Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 14 x^{14} + 68 x^{13} + 64 x^{12} - 456 x^{11} - 54 x^{10} + 1532 x^{9} - 400 x^{8} + \cdots - 49 \) |
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 | 1.6 | ||
Root | \(1.44011\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.44011 | −1.01832 | −0.509158 | − | 0.860673i | \(-0.670043\pi\) | ||||
−0.509158 | + | 0.860673i | \(0.670043\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.0739309 | 0.0369655 | ||||||||
\(5\) | 3.20961 | 1.43538 | 0.717692 | − | 0.696361i | \(-0.245199\pi\) | ||||
0.717692 | + | 0.696361i | \(0.245199\pi\) | |||||||
\(6\) | −1.44011 | −0.587924 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.77376 | 0.980673 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.62221 | −1.46167 | ||||||||
\(11\) | −3.71531 | −1.12021 | −0.560103 | − | 0.828423i | \(-0.689239\pi\) | ||||
−0.560103 | + | 0.828423i | \(0.689239\pi\) | |||||||
\(12\) | 0.0739309 | 0.0213420 | ||||||||
\(13\) | 1.13302 | 0.314242 | 0.157121 | − | 0.987579i | \(-0.449779\pi\) | ||||
0.157121 | + | 0.987579i | \(0.449779\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.20961 | 0.828719 | ||||||||
\(16\) | −4.14240 | −1.03560 | ||||||||
\(17\) | −5.67373 | −1.37608 | −0.688041 | − | 0.725672i | \(-0.741529\pi\) | ||||
−0.688041 | + | 0.725672i | \(0.741529\pi\) | |||||||
\(18\) | −1.44011 | −0.339438 | ||||||||
\(19\) | 3.14749 | 0.722083 | 0.361041 | − | 0.932550i | \(-0.382421\pi\) | ||||
0.361041 | + | 0.932550i | \(0.382421\pi\) | |||||||
\(20\) | 0.237290 | 0.0530596 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.35047 | 1.14072 | ||||||||
\(23\) | −4.86181 | −1.01376 | −0.506879 | − | 0.862017i | \(-0.669201\pi\) | ||||
−0.506879 | + | 0.862017i | \(0.669201\pi\) | |||||||
\(24\) | 2.77376 | 0.566192 | ||||||||
\(25\) | 5.30163 | 1.06033 | ||||||||
\(26\) | −1.63167 | −0.319998 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.25032 | 0.417874 | 0.208937 | − | 0.977929i | \(-0.433000\pi\) | ||||
0.208937 | + | 0.977929i | \(0.433000\pi\) | |||||||
\(30\) | −4.62221 | −0.843897 | ||||||||
\(31\) | −1.73959 | −0.312439 | −0.156219 | − | 0.987722i | \(-0.549931\pi\) | ||||
−0.156219 | + | 0.987722i | \(0.549931\pi\) | |||||||
\(32\) | 0.418005 | 0.0738935 | ||||||||
\(33\) | −3.71531 | −0.646752 | ||||||||
\(34\) | 8.17082 | 1.40128 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0739309 | 0.0123218 | ||||||||
\(37\) | −4.53215 | −0.745081 | −0.372540 | − | 0.928016i | \(-0.621513\pi\) | ||||
−0.372540 | + | 0.928016i | \(0.621513\pi\) | |||||||
\(38\) | −4.53274 | −0.735308 | ||||||||
\(39\) | 1.13302 | 0.181428 | ||||||||
\(40\) | 8.90270 | 1.40764 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.99210 | −1.06629 | −0.533143 | − | 0.846025i | \(-0.678989\pi\) | ||||
−0.533143 | + | 0.846025i | \(0.678989\pi\) | |||||||
\(44\) | −0.274676 | −0.0414090 | ||||||||
\(45\) | 3.20961 | 0.478461 | ||||||||
\(46\) | 7.00157 | 1.03232 | ||||||||
\(47\) | −6.44011 | −0.939387 | −0.469694 | − | 0.882830i | \(-0.655636\pi\) | ||||
−0.469694 | + | 0.882830i | \(0.655636\pi\) | |||||||
\(48\) | −4.14240 | −0.597903 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.63495 | −1.07975 | ||||||||
\(51\) | −5.67373 | −0.794481 | ||||||||
\(52\) | 0.0837649 | 0.0116161 | ||||||||
\(53\) | 3.39697 | 0.466610 | 0.233305 | − | 0.972404i | \(-0.425046\pi\) | ||||
0.233305 | + | 0.972404i | \(0.425046\pi\) | |||||||
\(54\) | −1.44011 | −0.195975 | ||||||||
\(55\) | −11.9247 | −1.60793 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.14749 | 0.416895 | ||||||||
\(58\) | −3.24072 | −0.425528 | ||||||||
\(59\) | −3.87745 | −0.504800 | −0.252400 | − | 0.967623i | \(-0.581220\pi\) | ||||
−0.252400 | + | 0.967623i | \(0.581220\pi\) | |||||||
\(60\) | 0.237290 | 0.0306340 | ||||||||
\(61\) | 8.17051 | 1.04613 | 0.523063 | − | 0.852294i | \(-0.324789\pi\) | ||||
0.523063 | + | 0.852294i | \(0.324789\pi\) | |||||||
\(62\) | 2.50520 | 0.318161 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.68282 | 0.960352 | ||||||||
\(65\) | 3.63655 | 0.451058 | ||||||||
\(66\) | 5.35047 | 0.658597 | ||||||||
\(67\) | −4.36043 | −0.532712 | −0.266356 | − | 0.963875i | \(-0.585820\pi\) | ||||
−0.266356 | + | 0.963875i | \(0.585820\pi\) | |||||||
\(68\) | −0.419464 | −0.0508675 | ||||||||
\(69\) | −4.86181 | −0.585293 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.54065 | 0.894910 | 0.447455 | − | 0.894306i | \(-0.352330\pi\) | ||||
0.447455 | + | 0.894306i | \(0.352330\pi\) | |||||||
\(72\) | 2.77376 | 0.326891 | ||||||||
\(73\) | −9.11677 | −1.06704 | −0.533519 | − | 0.845788i | \(-0.679131\pi\) | ||||
−0.533519 | + | 0.845788i | \(0.679131\pi\) | |||||||
\(74\) | 6.52682 | 0.758727 | ||||||||
\(75\) | 5.30163 | 0.612179 | ||||||||
\(76\) | 0.232697 | 0.0266921 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.63167 | −0.184751 | ||||||||
\(79\) | 0.0474074 | 0.00533375 | 0.00266688 | − | 0.999996i | \(-0.499151\pi\) | ||||
0.00266688 | + | 0.999996i | \(0.499151\pi\) | |||||||
\(80\) | −13.2955 | −1.48648 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.44011 | −0.159034 | ||||||||
\(83\) | −8.03200 | −0.881626 | −0.440813 | − | 0.897599i | \(-0.645310\pi\) | ||||
−0.440813 | + | 0.897599i | \(0.645310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.2105 | −1.97520 | ||||||||
\(86\) | 10.0694 | 1.08581 | ||||||||
\(87\) | 2.25032 | 0.241260 | ||||||||
\(88\) | −10.3054 | −1.09856 | ||||||||
\(89\) | −9.30187 | −0.985996 | −0.492998 | − | 0.870030i | \(-0.664099\pi\) | ||||
−0.492998 | + | 0.870030i | \(0.664099\pi\) | |||||||
\(90\) | −4.62221 | −0.487224 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.359438 | −0.0374740 | ||||||||
\(93\) | −1.73959 | −0.180387 | ||||||||
\(94\) | 9.27450 | 0.956592 | ||||||||
\(95\) | 10.1022 | 1.03647 | ||||||||
\(96\) | 0.418005 | 0.0426624 | ||||||||
\(97\) | −17.8996 | −1.81743 | −0.908714 | − | 0.417420i | \(-0.862934\pi\) | ||||
−0.908714 | + | 0.417420i | \(0.862934\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.71531 | −0.373402 | ||||||||
\(100\) | 0.391954 | 0.0391954 | ||||||||
\(101\) | −3.11847 | −0.310300 | −0.155150 | − | 0.987891i | \(-0.549586\pi\) | ||||
−0.155150 | + | 0.987891i | \(0.549586\pi\) | |||||||
\(102\) | 8.17082 | 0.809032 | ||||||||
\(103\) | 2.85378 | 0.281192 | 0.140596 | − | 0.990067i | \(-0.455098\pi\) | ||||
0.140596 | + | 0.990067i | \(0.455098\pi\) | |||||||
\(104\) | 3.14272 | 0.308169 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.89203 | −0.475156 | ||||||||
\(107\) | 12.8370 | 1.24100 | 0.620500 | − | 0.784206i | \(-0.286930\pi\) | ||||
0.620500 | + | 0.784206i | \(0.286930\pi\) | |||||||
\(108\) | 0.0739309 | 0.00711401 | ||||||||
\(109\) | −19.4326 | −1.86131 | −0.930655 | − | 0.365899i | \(-0.880762\pi\) | ||||
−0.930655 | + | 0.365899i | \(0.880762\pi\) | |||||||
\(110\) | 17.1729 | 1.63738 | ||||||||
\(111\) | −4.53215 | −0.430173 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.96160 | −0.843037 | −0.421518 | − | 0.906820i | \(-0.638503\pi\) | ||||
−0.421518 | + | 0.906820i | \(0.638503\pi\) | |||||||
\(114\) | −4.53274 | −0.424530 | ||||||||
\(115\) | −15.6045 | −1.45513 | ||||||||
\(116\) | 0.166368 | 0.0154469 | ||||||||
\(117\) | 1.13302 | 0.104747 | ||||||||
\(118\) | 5.58397 | 0.514046 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.90270 | 0.812702 | ||||||||
\(121\) | 2.80350 | 0.254863 | ||||||||
\(122\) | −11.7665 | −1.06529 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −0.128609 | −0.0115495 | ||||||||
\(125\) | 0.968108 | 0.0865902 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.5846 | 1.38291 | 0.691455 | − | 0.722420i | \(-0.256970\pi\) | ||||
0.691455 | + | 0.722420i | \(0.256970\pi\) | |||||||
\(128\) | −11.9001 | −1.05183 | ||||||||
\(129\) | −6.99210 | −0.615620 | ||||||||
\(130\) | −5.23704 | −0.459319 | ||||||||
\(131\) | 11.1927 | 0.977913 | 0.488957 | − | 0.872308i | \(-0.337378\pi\) | ||||
0.488957 | + | 0.872308i | \(0.337378\pi\) | |||||||
\(132\) | −0.274676 | −0.0239075 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.27953 | 0.542468 | ||||||||
\(135\) | 3.20961 | 0.276240 | ||||||||
\(136\) | −15.7376 | −1.34949 | ||||||||
\(137\) | −9.63284 | −0.822989 | −0.411494 | − | 0.911412i | \(-0.634993\pi\) | ||||
−0.411494 | + | 0.911412i | \(0.634993\pi\) | |||||||
\(138\) | 7.00157 | 0.596013 | ||||||||
\(139\) | −12.4957 | −1.05987 | −0.529935 | − | 0.848039i | \(-0.677784\pi\) | ||||
−0.529935 | + | 0.848039i | \(0.677784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.44011 | −0.542355 | ||||||||
\(142\) | −10.8594 | −0.911301 | ||||||||
\(143\) | −4.20950 | −0.352016 | ||||||||
\(144\) | −4.14240 | −0.345200 | ||||||||
\(145\) | 7.22267 | 0.599810 | ||||||||
\(146\) | 13.1292 | 1.08658 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.335066 | −0.0275423 | ||||||||
\(149\) | −13.7960 | −1.13021 | −0.565105 | − | 0.825019i | \(-0.691165\pi\) | ||||
−0.565105 | + | 0.825019i | \(0.691165\pi\) | |||||||
\(150\) | −7.63495 | −0.623391 | ||||||||
\(151\) | 15.3274 | 1.24733 | 0.623663 | − | 0.781694i | \(-0.285644\pi\) | ||||
0.623663 | + | 0.781694i | \(0.285644\pi\) | |||||||
\(152\) | 8.73037 | 0.708127 | ||||||||
\(153\) | −5.67373 | −0.458694 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.58340 | −0.448470 | ||||||||
\(156\) | 0.0837649 | 0.00670656 | ||||||||
\(157\) | −5.91126 | −0.471770 | −0.235885 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235885 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(158\) | −0.0682721 | −0.00543144 | ||||||||
\(159\) | 3.39697 | 0.269398 | ||||||||
\(160\) | 1.34163 | 0.106066 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.44011 | −0.113146 | ||||||||
\(163\) | 9.18322 | 0.719285 | 0.359643 | − | 0.933090i | \(-0.382899\pi\) | ||||
0.359643 | + | 0.933090i | \(0.382899\pi\) | |||||||
\(164\) | 0.0739309 | 0.00577304 | ||||||||
\(165\) | −11.9247 | −0.928337 | ||||||||
\(166\) | 11.5670 | 0.897773 | ||||||||
\(167\) | −20.1802 | −1.56159 | −0.780795 | − | 0.624787i | \(-0.785186\pi\) | ||||
−0.780795 | + | 0.624787i | \(0.785186\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7163 | −0.901252 | ||||||||
\(170\) | 26.2252 | 2.01138 | ||||||||
\(171\) | 3.14749 | 0.240694 | ||||||||
\(172\) | −0.516932 | −0.0394157 | ||||||||
\(173\) | −22.8081 | −1.73407 | −0.867033 | − | 0.498250i | \(-0.833976\pi\) | ||||
−0.867033 | + | 0.498250i | \(0.833976\pi\) | |||||||
\(174\) | −3.24072 | −0.245679 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.3903 | 1.16009 | ||||||||
\(177\) | −3.87745 | −0.291447 | ||||||||
\(178\) | 13.3958 | 1.00405 | ||||||||
\(179\) | 22.3973 | 1.67405 | 0.837025 | − | 0.547165i | \(-0.184293\pi\) | ||||
0.837025 | + | 0.547165i | \(0.184293\pi\) | |||||||
\(180\) | 0.237290 | 0.0176865 | ||||||||
\(181\) | 18.9086 | 1.40546 | 0.702732 | − | 0.711455i | \(-0.251963\pi\) | ||||
0.702732 | + | 0.711455i | \(0.251963\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.17051 | 0.603981 | ||||||||
\(184\) | −13.4855 | −0.994165 | ||||||||
\(185\) | −14.5465 | −1.06948 | ||||||||
\(186\) | 2.50520 | 0.183691 | ||||||||
\(187\) | 21.0796 | 1.54150 | ||||||||
\(188\) | −0.476124 | −0.0347249 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.5484 | −1.05545 | ||||||||
\(191\) | 19.3875 | 1.40283 | 0.701416 | − | 0.712752i | \(-0.252552\pi\) | ||||
0.701416 | + | 0.712752i | \(0.252552\pi\) | |||||||
\(192\) | 7.68282 | 0.554460 | ||||||||
\(193\) | −8.99357 | −0.647371 | −0.323686 | − | 0.946165i | \(-0.604922\pi\) | ||||
−0.323686 | + | 0.946165i | \(0.604922\pi\) | |||||||
\(194\) | 25.7775 | 1.85071 | ||||||||
\(195\) | 3.63655 | 0.260418 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.6318 | −1.18497 | −0.592484 | − | 0.805583i | \(-0.701852\pi\) | ||||
−0.592484 | + | 0.805583i | \(0.701852\pi\) | |||||||
\(198\) | 5.35047 | 0.380241 | ||||||||
\(199\) | 8.98803 | 0.637144 | 0.318572 | − | 0.947899i | \(-0.396797\pi\) | ||||
0.318572 | + | 0.947899i | \(0.396797\pi\) | |||||||
\(200\) | 14.7054 | 1.03983 | ||||||||
\(201\) | −4.36043 | −0.307561 | ||||||||
\(202\) | 4.49096 | 0.315983 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.419464 | −0.0293684 | ||||||||
\(205\) | 3.20961 | 0.224169 | ||||||||
\(206\) | −4.10978 | −0.286342 | ||||||||
\(207\) | −4.86181 | −0.337919 | ||||||||
\(208\) | −4.69340 | −0.325429 | ||||||||
\(209\) | −11.6939 | −0.808882 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.8993 | 1.78298 | 0.891490 | − | 0.453040i | \(-0.149661\pi\) | ||||
0.891490 | + | 0.453040i | \(0.149661\pi\) | |||||||
\(212\) | 0.251141 | 0.0172485 | ||||||||
\(213\) | 7.54065 | 0.516677 | ||||||||
\(214\) | −18.4868 | −1.26373 | ||||||||
\(215\) | −22.4419 | −1.53053 | ||||||||
\(216\) | 2.77376 | 0.188731 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 27.9852 | 1.89540 | ||||||||
\(219\) | −9.11677 | −0.616054 | ||||||||
\(220\) | −0.881604 | −0.0594377 | ||||||||
\(221\) | −6.42843 | −0.432423 | ||||||||
\(222\) | 6.52682 | 0.438051 | ||||||||
\(223\) | 18.1127 | 1.21292 | 0.606458 | − | 0.795115i | \(-0.292590\pi\) | ||||
0.606458 | + | 0.795115i | \(0.292590\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.30163 | 0.353442 | ||||||||
\(226\) | 12.9057 | 0.858477 | ||||||||
\(227\) | −12.9994 | −0.862802 | −0.431401 | − | 0.902160i | \(-0.641981\pi\) | ||||
−0.431401 | + | 0.902160i | \(0.641981\pi\) | |||||||
\(228\) | 0.232697 | 0.0154107 | ||||||||
\(229\) | 5.48370 | 0.362373 | 0.181187 | − | 0.983449i | \(-0.442006\pi\) | ||||
0.181187 | + | 0.983449i | \(0.442006\pi\) | |||||||
\(230\) | 22.4723 | 1.48178 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.24186 | 0.409798 | ||||||||
\(233\) | 9.19946 | 0.602676 | 0.301338 | − | 0.953517i | \(-0.402567\pi\) | ||||
0.301338 | + | 0.953517i | \(0.402567\pi\) | |||||||
\(234\) | −1.63167 | −0.106666 | ||||||||
\(235\) | −20.6703 | −1.34838 | ||||||||
\(236\) | −0.286663 | −0.0186602 | ||||||||
\(237\) | 0.0474074 | 0.00307944 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.823059 | 0.0532393 | 0.0266196 | − | 0.999646i | \(-0.491526\pi\) | ||||
0.0266196 | + | 0.999646i | \(0.491526\pi\) | |||||||
\(240\) | −13.2955 | −0.858221 | ||||||||
\(241\) | 6.48256 | 0.417578 | 0.208789 | − | 0.977961i | \(-0.433048\pi\) | ||||
0.208789 | + | 0.977961i | \(0.433048\pi\) | |||||||
\(242\) | −4.03736 | −0.259531 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.604053 | 0.0386706 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.44011 | −0.0918184 | ||||||||
\(247\) | 3.56615 | 0.226909 | ||||||||
\(248\) | −4.82520 | −0.306400 | ||||||||
\(249\) | −8.03200 | −0.509007 | ||||||||
\(250\) | −1.39419 | −0.0881761 | ||||||||
\(251\) | 11.0992 | 0.700575 | 0.350287 | − | 0.936642i | \(-0.386084\pi\) | ||||
0.350287 | + | 0.936642i | \(0.386084\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0631 | 1.13562 | ||||||||
\(254\) | −22.4436 | −1.40824 | ||||||||
\(255\) | −18.2105 | −1.14039 | ||||||||
\(256\) | 1.77195 | 0.110747 | ||||||||
\(257\) | −9.44160 | −0.588951 | −0.294475 | − | 0.955659i | \(-0.595145\pi\) | ||||
−0.294475 | + | 0.955659i | \(0.595145\pi\) | |||||||
\(258\) | 10.0694 | 0.626895 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.268853 | 0.0166736 | ||||||||
\(261\) | 2.25032 | 0.139291 | ||||||||
\(262\) | −16.1188 | −0.995824 | ||||||||
\(263\) | −12.5414 | −0.773333 | −0.386666 | − | 0.922220i | \(-0.626374\pi\) | ||||
−0.386666 | + | 0.922220i | \(0.626374\pi\) | |||||||
\(264\) | −10.3054 | −0.634252 | ||||||||
\(265\) | 10.9030 | 0.669765 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.30187 | −0.569265 | ||||||||
\(268\) | −0.322371 | −0.0196919 | ||||||||
\(269\) | 2.28195 | 0.139133 | 0.0695666 | − | 0.997577i | \(-0.477838\pi\) | ||||
0.0695666 | + | 0.997577i | \(0.477838\pi\) | |||||||
\(270\) | −4.62221 | −0.281299 | ||||||||
\(271\) | −12.2113 | −0.741781 | −0.370891 | − | 0.928677i | \(-0.620948\pi\) | ||||
−0.370891 | + | 0.928677i | \(0.620948\pi\) | |||||||
\(272\) | 23.5028 | 1.42507 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.8724 | 0.838062 | ||||||||
\(275\) | −19.6972 | −1.18778 | ||||||||
\(276\) | −0.359438 | −0.0216356 | ||||||||
\(277\) | −24.7287 | −1.48580 | −0.742901 | − | 0.669401i | \(-0.766551\pi\) | ||||
−0.742901 | + | 0.669401i | \(0.766551\pi\) | |||||||
\(278\) | 17.9952 | 1.07928 | ||||||||
\(279\) | −1.73959 | −0.104146 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.87088 | −0.290572 | −0.145286 | − | 0.989390i | \(-0.546410\pi\) | ||||
−0.145286 | + | 0.989390i | \(0.546410\pi\) | |||||||
\(282\) | 9.27450 | 0.552289 | ||||||||
\(283\) | 4.43504 | 0.263636 | 0.131818 | − | 0.991274i | \(-0.457919\pi\) | ||||
0.131818 | + | 0.991274i | \(0.457919\pi\) | |||||||
\(284\) | 0.557487 | 0.0330808 | ||||||||
\(285\) | 10.1022 | 0.598404 | ||||||||
\(286\) | 6.06217 | 0.358463 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.418005 | 0.0246312 | ||||||||
\(289\) | 15.1912 | 0.893601 | ||||||||
\(290\) | −10.4015 | −0.610795 | ||||||||
\(291\) | −17.8996 | −1.04929 | ||||||||
\(292\) | −0.674011 | −0.0394435 | ||||||||
\(293\) | 10.4636 | 0.611289 | 0.305644 | − | 0.952146i | \(-0.401128\pi\) | ||||
0.305644 | + | 0.952146i | \(0.401128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.4451 | −0.724582 | ||||||||
\(296\) | −12.5711 | −0.730680 | ||||||||
\(297\) | −3.71531 | −0.215584 | ||||||||
\(298\) | 19.8678 | 1.15091 | ||||||||
\(299\) | −5.50851 | −0.318566 | ||||||||
\(300\) | 0.391954 | 0.0226295 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −22.0732 | −1.27017 | ||||||||
\(303\) | −3.11847 | −0.179152 | ||||||||
\(304\) | −13.0381 | −0.747788 | ||||||||
\(305\) | 26.2242 | 1.50159 | ||||||||
\(306\) | 8.17082 | 0.467095 | ||||||||
\(307\) | −4.63816 | −0.264714 | −0.132357 | − | 0.991202i | \(-0.542254\pi\) | ||||
−0.132357 | + | 0.991202i | \(0.542254\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.85378 | 0.162346 | ||||||||
\(310\) | 8.04074 | 0.456683 | ||||||||
\(311\) | 4.98755 | 0.282818 | 0.141409 | − | 0.989951i | \(-0.454837\pi\) | ||||
0.141409 | + | 0.989951i | \(0.454837\pi\) | |||||||
\(312\) | 3.14272 | 0.177921 | ||||||||
\(313\) | 12.0497 | 0.681087 | 0.340544 | − | 0.940229i | \(-0.389389\pi\) | ||||
0.340544 | + | 0.940229i | \(0.389389\pi\) | |||||||
\(314\) | 8.51289 | 0.480410 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.00350487 | 0.000197165 0 | ||||||||
\(317\) | 17.2675 | 0.969840 | 0.484920 | − | 0.874559i | \(-0.338849\pi\) | ||||
0.484920 | + | 0.874559i | \(0.338849\pi\) | |||||||
\(318\) | −4.89203 | −0.274332 | ||||||||
\(319\) | −8.36064 | −0.468106 | ||||||||
\(320\) | 24.6589 | 1.37847 | ||||||||
\(321\) | 12.8370 | 0.716492 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.8580 | −0.993645 | ||||||||
\(324\) | 0.0739309 | 0.00410727 | ||||||||
\(325\) | 6.00683 | 0.333199 | ||||||||
\(326\) | −13.2249 | −0.732459 | ||||||||
\(327\) | −19.4326 | −1.07463 | ||||||||
\(328\) | 2.77376 | 0.153155 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 17.1729 | 0.945339 | ||||||||
\(331\) | −11.7004 | −0.643110 | −0.321555 | − | 0.946891i | \(-0.604205\pi\) | ||||
−0.321555 | + | 0.946891i | \(0.604205\pi\) | |||||||
\(332\) | −0.593813 | −0.0325897 | ||||||||
\(333\) | −4.53215 | −0.248360 | ||||||||
\(334\) | 29.0618 | 1.59019 | ||||||||
\(335\) | −13.9953 | −0.764646 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6186 | 0.687377 | 0.343689 | − | 0.939084i | \(-0.388324\pi\) | ||||
0.343689 | + | 0.939084i | \(0.388324\pi\) | |||||||
\(338\) | 16.8728 | 0.917758 | ||||||||
\(339\) | −8.96160 | −0.486728 | ||||||||
\(340\) | −1.34632 | −0.0730144 | ||||||||
\(341\) | 6.46310 | 0.349996 | ||||||||
\(342\) | −4.53274 | −0.245103 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −19.3944 | −1.04568 | ||||||||
\(345\) | −15.6045 | −0.840120 | ||||||||
\(346\) | 32.8463 | 1.76583 | ||||||||
\(347\) | −22.2243 | −1.19306 | −0.596530 | − | 0.802591i | \(-0.703454\pi\) | ||||
−0.596530 | + | 0.802591i | \(0.703454\pi\) | |||||||
\(348\) | 0.166368 | 0.00891828 | ||||||||
\(349\) | 27.5451 | 1.47445 | 0.737227 | − | 0.675645i | \(-0.236135\pi\) | ||||
0.737227 | + | 0.675645i | \(0.236135\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.13302 | 0.0604759 | ||||||||
\(352\) | −1.55302 | −0.0827760 | ||||||||
\(353\) | −8.11789 | −0.432072 | −0.216036 | − | 0.976385i | \(-0.569313\pi\) | ||||
−0.216036 | + | 0.976385i | \(0.569313\pi\) | |||||||
\(354\) | 5.58397 | 0.296785 | ||||||||
\(355\) | 24.2026 | 1.28454 | ||||||||
\(356\) | −0.687696 | −0.0364478 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −32.2546 | −1.70471 | ||||||||
\(359\) | −16.6316 | −0.877782 | −0.438891 | − | 0.898540i | \(-0.644629\pi\) | ||||
−0.438891 | + | 0.898540i | \(0.644629\pi\) | |||||||
\(360\) | 8.90270 | 0.469214 | ||||||||
\(361\) | −9.09334 | −0.478597 | ||||||||
\(362\) | −27.2305 | −1.43121 | ||||||||
\(363\) | 2.80350 | 0.147145 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −29.2613 | −1.53161 | ||||||||
\(366\) | −11.7665 | −0.615043 | ||||||||
\(367\) | 23.5211 | 1.22779 | 0.613897 | − | 0.789386i | \(-0.289601\pi\) | ||||
0.613897 | + | 0.789386i | \(0.289601\pi\) | |||||||
\(368\) | 20.1396 | 1.04985 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 20.9486 | 1.08906 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.128609 | −0.00666808 | ||||||||
\(373\) | 14.4062 | 0.745923 | 0.372962 | − | 0.927847i | \(-0.378342\pi\) | ||||
0.372962 | + | 0.927847i | \(0.378342\pi\) | |||||||
\(374\) | −30.3571 | −1.56973 | ||||||||
\(375\) | 0.968108 | 0.0499929 | ||||||||
\(376\) | −17.8633 | −0.921231 | ||||||||
\(377\) | 2.54965 | 0.131314 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.88799 | 0.251079 | 0.125540 | − | 0.992089i | \(-0.459934\pi\) | ||||
0.125540 | + | 0.992089i | \(0.459934\pi\) | |||||||
\(380\) | 0.746866 | 0.0383134 | ||||||||
\(381\) | 15.5846 | 0.798423 | ||||||||
\(382\) | −27.9203 | −1.42852 | ||||||||
\(383\) | 22.8952 | 1.16989 | 0.584944 | − | 0.811074i | \(-0.301116\pi\) | ||||
0.584944 | + | 0.811074i | \(0.301116\pi\) | |||||||
\(384\) | −11.9001 | −0.607277 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.9518 | 0.659228 | ||||||||
\(387\) | −6.99210 | −0.355428 | ||||||||
\(388\) | −1.32333 | −0.0671821 | ||||||||
\(389\) | 13.6469 | 0.691925 | 0.345962 | − | 0.938248i | \(-0.387553\pi\) | ||||
0.345962 | + | 0.938248i | \(0.387553\pi\) | |||||||
\(390\) | −5.23704 | −0.265188 | ||||||||
\(391\) | 27.5846 | 1.39501 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.1927 | 0.564599 | ||||||||
\(394\) | 23.9517 | 1.20667 | ||||||||
\(395\) | 0.152160 | 0.00765598 | ||||||||
\(396\) | −0.274676 | −0.0138030 | ||||||||
\(397\) | 7.08009 | 0.355339 | 0.177670 | − | 0.984090i | \(-0.443144\pi\) | ||||
0.177670 | + | 0.984090i | \(0.443144\pi\) | |||||||
\(398\) | −12.9438 | −0.648814 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −21.9614 | −1.09807 | ||||||||
\(401\) | −29.9703 | −1.49665 | −0.748323 | − | 0.663335i | \(-0.769141\pi\) | ||||
−0.748323 | + | 0.663335i | \(0.769141\pi\) | |||||||
\(402\) | 6.27953 | 0.313194 | ||||||||
\(403\) | −1.97098 | −0.0981815 | ||||||||
\(404\) | −0.230552 | −0.0114704 | ||||||||
\(405\) | 3.20961 | 0.159487 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.8383 | 0.834645 | ||||||||
\(408\) | −15.7376 | −0.779126 | ||||||||
\(409\) | −13.3731 | −0.661258 | −0.330629 | − | 0.943761i | \(-0.607261\pi\) | ||||
−0.330629 | + | 0.943761i | \(0.607261\pi\) | |||||||
\(410\) | −4.62221 | −0.228275 | ||||||||
\(411\) | −9.63284 | −0.475153 | ||||||||
\(412\) | 0.210983 | 0.0103944 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.00157 | 0.344108 | ||||||||
\(415\) | −25.7796 | −1.26547 | ||||||||
\(416\) | 0.473606 | 0.0232205 | ||||||||
\(417\) | −12.4957 | −0.611916 | ||||||||
\(418\) | 16.8405 | 0.823697 | ||||||||
\(419\) | −24.2251 | −1.18348 | −0.591738 | − | 0.806131i | \(-0.701558\pi\) | ||||
−0.591738 | + | 0.806131i | \(0.701558\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.2818 | −0.647314 | −0.323657 | − | 0.946174i | \(-0.604912\pi\) | ||||
−0.323657 | + | 0.946174i | \(0.604912\pi\) | |||||||
\(422\) | −37.2979 | −1.81564 | ||||||||
\(423\) | −6.44011 | −0.313129 | ||||||||
\(424\) | 9.42239 | 0.457592 | ||||||||
\(425\) | −30.0800 | −1.45909 | ||||||||
\(426\) | −10.8594 | −0.526140 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.949052 | 0.0458742 | ||||||||
\(429\) | −4.20950 | −0.203237 | ||||||||
\(430\) | 32.3190 | 1.55856 | ||||||||
\(431\) | 16.2256 | 0.781562 | 0.390781 | − | 0.920484i | \(-0.372205\pi\) | ||||
0.390781 | + | 0.920484i | \(0.372205\pi\) | |||||||
\(432\) | −4.14240 | −0.199301 | ||||||||
\(433\) | −1.61340 | −0.0775351 | −0.0387675 | − | 0.999248i | \(-0.512343\pi\) | ||||
−0.0387675 | + | 0.999248i | \(0.512343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.22267 | 0.346300 | ||||||||
\(436\) | −1.43667 | −0.0688042 | ||||||||
\(437\) | −15.3025 | −0.732017 | ||||||||
\(438\) | 13.1292 | 0.627337 | ||||||||
\(439\) | −15.4861 | −0.739113 | −0.369556 | − | 0.929208i | \(-0.620490\pi\) | ||||
−0.369556 | + | 0.929208i | \(0.620490\pi\) | |||||||
\(440\) | −33.0763 | −1.57685 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.25768 | 0.440343 | ||||||||
\(443\) | −12.9825 | −0.616817 | −0.308409 | − | 0.951254i | \(-0.599796\pi\) | ||||
−0.308409 | + | 0.951254i | \(0.599796\pi\) | |||||||
\(444\) | −0.335066 | −0.0159015 | ||||||||
\(445\) | −29.8554 | −1.41528 | ||||||||
\(446\) | −26.0844 | −1.23513 | ||||||||
\(447\) | −13.7960 | −0.652528 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.4508 | −1.20110 | −0.600549 | − | 0.799588i | \(-0.705051\pi\) | ||||
−0.600549 | + | 0.799588i | \(0.705051\pi\) | |||||||
\(450\) | −7.63495 | −0.359915 | ||||||||
\(451\) | −3.71531 | −0.174947 | ||||||||
\(452\) | −0.662540 | −0.0311633 | ||||||||
\(453\) | 15.3274 | 0.720144 | ||||||||
\(454\) | 18.7207 | 0.878604 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.73037 | 0.408837 | ||||||||
\(457\) | 14.1521 | 0.662009 | 0.331004 | − | 0.943629i | \(-0.392613\pi\) | ||||
0.331004 | + | 0.943629i | \(0.392613\pi\) | |||||||
\(458\) | −7.89716 | −0.369010 | ||||||||
\(459\) | −5.67373 | −0.264827 | ||||||||
\(460\) | −1.15366 | −0.0537896 | ||||||||
\(461\) | 1.10138 | 0.0512963 | 0.0256481 | − | 0.999671i | \(-0.491835\pi\) | ||||
0.0256481 | + | 0.999671i | \(0.491835\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.5041 | −0.859958 | −0.429979 | − | 0.902839i | \(-0.641479\pi\) | ||||
−0.429979 | + | 0.902839i | \(0.641479\pi\) | |||||||
\(464\) | −9.32173 | −0.432750 | ||||||||
\(465\) | −5.58340 | −0.258924 | ||||||||
\(466\) | −13.2483 | −0.613714 | ||||||||
\(467\) | 26.1402 | 1.20962 | 0.604812 | − | 0.796368i | \(-0.293248\pi\) | ||||
0.604812 | + | 0.796368i | \(0.293248\pi\) | |||||||
\(468\) | 0.0837649 | 0.00387204 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 29.7676 | 1.37308 | ||||||||
\(471\) | −5.91126 | −0.272377 | ||||||||
\(472\) | −10.7551 | −0.495044 | ||||||||
\(473\) | 25.9778 | 1.19446 | ||||||||
\(474\) | −0.0682721 | −0.00313584 | ||||||||
\(475\) | 16.6868 | 0.765643 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.39697 | 0.155537 | ||||||||
\(478\) | −1.18530 | −0.0542143 | ||||||||
\(479\) | −31.4816 | −1.43843 | −0.719216 | − | 0.694787i | \(-0.755499\pi\) | ||||
−0.719216 | + | 0.694787i | \(0.755499\pi\) | |||||||
\(480\) | 1.34163 | 0.0612369 | ||||||||
\(481\) | −5.13500 | −0.234136 | ||||||||
\(482\) | −9.33563 | −0.425226 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.207265 | 0.00942115 | ||||||||
\(485\) | −57.4508 | −2.60871 | ||||||||
\(486\) | −1.44011 | −0.0653249 | ||||||||
\(487\) | 14.3104 | 0.648468 | 0.324234 | − | 0.945977i | \(-0.394893\pi\) | ||||
0.324234 | + | 0.945977i | \(0.394893\pi\) | |||||||
\(488\) | 22.6630 | 1.02591 | ||||||||
\(489\) | 9.18322 | 0.415279 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.7811 | −0.982969 | −0.491485 | − | 0.870886i | \(-0.663546\pi\) | ||||
−0.491485 | + | 0.870886i | \(0.663546\pi\) | |||||||
\(492\) | 0.0739309 | 0.00333306 | ||||||||
\(493\) | −12.7677 | −0.575029 | ||||||||
\(494\) | −5.13567 | −0.231065 | ||||||||
\(495\) | −11.9247 | −0.535975 | ||||||||
\(496\) | 7.20606 | 0.323561 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.5670 | 0.518330 | ||||||||
\(499\) | −6.73070 | −0.301308 | −0.150654 | − | 0.988587i | \(-0.548138\pi\) | ||||
−0.150654 | + | 0.988587i | \(0.548138\pi\) | |||||||
\(500\) | 0.0715731 | 0.00320085 | ||||||||
\(501\) | −20.1802 | −0.901585 | ||||||||
\(502\) | −15.9841 | −0.713406 | ||||||||
\(503\) | 14.8815 | 0.663535 | 0.331768 | − | 0.943361i | \(-0.392355\pi\) | ||||
0.331768 | + | 0.943361i | \(0.392355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0091 | −0.445399 | ||||||||
\(506\) | −26.0130 | −1.15642 | ||||||||
\(507\) | −11.7163 | −0.520338 | ||||||||
\(508\) | 1.15218 | 0.0511199 | ||||||||
\(509\) | 1.57147 | 0.0696542 | 0.0348271 | − | 0.999393i | \(-0.488912\pi\) | ||||
0.0348271 | + | 0.999393i | \(0.488912\pi\) | |||||||
\(510\) | 26.2252 | 1.16127 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 21.2485 | 0.939059 | ||||||||
\(513\) | 3.14749 | 0.138965 | ||||||||
\(514\) | 13.5970 | 0.599737 | ||||||||
\(515\) | 9.15954 | 0.403618 | ||||||||
\(516\) | −0.516932 | −0.0227567 | ||||||||
\(517\) | 23.9270 | 1.05231 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.8081 | −1.00116 | ||||||||
\(520\) | 10.0869 | 0.442340 | ||||||||
\(521\) | 4.01664 | 0.175972 | 0.0879861 | − | 0.996122i | \(-0.471957\pi\) | ||||
0.0879861 | + | 0.996122i | \(0.471957\pi\) | |||||||
\(522\) | −3.24072 | −0.141843 | ||||||||
\(523\) | −8.94282 | −0.391042 | −0.195521 | − | 0.980699i | \(-0.562640\pi\) | ||||
−0.195521 | + | 0.980699i | \(0.562640\pi\) | |||||||
\(524\) | 0.827489 | 0.0361490 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.0610 | 0.787496 | ||||||||
\(527\) | 9.86995 | 0.429942 | ||||||||
\(528\) | 15.3903 | 0.669775 | ||||||||
\(529\) | 0.637219 | 0.0277052 | ||||||||
\(530\) | −15.7015 | −0.682031 | ||||||||
\(531\) | −3.87745 | −0.168267 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.13302 | 0.0490764 | ||||||||
\(534\) | 13.3958 | 0.579691 | ||||||||
\(535\) | 41.2019 | 1.78131 | ||||||||
\(536\) | −12.0948 | −0.522416 | ||||||||
\(537\) | 22.3973 | 0.966513 | ||||||||
\(538\) | −3.28628 | −0.141681 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.237290 | 0.0102113 | ||||||||
\(541\) | 22.1175 | 0.950907 | 0.475453 | − | 0.879741i | \(-0.342284\pi\) | ||||
0.475453 | + | 0.879741i | \(0.342284\pi\) | |||||||
\(542\) | 17.5856 | 0.755367 | ||||||||
\(543\) | 18.9086 | 0.811445 | ||||||||
\(544\) | −2.37165 | −0.101683 | ||||||||
\(545\) | −62.3713 | −2.67169 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.20726 | −0.137133 | −0.0685663 | − | 0.997647i | \(-0.521842\pi\) | ||||
−0.0685663 | + | 0.997647i | \(0.521842\pi\) | |||||||
\(548\) | −0.712165 | −0.0304222 | ||||||||
\(549\) | 8.17051 | 0.348709 | ||||||||
\(550\) | 28.3662 | 1.20954 | ||||||||
\(551\) | 7.08286 | 0.301740 | ||||||||
\(552\) | −13.4855 | −0.573981 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 35.6121 | 1.51302 | ||||||||
\(555\) | −14.5465 | −0.617463 | ||||||||
\(556\) | −0.923817 | −0.0391786 | ||||||||
\(557\) | −36.1547 | −1.53192 | −0.765962 | − | 0.642886i | \(-0.777737\pi\) | ||||
−0.765962 | + | 0.642886i | \(0.777737\pi\) | |||||||
\(558\) | 2.50520 | 0.106054 | ||||||||
\(559\) | −7.92216 | −0.335072 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.0796 | 0.889983 | ||||||||
\(562\) | 7.01463 | 0.295894 | ||||||||
\(563\) | 37.3991 | 1.57619 | 0.788093 | − | 0.615557i | \(-0.211069\pi\) | ||||
0.788093 | + | 0.615557i | \(0.211069\pi\) | |||||||
\(564\) | −0.476124 | −0.0200484 | ||||||||
\(565\) | −28.7633 | −1.21008 | ||||||||
\(566\) | −6.38697 | −0.268464 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.9160 | 0.877614 | ||||||||
\(569\) | −38.4021 | −1.60990 | −0.804950 | − | 0.593342i | \(-0.797808\pi\) | ||||
−0.804950 | + | 0.593342i | \(0.797808\pi\) | |||||||
\(570\) | −14.5484 | −0.609363 | ||||||||
\(571\) | 35.3708 | 1.48022 | 0.740112 | − | 0.672484i | \(-0.234773\pi\) | ||||
0.740112 | + | 0.672484i | \(0.234773\pi\) | |||||||
\(572\) | −0.311212 | −0.0130124 | ||||||||
\(573\) | 19.3875 | 0.809925 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.7755 | −1.07491 | ||||||||
\(576\) | 7.68282 | 0.320117 | ||||||||
\(577\) | 7.03644 | 0.292931 | 0.146465 | − | 0.989216i | \(-0.453210\pi\) | ||||
0.146465 | + | 0.989216i | \(0.453210\pi\) | |||||||
\(578\) | −21.8771 | −0.909967 | ||||||||
\(579\) | −8.99357 | −0.373760 | ||||||||
\(580\) | 0.533979 | 0.0221723 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 25.7775 | 1.06851 | ||||||||
\(583\) | −12.6208 | −0.522700 | ||||||||
\(584\) | −25.2877 | −1.04641 | ||||||||
\(585\) | 3.63655 | 0.150353 | ||||||||
\(586\) | −15.0687 | −0.622484 | ||||||||
\(587\) | −42.9014 | −1.77073 | −0.885365 | − | 0.464897i | \(-0.846091\pi\) | ||||
−0.885365 | + | 0.464897i | \(0.846091\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.47532 | −0.225607 | ||||||||
\(590\) | 17.9224 | 0.737853 | ||||||||
\(591\) | −16.6318 | −0.684141 | ||||||||
\(592\) | 18.7740 | 0.771605 | ||||||||
\(593\) | −29.8073 | −1.22404 | −0.612019 | − | 0.790843i | \(-0.709642\pi\) | ||||
−0.612019 | + | 0.790843i | \(0.709642\pi\) | |||||||
\(594\) | 5.35047 | 0.219532 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.01995 | −0.0417788 | ||||||||
\(597\) | 8.98803 | 0.367855 | ||||||||
\(598\) | 7.93289 | 0.324400 | ||||||||
\(599\) | −4.94543 | −0.202065 | −0.101032 | − | 0.994883i | \(-0.532215\pi\) | ||||
−0.101032 | + | 0.994883i | \(0.532215\pi\) | |||||||
\(600\) | 14.7054 | 0.600347 | ||||||||
\(601\) | 31.4634 | 1.28342 | 0.641709 | − | 0.766948i | \(-0.278226\pi\) | ||||
0.641709 | + | 0.766948i | \(0.278226\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.36043 | −0.177571 | ||||||||
\(604\) | 1.13317 | 0.0461080 | ||||||||
\(605\) | 8.99815 | 0.365827 | ||||||||
\(606\) | 4.49096 | 0.182433 | ||||||||
\(607\) | 19.3517 | 0.785461 | 0.392730 | − | 0.919654i | \(-0.371531\pi\) | ||||
0.392730 | + | 0.919654i | \(0.371531\pi\) | |||||||
\(608\) | 1.31566 | 0.0533572 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −37.7658 | −1.52909 | ||||||||
\(611\) | −7.29675 | −0.295195 | ||||||||
\(612\) | −0.419464 | −0.0169558 | ||||||||
\(613\) | −24.5783 | −0.992708 | −0.496354 | − | 0.868120i | \(-0.665328\pi\) | ||||
−0.496354 | + | 0.868120i | \(0.665328\pi\) | |||||||
\(614\) | 6.67948 | 0.269562 | ||||||||
\(615\) | 3.20961 | 0.129424 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.2037 | −1.65880 | −0.829399 | − | 0.558657i | \(-0.811317\pi\) | ||||
−0.829399 | + | 0.558657i | \(0.811317\pi\) | |||||||
\(618\) | −4.10978 | −0.165319 | ||||||||
\(619\) | 10.0042 | 0.402102 | 0.201051 | − | 0.979581i | \(-0.435564\pi\) | ||||
0.201051 | + | 0.979581i | \(0.435564\pi\) | |||||||
\(620\) | −0.412786 | −0.0165779 | ||||||||
\(621\) | −4.86181 | −0.195098 | ||||||||
\(622\) | −7.18264 | −0.287998 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.69340 | −0.187886 | ||||||||
\(625\) | −23.4009 | −0.936035 | ||||||||
\(626\) | −17.3529 | −0.693561 | ||||||||
\(627\) | −11.6939 | −0.467008 | ||||||||
\(628\) | −0.437025 | −0.0174392 | ||||||||
\(629\) | 25.7142 | 1.02529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0998 | −0.800162 | −0.400081 | − | 0.916480i | \(-0.631018\pi\) | ||||
−0.400081 | + | 0.916480i | \(0.631018\pi\) | |||||||
\(632\) | 0.131497 | 0.00523066 | ||||||||
\(633\) | 25.8993 | 1.02940 | ||||||||
\(634\) | −24.8672 | −0.987603 | ||||||||
\(635\) | 50.0205 | 1.98500 | ||||||||
\(636\) | 0.251141 | 0.00995841 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.0403 | 0.476679 | ||||||||
\(639\) | 7.54065 | 0.298303 | ||||||||
\(640\) | −38.1949 | −1.50979 | ||||||||
\(641\) | 11.2048 | 0.442564 | 0.221282 | − | 0.975210i | \(-0.428976\pi\) | ||||
0.221282 | + | 0.975210i | \(0.428976\pi\) | |||||||
\(642\) | −18.4868 | −0.729615 | ||||||||
\(643\) | −11.0643 | −0.436334 | −0.218167 | − | 0.975911i | \(-0.570008\pi\) | ||||
−0.218167 | + | 0.975911i | \(0.570008\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −22.4419 | −0.883651 | ||||||||
\(646\) | 25.7175 | 1.01184 | ||||||||
\(647\) | −0.620088 | −0.0243782 | −0.0121891 | − | 0.999926i | \(-0.503880\pi\) | ||||
−0.0121891 | + | 0.999926i | \(0.503880\pi\) | |||||||
\(648\) | 2.77376 | 0.108964 | ||||||||
\(649\) | 14.4059 | 0.565481 | ||||||||
\(650\) | −8.65053 | −0.339302 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.678924 | 0.0265887 | ||||||||
\(653\) | 32.5395 | 1.27337 | 0.636684 | − | 0.771125i | \(-0.280306\pi\) | ||||
0.636684 | + | 0.771125i | \(0.280306\pi\) | |||||||
\(654\) | 27.9852 | 1.09431 | ||||||||
\(655\) | 35.9244 | 1.40368 | ||||||||
\(656\) | −4.14240 | −0.161733 | ||||||||
\(657\) | −9.11677 | −0.355679 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.2250 | −1.56694 | −0.783472 | − | 0.621427i | \(-0.786553\pi\) | ||||
−0.783472 | + | 0.621427i | \(0.786553\pi\) | |||||||
\(660\) | −0.881604 | −0.0343164 | ||||||||
\(661\) | 8.07046 | 0.313904 | 0.156952 | − | 0.987606i | \(-0.449833\pi\) | ||||
0.156952 | + | 0.987606i | \(0.449833\pi\) | |||||||
\(662\) | 16.8499 | 0.654888 | ||||||||
\(663\) | −6.42843 | −0.249659 | ||||||||
\(664\) | −22.2788 | −0.864587 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.52682 | 0.252909 | ||||||||
\(667\) | −10.9406 | −0.423623 | ||||||||
\(668\) | −1.49194 | −0.0577249 | ||||||||
\(669\) | 18.1127 | 0.700278 | ||||||||
\(670\) | 20.1549 | 0.778650 | ||||||||
\(671\) | −30.3559 | −1.17188 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.65901 | −0.333780 | −0.166890 | − | 0.985976i | \(-0.553373\pi\) | ||||
−0.166890 | + | 0.985976i | \(0.553373\pi\) | |||||||
\(674\) | −18.1722 | −0.699967 | ||||||||
\(675\) | 5.30163 | 0.204060 | ||||||||
\(676\) | −0.866195 | −0.0333152 | ||||||||
\(677\) | −41.8965 | −1.61021 | −0.805106 | − | 0.593131i | \(-0.797892\pi\) | ||||
−0.805106 | + | 0.593131i | \(0.797892\pi\) | |||||||
\(678\) | 12.9057 | 0.495642 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −50.5115 | −1.93703 | ||||||||
\(681\) | −12.9994 | −0.498139 | ||||||||
\(682\) | −9.30760 | −0.356406 | ||||||||
\(683\) | 3.33986 | 0.127796 | 0.0638981 | − | 0.997956i | \(-0.479647\pi\) | ||||
0.0638981 | + | 0.997956i | \(0.479647\pi\) | |||||||
\(684\) | 0.232697 | 0.00889737 | ||||||||
\(685\) | −30.9177 | −1.18130 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.48370 | 0.209216 | ||||||||
\(688\) | 28.9640 | 1.10424 | ||||||||
\(689\) | 3.84883 | 0.146629 | ||||||||
\(690\) | 22.4723 | 0.855507 | ||||||||
\(691\) | −37.2226 | −1.41602 | −0.708008 | − | 0.706205i | \(-0.750406\pi\) | ||||
−0.708008 | + | 0.706205i | \(0.750406\pi\) | |||||||
\(692\) | −1.68622 | −0.0641006 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.0055 | 1.21491 | ||||||||
\(695\) | −40.1063 | −1.52132 | ||||||||
\(696\) | 6.24186 | 0.236597 | ||||||||
\(697\) | −5.67373 | −0.214908 | ||||||||
\(698\) | −39.6681 | −1.50146 | ||||||||
\(699\) | 9.19946 | 0.347955 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.14668 | 0.345465 | 0.172733 | − | 0.984969i | \(-0.444740\pi\) | ||||
0.172733 | + | 0.984969i | \(0.444740\pi\) | |||||||
\(702\) | −1.63167 | −0.0615836 | ||||||||
\(703\) | −14.2649 | −0.538010 | ||||||||
\(704\) | −28.5440 | −1.07579 | ||||||||
\(705\) | −20.6703 | −0.778488 | ||||||||
\(706\) | 11.6907 | 0.439985 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.286663 | −0.0107735 | ||||||||
\(709\) | −6.00600 | −0.225560 | −0.112780 | − | 0.993620i | \(-0.535976\pi\) | ||||
−0.112780 | + | 0.993620i | \(0.535976\pi\) | |||||||
\(710\) | −34.8545 | −1.30807 | ||||||||
\(711\) | 0.0474074 | 0.00177792 | ||||||||
\(712\) | −25.8012 | −0.966939 | ||||||||
\(713\) | 8.45754 | 0.316737 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.5109 | −0.505278 | ||||||||
\(716\) | 1.65585 | 0.0618820 | ||||||||
\(717\) | 0.823059 | 0.0307377 | ||||||||
\(718\) | 23.9514 | 0.893859 | ||||||||
\(719\) | −33.9920 | −1.26769 | −0.633844 | − | 0.773461i | \(-0.718524\pi\) | ||||
−0.633844 | + | 0.773461i | \(0.718524\pi\) | |||||||
\(720\) | −13.2955 | −0.495494 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.0954 | 0.487362 | ||||||||
\(723\) | 6.48256 | 0.241089 | ||||||||
\(724\) | 1.39793 | 0.0519536 | ||||||||
\(725\) | 11.9304 | 0.443083 | ||||||||
\(726\) | −4.03736 | −0.149840 | ||||||||
\(727\) | −16.9197 | −0.627516 | −0.313758 | − | 0.949503i | \(-0.601588\pi\) | ||||
−0.313758 | + | 0.949503i | \(0.601588\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 42.1397 | 1.55966 | ||||||||
\(731\) | 39.6713 | 1.46730 | ||||||||
\(732\) | 0.604053 | 0.0223265 | ||||||||
\(733\) | 41.7959 | 1.54377 | 0.771884 | − | 0.635763i | \(-0.219315\pi\) | ||||
0.771884 | + | 0.635763i | \(0.219315\pi\) | |||||||
\(734\) | −33.8731 | −1.25028 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.03226 | −0.0749101 | ||||||||
\(737\) | 16.2003 | 0.596747 | ||||||||
\(738\) | −1.44011 | −0.0530114 | ||||||||
\(739\) | −9.12094 | −0.335519 | −0.167760 | − | 0.985828i | \(-0.553653\pi\) | ||||
−0.167760 | + | 0.985828i | \(0.553653\pi\) | |||||||
\(740\) | −1.07543 | −0.0395337 | ||||||||
\(741\) | 3.56615 | 0.131006 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.7676 | 1.16544 | 0.582720 | − | 0.812673i | \(-0.301988\pi\) | ||||
0.582720 | + | 0.812673i | \(0.301988\pi\) | |||||||
\(744\) | −4.82520 | −0.176900 | ||||||||
\(745\) | −44.2798 | −1.62229 | ||||||||
\(746\) | −20.7465 | −0.759585 | ||||||||
\(747\) | −8.03200 | −0.293875 | ||||||||
\(748\) | 1.55844 | 0.0569821 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.39419 | −0.0509085 | ||||||||
\(751\) | −2.28714 | −0.0834590 | −0.0417295 | − | 0.999129i | \(-0.513287\pi\) | ||||
−0.0417295 | + | 0.999129i | \(0.513287\pi\) | |||||||
\(752\) | 26.6775 | 0.972828 | ||||||||
\(753\) | 11.0992 | 0.404477 | ||||||||
\(754\) | −3.67179 | −0.133719 | ||||||||
\(755\) | 49.1950 | 1.79039 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.8962 | 1.26832 | 0.634162 | − | 0.773201i | \(-0.281345\pi\) | ||||
0.634162 | + | 0.773201i | \(0.281345\pi\) | |||||||
\(758\) | −7.03927 | −0.255678 | ||||||||
\(759\) | 18.0631 | 0.655650 | ||||||||
\(760\) | 28.0211 | 1.01643 | ||||||||
\(761\) | −21.0081 | −0.761544 | −0.380772 | − | 0.924669i | \(-0.624342\pi\) | ||||
−0.380772 | + | 0.924669i | \(0.624342\pi\) | |||||||
\(762\) | −22.4436 | −0.813046 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.43334 | 0.0518563 | ||||||||
\(765\) | −18.2105 | −0.658402 | ||||||||
\(766\) | −32.9717 | −1.19131 | ||||||||
\(767\) | −4.39321 | −0.158630 | ||||||||
\(768\) | 1.77195 | 0.0639397 | ||||||||
\(769\) | 18.4285 | 0.664548 | 0.332274 | − | 0.943183i | \(-0.392184\pi\) | ||||
0.332274 | + | 0.943183i | \(0.392184\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.44160 | −0.340031 | ||||||||
\(772\) | −0.664903 | −0.0239304 | ||||||||
\(773\) | 53.0919 | 1.90958 | 0.954791 | − | 0.297277i | \(-0.0960783\pi\) | ||||
0.954791 | + | 0.297277i | \(0.0960783\pi\) | |||||||
\(774\) | 10.0694 | 0.361938 | ||||||||
\(775\) | −9.22264 | −0.331287 | ||||||||
\(776\) | −49.6492 | −1.78230 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.6531 | −0.704597 | ||||||||
\(779\) | 3.14749 | 0.112770 | ||||||||
\(780\) | 0.268853 | 0.00962649 | ||||||||
\(781\) | −28.0158 | −1.00248 | ||||||||
\(782\) | −39.7250 | −1.42056 | ||||||||
\(783\) | 2.25032 | 0.0804200 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.9729 | −0.677171 | ||||||||
\(786\) | −16.1188 | −0.574939 | ||||||||
\(787\) | 23.7459 | 0.846451 | 0.423226 | − | 0.906024i | \(-0.360898\pi\) | ||||
0.423226 | + | 0.906024i | \(0.360898\pi\) | |||||||
\(788\) | −1.22960 | −0.0438029 | ||||||||
\(789\) | −12.5414 | −0.446484 | ||||||||
\(790\) | −0.219127 | −0.00779620 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.3054 | −0.366185 | ||||||||
\(793\) | 9.25732 | 0.328737 | ||||||||
\(794\) | −10.1961 | −0.361847 | ||||||||
\(795\) | 10.9030 | 0.386689 | ||||||||
\(796\) | 0.664493 | 0.0235523 | ||||||||
\(797\) | 49.8669 | 1.76638 | 0.883189 | − | 0.469018i | \(-0.155392\pi\) | ||||
0.883189 | + | 0.469018i | \(0.155392\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.5395 | 1.29267 | ||||||||
\(800\) | 2.21611 | 0.0783512 | ||||||||
\(801\) | −9.30187 | −0.328665 | ||||||||
\(802\) | 43.1607 | 1.52406 | ||||||||
\(803\) | 33.8716 | 1.19530 | ||||||||
\(804\) | −0.322371 | −0.0113691 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.83844 | 0.0999797 | ||||||||
\(807\) | 2.28195 | 0.0803286 | ||||||||
\(808\) | −8.64990 | −0.304302 | ||||||||
\(809\) | 8.65135 | 0.304165 | 0.152083 | − | 0.988368i | \(-0.451402\pi\) | ||||
0.152083 | + | 0.988368i | \(0.451402\pi\) | |||||||
\(810\) | −4.62221 | −0.162408 | ||||||||
\(811\) | 42.3391 | 1.48673 | 0.743363 | − | 0.668888i | \(-0.233229\pi\) | ||||
0.743363 | + | 0.668888i | \(0.233229\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.2113 | −0.428268 | ||||||||
\(814\) | −24.2491 | −0.849931 | ||||||||
\(815\) | 29.4746 | 1.03245 | ||||||||
\(816\) | 23.5028 | 0.822764 | ||||||||
\(817\) | −22.0075 | −0.769946 | ||||||||
\(818\) | 19.2588 | 0.673369 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.237290 | 0.00828652 | ||||||||
\(821\) | 14.9198 | 0.520703 | 0.260352 | − | 0.965514i | \(-0.416162\pi\) | ||||
0.260352 | + | 0.965514i | \(0.416162\pi\) | |||||||
\(822\) | 13.8724 | 0.483855 | ||||||||
\(823\) | −42.3059 | −1.47469 | −0.737346 | − | 0.675516i | \(-0.763921\pi\) | ||||
−0.737346 | + | 0.675516i | \(0.763921\pi\) | |||||||
\(824\) | 7.91571 | 0.275757 | ||||||||
\(825\) | −19.6972 | −0.685767 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.8508 | 0.655507 | 0.327754 | − | 0.944763i | \(-0.393708\pi\) | ||||
0.327754 | + | 0.944763i | \(0.393708\pi\) | |||||||
\(828\) | −0.359438 | −0.0124913 | ||||||||
\(829\) | −19.0982 | −0.663307 | −0.331654 | − | 0.943401i | \(-0.607606\pi\) | ||||
−0.331654 | + | 0.943401i | \(0.607606\pi\) | |||||||
\(830\) | 37.1256 | 1.28865 | ||||||||
\(831\) | −24.7287 | −0.857829 | ||||||||
\(832\) | 8.70476 | 0.301783 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 17.9952 | 0.623123 | ||||||||
\(835\) | −64.7706 | −2.24148 | ||||||||
\(836\) | −0.864539 | −0.0299007 | ||||||||
\(837\) | −1.73959 | −0.0601289 | ||||||||
\(838\) | 34.8870 | 1.20515 | ||||||||
\(839\) | −48.6318 | −1.67895 | −0.839477 | − | 0.543395i | \(-0.817139\pi\) | ||||
−0.839477 | + | 0.543395i | \(0.817139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.9360 | −0.825381 | ||||||||
\(842\) | 19.1273 | 0.659170 | ||||||||
\(843\) | −4.87088 | −0.167762 | ||||||||
\(844\) | 1.91476 | 0.0659087 | ||||||||
\(845\) | −37.6047 | −1.29364 | ||||||||
\(846\) | 9.27450 | 0.318864 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.0716 | −0.483221 | ||||||||
\(849\) | 4.43504 | 0.152210 | ||||||||
\(850\) | 43.3187 | 1.48582 | ||||||||
\(851\) | 22.0345 | 0.755332 | ||||||||
\(852\) | 0.557487 | 0.0190992 | ||||||||
\(853\) | −44.9375 | −1.53863 | −0.769316 | − | 0.638868i | \(-0.779403\pi\) | ||||
−0.769316 | + | 0.638868i | \(0.779403\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.1022 | 0.345488 | ||||||||
\(856\) | 35.6068 | 1.21702 | ||||||||
\(857\) | −5.26810 | −0.179955 | −0.0899774 | − | 0.995944i | \(-0.528679\pi\) | ||||
−0.0899774 | + | 0.995944i | \(0.528679\pi\) | |||||||
\(858\) | 6.06217 | 0.206959 | ||||||||
\(859\) | −22.2259 | −0.758336 | −0.379168 | − | 0.925328i | \(-0.623790\pi\) | ||||
−0.379168 | + | 0.925328i | \(0.623790\pi\) | |||||||
\(860\) | −1.65915 | −0.0565767 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.3668 | −0.795876 | ||||||||
\(863\) | −1.76373 | −0.0600380 | −0.0300190 | − | 0.999549i | \(-0.509557\pi\) | ||||
−0.0300190 | + | 0.999549i | \(0.509557\pi\) | |||||||
\(864\) | 0.418005 | 0.0142208 | ||||||||
\(865\) | −73.2052 | −2.48905 | ||||||||
\(866\) | 2.32348 | 0.0789551 | ||||||||
\(867\) | 15.1912 | 0.515921 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.176133 | −0.00597491 | ||||||||
\(870\) | −10.4015 | −0.352643 | ||||||||
\(871\) | −4.94044 | −0.167401 | ||||||||
\(872\) | −53.9015 | −1.82533 | ||||||||
\(873\) | −17.8996 | −0.605809 | ||||||||
\(874\) | 22.0373 | 0.745424 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.674011 | −0.0227727 | ||||||||
\(877\) | 30.4164 | 1.02709 | 0.513544 | − | 0.858063i | \(-0.328332\pi\) | ||||
0.513544 | + | 0.858063i | \(0.328332\pi\) | |||||||
\(878\) | 22.3018 | 0.752649 | ||||||||
\(879\) | 10.4636 | 0.352928 | ||||||||
\(880\) | 49.3968 | 1.66517 | ||||||||
\(881\) | −30.7584 | −1.03628 | −0.518138 | − | 0.855297i | \(-0.673375\pi\) | ||||
−0.518138 | + | 0.855297i | \(0.673375\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.3820 | 1.35896 | 0.679482 | − | 0.733693i | \(-0.262205\pi\) | ||||
0.679482 | + | 0.733693i | \(0.262205\pi\) | |||||||
\(884\) | −0.475260 | −0.0159847 | ||||||||
\(885\) | −12.4451 | −0.418338 | ||||||||
\(886\) | 18.6963 | 0.628114 | ||||||||
\(887\) | −15.3104 | −0.514073 | −0.257037 | − | 0.966402i | \(-0.582746\pi\) | ||||
−0.257037 | + | 0.966402i | \(0.582746\pi\) | |||||||
\(888\) | −12.5711 | −0.421859 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 42.9952 | 1.44120 | ||||||||
\(891\) | −3.71531 | −0.124467 | ||||||||
\(892\) | 1.33909 | 0.0448360 | ||||||||
\(893\) | −20.2702 | −0.678315 | ||||||||
\(894\) | 19.8678 | 0.664479 | ||||||||
\(895\) | 71.8866 | 2.40290 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.50851 | −0.183924 | ||||||||
\(898\) | 36.6521 | 1.22310 | ||||||||
\(899\) | −3.91463 | −0.130560 | ||||||||
\(900\) | 0.391954 | 0.0130651 | ||||||||
\(901\) | −19.2735 | −0.642094 | ||||||||
\(902\) | 5.35047 | 0.178151 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.8573 | −0.826743 | ||||||||
\(905\) | 60.6893 | 2.01738 | ||||||||
\(906\) | −22.0732 | −0.733333 | ||||||||
\(907\) | −37.4485 | −1.24346 | −0.621728 | − | 0.783233i | \(-0.713569\pi\) | ||||
−0.621728 | + | 0.783233i | \(0.713569\pi\) | |||||||
\(908\) | −0.961060 | −0.0318939 | ||||||||
\(909\) | −3.11847 | −0.103433 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.5170 | −0.480969 | −0.240485 | − | 0.970653i | \(-0.577306\pi\) | ||||
−0.240485 | + | 0.970653i | \(0.577306\pi\) | |||||||
\(912\) | −13.0381 | −0.431736 | ||||||||
\(913\) | 29.8413 | 0.987604 | ||||||||
\(914\) | −20.3807 | −0.674133 | ||||||||
\(915\) | 26.2242 | 0.866945 | ||||||||
\(916\) | 0.405415 | 0.0133953 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.17082 | 0.269677 | ||||||||
\(919\) | 9.79265 | 0.323030 | 0.161515 | − | 0.986870i | \(-0.448362\pi\) | ||||
0.161515 | + | 0.986870i | \(0.448362\pi\) | |||||||
\(920\) | −43.2833 | −1.42701 | ||||||||
\(921\) | −4.63816 | −0.152832 | ||||||||
\(922\) | −1.58611 | −0.0522357 | ||||||||
\(923\) | 8.54368 | 0.281219 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.0278 | −0.790028 | ||||||||
\(926\) | 26.6480 | 0.875708 | ||||||||
\(927\) | 2.85378 | 0.0937305 | ||||||||
\(928\) | 0.940645 | 0.0308782 | ||||||||
\(929\) | 34.6323 | 1.13625 | 0.568124 | − | 0.822943i | \(-0.307669\pi\) | ||||
0.568124 | + | 0.822943i | \(0.307669\pi\) | |||||||
\(930\) | 8.04074 | 0.263666 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.680124 | 0.0222782 | ||||||||
\(933\) | 4.98755 | 0.163285 | ||||||||
\(934\) | −37.6449 | −1.23178 | ||||||||
\(935\) | 67.6575 | 2.21264 | ||||||||
\(936\) | 3.14272 | 0.102723 | ||||||||
\(937\) | 26.5941 | 0.868793 | 0.434396 | − | 0.900722i | \(-0.356962\pi\) | ||||
0.434396 | + | 0.900722i | \(0.356962\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.0497 | 0.393226 | ||||||||
\(940\) | −1.52817 | −0.0498435 | ||||||||
\(941\) | 48.6579 | 1.58620 | 0.793101 | − | 0.609091i | \(-0.208465\pi\) | ||||
0.793101 | + | 0.609091i | \(0.208465\pi\) | |||||||
\(942\) | 8.51289 | 0.277365 | ||||||||
\(943\) | −4.86181 | −0.158322 | ||||||||
\(944\) | 16.0619 | 0.522771 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −37.4110 | −1.21634 | ||||||||
\(947\) | 20.1400 | 0.654462 | 0.327231 | − | 0.944944i | \(-0.393885\pi\) | ||||
0.327231 | + | 0.944944i | \(0.393885\pi\) | |||||||
\(948\) | 0.00350487 | 0.000113833 0 | ||||||||
\(949\) | −10.3294 | −0.335308 | ||||||||
\(950\) | −24.0309 | −0.779665 | ||||||||
\(951\) | 17.2675 | 0.559937 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.71373 | 0.0879063 | 0.0439531 | − | 0.999034i | \(-0.486005\pi\) | ||||
0.0439531 | + | 0.999034i | \(0.486005\pi\) | |||||||
\(954\) | −4.89203 | −0.158385 | ||||||||
\(955\) | 62.2265 | 2.01360 | ||||||||
\(956\) | 0.0608495 | 0.00196801 | ||||||||
\(957\) | −8.36064 | −0.270261 | ||||||||
\(958\) | 45.3371 | 1.46478 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 24.6589 | 0.795862 | ||||||||
\(961\) | −27.9738 | −0.902382 | ||||||||
\(962\) | 7.39499 | 0.238424 | ||||||||
\(963\) | 12.8370 | 0.413667 | ||||||||
\(964\) | 0.479262 | 0.0154360 | ||||||||
\(965\) | −28.8659 | −0.929226 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.3281 | −1.45765 | −0.728827 | − | 0.684698i | \(-0.759934\pi\) | ||||
−0.728827 | + | 0.684698i | \(0.759934\pi\) | |||||||
\(968\) | 7.77623 | 0.249938 | ||||||||
\(969\) | −17.8580 | −0.573681 | ||||||||
\(970\) | 82.7357 | 2.65648 | ||||||||
\(971\) | −55.2056 | −1.77163 | −0.885816 | − | 0.464036i | \(-0.846401\pi\) | ||||
−0.885816 | + | 0.464036i | \(0.846401\pi\) | |||||||
\(972\) | 0.0739309 | 0.00237134 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −20.6087 | −0.660345 | ||||||||
\(975\) | 6.00683 | 0.192373 | ||||||||
\(976\) | −33.8455 | −1.08337 | ||||||||
\(977\) | −26.8269 | −0.858268 | −0.429134 | − | 0.903241i | \(-0.641181\pi\) | ||||
−0.429134 | + | 0.903241i | \(0.641181\pi\) | |||||||
\(978\) | −13.2249 | −0.422885 | ||||||||
\(979\) | 34.5593 | 1.10452 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.4326 | −0.620436 | ||||||||
\(982\) | 31.3673 | 1.00097 | ||||||||
\(983\) | 19.9926 | 0.637664 | 0.318832 | − | 0.947811i | \(-0.396709\pi\) | ||||
0.318832 | + | 0.947811i | \(0.396709\pi\) | |||||||
\(984\) | 2.77376 | 0.0884243 | ||||||||
\(985\) | −53.3817 | −1.70088 | ||||||||
\(986\) | 18.3870 | 0.585561 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.263649 | 0.00838779 | ||||||||
\(989\) | 33.9943 | 1.08095 | ||||||||
\(990\) | 17.1729 | 0.545792 | ||||||||
\(991\) | 11.1839 | 0.355267 | 0.177633 | − | 0.984097i | \(-0.443156\pi\) | ||||
0.177633 | + | 0.984097i | \(0.443156\pi\) | |||||||
\(992\) | −0.727156 | −0.0230872 | ||||||||
\(993\) | −11.7004 | −0.371300 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.8481 | 0.914546 | ||||||||
\(996\) | −0.593813 | −0.0188157 | ||||||||
\(997\) | 45.4682 | 1.43999 | 0.719996 | − | 0.693979i | \(-0.244144\pi\) | ||||
0.719996 | + | 0.693979i | \(0.244144\pi\) | |||||||
\(998\) | 9.69298 | 0.306826 | ||||||||
\(999\) | −4.53215 | −0.143391 |
(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 | 6027.2.a.bm.1.6 | yes | 16 | |
7.6 | odd | 2 | 6027.2.a.bl.1.6 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bl.1.6 | ✓ | 16 | 7.6 | odd | 2 | ||
6027.2.a.bm.1.6 | yes | 16 | 1.1 | even | 1 | trivial |