Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 4 x^{13} - 22 x^{12} + 98 x^{11} + 164 x^{10} - 912 x^{9} - 374 x^{8} + 3996 x^{7} - 817 x^{6} - 8194 x^{5} + 4418 x^{4} + 6430 x^{3} - 4327 x^{2} - 922 x + 358 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(3.36433\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.36433 | 1.94239 | 0.971197 | − | 0.238277i | \(-0.0765826\pi\) | ||||
0.971197 | + | 0.238277i | \(0.0765826\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.01748 | 1.34946 | 0.674728 | − | 0.738066i | \(-0.264261\pi\) | ||||
0.674728 | + | 0.738066i | \(0.264261\pi\) | |||||||
\(6\) | 3.36433 | 1.37348 | ||||||||
\(7\) | −1.60598 | −0.607002 | −0.303501 | − | 0.952831i | \(-0.598156\pi\) | ||||
−0.303501 | + | 0.952831i | \(0.598156\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.31869 | 2.77290 | ||||||||
\(10\) | 3.01748 | 0.954210 | ||||||||
\(11\) | 4.74435 | 1.43047 | 0.715237 | − | 0.698882i | \(-0.246319\pi\) | ||||
0.715237 | + | 0.698882i | \(0.246319\pi\) | |||||||
\(12\) | 3.36433 | 0.971197 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.60598 | −0.429215 | ||||||||
\(15\) | 10.1518 | 2.62118 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.15064 | −0.764142 | −0.382071 | − | 0.924133i | \(-0.624789\pi\) | ||||
−0.382071 | + | 0.924133i | \(0.624789\pi\) | |||||||
\(18\) | 8.31869 | 1.96073 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 3.01748 | 0.674728 | ||||||||
\(21\) | −5.40303 | −1.17904 | ||||||||
\(22\) | 4.74435 | 1.01150 | ||||||||
\(23\) | −4.43766 | −0.925317 | −0.462658 | − | 0.886537i | \(-0.653104\pi\) | ||||
−0.462658 | + | 0.886537i | \(0.653104\pi\) | |||||||
\(24\) | 3.36433 | 0.686740 | ||||||||
\(25\) | 4.10516 | 0.821033 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.8938 | 3.44366 | ||||||||
\(28\) | −1.60598 | −0.303501 | ||||||||
\(29\) | 1.98215 | 0.368076 | 0.184038 | − | 0.982919i | \(-0.441083\pi\) | ||||
0.184038 | + | 0.982919i | \(0.441083\pi\) | |||||||
\(30\) | 10.1518 | 1.85345 | ||||||||
\(31\) | −3.75696 | −0.674771 | −0.337385 | − | 0.941367i | \(-0.609543\pi\) | ||||
−0.337385 | + | 0.941367i | \(0.609543\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 15.9615 | 2.77855 | ||||||||
\(34\) | −3.15064 | −0.540330 | ||||||||
\(35\) | −4.84600 | −0.819123 | ||||||||
\(36\) | 8.31869 | 1.38645 | ||||||||
\(37\) | −8.45099 | −1.38933 | −0.694667 | − | 0.719332i | \(-0.744448\pi\) | ||||
−0.694667 | + | 0.719332i | \(0.744448\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.01748 | 0.477105 | ||||||||
\(41\) | −6.86672 | −1.07240 | −0.536200 | − | 0.844091i | \(-0.680141\pi\) | ||||
−0.536200 | + | 0.844091i | \(0.680141\pi\) | |||||||
\(42\) | −5.40303 | −0.833706 | ||||||||
\(43\) | 4.39270 | 0.669880 | 0.334940 | − | 0.942239i | \(-0.391284\pi\) | ||||
0.334940 | + | 0.942239i | \(0.391284\pi\) | |||||||
\(44\) | 4.74435 | 0.715237 | ||||||||
\(45\) | 25.1014 | 3.74190 | ||||||||
\(46\) | −4.43766 | −0.654298 | ||||||||
\(47\) | −12.7582 | −1.86098 | −0.930489 | − | 0.366320i | \(-0.880618\pi\) | ||||
−0.930489 | + | 0.366320i | \(0.880618\pi\) | |||||||
\(48\) | 3.36433 | 0.485599 | ||||||||
\(49\) | −4.42084 | −0.631548 | ||||||||
\(50\) | 4.10516 | 0.580558 | ||||||||
\(51\) | −10.5998 | −1.48426 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.81896 | −1.34874 | −0.674369 | − | 0.738395i | \(-0.735584\pi\) | ||||
−0.674369 | + | 0.738395i | \(0.735584\pi\) | |||||||
\(54\) | 17.8938 | 2.43504 | ||||||||
\(55\) | 14.3160 | 1.93036 | ||||||||
\(56\) | −1.60598 | −0.214608 | ||||||||
\(57\) | 3.36433 | 0.445616 | ||||||||
\(58\) | 1.98215 | 0.260269 | ||||||||
\(59\) | −5.56162 | −0.724061 | −0.362031 | − | 0.932166i | \(-0.617916\pi\) | ||||
−0.362031 | + | 0.932166i | \(0.617916\pi\) | |||||||
\(60\) | 10.1518 | 1.31059 | ||||||||
\(61\) | 7.01205 | 0.897801 | 0.448901 | − | 0.893582i | \(-0.351816\pi\) | ||||
0.448901 | + | 0.893582i | \(0.351816\pi\) | |||||||
\(62\) | −3.75696 | −0.477135 | ||||||||
\(63\) | −13.3596 | −1.68315 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 15.9615 | 1.96473 | ||||||||
\(67\) | 4.31241 | 0.526844 | 0.263422 | − | 0.964681i | \(-0.415149\pi\) | ||||
0.263422 | + | 0.964681i | \(0.415149\pi\) | |||||||
\(68\) | −3.15064 | −0.382071 | ||||||||
\(69\) | −14.9297 | −1.79733 | ||||||||
\(70\) | −4.84600 | −0.579207 | ||||||||
\(71\) | 0.512626 | 0.0608375 | 0.0304187 | − | 0.999537i | \(-0.490316\pi\) | ||||
0.0304187 | + | 0.999537i | \(0.490316\pi\) | |||||||
\(72\) | 8.31869 | 0.980367 | ||||||||
\(73\) | −0.764448 | −0.0894719 | −0.0447359 | − | 0.998999i | \(-0.514245\pi\) | ||||
−0.0447359 | + | 0.998999i | \(0.514245\pi\) | |||||||
\(74\) | −8.45099 | −0.982407 | ||||||||
\(75\) | 13.8111 | 1.59477 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −7.61931 | −0.868301 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.84387 | −0.207452 | −0.103726 | − | 0.994606i | \(-0.533077\pi\) | ||||
−0.103726 | + | 0.994606i | \(0.533077\pi\) | |||||||
\(80\) | 3.01748 | 0.337364 | ||||||||
\(81\) | 35.2445 | 3.91606 | ||||||||
\(82\) | −6.86672 | −0.758302 | ||||||||
\(83\) | −15.5237 | −1.70395 | −0.851975 | − | 0.523582i | \(-0.824595\pi\) | ||||
−0.851975 | + | 0.523582i | \(0.824595\pi\) | |||||||
\(84\) | −5.40303 | −0.589519 | ||||||||
\(85\) | −9.50697 | −1.03118 | ||||||||
\(86\) | 4.39270 | 0.473677 | ||||||||
\(87\) | 6.66860 | 0.714949 | ||||||||
\(88\) | 4.74435 | 0.505749 | ||||||||
\(89\) | −6.85279 | −0.726394 | −0.363197 | − | 0.931712i | \(-0.618315\pi\) | ||||
−0.363197 | + | 0.931712i | \(0.618315\pi\) | |||||||
\(90\) | 25.1014 | 2.64592 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.43766 | −0.462658 | ||||||||
\(93\) | −12.6397 | −1.31067 | ||||||||
\(94\) | −12.7582 | −1.31591 | ||||||||
\(95\) | 3.01748 | 0.309587 | ||||||||
\(96\) | 3.36433 | 0.343370 | ||||||||
\(97\) | −0.986823 | −0.100197 | −0.0500983 | − | 0.998744i | \(-0.515953\pi\) | ||||
−0.0500983 | + | 0.998744i | \(0.515953\pi\) | |||||||
\(98\) | −4.42084 | −0.446572 | ||||||||
\(99\) | 39.4667 | 3.96656 | ||||||||
\(100\) | 4.10516 | 0.410516 | ||||||||
\(101\) | 5.62489 | 0.559698 | 0.279849 | − | 0.960044i | \(-0.409716\pi\) | ||||
0.279849 | + | 0.960044i | \(0.409716\pi\) | |||||||
\(102\) | −10.5998 | −1.04953 | ||||||||
\(103\) | 11.9279 | 1.17529 | 0.587646 | − | 0.809118i | \(-0.300055\pi\) | ||||
0.587646 | + | 0.809118i | \(0.300055\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.3035 | −1.59106 | ||||||||
\(106\) | −9.81896 | −0.953702 | ||||||||
\(107\) | −0.978249 | −0.0945709 | −0.0472854 | − | 0.998881i | \(-0.515057\pi\) | ||||
−0.0472854 | + | 0.998881i | \(0.515057\pi\) | |||||||
\(108\) | 17.8938 | 1.72183 | ||||||||
\(109\) | −11.2693 | −1.07941 | −0.539703 | − | 0.841855i | \(-0.681464\pi\) | ||||
−0.539703 | + | 0.841855i | \(0.681464\pi\) | |||||||
\(110\) | 14.3160 | 1.36497 | ||||||||
\(111\) | −28.4319 | −2.69863 | ||||||||
\(112\) | −1.60598 | −0.151751 | ||||||||
\(113\) | 15.2293 | 1.43266 | 0.716328 | − | 0.697764i | \(-0.245821\pi\) | ||||
0.716328 | + | 0.697764i | \(0.245821\pi\) | |||||||
\(114\) | 3.36433 | 0.315098 | ||||||||
\(115\) | −13.3905 | −1.24867 | ||||||||
\(116\) | 1.98215 | 0.184038 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.56162 | −0.511989 | ||||||||
\(119\) | 5.05985 | 0.463836 | ||||||||
\(120\) | 10.1518 | 0.926726 | ||||||||
\(121\) | 11.5088 | 1.04626 | ||||||||
\(122\) | 7.01205 | 0.634841 | ||||||||
\(123\) | −23.1019 | −2.08303 | ||||||||
\(124\) | −3.75696 | −0.337385 | ||||||||
\(125\) | −2.70015 | −0.241509 | ||||||||
\(126\) | −13.3596 | −1.19017 | ||||||||
\(127\) | 6.56275 | 0.582350 | 0.291175 | − | 0.956670i | \(-0.405954\pi\) | ||||
0.291175 | + | 0.956670i | \(0.405954\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 14.7785 | 1.30117 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.4259 | −1.43513 | −0.717567 | − | 0.696489i | \(-0.754744\pi\) | ||||
−0.717567 | + | 0.696489i | \(0.754744\pi\) | |||||||
\(132\) | 15.9615 | 1.38927 | ||||||||
\(133\) | −1.60598 | −0.139256 | ||||||||
\(134\) | 4.31241 | 0.372535 | ||||||||
\(135\) | 53.9941 | 4.64708 | ||||||||
\(136\) | −3.15064 | −0.270165 | ||||||||
\(137\) | 19.7835 | 1.69022 | 0.845111 | − | 0.534590i | \(-0.179534\pi\) | ||||
0.845111 | + | 0.534590i | \(0.179534\pi\) | |||||||
\(138\) | −14.9297 | −1.27090 | ||||||||
\(139\) | 17.9507 | 1.52256 | 0.761281 | − | 0.648423i | \(-0.224571\pi\) | ||||
0.761281 | + | 0.648423i | \(0.224571\pi\) | |||||||
\(140\) | −4.84600 | −0.409562 | ||||||||
\(141\) | −42.9228 | −3.61475 | ||||||||
\(142\) | 0.512626 | 0.0430186 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.31869 | 0.693224 | ||||||||
\(145\) | 5.98109 | 0.496703 | ||||||||
\(146\) | −0.764448 | −0.0632662 | ||||||||
\(147\) | −14.8731 | −1.22672 | ||||||||
\(148\) | −8.45099 | −0.694667 | ||||||||
\(149\) | −5.34727 | −0.438066 | −0.219033 | − | 0.975717i | \(-0.570290\pi\) | ||||
−0.219033 | + | 0.975717i | \(0.570290\pi\) | |||||||
\(150\) | 13.8111 | 1.12767 | ||||||||
\(151\) | −5.24105 | −0.426510 | −0.213255 | − | 0.976997i | \(-0.568407\pi\) | ||||
−0.213255 | + | 0.976997i | \(0.568407\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −26.2092 | −2.11889 | ||||||||
\(154\) | −7.61931 | −0.613982 | ||||||||
\(155\) | −11.3366 | −0.910574 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.18765 | −0.174593 | −0.0872967 | − | 0.996182i | \(-0.527823\pi\) | ||||
−0.0872967 | + | 0.996182i | \(0.527823\pi\) | |||||||
\(158\) | −1.84387 | −0.146691 | ||||||||
\(159\) | −33.0342 | −2.61978 | ||||||||
\(160\) | 3.01748 | 0.238552 | ||||||||
\(161\) | 7.12678 | 0.561669 | ||||||||
\(162\) | 35.2445 | 2.76907 | ||||||||
\(163\) | 6.48287 | 0.507778 | 0.253889 | − | 0.967233i | \(-0.418290\pi\) | ||||
0.253889 | + | 0.967233i | \(0.418290\pi\) | |||||||
\(164\) | −6.86672 | −0.536200 | ||||||||
\(165\) | 48.1635 | 3.74953 | ||||||||
\(166\) | −15.5237 | −1.20488 | ||||||||
\(167\) | 7.51569 | 0.581581 | 0.290791 | − | 0.956787i | \(-0.406082\pi\) | ||||
0.290791 | + | 0.956787i | \(0.406082\pi\) | |||||||
\(168\) | −5.40303 | −0.416853 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −9.50697 | −0.729152 | ||||||||
\(171\) | 8.31869 | 0.636146 | ||||||||
\(172\) | 4.39270 | 0.334940 | ||||||||
\(173\) | 18.9342 | 1.43954 | 0.719769 | − | 0.694214i | \(-0.244248\pi\) | ||||
0.719769 | + | 0.694214i | \(0.244248\pi\) | |||||||
\(174\) | 6.66860 | 0.505545 | ||||||||
\(175\) | −6.59280 | −0.498369 | ||||||||
\(176\) | 4.74435 | 0.357619 | ||||||||
\(177\) | −18.7111 | −1.40641 | ||||||||
\(178\) | −6.85279 | −0.513638 | ||||||||
\(179\) | −5.62248 | −0.420244 | −0.210122 | − | 0.977675i | \(-0.567386\pi\) | ||||
−0.210122 | + | 0.977675i | \(0.567386\pi\) | |||||||
\(180\) | 25.1014 | 1.87095 | ||||||||
\(181\) | 10.2724 | 0.763538 | 0.381769 | − | 0.924258i | \(-0.375315\pi\) | ||||
0.381769 | + | 0.924258i | \(0.375315\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.5908 | 1.74388 | ||||||||
\(184\) | −4.43766 | −0.327149 | ||||||||
\(185\) | −25.5007 | −1.87485 | ||||||||
\(186\) | −12.6397 | −0.926784 | ||||||||
\(187\) | −14.9477 | −1.09309 | ||||||||
\(188\) | −12.7582 | −0.930489 | ||||||||
\(189\) | −28.7370 | −2.09031 | ||||||||
\(190\) | 3.01748 | 0.218911 | ||||||||
\(191\) | −17.6817 | −1.27941 | −0.639703 | − | 0.768622i | \(-0.720943\pi\) | ||||
−0.639703 | + | 0.768622i | \(0.720943\pi\) | |||||||
\(192\) | 3.36433 | 0.242799 | ||||||||
\(193\) | −1.74232 | −0.125415 | −0.0627075 | − | 0.998032i | \(-0.519974\pi\) | ||||
−0.0627075 | + | 0.998032i | \(0.519974\pi\) | |||||||
\(194\) | −0.986823 | −0.0708497 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.42084 | −0.315774 | ||||||||
\(197\) | 24.5715 | 1.75065 | 0.875324 | − | 0.483536i | \(-0.160648\pi\) | ||||
0.875324 | + | 0.483536i | \(0.160648\pi\) | |||||||
\(198\) | 39.4667 | 2.80478 | ||||||||
\(199\) | −15.6179 | −1.10712 | −0.553561 | − | 0.832808i | \(-0.686732\pi\) | ||||
−0.553561 | + | 0.832808i | \(0.686732\pi\) | |||||||
\(200\) | 4.10516 | 0.290279 | ||||||||
\(201\) | 14.5083 | 1.02334 | ||||||||
\(202\) | 5.62489 | 0.395766 | ||||||||
\(203\) | −3.18329 | −0.223423 | ||||||||
\(204\) | −10.5998 | −0.742132 | ||||||||
\(205\) | −20.7202 | −1.44716 | ||||||||
\(206\) | 11.9279 | 0.831056 | ||||||||
\(207\) | −36.9155 | −2.56581 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.74435 | 0.328173 | ||||||||
\(210\) | −16.3035 | −1.12505 | ||||||||
\(211\) | 6.76086 | 0.465437 | 0.232718 | − | 0.972544i | \(-0.425238\pi\) | ||||
0.232718 | + | 0.972544i | \(0.425238\pi\) | |||||||
\(212\) | −9.81896 | −0.674369 | ||||||||
\(213\) | 1.72464 | 0.118170 | ||||||||
\(214\) | −0.978249 | −0.0668717 | ||||||||
\(215\) | 13.2549 | 0.903974 | ||||||||
\(216\) | 17.8938 | 1.21752 | ||||||||
\(217\) | 6.03360 | 0.409587 | ||||||||
\(218\) | −11.2693 | −0.763256 | ||||||||
\(219\) | −2.57185 | −0.173790 | ||||||||
\(220\) | 14.3160 | 0.965181 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −28.4319 | −1.90822 | ||||||||
\(223\) | −1.03472 | −0.0692903 | −0.0346451 | − | 0.999400i | \(-0.511030\pi\) | ||||
−0.0346451 | + | 0.999400i | \(0.511030\pi\) | |||||||
\(224\) | −1.60598 | −0.107304 | ||||||||
\(225\) | 34.1496 | 2.27664 | ||||||||
\(226\) | 15.2293 | 1.01304 | ||||||||
\(227\) | 15.5518 | 1.03221 | 0.516104 | − | 0.856526i | \(-0.327382\pi\) | ||||
0.516104 | + | 0.856526i | \(0.327382\pi\) | |||||||
\(228\) | 3.36433 | 0.222808 | ||||||||
\(229\) | −1.43041 | −0.0945243 | −0.0472621 | − | 0.998883i | \(-0.515050\pi\) | ||||
−0.0472621 | + | 0.998883i | \(0.515050\pi\) | |||||||
\(230\) | −13.3905 | −0.882946 | ||||||||
\(231\) | −25.6338 | −1.68658 | ||||||||
\(232\) | 1.98215 | 0.130135 | ||||||||
\(233\) | 1.48502 | 0.0972871 | 0.0486436 | − | 0.998816i | \(-0.484510\pi\) | ||||
0.0486436 | + | 0.998816i | \(0.484510\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −38.4976 | −2.51131 | ||||||||
\(236\) | −5.56162 | −0.362031 | ||||||||
\(237\) | −6.20340 | −0.402954 | ||||||||
\(238\) | 5.05985 | 0.327981 | ||||||||
\(239\) | 7.28803 | 0.471423 | 0.235712 | − | 0.971823i | \(-0.424258\pi\) | ||||
0.235712 | + | 0.971823i | \(0.424258\pi\) | |||||||
\(240\) | 10.1518 | 0.655294 | ||||||||
\(241\) | 10.0796 | 0.649282 | 0.324641 | − | 0.945837i | \(-0.394757\pi\) | ||||
0.324641 | + | 0.945837i | \(0.394757\pi\) | |||||||
\(242\) | 11.5088 | 0.739815 | ||||||||
\(243\) | 64.8927 | 4.16287 | ||||||||
\(244\) | 7.01205 | 0.448901 | ||||||||
\(245\) | −13.3398 | −0.852247 | ||||||||
\(246\) | −23.1019 | −1.47292 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.75696 | −0.238568 | ||||||||
\(249\) | −52.2269 | −3.30974 | ||||||||
\(250\) | −2.70015 | −0.170772 | ||||||||
\(251\) | 19.6753 | 1.24190 | 0.620948 | − | 0.783852i | \(-0.286748\pi\) | ||||
0.620948 | + | 0.783852i | \(0.286748\pi\) | |||||||
\(252\) | −13.3596 | −0.841577 | ||||||||
\(253\) | −21.0538 | −1.32364 | ||||||||
\(254\) | 6.56275 | 0.411783 | ||||||||
\(255\) | −31.9846 | −2.00295 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.1766 | 1.07145 | 0.535723 | − | 0.844394i | \(-0.320039\pi\) | ||||
0.535723 | + | 0.844394i | \(0.320039\pi\) | |||||||
\(258\) | 14.7785 | 0.920067 | ||||||||
\(259\) | 13.5721 | 0.843329 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.4889 | 1.02064 | ||||||||
\(262\) | −16.4259 | −1.01479 | ||||||||
\(263\) | −7.47064 | −0.460660 | −0.230330 | − | 0.973113i | \(-0.573980\pi\) | ||||
−0.230330 | + | 0.973113i | \(0.573980\pi\) | |||||||
\(264\) | 15.9615 | 0.982364 | ||||||||
\(265\) | −29.6285 | −1.82006 | ||||||||
\(266\) | −1.60598 | −0.0984688 | ||||||||
\(267\) | −23.0550 | −1.41094 | ||||||||
\(268\) | 4.31241 | 0.263422 | ||||||||
\(269\) | 12.2533 | 0.747098 | 0.373549 | − | 0.927610i | \(-0.378141\pi\) | ||||
0.373549 | + | 0.927610i | \(0.378141\pi\) | |||||||
\(270\) | 53.9941 | 3.28598 | ||||||||
\(271\) | −2.46954 | −0.150014 | −0.0750069 | − | 0.997183i | \(-0.523898\pi\) | ||||
−0.0750069 | + | 0.997183i | \(0.523898\pi\) | |||||||
\(272\) | −3.15064 | −0.191035 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.7835 | 1.19517 | ||||||||
\(275\) | 19.4763 | 1.17447 | ||||||||
\(276\) | −14.9297 | −0.898665 | ||||||||
\(277\) | 17.7074 | 1.06393 | 0.531967 | − | 0.846765i | \(-0.321453\pi\) | ||||
0.531967 | + | 0.846765i | \(0.321453\pi\) | |||||||
\(278\) | 17.9507 | 1.07661 | ||||||||
\(279\) | −31.2530 | −1.87107 | ||||||||
\(280\) | −4.84600 | −0.289604 | ||||||||
\(281\) | 29.7058 | 1.77210 | 0.886050 | − | 0.463589i | \(-0.153439\pi\) | ||||
0.886050 | + | 0.463589i | \(0.153439\pi\) | |||||||
\(282\) | −42.9228 | −2.55602 | ||||||||
\(283\) | −15.4985 | −0.921289 | −0.460645 | − | 0.887585i | \(-0.652382\pi\) | ||||
−0.460645 | + | 0.887585i | \(0.652382\pi\) | |||||||
\(284\) | 0.512626 | 0.0304187 | ||||||||
\(285\) | 10.1518 | 0.601339 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.0278 | 0.650950 | ||||||||
\(288\) | 8.31869 | 0.490183 | ||||||||
\(289\) | −7.07349 | −0.416087 | ||||||||
\(290\) | 5.98109 | 0.351222 | ||||||||
\(291\) | −3.31999 | −0.194621 | ||||||||
\(292\) | −0.764448 | −0.0447359 | ||||||||
\(293\) | −14.1662 | −0.827598 | −0.413799 | − | 0.910368i | \(-0.635798\pi\) | ||||
−0.413799 | + | 0.910368i | \(0.635798\pi\) | |||||||
\(294\) | −14.8731 | −0.867419 | ||||||||
\(295\) | −16.7821 | −0.977089 | ||||||||
\(296\) | −8.45099 | −0.491204 | ||||||||
\(297\) | 84.8944 | 4.92607 | ||||||||
\(298\) | −5.34727 | −0.309759 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 13.8111 | 0.797385 | ||||||||
\(301\) | −7.05457 | −0.406619 | ||||||||
\(302\) | −5.24105 | −0.301588 | ||||||||
\(303\) | 18.9240 | 1.08715 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 21.1587 | 1.21154 | ||||||||
\(306\) | −26.2092 | −1.49828 | ||||||||
\(307\) | 21.1538 | 1.20731 | 0.603655 | − | 0.797245i | \(-0.293710\pi\) | ||||
0.603655 | + | 0.797245i | \(0.293710\pi\) | |||||||
\(308\) | −7.61931 | −0.434151 | ||||||||
\(309\) | 40.1294 | 2.28288 | ||||||||
\(310\) | −11.3366 | −0.643873 | ||||||||
\(311\) | 11.3516 | 0.643690 | 0.321845 | − | 0.946792i | \(-0.395697\pi\) | ||||
0.321845 | + | 0.946792i | \(0.395697\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.5500 | −1.16155 | −0.580777 | − | 0.814063i | \(-0.697251\pi\) | ||||
−0.580777 | + | 0.814063i | \(0.697251\pi\) | |||||||
\(314\) | −2.18765 | −0.123456 | ||||||||
\(315\) | −40.3123 | −2.27134 | ||||||||
\(316\) | −1.84387 | −0.103726 | ||||||||
\(317\) | −1.70454 | −0.0957367 | −0.0478683 | − | 0.998854i | \(-0.515243\pi\) | ||||
−0.0478683 | + | 0.998854i | \(0.515243\pi\) | |||||||
\(318\) | −33.0342 | −1.85246 | ||||||||
\(319\) | 9.40401 | 0.526523 | ||||||||
\(320\) | 3.01748 | 0.168682 | ||||||||
\(321\) | −3.29115 | −0.183694 | ||||||||
\(322\) | 7.12678 | 0.397160 | ||||||||
\(323\) | −3.15064 | −0.175306 | ||||||||
\(324\) | 35.2445 | 1.95803 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.48287 | 0.359053 | ||||||||
\(327\) | −37.9137 | −2.09663 | ||||||||
\(328\) | −6.86672 | −0.379151 | ||||||||
\(329\) | 20.4894 | 1.12962 | ||||||||
\(330\) | 48.1635 | 2.65132 | ||||||||
\(331\) | 9.04476 | 0.497145 | 0.248573 | − | 0.968613i | \(-0.420039\pi\) | ||||
0.248573 | + | 0.968613i | \(0.420039\pi\) | |||||||
\(332\) | −15.5237 | −0.851975 | ||||||||
\(333\) | −70.3011 | −3.85248 | ||||||||
\(334\) | 7.51569 | 0.411240 | ||||||||
\(335\) | 13.0126 | 0.710954 | ||||||||
\(336\) | −5.40303 | −0.294759 | ||||||||
\(337\) | 22.5298 | 1.22727 | 0.613637 | − | 0.789588i | \(-0.289706\pi\) | ||||
0.613637 | + | 0.789588i | \(0.289706\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 51.2365 | 2.78278 | ||||||||
\(340\) | −9.50697 | −0.515588 | ||||||||
\(341\) | −17.8243 | −0.965242 | ||||||||
\(342\) | 8.31869 | 0.449823 | ||||||||
\(343\) | 18.3416 | 0.990353 | ||||||||
\(344\) | 4.39270 | 0.236838 | ||||||||
\(345\) | −45.0501 | −2.42542 | ||||||||
\(346\) | 18.9342 | 1.01791 | ||||||||
\(347\) | 30.5928 | 1.64231 | 0.821154 | − | 0.570707i | \(-0.193331\pi\) | ||||
0.821154 | + | 0.570707i | \(0.193331\pi\) | |||||||
\(348\) | 6.66860 | 0.357475 | ||||||||
\(349\) | 16.8111 | 0.899875 | 0.449937 | − | 0.893060i | \(-0.351446\pi\) | ||||
0.449937 | + | 0.893060i | \(0.351446\pi\) | |||||||
\(350\) | −6.59280 | −0.352400 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.74435 | 0.252875 | ||||||||
\(353\) | 12.5945 | 0.670338 | 0.335169 | − | 0.942158i | \(-0.391207\pi\) | ||||
0.335169 | + | 0.942158i | \(0.391207\pi\) | |||||||
\(354\) | −18.7111 | −0.994484 | ||||||||
\(355\) | 1.54684 | 0.0820975 | ||||||||
\(356\) | −6.85279 | −0.363197 | ||||||||
\(357\) | 17.0230 | 0.900952 | ||||||||
\(358\) | −5.62248 | −0.297157 | ||||||||
\(359\) | 17.9825 | 0.949078 | 0.474539 | − | 0.880234i | \(-0.342615\pi\) | ||||
0.474539 | + | 0.880234i | \(0.342615\pi\) | |||||||
\(360\) | 25.1014 | 1.32296 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 10.2724 | 0.539903 | ||||||||
\(363\) | 38.7194 | 2.03224 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.30670 | −0.120738 | ||||||||
\(366\) | 23.5908 | 1.23311 | ||||||||
\(367\) | 24.7904 | 1.29405 | 0.647023 | − | 0.762470i | \(-0.276014\pi\) | ||||
0.647023 | + | 0.762470i | \(0.276014\pi\) | |||||||
\(368\) | −4.43766 | −0.231329 | ||||||||
\(369\) | −57.1221 | −2.97366 | ||||||||
\(370\) | −25.5007 | −1.32572 | ||||||||
\(371\) | 15.7690 | 0.818687 | ||||||||
\(372\) | −12.6397 | −0.655336 | ||||||||
\(373\) | −11.3778 | −0.589118 | −0.294559 | − | 0.955633i | \(-0.595173\pi\) | ||||
−0.294559 | + | 0.955633i | \(0.595173\pi\) | |||||||
\(374\) | −14.9477 | −0.772928 | ||||||||
\(375\) | −9.08419 | −0.469105 | ||||||||
\(376\) | −12.7582 | −0.657955 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −28.7370 | −1.47807 | ||||||||
\(379\) | 17.2668 | 0.886934 | 0.443467 | − | 0.896291i | \(-0.353748\pi\) | ||||
0.443467 | + | 0.896291i | \(0.353748\pi\) | |||||||
\(380\) | 3.01748 | 0.154793 | ||||||||
\(381\) | 22.0792 | 1.13115 | ||||||||
\(382\) | −17.6817 | −0.904676 | ||||||||
\(383\) | −31.1832 | −1.59339 | −0.796694 | − | 0.604383i | \(-0.793420\pi\) | ||||
−0.796694 | + | 0.604383i | \(0.793420\pi\) | |||||||
\(384\) | 3.36433 | 0.171685 | ||||||||
\(385\) | −22.9911 | −1.17173 | ||||||||
\(386\) | −1.74232 | −0.0886818 | ||||||||
\(387\) | 36.5415 | 1.85751 | ||||||||
\(388\) | −0.986823 | −0.0500983 | ||||||||
\(389\) | −25.4245 | −1.28907 | −0.644536 | − | 0.764574i | \(-0.722949\pi\) | ||||
−0.644536 | + | 0.764574i | \(0.722949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.9815 | 0.707073 | ||||||||
\(392\) | −4.42084 | −0.223286 | ||||||||
\(393\) | −55.2620 | −2.78760 | ||||||||
\(394\) | 24.5715 | 1.23790 | ||||||||
\(395\) | −5.56385 | −0.279948 | ||||||||
\(396\) | 39.4667 | 1.98328 | ||||||||
\(397\) | −17.5256 | −0.879586 | −0.439793 | − | 0.898099i | \(-0.644948\pi\) | ||||
−0.439793 | + | 0.898099i | \(0.644948\pi\) | |||||||
\(398\) | −15.6179 | −0.782854 | ||||||||
\(399\) | −5.40303 | −0.270490 | ||||||||
\(400\) | 4.10516 | 0.205258 | ||||||||
\(401\) | 19.1479 | 0.956202 | 0.478101 | − | 0.878305i | \(-0.341325\pi\) | ||||
0.478101 | + | 0.878305i | \(0.341325\pi\) | |||||||
\(402\) | 14.5083 | 0.723610 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.62489 | 0.279849 | ||||||||
\(405\) | 106.350 | 5.28455 | ||||||||
\(406\) | −3.18329 | −0.157984 | ||||||||
\(407\) | −40.0944 | −1.98741 | ||||||||
\(408\) | −10.5998 | −0.524767 | ||||||||
\(409\) | −3.57350 | −0.176698 | −0.0883490 | − | 0.996090i | \(-0.528159\pi\) | ||||
−0.0883490 | + | 0.996090i | \(0.528159\pi\) | |||||||
\(410\) | −20.7202 | −1.02330 | ||||||||
\(411\) | 66.5583 | 3.28308 | ||||||||
\(412\) | 11.9279 | 0.587646 | ||||||||
\(413\) | 8.93183 | 0.439507 | ||||||||
\(414\) | −36.9155 | −1.81430 | ||||||||
\(415\) | −46.8425 | −2.29941 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 60.3921 | 2.95741 | ||||||||
\(418\) | 4.74435 | 0.232054 | ||||||||
\(419\) | 9.65745 | 0.471797 | 0.235899 | − | 0.971778i | \(-0.424197\pi\) | ||||
0.235899 | + | 0.971778i | \(0.424197\pi\) | |||||||
\(420\) | −16.3035 | −0.795530 | ||||||||
\(421\) | 11.6457 | 0.567577 | 0.283788 | − | 0.958887i | \(-0.408409\pi\) | ||||
0.283788 | + | 0.958887i | \(0.408409\pi\) | |||||||
\(422\) | 6.76086 | 0.329114 | ||||||||
\(423\) | −106.132 | −5.16030 | ||||||||
\(424\) | −9.81896 | −0.476851 | ||||||||
\(425\) | −12.9339 | −0.627385 | ||||||||
\(426\) | 1.72464 | 0.0835591 | ||||||||
\(427\) | −11.2612 | −0.544967 | ||||||||
\(428\) | −0.978249 | −0.0472854 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.2549 | 0.639206 | ||||||||
\(431\) | −35.6809 | −1.71869 | −0.859344 | − | 0.511398i | \(-0.829128\pi\) | ||||
−0.859344 | + | 0.511398i | \(0.829128\pi\) | |||||||
\(432\) | 17.8938 | 0.860916 | ||||||||
\(433\) | −12.4345 | −0.597565 | −0.298782 | − | 0.954321i | \(-0.596580\pi\) | ||||
−0.298782 | + | 0.954321i | \(0.596580\pi\) | |||||||
\(434\) | 6.03360 | 0.289622 | ||||||||
\(435\) | 20.1223 | 0.964793 | ||||||||
\(436\) | −11.2693 | −0.539703 | ||||||||
\(437\) | −4.43766 | −0.212282 | ||||||||
\(438\) | −2.57185 | −0.122888 | ||||||||
\(439\) | 22.1563 | 1.05746 | 0.528732 | − | 0.848789i | \(-0.322668\pi\) | ||||
0.528732 | + | 0.848789i | \(0.322668\pi\) | |||||||
\(440\) | 14.3160 | 0.682486 | ||||||||
\(441\) | −36.7756 | −1.75122 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.3851 | −1.34862 | −0.674309 | − | 0.738449i | \(-0.735558\pi\) | ||||
−0.674309 | + | 0.738449i | \(0.735558\pi\) | |||||||
\(444\) | −28.4319 | −1.34932 | ||||||||
\(445\) | −20.6781 | −0.980237 | ||||||||
\(446\) | −1.03472 | −0.0489956 | ||||||||
\(447\) | −17.9900 | −0.850897 | ||||||||
\(448\) | −1.60598 | −0.0758753 | ||||||||
\(449\) | −19.4234 | −0.916648 | −0.458324 | − | 0.888785i | \(-0.651550\pi\) | ||||
−0.458324 | + | 0.888785i | \(0.651550\pi\) | |||||||
\(450\) | 34.1496 | 1.60983 | ||||||||
\(451\) | −32.5781 | −1.53404 | ||||||||
\(452\) | 15.2293 | 0.716328 | ||||||||
\(453\) | −17.6326 | −0.828452 | ||||||||
\(454\) | 15.5518 | 0.729882 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.36433 | 0.157549 | ||||||||
\(457\) | −1.69519 | −0.0792979 | −0.0396489 | − | 0.999214i | \(-0.512624\pi\) | ||||
−0.0396489 | + | 0.999214i | \(0.512624\pi\) | |||||||
\(458\) | −1.43041 | −0.0668388 | ||||||||
\(459\) | −56.3769 | −2.63145 | ||||||||
\(460\) | −13.3905 | −0.624337 | ||||||||
\(461\) | −32.8331 | −1.52919 | −0.764594 | − | 0.644512i | \(-0.777060\pi\) | ||||
−0.764594 | + | 0.644512i | \(0.777060\pi\) | |||||||
\(462\) | −25.6338 | −1.19259 | ||||||||
\(463\) | 26.2428 | 1.21960 | 0.609802 | − | 0.792554i | \(-0.291249\pi\) | ||||
0.609802 | + | 0.792554i | \(0.291249\pi\) | |||||||
\(464\) | 1.98215 | 0.0920190 | ||||||||
\(465\) | −38.1399 | −1.76869 | ||||||||
\(466\) | 1.48502 | 0.0687924 | ||||||||
\(467\) | −16.6106 | −0.768648 | −0.384324 | − | 0.923198i | \(-0.625566\pi\) | ||||
−0.384324 | + | 0.923198i | \(0.625566\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.92563 | −0.319796 | ||||||||
\(470\) | −38.4976 | −1.77576 | ||||||||
\(471\) | −7.35996 | −0.339129 | ||||||||
\(472\) | −5.56162 | −0.255994 | ||||||||
\(473\) | 20.8405 | 0.958246 | ||||||||
\(474\) | −6.20340 | −0.284931 | ||||||||
\(475\) | 4.10516 | 0.188358 | ||||||||
\(476\) | 5.05985 | 0.231918 | ||||||||
\(477\) | −81.6809 | −3.73991 | ||||||||
\(478\) | 7.28803 | 0.333347 | ||||||||
\(479\) | 22.7182 | 1.03802 | 0.519012 | − | 0.854767i | \(-0.326300\pi\) | ||||
0.519012 | + | 0.854767i | \(0.326300\pi\) | |||||||
\(480\) | 10.1518 | 0.463363 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.0796 | 0.459112 | ||||||||
\(483\) | 23.9768 | 1.09098 | ||||||||
\(484\) | 11.5088 | 0.523128 | ||||||||
\(485\) | −2.97771 | −0.135211 | ||||||||
\(486\) | 64.8927 | 2.94359 | ||||||||
\(487\) | −16.0162 | −0.725765 | −0.362883 | − | 0.931835i | \(-0.618207\pi\) | ||||
−0.362883 | + | 0.931835i | \(0.618207\pi\) | |||||||
\(488\) | 7.01205 | 0.317421 | ||||||||
\(489\) | 21.8105 | 0.986305 | ||||||||
\(490\) | −13.3398 | −0.602630 | ||||||||
\(491\) | −10.4778 | −0.472856 | −0.236428 | − | 0.971649i | \(-0.575977\pi\) | ||||
−0.236428 | + | 0.971649i | \(0.575977\pi\) | |||||||
\(492\) | −23.1019 | −1.04151 | ||||||||
\(493\) | −6.24504 | −0.281262 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 119.090 | 5.35270 | ||||||||
\(496\) | −3.75696 | −0.168693 | ||||||||
\(497\) | −0.823265 | −0.0369285 | ||||||||
\(498\) | −52.2269 | −2.34034 | ||||||||
\(499\) | 12.8864 | 0.576873 | 0.288437 | − | 0.957499i | \(-0.406865\pi\) | ||||
0.288437 | + | 0.957499i | \(0.406865\pi\) | |||||||
\(500\) | −2.70015 | −0.120754 | ||||||||
\(501\) | 25.2852 | 1.12966 | ||||||||
\(502\) | 19.6753 | 0.878153 | ||||||||
\(503\) | 15.6110 | 0.696060 | 0.348030 | − | 0.937483i | \(-0.386851\pi\) | ||||
0.348030 | + | 0.937483i | \(0.386851\pi\) | |||||||
\(504\) | −13.3596 | −0.595085 | ||||||||
\(505\) | 16.9730 | 0.755288 | ||||||||
\(506\) | −21.0538 | −0.935956 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.56275 | 0.291175 | ||||||||
\(509\) | −32.9207 | −1.45919 | −0.729593 | − | 0.683882i | \(-0.760290\pi\) | ||||
−0.729593 | + | 0.683882i | \(0.760290\pi\) | |||||||
\(510\) | −31.9846 | −1.41630 | ||||||||
\(511\) | 1.22769 | 0.0543096 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 17.8938 | 0.790031 | ||||||||
\(514\) | 17.1766 | 0.757627 | ||||||||
\(515\) | 35.9922 | 1.58600 | ||||||||
\(516\) | 14.7785 | 0.650586 | ||||||||
\(517\) | −60.5294 | −2.66208 | ||||||||
\(518\) | 13.5721 | 0.596323 | ||||||||
\(519\) | 63.7007 | 2.79615 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.9328 | −0.960892 | −0.480446 | − | 0.877024i | \(-0.659525\pi\) | ||||
−0.480446 | + | 0.877024i | \(0.659525\pi\) | |||||||
\(522\) | 16.4889 | 0.721699 | ||||||||
\(523\) | 25.5453 | 1.11702 | 0.558509 | − | 0.829498i | \(-0.311374\pi\) | ||||
0.558509 | + | 0.829498i | \(0.311374\pi\) | |||||||
\(524\) | −16.4259 | −0.717567 | ||||||||
\(525\) | −22.1803 | −0.968028 | ||||||||
\(526\) | −7.47064 | −0.325736 | ||||||||
\(527\) | 11.8368 | 0.515621 | ||||||||
\(528\) | 15.9615 | 0.694636 | ||||||||
\(529\) | −3.30715 | −0.143789 | ||||||||
\(530\) | −29.6285 | −1.28698 | ||||||||
\(531\) | −46.2654 | −2.00775 | ||||||||
\(532\) | −1.60598 | −0.0696279 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −23.0550 | −0.997688 | ||||||||
\(535\) | −2.95184 | −0.127619 | ||||||||
\(536\) | 4.31241 | 0.186268 | ||||||||
\(537\) | −18.9159 | −0.816280 | ||||||||
\(538\) | 12.2533 | 0.528278 | ||||||||
\(539\) | −20.9740 | −0.903414 | ||||||||
\(540\) | 53.9941 | 2.32354 | ||||||||
\(541\) | −39.5212 | −1.69915 | −0.849575 | − | 0.527468i | \(-0.823142\pi\) | ||||
−0.849575 | + | 0.527468i | \(0.823142\pi\) | |||||||
\(542\) | −2.46954 | −0.106076 | ||||||||
\(543\) | 34.5596 | 1.48309 | ||||||||
\(544\) | −3.15064 | −0.135082 | ||||||||
\(545\) | −34.0050 | −1.45661 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.72014 | 0.0735480 | 0.0367740 | − | 0.999324i | \(-0.488292\pi\) | ||||
0.0367740 | + | 0.999324i | \(0.488292\pi\) | |||||||
\(548\) | 19.7835 | 0.845111 | ||||||||
\(549\) | 58.3311 | 2.48951 | ||||||||
\(550\) | 19.4763 | 0.830473 | ||||||||
\(551\) | 1.98215 | 0.0844425 | ||||||||
\(552\) | −14.9297 | −0.635452 | ||||||||
\(553\) | 2.96122 | 0.125924 | ||||||||
\(554\) | 17.7074 | 0.752315 | ||||||||
\(555\) | −85.7925 | −3.64169 | ||||||||
\(556\) | 17.9507 | 0.761281 | ||||||||
\(557\) | 25.0279 | 1.06046 | 0.530232 | − | 0.847852i | \(-0.322105\pi\) | ||||
0.530232 | + | 0.847852i | \(0.322105\pi\) | |||||||
\(558\) | −31.2530 | −1.32305 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.84600 | −0.204781 | ||||||||
\(561\) | −50.2890 | −2.12320 | ||||||||
\(562\) | 29.7058 | 1.25306 | ||||||||
\(563\) | −0.0275168 | −0.00115969 | −0.000579847 | − | 1.00000i | \(-0.500185\pi\) | ||||
−0.000579847 | 1.00000i | \(0.500185\pi\) | ||||||||
\(564\) | −42.9228 | −1.80738 | ||||||||
\(565\) | 45.9542 | 1.93331 | ||||||||
\(566\) | −15.4985 | −0.651450 | ||||||||
\(567\) | −56.6019 | −2.37706 | ||||||||
\(568\) | 0.512626 | 0.0215093 | ||||||||
\(569\) | −33.3603 | −1.39854 | −0.699269 | − | 0.714859i | \(-0.746491\pi\) | ||||
−0.699269 | + | 0.714859i | \(0.746491\pi\) | |||||||
\(570\) | 10.1518 | 0.425211 | ||||||||
\(571\) | −0.291209 | −0.0121867 | −0.00609336 | − | 0.999981i | \(-0.501940\pi\) | ||||
−0.00609336 | + | 0.999981i | \(0.501940\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −59.4871 | −2.48511 | ||||||||
\(574\) | 11.0278 | 0.460291 | ||||||||
\(575\) | −18.2173 | −0.759715 | ||||||||
\(576\) | 8.31869 | 0.346612 | ||||||||
\(577\) | 8.64988 | 0.360099 | 0.180050 | − | 0.983658i | \(-0.442374\pi\) | ||||
0.180050 | + | 0.983658i | \(0.442374\pi\) | |||||||
\(578\) | −7.07349 | −0.294218 | ||||||||
\(579\) | −5.86174 | −0.243605 | ||||||||
\(580\) | 5.98109 | 0.248351 | ||||||||
\(581\) | 24.9308 | 1.03430 | ||||||||
\(582\) | −3.31999 | −0.137618 | ||||||||
\(583\) | −46.5845 | −1.92933 | ||||||||
\(584\) | −0.764448 | −0.0316331 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.1662 | −0.585200 | ||||||||
\(587\) | 34.8523 | 1.43851 | 0.719254 | − | 0.694747i | \(-0.244484\pi\) | ||||
0.719254 | + | 0.694747i | \(0.244484\pi\) | |||||||
\(588\) | −14.8731 | −0.613358 | ||||||||
\(589\) | −3.75696 | −0.154803 | ||||||||
\(590\) | −16.7821 | −0.690906 | ||||||||
\(591\) | 82.6666 | 3.40045 | ||||||||
\(592\) | −8.45099 | −0.347333 | ||||||||
\(593\) | −29.5726 | −1.21440 | −0.607200 | − | 0.794549i | \(-0.707707\pi\) | ||||
−0.607200 | + | 0.794549i | \(0.707707\pi\) | |||||||
\(594\) | 84.8944 | 3.48326 | ||||||||
\(595\) | 15.2680 | 0.625926 | ||||||||
\(596\) | −5.34727 | −0.219033 | ||||||||
\(597\) | −52.5437 | −2.15047 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.2670 | 0.419497 | 0.209748 | − | 0.977755i | \(-0.432736\pi\) | ||||
0.209748 | + | 0.977755i | \(0.432736\pi\) | |||||||
\(600\) | 13.8111 | 0.563836 | ||||||||
\(601\) | −25.1219 | −1.02474 | −0.512372 | − | 0.858764i | \(-0.671233\pi\) | ||||
−0.512372 | + | 0.858764i | \(0.671233\pi\) | |||||||
\(602\) | −7.05457 | −0.287523 | ||||||||
\(603\) | 35.8736 | 1.46089 | ||||||||
\(604\) | −5.24105 | −0.213255 | ||||||||
\(605\) | 34.7276 | 1.41188 | ||||||||
\(606\) | 18.9240 | 0.768734 | ||||||||
\(607\) | 1.68508 | 0.0683953 | 0.0341977 | − | 0.999415i | \(-0.489112\pi\) | ||||
0.0341977 | + | 0.999415i | \(0.489112\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −10.7096 | −0.433976 | ||||||||
\(610\) | 21.1587 | 0.856691 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −26.2092 | −1.05944 | ||||||||
\(613\) | −4.01859 | −0.162309 | −0.0811547 | − | 0.996702i | \(-0.525861\pi\) | ||||
−0.0811547 | + | 0.996702i | \(0.525861\pi\) | |||||||
\(614\) | 21.1538 | 0.853697 | ||||||||
\(615\) | −69.7094 | −2.81095 | ||||||||
\(616\) | −7.61931 | −0.306991 | ||||||||
\(617\) | 13.5199 | 0.544293 | 0.272146 | − | 0.962256i | \(-0.412267\pi\) | ||||
0.272146 | + | 0.962256i | \(0.412267\pi\) | |||||||
\(618\) | 40.1294 | 1.61424 | ||||||||
\(619\) | 27.5059 | 1.10555 | 0.552777 | − | 0.833329i | \(-0.313568\pi\) | ||||
0.552777 | + | 0.833329i | \(0.313568\pi\) | |||||||
\(620\) | −11.3366 | −0.455287 | ||||||||
\(621\) | −79.4067 | −3.18648 | ||||||||
\(622\) | 11.3516 | 0.455157 | ||||||||
\(623\) | 11.0054 | 0.440923 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.6735 | −1.14694 | ||||||||
\(626\) | −20.5500 | −0.821342 | ||||||||
\(627\) | 15.9615 | 0.637442 | ||||||||
\(628\) | −2.18765 | −0.0872967 | ||||||||
\(629\) | 26.6260 | 1.06165 | ||||||||
\(630\) | −40.3123 | −1.60608 | ||||||||
\(631\) | 9.68396 | 0.385513 | 0.192756 | − | 0.981247i | \(-0.438257\pi\) | ||||
0.192756 | + | 0.981247i | \(0.438257\pi\) | |||||||
\(632\) | −1.84387 | −0.0733454 | ||||||||
\(633\) | 22.7457 | 0.904062 | ||||||||
\(634\) | −1.70454 | −0.0676961 | ||||||||
\(635\) | 19.8029 | 0.785856 | ||||||||
\(636\) | −33.0342 | −1.30989 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.40401 | 0.372308 | ||||||||
\(639\) | 4.26437 | 0.168696 | ||||||||
\(640\) | 3.01748 | 0.119276 | ||||||||
\(641\) | 14.2237 | 0.561802 | 0.280901 | − | 0.959737i | \(-0.409367\pi\) | ||||
0.280901 | + | 0.959737i | \(0.409367\pi\) | |||||||
\(642\) | −3.29115 | −0.129891 | ||||||||
\(643\) | −30.6473 | −1.20861 | −0.604306 | − | 0.796752i | \(-0.706550\pi\) | ||||
−0.604306 | + | 0.796752i | \(0.706550\pi\) | |||||||
\(644\) | 7.12678 | 0.280835 | ||||||||
\(645\) | 44.5937 | 1.75587 | ||||||||
\(646\) | −3.15064 | −0.123960 | ||||||||
\(647\) | −0.270247 | −0.0106245 | −0.00531226 | − | 0.999986i | \(-0.501691\pi\) | ||||
−0.00531226 | + | 0.999986i | \(0.501691\pi\) | |||||||
\(648\) | 35.2445 | 1.38454 | ||||||||
\(649\) | −26.3863 | −1.03575 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.2990 | 0.795580 | ||||||||
\(652\) | 6.48287 | 0.253889 | ||||||||
\(653\) | 27.9086 | 1.09215 | 0.546075 | − | 0.837736i | \(-0.316121\pi\) | ||||
0.546075 | + | 0.837736i | \(0.316121\pi\) | |||||||
\(654\) | −37.9137 | −1.48254 | ||||||||
\(655\) | −49.5647 | −1.93665 | ||||||||
\(656\) | −6.86672 | −0.268100 | ||||||||
\(657\) | −6.35921 | −0.248096 | ||||||||
\(658\) | 20.4894 | 0.798760 | ||||||||
\(659\) | 33.3056 | 1.29740 | 0.648701 | − | 0.761043i | \(-0.275313\pi\) | ||||
0.648701 | + | 0.761043i | \(0.275313\pi\) | |||||||
\(660\) | 48.1635 | 1.87476 | ||||||||
\(661\) | −10.9624 | −0.426389 | −0.213195 | − | 0.977010i | \(-0.568387\pi\) | ||||
−0.213195 | + | 0.977010i | \(0.568387\pi\) | |||||||
\(662\) | 9.04476 | 0.351535 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.5237 | −0.602438 | ||||||||
\(665\) | −4.84600 | −0.187920 | ||||||||
\(666\) | −70.3011 | −2.72411 | ||||||||
\(667\) | −8.79611 | −0.340587 | ||||||||
\(668\) | 7.51569 | 0.290791 | ||||||||
\(669\) | −3.48115 | −0.134589 | ||||||||
\(670\) | 13.0126 | 0.502720 | ||||||||
\(671\) | 33.2676 | 1.28428 | ||||||||
\(672\) | −5.40303 | −0.208426 | ||||||||
\(673\) | 5.63771 | 0.217318 | 0.108659 | − | 0.994079i | \(-0.465344\pi\) | ||||
0.108659 | + | 0.994079i | \(0.465344\pi\) | |||||||
\(674\) | 22.5298 | 0.867814 | ||||||||
\(675\) | 73.4570 | 2.82736 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.4262 | 1.05407 | 0.527037 | − | 0.849842i | \(-0.323303\pi\) | ||||
0.527037 | + | 0.849842i | \(0.323303\pi\) | |||||||
\(678\) | 51.2365 | 1.96772 | ||||||||
\(679\) | 1.58481 | 0.0608196 | ||||||||
\(680\) | −9.50697 | −0.364576 | ||||||||
\(681\) | 52.3213 | 2.00496 | ||||||||
\(682\) | −17.8243 | −0.682529 | ||||||||
\(683\) | −12.4989 | −0.478258 | −0.239129 | − | 0.970988i | \(-0.576862\pi\) | ||||
−0.239129 | + | 0.970988i | \(0.576862\pi\) | |||||||
\(684\) | 8.31869 | 0.318073 | ||||||||
\(685\) | 59.6964 | 2.28088 | ||||||||
\(686\) | 18.3416 | 0.700286 | ||||||||
\(687\) | −4.81237 | −0.183603 | ||||||||
\(688\) | 4.39270 | 0.167470 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −45.0501 | −1.71503 | ||||||||
\(691\) | −49.5378 | −1.88451 | −0.942254 | − | 0.334900i | \(-0.891298\pi\) | ||||
−0.942254 | + | 0.334900i | \(0.891298\pi\) | |||||||
\(692\) | 18.9342 | 0.719769 | ||||||||
\(693\) | −63.3827 | −2.40771 | ||||||||
\(694\) | 30.5928 | 1.16129 | ||||||||
\(695\) | 54.1659 | 2.05463 | ||||||||
\(696\) | 6.66860 | 0.252773 | ||||||||
\(697\) | 21.6345 | 0.819466 | ||||||||
\(698\) | 16.8111 | 0.636308 | ||||||||
\(699\) | 4.99610 | 0.188970 | ||||||||
\(700\) | −6.59280 | −0.249184 | ||||||||
\(701\) | −30.4261 | −1.14918 | −0.574589 | − | 0.818442i | \(-0.694838\pi\) | ||||
−0.574589 | + | 0.818442i | \(0.694838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.45099 | −0.318735 | ||||||||
\(704\) | 4.74435 | 0.178809 | ||||||||
\(705\) | −129.519 | −4.87795 | ||||||||
\(706\) | 12.5945 | 0.474001 | ||||||||
\(707\) | −9.03345 | −0.339738 | ||||||||
\(708\) | −18.7111 | −0.703206 | ||||||||
\(709\) | −34.3500 | −1.29004 | −0.645021 | − | 0.764165i | \(-0.723151\pi\) | ||||
−0.645021 | + | 0.764165i | \(0.723151\pi\) | |||||||
\(710\) | 1.54684 | 0.0580517 | ||||||||
\(711\) | −15.3386 | −0.575243 | ||||||||
\(712\) | −6.85279 | −0.256819 | ||||||||
\(713\) | 16.6721 | 0.624377 | ||||||||
\(714\) | 17.0230 | 0.637069 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.62248 | −0.210122 | ||||||||
\(717\) | 24.5193 | 0.915690 | ||||||||
\(718\) | 17.9825 | 0.671100 | ||||||||
\(719\) | −20.4893 | −0.764121 | −0.382060 | − | 0.924137i | \(-0.624785\pi\) | ||||
−0.382060 | + | 0.924137i | \(0.624785\pi\) | |||||||
\(720\) | 25.1014 | 0.935476 | ||||||||
\(721\) | −19.1559 | −0.713404 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 33.9109 | 1.26116 | ||||||||
\(724\) | 10.2724 | 0.381769 | ||||||||
\(725\) | 8.13705 | 0.302202 | ||||||||
\(726\) | 38.7194 | 1.43701 | ||||||||
\(727\) | 8.97463 | 0.332851 | 0.166425 | − | 0.986054i | \(-0.446778\pi\) | ||||
0.166425 | + | 0.986054i | \(0.446778\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 112.586 | 4.16987 | ||||||||
\(730\) | −2.30670 | −0.0853749 | ||||||||
\(731\) | −13.8398 | −0.511883 | ||||||||
\(732\) | 23.5908 | 0.871942 | ||||||||
\(733\) | 30.7616 | 1.13621 | 0.568103 | − | 0.822958i | \(-0.307678\pi\) | ||||
0.568103 | + | 0.822958i | \(0.307678\pi\) | |||||||
\(734\) | 24.7904 | 0.915029 | ||||||||
\(735\) | −44.8793 | −1.65540 | ||||||||
\(736\) | −4.43766 | −0.163574 | ||||||||
\(737\) | 20.4596 | 0.753637 | ||||||||
\(738\) | −57.1221 | −2.10269 | ||||||||
\(739\) | −25.8774 | −0.951914 | −0.475957 | − | 0.879469i | \(-0.657898\pi\) | ||||
−0.475957 | + | 0.879469i | \(0.657898\pi\) | |||||||
\(740\) | −25.5007 | −0.937423 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.7690 | 0.578899 | ||||||||
\(743\) | −3.70756 | −0.136017 | −0.0680086 | − | 0.997685i | \(-0.521665\pi\) | ||||
−0.0680086 | + | 0.997685i | \(0.521665\pi\) | |||||||
\(744\) | −12.6397 | −0.463392 | ||||||||
\(745\) | −16.1353 | −0.591151 | ||||||||
\(746\) | −11.3778 | −0.416569 | ||||||||
\(747\) | −129.137 | −4.72488 | ||||||||
\(748\) | −14.9477 | −0.546543 | ||||||||
\(749\) | 1.57105 | 0.0574047 | ||||||||
\(750\) | −9.08419 | −0.331708 | ||||||||
\(751\) | 26.1045 | 0.952566 | 0.476283 | − | 0.879292i | \(-0.341984\pi\) | ||||
0.476283 | + | 0.879292i | \(0.341984\pi\) | |||||||
\(752\) | −12.7582 | −0.465245 | ||||||||
\(753\) | 66.1943 | 2.41225 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.8147 | −0.575557 | ||||||||
\(756\) | −28.7370 | −1.04516 | ||||||||
\(757\) | −0.521137 | −0.0189411 | −0.00947053 | − | 0.999955i | \(-0.503015\pi\) | ||||
−0.00947053 | + | 0.999955i | \(0.503015\pi\) | |||||||
\(758\) | 17.2668 | 0.627157 | ||||||||
\(759\) | −70.8319 | −2.57103 | ||||||||
\(760\) | 3.01748 | 0.109455 | ||||||||
\(761\) | −48.2179 | −1.74790 | −0.873949 | − | 0.486018i | \(-0.838449\pi\) | ||||
−0.873949 | + | 0.486018i | \(0.838449\pi\) | |||||||
\(762\) | 22.0792 | 0.799846 | ||||||||
\(763\) | 18.0983 | 0.655202 | ||||||||
\(764\) | −17.6817 | −0.639703 | ||||||||
\(765\) | −79.0856 | −2.85934 | ||||||||
\(766\) | −31.1832 | −1.12670 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.36433 | 0.121400 | ||||||||
\(769\) | −11.6926 | −0.421646 | −0.210823 | − | 0.977524i | \(-0.567614\pi\) | ||||
−0.210823 | + | 0.977524i | \(0.567614\pi\) | |||||||
\(770\) | −22.9911 | −0.828541 | ||||||||
\(771\) | 57.7876 | 2.08117 | ||||||||
\(772\) | −1.74232 | −0.0627075 | ||||||||
\(773\) | −1.49281 | −0.0536927 | −0.0268463 | − | 0.999640i | \(-0.508546\pi\) | ||||
−0.0268463 | + | 0.999640i | \(0.508546\pi\) | |||||||
\(774\) | 36.5415 | 1.31346 | ||||||||
\(775\) | −15.4230 | −0.554009 | ||||||||
\(776\) | −0.986823 | −0.0354249 | ||||||||
\(777\) | 45.6609 | 1.63808 | ||||||||
\(778\) | −25.4245 | −0.911512 | ||||||||
\(779\) | −6.86672 | −0.246026 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.43207 | 0.0870264 | ||||||||
\(782\) | 13.9815 | 0.499976 | ||||||||
\(783\) | 35.4682 | 1.26753 | ||||||||
\(784\) | −4.42084 | −0.157887 | ||||||||
\(785\) | −6.60118 | −0.235606 | ||||||||
\(786\) | −55.2620 | −1.97113 | ||||||||
\(787\) | 23.6691 | 0.843713 | 0.421856 | − | 0.906663i | \(-0.361379\pi\) | ||||
0.421856 | + | 0.906663i | \(0.361379\pi\) | |||||||
\(788\) | 24.5715 | 0.875324 | ||||||||
\(789\) | −25.1337 | −0.894783 | ||||||||
\(790\) | −5.56385 | −0.197953 | ||||||||
\(791\) | −24.4580 | −0.869625 | ||||||||
\(792\) | 39.4667 | 1.40239 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −17.5256 | −0.621961 | ||||||||
\(795\) | −99.6798 | −3.53528 | ||||||||
\(796\) | −15.6179 | −0.553561 | ||||||||
\(797\) | −36.5242 | −1.29376 | −0.646878 | − | 0.762594i | \(-0.723926\pi\) | ||||
−0.646878 | + | 0.762594i | \(0.723926\pi\) | |||||||
\(798\) | −5.40303 | −0.191265 | ||||||||
\(799\) | 40.1965 | 1.42205 | ||||||||
\(800\) | 4.10516 | 0.145139 | ||||||||
\(801\) | −57.0062 | −2.01422 | ||||||||
\(802\) | 19.1479 | 0.676137 | ||||||||
\(803\) | −3.62681 | −0.127987 | ||||||||
\(804\) | 14.5083 | 0.511670 | ||||||||
\(805\) | 21.5049 | 0.757948 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 41.2242 | 1.45116 | ||||||||
\(808\) | 5.62489 | 0.197883 | ||||||||
\(809\) | 39.8942 | 1.40261 | 0.701303 | − | 0.712863i | \(-0.252602\pi\) | ||||
0.701303 | + | 0.712863i | \(0.252602\pi\) | |||||||
\(810\) | 106.350 | 3.73674 | ||||||||
\(811\) | −14.6962 | −0.516052 | −0.258026 | − | 0.966138i | \(-0.583072\pi\) | ||||
−0.258026 | + | 0.966138i | \(0.583072\pi\) | |||||||
\(812\) | −3.18329 | −0.111712 | ||||||||
\(813\) | −8.30833 | −0.291386 | ||||||||
\(814\) | −40.0944 | −1.40531 | ||||||||
\(815\) | 19.5619 | 0.685224 | ||||||||
\(816\) | −10.5998 | −0.371066 | ||||||||
\(817\) | 4.39270 | 0.153681 | ||||||||
\(818\) | −3.57350 | −0.124944 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.7202 | −0.723579 | ||||||||
\(821\) | 20.5084 | 0.715749 | 0.357874 | − | 0.933770i | \(-0.383502\pi\) | ||||
0.357874 | + | 0.933770i | \(0.383502\pi\) | |||||||
\(822\) | 66.5583 | 2.32149 | ||||||||
\(823\) | 26.9934 | 0.940931 | 0.470465 | − | 0.882418i | \(-0.344086\pi\) | ||||
0.470465 | + | 0.882418i | \(0.344086\pi\) | |||||||
\(824\) | 11.9279 | 0.415528 | ||||||||
\(825\) | 65.5247 | 2.28128 | ||||||||
\(826\) | 8.93183 | 0.310778 | ||||||||
\(827\) | 10.9795 | 0.381796 | 0.190898 | − | 0.981610i | \(-0.438860\pi\) | ||||
0.190898 | + | 0.981610i | \(0.438860\pi\) | |||||||
\(828\) | −36.9155 | −1.28290 | ||||||||
\(829\) | 9.08917 | 0.315680 | 0.157840 | − | 0.987465i | \(-0.449547\pi\) | ||||
0.157840 | + | 0.987465i | \(0.449547\pi\) | |||||||
\(830\) | −46.8425 | −1.62593 | ||||||||
\(831\) | 59.5734 | 2.06658 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.9285 | 0.482592 | ||||||||
\(834\) | 60.3921 | 2.09121 | ||||||||
\(835\) | 22.6784 | 0.784818 | ||||||||
\(836\) | 4.74435 | 0.164087 | ||||||||
\(837\) | −67.2264 | −2.32368 | ||||||||
\(838\) | 9.65745 | 0.333611 | ||||||||
\(839\) | −1.83497 | −0.0633502 | −0.0316751 | − | 0.999498i | \(-0.510084\pi\) | ||||
−0.0316751 | + | 0.999498i | \(0.510084\pi\) | |||||||
\(840\) | −16.3035 | −0.562525 | ||||||||
\(841\) | −25.0711 | −0.864520 | ||||||||
\(842\) | 11.6457 | 0.401338 | ||||||||
\(843\) | 99.9401 | 3.44212 | ||||||||
\(844\) | 6.76086 | 0.232718 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −106.132 | −3.64888 | ||||||||
\(847\) | −18.4829 | −0.635080 | ||||||||
\(848\) | −9.81896 | −0.337184 | ||||||||
\(849\) | −52.1420 | −1.78951 | ||||||||
\(850\) | −12.9339 | −0.443628 | ||||||||
\(851\) | 37.5026 | 1.28557 | ||||||||
\(852\) | 1.72464 | 0.0590852 | ||||||||
\(853\) | −0.647190 | −0.0221594 | −0.0110797 | − | 0.999939i | \(-0.503527\pi\) | ||||
−0.0110797 | + | 0.999939i | \(0.503527\pi\) | |||||||
\(854\) | −11.2612 | −0.385350 | ||||||||
\(855\) | 25.1014 | 0.858451 | ||||||||
\(856\) | −0.978249 | −0.0334359 | ||||||||
\(857\) | 34.2606 | 1.17032 | 0.585161 | − | 0.810917i | \(-0.301031\pi\) | ||||
0.585161 | + | 0.810917i | \(0.301031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −55.5935 | −1.89683 | −0.948414 | − | 0.317036i | \(-0.897313\pi\) | ||||
−0.948414 | + | 0.317036i | \(0.897313\pi\) | |||||||
\(860\) | 13.2549 | 0.451987 | ||||||||
\(861\) | 37.1011 | 1.26440 | ||||||||
\(862\) | −35.6809 | −1.21530 | ||||||||
\(863\) | −3.48869 | −0.118756 | −0.0593781 | − | 0.998236i | \(-0.518912\pi\) | ||||
−0.0593781 | + | 0.998236i | \(0.518912\pi\) | |||||||
\(864\) | 17.8938 | 0.608760 | ||||||||
\(865\) | 57.1334 | 1.94259 | ||||||||
\(866\) | −12.4345 | −0.422542 | ||||||||
\(867\) | −23.7975 | −0.808206 | ||||||||
\(868\) | 6.03360 | 0.204794 | ||||||||
\(869\) | −8.74798 | −0.296755 | ||||||||
\(870\) | 20.1223 | 0.682211 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −11.2693 | −0.381628 | ||||||||
\(873\) | −8.20907 | −0.277835 | ||||||||
\(874\) | −4.43766 | −0.150106 | ||||||||
\(875\) | 4.33638 | 0.146596 | ||||||||
\(876\) | −2.57185 | −0.0868948 | ||||||||
\(877\) | 8.78684 | 0.296710 | 0.148355 | − | 0.988934i | \(-0.452602\pi\) | ||||
0.148355 | + | 0.988934i | \(0.452602\pi\) | |||||||
\(878\) | 22.1563 | 0.747739 | ||||||||
\(879\) | −47.6597 | −1.60752 | ||||||||
\(880\) | 14.3160 | 0.482591 | ||||||||
\(881\) | 8.39000 | 0.282666 | 0.141333 | − | 0.989962i | \(-0.454861\pi\) | ||||
0.141333 | + | 0.989962i | \(0.454861\pi\) | |||||||
\(882\) | −36.7756 | −1.23830 | ||||||||
\(883\) | −26.2560 | −0.883586 | −0.441793 | − | 0.897117i | \(-0.645658\pi\) | ||||
−0.441793 | + | 0.897117i | \(0.645658\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −56.4603 | −1.89789 | ||||||||
\(886\) | −28.3851 | −0.953617 | ||||||||
\(887\) | 57.8010 | 1.94077 | 0.970384 | − | 0.241567i | \(-0.0776615\pi\) | ||||
0.970384 | + | 0.241567i | \(0.0776615\pi\) | |||||||
\(888\) | −28.4319 | −0.954111 | ||||||||
\(889\) | −10.5396 | −0.353488 | ||||||||
\(890\) | −20.6781 | −0.693132 | ||||||||
\(891\) | 167.212 | 5.60182 | ||||||||
\(892\) | −1.03472 | −0.0346451 | ||||||||
\(893\) | −12.7582 | −0.426938 | ||||||||
\(894\) | −17.9900 | −0.601675 | ||||||||
\(895\) | −16.9657 | −0.567101 | ||||||||
\(896\) | −1.60598 | −0.0536519 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.4234 | −0.648168 | ||||||||
\(899\) | −7.44687 | −0.248367 | ||||||||
\(900\) | 34.1496 | 1.13832 | ||||||||
\(901\) | 30.9360 | 1.03063 | ||||||||
\(902\) | −32.5781 | −1.08473 | ||||||||
\(903\) | −23.7339 | −0.789814 | ||||||||
\(904\) | 15.2293 | 0.506520 | ||||||||
\(905\) | 30.9966 | 1.03036 | ||||||||
\(906\) | −17.6326 | −0.585804 | ||||||||
\(907\) | −7.29698 | −0.242292 | −0.121146 | − | 0.992635i | \(-0.538657\pi\) | ||||
−0.121146 | + | 0.992635i | \(0.538657\pi\) | |||||||
\(908\) | 15.5518 | 0.516104 | ||||||||
\(909\) | 46.7917 | 1.55198 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.2188 | 0.835536 | 0.417768 | − | 0.908554i | \(-0.362813\pi\) | ||||
0.417768 | + | 0.908554i | \(0.362813\pi\) | |||||||
\(912\) | 3.36433 | 0.111404 | ||||||||
\(913\) | −73.6500 | −2.43746 | ||||||||
\(914\) | −1.69519 | −0.0560721 | ||||||||
\(915\) | 71.1848 | 2.35330 | ||||||||
\(916\) | −1.43041 | −0.0472621 | ||||||||
\(917\) | 26.3796 | 0.871130 | ||||||||
\(918\) | −56.3769 | −1.86071 | ||||||||
\(919\) | −28.1990 | −0.930200 | −0.465100 | − | 0.885258i | \(-0.653982\pi\) | ||||
−0.465100 | + | 0.885258i | \(0.653982\pi\) | |||||||
\(920\) | −13.3905 | −0.441473 | ||||||||
\(921\) | 71.1682 | 2.34507 | ||||||||
\(922\) | −32.8331 | −1.08130 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −25.6338 | −0.843292 | ||||||||
\(925\) | −34.6927 | −1.14069 | ||||||||
\(926\) | 26.2428 | 0.862391 | ||||||||
\(927\) | 99.2245 | 3.25896 | ||||||||
\(928\) | 1.98215 | 0.0650673 | ||||||||
\(929\) | −7.39808 | −0.242723 | −0.121362 | − | 0.992608i | \(-0.538726\pi\) | ||||
−0.121362 | + | 0.992608i | \(0.538726\pi\) | |||||||
\(930\) | −38.1399 | −1.25066 | ||||||||
\(931\) | −4.42084 | −0.144887 | ||||||||
\(932\) | 1.48502 | 0.0486436 | ||||||||
\(933\) | 38.1904 | 1.25030 | ||||||||
\(934\) | −16.6106 | −0.543516 | ||||||||
\(935\) | −45.1044 | −1.47507 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.5732 | −0.900777 | −0.450389 | − | 0.892833i | \(-0.648715\pi\) | ||||
−0.450389 | + | 0.892833i | \(0.648715\pi\) | |||||||
\(938\) | −6.92563 | −0.226130 | ||||||||
\(939\) | −69.1368 | −2.25619 | ||||||||
\(940\) | −38.4976 | −1.25565 | ||||||||
\(941\) | −38.8296 | −1.26581 | −0.632904 | − | 0.774231i | \(-0.718137\pi\) | ||||
−0.632904 | + | 0.774231i | \(0.718137\pi\) | |||||||
\(942\) | −7.35996 | −0.239800 | ||||||||
\(943\) | 30.4722 | 0.992310 | ||||||||
\(944\) | −5.56162 | −0.181015 | ||||||||
\(945\) | −86.7133 | −2.82078 | ||||||||
\(946\) | 20.8405 | 0.677582 | ||||||||
\(947\) | 26.7230 | 0.868380 | 0.434190 | − | 0.900821i | \(-0.357035\pi\) | ||||
0.434190 | + | 0.900821i | \(0.357035\pi\) | |||||||
\(948\) | −6.20340 | −0.201477 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.10516 | 0.133189 | ||||||||
\(951\) | −5.73464 | −0.185958 | ||||||||
\(952\) | 5.05985 | 0.163991 | ||||||||
\(953\) | 44.4391 | 1.43952 | 0.719761 | − | 0.694222i | \(-0.244251\pi\) | ||||
0.719761 | + | 0.694222i | \(0.244251\pi\) | |||||||
\(954\) | −81.6809 | −2.64452 | ||||||||
\(955\) | −53.3542 | −1.72650 | ||||||||
\(956\) | 7.28803 | 0.235712 | ||||||||
\(957\) | 31.6382 | 1.02272 | ||||||||
\(958\) | 22.7182 | 0.733993 | ||||||||
\(959\) | −31.7719 | −1.02597 | ||||||||
\(960\) | 10.1518 | 0.327647 | ||||||||
\(961\) | −16.8852 | −0.544684 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.13775 | −0.262235 | ||||||||
\(964\) | 10.0796 | 0.324641 | ||||||||
\(965\) | −5.25741 | −0.169242 | ||||||||
\(966\) | 23.9768 | 0.771442 | ||||||||
\(967\) | 15.9816 | 0.513933 | 0.256966 | − | 0.966420i | \(-0.417277\pi\) | ||||
0.256966 | + | 0.966420i | \(0.417277\pi\) | |||||||
\(968\) | 11.5088 | 0.369908 | ||||||||
\(969\) | −10.5998 | −0.340514 | ||||||||
\(970\) | −2.97771 | −0.0956086 | ||||||||
\(971\) | 36.6172 | 1.17510 | 0.587551 | − | 0.809187i | \(-0.300092\pi\) | ||||
0.587551 | + | 0.809187i | \(0.300092\pi\) | |||||||
\(972\) | 64.8927 | 2.08143 | ||||||||
\(973\) | −28.8285 | −0.924198 | ||||||||
\(974\) | −16.0162 | −0.513193 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.01205 | 0.224450 | ||||||||
\(977\) | 24.9648 | 0.798695 | 0.399347 | − | 0.916800i | \(-0.369237\pi\) | ||||
0.399347 | + | 0.916800i | \(0.369237\pi\) | |||||||
\(978\) | 21.8105 | 0.697423 | ||||||||
\(979\) | −32.5120 | −1.03909 | ||||||||
\(980\) | −13.3398 | −0.426123 | ||||||||
\(981\) | −93.7461 | −2.99308 | ||||||||
\(982\) | −10.4778 | −0.334360 | ||||||||
\(983\) | −16.5472 | −0.527774 | −0.263887 | − | 0.964554i | \(-0.585005\pi\) | ||||
−0.263887 | + | 0.964554i | \(0.585005\pi\) | |||||||
\(984\) | −23.1019 | −0.736461 | ||||||||
\(985\) | 74.1440 | 2.36242 | ||||||||
\(986\) | −6.24504 | −0.198883 | ||||||||
\(987\) | 68.9331 | 2.19416 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.4933 | −0.619851 | ||||||||
\(990\) | 119.090 | 3.78493 | ||||||||
\(991\) | −34.7410 | −1.10358 | −0.551792 | − | 0.833982i | \(-0.686056\pi\) | ||||
−0.551792 | + | 0.833982i | \(0.686056\pi\) | |||||||
\(992\) | −3.75696 | −0.119284 | ||||||||
\(993\) | 30.4295 | 0.965652 | ||||||||
\(994\) | −0.823265 | −0.0261124 | ||||||||
\(995\) | −47.1266 | −1.49401 | ||||||||
\(996\) | −52.2269 | −1.65487 | ||||||||
\(997\) | 14.9452 | 0.473318 | 0.236659 | − | 0.971593i | \(-0.423948\pi\) | ||||
0.236659 | + | 0.971593i | \(0.423948\pi\) | |||||||
\(998\) | 12.8864 | 0.407911 | ||||||||
\(999\) | −151.220 | −4.78440 |
(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 | 6422.2.a.bn.1.14 | 14 | ||
13.2 | odd | 12 | 494.2.m.b.381.8 | yes | 28 | ||
13.7 | odd | 12 | 494.2.m.b.153.8 | ✓ | 28 | ||
13.12 | even | 2 | 6422.2.a.bm.1.14 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.m.b.153.8 | ✓ | 28 | 13.7 | odd | 12 | ||
494.2.m.b.381.8 | yes | 28 | 13.2 | odd | 12 | ||
6422.2.a.bm.1.14 | 14 | 13.12 | even | 2 | |||
6422.2.a.bn.1.14 | 14 | 1.1 | even | 1 | trivial |