Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6348,2,Mod(1,6348)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6348, 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("6348.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6348 = 2^{2} \cdot 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6348.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: | \(50.6890352031\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 14x^{8} + 65x^{7} + 57x^{6} - 354x^{5} - 46x^{4} + 714x^{3} - 74x^{2} - 323x - 23 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 276) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.84010\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6348.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.80838 | −0.808731 | −0.404365 | − | 0.914598i | \(-0.632508\pi\) | ||||
−0.404365 | + | 0.914598i | \(0.632508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.41002 | −1.28887 | −0.644433 | − | 0.764661i | \(-0.722907\pi\) | ||||
−0.644433 | + | 0.764661i | \(0.722907\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.92751 | −0.581165 | −0.290582 | − | 0.956850i | \(-0.593849\pi\) | ||||
−0.290582 | + | 0.956850i | \(0.593849\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.29803 | 1.46941 | 0.734704 | − | 0.678387i | \(-0.237321\pi\) | ||||
0.734704 | + | 0.678387i | \(0.237321\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.80838 | −0.466921 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.758011 | −0.183845 | −0.0919224 | − | 0.995766i | \(-0.529301\pi\) | ||||
−0.0919224 | + | 0.995766i | \(0.529301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.73895 | 1.08719 | 0.543595 | − | 0.839348i | \(-0.317063\pi\) | ||||
0.543595 | + | 0.839348i | \(0.317063\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.41002 | −0.744127 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.72977 | −0.345955 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.26626 | 0.792225 | 0.396112 | − | 0.918202i | \(-0.370359\pi\) | ||||
0.396112 | + | 0.918202i | \(0.370359\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.42219 | −0.614643 | −0.307321 | − | 0.951606i | \(-0.599433\pi\) | ||||
−0.307321 | + | 0.951606i | \(0.599433\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.92751 | −0.335536 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.16660 | 1.04235 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.67687 | −0.604474 | −0.302237 | − | 0.953233i | \(-0.597733\pi\) | ||||
−0.302237 | + | 0.953233i | \(0.597733\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.29803 | 0.848364 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.03987 | −1.09944 | −0.549722 | − | 0.835348i | \(-0.685266\pi\) | ||||
−0.549722 | + | 0.835348i | \(0.685266\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.67323 | −0.560162 | −0.280081 | − | 0.959976i | \(-0.590361\pi\) | ||||
−0.280081 | + | 0.959976i | \(0.590361\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.80838 | −0.269577 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.3519 | 1.50998 | 0.754989 | − | 0.655738i | \(-0.227642\pi\) | ||||
0.754989 | + | 0.655738i | \(0.227642\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.62823 | 0.661175 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.758011 | −0.106143 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.86365 | 1.08016 | 0.540078 | − | 0.841615i | \(-0.318395\pi\) | ||||
0.540078 | + | 0.841615i | \(0.318395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.48566 | 0.470006 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.73895 | 0.627689 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8055 | 1.40676 | 0.703378 | − | 0.710816i | \(-0.251674\pi\) | ||||
0.703378 | + | 0.710816i | \(0.251674\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.8972 | −1.65132 | −0.825658 | − | 0.564171i | \(-0.809196\pi\) | ||||
−0.825658 | + | 0.564171i | \(0.809196\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.41002 | −0.429622 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.58083 | −1.18836 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.20464 | −0.758018 | −0.379009 | − | 0.925393i | \(-0.623735\pi\) | ||||
−0.379009 | + | 0.925393i | \(0.623735\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.7922 | −1.75551 | −0.877756 | − | 0.479108i | \(-0.840960\pi\) | ||||
−0.877756 | + | 0.479108i | \(0.840960\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.59888 | −0.889382 | −0.444691 | − | 0.895684i | \(-0.646686\pi\) | ||||
−0.444691 | + | 0.895684i | \(0.646686\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.72977 | −0.199737 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.57283 | 0.749043 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.36068 | 0.715633 | 0.357816 | − | 0.933792i | \(-0.383521\pi\) | ||||
0.357816 | + | 0.933792i | \(0.383521\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.77918 | −1.07340 | −0.536702 | − | 0.843772i | \(-0.680330\pi\) | ||||
−0.536702 | + | 0.843772i | \(0.680330\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.37077 | 0.148681 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.26626 | 0.457391 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.1469 | 1.18157 | 0.590784 | − | 0.806830i | \(-0.298819\pi\) | ||||
0.590784 | + | 0.806830i | \(0.298819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.0664 | −1.89387 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.42219 | −0.354864 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.56981 | −0.879243 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.62022 | 0.773717 | 0.386858 | − | 0.922139i | \(-0.373560\pi\) | ||||
0.386858 | + | 0.922139i | \(0.373560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.92751 | −0.193722 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.91174 | 0.886752 | 0.443376 | − | 0.896336i | \(-0.353781\pi\) | ||||
0.443376 | + | 0.896336i | \(0.353781\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.885137 | −0.0872152 | −0.0436076 | − | 0.999049i | \(-0.513885\pi\) | ||||
−0.0436076 | + | 0.999049i | \(0.513885\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.16660 | 0.601798 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.91236 | −0.764917 | −0.382458 | − | 0.923973i | \(-0.624922\pi\) | ||||
−0.382458 | + | 0.923973i | \(0.624922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.75994 | −0.168571 | −0.0842856 | − | 0.996442i | \(-0.526861\pi\) | ||||
−0.0842856 | + | 0.996442i | \(0.526861\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.67687 | −0.348993 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.7242 | 1.57328 | 0.786642 | − | 0.617409i | \(-0.211818\pi\) | ||||
0.786642 | + | 0.617409i | \(0.211818\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.29803 | 0.489803 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.58483 | 0.236951 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.28472 | −0.662248 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.03987 | −0.634764 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1700 | 1.08851 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.27902 | 0.113495 | 0.0567473 | − | 0.998389i | \(-0.481927\pi\) | ||||
0.0567473 | + | 0.998389i | \(0.481927\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.67323 | −0.323410 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.0849 | −0.881121 | −0.440560 | − | 0.897723i | \(-0.645220\pi\) | ||||
−0.440560 | + | 0.897723i | \(0.645220\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.1599 | −1.40124 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.80838 | −0.155640 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.53140 | 0.558015 | 0.279007 | − | 0.960289i | \(-0.409995\pi\) | ||||
0.279007 | + | 0.960289i | \(0.409995\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.55305 | −0.725461 | −0.362730 | − | 0.931894i | \(-0.618155\pi\) | ||||
−0.362730 | + | 0.931894i | \(0.618155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.3519 | 0.871786 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.2120 | −0.853968 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.71501 | −0.640696 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.62823 | 0.381730 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.23686 | 0.265174 | 0.132587 | − | 0.991171i | \(-0.457672\pi\) | ||||
0.132587 | + | 0.991171i | \(0.457672\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.02936 | 0.572041 | 0.286021 | − | 0.958223i | \(-0.407667\pi\) | ||||
0.286021 | + | 0.958223i | \(0.407667\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.758011 | −0.0612816 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.18860 | 0.497081 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0537 | −1.60046 | −0.800230 | − | 0.599693i | \(-0.795289\pi\) | ||||
−0.800230 | + | 0.599693i | \(0.795289\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.86365 | 0.623628 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.8460 | −1.16283 | −0.581414 | − | 0.813608i | \(-0.697500\pi\) | ||||
−0.581414 | + | 0.813608i | \(0.697500\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.48566 | 0.271358 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.6323 | −1.90611 | −0.953053 | − | 0.302805i | \(-0.902077\pi\) | ||||
−0.953053 | + | 0.302805i | \(0.902077\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.0691 | 1.15916 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.73895 | 0.362396 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.6072 | −1.18659 | −0.593296 | − | 0.804985i | \(-0.702173\pi\) | ||||
−0.593296 | + | 0.804985i | \(0.702173\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.89856 | 0.445889 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.8055 | 0.812191 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.1421 | −1.35601 | −0.678003 | − | 0.735059i | \(-0.737154\pi\) | ||||
−0.678003 | + | 0.735059i | \(0.737154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.6007 | −1.97721 | −0.988607 | − | 0.150516i | \(-0.951906\pi\) | ||||
−0.988607 | + | 0.150516i | \(0.951906\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.8972 | −0.953388 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.64917 | 0.488856 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.46107 | 0.106844 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.41002 | −0.248042 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.7928 | −1.79394 | −0.896972 | − | 0.442087i | \(-0.854238\pi\) | ||||
−0.896972 | + | 0.442087i | \(0.854238\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.71905 | −0.339684 | −0.169842 | − | 0.985471i | \(-0.554326\pi\) | ||||
−0.169842 | + | 0.985471i | \(0.554326\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.58083 | −0.686098 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.1321 | −0.793128 | −0.396564 | − | 0.918007i | \(-0.629798\pi\) | ||||
−0.396564 | + | 0.918007i | \(0.629798\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.88804 | −0.559168 | −0.279584 | − | 0.960121i | \(-0.590197\pi\) | ||||
−0.279584 | + | 0.960121i | \(0.590197\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.20464 | −0.437642 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.5480 | −1.02107 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.7307 | 0.889154 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.13435 | −0.631836 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.6582 | −1.28448 | −0.642242 | − | 0.766502i | \(-0.721996\pi\) | ||||
−0.642242 | + | 0.766502i | \(0.721996\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.7922 | −1.01355 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.64258 | 0.453020 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.6697 | 0.792192 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.59888 | −0.513485 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.01597 | −0.270143 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.1363 | 1.54932 | 0.774661 | − | 0.632377i | \(-0.217921\pi\) | ||||
0.774661 | + | 0.632377i | \(0.217921\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.72977 | −0.115318 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.3327 | 0.818551 | 0.409276 | − | 0.912411i | \(-0.365781\pi\) | ||||
0.409276 | + | 0.912411i | \(0.365781\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.4857 | −0.758998 | −0.379499 | − | 0.925192i | \(-0.623904\pi\) | ||||
−0.379499 | + | 0.925192i | \(0.623904\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.57283 | 0.432460 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.35110 | −0.350562 | −0.175281 | − | 0.984518i | \(-0.556083\pi\) | ||||
−0.175281 | + | 0.984518i | \(0.556083\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.7201 | −1.22117 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.36068 | 0.413171 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.4413 | 0.740079 | 0.370039 | − | 0.929016i | \(-0.379344\pi\) | ||||
0.370039 | + | 0.929016i | \(0.379344\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50702 | 0.225907 | 0.112954 | − | 0.993600i | \(-0.463969\pi\) | ||||
0.112954 | + | 0.993600i | \(0.463969\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.36958 | −0.534713 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.1071 | 1.59753 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.77918 | −0.619730 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.8422 | −0.747473 | −0.373737 | − | 0.927535i | \(-0.621924\pi\) | ||||
−0.373737 | + | 0.927535i | \(0.621924\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.37077 | 0.0858410 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.5236 | −1.59212 | −0.796059 | − | 0.605219i | \(-0.793086\pi\) | ||||
−0.796059 | + | 0.605219i | \(0.793086\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.5382 | 0.779085 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.26626 | 0.264075 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.59494 | −0.221674 | −0.110837 | − | 0.993839i | \(-0.535353\pi\) | ||||
−0.110837 | + | 0.993839i | \(0.535353\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.2204 | −0.873555 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.1469 | 0.682179 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.2119 | 0.988454 | 0.494227 | − | 0.869333i | \(-0.335451\pi\) | ||||
0.494227 | + | 0.869333i | \(0.335451\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.34094 | −0.263693 | −0.131847 | − | 0.991270i | \(-0.542091\pi\) | ||||
−0.131847 | + | 0.991270i | \(0.542091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.0664 | −1.09343 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.33415 | 0.201057 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.6009 | 1.71846 | 0.859230 | − | 0.511589i | \(-0.170943\pi\) | ||||
0.859230 | + | 0.511589i | \(0.170943\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.42219 | −0.204881 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.3291 | −0.675836 | −0.337918 | − | 0.941176i | \(-0.609723\pi\) | ||||
−0.337918 | + | 0.941176i | \(0.609723\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.33421 | −0.317086 | −0.158543 | − | 0.987352i | \(-0.550680\pi\) | ||||
−0.158543 | + | 0.987352i | \(0.550680\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.56981 | −0.507631 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.0061 | 1.41704 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4254 | −0.966201 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.62022 | 0.446705 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.6546 | −1.38192 | −0.690959 | − | 0.722894i | \(-0.742811\pi\) | ||||
−0.690959 | + | 0.722894i | \(0.742811\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.5404 | −1.13769 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.92751 | −0.111845 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5258 | 0.721974 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.91174 | 0.511966 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.3230 | 1.33547 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.5823 | −1.11762 | −0.558809 | − | 0.829296i | \(-0.688742\pi\) | ||||
−0.558809 | + | 0.829296i | \(0.688742\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.885137 | −0.0503537 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.91968 | −0.108855 | −0.0544275 | − | 0.998518i | \(-0.517333\pi\) | ||||
−0.0544275 | + | 0.998518i | \(0.517333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.6859 | −0.717047 | −0.358524 | − | 0.933521i | \(-0.616720\pi\) | ||||
−0.358524 | + | 0.933521i | \(0.616720\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.16660 | 0.347448 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.12473 | 0.175503 | 0.0877513 | − | 0.996142i | \(-0.472032\pi\) | ||||
0.0877513 | + | 0.996142i | \(0.472032\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.22324 | −0.460413 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.91236 | −0.441625 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.59218 | −0.199874 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.16439 | −0.508349 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.75994 | −0.0973247 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −35.3001 | −1.94616 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.8689 | −0.707337 | −0.353669 | − | 0.935371i | \(-0.615066\pi\) | ||||
−0.353669 | + | 0.935371i | \(0.615066\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.67687 | −0.201491 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.2203 | 0.613032 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.4541 | −0.841840 | −0.420920 | − | 0.907098i | \(-0.638293\pi\) | ||||
−0.420920 | + | 0.907098i | \(0.638293\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.7242 | 0.908336 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.59628 | 0.357209 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.08779 | 0.436700 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.1546 | −0.974587 | −0.487294 | − | 0.873238i | \(-0.662016\pi\) | ||||
−0.487294 | + | 0.873238i | \(0.662016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.8805 | 1.17123 | 0.585617 | − | 0.810588i | \(-0.300852\pi\) | ||||
0.585617 | + | 0.810588i | \(0.300852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.29803 | 0.282788 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0997 | 0.644002 | 0.322001 | − | 0.946739i | \(-0.395645\pi\) | ||||
0.322001 | + | 0.946739i | \(0.395645\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.7499 | 1.41974 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.58483 | 0.136804 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.54542 | −0.187120 | −0.0935601 | − | 0.995614i | \(-0.529825\pi\) | ||||
−0.0935601 | + | 0.995614i | \(0.529825\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.45764 | 0.181981 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.28472 | −0.382349 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.7416 | 0.719270 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.1379 | −1.36439 | −0.682194 | − | 0.731171i | \(-0.738974\pi\) | ||||
−0.682194 | + | 0.731171i | \(0.738974\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.03987 | −0.366481 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.8152 | −1.39218 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.4617 | 0.748798 | 0.374399 | − | 0.927268i | \(-0.377849\pi\) | ||||
0.374399 | + | 0.927268i | \(0.377849\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.1700 | 0.628454 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.6028 | 1.16410 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.9789 | −1.43718 | −0.718590 | − | 0.695434i | \(-0.755212\pi\) | ||||
−0.718590 | + | 0.695434i | \(0.755212\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.27902 | 0.0655261 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.4801 | −0.944291 | −0.472145 | − | 0.881521i | \(-0.656520\pi\) | ||||
−0.472145 | + | 0.881521i | \(0.656520\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.8862 | −0.605774 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.67323 | −0.186721 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.7151 | 1.30381 | 0.651903 | − | 0.758302i | \(-0.273971\pi\) | ||||
0.651903 | + | 0.758302i | \(0.273971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.0849 | −0.508715 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.5025 | −0.578754 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.9380 | −1.40217 | −0.701085 | − | 0.713078i | \(-0.747300\pi\) | ||||
−0.701085 | + | 0.713078i | \(0.747300\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.1599 | −0.809007 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.4261 | 1.21978 | 0.609890 | − | 0.792486i | \(-0.291213\pi\) | ||||
0.609890 | + | 0.792486i | \(0.291213\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.1308 | −0.903162 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.80838 | −0.0898590 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.08718 | 0.351299 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.1790 | −1.78894 | −0.894469 | − | 0.447130i | \(-0.852446\pi\) | ||||
−0.894469 | + | 0.447130i | \(0.852446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.53140 | 0.322170 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.8470 | −1.81312 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.6844 | 0.868095 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.55305 | −0.418845 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.28020 | 0.404514 | 0.202257 | − | 0.979332i | \(-0.435172\pi\) | ||||
0.202257 | + | 0.979332i | \(0.435172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.7531 | 1.74250 | 0.871250 | − | 0.490840i | \(-0.163310\pi\) | ||||
0.871250 | + | 0.490840i | \(0.163310\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.3519 | 0.503326 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.31119 | 0.0636020 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.9797 | 2.12832 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.2120 | −0.493039 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.8226 | 1.05116 | 0.525578 | − | 0.850745i | \(-0.323849\pi\) | ||||
0.525578 | + | 0.850745i | \(0.323849\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.3982 | 1.46085 | 0.730423 | − | 0.682995i | \(-0.239323\pi\) | ||||
0.730423 | + | 0.682995i | \(0.239323\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.71501 | −0.369906 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.7108 | 0.988471 | 0.494235 | − | 0.869328i | \(-0.335448\pi\) | ||||
0.494235 | + | 0.869328i | \(0.335448\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.62823 | 0.220392 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.6057 | 1.16905 | 0.584527 | − | 0.811374i | \(-0.301280\pi\) | ||||
0.584527 | + | 0.811374i | \(0.301280\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.1578 | −0.955570 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.23686 | 0.153098 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.3310 | 1.85614 | 0.928072 | − | 0.372402i | \(-0.121466\pi\) | ||||
0.928072 | + | 0.372402i | \(0.121466\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.5694 | 0.638958 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.02936 | 0.330268 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 32.6708 | 1.53163 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.1738 | 0.803355 | 0.401678 | − | 0.915781i | \(-0.368427\pi\) | ||||
0.401678 | + | 0.915781i | \(0.368427\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.758011 | −0.0353809 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.59212 | 0.0741524 | 0.0370762 | − | 0.999312i | \(-0.488196\pi\) | ||||
0.0370762 | + | 0.999312i | \(0.488196\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5914 | −0.678122 | −0.339061 | − | 0.940764i | \(-0.610109\pi\) | ||||
−0.339061 | + | 0.940764i | \(0.610109\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.18860 | 0.286990 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.5473 | −1.36728 | −0.683642 | − | 0.729817i | \(-0.739605\pi\) | ||||
−0.683642 | + | 0.729817i | \(0.739605\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.1579 | 0.976983 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.0537 | −0.924026 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.08017 | 0.325547 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.19731 | −0.376118 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.86365 | 0.360052 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.16929 | 0.144808 | 0.0724042 | − | 0.997375i | \(-0.476933\pi\) | ||||
0.0724042 | + | 0.997375i | \(0.476933\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.4802 | −0.888219 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.7802 | −0.625728 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.8315 | 1.44242 | 0.721212 | − | 0.692715i | \(-0.243585\pi\) | ||||
0.721212 | + | 0.692715i | \(0.243585\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.8460 | −0.671359 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.1533 | 0.503342 | 0.251671 | − | 0.967813i | \(-0.419020\pi\) | ||||
0.251671 | + | 0.967813i | \(0.419020\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.23387 | −0.145646 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.48566 | 0.156669 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 50.4417 | 2.26262 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.88983 | 0.174133 | 0.0870664 | − | 0.996203i | \(-0.472251\pi\) | ||||
0.0870664 | + | 0.996203i | \(0.472251\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.6323 | −1.10049 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.6158 | 1.67720 | 0.838602 | − | 0.544745i | \(-0.183374\pi\) | ||||
0.838602 | + | 0.544745i | \(0.183374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.1158 | −0.717143 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.0691 | 0.669243 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.7613 | 0.875904 | 0.437952 | − | 0.898998i | \(-0.355704\pi\) | ||||
0.437952 | + | 0.898998i | \(0.355704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.9123 | 1.14629 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.73895 | 0.209230 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.60066 | 0.0705336 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.9533 | −0.877546 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.6072 | −0.685079 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.4915 | 1.20442 | 0.602212 | − | 0.798336i | \(-0.294286\pi\) | ||||
0.602212 | + | 0.798336i | \(0.294286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.12792 | −0.355409 | −0.177705 | − | 0.984084i | \(-0.556867\pi\) | ||||
−0.177705 | + | 0.984084i | \(0.556867\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.89856 | 0.257434 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.59406 | 0.112999 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.8055 | 0.468919 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −37.2975 | −1.61553 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.3085 | 0.618612 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.1421 | −0.782891 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.92093 | −0.384252 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.4068 | 1.00634 | 0.503168 | − | 0.864189i | \(-0.332168\pi\) | ||||
0.503168 | + | 0.864189i | \(0.332168\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.6007 | −1.14155 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.18263 | 0.136329 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.3796 | 0.700339 | 0.350170 | − | 0.936686i | \(-0.386124\pi\) | ||||
0.350170 | + | 0.936686i | \(0.386124\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.8972 | −0.550439 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.2176 | 0.861298 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.6900 | −0.922354 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.64917 | 0.282241 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.1105 | 0.809739 | 0.404870 | − | 0.914374i | \(-0.367317\pi\) | ||||
0.404870 | + | 0.914374i | \(0.367317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.4609 | −0.823107 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.46107 | 0.0616865 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.2704 | 0.854295 | 0.427147 | − | 0.904182i | \(-0.359519\pi\) | ||||
0.427147 | + | 0.904182i | \(0.359519\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.2437 | −1.27236 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.41002 | −0.143207 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.5611 | −0.778122 | −0.389061 | − | 0.921212i | \(-0.627201\pi\) | ||||
−0.389061 | + | 0.921212i | \(0.627201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.7442 | −1.95619 | −0.978093 | − | 0.208169i | \(-0.933250\pi\) | ||||
−0.978093 | + | 0.208169i | \(0.933250\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.7928 | −1.03573 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.8223 | −1.49130 | −0.745650 | − | 0.666338i | \(-0.767861\pi\) | ||||
−0.745650 | + | 0.666338i | \(0.767861\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.71905 | −0.196117 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.3472 | 1.38347 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.1572 | −0.627748 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.58083 | −0.396119 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.0185507 | 0.000765668 0 | 0.000382834 | − | 1.00000i | \(-0.499878\pi\) | ||||
0.000382834 | 1.00000i | \(0.499878\pi\) | ||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.2176 | −0.668233 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.1321 | −0.457913 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.49894 | −0.266880 | −0.133440 | − | 0.991057i | \(-0.542602\pi\) | ||||
−0.133440 | + | 0.991057i | \(0.542602\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.67435 | −0.191630 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.88804 | −0.322836 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.49989 | −0.306437 | −0.153219 | − | 0.988192i | \(-0.548964\pi\) | ||||
−0.153219 | + | 0.988192i | \(0.548964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.7294 | 1.04953 | 0.524763 | − | 0.851248i | \(-0.324154\pi\) | ||||
0.524763 | + | 0.851248i | \(0.324154\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.20464 | −0.252673 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.1735 | 0.535580 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.9734 | 1.17599 | 0.587997 | − | 0.808863i | \(-0.299917\pi\) | ||||
0.587997 | + | 0.808863i | \(0.299917\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.5480 | −0.589516 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 54.8446 | 2.21877 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.35394 | 0.0950747 | 0.0475374 | − | 0.998869i | \(-0.484863\pi\) | ||||
0.0475374 | + | 0.998869i | \(0.484863\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.7307 | 0.513353 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.2703 | 0.614757 | 0.307379 | − | 0.951587i | \(-0.400548\pi\) | ||||
0.307379 | + | 0.951587i | \(0.400548\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.4977 | −0.462131 | −0.231066 | − | 0.972938i | \(-0.574221\pi\) | ||||
−0.231066 | + | 0.972938i | \(0.574221\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −38.0111 | −1.52288 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.3590 | −0.534361 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.13435 | −0.364791 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.78711 | 0.111129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.1283 | −0.562440 | −0.281220 | − | 0.959643i | \(-0.590739\pi\) | ||||
−0.281220 | + | 0.959643i | \(0.590739\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.6582 | −0.741598 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.31295 | −0.0917865 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.5205 | 0.971537 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.7922 | −0.585171 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.8912 | −0.983144 | −0.491572 | − | 0.870837i | \(-0.663578\pi\) | ||||
−0.491572 | + | 0.870837i | \(0.663578\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.5235 | 0.927678 | 0.463839 | − | 0.885919i | \(-0.346472\pi\) | ||||
0.463839 | + | 0.885919i | \(0.346472\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.64258 | 0.261551 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.0221 | −0.787149 | −0.393575 | − | 0.919293i | \(-0.628762\pi\) | ||||
−0.393575 | + | 0.919293i | \(0.628762\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.8277 | −0.817557 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.6697 | 0.457373 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.46797 | −0.292244 | −0.146122 | − | 0.989267i | \(-0.546679\pi\) | ||||
−0.146122 | + | 0.989267i | \(0.546679\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.2373 | 0.712589 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.59888 | −0.296461 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.9051 | 0.424804 | 0.212402 | − | 0.977182i | \(-0.431871\pi\) | ||||
0.212402 | + | 0.977182i | \(0.431871\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.2616 | 0.671398 | 0.335699 | − | 0.941969i | \(-0.391028\pi\) | ||||
0.335699 | + | 0.941969i | \(0.391028\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.01597 | −0.155967 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 29.2232 | 1.13323 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.1363 | 0.894501 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.8594 | 0.959686 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.05328 | −0.271884 | −0.135942 | − | 0.990717i | \(-0.543406\pi\) | ||||
−0.135942 | + | 0.990717i | \(0.543406\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.72977 | −0.0665790 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.1331 | 1.00437 | 0.502187 | − | 0.864759i | \(-0.332529\pi\) | ||||
0.502187 | + | 0.864759i | \(0.332529\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.9851 | −0.997217 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.3327 | 0.472591 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.22451 | −0.161647 | −0.0808233 | − | 0.996728i | \(-0.525755\pi\) | ||||
−0.0808233 | + | 0.996728i | \(0.525755\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.8112 | −0.451284 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.4857 | −0.438208 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 41.6619 | 1.58719 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.2154 | 1.33966 | 0.669829 | − | 0.742516i | \(-0.266367\pi\) | ||||
0.669829 | + | 0.742516i | \(0.266367\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.57283 | 0.249681 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.4671 | 0.586702 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.33630 | 0.202127 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.35110 | −0.202397 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.7455 | 1.46340 | 0.731698 | − | 0.681629i | \(-0.238728\pi\) | ||||
0.731698 | + | 0.681629i | \(0.238728\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.4245 | −0.657177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.7201 | −0.705040 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.3892 | −1.14290 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.1192 | −0.530258 | −0.265129 | − | 0.964213i | \(-0.585415\pi\) | ||||
−0.265129 | + | 0.964213i | \(0.585415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.36068 | 0.238544 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.4671 | 0.690631 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.4413 | 0.427285 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.7130 | 1.77940 | 0.889698 | − | 0.456550i | \(-0.150915\pi\) | ||||
0.889698 | + | 0.456550i | \(0.150915\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.01833 | 0.112409 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.50702 | 0.130427 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.37966 | −0.274074 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.7935 | −1.36460 | −0.682298 | − | 0.731075i | \(-0.739019\pi\) | ||||
−0.682298 | + | 0.731075i | \(0.739019\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.78435 | 0.102983 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.7615 | 0.914588 | 0.457294 | − | 0.889316i | \(-0.348819\pi\) | ||||
0.457294 | + | 0.889316i | \(0.348819\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.36958 | −0.308717 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.9595 | 0.440533 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.7732 | 0.690585 | 0.345292 | − | 0.938495i | \(-0.387780\pi\) | ||||
0.345292 | + | 0.938495i | \(0.387780\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.1071 | 0.922332 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.4315 | −1.11642 | −0.558212 | − | 0.829698i | \(-0.688513\pi\) | ||||
−0.558212 | + | 0.829698i | \(0.688513\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.85347 | −0.214454 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.77918 | −0.357801 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.9813 | 0.985875 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.2616 | 1.32321 | 0.661603 | − | 0.749854i | \(-0.269876\pi\) | ||||
0.661603 | + | 0.749854i | \(0.269876\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.8422 | −0.431554 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.7117 | −0.462628 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.6441 | −1.58627 | −0.793136 | − | 0.609045i | \(-0.791553\pi\) | ||||
−0.793136 | + | 0.609045i | \(0.791553\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.10891 | −0.112698 | −0.0563490 | − | 0.998411i | \(-0.517946\pi\) | ||||
−0.0563490 | + | 0.998411i | \(0.517946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.00141 | 0.217266 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.37077 | 0.0495603 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 57.2479 | 2.06710 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.6155 | −1.60887 | −0.804437 | − | 0.594038i | \(-0.797533\pi\) | ||||
−0.804437 | + | 0.594038i | \(0.797533\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.5236 | −0.919210 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.1132 | 0.615519 | 0.307759 | − | 0.951464i | \(-0.400421\pi\) | ||||
0.307759 | + | 0.951464i | \(0.400421\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.91961 | 0.212639 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.5382 | 0.449805 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.3616 | −1.19530 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.5121 | 1.02024 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.26626 | 0.152464 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.2647 | 1.29434 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.7737 | −1.56036 | −0.780182 | − | 0.625553i | \(-0.784873\pi\) | ||||
−0.780182 | + | 0.625553i | \(0.784873\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.59494 | −0.127983 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −57.0300 | −2.02775 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −68.3297 | −2.42646 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.2204 | −0.504347 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.7708 | 1.01911 | 0.509557 | − | 0.860437i | \(-0.329809\pi\) | ||||
0.509557 | + | 0.860437i | \(0.329809\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.84685 | −0.277601 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.1469 | 0.393856 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.6469 | 0.516877 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.2119 | 0.570684 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.3028 | −0.467703 | −0.233851 | − | 0.972272i | \(-0.575133\pi\) | ||||
−0.233851 | + | 0.972272i | \(0.575133\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.9548 | −1.61369 | −0.806846 | − | 0.590762i | \(-0.798827\pi\) | ||||
−0.806846 | + | 0.590762i | \(0.798827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.34094 | −0.152243 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.8471 | 0.940414 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.4072 | −0.609003 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.0664 | −0.631290 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.1024 | −1.67879 | −0.839393 | − | 0.543525i | \(-0.817089\pi\) | ||||
−0.839393 | + | 0.543525i | \(0.817089\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.7767 | 1.00309 | 0.501547 | − | 0.865130i | \(-0.332764\pi\) | ||||
0.501547 | + | 0.865130i | \(0.332764\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.33415 | 0.116080 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.0915 | 1.63753 | 0.818766 | − | 0.574128i | \(-0.194659\pi\) | ||||
0.818766 | + | 0.574128i | \(0.194659\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.9669 | −0.971330 | −0.485665 | − | 0.874145i | \(-0.661423\pi\) | ||||
−0.485665 | + | 0.874145i | \(0.661423\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.6009 | 0.992153 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.50825 | −0.121554 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.5445 | 1.54153 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.42219 | −0.118288 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.5797 | 0.641443 | 0.320722 | − | 0.947174i | \(-0.396075\pi\) | ||||
0.320722 | + | 0.947174i | \(0.396075\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.7990 | −0.372380 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.3291 | −0.390194 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −27.2506 | −0.937450 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.8410 | 0.853548 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.33421 | −0.183070 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.6988 | 1.49622 | 0.748109 | − | 0.663576i | \(-0.230962\pi\) | ||||
0.748109 | + | 0.663576i | \(0.230962\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.56981 | −0.293081 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.9455 | −1.22787 | −0.613937 | − | 0.789355i | \(-0.710415\pi\) | ||||
−0.613937 | + | 0.789355i | \(0.710415\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.7971 | −0.948426 | −0.474213 | − | 0.880410i | \(-0.657267\pi\) | ||||
−0.474213 | + | 0.880410i | \(0.657267\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.0061 | 0.818126 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.73210 | −0.229163 | −0.114582 | − | 0.993414i | \(-0.536553\pi\) | ||||
−0.114582 | + | 0.993414i | \(0.536553\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.2236 | 0.959633 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.4254 | −0.557836 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.2602 | −0.415900 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.8724 | −1.11384 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.62022 | 0.257906 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −41.4998 | −1.40295 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.5250 | 0.422940 | 0.211470 | − | 0.977384i | \(-0.432175\pi\) | ||||
0.211470 | + | 0.977384i | \(0.432175\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.6546 | −0.797850 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.8983 | −1.00730 | −0.503649 | − | 0.863908i | \(-0.668009\pi\) | ||||
−0.503649 | + | 0.863908i | \(0.668009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.3188 | 0.650129 | 0.325064 | − | 0.945692i | \(-0.394614\pi\) | ||||
0.325064 | + | 0.945692i | \(0.394614\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.5404 | −0.656844 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −52.7571 | −1.77141 | −0.885705 | − | 0.464248i | \(-0.846324\pi\) | ||||
−0.885705 | + | 0.464248i | \(0.846324\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.36148 | −0.146279 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.92751 | −0.0645739 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 49.0571 | 1.64163 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.8078 | 1.09664 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.5999 | −0.486935 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.96074 | −0.198581 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.5258 | 0.416832 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 48.1041 | 1.59903 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.82536 | 0.193428 | 0.0967140 | − | 0.995312i | \(-0.469167\pi\) | ||||
0.0967140 | + | 0.995312i | \(0.469167\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.91174 | 0.295584 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.9253 | −1.19026 | −0.595129 | − | 0.803630i | \(-0.702899\pi\) | ||||
−0.595129 | + | 0.803630i | \(0.702899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.8494 | 0.623825 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23.3230 | 0.771034 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 34.3897 | 1.13565 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.76019 | −0.190011 | −0.0950055 | − | 0.995477i | \(-0.530287\pi\) | ||||
−0.0950055 | + | 0.995477i | \(0.530287\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.5823 | −0.645257 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −78.3695 | −2.57956 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.36015 | 0.209120 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.885137 | −0.0290717 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.7791 | 0.648932 | 0.324466 | − | 0.945897i | \(-0.394815\pi\) | ||||
0.324466 | + | 0.945897i | \(0.394815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.9329 | 0.718823 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.91968 | −0.0628474 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.64217 | −0.0864081 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.548515 | 0.0179192 | 0.00895961 | − | 0.999960i | \(-0.497148\pi\) | ||||
0.00895961 | + | 0.999960i | \(0.497148\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.6859 | −0.413987 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.1280 | 1.47113 | 0.735565 | − | 0.677454i | \(-0.236917\pi\) | ||||
0.735565 | + | 0.677454i | \(0.236917\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.16660 | 0.200599 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.89487 | 0.126566 | 0.0632831 | − | 0.997996i | \(-0.479843\pi\) | ||||
0.0632831 | + | 0.997996i | \(0.479843\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.2591 | −1.30687 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.12473 | 0.101326 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.2589 | −1.56326 | −0.781629 | − | 0.623743i | \(-0.785611\pi\) | ||||
−0.781629 | + | 0.623743i | \(0.785611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.8347 | 1.45082 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.22324 | −0.265820 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.2722 | −0.719206 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.2886 | −0.622214 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.91236 | −0.254972 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.53381 | 0.274713 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.3950 | −1.68491 | −0.842456 | − | 0.538766i | \(-0.818891\pi\) | ||||
−0.842456 | + | 0.538766i | \(0.818891\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.59218 | −0.115397 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.443074 | 0.0142189 | 0.00710946 | − | 0.999975i | \(-0.497737\pi\) | ||||
0.00710946 | + | 0.999975i | \(0.497737\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.1661 | 0.935021 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.16439 | −0.293495 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.6871 | 1.68561 | 0.842805 | − | 0.538219i | \(-0.180903\pi\) | ||||
0.842805 | + | 0.538219i | \(0.180903\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.4857 | −0.686686 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.75994 | −0.0561904 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.9658 | 0.509231 | 0.254615 | − | 0.967042i | \(-0.418051\pi\) | ||||
0.254615 | + | 0.967042i | \(0.418051\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.1310 | 0.641427 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −35.3001 | −1.12362 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.7399 | −0.690590 | −0.345295 | − | 0.938494i | \(-0.612221\pi\) | ||||
−0.345295 | + | 0.938494i | \(0.612221\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.8689 | −0.408381 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.2645 | 0.452216 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.2016 | 1.01984 | 0.509918 | − | 0.860223i | \(-0.329676\pi\) | ||||
0.509918 | + | 0.860223i | \(0.329676\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.67687 | −0.116331 |
(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 | 6348.2.a.s.1.3 | 10 | ||
23.2 | even | 11 | 276.2.i.a.73.1 | ✓ | 20 | ||
23.12 | even | 11 | 276.2.i.a.121.1 | yes | 20 | ||
23.22 | odd | 2 | 6348.2.a.t.1.8 | 10 | |||
69.2 | odd | 22 | 828.2.q.c.73.2 | 20 | |||
69.35 | odd | 22 | 828.2.q.c.397.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.73.1 | ✓ | 20 | 23.2 | even | 11 | ||
276.2.i.a.121.1 | yes | 20 | 23.12 | even | 11 | ||
828.2.q.c.73.2 | 20 | 69.2 | odd | 22 | |||
828.2.q.c.397.2 | 20 | 69.35 | odd | 22 | |||
6348.2.a.s.1.3 | 10 | 1.1 | even | 1 | trivial | ||
6348.2.a.t.1.8 | 10 | 23.22 | odd | 2 |