Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,2,Mod(1,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, 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("3332.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.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: | \(26.6061539535\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 5 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.1 |
$q$-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 | ||||||||
\(3\) | −1.79129 | −1.03420 | −0.517100 | − | 0.855925i | \(-0.672989\pi\) | ||||
−0.517100 | + | 0.855925i | \(0.672989\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.79129 | 1.24830 | 0.624151 | − | 0.781304i | \(-0.285445\pi\) | ||||
0.624151 | + | 0.781304i | \(0.285445\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.208712 | 0.0695707 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.58258 | 1.68321 | 0.841605 | − | 0.540094i | \(-0.181611\pi\) | ||||
0.841605 | + | 0.540094i | \(0.181611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.00000 | −1.29099 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.58258 | −1.58108 | −0.790538 | − | 0.612413i | \(-0.790199\pi\) | ||||
−0.790538 | + | 0.612413i | \(0.790199\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.79129 | 0.558258 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.79129 | −0.860541 | −0.430270 | − | 0.902700i | \(-0.641582\pi\) | ||||
−0.430270 | + | 0.902700i | \(0.641582\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.0000 | −1.74078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.58258 | −0.588972 | −0.294486 | − | 0.955656i | \(-0.595148\pi\) | ||||
−0.294486 | + | 0.955656i | \(0.595148\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.16515 | 1.14734 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.79129 | −0.904447 | −0.452224 | − | 0.891905i | \(-0.649369\pi\) | ||||
−0.452224 | + | 0.891905i | \(0.649369\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.79129 | 0.273169 | 0.136584 | − | 0.990628i | \(-0.456388\pi\) | ||||
0.136584 | + | 0.990628i | \(0.456388\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.582576 | 0.0868453 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.58258 | −1.10603 | −0.553016 | − | 0.833171i | \(-0.686523\pi\) | ||||
−0.553016 | + | 0.833171i | \(0.686523\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.79129 | 0.250830 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.20871 | −0.715472 | −0.357736 | − | 0.933823i | \(-0.616451\pi\) | ||||
−0.357736 | + | 0.933823i | \(0.616451\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.5826 | 2.10115 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.58258 | 0.474524 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.41742 | −0.314722 | −0.157361 | − | 0.987541i | \(-0.550299\pi\) | ||||
−0.157361 | + | 0.987541i | \(0.550299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.20871 | −0.282797 | −0.141398 | − | 0.989953i | \(-0.545160\pi\) | ||||
−0.141398 | + | 0.989953i | \(0.545160\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.1652 | −1.38487 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.9564 | 1.46071 | 0.730356 | − | 0.683067i | \(-0.239354\pi\) | ||||
0.730356 | + | 0.683067i | \(0.239354\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.5826 | 1.63515 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5826 | 1.61196 | 0.805978 | − | 0.591946i | \(-0.201640\pi\) | ||||
0.805978 | + | 0.591946i | \(0.201640\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.2087 | −1.19484 | −0.597420 | − | 0.801929i | \(-0.703807\pi\) | ||||
−0.597420 | + | 0.801929i | \(0.703807\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.00000 | −0.577350 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.58258 | −1.06473 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.417424 | 0.0458183 | 0.0229091 | − | 0.999738i | \(-0.492707\pi\) | ||||
0.0229091 | + | 0.999738i | \(0.492707\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.79129 | −0.302758 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.16515 | −0.759505 | −0.379752 | − | 0.925088i | \(-0.623991\pi\) | ||||
−0.379752 | + | 0.925088i | \(0.623991\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.58258 | 0.889972 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.58258 | −0.572760 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.20871 | −0.528865 | −0.264432 | − | 0.964404i | \(-0.585185\pi\) | ||||
−0.264432 | + | 0.964404i | \(0.585185\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.16515 | 0.117102 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.1652 | 1.90700 | 0.953502 | − | 0.301387i | \(-0.0974496\pi\) | ||||
0.953502 | + | 0.301387i | \(0.0974496\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.58258 | −0.155936 | −0.0779679 | − | 0.996956i | \(-0.524843\pi\) | ||||
−0.0779679 | + | 0.996956i | \(0.524843\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.5826 | 1.50642 | 0.753212 | − | 0.657778i | \(-0.228503\pi\) | ||||
0.753212 | + | 0.657778i | \(0.228503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4174 | 0.997808 | 0.498904 | − | 0.866657i | \(-0.333736\pi\) | ||||
0.498904 | + | 0.866657i | \(0.333736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.41742 | 0.609115 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.4174 | −0.979989 | −0.489994 | − | 0.871726i | \(-0.663001\pi\) | ||||
−0.489994 | + | 0.871726i | \(0.663001\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.1652 | −1.97366 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.834849 | −0.0771818 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.1652 | 1.83320 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.3739 | 0.935380 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.16515 | −0.551428 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.2087 | 1.34955 | 0.674777 | − | 0.738021i | \(-0.264240\pi\) | ||||
0.674777 | + | 0.738021i | \(0.264240\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.20871 | −0.282511 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.9564 | 1.20118 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.5390 | −1.41302 | −0.706512 | − | 0.707701i | \(-0.749732\pi\) | ||||
−0.706512 | + | 0.707701i | \(0.749732\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.7913 | −1.08494 | −0.542471 | − | 0.840074i | \(-0.682511\pi\) | ||||
−0.542471 | + | 0.840074i | \(0.682511\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.5826 | 1.14386 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −22.3303 | −1.86735 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.5390 | −1.35493 | −0.677464 | − | 0.735556i | \(-0.736921\pi\) | ||||
−0.677464 | + | 0.735556i | \(0.736921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.9564 | 1.37990 | 0.689948 | − | 0.723859i | \(-0.257633\pi\) | ||||
0.689948 | + | 0.723859i | \(0.257633\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.208712 | −0.0168734 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.3739 | −1.07421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.1652 | −1.05069 | −0.525347 | − | 0.850888i | \(-0.676064\pi\) | ||||
−0.525347 | + | 0.850888i | \(0.676064\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.33030 | 0.739941 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.58258 | 0.750565 | 0.375283 | − | 0.926910i | \(-0.377546\pi\) | ||||
0.375283 | + | 0.926910i | \(0.377546\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −27.9129 | −2.17301 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.79129 | −0.757673 | −0.378836 | − | 0.925464i | \(-0.623676\pi\) | ||||
−0.378836 | + | 0.925464i | \(0.623676\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.417424 | −0.0319212 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −25.3739 | −1.92914 | −0.964570 | − | 0.263829i | \(-0.915015\pi\) | ||||
−0.964570 | + | 0.263829i | \(0.915015\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.33030 | 0.325485 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.7913 | −1.32978 | −0.664892 | − | 0.746940i | \(-0.731522\pi\) | ||||
−0.664892 | + | 0.746940i | \(0.731522\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.1652 | 1.27588 | 0.637938 | − | 0.770088i | \(-0.279788\pi\) | ||||
0.637938 | + | 0.770088i | \(0.279788\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.95644 | 0.292468 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.0000 | −0.735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.58258 | −0.408238 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.20871 | −0.232174 | −0.116087 | − | 0.993239i | \(-0.537035\pi\) | ||||
−0.116087 | + | 0.993239i | \(0.537035\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.74773 | −0.485712 | −0.242856 | − | 0.970062i | \(-0.578084\pi\) | ||||
−0.242856 | + | 0.970062i | \(0.578084\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.0000 | 1.43223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.83485 | 0.344469 | 0.172234 | − | 0.985056i | \(-0.444901\pi\) | ||||
0.172234 | + | 0.985056i | \(0.444901\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5390 | 1.17242 | 0.586210 | − | 0.810159i | \(-0.300619\pi\) | ||||
0.586210 | + | 0.810159i | \(0.300619\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.4174 | −1.51067 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.1652 | −1.12902 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.58258 | −0.109997 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.1652 | −0.772310 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.9129 | −1.64623 | −0.823115 | − | 0.567874i | \(-0.807766\pi\) | ||||
−0.823115 | + | 0.567874i | \(0.807766\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.3303 | −1.66708 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.00000 | 0.340997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.2867 | 1.23570 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.16515 | 0.211954 | 0.105977 | − | 0.994369i | \(-0.466203\pi\) | ||||
0.105977 | + | 0.994369i | \(0.466203\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.582576 | 0.0388384 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.6261 | −0.904398 | −0.452199 | − | 0.891917i | \(-0.649360\pi\) | ||||
−0.452199 | + | 0.891917i | \(0.649360\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.7477 | 0.710230 | 0.355115 | − | 0.934823i | \(-0.384442\pi\) | ||||
0.355115 | + | 0.934823i | \(0.384442\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7477 | −0.835131 | −0.417566 | − | 0.908647i | \(-0.637117\pi\) | ||||
−0.417566 | + | 0.908647i | \(0.637117\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.1652 | −1.38066 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.9129 | 1.16357 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.37386 | −0.0888678 | −0.0444339 | − | 0.999012i | \(-0.514148\pi\) | ||||
−0.0444339 | + | 0.999012i | \(0.514148\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.5390 | −1.25862 | −0.629309 | − | 0.777155i | \(-0.716662\pi\) | ||||
−0.629309 | + | 0.777155i | \(0.716662\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.16515 | 0.138895 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.00000 | 0.509028 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.747727 | −0.0473853 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.5826 | 1.23604 | 0.618021 | − | 0.786162i | \(-0.287935\pi\) | ||||
0.618021 | + | 0.786162i | \(0.287935\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −42.3303 | −2.66128 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.00000 | 0.313112 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.3303 | −1.76720 | −0.883598 | − | 0.468247i | \(-0.844886\pi\) | ||||
−0.883598 | + | 0.468247i | \(0.844886\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.33030 | −0.390343 | −0.195172 | − | 0.980769i | \(-0.562526\pi\) | ||||
−0.195172 | + | 0.980769i | \(0.562526\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.5390 | −0.893125 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.8348 | 0.785480 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.1652 | 1.29046 | 0.645231 | − | 0.763988i | \(-0.276761\pi\) | ||||
0.645231 | + | 0.763988i | \(0.276761\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.1652 | −0.921217 | −0.460609 | − | 0.887603i | \(-0.652369\pi\) | ||||
−0.460609 | + | 0.887603i | \(0.652369\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.5826 | 0.939665 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.747727 | 0.0449266 | 0.0224633 | − | 0.999748i | \(-0.492849\pi\) | ||||
0.0224633 | + | 0.999748i | \(0.492849\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.20871 | 0.310726 | 0.155363 | − | 0.987857i | \(-0.450345\pi\) | ||||
0.155363 | + | 0.987857i | \(0.450345\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.1216 | 0.898885 | 0.449443 | − | 0.893309i | \(-0.351623\pi\) | ||||
0.449443 | + | 0.893309i | \(0.351623\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.0000 | 0.592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.33030 | 0.546952 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.7477 | 0.861571 | 0.430786 | − | 0.902454i | \(-0.358236\pi\) | ||||
0.430786 | + | 0.902454i | \(0.358236\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.74773 | −0.392868 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 27.9129 | 1.61967 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 30.3303 | 1.75405 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −34.3303 | −1.97222 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.16515 | −0.353016 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.58258 | 0.0903224 | 0.0451612 | − | 0.998980i | \(-0.485620\pi\) | ||||
0.0451612 | + | 0.998980i | \(0.485620\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.83485 | 0.161269 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.7913 | 1.40578 | 0.702892 | − | 0.711296i | \(-0.251891\pi\) | ||||
0.702892 | + | 0.711296i | \(0.251891\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.7042 | −1.05722 | −0.528611 | − | 0.848864i | \(-0.677287\pi\) | ||||
−0.528611 | + | 0.848864i | \(0.677287\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.3303 | −1.47886 | −0.739429 | − | 0.673235i | \(-0.764904\pi\) | ||||
−0.739429 | + | 0.673235i | \(0.764904\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.9129 | −1.55794 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000 | 0.111283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.1652 | −0.619331 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.6606 | −1.03193 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.37386 | 0.350339 | 0.175170 | − | 0.984538i | \(-0.443953\pi\) | ||||
0.175170 | + | 0.984538i | \(0.443953\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.747727 | −0.0409752 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 33.3739 | 1.82341 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.16515 | 0.0634698 | 0.0317349 | − | 0.999496i | \(-0.489897\pi\) | ||||
0.0317349 | + | 0.999496i | \(0.489897\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.6606 | 1.01350 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.7477 | −1.44847 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 37.9129 | 2.04116 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.1652 | 1.02884 | 0.514420 | − | 0.857539i | \(-0.328007\pi\) | ||||
0.514420 | + | 0.857539i | \(0.328007\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.58258 | −0.512944 | −0.256472 | − | 0.966552i | \(-0.582560\pi\) | ||||
−0.256472 | + | 0.966552i | \(0.582560\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.0000 | −1.06752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.83485 | 0.470232 | 0.235116 | − | 0.971967i | \(-0.424453\pi\) | ||||
0.235116 | + | 0.971967i | \(0.424453\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.9129 | 2.01221 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.95644 | −0.208813 | −0.104406 | − | 0.994535i | \(-0.533294\pi\) | ||||
−0.104406 | + | 0.994535i | \(0.533294\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −36.1216 | −1.89589 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.4955 | −1.49152 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.6261 | −0.763478 | −0.381739 | − | 0.924270i | \(-0.624675\pi\) | ||||
−0.381739 | + | 0.924270i | \(0.624675\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.20871 | −0.0629230 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.1216 | −1.24897 | −0.624484 | − | 0.781037i | \(-0.714691\pi\) | ||||
−0.624484 | + | 0.781037i | \(0.714691\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.0436 | 0.570287 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.3303 | −1.35250 | −0.676248 | − | 0.736674i | \(-0.736395\pi\) | ||||
−0.676248 | + | 0.736674i | \(0.736395\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.2432 | −1.39571 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.5826 | 0.898428 | 0.449214 | − | 0.893424i | \(-0.351704\pi\) | ||||
0.449214 | + | 0.893424i | \(0.351704\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.373864 | 0.0190046 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.1216 | 1.07091 | 0.535454 | − | 0.844565i | \(-0.320141\pi\) | ||||
0.535454 | + | 0.844565i | \(0.320141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.58258 | 0.383467 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.4955 | 1.08430 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.9129 | −1.40445 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.2867 | 1.41967 | 0.709835 | − | 0.704368i | \(-0.248769\pi\) | ||||
0.709835 | + | 0.704368i | \(0.248769\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.1652 | −1.05694 | −0.528469 | − | 0.848953i | \(-0.677234\pi\) | ||||
−0.528469 | + | 0.848953i | \(0.677234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.1652 | 0.954684 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −26.7477 | −1.32911 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.0000 | −0.991363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.00000 | 0.197787 | 0.0988936 | − | 0.995098i | \(-0.468470\pi\) | ||||
0.0988936 | + | 0.995098i | \(0.468470\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.6261 | 1.46135 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.16515 | 0.0571950 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.9129 | 1.12205 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.7913 | 1.40655 | 0.703273 | − | 0.710920i | \(-0.251721\pi\) | ||||
0.703273 | + | 0.710920i | \(0.251721\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7913 | −0.672146 | −0.336073 | − | 0.941836i | \(-0.609099\pi\) | ||||
−0.336073 | + | 0.941836i | \(0.609099\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.58258 | −0.0769475 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.79129 | −0.135397 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 40.0000 | 1.93122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.58258 | −0.461576 | −0.230788 | − | 0.973004i | \(-0.574130\pi\) | ||||
−0.230788 | + | 0.973004i | \(0.574130\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.4174 | −1.17343 | −0.586713 | − | 0.809795i | \(-0.699578\pi\) | ||||
−0.586713 | + | 0.809795i | \(0.699578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.1652 | 0.725448 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.9564 | 1.00020 | 0.500098 | − | 0.865969i | \(-0.333297\pi\) | ||||
0.500098 | + | 0.865969i | \(0.333297\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.3303 | −1.82113 | −0.910564 | − | 0.413369i | \(-0.864352\pi\) | ||||
−0.910564 | + | 0.413369i | \(0.864352\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.0000 | −0.948091 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.6261 | 1.40127 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.58258 | 0.357844 | 0.178922 | − | 0.983863i | \(-0.442739\pi\) | ||||
0.178922 | + | 0.983863i | \(0.442739\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.3303 | −1.52237 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.3739 | −1.42709 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.20871 | 0.243653 | 0.121827 | − | 0.992551i | \(-0.461125\pi\) | ||||
0.121827 | + | 0.992551i | \(0.461125\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.00000 | −0.233380 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.25227 | −0.151473 | −0.0757367 | − | 0.997128i | \(-0.524131\pi\) | ||||
−0.0757367 | + | 0.997128i | \(0.524131\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6261 | 0.865630 | 0.432815 | − | 0.901483i | \(-0.357520\pi\) | ||||
0.432815 | + | 0.901483i | \(0.357520\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 23.9564 | 1.11095 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.8348 | −0.593926 | −0.296963 | − | 0.954889i | \(-0.595974\pi\) | ||||
−0.296963 | + | 0.954889i | \(0.595974\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.5826 | 1.08663 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.0000 | 0.459800 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.58258 | −0.256146 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.08712 | −0.0497759 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.8693 | −1.59322 | −0.796610 | − | 0.604494i | \(-0.793375\pi\) | ||||
−0.796610 | + | 0.604494i | \(0.793375\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.3303 | 0.653406 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.5390 | −0.660183 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.25227 | −0.238003 | −0.119002 | − | 0.992894i | \(-0.537969\pi\) | ||||
−0.119002 | + | 0.992894i | \(0.537969\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.1652 | −0.776235 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.9564 | 1.08114 | 0.540569 | − | 0.841299i | \(-0.318209\pi\) | ||||
0.540569 | + | 0.841299i | \(0.318209\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.25227 | 0.146179 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.58258 | −0.428975 | −0.214488 | − | 0.976727i | \(-0.568808\pi\) | ||||
−0.214488 | + | 0.976727i | \(0.568808\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.5390 | 0.783585 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.791288 | −0.0352818 | −0.0176409 | − | 0.999844i | \(-0.505616\pi\) | ||||
−0.0176409 | + | 0.999844i | \(0.505616\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53.4955 | 2.38052 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.37386 | −0.238662 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.3303 | 1.25572 | 0.627859 | − | 0.778327i | \(-0.283931\pi\) | ||||
0.627859 | + | 0.778327i | \(0.283931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.0000 | −0.441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.41742 | −0.194655 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.3303 | −1.86168 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 45.4519 | 1.99512 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.9564 | 1.26860 | 0.634302 | − | 0.773085i | \(-0.281287\pi\) | ||||
0.634302 | + | 0.773085i | \(0.281287\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.0780 | −1.35895 | −0.679474 | − | 0.733700i | \(-0.737792\pi\) | ||||
−0.679474 | + | 0.733700i | \(0.737792\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.79129 | 0.208712 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 34.4955 | 1.49980 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.504546 | −0.0218954 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.1652 | 1.00339 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.4955 | 1.88047 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 31.8693 | 1.37526 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.1652 | 1.33989 | 0.669947 | − | 0.742409i | \(-0.266317\pi\) | ||||
0.669947 | + | 0.742409i | \(0.266317\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −30.7477 | −1.31951 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.0780 | 1.24557 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.00000 | −0.342055 | −0.171028 | − | 0.985266i | \(-0.554709\pi\) | ||||
−0.171028 | + | 0.985266i | \(0.554709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.460985 | −0.0196744 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.9129 | 0.760359 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.3303 | 0.522452 | 0.261226 | − | 0.965278i | \(-0.415873\pi\) | ||||
0.261226 | + | 0.965278i | \(0.415873\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.16515 | −0.303054 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.0000 | 0.422200 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0000 | 0.505740 | 0.252870 | − | 0.967500i | \(-0.418626\pi\) | ||||
0.252870 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.0780 | −1.22332 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.04356 | −0.295281 | −0.147641 | − | 0.989041i | \(-0.547168\pi\) | ||||
−0.147641 | + | 0.989041i | \(0.547168\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.41742 | −0.268561 | −0.134280 | − | 0.990943i | \(-0.542872\pi\) | ||||
−0.134280 | + | 0.990943i | \(0.542872\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.74773 | 0.240115 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.1652 | −0.882648 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.9129 | 1.49507 | 0.747536 | − | 0.664221i | \(-0.231237\pi\) | ||||
0.747536 | + | 0.664221i | \(0.231237\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.0871 | 0.502324 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.0780 | −1.20429 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.33030 | −0.0963462 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.5826 | −1.46865 | −0.734325 | − | 0.678798i | \(-0.762501\pi\) | ||||
−0.734325 | + | 0.678798i | \(0.762501\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.58258 | 0.394843 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.66061 | −0.356250 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.0780 | 1.60474 | 0.802371 | − | 0.596825i | \(-0.203571\pi\) | ||||
0.802371 | + | 0.596825i | \(0.203571\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.6261 | −1.21252 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.7913 | −0.726932 | −0.363466 | − | 0.931607i | \(-0.618407\pi\) | ||||
−0.363466 | + | 0.931607i | \(0.618407\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.4955 | −1.28473 | −0.642363 | − | 0.766400i | \(-0.722046\pi\) | ||||
−0.642363 | + | 0.766400i | \(0.722046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.49545 | 0.101623 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 56.2867 | 2.28838 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.6261 | 1.04013 | 0.520066 | − | 0.854126i | \(-0.325907\pi\) | ||||
0.520066 | + | 0.854126i | \(0.325907\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.3303 | 1.22703 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.2867 | 1.46561 | 0.732804 | − | 0.680440i | \(-0.238211\pi\) | ||||
0.732804 | + | 0.680440i | \(0.238211\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 28.9564 | 1.16764 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.4955 | 1.59003 | 0.795014 | − | 0.606592i | \(-0.207464\pi\) | ||||
0.795014 | + | 0.606592i | \(0.207464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.6606 | −1.79506 | −0.897531 | − | 0.440952i | \(-0.854641\pi\) | ||||
−0.897531 | + | 0.440952i | \(0.854641\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −37.9129 | −1.52139 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1652 | −1.24661 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.0000 | 0.798723 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.58258 | 0.142847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.95644 | 0.157503 | 0.0787517 | − | 0.996894i | \(-0.474907\pi\) | ||||
0.0787517 | + | 0.996894i | \(0.474907\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 42.8348 | 1.70253 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 42.4519 | 1.68465 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.83485 | 0.112145 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.91288 | 0.154549 | 0.0772747 | − | 0.997010i | \(-0.475378\pi\) | ||||
0.0772747 | + | 0.997010i | \(0.475378\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.9564 | 0.826441 | 0.413221 | − | 0.910631i | \(-0.364404\pi\) | ||||
0.413221 | + | 0.910631i | \(0.364404\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.95644 | −0.352659 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.1652 | 0.910716 | 0.455358 | − | 0.890308i | \(-0.349511\pi\) | ||||
0.455358 | + | 0.890308i | \(0.349511\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.4955 | −0.529743 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.9129 | −1.01405 | −0.507025 | − | 0.861932i | \(-0.669255\pi\) | ||||
−0.507025 | + | 0.861932i | \(0.669255\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.4955 | −1.30878 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.13068 | −0.0831258 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.04356 | −0.157515 | −0.0787574 | − | 0.996894i | \(-0.525095\pi\) | ||||
−0.0787574 | + | 0.996894i | \(0.525095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.4955 | 0.447121 | 0.223561 | − | 0.974690i | \(-0.428232\pi\) | ||||
0.223561 | + | 0.974690i | \(0.428232\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.16515 | −0.278271 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.66970 | −0.219203 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.3303 | −0.476006 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 51.0780 | 1.96891 | 0.984457 | − | 0.175628i | \(-0.0561955\pi\) | ||||
0.984457 | + | 0.175628i | \(0.0561955\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.9564 | 0.537184 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.1652 | 1.73584 | 0.867919 | − | 0.496706i | \(-0.165457\pi\) | ||||
0.867919 | + | 0.496706i | \(0.165457\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.4083 | 0.935329 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.25227 | 0.200973 | 0.100486 | − | 0.994938i | \(-0.467960\pi\) | ||||
0.100486 | + | 0.994938i | \(0.467960\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.1652 | −1.76388 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.2523 | −0.734520 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.8348 | 0.793745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.3739 | 1.26960 | 0.634801 | − | 0.772676i | \(-0.281082\pi\) | ||||
0.634801 | + | 0.772676i | \(0.281082\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.7042 | −1.35434 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.79129 | 0.219361 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.8348 | 0.863693 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.16515 | 0.270239 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 37.9129 | 1.42788 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.1652 | 1.84644 | 0.923218 | − | 0.384277i | \(-0.125549\pi\) | ||||
0.923218 | + | 0.384277i | \(0.125549\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.08712 | −0.0782732 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.3303 | 1.36058 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −62.3303 | −2.33102 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.46099 | 0.0919072 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 50.8693 | 1.89711 | 0.948553 | − | 0.316619i | \(-0.102548\pi\) | ||||
0.948553 | + | 0.316619i | \(0.102548\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 35.0000 | 1.30166 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.33030 | 0.160602 | 0.0803010 | − | 0.996771i | \(-0.474412\pi\) | ||||
0.0803010 | + | 0.996771i | \(0.474412\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.8693 | 0.921086 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.79129 | −0.0662532 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.7477 | −0.470848 | −0.235424 | − | 0.971893i | \(-0.575648\pi\) | ||||
−0.235424 | + | 0.971893i | \(0.575648\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 66.7477 | 2.45868 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.04356 | 0.259102 | 0.129551 | − | 0.991573i | \(-0.458646\pi\) | ||||
0.129551 | + | 0.991573i | \(0.458646\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.3303 | −0.526437 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.8348 | 0.984475 | 0.492238 | − | 0.870461i | \(-0.336179\pi\) | ||||
0.492238 | + | 0.870461i | \(0.336179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −46.1652 | −1.69136 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0871215 | 0.00318761 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.1652 | 0.918289 | 0.459145 | − | 0.888361i | \(-0.348156\pi\) | ||||
0.459145 | + | 0.888361i | \(0.348156\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −35.0780 | −1.27831 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.3303 | 1.72253 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.6170 | −1.51260 | −0.756299 | − | 0.654227i | \(-0.772994\pi\) | ||||
−0.756299 | + | 0.654227i | \(0.772994\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 75.8258 | 2.75230 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.8348 | 0.465263 | 0.232631 | − | 0.972565i | \(-0.425266\pi\) | ||||
0.232631 | + | 0.972565i | \(0.425266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.582576 | −0.0210631 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.66970 | 0.349153 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.4955 | 0.630902 | 0.315451 | − | 0.948942i | \(-0.397844\pi\) | ||||
0.315451 | + | 0.948942i | \(0.397844\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50.7477 | 1.82763 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.9129 | 0.500411 | 0.250206 | − | 0.968193i | \(-0.419502\pi\) | ||||
0.250206 | + | 0.968193i | \(0.419502\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.3739 | −0.480403 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.5826 | 0.414989 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 75.8258 | 2.71326 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.7477 | −1.31158 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.3303 | 0.510820 | 0.255410 | − | 0.966833i | \(-0.417790\pi\) | ||||
0.255410 | + | 0.966833i | \(0.417790\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.3394 | 0.403693 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.83485 | 0.313735 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 26.0436 | 0.923670 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.0780 | −1.45506 | −0.727529 | − | 0.686077i | \(-0.759331\pi\) | ||||
−0.727529 | + | 0.686077i | \(0.759331\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.58258 | 0.268252 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.49545 | −0.0528393 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −56.9909 | −2.01117 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.9129 | −1.33460 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.4955 | 0.966689 | 0.483344 | − | 0.875430i | \(-0.339422\pi\) | ||||
0.483344 | + | 0.875430i | \(0.339422\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.7042 | −1.81558 | −0.907789 | − | 0.419426i | \(-0.862231\pi\) | ||||
−0.907789 | + | 0.419426i | \(0.862231\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.1652 | 0.952723 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.7477 | 0.936932 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.58258 | −0.125338 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −53.0780 | −1.85018 | −0.925092 | − | 0.379743i | \(-0.876012\pi\) | ||||
−0.925092 | + | 0.379743i | \(0.876012\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −27.9129 | −0.971802 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.66970 | 0.127608 | 0.0638039 | − | 0.997962i | \(-0.479677\pi\) | ||||
0.0638039 | + | 0.997962i | \(0.479677\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.33939 | −0.0464631 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.3303 | −0.945804 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.9564 | −0.828056 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.8348 | 1.13358 | 0.566792 | − | 0.823861i | \(-0.308184\pi\) | ||||
0.566792 | + | 0.823861i | \(0.308184\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.33030 | −0.321353 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.37386 | 0.288070 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.0871 | −0.929628 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.1652 | 0.931209 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.4955 | −1.48926 | −0.744628 | − | 0.667480i | \(-0.767373\pi\) | ||||
−0.744628 | + | 0.667480i | \(0.767373\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.16515 | −0.0398473 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −56.2867 | −1.92272 | −0.961359 | − | 0.275297i | \(-0.911224\pi\) | ||||
−0.961359 | + | 0.275297i | \(0.911224\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.9129 | 1.29357 | 0.646785 | − | 0.762672i | \(-0.276113\pi\) | ||||
0.646785 | + | 0.762672i | \(0.276113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.37386 | 0.0808073 | 0.0404036 | − | 0.999183i | \(-0.487136\pi\) | ||||
0.0404036 | + | 0.999183i | \(0.487136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −70.8258 | −2.40815 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.79129 | −0.0608353 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −55.8258 | −1.89376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.8258 | −1.62051 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.08712 | −0.0367935 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.9129 | 0.739945 | 0.369973 | − | 0.929043i | \(-0.379367\pi\) | ||||
0.369973 | + | 0.929043i | \(0.379367\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.4174 | −0.891038 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.12159 | −0.0377873 | −0.0188937 | − | 0.999821i | \(-0.506014\pi\) | ||||
−0.0188937 | + | 0.999821i | \(0.506014\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.46099 | −0.0828187 | −0.0414094 | − | 0.999142i | \(-0.513185\pi\) | ||||
−0.0414094 | + | 0.999142i | \(0.513185\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.0871 | 0.406304 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.7913 | −0.832410 | −0.416205 | − | 0.909271i | \(-0.636640\pi\) | ||||
−0.416205 | + | 0.909271i | \(0.636640\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −53.4955 | −1.79217 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.1652 | 0.507482 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −49.6606 | −1.65997 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −54.3303 | −1.81404 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.20871 | 0.173527 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 47.9129 | 1.59268 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.41742 | −0.146678 | −0.0733391 | − | 0.997307i | \(-0.523366\pi\) | ||||
−0.0733391 | + | 0.997307i | \(0.523366\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.00000 | 0.132672 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.3303 | −1.53499 | −0.767496 | − | 0.641054i | \(-0.778497\pi\) | ||||
−0.767496 | + | 0.641054i | \(0.778497\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.33030 | 0.0771218 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.0436 | 0.365089 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.1216 | −1.85128 | −0.925640 | − | 0.378405i | \(-0.876473\pi\) | ||||
−0.925640 | + | 0.378405i | \(0.876473\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.83485 | −0.0934114 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −54.3303 | −1.78830 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.330303 | −0.0108486 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.37386 | 0.274738 | 0.137369 | − | 0.990520i | \(-0.456135\pi\) | ||||
0.137369 | + | 0.990520i | \(0.456135\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −44.4083 | −1.45386 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.5826 | −0.509605 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.6606 | 1.85102 | 0.925511 | − | 0.378722i | \(-0.123636\pi\) | ||||
0.925511 | + | 0.378722i | \(0.123636\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.5045 | 1.09338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.2867 | 1.80230 | 0.901148 | − | 0.433511i | \(-0.142726\pi\) | ||||
0.901148 | + | 0.433511i | \(0.142726\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.9129 | 1.43000 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.9129 | 1.49197 | 0.745984 | − | 0.665964i | \(-0.231979\pi\) | ||||
0.745984 | + | 0.665964i | \(0.231979\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.8348 | 1.32556 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 47.1652 | 1.52943 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.7042 | −1.90161 | −0.950807 | − | 0.309783i | \(-0.899744\pi\) | ||||
−0.950807 | + | 0.309783i | \(0.899744\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.95644 | −0.289824 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.04356 | −0.259470 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.25227 | 0.104803 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.8348 | −0.606315 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.46099 | 0.239929 | 0.119965 | − | 0.992778i | \(-0.461722\pi\) | ||||
0.119965 | + | 0.992778i | \(0.461722\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.58258 | −0.115089 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.8348 | 1.24627 | 0.623135 | − | 0.782114i | \(-0.285859\pi\) | ||||
0.623135 | + | 0.782114i | \(0.285859\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20.0000 | 0.640513 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.4610 | −0.526634 | −0.263317 | − | 0.964709i | \(-0.584816\pi\) | ||||
−0.263317 | + | 0.964709i | \(0.584816\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.0000 | −1.27841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.17424 | 0.0694182 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.3739 | 0.713615 | 0.356808 | − | 0.934178i | \(-0.383865\pi\) | ||||
0.356808 | + | 0.934178i | \(0.383865\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.4955 | 0.430001 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.5826 | −0.431901 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.0780 | −0.606034 | −0.303017 | − | 0.952985i | \(-0.597994\pi\) | ||||
−0.303017 | + | 0.952985i | \(0.597994\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.4174 | −0.362321 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46.1652 | 1.46353 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.7042 | −1.63749 | −0.818744 | − | 0.574159i | \(-0.805329\pi\) | ||||
−0.818744 | + | 0.574159i | \(0.805329\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.9129 | −0.566738 |
(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 | 3332.2.a.m.1.1 | yes | 2 | |
7.6 | odd | 2 | 3332.2.a.i.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3332.2.a.i.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
3332.2.a.m.1.1 | yes | 2 | 1.1 | even | 1 | trivial |