Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7220,2,Mod(1,7220)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7220, 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("7220.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7220 = 2^{2} \cdot 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7220.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: | \(57.6519902594\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.133593.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 3x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 380) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.52082\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7220.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.52082 | 1.45540 | 0.727698 | − | 0.685898i | \(-0.240590\pi\) | ||||
0.727698 | + | 0.685898i | \(0.240590\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.72743 | 1.03087 | 0.515435 | − | 0.856928i | \(-0.327630\pi\) | ||||
0.515435 | + | 0.856928i | \(0.327630\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.35453 | 1.11818 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.31421 | 0.999273 | 0.499636 | − | 0.866235i | \(-0.333467\pi\) | ||||
0.499636 | + | 0.866235i | \(0.333467\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.24825 | −0.900902 | −0.450451 | − | 0.892801i | \(-0.648737\pi\) | ||||
−0.450451 | + | 0.892801i | \(0.648737\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.52082 | 0.650873 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.35453 | −0.571058 | −0.285529 | − | 0.958370i | \(-0.592169\pi\) | ||||
−0.285529 | + | 0.958370i | \(0.592169\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.87535 | 1.50033 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.14793 | 0.447873 | 0.223937 | − | 0.974604i | \(-0.428109\pi\) | ||||
0.223937 | + | 0.974604i | \(0.428109\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.893714 | 0.171995 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.93403 | 0.730532 | 0.365266 | − | 0.930903i | \(-0.380978\pi\) | ||||
0.365266 | + | 0.930903i | \(0.380978\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.1896 | 1.83010 | 0.915050 | − | 0.403340i | \(-0.132151\pi\) | ||||
0.915050 | + | 0.403340i | \(0.132151\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.35453 | 1.45434 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.72743 | 0.461019 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.68579 | 0.605940 | 0.302970 | − | 0.953000i | \(-0.402022\pi\) | ||||
0.302970 | + | 0.953000i | \(0.402022\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.18825 | −1.31117 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.727427 | 0.113605 | 0.0568025 | − | 0.998385i | \(-0.481909\pi\) | ||||
0.0568025 | + | 0.998385i | \(0.481909\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.37289 | −0.361863 | −0.180931 | − | 0.983496i | \(-0.557911\pi\) | ||||
−0.180931 | + | 0.983496i | \(0.557911\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.35453 | 0.500064 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.0233 | −1.60791 | −0.803955 | − | 0.594690i | \(-0.797275\pi\) | ||||
−0.803955 | + | 0.594690i | \(0.797275\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.438860 | 0.0626942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.93535 | −0.831116 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.98296 | 1.23390 | 0.616952 | − | 0.787001i | \(-0.288367\pi\) | ||||
0.616952 | + | 0.787001i | \(0.288367\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.31421 | 0.446888 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.9757 | 1.42891 | 0.714456 | − | 0.699681i | \(-0.246674\pi\) | ||||
0.714456 | + | 0.699681i | \(0.246674\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.45485 | −1.08253 | −0.541267 | − | 0.840851i | \(-0.682055\pi\) | ||||
−0.541267 | + | 0.840851i | \(0.682055\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.14925 | 1.15270 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.24825 | −0.402895 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.75071 | 1.19124 | 0.595619 | − | 0.803267i | \(-0.296907\pi\) | ||||
0.595619 | + | 0.803267i | \(0.296907\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.41453 | 0.651833 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.91699 | −0.820896 | −0.410448 | − | 0.911884i | \(-0.634628\pi\) | ||||
−0.410448 | + | 0.911884i | \(0.634628\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.48050 | −0.290320 | −0.145160 | − | 0.989408i | \(-0.546370\pi\) | ||||
−0.145160 | + | 0.989408i | \(0.546370\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.52082 | 0.291079 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.03927 | 1.03012 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9990 | −1.34999 | −0.674994 | − | 0.737823i | \(-0.735854\pi\) | ||||
−0.674994 | + | 0.737823i | \(0.735854\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.81071 | −0.867856 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.68711 | 0.514477 | 0.257238 | − | 0.966348i | \(-0.417187\pi\) | ||||
0.257238 | + | 0.966348i | \(0.417187\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.35453 | −0.255385 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.91699 | 1.06321 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.54410 | −0.905673 | −0.452836 | − | 0.891594i | \(-0.649588\pi\) | ||||
−0.452836 | + | 0.891594i | \(0.649588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.85936 | −0.928713 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 25.6861 | 2.66352 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.22989 | −0.734084 | −0.367042 | − | 0.930204i | \(-0.619629\pi\) | ||||
−0.367042 | + | 0.930204i | \(0.619629\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.1176 | 1.11736 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.77635 | −0.574768 | −0.287384 | − | 0.957815i | \(-0.592786\pi\) | ||||
−0.287384 | + | 0.957815i | \(0.592786\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.0576 | 1.48367 | 0.741836 | − | 0.670581i | \(-0.233955\pi\) | ||||
0.741836 | + | 0.670581i | \(0.233955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.87535 | 0.670966 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.1896 | 1.46843 | 0.734215 | − | 0.678917i | \(-0.237550\pi\) | ||||
0.734215 | + | 0.678917i | \(0.237550\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.6211 | 1.20889 | 0.604443 | − | 0.796648i | \(-0.293396\pi\) | ||||
0.604443 | + | 0.796648i | \(0.293396\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.29121 | 0.881882 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.10761 | 0.574555 | 0.287278 | − | 0.957847i | \(-0.407250\pi\) | ||||
0.287278 | + | 0.957847i | \(0.407250\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.14793 | 0.200295 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.8964 | −1.00737 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.42182 | −0.588687 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0159950 | −0.00145409 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.83371 | 0.165340 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.12228 | 0.809472 | 0.404736 | − | 0.914434i | \(-0.367364\pi\) | ||||
0.404736 | + | 0.914434i | \(0.367364\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.98164 | −0.526654 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.2656 | 1.94535 | 0.972676 | − | 0.232169i | \(-0.0745821\pi\) | ||||
0.972676 | + | 0.232169i | \(0.0745821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.893714 | 0.0769187 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.62711 | −0.651628 | −0.325814 | − | 0.945434i | \(-0.605638\pi\) | ||||
−0.325814 | + | 0.945434i | \(0.605638\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.9183 | 1.43499 | 0.717496 | − | 0.696562i | \(-0.245288\pi\) | ||||
0.717496 | + | 0.696562i | \(0.245288\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −27.7877 | −2.34015 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.7654 | −0.900246 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.93403 | 0.326704 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.10629 | 0.0912449 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.3962 | −1.01553 | −0.507767 | − | 0.861494i | \(-0.669529\pi\) | ||||
−0.507767 | + | 0.861494i | \(0.669529\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.4549 | 1.17632 | 0.588160 | − | 0.808745i | \(-0.299853\pi\) | ||||
0.588160 | + | 0.808745i | \(0.299853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.89836 | −0.638544 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.1896 | 0.818446 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.2128 | −1.45354 | −0.726772 | − | 0.686879i | \(-0.758980\pi\) | ||||
−0.726772 | + | 0.686879i | \(0.758980\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.6444 | 1.79582 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.85831 | 0.461700 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.2642 | 1.50889 | 0.754446 | − | 0.656362i | \(-0.227906\pi\) | ||||
0.754446 | + | 0.656362i | \(0.227906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.35453 | 0.650400 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.68579 | −0.439979 | −0.219990 | − | 0.975502i | \(-0.570602\pi\) | ||||
−0.219990 | + | 0.975502i | \(0.570602\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.44889 | −0.188376 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.15521 | 0.696058 | 0.348029 | − | 0.937484i | \(-0.386851\pi\) | ||||
0.348029 | + | 0.937484i | \(0.386851\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.72743 | 0.206174 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27.6677 | 2.07963 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.1810 | −0.910448 | −0.455224 | − | 0.890377i | \(-0.650441\pi\) | ||||
−0.455224 | + | 0.890377i | \(0.650441\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.4122 | −1.14558 | −0.572789 | − | 0.819703i | \(-0.694138\pi\) | ||||
−0.572789 | + | 0.819703i | \(0.694138\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.3132 | −1.57551 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.68579 | 0.270984 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.80342 | −0.570643 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.43754 | 0.177305 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.2482 | −1.17568 | −0.587841 | − | 0.808977i | \(-0.700022\pi\) | ||||
−0.587841 | + | 0.808977i | \(0.700022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.851028 | −0.0612583 | −0.0306292 | − | 0.999531i | \(-0.509751\pi\) | ||||
−0.0306292 | + | 0.999531i | \(0.509751\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.18825 | −0.586372 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.9843 | 1.42382 | 0.711910 | − | 0.702270i | \(-0.247830\pi\) | ||||
0.711910 | + | 0.702270i | \(0.247830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.45722 | −0.457740 | −0.228870 | − | 0.973457i | \(-0.573503\pi\) | ||||
−0.228870 | + | 0.973457i | \(0.573503\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.5798 | 1.73372 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.7298 | 0.753084 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.727427 | 0.0508057 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.20529 | 0.500802 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5441 | −0.725886 | −0.362943 | − | 0.931811i | \(-0.618228\pi\) | ||||
−0.362943 | + | 0.931811i | \(0.618228\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −17.4365 | −1.19473 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.37289 | −0.161830 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.7913 | 1.88660 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.25289 | −0.422531 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.64811 | 0.514467 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.72638 | −0.651327 | −0.325663 | − | 0.945486i | \(-0.605588\pi\) | ||||
−0.325663 | + | 0.945486i | \(0.605588\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.35453 | 0.223636 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.5798 | −1.49867 | −0.749336 | − | 0.662190i | \(-0.769627\pi\) | ||||
−0.749336 | + | 0.662190i | \(0.769627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.2239 | −1.07211 | −0.536053 | − | 0.844184i | \(-0.680085\pi\) | ||||
−0.536053 | + | 0.844184i | \(0.680085\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22.7864 | 1.49923 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.6628 | −1.22264 | −0.611320 | − | 0.791384i | \(-0.709361\pi\) | ||||
−0.611320 | + | 0.791384i | \(0.709361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0233 | −0.719079 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −30.2472 | −1.96477 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.602780 | 0.0389906 | 0.0194953 | − | 0.999810i | \(-0.493794\pi\) | ||||
0.0194953 | + | 0.999810i | \(0.493794\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.8816 | −1.40952 | −0.704759 | − | 0.709447i | \(-0.748945\pi\) | ||||
−0.704759 | + | 0.709447i | \(0.748945\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.3705 | −1.43507 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.438860 | 0.0280377 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.8154 | 0.748768 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.27257 | 0.522160 | 0.261080 | − | 0.965317i | \(-0.415921\pi\) | ||||
0.261080 | + | 0.965317i | \(0.415921\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.11868 | 0.447548 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.93535 | −0.371686 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.1909 | −0.885203 | −0.442602 | − | 0.896718i | \(-0.645944\pi\) | ||||
−0.442602 | + | 0.896718i | \(0.645944\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0527 | 0.624645 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.1968 | 0.816864 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.5431 | −1.14341 | −0.571707 | − | 0.820458i | \(-0.693719\pi\) | ||||
−0.571707 | + | 0.820458i | \(0.693719\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.98296 | 0.551819 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.5381 | −1.31811 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.66743 | −0.406520 | −0.203260 | − | 0.979125i | \(-0.565154\pi\) | ||||
−0.203260 | + | 0.979125i | \(0.565154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.0662 | 1.34043 | 0.670214 | − | 0.742168i | \(-0.266202\pi\) | ||||
0.670214 | + | 0.742168i | \(0.266202\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.3328 | −1.35165 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.31421 | 0.199855 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.4624 | −1.46980 | −0.734902 | − | 0.678173i | \(-0.762772\pi\) | ||||
−0.734902 | + | 0.678173i | \(0.762772\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 34.1812 | 2.04638 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.6628 | −1.11333 | −0.556664 | − | 0.830738i | \(-0.687919\pi\) | ||||
−0.556664 | + | 0.830738i | \(0.687919\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.49622 | 0.267273 | 0.133636 | − | 0.991030i | \(-0.457335\pi\) | ||||
0.133636 | + | 0.991030i | \(0.457335\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.98400 | 0.117112 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4562 | −0.673893 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.2252 | −1.06838 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.27021 | −0.0742063 | −0.0371031 | − | 0.999311i | \(-0.511813\pi\) | ||||
−0.0371031 | + | 0.999311i | \(0.511813\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.9757 | 0.639028 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.96196 | 0.171870 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.97699 | −0.403490 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.47190 | −0.373034 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.5611 | −0.836516 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.45485 | −0.484124 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.65275 | 0.493839 | 0.246919 | − | 0.969036i | \(-0.420582\pi\) | ||||
0.246919 | + | 0.969036i | \(0.420582\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 37.9576 | 2.15933 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8497 | 1.35239 | 0.676196 | − | 0.736721i | \(-0.263627\pi\) | ||||
0.676196 | + | 0.736721i | \(0.263627\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.776351 | −0.0438819 | −0.0219410 | − | 0.999759i | \(-0.506985\pi\) | ||||
−0.0219410 | + | 0.999759i | \(0.506985\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.14925 | 0.515502 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.8423 | 0.777462 | 0.388731 | − | 0.921351i | \(-0.372914\pi\) | ||||
0.388731 | + | 0.921351i | \(0.372914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.0382 | 0.730001 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 38.2902 | 2.13715 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.24825 | −0.180180 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 31.8156 | 1.75941 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −30.0652 | −1.65755 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.6993 | −1.57746 | −0.788728 | − | 0.614742i | \(-0.789260\pi\) | ||||
−0.788728 | + | 0.614742i | \(0.789260\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.3641 | 0.677548 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.75071 | 0.532738 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.3256 | 1.92431 | 0.962153 | − | 0.272510i | \(-0.0878537\pi\) | ||||
0.962153 | + | 0.272510i | \(0.0878537\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.3962 | 0.836205 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.7704 | 1.82877 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8950 | −0.966241 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.41453 | 0.291509 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.0062 | 1.39609 | 0.698044 | − | 0.716055i | \(-0.254054\pi\) | ||||
0.698044 | + | 0.716055i | \(0.254054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.44757 | 0.131015 | 0.0655077 | − | 0.997852i | \(-0.479133\pi\) | ||||
0.0655077 | + | 0.997852i | \(0.479133\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.90300 | −0.154951 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.85103 | −0.258194 | −0.129097 | − | 0.991632i | \(-0.541208\pi\) | ||||
−0.129097 | + | 0.991632i | \(0.541208\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.91699 | −0.367116 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16.1882 | −0.856773 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.34752 | −0.387787 | −0.193894 | − | 0.981023i | \(-0.562112\pi\) | ||||
−0.193894 | + | 0.981023i | \(0.562112\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0403205 | −0.00211628 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.48050 | −0.129835 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.0357 | 0.680457 | 0.340228 | − | 0.940343i | \(-0.389496\pi\) | ||||
0.340228 | + | 0.940343i | \(0.389496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.44018 | 0.127031 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.5004 | 1.27200 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.5514 | 1.47833 | 0.739167 | − | 0.673522i | \(-0.235219\pi\) | ||||
0.739167 | + | 0.673522i | \(0.235219\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.52082 | 0.130175 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.7787 | −0.658137 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.2128 | −0.678698 | −0.339349 | − | 0.940661i | \(-0.610207\pi\) | ||||
−0.339349 | + | 0.940661i | \(0.610207\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.9956 | 1.17810 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.6617 | 1.92442 | 0.962212 | − | 0.272300i | \(-0.0877844\pi\) | ||||
0.962212 | + | 0.272300i | \(0.0877844\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.03927 | 0.460684 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.95995 | −0.404627 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.6447 | −1.30024 | −0.650119 | − | 0.759833i | \(-0.725281\pi\) | ||||
−0.650119 | + | 0.759833i | \(0.725281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.05736 | −0.255762 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 56.1275 | 2.83126 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.9990 | −0.603733 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.2731 | −1.66993 | −0.834965 | − | 0.550303i | \(-0.814512\pi\) | ||||
−0.834965 | + | 0.550303i | \(0.814512\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.41349 | −0.470087 | −0.235044 | − | 0.971985i | \(-0.575523\pi\) | ||||
−0.235044 | + | 0.971985i | \(0.575523\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.0982 | −1.64874 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.81071 | −0.388117 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.2155 | 0.605499 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.51090 | 0.124156 | 0.0620779 | − | 0.998071i | \(-0.480227\pi\) | ||||
0.0620779 | + | 0.998071i | \(0.480227\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.2266 | −0.948376 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.9354 | 1.47302 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.68711 | 0.230081 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 42.6480 | 2.08848 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.5638 | −1.93282 | −0.966409 | − | 0.257011i | \(-0.917262\pi\) | ||||
−0.966409 | + | 0.257011i | \(0.917262\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.1578 | 0.690011 | 0.345006 | − | 0.938601i | \(-0.387877\pi\) | ||||
0.345006 | + | 0.938601i | \(0.387877\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −36.9780 | −1.79793 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.35453 | −0.114212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.0600 | −1.11595 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −27.1376 | −1.31022 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.52574 | 0.314334 | 0.157167 | − | 0.987572i | \(-0.449764\pi\) | ||||
0.157167 | + | 0.987572i | \(0.449764\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.60146 | 0.413360 | 0.206680 | − | 0.978409i | \(-0.433734\pi\) | ||||
0.206680 | + | 0.978409i | \(0.433734\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.91699 | 0.475483 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.5588 | 0.551670 | 0.275835 | − | 0.961205i | \(-0.411046\pi\) | ||||
0.275835 | + | 0.961205i | \(0.411046\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.47217 | 0.0701033 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.3926 | −0.541278 | −0.270639 | − | 0.962681i | \(-0.587235\pi\) | ||||
−0.270639 | + | 0.962681i | \(0.587235\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.54410 | −0.405029 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −31.2485 | −1.47800 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.2252 | −0.812909 | −0.406455 | − | 0.913671i | \(-0.633235\pi\) | ||||
−0.406455 | + | 0.913671i | \(0.633235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.41085 | 0.113522 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 36.4381 | 1.71201 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.85936 | −0.415333 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.1885 | −1.22505 | −0.612524 | − | 0.790452i | \(-0.709846\pi\) | ||||
−0.612524 | + | 0.790452i | \(0.709846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.10428 | −0.0982194 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 40.4332 | 1.88316 | 0.941580 | − | 0.336789i | \(-0.109341\pi\) | ||||
0.941580 | + | 0.336789i | \(0.109341\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.48542 | 0.440825 | 0.220412 | − | 0.975407i | \(-0.429260\pi\) | ||||
0.220412 | + | 0.975407i | \(0.429260\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.6861 | 1.19116 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.2462 | −1.81610 | −0.908048 | − | 0.418867i | \(-0.862427\pi\) | ||||
−0.908048 | + | 0.418867i | \(0.862427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.5943 | 1.22801 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −45.9113 | −2.11548 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.86428 | −0.361600 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.1336 | 1.37972 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.45354 | 0.249178 | 0.124589 | − | 0.992208i | \(-0.460239\pi\) | ||||
0.124589 | + | 0.992208i | \(0.460239\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.9723 | −0.545892 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.7677 | 0.671956 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.22989 | −0.328292 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.0662 | −1.13586 | −0.567930 | − | 0.823077i | \(-0.692256\pi\) | ||||
−0.567930 | + | 0.823077i | \(0.692256\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 48.5617 | 2.19604 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.6824 | 1.33955 | 0.669773 | − | 0.742566i | \(-0.266391\pi\) | ||||
0.669773 | + | 0.742566i | \(0.266391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.26281 | −0.417176 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.1176 | 0.499701 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.8656 | −0.846238 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.7104 | −0.613761 | −0.306881 | − | 0.951748i | \(-0.599285\pi\) | ||||
−0.306881 | + | 0.951748i | \(0.599285\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.3328 | −0.640344 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.6507 | 1.63417 | 0.817086 | − | 0.576516i | \(-0.195588\pi\) | ||||
0.817086 | + | 0.576516i | \(0.195588\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.77635 | −0.257044 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.17321 | −0.274162 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.6504 | 0.560718 | 0.280359 | − | 0.959895i | \(-0.409546\pi\) | ||||
0.280359 | + | 0.959895i | \(0.409546\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.76538 | −0.299283 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.0576 | 0.663519 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −36.5335 | −1.60674 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.0786 | 1.01304 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.3339 | −0.715601 | −0.357800 | − | 0.933798i | \(-0.616473\pi\) | ||||
−0.357800 | + | 0.933798i | \(0.616473\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.13468 | 0.399432 | 0.199716 | − | 0.979854i | \(-0.435998\pi\) | ||||
0.199716 | + | 0.979854i | \(0.435998\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.87535 | 0.300065 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.9917 | −1.04509 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.3864 | −0.799409 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.8183 | 1.59778 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.36286 | −0.102347 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.1896 | 0.656702 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −30.7060 | −1.32506 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.45447 | 0.0626486 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.91909 | −0.125501 | −0.0627507 | − | 0.998029i | \(-0.519987\pi\) | ||||
−0.0627507 | + | 0.998029i | \(0.519987\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −38.8513 | −1.66727 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.6211 | 0.540630 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.47945 | 0.148771 | 0.0743853 | − | 0.997230i | \(-0.476301\pi\) | ||||
0.0743853 | + | 0.997230i | \(0.476301\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.3621 | −1.21046 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.7263 | −1.39166 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.29121 | 0.394390 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.9256 | 0.674789 | 0.337395 | − | 0.941363i | \(-0.390454\pi\) | ||||
0.337395 | + | 0.941363i | \(0.390454\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.70775 | 0.326003 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.6710 | −0.830511 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.6274 | −0.827195 | −0.413598 | − | 0.910460i | \(-0.635728\pi\) | ||||
−0.413598 | + | 0.910460i | \(0.635728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.10761 | 0.256949 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.3031 | −0.894648 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.7544 | 0.492770 | 0.246385 | − | 0.969172i | \(-0.420757\pi\) | ||||
0.246385 | + | 0.969172i | \(0.420757\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.4868 | 1.35953 | 0.679766 | − | 0.733429i | \(-0.262081\pi\) | ||||
0.679766 | + | 0.733429i | \(0.262081\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −40.9589 | −1.71108 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.14793 | 0.0895747 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.7287 | 1.07110 | 0.535551 | − | 0.844503i | \(-0.320104\pi\) | ||||
0.535551 | + | 0.844503i | \(0.320104\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.14529 | −0.0891551 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.7837 | 0.530359 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.7714 | 1.23301 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.8964 | −0.450509 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.6558 | −1.71932 | −0.859659 | − | 0.510869i | \(-0.829324\pi\) | ||||
−0.859659 | + | 0.510869i | \(0.829324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 50.3768 | 2.07222 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.6653 | 0.725428 | 0.362714 | − | 0.931900i | \(-0.381850\pi\) | ||||
0.362714 | + | 0.931900i | \(0.381850\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.42182 | −0.263269 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.2775 | −0.666193 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.3851 | 1.07807 | 0.539033 | − | 0.842285i | \(-0.318790\pi\) | ||||
0.539033 | + | 0.842285i | \(0.318790\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.46838 | −0.386223 | −0.193112 | − | 0.981177i | \(-0.561858\pi\) | ||||
−0.193112 | + | 0.981177i | \(0.561858\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.7091 | 1.33202 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.0159950 | −0.000650289 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.26529 | 0.335478 | 0.167739 | − | 0.985831i | \(-0.446353\pi\) | ||||
0.167739 | + | 0.985831i | \(0.446353\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.0479 | 1.09604 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.8063 | 1.44857 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.80834 | 0.274986 | 0.137493 | − | 0.990503i | \(-0.456095\pi\) | ||||
0.137493 | + | 0.990503i | \(0.456095\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.83371 | 0.0739425 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.01336 | 0.242089 | 0.121044 | − | 0.992647i | \(-0.461376\pi\) | ||||
0.121044 | + | 0.992647i | \(0.461376\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.2299 | 0.531754 | 0.265877 | − | 0.964007i | \(-0.414338\pi\) | ||||
0.265877 | + | 0.964007i | \(0.414338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.91963 | 0.0770322 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.3034 | −0.933631 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.67831 | −0.346027 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.7864 | −0.946921 | −0.473460 | − | 0.880815i | \(-0.656995\pi\) | ||||
−0.473460 | + | 0.880815i | \(0.656995\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.5798 | −1.05645 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.12228 | 0.362007 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.42552 | −0.0564813 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.2033 | −0.917908 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.2848 | −0.485219 | −0.242610 | − | 0.970124i | \(-0.578003\pi\) | ||||
−0.242610 | + | 0.970124i | \(0.578003\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1552 | 1.14977 | 0.574885 | − | 0.818234i | \(-0.305047\pi\) | ||||
0.574885 | + | 0.818234i | \(0.305047\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.98164 | −0.235527 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.7499 | −1.44479 | −0.722394 | − | 0.691481i | \(-0.756958\pi\) | ||||
−0.722394 | + | 0.691481i | \(0.756958\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.3757 | 1.42787 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 70.0569 | 2.74574 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.7707 | 0.969351 | 0.484675 | − | 0.874694i | \(-0.338938\pi\) | ||||
0.484675 | + | 0.874694i | \(0.338938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.2656 | 0.869987 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.32092 | −0.324630 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.2312 | −0.866005 | −0.433002 | − | 0.901393i | \(-0.642546\pi\) | ||||
−0.433002 | + | 0.901393i | \(0.642546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.9369 | −1.59226 | −0.796130 | − | 0.605126i | \(-0.793123\pi\) | ||||
−0.796130 | + | 0.605126i | \(0.793123\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.2795 | 0.748754 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.45001 | 0.327186 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.5185 | −0.947938 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.0212 | −1.08175 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.5992 | 1.29515 | 0.647577 | − | 0.762000i | \(-0.275783\pi\) | ||||
0.647577 | + | 0.762000i | \(0.275783\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.893714 | 0.0343991 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.5883 | −1.13717 | −0.568585 | − | 0.822624i | \(-0.692509\pi\) | ||||
−0.568585 | + | 0.822624i | \(0.692509\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.7190 | −0.756745 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −56.9195 | −2.18116 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.0567 | −1.57099 | −0.785495 | − | 0.618868i | \(-0.787592\pi\) | ||||
−0.785495 | + | 0.618868i | \(0.787592\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.62711 | −0.291417 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −40.8976 | −1.56034 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.1789 | −1.11163 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.22497 | 0.0466000 | 0.0233000 | − | 0.999729i | \(-0.492583\pi\) | ||||
0.0233000 | + | 0.999729i | \(0.492583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 30.3225 | 1.15186 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.9183 | 0.641748 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.71275 | −0.0648751 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −47.0455 | −1.77942 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.0201 | 1.66262 | 0.831309 | − | 0.555811i | \(-0.187592\pi\) | ||||
0.831309 | + | 0.555811i | \(0.187592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.7877 | −1.04655 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.7546 | −0.592512 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.3251 | 0.613102 | 0.306551 | − | 0.951854i | \(-0.400825\pi\) | ||||
0.306551 | + | 0.951854i | \(0.400825\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.2509 | −1.50953 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.8864 | 0.819653 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.7654 | −0.402602 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.51950 | 0.0567468 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.1715 | 0.379332 | 0.189666 | − | 0.981849i | \(-0.439259\pi\) | ||||
0.189666 | + | 0.981849i | \(0.439259\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.0686 | 1.52947 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −55.1595 | −2.05141 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.93403 | 0.146106 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.04296 | 0.298297 | 0.149148 | − | 0.988815i | \(-0.452347\pi\) | ||||
0.149148 | + | 0.988815i | \(0.452347\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −32.9600 | −1.22074 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.58706 | 0.206645 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.2325 | 1.52296 | 0.761479 | − | 0.648190i | \(-0.224474\pi\) | ||||
0.761479 | + | 0.648190i | \(0.224474\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.10629 | 0.0408060 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.3159 | 1.19037 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.0506 | 1.21579 | 0.607893 | − | 0.794019i | \(-0.292015\pi\) | ||||
0.607893 | + | 0.794019i | \(0.292015\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.7867 | −1.27620 | −0.638099 | − | 0.769954i | \(-0.720279\pi\) | ||||
−0.638099 | + | 0.769954i | \(0.720279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.3962 | −0.454161 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.7231 | 0.575276 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41.4284 | 1.51376 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.4701 | 1.58625 | 0.793123 | − | 0.609062i | \(-0.208454\pi\) | ||||
0.793123 | + | 0.609062i | \(0.208454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.8537 | 0.759950 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.4549 | 0.526066 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.16989 | −0.224248 | −0.112124 | − | 0.993694i | \(-0.535765\pi\) | ||||
−0.112124 | + | 0.993694i | \(0.535765\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.9449 | 0.651359 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.81318 | −0.355728 | −0.177864 | − | 0.984055i | \(-0.556919\pi\) | ||||
−0.177864 | + | 0.984055i | \(0.556919\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.4232 | 1.24621 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.89836 | −0.285566 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.6517 | −1.28731 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.4903 | −1.49618 | −0.748090 | − | 0.663597i | \(-0.769029\pi\) | ||||
−0.748090 | + | 0.663597i | \(0.769029\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.7727 | −1.28832 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −41.7169 | −1.50045 | −0.750226 | − | 0.661181i | \(-0.770055\pi\) | ||||
−0.750226 | + | 0.661181i | \(0.770055\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.1896 | 0.366020 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.3411 | 0.909107 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.9244 | −0.820299 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.51590 | 0.125648 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.2128 | −0.650044 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.0342 | 0.464621 | 0.232310 | − | 0.972642i | \(-0.425371\pi\) | ||||
0.232310 | + | 0.972642i | \(0.425371\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −46.7437 | −1.66412 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.6580 | 0.592292 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.4635 | 0.975256 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22.6444 | 0.803115 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.1911 | −1.17569 | −0.587844 | − | 0.808974i | \(-0.700023\pi\) | ||||
−0.587844 | + | 0.808974i | \(0.700023\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.9547 | 0.918210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −28.6615 | −1.01270 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.22090 | −0.290109 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.85831 | 0.206478 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.8074 | −0.591648 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.5271 | −1.03812 | −0.519058 | − | 0.854739i | \(-0.673717\pi\) | ||||
−0.519058 | + | 0.854739i | \(0.673717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.8194 | −1.01199 | −0.505993 | − | 0.862537i | \(-0.668874\pi\) | ||||
−0.505993 | + | 0.862537i | \(0.668874\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 55.6250 | 1.95085 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.2642 | 0.674797 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29.7190 | −1.03847 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.8056 | −0.656320 | −0.328160 | − | 0.944622i | \(-0.606428\pi\) | ||||
−0.328160 | + | 0.944622i | \(0.606428\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.56958 | 0.263859 | 0.131929 | − | 0.991259i | \(-0.457883\pi\) | ||||
0.131929 | + | 0.991259i | \(0.457883\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.35453 | 0.290868 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.9367 | −1.21487 | −0.607434 | − | 0.794370i | \(-0.707801\pi\) | ||||
−0.607434 | + | 0.794370i | \(0.707801\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.8376 | 1.59201 | 0.796003 | − | 0.605293i | \(-0.206944\pi\) | ||||
0.796003 | + | 0.605293i | \(0.206944\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −61.6653 | −2.13915 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.03331 | −0.0358020 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.68579 | −0.196765 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.10656 | 0.314769 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.0100 | −0.483680 | −0.241840 | − | 0.970316i | \(-0.577751\pi\) | ||||
−0.241840 | + | 0.970316i | \(0.577751\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.5234 | −0.466323 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −47.0455 | −1.62033 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.44889 | −0.0842444 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0436252 | −0.00149898 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.3342 | 0.388988 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.91680 | 0.271384 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.5515 | −1.28574 | −0.642869 | − | 0.765976i | \(-0.722256\pi\) | ||||
−0.642869 | + | 0.765976i | \(0.722256\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.06756 | −0.138945 | −0.0694726 | − | 0.997584i | \(-0.522132\pi\) | ||||
−0.0694726 | + | 0.997584i | \(0.522132\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.6357 | 0.431125 | 0.215562 | − | 0.976490i | \(-0.430842\pi\) | ||||
0.215562 | + | 0.976490i | \(0.430842\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.00132 | 0.170445 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.5147 | 0.494085 | 0.247042 | − | 0.969005i | \(-0.420541\pi\) | ||||
0.247042 | + | 0.969005i | \(0.420541\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.15521 | 0.311286 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −28.8790 | −0.980781 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.7671 | −1.34901 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.6727 | −1.07319 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.2529 | −0.820836 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.72743 | 0.0922039 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.93508 | −0.0653431 | −0.0326715 | − | 0.999466i | \(-0.510402\pi\) | ||||
−0.0326715 | + | 0.999466i | \(0.510402\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.20196 | −0.108000 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.9037 | 0.535811 | 0.267905 | − | 0.963445i | \(-0.413669\pi\) | ||||
0.267905 | + | 0.963445i | \(0.413669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.0431 | −1.17930 | −0.589648 | − | 0.807660i | \(-0.700733\pi\) | ||||
−0.589648 | + | 0.807660i | \(0.700733\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 27.6677 | 0.930040 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.1761 | 0.543141 | 0.271571 | − | 0.962419i | \(-0.412457\pi\) | ||||
0.271571 | + | 0.962419i | \(0.412457\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.8804 | 0.834460 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.8863 | −0.867225 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.1810 | −0.407165 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.5877 | −0.587238 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40.0861 | 1.33695 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.1507 | −0.704631 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.3145 | −0.542912 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.4122 | −0.512318 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.9951 | −0.763539 | −0.381770 | − | 0.924258i | \(-0.624685\pi\) | ||||
−0.381770 | + | 0.924258i | \(0.624685\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.3770 | −0.642693 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.0833 | 0.764783 | 0.382392 | − | 0.924000i | \(-0.375101\pi\) | ||||
0.382392 | + | 0.924000i | \(0.375101\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.5341 | 0.514103 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.3132 | −0.704592 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 60.7277 | 2.00541 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5454 | 0.413835 | 0.206918 | − | 0.978358i | \(-0.433657\pi\) | ||||
0.206918 | + | 0.978358i | \(0.433657\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.8120 | 0.718731 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.4681 | 0.739547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.68579 | 0.121188 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 50.5113 | 1.65901 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.2988 | −1.74868 | −0.874338 | − | 0.485318i | \(-0.838704\pi\) | ||||
−0.874338 | + | 0.485318i | \(0.838704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 60.1208 | 1.96827 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.80342 | −0.255199 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.1205 | −1.14734 | −0.573668 | − | 0.819088i | \(-0.694480\pi\) | ||||
−0.573668 | + | 0.819088i | \(0.694480\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.95704 | −0.0638656 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.1580 | −0.428937 | −0.214469 | − | 0.976731i | \(-0.568802\pi\) | ||||
−0.214469 | + | 0.976731i | \(0.568802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.56246 | 0.0508807 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.43754 | 0.0792932 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.4502 | −0.339586 | −0.169793 | − | 0.985480i | \(-0.554310\pi\) | ||||
−0.169793 | + | 0.985480i | \(0.554310\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.05728 | 0.261550 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.8940 | 1.13152 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.34233 | −0.140662 | −0.0703310 | − | 0.997524i | \(-0.522406\pi\) | ||||
−0.0703310 | + | 0.997524i | \(0.522406\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.2482 | −0.525781 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.8670 | 1.06244 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.8024 | −0.671744 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 72.8272 | 2.34927 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 50.9539 | 1.64197 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.851028 | −0.0273955 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.6820 | −0.504299 | −0.252149 | − | 0.967688i | \(-0.581137\pi\) | ||||
−0.252149 | + | 0.967688i | \(0.581137\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.67735 | −0.0859202 | −0.0429601 | − | 0.999077i | \(-0.513679\pi\) | ||||
−0.0429601 | + | 0.999077i | \(0.513679\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 46.1435 | 1.47929 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.18825 | −0.262234 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.87156 | −0.0918693 | −0.0459347 | − | 0.998944i | \(-0.514627\pi\) | ||||
−0.0459347 | + | 0.998944i | \(0.514627\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.3170 | −0.905014 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.3380 | 1.35175 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.9089 | 1.08153 | 0.540764 | − | 0.841175i | \(-0.318135\pi\) | ||||
0.540764 | + | 0.841175i | \(0.318135\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.9843 | 0.636752 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −75.7889 | −2.41239 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.09680 | −0.162069 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.1298 | 1.27477 | 0.637383 | − | 0.770547i | \(-0.280017\pi\) | ||||
0.637383 | + | 0.770547i | \(0.280017\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −72.3458 | −2.29582 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.45722 | −0.204708 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.50738 | 0.111080 | 0.0555399 | − | 0.998456i | \(-0.482312\pi\) | ||||
0.0555399 | + | 0.998456i | \(0.482312\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.29404 | 0.104219 |
(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 | 7220.2.a.p.1.4 | 4 | ||
19.8 | odd | 6 | 380.2.i.c.121.4 | ✓ | 8 | ||
19.12 | odd | 6 | 380.2.i.c.201.4 | yes | 8 | ||
19.18 | odd | 2 | 7220.2.a.r.1.1 | 4 | |||
57.8 | even | 6 | 3420.2.t.w.1261.3 | 8 | |||
57.50 | even | 6 | 3420.2.t.w.3241.3 | 8 | |||
76.27 | even | 6 | 1520.2.q.m.881.1 | 8 | |||
76.31 | even | 6 | 1520.2.q.m.961.1 | 8 | |||
95.8 | even | 12 | 1900.2.s.d.349.2 | 16 | |||
95.12 | even | 12 | 1900.2.s.d.49.2 | 16 | |||
95.27 | even | 12 | 1900.2.s.d.349.7 | 16 | |||
95.69 | odd | 6 | 1900.2.i.d.201.1 | 8 | |||
95.84 | odd | 6 | 1900.2.i.d.501.1 | 8 | |||
95.88 | even | 12 | 1900.2.s.d.49.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.c.121.4 | ✓ | 8 | 19.8 | odd | 6 | ||
380.2.i.c.201.4 | yes | 8 | 19.12 | odd | 6 | ||
1520.2.q.m.881.1 | 8 | 76.27 | even | 6 | |||
1520.2.q.m.961.1 | 8 | 76.31 | even | 6 | |||
1900.2.i.d.201.1 | 8 | 95.69 | odd | 6 | |||
1900.2.i.d.501.1 | 8 | 95.84 | odd | 6 | |||
1900.2.s.d.49.2 | 16 | 95.12 | even | 12 | |||
1900.2.s.d.49.7 | 16 | 95.88 | even | 12 | |||
1900.2.s.d.349.2 | 16 | 95.8 | even | 12 | |||
1900.2.s.d.349.7 | 16 | 95.27 | even | 12 | |||
3420.2.t.w.1261.3 | 8 | 57.8 | even | 6 | |||
3420.2.t.w.3241.3 | 8 | 57.50 | even | 6 | |||
7220.2.a.p.1.4 | 4 | 1.1 | even | 1 | trivial | ||
7220.2.a.r.1.1 | 4 | 19.18 | odd | 2 |