Properties

Label 536.1.h.a.133.1
Level $536$
Weight $1$
Character 536.133
Self dual yes
Analytic conductor $0.267$
Analytic rank $0$
Dimension $3$
Projective image $D_{7}$
CM discriminant -536
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [536,1,Mod(133,536)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(536, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("536.133");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 536 = 2^{3} \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 536.h (of order \(2\), degree \(1\), minimal)

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: \(0.267498846771\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{7}\)
Projective field: Galois closure of 7.1.153990656.1

Embedding invariants

Embedding label 133.1
Root \(-1.24698\) of defining polynomial
Character \(\chi\) \(=\) 536.133

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.24698 q^{3} +1.00000 q^{4} +1.80194 q^{5} +1.24698 q^{6} -1.00000 q^{8} +0.554958 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.24698 q^{3} +1.00000 q^{4} +1.80194 q^{5} +1.24698 q^{6} -1.00000 q^{8} +0.554958 q^{9} -1.80194 q^{10} +0.445042 q^{11} -1.24698 q^{12} +0.445042 q^{13} -2.24698 q^{15} +1.00000 q^{16} -1.80194 q^{17} -0.554958 q^{18} +1.80194 q^{20} -0.445042 q^{22} +1.24698 q^{23} +1.24698 q^{24} +2.24698 q^{25} -0.445042 q^{26} +0.554958 q^{27} +2.24698 q^{30} -1.00000 q^{32} -0.554958 q^{33} +1.80194 q^{34} +0.554958 q^{36} -0.554958 q^{39} -1.80194 q^{40} +1.80194 q^{43} +0.445042 q^{44} +1.00000 q^{45} -1.24698 q^{46} -0.445042 q^{47} -1.24698 q^{48} +1.00000 q^{49} -2.24698 q^{50} +2.24698 q^{51} +0.445042 q^{52} -1.24698 q^{53} -0.554958 q^{54} +0.801938 q^{55} -2.24698 q^{60} -1.24698 q^{61} +1.00000 q^{64} +0.801938 q^{65} +0.554958 q^{66} -1.00000 q^{67} -1.80194 q^{68} -1.55496 q^{69} -1.80194 q^{71} -0.554958 q^{72} -0.445042 q^{73} -2.80194 q^{75} +0.554958 q^{78} +1.80194 q^{80} -1.24698 q^{81} -3.24698 q^{85} -1.80194 q^{86} -0.445042 q^{88} +1.24698 q^{89} -1.00000 q^{90} +1.24698 q^{92} +0.445042 q^{94} +1.24698 q^{96} -1.00000 q^{98} +0.246980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} + q^{3} + 3 q^{4} + q^{5} - q^{6} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{2} + q^{3} + 3 q^{4} + q^{5} - q^{6} - 3 q^{8} + 2 q^{9} - q^{10} + q^{11} + q^{12} + q^{13} - 2 q^{15} + 3 q^{16} - q^{17} - 2 q^{18} + q^{20} - q^{22} - q^{23} - q^{24} + 2 q^{25} - q^{26} + 2 q^{27} + 2 q^{30} - 3 q^{32} - 2 q^{33} + q^{34} + 2 q^{36} - 2 q^{39} - q^{40} + q^{43} + q^{44} + 3 q^{45} + q^{46} - q^{47} + q^{48} + 3 q^{49} - 2 q^{50} + 2 q^{51} + q^{52} + q^{53} - 2 q^{54} - 2 q^{55} - 2 q^{60} + q^{61} + 3 q^{64} - 2 q^{65} + 2 q^{66} - 3 q^{67} - q^{68} - 5 q^{69} - q^{71} - 2 q^{72} - q^{73} - 4 q^{75} + 2 q^{78} + q^{80} + q^{81} - 5 q^{85} - q^{86} - q^{88} - q^{89} - 3 q^{90} - q^{92} + q^{94} - q^{96} - 3 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/536\mathbb{Z}\right)^\times\).

\(n\) \(135\) \(269\) \(337\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −1.00000
\(3\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(4\) 1.00000 1.00000
\(5\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(6\) 1.24698 1.24698
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) −1.00000 −1.00000
\(9\) 0.554958 0.554958
\(10\) −1.80194 −1.80194
\(11\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(12\) −1.24698 −1.24698
\(13\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(14\) 0 0
\(15\) −2.24698 −2.24698
\(16\) 1.00000 1.00000
\(17\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(18\) −0.554958 −0.554958
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 1.80194 1.80194
\(21\) 0 0
\(22\) −0.445042 −0.445042
\(23\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(24\) 1.24698 1.24698
\(25\) 2.24698 2.24698
\(26\) −0.445042 −0.445042
\(27\) 0.554958 0.554958
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 2.24698 2.24698
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −1.00000 −1.00000
\(33\) −0.554958 −0.554958
\(34\) 1.80194 1.80194
\(35\) 0 0
\(36\) 0.554958 0.554958
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) −0.554958 −0.554958
\(40\) −1.80194 −1.80194
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(44\) 0.445042 0.445042
\(45\) 1.00000 1.00000
\(46\) −1.24698 −1.24698
\(47\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(48\) −1.24698 −1.24698
\(49\) 1.00000 1.00000
\(50\) −2.24698 −2.24698
\(51\) 2.24698 2.24698
\(52\) 0.445042 0.445042
\(53\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(54\) −0.554958 −0.554958
\(55\) 0.801938 0.801938
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) −2.24698 −2.24698
\(61\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0.801938 0.801938
\(66\) 0.554958 0.554958
\(67\) −1.00000 −1.00000
\(68\) −1.80194 −1.80194
\(69\) −1.55496 −1.55496
\(70\) 0 0
\(71\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(72\) −0.554958 −0.554958
\(73\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(74\) 0 0
\(75\) −2.80194 −2.80194
\(76\) 0 0
\(77\) 0 0
\(78\) 0.554958 0.554958
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 1.80194 1.80194
\(81\) −1.24698 −1.24698
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) −3.24698 −3.24698
\(86\) −1.80194 −1.80194
\(87\) 0 0
\(88\) −0.445042 −0.445042
\(89\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(90\) −1.00000 −1.00000
\(91\) 0 0
\(92\) 1.24698 1.24698
\(93\) 0 0
\(94\) 0.445042 0.445042
\(95\) 0 0
\(96\) 1.24698 1.24698
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −1.00000 −1.00000
\(99\) 0.246980 0.246980
\(100\) 2.24698 2.24698
\(101\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(102\) −2.24698 −2.24698
\(103\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(104\) −0.445042 −0.445042
\(105\) 0 0
\(106\) 1.24698 1.24698
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0.554958 0.554958
\(109\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(110\) −0.801938 −0.801938
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 2.24698 2.24698
\(116\) 0 0
\(117\) 0.246980 0.246980
\(118\) 0 0
\(119\) 0 0
\(120\) 2.24698 2.24698
\(121\) −0.801938 −0.801938
\(122\) 1.24698 1.24698
\(123\) 0 0
\(124\) 0 0
\(125\) 2.24698 2.24698
\(126\) 0 0
\(127\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(128\) −1.00000 −1.00000
\(129\) −2.24698 −2.24698
\(130\) −0.801938 −0.801938
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) −0.554958 −0.554958
\(133\) 0 0
\(134\) 1.00000 1.00000
\(135\) 1.00000 1.00000
\(136\) 1.80194 1.80194
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 1.55496 1.55496
\(139\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0.554958 0.554958
\(142\) 1.80194 1.80194
\(143\) 0.198062 0.198062
\(144\) 0.554958 0.554958
\(145\) 0 0
\(146\) 0.445042 0.445042
\(147\) −1.24698 −1.24698
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 2.80194 2.80194
\(151\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(152\) 0 0
\(153\) −1.00000 −1.00000
\(154\) 0 0
\(155\) 0 0
\(156\) −0.554958 −0.554958
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 1.55496 1.55496
\(160\) −1.80194 −1.80194
\(161\) 0 0
\(162\) 1.24698 1.24698
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) −1.00000 −1.00000
\(166\) 0 0
\(167\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(168\) 0 0
\(169\) −0.801938 −0.801938
\(170\) 3.24698 3.24698
\(171\) 0 0
\(172\) 1.80194 1.80194
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.445042 0.445042
\(177\) 0 0
\(178\) −1.24698 −1.24698
\(179\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(180\) 1.00000 1.00000
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 1.55496 1.55496
\(184\) −1.24698 −1.24698
\(185\) 0 0
\(186\) 0 0
\(187\) −0.801938 −0.801938
\(188\) −0.445042 −0.445042
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −1.24698 −1.24698
\(193\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(194\) 0 0
\(195\) −1.00000 −1.00000
\(196\) 1.00000 1.00000
\(197\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(198\) −0.246980 −0.246980
\(199\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(200\) −2.24698 −2.24698
\(201\) 1.24698 1.24698
\(202\) 1.24698 1.24698
\(203\) 0 0
\(204\) 2.24698 2.24698
\(205\) 0 0
\(206\) −1.24698 −1.24698
\(207\) 0.692021 0.692021
\(208\) 0.445042 0.445042
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) −1.24698 −1.24698
\(213\) 2.24698 2.24698
\(214\) 0 0
\(215\) 3.24698 3.24698
\(216\) −0.554958 −0.554958
\(217\) 0 0
\(218\) −1.80194 −1.80194
\(219\) 0.554958 0.554958
\(220\) 0.801938 0.801938
\(221\) −0.801938 −0.801938
\(222\) 0 0
\(223\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(224\) 0 0
\(225\) 1.24698 1.24698
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(230\) −2.24698 −2.24698
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) −0.246980 −0.246980
\(235\) −0.801938 −0.801938
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −2.24698 −2.24698
\(241\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(242\) 0.801938 0.801938
\(243\) 1.00000 1.00000
\(244\) −1.24698 −1.24698
\(245\) 1.80194 1.80194
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −2.24698 −2.24698
\(251\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(252\) 0 0
\(253\) 0.554958 0.554958
\(254\) 1.80194 1.80194
\(255\) 4.04892 4.04892
\(256\) 1.00000 1.00000
\(257\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(258\) 2.24698 2.24698
\(259\) 0 0
\(260\) 0.801938 0.801938
\(261\) 0 0
\(262\) 0 0
\(263\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(264\) 0.554958 0.554958
\(265\) −2.24698 −2.24698
\(266\) 0 0
\(267\) −1.55496 −1.55496
\(268\) −1.00000 −1.00000
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −1.00000 −1.00000
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −1.80194 −1.80194
\(273\) 0 0
\(274\) 0 0
\(275\) 1.00000 1.00000
\(276\) −1.55496 −1.55496
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 2.00000 2.00000
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −0.554958 −0.554958
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −1.80194 −1.80194
\(285\) 0 0
\(286\) −0.198062 −0.198062
\(287\) 0 0
\(288\) −0.554958 −0.554958
\(289\) 2.24698 2.24698
\(290\) 0 0
\(291\) 0 0
\(292\) −0.445042 −0.445042
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 1.24698 1.24698
\(295\) 0 0
\(296\) 0 0
\(297\) 0.246980 0.246980
\(298\) 0 0
\(299\) 0.554958 0.554958
\(300\) −2.80194 −2.80194
\(301\) 0 0
\(302\) 0.445042 0.445042
\(303\) 1.55496 1.55496
\(304\) 0 0
\(305\) −2.24698 −2.24698
\(306\) 1.00000 1.00000
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −1.55496 −1.55496
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0.554958 0.554958
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) −1.55496 −1.55496
\(319\) 0 0
\(320\) 1.80194 1.80194
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −1.24698 −1.24698
\(325\) 1.00000 1.00000
\(326\) 0 0
\(327\) −2.24698 −2.24698
\(328\) 0 0
\(329\) 0 0
\(330\) 1.00000 1.00000
\(331\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0.445042 0.445042
\(335\) −1.80194 −1.80194
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0.801938 0.801938
\(339\) 0 0
\(340\) −3.24698 −3.24698
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) −1.80194 −1.80194
\(345\) −2.80194 −2.80194
\(346\) 0 0
\(347\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0.246980 0.246980
\(352\) −0.445042 −0.445042
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) −3.24698 −3.24698
\(356\) 1.24698 1.24698
\(357\) 0 0
\(358\) 1.24698 1.24698
\(359\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(360\) −1.00000 −1.00000
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) 1.00000 1.00000
\(364\) 0 0
\(365\) −0.801938 −0.801938
\(366\) −1.55496 −1.55496
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 1.24698 1.24698
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(374\) 0.801938 0.801938
\(375\) −2.80194 −2.80194
\(376\) 0.445042 0.445042
\(377\) 0 0
\(378\) 0 0
\(379\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(380\) 0 0
\(381\) 2.24698 2.24698
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 1.24698 1.24698
\(385\) 0 0
\(386\) −1.24698 −1.24698
\(387\) 1.00000 1.00000
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 1.00000 1.00000
\(391\) −2.24698 −2.24698
\(392\) −1.00000 −1.00000
\(393\) 0 0
\(394\) −0.445042 −0.445042
\(395\) 0 0
\(396\) 0.246980 0.246980
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 1.80194 1.80194
\(399\) 0 0
\(400\) 2.24698 2.24698
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) −1.24698 −1.24698
\(403\) 0 0
\(404\) −1.24698 −1.24698
\(405\) −2.24698 −2.24698
\(406\) 0 0
\(407\) 0 0
\(408\) −2.24698 −2.24698
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.24698 1.24698
\(413\) 0 0
\(414\) −0.692021 −0.692021
\(415\) 0 0
\(416\) −0.445042 −0.445042
\(417\) 2.49396 2.49396
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) −0.246980 −0.246980
\(424\) 1.24698 1.24698
\(425\) −4.04892 −4.04892
\(426\) −2.24698 −2.24698
\(427\) 0 0
\(428\) 0 0
\(429\) −0.246980 −0.246980
\(430\) −3.24698 −3.24698
\(431\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(432\) 0.554958 0.554958
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.80194 1.80194
\(437\) 0 0
\(438\) −0.554958 −0.554958
\(439\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(440\) −0.801938 −0.801938
\(441\) 0.554958 0.554958
\(442\) 0.801938 0.801938
\(443\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(444\) 0 0
\(445\) 2.24698 2.24698
\(446\) 1.80194 1.80194
\(447\) 0 0
\(448\) 0 0
\(449\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(450\) −1.24698 −1.24698
\(451\) 0 0
\(452\) 0 0
\(453\) 0.554958 0.554958
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(458\) 2.00000 2.00000
\(459\) −1.00000 −1.00000
\(460\) 2.24698 2.24698
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0.246980 0.246980
\(469\) 0 0
\(470\) 0.801938 0.801938
\(471\) 0 0
\(472\) 0 0
\(473\) 0.801938 0.801938
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.692021 −0.692021
\(478\) 0 0
\(479\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(480\) 2.24698 2.24698
\(481\) 0 0
\(482\) 0.445042 0.445042
\(483\) 0 0
\(484\) −0.801938 −0.801938
\(485\) 0 0
\(486\) −1.00000 −1.00000
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 1.24698 1.24698
\(489\) 0 0
\(490\) −1.80194 −1.80194
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0.445042 0.445042
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(500\) 2.24698 2.24698
\(501\) 0.554958 0.554958
\(502\) −1.80194 −1.80194
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) −2.24698 −2.24698
\(506\) −0.554958 −0.554958
\(507\) 1.00000 1.00000
\(508\) −1.80194 −1.80194
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) −4.04892 −4.04892
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 0.445042 0.445042
\(515\) 2.24698 2.24698
\(516\) −2.24698 −2.24698
\(517\) −0.198062 −0.198062
\(518\) 0 0
\(519\) 0 0
\(520\) −0.801938 −0.801938
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −1.24698 −1.24698
\(527\) 0 0
\(528\) −0.554958 −0.554958
\(529\) 0.554958 0.554958
\(530\) 2.24698 2.24698
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 1.55496 1.55496
\(535\) 0 0
\(536\) 1.00000 1.00000
\(537\) 1.55496 1.55496
\(538\) 0 0
\(539\) 0.445042 0.445042
\(540\) 1.00000 1.00000
\(541\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.80194 1.80194
\(545\) 3.24698 3.24698
\(546\) 0 0
\(547\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(548\) 0 0
\(549\) −0.692021 −0.692021
\(550\) −1.00000 −1.00000
\(551\) 0 0
\(552\) 1.55496 1.55496
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −2.00000 −2.00000
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0.801938 0.801938
\(560\) 0 0
\(561\) 1.00000 1.00000
\(562\) 0 0
\(563\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(564\) 0.554958 0.554958
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 1.80194 1.80194
\(569\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0.198062 0.198062
\(573\) 0 0
\(574\) 0 0
\(575\) 2.80194 2.80194
\(576\) 0.554958 0.554958
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −2.24698 −2.24698
\(579\) −1.55496 −1.55496
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.554958 −0.554958
\(584\) 0.445042 0.445042
\(585\) 0.445042 0.445042
\(586\) 0 0
\(587\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(588\) −1.24698 −1.24698
\(589\) 0 0
\(590\) 0 0
\(591\) −0.554958 −0.554958
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) −0.246980 −0.246980
\(595\) 0 0
\(596\) 0 0
\(597\) 2.24698 2.24698
\(598\) −0.554958 −0.554958
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 2.80194 2.80194
\(601\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(602\) 0 0
\(603\) −0.554958 −0.554958
\(604\) −0.445042 −0.445042
\(605\) −1.44504 −1.44504
\(606\) −1.55496 −1.55496
\(607\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 2.24698 2.24698
\(611\) −0.198062 −0.198062
\(612\) −1.00000 −1.00000
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(618\) 1.55496 1.55496
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0.692021 0.692021
\(622\) 0 0
\(623\) 0 0
\(624\) −0.554958 −0.554958
\(625\) 1.80194 1.80194
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.24698 −3.24698
\(636\) 1.55496 1.55496
\(637\) 0.445042 0.445042
\(638\) 0 0
\(639\) −1.00000 −1.00000
\(640\) −1.80194 −1.80194
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) −4.04892 −4.04892
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 1.24698 1.24698
\(649\) 0 0
\(650\) −1.00000 −1.00000
\(651\) 0 0
\(652\) 0 0
\(653\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(654\) 2.24698 2.24698
\(655\) 0 0
\(656\) 0 0
\(657\) −0.246980 −0.246980
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −1.00000 −1.00000
\(661\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(662\) −1.80194 −1.80194
\(663\) 1.00000 1.00000
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.445042 −0.445042
\(669\) 2.24698 2.24698
\(670\) 1.80194 1.80194
\(671\) −0.554958 −0.554958
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 1.24698 1.24698
\(676\) −0.801938 −0.801938
\(677\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3.24698 3.24698
\(681\) 0 0
\(682\) 0 0
\(683\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2.49396 2.49396
\(688\) 1.80194 1.80194
\(689\) −0.554958 −0.554958
\(690\) 2.80194 2.80194
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.80194 −1.80194
\(695\) −3.60388 −3.60388
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(702\) −0.246980 −0.246980
\(703\) 0 0
\(704\) 0.445042 0.445042
\(705\) 1.00000 1.00000
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 3.24698 3.24698
\(711\) 0 0
\(712\) −1.24698 −1.24698
\(713\) 0 0
\(714\) 0 0
\(715\) 0.356896 0.356896
\(716\) −1.24698 −1.24698
\(717\) 0 0
\(718\) −2.00000 −2.00000
\(719\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(720\) 1.00000 1.00000
\(721\) 0 0
\(722\) −1.00000 −1.00000
\(723\) 0.554958 0.554958
\(724\) 0 0
\(725\) 0 0
\(726\) −1.00000 −1.00000
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0.801938 0.801938
\(731\) −3.24698 −3.24698
\(732\) 1.55496 1.55496
\(733\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(734\) 0 0
\(735\) −2.24698 −2.24698
\(736\) −1.24698 −1.24698
\(737\) −0.445042 −0.445042
\(738\) 0 0
\(739\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −0.445042 −0.445042
\(747\) 0 0
\(748\) −0.801938 −0.801938
\(749\) 0 0
\(750\) 2.80194 2.80194
\(751\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(752\) −0.445042 −0.445042
\(753\) −2.24698 −2.24698
\(754\) 0 0
\(755\) −0.801938 −0.801938
\(756\) 0 0
\(757\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(758\) −0.445042 −0.445042
\(759\) −0.692021 −0.692021
\(760\) 0 0
\(761\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(762\) −2.24698 −2.24698
\(763\) 0 0
\(764\) 0 0
\(765\) −1.80194 −1.80194
\(766\) 0 0
\(767\) 0 0
\(768\) −1.24698 −1.24698
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0.554958 0.554958
\(772\) 1.24698 1.24698
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −1.00000 −1.00000
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −1.00000 −1.00000
\(781\) −0.801938 −0.801938
\(782\) 2.24698 2.24698
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(788\) 0.445042 0.445042
\(789\) −1.55496 −1.55496
\(790\) 0 0
\(791\) 0 0
\(792\) −0.246980 −0.246980
\(793\) −0.554958 −0.554958
\(794\) 0 0
\(795\) 2.80194 2.80194
\(796\) −1.80194 −1.80194
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0.801938 0.801938
\(800\) −2.24698 −2.24698
\(801\) 0.692021 0.692021
\(802\) 0 0
\(803\) −0.198062 −0.198062
\(804\) 1.24698 1.24698
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 1.24698 1.24698
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 2.24698 2.24698
\(811\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 2.24698 2.24698
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(824\) −1.24698 −1.24698
\(825\) −1.24698 −1.24698
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0.692021 0.692021
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.445042 0.445042
\(833\) −1.80194 −1.80194
\(834\) −2.49396 −2.49396
\(835\) −0.801938 −0.801938
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.44504 −1.44504
\(846\) 0.246980 0.246980
\(847\) 0 0
\(848\) −1.24698 −1.24698
\(849\) 0 0
\(850\) 4.04892 4.04892
\(851\) 0 0
\(852\) 2.24698 2.24698
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0.246980 0.246980
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 3.24698 3.24698
\(861\) 0 0
\(862\) 0.445042 0.445042
\(863\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(864\) −0.554958 −0.554958
\(865\) 0 0
\(866\) 0 0
\(867\) −2.80194 −2.80194
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −0.445042 −0.445042
\(872\) −1.80194 −1.80194
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0.554958 0.554958
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) −1.24698 −1.24698
\(879\) 0 0
\(880\) 0.801938 0.801938
\(881\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(882\) −0.554958 −0.554958
\(883\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(884\) −0.801938 −0.801938
\(885\) 0 0
\(886\) −0.445042 −0.445042
\(887\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −2.24698 −2.24698
\(891\) −0.554958 −0.554958
\(892\) −1.80194 −1.80194
\(893\) 0 0
\(894\) 0 0
\(895\) −2.24698 −2.24698
\(896\) 0 0
\(897\) −0.692021 −0.692021
\(898\) 1.80194 1.80194
\(899\) 0 0
\(900\) 1.24698 1.24698
\(901\) 2.24698 2.24698
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) −0.554958 −0.554958
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) −0.692021 −0.692021
\(910\) 0 0
\(911\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 1.80194 1.80194
\(915\) 2.80194 2.80194
\(916\) −2.00000 −2.00000
\(917\) 0 0
\(918\) 1.00000 1.00000
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) −2.24698 −2.24698
\(921\) 0 0
\(922\) 0 0
\(923\) −0.801938 −0.801938
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0.692021 0.692021
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.44504 −1.44504
\(936\) −0.246980 −0.246980
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −0.801938 −0.801938
\(941\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −0.801938 −0.801938
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) −0.198062 −0.198062
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(954\) 0.692021 0.692021
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0.445042 0.445042
\(959\) 0 0
\(960\) −2.24698 −2.24698
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) −0.445042 −0.445042
\(965\) 2.24698 2.24698
\(966\) 0 0
\(967\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(968\) 0.801938 0.801938
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 1.00000 1.00000
\(973\) 0 0
\(974\) 0 0
\(975\) −1.24698 −1.24698
\(976\) −1.24698 −1.24698
\(977\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(978\) 0 0
\(979\) 0.554958 0.554958
\(980\) 1.80194 1.80194
\(981\) 1.00000 1.00000
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0.801938 0.801938
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 2.24698 2.24698
\(990\) −0.445042 −0.445042
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) −2.24698 −2.24698
\(994\) 0 0
\(995\) −3.24698 −3.24698
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 1.24698 1.24698
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 536.1.h.a.133.1 3
4.3 odd 2 2144.1.h.a.401.3 3
8.3 odd 2 2144.1.h.b.401.1 3
8.5 even 2 536.1.h.b.133.3 yes 3
67.66 odd 2 536.1.h.b.133.3 yes 3
268.267 even 2 2144.1.h.b.401.1 3
536.133 odd 2 CM 536.1.h.a.133.1 3
536.267 even 2 2144.1.h.a.401.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
536.1.h.a.133.1 3 1.1 even 1 trivial
536.1.h.a.133.1 3 536.133 odd 2 CM
536.1.h.b.133.3 yes 3 8.5 even 2
536.1.h.b.133.3 yes 3 67.66 odd 2
2144.1.h.a.401.3 3 4.3 odd 2
2144.1.h.a.401.3 3 536.267 even 2
2144.1.h.b.401.1 3 8.3 odd 2
2144.1.h.b.401.1 3 268.267 even 2