Properties

Label 1352.1.g.c.339.2
Level $1352$
Weight $1$
Character 1352.339
Self dual yes
Analytic conductor $0.675$
Analytic rank $0$
Dimension $3$
Projective image $D_{7}$
CM discriminant -8
Inner twists $2$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1352,1,Mod(339,1352)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1352, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1352.339");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1352 = 2^{3} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1352.g (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: \(0.674735897080\)
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 7.1.2471326208.1
Artin image: $D_7$
Artin field: Galois closure of 7.1.2471326208.1

Embedding invariants

Embedding label 339.2
Root \(0.445042\) of defining polynomial
Character \(\chi\) \(=\) 1352.339

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.445042 q^{3} +1.00000 q^{4} -0.445042 q^{6} +1.00000 q^{8} -0.801938 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.445042 q^{3} +1.00000 q^{4} -0.445042 q^{6} +1.00000 q^{8} -0.801938 q^{9} +1.24698 q^{11} -0.445042 q^{12} +1.00000 q^{16} +1.24698 q^{17} -0.801938 q^{18} -1.80194 q^{19} +1.24698 q^{22} -0.445042 q^{24} +1.00000 q^{25} +0.801938 q^{27} +1.00000 q^{32} -0.554958 q^{33} +1.24698 q^{34} -0.801938 q^{36} -1.80194 q^{38} -1.80194 q^{41} -1.80194 q^{43} +1.24698 q^{44} -0.445042 q^{48} +1.00000 q^{49} +1.00000 q^{50} -0.554958 q^{51} +0.801938 q^{54} +0.801938 q^{57} -0.445042 q^{59} +1.00000 q^{64} -0.554958 q^{66} -0.445042 q^{67} +1.24698 q^{68} -0.801938 q^{72} -0.445042 q^{73} -0.445042 q^{75} -1.80194 q^{76} +0.445042 q^{81} -1.80194 q^{82} -1.80194 q^{83} -1.80194 q^{86} +1.24698 q^{88} -0.445042 q^{89} -0.445042 q^{96} +1.24698 q^{97} +1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{6} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{6} + 3 q^{8} + 2 q^{9} - q^{11} - q^{12} + 3 q^{16} - q^{17} + 2 q^{18} - q^{19} - q^{22} - q^{24} + 3 q^{25} - 2 q^{27} + 3 q^{32} - 2 q^{33} - q^{34} + 2 q^{36} - q^{38} - q^{41} - q^{43} - q^{44} - q^{48} + 3 q^{49} + 3 q^{50} - 2 q^{51} - 2 q^{54} - 2 q^{57} - q^{59} + 3 q^{64} - 2 q^{66} - q^{67} - q^{68} + 2 q^{72} - q^{73} - q^{75} - q^{76} + q^{81} - q^{82} - q^{83} - q^{86} - q^{88} - q^{89} - q^{96} - q^{97} + 3 q^{98} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1352\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(1015\) \(1185\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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
\(3\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(4\) 1.00000 1.00000
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) −0.445042 −0.445042
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 1.00000 1.00000
\(9\) −0.801938 −0.801938
\(10\) 0 0
\(11\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(12\) −0.445042 −0.445042
\(13\) 0 0
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(18\) −0.801938 −0.801938
\(19\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.24698 1.24698
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −0.445042 −0.445042
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) 0.801938 0.801938
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.00000 1.00000
\(33\) −0.554958 −0.554958
\(34\) 1.24698 1.24698
\(35\) 0 0
\(36\) −0.801938 −0.801938
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −1.80194 −1.80194
\(39\) 0 0
\(40\) 0 0
\(41\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(42\) 0 0
\(43\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(44\) 1.24698 1.24698
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −0.445042 −0.445042
\(49\) 1.00000 1.00000
\(50\) 1.00000 1.00000
\(51\) −0.554958 −0.554958
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0.801938 0.801938
\(55\) 0 0
\(56\) 0 0
\(57\) 0.801938 0.801938
\(58\) 0 0
\(59\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) −0.554958 −0.554958
\(67\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(68\) 1.24698 1.24698
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −0.801938 −0.801938
\(73\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(74\) 0 0
\(75\) −0.445042 −0.445042
\(76\) −1.80194 −1.80194
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 0.445042 0.445042
\(82\) −1.80194 −1.80194
\(83\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.80194 −1.80194
\(87\) 0 0
\(88\) 1.24698 1.24698
\(89\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.445042 −0.445042
\(97\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(98\) 1.00000 1.00000
\(99\) −1.00000 −1.00000
\(100\) 1.00000 1.00000
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) −0.554958 −0.554958
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(108\) 0.801938 0.801938
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(114\) 0.801938 0.801938
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.445042 −0.445042
\(119\) 0 0
\(120\) 0 0
\(121\) 0.554958 0.554958
\(122\) 0 0
\(123\) 0.801938 0.801938
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 1.00000 1.00000
\(129\) 0.801938 0.801938
\(130\) 0 0
\(131\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(132\) −0.554958 −0.554958
\(133\) 0 0
\(134\) −0.445042 −0.445042
\(135\) 0 0
\(136\) 1.24698 1.24698
\(137\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(138\) 0 0
\(139\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.801938 −0.801938
\(145\) 0 0
\(146\) −0.445042 −0.445042
\(147\) −0.445042 −0.445042
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −0.445042 −0.445042
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) −1.80194 −1.80194
\(153\) −1.00000 −1.00000
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.445042 0.445042
\(163\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(164\) −1.80194 −1.80194
\(165\) 0 0
\(166\) −1.80194 −1.80194
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 1.44504 1.44504
\(172\) −1.80194 −1.80194
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.24698 1.24698
\(177\) 0.198062 0.198062
\(178\) −0.445042 −0.445042
\(179\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.55496 1.55496
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −0.445042 −0.445042
\(193\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(194\) 1.24698 1.24698
\(195\) 0 0
\(196\) 1.00000 1.00000
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −1.00000 −1.00000
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.00000 1.00000
\(201\) 0.198062 0.198062
\(202\) 0 0
\(203\) 0 0
\(204\) −0.554958 −0.554958
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.24698 −2.24698
\(210\) 0 0
\(211\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.80194 −1.80194
\(215\) 0 0
\(216\) 0.801938 0.801938
\(217\) 0 0
\(218\) 0 0
\(219\) 0.198062 0.198062
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −0.801938 −0.801938
\(226\) −0.445042 −0.445042
\(227\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(228\) 0.801938 0.801938
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.445042 −0.445042
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(242\) 0.554958 0.554958
\(243\) −1.00000 −1.00000
\(244\) 0 0
\(245\) 0 0
\(246\) 0.801938 0.801938
\(247\) 0 0
\(248\) 0 0
\(249\) 0.801938 0.801938
\(250\) 0 0
\(251\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(258\) 0.801938 0.801938
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −1.80194 −1.80194
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −0.554958 −0.554958
\(265\) 0 0
\(266\) 0 0
\(267\) 0.198062 0.198062
\(268\) −0.445042 −0.445042
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 1.24698 1.24698
\(273\) 0 0
\(274\) −0.445042 −0.445042
\(275\) 1.24698 1.24698
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 1.24698 1.24698
\(279\) 0 0
\(280\) 0 0
\(281\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(282\) 0 0
\(283\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.801938 −0.801938
\(289\) 0.554958 0.554958
\(290\) 0 0
\(291\) −0.554958 −0.554958
\(292\) −0.445042 −0.445042
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) −0.445042 −0.445042
\(295\) 0 0
\(296\) 0 0
\(297\) 1.00000 1.00000
\(298\) 0 0
\(299\) 0 0
\(300\) −0.445042 −0.445042
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.80194 −1.80194
\(305\) 0 0
\(306\) −1.00000 −1.00000
\(307\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0.801938 0.801938
\(322\) 0 0
\(323\) −2.24698 −2.24698
\(324\) 0.445042 0.445042
\(325\) 0 0
\(326\) 1.24698 1.24698
\(327\) 0 0
\(328\) −1.80194 −1.80194
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(332\) −1.80194 −1.80194
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(338\) 0 0
\(339\) 0.198062 0.198062
\(340\) 0 0
\(341\) 0 0
\(342\) 1.44504 1.44504
\(343\) 0 0
\(344\) −1.80194 −1.80194
\(345\) 0 0
\(346\) 0 0
\(347\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.24698 1.24698
\(353\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(354\) 0.198062 0.198062
\(355\) 0 0
\(356\) −0.445042 −0.445042
\(357\) 0 0
\(358\) 1.24698 1.24698
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 2.24698 2.24698
\(362\) 0 0
\(363\) −0.246980 −0.246980
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 1.44504 1.44504
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 1.55496 1.55496
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −0.445042 −0.445042
\(385\) 0 0
\(386\) −1.80194 −1.80194
\(387\) 1.44504 1.44504
\(388\) 1.24698 1.24698
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.00000 1.00000
\(393\) 0.801938 0.801938
\(394\) 0 0
\(395\) 0 0
\(396\) −1.00000 −1.00000
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 1.00000
\(401\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(402\) 0.198062 0.198062
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.554958 −0.554958
\(409\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(410\) 0 0
\(411\) 0.198062 0.198062
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −0.554958 −0.554958
\(418\) −2.24698 −2.24698
\(419\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 1.24698 1.24698
\(423\) 0 0
\(424\) 0 0
\(425\) 1.24698 1.24698
\(426\) 0 0
\(427\) 0 0
\(428\) −1.80194 −1.80194
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0.801938 0.801938
\(433\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0.198062 0.198062
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −0.801938 −0.801938
\(442\) 0 0
\(443\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(450\) −0.801938 −0.801938
\(451\) −2.24698 −2.24698
\(452\) −0.445042 −0.445042
\(453\) 0 0
\(454\) −0.445042 −0.445042
\(455\) 0 0
\(456\) 0.801938 0.801938
\(457\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(458\) 0 0
\(459\) 1.00000 1.00000
\(460\) 0 0
\(461\) 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
\(466\) −0.445042 −0.445042
\(467\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.445042 −0.445042
\(473\) −2.24698 −2.24698
\(474\) 0 0
\(475\) −1.80194 −1.80194
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 2.00000 2.00000
\(483\) 0 0
\(484\) 0.554958 0.554958
\(485\) 0 0
\(486\) −1.00000 −1.00000
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −0.554958 −0.554958
\(490\) 0 0
\(491\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(492\) 0.801938 0.801938
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0.801938 0.801938
\(499\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 1.24698 1.24698
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 1.00000
\(513\) −1.44504 −1.44504
\(514\) −1.80194 −1.80194
\(515\) 0 0
\(516\) 0.801938 0.801938
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(522\) 0 0
\(523\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(524\) −1.80194 −1.80194
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −0.554958 −0.554958
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0.356896 0.356896
\(532\) 0 0
\(533\) 0 0
\(534\) 0.198062 0.198062
\(535\) 0 0
\(536\) −0.445042 −0.445042
\(537\) −0.554958 −0.554958
\(538\) 0 0
\(539\) 1.24698 1.24698
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.24698 1.24698
\(545\) 0 0
\(546\) 0 0
\(547\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(548\) −0.445042 −0.445042
\(549\) 0 0
\(550\) 1.24698 1.24698
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 1.24698 1.24698
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.692021 −0.692021
\(562\) 1.24698 1.24698
\(563\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.80194 −1.80194
\(567\) 0 0
\(568\) 0 0
\(569\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(570\) 0 0
\(571\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.801938 −0.801938
\(577\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(578\) 0.554958 0.554958
\(579\) 0.801938 0.801938
\(580\) 0 0
\(581\) 0 0
\(582\) −0.554958 −0.554958
\(583\) 0 0
\(584\) −0.445042 −0.445042
\(585\) 0 0
\(586\) 0 0
\(587\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(588\) −0.445042 −0.445042
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(594\) 1.00000 1.00000
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) −0.445042 −0.445042
\(601\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(602\) 0 0
\(603\) 0.356896 0.356896
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) −1.80194 −1.80194
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −1.00000 −1.00000
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 1.24698 1.24698
\(615\) 0 0
\(616\) 0 0
\(617\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(618\) 0 0
\(619\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 1.24698 1.24698
\(627\) 1.00000 1.00000
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) −0.554958 −0.554958
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(642\) 0.801938 0.801938
\(643\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.24698 −2.24698
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0.445042 0.445042
\(649\) −0.554958 −0.554958
\(650\) 0 0
\(651\) 0 0
\(652\) 1.24698 1.24698
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.80194 −1.80194
\(657\) 0.356896 0.356896
\(658\) 0 0
\(659\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 2.00000 2.00000
\(663\) 0 0
\(664\) −1.80194 −1.80194
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(674\) −1.80194 −1.80194
\(675\) 0.801938 0.801938
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0.198062 0.198062
\(679\) 0 0
\(680\) 0 0
\(681\) 0.198062 0.198062
\(682\) 0 0
\(683\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(684\) 1.44504 1.44504
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.80194 −1.80194
\(689\) 0 0
\(690\) 0 0
\(691\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 2.00000 2.00000
\(695\) 0 0
\(696\) 0 0
\(697\) −2.24698 −2.24698
\(698\) 0 0
\(699\) 0.198062 0.198062
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.24698 1.24698
\(705\) 0 0
\(706\) 1.24698 1.24698
\(707\) 0 0
\(708\) 0.198062 0.198062
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.445042 −0.445042
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.24698 1.24698
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.24698 2.24698
\(723\) −0.890084 −0.890084
\(724\) 0 0
\(725\) 0 0
\(726\) −0.246980 −0.246980
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.24698 −2.24698
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −0.554958 −0.554958
\(738\) 1.44504 1.44504
\(739\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.44504 1.44504
\(748\) 1.55496 1.55496
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) −0.554958 −0.554958
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −0.445042 −0.445042
\(759\) 0 0
\(760\) 0 0
\(761\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.445042 −0.445042
\(769\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(770\) 0 0
\(771\) 0.801938 0.801938
\(772\) −1.80194 −1.80194
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 1.44504 1.44504
\(775\) 0 0
\(776\) 1.24698 1.24698
\(777\) 0 0
\(778\) 0 0
\(779\) 3.24698 3.24698
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) 0.801938 0.801938
\(787\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −1.00000 −1.00000
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000 1.00000
\(801\) 0.356896 0.356896
\(802\) 1.24698 1.24698
\(803\) −0.554958 −0.554958
\(804\) 0.198062 0.198062
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(810\) 0 0
\(811\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) −0.554958 −0.554958
\(817\) 3.24698 3.24698
\(818\) −0.445042 −0.445042
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0.198062 0.198062
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) −0.554958 −0.554958
\(826\) 0 0
\(827\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.24698 1.24698
\(834\) −0.554958 −0.554958
\(835\) 0 0
\(836\) −2.24698 −2.24698
\(837\) 0 0
\(838\) 2.00000 2.00000
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) −0.554958 −0.554958
\(844\) 1.24698 1.24698
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0.801938 0.801938
\(850\) 1.24698 1.24698
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.80194 −1.80194
\(857\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(858\) 0 0
\(859\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0.801938 0.801938
\(865\) 0 0
\(866\) −0.445042 −0.445042
\(867\) −0.246980 −0.246980
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −1.00000 −1.00000
\(874\) 0 0
\(875\) 0 0
\(876\) 0.198062 0.198062
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(882\) −0.801938 −0.801938
\(883\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.24698 1.24698
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.554958 0.554958
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −1.80194 −1.80194
\(899\) 0 0
\(900\) −0.801938 −0.801938
\(901\) 0 0
\(902\) −2.24698 −2.24698
\(903\) 0 0
\(904\) −0.445042 −0.445042
\(905\) 0 0
\(906\) 0 0
\(907\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(908\) −0.445042 −0.445042
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0.801938 0.801938
\(913\) −2.24698 −2.24698
\(914\) 2.00000 2.00000
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 1.00000 1.00000
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) −0.554958 −0.554958
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(930\) 0 0
\(931\) −1.80194 −1.80194
\(932\) −0.445042 −0.445042
\(933\) 0 0
\(934\) −0.445042 −0.445042
\(935\) 0 0
\(936\) 0 0
\(937\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(938\) 0 0
\(939\) −0.554958 −0.554958
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −0.445042 −0.445042
\(945\) 0 0
\(946\) −2.24698 −2.24698
\(947\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −1.80194 −1.80194
\(951\) 0 0
\(952\) 0 0
\(953\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 1.44504 1.44504
\(964\) 2.00000 2.00000
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0.554958 0.554958
\(969\) 1.00000 1.00000
\(970\) 0 0
\(971\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(972\) −1.00000 −1.00000
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(978\) −0.554958 −0.554958
\(979\) −0.554958 −0.554958
\(980\) 0 0
\(981\) 0 0
\(982\) −0.445042 −0.445042
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0.801938 0.801938
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) −0.890084 −0.890084
\(994\) 0 0
\(995\) 0 0
\(996\) 0.801938 0.801938
\(997\) 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 1352.1.g.c.339.2 yes 3
8.3 odd 2 CM 1352.1.g.c.339.2 yes 3
13.2 odd 12 1352.1.p.c.147.5 12
13.3 even 3 1352.1.n.b.867.2 6
13.4 even 6 1352.1.n.c.315.2 6
13.5 odd 4 1352.1.h.a.675.2 6
13.6 odd 12 1352.1.p.c.699.2 12
13.7 odd 12 1352.1.p.c.699.5 12
13.8 odd 4 1352.1.h.a.675.5 6
13.9 even 3 1352.1.n.b.315.2 6
13.10 even 6 1352.1.n.c.867.2 6
13.11 odd 12 1352.1.p.c.147.2 12
13.12 even 2 1352.1.g.b.339.2 3
104.3 odd 6 1352.1.n.b.867.2 6
104.11 even 12 1352.1.p.c.147.2 12
104.19 even 12 1352.1.p.c.699.2 12
104.35 odd 6 1352.1.n.b.315.2 6
104.43 odd 6 1352.1.n.c.315.2 6
104.51 odd 2 1352.1.g.b.339.2 3
104.59 even 12 1352.1.p.c.699.5 12
104.67 even 12 1352.1.p.c.147.5 12
104.75 odd 6 1352.1.n.c.867.2 6
104.83 even 4 1352.1.h.a.675.2 6
104.99 even 4 1352.1.h.a.675.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1352.1.g.b.339.2 3 13.12 even 2
1352.1.g.b.339.2 3 104.51 odd 2
1352.1.g.c.339.2 yes 3 1.1 even 1 trivial
1352.1.g.c.339.2 yes 3 8.3 odd 2 CM
1352.1.h.a.675.2 6 13.5 odd 4
1352.1.h.a.675.2 6 104.83 even 4
1352.1.h.a.675.5 6 13.8 odd 4
1352.1.h.a.675.5 6 104.99 even 4
1352.1.n.b.315.2 6 13.9 even 3
1352.1.n.b.315.2 6 104.35 odd 6
1352.1.n.b.867.2 6 13.3 even 3
1352.1.n.b.867.2 6 104.3 odd 6
1352.1.n.c.315.2 6 13.4 even 6
1352.1.n.c.315.2 6 104.43 odd 6
1352.1.n.c.867.2 6 13.10 even 6
1352.1.n.c.867.2 6 104.75 odd 6
1352.1.p.c.147.2 12 13.11 odd 12
1352.1.p.c.147.2 12 104.11 even 12
1352.1.p.c.147.5 12 13.2 odd 12
1352.1.p.c.147.5 12 104.67 even 12
1352.1.p.c.699.2 12 13.6 odd 12
1352.1.p.c.699.2 12 104.19 even 12
1352.1.p.c.699.5 12 13.7 odd 12
1352.1.p.c.699.5 12 104.59 even 12