Properties

Label 151.1.b.a.150.2
Level $151$
Weight $1$
Character 151.150
Self dual yes
Analytic conductor $0.075$
Analytic rank $0$
Dimension $3$
Projective image $D_{7}$
CM discriminant -151
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] = [151,1,Mod(150,151)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(151, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("151.150");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 151 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 151.b (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: \(0.0753588169076\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{7}\)
Projective field: Galois closure of 7.1.3442951.1
Artin image: $D_7$
Artin field: Galois closure of 7.1.3442951.1

Embedding invariants

Embedding label 150.2
Root \(0.445042\) of defining polynomial
Character \(\chi\) \(=\) 151.150

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.445042 q^{2} -0.801938 q^{4} +1.24698 q^{5} +0.801938 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.445042 q^{2} -0.801938 q^{4} +1.24698 q^{5} +0.801938 q^{8} +1.00000 q^{9} -0.554958 q^{10} -1.80194 q^{11} +0.445042 q^{16} -1.80194 q^{17} -0.445042 q^{18} -0.445042 q^{19} -1.00000 q^{20} +0.801938 q^{22} +0.554958 q^{25} -0.445042 q^{29} +1.24698 q^{31} -1.00000 q^{32} +0.801938 q^{34} -0.801938 q^{36} -1.80194 q^{37} +0.198062 q^{38} +1.00000 q^{40} +1.24698 q^{43} +1.44504 q^{44} +1.24698 q^{45} -0.445042 q^{47} +1.00000 q^{49} -0.246980 q^{50} -2.24698 q^{55} +0.198062 q^{58} +1.24698 q^{59} -0.554958 q^{62} +1.44504 q^{68} +0.801938 q^{72} +0.801938 q^{74} +0.356896 q^{76} +0.554958 q^{80} +1.00000 q^{81} -2.24698 q^{85} -0.554958 q^{86} -1.44504 q^{88} -0.554958 q^{90} +0.198062 q^{94} -0.554958 q^{95} -0.445042 q^{97} -0.445042 q^{98} -1.80194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{2} + 2 q^{4} - q^{5} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{2} + 2 q^{4} - q^{5} - 2 q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + q^{16} - q^{17} - q^{18} - q^{19} - 3 q^{20} - 2 q^{22} + 2 q^{25} - q^{29} - q^{31} - 3 q^{32} - 2 q^{34} + 2 q^{36} - q^{37} + 5 q^{38} + 3 q^{40} - q^{43} + 4 q^{44} - q^{45} - q^{47} + 3 q^{49} + 4 q^{50} - 2 q^{55} + 5 q^{58} - q^{59} - 2 q^{62} + 4 q^{68} - 2 q^{72} - 2 q^{74} - 3 q^{76} + 2 q^{80} + 3 q^{81} - 2 q^{85} - 2 q^{86} - 4 q^{88} - 2 q^{90} + 5 q^{94} - 2 q^{95} - q^{97} - q^{98} - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/151\mathbb{Z}\right)^\times\).

\(n\) \(6\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) −0.801938 −0.801938
\(5\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0.801938 0.801938
\(9\) 1.00000 1.00000
\(10\) −0.554958 −0.554958
\(11\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.445042 0.445042
\(17\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(18\) −0.445042 −0.445042
\(19\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(20\) −1.00000 −1.00000
\(21\) 0 0
\(22\) 0.801938 0.801938
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0.554958 0.554958
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(30\) 0 0
\(31\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) 0.801938 0.801938
\(35\) 0 0
\(36\) −0.801938 −0.801938
\(37\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(38\) 0.198062 0.198062
\(39\) 0 0
\(40\) 1.00000 1.00000
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(44\) 1.44504 1.44504
\(45\) 1.24698 1.24698
\(46\) 0 0
\(47\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(48\) 0 0
\(49\) 1.00000 1.00000
\(50\) −0.246980 −0.246980
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) −2.24698 −2.24698
\(56\) 0 0
\(57\) 0 0
\(58\) 0.198062 0.198062
\(59\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) −0.554958 −0.554958
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 1.44504 1.44504
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0.801938 0.801938
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0.801938 0.801938
\(75\) 0 0
\(76\) 0.356896 0.356896
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0.554958 0.554958
\(81\) 1.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) −2.24698 −2.24698
\(86\) −0.554958 −0.554958
\(87\) 0 0
\(88\) −1.44504 −1.44504
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −0.554958 −0.554958
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0.198062 0.198062
\(95\) −0.554958 −0.554958
\(96\) 0 0
\(97\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(98\) −0.445042 −0.445042
\(99\) −1.80194 −1.80194
\(100\) −0.445042 −0.445042
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 1.00000 1.00000
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.356896 0.356896
\(117\) 0 0
\(118\) −0.554958 −0.554958
\(119\) 0 0
\(120\) 0 0
\(121\) 2.24698 2.24698
\(122\) 0 0
\(123\) 0 0
\(124\) −1.00000 −1.00000
\(125\) −0.554958 −0.554958
\(126\) 0 0
\(127\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −1.44504 −1.44504
\(137\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(138\) 0 0
\(139\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.445042 0.445042
\(145\) −0.554958 −0.554958
\(146\) 0 0
\(147\) 0 0
\(148\) 1.44504 1.44504
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 1.00000 1.00000
\(152\) −0.356896 −0.356896
\(153\) −1.80194 −1.80194
\(154\) 0 0
\(155\) 1.55496 1.55496
\(156\) 0 0
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −1.24698 −1.24698
\(161\) 0 0
\(162\) −0.445042 −0.445042
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 1.00000 1.00000
\(171\) −0.445042 −0.445042
\(172\) −1.00000 −1.00000
\(173\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.801938 −0.801938
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −1.00000 −1.00000
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.24698 −2.24698
\(186\) 0 0
\(187\) 3.24698 3.24698
\(188\) 0.356896 0.356896
\(189\) 0 0
\(190\) 0.246980 0.246980
\(191\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(192\) 0 0
\(193\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(194\) 0.198062 0.198062
\(195\) 0 0
\(196\) −0.801938 −0.801938
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0.801938 0.801938
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0.445042 0.445042
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0.801938 0.801938
\(207\) 0 0
\(208\) 0 0
\(209\) 0.801938 0.801938
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.55496 1.55496
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 1.80194 1.80194
\(221\) 0 0
\(222\) 0 0
\(223\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(224\) 0 0
\(225\) 0.554958 0.554958
\(226\) 0 0
\(227\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(228\) 0 0
\(229\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.356896 −0.356896
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −0.554958 −0.554958
\(236\) −1.00000 −1.00000
\(237\) 0 0
\(238\) 0 0
\(239\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(240\) 0 0
\(241\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(242\) −1.00000 −1.00000
\(243\) 0 0
\(244\) 0 0
\(245\) 1.24698 1.24698
\(246\) 0 0
\(247\) 0 0
\(248\) 1.00000 1.00000
\(249\) 0 0
\(250\) 0.246980 0.246980
\(251\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(252\) 0 0
\(253\) 0 0
\(254\) −0.554958 −0.554958
\(255\) 0 0
\(256\) −0.445042 −0.445042
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.445042 −0.445042
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −0.801938 −0.801938
\(273\) 0 0
\(274\) −0.554958 −0.554958
\(275\) −1.00000 −1.00000
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0.198062 0.198062
\(279\) 1.24698 1.24698
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −1.00000
\(289\) 2.24698 2.24698
\(290\) 0.246980 0.246980
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 1.55496 1.55496
\(296\) −1.44504 −1.44504
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −0.445042 −0.445042
\(303\) 0 0
\(304\) −0.198062 −0.198062
\(305\) 0 0
\(306\) 0.801938 0.801938
\(307\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.692021 −0.692021
\(311\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(312\) 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
\(319\) 0.801938 0.801938
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.801938 0.801938
\(324\) −0.801938 −0.801938
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(332\) 0 0
\(333\) −1.80194 −1.80194
\(334\) −0.890084 −0.890084
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −0.445042 −0.445042
\(339\) 0 0
\(340\) 1.80194 1.80194
\(341\) −2.24698 −2.24698
\(342\) 0.198062 0.198062
\(343\) 0 0
\(344\) 1.00000 1.00000
\(345\) 0 0
\(346\) 0.198062 0.198062
\(347\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(348\) 0 0
\(349\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.80194 1.80194
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 1.00000 1.00000
\(361\) −0.801938 −0.801938
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 1.00000 1.00000
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −1.44504 −1.44504
\(375\) 0 0
\(376\) −0.356896 −0.356896
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0.445042 0.445042
\(381\) 0 0
\(382\) 0.198062 0.198062
\(383\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.554958 −0.554958
\(387\) 1.24698 1.24698
\(388\) 0.356896 0.356896
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.801938 0.801938
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 1.44504 1.44504
\(397\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.246980 0.246980
\(401\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.24698 1.24698
\(406\) 0 0
\(407\) 3.24698 3.24698
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.44504 1.44504
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) −0.356896 −0.356896
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) −0.445042 −0.445042
\(424\) 0 0
\(425\) −1.00000 −1.00000
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) −0.692021 −0.692021
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(440\) −1.80194 −1.80194
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.801938 0.801938
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) −0.246980 −0.246980
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.801938 0.801938
\(455\) 0 0
\(456\) 0 0
\(457\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(458\) 0.198062 0.198062
\(459\) 0 0
\(460\) 0 0
\(461\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(462\) 0 0
\(463\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(464\) −0.198062 −0.198062
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0.246980 0.246980
\(471\) 0 0
\(472\) 1.00000 1.00000
\(473\) −2.24698 −2.24698
\(474\) 0 0
\(475\) −0.246980 −0.246980
\(476\) 0 0
\(477\) 0 0
\(478\) 0.801938 0.801938
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.801938 0.801938
\(483\) 0 0
\(484\) −1.80194 −1.80194
\(485\) −0.554958 −0.554958
\(486\) 0 0
\(487\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.554958 −0.554958
\(491\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(492\) 0 0
\(493\) 0.801938 0.801938
\(494\) 0 0
\(495\) −2.24698 −2.24698
\(496\) 0.554958 0.554958
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0.445042 0.445042
\(501\) 0 0
\(502\) −0.890084 −0.890084
\(503\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −1.00000 −1.00000
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.801938 −0.801938
\(513\) 0 0
\(514\) 0 0
\(515\) −2.24698 −2.24698
\(516\) 0 0
\(517\) 0.801938 0.801938
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(522\) 0.198062 0.198062
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.24698 −2.24698
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 1.24698 1.24698
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0.801938 0.801938
\(539\) −1.80194 −1.80194
\(540\) 0 0
\(541\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.80194 1.80194
\(545\) 0 0
\(546\) 0 0
\(547\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(548\) −1.00000 −1.00000
\(549\) 0 0
\(550\) 0.445042 0.445042
\(551\) 0.198062 0.198062
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.356896 0.356896
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) −0.554958 −0.554958
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(570\) 0 0
\(571\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(578\) −1.00000 −1.00000
\(579\) 0 0
\(580\) 0.445042 0.445042
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) −0.554958 −0.554958
\(590\) −0.692021 −0.692021
\(591\) 0 0
\(592\) −0.801938 −0.801938
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.801938 −0.801938
\(605\) 2.80194 2.80194
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0.445042 0.445042
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.44504 1.44504
\(613\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(614\) 0.801938 0.801938
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) −1.24698 −1.24698
\(621\) 0 0
\(622\) −0.554958 −0.554958
\(623\) 0 0
\(624\) 0 0
\(625\) −1.24698 −1.24698
\(626\) −0.554958 −0.554958
\(627\) 0 0
\(628\) 0 0
\(629\) 3.24698 3.24698
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.55496 1.55496
\(636\) 0 0
\(637\) 0 0
\(638\) −0.356896 −0.356896
\(639\) 0 0
\(640\) 1.24698 1.24698
\(641\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(642\) 0 0
\(643\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.356896 −0.356896
\(647\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(648\) 0.801938 0.801938
\(649\) −2.24698 −2.24698
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0.801938 0.801938
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.801938 0.801938
\(667\) 0 0
\(668\) −1.60388 −1.60388
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −0.801938 −0.801938
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.80194 −1.80194
\(681\) 0 0
\(682\) 1.00000 1.00000
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0.356896 0.356896
\(685\) 1.55496 1.55496
\(686\) 0 0
\(687\) 0 0
\(688\) 0.554958 0.554958
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0.356896 0.356896
\(693\) 0 0
\(694\) −0.890084 −0.890084
\(695\) −0.554958 −0.554958
\(696\) 0 0
\(697\) 0 0
\(698\) 0.801938 0.801938
\(699\) 0 0
\(700\) 0 0
\(701\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(702\) 0 0
\(703\) 0.801938 0.801938
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0.554958 0.554958
\(721\) 0 0
\(722\) 0.356896 0.356896
\(723\) 0 0
\(724\) 0 0
\(725\) −0.246980 −0.246980
\(726\) 0 0
\(727\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 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 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 1.80194 1.80194
\(741\) 0 0
\(742\) 0 0
\(743\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) −2.60388 −2.60388
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) −0.198062 −0.198062
\(753\) 0 0
\(754\) 0 0
\(755\) 1.24698 1.24698
\(756\) 0 0
\(757\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −0.445042 −0.445042
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.356896 0.356896
\(765\) −2.24698 −2.24698
\(766\) −0.554958 −0.554958
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 −1.00000
\(773\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(774\) −0.554958 −0.554958
\(775\) 0.692021 0.692021
\(776\) −0.356896 −0.356896
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.445042 0.445042
\(785\) 0 0
\(786\) 0 0
\(787\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −1.44504 −1.44504
\(793\) 0 0
\(794\) 0.198062 0.198062
\(795\) 0 0
\(796\) 0 0
\(797\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(798\) 0 0
\(799\) 0.801938 0.801938
\(800\) −0.554958 −0.554958
\(801\) 0 0
\(802\) 0.198062 0.198062
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) −0.554958 −0.554958
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −1.44504 −1.44504
\(815\) 0 0
\(816\) 0 0
\(817\) −0.554958 −0.554958
\(818\) 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 \(0.571429\pi\)
\(824\) −1.44504 −1.44504
\(825\) 0 0
\(826\) 0 0
\(827\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(828\) 0 0
\(829\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.80194 −1.80194
\(834\) 0 0
\(835\) 2.49396 2.49396
\(836\) −0.643104 −0.643104
\(837\) 0 0
\(838\) 0 0
\(839\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(840\) 0 0
\(841\) −0.801938 −0.801938
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.24698 1.24698
\(846\) 0.198062 0.198062
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0.445042 0.445042
\(851\) 0 0
\(852\) 0 0
\(853\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(854\) 0 0
\(855\) −0.554958 −0.554958
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) −1.24698 −1.24698
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) −0.554958 −0.554958
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −0.445042 −0.445042
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0.801938 0.801938
\(879\) 0 0
\(880\) −1.00000 −1.00000
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −0.445042 −0.445042
\(883\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.80194 −1.80194
\(892\) 1.44504 1.44504
\(893\) 0.198062 0.198062
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −0.554958 −0.554958
\(900\) −0.445042 −0.445042
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(908\) 1.44504 1.44504
\(909\) 0 0
\(910\) 0 0
\(911\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −0.554958 −0.554958
\(915\) 0 0
\(916\) 0.356896 0.356896
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0.801938 0.801938
\(923\) 0 0
\(924\) 0 0
\(925\) −1.00000 −1.00000
\(926\) 0.801938 0.801938
\(927\) −1.80194 −1.80194
\(928\) 0.445042 0.445042
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) −0.445042 −0.445042
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4.04892 4.04892
\(936\) 0 0
\(937\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0.445042 0.445042
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0.554958 0.554958
\(945\) 0 0
\(946\) 1.00000 1.00000
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0.109916 0.109916
\(951\) 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 0
\(955\) −0.554958 −0.554958
\(956\) 1.44504 1.44504
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 0.554958 0.554958
\(962\) 0 0
\(963\) 0 0
\(964\) 1.44504 1.44504
\(965\) 1.55496 1.55496
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 1.80194 1.80194
\(969\) 0 0
\(970\) 0.246980 0.246980
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0.198062 0.198062
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −1.00000 −1.00000
\(981\) 0 0
\(982\) −0.554958 −0.554958
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −0.356896 −0.356896
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 1.00000 1.00000
\(991\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(992\) −1.24698 −1.24698
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(998\) 0 0
\(999\) 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 151.1.b.a.150.2 3
3.2 odd 2 1359.1.d.b.1207.2 3
4.3 odd 2 2416.1.e.a.2113.3 3
5.2 odd 4 3775.1.c.c.3774.3 6
5.3 odd 4 3775.1.c.c.3774.4 6
5.4 even 2 3775.1.d.d.301.2 3
151.150 odd 2 CM 151.1.b.a.150.2 3
453.452 even 2 1359.1.d.b.1207.2 3
604.603 even 2 2416.1.e.a.2113.3 3
755.452 even 4 3775.1.c.c.3774.3 6
755.603 even 4 3775.1.c.c.3774.4 6
755.754 odd 2 3775.1.d.d.301.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
151.1.b.a.150.2 3 1.1 even 1 trivial
151.1.b.a.150.2 3 151.150 odd 2 CM
1359.1.d.b.1207.2 3 3.2 odd 2
1359.1.d.b.1207.2 3 453.452 even 2
2416.1.e.a.2113.3 3 4.3 odd 2
2416.1.e.a.2113.3 3 604.603 even 2
3775.1.c.c.3774.3 6 5.2 odd 4
3775.1.c.c.3774.3 6 755.452 even 4
3775.1.c.c.3774.4 6 5.3 odd 4
3775.1.c.c.3774.4 6 755.603 even 4
3775.1.d.d.301.2 3 5.4 even 2
3775.1.d.d.301.2 3 755.754 odd 2