Properties

Label 2255.1.h.i.2254.4
Level $2255$
Weight $1$
Character 2255.2254
Self dual yes
Analytic conductor $1.125$
Analytic rank $0$
Dimension $4$
Projective image $D_{10}$
CM discriminant -2255
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2255,1,Mod(2254,2255)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2255, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 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("2255.2254");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2255 = 5 \cdot 11 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2255.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: \(1.12539160349\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{20})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 5x^{2} + 5 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{10}\)
Projective field: Galois closure of 10.2.129287396253125.1

Embedding invariants

Embedding label 2254.4
Root \(-1.17557\) of defining polynomial
Character \(\chi\) \(=\) 2255.2254

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.90211 q^{2} +1.17557 q^{3} +2.61803 q^{4} -1.00000 q^{5} +2.23607 q^{6} +3.07768 q^{8} +0.381966 q^{9} +O(q^{10})\) \(q+1.90211 q^{2} +1.17557 q^{3} +2.61803 q^{4} -1.00000 q^{5} +2.23607 q^{6} +3.07768 q^{8} +0.381966 q^{9} -1.90211 q^{10} -1.00000 q^{11} +3.07768 q^{12} -1.17557 q^{15} +3.23607 q^{16} +0.726543 q^{18} -1.61803 q^{19} -2.61803 q^{20} -1.90211 q^{22} +3.61803 q^{24} +1.00000 q^{25} -0.726543 q^{27} -0.618034 q^{29} -2.23607 q^{30} -1.61803 q^{31} +3.07768 q^{32} -1.17557 q^{33} +1.00000 q^{36} -3.07768 q^{38} -3.07768 q^{40} +1.00000 q^{41} -2.61803 q^{44} -0.381966 q^{45} +3.80423 q^{48} +1.00000 q^{49} +1.90211 q^{50} +1.90211 q^{53} -1.38197 q^{54} +1.00000 q^{55} -1.90211 q^{57} -1.17557 q^{58} +0.618034 q^{59} -3.07768 q^{60} -3.07768 q^{62} +2.61803 q^{64} -2.23607 q^{66} +1.90211 q^{67} +1.17557 q^{72} +1.17557 q^{73} +1.17557 q^{75} -4.23607 q^{76} -0.618034 q^{79} -3.23607 q^{80} -1.23607 q^{81} +1.90211 q^{82} -1.17557 q^{83} -0.726543 q^{87} -3.07768 q^{88} -0.726543 q^{90} -1.90211 q^{93} +1.61803 q^{95} +3.61803 q^{96} +1.90211 q^{98} -0.381966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{4} - 4 q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{4} - 4 q^{5} + 6 q^{9} - 4 q^{11} + 4 q^{16} - 2 q^{19} - 6 q^{20} + 10 q^{24} + 4 q^{25} + 2 q^{29} - 2 q^{31} + 4 q^{36} + 4 q^{41} - 6 q^{44} - 6 q^{45} + 4 q^{49} - 10 q^{54} + 4 q^{55} - 2 q^{59} + 6 q^{64} - 8 q^{76} + 2 q^{79} - 4 q^{80} + 4 q^{81} + 2 q^{95} + 10 q^{96} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2255\mathbb{Z}\right)^\times\).

\(n\) \(452\) \(826\) \(1641\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(3\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(4\) 2.61803 2.61803
\(5\) −1.00000 −1.00000
\(6\) 2.23607 2.23607
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 3.07768 3.07768
\(9\) 0.381966 0.381966
\(10\) −1.90211 −1.90211
\(11\) −1.00000 −1.00000
\(12\) 3.07768 3.07768
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) −1.17557 −1.17557
\(16\) 3.23607 3.23607
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0.726543 0.726543
\(19\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(20\) −2.61803 −2.61803
\(21\) 0 0
\(22\) −1.90211 −1.90211
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 3.61803 3.61803
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) −0.726543 −0.726543
\(28\) 0 0
\(29\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(30\) −2.23607 −2.23607
\(31\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(32\) 3.07768 3.07768
\(33\) −1.17557 −1.17557
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 1.00000
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) −3.07768 −3.07768
\(39\) 0 0
\(40\) −3.07768 −3.07768
\(41\) 1.00000 1.00000
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) −2.61803 −2.61803
\(45\) −0.381966 −0.381966
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 3.80423 3.80423
\(49\) 1.00000 1.00000
\(50\) 1.90211 1.90211
\(51\) 0 0
\(52\) 0 0
\(53\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(54\) −1.38197 −1.38197
\(55\) 1.00000 1.00000
\(56\) 0 0
\(57\) −1.90211 −1.90211
\(58\) −1.17557 −1.17557
\(59\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(60\) −3.07768 −3.07768
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) −3.07768 −3.07768
\(63\) 0 0
\(64\) 2.61803 2.61803
\(65\) 0 0
\(66\) −2.23607 −2.23607
\(67\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 1.17557 1.17557
\(73\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(74\) 0 0
\(75\) 1.17557 1.17557
\(76\) −4.23607 −4.23607
\(77\) 0 0
\(78\) 0 0
\(79\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(80\) −3.23607 −3.23607
\(81\) −1.23607 −1.23607
\(82\) 1.90211 1.90211
\(83\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.726543 −0.726543
\(88\) −3.07768 −3.07768
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −0.726543 −0.726543
\(91\) 0 0
\(92\) 0 0
\(93\) −1.90211 −1.90211
\(94\) 0 0
\(95\) 1.61803 1.61803
\(96\) 3.61803 3.61803
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 1.90211 1.90211
\(99\) −0.381966 −0.381966
\(100\) 2.61803 2.61803
\(101\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 3.61803 3.61803
\(107\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(108\) −1.90211 −1.90211
\(109\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(110\) 1.90211 1.90211
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) −3.61803 −3.61803
\(115\) 0 0
\(116\) −1.61803 −1.61803
\(117\) 0 0
\(118\) 1.17557 1.17557
\(119\) 0 0
\(120\) −3.61803 −3.61803
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 1.17557 1.17557
\(124\) −4.23607 −4.23607
\(125\) −1.00000 −1.00000
\(126\) 0 0
\(127\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(128\) 1.90211 1.90211
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) −3.07768 −3.07768
\(133\) 0 0
\(134\) 3.61803 3.61803
\(135\) 0.726543 0.726543
\(136\) 0 0
\(137\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.23607 1.23607
\(145\) 0.618034 0.618034
\(146\) 2.23607 2.23607
\(147\) 1.17557 1.17557
\(148\) 0 0
\(149\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) 2.23607 2.23607
\(151\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(152\) −4.97980 −4.97980
\(153\) 0 0
\(154\) 0 0
\(155\) 1.61803 1.61803
\(156\) 0 0
\(157\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(158\) −1.17557 −1.17557
\(159\) 2.23607 2.23607
\(160\) −3.07768 −3.07768
\(161\) 0 0
\(162\) −2.35114 −2.35114
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 2.61803 2.61803
\(165\) 1.17557 1.17557
\(166\) −2.23607 −2.23607
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) −0.618034 −0.618034
\(172\) 0 0
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) −1.38197 −1.38197
\(175\) 0 0
\(176\) −3.23607 −3.23607
\(177\) 0.726543 0.726543
\(178\) 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
\(185\) 0 0
\(186\) −3.61803 −3.61803
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 3.07768 3.07768
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 3.07768 3.07768
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2.61803 2.61803
\(197\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(198\) −0.726543 −0.726543
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 3.07768 3.07768
\(201\) 2.23607 2.23607
\(202\) 1.17557 1.17557
\(203\) 0 0
\(204\) 0 0
\(205\) −1.00000 −1.00000
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.61803 1.61803
\(210\) 0 0
\(211\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(212\) 4.97980 4.97980
\(213\) 0 0
\(214\) −3.61803 −3.61803
\(215\) 0 0
\(216\) −2.23607 −2.23607
\(217\) 0 0
\(218\) 3.07768 3.07768
\(219\) 1.38197 1.38197
\(220\) 2.61803 2.61803
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) 0.381966 0.381966
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) −4.97980 −4.97980
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.90211 −1.90211
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.61803 1.61803
\(237\) −0.726543 −0.726543
\(238\) 0 0
\(239\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(240\) −3.80423 −3.80423
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.90211 1.90211
\(243\) −0.726543 −0.726543
\(244\) 0 0
\(245\) −1.00000 −1.00000
\(246\) 2.23607 2.23607
\(247\) 0 0
\(248\) −4.97980 −4.97980
\(249\) −1.38197 −1.38197
\(250\) −1.90211 −1.90211
\(251\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −2.23607 −2.23607
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.236068 −0.236068
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −3.61803 −3.61803
\(265\) −1.90211 −1.90211
\(266\) 0 0
\(267\) 0 0
\(268\) 4.97980 4.97980
\(269\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(270\) 1.38197 1.38197
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −3.61803 −3.61803
\(275\) −1.00000 −1.00000
\(276\) 0 0
\(277\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(278\) 0 0
\(279\) −0.618034 −0.618034
\(280\) 0 0
\(281\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(282\) 0 0
\(283\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(284\) 0 0
\(285\) 1.90211 1.90211
\(286\) 0 0
\(287\) 0 0
\(288\) 1.17557 1.17557
\(289\) 1.00000 1.00000
\(290\) 1.17557 1.17557
\(291\) 0 0
\(292\) 3.07768 3.07768
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 2.23607 2.23607
\(295\) −0.618034 −0.618034
\(296\) 0 0
\(297\) 0.726543 0.726543
\(298\) −3.07768 −3.07768
\(299\) 0 0
\(300\) 3.07768 3.07768
\(301\) 0 0
\(302\) 1.17557 1.17557
\(303\) 0.726543 0.726543
\(304\) −5.23607 −5.23607
\(305\) 0 0
\(306\) 0 0
\(307\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 3.07768 3.07768
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(314\) −2.23607 −2.23607
\(315\) 0 0
\(316\) −1.61803 −1.61803
\(317\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(318\) 4.25325 4.25325
\(319\) 0.618034 0.618034
\(320\) −2.61803 −2.61803
\(321\) −2.23607 −2.23607
\(322\) 0 0
\(323\) 0 0
\(324\) −3.23607 −3.23607
\(325\) 0 0
\(326\) 0 0
\(327\) 1.90211 1.90211
\(328\) 3.07768 3.07768
\(329\) 0 0
\(330\) 2.23607 2.23607
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −3.07768 −3.07768
\(333\) 0 0
\(334\) 0 0
\(335\) −1.90211 −1.90211
\(336\) 0 0
\(337\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(338\) 1.90211 1.90211
\(339\) 0 0
\(340\) 0 0
\(341\) 1.61803 1.61803
\(342\) −1.17557 −1.17557
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) −1.90211 −1.90211
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.07768 −3.07768
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 1.38197 1.38197
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) −1.17557 −1.17557
\(361\) 1.61803 1.61803
\(362\) 0 0
\(363\) 1.17557 1.17557
\(364\) 0 0
\(365\) −1.17557 −1.17557
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0.381966 0.381966
\(370\) 0 0
\(371\) 0 0
\(372\) −4.97980 −4.97980
\(373\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(374\) 0 0
\(375\) −1.17557 −1.17557
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(380\) 4.23607 4.23607
\(381\) −1.38197 −1.38197
\(382\) 0 0
\(383\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(384\) 2.23607 2.23607
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 3.07768 3.07768
\(393\) 0 0
\(394\) −3.61803 −3.61803
\(395\) 0.618034 0.618034
\(396\) −1.00000 −1.00000
\(397\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 3.23607 3.23607
\(401\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(402\) 4.25325 4.25325
\(403\) 0 0
\(404\) 1.61803 1.61803
\(405\) 1.23607 1.23607
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) −1.90211 −1.90211
\(411\) −2.23607 −2.23607
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 1.17557 1.17557
\(416\) 0 0
\(417\) 0 0
\(418\) 3.07768 3.07768
\(419\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 3.07768 3.07768
\(423\) 0 0
\(424\) 5.85410 5.85410
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −4.97980 −4.97980
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −2.35114 −2.35114
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0.726543 0.726543
\(436\) 4.23607 4.23607
\(437\) 0 0
\(438\) 2.62866 2.62866
\(439\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(440\) 3.07768 3.07768
\(441\) 0.381966 0.381966
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1.90211 −1.90211
\(448\) 0 0
\(449\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) 0.726543 0.726543
\(451\) −1.00000 −1.00000
\(452\) 0 0
\(453\) 0.726543 0.726543
\(454\) 0 0
\(455\) 0 0
\(456\) −5.85410 −5.85410
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(464\) −2.00000 −2.00000
\(465\) 1.90211 1.90211
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.38197 −1.38197
\(472\) 1.90211 1.90211
\(473\) 0 0
\(474\) −1.38197 −1.38197
\(475\) −1.61803 −1.61803
\(476\) 0 0
\(477\) 0.726543 0.726543
\(478\) 1.17557 1.17557
\(479\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) −3.61803 −3.61803
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 2.61803 2.61803
\(485\) 0 0
\(486\) −1.38197 −1.38197
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −1.90211 −1.90211
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 3.07768 3.07768
\(493\) 0 0
\(494\) 0 0
\(495\) 0.381966 0.381966
\(496\) −5.23607 −5.23607
\(497\) 0 0
\(498\) −2.62866 −2.62866
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) −2.61803 −2.61803
\(501\) 0 0
\(502\) −1.17557 −1.17557
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) −0.618034 −0.618034
\(506\) 0 0
\(507\) 1.17557 1.17557
\(508\) −3.07768 −3.07768
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1.17557 1.17557
\(514\) −2.23607 −2.23607
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −0.449028 −0.449028
\(523\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −3.80423 −3.80423
\(529\) 1.00000 1.00000
\(530\) −3.61803 −3.61803
\(531\) 0.236068 0.236068
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 1.90211 1.90211
\(536\) 5.85410 5.85410
\(537\) 0 0
\(538\) −3.07768 −3.07768
\(539\) −1.00000 −1.00000
\(540\) 1.90211 1.90211
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.61803 −1.61803
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −4.97980 −4.97980
\(549\) 0 0
\(550\) −1.90211 −1.90211
\(551\) 1.00000 1.00000
\(552\) 0 0
\(553\) 0 0
\(554\) −2.23607 −2.23607
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) −1.17557 −1.17557
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 3.07768 3.07768
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 3.61803 3.61803
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 3.61803 3.61803
\(571\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(578\) 1.90211 1.90211
\(579\) 0 0
\(580\) 1.61803 1.61803
\(581\) 0 0
\(582\) 0 0
\(583\) −1.90211 −1.90211
\(584\) 3.61803 3.61803
\(585\) 0 0
\(586\) 0 0
\(587\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(588\) 3.07768 3.07768
\(589\) 2.61803 2.61803
\(590\) −1.17557 −1.17557
\(591\) −2.23607 −2.23607
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 1.38197 1.38197
\(595\) 0 0
\(596\) −4.23607 −4.23607
\(597\) 0 0
\(598\) 0 0
\(599\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(600\) 3.61803 3.61803
\(601\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0.726543 0.726543
\(604\) 1.61803 1.61803
\(605\) −1.00000 −1.00000
\(606\) 1.38197 1.38197
\(607\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(608\) −4.97980 −4.97980
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(614\) 2.23607 2.23607
\(615\) −1.17557 −1.17557
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(620\) 4.23607 4.23607
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 3.61803 3.61803
\(627\) 1.90211 1.90211
\(628\) −3.07768 −3.07768
\(629\) 0 0
\(630\) 0 0
\(631\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(632\) −1.90211 −1.90211
\(633\) 1.90211 1.90211
\(634\) −2.23607 −2.23607
\(635\) 1.17557 1.17557
\(636\) 5.85410 5.85410
\(637\) 0 0
\(638\) 1.17557 1.17557
\(639\) 0 0
\(640\) −1.90211 −1.90211
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) −4.25325 −4.25325
\(643\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) −3.80423 −3.80423
\(649\) −0.618034 −0.618034
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(654\) 3.61803 3.61803
\(655\) 0 0
\(656\) 3.23607 3.23607
\(657\) 0.449028 0.449028
\(658\) 0 0
\(659\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(660\) 3.07768 3.07768
\(661\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −3.61803 −3.61803
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) −3.61803 −3.61803
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 3.61803 3.61803
\(675\) −0.726543 −0.726543
\(676\) 2.61803 2.61803
\(677\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 3.07768 3.07768
\(683\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(684\) −1.61803 −1.61803
\(685\) 1.90211 1.90211
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) −2.23607 −2.23607
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −2.61803 −2.61803
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 1.90211 1.90211
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) −0.236068 −0.236068
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0.726543 0.726543
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −1.23607 −1.23607
\(721\) 0 0
\(722\) 3.07768 3.07768
\(723\) 0 0
\(724\) 0 0
\(725\) −0.618034 −0.618034
\(726\) 2.23607 2.23607
\(727\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(728\) 0 0
\(729\) 0.381966 0.381966
\(730\) −2.23607 −2.23607
\(731\) 0 0
\(732\) 0 0
\(733\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(734\) 0 0
\(735\) −1.17557 −1.17557
\(736\) 0 0
\(737\) −1.90211 −1.90211
\(738\) 0.726543 0.726543
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(744\) −5.85410 −5.85410
\(745\) 1.61803 1.61803
\(746\) 3.61803 3.61803
\(747\) −0.449028 −0.449028
\(748\) 0 0
\(749\) 0 0
\(750\) −2.23607 −2.23607
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) −0.726543 −0.726543
\(754\) 0 0
\(755\) −0.618034 −0.618034
\(756\) 0 0
\(757\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(758\) −1.17557 −1.17557
\(759\) 0 0
\(760\) 4.97980 4.97980
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) −2.62866 −2.62866
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 3.61803 3.61803
\(767\) 0 0
\(768\) 1.17557 1.17557
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −1.38197 −1.38197
\(772\) 0 0
\(773\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(774\) 0 0
\(775\) −1.61803 −1.61803
\(776\) 0 0
\(777\) 0 0
\(778\) 3.07768 3.07768
\(779\) −1.61803 −1.61803
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.449028 0.449028
\(784\) 3.23607 3.23607
\(785\) 1.17557 1.17557
\(786\) 0 0
\(787\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(788\) −4.97980 −4.97980
\(789\) 0 0
\(790\) 1.17557 1.17557
\(791\) 0 0
\(792\) −1.17557 −1.17557
\(793\) 0 0
\(794\) −3.61803 −3.61803
\(795\) −2.23607 −2.23607
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 3.07768 3.07768
\(801\) 0 0
\(802\) 1.17557 1.17557
\(803\) −1.17557 −1.17557
\(804\) 5.85410 5.85410
\(805\) 0 0
\(806\) 0 0
\(807\) −1.90211 −1.90211
\(808\) 1.90211 1.90211
\(809\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(810\) 2.35114 2.35114
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) −2.61803 −2.61803
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) −4.25325 −4.25325
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) −1.17557 −1.17557
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(830\) 2.23607 2.23607
\(831\) −1.38197 −1.38197
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 4.23607 4.23607
\(837\) 1.17557 1.17557
\(838\) −3.07768 −3.07768
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) −0.618034 −0.618034
\(842\) 0 0
\(843\) 1.90211 1.90211
\(844\) 4.23607 4.23607
\(845\) −1.00000 −1.00000
\(846\) 0 0
\(847\) 0 0
\(848\) 6.15537 6.15537
\(849\) 2.23607 2.23607
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0.618034 0.618034
\(856\) −5.85410 −5.85410
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) −2.23607 −2.23607
\(865\) 0 0
\(866\) 0 0
\(867\) 1.17557 1.17557
\(868\) 0 0
\(869\) 0.618034 0.618034
\(870\) 1.38197 1.38197
\(871\) 0 0
\(872\) 4.97980 4.97980
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 3.61803 3.61803
\(877\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(878\) 3.07768 3.07768
\(879\) 0 0
\(880\) 3.23607 3.23607
\(881\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(882\) 0.726543 0.726543
\(883\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(884\) 0 0
\(885\) −0.726543 −0.726543
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.23607 1.23607
\(892\) 0 0
\(893\) 0 0
\(894\) −3.61803 −3.61803
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −3.07768 −3.07768
\(899\) 1.00000 1.00000
\(900\) 1.00000 1.00000
\(901\) 0 0
\(902\) −1.90211 −1.90211
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 1.38197 1.38197
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) 0.236068 0.236068
\(910\) 0 0
\(911\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(912\) −6.15537 −6.15537
\(913\) 1.17557 1.17557
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 1.38197 1.38197
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) −3.61803 −3.61803
\(927\) 0 0
\(928\) −1.90211 −1.90211
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 3.61803 3.61803
\(931\) −1.61803 −1.61803
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 2.23607 2.23607
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) −2.62866 −2.62866
\(943\) 0 0
\(944\) 2.00000 2.00000
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) −1.90211 −1.90211
\(949\) 0 0
\(950\) −3.07768 −3.07768
\(951\) −1.38197 −1.38197
\(952\) 0 0
\(953\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(954\) 1.38197 1.38197
\(955\) 0 0
\(956\) 1.61803 1.61803
\(957\) 0.726543 0.726543
\(958\) −3.07768 −3.07768
\(959\) 0 0
\(960\) −3.07768 −3.07768
\(961\) 1.61803 1.61803
\(962\) 0 0
\(963\) −0.726543 −0.726543
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 3.07768 3.07768
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −1.90211 −1.90211
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −2.61803 −2.61803
\(981\) 0.618034 0.618034
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 3.61803 3.61803
\(985\) 1.90211 1.90211
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0.726543 0.726543
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) −4.97980 −4.97980
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) −3.61803 −3.61803
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 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 2255.1.h.i.2254.4 yes 4
5.4 even 2 inner 2255.1.h.i.2254.1 4
11.10 odd 2 2255.1.h.j.2254.1 yes 4
41.40 even 2 2255.1.h.j.2254.4 yes 4
55.54 odd 2 2255.1.h.j.2254.4 yes 4
205.204 even 2 2255.1.h.j.2254.1 yes 4
451.450 odd 2 inner 2255.1.h.i.2254.1 4
2255.2254 odd 2 CM 2255.1.h.i.2254.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2255.1.h.i.2254.1 4 5.4 even 2 inner
2255.1.h.i.2254.1 4 451.450 odd 2 inner
2255.1.h.i.2254.4 yes 4 1.1 even 1 trivial
2255.1.h.i.2254.4 yes 4 2255.2254 odd 2 CM
2255.1.h.j.2254.1 yes 4 11.10 odd 2
2255.1.h.j.2254.1 yes 4 205.204 even 2
2255.1.h.j.2254.4 yes 4 41.40 even 2
2255.1.h.j.2254.4 yes 4 55.54 odd 2