Properties

Label 2013.1.bm.d.1280.4
Level $2013$
Weight $1$
Character 2013.1280
Analytic conductor $1.005$
Analytic rank $0$
Dimension $16$
Projective image $D_{20}$
CM discriminant -183
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2013,1,Mod(548,2013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2013, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6, 5]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2013.548");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2013.bm (of order \(10\), degree \(4\), 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: no
Analytic conductor: \(1.00461787043\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{40})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{20}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{20} - \cdots)\)

Embedding invariants

Embedding label 1280.4
Root \(-0.453990 - 0.891007i\) of defining polynomial
Character \(\chi\) \(=\) 2013.1280
Dual form 2013.1.bm.d.1829.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.59811 + 1.16110i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.896802 + 2.76007i) q^{4} +(-1.59811 + 1.16110i) q^{6} +(-1.16110 + 3.57349i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(1.59811 + 1.16110i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.896802 + 2.76007i) q^{4} +(-1.59811 + 1.16110i) q^{6} +(-1.16110 + 3.57349i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.453990 - 0.891007i) q^{11} -2.90211 q^{12} +(0.951057 + 0.690983i) q^{13} +(-3.65688 + 2.65688i) q^{16} +(-0.734572 + 0.533698i) q^{17} +(-0.610425 - 1.87869i) q^{18} +(0.587785 - 1.80902i) q^{19} +(1.76007 - 0.896802i) q^{22} -0.312869 q^{23} +(-3.03979 - 2.20854i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.717598 + 2.20854i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-0.0966818 - 0.297556i) q^{29} -5.17160 q^{32} +(0.707107 + 0.707107i) q^{33} -1.79360 q^{34} +(0.896802 - 2.76007i) q^{36} +(3.03979 - 2.20854i) q^{38} +(-0.951057 + 0.690983i) q^{39} +(2.86638 + 0.453990i) q^{44} +(-0.500000 - 0.363271i) q^{46} +(-1.39680 - 4.29892i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(1.59811 - 1.16110i) q^{50} +(-0.280582 - 0.863541i) q^{51} +(-1.05425 + 3.24466i) q^{52} +(-1.59811 - 1.16110i) q^{53} +1.97538 q^{54} +(1.53884 + 1.11803i) q^{57} +(0.190983 - 0.587785i) q^{58} +(0.550672 + 1.69480i) q^{59} +(0.809017 - 0.587785i) q^{61} +(-4.60793 - 3.34786i) q^{64} +(0.309017 + 1.95106i) q^{66} +(-2.13181 - 1.54885i) q^{68} +(0.0966818 - 0.297556i) q^{69} +(1.14412 - 0.831254i) q^{71} +(3.03979 - 2.20854i) q^{72} +(0.500000 + 1.53884i) q^{73} +(0.809017 + 0.587785i) q^{75} +5.52015 q^{76} -2.32219 q^{78} +(0.309017 + 0.951057i) q^{81} +0.312869 q^{87} +(2.65688 + 2.65688i) q^{88} -0.907981 q^{89} +(-0.280582 - 0.863541i) q^{92} +(1.59811 - 4.91849i) q^{96} -1.97538 q^{98} +(-0.891007 + 0.453990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{3} - 4 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{3} - 4 q^{4} - 4 q^{9} - 16 q^{12} - 16 q^{16} + 4 q^{22} - 4 q^{25} + 4 q^{27} + 8 q^{34} - 4 q^{36} - 8 q^{46} - 4 q^{48} - 4 q^{49} - 20 q^{52} + 12 q^{58} + 4 q^{61} - 16 q^{64} - 4 q^{66} + 8 q^{73} + 4 q^{75} + 40 q^{76} - 4 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2013\mathbb{Z}\right)^\times\).

\(n\) \(1222\) \(1343\) \(1465\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.59811 + 1.16110i 1.59811 + 1.16110i 0.891007 + 0.453990i \(0.150000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(4\) 0.896802 + 2.76007i 0.896802 + 2.76007i
\(5\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(6\) −1.59811 + 1.16110i −1.59811 + 1.16110i
\(7\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(8\) −1.16110 + 3.57349i −1.16110 + 3.57349i
\(9\) −0.809017 0.587785i −0.809017 0.587785i
\(10\) 0 0
\(11\) 0.453990 0.891007i 0.453990 0.891007i
\(12\) −2.90211 −2.90211
\(13\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −3.65688 + 2.65688i −3.65688 + 2.65688i
\(17\) −0.734572 + 0.533698i −0.734572 + 0.533698i −0.891007 0.453990i \(-0.850000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(18\) −0.610425 1.87869i −0.610425 1.87869i
\(19\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.76007 0.896802i 1.76007 0.896802i
\(23\) −0.312869 −0.312869 −0.156434 0.987688i \(-0.550000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(24\) −3.03979 2.20854i −3.03979 2.20854i
\(25\) 0.309017 0.951057i 0.309017 0.951057i
\(26\) 0.717598 + 2.20854i 0.717598 + 2.20854i
\(27\) 0.809017 0.587785i 0.809017 0.587785i
\(28\) 0 0
\(29\) −0.0966818 0.297556i −0.0966818 0.297556i 0.891007 0.453990i \(-0.150000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(32\) −5.17160 −5.17160
\(33\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(34\) −1.79360 −1.79360
\(35\) 0 0
\(36\) 0.896802 2.76007i 0.896802 2.76007i
\(37\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(38\) 3.03979 2.20854i 3.03979 2.20854i
\(39\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(40\) 0 0
\(41\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 2.86638 + 0.453990i 2.86638 + 0.453990i
\(45\) 0 0
\(46\) −0.500000 0.363271i −0.500000 0.363271i
\(47\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(48\) −1.39680 4.29892i −1.39680 4.29892i
\(49\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(50\) 1.59811 1.16110i 1.59811 1.16110i
\(51\) −0.280582 0.863541i −0.280582 0.863541i
\(52\) −1.05425 + 3.24466i −1.05425 + 3.24466i
\(53\) −1.59811 1.16110i −1.59811 1.16110i −0.891007 0.453990i \(-0.850000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(54\) 1.97538 1.97538
\(55\) 0 0
\(56\) 0 0
\(57\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(58\) 0.190983 0.587785i 0.190983 0.587785i
\(59\) 0.550672 + 1.69480i 0.550672 + 1.69480i 0.707107 + 0.707107i \(0.250000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(60\) 0 0
\(61\) 0.809017 0.587785i 0.809017 0.587785i
\(62\) 0 0
\(63\) 0 0
\(64\) −4.60793 3.34786i −4.60793 3.34786i
\(65\) 0 0
\(66\) 0.309017 + 1.95106i 0.309017 + 1.95106i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −2.13181 1.54885i −2.13181 1.54885i
\(69\) 0.0966818 0.297556i 0.0966818 0.297556i
\(70\) 0 0
\(71\) 1.14412 0.831254i 1.14412 0.831254i 0.156434 0.987688i \(-0.450000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(72\) 3.03979 2.20854i 3.03979 2.20854i
\(73\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(74\) 0 0
\(75\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(76\) 5.52015 5.52015
\(77\) 0 0
\(78\) −2.32219 −2.32219
\(79\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(82\) 0 0
\(83\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.312869 0.312869
\(88\) 2.65688 + 2.65688i 2.65688 + 2.65688i
\(89\) −0.907981 −0.907981 −0.453990 0.891007i \(-0.650000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.280582 0.863541i −0.280582 0.863541i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.59811 4.91849i 1.59811 4.91849i
\(97\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(98\) −1.97538 −1.97538
\(99\) −0.891007 + 0.453990i −0.891007 + 0.453990i
\(100\) 2.90211 2.90211
\(101\) −1.14412 0.831254i −1.14412 0.831254i −0.156434 0.987688i \(-0.550000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(102\) 0.554254 1.70582i 0.554254 1.70582i
\(103\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(104\) −3.57349 + 2.59629i −3.57349 + 2.59629i
\(105\) 0 0
\(106\) −1.20582 3.71113i −1.20582 3.71113i
\(107\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(108\) 2.34786 + 1.70582i 2.34786 + 1.70582i
\(109\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(114\) 1.16110 + 3.57349i 1.16110 + 3.57349i
\(115\) 0 0
\(116\) 0.734572 0.533698i 0.734572 0.533698i
\(117\) −0.363271 1.11803i −0.363271 1.11803i
\(118\) −1.08779 + 3.34786i −1.08779 + 3.34786i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.587785 0.809017i −0.587785 0.809017i
\(122\) 1.97538 1.97538
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(128\) −1.87869 5.78203i −1.87869 5.78203i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) −1.31753 + 2.58580i −1.31753 + 2.58580i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −1.05425 3.24466i −1.05425 3.24466i
\(137\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(138\) 0.500000 0.363271i 0.500000 0.363271i
\(139\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.79360 2.79360
\(143\) 1.04744 0.533698i 1.04744 0.533698i
\(144\) 4.52015 4.52015
\(145\) 0 0
\(146\) −0.987688 + 3.03979i −0.987688 + 3.03979i
\(147\) −0.309017 0.951057i −0.309017 0.951057i
\(148\) 0 0
\(149\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) 0.610425 + 1.87869i 0.610425 + 1.87869i
\(151\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(152\) 5.78203 + 4.20089i 5.78203 + 4.20089i
\(153\) 0.907981 0.907981
\(154\) 0 0
\(155\) 0 0
\(156\) −2.76007 2.00531i −2.76007 2.00531i
\(157\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(158\) 0 0
\(159\) 1.59811 1.16110i 1.59811 1.16110i
\(160\) 0 0
\(161\) 0 0
\(162\) −0.610425 + 1.87869i −0.610425 + 1.87869i
\(163\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(168\) 0 0
\(169\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(170\) 0 0
\(171\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(172\) 0 0
\(173\) −0.437016 + 1.34500i −0.437016 + 1.34500i 0.453990 + 0.891007i \(0.350000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(174\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(175\) 0 0
\(176\) 0.707107 + 4.46450i 0.707107 + 4.46450i
\(177\) −1.78201 −1.78201
\(178\) −1.45106 1.05425i −1.45106 1.05425i
\(179\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(180\) 0 0
\(181\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(182\) 0 0
\(183\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(184\) 0.363271 1.11803i 0.363271 1.11803i
\(185\) 0 0
\(186\) 0 0
\(187\) 0.142040 + 0.896802i 0.142040 + 0.896802i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.550672 1.69480i −0.550672 1.69480i −0.707107 0.707107i \(-0.750000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(192\) 4.60793 3.34786i 4.60793 3.34786i
\(193\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −2.34786 1.70582i −2.34786 1.70582i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −1.95106 0.309017i −1.95106 0.309017i
\(199\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(200\) 3.03979 + 2.20854i 3.03979 + 2.20854i
\(201\) 0 0
\(202\) −0.863271 2.65688i −0.863271 2.65688i
\(203\) 0 0
\(204\) 2.13181 1.54885i 2.13181 1.54885i
\(205\) 0 0
\(206\) −0.717598 + 2.20854i −0.717598 + 2.20854i
\(207\) 0.253116 + 0.183900i 0.253116 + 0.183900i
\(208\) −5.31375 −5.31375
\(209\) −1.34500 1.34500i −1.34500 1.34500i
\(210\) 0 0
\(211\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(212\) 1.77152 5.45218i 1.77152 5.45218i
\(213\) 0.437016 + 1.34500i 0.437016 + 1.34500i
\(214\) 0 0
\(215\) 0 0
\(216\) 1.16110 + 3.57349i 1.16110 + 3.57349i
\(217\) 0 0
\(218\) −0.987688 0.717598i −0.987688 0.717598i
\(219\) −1.61803 −1.61803
\(220\) 0 0
\(221\) −1.06740 −1.06740
\(222\) 0 0
\(223\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(224\) 0 0
\(225\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(226\) 0 0
\(227\) 0.437016 + 1.34500i 0.437016 + 1.34500i 0.891007 + 0.453990i \(0.150000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(228\) −1.70582 + 5.24997i −1.70582 + 5.24997i
\(229\) −0.951057 0.690983i −0.951057 0.690983i 1.00000i \(-0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.17557 1.17557
\(233\) −1.44168 1.04744i −1.44168 1.04744i −0.987688 0.156434i \(-0.950000\pi\)
−0.453990 0.891007i \(-0.650000\pi\)
\(234\) 0.717598 2.20854i 0.717598 2.20854i
\(235\) 0 0
\(236\) −4.18391 + 3.03979i −4.18391 + 3.03979i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 1.97538i 1.97538i
\(243\) −1.00000 −1.00000
\(244\) 2.34786 + 1.70582i 2.34786 + 1.70582i
\(245\) 0 0
\(246\) 0 0
\(247\) 1.80902 1.31433i 1.80902 1.31433i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0.734572 + 0.533698i 0.734572 + 0.533698i 0.891007 0.453990i \(-0.150000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(252\) 0 0
\(253\) −0.142040 + 0.278768i −0.142040 + 0.278768i
\(254\) 0 0
\(255\) 0 0
\(256\) 1.95106 6.00473i 1.95106 6.00473i
\(257\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.0966818 + 0.297556i −0.0966818 + 0.297556i
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −3.34786 + 1.70582i −3.34786 + 1.70582i
\(265\) 0 0
\(266\) 0 0
\(267\) 0.280582 0.863541i 0.280582 0.863541i
\(268\) 0 0
\(269\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(270\) 0 0
\(271\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(272\) 1.26827 3.90333i 1.26827 3.90333i
\(273\) 0 0
\(274\) 0 0
\(275\) −0.707107 0.707107i −0.707107 0.707107i
\(276\) 0.907981 0.907981
\(277\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.253116 + 0.183900i −0.253116 + 0.183900i −0.707107 0.707107i \(-0.750000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(282\) 0 0
\(283\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(284\) 3.32037 + 2.41239i 3.32037 + 2.41239i
\(285\) 0 0
\(286\) 2.29360 + 0.363271i 2.29360 + 0.363271i
\(287\) 0 0
\(288\) 4.18391 + 3.03979i 4.18391 + 3.03979i
\(289\) −0.0542543 + 0.166977i −0.0542543 + 0.166977i
\(290\) 0 0
\(291\) 0 0
\(292\) −3.79892 + 2.76007i −3.79892 + 2.76007i
\(293\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(294\) 0.610425 1.87869i 0.610425 1.87869i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.156434 0.987688i −0.156434 0.987688i
\(298\) 0 0
\(299\) −0.297556 0.216187i −0.297556 0.216187i
\(300\) −0.896802 + 2.76007i −0.896802 + 2.76007i
\(301\) 0 0
\(302\) 0 0
\(303\) 1.14412 0.831254i 1.14412 0.831254i
\(304\) 2.65688 + 8.17702i 2.65688 + 8.17702i
\(305\) 0 0
\(306\) 1.45106 + 1.05425i 1.45106 + 1.05425i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −1.17557 −1.17557
\(310\) 0 0
\(311\) 0.437016 1.34500i 0.437016 1.34500i −0.453990 0.891007i \(-0.650000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(312\) −1.36495 4.20089i −1.36495 4.20089i
\(313\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(318\) 3.90211 3.90211
\(319\) −0.309017 0.0489435i −0.309017 0.0489435i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.533698 + 1.64255i 0.533698 + 1.64255i
\(324\) −2.34786 + 1.70582i −2.34786 + 1.70582i
\(325\) 0.951057 0.690983i 0.951057 0.690983i
\(326\) 0.717598 + 2.20854i 0.717598 + 2.20854i
\(327\) 0.190983 0.587785i 0.190983 0.587785i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(338\) −0.233162 + 0.717598i −0.233162 + 0.717598i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) −3.75739 −3.75739
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −2.26007 + 1.64204i −2.26007 + 1.64204i
\(347\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(348\) 0.280582 + 0.863541i 0.280582 + 0.863541i
\(349\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(350\) 0 0
\(351\) 1.17557 1.17557
\(352\) −2.34786 + 4.60793i −2.34786 + 4.60793i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) −2.84786 2.06909i −2.84786 2.06909i
\(355\) 0 0
\(356\) −0.814279 2.50609i −0.814279 2.50609i
\(357\) 0 0
\(358\) 0 0
\(359\) 0.550672 + 1.69480i 0.550672 + 1.69480i 0.707107 + 0.707107i \(0.250000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(360\) 0 0
\(361\) −2.11803 1.53884i −2.11803 1.53884i
\(362\) 0 0
\(363\) 0.951057 0.309017i 0.951057 0.309017i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.610425 + 1.87869i −0.610425 + 1.87869i
\(367\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(368\) 1.14412 0.831254i 1.14412 0.831254i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −0.814279 + 1.59811i −0.814279 + 1.59811i
\(375\) 0 0
\(376\) 0 0
\(377\) 0.113656 0.349798i 0.113656 0.349798i
\(378\) 0 0
\(379\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.08779 3.34786i 1.08779 3.34786i
\(383\) −0.734572 0.533698i −0.734572 0.533698i 0.156434 0.987688i \(-0.450000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(384\) 6.07958 6.07958
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.437016 1.34500i −0.437016 1.34500i −0.891007 0.453990i \(-0.850000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(390\) 0 0
\(391\) 0.229825 0.166977i 0.229825 0.166977i
\(392\) −1.16110 3.57349i −1.16110 3.57349i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −2.05210 2.05210i −2.05210 2.05210i
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0.987688 + 0.717598i 0.987688 + 0.717598i
\(399\) 0 0
\(400\) 1.39680 + 4.29892i 1.39680 + 4.29892i
\(401\) 1.59811 1.16110i 1.59811 1.16110i 0.707107 0.707107i \(-0.250000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.26827 3.90333i 1.26827 3.90333i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 3.41164 3.41164
\(409\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −2.76007 + 2.00531i −2.76007 + 2.00531i
\(413\) 0 0
\(414\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(415\) 0 0
\(416\) −4.91849 3.57349i −4.91849 3.57349i
\(417\) 0 0
\(418\) −0.587785 3.71113i −0.587785 3.71113i
\(419\) 1.97538 1.97538 0.987688 0.156434i \(-0.0500000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(420\) 0 0
\(421\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 6.00473 4.36269i 6.00473 4.36269i
\(425\) 0.280582 + 0.863541i 0.280582 + 0.863541i
\(426\) −0.863271 + 2.65688i −0.863271 + 2.65688i
\(427\) 0 0
\(428\) 0 0
\(429\) 0.183900 + 1.16110i 0.183900 + 1.16110i
\(430\) 0 0
\(431\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(432\) −1.39680 + 4.29892i −1.39680 + 4.29892i
\(433\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.554254 1.70582i −0.554254 1.70582i
\(437\) −0.183900 + 0.565985i −0.183900 + 0.565985i
\(438\) −2.58580 1.87869i −2.58580 1.87869i
\(439\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) −1.70582 1.23935i −1.70582 1.23935i
\(443\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(450\) −1.97538 −1.97538
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −0.863271 + 2.65688i −0.863271 + 2.65688i
\(455\) 0 0
\(456\) −5.78203 + 4.20089i −5.78203 + 4.20089i
\(457\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(458\) −0.717598 2.20854i −0.717598 2.20854i
\(459\) −0.280582 + 0.863541i −0.280582 + 0.863541i
\(460\) 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 \(0.900000\pi\)
\(464\) 1.14412 + 0.831254i 1.14412 + 0.831254i
\(465\) 0 0
\(466\) −1.08779 3.34786i −1.08779 3.34786i
\(467\) 1.44168 1.04744i 1.44168 1.04744i 0.453990 0.891007i \(-0.350000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(468\) 2.76007 2.00531i 2.76007 2.00531i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −6.69572 −6.69572
\(473\) 0 0
\(474\) 0 0
\(475\) −1.53884 1.11803i −1.53884 1.11803i
\(476\) 0 0
\(477\) 0.610425 + 1.87869i 0.610425 + 1.87869i
\(478\) 0 0
\(479\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.70582 2.34786i 1.70582 2.34786i
\(485\) 0 0
\(486\) −1.59811 1.16110i −1.59811 1.16110i
\(487\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(488\) 1.16110 + 3.57349i 1.16110 + 3.57349i
\(489\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(490\) 0 0
\(491\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0.229825 + 0.166977i 0.229825 + 0.166977i
\(494\) 4.41708 4.41708
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.554254 + 1.70582i 0.554254 + 1.70582i
\(503\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −0.550672 + 0.280582i −0.550672 + 0.280582i
\(507\) −0.381966 −0.381966
\(508\) 0 0
\(509\) −0.550672 + 1.69480i −0.550672 + 1.69480i 0.156434 + 0.987688i \(0.450000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 5.17160 3.75739i 5.17160 3.75739i
\(513\) −0.587785 1.80902i −0.587785 1.80902i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.14412 0.831254i −1.14412 0.831254i
\(520\) 0 0
\(521\) 0.280582 + 0.863541i 0.280582 + 0.863541i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(522\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(523\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −4.46450 0.707107i −4.46450 0.707107i
\(529\) −0.902113 −0.902113
\(530\) 0 0
\(531\) 0.550672 1.69480i 0.550672 1.69480i
\(532\) 0 0
\(533\) 0 0
\(534\) 1.45106 1.05425i 1.45106 1.05425i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.156434 + 0.987688i 0.156434 + 0.987688i
\(540\) 0 0
\(541\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(542\) 0.377263 1.16110i 0.377263 1.16110i
\(543\) 0 0
\(544\) 3.79892 2.76007i 3.79892 2.76007i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(548\) 0 0
\(549\) −1.00000 −1.00000
\(550\) −0.309017 1.95106i −0.309017 1.95106i
\(551\) −0.595112 −0.595112
\(552\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.550672 + 1.69480i 0.550672 + 1.69480i 0.707107 + 0.707107i \(0.250000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −0.896802 0.142040i −0.896802 0.142040i
\(562\) −0.618034 −0.618034
\(563\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.987688 0.717598i 0.987688 0.717598i
\(567\) 0 0
\(568\) 1.64204 + 5.05368i 1.64204 + 5.05368i
\(569\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(570\) 0 0
\(571\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(572\) 2.41239 + 2.41239i 2.41239 + 2.41239i
\(573\) 1.78201 1.78201
\(574\) 0 0
\(575\) −0.0966818 + 0.297556i −0.0966818 + 0.297556i
\(576\) 1.76007 + 5.41695i 1.76007 + 5.41695i
\(577\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(578\) −0.280582 + 0.203854i −0.280582 + 0.203854i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.76007 + 0.896802i −1.76007 + 0.896802i
\(584\) −6.07958 −6.07958
\(585\) 0 0
\(586\) 0 0
\(587\) −0.610425 1.87869i −0.610425 1.87869i −0.453990 0.891007i \(-0.650000\pi\)
−0.156434 0.987688i \(-0.550000\pi\)
\(588\) 2.34786 1.70582i 2.34786 1.70582i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.907981 −0.907981 −0.453990 0.891007i \(-0.650000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(594\) 0.896802 1.76007i 0.896802 1.76007i
\(595\) 0 0
\(596\) 0 0
\(597\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(598\) −0.224514 0.690983i −0.224514 0.690983i
\(599\) −1.59811 + 1.16110i −1.59811 + 1.16110i −0.707107 + 0.707107i \(0.750000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(600\) −3.03979 + 2.20854i −3.03979 + 2.20854i
\(601\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 2.79360 2.79360
\(607\) 1.61803 + 1.17557i 1.61803 + 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(608\) −3.03979 + 9.35552i −3.03979 + 9.35552i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.814279 + 2.50609i 0.814279 + 2.50609i
\(613\) 0.363271 1.11803i 0.363271 1.11803i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(618\) −1.87869 1.36495i −1.87869 1.36495i
\(619\) −0.587785 + 1.80902i −0.587785 + 1.80902i 1.00000i \(0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(620\) 0 0
\(621\) −0.253116 + 0.183900i −0.253116 + 0.183900i
\(622\) 2.26007 1.64204i 2.26007 1.64204i
\(623\) 0 0
\(624\) 1.64204 5.05368i 1.64204 5.05368i
\(625\) −0.809017 0.587785i −0.809017 0.587785i
\(626\) 0 0
\(627\) 1.69480 0.863541i 1.69480 0.863541i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 4.63791 + 3.36964i 4.63791 + 3.36964i
\(637\) −1.17557 −1.17557
\(638\) −0.437016 0.437016i −0.437016 0.437016i
\(639\) −1.41421 −1.41421
\(640\) 0 0
\(641\) 0.437016 1.34500i 0.437016 1.34500i −0.453990 0.891007i \(-0.650000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(642\) 0 0
\(643\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1.05425 + 3.24466i −1.05425 + 3.24466i
\(647\) −0.253116 0.183900i −0.253116 0.183900i 0.453990 0.891007i \(-0.350000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) −3.75739 −3.75739
\(649\) 1.76007 + 0.278768i 1.76007 + 0.278768i
\(650\) 2.32219 2.32219
\(651\) 0 0
\(652\) −1.05425 + 3.24466i −1.05425 + 3.24466i
\(653\) 0.550672 + 1.69480i 0.550672 + 1.69480i 0.707107 + 0.707107i \(0.250000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(654\) 0.987688 0.717598i 0.987688 0.717598i
\(655\) 0 0
\(656\) 0 0
\(657\) 0.500000 1.53884i 0.500000 1.53884i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0.329843 1.01515i 0.329843 1.01515i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0.0302487 + 0.0930960i 0.0302487 + 0.0930960i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.156434 0.987688i −0.156434 0.987688i
\(672\) 0 0
\(673\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(674\) 0 0
\(675\) −0.309017 0.951057i −0.309017 0.951057i
\(676\) −0.896802 + 0.651565i −0.896802 + 0.651565i
\(677\) −1.44168 + 1.04744i −1.44168 + 1.04744i −0.453990 + 0.891007i \(0.650000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −1.41421 −1.41421
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) −4.46589 3.24466i −4.46589 3.24466i
\(685\) 0 0
\(686\) 0 0
\(687\) 0.951057 0.690983i 0.951057 0.690983i
\(688\) 0 0
\(689\) −0.717598 2.20854i −0.717598 2.20854i
\(690\) 0 0
\(691\) 1.53884 + 1.11803i 1.53884 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(692\) −4.10421 −4.10421
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(697\) 0 0
\(698\) 0 0
\(699\) 1.44168 1.04744i 1.44168 1.04744i
\(700\) 0 0
\(701\) −0.550672 + 1.69480i −0.550672 + 1.69480i 0.156434 + 0.987688i \(0.450000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(702\) 1.87869 + 1.36495i 1.87869 + 1.36495i
\(703\) 0 0
\(704\) −5.07492 + 2.58580i −5.07492 + 2.58580i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) −1.59811 4.91849i −1.59811 4.91849i
\(709\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.05425 3.24466i 1.05425 3.24466i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) −1.08779 + 3.34786i −1.08779 + 3.34786i
\(719\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.59811 4.91849i −1.59811 4.91849i
\(723\) 0 0
\(724\) 0 0
\(725\) −0.312869 −0.312869
\(726\) 1.87869 + 0.610425i 1.87869 + 0.610425i
\(727\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(728\) 0 0
\(729\) 0.309017 0.951057i 0.309017 0.951057i
\(730\) 0 0
\(731\) 0 0
\(732\) −2.34786 + 1.70582i −2.34786 + 1.70582i
\(733\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 1.61803 1.61803
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(740\) 0 0
\(741\) 0.690983 + 2.12663i 0.690983 + 2.12663i
\(742\) 0 0
\(743\) −1.14412 + 0.831254i −1.14412 + 0.831254i −0.987688 0.156434i \(-0.950000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) −2.34786 + 1.19629i −2.34786 + 1.19629i
\(749\) 0 0
\(750\) 0 0
\(751\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(752\) 0 0
\(753\) −0.734572 + 0.533698i −0.734572 + 0.533698i
\(754\) 0.587785 0.427051i 0.587785 0.427051i
\(755\) 0 0
\(756\) 0 0
\(757\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(758\) 3.19623 3.19623
\(759\) −0.221232 0.221232i −0.221232 0.221232i
\(760\) 0 0
\(761\) 1.44168 + 1.04744i 1.44168 + 1.04744i 0.987688 + 0.156434i \(0.0500000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4.18391 3.03979i 4.18391 3.03979i
\(765\) 0 0
\(766\) −0.554254 1.70582i −0.554254 1.70582i
\(767\) −0.647354 + 1.99235i −0.647354 + 1.99235i
\(768\) 5.10793 + 3.71113i 5.10793 + 3.71113i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.863271 2.65688i 0.863271 2.65688i
\(779\) 0 0
\(780\) 0 0
\(781\) −0.221232 1.39680i −0.221232 1.39680i
\(782\) 0.561163 0.561163
\(783\) −0.253116 0.183900i −0.253116 0.183900i
\(784\) 1.39680 4.29892i 1.39680 4.29892i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −0.587785 3.71113i −0.587785 3.71113i
\(793\) 1.17557 1.17557
\(794\) 0 0
\(795\) 0 0
\(796\) 0.554254 + 1.70582i 0.554254 + 1.70582i
\(797\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.59811 + 4.91849i −1.59811 + 4.91849i
\(801\) 0.734572 + 0.533698i 0.734572 + 0.533698i
\(802\) 3.90211 3.90211
\(803\) 1.59811 + 0.253116i 1.59811 + 0.253116i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 4.29892 3.12334i 4.29892 3.12334i
\(809\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(810\) 0 0
\(811\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(812\) 0 0
\(813\) 0.618034 0.618034
\(814\) 0 0
\(815\) 0 0
\(816\) 3.32037 + 2.41239i 3.32037 + 2.41239i
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0.0966818 + 0.297556i 0.0966818 + 0.297556i 0.987688 0.156434i \(-0.0500000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(822\) 0 0
\(823\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(824\) −4.41708 −4.41708
\(825\) 0.891007 0.453990i 0.891007 0.453990i
\(826\) 0 0
\(827\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(828\) −0.280582 + 0.863541i −0.280582 + 0.863541i
\(829\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −2.06909 6.36801i −2.06909 6.36801i
\(833\) 0.280582 0.863541i 0.280582 0.863541i
\(834\) 0 0
\(835\) 0 0
\(836\) 2.50609 4.91849i 2.50609 4.91849i
\(837\) 0 0
\(838\) 3.15688 + 2.29360i 3.15688 + 2.29360i
\(839\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(840\) 0 0
\(841\) 0.729825 0.530249i 0.729825 0.530249i
\(842\) 0 0
\(843\) −0.0966818 0.297556i −0.0966818 0.297556i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 8.92899 8.92899
\(849\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(850\) −0.554254 + 1.70582i −0.554254 + 1.70582i
\(851\) 0 0
\(852\) −3.32037 + 2.41239i −3.32037 + 2.41239i
\(853\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) −1.05425 + 2.06909i −1.05425 + 2.06909i
\(859\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(864\) −4.18391 + 3.03979i −4.18391 + 3.03979i
\(865\) 0 0
\(866\) 0 0
\(867\) −0.142040 0.103198i −0.142040 0.103198i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0.717598 2.20854i 0.717598 2.20854i
\(873\) 0 0
\(874\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(875\) 0 0
\(876\) −1.45106 4.46589i −1.45106 4.46589i
\(877\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(878\) −2.58580 1.87869i −2.58580 1.87869i
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 1.59811 + 1.16110i 1.59811 + 1.16110i
\(883\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(884\) −0.957243 2.94609i −0.957243 2.94609i
\(885\) 0 0
\(886\) 0 0
\(887\) −0.550672 1.69480i −0.550672 1.69480i −0.707107 0.707107i \(-0.750000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.987688 + 0.156434i 0.987688 + 0.156434i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0.297556 0.216187i 0.297556 0.216187i
\(898\) 0 0
\(899\) 0 0
\(900\) −2.34786 1.70582i −2.34786 1.70582i
\(901\) 1.79360 1.79360
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(908\) −3.32037 + 2.41239i −3.32037 + 2.41239i
\(909\) 0.437016 + 1.34500i 0.437016 + 1.34500i
\(910\) 0 0
\(911\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(912\) −8.59783 −8.59783
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 1.05425 3.24466i 1.05425 3.24466i
\(917\) 0 0
\(918\) −1.45106 + 1.05425i −1.45106 + 1.05425i
\(919\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1.66251 1.66251
\(924\) 0 0
\(925\) 0 0
\(926\) −3.03979 2.20854i −3.03979 2.20854i
\(927\) 0.363271 1.11803i 0.363271 1.11803i
\(928\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(929\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(930\) 0 0
\(931\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(932\) 1.59811 4.91849i 1.59811 4.91849i
\(933\) 1.14412 + 0.831254i 1.14412 + 0.831254i
\(934\) 3.52015 3.52015
\(935\) 0 0
\(936\) 4.41708 4.41708
\(937\) −0.951057 0.690983i −0.951057 0.690983i 1.00000i \(-0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.59811 + 1.16110i −1.59811 + 1.16110i −0.707107 + 0.707107i \(0.750000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −6.51660 4.73459i −6.51660 4.73459i
\(945\) 0 0
\(946\) 0 0
\(947\) −1.97538 −1.97538 −0.987688 0.156434i \(-0.950000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(948\) 0 0
\(949\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(950\) −1.16110 3.57349i −1.16110 3.57349i
\(951\) 0 0
\(952\) 0 0
\(953\) 0.610425 + 1.87869i 0.610425 + 1.87869i 0.453990 + 0.891007i \(0.350000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(954\) −1.20582 + 3.71113i −1.20582 + 3.71113i
\(955\) 0 0
\(956\) 0 0
\(957\) 0.142040 0.278768i 0.142040 0.278768i
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(968\) 3.57349 1.16110i 3.57349 1.16110i
\(969\) −1.72708 −1.72708
\(970\) 0 0
\(971\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(972\) −0.896802 2.76007i −0.896802 2.76007i
\(973\) 0 0
\(974\) 2.58580 1.87869i 2.58580 1.87869i
\(975\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(976\) −1.39680 + 4.29892i −1.39680 + 4.29892i
\(977\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(978\) −2.32219 −2.32219
\(979\) −0.412215 + 0.809017i −0.412215 + 0.809017i
\(980\) 0 0
\(981\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(982\) 0 0
\(983\) 0.280582 + 0.863541i 0.280582 + 0.863541i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0.173409 + 0.533698i 0.173409 + 0.533698i
\(987\) 0 0
\(988\) 5.24997 + 3.81433i 5.24997 + 3.81433i
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(998\) 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 2013.1.bm.d.1280.4 yes 16
3.2 odd 2 inner 2013.1.bm.d.1280.1 16
11.3 even 5 inner 2013.1.bm.d.1829.4 yes 16
33.14 odd 10 inner 2013.1.bm.d.1829.1 yes 16
61.60 even 2 inner 2013.1.bm.d.1280.1 16
183.182 odd 2 CM 2013.1.bm.d.1280.4 yes 16
671.487 even 10 inner 2013.1.bm.d.1829.1 yes 16
2013.1829 odd 10 inner 2013.1.bm.d.1829.4 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.1.bm.d.1280.1 16 3.2 odd 2 inner
2013.1.bm.d.1280.1 16 61.60 even 2 inner
2013.1.bm.d.1280.4 yes 16 1.1 even 1 trivial
2013.1.bm.d.1280.4 yes 16 183.182 odd 2 CM
2013.1.bm.d.1829.1 yes 16 33.14 odd 10 inner
2013.1.bm.d.1829.1 yes 16 671.487 even 10 inner
2013.1.bm.d.1829.4 yes 16 11.3 even 5 inner
2013.1.bm.d.1829.4 yes 16 2013.1829 odd 10 inner