Properties

Label 1067.1.bg.a.824.1
Level $1067$
Weight $1$
Character 1067.824
Analytic conductor $0.533$
Analytic rank $0$
Dimension $16$
Projective image $D_{48}$
CM discriminant -11
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1067,1,Mod(32,1067)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1067, base_ring=CyclotomicField(48))
 
chi = DirichletCharacter(H, H._module([24, 37]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1067.32");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1067 = 11 \cdot 97 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1067.bg (of order \(48\), degree \(16\), 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: \(0.532502368479\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\Q(\zeta_{48})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{48}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{48} - \cdots)\)

Embedding invariants

Embedding label 824.1
Root \(0.991445 - 0.130526i\) of defining polynomial
Character \(\chi\) \(=\) 1067.824
Dual form 1067.1.bg.a.483.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.410670 + 0.315118i) q^{3} +(0.965926 - 0.258819i) q^{4} +(-1.18270 - 0.583242i) q^{5} +(-0.189469 - 0.707107i) q^{9} +O(q^{10})\) \(q+(0.410670 + 0.315118i) q^{3} +(0.965926 - 0.258819i) q^{4} +(-1.18270 - 0.583242i) q^{5} +(-0.189469 - 0.707107i) q^{9} +(0.130526 - 0.991445i) q^{11} +(0.478235 + 0.198092i) q^{12} +(-0.301908 - 0.612210i) q^{15} +(0.866025 - 0.500000i) q^{16} +(-1.29335 - 0.257264i) q^{20} +(0.665060 + 0.583242i) q^{23} +(0.449843 + 0.586247i) q^{25} +(0.343105 - 0.828328i) q^{27} +(-0.465926 + 0.607206i) q^{31} +(0.366025 - 0.366025i) q^{33} +(-0.366025 - 0.633975i) q^{36} +(1.31587 + 1.50046i) q^{37} +(-0.130526 - 0.991445i) q^{44} +(-0.188330 + 0.946800i) q^{45} +(-0.707107 - 0.707107i) q^{47} +(0.513210 + 0.0675653i) q^{48} +(-0.991445 - 0.130526i) q^{49} +(0.158919 + 1.20711i) q^{53} +(-0.732626 + 1.09645i) q^{55} +(-1.13053 + 0.991445i) q^{59} +(-0.450073 - 0.513210i) q^{60} +(0.707107 - 0.707107i) q^{64} +(0.357164 + 0.534534i) q^{67} +(0.0893301 + 0.449093i) q^{69} +(0.0420463 - 0.123864i) q^{71} +0.382507i q^{75} +(-1.31587 + 0.0862466i) q^{80} +(-0.232051 + 0.133975i) q^{81} +(0.793353 + 0.391239i) q^{92} +(-0.382683 + 0.102540i) q^{93} +(0.991445 - 0.130526i) q^{97} +(-0.725788 + 0.0955518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{15} - 8 q^{20} + 8 q^{31} - 8 q^{33} + 8 q^{36} - 24 q^{45} - 16 q^{59} + 8 q^{69} + 24 q^{81}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1067\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(486\)
\(\chi(n)\) \(e\left(\frac{7}{48}\right)\) \(-1\)

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 0 0.991445 0.130526i \(-0.0416667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(3\) 0.410670 + 0.315118i 0.410670 + 0.315118i 0.793353 0.608761i \(-0.208333\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(4\) 0.965926 0.258819i 0.965926 0.258819i
\(5\) −1.18270 0.583242i −1.18270 0.583242i −0.258819 0.965926i \(-0.583333\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(6\) 0 0
\(7\) 0 0 0.0654031 0.997859i \(-0.479167\pi\)
−0.0654031 + 0.997859i \(0.520833\pi\)
\(8\) 0 0
\(9\) −0.189469 0.707107i −0.189469 0.707107i
\(10\) 0 0
\(11\) 0.130526 0.991445i 0.130526 0.991445i
\(12\) 0.478235 + 0.198092i 0.478235 + 0.198092i
\(13\) 0 0 0.442289 0.896873i \(-0.354167\pi\)
−0.442289 + 0.896873i \(0.645833\pi\)
\(14\) 0 0
\(15\) −0.301908 0.612210i −0.301908 0.612210i
\(16\) 0.866025 0.500000i 0.866025 0.500000i
\(17\) 0 0 0.997859 0.0654031i \(-0.0208333\pi\)
−0.997859 + 0.0654031i \(0.979167\pi\)
\(18\) 0 0
\(19\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(20\) −1.29335 0.257264i −1.29335 0.257264i
\(21\) 0 0
\(22\) 0 0
\(23\) 0.665060 + 0.583242i 0.665060 + 0.583242i 0.923880 0.382683i \(-0.125000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(24\) 0 0
\(25\) 0.449843 + 0.586247i 0.449843 + 0.586247i
\(26\) 0 0
\(27\) 0.343105 0.828328i 0.343105 0.828328i
\(28\) 0 0
\(29\) 0 0 0.946930 0.321439i \(-0.104167\pi\)
−0.946930 + 0.321439i \(0.895833\pi\)
\(30\) 0 0
\(31\) −0.465926 + 0.607206i −0.465926 + 0.607206i −0.965926 0.258819i \(-0.916667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(32\) 0 0
\(33\) 0.366025 0.366025i 0.366025 0.366025i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.366025 0.633975i −0.366025 0.633975i
\(37\) 1.31587 + 1.50046i 1.31587 + 1.50046i 0.707107 + 0.707107i \(0.250000\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.321439 0.946930i \(-0.604167\pi\)
0.321439 + 0.946930i \(0.395833\pi\)
\(42\) 0 0
\(43\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(44\) −0.130526 0.991445i −0.130526 0.991445i
\(45\) −0.188330 + 0.946800i −0.188330 + 0.946800i
\(46\) 0 0
\(47\) −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(48\) 0.513210 + 0.0675653i 0.513210 + 0.0675653i
\(49\) −0.991445 0.130526i −0.991445 0.130526i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.158919 + 1.20711i 0.158919 + 1.20711i 0.866025 + 0.500000i \(0.166667\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(54\) 0 0
\(55\) −0.732626 + 1.09645i −0.732626 + 1.09645i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.13053 + 0.991445i −1.13053 + 0.991445i −0.130526 + 0.991445i \(0.541667\pi\)
−1.00000 \(\pi\)
\(60\) −0.450073 0.513210i −0.450073 0.513210i
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.707107 0.707107i 0.707107 0.707107i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.357164 + 0.534534i 0.357164 + 0.534534i 0.965926 0.258819i \(-0.0833333\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(68\) 0 0
\(69\) 0.0893301 + 0.449093i 0.0893301 + 0.449093i
\(70\) 0 0
\(71\) 0.0420463 0.123864i 0.0420463 0.123864i −0.923880 0.382683i \(-0.875000\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(72\) 0 0
\(73\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(74\) 0 0
\(75\) 0.382507i 0.382507i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(80\) −1.31587 + 0.0862466i −1.31587 + 0.0862466i
\(81\) −0.232051 + 0.133975i −0.232051 + 0.133975i
\(82\) 0 0
\(83\) 0 0 −0.0654031 0.997859i \(-0.520833\pi\)
0.0654031 + 0.997859i \(0.479167\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.793353 + 0.391239i 0.793353 + 0.391239i
\(93\) −0.382683 + 0.102540i −0.382683 + 0.102540i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.991445 0.130526i 0.991445 0.130526i
\(98\) 0 0
\(99\) −0.725788 + 0.0955518i −0.725788 + 0.0955518i
\(100\) 0.586247 + 0.449843i 0.586247 + 0.449843i
\(101\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(102\) 0 0
\(103\) −0.226078 0.130526i −0.226078 0.130526i 0.382683 0.923880i \(-0.375000\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.946930 0.321439i \(-0.895833\pi\)
0.946930 + 0.321439i \(0.104167\pi\)
\(108\) 0.117027 0.888905i 0.117027 0.888905i
\(109\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(110\) 0 0
\(111\) 0.0675653 + 1.03085i 0.0675653 + 1.03085i
\(112\) 0 0
\(113\) 1.37413 0.793353i 1.37413 0.793353i 0.382683 0.923880i \(-0.375000\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(114\) 0 0
\(115\) −0.446394 1.07769i −0.446394 1.07769i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.965926 0.258819i −0.965926 0.258819i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(125\) 0.0671594 + 0.337633i 0.0671594 + 0.337633i
\(126\) 0 0
\(127\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(132\) 0.258819 0.448288i 0.258819 0.448288i
\(133\) 0 0
\(134\) 0 0
\(135\) −0.888905 + 0.779549i −0.888905 + 0.779549i
\(136\) 0 0
\(137\) −1.95737 0.128293i −1.95737 0.128293i −0.965926 0.258819i \(-0.916667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(138\) 0 0
\(139\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(140\) 0 0
\(141\) −0.0675653 0.513210i −0.0675653 0.513210i
\(142\) 0 0
\(143\) 0 0
\(144\) −0.517638 0.517638i −0.517638 0.517638i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.366025 0.366025i −0.366025 0.366025i
\(148\) 1.65938 + 1.10876i 1.65938 + 1.10876i
\(149\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(150\) 0 0
\(151\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.905198 0.446394i 0.905198 0.446394i
\(156\) 0 0
\(157\) 1.18270 + 1.34861i 1.18270 + 1.34861i 0.923880 + 0.382683i \(0.125000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(158\) 0 0
\(159\) −0.315118 + 0.545801i −0.315118 + 0.545801i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.12484 + 1.46593i −1.12484 + 1.46593i −0.258819 + 0.965926i \(0.583333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(164\) 0 0
\(165\) −0.646379 + 0.219416i −0.646379 + 0.219416i
\(166\) 0 0
\(167\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(168\) 0 0
\(169\) −0.608761 0.793353i −0.608761 0.793353i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.659346 0.751840i \(-0.270833\pi\)
−0.659346 + 0.751840i \(0.729167\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.382683 0.923880i −0.382683 0.923880i
\(177\) −0.776695 + 0.0509073i −0.776695 + 0.0509073i
\(178\) 0 0
\(179\) 0.491445 + 0.996552i 0.491445 + 0.996552i 0.991445 + 0.130526i \(0.0416667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) 0.0631369 + 0.963282i 0.0631369 + 0.963282i
\(181\) 0.735499 1.49144i 0.735499 1.49144i −0.130526 0.991445i \(-0.541667\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.681144 2.54206i −0.681144 2.54206i
\(186\) 0 0
\(187\) 0 0
\(188\) −0.866025 0.500000i −0.866025 0.500000i
\(189\) 0 0
\(190\) 0 0
\(191\) 1.53264 + 1.17604i 1.53264 + 1.17604i 0.923880 + 0.382683i \(0.125000\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(192\) 0.513210 0.0675653i 0.513210 0.0675653i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.991445 + 0.130526i −0.991445 + 0.130526i
\(197\) 0 0 −0.793353 0.608761i \(-0.791667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(198\) 0 0
\(199\) −1.69855 0.837633i −1.69855 0.837633i −0.991445 0.130526i \(-0.958333\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(200\) 0 0
\(201\) −0.0217648 + 0.332066i −0.0217648 + 0.332066i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.286407 0.580775i 0.286407 0.580775i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.997859 0.0654031i \(-0.0208333\pi\)
−0.997859 + 0.0654031i \(0.979167\pi\)
\(212\) 0.465926 + 1.12484i 0.465926 + 1.12484i
\(213\) 0.0562991 0.0376178i 0.0562991 0.0376178i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.423880 + 1.24871i −0.423880 + 1.24871i
\(221\) 0 0
\(222\) 0 0
\(223\) −1.05217 + 0.357164i −1.05217 + 0.357164i −0.793353 0.608761i \(-0.791667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(224\) 0 0
\(225\) 0.329308 0.429162i 0.329308 0.429162i
\(226\) 0 0
\(227\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(228\) 0 0
\(229\) −0.793353 + 1.37413i −0.793353 + 1.37413i 0.130526 + 0.991445i \(0.458333\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.896873 0.442289i \(-0.145833\pi\)
−0.896873 + 0.442289i \(0.854167\pi\)
\(234\) 0 0
\(235\) 0.423880 + 1.24871i 0.423880 + 1.24871i
\(236\) −0.835400 + 1.25026i −0.835400 + 1.25026i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(240\) −0.567565 0.379235i −0.567565 0.379235i
\(241\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(242\) 0 0
\(243\) −1.02642 0.135131i −1.02642 0.135131i
\(244\) 0 0
\(245\) 1.09645 + 0.732626i 1.09645 + 0.732626i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.130526 0.00855514i −0.130526 0.00855514i 1.00000i \(-0.5\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(252\) 0 0
\(253\) 0.665060 0.583242i 0.665060 0.583242i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.500000 0.866025i 0.500000 0.866025i
\(257\) 0.382683 0.0761205i 0.382683 0.0761205i 1.00000i \(-0.5\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(264\) 0 0
\(265\) 0.516083 1.52033i 0.516083 1.52033i
\(266\) 0 0
\(267\) 0 0
\(268\) 0.483342 + 0.423880i 0.483342 + 0.423880i
\(269\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(270\) 0 0
\(271\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.639947 0.369474i 0.639947 0.369474i
\(276\) 0.202520 + 0.410670i 0.202520 + 0.410670i
\(277\) 0 0 −0.0654031 0.997859i \(-0.520833\pi\)
0.0654031 + 0.997859i \(0.479167\pi\)
\(278\) 0 0
\(279\) 0.517638 + 0.214413i 0.517638 + 0.214413i
\(280\) 0 0
\(281\) 0 0 −0.946930 0.321439i \(-0.895833\pi\)
0.946930 + 0.321439i \(0.104167\pi\)
\(282\) 0 0
\(283\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(284\) 0.00855514 0.130526i 0.00855514 0.130526i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 0.991445 0.130526i 0.991445 0.130526i
\(290\) 0 0
\(291\) 0.448288 + 0.258819i 0.448288 + 0.258819i
\(292\) 0 0
\(293\) 0 0 0.991445 0.130526i \(-0.0416667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(294\) 0 0
\(295\) 1.91532 0.513210i 1.91532 0.513210i
\(296\) 0 0
\(297\) −0.776457 0.448288i −0.776457 0.448288i
\(298\) 0 0
\(299\) 0 0
\(300\) 0.0990002 + 0.369474i 0.0990002 + 0.369474i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(308\) 0 0
\(309\) −0.0517123 0.124844i −0.0517123 0.124844i
\(310\) 0 0
\(311\) 1.75928 + 0.349942i 1.75928 + 0.349942i 0.965926 0.258819i \(-0.0833333\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(312\) 0 0
\(313\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.206647 0.608761i 0.206647 0.608761i −0.793353 0.608761i \(-0.791667\pi\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.24871 + 0.423880i −1.24871 + 0.423880i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.189469 + 0.189469i −0.189469 + 0.189469i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.65938 0.108761i −1.65938 0.108761i −0.793353 0.608761i \(-0.791667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(332\) 0 0
\(333\) 0.811670 1.21475i 0.811670 1.21475i
\(334\) 0 0
\(335\) −0.110655 0.840506i −0.110655 0.840506i
\(336\) 0 0
\(337\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(338\) 0 0
\(339\) 0.814313 + 0.107206i 0.814313 + 0.107206i
\(340\) 0 0
\(341\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0.156279 0.583242i 0.156279 0.583242i
\(346\) 0 0
\(347\) 0 0 −0.321439 0.946930i \(-0.604167\pi\)
0.321439 + 0.946930i \(0.395833\pi\)
\(348\) 0 0
\(349\) 0 0 0.896873 0.442289i \(-0.145833\pi\)
−0.896873 + 0.442289i \(0.854167\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.923880 1.60021i 0.923880 1.60021i 0.130526 0.991445i \(-0.458333\pi\)
0.793353 0.608761i \(-0.208333\pi\)
\(354\) 0 0
\(355\) −0.121971 + 0.121971i −0.121971 + 0.121971i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.946930 0.321439i \(-0.104167\pi\)
−0.946930 + 0.321439i \(0.895833\pi\)
\(360\) 0 0
\(361\) 0.382683 0.923880i 0.382683 0.923880i
\(362\) 0 0
\(363\) −0.315118 0.410670i −0.315118 0.410670i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0.0862466 0.0983454i 0.0862466 0.0983454i −0.707107 0.707107i \(-0.750000\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(368\) 0.867580 + 0.172572i 0.867580 + 0.172572i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −0.343105 + 0.198092i −0.343105 + 0.198092i
\(373\) 0 0 −0.442289 0.896873i \(-0.645833\pi\)
0.442289 + 0.896873i \(0.354167\pi\)
\(374\) 0 0
\(375\) −0.0788139 + 0.159819i −0.0788139 + 0.159819i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.478235 1.78480i −0.478235 1.78480i −0.608761 0.793353i \(-0.708333\pi\)
0.130526 0.991445i \(-0.458333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.75928 + 0.867580i 1.75928 + 0.867580i 0.965926 + 0.258819i \(0.0833333\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.923880 0.382683i 0.923880 0.382683i
\(389\) −1.58671 −1.58671 −0.793353 0.608761i \(-0.791667\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −0.676327 + 0.280144i −0.676327 + 0.280144i
\(397\) −0.500000 1.86603i −0.500000 1.86603i −0.500000 0.866025i \(-0.666667\pi\)
1.00000i \(-0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.682699 + 0.282783i 0.682699 + 0.282783i
\(401\) 0.284338 0.576581i 0.284338 0.576581i −0.707107 0.707107i \(-0.750000\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.352586 0.0231097i 0.352586 0.0231097i
\(406\) 0 0
\(407\) 1.65938 1.10876i 1.65938 1.10876i
\(408\) 0 0
\(409\) 0 0 0.659346 0.751840i \(-0.270833\pi\)
−0.659346 + 0.751840i \(0.729167\pi\)
\(410\) 0 0
\(411\) −0.763406 0.669489i −0.763406 0.669489i
\(412\) −0.252157 0.0675653i −0.252157 0.0675653i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.20711 1.57313i 1.20711 1.57313i 0.500000 0.866025i \(-0.333333\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(420\) 0 0
\(421\) 1.40211 1.40211i 1.40211 1.40211i 0.608761 0.793353i \(-0.291667\pi\)
0.793353 0.608761i \(-0.208333\pi\)
\(422\) 0 0
\(423\) −0.366025 + 0.633975i −0.366025 + 0.633975i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(432\) −0.117027 0.888905i −0.117027 0.888905i
\(433\) 0.0255190 0.128293i 0.0255190 0.128293i −0.965926 0.258819i \(-0.916667\pi\)
0.991445 + 0.130526i \(0.0416667\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(440\) 0 0
\(441\) 0.0955518 + 0.725788i 0.0955518 + 0.725788i
\(442\) 0 0
\(443\) −0.835400 + 1.25026i −0.835400 + 1.25026i 0.130526 + 0.991445i \(0.458333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(444\) 0.332066 + 0.978235i 0.332066 + 0.978235i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.965926 1.67303i −0.965926 1.67303i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 0.965926i \(-0.583333\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 1.12197 1.12197i 1.12197 1.12197i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.710111 0.925435i −0.710111 0.925435i
\(461\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(462\) 0 0
\(463\) 1.21752i 1.21752i 0.793353 + 0.608761i \(0.208333\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(464\) 0 0
\(465\) 0.512405 + 0.101924i 0.512405 + 0.101924i
\(466\) 0 0
\(467\) 0.758819 + 1.83195i 0.758819 + 1.83195i 0.500000 + 0.866025i \(0.333333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0.0607275 + 0.926523i 0.0607275 + 0.926523i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.823443 0.341081i 0.823443 0.341081i
\(478\) 0 0
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.00000 −1.00000
\(485\) −1.24871 0.423880i −1.24871 0.423880i
\(486\) 0 0
\(487\) −0.991445 + 0.130526i −0.991445 + 0.130526i −0.608761 0.793353i \(-0.708333\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(488\) 0 0
\(489\) −0.923880 + 0.247553i −0.923880 + 0.247553i
\(490\) 0 0
\(491\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0.914118 + 0.310301i 0.914118 + 0.310301i
\(496\) −0.0999004 + 0.758819i −0.0999004 + 0.758819i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.128293 + 1.95737i 0.128293 + 1.95737i 0.258819 + 0.965926i \(0.416667\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(500\) 0.152257 + 0.308746i 0.152257 + 0.308746i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.517638i 0.517638i
\(508\) 0 0
\(509\) −1.91532 0.513210i −1.91532 0.513210i −0.991445 0.130526i \(-0.958333\pi\)
−0.923880 0.382683i \(-0.875000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.191254 + 0.286231i 0.191254 + 0.286231i
\(516\) 0 0
\(517\) −0.793353 + 0.608761i −0.793353 + 0.608761i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.965926 + 1.67303i 0.965926 + 1.67303i 0.707107 + 0.707107i \(0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(522\) 0 0
\(523\) 0 0 0.751840 0.659346i \(-0.229167\pi\)
−0.751840 + 0.659346i \(0.770833\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0.133975 0.500000i 0.133975 0.500000i
\(529\) −0.0283924 0.215662i −0.0283924 0.215662i
\(530\) 0 0
\(531\) 0.915257 + 0.611555i 0.915257 + 0.611555i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −0.112210 + 0.564117i −0.112210 + 0.564117i
\(538\) 0 0
\(539\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(540\) −0.656854 + 0.983052i −0.656854 + 0.983052i
\(541\) 0 0 −0.321439 0.946930i \(-0.604167\pi\)
0.321439 + 0.946930i \(0.395833\pi\)
\(542\) 0 0
\(543\) 0.772029 0.380722i 0.772029 0.380722i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) −1.92388 + 0.382683i −1.92388 + 0.382683i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.521325 1.25859i 0.521325 1.25859i
\(556\) 0 0
\(557\) 0 0 −0.608761 0.793353i \(-0.708333\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(564\) −0.198092 0.478235i −0.198092 0.478235i
\(565\) −2.08790 + 0.136848i −2.08790 + 0.136848i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.442289 0.896873i \(-0.354167\pi\)
−0.442289 + 0.896873i \(0.645833\pi\)
\(570\) 0 0
\(571\) 0 0 0.130526 0.991445i \(-0.458333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(572\) 0 0
\(573\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(574\) 0 0
\(575\) −0.0427512 + 0.652257i −0.0427512 + 0.652257i
\(576\) −0.633975 0.366025i −0.633975 0.366025i
\(577\) −0.349942 0.172572i −0.349942 0.172572i 0.258819 0.965926i \(-0.416667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.21752 1.21752
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.49144 0.735499i −1.49144 0.735499i −0.500000 0.866025i \(-0.666667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(588\) −0.448288 0.258819i −0.448288 0.258819i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.88981 + 0.641502i 1.88981 + 0.641502i
\(593\) 0 0 0.130526 0.991445i \(-0.458333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.433591 0.879235i −0.433591 0.879235i
\(598\) 0 0
\(599\) −1.99144 + 0.130526i −1.99144 + 0.130526i −0.991445 + 0.130526i \(0.958333\pi\)
−1.00000 \(1.00000\pi\)
\(600\) 0 0
\(601\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(602\) 0 0
\(603\) 0.310301 0.353831i 0.310301 0.353831i
\(604\) 0 0
\(605\) 0.991445 + 0.869474i 0.991445 + 0.869474i
\(606\) 0 0
\(607\) 0 0 −0.608761 0.793353i \(-0.708333\pi\)
0.608761 + 0.793353i \(0.291667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.608761 0.793353i \(-0.291667\pi\)
−0.608761 + 0.793353i \(0.708333\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.793353 1.37413i 0.793353 1.37413i −0.130526 0.991445i \(-0.541667\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(618\) 0 0
\(619\) −1.24871 1.42388i −1.24871 1.42388i −0.866025 0.500000i \(-0.833333\pi\)
−0.382683 0.923880i \(-0.625000\pi\)
\(620\) 0.758819 0.665466i 0.758819 0.665466i
\(621\) 0.711301 0.350775i 0.711301 0.350775i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.308746 1.15226i 0.308746 1.15226i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.49144 + 0.996552i 1.49144 + 0.996552i
\(629\) 0 0
\(630\) 0 0
\(631\) 0.991445 + 0.130526i 0.991445 + 0.130526i 0.608761 0.793353i \(-0.291667\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −0.163117 + 0.608761i −0.163117 + 0.608761i
\(637\) 0 0
\(638\) 0 0
\(639\) −0.0955518 0.00626280i −0.0955518 0.00626280i
\(640\) 0 0
\(641\) 0.293353 0.257264i 0.293353 0.257264i −0.500000 0.866025i \(-0.666667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(642\) 0 0
\(643\) 0.991445 + 1.71723i 0.991445 + 1.71723i 0.608761 + 0.793353i \(0.291667\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.57313 + 1.20711i −1.57313 + 1.20711i −0.707107 + 0.707107i \(0.750000\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) 0 0
\(649\) 0.835400 + 1.25026i 0.835400 + 1.25026i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(653\) 0.483342 1.42388i 0.483342 1.42388i −0.382683 0.923880i \(-0.625000\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(660\) −0.567565 + 0.379235i −0.567565 + 0.379235i
\(661\) 0.465926 + 1.12484i 0.465926 + 1.12484i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −0.544645 0.184882i −0.544645 0.184882i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(674\) 0 0
\(675\) 0.639947 0.171473i 0.639947 0.171473i
\(676\) −0.793353 0.608761i −0.793353 0.608761i
\(677\) 0 0 0.991445 0.130526i \(-0.0416667\pi\)
−0.991445 + 0.130526i \(0.958333\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.739288 + 0.198092i −0.739288 + 0.198092i −0.608761 0.793353i \(-0.708333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(684\) 0 0
\(685\) 2.24015 + 1.29335i 2.24015 + 1.29335i
\(686\) 0 0
\(687\) −0.758819 + 0.314313i −0.758819 + 0.314313i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 1.30656 + 0.541196i 1.30656 + 0.541196i 0.923880 0.382683i \(-0.125000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.608761 0.793353i −0.608761 0.793353i
\(705\) −0.219416 + 0.646379i −0.219416 + 0.646379i
\(706\) 0 0
\(707\) 0 0
\(708\) −0.737054 + 0.250196i −0.737054 + 0.250196i
\(709\) −0.923880 1.38268i −0.923880 1.38268i −0.923880 0.382683i \(-0.875000\pi\)
1.00000i \(-0.5\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.664017 + 0.132081i −0.664017 + 0.132081i
\(714\) 0 0
\(715\) 0 0
\(716\) 0.732626 + 0.835400i 0.732626 + 0.835400i
\(717\) 0 0
\(718\) 0 0
\(719\) −0.389345 0.0255190i −0.389345 0.0255190i −0.130526 0.991445i \(-0.541667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(720\) 0.310301 + 0.914118i 0.310301 + 0.914118i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0.324423 1.63099i 0.324423 1.63099i
\(725\) 0 0
\(726\) 0 0
\(727\) −1.20711 0.158919i −1.20711 0.158919i −0.500000 0.866025i \(-0.666667\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(728\) 0 0
\(729\) −0.189469 0.189469i −0.189469 0.189469i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(734\) 0 0
\(735\) 0.219416 + 0.646379i 0.219416 + 0.646379i
\(736\) 0 0
\(737\) 0.576581 0.284338i 0.576581 0.284338i
\(738\) 0 0
\(739\) 0 0 −0.659346 0.751840i \(-0.729167\pi\)
0.659346 + 0.751840i \(0.270833\pi\)
\(740\) −1.31587 2.27915i −1.31587 2.27915i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.12484 1.46593i −1.12484 1.46593i −0.866025 0.500000i \(-0.833333\pi\)
−0.258819 0.965926i \(-0.583333\pi\)
\(752\) −0.965926 0.258819i −0.965926 0.258819i
\(753\) −0.0509073 0.0446445i −0.0509073 0.0446445i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.57469 + 1.05217i −1.57469 + 1.05217i −0.608761 + 0.793353i \(0.708333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(758\) 0 0
\(759\) 0.456911 0.0299475i 0.456911 0.0299475i
\(760\) 0 0
\(761\) 0 0 −0.442289 0.896873i \(-0.645833\pi\)
0.442289 + 0.896873i \(0.354167\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1.78480 + 0.739288i 1.78480 + 0.739288i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.478235 0.198092i 0.478235 0.198092i
\(769\) 0 0 0.0654031 0.997859i \(-0.479167\pi\)
−0.0654031 + 0.997859i \(0.520833\pi\)
\(770\) 0 0
\(771\) 0.181144 + 0.0893301i 0.181144 + 0.0893301i
\(772\) 0 0
\(773\) 1.46593 + 1.12484i 1.46593 + 1.12484i 0.965926 + 0.258819i \(0.0833333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(774\) 0 0
\(775\) −0.565566 −0.565566
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −0.117317 0.0578541i −0.117317 0.0578541i
\(782\) 0 0
\(783\) 0 0
\(784\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(785\) −0.612210 2.28480i −0.612210 2.28480i
\(786\) 0 0
\(787\) 0 0 0.130526 0.991445i \(-0.458333\pi\)
−0.130526 + 0.991445i \(0.541667\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0.691024 0.461727i 0.691024 0.461727i
\(796\) −1.85747 0.369474i −1.85747 0.369474i
\(797\) −1.31587 + 1.50046i −1.31587 + 1.50046i −0.608761 + 0.793353i \(0.708333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0.0649219 + 0.326384i 0.0649219 + 0.326384i
\(805\) 0 0
\(806\) 0 0
\(807\) −0.545801 + 0.711301i −0.545801 + 0.711301i
\(808\) 0 0
\(809\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(810\) 0 0
\(811\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2.18534 1.07769i 2.18534 1.07769i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(822\) 0 0
\(823\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0.379235 + 0.0499272i 0.379235 + 0.0499272i
\(826\) 0 0
\(827\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(828\) 0.126332 0.635113i 0.126332 0.635113i
\(829\) 0.0675653 + 0.513210i 0.0675653 + 0.513210i 0.991445 + 0.130526i \(0.0416667\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0.343105 + 0.594275i 0.343105 + 0.594275i
\(838\) 0 0
\(839\) −1.75928 + 0.349942i −1.75928 + 0.349942i −0.965926 0.258819i \(-0.916667\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(840\) 0 0
\(841\) 0.793353 0.608761i 0.793353 0.608761i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0.257264 + 1.29335i 0.257264 + 1.29335i
\(846\) 0 0
\(847\) 0 0
\(848\) 0.741181 + 0.965926i 0.741181 + 0.965926i
\(849\) 0 0
\(850\) 0 0
\(851\) 1.76537i 1.76537i
\(852\) 0.0446445 0.0509073i 0.0446445 0.0509073i
\(853\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(858\) 0 0
\(859\) −0.0983454 1.50046i −0.0983454 1.50046i −0.707107 0.707107i \(-0.750000\pi\)
0.608761 0.793353i \(-0.291667\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.85747 0.630526i −1.85747 0.630526i −0.991445 0.130526i \(-0.958333\pi\)
−0.866025 0.500000i \(-0.833333\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0.448288 + 0.258819i 0.448288 + 0.258819i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −0.280144 0.676327i −0.280144 0.676327i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −0.0862466 + 1.31587i −0.0862466 + 1.31587i
\(881\) −1.70711 + 0.707107i −1.70711 + 0.707107i −0.707107 + 0.707107i \(0.750000\pi\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) −1.88981 0.641502i −1.88981 0.641502i −0.965926 0.258819i \(-0.916667\pi\)
−0.923880 0.382683i \(-0.875000\pi\)
\(884\) 0 0
\(885\) 0.948288 + 0.392794i 0.948288 + 0.392794i
\(886\) 0 0
\(887\) 0 0 −0.0654031 0.997859i \(-0.520833\pi\)
0.0654031 + 0.997859i \(0.479167\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.102540 + 0.247553i 0.102540 + 0.247553i
\(892\) −0.923880 + 0.617317i −0.923880 + 0.617317i
\(893\) 0 0
\(894\) 0 0
\(895\) 1.46525i 1.46525i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0.207012 0.499770i 0.207012 0.499770i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.73975 + 1.33496i −1.73975 + 1.33496i
\(906\) 0 0
\(907\) −0.382683 + 0.0761205i −0.382683 + 0.0761205i −0.382683 0.923880i \(-0.625000\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.50046 1.31587i 1.50046 1.31587i 0.707107 0.707107i \(-0.250000\pi\)
0.793353 0.608761i \(-0.208333\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.410670 + 1.53264i −0.410670 + 1.53264i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −0.287706 + 1.44639i −0.287706 + 1.44639i
\(926\) 0 0
\(927\) −0.0494613 + 0.184592i −0.0494613 + 0.184592i
\(928\) 0 0
\(929\) 0.0420463 + 0.123864i 0.0420463 + 0.123864i 0.965926 0.258819i \(-0.0833333\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0.612210 + 0.698092i 0.612210 + 0.698092i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(938\) 0 0
\(939\) 0.545801 0.711301i 0.545801 0.711301i
\(940\) 0.732626 + 1.09645i 0.732626 + 1.09645i
\(941\) 0 0 0.946930 0.321439i \(-0.104167\pi\)
−0.946930 + 0.321439i \(0.895833\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −0.483342 + 1.42388i −0.483342 + 1.42388i
\(945\) 0 0
\(946\) 0 0
\(947\) −0.293353 0.257264i −0.293353 0.257264i 0.500000 0.866025i \(-0.333333\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0.276695 0.184882i 0.276695 0.184882i
\(952\) 0 0
\(953\) 0 0 0.997859 0.0654031i \(-0.0208333\pi\)
−0.997859 + 0.0654031i \(0.979167\pi\)
\(954\) 0 0
\(955\) −1.12674 2.28480i −1.12674 2.28480i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −0.646379 0.219416i −0.646379 0.219416i
\(961\) 0.107206 + 0.400100i 0.107206 + 0.400100i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 −0.793353 0.608761i \(-0.791667\pi\)
0.793353 + 0.608761i \(0.208333\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(972\) −1.02642 + 0.135131i −1.02642 + 0.135131i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −0.123864 + 1.88981i −0.123864 + 1.88981i 0.258819 + 0.965926i \(0.416667\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 1.24871 + 0.423880i 1.24871 + 0.423880i
\(981\) 0 0
\(982\) 0 0
\(983\) 0.837633 1.69855i 0.837633 1.69855i 0.130526 0.991445i \(-0.458333\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −1.29335 + 1.47479i −1.29335 + 1.47479i −0.500000 + 0.866025i \(0.666667\pi\)
−0.793353 + 0.608761i \(0.791667\pi\)
\(992\) 0 0
\(993\) −0.647184 0.567565i −0.647184 0.567565i
\(994\) 0 0
\(995\) 1.52033 + 1.98133i 1.52033 + 1.98133i
\(996\) 0 0
\(997\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(998\) 0 0
\(999\) 1.69435 0.575155i 1.69435 0.575155i
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 1067.1.bg.a.824.1 yes 16
11.10 odd 2 CM 1067.1.bg.a.824.1 yes 16
97.95 even 48 inner 1067.1.bg.a.483.1 16
1067.483 odd 48 inner 1067.1.bg.a.483.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1067.1.bg.a.483.1 16 97.95 even 48 inner
1067.1.bg.a.483.1 16 1067.483 odd 48 inner
1067.1.bg.a.824.1 yes 16 1.1 even 1 trivial
1067.1.bg.a.824.1 yes 16 11.10 odd 2 CM