Properties

Label 817.1.bz.a.56.1
Level $817$
Weight $1$
Character 817.56
Analytic conductor $0.408$
Analytic rank $0$
Dimension $12$
Projective image $D_{21}$
CM discriminant -19
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [817,1,Mod(56,817)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(817, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 32]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("817.56");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 817 = 19 \cdot 43 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 817.bz (of order \(42\), degree \(12\), 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: \(0.407736115321\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\Q(\zeta_{21})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{21}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{21} - \cdots)\)

Embedding invariants

Embedding label 56.1
Root \(-0.733052 + 0.680173i\) of defining polynomial
Character \(\chi\) \(=\) 817.56
Dual form 817.1.bz.a.569.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.900969 - 0.433884i) q^{4} +(0.440071 + 0.0663300i) q^{5} +(-0.955573 + 1.65510i) q^{7} +(0.0747301 - 0.997204i) q^{9} +O(q^{10})\) \(q+(-0.900969 - 0.433884i) q^{4} +(0.440071 + 0.0663300i) q^{5} +(-0.955573 + 1.65510i) q^{7} +(0.0747301 - 0.997204i) q^{9} +(1.78181 - 0.858075i) q^{11} +(0.623490 + 0.781831i) q^{16} +(1.44973 - 0.218511i) q^{17} +(0.0747301 + 0.997204i) q^{19} +(-0.367711 - 0.250701i) q^{20} +(0.603718 + 0.411608i) q^{23} +(-0.766310 - 0.236375i) q^{25} +(1.57906 - 1.07659i) q^{28} +(-0.530303 + 0.664979i) q^{35} +(-0.500000 + 0.866025i) q^{36} +1.00000 q^{43} -1.97766 q^{44} +(0.0990311 - 0.433884i) q^{45} +(-1.12349 - 0.541044i) q^{47} +(-1.32624 - 2.29711i) q^{49} +(0.841040 - 0.259426i) q^{55} +(-1.40097 - 0.432142i) q^{61} +(1.57906 + 1.07659i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(-1.40097 - 0.432142i) q^{68} +(0.455573 + 1.16078i) q^{73} +(0.365341 - 0.930874i) q^{76} +(-0.282450 + 3.76903i) q^{77} +(0.222521 + 0.385418i) q^{80} +(-0.988831 - 0.149042i) q^{81} +(-1.40097 + 1.29991i) q^{83} +0.652478 q^{85} +(-0.365341 - 0.632789i) q^{92} +(-0.0332580 + 0.443797i) q^{95} +(-0.722521 - 1.84095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{4} + 2 q^{5} - q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{4} + 2 q^{5} - q^{7} + q^{9} + 2 q^{11} - 2 q^{16} - q^{17} + q^{19} + 2 q^{20} - q^{23} + 3 q^{25} - q^{28} + 4 q^{35} - 6 q^{36} + 12 q^{43} + 2 q^{44} + 10 q^{45} - 4 q^{47} - 7 q^{49} - 2 q^{55} - 8 q^{61} - q^{63} - 2 q^{64} - 8 q^{68} - 5 q^{73} + q^{76} - 6 q^{77} + 2 q^{80} + q^{81} - 8 q^{83} - 10 q^{85} - q^{92} + 2 q^{95} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/817\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(476\)
\(\chi(n)\) \(-1\) \(e\left(\frac{16}{21}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(3\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(4\) −0.900969 0.433884i −0.900969 0.433884i
\(5\) 0.440071 + 0.0663300i 0.440071 + 0.0663300i 0.365341 0.930874i \(-0.380952\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(6\) 0 0
\(7\) −0.955573 + 1.65510i −0.955573 + 1.65510i −0.222521 + 0.974928i \(0.571429\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(8\) 0 0
\(9\) 0.0747301 0.997204i 0.0747301 0.997204i
\(10\) 0 0
\(11\) 1.78181 0.858075i 1.78181 0.858075i 0.826239 0.563320i \(-0.190476\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(12\) 0 0
\(13\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(17\) 1.44973 0.218511i 1.44973 0.218511i 0.623490 0.781831i \(-0.285714\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(18\) 0 0
\(19\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(20\) −0.367711 0.250701i −0.367711 0.250701i
\(21\) 0 0
\(22\) 0 0
\(23\) 0.603718 + 0.411608i 0.603718 + 0.411608i 0.826239 0.563320i \(-0.190476\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(24\) 0 0
\(25\) −0.766310 0.236375i −0.766310 0.236375i
\(26\) 0 0
\(27\) 0 0
\(28\) 1.57906 1.07659i 1.57906 1.07659i
\(29\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(30\) 0 0
\(31\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.530303 + 0.664979i −0.530303 + 0.664979i
\(36\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(42\) 0 0
\(43\) 1.00000 1.00000
\(44\) −1.97766 −1.97766
\(45\) 0.0990311 0.433884i 0.0990311 0.433884i
\(46\) 0 0
\(47\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(48\) 0 0
\(49\) −1.32624 2.29711i −1.32624 2.29711i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(54\) 0 0
\(55\) 0.841040 0.259426i 0.841040 0.259426i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(60\) 0 0
\(61\) −1.40097 0.432142i −1.40097 0.432142i −0.500000 0.866025i \(-0.666667\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(62\) 0 0
\(63\) 1.57906 + 1.07659i 1.57906 + 1.07659i
\(64\) −0.222521 0.974928i −0.222521 0.974928i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(68\) −1.40097 0.432142i −1.40097 0.432142i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(72\) 0 0
\(73\) 0.455573 + 1.16078i 0.455573 + 1.16078i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0.365341 0.930874i 0.365341 0.930874i
\(77\) −0.282450 + 3.76903i −0.282450 + 3.76903i
\(78\) 0 0
\(79\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(81\) −0.988831 0.149042i −0.988831 0.149042i
\(82\) 0 0
\(83\) −1.40097 + 1.29991i −1.40097 + 1.29991i −0.500000 + 0.866025i \(0.666667\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(84\) 0 0
\(85\) 0.652478 0.652478
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.365341 0.632789i −0.365341 0.632789i
\(93\) 0 0
\(94\) 0 0
\(95\) −0.0332580 + 0.443797i −0.0332580 + 0.443797i
\(96\) 0 0
\(97\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(98\) 0 0
\(99\) −0.722521 1.84095i −0.722521 1.84095i
\(100\) 0.587862 + 0.545456i 0.587862 + 0.545456i
\(101\) −0.367711 + 0.250701i −0.367711 + 0.250701i −0.733052 0.680173i \(-0.761905\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(102\) 0 0
\(103\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(108\) 0 0
\(109\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.88980 + 0.284841i −1.88980 + 0.284841i
\(113\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(114\) 0 0
\(115\) 0.238377 + 0.221181i 0.238377 + 0.221181i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.02366 + 2.60825i −1.02366 + 2.60825i
\(120\) 0 0
\(121\) 1.81507 2.27603i 1.81507 2.27603i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −0.722521 0.347948i −0.722521 0.347948i
\(126\) 0 0
\(127\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.222521 0.974928i 0.222521 0.974928i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(132\) 0 0
\(133\) −1.72188 0.829215i −1.72188 0.829215i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.03030 1.29196i 1.03030 1.29196i 0.0747301 0.997204i \(-0.476190\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(138\) 0 0
\(139\) −0.162592 + 0.414278i −0.162592 + 0.414278i −0.988831 0.149042i \(-0.952381\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(140\) 0.766310 0.369035i 0.766310 0.369035i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0.826239 0.563320i 0.826239 0.563320i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.21135 0.825886i −1.21135 0.825886i −0.222521 0.974928i \(-0.571429\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(150\) 0 0
\(151\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(152\) 0 0
\(153\) −0.109562 1.46200i −0.109562 1.46200i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.48883 + 1.01507i −1.48883 + 1.01507i −0.500000 + 0.866025i \(0.666667\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.25815 + 0.605893i −1.25815 + 0.605893i
\(162\) 0 0
\(163\) 0.0546039 0.728639i 0.0546039 0.728639i −0.900969 0.433884i \(-0.857143\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(168\) 0 0
\(169\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(170\) 0 0
\(171\) 1.00000 1.00000
\(172\) −0.900969 0.433884i −0.900969 0.433884i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 1.12349 1.04245i 1.12349 1.04245i
\(176\) 1.78181 + 0.858075i 1.78181 + 0.858075i
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(181\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.39564 1.63332i 2.39564 1.63332i
\(188\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(189\) 0 0
\(190\) 0 0
\(191\) 0.0546039 + 0.728639i 0.0546039 + 0.728639i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(192\) 0 0
\(193\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.198220 + 2.64506i 0.198220 + 2.64506i
\(197\) 1.57906 + 0.487076i 1.57906 + 0.487076i 0.955573 0.294755i \(-0.0952381\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(198\) 0 0
\(199\) 0.0931869 + 0.116853i 0.0931869 + 0.116853i 0.826239 0.563320i \(-0.190476\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.455573 0.571270i 0.455573 0.571270i
\(208\) 0 0
\(209\) 0.988831 + 1.71271i 0.988831 + 1.71271i
\(210\) 0 0
\(211\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.440071 + 0.0663300i 0.440071 + 0.0663300i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.870312 0.131178i −0.870312 0.131178i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(224\) 0 0
\(225\) −0.292981 + 0.746503i −0.292981 + 0.746503i
\(226\) 0 0
\(227\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(228\) 0 0
\(229\) −0.914101 0.848162i −0.914101 0.848162i 0.0747301 0.997204i \(-0.476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i 0.365341 0.930874i \(-0.380952\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(234\) 0 0
\(235\) −0.458528 0.312619i −0.458528 0.312619i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.0931869 + 1.24349i 0.0931869 + 1.24349i 0.826239 + 0.563320i \(0.190476\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(240\) 0 0
\(241\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 1.07473 + 0.997204i 1.07473 + 0.997204i
\(245\) −0.431272 1.09886i −0.431272 1.09886i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.0747301 + 0.129436i −0.0747301 + 0.129436i −0.900969 0.433884i \(-0.857143\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(252\) −0.955573 1.65510i −0.955573 1.65510i
\(253\) 1.42890 + 0.215372i 1.42890 + 0.215372i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.63402 0.246289i −1.63402 0.246289i −0.733052 0.680173i \(-0.761905\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(270\) 0 0
\(271\) −0.365341 0.930874i −0.365341 0.930874i −0.988831 0.149042i \(-0.952381\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(272\) 1.07473 + 0.997204i 1.07473 + 0.997204i
\(273\) 0 0
\(274\) 0 0
\(275\) −1.56825 + 0.236375i −1.56825 + 0.236375i
\(276\) 0 0
\(277\) −0.0747301 0.997204i −0.0747301 0.997204i −0.900969 0.433884i \(-0.857143\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(282\) 0 0
\(283\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i 0.365341 0.930874i \(-0.380952\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.09839 0.338809i 1.09839 0.338809i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.0931869 1.24349i 0.0931869 1.24349i
\(293\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −0.955573 + 1.65510i −0.955573 + 1.65510i
\(302\) 0 0
\(303\) 0 0
\(304\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(305\) −0.587862 0.283099i −0.587862 0.283099i
\(306\) 0 0
\(307\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(308\) 1.88980 3.27323i 1.88980 3.27323i
\(309\) 0 0
\(310\) 0 0
\(311\) 0.698220 1.77904i 0.698220 1.77904i 0.0747301 0.997204i \(-0.476190\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(312\) 0 0
\(313\) −0.955573 + 0.294755i −0.955573 + 0.294755i −0.733052 0.680173i \(-0.761905\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(314\) 0 0
\(315\) 0.623490 + 0.578514i 0.623490 + 0.578514i
\(316\) 0 0
\(317\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.0332580 0.443797i −0.0332580 0.443797i
\(321\) 0 0
\(322\) 0 0
\(323\) 0.326239 + 1.42935i 0.326239 + 1.42935i
\(324\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.96906 1.34248i 1.96906 1.34248i
\(330\) 0 0
\(331\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(332\) 1.82624 0.563320i 1.82624 0.563320i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −0.587862 0.283099i −0.587862 0.283099i
\(341\) 0 0
\(342\) 0 0
\(343\) 3.15813 3.15813
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.109562 + 0.101659i −0.109562 + 0.101659i −0.733052 0.680173i \(-0.761905\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(348\) 0 0
\(349\) 1.78181 + 0.268565i 1.78181 + 0.268565i 0.955573 0.294755i \(-0.0952381\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −0.134659 + 1.79690i −0.134659 + 1.79690i 0.365341 + 0.930874i \(0.380952\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.826239 + 0.563320i −0.826239 + 0.563320i −0.900969 0.433884i \(-0.857143\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(360\) 0 0
\(361\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.123490 + 0.541044i 0.123490 + 0.541044i
\(366\) 0 0
\(367\) −0.367711 0.250701i −0.367711 0.250701i 0.365341 0.930874i \(-0.380952\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(368\) 0.0546039 + 0.728639i 0.0546039 + 0.728639i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(380\) 0.222521 0.385418i 0.222521 0.385418i
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(384\) 0 0
\(385\) −0.374298 + 1.63991i −0.374298 + 1.63991i
\(386\) 0 0
\(387\) 0.0747301 0.997204i 0.0747301 0.997204i
\(388\) 0 0
\(389\) 0.440071 1.92808i 0.440071 1.92808i 0.0747301 0.997204i \(-0.476190\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(390\) 0 0
\(391\) 0.965168 + 0.464800i 0.965168 + 0.464800i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −0.147791 + 1.97213i −0.147791 + 1.97213i
\(397\) 0.0546039 0.139129i 0.0546039 0.139129i −0.900969 0.433884i \(-0.857143\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.292981 0.746503i −0.292981 0.746503i
\(401\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.440071 0.0663300i 0.440071 0.0663300i
\(405\) −0.425270 0.131178i −0.425270 0.131178i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −0.702749 + 0.479126i −0.702749 + 0.479126i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.48883 + 0.716983i −1.48883 + 0.716983i −0.988831 0.149042i \(-0.952381\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0 0
\(421\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(422\) 0 0
\(423\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(424\) 0 0
\(425\) −1.16259 0.175233i −1.16259 0.175233i
\(426\) 0 0
\(427\) 2.05397 1.90580i 2.05397 1.90580i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.365341 + 0.632789i −0.365341 + 0.632789i
\(438\) 0 0
\(439\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(440\) 0 0
\(441\) −2.38980 + 1.15087i −2.38980 + 1.15087i
\(442\) 0 0
\(443\) 0.266948 + 0.680173i 0.266948 + 0.680173i 1.00000 \(0\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 1.82624 + 0.563320i 1.82624 + 0.563320i
\(449\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.23305 1.54620i −1.23305 1.54620i −0.733052 0.680173i \(-0.761905\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.118803 0.302705i −0.118803 0.302705i
\(461\) 1.57906 0.487076i 1.57906 0.487076i 0.623490 0.781831i \(-0.285714\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(462\) 0 0
\(463\) −0.535628 + 1.36476i −0.535628 + 1.36476i 0.365341 + 0.930874i \(0.380952\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.78181 0.858075i 1.78181 0.858075i
\(474\) 0 0
\(475\) 0.178448 0.781831i 0.178448 0.781831i
\(476\) 2.05397 1.90580i 2.05397 1.90580i
\(477\) 0 0
\(478\) 0 0
\(479\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −2.62285 + 1.26310i −2.62285 + 1.26310i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.19158 + 0.367554i 1.19158 + 0.367554i 0.826239 0.563320i \(-0.190476\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −0.195850 0.858075i −0.195850 0.858075i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1.23305 + 0.185853i −1.23305 + 0.185853i −0.733052 0.680173i \(-0.761905\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(501\) 0 0
\(502\) 0 0
\(503\) −0.722521 1.84095i −0.722521 1.84095i −0.500000 0.866025i \(-0.666667\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(504\) 0 0
\(505\) −0.178448 + 0.0859360i −0.178448 + 0.0859360i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) 0 0
\(511\) −2.35654 0.355192i −2.35654 0.355192i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −2.46610 −2.46610
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(522\) 0 0
\(523\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.170287 0.433884i −0.170287 0.433884i
\(530\) 0 0
\(531\) 0 0
\(532\) 1.19158 + 1.49419i 1.19158 + 1.49419i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.33420 2.95501i −4.33420 2.95501i
\(540\) 0 0
\(541\) 0.698220 + 0.215372i 0.698220 + 0.215372i 0.623490 0.781831i \(-0.285714\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(548\) −1.48883 + 0.716983i −1.48883 + 0.716983i
\(549\) −0.535628 + 1.36476i −0.535628 + 1.36476i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0.326239 0.302705i 0.326239 0.302705i
\(557\) −0.0332580 + 0.145713i −0.0332580 + 0.145713i −0.988831 0.149042i \(-0.952381\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.850540 −0.850540
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.19158 1.49419i 1.19158 1.49419i
\(568\) 0 0
\(569\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(570\) 0 0
\(571\) −1.88980 + 0.582926i −1.88980 + 0.582926i −0.900969 + 0.433884i \(0.857143\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.365341 0.458123i −0.365341 0.458123i
\(576\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(577\) 0.698220 + 0.215372i 0.698220 + 0.215372i 0.623490 0.781831i \(-0.285714\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.812753 3.56090i −0.812753 3.56090i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.21135 + 0.825886i −1.21135 + 0.825886i −0.988831 0.149042i \(-0.952381\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.109562 + 1.46200i −0.109562 + 1.46200i 0.623490 + 0.781831i \(0.285714\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(594\) 0 0
\(595\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(596\) 0.733052 + 1.26968i 0.733052 + 1.26968i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.949729 0.881219i 0.949729 0.881219i
\(606\) 0 0
\(607\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.535628 + 1.36476i −0.535628 + 1.36476i
\(613\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.48883 + 1.01507i −1.48883 + 1.01507i −0.500000 + 0.866025i \(0.666667\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(618\) 0 0
\(619\) 0.988831 0.149042i 0.988831 0.149042i 0.365341 0.930874i \(-0.380952\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.367711 + 0.250701i 0.367711 + 0.250701i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.78181 0.268565i 1.78181 0.268565i
\(629\) 0 0
\(630\) 0 0
\(631\) 1.32091 + 1.22563i 1.32091 + 1.22563i 0.955573 + 0.294755i \(0.0952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(642\) 0 0
\(643\) −0.162592 + 0.712362i −0.162592 + 0.712362i 0.826239 + 0.563320i \(0.190476\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(644\) 1.39644 1.39644
\(645\) 0 0
\(646\) 0 0
\(647\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.365341 + 0.632789i −0.365341 + 0.632789i
\(653\) 0.455573 0.571270i 0.455573 0.571270i −0.500000 0.866025i \(-0.666667\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(654\) 0 0
\(655\) 0.162592 0.414278i 0.162592 0.414278i
\(656\) 0 0
\(657\) 1.19158 0.367554i 1.19158 0.367554i
\(658\) 0 0
\(659\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(660\) 0 0
\(661\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.702749 0.479126i −0.702749 0.479126i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.86707 + 0.432142i −2.86707 + 0.432142i
\(672\) 0 0
\(673\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0.955573 0.294755i 0.955573 0.294755i
\(677\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(684\) −0.900969 0.433884i −0.900969 0.433884i
\(685\) 0.539102 0.500214i 0.539102 0.500214i
\(686\) 0 0
\(687\) 0 0
\(688\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(689\) 0 0
\(690\) 0 0
\(691\) −1.21135 + 1.12397i −1.21135 + 1.12397i −0.222521 + 0.974928i \(0.571429\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(692\) 0 0
\(693\) 3.73738 + 0.563320i 3.73738 + 0.563320i
\(694\) 0 0
\(695\) −0.0990311 + 0.171527i −0.0990311 + 0.171527i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.46453 + 0.451748i −1.46453 + 0.451748i
\(701\) −0.658322 1.67738i −0.658322 1.67738i −0.733052 0.680173i \(-0.761905\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.23305 1.54620i −1.23305 1.54620i
\(705\) 0 0
\(706\) 0 0
\(707\) −0.0635609 0.848162i −0.0635609 0.848162i
\(708\) 0 0
\(709\) −0.425270 1.86323i −0.425270 1.86323i −0.500000 0.866025i \(-0.666667\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.57906 0.487076i 1.57906 0.487076i 0.623490 0.781831i \(-0.285714\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(720\) 0.400969 0.193096i 0.400969 0.193096i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.32091 + 0.636119i 1.32091 + 0.636119i 0.955573 0.294755i \(-0.0952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(728\) 0 0
\(729\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(730\) 0 0
\(731\) 1.44973 0.218511i 1.44973 0.218511i
\(732\) 0 0
\(733\) −0.0332580 + 0.145713i −0.0332580 + 0.145713i −0.988831 0.149042i \(-0.952381\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.455573 0.571270i 0.455573 0.571270i −0.500000 0.866025i \(-0.666667\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(744\) 0 0
\(745\) −0.478300 0.443797i −0.478300 0.443797i
\(746\) 0 0
\(747\) 1.19158 + 1.49419i 1.19158 + 1.49419i
\(748\) −2.86707 + 0.432142i −2.86707 + 0.432142i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(752\) −0.277479 1.21572i −0.277479 1.21572i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.95557 0.294755i 1.95557 0.294755i 0.955573 0.294755i \(-0.0952381\pi\)
1.00000 \(0\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.266948 + 0.680173i 0.266948 + 0.680173i 1.00000 \(0\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.266948 0.680173i 0.266948 0.680173i
\(765\) 0.0487597 0.650653i 0.0487597 0.650653i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 1.44973 + 0.218511i 1.44973 + 0.218511i 0.826239 0.563320i \(-0.190476\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.969059 2.46912i 0.969059 2.46912i
\(785\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(786\) 0 0
\(787\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(788\) −1.21135 1.12397i −1.21135 1.12397i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −0.0332580 0.145713i −0.0332580 0.145713i
\(797\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(798\) 0 0
\(799\) −1.74698 0.538872i −1.74698 0.538872i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.80778 + 1.67738i 1.80778 + 1.67738i
\(804\) 0 0
\(805\) −0.593864 + 0.183183i −0.593864 + 0.183183i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −0.914101 + 1.14625i −0.914101 + 1.14625i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(810\) 0 0
\(811\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0.0723603 0.317031i 0.0723603 0.317031i
\(816\) 0 0
\(817\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −0.658322 0.317031i −0.658322 0.317031i 0.0747301 0.997204i \(-0.476190\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(822\) 0 0
\(823\) −0.0747301 0.129436i −0.0747301 0.129436i 0.826239 0.563320i \(-0.190476\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(828\) −0.658322 + 0.317031i −0.658322 + 0.317031i
\(829\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.42463 3.04039i −2.42463 3.04039i
\(834\) 0 0
\(835\) 0 0
\(836\) −0.147791 1.97213i −0.147791 1.97213i
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(840\) 0 0
\(841\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −0.367711 + 0.250701i −0.367711 + 0.250701i
\(846\) 0 0
\(847\) 2.03262 + 5.17903i 2.03262 + 5.17903i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0.988831 1.71271i 0.988831 1.71271i 0.365341 0.930874i \(-0.380952\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(854\) 0 0
\(855\) 0.440071 + 0.0663300i 0.440071 + 0.0663300i
\(856\) 0 0
\(857\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(858\) 0 0
\(859\) −1.97766 −1.97766 −0.988831 0.149042i \(-0.952381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(860\) −0.367711 0.250701i −0.367711 0.250701i
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.26631 0.863355i 1.26631 0.863355i
\(876\) 0 0
\(877\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0.727208 + 0.495802i 0.727208 + 0.495802i
\(881\) 0.222521 + 0.974928i 0.222521 + 0.974928i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(882\) 0 0
\(883\) −1.63402 1.11406i −1.63402 1.11406i −0.900969 0.433884i \(-0.857143\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.88980 + 0.582926i −1.88980 + 0.582926i
\(892\) 0 0
\(893\) 0.455573 1.16078i 0.455573 1.16078i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0.587862 0.545456i 0.587862 0.545456i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(908\) 0 0
\(909\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(910\) 0 0
\(911\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(912\) 0 0
\(913\) −1.38084 + 3.51833i −1.38084 + 3.51833i
\(914\) 0 0
\(915\) 0 0
\(916\) 0.455573 + 1.16078i 0.455573 + 1.16078i
\(917\) 1.40097 + 1.29991i 1.40097 + 1.29991i
\(918\) 0 0
\(919\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.78181 0.268565i 1.78181 0.268565i 0.826239 0.563320i \(-0.190476\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(930\) 0 0
\(931\) 2.19158 1.49419i 2.19158 1.49419i
\(932\) −0.109562 0.101659i −0.109562 0.101659i
\(933\) 0 0
\(934\) 0 0
\(935\) 1.16259 0.559875i 1.16259 0.559875i
\(936\) 0 0
\(937\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i 0.826239 + 0.563320i \(0.190476\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(941\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(954\) 0 0
\(955\) −0.0243010 + 0.324275i −0.0243010 + 0.324275i
\(956\) 0.455573 1.16078i 0.455573 1.16078i
\(957\) 0 0
\(958\) 0 0
\(959\) 1.15379 + 2.93982i 1.15379 + 2.93982i
\(960\) 0 0
\(961\) 0.826239 0.563320i 0.826239 0.563320i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0.326239 + 1.42935i 0.326239 + 1.42935i 0.826239 + 0.563320i \(0.190476\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(972\) 0 0
\(973\) −0.530303 0.664979i −0.530303 0.664979i
\(974\) 0 0
\(975\) 0 0
\(976\) −0.535628 1.36476i −0.535628 1.36476i
\(977\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −0.0882162 + 1.17716i −0.0882162 + 1.17716i
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(984\) 0 0
\(985\) 0.662592 + 0.319088i 0.662592 + 0.319088i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.603718 + 0.411608i 0.603718 + 0.411608i
\(990\) 0 0
\(991\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0.0332580 + 0.0576046i 0.0332580 + 0.0576046i
\(996\) 0 0
\(997\) 1.03030 1.29196i 1.03030 1.29196i 0.0747301 0.997204i \(-0.476190\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(998\) 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 817.1.bz.a.56.1 12
19.18 odd 2 CM 817.1.bz.a.56.1 12
43.10 even 21 inner 817.1.bz.a.569.1 yes 12
817.569 odd 42 inner 817.1.bz.a.569.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
817.1.bz.a.56.1 12 1.1 even 1 trivial
817.1.bz.a.56.1 12 19.18 odd 2 CM
817.1.bz.a.569.1 yes 12 43.10 even 21 inner
817.1.bz.a.569.1 yes 12 817.569 odd 42 inner