Properties

Label 1859.1.k.a.1374.3
Level $1859$
Weight $1$
Character 1859.1374
Analytic conductor $0.928$
Analytic rank $0$
Dimension $6$
Projective image $D_{7}$
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] = [1859,1,Mod(1374,1859)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1859, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1859.1374");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1859.k (of order \(6\), degree \(2\), not 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: \(0.927761858485\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.64827.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{7}\)
Projective field: Galois closure of 7.1.6424482779.1
Artin image: $C_3\times D_7$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{21} - \cdots)\)

Embedding invariants

Embedding label 1374.3
Root \(-0.623490 + 1.07992i\) of defining polynomial
Character \(\chi\) \(=\) 1859.1374
Dual form 1859.1.k.a.1836.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.900969 - 1.56052i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.24698 q^{5} +(-1.12349 - 1.94594i) q^{9} +O(q^{10})\) \(q+(0.900969 - 1.56052i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.24698 q^{5} +(-1.12349 - 1.94594i) q^{9} +(-0.500000 + 0.866025i) q^{11} -1.80194 q^{12} +(1.12349 - 1.94594i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.623490 - 1.07992i) q^{20} +(0.222521 - 0.385418i) q^{23} +0.554958 q^{25} -2.24698 q^{27} -0.445042 q^{31} +(0.900969 + 1.56052i) q^{33} +(-1.12349 + 1.94594i) q^{36} +(0.900969 - 1.56052i) q^{37} +1.00000 q^{44} +(-1.40097 - 2.42655i) q^{45} -0.445042 q^{47} +(0.900969 + 1.56052i) q^{48} +(-0.500000 + 0.866025i) q^{49} +1.24698 q^{53} +(-0.623490 + 1.07992i) q^{55} +(0.900969 + 1.56052i) q^{59} -2.24698 q^{60} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{67} +(-0.400969 - 0.694498i) q^{69} +(0.900969 + 1.56052i) q^{71} +(0.500000 - 0.866025i) q^{75} +(-0.623490 + 1.07992i) q^{80} +(-0.900969 + 1.56052i) q^{81} +(0.222521 - 0.385418i) q^{89} -0.445042 q^{92} +(-0.400969 + 0.694498i) q^{93} +(-0.623490 - 1.07992i) q^{97} +2.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{3} - 3 q^{4} - 2 q^{5} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{3} - 3 q^{4} - 2 q^{5} - 2 q^{9} - 3 q^{11} - 2 q^{12} + 2 q^{15} - 3 q^{16} + q^{20} + q^{23} + 4 q^{25} - 4 q^{27} - 2 q^{31} + q^{33} - 2 q^{36} + q^{37} + 6 q^{44} - 4 q^{45} - 2 q^{47} + q^{48} - 3 q^{49} - 2 q^{53} + q^{55} + q^{59} - 4 q^{60} + 6 q^{64} - 6 q^{67} + 2 q^{69} + q^{71} + 3 q^{75} + q^{80} - q^{81} + q^{89} - 2 q^{92} + 2 q^{93} + q^{97} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1859\mathbb{Z}\right)^\times\).

\(n\) \(508\) \(1354\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(4\) −0.500000 0.866025i −0.500000 0.866025i
\(5\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(6\) 0 0
\(7\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(8\) 0 0
\(9\) −1.12349 1.94594i −1.12349 1.94594i
\(10\) 0 0
\(11\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(12\) −1.80194 −1.80194
\(13\) 0 0
\(14\) 0 0
\(15\) 1.12349 1.94594i 1.12349 1.94594i
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 0 0
\(19\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) −0.623490 1.07992i −0.623490 1.07992i
\(21\) 0 0
\(22\) 0 0
\(23\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(24\) 0 0
\(25\) 0.554958 0.554958
\(26\) 0 0
\(27\) −2.24698 −2.24698
\(28\) 0 0
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(32\) 0 0
\(33\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(34\) 0 0
\(35\) 0 0
\(36\) −1.12349 + 1.94594i −1.12349 + 1.94594i
\(37\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0 0
\(43\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(44\) 1.00000 1.00000
\(45\) −1.40097 2.42655i −1.40097 2.42655i
\(46\) 0 0
\(47\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(48\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(49\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(54\) 0 0
\(55\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(60\) −2.24698 −2.24698
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) −0.400969 0.694498i −0.400969 0.694498i
\(70\) 0 0
\(71\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0.500000 0.866025i 0.500000 0.866025i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(81\) −0.900969 + 1.56052i −0.900969 + 1.56052i
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.445042 −0.445042
\(93\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(98\) 0 0
\(99\) 2.24698 2.24698
\(100\) −0.277479 0.480608i −0.277479 0.480608i
\(101\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(102\) 0 0
\(103\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(108\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −1.62349 2.81197i −1.62349 2.81197i
\(112\) 0 0
\(113\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(114\) 0 0
\(115\) 0.277479 0.480608i 0.277479 0.480608i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.500000 0.866025i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(125\) −0.554958 −0.554958
\(126\) 0 0
\(127\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0.900969 1.56052i 0.900969 1.56052i
\(133\) 0 0
\(134\) 0 0
\(135\) −2.80194 −2.80194
\(136\) 0 0
\(137\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(138\) 0 0
\(139\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(140\) 0 0
\(141\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(142\) 0 0
\(143\) 0 0
\(144\) 2.24698 2.24698
\(145\) 0 0
\(146\) 0 0
\(147\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(148\) −1.80194 −1.80194
\(149\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.554958 −0.554958
\(156\) 0 0
\(157\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(158\) 0 0
\(159\) 1.12349 1.94594i 1.12349 1.94594i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(164\) 0 0
\(165\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(166\) 0 0
\(167\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.500000 0.866025i −0.500000 0.866025i
\(177\) 3.24698 3.24698
\(178\) 0 0
\(179\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(180\) −1.40097 + 2.42655i −1.40097 + 2.42655i
\(181\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.12349 1.94594i 1.12349 1.94594i
\(186\) 0 0
\(187\) 0 0
\(188\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(189\) 0 0
\(190\) 0 0
\(191\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(192\) 0.900969 1.56052i 0.900969 1.56052i
\(193\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.00000 1.00000
\(197\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) 0 0
\(199\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(200\) 0 0
\(201\) 1.80194 + 3.12105i 1.80194 + 3.12105i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.00000 −1.00000
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(212\) −0.623490 1.07992i −0.623490 1.07992i
\(213\) 3.24698 3.24698
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 1.24698 1.24698
\(221\) 0 0
\(222\) 0 0
\(223\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(224\) 0 0
\(225\) −0.623490 1.07992i −0.623490 1.07992i
\(226\) 0 0
\(227\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) 0 0
\(229\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −0.554958 −0.554958
\(236\) 0.900969 1.56052i 0.900969 1.56052i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(244\) 0 0
\(245\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(252\) 0 0
\(253\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.500000 0.866025i
\(257\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) 1.55496 1.55496
\(266\) 0 0
\(267\) −0.400969 0.694498i −0.400969 0.694498i
\(268\) 2.00000 2.00000
\(269\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(270\) 0 0
\(271\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(276\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(277\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(278\) 0 0
\(279\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(284\) 0.900969 1.56052i 0.900969 1.56052i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(290\) 0 0
\(291\) −2.24698 −2.24698
\(292\) 0 0
\(293\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(294\) 0 0
\(295\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(296\) 0 0
\(297\) 1.12349 1.94594i 1.12349 1.94594i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.00000 −1.00000
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 1.12349 1.94594i 1.12349 1.94594i
\(310\) 0 0
\(311\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(312\) 0 0
\(313\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.24698 1.24698
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.80194 1.80194
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(332\) 0 0
\(333\) −4.04892 −4.04892
\(334\) 0 0
\(335\) −1.24698 + 2.15983i −1.24698 + 2.15983i
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) −2.24698 −2.24698
\(340\) 0 0
\(341\) 0.222521 0.385418i 0.222521 0.385418i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −0.500000 0.866025i −0.500000 0.866025i
\(346\) 0 0
\(347\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(348\) 0 0
\(349\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(354\) 0 0
\(355\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(356\) −0.445042 −0.445042
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(362\) 0 0
\(363\) −1.80194 −1.80194
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(368\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0.801938 0.801938
\(373\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(374\) 0 0
\(375\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(389\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −1.12349 1.94594i −1.12349 1.94594i
\(397\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.277479 + 0.480608i −0.277479 + 0.480608i
\(401\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.12349 + 1.94594i −1.12349 + 1.94594i
\(406\) 0 0
\(407\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(408\) 0 0
\(409\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(410\) 0 0
\(411\) 0.801938 0.801938
\(412\) −0.623490 1.07992i −0.623490 1.07992i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(420\) 0 0
\(421\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(422\) 0 0
\(423\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 1.12349 1.94594i 1.12349 1.94594i
\(433\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 2.24698 2.24698
\(442\) 0 0
\(443\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(444\) −1.62349 + 2.81197i −1.62349 + 2.81197i
\(445\) 0.277479 0.480608i 0.277479 0.480608i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.554958 −0.554958
\(461\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 0 0
\(463\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(464\) 0 0
\(465\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(466\) 0 0
\(467\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.62349 + 2.81197i −1.62349 + 2.81197i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.40097 2.42655i −1.40097 2.42655i
\(478\) 0 0
\(479\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(485\) −0.777479 1.34663i −0.777479 1.34663i
\(486\) 0 0
\(487\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(488\) 0 0
\(489\) 0.801938 0.801938
\(490\) 0 0
\(491\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 2.80194 2.80194
\(496\) 0.222521 0.385418i 0.222521 0.385418i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(500\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.55496 1.55496
\(516\) 0 0
\(517\) 0.222521 0.385418i 0.222521 0.385418i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(522\) 0 0
\(523\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1.80194 −1.80194
\(529\) 0.400969 + 0.694498i 0.400969 + 0.694498i
\(530\) 0 0
\(531\) 2.02446 3.50647i 2.02446 3.50647i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.62349 2.81197i −1.62349 2.81197i
\(538\) 0 0
\(539\) −0.500000 0.866025i −0.500000 0.866025i
\(540\) 1.40097 + 2.42655i 1.40097 + 2.42655i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0.222521 0.385418i 0.222521 0.385418i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −2.02446 3.50647i −2.02446 3.50647i
\(556\) 0 0
\(557\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(564\) 0.801938 0.801938
\(565\) −0.777479 1.34663i −0.777479 1.34663i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0.801938 0.801938
\(574\) 0 0
\(575\) 0.123490 0.213891i 0.123490 0.213891i
\(576\) −1.12349 1.94594i −1.12349 1.94594i
\(577\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(588\) 0.900969 1.56052i 0.900969 1.56052i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 3.24698 3.24698
\(598\) 0 0
\(599\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(600\) 0 0
\(601\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 4.49396 4.49396
\(604\) 0 0
\(605\) −0.623490 1.07992i −0.623490 1.07992i
\(606\) 0 0
\(607\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(618\) 0 0
\(619\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(620\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(621\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −1.24698 −1.24698
\(626\) 0 0
\(627\) 0 0
\(628\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(629\) 0 0
\(630\) 0 0
\(631\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) −2.24698 −2.24698
\(637\) 0 0
\(638\) 0 0
\(639\) 2.02446 3.50647i 2.02446 3.50647i
\(640\) 0 0
\(641\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(642\) 0 0
\(643\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(648\) 0 0
\(649\) −1.80194 −1.80194
\(650\) 0 0
\(651\) 0 0
\(652\) 0.222521 0.385418i 0.222521 0.385418i
\(653\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(660\) 1.12349 1.94594i 1.12349 1.94594i
\(661\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−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
\(669\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) 0 0
\(675\) −1.24698 −1.24698
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(684\) 0 0
\(685\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(686\) 0 0
\(687\) −1.62349 + 2.81197i −1.62349 + 2.81197i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(692\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(705\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(706\) 0 0
\(707\) 0 0
\(708\) −1.62349 2.81197i −1.62349 2.81197i
\(709\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.0990311 + 0.171527i −0.0990311 + 0.171527i
\(714\) 0 0
\(715\) 0 0
\(716\) −1.80194 −1.80194
\(717\) 0 0
\(718\) 0 0
\(719\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(720\) 2.80194 2.80194
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(725\) 0 0
\(726\) 0 0
\(727\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(736\) 0 0
\(737\) −1.00000 1.73205i −1.00000 1.73205i
\(738\) 0 0
\(739\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) −2.24698 −2.24698
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(752\) 0.222521 0.385418i 0.222521 0.385418i
\(753\) −2.24698 −2.24698
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(758\) 0 0
\(759\) 0.801938 0.801938
\(760\) 0 0
\(761\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.222521 0.385418i 0.222521 0.385418i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1.80194 −1.80194
\(769\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) −1.62349 2.81197i −1.62349 2.81197i
\(772\) 0 0
\(773\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(774\) 0 0
\(775\) −0.246980 −0.246980
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −1.80194 −1.80194
\(782\) 0 0
\(783\) 0 0
\(784\) −0.500000 0.866025i −0.500000 0.866025i
\(785\) −2.24698 −2.24698
\(786\) 0 0
\(787\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 1.40097 2.42655i 1.40097 2.42655i
\(796\) 0.900969 1.56052i 0.900969 1.56052i
\(797\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −1.00000 −1.00000
\(802\) 0 0
\(803\) 0 0
\(804\) 1.80194 3.12105i 1.80194 3.12105i
\(805\) 0 0
\(806\) 0 0
\(807\) 3.24698 3.24698
\(808\) 0 0
\(809\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(822\) 0 0
\(823\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(824\) 0 0
\(825\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(829\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.00000 1.00000
\(838\) 0 0
\(839\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(840\) 0 0
\(841\) −0.500000 0.866025i −0.500000 0.866025i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(849\) 0 0
\(850\) 0 0
\(851\) −0.400969 0.694498i −0.400969 0.694498i
\(852\) −1.62349 2.81197i −1.62349 2.81197i
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −1.40097 + 2.42655i −1.40097 + 2.42655i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −0.623490 1.07992i −0.623490 1.07992i
\(881\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(882\) 0 0
\(883\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(884\) 0 0
\(885\) 4.04892 4.04892
\(886\) 0 0
\(887\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.900969 1.56052i −0.900969 1.56052i
\(892\) 1.24698 1.24698
\(893\) 0 0
\(894\) 0 0
\(895\) 1.12349 1.94594i 1.12349 1.94594i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −0.554958 −0.554958
\(906\) 0 0
\(907\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0.500000 0.866025i 0.500000 0.866025i
\(926\) 0 0
\(927\) −1.40097 2.42655i −1.40097 2.42655i
\(928\) 0 0
\(929\) −0.623490 1.07992i −0.623490 1.07992i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.400969 + 0.694498i −0.400969 + 0.694498i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 1.12349 1.94594i 1.12349 1.94594i
\(940\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −1.80194 −1.80194
\(945\) 0 0
\(946\) 0 0
\(947\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −1.62349 + 2.81197i −1.62349 + 2.81197i
\(952\) 0 0
\(953\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(954\) 0 0
\(955\) 0.277479 + 0.480608i 0.277479 + 0.480608i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.12349 1.94594i 1.12349 1.94594i
\(961\) −0.801938 −0.801938
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(972\) 0.500000 0.866025i 0.500000 0.866025i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(978\) 0 0
\(979\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(980\) 1.24698 1.24698
\(981\) 0 0
\(982\) 0 0
\(983\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(992\) 0 0
\(993\) −2.24698 −2.24698
\(994\) 0 0
\(995\) 1.12349 + 1.94594i 1.12349 + 1.94594i
\(996\) 0 0
\(997\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(998\) 0 0
\(999\) −2.02446 + 3.50647i −2.02446 + 3.50647i
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 1859.1.k.a.1374.3 6
11.10 odd 2 CM 1859.1.k.a.1374.3 6
13.2 odd 12 1859.1.i.c.868.5 12
13.3 even 3 inner 1859.1.k.a.1836.3 6
13.4 even 6 1859.1.c.b.846.1 yes 3
13.5 odd 4 1859.1.i.c.1330.5 12
13.6 odd 12 1859.1.d.a.1858.1 6
13.7 odd 12 1859.1.d.a.1858.2 6
13.8 odd 4 1859.1.i.c.1330.6 12
13.9 even 3 1859.1.c.a.846.1 3
13.10 even 6 1859.1.k.b.1836.3 6
13.11 odd 12 1859.1.i.c.868.6 12
13.12 even 2 1859.1.k.b.1374.3 6
143.10 odd 6 1859.1.k.b.1836.3 6
143.21 even 4 1859.1.i.c.1330.6 12
143.32 even 12 1859.1.d.a.1858.1 6
143.43 odd 6 1859.1.c.b.846.1 yes 3
143.54 even 12 1859.1.i.c.868.5 12
143.76 even 12 1859.1.i.c.868.6 12
143.87 odd 6 1859.1.c.a.846.1 3
143.98 even 12 1859.1.d.a.1858.2 6
143.109 even 4 1859.1.i.c.1330.5 12
143.120 odd 6 inner 1859.1.k.a.1836.3 6
143.142 odd 2 1859.1.k.b.1374.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.1.c.a.846.1 3 13.9 even 3
1859.1.c.a.846.1 3 143.87 odd 6
1859.1.c.b.846.1 yes 3 13.4 even 6
1859.1.c.b.846.1 yes 3 143.43 odd 6
1859.1.d.a.1858.1 6 13.6 odd 12
1859.1.d.a.1858.1 6 143.32 even 12
1859.1.d.a.1858.2 6 13.7 odd 12
1859.1.d.a.1858.2 6 143.98 even 12
1859.1.i.c.868.5 12 13.2 odd 12
1859.1.i.c.868.5 12 143.54 even 12
1859.1.i.c.868.6 12 13.11 odd 12
1859.1.i.c.868.6 12 143.76 even 12
1859.1.i.c.1330.5 12 13.5 odd 4
1859.1.i.c.1330.5 12 143.109 even 4
1859.1.i.c.1330.6 12 13.8 odd 4
1859.1.i.c.1330.6 12 143.21 even 4
1859.1.k.a.1374.3 6 1.1 even 1 trivial
1859.1.k.a.1374.3 6 11.10 odd 2 CM
1859.1.k.a.1836.3 6 13.3 even 3 inner
1859.1.k.a.1836.3 6 143.120 odd 6 inner
1859.1.k.b.1374.3 6 13.12 even 2
1859.1.k.b.1374.3 6 143.142 odd 2
1859.1.k.b.1836.3 6 13.10 even 6
1859.1.k.b.1836.3 6 143.10 odd 6