Properties

Label 799.1.e.a.140.1
Level $799$
Weight $1$
Character 799.140
Analytic conductor $0.399$
Analytic rank $0$
Dimension $2$
Projective image $D_{4}$
CM discriminant -47
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [799,1,Mod(140,799)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(799, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("799.140");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 799.e (of order \(4\), degree \(2\), 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: \(0.398752945094\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{4}\)
Projective field: Galois closure of 4.2.230911.1

Embedding invariants

Embedding label 140.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 799.140
Dual form 799.1.e.a.234.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000i q^{2} +(1.00000 - 1.00000i) q^{3} -3.00000 q^{4} +(-2.00000 - 2.00000i) q^{6} +(-1.00000 - 1.00000i) q^{7} +4.00000i q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-2.00000i q^{2} +(1.00000 - 1.00000i) q^{3} -3.00000 q^{4} +(-2.00000 - 2.00000i) q^{6} +(-1.00000 - 1.00000i) q^{7} +4.00000i q^{8} -1.00000i q^{9} +(-3.00000 + 3.00000i) q^{12} +(-2.00000 + 2.00000i) q^{14} +5.00000 q^{16} +1.00000 q^{17} -2.00000 q^{18} -2.00000 q^{21} +(4.00000 + 4.00000i) q^{24} -1.00000i q^{25} +(3.00000 + 3.00000i) q^{28} -6.00000i q^{32} -2.00000i q^{34} +3.00000i q^{36} +(-1.00000 + 1.00000i) q^{37} +4.00000i q^{42} -1.00000 q^{47} +(5.00000 - 5.00000i) q^{48} +1.00000i q^{49} -2.00000 q^{50} +(1.00000 - 1.00000i) q^{51} +(4.00000 - 4.00000i) q^{56} -2.00000i q^{59} +(1.00000 + 1.00000i) q^{61} +(-1.00000 + 1.00000i) q^{63} -7.00000 q^{64} -3.00000 q^{68} +(1.00000 - 1.00000i) q^{71} +4.00000 q^{72} +(2.00000 + 2.00000i) q^{74} +(-1.00000 - 1.00000i) q^{75} +(1.00000 + 1.00000i) q^{79} +1.00000 q^{81} +6.00000 q^{84} +2.00000 q^{89} +2.00000i q^{94} +(-6.00000 - 6.00000i) q^{96} +(-1.00000 + 1.00000i) q^{97} +2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} - 6 q^{4} - 4 q^{6} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} - 6 q^{4} - 4 q^{6} - 2 q^{7} - 6 q^{12} - 4 q^{14} + 10 q^{16} + 2 q^{17} - 4 q^{18} - 4 q^{21} + 8 q^{24} + 6 q^{28} - 2 q^{37} - 2 q^{47} + 10 q^{48} - 4 q^{50} + 2 q^{51} + 8 q^{56} + 2 q^{61} - 2 q^{63} - 14 q^{64} - 6 q^{68} + 2 q^{71} + 8 q^{72} + 4 q^{74} - 2 q^{75} + 2 q^{79} + 2 q^{81} + 12 q^{84} + 4 q^{89} - 12 q^{96} - 2 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/799\mathbb{Z}\right)^\times\).

\(n\) \(52\) \(377\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(3\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(4\) −3.00000 −3.00000
\(5\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(6\) −2.00000 2.00000i −2.00000 2.00000i
\(7\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(8\) 4.00000i 4.00000i
\(9\) 1.00000i 1.00000i
\(10\) 0 0
\(11\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(12\) −3.00000 + 3.00000i −3.00000 + 3.00000i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(15\) 0 0
\(16\) 5.00000 5.00000
\(17\) 1.00000 1.00000
\(18\) −2.00000 −2.00000
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) −2.00000 −2.00000
\(22\) 0 0
\(23\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(24\) 4.00000 + 4.00000i 4.00000 + 4.00000i
\(25\) 1.00000i 1.00000i
\(26\) 0 0
\(27\) 0 0
\(28\) 3.00000 + 3.00000i 3.00000 + 3.00000i
\(29\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(30\) 0 0
\(31\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(32\) 6.00000i 6.00000i
\(33\) 0 0
\(34\) 2.00000i 2.00000i
\(35\) 0 0
\(36\) 3.00000i 3.00000i
\(37\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(42\) 4.00000i 4.00000i
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.00000 −1.00000
\(48\) 5.00000 5.00000i 5.00000 5.00000i
\(49\) 1.00000i 1.00000i
\(50\) −2.00000 −2.00000
\(51\) 1.00000 1.00000i 1.00000 1.00000i
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 4.00000 4.00000i 4.00000 4.00000i
\(57\) 0 0
\(58\) 0 0
\(59\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(64\) −7.00000 −7.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −3.00000 −3.00000
\(69\) 0 0
\(70\) 0 0
\(71\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(72\) 4.00000 4.00000
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(75\) −1.00000 1.00000i −1.00000 1.00000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 1.00000 1.00000
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 6.00000 6.00000
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 2.00000i 2.00000i
\(95\) 0 0
\(96\) −6.00000 6.00000i −6.00000 6.00000i
\(97\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(98\) 2.00000 2.00000
\(99\) 0 0
\(100\) 3.00000i 3.00000i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −2.00000 2.00000i −2.00000 2.00000i
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(108\) 0 0
\(109\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(110\) 0 0
\(111\) 2.00000i 2.00000i
\(112\) −5.00000 5.00000i −5.00000 5.00000i
\(113\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −4.00000 −4.00000
\(119\) −1.00000 1.00000i −1.00000 1.00000i
\(120\) 0 0
\(121\) 1.00000i 1.00000i
\(122\) 2.00000 2.00000i 2.00000 2.00000i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 8.00000i 8.00000i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 4.00000i 4.00000i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(140\) 0 0
\(141\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(142\) −2.00000 2.00000i −2.00000 2.00000i
\(143\) 0 0
\(144\) 5.00000i 5.00000i
\(145\) 0 0
\(146\) 0 0
\(147\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(148\) 3.00000 3.00000i 3.00000 3.00000i
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 1.00000i 1.00000i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 2.00000 2.00000i 2.00000 2.00000i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 2.00000i 2.00000i
\(163\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(168\) 8.00000i 8.00000i
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(176\) 0 0
\(177\) −2.00000 2.00000i −2.00000 2.00000i
\(178\) 4.00000i 4.00000i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(182\) 0 0
\(183\) 2.00000 2.00000
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 3.00000 3.00000
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) −7.00000 + 7.00000i −7.00000 + 7.00000i
\(193\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(194\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(195\) 0 0
\(196\) 3.00000i 3.00000i
\(197\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(200\) 4.00000 4.00000
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) −3.00000 + 3.00000i −3.00000 + 3.00000i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(212\) 0 0
\(213\) 2.00000i 2.00000i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 4.00000 4.00000
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) −6.00000 + 6.00000i −6.00000 + 6.00000i
\(225\) −1.00000 −1.00000
\(226\) 0 0
\(227\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6.00000i 6.00000i
\(237\) 2.00000 2.00000
\(238\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(239\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(242\) 2.00000 2.00000
\(243\) 1.00000 1.00000i 1.00000 1.00000i
\(244\) −3.00000 3.00000i −3.00000 3.00000i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 3.00000 3.00000i 3.00000 3.00000i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 9.00000 9.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 2.00000 2.00000
\(260\) 0 0
\(261\) 0 0
\(262\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(263\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.00000 2.00000i 2.00000 2.00000i
\(268\) 0 0
\(269\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 5.00000 5.00000
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(283\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(284\) −3.00000 + 3.00000i −3.00000 + 3.00000i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −6.00000 −6.00000
\(289\) 1.00000 1.00000
\(290\) 0 0
\(291\) 2.00000i 2.00000i
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 2.00000 2.00000i 2.00000 2.00000i
\(295\) 0 0
\(296\) −4.00000 4.00000i −4.00000 4.00000i
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 3.00000 + 3.00000i 3.00000 + 3.00000i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) −2.00000 −2.00000
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(312\) 0 0
\(313\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −3.00000 3.00000i −3.00000 3.00000i
\(317\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −3.00000 −3.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(330\) 0 0
\(331\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(334\) 0 0
\(335\) 0 0
\(336\) −10.0000 −10.0000
\(337\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(338\) 2.00000i 2.00000i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(347\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) −4.00000 + 4.00000i −4.00000 + 4.00000i
\(355\) 0 0
\(356\) −6.00000 −6.00000
\(357\) −2.00000 −2.00000
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −1.00000 −1.00000
\(362\) 0 0
\(363\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(364\) 0 0
\(365\) 0 0
\(366\) 4.00000i 4.00000i
\(367\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 4.00000i 4.00000i
\(377\) 0 0
\(378\) 0 0
\(379\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 8.00000 + 8.00000i 8.00000 + 8.00000i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 3.00000 3.00000i 3.00000 3.00000i
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −4.00000 −4.00000
\(393\) 2.00000i 2.00000i
\(394\) 2.00000 2.00000i 2.00000 2.00000i
\(395\) 0 0
\(396\) 0 0
\(397\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 5.00000i 5.00000i
\(401\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 4.00000 + 4.00000i 4.00000 + 4.00000i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 1.00000i 1.00000i
\(424\) 0 0
\(425\) 1.00000i 1.00000i
\(426\) −4.00000 −4.00000
\(427\) 2.00000i 2.00000i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 6.00000i 6.00000i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 7.00000 + 7.00000i 7.00000 + 7.00000i
\(449\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(450\) 2.00000i 2.00000i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 8.00000 8.00000
\(473\) 0 0
\(474\) 4.00000i 4.00000i
\(475\) 0 0
\(476\) 3.00000 + 3.00000i 3.00000 + 3.00000i
\(477\) 0 0
\(478\) 4.00000i 4.00000i
\(479\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(480\) 0 0
\(481\) 0 0
\(482\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(483\) 0 0
\(484\) 3.00000i 3.00000i
\(485\) 0 0
\(486\) −2.00000 2.00000i −2.00000 2.00000i
\(487\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(488\) −4.00000 + 4.00000i −4.00000 + 4.00000i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.00000 −2.00000
\(498\) 0 0
\(499\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) −4.00000 4.00000i −4.00000 4.00000i
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 1.00000i 1.00000 1.00000i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 10.0000i 10.0000i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 4.00000i 4.00000i
\(519\) 2.00000i 2.00000i
\(520\) 0 0
\(521\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(524\) 3.00000 3.00000i 3.00000 3.00000i
\(525\) 2.00000i 2.00000i
\(526\) −4.00000 −4.00000
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000i 1.00000i
\(530\) 0 0
\(531\) −2.00000 −2.00000
\(532\) 0 0
\(533\) 0 0
\(534\) −4.00000 4.00000i −4.00000 4.00000i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −2.00000 2.00000i −2.00000 2.00000i
\(539\) 0 0
\(540\) 0 0
\(541\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 6.00000i 6.00000i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(548\) 0 0
\(549\) 1.00000 1.00000i 1.00000 1.00000i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 2.00000i 2.00000i
\(554\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 3.00000 3.00000i 3.00000 3.00000i
\(565\) 0 0
\(566\) 2.00000 2.00000i 2.00000 2.00000i
\(567\) −1.00000 1.00000i −1.00000 1.00000i
\(568\) 4.00000 + 4.00000i 4.00000 + 4.00000i
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 7.00000i 7.00000i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 2.00000i 2.00000i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 4.00000 4.00000
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) −3.00000 3.00000i −3.00000 3.00000i
\(589\) 0 0
\(590\) 0 0
\(591\) 2.00000 2.00000
\(592\) −5.00000 + 5.00000i −5.00000 + 5.00000i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 4.00000 4.00000i 4.00000 4.00000i
\(601\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 3.00000i 3.00000i
\(613\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(618\) 0 0
\(619\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.00000 2.00000i −2.00000 2.00000i
\(624\) 0 0
\(625\) −1.00000 −1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) −4.00000 + 4.00000i −4.00000 + 4.00000i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −1.00000 1.00000i −1.00000 1.00000i
\(640\) 0 0
\(641\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(642\) 0 0
\(643\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 4.00000i 4.00000i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 2.00000 2.00000i 2.00000 2.00000i
\(659\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(662\) 4.00000 4.00000
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 2.00000 2.00000i 2.00000 2.00000i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 12.0000i 12.0000i
\(673\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(674\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(675\) 0 0
\(676\) −3.00000 −3.00000
\(677\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(678\) 0 0
\(679\) 2.00000 2.00000
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(692\) 3.00000 3.00000i 3.00000 3.00000i
\(693\) 0 0
\(694\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 3.00000 3.00000i 3.00000 3.00000i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 6.00000 + 6.00000i 6.00000 + 6.00000i
\(709\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 1.00000 1.00000i 1.00000 1.00000i
\(712\) 8.00000i 8.00000i
\(713\) 0 0
\(714\) 4.00000i 4.00000i
\(715\) 0 0
\(716\) 0 0
\(717\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(718\) 0 0
\(719\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.00000i 2.00000i
\(723\) 2.00000i 2.00000i
\(724\) 0 0
\(725\) 0 0
\(726\) 2.00000 2.00000i 2.00000 2.00000i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.00000i 1.00000i
\(730\) 0 0
\(731\) 0 0
\(732\) −6.00000 −6.00000
\(733\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 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
\(751\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(752\) −5.00000 −5.00000
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) −2.00000 2.00000i −2.00000 2.00000i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 9.00000 9.00000i 9.00000 9.00000i
\(769\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −4.00000 4.00000i −4.00000 4.00000i
\(777\) 2.00000 2.00000i 2.00000 2.00000i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 5.00000i 5.00000i
\(785\) 0 0
\(786\) 4.00000 4.00000
\(787\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(788\) −3.00000 3.00000i −3.00000 3.00000i
\(789\) −2.00000 2.00000i −2.00000 2.00000i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) −1.00000 −1.00000
\(800\) −6.00000 −6.00000
\(801\) 2.00000i 2.00000i
\(802\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2.00000i 2.00000i
\(808\) 0 0
\(809\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(810\) 0 0
\(811\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 5.00000 5.00000i 5.00000 5.00000i
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(822\) 0 0
\(823\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 4.00000 + 4.00000i 4.00000 + 4.00000i
\(827\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 2.00000i 2.00000i
\(832\) 0 0
\(833\) 1.00000i 1.00000i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(840\) 0 0
\(841\) 1.00000i 1.00000i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 2.00000 2.00000
\(847\) 1.00000 1.00000i 1.00000 1.00000i
\(848\) 0 0
\(849\) 2.00000 2.00000
\(850\) −2.00000 −2.00000
\(851\) 0 0
\(852\) 6.00000i 6.00000i
\(853\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(854\) −4.00000 −4.00000
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 2.00000 2.00000i 2.00000 2.00000i
\(863\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1.00000 1.00000i 1.00000 1.00000i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(878\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(882\) 2.00000i 2.00000i
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(888\) −8.00000 −8.00000
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 8.00000 8.00000i 8.00000 8.00000i
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 3.00000 3.00000
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.00000 2.00000
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 10.0000i 10.0000i
\(945\) 0 0
\(946\) 0 0
\(947\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(948\) −6.00000 −6.00000
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 4.00000 4.00000i 4.00000 4.00000i
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 6.00000 6.00000
\(957\) 0 0
\(958\) −2.00000 2.00000i −2.00000 2.00000i
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000i 1.00000i
\(962\) 0 0
\(963\) 0 0
\(964\) 3.00000 3.00000i 3.00000 3.00000i
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −4.00000 −4.00000
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) −3.00000 + 3.00000i −3.00000 + 3.00000i
\(973\) 0 0
\(974\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(975\) 0 0
\(976\) 5.00000 + 5.00000i 5.00000 + 5.00000i
\(977\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 2.00000 2.00000
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(992\) 0 0
\(993\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(994\) 4.00000i 4.00000i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(998\) 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 799.1.e.a.140.1 2
17.13 even 4 inner 799.1.e.a.234.1 yes 2
47.46 odd 2 CM 799.1.e.a.140.1 2
799.234 odd 4 inner 799.1.e.a.234.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
799.1.e.a.140.1 2 1.1 even 1 trivial
799.1.e.a.140.1 2 47.46 odd 2 CM
799.1.e.a.234.1 yes 2 17.13 even 4 inner
799.1.e.a.234.1 yes 2 799.234 odd 4 inner