Properties

Label 1200.1.r.a.701.1
Level $1200$
Weight $1$
Character 1200.701
Analytic conductor $0.599$
Analytic rank $0$
Dimension $4$
Projective image $D_{4}$
CM discriminant -15
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1200,1,Mod(101,1200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2, 0]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1200.101");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1200.r (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: \(0.598878015160\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 240)
Projective image: \(D_{4}\)
Projective field: Galois closure of 4.0.92160.2

Embedding invariants

Embedding label 701.1
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1200.701
Dual form 1200.1.r.a.101.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000i q^{4} -1.00000i q^{6} +(0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(0.707107 + 0.707107i) q^{12} -1.00000 q^{16} -1.41421i q^{17} +(0.707107 + 0.707107i) q^{18} +(1.00000 + 1.00000i) q^{19} +1.41421 q^{23} -1.00000 q^{24} +(0.707107 + 0.707107i) q^{27} +(0.707107 - 0.707107i) q^{32} +(1.00000 + 1.00000i) q^{34} -1.00000 q^{36} -1.41421 q^{38} +(-1.00000 + 1.00000i) q^{46} +1.41421i q^{47} +(0.707107 - 0.707107i) q^{48} +1.00000 q^{49} +(1.00000 + 1.00000i) q^{51} -1.00000 q^{54} -1.41421 q^{57} +(1.00000 + 1.00000i) q^{61} +1.00000i q^{64} -1.41421 q^{68} +(-1.00000 + 1.00000i) q^{69} +(0.707107 - 0.707107i) q^{72} +(1.00000 - 1.00000i) q^{76} -2.00000 q^{79} -1.00000 q^{81} -1.41421i q^{92} +(-1.00000 - 1.00000i) q^{94} +1.00000i q^{96} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{16} + 4 q^{19} - 4 q^{24} + 4 q^{34} - 4 q^{36} - 4 q^{46} + 4 q^{49} + 4 q^{51} - 4 q^{54} + 4 q^{61} - 4 q^{69} + 4 q^{76} - 8 q^{79} - 4 q^{81} - 4 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).

\(n\) \(401\) \(577\) \(751\) \(901\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(3\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(4\) 1.00000i 1.00000i
\(5\) 0 0
\(6\) 1.00000i 1.00000i
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(9\) 1.00000i 1.00000i
\(10\) 0 0
\(11\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(12\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(13\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.00000 −1.00000
\(17\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(18\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(19\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(24\) −1.00000 −1.00000
\(25\) 0 0
\(26\) 0 0
\(27\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(28\) 0 0
\(29\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0.707107 0.707107i 0.707107 0.707107i
\(33\) 0 0
\(34\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(35\) 0 0
\(36\) −1.00000 −1.00000
\(37\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) −1.41421 −1.41421
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(47\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(48\) 0.707107 0.707107i 0.707107 0.707107i
\(49\) 1.00000 1.00000
\(50\) 0 0
\(51\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(52\) 0 0
\(53\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(54\) −1.00000 −1.00000
\(55\) 0 0
\(56\) 0 0
\(57\) −1.41421 −1.41421
\(58\) 0 0
\(59\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(68\) −1.41421 −1.41421
\(69\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0.707107 0.707107i 0.707107 0.707107i
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 1.00000 1.00000i 1.00000 1.00000i
\(77\) 0 0
\(78\) 0 0
\(79\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) −1.00000 −1.00000
\(82\) 0 0
\(83\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.41421i 1.41421i
\(93\) 0 0
\(94\) −1.00000 1.00000i −1.00000 1.00000i
\(95\) 0 0
\(96\) 1.00000i 1.00000i
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(102\) −1.41421 −1.41421
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(108\) 0.707107 0.707107i 0.707107 0.707107i
\(109\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(114\) 1.00000 1.00000i 1.00000 1.00000i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000i 1.00000i
\(122\) −1.41421 −1.41421
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −0.707107 0.707107i −0.707107 0.707107i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 1.00000 1.00000i 1.00000 1.00000i
\(137\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(138\) 1.41421i 1.41421i
\(139\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(140\) 0 0
\(141\) −1.00000 1.00000i −1.00000 1.00000i
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000i 1.00000i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(148\) 0 0
\(149\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 1.41421i 1.41421i
\(153\) −1.41421 −1.41421
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(158\) 1.41421 1.41421i 1.41421 1.41421i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.707107 0.707107i 0.707107 0.707107i
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) 0 0
\(169\) 1.00000i 1.00000i
\(170\) 0 0
\(171\) 1.00000 1.00000i 1.00000 1.00000i
\(172\) 0 0
\(173\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(180\) 0 0
\(181\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) −1.41421 −1.41421
\(184\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 1.41421 1.41421
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −0.707107 0.707107i −0.707107 0.707107i
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.00000i 1.00000i
\(197\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(198\) 0 0
\(199\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 1.00000 1.00000i 1.00000 1.00000i
\(205\) 0 0
\(206\) 0 0
\(207\) 1.41421i 1.41421i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 1.00000i 1.00000i
\(217\) 0 0
\(218\) −1.41421 −1.41421
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(227\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(228\) 1.41421i 1.41421i
\(229\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 1.41421 1.41421i 1.41421 1.41421i
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(243\) 0.707107 0.707107i 0.707107 0.707107i
\(244\) 1.00000 1.00000i 1.00000 1.00000i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(270\) 0 0
\(271\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(272\) 1.41421i 1.41421i
\(273\) 0 0
\(274\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(275\) 0 0
\(276\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(277\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(278\) 1.41421i 1.41421i
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 1.41421 1.41421
\(283\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.707107 0.707107i −0.707107 0.707107i
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(294\) 1.00000i 1.00000i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.00000 1.00000i −1.00000 1.00000i
\(305\) 0 0
\(306\) 1.00000 1.00000i 1.00000 1.00000i
\(307\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 2.00000i 2.00000i
\(317\) −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i \(0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.41421 1.41421i 1.41421 1.41421i
\(324\) 1.00000i 1.00000i
\(325\) 0 0
\(326\) 0 0
\(327\) −1.41421 −1.41421
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(339\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(340\) 0 0
\(341\) 0 0
\(342\) 1.41421i 1.41421i
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(348\) 0 0
\(349\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 1.00000i 1.00000i
\(362\) 1.41421i 1.41421i
\(363\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(364\) 0 0
\(365\) 0 0
\(366\) 1.00000 1.00000i 1.00000 1.00000i
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) −1.41421 −1.41421
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(377\) 0 0
\(378\) 0 0
\(379\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(384\) 1.00000 1.00000
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(390\) 0 0
\(391\) 2.00000i 2.00000i
\(392\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(393\) 0 0
\(394\) 2.00000 2.00000
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(398\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 1.41421i 1.41421i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(412\) 0 0
\(413\) 0 0
\(414\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(415\) 0 0
\(416\) 0 0
\(417\) 1.41421i 1.41421i
\(418\) 0 0
\(419\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(420\) 0 0
\(421\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(422\) 1.41421 1.41421
\(423\) 1.41421 1.41421
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −0.707107 0.707107i −0.707107 0.707107i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.00000 1.00000i 1.00000 1.00000i
\(437\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(438\) 0 0
\(439\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 1.00000i 1.00000i
\(442\) 0 0
\(443\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −1.41421 −1.41421
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) −1.00000 1.00000i −1.00000 1.00000i
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 1.41421i 1.41421i
\(459\) 1.00000 1.00000i 1.00000 1.00000i
\(460\) 0 0
\(461\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(467\) 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i \(-0.250000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 2.00000i 2.00000i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.00000 −1.00000
\(485\) 0 0
\(486\) 1.00000i 1.00000i
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 1.41421i 1.41421i
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(502\) 0 0
\(503\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(508\) 0 0
\(509\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(513\) 1.41421i 1.41421i
\(514\) −1.00000 1.00000i −1.00000 1.00000i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 1.00000 1.00000i 1.00000 1.00000i
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(542\) 1.41421 1.41421i 1.41421 1.41421i
\(543\) 1.41421i 1.41421i
\(544\) −1.00000 1.00000i −1.00000 1.00000i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(548\) 1.41421i 1.41421i
\(549\) 1.00000 1.00000i 1.00000 1.00000i
\(550\) 0 0
\(551\) 0 0
\(552\) −1.41421 −1.41421
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −1.00000 1.00000i −1.00000 1.00000i
\(557\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i \(0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(564\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.00000 1.00000
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 0.707107 0.707107i 0.707107 0.707107i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(589\) 0 0
\(590\) 0 0
\(591\) 2.00000 2.00000
\(592\) 0 0
\(593\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 1.41421 1.41421
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1.41421i 1.41421i
\(613\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(618\) 0 0
\(619\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) −1.41421 1.41421i −1.41421 1.41421i
\(633\) 1.41421 1.41421
\(634\) 2.00000i 2.00000i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 2.00000i 2.00000i
\(647\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) −0.707107 0.707107i −0.707107 0.707107i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(654\) 1.00000 1.00000i 1.00000 1.00000i
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(660\) 0 0
\(661\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(662\) 1.41421i 1.41421i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.41421i 1.41421i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −1.00000 −1.00000
\(677\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(678\) −1.41421 −1.41421
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(684\) −1.00000 1.00000i −1.00000 1.00000i
\(685\) 0 0
\(686\) 0 0
\(687\) 1.41421i 1.41421i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 2.00000 2.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 1.41421 1.41421
\(699\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(700\) 0 0
\(701\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.00000 1.00000i −1.00000 1.00000i
\(707\) 0 0
\(708\) 0 0
\(709\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(710\) 0 0
\(711\) 2.00000i 2.00000i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.707107 0.707107i −0.707107 0.707107i
\(723\) 0 0
\(724\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(725\) 0 0
\(726\) −1.00000 −1.00000
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.00000i 1.00000i
\(730\) 0 0
\(731\) 0 0
\(732\) 1.41421i 1.41421i
\(733\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 1.00000 1.00000i 1.00000 1.00000i
\(737\) 0 0
\(738\) 0 0
\(739\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 1.41421i 1.41421i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) 1.41421i 1.41421i
\(759\) 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
\(766\) −1.00000 1.00000i −1.00000 1.00000i
\(767\) 0 0
\(768\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) −1.00000 1.00000i −1.00000 1.00000i
\(772\) 0 0
\(773\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(783\) 0 0
\(784\) −1.00000 −1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(788\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(789\) 1.00000 1.00000i 1.00000 1.00000i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −2.00000 −2.00000
\(797\) −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i \(0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(798\) 0 0
\(799\) 2.00000 2.00000
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(810\) 0 0
\(811\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(812\) 0 0
\(813\) 1.41421 1.41421i 1.41421 1.41421i
\(814\) 0 0
\(815\) 0 0
\(816\) −1.00000 1.00000i −1.00000 1.00000i
\(817\) 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 \(0.750000\pi\)
\(822\) 1.41421i 1.41421i
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(828\) −1.41421 −1.41421
\(829\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.41421i 1.41421i
\(834\) −1.00000 1.00000i −1.00000 1.00000i
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 1.00000i 1.00000i
\(842\) 1.41421i 1.41421i
\(843\) 0 0
\(844\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(845\) 0 0
\(846\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(858\) 0 0
\(859\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(864\) 1.00000 1.00000
\(865\) 0 0
\(866\) 0 0
\(867\) 0.707107 0.707107i 0.707107 0.707107i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 1.41421i 1.41421i
\(873\) 0 0
\(874\) −2.00000 −2.00000
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(878\) −1.41421 1.41421i −1.41421 1.41421i
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(883\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 1.00000 1.00000i 1.00000 1.00000i
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 1.41421 1.41421
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(917\) 0 0
\(918\) 1.41421i 1.41421i
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(932\) 1.41421i 1.41421i
\(933\) 0 0
\(934\) 2.00000i 2.00000i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(948\) −1.41421 1.41421i −1.41421 1.41421i
\(949\) 0 0
\(950\) 0 0
\(951\) 2.00000i 2.00000i
\(952\) 0 0
\(953\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −1.00000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0.707107 0.707107i 0.707107 0.707107i
\(969\) 2.00000i 2.00000i
\(970\) 0 0
\(971\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(972\) −0.707107 0.707107i −0.707107 0.707107i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −1.00000 1.00000i −1.00000 1.00000i
\(977\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 1.00000 1.00000i 1.00000 1.00000i
\(982\) 0 0
\(983\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(992\) 0 0
\(993\) 1.41421i 1.41421i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(998\) 1.41421 1.41421
\(999\) 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 1200.1.r.a.701.1 4
3.2 odd 2 inner 1200.1.r.a.701.2 4
5.2 odd 4 240.1.bm.a.29.1 4
5.3 odd 4 240.1.bm.a.29.2 yes 4
5.4 even 2 inner 1200.1.r.a.701.2 4
15.2 even 4 240.1.bm.a.29.2 yes 4
15.8 even 4 240.1.bm.a.29.1 4
15.14 odd 2 CM 1200.1.r.a.701.1 4
16.5 even 4 inner 1200.1.r.a.101.2 4
20.3 even 4 960.1.bm.a.209.2 4
20.7 even 4 960.1.bm.a.209.1 4
40.3 even 4 1920.1.bm.b.929.1 4
40.13 odd 4 1920.1.bm.a.929.2 4
40.27 even 4 1920.1.bm.b.929.2 4
40.37 odd 4 1920.1.bm.a.929.1 4
48.5 odd 4 inner 1200.1.r.a.101.1 4
60.23 odd 4 960.1.bm.a.209.1 4
60.47 odd 4 960.1.bm.a.209.2 4
80.3 even 4 1920.1.bm.b.1889.1 4
80.13 odd 4 1920.1.bm.a.1889.2 4
80.27 even 4 960.1.bm.a.689.1 4
80.37 odd 4 240.1.bm.a.149.1 yes 4
80.43 even 4 960.1.bm.a.689.2 4
80.53 odd 4 240.1.bm.a.149.2 yes 4
80.67 even 4 1920.1.bm.b.1889.2 4
80.69 even 4 inner 1200.1.r.a.101.1 4
80.77 odd 4 1920.1.bm.a.1889.1 4
120.53 even 4 1920.1.bm.a.929.1 4
120.77 even 4 1920.1.bm.a.929.2 4
120.83 odd 4 1920.1.bm.b.929.2 4
120.107 odd 4 1920.1.bm.b.929.1 4
240.53 even 4 240.1.bm.a.149.1 yes 4
240.77 even 4 1920.1.bm.a.1889.2 4
240.83 odd 4 1920.1.bm.b.1889.2 4
240.107 odd 4 960.1.bm.a.689.2 4
240.149 odd 4 inner 1200.1.r.a.101.2 4
240.173 even 4 1920.1.bm.a.1889.1 4
240.197 even 4 240.1.bm.a.149.2 yes 4
240.203 odd 4 960.1.bm.a.689.1 4
240.227 odd 4 1920.1.bm.b.1889.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.1.bm.a.29.1 4 5.2 odd 4
240.1.bm.a.29.1 4 15.8 even 4
240.1.bm.a.29.2 yes 4 5.3 odd 4
240.1.bm.a.29.2 yes 4 15.2 even 4
240.1.bm.a.149.1 yes 4 80.37 odd 4
240.1.bm.a.149.1 yes 4 240.53 even 4
240.1.bm.a.149.2 yes 4 80.53 odd 4
240.1.bm.a.149.2 yes 4 240.197 even 4
960.1.bm.a.209.1 4 20.7 even 4
960.1.bm.a.209.1 4 60.23 odd 4
960.1.bm.a.209.2 4 20.3 even 4
960.1.bm.a.209.2 4 60.47 odd 4
960.1.bm.a.689.1 4 80.27 even 4
960.1.bm.a.689.1 4 240.203 odd 4
960.1.bm.a.689.2 4 80.43 even 4
960.1.bm.a.689.2 4 240.107 odd 4
1200.1.r.a.101.1 4 48.5 odd 4 inner
1200.1.r.a.101.1 4 80.69 even 4 inner
1200.1.r.a.101.2 4 16.5 even 4 inner
1200.1.r.a.101.2 4 240.149 odd 4 inner
1200.1.r.a.701.1 4 1.1 even 1 trivial
1200.1.r.a.701.1 4 15.14 odd 2 CM
1200.1.r.a.701.2 4 3.2 odd 2 inner
1200.1.r.a.701.2 4 5.4 even 2 inner
1920.1.bm.a.929.1 4 40.37 odd 4
1920.1.bm.a.929.1 4 120.53 even 4
1920.1.bm.a.929.2 4 40.13 odd 4
1920.1.bm.a.929.2 4 120.77 even 4
1920.1.bm.a.1889.1 4 80.77 odd 4
1920.1.bm.a.1889.1 4 240.173 even 4
1920.1.bm.a.1889.2 4 80.13 odd 4
1920.1.bm.a.1889.2 4 240.77 even 4
1920.1.bm.b.929.1 4 40.3 even 4
1920.1.bm.b.929.1 4 120.107 odd 4
1920.1.bm.b.929.2 4 40.27 even 4
1920.1.bm.b.929.2 4 120.83 odd 4
1920.1.bm.b.1889.1 4 80.3 even 4
1920.1.bm.b.1889.1 4 240.227 odd 4
1920.1.bm.b.1889.2 4 80.67 even 4
1920.1.bm.b.1889.2 4 240.83 odd 4