Properties

Label 1260.1.u.b.307.1
Level $1260$
Weight $1$
Character 1260.307
Analytic conductor $0.629$
Analytic rank $0$
Dimension $4$
Projective image $D_{4}$
CM discriminant -84
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1260,1,Mod(307,1260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1260, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 1, 2]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1260.307");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1260.u (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: \(0.628821915918\)
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: yes
Projective image: \(D_{4}\)
Projective field: Galois closure of 4.2.220500.3

Embedding invariants

Embedding label 307.1
Root \(-0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1260.307
Dual form 1260.1.u.b.1063.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +1.00000 q^{5} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +1.00000 q^{5} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.707107 + 0.707107i) q^{10} +1.41421i q^{11} -1.00000 q^{14} -1.00000 q^{16} +(-1.00000 + 1.00000i) q^{17} -1.41421i q^{19} -1.00000i q^{20} +(-1.00000 - 1.00000i) q^{22} +1.00000 q^{25} +(0.707107 - 0.707107i) q^{28} -1.41421 q^{31} +(0.707107 - 0.707107i) q^{32} -1.41421i q^{34} +(0.707107 + 0.707107i) q^{35} +(1.00000 + 1.00000i) q^{37} +(1.00000 + 1.00000i) q^{38} +(0.707107 + 0.707107i) q^{40} -2.00000i q^{41} +1.41421 q^{44} +1.00000i q^{49} +(-0.707107 + 0.707107i) q^{50} +1.41421i q^{55} +1.00000i q^{56} +(1.00000 - 1.00000i) q^{62} +1.00000i q^{64} +(1.00000 + 1.00000i) q^{68} -1.00000 q^{70} -1.41421i q^{71} -1.41421 q^{74} -1.41421 q^{76} +(-1.00000 + 1.00000i) q^{77} -1.00000 q^{80} +(1.41421 + 1.41421i) q^{82} +(-1.00000 + 1.00000i) q^{85} +(-1.00000 + 1.00000i) q^{88} -1.41421i q^{95} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{5} - 4 q^{14} - 4 q^{16} - 4 q^{17} - 4 q^{22} + 4 q^{25} + 4 q^{37} + 4 q^{38} + 4 q^{62} + 4 q^{68} - 4 q^{70} - 4 q^{77} - 4 q^{80} - 4 q^{85} - 4 q^{88}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(3\) 0 0
\(4\) 1.00000i 1.00000i
\(5\) 1.00000 1.00000
\(6\) 0 0
\(7\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(8\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(9\) 0 0
\(10\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(11\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(12\) 0 0
\(13\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(14\) −1.00000 −1.00000
\(15\) 0 0
\(16\) −1.00000 −1.00000
\(17\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(20\) 1.00000i 1.00000i
\(21\) 0 0
\(22\) −1.00000 1.00000i −1.00000 1.00000i
\(23\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(24\) 0 0
\(25\) 1.00000 1.00000
\(26\) 0 0
\(27\) 0 0
\(28\) 0.707107 0.707107i 0.707107 0.707107i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(32\) 0.707107 0.707107i 0.707107 0.707107i
\(33\) 0 0
\(34\) 1.41421i 1.41421i
\(35\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(36\) 0 0
\(37\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(38\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(39\) 0 0
\(40\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(41\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(42\) 0 0
\(43\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) 1.41421 1.41421
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(48\) 0 0
\(49\) 1.00000i 1.00000i
\(50\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(54\) 0 0
\(55\) 1.41421i 1.41421i
\(56\) 1.00000i 1.00000i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 1.00000 1.00000i 1.00000 1.00000i
\(63\) 0 0
\(64\) 1.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(68\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(69\) 0 0
\(70\) −1.00000 −1.00000
\(71\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(72\) 0 0
\(73\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(74\) −1.41421 −1.41421
\(75\) 0 0
\(76\) −1.41421 −1.41421
\(77\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −1.00000 −1.00000
\(81\) 0 0
\(82\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(83\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(84\) 0 0
\(85\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(86\) 0 0
\(87\) 0 0
\(88\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.41421i 1.41421i
\(96\) 0 0
\(97\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(98\) −0.707107 0.707107i −0.707107 0.707107i
\(99\) 0 0
\(100\) 1.00000i 1.00000i
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i \(-0.250000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −1.00000 1.00000i −1.00000 1.00000i
\(111\) 0 0
\(112\) −0.707107 0.707107i −0.707107 0.707107i
\(113\) 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
\(118\) 0 0
\(119\) −1.41421 −1.41421
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 1.41421i 1.41421i
\(125\) 1.00000 1.00000
\(126\) 0 0
\(127\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(128\) −0.707107 0.707107i −0.707107 0.707107i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 1.00000 1.00000i 1.00000 1.00000i
\(134\) 0 0
\(135\) 0 0
\(136\) −1.41421 −1.41421
\(137\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(138\) 0 0
\(139\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(140\) 0.707107 0.707107i 0.707107 0.707107i
\(141\) 0 0
\(142\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 1.00000 1.00000i 1.00000 1.00000i
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 1.00000 1.00000i 1.00000 1.00000i
\(153\) 0 0
\(154\) 1.41421i 1.41421i
\(155\) −1.41421 −1.41421
\(156\) 0 0
\(157\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.707107 0.707107i 0.707107 0.707107i
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) −2.00000 −2.00000
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(168\) 0 0
\(169\) 1.00000i 1.00000i
\(170\) 1.41421i 1.41421i
\(171\) 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
\(175\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(176\) 1.41421i 1.41421i
\(177\) 0 0
\(178\) 0 0
\(179\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(186\) 0 0
\(187\) −1.41421 1.41421i −1.41421 1.41421i
\(188\) 0 0
\(189\) 0 0
\(190\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(191\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.00000 1.00000
\(197\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(198\) 0 0
\(199\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(200\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2.00000i 2.00000i
\(206\) 2.00000i 2.00000i
\(207\) 0 0
\(208\) 0 0
\(209\) 2.00000 2.00000
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.00000 1.00000i −1.00000 1.00000i
\(218\) 0 0
\(219\) 0 0
\(220\) 1.41421 1.41421
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(224\) 1.00000 1.00000
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(228\) 0 0
\(229\) 0 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 1.00000 1.00000i 1.00000 1.00000i
\(239\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0.707107 0.707107i 0.707107 0.707107i
\(243\) 0 0
\(244\) 0 0
\(245\) 1.00000i 1.00000i
\(246\) 0 0
\(247\) 0 0
\(248\) −1.00000 1.00000i −1.00000 1.00000i
\(249\) 0 0
\(250\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 1.41421i 1.41421i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.41421i 1.41421i
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(272\) 1.00000 1.00000i 1.00000 1.00000i
\(273\) 0 0
\(274\) 0 0
\(275\) 1.41421i 1.41421i
\(276\) 0 0
\(277\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(278\) −1.00000 1.00000i −1.00000 1.00000i
\(279\) 0 0
\(280\) 1.00000i 1.00000i
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(284\) −1.41421 −1.41421
\(285\) 0 0
\(286\) 0 0
\(287\) 1.41421 1.41421i 1.41421 1.41421i
\(288\) 0 0
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.41421i 1.41421i
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.41421i 1.41421i
\(305\) 0 0
\(306\) 0 0
\(307\) 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(309\) 0 0
\(310\) 1.00000 1.00000i 1.00000 1.00000i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.00000i 1.00000i
\(321\) 0 0
\(322\) 0 0
\(323\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 1.41421 1.41421i 1.41421 1.41421i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(338\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(339\) 0 0
\(340\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(341\) 2.00000i 2.00000i
\(342\) 0 0
\(343\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(344\) 0 0
\(345\) 0 0
\(346\) 1.41421 1.41421
\(347\) −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
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) −1.00000 −1.00000
\(351\) 0 0
\(352\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(353\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 1.41421i 1.41421i
\(356\) 0 0
\(357\) 0 0
\(358\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(359\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(360\) 0 0
\(361\) −1.00000 −1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −1.41421 −1.41421
\(371\) 0 0
\(372\) 0 0
\(373\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(374\) 2.00000 2.00000
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) −1.41421 −1.41421
\(381\) 0 0
\(382\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(383\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(384\) 0 0
\(385\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(386\) 1.41421i 1.41421i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(398\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(399\) 0 0
\(400\) −1.00000 −1.00000
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(411\) 0 0
\(412\) −1.41421 1.41421i −1.41421 1.41421i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(432\) 0 0
\(433\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(434\) 1.41421 1.41421
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(440\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(441\) 0 0
\(442\) 0 0
\(443\) 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 2.82843 2.82843
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 1.41421i 1.41421i
\(476\) 1.41421i 1.41421i
\(477\) 0 0
\(478\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000i 1.00000i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.707107 0.707107i −0.707107 0.707107i
\(491\) 1.41421i 1.41421i 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
\(496\) 1.41421 1.41421
\(497\) 1.00000 1.00000i 1.00000 1.00000i
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 1.00000i 1.00000i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(513\) 0 0
\(514\) 1.41421i 1.41421i
\(515\) 1.41421 1.41421i 1.41421 1.41421i
\(516\) 0 0
\(517\) 0 0
\(518\) −1.00000 1.00000i −1.00000 1.00000i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i \(0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 2.00000 2.00000
\(527\) 1.41421 1.41421i 1.41421 1.41421i
\(528\) 0 0
\(529\) 1.00000i 1.00000i
\(530\) 0 0
\(531\) 0 0
\(532\) −1.00000 1.00000i −1.00000 1.00000i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.41421 −1.41421
\(540\) 0 0
\(541\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(542\) 1.00000 1.00000i 1.00000 1.00000i
\(543\) 0 0
\(544\) 1.41421i 1.41421i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −1.00000 1.00000i −1.00000 1.00000i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 1.41421 1.41421
\(555\) 0 0
\(556\) 1.41421 1.41421
\(557\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.707107 0.707107i −0.707107 0.707107i
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 1.00000 1.00000i 1.00000 1.00000i
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 2.00000i 2.00000i
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(578\) 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
\(586\) 1.41421 1.41421
\(587\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) 0 0
\(589\) 2.00000i 2.00000i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 1.00000i −1.00000 1.00000i
\(593\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) −1.41421 −1.41421
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.00000 −1.00000
\(606\) 0 0
\(607\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(608\) −1.00000 1.00000i −1.00000 1.00000i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(614\) −2.00000 −2.00000
\(615\) 0 0
\(616\) −1.41421 −1.41421
\(617\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(618\) 0 0
\(619\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(620\) 1.41421i 1.41421i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.00000 −2.00000
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.707107 0.707107i −0.707107 0.707107i
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i \(0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.00000 −2.00000
\(647\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) 0 0
\(649\) 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 \(0.250000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 2.00000i 2.00000i
\(657\) 0 0
\(658\) 0 0
\(659\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.00000 1.00000i 1.00000 1.00000i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(674\) 1.41421 1.41421
\(675\) 0 0
\(676\) −1.00000 −1.00000
\(677\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.41421 −1.41421
\(681\) 0 0
\(682\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(683\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 1.00000i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(692\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(693\) 0 0
\(694\) 2.00000i 2.00000i
\(695\) 1.41421i 1.41421i
\(696\) 0 0
\(697\) 2.00000 + 2.00000i 2.00000 + 2.00000i
\(698\) 0 0
\(699\) 0 0
\(700\) 0.707107 0.707107i 0.707107 0.707107i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 1.41421 1.41421i 1.41421 1.41421i
\(704\) −1.41421 −1.41421
\(705\) 0 0
\(706\) 1.41421 1.41421
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.41421i 1.41421i
\(717\) 0 0
\(718\) 1.00000 1.00000i 1.00000 1.00000i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 2.00000 2.00000
\(722\) 0.707107 0.707107i 0.707107 0.707107i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 1.00000 1.00000i 1.00000 1.00000i
\(741\) 0 0
\(742\) 0 0
\(743\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1.41421i 1.41421i
\(747\) 0 0
\(748\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 1.00000 1.00000i 1.00000 1.00000i
\(761\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −1.41421 −1.41421
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 1.41421i 1.41421i
\(771\) 0 0
\(772\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(773\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) −1.41421 −1.41421
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.82843 −2.82843
\(780\) 0 0
\(781\) 2.00000 2.00000
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000i 1.00000i
\(785\) 0 0
\(786\) 0 0
\(787\) −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −1.41421 −1.41421
\(797\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.707107 0.707107i 0.707107 0.707107i
\(801\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 2.00000i 2.00000i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) −2.00000 −2.00000
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(824\) 2.00000 2.00000
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.00000 1.00000i −1.00000 1.00000i
\(834\) 0 0
\(835\) 0 0
\(836\) 2.00000i 2.00000i
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.00000i 1.00000i
\(846\) 0 0
\(847\) −0.707107 0.707107i −0.707107 0.707107i
\(848\) 0 0
\(849\) 0 0
\(850\) 1.41421i 1.41421i
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(858\) 0 0
\(859\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −1.00000 1.00000i −1.00000 1.00000i
\(863\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(864\) 0 0
\(865\) −1.00000 1.00000i −1.00000 1.00000i
\(866\) 0 0
\(867\) 0 0
\(868\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(876\) 0 0
\(877\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(878\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(879\) 0 0
\(880\) 1.41421i 1.41421i
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −2.00000 −2.00000
\(887\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 1.41421 1.41421
\(896\) 1.00000i 1.00000i
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) −2.00000 + 2.00000i −2.00000 + 2.00000i
\(903\) 0 0
\(904\) 0 0
\(905\) 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
\(911\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −1.41421 −1.41421
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −1.41421 1.41421i −1.41421 1.41421i
\(923\) 0 0
\(924\) 0 0
\(925\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(930\) 0 0
\(931\) 1.41421 1.41421
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.41421 1.41421i −1.41421 1.41421i
\(936\) 0 0
\(937\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i \(-0.250000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(951\) 0 0
\(952\) −1.00000 1.00000i −1.00000 1.00000i
\(953\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(954\) 0 0
\(955\) 1.41421i 1.41421i
\(956\) 1.41421i 1.41421i
\(957\) 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
\(965\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(966\) 0 0
\(967\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(968\) −0.707107 0.707107i −0.707107 0.707107i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 1.00000 1.00000
\(981\) 0 0
\(982\) −1.00000 1.00000i −1.00000 1.00000i
\(983\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
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
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(993\) 0 0
\(994\) 1.41421i 1.41421i
\(995\) 1.41421i 1.41421i
\(996\) 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 1260.1.u.b.307.1 yes 4
3.2 odd 2 1260.1.u.a.307.2 yes 4
4.3 odd 2 inner 1260.1.u.b.307.2 yes 4
5.3 odd 4 1260.1.u.a.1063.2 yes 4
7.6 odd 2 1260.1.u.a.307.1 4
12.11 even 2 1260.1.u.a.307.1 4
15.8 even 4 inner 1260.1.u.b.1063.1 yes 4
20.3 even 4 1260.1.u.a.1063.1 yes 4
21.20 even 2 inner 1260.1.u.b.307.2 yes 4
28.27 even 2 1260.1.u.a.307.2 yes 4
35.13 even 4 inner 1260.1.u.b.1063.2 yes 4
60.23 odd 4 inner 1260.1.u.b.1063.2 yes 4
84.83 odd 2 CM 1260.1.u.b.307.1 yes 4
105.83 odd 4 1260.1.u.a.1063.1 yes 4
140.83 odd 4 inner 1260.1.u.b.1063.1 yes 4
420.83 even 4 1260.1.u.a.1063.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1260.1.u.a.307.1 4 7.6 odd 2
1260.1.u.a.307.1 4 12.11 even 2
1260.1.u.a.307.2 yes 4 3.2 odd 2
1260.1.u.a.307.2 yes 4 28.27 even 2
1260.1.u.a.1063.1 yes 4 20.3 even 4
1260.1.u.a.1063.1 yes 4 105.83 odd 4
1260.1.u.a.1063.2 yes 4 5.3 odd 4
1260.1.u.a.1063.2 yes 4 420.83 even 4
1260.1.u.b.307.1 yes 4 1.1 even 1 trivial
1260.1.u.b.307.1 yes 4 84.83 odd 2 CM
1260.1.u.b.307.2 yes 4 4.3 odd 2 inner
1260.1.u.b.307.2 yes 4 21.20 even 2 inner
1260.1.u.b.1063.1 yes 4 15.8 even 4 inner
1260.1.u.b.1063.1 yes 4 140.83 odd 4 inner
1260.1.u.b.1063.2 yes 4 35.13 even 4 inner
1260.1.u.b.1063.2 yes 4 60.23 odd 4 inner