Properties

Label 700.1.bf.a.507.2
Level $700$
Weight $1$
Character 700.507
Analytic conductor $0.349$
Analytic rank $0$
Dimension $8$
Projective image $D_{6}$
CM discriminant -20
Inner twists $16$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [700,1,Mod(143,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 2]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.143");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 700.bf (of order \(12\), degree \(4\), 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: \(0.349345508843\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{6}\)
Projective field: Galois closure of 6.0.6722800.1

Embedding invariants

Embedding label 507.2
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 700.507
Dual form 700.1.bf.a.243.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 + 0.258819i) q^{2} +(-0.448288 - 1.67303i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.73205 + 1.00000i) q^{9} +O(q^{10})\) \(q+(0.965926 + 0.258819i) q^{2} +(-0.448288 - 1.67303i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.73205 + 1.00000i) q^{9} +(0.448288 - 1.67303i) q^{12} -1.00000i q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.93185 + 0.517638i) q^{18} +(-1.50000 + 0.866025i) q^{21} +(-0.258819 + 0.965926i) q^{23} +(0.866025 - 1.50000i) q^{24} +(1.22474 + 1.22474i) q^{27} +(0.258819 - 0.965926i) q^{28} -1.00000i q^{29} +(0.258819 + 0.965926i) q^{32} -2.00000 q^{36} +1.73205i q^{41} +(-1.67303 + 0.448288i) q^{42} +(0.707107 + 0.707107i) q^{43} +(-0.500000 + 0.866025i) q^{46} +(1.22474 - 1.22474i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.866025 + 1.50000i) q^{54} +(0.500000 - 0.866025i) q^{56} +(0.258819 - 0.965926i) q^{58} +(1.50000 - 0.866025i) q^{61} +(1.41421 + 1.41421i) q^{63} +1.00000i q^{64} +(-0.258819 - 0.965926i) q^{67} +1.73205 q^{69} +(-1.93185 - 0.517638i) q^{72} +(0.500000 - 0.866025i) q^{81} +(-0.448288 + 1.67303i) q^{82} +(-1.22474 + 1.22474i) q^{83} -1.73205 q^{84} +(0.500000 + 0.866025i) q^{86} +(-1.67303 + 0.448288i) q^{87} +(0.866025 + 1.50000i) q^{89} +(-0.707107 + 0.707107i) q^{92} +(1.50000 - 0.866025i) q^{96} +(-0.965926 + 0.258819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{16} - 12 q^{21} - 16 q^{36} - 4 q^{46} + 4 q^{56} + 12 q^{61} + 4 q^{81} + 4 q^{86} + 12 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(3\) −0.448288 1.67303i −0.448288 1.67303i −0.707107 0.707107i \(-0.750000\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(4\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(5\) 0 0
\(6\) 1.73205i 1.73205i
\(7\) −0.258819 0.965926i −0.258819 0.965926i
\(8\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(9\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(10\) 0 0
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 0.448288 1.67303i 0.448288 1.67303i
\(13\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(14\) 1.00000i 1.00000i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(17\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(18\) −1.93185 + 0.517638i −1.93185 + 0.517638i
\(19\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) 0 0
\(21\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(22\) 0 0
\(23\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(24\) 0.866025 1.50000i 0.866025 1.50000i
\(25\) 0 0
\(26\) 0 0
\(27\) 1.22474 + 1.22474i 1.22474 + 1.22474i
\(28\) 0.258819 0.965926i 0.258819 0.965926i
\(29\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −2.00000
\(37\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) −1.67303 + 0.448288i −1.67303 + 0.448288i
\(43\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(47\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(48\) 1.22474 1.22474i 1.22474 1.22474i
\(49\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(54\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(55\) 0 0
\(56\) 0.500000 0.866025i 0.500000 0.866025i
\(57\) 0 0
\(58\) 0.258819 0.965926i 0.258819 0.965926i
\(59\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 1.50000 0.866025i 1.50000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
1.00000 \(0\)
\(62\) 0 0
\(63\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(64\) 1.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(68\) 0 0
\(69\) 1.73205 1.73205
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −1.93185 0.517638i −1.93185 0.517638i
\(73\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) 0 0
\(81\) 0.500000 0.866025i 0.500000 0.866025i
\(82\) −0.448288 + 1.67303i −0.448288 + 1.67303i
\(83\) −1.22474 + 1.22474i −1.22474 + 1.22474i −0.258819 + 0.965926i \(0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(84\) −1.73205 −1.73205
\(85\) 0 0
\(86\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(87\) −1.67303 + 0.448288i −1.67303 + 0.448288i
\(88\) 0 0
\(89\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 1.50000 0.866025i 1.50000 0.866025i
\(97\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(98\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(99\) 0 0
\(100\) 0 0
\(101\) −1.50000 0.866025i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −1.67303 0.448288i −1.67303 0.448288i −0.707107 0.707107i \(-0.750000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(108\) 0.448288 + 1.67303i 0.448288 + 1.67303i
\(109\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(110\) 0 0
\(111\) 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
\(116\) 0.500000 0.866025i 0.500000 0.866025i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.500000 0.866025i
\(122\) 1.67303 0.448288i 1.67303 0.448288i
\(123\) 2.89778 0.776457i 2.89778 0.776457i
\(124\) 0 0
\(125\) 0 0
\(126\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(127\) −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i \(0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(129\) 0.866025 1.50000i 0.866025 1.50000i
\(130\) 0 0
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.00000i 1.00000i
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(138\) 1.67303 + 0.448288i 1.67303 + 0.448288i
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.73205 1.00000i −1.73205 1.00000i
\(145\) 0 0
\(146\) 0 0
\(147\) 1.22474 + 1.22474i 1.22474 + 1.22474i
\(148\) 0 0
\(149\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) 0 0
\(151\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.00000 1.00000
\(162\) 0.707107 0.707107i 0.707107 0.707107i
\(163\) 0.517638 1.93185i 0.517638 1.93185i 0.258819 0.965926i \(-0.416667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(164\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(165\) 0 0
\(166\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(167\) −1.22474 1.22474i −1.22474 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 0.965926i \(-0.583333\pi\)
\(168\) −1.67303 0.448288i −1.67303 0.448288i
\(169\) 1.00000i 1.00000i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(173\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(174\) −1.73205 −1.73205
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0.448288 + 1.67303i 0.448288 + 1.67303i
\(179\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(180\) 0 0
\(181\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(182\) 0 0
\(183\) −2.12132 2.12132i −2.12132 2.12132i
\(184\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.866025 1.50000i 0.866025 1.50000i
\(190\) 0 0
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) 1.67303 0.448288i 1.67303 0.448288i
\(193\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(194\) 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
\(199\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) 0 0
\(201\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(202\) −1.22474 1.22474i −1.22474 1.22474i
\(203\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(204\) 0 0
\(205\) 0 0
\(206\) −1.50000 0.866025i −1.50000 0.866025i
\(207\) −0.517638 1.93185i −0.517638 1.93185i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(215\) 0 0
\(216\) 1.73205i 1.73205i
\(217\) 0 0
\(218\) −0.707107 0.707107i −0.707107 0.707107i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(224\) 0.866025 0.500000i 0.866025 0.500000i
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(228\) 0 0
\(229\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.707107 0.707107i 0.707107 0.707107i
\(233\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) −0.258819 0.965926i −0.258819 0.965926i
\(243\) 0 0
\(244\) 1.73205 1.73205
\(245\) 0 0
\(246\) 3.00000 3.00000
\(247\) 0 0
\(248\) 0 0
\(249\) 2.59808 + 1.50000i 2.59808 + 1.50000i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0.517638 + 1.93185i 0.517638 + 1.93185i
\(253\) 0 0
\(254\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(258\) 1.22474 1.22474i 1.22474 1.22474i
\(259\) 0 0
\(260\) 0 0
\(261\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(262\) 0 0
\(263\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.12132 2.12132i 2.12132 2.12132i
\(268\) 0.258819 0.965926i 0.258819 0.965926i
\(269\) −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(277\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.67303 0.448288i 1.67303 0.448288i
\(288\) −1.41421 1.41421i −1.41421 1.41421i
\(289\) 0.866025 0.500000i 0.866025 0.500000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(294\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0.965926 0.258819i 0.965926 0.258819i
\(299\) 0 0
\(300\) 0 0
\(301\) 0.500000 0.866025i 0.500000 0.866025i
\(302\) 0 0
\(303\) −0.776457 + 2.89778i −0.776457 + 2.89778i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.22474 + 1.22474i 1.22474 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(308\) 0 0
\(309\) 3.00000i 3.00000i
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 1.73205i 1.73205i
\(322\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(323\) 0 0
\(324\) 0.866025 0.500000i 0.866025 0.500000i
\(325\) 0 0
\(326\) 1.00000 1.73205i 1.00000 1.73205i
\(327\) −0.448288 + 1.67303i −0.448288 + 1.67303i
\(328\) −1.22474 + 1.22474i −1.22474 + 1.22474i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) −1.67303 + 0.448288i −1.67303 + 0.448288i
\(333\) 0 0
\(334\) −0.866025 1.50000i −0.866025 1.50000i
\(335\) 0 0
\(336\) −1.50000 0.866025i −1.50000 0.866025i
\(337\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(338\) 0.258819 0.965926i 0.258819 0.965926i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(344\) 1.00000i 1.00000i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(348\) −1.67303 0.448288i −1.67303 0.448288i
\(349\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.73205i 1.73205i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) 0 0
\(361\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(362\) 0.448288 1.67303i 0.448288 1.67303i
\(363\) −1.22474 + 1.22474i −1.22474 + 1.22474i
\(364\) 0 0
\(365\) 0 0
\(366\) −1.50000 2.59808i −1.50000 2.59808i
\(367\) 1.67303 0.448288i 1.67303 0.448288i 0.707107 0.707107i \(-0.250000\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(368\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(369\) −1.73205 3.00000i −1.73205 3.00000i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 1.22474 1.22474i 1.22474 1.22474i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 3.00000 + 1.73205i 3.00000 + 1.73205i
\(382\) 0 0
\(383\) 1.67303 + 0.448288i 1.67303 + 0.448288i 0.965926 0.258819i \(-0.0833333\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(384\) 1.73205 1.73205
\(385\) 0 0
\(386\) 0 0
\(387\) −1.93185 0.517638i −1.93185 0.517638i
\(388\) 0 0
\(389\) −1.73205 1.00000i −1.73205 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 0.500000i \(-0.833333\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.965926 0.258819i −0.965926 0.258819i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) −1.67303 + 0.448288i −1.67303 + 0.448288i
\(403\) 0 0
\(404\) −0.866025 1.50000i −0.866025 1.50000i
\(405\) 0 0
\(406\) −1.00000 −1.00000
\(407\) 0 0
\(408\) 0 0
\(409\) 0.866025 1.50000i 0.866025 1.50000i 1.00000i \(-0.5\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.22474 1.22474i −1.22474 1.22474i
\(413\) 0 0
\(414\) 2.00000i 2.00000i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.22474 1.22474i −1.22474 1.22474i
\(428\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −0.448288 + 1.67303i −0.448288 + 1.67303i
\(433\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.500000 0.866025i −0.500000 0.866025i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 1.00000 1.73205i 1.00000 1.73205i
\(442\) 0 0
\(443\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −1.22474 1.22474i −1.22474 1.22474i
\(448\) 0.965926 0.258819i 0.965926 0.258819i
\(449\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(464\) 0.866025 0.500000i 0.866025 0.500000i
\(465\) 0 0
\(466\) 0 0
\(467\) −0.448288 + 1.67303i −0.448288 + 1.67303i 0.258819 + 0.965926i \(0.416667\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) 0 0
\(469\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −0.448288 1.67303i −0.448288 1.67303i
\(484\) 1.00000i 1.00000i
\(485\) 0 0
\(486\) 0 0
\(487\) 0.517638 + 1.93185i 0.517638 + 1.93185i 0.258819 + 0.965926i \(0.416667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(488\) 1.67303 + 0.448288i 1.67303 + 0.448288i
\(489\) −3.46410 −3.46410
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 2.89778 + 0.776457i 2.89778 + 0.776457i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 2.12132 + 2.12132i 2.12132 + 2.12132i
\(499\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(500\) 0 0
\(501\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(502\) 0 0
\(503\) 1.22474 1.22474i 1.22474 1.22474i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(504\) 2.00000i 2.00000i
\(505\) 0 0
\(506\) 0 0
\(507\) −1.67303 + 0.448288i −1.67303 + 0.448288i
\(508\) −1.93185 + 0.517638i −1.93185 + 0.517638i
\(509\) 0.866025 + 1.50000i 0.866025 + 1.50000i 0.866025 + 0.500000i \(0.166667\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 1.50000 0.866025i 1.50000 0.866025i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0.517638 + 1.93185i 0.517638 + 1.93185i
\(523\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 1.00000 1.00000
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 2.59808 1.50000i 2.59808 1.50000i
\(535\) 0 0
\(536\) 0.500000 0.866025i 0.500000 0.866025i
\(537\) 0 0
\(538\) −1.22474 + 1.22474i −1.22474 + 1.22474i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −2.89778 + 0.776457i −2.89778 + 0.776457i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(548\) 0 0
\(549\) −1.73205 + 3.00000i −1.73205 + 3.00000i
\(550\) 0 0
\(551\) 0 0
\(552\) 1.22474 + 1.22474i 1.22474 + 1.22474i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.93185 0.517638i −1.93185 0.517638i
\(563\) −0.448288 1.67303i −0.448288 1.67303i −0.707107 0.707107i \(-0.750000\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.965926 0.258819i −0.965926 0.258819i
\(568\) 0 0
\(569\) 1.73205 1.00000i 1.73205 1.00000i 0.866025 0.500000i \(-0.166667\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(570\) 0 0
\(571\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 1.73205 1.73205
\(575\) 0 0
\(576\) −1.00000 1.73205i −1.00000 1.73205i
\(577\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(578\) 0.965926 0.258819i 0.965926 0.258819i
\(579\) 0 0
\(580\) 0 0
\(581\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(582\) 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 \(0.750000\pi\)
\(588\) 0.448288 + 1.67303i 0.448288 + 1.67303i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.00000 1.00000
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0.707107 0.707107i 0.707107 0.707107i
\(603\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(604\) 0 0
\(605\) 0 0
\(606\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(607\) 0.448288 1.67303i 0.448288 1.67303i −0.258819 0.965926i \(-0.583333\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(608\) 0 0
\(609\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(614\) 0.866025 + 1.50000i 0.866025 + 1.50000i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(618\) −0.776457 + 2.89778i −0.776457 + 2.89778i
\(619\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(622\) 0 0
\(623\) 1.22474 1.22474i 1.22474 1.22474i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 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 0
\(641\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(642\) 0.448288 1.67303i 0.448288 1.67303i
\(643\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(644\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(645\) 0 0
\(646\) 0 0
\(647\) −1.67303 + 0.448288i −1.67303 + 0.448288i −0.965926 0.258819i \(-0.916667\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(648\) 0.965926 0.258819i 0.965926 0.258819i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 1.41421 1.41421i 1.41421 1.41421i
\(653\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(654\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(655\) 0 0
\(656\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 1.50000 + 0.866025i 1.50000 + 0.866025i 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −1.73205 −1.73205
\(665\) 0 0
\(666\) 0 0
\(667\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(668\) −0.448288 1.67303i −0.448288 1.67303i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −1.22474 1.22474i −1.22474 1.22474i
\(673\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0.500000 0.866025i 0.500000 0.866025i
\(677\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(687\) 0 0
\(688\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 1.00000i 1.00000i
\(695\) 0 0
\(696\) −1.50000 0.866025i −1.50000 0.866025i
\(697\) 0 0
\(698\) −1.67303 0.448288i −1.67303 0.448288i
\(699\) 0 0
\(700\) 0 0
\(701\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.448288 + 1.67303i −0.448288 + 1.67303i
\(708\) 0 0
\(709\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.448288 + 1.67303i −0.448288 + 1.67303i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(720\) 0 0
\(721\) 1.73205i 1.73205i
\(722\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(723\) 0 0
\(724\) 0.866025 1.50000i 0.866025 1.50000i
\(725\) 0 0
\(726\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(727\) 1.22474 + 1.22474i 1.22474 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(728\) 0 0
\(729\) 1.00000i 1.00000i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.776457 2.89778i −0.776457 2.89778i
\(733\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(734\) 1.73205 1.73205
\(735\) 0 0
\(736\) −1.00000 −1.00000
\(737\) 0 0
\(738\) −0.896575 3.34607i −0.896575 3.34607i
\(739\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.896575 3.34607i 0.896575 3.34607i
\(748\) 0 0
\(749\) 1.00000i 1.00000i
\(750\) 0 0
\(751\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.50000 0.866025i 1.50000 0.866025i
\(757\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 2.44949 + 2.44949i 2.44949 + 2.44949i
\(763\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(764\) 0 0
\(765\) 0 0
\(766\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(767\) 0 0
\(768\) 1.67303 + 0.448288i 1.67303 + 0.448288i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(774\) −1.73205 1.00000i −1.73205 1.00000i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −1.41421 1.41421i −1.41421 1.41421i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 1.22474 1.22474i 1.22474 1.22474i
\(784\) −0.866025 0.500000i −0.866025 0.500000i
\(785\) 0 0
\(786\) 0 0
\(787\) 1.67303 0.448288i 1.67303 0.448288i 0.707107 0.707107i \(-0.250000\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(788\) 0 0
\(789\) −0.866025 1.50000i −0.866025 1.50000i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −3.00000 1.73205i −3.00000 1.73205i
\(802\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(803\) 0 0
\(804\) −1.73205 −1.73205
\(805\) 0 0
\(806\) 0 0
\(807\) 2.89778 + 0.776457i 2.89778 + 0.776457i
\(808\) −0.448288 1.67303i −0.448288 1.67303i
\(809\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) −0.965926 0.258819i −0.965926 0.258819i
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 1.22474 1.22474i 1.22474 1.22474i
\(819\) 0 0
\(820\) 0 0
\(821\) −1.00000 1.73205i −1.00000 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(822\) 0 0
\(823\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(824\) −0.866025 1.50000i −0.866025 1.50000i
\(825\) 0 0
\(826\) 0 0
\(827\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(828\) 0.517638 1.93185i 0.517638 1.93185i
\(829\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 0 0
\(842\) −0.965926 0.258819i −0.965926 0.258819i
\(843\) 0.896575 + 3.34607i 0.896575 + 3.34607i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(854\) −0.866025 1.50000i −0.866025 1.50000i
\(855\) 0 0
\(856\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(857\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(858\) 0 0
\(859\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(860\) 0 0
\(861\) −1.50000 2.59808i −1.50000 2.59808i
\(862\) 0 0
\(863\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(864\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(865\) 0 0
\(866\) 0 0
\(867\) −1.22474 1.22474i −1.22474 1.22474i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −0.258819 0.965926i −0.258819 0.965926i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(882\) 1.41421 1.41421i 1.41421 1.41421i
\(883\) 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.500000 0.866025i 0.500000 0.866025i
\(887\) 0.448288 1.67303i 0.448288 1.67303i −0.258819 0.965926i \(-0.583333\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(888\) 0 0
\(889\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) −0.866025 1.50000i −0.866025 1.50000i
\(895\) 0 0
\(896\) 1.00000 1.00000
\(897\) 0 0
\(898\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) −1.67303 0.448288i −1.67303 0.448288i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(908\) 0 0
\(909\) 3.46410 3.46410
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(920\) 0 0
\(921\) 1.50000 2.59808i 1.50000 2.59808i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(927\) 3.34607 0.896575i 3.34607 0.896575i
\(928\) 0.965926 0.258819i 0.965926 0.258819i
\(929\) −0.866025 1.50000i −0.866025 1.50000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(-0.5\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −0.866025 + 1.50000i −0.866025 + 1.50000i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(938\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(942\) 0 0
\(943\) −1.67303 0.448288i −1.67303 0.448288i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(962\) 0 0
\(963\) −1.93185 + 0.517638i −1.93185 + 0.517638i
\(964\) 0 0
\(965\) 0 0
\(966\) 1.73205i 1.73205i
\(967\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(968\) 0.258819 0.965926i 0.258819 0.965926i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 2.00000i 2.00000i
\(975\) 0 0
\(976\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(977\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(978\) −3.34607 0.896575i −3.34607 0.896575i
\(979\) 0 0
\(980\) 0 0
\(981\) 2.00000 2.00000
\(982\) 0 0
\(983\) 0.448288 + 1.67303i 0.448288 + 1.67303i 0.707107 + 0.707107i \(0.250000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(984\) 2.59808 + 1.50000i 2.59808 + 1.50000i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(990\) 0 0
\(991\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 1.50000 + 2.59808i 1.50000 + 2.59808i
\(997\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(998\) 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 700.1.bf.a.507.2 yes 8
4.3 odd 2 inner 700.1.bf.a.507.1 yes 8
5.2 odd 4 inner 700.1.bf.a.143.1 8
5.3 odd 4 inner 700.1.bf.a.143.2 yes 8
5.4 even 2 inner 700.1.bf.a.507.1 yes 8
7.5 odd 6 inner 700.1.bf.a.607.1 yes 8
20.3 even 4 inner 700.1.bf.a.143.1 8
20.7 even 4 inner 700.1.bf.a.143.2 yes 8
20.19 odd 2 CM 700.1.bf.a.507.2 yes 8
28.19 even 6 inner 700.1.bf.a.607.2 yes 8
35.12 even 12 inner 700.1.bf.a.243.2 yes 8
35.19 odd 6 inner 700.1.bf.a.607.2 yes 8
35.33 even 12 inner 700.1.bf.a.243.1 yes 8
140.19 even 6 inner 700.1.bf.a.607.1 yes 8
140.47 odd 12 inner 700.1.bf.a.243.1 yes 8
140.103 odd 12 inner 700.1.bf.a.243.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
700.1.bf.a.143.1 8 5.2 odd 4 inner
700.1.bf.a.143.1 8 20.3 even 4 inner
700.1.bf.a.143.2 yes 8 5.3 odd 4 inner
700.1.bf.a.143.2 yes 8 20.7 even 4 inner
700.1.bf.a.243.1 yes 8 35.33 even 12 inner
700.1.bf.a.243.1 yes 8 140.47 odd 12 inner
700.1.bf.a.243.2 yes 8 35.12 even 12 inner
700.1.bf.a.243.2 yes 8 140.103 odd 12 inner
700.1.bf.a.507.1 yes 8 4.3 odd 2 inner
700.1.bf.a.507.1 yes 8 5.4 even 2 inner
700.1.bf.a.507.2 yes 8 1.1 even 1 trivial
700.1.bf.a.507.2 yes 8 20.19 odd 2 CM
700.1.bf.a.607.1 yes 8 7.5 odd 6 inner
700.1.bf.a.607.1 yes 8 140.19 even 6 inner
700.1.bf.a.607.2 yes 8 28.19 even 6 inner
700.1.bf.a.607.2 yes 8 35.19 odd 6 inner