Properties

Label 2960.1.ez.a.1099.2
Level $2960$
Weight $1$
Character 2960.1099
Analytic conductor $1.477$
Analytic rank $0$
Dimension $8$
Projective image $S_{4}$
CM/RM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2960,1,Mod(1099,2960)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2960, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 6, 4]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2960.1099");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2960.ez (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: \(1.47723243739\)
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: \(S_{4}\)
Projective field: Galois closure of 4.0.14018560.7

Embedding invariants

Embedding label 1099.2
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 2960.1099
Dual form 2960.1.ez.a.1379.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.258819 - 0.965926i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.258819 + 0.965926i) q^{5} +1.00000 q^{6} +(-1.22474 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.258819 - 0.965926i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.258819 + 0.965926i) q^{5} +1.00000 q^{6} +(-1.22474 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000 q^{10} +(1.00000 - 1.00000i) q^{11} +(0.258819 - 0.965926i) q^{12} +(0.965926 - 0.258819i) q^{13} +(-1.00000 + 1.00000i) q^{14} +(-0.866025 + 0.500000i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.22474 + 0.707107i) q^{17} +(1.36603 - 0.366025i) q^{19} +(0.258819 - 0.965926i) q^{20} +(0.366025 - 1.36603i) q^{21} +(-0.707107 - 1.22474i) q^{22} -1.41421i q^{23} +(-0.866025 - 0.500000i) q^{24} +(-0.866025 + 0.500000i) q^{25} -1.00000i q^{26} +(0.707107 + 0.707107i) q^{27} +(0.707107 + 1.22474i) q^{28} +(0.258819 + 0.965926i) q^{30} +1.00000i q^{31} +(0.965926 - 0.258819i) q^{32} +(1.22474 + 0.707107i) q^{33} +(0.366025 + 1.36603i) q^{34} +(0.366025 - 1.36603i) q^{35} +(-0.258819 - 0.965926i) q^{37} -1.41421i q^{38} +(0.500000 + 0.866025i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(0.866025 + 0.500000i) q^{41} +(-1.22474 - 0.707107i) q^{42} +(0.707107 + 0.707107i) q^{43} +(-1.36603 + 0.366025i) q^{44} +(-1.36603 - 0.366025i) q^{46} +(-0.707107 + 0.707107i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.258819 + 0.965926i) q^{50} +(-1.00000 - 1.00000i) q^{51} +(-0.965926 - 0.258819i) q^{52} +(0.965926 + 0.258819i) q^{53} +(0.866025 - 0.500000i) q^{54} +(1.22474 + 0.707107i) q^{55} +(1.36603 - 0.366025i) q^{56} +(0.707107 + 1.22474i) q^{57} +1.00000 q^{60} +(0.366025 + 1.36603i) q^{61} +(0.965926 + 0.258819i) q^{62} -1.00000i q^{64} +(0.500000 + 0.866025i) q^{65} +(1.00000 - 1.00000i) q^{66} +1.41421 q^{68} +(1.36603 - 0.366025i) q^{69} +(-1.22474 - 0.707107i) q^{70} +(1.00000 - 1.73205i) q^{71} -1.00000 q^{74} +(-0.707107 - 0.707107i) q^{75} +(-1.36603 - 0.366025i) q^{76} +(-1.93185 + 0.517638i) q^{77} +(0.965926 - 0.258819i) q^{78} +(-1.73205 - 1.00000i) q^{79} +(-0.707107 + 0.707107i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.707107 - 0.707107i) q^{82} +(-1.00000 + 1.00000i) q^{84} +(-1.00000 - 1.00000i) q^{85} +(0.866025 - 0.500000i) q^{86} +1.41421i q^{88} +(-1.36603 - 0.366025i) q^{91} +(-0.707107 + 1.22474i) q^{92} +(-0.965926 + 0.258819i) q^{93} +(0.707107 + 1.22474i) q^{95} +(0.500000 + 0.866025i) q^{96} +(0.965926 - 0.258819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{6} + 8 q^{10} + 8 q^{11} - 8 q^{14} + 4 q^{16} + 4 q^{19} - 4 q^{21} - 4 q^{34} - 4 q^{35} + 4 q^{39} - 4 q^{44} - 4 q^{46} + 4 q^{49} - 8 q^{51} + 4 q^{56} + 8 q^{60} - 4 q^{61} + 4 q^{65} + 8 q^{66} + 4 q^{69} + 8 q^{71} - 8 q^{74} - 4 q^{76} - 4 q^{81} - 8 q^{84} - 8 q^{85} - 4 q^{91} + 4 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2960\mathbb{Z}\right)^\times\).

\(n\) \(741\) \(1777\) \(2481\) \(2591\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.258819 0.965926i 0.258819 0.965926i
\(3\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(4\) −0.866025 0.500000i −0.866025 0.500000i
\(5\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(6\) 1.00000 1.00000
\(7\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(8\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(9\) 0 0
\(10\) 1.00000 1.00000
\(11\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(12\) 0.258819 0.965926i 0.258819 0.965926i
\(13\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(14\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(15\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(16\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(17\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(18\) 0 0
\(19\) 1.36603 0.366025i 1.36603 0.366025i 0.500000 0.866025i \(-0.333333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) 0.258819 0.965926i 0.258819 0.965926i
\(21\) 0.366025 1.36603i 0.366025 1.36603i
\(22\) −0.707107 1.22474i −0.707107 1.22474i
\(23\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(24\) −0.866025 0.500000i −0.866025 0.500000i
\(25\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(26\) 1.00000i 1.00000i
\(27\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(28\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(29\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(30\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(31\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0.965926 0.258819i 0.965926 0.258819i
\(33\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(34\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(35\) 0.366025 1.36603i 0.366025 1.36603i
\(36\) 0 0
\(37\) −0.258819 0.965926i −0.258819 0.965926i
\(38\) 1.41421i 1.41421i
\(39\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(40\) −0.866025 0.500000i −0.866025 0.500000i
\(41\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(42\) −1.22474 0.707107i −1.22474 0.707107i
\(43\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(44\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(45\) 0 0
\(46\) −1.36603 0.366025i −1.36603 0.366025i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(49\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(50\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(51\) −1.00000 1.00000i −1.00000 1.00000i
\(52\) −0.965926 0.258819i −0.965926 0.258819i
\(53\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(54\) 0.866025 0.500000i 0.866025 0.500000i
\(55\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(56\) 1.36603 0.366025i 1.36603 0.366025i
\(57\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(58\) 0 0
\(59\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(60\) 1.00000 1.00000
\(61\) 0.366025 + 1.36603i 0.366025 + 1.36603i 0.866025 + 0.500000i \(0.166667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(62\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(63\) 0 0
\(64\) 1.00000i 1.00000i
\(65\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(66\) 1.00000 1.00000i 1.00000 1.00000i
\(67\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(68\) 1.41421 1.41421
\(69\) 1.36603 0.366025i 1.36603 0.366025i
\(70\) −1.22474 0.707107i −1.22474 0.707107i
\(71\) 1.00000 1.73205i 1.00000 1.73205i 0.500000 0.866025i \(-0.333333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) −1.00000 −1.00000
\(75\) −0.707107 0.707107i −0.707107 0.707107i
\(76\) −1.36603 0.366025i −1.36603 0.366025i
\(77\) −1.93185 + 0.517638i −1.93185 + 0.517638i
\(78\) 0.965926 0.258819i 0.965926 0.258819i
\(79\) −1.73205 1.00000i −1.73205 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 0.500000i \(-0.833333\pi\)
\(80\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(81\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(82\) 0.707107 0.707107i 0.707107 0.707107i
\(83\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(84\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(85\) −1.00000 1.00000i −1.00000 1.00000i
\(86\) 0.866025 0.500000i 0.866025 0.500000i
\(87\) 0 0
\(88\) 1.41421i 1.41421i
\(89\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) 0 0
\(91\) −1.36603 0.366025i −1.36603 0.366025i
\(92\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(93\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(94\) 0 0
\(95\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(96\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0.965926 0.258819i 0.965926 0.258819i
\(99\) 0 0
\(100\) 1.00000 1.00000
\(101\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(102\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(105\) 1.41421 1.41421
\(106\) 0.500000 0.866025i 0.500000 0.866025i
\(107\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(108\) −0.258819 0.965926i −0.258819 0.965926i
\(109\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(110\) 1.00000 1.00000i 1.00000 1.00000i
\(111\) 0.866025 0.500000i 0.866025 0.500000i
\(112\) 1.41421i 1.41421i
\(113\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) 1.36603 0.366025i 1.36603 0.366025i
\(115\) 1.36603 0.366025i 1.36603 0.366025i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.00000 2.00000
\(120\) 0.258819 0.965926i 0.258819 0.965926i
\(121\) 1.00000i 1.00000i
\(122\) 1.41421 1.41421
\(123\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(124\) 0.500000 0.866025i 0.500000 0.866025i
\(125\) −0.707107 0.707107i −0.707107 0.707107i
\(126\) 0 0
\(127\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(128\) −0.965926 0.258819i −0.965926 0.258819i
\(129\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(130\) 0.965926 0.258819i 0.965926 0.258819i
\(131\) −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i \(0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) −0.707107 1.22474i −0.707107 1.22474i
\(133\) −1.93185 0.517638i −1.93185 0.517638i
\(134\) 0 0
\(135\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(136\) 0.366025 1.36603i 0.366025 1.36603i
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 1.41421i 1.41421i
\(139\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(140\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(141\) 0 0
\(142\) −1.41421 1.41421i −1.41421 1.41421i
\(143\) 0.707107 1.22474i 0.707107 1.22474i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(148\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(149\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(150\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(151\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(152\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(153\) 0 0
\(154\) 2.00000i 2.00000i
\(155\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(156\) 1.00000i 1.00000i
\(157\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(158\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(159\) 1.00000i 1.00000i
\(160\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(161\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(162\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(163\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) −0.500000 0.866025i −0.500000 0.866025i
\(165\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(166\) 0 0
\(167\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(168\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(169\) 0 0
\(170\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(171\) 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 \(0.0833333\pi\)
\(174\) 0 0
\(175\) 1.41421 1.41421
\(176\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(177\) 0 0
\(178\) 0 0
\(179\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(182\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(183\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(184\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(185\) 0.866025 0.500000i 0.866025 0.500000i
\(186\) 1.00000i 1.00000i
\(187\) −0.517638 + 1.93185i −0.517638 + 1.93185i
\(188\) 0 0
\(189\) −0.366025 1.36603i −0.366025 1.36603i
\(190\) 1.36603 0.366025i 1.36603 0.366025i
\(191\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(192\) 0.965926 0.258819i 0.965926 0.258819i
\(193\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(194\) 0 0
\(195\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(196\) 1.00000i 1.00000i
\(197\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(198\) 0 0
\(199\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) 0.258819 0.965926i 0.258819 0.965926i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(205\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(206\) 0 0
\(207\) 0 0
\(208\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(209\) 1.00000 1.73205i 1.00000 1.73205i
\(210\) 0.366025 1.36603i 0.366025 1.36603i
\(211\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(212\) −0.707107 0.707107i −0.707107 0.707107i
\(213\) 1.93185 + 0.517638i 1.93185 + 0.517638i
\(214\) 1.00000i 1.00000i
\(215\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(216\) −1.00000 −1.00000
\(217\) 0.707107 1.22474i 0.707107 1.22474i
\(218\) 0 0
\(219\) 0 0
\(220\) −0.707107 1.22474i −0.707107 1.22474i
\(221\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(222\) −0.258819 0.965926i −0.258819 0.965926i
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) −1.36603 0.366025i −1.36603 0.366025i
\(225\) 0 0
\(226\) 0 0
\(227\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(228\) 1.41421i 1.41421i
\(229\) −1.36603 + 0.366025i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 1.41421i 1.41421i
\(231\) −1.00000 1.73205i −1.00000 1.73205i
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0.517638 1.93185i 0.517638 1.93185i
\(238\) 0.517638 1.93185i 0.517638 1.93185i
\(239\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(240\) −0.866025 0.500000i −0.866025 0.500000i
\(241\) −1.00000 + 1.73205i −1.00000 + 1.73205i −0.500000 + 0.866025i \(0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) −0.965926 0.258819i −0.965926 0.258819i
\(243\) 0 0
\(244\) 0.366025 1.36603i 0.366025 1.36603i
\(245\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(246\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(247\) 1.22474 0.707107i 1.22474 0.707107i
\(248\) −0.707107 0.707107i −0.707107 0.707107i
\(249\) 0 0
\(250\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(251\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(252\) 0 0
\(253\) −1.41421 1.41421i −1.41421 1.41421i
\(254\) 1.36603 0.366025i 1.36603 0.366025i
\(255\) 0.707107 1.22474i 0.707107 1.22474i
\(256\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(257\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(259\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(260\) 1.00000i 1.00000i
\(261\) 0 0
\(262\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(265\) 1.00000i 1.00000i
\(266\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(270\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(271\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(272\) −1.22474 0.707107i −1.22474 0.707107i
\(273\) 1.41421i 1.41421i
\(274\) 0 0
\(275\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(276\) −1.36603 0.366025i −1.36603 0.366025i
\(277\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(281\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(284\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(285\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(286\) −1.00000 1.00000i −1.00000 1.00000i
\(287\) −0.707107 1.22474i −0.707107 1.22474i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.500000 0.866025i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(294\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(295\) 0 0
\(296\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(297\) 1.41421 1.41421
\(298\) 0 0
\(299\) −0.366025 1.36603i −0.366025 1.36603i
\(300\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(301\) −0.366025 1.36603i −0.366025 1.36603i
\(302\) −0.707107 0.707107i −0.707107 0.707107i
\(303\) 0 0
\(304\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(305\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(306\) 0 0
\(307\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(308\) 1.93185 + 0.517638i 1.93185 + 0.517638i
\(309\) 0 0
\(310\) 1.00000i 1.00000i
\(311\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(312\) −0.965926 0.258819i −0.965926 0.258819i
\(313\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(314\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(315\) 0 0
\(316\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(317\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(318\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(319\) 0 0
\(320\) 0.965926 0.258819i 0.965926 0.258819i
\(321\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(322\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(323\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(324\) 0.866025 0.500000i 0.866025 0.500000i
\(325\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(326\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(327\) 0 0
\(328\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(329\) 0 0
\(330\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(331\) −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 1.36603 0.366025i 1.36603 0.366025i
\(337\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(341\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(342\) 0 0
\(343\) 0 0
\(344\) −1.00000 −1.00000
\(345\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(346\) 0 0
\(347\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(348\) 0 0
\(349\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(350\) 0.366025 1.36603i 0.366025 1.36603i
\(351\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(352\) 0.707107 1.22474i 0.707107 1.22474i
\(353\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(354\) 0 0
\(355\) 1.93185 + 0.517638i 1.93185 + 0.517638i
\(356\) 0 0
\(357\) 0.517638 + 1.93185i 0.517638 + 1.93185i
\(358\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(359\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(360\) 0 0
\(361\) 0.866025 0.500000i 0.866025 0.500000i
\(362\) 1.41421i 1.41421i
\(363\) 0.965926 0.258819i 0.965926 0.258819i
\(364\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(365\) 0 0
\(366\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(367\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(368\) 1.22474 0.707107i 1.22474 0.707107i
\(369\) 0 0
\(370\) −0.258819 0.965926i −0.258819 0.965926i
\(371\) −1.00000 1.00000i −1.00000 1.00000i
\(372\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(373\) 0.258819 + 0.965926i 0.258819 + 0.965926i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(374\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(375\) 0.500000 0.866025i 0.500000 0.866025i
\(376\) 0 0
\(377\) 0 0
\(378\) −1.41421 −1.41421
\(379\) 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i \(-0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(380\) 1.41421i 1.41421i
\(381\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(382\) −0.965926 0.258819i −0.965926 0.258819i
\(383\) −0.707107 + 1.22474i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(384\) 1.00000i 1.00000i
\(385\) −1.00000 1.73205i −1.00000 1.73205i
\(386\) −1.36603 0.366025i −1.36603 0.366025i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(390\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(391\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(392\) −0.965926 0.258819i −0.965926 0.258819i
\(393\) −1.41421 −1.41421
\(394\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(395\) 0.517638 1.93185i 0.517638 1.93185i
\(396\) 0 0
\(397\) −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(398\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(399\) 2.00000i 2.00000i
\(400\) −0.866025 0.500000i −0.866025 0.500000i
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(404\) 0 0
\(405\) −0.965926 0.258819i −0.965926 0.258819i
\(406\) 0 0
\(407\) −1.22474 0.707107i −1.22474 0.707107i
\(408\) 1.41421 1.41421
\(409\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(410\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.866025 0.500000i 0.866025 0.500000i
\(417\) 0 0
\(418\) −1.41421 1.41421i −1.41421 1.41421i
\(419\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(420\) −1.22474 0.707107i −1.22474 0.707107i
\(421\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(425\) 0.707107 1.22474i 0.707107 1.22474i
\(426\) 1.00000 1.73205i 1.00000 1.73205i
\(427\) 0.517638 1.93185i 0.517638 1.93185i
\(428\) −0.965926 0.258819i −0.965926 0.258819i
\(429\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(430\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(431\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(432\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(433\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(434\) −1.00000 1.00000i −1.00000 1.00000i
\(435\) 0 0
\(436\) 0 0
\(437\) −0.517638 1.93185i −0.517638 1.93185i
\(438\) 0 0
\(439\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(440\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(441\) 0 0
\(442\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(443\) −0.707107 0.707107i −0.707107 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(444\) −1.00000 −1.00000
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(449\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(450\) 0 0
\(451\) 1.36603 0.366025i 1.36603 0.366025i
\(452\) 0 0
\(453\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(454\) −1.00000 −1.00000
\(455\) 1.41421i 1.41421i
\(456\) −1.36603 0.366025i −1.36603 0.366025i
\(457\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(458\) 1.41421i 1.41421i
\(459\) −1.36603 0.366025i −1.36603 0.366025i
\(460\) −1.36603 0.366025i −1.36603 0.366025i
\(461\) 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i \(-0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) −1.93185 + 0.517638i −1.93185 + 0.517638i
\(463\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(464\) 0 0
\(465\) −0.500000 0.866025i −0.500000 0.866025i
\(466\) 0 0
\(467\) 0.707107 0.707107i 0.707107 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.00000 −1.00000
\(472\) 0 0
\(473\) 1.41421 1.41421
\(474\) −1.73205 1.00000i −1.73205 1.00000i
\(475\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(476\) −1.73205 1.00000i −1.73205 1.00000i
\(477\) 0 0
\(478\) 0 0
\(479\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(480\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(481\) −0.500000 0.866025i −0.500000 0.866025i
\(482\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(483\) −1.93185 0.517638i −1.93185 0.517638i
\(484\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(488\) −1.22474 0.707107i −1.22474 0.707107i
\(489\) 1.00000i 1.00000i
\(490\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(491\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(492\) 0.707107 0.707107i 0.707107 0.707107i
\(493\) 0 0
\(494\) −0.366025 1.36603i −0.366025 1.36603i
\(495\) 0 0
\(496\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(497\) −2.44949 + 1.41421i −2.44949 + 1.41421i
\(498\) 0 0
\(499\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(500\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(501\) 0 0
\(502\) 0 0
\(503\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(507\) 0 0
\(508\) 1.41421i 1.41421i
\(509\) 1.36603 + 0.366025i 1.36603 + 0.366025i 0.866025 0.500000i \(-0.166667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(510\) −1.00000 1.00000i −1.00000 1.00000i
\(511\) 0 0
\(512\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(513\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(514\) 0 0
\(515\) 0 0
\(516\) 0.866025 0.500000i 0.866025 0.500000i
\(517\) 0 0
\(518\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(519\) 0 0
\(520\) −0.965926 0.258819i −0.965926 0.258819i
\(521\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(524\) 1.00000 1.00000i 1.00000 1.00000i
\(525\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(526\) 0 0
\(527\) −0.707107 1.22474i −0.707107 1.22474i
\(528\) 1.41421i 1.41421i
\(529\) −1.00000 −1.00000
\(530\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(531\) 0 0
\(532\) 1.41421 + 1.41421i 1.41421 + 1.41421i
\(533\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(534\) 0 0
\(535\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(536\) 0 0
\(537\) 0.707107 1.22474i 0.707107 1.22474i
\(538\) 0 0
\(539\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(540\) 0.866025 0.500000i 0.866025 0.500000i
\(541\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(542\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(543\) −0.707107 1.22474i −0.707107 1.22474i
\(544\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(545\) 0 0
\(546\) −1.36603 0.366025i −1.36603 0.366025i
\(547\) −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
\(549\) 0 0
\(550\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(551\) 0 0
\(552\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(553\) 1.41421 + 2.44949i 1.41421 + 2.44949i
\(554\) 1.00000 1.00000
\(555\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(556\) 0 0
\(557\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(558\) 0 0
\(559\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(560\) 1.36603 0.366025i 1.36603 0.366025i
\(561\) −2.00000 −2.00000
\(562\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(563\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.00000i 1.00000i
\(567\) 1.22474 0.707107i 1.22474 0.707107i
\(568\) 0.517638 + 1.93185i 0.517638 + 1.93185i
\(569\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(570\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(571\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(572\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(573\) 0.965926 0.258819i 0.965926 0.258819i
\(574\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(575\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(576\) 0 0
\(577\) 1.22474 0.707107i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(578\) −0.707107 0.707107i −0.707107 0.707107i
\(579\) 1.36603 0.366025i 1.36603 0.366025i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.22474 0.707107i 1.22474 0.707107i
\(584\) 0 0
\(585\) 0 0
\(586\) −1.00000 −1.00000
\(587\) −0.965926 + 0.258819i −0.965926 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(588\) 0.965926 0.258819i 0.965926 0.258819i
\(589\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(590\) 0 0
\(591\) 1.00000i 1.00000i
\(592\) 0.707107 0.707107i 0.707107 0.707107i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0.366025 1.36603i 0.366025 1.36603i
\(595\) 0.517638 + 1.93185i 0.517638 + 1.93185i
\(596\) 0 0
\(597\) −0.258819 0.965926i −0.258819 0.965926i
\(598\) −1.41421 −1.41421
\(599\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(600\) 1.00000 1.00000
\(601\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(602\) −1.41421 −1.41421
\(603\) 0 0
\(604\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(605\) 0.965926 0.258819i 0.965926 0.258819i
\(606\) 0 0
\(607\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(608\) 1.22474 0.707107i 1.22474 0.707107i
\(609\) 0 0
\(610\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(614\) −0.500000 0.866025i −0.500000 0.866025i
\(615\) −1.00000 −1.00000
\(616\) 1.00000 1.73205i 1.00000 1.73205i
\(617\) −0.707107 1.22474i −0.707107 1.22474i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 0.965926i \(-0.416667\pi\)
\(618\) 0 0
\(619\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(620\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(621\) 1.00000 1.00000i 1.00000 1.00000i
\(622\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(623\) 0 0
\(624\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(625\) 0.500000 0.866025i 0.500000 0.866025i
\(626\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(627\) 1.93185 + 0.517638i 1.93185 + 0.517638i
\(628\) 0.707107 0.707107i 0.707107 0.707107i
\(629\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(630\) 0 0
\(631\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(632\) 1.93185 0.517638i 1.93185 0.517638i
\(633\) 0 0
\(634\) −0.866025 0.500000i −0.866025 0.500000i
\(635\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(636\) 0.500000 0.866025i 0.500000 0.866025i
\(637\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(638\) 0 0
\(639\) 0 0
\(640\) 1.00000i 1.00000i
\(641\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(642\) 0.965926 0.258819i 0.965926 0.258819i
\(643\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(644\) 1.73205 1.00000i 1.73205 1.00000i
\(645\) −0.965926 0.258819i −0.965926 0.258819i
\(646\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(647\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(648\) −0.258819 0.965926i −0.258819 0.965926i
\(649\) 0 0
\(650\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(651\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(652\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(653\) 0.965926 0.258819i 0.965926 0.258819i 0.258819 0.965926i \(-0.416667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(654\) 0 0
\(655\) −1.41421 −1.41421
\(656\) 1.00000i 1.00000i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(660\) 1.00000 1.00000i 1.00000 1.00000i
\(661\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(662\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(663\) −1.22474 0.707107i −1.22474 0.707107i
\(664\) 0 0
\(665\) 2.00000i 2.00000i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(672\) 1.41421i 1.41421i
\(673\) 1.22474 + 0.707107i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(674\) 1.00000 1.00000i 1.00000 1.00000i
\(675\) −0.965926 0.258819i −0.965926 0.258819i
\(676\) 0 0
\(677\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1.41421 1.41421
\(681\) 0.866025 0.500000i 0.866025 0.500000i
\(682\) 1.22474 0.707107i 1.22474 0.707107i
\(683\) −0.258819 + 0.965926i −0.258819 + 0.965926i 0.707107 + 0.707107i \(0.250000\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −0.707107 1.22474i −0.707107 1.22474i
\(688\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(689\) 1.00000 1.00000
\(690\) 1.36603 0.366025i 1.36603 0.366025i
\(691\) −0.366025 + 1.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i \(0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −1.41421 −1.41421
\(698\) 0 0
\(699\) 0 0
\(700\) −1.22474 0.707107i −1.22474 0.707107i
\(701\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(702\) 0.707107 0.707107i 0.707107 0.707107i
\(703\) −0.707107 1.22474i −0.707107 1.22474i
\(704\) −1.00000 1.00000i −1.00000 1.00000i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(710\) 1.00000 1.73205i 1.00000 1.73205i
\(711\) 0 0
\(712\) 0 0
\(713\) 1.41421 1.41421
\(714\) 2.00000 2.00000
\(715\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(716\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(717\) 0 0
\(718\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(719\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.258819 0.965926i −0.258819 0.965926i
\(723\) −1.93185 0.517638i −1.93185 0.517638i
\(724\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(725\) 0 0
\(726\) 1.00000i 1.00000i
\(727\) −1.22474 0.707107i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(728\) 1.22474 0.707107i 1.22474 0.707107i
\(729\) 1.00000i 1.00000i
\(730\) 0 0
\(731\) −1.36603 0.366025i −1.36603 0.366025i
\(732\) 1.41421 1.41421
\(733\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(734\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(735\) −0.866025 0.500000i −0.866025 0.500000i
\(736\) −0.366025 1.36603i −0.366025 1.36603i
\(737\) 0 0
\(738\) 0 0
\(739\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(740\) −1.00000 −1.00000
\(741\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(742\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(743\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0.500000 0.866025i 0.500000 0.866025i
\(745\) 0 0
\(746\) 1.00000 1.00000
\(747\) 0 0
\(748\) 1.41421 1.41421i 1.41421 1.41421i
\(749\) −1.36603 0.366025i −1.36603 0.366025i
\(750\) −0.707107 0.707107i −0.707107 0.707107i
\(751\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(756\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(757\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(758\) 0.707107 1.22474i 0.707107 1.22474i
\(759\) 1.00000 1.73205i 1.00000 1.73205i
\(760\) −1.36603 0.366025i −1.36603 0.366025i
\(761\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(763\) 0 0
\(764\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(765\) 0 0
\(766\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(767\) 0 0
\(768\) −0.965926 0.258819i −0.965926 0.258819i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) −1.93185 + 0.517638i −1.93185 + 0.517638i
\(771\) 0 0
\(772\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(773\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(774\) 0 0
\(775\) −0.500000 0.866025i −0.500000 0.866025i
\(776\) 0 0
\(777\) −1.41421 −1.41421
\(778\) 0 0
\(779\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(780\) 0.965926 0.258819i 0.965926 0.258819i
\(781\) −0.732051 2.73205i −0.732051 2.73205i
\(782\) 1.93185 0.517638i 1.93185 0.517638i
\(783\) 0 0
\(784\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(785\) −1.00000 −1.00000
\(786\) −0.366025 + 1.36603i −0.366025 + 1.36603i
\(787\) −0.707107 + 0.707107i −0.707107 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(788\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(789\) 0 0
\(790\) −1.73205 1.00000i −1.73205 1.00000i
\(791\) 0 0
\(792\) 0 0
\(793\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(794\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(795\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(796\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(797\) 0.258819 0.965926i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(798\) −1.93185 0.517638i −1.93185 0.517638i
\(799\) 0 0
\(800\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) −1.93185 0.517638i −1.93185 0.517638i
\(806\) 1.00000 1.00000
\(807\) 0 0
\(808\) 0 0
\(809\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(810\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(811\) −0.366025 1.36603i −0.366025 1.36603i −0.866025 0.500000i \(-0.833333\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(812\) 0 0
\(813\) −0.707107 0.707107i −0.707107 0.707107i
\(814\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(815\) 1.00000i 1.00000i
\(816\) 0.366025 1.36603i 0.366025 1.36603i
\(817\) 1.22474 + 0.707107i 1.22474 + 0.707107i
\(818\) −0.258819 0.965926i −0.258819 0.965926i
\(819\) 0 0
\(820\) 0.707107 0.707107i 0.707107 0.707107i
\(821\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(822\) 0 0
\(823\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(824\) 0 0
\(825\) −1.41421 −1.41421
\(826\) 0 0
\(827\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(828\) 0 0
\(829\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(830\) 0 0
\(831\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(832\) −0.258819 0.965926i −0.258819 0.965926i
\(833\) −1.22474 0.707107i −1.22474 0.707107i
\(834\) 0 0
\(835\) 0 0
\(836\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(837\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(838\) 0 0
\(839\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(840\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(841\) 1.00000i 1.00000i
\(842\) 0 0
\(843\) −0.707107 0.707107i −0.707107 0.707107i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(848\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(849\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(850\) −1.00000 1.00000i −1.00000 1.00000i
\(851\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(852\) −1.41421 1.41421i −1.41421 1.41421i
\(853\) 0.965926 + 0.258819i 0.965926 + 0.258819i 0.707107 0.707107i \(-0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(854\) −1.73205 1.00000i −1.73205 1.00000i
\(855\) 0 0
\(856\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0.707107 1.22474i 0.707107 1.22474i
\(859\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(860\) 0.866025 0.500000i 0.866025 0.500000i
\(861\) 1.00000 1.00000i 1.00000 1.00000i
\(862\) 0.707107 0.707107i 0.707107 0.707107i
\(863\) 0.707107 + 1.22474i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(864\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(865\) 0 0
\(866\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(867\) 0.965926 + 0.258819i 0.965926 + 0.258819i
\(868\) −1.22474 + 0.707107i −1.22474 + 0.707107i
\(869\) −2.73205 + 0.732051i −2.73205 + 0.732051i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) −2.00000 −2.00000
\(875\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(876\) 0 0
\(877\) 0.707107 + 0.707107i 0.707107 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(878\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(879\) 0.866025 0.500000i 0.866025 0.500000i
\(880\) 1.41421i 1.41421i
\(881\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(882\) 0 0
\(883\) −0.258819 0.965926i −0.258819 0.965926i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(884\) 1.36603 0.366025i 1.36603 0.366025i
\(885\) 0 0
\(886\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(889\) 2.00000i 2.00000i
\(890\) 0 0
\(891\) 0.366025 + 1.36603i 0.366025 + 1.36603i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0.707107 1.22474i 0.707107 1.22474i
\(896\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(897\) 1.22474 0.707107i 1.22474 0.707107i
\(898\) −0.707107 0.707107i −0.707107 0.707107i
\(899\) 0 0
\(900\) 0 0
\(901\) −1.36603 + 0.366025i −1.36603 + 0.366025i
\(902\) 1.41421i 1.41421i
\(903\) 1.22474 0.707107i 1.22474 0.707107i
\(904\) 0 0
\(905\) −0.707107 1.22474i −0.707107 1.22474i
\(906\) 0.500000 0.866025i 0.500000 0.866025i
\(907\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(908\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(909\) 0 0
\(910\) −1.36603 0.366025i −1.36603 0.366025i
\(911\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(912\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(913\) 0 0
\(914\) 0 0
\(915\) −1.00000 1.00000i −1.00000 1.00000i
\(916\) 1.36603 + 0.366025i 1.36603 + 0.366025i
\(917\) 1.41421 1.41421i 1.41421 1.41421i
\(918\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) −0.707107 + 1.22474i −0.707107 + 1.22474i
\(921\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(922\) 0.707107 1.22474i 0.707107 1.22474i
\(923\) 0.517638 1.93185i 0.517638 1.93185i
\(924\) 2.00000i 2.00000i
\(925\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(930\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(931\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(932\) 0 0
\(933\) 0.707107 0.707107i 0.707107 0.707107i
\(934\) −0.500000 0.866025i −0.500000 0.866025i
\(935\) −2.00000 −2.00000
\(936\) 0 0
\(937\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(938\) 0 0
\(939\) 1.00000 1.00000i 1.00000 1.00000i
\(940\) 0 0
\(941\) −1.36603 0.366025i −1.36603 0.366025i −0.500000 0.866025i \(-0.666667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(942\) −0.258819 + 0.965926i −0.258819 + 0.965926i
\(943\) 0.707107 1.22474i 0.707107 1.22474i
\(944\) 0 0
\(945\) 1.22474 0.707107i 1.22474 0.707107i
\(946\) 0.366025 1.36603i 0.366025 1.36603i
\(947\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(948\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(949\) 0 0
\(950\) 0.707107 + 1.22474i 0.707107 + 1.22474i
\(951\) 1.00000 1.00000
\(952\) −1.41421 + 1.41421i −1.41421 + 1.41421i
\(953\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(954\) 0 0
\(955\) 0.965926 0.258819i 0.965926 0.258819i
\(956\) 0 0
\(957\) 0 0
\(958\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(959\) 0 0
\(960\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(961\) 0 0
\(962\) −0.965926 + 0.258819i −0.965926 + 0.258819i
\(963\) 0 0
\(964\) 1.73205 1.00000i 1.73205 1.00000i
\(965\) 1.36603 0.366025i 1.36603 0.366025i
\(966\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(967\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(969\) −1.73205 1.00000i −1.73205 1.00000i
\(970\) 0 0
\(971\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −1.36603 0.366025i −1.36603 0.366025i
\(975\) −0.866025 0.500000i −0.866025 0.500000i
\(976\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(977\) −1.22474 + 0.707107i −1.22474 + 0.707107i −0.965926 0.258819i \(-0.916667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(978\) −0.965926 0.258819i −0.965926 0.258819i
\(979\) 0 0
\(980\) 0.965926 0.258819i 0.965926 0.258819i
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(984\) −0.500000 0.866025i −0.500000 0.866025i
\(985\) 1.00000i 1.00000i
\(986\) 0 0
\(987\) 0 0
\(988\) −1.41421 −1.41421
\(989\) 1.00000 1.00000i 1.00000 1.00000i
\(990\) 0 0
\(991\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(992\) 0.258819 + 0.965926i 0.258819 + 0.965926i
\(993\) 1.41421i 1.41421i
\(994\) 0.732051 + 2.73205i 0.732051 + 2.73205i
\(995\) −0.258819 0.965926i −0.258819 0.965926i
\(996\) 0 0
\(997\) −0.965926 0.258819i −0.965926 0.258819i −0.258819 0.965926i \(-0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(998\) 0 0
\(999\) 0.500000 0.866025i 0.500000 0.866025i
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 2960.1.ez.a.1099.2 yes 8
5.4 even 2 inner 2960.1.ez.a.1099.1 8
16.3 odd 4 inner 2960.1.ez.a.2579.2 yes 8
37.10 even 3 inner 2960.1.ez.a.2859.1 yes 8
80.19 odd 4 inner 2960.1.ez.a.2579.1 yes 8
185.84 even 6 inner 2960.1.ez.a.2859.2 yes 8
592.195 odd 12 inner 2960.1.ez.a.1379.1 yes 8
2960.1379 odd 12 inner 2960.1.ez.a.1379.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2960.1.ez.a.1099.1 8 5.4 even 2 inner
2960.1.ez.a.1099.2 yes 8 1.1 even 1 trivial
2960.1.ez.a.1379.1 yes 8 592.195 odd 12 inner
2960.1.ez.a.1379.2 yes 8 2960.1379 odd 12 inner
2960.1.ez.a.2579.1 yes 8 80.19 odd 4 inner
2960.1.ez.a.2579.2 yes 8 16.3 odd 4 inner
2960.1.ez.a.2859.1 yes 8 37.10 even 3 inner
2960.1.ez.a.2859.2 yes 8 185.84 even 6 inner