Properties

Label 3332.1.be.a.407.1
Level $3332$
Weight $1$
Character 3332.407
Analytic conductor $1.663$
Analytic rank $0$
Dimension $6$
Projective image $D_{7}$
CM discriminant -68
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3332,1,Mod(407,3332)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3332, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 10, 7]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3332.407");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.be (of order \(14\), degree \(6\), 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: \(1.66288462209\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{14})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{7}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{7} - \cdots)\)

Embedding invariants

Embedding label 407.1
Root \(0.900969 + 0.433884i\) of defining polynomial
Character \(\chi\) \(=\) 3332.407
Dual form 3332.1.be.a.1359.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.222521 + 0.974928i) q^{2} +(-0.777479 + 0.974928i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.777479 - 0.974928i) q^{6} +(-0.623490 + 0.781831i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.123490 - 0.541044i) q^{9} +O(q^{10})\) \(q+(-0.222521 + 0.974928i) q^{2} +(-0.777479 + 0.974928i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(-0.777479 - 0.974928i) q^{6} +(-0.623490 + 0.781831i) q^{7} +(0.623490 - 0.781831i) q^{8} +(-0.123490 - 0.541044i) q^{9} +(-0.0990311 + 0.433884i) q^{11} +(1.12349 - 0.541044i) q^{12} +(0.0990311 - 0.433884i) q^{13} +(-0.623490 - 0.781831i) q^{14} +(0.623490 + 0.781831i) q^{16} +(-0.900969 + 0.433884i) q^{17} +0.554958 q^{18} +(-0.277479 - 1.21572i) q^{21} +(-0.400969 - 0.193096i) q^{22} +(-0.400969 - 0.193096i) q^{23} +(0.277479 + 1.21572i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(0.400969 + 0.193096i) q^{26} +(-0.500000 - 0.240787i) q^{27} +(0.900969 - 0.433884i) q^{28} -1.24698 q^{31} +(-0.900969 + 0.433884i) q^{32} +(-0.346011 - 0.433884i) q^{33} +(-0.222521 - 0.974928i) q^{34} +(-0.123490 + 0.541044i) q^{36} +(0.346011 + 0.433884i) q^{39} +1.24698 q^{42} +(0.277479 - 0.347948i) q^{44} +(0.277479 - 0.347948i) q^{46} -1.24698 q^{48} +(-0.222521 - 0.974928i) q^{49} +1.00000 q^{50} +(0.277479 - 1.21572i) q^{51} +(-0.277479 + 0.347948i) q^{52} +(-1.12349 - 0.541044i) q^{53} +(0.346011 - 0.433884i) q^{54} +(0.222521 + 0.974928i) q^{56} +(0.277479 - 1.21572i) q^{62} +(0.500000 + 0.240787i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.500000 - 0.240787i) q^{66} +1.00000 q^{68} +(0.500000 - 0.240787i) q^{69} +(1.12349 + 0.541044i) q^{71} +(-0.500000 - 0.240787i) q^{72} +(1.12349 + 0.541044i) q^{75} +(-0.277479 - 0.347948i) q^{77} +(-0.500000 + 0.240787i) q^{78} +0.445042 q^{79} +(1.12349 - 0.541044i) q^{81} +(-0.277479 + 1.21572i) q^{84} +(0.277479 + 0.347948i) q^{88} +(-0.277479 - 1.21572i) q^{89} +(0.277479 + 0.347948i) q^{91} +(0.277479 + 0.347948i) q^{92} +(0.969501 - 1.21572i) q^{93} +(0.277479 - 1.21572i) q^{96} +1.00000 q^{98} +0.246980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 5 q^{3} - q^{4} - 5 q^{6} + q^{7} - q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 5 q^{3} - q^{4} - 5 q^{6} + q^{7} - q^{8} + 4 q^{9} - 5 q^{11} + 2 q^{12} + 5 q^{13} + q^{14} - q^{16} - q^{17} + 4 q^{18} - 2 q^{21} + 2 q^{22} + 2 q^{23} + 2 q^{24} - q^{25} - 2 q^{26} - 3 q^{27} + q^{28} + 2 q^{31} - q^{32} + 3 q^{33} - q^{34} + 4 q^{36} - 3 q^{39} - 2 q^{42} + 2 q^{44} + 2 q^{46} + 2 q^{48} - q^{49} + 6 q^{50} + 2 q^{51} - 2 q^{52} - 2 q^{53} - 3 q^{54} + q^{56} + 2 q^{62} + 3 q^{63} - q^{64} + 3 q^{66} + 6 q^{68} + 3 q^{69} + 2 q^{71} - 3 q^{72} + 2 q^{75} - 2 q^{77} - 3 q^{78} + 2 q^{79} + 2 q^{81} - 2 q^{84} + 2 q^{88} - 2 q^{89} + 2 q^{91} + 2 q^{92} - 4 q^{93} + 2 q^{96} + 6 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(885\) \(1667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{7}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(3\) −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i \(0.428571\pi\)
−1.00000 \(\pi\)
\(4\) −0.900969 0.433884i −0.900969 0.433884i
\(5\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(6\) −0.777479 0.974928i −0.777479 0.974928i
\(7\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(8\) 0.623490 0.781831i 0.623490 0.781831i
\(9\) −0.123490 0.541044i −0.123490 0.541044i
\(10\) 0 0
\(11\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i 0.900969 + 0.433884i \(0.142857\pi\)
−1.00000 \(\pi\)
\(12\) 1.12349 0.541044i 1.12349 0.541044i
\(13\) 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
1.00000 \(0\)
\(14\) −0.623490 0.781831i −0.623490 0.781831i
\(15\) 0 0
\(16\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(17\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(18\) 0.554958 0.554958
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) −0.277479 1.21572i −0.277479 1.21572i
\(22\) −0.400969 0.193096i −0.400969 0.193096i
\(23\) −0.400969 0.193096i −0.400969 0.193096i 0.222521 0.974928i \(-0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(24\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(25\) −0.222521 0.974928i −0.222521 0.974928i
\(26\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(27\) −0.500000 0.240787i −0.500000 0.240787i
\(28\) 0.900969 0.433884i 0.900969 0.433884i
\(29\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(30\) 0 0
\(31\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(32\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(33\) −0.346011 0.433884i −0.346011 0.433884i
\(34\) −0.222521 0.974928i −0.222521 0.974928i
\(35\) 0 0
\(36\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(37\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(38\) 0 0
\(39\) 0.346011 + 0.433884i 0.346011 + 0.433884i
\(40\) 0 0
\(41\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(42\) 1.24698 1.24698
\(43\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(44\) 0.277479 0.347948i 0.277479 0.347948i
\(45\) 0 0
\(46\) 0.277479 0.347948i 0.277479 0.347948i
\(47\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(48\) −1.24698 −1.24698
\(49\) −0.222521 0.974928i −0.222521 0.974928i
\(50\) 1.00000 1.00000
\(51\) 0.277479 1.21572i 0.277479 1.21572i
\(52\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(53\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(54\) 0.346011 0.433884i 0.346011 0.433884i
\(55\) 0 0
\(56\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(60\) 0 0
\(61\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(62\) 0.277479 1.21572i 0.277479 1.21572i
\(63\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(64\) −0.222521 0.974928i −0.222521 0.974928i
\(65\) 0 0
\(66\) 0.500000 0.240787i 0.500000 0.240787i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 1.00000 1.00000
\(69\) 0.500000 0.240787i 0.500000 0.240787i
\(70\) 0 0
\(71\) 1.12349 + 0.541044i 1.12349 + 0.541044i 0.900969 0.433884i \(-0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(72\) −0.500000 0.240787i −0.500000 0.240787i
\(73\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(74\) 0 0
\(75\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(76\) 0 0
\(77\) −0.277479 0.347948i −0.277479 0.347948i
\(78\) −0.500000 + 0.240787i −0.500000 + 0.240787i
\(79\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(80\) 0 0
\(81\) 1.12349 0.541044i 1.12349 0.541044i
\(82\) 0 0
\(83\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(84\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(89\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(90\) 0 0
\(91\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(92\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(93\) 0.969501 1.21572i 0.969501 1.21572i
\(94\) 0 0
\(95\) 0 0
\(96\) 0.277479 1.21572i 0.277479 1.21572i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1.00000 1.00000
\(99\) 0.246980 0.246980
\(100\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(101\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(102\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(103\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(104\) −0.277479 0.347948i −0.277479 0.347948i
\(105\) 0 0
\(106\) 0.777479 0.974928i 0.777479 0.974928i
\(107\) −0.400969 1.75676i −0.400969 1.75676i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(108\) 0.346011 + 0.433884i 0.346011 + 0.433884i
\(109\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.00000 −1.00000
\(113\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.246980 −0.246980
\(118\) 0 0
\(119\) 0.222521 0.974928i 0.222521 0.974928i
\(120\) 0 0
\(121\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(122\) 0 0
\(123\) 0 0
\(124\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(125\) 0 0
\(126\) −0.346011 + 0.433884i −0.346011 + 0.433884i
\(127\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) 0.277479 + 0.347948i 0.277479 + 0.347948i 0.900969 0.433884i \(-0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(132\) 0.123490 + 0.541044i 0.123490 + 0.541044i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(137\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(138\) 0.123490 + 0.541044i 0.123490 + 0.541044i
\(139\) 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.777479 + 0.974928i −0.777479 + 0.974928i
\(143\) 0.178448 + 0.0859360i 0.178448 + 0.0859360i
\(144\) 0.346011 0.433884i 0.346011 0.433884i
\(145\) 0 0
\(146\) 0 0
\(147\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(148\) 0 0
\(149\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(150\) −0.777479 + 0.974928i −0.777479 + 0.974928i
\(151\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(152\) 0 0
\(153\) 0.346011 + 0.433884i 0.346011 + 0.433884i
\(154\) 0.400969 0.193096i 0.400969 0.193096i
\(155\) 0 0
\(156\) −0.123490 0.541044i −0.123490 0.541044i
\(157\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(158\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(159\) 1.40097 0.674671i 1.40097 0.674671i
\(160\) 0 0
\(161\) 0.400969 0.193096i 0.400969 0.193096i
\(162\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(163\) −1.24698 1.56366i −1.24698 1.56366i −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 0.781831i \(-0.714286\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.62349 + 0.781831i −1.62349 + 0.781831i −0.623490 + 0.781831i \(0.714286\pi\)
−1.00000 \(1.00000\pi\)
\(168\) −1.12349 0.541044i −1.12349 0.541044i
\(169\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(174\) 0 0
\(175\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(176\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(177\) 0 0
\(178\) 1.24698 1.24698
\(179\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(180\) 0 0
\(181\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(182\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(183\) 0 0
\(184\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(185\) 0 0
\(186\) 0.969501 + 1.21572i 0.969501 + 1.21572i
\(187\) −0.0990311 0.433884i −0.0990311 0.433884i
\(188\) 0 0
\(189\) 0.500000 0.240787i 0.500000 0.240787i
\(190\) 0 0
\(191\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(192\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(193\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −0.0549581 + 0.240787i −0.0549581 + 0.240787i
\(199\) −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i \(0.428571\pi\)
−1.00000 \(\pi\)
\(200\) −0.900969 0.433884i −0.900969 0.433884i
\(201\) 0 0
\(202\) −0.277479 0.347948i −0.277479 0.347948i
\(203\) 0 0
\(204\) −0.777479 + 0.974928i −0.777479 + 0.974928i
\(205\) 0 0
\(206\) 0 0
\(207\) −0.0549581 + 0.240787i −0.0549581 + 0.240787i
\(208\) 0.400969 0.193096i 0.400969 0.193096i
\(209\) 0 0
\(210\) 0 0
\(211\) −0.400969 1.75676i −0.400969 1.75676i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(212\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(213\) −1.40097 + 0.674671i −1.40097 + 0.674671i
\(214\) 1.80194 1.80194
\(215\) 0 0
\(216\) −0.500000 + 0.240787i −0.500000 + 0.240787i
\(217\) 0.777479 0.974928i 0.777479 0.974928i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(222\) 0 0
\(223\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(224\) 0.222521 0.974928i 0.222521 0.974928i
\(225\) −0.500000 + 0.240787i −0.500000 + 0.240787i
\(226\) 0 0
\(227\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(228\) 0 0
\(229\) −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(230\) 0 0
\(231\) 0.554958 0.554958
\(232\) 0 0
\(233\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(234\) 0.0549581 0.240787i 0.0549581 0.240787i
\(235\) 0 0
\(236\) 0 0
\(237\) −0.346011 + 0.433884i −0.346011 + 0.433884i
\(238\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(239\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(240\) 0 0
\(241\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(242\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(243\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −0.777479 + 0.974928i −0.777479 + 0.974928i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(252\) −0.346011 0.433884i −0.346011 0.433884i
\(253\) 0.123490 0.154851i 0.123490 0.154851i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(257\) −1.80194 + 0.867767i −1.80194 + 0.867767i −0.900969 + 0.433884i \(0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −0.554958 −0.554958
\(265\) 0 0
\(266\) 0 0
\(267\) 1.40097 + 0.674671i 1.40097 + 0.674671i
\(268\) 0 0
\(269\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(270\) 0 0
\(271\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(272\) −0.900969 0.433884i −0.900969 0.433884i
\(273\) −0.554958 −0.554958
\(274\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(275\) 0.445042 0.445042
\(276\) −0.554958 −0.554958
\(277\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(278\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(279\) 0.153989 + 0.674671i 0.153989 + 0.674671i
\(280\) 0 0
\(281\) −0.445042 + 1.94986i −0.445042 + 1.94986i −0.222521 + 0.974928i \(0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(282\) 0 0
\(283\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i 0.900969 + 0.433884i \(0.142857\pi\)
−1.00000 \(\pi\)
\(284\) −0.777479 0.974928i −0.777479 0.974928i
\(285\) 0 0
\(286\) −0.123490 + 0.154851i −0.123490 + 0.154851i
\(287\) 0 0
\(288\) 0.346011 + 0.433884i 0.346011 + 0.433884i
\(289\) 0.623490 0.781831i 0.623490 0.781831i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(294\) −0.777479 + 0.974928i −0.777479 + 0.974928i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.153989 0.193096i 0.153989 0.193096i
\(298\) −1.12349 0.541044i −1.12349 0.541044i
\(299\) −0.123490 + 0.154851i −0.123490 + 0.154851i
\(300\) −0.777479 0.974928i −0.777479 0.974928i
\(301\) 0 0
\(302\) 0 0
\(303\) −0.123490 0.541044i −0.123490 0.541044i
\(304\) 0 0
\(305\) 0 0
\(306\) −0.500000 + 0.240787i −0.500000 + 0.240787i
\(307\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(308\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(309\) 0 0
\(310\) 0 0
\(311\) 1.80194 0.867767i 1.80194 0.867767i 0.900969 0.433884i \(-0.142857\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(312\) 0.554958 0.554958
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0.400969 0.193096i 0.400969 0.193096i
\(315\) 0 0
\(316\) −0.400969 0.193096i −0.400969 0.193096i
\(317\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(318\) 0.346011 + 1.51597i 0.346011 + 1.51597i
\(319\) 0 0
\(320\) 0 0
\(321\) 2.02446 + 0.974928i 2.02446 + 0.974928i
\(322\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(323\) 0 0
\(324\) −1.24698 −1.24698
\(325\) −0.445042 −0.445042
\(326\) 1.80194 0.867767i 1.80194 0.867767i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.400969 1.75676i −0.400969 1.75676i
\(335\) 0 0
\(336\) 0.777479 0.974928i 0.777479 0.974928i
\(337\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(338\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(339\) 0 0
\(340\) 0 0
\(341\) 0.123490 0.541044i 0.123490 0.541044i
\(342\) 0 0
\(343\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.62349 0.781831i −1.62349 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(350\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(351\) −0.153989 + 0.193096i −0.153989 + 0.193096i
\(352\) −0.0990311 0.433884i −0.0990311 0.433884i
\(353\) 1.24698 + 1.56366i 1.24698 + 1.56366i 0.623490 + 0.781831i \(0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(357\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(358\) 0 0
\(359\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(364\) −0.0990311 0.433884i −0.0990311 0.433884i
\(365\) 0 0
\(366\) 0 0
\(367\) −0.400969 1.75676i −0.400969 1.75676i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(368\) −0.0990311 0.433884i −0.0990311 0.433884i
\(369\) 0 0
\(370\) 0 0
\(371\) 1.12349 0.541044i 1.12349 0.541044i
\(372\) −1.40097 + 0.674671i −1.40097 + 0.674671i
\(373\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(374\) 0.445042 0.445042
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0.123490 + 0.541044i 0.123490 + 0.541044i
\(379\) 0.445042 1.94986i 0.445042 1.94986i 0.222521 0.974928i \(-0.428571\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(384\) −0.777479 + 0.974928i −0.777479 + 0.974928i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i \(0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(390\) 0 0
\(391\) 0.445042 0.445042
\(392\) −0.900969 0.433884i −0.900969 0.433884i
\(393\) −0.554958 −0.554958
\(394\) 0 0
\(395\) 0 0
\(396\) −0.222521 0.107160i −0.222521 0.107160i
\(397\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(398\) −0.777479 0.974928i −0.777479 0.974928i
\(399\) 0 0
\(400\) 0.623490 0.781831i 0.623490 0.781831i
\(401\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(402\) 0 0
\(403\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(404\) 0.400969 0.193096i 0.400969 0.193096i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.777479 0.974928i −0.777479 0.974928i
\(409\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(410\) 0 0
\(411\) −1.55496 −1.55496
\(412\) 0 0
\(413\) 0 0
\(414\) −0.222521 0.107160i −0.222521 0.107160i
\(415\) 0 0
\(416\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(417\) 0.123490 + 0.541044i 0.123490 + 0.541044i
\(418\) 0 0
\(419\) −0.400969 0.193096i −0.400969 0.193096i 0.222521 0.974928i \(-0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(420\) 0 0
\(421\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(422\) 1.80194 1.80194
\(423\) 0 0
\(424\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(425\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(426\) −0.346011 1.51597i −0.346011 1.51597i
\(427\) 0 0
\(428\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(429\) −0.222521 + 0.107160i −0.222521 + 0.107160i
\(430\) 0 0
\(431\) −1.24698 1.56366i −1.24698 1.56366i −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 0.781831i \(-0.714286\pi\)
\(432\) −0.123490 0.541044i −0.123490 0.541044i
\(433\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(434\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i 0.900969 + 0.433884i \(0.142857\pi\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −0.500000 + 0.240787i −0.500000 + 0.240787i
\(442\) −0.445042 −0.445042
\(443\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −0.969501 1.21572i −0.969501 1.21572i
\(448\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(449\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(450\) −0.123490 0.541044i −0.123490 0.541044i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.277479 1.21572i 0.277479 1.21572i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(458\) 1.62349 0.781831i 1.62349 0.781831i
\(459\) 0.554958 0.554958
\(460\) 0 0
\(461\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(462\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(463\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(468\) 0.222521 + 0.107160i 0.222521 + 0.107160i
\(469\) 0 0
\(470\) 0 0
\(471\) 0.554958 0.554958
\(472\) 0 0
\(473\) 0 0
\(474\) −0.346011 0.433884i −0.346011 0.433884i
\(475\) 0 0
\(476\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(477\) −0.153989 + 0.674671i −0.153989 + 0.674671i
\(478\) 0 0
\(479\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i 0.900969 + 0.433884i \(0.142857\pi\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(484\) −0.500000 0.626980i −0.500000 0.626980i
\(485\) 0 0
\(486\) −0.900969 0.433884i −0.900969 0.433884i
\(487\) −1.24698 + 1.56366i −1.24698 + 1.56366i −0.623490 + 0.781831i \(0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(488\) 0 0
\(489\) 2.49396 2.49396
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.777479 0.974928i −0.777479 0.974928i
\(497\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(498\) 0 0
\(499\) −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0.500000 2.19064i 0.500000 2.19064i
\(502\) 0 0
\(503\) −0.400969 + 1.75676i −0.400969 + 1.75676i 0.222521 + 0.974928i \(0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(504\) 0.500000 0.240787i 0.500000 0.240787i
\(505\) 0 0
\(506\) 0.123490 + 0.154851i 0.123490 + 0.154851i
\(507\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(508\) 0 0
\(509\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.900969 0.433884i −0.900969 0.433884i
\(513\) 0 0
\(514\) −0.445042 1.94986i −0.445042 1.94986i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(524\) −0.0990311 0.433884i −0.0990311 0.433884i
\(525\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(526\) 0 0
\(527\) 1.12349 0.541044i 1.12349 0.541044i
\(528\) 0.123490 0.541044i 0.123490 0.541044i
\(529\) −0.500000 0.626980i −0.500000 0.626980i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.969501 + 1.21572i −0.969501 + 1.21572i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.445042 0.445042
\(540\) 0 0
\(541\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.623490 0.781831i 0.623490 0.781831i
\(545\) 0 0
\(546\) 0.123490 0.541044i 0.123490 0.541044i
\(547\) 1.12349 1.40881i 1.12349 1.40881i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(548\) −0.277479 1.21572i −0.277479 1.21572i
\(549\) 0 0
\(550\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(551\) 0 0
\(552\) 0.123490 0.541044i 0.123490 0.541044i
\(553\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(554\) 0 0
\(555\) 0 0
\(556\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(557\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(558\) −0.692021 −0.692021
\(559\) 0 0
\(560\) 0 0
\(561\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(562\) −1.80194 0.867767i −1.80194 0.867767i
\(563\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −0.400969 0.193096i −0.400969 0.193096i
\(567\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(568\) 1.12349 0.541044i 1.12349 0.541044i
\(569\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(570\) 0 0
\(571\) 1.12349 0.541044i 1.12349 0.541044i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(572\) −0.123490 0.154851i −0.123490 0.154851i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(576\) −0.500000 + 0.240787i −0.500000 + 0.240787i
\(577\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(578\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.346011 0.433884i 0.346011 0.433884i
\(584\) 0 0
\(585\) 0 0
\(586\) 0.0990311 0.433884i 0.0990311 0.433884i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −0.777479 0.974928i −0.777479 0.974928i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i \(0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(594\) 0.153989 + 0.193096i 0.153989 + 0.193096i
\(595\) 0 0
\(596\) 0.777479 0.974928i 0.777479 0.974928i
\(597\) −0.346011 1.51597i −0.346011 1.51597i
\(598\) −0.123490 0.154851i −0.123490 0.154851i
\(599\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(600\) 1.12349 0.541044i 1.12349 0.541044i
\(601\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0.554958 0.554958
\(607\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.123490 0.541044i −0.123490 0.541044i
\(613\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.445042 −0.445042
\(617\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(618\) 0 0
\(619\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0.153989 + 0.193096i 0.153989 + 0.193096i
\(622\) 0.445042 + 1.94986i 0.445042 + 1.94986i
\(623\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(624\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(625\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(632\) 0.277479 0.347948i 0.277479 0.347948i
\(633\) 2.02446 + 0.974928i 2.02446 + 0.974928i
\(634\) 0 0
\(635\) 0 0
\(636\) −1.55496 −1.55496
\(637\) −0.445042 −0.445042
\(638\) 0 0
\(639\) 0.153989 0.674671i 0.153989 0.674671i
\(640\) 0 0
\(641\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(642\) −1.40097 + 1.75676i −1.40097 + 1.75676i
\(643\) 1.12349 + 1.40881i 1.12349 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(644\) −0.445042 −0.445042
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(648\) 0.277479 1.21572i 0.277479 1.21572i
\(649\) 0 0
\(650\) 0.0990311 0.433884i 0.0990311 0.433884i
\(651\) 0.346011 + 1.51597i 0.346011 + 1.51597i
\(652\) 0.445042 + 1.94986i 0.445042 + 1.94986i
\(653\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(660\) 0 0
\(661\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(662\) 0 0
\(663\) −0.500000 0.240787i −0.500000 0.240787i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.80194 1.80194
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(673\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(674\) 0 0
\(675\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(676\) −0.500000 0.626980i −0.500000 0.626980i
\(677\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.969501 1.21572i 0.969501 1.21572i
\(682\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(683\) −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i \(0.428571\pi\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(687\) 2.24698 2.24698
\(688\) 0 0
\(689\) −0.346011 + 0.433884i −0.346011 + 0.433884i
\(690\) 0 0
\(691\) −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i \(0.428571\pi\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) −0.153989 + 0.193096i −0.153989 + 0.193096i
\(694\) 1.12349 1.40881i 1.12349 1.40881i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 1.62349 0.781831i 1.62349 0.781831i
\(699\) 0 0
\(700\) −0.623490 0.781831i −0.623490 0.781831i
\(701\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(702\) −0.153989 0.193096i −0.153989 0.193096i
\(703\) 0 0
\(704\) 0.445042 0.445042
\(705\) 0 0
\(706\) −1.80194 + 0.867767i −1.80194 + 0.867767i
\(707\) −0.0990311 0.433884i −0.0990311 0.433884i
\(708\) 0 0
\(709\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(710\) 0 0
\(711\) −0.0549581 0.240787i −0.0549581 0.240787i
\(712\) −1.12349 0.541044i −1.12349 0.541044i
\(713\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(714\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.277479 + 0.347948i 0.277479 + 0.347948i 0.900969 0.433884i \(-0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −0.222521 0.974928i −0.222521 0.974928i
\(727\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(728\) 0.445042 0.445042
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.445042 + 1.94986i −0.445042 + 1.94986i −0.222521 + 0.974928i \(0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(734\) 1.80194 1.80194
\(735\) 0 0
\(736\) 0.445042 0.445042
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(743\) −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i \(0.428571\pi\)
−1.00000 \(\pi\)
\(744\) −0.346011 1.51597i −0.346011 1.51597i
\(745\) 0 0
\(746\) 0.0990311 0.433884i 0.0990311 0.433884i
\(747\) 0 0
\(748\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(749\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(750\) 0 0
\(751\) 0.277479 + 0.347948i 0.277479 + 0.347948i 0.900969 0.433884i \(-0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.554958 −0.554958
\(757\) −1.80194 0.867767i −1.80194 0.867767i −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 0.433884i \(-0.857143\pi\)
\(758\) 1.80194 + 0.867767i 1.80194 + 0.867767i
\(759\) 0.0549581 + 0.240787i 0.0549581 + 0.240787i
\(760\) 0 0
\(761\) 1.62349 + 0.781831i 1.62349 + 0.781831i 1.00000 \(0\)
0.623490 + 0.781831i \(0.285714\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.777479 0.974928i −0.777479 0.974928i
\(769\) −0.445042 1.94986i −0.445042 1.94986i −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(770\) 0 0
\(771\) 0.554958 2.43143i 0.554958 2.43143i
\(772\) 0 0
\(773\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(774\) 0 0
\(775\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(776\) 0 0
\(777\) 0 0
\(778\) −1.12349 1.40881i −1.12349 1.40881i
\(779\) 0 0
\(780\) 0 0
\(781\) −0.346011 + 0.433884i −0.346011 + 0.433884i
\(782\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(783\) 0 0
\(784\) 0.623490 0.781831i 0.623490 0.781831i
\(785\) 0 0
\(786\) 0.123490 0.541044i 0.123490 0.541044i
\(787\) 1.12349 1.40881i 1.12349 1.40881i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.153989 0.193096i 0.153989 0.193096i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 1.12349 0.541044i 1.12349 0.541044i
\(797\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(801\) −0.623490 + 0.300257i −0.623490 + 0.300257i
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −0.500000 0.240787i −0.500000 0.240787i
\(807\) 0 0
\(808\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(809\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(810\) 0 0
\(811\) 1.12349 + 0.541044i 1.12349 + 0.541044i 0.900969 0.433884i \(-0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 1.12349 0.541044i 1.12349 0.541044i
\(817\) 0 0
\(818\) −0.277479 1.21572i −0.277479 1.21572i
\(819\) 0.153989 0.193096i 0.153989 0.193096i
\(820\) 0 0
\(821\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(822\) 0.346011 1.51597i 0.346011 1.51597i
\(823\) −0.777479 0.974928i −0.777479 0.974928i 0.222521 0.974928i \(-0.428571\pi\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) −0.346011 + 0.433884i −0.346011 + 0.433884i
\(826\) 0 0
\(827\) 1.12349 + 1.40881i 1.12349 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(828\) 0.153989 0.193096i 0.153989 0.193096i
\(829\) 1.62349 + 0.781831i 1.62349 + 0.781831i 1.00000 \(0\)
0.623490 + 0.781831i \(0.285714\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −0.445042 −0.445042
\(833\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(834\) −0.554958 −0.554958
\(835\) 0 0
\(836\) 0 0
\(837\) 0.623490 + 0.300257i 0.623490 + 0.300257i
\(838\) 0.277479 0.347948i 0.277479 0.347948i
\(839\) 1.12349 + 1.40881i 1.12349 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(840\) 0 0
\(841\) 0.623490 0.781831i 0.623490 0.781831i
\(842\) −0.277479 1.21572i −0.277479 1.21572i
\(843\) −1.55496 1.94986i −1.55496 1.94986i
\(844\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(845\) 0 0
\(846\) 0 0
\(847\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(848\) −0.277479 1.21572i −0.277479 1.21572i
\(849\) −0.346011 0.433884i −0.346011 0.433884i
\(850\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(851\) 0 0
\(852\) 1.55496 1.55496
\(853\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.62349 0.781831i −1.62349 0.781831i
\(857\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(858\) −0.0549581 0.240787i −0.0549581 0.240787i
\(859\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 1.80194 0.867767i 1.80194 0.867767i
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0.554958 0.554958
\(865\) 0 0
\(866\) −0.277479 0.347948i −0.277479 0.347948i
\(867\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(868\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(869\) −0.0440730 + 0.193096i −0.0440730 + 0.193096i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(878\) −0.400969 0.193096i −0.400969 0.193096i
\(879\) 0.346011 0.433884i 0.346011 0.433884i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −0.123490 0.541044i −0.123490 0.541044i
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0.0990311 0.433884i 0.0990311 0.433884i
\(885\) 0 0
\(886\) 0 0
\(887\) 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.123490 + 0.541044i 0.123490 + 0.541044i
\(892\) 0 0
\(893\) 0 0
\(894\) 1.40097 0.674671i 1.40097 0.674671i
\(895\) 0 0
\(896\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(897\) −0.0549581 0.240787i −0.0549581 0.240787i
\(898\) 0 0
\(899\) 0 0
\(900\) 0.554958 0.554958
\(901\) 1.24698 1.24698
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0.277479 + 1.21572i 0.277479 + 1.21572i 0.900969 + 0.433884i \(0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(908\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(909\) 0.222521 + 0.107160i 0.222521 + 0.107160i
\(910\) 0 0
\(911\) −0.400969 + 0.193096i −0.400969 + 0.193096i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.400969 0.193096i 0.400969 0.193096i
\(915\) 0 0
\(916\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(917\) −0.445042 −0.445042
\(918\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(919\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −0.277479 1.21572i −0.277479 1.21572i
\(923\) 0.346011 0.433884i 0.346011 0.433884i
\(924\) −0.500000 0.240787i −0.500000 0.240787i
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.554958 + 2.43143i −0.554958 + 2.43143i
\(934\) 0 0
\(935\) 0 0
\(936\) −0.153989 + 0.193096i −0.153989 + 0.193096i
\(937\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(942\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.24698 1.56366i −1.24698 1.56366i −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 0.781831i \(-0.714286\pi\)
\(948\) 0.500000 0.240787i 0.500000 0.240787i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) −0.623490 0.781831i −0.623490 0.781831i
\(953\) 1.62349 + 0.781831i 1.62349 + 0.781831i 1.00000 \(0\)
0.623490 + 0.781831i \(0.285714\pi\)
\(954\) −0.623490 0.300257i −0.623490 0.300257i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −0.400969 0.193096i −0.400969 0.193096i
\(959\) −1.24698 −1.24698
\(960\) 0 0
\(961\) 0.554958 0.554958
\(962\) 0 0
\(963\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(964\) 0 0
\(965\) 0 0
\(966\) −0.500000 0.240787i −0.500000 0.240787i
\(967\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(968\) 0.722521 0.347948i 0.722521 0.347948i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(972\) 0.623490 0.781831i 0.623490 0.781831i
\(973\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(974\) −1.24698 1.56366i −1.24698 1.56366i
\(975\) 0.346011 0.433884i 0.346011 0.433884i
\(976\) 0 0
\(977\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(978\) −0.554958 + 2.43143i −0.554958 + 2.43143i
\(979\) 0.554958 0.554958
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −0.400969 + 1.75676i −0.400969 + 1.75676i 0.222521 + 0.974928i \(0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(992\) 1.12349 0.541044i 1.12349 0.541044i
\(993\) 0 0
\(994\) −0.277479 1.21572i −0.277479 1.21572i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(998\) 0.445042 0.445042
\(999\) 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 3332.1.be.a.407.1 6
4.3 odd 2 3332.1.be.b.407.1 yes 6
17.16 even 2 3332.1.be.b.407.1 yes 6
49.36 even 7 inner 3332.1.be.a.1359.1 yes 6
68.67 odd 2 CM 3332.1.be.a.407.1 6
196.183 odd 14 3332.1.be.b.1359.1 yes 6
833.526 even 14 3332.1.be.b.1359.1 yes 6
3332.1359 odd 14 inner 3332.1.be.a.1359.1 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3332.1.be.a.407.1 6 1.1 even 1 trivial
3332.1.be.a.407.1 6 68.67 odd 2 CM
3332.1.be.a.1359.1 yes 6 49.36 even 7 inner
3332.1.be.a.1359.1 yes 6 3332.1359 odd 14 inner
3332.1.be.b.407.1 yes 6 4.3 odd 2
3332.1.be.b.407.1 yes 6 17.16 even 2
3332.1.be.b.1359.1 yes 6 196.183 odd 14
3332.1.be.b.1359.1 yes 6 833.526 even 14