Properties

Label 696.1.bb.a.125.1
Level $696$
Weight $1$
Character 696.125
Analytic conductor $0.347$
Analytic rank $0$
Dimension $12$
Projective image $D_{14}$
CM discriminant -24
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [696,1,Mod(5,696)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(696, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 7, 7, 11]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("696.5");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 696.bb (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: \(0.347349248793\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{14})\)
Coefficient field: \(\Q(\zeta_{28})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{14}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{14} - \cdots)\)

Embedding invariants

Embedding label 125.1
Root \(-0.781831 - 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 696.125
Dual form 696.1.bb.a.245.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.433884 - 0.900969i) q^{2} +(0.781831 - 0.623490i) q^{3} +(-0.623490 + 0.781831i) q^{4} +(-0.781831 + 0.376510i) q^{5} +(-0.900969 - 0.433884i) q^{6} +(1.12349 + 1.40881i) q^{7} +(0.974928 + 0.222521i) q^{8} +(0.222521 - 0.974928i) q^{9} +O(q^{10})\) \(q+(-0.433884 - 0.900969i) q^{2} +(0.781831 - 0.623490i) q^{3} +(-0.623490 + 0.781831i) q^{4} +(-0.781831 + 0.376510i) q^{5} +(-0.900969 - 0.433884i) q^{6} +(1.12349 + 1.40881i) q^{7} +(0.974928 + 0.222521i) q^{8} +(0.222521 - 0.974928i) q^{9} +(0.678448 + 0.541044i) q^{10} +(0.433884 - 0.0990311i) q^{11} +1.00000i q^{12} +(0.781831 - 1.62349i) q^{14} +(-0.376510 + 0.781831i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-0.974928 + 0.222521i) q^{18} +(0.193096 - 0.846011i) q^{20} +(1.75676 + 0.400969i) q^{21} +(-0.277479 - 0.347948i) q^{22} +(0.900969 - 0.433884i) q^{24} +(-0.153989 + 0.193096i) q^{25} +(-0.433884 - 0.900969i) q^{27} -1.80194 q^{28} +(0.974928 + 0.222521i) q^{29} +0.867767 q^{30} +(-0.846011 - 1.75676i) q^{31} +(-0.781831 + 0.623490i) q^{32} +(0.277479 - 0.347948i) q^{33} +(-1.40881 - 0.678448i) q^{35} +(0.623490 + 0.781831i) q^{36} +(-0.846011 + 0.193096i) q^{40} +(-0.400969 - 1.75676i) q^{42} +(-0.193096 + 0.400969i) q^{44} +(0.193096 + 0.846011i) q^{45} +(-0.781831 - 0.623490i) q^{48} +(-0.500000 + 2.19064i) q^{49} +(0.240787 + 0.0549581i) q^{50} +(-1.40881 + 0.678448i) q^{53} +(-0.623490 + 0.781831i) q^{54} +(-0.301938 + 0.240787i) q^{55} +(0.781831 + 1.62349i) q^{56} +(-0.222521 - 0.974928i) q^{58} -1.94986 q^{59} +(-0.376510 - 0.781831i) q^{60} +(-1.21572 + 1.52446i) q^{62} +(1.62349 - 0.781831i) q^{63} +(0.900969 + 0.433884i) q^{64} +(-0.433884 - 0.0990311i) q^{66} +1.56366i q^{70} +(0.433884 - 0.900969i) q^{72} +(0.678448 - 1.40881i) q^{73} +0.246980i q^{75} +(0.626980 + 0.500000i) q^{77} +(0.541044 + 0.678448i) q^{80} +(-0.900969 - 0.433884i) q^{81} +(1.21572 - 1.52446i) q^{83} +(-1.40881 + 1.12349i) q^{84} +(0.900969 - 0.433884i) q^{87} +0.445042 q^{88} +(0.678448 - 0.541044i) q^{90} +(-1.75676 - 0.846011i) q^{93} +(-0.222521 + 0.974928i) q^{96} +(1.52446 + 1.21572i) q^{97} +(2.19064 - 0.500000i) q^{98} -0.445042i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{9} - 14 q^{15} - 2 q^{16} - 4 q^{22} + 2 q^{24} - 12 q^{25} - 4 q^{28} + 4 q^{33} - 2 q^{36} + 4 q^{42} - 6 q^{49} + 2 q^{54} + 14 q^{55} - 2 q^{58} - 14 q^{60} + 10 q^{63} + 2 q^{64} - 2 q^{81} + 2 q^{87} + 4 q^{88} - 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/696\mathbb{Z}\right)^\times\).

\(n\) \(175\) \(233\) \(349\) \(553\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{5}{14}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.433884 0.900969i −0.433884 0.900969i
\(3\) 0.781831 0.623490i 0.781831 0.623490i
\(4\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(5\) −0.781831 + 0.376510i −0.781831 + 0.376510i −0.781831 0.623490i \(-0.785714\pi\)
1.00000i \(0.5\pi\)
\(6\) −0.900969 0.433884i −0.900969 0.433884i
\(7\) 1.12349 + 1.40881i 1.12349 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(8\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(9\) 0.222521 0.974928i 0.222521 0.974928i
\(10\) 0.678448 + 0.541044i 0.678448 + 0.541044i
\(11\) 0.433884 0.0990311i 0.433884 0.0990311i 1.00000i \(-0.5\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(12\) 1.00000i 1.00000i
\(13\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(14\) 0.781831 1.62349i 0.781831 1.62349i
\(15\) −0.376510 + 0.781831i −0.376510 + 0.781831i
\(16\) −0.222521 0.974928i −0.222521 0.974928i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(19\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(20\) 0.193096 0.846011i 0.193096 0.846011i
\(21\) 1.75676 + 0.400969i 1.75676 + 0.400969i
\(22\) −0.277479 0.347948i −0.277479 0.347948i
\(23\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(24\) 0.900969 0.433884i 0.900969 0.433884i
\(25\) −0.153989 + 0.193096i −0.153989 + 0.193096i
\(26\) 0 0
\(27\) −0.433884 0.900969i −0.433884 0.900969i
\(28\) −1.80194 −1.80194
\(29\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(30\) 0.867767 0.867767
\(31\) −0.846011 1.75676i −0.846011 1.75676i −0.623490 0.781831i \(-0.714286\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(32\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(33\) 0.277479 0.347948i 0.277479 0.347948i
\(34\) 0 0
\(35\) −1.40881 0.678448i −1.40881 0.678448i
\(36\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(37\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.846011 + 0.193096i −0.846011 + 0.193096i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −0.400969 1.75676i −0.400969 1.75676i
\(43\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(44\) −0.193096 + 0.400969i −0.193096 + 0.400969i
\(45\) 0.193096 + 0.846011i 0.193096 + 0.846011i
\(46\) 0 0
\(47\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(48\) −0.781831 0.623490i −0.781831 0.623490i
\(49\) −0.500000 + 2.19064i −0.500000 + 2.19064i
\(50\) 0.240787 + 0.0549581i 0.240787 + 0.0549581i
\(51\) 0 0
\(52\) 0 0
\(53\) −1.40881 + 0.678448i −1.40881 + 0.678448i −0.974928 0.222521i \(-0.928571\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(54\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(55\) −0.301938 + 0.240787i −0.301938 + 0.240787i
\(56\) 0.781831 + 1.62349i 0.781831 + 1.62349i
\(57\) 0 0
\(58\) −0.222521 0.974928i −0.222521 0.974928i
\(59\) −1.94986 −1.94986 −0.974928 0.222521i \(-0.928571\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(60\) −0.376510 0.781831i −0.376510 0.781831i
\(61\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(62\) −1.21572 + 1.52446i −1.21572 + 1.52446i
\(63\) 1.62349 0.781831i 1.62349 0.781831i
\(64\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(65\) 0 0
\(66\) −0.433884 0.0990311i −0.433884 0.0990311i
\(67\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.56366i 1.56366i
\(71\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(72\) 0.433884 0.900969i 0.433884 0.900969i
\(73\) 0.678448 1.40881i 0.678448 1.40881i −0.222521 0.974928i \(-0.571429\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(74\) 0 0
\(75\) 0.246980i 0.246980i
\(76\) 0 0
\(77\) 0.626980 + 0.500000i 0.626980 + 0.500000i
\(78\) 0 0
\(79\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(80\) 0.541044 + 0.678448i 0.541044 + 0.678448i
\(81\) −0.900969 0.433884i −0.900969 0.433884i
\(82\) 0 0
\(83\) 1.21572 1.52446i 1.21572 1.52446i 0.433884 0.900969i \(-0.357143\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(84\) −1.40881 + 1.12349i −1.40881 + 1.12349i
\(85\) 0 0
\(86\) 0 0
\(87\) 0.900969 0.433884i 0.900969 0.433884i
\(88\) 0.445042 0.445042
\(89\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(90\) 0.678448 0.541044i 0.678448 0.541044i
\(91\) 0 0
\(92\) 0 0
\(93\) −1.75676 0.846011i −1.75676 0.846011i
\(94\) 0 0
\(95\) 0 0
\(96\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(97\) 1.52446 + 1.21572i 1.52446 + 1.21572i 0.900969 + 0.433884i \(0.142857\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(98\) 2.19064 0.500000i 2.19064 0.500000i
\(99\) 0.445042i 0.445042i
\(100\) −0.0549581 0.240787i −0.0549581 0.240787i
\(101\) −0.541044 + 1.12349i −0.541044 + 1.12349i 0.433884 + 0.900969i \(0.357143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(102\) 0 0
\(103\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(104\) 0 0
\(105\) −1.52446 + 0.347948i −1.52446 + 0.347948i
\(106\) 1.22252 + 0.974928i 1.22252 + 0.974928i
\(107\) −0.347948 + 1.52446i −0.347948 + 1.52446i 0.433884 + 0.900969i \(0.357143\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(108\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(109\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(110\) 0.347948 + 0.167563i 0.347948 + 0.167563i
\(111\) 0 0
\(112\) 1.12349 1.40881i 1.12349 1.40881i
\(113\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(117\) 0 0
\(118\) 0.846011 + 1.75676i 0.846011 + 1.75676i
\(119\) 0 0
\(120\) −0.541044 + 0.678448i −0.541044 + 0.678448i
\(121\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(122\) 0 0
\(123\) 0 0
\(124\) 1.90097 + 0.433884i 1.90097 + 0.433884i
\(125\) 0.240787 1.05496i 0.240787 1.05496i
\(126\) −1.40881 1.12349i −1.40881 1.12349i
\(127\) −1.52446 + 0.347948i −1.52446 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(128\) 1.00000i 1.00000i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.193096 0.400969i 0.193096 0.400969i −0.781831 0.623490i \(-0.785714\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(132\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(133\) 0 0
\(134\) 0 0
\(135\) 0.678448 + 0.541044i 0.678448 + 0.541044i
\(136\) 0 0
\(137\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(138\) 0 0
\(139\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(140\) 1.40881 0.678448i 1.40881 0.678448i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) −0.846011 + 0.193096i −0.846011 + 0.193096i
\(146\) −1.56366 −1.56366
\(147\) 0.974928 + 2.02446i 0.974928 + 2.02446i
\(148\) 0 0
\(149\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(150\) 0.222521 0.107160i 0.222521 0.107160i
\(151\) −1.62349 0.781831i −1.62349 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0.178448 0.781831i 0.178448 0.781831i
\(155\) 1.32288 + 1.05496i 1.32288 + 1.05496i
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) −0.678448 + 1.40881i −0.678448 + 1.40881i
\(160\) 0.376510 0.781831i 0.376510 0.781831i
\(161\) 0 0
\(162\) 1.00000i 1.00000i
\(163\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(164\) 0 0
\(165\) −0.0859360 + 0.376510i −0.0859360 + 0.376510i
\(166\) −1.90097 0.433884i −1.90097 0.433884i
\(167\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(168\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(169\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.867767 −0.867767 −0.433884 0.900969i \(-0.642857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(174\) −0.781831 0.623490i −0.781831 0.623490i
\(175\) −0.445042 −0.445042
\(176\) −0.193096 0.400969i −0.193096 0.400969i
\(177\) −1.52446 + 1.21572i −1.52446 + 1.21572i
\(178\) 0 0
\(179\) 0.781831 0.376510i 0.781831 0.376510i 1.00000i \(-0.5\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(180\) −0.781831 0.376510i −0.781831 0.376510i
\(181\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 1.94986i 1.94986i
\(187\) 0 0
\(188\) 0 0
\(189\) 0.781831 1.62349i 0.781831 1.62349i
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0.974928 0.222521i 0.974928 0.222521i
\(193\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(194\) 0.433884 1.90097i 0.433884 1.90097i
\(195\) 0 0
\(196\) −1.40097 1.75676i −1.40097 1.75676i
\(197\) 1.40881 + 0.678448i 1.40881 + 0.678448i 0.974928 0.222521i \(-0.0714286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(198\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(199\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(200\) −0.193096 + 0.153989i −0.193096 + 0.153989i
\(201\) 0 0
\(202\) 1.24698 1.24698
\(203\) 0.781831 + 1.62349i 0.781831 + 1.62349i
\(204\) 0 0
\(205\) 0 0
\(206\) −0.974928 + 0.777479i −0.974928 + 0.777479i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(211\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(212\) 0.347948 1.52446i 0.347948 1.52446i
\(213\) 0 0
\(214\) 1.52446 0.347948i 1.52446 0.347948i
\(215\) 0 0
\(216\) −0.222521 0.974928i −0.222521 0.974928i
\(217\) 1.52446 3.16557i 1.52446 3.16557i
\(218\) 0 0
\(219\) −0.347948 1.52446i −0.347948 1.52446i
\(220\) 0.386193i 0.386193i
\(221\) 0 0
\(222\) 0 0
\(223\) 0.277479 1.21572i 0.277479 1.21572i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(224\) −1.75676 0.400969i −1.75676 0.400969i
\(225\) 0.153989 + 0.193096i 0.153989 + 0.193096i
\(226\) 0 0
\(227\) −0.781831 + 0.376510i −0.781831 + 0.376510i −0.781831 0.623490i \(-0.785714\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(230\) 0 0
\(231\) 0.801938 0.801938
\(232\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.21572 1.52446i 1.21572 1.52446i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(240\) 0.846011 + 0.193096i 0.846011 + 0.193096i
\(241\) 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
1.00000 \(0\)
\(242\) 0.626980 + 0.500000i 0.626980 + 0.500000i
\(243\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(244\) 0 0
\(245\) −0.433884 1.90097i −0.433884 1.90097i
\(246\) 0 0
\(247\) 0 0
\(248\) −0.433884 1.90097i −0.433884 1.90097i
\(249\) 1.94986i 1.94986i
\(250\) −1.05496 + 0.240787i −1.05496 + 0.240787i
\(251\) −1.40881 1.12349i −1.40881 1.12349i −0.974928 0.222521i \(-0.928571\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(252\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(253\) 0 0
\(254\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(255\) 0 0
\(256\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(257\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.433884 0.900969i 0.433884 0.900969i
\(262\) −0.445042 −0.445042
\(263\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(264\) 0.347948 0.277479i 0.347948 0.277479i
\(265\) 0.846011 1.06086i 0.846011 1.06086i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.21572 + 0.277479i 1.21572 + 0.277479i 0.781831 0.623490i \(-0.214286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(270\) 0.193096 0.846011i 0.193096 0.846011i
\(271\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.0476909 + 0.0990311i −0.0476909 + 0.0990311i
\(276\) 0 0
\(277\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(278\) 0 0
\(279\) −1.90097 + 0.433884i −1.90097 + 0.433884i
\(280\) −1.22252 0.974928i −1.22252 0.974928i
\(281\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(282\) 0 0
\(283\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(289\) −1.00000 −1.00000
\(290\) 0.541044 + 0.678448i 0.541044 + 0.678448i
\(291\) 1.94986 1.94986
\(292\) 0.678448 + 1.40881i 0.678448 + 1.40881i
\(293\) 0.974928 0.777479i 0.974928 0.777479i 1.00000i \(-0.5\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(294\) 1.40097 1.75676i 1.40097 1.75676i
\(295\) 1.52446 0.734141i 1.52446 0.734141i
\(296\) 0 0
\(297\) −0.277479 0.347948i −0.277479 0.347948i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.193096 0.153989i −0.193096 0.153989i
\(301\) 0 0
\(302\) 1.80194i 1.80194i
\(303\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) −0.781831 + 0.178448i −0.781831 + 0.178448i
\(309\) −0.974928 0.777479i −0.974928 0.777479i
\(310\) 0.376510 1.64960i 0.376510 1.64960i
\(311\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(312\) 0 0
\(313\) 1.62349 + 0.781831i 1.62349 + 0.781831i 1.00000 \(0\)
0.623490 + 0.781831i \(0.285714\pi\)
\(314\) 0 0
\(315\) −0.974928 + 1.22252i −0.974928 + 1.22252i
\(316\) 0 0
\(317\) −0.193096 0.400969i −0.193096 0.400969i 0.781831 0.623490i \(-0.214286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(318\) 1.56366 1.56366
\(319\) 0.445042 0.445042
\(320\) −0.867767 −0.867767
\(321\) 0.678448 + 1.40881i 0.678448 + 1.40881i
\(322\) 0 0
\(323\) 0 0
\(324\) 0.900969 0.433884i 0.900969 0.433884i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0.376510 0.0859360i 0.376510 0.0859360i
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0.433884 + 1.90097i 0.433884 + 1.90097i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 1.80194i 1.80194i
\(337\) −0.846011 + 0.193096i −0.846011 + 0.193096i −0.623490 0.781831i \(-0.714286\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(338\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(339\) 0 0
\(340\) 0 0
\(341\) −0.541044 0.678448i −0.541044 0.678448i
\(342\) 0 0
\(343\) −2.02446 + 0.974928i −2.02446 + 0.974928i
\(344\) 0 0
\(345\) 0 0
\(346\) 0.376510 + 0.781831i 0.376510 + 0.781831i
\(347\) 1.94986 1.94986 0.974928 0.222521i \(-0.0714286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(348\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0.193096 + 0.400969i 0.193096 + 0.400969i
\(351\) 0 0
\(352\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(353\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(354\) 1.75676 + 0.846011i 1.75676 + 0.846011i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.678448 0.541044i −0.678448 0.541044i
\(359\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(360\) 0.867767i 0.867767i
\(361\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(362\) 0 0
\(363\) −0.347948 + 0.722521i −0.347948 + 0.722521i
\(364\) 0 0
\(365\) 1.35690i 1.35690i
\(366\) 0 0
\(367\) 1.22252 + 0.974928i 1.22252 + 0.974928i 1.00000 \(0\)
0.222521 + 0.974928i \(0.428571\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2.53859 1.22252i −2.53859 1.22252i
\(372\) 1.75676 0.846011i 1.75676 0.846011i
\(373\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(374\) 0 0
\(375\) −0.469501 0.974928i −0.469501 0.974928i
\(376\) 0 0
\(377\) 0 0
\(378\) −1.80194 −1.80194
\(379\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(380\) 0 0
\(381\) −0.974928 + 1.22252i −0.974928 + 1.22252i
\(382\) 0 0
\(383\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(384\) −0.623490 0.781831i −0.623490 0.781831i
\(385\) −0.678448 0.154851i −0.678448 0.154851i
\(386\) 0 0
\(387\) 0 0
\(388\) −1.90097 + 0.433884i −1.90097 + 0.433884i
\(389\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.974928 + 2.02446i −0.974928 + 2.02446i
\(393\) −0.0990311 0.433884i −0.0990311 0.433884i
\(394\) 1.56366i 1.56366i
\(395\) 0 0
\(396\) 0.347948 + 0.277479i 0.347948 + 0.277479i
\(397\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(398\) 0.433884 + 0.0990311i 0.433884 + 0.0990311i
\(399\) 0 0
\(400\) 0.222521 + 0.107160i 0.222521 + 0.107160i
\(401\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.541044 1.12349i −0.541044 1.12349i
\(405\) 0.867767 0.867767
\(406\) 1.12349 1.40881i 1.12349 1.40881i
\(407\) 0 0
\(408\) 0 0
\(409\) −0.678448 + 0.541044i −0.678448 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(413\) −2.19064 2.74698i −2.19064 2.74698i
\(414\) 0 0
\(415\) −0.376510 + 1.64960i −0.376510 + 1.64960i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.347948 + 1.52446i 0.347948 + 1.52446i 0.781831 + 0.623490i \(0.214286\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(420\) 0.678448 1.40881i 0.678448 1.40881i
\(421\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −1.52446 + 0.347948i −1.52446 + 0.347948i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −0.974928 1.22252i −0.974928 1.22252i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(432\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(433\) 0.678448 + 1.40881i 0.678448 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(434\) −3.51352 −3.51352
\(435\) −0.541044 + 0.678448i −0.541044 + 0.678448i
\(436\) 0 0
\(437\) 0 0
\(438\) −1.22252 + 0.974928i −1.22252 + 0.974928i
\(439\) 0.777479 0.974928i 0.777479 0.974928i −0.222521 0.974928i \(-0.571429\pi\)
1.00000 \(0\)
\(440\) −0.347948 + 0.167563i −0.347948 + 0.167563i
\(441\) 2.02446 + 0.974928i 2.02446 + 0.974928i
\(442\) 0 0
\(443\) 1.75676 + 0.400969i 1.75676 + 0.400969i 0.974928 0.222521i \(-0.0714286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −1.21572 + 0.277479i −1.21572 + 0.277479i
\(447\) 0 0
\(448\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(449\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(450\) 0.107160 0.222521i 0.107160 0.222521i
\(451\) 0 0
\(452\) 0 0
\(453\) −1.75676 + 0.400969i −1.75676 + 0.400969i
\(454\) 0.678448 + 0.541044i 0.678448 + 0.541044i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.777479 0.974928i −0.777479 0.974928i 0.222521 0.974928i \(-0.428571\pi\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.347948 0.277479i 0.347948 0.277479i −0.433884 0.900969i \(-0.642857\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(462\) −0.347948 0.722521i −0.347948 0.722521i
\(463\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(464\) 1.00000i 1.00000i
\(465\) 1.69202 1.69202
\(466\) 0 0
\(467\) 1.40881 1.12349i 1.40881 1.12349i 0.433884 0.900969i \(-0.357143\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.90097 0.433884i −1.90097 0.433884i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.347948 + 1.52446i 0.347948 + 1.52446i
\(478\) 0 0
\(479\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(480\) −0.193096 0.846011i −0.193096 0.846011i
\(481\) 0 0
\(482\) −0.433884 + 0.0990311i −0.433884 + 0.0990311i
\(483\) 0 0
\(484\) 0.178448 0.781831i 0.178448 0.781831i
\(485\) −1.64960 0.376510i −1.64960 0.376510i
\(486\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(487\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −1.52446 + 1.21572i −1.52446 + 1.21572i
\(491\) 0.541044 + 1.12349i 0.541044 + 1.12349i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0.167563 + 0.347948i 0.167563 + 0.347948i
\(496\) −1.52446 + 1.21572i −1.52446 + 1.21572i
\(497\) 0 0
\(498\) −1.75676 + 0.846011i −1.75676 + 0.846011i
\(499\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(500\) 0.674671 + 0.846011i 0.674671 + 0.846011i
\(501\) 0 0
\(502\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(503\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(504\) 1.75676 0.400969i 1.75676 0.400969i
\(505\) 1.08209i 1.08209i
\(506\) 0 0
\(507\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(508\) 0.678448 1.40881i 0.678448 1.40881i
\(509\) 0.347948 + 1.52446i 0.347948 + 1.52446i 0.781831 + 0.623490i \(0.214286\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(510\) 0 0
\(511\) 2.74698 0.626980i 2.74698 0.626980i
\(512\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.674671 + 0.846011i 0.674671 + 0.846011i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.678448 + 0.541044i −0.678448 + 0.541044i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −1.00000 −1.00000
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0.193096 + 0.400969i 0.193096 + 0.400969i
\(525\) −0.347948 + 0.277479i −0.347948 + 0.277479i
\(526\) 0 0
\(527\) 0 0
\(528\) −0.400969 0.193096i −0.400969 0.193096i
\(529\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(530\) −1.32288 0.301938i −1.32288 0.301938i
\(531\) −0.433884 + 1.90097i −0.433884 + 1.90097i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −0.301938 1.32288i −0.301938 1.32288i
\(536\) 0 0
\(537\) 0.376510 0.781831i 0.376510 0.781831i
\(538\) −0.277479 1.21572i −0.277479 1.21572i
\(539\) 1.00000i 1.00000i
\(540\) −0.846011 + 0.193096i −0.846011 + 0.193096i
\(541\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0.109916 0.109916
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.781831 + 0.376510i 0.781831 + 0.376510i 0.781831 0.623490i \(-0.214286\pi\)
1.00000i \(0.5\pi\)
\(558\) 1.21572 + 1.52446i 1.21572 + 1.52446i
\(559\) 0 0
\(560\) −0.347948 + 1.52446i −0.347948 + 1.52446i
\(561\) 0 0
\(562\) 0 0
\(563\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.400969 1.75676i −0.400969 1.75676i
\(568\) 0 0
\(569\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(570\) 0 0
\(571\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.623490 0.781831i 0.623490 0.781831i
\(577\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(578\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(579\) 0 0
\(580\) 0.376510 0.781831i 0.376510 0.781831i
\(581\) 3.51352 3.51352
\(582\) −0.846011 1.75676i −0.846011 1.75676i
\(583\) −0.544073 + 0.433884i −0.544073 + 0.433884i
\(584\) 0.974928 1.22252i 0.974928 1.22252i
\(585\) 0 0
\(586\) −1.12349 0.541044i −1.12349 0.541044i
\(587\) −0.974928 1.22252i −0.974928 1.22252i −0.974928 0.222521i \(-0.928571\pi\)
1.00000i \(-0.5\pi\)
\(588\) −2.19064 0.500000i −2.19064 0.500000i
\(589\) 0 0
\(590\) −1.32288 1.05496i −1.32288 1.05496i
\(591\) 1.52446 0.347948i 1.52446 0.347948i
\(592\) 0 0
\(593\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(594\) −0.193096 + 0.400969i −0.193096 + 0.400969i
\(595\) 0 0
\(596\) 0 0
\(597\) 0.445042i 0.445042i
\(598\) 0 0
\(599\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(600\) −0.0549581 + 0.240787i −0.0549581 + 0.240787i
\(601\) −0.846011 0.193096i −0.846011 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.62349 0.781831i 1.62349 0.781831i
\(605\) 0.433884 0.544073i 0.433884 0.544073i
\(606\) 0.974928 0.777479i 0.974928 0.777479i
\(607\) −0.376510 0.781831i −0.376510 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(617\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(618\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(619\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(620\) −1.64960 + 0.376510i −1.64960 + 0.376510i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.153989 + 0.674671i 0.153989 + 0.674671i
\(626\) 1.80194i 1.80194i
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 1.52446 + 0.347948i 1.52446 + 0.347948i
\(631\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(635\) 1.06086 0.846011i 1.06086 0.846011i
\(636\) −0.678448 1.40881i −0.678448 1.40881i
\(637\) 0 0
\(638\) −0.193096 0.400969i −0.193096 0.400969i
\(639\) 0 0
\(640\) 0.376510 + 0.781831i 0.376510 + 0.781831i
\(641\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(642\) 0.974928 1.22252i 0.974928 1.22252i
\(643\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(648\) −0.781831 0.623490i −0.781831 0.623490i
\(649\) −0.846011 + 0.193096i −0.846011 + 0.193096i
\(650\) 0 0
\(651\) −0.781831 3.42543i −0.781831 3.42543i
\(652\) 0 0
\(653\) −0.781831 + 1.62349i −0.781831 + 1.62349i 1.00000i \(0.5\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(654\) 0 0
\(655\) 0.386193i 0.386193i
\(656\) 0 0
\(657\) −1.22252 0.974928i −1.22252 0.974928i
\(658\) 0 0
\(659\) −1.21572 0.277479i −1.21572 0.277479i −0.433884 0.900969i \(-0.642857\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(660\) −0.240787 0.301938i −0.240787 0.301938i
\(661\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 1.52446 1.21572i 1.52446 1.21572i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −0.541044 1.12349i −0.541044 1.12349i
\(670\) 0 0
\(671\) 0 0
\(672\) −1.62349 + 0.781831i −1.62349 + 0.781831i
\(673\) −0.400969 0.193096i −0.400969 0.193096i 0.222521 0.974928i \(-0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(674\) 0.541044 + 0.678448i 0.541044 + 0.678448i
\(675\) 0.240787 + 0.0549581i 0.240787 + 0.0549581i
\(676\) 0.222521 0.974928i 0.222521 0.974928i
\(677\) −0.347948 0.277479i −0.347948 0.277479i 0.433884 0.900969i \(-0.357143\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(678\) 0 0
\(679\) 3.51352i 3.51352i
\(680\) 0 0
\(681\) −0.376510 + 0.781831i −0.376510 + 0.781831i
\(682\) −0.376510 + 0.781831i −0.376510 + 0.781831i
\(683\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.75676 + 1.40097i 1.75676 + 1.40097i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(692\) 0.541044 0.678448i 0.541044 0.678448i
\(693\) 0.626980 0.500000i 0.626980 0.500000i
\(694\) −0.846011 1.75676i −0.846011 1.75676i
\(695\) 0 0
\(696\) 0.974928 0.222521i 0.974928 0.222521i
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.277479 0.347948i 0.277479 0.347948i
\(701\) 1.75676 0.846011i 1.75676 0.846011i 0.781831 0.623490i \(-0.214286\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.433884 + 0.0990311i 0.433884 + 0.0990311i
\(705\) 0 0
\(706\) 0 0
\(707\) −2.19064 + 0.500000i −2.19064 + 0.500000i
\(708\) 1.94986i 1.94986i
\(709\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.193096 + 0.846011i −0.193096 + 0.846011i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(720\) 0.781831 0.376510i 0.781831 0.376510i
\(721\) 1.40097 1.75676i 1.40097 1.75676i
\(722\) 0.781831 0.623490i 0.781831 0.623490i
\(723\) −0.193096 0.400969i −0.193096 0.400969i
\(724\) 0 0
\(725\) −0.193096 + 0.153989i −0.193096 + 0.153989i
\(726\) 0.801938 0.801938
\(727\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(728\) 0 0
\(729\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(730\) 1.22252 0.588735i 1.22252 0.588735i
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(734\) 0.347948 1.52446i 0.347948 1.52446i
\(735\) −1.52446 1.21572i −1.52446 1.21572i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2.81762i 2.81762i
\(743\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(744\) −1.52446 1.21572i −1.52446 1.21572i
\(745\) 0 0
\(746\) 0 0
\(747\) −1.21572 1.52446i −1.21572 1.52446i
\(748\) 0 0
\(749\) −2.53859 + 1.22252i −2.53859 + 1.22252i
\(750\) −0.674671 + 0.846011i −0.674671 + 0.846011i
\(751\) −1.22252 + 0.974928i −1.22252 + 0.974928i −0.222521 + 0.974928i \(0.571429\pi\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) −1.80194 −1.80194
\(754\) 0 0
\(755\) 1.56366 1.56366
\(756\) 0.781831 + 1.62349i 0.781831 + 1.62349i
\(757\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(762\) 1.52446 + 0.347948i 1.52446 + 0.347948i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(769\) −0.678448 + 1.40881i −0.678448 + 1.40881i 0.222521 + 0.974928i \(0.428571\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(770\) 0.154851 + 0.678448i 0.154851 + 0.678448i
\(771\) 0 0
\(772\) 0 0
\(773\) 1.40881 + 1.12349i 1.40881 + 1.12349i 0.974928 + 0.222521i \(0.0714286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(774\) 0 0
\(775\) 0.469501 + 0.107160i 0.469501 + 0.107160i
\(776\) 1.21572 + 1.52446i 1.21572 + 1.52446i
\(777\) 0 0
\(778\) −1.62349 + 0.781831i −1.62349 + 0.781831i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.222521 0.974928i −0.222521 0.974928i
\(784\) 2.24698 2.24698
\(785\) 0 0
\(786\) −0.347948 + 0.277479i −0.347948 + 0.277479i
\(787\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(788\) −1.40881 + 0.678448i −1.40881 + 0.678448i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.0990311 0.433884i 0.0990311 0.433884i
\(793\) 0 0
\(794\) 0 0
\(795\) 1.35690i 1.35690i
\(796\) −0.0990311 0.433884i −0.0990311 0.433884i
\(797\) 0.193096 0.400969i 0.193096 0.400969i −0.781831 0.623490i \(-0.785714\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.246980i 0.246980i
\(801\) 0 0
\(802\) 0 0
\(803\) 0.154851 0.678448i 0.154851 0.678448i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.12349 0.541044i 1.12349 0.541044i
\(808\) −0.777479 + 0.974928i −0.777479 + 0.974928i
\(809\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(810\) −0.376510 0.781831i −0.376510 0.781831i
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −1.75676 0.400969i −1.75676 0.400969i
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0.781831 + 0.376510i 0.781831 + 0.376510i
\(819\) 0 0
\(820\) 0 0
\(821\) −0.433884 + 1.90097i −0.433884 + 1.90097i 1.00000i \(0.5\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(822\) 0 0
\(823\) 1.90097 0.433884i 1.90097 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
1.00000 \(0\)
\(824\) 1.24698i 1.24698i
\(825\) 0.0244587 + 0.107160i 0.0244587 + 0.107160i
\(826\) −1.52446 + 3.16557i −1.52446 + 3.16557i
\(827\) 0.781831 1.62349i 0.781831 1.62349i 1.00000i \(-0.5\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 1.64960 0.376510i 1.64960 0.376510i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.21572 + 1.52446i −1.21572 + 1.52446i
\(838\) 1.22252 0.974928i 1.22252 0.974928i
\(839\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(840\) −1.56366 −1.56366
\(841\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0.541044 0.678448i 0.541044 0.678448i
\(846\) 0 0
\(847\) −1.30194 0.626980i −1.30194 0.626980i
\(848\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −0.678448 + 1.40881i −0.678448 + 1.40881i
\(857\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(858\) 0 0
\(859\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(864\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(865\) 0.678448 0.326723i 0.678448 0.326723i
\(866\) 0.974928 1.22252i 0.974928 1.22252i
\(867\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(868\) 1.52446 + 3.16557i 1.52446 + 3.16557i
\(869\) 0 0
\(870\) 0.846011 + 0.193096i 0.846011 + 0.193096i
\(871\) 0 0
\(872\) 0 0
\(873\) 1.52446 1.21572i 1.52446 1.21572i
\(874\) 0 0
\(875\) 1.75676 0.846011i 1.75676 0.846011i
\(876\) 1.40881 + 0.678448i 1.40881 + 0.678448i
\(877\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(878\) −1.21572 0.277479i −1.21572 0.277479i
\(879\) 0.277479 1.21572i 0.277479 1.21572i
\(880\) 0.301938 + 0.240787i 0.301938 + 0.240787i
\(881\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(882\) 2.24698i 2.24698i
\(883\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(884\) 0 0
\(885\) 0.734141 1.52446i 0.734141 1.52446i
\(886\) −0.400969 1.75676i −0.400969 1.75676i
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) −2.20291 1.75676i −2.20291 1.75676i
\(890\) 0 0
\(891\) −0.433884 0.0990311i −0.433884 0.0990311i
\(892\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(893\) 0 0
\(894\) 0 0
\(895\) −0.469501 + 0.588735i −0.469501 + 0.588735i
\(896\) 1.40881 1.12349i 1.40881 1.12349i
\(897\) 0 0
\(898\) 0 0
\(899\) −0.433884 1.90097i −0.433884 1.90097i
\(900\) −0.246980 −0.246980
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 1.12349 + 1.40881i 1.12349 + 1.40881i
\(907\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(908\) 0.193096 0.846011i 0.193096 0.846011i
\(909\) 0.974928 + 0.777479i 0.974928 + 0.777479i
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0.376510 0.781831i 0.376510 0.781831i
\(914\) −0.541044 + 1.12349i −0.541044 + 1.12349i
\(915\) 0 0
\(916\) 0 0
\(917\) 0.781831 0.178448i 0.781831 0.178448i
\(918\) 0 0
\(919\) 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
1.00000 \(0\)
\(920\) 0 0
\(921\) 0 0
\(922\) −0.400969 0.193096i −0.400969 0.193096i
\(923\) 0 0
\(924\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(925\) 0 0
\(926\) −0.781831 1.62349i −0.781831 1.62349i
\(927\) −1.24698 −1.24698
\(928\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) −0.734141 1.52446i −0.734141 1.52446i
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −1.62349 0.781831i −1.62349 0.781831i
\(935\) 0 0
\(936\) 0 0
\(937\) −0.445042 + 1.94986i −0.445042 + 1.94986i −0.222521 + 0.974928i \(0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(938\) 0 0
\(939\) 1.75676 0.400969i 1.75676 0.400969i
\(940\) 0 0
\(941\) −0.347948 1.52446i −0.347948 1.52446i −0.781831 0.623490i \(-0.785714\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0.433884 + 1.90097i 0.433884 + 1.90097i
\(945\) 1.56366i 1.56366i
\(946\) 0 0
\(947\) −0.974928 0.777479i −0.974928 0.777479i 1.00000i \(-0.5\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −0.400969 0.193096i −0.400969 0.193096i
\(952\) 0 0
\(953\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(954\) 1.22252 0.974928i 1.22252 0.974928i
\(955\) 0 0
\(956\) 0 0
\(957\) 0.347948 0.277479i 0.347948 0.277479i
\(958\) 0 0
\(959\) 0 0
\(960\) −0.678448 + 0.541044i −0.678448 + 0.541044i
\(961\) −1.74698 + 2.19064i −1.74698 + 2.19064i
\(962\) 0 0
\(963\) 1.40881 + 0.678448i 1.40881 + 0.678448i
\(964\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(965\) 0 0
\(966\) 0 0
\(967\) 0.678448 + 0.541044i 0.678448 + 0.541044i 0.900969 0.433884i \(-0.142857\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(968\) −0.781831 + 0.178448i −0.781831 + 0.178448i
\(969\) 0 0
\(970\) 0.376510 + 1.64960i 0.376510 + 1.64960i
\(971\) −0.541044 + 1.12349i −0.541044 + 1.12349i 0.433884 + 0.900969i \(0.357143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(972\) 0.433884 0.900969i 0.433884 0.900969i
\(973\) 0 0
\(974\) 0.445042i 0.445042i
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 1.75676 + 0.846011i 1.75676 + 0.846011i
\(981\) 0 0
\(982\) 0.777479 0.974928i 0.777479 0.974928i
\(983\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(984\) 0 0
\(985\) −1.35690 −1.35690
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0.240787 0.301938i 0.240787 0.301938i
\(991\) −1.80194 + 0.867767i −1.80194 + 0.867767i −0.900969 + 0.433884i \(0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(992\) 1.75676 + 0.846011i 1.75676 + 0.846011i
\(993\) 0 0
\(994\) 0 0
\(995\) 0.0859360 0.376510i 0.0859360 0.376510i
\(996\) 1.52446 + 1.21572i 1.52446 + 1.21572i
\(997\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 696.1.bb.a.125.1 12
3.2 odd 2 inner 696.1.bb.a.125.2 yes 12
4.3 odd 2 2784.1.ch.a.1169.1 12
8.3 odd 2 2784.1.ch.a.1169.2 12
8.5 even 2 inner 696.1.bb.a.125.2 yes 12
12.11 even 2 2784.1.ch.a.1169.2 12
24.5 odd 2 CM 696.1.bb.a.125.1 12
24.11 even 2 2784.1.ch.a.1169.1 12
29.13 even 14 inner 696.1.bb.a.245.1 yes 12
87.71 odd 14 inner 696.1.bb.a.245.2 yes 12
116.71 odd 14 2784.1.ch.a.593.1 12
232.13 even 14 inner 696.1.bb.a.245.2 yes 12
232.187 odd 14 2784.1.ch.a.593.2 12
348.71 even 14 2784.1.ch.a.593.2 12
696.245 odd 14 inner 696.1.bb.a.245.1 yes 12
696.419 even 14 2784.1.ch.a.593.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
696.1.bb.a.125.1 12 1.1 even 1 trivial
696.1.bb.a.125.1 12 24.5 odd 2 CM
696.1.bb.a.125.2 yes 12 3.2 odd 2 inner
696.1.bb.a.125.2 yes 12 8.5 even 2 inner
696.1.bb.a.245.1 yes 12 29.13 even 14 inner
696.1.bb.a.245.1 yes 12 696.245 odd 14 inner
696.1.bb.a.245.2 yes 12 87.71 odd 14 inner
696.1.bb.a.245.2 yes 12 232.13 even 14 inner
2784.1.ch.a.593.1 12 116.71 odd 14
2784.1.ch.a.593.1 12 696.419 even 14
2784.1.ch.a.593.2 12 232.187 odd 14
2784.1.ch.a.593.2 12 348.71 even 14
2784.1.ch.a.1169.1 12 4.3 odd 2
2784.1.ch.a.1169.1 12 24.11 even 2
2784.1.ch.a.1169.2 12 8.3 odd 2
2784.1.ch.a.1169.2 12 12.11 even 2