Properties

Label 696.1.bb.a.5.2
Level $696$
Weight $1$
Character 696.5
Analytic conductor $0.347$
Analytic rank $0$
Dimension $12$
Projective image $D_{14}$
CM discriminant -24
Inner twists $8$

Related objects

Downloads

Learn more

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 5.2
Root \(-0.974928 - 0.222521i\) of defining polynomial
Character \(\chi\) \(=\) 696.5
Dual form 696.1.bb.a.557.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.781831 - 0.623490i) q^{2} +(0.974928 - 0.222521i) q^{3} +(0.222521 - 0.974928i) q^{4} +(-0.974928 - 1.22252i) q^{5} +(0.623490 - 0.781831i) q^{6} +(0.277479 + 1.21572i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(0.900969 - 0.433884i) q^{9} +O(q^{10})\) \(q+(0.781831 - 0.623490i) q^{2} +(0.974928 - 0.222521i) q^{3} +(0.222521 - 0.974928i) q^{4} +(-0.974928 - 1.22252i) q^{5} +(0.623490 - 0.781831i) q^{6} +(0.277479 + 1.21572i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(0.900969 - 0.433884i) q^{9} +(-1.52446 - 0.347948i) q^{10} +(-0.781831 + 1.62349i) q^{11} -1.00000i q^{12} +(0.974928 + 0.777479i) q^{14} +(-1.22252 - 0.974928i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(0.433884 - 0.900969i) q^{18} +(-1.40881 + 0.678448i) q^{20} +(0.541044 + 1.12349i) q^{21} +(0.400969 + 1.75676i) q^{22} +(-0.623490 - 0.781831i) q^{24} +(-0.321552 + 1.40881i) q^{25} +(0.781831 - 0.623490i) q^{27} +1.24698 q^{28} +(-0.433884 - 0.900969i) q^{29} -1.56366 q^{30} +(-0.678448 + 0.541044i) q^{31} +(-0.974928 + 0.222521i) q^{32} +(-0.400969 + 1.75676i) q^{33} +(1.21572 - 1.52446i) q^{35} +(-0.222521 - 0.974928i) q^{36} +(-0.678448 + 1.40881i) q^{40} +(1.12349 + 0.541044i) q^{42} +(1.40881 + 1.12349i) q^{44} +(-1.40881 - 0.678448i) q^{45} +(-0.974928 - 0.222521i) q^{48} +(-0.500000 + 0.240787i) q^{49} +(0.626980 + 1.30194i) q^{50} +(1.21572 + 1.52446i) q^{53} +(0.222521 - 0.974928i) q^{54} +(2.74698 - 0.626980i) q^{55} +(0.974928 - 0.777479i) q^{56} +(-0.900969 - 0.433884i) q^{58} +0.867767 q^{59} +(-1.22252 + 0.974928i) q^{60} +(-0.193096 + 0.846011i) q^{62} +(0.777479 + 0.974928i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(0.781831 + 1.62349i) q^{66} -1.94986i q^{70} +(-0.781831 - 0.623490i) q^{72} +(-1.52446 - 1.21572i) q^{73} +1.44504i q^{75} +(-2.19064 - 0.500000i) q^{77} +(0.347948 + 1.52446i) q^{80} +(0.623490 - 0.781831i) q^{81} +(0.193096 - 0.846011i) q^{83} +(1.21572 - 0.277479i) q^{84} +(-0.623490 - 0.781831i) q^{87} +1.80194 q^{88} +(-1.52446 + 0.347948i) q^{90} +(-0.541044 + 0.678448i) q^{93} +(-0.900969 + 0.433884i) q^{96} +(-0.846011 - 0.193096i) q^{97} +(-0.240787 + 0.500000i) q^{98} +1.80194i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/696\mathbb{Z}\right)^\times\).

\(n\) \(175\) \(233\) \(349\) \(553\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{11}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.781831 0.623490i 0.781831 0.623490i
\(3\) 0.974928 0.222521i 0.974928 0.222521i
\(4\) 0.222521 0.974928i 0.222521 0.974928i
\(5\) −0.974928 1.22252i −0.974928 1.22252i −0.974928 0.222521i \(-0.928571\pi\)
1.00000i \(-0.5\pi\)
\(6\) 0.623490 0.781831i 0.623490 0.781831i
\(7\) 0.277479 + 1.21572i 0.277479 + 1.21572i 0.900969 + 0.433884i \(0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(8\) −0.433884 0.900969i −0.433884 0.900969i
\(9\) 0.900969 0.433884i 0.900969 0.433884i
\(10\) −1.52446 0.347948i −1.52446 0.347948i
\(11\) −0.781831 + 1.62349i −0.781831 + 1.62349i 1.00000i \(0.5\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(12\) 1.00000i 1.00000i
\(13\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(14\) 0.974928 + 0.777479i 0.974928 + 0.777479i
\(15\) −1.22252 0.974928i −1.22252 0.974928i
\(16\) −0.900969 0.433884i −0.900969 0.433884i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0.433884 0.900969i 0.433884 0.900969i
\(19\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(20\) −1.40881 + 0.678448i −1.40881 + 0.678448i
\(21\) 0.541044 + 1.12349i 0.541044 + 1.12349i
\(22\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(23\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(24\) −0.623490 0.781831i −0.623490 0.781831i
\(25\) −0.321552 + 1.40881i −0.321552 + 1.40881i
\(26\) 0 0
\(27\) 0.781831 0.623490i 0.781831 0.623490i
\(28\) 1.24698 1.24698
\(29\) −0.433884 0.900969i −0.433884 0.900969i
\(30\) −1.56366 −1.56366
\(31\) −0.678448 + 0.541044i −0.678448 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(32\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(33\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(34\) 0 0
\(35\) 1.21572 1.52446i 1.21572 1.52446i
\(36\) −0.222521 0.974928i −0.222521 0.974928i
\(37\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.678448 + 1.40881i −0.678448 + 1.40881i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(43\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(44\) 1.40881 + 1.12349i 1.40881 + 1.12349i
\(45\) −1.40881 0.678448i −1.40881 0.678448i
\(46\) 0 0
\(47\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(48\) −0.974928 0.222521i −0.974928 0.222521i
\(49\) −0.500000 + 0.240787i −0.500000 + 0.240787i
\(50\) 0.626980 + 1.30194i 0.626980 + 1.30194i
\(51\) 0 0
\(52\) 0 0
\(53\) 1.21572 + 1.52446i 1.21572 + 1.52446i 0.781831 + 0.623490i \(0.214286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(54\) 0.222521 0.974928i 0.222521 0.974928i
\(55\) 2.74698 0.626980i 2.74698 0.626980i
\(56\) 0.974928 0.777479i 0.974928 0.777479i
\(57\) 0 0
\(58\) −0.900969 0.433884i −0.900969 0.433884i
\(59\) 0.867767 0.867767 0.433884 0.900969i \(-0.357143\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(60\) −1.22252 + 0.974928i −1.22252 + 0.974928i
\(61\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(62\) −0.193096 + 0.846011i −0.193096 + 0.846011i
\(63\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(64\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(65\) 0 0
\(66\) 0.781831 + 1.62349i 0.781831 + 1.62349i
\(67\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.94986i 1.94986i
\(71\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(72\) −0.781831 0.623490i −0.781831 0.623490i
\(73\) −1.52446 1.21572i −1.52446 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
−0.623490 0.781831i \(-0.714286\pi\)
\(74\) 0 0
\(75\) 1.44504i 1.44504i
\(76\) 0 0
\(77\) −2.19064 0.500000i −2.19064 0.500000i
\(78\) 0 0
\(79\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(80\) 0.347948 + 1.52446i 0.347948 + 1.52446i
\(81\) 0.623490 0.781831i 0.623490 0.781831i
\(82\) 0 0
\(83\) 0.193096 0.846011i 0.193096 0.846011i −0.781831 0.623490i \(-0.785714\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(84\) 1.21572 0.277479i 1.21572 0.277479i
\(85\) 0 0
\(86\) 0 0
\(87\) −0.623490 0.781831i −0.623490 0.781831i
\(88\) 1.80194 1.80194
\(89\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(90\) −1.52446 + 0.347948i −1.52446 + 0.347948i
\(91\) 0 0
\(92\) 0 0
\(93\) −0.541044 + 0.678448i −0.541044 + 0.678448i
\(94\) 0 0
\(95\) 0 0
\(96\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(97\) −0.846011 0.193096i −0.846011 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(98\) −0.240787 + 0.500000i −0.240787 + 0.500000i
\(99\) 1.80194i 1.80194i
\(100\) 1.30194 + 0.626980i 1.30194 + 0.626980i
\(101\) −0.347948 0.277479i −0.347948 0.277479i 0.433884 0.900969i \(-0.357143\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(102\) 0 0
\(103\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(104\) 0 0
\(105\) 0.846011 1.75676i 0.846011 1.75676i
\(106\) 1.90097 + 0.433884i 1.90097 + 0.433884i
\(107\) −1.75676 + 0.846011i −1.75676 + 0.846011i −0.781831 + 0.623490i \(0.785714\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(108\) −0.433884 0.900969i −0.433884 0.900969i
\(109\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(110\) 1.75676 2.20291i 1.75676 2.20291i
\(111\) 0 0
\(112\) 0.277479 1.21572i 0.277479 1.21572i
\(113\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(117\) 0 0
\(118\) 0.678448 0.541044i 0.678448 0.541044i
\(119\) 0 0
\(120\) −0.347948 + 1.52446i −0.347948 + 1.52446i
\(121\) −1.40097 1.75676i −1.40097 1.75676i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.376510 + 0.781831i 0.376510 + 0.781831i
\(125\) 0.626980 0.301938i 0.626980 0.301938i
\(126\) 1.21572 + 0.277479i 1.21572 + 0.277479i
\(127\) 0.846011 1.75676i 0.846011 1.75676i 0.222521 0.974928i \(-0.428571\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(128\) 1.00000i 1.00000i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.40881 1.12349i −1.40881 1.12349i −0.974928 0.222521i \(-0.928571\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(132\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(133\) 0 0
\(134\) 0 0
\(135\) −1.52446 0.347948i −1.52446 0.347948i
\(136\) 0 0
\(137\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(138\) 0 0
\(139\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(140\) −1.21572 1.52446i −1.21572 1.52446i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) −0.678448 + 1.40881i −0.678448 + 1.40881i
\(146\) −1.94986 −1.94986
\(147\) −0.433884 + 0.346011i −0.433884 + 0.346011i
\(148\) 0 0
\(149\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(150\) 0.900969 + 1.12978i 0.900969 + 1.12978i
\(151\) −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i \(0.428571\pi\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −2.02446 + 0.974928i −2.02446 + 0.974928i
\(155\) 1.32288 + 0.301938i 1.32288 + 0.301938i
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 1.52446 + 1.21572i 1.52446 + 1.21572i
\(160\) 1.22252 + 0.974928i 1.22252 + 0.974928i
\(161\) 0 0
\(162\) 1.00000i 1.00000i
\(163\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(164\) 0 0
\(165\) 2.53859 1.22252i 2.53859 1.22252i
\(166\) −0.376510 0.781831i −0.376510 0.781831i
\(167\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(168\) 0.777479 0.974928i 0.777479 0.974928i
\(169\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.56366 1.56366 0.781831 0.623490i \(-0.214286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(174\) −0.974928 0.222521i −0.974928 0.222521i
\(175\) −1.80194 −1.80194
\(176\) 1.40881 1.12349i 1.40881 1.12349i
\(177\) 0.846011 0.193096i 0.846011 0.193096i
\(178\) 0 0
\(179\) 0.974928 + 1.22252i 0.974928 + 1.22252i 0.974928 + 0.222521i \(0.0714286\pi\)
1.00000i \(0.5\pi\)
\(180\) −0.974928 + 1.22252i −0.974928 + 1.22252i
\(181\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0.867767i 0.867767i
\(187\) 0 0
\(188\) 0 0
\(189\) 0.974928 + 0.777479i 0.974928 + 0.777479i
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(193\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(194\) −0.781831 + 0.376510i −0.781831 + 0.376510i
\(195\) 0 0
\(196\) 0.123490 + 0.541044i 0.123490 + 0.541044i
\(197\) −1.21572 + 1.52446i −1.21572 + 1.52446i −0.433884 + 0.900969i \(0.642857\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(198\) 1.12349 + 1.40881i 1.12349 + 1.40881i
\(199\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(200\) 1.40881 0.321552i 1.40881 0.321552i
\(201\) 0 0
\(202\) −0.445042 −0.445042
\(203\) 0.974928 0.777479i 0.974928 0.777479i
\(204\) 0 0
\(205\) 0 0
\(206\) 0.433884 0.0990311i 0.433884 0.0990311i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) −0.433884 1.90097i −0.433884 1.90097i
\(211\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(212\) 1.75676 0.846011i 1.75676 0.846011i
\(213\) 0 0
\(214\) −0.846011 + 1.75676i −0.846011 + 1.75676i
\(215\) 0 0
\(216\) −0.900969 0.433884i −0.900969 0.433884i
\(217\) −0.846011 0.674671i −0.846011 0.674671i
\(218\) 0 0
\(219\) −1.75676 0.846011i −1.75676 0.846011i
\(220\) 2.81762i 2.81762i
\(221\) 0 0
\(222\) 0 0
\(223\) −0.400969 + 0.193096i −0.400969 + 0.193096i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(224\) −0.541044 1.12349i −0.541044 1.12349i
\(225\) 0.321552 + 1.40881i 0.321552 + 1.40881i
\(226\) 0 0
\(227\) −0.974928 1.22252i −0.974928 1.22252i −0.974928 0.222521i \(-0.928571\pi\)
1.00000i \(-0.5\pi\)
\(228\) 0 0
\(229\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(230\) 0 0
\(231\) −2.24698 −2.24698
\(232\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.193096 0.846011i 0.193096 0.846011i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(240\) 0.678448 + 1.40881i 0.678448 + 1.40881i
\(241\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(242\) −2.19064 0.500000i −2.19064 0.500000i
\(243\) 0.433884 0.900969i 0.433884 0.900969i
\(244\) 0 0
\(245\) 0.781831 + 0.376510i 0.781831 + 0.376510i
\(246\) 0 0
\(247\) 0 0
\(248\) 0.781831 + 0.376510i 0.781831 + 0.376510i
\(249\) 0.867767i 0.867767i
\(250\) 0.301938 0.626980i 0.301938 0.626980i
\(251\) 1.21572 + 0.277479i 1.21572 + 0.277479i 0.781831 0.623490i \(-0.214286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(252\) 1.12349 0.541044i 1.12349 0.541044i
\(253\) 0 0
\(254\) −0.433884 1.90097i −0.433884 1.90097i
\(255\) 0 0
\(256\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(257\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.781831 0.623490i −0.781831 0.623490i
\(262\) −1.80194 −1.80194
\(263\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(264\) 1.75676 0.400969i 1.75676 0.400969i
\(265\) 0.678448 2.97247i 0.678448 2.97247i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.193096 + 0.400969i 0.193096 + 0.400969i 0.974928 0.222521i \(-0.0714286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(270\) −1.40881 + 0.678448i −1.40881 + 0.678448i
\(271\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.03579 1.62349i −2.03579 1.62349i
\(276\) 0 0
\(277\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(278\) 0 0
\(279\) −0.376510 + 0.781831i −0.376510 + 0.781831i
\(280\) −1.90097 0.433884i −1.90097 0.433884i
\(281\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(282\) 0 0
\(283\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(289\) −1.00000 −1.00000
\(290\) 0.347948 + 1.52446i 0.347948 + 1.52446i
\(291\) −0.867767 −0.867767
\(292\) −1.52446 + 1.21572i −1.52446 + 1.21572i
\(293\) −0.433884 + 0.0990311i −0.433884 + 0.0990311i −0.433884 0.900969i \(-0.642857\pi\)
1.00000i \(0.5\pi\)
\(294\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(295\) −0.846011 1.06086i −0.846011 1.06086i
\(296\) 0 0
\(297\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.40881 + 0.321552i 1.40881 + 0.321552i
\(301\) 0 0
\(302\) 1.24698i 1.24698i
\(303\) −0.400969 0.193096i −0.400969 0.193096i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) −0.974928 + 2.02446i −0.974928 + 2.02446i
\(309\) 0.433884 + 0.0990311i 0.433884 + 0.0990311i
\(310\) 1.22252 0.588735i 1.22252 0.588735i
\(311\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(312\) 0 0
\(313\) 0.777479 0.974928i 0.777479 0.974928i −0.222521 0.974928i \(-0.571429\pi\)
1.00000 \(0\)
\(314\) 0 0
\(315\) 0.433884 1.90097i 0.433884 1.90097i
\(316\) 0 0
\(317\) 1.40881 1.12349i 1.40881 1.12349i 0.433884 0.900969i \(-0.357143\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(318\) 1.94986 1.94986
\(319\) 1.80194 1.80194
\(320\) 1.56366 1.56366
\(321\) −1.52446 + 1.21572i −1.52446 + 1.21572i
\(322\) 0 0
\(323\) 0 0
\(324\) −0.623490 0.781831i −0.623490 0.781831i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 1.22252 2.53859i 1.22252 2.53859i
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) −0.781831 0.376510i −0.781831 0.376510i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 1.24698i 1.24698i
\(337\) −0.678448 + 1.40881i −0.678448 + 1.40881i 0.222521 + 0.974928i \(0.428571\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(338\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(339\) 0 0
\(340\) 0 0
\(341\) −0.347948 1.52446i −0.347948 1.52446i
\(342\) 0 0
\(343\) 0.346011 + 0.433884i 0.346011 + 0.433884i
\(344\) 0 0
\(345\) 0 0
\(346\) 1.22252 0.974928i 1.22252 0.974928i
\(347\) −0.867767 −0.867767 −0.433884 0.900969i \(-0.642857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(348\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) −1.40881 + 1.12349i −1.40881 + 1.12349i
\(351\) 0 0
\(352\) 0.400969 1.75676i 0.400969 1.75676i
\(353\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(354\) 0.541044 0.678448i 0.541044 0.678448i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 1.52446 + 0.347948i 1.52446 + 0.347948i
\(359\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(360\) 1.56366i 1.56366i
\(361\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(362\) 0 0
\(363\) −1.75676 1.40097i −1.75676 1.40097i
\(364\) 0 0
\(365\) 3.04892i 3.04892i
\(366\) 0 0
\(367\) 1.90097 + 0.433884i 1.90097 + 0.433884i 1.00000 \(0\)
0.900969 + 0.433884i \(0.142857\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.51597 + 1.90097i −1.51597 + 1.90097i
\(372\) 0.541044 + 0.678448i 0.541044 + 0.678448i
\(373\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(374\) 0 0
\(375\) 0.544073 0.433884i 0.544073 0.433884i
\(376\) 0 0
\(377\) 0 0
\(378\) 1.24698 1.24698
\(379\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(380\) 0 0
\(381\) 0.433884 1.90097i 0.433884 1.90097i
\(382\) 0 0
\(383\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(384\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(385\) 1.52446 + 3.16557i 1.52446 + 3.16557i
\(386\) 0 0
\(387\) 0 0
\(388\) −0.376510 + 0.781831i −0.376510 + 0.781831i
\(389\) 1.24698i 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.433884 + 0.346011i 0.433884 + 0.346011i
\(393\) −1.62349 0.781831i −1.62349 0.781831i
\(394\) 1.94986i 1.94986i
\(395\) 0 0
\(396\) 1.75676 + 0.400969i 1.75676 + 0.400969i
\(397\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(398\) −0.781831 1.62349i −0.781831 1.62349i
\(399\) 0 0
\(400\) 0.900969 1.12978i 0.900969 1.12978i
\(401\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.347948 + 0.277479i −0.347948 + 0.277479i
\(405\) −1.56366 −1.56366
\(406\) 0.277479 1.21572i 0.277479 1.21572i
\(407\) 0 0
\(408\) 0 0
\(409\) 1.52446 0.347948i 1.52446 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.277479 0.347948i 0.277479 0.347948i
\(413\) 0.240787 + 1.05496i 0.240787 + 1.05496i
\(414\) 0 0
\(415\) −1.22252 + 0.588735i −1.22252 + 0.588735i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.75676 + 0.846011i 1.75676 + 0.846011i 0.974928 + 0.222521i \(0.0714286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(420\) −1.52446 1.21572i −1.52446 1.21572i
\(421\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0.846011 1.75676i 0.846011 1.75676i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0.433884 + 1.90097i 0.433884 + 1.90097i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(432\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(433\) −1.52446 + 1.21572i −1.52446 + 1.21572i −0.623490 + 0.781831i \(0.714286\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(434\) −1.08209 −1.08209
\(435\) −0.347948 + 1.52446i −0.347948 + 1.52446i
\(436\) 0 0
\(437\) 0 0
\(438\) −1.90097 + 0.433884i −1.90097 + 0.433884i
\(439\) 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
1.00000 \(0\)
\(440\) −1.75676 2.20291i −1.75676 2.20291i
\(441\) −0.346011 + 0.433884i −0.346011 + 0.433884i
\(442\) 0 0
\(443\) 0.541044 + 1.12349i 0.541044 + 1.12349i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.193096 + 0.400969i −0.193096 + 0.400969i
\(447\) 0 0
\(448\) −1.12349 0.541044i −1.12349 0.541044i
\(449\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(450\) 1.12978 + 0.900969i 1.12978 + 0.900969i
\(451\) 0 0
\(452\) 0 0
\(453\) −0.541044 + 1.12349i −0.541044 + 1.12349i
\(454\) −1.52446 0.347948i −1.52446 0.347948i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.75676 0.400969i 1.75676 0.400969i 0.781831 0.623490i \(-0.214286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(462\) −1.75676 + 1.40097i −1.75676 + 1.40097i
\(463\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(464\) 1.00000i 1.00000i
\(465\) 1.35690 1.35690
\(466\) 0 0
\(467\) −1.21572 + 0.277479i −1.21572 + 0.277479i −0.781831 0.623490i \(-0.785714\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −0.376510 0.781831i −0.376510 0.781831i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.75676 + 0.846011i 1.75676 + 0.846011i
\(478\) 0 0
\(479\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(480\) 1.40881 + 0.678448i 1.40881 + 0.678448i
\(481\) 0 0
\(482\) 0.781831 1.62349i 0.781831 1.62349i
\(483\) 0 0
\(484\) −2.02446 + 0.974928i −2.02446 + 0.974928i
\(485\) 0.588735 + 1.22252i 0.588735 + 1.22252i
\(486\) −0.222521 0.974928i −0.222521 0.974928i
\(487\) −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i \(0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0.846011 0.193096i 0.846011 0.193096i
\(491\) 0.347948 0.277479i 0.347948 0.277479i −0.433884 0.900969i \(-0.642857\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 2.20291 1.75676i 2.20291 1.75676i
\(496\) 0.846011 0.193096i 0.846011 0.193096i
\(497\) 0 0
\(498\) −0.541044 0.678448i −0.541044 0.678448i
\(499\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(500\) −0.154851 0.678448i −0.154851 0.678448i
\(501\) 0 0
\(502\) 1.12349 0.541044i 1.12349 0.541044i
\(503\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(504\) 0.541044 1.12349i 0.541044 1.12349i
\(505\) 0.695895i 0.695895i
\(506\) 0 0
\(507\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(508\) −1.52446 1.21572i −1.52446 1.21572i
\(509\) 1.75676 + 0.846011i 1.75676 + 0.846011i 0.974928 + 0.222521i \(0.0714286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(510\) 0 0
\(511\) 1.05496 2.19064i 1.05496 2.19064i
\(512\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(513\) 0 0
\(514\) 0 0
\(515\) −0.154851 0.678448i −0.154851 0.678448i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 1.52446 0.347948i 1.52446 0.347948i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) −1.00000 −1.00000
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −1.40881 + 1.12349i −1.40881 + 1.12349i
\(525\) −1.75676 + 0.400969i −1.75676 + 0.400969i
\(526\) 0 0
\(527\) 0 0
\(528\) 1.12349 1.40881i 1.12349 1.40881i
\(529\) −0.222521 0.974928i −0.222521 0.974928i
\(530\) −1.32288 2.74698i −1.32288 2.74698i
\(531\) 0.781831 0.376510i 0.781831 0.376510i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 2.74698 + 1.32288i 2.74698 + 1.32288i
\(536\) 0 0
\(537\) 1.22252 + 0.974928i 1.22252 + 0.974928i
\(538\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(539\) 1.00000i 1.00000i
\(540\) −0.678448 + 1.40881i −0.678448 + 1.40881i
\(541\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −2.60388 −2.60388
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.974928 1.22252i 0.974928 1.22252i 1.00000i \(-0.5\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(558\) 0.193096 + 0.846011i 0.193096 + 0.846011i
\(559\) 0 0
\(560\) −1.75676 + 0.846011i −1.75676 + 0.846011i
\(561\) 0 0
\(562\) 0 0
\(563\) 0.445042i 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(568\) 0 0
\(569\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(570\) 0 0
\(571\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(577\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(578\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(579\) 0 0
\(580\) 1.22252 + 0.974928i 1.22252 + 0.974928i
\(581\) 1.08209 1.08209
\(582\) −0.678448 + 0.541044i −0.678448 + 0.541044i
\(583\) −3.42543 + 0.781831i −3.42543 + 0.781831i
\(584\) −0.433884 + 1.90097i −0.433884 + 1.90097i
\(585\) 0 0
\(586\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(587\) 0.433884 + 1.90097i 0.433884 + 1.90097i 0.433884 + 0.900969i \(0.357143\pi\)
1.00000i \(0.500000\pi\)
\(588\) 0.240787 + 0.500000i 0.240787 + 0.500000i
\(589\) 0 0
\(590\) −1.32288 0.301938i −1.32288 0.301938i
\(591\) −0.846011 + 1.75676i −0.846011 + 1.75676i
\(592\) 0 0
\(593\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(594\) 1.40881 + 1.12349i 1.40881 + 1.12349i
\(595\) 0 0
\(596\) 0 0
\(597\) 1.80194i 1.80194i
\(598\) 0 0
\(599\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(600\) 1.30194 0.626980i 1.30194 0.626980i
\(601\) −0.678448 1.40881i −0.678448 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(605\) −0.781831 + 3.42543i −0.781831 + 3.42543i
\(606\) −0.433884 + 0.0990311i −0.433884 + 0.0990311i
\(607\) −1.22252 + 0.974928i −1.22252 + 0.974928i −0.222521 + 0.974928i \(0.571429\pi\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0.777479 0.974928i 0.777479 0.974928i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0.500000 + 2.19064i 0.500000 + 2.19064i
\(617\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(618\) 0.400969 0.193096i 0.400969 0.193096i
\(619\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(620\) 0.588735 1.22252i 0.588735 1.22252i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.321552 + 0.154851i 0.321552 + 0.154851i
\(626\) 1.24698i 1.24698i
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −0.846011 1.75676i −0.846011 1.75676i
\(631\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0.400969 1.75676i 0.400969 1.75676i
\(635\) −2.97247 + 0.678448i −2.97247 + 0.678448i
\(636\) 1.52446 1.21572i 1.52446 1.21572i
\(637\) 0 0
\(638\) 1.40881 1.12349i 1.40881 1.12349i
\(639\) 0 0
\(640\) 1.22252 0.974928i 1.22252 0.974928i
\(641\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(642\) −0.433884 + 1.90097i −0.433884 + 1.90097i
\(643\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(648\) −0.974928 0.222521i −0.974928 0.222521i
\(649\) −0.678448 + 1.40881i −0.678448 + 1.40881i
\(650\) 0 0
\(651\) −0.974928 0.469501i −0.974928 0.469501i
\(652\) 0 0
\(653\) −0.974928 0.777479i −0.974928 0.777479i 1.00000i \(-0.5\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(654\) 0 0
\(655\) 2.81762i 2.81762i
\(656\) 0 0
\(657\) −1.90097 0.433884i −1.90097 0.433884i
\(658\) 0 0
\(659\) −0.193096 0.400969i −0.193096 0.400969i 0.781831 0.623490i \(-0.214286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(660\) −0.626980 2.74698i −0.626980 2.74698i
\(661\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.846011 + 0.193096i −0.846011 + 0.193096i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −0.347948 + 0.277479i −0.347948 + 0.277479i
\(670\) 0 0
\(671\) 0 0
\(672\) −0.777479 0.974928i −0.777479 0.974928i
\(673\) 1.12349 1.40881i 1.12349 1.40881i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(674\) 0.347948 + 1.52446i 0.347948 + 1.52446i
\(675\) 0.626980 + 1.30194i 0.626980 + 1.30194i
\(676\) 0.900969 0.433884i 0.900969 0.433884i
\(677\) −1.75676 0.400969i −1.75676 0.400969i −0.781831 0.623490i \(-0.785714\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(678\) 0 0
\(679\) 1.08209i 1.08209i
\(680\) 0 0
\(681\) −1.22252 0.974928i −1.22252 0.974928i
\(682\) −1.22252 0.974928i −1.22252 0.974928i
\(683\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.541044 + 0.123490i 0.541044 + 0.123490i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(692\) 0.347948 1.52446i 0.347948 1.52446i
\(693\) −2.19064 + 0.500000i −2.19064 + 0.500000i
\(694\) −0.678448 + 0.541044i −0.678448 + 0.541044i
\(695\) 0 0
\(696\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(701\) 0.541044 + 0.678448i 0.541044 + 0.678448i 0.974928 0.222521i \(-0.0714286\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.781831 1.62349i −0.781831 1.62349i
\(705\) 0 0
\(706\) 0 0
\(707\) 0.240787 0.500000i 0.240787 0.500000i
\(708\) 0.867767i 0.867767i
\(709\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.40881 0.678448i 1.40881 0.678448i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(720\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(721\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(722\) 0.974928 0.222521i 0.974928 0.222521i
\(723\) 1.40881 1.12349i 1.40881 1.12349i
\(724\) 0 0
\(725\) 1.40881 0.321552i 1.40881 0.321552i
\(726\) −2.24698 −2.24698
\(727\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(728\) 0 0
\(729\) 0.222521 0.974928i 0.222521 0.974928i
\(730\) 1.90097 + 2.38374i 1.90097 + 2.38374i
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(734\) 1.75676 0.846011i 1.75676 0.846011i
\(735\) 0.846011 + 0.193096i 0.846011 + 0.193096i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2.43143i 2.43143i
\(743\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(744\) 0.846011 + 0.193096i 0.846011 + 0.193096i
\(745\) 0 0
\(746\) 0 0
\(747\) −0.193096 0.846011i −0.193096 0.846011i
\(748\) 0 0
\(749\) −1.51597 1.90097i −1.51597 1.90097i
\(750\) 0.154851 0.678448i 0.154851 0.678448i
\(751\) −1.90097 + 0.433884i −1.90097 + 0.433884i −0.900969 + 0.433884i \(0.857143\pi\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 1.24698 1.24698
\(754\) 0 0
\(755\) 1.94986 1.94986
\(756\) 0.974928 0.777479i 0.974928 0.777479i
\(757\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(762\) −0.846011 1.75676i −0.846011 1.75676i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(769\) 1.52446 + 1.21572i 1.52446 + 1.21572i 0.900969 + 0.433884i \(0.142857\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(770\) 3.16557 + 1.52446i 3.16557 + 1.52446i
\(771\) 0 0
\(772\) 0 0
\(773\) −1.21572 0.277479i −1.21572 0.277479i −0.433884 0.900969i \(-0.642857\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(774\) 0 0
\(775\) −0.544073 1.12978i −0.544073 1.12978i
\(776\) 0.193096 + 0.846011i 0.193096 + 0.846011i
\(777\) 0 0
\(778\) −0.777479 0.974928i −0.777479 0.974928i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.900969 0.433884i −0.900969 0.433884i
\(784\) 0.554958 0.554958
\(785\) 0 0
\(786\) −1.75676 + 0.400969i −1.75676 + 0.400969i
\(787\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(788\) 1.21572 + 1.52446i 1.21572 + 1.52446i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 1.62349 0.781831i 1.62349 0.781831i
\(793\) 0 0
\(794\) 0 0
\(795\) 3.04892i 3.04892i
\(796\) −1.62349 0.781831i −1.62349 0.781831i
\(797\) −1.40881 1.12349i −1.40881 1.12349i −0.974928 0.222521i \(-0.928571\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.44504i 1.44504i
\(801\) 0 0
\(802\) 0 0
\(803\) 3.16557 1.52446i 3.16557 1.52446i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(808\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(809\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(810\) −1.22252 + 0.974928i −1.22252 + 0.974928i
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −0.541044 1.12349i −0.541044 1.12349i
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0.974928 1.22252i 0.974928 1.22252i
\(819\) 0 0
\(820\) 0 0
\(821\) 0.781831 0.376510i 0.781831 0.376510i 1.00000i \(-0.5\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(822\) 0 0
\(823\) 0.376510 0.781831i 0.376510 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
1.00000 \(0\)
\(824\) 0.445042i 0.445042i
\(825\) −2.34601 1.12978i −2.34601 1.12978i
\(826\) 0.846011 + 0.674671i 0.846011 + 0.674671i
\(827\) 0.974928 + 0.777479i 0.974928 + 0.777479i 0.974928 0.222521i \(-0.0714286\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) −0.588735 + 1.22252i −0.588735 + 1.22252i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −0.193096 + 0.846011i −0.193096 + 0.846011i
\(838\) 1.90097 0.433884i 1.90097 0.433884i
\(839\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(840\) −1.94986 −1.94986
\(841\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0.347948 1.52446i 0.347948 1.52446i
\(846\) 0 0
\(847\) 1.74698 2.19064i 1.74698 2.19064i
\(848\) −0.433884 1.90097i −0.433884 1.90097i
\(849\) 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
\(856\) 1.52446 + 1.21572i 1.52446 + 1.21572i
\(857\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(858\) 0 0
\(859\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(864\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(865\) −1.52446 1.91161i −1.52446 1.91161i
\(866\) −0.433884 + 1.90097i −0.433884 + 1.90097i
\(867\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(868\) −0.846011 + 0.674671i −0.846011 + 0.674671i
\(869\) 0 0
\(870\) 0.678448 + 1.40881i 0.678448 + 1.40881i
\(871\) 0 0
\(872\) 0 0
\(873\) −0.846011 + 0.193096i −0.846011 + 0.193096i
\(874\) 0 0
\(875\) 0.541044 + 0.678448i 0.541044 + 0.678448i
\(876\) −1.21572 + 1.52446i −1.21572 + 1.52446i
\(877\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(878\) −0.193096 0.400969i −0.193096 0.400969i
\(879\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(880\) −2.74698 0.626980i −2.74698 0.626980i
\(881\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(882\) 0.554958i 0.554958i
\(883\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(884\) 0 0
\(885\) −1.06086 0.846011i −1.06086 0.846011i
\(886\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 2.37047 + 0.541044i 2.37047 + 0.541044i
\(890\) 0 0
\(891\) 0.781831 + 1.62349i 0.781831 + 1.62349i
\(892\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(893\) 0 0
\(894\) 0 0
\(895\) 0.544073 2.38374i 0.544073 2.38374i
\(896\) −1.21572 + 0.277479i −1.21572 + 0.277479i
\(897\) 0 0
\(898\) 0 0
\(899\) 0.781831 + 0.376510i 0.781831 + 0.376510i
\(900\) 1.44504 1.44504
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(907\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(908\) −1.40881 + 0.678448i −1.40881 + 0.678448i
\(909\) −0.433884 0.0990311i −0.433884 0.0990311i
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 1.22252 + 0.974928i 1.22252 + 0.974928i
\(914\) −0.347948 0.277479i −0.347948 0.277479i
\(915\) 0 0
\(916\) 0 0
\(917\) 0.974928 2.02446i 0.974928 2.02446i
\(918\) 0 0
\(919\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(920\) 0 0
\(921\) 0 0
\(922\) 1.12349 1.40881i 1.12349 1.40881i
\(923\) 0 0
\(924\) −0.500000 + 2.19064i −0.500000 + 2.19064i
\(925\) 0 0
\(926\) −0.974928 + 0.777479i −0.974928 + 0.777479i
\(927\) 0.445042 0.445042
\(928\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) 1.06086 0.846011i 1.06086 0.846011i
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −0.777479 + 0.974928i −0.777479 + 0.974928i
\(935\) 0 0
\(936\) 0 0
\(937\) −1.80194 + 0.867767i −1.80194 + 0.867767i −0.900969 + 0.433884i \(0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(938\) 0 0
\(939\) 0.541044 1.12349i 0.541044 1.12349i
\(940\) 0 0
\(941\) −1.75676 0.846011i −1.75676 0.846011i −0.974928 0.222521i \(-0.928571\pi\)
−0.781831 0.623490i \(-0.785714\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) −0.781831 0.376510i −0.781831 0.376510i
\(945\) 1.94986i 1.94986i
\(946\) 0 0
\(947\) 0.433884 + 0.0990311i 0.433884 + 0.0990311i 0.433884 0.900969i \(-0.357143\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 1.12349 1.40881i 1.12349 1.40881i
\(952\) 0 0
\(953\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(954\) 1.90097 0.433884i 1.90097 0.433884i
\(955\) 0 0
\(956\) 0 0
\(957\) 1.75676 0.400969i 1.75676 0.400969i
\(958\) 0 0
\(959\) 0 0
\(960\) 1.52446 0.347948i 1.52446 0.347948i
\(961\) −0.0549581 + 0.240787i −0.0549581 + 0.240787i
\(962\) 0 0
\(963\) −1.21572 + 1.52446i −1.21572 + 1.52446i
\(964\) −0.400969 1.75676i −0.400969 1.75676i
\(965\) 0 0
\(966\) 0 0
\(967\) −1.52446 0.347948i −1.52446 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(968\) −0.974928 + 2.02446i −0.974928 + 2.02446i
\(969\) 0 0
\(970\) 1.22252 + 0.588735i 1.22252 + 0.588735i
\(971\) −0.347948 0.277479i −0.347948 0.277479i 0.433884 0.900969i \(-0.357143\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(972\) −0.781831 0.623490i −0.781831 0.623490i
\(973\) 0 0
\(974\) 1.80194i 1.80194i
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.541044 0.678448i 0.541044 0.678448i
\(981\) 0 0
\(982\) 0.0990311 0.433884i 0.0990311 0.433884i
\(983\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(984\) 0 0
\(985\) 3.04892 3.04892
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0.626980 2.74698i 0.626980 2.74698i
\(991\) 1.24698 + 1.56366i 1.24698 + 1.56366i 0.623490 + 0.781831i \(0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(992\) 0.541044 0.678448i 0.541044 0.678448i
\(993\) 0 0
\(994\) 0 0
\(995\) −2.53859 + 1.22252i −2.53859 + 1.22252i
\(996\) −0.846011 0.193096i −0.846011 0.193096i
\(997\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(998\) 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.5.2 yes 12
3.2 odd 2 inner 696.1.bb.a.5.1 12
4.3 odd 2 2784.1.ch.a.1745.1 12
8.3 odd 2 2784.1.ch.a.1745.2 12
8.5 even 2 inner 696.1.bb.a.5.1 12
12.11 even 2 2784.1.ch.a.1745.2 12
24.5 odd 2 CM 696.1.bb.a.5.2 yes 12
24.11 even 2 2784.1.ch.a.1745.1 12
29.6 even 14 inner 696.1.bb.a.557.2 yes 12
87.35 odd 14 inner 696.1.bb.a.557.1 yes 12
116.35 odd 14 2784.1.ch.a.209.1 12
232.35 odd 14 2784.1.ch.a.209.2 12
232.93 even 14 inner 696.1.bb.a.557.1 yes 12
348.35 even 14 2784.1.ch.a.209.2 12
696.35 even 14 2784.1.ch.a.209.1 12
696.557 odd 14 inner 696.1.bb.a.557.2 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
696.1.bb.a.5.1 12 3.2 odd 2 inner
696.1.bb.a.5.1 12 8.5 even 2 inner
696.1.bb.a.5.2 yes 12 1.1 even 1 trivial
696.1.bb.a.5.2 yes 12 24.5 odd 2 CM
696.1.bb.a.557.1 yes 12 87.35 odd 14 inner
696.1.bb.a.557.1 yes 12 232.93 even 14 inner
696.1.bb.a.557.2 yes 12 29.6 even 14 inner
696.1.bb.a.557.2 yes 12 696.557 odd 14 inner
2784.1.ch.a.209.1 12 116.35 odd 14
2784.1.ch.a.209.1 12 696.35 even 14
2784.1.ch.a.209.2 12 232.35 odd 14
2784.1.ch.a.209.2 12 348.35 even 14
2784.1.ch.a.1745.1 12 4.3 odd 2
2784.1.ch.a.1745.1 12 24.11 even 2
2784.1.ch.a.1745.2 12 8.3 odd 2
2784.1.ch.a.1745.2 12 12.11 even 2