Properties

Label 3332.1.be.c.2787.1
Level $3332$
Weight $1$
Character 3332.2787
Analytic conductor $1.663$
Analytic rank $0$
Dimension $12$
Projective image $D_{14}$
CM discriminant -68
Inner twists $8$

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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: \(12\)
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: \(\Z[a_1, \ldots, a_{7}]\)
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 2787.1
Root \(0.781831 + 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 3332.2787
Dual form 3332.1.be.c.2311.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.623490 + 0.781831i) q^{2} +(-0.781831 - 0.376510i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(0.781831 - 0.376510i) q^{6} +(-0.433884 + 0.900969i) q^{7} +(0.900969 + 0.433884i) q^{8} +(-0.153989 - 0.193096i) q^{9} +(0.974928 - 1.22252i) q^{11} +(-0.193096 + 0.846011i) q^{12} +(-0.777479 + 0.974928i) q^{13} +(-0.433884 - 0.900969i) q^{14} +(-0.900969 + 0.433884i) q^{16} +(-0.222521 + 0.974928i) q^{17} +0.246980 q^{18} +(0.678448 - 0.541044i) q^{21} +(0.347948 + 1.52446i) q^{22} +(-0.347948 - 1.52446i) q^{23} +(-0.541044 - 0.678448i) q^{24} +(0.623490 + 0.781831i) q^{25} +(-0.277479 - 1.21572i) q^{26} +(0.240787 + 1.05496i) q^{27} +(0.974928 + 0.222521i) q^{28} -0.867767 q^{31} +(0.222521 - 0.974928i) q^{32} +(-1.22252 + 0.588735i) q^{33} +(-0.623490 - 0.781831i) q^{34} +(-0.153989 + 0.193096i) q^{36} +(0.974928 - 0.469501i) q^{39} +0.867767i q^{42} +(-1.40881 - 0.678448i) q^{44} +(1.40881 + 0.678448i) q^{46} +0.867767 q^{48} +(-0.623490 - 0.781831i) q^{49} -1.00000 q^{50} +(0.541044 - 0.678448i) q^{51} +(1.12349 + 0.541044i) q^{52} +(0.400969 + 1.75676i) q^{53} +(-0.974928 - 0.469501i) q^{54} +(-0.781831 + 0.623490i) q^{56} +(0.541044 - 0.678448i) q^{62} +(0.240787 - 0.0549581i) q^{63} +(0.623490 + 0.781831i) q^{64} +(0.301938 - 1.32288i) q^{66} +1.00000 q^{68} +(-0.301938 + 1.32288i) q^{69} +(0.193096 + 0.846011i) q^{71} +(-0.0549581 - 0.240787i) q^{72} +(-0.193096 - 0.846011i) q^{75} +(0.678448 + 1.40881i) q^{77} +(-0.240787 + 1.05496i) q^{78} -1.56366 q^{79} +(0.153989 - 0.674671i) q^{81} +(-0.678448 - 0.541044i) q^{84} +(1.40881 - 0.678448i) q^{88} +(1.12349 + 1.40881i) q^{89} +(-0.541044 - 1.12349i) q^{91} +(-1.40881 + 0.678448i) q^{92} +(0.678448 + 0.326723i) q^{93} +(-0.541044 + 0.678448i) q^{96} +1.00000 q^{98} -0.386193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} - 2 q^{4} + 2 q^{8} - 12 q^{9} - 10 q^{13} - 2 q^{16} - 2 q^{17} - 16 q^{18} - 2 q^{25} - 4 q^{26} + 2 q^{32} - 14 q^{33} + 2 q^{34} - 12 q^{36} + 2 q^{49} - 12 q^{50} + 4 q^{52} - 4 q^{53}+ \cdots + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(3\) −0.781831 0.376510i −0.781831 0.376510i 1.00000i \(-0.5\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(4\) −0.222521 0.974928i −0.222521 0.974928i
\(5\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(6\) 0.781831 0.376510i 0.781831 0.376510i
\(7\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(8\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(9\) −0.153989 0.193096i −0.153989 0.193096i
\(10\) 0 0
\(11\) 0.974928 1.22252i 0.974928 1.22252i 1.00000i \(-0.5\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(12\) −0.193096 + 0.846011i −0.193096 + 0.846011i
\(13\) −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i \(0.428571\pi\)
−1.00000 \(\pi\)
\(14\) −0.433884 0.900969i −0.433884 0.900969i
\(15\) 0 0
\(16\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(17\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(18\) 0.246980 0.246980
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0.678448 0.541044i 0.678448 0.541044i
\(22\) 0.347948 + 1.52446i 0.347948 + 1.52446i
\(23\) −0.347948 1.52446i −0.347948 1.52446i −0.781831 0.623490i \(-0.785714\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(24\) −0.541044 0.678448i −0.541044 0.678448i
\(25\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(26\) −0.277479 1.21572i −0.277479 1.21572i
\(27\) 0.240787 + 1.05496i 0.240787 + 1.05496i
\(28\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(29\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(30\) 0 0
\(31\) −0.867767 −0.867767 −0.433884 0.900969i \(-0.642857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(32\) 0.222521 0.974928i 0.222521 0.974928i
\(33\) −1.22252 + 0.588735i −1.22252 + 0.588735i
\(34\) −0.623490 0.781831i −0.623490 0.781831i
\(35\) 0 0
\(36\) −0.153989 + 0.193096i −0.153989 + 0.193096i
\(37\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(38\) 0 0
\(39\) 0.974928 0.469501i 0.974928 0.469501i
\(40\) 0 0
\(41\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(42\) 0.867767i 0.867767i
\(43\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(44\) −1.40881 0.678448i −1.40881 0.678448i
\(45\) 0 0
\(46\) 1.40881 + 0.678448i 1.40881 + 0.678448i
\(47\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(48\) 0.867767 0.867767
\(49\) −0.623490 0.781831i −0.623490 0.781831i
\(50\) −1.00000 −1.00000
\(51\) 0.541044 0.678448i 0.541044 0.678448i
\(52\) 1.12349 + 0.541044i 1.12349 + 0.541044i
\(53\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(54\) −0.974928 0.469501i −0.974928 0.469501i
\(55\) 0 0
\(56\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(60\) 0 0
\(61\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(62\) 0.541044 0.678448i 0.541044 0.678448i
\(63\) 0.240787 0.0549581i 0.240787 0.0549581i
\(64\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(65\) 0 0
\(66\) 0.301938 1.32288i 0.301938 1.32288i
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 1.00000 1.00000
\(69\) −0.301938 + 1.32288i −0.301938 + 1.32288i
\(70\) 0 0
\(71\) 0.193096 + 0.846011i 0.193096 + 0.846011i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(72\) −0.0549581 0.240787i −0.0549581 0.240787i
\(73\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(74\) 0 0
\(75\) −0.193096 0.846011i −0.193096 0.846011i
\(76\) 0 0
\(77\) 0.678448 + 1.40881i 0.678448 + 1.40881i
\(78\) −0.240787 + 1.05496i −0.240787 + 1.05496i
\(79\) −1.56366 −1.56366 −0.781831 0.623490i \(-0.785714\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(80\) 0 0
\(81\) 0.153989 0.674671i 0.153989 0.674671i
\(82\) 0 0
\(83\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(84\) −0.678448 0.541044i −0.678448 0.541044i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 1.40881 0.678448i 1.40881 0.678448i
\(89\) 1.12349 + 1.40881i 1.12349 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(90\) 0 0
\(91\) −0.541044 1.12349i −0.541044 1.12349i
\(92\) −1.40881 + 0.678448i −1.40881 + 0.678448i
\(93\) 0.678448 + 0.326723i 0.678448 + 0.326723i
\(94\) 0 0
\(95\) 0 0
\(96\) −0.541044 + 0.678448i −0.541044 + 0.678448i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1.00000 1.00000
\(99\) −0.386193 −0.386193
\(100\) 0.623490 0.781831i 0.623490 0.781831i
\(101\) 1.12349 + 0.541044i 1.12349 + 0.541044i 0.900969 0.433884i \(-0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(102\) 0.193096 + 0.846011i 0.193096 + 0.846011i
\(103\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(104\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(105\) 0 0
\(106\) −1.62349 0.781831i −1.62349 0.781831i
\(107\) 1.21572 + 1.52446i 1.21572 + 1.52446i 0.781831 + 0.623490i \(0.214286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(108\) 0.974928 0.469501i 0.974928 0.469501i
\(109\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000i 1.00000i
\(113\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.307979 0.307979
\(118\) 0 0
\(119\) −0.781831 0.623490i −0.781831 0.623490i
\(120\) 0 0
\(121\) −0.321552 1.40881i −0.321552 1.40881i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.193096 + 0.846011i 0.193096 + 0.846011i
\(125\) 0 0
\(126\) −0.107160 + 0.222521i −0.107160 + 0.222521i
\(127\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(128\) −1.00000 −1.00000
\(129\) 0 0
\(130\) 0 0
\(131\) −1.40881 + 0.678448i −1.40881 + 0.678448i −0.974928 0.222521i \(-0.928571\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(132\) 0.846011 + 1.06086i 0.846011 + 1.06086i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(137\) −1.62349 + 0.781831i −1.62349 + 0.781831i −0.623490 + 0.781831i \(0.714286\pi\)
−1.00000 \(1.00000\pi\)
\(138\) −0.846011 1.06086i −0.846011 1.06086i
\(139\) 1.40881 + 0.678448i 1.40881 + 0.678448i 0.974928 0.222521i \(-0.0714286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.781831 0.376510i −0.781831 0.376510i
\(143\) 0.433884 + 1.90097i 0.433884 + 1.90097i
\(144\) 0.222521 + 0.107160i 0.222521 + 0.107160i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.193096 + 0.846011i 0.193096 + 0.846011i
\(148\) 0 0
\(149\) −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i \(0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(150\) 0.781831 + 0.376510i 0.781831 + 0.376510i
\(151\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(152\) 0 0
\(153\) 0.222521 0.107160i 0.222521 0.107160i
\(154\) −1.52446 0.347948i −1.52446 0.347948i
\(155\) 0 0
\(156\) −0.674671 0.846011i −0.674671 0.846011i
\(157\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(158\) 0.974928 1.22252i 0.974928 1.22252i
\(159\) 0.347948 1.52446i 0.347948 1.52446i
\(160\) 0 0
\(161\) 1.52446 + 0.347948i 1.52446 + 0.347948i
\(162\) 0.431468 + 0.541044i 0.431468 + 0.541044i
\(163\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.433884 + 1.90097i −0.433884 + 1.90097i 1.00000i \(0.5\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(168\) 0.846011 0.193096i 0.846011 0.193096i
\(169\) −0.123490 0.541044i −0.123490 0.541044i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(174\) 0 0
\(175\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(176\) −0.347948 + 1.52446i −0.347948 + 1.52446i
\(177\) 0 0
\(178\) −1.80194 −1.80194
\(179\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(180\) 0 0
\(181\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(182\) 1.21572 + 0.277479i 1.21572 + 0.277479i
\(183\) 0 0
\(184\) 0.347948 1.52446i 0.347948 1.52446i
\(185\) 0 0
\(186\) −0.678448 + 0.326723i −0.678448 + 0.326723i
\(187\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(188\) 0 0
\(189\) −1.05496 0.240787i −1.05496 0.240787i
\(190\) 0 0
\(191\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(192\) −0.193096 0.846011i −0.193096 0.846011i
\(193\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0.240787 0.301938i 0.240787 0.301938i
\(199\) −0.781831 0.376510i −0.781831 0.376510i 1.00000i \(-0.5\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(200\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(201\) 0 0
\(202\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(203\) 0 0
\(204\) −0.781831 0.376510i −0.781831 0.376510i
\(205\) 0 0
\(206\) 0 0
\(207\) −0.240787 + 0.301938i −0.240787 + 0.301938i
\(208\) 0.277479 1.21572i 0.277479 1.21572i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.21572 + 1.52446i 1.21572 + 1.52446i 0.781831 + 0.623490i \(0.214286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(212\) 1.62349 0.781831i 1.62349 0.781831i
\(213\) 0.167563 0.734141i 0.167563 0.734141i
\(214\) −1.94986 −1.94986
\(215\) 0 0
\(216\) −0.240787 + 1.05496i −0.240787 + 1.05496i
\(217\) 0.376510 0.781831i 0.376510 0.781831i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.777479 0.974928i −0.777479 0.974928i
\(222\) 0 0
\(223\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(224\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(225\) 0.0549581 0.240787i 0.0549581 0.240787i
\(226\) 0 0
\(227\) 0.867767 0.867767 0.433884 0.900969i \(-0.357143\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(228\) 0 0
\(229\) −0.400969 + 0.193096i −0.400969 + 0.193096i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(230\) 0 0
\(231\) 1.35690i 1.35690i
\(232\) 0 0
\(233\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(234\) −0.192021 + 0.240787i −0.192021 + 0.240787i
\(235\) 0 0
\(236\) 0 0
\(237\) 1.22252 + 0.588735i 1.22252 + 0.588735i
\(238\) 0.974928 0.222521i 0.974928 0.222521i
\(239\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(240\) 0 0
\(241\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(242\) 1.30194 + 0.626980i 1.30194 + 0.626980i
\(243\) 0.300257 0.376510i 0.300257 0.376510i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −0.781831 0.376510i −0.781831 0.376510i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(252\) −0.107160 0.222521i −0.107160 0.222521i
\(253\) −2.20291 1.06086i −2.20291 1.06086i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.623490 0.781831i 0.623490 0.781831i
\(257\) 0.445042 1.94986i 0.445042 1.94986i 0.222521 0.974928i \(-0.428571\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.347948 1.52446i 0.347948 1.52446i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −1.35690 −1.35690
\(265\) 0 0
\(266\) 0 0
\(267\) −0.347948 1.52446i −0.347948 1.52446i
\(268\) 0 0
\(269\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(270\) 0 0
\(271\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(272\) −0.222521 0.974928i −0.222521 0.974928i
\(273\) 1.08209i 1.08209i
\(274\) 0.400969 1.75676i 0.400969 1.75676i
\(275\) 1.56366 1.56366
\(276\) 1.35690 1.35690
\(277\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(278\) −1.40881 + 0.678448i −1.40881 + 0.678448i
\(279\) 0.133627 + 0.167563i 0.133627 + 0.167563i
\(280\) 0 0
\(281\) 1.24698 1.56366i 1.24698 1.56366i 0.623490 0.781831i \(-0.285714\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(282\) 0 0
\(283\) −0.974928 + 1.22252i −0.974928 + 1.22252i 1.00000i \(0.5\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(284\) 0.781831 0.376510i 0.781831 0.376510i
\(285\) 0 0
\(286\) −1.75676 0.846011i −1.75676 0.846011i
\(287\) 0 0
\(288\) −0.222521 + 0.107160i −0.222521 + 0.107160i
\(289\) −0.900969 0.433884i −0.900969 0.433884i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(294\) −0.781831 0.376510i −0.781831 0.376510i
\(295\) 0 0
\(296\) 0 0
\(297\) 1.52446 + 0.734141i 1.52446 + 0.734141i
\(298\) −0.400969 1.75676i −0.400969 1.75676i
\(299\) 1.75676 + 0.846011i 1.75676 + 0.846011i
\(300\) −0.781831 + 0.376510i −0.781831 + 0.376510i
\(301\) 0 0
\(302\) 0 0
\(303\) −0.674671 0.846011i −0.674671 0.846011i
\(304\) 0 0
\(305\) 0 0
\(306\) −0.0549581 + 0.240787i −0.0549581 + 0.240787i
\(307\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(308\) 1.22252 0.974928i 1.22252 0.974928i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(312\) 1.08209 1.08209
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0.277479 1.21572i 0.277479 1.21572i
\(315\) 0 0
\(316\) 0.347948 + 1.52446i 0.347948 + 1.52446i
\(317\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(318\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(319\) 0 0
\(320\) 0 0
\(321\) −0.376510 1.64960i −0.376510 1.64960i
\(322\) −1.22252 + 0.974928i −1.22252 + 0.974928i
\(323\) 0 0
\(324\) −0.692021 −0.692021
\(325\) −1.24698 −1.24698
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −1.21572 1.52446i −1.21572 1.52446i
\(335\) 0 0
\(336\) −0.376510 + 0.781831i −0.376510 + 0.781831i
\(337\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(338\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(339\) 0 0
\(340\) 0 0
\(341\) −0.846011 + 1.06086i −0.846011 + 1.06086i
\(342\) 0 0
\(343\) 0.974928 0.222521i 0.974928 0.222521i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.433884 1.90097i −0.433884 1.90097i −0.433884 0.900969i \(-0.642857\pi\)
1.00000i \(-0.5\pi\)
\(348\) 0 0
\(349\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(350\) 0.433884 0.900969i 0.433884 0.900969i
\(351\) −1.21572 0.585458i −1.21572 0.585458i
\(352\) −0.974928 1.22252i −0.974928 1.22252i
\(353\) −1.80194 + 0.867767i −1.80194 + 0.867767i −0.900969 + 0.433884i \(0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.12349 1.40881i 1.12349 1.40881i
\(357\) 0.376510 + 0.781831i 0.376510 + 0.781831i
\(358\) 0 0
\(359\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) −0.279032 + 1.22252i −0.279032 + 1.22252i
\(364\) −0.974928 + 0.777479i −0.974928 + 0.777479i
\(365\) 0 0
\(366\) 0 0
\(367\) −1.21572 1.52446i −1.21572 1.52446i −0.781831 0.623490i \(-0.785714\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(368\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(369\) 0 0
\(370\) 0 0
\(371\) −1.75676 0.400969i −1.75676 0.400969i
\(372\) 0.167563 0.734141i 0.167563 0.734141i
\(373\) −1.24698 −1.24698 −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(374\) −1.56366 −1.56366
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0.846011 0.674671i 0.846011 0.674671i
\(379\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(384\) 0.781831 + 0.376510i 0.781831 + 0.376510i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.400969 0.193096i −0.400969 0.193096i 0.222521 0.974928i \(-0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(390\) 0 0
\(391\) 1.56366 1.56366
\(392\) −0.222521 0.974928i −0.222521 0.974928i
\(393\) 1.35690 1.35690
\(394\) 0 0
\(395\) 0 0
\(396\) 0.0859360 + 0.376510i 0.0859360 + 0.376510i
\(397\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(398\) 0.781831 0.376510i 0.781831 0.376510i
\(399\) 0 0
\(400\) −0.900969 0.433884i −0.900969 0.433884i
\(401\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(402\) 0 0
\(403\) 0.674671 0.846011i 0.674671 0.846011i
\(404\) 0.277479 1.21572i 0.277479 1.21572i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.781831 0.376510i 0.781831 0.376510i
\(409\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(410\) 0 0
\(411\) 1.56366 1.56366
\(412\) 0 0
\(413\) 0 0
\(414\) −0.0859360 0.376510i −0.0859360 0.376510i
\(415\) 0 0
\(416\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(417\) −0.846011 1.06086i −0.846011 1.06086i
\(418\) 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 0
\(421\) −0.400969 + 1.75676i −0.400969 + 1.75676i 0.222521 + 0.974928i \(0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(422\) −1.94986 −1.94986
\(423\) 0 0
\(424\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(425\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(426\) 0.469501 + 0.588735i 0.469501 + 0.588735i
\(427\) 0 0
\(428\) 1.21572 1.52446i 1.21572 1.52446i
\(429\) 0.376510 1.64960i 0.376510 1.64960i
\(430\) 0 0
\(431\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(432\) −0.674671 0.846011i −0.674671 0.846011i
\(433\) 1.12349 + 0.541044i 1.12349 + 0.541044i 0.900969 0.433884i \(-0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(434\) 0.376510 + 0.781831i 0.376510 + 0.781831i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0.974928 1.22252i 0.974928 1.22252i 1.00000i \(-0.5\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(440\) 0 0
\(441\) −0.0549581 + 0.240787i −0.0549581 + 0.240787i
\(442\) 1.24698 1.24698
\(443\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.40881 0.678448i 1.40881 0.678448i
\(448\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(449\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(450\) 0.153989 + 0.193096i 0.153989 + 0.193096i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −0.541044 + 0.678448i −0.541044 + 0.678448i
\(455\) 0 0
\(456\) 0 0
\(457\) 1.12349 0.541044i 1.12349 0.541044i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(458\) 0.0990311 0.433884i 0.0990311 0.433884i
\(459\) −1.08209 −1.08209
\(460\) 0 0
\(461\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(462\) 1.06086 + 0.846011i 1.06086 + 0.846011i
\(463\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(468\) −0.0685317 0.300257i −0.0685317 0.300257i
\(469\) 0 0
\(470\) 0 0
\(471\) 1.08209 1.08209
\(472\) 0 0
\(473\) 0 0
\(474\) −1.22252 + 0.588735i −1.22252 + 0.588735i
\(475\) 0 0
\(476\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(477\) 0.277479 0.347948i 0.277479 0.347948i
\(478\) 0 0
\(479\) −0.974928 + 1.22252i −0.974928 + 1.22252i 1.00000i \(0.5\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −1.06086 0.846011i −1.06086 0.846011i
\(484\) −1.30194 + 0.626980i −1.30194 + 0.626980i
\(485\) 0 0
\(486\) 0.107160 + 0.469501i 0.107160 + 0.469501i
\(487\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.781831 0.376510i 0.781831 0.376510i
\(497\) −0.846011 0.193096i −0.846011 0.193096i
\(498\) 0 0
\(499\) 0.974928 + 1.22252i 0.974928 + 1.22252i 0.974928 + 0.222521i \(0.0714286\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) 1.05496 1.32288i 1.05496 1.32288i
\(502\) 0 0
\(503\) 1.21572 1.52446i 1.21572 1.52446i 0.433884 0.900969i \(-0.357143\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(504\) 0.240787 + 0.0549581i 0.240787 + 0.0549581i
\(505\) 0 0
\(506\) 2.20291 1.06086i 2.20291 1.06086i
\(507\) −0.107160 + 0.469501i −0.107160 + 0.469501i
\(508\) 0 0
\(509\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(513\) 0 0
\(514\) 1.24698 + 1.56366i 1.24698 + 1.56366i
\(515\) 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 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(524\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(525\) 0.846011 + 0.193096i 0.846011 + 0.193096i
\(526\) 0 0
\(527\) 0.193096 0.846011i 0.193096 0.846011i
\(528\) 0.846011 1.06086i 0.846011 1.06086i
\(529\) −1.30194 + 0.626980i −1.30194 + 0.626980i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 1.40881 + 0.678448i 1.40881 + 0.678448i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.56366 −1.56366
\(540\) 0 0
\(541\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(545\) 0 0
\(546\) −0.846011 0.674671i −0.846011 0.674671i
\(547\) −1.75676 0.846011i −1.75676 0.846011i −0.974928 0.222521i \(-0.928571\pi\)
−0.781831 0.623490i \(-0.785714\pi\)
\(548\) 1.12349 + 1.40881i 1.12349 + 1.40881i
\(549\) 0 0
\(550\) −0.974928 + 1.22252i −0.974928 + 1.22252i
\(551\) 0 0
\(552\) −0.846011 + 1.06086i −0.846011 + 1.06086i
\(553\) 0.678448 1.40881i 0.678448 1.40881i
\(554\) 0 0
\(555\) 0 0
\(556\) 0.347948 1.52446i 0.347948 1.52446i
\(557\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(558\) −0.214321 −0.214321
\(559\) 0 0
\(560\) 0 0
\(561\) −0.301938 1.32288i −0.301938 1.32288i
\(562\) 0.445042 + 1.94986i 0.445042 + 1.94986i
\(563\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −0.347948 1.52446i −0.347948 1.52446i
\(567\) 0.541044 + 0.431468i 0.541044 + 0.431468i
\(568\) −0.193096 + 0.846011i −0.193096 + 0.846011i
\(569\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(570\) 0 0
\(571\) 0.193096 0.846011i 0.193096 0.846011i −0.781831 0.623490i \(-0.785714\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(572\) 1.75676 0.846011i 1.75676 0.846011i
\(573\) 0 0
\(574\) 0 0
\(575\) 0.974928 1.22252i 0.974928 1.22252i
\(576\) 0.0549581 0.240787i 0.0549581 0.240787i
\(577\) 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(578\) 0.900969 0.433884i 0.900969 0.433884i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2.53859 + 1.22252i 2.53859 + 1.22252i
\(584\) 0 0
\(585\) 0 0
\(586\) −0.777479 + 0.974928i −0.777479 + 0.974928i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0.781831 0.376510i 0.781831 0.376510i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(594\) −1.52446 + 0.734141i −1.52446 + 0.734141i
\(595\) 0 0
\(596\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(597\) 0.469501 + 0.588735i 0.469501 + 0.588735i
\(598\) −1.75676 + 0.846011i −1.75676 + 0.846011i
\(599\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(600\) 0.193096 0.846011i 0.193096 0.846011i
\(601\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 1.08209 1.08209
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.153989 0.193096i −0.153989 0.193096i
\(613\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 1.56366i 1.56366i
\(617\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 1.52446 0.734141i 1.52446 0.734141i
\(622\) 0 0
\(623\) −1.75676 + 0.400969i −1.75676 + 0.400969i
\(624\) −0.674671 + 0.846011i −0.674671 + 0.846011i
\(625\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(632\) −1.40881 0.678448i −1.40881 0.678448i
\(633\) −0.376510 1.64960i −0.376510 1.64960i
\(634\) 0 0
\(635\) 0 0
\(636\) −1.56366 −1.56366
\(637\) 1.24698 1.24698
\(638\) 0 0
\(639\) 0.133627 0.167563i 0.133627 0.167563i
\(640\) 0 0
\(641\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(642\) 1.52446 + 0.734141i 1.52446 + 0.734141i
\(643\) −1.75676 + 0.846011i −1.75676 + 0.846011i −0.781831 + 0.623490i \(0.785714\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(644\) 1.56366i 1.56366i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(648\) 0.431468 0.541044i 0.431468 0.541044i
\(649\) 0 0
\(650\) 0.777479 0.974928i 0.777479 0.974928i
\(651\) −0.588735 + 0.469501i −0.588735 + 0.469501i
\(652\) 0 0
\(653\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(660\) 0 0
\(661\) −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(662\) 0 0
\(663\) 0.240787 + 1.05496i 0.240787 + 1.05496i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.94986 1.94986
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −0.376510 0.781831i −0.376510 0.781831i
\(673\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(674\) 0 0
\(675\) −0.674671 + 0.846011i −0.674671 + 0.846011i
\(676\) −0.500000 + 0.240787i −0.500000 + 0.240787i
\(677\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −0.678448 0.326723i −0.678448 0.326723i
\(682\) −0.301938 1.32288i −0.301938 1.32288i
\(683\) −0.781831 0.376510i −0.781831 0.376510i 1.00000i \(-0.5\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(687\) 0.386193 0.386193
\(688\) 0 0
\(689\) −2.02446 0.974928i −2.02446 0.974928i
\(690\) 0 0
\(691\) −0.781831 0.376510i −0.781831 0.376510i 1.00000i \(-0.5\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(692\) 0 0
\(693\) 0.167563 0.347948i 0.167563 0.347948i
\(694\) 1.75676 + 0.846011i 1.75676 + 0.846011i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(699\) 0 0
\(700\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(701\) 1.12349 + 1.40881i 1.12349 + 1.40881i 0.900969 + 0.433884i \(0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(702\) 1.21572 0.585458i 1.21572 0.585458i
\(703\) 0 0
\(704\) 1.56366 1.56366
\(705\) 0 0
\(706\) 0.445042 1.94986i 0.445042 1.94986i
\(707\) −0.974928 + 0.777479i −0.974928 + 0.777479i
\(708\) 0 0
\(709\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(710\) 0 0
\(711\) 0.240787 + 0.301938i 0.240787 + 0.301938i
\(712\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(713\) 0.301938 + 1.32288i 0.301938 + 1.32288i
\(714\) −0.846011 0.193096i −0.846011 0.193096i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.40881 + 0.678448i −1.40881 + 0.678448i −0.974928 0.222521i \(-0.928571\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −0.781831 0.980386i −0.781831 0.980386i
\(727\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(728\) 1.24698i 1.24698i
\(729\) −1.00000 + 0.481575i −1.00000 + 0.481575i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 1.24698 1.56366i 1.24698 1.56366i 0.623490 0.781831i \(-0.285714\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(734\) 1.94986 1.94986
\(735\) 0 0
\(736\) −1.56366 −1.56366
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.40881 1.12349i 1.40881 1.12349i
\(743\) 0.781831 + 0.376510i 0.781831 + 0.376510i 0.781831 0.623490i \(-0.214286\pi\)
1.00000i \(0.5\pi\)
\(744\) 0.469501 + 0.588735i 0.469501 + 0.588735i
\(745\) 0 0
\(746\) 0.777479 0.974928i 0.777479 0.974928i
\(747\) 0 0
\(748\) 0.974928 1.22252i 0.974928 1.22252i
\(749\) −1.90097 + 0.433884i −1.90097 + 0.433884i
\(750\) 0 0
\(751\) −1.40881 + 0.678448i −1.40881 + 0.678448i −0.974928 0.222521i \(-0.928571\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.08209i 1.08209i
\(757\) 0.445042 + 1.94986i 0.445042 + 1.94986i 0.222521 + 0.974928i \(0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(758\) 0 0
\(759\) 1.32288 + 1.65883i 1.32288 + 1.65883i
\(760\) 0 0
\(761\) −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.781831 + 0.376510i −0.781831 + 0.376510i
\(769\) −1.24698 1.56366i −1.24698 1.56366i −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 0.781831i \(-0.714286\pi\)
\(770\) 0 0
\(771\) −1.08209 + 1.35690i −1.08209 + 1.35690i
\(772\) 0 0
\(773\) 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(774\) 0 0
\(775\) −0.541044 0.678448i −0.541044 0.678448i
\(776\) 0 0
\(777\) 0 0
\(778\) 0.400969 0.193096i 0.400969 0.193096i
\(779\) 0 0
\(780\) 0 0
\(781\) 1.22252 + 0.588735i 1.22252 + 0.588735i
\(782\) −0.974928 + 1.22252i −0.974928 + 1.22252i
\(783\) 0 0
\(784\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(785\) 0 0
\(786\) −0.846011 + 1.06086i −0.846011 + 1.06086i
\(787\) −1.75676 0.846011i −1.75676 0.846011i −0.974928 0.222521i \(-0.928571\pi\)
−0.781831 0.623490i \(-0.785714\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0