Properties

Label 2523.1.h.c.1952.3
Level $2523$
Weight $1$
Character 2523.1952
Analytic conductor $1.259$
Analytic rank $0$
Dimension $24$
Projective image $D_{5}$
CM discriminant -3
Inner twists $24$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2523,1,Mod(236,2523)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2523, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2523.236");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2523 = 3 \cdot 29^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2523.h (of order \(14\), degree \(6\), not 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: \(1.25914102687\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{14})\)
Coefficient field: 24.0.326829122755018756096000000000000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{24} - 3 x^{22} + 8 x^{20} - 21 x^{18} + 55 x^{16} - 144 x^{14} + 377 x^{12} - 144 x^{10} + 55 x^{8} + \cdots + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.6365529.1

Embedding invariants

Embedding label 1952.3
Root \(0.483198 - 0.385338i\) of defining polynomial
Character \(\chi\) \(=\) 2523.1952
Dual form 2523.1.h.c.2333.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.781831 - 0.623490i) q^{3} +(-0.623490 + 0.781831i) q^{4} +(-1.00883 - 1.26503i) q^{7} +(0.222521 - 0.974928i) q^{9} +O(q^{10})\) \(q+(0.781831 - 0.623490i) q^{3} +(-0.623490 + 0.781831i) q^{4} +(-1.00883 - 1.26503i) q^{7} +(0.222521 - 0.974928i) q^{9} +1.00000i q^{12} +(0.137526 + 0.602539i) q^{13} +(-0.222521 - 0.974928i) q^{16} +(-0.483198 - 0.385338i) q^{19} +(-1.57747 - 0.360046i) q^{21} +(0.623490 - 0.781831i) q^{25} +(-0.433884 - 0.900969i) q^{27} +1.61803 q^{28} +(-0.702039 - 1.45780i) q^{31} +(0.623490 + 0.781831i) q^{36} +(-0.602539 - 0.137526i) q^{37} +(0.483198 + 0.385338i) q^{39} +(0.702039 - 1.45780i) q^{43} +(-0.781831 - 0.623490i) q^{48} +(-0.360046 + 1.57747i) q^{49} +(-0.556829 - 0.268155i) q^{52} -0.618034 q^{57} +(-1.26503 + 1.00883i) q^{61} +(-1.45780 + 0.702039i) q^{63} +(0.900969 + 0.433884i) q^{64} +(0.137526 - 0.602539i) q^{67} +(0.268155 - 0.556829i) q^{73} -1.00000i q^{75} +(0.602539 - 0.137526i) q^{76} +(0.602539 + 0.137526i) q^{79} +(-0.900969 - 0.433884i) q^{81} +(1.26503 - 1.00883i) q^{84} +(0.623490 - 0.781831i) q^{91} +(-1.45780 - 0.702039i) q^{93} +(-1.26503 - 1.00883i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{4} + 2 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{4} + 2 q^{7} + 4 q^{9} - 2 q^{13} - 4 q^{16} - 4 q^{25} + 12 q^{28} - 4 q^{36} - 2 q^{49} + 2 q^{52} + 12 q^{57} - 2 q^{63} + 4 q^{64} - 2 q^{67} - 4 q^{81} - 4 q^{91} - 2 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2523\mathbb{Z}\right)^\times\).

\(n\) \(842\) \(1684\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{14}\right)\)

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 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(3\) 0.781831 0.623490i 0.781831 0.623490i
\(4\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(5\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(6\) 0 0
\(7\) −1.00883 1.26503i −1.00883 1.26503i −0.963963 0.266037i \(-0.914286\pi\)
−0.0448648 0.998993i \(-0.514286\pi\)
\(8\) 0 0
\(9\) 0.222521 0.974928i 0.222521 0.974928i
\(10\) 0 0
\(11\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(12\) 1.00000i 1.00000i
\(13\) 0.137526 + 0.602539i 0.137526 + 0.602539i 0.995974 + 0.0896393i \(0.0285714\pi\)
−0.858449 + 0.512899i \(0.828571\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.222521 0.974928i −0.222521 0.974928i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) −0.483198 0.385338i −0.483198 0.385338i 0.351375 0.936235i \(-0.385714\pi\)
−0.834573 + 0.550897i \(0.814286\pi\)
\(20\) 0 0
\(21\) −1.57747 0.360046i −1.57747 0.360046i
\(22\) 0 0
\(23\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(24\) 0 0
\(25\) 0.623490 0.781831i 0.623490 0.781831i
\(26\) 0 0
\(27\) −0.433884 0.900969i −0.433884 0.900969i
\(28\) 1.61803 1.61803
\(29\) 0 0
\(30\) 0 0
\(31\) −0.702039 1.45780i −0.702039 1.45780i −0.880596 0.473869i \(-0.842857\pi\)
0.178557 0.983930i \(-0.442857\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(37\) −0.602539 0.137526i −0.602539 0.137526i −0.0896393 0.995974i \(-0.528571\pi\)
−0.512899 + 0.858449i \(0.671429\pi\)
\(38\) 0 0
\(39\) 0.483198 + 0.385338i 0.483198 + 0.385338i
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 0.702039 1.45780i 0.702039 1.45780i −0.178557 0.983930i \(-0.557143\pi\)
0.880596 0.473869i \(-0.157143\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 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
\(49\) −0.360046 + 1.57747i −0.360046 + 1.57747i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.556829 0.268155i −0.556829 0.268155i
\(53\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.618034 −0.618034
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −1.26503 + 1.00883i −1.26503 + 1.00883i −0.266037 + 0.963963i \(0.585714\pi\)
−0.998993 + 0.0448648i \(0.985714\pi\)
\(62\) 0 0
\(63\) −1.45780 + 0.702039i −1.45780 + 0.702039i
\(64\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.137526 0.602539i 0.137526 0.602539i −0.858449 0.512899i \(-0.828571\pi\)
0.995974 0.0896393i \(-0.0285714\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(72\) 0 0
\(73\) 0.268155 0.556829i 0.268155 0.556829i −0.722795 0.691063i \(-0.757143\pi\)
0.990950 + 0.134233i \(0.0428571\pi\)
\(74\) 0 0
\(75\) 1.00000i 1.00000i
\(76\) 0.602539 0.137526i 0.602539 0.137526i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.602539 + 0.137526i 0.602539 + 0.137526i 0.512899 0.858449i \(-0.328571\pi\)
0.0896393 + 0.995974i \(0.471429\pi\)
\(80\) 0 0
\(81\) −0.900969 0.433884i −0.900969 0.433884i
\(82\) 0 0
\(83\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(84\) 1.26503 1.00883i 1.26503 1.00883i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(90\) 0 0
\(91\) 0.623490 0.781831i 0.623490 0.781831i
\(92\) 0 0
\(93\) −1.45780 0.702039i −1.45780 0.702039i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.26503 1.00883i −1.26503 1.00883i −0.998993 0.0448648i \(-0.985714\pi\)
−0.266037 0.963963i \(-0.585714\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(101\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(102\) 0 0
\(103\) 0.360046 + 1.57747i 0.360046 + 1.57747i 0.753071 + 0.657939i \(0.228571\pi\)
−0.393025 + 0.919528i \(0.628571\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(108\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(109\) 1.00883 + 1.26503i 1.00883 + 1.26503i 0.963963 + 0.266037i \(0.0857143\pi\)
0.0448648 + 0.998993i \(0.485714\pi\)
\(110\) 0 0
\(111\) −0.556829 + 0.268155i −0.556829 + 0.268155i
\(112\) −1.00883 + 1.26503i −1.00883 + 1.26503i
\(113\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.618034 0.618034
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.900969 0.433884i 0.900969 0.433884i
\(122\) 0 0
\(123\) 0 0
\(124\) 1.57747 + 0.360046i 1.57747 + 0.360046i
\(125\) 0 0
\(126\) 0 0
\(127\) 1.57747 0.360046i 1.57747 0.360046i 0.657939 0.753071i \(-0.271429\pi\)
0.919528 + 0.393025i \(0.128571\pi\)
\(128\) 0 0
\(129\) −0.360046 1.57747i −0.360046 1.57747i
\(130\) 0 0
\(131\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(132\) 0 0
\(133\) 1.00000i 1.00000i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(138\) 0 0
\(139\) 1.45780 + 0.702039i 1.45780 + 0.702039i 0.983930 0.178557i \(-0.0571429\pi\)
0.473869 + 0.880596i \(0.342857\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0.702039 + 1.45780i 0.702039 + 1.45780i
\(148\) 0.483198 0.385338i 0.483198 0.385338i
\(149\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(150\) 0 0
\(151\) 0.556829 + 0.268155i 0.556829 + 0.268155i 0.691063 0.722795i \(-0.257143\pi\)
−0.134233 + 0.990950i \(0.542857\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.602539 + 0.137526i −0.602539 + 0.137526i
\(157\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.57747 + 0.360046i −1.57747 + 0.360046i −0.919528 0.393025i \(-0.871429\pi\)
−0.657939 + 0.753071i \(0.728571\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(168\) 0 0
\(169\) 0.556829 0.268155i 0.556829 0.268155i
\(170\) 0 0
\(171\) −0.483198 + 0.385338i −0.483198 + 0.385338i
\(172\) 0.702039 + 1.45780i 0.702039 + 1.45780i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −1.61803 −1.61803
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(180\) 0 0
\(181\) 0.385338 + 0.483198i 0.385338 + 0.483198i 0.936235 0.351375i \(-0.114286\pi\)
−0.550897 + 0.834573i \(0.685714\pi\)
\(182\) 0 0
\(183\) −0.360046 + 1.57747i −0.360046 + 1.57747i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −0.702039 + 1.45780i −0.702039 + 1.45780i
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0.974928 0.222521i 0.974928 0.222521i
\(193\) 1.26503 + 1.00883i 1.26503 + 1.00883i 0.998993 + 0.0448648i \(0.0142857\pi\)
0.266037 + 0.963963i \(0.414286\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.00883 1.26503i −1.00883 1.26503i
\(197\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(198\) 0 0
\(199\) 0.385338 0.483198i 0.385338 0.483198i −0.550897 0.834573i \(-0.685714\pi\)
0.936235 + 0.351375i \(0.114286\pi\)
\(200\) 0 0
\(201\) −0.268155 0.556829i −0.268155 0.556829i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0.556829 0.268155i 0.556829 0.268155i
\(209\) 0 0
\(210\) 0 0
\(211\) −1.94986 0.445042i −1.94986 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
−0.974928 0.222521i \(-0.928571\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.13592 + 2.35877i −1.13592 + 2.35877i
\(218\) 0 0
\(219\) −0.137526 0.602539i −0.137526 0.602539i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0.360046 1.57747i 0.360046 1.57747i −0.393025 0.919528i \(-0.628571\pi\)
0.753071 0.657939i \(-0.228571\pi\)
\(224\) 0 0
\(225\) −0.623490 0.781831i −0.623490 0.781831i
\(226\) 0 0
\(227\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(228\) 0.385338 0.483198i 0.385338 0.483198i
\(229\) −1.56366 + 1.24698i −1.56366 + 1.24698i −0.781831 + 0.623490i \(0.785714\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0.556829 0.268155i 0.556829 0.268155i
\(238\) 0 0
\(239\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(240\) 0 0
\(241\) −0.360046 + 1.57747i −0.360046 + 1.57747i 0.393025 + 0.919528i \(0.371429\pi\)
−0.753071 + 0.657939i \(0.771429\pi\)
\(242\) 0 0
\(243\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(244\) 1.61803i 1.61803i
\(245\) 0 0
\(246\) 0 0
\(247\) 0.165729 0.344139i 0.165729 0.344139i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(252\) 0.360046 1.57747i 0.360046 1.57747i
\(253\) 0 0
\(254\) 0 0
\(255\) 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
\(259\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.385338 + 0.483198i 0.385338 + 0.483198i
\(269\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(270\) 0 0
\(271\) 1.56366 + 1.24698i 1.56366 + 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(272\) 0 0
\(273\) 1.00000i 1.00000i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −0.137526 0.602539i −0.137526 0.602539i −0.995974 0.0896393i \(-0.971429\pi\)
0.858449 0.512899i \(-0.171429\pi\)
\(278\) 0 0
\(279\) −1.57747 + 0.360046i −1.57747 + 0.360046i
\(280\) 0 0
\(281\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(282\) 0 0
\(283\) −0.385338 0.483198i −0.385338 0.483198i 0.550897 0.834573i \(-0.314286\pi\)
−0.936235 + 0.351375i \(0.885714\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) −1.61803 −1.61803
\(292\) 0.268155 + 0.556829i 0.268155 + 0.556829i
\(293\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(301\) −2.55239 + 0.582567i −2.55239 + 0.582567i
\(302\) 0 0
\(303\) 0 0
\(304\) −0.268155 + 0.556829i −0.268155 + 0.556829i
\(305\) 0 0
\(306\) 0 0
\(307\) 0.618034i 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(308\) 0 0
\(309\) 1.26503 + 1.00883i 1.26503 + 1.00883i
\(310\) 0 0
\(311\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(312\) 0 0
\(313\) 1.45780 + 0.702039i 1.45780 + 0.702039i 0.983930 0.178557i \(-0.0571429\pi\)
0.473869 + 0.880596i \(0.342857\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.483198 + 0.385338i −0.483198 + 0.385338i
\(317\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.900969 0.433884i 0.900969 0.433884i
\(325\) 0.556829 + 0.268155i 0.556829 + 0.268155i
\(326\) 0 0
\(327\) 1.57747 + 0.360046i 1.57747 + 0.360046i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.61803i 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(332\) 0 0
\(333\) −0.268155 + 0.556829i −0.268155 + 0.556829i
\(334\) 0 0
\(335\) 0 0
\(336\) 1.61803i 1.61803i
\(337\) 1.94986 0.445042i 1.94986 0.445042i 0.974928 0.222521i \(-0.0714286\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.900969 0.433884i 0.900969 0.433884i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(350\) 0 0
\(351\) 0.483198 0.385338i 0.483198 0.385338i
\(352\) 0 0
\(353\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(360\) 0 0
\(361\) −0.137526 0.602539i −0.137526 0.602539i
\(362\) 0 0
\(363\) 0.433884 0.900969i 0.433884 0.900969i
\(364\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(365\) 0 0
\(366\) 0 0
\(367\) 1.26503 + 1.00883i 1.26503 + 1.00883i 0.998993 + 0.0448648i \(0.0142857\pi\)
0.266037 + 0.963963i \(0.414286\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 1.45780 0.702039i 1.45780 0.702039i
\(373\) −1.00883 + 1.26503i −1.00883 + 1.26503i −0.0448648 + 0.998993i \(0.514286\pi\)
−0.963963 + 0.266037i \(0.914286\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.867767 + 1.80194i 0.867767 + 1.80194i 0.433884 + 0.900969i \(0.357143\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(380\) 0 0
\(381\) 1.00883 1.26503i 1.00883 1.26503i
\(382\) 0 0
\(383\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.26503 1.00883i −1.26503 1.00883i
\(388\) 1.57747 0.360046i 1.57747 0.360046i
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.360046 1.57747i 0.360046 1.57747i −0.393025 0.919528i \(-0.628571\pi\)
0.753071 0.657939i \(-0.228571\pi\)
\(398\) 0 0
\(399\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(400\) −0.900969 0.433884i −0.900969 0.433884i
\(401\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(402\) 0 0
\(403\) 0.781831 0.623490i 0.781831 0.623490i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.483198 0.385338i 0.483198 0.385338i −0.351375 0.936235i \(-0.614286\pi\)
0.834573 + 0.550897i \(0.185714\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.45780 0.702039i −1.45780 0.702039i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.57747 0.360046i 1.57747 0.360046i
\(418\) 0 0
\(419\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(420\) 0 0
\(421\) 0.268155 0.556829i 0.268155 0.556829i −0.722795 0.691063i \(-0.757143\pi\)
0.990950 + 0.134233i \(0.0428571\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2.55239 + 0.582567i 2.55239 + 0.582567i
\(428\) 0 0
\(429\) 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
\(433\) −0.268155 0.556829i −0.268155 0.556829i 0.722795 0.691063i \(-0.242857\pi\)
−0.990950 + 0.134233i \(0.957143\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.61803 −1.61803
\(437\) 0 0
\(438\) 0 0
\(439\) −0.385338 + 0.483198i −0.385338 + 0.483198i −0.936235 0.351375i \(-0.885714\pi\)
0.550897 + 0.834573i \(0.314286\pi\)
\(440\) 0 0
\(441\) 1.45780 + 0.702039i 1.45780 + 0.702039i
\(442\) 0 0
\(443\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(444\) 0.137526 0.602539i 0.137526 0.602539i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.360046 1.57747i −0.360046 1.57747i
\(449\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0.602539 0.137526i 0.602539 0.137526i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.00883 + 1.26503i 1.00883 + 1.26503i 0.963963 + 0.266037i \(0.0857143\pi\)
0.0448648 + 0.998993i \(0.485714\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(462\) 0 0
\(463\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(468\) −0.385338 + 0.483198i −0.385338 + 0.483198i
\(469\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(470\) 0 0
\(471\) 0.385338 + 0.483198i 0.385338 + 0.483198i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −0.602539 + 0.137526i −0.602539 + 0.137526i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(480\) 0 0
\(481\) 0.381966i 0.381966i
\(482\) 0 0
\(483\) 0 0
\(484\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(485\) 0 0
\(486\) 0 0
\(487\) −0.556829 0.268155i −0.556829 0.268155i 0.134233 0.990950i \(-0.457143\pi\)
−0.691063 + 0.722795i \(0.742857\pi\)
\(488\) 0 0
\(489\) −1.00883 + 1.26503i −1.00883 + 1.26503i
\(490\) 0 0
\(491\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −1.26503 + 1.00883i −1.26503 + 1.00883i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.45780 0.702039i −1.45780 0.702039i −0.473869 0.880596i \(-0.657143\pi\)
−0.983930 + 0.178557i \(0.942857\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.268155 0.556829i 0.268155 0.556829i
\(508\) −0.702039 + 1.45780i −0.702039 + 1.45780i
\(509\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(510\) 0 0
\(511\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(512\) 0 0
\(513\) −0.137526 + 0.602539i −0.137526 + 0.602539i
\(514\) 0 0
\(515\) 0 0
\(516\) 1.45780 + 0.702039i 1.45780 + 0.702039i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(524\) 0 0
\(525\) −1.26503 + 1.00883i −1.26503 + 1.00883i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(530\) 0 0
\(531\) 0 0
\(532\) −0.781831 0.623490i −0.781831 0.623490i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.56366 1.24698i −1.56366 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
−0.781831 0.623490i \(-0.785714\pi\)
\(542\) 0 0
\(543\) 0.602539 + 0.137526i 0.602539 + 0.137526i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.385338 0.483198i 0.385338 0.483198i −0.550897 0.834573i \(-0.685714\pi\)
0.936235 + 0.351375i \(0.114286\pi\)
\(548\) 0 0
\(549\) 0.702039 + 1.45780i 0.702039 + 1.45780i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −0.433884 0.900969i −0.433884 0.900969i
\(554\) 0 0
\(555\) 0 0
\(556\) −1.45780 + 0.702039i −1.45780 + 0.702039i
\(557\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(558\) 0 0
\(559\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.360046 + 1.57747i 0.360046 + 1.57747i
\(568\) 0 0
\(569\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(570\) 0 0
\(571\) −0.137526 + 0.602539i −0.137526 + 0.602539i 0.858449 + 0.512899i \(0.171429\pi\)
−0.995974 + 0.0896393i \(0.971429\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.623490 0.781831i 0.623490 0.781831i
\(577\) 1.26503 1.00883i 1.26503 1.00883i 0.266037 0.963963i \(-0.414286\pi\)
0.998993 0.0448648i \(-0.0142857\pi\)
\(578\) 0 0
\(579\) 1.61803 1.61803
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(588\) −1.57747 0.360046i −1.57747 0.360046i
\(589\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(590\) 0 0
\(591\) 0 0
\(592\) 0.618034i 0.618034i
\(593\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0.618034i 0.618034i
\(598\) 0 0
\(599\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(600\) 0 0
\(601\) −1.57747 0.360046i −1.57747 0.360046i −0.657939 0.753071i \(-0.728571\pi\)
−0.919528 + 0.393025i \(0.871429\pi\)
\(602\) 0 0
\(603\) −0.556829 0.268155i −0.556829 0.268155i
\(604\) −0.556829 + 0.268155i −0.556829 + 0.268155i
\(605\) 0 0
\(606\) 0 0
\(607\) −0.867767 1.80194i −0.867767 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.00883 1.26503i 1.00883 1.26503i 0.0448648 0.998993i \(-0.485714\pi\)
0.963963 0.266037i \(-0.0857143\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(618\) 0 0
\(619\) 0.483198 + 0.385338i 0.483198 + 0.385338i 0.834573 0.550897i \(-0.185714\pi\)
−0.351375 + 0.936235i \(0.614286\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0.268155 0.556829i 0.268155 0.556829i
\(625\) −0.222521 0.974928i −0.222521 0.974928i
\(626\) 0 0
\(627\) 0 0
\(628\) −0.483198 0.385338i −0.483198 0.385338i
\(629\) 0 0
\(630\) 0 0
\(631\) −1.24698 1.56366i −1.24698 1.56366i −0.623490 0.781831i \(-0.714286\pi\)
−0.623490 0.781831i \(-0.714286\pi\)
\(632\) 0 0
\(633\) −1.80194 + 0.867767i −1.80194 + 0.867767i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.00000 −1.00000
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(642\) 0 0
\(643\) 1.80194 0.867767i 1.80194 0.867767i 0.900969 0.433884i \(-0.142857\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(644\) 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 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0.582567 + 2.55239i 0.582567 + 2.55239i
\(652\) 0.702039 1.45780i 0.702039 1.45780i
\(653\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.483198 0.385338i −0.483198 0.385338i
\(658\) 0 0
\(659\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(660\) 0 0
\(661\) −1.80194 0.867767i −1.80194 0.867767i −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 0.433884i \(-0.857143\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −0.702039 1.45780i −0.702039 1.45780i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.80194 + 0.867767i 1.80194 + 0.867767i 0.900969 + 0.433884i \(0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(674\) 0 0
\(675\) −0.974928 0.222521i −0.974928 0.222521i
\(676\) −0.137526 + 0.602539i −0.137526 + 0.602539i
\(677\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(678\) 0 0
\(679\) 2.61803i 2.61803i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(684\) 0.618034i 0.618034i
\(685\) 0 0
\(686\) 0 0
\(687\) −0.445042 + 1.94986i −0.445042 + 1.94986i
\(688\) −1.57747 0.360046i −1.57747 0.360046i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.556829 + 0.268155i −0.556829 + 0.268155i −0.691063 0.722795i \(-0.742857\pi\)
0.134233 + 0.990950i \(0.457143\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 1.00883 1.26503i 1.00883 1.26503i
\(701\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(702\) 0 0
\(703\) 0.238152 + 0.298633i 0.238152 + 0.298633i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0.137526 + 0.602539i 0.137526 + 0.602539i 0.995974 + 0.0896393i \(0.0285714\pi\)
−0.858449 + 0.512899i \(0.828571\pi\)
\(710\) 0 0
\(711\) 0.268155 0.556829i 0.268155 0.556829i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(720\) 0 0
\(721\) 1.63232 2.04686i 1.63232 2.04686i
\(722\) 0 0
\(723\) 0.702039 + 1.45780i 0.702039 + 1.45780i
\(724\) −0.618034 −0.618034
\(725\) 0 0
\(726\) 0 0
\(727\) 0.268155 + 0.556829i 0.268155 + 0.556829i 0.990950 0.134233i \(-0.0428571\pi\)
−0.722795 + 0.691063i \(0.757143\pi\)
\(728\) 0 0
\(729\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(730\) 0 0
\(731\) 0 0
\(732\) −1.00883 1.26503i −1.00883 1.26503i
\(733\) 1.57747 + 0.360046i 1.57747 + 0.360046i 0.919528 0.393025i \(-0.128571\pi\)
0.657939 + 0.753071i \(0.271429\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.702039 1.45780i 0.702039 1.45780i −0.178557 0.983930i \(-0.557143\pi\)
0.880596 0.473869i \(-0.157143\pi\)
\(740\) 0 0
\(741\) −0.0849954 0.372389i −0.0849954 0.372389i
\(742\) 0 0
\(743\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.26503 1.00883i 1.26503 1.00883i 0.266037 0.963963i \(-0.414286\pi\)
0.998993 0.0448648i \(-0.0142857\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.702039 1.45780i −0.702039 1.45780i
\(757\) 1.56366 1.24698i 1.56366 1.24698i 0.781831 0.623490i \(-0.214286\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(762\) 0 0
\(763\) 0.582567 2.55239i 0.582567 2.55239i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(769\) −0.702039 + 1.45780i −0.702039 + 1.45780i 0.178557 + 0.983930i \(0.442857\pi\)
−0.880596 + 0.473869i \(0.842857\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.57747 + 0.360046i −1.57747 + 0.360046i
\(773\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(774\) 0 0
\(775\) −1.57747 0.360046i −1.57747 0.360046i
\(776\) 0 0
\(777\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.61803 1.61803
\(785\) 0 0
\(786\) 0 0
\(787\) −1.24698 + 1.56366i −1.24698 + 1.56366i −0.623490 + 0.781831i \(0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.781831 0.623490i −0.781831 0.623490i
\(794\) 0 0
\(795\) 0 0
\(796\) 0.137526 + 0.602539i 0.137526 + 0.602539i
\(797\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(798\) 0 0