Properties

Label 77.1.j.a.48.1
Level $77$
Weight $1$
Character 77.48
Analytic conductor $0.038$
Analytic rank $0$
Dimension $4$
Projective image $D_{5}$
CM discriminant -7
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 77 = 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 77.j (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.0384280059727\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.717409.1

Embedding invariants

Embedding label 48.1
Root \(-0.309017 - 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 77.48
Dual form 77.1.j.a.69.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.363271i) q^{2} +(-0.190983 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.363271i) q^{2} +(-0.190983 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.809017 + 0.587785i) q^{11} +(0.190983 - 0.587785i) q^{14} +(0.190983 + 0.587785i) q^{18} +0.618034 q^{22} +0.618034 q^{23} +(0.309017 - 0.951057i) q^{25} +(0.500000 - 0.363271i) q^{28} +(-0.500000 - 1.53884i) q^{29} +1.00000 q^{32} +(-0.190983 + 0.587785i) q^{36} +(0.190983 + 0.587785i) q^{37} -1.61803 q^{43} +(0.500000 + 0.363271i) q^{44} +(-0.309017 - 0.224514i) q^{46} +(-0.809017 + 0.587785i) q^{49} +(-0.500000 + 0.363271i) q^{50} +(1.30902 + 0.951057i) q^{53} -1.00000 q^{56} +(-0.309017 + 0.951057i) q^{58} +(0.309017 - 0.951057i) q^{63} +(-0.500000 - 0.363271i) q^{64} -1.61803 q^{67} +(1.30902 - 0.951057i) q^{71} +(0.809017 - 0.587785i) q^{72} +(0.118034 - 0.363271i) q^{74} +(-0.809017 - 0.587785i) q^{77} +(1.30902 + 0.951057i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.809017 + 0.587785i) q^{86} +(-0.309017 - 0.951057i) q^{88} +(-0.118034 - 0.363271i) q^{92} +0.618034 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 3q^{4} - q^{7} + q^{8} - q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 3q^{4} - q^{7} + q^{8} - q^{9} - q^{11} + 3q^{14} + 3q^{18} - 2q^{22} - 2q^{23} - q^{25} + 2q^{28} - 2q^{29} + 4q^{32} - 3q^{36} + 3q^{37} - 2q^{43} + 2q^{44} + q^{46} - q^{49} - 2q^{50} + 3q^{53} - 4q^{56} + q^{58} - q^{63} - 2q^{64} - 2q^{67} + 3q^{71} + q^{72} - 4q^{74} - q^{77} + 3q^{79} - q^{81} + q^{86} + q^{88} + 4q^{92} - 2q^{98} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/77\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(3\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(4\) −0.190983 0.587785i −0.190983 0.587785i
\(5\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(6\) 0 0
\(7\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(8\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(9\) −0.809017 0.587785i −0.809017 0.587785i
\(10\) 0 0
\(11\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(12\) 0 0
\(13\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(14\) 0.190983 0.587785i 0.190983 0.587785i
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(19\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.618034 0.618034
\(23\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(24\) 0 0
\(25\) 0.309017 0.951057i 0.309017 0.951057i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.500000 0.363271i 0.500000 0.363271i
\(29\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(32\) 1.00000 1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(37\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(42\) 0 0
\(43\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(44\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(45\) 0 0
\(46\) −0.309017 0.224514i −0.309017 0.224514i
\(47\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(48\) 0 0
\(49\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(50\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(51\) 0 0
\(52\) 0 0
\(53\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 −1.00000
\(57\) 0 0
\(58\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(59\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(60\) 0 0
\(61\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(62\) 0 0
\(63\) 0.309017 0.951057i 0.309017 0.951057i
\(64\) −0.500000 0.363271i −0.500000 0.363271i
\(65\) 0 0
\(66\) 0 0
\(67\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(72\) 0.809017 0.587785i 0.809017 0.587785i
\(73\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(74\) 0.118034 0.363271i 0.118034 0.363271i
\(75\) 0 0
\(76\) 0 0
\(77\) −0.809017 0.587785i −0.809017 0.587785i
\(78\) 0 0
\(79\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(82\) 0 0
\(83\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(87\) 0 0
\(88\) −0.309017 0.951057i −0.309017 0.951057i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.118034 0.363271i −0.118034 0.363271i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(98\) 0.618034 0.618034
\(99\) 1.00000 1.00000
\(100\) −0.618034 −0.618034
\(101\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −0.309017 0.951057i −0.309017 0.951057i
\(107\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(108\) 0 0
\(109\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.309017 0.951057i 0.309017 0.951057i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(127\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(128\) −0.190983 0.587785i −0.190983 0.587785i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(135\) 0 0
\(136\) 0 0
\(137\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.00000 −1.00000
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0.309017 0.224514i 0.309017 0.224514i
\(149\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) 0 0
\(151\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(158\) −0.309017 0.951057i −0.309017 0.951057i
\(159\) 0 0
\(160\) 0 0
\(161\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(162\) 0.190983 0.587785i 0.190983 0.587785i
\(163\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(168\) 0 0
\(169\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(173\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(174\) 0 0
\(175\) 1.00000 1.00000
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(180\) 0 0
\(181\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(192\) 0 0
\(193\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(197\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(198\) −0.500000 0.363271i −0.500000 0.363271i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(201\) 0 0
\(202\) 0 0
\(203\) 1.30902 0.951057i 1.30902 0.951057i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.500000 0.363271i −0.500000 0.363271i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(212\) 0.309017 0.951057i 0.309017 0.951057i
\(213\) 0 0
\(214\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −0.309017 0.224514i −0.309017 0.224514i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(224\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(225\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(226\) 0.809017 0.587785i 0.809017 0.587785i
\(227\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.61803 1.61803
\(233\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(252\) −0.618034 −0.618034
\(253\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(254\) 0.381966 0.381966
\(255\) 0 0
\(256\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(257\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(258\) 0 0
\(259\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(260\) 0 0
\(261\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(262\) 0 0
\(263\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(269\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(270\) 0 0
\(271\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0.381966 0.381966
\(275\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(276\) 0 0
\(277\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(282\) 0 0
\(283\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(284\) −0.809017 0.587785i −0.809017 0.587785i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.809017 0.587785i −0.809017 0.587785i
\(289\) 0.309017 0.951057i 0.309017 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.618034 −0.618034
\(297\) 0 0
\(298\) 1.23607 1.23607
\(299\) 0 0
\(300\) 0 0
\(301\) −0.500000 1.53884i −0.500000 1.53884i
\(302\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(312\) 0 0
\(313\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.309017 0.951057i 0.309017 0.951057i
\(317\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(318\) 0 0
\(319\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.118034 0.363271i 0.118034 0.363271i
\(323\) 0 0
\(324\) 0.500000 0.363271i 0.500000 0.363271i
\(325\) 0 0
\(326\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(332\) 0 0
\(333\) 0.190983 0.587785i 0.190983 0.587785i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(338\) 0.190983 0.587785i 0.190983 0.587785i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.809017 0.587785i −0.809017 0.587785i
\(344\) 0.500000 1.53884i 0.500000 1.53884i
\(345\) 0 0
\(346\) 0 0
\(347\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(348\) 0 0
\(349\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(350\) −0.500000 0.363271i −0.500000 0.363271i
\(351\) 0 0
\(352\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(359\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(360\) 0 0
\(361\) −0.809017 0.587785i −0.809017 0.587785i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(372\) 0 0
\(373\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(383\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −1.00000 −1.00000
\(387\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(388\) 0 0
\(389\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.309017 0.951057i −0.309017 0.951057i
\(393\) 0 0
\(394\) −0.309017 0.224514i −0.309017 0.224514i
\(395\) 0 0
\(396\) −0.190983 0.587785i −0.190983 0.587785i
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) −1.00000 −1.00000
\(407\) −0.500000 0.363271i −0.500000 0.363271i
\(408\) 0 0
\(409\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(422\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(423\) 0 0
\(424\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −0.381966 −0.381966
\(429\) 0 0
\(430\) 0 0
\(431\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(432\) 0 0
\(433\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.118034 0.363271i −0.118034 0.363271i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.190983 0.587785i 0.190983 0.587785i
\(449\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) 0.618034 0.618034
\(451\) 0 0
\(452\) 1.00000 1.00000
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(467\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(468\) 0 0
\(469\) −0.500000 1.53884i −0.500000 1.53884i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.30902 0.951057i 1.30902 0.951057i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.500000 1.53884i −0.500000 1.53884i
\(478\) 0.809017 0.587785i 0.809017 0.587785i
\(479\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.618034 −0.618034
\(485\) 0 0
\(486\) 0 0
\(487\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(498\) 0 0
\(499\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(504\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(505\) 0 0
\(506\) 0.381966 0.381966
\(507\) 0 0
\(508\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(509\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0.381966 0.381966
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(522\) 0.809017 0.587785i 0.809017 0.587785i
\(523\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.618034 −0.618034
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.500000 1.53884i 0.500000 1.53884i
\(537\) 0 0
\(538\) 0 0
\(539\) 0.309017 0.951057i 0.309017 0.951057i
\(540\) 0 0
\(541\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(548\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(549\) 0 0
\(550\) 0.190983 0.587785i 0.190983 0.587785i
\(551\) 0 0
\(552\) 0 0
\(553\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(554\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.00000 −1.00000
\(563\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(568\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(569\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(570\) 0 0
\(571\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.190983 0.587785i 0.190983 0.587785i
\(576\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(577\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(578\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.61803 −1.61803
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.00000 + 0.726543i 1.00000 + 0.726543i
\(597\) 0 0
\(598\) 0 0
\(599\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(600\) 0 0
\(601\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(602\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(603\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(604\) −0.381966 −0.381966
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0.809017 0.587785i 0.809017 0.587785i
\(617\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(618\) 0 0
\(619\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.809017 0.587785i −0.809017 0.587785i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(632\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(633\) 0 0
\(634\) −0.309017 0.951057i −0.309017 0.951057i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −0.309017 0.951057i −0.309017 0.951057i
\(639\) −1.61803 −1.61803
\(640\) 0 0
\(641\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(642\) 0 0
\(643\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(644\) 0.309017 0.224514i 0.309017 0.224514i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(648\) −1.00000 −1.00000
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(653\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) −0.309017 0.224514i −0.309017 0.224514i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(667\) −0.309017 0.951057i −0.309017 0.951057i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(674\) 0.118034 0.363271i 0.118034 0.363271i
\(675\) 0 0
\(676\) 0.500000 0.363271i 0.500000 0.363271i
\(677\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(692\) 0 0
\(693\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(694\) −1.00000 −1.00000
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.190983 0.587785i −0.190983 0.587785i
\(701\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.618034 0.618034
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(710\) 0 0
\(711\) −0.500000 1.53884i −0.500000 1.53884i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.381966 −0.381966
\(717\) 0 0
\(718\) 0.118034 0.363271i 0.118034 0.363271i
\(719\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(723\) 0 0
\(724\) 0 0
\(725\) −1.61803 −1.61803
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0.309017 0.951057i 0.309017 0.951057i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.618034 0.618034
\(737\) 1.30902 0.951057i 1.30902 0.951057i
\(738\) 0 0
\(739\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.809017 0.587785i 0.809017 0.587785i
\(743\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(744\) 0 0
\(745\) 0 0
\(746\) −1.00000 0.726543i −1.00000 0.726543i
\(747\) 0 0
\(748\) 0 0
\(749\) 0.618034 0.618034
\(750\) 0 0
\(751\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(758\) 0.381966 0.381966
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(762\) 0 0
\(763\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(764\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.809017 0.587785i −0.809017 0.587785i
\(773\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(774\) −0.309017 0.951057i −0.309017 0.951057i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.118034 0.363271i 0.118034 0.363271i
\(779\) 0 0
\(780\) 0 0
\(781\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(788\) −0.118034 0.363271i −0.118034 0.363271i
\(789\) 0 0
\(790\) 0 0
\(791\) −1.61803 −1.61803
\(792\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.309017 0.951057i 0.309017 0.951057i
\(801\) 0 0
\(802\) 0.381966 0.381966
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0