Properties

Label 552.1.h.d.275.1
Level $552$
Weight $1$
Character 552.275
Analytic conductor $0.275$
Analytic rank $0$
Dimension $2$
Projective image $D_{6}$
CM discriminant -23
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 552.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.275483886973\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{6}\)
Projective field: Galois closure of 6.2.7312896.1

Embedding invariants

Embedding label 275.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 552.275
Dual form 552.1.h.d.275.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{12} +1.73205i q^{13} +(-0.500000 + 0.866025i) q^{16} -1.00000 q^{18} +1.00000 q^{23} +(-0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(1.50000 + 0.866025i) q^{26} -1.00000 q^{27} -1.00000 q^{29} -1.73205i q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{36} +(1.50000 + 0.866025i) q^{39} +1.73205i q^{41} +(0.500000 - 0.866025i) q^{46} -1.00000 q^{47} +(0.500000 + 0.866025i) q^{48} -1.00000 q^{49} +(0.500000 - 0.866025i) q^{50} +(1.50000 - 0.866025i) q^{52} +(-0.500000 + 0.866025i) q^{54} +(-0.500000 + 0.866025i) q^{58} +(-1.50000 - 0.866025i) q^{62} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{69} +1.00000 q^{71} +(0.500000 + 0.866025i) q^{72} +1.00000 q^{73} +(0.500000 - 0.866025i) q^{75} +(1.50000 - 0.866025i) q^{78} +(-0.500000 + 0.866025i) q^{81} +(1.50000 + 0.866025i) q^{82} +(-0.500000 + 0.866025i) q^{87} +(-0.500000 - 0.866025i) q^{92} +(-1.50000 - 0.866025i) q^{93} +(-0.500000 + 0.866025i) q^{94} +1.00000 q^{96} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} - q^{6} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} - q^{6} - 2q^{8} - q^{9} - 2q^{12} - q^{16} - 2q^{18} + 2q^{23} - q^{24} + 2q^{25} + 3q^{26} - 2q^{27} - 2q^{29} + q^{32} - q^{36} + 3q^{39} + q^{46} - 2q^{47} + q^{48} - 2q^{49} + q^{50} + 3q^{52} - q^{54} - q^{58} - 3q^{62} + 2q^{64} + q^{69} + 2q^{71} + q^{72} + 2q^{73} + q^{75} + 3q^{78} - q^{81} + 3q^{82} - q^{87} - q^{92} - 3q^{93} - q^{94} + 2q^{96} - q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(185\) \(277\) \(415\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.500000 0.866025i
\(3\) 0.500000 0.866025i 0.500000 0.866025i
\(4\) −0.500000 0.866025i −0.500000 0.866025i
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) −0.500000 0.866025i −0.500000 0.866025i
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −1.00000 −1.00000
\(9\) −0.500000 0.866025i −0.500000 0.866025i
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −1.00000 −1.00000
\(13\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −1.00000 −1.00000
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 1.00000
\(24\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(25\) 1.00000 1.00000
\(26\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(27\) −1.00000 −1.00000
\(28\) 0 0
\(29\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(32\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(40\) 0 0
\(41\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0.500000 0.866025i 0.500000 0.866025i
\(47\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(48\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(49\) −1.00000 −1.00000
\(50\) 0.500000 0.866025i 0.500000 0.866025i
\(51\) 0 0
\(52\) 1.50000 0.866025i 1.50000 0.866025i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) −1.50000 0.866025i −1.50000 0.866025i
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0.500000 0.866025i 0.500000 0.866025i
\(70\) 0 0
\(71\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(72\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(73\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 0 0
\(75\) 0.500000 0.866025i 0.500000 0.866025i
\(76\) 0 0
\(77\) 0 0
\(78\) 1.50000 0.866025i 1.50000 0.866025i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(82\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.500000 0.866025i −0.500000 0.866025i
\(93\) −1.50000 0.866025i −1.50000 0.866025i
\(94\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(95\) 0 0
\(96\) 1.00000 1.00000
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.500000 0.866025i
\(101\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 1.73205i 1.73205i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(117\) 1.50000 0.866025i 1.50000 0.866025i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) 0 0
\(123\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(124\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(125\) 0 0
\(126\) 0 0
\(127\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(128\) 0.500000 0.866025i 0.500000 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) −0.500000 0.866025i −0.500000 0.866025i
\(139\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(142\) 0.500000 0.866025i 0.500000 0.866025i
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0.500000 0.866025i 0.500000 0.866025i
\(147\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −0.500000 0.866025i −0.500000 0.866025i
\(151\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 1.73205i 1.73205i
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(163\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) 1.50000 0.866025i 1.50000 0.866025i
\(165\) 0 0
\(166\) 0 0
\(167\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −2.00000 −2.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(174\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.00000 −1.00000
\(185\) 0 0
\(186\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(187\) 0 0
\(188\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0.500000 0.866025i 0.500000 0.866025i
\(193\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(197\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −1.00000 −1.00000
\(201\) 0 0
\(202\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.500000 0.866025i −0.500000 0.866025i
\(208\) −1.50000 0.866025i −1.50000 0.866025i
\(209\) 0 0
\(210\) 0 0
\(211\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0.500000 0.866025i 0.500000 0.866025i
\(214\) 0 0
\(215\) 0 0
\(216\) 1.00000 1.00000
\(217\) 0 0
\(218\) 0 0
\(219\) 0.500000 0.866025i 0.500000 0.866025i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −0.500000 0.866025i −0.500000 0.866025i
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.00000 1.00000
\(233\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(234\) 1.73205i 1.73205i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(243\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(244\) 0 0
\(245\) 0 0
\(246\) 1.50000 0.866025i 1.50000 0.866025i
\(247\) 0 0
\(248\) 1.73205i 1.73205i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1.50000 0.866025i −1.50000 0.866025i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.500000 0.866025i
\(257\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(262\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.00000 −1.00000
\(277\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(278\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(279\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −0.500000 0.866025i −0.500000 0.866025i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.500000 0.866025i 0.500000 0.866025i
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) −0.500000 0.866025i −0.500000 0.866025i
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.73205i 1.73205i
\(300\) −1.00000 −1.00000
\(301\) 0 0
\(302\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(303\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(312\) −1.50000 0.866025i −1.50000 0.866025i
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.00000 1.00000
\(325\) 1.73205i 1.73205i
\(326\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(327\) 0 0
\(328\) 1.73205i 1.73205i
\(329\) 0 0
\(330\) 0 0
\(331\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 1.00000 1.73205i 1.00000 1.73205i
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 1.00000 1.00000
\(349\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(350\) 0 0
\(351\) 1.73205i 1.73205i
\(352\) 0 0
\(353\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −1.50000 0.866025i −1.50000 0.866025i
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(369\) 1.50000 0.866025i 1.50000 0.866025i
\(370\) 0 0
\(371\) 0 0
\(372\) 1.73205i 1.73205i
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.00000 1.00000
\(377\) 1.73205i 1.73205i
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) −1.50000 0.866025i −1.50000 0.866025i
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −0.500000 0.866025i −0.500000 0.866025i
\(385\) 0 0
\(386\) 0.500000 0.866025i 0.500000 0.866025i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.00000 1.00000
\(393\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(394\) 0.500000 0.866025i 0.500000 0.866025i
\(395\) 0 0
\(396\) 0 0
\(397\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 3.00000 3.00000
\(404\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −1.00000 −1.00000
\(415\) 0 0
\(416\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(417\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(423\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(424\) 0 0
\(425\) 0 0
\(426\) −0.500000 0.866025i −0.500000 0.866025i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0.500000 0.866025i 0.500000 0.866025i
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.500000 0.866025i −0.500000 0.866025i
\(439\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(442\) 0 0
\(443\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) −1.00000 −1.00000
\(451\) 0 0
\(452\) 0 0
\(453\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0.500000 0.866025i 0.500000 0.866025i
\(465\) 0 0
\(466\) −1.50000 0.866025i −1.50000 0.866025i
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) −1.50000 0.866025i −1.50000 0.866025i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(485\) 0 0
\(486\) 1.00000 1.00000
\(487\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0 0
\(489\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(490\) 0 0
\(491\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(492\) 1.73205i 1.73205i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(497\) 0 0
\(498\) 0 0
\(499\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0 0
\(501\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(508\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(509\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) −1.50000 0.866025i −1.50000 0.866025i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 1.00000 1.73205i 1.00000 1.73205i
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 1.00000 1.00000
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 1.50000 0.866025i 1.50000 0.866025i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.00000 −3.00000
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.50000 0.866025i −1.50000 0.866025i
\(538\) 0.500000 0.866025i 0.500000 0.866025i
\(539\) 0 0
\(540\) 0 0
\(541\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(553\) 0 0
\(554\) −1.50000 0.866025i −1.50000 0.866025i
\(555\) 0 0
\(556\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 1.73205i 1.73205i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 1.00000 1.00000
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −1.00000 −1.00000
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 1.00000
\(576\) −0.500000 0.866025i −0.500000 0.866025i
\(577\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(578\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(579\) 0.500000 0.866025i 0.500000 0.866025i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −1.00000 −1.00000
\(585\) 0 0
\(586\) 0 0
\(587\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) 1.00000 1.00000
\(589\) 0 0
\(590\) 0 0
\(591\) 0.500000 0.866025i 0.500000 0.866025i
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(599\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(600\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(601\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.50000 0.866025i 1.50000 0.866025i
\(605\) 0 0
\(606\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.73205i 1.73205i
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) 1.00000 1.73205i 1.00000 1.73205i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) −1.00000 −1.00000
\(622\) 0.500000 0.866025i 0.500000 0.866025i
\(623\) 0 0
\(624\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(634\) 1.00000 1.73205i 1.00000 1.73205i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.73205i 1.73205i
\(638\) 0 0
\(639\) −0.500000 0.866025i −0.500000 0.866025i
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) 0.500000 0.866025i 0.500000 0.866025i
\(649\) 0 0
\(650\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(651\) 0 0
\(652\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(653\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.50000 0.866025i −1.50000 0.866025i
\(657\) −0.500000 0.866025i −0.500000 0.866025i
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0.500000 0.866025i 0.500000 0.866025i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.00000 −1.00000
\(668\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(674\) 0 0
\(675\) −1.00000 −1.00000
\(676\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(692\) −1.00000 1.73205i −1.00000 1.73205i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0.500000 0.866025i 0.500000 0.866025i
\(697\) 0 0
\(698\) −1.50000 0.866025i −1.50000 0.866025i
\(699\) −1.50000 0.866025i −1.50000 0.866025i
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) −1.50000 0.866025i −1.50000 0.866025i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.73205i 1.73205i
\(714\) 0 0
\(715\) 0 0
\(716\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(717\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(718\) 0 0
\(719\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.500000 0.866025i 0.500000 0.866025i
\(723\) 0 0
\(724\) 0 0
\(725\) −1.00000 −1.00000
\(726\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(737\) 0 0
\(738\) 1.73205i 1.73205i
\(739\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0.500000 0.866025i 0.500000 0.866025i
\(753\) 0 0
\(754\) −1.50000 0.866025i −1.50000 0.866025i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(762\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1.00000 −1.00000
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −1.50000 0.866025i −1.50000 0.866025i
\(772\) −0.500000 0.866025i −0.500000 0.866025i
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 1.73205i 1.73205i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 1.00000 1.00000
\(784\) 0.500000 0.866025i 0.500000 0.866025i
\(785\) 0 0
\(786\) 1.50000 0.866025i 1.50000 0.866025i
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) −0.500000 0.866025i −0.500000 0.866025i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 1.50000 2.59808i 1.50000 2.59808i
\(807\) 0.500000 0.866025i 0.500000 0.866025i
\(808\) 2.00000 2.00000
\(809\