Properties

Label 1960.1.bi.b.1059.1
Level $1960$
Weight $1$
Character 1960.1059
Analytic conductor $0.978$
Analytic rank $0$
Dimension $2$
Projective image $D_{3}$
CM discriminant -40
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1960.bi (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.978167424761\)
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: no (minimal twist has level 280)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.1960.1
Artin image: $C_6\times S_3$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{12} - \cdots)\)

Embedding invariants

Embedding label 1059.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1960.1059
Dual form 1960.1.bi.b.459.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} -1.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +1.00000 q^{20} +1.00000 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(0.500000 + 0.866025i) q^{32} +1.00000 q^{36} +(-0.500000 + 0.866025i) q^{37} +(0.500000 + 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{40} +1.00000 q^{41} +(0.500000 - 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(0.500000 + 0.866025i) q^{46} +(0.500000 - 0.866025i) q^{47} -1.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{53} -1.00000 q^{55} +(1.00000 + 1.73205i) q^{59} +1.00000 q^{64} +(0.500000 - 0.866025i) q^{65} +(0.500000 - 0.866025i) q^{72} +(0.500000 + 0.866025i) q^{74} +1.00000 q^{76} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.500000 - 0.866025i) q^{82} +(-0.500000 - 0.866025i) q^{88} +(1.00000 - 1.73205i) q^{89} -1.00000 q^{90} +1.00000 q^{92} +(-0.500000 - 0.866025i) q^{94} +(-0.500000 - 0.866025i) q^{95} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} - q^{5} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{4} - q^{5} - 2q^{8} - q^{9} + q^{10} + q^{11} - 2q^{13} - q^{16} + q^{18} - q^{19} + 2q^{20} + 2q^{22} - q^{23} - q^{25} - q^{26} + q^{32} + 2q^{36} - q^{37} + q^{38} + q^{40} + 2q^{41} + q^{44} - q^{45} + q^{46} + q^{47} - 2q^{50} + q^{52} - q^{53} - 2q^{55} + 2q^{59} + 2q^{64} + q^{65} + q^{72} + q^{74} + 2q^{76} - q^{80} - q^{81} + q^{82} - q^{88} + 2q^{89} - 2q^{90} + 2q^{92} - q^{94} - q^{95} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\)

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