Properties

Label 155.1.c.b.154.1
Level 155
Weight 1
Character 155.154
Analytic conductor 0.077
Analytic rank 0
Dimension 2
Projective image \(D_{6}\)
CM disc. -31
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 155 = 5 \cdot 31 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 155.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.0773550769581\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Projective image \(D_{6}\)
Projective field Galois closure of 6.2.120125.1

Embedding invariants

Embedding label 154.1
Root \(0.500000 - 0.866025i\)
Character \(\chi\) = 155.154
Dual form 155.1.c.b.154.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205i q^{2} -2.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +1.73205i q^{7} +1.73205i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.73205i q^{2} -2.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +1.73205i q^{7} +1.73205i q^{8} -1.00000 q^{9} +(-1.50000 - 0.866025i) q^{10} +3.00000 q^{14} +1.00000 q^{16} +1.73205i q^{18} +1.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(-0.500000 - 0.866025i) q^{25} -3.46410i q^{28} -1.00000 q^{31} +(1.50000 + 0.866025i) q^{35} +2.00000 q^{36} -1.73205i q^{38} +(1.50000 + 0.866025i) q^{40} -1.00000 q^{41} +(-0.500000 + 0.866025i) q^{45} -2.00000 q^{49} +(-1.50000 + 0.866025i) q^{50} -3.00000 q^{56} -1.00000 q^{59} +1.73205i q^{62} -1.73205i q^{63} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{70} +1.00000 q^{71} -1.73205i q^{72} -2.00000 q^{76} +(0.500000 - 0.866025i) q^{80} +1.00000 q^{81} +1.73205i q^{82} +(1.50000 + 0.866025i) q^{90} +(0.500000 - 0.866025i) q^{95} -1.73205i q^{97} +3.46410i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{4} + q^{5} - 2q^{9} + O(q^{10}) \) \( 2q - 4q^{4} + q^{5} - 2q^{9} - 3q^{10} + 6q^{14} + 2q^{16} + 2q^{19} - 2q^{20} - q^{25} - 2q^{31} + 3q^{35} + 4q^{36} + 3q^{40} - 2q^{41} - q^{45} - 4q^{49} - 3q^{50} - 6q^{56} - 2q^{59} + 2q^{64} + 3q^{70} + 2q^{71} - 4q^{76} + q^{80} + 2q^{81} + 3q^{90} + q^{95} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/155\mathbb{Z}\right)^\times\).

\(n\) \(32\) \(96\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) −2.00000 −2.00000
\(5\) 0.500000 0.866025i 0.500000 0.866025i
\(6\) 0 0
\(7\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 1.73205i 1.73205i
\(9\) −1.00000 −1.00000
\(10\) −1.50000 0.866025i −1.50000 0.866025i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 3.00000 3.00000
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 1.73205i 1.73205i
\(19\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.500000 0.866025i
\(26\) 0 0
\(27\) 0 0
\(28\) 3.46410i 3.46410i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −1.00000 −1.00000
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(36\) 2.00000 2.00000
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 1.73205i 1.73205i
\(39\) 0 0
\(40\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(41\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −2.00000 −2.00000
\(50\) −1.50000 + 0.866025i −1.50000 + 0.866025i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −3.00000 −3.00000
\(57\) 0 0
\(58\) 0 0
\(59\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 1.73205i 1.73205i
\(63\) 1.73205i 1.73205i
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 1.50000 2.59808i 1.50000 2.59808i
\(71\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(72\) 1.73205i 1.73205i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −2.00000 −2.00000
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0.500000 0.866025i 0.500000 0.866025i
\(81\) 1.00000 1.00000
\(82\) 1.73205i 1.73205i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.500000 0.866025i 0.500000 0.866025i
\(96\) 0 0
\(97\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(98\) 3.46410i 3.46410i
\(99\) 0 0
\(100\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(101\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(102\) 0 0
\(103\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(108\) 0 0
\(109\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.73205i 1.73205i
\(113\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.73205i 1.73205i
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 0 0
\(124\) 2.00000 2.00000
\(125\) −1.00000 −1.00000
\(126\) −3.00000 −3.00000
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 1.73205i 1.73205i
\(129\) 0 0
\(130\) 0 0
\(131\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 1.73205i 1.73205i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −3.00000 1.73205i −3.00000 1.73205i
\(141\) 0 0
\(142\) 1.73205i 1.73205i
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 1.73205i 1.73205i
\(153\) 0 0
\(154\) 0 0
\(155\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(156\) 0 0
\(157\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.73205i 1.73205i
\(163\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) 2.00000 2.00000
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) −1.00000 −1.00000
\(172\) 0 0
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 1.50000 0.866025i 1.50000 0.866025i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 1.00000 1.73205i 1.00000 1.73205i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −1.50000 0.866025i −1.50000 0.866025i
\(191\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0 0
\(193\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(194\) −3.00000 −3.00000
\(195\) 0 0
\(196\) 4.00000 4.00000
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.50000 0.866025i 1.50000 0.866025i
\(201\) 0 0
\(202\) 1.73205i 1.73205i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(206\) 3.00000 3.00000
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −3.00000 −3.00000
\(215\) 0 0
\(216\) 0 0
\(217\) 1.73205i 1.73205i
\(218\) 1.73205i 1.73205i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(226\) −3.00000 −3.00000
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 2.00000 2.00000
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.73205i 1.73205i
\(243\) 0 0
\(244\) 0 0
\(245\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(246\) 0 0
\(247\) 0 0
\(248\) 1.73205i 1.73205i
\(249\) 0 0
\(250\) 1.73205i 1.73205i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 3.46410i 3.46410i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −2.00000 −2.00000
\(257\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 3.46410i 3.46410i
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 3.00000 3.00000
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) 1.00000 1.00000
\(280\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(281\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) −2.00000 −2.00000
\(285\) 0 0
\(286\) 0 0
\(287\) 1.73205i 1.73205i
\(288\) 0 0
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(296\) 0 0
\(297\) 0 0
\(298\) 3.46410i 3.46410i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 1.00000 1.00000
\(305\) 0 0
\(306\) 0 0
\(307\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(311\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 3.00000 3.00000
\(315\) −1.50000 0.866025i −1.50000 0.866025i
\(316\) 0 0
\(317\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.500000 0.866025i 0.500000 0.866025i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −2.00000 −2.00000
\(325\) 0 0
\(326\) 3.00000 3.00000
\(327\) 0 0
\(328\) 1.73205i 1.73205i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 1.73205i 1.73205i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 1.73205i 1.73205i
\(343\) 1.73205i 1.73205i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(350\) −1.50000 2.59808i −1.50000 2.59808i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0.500000 0.866025i 0.500000 0.866025i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(360\) −1.50000 0.866025i −1.50000 0.866025i
\(361\) 0 0
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 1.00000 1.00000
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(380\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(381\) 0 0
\(382\) 1.73205i 1.73205i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −3.00000 −3.00000
\(387\) 0 0
\(388\) 3.46410i 3.46410i
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 3.46410i 3.46410i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.500000 0.866025i −0.500000 0.866025i
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −2.00000 −2.00000
\(405\) 0.500000 0.866025i 0.500000 0.866025i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(411\) 0 0
\(412\) 3.46410i 3.46410i
\(413\) 1.73205i 1.73205i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0 0
\(421\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) 1.73205i 1.73205i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 3.46410i 3.46410i
\(429\) 0 0
\(430\) 0 0
\(431\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) −3.00000 −3.00000
\(435\) 0 0
\(436\) −2.00000 −2.00000
\(437\) 0 0
\(438\) 0 0
\(439\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 2.00000 2.00000
\(442\) 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
\(448\) 1.73205i 1.73205i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 1.50000 0.866025i 1.50000 0.866025i
\(451\) 0 0
\(452\) 3.46410i 3.46410i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 3.00000 3.00000
\(467\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.73205i 1.73205i
\(473\) 0 0
\(474\) 0 0
\(475\) −0.500000 0.866025i −0.500000 0.866025i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −2.00000 −2.00000
\(485\) −1.50000 0.866025i −1.50000 0.866025i
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 3.00000 + 1.73205i 3.00000 + 1.73205i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −1.00000 −1.00000
\(497\) 1.73205i 1.73205i
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 2.00000 2.00000
\(501\) 0 0
\(502\) 0 0
\(503\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(504\) 3.00000 3.00000
\(505\) 0.500000 0.866025i 0.500000 0.866025i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.73205i 1.73205i
\(513\) 0 0
\(514\) 3.00000 3.00000
\(515\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 4.00000 4.00000
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −1.00000 −1.00000
\(530\) 0 0
\(531\) 1.00000 1.00000
\(532\) 3.46410i 3.46410i
\(533\) 0 0
\(534\) 0 0
\(535\) −1.50000 0.866025i −1.50000 0.866025i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.500000 0.866025i 0.500000 0.866025i
\(546\) 0 0
\(547\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 1.73205i 1.73205i
\(559\) 0 0
\(560\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(561\) 0 0
\(562\) 1.73205i 1.73205i
\(563\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(564\) 0 0
\(565\) −1.50000 0.866025i −1.50000 0.866025i
\(566\) 0 0
\(567\) 1.73205i 1.73205i
\(568\) 1.73205i 1.73205i
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −3.00000 −3.00000
\(575\) 0 0
\(576\) −1.00000 −1.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 1.73205i 1.73205i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) −1.00000 −1.00000
\(590\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(591\) 0 0
\(592\) 0 0
\(593\) 1.73205i 1.73205i 0.500000 + 0.866025i \(0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −4.00000 −4.00000
\(597\) 0 0
\(598\) 0 0
\(599\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.500000 0.866025i 0.500000 0.866025i
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(614\) −3.00000 −3.00000
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 1.00000 1.73205i 1.00000 1.73205i
\(621\) 0 0
\(622\) 1.73205i 1.73205i
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) 0 0
\(628\) 3.46410i 3.46410i
\(629\) 0 0
\(630\) −1.50000 + 2.59808i −1.50000 + 2.59808i
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 3.00000 3.00000
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −1.00000 −1.00000
\(640\) −1.50000 0.866025i −1.50000 0.866025i
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.73205i 1.73205i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 3.46410i 3.46410i
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(656\) −1.00000 −1.00000
\(657\) 0 0
\(658\) 0 0
\(659\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(660\) 0 0
\(661\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 2.00000 2.00000
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 3.00000 3.00000
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(684\) 2.00000 2.00000
\(685\) 0 0
\(686\) −3.00000 −3.00000
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 3.46410i 3.46410i
\(699\) 0 0
\(700\) −3.00000 + 1.73205i −3.00000 + 1.73205i
\(701\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.73205i 1.73205i
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) −1.50000 0.866025i −1.50000 0.866025i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 1.73205i 1.73205i
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(721\) −3.00000 −3.00000
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(728\) 0 0
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 1.73205i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 1.73205i 1.73205i
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 1.00000 1.73205i 1.00000 1.73205i
\(746\) 3.00000 3.00000
\(747\) 0 0
\(748\) 0 0
\(749\) 3.00000 3.00000
\(750\) 0 0
\(751\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 3.46410i 3.46410i
\(759\) 0 0
\(760\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 1.73205i 1.73205i
\(764\) 2.00000 2.00000
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 3.46410i 3.46410i
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(776\) 3.00000 3.00000
\(777\) 0 0
\(778\) 0 0
\(779\) −1.00000 −1.00000
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −2.00000 −2.00000
\(785\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.00000 3.00000
\(792\) 0 0
\(793\) 0 0
\(794\) −3.00000 −3.00000
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 1.73205i 1.73205i
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) −1.50000 0.866025i −1.50000 0.866025i
\(811\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.50000 + 0.866025i 1.50000 + 0.866025i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 1.00000 1.73205i 1.00000 1.73205i
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0