Properties

Label 1099.1.b.d.1098.1
Level 1099
Weight 1
Character 1099.1098
Analytic conductor 0.548
Analytic rank 0
Dimension 2
Projective image \(S_{4}\)
CM/RM no
Inner twists 2

Related objects

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Newspace parameters

Level: \( N \) \(=\) \( 1099 = 7 \cdot 157 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1099.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.548472448884\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-2}) \)
Defining polynomial: \(x^{2} + 2\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(S_{4}\)
Projective field Galois closure of 4.2.1099.1
Artin image $\GL(2,3)$
Artin field Galois closure of 8.2.1327373299.2

Embedding invariants

Embedding label 1098.1
Root \(1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 1099.1098
Dual form 1099.1.b.d.1098.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} -1.41421i q^{3} -1.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} +1.00000 q^{7} -1.00000 q^{9} +O(q^{10})\) \(q-1.41421i q^{2} -1.41421i q^{3} -1.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} +1.00000 q^{7} -1.00000 q^{9} -1.41421i q^{10} -1.00000 q^{11} +1.41421i q^{12} +1.41421i q^{13} -1.41421i q^{14} -1.41421i q^{15} -1.00000 q^{16} +1.41421i q^{17} +1.41421i q^{18} -1.41421i q^{19} -1.00000 q^{20} -1.41421i q^{21} +1.41421i q^{22} -1.41421i q^{23} +2.00000 q^{26} -1.00000 q^{28} -2.00000 q^{30} +1.41421i q^{31} +1.41421i q^{32} +1.41421i q^{33} +2.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} -1.00000 q^{37} -2.00000 q^{38} +2.00000 q^{39} -2.00000 q^{42} +1.41421i q^{43} +1.00000 q^{44} -1.00000 q^{45} -2.00000 q^{46} +1.41421i q^{48} +1.00000 q^{49} +2.00000 q^{51} -1.41421i q^{52} -1.00000 q^{55} -2.00000 q^{57} +1.00000 q^{59} +1.41421i q^{60} +1.00000 q^{61} +2.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} +1.41421i q^{65} +2.00000 q^{66} +1.00000 q^{67} -1.41421i q^{68} -2.00000 q^{69} -1.41421i q^{70} -1.00000 q^{71} +1.00000 q^{73} +1.41421i q^{74} +1.41421i q^{76} -1.00000 q^{77} -2.82843i q^{78} +1.41421i q^{79} -1.00000 q^{80} -1.00000 q^{81} +1.41421i q^{84} +1.41421i q^{85} +2.00000 q^{86} +1.41421i q^{90} +1.41421i q^{91} +1.41421i q^{92} +2.00000 q^{93} -1.41421i q^{95} +2.00000 q^{96} -1.00000 q^{97} -1.41421i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} + 2q^{5} - 4q^{6} + 2q^{7} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} + 2q^{5} - 4q^{6} + 2q^{7} - 2q^{9} - 2q^{11} - 2q^{16} - 2q^{20} + 4q^{26} - 2q^{28} - 4q^{30} + 4q^{34} + 2q^{35} + 2q^{36} - 2q^{37} - 4q^{38} + 4q^{39} - 4q^{42} + 2q^{44} - 2q^{45} - 4q^{46} + 2q^{49} + 4q^{51} - 2q^{55} - 4q^{57} + 2q^{59} + 2q^{61} + 4q^{62} - 2q^{63} + 2q^{64} + 4q^{66} + 2q^{67} - 4q^{69} - 2q^{71} + 2q^{73} - 2q^{77} - 2q^{80} - 2q^{81} + 4q^{86} + 4q^{93} + 4q^{96} - 2q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1099\mathbb{Z}\right)^\times\).

\(n\) \(162\) \(472\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(3\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(4\) −1.00000 −1.00000
\(5\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(6\) −2.00000 −2.00000
\(7\) 1.00000 1.00000
\(8\) 0 0
\(9\) −1.00000 −1.00000
\(10\) − 1.41421i − 1.41421i
\(11\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 1.41421i 1.41421i
\(13\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(14\) − 1.41421i − 1.41421i
\(15\) − 1.41421i − 1.41421i
\(16\) −1.00000 −1.00000
\(17\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 1.41421i 1.41421i
\(19\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(20\) −1.00000 −1.00000
\(21\) − 1.41421i − 1.41421i
\(22\) 1.41421i 1.41421i
\(23\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.00000 2.00000
\(27\) 0 0
\(28\) −1.00000 −1.00000
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) −2.00000 −2.00000
\(31\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(32\) 1.41421i 1.41421i
\(33\) 1.41421i 1.41421i
\(34\) 2.00000 2.00000
\(35\) 1.00000 1.00000
\(36\) 1.00000 1.00000
\(37\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) −2.00000 −2.00000
\(39\) 2.00000 2.00000
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) −2.00000 −2.00000
\(43\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) 1.00000 1.00000
\(45\) −1.00000 −1.00000
\(46\) −2.00000 −2.00000
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 1.41421i 1.41421i
\(49\) 1.00000 1.00000
\(50\) 0 0
\(51\) 2.00000 2.00000
\(52\) − 1.41421i − 1.41421i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) −1.00000 −1.00000
\(56\) 0 0
\(57\) −2.00000 −2.00000
\(58\) 0 0
\(59\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) 1.41421i 1.41421i
\(61\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 2.00000 2.00000
\(63\) −1.00000 −1.00000
\(64\) 1.00000 1.00000
\(65\) 1.41421i 1.41421i
\(66\) 2.00000 2.00000
\(67\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) − 1.41421i − 1.41421i
\(69\) −2.00000 −2.00000
\(70\) − 1.41421i − 1.41421i
\(71\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(72\) 0 0
\(73\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 1.41421i 1.41421i
\(75\) 0 0
\(76\) 1.41421i 1.41421i
\(77\) −1.00000 −1.00000
\(78\) − 2.82843i − 2.82843i
\(79\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(80\) −1.00000 −1.00000
\(81\) −1.00000 −1.00000
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 1.41421i 1.41421i
\(85\) 1.41421i 1.41421i
\(86\) 2.00000 2.00000
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 1.41421i 1.41421i
\(91\) 1.41421i 1.41421i
\(92\) 1.41421i 1.41421i
\(93\) 2.00000 2.00000
\(94\) 0 0
\(95\) − 1.41421i − 1.41421i
\(96\) 2.00000 2.00000
\(97\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(98\) − 1.41421i − 1.41421i
\(99\) 1.00000 1.00000
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) − 2.82843i − 2.82843i
\(103\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) 0 0
\(105\) − 1.41421i − 1.41421i
\(106\) 0 0
\(107\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(108\) 0 0
\(109\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 1.41421i 1.41421i
\(111\) 1.41421i 1.41421i
\(112\) −1.00000 −1.00000
\(113\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) 2.82843i 2.82843i
\(115\) − 1.41421i − 1.41421i
\(116\) 0 0
\(117\) − 1.41421i − 1.41421i
\(118\) − 1.41421i − 1.41421i
\(119\) 1.41421i 1.41421i
\(120\) 0 0
\(121\) 0 0
\(122\) − 1.41421i − 1.41421i
\(123\) 0 0
\(124\) − 1.41421i − 1.41421i
\(125\) −1.00000 −1.00000
\(126\) 1.41421i 1.41421i
\(127\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) 0 0
\(129\) 2.00000 2.00000
\(130\) 2.00000 2.00000
\(131\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) − 1.41421i − 1.41421i
\(133\) − 1.41421i − 1.41421i
\(134\) − 1.41421i − 1.41421i
\(135\) 0 0
\(136\) 0 0
\(137\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(138\) 2.82843i 2.82843i
\(139\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(140\) −1.00000 −1.00000
\(141\) 0 0
\(142\) 1.41421i 1.41421i
\(143\) − 1.41421i − 1.41421i
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) − 1.41421i − 1.41421i
\(147\) − 1.41421i − 1.41421i
\(148\) 1.00000 1.00000
\(149\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) − 1.41421i − 1.41421i
\(154\) 1.41421i 1.41421i
\(155\) 1.41421i 1.41421i
\(156\) −2.00000 −2.00000
\(157\) −1.00000 −1.00000
\(158\) 2.00000 2.00000
\(159\) 0 0
\(160\) 1.41421i 1.41421i
\(161\) − 1.41421i − 1.41421i
\(162\) 1.41421i 1.41421i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 1.41421i 1.41421i
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) −1.00000 −1.00000
\(170\) 2.00000 2.00000
\(171\) 1.41421i 1.41421i
\(172\) − 1.41421i − 1.41421i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 1.00000
\(177\) − 1.41421i − 1.41421i
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 1.00000 1.00000
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 2.00000 2.00000
\(183\) − 1.41421i − 1.41421i
\(184\) 0 0
\(185\) −1.00000 −1.00000
\(186\) − 2.82843i − 2.82843i
\(187\) − 1.41421i − 1.41421i
\(188\) 0 0
\(189\) 0 0
\(190\) −2.00000 −2.00000
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) − 1.41421i − 1.41421i
\(193\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(194\) 1.41421i 1.41421i
\(195\) 2.00000 2.00000
\(196\) −1.00000 −1.00000
\(197\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(198\) − 1.41421i − 1.41421i
\(199\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(200\) 0 0
\(201\) − 1.41421i − 1.41421i
\(202\) 0 0
\(203\) 0 0
\(204\) −2.00000 −2.00000
\(205\) 0 0
\(206\) 1.41421i 1.41421i
\(207\) 1.41421i 1.41421i
\(208\) − 1.41421i − 1.41421i
\(209\) 1.41421i 1.41421i
\(210\) −2.00000 −2.00000
\(211\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(212\) 0 0
\(213\) 1.41421i 1.41421i
\(214\) −2.00000 −2.00000
\(215\) 1.41421i 1.41421i
\(216\) 0 0
\(217\) 1.41421i 1.41421i
\(218\) − 1.41421i − 1.41421i
\(219\) − 1.41421i − 1.41421i
\(220\) 1.00000 1.00000
\(221\) −2.00000 −2.00000
\(222\) 2.00000 2.00000
\(223\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(224\) 1.41421i 1.41421i
\(225\) 0 0
\(226\) − 1.41421i − 1.41421i
\(227\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) 2.00000 2.00000
\(229\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) −2.00000 −2.00000
\(231\) 1.41421i 1.41421i
\(232\) 0 0
\(233\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(234\) −2.00000 −2.00000
\(235\) 0 0
\(236\) −1.00000 −1.00000
\(237\) 2.00000 2.00000
\(238\) 2.00000 2.00000
\(239\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 1.41421i 1.41421i
\(241\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) 0 0
\(243\) 1.41421i 1.41421i
\(244\) −1.00000 −1.00000
\(245\) 1.00000 1.00000
\(246\) 0 0
\(247\) 2.00000 2.00000
\(248\) 0 0
\(249\) 0 0
\(250\) 1.41421i 1.41421i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 1.00000 1.00000
\(253\) 1.41421i 1.41421i
\(254\) 1.41421i 1.41421i
\(255\) 2.00000 2.00000
\(256\) 1.00000 1.00000
\(257\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(258\) − 2.82843i − 2.82843i
\(259\) −1.00000 −1.00000
\(260\) − 1.41421i − 1.41421i
\(261\) 0 0
\(262\) 1.41421i 1.41421i
\(263\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2.00000 −2.00000
\(267\) 0 0
\(268\) −1.00000 −1.00000
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) − 1.41421i − 1.41421i
\(273\) 2.00000 2.00000
\(274\) −2.00000 −2.00000
\(275\) 0 0
\(276\) 2.00000 2.00000
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) − 1.41421i − 1.41421i
\(279\) − 1.41421i − 1.41421i
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 1.00000 1.00000
\(285\) −2.00000 −2.00000
\(286\) −2.00000 −2.00000
\(287\) 0 0
\(288\) − 1.41421i − 1.41421i
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 1.41421i 1.41421i
\(292\) −1.00000 −1.00000
\(293\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) −2.00000 −2.00000
\(295\) 1.00000 1.00000
\(296\) 0 0
\(297\) 0 0
\(298\) −2.00000 −2.00000
\(299\) 2.00000 2.00000
\(300\) 0 0
\(301\) 1.41421i 1.41421i
\(302\) 0 0
\(303\) 0 0
\(304\) 1.41421i 1.41421i
\(305\) 1.00000 1.00000
\(306\) −2.00000 −2.00000
\(307\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(308\) 1.00000 1.00000
\(309\) 1.41421i 1.41421i
\(310\) 2.00000 2.00000
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 1.41421i 1.41421i
\(315\) −1.00000 −1.00000
\(316\) − 1.41421i − 1.41421i
\(317\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.00000 1.00000
\(321\) −2.00000 −2.00000
\(322\) −2.00000 −2.00000
\(323\) 2.00000 2.00000
\(324\) 1.00000 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) − 1.41421i − 1.41421i
\(328\) 0 0
\(329\) 0 0
\(330\) 2.00000 2.00000
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 1.00000 1.00000
\(334\) 0 0
\(335\) 1.00000 1.00000
\(336\) 1.41421i 1.41421i
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 1.41421i 1.41421i
\(339\) − 1.41421i − 1.41421i
\(340\) − 1.41421i − 1.41421i
\(341\) − 1.41421i − 1.41421i
\(342\) 2.00000 2.00000
\(343\) 1.00000 1.00000
\(344\) 0 0
\(345\) −2.00000 −2.00000
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) − 1.41421i − 1.41421i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) −2.00000 −2.00000
\(355\) −1.00000 −1.00000
\(356\) 0 0
\(357\) 2.00000 2.00000
\(358\) 0 0
\(359\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(360\) 0 0
\(361\) −1.00000 −1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) − 1.41421i − 1.41421i
\(365\) 1.00000 1.00000
\(366\) −2.00000 −2.00000
\(367\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 1.41421i 1.41421i
\(369\) 0 0
\(370\) 1.41421i 1.41421i
\(371\) 0 0
\(372\) −2.00000 −2.00000
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −2.00000 −2.00000
\(375\) 1.41421i 1.41421i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(380\) 1.41421i 1.41421i
\(381\) 1.41421i 1.41421i
\(382\) 0 0
\(383\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(384\) 0 0
\(385\) −1.00000 −1.00000
\(386\) 1.41421i 1.41421i
\(387\) − 1.41421i − 1.41421i
\(388\) 1.00000 1.00000
\(389\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(390\) − 2.82843i − 2.82843i
\(391\) 2.00000 2.00000
\(392\) 0 0
\(393\) 1.41421i 1.41421i
\(394\) 1.41421i 1.41421i
\(395\) 1.41421i 1.41421i
\(396\) −1.00000 −1.00000
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 2.00000 2.00000
\(399\) −2.00000 −2.00000
\(400\) 0 0
\(401\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(402\) −2.00000 −2.00000
\(403\) −2.00000 −2.00000
\(404\) 0 0
\(405\) −1.00000 −1.00000
\(406\) 0 0
\(407\) 1.00000 1.00000
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) −2.00000 −2.00000
\(412\) 1.00000 1.00000
\(413\) 1.00000 1.00000
\(414\) 2.00000 2.00000
\(415\) 0 0
\(416\) −2.00000 −2.00000
\(417\) − 1.41421i − 1.41421i
\(418\) 2.00000 2.00000
\(419\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(420\) 1.41421i 1.41421i
\(421\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(422\) −2.00000 −2.00000
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 2.00000 2.00000
\(427\) 1.00000 1.00000
\(428\) 1.41421i 1.41421i
\(429\) −2.00000 −2.00000
\(430\) 2.00000 2.00000
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 2.00000 2.00000
\(435\) 0 0
\(436\) −1.00000 −1.00000
\(437\) −2.00000 −2.00000
\(438\) −2.00000 −2.00000
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −1.00000 −1.00000
\(442\) 2.82843i 2.82843i
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) − 1.41421i − 1.41421i
\(445\) 0 0
\(446\) 1.41421i 1.41421i
\(447\) −2.00000 −2.00000
\(448\) 1.00000 1.00000
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −1.00000 −1.00000
\(453\) 0 0
\(454\) − 1.41421i − 1.41421i
\(455\) 1.41421i 1.41421i
\(456\) 0 0
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) − 1.41421i − 1.41421i
\(459\) 0 0
\(460\) 1.41421i 1.41421i
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 2.00000 2.00000
\(463\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(464\) 0 0
\(465\) 2.00000 2.00000
\(466\) − 1.41421i − 1.41421i
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 1.41421i 1.41421i
\(469\) 1.00000 1.00000
\(470\) 0 0
\(471\) 1.41421i 1.41421i
\(472\) 0 0
\(473\) − 1.41421i − 1.41421i
\(474\) − 2.82843i − 2.82843i
\(475\) 0 0
\(476\) − 1.41421i − 1.41421i
\(477\) 0 0
\(478\) 1.41421i 1.41421i
\(479\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 2.00000 2.00000
\(481\) − 1.41421i − 1.41421i
\(482\) − 1.41421i − 1.41421i
\(483\) −2.00000 −2.00000
\(484\) 0 0
\(485\) −1.00000 −1.00000
\(486\) 2.00000 2.00000
\(487\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) − 1.41421i − 1.41421i
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) − 2.82843i − 2.82843i
\(495\) 1.00000 1.00000
\(496\) − 1.41421i − 1.41421i
\(497\) −1.00000 −1.00000
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 1.00000 1.00000
\(501\) 0 0
\(502\) 0 0
\(503\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 2.00000 2.00000
\(507\) 1.41421i 1.41421i
\(508\) 1.00000 1.00000
\(509\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(510\) − 2.82843i − 2.82843i
\(511\) 1.00000 1.00000
\(512\) − 1.41421i − 1.41421i
\(513\) 0 0
\(514\) 2.00000 2.00000
\(515\) −1.00000 −1.00000
\(516\) −2.00000 −2.00000
\(517\) 0 0
\(518\) 1.41421i 1.41421i
\(519\) 0 0
\(520\) 0 0
\(521\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(524\) 1.00000 1.00000
\(525\) 0 0
\(526\) − 1.41421i − 1.41421i
\(527\) −2.00000 −2.00000
\(528\) − 1.41421i − 1.41421i
\(529\) −1.00000 −1.00000
\(530\) 0 0
\(531\) −1.00000 −1.00000
\(532\) 1.41421i 1.41421i
\(533\) 0 0
\(534\) 0 0
\(535\) − 1.41421i − 1.41421i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.00000 −1.00000
\(540\) 0 0
\(541\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(542\) 1.41421i 1.41421i
\(543\) 0 0
\(544\) −2.00000 −2.00000
\(545\) 1.00000 1.00000
\(546\) − 2.82843i − 2.82843i
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 1.41421i 1.41421i
\(549\) −1.00000 −1.00000
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1.41421i 1.41421i
\(554\) 0 0
\(555\) 1.41421i 1.41421i
\(556\) −1.00000 −1.00000
\(557\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(558\) −2.00000 −2.00000
\(559\) −2.00000 −2.00000
\(560\) −1.00000 −1.00000
\(561\) −2.00000 −2.00000
\(562\) 0 0
\(563\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 1.00000 1.00000
\(566\) 0 0
\(567\) −1.00000 −1.00000
\(568\) 0 0
\(569\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(570\) 2.82843i 2.82843i
\(571\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(572\) 1.41421i 1.41421i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −1.00000 −1.00000
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 1.41421i 1.41421i
\(579\) 1.41421i 1.41421i
\(580\) 0 0
\(581\) 0 0
\(582\) 2.00000 2.00000
\(583\) 0 0
\(584\) 0 0
\(585\) − 1.41421i − 1.41421i
\(586\) 1.41421i 1.41421i
\(587\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(588\) 1.41421i 1.41421i
\(589\) 2.00000 2.00000
\(590\) − 1.41421i − 1.41421i
\(591\) 1.41421i 1.41421i
\(592\) 1.00000 1.00000
\(593\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(594\) 0 0
\(595\) 1.41421i 1.41421i
\(596\) 1.41421i 1.41421i
\(597\) 2.00000 2.00000
\(598\) − 2.82843i − 2.82843i
\(599\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 2.00000 2.00000
\(603\) −1.00000 −1.00000
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) 2.00000 2.00000
\(609\) 0 0
\(610\) − 1.41421i − 1.41421i
\(611\) 0 0
\(612\) 1.41421i 1.41421i
\(613\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(614\) 1.41421i 1.41421i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(618\) 2.00000 2.00000
\(619\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(620\) − 1.41421i − 1.41421i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −2.00000 −2.00000
\(625\) −1.00000 −1.00000
\(626\) 0 0
\(627\) 2.00000 2.00000
\(628\) 1.00000 1.00000
\(629\) − 1.41421i − 1.41421i
\(630\) 1.41421i 1.41421i
\(631\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(632\) 0 0
\(633\) −2.00000 −2.00000
\(634\) 2.82843i 2.82843i
\(635\) −1.00000 −1.00000
\(636\) 0 0
\(637\) 1.41421i 1.41421i
\(638\) 0 0
\(639\) 1.00000 1.00000
\(640\) 0 0
\(641\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 2.82843i 2.82843i
\(643\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(644\) 1.41421i 1.41421i
\(645\) 2.00000 2.00000
\(646\) − 2.82843i − 2.82843i
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0 0
\(649\) −1.00000 −1.00000
\(650\) 0 0
\(651\) 2.00000 2.00000
\(652\) 0 0
\(653\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) −2.00000 −2.00000
\(655\) −1.00000 −1.00000
\(656\) 0 0
\(657\) −1.00000 −1.00000
\(658\) 0 0
\(659\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(660\) − 1.41421i − 1.41421i
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 2.82843i 2.82843i
\(664\) 0 0
\(665\) − 1.41421i − 1.41421i
\(666\) − 1.41421i − 1.41421i
\(667\) 0 0
\(668\) 0 0
\(669\) 1.41421i 1.41421i
\(670\) − 1.41421i − 1.41421i
\(671\) −1.00000 −1.00000
\(672\) 2.00000 2.00000
\(673\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 1.00000 1.00000
\(677\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(678\) −2.00000 −2.00000
\(679\) −1.00000 −1.00000
\(680\) 0 0
\(681\) − 1.41421i − 1.41421i
\(682\) −2.00000 −2.00000
\(683\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(684\) − 1.41421i − 1.41421i
\(685\) − 1.41421i − 1.41421i
\(686\) − 1.41421i − 1.41421i
\(687\) − 1.41421i − 1.41421i
\(688\) − 1.41421i − 1.41421i
\(689\) 0 0
\(690\) 2.82843i 2.82843i
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) 1.00000 1.00000
\(694\) 0 0
\(695\) 1.00000 1.00000
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) − 1.41421i − 1.41421i
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 1.41421i 1.41421i
\(704\) −1.00000 −1.00000
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 1.41421i 1.41421i
\(709\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 1.41421i 1.41421i
\(711\) − 1.41421i − 1.41421i
\(712\) 0 0
\(713\) 2.00000 2.00000
\(714\) − 2.82843i − 2.82843i
\(715\) − 1.41421i − 1.41421i
\(716\) 0 0
\(717\) 1.41421i 1.41421i
\(718\) 2.00000 2.00000
\(719\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(720\) 1.00000 1.00000
\(721\) −1.00000 −1.00000
\(722\) 1.41421i 1.41421i
\(723\) − 1.41421i − 1.41421i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(728\) 0 0
\(729\) 1.00000 1.00000
\(730\) − 1.41421i − 1.41421i
\(731\) −2.00000 −2.00000
\(732\) 1.41421i 1.41421i
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 1.41421i 1.41421i
\(735\) − 1.41421i − 1.41421i
\(736\) 2.00000 2.00000
\(737\) −1.00000 −1.00000
\(738\) 0 0
\(739\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 1.00000 1.00000
\(741\) − 2.82843i − 2.82843i
\(742\) 0 0
\(743\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0 0
\(745\) − 1.41421i − 1.41421i
\(746\) 0 0
\(747\) 0 0
\(748\) 1.41421i 1.41421i
\(749\) − 1.41421i − 1.41421i
\(750\) 2.00000 2.00000
\(751\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −2.00000 −2.00000
\(759\) 2.00000 2.00000
\(760\) 0 0
\(761\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(762\) 2.00000 2.00000
\(763\) 1.00000 1.00000
\(764\) 0 0
\(765\) − 1.41421i − 1.41421i
\(766\) − 1.41421i − 1.41421i
\(767\) 1.41421i 1.41421i
\(768\) − 1.41421i − 1.41421i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 1.41421i 1.41421i
\(771\) 2.00000 2.00000
\(772\) 1.00000 1.00000
\(773\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(774\) −2.00000 −2.00000
\(775\) 0 0
\(776\) 0 0
\(777\) 1.41421i 1.41421i
\(778\) − 1.41421i − 1.41421i
\(779\) 0 0
\(780\) −2.00000 −2.00000
\(781\) 1.00000 1.00000
\(782\) − 2.82843i − 2.82843i
\(783\) 0 0
\(784\) −1.00000 −1.00000
\(785\) −1.00000 −1.00000
\(786\) 2.00000 2.00000
\(787\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(788\) 1.00000 1.00000
\(789\) − 1.41421i − 1.41421i
\(790\) 2.00000 2.00000
\(791\) 1.00000 1.00000
\(792\) 0 0
\(793\) 1.41421i 1.41421i
\(794\) 0 0
\(795\) 0 0
\(796\) − 1.41421i − 1.41421i
\(797\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(798\) 2.82843i 2.82843i
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 2.00000 2.00000
\(803\) −1.00000 −1.00000
\(804\) 1.41421i 1.41421i
\(805\) − 1.41421i − 1.41421i
\(806\) 2.82843i 2.82843i
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 1.41421i 1.41421i
\(811\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(812\) 0 0
\(813\) 1.41421i 1.41421i
\(814\) − 1.41421i − 1.41421i
\(815\) 0 0
\(816\) −2.00000 −2.00000
\(817\) 2.00000 2.00000
\(818\) 0 0
\(819\) − 1.41421i − 1.41421i
\(820\) 0 0
\(821\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(822\) 2.82843i 2.82843i
\(823\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) − 1.41421i − 1.41421i
\(827\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(828\) − 1.41421i − 1.41421i
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.41421i 1.41421i
\(833\) 1.41421i 1.41421i
\(834\) −2.00000 −2.00000
\(835\) 0 0
\(836\) − 1.41421i − 1.41421i
\(837\) 0 0
\(838\) −2.00000 −2.00000
\(839\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 2.00000 2.00000
\(843\) 0 0
\(844\) 1.41421i 1.41421i
\(845\) −1.00000 −1.00000
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.41421i 1.41421i
\(852\) − 1.41421i − 1.41421i
\(853\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(854\) − 1.41421i − 1.41421i
\(855\) 1.41421i 1.41421i
\(856\) 0 0
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 2.82843i 2.82843i
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) − 1.41421i − 1.41421i
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1.41421i 1.41421i
\(868\) − 1.41421i − 1.41421i
\(869\) − 1.41421i − 1.41421i
\(870\) 0 0
\(871\) 1.41421i 1.41421i
\(872\) 0 0
\(873\) 1.00000 1.00000
\(874\) 2.82843i 2.82843i
\(875\) −1.00000 −1.00000
\(876\) 1.41421i 1.41421i
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 1.41421i 1.41421i
\(880\) 1.00000 1.00000
\(881\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(882\) 1.41421i 1.41421i
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 2.00000 2.00000
\(885\) − 1.41421i − 1.41421i
\(886\) 0 0
\(887\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(888\) 0 0
\(889\) −1.00000 −1.00000
\(890\) 0 0
\(891\) 1.00000 1.00000
\(892\) 1.00000 1.00000
\(893\) 0 0
\(894\) 2.82843i 2.82843i
\(895\) 0 0
\(896\) 0 0
\(897\) − 2.82843i − 2.82843i
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 2.00000 2.00000
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(908\) −1.00000 −1.00000
\(909\) 0 0
\(910\) 2.00000 2.00000
\(911\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(912\) 2.00000 2.00000
\(913\) 0 0
\(914\) 0 0
\(915\) − 1.41421i − 1.41421i
\(916\) −1.00000 −1.00000
\(917\) −1.00000 −1.00000
\(918\) 0 0
\(919\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(920\) 0 0
\(921\) 1.41421i 1.41421i
\(922\) 0 0
\(923\) − 1.41421i − 1.41421i
\(924\) − 1.41421i − 1.41421i
\(925\) 0 0
\(926\) −2.00000 −2.00000
\(927\) 1.00000 1.00000
\(928\) 0 0
\(929\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(930\) − 2.82843i − 2.82843i
\(931\) − 1.41421i − 1.41421i
\(932\) −1.00000 −1.00000
\(933\) 0 0
\(934\) 0 0
\(935\) − 1.41421i − 1.41421i
\(936\) 0 0
\(937\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(938\) − 1.41421i − 1.41421i
\(939\) 0 0
\(940\) 0 0
\(941\) − 1.41421i − 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(942\) 2.00000 2.00000
\(943\) 0 0
\(944\) −1.00000 −1.00000
\(945\) 0 0
\(946\) −2.00000 −2.00000
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) −2.00000 −2.00000
\(949\) 1.41421i 1.41421i
\(950\) 0 0
\(951\) 2.82843i 2.82843i
\(952\) 0 0
\(953\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 1.00000 1.00000
\(957\) 0 0
\(958\) − 1.41421i − 1.41421i
\(959\) − 1.41421i − 1.41421i
\(960\) − 1.41421i − 1.41421i
\(961\) −1.00000 −1.00000
\(962\) −2.00000 −2.00000
\(963\) 1.41421i 1.41421i
\(964\) −1.00000 −1.00000
\(965\) −1.00000 −1.00000
\(966\) 2.82843i 2.82843i
\(967\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(968\) 0 0
\(969\) − 2.82843i − 2.82843i
\(970\) 1.41421i 1.41421i
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) − 1.41421i − 1.41421i
\(973\) 1.00000 1.00000
\(974\) 1.41421i 1.41421i
\(975\) 0 0
\(976\) −1.00000 −1.00000
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −1.00000 −1.00000
\(981\) −1.00000 −1.00000
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) −1.00000 −1.00000
\(986\) 0 0
\(987\) 0 0
\(988\) −2.00000 −2.00000
\(989\) 2.00000 2.00000
\(990\) − 1.41421i − 1.41421i
\(991\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(992\) −2.00000 −2.00000
\(993\) 0 0
\(994\) 1.41421i 1.41421i
\(995\) 1.41421i 1.41421i
\(996\) 0 0
\(997\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1099.1.b.d.1098.1 yes 2
7.6 odd 2 1099.1.b.c.1098.1 2
157.156 even 2 1099.1.b.c.1098.2 yes 2
1099.1098 odd 2 inner 1099.1.b.d.1098.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1099.1.b.c.1098.1 2 7.6 odd 2
1099.1.b.c.1098.2 yes 2 157.156 even 2
1099.1.b.d.1098.1 yes 2 1.1 even 1 trivial
1099.1.b.d.1098.2 yes 2 1099.1098 odd 2 inner