Properties

Label 287.1.d.a.286.3
Level $287$
Weight $1$
Character 287.286
Self dual yes
Analytic conductor $0.143$
Analytic rank $0$
Dimension $3$
Projective image $D_{7}$
CM discriminant -287
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 287.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.143231658626\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Defining polynomial: \(x^{3} - x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{7}\)
Projective field Galois closure of 7.1.23639903.1
Artin image $D_7$
Artin field Galois closure of 7.1.23639903.1

Embedding invariants

Embedding label 286.3
Root \(0.445042\) of defining polynomial
Character \(\chi\) \(=\) 287.286

$q$-expansion

\(f(q)\) \(=\) \(q+1.24698 q^{2} -0.445042 q^{3} +0.554958 q^{4} -0.554958 q^{6} +1.00000 q^{7} -0.554958 q^{8} -0.801938 q^{9} +O(q^{10})\) \(q+1.24698 q^{2} -0.445042 q^{3} +0.554958 q^{4} -0.554958 q^{6} +1.00000 q^{7} -0.554958 q^{8} -0.801938 q^{9} -0.246980 q^{12} +1.24698 q^{13} +1.24698 q^{14} -1.24698 q^{16} -1.80194 q^{17} -1.00000 q^{18} -1.80194 q^{19} -0.445042 q^{21} -0.445042 q^{23} +0.246980 q^{24} +1.00000 q^{25} +1.55496 q^{26} +0.801938 q^{27} +0.554958 q^{28} -1.00000 q^{32} -2.24698 q^{34} -0.445042 q^{36} +1.24698 q^{37} -2.24698 q^{38} -0.554958 q^{39} +1.00000 q^{41} -0.554958 q^{42} -1.80194 q^{43} -0.554958 q^{46} +1.24698 q^{47} +0.554958 q^{48} +1.00000 q^{49} +1.24698 q^{50} +0.801938 q^{51} +0.692021 q^{52} +1.00000 q^{54} -0.554958 q^{56} +0.801938 q^{57} -0.801938 q^{63} -1.00000 q^{68} +0.198062 q^{69} +0.445042 q^{72} +1.55496 q^{74} -0.445042 q^{75} -1.00000 q^{76} -0.692021 q^{78} +0.445042 q^{81} +1.24698 q^{82} -0.246980 q^{84} -2.24698 q^{86} +1.24698 q^{89} +1.24698 q^{91} -0.246980 q^{92} +1.55496 q^{94} +0.445042 q^{96} -0.445042 q^{97} +1.24698 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - q^{2} - q^{3} + 2q^{4} - 2q^{6} + 3q^{7} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 3q - q^{2} - q^{3} + 2q^{4} - 2q^{6} + 3q^{7} - 2q^{8} + 2q^{9} + 4q^{12} - q^{13} - q^{14} + q^{16} - q^{17} - 3q^{18} - q^{19} - q^{21} - q^{23} - 4q^{24} + 3q^{25} + 5q^{26} - 2q^{27} + 2q^{28} - 3q^{32} - 2q^{34} - q^{36} - q^{37} - 2q^{38} - 2q^{39} + 3q^{41} - 2q^{42} - q^{43} - 2q^{46} - q^{47} + 2q^{48} + 3q^{49} - q^{50} - 2q^{51} - 3q^{52} + 3q^{54} - 2q^{56} - 2q^{57} + 2q^{63} - 3q^{68} + 5q^{69} + q^{72} + 5q^{74} - q^{75} - 3q^{76} + 3q^{78} + q^{81} - q^{82} + 4q^{84} - 2q^{86} - q^{89} - q^{91} + 4q^{92} + 5q^{94} + q^{96} - q^{97} - q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(3\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(4\) 0.554958 0.554958
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) −0.554958 −0.554958
\(7\) 1.00000 1.00000
\(8\) −0.554958 −0.554958
\(9\) −0.801938 −0.801938
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) −0.246980 −0.246980
\(13\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(14\) 1.24698 1.24698
\(15\) 0 0
\(16\) −1.24698 −1.24698
\(17\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(18\) −1.00000 −1.00000
\(19\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(20\) 0 0
\(21\) −0.445042 −0.445042
\(22\) 0 0
\(23\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(24\) 0.246980 0.246980
\(25\) 1.00000 1.00000
\(26\) 1.55496 1.55496
\(27\) 0.801938 0.801938
\(28\) 0.554958 0.554958
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) −2.24698 −2.24698
\(35\) 0 0
\(36\) −0.445042 −0.445042
\(37\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(38\) −2.24698 −2.24698
\(39\) −0.554958 −0.554958
\(40\) 0 0
\(41\) 1.00000 1.00000
\(42\) −0.554958 −0.554958
\(43\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.554958 −0.554958
\(47\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(48\) 0.554958 0.554958
\(49\) 1.00000 1.00000
\(50\) 1.24698 1.24698
\(51\) 0.801938 0.801938
\(52\) 0.692021 0.692021
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 1.00000 1.00000
\(55\) 0 0
\(56\) −0.554958 −0.554958
\(57\) 0.801938 0.801938
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) −0.801938 −0.801938
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −1.00000 −1.00000
\(69\) 0.198062 0.198062
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0.445042 0.445042
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 1.55496 1.55496
\(75\) −0.445042 −0.445042
\(76\) −1.00000 −1.00000
\(77\) 0 0
\(78\) −0.692021 −0.692021
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 0.445042 0.445042
\(82\) 1.24698 1.24698
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −0.246980 −0.246980
\(85\) 0 0
\(86\) −2.24698 −2.24698
\(87\) 0 0
\(88\) 0 0
\(89\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(90\) 0 0
\(91\) 1.24698 1.24698
\(92\) −0.246980 −0.246980
\(93\) 0 0
\(94\) 1.55496 1.55496
\(95\) 0 0
\(96\) 0.445042 0.445042
\(97\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(98\) 1.24698 1.24698
\(99\) 0 0
\(100\) 0.554958 0.554958
\(101\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(102\) 1.00000 1.00000
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −0.692021 −0.692021
\(105\) 0 0
\(106\) 0 0
\(107\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(108\) 0.445042 0.445042
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −0.554958 −0.554958
\(112\) −1.24698 −1.24698
\(113\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(114\) 1.00000 1.00000
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −1.00000
\(118\) 0 0
\(119\) −1.80194 −1.80194
\(120\) 0 0
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) −0.445042 −0.445042
\(124\) 0 0
\(125\) 0 0
\(126\) −1.00000 −1.00000
\(127\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(128\) 1.00000 1.00000
\(129\) 0.801938 0.801938
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −1.80194 −1.80194
\(134\) 0 0
\(135\) 0 0
\(136\) 1.00000 1.00000
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0.246980 0.246980
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) −0.554958 −0.554958
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) −0.445042 −0.445042
\(148\) 0.692021 0.692021
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −0.554958 −0.554958
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 1.00000 1.00000
\(153\) 1.44504 1.44504
\(154\) 0 0
\(155\) 0 0
\(156\) −0.307979 −0.307979
\(157\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.445042 −0.445042
\(162\) 0.554958 0.554958
\(163\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(164\) 0.554958 0.554958
\(165\) 0 0
\(166\) 0 0
\(167\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(168\) 0.246980 0.246980
\(169\) 0.554958 0.554958
\(170\) 0 0
\(171\) 1.44504 1.44504
\(172\) −1.00000 −1.00000
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 1.00000 1.00000
\(176\) 0 0
\(177\) 0 0
\(178\) 1.55496 1.55496
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(182\) 1.55496 1.55496
\(183\) 0 0
\(184\) 0.246980 0.246980
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0.692021 0.692021
\(189\) 0.801938 0.801938
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) −0.554958 −0.554958
\(195\) 0 0
\(196\) 0.554958 0.554958
\(197\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(198\) 0 0
\(199\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(200\) −0.554958 −0.554958
\(201\) 0 0
\(202\) −0.554958 −0.554958
\(203\) 0 0
\(204\) 0.445042 0.445042
\(205\) 0 0
\(206\) 0 0
\(207\) 0.356896 0.356896
\(208\) −1.55496 −1.55496
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −2.24698 −2.24698
\(215\) 0 0
\(216\) −0.445042 −0.445042
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.24698 −2.24698
\(222\) −0.692021 −0.692021
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) −1.00000 −1.00000
\(225\) −0.801938 −0.801938
\(226\) −0.554958 −0.554958
\(227\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(228\) 0.445042 0.445042
\(229\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) −1.24698 −1.24698
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) −2.24698 −2.24698
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.24698 1.24698
\(243\) −1.00000 −1.00000
\(244\) 0 0
\(245\) 0 0
\(246\) −0.554958 −0.554958
\(247\) −2.24698 −2.24698
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −0.445042 −0.445042
\(253\) 0 0
\(254\) 1.55496 1.55496
\(255\) 0 0
\(256\) 1.24698 1.24698
\(257\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(258\) 1.00000 1.00000
\(259\) 1.24698 1.24698
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2.24698 −2.24698
\(267\) −0.554958 −0.554958
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 2.24698 2.24698
\(273\) −0.554958 −0.554958
\(274\) 0 0
\(275\) 0 0
\(276\) 0.109916 0.109916
\(277\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −0.692021 −0.692021
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.00000 1.00000
\(288\) 0.801938 0.801938
\(289\) 2.24698 2.24698
\(290\) 0 0
\(291\) 0.198062 0.198062
\(292\) 0 0
\(293\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(294\) −0.554958 −0.554958
\(295\) 0 0
\(296\) −0.692021 −0.692021
\(297\) 0 0
\(298\) 0 0
\(299\) −0.554958 −0.554958
\(300\) −0.246980 −0.246980
\(301\) −1.80194 −1.80194
\(302\) 0 0
\(303\) 0.198062 0.198062
\(304\) 2.24698 2.24698
\(305\) 0 0
\(306\) 1.80194 1.80194
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(312\) 0.307979 0.307979
\(313\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(314\) −2.24698 −2.24698
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0.801938 0.801938
\(322\) −0.554958 −0.554958
\(323\) 3.24698 3.24698
\(324\) 0.246980 0.246980
\(325\) 1.24698 1.24698
\(326\) −0.554958 −0.554958
\(327\) 0 0
\(328\) −0.554958 −0.554958
\(329\) 1.24698 1.24698
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −1.00000 −1.00000
\(334\) −2.24698 −2.24698
\(335\) 0 0
\(336\) 0.554958 0.554958
\(337\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(338\) 0.692021 0.692021
\(339\) 0.198062 0.198062
\(340\) 0 0
\(341\) 0 0
\(342\) 1.80194 1.80194
\(343\) 1.00000 1.00000
\(344\) 1.00000 1.00000
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 1.24698 1.24698
\(351\) 1.00000 1.00000
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.692021 0.692021
\(357\) 0.801938 0.801938
\(358\) 0 0
\(359\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(360\) 0 0
\(361\) 2.24698 2.24698
\(362\) −0.554958 −0.554958
\(363\) −0.445042 −0.445042
\(364\) 0.692021 0.692021
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0.554958 0.554958
\(369\) −0.801938 −0.801938
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −0.692021 −0.692021
\(377\) 0 0
\(378\) 1.00000 1.00000
\(379\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(380\) 0 0
\(381\) −0.554958 −0.554958
\(382\) 0 0
\(383\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(384\) −0.445042 −0.445042
\(385\) 0 0
\(386\) 0 0
\(387\) 1.44504 1.44504
\(388\) −0.246980 −0.246980
\(389\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(390\) 0 0
\(391\) 0.801938 0.801938
\(392\) −0.554958 −0.554958
\(393\) 0 0
\(394\) −2.24698 −2.24698
\(395\) 0 0
\(396\) 0 0
\(397\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(398\) 1.55496 1.55496
\(399\) 0.801938 0.801938
\(400\) −1.24698 −1.24698
\(401\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.246980 −0.246980
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.445042 −0.445042
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.445042 0.445042
\(415\) 0 0
\(416\) −1.24698 −1.24698
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) −1.00000 −1.00000
\(424\) 0 0
\(425\) −1.80194 −1.80194
\(426\) 0 0
\(427\) 0 0
\(428\) −1.00000 −1.00000
\(429\) 0 0
\(430\) 0 0
\(431\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(432\) −1.00000 −1.00000
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.801938 0.801938
\(438\) 0 0
\(439\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(440\) 0 0
\(441\) −0.801938 −0.801938
\(442\) −2.80194 −2.80194
\(443\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(444\) −0.307979 −0.307979
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(450\) −1.00000 −1.00000
\(451\) 0 0
\(452\) −0.246980 −0.246980
\(453\) 0 0
\(454\) 2.49396 2.49396
\(455\) 0 0
\(456\) −0.445042 −0.445042
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −0.554958 −0.554958
\(459\) −1.44504 −1.44504
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −0.554958 −0.554958
\(469\) 0 0
\(470\) 0 0
\(471\) 0.801938 0.801938
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.80194 −1.80194
\(476\) −1.00000 −1.00000
\(477\) 0 0
\(478\) 0 0
\(479\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(480\) 0 0
\(481\) 1.55496 1.55496
\(482\) 0 0
\(483\) 0.198062 0.198062
\(484\) 0.554958 0.554958
\(485\) 0 0
\(486\) −1.24698 −1.24698
\(487\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(488\) 0 0
\(489\) 0.198062 0.198062
\(490\) 0 0
\(491\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(492\) −0.246980 −0.246980
\(493\) 0 0
\(494\) −2.80194 −2.80194
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0.801938 0.801938
\(502\) 0 0
\(503\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(504\) 0.445042 0.445042
\(505\) 0 0
\(506\) 0 0
\(507\) −0.246980 −0.246980
\(508\) 0.692021 0.692021
\(509\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.554958 0.554958
\(513\) −1.44504 −1.44504
\(514\) −0.554958 −0.554958
\(515\) 0 0
\(516\) 0.445042 0.445042
\(517\) 0 0
\(518\) 1.55496 1.55496
\(519\) 0 0
\(520\) 0 0
\(521\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) −0.445042 −0.445042
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.801938 −0.801938
\(530\) 0 0
\(531\) 0 0
\(532\) −1.00000 −1.00000
\(533\) 1.24698 1.24698
\(534\) −0.692021 −0.692021
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(542\) 0 0
\(543\) 0.198062 0.198062
\(544\) 1.80194 1.80194
\(545\) 0 0
\(546\) −0.692021 −0.692021
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) −0.109916 −0.109916
\(553\) 0 0
\(554\) −0.554958 −0.554958
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) −2.24698 −2.24698
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(564\) −0.307979 −0.307979
\(565\) 0 0
\(566\) 0 0
\(567\) 0.445042 0.445042
\(568\) 0 0
\(569\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 1.24698 1.24698
\(575\) −0.445042 −0.445042
\(576\) 0 0
\(577\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(578\) 2.80194 2.80194
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0.246980 0.246980
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 2.49396 2.49396
\(587\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(588\) −0.246980 −0.246980
\(589\) 0 0
\(590\) 0 0
\(591\) 0.801938 0.801938
\(592\) −1.55496 −1.55496
\(593\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.554958 −0.554958
\(598\) −0.692021 −0.692021
\(599\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(600\) 0.246980 0.246980
\(601\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(602\) −2.24698 −2.24698
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0.246980 0.246980
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 1.80194 1.80194
\(609\) 0 0
\(610\) 0 0
\(611\) 1.55496 1.55496
\(612\) 0.801938 0.801938
\(613\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) −0.356896 −0.356896
\(622\) −2.24698 −2.24698
\(623\) 1.24698 1.24698
\(624\) 0.692021 0.692021
\(625\) 1.00000 1.00000
\(626\) −2.24698 −2.24698
\(627\) 0 0
\(628\) −1.00000 −1.00000
\(629\) −2.24698 −2.24698
\(630\) 0 0
\(631\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.24698 1.24698
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 1.00000 1.00000
\(643\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(644\) −0.246980 −0.246980
\(645\) 0 0
\(646\) 4.04892 4.04892
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) −0.246980 −0.246980
\(649\) 0 0
\(650\) 1.55496 1.55496
\(651\) 0 0
\(652\) −0.246980 −0.246980
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.24698 −1.24698
\(657\) 0 0
\(658\) 1.55496 1.55496
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 1.00000 1.00000
\(664\) 0 0
\(665\) 0 0
\(666\) −1.24698 −1.24698
\(667\) 0 0
\(668\) −1.00000 −1.00000
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0.445042 0.445042
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) −0.554958 −0.554958
\(675\) 0.801938 0.801938
\(676\) 0.307979 0.307979
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0.246980 0.246980
\(679\) −0.445042 −0.445042
\(680\) 0 0
\(681\) −0.890084 −0.890084
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0.801938 0.801938
\(685\) 0 0
\(686\) 1.24698 1.24698
\(687\) 0.198062 0.198062
\(688\) 2.24698 2.24698
\(689\) 0 0
\(690\) 0 0
\(691\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −1.80194 −1.80194
\(698\) 0 0
\(699\) 0 0
\(700\) 0.554958 0.554958
\(701\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(702\) 1.24698 1.24698
\(703\) −2.24698 −2.24698
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.445042 −0.445042
\(708\) 0 0
\(709\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.692021 −0.692021
\(713\) 0 0
\(714\) 1.00000 1.00000
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 1.55496 1.55496
\(719\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.80194 2.80194
\(723\) 0 0
\(724\) −0.246980 −0.246980
\(725\) 0 0
\(726\) −0.554958 −0.554958
\(727\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(728\) −0.692021 −0.692021
\(729\) 0 0
\(730\) 0 0
\(731\) 3.24698 3.24698
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.445042 0.445042
\(737\) 0 0
\(738\) −1.00000 −1.00000
\(739\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(740\) 0 0
\(741\) 1.00000 1.00000
\(742\) 0 0
\(743\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −2.24698 −2.24698
\(747\) 0 0
\(748\) 0 0
\(749\) −1.80194 −1.80194
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) −1.55496 −1.55496
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0.445042 0.445042
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −0.554958 −0.554958
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) −0.692021 −0.692021
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −0.554958 −0.554958
\(767\) 0 0
\(768\) −0.554958 −0.554958
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0.198062 0.198062
\(772\) 0 0
\(773\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(774\) 1.80194 1.80194
\(775\) 0 0
\(776\) 0.246980 0.246980
\(777\) −0.554958 −0.554958
\(778\) 1.55496 1.55496
\(779\) −1.80194 −1.80194
\(780\) 0 0
\(781\) 0 0
\(782\) 1.00000 1.00000
\(783\) 0 0
\(784\) −1.24698 −1.24698
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) −1.00000 −1.00000
\(789\) 0 0
\(790\) 0 0
\(791\) −0.445042 −0.445042
\(792\) 0 0
\(793\) 0 0
\(794\) 2.49396 2.49396
\(795\) 0 0
\(796\) 0.692021 0.692021
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 1.00000 1.00000
\(799\) −2.24698 −2.24698
\(800\) −1.00000 −1.00000
\(801\) −1.00000 −1.00000
\(802\) 1.55496 1.55496
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0.246980 0.246980
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) −1.00000 −1.00000
\(817\) 3.24698 3.24698
\(818\) 0 0
\(819\) −1.00000 −1.00000
\(820\) 0 0
\(821\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0.198062 0.198062
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0.198062 0.198062
\(832\) 0 0
\(833\) −1.80194 −1.80194
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(840\) 0 0
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) −1.24698 −1.24698
\(847\) 1.00000 1.00000
\(848\) 0 0
\(849\) 0 0
\(850\) −2.24698 −2.24698
\(851\) −0.554958 −0.554958
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1.00000 1.00000
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0 0
\(861\) −0.445042 −0.445042
\(862\) 2.49396 2.49396
\(863\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(864\) −0.801938 −0.801938
\(865\) 0 0
\(866\) 0 0
\(867\) −1.00000 −1.00000
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0.356896 0.356896
\(874\) 1.00000 1.00000
\(875\) 0 0
\(876\) 0 0
\(877\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(878\) −0.554958 −0.554958
\(879\) −0.890084 −0.890084
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −1.00000 −1.00000
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) −1.24698 −1.24698
\(885\) 0 0
\(886\) 1.55496 1.55496
\(887\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(888\) 0.307979 0.307979
\(889\) 1.24698 1.24698
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2.24698 −2.24698
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 1.00000
\(897\) 0.246980 0.246980
\(898\) −0.554958 −0.554958
\(899\) 0 0
\(900\) −0.445042 −0.445042
\(901\) 0 0
\(902\) 0 0
\(903\) 0.801938 0.801938
\(904\) 0.246980 0.246980
\(905\) 0 0
\(906\) 0 0
\(907\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(908\) 1.10992 1.10992
\(909\) 0.356896 0.356896
\(910\) 0 0
\(911\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(912\) −1.00000 −1.00000
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.246980 −0.246980
\(917\) 0 0
\(918\) −1.80194 −1.80194
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.24698 1.24698
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(930\) 0 0
\(931\) −1.80194 −1.80194
\(932\) 0 0
\(933\) 0.801938 0.801938
\(934\) 0 0
\(935\) 0 0
\(936\) 0.554958 0.554958
\(937\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(938\) 0 0
\(939\) 0.801938 0.801938
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 1.00000 1.00000
\(943\) −0.445042 −0.445042
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −2.24698 −2.24698
\(951\) 0 0
\(952\) 1.00000 1.00000
\(953\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −0.554958 −0.554958
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 1.93900 1.93900
\(963\) 1.44504 1.44504
\(964\) 0 0
\(965\) 0 0
\(966\) 0.246980 0.246980
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −0.554958 −0.554958
\(969\) −1.44504 −1.44504
\(970\) 0 0
\(971\) −1.80194 −1.80194 −0.900969 0.433884i \(-0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(972\) −0.554958 −0.554958
\(973\) 0 0
\(974\) −2.24698 −2.24698
\(975\) −0.554958 −0.554958
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0.246980 0.246980
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) −0.554958 −0.554958
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0.246980 0.246980
\(985\) 0 0
\(986\) 0 0
\(987\) −0.554958 −0.554958
\(988\) −1.24698 −1.24698
\(989\) 0.801938 0.801938
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(998\) 0 0
\(999\) 1.00000 1.00000
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 287.1.d.a.286.3 3
3.2 odd 2 2583.1.f.b.2008.1 3
7.2 even 3 2009.1.i.b.1844.1 6
7.3 odd 6 2009.1.i.a.901.1 6
7.4 even 3 2009.1.i.b.901.1 6
7.5 odd 6 2009.1.i.a.1844.1 6
7.6 odd 2 287.1.d.b.286.3 yes 3
21.20 even 2 2583.1.f.a.2008.1 3
41.40 even 2 287.1.d.b.286.3 yes 3
123.122 odd 2 2583.1.f.a.2008.1 3
287.40 odd 6 2009.1.i.b.1844.1 6
287.81 even 6 2009.1.i.a.901.1 6
287.122 odd 6 2009.1.i.b.901.1 6
287.163 even 6 2009.1.i.a.1844.1 6
287.286 odd 2 CM 287.1.d.a.286.3 3
861.860 even 2 2583.1.f.b.2008.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.1.d.a.286.3 3 1.1 even 1 trivial
287.1.d.a.286.3 3 287.286 odd 2 CM
287.1.d.b.286.3 yes 3 7.6 odd 2
287.1.d.b.286.3 yes 3 41.40 even 2
2009.1.i.a.901.1 6 7.3 odd 6
2009.1.i.a.901.1 6 287.81 even 6
2009.1.i.a.1844.1 6 7.5 odd 6
2009.1.i.a.1844.1 6 287.163 even 6
2009.1.i.b.901.1 6 7.4 even 3
2009.1.i.b.901.1 6 287.122 odd 6
2009.1.i.b.1844.1 6 7.2 even 3
2009.1.i.b.1844.1 6 287.40 odd 6
2583.1.f.a.2008.1 3 21.20 even 2
2583.1.f.a.2008.1 3 123.122 odd 2
2583.1.f.b.2008.1 3 3.2 odd 2
2583.1.f.b.2008.1 3 861.860 even 2