Properties

Label 2015.1.h.c.2014.4
Level 2015
Weight 1
Character 2015.2014
Self dual yes
Analytic conductor 1.006
Analytic rank 0
Dimension 6
Projective image \(D_{13}\)
CM discriminant -2015
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 2015 = 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2015.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(1.00561600046\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{26})^+\)
Defining polynomial: \(x^{6} - x^{5} - 5 x^{4} + 4 x^{3} + 6 x^{2} - 3 x - 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image \(D_{13}\)
Projective field Galois closure of \(\mathbb{Q}[x]/(x^{13} - \cdots)\)

Embedding invariants

Embedding label 2014.4
Root \(-0.241073\) of defining polynomial
Character \(\chi\) \(=\) 2015.2014

$q$-expansion

\(f(q)\) \(=\) \(q+0.241073 q^{2} +0.709210 q^{3} -0.941884 q^{4} +1.00000 q^{5} +0.170972 q^{6} +1.77091 q^{7} -0.468136 q^{8} -0.497021 q^{9} +O(q^{10})\) \(q+0.241073 q^{2} +0.709210 q^{3} -0.941884 q^{4} +1.00000 q^{5} +0.170972 q^{6} +1.77091 q^{7} -0.468136 q^{8} -0.497021 q^{9} +0.241073 q^{10} -1.13613 q^{11} -0.667993 q^{12} -1.00000 q^{13} +0.426920 q^{14} +0.709210 q^{15} +0.829028 q^{16} +1.94188 q^{17} -0.119819 q^{18} -0.941884 q^{20} +1.25595 q^{21} -0.273891 q^{22} +1.49702 q^{23} -0.332007 q^{24} +1.00000 q^{25} -0.241073 q^{26} -1.06170 q^{27} -1.66799 q^{28} +0.170972 q^{30} -1.00000 q^{31} +0.667993 q^{32} -0.805754 q^{33} +0.468136 q^{34} +1.77091 q^{35} +0.468136 q^{36} -0.709210 q^{39} -0.468136 q^{40} +0.302776 q^{42} -0.241073 q^{43} +1.07010 q^{44} -0.497021 q^{45} +0.360892 q^{46} -1.49702 q^{47} +0.587955 q^{48} +2.13613 q^{49} +0.241073 q^{50} +1.37720 q^{51} +0.941884 q^{52} -1.13613 q^{53} -0.255948 q^{54} -1.13613 q^{55} -0.829028 q^{56} -0.667993 q^{60} -0.241073 q^{62} -0.880181 q^{63} -0.667993 q^{64} -1.00000 q^{65} -0.194246 q^{66} +1.13613 q^{67} -1.82903 q^{68} +1.06170 q^{69} +0.426920 q^{70} +0.232674 q^{72} +0.709210 q^{75} -2.01199 q^{77} -0.170972 q^{78} +0.829028 q^{80} -0.255948 q^{81} -1.18296 q^{84} +1.94188 q^{85} -0.0581164 q^{86} +0.531864 q^{88} -1.77091 q^{89} -0.119819 q^{90} -1.77091 q^{91} -1.41002 q^{92} -0.709210 q^{93} -0.360892 q^{94} +0.473747 q^{96} -0.709210 q^{97} +0.514964 q^{98} +0.564681 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} + q^{3} + 5q^{4} + 6q^{5} + 2q^{6} - q^{7} - 2q^{8} + 5q^{9} + O(q^{10}) \) \( 6q - q^{2} + q^{3} + 5q^{4} + 6q^{5} + 2q^{6} - q^{7} - 2q^{8} + 5q^{9} - q^{10} + q^{11} + 3q^{12} - 6q^{13} - 2q^{14} + q^{15} + 4q^{16} + q^{17} - 3q^{18} + 5q^{20} + 2q^{21} + 2q^{22} + q^{23} - 9q^{24} + 6q^{25} + q^{26} + 2q^{27} - 3q^{28} + 2q^{30} - 6q^{31} - 3q^{32} - 2q^{33} + 2q^{34} - q^{35} + 2q^{36} - q^{39} - 2q^{40} - 9q^{42} + q^{43} + 3q^{44} + 5q^{45} + 2q^{46} - q^{47} + 5q^{48} + 5q^{49} - q^{50} - 2q^{51} - 5q^{52} + q^{53} + 4q^{54} + q^{55} - 4q^{56} + 3q^{60} + q^{62} - 3q^{63} + 3q^{64} - 6q^{65} - 4q^{66} - q^{67} - 10q^{68} - 2q^{69} - 2q^{70} - 6q^{72} + q^{75} + 2q^{77} - 2q^{78} + 4q^{80} + 4q^{81} + 6q^{84} + q^{85} - 11q^{86} + 4q^{88} + q^{89} - 3q^{90} + q^{91} + 3q^{92} - q^{93} - 2q^{94} - 7q^{96} - q^{97} - 3q^{98} + 3q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2015\mathbb{Z}\right)^\times\).

\(n\) \(716\) \(807\) \(1861\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(3\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(4\) −0.941884 −0.941884
\(5\) 1.00000 1.00000
\(6\) 0.170972 0.170972
\(7\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(8\) −0.468136 −0.468136
\(9\) −0.497021 −0.497021
\(10\) 0.241073 0.241073
\(11\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(12\) −0.667993 −0.667993
\(13\) −1.00000 −1.00000
\(14\) 0.426920 0.426920
\(15\) 0.709210 0.709210
\(16\) 0.829028 0.829028
\(17\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(18\) −0.119819 −0.119819
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −0.941884 −0.941884
\(21\) 1.25595 1.25595
\(22\) −0.273891 −0.273891
\(23\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(24\) −0.332007 −0.332007
\(25\) 1.00000 1.00000
\(26\) −0.241073 −0.241073
\(27\) −1.06170 −1.06170
\(28\) −1.66799 −1.66799
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0.170972 0.170972
\(31\) −1.00000 −1.00000
\(32\) 0.667993 0.667993
\(33\) −0.805754 −0.805754
\(34\) 0.468136 0.468136
\(35\) 1.77091 1.77091
\(36\) 0.468136 0.468136
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) −0.709210 −0.709210
\(40\) −0.468136 −0.468136
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0.302776 0.302776
\(43\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(44\) 1.07010 1.07010
\(45\) −0.497021 −0.497021
\(46\) 0.360892 0.360892
\(47\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(48\) 0.587955 0.587955
\(49\) 2.13613 2.13613
\(50\) 0.241073 0.241073
\(51\) 1.37720 1.37720
\(52\) 0.941884 0.941884
\(53\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(54\) −0.255948 −0.255948
\(55\) −1.13613 −1.13613
\(56\) −0.829028 −0.829028
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) −0.667993 −0.667993
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) −0.241073 −0.241073
\(63\) −0.880181 −0.880181
\(64\) −0.667993 −0.667993
\(65\) −1.00000 −1.00000
\(66\) −0.194246 −0.194246
\(67\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(68\) −1.82903 −1.82903
\(69\) 1.06170 1.06170
\(70\) 0.426920 0.426920
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0.232674 0.232674
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0.709210 0.709210
\(76\) 0 0
\(77\) −2.01199 −2.01199
\(78\) −0.170972 −0.170972
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 0.829028 0.829028
\(81\) −0.255948 −0.255948
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −1.18296 −1.18296
\(85\) 1.94188 1.94188
\(86\) −0.0581164 −0.0581164
\(87\) 0 0
\(88\) 0.531864 0.531864
\(89\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(90\) −0.119819 −0.119819
\(91\) −1.77091 −1.77091
\(92\) −1.41002 −1.41002
\(93\) −0.709210 −0.709210
\(94\) −0.360892 −0.360892
\(95\) 0 0
\(96\) 0.473747 0.473747
\(97\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(98\) 0.514964 0.514964
\(99\) 0.564681 0.564681
\(100\) −0.941884 −0.941884
\(101\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(102\) 0.332007 0.332007
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0.468136 0.468136
\(105\) 1.25595 1.25595
\(106\) −0.273891 −0.273891
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 1.00000 1.00000
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −0.273891 −0.273891
\(111\) 0 0
\(112\) 1.46814 1.46814
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 1.49702 1.49702
\(116\) 0 0
\(117\) 0.497021 0.497021
\(118\) 0 0
\(119\) 3.43891 3.43891
\(120\) −0.332007 −0.332007
\(121\) 0.290790 0.290790
\(122\) 0 0
\(123\) 0 0
\(124\) 0.941884 0.941884
\(125\) 1.00000 1.00000
\(126\) −0.212188 −0.212188
\(127\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(128\) −0.829028 −0.829028
\(129\) −0.170972 −0.170972
\(130\) −0.241073 −0.241073
\(131\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(132\) 0.758927 0.758927
\(133\) 0 0
\(134\) 0.273891 0.273891
\(135\) −1.06170 −1.06170
\(136\) −0.909066 −0.909066
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0.255948 0.255948
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −1.66799 −1.66799
\(141\) −1.06170 −1.06170
\(142\) 0 0
\(143\) 1.13613 1.13613
\(144\) −0.412045 −0.412045
\(145\) 0 0
\(146\) 0 0
\(147\) 1.51496 1.51496
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 0.170972 0.170972
\(151\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(152\) 0 0
\(153\) −0.965158 −0.965158
\(154\) −0.485036 −0.485036
\(155\) −1.00000 −1.00000
\(156\) 0.667993 0.667993
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) −0.805754 −0.805754
\(160\) 0.667993 0.667993
\(161\) 2.65109 2.65109
\(162\) −0.0617023 −0.0617023
\(163\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(164\) 0 0
\(165\) −0.805754 −0.805754
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) −0.587955 −0.587955
\(169\) 1.00000 1.00000
\(170\) 0.468136 0.468136
\(171\) 0 0
\(172\) 0.227063 0.227063
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 1.77091 1.77091
\(176\) −0.941884 −0.941884
\(177\) 0 0
\(178\) −0.426920 −0.426920
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.468136 0.468136
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −0.426920 −0.426920
\(183\) 0 0
\(184\) −0.700810 −0.700810
\(185\) 0 0
\(186\) −0.170972 −0.170972
\(187\) −2.20623 −2.20623
\(188\) 1.41002 1.41002
\(189\) −1.88018 −1.88018
\(190\) 0 0
\(191\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(192\) −0.473747 −0.473747
\(193\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(194\) −0.170972 −0.170972
\(195\) −0.709210 −0.709210
\(196\) −2.01199 −2.01199
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0.136129 0.136129
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −0.468136 −0.468136
\(201\) 0.805754 0.805754
\(202\) 0.0581164 0.0581164
\(203\) 0 0
\(204\) −1.29716 −1.29716
\(205\) 0 0
\(206\) 0 0
\(207\) −0.744052 −0.744052
\(208\) −0.829028 −0.829028
\(209\) 0 0
\(210\) 0.302776 0.302776
\(211\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(212\) 1.07010 1.07010
\(213\) 0 0
\(214\) 0 0
\(215\) −0.241073 −0.241073
\(216\) 0.497021 0.497021
\(217\) −1.77091 −1.77091
\(218\) 0 0
\(219\) 0 0
\(220\) 1.07010 1.07010
\(221\) −1.94188 −1.94188
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 1.18296 1.18296
\(225\) −0.497021 −0.497021
\(226\) 0 0
\(227\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(228\) 0 0
\(229\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(230\) 0.360892 0.360892
\(231\) −1.42692 −1.42692
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0.119819 0.119819
\(235\) −1.49702 −1.49702
\(236\) 0 0
\(237\) 0 0
\(238\) 0.829028 0.829028
\(239\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(240\) 0.587955 0.587955
\(241\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(242\) 0.0701018 0.0701018
\(243\) 0.880181 0.880181
\(244\) 0 0
\(245\) 2.13613 2.13613
\(246\) 0 0
\(247\) 0 0
\(248\) 0.468136 0.468136
\(249\) 0 0
\(250\) 0.241073 0.241073
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0.829028 0.829028
\(253\) −1.70081 −1.70081
\(254\) 0.468136 0.468136
\(255\) 1.37720 1.37720
\(256\) 0.468136 0.468136
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) −0.0412167 −0.0412167
\(259\) 0 0
\(260\) 0.941884 0.941884
\(261\) 0 0
\(262\) −0.468136 −0.468136
\(263\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(264\) 0.377203 0.377203
\(265\) −1.13613 −1.13613
\(266\) 0 0
\(267\) −1.25595 −1.25595
\(268\) −1.07010 −1.07010
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −0.255948 −0.255948
\(271\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(272\) 1.60988 1.60988
\(273\) −1.25595 −1.25595
\(274\) 0 0
\(275\) −1.13613 −1.13613
\(276\) −1.00000 −1.00000
\(277\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(278\) 0 0
\(279\) 0.497021 0.497021
\(280\) −0.829028 −0.829028
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −0.255948 −0.255948
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0.273891 0.273891
\(287\) 0 0
\(288\) −0.332007 −0.332007
\(289\) 2.77091 2.77091
\(290\) 0 0
\(291\) −0.502979 −0.502979
\(292\) 0 0
\(293\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(294\) 0.365217 0.365217
\(295\) 0 0
\(296\) 0 0
\(297\) 1.20623 1.20623
\(298\) 0 0
\(299\) −1.49702 −1.49702
\(300\) −0.667993 −0.667993
\(301\) −0.426920 −0.426920
\(302\) −0.0581164 −0.0581164
\(303\) 0.170972 0.170972
\(304\) 0 0
\(305\) 0 0
\(306\) −0.232674 −0.232674
\(307\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(308\) 1.89506 1.89506
\(309\) 0 0
\(310\) −0.241073 −0.241073
\(311\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(312\) 0.332007 0.332007
\(313\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(314\) 0 0
\(315\) −0.880181 −0.880181
\(316\) 0 0
\(317\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(318\) −0.194246 −0.194246
\(319\) 0 0
\(320\) −0.667993 −0.667993
\(321\) 0 0
\(322\) 0.639108 0.639108
\(323\) 0 0
\(324\) 0.241073 0.241073
\(325\) −1.00000 −1.00000
\(326\) −0.468136 −0.468136
\(327\) 0 0
\(328\) 0 0
\(329\) −2.65109 −2.65109
\(330\) −0.194246 −0.194246
\(331\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.13613 1.13613
\(336\) 1.04122 1.04122
\(337\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(338\) 0.241073 0.241073
\(339\) 0 0
\(340\) −1.82903 −1.82903
\(341\) 1.13613 1.13613
\(342\) 0 0
\(343\) 2.01199 2.01199
\(344\) 0.112855 0.112855
\(345\) 1.06170 1.06170
\(346\) 0 0
\(347\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0.426920 0.426920
\(351\) 1.06170 1.06170
\(352\) −0.758927 −0.758927
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.66799 1.66799
\(357\) 2.43891 2.43891
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0.232674 0.232674
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) 0.206231 0.206231
\(364\) 1.66799 1.66799
\(365\) 0 0
\(366\) 0 0
\(367\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(368\) 1.24107 1.24107
\(369\) 0 0
\(370\) 0 0
\(371\) −2.01199 −2.01199
\(372\) 0.667993 0.667993
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −0.531864 −0.531864
\(375\) 0.709210 0.709210
\(376\) 0.700810 0.700810
\(377\) 0 0
\(378\) −0.453262 −0.453262
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 1.37720 1.37720
\(382\) 0.0581164 0.0581164
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −0.587955 −0.587955
\(385\) −2.01199 −2.01199
\(386\) −0.360892 −0.360892
\(387\) 0.119819 0.119819
\(388\) 0.667993 0.667993
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) −0.170972 −0.170972
\(391\) 2.90704 2.90704
\(392\) −1.00000 −1.00000
\(393\) −1.37720 −1.37720
\(394\) 0 0
\(395\) 0 0
\(396\) −0.531864 −0.531864
\(397\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.829028 0.829028
\(401\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(402\) 0.194246 0.194246
\(403\) 1.00000 1.00000
\(404\) −0.227063 −0.227063
\(405\) −0.255948 −0.255948
\(406\) 0 0
\(407\) 0 0
\(408\) −0.644719 −0.644719
\(409\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.179371 −0.179371
\(415\) 0 0
\(416\) −0.667993 −0.667993
\(417\) 0 0
\(418\) 0 0
\(419\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(420\) −1.18296 −1.18296
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) −0.170972 −0.170972
\(423\) 0.744052 0.744052
\(424\) 0.531864 0.531864
\(425\) 1.94188 1.94188
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0.805754 0.805754
\(430\) −0.0581164 −0.0581164
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −0.880181 −0.880181
\(433\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(434\) −0.426920 −0.426920
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(440\) 0.531864 0.531864
\(441\) −1.06170 −1.06170
\(442\) −0.468136 −0.468136
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) −1.77091 −1.77091
\(446\) 0 0
\(447\) 0 0
\(448\) −1.18296 −1.18296
\(449\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(450\) −0.119819 −0.119819
\(451\) 0 0
\(452\) 0 0
\(453\) −0.170972 −0.170972
\(454\) −0.468136 −0.468136
\(455\) −1.77091 −1.77091
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −0.426920 −0.426920
\(459\) −2.06170 −2.06170
\(460\) −1.41002 −1.41002
\(461\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(462\) −0.343992 −0.343992
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) −0.709210 −0.709210
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −0.468136 −0.468136
\(469\) 2.01199 2.01199
\(470\) −0.360892 −0.360892
\(471\) 0 0
\(472\) 0 0
\(473\) 0.273891 0.273891
\(474\) 0 0
\(475\) 0 0
\(476\) −3.23905 −3.23905
\(477\) 0.564681 0.564681
\(478\) −0.426920 −0.426920
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0.473747 0.473747
\(481\) 0 0
\(482\) 0.170972 0.170972
\(483\) 1.88018 1.88018
\(484\) −0.273891 −0.273891
\(485\) −0.709210 −0.709210
\(486\) 0.212188 0.212188
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −1.37720 −1.37720
\(490\) 0.514964 0.514964
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0.564681 0.564681
\(496\) −0.829028 −0.829028
\(497\) 0 0
\(498\) 0 0
\(499\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(500\) −0.941884 −0.941884
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0.412045 0.412045
\(505\) 0.241073 0.241073
\(506\) −0.410020 −0.410020
\(507\) 0.709210 0.709210
\(508\) −1.82903 −1.82903
\(509\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(510\) 0.332007 0.332007
\(511\) 0 0
\(512\) 0.941884 0.941884
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0.161035 0.161035
\(517\) 1.70081 1.70081
\(518\) 0 0
\(519\) 0 0
\(520\) 0.468136 0.468136
\(521\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(522\) 0 0
\(523\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(524\) 1.82903 1.82903
\(525\) 1.25595 1.25595
\(526\) −0.0581164 −0.0581164
\(527\) −1.94188 −1.94188
\(528\) −0.667993 −0.667993
\(529\) 1.24107 1.24107
\(530\) −0.273891 −0.273891
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.302776 −0.302776
\(535\) 0 0
\(536\) −0.531864 −0.531864
\(537\) 0 0
\(538\) 0 0
\(539\) −2.42692 −2.42692
\(540\) 1.00000 1.00000
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0.468136 0.468136
\(543\) 0 0
\(544\) 1.29716 1.29716
\(545\) 0 0
\(546\) −0.302776 −0.302776
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −0.273891 −0.273891
\(551\) 0 0
\(552\) −0.497021 −0.497021
\(553\) 0 0
\(554\) 0.360892 0.360892
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0.119819 0.119819
\(559\) 0.241073 0.241073
\(560\) 1.46814 1.46814
\(561\) −1.56468 −1.56468
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 1.00000 1.00000
\(565\) 0 0
\(566\) 0 0
\(567\) −0.453262 −0.453262
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) −1.07010 −1.07010
\(573\) 0.170972 0.170972
\(574\) 0 0
\(575\) 1.49702 1.49702
\(576\) 0.332007 0.332007
\(577\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(578\) 0.667993 0.667993
\(579\) −1.06170 −1.06170
\(580\) 0 0
\(581\) 0 0
\(582\) −0.121255 −0.121255
\(583\) 1.29079 1.29079
\(584\) 0 0
\(585\) 0.497021 0.497021
\(586\) 0.426920 0.426920
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −1.42692 −1.42692
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(594\) 0.290790 0.290790
\(595\) 3.43891 3.43891
\(596\) 0 0
\(597\) 0 0
\(598\) −0.360892 −0.360892
\(599\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(600\) −0.332007 −0.332007
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) −0.102919 −0.102919
\(603\) −0.564681 −0.564681
\(604\) 0.227063 0.227063
\(605\) 0.290790 0.290790
\(606\) 0.0412167 0.0412167
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.49702 1.49702
\(612\) 0.909066 0.909066
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0.0581164 0.0581164
\(615\) 0 0
\(616\) 0.941884 0.941884
\(617\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(618\) 0 0
\(619\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(620\) 0.941884 0.941884
\(621\) −1.58939 −1.58939
\(622\) −0.360892 −0.360892
\(623\) −3.13613 −3.13613
\(624\) −0.587955 −0.587955
\(625\) 1.00000 1.00000
\(626\) 0.360892 0.360892
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −0.212188 −0.212188
\(631\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(632\) 0 0
\(633\) −0.502979 −0.502979
\(634\) −0.468136 −0.468136
\(635\) 1.94188 1.94188
\(636\) 0.758927 0.758927
\(637\) −2.13613 −2.13613
\(638\) 0 0
\(639\) 0 0
\(640\) −0.829028 −0.829028
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) −2.49702 −2.49702
\(645\) −0.170972 −0.170972
\(646\) 0 0
\(647\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(648\) 0.119819 0.119819
\(649\) 0 0
\(650\) −0.241073 −0.241073
\(651\) −1.25595 −1.25595
\(652\) 1.82903 1.82903
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) −1.94188 −1.94188
\(656\) 0 0
\(657\) 0 0
\(658\) −0.639108 −0.639108
\(659\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(660\) 0.758927 0.758927
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0.468136 0.468136
\(663\) −1.37720 −1.37720
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0.273891 0.273891
\(671\) 0 0
\(672\) 0.838965 0.838965
\(673\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(674\) −0.273891 −0.273891
\(675\) −1.06170 −1.06170
\(676\) −0.941884 −0.941884
\(677\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(678\) 0 0
\(679\) −1.25595 −1.25595
\(680\) −0.909066 −0.909066
\(681\) −1.37720 −1.37720
\(682\) 0.273891 0.273891
\(683\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.485036 0.485036
\(687\) −1.25595 −1.25595
\(688\) −0.199857 −0.199857
\(689\) 1.13613 1.13613
\(690\) 0.255948 0.255948
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 1.00000 1.00000
\(694\) −0.273891 −0.273891
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.66799 −1.66799
\(701\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(702\) 0.255948 0.255948
\(703\) 0 0
\(704\) 0.758927 0.758927
\(705\) −1.06170 −1.06170
\(706\) 0 0
\(707\) 0.426920 0.426920
\(708\) 0 0
\(709\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.829028 0.829028
\(713\) −1.49702 −1.49702
\(714\) 0.587955 0.587955
\(715\) 1.13613 1.13613
\(716\) 0 0
\(717\) −1.25595 −1.25595
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −0.412045 −0.412045
\(721\) 0 0
\(722\) 0.241073 0.241073
\(723\) 0.502979 0.502979
\(724\) 0 0
\(725\) 0 0
\(726\) 0.0497169 0.0497169
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0.829028 0.829028
\(729\) 0.880181 0.880181
\(730\) 0 0
\(731\) −0.468136 −0.468136
\(732\) 0 0
\(733\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(734\) −0.426920 −0.426920
\(735\) 1.51496 1.51496
\(736\) 1.00000 1.00000
\(737\) −1.29079 −1.29079
\(738\) 0 0
\(739\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.485036 −0.485036
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0.332007 0.332007
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 2.07801 2.07801
\(749\) 0 0
\(750\) 0.170972 0.170972
\(751\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(752\) −1.24107 −1.24107
\(753\) 0 0
\(754\) 0 0
\(755\) −0.241073 −0.241073
\(756\) 1.77091 1.77091
\(757\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(758\) 0 0
\(759\) −1.20623 −1.20623
\(760\) 0 0
\(761\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(762\) 0.332007 0.332007
\(763\) 0 0
\(764\) −0.227063 −0.227063
\(765\) −0.965158 −0.965158
\(766\) 0 0
\(767\) 0 0
\(768\) 0.332007 0.332007
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) −0.485036 −0.485036
\(771\) 0 0
\(772\) 1.41002 1.41002
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0.0288851 0.0288851
\(775\) −1.00000 −1.00000
\(776\) 0.332007 0.332007
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0.667993 0.667993
\(781\) 0 0
\(782\) 0.700810 0.700810
\(783\) 0 0
\(784\) 1.77091 1.77091
\(785\) 0 0
\(786\) −0.332007 −0.332007
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) −0.170972 −0.170972
\(790\) 0 0
\(791\) 0 0
\(792\) −0.264348 −0.264348
\(793\) 0 0
\(794\) 0.273891 0.273891
\(795\) −0.805754 −0.805754
\(796\) 0 0
\(797\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(798\) 0 0
\(799\) −2.90704 −2.90704
\(800\) 0.667993 0.667993
\(801\) 0.880181 0.880181
\(802\) 0.360892 0.360892
\(803\) 0 0
\(804\) −0.758927 −0.758927
\(805\) 2.65109 2.65109
\(806\) 0.241073 0.241073
\(807\) 0 0
\(808\) −0.112855 −0.112855
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) −0.0617023 −0.0617023
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 1.37720 1.37720
\(814\) 0 0
\(815\) −1.94188 −1.94188
\(816\) 1.14174 1.14174
\(817\) 0 0
\(818\) 0.360892 0.360892
\(819\) 0.880181 0.880181
\(820\) 0 0
\(821\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(822\) 0 0
\(823\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(824\) 0 0
\(825\) −0.805754 −0.805754
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0.700810 0.700810
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 1.06170 1.06170
\(832\) 0.667993 0.667993
\(833\) 4.14811 4.14811
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.06170 1.06170
\(838\) −0.170972 −0.170972
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) −0.587955 −0.587955
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0.667993 0.667993
\(845\) 1.00000 1.00000
\(846\) 0.179371 0.179371
\(847\) 0.514964 0.514964
\(848\) −0.941884 −0.941884
\(849\) 0 0
\(850\) 0.468136 0.468136
\(851\) 0 0
\(852\) 0 0
\(853\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0.194246 0.194246
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0.227063 0.227063
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) −0.709210 −0.709210
\(865\) 0 0
\(866\) −0.0581164 −0.0581164
\(867\) 1.96516 1.96516
\(868\) 1.66799 1.66799
\(869\) 0 0
\(870\) 0 0
\(871\) −1.13613 −1.13613
\(872\) 0 0
\(873\) 0.352493 0.352493
\(874\) 0 0
\(875\) 1.77091 1.77091
\(876\) 0 0
\(877\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(878\) −0.360892 −0.360892
\(879\) 1.25595 1.25595
\(880\) −0.941884 −0.941884
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −0.255948 −0.255948
\(883\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(884\) 1.82903 1.82903
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 3.43891 3.43891
\(890\) −0.426920 −0.426920
\(891\) 0.290790 0.290790
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −1.46814 −1.46814
\(897\) −1.06170 −1.06170
\(898\) −0.0581164 −0.0581164
\(899\) 0 0
\(900\) 0.468136 0.468136
\(901\) −2.20623 −2.20623
\(902\) 0 0
\(903\) −0.302776 −0.302776
\(904\) 0 0
\(905\) 0 0
\(906\) −0.0412167 −0.0412167
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 1.82903 1.82903
\(909\) −0.119819 −0.119819
\(910\) −0.426920 −0.426920
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 1.66799 1.66799
\(917\) −3.43891 −3.43891
\(918\) −0.497021 −0.497021
\(919\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(920\) −0.700810 −0.700810
\(921\) 0.170972 0.170972
\(922\) 0.170972 0.170972
\(923\) 0 0
\(924\) 1.34399 1.34399
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(930\) −0.170972 −0.170972
\(931\) 0 0
\(932\) 0 0
\(933\) −1.06170 −1.06170
\(934\) 0 0
\(935\) −2.20623 −2.20623
\(936\) −0.232674 −0.232674
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0.485036 0.485036
\(939\) 1.06170 1.06170
\(940\) 1.41002 1.41002
\(941\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −1.88018 −1.88018
\(946\) 0.0660277 0.0660277
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −1.37720 −1.37720
\(952\) −1.60988 −1.60988
\(953\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(954\) 0.136129 0.136129
\(955\) 0.241073 0.241073
\(956\) 1.66799 1.66799
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −0.473747 −0.473747
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) −0.667993 −0.667993
\(965\) −1.49702 −1.49702
\(966\) 0.453262 0.453262
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −0.136129 −0.136129
\(969\) 0 0
\(970\) −0.170972 −0.170972
\(971\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(972\) −0.829028 −0.829028
\(973\) 0 0
\(974\) 0 0
\(975\) −0.709210 −0.709210
\(976\) 0 0
\(977\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(978\) −0.332007 −0.332007
\(979\) 2.01199 2.01199
\(980\) −2.01199 −2.01199
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −1.88018 −1.88018
\(988\) 0 0
\(989\) −0.360892 −0.360892
\(990\) 0.136129 0.136129
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) −0.667993 −0.667993
\(993\) 1.37720 1.37720
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) −0.0581164 −0.0581164
\(999\) 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 2015.1.h.c.2014.4 yes 6
5.4 even 2 2015.1.h.d.2014.3 yes 6
13.12 even 2 2015.1.h.e.2014.3 yes 6
31.30 odd 2 2015.1.h.b.2014.4 6
65.64 even 2 2015.1.h.b.2014.4 6
155.154 odd 2 2015.1.h.e.2014.3 yes 6
403.402 odd 2 2015.1.h.d.2014.3 yes 6
2015.2014 odd 2 CM 2015.1.h.c.2014.4 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2015.1.h.b.2014.4 6 31.30 odd 2
2015.1.h.b.2014.4 6 65.64 even 2
2015.1.h.c.2014.4 yes 6 1.1 even 1 trivial
2015.1.h.c.2014.4 yes 6 2015.2014 odd 2 CM
2015.1.h.d.2014.3 yes 6 5.4 even 2
2015.1.h.d.2014.3 yes 6 403.402 odd 2
2015.1.h.e.2014.3 yes 6 13.12 even 2
2015.1.h.e.2014.3 yes 6 155.154 odd 2