Properties

Label 2015.1.h.b.2014.3
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 2014.3
Root \(0.709210\) of defining polynomial
Character \(\chi\) \(=\) 2015.2014

$q$-expansion

\(f(q)\) \(=\) \(q-0.709210 q^{2} +1.77091 q^{3} -0.497021 q^{4} +1.00000 q^{5} -1.25595 q^{6} +0.241073 q^{7} +1.06170 q^{8} +2.13613 q^{9} +O(q^{10})\) \(q-0.709210 q^{2} +1.77091 q^{3} -0.497021 q^{4} +1.00000 q^{5} -1.25595 q^{6} +0.241073 q^{7} +1.06170 q^{8} +2.13613 q^{9} -0.709210 q^{10} -1.94188 q^{11} -0.880181 q^{12} +1.00000 q^{13} -0.170972 q^{14} +1.77091 q^{15} -0.255948 q^{16} -1.49702 q^{17} -1.51496 q^{18} -0.497021 q^{20} +0.426920 q^{21} +1.37720 q^{22} +1.13613 q^{23} +1.88018 q^{24} +1.00000 q^{25} -0.709210 q^{26} +2.01199 q^{27} -0.119819 q^{28} -1.25595 q^{30} +1.00000 q^{31} -0.880181 q^{32} -3.43891 q^{33} +1.06170 q^{34} +0.241073 q^{35} -1.06170 q^{36} +1.77091 q^{39} +1.06170 q^{40} -0.302776 q^{42} -0.709210 q^{43} +0.965158 q^{44} +2.13613 q^{45} -0.805754 q^{46} +1.13613 q^{47} -0.453262 q^{48} -0.941884 q^{49} -0.709210 q^{50} -2.65109 q^{51} -0.497021 q^{52} -1.94188 q^{53} -1.42692 q^{54} -1.94188 q^{55} +0.255948 q^{56} -0.880181 q^{60} -0.709210 q^{62} +0.514964 q^{63} +0.880181 q^{64} +1.00000 q^{65} +2.43891 q^{66} -1.94188 q^{67} +0.744052 q^{68} +2.01199 q^{69} -0.170972 q^{70} +2.26793 q^{72} +1.77091 q^{75} -0.468136 q^{77} -1.25595 q^{78} -0.255948 q^{80} +1.42692 q^{81} -0.212188 q^{84} -1.49702 q^{85} +0.502979 q^{86} -2.06170 q^{88} +0.241073 q^{89} -1.51496 q^{90} +0.241073 q^{91} -0.564681 q^{92} +1.77091 q^{93} -0.805754 q^{94} -1.55872 q^{96} +1.77091 q^{97} +0.667993 q^{98} -4.14811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} - q^{3} + 5q^{4} + 6q^{5} - 2q^{6} - q^{7} - 2q^{8} + 5q^{9} + O(q^{10}) \) \( 6q - q^{2} - q^{3} + 5q^{4} + 6q^{5} - 2q^{6} - q^{7} - 2q^{8} + 5q^{9} - q^{10} - q^{11} - 3q^{12} + 6q^{13} - 2q^{14} - q^{15} + 4q^{16} - q^{17} - 3q^{18} + 5q^{20} - 2q^{21} - 2q^{22} - q^{23} + 9q^{24} + 6q^{25} - q^{26} - 2q^{27} - 3q^{28} - 2q^{30} + 6q^{31} - 3q^{32} - 2q^{33} - 2q^{34} - q^{35} + 2q^{36} - q^{39} - 2q^{40} + 9q^{42} - q^{43} - 3q^{44} + 5q^{45} - 2q^{46} - q^{47} - 5q^{48} + 5q^{49} - q^{50} - 2q^{51} + 5q^{52} - q^{53} - 4q^{54} - q^{55} - 4q^{56} - 3q^{60} - q^{62} - 3q^{63} + 3q^{64} + 6q^{65} - 4q^{66} - q^{67} + 10q^{68} - 2q^{69} - 2q^{70} - 6q^{72} - q^{75} - 2q^{77} - 2q^{78} + 4q^{80} + 4q^{81} - 6q^{84} - q^{85} + 11q^{86} - 4q^{88} - q^{89} - 3q^{90} - q^{91} - 3q^{92} - q^{93} - 2q^{94} + 7q^{96} - q^{97} - 3q^{98} - 3q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(3\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(4\) −0.497021 −0.497021
\(5\) 1.00000 1.00000
\(6\) −1.25595 −1.25595
\(7\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(8\) 1.06170 1.06170
\(9\) 2.13613 2.13613
\(10\) −0.709210 −0.709210
\(11\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(12\) −0.880181 −0.880181
\(13\) 1.00000 1.00000
\(14\) −0.170972 −0.170972
\(15\) 1.77091 1.77091
\(16\) −0.255948 −0.255948
\(17\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(18\) −1.51496 −1.51496
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −0.497021 −0.497021
\(21\) 0.426920 0.426920
\(22\) 1.37720 1.37720
\(23\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(24\) 1.88018 1.88018
\(25\) 1.00000 1.00000
\(26\) −0.709210 −0.709210
\(27\) 2.01199 2.01199
\(28\) −0.119819 −0.119819
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) −1.25595 −1.25595
\(31\) 1.00000 1.00000
\(32\) −0.880181 −0.880181
\(33\) −3.43891 −3.43891
\(34\) 1.06170 1.06170
\(35\) 0.241073 0.241073
\(36\) −1.06170 −1.06170
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 1.77091 1.77091
\(40\) 1.06170 1.06170
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) −0.302776 −0.302776
\(43\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(44\) 0.965158 0.965158
\(45\) 2.13613 2.13613
\(46\) −0.805754 −0.805754
\(47\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(48\) −0.453262 −0.453262
\(49\) −0.941884 −0.941884
\(50\) −0.709210 −0.709210
\(51\) −2.65109 −2.65109
\(52\) −0.497021 −0.497021
\(53\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(54\) −1.42692 −1.42692
\(55\) −1.94188 −1.94188
\(56\) 0.255948 0.255948
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) −0.880181 −0.880181
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) −0.709210 −0.709210
\(63\) 0.514964 0.514964
\(64\) 0.880181 0.880181
\(65\) 1.00000 1.00000
\(66\) 2.43891 2.43891
\(67\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(68\) 0.744052 0.744052
\(69\) 2.01199 2.01199
\(70\) −0.170972 −0.170972
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 2.26793 2.26793
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 1.77091 1.77091
\(76\) 0 0
\(77\) −0.468136 −0.468136
\(78\) −1.25595 −1.25595
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −0.255948 −0.255948
\(81\) 1.42692 1.42692
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −0.212188 −0.212188
\(85\) −1.49702 −1.49702
\(86\) 0.502979 0.502979
\(87\) 0 0
\(88\) −2.06170 −2.06170
\(89\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(90\) −1.51496 −1.51496
\(91\) 0.241073 0.241073
\(92\) −0.564681 −0.564681
\(93\) 1.77091 1.77091
\(94\) −0.805754 −0.805754
\(95\) 0 0
\(96\) −1.55872 −1.55872
\(97\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(98\) 0.667993 0.667993
\(99\) −4.14811 −4.14811
\(100\) −0.497021 −0.497021
\(101\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(102\) 1.88018 1.88018
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 1.06170 1.06170
\(105\) 0.426920 0.426920
\(106\) 1.37720 1.37720
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −1.00000 −1.00000
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 1.37720 1.37720
\(111\) 0 0
\(112\) −0.0617023 −0.0617023
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 1.13613 1.13613
\(116\) 0 0
\(117\) 2.13613 2.13613
\(118\) 0 0
\(119\) −0.360892 −0.360892
\(120\) 1.88018 1.88018
\(121\) 2.77091 2.77091
\(122\) 0 0
\(123\) 0 0
\(124\) −0.497021 −0.497021
\(125\) 1.00000 1.00000
\(126\) −0.365217 −0.365217
\(127\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(128\) 0.255948 0.255948
\(129\) −1.25595 −1.25595
\(130\) −0.709210 −0.709210
\(131\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(132\) 1.70921 1.70921
\(133\) 0 0
\(134\) 1.37720 1.37720
\(135\) 2.01199 2.01199
\(136\) −1.58939 −1.58939
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) −1.42692 −1.42692
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −0.119819 −0.119819
\(141\) 2.01199 2.01199
\(142\) 0 0
\(143\) −1.94188 −1.94188
\(144\) −0.546738 −0.546738
\(145\) 0 0
\(146\) 0 0
\(147\) −1.66799 −1.66799
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −1.25595 −1.25595
\(151\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(152\) 0 0
\(153\) −3.19783 −3.19783
\(154\) 0.332007 0.332007
\(155\) 1.00000 1.00000
\(156\) −0.880181 −0.880181
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) −3.43891 −3.43891
\(160\) −0.880181 −0.880181
\(161\) 0.273891 0.273891
\(162\) −1.01199 −1.01199
\(163\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(164\) 0 0
\(165\) −3.43891 −3.43891
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0.453262 0.453262
\(169\) 1.00000 1.00000
\(170\) 1.06170 1.06170
\(171\) 0 0
\(172\) 0.352493 0.352493
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0.241073 0.241073
\(176\) 0.497021 0.497021
\(177\) 0 0
\(178\) −0.170972 −0.170972
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −1.06170 −1.06170
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −0.170972 −0.170972
\(183\) 0 0
\(184\) 1.20623 1.20623
\(185\) 0 0
\(186\) −1.25595 −1.25595
\(187\) 2.90704 2.90704
\(188\) −0.564681 −0.564681
\(189\) 0.485036 0.485036
\(190\) 0 0
\(191\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(192\) 1.55872 1.55872
\(193\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(194\) −1.25595 −1.25595
\(195\) 1.77091 1.77091
\(196\) 0.468136 0.468136
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 2.94188 2.94188
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.06170 1.06170
\(201\) −3.43891 −3.43891
\(202\) 0.502979 0.502979
\(203\) 0 0
\(204\) 1.31765 1.31765
\(205\) 0 0
\(206\) 0 0
\(207\) 2.42692 2.42692
\(208\) −0.255948 −0.255948
\(209\) 0 0
\(210\) −0.302776 −0.302776
\(211\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(212\) 0.965158 0.965158
\(213\) 0 0
\(214\) 0 0
\(215\) −0.709210 −0.709210
\(216\) 2.13613 2.13613
\(217\) 0.241073 0.241073
\(218\) 0 0
\(219\) 0 0
\(220\) 0.965158 0.965158
\(221\) −1.49702 −1.49702
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) −0.212188 −0.212188
\(225\) 2.13613 2.13613
\(226\) 0 0
\(227\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(228\) 0 0
\(229\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(230\) −0.805754 −0.805754
\(231\) −0.829028 −0.829028
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) −1.51496 −1.51496
\(235\) 1.13613 1.13613
\(236\) 0 0
\(237\) 0 0
\(238\) 0.255948 0.255948
\(239\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(240\) −0.453262 −0.453262
\(241\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(242\) −1.96516 −1.96516
\(243\) 0.514964 0.514964
\(244\) 0 0
\(245\) −0.941884 −0.941884
\(246\) 0 0
\(247\) 0 0
\(248\) 1.06170 1.06170
\(249\) 0 0
\(250\) −0.709210 −0.709210
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −0.255948 −0.255948
\(253\) −2.20623 −2.20623
\(254\) 1.06170 1.06170
\(255\) −2.65109 −2.65109
\(256\) −1.06170 −1.06170
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0.890731 0.890731
\(259\) 0 0
\(260\) −0.497021 −0.497021
\(261\) 0 0
\(262\) 1.06170 1.06170
\(263\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(264\) −3.65109 −3.65109
\(265\) −1.94188 −1.94188
\(266\) 0 0
\(267\) 0.426920 0.426920
\(268\) 0.965158 0.965158
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −1.42692 −1.42692
\(271\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(272\) 0.383160 0.383160
\(273\) 0.426920 0.426920
\(274\) 0 0
\(275\) −1.94188 −1.94188
\(276\) −1.00000 −1.00000
\(277\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(278\) 0 0
\(279\) 2.13613 2.13613
\(280\) 0.255948 0.255948
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −1.42692 −1.42692
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 1.37720 1.37720
\(287\) 0 0
\(288\) −1.88018 −1.88018
\(289\) 1.24107 1.24107
\(290\) 0 0
\(291\) 3.13613 3.13613
\(292\) 0 0
\(293\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(294\) 1.18296 1.18296
\(295\) 0 0
\(296\) 0 0
\(297\) −3.90704 −3.90704
\(298\) 0 0
\(299\) 1.13613 1.13613
\(300\) −0.880181 −0.880181
\(301\) −0.170972 −0.170972
\(302\) 0.502979 0.502979
\(303\) −1.25595 −1.25595
\(304\) 0 0
\(305\) 0 0
\(306\) 2.26793 2.26793
\(307\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(308\) 0.232674 0.232674
\(309\) 0 0
\(310\) −0.709210 −0.709210
\(311\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(312\) 1.88018 1.88018
\(313\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(314\) 0 0
\(315\) 0.514964 0.514964
\(316\) 0 0
\(317\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(318\) 2.43891 2.43891
\(319\) 0 0
\(320\) 0.880181 0.880181
\(321\) 0 0
\(322\) −0.194246 −0.194246
\(323\) 0 0
\(324\) −0.709210 −0.709210
\(325\) 1.00000 1.00000
\(326\) 1.06170 1.06170
\(327\) 0 0
\(328\) 0 0
\(329\) 0.273891 0.273891
\(330\) 2.43891 2.43891
\(331\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.94188 −1.94188
\(336\) −0.109269 −0.109269
\(337\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(338\) −0.709210 −0.709210
\(339\) 0 0
\(340\) 0.744052 0.744052
\(341\) −1.94188 −1.94188
\(342\) 0 0
\(343\) −0.468136 −0.468136
\(344\) −0.752970 −0.752970
\(345\) 2.01199 2.01199
\(346\) 0 0
\(347\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) −0.170972 −0.170972
\(351\) 2.01199 2.01199
\(352\) 1.70921 1.70921
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.119819 −0.119819
\(357\) −0.639108 −0.639108
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 2.26793 2.26793
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) 4.90704 4.90704
\(364\) −0.119819 −0.119819
\(365\) 0 0
\(366\) 0 0
\(367\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(368\) −0.290790 −0.290790
\(369\) 0 0
\(370\) 0 0
\(371\) −0.468136 −0.468136
\(372\) −0.880181 −0.880181
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −2.06170 −2.06170
\(375\) 1.77091 1.77091
\(376\) 1.20623 1.20623
\(377\) 0 0
\(378\) −0.343992 −0.343992
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) −2.65109 −2.65109
\(382\) 0.502979 0.502979
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0.453262 0.453262
\(385\) −0.468136 −0.468136
\(386\) −0.805754 −0.805754
\(387\) −1.51496 −1.51496
\(388\) −0.880181 −0.880181
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) −1.25595 −1.25595
\(391\) −1.70081 −1.70081
\(392\) −1.00000 −1.00000
\(393\) −2.65109 −2.65109
\(394\) 0 0
\(395\) 0 0
\(396\) 2.06170 2.06170
\(397\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.255948 −0.255948
\(401\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(402\) 2.43891 2.43891
\(403\) 1.00000 1.00000
\(404\) 0.352493 0.352493
\(405\) 1.42692 1.42692
\(406\) 0 0
\(407\) 0 0
\(408\) −2.81467 −2.81467
\(409\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −1.72120 −1.72120
\(415\) 0 0
\(416\) −0.880181 −0.880181
\(417\) 0 0
\(418\) 0 0
\(419\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(420\) −0.212188 −0.212188
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) −1.25595 −1.25595
\(423\) 2.42692 2.42692
\(424\) −2.06170 −2.06170
\(425\) −1.49702 −1.49702
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −3.43891 −3.43891
\(430\) 0.502979 0.502979
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −0.514964 −0.514964
\(433\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(434\) −0.170972 −0.170972
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(440\) −2.06170 −2.06170
\(441\) −2.01199 −2.01199
\(442\) 1.06170 1.06170
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0.241073 0.241073
\(446\) 0 0
\(447\) 0 0
\(448\) 0.212188 0.212188
\(449\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(450\) −1.51496 −1.51496
\(451\) 0 0
\(452\) 0 0
\(453\) −1.25595 −1.25595
\(454\) 1.06170 1.06170
\(455\) 0.241073 0.241073
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −0.170972 −0.170972
\(459\) −3.01199 −3.01199
\(460\) −0.564681 −0.564681
\(461\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(462\) 0.587955 0.587955
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 1.77091 1.77091
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −1.06170 −1.06170
\(469\) −0.468136 −0.468136
\(470\) −0.805754 −0.805754
\(471\) 0 0
\(472\) 0 0
\(473\) 1.37720 1.37720
\(474\) 0 0
\(475\) 0 0
\(476\) 0.179371 0.179371
\(477\) −4.14811 −4.14811
\(478\) −0.170972 −0.170972
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) −1.55872 −1.55872
\(481\) 0 0
\(482\) −1.25595 −1.25595
\(483\) 0.485036 0.485036
\(484\) −1.37720 −1.37720
\(485\) 1.77091 1.77091
\(486\) −0.365217 −0.365217
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −2.65109 −2.65109
\(490\) 0.667993 0.667993
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −4.14811 −4.14811
\(496\) −0.255948 −0.255948
\(497\) 0 0
\(498\) 0 0
\(499\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(500\) −0.497021 −0.497021
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0.546738 0.546738
\(505\) −0.709210 −0.709210
\(506\) 1.56468 1.56468
\(507\) 1.77091 1.77091
\(508\) 0.744052 0.744052
\(509\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(510\) 1.88018 1.88018
\(511\) 0 0
\(512\) 0.497021 0.497021
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0.624233 0.624233
\(517\) −2.20623 −2.20623
\(518\) 0 0
\(519\) 0 0
\(520\) 1.06170 1.06170
\(521\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(522\) 0 0
\(523\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(524\) 0.744052 0.744052
\(525\) 0.426920 0.426920
\(526\) 0.502979 0.502979
\(527\) −1.49702 −1.49702
\(528\) 0.880181 0.880181
\(529\) 0.290790 0.290790
\(530\) 1.37720 1.37720
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.302776 −0.302776
\(535\) 0 0
\(536\) −2.06170 −2.06170
\(537\) 0 0
\(538\) 0 0
\(539\) 1.82903 1.82903
\(540\) −1.00000 −1.00000
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 1.06170 1.06170
\(543\) 0 0
\(544\) 1.31765 1.31765
\(545\) 0 0
\(546\) −0.302776 −0.302776
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 1.37720 1.37720
\(551\) 0 0
\(552\) 2.13613 2.13613
\(553\) 0 0
\(554\) −0.805754 −0.805754
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) −1.51496 −1.51496
\(559\) −0.709210 −0.709210
\(560\) −0.0617023 −0.0617023
\(561\) 5.14811 5.14811
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) −1.00000 −1.00000
\(565\) 0 0
\(566\) 0 0
\(567\) 0.343992 0.343992
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0.965158 0.965158
\(573\) −1.25595 −1.25595
\(574\) 0 0
\(575\) 1.13613 1.13613
\(576\) 1.88018 1.88018
\(577\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(578\) −0.880181 −0.880181
\(579\) 2.01199 2.01199
\(580\) 0 0
\(581\) 0 0
\(582\) −2.22417 −2.22417
\(583\) 3.77091 3.77091
\(584\) 0 0
\(585\) 2.13613 2.13613
\(586\) −0.170972 −0.170972
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0.829028 0.829028
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(594\) 2.77091 2.77091
\(595\) −0.360892 −0.360892
\(596\) 0 0
\(597\) 0 0
\(598\) −0.805754 −0.805754
\(599\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(600\) 1.88018 1.88018
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0.121255 0.121255
\(603\) −4.14811 −4.14811
\(604\) 0.352493 0.352493
\(605\) 2.77091 2.77091
\(606\) 0.890731 0.890731
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.13613 1.13613
\(612\) 1.58939 1.58939
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0.502979 0.502979
\(615\) 0 0
\(616\) −0.497021 −0.497021
\(617\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(618\) 0 0
\(619\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(620\) −0.497021 −0.497021
\(621\) 2.28588 2.28588
\(622\) −0.805754 −0.805754
\(623\) 0.0581164 0.0581164
\(624\) −0.453262 −0.453262
\(625\) 1.00000 1.00000
\(626\) −0.805754 −0.805754
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −0.365217 −0.365217
\(631\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(632\) 0 0
\(633\) 3.13613 3.13613
\(634\) 1.06170 1.06170
\(635\) −1.49702 −1.49702
\(636\) 1.70921 1.70921
\(637\) −0.941884 −0.941884
\(638\) 0 0
\(639\) 0 0
\(640\) 0.255948 0.255948
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) −0.136129 −0.136129
\(645\) −1.25595 −1.25595
\(646\) 0 0
\(647\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(648\) 1.51496 1.51496
\(649\) 0 0
\(650\) −0.709210 −0.709210
\(651\) 0.426920 0.426920
\(652\) 0.744052 0.744052
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) −1.49702 −1.49702
\(656\) 0 0
\(657\) 0 0
\(658\) −0.194246 −0.194246
\(659\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(660\) 1.70921 1.70921
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 1.06170 1.06170
\(663\) −2.65109 −2.65109
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 1.37720 1.37720
\(671\) 0 0
\(672\) −0.375767 −0.375767
\(673\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(674\) 1.37720 1.37720
\(675\) 2.01199 2.01199
\(676\) −0.497021 −0.497021
\(677\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(678\) 0 0
\(679\) 0.426920 0.426920
\(680\) −1.58939 −1.58939
\(681\) −2.65109 −2.65109
\(682\) 1.37720 1.37720
\(683\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.332007 0.332007
\(687\) 0.426920 0.426920
\(688\) 0.181521 0.181521
\(689\) −1.94188 −1.94188
\(690\) −1.42692 −1.42692
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) −1.00000 −1.00000
\(694\) 1.37720 1.37720
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.119819 −0.119819
\(701\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(702\) −1.42692 −1.42692
\(703\) 0 0
\(704\) −1.70921 −1.70921
\(705\) 2.01199 2.01199
\(706\) 0 0
\(707\) −0.170972 −0.170972
\(708\) 0 0
\(709\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.255948 0.255948
\(713\) 1.13613 1.13613
\(714\) 0.453262 0.453262
\(715\) −1.94188 −1.94188
\(716\) 0 0
\(717\) 0.426920 0.426920
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −0.546738 −0.546738
\(721\) 0 0
\(722\) −0.709210 −0.709210
\(723\) 3.13613 3.13613
\(724\) 0 0
\(725\) 0 0
\(726\) −3.48012 −3.48012
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0.255948 0.255948
\(729\) −0.514964 −0.514964
\(730\) 0 0
\(731\) 1.06170 1.06170
\(732\) 0 0
\(733\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(734\) −0.170972 −0.170972
\(735\) −1.66799 −1.66799
\(736\) −1.00000 −1.00000
\(737\) 3.77091 3.77091
\(738\) 0 0
\(739\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.332007 0.332007
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 1.88018 1.88018
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) −1.44486 −1.44486
\(749\) 0 0
\(750\) −1.25595 −1.25595
\(751\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(752\) −0.290790 −0.290790
\(753\) 0 0
\(754\) 0 0
\(755\) −0.709210 −0.709210
\(756\) −0.241073 −0.241073
\(757\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(758\) 0 0
\(759\) −3.90704 −3.90704
\(760\) 0 0
\(761\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(762\) 1.88018 1.88018
\(763\) 0 0
\(764\) 0.352493 0.352493
\(765\) −3.19783 −3.19783
\(766\) 0 0
\(767\) 0 0
\(768\) −1.88018 −1.88018
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0.332007 0.332007
\(771\) 0 0
\(772\) −0.564681 −0.564681
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 1.07443 1.07443
\(775\) 1.00000 1.00000
\(776\) 1.88018 1.88018
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −0.880181 −0.880181
\(781\) 0 0
\(782\) 1.20623 1.20623
\(783\) 0 0
\(784\) 0.241073 0.241073
\(785\) 0 0
\(786\) 1.88018 1.88018
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) −1.25595 −1.25595
\(790\) 0 0
\(791\) 0 0
\(792\) −4.40406 −4.40406
\(793\) 0 0
\(794\) 1.37720 1.37720
\(795\) −3.43891 −3.43891
\(796\) 0 0
\(797\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(798\) 0 0
\(799\) −1.70081 −1.70081
\(800\) −0.880181 −0.880181
\(801\) 0.514964 0.514964
\(802\) −0.805754 −0.805754
\(803\) 0 0
\(804\) 1.70921 1.70921
\(805\) 0.273891 0.273891
\(806\) −0.709210 −0.709210
\(807\) 0 0
\(808\) −0.752970 −0.752970
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) −1.01199 −1.01199
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) −2.65109 −2.65109
\(814\) 0 0
\(815\) −1.49702 −1.49702
\(816\) 0.678542 0.678542
\(817\) 0 0
\(818\) −0.805754 −0.805754
\(819\) 0.514964 0.514964
\(820\) 0 0
\(821\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(822\) 0 0
\(823\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(824\) 0 0
\(825\) −3.43891 −3.43891
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) −1.20623 −1.20623
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 2.01199 2.01199
\(832\) 0.880181 0.880181
\(833\) 1.41002 1.41002
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 2.01199 2.01199
\(838\) −1.25595 −1.25595
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0.453262 0.453262
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) −0.880181 −0.880181
\(845\) 1.00000 1.00000
\(846\) −1.72120 −1.72120
\(847\) 0.667993 0.667993
\(848\) 0.497021 0.497021
\(849\) 0 0
\(850\) 1.06170 1.06170
\(851\) 0 0
\(852\) 0 0
\(853\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 2.43891 2.43891
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 0.352493 0.352493
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) −1.77091 −1.77091
\(865\) 0 0
\(866\) 0.502979 0.502979
\(867\) 2.19783 2.19783
\(868\) −0.119819 −0.119819
\(869\) 0 0
\(870\) 0 0
\(871\) −1.94188 −1.94188
\(872\) 0 0
\(873\) 3.78290 3.78290
\(874\) 0 0
\(875\) 0.241073 0.241073
\(876\) 0 0
\(877\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(878\) −0.805754 −0.805754
\(879\) 0.426920 0.426920
\(880\) 0.497021 0.497021
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 1.42692 1.42692
\(883\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(884\) 0.744052 0.744052
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) −0.360892 −0.360892
\(890\) −0.170972 −0.170972
\(891\) −2.77091 −2.77091
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0.0617023 0.0617023
\(897\) 2.01199 2.01199
\(898\) 0.502979 0.502979
\(899\) 0 0
\(900\) −1.06170 −1.06170
\(901\) 2.90704 2.90704
\(902\) 0 0
\(903\) −0.302776 −0.302776
\(904\) 0 0
\(905\) 0 0
\(906\) 0.890731 0.890731
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0.744052 0.744052
\(909\) −1.51496 −1.51496
\(910\) −0.170972 −0.170972
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.119819 −0.119819
\(917\) −0.360892 −0.360892
\(918\) 2.13613 2.13613
\(919\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(920\) 1.20623 1.20623
\(921\) −1.25595 −1.25595
\(922\) −1.25595 −1.25595
\(923\) 0 0
\(924\) 0.412045 0.412045
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(930\) −1.25595 −1.25595
\(931\) 0 0
\(932\) 0 0
\(933\) 2.01199 2.01199
\(934\) 0 0
\(935\) 2.90704 2.90704
\(936\) 2.26793 2.26793
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0.332007 0.332007
\(939\) 2.01199 2.01199
\(940\) −0.564681 −0.564681
\(941\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0.485036 0.485036
\(946\) −0.976726 −0.976726
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −2.65109 −2.65109
\(952\) −0.383160 −0.383160
\(953\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(954\) 2.94188 2.94188
\(955\) −0.709210 −0.709210
\(956\) −0.119819 −0.119819
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.55872 1.55872
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) −0.880181 −0.880181
\(965\) 1.13613 1.13613
\(966\) −0.343992 −0.343992
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 2.94188 2.94188
\(969\) 0 0
\(970\) −1.25595 −1.25595
\(971\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(972\) −0.255948 −0.255948
\(973\) 0 0
\(974\) 0 0
\(975\) 1.77091 1.77091
\(976\) 0 0
\(977\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(978\) 1.88018 1.88018
\(979\) −0.468136 −0.468136
\(980\) 0.468136 0.468136
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0.485036 0.485036
\(988\) 0 0
\(989\) −0.805754 −0.805754
\(990\) 2.94188 2.94188
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) −0.880181 −0.880181
\(993\) −2.65109 −2.65109
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0.502979 0.502979
\(999\) 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.b.2014.3 6
5.4 even 2 2015.1.h.e.2014.4 yes 6
13.12 even 2 2015.1.h.d.2014.4 yes 6
31.30 odd 2 2015.1.h.c.2014.3 yes 6
65.64 even 2 2015.1.h.c.2014.3 yes 6
155.154 odd 2 2015.1.h.d.2014.4 yes 6
403.402 odd 2 2015.1.h.e.2014.4 yes 6
2015.2014 odd 2 CM 2015.1.h.b.2014.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2015.1.h.b.2014.3 6 1.1 even 1 trivial
2015.1.h.b.2014.3 6 2015.2014 odd 2 CM
2015.1.h.c.2014.3 yes 6 31.30 odd 2
2015.1.h.c.2014.3 yes 6 65.64 even 2
2015.1.h.d.2014.4 yes 6 13.12 even 2
2015.1.h.d.2014.4 yes 6 155.154 odd 2
2015.1.h.e.2014.4 yes 6 5.4 even 2
2015.1.h.e.2014.4 yes 6 403.402 odd 2