Properties

Label 2015.1.h.c.2014.2
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

Related objects

Downloads

Learn more about

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 2014.2
Root \(1.49702\) of defining polynomial
Character \(\chi\) \(=\) 2015.2014

$q$-expansion

\(f(q)\) \(=\) \(q-1.49702 q^{2} -1.13613 q^{3} +1.24107 q^{4} +1.00000 q^{5} +1.70081 q^{6} -1.94188 q^{7} -0.360892 q^{8} +0.290790 q^{9} +O(q^{10})\) \(q-1.49702 q^{2} -1.13613 q^{3} +1.24107 q^{4} +1.00000 q^{5} +1.70081 q^{6} -1.94188 q^{7} -0.360892 q^{8} +0.290790 q^{9} -1.49702 q^{10} -1.77091 q^{11} -1.41002 q^{12} -1.00000 q^{13} +2.90704 q^{14} -1.13613 q^{15} -0.700810 q^{16} -0.241073 q^{17} -0.435319 q^{18} +1.24107 q^{20} +2.20623 q^{21} +2.65109 q^{22} +0.709210 q^{23} +0.410020 q^{24} +1.00000 q^{25} +1.49702 q^{26} +0.805754 q^{27} -2.41002 q^{28} +1.70081 q^{30} -1.00000 q^{31} +1.41002 q^{32} +2.01199 q^{33} +0.360892 q^{34} -1.94188 q^{35} +0.360892 q^{36} +1.13613 q^{39} -0.360892 q^{40} -3.30278 q^{42} +1.49702 q^{43} -2.19783 q^{44} +0.290790 q^{45} -1.06170 q^{46} -0.709210 q^{47} +0.796211 q^{48} +2.77091 q^{49} -1.49702 q^{50} +0.273891 q^{51} -1.24107 q^{52} -1.77091 q^{53} -1.20623 q^{54} -1.77091 q^{55} +0.700810 q^{56} -1.41002 q^{60} +1.49702 q^{62} -0.564681 q^{63} -1.41002 q^{64} -1.00000 q^{65} -3.01199 q^{66} +1.77091 q^{67} -0.299190 q^{68} -0.805754 q^{69} +2.90704 q^{70} -0.104944 q^{72} -1.13613 q^{75} +3.43891 q^{77} -1.70081 q^{78} -0.700810 q^{80} -1.20623 q^{81} +2.73809 q^{84} -0.241073 q^{85} -2.24107 q^{86} +0.639108 q^{88} +1.94188 q^{89} -0.435319 q^{90} +1.94188 q^{91} +0.880181 q^{92} +1.13613 q^{93} +1.06170 q^{94} -1.60197 q^{96} +1.13613 q^{97} -4.14811 q^{98} -0.514964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - q^{2} + q^{3} + 5q^{4} + 6q^{5} + 2q^{6} - q^{7} - 2q^{8} + 5q^{9} + O(q^{10}) \) \( 6q - q^{2} + q^{3} + 5q^{4} + 6q^{5} + 2q^{6} - q^{7} - 2q^{8} + 5q^{9} - q^{10} + q^{11} + 3q^{12} - 6q^{13} - 2q^{14} + q^{15} + 4q^{16} + q^{17} - 3q^{18} + 5q^{20} + 2q^{21} + 2q^{22} + q^{23} - 9q^{24} + 6q^{25} + q^{26} + 2q^{27} - 3q^{28} + 2q^{30} - 6q^{31} - 3q^{32} - 2q^{33} + 2q^{34} - q^{35} + 2q^{36} - q^{39} - 2q^{40} - 9q^{42} + q^{43} + 3q^{44} + 5q^{45} + 2q^{46} - q^{47} + 5q^{48} + 5q^{49} - q^{50} - 2q^{51} - 5q^{52} + q^{53} + 4q^{54} + q^{55} - 4q^{56} + 3q^{60} + q^{62} - 3q^{63} + 3q^{64} - 6q^{65} - 4q^{66} - q^{67} - 10q^{68} - 2q^{69} - 2q^{70} - 6q^{72} + q^{75} + 2q^{77} - 2q^{78} + 4q^{80} + 4q^{81} + 6q^{84} + q^{85} - 11q^{86} + 4q^{88} + q^{89} - 3q^{90} + q^{91} + 3q^{92} - q^{93} - 2q^{94} - 7q^{96} - q^{97} - 3q^{98} + 3q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(3\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(4\) 1.24107 1.24107
\(5\) 1.00000 1.00000
\(6\) 1.70081 1.70081
\(7\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(8\) −0.360892 −0.360892
\(9\) 0.290790 0.290790
\(10\) −1.49702 −1.49702
\(11\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(12\) −1.41002 −1.41002
\(13\) −1.00000 −1.00000
\(14\) 2.90704 2.90704
\(15\) −1.13613 −1.13613
\(16\) −0.700810 −0.700810
\(17\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(18\) −0.435319 −0.435319
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 1.24107 1.24107
\(21\) 2.20623 2.20623
\(22\) 2.65109 2.65109
\(23\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(24\) 0.410020 0.410020
\(25\) 1.00000 1.00000
\(26\) 1.49702 1.49702
\(27\) 0.805754 0.805754
\(28\) −2.41002 −2.41002
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 1.70081 1.70081
\(31\) −1.00000 −1.00000
\(32\) 1.41002 1.41002
\(33\) 2.01199 2.01199
\(34\) 0.360892 0.360892
\(35\) −1.94188 −1.94188
\(36\) 0.360892 0.360892
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 1.13613 1.13613
\(40\) −0.360892 −0.360892
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) −3.30278 −3.30278
\(43\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(44\) −2.19783 −2.19783
\(45\) 0.290790 0.290790
\(46\) −1.06170 −1.06170
\(47\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(48\) 0.796211 0.796211
\(49\) 2.77091 2.77091
\(50\) −1.49702 −1.49702
\(51\) 0.273891 0.273891
\(52\) −1.24107 −1.24107
\(53\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(54\) −1.20623 −1.20623
\(55\) −1.77091 −1.77091
\(56\) 0.700810 0.700810
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) −1.41002 −1.41002
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 1.49702 1.49702
\(63\) −0.564681 −0.564681
\(64\) −1.41002 −1.41002
\(65\) −1.00000 −1.00000
\(66\) −3.01199 −3.01199
\(67\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(68\) −0.299190 −0.299190
\(69\) −0.805754 −0.805754
\(70\) 2.90704 2.90704
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −0.104944 −0.104944
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −1.13613 −1.13613
\(76\) 0 0
\(77\) 3.43891 3.43891
\(78\) −1.70081 −1.70081
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −0.700810 −0.700810
\(81\) −1.20623 −1.20623
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 2.73809 2.73809
\(85\) −0.241073 −0.241073
\(86\) −2.24107 −2.24107
\(87\) 0 0
\(88\) 0.639108 0.639108
\(89\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(90\) −0.435319 −0.435319
\(91\) 1.94188 1.94188
\(92\) 0.880181 0.880181
\(93\) 1.13613 1.13613
\(94\) 1.06170 1.06170
\(95\) 0 0
\(96\) −1.60197 −1.60197
\(97\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(98\) −4.14811 −4.14811
\(99\) −0.514964 −0.514964
\(100\) 1.24107 1.24107
\(101\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(102\) −0.410020 −0.410020
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0.360892 0.360892
\(105\) 2.20623 2.20623
\(106\) 2.65109 2.65109
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 1.00000 1.00000
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 2.65109 2.65109
\(111\) 0 0
\(112\) 1.36089 1.36089
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0.709210 0.709210
\(116\) 0 0
\(117\) −0.290790 −0.290790
\(118\) 0 0
\(119\) 0.468136 0.468136
\(120\) 0.410020 0.410020
\(121\) 2.13613 2.13613
\(122\) 0 0
\(123\) 0 0
\(124\) −1.24107 −1.24107
\(125\) 1.00000 1.00000
\(126\) 0.845339 0.845339
\(127\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(128\) 0.700810 0.700810
\(129\) −1.70081 −1.70081
\(130\) 1.49702 1.49702
\(131\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(132\) 2.49702 2.49702
\(133\) 0 0
\(134\) −2.65109 −2.65109
\(135\) 0.805754 0.805754
\(136\) 0.0870014 0.0870014
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 1.20623 1.20623
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) −2.41002 −2.41002
\(141\) 0.805754 0.805754
\(142\) 0 0
\(143\) 1.77091 1.77091
\(144\) −0.203789 −0.203789
\(145\) 0 0
\(146\) 0 0
\(147\) −3.14811 −3.14811
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 1.70081 1.70081
\(151\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(152\) 0 0
\(153\) −0.0701018 −0.0701018
\(154\) −5.14811 −5.14811
\(155\) −1.00000 −1.00000
\(156\) 1.41002 1.41002
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) 2.01199 2.01199
\(160\) 1.41002 1.41002
\(161\) −1.37720 −1.37720
\(162\) 1.80575 1.80575
\(163\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(164\) 0 0
\(165\) 2.01199 2.01199
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) −0.796211 −0.796211
\(169\) 1.00000 1.00000
\(170\) 0.360892 0.360892
\(171\) 0 0
\(172\) 1.85791 1.85791
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) −1.94188 −1.94188
\(176\) 1.24107 1.24107
\(177\) 0 0
\(178\) −2.90704 −2.90704
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.360892 0.360892
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −2.90704 −2.90704
\(183\) 0 0
\(184\) −0.255948 −0.255948
\(185\) 0 0
\(186\) −1.70081 −1.70081
\(187\) 0.426920 0.426920
\(188\) −0.880181 −0.880181
\(189\) −1.56468 −1.56468
\(190\) 0 0
\(191\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(192\) 1.60197 1.60197
\(193\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(194\) −1.70081 −1.70081
\(195\) 1.13613 1.13613
\(196\) 3.43891 3.43891
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0.770912 0.770912
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −0.360892 −0.360892
\(201\) −2.01199 −2.01199
\(202\) 2.24107 2.24107
\(203\) 0 0
\(204\) 0.339918 0.339918
\(205\) 0 0
\(206\) 0 0
\(207\) 0.206231 0.206231
\(208\) 0.700810 0.700810
\(209\) 0 0
\(210\) −3.30278 −3.30278
\(211\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(212\) −2.19783 −2.19783
\(213\) 0 0
\(214\) 0 0
\(215\) 1.49702 1.49702
\(216\) −0.290790 −0.290790
\(217\) 1.94188 1.94188
\(218\) 0 0
\(219\) 0 0
\(220\) −2.19783 −2.19783
\(221\) 0.241073 0.241073
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) −2.73809 −2.73809
\(225\) 0.290790 0.290790
\(226\) 0 0
\(227\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(228\) 0 0
\(229\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(230\) −1.06170 −1.06170
\(231\) −3.90704 −3.90704
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0.435319 0.435319
\(235\) −0.709210 −0.709210
\(236\) 0 0
\(237\) 0 0
\(238\) −0.700810 −0.700810
\(239\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(240\) 0.796211 0.796211
\(241\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(242\) −3.19783 −3.19783
\(243\) 0.564681 0.564681
\(244\) 0 0
\(245\) 2.77091 2.77091
\(246\) 0 0
\(247\) 0 0
\(248\) 0.360892 0.360892
\(249\) 0 0
\(250\) −1.49702 −1.49702
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −0.700810 −0.700810
\(253\) −1.25595 −1.25595
\(254\) 0.360892 0.360892
\(255\) 0.273891 0.273891
\(256\) 0.360892 0.360892
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 2.54615 2.54615
\(259\) 0 0
\(260\) −1.24107 −1.24107
\(261\) 0 0
\(262\) −0.360892 −0.360892
\(263\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(264\) −0.726109 −0.726109
\(265\) −1.77091 −1.77091
\(266\) 0 0
\(267\) −2.20623 −2.20623
\(268\) 2.19783 2.19783
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −1.20623 −1.20623
\(271\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(272\) 0.168947 0.168947
\(273\) −2.20623 −2.20623
\(274\) 0 0
\(275\) −1.77091 −1.77091
\(276\) −1.00000 −1.00000
\(277\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(278\) 0 0
\(279\) −0.290790 −0.290790
\(280\) 0.700810 0.700810
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −1.20623 −1.20623
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −2.65109 −2.65109
\(287\) 0 0
\(288\) 0.410020 0.410020
\(289\) −0.941884 −0.941884
\(290\) 0 0
\(291\) −1.29079 −1.29079
\(292\) 0 0
\(293\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(294\) 4.71280 4.71280
\(295\) 0 0
\(296\) 0 0
\(297\) −1.42692 −1.42692
\(298\) 0 0
\(299\) −0.709210 −0.709210
\(300\) −1.41002 −1.41002
\(301\) −2.90704 −2.90704
\(302\) −2.24107 −2.24107
\(303\) 1.70081 1.70081
\(304\) 0 0
\(305\) 0 0
\(306\) 0.104944 0.104944
\(307\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(308\) 4.26793 4.26793
\(309\) 0 0
\(310\) 1.49702 1.49702
\(311\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(312\) −0.410020 −0.410020
\(313\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(314\) 0 0
\(315\) −0.564681 −0.564681
\(316\) 0 0
\(317\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(318\) −3.01199 −3.01199
\(319\) 0 0
\(320\) −1.41002 −1.41002
\(321\) 0 0
\(322\) 2.06170 2.06170
\(323\) 0 0
\(324\) −1.49702 −1.49702
\(325\) −1.00000 −1.00000
\(326\) −0.360892 −0.360892
\(327\) 0 0
\(328\) 0 0
\(329\) 1.37720 1.37720
\(330\) −3.01199 −3.01199
\(331\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.77091 1.77091
\(336\) −1.54615 −1.54615
\(337\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(338\) −1.49702 −1.49702
\(339\) 0 0
\(340\) −0.299190 −0.299190
\(341\) 1.77091 1.77091
\(342\) 0 0
\(343\) −3.43891 −3.43891
\(344\) −0.540263 −0.540263
\(345\) −0.805754 −0.805754
\(346\) 0 0
\(347\) −1.77091 −1.77091 −0.885456 0.464723i \(-0.846154\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 2.90704 2.90704
\(351\) −0.805754 −0.805754
\(352\) −2.49702 −2.49702
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 2.41002 2.41002
\(357\) −0.531864 −0.531864
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) −0.104944 −0.104944
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) −2.42692 −2.42692
\(364\) 2.41002 2.41002
\(365\) 0 0
\(366\) 0 0
\(367\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(368\) −0.497021 −0.497021
\(369\) 0 0
\(370\) 0 0
\(371\) 3.43891 3.43891
\(372\) 1.41002 1.41002
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) −0.639108 −0.639108
\(375\) −1.13613 −1.13613
\(376\) 0.255948 0.255948
\(377\) 0 0
\(378\) 2.34236 2.34236
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0.273891 0.273891
\(382\) 2.24107 2.24107
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) −0.796211 −0.796211
\(385\) 3.43891 3.43891
\(386\) 1.06170 1.06170
\(387\) 0.435319 0.435319
\(388\) 1.41002 1.41002
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) −1.70081 −1.70081
\(391\) −0.170972 −0.170972
\(392\) −1.00000 −1.00000
\(393\) −0.273891 −0.273891
\(394\) 0 0
\(395\) 0 0
\(396\) −0.639108 −0.639108
\(397\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.700810 −0.700810
\(401\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(402\) 3.01199 3.01199
\(403\) 1.00000 1.00000
\(404\) −1.85791 −1.85791
\(405\) −1.20623 −1.20623
\(406\) 0 0
\(407\) 0 0
\(408\) −0.0988449 −0.0988449
\(409\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −0.308733 −0.308733
\(415\) 0 0
\(416\) −1.41002 −1.41002
\(417\) 0 0
\(418\) 0 0
\(419\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(420\) 2.73809 2.73809
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) −1.70081 −1.70081
\(423\) −0.206231 −0.206231
\(424\) 0.639108 0.639108
\(425\) −0.241073 −0.241073
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2.01199 −2.01199
\(430\) −2.24107 −2.24107
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −0.564681 −0.564681
\(433\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(434\) −2.90704 −2.90704
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(440\) 0.639108 0.639108
\(441\) 0.805754 0.805754
\(442\) −0.360892 −0.360892
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 1.94188 1.94188
\(446\) 0 0
\(447\) 0 0
\(448\) 2.73809 2.73809
\(449\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(450\) −0.435319 −0.435319
\(451\) 0 0
\(452\) 0 0
\(453\) −1.70081 −1.70081
\(454\) −0.360892 −0.360892
\(455\) 1.94188 1.94188
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −2.90704 −2.90704
\(459\) −0.194246 −0.194246
\(460\) 0.880181 0.880181
\(461\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(462\) 5.84893 5.84893
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 1.13613 1.13613
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) −0.360892 −0.360892
\(469\) −3.43891 −3.43891
\(470\) 1.06170 1.06170
\(471\) 0 0
\(472\) 0 0
\(473\) −2.65109 −2.65109
\(474\) 0 0
\(475\) 0 0
\(476\) 0.580992 0.580992
\(477\) −0.514964 −0.514964
\(478\) −2.90704 −2.90704
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) −1.60197 −1.60197
\(481\) 0 0
\(482\) 1.70081 1.70081
\(483\) 1.56468 1.56468
\(484\) 2.65109 2.65109
\(485\) 1.13613 1.13613
\(486\) −0.845339 −0.845339
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) −0.273891 −0.273891
\(490\) −4.14811 −4.14811
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −0.514964 −0.514964
\(496\) 0.700810 0.700810
\(497\) 0 0
\(498\) 0 0
\(499\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(500\) 1.24107 1.24107
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0.203789 0.203789
\(505\) −1.49702 −1.49702
\(506\) 1.88018 1.88018
\(507\) −1.13613 −1.13613
\(508\) −0.299190 −0.299190
\(509\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(510\) −0.410020 −0.410020
\(511\) 0 0
\(512\) −1.24107 −1.24107
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) −2.11083 −2.11083
\(517\) 1.25595 1.25595
\(518\) 0 0
\(519\) 0 0
\(520\) 0.360892 0.360892
\(521\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(522\) 0 0
\(523\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(524\) 0.299190 0.299190
\(525\) 2.20623 2.20623
\(526\) −2.24107 −2.24107
\(527\) 0.241073 0.241073
\(528\) −1.41002 −1.41002
\(529\) −0.497021 −0.497021
\(530\) 2.65109 2.65109
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 3.30278 3.30278
\(535\) 0 0
\(536\) −0.639108 −0.639108
\(537\) 0 0
\(538\) 0 0
\(539\) −4.90704 −4.90704
\(540\) 1.00000 1.00000
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0.360892 0.360892
\(543\) 0 0
\(544\) −0.339918 −0.339918
\(545\) 0 0
\(546\) 3.30278 3.30278
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 2.65109 2.65109
\(551\) 0 0
\(552\) 0.290790 0.290790
\(553\) 0 0
\(554\) −1.06170 −1.06170
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0.435319 0.435319
\(559\) −1.49702 −1.49702
\(560\) 1.36089 1.36089
\(561\) −0.485036 −0.485036
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 1.00000 1.00000
\(565\) 0 0
\(566\) 0 0
\(567\) 2.34236 2.34236
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 2.19783 2.19783
\(573\) 1.70081 1.70081
\(574\) 0 0
\(575\) 0.709210 0.709210
\(576\) −0.410020 −0.410020
\(577\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(578\) 1.41002 1.41002
\(579\) 0.805754 0.805754
\(580\) 0 0
\(581\) 0 0
\(582\) 1.93234 1.93234
\(583\) 3.13613 3.13613
\(584\) 0 0
\(585\) −0.290790 −0.290790
\(586\) 2.90704 2.90704
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −3.90704 −3.90704
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(594\) 2.13613 2.13613
\(595\) 0.468136 0.468136
\(596\) 0 0
\(597\) 0 0
\(598\) 1.06170 1.06170
\(599\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(600\) 0.410020 0.410020
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 4.35190 4.35190
\(603\) 0.514964 0.514964
\(604\) 1.85791 1.85791
\(605\) 2.13613 2.13613
\(606\) −2.54615 −2.54615
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.709210 0.709210
\(612\) −0.0870014 −0.0870014
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 2.24107 2.24107
\(615\) 0 0
\(616\) −1.24107 −1.24107
\(617\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(618\) 0 0
\(619\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(620\) −1.24107 −1.24107
\(621\) 0.571449 0.571449
\(622\) 1.06170 1.06170
\(623\) −3.77091 −3.77091
\(624\) −0.796211 −0.796211
\(625\) 1.00000 1.00000
\(626\) −1.06170 −1.06170
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.845339 0.845339
\(631\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(632\) 0 0
\(633\) −1.29079 −1.29079
\(634\) −0.360892 −0.360892
\(635\) −0.241073 −0.241073
\(636\) 2.49702 2.49702
\(637\) −2.77091 −2.77091
\(638\) 0 0
\(639\) 0 0
\(640\) 0.700810 0.700810
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) −1.70921 −1.70921
\(645\) −1.70081 −1.70081
\(646\) 0 0
\(647\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(648\) 0.435319 0.435319
\(649\) 0 0
\(650\) 1.49702 1.49702
\(651\) −2.20623 −2.20623
\(652\) 0.299190 0.299190
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0.241073 0.241073
\(656\) 0 0
\(657\) 0 0
\(658\) −2.06170 −2.06170
\(659\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(660\) 2.49702 2.49702
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0.360892 0.360892
\(663\) −0.273891 −0.273891
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) −2.65109 −2.65109
\(671\) 0 0
\(672\) 3.11083 3.11083
\(673\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(674\) 2.65109 2.65109
\(675\) 0.805754 0.805754
\(676\) 1.24107 1.24107
\(677\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(678\) 0 0
\(679\) −2.20623 −2.20623
\(680\) 0.0870014 0.0870014
\(681\) −0.273891 −0.273891
\(682\) −2.65109 −2.65109
\(683\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 5.14811 5.14811
\(687\) −2.20623 −2.20623
\(688\) −1.04913 −1.04913
\(689\) 1.77091 1.77091
\(690\) 1.20623 1.20623
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 1.00000 1.00000
\(694\) 2.65109 2.65109
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −2.41002 −2.41002
\(701\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(702\) 1.20623 1.20623
\(703\) 0 0
\(704\) 2.49702 2.49702
\(705\) 0.805754 0.805754
\(706\) 0 0
\(707\) 2.90704 2.90704
\(708\) 0 0
\(709\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.700810 −0.700810
\(713\) −0.709210 −0.709210
\(714\) 0.796211 0.796211
\(715\) 1.77091 1.77091
\(716\) 0 0
\(717\) −2.20623 −2.20623
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −0.203789 −0.203789
\(721\) 0 0
\(722\) −1.49702 −1.49702
\(723\) 1.29079 1.29079
\(724\) 0 0
\(725\) 0 0
\(726\) 3.63315 3.63315
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) −0.700810 −0.700810
\(729\) 0.564681 0.564681
\(730\) 0 0
\(731\) −0.360892 −0.360892
\(732\) 0 0
\(733\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(734\) −2.90704 −2.90704
\(735\) −3.14811 −3.14811
\(736\) 1.00000 1.00000
\(737\) −3.13613 −3.13613
\(738\) 0 0
\(739\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −5.14811 −5.14811
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) −0.410020 −0.410020
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0.529839 0.529839
\(749\) 0 0
\(750\) 1.70081 1.70081
\(751\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(752\) 0.497021 0.497021
\(753\) 0 0
\(754\) 0 0
\(755\) 1.49702 1.49702
\(756\) −1.94188 −1.94188
\(757\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(758\) 0 0
\(759\) 1.42692 1.42692
\(760\) 0 0
\(761\) 1.49702 1.49702 0.748511 0.663123i \(-0.230769\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(762\) −0.410020 −0.410020
\(763\) 0 0
\(764\) −1.85791 −1.85791
\(765\) −0.0701018 −0.0701018
\(766\) 0 0
\(767\) 0 0
\(768\) −0.410020 −0.410020
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) −5.14811 −5.14811
\(771\) 0 0
\(772\) −0.880181 −0.880181
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) −0.651682 −0.651682
\(775\) −1.00000 −1.00000
\(776\) −0.410020 −0.410020
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 1.41002 1.41002
\(781\) 0 0
\(782\) 0.255948 0.255948
\(783\) 0 0
\(784\) −1.94188 −1.94188
\(785\) 0 0
\(786\) 0.410020 0.410020
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) −1.70081 −1.70081
\(790\) 0 0
\(791\) 0 0
\(792\) 0.185846 0.185846
\(793\) 0 0
\(794\) −2.65109 −2.65109
\(795\) 2.01199 2.01199
\(796\) 0 0
\(797\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(798\) 0 0
\(799\) 0.170972 0.170972
\(800\) 1.41002 1.41002
\(801\) 0.564681 0.564681
\(802\) −1.06170 −1.06170
\(803\) 0 0
\(804\) −2.49702 −2.49702
\(805\) −1.37720 −1.37720
\(806\) −1.49702 −1.49702
\(807\) 0 0
\(808\) 0.540263 0.540263
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 1.80575 1.80575
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0.273891 0.273891
\(814\) 0 0
\(815\) 0.241073 0.241073
\(816\) −0.191945 −0.191945
\(817\) 0 0
\(818\) −1.06170 −1.06170
\(819\) 0.564681 0.564681
\(820\) 0 0
\(821\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(822\) 0 0
\(823\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(824\) 0 0
\(825\) 2.01199 2.01199
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0.255948 0.255948
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) −0.805754 −0.805754
\(832\) 1.41002 1.41002
\(833\) −0.667993 −0.667993
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −0.805754 −0.805754
\(838\) −1.70081 −1.70081
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) −0.796211 −0.796211
\(841\) 1.00000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 1.41002 1.41002
\(845\) 1.00000 1.00000
\(846\) 0.308733 0.308733
\(847\) −4.14811 −4.14811
\(848\) 1.24107 1.24107
\(849\) 0 0
\(850\) 0.360892 0.360892
\(851\) 0 0
\(852\) 0 0
\(853\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 3.01199 3.01199
\(859\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(860\) 1.85791 1.85791
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 1.13613 1.13613
\(865\) 0 0
\(866\) −2.24107 −2.24107
\(867\) 1.07010 1.07010
\(868\) 2.41002 2.41002
\(869\) 0 0
\(870\) 0 0
\(871\) −1.77091 −1.77091
\(872\) 0 0
\(873\) 0.330375 0.330375
\(874\) 0 0
\(875\) −1.94188 −1.94188
\(876\) 0 0
\(877\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(878\) 1.06170 1.06170
\(879\) 2.20623 2.20623
\(880\) 1.24107 1.24107
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −1.20623 −1.20623
\(883\) −0.241073 −0.241073 −0.120537 0.992709i \(-0.538462\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(884\) 0.299190 0.299190
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0.468136 0.468136
\(890\) −2.90704 −2.90704
\(891\) 2.13613 2.13613
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) −1.36089 −1.36089
\(897\) 0.805754 0.805754
\(898\) −2.24107 −2.24107
\(899\) 0 0
\(900\) 0.360892 0.360892
\(901\) 0.426920 0.426920
\(902\) 0 0
\(903\) 3.30278 3.30278
\(904\) 0 0
\(905\) 0 0
\(906\) 2.54615 2.54615
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) 0.299190 0.299190
\(909\) −0.435319 −0.435319
\(910\) −2.90704 −2.90704
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 2.41002 2.41002
\(917\) −0.468136 −0.468136
\(918\) 0.290790 0.290790
\(919\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(920\) −0.255948 −0.255948
\(921\) 1.70081 1.70081
\(922\) 1.70081 1.70081
\(923\) 0 0
\(924\) −4.84893 −4.84893
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0.709210 0.709210 0.354605 0.935016i \(-0.384615\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(930\) −1.70081 −1.70081
\(931\) 0 0
\(932\) 0 0
\(933\) 0.805754 0.805754
\(934\) 0 0
\(935\) 0.426920 0.426920
\(936\) 0.104944 0.104944
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 5.14811 5.14811
\(939\) −0.805754 −0.805754
\(940\) −0.880181 −0.880181
\(941\) −1.13613 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) −1.56468 −1.56468
\(946\) 3.96874 3.96874
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −0.273891 −0.273891
\(952\) −0.168947 −0.168947
\(953\) 1.94188 1.94188 0.970942 0.239316i \(-0.0769231\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(954\) 0.770912 0.770912
\(955\) −1.49702 −1.49702
\(956\) 2.41002 2.41002
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.60197 1.60197
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) −1.41002 −1.41002
\(965\) −0.709210 −0.709210
\(966\) −2.34236 −2.34236
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −0.770912 −0.770912
\(969\) 0 0
\(970\) −1.70081 −1.70081
\(971\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(972\) 0.700810 0.700810
\(973\) 0 0
\(974\) 0 0
\(975\) 1.13613 1.13613
\(976\) 0 0
\(977\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(978\) 0.410020 0.410020
\(979\) −3.43891 −3.43891
\(980\) 3.43891 3.43891
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −1.56468 −1.56468
\(988\) 0 0
\(989\) 1.06170 1.06170
\(990\) 0.770912 0.770912
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) −1.41002 −1.41002
\(993\) 0.273891 0.273891
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) −2.24107 −2.24107
\(999\) 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.2014.2 yes 6
5.4 even 2 2015.1.h.d.2014.5 yes 6
13.12 even 2 2015.1.h.e.2014.5 yes 6
31.30 odd 2 2015.1.h.b.2014.2 6
65.64 even 2 2015.1.h.b.2014.2 6
155.154 odd 2 2015.1.h.e.2014.5 yes 6
403.402 odd 2 2015.1.h.d.2014.5 yes 6
2015.2014 odd 2 CM 2015.1.h.c.2014.2 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2015.1.h.b.2014.2 6 31.30 odd 2
2015.1.h.b.2014.2 6 65.64 even 2
2015.1.h.c.2014.2 yes 6 1.1 even 1 trivial
2015.1.h.c.2014.2 yes 6 2015.2014 odd 2 CM
2015.1.h.d.2014.5 yes 6 5.4 even 2
2015.1.h.d.2014.5 yes 6 403.402 odd 2
2015.1.h.e.2014.5 yes 6 13.12 even 2
2015.1.h.e.2014.5 yes 6 155.154 odd 2