Properties

Label 3311.1.h.o.3310.1
Level 3311
Weight 1
Character 3311.3310
Self dual Yes
Analytic conductor 1.652
Analytic rank 0
Dimension 6
Projective image \(D_{18}\)
CM disc. -3311
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 3311 = 7 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 3311.h (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(1.65240425683\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{36})^+\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Projective image \(D_{18}\)
Projective field Galois closure of \(\mathbb{Q}[x]/(x^{18} - \cdots)\)

Embedding invariants

Embedding label 3310.1
Root \(1.96962\)
Character \(\chi\) = 3311.3310

$q$-expansion

\(f(q)\) \(=\) \(q-1.53209 q^{2} -1.96962 q^{3} +1.34730 q^{4} +1.28558 q^{5} +3.01763 q^{6} -1.00000 q^{7} -0.532089 q^{8} +2.87939 q^{9} +O(q^{10})\) \(q-1.53209 q^{2} -1.96962 q^{3} +1.34730 q^{4} +1.28558 q^{5} +3.01763 q^{6} -1.00000 q^{7} -0.532089 q^{8} +2.87939 q^{9} -1.96962 q^{10} -1.00000 q^{11} -2.65366 q^{12} -1.73205 q^{13} +1.53209 q^{14} -2.53209 q^{15} -0.532089 q^{16} +0.684040 q^{17} -4.41147 q^{18} +1.73205 q^{20} +1.96962 q^{21} +1.53209 q^{22} +1.00000 q^{23} +1.04801 q^{24} +0.652704 q^{25} +2.65366 q^{26} -3.70167 q^{27} -1.34730 q^{28} +0.347296 q^{29} +3.87939 q^{30} +1.34730 q^{32} +1.96962 q^{33} -1.04801 q^{34} -1.28558 q^{35} +3.87939 q^{36} +3.41147 q^{39} -0.684040 q^{40} -0.684040 q^{41} -3.01763 q^{42} +1.00000 q^{43} -1.34730 q^{44} +3.70167 q^{45} -1.53209 q^{46} +1.04801 q^{48} +1.00000 q^{49} -1.00000 q^{50} -1.34730 q^{51} -2.33359 q^{52} -1.87939 q^{53} +5.67128 q^{54} -1.28558 q^{55} +0.532089 q^{56} -0.532089 q^{58} -3.41147 q^{60} -2.87939 q^{63} -1.53209 q^{64} -2.22668 q^{65} -3.01763 q^{66} +1.53209 q^{67} +0.921605 q^{68} -1.96962 q^{69} +1.96962 q^{70} -1.53209 q^{72} -1.28558 q^{75} +1.00000 q^{77} -5.22668 q^{78} -0.684040 q^{80} +4.41147 q^{81} +1.04801 q^{82} -1.96962 q^{83} +2.65366 q^{84} +0.879385 q^{85} -1.53209 q^{86} -0.684040 q^{87} +0.532089 q^{88} -5.67128 q^{90} +1.73205 q^{91} +1.34730 q^{92} -2.65366 q^{96} -1.53209 q^{98} -2.87939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{4} - 6q^{7} + 6q^{8} + 6q^{9} + O(q^{10}) \) \( 6q + 6q^{4} - 6q^{7} + 6q^{8} + 6q^{9} - 6q^{11} - 6q^{15} + 6q^{16} - 6q^{18} + 6q^{23} + 6q^{25} - 6q^{28} + 12q^{30} + 6q^{32} + 12q^{36} + 6q^{43} - 6q^{44} + 6q^{49} - 6q^{50} - 6q^{51} - 6q^{56} + 6q^{58} - 6q^{63} + 6q^{77} - 18q^{78} + 6q^{81} - 6q^{85} - 6q^{88} + 6q^{92} - 6q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3311\mathbb{Z}\right)^\times\).

\(n\) \(904\) \(1893\) \(2927\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(3\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(4\) 1.34730 1.34730
\(5\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(6\) 3.01763 3.01763
\(7\) −1.00000 −1.00000
\(8\) −0.532089 −0.532089
\(9\) 2.87939 2.87939
\(10\) −1.96962 −1.96962
\(11\) −1.00000 −1.00000
\(12\) −2.65366 −2.65366
\(13\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(14\) 1.53209 1.53209
\(15\) −2.53209 −2.53209
\(16\) −0.532089 −0.532089
\(17\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(18\) −4.41147 −4.41147
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 1.73205 1.73205
\(21\) 1.96962 1.96962
\(22\) 1.53209 1.53209
\(23\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 1.04801 1.04801
\(25\) 0.652704 0.652704
\(26\) 2.65366 2.65366
\(27\) −3.70167 −3.70167
\(28\) −1.34730 −1.34730
\(29\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(30\) 3.87939 3.87939
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 1.34730 1.34730
\(33\) 1.96962 1.96962
\(34\) −1.04801 −1.04801
\(35\) −1.28558 −1.28558
\(36\) 3.87939 3.87939
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 3.41147 3.41147
\(40\) −0.684040 −0.684040
\(41\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(42\) −3.01763 −3.01763
\(43\) 1.00000 1.00000
\(44\) −1.34730 −1.34730
\(45\) 3.70167 3.70167
\(46\) −1.53209 −1.53209
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 1.04801 1.04801
\(49\) 1.00000 1.00000
\(50\) −1.00000 −1.00000
\(51\) −1.34730 −1.34730
\(52\) −2.33359 −2.33359
\(53\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(54\) 5.67128 5.67128
\(55\) −1.28558 −1.28558
\(56\) 0.532089 0.532089
\(57\) 0 0
\(58\) −0.532089 −0.532089
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) −3.41147 −3.41147
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) −2.87939 −2.87939
\(64\) −1.53209 −1.53209
\(65\) −2.22668 −2.22668
\(66\) −3.01763 −3.01763
\(67\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(68\) 0.921605 0.921605
\(69\) −1.96962 −1.96962
\(70\) 1.96962 1.96962
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −1.53209 −1.53209
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) −1.28558 −1.28558
\(76\) 0 0
\(77\) 1.00000 1.00000
\(78\) −5.22668 −5.22668
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −0.684040 −0.684040
\(81\) 4.41147 4.41147
\(82\) 1.04801 1.04801
\(83\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(84\) 2.65366 2.65366
\(85\) 0.879385 0.879385
\(86\) −1.53209 −1.53209
\(87\) −0.684040 −0.684040
\(88\) 0.532089 0.532089
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −5.67128 −5.67128
\(91\) 1.73205 1.73205
\(92\) 1.34730 1.34730
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −2.65366 −2.65366
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −1.53209 −1.53209
\(99\) −2.87939 −2.87939
\(100\) 0.879385 0.879385
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 2.06418 2.06418
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0.921605 0.921605
\(105\) 2.53209 2.53209
\(106\) 2.87939 2.87939
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −4.98724 −4.98724
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 1.96962 1.96962
\(111\) 0 0
\(112\) 0.532089 0.532089
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 1.28558 1.28558
\(116\) 0.467911 0.467911
\(117\) −4.98724 −4.98724
\(118\) 0 0
\(119\) −0.684040 −0.684040
\(120\) 1.34730 1.34730
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 1.34730 1.34730
\(124\) 0 0
\(125\) −0.446476 −0.446476
\(126\) 4.41147 4.41147
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 1.00000 1.00000
\(129\) −1.96962 −1.96962
\(130\) 3.41147 3.41147
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 2.65366 2.65366
\(133\) 0 0
\(134\) −2.34730 −2.34730
\(135\) −4.75877 −4.75877
\(136\) −0.363970 −0.363970
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 3.01763 3.01763
\(139\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(140\) −1.73205 −1.73205
\(141\) 0 0
\(142\) 0 0
\(143\) 1.73205 1.73205
\(144\) −1.53209 −1.53209
\(145\) 0.446476 0.446476
\(146\) 0 0
\(147\) −1.96962 −1.96962
\(148\) 0 0
\(149\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(150\) 1.96962 1.96962
\(151\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) 0 0
\(153\) 1.96962 1.96962
\(154\) −1.53209 −1.53209
\(155\) 0 0
\(156\) 4.59627 4.59627
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 3.70167 3.70167
\(160\) 1.73205 1.73205
\(161\) −1.00000 −1.00000
\(162\) −6.75877 −6.75877
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) −0.921605 −0.921605
\(165\) 2.53209 2.53209
\(166\) 3.01763 3.01763
\(167\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(168\) −1.04801 −1.04801
\(169\) 2.00000 2.00000
\(170\) −1.34730 −1.34730
\(171\) 0 0
\(172\) 1.34730 1.34730
\(173\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(174\) 1.04801 1.04801
\(175\) −0.652704 −0.652704
\(176\) 0.532089 0.532089
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 4.98724 4.98724
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −2.65366 −2.65366
\(183\) 0 0
\(184\) −0.532089 −0.532089
\(185\) 0 0
\(186\) 0 0
\(187\) −0.684040 −0.684040
\(188\) 0 0
\(189\) 3.70167 3.70167
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 3.01763 3.01763
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 4.38571 4.38571
\(196\) 1.34730 1.34730
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 4.41147 4.41147
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −0.347296 −0.347296
\(201\) −3.01763 −3.01763
\(202\) 0 0
\(203\) −0.347296 −0.347296
\(204\) −1.81521 −1.81521
\(205\) −0.879385 −0.879385
\(206\) 0 0
\(207\) 2.87939 2.87939
\(208\) 0.921605 0.921605
\(209\) 0 0
\(210\) −3.87939 −3.87939
\(211\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(212\) −2.53209 −2.53209
\(213\) 0 0
\(214\) 0 0
\(215\) 1.28558 1.28558
\(216\) 1.96962 1.96962
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −1.73205 −1.73205
\(221\) −1.18479 −1.18479
\(222\) 0 0
\(223\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(224\) −1.34730 −1.34730
\(225\) 1.87939 1.87939
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) −1.96962 −1.96962
\(231\) −1.96962 −1.96962
\(232\) −0.184793 −0.184793
\(233\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(234\) 7.64090 7.64090
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 1.04801 1.04801
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 1.34730 1.34730
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −1.53209 −1.53209
\(243\) −4.98724 −4.98724
\(244\) 0 0
\(245\) 1.28558 1.28558
\(246\) −2.06418 −2.06418
\(247\) 0 0
\(248\) 0 0
\(249\) 3.87939 3.87939
\(250\) 0.684040 0.684040
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −3.87939 −3.87939
\(253\) −1.00000 −1.00000
\(254\) 0 0
\(255\) −1.73205 −1.73205
\(256\) 0 0
\(257\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(258\) 3.01763 3.01763
\(259\) 0 0
\(260\) −3.00000 −3.00000
\(261\) 1.00000 1.00000
\(262\) 0 0
\(263\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) −1.04801 −1.04801
\(265\) −2.41609 −2.41609
\(266\) 0 0
\(267\) 0 0
\(268\) 2.06418 2.06418
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 7.29086 7.29086
\(271\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(272\) −0.363970 −0.363970
\(273\) −3.41147 −3.41147
\(274\) 0 0
\(275\) −0.652704 −0.652704
\(276\) −2.65366 −2.65366
\(277\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(278\) −1.96962 −1.96962
\(279\) 0 0
\(280\) 0.684040 0.684040
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −2.65366 −2.65366
\(287\) 0.684040 0.684040
\(288\) 3.87939 3.87939
\(289\) −0.532089 −0.532089
\(290\) −0.684040 −0.684040
\(291\) 0 0
\(292\) 0 0
\(293\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(294\) 3.01763 3.01763
\(295\) 0 0
\(296\) 0 0
\(297\) 3.70167 3.70167
\(298\) −2.34730 −2.34730
\(299\) −1.73205 −1.73205
\(300\) −1.73205 −1.73205
\(301\) −1.00000 −1.00000
\(302\) −1.53209 −1.53209
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) −3.01763 −3.01763
\(307\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(308\) 1.34730 1.34730
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) −1.81521 −1.81521
\(313\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(314\) 0 0
\(315\) −3.70167 −3.70167
\(316\) 0 0
\(317\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) −5.67128 −5.67128
\(319\) −0.347296 −0.347296
\(320\) −1.96962 −1.96962
\(321\) 0 0
\(322\) 1.53209 1.53209
\(323\) 0 0
\(324\) 5.94356 5.94356
\(325\) −1.13052 −1.13052
\(326\) 0 0
\(327\) 0 0
\(328\) 0.363970 0.363970
\(329\) 0 0
\(330\) −3.87939 −3.87939
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −2.65366 −2.65366
\(333\) 0 0
\(334\) −3.01763 −3.01763
\(335\) 1.96962 1.96962
\(336\) −1.04801 −1.04801
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −3.06418 −3.06418
\(339\) 0 0
\(340\) 1.18479 1.18479
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) −0.532089 −0.532089
\(345\) −2.53209 −2.53209
\(346\) −1.96962 −1.96962
\(347\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(348\) −0.921605 −0.921605
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 1.00000 1.00000
\(351\) 6.41147 6.41147
\(352\) −1.34730 −1.34730
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.34730 1.34730
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) −1.96962 −1.96962
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) −1.96962 −1.96962
\(364\) 2.33359 2.33359
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) −0.532089 −0.532089
\(369\) −1.96962 −1.96962
\(370\) 0 0
\(371\) 1.87939 1.87939
\(372\) 0 0
\(373\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(374\) 1.04801 1.04801
\(375\) 0.879385 0.879385
\(376\) 0 0
\(377\) −0.601535 −0.601535
\(378\) −5.67128 −5.67128
\(379\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) −1.96962 −1.96962
\(385\) 1.28558 1.28558
\(386\) 0 0
\(387\) 2.87939 2.87939
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) −6.71929 −6.71929
\(391\) 0.684040 0.684040
\(392\) −0.532089 −0.532089
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −3.87939 −3.87939
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.347296 −0.347296
\(401\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 4.62327 4.62327
\(403\) 0 0
\(404\) 0 0
\(405\) 5.67128 5.67128
\(406\) 0.532089 0.532089
\(407\) 0 0
\(408\) 0.716881 0.716881
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 1.34730 1.34730
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) −4.41147 −4.41147
\(415\) −2.53209 −2.53209
\(416\) −2.33359 −2.33359
\(417\) −2.53209 −2.53209
\(418\) 0 0
\(419\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(420\) 3.41147 3.41147
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 2.87939 2.87939
\(423\) 0 0
\(424\) 1.00000 1.00000
\(425\) 0.446476 0.446476
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −3.41147 −3.41147
\(430\) −1.96962 −1.96962
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 1.96962 1.96962
\(433\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(434\) 0 0
\(435\) −0.879385 −0.879385
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0.684040 0.684040
\(441\) 2.87939 2.87939
\(442\) 1.81521 1.81521
\(443\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −1.04801 −1.04801
\(447\) −3.01763 −3.01763
\(448\) 1.53209 1.53209
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) −2.87939 −2.87939
\(451\) 0.684040 0.684040
\(452\) 0 0
\(453\) −1.96962 −1.96962
\(454\) 0 0
\(455\) 2.22668 2.22668
\(456\) 0 0
\(457\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(458\) 0 0
\(459\) −2.53209 −2.53209
\(460\) 1.73205 1.73205
\(461\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(462\) 3.01763 3.01763
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) −0.184793 −0.184793
\(465\) 0 0
\(466\) −2.87939 −2.87939
\(467\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(468\) −6.71929 −6.71929
\(469\) −1.53209 −1.53209
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.00000 −1.00000
\(474\) 0 0
\(475\) 0 0
\(476\) −0.921605 −0.921605
\(477\) −5.41147 −5.41147
\(478\) 0 0
\(479\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) −3.41147 −3.41147
\(481\) 0 0
\(482\) 0 0
\(483\) 1.96962 1.96962
\(484\) 1.34730 1.34730
\(485\) 0 0
\(486\) 7.64090 7.64090
\(487\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −1.96962 −1.96962
\(491\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(492\) 1.81521 1.81521
\(493\) 0.237565 0.237565
\(494\) 0 0
\(495\) −3.70167 −3.70167
\(496\) 0 0
\(497\) 0 0
\(498\) −5.94356 −5.94356
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) −0.601535 −0.601535
\(501\) −3.87939 −3.87939
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 1.53209 1.53209
\(505\) 0 0
\(506\) 1.53209 1.53209
\(507\) −3.93923 −3.93923
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 2.65366 2.65366
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 1.04801 1.04801
\(515\) 0 0
\(516\) −2.65366 −2.65366
\(517\) 0 0
\(518\) 0 0
\(519\) −2.53209 −2.53209
\(520\) 1.18479 1.18479
\(521\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(522\) −1.53209 −1.53209
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 1.28558 1.28558
\(526\) 1.53209 1.53209
\(527\) 0 0
\(528\) −1.04801 −1.04801
\(529\) 0 0
\(530\) 3.70167 3.70167
\(531\) 0 0
\(532\) 0 0
\(533\) 1.18479 1.18479
\(534\) 0 0
\(535\) 0 0
\(536\) −0.815207 −0.815207
\(537\) 0 0
\(538\) 0 0
\(539\) −1.00000 −1.00000
\(540\) −6.41147 −6.41147
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) −1.04801 −1.04801
\(543\) 0 0
\(544\) 0.921605 0.921605
\(545\) 0 0
\(546\) 5.22668 5.22668
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 1.00000 1.00000
\(551\) 0 0
\(552\) 1.04801 1.04801
\(553\) 0 0
\(554\) 0.532089 0.532089
\(555\) 0 0
\(556\) 1.73205 1.73205
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) −1.73205 −1.73205
\(560\) 0.684040 0.684040
\(561\) 1.34730 1.34730
\(562\) 0 0
\(563\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −2.65366 −2.65366
\(567\) −4.41147 −4.41147
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(572\) 2.33359 2.33359
\(573\) 0 0
\(574\) −1.04801 −1.04801
\(575\) 0.652704 0.652704
\(576\) −4.41147 −4.41147
\(577\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(578\) 0.815207 0.815207
\(579\) 0 0
\(580\) 0.601535 0.601535
\(581\) 1.96962 1.96962
\(582\) 0 0
\(583\) 1.87939 1.87939
\(584\) 0 0
\(585\) −6.41147 −6.41147
\(586\) −2.65366 −2.65366
\(587\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(588\) −2.65366 −2.65366
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) −5.67128 −5.67128
\(595\) −0.879385 −0.879385
\(596\) 2.06418 2.06418
\(597\) 0 0
\(598\) 2.65366 2.65366
\(599\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(600\) 0.684040 0.684040
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 1.53209 1.53209
\(603\) 4.41147 4.41147
\(604\) 1.34730 1.34730
\(605\) 1.28558 1.28558
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0.684040 0.684040
\(610\) 0 0
\(611\) 0 0
\(612\) 2.65366 2.65366
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) −3.01763 −3.01763
\(615\) 1.73205 1.73205
\(616\) −0.532089 −0.532089
\(617\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) −3.70167 −3.70167
\(622\) 0 0
\(623\) 0 0
\(624\) −1.81521 −1.81521
\(625\) −1.22668 −1.22668
\(626\) −1.04801 −1.04801
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 5.67128 5.67128
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 3.70167 3.70167
\(634\) 1.53209 1.53209
\(635\) 0 0
\(636\) 4.98724 4.98724
\(637\) −1.73205 −1.73205
\(638\) 0.532089 0.532089
\(639\) 0 0
\(640\) 1.28558 1.28558
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) −1.34730 −1.34730
\(645\) −2.53209 −2.53209
\(646\) 0 0
\(647\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) −2.34730 −2.34730
\(649\) 0 0
\(650\) 1.73205 1.73205
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.363970 0.363970
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 3.41147 3.41147
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 2.33359 2.33359
\(664\) 1.04801 1.04801
\(665\) 0 0
\(666\) 0 0
\(667\) 0.347296 0.347296
\(668\) 2.65366 2.65366
\(669\) −1.34730 −1.34730
\(670\) −3.01763 −3.01763
\(671\) 0 0
\(672\) 2.65366 2.65366
\(673\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) 0 0
\(675\) −2.41609 −2.41609
\(676\) 2.69459 2.69459
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −0.467911 −0.467911
\(681\) 0 0
\(682\) 0 0
\(683\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.53209 1.53209
\(687\) 0 0
\(688\) −0.532089 −0.532089
\(689\) 3.25519 3.25519
\(690\) 3.87939 3.87939
\(691\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(692\) 1.73205 1.73205
\(693\) 2.87939 2.87939
\(694\) −2.34730 −2.34730
\(695\) 1.65270 1.65270
\(696\) 0.363970 0.363970
\(697\) −0.467911 −0.467911
\(698\) 0 0
\(699\) −3.70167 −3.70167
\(700\) −0.879385 −0.879385
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) −9.82295 −9.82295
\(703\) 0 0
\(704\) 1.53209 1.53209
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) −2.06418 −2.06418
\(715\) 2.22668 2.22668
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −1.96962 −1.96962
\(721\) 0 0
\(722\) −1.53209 −1.53209
\(723\) 0 0
\(724\) 0 0
\(725\) 0.226682 0.226682
\(726\) 3.01763 3.01763
\(727\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(728\) −0.921605 −0.921605
\(729\) 5.41147 5.41147
\(730\) 0 0
\(731\) 0.684040 0.684040
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) −2.53209 −2.53209
\(736\) 1.34730 1.34730
\(737\) −1.53209 −1.53209
\(738\) 3.01763 3.01763
\(739\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −2.87939 −2.87939
\(743\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(744\) 0 0
\(745\) 1.96962 1.96962
\(746\) −2.34730 −2.34730
\(747\) −5.67128 −5.67128
\(748\) −0.921605 −0.921605
\(749\) 0 0
\(750\) −1.34730 −1.34730
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0.921605 0.921605
\(755\) 1.28558 1.28558
\(756\) 4.98724 4.98724
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −2.87939 −2.87939
\(759\) 1.96962 1.96962
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 2.53209 2.53209
\(766\) −2.65366 −2.65366
\(767\) 0 0
\(768\) 0 0
\(769\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(770\) −1.96962 −1.96962
\(771\) 1.34730 1.34730
\(772\) 0 0
\(773\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(774\) −4.41147 −4.41147
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 5.90885 5.90885
\(781\) 0 0
\(782\) −1.04801 −1.04801
\(783\) −1.28558 −1.28558
\(784\) −0.532089 −0.532089
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 1.96962 1.96962
\(790\) 0 0
\(791\) 0 0
\(792\) 1.53209 1.53209
\(793\) 0 0
\(794\) 0 0
\(795\) 4.75877 4.75877
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.879385 0.879385
\(801\) 0 0
\(802\) 1.53209 1.53209
\(803\) 0 0
\(804\) −4.06564 −4.06564
\(805\) −1.28558 −1.28558
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) −8.68891 −8.68891
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −0.467911 −0.467911
\(813\) −1.34730 −1.34730
\(814\) 0 0
\(815\) 0 0
\(816\) 0.716881 0.716881
\(817\) 0 0
\(818\) 0 0
\(819\) 4.98724 4.98724
\(820\) −1.18479 −1.18479
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(824\) 0 0
\(825\) 1.28558 1.28558
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 3.87939 3.87939
\(829\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(830\) 3.87939 3.87939
\(831\) 0.684040 0.684040
\(832\) 2.65366 2.65366
\(833\) 0.684040 0.684040
\(834\) 3.87939 3.87939
\(835\) 2.53209 2.53209
\(836\) 0 0
\(837\) 0 0
\(838\) 1.96962 1.96962
\(839\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(840\) −1.34730 −1.34730
\(841\) −0.879385 −0.879385
\(842\) 0 0
\(843\) 0 0
\(844\) −2.53209 −2.53209
\(845\) 2.57115 2.57115
\(846\) 0 0
\(847\) −1.00000 −1.00000
\(848\) 1.00000 1.00000
\(849\) −3.41147 −3.41147
\(850\) −0.684040 −0.684040
\(851\) 0 0
\(852\) 0 0
\(853\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(858\) 5.22668 5.22668
\(859\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(860\) 1.73205 1.73205
\(861\) −1.34730 −1.34730
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) −4.98724 −4.98724
\(865\) 1.65270 1.65270
\(866\) −2.65366 −2.65366
\(867\) 1.04801 1.04801
\(868\) 0 0
\(869\) 0 0
\(870\) 1.34730 1.34730
\(871\) −2.65366 −2.65366
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0.446476 0.446476
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) −2.65366 −2.65366
\(879\) −3.41147 −3.41147
\(880\) 0.684040 0.684040
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −4.41147 −4.41147
\(883\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(884\) −1.59627 −1.59627
\(885\) 0 0
\(886\) −2.87939 −2.87939
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −4.41147 −4.41147
\(892\) 0.921605 0.921605
\(893\) 0 0
\(894\) 4.62327 4.62327
\(895\) 0 0
\(896\) −1.00000 −1.00000
\(897\) 3.41147 3.41147
\(898\) 0 0
\(899\) 0 0
\(900\) 2.53209 2.53209
\(901\) −1.28558 −1.28558
\(902\) −1.04801 −1.04801
\(903\) 1.96962 1.96962
\(904\) 0 0
\(905\) 0 0
\(906\) 3.01763 3.01763
\(907\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) −3.41147 −3.41147
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 1.96962 1.96962
\(914\) −0.532089 −0.532089
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 3.87939 3.87939
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) −0.684040 −0.684040
\(921\) −3.87939 −3.87939
\(922\) 3.01763 3.01763
\(923\) 0 0
\(924\) −2.65366 −2.65366
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0.467911 0.467911
\(929\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 2.53209 2.53209
\(933\) 0 0
\(934\) −3.01763 −3.01763
\(935\) −0.879385 −0.879385
\(936\) 2.65366 2.65366
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 2.34730 2.34730
\(939\) −1.34730 −1.34730
\(940\) 0 0
\(941\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(942\) 0 0
\(943\) −0.684040 −0.684040
\(944\) 0 0
\(945\) 4.75877 4.75877
\(946\) 1.53209 1.53209
\(947\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 1.96962 1.96962
\(952\) 0.363970 0.363970
\(953\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(954\) 8.29086 8.29086
\(955\) 0 0
\(956\) 0 0
\(957\) 0.684040 0.684040
\(958\) 2.65366 2.65366
\(959\) 0 0
\(960\) 3.87939 3.87939
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) −3.01763 −3.01763
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −0.532089 −0.532089
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −6.71929 −6.71929
\(973\) −1.28558 −1.28558
\(974\) 2.87939 2.87939
\(975\) 2.22668 2.22668
\(976\) 0 0
\(977\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 1.73205 1.73205
\(981\) 0 0
\(982\) 2.87939 2.87939
\(983\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(984\) −0.716881 −0.716881
\(985\) 0 0
\(986\) −0.363970 −0.363970
\(987\) 0 0
\(988\) 0 0
\(989\) 1.00000 1.00000
\(990\) 5.67128 5.67128
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 5.22668 5.22668
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))