Properties

Label 3311.1.h.o.3310.4
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

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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 3310.4
Root \(-0.684040\)
Character \(\chi\) = 3311.3310

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.347296 q^{2}\) \(+0.684040 q^{3}\) \(-0.879385 q^{4}\) \(-1.96962 q^{5}\) \(-0.237565 q^{6}\) \(-1.00000 q^{7}\) \(+0.652704 q^{8}\) \(-0.532089 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.347296 q^{2}\) \(+0.684040 q^{3}\) \(-0.879385 q^{4}\) \(-1.96962 q^{5}\) \(-0.237565 q^{6}\) \(-1.00000 q^{7}\) \(+0.652704 q^{8}\) \(-0.532089 q^{9}\) \(+0.684040 q^{10}\) \(-1.00000 q^{11}\) \(-0.601535 q^{12}\) \(-1.73205 q^{13}\) \(+0.347296 q^{14}\) \(-1.34730 q^{15}\) \(+0.652704 q^{16}\) \(+1.28558 q^{17}\) \(+0.184793 q^{18}\) \(+1.73205 q^{20}\) \(-0.684040 q^{21}\) \(+0.347296 q^{22}\) \(+1.00000 q^{23}\) \(+0.446476 q^{24}\) \(+2.87939 q^{25}\) \(+0.601535 q^{26}\) \(-1.04801 q^{27}\) \(+0.879385 q^{28}\) \(-1.87939 q^{29}\) \(+0.467911 q^{30}\) \(-0.879385 q^{32}\) \(-0.684040 q^{33}\) \(-0.446476 q^{34}\) \(+1.96962 q^{35}\) \(+0.467911 q^{36}\) \(-1.18479 q^{39}\) \(-1.28558 q^{40}\) \(-1.28558 q^{41}\) \(+0.237565 q^{42}\) \(+1.00000 q^{43}\) \(+0.879385 q^{44}\) \(+1.04801 q^{45}\) \(-0.347296 q^{46}\) \(+0.446476 q^{48}\) \(+1.00000 q^{49}\) \(-1.00000 q^{50}\) \(+0.879385 q^{51}\) \(+1.52314 q^{52}\) \(+1.53209 q^{53}\) \(+0.363970 q^{54}\) \(+1.96962 q^{55}\) \(-0.652704 q^{56}\) \(+0.652704 q^{58}\) \(+1.18479 q^{60}\) \(+0.532089 q^{63}\) \(-0.347296 q^{64}\) \(+3.41147 q^{65}\) \(+0.237565 q^{66}\) \(+0.347296 q^{67}\) \(-1.13052 q^{68}\) \(+0.684040 q^{69}\) \(-0.684040 q^{70}\) \(-0.347296 q^{72}\) \(+1.96962 q^{75}\) \(+1.00000 q^{77}\) \(+0.411474 q^{78}\) \(-1.28558 q^{80}\) \(-0.184793 q^{81}\) \(+0.446476 q^{82}\) \(+0.684040 q^{83}\) \(+0.601535 q^{84}\) \(-2.53209 q^{85}\) \(-0.347296 q^{86}\) \(-1.28558 q^{87}\) \(-0.652704 q^{88}\) \(-0.363970 q^{90}\) \(+1.73205 q^{91}\) \(-0.879385 q^{92}\) \(-0.601535 q^{96}\) \(-0.347296 q^{98}\) \(+0.532089 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(6q \) \(\mathstrut +\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 6q^{16} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 6q^{32} \) \(\mathstrut +\mathstrut 12q^{36} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 6q^{50} \) \(\mathstrut -\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 18q^{78} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(3\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(4\) −0.879385 −0.879385
\(5\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(6\) −0.237565 −0.237565
\(7\) −1.00000 −1.00000
\(8\) 0.652704 0.652704
\(9\) −0.532089 −0.532089
\(10\) 0.684040 0.684040
\(11\) −1.00000 −1.00000
\(12\) −0.601535 −0.601535
\(13\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(14\) 0.347296 0.347296
\(15\) −1.34730 −1.34730
\(16\) 0.652704 0.652704
\(17\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(18\) 0.184793 0.184793
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 1.73205 1.73205
\(21\) −0.684040 −0.684040
\(22\) 0.347296 0.347296
\(23\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) 0.446476 0.446476
\(25\) 2.87939 2.87939
\(26\) 0.601535 0.601535
\(27\) −1.04801 −1.04801
\(28\) 0.879385 0.879385
\(29\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(30\) 0.467911 0.467911
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) −0.879385 −0.879385
\(33\) −0.684040 −0.684040
\(34\) −0.446476 −0.446476
\(35\) 1.96962 1.96962
\(36\) 0.467911 0.467911
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) −1.18479 −1.18479
\(40\) −1.28558 −1.28558
\(41\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(42\) 0.237565 0.237565
\(43\) 1.00000 1.00000
\(44\) 0.879385 0.879385
\(45\) 1.04801 1.04801
\(46\) −0.347296 −0.347296
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0.446476 0.446476
\(49\) 1.00000 1.00000
\(50\) −1.00000 −1.00000
\(51\) 0.879385 0.879385
\(52\) 1.52314 1.52314
\(53\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(54\) 0.363970 0.363970
\(55\) 1.96962 1.96962
\(56\) −0.652704 −0.652704
\(57\) 0 0
\(58\) 0.652704 0.652704
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 1.18479 1.18479
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0.532089 0.532089
\(64\) −0.347296 −0.347296
\(65\) 3.41147 3.41147
\(66\) 0.237565 0.237565
\(67\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(68\) −1.13052 −1.13052
\(69\) 0.684040 0.684040
\(70\) −0.684040 −0.684040
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −0.347296 −0.347296
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 1.96962 1.96962
\(76\) 0 0
\(77\) 1.00000 1.00000
\(78\) 0.411474 0.411474
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −1.28558 −1.28558
\(81\) −0.184793 −0.184793
\(82\) 0.446476 0.446476
\(83\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(84\) 0.601535 0.601535
\(85\) −2.53209 −2.53209
\(86\) −0.347296 −0.347296
\(87\) −1.28558 −1.28558
\(88\) −0.652704 −0.652704
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −0.363970 −0.363970
\(91\) 1.73205 1.73205
\(92\) −0.879385 −0.879385
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −0.601535 −0.601535
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.347296 −0.347296
\(99\) 0.532089 0.532089
\(100\) −2.53209 −2.53209
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −0.305407 −0.305407
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −1.13052 −1.13052
\(105\) 1.34730 1.34730
\(106\) −0.532089 −0.532089
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0.921605 0.921605
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −0.684040 −0.684040
\(111\) 0 0
\(112\) −0.652704 −0.652704
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) −1.96962 −1.96962
\(116\) 1.65270 1.65270
\(117\) 0.921605 0.921605
\(118\) 0 0
\(119\) −1.28558 −1.28558
\(120\) −0.879385 −0.879385
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) −0.879385 −0.879385
\(124\) 0 0
\(125\) −3.70167 −3.70167
\(126\) −0.184793 −0.184793
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 1.00000 1.00000
\(129\) 0.684040 0.684040
\(130\) −1.18479 −1.18479
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0.601535 0.601535
\(133\) 0 0
\(134\) −0.120615 −0.120615
\(135\) 2.06418 2.06418
\(136\) 0.839100 0.839100
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) −0.237565 −0.237565
\(139\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(140\) −1.73205 −1.73205
\(141\) 0 0
\(142\) 0 0
\(143\) 1.73205 1.73205
\(144\) −0.347296 −0.347296
\(145\) 3.70167 3.70167
\(146\) 0 0
\(147\) 0.684040 0.684040
\(148\) 0 0
\(149\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(150\) −0.684040 −0.684040
\(151\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) 0 0
\(153\) −0.684040 −0.684040
\(154\) −0.347296 −0.347296
\(155\) 0 0
\(156\) 1.04189 1.04189
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 1.04801 1.04801
\(160\) 1.73205 1.73205
\(161\) −1.00000 −1.00000
\(162\) 0.0641778 0.0641778
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 1.13052 1.13052
\(165\) 1.34730 1.34730
\(166\) −0.237565 −0.237565
\(167\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(168\) −0.446476 −0.446476
\(169\) 2.00000 2.00000
\(170\) 0.879385 0.879385
\(171\) 0 0
\(172\) −0.879385 −0.879385
\(173\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(174\) 0.446476 0.446476
\(175\) −2.87939 −2.87939
\(176\) −0.652704 −0.652704
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −0.921605 −0.921605
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −0.601535 −0.601535
\(183\) 0 0
\(184\) 0.652704 0.652704
\(185\) 0 0
\(186\) 0 0
\(187\) −1.28558 −1.28558
\(188\) 0 0
\(189\) 1.04801 1.04801
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −0.237565 −0.237565
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 2.33359 2.33359
\(196\) −0.879385 −0.879385
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −0.184793 −0.184793
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 1.87939 1.87939
\(201\) 0.237565 0.237565
\(202\) 0 0
\(203\) 1.87939 1.87939
\(204\) −0.773318 −0.773318
\(205\) 2.53209 2.53209
\(206\) 0 0
\(207\) −0.532089 −0.532089
\(208\) −1.13052 −1.13052
\(209\) 0 0
\(210\) −0.467911 −0.467911
\(211\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(212\) −1.34730 −1.34730
\(213\) 0 0
\(214\) 0 0
\(215\) −1.96962 −1.96962
\(216\) −0.684040 −0.684040
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −1.73205 −1.73205
\(221\) −2.22668 −2.22668
\(222\) 0 0
\(223\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(224\) 0.879385 0.879385
\(225\) −1.53209 −1.53209
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0.684040 0.684040
\(231\) 0.684040 0.684040
\(232\) −1.22668 −1.22668
\(233\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(234\) −0.320070 −0.320070
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0.446476 0.446476
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −0.879385 −0.879385
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) −0.347296 −0.347296
\(243\) 0.921605 0.921605
\(244\) 0 0
\(245\) −1.96962 −1.96962
\(246\) 0.305407 0.305407
\(247\) 0 0
\(248\) 0 0
\(249\) 0.467911 0.467911
\(250\) 1.28558 1.28558
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −0.467911 −0.467911
\(253\) −1.00000 −1.00000
\(254\) 0 0
\(255\) −1.73205 −1.73205
\(256\) 0 0
\(257\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(258\) −0.237565 −0.237565
\(259\) 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 \(0.666667\pi\)
\(264\) −0.446476 −0.446476
\(265\) −3.01763 −3.01763
\(266\) 0 0
\(267\) 0 0
\(268\) −0.305407 −0.305407
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −0.716881 −0.716881
\(271\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(272\) 0.839100 0.839100
\(273\) 1.18479 1.18479
\(274\) 0 0
\(275\) −2.87939 −2.87939
\(276\) −0.601535 −0.601535
\(277\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(278\) 0.684040 0.684040
\(279\) 0 0
\(280\) 1.28558 1.28558
\(281\) 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
\(286\) −0.601535 −0.601535
\(287\) 1.28558 1.28558
\(288\) 0.467911 0.467911
\(289\) 0.652704 0.652704
\(290\) −1.28558 −1.28558
\(291\) 0 0
\(292\) 0 0
\(293\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(294\) −0.237565 −0.237565
\(295\) 0 0
\(296\) 0 0
\(297\) 1.04801 1.04801
\(298\) −0.120615 −0.120615
\(299\) −1.73205 −1.73205
\(300\) −1.73205 −1.73205
\(301\) −1.00000 −1.00000
\(302\) −0.347296 −0.347296
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0.237565 0.237565
\(307\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(308\) −0.879385 −0.879385
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) −0.773318 −0.773318
\(313\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(314\) 0 0
\(315\) −1.04801 −1.04801
\(316\) 0 0
\(317\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) −0.363970 −0.363970
\(319\) 1.87939 1.87939
\(320\) 0.684040 0.684040
\(321\) 0 0
\(322\) 0.347296 0.347296
\(323\) 0 0
\(324\) 0.162504 0.162504
\(325\) −4.98724 −4.98724
\(326\) 0 0
\(327\) 0 0
\(328\) −0.839100 −0.839100
\(329\) 0 0
\(330\) −0.467911 −0.467911
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −0.601535 −0.601535
\(333\) 0 0
\(334\) 0.237565 0.237565
\(335\) −0.684040 −0.684040
\(336\) −0.446476 −0.446476
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −0.694593 −0.694593
\(339\) 0 0
\(340\) 2.22668 2.22668
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) 0.652704 0.652704
\(345\) −1.34730 −1.34730
\(346\) 0.684040 0.684040
\(347\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(348\) 1.13052 1.13052
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 1.00000 1.00000
\(351\) 1.81521 1.81521
\(352\) 0.879385 0.879385
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −0.879385 −0.879385
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0.684040 0.684040
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) 0.684040 0.684040
\(364\) −1.52314 −1.52314
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0.652704 0.652704
\(369\) 0.684040 0.684040
\(370\) 0 0
\(371\) −1.53209 −1.53209
\(372\) 0 0
\(373\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(374\) 0.446476 0.446476
\(375\) −2.53209 −2.53209
\(376\) 0 0
\(377\) 3.25519 3.25519
\(378\) −0.363970 −0.363970
\(379\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 0.684040 0.684040
\(385\) −1.96962 −1.96962
\(386\) 0 0
\(387\) −0.532089 −0.532089
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) −0.810446 −0.810446
\(391\) 1.28558 1.28558
\(392\) 0.652704 0.652704
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −0.467911 −0.467911
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.87939 1.87939
\(401\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) −0.0825054 −0.0825054
\(403\) 0 0
\(404\) 0 0
\(405\) 0.363970 0.363970
\(406\) −0.652704 −0.652704
\(407\) 0 0
\(408\) 0.573978 0.573978
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) −0.879385 −0.879385
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.184793 0.184793
\(415\) −1.34730 −1.34730
\(416\) 1.52314 1.52314
\(417\) −1.34730 −1.34730
\(418\) 0 0
\(419\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(420\) −1.18479 −1.18479
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) −0.532089 −0.532089
\(423\) 0 0
\(424\) 1.00000 1.00000
\(425\) 3.70167 3.70167
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 1.18479 1.18479
\(430\) 0.684040 0.684040
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −0.684040 −0.684040
\(433\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(434\) 0 0
\(435\) 2.53209 2.53209
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 1.28558 1.28558
\(441\) −0.532089 −0.532089
\(442\) 0.773318 0.773318
\(443\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.446476 −0.446476
\(447\) 0.237565 0.237565
\(448\) 0.347296 0.347296
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0.532089 0.532089
\(451\) 1.28558 1.28558
\(452\) 0 0
\(453\) 0.684040 0.684040
\(454\) 0 0
\(455\) −3.41147 −3.41147
\(456\) 0 0
\(457\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(458\) 0 0
\(459\) −1.34730 −1.34730
\(460\) 1.73205 1.73205
\(461\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(462\) −0.237565 −0.237565
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) −1.22668 −1.22668
\(465\) 0 0
\(466\) 0.532089 0.532089
\(467\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(468\) −0.810446 −0.810446
\(469\) −0.347296 −0.347296
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.00000 −1.00000
\(474\) 0 0
\(475\) 0 0
\(476\) 1.13052 1.13052
\(477\) −0.815207 −0.815207
\(478\) 0 0
\(479\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 1.18479 1.18479
\(481\) 0 0
\(482\) 0 0
\(483\) −0.684040 −0.684040
\(484\) −0.879385 −0.879385
\(485\) 0 0
\(486\) −0.320070 −0.320070
\(487\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0.684040 0.684040
\(491\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(492\) 0.773318 0.773318
\(493\) −2.41609 −2.41609
\(494\) 0 0
\(495\) −1.04801 −1.04801
\(496\) 0 0
\(497\) 0 0
\(498\) −0.162504 −0.162504
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 3.25519 3.25519
\(501\) −0.467911 −0.467911
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0.347296 0.347296
\(505\) 0 0
\(506\) 0.347296 0.347296
\(507\) 1.36808 1.36808
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0.601535 0.601535
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) 0.446476 0.446476
\(515\) 0 0
\(516\) −0.601535 −0.601535
\(517\) 0 0
\(518\) 0 0
\(519\) −1.34730 −1.34730
\(520\) 2.22668 2.22668
\(521\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(522\) −0.347296 −0.347296
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) −1.96962 −1.96962
\(526\) 0.347296 0.347296
\(527\) 0 0
\(528\) −0.446476 −0.446476
\(529\) 0 0
\(530\) 1.04801 1.04801
\(531\) 0 0
\(532\) 0 0
\(533\) 2.22668 2.22668
\(534\) 0 0
\(535\) 0 0
\(536\) 0.226682 0.226682
\(537\) 0 0
\(538\) 0 0
\(539\) −1.00000 −1.00000
\(540\) −1.81521 −1.81521
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) −0.446476 −0.446476
\(543\) 0 0
\(544\) −1.13052 −1.13052
\(545\) 0 0
\(546\) −0.411474 −0.411474
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 1.00000 1.00000
\(551\) 0 0
\(552\) 0.446476 0.446476
\(553\) 0 0
\(554\) −0.652704 −0.652704
\(555\) 0 0
\(556\) 1.73205 1.73205
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) −1.73205 −1.73205
\(560\) 1.28558 1.28558
\(561\) −0.879385 −0.879385
\(562\) 0 0
\(563\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −0.601535 −0.601535
\(567\) 0.184793 0.184793
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(572\) −1.52314 −1.52314
\(573\) 0 0
\(574\) −0.446476 −0.446476
\(575\) 2.87939 2.87939
\(576\) 0.184793 0.184793
\(577\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(578\) −0.226682 −0.226682
\(579\) 0 0
\(580\) −3.25519 −3.25519
\(581\) −0.684040 −0.684040
\(582\) 0 0
\(583\) −1.53209 −1.53209
\(584\) 0 0
\(585\) −1.81521 −1.81521
\(586\) −0.601535 −0.601535
\(587\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(588\) −0.601535 −0.601535
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) −0.363970 −0.363970
\(595\) 2.53209 2.53209
\(596\) −0.305407 −0.305407
\(597\) 0 0
\(598\) 0.601535 0.601535
\(599\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(600\) 1.28558 1.28558
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0.347296 0.347296
\(603\) −0.184793 −0.184793
\(604\) −0.879385 −0.879385
\(605\) −1.96962 −1.96962
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 1.28558 1.28558
\(610\) 0 0
\(611\) 0 0
\(612\) 0.601535 0.601535
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0.237565 0.237565
\(615\) 1.73205 1.73205
\(616\) 0.652704 0.652704
\(617\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) −1.04801 −1.04801
\(622\) 0 0
\(623\) 0 0
\(624\) −0.773318 −0.773318
\(625\) 4.41147 4.41147
\(626\) −0.446476 −0.446476
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.363970 0.363970
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 1.04801 1.04801
\(634\) 0.347296 0.347296
\(635\) 0 0
\(636\) −0.921605 −0.921605
\(637\) −1.73205 −1.73205
\(638\) −0.652704 −0.652704
\(639\) 0 0
\(640\) −1.96962 −1.96962
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0.879385 0.879385
\(645\) −1.34730 −1.34730
\(646\) 0 0
\(647\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) −0.120615 −0.120615
\(649\) 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
\(656\) −0.839100 −0.839100
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −1.18479 −1.18479
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) −1.52314 −1.52314
\(664\) 0.446476 0.446476
\(665\) 0 0
\(666\) 0 0
\(667\) −1.87939 −1.87939
\(668\) 0.601535 0.601535
\(669\) 0.879385 0.879385
\(670\) 0.237565 0.237565
\(671\) 0 0
\(672\) 0.601535 0.601535
\(673\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) 0 0
\(675\) −3.01763 −3.01763
\(676\) −1.75877 −1.75877
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.65270 −1.65270
\(681\) 0 0
\(682\) 0 0
\(683\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.347296 0.347296
\(687\) 0 0
\(688\) 0.652704 0.652704
\(689\) −2.65366 −2.65366
\(690\) 0.467911 0.467911
\(691\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(692\) 1.73205 1.73205
\(693\) −0.532089 −0.532089
\(694\) −0.120615 −0.120615
\(695\) 3.87939 3.87939
\(696\) −0.839100 −0.839100
\(697\) −1.65270 −1.65270
\(698\) 0 0
\(699\) −1.04801 −1.04801
\(700\) 2.53209 2.53209
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) −0.630415 −0.630415
\(703\) 0 0
\(704\) 0.347296 0.347296
\(705\) 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
\(714\) 0.305407 0.305407
\(715\) −3.41147 −3.41147
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) 0.684040 0.684040
\(721\) 0 0
\(722\) −0.347296 −0.347296
\(723\) 0 0
\(724\) 0 0
\(725\) −5.41147 −5.41147
\(726\) −0.237565 −0.237565
\(727\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(728\) 1.13052 1.13052
\(729\) 0.815207 0.815207
\(730\) 0 0
\(731\) 1.28558 1.28558
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) −1.34730 −1.34730
\(736\) −0.879385 −0.879385
\(737\) −0.347296 −0.347296
\(738\) −0.237565 −0.237565
\(739\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.532089 0.532089
\(743\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(744\) 0 0
\(745\) −0.684040 −0.684040
\(746\) −0.120615 −0.120615
\(747\) −0.363970 −0.363970
\(748\) 1.13052 1.13052
\(749\) 0 0
\(750\) 0.879385 0.879385
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −1.13052 −1.13052
\(755\) −1.96962 −1.96962
\(756\) −0.921605 −0.921605
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0.532089 0.532089
\(759\) −0.684040 −0.684040
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 1.34730 1.34730
\(766\) −0.601535 −0.601535
\(767\) 0 0
\(768\) 0 0
\(769\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(770\) 0.684040 0.684040
\(771\) −0.879385 −0.879385
\(772\) 0 0
\(773\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(774\) 0.184793 0.184793
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −2.05212 −2.05212
\(781\) 0 0
\(782\) −0.446476 −0.446476
\(783\) 1.96962 1.96962
\(784\) 0.652704 0.652704
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) −0.684040 −0.684040
\(790\) 0 0
\(791\) 0 0
\(792\) 0.347296 0.347296
\(793\) 0 0
\(794\) 0 0
\(795\) −2.06418 −2.06418
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −2.53209 −2.53209
\(801\) 0 0
\(802\) 0.347296 0.347296
\(803\) 0 0
\(804\) −0.208911 −0.208911
\(805\) 1.96962 1.96962
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) −0.126406 −0.126406
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −1.65270 −1.65270
\(813\) 0.879385 0.879385
\(814\) 0 0
\(815\) 0 0
\(816\) 0.573978 0.573978
\(817\) 0 0
\(818\) 0 0
\(819\) −0.921605 −0.921605
\(820\) −2.22668 −2.22668
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(824\) 0 0
\(825\) −1.96962 −1.96962
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0.467911 0.467911
\(829\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(830\) 0.467911 0.467911
\(831\) 1.28558 1.28558
\(832\) 0.601535 0.601535
\(833\) 1.28558 1.28558
\(834\) 0.467911 0.467911
\(835\) 1.34730 1.34730
\(836\) 0 0
\(837\) 0 0
\(838\) −0.684040 −0.684040
\(839\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(840\) 0.879385 0.879385
\(841\) 2.53209 2.53209
\(842\) 0 0
\(843\) 0 0
\(844\) −1.34730 −1.34730
\(845\) −3.93923 −3.93923
\(846\) 0 0
\(847\) −1.00000 −1.00000
\(848\) 1.00000 1.00000
\(849\) 1.18479 1.18479
\(850\) −1.28558 −1.28558
\(851\) 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
\(857\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(858\) −0.411474 −0.411474
\(859\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(860\) 1.73205 1.73205
\(861\) 0.879385 0.879385
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0.921605 0.921605
\(865\) 3.87939 3.87939
\(866\) −0.601535 −0.601535
\(867\) 0.446476 0.446476
\(868\) 0 0
\(869\) 0 0
\(870\) −0.879385 −0.879385
\(871\) −0.601535 −0.601535
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 3.70167 3.70167
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) −0.601535 −0.601535
\(879\) 1.18479 1.18479
\(880\) 1.28558 1.28558
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0.184793 0.184793
\(883\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(884\) 1.95811 1.95811
\(885\) 0 0
\(886\) 0.532089 0.532089
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.184793 0.184793
\(892\) −1.13052 −1.13052
\(893\) 0 0
\(894\) −0.0825054 −0.0825054
\(895\) 0 0
\(896\) −1.00000 −1.00000
\(897\) −1.18479 −1.18479
\(898\) 0 0
\(899\) 0 0
\(900\) 1.34730 1.34730
\(901\) 1.96962 1.96962
\(902\) −0.446476 −0.446476
\(903\) −0.684040 −0.684040
\(904\) 0 0
\(905\) 0 0
\(906\) −0.237565 −0.237565
\(907\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 1.18479 1.18479
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) −0.684040 −0.684040
\(914\) 0.652704 0.652704
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0.467911 0.467911
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) −1.28558 −1.28558
\(921\) −0.467911 −0.467911
\(922\) −0.237565 −0.237565
\(923\) 0 0
\(924\) −0.601535 −0.601535
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 1.65270 1.65270
\(929\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.34730 1.34730
\(933\) 0 0
\(934\) 0.237565 0.237565
\(935\) 2.53209 2.53209
\(936\) 0.601535 0.601535
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0.120615 0.120615
\(939\) 0.879385 0.879385
\(940\) 0 0
\(941\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(942\) 0 0
\(943\) −1.28558 −1.28558
\(944\) 0 0
\(945\) −2.06418 −2.06418
\(946\) 0.347296 0.347296
\(947\) −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
\(951\) −0.684040 −0.684040
\(952\) −0.839100 −0.839100
\(953\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(954\) 0.283119 0.283119
\(955\) 0 0
\(956\) 0 0
\(957\) 1.28558 1.28558
\(958\) 0.601535 0.601535
\(959\) 0 0
\(960\) 0.467911 0.467911
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0.237565 0.237565
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 0.652704 0.652704
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) −0.810446 −0.810446
\(973\) 1.96962 1.96962
\(974\) −0.532089 −0.532089
\(975\) −3.41147 −3.41147
\(976\) 0 0
\(977\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 1.73205 1.73205
\(981\) 0 0
\(982\) −0.532089 −0.532089
\(983\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(984\) −0.573978 −0.573978
\(985\) 0 0
\(986\) 0.839100 0.839100
\(987\) 0 0
\(988\) 0 0
\(989\) 1.00000 1.00000
\(990\) 0.363970 0.363970
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) −0.411474 −0.411474
\(997\) 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 \(a_p\))