Properties

Label 3311.1.h.o.3310.5
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 3310.5
Root \(1.28558\)
Character \(\chi\) = 3311.3310

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.87939 q^{2}\) \(-1.28558 q^{3}\) \(+2.53209 q^{4}\) \(-0.684040 q^{5}\) \(-2.41609 q^{6}\) \(-1.00000 q^{7}\) \(+2.87939 q^{8}\) \(+0.652704 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.87939 q^{2}\) \(-1.28558 q^{3}\) \(+2.53209 q^{4}\) \(-0.684040 q^{5}\) \(-2.41609 q^{6}\) \(-1.00000 q^{7}\) \(+2.87939 q^{8}\) \(+0.652704 q^{9}\) \(-1.28558 q^{10}\) \(-1.00000 q^{11}\) \(-3.25519 q^{12}\) \(+1.73205 q^{13}\) \(-1.87939 q^{14}\) \(+0.879385 q^{15}\) \(+2.87939 q^{16}\) \(+1.96962 q^{17}\) \(+1.22668 q^{18}\) \(-1.73205 q^{20}\) \(+1.28558 q^{21}\) \(-1.87939 q^{22}\) \(+1.00000 q^{23}\) \(-3.70167 q^{24}\) \(-0.532089 q^{25}\) \(+3.25519 q^{26}\) \(+0.446476 q^{27}\) \(-2.53209 q^{28}\) \(+1.53209 q^{29}\) \(+1.65270 q^{30}\) \(+2.53209 q^{32}\) \(+1.28558 q^{33}\) \(+3.70167 q^{34}\) \(+0.684040 q^{35}\) \(+1.65270 q^{36}\) \(-2.22668 q^{39}\) \(-1.96962 q^{40}\) \(-1.96962 q^{41}\) \(+2.41609 q^{42}\) \(+1.00000 q^{43}\) \(-2.53209 q^{44}\) \(-0.446476 q^{45}\) \(+1.87939 q^{46}\) \(-3.70167 q^{48}\) \(+1.00000 q^{49}\) \(-1.00000 q^{50}\) \(-2.53209 q^{51}\) \(+4.38571 q^{52}\) \(+0.347296 q^{53}\) \(+0.839100 q^{54}\) \(+0.684040 q^{55}\) \(-2.87939 q^{56}\) \(+2.87939 q^{58}\) \(+2.22668 q^{60}\) \(-0.652704 q^{63}\) \(+1.87939 q^{64}\) \(-1.18479 q^{65}\) \(+2.41609 q^{66}\) \(-1.87939 q^{67}\) \(+4.98724 q^{68}\) \(-1.28558 q^{69}\) \(+1.28558 q^{70}\) \(+1.87939 q^{72}\) \(+0.684040 q^{75}\) \(+1.00000 q^{77}\) \(-4.18479 q^{78}\) \(-1.96962 q^{80}\) \(-1.22668 q^{81}\) \(-3.70167 q^{82}\) \(-1.28558 q^{83}\) \(+3.25519 q^{84}\) \(-1.34730 q^{85}\) \(+1.87939 q^{86}\) \(-1.96962 q^{87}\) \(-2.87939 q^{88}\) \(-0.839100 q^{90}\) \(-1.73205 q^{91}\) \(+2.53209 q^{92}\) \(-3.25519 q^{96}\) \(+1.87939 q^{98}\) \(-0.652704 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(6q \) \(\mathstrut +\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 6q^{4} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 6q^{16} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 6q^{25} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 6q^{32} \) \(\mathstrut +\mathstrut 12q^{36} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 6q^{50} \) \(\mathstrut -\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 18q^{78} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(3\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(4\) 2.53209 2.53209
\(5\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(6\) −2.41609 −2.41609
\(7\) −1.00000 −1.00000
\(8\) 2.87939 2.87939
\(9\) 0.652704 0.652704
\(10\) −1.28558 −1.28558
\(11\) −1.00000 −1.00000
\(12\) −3.25519 −3.25519
\(13\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(14\) −1.87939 −1.87939
\(15\) 0.879385 0.879385
\(16\) 2.87939 2.87939
\(17\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(18\) 1.22668 1.22668
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) −1.73205 −1.73205
\(21\) 1.28558 1.28558
\(22\) −1.87939 −1.87939
\(23\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) −3.70167 −3.70167
\(25\) −0.532089 −0.532089
\(26\) 3.25519 3.25519
\(27\) 0.446476 0.446476
\(28\) −2.53209 −2.53209
\(29\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(30\) 1.65270 1.65270
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 2.53209 2.53209
\(33\) 1.28558 1.28558
\(34\) 3.70167 3.70167
\(35\) 0.684040 0.684040
\(36\) 1.65270 1.65270
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) −2.22668 −2.22668
\(40\) −1.96962 −1.96962
\(41\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(42\) 2.41609 2.41609
\(43\) 1.00000 1.00000
\(44\) −2.53209 −2.53209
\(45\) −0.446476 −0.446476
\(46\) 1.87939 1.87939
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −3.70167 −3.70167
\(49\) 1.00000 1.00000
\(50\) −1.00000 −1.00000
\(51\) −2.53209 −2.53209
\(52\) 4.38571 4.38571
\(53\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(54\) 0.839100 0.839100
\(55\) 0.684040 0.684040
\(56\) −2.87939 −2.87939
\(57\) 0 0
\(58\) 2.87939 2.87939
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 2.22668 2.22668
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) −0.652704 −0.652704
\(64\) 1.87939 1.87939
\(65\) −1.18479 −1.18479
\(66\) 2.41609 2.41609
\(67\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(68\) 4.98724 4.98724
\(69\) −1.28558 −1.28558
\(70\) 1.28558 1.28558
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 1.87939 1.87939
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0 0
\(75\) 0.684040 0.684040
\(76\) 0 0
\(77\) 1.00000 1.00000
\(78\) −4.18479 −4.18479
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −1.96962 −1.96962
\(81\) −1.22668 −1.22668
\(82\) −3.70167 −3.70167
\(83\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(84\) 3.25519 3.25519
\(85\) −1.34730 −1.34730
\(86\) 1.87939 1.87939
\(87\) −1.96962 −1.96962
\(88\) −2.87939 −2.87939
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −0.839100 −0.839100
\(91\) −1.73205 −1.73205
\(92\) 2.53209 2.53209
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −3.25519 −3.25519
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1.87939 1.87939
\(99\) −0.652704 −0.652704
\(100\) −1.34730 −1.34730
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −4.75877 −4.75877
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 4.98724 4.98724
\(105\) −0.879385 −0.879385
\(106\) 0.652704 0.652704
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 1.13052 1.13052
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 1.28558 1.28558
\(111\) 0 0
\(112\) −2.87939 −2.87939
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) −0.684040 −0.684040
\(116\) 3.87939 3.87939
\(117\) 1.13052 1.13052
\(118\) 0 0
\(119\) −1.96962 −1.96962
\(120\) 2.53209 2.53209
\(121\) 1.00000 1.00000
\(122\) 0 0
\(123\) 2.53209 2.53209
\(124\) 0 0
\(125\) 1.04801 1.04801
\(126\) −1.22668 −1.22668
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 1.00000 1.00000
\(129\) −1.28558 −1.28558
\(130\) −2.22668 −2.22668
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 3.25519 3.25519
\(133\) 0 0
\(134\) −3.53209 −3.53209
\(135\) −0.305407 −0.305407
\(136\) 5.67128 5.67128
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) −2.41609 −2.41609
\(139\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(140\) 1.73205 1.73205
\(141\) 0 0
\(142\) 0 0
\(143\) −1.73205 −1.73205
\(144\) 1.87939 1.87939
\(145\) −1.04801 −1.04801
\(146\) 0 0
\(147\) −1.28558 −1.28558
\(148\) 0 0
\(149\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(150\) 1.28558 1.28558
\(151\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) 0 0
\(153\) 1.28558 1.28558
\(154\) 1.87939 1.87939
\(155\) 0 0
\(156\) −5.63816 −5.63816
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) −0.446476 −0.446476
\(160\) −1.73205 −1.73205
\(161\) −1.00000 −1.00000
\(162\) −2.30541 −2.30541
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) −4.98724 −4.98724
\(165\) −0.879385 −0.879385
\(166\) −2.41609 −2.41609
\(167\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(168\) 3.70167 3.70167
\(169\) 2.00000 2.00000
\(170\) −2.53209 −2.53209
\(171\) 0 0
\(172\) 2.53209 2.53209
\(173\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(174\) −3.70167 −3.70167
\(175\) 0.532089 0.532089
\(176\) −2.87939 −2.87939
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −1.13052 −1.13052
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −3.25519 −3.25519
\(183\) 0 0
\(184\) 2.87939 2.87939
\(185\) 0 0
\(186\) 0 0
\(187\) −1.96962 −1.96962
\(188\) 0 0
\(189\) −0.446476 −0.446476
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) −2.41609 −2.41609
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 1.52314 1.52314
\(196\) 2.53209 2.53209
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −1.22668 −1.22668
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −1.53209 −1.53209
\(201\) 2.41609 2.41609
\(202\) 0 0
\(203\) −1.53209 −1.53209
\(204\) −6.41147 −6.41147
\(205\) 1.34730 1.34730
\(206\) 0 0
\(207\) 0.652704 0.652704
\(208\) 4.98724 4.98724
\(209\) 0 0
\(210\) −1.65270 −1.65270
\(211\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(212\) 0.879385 0.879385
\(213\) 0 0
\(214\) 0 0
\(215\) −0.684040 −0.684040
\(216\) 1.28558 1.28558
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 1.73205 1.73205
\(221\) 3.41147 3.41147
\(222\) 0 0
\(223\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(224\) −2.53209 −2.53209
\(225\) −0.347296 −0.347296
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) −1.28558 −1.28558
\(231\) −1.28558 −1.28558
\(232\) 4.41147 4.41147
\(233\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(234\) 2.12467 2.12467
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) −3.70167 −3.70167
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 2.53209 2.53209
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 1.87939 1.87939
\(243\) 1.13052 1.13052
\(244\) 0 0
\(245\) −0.684040 −0.684040
\(246\) 4.75877 4.75877
\(247\) 0 0
\(248\) 0 0
\(249\) 1.65270 1.65270
\(250\) 1.96962 1.96962
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) −1.65270 −1.65270
\(253\) −1.00000 −1.00000
\(254\) 0 0
\(255\) 1.73205 1.73205
\(256\) 0 0
\(257\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(258\) −2.41609 −2.41609
\(259\) 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 \(0.666667\pi\)
\(264\) 3.70167 3.70167
\(265\) −0.237565 −0.237565
\(266\) 0 0
\(267\) 0 0
\(268\) −4.75877 −4.75877
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) −0.573978 −0.573978
\(271\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(272\) 5.67128 5.67128
\(273\) 2.22668 2.22668
\(274\) 0 0
\(275\) 0.532089 0.532089
\(276\) −3.25519 −3.25519
\(277\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(278\) −1.28558 −1.28558
\(279\) 0 0
\(280\) 1.96962 1.96962
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −3.25519 −3.25519
\(287\) 1.96962 1.96962
\(288\) 1.65270 1.65270
\(289\) 2.87939 2.87939
\(290\) −1.96962 −1.96962
\(291\) 0 0
\(292\) 0 0
\(293\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(294\) −2.41609 −2.41609
\(295\) 0 0
\(296\) 0 0
\(297\) −0.446476 −0.446476
\(298\) −3.53209 −3.53209
\(299\) 1.73205 1.73205
\(300\) 1.73205 1.73205
\(301\) −1.00000 −1.00000
\(302\) 1.87939 1.87939
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 2.41609 2.41609
\(307\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(308\) 2.53209 2.53209
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) −6.41147 −6.41147
\(313\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(314\) 0 0
\(315\) 0.446476 0.446476
\(316\) 0 0
\(317\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(318\) −0.839100 −0.839100
\(319\) −1.53209 −1.53209
\(320\) −1.28558 −1.28558
\(321\) 0 0
\(322\) −1.87939 −1.87939
\(323\) 0 0
\(324\) −3.10607 −3.10607
\(325\) −0.921605 −0.921605
\(326\) 0 0
\(327\) 0 0
\(328\) −5.67128 −5.67128
\(329\) 0 0
\(330\) −1.65270 −1.65270
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −3.25519 −3.25519
\(333\) 0 0
\(334\) 2.41609 2.41609
\(335\) 1.28558 1.28558
\(336\) 3.70167 3.70167
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 3.75877 3.75877
\(339\) 0 0
\(340\) −3.41147 −3.41147
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) 2.87939 2.87939
\(345\) 0.879385 0.879385
\(346\) −1.28558 −1.28558
\(347\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(348\) −4.98724 −4.98724
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 1.00000 1.00000
\(351\) 0.773318 0.773318
\(352\) −2.53209 −2.53209
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.53209 2.53209
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) −1.28558 −1.28558
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) −1.28558 −1.28558
\(364\) −4.38571 −4.38571
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 2.87939 2.87939
\(369\) −1.28558 −1.28558
\(370\) 0 0
\(371\) −0.347296 −0.347296
\(372\) 0 0
\(373\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(374\) −3.70167 −3.70167
\(375\) −1.34730 −1.34730
\(376\) 0 0
\(377\) 2.65366 2.65366
\(378\) −0.839100 −0.839100
\(379\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) −1.28558 −1.28558
\(385\) −0.684040 −0.684040
\(386\) 0 0
\(387\) 0.652704 0.652704
\(388\) 0 0
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 2.86257 2.86257
\(391\) 1.96962 1.96962
\(392\) 2.87939 2.87939
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −1.65270 −1.65270
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −1.53209 −1.53209
\(401\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 4.54077 4.54077
\(403\) 0 0
\(404\) 0 0
\(405\) 0.839100 0.839100
\(406\) −2.87939 −2.87939
\(407\) 0 0
\(408\) −7.29086 −7.29086
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 2.53209 2.53209
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 1.22668 1.22668
\(415\) 0.879385 0.879385
\(416\) 4.38571 4.38571
\(417\) 0.879385 0.879385
\(418\) 0 0
\(419\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(420\) −2.22668 −2.22668
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0.652704 0.652704
\(423\) 0 0
\(424\) 1.00000 1.00000
\(425\) −1.04801 −1.04801
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 2.22668 2.22668
\(430\) −1.28558 −1.28558
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 1.28558 1.28558
\(433\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(434\) 0 0
\(435\) 1.34730 1.34730
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 1.96962 1.96962
\(441\) 0.652704 0.652704
\(442\) 6.41147 6.41147
\(443\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 3.70167 3.70167
\(447\) 2.41609 2.41609
\(448\) −1.87939 −1.87939
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) −0.652704 −0.652704
\(451\) 1.96962 1.96962
\(452\) 0 0
\(453\) −1.28558 −1.28558
\(454\) 0 0
\(455\) 1.18479 1.18479
\(456\) 0 0
\(457\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(458\) 0 0
\(459\) 0.879385 0.879385
\(460\) −1.73205 −1.73205
\(461\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(462\) −2.41609 −2.41609
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 4.41147 4.41147
\(465\) 0 0
\(466\) −0.652704 −0.652704
\(467\) 1.28558 1.28558 0.642788 0.766044i \(-0.277778\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(468\) 2.86257 2.86257
\(469\) 1.87939 1.87939
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.00000 −1.00000
\(474\) 0 0
\(475\) 0 0
\(476\) −4.98724 −4.98724
\(477\) 0.226682 0.226682
\(478\) 0 0
\(479\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 2.22668 2.22668
\(481\) 0 0
\(482\) 0 0
\(483\) 1.28558 1.28558
\(484\) 2.53209 2.53209
\(485\) 0 0
\(486\) 2.12467 2.12467
\(487\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −1.28558 −1.28558
\(491\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(492\) 6.41147 6.41147
\(493\) 3.01763 3.01763
\(494\) 0 0
\(495\) 0.446476 0.446476
\(496\) 0 0
\(497\) 0 0
\(498\) 3.10607 3.10607
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 2.65366 2.65366
\(501\) −1.65270 −1.65270
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) −1.87939 −1.87939
\(505\) 0 0
\(506\) −1.87939 −1.87939
\(507\) −2.57115 −2.57115
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 3.25519 3.25519
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 0 0
\(514\) −3.70167 −3.70167
\(515\) 0 0
\(516\) −3.25519 −3.25519
\(517\) 0 0
\(518\) 0 0
\(519\) 0.879385 0.879385
\(520\) −3.41147 −3.41147
\(521\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(522\) 1.87939 1.87939
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) −0.684040 −0.684040
\(526\) −1.87939 −1.87939
\(527\) 0 0
\(528\) 3.70167 3.70167
\(529\) 0 0
\(530\) −0.446476 −0.446476
\(531\) 0 0
\(532\) 0 0
\(533\) −3.41147 −3.41147
\(534\) 0 0
\(535\) 0 0
\(536\) −5.41147 −5.41147
\(537\) 0 0
\(538\) 0 0
\(539\) −1.00000 −1.00000
\(540\) −0.773318 −0.773318
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 3.70167 3.70167
\(543\) 0 0
\(544\) 4.98724 4.98724
\(545\) 0 0
\(546\) 4.18479 4.18479
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 1.00000 1.00000
\(551\) 0 0
\(552\) −3.70167 −3.70167
\(553\) 0 0
\(554\) −2.87939 −2.87939
\(555\) 0 0
\(556\) −1.73205 −1.73205
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 1.73205 1.73205
\(560\) 1.96962 1.96962
\(561\) 2.53209 2.53209
\(562\) 0 0
\(563\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −3.25519 −3.25519
\(567\) 1.22668 1.22668
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(572\) −4.38571 −4.38571
\(573\) 0 0
\(574\) 3.70167 3.70167
\(575\) −0.532089 −0.532089
\(576\) 1.22668 1.22668
\(577\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(578\) 5.41147 5.41147
\(579\) 0 0
\(580\) −2.65366 −2.65366
\(581\) 1.28558 1.28558
\(582\) 0 0
\(583\) −0.347296 −0.347296
\(584\) 0 0
\(585\) −0.773318 −0.773318
\(586\) −3.25519 −3.25519
\(587\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) −3.25519 −3.25519
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) −0.839100 −0.839100
\(595\) 1.34730 1.34730
\(596\) −4.75877 −4.75877
\(597\) 0 0
\(598\) 3.25519 3.25519
\(599\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(600\) 1.96962 1.96962
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) −1.87939 −1.87939
\(603\) −1.22668 −1.22668
\(604\) 2.53209 2.53209
\(605\) −0.684040 −0.684040
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 1.96962 1.96962
\(610\) 0 0
\(611\) 0 0
\(612\) 3.25519 3.25519
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 2.41609 2.41609
\(615\) −1.73205 −1.73205
\(616\) 2.87939 2.87939
\(617\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0.446476 0.446476
\(622\) 0 0
\(623\) 0 0
\(624\) −6.41147 −6.41147
\(625\) −0.184793 −0.184793
\(626\) 3.70167 3.70167
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0.839100 0.839100
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) −0.446476 −0.446476
\(634\) −1.87939 −1.87939
\(635\) 0 0
\(636\) −1.13052 −1.13052
\(637\) 1.73205 1.73205
\(638\) −2.87939 −2.87939
\(639\) 0 0
\(640\) −0.684040 −0.684040
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) −2.53209 −2.53209
\(645\) 0.879385 0.879385
\(646\) 0 0
\(647\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) −3.53209 −3.53209
\(649\) 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
\(656\) −5.67128 −5.67128
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) −2.22668 −2.22668
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) −4.38571 −4.38571
\(664\) −3.70167 −3.70167
\(665\) 0 0
\(666\) 0 0
\(667\) 1.53209 1.53209
\(668\) 3.25519 3.25519
\(669\) −2.53209 −2.53209
\(670\) 2.41609 2.41609
\(671\) 0 0
\(672\) 3.25519 3.25519
\(673\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(674\) 0 0
\(675\) −0.237565 −0.237565
\(676\) 5.06418 5.06418
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3.87939 −3.87939
\(681\) 0 0
\(682\) 0 0
\(683\) 0.347296 0.347296 0.173648 0.984808i \(-0.444444\pi\)
0.173648 + 0.984808i \(0.444444\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.87939 −1.87939
\(687\) 0 0
\(688\) 2.87939 2.87939
\(689\) 0.601535 0.601535
\(690\) 1.65270 1.65270
\(691\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(692\) −1.73205 −1.73205
\(693\) 0.652704 0.652704
\(694\) −3.53209 −3.53209
\(695\) 0.467911 0.467911
\(696\) −5.67128 −5.67128
\(697\) −3.87939 −3.87939
\(698\) 0 0
\(699\) 0.446476 0.446476
\(700\) 1.34730 1.34730
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 1.45336 1.45336
\(703\) 0 0
\(704\) −1.87939 −1.87939
\(705\) 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
\(714\) 4.75877 4.75877
\(715\) 1.18479 1.18479
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(720\) −1.28558 −1.28558
\(721\) 0 0
\(722\) 1.87939 1.87939
\(723\) 0 0
\(724\) 0 0
\(725\) −0.815207 −0.815207
\(726\) −2.41609 −2.41609
\(727\) −0.684040 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(728\) −4.98724 −4.98724
\(729\) −0.226682 −0.226682
\(730\) 0 0
\(731\) 1.96962 1.96962
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) 0.879385 0.879385
\(736\) 2.53209 2.53209
\(737\) 1.87939 1.87939
\(738\) −2.41609 −2.41609
\(739\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.652704 −0.652704
\(743\) −1.53209 −1.53209 −0.766044 0.642788i \(-0.777778\pi\)
−0.766044 + 0.642788i \(0.777778\pi\)
\(744\) 0 0
\(745\) 1.28558 1.28558
\(746\) −3.53209 −3.53209
\(747\) −0.839100 −0.839100
\(748\) −4.98724 −4.98724
\(749\) 0 0
\(750\) −2.53209 −2.53209
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 4.98724 4.98724
\(755\) −0.684040 −0.684040
\(756\) −1.13052 −1.13052
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −0.652704 −0.652704
\(759\) 1.28558 1.28558
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.879385 −0.879385
\(766\) −3.25519 −3.25519
\(767\) 0 0
\(768\) 0 0
\(769\) −1.28558 −1.28558 −0.642788 0.766044i \(-0.722222\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(770\) −1.28558 −1.28558
\(771\) 2.53209 2.53209
\(772\) 0 0
\(773\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(774\) 1.22668 1.22668
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 3.85673 3.85673
\(781\) 0 0
\(782\) 3.70167 3.70167
\(783\) 0.684040 0.684040
\(784\) 2.87939 2.87939
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 1.28558 1.28558
\(790\) 0 0
\(791\) 0 0
\(792\) −1.87939 −1.87939
\(793\) 0 0
\(794\) 0 0
\(795\) 0.305407 0.305407
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.34730 −1.34730
\(801\) 0 0
\(802\) −1.87939 −1.87939
\(803\) 0 0
\(804\) 6.11776 6.11776
\(805\) 0.684040 0.684040
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 1.57699 1.57699
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −3.87939 −3.87939
\(813\) −2.53209 −2.53209
\(814\) 0 0
\(815\) 0 0
\(816\) −7.29086 −7.29086
\(817\) 0 0
\(818\) 0 0
\(819\) −1.13052 −1.13052
\(820\) 3.41147 3.41147
\(821\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(822\) 0 0
\(823\) −0.347296 −0.347296 −0.173648 0.984808i \(-0.555556\pi\)
−0.173648 + 0.984808i \(0.555556\pi\)
\(824\) 0 0
\(825\) −0.684040 −0.684040
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 1.65270 1.65270
\(829\) −1.96962 −1.96962 −0.984808 0.173648i \(-0.944444\pi\)
−0.984808 + 0.173648i \(0.944444\pi\)
\(830\) 1.65270 1.65270
\(831\) 1.96962 1.96962
\(832\) 3.25519 3.25519
\(833\) 1.96962 1.96962
\(834\) 1.65270 1.65270
\(835\) −0.879385 −0.879385
\(836\) 0 0
\(837\) 0 0
\(838\) 1.28558 1.28558
\(839\) 1.73205 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(840\) −2.53209 −2.53209
\(841\) 1.34730 1.34730
\(842\) 0 0
\(843\) 0 0
\(844\) 0.879385 0.879385
\(845\) −1.36808 −1.36808
\(846\) 0 0
\(847\) −1.00000 −1.00000
\(848\) 1.00000 1.00000
\(849\) 2.22668 2.22668
\(850\) −1.96962 −1.96962
\(851\) 0 0
\(852\) 0 0
\(853\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(858\) 4.18479 4.18479
\(859\) 1.96962 1.96962 0.984808 0.173648i \(-0.0555556\pi\)
0.984808 + 0.173648i \(0.0555556\pi\)
\(860\) −1.73205 −1.73205
\(861\) −2.53209 −2.53209
\(862\) 0 0
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 1.13052 1.13052
\(865\) 0.467911 0.467911
\(866\) −3.25519 −3.25519
\(867\) −3.70167 −3.70167
\(868\) 0 0
\(869\) 0 0
\(870\) 2.53209 2.53209
\(871\) −3.25519 −3.25519
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.04801 −1.04801
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) −3.25519 −3.25519
\(879\) 2.22668 2.22668
\(880\) 1.96962 1.96962
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 1.22668 1.22668
\(883\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(884\) 8.63816 8.63816
\(885\) 0 0
\(886\) −0.652704 −0.652704
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.22668 1.22668
\(892\) 4.98724 4.98724
\(893\) 0 0
\(894\) 4.54077 4.54077
\(895\) 0 0
\(896\) −1.00000 −1.00000
\(897\) −2.22668 −2.22668
\(898\) 0 0
\(899\) 0 0
\(900\) −0.879385 −0.879385
\(901\) 0.684040 0.684040
\(902\) 3.70167 3.70167
\(903\) 1.28558 1.28558
\(904\) 0 0
\(905\) 0 0
\(906\) −2.41609 −2.41609
\(907\) 1.87939 1.87939 0.939693 0.342020i \(-0.111111\pi\)
0.939693 + 0.342020i \(0.111111\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 2.22668 2.22668
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 1.28558 1.28558
\(914\) 2.87939 2.87939
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 1.65270 1.65270
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) −1.96962 −1.96962
\(921\) −1.65270 −1.65270
\(922\) −2.41609 −2.41609
\(923\) 0 0
\(924\) −3.25519 −3.25519
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 3.87939 3.87939
\(929\) −1.73205 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −0.879385 −0.879385
\(933\) 0 0
\(934\) 2.41609 2.41609
\(935\) 1.34730 1.34730
\(936\) 3.25519 3.25519
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 3.53209 3.53209
\(939\) −2.53209 −2.53209
\(940\) 0 0
\(941\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(942\) 0 0
\(943\) −1.96962 −1.96962
\(944\) 0 0
\(945\) 0.305407 0.305407
\(946\) −1.87939 −1.87939
\(947\) −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
\(951\) 1.28558 1.28558
\(952\) −5.67128 −5.67128
\(953\) −1.87939 −1.87939 −0.939693 0.342020i \(-0.888889\pi\)
−0.939693 + 0.342020i \(0.888889\pi\)
\(954\) 0.426022 0.426022
\(955\) 0 0
\(956\) 0 0
\(957\) 1.96962 1.96962
\(958\) 3.25519 3.25519
\(959\) 0 0
\(960\) 1.65270 1.65270
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 2.41609 2.41609
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) 2.87939 2.87939
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 2.86257 2.86257
\(973\) 0.684040 0.684040
\(974\) 0.652704 0.652704
\(975\) 1.18479 1.18479
\(976\) 0 0
\(977\) 1.53209 1.53209 0.766044 0.642788i \(-0.222222\pi\)
0.766044 + 0.642788i \(0.222222\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −1.73205 −1.73205
\(981\) 0 0
\(982\) 0.652704 0.652704
\(983\) 0.684040 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(984\) 7.29086 7.29086
\(985\) 0 0
\(986\) 5.67128 5.67128
\(987\) 0 0
\(988\) 0 0
\(989\) 1.00000 1.00000
\(990\) 0.839100 0.839100
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 4.18479 4.18479
\(997\) 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 \(a_p\))