Properties

Label 799.1.c.d.798.1
Level $799$
Weight $1$
Character 799.798
Analytic conductor $0.399$
Analytic rank $0$
Dimension $4$
Projective image $D_{10}$
CM discriminant -47
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 799.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.398752945094\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{10}\)
Projective field: Galois closure of 10.2.6928449225617.1

Embedding invariants

Embedding label 798.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 799.798
Dual form 799.1.c.d.798.2

$q$-expansion

\(f(q)\) \(=\) \(q-0.618034 q^{2} -1.17557i q^{3} -0.618034 q^{4} +0.726543i q^{6} -1.90211i q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\) \(q-0.618034 q^{2} -1.17557i q^{3} -0.618034 q^{4} +0.726543i q^{6} -1.90211i q^{7} +1.00000 q^{8} -0.381966 q^{9} +0.726543i q^{12} +1.17557i q^{14} +(-0.809017 + 0.587785i) q^{17} +0.236068 q^{18} -2.23607 q^{21} -1.17557i q^{24} -1.00000 q^{25} -0.726543i q^{27} +1.17557i q^{28} -1.00000 q^{32} +(0.500000 - 0.363271i) q^{34} +0.236068 q^{36} -1.17557i q^{37} +1.38197 q^{42} +1.00000 q^{47} -2.61803 q^{49} +0.618034 q^{50} +(0.690983 + 0.951057i) q^{51} +0.618034 q^{53} +0.449028i q^{54} -1.90211i q^{56} -0.618034 q^{59} +1.90211i q^{61} +0.726543i q^{63} +0.618034 q^{64} +(0.500000 - 0.363271i) q^{68} +1.17557i q^{71} -0.381966 q^{72} +0.726543i q^{74} +1.17557i q^{75} -1.17557i q^{79} -1.23607 q^{81} +2.00000 q^{83} +1.38197 q^{84} +0.618034 q^{89} -0.618034 q^{94} +1.17557i q^{96} -1.90211i q^{97} +1.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 2 q^{4} + 4 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 2 q^{4} + 4 q^{8} - 6 q^{9} - q^{17} - 8 q^{18} - 4 q^{25} - 4 q^{32} + 2 q^{34} - 8 q^{36} + 10 q^{42} + 4 q^{47} - 6 q^{49} - 2 q^{50} + 5 q^{51} - 2 q^{53} + 2 q^{59} - 2 q^{64} + 2 q^{68} - 6 q^{72} + 4 q^{81} + 8 q^{83} + 10 q^{84} - 2 q^{89} + 2 q^{94} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/799\mathbb{Z}\right)^\times\).

\(n\) \(52\) \(377\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(3\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(4\) −0.618034 −0.618034
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0.726543i 0.726543i
\(7\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(8\) 1.00000 1.00000
\(9\) −0.381966 −0.381966
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0.726543i 0.726543i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 1.17557i 1.17557i
\(15\) 0 0
\(16\) 0 0
\(17\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(18\) 0.236068 0.236068
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) −2.23607 −2.23607
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.17557i 1.17557i
\(25\) −1.00000 −1.00000
\(26\) 0 0
\(27\) 0.726543i 0.726543i
\(28\) 1.17557i 1.17557i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) 0.500000 0.363271i 0.500000 0.363271i
\(35\) 0 0
\(36\) 0.236068 0.236068
\(37\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 1.38197 1.38197
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.00000 1.00000
\(48\) 0 0
\(49\) −2.61803 −2.61803
\(50\) 0.618034 0.618034
\(51\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(52\) 0 0
\(53\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(54\) 0.449028i 0.449028i
\(55\) 0 0
\(56\) 1.90211i 1.90211i
\(57\) 0 0
\(58\) 0 0
\(59\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(60\) 0 0
\(61\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(62\) 0 0
\(63\) 0.726543i 0.726543i
\(64\) 0.618034 0.618034
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0.500000 0.363271i 0.500000 0.363271i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(72\) −0.381966 −0.381966
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0.726543i 0.726543i
\(75\) 1.17557i 1.17557i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(80\) 0 0
\(81\) −1.23607 −1.23607
\(82\) 0 0
\(83\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(84\) 1.38197 1.38197
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −0.618034 −0.618034
\(95\) 0 0
\(96\) 1.17557i 1.17557i
\(97\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(98\) 1.61803 1.61803
\(99\) 0 0
\(100\) 0.618034 0.618034
\(101\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(102\) −0.427051 0.587785i −0.427051 0.587785i
\(103\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −0.381966 −0.381966
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0.449028i 0.449028i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) −1.38197 −1.38197
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.381966 0.381966
\(119\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) 1.17557i 1.17557i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0.449028i 0.449028i
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0.618034 0.618034
\(129\) 0 0
\(130\) 0 0
\(131\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 1.17557i 1.17557i
\(142\) 0.726543i 0.726543i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 3.07768i 3.07768i
\(148\) 0.726543i 0.726543i
\(149\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(150\) 0.726543i 0.726543i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0.309017 0.224514i 0.309017 0.224514i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(158\) 0.726543i 0.726543i
\(159\) 0.726543i 0.726543i
\(160\) 0 0
\(161\) 0 0
\(162\) 0.763932 0.763932
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −1.23607 −1.23607
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) −2.23607 −2.23607
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(174\) 0 0
\(175\) 1.90211i 1.90211i
\(176\) 0 0
\(177\) 0.726543i 0.726543i
\(178\) −0.381966 −0.381966
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 2.23607 2.23607
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.618034 −0.618034
\(189\) −1.38197 −1.38197
\(190\) 0 0
\(191\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(192\) 0.726543i 0.726543i
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 1.17557i 1.17557i
\(195\) 0 0
\(196\) 1.61803 1.61803
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −1.00000 −1.00000
\(201\) 0 0
\(202\) −1.00000 −1.00000
\(203\) 0 0
\(204\) −0.427051 0.587785i −0.427051 0.587785i
\(205\) 0 0
\(206\) −1.00000 −1.00000
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) −0.381966 −0.381966
\(213\) 1.38197 1.38197
\(214\) 0 0
\(215\) 0 0
\(216\) 0.726543i 0.726543i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0.854102 0.854102
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 1.90211i 1.90211i
\(225\) 0.381966 0.381966
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.381966 0.381966
\(237\) −1.38197 −1.38197
\(238\) −0.690983 0.951057i −0.690983 0.951057i
\(239\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) 0 0
\(241\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(242\) 0.618034 0.618034
\(243\) 0.726543i 0.726543i
\(244\) 1.17557i 1.17557i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 2.35114i 2.35114i
\(250\) 0 0
\(251\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(252\) 0.449028i 0.449028i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −1.00000 −1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −2.23607 −2.23607
\(260\) 0 0
\(261\) 0 0
\(262\) 1.17557i 1.17557i
\(263\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.726543i 0.726543i
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0.726543i 0.726543i
\(283\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(284\) 0.726543i 0.726543i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.381966 0.381966
\(289\) 0.309017 0.951057i 0.309017 0.951057i
\(290\) 0 0
\(291\) −2.23607 −2.23607
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 1.90211i 1.90211i
\(295\) 0 0
\(296\) 1.17557i 1.17557i
\(297\) 0 0
\(298\) −1.00000 −1.00000
\(299\) 0 0
\(300\) 0.726543i 0.726543i
\(301\) 0 0
\(302\) 0 0
\(303\) 1.90211i 1.90211i
\(304\) 0 0
\(305\) 0 0
\(306\) −0.190983 + 0.138757i −0.190983 + 0.138757i
\(307\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(308\) 0 0
\(309\) 1.90211i 1.90211i
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 0.381966 0.381966
\(315\) 0 0
\(316\) 0.726543i 0.726543i
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0.449028i 0.449028i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.763932 0.763932
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.90211i 1.90211i
\(330\) 0 0
\(331\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(332\) −1.23607 −1.23607
\(333\) 0.449028i 0.449028i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(338\) −0.618034 −0.618034
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 3.07768i 3.07768i
\(344\) 0 0
\(345\) 0 0
\(346\) 1.17557i 1.17557i
\(347\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 1.17557i 1.17557i
\(351\) 0 0
\(352\) 0 0
\(353\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(354\) 0.449028i 0.449028i
\(355\) 0 0
\(356\) −0.381966 −0.381966
\(357\) 1.80902 1.31433i 1.80902 1.31433i
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 1.00000 1.00000
\(362\) 0 0
\(363\) 1.17557i 1.17557i
\(364\) 0 0
\(365\) 0 0
\(366\) −1.38197 −1.38197
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.17557i 1.17557i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.00000 1.00000
\(377\) 0 0
\(378\) 0.854102 0.854102
\(379\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.23607 1.23607
\(383\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(384\) 0.726543i 0.726543i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 1.17557i 1.17557i
\(389\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −2.61803 −2.61803
\(393\) −2.23607 −2.23607
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −1.00000 −1.00000
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.00000 −1.00000
\(413\) 1.17557i 1.17557i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) −0.381966 −0.381966
\(424\) 0.618034 0.618034
\(425\) 0.809017 0.587785i 0.809017 0.587785i
\(426\) −0.854102 −0.854102
\(427\) 3.61803 3.61803
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1.00000 1.00000
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0.854102 0.854102
\(445\) 0 0
\(446\) 0 0
\(447\) 1.90211i 1.90211i
\(448\) 1.17557i 1.17557i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) −0.236068 −0.236068
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(458\) 0 0
\(459\) 0.427051 + 0.587785i 0.427051 + 0.587785i
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0.726543i 0.726543i
\(472\) −0.618034 −0.618034
\(473\) 0 0
\(474\) 0.854102 0.854102
\(475\) 0 0
\(476\) −0.690983 0.951057i −0.690983 0.951057i
\(477\) −0.236068 −0.236068
\(478\) 1.00000 1.00000
\(479\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.726543i 0.726543i
\(483\) 0 0
\(484\) 0.618034 0.618034
\(485\) 0 0
\(486\) 0.449028i 0.449028i
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 1.90211i 1.90211i
\(489\) 0 0
\(490\) 0 0
\(491\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.23607 2.23607
\(498\) 1.45309i 1.45309i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.00000 −1.00000
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0.726543i 0.726543i
\(505\) 0 0
\(506\) 0 0
\(507\) 1.17557i 1.17557i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 1.38197 1.38197
\(519\) 2.23607 2.23607
\(520\) 0 0
\(521\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(522\) 0 0
\(523\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(524\) 1.17557i 1.17557i
\(525\) 2.23607 2.23607
\(526\) 0.381966 0.381966
\(527\) 0 0
\(528\) 0 0
\(529\) −1.00000 −1.00000
\(530\) 0 0
\(531\) 0.236068 0.236068
\(532\) 0 0
\(533\) 0 0
\(534\) 0.449028i 0.449028i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(542\) −1.00000 −1.00000
\(543\) 0 0
\(544\) 0.809017 0.587785i 0.809017 0.587785i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 0 0
\(549\) 0.726543i 0.726543i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −2.23607 −2.23607
\(554\) 0.726543i 0.726543i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0.726543i 0.726543i
\(565\) 0 0
\(566\) 1.17557i 1.17557i
\(567\) 2.35114i 2.35114i
\(568\) 1.17557i 1.17557i
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(572\) 0 0
\(573\) 2.35114i 2.35114i
\(574\) 0 0
\(575\) 0 0
\(576\) −0.236068 −0.236068
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(579\) 0 0
\(580\) 0 0
\(581\) 3.80423i 3.80423i
\(582\) 1.38197 1.38197
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 1.90211i 1.90211i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.00000 −1.00000
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 1.17557i 1.17557i
\(601\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 1.17557i 1.17557i
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.190983 + 0.138757i −0.190983 + 0.138757i
\(613\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) −1.00000 −1.00000
\(615\) 0 0
\(616\) 0 0
\(617\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(618\) 1.17557i 1.17557i
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.17557i 1.17557i
\(624\) 0 0
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0.381966 0.381966
\(629\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 1.17557i 1.17557i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0.449028i 0.449028i
\(637\) 0 0
\(638\) 0 0
\(639\) 0.449028i 0.449028i
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(648\) −1.23607 −1.23607
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.17557i 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 1.17557i 1.17557i
\(659\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(660\) 0 0
\(661\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(662\) 0.381966 0.381966
\(663\) 0 0
\(664\) 2.00000 2.00000
\(665\) 0 0
\(666\) 0.277515i 0.277515i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 2.23607 2.23607
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 1.17557i 1.17557i
\(675\) 0.726543i 0.726543i
\(676\) −0.618034 −0.618034
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) −3.61803 −3.61803
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.90211i 1.90211i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 1.17557i 1.17557i
\(693\) 0 0
\(694\) 0.726543i 0.726543i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 1.17557i 1.17557i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.381966 0.381966
\(707\) 3.07768i 3.07768i
\(708\) 0.449028i 0.449028i
\(709\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(710\) 0 0
\(711\) 0.449028i 0.449028i
\(712\) 0.618034 0.618034
\(713\) 0 0
\(714\) −1.11803 + 0.812299i −1.11803 + 0.812299i
\(715\) 0 0
\(716\) 0 0
\(717\) 1.90211i 1.90211i
\(718\) 0 0
\(719\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(720\) 0 0
\(721\) 3.07768i 3.07768i
\(722\) −0.618034 −0.618034
\(723\) −1.38197 −1.38197
\(724\) 0 0
\(725\) 0 0
\(726\) 0.726543i 0.726543i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −0.381966 −0.381966
\(730\) 0 0
\(731\) 0 0
\(732\) −1.38197 −1.38197
\(733\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.726543i 0.726543i
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.763932 −0.763932
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 1.90211i 1.90211i
\(754\) 0 0
\(755\) 0 0
\(756\) 0.854102 0.854102
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 1.17557i 1.17557i
\(759\) 0 0
\(760\) 0 0
\(761\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1.23607 1.23607
\(765\) 0 0
\(766\) 1.00000 1.00000
\(767\) 0 0
\(768\) 1.17557i 1.17557i
\(769\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.90211i 1.90211i
\(777\) 2.62866i 2.62866i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 1.38197 1.38197
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 0.726543i 0.726543i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0.726543i 0.726543i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(800\) 1.00000 1.00000
\(801\) −0.236068 −0.236068
\(802\) 0.726543i 0.726543i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 1.61803 1.61803
\(809\) 0 0