Properties

Label 1400.1.bs.c.1021.1
Level $1400$
Weight $1$
Character 1400.1021
Analytic conductor $0.699$
Analytic rank $0$
Dimension $8$
Projective image $D_{10}$
CM discriminant -56
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1400.bs (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.698691017686\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
Defining polynomial: \(x^{8} - x^{6} + x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{10}\)
Projective field: Galois closure of 10.0.10504375000000000000.2

Embedding invariants

Embedding label 1021.1
Root \(-0.587785 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 1400.1021
Dual form 1400.1.bs.c.181.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(-0.951057 - 0.690983i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.951057 - 0.309017i) q^{5} +(0.951057 - 0.690983i) q^{6} -1.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.118034 + 0.363271i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(-0.951057 - 0.690983i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.951057 - 0.309017i) q^{5} +(0.951057 - 0.690983i) q^{6} -1.00000 q^{7} +(0.809017 - 0.587785i) q^{8} +(0.118034 + 0.363271i) q^{9} +(0.587785 - 0.809017i) q^{10} +(0.363271 + 1.11803i) q^{12} +(-0.363271 - 1.11803i) q^{13} +(0.309017 - 0.951057i) q^{14} +(0.690983 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} -0.381966 q^{18} +(0.587785 + 0.809017i) q^{20} +(0.951057 + 0.690983i) q^{21} +(-0.500000 + 1.53884i) q^{23} -1.17557 q^{24} +(0.809017 + 0.587785i) q^{25} +1.17557 q^{26} +(-0.224514 + 0.690983i) q^{27} +(0.809017 + 0.587785i) q^{28} +(-1.11803 + 0.363271i) q^{30} -1.00000 q^{32} +(0.951057 + 0.309017i) q^{35} +(0.118034 - 0.363271i) q^{36} +(-0.427051 + 1.31433i) q^{39} +(-0.951057 + 0.309017i) q^{40} +(-0.951057 + 0.690983i) q^{42} -0.381966i q^{45} +(-1.30902 - 0.951057i) q^{46} +(0.363271 - 1.11803i) q^{48} +1.00000 q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.363271 + 1.11803i) q^{52} +(-0.587785 - 0.427051i) q^{54} +(-0.809017 + 0.587785i) q^{56} +(0.587785 + 1.80902i) q^{59} -1.17557i q^{60} +(-0.587785 + 1.80902i) q^{61} +(-0.118034 - 0.363271i) q^{63} +(0.309017 - 0.951057i) q^{64} +1.17557i q^{65} +(1.53884 - 1.11803i) q^{69} +(-0.587785 + 0.809017i) q^{70} +(0.500000 + 0.363271i) q^{71} +(0.309017 + 0.224514i) q^{72} +(-0.363271 - 1.11803i) q^{75} +(-1.11803 - 0.812299i) q^{78} +(-1.30902 - 0.951057i) q^{79} -1.00000i q^{80} +(1.00000 - 0.726543i) q^{81} +(-1.53884 + 1.11803i) q^{83} +(-0.363271 - 1.11803i) q^{84} +(0.363271 + 0.118034i) q^{90} +(0.363271 + 1.11803i) q^{91} +(1.30902 - 0.951057i) q^{92} +(0.951057 + 0.690983i) q^{96} +(-0.309017 + 0.951057i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 2q^{4} - 8q^{7} + 2q^{8} - 8q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 2q^{4} - 8q^{7} + 2q^{8} - 8q^{9} - 2q^{14} + 10q^{15} - 2q^{16} - 12q^{18} - 4q^{23} + 2q^{25} + 2q^{28} - 8q^{32} - 8q^{36} + 10q^{39} - 6q^{46} + 8q^{49} - 2q^{50} - 2q^{56} + 8q^{63} - 2q^{64} + 4q^{71} - 2q^{72} - 6q^{79} + 8q^{81} + 6q^{92} + 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(3\) −0.951057 0.690983i −0.951057 0.690983i 1.00000i \(-0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(4\) −0.809017 0.587785i −0.809017 0.587785i
\(5\) −0.951057 0.309017i −0.951057 0.309017i
\(6\) 0.951057 0.690983i 0.951057 0.690983i
\(7\) −1.00000 −1.00000
\(8\) 0.809017 0.587785i 0.809017 0.587785i
\(9\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(10\) 0.587785 0.809017i 0.587785 0.809017i
\(11\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(12\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(13\) −0.363271 1.11803i −0.363271 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(14\) 0.309017 0.951057i 0.309017 0.951057i
\(15\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(16\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(17\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) −0.381966 −0.381966
\(19\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(20\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(21\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(22\) 0 0
\(23\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(24\) −1.17557 −1.17557
\(25\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(26\) 1.17557 1.17557
\(27\) −0.224514 + 0.690983i −0.224514 + 0.690983i
\(28\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(29\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(30\) −1.11803 + 0.363271i −1.11803 + 0.363271i
\(31\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(36\) 0.118034 0.363271i 0.118034 0.363271i
\(37\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(38\) 0 0
\(39\) −0.427051 + 1.31433i −0.427051 + 1.31433i
\(40\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(41\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(42\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0.381966i 0.381966i
\(46\) −1.30902 0.951057i −1.30902 0.951057i
\(47\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(48\) 0.363271 1.11803i 0.363271 1.11803i
\(49\) 1.00000 1.00000
\(50\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(51\) 0 0
\(52\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(53\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(54\) −0.587785 0.427051i −0.587785 0.427051i
\(55\) 0 0
\(56\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(57\) 0 0
\(58\) 0 0
\(59\) 0.587785 + 1.80902i 0.587785 + 1.80902i 0.587785 + 0.809017i \(0.300000\pi\)
1.00000i \(0.5\pi\)
\(60\) 1.17557i 1.17557i
\(61\) −0.587785 + 1.80902i −0.587785 + 1.80902i 1.00000i \(0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(62\) 0 0
\(63\) −0.118034 0.363271i −0.118034 0.363271i
\(64\) 0.309017 0.951057i 0.309017 0.951057i
\(65\) 1.17557i 1.17557i
\(66\) 0 0
\(67\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(68\) 0 0
\(69\) 1.53884 1.11803i 1.53884 1.11803i
\(70\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(71\) 0.500000 + 0.363271i 0.500000 + 0.363271i 0.809017 0.587785i \(-0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(72\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(73\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(74\) 0 0
\(75\) −0.363271 1.11803i −0.363271 1.11803i
\(76\) 0 0
\(77\) 0 0
\(78\) −1.11803 0.812299i −1.11803 0.812299i
\(79\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(80\) 1.00000i 1.00000i
\(81\) 1.00000 0.726543i 1.00000 0.726543i
\(82\) 0 0
\(83\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(84\) −0.363271 1.11803i −0.363271 1.11803i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(90\) 0.363271 + 0.118034i 0.363271 + 0.118034i
\(91\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(92\) 1.30902 0.951057i 1.30902 0.951057i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(97\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(98\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(99\) 0 0
\(100\) −0.309017 0.951057i −0.309017 0.951057i
\(101\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(104\) −0.951057 0.690983i −0.951057 0.690983i
\(105\) −0.690983 0.951057i −0.690983 0.951057i
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0.587785 0.427051i 0.587785 0.427051i
\(109\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.309017 0.951057i −0.309017 0.951057i
\(113\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0.951057 1.30902i 0.951057 1.30902i
\(116\) 0 0
\(117\) 0.363271 0.263932i 0.363271 0.263932i
\(118\) −1.90211 −1.90211
\(119\) 0 0
\(120\) 1.11803 + 0.363271i 1.11803 + 0.363271i
\(121\) −0.809017 0.587785i −0.809017 0.587785i
\(122\) −1.53884 1.11803i −1.53884 1.11803i
\(123\) 0 0
\(124\) 0 0
\(125\) −0.587785 0.809017i −0.587785 0.809017i
\(126\) 0.381966 0.381966
\(127\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(128\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(129\) 0 0
\(130\) −1.11803 0.363271i −1.11803 0.363271i
\(131\) 1.53884 1.11803i 1.53884 1.11803i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0.427051 0.587785i 0.427051 0.587785i
\(136\) 0 0
\(137\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(139\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(140\) −0.587785 0.809017i −0.587785 0.809017i
\(141\) 0 0
\(142\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(143\) 0 0
\(144\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.951057 0.690983i −0.951057 0.690983i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) 1.17557 1.17557
\(151\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 1.11803 0.812299i 1.11803 0.812299i
\(157\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(158\) 1.30902 0.951057i 1.30902 0.951057i
\(159\) 0 0
\(160\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(161\) 0.500000 1.53884i 0.500000 1.53884i
\(162\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(163\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −0.587785 1.80902i −0.587785 1.80902i
\(167\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(168\) 1.17557 1.17557
\(169\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.587785 + 1.80902i −0.587785 + 1.80902i 1.00000i \(0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(174\) 0 0
\(175\) −0.809017 0.587785i −0.809017 0.587785i
\(176\) 0 0
\(177\) 0.690983 2.12663i 0.690983 2.12663i
\(178\) 0 0
\(179\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(180\) −0.224514 + 0.309017i −0.224514 + 0.309017i
\(181\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(182\) −1.17557 −1.17557
\(183\) 1.80902 1.31433i 1.80902 1.31433i
\(184\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0.224514 0.690983i 0.224514 0.690983i
\(190\) 0 0
\(191\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(192\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(193\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(194\) 0 0
\(195\) 0.812299 1.11803i 0.812299 1.11803i
\(196\) −0.809017 0.587785i −0.809017 0.587785i
\(197\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.00000 1.00000
\(201\) 0 0
\(202\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.618034 −0.618034
\(208\) 0.951057 0.690983i 0.951057 0.690983i
\(209\) 0 0
\(210\) 1.11803 0.363271i 1.11803 0.363271i
\(211\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(212\) 0 0
\(213\) −0.224514 0.690983i −0.224514 0.690983i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.224514 + 0.690983i 0.224514 + 0.690983i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(224\) 1.00000 1.00000
\(225\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(226\) 0.618034 0.618034
\(227\) 0.363271 1.11803i 0.363271 1.11803i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(228\) 0 0
\(229\) −1.53884 1.11803i −1.53884 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(230\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(231\) 0 0
\(232\) 0 0
\(233\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(234\) 0.138757 + 0.427051i 0.138757 + 0.427051i
\(235\) 0 0
\(236\) 0.587785 1.80902i 0.587785 1.80902i
\(237\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(238\) 0 0
\(239\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) −0.690983 + 0.951057i −0.690983 + 0.951057i
\(241\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(242\) 0.809017 0.587785i 0.809017 0.587785i
\(243\) −0.726543 −0.726543
\(244\) 1.53884 1.11803i 1.53884 1.11803i
\(245\) −0.951057 0.309017i −0.951057 0.309017i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 2.23607 2.23607
\(250\) 0.951057 0.309017i 0.951057 0.309017i
\(251\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(252\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(253\) 0 0
\(254\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(255\) 0 0
\(256\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.690983 0.951057i 0.690983 0.951057i
\(261\) 0 0
\(262\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(263\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(270\) 0.427051 + 0.587785i 0.427051 + 0.587785i
\(271\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(272\) 0 0
\(273\) 0.427051 1.31433i 0.427051 1.31433i
\(274\) −2.00000 −2.00000
\(275\) 0 0
\(276\) −1.90211 −1.90211
\(277\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.951057 0.309017i 0.951057 0.309017i
\(281\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(282\) 0 0
\(283\) −0.951057 + 0.690983i −0.951057 + 0.690983i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(0.5\pi\)
\(284\) −0.190983 0.587785i −0.190983 0.587785i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.118034 0.363271i −0.118034 0.363271i
\(289\) 0.309017 0.951057i 0.309017 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0.951057 0.690983i 0.951057 0.690983i
\(295\) 1.90211i 1.90211i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.90211 1.90211
\(300\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(301\) 0 0
\(302\) 0.500000 1.53884i 0.500000 1.53884i
\(303\) −1.11803 0.812299i −1.11803 0.812299i
\(304\) 0 0
\(305\) 1.11803 1.53884i 1.11803 1.53884i
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(312\) 0.427051 + 1.31433i 0.427051 + 1.31433i
\(313\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(314\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(315\) 0.381966i 0.381966i
\(316\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(317\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(321\) 0 0
\(322\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(323\) 0 0
\(324\) −1.23607 −1.23607
\(325\) 0.363271 1.11803i 0.363271 1.11803i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(332\) 1.90211 1.90211
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(337\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(338\) −0.118034 0.363271i −0.118034 0.363271i
\(339\) −0.224514 + 0.690983i −0.224514 + 0.690983i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) 0 0
\(345\) −1.80902 + 0.587785i −1.80902 + 0.587785i
\(346\) −1.53884 1.11803i −1.53884 1.11803i
\(347\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(348\) 0 0
\(349\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(350\) 0.809017 0.587785i 0.809017 0.587785i
\(351\) 0.854102 0.854102
\(352\) 0 0
\(353\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(354\) 1.80902 + 1.31433i 1.80902 + 1.31433i
\(355\) −0.363271 0.500000i −0.363271 0.500000i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(360\) −0.224514 0.309017i −0.224514 0.309017i
\(361\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(362\) −0.587785 1.80902i −0.587785 1.80902i
\(363\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(364\) 0.363271 1.11803i 0.363271 1.11803i
\(365\) 0 0
\(366\) 0.690983 + 2.12663i 0.690983 + 2.12663i
\(367\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(368\) −1.61803 −1.61803
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(374\) 0 0
\(375\) 1.17557i 1.17557i
\(376\) 0 0
\(377\) 0 0
\(378\) 0.587785 + 0.427051i 0.587785 + 0.427051i
\(379\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(380\) 0 0
\(381\) −1.90211 + 1.38197i −1.90211 + 1.38197i
\(382\) −1.61803 −1.61803
\(383\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(384\) −0.363271 1.11803i −0.363271 1.11803i
\(385\) 0 0
\(386\) 0.190983 0.587785i 0.190983 0.587785i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(390\) 0.812299 + 1.11803i 0.812299 + 1.11803i
\(391\) 0 0
\(392\) 0.809017 0.587785i 0.809017 0.587785i
\(393\) −2.23607 −2.23607
\(394\) 0 0
\(395\) 0.951057 + 1.30902i 0.951057 + 1.30902i
\(396\) 0 0
\(397\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(401\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.951057 0.690983i −0.951057 0.690983i
\(405\) −1.17557 + 0.381966i −1.17557 + 0.381966i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(410\) 0 0
\(411\) 0.726543 2.23607i 0.726543 2.23607i
\(412\) 0 0
\(413\) −0.587785 1.80902i −0.587785 1.80902i
\(414\) 0.190983 0.587785i 0.190983 0.587785i
\(415\) 1.80902 0.587785i 1.80902 0.587785i
\(416\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(417\) 0 0
\(418\) 0 0
\(419\) 0.951057 0.690983i 0.951057 0.690983i 1.00000i \(-0.5\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(420\) 1.17557i 1.17557i
\(421\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0.726543 0.726543
\(427\) 0.587785 1.80902i 0.587785 1.80902i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(432\) −0.726543 −0.726543
\(433\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(440\) 0 0
\(441\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(449\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) −0.309017 0.224514i −0.309017 0.224514i
\(451\) 0 0
\(452\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(453\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(454\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(455\) 1.17557i 1.17557i
\(456\) 0 0
\(457\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(458\) 1.53884 1.11803i 1.53884 1.11803i
\(459\) 0 0
\(460\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(461\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(462\) 0 0
\(463\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.190983 0.587785i −0.190983 0.587785i
\(467\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(468\) −0.449028 −0.449028
\(469\) 0 0
\(470\) 0 0
\(471\) −1.80902 1.31433i −1.80902 1.31433i
\(472\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(473\) 0 0
\(474\) −1.90211 −1.90211
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −1.30902 0.951057i −1.30902 0.951057i
\(479\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(480\) −0.690983 0.951057i −0.690983 0.951057i
\(481\) 0 0
\(482\) 0 0
\(483\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(484\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(485\) 0 0
\(486\) 0.224514 0.690983i 0.224514 0.690983i
\(487\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(488\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(489\) 0 0
\(490\) 0.587785 0.809017i 0.587785 0.809017i
\(491\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.500000 0.363271i −0.500000 0.363271i
\(498\) −0.690983 + 2.12663i −0.690983 + 2.12663i
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 1.00000i 1.00000i
\(501\) 0 0
\(502\) 0.587785 1.80902i 0.587785 1.80902i
\(503\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(504\) −0.309017 0.224514i −0.309017 0.224514i
\(505\) −1.11803 0.363271i −1.11803 0.363271i
\(506\) 0 0
\(507\) 0.449028 0.449028
\(508\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(509\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.309017 0.951057i −0.309017 0.951057i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 1.80902 1.31433i 1.80902 1.31433i
\(520\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(521\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) 0 0
\(523\) −0.363271 + 1.11803i −0.363271 + 1.11803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(524\) −1.90211 −1.90211
\(525\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(526\) −1.61803 −1.61803
\(527\) 0 0
\(528\) 0 0
\(529\) −1.30902 0.951057i −1.30902 0.951057i
\(530\) 0 0
\(531\) −0.587785 + 0.427051i −0.587785 + 0.427051i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.587785 1.80902i −0.587785 1.80902i
\(539\) 0 0
\(540\) −0.690983 + 0.224514i −0.690983 + 0.224514i
\(541\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(542\) 0 0
\(543\) 2.23607 2.23607
\(544\) 0 0
\(545\) 0 0
\(546\) 1.11803 + 0.812299i 1.11803 + 0.812299i
\(547\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(548\) 0.618034 1.90211i 0.618034 1.90211i
\(549\) −0.726543 −0.726543
\(550\) 0 0
\(551\) 0 0
\(552\) 0.587785 1.80902i 0.587785 1.80902i
\(553\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.00000i 1.00000i
\(561\) 0 0
\(562\) −0.190983 0.587785i −0.190983 0.587785i
\(563\) −0.363271 1.11803i −0.363271 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(564\) 0 0
\(565\) 0.618034i 0.618034i
\(566\) −0.363271 1.11803i −0.363271 1.11803i
\(567\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(568\) 0.618034 0.618034
\(569\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(572\) 0 0
\(573\) 0.587785 1.80902i 0.587785 1.80902i
\(574\) 0 0
\(575\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(576\) 0.381966 0.381966
\(577\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(578\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(579\) 0.587785 + 0.427051i 0.587785 + 0.427051i
\(580\) 0 0
\(581\) 1.53884 1.11803i 1.53884 1.11803i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −0.427051 + 0.138757i −0.427051 + 0.138757i
\(586\) 0 0
\(587\) −0.587785 1.80902i −0.587785 1.80902i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(-0.5\pi\)
\(588\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(589\) 0 0
\(590\) 1.80902 + 0.587785i 1.80902 + 0.587785i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(599\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(600\) −0.951057 0.690983i −0.951057 0.690983i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(605\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(606\) 1.11803 0.812299i 1.11803 0.812299i
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(620\) 0 0
\(621\) −0.951057 0.690983i −0.951057 0.690983i
\(622\) 0 0
\(623\) 0 0
\(624\) −1.38197 −1.38197
\(625\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(626\) 0 0
\(627\) 0 0
\(628\) −1.53884 1.11803i −1.53884 1.11803i
\(629\) 0 0
\(630\) −0.363271 0.118034i −0.363271 0.118034i
\(631\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(632\) −1.61803 −1.61803
\(633\) 0 0
\(634\) 0 0
\(635\) −1.17557 + 1.61803i −1.17557 + 1.61803i
\(636\) 0 0
\(637\) −0.363271 1.11803i −0.363271 1.11803i
\(638\) 0 0
\(639\) −0.0729490 + 0.224514i −0.0729490 + 0.224514i
\(640\) −0.587785 0.809017i −0.587785 0.809017i
\(641\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(642\) 0 0
\(643\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(644\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(648\) 0.381966 1.17557i 0.381966 1.17557i
\(649\) 0 0
\(650\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(654\) 0 0
\(655\) −1.80902 + 0.587785i −1.80902 + 0.587785i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(660\) 0 0
\(661\) −0.587785 + 1.80902i −0.587785 + 1.80902i 1.00000i \(0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −0.951057 0.690983i −0.951057 0.690983i
\(673\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(674\) −1.61803 −1.61803
\(675\) −0.587785 + 0.427051i −0.587785 + 0.427051i
\(676\) 0.381966 0.381966
\(677\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(678\) −0.587785 0.427051i −0.587785 0.427051i
\(679\) 0 0
\(680\) 0 0
\(681\) −1.11803 + 0.812299i −1.11803 + 0.812299i
\(682\) 0 0
\(683\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(684\) 0 0
\(685\) 2.00000i 2.00000i
\(686\) 0.309017 0.951057i 0.309017 0.951057i
\(687\) 0.690983 + 2.12663i 0.690983 + 2.12663i
\(688\) 0 0
\(689\) 0 0
\(690\) 1.90211i 1.90211i
\(691\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(692\) 1.53884 1.11803i 1.53884 1.11803i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(699\) 0.726543 0.726543
\(700\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) −0.263932 + 0.812299i −0.263932 + 0.812299i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.17557 −1.17557
\(708\) −1.80902 + 1.31433i −1.80902 + 1.31433i
\(709\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(710\) 0.587785 0.190983i 0.587785 0.190983i
\(711\) 0.190983 0.587785i 0.190983 0.587785i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 1.53884 1.11803i 1.53884 1.11803i
\(718\) 1.61803 1.61803
\(719\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(720\) 0.363271 0.118034i 0.363271 0.118034i
\(721\) 0 0
\(722\) −0.809017 0.587785i −0.809017 0.587785i
\(723\) 0 0
\(724\) 1.90211 1.90211
\(725\) 0 0
\(726\) −1.17557 −1.17557
\(727\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(728\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(729\) −0.309017 0.224514i −0.309017 0.224514i
\(730\) 0 0
\(731\) 0 0
\(732\) −2.23607 −2.23607
\(733\) 1.53884 1.11803i 1.53884 1.11803i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(734\) 0 0
\(735\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(736\) 0.500000 1.53884i 0.500000 1.53884i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.587785 0.427051i −0.587785 0.427051i
\(748\) 0 0
\(749\) 0 0
\(750\) −1.11803 0.363271i −1.11803 0.363271i
\(751\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(752\) 0 0
\(753\) 1.80902 + 1.31433i 1.80902 + 1.31433i
\(754\) 0 0
\(755\) 1.53884 + 0.500000i 1.53884 + 0.500000i
\(756\) −0.587785 + 0.427051i −0.587785 + 0.427051i
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(762\) −0.726543 2.23607i −0.726543 2.23607i
\(763\) 0 0
\(764\) 0.500000 1.53884i 0.500000 1.53884i
\(765\) 0 0
\(766\) 0 0
\(767\) 1.80902 1.31433i 1.80902 1.31433i
\(768\) 1.17557 1.17557
\(769\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(773\) 0.363271 1.11803i 0.363271 1.11803i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −1.31433 + 0.427051i −1.31433 + 0.427051i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(785\) −1.80902 0.587785i −1.80902 0.587785i
\(786\) 0.690983 2.12663i 0.690983 2.12663i
\(787\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(788\) 0 0
\(789\) 0.587785 1.80902i 0.587785 1.80902i
\(790\) −1.53884 + 0.500000i −1.53884 + 0.500000i
\(791\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(792\) 0 0
\(793\) 2.23607 2.23607
\(794\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(795\) 0 0
\(796\) 0 0
\(797\) 1.53884 + 1.11803i 1.53884 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)