Properties

Label 1045.1.w.f.664.4
Level $1045$
Weight $1$
Character 1045.664
Analytic conductor $0.522$
Analytic rank $0$
Dimension $16$
Projective image $D_{20}$
CM discriminant -95
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1045.w (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.521522938201\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{40})\)
Defining polynomial: \(x^{16} - x^{12} + x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{20}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{20} + \cdots)\)

Embedding invariants

Embedding label 664.4
Root \(0.987688 + 0.156434i\) of defining polynomial
Character \(\chi\) \(=\) 1045.664
Dual form 1045.1.w.f.949.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.44168 + 1.04744i) q^{2} +(-0.610425 + 1.87869i) q^{3} +(0.672288 + 2.06909i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-2.84786 + 2.06909i) q^{6} +(-0.647354 + 1.99235i) q^{8} +(-2.34786 - 1.70582i) q^{9} +O(q^{10})\) \(q+(1.44168 + 1.04744i) q^{2} +(-0.610425 + 1.87869i) q^{3} +(0.672288 + 2.06909i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-2.84786 + 2.06909i) q^{6} +(-0.647354 + 1.99235i) q^{8} +(-2.34786 - 1.70582i) q^{9} +1.78201 q^{10} +(0.587785 - 0.809017i) q^{11} -4.29757 q^{12} +(-0.734572 - 0.533698i) q^{13} +(0.610425 + 1.87869i) q^{15} +(-1.26007 + 0.915497i) q^{16} +(-1.59811 - 4.91849i) q^{18} +(-0.309017 + 0.951057i) q^{19} +(1.76007 + 1.27877i) q^{20} +(1.69480 - 0.550672i) q^{22} +(-3.34786 - 2.43236i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-0.500000 - 1.53884i) q^{26} +(3.03979 - 2.20854i) q^{27} +(-1.08779 + 3.34786i) q^{30} -0.680668 q^{32} +(1.16110 + 1.59811i) q^{33} +(1.95106 - 6.00473i) q^{36} +(-0.0966818 - 0.297556i) q^{37} +(-1.44168 + 1.04744i) q^{38} +(1.45106 - 1.05425i) q^{39} +(0.647354 + 1.99235i) q^{40} +(2.06909 + 0.672288i) q^{44} -2.90211 q^{45} +(-0.950759 - 2.92614i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(1.44168 - 1.04744i) q^{50} +(0.610425 - 1.87869i) q^{52} +(-1.14412 - 0.831254i) q^{53} +6.69572 q^{54} -1.00000i q^{55} +(-1.59811 - 1.16110i) q^{57} +(-3.47681 + 2.52605i) q^{60} +(-0.951057 + 0.690983i) q^{61} +(0.278768 + 0.202537i) q^{64} -0.907981 q^{65} +3.52015i q^{66} +0.312869 q^{67} +(4.91849 - 3.57349i) q^{72} +(0.172288 - 0.530249i) q^{74} +(1.59811 + 1.16110i) q^{75} -2.17557 q^{76} +3.19623 q^{78} +(-0.481305 + 1.48131i) q^{80} +(1.39680 + 4.29892i) q^{81} +(1.23134 + 1.69480i) q^{88} +(-4.18391 - 3.03979i) q^{90} +(0.309017 + 0.951057i) q^{95} +(0.415497 - 1.27877i) q^{96} +(-1.44168 - 1.04744i) q^{97} -1.78201 q^{98} +(-2.76007 + 0.896802i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{4} + 4q^{5} - 12q^{6} - 4q^{9} + O(q^{10}) \) \( 16q - 4q^{4} + 4q^{5} - 12q^{6} - 4q^{9} + 4q^{16} + 4q^{19} + 4q^{20} - 20q^{24} - 4q^{25} - 8q^{26} - 8q^{30} + 16q^{36} + 8q^{39} - 16q^{45} - 4q^{49} + 40q^{54} + 4q^{64} - 12q^{74} - 16q^{76} + 16q^{80} + 4q^{81} - 4q^{95} + 12q^{96} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).

\(n\) \(496\) \(761\) \(837\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.44168 + 1.04744i 1.44168 + 1.04744i 0.987688 + 0.156434i \(0.0500000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(3\) −0.610425 + 1.87869i −0.610425 + 1.87869i −0.156434 + 0.987688i \(0.550000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(4\) 0.672288 + 2.06909i 0.672288 + 2.06909i
\(5\) 0.809017 0.587785i 0.809017 0.587785i
\(6\) −2.84786 + 2.06909i −2.84786 + 2.06909i
\(7\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(8\) −0.647354 + 1.99235i −0.647354 + 1.99235i
\(9\) −2.34786 1.70582i −2.34786 1.70582i
\(10\) 1.78201 1.78201
\(11\) 0.587785 0.809017i 0.587785 0.809017i
\(12\) −4.29757 −4.29757
\(13\) −0.734572 0.533698i −0.734572 0.533698i 0.156434 0.987688i \(-0.450000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(14\) 0 0
\(15\) 0.610425 + 1.87869i 0.610425 + 1.87869i
\(16\) −1.26007 + 0.915497i −1.26007 + 0.915497i
\(17\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(18\) −1.59811 4.91849i −1.59811 4.91849i
\(19\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(20\) 1.76007 + 1.27877i 1.76007 + 1.27877i
\(21\) 0 0
\(22\) 1.69480 0.550672i 1.69480 0.550672i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −3.34786 2.43236i −3.34786 2.43236i
\(25\) 0.309017 0.951057i 0.309017 0.951057i
\(26\) −0.500000 1.53884i −0.500000 1.53884i
\(27\) 3.03979 2.20854i 3.03979 2.20854i
\(28\) 0 0
\(29\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(30\) −1.08779 + 3.34786i −1.08779 + 3.34786i
\(31\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(32\) −0.680668 −0.680668
\(33\) 1.16110 + 1.59811i 1.16110 + 1.59811i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.95106 6.00473i 1.95106 6.00473i
\(37\) −0.0966818 0.297556i −0.0966818 0.297556i 0.891007 0.453990i \(-0.150000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(38\) −1.44168 + 1.04744i −1.44168 + 1.04744i
\(39\) 1.45106 1.05425i 1.45106 1.05425i
\(40\) 0.647354 + 1.99235i 0.647354 + 1.99235i
\(41\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 2.06909 + 0.672288i 2.06909 + 0.672288i
\(45\) −2.90211 −2.90211
\(46\) 0 0
\(47\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(48\) −0.950759 2.92614i −0.950759 2.92614i
\(49\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(50\) 1.44168 1.04744i 1.44168 1.04744i
\(51\) 0 0
\(52\) 0.610425 1.87869i 0.610425 1.87869i
\(53\) −1.14412 0.831254i −1.14412 0.831254i −0.156434 0.987688i \(-0.550000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(54\) 6.69572 6.69572
\(55\) 1.00000i 1.00000i
\(56\) 0 0
\(57\) −1.59811 1.16110i −1.59811 1.16110i
\(58\) 0 0
\(59\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(60\) −3.47681 + 2.52605i −3.47681 + 2.52605i
\(61\) −0.951057 + 0.690983i −0.951057 + 0.690983i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.278768 + 0.202537i 0.278768 + 0.202537i
\(65\) −0.907981 −0.907981
\(66\) 3.52015i 3.52015i
\(67\) 0.312869 0.312869 0.156434 0.987688i \(-0.450000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(72\) 4.91849 3.57349i 4.91849 3.57349i
\(73\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(74\) 0.172288 0.530249i 0.172288 0.530249i
\(75\) 1.59811 + 1.16110i 1.59811 + 1.16110i
\(76\) −2.17557 −2.17557
\(77\) 0 0
\(78\) 3.19623 3.19623
\(79\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(80\) −0.481305 + 1.48131i −0.481305 + 1.48131i
\(81\) 1.39680 + 4.29892i 1.39680 + 4.29892i
\(82\) 0 0
\(83\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 1.23134 + 1.69480i 1.23134 + 1.69480i
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) −4.18391 3.03979i −4.18391 3.03979i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(96\) 0.415497 1.27877i 0.415497 1.27877i
\(97\) −1.44168 1.04744i −1.44168 1.04744i −0.987688 0.156434i \(-0.950000\pi\)
−0.453990 0.891007i \(-0.650000\pi\)
\(98\) −1.78201 −1.78201
\(99\) −2.76007 + 0.896802i −2.76007 + 0.896802i
\(100\) 2.17557 2.17557
\(101\) 1.53884 + 1.11803i 1.53884 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(102\) 0 0
\(103\) 0.280582 + 0.863541i 0.280582 + 0.863541i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(104\) 1.53884 1.11803i 1.53884 1.11803i
\(105\) 0 0
\(106\) −0.778768 2.39680i −0.778768 2.39680i
\(107\) 0.0966818 0.297556i 0.0966818 0.297556i −0.891007 0.453990i \(-0.850000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(108\) 6.61328 + 4.80483i 6.61328 + 4.80483i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 1.04744 1.44168i 1.04744 1.44168i
\(111\) 0.618034 0.618034
\(112\) 0 0
\(113\) 0.280582 0.863541i 0.280582 0.863541i −0.707107 0.707107i \(-0.750000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(114\) −1.08779 3.34786i −1.08779 3.34786i
\(115\) 0 0
\(116\) 0 0
\(117\) 0.814279 + 2.50609i 0.814279 + 2.50609i
\(118\) 0 0
\(119\) 0 0
\(120\) −4.13818 −4.13818
\(121\) −0.309017 0.951057i −0.309017 0.951057i
\(122\) −2.09488 −2.09488
\(123\) 0 0
\(124\) 0 0
\(125\) −0.309017 0.951057i −0.309017 0.951057i
\(126\) 0 0
\(127\) −1.14412 + 0.831254i −1.14412 + 0.831254i −0.987688 0.156434i \(-0.950000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(128\) 0.400087 + 1.23134i 0.400087 + 1.23134i
\(129\) 0 0
\(130\) −1.30902 0.951057i −1.30902 0.951057i
\(131\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(132\) −2.52605 + 3.47681i −2.52605 + 3.47681i
\(133\) 0 0
\(134\) 0.451057 + 0.327712i 0.451057 + 0.327712i
\(135\) 1.16110 3.57349i 1.16110 3.57349i
\(136\) 0 0
\(137\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(138\) 0 0
\(139\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.863541 + 0.280582i −0.863541 + 0.280582i
\(144\) 4.52015 4.52015
\(145\) 0 0
\(146\) 0 0
\(147\) −0.610425 1.87869i −0.610425 1.87869i
\(148\) 0.550672 0.400087i 0.550672 0.400087i
\(149\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(150\) 1.08779 + 3.34786i 1.08779 + 3.34786i
\(151\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(152\) −1.69480 1.23134i −1.69480 1.23134i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 3.15688 + 2.29360i 3.15688 + 2.29360i
\(157\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(158\) 0 0
\(159\) 2.26007 1.64204i 2.26007 1.64204i
\(160\) −0.550672 + 0.400087i −0.550672 + 0.400087i
\(161\) 0 0
\(162\) −2.48912 + 7.66072i −2.48912 + 7.66072i
\(163\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(164\) 0 0
\(165\) 1.87869 + 0.610425i 1.87869 + 0.610425i
\(166\) 0 0
\(167\) 1.59811 + 1.16110i 1.59811 + 1.16110i 0.891007 + 0.453990i \(0.150000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) 0 0
\(169\) −0.0542543 0.166977i −0.0542543 0.166977i
\(170\) 0 0
\(171\) 2.34786 1.70582i 2.34786 1.70582i
\(172\) 0 0
\(173\) −0.437016 + 1.34500i −0.437016 + 1.34500i 0.453990 + 0.891007i \(0.350000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.55754i 1.55754i
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(180\) −1.95106 6.00473i −1.95106 6.00473i
\(181\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(182\) 0 0
\(183\) −0.717598 2.20854i −0.717598 2.20854i
\(184\) 0 0
\(185\) −0.253116 0.183900i −0.253116 0.183900i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −0.550672 + 1.69480i −0.550672 + 1.69480i
\(191\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(192\) −0.550672 + 0.400087i −0.550672 + 0.400087i
\(193\) 1.59811 1.16110i 1.59811 1.16110i 0.707107 0.707107i \(-0.250000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(194\) −0.981305 3.02015i −0.981305 3.02015i
\(195\) 0.554254 1.70582i 0.554254 1.70582i
\(196\) −1.76007 1.27877i −1.76007 1.27877i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −4.91849 1.59811i −4.91849 1.59811i
\(199\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(200\) 1.69480 + 1.23134i 1.69480 + 1.23134i
\(201\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(202\) 1.04744 + 3.22369i 1.04744 + 3.22369i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(207\) 0 0
\(208\) 1.41421 1.41421
\(209\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(210\) 0 0
\(211\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(212\) 0.950759 2.92614i 0.950759 2.92614i
\(213\) 0 0
\(214\) 0.451057 0.327712i 0.451057 0.327712i
\(215\) 0 0
\(216\) 2.43236 + 7.48604i 2.43236 + 7.48604i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 2.06909 0.672288i 2.06909 0.672288i
\(221\) 0 0
\(222\) 0.891007 + 0.647354i 0.891007 + 0.647354i
\(223\) 0.437016 1.34500i 0.437016 1.34500i −0.453990 0.891007i \(-0.650000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(224\) 0 0
\(225\) −2.34786 + 1.70582i −2.34786 + 1.70582i
\(226\) 1.30902 0.951057i 1.30902 0.951057i
\(227\) 0.610425 + 1.87869i 0.610425 + 1.87869i 0.453990 + 0.891007i \(0.350000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(228\) 1.32802 4.08723i 1.32802 4.08723i
\(229\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(234\) −1.45106 + 4.46589i −1.45106 + 4.46589i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(240\) −2.48912 1.80845i −2.48912 1.80845i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0.550672 1.69480i 0.550672 1.69480i
\(243\) −5.17160 −5.17160
\(244\) −2.06909 1.50328i −2.06909 1.50328i
\(245\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(246\) 0 0
\(247\) 0.734572 0.533698i 0.734572 0.533698i
\(248\) 0 0
\(249\) 0 0
\(250\) 0.550672 1.69480i 0.550672 1.69480i
\(251\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −2.52015 −2.52015
\(255\) 0 0
\(256\) −0.606480 + 1.86655i −0.606480 + 1.86655i
\(257\) −0.280582 0.863541i −0.280582 0.863541i −0.987688 0.156434i \(-0.950000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.610425 1.87869i −0.610425 1.87869i
\(261\) 0 0
\(262\) −2.33269 1.69480i −2.33269 1.69480i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −3.93564 + 1.27877i −3.93564 + 1.27877i
\(265\) −1.41421 −1.41421
\(266\) 0 0
\(267\) 0 0
\(268\) 0.210338 + 0.647354i 0.210338 + 0.647354i
\(269\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(270\) 5.41695 3.93564i 5.41695 3.93564i
\(271\) −0.587785 1.80902i −0.587785 1.80902i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(-0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.587785 0.809017i −0.587785 0.809017i
\(276\) 0 0
\(277\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(282\) 0 0
\(283\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(284\) 0 0
\(285\) −1.97538 −1.97538
\(286\) −1.53884 0.500000i −1.53884 0.500000i
\(287\) 0 0
\(288\) 1.59811 + 1.16110i 1.59811 + 1.16110i
\(289\) 0.309017 0.951057i 0.309017 0.951057i
\(290\) 0 0
\(291\) 2.84786 2.06909i 2.84786 2.06909i
\(292\) 0 0
\(293\) 0.550672 + 1.69480i 0.550672 + 1.69480i 0.707107 + 0.707107i \(0.250000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(294\) 1.08779 3.34786i 1.08779 3.34786i
\(295\) 0 0
\(296\) 0.655423 0.655423
\(297\) 3.75739i 3.75739i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.32802 + 4.08723i −1.32802 + 4.08723i
\(301\) 0 0
\(302\) 0 0
\(303\) −3.03979 + 2.20854i −3.03979 + 2.20854i
\(304\) −0.481305 1.48131i −0.481305 1.48131i
\(305\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(306\) 0 0
\(307\) −1.41421 −1.41421 −0.707107 0.707107i \(-0.750000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) 0 0
\(309\) −1.79360 −1.79360
\(310\) 0 0
\(311\) −0.587785 + 1.80902i −0.587785 + 1.80902i 1.00000i \(0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(312\) 1.16110 + 3.57349i 1.16110 + 3.57349i
\(313\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.14412 + 0.831254i 1.14412 + 0.831254i 0.987688 0.156434i \(-0.0500000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(318\) 4.97824 4.97824
\(319\) 0 0
\(320\) 0.344577 0.344577
\(321\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(322\) 0 0
\(323\) 0 0
\(324\) −7.95579 + 5.78022i −7.95579 + 5.78022i
\(325\) −0.734572 + 0.533698i −0.734572 + 0.533698i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 2.06909 + 2.84786i 2.06909 + 2.84786i
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) −0.280582 + 0.863541i −0.280582 + 0.863541i
\(334\) 1.08779 + 3.34786i 1.08779 + 3.34786i
\(335\) 0.253116 0.183900i 0.253116 0.183900i
\(336\) 0 0
\(337\) −0.437016 1.34500i −0.437016 1.34500i −0.891007 0.453990i \(-0.850000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(338\) 0.0966818 0.297556i 0.0966818 0.297556i
\(339\) 1.45106 + 1.05425i 1.45106 + 1.05425i
\(340\) 0 0
\(341\) 0 0
\(342\) 5.17160 5.17160
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −2.03884 + 1.48131i −2.03884 + 1.48131i
\(347\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(348\) 0 0
\(349\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) −3.41164 −3.41164
\(352\) −0.400087 + 0.550672i −0.400087 + 0.550672i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(360\) 1.87869 5.78203i 1.87869 5.78203i
\(361\) −0.809017 0.587785i −0.809017 0.587785i
\(362\) 0 0
\(363\) 1.97538 1.97538
\(364\) 0 0
\(365\) 0 0
\(366\) 1.27877 3.93564i 1.27877 3.93564i
\(367\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −0.172288 0.530249i −0.172288 0.530249i
\(371\) 0 0
\(372\) 0 0
\(373\) −0.312869 −0.312869 −0.156434 0.987688i \(-0.550000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(374\) 0 0
\(375\) 1.97538 1.97538
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(380\) −1.76007 + 1.27877i −1.76007 + 1.27877i
\(381\) −0.863271 2.65688i −0.863271 2.65688i
\(382\) 0.340334 1.04744i 0.340334 1.04744i
\(383\) 1.14412 + 0.831254i 1.14412 + 0.831254i 0.987688 0.156434i \(-0.0500000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(384\) −2.55754 −2.55754
\(385\) 0 0
\(386\) 3.52015 3.52015
\(387\) 0 0
\(388\) 1.19803 3.68715i 1.19803 3.68715i
\(389\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(390\) 2.58580 1.87869i 2.58580 1.87869i
\(391\) 0 0
\(392\) −0.647354 1.99235i −0.647354 1.99235i
\(393\) 0.987688 3.03979i 0.987688 3.03979i
\(394\) 0 0
\(395\) 0 0
\(396\) −3.71113 5.10793i −3.71113 5.10793i
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 2.33269 + 1.69480i 2.33269 + 1.69480i
\(399\) 0 0
\(400\) 0.481305 + 1.48131i 0.481305 + 1.48131i
\(401\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(402\) −0.891007 + 0.647354i −0.891007 + 0.647354i
\(403\) 0 0
\(404\) −1.27877 + 3.93564i −1.27877 + 3.93564i
\(405\) 3.65688 + 2.65688i 3.65688 + 2.65688i
\(406\) 0 0
\(407\) −0.297556 0.0966818i −0.297556 0.0966818i
\(408\) 0 0
\(409\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.59811 + 1.16110i −1.59811 + 1.16110i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(417\) 0 0
\(418\) 1.78201i 1.78201i
\(419\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(420\) 0 0
\(421\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 2.39680 1.74138i 2.39680 1.74138i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0.680668 0.680668
\(429\) 1.79360i 1.79360i
\(430\) 0 0
\(431\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(432\) −1.80845 + 5.56584i −1.80845 + 5.56584i
\(433\) −0.550672 1.69480i −0.550672 1.69480i −0.707107 0.707107i \(-0.750000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 1.99235 + 0.647354i 1.99235 + 0.647354i
\(441\) 2.90211 2.90211
\(442\) 0 0
\(443\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(444\) 0.415497 + 1.27877i 0.415497 + 1.27877i
\(445\) 0 0
\(446\) 2.03884 1.48131i 2.03884 1.48131i
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(450\) −5.17160 −5.17160
\(451\) 0 0
\(452\) 1.97538 1.97538
\(453\) 0 0
\(454\) −1.08779 + 3.34786i −1.08779 + 3.34786i
\(455\) 0 0
\(456\) 3.34786 2.43236i 3.34786 2.43236i
\(457\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(468\) −4.63791 + 3.36964i −4.63791 + 3.36964i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(476\) 0 0
\(477\) 1.26827 + 3.90333i 1.26827 + 3.90333i
\(478\) 0.891007 0.647354i 0.891007 0.647354i
\(479\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(480\) −0.415497 1.27877i −0.415497 1.27877i
\(481\) −0.0877853 + 0.270175i −0.0877853 + 0.270175i
\(482\) 0 0
\(483\) 0 0
\(484\) 1.76007 1.27877i 1.76007 1.27877i
\(485\) −1.78201 −1.78201
\(486\) −7.45579 5.41695i −7.45579 5.41695i
\(487\) −0.437016 + 1.34500i −0.437016 + 1.34500i 0.453990 + 0.891007i \(0.350000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(488\) −0.761010 2.34215i −0.761010 2.34215i
\(489\) 0 0
\(490\) −1.44168 + 1.04744i −1.44168 + 1.04744i
\(491\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 1.61803 1.61803
\(495\) −1.70582 + 2.34786i −1.70582 + 2.34786i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(500\) 1.76007 1.27877i 1.76007 1.27877i
\(501\) −3.15688 + 2.29360i −3.15688 + 2.29360i
\(502\) −0.891007 2.74224i −0.891007 2.74224i
\(503\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(504\) 0 0
\(505\) 1.90211 1.90211
\(506\) 0 0
\(507\) 0.346818 0.346818
\(508\) −2.48912 1.80845i −2.48912 1.80845i
\(509\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.78201 + 1.29471i −1.78201 + 1.29471i
\(513\) 1.16110 + 3.57349i 1.16110 + 3.57349i
\(514\) 0.500000 1.53884i 0.500000 1.53884i
\(515\) 0.734572 + 0.533698i 0.734572 + 0.533698i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −2.26007 1.64204i −2.26007 1.64204i
\(520\) 0.587785 1.80902i 0.587785 1.80902i
\(521\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(522\) 0 0
\(523\) 0.734572 0.533698i 0.734572 0.533698i −0.156434 0.987688i \(-0.550000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(524\) −1.08779 3.34786i −1.08779 3.34786i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −2.92614 0.950759i −2.92614 0.950759i
\(529\) 1.00000 1.00000
\(530\) −2.03884 1.48131i −2.03884 1.48131i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −0.0966818 0.297556i −0.0966818 0.297556i
\(536\) −0.202537 + 0.623345i −0.202537 + 0.623345i
\(537\) 0 0
\(538\) 0 0
\(539\) 1.00000i 1.00000i
\(540\) 8.17447 8.17447
\(541\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(542\) 1.04744 3.22369i 1.04744 3.22369i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.610425 + 1.87869i −0.610425 + 1.87869i −0.156434 + 0.987688i \(0.550000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(548\) 0 0
\(549\) 3.41164 3.41164
\(550\) 1.78201i 1.78201i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.500000 0.363271i 0.500000 0.363271i
\(556\) 0 0
\(557\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.44168 1.04744i −1.44168 1.04744i −0.987688 0.156434i \(-0.950000\pi\)
−0.453990 0.891007i \(-0.650000\pi\)
\(564\) 0 0
\(565\) −0.280582 0.863541i −0.280582 0.863541i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(570\) −2.84786 2.06909i −2.84786 2.06909i
\(571\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(572\) −1.16110 1.59811i −1.16110 1.59811i
\(573\) 1.22085 1.22085
\(574\) 0 0
\(575\) 0 0
\(576\) −0.309017 0.951057i −0.309017 0.951057i
\(577\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(578\) 1.44168 1.04744i 1.44168 1.04744i
\(579\) 1.20582 + 3.71113i 1.20582 + 3.71113i
\(580\) 0 0
\(581\) 0 0
\(582\) 6.27295 6.27295
\(583\) −1.34500 + 0.437016i −1.34500 + 0.437016i
\(584\) 0 0
\(585\) 2.13181 + 1.54885i 2.13181 + 1.54885i
\(586\) −0.981305 + 3.02015i −0.981305 + 3.02015i
\(587\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(588\) 3.47681 2.52605i 3.47681 2.52605i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.394238 + 0.286431i 0.394238 + 0.286431i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 3.93564 5.41695i 3.93564 5.41695i
\(595\) 0 0
\(596\) 0 0
\(597\) −0.987688 + 3.03979i −0.987688 + 3.03979i
\(598\) 0 0
\(599\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(600\) −3.34786 + 2.43236i −3.34786 + 2.43236i
\(601\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(602\) 0 0
\(603\) −0.734572 0.533698i −0.734572 0.533698i
\(604\) 0 0
\(605\) −0.809017 0.587785i −0.809017 0.587785i
\(606\) −6.69572 −6.69572
\(607\) −1.59811 1.16110i −1.59811 1.16110i −0.891007 0.453990i \(-0.850000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(608\) 0.210338 0.647354i 0.210338 0.647354i
\(609\) 0 0
\(610\) −1.69480 + 1.23134i −1.69480 + 1.23134i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(614\) −2.03884 1.48131i −2.03884 1.48131i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) −2.58580 1.87869i −2.58580 1.87869i
\(619\) −0.363271 + 1.11803i −0.363271 + 1.11803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −2.74224 + 1.99235i −2.74224 + 1.99235i
\(623\) 0 0
\(624\) −0.863271 + 2.65688i −0.863271 + 2.65688i
\(625\) −0.809017 0.587785i −0.809017 0.587785i
\(626\) 0 0
\(627\) −1.87869 + 0.610425i −1.87869 + 0.610425i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.587785 1.80902i −0.587785 1.80902i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(-0.5\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0.778768 + 2.39680i 0.778768 + 2.39680i
\(635\) −0.437016 + 1.34500i −0.437016 + 1.34500i
\(636\) 4.91695 + 3.57237i 4.91695 + 3.57237i
\(637\) 0.907981 0.907981
\(638\) 0 0
\(639\) 0 0
\(640\) 1.04744 + 0.761010i 1.04744 + 0.761010i
\(641\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(642\) 0.340334 + 1.04744i 0.340334 + 1.04744i
\(643\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(648\) −9.46917 −9.46917
\(649\) 0 0
\(650\) −1.61803 −1.61803
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(654\) 0 0
\(655\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 4.29757i 4.29757i
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(667\) 0 0
\(668\) −1.32802 + 4.08723i −1.32802 + 4.08723i
\(669\) 2.26007 + 1.64204i 2.26007 + 1.64204i
\(670\) 0.557537 0.557537
\(671\) 1.17557i 1.17557i
\(672\) 0 0
\(673\) −0.253116 0.183900i −0.253116 0.183900i 0.453990 0.891007i \(-0.350000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(674\) 0.778768 2.39680i 0.778768 2.39680i
\(675\) −1.16110 3.57349i −1.16110 3.57349i
\(676\) 0.309017 0.224514i 0.309017 0.224514i
\(677\) 1.59811 1.16110i 1.59811 1.16110i 0.707107 0.707107i \(-0.250000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(678\) 0.987688 + 3.03979i 0.987688 + 3.03979i
\(679\) 0 0
\(680\) 0 0
\(681\) −3.90211 −3.90211
\(682\) 0 0
\(683\) 1.78201 1.78201 0.891007 0.453990i \(-0.150000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(684\) 5.10793 + 3.71113i 5.10793 + 3.71113i
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0.396802 + 1.22123i 0.396802 + 1.22123i
\(690\) 0 0
\(691\) 1.53884 + 1.11803i 1.53884 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(692\) −3.07672 −3.07672
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −0.891007 + 0.647354i −0.891007 + 0.647354i
\(699\) 0 0
\(700\) 0 0
\(701\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(702\) −4.91849 3.57349i −4.91849 3.57349i
\(703\) 0.312869 0.312869
\(704\) 0.327712 0.106480i 0.327712 0.106480i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −0.533698 + 0.734572i −0.533698 + 0.734572i
\(716\) 0 0
\(717\) 0.987688 + 0.717598i 0.987688 + 0.717598i
\(718\) −0.647354 + 1.99235i −0.647354 + 1.99235i
\(719\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(720\) 3.65688 2.65688i 3.65688 2.65688i
\(721\) 0 0
\(722\) −0.550672 1.69480i −0.550672 1.69480i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 2.84786 + 2.06909i 2.84786 + 2.06909i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.76007 5.41695i 1.76007 5.41695i
\(730\) 0 0
\(731\) 0 0
\(732\) 4.08723 2.96955i 4.08723 2.96955i
\(733\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(734\) 0 0
\(735\) −1.59811 1.16110i −1.59811 1.16110i
\(736\) 0 0
\(737\) 0.183900 0.253116i 0.183900 0.253116i
\(738\) 0 0
\(739\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(740\) 0.210338 0.647354i 0.210338 0.647354i
\(741\) 0.554254 + 1.70582i 0.554254 + 1.70582i
\(742\) 0 0
\(743\) −1.44168 + 1.04744i −1.44168 + 1.04744i −0.453990 + 0.891007i \(0.650000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −0.451057 0.327712i −0.451057 0.327712i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 2.84786 + 2.06909i 2.84786 + 2.06909i
\(751\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(752\) 0 0
\(753\) 2.58580 1.87869i 2.58580 1.87869i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −2.09488 −2.09488
\(761\) −0.951057 0.690983i −0.951057 0.690983i 1.00000i \(-0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(762\) 1.53836 4.73459i 1.53836 4.73459i
\(763\) 0 0
\(764\) 1.08779 0.790322i 1.08779 0.790322i
\(765\) 0 0
\(766\) 0.778768 + 2.39680i 0.778768 + 2.39680i
\(767\) 0 0
\(768\) −3.13647 2.27878i −3.13647 2.27878i
\(769\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(770\) 0 0
\(771\) 1.79360 1.79360
\(772\) 3.47681 + 2.52605i 3.47681 + 2.52605i
\(773\) 0.610425 1.87869i 0.610425 1.87869i 0.156434 0.987688i \(-0.450000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 3.02015 2.19427i 3.02015 2.19427i
\(777\) 0 0
\(778\) −0.340334 + 1.04744i −0.340334 + 1.04744i
\(779\) 0 0
\(780\) 3.90211 3.90211
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.481305 1.48131i 0.481305 1.48131i
\(785\) 0 0
\(786\) 4.60793 3.34786i 4.60793 3.34786i
\(787\) 0.253116 0.183900i 0.253116 0.183900i −0.453990 0.891007i \(-0.650000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 6.07958i 6.07958i
\(793\) 1.06740 1.06740
\(794\) 0 0
\(795\) 0.863271 2.65688i 0.863271 2.65688i
\(796\) 1.08779 + 3.34786i 1.08779 + 3.34786i
\(797\) −1.44168 + 1.04744i −1.44168 + 1.04744i −0.453990 + 0.891007i \(0.650000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(798\) 0 0