Properties

Label 1441.1.u.a.130.1
Level $1441$
Weight $1$
Character 1441.130
Analytic conductor $0.719$
Analytic rank $0$
Dimension $20$
Projective image $D_{25}$
CM discriminant -131
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1441.u (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.719152683204\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{50})\)
Defining polynomial: \(x^{20} - x^{15} + x^{10} - x^{5} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{25}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{25} + \cdots)\)

Embedding invariants

Embedding label 130.1
Root \(-0.535827 - 0.844328i\) of defining polynomial
Character \(\chi\) \(=\) 1441.130
Dual form 1441.1.u.a.654.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.56720 + 1.13864i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.115808 - 0.356420i) q^{5} +(-1.41789 - 1.03016i) q^{7} +(0.850604 - 2.61789i) q^{9} +O(q^{10})\) \(q+(-1.56720 + 1.13864i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.115808 - 0.356420i) q^{5} +(-1.41789 - 1.03016i) q^{7} +(0.850604 - 2.61789i) q^{9} +(-0.637424 - 0.770513i) q^{11} +1.93717 q^{12} +(-0.574633 + 1.76854i) q^{13} +(0.587328 + 0.426719i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.115808 + 0.356420i) q^{20} +3.39510 q^{21} +(0.695393 - 0.505233i) q^{25} +(1.04914 + 3.22894i) q^{27} +(0.541587 + 1.66683i) q^{28} +(1.87631 + 0.481754i) q^{33} +(-0.202967 + 0.624667i) q^{35} +(-2.22691 + 1.61795i) q^{36} +(-1.11316 - 3.42596i) q^{39} +(-0.101597 + 0.0738147i) q^{41} -0.851559 q^{43} +(0.0627905 + 0.998027i) q^{44} -1.03158 q^{45} +(-1.56720 - 1.13864i) q^{48} +(0.640176 + 1.97026i) q^{49} +(1.50441 - 1.09302i) q^{52} +(-0.500000 + 1.53884i) q^{53} +(-0.200808 + 0.316423i) q^{55} +(1.60528 + 1.16630i) q^{59} +(-0.224339 - 0.690446i) q^{60} +(-0.115808 - 0.356420i) q^{61} +(-3.90291 + 2.83563i) q^{63} +(0.309017 - 0.951057i) q^{64} +0.696891 q^{65} +(-0.514543 + 1.58360i) q^{75} +(0.110048 + 1.74915i) q^{77} +(0.303189 - 0.220280i) q^{80} +(-3.09390 - 2.24785i) q^{81} +(-2.74670 - 1.99559i) q^{84} +0.618034 q^{89} +(2.63665 - 1.91564i) q^{91} +(-2.55932 + 1.01330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} - 5q^{25} + 20q^{33} + 15q^{35} - 5q^{36} - 10q^{39} - 10q^{45} - 5q^{49} - 10q^{53} - 10q^{63} - 5q^{64} - 10q^{75} - 5q^{81} - 10q^{89} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1441\mathbb{Z}\right)^\times\).

\(n\) \(133\) \(1311\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

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 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(3\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(4\) −0.809017 0.587785i −0.809017 0.587785i
\(5\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(6\) 0 0
\(7\) −1.41789 1.03016i −1.41789 1.03016i −0.992115 0.125333i \(-0.960000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(8\) 0 0
\(9\) 0.850604 2.61789i 0.850604 2.61789i
\(10\) 0 0
\(11\) −0.637424 0.770513i −0.637424 0.770513i
\(12\) 1.93717 1.93717
\(13\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(14\) 0 0
\(15\) 0.587328 + 0.426719i 0.587328 + 0.426719i
\(16\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(17\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(18\) 0 0
\(19\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(20\) −0.115808 + 0.356420i −0.115808 + 0.356420i
\(21\) 3.39510 3.39510
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) 0.695393 0.505233i 0.695393 0.505233i
\(26\) 0 0
\(27\) 1.04914 + 3.22894i 1.04914 + 3.22894i
\(28\) 0.541587 + 1.66683i 0.541587 + 1.66683i
\(29\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(30\) 0 0
\(31\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(32\) 0 0
\(33\) 1.87631 + 0.481754i 1.87631 + 0.481754i
\(34\) 0 0
\(35\) −0.202967 + 0.624667i −0.202967 + 0.624667i
\(36\) −2.22691 + 1.61795i −2.22691 + 1.61795i
\(37\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(38\) 0 0
\(39\) −1.11316 3.42596i −1.11316 3.42596i
\(40\) 0 0
\(41\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(42\) 0 0
\(43\) −0.851559 −0.851559 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(44\) 0.0627905 + 0.998027i 0.0627905 + 0.998027i
\(45\) −1.03158 −1.03158
\(46\) 0 0
\(47\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(48\) −1.56720 1.13864i −1.56720 1.13864i
\(49\) 0.640176 + 1.97026i 0.640176 + 1.97026i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.50441 1.09302i 1.50441 1.09302i
\(53\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(54\) 0 0
\(55\) −0.200808 + 0.316423i −0.200808 + 0.316423i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(60\) −0.224339 0.690446i −0.224339 0.690446i
\(61\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(62\) 0 0
\(63\) −3.90291 + 2.83563i −3.90291 + 2.83563i
\(64\) 0.309017 0.951057i 0.309017 0.951057i
\(65\) 0.696891 0.696891
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(72\) 0 0
\(73\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(74\) 0 0
\(75\) −0.514543 + 1.58360i −0.514543 + 1.58360i
\(76\) 0 0
\(77\) 0.110048 + 1.74915i 0.110048 + 1.74915i
\(78\) 0 0
\(79\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(80\) 0.303189 0.220280i 0.303189 0.220280i
\(81\) −3.09390 2.24785i −3.09390 2.24785i
\(82\) 0 0
\(83\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(84\) −2.74670 1.99559i −2.74670 1.99559i
\(85\) 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
\(91\) 2.63665 1.91564i 2.63665 1.91564i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(98\) 0 0
\(99\) −2.55932 + 1.01330i −2.55932 + 1.01330i
\(100\) −0.859553 −0.859553
\(101\) −0.263146 + 0.809880i −0.263146 + 0.809880i 0.728969 + 0.684547i \(0.240000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(104\) 0 0
\(105\) −0.393180 1.21008i −0.393180 1.21008i
\(106\) 0 0
\(107\) 1.60528 1.16630i 1.60528 1.16630i 0.728969 0.684547i \(-0.240000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(108\) 1.04914 3.22894i 1.04914 3.22894i
\(109\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.541587 1.66683i 0.541587 1.66683i
\(113\) 1.03137 0.749337i 1.03137 0.749337i 0.0627905 0.998027i \(-0.480000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 4.14106 + 3.00866i 4.14106 + 3.00866i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(122\) 0 0
\(123\) 0.0751750 0.231365i 0.0751750 0.231365i
\(124\) 0 0
\(125\) −0.563797 0.409622i −0.563797 0.409622i
\(126\) 0 0
\(127\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(128\) 0 0
\(129\) 1.33456 0.969617i 1.33456 0.969617i
\(130\) 0 0
\(131\) 1.00000 1.00000
\(132\) −1.23480 1.49261i −1.23480 1.49261i
\(133\) 0 0
\(134\) 0 0
\(135\) 1.02936 0.747873i 1.02936 0.747873i
\(136\) 0 0
\(137\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(140\) 0.531374 0.386066i 0.531374 0.386066i
\(141\) 0 0
\(142\) 0 0
\(143\) 1.72897 0.684547i 1.72897 0.684547i
\(144\) 2.75261 2.75261
\(145\) 0 0
\(146\) 0 0
\(147\) −3.24670 2.35886i −3.24670 2.35886i
\(148\) 0 0
\(149\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(150\) 0 0
\(151\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.11316 + 3.42596i −1.11316 + 3.42596i
\(157\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0 0
\(159\) −0.968583 2.98099i −0.968583 2.98099i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(164\) 0.125581 0.125581
\(165\) −0.0455845 0.724545i −0.0455845 0.724545i
\(166\) 0 0
\(167\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(168\) 0 0
\(169\) −1.98851 1.44474i −1.98851 1.44474i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.688925 + 0.500534i 0.688925 + 0.500534i
\(173\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(174\) 0 0
\(175\) −1.50646 −1.50646
\(176\) 0.535827 0.844328i 0.535827 0.844328i
\(177\) −3.84378 −3.84378
\(178\) 0 0
\(179\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(180\) 0.834563 + 0.606346i 0.834563 + 0.606346i
\(181\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(182\) 0 0
\(183\) 0.587328 + 0.426719i 0.587328 + 0.426719i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 1.83875 5.65908i 1.83875 5.65908i
\(190\) 0 0
\(191\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(192\) 0.598617 + 1.84235i 0.598617 + 1.84235i
\(193\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(194\) 0 0
\(195\) −1.09217 + 0.793506i −1.09217 + 0.793506i
\(196\) 0.640176 1.97026i 0.640176 1.97026i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.0380748 + 0.0276630i 0.0380748 + 0.0276630i
\(206\) 0 0
\(207\) 0 0
\(208\) −1.85955 −1.85955
\(209\) 0 0
\(210\) 0 0
\(211\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(212\) 1.30902 0.951057i 1.30902 0.951057i
\(213\) 0 0
\(214\) 0 0
\(215\) 0.0986173 + 0.303513i 0.0986173 + 0.303513i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.348445 0.137959i 0.348445 0.137959i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(224\) 0 0
\(225\) −0.731139 2.25022i −0.731139 2.25022i
\(226\) 0 0
\(227\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(228\) 0 0
\(229\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(230\) 0 0
\(231\) −2.16412 2.61597i −2.16412 2.61597i
\(232\) 0 0
\(233\) 0.450527 1.38658i 0.450527 1.38658i −0.425779 0.904827i \(-0.640000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −0.613161 1.88711i −0.613161 1.88711i
\(237\) 0 0
\(238\) 0 0
\(239\) −1.17950 + 0.856954i −1.17950 + 0.856954i −0.992115 0.125333i \(-0.960000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(240\) −0.224339 + 0.690446i −0.224339 + 0.690446i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 4.01314 4.01314
\(244\) −0.115808 + 0.356420i −0.115808 + 0.356420i
\(245\) 0.628103 0.456344i 0.628103 0.456344i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(252\) 4.82427 4.82427
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(257\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.563797 0.409622i −0.563797 0.409622i
\(261\) 0 0
\(262\) 0 0
\(263\) 1.93717 1.93717 0.968583 0.248690i \(-0.0800000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(264\) 0 0
\(265\) 0.606379 0.606379
\(266\) 0 0
\(267\) −0.968583 + 0.703717i −0.968583 + 0.703717i
\(268\) 0 0
\(269\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(270\) 0 0
\(271\) −0.866986 0.629902i −0.866986 0.629902i 0.0627905 0.998027i \(-0.480000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(272\) 0 0
\(273\) −1.95094 + 6.00438i −1.95094 + 6.00438i
\(274\) 0 0
\(275\) −0.832549 0.213762i −0.832549 0.213762i
\(276\) 0 0
\(277\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(282\) 0 0
\(283\) −1.56720 + 1.13864i −1.56720 + 1.13864i −0.637424 + 0.770513i \(0.720000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.220095 0.220095
\(288\) 0 0
\(289\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(294\) 0 0
\(295\) 0.229790 0.707220i 0.229790 0.707220i
\(296\) 0 0
\(297\) 1.81919 2.86658i 1.81919 2.86658i
\(298\) 0 0
\(299\) 0 0
\(300\) 1.34709 0.978720i 1.34709 0.978720i
\(301\) 1.20742 + 0.877242i 1.20742 + 0.877242i
\(302\) 0 0
\(303\) −0.509758 1.56887i −0.509758 1.56887i
\(304\) 0 0
\(305\) −0.113624 + 0.0825527i −0.113624 + 0.0825527i
\(306\) 0 0
\(307\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(308\) 0.939097 1.47978i 0.939097 1.47978i
\(309\) 0 0
\(310\) 0 0
\(311\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(312\) 0 0
\(313\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(314\) 0 0
\(315\) 1.46267 + 1.06269i 1.46267 + 1.06269i
\(316\) 0 0
\(317\) −0.393950 + 1.21245i −0.393950 + 1.21245i 0.535827 + 0.844328i \(0.320000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.374763 −0.374763
\(321\) −1.18779 + 3.65565i −1.18779 + 3.65565i
\(322\) 0 0
\(323\) 0 0
\(324\) 1.18176 + 3.63709i 1.18176 + 3.63709i
\(325\) 0.493928 + 1.52015i 0.493928 + 1.52015i
\(326\) 0 0
\(327\) −0.196811 + 0.142991i −0.196811 + 0.142991i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 1.04914 + 3.22894i 1.04914 + 3.22894i
\(337\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(338\) 0 0
\(339\) −0.763146 + 2.34872i −0.763146 + 2.34872i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.580394 1.78627i 0.580394 1.78627i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(348\) 0 0
\(349\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(350\) 0 0
\(351\) −6.31337 −6.31337
\(352\) 0 0
\(353\) 0.125581 0.125581 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.500000 0.363271i −0.500000 0.363271i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(360\) 0 0
\(361\) 0.309017 0.951057i 0.309017 0.951057i
\(362\) 0 0
\(363\) −0.824805 1.75280i −0.824805 1.75280i
\(364\) −3.25908 −3.25908
\(365\) 0 0
\(366\) 0 0
\(367\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(368\) 0 0
\(369\) 0.106820 + 0.328757i 0.106820 + 0.328757i
\(370\) 0 0
\(371\) 2.29420 1.66683i 2.29420 1.66683i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 1.34999 1.34999
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(384\) 0 0
\(385\) 0.610690 0.241789i 0.610690 0.241789i
\(386\) 0 0
\(387\) −0.724339 + 2.22929i −0.724339 + 2.22929i
\(388\) 0 0
\(389\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −1.56720 + 1.13864i −1.56720 + 1.13864i
\(394\) 0 0
\(395\) 0 0
\(396\) 2.66613 + 0.684547i 2.66613 + 0.684547i
\(397\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.695393 + 0.505233i 0.695393 + 0.505233i
\(401\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.688925 0.500534i 0.688925 0.500534i
\(405\) −0.442881 + 1.36305i −0.442881 + 1.36305i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.07463 3.30738i −1.07463 3.30738i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) −0.393180 + 1.21008i −0.393180 + 1.21008i
\(421\) 0.688925 0.500534i 0.688925 0.500534i −0.187381 0.982287i \(-0.560000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.202967 + 0.624667i −0.202967 + 0.624667i
\(428\) −1.98423 −1.98423
\(429\) −1.93019 + 3.04149i −1.93019 + 3.04149i
\(430\) 0 0
\(431\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(432\) −2.74670 + 1.99559i −2.74670 + 1.99559i
\(433\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.101597 0.0738147i −0.101597 0.0738147i
\(437\) 0 0
\(438\) 0 0
\(439\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(440\) 0 0
\(441\) 5.70246 5.70246
\(442\) 0 0
\(443\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) 0 0
\(445\) −0.0715733 0.220280i −0.0715733 0.220280i
\(446\) 0 0
\(447\) 0 0
\(448\) −1.41789 + 1.03016i −1.41789 + 1.03016i
\(449\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(450\) 0 0
\(451\) 0.121636 + 0.0312307i 0.121636 + 0.0312307i
\(452\) −1.27485 −1.27485
\(453\) 0.641510 1.97437i 0.641510 1.97437i
\(454\) 0 0
\(455\) −0.988118 0.717909i −0.988118 0.717909i
\(456\) 0 0
\(457\) −0.393950 1.21245i −0.393950 1.21245i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 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
\(467\) 0.541587 + 1.66683i 0.541587 + 1.66683i 0.728969 + 0.684547i \(0.240000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(468\) −1.58174 4.86811i −1.58174 4.86811i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.542804 + 0.656137i 0.542804 + 0.656137i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 3.60322 + 2.61789i 3.60322 + 2.61789i
\(478\) 0 0
\(479\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.728969 0.684547i 0.728969 0.684547i
\(485\) 0 0
\(486\) 0 0
\(487\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(492\) −0.196811 + 0.142991i −0.196811 + 0.142991i
\(493\) 0 0
\(494\) 0 0
\(495\) 0.657552 + 0.794843i 0.657552 + 0.794843i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(500\) 0.215351 + 0.662783i 0.215351 + 0.662783i
\(501\) −0.968583 2.98099i −0.968583 2.98099i
\(502\) 0 0
\(503\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(504\) 0 0
\(505\) 0.319132 0.319132
\(506\) 0 0
\(507\) 4.76143 4.76143
\(508\) 0 0
\(509\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) −1.64961 −1.64961
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(522\) 0 0
\(523\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(524\) −0.809017 0.587785i −0.809017 0.587785i
\(525\) 2.36093 1.71532i 2.36093 1.71532i
\(526\) 0 0
\(527\) 0 0
\(528\) 0.121636 + 1.93334i 0.121636 + 1.93334i
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 4.41870 3.21038i 4.41870 3.21038i
\(532\) 0 0
\(533\) −0.0721631 0.222095i −0.0721631 0.222095i
\(534\) 0 0
\(535\) −0.601597 0.437086i −0.601597 0.437086i
\(536\) 0 0
\(537\) 0.872746 2.68604i 0.872746 2.68604i
\(538\) 0 0
\(539\) 1.11005 1.74915i 1.11005 1.74915i
\(540\) −1.27236 −1.27236
\(541\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −0.0145433 0.0447596i −0.0145433 0.0447596i
\(546\) 0 0
\(547\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(548\) 0 0
\(549\) −1.03158 −1.03158
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.688925 + 0.500534i 0.688925 + 0.500534i 0.876307 0.481754i \(-0.160000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(558\) 0 0
\(559\) 0.489334 1.50602i 0.489334 1.50602i
\(560\) −0.656814 −0.656814
\(561\) 0 0
\(562\) 0 0
\(563\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(564\) 0 0
\(565\) −0.386520 0.280823i −0.386520 0.280823i
\(566\) 0 0
\(567\) 2.07117 + 6.37442i 2.07117 + 6.37442i
\(568\) 0 0
\(569\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) −1.80113 0.462452i −1.80113 0.462452i
\(573\) −3.60226 −3.60226
\(574\) 0 0
\(575\) 0 0
\(576\) −2.22691 1.61795i −2.22691 1.61795i
\(577\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i 0.968583 0.248690i \(-0.0800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(578\) 0 0
\(579\) −2.28488 1.66006i −2.28488 1.66006i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.50441 0.595638i 1.50441 0.595638i
\(584\) 0 0
\(585\) 0.592778 1.82438i 0.592778 1.82438i
\(586\) 0 0
\(587\) 1.50441 + 1.09302i 1.50441 + 1.09302i 0.968583 + 0.248690i \(0.0800000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(588\) 1.24013 + 3.81672i 1.24013 + 3.81672i
\(589\) 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
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(600\) 0 0
\(601\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.07165 1.07165
\(605\) 0.371808 0.0469702i 0.371808 0.0469702i
\(606\) 0 0
\(607\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(614\) 0 0
\(615\) −0.0911690 −0.0911690
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.876307 0.636674i −0.876307 0.636674i
\(624\) 2.91429 2.11736i 2.91429 2.11736i
\(625\) 0.184911 0.569097i 0.184911 0.569097i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(632\) 0 0
\(633\) −0.763146 2.34872i −0.763146 2.34872i
\(634\) 0 0
\(635\) 0 0
\(636\) −0.968583 + 2.98099i −0.968583 + 2.98099i
\(637\) −3.85235 −3.85235
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.41789 + 1.03016i −1.41789 + 1.03016i −0.425779 + 0.904827i \(0.640000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(642\) 0 0
\(643\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(644\) 0 0
\(645\) −0.500144 0.363376i −0.500144 0.363376i
\(646\) 0 0
\(647\) −0.574633 + 1.76854i −0.574633 + 1.76854i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(648\) 0 0
\(649\) −0.124591 1.98031i −0.124591 1.98031i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.60528 + 1.16630i 1.60528 + 1.16630i 0.876307 + 0.481754i \(0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(654\) 0 0
\(655\) −0.115808 0.356420i −0.115808 0.356420i
\(656\) −0.101597 0.0738147i −0.101597 0.0738147i
\(657\) 0 0
\(658\) 0 0
\(659\) 1.75261 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(660\) −0.388998 + 0.612963i −0.388998 + 0.612963i
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.30902 0.951057i 1.30902 0.951057i
\(669\) 0 0
\(670\) 0 0
\(671\) −0.200808 + 0.316423i −0.200808 + 0.316423i
\(672\) 0 0
\(673\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(674\) 0 0
\(675\) 2.36093 + 1.71532i 2.36093 + 1.71532i
\(676\) 0.759544 + 2.33764i 0.759544 + 2.33764i
\(677\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.263146 0.809880i −0.263146 0.809880i
\(689\) −2.43419 1.76854i −2.43419 1.76854i
\(690\) 0 0
\(691\) 0.541587 1.66683i 0.541587 1.66683i −0.187381 0.982287i \(-0.560000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(692\) 0 0
\(693\) 4.67270 + 1.19975i 4.67270 + 1.19975i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0.872746 + 2.68604i 0.872746 + 2.68604i
\(700\) 1.21875 + 0.885477i 1.21875 + 0.885477i
\(701\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.929776 + 0.368125i −0.929776 + 0.368125i
\(705\) 0 0
\(706\) 0 0
\(707\) 1.20742 0.877242i 1.20742 0.877242i
\(708\) 3.10969 + 2.25932i 3.10969 + 2.25932i
\(709\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −0.444215 0.536964i −0.444215 0.536964i
\(716\) 1.45794 1.45794
\(717\) 0.872746 2.68604i 0.872746 2.68604i
\(718\) 0 0
\(719\) 1.03137 + 0.749337i 1.03137 + 0.749337i 0.968583 0.248690i \(-0.0800000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(720\) −0.318775 0.981088i −0.318775 0.981088i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −3.19549 + 2.32166i −3.19549 + 2.32166i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.224339 0.690446i −0.224339 0.690446i
\(733\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(734\) 0 0
\(735\) −0.464754 + 1.43036i −0.464754 + 1.43036i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.598617 1.84235i 0.598617 1.84235i 0.0627905 0.998027i \(-0.480000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.47759 −3.47759
\(750\) 0 0
\(751\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.324914 + 0.236064i 0.324914 + 0.236064i
\(756\) −4.81390 + 3.49750i −4.81390 + 3.49750i
\(757\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(758\) 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 0
\(763\) −0.178061 0.129369i −0.178061 0.129369i
\(764\) −0.574633 1.76854i −0.574633 1.76854i
\(765\) 0 0
\(766\) 0 0
\(767\) −2.98509 + 2.16880i −2.98509 + 2.16880i
\(768\) 0.598617 1.84235i 0.598617 1.84235i
\(769\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.450527 1.38658i 0.450527 1.38658i
\(773\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 1.34999 1.34999
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −1.67600 + 1.21769i −1.67600 + 1.21769i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.598617 + 1.84235i 0.598617 + 1.84235i 0.535827 + 0.844328i \(0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(788\) 0 0
\(789\) −3.03593 + 2.20573i −3.03593 + 2.20573i
\(790\) 0 0
\(791\) −2.23432 −2.23432
\(792\) 0 0
\(793\) 0.696891 0.696891
\(794\) 0 0
\(795\) −0.950317 + 0.690446i −0.950317 + 0.690446i
\(796\) 0 0
\(797\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0.525702 1.61795i 0.525702 1.61795i
\(802\) 0 0
\(803\) 0 0
\(804\) 0