Properties

Label 1375.1.ch.a.1011.1
Level $1375$
Weight $1$
Character 1375.1011
Analytic conductor $0.686$
Analytic rank $0$
Dimension $20$
Projective image $D_{25}$
CM discriminant -11
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1375 = 5^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1375.ch (of order \(50\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.686214392370\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{50})\)
Defining polynomial: \(x^{20} - x^{15} + x^{10} - x^{5} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
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 1011.1
Root \(0.929776 + 0.368125i\) of defining polynomial
Character \(\chi\) \(=\) 1375.1011
Dual form 1375.1.ch.a.1341.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.939097 + 1.47978i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-0.882067 + 1.87449i) q^{9} +O(q^{10})\) \(q+(0.939097 + 1.47978i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.309017 - 0.951057i) q^{5} +(-0.882067 + 1.87449i) q^{9} +(0.728969 - 0.684547i) q^{11} +(1.53583 - 0.844328i) q^{12} +(1.69755 - 0.435857i) q^{15} +(-0.992115 - 0.125333i) q^{16} +(-0.929776 - 0.368125i) q^{20} +(-0.200808 + 1.05267i) q^{23} +(-0.809017 - 0.587785i) q^{25} +(-1.86338 + 0.235400i) q^{27} +(-0.0235315 - 0.374023i) q^{31} +(1.69755 + 0.435857i) q^{33} +(1.81540 + 0.998027i) q^{36} +(1.60528 + 0.202793i) q^{37} +(-0.637424 - 0.770513i) q^{44} +(1.51017 + 1.41814i) q^{45} +(-0.393950 + 0.476203i) q^{47} +(-0.746226 - 1.58581i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.41213 - 0.362574i) q^{53} +(-0.425779 - 0.904827i) q^{55} +(-1.73879 + 0.955910i) q^{59} +(-0.328407 - 1.72157i) q^{60} +(-0.187381 + 0.982287i) q^{64} +(-1.80113 + 0.713118i) q^{67} +(-1.74630 + 0.691409i) q^{69} +(-1.11716 + 1.35041i) q^{71} +(0.110048 - 1.74915i) q^{75} +(-0.425779 + 0.904827i) q^{80} +(-0.777718 - 0.940099i) q^{81} +(-1.11716 - 0.614163i) q^{89} +(1.03799 + 0.266509i) q^{92} +(0.531374 - 0.386066i) q^{93} +(1.84489 + 0.730444i) q^{97} +(0.640176 + 1.97026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 5q^{5} + O(q^{10}) \) \( 20q - 5q^{5} + 20q^{12} - 5q^{25} - 5q^{27} - 5q^{48} - 5q^{49} - 5q^{59} - 5q^{60} - 5q^{67} - 5q^{69} - 5q^{81} - 5q^{92} - 10q^{93} - 5q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1375\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(1002\)
\(\chi(n)\) \(-1\) \(e\left(\frac{19}{25}\right)\)

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 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(3\) 0.939097 + 1.47978i 0.939097 + 1.47978i 0.876307 + 0.481754i \(0.160000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(4\) 0.0627905 0.998027i 0.0627905 0.998027i
\(5\) 0.309017 0.951057i 0.309017 0.951057i
\(6\) 0 0
\(7\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(8\) 0 0
\(9\) −0.882067 + 1.87449i −0.882067 + 1.87449i
\(10\) 0 0
\(11\) 0.728969 0.684547i 0.728969 0.684547i
\(12\) 1.53583 0.844328i 1.53583 0.844328i
\(13\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(14\) 0 0
\(15\) 1.69755 0.435857i 1.69755 0.435857i
\(16\) −0.992115 0.125333i −0.992115 0.125333i
\(17\) 0 0 −0.0627905 0.998027i \(-0.520000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(18\) 0 0
\(19\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(20\) −0.929776 0.368125i −0.929776 0.368125i
\(21\) 0 0
\(22\) 0 0
\(23\) −0.200808 + 1.05267i −0.200808 + 1.05267i 0.728969 + 0.684547i \(0.240000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(24\) 0 0
\(25\) −0.809017 0.587785i −0.809017 0.587785i
\(26\) 0 0
\(27\) −1.86338 + 0.235400i −1.86338 + 0.235400i
\(28\) 0 0
\(29\) 0 0 −0.929776 0.368125i \(-0.880000\pi\)
0.929776 + 0.368125i \(0.120000\pi\)
\(30\) 0 0
\(31\) −0.0235315 0.374023i −0.0235315 0.374023i −0.992115 0.125333i \(-0.960000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(32\) 0 0
\(33\) 1.69755 + 0.435857i 1.69755 + 0.435857i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.81540 + 0.998027i 1.81540 + 0.998027i
\(37\) 1.60528 + 0.202793i 1.60528 + 0.202793i 0.876307 0.481754i \(-0.160000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.187381 0.982287i \(-0.560000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(42\) 0 0
\(43\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(44\) −0.637424 0.770513i −0.637424 0.770513i
\(45\) 1.51017 + 1.41814i 1.51017 + 1.41814i
\(46\) 0 0
\(47\) −0.393950 + 0.476203i −0.393950 + 0.476203i −0.929776 0.368125i \(-0.880000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(48\) −0.746226 1.58581i −0.746226 1.58581i
\(49\) −0.809017 0.587785i −0.809017 0.587785i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.41213 0.362574i 1.41213 0.362574i 0.535827 0.844328i \(-0.320000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(54\) 0 0
\(55\) −0.425779 0.904827i −0.425779 0.904827i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.73879 + 0.955910i −1.73879 + 0.955910i −0.809017 + 0.587785i \(0.800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(60\) −0.328407 1.72157i −0.328407 1.72157i
\(61\) 0 0 0.187381 0.982287i \(-0.440000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.187381 + 0.982287i −0.187381 + 0.982287i
\(65\) 0 0
\(66\) 0 0
\(67\) −1.80113 + 0.713118i −1.80113 + 0.713118i −0.809017 + 0.587785i \(0.800000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(68\) 0 0
\(69\) −1.74630 + 0.691409i −1.74630 + 0.691409i
\(70\) 0 0
\(71\) −1.11716 + 1.35041i −1.11716 + 1.35041i −0.187381 + 0.982287i \(0.560000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(72\) 0 0
\(73\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(74\) 0 0
\(75\) 0.110048 1.74915i 0.110048 1.74915i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.535827 0.844328i \(-0.680000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(80\) −0.425779 + 0.904827i −0.425779 + 0.904827i
\(81\) −0.777718 0.940099i −0.777718 0.940099i
\(82\) 0 0
\(83\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.11716 0.614163i −1.11716 0.614163i −0.187381 0.982287i \(-0.560000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.03799 + 0.266509i 1.03799 + 0.266509i
\(93\) 0.531374 0.386066i 0.531374 0.386066i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.84489 + 0.730444i 1.84489 + 0.730444i 0.968583 + 0.248690i \(0.0800000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(98\) 0 0
\(99\) 0.640176 + 1.97026i 0.640176 + 1.97026i
\(100\) −0.637424 + 0.770513i −0.637424 + 0.770513i
\(101\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(102\) 0 0
\(103\) 0.121636 1.93334i 0.121636 1.93334i −0.187381 0.982287i \(-0.560000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(108\) 0.117933 + 1.87449i 0.117933 + 1.87449i
\(109\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(110\) 0 0
\(111\) 1.20742 + 2.56590i 1.20742 + 2.56590i
\(112\) 0 0
\(113\) −1.11716 + 0.614163i −1.11716 + 0.614163i −0.929776 0.368125i \(-0.880000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(114\) 0 0
\(115\) 0.939097 + 0.516273i 0.939097 + 0.516273i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.0627905 0.998027i 0.0627905 0.998027i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.374763 −0.374763
\(125\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(126\) 0 0
\(127\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(132\) 0.541587 1.66683i 0.541587 1.66683i
\(133\) 0 0
\(134\) 0 0
\(135\) −0.351939 + 1.84493i −0.351939 + 1.84493i
\(136\) 0 0
\(137\) −1.62954 + 0.895846i −1.62954 + 0.895846i −0.637424 + 0.770513i \(0.720000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.425779 0.904827i \(-0.640000\pi\)
0.425779 + 0.904827i \(0.360000\pi\)
\(140\) 0 0
\(141\) −1.07463 0.135758i −1.07463 0.135758i
\(142\) 0 0
\(143\) 0 0
\(144\) 1.11005 1.74915i 1.11005 1.74915i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.110048 1.74915i 0.110048 1.74915i
\(148\) 0.303189 1.58937i 0.303189 1.58937i
\(149\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(150\) 0 0
\(151\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.362989 0.0931997i −0.362989 0.0931997i
\(156\) 0 0
\(157\) −0.101597 + 0.0738147i −0.101597 + 0.0738147i −0.637424 0.770513i \(-0.720000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(158\) 0 0
\(159\) 1.86266 + 1.74915i 1.86266 + 1.74915i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0.0702235 + 0.368125i 0.0702235 + 0.368125i 1.00000 \(0\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(164\) 0 0
\(165\) 0.939097 1.47978i 0.939097 1.47978i
\(166\) 0 0
\(167\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(168\) 0 0
\(169\) −0.637424 0.770513i −0.637424 0.770513i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.425779 0.904827i \(-0.640000\pi\)
0.425779 + 0.904827i \(0.360000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(177\) −3.04743 1.67534i −3.04743 1.67534i
\(178\) 0 0
\(179\) 1.18532 1.43281i 1.18532 1.43281i 0.309017 0.951057i \(-0.400000\pi\)
0.876307 0.481754i \(-0.160000\pi\)
\(180\) 1.51017 1.41814i 1.51017 1.41814i
\(181\) 1.50441 0.595638i 1.50441 0.595638i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.688925 1.46404i 0.688925 1.46404i
\(186\) 0 0
\(187\) 0 0
\(188\) 0.450527 + 0.423073i 0.450527 + 0.423073i
\(189\) 0 0
\(190\) 0 0
\(191\) −1.11716 + 0.614163i −1.11716 + 0.614163i −0.929776 0.368125i \(-0.880000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(192\) −1.62954 + 0.645180i −1.62954 + 0.645180i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.637424 + 0.770513i −0.637424 + 0.770513i
\(197\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(198\) 0 0
\(199\) 1.50441 1.09302i 1.50441 1.09302i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(200\) 0 0
\(201\) −2.74670 1.99559i −2.74670 1.99559i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.79609 1.30494i −1.79609 1.30494i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(212\) −0.273190 1.43211i −0.273190 1.43211i
\(213\) −3.04743 0.384980i −3.04743 0.384980i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.929776 + 0.368125i −0.929776 + 0.368125i
\(221\) 0 0
\(222\) 0 0
\(223\) 0.844844 0.106729i 0.844844 0.106729i 0.309017 0.951057i \(-0.400000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(224\) 0 0
\(225\) 1.81540 0.998027i 1.81540 0.998027i
\(226\) 0 0
\(227\) 0 0 0.187381 0.982287i \(-0.440000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(228\) 0 0
\(229\) 0.121636 0.0312307i 0.121636 0.0312307i −0.187381 0.982287i \(-0.560000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.0627905 0.998027i \(-0.520000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(234\) 0 0
\(235\) 0.331159 + 0.521823i 0.331159 + 0.521823i
\(236\) 0.844844 + 1.79538i 0.844844 + 1.79538i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(240\) −1.73879 + 0.219661i −1.73879 + 0.219661i
\(241\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(242\) 0 0
\(243\) 0.0803940 0.247427i 0.0803940 0.247427i
\(244\) 0 0
\(245\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(252\) 0 0
\(253\) 0.574221 + 0.904827i 0.574221 + 0.904827i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.968583 + 0.248690i 0.968583 + 0.248690i
\(257\) 0.331159 1.01920i 0.331159 1.01920i −0.637424 0.770513i \(-0.720000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(264\) 0 0
\(265\) 0.0915446 1.45506i 0.0915446 1.45506i
\(266\) 0 0
\(267\) −0.140294 2.22991i −0.140294 2.22991i
\(268\) 0.598617 + 1.84235i 0.598617 + 1.84235i
\(269\) 0.0672897 0.106032i 0.0672897 0.106032i −0.809017 0.587785i \(-0.800000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(270\) 0 0
\(271\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.992115 + 0.125333i −0.992115 + 0.125333i
\(276\) 0.580394 + 1.78627i 0.580394 + 1.78627i
\(277\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(278\) 0 0
\(279\) 0.721858 + 0.285804i 0.721858 + 0.285804i
\(280\) 0 0
\(281\) 0 0 −0.0627905 0.998027i \(-0.520000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.968583 0.248690i \(-0.920000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(284\) 1.27760 + 1.19975i 1.27760 + 1.19975i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.992115 + 0.125333i −0.992115 + 0.125333i
\(290\) 0 0
\(291\) 0.651635 + 3.41599i 0.651635 + 3.41599i
\(292\) 0 0
\(293\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(294\) 0 0
\(295\) 0.371808 + 1.94908i 0.371808 + 1.94908i
\(296\) 0 0
\(297\) −1.19721 + 1.44717i −1.19721 + 1.44717i
\(298\) 0 0
\(299\) 0 0
\(300\) −1.73879 0.219661i −1.73879 0.219661i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 2.97515 1.63560i 2.97515 1.63560i
\(310\) 0 0
\(311\) −0.362989 + 1.90285i −0.362989 + 1.90285i 0.0627905 + 0.998027i \(0.480000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(312\) 0 0
\(313\) −1.35556 1.27295i −1.35556 1.27295i −0.929776 0.368125i \(-0.880000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.791759 0.313480i 0.791759 0.313480i 0.0627905 0.998027i \(-0.480000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.876307 + 0.481754i 0.876307 + 0.481754i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.987078 + 0.717154i −0.987078 + 0.717154i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.23480 1.49261i −1.23480 1.49261i −0.809017 0.587785i \(-0.800000\pi\)
−0.425779 0.904827i \(-0.640000\pi\)
\(332\) 0 0
\(333\) −1.79609 + 2.83019i −1.79609 + 2.83019i
\(334\) 0 0
\(335\) 0.121636 + 1.93334i 0.121636 + 1.93334i
\(336\) 0 0
\(337\) 0 0 −0.187381 0.982287i \(-0.560000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(338\) 0 0
\(339\) −1.95795 1.07639i −1.95795 1.07639i
\(340\) 0 0
\(341\) −0.273190 0.256543i −0.273190 0.256543i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0.117933 + 1.87449i 0.117933 + 1.87449i
\(346\) 0 0
\(347\) 0 0 −0.929776 0.368125i \(-0.880000\pi\)
0.929776 + 0.368125i \(0.120000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.125581 1.99605i 0.125581 1.99605i 0.0627905 0.998027i \(-0.480000\pi\)
0.0627905 0.998027i \(-0.480000\pi\)
\(354\) 0 0
\(355\) 0.939097 + 1.47978i 0.939097 + 1.47978i
\(356\) −0.683098 + 1.07639i −0.683098 + 1.07639i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(360\) 0 0
\(361\) −0.425779 0.904827i −0.425779 0.904827i
\(362\) 0 0
\(363\) 1.53583 0.844328i 1.53583 0.844328i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 1.18532 + 1.43281i 1.18532 + 1.43281i 0.876307 + 0.481754i \(0.160000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(368\) 0.331159 1.01920i 0.331159 1.01920i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −0.351939 0.554566i −0.351939 0.554566i
\(373\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(374\) 0 0
\(375\) −1.62954 0.645180i −1.62954 0.645180i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.0388067 0.616814i 0.0388067 0.616814i −0.929776 0.368125i \(-0.880000\pi\)
0.968583 0.248690i \(-0.0800000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.238883 + 0.288760i 0.238883 + 0.288760i 0.876307 0.481754i \(-0.160000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.844844 1.79538i 0.844844 1.79538i
\(389\) 0.362576 + 0.770513i 0.362576 + 0.770513i 1.00000 \(0\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 2.00657 0.515199i 2.00657 0.515199i
\(397\) −0.0800484 + 1.27233i −0.0800484 + 1.27233i 0.728969 + 0.684547i \(0.240000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(401\) 0.450527 + 1.38658i 0.450527 + 1.38658i 0.876307 + 0.481754i \(0.160000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −1.13442 + 0.449147i −1.13442 + 0.449147i
\(406\) 0 0
\(407\) 1.30902 0.951057i 1.30902 0.951057i
\(408\) 0 0
\(409\) 0 0 −0.728969 0.684547i \(-0.760000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(410\) 0 0
\(411\) −2.85595 1.57007i −2.85595 1.57007i
\(412\) −1.92189 0.242791i −1.92189 0.242791i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.26480 + 1.52888i 1.26480 + 1.52888i 0.728969 + 0.684547i \(0.240000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(420\) 0 0
\(421\) −0.683098 1.07639i −0.683098 1.07639i −0.992115 0.125333i \(-0.960000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(422\) 0 0
\(423\) −0.545148 1.15850i −0.545148 1.15850i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(432\) 1.87819 1.87819
\(433\) 1.50441 0.595638i 1.50441 0.595638i 0.535827 0.844328i \(-0.320000\pi\)
0.968583 + 0.248690i \(0.0800000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.187381 0.982287i \(-0.440000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(440\) 0 0
\(441\) 1.81540 0.998027i 1.81540 0.998027i
\(442\) 0 0
\(443\) −1.98423 −1.98423 −0.992115 0.125333i \(-0.960000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(444\) 2.63665 1.04392i 2.63665 1.04392i
\(445\) −0.929324 + 0.872693i −0.929324 + 0.872693i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.866986 + 0.629902i −0.866986 + 0.629902i −0.929776 0.368125i \(-0.880000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0.542804 + 1.15352i 0.542804 + 1.15352i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0.574221 0.904827i 0.574221 0.904827i
\(461\) 0 0 0.992115 0.125333i \(-0.0400000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(462\) 0 0
\(463\) 1.26480 + 0.159781i 1.26480 + 0.159781i 0.728969 0.684547i \(-0.240000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(464\) 0 0
\(465\) −0.202967 0.624667i −0.202967 0.624667i
\(466\) 0 0
\(467\) 0.598617 + 0.153699i 0.598617 + 0.153699i 0.535827 0.844328i \(-0.320000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.204639 0.0810224i −0.204639 0.0810224i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.565955 + 2.96684i −0.565955 + 2.96684i
\(478\) 0 0
\(479\) 0 0 0.968583 0.248690i \(-0.0800000\pi\)
−0.968583 + 0.248690i \(0.920000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.992115 0.125333i −0.992115 0.125333i
\(485\) 1.26480 1.52888i 1.26480 1.52888i
\(486\) 0 0
\(487\) −0.851559 + 1.80965i −0.851559 + 1.80965i −0.425779 + 0.904827i \(0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(488\) 0 0
\(489\) −0.478797 + 0.449620i −0.478797 + 0.449620i
\(490\) 0 0
\(491\) 0 0 0.425779 0.904827i \(-0.360000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 2.07165 2.07165
\(496\) −0.0235315 + 0.374023i −0.0235315 + 0.374023i
\(497\) 0 0
\(498\) 0 0
\(499\) 1.45794 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(500\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.535827 0.844328i \(-0.680000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.541587 1.66683i 0.541587 1.66683i
\(508\) 0 0
\(509\) 0.791759 1.68257i 0.791759 1.68257i 0.0627905 0.998027i \(-0.480000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.80113 0.713118i −1.80113 0.713118i
\(516\) 0 0
\(517\) 0.0388067 + 0.616814i 0.0388067 + 0.616814i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.87631 0.481754i 1.87631 0.481754i 0.876307 0.481754i \(-0.160000\pi\)
1.00000 \(0\)
\(522\) 0 0
\(523\) 0 0 0.187381 0.982287i \(-0.440000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) −1.62954 0.645180i −1.62954 0.645180i
\(529\) −0.138017 0.0546449i −0.138017 0.0546449i
\(530\) 0 0
\(531\) −0.258109 4.10252i −0.258109 4.10252i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 3.23338 + 0.408471i 3.23338 + 0.408471i
\(538\) 0 0
\(539\) −0.992115 + 0.125333i −0.992115 + 0.125333i
\(540\) 1.81919 + 0.467088i 1.81919 + 0.467088i
\(541\) 0 0 −0.187381 0.982287i \(-0.560000\pi\)
0.187381 + 0.982287i \(0.440000\pi\)
\(542\) 0 0
\(543\) 2.29420 + 1.66683i 2.29420 + 1.66683i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(548\) 0.791759 + 1.68257i 0.791759 + 1.68257i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 2.81343 0.355418i 2.81343 0.355418i
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.728969 0.684547i \(-0.760000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(564\) −0.202967 + 1.06399i −0.202967 + 1.06399i
\(565\) 0.238883 + 1.25227i 0.238883 + 1.25227i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.929776 0.368125i \(-0.120000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(570\) 0 0
\(571\) 0 0 0.637424 0.770513i \(-0.280000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(572\) 0 0
\(573\) −1.95795 1.07639i −1.95795 1.07639i
\(574\) 0 0
\(575\) 0.781202 0.733597i 0.781202 0.733597i
\(576\) −1.67600 1.21769i −1.67600 1.21769i
\(577\) 0.362576 + 0.770513i 0.362576 + 0.770513i 1.00000 \(0\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.781202 1.23098i 0.781202 1.23098i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.371808 + 1.94908i 0.371808 + 1.94908i 0.309017 + 0.951057i \(0.400000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(588\) −1.73879 0.219661i −1.73879 0.219661i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.56720 0.402389i −1.56720 0.402389i
\(593\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 3.03021 + 1.19975i 3.03021 + 1.19975i
\(598\) 0 0
\(599\) −0.263146 0.809880i −0.263146 0.809880i −0.992115 0.125333i \(-0.960000\pi\)
0.728969 0.684547i \(-0.240000\pi\)
\(600\) 0 0
\(601\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(602\) 0 0
\(603\) 0.251987 4.00522i 0.251987 4.00522i
\(604\) 0 0
\(605\) −0.929776 0.368125i −0.929776 0.368125i
\(606\) 0 0
\(607\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.876307 0.481754i \(-0.160000\pi\)
−0.876307 + 0.481754i \(0.840000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.542804 + 0.656137i 0.542804 + 0.656137i 0.968583 0.248690i \(-0.0800000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(618\) 0 0
\(619\) −0.362989 0.0931997i −0.362989 0.0931997i 0.0627905 0.998027i \(-0.480000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(620\) −0.115808 + 0.356420i −0.115808 + 0.356420i
\(621\) 0.126383 2.00880i 0.126383 2.00880i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.0672897 + 0.106032i 0.0672897 + 0.106032i
\(629\) 0 0
\(630\) 0 0
\(631\) 1.87631 + 0.481754i 1.87631 + 0.481754i 1.00000 \(0\)
0.876307 + 0.481754i \(0.160000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 1.86266 1.74915i 1.86266 1.74915i
\(637\) 0 0
\(638\) 0 0
\(639\) −1.54592 3.28525i −1.54592 3.28525i
\(640\) 0 0
\(641\) −1.73879 0.219661i −1.73879 0.219661i −0.809017 0.587785i \(-0.800000\pi\)
−0.929776 + 0.368125i \(0.880000\pi\)
\(642\) 0 0
\(643\) −0.115808 0.356420i −0.115808 0.356420i 0.876307 0.481754i \(-0.160000\pi\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.121636 1.93334i 0.121636 1.93334i −0.187381 0.982287i \(-0.560000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(648\) 0 0
\(649\) −0.613161 + 1.88711i −0.613161 + 1.88711i
\(650\) 0 0
\(651\) 0 0
\(652\) 0.371808 0.0469702i 0.371808 0.0469702i
\(653\) 0.348445 + 0.137959i 0.348445 + 0.137959i 0.535827 0.844328i \(-0.320000\pi\)
−0.187381 + 0.982287i \(0.560000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.728969 0.684547i \(-0.760000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(660\) −1.41789 1.03016i −1.41789 1.03016i
\(661\) −1.62954 0.895846i −1.62954 0.895846i −0.992115 0.125333i \(-0.960000\pi\)
−0.637424 0.770513i \(-0.720000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0.951325 + 1.14995i 0.951325 + 1.14995i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.425779 0.904827i \(-0.640000\pi\)
0.425779 + 0.904827i \(0.360000\pi\)
\(674\) 0 0
\(675\) 1.64587 + 0.904827i 1.64587 + 0.904827i
\(676\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(677\) 0 0 −0.876307 0.481754i \(-0.840000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.116762 + 0.0462295i −0.116762 + 0.0462295i −0.425779 0.904827i \(-0.640000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(684\) 0 0
\(685\) 0.348445 + 1.82662i 0.348445 + 1.82662i
\(686\) 0 0
\(687\) 0.160442 + 0.150665i 0.160442 + 0.150665i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.939097 0.516273i 0.939097 0.516273i 0.0627905 0.998027i \(-0.480000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.535827 + 0.844328i 0.535827 + 0.844328i
\(705\) −0.461193 + 0.980086i −0.461193 + 0.980086i
\(706\) 0 0
\(707\) 0 0
\(708\) −1.86338 + 2.93622i −1.86338 + 2.93622i
\(709\) −0.273190 1.43211i −0.273190 1.43211i −0.809017 0.587785i \(-0.800000\pi\)
0.535827 0.844328i \(-0.320000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.398449 + 0.0503358i 0.398449 + 0.0503358i
\(714\) 0 0
\(715\) 0 0
\(716\) −1.35556 1.27295i −1.35556 1.27295i
\(717\) 0 0
\(718\) 0 0
\(719\) 0.00788530 + 0.125333i 0.00788530 + 0.125333i 1.00000 \(0\)
−0.992115 + 0.125333i \(0.960000\pi\)
\(720\) −1.32052 1.59624i −1.32052 1.59624i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −0.500000 1.53884i −0.500000 1.53884i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.371808 1.94908i 0.371808 1.94908i 0.0627905 0.998027i \(-0.480000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(728\) 0 0
\(729\) −0.740128 + 0.190032i −0.740128 + 0.190032i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.0627905 0.998027i \(-0.520000\pi\)
0.0627905 + 0.998027i \(0.480000\pi\)
\(734\) 0 0
\(735\) −1.62954 0.645180i −1.62954 0.645180i
\(736\) 0 0
\(737\) −0.824805 + 1.75280i −0.824805 + 1.75280i
\(738\) 0 0
\(739\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(740\) −1.41789 0.779494i −1.41789 0.779494i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −1.27485 −1.27485 −0.637424 0.770513i \(-0.720000\pi\)
−0.637424 + 0.770513i \(0.720000\pi\)
\(752\) 0.450527 0.423073i 0.450527 0.423073i
\(753\) 1.36914 + 2.15743i 1.36914 + 2.15743i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −0.613161 + 1.88711i −0.613161 + 1.88711i −0.187381 + 0.982287i \(0.560000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(758\) 0 0
\(759\) −0.799696 + 1.69944i −0.799696 + 1.69944i
\(760\) 0 0
\(761\) 0 0 0.728969 0.684547i \(-0.240000\pi\)
−0.728969 + 0.684547i \(0.760000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.542804 + 1.15352i 0.542804 + 1.15352i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.541587 + 1.66683i 0.541587 + 1.66683i
\(769\) 0 0 0.535827 0.844328i \(-0.320000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(770\) 0 0
\(771\) 1.81919 0.467088i 1.81919 0.467088i
\(772\) 0 0
\(773\) −0.273190 + 1.43211i −0.273190 + 1.43211i 0.535827 + 0.844328i \(0.320000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(774\) 0 0
\(775\) −0.200808 + 0.316423i −0.200808 + 0.316423i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0.110048 + 1.74915i 0.110048 + 1.74915i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.728969 + 0.684547i 0.728969 + 0.684547i
\(785\) 0.0388067 + 0.119435i 0.0388067 + 0.119435i
\(786\) 0 0
\(787\) 0 0 −0.992115 0.125333i \(-0.960000\pi\)
0.992115 + 0.125333i \(0.0400000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 2.23914 1.23098i 2.23914 1.23098i
\(796\) −0.996398 1.57007i −0.996398 1.57007i
\(797\) 0.812619 0.982287i 0.812619 0.982287i −0.187381 0.982287i \(-0.560000\pi\)
1.00000 \(0\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 2.13665 1.55237i 2.13665 1.55237i
\(802\) 0 0