Properties

Label 471.1.o.a.353.1
Level $471$
Weight $1$
Character 471.353
Analytic conductor $0.235$
Analytic rank $0$
Dimension $12$
Projective image $D_{13}$
CM discriminant -3
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 471 = 3 \cdot 157 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 471.o (of order \(26\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.235059620950\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\Q(\zeta_{26})\)
Defining polynomial: \(x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{13}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{13} - \cdots)\)

Embedding invariants

Embedding label 353.1
Root \(0.970942 - 0.239316i\) of defining polynomial
Character \(\chi\) \(=\) 471.353
Dual form 471.1.o.a.467.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.748511 + 0.663123i) q^{3} +(-0.748511 - 0.663123i) q^{4} +(-1.32555 + 1.17433i) q^{7} +(0.120537 - 0.992709i) q^{9} +O(q^{10})\) \(q+(-0.748511 + 0.663123i) q^{3} +(-0.748511 - 0.663123i) q^{4} +(-1.32555 + 1.17433i) q^{7} +(0.120537 - 0.992709i) q^{9} +1.00000 q^{12} -1.94188 q^{13} +(0.120537 + 0.992709i) q^{16} +(-1.32555 + 0.695701i) q^{19} +(0.213460 - 1.75800i) q^{21} +(-0.354605 - 0.935016i) q^{25} +(0.568065 + 0.822984i) q^{27} +1.77091 q^{28} +(0.688601 - 0.169725i) q^{31} +(-0.748511 + 0.663123i) q^{36} +(1.00599 + 1.45743i) q^{37} +(1.45352 - 1.28771i) q^{39} +(-0.180446 - 0.159861i) q^{43} +(-0.748511 - 0.663123i) q^{48} +(0.257482 - 2.12055i) q^{49} +(1.45352 + 1.28771i) q^{52} +(0.530851 - 1.39974i) q^{57} +(-0.627974 + 0.329586i) q^{61} +(1.00599 + 1.45743i) q^{63} +(0.568065 - 0.822984i) q^{64} +(0.213460 - 0.112032i) q^{67} +(-0.850405 + 0.753393i) q^{73} +(0.885456 + 0.464723i) q^{75} +(1.45352 + 0.358261i) q^{76} +(0.530851 + 1.39974i) q^{79} +(-0.970942 - 0.239316i) q^{81} +(-1.32555 + 1.17433i) q^{84} +(2.57406 - 2.28042i) q^{91} +(-0.402877 + 0.583668i) q^{93} +(0.645395 - 0.935016i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - q^{3} - q^{4} - 2q^{7} - q^{9} + O(q^{10}) \) \( 12q - q^{3} - q^{4} - 2q^{7} - q^{9} + 12q^{12} - 2q^{13} - q^{16} - 2q^{19} - 2q^{21} - q^{25} - q^{27} - 2q^{28} - 2q^{31} - q^{36} - 2q^{37} - 2q^{39} - 2q^{43} - q^{48} - 3q^{49} - 2q^{52} - 2q^{57} - 2q^{61} - 2q^{63} - q^{64} - 2q^{67} - 2q^{73} - q^{75} - 2q^{76} - 2q^{79} - q^{81} - 2q^{84} + 9q^{91} - 2q^{93} + 11q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).

\(n\) \(158\) \(319\)
\(\chi(n)\) \(-1\) \(e\left(\frac{9}{13}\right)\)

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 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(3\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(4\) −0.748511 0.663123i −0.748511 0.663123i
\(5\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(6\) 0 0
\(7\) −1.32555 + 1.17433i −1.32555 + 1.17433i −0.354605 + 0.935016i \(0.615385\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(8\) 0 0
\(9\) 0.120537 0.992709i 0.120537 0.992709i
\(10\) 0 0
\(11\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(12\) 1.00000 1.00000
\(13\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.120537 + 0.992709i 0.120537 + 0.992709i
\(17\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(18\) 0 0
\(19\) −1.32555 + 0.695701i −1.32555 + 0.695701i −0.970942 0.239316i \(-0.923077\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(20\) 0 0
\(21\) 0.213460 1.75800i 0.213460 1.75800i
\(22\) 0 0
\(23\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(24\) 0 0
\(25\) −0.354605 0.935016i −0.354605 0.935016i
\(26\) 0 0
\(27\) 0.568065 + 0.822984i 0.568065 + 0.822984i
\(28\) 1.77091 1.77091
\(29\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(30\) 0 0
\(31\) 0.688601 0.169725i 0.688601 0.169725i 0.120537 0.992709i \(-0.461538\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(37\) 1.00599 + 1.45743i 1.00599 + 1.45743i 0.885456 + 0.464723i \(0.153846\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(38\) 0 0
\(39\) 1.45352 1.28771i 1.45352 1.28771i
\(40\) 0 0
\(41\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(42\) 0 0
\(43\) −0.180446 0.159861i −0.180446 0.159861i 0.568065 0.822984i \(-0.307692\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(48\) −0.748511 0.663123i −0.748511 0.663123i
\(49\) 0.257482 2.12055i 0.257482 2.12055i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.45352 + 1.28771i 1.45352 + 1.28771i
\(53\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.530851 1.39974i 0.530851 1.39974i
\(58\) 0 0
\(59\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(60\) 0 0
\(61\) −0.627974 + 0.329586i −0.627974 + 0.329586i −0.748511 0.663123i \(-0.769231\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(62\) 0 0
\(63\) 1.00599 + 1.45743i 1.00599 + 1.45743i
\(64\) 0.568065 0.822984i 0.568065 0.822984i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.213460 0.112032i 0.213460 0.112032i −0.354605 0.935016i \(-0.615385\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(72\) 0 0
\(73\) −0.850405 + 0.753393i −0.850405 + 0.753393i −0.970942 0.239316i \(-0.923077\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(74\) 0 0
\(75\) 0.885456 + 0.464723i 0.885456 + 0.464723i
\(76\) 1.45352 + 0.358261i 1.45352 + 0.358261i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.530851 + 1.39974i 0.530851 + 1.39974i 0.885456 + 0.464723i \(0.153846\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(80\) 0 0
\(81\) −0.970942 0.239316i −0.970942 0.239316i
\(82\) 0 0
\(83\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(84\) −1.32555 + 1.17433i −1.32555 + 1.17433i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(90\) 0 0
\(91\) 2.57406 2.28042i 2.57406 2.28042i
\(92\) 0 0
\(93\) −0.402877 + 0.583668i −0.402877 + 0.583668i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.645395 0.935016i 0.645395 0.935016i −0.354605 0.935016i \(-0.615385\pi\)
1.00000 \(0\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.354605 + 0.935016i −0.354605 + 0.935016i
\(101\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(102\) 0 0
\(103\) −1.94188 + 0.478631i −1.94188 + 0.478631i −0.970942 + 0.239316i \(0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0.120537 0.992709i 0.120537 0.992709i
\(109\) −0.180446 0.159861i −0.180446 0.159861i 0.568065 0.822984i \(-0.307692\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(110\) 0 0
\(111\) −1.71945 0.423807i −1.71945 0.423807i
\(112\) −1.32555 1.17433i −1.32555 1.17433i
\(113\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.234068 + 1.92773i −0.234068 + 1.92773i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.627974 0.329586i −0.627974 0.329586i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.10312 0.271894i −1.10312 0.271894i −0.354605 0.935016i \(-0.615385\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(128\) 0 0
\(129\) 0.241073 0.241073
\(130\) 0 0
\(131\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(132\) 0 0
\(133\) 0.940091 2.47882i 0.940091 2.47882i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(138\) 0 0
\(139\) −1.71945 0.902438i −1.71945 0.902438i −0.970942 0.239316i \(-0.923077\pi\)
−0.748511 0.663123i \(-0.769231\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 1.21346 + 1.75800i 1.21346 + 1.75800i
\(148\) 0.213460 1.75800i 0.213460 1.75800i
\(149\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(150\) 0 0
\(151\) −0.0854858 0.225408i −0.0854858 0.225408i 0.885456 0.464723i \(-0.153846\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.94188 −1.94188
\(157\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0.251489 + 0.663123i 0.251489 + 0.663123i 1.00000 \(0\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(168\) 0 0
\(169\) 2.77091 2.77091
\(170\) 0 0
\(171\) 0.530851 + 1.39974i 0.530851 + 1.39974i
\(172\) 0.0290582 + 0.239316i 0.0290582 + 0.239316i
\(173\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(174\) 0 0
\(175\) 1.56806 + 0.822984i 1.56806 + 0.822984i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0 0
\(181\) −0.709210 + 1.87003i −0.709210 + 1.87003i −0.354605 + 0.935016i \(0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(182\) 0 0
\(183\) 0.251489 0.663123i 0.251489 0.663123i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −1.71945 0.423807i −1.71945 0.423807i
\(190\) 0 0
\(191\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(192\) 0.120537 + 0.992709i 0.120537 + 0.992709i
\(193\) −0.180446 + 0.159861i −0.180446 + 0.159861i −0.748511 0.663123i \(-0.769231\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.59892 + 1.41652i −1.59892 + 1.41652i
\(197\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(198\) 0 0
\(199\) −0.627974 0.329586i −0.627974 0.329586i 0.120537 0.992709i \(-0.461538\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(200\) 0 0
\(201\) −0.0854858 + 0.225408i −0.0854858 + 0.225408i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −0.234068 1.92773i −0.234068 1.92773i
\(209\) 0 0
\(210\) 0 0
\(211\) −1.10312 + 0.271894i −1.10312 + 0.271894i −0.748511 0.663123i \(-0.769231\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −0.713460 + 1.03363i −0.713460 + 1.03363i
\(218\) 0 0
\(219\) 0.136945 1.12785i 0.136945 1.12785i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.45352 1.28771i 1.45352 1.28771i 0.568065 0.822984i \(-0.307692\pi\)
0.885456 0.464723i \(-0.153846\pi\)
\(224\) 0 0
\(225\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(226\) 0 0
\(227\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(228\) −1.32555 + 0.695701i −1.32555 + 0.695701i
\(229\) 0.688601 + 1.81569i 0.688601 + 1.81569i 0.568065 + 0.822984i \(0.307692\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −1.32555 0.695701i −1.32555 0.695701i
\(238\) 0 0
\(239\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(240\) 0 0
\(241\) 1.12054 0.992709i 1.12054 0.992709i 0.120537 0.992709i \(-0.461538\pi\)
1.00000 \(0\)
\(242\) 0 0
\(243\) 0.885456 0.464723i 0.885456 0.464723i
\(244\) 0.688601 + 0.169725i 0.688601 + 0.169725i
\(245\) 0 0
\(246\) 0 0
\(247\) 2.57406 1.35097i 2.57406 1.35097i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(252\) 0.213460 1.75800i 0.213460 1.75800i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(257\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(258\) 0 0
\(259\) −3.04500 0.750525i −3.04500 0.750525i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.234068 0.0576926i −0.234068 0.0576926i
\(269\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(270\) 0 0
\(271\) 1.45352 + 1.28771i 1.45352 + 1.28771i 0.885456 + 0.464723i \(0.153846\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(272\) 0 0
\(273\) −0.414514 + 3.41383i −0.414514 + 3.41383i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.136945 + 0.198399i 0.136945 + 0.198399i 0.885456 0.464723i \(-0.153846\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(278\) 0 0
\(279\) −0.0854858 0.704039i −0.0854858 0.704039i
\(280\) 0 0
\(281\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(282\) 0 0
\(283\) 0.688601 0.169725i 0.688601 0.169725i 0.120537 0.992709i \(-0.461538\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.354605 0.935016i −0.354605 0.935016i
\(290\) 0 0
\(291\) 0.136945 + 1.12785i 0.136945 + 1.12785i
\(292\) 1.13613 1.13613
\(293\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −0.354605 0.935016i −0.354605 0.935016i
\(301\) 0.426920 0.426920
\(302\) 0 0
\(303\) 0 0
\(304\) −0.850405 1.23202i −0.850405 1.23202i
\(305\) 0 0
\(306\) 0 0
\(307\) 0.530851 0.470293i 0.530851 0.470293i −0.354605 0.935016i \(-0.615385\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(308\) 0 0
\(309\) 1.13613 1.64597i 1.13613 1.64597i
\(310\) 0 0
\(311\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(312\) 0 0
\(313\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.530851 1.39974i 0.530851 1.39974i
\(317\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.568065 + 0.822984i 0.568065 + 0.822984i
\(325\) 0.688601 + 1.81569i 0.688601 + 1.81569i
\(326\) 0 0
\(327\) 0.241073 0.241073
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.850405 + 1.23202i −0.850405 + 1.23202i 0.120537 + 0.992709i \(0.461538\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(332\) 0 0
\(333\) 1.56806 0.822984i 1.56806 0.822984i
\(334\) 0 0
\(335\) 0 0
\(336\) 1.77091 1.77091
\(337\) −0.0854858 0.704039i −0.0854858 0.704039i −0.970942 0.239316i \(-0.923077\pi\)
0.885456 0.464723i \(-0.153846\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.14294 + 1.65583i 1.14294 + 1.65583i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(348\) 0 0
\(349\) −0.180446 1.48611i −0.180446 1.48611i −0.748511 0.663123i \(-0.769231\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(350\) 0 0
\(351\) −1.10312 1.59814i −1.10312 1.59814i
\(352\) 0 0
\(353\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(360\) 0 0
\(361\) 0.705010 1.02138i 0.705010 1.02138i
\(362\) 0 0
\(363\) 0.120537 0.992709i 0.120537 0.992709i
\(364\) −3.43891 −3.43891
\(365\) 0 0
\(366\) 0 0
\(367\) −1.32555 + 0.695701i −1.32555 + 0.695701i −0.970942 0.239316i \(-0.923077\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0.688601 0.169725i 0.688601 0.169725i
\(373\) 1.00599 + 0.527986i 1.00599 + 0.527986i 0.885456 0.464723i \(-0.153846\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.850405 + 1.23202i −0.850405 + 1.23202i 0.120537 + 0.992709i \(0.461538\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(380\) 0 0
\(381\) 1.00599 0.527986i 1.00599 0.527986i
\(382\) 0 0
\(383\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.180446 + 0.159861i −0.180446 + 0.159861i
\(388\) −1.10312 + 0.271894i −1.10312 + 0.271894i
\(389\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −1.10312 + 0.271894i −1.10312 + 0.271894i −0.748511 0.663123i \(-0.769231\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(398\) 0 0
\(399\) 0.940091 + 2.47882i 0.940091 + 2.47882i
\(400\) 0.885456 0.464723i 0.885456 0.464723i
\(401\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(402\) 0 0
\(403\) −1.33718 + 0.329586i −1.33718 + 0.329586i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.0854858 + 0.704039i −0.0854858 + 0.704039i 0.885456 + 0.464723i \(0.153846\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.77091 + 0.929446i 1.77091 + 0.929446i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 1.88546 0.464723i 1.88546 0.464723i
\(418\) 0 0
\(419\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(420\) 0 0
\(421\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.445365 1.17433i 0.445365 1.17433i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(432\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(433\) 0.0290582 + 0.239316i 0.0290582 + 0.239316i 1.00000 \(0\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.0290582 + 0.239316i 0.0290582 + 0.239316i
\(437\) 0 0
\(438\) 0 0
\(439\) 1.45352 + 0.358261i 1.45352 + 0.358261i 0.885456 0.464723i \(-0.153846\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(440\) 0 0
\(441\) −2.07406 0.511209i −2.07406 0.511209i
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 1.00599 + 1.45743i 1.00599 + 1.45743i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.213460 + 1.75800i 0.213460 + 1.75800i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0.213460 + 0.112032i 0.213460 + 0.112032i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.402877 1.06230i −0.402877 1.06230i −0.970942 0.239316i \(-0.923077\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(462\) 0 0
\(463\) −1.32555 + 0.695701i −1.32555 + 0.695701i −0.970942 0.239316i \(-0.923077\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(468\) 1.45352 1.28771i 1.45352 1.28771i
\(469\) −0.151388 + 0.399177i −0.151388 + 0.399177i
\(470\) 0 0
\(471\) 0.120537 0.992709i 0.120537 0.992709i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 1.12054 + 0.992709i 1.12054 + 0.992709i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(480\) 0 0
\(481\) −1.95352 2.83016i −1.95352 2.83016i
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) −0.234068 1.92773i −0.234068 1.92773i −0.354605 0.935016i \(-0.615385\pi\)
0.120537 0.992709i \(-0.461538\pi\)
\(488\) 0 0
\(489\) −0.627974 0.329586i −0.627974 0.329586i
\(490\) 0 0
\(491\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.251489 + 0.663123i 0.251489 + 0.663123i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −2.07406 + 1.83745i −2.07406 + 1.83745i
\(508\) 0.645395 + 0.935016i 0.645395 + 0.935016i
\(509\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(510\) 0 0
\(511\) 0.242518 1.99732i 0.242518 1.99732i
\(512\) 0 0
\(513\) −1.32555 0.695701i −1.32555 0.695701i
\(514\) 0 0
\(515\) 0 0
\(516\) −0.180446 0.159861i −0.180446 0.159861i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −0.850405 0.753393i −0.850405 0.753393i 0.120537 0.992709i \(-0.461538\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(524\) 0 0
\(525\) −1.71945 + 0.423807i −1.71945 + 0.423807i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(530\) 0 0
\(531\) 0 0
\(532\) −2.34743 + 1.23202i −2.34743 + 1.23202i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −0.234068 0.0576926i −0.234068 0.0576926i 0.120537 0.992709i \(-0.461538\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(542\) 0 0
\(543\) −0.709210 1.87003i −0.709210 1.87003i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.71945 0.423807i −1.71945 0.423807i −0.748511 0.663123i \(-0.769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(548\) 0 0
\(549\) 0.251489 + 0.663123i 0.251489 + 0.663123i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −2.34743 1.23202i −2.34743 1.23202i
\(554\) 0 0
\(555\) 0 0
\(556\) 0.688601 + 1.81569i 0.688601 + 1.81569i
\(557\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(558\) 0 0
\(559\) 0.350405 + 0.310432i 0.350405 + 0.310432i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1.56806 0.822984i 1.56806 0.822984i
\(568\) 0 0
\(569\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(570\) 0 0
\(571\) 0.688601 1.81569i 0.688601 1.81569i 0.120537 0.992709i \(-0.461538\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.748511 0.663123i −0.748511 0.663123i
\(577\) 0.213460 + 1.75800i 0.213460 + 1.75800i 0.568065 + 0.822984i \(0.307692\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(578\) 0 0
\(579\) 0.0290582 0.239316i 0.0290582 0.239316i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(588\) 0.257482 2.12055i 0.257482 2.12055i
\(589\) −0.794696 + 0.704039i −0.794696 + 0.704039i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.32555 + 1.17433i −1.32555 + 1.17433i
\(593\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0.688601 0.169725i 0.688601 0.169725i
\(598\) 0 0
\(599\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(600\) 0 0
\(601\) 0.645395 + 0.935016i 0.645395 + 0.935016i 1.00000 \(0\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(602\) 0 0
\(603\) −0.0854858 0.225408i −0.0854858 0.225408i
\(604\) −0.0854858 + 0.225408i −0.0854858 + 0.225408i
\(605\) 0 0
\(606\) 0 0
\(607\) 0.0290582 0.239316i 0.0290582 0.239316i −0.970942 0.239316i \(-0.923077\pi\)
1.00000 \(0\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.0854858 0.704039i −0.0854858 0.704039i −0.970942 0.239316i \(-0.923077\pi\)
0.885456 0.464723i \(-0.153846\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(618\) 0 0
\(619\) −0.0854858 + 0.704039i −0.0854858 + 0.704039i 0.885456 + 0.464723i \(0.153846\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 1.45352 + 1.28771i 1.45352 + 1.28771i
\(625\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.00000 1.00000
\(629\) 0 0
\(630\) 0 0
\(631\) −0.850405 + 0.753393i −0.850405 + 0.753393i −0.970942 0.239316i \(-0.923077\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(632\) 0 0
\(633\) 0.645395 0.935016i 0.645395 0.935016i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −0.500000 + 4.11787i −0.500000 + 4.11787i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 0.241073 + 1.98542i 0.241073 + 1.98542i 0.120537 + 0.992709i \(0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −0.151388 1.24679i −0.151388 1.24679i
\(652\) 0.251489 0.663123i 0.251489 0.663123i
\(653\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0.645395 + 0.935016i 0.645395 + 0.935016i
\(658\) 0 0
\(659\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(660\) 0 0
\(661\) 1.00599 + 0.527986i 1.00599 + 0.527986i 0.885456 0.464723i \(-0.153846\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −0.234068 + 1.92773i −0.234068 + 1.92773i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.45352 + 1.28771i 1.45352 + 1.28771i 0.885456 + 0.464723i \(0.153846\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(674\) 0 0
\(675\) 0.568065 0.822984i 0.568065 0.822984i
\(676\) −2.07406 1.83745i −2.07406 1.83745i
\(677\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(678\) 0 0
\(679\) 0.242518 + 1.99732i 0.242518 + 1.99732i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(684\) 0.530851 1.39974i 0.530851 1.39974i
\(685\) 0 0
\(686\) 0 0
\(687\) −1.71945 0.902438i −1.71945 0.902438i
\(688\) 0.136945 0.198399i 0.136945 0.198399i
\(689\) 0 0
\(690\) 0 0
\(691\) −1.10312 1.59814i −1.10312 1.59814i −0.748511 0.663123i \(-0.769231\pi\)
−0.354605 0.935016i \(-0.615385\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.627974 1.65583i −0.627974 1.65583i
\(701\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(702\) 0 0
\(703\) −2.34743 1.23202i −2.34743 1.23202i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.10312 0.271894i −1.10312 0.271894i −0.354605 0.935016i \(-0.615385\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(710\) 0 0
\(711\) 1.45352 0.358261i 1.45352 0.358261i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(720\) 0 0
\(721\) 2.01199 2.91486i 2.01199 2.91486i
\(722\) 0 0
\(723\) −0.180446 + 1.48611i −0.180446 + 1.48611i
\(724\) 1.77091 0.929446i 1.77091 0.929446i
\(725\) 0 0
\(726\) 0 0
\(727\) 1.45352 0.358261i 1.45352 0.358261i 0.568065 0.822984i \(-0.307692\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(728\) 0 0
\(729\) −0.354605 + 0.935016i −0.354605 + 0.935016i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.627974 + 0.329586i −0.627974 + 0.329586i
\(733\) 1.45352 + 1.28771i 1.45352 + 1.28771i 0.885456 + 0.464723i \(0.153846\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.688601 + 0.169725i 0.688601 + 0.169725i 0.568065 0.822984i \(-0.307692\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(740\) 0 0
\(741\) −1.03085 + 2.71813i −1.03085 + 2.71813i
\(742\) 0 0
\(743\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.136945 + 0.198399i 0.136945 + 0.198399i 0.885456 0.464723i \(-0.153846\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 1.00599 + 1.45743i 1.00599 + 1.45743i
\(757\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(762\) 0 0
\(763\) 0.426920 0.426920
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.568065 0.822984i 0.568065 0.822984i
\(769\) 0.136945 + 1.12785i 0.136945 + 1.12785i 0.885456 + 0.464723i \(0.153846\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.241073 0.241073
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) −0.402877 0.583668i −0.402877 0.583668i
\(776\) 0 0
\(777\) 2.77690 1.45743i 2.77690 1.45743i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 2.13613 2.13613
\(785\) 0 0
\(786\) 0 0
\(787\) 0.688601 1.81569i 0.688601 1.81569i 0.120537 0.992709i \(-0.461538\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 1.21945 0.640018i 1.21945 0.640018i
\(794\) 0 0
\(795\) 0 0
\(796\) 0.251489 + 0.663123i 0.251489 + 0.663123i
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0.213460 0.112032i 0.213460 0.112032i
\(805\) 0 0