Properties

Label 448.1.bf.a.293.1
Level $448$
Weight $1$
Character 448.293
Analytic conductor $0.224$
Analytic rank $0$
Dimension $8$
Projective image $D_{16}$
CM discriminant -7
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 448.bf (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.223581125660\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{16})\)
Defining polynomial: \(x^{8} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{16}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{16} - \cdots)\)

Embedding invariants

Embedding label 293.1
Root \(-0.923880 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 448.293
Dual form 448.1.bf.a.237.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.923880 + 0.382683i) q^{2} +(0.707107 + 0.707107i) q^{4} +(0.382683 - 0.923880i) q^{7} +(0.382683 + 0.923880i) q^{8} +(-0.382683 - 0.923880i) q^{9} +O(q^{10})\) \(q+(0.923880 + 0.382683i) q^{2} +(0.707107 + 0.707107i) q^{4} +(0.382683 - 0.923880i) q^{7} +(0.382683 + 0.923880i) q^{8} +(-0.382683 - 0.923880i) q^{9} +(-1.63099 + 1.08979i) q^{11} +(0.707107 - 0.707107i) q^{14} +1.00000i q^{16} -1.00000i q^{18} +(-1.92388 + 0.382683i) q^{22} +(-0.707107 + 0.292893i) q^{23} +(-0.923880 - 0.382683i) q^{25} +(0.923880 - 0.382683i) q^{28} +(0.324423 + 0.216773i) q^{29} +(-0.382683 + 0.923880i) q^{32} +(0.382683 - 0.923880i) q^{36} +(1.63099 + 0.324423i) q^{37} +(-0.923880 - 1.38268i) q^{43} +(-1.92388 - 0.382683i) q^{44} -0.765367 q^{46} +(-0.707107 - 0.707107i) q^{49} +(-0.707107 - 0.707107i) q^{50} +(0.923880 - 0.617317i) q^{53} +1.00000 q^{56} +(0.216773 + 0.324423i) q^{58} -1.00000 q^{63} +(-0.707107 + 0.707107i) q^{64} +(-0.617317 + 0.923880i) q^{67} +(0.541196 - 1.30656i) q^{71} +(0.707107 - 0.707107i) q^{72} +(1.38268 + 0.923880i) q^{74} +(0.382683 + 1.92388i) q^{77} +(1.30656 + 1.30656i) q^{79} +(-0.707107 + 0.707107i) q^{81} +(-0.324423 - 1.63099i) q^{86} +(-1.63099 - 1.08979i) q^{88} +(-0.707107 - 0.292893i) q^{92} +(-0.382683 - 0.923880i) q^{98} +(1.63099 + 1.08979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q - 8q^{22} - 8q^{44} + 8q^{56} - 8q^{63} - 8q^{67} + 8q^{74} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{9}{16}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(3\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(4\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(5\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(6\) 0 0
\(7\) 0.382683 0.923880i 0.382683 0.923880i
\(8\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(9\) −0.382683 0.923880i −0.382683 0.923880i
\(10\) 0 0
\(11\) −1.63099 + 1.08979i −1.63099 + 1.08979i −0.707107 + 0.707107i \(0.750000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(12\) 0 0
\(13\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(14\) 0.707107 0.707107i 0.707107 0.707107i
\(15\) 0 0
\(16\) 1.00000i 1.00000i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 1.00000i 1.00000i
\(19\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.92388 + 0.382683i −1.92388 + 0.382683i
\(23\) −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i \(-0.750000\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −0.923880 0.382683i −0.923880 0.382683i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.923880 0.382683i 0.923880 0.382683i
\(29\) 0.324423 + 0.216773i 0.324423 + 0.216773i 0.707107 0.707107i \(-0.250000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.382683 0.923880i 0.382683 0.923880i
\(37\) 1.63099 + 0.324423i 1.63099 + 0.324423i 0.923880 0.382683i \(-0.125000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(42\) 0 0
\(43\) −0.923880 1.38268i −0.923880 1.38268i −0.923880 0.382683i \(-0.875000\pi\)
1.00000i \(-0.5\pi\)
\(44\) −1.92388 0.382683i −1.92388 0.382683i
\(45\) 0 0
\(46\) −0.765367 −0.765367
\(47\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(48\) 0 0
\(49\) −0.707107 0.707107i −0.707107 0.707107i
\(50\) −0.707107 0.707107i −0.707107 0.707107i
\(51\) 0 0
\(52\) 0 0
\(53\) 0.923880 0.617317i 0.923880 0.617317i 1.00000i \(-0.5\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 1.00000
\(57\) 0 0
\(58\) 0.216773 + 0.324423i 0.216773 + 0.324423i
\(59\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(60\) 0 0
\(61\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(62\) 0 0
\(63\) −1.00000 −1.00000
\(64\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.617317 + 0.923880i −0.617317 + 0.923880i 0.382683 + 0.923880i \(0.375000\pi\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0.541196 1.30656i 0.541196 1.30656i −0.382683 0.923880i \(-0.625000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(72\) 0.707107 0.707107i 0.707107 0.707107i
\(73\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(74\) 1.38268 + 0.923880i 1.38268 + 0.923880i
\(75\) 0 0
\(76\) 0 0
\(77\) 0.382683 + 1.92388i 0.382683 + 1.92388i
\(78\) 0 0
\(79\) 1.30656 + 1.30656i 1.30656 + 1.30656i 0.923880 + 0.382683i \(0.125000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(80\) 0 0
\(81\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(82\) 0 0
\(83\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.324423 1.63099i −0.324423 1.63099i
\(87\) 0 0
\(88\) −1.63099 1.08979i −1.63099 1.08979i
\(89\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.707107 0.292893i −0.707107 0.292893i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) −0.382683 0.923880i −0.382683 0.923880i
\(99\) 1.63099 + 1.08979i 1.63099 + 1.08979i
\(100\) −0.382683 0.923880i −0.382683 0.923880i
\(101\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1.08979 0.216773i 1.08979 0.216773i
\(107\) 0.617317 + 0.923880i 0.617317 + 0.923880i 1.00000 \(0\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(108\) 0 0
\(109\) −1.92388 + 0.382683i −1.92388 + 0.382683i −0.923880 + 0.382683i \(0.875000\pi\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(113\) 0.541196 + 0.541196i 0.541196 + 0.541196i 0.923880 0.382683i \(-0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.0761205 + 0.382683i 0.0761205 + 0.382683i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.08979 2.63099i 1.08979 2.63099i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.923880 0.382683i −0.923880 0.382683i
\(127\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(128\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.923880 + 0.617317i −0.923880 + 0.617317i
\(135\) 0 0
\(136\) 0 0
\(137\) 0.707107 + 1.70711i 0.707107 + 1.70711i 0.707107 + 0.707107i \(0.250000\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.00000 1.00000i 1.00000 1.00000i
\(143\) 0 0
\(144\) 0.923880 0.382683i 0.923880 0.382683i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0.923880 + 1.38268i 0.923880 + 1.38268i
\(149\) −0.617317 0.923880i −0.617317 0.923880i 0.382683 0.923880i \(-0.375000\pi\)
−1.00000 \(\pi\)
\(150\) 0 0
\(151\) 1.70711 0.707107i 1.70711 0.707107i 0.707107 0.707107i \(-0.250000\pi\)
1.00000 \(0\)
\(152\) 0 0
\(153\) 0 0
\(154\) −0.382683 + 1.92388i −0.382683 + 1.92388i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(158\) 0.707107 + 1.70711i 0.707107 + 1.70711i
\(159\) 0 0
\(160\) 0 0
\(161\) 0.765367i 0.765367i
\(162\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(163\) 0.324423 + 0.216773i 0.324423 + 0.216773i 0.707107 0.707107i \(-0.250000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(168\) 0 0
\(169\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.324423 1.63099i 0.324423 1.63099i
\(173\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(174\) 0 0
\(175\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(176\) −1.08979 1.63099i −1.08979 1.63099i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.324423 1.63099i −0.324423 1.63099i −0.707107 0.707107i \(-0.750000\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(180\) 0 0
\(181\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.541196 0.541196i −0.541196 0.541196i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.84776 −1.84776 −0.923880 0.382683i \(-0.875000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(192\) 0 0
\(193\) 0.765367 0.765367 0.382683 0.923880i \(-0.375000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.00000i 1.00000i
\(197\) −0.324423 + 1.63099i −0.324423 + 1.63099i 0.382683 + 0.923880i \(0.375000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(198\) 1.08979 + 1.63099i 1.08979 + 1.63099i
\(199\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(200\) 1.00000i 1.00000i
\(201\) 0 0
\(202\) 0 0
\(203\) 0.324423 0.216773i 0.324423 0.216773i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −0.382683 + 0.0761205i −0.382683 + 0.0761205i −0.382683 0.923880i \(-0.625000\pi\)
1.00000i \(0.5\pi\)
\(212\) 1.08979 + 0.216773i 1.08979 + 0.216773i
\(213\) 0 0
\(214\) 0.216773 + 1.08979i 0.216773 + 1.08979i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −1.92388 0.382683i −1.92388 0.382683i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(225\) 1.00000i 1.00000i
\(226\) 0.292893 + 0.707107i 0.292893 + 0.707107i
\(227\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(228\) 0 0
\(229\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.0761205 + 0.382683i −0.0761205 + 0.382683i
\(233\) −1.70711 + 0.707107i −1.70711 + 0.707107i −0.707107 + 0.707107i \(0.750000\pi\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(240\) 0 0
\(241\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(242\) 2.01367 2.01367i 2.01367 2.01367i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(252\) −0.707107 0.707107i −0.707107 0.707107i
\(253\) 0.834089 1.24830i 0.834089 1.24830i
\(254\) 1.30656 + 0.541196i 1.30656 + 0.541196i
\(255\) 0 0
\(256\) −1.00000 −1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0.923880 1.38268i 0.923880 1.38268i
\(260\) 0 0
\(261\) 0.0761205 0.382683i 0.0761205 0.382683i
\(262\) 0 0
\(263\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −1.08979 + 0.216773i −1.08979 + 0.216773i
\(269\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(270\) 0 0
\(271\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 1.84776i 1.84776i
\(275\) 1.92388 0.382683i 1.92388 0.382683i
\(276\) 0 0
\(277\) −1.08979 1.63099i −1.08979 1.63099i −0.707107 0.707107i \(-0.750000\pi\)
−0.382683 0.923880i \(-0.625000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.70711 0.707107i −1.70711 0.707107i −0.707107 0.707107i \(-0.750000\pi\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(284\) 1.30656 0.541196i 1.30656 0.541196i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000 1.00000
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.324423 + 1.63099i 0.324423 + 1.63099i
\(297\) 0 0
\(298\) −0.216773 1.08979i −0.216773 1.08979i
\(299\) 0 0
\(300\) 0 0
\(301\) −1.63099 + 0.324423i −1.63099 + 0.324423i
\(302\) 1.84776 1.84776
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(308\) −1.08979 + 1.63099i −1.08979 + 1.63099i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(312\) 0 0
\(313\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.84776i 1.84776i
\(317\) −0.216773 + 0.324423i −0.216773 + 0.324423i −0.923880 0.382683i \(-0.875000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(318\) 0 0
\(319\) −0.765367 −0.765367
\(320\) 0 0
\(321\) 0 0
\(322\) −0.292893 + 0.707107i −0.292893 + 0.707107i
\(323\) 0 0
\(324\) −1.00000 −1.00000
\(325\) 0 0
\(326\) 0.216773 + 0.324423i 0.216773 + 0.324423i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.324423 + 0.216773i −0.324423 + 0.216773i −0.707107 0.707107i \(-0.750000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(332\) 0 0
\(333\) −0.324423 1.63099i −0.324423 1.63099i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.541196 + 0.541196i −0.541196 + 0.541196i −0.923880 0.382683i \(-0.875000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(338\) −1.00000 −1.00000
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(344\) 0.923880 1.38268i 0.923880 1.38268i
\(345\) 0 0
\(346\) 0 0
\(347\) 0.382683 + 0.0761205i 0.382683 + 0.0761205i 0.382683 0.923880i \(-0.375000\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(350\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(351\) 0 0
\(352\) −0.382683 1.92388i −0.382683 1.92388i
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0.324423 1.63099i 0.324423 1.63099i
\(359\) −0.707107 0.292893i −0.707107 0.292893i 1.00000i \(-0.5\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(360\) 0 0
\(361\) 0.923880 0.382683i 0.923880 0.382683i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(368\) −0.292893 0.707107i −0.292893 0.707107i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.216773 1.08979i −0.216773 1.08979i
\(372\) 0 0
\(373\) −1.63099 + 1.08979i −1.63099 + 1.08979i −0.707107 + 0.707107i \(0.750000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.216773 1.08979i 0.216773 1.08979i −0.707107 0.707107i \(-0.750000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.70711 0.707107i −1.70711 0.707107i
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.707107 + 0.292893i 0.707107 + 0.292893i
\(387\) −0.923880 + 1.38268i −0.923880 + 1.38268i
\(388\) 0 0
\(389\) 0.324423 1.63099i 0.324423 1.63099i −0.382683 0.923880i \(-0.625000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.382683 0.923880i 0.382683 0.923880i
\(393\) 0 0
\(394\) −0.923880 + 1.38268i −0.923880 + 1.38268i
\(395\) 0 0
\(396\) 0.382683 + 1.92388i 0.382683 + 1.92388i
\(397\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.382683 0.923880i 0.382683 0.923880i
\(401\) 0.541196 0.541196i 0.541196 0.541196i −0.382683 0.923880i \(-0.625000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0.382683 0.0761205i 0.382683 0.0761205i
\(407\) −3.01367 + 1.24830i −3.01367 + 1.24830i
\(408\) 0 0
\(409\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.292893 + 0.707107i 0.292893 + 0.707107i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(420\) 0 0
\(421\) 0.382683 + 0.0761205i 0.382683 + 0.0761205i 0.382683 0.923880i \(-0.375000\pi\)
1.00000i \(0.5\pi\)
\(422\) −0.382683 0.0761205i −0.382683 0.0761205i
\(423\) 0 0
\(424\) 0.923880 + 0.617317i 0.923880 + 0.617317i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −0.216773 + 1.08979i −0.216773 + 1.08979i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(432\) 0 0
\(433\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.63099 1.08979i −1.63099 1.08979i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(440\) 0 0
\(441\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(442\) 0 0
\(443\) 0.324423 1.63099i 0.324423 1.63099i −0.382683 0.923880i \(-0.625000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(449\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(450\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(451\) 0 0
\(452\) 0.765367i 0.765367i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.541196 + 1.30656i 0.541196 + 1.30656i 0.923880 + 0.382683i \(0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(462\) 0 0
\(463\) −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i \(-0.375000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(464\) −0.216773 + 0.324423i −0.216773 + 0.324423i
\(465\) 0 0
\(466\) −1.84776 −1.84776
\(467\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(468\) 0 0
\(469\) 0.617317 + 0.923880i 0.617317 + 0.923880i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.01367 + 1.24830i 3.01367 + 1.24830i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.923880 0.617317i −0.923880 0.617317i
\(478\) 1.30656 0.541196i 1.30656 0.541196i
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 2.63099 1.08979i 2.63099 1.08979i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.70711 + 0.707107i 1.70711 + 0.707107i 1.00000 \(0\)
0.707107 + 0.707107i \(0.250000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.617317 0.923880i −0.617317 0.923880i 0.382683 0.923880i \(-0.375000\pi\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.00000 1.00000i −1.00000 1.00000i
\(498\) 0 0
\(499\) 0.216773 + 1.08979i 0.216773 + 1.08979i 0.923880 + 0.382683i \(0.125000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(504\) −0.382683 0.923880i −0.382683 0.923880i
\(505\) 0 0
\(506\) 1.24830 0.834089i 1.24830 0.834089i
\(507\) 0 0
\(508\) 1.00000 + 1.00000i 1.00000 + 1.00000i
\(509\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.923880 0.382683i −0.923880 0.382683i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 1.38268 0.923880i 1.38268 0.923880i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(522\) 0.216773 0.324423i 0.216773 0.324423i
\(523\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.292893 + 0.292893i −0.292893 + 0.292893i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −1.08979 0.216773i −1.08979 0.216773i
\(537\) 0 0
\(538\) 0 0
\(539\) 1.92388 + 0.382683i 1.92388 + 0.382683i
\(540\) 0 0
\(541\) 0.923880 + 0.617317i 0.923880 + 0.617317i 0.923880 0.382683i \(-0.125000\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.324423 0.216773i −0.324423 0.216773i 0.382683 0.923880i \(-0.375000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(548\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(549\) 0 0
\(550\) 1.92388 + 0.382683i 1.92388 + 0.382683i
\(551\) 0 0
\(552\) 0 0
\(553\) 1.70711 0.707107i 1.70711 0.707107i
\(554\) −0.382683 1.92388i −0.382683 1.92388i
\(555\) 0 0
\(556\) 0 0
\(557\) 1.92388 0.382683i 1.92388 0.382683i 0.923880 0.382683i \(-0.125000\pi\)
1.00000 \(0\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.30656 1.30656i −1.30656 1.30656i
\(563\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(568\) 1.41421 1.41421
\(569\) −0.541196 + 1.30656i −0.541196 + 1.30656i 0.382683 + 0.923880i \(0.375000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(570\) 0 0
\(571\) −0.0761205 + 0.382683i −0.0761205 + 0.382683i 0.923880 + 0.382683i \(0.125000\pi\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.765367 0.765367
\(576\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0.382683 0.923880i 0.382683 0.923880i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.834089 + 2.01367i −0.834089 + 2.01367i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −0.324423 + 1.63099i −0.324423 + 1.63099i
\(593\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.216773 1.08979i 0.216773 1.08979i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(600\) 0 0
\(601\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(602\) −1.63099 0.324423i −1.63099 0.324423i
\(603\) 1.08979 + 0.216773i 1.08979 + 0.216773i
\(604\) 1.70711 + 0.707107i 1.70711 + 0.707107i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.382683 0.0761205i −0.382683 0.0761205i 1.00000i \(-0.5\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.63099 + 1.08979i −1.63099 + 1.08979i
\(617\) 1.30656 0.541196i 1.30656 0.541196i 0.382683 0.923880i \(-0.375000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(618\) 0 0
\(619\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.541196 + 1.30656i 0.541196 + 1.30656i 0.923880 + 0.382683i \(0.125000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(632\) −0.707107 + 1.70711i −0.707107 + 1.70711i
\(633\) 0 0
\(634\) −0.324423 + 0.216773i −0.324423 + 0.216773i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −0.707107 0.292893i −0.707107 0.292893i
\(639\) −1.41421 −1.41421
\(640\) 0 0
\(641\) −0.765367 −0.765367 −0.382683 0.923880i \(-0.625000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(642\) 0 0
\(643\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(644\) −0.541196 + 0.541196i −0.541196 + 0.541196i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(648\) −0.923880 0.382683i −0.923880 0.382683i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.0761205 + 0.382683i 0.0761205 + 0.382683i
\(653\) −0.382683 1.92388i −0.382683 1.92388i −0.382683 0.923880i \(-0.625000\pi\)
1.00000i \(-0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.92388 + 0.382683i −1.92388 + 0.382683i −0.923880 + 0.382683i \(0.875000\pi\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(662\) −0.382683 + 0.0761205i −0.382683 + 0.0761205i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.324423 1.63099i 0.324423 1.63099i
\(667\) −0.292893 0.0582601i −0.292893 0.0582601i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(674\) −0.707107 + 0.292893i −0.707107 + 0.292893i
\(675\) 0 0
\(676\) −0.923880 0.382683i −0.923880 0.382683i
\(677\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.923880 + 1.38268i 0.923880 + 1.38268i 0.923880 + 0.382683i \(0.125000\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −1.00000
\(687\) 0 0
\(688\) 1.38268 0.923880i 1.38268 0.923880i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(692\) 0 0
\(693\) 1.63099 1.08979i 1.63099 1.08979i
\(694\) 0.324423 + 0.216773i 0.324423 + 0.216773i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.00000 −1.00000
\(701\) 0.923880 1.38268i 0.923880 1.38268i 1.00000i \(-0.5\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.382683 1.92388i 0.382683 1.92388i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.382683 + 1.92388i −0.382683 + 1.92388i 1.00000i \(0.5\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(710\) 0 0
\(711\) 0.707107 1.70711i 0.707107 1.70711i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.923880 1.38268i 0.923880 1.38268i
\(717\) 0 0
\(718\) −0.541196 0.541196i −0.541196 0.541196i
\(719\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000 1.00000
\(723\) 0 0
\(724\) 0 0
\(725\) −0.216773 0.324423i −0.216773 0.324423i
\(726\) 0 0
\(727\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(728\) 0 0
\(729\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.765367i 0.765367i
\(737\) 2.17958i 2.17958i
\(738\) 0 0
\(739\) −1.63099 1.08979i −1.63099 1.08979i −0.923880 0.382683i \(-0.875000\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.216773 1.08979i 0.216773 1.08979i
\(743\) −1.70711 0.707107i −1.70711 0.707107i −0.707107 0.707107i \(-0.750000\pi\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −1.92388 + 0.382683i −1.92388 + 0.382683i
\(747\) 0 0
\(748\) 0 0
\(749\) 1.08979 0.216773i 1.08979 0.216773i
\(750\) 0 0
\(751\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −0.923880 + 0.617317i −0.923880 + 0.617317i −0.923880 0.382683i \(-0.875000\pi\)
1.00000i \(0.5\pi\)
\(758\) 0.617317 0.923880i 0.617317 0.923880i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(762\) 0 0
\(763\) −0.382683 + 1.92388i −0.382683 + 1.92388i
\(764\) −1.30656 1.30656i −1.30656 1.30656i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.541196 + 0.541196i 0.541196 + 0.541196i
\(773\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(774\) −1.38268 + 0.923880i −1.38268 + 0.923880i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.923880 1.38268i 0.923880 1.38268i
\(779\) 0 0
\(780\) 0 0
\(781\) 0.541196 + 2.72078i 0.541196 + 2.72078i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.707107 0.707107i 0.707107 0.707107i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(788\) −1.38268 + 0.923880i −1.38268 + 0.923880i
\(789\) 0 0
\(790\) 0 0
\(791\) 0.707107 0.292893i 0.707107 0.292893i
\(792\) −0.382683 + 1.92388i −0.382683 + 1.92388i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.707107 0.707107i 0.707107 0.707107i
\(801\) 0 0
\(802\) 0.707107 0.292893i 0.707107 0.292893i
\(803\) 0 0
\(804\) 0 0
\(805\) 0