Properties

Label 799.1.h.b.93.3
Level $799$
Weight $1$
Character 799.93
Analytic conductor $0.399$
Analytic rank $0$
Dimension $16$
Projective image $D_{40}$
CM discriminant -47
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 799.h (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.398752945094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\Q(\zeta_{40})\)
Defining polynomial: \(x^{16} - x^{12} + x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{40}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{40} + \cdots)\)

Embedding invariants

Embedding label 93.3
Root \(-0.156434 + 0.987688i\) of defining polynomial
Character \(\chi\) \(=\) 799.93
Dual form 799.1.h.b.610.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.831254 - 0.831254i) q^{2} +(-0.581990 + 1.40505i) q^{3} -0.381966i q^{4} +(0.684170 + 1.65173i) q^{6} +(-1.57547 + 0.652583i) q^{7} +(0.513743 + 0.513743i) q^{8} +(-0.928339 - 0.928339i) q^{9} +O(q^{10})\) \(q+(0.831254 - 0.831254i) q^{2} +(-0.581990 + 1.40505i) q^{3} -0.381966i q^{4} +(0.684170 + 1.65173i) q^{6} +(-1.57547 + 0.652583i) q^{7} +(0.513743 + 0.513743i) q^{8} +(-0.928339 - 0.928339i) q^{9} +(0.536680 + 0.222300i) q^{12} +(-0.767157 + 1.85208i) q^{14} +1.23607 q^{16} +(-0.309017 + 0.951057i) q^{17} -1.54337 q^{18} -2.59341i q^{21} +(-1.02083 + 0.422840i) q^{24} +(0.707107 + 0.707107i) q^{25} +(0.439596 - 0.182086i) q^{27} +(0.249264 + 0.601777i) q^{28} +(0.513743 - 0.513743i) q^{32} +(0.533698 + 1.04744i) q^{34} +(-0.354594 + 0.354594i) q^{36} +(0.497066 - 1.20002i) q^{37} +(-2.15578 - 2.15578i) q^{42} -1.00000i q^{47} +(-0.719379 + 1.73673i) q^{48} +(1.34915 - 1.34915i) q^{49} +1.17557 q^{50} +(-1.15643 - 0.987688i) q^{51} +(0.221232 - 0.221232i) q^{53} +(0.214055 - 0.516776i) q^{54} +(-1.14465 - 0.474129i) q^{56} +(1.14412 + 1.14412i) q^{59} +(1.79671 - 0.744220i) q^{61} +(2.06839 + 0.856755i) q^{63} +0.381966i q^{64} +(0.363271 + 0.118034i) q^{68} +(0.763007 - 1.84206i) q^{71} -0.953855i q^{72} +(-0.584336 - 1.41071i) q^{74} +(-1.40505 + 0.581990i) q^{75} +(0.763007 + 1.84206i) q^{79} -0.589244i q^{81} +(-1.00000 + 1.00000i) q^{83} -0.990595 q^{84} -1.17557i q^{89} +(-0.831254 - 0.831254i) q^{94} +(0.422840 + 1.02083i) q^{96} +(-0.431351 - 0.178671i) q^{97} -2.24297i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{3} - 4q^{9} + O(q^{10}) \) \( 16q - 4q^{3} - 4q^{9} - 16q^{16} + 4q^{17} - 20q^{24} - 4q^{27} - 4q^{28} + 4q^{36} - 20q^{42} + 24q^{48} + 4q^{49} - 16q^{51} + 4q^{53} + 20q^{54} + 20q^{56} + 4q^{61} - 4q^{63} - 4q^{71} - 4q^{79} - 16q^{83} + 32q^{84} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/799\mathbb{Z}\right)^\times\).

\(n\) \(52\) \(377\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.831254 0.831254i 0.831254 0.831254i −0.156434 0.987688i \(-0.550000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(3\) −0.581990 + 1.40505i −0.581990 + 1.40505i 0.309017 + 0.951057i \(0.400000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(4\) 0.381966i 0.381966i
\(5\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(6\) 0.684170 + 1.65173i 0.684170 + 1.65173i
\(7\) −1.57547 + 0.652583i −1.57547 + 0.652583i −0.987688 0.156434i \(-0.950000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(8\) 0.513743 + 0.513743i 0.513743 + 0.513743i
\(9\) −0.928339 0.928339i −0.928339 0.928339i
\(10\) 0 0
\(11\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(12\) 0.536680 + 0.222300i 0.536680 + 0.222300i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −0.767157 + 1.85208i −0.767157 + 1.85208i
\(15\) 0 0
\(16\) 1.23607 1.23607
\(17\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(18\) −1.54337 −1.54337
\(19\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(20\) 0 0
\(21\) 2.59341i 2.59341i
\(22\) 0 0
\(23\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(24\) −1.02083 + 0.422840i −1.02083 + 0.422840i
\(25\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(26\) 0 0
\(27\) 0.439596 0.182086i 0.439596 0.182086i
\(28\) 0.249264 + 0.601777i 0.249264 + 0.601777i
\(29\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(30\) 0 0
\(31\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(32\) 0.513743 0.513743i 0.513743 0.513743i
\(33\) 0 0
\(34\) 0.533698 + 1.04744i 0.533698 + 1.04744i
\(35\) 0 0
\(36\) −0.354594 + 0.354594i −0.354594 + 0.354594i
\(37\) 0.497066 1.20002i 0.497066 1.20002i −0.453990 0.891007i \(-0.650000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(42\) −2.15578 2.15578i −2.15578 2.15578i
\(43\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.00000i 1.00000i
\(48\) −0.719379 + 1.73673i −0.719379 + 1.73673i
\(49\) 1.34915 1.34915i 1.34915 1.34915i
\(50\) 1.17557 1.17557
\(51\) −1.15643 0.987688i −1.15643 0.987688i
\(52\) 0 0
\(53\) 0.221232 0.221232i 0.221232 0.221232i −0.587785 0.809017i \(-0.700000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(54\) 0.214055 0.516776i 0.214055 0.516776i
\(55\) 0 0
\(56\) −1.14465 0.474129i −1.14465 0.474129i
\(57\) 0 0
\(58\) 0 0
\(59\) 1.14412 + 1.14412i 1.14412 + 1.14412i 0.987688 + 0.156434i \(0.0500000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(60\) 0 0
\(61\) 1.79671 0.744220i 1.79671 0.744220i 0.809017 0.587785i \(-0.200000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(62\) 0 0
\(63\) 2.06839 + 0.856755i 2.06839 + 0.856755i
\(64\) 0.381966i 0.381966i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0.363271 + 0.118034i 0.363271 + 0.118034i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.763007 1.84206i 0.763007 1.84206i 0.309017 0.951057i \(-0.400000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(72\) 0.953855i 0.953855i
\(73\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(74\) −0.584336 1.41071i −0.584336 1.41071i
\(75\) −1.40505 + 0.581990i −1.40505 + 0.581990i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.763007 + 1.84206i 0.763007 + 1.84206i 0.453990 + 0.891007i \(0.350000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(80\) 0 0
\(81\) 0.589244i 0.589244i
\(82\) 0 0
\(83\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(84\) −0.990595 −0.990595
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −0.831254 0.831254i −0.831254 0.831254i
\(95\) 0 0
\(96\) 0.422840 + 1.02083i 0.422840 + 1.02083i
\(97\) −0.431351 0.178671i −0.431351 0.178671i 0.156434 0.987688i \(-0.450000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(98\) 2.24297i 2.24297i
\(99\) 0 0
\(100\) 0.270091 0.270091i 0.270091 0.270091i
\(101\) −1.78201 −1.78201 −0.891007 0.453990i \(-0.850000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(102\) −1.78231 + 0.140271i −1.78231 + 0.140271i
\(103\) −0.907981 −0.907981 −0.453990 0.891007i \(-0.650000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.367799i 0.367799i
\(107\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(108\) −0.0695508 0.167911i −0.0695508 0.167911i
\(109\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(110\) 0 0
\(111\) 1.39680 + 1.39680i 1.39680 + 1.39680i
\(112\) −1.94739 + 0.806636i −1.94739 + 0.806636i
\(113\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 1.90211 1.90211
\(119\) −0.133795 1.70002i −0.133795 1.70002i
\(120\) 0 0
\(121\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(122\) 0.874883 2.11215i 0.874883 2.11215i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 2.43154 1.00718i 2.43154 1.00718i
\(127\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(128\) 0.831254 + 0.831254i 0.831254 + 0.831254i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.431351 + 0.178671i 0.431351 + 0.178671i 0.587785 0.809017i \(-0.300000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.647354 + 0.329843i −0.647354 + 0.329843i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(140\) 0 0
\(141\) 1.40505 + 0.581990i 1.40505 + 0.581990i
\(142\) −0.896969 2.16547i −0.896969 2.16547i
\(143\) 0 0
\(144\) −1.14749 1.14749i −1.14749 1.14749i
\(145\) 0 0
\(146\) 0 0
\(147\) 1.11042 + 2.68080i 1.11042 + 2.68080i
\(148\) −0.458368 0.189862i −0.458368 0.189862i
\(149\) 0.907981i 0.907981i −0.891007 0.453990i \(-0.850000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(150\) −0.684170 + 1.65173i −0.684170 + 1.65173i
\(151\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(152\) 0 0
\(153\) 1.16977 0.596030i 1.16977 0.596030i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.97538i 1.97538i 0.156434 + 0.987688i \(0.450000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(158\) 2.16547 + 0.896969i 2.16547 + 0.896969i
\(159\) 0.182086 + 0.439596i 0.182086 + 0.439596i
\(160\) 0 0
\(161\) 0 0
\(162\) −0.489811 0.489811i −0.489811 0.489811i
\(163\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.66251i 1.66251i
\(167\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(168\) 1.33235 1.33235i 1.33235 1.33235i
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.399903 + 0.965451i −0.399903 + 0.965451i 0.587785 + 0.809017i \(0.300000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(174\) 0 0
\(175\) −1.57547 0.652583i −1.57547 0.652583i
\(176\) 0 0
\(177\) −2.27341 + 0.941679i −2.27341 + 0.941679i
\(178\) −0.977198 0.977198i −0.977198 0.977198i
\(179\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(180\) 0 0
\(181\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(182\) 0 0
\(183\) 2.95758i 2.95758i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.381966 −0.381966
\(189\) −0.573745 + 0.573745i −0.573745 + 0.573745i
\(190\) 0 0
\(191\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(192\) −0.536680 0.222300i −0.536680 0.222300i
\(193\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(194\) −0.507083 + 0.210041i −0.507083 + 0.210041i
\(195\) 0 0
\(196\) −0.515328 0.515328i −0.515328 0.515328i
\(197\) 1.70711 0.707107i 1.70711 0.707107i 0.707107 0.707107i \(-0.250000\pi\)
1.00000 \(0\)
\(198\) 0 0
\(199\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(200\) 0.726543i 0.726543i
\(201\) 0 0
\(202\) −1.48131 + 1.48131i −1.48131 + 1.48131i
\(203\) 0 0
\(204\) −0.377263 + 0.441719i −0.377263 + 0.441719i
\(205\) 0 0
\(206\) −0.754763 + 0.754763i −0.754763 + 0.754763i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(212\) −0.0845030 0.0845030i −0.0845030 0.0845030i
\(213\) 2.14412 + 2.14412i 2.14412 + 2.14412i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.319385 + 0.132294i 0.319385 + 0.132294i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 2.32219 2.32219
\(223\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(224\) −0.474129 + 1.14465i −0.474129 + 1.14465i
\(225\) 1.31287i 1.31287i
\(226\) 0 0
\(227\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.437016 0.437016i 0.437016 0.437016i
\(237\) −3.03225 −3.03225
\(238\) −1.52437 1.30193i −1.52437 1.30193i
\(239\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(240\) 0 0
\(241\) −0.497066 + 1.20002i −0.497066 + 1.20002i 0.453990 + 0.891007i \(0.350000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(242\) 1.17557i 1.17557i
\(243\) 1.26751 + 0.525020i 1.26751 + 0.525020i
\(244\) −0.284267 0.686280i −0.284267 0.686280i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −0.823057 1.98704i −0.823057 1.98704i
\(250\) 0 0
\(251\) 1.78201i 1.78201i −0.453990 0.891007i \(-0.650000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(252\) 0.327251 0.790055i 0.327251 0.790055i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(258\) 0 0
\(259\) 2.21498i 2.21498i
\(260\) 0 0
\(261\) 0 0
\(262\) 0.507083 0.210041i 0.507083 0.210041i
\(263\) −1.14412 1.14412i −1.14412 1.14412i −0.987688 0.156434i \(-0.950000\pi\)
−0.156434 0.987688i \(-0.550000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.65173 + 0.684170i 1.65173 + 0.684170i
\(268\) 0 0
\(269\) −0.292893 + 0.707107i −0.292893 + 0.707107i 0.707107 + 0.707107i \(0.250000\pi\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 1.78201 1.78201 0.891007 0.453990i \(-0.150000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(272\) −0.381966 + 1.17557i −0.381966 + 1.17557i
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.84206 + 0.763007i 1.84206 + 0.763007i 0.951057 + 0.309017i \(0.100000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(282\) 1.65173 0.684170i 1.65173 0.684170i
\(283\) −0.652583 1.57547i −0.652583 1.57547i −0.809017 0.587785i \(-0.800000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(284\) −0.703605 0.291443i −0.703605 0.291443i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.953855 −0.953855
\(289\) −0.809017 0.587785i −0.809017 0.587785i
\(290\) 0 0
\(291\) 0.502083 0.502083i 0.502083 0.502083i
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 3.15147 + 1.30538i 3.15147 + 1.30538i
\(295\) 0 0
\(296\) 0.871868 0.361140i 0.871868 0.361140i
\(297\) 0 0
\(298\) −0.754763 0.754763i −0.754763 0.754763i
\(299\) 0 0
\(300\) 0.222300 + 0.536680i 0.222300 + 0.536680i
\(301\) 0 0
\(302\) 0 0
\(303\) 1.03711 2.50381i 1.03711 2.50381i
\(304\) 0 0
\(305\) 0 0
\(306\) 0.476928 1.46783i 0.476928 1.46783i
\(307\) 1.78201 1.78201 0.891007 0.453990i \(-0.150000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(308\) 0 0
\(309\) 0.528435 1.27576i 0.528435 1.27576i
\(310\) 0 0
\(311\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(312\) 0 0
\(313\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(314\) 1.64204 + 1.64204i 1.64204 + 1.64204i
\(315\) 0 0
\(316\) 0.703605 0.291443i 0.703605 0.291443i
\(317\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(318\) 0.516776 + 0.214055i 0.516776 + 0.214055i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.225071 −0.225071
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.652583 + 1.57547i 0.652583 + 1.57547i
\(330\) 0 0
\(331\) 0.831254 + 0.831254i 0.831254 + 0.831254i 0.987688 0.156434i \(-0.0500000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(332\) 0.381966 + 0.381966i 0.381966 + 0.381966i
\(333\) −1.57547 + 0.652583i −1.57547 + 0.652583i
\(334\) 0 0
\(335\) 0 0
\(336\) 3.20563i 3.20563i
\(337\) 0.399903 0.965451i 0.399903 0.965451i −0.587785 0.809017i \(-0.700000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(338\) −0.831254 + 0.831254i −0.831254 + 0.831254i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.592533 + 1.43050i −0.592533 + 1.43050i
\(344\) 0 0
\(345\) 0 0
\(346\) 0.470114 + 1.13496i 0.470114 + 1.13496i
\(347\) 1.40505 0.581990i 1.40505 0.581990i 0.453990 0.891007i \(-0.350000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(350\) −1.85208 + 0.767157i −1.85208 + 0.767157i
\(351\) 0 0
\(352\) 0 0
\(353\) 1.97538i 1.97538i −0.156434 0.987688i \(-0.550000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(354\) −1.10701 + 2.67256i −1.10701 + 2.67256i
\(355\) 0 0
\(356\) −0.449028 −0.449028
\(357\) 2.46648 + 0.801408i 2.46648 + 0.801408i
\(358\) 0 0
\(359\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(360\) 0 0
\(361\) 1.00000i 1.00000i
\(362\) 0 0
\(363\) −0.581990 1.40505i −0.581990 1.40505i
\(364\) 0 0
\(365\) 0 0
\(366\) 2.45850 + 2.45850i 2.45850 + 2.45850i
\(367\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −0.204173 + 0.492917i −0.204173 + 0.492917i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.513743 0.513743i 0.513743 0.513743i
\(377\) 0 0
\(378\) 0.953855i 0.953855i
\(379\) −0.965451 0.399903i −0.965451 0.399903i −0.156434 0.987688i \(-0.550000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.17557 1.17557i −1.17557 1.17557i
\(383\) −0.642040 0.642040i −0.642040 0.642040i 0.309017 0.951057i \(-0.400000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(384\) −1.65173 + 0.684170i −1.65173 + 0.684170i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.0682464 + 0.164761i −0.0682464 + 0.164761i
\(389\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.38623 1.38623
\(393\) −0.502083 + 0.502083i −0.502083 + 0.502083i
\(394\) 0.831254 2.00682i 0.831254 2.00682i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.0600500 + 0.144974i 0.0600500 + 0.144974i 0.951057 0.309017i \(-0.100000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.874032 + 0.874032i 0.874032 + 0.874032i
\(401\) −1.40505 + 0.581990i −1.40505 + 0.581990i −0.951057 0.309017i \(-0.900000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.680668i 0.680668i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.0866922 1.10153i −0.0866922 1.10153i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.346818i 0.346818i
\(413\) −2.54917 1.05590i −2.54917 1.05590i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) −0.928339 + 0.928339i −0.928339 + 0.928339i
\(424\) 0.227313 0.227313
\(425\) −0.891007 + 0.453990i −0.891007 + 0.453990i
\(426\) 3.56462 3.56462
\(427\) −2.34500 + 2.34500i −2.34500 + 2.34500i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0.178671 + 0.431351i 0.178671 + 0.431351i 0.987688 0.156434i \(-0.0500000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(432\) 0.543370 0.225071i 0.543370 0.225071i
\(433\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0.707107 1.70711i 0.707107 1.70711i 1.00000i \(-0.5\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(440\) 0 0
\(441\) −2.50493 −2.50493
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0.533531 0.533531i 0.533531 0.533531i
\(445\) 0 0
\(446\) 0 0
\(447\) 1.27576 + 0.528435i 1.27576 + 0.528435i
\(448\) −0.249264 0.601777i −0.249264 0.601777i
\(449\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(450\) −1.09133 1.09133i −1.09133 1.09133i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.26007 + 1.26007i −1.26007 + 1.26007i −0.309017 + 0.951057i \(0.600000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(458\) 0 0
\(459\) 0.0373320 + 0.474348i 0.0373320 + 0.474348i
\(460\) 0 0
\(461\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −2.77550 1.14965i −2.77550 1.14965i
\(472\) 1.17557i 1.17557i
\(473\) 0 0
\(474\) −2.52057 + 2.52057i −2.52057 + 2.52057i
\(475\) 0 0
\(476\) −0.649351 + 0.0511050i −0.649351 + 0.0511050i
\(477\) −0.410756 −0.410756
\(478\) −1.58114 + 1.58114i −1.58114 + 1.58114i
\(479\) 0.652583 1.57547i 0.652583 1.57547i −0.156434 0.987688i \(-0.550000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.584336 + 1.41071i 0.584336 + 1.41071i
\(483\) 0 0
\(484\) 0.270091 + 0.270091i 0.270091 + 0.270091i
\(485\) 0 0
\(486\) 1.49005 0.617198i 1.49005 0.617198i
\(487\) −0.707107 1.70711i −0.707107 1.70711i −0.707107 0.707107i \(-0.750000\pi\)
1.00000i \(-0.5\pi\)
\(488\) 1.30538 + 0.540707i 1.30538 + 0.540707i
\(489\) 0 0
\(490\) 0 0
\(491\) −1.39680 + 1.39680i −1.39680 + 1.39680i −0.587785 + 0.809017i \(0.700000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.40005i 3.40005i
\(498\) −2.33590 0.967562i −2.33590 0.967562i
\(499\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.48131 1.48131i −1.48131 1.48131i
\(503\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(504\) 0.622469 + 1.50277i 0.622469 + 1.50277i
\(505\) 0 0
\(506\) 0 0
\(507\) 0.581990 1.40505i 0.581990 1.40505i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 1.84121 + 1.84121i 1.84121 + 1.84121i
\(519\) −1.12377 1.12377i −1.12377 1.12377i
\(520\) 0 0
\(521\) −0.399903 0.965451i −0.399903 0.965451i −0.987688 0.156434i \(-0.950000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0.0682464 0.164761i 0.0682464 0.164761i
\(525\) 1.83382 1.83382i 1.83382 1.83382i
\(526\) −1.90211 −1.90211
\(527\) 0 0
\(528\) 0 0
\(529\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(530\) 0 0
\(531\) 2.12427i 2.12427i
\(532\) 0 0
\(533\) 0 0
\(534\) 1.94173 0.804290i 1.94173 0.804290i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0.344317 + 0.831254i 0.344317 + 0.831254i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.399903 + 0.965451i −0.399903 + 0.965451i 0.587785 + 0.809017i \(0.300000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(542\) 1.48131 1.48131i 1.48131 1.48131i
\(543\) 0 0
\(544\) 0.329843 + 0.647354i 0.329843 + 0.647354i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(548\) 0 0
\(549\) −2.35884 0.977063i −2.35884 0.977063i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −2.40420 2.40420i −2.40420 2.40420i
\(554\) 2.16547 0.896969i 2.16547 0.896969i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(564\) 0.222300 0.536680i 0.222300 0.536680i
\(565\) 0 0
\(566\) −1.85208 0.767157i −1.85208 0.767157i
\(567\) 0.384530 + 0.928339i 0.384530 + 0.928339i
\(568\) 1.33834 0.554357i 1.33834 0.554357i
\(569\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(570\) 0 0
\(571\) 0.144974 0.0600500i 0.144974 0.0600500i −0.309017 0.951057i \(-0.600000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(572\) 0 0
\(573\) 1.98704 + 0.823057i 1.98704 + 0.823057i
\(574\) 0 0
\(575\) 0 0
\(576\) 0.354594 0.354594i 0.354594 0.354594i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −1.16110 + 0.183900i −1.16110 + 0.183900i
\(579\) 0 0
\(580\) 0 0
\(581\) 0.922891 2.22806i 0.922891 2.22806i
\(582\) 0.834717i 0.834717i
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(588\) 1.02398 0.424145i 1.02398 0.424145i
\(589\) 0 0
\(590\) 0 0
\(591\) 2.81009i 2.81009i
\(592\) 0.614407 1.48331i 0.614407 1.48331i
\(593\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.346818 −0.346818
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −1.02083 0.422840i −1.02083 0.422840i
\(601\) 0.744220 + 1.79671i 0.744220 + 1.79671i 0.587785 + 0.809017i \(0.300000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −1.21920 2.94341i −1.21920 2.94341i
\(607\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.227663 0.446814i −0.227663 0.446814i
\(613\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(614\) 1.48131 1.48131i 1.48131 1.48131i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.144974 0.0600500i −0.144974 0.0600500i 0.309017 0.951057i \(-0.400000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(618\) −0.621213 1.49974i −0.621213 1.49974i
\(619\) −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i \(-0.750000\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.767157 + 1.85208i 0.767157 + 1.85208i
\(624\) 0 0
\(625\) 1.00000i 1.00000i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.754527 0.754527
\(629\) 0.987688 + 0.843566i 0.987688 + 0.843566i
\(630\) 0 0
\(631\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(632\) −0.554357 + 1.33834i −0.554357 + 1.33834i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0.167911 0.0695508i 0.167911 0.0695508i
\(637\) 0 0
\(638\) 0 0
\(639\) −2.41839 + 1.00173i −2.41839 + 1.00173i
\(640\) 0 0
\(641\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(642\) 0 0
\(643\) −0.744220 + 1.79671i −0.744220 + 1.79671i −0.156434 + 0.987688i \(0.550000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.97538 1.97538 0.987688 0.156434i \(-0.0500000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(648\) 0.302720 0.302720i 0.302720 0.302720i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.20002 + 0.497066i −1.20002 + 0.497066i −0.891007 0.453990i \(-0.850000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 1.85208 + 0.767157i 1.85208 + 0.767157i
\(659\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(660\) 0 0
\(661\) 1.34500 1.34500i 1.34500 1.34500i 0.453990 0.891007i \(-0.350000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(662\) 1.38197 1.38197
\(663\) 0 0
\(664\) −1.02749 −1.02749
\(665\) 0 0
\(666\) −0.767157 + 1.85208i −0.767157 + 1.85208i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −1.33235 1.33235i −1.33235 1.33235i
\(673\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(674\) −0.470114 1.13496i −0.470114 1.13496i
\(675\) 0.439596 + 0.182086i 0.439596 + 0.182086i
\(676\) 0.381966i 0.381966i
\(677\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(678\) 0 0
\(679\) 0.796180 0.796180
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.744220 1.79671i 0.744220 1.79671i 0.156434 0.987688i \(-0.450000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.696564 + 1.68165i 0.696564 + 1.68165i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(692\) 0.368770 + 0.152749i 0.368770 + 0.152749i
\(693\) 0 0
\(694\) 0.684170 1.65173i 0.684170 1.65173i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.249264 + 0.601777i −0.249264 + 0.601777i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.64204 1.64204i −1.64204 1.64204i
\(707\) 2.80751 1.16291i 2.80751 1.16291i
\(708\) 0.359689 + 0.868367i 0.359689 + 0.868367i
\(709\) −1.57547 0.652583i −1.57547 0.652583i −0.587785 0.809017i \(-0.700000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(710\) 0 0
\(711\) 1.00173 2.41839i 1.00173 2.41839i
\(712\) 0.603941 0.603941i 0.603941 0.603941i
\(713\) 0 0
\(714\) 2.71644 1.38410i 2.71644 1.38410i
\(715\) 0 0
\(716\) 0 0
\(717\) 1.10701 2.67256i 1.10701 2.67256i
\(718\) 0 0
\(719\) −1.79671 0.744220i −1.79671 0.744220i −0.987688 0.156434i \(-0.950000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(720\) 0 0
\(721\) 1.43050 0.592533i 1.43050 0.592533i
\(722\) −0.831254 0.831254i −0.831254 0.831254i
\(723\) −1.39680 1.39680i −1.39680 1.39680i
\(724\) 0 0
\(725\) 0 0
\(726\) −1.65173 0.684170i −1.65173 0.684170i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −1.05870 + 1.05870i −1.05870 + 1.05870i
\(730\) 0 0
\(731\) 0 0
\(732\) 1.12970 1.12970
\(733\) 1.34500 1.34500i 1.34500 1.34500i 0.453990 0.891007i \(-0.350000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.39680 + 1.39680i 1.39680 + 1.39680i 0.809017 + 0.587785i \(0.200000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.240020 + 0.579458i 0.240020 + 0.579458i
\(743\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.85668 1.85668
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(752\) 1.23607i 1.23607i
\(753\) 2.50381 + 1.03711i 2.50381 + 1.03711i
\(754\) 0 0
\(755\) 0 0
\(756\) 0.219151 + 0.219151i 0.219151 + 0.219151i
\(757\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(758\) −1.13496 + 0.470114i −1.13496 + 0.470114i
\(759\) 0 0
\(760\) 0 0
\(761\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −0.540182 −0.540182
\(765\) 0 0
\(766\) −1.06740 −1.06740
\(767\) 0 0
\(768\) −0.581990 + 1.40505i −0.581990 + 1.40505i
\(769\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.34500 1.34500i −1.34500 1.34500i −0.891007 0.453990i \(-0.850000\pi\)
−0.453990 0.891007i \(-0.650000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.129812 0.313395i −0.129812 0.313395i
\(777\) −3.11215 1.28910i −3.11215 1.28910i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.66764 1.66764i 1.66764 1.66764i
\(785\) 0 0
\(786\) 0.834717i 0.834717i
\(787\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(788\) −0.270091 0.652057i −0.270091 0.652057i
\(789\) 2.27341 0.941679i 2.27341 0.941679i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0.170427 + 0.0705930i 0.170427 + 0.0705930i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(798\) 0 0
\(799\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(800\) 0.726543 0.726543