Properties

Label 799.1.h.b.610.4
Level $799$
Weight $1$
Character 799.610
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 610.4
Root \(0.891007 - 0.453990i\) of defining polynomial
Character \(\chi\) \(=\) 799.610
Dual form 799.1.h.b.93.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.34500 + 1.34500i) q^{2} +(0.178671 + 0.431351i) q^{3} +2.61803i q^{4} +(-0.339853 + 0.820478i) q^{6} +(-1.40505 - 0.581990i) q^{7} +(-2.17625 + 2.17625i) q^{8} +(0.552967 - 0.552967i) q^{9} +O(q^{10})\) \(q+(1.34500 + 1.34500i) q^{2} +(0.178671 + 0.431351i) q^{3} +2.61803i q^{4} +(-0.339853 + 0.820478i) q^{6} +(-1.40505 - 0.581990i) q^{7} +(-2.17625 + 2.17625i) q^{8} +(0.552967 - 0.552967i) q^{9} +(-1.12929 + 0.467768i) q^{12} +(-1.10701 - 2.67256i) q^{14} -3.23607 q^{16} +(0.809017 + 0.587785i) q^{17} +1.48748 q^{18} -0.710053i q^{21} +(-1.32756 - 0.549894i) q^{24} +(0.707107 - 0.707107i) q^{25} +(0.768673 + 0.318395i) q^{27} +(1.52367 - 3.67846i) q^{28} +(-2.17625 - 2.17625i) q^{32} +(0.297556 + 1.87869i) q^{34} +(1.44769 + 1.44769i) q^{36} +(-0.744220 - 1.79671i) q^{37} +(0.955019 - 0.955019i) q^{42} +1.00000i q^{47} +(-0.578193 - 1.39588i) q^{48} +(0.928339 + 0.928339i) q^{49} +1.90211 q^{50} +(-0.108993 + 0.453990i) q^{51} +(-1.26007 - 1.26007i) q^{53} +(0.605623 + 1.46210i) q^{54} +(4.32429 - 1.79118i) q^{56} +(-0.437016 + 0.437016i) q^{59} +(0.144974 + 0.0600500i) q^{61} +(-1.09877 + 0.455123i) q^{63} -2.61803i q^{64} +(-1.53884 + 2.11803i) q^{68} +(-0.652583 - 1.57547i) q^{71} +2.40679i q^{72} +(1.41559 - 3.41754i) q^{74} +(0.431351 + 0.178671i) q^{75} +(-0.652583 + 1.57547i) q^{79} -0.393557i q^{81} +(-1.00000 - 1.00000i) q^{83} +1.85894 q^{84} +1.90211i q^{89} +(-1.34500 + 1.34500i) q^{94} +(0.549894 - 1.32756i) q^{96} +(-1.84206 + 0.763007i) q^{97} +2.49723i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{3} - 4q^{9} + O(q^{10}) \) \( 16q - 4q^{3} - 4q^{9} - 16q^{16} + 4q^{17} - 20q^{24} - 4q^{27} - 4q^{28} + 4q^{36} - 20q^{42} + 24q^{48} + 4q^{49} - 16q^{51} + 4q^{53} + 20q^{54} + 20q^{56} + 4q^{61} - 4q^{63} - 4q^{71} - 4q^{79} - 16q^{83} + 32q^{84} + O(q^{100}) \)

Character values

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

\(n\) \(52\) \(377\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.34500 + 1.34500i 1.34500 + 1.34500i 0.891007 + 0.453990i \(0.150000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(3\) 0.178671 + 0.431351i 0.178671 + 0.431351i 0.987688 0.156434i \(-0.0500000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) 2.61803i 2.61803i
\(5\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(6\) −0.339853 + 0.820478i −0.339853 + 0.820478i
\(7\) −1.40505 0.581990i −1.40505 0.581990i −0.453990 0.891007i \(-0.650000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(8\) −2.17625 + 2.17625i −2.17625 + 2.17625i
\(9\) 0.552967 0.552967i 0.552967 0.552967i
\(10\) 0 0
\(11\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(12\) −1.12929 + 0.467768i −1.12929 + 0.467768i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −1.10701 2.67256i −1.10701 2.67256i
\(15\) 0 0
\(16\) −3.23607 −3.23607
\(17\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(18\) 1.48748 1.48748
\(19\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(20\) 0 0
\(21\) 0.710053i 0.710053i
\(22\) 0 0
\(23\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(24\) −1.32756 0.549894i −1.32756 0.549894i
\(25\) 0.707107 0.707107i 0.707107 0.707107i
\(26\) 0 0
\(27\) 0.768673 + 0.318395i 0.768673 + 0.318395i
\(28\) 1.52367 3.67846i 1.52367 3.67846i
\(29\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(32\) −2.17625 2.17625i −2.17625 2.17625i
\(33\) 0 0
\(34\) 0.297556 + 1.87869i 0.297556 + 1.87869i
\(35\) 0 0
\(36\) 1.44769 + 1.44769i 1.44769 + 1.44769i
\(37\) −0.744220 1.79671i −0.744220 1.79671i −0.587785 0.809017i \(-0.700000\pi\)
−0.156434 0.987688i \(-0.550000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(42\) 0.955019 0.955019i 0.955019 0.955019i
\(43\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.00000i 1.00000i
\(48\) −0.578193 1.39588i −0.578193 1.39588i
\(49\) 0.928339 + 0.928339i 0.928339 + 0.928339i
\(50\) 1.90211 1.90211
\(51\) −0.108993 + 0.453990i −0.108993 + 0.453990i
\(52\) 0 0
\(53\) −1.26007 1.26007i −1.26007 1.26007i −0.951057 0.309017i \(-0.900000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(54\) 0.605623 + 1.46210i 0.605623 + 1.46210i
\(55\) 0 0
\(56\) 4.32429 1.79118i 4.32429 1.79118i
\(57\) 0 0
\(58\) 0 0
\(59\) −0.437016 + 0.437016i −0.437016 + 0.437016i −0.891007 0.453990i \(-0.850000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(60\) 0 0
\(61\) 0.144974 + 0.0600500i 0.144974 + 0.0600500i 0.453990 0.891007i \(-0.350000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(62\) 0 0
\(63\) −1.09877 + 0.455123i −1.09877 + 0.455123i
\(64\) 2.61803i 2.61803i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −1.53884 + 2.11803i −1.53884 + 2.11803i
\(69\) 0 0
\(70\) 0 0
\(71\) −0.652583 1.57547i −0.652583 1.57547i −0.809017 0.587785i \(-0.800000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(72\) 2.40679i 2.40679i
\(73\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(74\) 1.41559 3.41754i 1.41559 3.41754i
\(75\) 0.431351 + 0.178671i 0.431351 + 0.178671i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.652583 + 1.57547i −0.652583 + 1.57547i 0.156434 + 0.987688i \(0.450000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(80\) 0 0
\(81\) 0.393557i 0.393557i
\(82\) 0 0
\(83\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(84\) 1.85894 1.85894
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −1.34500 + 1.34500i −1.34500 + 1.34500i
\(95\) 0 0
\(96\) 0.549894 1.32756i 0.549894 1.32756i
\(97\) −1.84206 + 0.763007i −1.84206 + 0.763007i −0.891007 + 0.453990i \(0.850000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(98\) 2.49723i 2.49723i
\(99\) 0 0
\(100\) 1.85123 + 1.85123i 1.85123 + 1.85123i
\(101\) 1.97538 1.97538 0.987688 0.156434i \(-0.0500000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(102\) −0.757212 + 0.464020i −0.757212 + 0.464020i
\(103\) −0.312869 −0.312869 −0.156434 0.987688i \(-0.550000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 3.38959i 3.38959i
\(107\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(108\) −0.833568 + 2.01241i −0.833568 + 2.01241i
\(109\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(110\) 0 0
\(111\) 0.642040 0.642040i 0.642040 0.642040i
\(112\) 4.54683 + 1.88336i 4.54683 + 1.88336i
\(113\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.17557 −1.17557
\(119\) −0.794622 1.29671i −0.794622 1.29671i
\(120\) 0 0
\(121\) −0.707107 0.707107i −0.707107 0.707107i
\(122\) 0.114222 + 0.275756i 0.114222 + 0.275756i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −2.08998 0.865696i −2.08998 0.865696i
\(127\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) 1.34500 1.34500i 1.34500 1.34500i
\(129\) 0 0
\(130\) 0 0
\(131\) 1.84206 0.763007i 1.84206 0.763007i 0.891007 0.453990i \(-0.150000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −3.03979 + 0.481456i −3.03979 + 0.481456i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(140\) 0 0
\(141\) −0.431351 + 0.178671i −0.431351 + 0.178671i
\(142\) 1.24129 2.99673i 1.24129 2.99673i
\(143\) 0 0
\(144\) −1.78944 + 1.78944i −1.78944 + 1.78944i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.234572 + 0.566307i −0.234572 + 0.566307i
\(148\) 4.70384 1.94839i 4.70384 1.94839i
\(149\) 0.312869i 0.312869i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(150\) 0.339853 + 0.820478i 0.339853 + 0.820478i
\(151\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(152\) 0 0
\(153\) 0.772385 0.122334i 0.772385 0.122334i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.907981i 0.907981i −0.891007 0.453990i \(-0.850000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(158\) −2.99673 + 1.24129i −2.99673 + 1.24129i
\(159\) 0.318395 0.768673i 0.318395 0.768673i
\(160\) 0 0
\(161\) 0 0
\(162\) 0.529334 0.529334i 0.529334 0.529334i
\(163\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 2.68999i 2.68999i
\(167\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(168\) 1.54525 + 1.54525i 1.54525 + 1.54525i
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.497066 + 1.20002i 0.497066 + 1.20002i 0.951057 + 0.309017i \(0.100000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(174\) 0 0
\(175\) −1.40505 + 0.581990i −1.40505 + 0.581990i
\(176\) 0 0
\(177\) −0.266589 0.110425i −0.266589 0.110425i
\(178\) −2.55834 + 2.55834i −2.55834 + 2.55834i
\(179\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(180\) 0 0
\(181\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(182\) 0 0
\(183\) 0.0732636i 0.0732636i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −2.61803 −2.61803
\(189\) −0.894719 0.894719i −0.894719 0.894719i
\(190\) 0 0
\(191\) 1.41421i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) 1.12929 0.467768i 1.12929 0.467768i
\(193\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(194\) −3.50381 1.45133i −3.50381 1.45133i
\(195\) 0 0
\(196\) −2.43042 + 2.43042i −2.43042 + 2.43042i
\(197\) 1.70711 + 0.707107i 1.70711 + 0.707107i 1.00000 \(0\)
0.707107 + 0.707107i \(0.250000\pi\)
\(198\) 0 0
\(199\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(200\) 3.07768i 3.07768i
\(201\) 0 0
\(202\) 2.65688 + 2.65688i 2.65688 + 2.65688i
\(203\) 0 0
\(204\) −1.18856 0.285349i −1.18856 0.285349i
\(205\) 0 0
\(206\) −0.420808 0.420808i −0.420808 0.420808i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(212\) 3.29892 3.29892i 3.29892 3.29892i
\(213\) 0.562984 0.562984i 0.562984 0.562984i
\(214\) 0 0
\(215\) 0 0
\(216\) −2.36573 + 0.979918i −2.36573 + 0.979918i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 1.72708 1.72708
\(223\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(224\) 1.79118 + 4.32429i 1.79118 + 4.32429i
\(225\) 0.782013i 0.782013i
\(226\) 0 0
\(227\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(228\) 0 0
\(229\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.14412 1.14412i −1.14412 1.14412i
\(237\) −0.796180 −0.796180
\(238\) 0.675301 2.81283i 0.675301 2.81283i
\(239\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(240\) 0 0
\(241\) 0.744220 + 1.79671i 0.744220 + 1.79671i 0.587785 + 0.809017i \(0.300000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(242\) 1.90211i 1.90211i
\(243\) 0.938434 0.388712i 0.938434 0.388712i
\(244\) −0.157213 + 0.379546i −0.157213 + 0.379546i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0.252679 0.610022i 0.252679 0.610022i
\(250\) 0 0
\(251\) 1.97538i 1.97538i −0.156434 0.987688i \(-0.550000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(252\) −1.19153 2.87660i −1.19153 2.87660i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(258\) 0 0
\(259\) 2.95758i 2.95758i
\(260\) 0 0
\(261\) 0 0
\(262\) 3.50381 + 1.45133i 3.50381 + 1.45133i
\(263\) 0.437016 0.437016i 0.437016 0.437016i −0.453990 0.891007i \(-0.650000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.820478 + 0.339853i −0.820478 + 0.339853i
\(268\) 0 0
\(269\) −0.292893 0.707107i −0.292893 0.707107i 0.707107 0.707107i \(-0.250000\pi\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −1.97538 −1.97538 −0.987688 0.156434i \(-0.950000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(272\) −2.61803 1.90211i −2.61803 1.90211i
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.57547 + 0.652583i −1.57547 + 0.652583i −0.987688 0.156434i \(-0.950000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(282\) −0.820478 0.339853i −0.820478 0.339853i
\(283\) −0.581990 + 1.40505i −0.581990 + 1.40505i 0.309017 + 0.951057i \(0.400000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(284\) 4.12464 1.70848i 4.12464 1.70848i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −2.40679 −2.40679
\(289\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(290\) 0 0
\(291\) −0.658248 0.658248i −0.658248 0.658248i
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) −1.07718 + 0.446183i −1.07718 + 0.446183i
\(295\) 0 0
\(296\) 5.52969 + 2.29047i 5.52969 + 2.29047i
\(297\) 0 0
\(298\) −0.420808 + 0.420808i −0.420808 + 0.420808i
\(299\) 0 0
\(300\) −0.467768 + 1.12929i −0.467768 + 1.12929i
\(301\) 0 0
\(302\) 0 0
\(303\) 0.352943 + 0.852080i 0.352943 + 0.852080i
\(304\) 0 0
\(305\) 0 0
\(306\) 1.20339 + 0.874317i 1.20339 + 0.874317i
\(307\) −1.97538 −1.97538 −0.987688 0.156434i \(-0.950000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(308\) 0 0
\(309\) −0.0559007 0.134956i −0.0559007 0.134956i
\(310\) 0 0
\(311\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(312\) 0 0
\(313\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(314\) 1.22123 1.22123i 1.22123 1.22123i
\(315\) 0 0
\(316\) −4.12464 1.70848i −4.12464 1.70848i
\(317\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(318\) 1.46210 0.605623i 1.46210 0.605623i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 1.03035 1.03035
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.581990 1.40505i 0.581990 1.40505i
\(330\) 0 0
\(331\) 1.34500 1.34500i 1.34500 1.34500i 0.453990 0.891007i \(-0.350000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(332\) 2.61803 2.61803i 2.61803 2.61803i
\(333\) −1.40505 0.581990i −1.40505 0.581990i
\(334\) 0 0
\(335\) 0 0
\(336\) 2.29778i 2.29778i
\(337\) −0.497066 1.20002i −0.497066 1.20002i −0.951057 0.309017i \(-0.900000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(338\) −1.34500 1.34500i −1.34500 1.34500i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.182086 0.439596i −0.182086 0.439596i
\(344\) 0 0
\(345\) 0 0
\(346\) −0.945476 + 2.28258i −0.945476 + 2.28258i
\(347\) −0.431351 0.178671i −0.431351 0.178671i 0.156434 0.987688i \(-0.450000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(348\) 0 0
\(349\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(350\) −2.67256 1.10701i −2.67256 1.10701i
\(351\) 0 0
\(352\) 0 0
\(353\) 0.907981i 0.907981i 0.891007 + 0.453990i \(0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(354\) −0.210041 0.507083i −0.210041 0.507083i
\(355\) 0 0
\(356\) −4.97980 −4.97980
\(357\) 0.417359 0.574445i 0.417359 0.574445i
\(358\) 0 0
\(359\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(360\) 0 0
\(361\) 1.00000i 1.00000i
\(362\) 0 0
\(363\) 0.178671 0.431351i 0.178671 0.431351i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.0985394 + 0.0985394i −0.0985394 + 0.0985394i
\(367\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.03711 + 2.50381i 1.03711 + 2.50381i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −2.17625 2.17625i −2.17625 2.17625i
\(377\) 0 0
\(378\) 2.40679i 2.40679i
\(379\) 1.20002 0.497066i 1.20002 0.497066i 0.309017 0.951057i \(-0.400000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.90211 + 1.90211i −1.90211 + 1.90211i
\(383\) −0.221232 + 0.221232i −0.221232 + 0.221232i −0.809017 0.587785i \(-0.800000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(384\) 0.820478 + 0.339853i 0.820478 + 0.339853i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −1.99758 4.82258i −1.99758 4.82258i
\(389\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −4.04060 −4.04060
\(393\) 0.658248 + 0.658248i 0.658248 + 0.658248i
\(394\) 1.34500 + 3.24711i 1.34500 + 3.24711i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.399903 0.965451i 0.399903 0.965451i −0.587785 0.809017i \(-0.700000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −2.28825 + 2.28825i −2.28825 + 2.28825i
\(401\) 0.431351 + 0.178671i 0.431351 + 0.178671i 0.587785 0.809017i \(-0.300000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 5.17160i 5.17160i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.750800 1.22519i −0.750800 1.22519i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0.819101i 0.819101i
\(413\) 0.868367 0.359689i 0.868367 0.359689i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 0.552967 + 0.552967i 0.552967 + 0.552967i
\(424\) 5.48447 5.48447
\(425\) 0.987688 0.156434i 0.987688 0.156434i
\(426\) 1.51442 1.51442
\(427\) −0.168746 0.168746i −0.168746 0.168746i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0.763007 1.84206i 0.763007 1.84206i 0.309017 0.951057i \(-0.400000\pi\)
0.453990 0.891007i \(-0.350000\pi\)
\(432\) −2.48748 1.03035i −2.48748 1.03035i
\(433\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0.707107 + 1.70711i 0.707107 + 1.70711i 0.707107 + 0.707107i \(0.250000\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 1.02668 1.02668
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 1.68088 + 1.68088i 1.68088 + 1.68088i
\(445\) 0 0
\(446\) 0 0
\(447\) −0.134956 + 0.0559007i −0.134956 + 0.0559007i
\(448\) −1.52367 + 3.67846i −1.52367 + 3.67846i
\(449\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(450\) 1.05181 1.05181i 1.05181 1.05181i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.39680 + 1.39680i 1.39680 + 1.39680i 0.809017 + 0.587785i \(0.200000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(458\) 0 0
\(459\) 0.434722 + 0.709401i 0.434722 + 0.709401i
\(460\) 0 0
\(461\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(462\) 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 \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0.391658 0.162230i 0.391658 0.162230i
\(472\) 1.90211i 1.90211i
\(473\) 0 0
\(474\) −1.07086 1.07086i −1.07086 1.07086i
\(475\) 0 0
\(476\) 3.39482 2.08035i 3.39482 2.08035i
\(477\) −1.39356 −1.39356
\(478\) 1.58114 + 1.58114i 1.58114 + 1.58114i
\(479\) 0.581990 + 1.40505i 0.581990 + 1.40505i 0.891007 + 0.453990i \(0.150000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.41559 + 3.41754i −1.41559 + 3.41754i
\(483\) 0 0
\(484\) 1.85123 1.85123i 1.85123 1.85123i
\(485\) 0 0
\(486\) 1.78501 + 0.739374i 1.78501 + 0.739374i
\(487\) −0.707107 + 1.70711i −0.707107 + 1.70711i 1.00000i \(0.5\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(488\) −0.446183 + 0.184815i −0.446183 + 0.184815i
\(489\) 0 0
\(490\) 0 0
\(491\) −0.642040 0.642040i −0.642040 0.642040i 0.309017 0.951057i \(-0.400000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.59341i 2.59341i
\(498\) 1.16033 0.480625i 1.16033 0.480625i
\(499\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 2.65688 2.65688i 2.65688 2.65688i
\(503\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(504\) 1.40073 3.38165i 1.40073 3.38165i
\(505\) 0 0
\(506\) 0 0
\(507\) −0.178671 0.431351i −0.178671 0.431351i
\(508\) 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
\(518\) −3.97794 + 3.97794i −3.97794 + 3.97794i
\(519\) −0.428820 + 0.428820i −0.428820 + 0.428820i
\(520\) 0 0
\(521\) 0.497066 1.20002i 0.497066 1.20002i −0.453990 0.891007i \(-0.650000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 1.99758 + 4.82258i 1.99758 + 4.82258i
\(525\) −0.502083 0.502083i −0.502083 0.502083i
\(526\) 1.17557 1.17557
\(527\) 0 0
\(528\) 0 0
\(529\) −0.707107 0.707107i −0.707107 0.707107i
\(530\) 0 0
\(531\) 0.483311i 0.483311i
\(532\) 0 0
\(533\) 0 0
\(534\) −1.56064 0.646439i −1.56064 0.646439i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0.557116 1.34500i 0.557116 1.34500i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.497066 + 1.20002i 0.497066 + 1.20002i 0.951057 + 0.309017i \(0.100000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(542\) −2.65688 2.65688i −2.65688 2.65688i
\(543\) 0 0
\(544\) −0.481456 3.03979i −0.481456 3.03979i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(548\) 0 0
\(549\) 0.113371 0.0469599i 0.113371 0.0469599i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1.83382 1.83382i 1.83382 1.83382i
\(554\) −2.99673 1.24129i −2.99673 1.24129i
\(555\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(564\) −0.467768 1.12929i −0.467768 1.12929i
\(565\) 0 0
\(566\) −2.67256 + 1.10701i −2.67256 + 1.10701i
\(567\) −0.229046 + 0.552967i −0.229046 + 0.552967i
\(568\) 4.84881 + 2.00844i 4.84881 + 2.00844i
\(569\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(570\) 0 0
\(571\) 0.965451 + 0.399903i 0.965451 + 0.399903i 0.809017 0.587785i \(-0.200000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(572\) 0 0
\(573\) −0.610022 + 0.252679i −0.610022 + 0.252679i
\(574\) 0 0
\(575\) 0 0
\(576\) −1.44769 1.44769i −1.44769 1.44769i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −0.863541 + 1.69480i −0.863541 + 1.69480i
\(579\) 0 0
\(580\) 0 0
\(581\) 0.823057 + 1.98704i 0.823057 + 1.98704i
\(582\) 1.77068i 1.77068i
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) −1.48261 0.614118i −1.48261 0.614118i
\(589\) 0 0
\(590\) 0 0
\(591\) 0.862702i 0.862702i
\(592\) 2.40835 + 5.81426i 2.40835 + 5.81426i
\(593\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.819101 −0.819101
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −1.32756 + 0.549894i −1.32756 + 0.549894i
\(601\) 0.0600500 0.144974i 0.0600500 0.144974i −0.891007 0.453990i \(-0.850000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −0.671338 + 1.62075i −0.671338 + 1.62075i
\(607\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.320274 + 2.02213i 0.320274 + 2.02213i
\(613\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(614\) −2.65688 2.65688i −2.65688 2.65688i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.965451 + 0.399903i −0.965451 + 0.399903i −0.809017 0.587785i \(-0.800000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(618\) 0.106329 0.256702i 0.106329 0.256702i
\(619\) −0.707107 0.292893i −0.707107 0.292893i 1.00000i \(-0.5\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.10701 2.67256i 1.10701 2.67256i
\(624\) 0 0
\(625\) 1.00000i 1.00000i
\(626\) 0 0
\(627\) 0 0
\(628\) 2.37713 2.37713
\(629\) 0.453990 1.89101i 0.453990 1.89101i
\(630\) 0 0
\(631\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(632\) −2.00844 4.84881i −2.00844 4.84881i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 2.01241 + 0.833568i 2.01241 + 0.833568i
\(637\) 0 0
\(638\) 0 0
\(639\) −1.23204 0.510328i −1.23204 0.510328i
\(640\) 0 0
\(641\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(642\) 0 0
\(643\) −0.0600500 0.144974i −0.0600500 0.144974i 0.891007 0.453990i \(-0.150000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.907981 0.907981 0.453990 0.891007i \(-0.350000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(648\) 0.856480 + 0.856480i 0.856480 + 0.856480i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.79671 + 0.744220i 1.79671 + 0.744220i 0.987688 + 0.156434i \(0.0500000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 2.67256 1.10701i 2.67256 1.10701i
\(659\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(660\) 0 0
\(661\) −0.831254 0.831254i −0.831254 0.831254i 0.156434 0.987688i \(-0.450000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(662\) 3.61803 3.61803
\(663\) 0 0
\(664\) 4.35250 4.35250
\(665\) 0 0
\(666\) −1.10701 2.67256i −1.10701 2.67256i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −1.54525 + 1.54525i −1.54525 + 1.54525i
\(673\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(674\) 0.945476 2.28258i 0.945476 2.28258i
\(675\) 0.768673 0.318395i 0.768673 0.318395i
\(676\) 2.61803i 2.61803i
\(677\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(678\) 0 0
\(679\) 3.03225 3.03225
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.0600500 + 0.144974i 0.0600500 + 0.144974i 0.951057 0.309017i \(-0.100000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.346349 0.836160i 0.346349 0.836160i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(692\) −3.14170 + 1.30134i −3.14170 + 1.30134i
\(693\) 0 0
\(694\) −0.339853 0.820478i −0.339853 0.820478i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −1.52367 3.67846i −1.52367 3.67846i
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.22123 + 1.22123i −1.22123 + 1.22123i
\(707\) −2.77550 1.14965i −2.77550 1.14965i
\(708\) 0.289096 0.697940i 0.289096 0.697940i
\(709\) −1.40505 + 0.581990i −1.40505 + 0.581990i −0.951057 0.309017i \(-0.900000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(710\) 0 0
\(711\) 0.510328 + 1.23204i 0.510328 + 1.23204i
\(712\) −4.13948 4.13948i −4.13948 4.13948i
\(713\) 0 0
\(714\) 1.33397 0.211281i 1.33397 0.211281i
\(715\) 0 0
\(716\) 0 0
\(717\) 0.210041 + 0.507083i 0.210041 + 0.507083i
\(718\) 0 0
\(719\) −0.144974 + 0.0600500i −0.144974 + 0.0600500i −0.453990 0.891007i \(-0.650000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(720\) 0 0
\(721\) 0.439596 + 0.182086i 0.439596 + 0.182086i
\(722\) −1.34500 + 1.34500i −1.34500 + 1.34500i
\(723\) −0.642040 + 0.642040i −0.642040 + 0.642040i
\(724\) 0 0
\(725\) 0 0
\(726\) 0.820478 0.339853i 0.820478 0.339853i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 0.0570554 + 0.0570554i 0.0570554 + 0.0570554i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.191807 −0.191807
\(733\) −0.831254 0.831254i −0.831254 0.831254i 0.156434 0.987688i \(-0.450000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.642040 0.642040i 0.642040 0.642040i −0.309017 0.951057i \(-0.600000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.97271 + 4.76253i −1.97271 + 4.76253i
\(743\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.10593 −1.10593
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(752\) 3.23607i 3.23607i
\(753\) 0.852080 0.352943i 0.852080 0.352943i
\(754\) 0 0
\(755\) 0 0
\(756\) 2.34240 2.34240i 2.34240 2.34240i
\(757\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(758\) 2.28258 + 0.945476i 2.28258 + 0.945476i
\(759\) 0 0
\(760\) 0 0
\(761\) 1.41421i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3.70246 −3.70246
\(765\) 0 0
\(766\) −0.595112 −0.595112
\(767\) 0 0
\(768\) 0.178671 + 0.431351i 0.178671 + 0.431351i
\(769\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.831254 0.831254i 0.831254 0.831254i −0.156434 0.987688i \(-0.550000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 2.34830 5.66929i 2.34830 5.66929i
\(777\) −1.27576 + 0.528435i −1.27576 + 0.528435i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −3.00417 3.00417i −3.00417 3.00417i
\(785\) 0 0
\(786\) 1.77068i 1.77068i
\(787\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(788\) −1.85123 + 4.46926i −1.85123 + 4.46926i
\(789\) 0.266589 + 0.110425i 0.266589 + 0.110425i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 1.83640 0.760661i 1.83640 0.760661i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(798\) 0 0
\(799\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(800\) −3.07768 −3.07768