Properties

Label 2240.2.g.o.449.7
Level $2240$
Weight $2$
Character 2240.449
Analytic conductor $17.886$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.8864900528\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 13 x^{8} + 56 x^{6} + 97 x^{4} + 61 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 1120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 449.7
Root \(1.28447i\) of defining polynomial
Character \(\chi\) \(=\) 2240.449
Dual form 2240.2.g.o.449.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.63460i q^{3} +(2.23081 + 0.153266i) q^{5} +1.00000i q^{7} +0.328072 q^{9} +O(q^{10})\) \(q+1.63460i q^{3} +(2.23081 + 0.153266i) q^{5} +1.00000i q^{7} +0.328072 q^{9} +1.24087 q^{11} -4.20355i q^{13} +(-0.250528 + 3.64649i) q^{15} +3.39596i q^{17} -6.46162 q^{19} -1.63460 q^{21} +2.15509i q^{23} +(4.95302 + 0.683813i) q^{25} +5.44008i q^{27} +3.96490 q^{29} +10.0611 q^{31} +2.02833i q^{33} +(-0.153266 + 2.23081i) q^{35} +6.76815i q^{37} +6.87113 q^{39} -0.131318 q^{41} +7.40498i q^{43} +(0.731866 + 0.0502822i) q^{45} +4.82702i q^{47} -1.00000 q^{49} -5.55105 q^{51} -10.0374i q^{53} +(2.76815 + 0.190183i) q^{55} -10.5622i q^{57} -10.9864 q^{59} +6.33030 q^{61} +0.328072i q^{63} +(0.644259 - 9.37731i) q^{65} -2.65614i q^{67} -3.52271 q^{69} -0.754563 q^{71} +6.03736i q^{73} +(-1.11776 + 8.09622i) q^{75} +1.24087i q^{77} +14.6652 q^{79} -7.90815 q^{81} -14.0813i q^{83} +(-0.520484 + 7.57574i) q^{85} +6.48105i q^{87} +12.6742 q^{89} +4.20355 q^{91} +16.4459i q^{93} +(-14.4146 - 0.990344i) q^{95} -0.914215i q^{97} +0.407096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{5} - 14q^{9} + O(q^{10}) \) \( 10q + 2q^{5} - 14q^{9} + 8q^{11} - 4q^{15} - 24q^{19} + 4q^{21} + 6q^{25} - 24q^{29} - 24q^{31} + 64q^{39} - 4q^{41} - 10q^{45} - 10q^{49} + 24q^{51} - 16q^{55} - 32q^{59} + 20q^{61} - 8q^{65} + 8q^{69} - 8q^{71} + 64q^{75} + 64q^{79} + 2q^{81} + 12q^{85} - 4q^{89} - 60q^{95} - 80q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).

\(n\) \(897\) \(1471\) \(1541\) \(1921\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.63460i 0.943739i 0.881668 + 0.471869i \(0.156421\pi\)
−0.881668 + 0.471869i \(0.843579\pi\)
\(4\) 0 0
\(5\) 2.23081 + 0.153266i 0.997648 + 0.0685425i
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 0.328072 0.109357
\(10\) 0 0
\(11\) 1.24087 0.374137 0.187069 0.982347i \(-0.440101\pi\)
0.187069 + 0.982347i \(0.440101\pi\)
\(12\) 0 0
\(13\) 4.20355i 1.16585i −0.812524 0.582927i \(-0.801907\pi\)
0.812524 0.582927i \(-0.198093\pi\)
\(14\) 0 0
\(15\) −0.250528 + 3.64649i −0.0646862 + 0.941519i
\(16\) 0 0
\(17\) 3.39596i 0.823641i 0.911265 + 0.411821i \(0.135107\pi\)
−0.911265 + 0.411821i \(0.864893\pi\)
\(18\) 0 0
\(19\) −6.46162 −1.48240 −0.741198 0.671286i \(-0.765742\pi\)
−0.741198 + 0.671286i \(0.765742\pi\)
\(20\) 0 0
\(21\) −1.63460 −0.356700
\(22\) 0 0
\(23\) 2.15509i 0.449367i 0.974432 + 0.224683i \(0.0721348\pi\)
−0.974432 + 0.224683i \(0.927865\pi\)
\(24\) 0 0
\(25\) 4.95302 + 0.683813i 0.990604 + 0.136763i
\(26\) 0 0
\(27\) 5.44008i 1.04694i
\(28\) 0 0
\(29\) 3.96490 0.736264 0.368132 0.929773i \(-0.379997\pi\)
0.368132 + 0.929773i \(0.379997\pi\)
\(30\) 0 0
\(31\) 10.0611 1.80703 0.903516 0.428555i \(-0.140977\pi\)
0.903516 + 0.428555i \(0.140977\pi\)
\(32\) 0 0
\(33\) 2.02833i 0.353088i
\(34\) 0 0
\(35\) −0.153266 + 2.23081i −0.0259066 + 0.377076i
\(36\) 0 0
\(37\) 6.76815i 1.11268i 0.830956 + 0.556338i \(0.187794\pi\)
−0.830956 + 0.556338i \(0.812206\pi\)
\(38\) 0 0
\(39\) 6.87113 1.10026
\(40\) 0 0
\(41\) −0.131318 −0.0205084 −0.0102542 0.999947i \(-0.503264\pi\)
−0.0102542 + 0.999947i \(0.503264\pi\)
\(42\) 0 0
\(43\) 7.40498i 1.12925i 0.825348 + 0.564625i \(0.190979\pi\)
−0.825348 + 0.564625i \(0.809021\pi\)
\(44\) 0 0
\(45\) 0.731866 + 0.0502822i 0.109100 + 0.00749562i
\(46\) 0 0
\(47\) 4.82702i 0.704093i 0.935983 + 0.352046i \(0.114514\pi\)
−0.935983 + 0.352046i \(0.885486\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) −5.55105 −0.777302
\(52\) 0 0
\(53\) 10.0374i 1.37874i −0.724411 0.689368i \(-0.757888\pi\)
0.724411 0.689368i \(-0.242112\pi\)
\(54\) 0 0
\(55\) 2.76815 + 0.190183i 0.373257 + 0.0256443i
\(56\) 0 0
\(57\) 10.5622i 1.39900i
\(58\) 0 0
\(59\) −10.9864 −1.43031 −0.715157 0.698964i \(-0.753645\pi\)
−0.715157 + 0.698964i \(0.753645\pi\)
\(60\) 0 0
\(61\) 6.33030 0.810512 0.405256 0.914203i \(-0.367182\pi\)
0.405256 + 0.914203i \(0.367182\pi\)
\(62\) 0 0
\(63\) 0.328072i 0.0413332i
\(64\) 0 0
\(65\) 0.644259 9.37731i 0.0799105 1.16311i
\(66\) 0 0
\(67\) 2.65614i 0.324500i −0.986750 0.162250i \(-0.948125\pi\)
0.986750 0.162250i \(-0.0518750\pi\)
\(68\) 0 0
\(69\) −3.52271 −0.424085
\(70\) 0 0
\(71\) −0.754563 −0.0895501 −0.0447751 0.998997i \(-0.514257\pi\)
−0.0447751 + 0.998997i \(0.514257\pi\)
\(72\) 0 0
\(73\) 6.03736i 0.706619i 0.935506 + 0.353310i \(0.114944\pi\)
−0.935506 + 0.353310i \(0.885056\pi\)
\(74\) 0 0
\(75\) −1.11776 + 8.09622i −0.129068 + 0.934871i
\(76\) 0 0
\(77\) 1.24087i 0.141411i
\(78\) 0 0
\(79\) 14.6652 1.64996 0.824980 0.565162i \(-0.191186\pi\)
0.824980 + 0.565162i \(0.191186\pi\)
\(80\) 0 0
\(81\) −7.90815 −0.878684
\(82\) 0 0
\(83\) 14.0813i 1.54562i −0.634639 0.772809i \(-0.718851\pi\)
0.634639 0.772809i \(-0.281149\pi\)
\(84\) 0 0
\(85\) −0.520484 + 7.57574i −0.0564544 + 0.821704i
\(86\) 0 0
\(87\) 6.48105i 0.694841i
\(88\) 0 0
\(89\) 12.6742 1.34346 0.671731 0.740795i \(-0.265551\pi\)
0.671731 + 0.740795i \(0.265551\pi\)
\(90\) 0 0
\(91\) 4.20355 0.440652
\(92\) 0 0
\(93\) 16.4459i 1.70537i
\(94\) 0 0
\(95\) −14.4146 0.990344i −1.47891 0.101607i
\(96\) 0 0
\(97\) 0.914215i 0.0928244i −0.998922 0.0464122i \(-0.985221\pi\)
0.998922 0.0464122i \(-0.0147788\pi\)
\(98\) 0 0
\(99\) 0.407096 0.0409146
\(100\) 0 0
\(101\) −13.4818 −1.34149 −0.670743 0.741689i \(-0.734025\pi\)
−0.670743 + 0.741689i \(0.734025\pi\)
\(102\) 0 0
\(103\) 0.516841i 0.0509258i −0.999676 0.0254629i \(-0.991894\pi\)
0.999676 0.0254629i \(-0.00810597\pi\)
\(104\) 0 0
\(105\) −3.64649 0.250528i −0.355861 0.0244491i
\(106\) 0 0
\(107\) 18.8486i 1.82216i 0.412228 + 0.911081i \(0.364751\pi\)
−0.412228 + 0.911081i \(0.635249\pi\)
\(108\) 0 0
\(109\) 0.345270 0.0330709 0.0165354 0.999863i \(-0.494736\pi\)
0.0165354 + 0.999863i \(0.494736\pi\)
\(110\) 0 0
\(111\) −11.0632 −1.05008
\(112\) 0 0
\(113\) 3.77026i 0.354677i 0.984150 + 0.177338i \(0.0567487\pi\)
−0.984150 + 0.177338i \(0.943251\pi\)
\(114\) 0 0
\(115\) −0.330301 + 4.80759i −0.0308007 + 0.448310i
\(116\) 0 0
\(117\) 1.37907i 0.127495i
\(118\) 0 0
\(119\) −3.39596 −0.311307
\(120\) 0 0
\(121\) −9.46024 −0.860021
\(122\) 0 0
\(123\) 0.214652i 0.0193545i
\(124\) 0 0
\(125\) 10.9444 + 2.28458i 0.978900 + 0.204339i
\(126\) 0 0
\(127\) 5.63895i 0.500376i 0.968197 + 0.250188i \(0.0804924\pi\)
−0.968197 + 0.250188i \(0.919508\pi\)
\(128\) 0 0
\(129\) −12.1042 −1.06572
\(130\) 0 0
\(131\) 10.5183 0.918987 0.459493 0.888181i \(-0.348031\pi\)
0.459493 + 0.888181i \(0.348031\pi\)
\(132\) 0 0
\(133\) 6.46162i 0.560293i
\(134\) 0 0
\(135\) −0.833777 + 12.1358i −0.0717601 + 1.04448i
\(136\) 0 0
\(137\) 6.96632i 0.595173i 0.954695 + 0.297586i \(0.0961816\pi\)
−0.954695 + 0.297586i \(0.903818\pi\)
\(138\) 0 0
\(139\) −10.3258 −0.875827 −0.437913 0.899017i \(-0.644282\pi\)
−0.437913 + 0.899017i \(0.644282\pi\)
\(140\) 0 0
\(141\) −7.89025 −0.664479
\(142\) 0 0
\(143\) 5.21607i 0.436189i
\(144\) 0 0
\(145\) 8.84494 + 0.607683i 0.734533 + 0.0504654i
\(146\) 0 0
\(147\) 1.63460i 0.134820i
\(148\) 0 0
\(149\) −0.773875 −0.0633983 −0.0316992 0.999497i \(-0.510092\pi\)
−0.0316992 + 0.999497i \(0.510092\pi\)
\(150\) 0 0
\(151\) −6.14607 −0.500160 −0.250080 0.968225i \(-0.580457\pi\)
−0.250080 + 0.968225i \(0.580457\pi\)
\(152\) 0 0
\(153\) 1.11412i 0.0900712i
\(154\) 0 0
\(155\) 22.4445 + 1.54202i 1.80278 + 0.123858i
\(156\) 0 0
\(157\) 18.5421i 1.47982i −0.672707 0.739909i \(-0.734869\pi\)
0.672707 0.739909i \(-0.265131\pi\)
\(158\) 0 0
\(159\) 16.4071 1.30117
\(160\) 0 0
\(161\) −2.15509 −0.169845
\(162\) 0 0
\(163\) 0.993429i 0.0778113i −0.999243 0.0389057i \(-0.987613\pi\)
0.999243 0.0389057i \(-0.0123872\pi\)
\(164\) 0 0
\(165\) −0.310874 + 4.52483i −0.0242015 + 0.352257i
\(166\) 0 0
\(167\) 3.22052i 0.249212i −0.992206 0.124606i \(-0.960233\pi\)
0.992206 0.124606i \(-0.0397666\pi\)
\(168\) 0 0
\(169\) −4.66981 −0.359216
\(170\) 0 0
\(171\) −2.11988 −0.162111
\(172\) 0 0
\(173\) 15.9187i 1.21028i −0.796120 0.605138i \(-0.793118\pi\)
0.796120 0.605138i \(-0.206882\pi\)
\(174\) 0 0
\(175\) −0.683813 + 4.95302i −0.0516914 + 0.374413i
\(176\) 0 0
\(177\) 17.9585i 1.34984i
\(178\) 0 0
\(179\) 9.84647 0.735960 0.367980 0.929834i \(-0.380049\pi\)
0.367980 + 0.929834i \(0.380049\pi\)
\(180\) 0 0
\(181\) −21.6562 −1.60969 −0.804845 0.593484i \(-0.797752\pi\)
−0.804845 + 0.593484i \(0.797752\pi\)
\(182\) 0 0
\(183\) 10.3475i 0.764911i
\(184\) 0 0
\(185\) −1.03732 + 15.0985i −0.0762656 + 1.11006i
\(186\) 0 0
\(187\) 4.21395i 0.308155i
\(188\) 0 0
\(189\) −5.44008 −0.395707
\(190\) 0 0
\(191\) −17.7197 −1.28215 −0.641077 0.767477i \(-0.721512\pi\)
−0.641077 + 0.767477i \(0.721512\pi\)
\(192\) 0 0
\(193\) 12.0238i 0.865490i 0.901516 + 0.432745i \(0.142455\pi\)
−0.901516 + 0.432745i \(0.857545\pi\)
\(194\) 0 0
\(195\) 15.3282 + 1.05311i 1.09767 + 0.0754147i
\(196\) 0 0
\(197\) 4.12069i 0.293587i −0.989167 0.146794i \(-0.953105\pi\)
0.989167 0.146794i \(-0.0468953\pi\)
\(198\) 0 0
\(199\) 9.86868 0.699572 0.349786 0.936830i \(-0.386254\pi\)
0.349786 + 0.936830i \(0.386254\pi\)
\(200\) 0 0
\(201\) 4.34174 0.306243
\(202\) 0 0
\(203\) 3.96490i 0.278282i
\(204\) 0 0
\(205\) −0.292945 0.0201265i −0.0204601 0.00140569i
\(206\) 0 0
\(207\) 0.707024i 0.0491416i
\(208\) 0 0
\(209\) −8.01804 −0.554620
\(210\) 0 0
\(211\) −6.93076 −0.477133 −0.238567 0.971126i \(-0.576678\pi\)
−0.238567 + 0.971126i \(0.576678\pi\)
\(212\) 0 0
\(213\) 1.23341i 0.0845119i
\(214\) 0 0
\(215\) −1.13493 + 16.5191i −0.0774015 + 1.12659i
\(216\) 0 0
\(217\) 10.0611i 0.682994i
\(218\) 0 0
\(219\) −9.86868 −0.666864
\(220\) 0 0
\(221\) 14.2751 0.960246
\(222\) 0 0
\(223\) 23.0625i 1.54438i −0.635391 0.772191i \(-0.719161\pi\)
0.635391 0.772191i \(-0.280839\pi\)
\(224\) 0 0
\(225\) 1.62495 + 0.224340i 0.108330 + 0.0149560i
\(226\) 0 0
\(227\) 2.86073i 0.189873i −0.995483 0.0949366i \(-0.969735\pi\)
0.995483 0.0949366i \(-0.0302648\pi\)
\(228\) 0 0
\(229\) 18.5227 1.22402 0.612009 0.790851i \(-0.290362\pi\)
0.612009 + 0.790851i \(0.290362\pi\)
\(230\) 0 0
\(231\) −2.02833 −0.133455
\(232\) 0 0
\(233\) 23.1112i 1.51407i −0.653376 0.757033i \(-0.726648\pi\)
0.653376 0.757033i \(-0.273352\pi\)
\(234\) 0 0
\(235\) −0.739815 + 10.7681i −0.0482602 + 0.702437i
\(236\) 0 0
\(237\) 23.9717i 1.55713i
\(238\) 0 0
\(239\) −9.01270 −0.582983 −0.291491 0.956573i \(-0.594151\pi\)
−0.291491 + 0.956573i \(0.594151\pi\)
\(240\) 0 0
\(241\) −12.4415 −0.801427 −0.400713 0.916203i \(-0.631238\pi\)
−0.400713 + 0.916203i \(0.631238\pi\)
\(242\) 0 0
\(243\) 3.39354i 0.217696i
\(244\) 0 0
\(245\) −2.23081 0.153266i −0.142521 0.00979178i
\(246\) 0 0
\(247\) 27.1617i 1.72826i
\(248\) 0 0
\(249\) 23.0173 1.45866
\(250\) 0 0
\(251\) 21.3984 1.35066 0.675329 0.737517i \(-0.264002\pi\)
0.675329 + 0.737517i \(0.264002\pi\)
\(252\) 0 0
\(253\) 2.67419i 0.168125i
\(254\) 0 0
\(255\) −12.3833 0.850785i −0.775474 0.0532782i
\(256\) 0 0
\(257\) 27.5737i 1.72000i 0.510296 + 0.859999i \(0.329536\pi\)
−0.510296 + 0.859999i \(0.670464\pi\)
\(258\) 0 0
\(259\) −6.76815 −0.420552
\(260\) 0 0
\(261\) 1.30077 0.0805159
\(262\) 0 0
\(263\) 6.77388i 0.417695i −0.977948 0.208848i \(-0.933029\pi\)
0.977948 0.208848i \(-0.0669712\pi\)
\(264\) 0 0
\(265\) 1.53838 22.3914i 0.0945020 1.37549i
\(266\) 0 0
\(267\) 20.7173i 1.26788i
\(268\) 0 0
\(269\) −14.5794 −0.888922 −0.444461 0.895798i \(-0.646605\pi\)
−0.444461 + 0.895798i \(0.646605\pi\)
\(270\) 0 0
\(271\) −23.3842 −1.42049 −0.710244 0.703956i \(-0.751415\pi\)
−0.710244 + 0.703956i \(0.751415\pi\)
\(272\) 0 0
\(273\) 6.87113i 0.415860i
\(274\) 0 0
\(275\) 6.14607 + 0.848524i 0.370622 + 0.0511679i
\(276\) 0 0
\(277\) 8.57577i 0.515268i −0.966243 0.257634i \(-0.917057\pi\)
0.966243 0.257634i \(-0.0829429\pi\)
\(278\) 0 0
\(279\) 3.30077 0.197612
\(280\) 0 0
\(281\) −3.49675 −0.208598 −0.104299 0.994546i \(-0.533260\pi\)
−0.104299 + 0.994546i \(0.533260\pi\)
\(282\) 0 0
\(283\) 18.2952i 1.08754i −0.839235 0.543769i \(-0.816997\pi\)
0.839235 0.543769i \(-0.183003\pi\)
\(284\) 0 0
\(285\) 1.61882 23.5622i 0.0958906 1.39571i
\(286\) 0 0
\(287\) 0.131318i 0.00775143i
\(288\) 0 0
\(289\) 5.46746 0.321615
\(290\) 0 0
\(291\) 1.49438 0.0876020
\(292\) 0 0
\(293\) 30.4752i 1.78038i 0.455592 + 0.890189i \(0.349428\pi\)
−0.455592 + 0.890189i \(0.650572\pi\)
\(294\) 0 0
\(295\) −24.5087 1.68384i −1.42695 0.0980372i
\(296\) 0 0
\(297\) 6.75044i 0.391700i
\(298\) 0 0
\(299\) 9.05901 0.523896
\(300\) 0 0
\(301\) −7.40498 −0.426816
\(302\) 0 0
\(303\) 22.0374i 1.26601i
\(304\) 0 0
\(305\) 14.1217 + 0.970217i 0.808606 + 0.0555545i
\(306\) 0 0
\(307\) 24.8725i 1.41955i −0.704430 0.709773i \(-0.748797\pi\)
0.704430 0.709773i \(-0.251203\pi\)
\(308\) 0 0
\(309\) 0.844830 0.0480607
\(310\) 0 0
\(311\) −7.42579 −0.421078 −0.210539 0.977585i \(-0.567522\pi\)
−0.210539 + 0.977585i \(0.567522\pi\)
\(312\) 0 0
\(313\) 8.10594i 0.458175i −0.973406 0.229088i \(-0.926426\pi\)
0.973406 0.229088i \(-0.0735742\pi\)
\(314\) 0 0
\(315\) −0.0502822 + 0.731866i −0.00283308 + 0.0412360i
\(316\) 0 0
\(317\) 14.6010i 0.820076i 0.912068 + 0.410038i \(0.134485\pi\)
−0.912068 + 0.410038i \(0.865515\pi\)
\(318\) 0 0
\(319\) 4.91994 0.275464
\(320\) 0 0
\(321\) −30.8100 −1.71964
\(322\) 0 0
\(323\) 21.9434i 1.22096i
\(324\) 0 0
\(325\) 2.87444 20.8203i 0.159445 1.15490i
\(326\) 0 0
\(327\) 0.564380i 0.0312103i
\(328\) 0 0
\(329\) −4.82702 −0.266122
\(330\) 0 0
\(331\) 29.7374 1.63452 0.817258 0.576271i \(-0.195493\pi\)
0.817258 + 0.576271i \(0.195493\pi\)
\(332\) 0 0
\(333\) 2.22044i 0.121679i
\(334\) 0 0
\(335\) 0.407096 5.92535i 0.0222420 0.323736i
\(336\) 0 0
\(337\) 7.88799i 0.429686i −0.976649 0.214843i \(-0.931076\pi\)
0.976649 0.214843i \(-0.0689241\pi\)
\(338\) 0 0
\(339\) −6.16289 −0.334722
\(340\) 0 0
\(341\) 12.4846 0.676078
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) −7.85850 0.539911i −0.423087 0.0290678i
\(346\) 0 0
\(347\) 3.28725i 0.176469i −0.996100 0.0882344i \(-0.971878\pi\)
0.996100 0.0882344i \(-0.0281225\pi\)
\(348\) 0 0
\(349\) 6.68073 0.357611 0.178806 0.983884i \(-0.442777\pi\)
0.178806 + 0.983884i \(0.442777\pi\)
\(350\) 0 0
\(351\) 22.8676 1.22058
\(352\) 0 0
\(353\) 26.3234i 1.40105i −0.713626 0.700527i \(-0.752948\pi\)
0.713626 0.700527i \(-0.247052\pi\)
\(354\) 0 0
\(355\) −1.68329 0.115649i −0.0893395 0.00613799i
\(356\) 0 0
\(357\) 5.55105i 0.293793i
\(358\) 0 0
\(359\) −8.27155 −0.436556 −0.218278 0.975887i \(-0.570044\pi\)
−0.218278 + 0.975887i \(0.570044\pi\)
\(360\) 0 0
\(361\) 22.7525 1.19750
\(362\) 0 0
\(363\) 15.4637i 0.811635i
\(364\) 0 0
\(365\) −0.925319 + 13.4682i −0.0484334 + 0.704957i
\(366\) 0 0
\(367\) 33.7548i 1.76198i −0.473130 0.880992i \(-0.656876\pi\)
0.473130 0.880992i \(-0.343124\pi\)
\(368\) 0 0
\(369\) −0.0430816 −0.00224274
\(370\) 0 0
\(371\) 10.0374 0.521114
\(372\) 0 0
\(373\) 28.0582i 1.45280i 0.687272 + 0.726400i \(0.258808\pi\)
−0.687272 + 0.726400i \(0.741192\pi\)
\(374\) 0 0
\(375\) −3.73439 + 17.8898i −0.192843 + 0.923826i
\(376\) 0 0
\(377\) 16.6667i 0.858377i
\(378\) 0 0
\(379\) −15.6585 −0.804322 −0.402161 0.915569i \(-0.631741\pi\)
−0.402161 + 0.915569i \(0.631741\pi\)
\(380\) 0 0
\(381\) −9.21744 −0.472224
\(382\) 0 0
\(383\) 18.6950i 0.955270i −0.878558 0.477635i \(-0.841494\pi\)
0.878558 0.477635i \(-0.158506\pi\)
\(384\) 0 0
\(385\) −0.190183 + 2.76815i −0.00969263 + 0.141078i
\(386\) 0 0
\(387\) 2.42937i 0.123492i
\(388\) 0 0
\(389\) 33.7798 1.71270 0.856352 0.516392i \(-0.172725\pi\)
0.856352 + 0.516392i \(0.172725\pi\)
\(390\) 0 0
\(391\) −7.31859 −0.370117
\(392\) 0 0
\(393\) 17.1932i 0.867284i
\(394\) 0 0
\(395\) 32.7152 + 2.24767i 1.64608 + 0.113092i
\(396\) 0 0
\(397\) 0.466183i 0.0233971i −0.999932 0.0116985i \(-0.996276\pi\)
0.999932 0.0116985i \(-0.00372384\pi\)
\(398\) 0 0
\(399\) 10.5622 0.528771
\(400\) 0 0
\(401\) 33.2221 1.65903 0.829516 0.558483i \(-0.188616\pi\)
0.829516 + 0.558483i \(0.188616\pi\)
\(402\) 0 0
\(403\) 42.2924i 2.10674i
\(404\) 0 0
\(405\) −17.6416 1.21205i −0.876617 0.0602271i
\(406\) 0 0
\(407\) 8.39841i 0.416294i
\(408\) 0 0
\(409\) 15.4588 0.764390 0.382195 0.924082i \(-0.375168\pi\)
0.382195 + 0.924082i \(0.375168\pi\)
\(410\) 0 0
\(411\) −11.3872 −0.561688
\(412\) 0 0
\(413\) 10.9864i 0.540608i
\(414\) 0 0
\(415\) 2.15817 31.4126i 0.105940 1.54198i
\(416\) 0 0
\(417\) 16.8787i 0.826551i
\(418\) 0 0
\(419\) −29.0268 −1.41805 −0.709025 0.705183i \(-0.750865\pi\)
−0.709025 + 0.705183i \(0.750865\pi\)
\(420\) 0 0
\(421\) 5.31745 0.259156 0.129578 0.991569i \(-0.458638\pi\)
0.129578 + 0.991569i \(0.458638\pi\)
\(422\) 0 0
\(423\) 1.58361i 0.0769977i
\(424\) 0 0
\(425\) −2.32220 + 16.8203i −0.112643 + 0.815902i
\(426\) 0 0
\(427\) 6.33030i 0.306345i
\(428\) 0 0
\(429\) 8.52620 0.411649
\(430\) 0 0
\(431\) 17.6480 0.850073 0.425036 0.905176i \(-0.360261\pi\)
0.425036 + 0.905176i \(0.360261\pi\)
\(432\) 0 0
\(433\) 18.5011i 0.889107i −0.895752 0.444554i \(-0.853362\pi\)
0.895752 0.444554i \(-0.146638\pi\)
\(434\) 0 0
\(435\) −0.993321 + 14.4580i −0.0476261 + 0.693207i
\(436\) 0 0
\(437\) 13.9254i 0.666140i
\(438\) 0 0
\(439\) 14.7444 0.703711 0.351855 0.936054i \(-0.385551\pi\)
0.351855 + 0.936054i \(0.385551\pi\)
\(440\) 0 0
\(441\) −0.328072 −0.0156225
\(442\) 0 0
\(443\) 18.0223i 0.856264i −0.903716 0.428132i \(-0.859172\pi\)
0.903716 0.428132i \(-0.140828\pi\)
\(444\) 0 0
\(445\) 28.2737 + 1.94252i 1.34030 + 0.0920842i
\(446\) 0 0
\(447\) 1.26498i 0.0598314i
\(448\) 0 0
\(449\) 2.46746 0.116447 0.0582233 0.998304i \(-0.481456\pi\)
0.0582233 + 0.998304i \(0.481456\pi\)
\(450\) 0 0
\(451\) −0.162948 −0.00767294
\(452\) 0 0
\(453\) 10.0464i 0.472020i
\(454\) 0 0
\(455\) 9.37731 + 0.644259i 0.439615 + 0.0302033i
\(456\) 0 0
\(457\) 1.73587i 0.0812004i 0.999175 + 0.0406002i \(0.0129270\pi\)
−0.999175 + 0.0406002i \(0.987073\pi\)
\(458\) 0 0
\(459\) −18.4743 −0.862306
\(460\) 0 0
\(461\) −9.00725 −0.419510 −0.209755 0.977754i \(-0.567267\pi\)
−0.209755 + 0.977754i \(0.567267\pi\)
\(462\) 0 0
\(463\) 39.1293i 1.81849i −0.416260 0.909246i \(-0.636659\pi\)
0.416260 0.909246i \(-0.363341\pi\)
\(464\) 0 0
\(465\) −2.52060 + 36.6878i −0.116890 + 1.70135i
\(466\) 0 0
\(467\) 6.47873i 0.299800i −0.988701 0.149900i \(-0.952105\pi\)
0.988701 0.149900i \(-0.0478952\pi\)
\(468\) 0 0
\(469\) 2.65614 0.122649
\(470\) 0 0
\(471\) 30.3089 1.39656
\(472\) 0 0
\(473\) 9.18864i 0.422494i
\(474\) 0 0
\(475\) −32.0045 4.41854i −1.46847 0.202736i
\(476\) 0 0
\(477\) 3.29298i 0.150775i
\(478\) 0 0
\(479\) −22.5651 −1.03103 −0.515514 0.856881i \(-0.672399\pi\)
−0.515514 + 0.856881i \(0.672399\pi\)
\(480\) 0 0
\(481\) 28.4502 1.29722
\(482\) 0 0
\(483\) 3.52271i 0.160289i
\(484\) 0 0
\(485\) 0.140118 2.03944i 0.00636242 0.0926061i
\(486\) 0 0
\(487\) 39.2500i 1.77859i −0.457339 0.889293i \(-0.651197\pi\)
0.457339 0.889293i \(-0.348803\pi\)
\(488\) 0 0
\(489\) 1.62386 0.0734336
\(490\) 0 0
\(491\) −33.7793 −1.52444 −0.762220 0.647318i \(-0.775891\pi\)
−0.762220 + 0.647318i \(0.775891\pi\)
\(492\) 0 0
\(493\) 13.4647i 0.606418i
\(494\) 0 0
\(495\) 0.908153 + 0.0623938i 0.0408184 + 0.00280439i
\(496\) 0 0
\(497\) 0.754563i 0.0338468i
\(498\) 0 0
\(499\) −11.6529 −0.521654 −0.260827 0.965386i \(-0.583995\pi\)
−0.260827 + 0.965386i \(0.583995\pi\)
\(500\) 0 0
\(501\) 5.26428 0.235191
\(502\) 0 0
\(503\) 15.0639i 0.671668i −0.941921 0.335834i \(-0.890982\pi\)
0.941921 0.335834i \(-0.109018\pi\)
\(504\) 0 0
\(505\) −30.0753 2.06629i −1.33833 0.0919488i
\(506\) 0 0
\(507\) 7.63329i 0.339006i
\(508\) 0 0
\(509\) −19.8458 −0.879649 −0.439825 0.898084i \(-0.644959\pi\)
−0.439825 + 0.898084i \(0.644959\pi\)
\(510\) 0 0
\(511\) −6.03736 −0.267077
\(512\) 0 0
\(513\) 35.1517i 1.55199i
\(514\) 0 0
\(515\) 0.0792139 1.15297i 0.00349058 0.0508061i
\(516\) 0 0
\(517\) 5.98971i 0.263427i
\(518\) 0 0
\(519\) 26.0208 1.14218
\(520\) 0 0
\(521\) −18.7964 −0.823484 −0.411742 0.911300i \(-0.635080\pi\)
−0.411742 + 0.911300i \(0.635080\pi\)
\(522\) 0 0
\(523\) 31.0907i 1.35950i −0.733444 0.679750i \(-0.762088\pi\)
0.733444 0.679750i \(-0.237912\pi\)
\(524\) 0 0
\(525\) −8.09622 1.11776i −0.353348 0.0487832i
\(526\) 0 0
\(527\) 34.1672i 1.48835i
\(528\) 0 0
\(529\) 18.3556 0.798070
\(530\) 0 0
\(531\) −3.60435 −0.156415
\(532\) 0 0
\(533\) 0.552000i 0.0239098i
\(534\) 0 0
\(535\) −2.88884 + 42.0476i −0.124895 + 1.81788i
\(536\) 0 0
\(537\) 16.0951i 0.694554i
\(538\) 0 0
\(539\) −1.24087 −0.0534482
\(540\) 0 0
\(541\) 35.8816 1.54267 0.771336 0.636428i \(-0.219589\pi\)
0.771336 + 0.636428i \(0.219589\pi\)
\(542\) 0 0
\(543\) 35.3993i 1.51913i
\(544\) 0 0
\(545\) 0.770232 + 0.0529181i 0.0329931 + 0.00226676i
\(546\) 0 0
\(547\) 25.4869i 1.08974i −0.838520 0.544871i \(-0.816579\pi\)
0.838520 0.544871i \(-0.183421\pi\)
\(548\) 0 0
\(549\) 2.07679 0.0886354
\(550\) 0 0
\(551\) −25.6197 −1.09144
\(552\) 0 0
\(553\) 14.6652i 0.623626i
\(554\) 0 0
\(555\) −24.6800 1.69561i −1.04761 0.0719748i
\(556\) 0 0
\(557\) 23.5917i 0.999612i −0.866137 0.499806i \(-0.833405\pi\)
0.866137 0.499806i \(-0.166595\pi\)
\(558\) 0 0
\(559\) 31.1272 1.31654
\(560\) 0 0
\(561\) −6.88814 −0.290818
\(562\) 0 0
\(563\) 1.25815i 0.0530245i −0.999648 0.0265123i \(-0.991560\pi\)
0.999648 0.0265123i \(-0.00844011\pi\)
\(564\) 0 0
\(565\) −0.577852 + 8.41074i −0.0243104 + 0.353842i
\(566\) 0 0
\(567\) 7.90815i 0.332111i
\(568\) 0 0
\(569\) −23.4899 −0.984747 −0.492373 0.870384i \(-0.663871\pi\)
−0.492373 + 0.870384i \(0.663871\pi\)
\(570\) 0 0
\(571\) −18.0476 −0.755269 −0.377634 0.925955i \(-0.623262\pi\)
−0.377634 + 0.925955i \(0.623262\pi\)
\(572\) 0 0
\(573\) 28.9647i 1.21002i
\(574\) 0 0
\(575\) −1.47368 + 10.6742i −0.0614565 + 0.445144i
\(576\) 0 0
\(577\) 45.4141i 1.89061i 0.326184 + 0.945306i \(0.394237\pi\)
−0.326184 + 0.945306i \(0.605763\pi\)
\(578\) 0 0
\(579\) −19.6541 −0.816796
\(580\) 0 0
\(581\) 14.0813 0.584189
\(582\) 0 0
\(583\) 12.4551i 0.515837i
\(584\) 0 0
\(585\) 0.211363 3.07643i 0.00873880 0.127195i
\(586\) 0 0
\(587\) 38.1946i 1.57646i 0.615381 + 0.788230i \(0.289002\pi\)
−0.615381 + 0.788230i \(0.710998\pi\)
\(588\) 0 0
\(589\) −65.0112 −2.67874
\(590\) 0 0
\(591\) 6.73569 0.277069
\(592\) 0 0
\(593\) 11.0544i 0.453952i 0.973900 + 0.226976i \(0.0728839\pi\)
−0.973900 + 0.226976i \(0.927116\pi\)
\(594\) 0 0
\(595\) −7.57574 0.520484i −0.310575 0.0213378i
\(596\) 0 0
\(597\) 16.1314i 0.660213i
\(598\) 0 0
\(599\) 10.4206 0.425773 0.212887 0.977077i \(-0.431714\pi\)
0.212887 + 0.977077i \(0.431714\pi\)
\(600\) 0 0
\(601\) −31.5047 −1.28510 −0.642552 0.766242i \(-0.722125\pi\)
−0.642552 + 0.766242i \(0.722125\pi\)
\(602\) 0 0
\(603\) 0.871407i 0.0354864i
\(604\) 0 0
\(605\) −21.1040 1.44993i −0.857999 0.0589480i
\(606\) 0 0
\(607\) 34.9493i 1.41855i −0.704932 0.709275i \(-0.749023\pi\)
0.704932 0.709275i \(-0.250977\pi\)
\(608\) 0 0
\(609\) −6.48105 −0.262625
\(610\) 0 0
\(611\) 20.2906 0.820869
\(612\) 0 0
\(613\) 37.9464i 1.53264i −0.642460 0.766319i \(-0.722086\pi\)
0.642460 0.766319i \(-0.277914\pi\)
\(614\) 0 0
\(615\) 0.0328988 0.478848i 0.00132661 0.0193090i
\(616\) 0 0
\(617\) 27.0081i 1.08731i −0.839310 0.543653i \(-0.817041\pi\)
0.839310 0.543653i \(-0.182959\pi\)
\(618\) 0 0
\(619\) 29.0656 1.16825 0.584123 0.811665i \(-0.301439\pi\)
0.584123 + 0.811665i \(0.301439\pi\)
\(620\) 0 0
\(621\) −11.7238 −0.470462
\(622\) 0 0
\(623\) 12.6742i 0.507781i
\(624\) 0 0
\(625\) 24.0648 + 6.77388i 0.962592 + 0.270955i
\(626\) 0 0
\(627\) 13.1063i 0.523416i
\(628\) 0 0
\(629\) −22.9844 −0.916447
\(630\) 0 0
\(631\) 38.8146 1.54518 0.772592 0.634903i \(-0.218960\pi\)
0.772592 + 0.634903i \(0.218960\pi\)
\(632\) 0 0
\(633\) 11.3290i 0.450289i
\(634\) 0 0
\(635\) −0.864257 + 12.5794i −0.0342970 + 0.499199i
\(636\) 0 0
\(637\) 4.20355i 0.166551i
\(638\) 0 0
\(639\) −0.247551 −0.00979297
\(640\) 0 0
\(641\) 40.2837 1.59111 0.795555 0.605881i \(-0.207179\pi\)
0.795555 + 0.605881i \(0.207179\pi\)
\(642\) 0 0
\(643\) 2.02226i 0.0797500i −0.999205 0.0398750i \(-0.987304\pi\)
0.999205 0.0398750i \(-0.0126960\pi\)
\(644\) 0 0
\(645\) −27.0022 1.85516i −1.06321 0.0730468i
\(646\) 0 0
\(647\) 8.08779i 0.317964i 0.987281 + 0.158982i \(0.0508212\pi\)
−0.987281 + 0.158982i \(0.949179\pi\)
\(648\) 0 0
\(649\) −13.6328 −0.535133
\(650\) 0 0
\(651\) −16.4459 −0.644568
\(652\) 0 0
\(653\) 25.0259i 0.979338i 0.871908 + 0.489669i \(0.162882\pi\)
−0.871908 + 0.489669i \(0.837118\pi\)
\(654\) 0 0
\(655\) 23.4643 + 1.61209i 0.916826 + 0.0629896i
\(656\) 0 0
\(657\) 1.98069i 0.0772740i
\(658\) 0 0
\(659\) 35.1054 1.36751 0.683756 0.729711i \(-0.260345\pi\)
0.683756 + 0.729711i \(0.260345\pi\)
\(660\) 0 0
\(661\) 7.69197 0.299183 0.149592 0.988748i \(-0.452204\pi\)
0.149592 + 0.988748i \(0.452204\pi\)
\(662\) 0 0
\(663\) 23.3341i 0.906221i
\(664\) 0 0
\(665\) 0.990344 14.4146i 0.0384039 0.558976i
\(666\) 0 0
\(667\) 8.54471i 0.330853i
\(668\) 0 0
\(669\) 37.6981 1.45749
\(670\) 0 0
\(671\) 7.85510 0.303243
\(672\) 0 0
\(673\) 4.07019i 0.156894i 0.996918 + 0.0784472i \(0.0249962\pi\)
−0.996918 + 0.0784472i \(0.975004\pi\)
\(674\) 0 0
\(675\) −3.71999 + 26.9448i −0.143183 + 1.03711i
\(676\) 0 0
\(677\) 32.6451i 1.25465i −0.778756 0.627327i \(-0.784149\pi\)
0.778756 0.627327i \(-0.215851\pi\)
\(678\) 0 0
\(679\) 0.914215 0.0350843
\(680\) 0 0
\(681\) 4.67616 0.179191
\(682\) 0 0
\(683\) 35.7284i 1.36711i 0.729900 + 0.683554i \(0.239567\pi\)
−0.729900 + 0.683554i \(0.760433\pi\)
\(684\) 0 0
\(685\) −1.06770 + 15.5405i −0.0407946 + 0.593773i
\(686\) 0 0
\(687\) 30.2773i 1.15515i
\(688\) 0 0
\(689\) −42.1925 −1.60741
\(690\) 0 0
\(691\) 27.9663 1.06389 0.531945 0.846779i \(-0.321461\pi\)
0.531945 + 0.846779i \(0.321461\pi\)
\(692\) 0 0
\(693\) 0.407096i 0.0154643i
\(694\) 0 0
\(695\) −23.0350 1.58260i −0.873767 0.0600313i
\(696\) 0 0
\(697\) 0.445949i 0.0168915i
\(698\) 0 0
\(699\) 37.7777 1.42888
\(700\) 0 0
\(701\) 19.7996 0.747822 0.373911 0.927465i \(-0.378017\pi\)
0.373911 + 0.927465i \(0.378017\pi\)
\(702\) 0 0
\(703\) 43.7332i 1.64943i
\(704\) 0 0
\(705\) −17.6017 1.20930i −0.662917 0.0455451i
\(706\) 0 0
\(707\) 13.4818i 0.507034i
\(708\) 0 0
\(709\) 8.46892 0.318057 0.159029 0.987274i \(-0.449164\pi\)
0.159029 + 0.987274i \(0.449164\pi\)
\(710\) 0 0
\(711\) 4.81123 0.180435
\(712\) 0 0
\(713\) 21.6826i 0.812020i
\(714\) 0 0
\(715\) 0.799444 11.6360i 0.0298975 0.435164i
\(716\) 0 0
\(717\) 14.7322i 0.550183i
\(718\) 0 0
\(719\) −11.2512 −0.419598 −0.209799 0.977745i \(-0.567281\pi\)
−0.209799 + 0.977745i \(0.567281\pi\)
\(720\) 0 0
\(721\) 0.516841 0.0192482
\(722\) 0 0
\(723\) 20.3369i 0.756338i
\(724\) 0 0
\(725\) 19.6382 + 2.71125i 0.729346 + 0.100693i
\(726\) 0 0
\(727\) 26.2716i 0.974360i 0.873302 + 0.487180i \(0.161974\pi\)
−0.873302 + 0.487180i \(0.838026\pi\)
\(728\) 0 0
\(729\) −29.2716 −1.08413
\(730\) 0 0
\(731\) −25.1470 −0.930096
\(732\) 0 0
\(733\) 48.7804i 1.80175i 0.434082 + 0.900873i \(0.357073\pi\)
−0.434082 + 0.900873i \(0.642927\pi\)
\(734\) 0 0
\(735\) 0.250528 3.64649i 0.00924088 0.134503i
\(736\) 0 0
\(737\) 3.29594i 0.121407i
\(738\) 0 0
\(739\) −37.5871 −1.38267 −0.691333 0.722537i \(-0.742976\pi\)
−0.691333 + 0.722537i \(0.742976\pi\)
\(740\) 0 0
\(741\) −44.3986 −1.63102
\(742\) 0 0
\(743\) 29.2572i 1.07334i −0.843792 0.536671i \(-0.819682\pi\)
0.843792 0.536671i \(-0.180318\pi\)
\(744\) 0 0
\(745\) −1.72637 0.118608i −0.0632492 0.00434548i
\(746\) 0 0
\(747\) 4.61967i 0.169025i
\(748\) 0 0
\(749\) −18.8486 −0.688712
\(750\) 0 0
\(751\) −41.4125 −1.51116 −0.755582 0.655054i \(-0.772646\pi\)
−0.755582 + 0.655054i \(0.772646\pi\)
\(752\) 0 0
\(753\) 34.9780i 1.27467i
\(754\) 0 0
\(755\) −13.7107 0.941980i −0.498983 0.0342822i
\(756\) 0 0
\(757\) 33.1411i 1.20453i 0.798295 + 0.602266i \(0.205736\pi\)
−0.798295 + 0.602266i \(0.794264\pi\)
\(758\) 0 0
\(759\) −4.37124 −0.158666
\(760\) 0 0
\(761\) 7.08166 0.256710 0.128355 0.991728i \(-0.459030\pi\)
0.128355 + 0.991728i \(0.459030\pi\)
\(762\) 0 0
\(763\) 0.345270i 0.0124996i
\(764\) 0 0
\(765\) −0.170756 + 2.48539i −0.00617370 + 0.0898594i
\(766\) 0 0
\(767\) 46.1820i 1.66754i
\(768\) 0 0
\(769\) −20.8844 −0.753112 −0.376556 0.926394i \(-0.622892\pi\)
−0.376556 + 0.926394i \(0.622892\pi\)
\(770\) 0 0
\(771\) −45.0720 −1.62323
\(772\) 0 0
\(773\) 50.0409i 1.79985i 0.436049 + 0.899923i \(0.356377\pi\)
−0.436049 + 0.899923i \(0.643623\pi\)
\(774\) 0 0
\(775\) 49.8329 + 6.87993i 1.79005 + 0.247134i
\(776\) 0 0
\(777\) 11.0632i 0.396892i
\(778\) 0 0
\(779\) 0.848524 0.0304015
\(780\) 0 0
\(781\) −0.936316 −0.0335040
\(782\) 0 0
\(783\) 21.5694i 0.770827i
\(784\) 0 0
\(785\) 2.84186 41.3638i 0.101430 1.47634i
\(786\) 0 0
\(787\) 23.0831i 0.822824i −0.911449 0.411412i \(-0.865036\pi\)
0.911449 0.411412i \(-0.134964\pi\)
\(788\) 0 0
\(789\) 11.0726 0.394195
\(790\) 0 0
\(791\) −3.77026 −0.134055
\(792\) 0 0
\(793\) 26.6097i 0.944939i
\(794\) 0 0
\(795\) 36.6011 + 2.51464i 1.29811 + 0.0891852i
\(796\) 0 0
\(797\) 0.553975i 0.0196228i −0.999952 0.00981140i \(-0.996877\pi\)
0.999952 0.00981140i \(-0.00312312\pi\)
\(798\) 0 0
\(799\) −16.3923 −0.579920
\(800\) 0 0
\(801\) 4.15805 0.146917
\(802\) 0 0