Properties

Label 1520.2.d.j.609.6
Level $1520$
Weight $2$
Character 1520.609
Analytic conductor $12.137$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5161984.1
Defining polynomial: \(x^{6} - 4 x^{3} + 25 x^{2} - 20 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 609.6
Root \(0.432320 - 0.432320i\) of defining polynomial
Character \(\chi\) \(=\) 1520.609
Dual form 1520.2.d.j.609.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.76156i q^{3} +(-2.19388 - 0.432320i) q^{5} +0.761557i q^{7} -4.62620 q^{9} +O(q^{10})\) \(q+2.76156i q^{3} +(-2.19388 - 0.432320i) q^{5} +0.761557i q^{7} -4.62620 q^{9} +0.864641 q^{11} -5.62620i q^{13} +(1.19388 - 6.05852i) q^{15} -3.62620i q^{17} +1.00000 q^{19} -2.10308 q^{21} -8.01395i q^{23} +(4.62620 + 1.89692i) q^{25} -4.49084i q^{27} +7.35548 q^{29} -8.11704 q^{31} +2.38776i q^{33} +(0.329237 - 1.67076i) q^{35} +0.476886i q^{37} +15.5371 q^{39} -2.65847 q^{41} +6.86464i q^{43} +(10.1493 + 2.00000i) q^{45} -1.25240i q^{47} +6.42003 q^{49} +10.0140 q^{51} -2.37380i q^{53} +(-1.89692 - 0.373802i) q^{55} +2.76156i q^{57} +4.49084 q^{59} -10.8646 q^{61} -3.52311i q^{63} +(-2.43232 + 12.3432i) q^{65} -1.03228i q^{67} +22.1310 q^{69} +10.1816 q^{71} -16.4017i q^{73} +(-5.23844 + 12.7755i) q^{75} +0.658473i q^{77} -12.5693 q^{79} -1.47689 q^{81} -0.270718i q^{83} +(-1.56768 + 7.95543i) q^{85} +20.3126i q^{87} -0.387755 q^{89} +4.28467 q^{91} -22.4157i q^{93} +(-2.19388 - 0.432320i) q^{95} -8.50479i q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{5} - 10q^{9} + O(q^{10}) \) \( 6q + 2q^{5} - 10q^{9} - 8q^{15} + 6q^{19} - 20q^{21} + 10q^{25} + 16q^{29} - 8q^{31} - 8q^{35} + 20q^{39} + 4q^{41} + 18q^{45} + 6q^{49} + 12q^{51} - 4q^{55} + 4q^{59} - 60q^{61} - 12q^{65} + 44q^{69} + 16q^{71} - 44q^{75} - 34q^{81} - 12q^{85} + 28q^{89} - 12q^{91} + 2q^{95} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 2.76156i 1.59439i 0.603725 + 0.797193i \(0.293683\pi\)
−0.603725 + 0.797193i \(0.706317\pi\)
\(4\) 0 0
\(5\) −2.19388 0.432320i −0.981132 0.193340i
\(6\) 0 0
\(7\) 0.761557i 0.287842i 0.989589 + 0.143921i \(0.0459710\pi\)
−0.989589 + 0.143921i \(0.954029\pi\)
\(8\) 0 0
\(9\) −4.62620 −1.54207
\(10\) 0 0
\(11\) 0.864641 0.260699 0.130350 0.991468i \(-0.458390\pi\)
0.130350 + 0.991468i \(0.458390\pi\)
\(12\) 0 0
\(13\) 5.62620i 1.56043i −0.625514 0.780213i \(-0.715111\pi\)
0.625514 0.780213i \(-0.284889\pi\)
\(14\) 0 0
\(15\) 1.19388 6.05852i 0.308258 1.56430i
\(16\) 0 0
\(17\) 3.62620i 0.879482i −0.898125 0.439741i \(-0.855070\pi\)
0.898125 0.439741i \(-0.144930\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −2.10308 −0.458930
\(22\) 0 0
\(23\) 8.01395i 1.67102i −0.549472 0.835512i \(-0.685171\pi\)
0.549472 0.835512i \(-0.314829\pi\)
\(24\) 0 0
\(25\) 4.62620 + 1.89692i 0.925240 + 0.379383i
\(26\) 0 0
\(27\) 4.49084i 0.864262i
\(28\) 0 0
\(29\) 7.35548 1.36588 0.682939 0.730475i \(-0.260701\pi\)
0.682939 + 0.730475i \(0.260701\pi\)
\(30\) 0 0
\(31\) −8.11704 −1.45786 −0.728931 0.684587i \(-0.759983\pi\)
−0.728931 + 0.684587i \(0.759983\pi\)
\(32\) 0 0
\(33\) 2.38776i 0.415655i
\(34\) 0 0
\(35\) 0.329237 1.67076i 0.0556512 0.282411i
\(36\) 0 0
\(37\) 0.476886i 0.0783995i 0.999231 + 0.0391998i \(0.0124809\pi\)
−0.999231 + 0.0391998i \(0.987519\pi\)
\(38\) 0 0
\(39\) 15.5371 2.48792
\(40\) 0 0
\(41\) −2.65847 −0.415184 −0.207592 0.978216i \(-0.566563\pi\)
−0.207592 + 0.978216i \(0.566563\pi\)
\(42\) 0 0
\(43\) 6.86464i 1.04685i 0.852072 + 0.523424i \(0.175346\pi\)
−0.852072 + 0.523424i \(0.824654\pi\)
\(44\) 0 0
\(45\) 10.1493 + 2.00000i 1.51297 + 0.298142i
\(46\) 0 0
\(47\) 1.25240i 0.182681i −0.995820 0.0913404i \(-0.970885\pi\)
0.995820 0.0913404i \(-0.0291151\pi\)
\(48\) 0 0
\(49\) 6.42003 0.917147
\(50\) 0 0
\(51\) 10.0140 1.40223
\(52\) 0 0
\(53\) 2.37380i 0.326067i −0.986621 0.163033i \(-0.947872\pi\)
0.986621 0.163033i \(-0.0521278\pi\)
\(54\) 0 0
\(55\) −1.89692 0.373802i −0.255780 0.0504034i
\(56\) 0 0
\(57\) 2.76156i 0.365777i
\(58\) 0 0
\(59\) 4.49084 0.584657 0.292329 0.956318i \(-0.405570\pi\)
0.292329 + 0.956318i \(0.405570\pi\)
\(60\) 0 0
\(61\) −10.8646 −1.39107 −0.695537 0.718490i \(-0.744834\pi\)
−0.695537 + 0.718490i \(0.744834\pi\)
\(62\) 0 0
\(63\) 3.52311i 0.443871i
\(64\) 0 0
\(65\) −2.43232 + 12.3432i −0.301692 + 1.53098i
\(66\) 0 0
\(67\) 1.03228i 0.126113i −0.998010 0.0630563i \(-0.979915\pi\)
0.998010 0.0630563i \(-0.0200848\pi\)
\(68\) 0 0
\(69\) 22.1310 2.66426
\(70\) 0 0
\(71\) 10.1816 1.20833 0.604166 0.796858i \(-0.293506\pi\)
0.604166 + 0.796858i \(0.293506\pi\)
\(72\) 0 0
\(73\) 16.4017i 1.91967i −0.280557 0.959837i \(-0.590519\pi\)
0.280557 0.959837i \(-0.409481\pi\)
\(74\) 0 0
\(75\) −5.23844 + 12.7755i −0.604883 + 1.47519i
\(76\) 0 0
\(77\) 0.658473i 0.0750400i
\(78\) 0 0
\(79\) −12.5693 −1.41416 −0.707081 0.707133i \(-0.749988\pi\)
−0.707081 + 0.707133i \(0.749988\pi\)
\(80\) 0 0
\(81\) −1.47689 −0.164098
\(82\) 0 0
\(83\) 0.270718i 0.0297152i −0.999890 0.0148576i \(-0.995271\pi\)
0.999890 0.0148576i \(-0.00472949\pi\)
\(84\) 0 0
\(85\) −1.56768 + 7.95543i −0.170039 + 0.862888i
\(86\) 0 0
\(87\) 20.3126i 2.17774i
\(88\) 0 0
\(89\) −0.387755 −0.0411020 −0.0205510 0.999789i \(-0.506542\pi\)
−0.0205510 + 0.999789i \(0.506542\pi\)
\(90\) 0 0
\(91\) 4.28467 0.449156
\(92\) 0 0
\(93\) 22.4157i 2.32440i
\(94\) 0 0
\(95\) −2.19388 0.432320i −0.225087 0.0443551i
\(96\) 0 0
\(97\) 8.50479i 0.863531i −0.901986 0.431765i \(-0.857891\pi\)
0.901986 0.431765i \(-0.142109\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 0 0
\(101\) 16.4157 1.63342 0.816710 0.577049i \(-0.195796\pi\)
0.816710 + 0.577049i \(0.195796\pi\)
\(102\) 0 0
\(103\) 9.64015i 0.949872i −0.880020 0.474936i \(-0.842471\pi\)
0.880020 0.474936i \(-0.157529\pi\)
\(104\) 0 0
\(105\) 4.61391 + 0.909206i 0.450271 + 0.0887294i
\(106\) 0 0
\(107\) 4.28467i 0.414215i −0.978318 0.207107i \(-0.933595\pi\)
0.978318 0.207107i \(-0.0664050\pi\)
\(108\) 0 0
\(109\) 13.4200 1.28541 0.642703 0.766116i \(-0.277813\pi\)
0.642703 + 0.766116i \(0.277813\pi\)
\(110\) 0 0
\(111\) −1.31695 −0.124999
\(112\) 0 0
\(113\) 10.3232i 0.971125i 0.874202 + 0.485563i \(0.161385\pi\)
−0.874202 + 0.485563i \(0.838615\pi\)
\(114\) 0 0
\(115\) −3.46460 + 17.5816i −0.323075 + 1.63950i
\(116\) 0 0
\(117\) 26.0279i 2.40628i
\(118\) 0 0
\(119\) 2.76156 0.253152
\(120\) 0 0
\(121\) −10.2524 −0.932036
\(122\) 0 0
\(123\) 7.34153i 0.661963i
\(124\) 0 0
\(125\) −9.32924 6.16160i −0.834432 0.551110i
\(126\) 0 0
\(127\) 16.9817i 1.50688i −0.657517 0.753440i \(-0.728393\pi\)
0.657517 0.753440i \(-0.271607\pi\)
\(128\) 0 0
\(129\) −18.9571 −1.66908
\(130\) 0 0
\(131\) −0.541436 −0.0473055 −0.0236528 0.999720i \(-0.507530\pi\)
−0.0236528 + 0.999720i \(0.507530\pi\)
\(132\) 0 0
\(133\) 0.761557i 0.0660354i
\(134\) 0 0
\(135\) −1.94148 + 9.85235i −0.167096 + 0.847955i
\(136\) 0 0
\(137\) 2.87859i 0.245935i 0.992411 + 0.122967i \(0.0392411\pi\)
−0.992411 + 0.122967i \(0.960759\pi\)
\(138\) 0 0
\(139\) 3.58767 0.304302 0.152151 0.988357i \(-0.451380\pi\)
0.152151 + 0.988357i \(0.451380\pi\)
\(140\) 0 0
\(141\) 3.45856 0.291264
\(142\) 0 0
\(143\) 4.86464i 0.406802i
\(144\) 0 0
\(145\) −16.1370 3.17992i −1.34011 0.264078i
\(146\) 0 0
\(147\) 17.7293i 1.46229i
\(148\) 0 0
\(149\) 16.8401 1.37959 0.689796 0.724004i \(-0.257700\pi\)
0.689796 + 0.724004i \(0.257700\pi\)
\(150\) 0 0
\(151\) 16.9817 1.38195 0.690975 0.722879i \(-0.257182\pi\)
0.690975 + 0.722879i \(0.257182\pi\)
\(152\) 0 0
\(153\) 16.7755i 1.35622i
\(154\) 0 0
\(155\) 17.8078 + 3.50916i 1.43036 + 0.281863i
\(156\) 0 0
\(157\) 14.8401i 1.18437i 0.805804 + 0.592183i \(0.201734\pi\)
−0.805804 + 0.592183i \(0.798266\pi\)
\(158\) 0 0
\(159\) 6.55539 0.519876
\(160\) 0 0
\(161\) 6.10308 0.480990
\(162\) 0 0
\(163\) 13.3694i 1.04717i 0.851972 + 0.523587i \(0.175407\pi\)
−0.851972 + 0.523587i \(0.824593\pi\)
\(164\) 0 0
\(165\) 1.03228 5.23844i 0.0803625 0.407812i
\(166\) 0 0
\(167\) 9.84632i 0.761931i −0.924589 0.380966i \(-0.875592\pi\)
0.924589 0.380966i \(-0.124408\pi\)
\(168\) 0 0
\(169\) −18.6541 −1.43493
\(170\) 0 0
\(171\) −4.62620 −0.353774
\(172\) 0 0
\(173\) 2.98168i 0.226693i −0.993556 0.113346i \(-0.963843\pi\)
0.993556 0.113346i \(-0.0361570\pi\)
\(174\) 0 0
\(175\) −1.44461 + 3.52311i −0.109202 + 0.266322i
\(176\) 0 0
\(177\) 12.4017i 0.932169i
\(178\) 0 0
\(179\) 11.7938 0.881512 0.440756 0.897627i \(-0.354710\pi\)
0.440756 + 0.897627i \(0.354710\pi\)
\(180\) 0 0
\(181\) 14.5693 1.08293 0.541465 0.840723i \(-0.317870\pi\)
0.541465 + 0.840723i \(0.317870\pi\)
\(182\) 0 0
\(183\) 30.0033i 2.21791i
\(184\) 0 0
\(185\) 0.206167 1.04623i 0.0151577 0.0769203i
\(186\) 0 0
\(187\) 3.13536i 0.229280i
\(188\) 0 0
\(189\) 3.42003 0.248771
\(190\) 0 0
\(191\) −13.2384 −0.957900 −0.478950 0.877842i \(-0.658983\pi\)
−0.478950 + 0.877842i \(0.658983\pi\)
\(192\) 0 0
\(193\) 2.54144i 0.182937i −0.995808 0.0914683i \(-0.970844\pi\)
0.995808 0.0914683i \(-0.0291560\pi\)
\(194\) 0 0
\(195\) −34.0864 6.71699i −2.44098 0.481014i
\(196\) 0 0
\(197\) 19.9109i 1.41859i −0.704911 0.709295i \(-0.749013\pi\)
0.704911 0.709295i \(-0.250987\pi\)
\(198\) 0 0
\(199\) −20.3126 −1.43992 −0.719960 0.694015i \(-0.755840\pi\)
−0.719960 + 0.694015i \(0.755840\pi\)
\(200\) 0 0
\(201\) 2.85069 0.201072
\(202\) 0 0
\(203\) 5.60162i 0.393157i
\(204\) 0 0
\(205\) 5.83237 + 1.14931i 0.407350 + 0.0802715i
\(206\) 0 0
\(207\) 37.0741i 2.57683i
\(208\) 0 0
\(209\) 0.864641 0.0598085
\(210\) 0 0
\(211\) −18.0419 −1.24205 −0.621026 0.783790i \(-0.713284\pi\)
−0.621026 + 0.783790i \(0.713284\pi\)
\(212\) 0 0
\(213\) 28.1170i 1.92655i
\(214\) 0 0
\(215\) 2.96772 15.0602i 0.202397 1.02710i
\(216\) 0 0
\(217\) 6.18159i 0.419634i
\(218\) 0 0
\(219\) 45.2943 3.06070
\(220\) 0 0
\(221\) −20.4017 −1.37237
\(222\) 0 0
\(223\) 13.5231i 0.905575i −0.891619 0.452787i \(-0.850430\pi\)
0.891619 0.452787i \(-0.149570\pi\)
\(224\) 0 0
\(225\) −21.4017 8.77551i −1.42678 0.585034i
\(226\) 0 0
\(227\) 13.6016i 0.902771i −0.892329 0.451386i \(-0.850930\pi\)
0.892329 0.451386i \(-0.149070\pi\)
\(228\) 0 0
\(229\) −13.5877 −0.897898 −0.448949 0.893557i \(-0.648202\pi\)
−0.448949 + 0.893557i \(0.648202\pi\)
\(230\) 0 0
\(231\) −1.81841 −0.119643
\(232\) 0 0
\(233\) 25.5510i 1.67390i −0.547277 0.836952i \(-0.684336\pi\)
0.547277 0.836952i \(-0.315664\pi\)
\(234\) 0 0
\(235\) −0.541436 + 2.74760i −0.0353194 + 0.179234i
\(236\) 0 0
\(237\) 34.7110i 2.25472i
\(238\) 0 0
\(239\) −11.3309 −0.732935 −0.366468 0.930431i \(-0.619433\pi\)
−0.366468 + 0.930431i \(0.619433\pi\)
\(240\) 0 0
\(241\) −1.25240 −0.0806739 −0.0403370 0.999186i \(-0.512843\pi\)
−0.0403370 + 0.999186i \(0.512843\pi\)
\(242\) 0 0
\(243\) 17.5510i 1.12590i
\(244\) 0 0
\(245\) −14.0848 2.77551i −0.899842 0.177321i
\(246\) 0 0
\(247\) 5.62620i 0.357986i
\(248\) 0 0
\(249\) 0.747604 0.0473775
\(250\) 0 0
\(251\) −10.5939 −0.668682 −0.334341 0.942452i \(-0.608514\pi\)
−0.334341 + 0.942452i \(0.608514\pi\)
\(252\) 0 0
\(253\) 6.92919i 0.435635i
\(254\) 0 0
\(255\) −21.9694 4.32924i −1.37578 0.271107i
\(256\) 0 0
\(257\) 0.153681i 0.00958637i −0.999989 0.00479319i \(-0.998474\pi\)
0.999989 0.00479319i \(-0.00152572\pi\)
\(258\) 0 0
\(259\) −0.363176 −0.0225666
\(260\) 0 0
\(261\) −34.0279 −2.10627
\(262\) 0 0
\(263\) 0.504792i 0.0311268i 0.999879 + 0.0155634i \(0.00495419\pi\)
−0.999879 + 0.0155634i \(0.995046\pi\)
\(264\) 0 0
\(265\) −1.02624 + 5.20783i −0.0630416 + 0.319915i
\(266\) 0 0
\(267\) 1.07081i 0.0655324i
\(268\) 0 0
\(269\) 3.49521 0.213107 0.106553 0.994307i \(-0.466019\pi\)
0.106553 + 0.994307i \(0.466019\pi\)
\(270\) 0 0
\(271\) −5.47252 −0.332432 −0.166216 0.986089i \(-0.553155\pi\)
−0.166216 + 0.986089i \(0.553155\pi\)
\(272\) 0 0
\(273\) 11.8324i 0.716127i
\(274\) 0 0
\(275\) 4.00000 + 1.64015i 0.241209 + 0.0989049i
\(276\) 0 0
\(277\) 12.9538i 0.778317i 0.921171 + 0.389158i \(0.127234\pi\)
−0.921171 + 0.389158i \(0.872766\pi\)
\(278\) 0 0
\(279\) 37.5510 2.24812
\(280\) 0 0
\(281\) 0.153681 0.00916785 0.00458393 0.999989i \(-0.498541\pi\)
0.00458393 + 0.999989i \(0.498541\pi\)
\(282\) 0 0
\(283\) 18.2341i 1.08390i −0.840410 0.541952i \(-0.817686\pi\)
0.840410 0.541952i \(-0.182314\pi\)
\(284\) 0 0
\(285\) 1.19388 6.05852i 0.0707192 0.358876i
\(286\) 0 0
\(287\) 2.02458i 0.119507i
\(288\) 0 0
\(289\) 3.85069 0.226511
\(290\) 0 0
\(291\) 23.4865 1.37680
\(292\) 0 0
\(293\) 2.03853i 0.119092i −0.998226 0.0595462i \(-0.981035\pi\)
0.998226 0.0595462i \(-0.0189654\pi\)
\(294\) 0 0
\(295\) −9.85235 1.94148i −0.573626 0.113037i
\(296\) 0 0
\(297\) 3.88296i 0.225312i
\(298\) 0 0
\(299\) −45.0881 −2.60751
\(300\) 0 0
\(301\) −5.22782 −0.301326
\(302\) 0 0
\(303\) 45.3328i 2.60430i
\(304\) 0 0
\(305\) 23.8357 + 4.69701i 1.36483 + 0.268950i
\(306\) 0 0
\(307\) 16.5414i 0.944070i −0.881580 0.472035i \(-0.843520\pi\)
0.881580 0.472035i \(-0.156480\pi\)
\(308\) 0 0
\(309\) 26.6218 1.51446
\(310\) 0 0
\(311\) 21.4725 1.21759 0.608797 0.793326i \(-0.291652\pi\)
0.608797 + 0.793326i \(0.291652\pi\)
\(312\) 0 0
\(313\) 1.12141i 0.0633856i 0.999498 + 0.0316928i \(0.0100898\pi\)
−0.999498 + 0.0316928i \(0.989910\pi\)
\(314\) 0 0
\(315\) −1.52311 + 7.72928i −0.0858178 + 0.435496i
\(316\) 0 0
\(317\) 29.8882i 1.67869i −0.543601 0.839344i \(-0.682940\pi\)
0.543601 0.839344i \(-0.317060\pi\)
\(318\) 0 0
\(319\) 6.35985 0.356083
\(320\) 0 0
\(321\) 11.8324 0.660418
\(322\) 0 0
\(323\) 3.62620i 0.201767i
\(324\) 0 0
\(325\) 10.6724 26.0279i 0.592000 1.44377i
\(326\) 0 0
\(327\) 37.0602i 2.04943i
\(328\) 0 0
\(329\) 0.953771 0.0525831
\(330\) 0 0
\(331\) −32.3126 −1.77606 −0.888030 0.459786i \(-0.847926\pi\)
−0.888030 + 0.459786i \(0.847926\pi\)
\(332\) 0 0
\(333\) 2.20617i 0.120897i
\(334\) 0 0
\(335\) −0.446274 + 2.26469i −0.0243825 + 0.123733i
\(336\) 0 0
\(337\) 26.3511i 1.43544i 0.696334 + 0.717718i \(0.254813\pi\)
−0.696334 + 0.717718i \(0.745187\pi\)
\(338\) 0 0
\(339\) −28.5081 −1.54835
\(340\) 0 0
\(341\) −7.01832 −0.380063
\(342\) 0 0
\(343\) 10.2201i 0.551835i
\(344\) 0 0
\(345\) −48.5527 9.56768i −2.61399 0.515107i
\(346\) 0 0
\(347\) 2.77551i 0.148997i 0.997221 + 0.0744986i \(0.0237356\pi\)
−0.997221 + 0.0744986i \(0.976264\pi\)
\(348\) 0 0
\(349\) −11.5510 −0.618312 −0.309156 0.951011i \(-0.600047\pi\)
−0.309156 + 0.951011i \(0.600047\pi\)
\(350\) 0 0
\(351\) −25.2663 −1.34862
\(352\) 0 0
\(353\) 8.40171i 0.447178i 0.974684 + 0.223589i \(0.0717773\pi\)
−0.974684 + 0.223589i \(0.928223\pi\)
\(354\) 0 0
\(355\) −22.3372 4.40171i −1.18553 0.233618i
\(356\) 0 0
\(357\) 7.62620i 0.403621i
\(358\) 0 0
\(359\) 22.7895 1.20278 0.601391 0.798955i \(-0.294613\pi\)
0.601391 + 0.798955i \(0.294613\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 28.3126i 1.48602i
\(364\) 0 0
\(365\) −7.09079 + 35.9833i −0.371149 + 1.88345i
\(366\) 0 0
\(367\) 4.06455i 0.212168i −0.994357 0.106084i \(-0.966169\pi\)
0.994357 0.106084i \(-0.0338312\pi\)
\(368\) 0 0
\(369\) 12.2986 0.640241
\(370\) 0 0
\(371\) 1.80779 0.0938556
\(372\) 0 0
\(373\) 18.4017i 0.952804i 0.879227 + 0.476402i \(0.158059\pi\)
−0.879227 + 0.476402i \(0.841941\pi\)
\(374\) 0 0
\(375\) 17.0156 25.7632i 0.878683 1.33041i
\(376\) 0 0
\(377\) 41.3834i 2.13135i
\(378\) 0 0
\(379\) 1.23844 0.0636145 0.0318073 0.999494i \(-0.489874\pi\)
0.0318073 + 0.999494i \(0.489874\pi\)
\(380\) 0 0
\(381\) 46.8959 2.40255
\(382\) 0 0
\(383\) 16.8646i 0.861743i 0.902413 + 0.430871i \(0.141794\pi\)
−0.902413 + 0.430871i \(0.858206\pi\)
\(384\) 0 0
\(385\) 0.284672 1.44461i 0.0145082 0.0736242i
\(386\) 0 0
\(387\) 31.7572i 1.61431i
\(388\) 0 0
\(389\) −8.59392 −0.435729 −0.217865 0.975979i \(-0.569909\pi\)
−0.217865 + 0.975979i \(0.569909\pi\)
\(390\) 0 0
\(391\) −29.0602 −1.46964
\(392\) 0 0
\(393\) 1.49521i 0.0754233i
\(394\) 0 0
\(395\) 27.5756 + 5.43398i 1.38748 + 0.273413i
\(396\) 0 0
\(397\) 16.0558i 0.805818i 0.915240 + 0.402909i \(0.132001\pi\)
−0.915240 + 0.402909i \(0.867999\pi\)
\(398\) 0 0
\(399\) −2.10308 −0.105286
\(400\) 0 0
\(401\) −14.8925 −0.743698 −0.371849 0.928293i \(-0.621276\pi\)
−0.371849 + 0.928293i \(0.621276\pi\)
\(402\) 0 0
\(403\) 45.6681i 2.27489i
\(404\) 0 0
\(405\) 3.24011 + 0.638488i 0.161002 + 0.0317267i
\(406\) 0 0
\(407\) 0.412335i 0.0204387i
\(408\) 0 0
\(409\) 18.3511 0.907404 0.453702 0.891153i \(-0.350103\pi\)
0.453702 + 0.891153i \(0.350103\pi\)
\(410\) 0 0
\(411\) −7.94940 −0.392115
\(412\) 0 0
\(413\) 3.42003i 0.168289i
\(414\) 0 0
\(415\) −0.117037 + 0.593923i −0.00574512 + 0.0291545i
\(416\) 0 0
\(417\) 9.90754i 0.485174i
\(418\) 0 0
\(419\) 34.7509 1.69769 0.848847 0.528639i \(-0.177297\pi\)
0.848847 + 0.528639i \(0.177297\pi\)
\(420\) 0 0
\(421\) −40.1589 −1.95722 −0.978612 0.205713i \(-0.934049\pi\)
−0.978612 + 0.205713i \(0.934049\pi\)
\(422\) 0 0
\(423\) 5.79383i 0.281706i
\(424\) 0 0
\(425\) 6.87859 16.7755i 0.333661 0.813732i
\(426\) 0 0
\(427\) 8.27405i 0.400409i
\(428\) 0 0
\(429\) 13.4340 0.648599
\(430\) 0 0
\(431\) −34.9571 −1.68382 −0.841912 0.539615i \(-0.818570\pi\)
−0.841912 + 0.539615i \(0.818570\pi\)
\(432\) 0 0
\(433\) 1.13536i 0.0545619i −0.999628 0.0272809i \(-0.991315\pi\)
0.999628 0.0272809i \(-0.00868487\pi\)
\(434\) 0 0
\(435\) 8.78154 44.5633i 0.421043 2.13665i
\(436\) 0 0
\(437\) 8.01395i 0.383359i
\(438\) 0 0
\(439\) −6.80009 −0.324551 −0.162275 0.986746i \(-0.551883\pi\)
−0.162275 + 0.986746i \(0.551883\pi\)
\(440\) 0 0
\(441\) −29.7003 −1.41430
\(442\) 0 0
\(443\) 38.0679i 1.80866i 0.426835 + 0.904330i \(0.359629\pi\)
−0.426835 + 0.904330i \(0.640371\pi\)
\(444\) 0 0
\(445\) 0.850688 + 0.167635i 0.0403265 + 0.00794664i
\(446\) 0 0
\(447\) 46.5048i 2.19960i
\(448\) 0 0
\(449\) 18.5414 0.875024 0.437512 0.899212i \(-0.355860\pi\)
0.437512 + 0.899212i \(0.355860\pi\)
\(450\) 0 0
\(451\) −2.29862 −0.108238
\(452\) 0 0
\(453\) 46.8959i 2.20336i
\(454\) 0 0
\(455\) −9.40005 1.85235i −0.440681 0.0868396i
\(456\) 0 0
\(457\) 16.3738i 0.765934i 0.923762 + 0.382967i \(0.125098\pi\)
−0.923762 + 0.382967i \(0.874902\pi\)
\(458\) 0 0
\(459\) −16.2847 −0.760103
\(460\) 0 0
\(461\) 1.70470 0.0793959 0.0396979 0.999212i \(-0.487360\pi\)
0.0396979 + 0.999212i \(0.487360\pi\)
\(462\) 0 0
\(463\) 10.0279i 0.466036i −0.972472 0.233018i \(-0.925140\pi\)
0.972472 0.233018i \(-0.0748602\pi\)
\(464\) 0 0
\(465\) −9.69075 + 49.1772i −0.449398 + 2.28054i
\(466\) 0 0
\(467\) 32.7509i 1.51553i −0.652526 0.757766i \(-0.726291\pi\)
0.652526 0.757766i \(-0.273709\pi\)
\(468\) 0 0
\(469\) 0.786137 0.0363004
\(470\) 0 0
\(471\) −40.9817 −1.88834
\(472\) 0 0
\(473\) 5.93545i 0.272912i
\(474\) 0 0
\(475\) 4.62620 + 1.89692i 0.212265 + 0.0870365i
\(476\) 0 0
\(477\) 10.9817i 0.502816i
\(478\) 0 0
\(479\) 27.2803 1.24647 0.623234 0.782035i \(-0.285818\pi\)
0.623234 + 0.782035i \(0.285818\pi\)
\(480\) 0 0
\(481\) 2.68305 0.122337
\(482\) 0 0
\(483\) 16.8540i 0.766884i
\(484\) 0 0
\(485\) −3.67680 + 18.6585i −0.166955 + 0.847238i
\(486\) 0 0
\(487\) 11.0741i 0.501817i 0.968011 + 0.250908i \(0.0807293\pi\)
−0.968011 + 0.250908i \(0.919271\pi\)
\(488\) 0 0
\(489\) −36.9205 −1.66960
\(490\) 0 0
\(491\) −8.11704 −0.366317 −0.183158 0.983083i \(-0.558632\pi\)
−0.183158 + 0.983083i \(0.558632\pi\)
\(492\) 0 0
\(493\) 26.6724i 1.20127i
\(494\) 0 0
\(495\) 8.77551 + 1.72928i 0.394430 + 0.0777254i
\(496\) 0 0
\(497\) 7.75386i 0.347808i
\(498\) 0 0
\(499\) 0.295298 0.0132193 0.00660967 0.999978i \(-0.497896\pi\)
0.00660967 + 0.999978i \(0.497896\pi\)
\(500\) 0 0
\(501\) 27.1912 1.21481
\(502\) 0 0
\(503\) 19.6016i 0.873993i 0.899463 + 0.436996i \(0.143958\pi\)
−0.899463 + 0.436996i \(0.856042\pi\)
\(504\) 0 0
\(505\) −36.0140 7.09683i −1.60260 0.315805i
\(506\) 0 0
\(507\) 51.5144i 2.28783i
\(508\) 0 0
\(509\) 1.79383 0.0795102 0.0397551 0.999209i \(-0.487342\pi\)
0.0397551 + 0.999209i \(0.487342\pi\)
\(510\) 0 0
\(511\) 12.4908 0.552562
\(512\) 0 0
\(513\) 4.49084i 0.198275i
\(514\) 0 0
\(515\) −4.16763 + 21.1493i −0.183648 + 0.931950i
\(516\) 0 0
\(517\) 1.08287i 0.0476247i
\(518\) 0 0
\(519\) 8.23407 0.361436
\(520\) 0 0
\(521\) −2.61850 −0.114719 −0.0573593 0.998354i \(-0.518268\pi\)
−0.0573593 + 0.998354i \(0.518268\pi\)
\(522\) 0 0
\(523\) 14.9956i 0.655713i 0.944728 + 0.327857i \(0.106326\pi\)
−0.944728 + 0.327857i \(0.893674\pi\)
\(524\) 0 0
\(525\) −9.72928 3.98937i −0.424621 0.174111i
\(526\) 0 0
\(527\) 29.4340i 1.28216i
\(528\) 0 0
\(529\) −41.2234 −1.79232
\(530\) 0 0
\(531\) −20.7755 −0.901580
\(532\) 0 0
\(533\) 14.9571i 0.647864i
\(534\) 0 0
\(535\) −1.85235 + 9.40005i −0.0800841 + 0.406399i
\(536\) 0 0
\(537\) 32.5693i 1.40547i
\(538\) 0 0
\(539\) 5.55102 0.239099
\(540\) 0 0
\(541\) 3.40608 0.146439 0.0732194 0.997316i \(-0.476673\pi\)
0.0732194 + 0.997316i \(0.476673\pi\)
\(542\) 0 0
\(543\) 40.2341i 1.72661i
\(544\) 0 0
\(545\) −29.4419 5.80175i −1.26115 0.248520i
\(546\) 0 0
\(547\) 4.74760i 0.202993i −0.994836 0.101496i \(-0.967637\pi\)
0.994836 0.101496i \(-0.0323630\pi\)
\(548\) 0 0
\(549\) 50.2620 2.14513
\(550\) 0 0
\(551\) 7.35548 0.313354
\(552\) 0 0
\(553\) 9.57227i 0.407054i
\(554\) 0 0
\(555\) 2.88922 + 0.569343i 0.122641 + 0.0241673i
\(556\) 0 0
\(557\) 43.0462i 1.82393i 0.410271 + 0.911964i \(0.365434\pi\)
−0.410271 + 0.911964i \(0.634566\pi\)
\(558\) 0 0
\(559\) 38.6218 1.63353
\(560\) 0 0
\(561\) 8.65847 0.365561
\(562\) 0 0
\(563\) 17.0096i 0.716869i 0.933555 + 0.358434i \(0.116689\pi\)
−0.933555 + 0.358434i \(0.883311\pi\)
\(564\) 0 0
\(565\) 4.46293 22.6478i 0.187757 0.952802i
\(566\) 0 0
\(567\) 1.12473i 0.0472343i
\(568\) 0 0
\(569\) 19.7572 0.828264 0.414132 0.910217i \(-0.364085\pi\)
0.414132 + 0.910217i \(0.364085\pi\)
\(570\) 0 0
\(571\) 11.3973 0.476964 0.238482 0.971147i \(-0.423350\pi\)
0.238482 + 0.971147i \(0.423350\pi\)
\(572\) 0 0
\(573\) 36.5587i 1.52726i
\(574\) 0 0
\(575\) 15.2018 37.0741i 0.633959 1.54610i
\(576\) 0 0
\(577\) 18.3372i 0.763386i −0.924289 0.381693i \(-0.875341\pi\)
0.924289 0.381693i \(-0.124659\pi\)
\(578\) 0 0
\(579\) 7.01832 0.291672
\(580\) 0 0
\(581\) 0.206167 0.00855327
\(582\) 0 0
\(583\) 2.05249i 0.0850053i
\(584\) 0 0
\(585\) 11.2524 57.1020i 0.465229 2.36088i
\(586\) 0 0
\(587\) 11.9475i 0.493127i 0.969127 + 0.246563i \(0.0793013\pi\)
−0.969127 + 0.246563i \(0.920699\pi\)
\(588\) 0 0
\(589\) −8.11704 −0.334457
\(590\) 0 0
\(591\) 54.9850 2.26178
\(592\) 0 0
\(593\) 24.3911i 1.00162i 0.865557 + 0.500811i \(0.166965\pi\)
−0.865557 + 0.500811i \(0.833035\pi\)
\(594\) 0 0
\(595\) −6.05852 1.19388i −0.248375 0.0489442i
\(596\) 0 0
\(597\) 56.0943i 2.29579i
\(598\) 0 0
\(599\) −21.0708 −0.860930 −0.430465 0.902607i \(-0.641650\pi\)
−0.430465 + 0.902607i \(0.641650\pi\)
\(600\) 0 0
\(601\) 32.3878 1.32112 0.660562 0.750771i \(-0.270318\pi\)
0.660562 + 0.750771i \(0.270318\pi\)
\(602\) 0 0
\(603\) 4.77551i 0.194474i
\(604\) 0 0
\(605\) 22.4925 + 4.43232i 0.914450 + 0.180199i
\(606\) 0 0
\(607\) 19.0183i 0.771930i −0.922513 0.385965i \(-0.873869\pi\)
0.922513 0.385965i \(-0.126131\pi\)
\(608\) 0 0
\(609\) −15.4692 −0.626843
\(610\) 0 0
\(611\) −7.04623 −0.285060
\(612\) 0 0
\(613\) 23.5756i 0.952210i 0.879389 + 0.476105i \(0.157952\pi\)
−0.879389 + 0.476105i \(0.842048\pi\)
\(614\) 0 0
\(615\) −3.17389 + 16.1064i −0.127984 + 0.649473i
\(616\) 0 0
\(617\) 26.2707i 1.05762i −0.848740 0.528810i \(-0.822639\pi\)
0.848740 0.528810i \(-0.177361\pi\)
\(618\) 0 0
\(619\) 11.4985 0.462165 0.231083 0.972934i \(-0.425773\pi\)
0.231083 + 0.972934i \(0.425773\pi\)
\(620\) 0 0
\(621\) −35.9894 −1.44420
\(622\) 0 0
\(623\) 0.295298i 0.0118309i
\(624\) 0 0
\(625\) 17.8034 + 17.5510i 0.712137 + 0.702041i
\(626\) 0 0
\(627\) 2.38776i 0.0953578i
\(628\) 0 0
\(629\) 1.72928 0.0689510
\(630\) 0 0
\(631\) 45.8130 1.82379 0.911893 0.410427i \(-0.134620\pi\)
0.911893 + 0.410427i \(0.134620\pi\)
\(632\) 0 0
\(633\) 49.8236i 1.98031i
\(634\) 0 0
\(635\) −7.34153 + 37.2557i −0.291340 + 1.47845i
\(636\) 0 0
\(637\) 36.1204i 1.43114i
\(638\) 0 0
\(639\) −47.1020 −1.86333
\(640\) 0 0
\(641\) 1.36943 0.0540894 0.0270447 0.999634i \(-0.491390\pi\)
0.0270447 + 0.999634i \(0.491390\pi\)
\(642\) 0 0
\(643\) 24.7389i 0.975606i −0.872954 0.487803i \(-0.837799\pi\)
0.872954 0.487803i \(-0.162201\pi\)
\(644\) 0 0
\(645\) 41.5896 + 8.19554i 1.63759 + 0.322699i
\(646\) 0 0
\(647\) 6.82611i 0.268362i 0.990957 + 0.134181i \(0.0428404\pi\)
−0.990957 + 0.134181i \(0.957160\pi\)
\(648\) 0 0
\(649\) 3.88296 0.152420
\(650\) 0 0
\(651\) 17.0708 0.669058
\(652\) 0 0
\(653\) 6.91713i 0.270688i −0.990799 0.135344i \(-0.956786\pi\)
0.990799 0.135344i \(-0.0432140\pi\)
\(654\) 0 0
\(655\) 1.18785 + 0.234074i 0.0464130 + 0.00914603i
\(656\) 0 0
\(657\) 75.8776i 2.96027i
\(658\) 0 0
\(659\) 9.44461 0.367910 0.183955 0.982935i \(-0.441110\pi\)
0.183955 + 0.982935i \(0.441110\pi\)
\(660\) 0 0
\(661\) −22.1955 −0.863306 −0.431653 0.902040i \(-0.642070\pi\)
−0.431653 + 0.902040i \(0.642070\pi\)
\(662\) 0 0
\(663\) 56.3405i 2.18808i
\(664\) 0 0
\(665\) 0.329237 1.67076i 0.0127673 0.0647894i
\(666\) 0 0
\(667\) 58.9465i 2.28242i
\(668\) 0 0
\(669\) 37.3449 1.44384
\(670\) 0 0
\(671\) −9.39401 −0.362652
\(672\) 0 0
\(673\) 12.2986i 0.474077i −0.971500 0.237039i \(-0.923823\pi\)
0.971500 0.237039i \(-0.0761768\pi\)
\(674\) 0 0
\(675\) 8.51875 20.7755i 0.327887 0.799650i
\(676\) 0 0
\(677\) 35.9527i 1.38178i −0.722962 0.690888i \(-0.757220\pi\)
0.722962 0.690888i \(-0.242780\pi\)
\(678\) 0 0
\(679\) 6.47689 0.248560
\(680\) 0 0
\(681\) 37.5616 1.43937
\(682\) 0 0
\(683\) 9.00958i 0.344742i −0.985032 0.172371i \(-0.944857\pi\)
0.985032 0.172371i \(-0.0551428\pi\)
\(684\) 0 0
\(685\) 1.24448 6.31528i 0.0475490 0.241295i
\(686\) 0 0
\(687\) 37.5231i 1.43160i
\(688\) 0 0
\(689\) −13.3555 −0.508803
\(690\) 0 0
\(691\) 9.11078 0.346590 0.173295 0.984870i \(-0.444559\pi\)
0.173295 + 0.984870i \(0.444559\pi\)
\(692\) 0 0
\(693\) 3.04623i 0.115717i
\(694\) 0 0
\(695\) −7.87090 1.55102i −0.298560 0.0588336i
\(696\) 0 0
\(697\) 9.64015i 0.365147i
\(698\) 0 0
\(699\) 70.5606 2.66885
\(700\) 0 0
\(701\) −14.7476 −0.557009 −0.278505 0.960435i \(-0.589839\pi\)
−0.278505 + 0.960435i \(0.589839\pi\)
\(702\) 0 0
\(703\) 0.476886i 0.0179861i
\(704\) 0 0
\(705\) −7.58767 1.49521i −0.285768 0.0563128i
\(706\) 0 0
\(707\) 12.5015i 0.470166i
\(708\) 0 0
\(709\) 8.63389 0.324253 0.162126 0.986770i \(-0.448165\pi\)
0.162126 + 0.986770i \(0.448165\pi\)
\(710\) 0 0
\(711\) 58.1483 2.18073
\(712\) 0 0
\(713\) 65.0496i 2.43613i
\(714\) 0 0
\(715\) −2.10308 + 10.6724i −0.0786509 + 0.399126i
\(716\) 0 0
\(717\) 31.2909i 1.16858i
\(718\) 0 0
\(719\) −38.2759 −1.42745 −0.713726 0.700425i \(-0.752994\pi\)
−0.713726 + 0.700425i \(0.752994\pi\)
\(720\) 0 0
\(721\) 7.34153 0.273413
\(722\) 0 0
\(723\) 3.45856i 0.128625i
\(724\) 0 0
\(725\) 34.0279 + 13.9527i 1.26376 + 0.518191i
\(726\) 0 0
\(727\) 31.1893i 1.15675i 0.815772 + 0.578373i \(0.196312\pi\)
−0.815772 + 0.578373i \(0.803688\pi\)
\(728\) 0 0
\(729\) 44.0375 1.63102
\(730\) 0 0
\(731\) 24.8925 0.920684
\(732\) 0 0
\(733\) 13.9634i 0.515748i 0.966179 + 0.257874i \(0.0830220\pi\)
−0.966179 + 0.257874i \(0.916978\pi\)
\(734\) 0 0
\(735\) 7.66473 38.8959i 0.282718 1.43470i
\(736\) 0 0
\(737\) 0.892548i 0.0328774i
\(738\) 0 0
\(739\) 9.02165 0.331867 0.165933 0.986137i \(-0.446936\pi\)
0.165933 + 0.986137i \(0.446936\pi\)
\(740\) 0 0
\(741\) 15.5371 0.570768
\(742\) 0 0
\(743\) 15.0342i 0.551550i −0.961222 0.275775i \(-0.911066\pi\)
0.961222 0.275775i \(-0.0889345\pi\)
\(744\) 0 0
\(745\) −36.9450 7.28030i −1.35356 0.266730i
\(746\) 0 0
\(747\) 1.25240i 0.0458228i
\(748\) 0 0
\(749\) 3.26302 0.119228
\(750\) 0 0
\(751\) −29.6681 −1.08260 −0.541301 0.840829i \(-0.682068\pi\)
−0.541301 + 0.840829i \(0.682068\pi\)
\(752\) 0 0
\(753\) 29.2557i 1.06614i
\(754\) 0 0
\(755\) −37.2557 7.34153i −1.35587 0.267186i
\(756\) 0 0
\(757\) 10.5819i 0.384604i 0.981336 + 0.192302i \(0.0615953\pi\)
−0.981336 + 0.192302i \(0.938405\pi\)
\(758\) 0 0
\(759\) 19.1354 0.694570
\(760\) 0 0
\(761\) −0.979789 −0.0355173 −0.0177587 0.999842i \(-0.505653\pi\)
−0.0177587 + 0.999842i \(0.505653\pi\)
\(762\) 0 0
\(763\) 10.2201i 0.369993i
\(764\) 0 0
\(765\) 7.25240 36.8034i 0.262211 1.33063i
\(766\) 0 0
\(767\) 25.2663i 0.912315i
\(768\) 0 0
\(769\) −43.1772 −1.55701 −0.778505 0.627638i \(-0.784022\pi\)
−0.778505 + 0.627638i \(0.784022\pi\)
\(770\) 0 0
\(771\) 0.424399 0.0152844
\(772\) 0 0
\(773\) 37.5250i 1.34968i −0.737964 0.674840i \(-0.764213\pi\)
0.737964 0.674840i \(-0.235787\pi\)
\(774\) 0 0
\(775\) −37.5510 15.3973i −1.34887 0.553089i
\(776\) 0 0
\(777\) 1.00293i 0.0359799i
\(778\) 0 0
\(779\) −2.65847 −0.0952497
\(780\) 0 0
\(781\) 8.80342 0.315011
\(782\) 0 0
\(783\) 33.0323i 1.18048i
\(784\) 0 0
\(785\) 6.41566 32.5573i 0.228985 1.16202i
\(786\) 0 0
\(787\) 22.5833i 0.805008i −0.915418 0.402504i \(-0.868140\pi\)
0.915418 0.402504i \(-0.131860\pi\)
\(788\) 0 0
\(789\) −1.39401 −0.0496282
\(790\) 0 0
\(791\) −7.86171 −0.279530
\(792\) 0 0
\(793\) 61.1266i 2.17067i
\(794\) 0 0
\(795\) −14.3817 2.83403i −0.510067 0.100513i
\(796\) 0 0
\(797\) 35.9806i 1.27450i 0.770657 + 0.637250i \(0.219928\pi\)
−0.770657 + 0.637250i \(0.780072\pi\)
\(798\) 0 0
\(799\) −4.54144 −0.160664
\(800\) 0 0
\(801\) 1.79383 0.0633820
\(802\) 0 0