Properties

Label 1560.2.l.e.1249.3
Level $1560$
Weight $2$
Character 1560.1249
Analytic conductor $12.457$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1560.l (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.4566627153\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.1698758656.6
Defining polynomial: \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1249.3
Root \(1.69230i\) of defining polynomial
Character \(\chi\) \(=\) 1560.1249
Dual form 1560.2.l.e.1249.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{3} +(0.489528 - 2.18183i) q^{5} -2.82843i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{3} +(0.489528 - 2.18183i) q^{5} -2.82843i q^{7} -1.00000 q^{9} -2.97906 q^{11} +1.00000i q^{13} +(-2.18183 - 0.489528i) q^{15} +1.44383i q^{17} -4.17113 q^{19} -2.82843 q^{21} -6.21302i q^{23} +(-4.52072 - 2.13613i) q^{25} +1.00000i q^{27} +0.828427 q^{29} +1.65685 q^{31} +2.97906i q^{33} +(-6.17113 - 1.38459i) q^{35} -0.0418875i q^{37} +1.00000 q^{39} -4.36365 q^{41} +8.99956i q^{43} +(-0.489528 + 2.18183i) q^{45} -4.40554i q^{47} -1.00000 q^{49} +1.44383 q^{51} +6.72730i q^{53} +(-1.45833 + 6.49978i) q^{55} +4.17113i q^{57} +2.97906 q^{59} +6.27226 q^{61} +2.82843i q^{63} +(2.18183 + 0.489528i) q^{65} +0.727302i q^{67} -6.21302 q^{69} -8.32176 q^{71} +6.87031i q^{73} +(-2.13613 + 4.52072i) q^{75} +8.42604i q^{77} -6.11190 q^{79} +1.00000 q^{81} -14.7059i q^{83} +(3.15019 + 0.706797i) q^{85} -0.828427i q^{87} -14.7478 q^{89} +2.82843 q^{91} -1.65685i q^{93} +(-2.04189 + 9.10069i) q^{95} -6.78654i q^{97} +2.97906 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{9} - 16 q^{11} - 4 q^{15} + 24 q^{19} - 4 q^{25} - 16 q^{29} - 32 q^{31} + 8 q^{35} + 8 q^{39} - 8 q^{41} - 8 q^{49} + 8 q^{51} - 36 q^{55} + 16 q^{59} + 24 q^{61} + 4 q^{65} - 8 q^{69} - 24 q^{71} - 4 q^{75} + 24 q^{79} + 8 q^{81} - 40 q^{85} + 8 q^{89} - 32 q^{95} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).

\(n\) \(391\) \(521\) \(781\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\) \(1\)

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
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) 0.489528 2.18183i 0.218924 0.975742i
\(6\) 0 0
\(7\) 2.82843i 1.06904i −0.845154 0.534522i \(-0.820491\pi\)
0.845154 0.534522i \(-0.179509\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −2.97906 −0.898219 −0.449110 0.893477i \(-0.648259\pi\)
−0.449110 + 0.893477i \(0.648259\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) 0 0
\(15\) −2.18183 0.489528i −0.563345 0.126396i
\(16\) 0 0
\(17\) 1.44383i 0.350181i 0.984552 + 0.175090i \(0.0560218\pi\)
−0.984552 + 0.175090i \(0.943978\pi\)
\(18\) 0 0
\(19\) −4.17113 −0.956924 −0.478462 0.878108i \(-0.658806\pi\)
−0.478462 + 0.878108i \(0.658806\pi\)
\(20\) 0 0
\(21\) −2.82843 −0.617213
\(22\) 0 0
\(23\) 6.21302i 1.29550i −0.761851 0.647752i \(-0.775709\pi\)
0.761851 0.647752i \(-0.224291\pi\)
\(24\) 0 0
\(25\) −4.52072 2.13613i −0.904145 0.427226i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 0.828427 0.153835 0.0769175 0.997037i \(-0.475492\pi\)
0.0769175 + 0.997037i \(0.475492\pi\)
\(30\) 0 0
\(31\) 1.65685 0.297580 0.148790 0.988869i \(-0.452462\pi\)
0.148790 + 0.988869i \(0.452462\pi\)
\(32\) 0 0
\(33\) 2.97906i 0.518587i
\(34\) 0 0
\(35\) −6.17113 1.38459i −1.04311 0.234039i
\(36\) 0 0
\(37\) 0.0418875i 0.00688626i −0.999994 0.00344313i \(-0.998904\pi\)
0.999994 0.00344313i \(-0.00109599\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) −4.36365 −0.681488 −0.340744 0.940156i \(-0.610679\pi\)
−0.340744 + 0.940156i \(0.610679\pi\)
\(42\) 0 0
\(43\) 8.99956i 1.37242i 0.727403 + 0.686210i \(0.240727\pi\)
−0.727403 + 0.686210i \(0.759273\pi\)
\(44\) 0 0
\(45\) −0.489528 + 2.18183i −0.0729745 + 0.325247i
\(46\) 0 0
\(47\) 4.40554i 0.642614i −0.946975 0.321307i \(-0.895878\pi\)
0.946975 0.321307i \(-0.104122\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 1.44383 0.202177
\(52\) 0 0
\(53\) 6.72730i 0.924066i 0.886863 + 0.462033i \(0.152880\pi\)
−0.886863 + 0.462033i \(0.847120\pi\)
\(54\) 0 0
\(55\) −1.45833 + 6.49978i −0.196641 + 0.876430i
\(56\) 0 0
\(57\) 4.17113i 0.552480i
\(58\) 0 0
\(59\) 2.97906 0.387840 0.193920 0.981017i \(-0.437880\pi\)
0.193920 + 0.981017i \(0.437880\pi\)
\(60\) 0 0
\(61\) 6.27226 0.803081 0.401540 0.915841i \(-0.368475\pi\)
0.401540 + 0.915841i \(0.368475\pi\)
\(62\) 0 0
\(63\) 2.82843i 0.356348i
\(64\) 0 0
\(65\) 2.18183 + 0.489528i 0.270622 + 0.0607185i
\(66\) 0 0
\(67\) 0.727302i 0.0888540i 0.999013 + 0.0444270i \(0.0141462\pi\)
−0.999013 + 0.0444270i \(0.985854\pi\)
\(68\) 0 0
\(69\) −6.21302 −0.747960
\(70\) 0 0
\(71\) −8.32176 −0.987612 −0.493806 0.869572i \(-0.664395\pi\)
−0.493806 + 0.869572i \(0.664395\pi\)
\(72\) 0 0
\(73\) 6.87031i 0.804110i 0.915616 + 0.402055i \(0.131704\pi\)
−0.915616 + 0.402055i \(0.868296\pi\)
\(74\) 0 0
\(75\) −2.13613 + 4.52072i −0.246659 + 0.522008i
\(76\) 0 0
\(77\) 8.42604i 0.960237i
\(78\) 0 0
\(79\) −6.11190 −0.687642 −0.343821 0.939035i \(-0.611721\pi\)
−0.343821 + 0.939035i \(0.611721\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 14.7059i 1.61418i −0.590425 0.807092i \(-0.701040\pi\)
0.590425 0.807092i \(-0.298960\pi\)
\(84\) 0 0
\(85\) 3.15019 + 0.706797i 0.341686 + 0.0766629i
\(86\) 0 0
\(87\) 0.828427i 0.0888167i
\(88\) 0 0
\(89\) −14.7478 −1.56326 −0.781632 0.623740i \(-0.785613\pi\)
−0.781632 + 0.623740i \(0.785613\pi\)
\(90\) 0 0
\(91\) 2.82843 0.296500
\(92\) 0 0
\(93\) 1.65685i 0.171808i
\(94\) 0 0
\(95\) −2.04189 + 9.10069i −0.209493 + 0.933711i
\(96\) 0 0
\(97\) 6.78654i 0.689069i −0.938774 0.344534i \(-0.888037\pi\)
0.938774 0.344534i \(-0.111963\pi\)
\(98\) 0 0
\(99\) 2.97906 0.299406
\(100\) 0 0
\(101\) 12.1421 1.20819 0.604094 0.796913i \(-0.293535\pi\)
0.604094 + 0.796913i \(0.293535\pi\)
\(102\) 0 0
\(103\) 2.81108i 0.276984i −0.990364 0.138492i \(-0.955775\pi\)
0.990364 0.138492i \(-0.0442255\pi\)
\(104\) 0 0
\(105\) −1.38459 + 6.17113i −0.135123 + 0.602241i
\(106\) 0 0
\(107\) 18.3842i 1.77726i −0.458621 0.888632i \(-0.651657\pi\)
0.458621 0.888632i \(-0.348343\pi\)
\(108\) 0 0
\(109\) −1.44383 −0.138294 −0.0691470 0.997606i \(-0.522028\pi\)
−0.0691470 + 0.997606i \(0.522028\pi\)
\(110\) 0 0
\(111\) −0.0418875 −0.00397579
\(112\) 0 0
\(113\) 3.40194i 0.320028i 0.987115 + 0.160014i \(0.0511539\pi\)
−0.987115 + 0.160014i \(0.948846\pi\)
\(114\) 0 0
\(115\) −13.5557 3.04145i −1.26408 0.283617i
\(116\) 0 0
\(117\) 1.00000i 0.0924500i
\(118\) 0 0
\(119\) 4.08378 0.374359
\(120\) 0 0
\(121\) −2.12522 −0.193202
\(122\) 0 0
\(123\) 4.36365i 0.393457i
\(124\) 0 0
\(125\) −6.87368 + 8.81774i −0.614801 + 0.788682i
\(126\) 0 0
\(127\) 15.8106i 1.40297i −0.712686 0.701484i \(-0.752521\pi\)
0.712686 0.701484i \(-0.247479\pi\)
\(128\) 0 0
\(129\) 8.99956 0.792367
\(130\) 0 0
\(131\) −19.1707 −1.67495 −0.837476 0.546475i \(-0.815970\pi\)
−0.837476 + 0.546475i \(0.815970\pi\)
\(132\) 0 0
\(133\) 11.7977i 1.02299i
\(134\) 0 0
\(135\) 2.18183 + 0.489528i 0.187782 + 0.0421319i
\(136\) 0 0
\(137\) 1.67824i 0.143381i −0.997427 0.0716907i \(-0.977161\pi\)
0.997427 0.0716907i \(-0.0228395\pi\)
\(138\) 0 0
\(139\) 12.3423 1.04686 0.523429 0.852069i \(-0.324653\pi\)
0.523429 + 0.852069i \(0.324653\pi\)
\(140\) 0 0
\(141\) −4.40554 −0.371013
\(142\) 0 0
\(143\) 2.97906i 0.249121i
\(144\) 0 0
\(145\) 0.405538 1.80748i 0.0336781 0.150103i
\(146\) 0 0
\(147\) 1.00000i 0.0824786i
\(148\) 0 0
\(149\) −0.677798 −0.0555274 −0.0277637 0.999615i \(-0.508839\pi\)
−0.0277637 + 0.999615i \(0.508839\pi\)
\(150\) 0 0
\(151\) −17.9991 −1.46475 −0.732374 0.680903i \(-0.761588\pi\)
−0.732374 + 0.680903i \(0.761588\pi\)
\(152\) 0 0
\(153\) 1.44383i 0.116727i
\(154\) 0 0
\(155\) 0.811077 3.61497i 0.0651473 0.290361i
\(156\) 0 0
\(157\) 12.8392i 1.02468i 0.858783 + 0.512340i \(0.171221\pi\)
−0.858783 + 0.512340i \(0.828779\pi\)
\(158\) 0 0
\(159\) 6.72730 0.533510
\(160\) 0 0
\(161\) −17.5731 −1.38495
\(162\) 0 0
\(163\) 15.3137i 1.19946i 0.800202 + 0.599731i \(0.204726\pi\)
−0.800202 + 0.599731i \(0.795274\pi\)
\(164\) 0 0
\(165\) 6.49978 + 1.45833i 0.506007 + 0.113531i
\(166\) 0 0
\(167\) 15.3922i 1.19109i −0.803324 0.595543i \(-0.796937\pi\)
0.803324 0.595543i \(-0.203063\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) 4.17113 0.318975
\(172\) 0 0
\(173\) 14.9706i 1.13819i −0.822272 0.569095i \(-0.807294\pi\)
0.822272 0.569095i \(-0.192706\pi\)
\(174\) 0 0
\(175\) −6.04189 + 12.7865i −0.456724 + 0.966572i
\(176\) 0 0
\(177\) 2.97906i 0.223920i
\(178\) 0 0
\(179\) 7.63950 0.571003 0.285502 0.958378i \(-0.407840\pi\)
0.285502 + 0.958378i \(0.407840\pi\)
\(180\) 0 0
\(181\) 15.0286 1.11706 0.558532 0.829483i \(-0.311365\pi\)
0.558532 + 0.829483i \(0.311365\pi\)
\(182\) 0 0
\(183\) 6.27226i 0.463659i
\(184\) 0 0
\(185\) −0.0913912 0.0205051i −0.00671922 0.00150757i
\(186\) 0 0
\(187\) 4.30126i 0.314539i
\(188\) 0 0
\(189\) 2.82843 0.205738
\(190\) 0 0
\(191\) −10.8877 −0.787804 −0.393902 0.919152i \(-0.628875\pi\)
−0.393902 + 0.919152i \(0.628875\pi\)
\(192\) 0 0
\(193\) 4.94690i 0.356086i 0.984023 + 0.178043i \(0.0569766\pi\)
−0.984023 + 0.178043i \(0.943023\pi\)
\(194\) 0 0
\(195\) 0.489528 2.18183i 0.0350558 0.156244i
\(196\) 0 0
\(197\) 26.3628i 1.87827i −0.343549 0.939135i \(-0.611629\pi\)
0.343549 0.939135i \(-0.388371\pi\)
\(198\) 0 0
\(199\) −6.11190 −0.433261 −0.216630 0.976254i \(-0.569507\pi\)
−0.216630 + 0.976254i \(0.569507\pi\)
\(200\) 0 0
\(201\) 0.727302 0.0512999
\(202\) 0 0
\(203\) 2.34315i 0.164457i
\(204\) 0 0
\(205\) −2.13613 + 9.52072i −0.149194 + 0.664956i
\(206\) 0 0
\(207\) 6.21302i 0.431835i
\(208\) 0 0
\(209\) 12.4260 0.859527
\(210\) 0 0
\(211\) 9.68585 0.666802 0.333401 0.942785i \(-0.391804\pi\)
0.333401 + 0.942785i \(0.391804\pi\)
\(212\) 0 0
\(213\) 8.32176i 0.570198i
\(214\) 0 0
\(215\) 19.6355 + 4.40554i 1.33913 + 0.300455i
\(216\) 0 0
\(217\) 4.68629i 0.318126i
\(218\) 0 0
\(219\) 6.87031 0.464253
\(220\) 0 0
\(221\) −1.44383 −0.0971227
\(222\) 0 0
\(223\) 9.21258i 0.616920i 0.951237 + 0.308460i \(0.0998136\pi\)
−0.951237 + 0.308460i \(0.900186\pi\)
\(224\) 0 0
\(225\) 4.52072 + 2.13613i 0.301382 + 0.142409i
\(226\) 0 0
\(227\) 20.3218i 1.34880i −0.738365 0.674401i \(-0.764402\pi\)
0.738365 0.674401i \(-0.235598\pi\)
\(228\) 0 0
\(229\) 16.4715 1.08847 0.544234 0.838933i \(-0.316820\pi\)
0.544234 + 0.838933i \(0.316820\pi\)
\(230\) 0 0
\(231\) 8.42604 0.554393
\(232\) 0 0
\(233\) 2.37339i 0.155486i 0.996973 + 0.0777428i \(0.0247713\pi\)
−0.996973 + 0.0777428i \(0.975229\pi\)
\(234\) 0 0
\(235\) −9.61212 2.15663i −0.627025 0.140683i
\(236\) 0 0
\(237\) 6.11190i 0.397010i
\(238\) 0 0
\(239\) 13.6363 0.882062 0.441031 0.897492i \(-0.354613\pi\)
0.441031 + 0.897492i \(0.354613\pi\)
\(240\) 0 0
\(241\) 1.07045 0.0689536 0.0344768 0.999405i \(-0.489024\pi\)
0.0344768 + 0.999405i \(0.489024\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −0.489528 + 2.18183i −0.0312748 + 0.139392i
\(246\) 0 0
\(247\) 4.17113i 0.265403i
\(248\) 0 0
\(249\) −14.7059 −0.931950
\(250\) 0 0
\(251\) 14.6262 0.923196 0.461598 0.887089i \(-0.347276\pi\)
0.461598 + 0.887089i \(0.347276\pi\)
\(252\) 0 0
\(253\) 18.5089i 1.16365i
\(254\) 0 0
\(255\) 0.706797 3.15019i 0.0442613 0.197273i
\(256\) 0 0
\(257\) 24.9403i 1.55573i −0.628429 0.777867i \(-0.716302\pi\)
0.628429 0.777867i \(-0.283698\pi\)
\(258\) 0 0
\(259\) −0.118476 −0.00736173
\(260\) 0 0
\(261\) −0.828427 −0.0512784
\(262\) 0 0
\(263\) 9.01691i 0.556007i −0.960580 0.278003i \(-0.910327\pi\)
0.960580 0.278003i \(-0.0896726\pi\)
\(264\) 0 0
\(265\) 14.6778 + 3.29320i 0.901650 + 0.202300i
\(266\) 0 0
\(267\) 14.7478i 0.902551i
\(268\) 0 0
\(269\) −8.28391 −0.505079 −0.252539 0.967587i \(-0.581266\pi\)
−0.252539 + 0.967587i \(0.581266\pi\)
\(270\) 0 0
\(271\) −19.9572 −1.21232 −0.606158 0.795344i \(-0.707290\pi\)
−0.606158 + 0.795344i \(0.707290\pi\)
\(272\) 0 0
\(273\) 2.82843i 0.171184i
\(274\) 0 0
\(275\) 13.4675 + 6.36365i 0.812120 + 0.383743i
\(276\) 0 0
\(277\) 22.6145i 1.35878i 0.733780 + 0.679388i \(0.237755\pi\)
−0.733780 + 0.679388i \(0.762245\pi\)
\(278\) 0 0
\(279\) −1.65685 −0.0991933
\(280\) 0 0
\(281\) −1.89572 −0.113089 −0.0565446 0.998400i \(-0.518008\pi\)
−0.0565446 + 0.998400i \(0.518008\pi\)
\(282\) 0 0
\(283\) 11.2299i 0.667550i −0.942653 0.333775i \(-0.891677\pi\)
0.942653 0.333775i \(-0.108323\pi\)
\(284\) 0 0
\(285\) 9.10069 + 2.04189i 0.539078 + 0.120951i
\(286\) 0 0
\(287\) 12.3423i 0.728541i
\(288\) 0 0
\(289\) 14.9153 0.877373
\(290\) 0 0
\(291\) −6.78654 −0.397834
\(292\) 0 0
\(293\) 27.6774i 1.61693i 0.588545 + 0.808464i \(0.299701\pi\)
−0.588545 + 0.808464i \(0.700299\pi\)
\(294\) 0 0
\(295\) 1.45833 6.49978i 0.0849074 0.378432i
\(296\) 0 0
\(297\) 2.97906i 0.172862i
\(298\) 0 0
\(299\) 6.21302 0.359308
\(300\) 0 0
\(301\) 25.4546 1.46718
\(302\) 0 0
\(303\) 12.1421i 0.697547i
\(304\) 0 0
\(305\) 3.07045 13.6850i 0.175813 0.783599i
\(306\) 0 0
\(307\) 24.9858i 1.42601i −0.701157 0.713007i \(-0.747333\pi\)
0.701157 0.713007i \(-0.252667\pi\)
\(308\) 0 0
\(309\) −2.81108 −0.159917
\(310\) 0 0
\(311\) 18.3842 1.04247 0.521235 0.853413i \(-0.325472\pi\)
0.521235 + 0.853413i \(0.325472\pi\)
\(312\) 0 0
\(313\) 8.61453i 0.486922i −0.969911 0.243461i \(-0.921717\pi\)
0.969911 0.243461i \(-0.0782828\pi\)
\(314\) 0 0
\(315\) 6.17113 + 1.38459i 0.347704 + 0.0780131i
\(316\) 0 0
\(317\) 15.0491i 0.845240i −0.906307 0.422620i \(-0.861111\pi\)
0.906307 0.422620i \(-0.138889\pi\)
\(318\) 0 0
\(319\) −2.46793 −0.138178
\(320\) 0 0
\(321\) −18.3842 −1.02610
\(322\) 0 0
\(323\) 6.02242i 0.335096i
\(324\) 0 0
\(325\) 2.13613 4.52072i 0.118491 0.250765i
\(326\) 0 0
\(327\) 1.44383i 0.0798441i
\(328\) 0 0
\(329\) −12.4607 −0.686983
\(330\) 0 0
\(331\) 22.6738 1.24626 0.623131 0.782117i \(-0.285860\pi\)
0.623131 + 0.782117i \(0.285860\pi\)
\(332\) 0 0
\(333\) 0.0418875i 0.00229542i
\(334\) 0 0
\(335\) 1.58685 + 0.356035i 0.0866986 + 0.0194523i
\(336\) 0 0
\(337\) 27.9282i 1.52135i −0.649134 0.760674i \(-0.724869\pi\)
0.649134 0.760674i \(-0.275131\pi\)
\(338\) 0 0
\(339\) 3.40194 0.184768
\(340\) 0 0
\(341\) −4.93586 −0.267292
\(342\) 0 0
\(343\) 16.9706i 0.916324i
\(344\) 0 0
\(345\) −3.04145 + 13.5557i −0.163746 + 0.729816i
\(346\) 0 0
\(347\) 19.7398i 1.05969i −0.848096 0.529843i \(-0.822251\pi\)
0.848096 0.529843i \(-0.177749\pi\)
\(348\) 0 0
\(349\) −30.7157 −1.64417 −0.822086 0.569364i \(-0.807190\pi\)
−0.822086 + 0.569364i \(0.807190\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 17.0072i 0.905201i −0.891713 0.452600i \(-0.850496\pi\)
0.891713 0.452600i \(-0.149504\pi\)
\(354\) 0 0
\(355\) −4.07374 + 18.1566i −0.216212 + 0.963654i
\(356\) 0 0
\(357\) 4.08378i 0.216136i
\(358\) 0 0
\(359\) 7.90203 0.417053 0.208527 0.978017i \(-0.433133\pi\)
0.208527 + 0.978017i \(0.433133\pi\)
\(360\) 0 0
\(361\) −1.60164 −0.0842968
\(362\) 0 0
\(363\) 2.12522i 0.111545i
\(364\) 0 0
\(365\) 14.9898 + 3.36321i 0.784603 + 0.176039i
\(366\) 0 0
\(367\) 34.1810i 1.78424i 0.451803 + 0.892118i \(0.350781\pi\)
−0.451803 + 0.892118i \(0.649219\pi\)
\(368\) 0 0
\(369\) 4.36365 0.227163
\(370\) 0 0
\(371\) 19.0277 0.987868
\(372\) 0 0
\(373\) 18.5098i 0.958402i 0.877705 + 0.479201i \(0.159074\pi\)
−0.877705 + 0.479201i \(0.840926\pi\)
\(374\) 0 0
\(375\) 8.81774 + 6.87368i 0.455346 + 0.354956i
\(376\) 0 0
\(377\) 0.828427i 0.0426662i
\(378\) 0 0
\(379\) 12.7994 0.657462 0.328731 0.944424i \(-0.393379\pi\)
0.328731 + 0.944424i \(0.393379\pi\)
\(380\) 0 0
\(381\) −15.8106 −0.810004
\(382\) 0 0
\(383\) 0.664032i 0.0339304i −0.999856 0.0169652i \(-0.994600\pi\)
0.999856 0.0169652i \(-0.00540046\pi\)
\(384\) 0 0
\(385\) 18.3842 + 4.12479i 0.936943 + 0.210219i
\(386\) 0 0
\(387\) 8.99956i 0.457473i
\(388\) 0 0
\(389\) −2.32580 −0.117923 −0.0589613 0.998260i \(-0.518779\pi\)
−0.0589613 + 0.998260i \(0.518779\pi\)
\(390\) 0 0
\(391\) 8.97056 0.453661
\(392\) 0 0
\(393\) 19.1707i 0.967034i
\(394\) 0 0
\(395\) −2.99195 + 13.3351i −0.150541 + 0.670961i
\(396\) 0 0
\(397\) 18.2433i 0.915603i −0.889054 0.457802i \(-0.848637\pi\)
0.889054 0.457802i \(-0.151363\pi\)
\(398\) 0 0
\(399\) 11.7977 0.590626
\(400\) 0 0
\(401\) 16.9919 0.848537 0.424269 0.905536i \(-0.360531\pi\)
0.424269 + 0.905536i \(0.360531\pi\)
\(402\) 0 0
\(403\) 1.65685i 0.0825338i
\(404\) 0 0
\(405\) 0.489528 2.18183i 0.0243248 0.108416i
\(406\) 0 0
\(407\) 0.124785i 0.00618538i
\(408\) 0 0
\(409\) 10.8111 0.534573 0.267287 0.963617i \(-0.413873\pi\)
0.267287 + 0.963617i \(0.413873\pi\)
\(410\) 0 0
\(411\) −1.67824 −0.0827813
\(412\) 0 0
\(413\) 8.42604i 0.414618i
\(414\) 0 0
\(415\) −32.0857 7.19896i −1.57503 0.353383i
\(416\) 0 0
\(417\) 12.3423i 0.604403i
\(418\) 0 0
\(419\) 5.08780 0.248555 0.124278 0.992247i \(-0.460339\pi\)
0.124278 + 0.992247i \(0.460339\pi\)
\(420\) 0 0
\(421\) 12.0945 0.589452 0.294726 0.955582i \(-0.404772\pi\)
0.294726 + 0.955582i \(0.404772\pi\)
\(422\) 0 0
\(423\) 4.40554i 0.214205i
\(424\) 0 0
\(425\) 3.08421 6.52717i 0.149606 0.316614i
\(426\) 0 0
\(427\) 17.7406i 0.858529i
\(428\) 0 0
\(429\) −2.97906 −0.143830
\(430\) 0 0
\(431\) −8.48931 −0.408916 −0.204458 0.978875i \(-0.565543\pi\)
−0.204458 + 0.978875i \(0.565543\pi\)
\(432\) 0 0
\(433\) 13.8453i 0.665365i −0.943039 0.332682i \(-0.892046\pi\)
0.943039 0.332682i \(-0.107954\pi\)
\(434\) 0 0
\(435\) −1.80748 0.405538i −0.0866622 0.0194441i
\(436\) 0 0
\(437\) 25.9153i 1.23970i
\(438\) 0 0
\(439\) −0.602516 −0.0287565 −0.0143783 0.999897i \(-0.504577\pi\)
−0.0143783 + 0.999897i \(0.504577\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 17.6721i 0.839626i 0.907611 + 0.419813i \(0.137904\pi\)
−0.907611 + 0.419813i \(0.862096\pi\)
\(444\) 0 0
\(445\) −7.21947 + 32.1771i −0.342236 + 1.52534i
\(446\) 0 0
\(447\) 0.677798i 0.0320587i
\(448\) 0 0
\(449\) −3.33509 −0.157393 −0.0786963 0.996899i \(-0.525076\pi\)
−0.0786963 + 0.996899i \(0.525076\pi\)
\(450\) 0 0
\(451\) 12.9996 0.612125
\(452\) 0 0
\(453\) 17.9991i 0.845673i
\(454\) 0 0
\(455\) 1.38459 6.17113i 0.0649108 0.289307i
\(456\) 0 0
\(457\) 38.9266i 1.82091i −0.413611 0.910454i \(-0.635733\pi\)
0.413611 0.910454i \(-0.364267\pi\)
\(458\) 0 0
\(459\) −1.44383 −0.0673923
\(460\) 0 0
\(461\) 28.3918 1.32234 0.661168 0.750238i \(-0.270061\pi\)
0.661168 + 0.750238i \(0.270061\pi\)
\(462\) 0 0
\(463\) 10.2259i 0.475238i −0.971358 0.237619i \(-0.923633\pi\)
0.971358 0.237619i \(-0.0763670\pi\)
\(464\) 0 0
\(465\) −3.61497 0.811077i −0.167640 0.0376128i
\(466\) 0 0
\(467\) 5.61584i 0.259870i −0.991522 0.129935i \(-0.958523\pi\)
0.991522 0.129935i \(-0.0414769\pi\)
\(468\) 0 0
\(469\) 2.05712 0.0949890
\(470\) 0 0
\(471\) 12.8392 0.591599
\(472\) 0 0
\(473\) 26.8102i 1.23273i
\(474\) 0 0
\(475\) 18.8565 + 8.91008i 0.865198 + 0.408823i
\(476\) 0 0
\(477\) 6.72730i 0.308022i
\(478\) 0 0
\(479\) 8.95006 0.408939 0.204469 0.978873i \(-0.434453\pi\)
0.204469 + 0.978873i \(0.434453\pi\)
\(480\) 0 0
\(481\) 0.0418875 0.00190991
\(482\) 0 0
\(483\) 17.5731i 0.799603i
\(484\) 0 0
\(485\) −14.8070 3.32220i −0.672353 0.150853i
\(486\) 0 0
\(487\) 18.3596i 0.831954i 0.909375 + 0.415977i \(0.136560\pi\)
−0.909375 + 0.415977i \(0.863440\pi\)
\(488\) 0 0
\(489\) 15.3137 0.692510
\(490\) 0 0
\(491\) −33.7981 −1.52529 −0.762644 0.646819i \(-0.776099\pi\)
−0.762644 + 0.646819i \(0.776099\pi\)
\(492\) 0 0
\(493\) 1.19611i 0.0538701i
\(494\) 0 0
\(495\) 1.45833 6.49978i 0.0655471 0.292143i
\(496\) 0 0
\(497\) 23.5375i 1.05580i
\(498\) 0 0
\(499\) −5.72898 −0.256464 −0.128232 0.991744i \(-0.540930\pi\)
−0.128232 + 0.991744i \(0.540930\pi\)
\(500\) 0 0
\(501\) −15.3922 −0.687673
\(502\) 0 0
\(503\) 20.2121i 0.901215i 0.892722 + 0.450607i \(0.148793\pi\)
−0.892722 + 0.450607i \(0.851207\pi\)
\(504\) 0 0
\(505\) 5.94392 26.4920i 0.264501 1.17888i
\(506\) 0 0
\(507\) 1.00000i 0.0444116i
\(508\) 0 0
\(509\) −6.02708 −0.267146 −0.133573 0.991039i \(-0.542645\pi\)
−0.133573 + 0.991039i \(0.542645\pi\)
\(510\) 0 0
\(511\) 19.4322 0.859629
\(512\) 0 0
\(513\) 4.17113i 0.184160i
\(514\) 0 0
\(515\) −6.13328 1.37610i −0.270265 0.0606383i
\(516\) 0 0
\(517\) 13.1243i 0.577208i
\(518\) 0 0
\(519\) −14.9706 −0.657135
\(520\) 0 0
\(521\) −1.95899 −0.0858249 −0.0429125 0.999079i \(-0.513664\pi\)
−0.0429125 + 0.999079i \(0.513664\pi\)
\(522\) 0 0
\(523\) 21.6859i 0.948256i 0.880456 + 0.474128i \(0.157237\pi\)
−0.880456 + 0.474128i \(0.842763\pi\)
\(524\) 0 0
\(525\) 12.7865 + 6.04189i 0.558050 + 0.263690i
\(526\) 0 0
\(527\) 2.39222i 0.104207i
\(528\) 0 0
\(529\) −15.6016 −0.678332
\(530\) 0 0
\(531\) −2.97906 −0.129280
\(532\) 0 0
\(533\) 4.36365i 0.189011i
\(534\) 0 0
\(535\) −40.1110 8.99956i −1.73415 0.389085i
\(536\) 0 0
\(537\) 7.63950i 0.329669i
\(538\) 0 0
\(539\) 2.97906 0.128317
\(540\) 0 0
\(541\) 39.3245 1.69069 0.845346 0.534220i \(-0.179394\pi\)
0.845346 + 0.534220i \(0.179394\pi\)
\(542\) 0 0
\(543\) 15.0286i 0.644937i
\(544\) 0 0
\(545\) −0.706797 + 3.15019i −0.0302758 + 0.134939i
\(546\) 0 0
\(547\) 14.1466i 0.604865i 0.953171 + 0.302432i \(0.0977987\pi\)
−0.953171 + 0.302432i \(0.902201\pi\)
\(548\) 0 0
\(549\) −6.27226 −0.267694
\(550\) 0 0
\(551\) −3.45548 −0.147208
\(552\) 0 0
\(553\) 17.2871i 0.735120i
\(554\) 0 0
\(555\) −0.0205051 + 0.0913912i −0.000870394 + 0.00387934i
\(556\) 0 0
\(557\) 29.7603i 1.26098i −0.776196 0.630491i \(-0.782853\pi\)
0.776196 0.630491i \(-0.217147\pi\)
\(558\) 0 0
\(559\) −8.99956 −0.380641
\(560\) 0 0
\(561\) −4.30126 −0.181599
\(562\) 0 0
\(563\) 28.6498i 1.20745i 0.797194 + 0.603723i \(0.206317\pi\)
−0.797194 + 0.603723i \(0.793683\pi\)
\(564\) 0 0
\(565\) 7.42245 + 1.66535i 0.312265 + 0.0700617i
\(566\) 0 0
\(567\) 2.82843i 0.118783i
\(568\) 0 0
\(569\) −39.7326 −1.66568 −0.832838 0.553517i \(-0.813285\pi\)
−0.832838 + 0.553517i \(0.813285\pi\)
\(570\) 0 0
\(571\) 30.5726 1.27943 0.639713 0.768614i \(-0.279053\pi\)
0.639713 + 0.768614i \(0.279053\pi\)
\(572\) 0 0
\(573\) 10.8877i 0.454839i
\(574\) 0 0
\(575\) −13.2718 + 28.0874i −0.553473 + 1.17132i
\(576\) 0 0
\(577\) 35.3116i 1.47004i −0.678045 0.735020i \(-0.737173\pi\)
0.678045 0.735020i \(-0.262827\pi\)
\(578\) 0 0
\(579\) 4.94690 0.205586
\(580\) 0 0
\(581\) −41.5946 −1.72564
\(582\) 0 0
\(583\) 20.0410i 0.830014i
\(584\) 0 0
\(585\) −2.18183 0.489528i −0.0902074 0.0202395i
\(586\) 0 0
\(587\) 19.5517i 0.806985i 0.914983 + 0.403492i \(0.132204\pi\)
−0.914983 + 0.403492i \(0.867796\pi\)
\(588\) 0 0
\(589\) −6.91096 −0.284761
\(590\) 0 0
\(591\) −26.3628 −1.08442
\(592\) 0 0
\(593\) 4.66491i 0.191565i −0.995402 0.0957824i \(-0.969465\pi\)
0.995402 0.0957824i \(-0.0305353\pi\)
\(594\) 0 0
\(595\) 1.99912 8.91008i 0.0819560 0.365278i
\(596\) 0 0
\(597\) 6.11190i 0.250143i
\(598\) 0 0
\(599\) 19.6497 0.802864 0.401432 0.915889i \(-0.368513\pi\)
0.401432 + 0.915889i \(0.368513\pi\)
\(600\) 0 0
\(601\) 44.2714 1.80587 0.902934 0.429780i \(-0.141409\pi\)
0.902934 + 0.429780i \(0.141409\pi\)
\(602\) 0 0
\(603\) 0.727302i 0.0296180i
\(604\) 0 0
\(605\) −1.04036 + 4.63687i −0.0422965 + 0.188515i
\(606\) 0 0
\(607\) 34.2648i 1.39077i 0.718640 + 0.695383i \(0.244765\pi\)
−0.718640 + 0.695383i \(0.755235\pi\)
\(608\) 0 0
\(609\) −2.34315 −0.0949491
\(610\) 0 0
\(611\) 4.40554 0.178229
\(612\) 0 0
\(613\) 33.7203i 1.36195i −0.732307 0.680975i \(-0.761556\pi\)
0.732307 0.680975i \(-0.238444\pi\)
\(614\) 0 0
\(615\) 9.52072 + 2.13613i 0.383913 + 0.0861371i
\(616\) 0 0
\(617\) 35.0901i 1.41267i −0.707876 0.706337i \(-0.750347\pi\)
0.707876 0.706337i \(-0.249653\pi\)
\(618\) 0 0
\(619\) −2.63907 −0.106073 −0.0530365 0.998593i \(-0.516890\pi\)
−0.0530365 + 0.998593i \(0.516890\pi\)
\(620\) 0 0
\(621\) 6.21302 0.249320
\(622\) 0 0
\(623\) 41.7131i 1.67120i
\(624\) 0 0
\(625\) 15.8739 + 19.3137i 0.634956 + 0.772548i
\(626\) 0 0
\(627\) 12.4260i 0.496248i
\(628\) 0 0
\(629\) 0.0604785 0.00241144
\(630\) 0 0
\(631\) −28.7683 −1.14525 −0.572624 0.819818i \(-0.694075\pi\)
−0.572624 + 0.819818i \(0.694075\pi\)
\(632\) 0 0
\(633\) 9.68585i 0.384978i
\(634\) 0 0
\(635\) −34.4961 7.73975i −1.36893 0.307143i
\(636\) 0 0
\(637\) 1.00000i 0.0396214i
\(638\) 0 0
\(639\) 8.32176 0.329204
\(640\) 0 0
\(641\) 35.1944 1.39009 0.695047 0.718965i \(-0.255384\pi\)
0.695047 + 0.718965i \(0.255384\pi\)
\(642\) 0 0
\(643\) 27.2709i 1.07546i 0.843117 + 0.537731i \(0.180718\pi\)
−0.843117 + 0.537731i \(0.819282\pi\)
\(644\) 0 0
\(645\) 4.40554 19.6355i 0.173468 0.773146i
\(646\) 0 0
\(647\) 4.22913i 0.166264i −0.996539 0.0831322i \(-0.973508\pi\)
0.996539 0.0831322i \(-0.0264924\pi\)
\(648\) 0 0
\(649\) −8.87478 −0.348365
\(650\) 0 0
\(651\) −4.68629 −0.183670
\(652\) 0 0
\(653\) 22.1400i 0.866406i 0.901296 + 0.433203i \(0.142617\pi\)
−0.901296 + 0.433203i \(0.857383\pi\)
\(654\) 0 0
\(655\) −9.38459 + 41.8271i −0.366686 + 1.63432i
\(656\) 0 0
\(657\) 6.87031i 0.268037i
\(658\) 0 0
\(659\) −27.0932 −1.05540 −0.527701 0.849430i \(-0.676946\pi\)
−0.527701 + 0.849430i \(0.676946\pi\)
\(660\) 0 0
\(661\) 19.0597 0.741335 0.370668 0.928766i \(-0.379129\pi\)
0.370668 + 0.928766i \(0.379129\pi\)
\(662\) 0 0
\(663\) 1.44383i 0.0560738i
\(664\) 0 0
\(665\) 25.7406 + 5.77533i 0.998179 + 0.223958i
\(666\) 0 0
\(667\) 5.14704i 0.199294i
\(668\) 0 0
\(669\) 9.21258 0.356179
\(670\) 0 0
\(671\) −18.6854 −0.721342
\(672\) 0 0
\(673\) 23.6213i 0.910533i −0.890355 0.455267i \(-0.849544\pi\)
0.890355 0.455267i \(-0.150456\pi\)
\(674\) 0 0
\(675\) 2.13613 4.52072i 0.0822197 0.174003i
\(676\) 0 0
\(677\) 18.8111i 0.722968i 0.932378 + 0.361484i \(0.117730\pi\)
−0.932378 + 0.361484i \(0.882270\pi\)
\(678\) 0 0
\(679\) −19.1952 −0.736645
\(680\) 0 0
\(681\) −20.3218 −0.778732
\(682\) 0 0
\(683\) 33.7827i 1.29266i 0.763059 + 0.646329i \(0.223697\pi\)
−0.763059 + 0.646329i \(0.776303\pi\)
\(684\) 0 0
\(685\) −3.66162 0.821544i −0.139903 0.0313896i
\(686\) 0 0
\(687\) 16.4715i 0.628428i
\(688\) 0 0
\(689\) −6.72730 −0.256290
\(690\) 0 0
\(691\) −47.3236 −1.80027 −0.900137 0.435606i \(-0.856534\pi\)
−0.900137 + 0.435606i \(0.856534\pi\)
\(692\) 0 0
\(693\) 8.42604i 0.320079i
\(694\) 0 0
\(695\) 6.04189 26.9287i 0.229182 1.02146i
\(696\) 0 0
\(697\) 6.30038i 0.238644i
\(698\) 0 0
\(699\) 2.37339 0.0897697
\(700\) 0 0
\(701\) −3.29636 −0.124502 −0.0622509 0.998061i \(-0.519828\pi\)
−0.0622509 + 0.998061i \(0.519828\pi\)
\(702\) 0 0
\(703\) 0.174718i 0.00658963i
\(704\) 0 0
\(705\) −2.15663 + 9.61212i −0.0812236 + 0.362013i
\(706\) 0 0
\(707\) 34.3431i 1.29161i
\(708\) 0 0
\(709\) −46.8404 −1.75913 −0.879565 0.475779i \(-0.842166\pi\)
−0.879565 + 0.475779i \(0.842166\pi\)
\(710\) 0 0
\(711\) 6.11190 0.229214
\(712\) 0 0
\(713\) 10.2941i 0.385516i
\(714\) 0 0
\(715\) −6.49978 1.45833i −0.243078 0.0545385i
\(716\) 0 0
\(717\) 13.6363i 0.509259i
\(718\) 0 0
\(719\) 20.0152 0.746442 0.373221 0.927742i \(-0.378253\pi\)
0.373221 + 0.927742i \(0.378253\pi\)
\(720\) 0 0
\(721\) −7.95093 −0.296108
\(722\) 0 0
\(723\) 1.07045i 0.0398104i
\(724\) 0 0
\(725\) −3.74509 1.76963i −0.139089 0.0657223i
\(726\) 0 0
\(727\) 10.8383i 0.401971i −0.979594 0.200986i \(-0.935586\pi\)
0.979594 0.200986i \(-0.0644144\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −12.9939 −0.480595
\(732\) 0 0
\(733\) 21.1952i 0.782864i −0.920207 0.391432i \(-0.871980\pi\)
0.920207 0.391432i \(-0.128020\pi\)
\(734\) 0 0
\(735\) 2.18183 + 0.489528i 0.0804778 + 0.0180565i
\(736\) 0 0
\(737\) 2.16667i 0.0798104i
\(738\) 0 0
\(739\) −7.07403 −0.260222 −0.130111 0.991499i \(-0.541533\pi\)
−0.130111 + 0.991499i \(0.541533\pi\)
\(740\) 0 0
\(741\) −4.17113 −0.153230
\(742\) 0 0
\(743\) 21.3913i 0.784772i −0.919801 0.392386i \(-0.871650\pi\)
0.919801 0.392386i \(-0.128350\pi\)
\(744\) 0 0
\(745\) −0.331801 + 1.47884i −0.0121563 + 0.0541804i
\(746\) 0 0
\(747\) 14.7059i 0.538061i
\(748\) 0 0
\(749\) −51.9982 −1.89997
\(750\) 0 0
\(751\) 18.2247 0.665028 0.332514 0.943098i \(-0.392103\pi\)
0.332514 + 0.943098i \(0.392103\pi\)
\(752\) 0 0
\(753\) 14.6262i 0.533007i
\(754\) 0 0
\(755\) −8.81108 + 39.2709i −0.320668 + 1.42922i
\(756\) 0 0
\(757\) 39.3708i 1.43096i −0.698635 0.715479i \(-0.746209\pi\)
0.698635 0.715479i \(-0.253791\pi\)
\(758\) 0 0
\(759\) 18.5089 0.671832
\(760\) 0 0
\(761\) −13.8610 −0.502462 −0.251231 0.967927i \(-0.580835\pi\)
−0.251231 + 0.967927i \(0.580835\pi\)
\(762\) 0 0
\(763\) 4.08378i 0.147843i
\(764\) 0 0
\(765\) −3.15019 0.706797i −0.113895 0.0255543i
\(766\) 0 0
\(767\) 2.97906i 0.107567i
\(768\) 0 0
\(769\) 12.6274 0.455356 0.227678 0.973736i \(-0.426887\pi\)
0.227678 + 0.973736i \(0.426887\pi\)
\(770\) 0 0
\(771\) −24.9403 −0.898204
\(772\) 0 0
\(773\) 34.7825i 1.25104i 0.780208 + 0.625520i \(0.215113\pi\)
−0.780208 + 0.625520i \(0.784887\pi\)
\(774\) 0 0
\(775\) −7.49018 3.53926i −0.269055 0.127134i
\(776\) 0 0
\(777\) 0.118476i 0.00425029i
\(778\) 0 0
\(779\) 18.2014 0.652132
\(780\) 0 0
\(781\) 24.7910 0.887092
\(782\) 0 0
\(783\) 0.828427i 0.0296056i
\(784\) 0 0
\(785\) 28.0129 + 6.28515i 0.999823 + 0.224327i
\(786\) 0 0
\(787\) 36.7835i 1.31119i 0.755112 + 0.655596i \(0.227582\pi\)
−0.755112 + 0.655596i \(0.772418\pi\)
\(788\) 0 0
\(789\) −9.01691 −0.321011
\(790\) 0 0
\(791\) 9.62215 0.342124
\(792\) 0 0
\(793\) 6.27226i 0.222734i
\(794\) 0 0
\(795\) 3.29320 14.6778i 0.116798 0.520568i
\(796\) 0 0
\(797\) 42.4413i 1.50335i 0.659535 + 0.751674i \(0.270753\pi\)
−0.659535 + 0.751674i \(0.729247\pi\)
\(798\) 0 0
\(799\) 6.36086 0.225031
\(800\) 0 0