Properties

Label 1680.2.t.k.1009.1
Level $1680$
Weight $2$
Character 1680.1009
Analytic conductor $13.415$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.t (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4148675396\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
Defining polynomial: \(x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} + 4 x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1009.1
Root \(0.403032 - 0.403032i\) of defining polynomial
Character \(\chi\) \(=\) 1680.1009
Dual form 1680.2.t.k.1009.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{3} +(-1.48119 + 1.67513i) q^{5} +1.00000i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{3} +(-1.48119 + 1.67513i) q^{5} +1.00000i q^{7} -1.00000 q^{9} -2.00000 q^{11} -1.35026i q^{13} +(1.67513 + 1.48119i) q^{15} -3.35026i q^{17} +5.35026 q^{19} +1.00000 q^{21} +4.96239i q^{23} +(-0.612127 - 4.96239i) q^{25} +1.00000i q^{27} -7.92478 q^{29} -4.57452 q^{31} +2.00000i q^{33} +(-1.67513 - 1.48119i) q^{35} -0.775746i q^{37} -1.35026 q^{39} +3.73813 q^{41} -12.6253i q^{43} +(1.48119 - 1.67513i) q^{45} -9.92478i q^{47} -1.00000 q^{49} -3.35026 q^{51} -8.57452i q^{53} +(2.96239 - 3.35026i) q^{55} -5.35026i q^{57} -8.62530 q^{59} -8.70052 q^{61} -1.00000i q^{63} +(2.26187 + 2.00000i) q^{65} -9.92478i q^{67} +4.96239 q^{69} -2.00000 q^{71} +9.35026i q^{73} +(-4.96239 + 0.612127i) q^{75} -2.00000i q^{77} +10.7005 q^{79} +1.00000 q^{81} +3.22425i q^{83} +(5.61213 + 4.96239i) q^{85} +7.92478i q^{87} -1.03761 q^{89} +1.35026 q^{91} +4.57452i q^{93} +(-7.92478 + 8.96239i) q^{95} -18.4993i q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{5} - 6 q^{9} + O(q^{10}) \) \( 6 q + 2 q^{5} - 6 q^{9} - 12 q^{11} + 12 q^{19} + 6 q^{21} - 2 q^{25} - 4 q^{29} - 4 q^{31} + 12 q^{39} + 4 q^{41} - 2 q^{45} - 6 q^{49} - 4 q^{55} + 32 q^{59} - 12 q^{61} + 32 q^{65} + 8 q^{69} - 12 q^{71} - 8 q^{75} + 24 q^{79} + 6 q^{81} + 32 q^{85} - 28 q^{89} - 12 q^{91} - 4 q^{95} + 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(421\) \(1121\) \(1471\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\) \(1\)

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
\(5\) −1.48119 + 1.67513i −0.662410 + 0.749141i
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 1.35026i 0.374495i −0.982313 0.187248i \(-0.940043\pi\)
0.982313 0.187248i \(-0.0599567\pi\)
\(14\) 0 0
\(15\) 1.67513 + 1.48119i 0.432517 + 0.382443i
\(16\) 0 0
\(17\) 3.35026i 0.812558i −0.913749 0.406279i \(-0.866826\pi\)
0.913749 0.406279i \(-0.133174\pi\)
\(18\) 0 0
\(19\) 5.35026 1.22743 0.613717 0.789526i \(-0.289674\pi\)
0.613717 + 0.789526i \(0.289674\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 4.96239i 1.03473i 0.855765 + 0.517365i \(0.173087\pi\)
−0.855765 + 0.517365i \(0.826913\pi\)
\(24\) 0 0
\(25\) −0.612127 4.96239i −0.122425 0.992478i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −7.92478 −1.47159 −0.735797 0.677202i \(-0.763192\pi\)
−0.735797 + 0.677202i \(0.763192\pi\)
\(30\) 0 0
\(31\) −4.57452 −0.821607 −0.410804 0.911724i \(-0.634752\pi\)
−0.410804 + 0.911724i \(0.634752\pi\)
\(32\) 0 0
\(33\) 2.00000i 0.348155i
\(34\) 0 0
\(35\) −1.67513 1.48119i −0.283149 0.250368i
\(36\) 0 0
\(37\) 0.775746i 0.127532i −0.997965 0.0637660i \(-0.979689\pi\)
0.997965 0.0637660i \(-0.0203111\pi\)
\(38\) 0 0
\(39\) −1.35026 −0.216215
\(40\) 0 0
\(41\) 3.73813 0.583799 0.291899 0.956449i \(-0.405713\pi\)
0.291899 + 0.956449i \(0.405713\pi\)
\(42\) 0 0
\(43\) 12.6253i 1.92534i −0.270677 0.962670i \(-0.587248\pi\)
0.270677 0.962670i \(-0.412752\pi\)
\(44\) 0 0
\(45\) 1.48119 1.67513i 0.220803 0.249714i
\(46\) 0 0
\(47\) 9.92478i 1.44768i −0.689969 0.723839i \(-0.742376\pi\)
0.689969 0.723839i \(-0.257624\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) −3.35026 −0.469130
\(52\) 0 0
\(53\) 8.57452i 1.17780i −0.808206 0.588900i \(-0.799561\pi\)
0.808206 0.588900i \(-0.200439\pi\)
\(54\) 0 0
\(55\) 2.96239 3.35026i 0.399448 0.451749i
\(56\) 0 0
\(57\) 5.35026i 0.708659i
\(58\) 0 0
\(59\) −8.62530 −1.12292 −0.561459 0.827504i \(-0.689760\pi\)
−0.561459 + 0.827504i \(0.689760\pi\)
\(60\) 0 0
\(61\) −8.70052 −1.11399 −0.556994 0.830517i \(-0.688045\pi\)
−0.556994 + 0.830517i \(0.688045\pi\)
\(62\) 0 0
\(63\) 1.00000i 0.125988i
\(64\) 0 0
\(65\) 2.26187 + 2.00000i 0.280550 + 0.248069i
\(66\) 0 0
\(67\) 9.92478i 1.21250i −0.795272 0.606252i \(-0.792672\pi\)
0.795272 0.606252i \(-0.207328\pi\)
\(68\) 0 0
\(69\) 4.96239 0.597401
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 9.35026i 1.09437i 0.837013 + 0.547183i \(0.184300\pi\)
−0.837013 + 0.547183i \(0.815700\pi\)
\(74\) 0 0
\(75\) −4.96239 + 0.612127i −0.573007 + 0.0706823i
\(76\) 0 0
\(77\) 2.00000i 0.227921i
\(78\) 0 0
\(79\) 10.7005 1.20390 0.601951 0.798533i \(-0.294390\pi\)
0.601951 + 0.798533i \(0.294390\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 3.22425i 0.353908i 0.984219 + 0.176954i \(0.0566244\pi\)
−0.984219 + 0.176954i \(0.943376\pi\)
\(84\) 0 0
\(85\) 5.61213 + 4.96239i 0.608721 + 0.538247i
\(86\) 0 0
\(87\) 7.92478i 0.849625i
\(88\) 0 0
\(89\) −1.03761 −0.109987 −0.0549933 0.998487i \(-0.517514\pi\)
−0.0549933 + 0.998487i \(0.517514\pi\)
\(90\) 0 0
\(91\) 1.35026 0.141546
\(92\) 0 0
\(93\) 4.57452i 0.474355i
\(94\) 0 0
\(95\) −7.92478 + 8.96239i −0.813065 + 0.919522i
\(96\) 0 0
\(97\) 18.4993i 1.87832i −0.343482 0.939159i \(-0.611606\pi\)
0.343482 0.939159i \(-0.388394\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) −17.6629 −1.75753 −0.878763 0.477259i \(-0.841630\pi\)
−0.878763 + 0.477259i \(0.841630\pi\)
\(102\) 0 0
\(103\) 6.70052i 0.660222i 0.943942 + 0.330111i \(0.107086\pi\)
−0.943942 + 0.330111i \(0.892914\pi\)
\(104\) 0 0
\(105\) −1.48119 + 1.67513i −0.144550 + 0.163476i
\(106\) 0 0
\(107\) 13.7381i 1.32812i −0.747681 0.664058i \(-0.768833\pi\)
0.747681 0.664058i \(-0.231167\pi\)
\(108\) 0 0
\(109\) 2.77575 0.265868 0.132934 0.991125i \(-0.457560\pi\)
0.132934 + 0.991125i \(0.457560\pi\)
\(110\) 0 0
\(111\) −0.775746 −0.0736306
\(112\) 0 0
\(113\) 12.0508i 1.13364i −0.823841 0.566821i \(-0.808173\pi\)
0.823841 0.566821i \(-0.191827\pi\)
\(114\) 0 0
\(115\) −8.31265 7.35026i −0.775159 0.685415i
\(116\) 0 0
\(117\) 1.35026i 0.124832i
\(118\) 0 0
\(119\) 3.35026 0.307118
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 3.73813i 0.337056i
\(124\) 0 0
\(125\) 9.21933 + 6.32487i 0.824602 + 0.565713i
\(126\) 0 0
\(127\) 2.70052i 0.239633i −0.992796 0.119816i \(-0.961769\pi\)
0.992796 0.119816i \(-0.0382306\pi\)
\(128\) 0 0
\(129\) −12.6253 −1.11160
\(130\) 0 0
\(131\) −20.6253 −1.80204 −0.901020 0.433777i \(-0.857181\pi\)
−0.901020 + 0.433777i \(0.857181\pi\)
\(132\) 0 0
\(133\) 5.35026i 0.463927i
\(134\) 0 0
\(135\) −1.67513 1.48119i −0.144172 0.127481i
\(136\) 0 0
\(137\) 22.4993i 1.92224i 0.276124 + 0.961122i \(0.410950\pi\)
−0.276124 + 0.961122i \(0.589050\pi\)
\(138\) 0 0
\(139\) −3.27504 −0.277785 −0.138893 0.990307i \(-0.544354\pi\)
−0.138893 + 0.990307i \(0.544354\pi\)
\(140\) 0 0
\(141\) −9.92478 −0.835817
\(142\) 0 0
\(143\) 2.70052i 0.225829i
\(144\) 0 0
\(145\) 11.7381 13.2750i 0.974799 1.10243i
\(146\) 0 0
\(147\) 1.00000i 0.0824786i
\(148\) 0 0
\(149\) 4.44851 0.364436 0.182218 0.983258i \(-0.441672\pi\)
0.182218 + 0.983258i \(0.441672\pi\)
\(150\) 0 0
\(151\) −1.29948 −0.105750 −0.0528749 0.998601i \(-0.516838\pi\)
−0.0528749 + 0.998601i \(0.516838\pi\)
\(152\) 0 0
\(153\) 3.35026i 0.270853i
\(154\) 0 0
\(155\) 6.77575 7.66291i 0.544241 0.615500i
\(156\) 0 0
\(157\) 2.64974i 0.211472i −0.994394 0.105736i \(-0.966280\pi\)
0.994394 0.105736i \(-0.0337199\pi\)
\(158\) 0 0
\(159\) −8.57452 −0.680003
\(160\) 0 0
\(161\) −4.96239 −0.391091
\(162\) 0 0
\(163\) 5.29948i 0.415087i 0.978226 + 0.207544i \(0.0665469\pi\)
−0.978226 + 0.207544i \(0.933453\pi\)
\(164\) 0 0
\(165\) −3.35026 2.96239i −0.260818 0.230622i
\(166\) 0 0
\(167\) 14.5501i 1.12592i 0.826485 + 0.562959i \(0.190337\pi\)
−0.826485 + 0.562959i \(0.809663\pi\)
\(168\) 0 0
\(169\) 11.1768 0.859753
\(170\) 0 0
\(171\) −5.35026 −0.409145
\(172\) 0 0
\(173\) 4.49929i 0.342075i 0.985265 + 0.171037i \(0.0547119\pi\)
−0.985265 + 0.171037i \(0.945288\pi\)
\(174\) 0 0
\(175\) 4.96239 0.612127i 0.375121 0.0462724i
\(176\) 0 0
\(177\) 8.62530i 0.648317i
\(178\) 0 0
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 0 0
\(181\) 10.6253 0.789772 0.394886 0.918730i \(-0.370784\pi\)
0.394886 + 0.918730i \(0.370784\pi\)
\(182\) 0 0
\(183\) 8.70052i 0.643161i
\(184\) 0 0
\(185\) 1.29948 + 1.14903i 0.0955394 + 0.0844784i
\(186\) 0 0
\(187\) 6.70052i 0.489991i
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) 13.8496 1.00212 0.501059 0.865413i \(-0.332944\pi\)
0.501059 + 0.865413i \(0.332944\pi\)
\(192\) 0 0
\(193\) 15.3258i 1.10318i −0.834116 0.551588i \(-0.814022\pi\)
0.834116 0.551588i \(-0.185978\pi\)
\(194\) 0 0
\(195\) 2.00000 2.26187i 0.143223 0.161976i
\(196\) 0 0
\(197\) 0.574515i 0.0409325i −0.999791 0.0204663i \(-0.993485\pi\)
0.999791 0.0204663i \(-0.00651507\pi\)
\(198\) 0 0
\(199\) −0.201231 −0.0142649 −0.00713244 0.999975i \(-0.502270\pi\)
−0.00713244 + 0.999975i \(0.502270\pi\)
\(200\) 0 0
\(201\) −9.92478 −0.700040
\(202\) 0 0
\(203\) 7.92478i 0.556210i
\(204\) 0 0
\(205\) −5.53690 + 6.26187i −0.386714 + 0.437348i
\(206\) 0 0
\(207\) 4.96239i 0.344910i
\(208\) 0 0
\(209\) −10.7005 −0.740171
\(210\) 0 0
\(211\) −6.44851 −0.443934 −0.221967 0.975054i \(-0.571248\pi\)
−0.221967 + 0.975054i \(0.571248\pi\)
\(212\) 0 0
\(213\) 2.00000i 0.137038i
\(214\) 0 0
\(215\) 21.1490 + 18.7005i 1.44235 + 1.27537i
\(216\) 0 0
\(217\) 4.57452i 0.310538i
\(218\) 0 0
\(219\) 9.35026 0.631832
\(220\) 0 0
\(221\) −4.52373 −0.304299
\(222\) 0 0
\(223\) 1.55149i 0.103896i 0.998650 + 0.0519478i \(0.0165429\pi\)
−0.998650 + 0.0519478i \(0.983457\pi\)
\(224\) 0 0
\(225\) 0.612127 + 4.96239i 0.0408085 + 0.330826i
\(226\) 0 0
\(227\) 13.1490i 0.872732i 0.899769 + 0.436366i \(0.143735\pi\)
−0.899769 + 0.436366i \(0.856265\pi\)
\(228\) 0 0
\(229\) −2.77575 −0.183426 −0.0917132 0.995785i \(-0.529234\pi\)
−0.0917132 + 0.995785i \(0.529234\pi\)
\(230\) 0 0
\(231\) −2.00000 −0.131590
\(232\) 0 0
\(233\) 0.0507852i 0.00332705i 0.999999 + 0.00166353i \(0.000529517\pi\)
−0.999999 + 0.00166353i \(0.999470\pi\)
\(234\) 0 0
\(235\) 16.6253 + 14.7005i 1.08452 + 0.958956i
\(236\) 0 0
\(237\) 10.7005i 0.695074i
\(238\) 0 0
\(239\) 5.84955 0.378376 0.189188 0.981941i \(-0.439414\pi\)
0.189188 + 0.981941i \(0.439414\pi\)
\(240\) 0 0
\(241\) −0.0752228 −0.00484553 −0.00242276 0.999997i \(-0.500771\pi\)
−0.00242276 + 0.999997i \(0.500771\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 1.48119 1.67513i 0.0946300 0.107020i
\(246\) 0 0
\(247\) 7.22425i 0.459668i
\(248\) 0 0
\(249\) 3.22425 0.204329
\(250\) 0 0
\(251\) −19.2243 −1.21342 −0.606712 0.794922i \(-0.707512\pi\)
−0.606712 + 0.794922i \(0.707512\pi\)
\(252\) 0 0
\(253\) 9.92478i 0.623965i
\(254\) 0 0
\(255\) 4.96239 5.61213i 0.310757 0.351445i
\(256\) 0 0
\(257\) 7.35026i 0.458497i 0.973368 + 0.229248i \(0.0736268\pi\)
−0.973368 + 0.229248i \(0.926373\pi\)
\(258\) 0 0
\(259\) 0.775746 0.0482025
\(260\) 0 0
\(261\) 7.92478 0.490531
\(262\) 0 0
\(263\) 12.9624i 0.799295i −0.916669 0.399648i \(-0.869133\pi\)
0.916669 0.399648i \(-0.130867\pi\)
\(264\) 0 0
\(265\) 14.3634 + 12.7005i 0.882339 + 0.780187i
\(266\) 0 0
\(267\) 1.03761i 0.0635008i
\(268\) 0 0
\(269\) −4.11142 −0.250678 −0.125339 0.992114i \(-0.540002\pi\)
−0.125339 + 0.992114i \(0.540002\pi\)
\(270\) 0 0
\(271\) 16.4241 0.997691 0.498846 0.866691i \(-0.333757\pi\)
0.498846 + 0.866691i \(0.333757\pi\)
\(272\) 0 0
\(273\) 1.35026i 0.0817216i
\(274\) 0 0
\(275\) 1.22425 + 9.92478i 0.0738253 + 0.598487i
\(276\) 0 0
\(277\) 11.0738i 0.665361i −0.943040 0.332680i \(-0.892047\pi\)
0.943040 0.332680i \(-0.107953\pi\)
\(278\) 0 0
\(279\) 4.57452 0.273869
\(280\) 0 0
\(281\) 14.3733 0.857438 0.428719 0.903438i \(-0.358965\pi\)
0.428719 + 0.903438i \(0.358965\pi\)
\(282\) 0 0
\(283\) 1.14903i 0.0683028i 0.999417 + 0.0341514i \(0.0108728\pi\)
−0.999417 + 0.0341514i \(0.989127\pi\)
\(284\) 0 0
\(285\) 8.96239 + 7.92478i 0.530886 + 0.469423i
\(286\) 0 0
\(287\) 3.73813i 0.220655i
\(288\) 0 0
\(289\) 5.77575 0.339750
\(290\) 0 0
\(291\) −18.4993 −1.08445
\(292\) 0 0
\(293\) 0.649738i 0.0379581i −0.999820 0.0189791i \(-0.993958\pi\)
0.999820 0.0189791i \(-0.00604158\pi\)
\(294\) 0 0
\(295\) 12.7757 14.4485i 0.743833 0.841225i
\(296\) 0 0
\(297\) 2.00000i 0.116052i
\(298\) 0 0
\(299\) 6.70052 0.387501
\(300\) 0 0
\(301\) 12.6253 0.727710
\(302\) 0 0
\(303\) 17.6629i 1.01471i
\(304\) 0 0
\(305\) 12.8872 14.5745i 0.737917 0.834534i
\(306\) 0 0
\(307\) 24.1016i 1.37555i −0.725924 0.687775i \(-0.758588\pi\)
0.725924 0.687775i \(-0.241412\pi\)
\(308\) 0 0
\(309\) 6.70052 0.381179
\(310\) 0 0
\(311\) −8.25202 −0.467929 −0.233964 0.972245i \(-0.575170\pi\)
−0.233964 + 0.972245i \(0.575170\pi\)
\(312\) 0 0
\(313\) 14.9018i 0.842297i 0.906992 + 0.421148i \(0.138373\pi\)
−0.906992 + 0.421148i \(0.861627\pi\)
\(314\) 0 0
\(315\) 1.67513 + 1.48119i 0.0943829 + 0.0834558i
\(316\) 0 0
\(317\) 10.1260i 0.568733i 0.958716 + 0.284367i \(0.0917833\pi\)
−0.958716 + 0.284367i \(0.908217\pi\)
\(318\) 0 0
\(319\) 15.8496 0.887405
\(320\) 0 0
\(321\) −13.7381 −0.766788
\(322\) 0 0
\(323\) 17.9248i 0.997361i
\(324\) 0 0
\(325\) −6.70052 + 0.826531i −0.371678 + 0.0458477i
\(326\) 0 0
\(327\) 2.77575i 0.153499i
\(328\) 0 0
\(329\) 9.92478 0.547171
\(330\) 0 0
\(331\) −27.8496 −1.53075 −0.765375 0.643585i \(-0.777446\pi\)
−0.765375 + 0.643585i \(0.777446\pi\)
\(332\) 0 0
\(333\) 0.775746i 0.0425106i
\(334\) 0 0
\(335\) 16.6253 + 14.7005i 0.908337 + 0.803175i
\(336\) 0 0
\(337\) 3.84955i 0.209699i −0.994488 0.104849i \(-0.966564\pi\)
0.994488 0.104849i \(-0.0334360\pi\)
\(338\) 0 0
\(339\) −12.0508 −0.654509
\(340\) 0 0
\(341\) 9.14903 0.495448
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) −7.35026 + 8.31265i −0.395725 + 0.447538i
\(346\) 0 0
\(347\) 9.58769i 0.514694i −0.966319 0.257347i \(-0.917152\pi\)
0.966319 0.257347i \(-0.0828484\pi\)
\(348\) 0 0
\(349\) 15.1490 0.810909 0.405455 0.914115i \(-0.367113\pi\)
0.405455 + 0.914115i \(0.367113\pi\)
\(350\) 0 0
\(351\) 1.35026 0.0720716
\(352\) 0 0
\(353\) 20.3488i 1.08306i 0.840681 + 0.541530i \(0.182155\pi\)
−0.840681 + 0.541530i \(0.817845\pi\)
\(354\) 0 0
\(355\) 2.96239 3.35026i 0.157227 0.177813i
\(356\) 0 0
\(357\) 3.35026i 0.177315i
\(358\) 0 0
\(359\) −31.4010 −1.65728 −0.828642 0.559779i \(-0.810886\pi\)
−0.828642 + 0.559779i \(0.810886\pi\)
\(360\) 0 0
\(361\) 9.62530 0.506595
\(362\) 0 0
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) −15.6629 13.8496i −0.819834 0.724919i
\(366\) 0 0
\(367\) 29.4010i 1.53472i 0.641215 + 0.767361i \(0.278431\pi\)
−0.641215 + 0.767361i \(0.721569\pi\)
\(368\) 0 0
\(369\) −3.73813 −0.194600
\(370\) 0 0
\(371\) 8.57452 0.445167
\(372\) 0 0
\(373\) 16.0000i 0.828449i −0.910175 0.414224i \(-0.864053\pi\)
0.910175 0.414224i \(-0.135947\pi\)
\(374\) 0 0
\(375\) 6.32487 9.21933i 0.326615 0.476084i
\(376\) 0 0
\(377\) 10.7005i 0.551105i
\(378\) 0 0
\(379\) 10.7005 0.549649 0.274824 0.961494i \(-0.411380\pi\)
0.274824 + 0.961494i \(0.411380\pi\)
\(380\) 0 0
\(381\) −2.70052 −0.138352
\(382\) 0 0
\(383\) 16.7757i 0.857201i −0.903494 0.428600i \(-0.859007\pi\)
0.903494 0.428600i \(-0.140993\pi\)
\(384\) 0 0
\(385\) 3.35026 + 2.96239i 0.170745 + 0.150977i
\(386\) 0 0
\(387\) 12.6253i 0.641780i
\(388\) 0 0
\(389\) 29.3258 1.48688 0.743439 0.668804i \(-0.233193\pi\)
0.743439 + 0.668804i \(0.233193\pi\)
\(390\) 0 0
\(391\) 16.6253 0.840778
\(392\) 0 0
\(393\) 20.6253i 1.04041i
\(394\) 0 0
\(395\) −15.8496 + 17.9248i −0.797478 + 0.901893i
\(396\) 0 0
\(397\) 18.3488i 0.920902i 0.887685 + 0.460451i \(0.152312\pi\)
−0.887685 + 0.460451i \(0.847688\pi\)
\(398\) 0 0
\(399\) 5.35026 0.267848
\(400\) 0 0
\(401\) −37.3258 −1.86396 −0.931981 0.362506i \(-0.881921\pi\)
−0.931981 + 0.362506i \(0.881921\pi\)
\(402\) 0 0
\(403\) 6.17679i 0.307688i
\(404\) 0 0
\(405\) −1.48119 + 1.67513i −0.0736011 + 0.0832379i
\(406\) 0 0
\(407\) 1.55149i 0.0769046i
\(408\) 0 0
\(409\) 22.3733 1.10629 0.553144 0.833086i \(-0.313428\pi\)
0.553144 + 0.833086i \(0.313428\pi\)
\(410\) 0 0
\(411\) 22.4993 1.10981
\(412\) 0 0
\(413\) 8.62530i 0.424423i
\(414\) 0 0
\(415\) −5.40105 4.77575i −0.265127 0.234432i
\(416\) 0 0
\(417\) 3.27504i 0.160379i
\(418\) 0 0
\(419\) 23.4763 1.14689 0.573445 0.819244i \(-0.305606\pi\)
0.573445 + 0.819244i \(0.305606\pi\)
\(420\) 0 0
\(421\) −25.2243 −1.22935 −0.614677 0.788779i \(-0.710714\pi\)
−0.614677 + 0.788779i \(0.710714\pi\)
\(422\) 0 0
\(423\) 9.92478i 0.482559i
\(424\) 0 0
\(425\) −16.6253 + 2.05079i −0.806446 + 0.0994777i
\(426\) 0 0
\(427\) 8.70052i 0.421048i
\(428\) 0 0
\(429\) 2.70052 0.130383
\(430\) 0 0
\(431\) 19.4010 0.934516 0.467258 0.884121i \(-0.345242\pi\)
0.467258 + 0.884121i \(0.345242\pi\)
\(432\) 0 0
\(433\) 6.49929i 0.312336i −0.987731 0.156168i \(-0.950086\pi\)
0.987731 0.156168i \(-0.0499141\pi\)
\(434\) 0 0
\(435\) −13.2750 11.7381i −0.636489 0.562800i
\(436\) 0 0
\(437\) 26.5501i 1.27006i
\(438\) 0 0
\(439\) −14.6497 −0.699194 −0.349597 0.936900i \(-0.613681\pi\)
−0.349597 + 0.936900i \(0.613681\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 19.1392i 0.909330i 0.890663 + 0.454665i \(0.150241\pi\)
−0.890663 + 0.454665i \(0.849759\pi\)
\(444\) 0 0
\(445\) 1.53690 1.73813i 0.0728562 0.0823955i
\(446\) 0 0
\(447\) 4.44851i 0.210407i
\(448\) 0 0
\(449\) 32.8021 1.54803 0.774013 0.633169i \(-0.218246\pi\)
0.774013 + 0.633169i \(0.218246\pi\)
\(450\) 0 0
\(451\) −7.47627 −0.352044
\(452\) 0 0
\(453\) 1.29948i 0.0610547i
\(454\) 0 0
\(455\) −2.00000 + 2.26187i −0.0937614 + 0.106038i
\(456\) 0 0
\(457\) 18.7005i 0.874774i −0.899273 0.437387i \(-0.855904\pi\)
0.899273 0.437387i \(-0.144096\pi\)
\(458\) 0 0
\(459\) 3.35026 0.156377
\(460\) 0 0
\(461\) −6.96239 −0.324271 −0.162135 0.986769i \(-0.551838\pi\)
−0.162135 + 0.986769i \(0.551838\pi\)
\(462\) 0 0
\(463\) 5.29948i 0.246288i 0.992389 + 0.123144i \(0.0392976\pi\)
−0.992389 + 0.123144i \(0.960702\pi\)
\(464\) 0 0
\(465\) −7.66291 6.77575i −0.355359 0.314218i
\(466\) 0 0
\(467\) 13.1490i 0.608465i 0.952598 + 0.304232i \(0.0983999\pi\)
−0.952598 + 0.304232i \(0.901600\pi\)
\(468\) 0 0
\(469\) 9.92478 0.458284
\(470\) 0 0
\(471\) −2.64974 −0.122093
\(472\) 0 0
\(473\) 25.2506i 1.16102i
\(474\) 0 0
\(475\) −3.27504 26.5501i −0.150269 1.21820i
\(476\) 0 0
\(477\) 8.57452i 0.392600i
\(478\) 0 0
\(479\) 5.14903 0.235265 0.117633 0.993057i \(-0.462469\pi\)
0.117633 + 0.993057i \(0.462469\pi\)
\(480\) 0 0
\(481\) −1.04746 −0.0477601
\(482\) 0 0
\(483\) 4.96239i 0.225797i
\(484\) 0 0
\(485\) 30.9887 + 27.4010i 1.40713 + 1.24422i
\(486\) 0 0
\(487\) 22.1768i 1.00493i 0.864599 + 0.502463i \(0.167573\pi\)
−0.864599 + 0.502463i \(0.832427\pi\)
\(488\) 0 0
\(489\) 5.29948 0.239651
\(490\) 0 0
\(491\) −2.00000 −0.0902587 −0.0451294 0.998981i \(-0.514370\pi\)
−0.0451294 + 0.998981i \(0.514370\pi\)
\(492\) 0 0
\(493\) 26.5501i 1.19576i
\(494\) 0 0
\(495\) −2.96239 + 3.35026i −0.133149 + 0.150583i
\(496\) 0 0
\(497\) 2.00000i 0.0897123i
\(498\) 0 0
\(499\) −6.55008 −0.293222 −0.146611 0.989194i \(-0.546837\pi\)
−0.146611 + 0.989194i \(0.546837\pi\)
\(500\) 0 0
\(501\) 14.5501 0.650050
\(502\) 0 0
\(503\) 8.77575i 0.391291i 0.980675 + 0.195646i \(0.0626802\pi\)
−0.980675 + 0.195646i \(0.937320\pi\)
\(504\) 0 0
\(505\) 26.1622 29.5877i 1.16420 1.31663i
\(506\) 0 0
\(507\) 11.1768i 0.496379i
\(508\) 0 0
\(509\) −13.1392 −0.582384 −0.291192 0.956665i \(-0.594052\pi\)
−0.291192 + 0.956665i \(0.594052\pi\)
\(510\) 0 0
\(511\) −9.35026 −0.413631
\(512\) 0 0
\(513\) 5.35026i 0.236220i
\(514\) 0 0
\(515\) −11.2243 9.92478i −0.494600 0.437338i
\(516\) 0 0
\(517\) 19.8496i 0.872982i
\(518\) 0 0
\(519\) 4.49929 0.197497
\(520\) 0 0
\(521\) −37.6629 −1.65004 −0.825021 0.565102i \(-0.808837\pi\)
−0.825021 + 0.565102i \(0.808837\pi\)
\(522\) 0 0
\(523\) 4.00000i 0.174908i −0.996169 0.0874539i \(-0.972127\pi\)
0.996169 0.0874539i \(-0.0278730\pi\)
\(524\) 0 0
\(525\) −0.612127 4.96239i −0.0267154 0.216576i
\(526\) 0 0
\(527\) 15.3258i 0.667603i
\(528\) 0 0
\(529\) −1.62530 −0.0706652
\(530\) 0 0
\(531\) 8.62530 0.374306
\(532\) 0 0
\(533\) 5.04746i 0.218630i
\(534\) 0 0
\(535\) 23.0132 + 20.3488i 0.994946 + 0.879757i
\(536\) 0 0
\(537\) 10.0000i 0.431532i
\(538\) 0 0
\(539\) 2.00000 0.0861461
\(540\) 0 0
\(541\) −22.4749 −0.966269 −0.483135 0.875546i \(-0.660502\pi\)
−0.483135 + 0.875546i \(0.660502\pi\)
\(542\) 0 0
\(543\) 10.6253i 0.455975i
\(544\) 0 0
\(545\) −4.11142 + 4.64974i −0.176114 + 0.199173i
\(546\) 0 0
\(547\) 25.9248i 1.10846i 0.832362 + 0.554232i \(0.186988\pi\)
−0.832362 + 0.554232i \(0.813012\pi\)
\(548\) 0 0
\(549\) 8.70052 0.371329
\(550\) 0 0
\(551\) −42.3996 −1.80629
\(552\) 0 0
\(553\) 10.7005i 0.455033i
\(554\) 0 0
\(555\) 1.14903 1.29948i 0.0487736 0.0551597i
\(556\) 0 0
\(557\) 28.5256i 1.20867i −0.796730 0.604335i \(-0.793439\pi\)
0.796730 0.604335i \(-0.206561\pi\)
\(558\) 0 0
\(559\) −17.0475 −0.721031
\(560\) 0 0
\(561\) 6.70052 0.282896
\(562\) 0 0
\(563\) 11.6267i 0.490008i −0.969522 0.245004i \(-0.921211\pi\)
0.969522 0.245004i \(-0.0787892\pi\)
\(564\) 0 0
\(565\) 20.1866 + 17.8496i 0.849258 + 0.750936i
\(566\) 0 0
\(567\) 1.00000i 0.0419961i
\(568\) 0 0
\(569\) −9.32582 −0.390959 −0.195479 0.980708i \(-0.562626\pi\)
−0.195479 + 0.980708i \(0.562626\pi\)
\(570\) 0 0
\(571\) 19.6991 0.824382 0.412191 0.911097i \(-0.364764\pi\)
0.412191 + 0.911097i \(0.364764\pi\)
\(572\) 0 0
\(573\) 13.8496i 0.578573i
\(574\) 0 0
\(575\) 24.6253 3.03761i 1.02695 0.126677i
\(576\) 0 0
\(577\) 32.7974i 1.36537i 0.730712 + 0.682686i \(0.239188\pi\)
−0.730712 + 0.682686i \(0.760812\pi\)
\(578\) 0 0
\(579\) −15.3258 −0.636920
\(580\) 0 0
\(581\) −3.22425 −0.133765
\(582\) 0 0
\(583\) 17.1490i 0.710240i
\(584\) 0 0
\(585\) −2.26187 2.00000i −0.0935166 0.0826898i
\(586\) 0 0
\(587\) 18.8218i 0.776859i −0.921479 0.388429i \(-0.873018\pi\)
0.921479 0.388429i \(-0.126982\pi\)
\(588\) 0 0
\(589\) −24.4749 −1.00847
\(590\) 0 0
\(591\) −0.574515 −0.0236324
\(592\) 0 0
\(593\) 33.7499i 1.38594i −0.720965 0.692971i \(-0.756301\pi\)
0.720965 0.692971i \(-0.243699\pi\)
\(594\) 0 0
\(595\) −4.96239 + 5.61213i −0.203438 + 0.230075i
\(596\) 0 0
\(597\) 0.201231i 0.00823583i
\(598\) 0 0
\(599\) −20.2981 −0.829356 −0.414678 0.909968i \(-0.636106\pi\)
−0.414678 + 0.909968i \(0.636106\pi\)
\(600\) 0 0
\(601\) −13.8496 −0.564935 −0.282468 0.959277i \(-0.591153\pi\)
−0.282468 + 0.959277i \(0.591153\pi\)
\(602\) 0 0
\(603\) 9.92478i 0.404168i
\(604\) 0 0
\(605\) 10.3684 11.7259i 0.421534 0.476726i
\(606\) 0 0
\(607\) 25.2506i 1.02489i 0.858720 + 0.512445i \(0.171260\pi\)
−0.858720 + 0.512445i \(0.828740\pi\)
\(608\) 0 0
\(609\) −7.92478 −0.321128
\(610\) 0 0
\(611\) −13.4010 −0.542148
\(612\) 0 0
\(613\) 9.14903i 0.369526i 0.982783 + 0.184763i \(0.0591517\pi\)
−0.982783 + 0.184763i \(0.940848\pi\)
\(614\) 0 0
\(615\) 6.26187 + 5.53690i 0.252503 + 0.223270i
\(616\) 0 0
\(617\) 15.9492i 0.642091i 0.947064 + 0.321046i \(0.104034\pi\)
−0.947064 + 0.321046i \(0.895966\pi\)
\(618\) 0 0
\(619\) 11.1735 0.449100 0.224550 0.974463i \(-0.427909\pi\)
0.224550 + 0.974463i \(0.427909\pi\)
\(620\) 0 0
\(621\) −4.96239 −0.199134
\(622\) 0 0
\(623\) 1.03761i 0.0415710i
\(624\) 0 0
\(625\) −24.2506 + 6.07522i −0.970024 + 0.243009i
\(626\) 0 0
\(627\) 10.7005i 0.427338i
\(628\) 0 0
\(629\) −2.59895 −0.103627
\(630\) 0 0
\(631\) 14.5501 0.579229 0.289615 0.957143i \(-0.406473\pi\)
0.289615 + 0.957143i \(0.406473\pi\)
\(632\) 0 0
\(633\) 6.44851i 0.256305i
\(634\) 0 0
\(635\) 4.52373 + 4.00000i 0.179519 + 0.158735i
\(636\) 0 0
\(637\) 1.35026i 0.0534993i
\(638\) 0 0
\(639\) 2.00000 0.0791188
\(640\) 0 0
\(641\) −38.7269 −1.52962 −0.764810 0.644256i \(-0.777167\pi\)
−0.764810 + 0.644256i \(0.777167\pi\)
\(642\) 0 0
\(643\) 11.9511i 0.471306i −0.971837 0.235653i \(-0.924277\pi\)
0.971837 0.235653i \(-0.0757229\pi\)
\(644\) 0 0
\(645\) 18.7005 21.1490i 0.736332 0.832742i
\(646\) 0 0
\(647\) 14.5501i 0.572023i 0.958226 + 0.286011i \(0.0923295\pi\)
−0.958226 + 0.286011i \(0.907671\pi\)
\(648\) 0 0
\(649\) 17.2506 0.677145
\(650\) 0 0
\(651\) −4.57452 −0.179289
\(652\) 0 0
\(653\) 49.9756i 1.95569i −0.209319 0.977847i \(-0.567125\pi\)
0.209319 0.977847i \(-0.432875\pi\)
\(654\) 0 0
\(655\) 30.5501 34.5501i 1.19369 1.34998i
\(656\) 0 0
\(657\) 9.35026i 0.364788i
\(658\) 0 0
\(659\) −16.9525 −0.660377 −0.330189 0.943915i \(-0.607112\pi\)
−0.330189 + 0.943915i \(0.607112\pi\)
\(660\) 0 0
\(661\) −15.6531 −0.608834 −0.304417 0.952539i \(-0.598462\pi\)
−0.304417 + 0.952539i \(0.598462\pi\)
\(662\) 0 0
\(663\) 4.52373i 0.175687i
\(664\) 0 0
\(665\) −8.96239 7.92478i −0.347547 0.307310i
\(666\) 0 0
\(667\) 39.3258i 1.52270i
\(668\) 0 0
\(669\) 1.55149 0.0599842
\(670\) 0 0
\(671\) 17.4010 0.671760
\(672\) 0 0
\(673\) 26.0263i 1.00324i −0.865088 0.501621i \(-0.832737\pi\)
0.865088 0.501621i \(-0.167263\pi\)
\(674\) 0 0
\(675\) 4.96239 0.612127i 0.191002 0.0235608i
\(676\) 0 0
\(677\) 35.4518i 1.36252i −0.732039 0.681262i \(-0.761431\pi\)
0.732039 0.681262i \(-0.238569\pi\)
\(678\) 0 0
\(679\) 18.4993 0.709938
\(680\) 0 0
\(681\) 13.1490 0.503872
\(682\) 0 0
\(683\) 23.6629i 0.905436i −0.891654 0.452718i \(-0.850454\pi\)
0.891654 0.452718i \(-0.149546\pi\)
\(684\) 0 0
\(685\) −37.6893 33.3258i −1.44003 1.27331i
\(686\) 0 0
\(687\) 2.77575i 0.105901i
\(688\) 0 0
\(689\) −11.5778 −0.441081
\(690\) 0 0
\(691\) 0.574515 0.0218556 0.0109278 0.999940i \(-0.496522\pi\)
0.0109278 + 0.999940i \(0.496522\pi\)
\(692\) 0 0
\(693\) 2.00000i 0.0759737i
\(694\) 0 0
\(695\) 4.85097 5.48612i 0.184008 0.208100i
\(696\) 0 0
\(697\) 12.5237i 0.474370i
\(698\) 0 0
\(699\) 0.0507852 0.00192087
\(700\) 0 0
\(701\) 42.7269 1.61377 0.806886 0.590707i \(-0.201151\pi\)
0.806886 + 0.590707i \(0.201151\pi\)
\(702\) 0 0
\(703\) 4.15045i 0.156537i
\(704\) 0 0
\(705\) 14.7005 16.6253i 0.553654 0.626145i
\(706\) 0 0
\(707\) 17.6629i 0.664282i
\(708\) 0 0
\(709\) −27.2506 −1.02342 −0.511709 0.859159i \(-0.670987\pi\)
−0.511709 + 0.859159i \(0.670987\pi\)
\(710\) 0 0
\(711\) −10.7005 −0.401301
\(712\) 0 0
\(713\) 22.7005i 0.850141i
\(714\) 0 0
\(715\) −4.52373 4.00000i −0.169178 0.149592i
\(716\) 0 0
\(717\) 5.84955i 0.218456i
\(718\) 0 0
\(719\) −10.7005 −0.399062 −0.199531 0.979891i \(-0.563942\pi\)
−0.199531 + 0.979891i \(0.563942\pi\)
\(720\) 0 0
\(721\) −6.70052 −0.249541
\(722\) 0 0
\(723\) 0.0752228i 0.00279757i
\(724\) 0 0
\(725\) 4.85097 + 39.3258i 0.180160 + 1.46052i
\(726\) 0 0
\(727\) 39.9511i 1.48171i −0.671668 0.740853i \(-0.734422\pi\)
0.671668 0.740853i \(-0.265578\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −42.2981 −1.56445
\(732\) 0 0
\(733\) 30.3488i 1.12096i 0.828168 + 0.560480i \(0.189383\pi\)
−0.828168 + 0.560480i \(0.810617\pi\)
\(734\) 0 0
\(735\) −1.67513 1.48119i −0.0617881 0.0546347i
\(736\) 0 0
\(737\) 19.8496i 0.731168i
\(738\) 0 0
\(739\) 37.2506 1.37029 0.685143 0.728409i \(-0.259740\pi\)
0.685143 + 0.728409i \(0.259740\pi\)
\(740\) 0 0
\(741\) −7.22425 −0.265390
\(742\) 0 0
\(743\) 26.3634i 0.967181i 0.875294 + 0.483590i \(0.160668\pi\)
−0.875294 + 0.483590i \(0.839332\pi\)
\(744\) 0 0
\(745\) −6.58910 + 7.45183i −0.241406 + 0.273014i
\(746\) 0 0
\(747\) 3.22425i 0.117969i
\(748\) 0 0
\(749\) 13.7381 0.501981
\(750\) 0 0
\(751\) −50.6516 −1.84830 −0.924152 0.382024i \(-0.875227\pi\)
−0.924152 + 0.382024i \(0.875227\pi\)
\(752\) 0 0
\(753\) 19.2243i 0.700571i
\(754\) 0 0
\(755\) 1.92478 2.17679i 0.0700498 0.0792216i
\(756\) 0 0
\(757\) 38.9525i 1.41575i 0.706336 + 0.707877i \(0.250347\pi\)
−0.706336 + 0.707877i \(0.749653\pi\)
\(758\) 0 0
\(759\) −9.92478 −0.360247
\(760\) 0 0
\(761\) 48.2130 1.74772 0.873860 0.486178i \(-0.161609\pi\)
0.873860 + 0.486178i \(0.161609\pi\)
\(762\) 0 0
\(763\) 2.77575i 0.100489i
\(764\) 0 0
\(765\) −5.61213 4.96239i −0.202907 0.179416i
\(766\) 0 0
\(767\) 11.6464i 0.420528i
\(768\) 0 0
\(769\) −4.44851 −0.160417 −0.0802086 0.996778i \(-0.525559\pi\)
−0.0802086 + 0.996778i \(0.525559\pi\)
\(770\) 0 0
\(771\) 7.35026 0.264713
\(772\) 0 0
\(773\) 39.3014i 1.41357i −0.707427 0.706786i \(-0.750144\pi\)
0.707427 0.706786i \(-0.249856\pi\)
\(774\) 0 0
\(775\) 2.80018 + 22.7005i 0.100586 + 0.815427i
\(776\) 0 0
\(777\) 0.775746i 0.0278297i
\(778\) 0 0
\(779\) 20.0000 0.716574
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) 7.92478i 0.283208i
\(784\) 0 0
\(785\) 4.43866 + 3.92478i 0.158423 + 0.140081i
\(786\) 0 0
\(787\) 0.897015i 0.0319751i −0.999872 0.0159876i \(-0.994911\pi\)
0.999872 0.0159876i \(-0.00508922\pi\)
\(788\) 0 0
\(789\) −12.9624 −0.461473
\(790\) 0 0
\(791\) 12.0508 0.428477
\(792\) 0 0
\(793\) 11.7480i 0.417183i
\(794\) 0 0
\(795\) 12.7005 14.3634i 0.450441 0.509419i
\(796\) 0 0
\(797\) 3.19982i 0.113343i 0.998393 + 0.0566717i \(0.0180488\pi\)
−0.998393 + 0.0566717i \(0.981951\pi\)
\(798\) 0 0
\(799\) −33.2506 −1.17632
\(800\) 0 0
\(801\) 1.03761 0.0366622
\(802\) 0