Properties

Label 1680.2.t.k.1009.3
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 1009.3
Root \(-0.854638 + 0.854638i\) of defining polynomial
Character \(\chi\) \(=\) 1680.1009
Dual form 1680.2.t.k.1009.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{3} +(2.17009 + 0.539189i) q^{5} +1.00000i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{3} +(2.17009 + 0.539189i) q^{5} +1.00000i q^{7} -1.00000 q^{9} -2.00000 q^{11} +0.921622i q^{13} +(0.539189 - 2.17009i) q^{15} -1.07838i q^{17} +3.07838 q^{19} +1.00000 q^{21} -2.34017i q^{23} +(4.41855 + 2.34017i) q^{25} +1.00000i q^{27} +6.68035 q^{29} +7.75872 q^{31} +2.00000i q^{33} +(-0.539189 + 2.17009i) q^{35} -10.8371i q^{37} +0.921622 q^{39} +6.49693 q^{41} +6.52359i q^{43} +(-2.17009 - 0.539189i) q^{45} +4.68035i q^{47} -1.00000 q^{49} -1.07838 q^{51} +3.75872i q^{53} +(-4.34017 - 1.07838i) q^{55} -3.07838i q^{57} +10.5236 q^{59} -4.15676 q^{61} -1.00000i q^{63} +(-0.496928 + 2.00000i) q^{65} +4.68035i q^{67} -2.34017 q^{69} -2.00000 q^{71} +7.07838i q^{73} +(2.34017 - 4.41855i) q^{75} -2.00000i q^{77} +6.15676 q^{79} +1.00000 q^{81} -6.83710i q^{83} +(0.581449 - 2.34017i) q^{85} -6.68035i q^{87} -8.34017 q^{89} -0.921622 q^{91} -7.75872i q^{93} +(6.68035 + 1.65983i) q^{95} +8.43907i q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{5} - 6 q^{9} + O(q^{10}) \) \( 6 q + 2 q^{5} - 6 q^{9} - 12 q^{11} + 12 q^{19} + 6 q^{21} - 2 q^{25} - 4 q^{29} - 4 q^{31} + 12 q^{39} + 4 q^{41} - 2 q^{45} - 6 q^{49} - 4 q^{55} + 32 q^{59} - 12 q^{61} + 32 q^{65} + 8 q^{69} - 12 q^{71} - 8 q^{75} + 24 q^{79} + 6 q^{81} + 32 q^{85} - 28 q^{89} - 12 q^{91} - 4 q^{95} + 12 q^{99} + O(q^{100}) \)

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
\(5\) 2.17009 + 0.539189i 0.970492 + 0.241133i
\(6\) 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
\(13\) 0.921622i 0.255612i 0.991799 + 0.127806i \(0.0407935\pi\)
−0.991799 + 0.127806i \(0.959207\pi\)
\(14\) 0 0
\(15\) 0.539189 2.17009i 0.139218 0.560314i
\(16\) 0 0
\(17\) 1.07838i 0.261545i −0.991412 0.130773i \(-0.958254\pi\)
0.991412 0.130773i \(-0.0417457\pi\)
\(18\) 0 0
\(19\) 3.07838 0.706228 0.353114 0.935580i \(-0.385123\pi\)
0.353114 + 0.935580i \(0.385123\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 2.34017i 0.487960i −0.969780 0.243980i \(-0.921547\pi\)
0.969780 0.243980i \(-0.0784531\pi\)
\(24\) 0 0
\(25\) 4.41855 + 2.34017i 0.883710 + 0.468035i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 6.68035 1.24051 0.620255 0.784401i \(-0.287029\pi\)
0.620255 + 0.784401i \(0.287029\pi\)
\(30\) 0 0
\(31\) 7.75872 1.39351 0.696754 0.717310i \(-0.254627\pi\)
0.696754 + 0.717310i \(0.254627\pi\)
\(32\) 0 0
\(33\) 2.00000i 0.348155i
\(34\) 0 0
\(35\) −0.539189 + 2.17009i −0.0911396 + 0.366812i
\(36\) 0 0
\(37\) 10.8371i 1.78161i −0.454387 0.890804i \(-0.650142\pi\)
0.454387 0.890804i \(-0.349858\pi\)
\(38\) 0 0
\(39\) 0.921622 0.147578
\(40\) 0 0
\(41\) 6.49693 1.01465 0.507325 0.861755i \(-0.330634\pi\)
0.507325 + 0.861755i \(0.330634\pi\)
\(42\) 0 0
\(43\) 6.52359i 0.994838i 0.867510 + 0.497419i \(0.165719\pi\)
−0.867510 + 0.497419i \(0.834281\pi\)
\(44\) 0 0
\(45\) −2.17009 0.539189i −0.323497 0.0803775i
\(46\) 0 0
\(47\) 4.68035i 0.682699i 0.939937 + 0.341349i \(0.110884\pi\)
−0.939937 + 0.341349i \(0.889116\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) −1.07838 −0.151003
\(52\) 0 0
\(53\) 3.75872i 0.516300i 0.966105 + 0.258150i \(0.0831129\pi\)
−0.966105 + 0.258150i \(0.916887\pi\)
\(54\) 0 0
\(55\) −4.34017 1.07838i −0.585229 0.145408i
\(56\) 0 0
\(57\) 3.07838i 0.407741i
\(58\) 0 0
\(59\) 10.5236 1.37005 0.685027 0.728517i \(-0.259790\pi\)
0.685027 + 0.728517i \(0.259790\pi\)
\(60\) 0 0
\(61\) −4.15676 −0.532218 −0.266109 0.963943i \(-0.585738\pi\)
−0.266109 + 0.963943i \(0.585738\pi\)
\(62\) 0 0
\(63\) 1.00000i 0.125988i
\(64\) 0 0
\(65\) −0.496928 + 2.00000i −0.0616364 + 0.248069i
\(66\) 0 0
\(67\) 4.68035i 0.571795i 0.958260 + 0.285898i \(0.0922917\pi\)
−0.958260 + 0.285898i \(0.907708\pi\)
\(68\) 0 0
\(69\) −2.34017 −0.281724
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 7.07838i 0.828461i 0.910172 + 0.414231i \(0.135949\pi\)
−0.910172 + 0.414231i \(0.864051\pi\)
\(74\) 0 0
\(75\) 2.34017 4.41855i 0.270220 0.510210i
\(76\) 0 0
\(77\) 2.00000i 0.227921i
\(78\) 0 0
\(79\) 6.15676 0.692689 0.346345 0.938107i \(-0.387423\pi\)
0.346345 + 0.938107i \(0.387423\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 6.83710i 0.750469i −0.926930 0.375235i \(-0.877562\pi\)
0.926930 0.375235i \(-0.122438\pi\)
\(84\) 0 0
\(85\) 0.581449 2.34017i 0.0630670 0.253827i
\(86\) 0 0
\(87\) 6.68035i 0.716208i
\(88\) 0 0
\(89\) −8.34017 −0.884057 −0.442028 0.897001i \(-0.645741\pi\)
−0.442028 + 0.897001i \(0.645741\pi\)
\(90\) 0 0
\(91\) −0.921622 −0.0966123
\(92\) 0 0
\(93\) 7.75872i 0.804542i
\(94\) 0 0
\(95\) 6.68035 + 1.65983i 0.685389 + 0.170295i
\(96\) 0 0
\(97\) 8.43907i 0.856858i 0.903576 + 0.428429i \(0.140933\pi\)
−0.903576 + 0.428429i \(0.859067\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) −5.81658 −0.578772 −0.289386 0.957213i \(-0.593451\pi\)
−0.289386 + 0.957213i \(0.593451\pi\)
\(102\) 0 0
\(103\) 2.15676i 0.212511i 0.994339 + 0.106256i \(0.0338862\pi\)
−0.994339 + 0.106256i \(0.966114\pi\)
\(104\) 0 0
\(105\) 2.17009 + 0.539189i 0.211779 + 0.0526194i
\(106\) 0 0
\(107\) 16.4969i 1.59482i −0.603439 0.797409i \(-0.706203\pi\)
0.603439 0.797409i \(-0.293797\pi\)
\(108\) 0 0
\(109\) 12.8371 1.22957 0.614786 0.788694i \(-0.289243\pi\)
0.614786 + 0.788694i \(0.289243\pi\)
\(110\) 0 0
\(111\) −10.8371 −1.02861
\(112\) 0 0
\(113\) 5.23513i 0.492480i −0.969209 0.246240i \(-0.920805\pi\)
0.969209 0.246240i \(-0.0791951\pi\)
\(114\) 0 0
\(115\) 1.26180 5.07838i 0.117663 0.473561i
\(116\) 0 0
\(117\) 0.921622i 0.0852040i
\(118\) 0 0
\(119\) 1.07838 0.0988547
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 6.49693i 0.585808i
\(124\) 0 0
\(125\) 8.32684 + 7.46081i 0.744775 + 0.667315i
\(126\) 0 0
\(127\) 1.84324i 0.163562i 0.996650 + 0.0817808i \(0.0260607\pi\)
−0.996650 + 0.0817808i \(0.973939\pi\)
\(128\) 0 0
\(129\) 6.52359 0.574370
\(130\) 0 0
\(131\) −1.47641 −0.128995 −0.0644973 0.997918i \(-0.520544\pi\)
−0.0644973 + 0.997918i \(0.520544\pi\)
\(132\) 0 0
\(133\) 3.07838i 0.266929i
\(134\) 0 0
\(135\) −0.539189 + 2.17009i −0.0464060 + 0.186771i
\(136\) 0 0
\(137\) 4.43907i 0.379255i −0.981856 0.189628i \(-0.939272\pi\)
0.981856 0.189628i \(-0.0607281\pi\)
\(138\) 0 0
\(139\) 13.6020 1.15370 0.576852 0.816849i \(-0.304281\pi\)
0.576852 + 0.816849i \(0.304281\pi\)
\(140\) 0 0
\(141\) 4.68035 0.394156
\(142\) 0 0
\(143\) 1.84324i 0.154140i
\(144\) 0 0
\(145\) 14.4969 + 3.60197i 1.20390 + 0.299127i
\(146\) 0 0
\(147\) 1.00000i 0.0824786i
\(148\) 0 0
\(149\) −15.6742 −1.28408 −0.642040 0.766671i \(-0.721912\pi\)
−0.642040 + 0.766671i \(0.721912\pi\)
\(150\) 0 0
\(151\) −5.84324 −0.475516 −0.237758 0.971324i \(-0.576413\pi\)
−0.237758 + 0.971324i \(0.576413\pi\)
\(152\) 0 0
\(153\) 1.07838i 0.0871817i
\(154\) 0 0
\(155\) 16.8371 + 4.18342i 1.35239 + 0.336020i
\(156\) 0 0
\(157\) 4.92162i 0.392788i −0.980525 0.196394i \(-0.937077\pi\)
0.980525 0.196394i \(-0.0629232\pi\)
\(158\) 0 0
\(159\) 3.75872 0.298086
\(160\) 0 0
\(161\) 2.34017 0.184431
\(162\) 0 0
\(163\) 9.84324i 0.770982i 0.922712 + 0.385491i \(0.125968\pi\)
−0.922712 + 0.385491i \(0.874032\pi\)
\(164\) 0 0
\(165\) −1.07838 + 4.34017i −0.0839516 + 0.337882i
\(166\) 0 0
\(167\) 19.2039i 1.48605i −0.669266 0.743023i \(-0.733391\pi\)
0.669266 0.743023i \(-0.266609\pi\)
\(168\) 0 0
\(169\) 12.1506 0.934662
\(170\) 0 0
\(171\) −3.07838 −0.235409
\(172\) 0 0
\(173\) 22.4391i 1.70601i −0.521902 0.853005i \(-0.674777\pi\)
0.521902 0.853005i \(-0.325223\pi\)
\(174\) 0 0
\(175\) −2.34017 + 4.41855i −0.176900 + 0.334011i
\(176\) 0 0
\(177\) 10.5236i 0.791001i
\(178\) 0 0
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 0 0
\(181\) −8.52359 −0.633553 −0.316777 0.948500i \(-0.602601\pi\)
−0.316777 + 0.948500i \(0.602601\pi\)
\(182\) 0 0
\(183\) 4.15676i 0.307276i
\(184\) 0 0
\(185\) 5.84324 23.5174i 0.429604 1.72904i
\(186\) 0 0
\(187\) 2.15676i 0.157718i
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) 0 0
\(191\) −15.3607 −1.11146 −0.555730 0.831363i \(-0.687561\pi\)
−0.555730 + 0.831363i \(0.687561\pi\)
\(192\) 0 0
\(193\) 8.36683i 0.602258i 0.953583 + 0.301129i \(0.0973635\pi\)
−0.953583 + 0.301129i \(0.902637\pi\)
\(194\) 0 0
\(195\) 2.00000 + 0.496928i 0.143223 + 0.0355858i
\(196\) 0 0
\(197\) 11.7587i 0.837774i 0.908038 + 0.418887i \(0.137580\pi\)
−0.908038 + 0.418887i \(0.862420\pi\)
\(198\) 0 0
\(199\) −22.5958 −1.60178 −0.800888 0.598814i \(-0.795639\pi\)
−0.800888 + 0.598814i \(0.795639\pi\)
\(200\) 0 0
\(201\) 4.68035 0.330126
\(202\) 0 0
\(203\) 6.68035i 0.468868i
\(204\) 0 0
\(205\) 14.0989 + 3.50307i 0.984710 + 0.244665i
\(206\) 0 0
\(207\) 2.34017i 0.162653i
\(208\) 0 0
\(209\) −6.15676 −0.425872
\(210\) 0 0
\(211\) 13.6742 0.941371 0.470685 0.882301i \(-0.344007\pi\)
0.470685 + 0.882301i \(0.344007\pi\)
\(212\) 0 0
\(213\) 2.00000i 0.137038i
\(214\) 0 0
\(215\) −3.51745 + 14.1568i −0.239888 + 0.965483i
\(216\) 0 0
\(217\) 7.75872i 0.526696i
\(218\) 0 0
\(219\) 7.07838 0.478312
\(220\) 0 0
\(221\) 0.993857 0.0668541
\(222\) 0 0
\(223\) 21.6742i 1.45141i 0.688005 + 0.725706i \(0.258487\pi\)
−0.688005 + 0.725706i \(0.741513\pi\)
\(224\) 0 0
\(225\) −4.41855 2.34017i −0.294570 0.156012i
\(226\) 0 0
\(227\) 11.5174i 0.764440i −0.924071 0.382220i \(-0.875160\pi\)
0.924071 0.382220i \(-0.124840\pi\)
\(228\) 0 0
\(229\) −12.8371 −0.848300 −0.424150 0.905592i \(-0.639427\pi\)
−0.424150 + 0.905592i \(0.639427\pi\)
\(230\) 0 0
\(231\) −2.00000 −0.131590
\(232\) 0 0
\(233\) 6.76487i 0.443181i −0.975140 0.221591i \(-0.928875\pi\)
0.975140 0.221591i \(-0.0711248\pi\)
\(234\) 0 0
\(235\) −2.52359 + 10.1568i −0.164621 + 0.662554i
\(236\) 0 0
\(237\) 6.15676i 0.399924i
\(238\) 0 0
\(239\) −23.3607 −1.51108 −0.755539 0.655104i \(-0.772625\pi\)
−0.755539 + 0.655104i \(0.772625\pi\)
\(240\) 0 0
\(241\) −14.6803 −0.945644 −0.472822 0.881158i \(-0.656765\pi\)
−0.472822 + 0.881158i \(0.656765\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −2.17009 0.539189i −0.138642 0.0344475i
\(246\) 0 0
\(247\) 2.83710i 0.180520i
\(248\) 0 0
\(249\) −6.83710 −0.433284
\(250\) 0 0
\(251\) −9.16290 −0.578357 −0.289179 0.957275i \(-0.593382\pi\)
−0.289179 + 0.957275i \(0.593382\pi\)
\(252\) 0 0
\(253\) 4.68035i 0.294251i
\(254\) 0 0
\(255\) −2.34017 0.581449i −0.146547 0.0364118i
\(256\) 0 0
\(257\) 5.07838i 0.316781i 0.987377 + 0.158390i \(0.0506304\pi\)
−0.987377 + 0.158390i \(0.949370\pi\)
\(258\) 0 0
\(259\) 10.8371 0.673385
\(260\) 0 0
\(261\) −6.68035 −0.413503
\(262\) 0 0
\(263\) 5.65983i 0.349000i −0.984657 0.174500i \(-0.944169\pi\)
0.984657 0.174500i \(-0.0558309\pi\)
\(264\) 0 0
\(265\) −2.02666 + 8.15676i −0.124497 + 0.501066i
\(266\) 0 0
\(267\) 8.34017i 0.510410i
\(268\) 0 0
\(269\) 27.8576 1.69851 0.849255 0.527984i \(-0.177052\pi\)
0.849255 + 0.527984i \(0.177052\pi\)
\(270\) 0 0
\(271\) −25.1194 −1.52590 −0.762948 0.646460i \(-0.776249\pi\)
−0.762948 + 0.646460i \(0.776249\pi\)
\(272\) 0 0
\(273\) 0.921622i 0.0557791i
\(274\) 0 0
\(275\) −8.83710 4.68035i −0.532897 0.282235i
\(276\) 0 0
\(277\) 28.1978i 1.69424i 0.531401 + 0.847121i \(0.321666\pi\)
−0.531401 + 0.847121i \(0.678334\pi\)
\(278\) 0 0
\(279\) −7.75872 −0.464503
\(280\) 0 0
\(281\) −20.3545 −1.21425 −0.607125 0.794606i \(-0.707677\pi\)
−0.607125 + 0.794606i \(0.707677\pi\)
\(282\) 0 0
\(283\) 23.5174i 1.39797i −0.715138 0.698984i \(-0.753636\pi\)
0.715138 0.698984i \(-0.246364\pi\)
\(284\) 0 0
\(285\) 1.65983 6.68035i 0.0983197 0.395710i
\(286\) 0 0
\(287\) 6.49693i 0.383502i
\(288\) 0 0
\(289\) 15.8371 0.931594
\(290\) 0 0
\(291\) 8.43907 0.494707
\(292\) 0 0
\(293\) 2.92162i 0.170683i −0.996352 0.0853415i \(-0.972802\pi\)
0.996352 0.0853415i \(-0.0271981\pi\)
\(294\) 0 0
\(295\) 22.8371 + 5.67420i 1.32963 + 0.330365i
\(296\) 0 0
\(297\) 2.00000i 0.116052i
\(298\) 0 0
\(299\) 2.15676 0.124728
\(300\) 0 0
\(301\) −6.52359 −0.376014
\(302\) 0 0
\(303\) 5.81658i 0.334154i
\(304\) 0 0
\(305\) −9.02052 2.24128i −0.516513 0.128335i
\(306\) 0 0
\(307\) 10.4703i 0.597570i −0.954321 0.298785i \(-0.903419\pi\)
0.954321 0.298785i \(-0.0965813\pi\)
\(308\) 0 0
\(309\) 2.15676 0.122694
\(310\) 0 0
\(311\) −23.8310 −1.35133 −0.675665 0.737209i \(-0.736143\pi\)
−0.675665 + 0.737209i \(0.736143\pi\)
\(312\) 0 0
\(313\) 32.7526i 1.85129i 0.378399 + 0.925643i \(0.376475\pi\)
−0.378399 + 0.925643i \(0.623525\pi\)
\(314\) 0 0
\(315\) 0.539189 2.17009i 0.0303799 0.122271i
\(316\) 0 0
\(317\) 17.9155i 1.00623i 0.864218 + 0.503117i \(0.167813\pi\)
−0.864218 + 0.503117i \(0.832187\pi\)
\(318\) 0 0
\(319\) −13.3607 −0.748055
\(320\) 0 0
\(321\) −16.4969 −0.920769
\(322\) 0 0
\(323\) 3.31965i 0.184710i
\(324\) 0 0
\(325\) −2.15676 + 4.07223i −0.119635 + 0.225887i
\(326\) 0 0
\(327\) 12.8371i 0.709893i
\(328\) 0 0
\(329\) −4.68035 −0.258036
\(330\) 0 0
\(331\) 1.36069 0.0747904 0.0373952 0.999301i \(-0.488094\pi\)
0.0373952 + 0.999301i \(0.488094\pi\)
\(332\) 0 0
\(333\) 10.8371i 0.593870i
\(334\) 0 0
\(335\) −2.52359 + 10.1568i −0.137878 + 0.554923i
\(336\) 0 0
\(337\) 25.3607i 1.38148i 0.723101 + 0.690742i \(0.242716\pi\)
−0.723101 + 0.690742i \(0.757284\pi\)
\(338\) 0 0
\(339\) −5.23513 −0.284333
\(340\) 0 0
\(341\) −15.5174 −0.840317
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) −5.07838 1.26180i −0.273411 0.0679328i
\(346\) 0 0
\(347\) 16.8638i 0.905294i 0.891690 + 0.452647i \(0.149520\pi\)
−0.891690 + 0.452647i \(0.850480\pi\)
\(348\) 0 0
\(349\) −9.51745 −0.509457 −0.254729 0.967013i \(-0.581986\pi\)
−0.254729 + 0.967013i \(0.581986\pi\)
\(350\) 0 0
\(351\) −0.921622 −0.0491926
\(352\) 0 0
\(353\) 35.7998i 1.90543i −0.303867 0.952715i \(-0.598278\pi\)
0.303867 0.952715i \(-0.401722\pi\)
\(354\) 0 0
\(355\) −4.34017 1.07838i −0.230352 0.0572343i
\(356\) 0 0
\(357\) 1.07838i 0.0570738i
\(358\) 0 0
\(359\) −22.3135 −1.17766 −0.588831 0.808256i \(-0.700412\pi\)
−0.588831 + 0.808256i \(0.700412\pi\)
\(360\) 0 0
\(361\) −9.52359 −0.501242
\(362\) 0 0
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) −3.81658 + 15.3607i −0.199769 + 0.804015i
\(366\) 0 0
\(367\) 20.3135i 1.06036i 0.847886 + 0.530178i \(0.177875\pi\)
−0.847886 + 0.530178i \(0.822125\pi\)
\(368\) 0 0
\(369\) −6.49693 −0.338217
\(370\) 0 0
\(371\) −3.75872 −0.195143
\(372\) 0 0
\(373\) 16.0000i 0.828449i −0.910175 0.414224i \(-0.864053\pi\)
0.910175 0.414224i \(-0.135947\pi\)
\(374\) 0 0
\(375\) 7.46081 8.32684i 0.385275 0.429996i
\(376\) 0 0
\(377\) 6.15676i 0.317089i
\(378\) 0 0
\(379\) 6.15676 0.316251 0.158126 0.987419i \(-0.449455\pi\)
0.158126 + 0.987419i \(0.449455\pi\)
\(380\) 0 0
\(381\) 1.84324 0.0944323
\(382\) 0 0
\(383\) 26.8371i 1.37131i −0.727926 0.685656i \(-0.759515\pi\)
0.727926 0.685656i \(-0.240485\pi\)
\(384\) 0 0
\(385\) 1.07838 4.34017i 0.0549592 0.221196i
\(386\) 0 0
\(387\) 6.52359i 0.331613i
\(388\) 0 0
\(389\) 5.63317 0.285613 0.142806 0.989751i \(-0.454387\pi\)
0.142806 + 0.989751i \(0.454387\pi\)
\(390\) 0 0
\(391\) −2.52359 −0.127623
\(392\) 0 0
\(393\) 1.47641i 0.0744750i
\(394\) 0 0
\(395\) 13.3607 + 3.31965i 0.672249 + 0.167030i
\(396\) 0 0
\(397\) 37.7998i 1.89712i −0.316604 0.948558i \(-0.602543\pi\)
0.316604 0.948558i \(-0.397457\pi\)
\(398\) 0 0
\(399\) 3.07838 0.154112
\(400\) 0 0
\(401\) −13.6332 −0.680808 −0.340404 0.940279i \(-0.610564\pi\)
−0.340404 + 0.940279i \(0.610564\pi\)
\(402\) 0 0
\(403\) 7.15061i 0.356197i
\(404\) 0 0
\(405\) 2.17009 + 0.539189i 0.107832 + 0.0267925i
\(406\) 0 0
\(407\) 21.6742i 1.07435i
\(408\) 0 0
\(409\) −12.3545 −0.610893 −0.305447 0.952209i \(-0.598806\pi\)
−0.305447 + 0.952209i \(0.598806\pi\)
\(410\) 0 0
\(411\) −4.43907 −0.218963
\(412\) 0 0
\(413\) 10.5236i 0.517832i
\(414\) 0 0
\(415\) 3.68649 14.8371i 0.180963 0.728325i
\(416\) 0 0
\(417\) 13.6020i 0.666091i
\(418\) 0 0
\(419\) 28.9939 1.41644 0.708221 0.705991i \(-0.249498\pi\)
0.708221 + 0.705991i \(0.249498\pi\)
\(420\) 0 0
\(421\) −15.1629 −0.738994 −0.369497 0.929232i \(-0.620470\pi\)
−0.369497 + 0.929232i \(0.620470\pi\)
\(422\) 0 0
\(423\) 4.68035i 0.227566i
\(424\) 0 0
\(425\) 2.52359 4.76487i 0.122412 0.231130i
\(426\) 0 0
\(427\) 4.15676i 0.201159i
\(428\) 0 0
\(429\) −1.84324 −0.0889927
\(430\) 0 0
\(431\) 10.3135 0.496784 0.248392 0.968660i \(-0.420098\pi\)
0.248392 + 0.968660i \(0.420098\pi\)
\(432\) 0 0
\(433\) 20.4391i 0.982239i 0.871092 + 0.491120i \(0.163412\pi\)
−0.871092 + 0.491120i \(0.836588\pi\)
\(434\) 0 0
\(435\) 3.60197 14.4969i 0.172701 0.695075i
\(436\) 0 0
\(437\) 7.20394i 0.344611i
\(438\) 0 0
\(439\) −16.9216 −0.807625 −0.403812 0.914842i \(-0.632315\pi\)
−0.403812 + 0.914842i \(0.632315\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 12.8104i 0.608642i 0.952569 + 0.304321i \(0.0984296\pi\)
−0.952569 + 0.304321i \(0.901570\pi\)
\(444\) 0 0
\(445\) −18.0989 4.49693i −0.857970 0.213175i
\(446\) 0 0
\(447\) 15.6742i 0.741364i
\(448\) 0 0
\(449\) 14.6270 0.690292 0.345146 0.938549i \(-0.387829\pi\)
0.345146 + 0.938549i \(0.387829\pi\)
\(450\) 0 0
\(451\) −12.9939 −0.611857
\(452\) 0 0
\(453\) 5.84324i 0.274540i
\(454\) 0 0
\(455\) −2.00000 0.496928i −0.0937614 0.0232964i
\(456\) 0 0
\(457\) 14.1568i 0.662225i −0.943591 0.331113i \(-0.892576\pi\)
0.943591 0.331113i \(-0.107424\pi\)
\(458\) 0 0
\(459\) 1.07838 0.0503344
\(460\) 0 0
\(461\) 0.340173 0.0158434 0.00792172 0.999969i \(-0.497478\pi\)
0.00792172 + 0.999969i \(0.497478\pi\)
\(462\) 0 0
\(463\) 9.84324i 0.457454i 0.973491 + 0.228727i \(0.0734564\pi\)
−0.973491 + 0.228727i \(0.926544\pi\)
\(464\) 0 0
\(465\) 4.18342 16.8371i 0.194001 0.780802i
\(466\) 0 0
\(467\) 11.5174i 0.532964i −0.963840 0.266482i \(-0.914139\pi\)
0.963840 0.266482i \(-0.0858613\pi\)
\(468\) 0 0
\(469\) −4.68035 −0.216118
\(470\) 0 0
\(471\) −4.92162 −0.226776
\(472\) 0 0
\(473\) 13.0472i 0.599910i
\(474\) 0 0
\(475\) 13.6020 + 7.20394i 0.624101 + 0.330539i
\(476\) 0 0
\(477\) 3.75872i 0.172100i
\(478\) 0 0
\(479\) −19.5174 −0.891775 −0.445887 0.895089i \(-0.647112\pi\)
−0.445887 + 0.895089i \(0.647112\pi\)
\(480\) 0 0
\(481\) 9.98771 0.455401
\(482\) 0 0
\(483\) 2.34017i 0.106482i
\(484\) 0 0
\(485\) −4.55025 + 18.3135i −0.206616 + 0.831574i
\(486\) 0 0
\(487\) 23.1506i 1.04905i 0.851394 + 0.524527i \(0.175758\pi\)
−0.851394 + 0.524527i \(0.824242\pi\)
\(488\) 0 0
\(489\) 9.84324 0.445127
\(490\) 0 0
\(491\) −2.00000 −0.0902587 −0.0451294 0.998981i \(-0.514370\pi\)
−0.0451294 + 0.998981i \(0.514370\pi\)
\(492\) 0 0
\(493\) 7.20394i 0.324449i
\(494\) 0 0
\(495\) 4.34017 + 1.07838i 0.195076 + 0.0484695i
\(496\) 0 0
\(497\) 2.00000i 0.0897123i
\(498\) 0 0
\(499\) 27.2039 1.21782 0.608908 0.793241i \(-0.291608\pi\)
0.608908 + 0.793241i \(0.291608\pi\)
\(500\) 0 0
\(501\) −19.2039 −0.857969
\(502\) 0 0
\(503\) 18.8371i 0.839905i 0.907546 + 0.419952i \(0.137953\pi\)
−0.907546 + 0.419952i \(0.862047\pi\)
\(504\) 0 0
\(505\) −12.6225 3.13624i −0.561693 0.139561i
\(506\) 0 0
\(507\) 12.1506i 0.539628i
\(508\) 0 0
\(509\) −6.81044 −0.301867 −0.150934 0.988544i \(-0.548228\pi\)
−0.150934 + 0.988544i \(0.548228\pi\)
\(510\) 0 0
\(511\) −7.07838 −0.313129
\(512\) 0 0
\(513\) 3.07838i 0.135914i
\(514\) 0 0
\(515\) −1.16290 + 4.68035i −0.0512434 + 0.206241i
\(516\) 0 0
\(517\) 9.36069i 0.411683i
\(518\) 0 0
\(519\) −22.4391 −0.984966
\(520\) 0 0
\(521\) −25.8166 −1.13105 −0.565523 0.824733i \(-0.691325\pi\)
−0.565523 + 0.824733i \(0.691325\pi\)
\(522\) 0 0
\(523\) 4.00000i 0.174908i −0.996169 0.0874539i \(-0.972127\pi\)
0.996169 0.0874539i \(-0.0278730\pi\)
\(524\) 0 0
\(525\) 4.41855 + 2.34017i 0.192841 + 0.102134i
\(526\) 0 0
\(527\) 8.36683i 0.364465i
\(528\) 0 0
\(529\) 17.5236 0.761895
\(530\) 0 0
\(531\) −10.5236 −0.456685
\(532\) 0 0
\(533\) 5.98771i 0.259357i
\(534\) 0 0
\(535\) 8.89496 35.7998i 0.384563 1.54776i
\(536\) 0 0
\(537\) 10.0000i 0.431532i
\(538\) 0 0
\(539\) 2.00000 0.0861461
\(540\) 0 0
\(541\) 25.8843 1.11285 0.556426 0.830897i \(-0.312172\pi\)
0.556426 + 0.830897i \(0.312172\pi\)
\(542\) 0 0
\(543\) 8.52359i 0.365782i
\(544\) 0 0
\(545\) 27.8576 + 6.92162i 1.19329 + 0.296490i
\(546\) 0 0
\(547\) 11.3197i 0.483993i 0.970277 + 0.241997i \(0.0778023\pi\)
−0.970277 + 0.241997i \(0.922198\pi\)
\(548\) 0 0
\(549\) 4.15676 0.177406
\(550\) 0 0
\(551\) 20.5646 0.876083
\(552\) 0 0
\(553\) 6.15676i 0.261812i
\(554\) 0 0
\(555\) −23.5174 5.84324i −0.998260 0.248032i
\(556\) 0 0
\(557\) 26.6491i 1.12916i 0.825378 + 0.564580i \(0.190962\pi\)
−0.825378 + 0.564580i \(0.809038\pi\)
\(558\) 0 0
\(559\) −6.01229 −0.254293
\(560\) 0 0
\(561\) 2.15676 0.0910583
\(562\) 0 0
\(563\) 46.3545i 1.95361i −0.214128 0.976806i \(-0.568691\pi\)
0.214128 0.976806i \(-0.431309\pi\)
\(564\) 0 0
\(565\) 2.82273 11.3607i 0.118753 0.477948i
\(566\) 0 0
\(567\) 1.00000i 0.0419961i
\(568\) 0 0
\(569\) 14.3668 0.602289 0.301145 0.953579i \(-0.402631\pi\)
0.301145 + 0.953579i \(0.402631\pi\)
\(570\) 0 0
\(571\) −38.7214 −1.62044 −0.810220 0.586126i \(-0.800652\pi\)
−0.810220 + 0.586126i \(0.800652\pi\)
\(572\) 0 0
\(573\) 15.3607i 0.641702i
\(574\) 0 0
\(575\) 5.47641 10.3402i 0.228382 0.431215i
\(576\) 0 0
\(577\) 43.4740i 1.80984i −0.425577 0.904922i \(-0.639929\pi\)
0.425577 0.904922i \(-0.360071\pi\)
\(578\) 0 0
\(579\) 8.36683 0.347714
\(580\) 0 0
\(581\) 6.83710 0.283651
\(582\) 0 0
\(583\) 7.51745i 0.311341i
\(584\) 0 0
\(585\) 0.496928 2.00000i 0.0205455 0.0826898i
\(586\) 0 0
\(587\) 36.0288i 1.48707i 0.668699 + 0.743533i \(0.266851\pi\)
−0.668699 + 0.743533i \(0.733149\pi\)
\(588\) 0 0
\(589\) 23.8843 0.984135
\(590\) 0 0
\(591\) 11.7587 0.483689
\(592\) 0 0
\(593\) 31.4863i 1.29299i 0.762920 + 0.646493i \(0.223765\pi\)
−0.762920 + 0.646493i \(0.776235\pi\)
\(594\) 0 0
\(595\) 2.34017 + 0.581449i 0.0959377 + 0.0238371i
\(596\) 0 0
\(597\) 22.5958i 0.924786i
\(598\) 0 0
\(599\) 29.0349 1.18633 0.593167 0.805080i \(-0.297877\pi\)
0.593167 + 0.805080i \(0.297877\pi\)
\(600\) 0 0
\(601\) 15.3607 0.626576 0.313288 0.949658i \(-0.398570\pi\)
0.313288 + 0.949658i \(0.398570\pi\)
\(602\) 0 0
\(603\) 4.68035i 0.190598i
\(604\) 0 0
\(605\) −15.1906 3.77432i −0.617586 0.153448i
\(606\) 0 0
\(607\) 13.0472i 0.529569i −0.964308 0.264784i \(-0.914699\pi\)
0.964308 0.264784i \(-0.0853008\pi\)
\(608\) 0 0
\(609\) 6.68035 0.270701
\(610\) 0 0
\(611\) −4.31351 −0.174506
\(612\) 0 0
\(613\) 15.5174i 0.626744i −0.949630 0.313372i \(-0.898541\pi\)
0.949630 0.313372i \(-0.101459\pi\)
\(614\) 0 0
\(615\) 3.50307 14.0989i 0.141257 0.568522i
\(616\) 0 0
\(617\) 22.7649i 0.916479i 0.888829 + 0.458240i \(0.151520\pi\)
−0.888829 + 0.458240i \(0.848480\pi\)
\(618\) 0 0
\(619\) 7.92777 0.318644 0.159322 0.987227i \(-0.449069\pi\)
0.159322 + 0.987227i \(0.449069\pi\)
\(620\) 0 0
\(621\) 2.34017 0.0939079
\(622\) 0 0
\(623\) 8.34017i 0.334142i
\(624\) 0 0
\(625\) 14.0472 + 20.6803i 0.561887 + 0.827214i
\(626\) 0 0
\(627\) 6.15676i 0.245877i
\(628\) 0 0
\(629\) −11.6865 −0.465971
\(630\) 0 0
\(631\) −19.2039 −0.764497 −0.382248 0.924060i \(-0.624850\pi\)
−0.382248 + 0.924060i \(0.624850\pi\)
\(632\) 0 0
\(633\) 13.6742i 0.543501i
\(634\) 0 0
\(635\) −0.993857 + 4.00000i −0.0394400 + 0.158735i
\(636\) 0 0
\(637\) 0.921622i 0.0365160i
\(638\) 0 0
\(639\) 2.00000 0.0791188
\(640\) 0 0
\(641\) −5.94668 −0.234880 −0.117440 0.993080i \(-0.537469\pi\)
−0.117440 + 0.993080i \(0.537469\pi\)
\(642\) 0 0
\(643\) 30.8904i 1.21820i 0.793094 + 0.609100i \(0.208469\pi\)
−0.793094 + 0.609100i \(0.791531\pi\)
\(644\) 0 0
\(645\) 14.1568 + 3.51745i 0.557422 + 0.138499i
\(646\) 0 0
\(647\) 19.2039i 0.754985i −0.926013 0.377492i \(-0.876786\pi\)
0.926013 0.377492i \(-0.123214\pi\)
\(648\) 0 0
\(649\) −21.0472 −0.826174
\(650\) 0 0
\(651\) 7.75872 0.304088
\(652\) 0 0
\(653\) 28.5548i 1.11744i −0.829358 0.558718i \(-0.811294\pi\)
0.829358 0.558718i \(-0.188706\pi\)
\(654\) 0 0
\(655\) −3.20394 0.796064i −0.125188 0.0311048i
\(656\) 0 0
\(657\) 7.07838i 0.276154i
\(658\) 0 0
\(659\) −27.9877 −1.09025 −0.545123 0.838356i \(-0.683517\pi\)
−0.545123 + 0.838356i \(0.683517\pi\)
\(660\) 0 0
\(661\) −22.1445 −0.861320 −0.430660 0.902514i \(-0.641719\pi\)
−0.430660 + 0.902514i \(0.641719\pi\)
\(662\) 0 0
\(663\) 0.993857i 0.0385982i
\(664\) 0 0
\(665\) −1.65983 + 6.68035i −0.0643653 + 0.259053i
\(666\) 0 0
\(667\) 15.6332i 0.605319i
\(668\) 0 0
\(669\) 21.6742 0.837973
\(670\) 0 0
\(671\) 8.31351 0.320940
\(672\) 0 0
\(673\) 2.21008i 0.0851923i 0.999092 + 0.0425962i \(0.0135629\pi\)
−0.999092 + 0.0425962i \(0.986437\pi\)
\(674\) 0 0
\(675\) −2.34017 + 4.41855i −0.0900733 + 0.170070i
\(676\) 0 0
\(677\) 19.5486i 0.751315i −0.926758 0.375658i \(-0.877417\pi\)
0.926758 0.375658i \(-0.122583\pi\)
\(678\) 0 0
\(679\) −8.43907 −0.323862
\(680\) 0 0
\(681\) −11.5174 −0.441350
\(682\) 0 0
\(683\) 11.8166i 0.452149i −0.974110 0.226074i \(-0.927411\pi\)
0.974110 0.226074i \(-0.0725893\pi\)
\(684\) 0 0
\(685\) 2.39350 9.63317i 0.0914508 0.368064i
\(686\) 0 0
\(687\) 12.8371i 0.489766i
\(688\) 0 0
\(689\) −3.46412 −0.131973
\(690\) 0 0
\(691\) −11.7587 −0.447323 −0.223661 0.974667i \(-0.571801\pi\)
−0.223661 + 0.974667i \(0.571801\pi\)
\(692\) 0 0
\(693\) 2.00000i 0.0759737i
\(694\) 0 0
\(695\) 29.5174 + 7.33403i 1.11966 + 0.278196i
\(696\) 0 0
\(697\) 7.00614i 0.265377i
\(698\) 0 0
\(699\) −6.76487 −0.255871
\(700\) 0 0
\(701\) 9.94668 0.375681 0.187840 0.982200i \(-0.439851\pi\)
0.187840 + 0.982200i \(0.439851\pi\)
\(702\) 0 0
\(703\) 33.3607i 1.25822i
\(704\) 0 0
\(705\) 10.1568 + 2.52359i 0.382526 + 0.0950439i
\(706\) 0 0
\(707\) 5.81658i 0.218755i
\(708\) 0 0
\(709\) 11.0472 0.414886 0.207443 0.978247i \(-0.433486\pi\)
0.207443 + 0.978247i \(0.433486\pi\)
\(710\) 0 0
\(711\) −6.15676 −0.230896
\(712\) 0 0
\(713\) 18.1568i 0.679976i
\(714\) 0 0
\(715\) 0.993857 4.00000i 0.0371681 0.149592i
\(716\) 0 0
\(717\) 23.3607i 0.872421i
\(718\) 0 0
\(719\) −6.15676 −0.229608 −0.114804 0.993388i \(-0.536624\pi\)
−0.114804 + 0.993388i \(0.536624\pi\)
\(720\) 0 0
\(721\) −2.15676 −0.0803218
\(722\) 0 0
\(723\) 14.6803i 0.545968i
\(724\) 0 0
\(725\) 29.5174 + 15.6332i 1.09625 + 0.580601i
\(726\) 0 0
\(727\) 2.89043i 0.107200i 0.998562 + 0.0536000i \(0.0170696\pi\)
−0.998562 + 0.0536000i \(0.982930\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 7.03489 0.260195
\(732\) 0 0
\(733\) 25.7998i 0.952936i −0.879192 0.476468i \(-0.841917\pi\)
0.879192 0.476468i \(-0.158083\pi\)
\(734\) 0 0
\(735\) −0.539189 + 2.17009i −0.0198883 + 0.0800448i
\(736\) 0 0
\(737\) 9.36069i 0.344806i
\(738\) 0 0
\(739\) −1.04718 −0.0385212 −0.0192606 0.999814i \(-0.506131\pi\)
−0.0192606 + 0.999814i \(0.506131\pi\)
\(740\) 0 0
\(741\) 2.83710 0.104224
\(742\) 0 0
\(743\) 9.97334i 0.365886i 0.983123 + 0.182943i \(0.0585624\pi\)
−0.983123 + 0.182943i \(0.941438\pi\)
\(744\) 0 0
\(745\) −34.0144 8.45136i −1.24619 0.309634i
\(746\) 0 0
\(747\) 6.83710i 0.250156i
\(748\) 0 0
\(749\) 16.4969 0.602785
\(750\) 0 0
\(751\) −3.26633 −0.119190 −0.0595950 0.998223i \(-0.518981\pi\)
−0.0595950 + 0.998223i \(0.518981\pi\)
\(752\) 0 0
\(753\) 9.16290i 0.333915i
\(754\) 0 0
\(755\) −12.6803 3.15061i −0.461485 0.114663i
\(756\) 0 0
\(757\) 49.9877i 1.81683i 0.418065 + 0.908417i \(0.362708\pi\)
−0.418065 + 0.908417i \(0.637292\pi\)
\(758\) 0 0
\(759\) 4.68035 0.169886
\(760\) 0 0
\(761\) 2.61265 0.0947083 0.0473542 0.998878i \(-0.484921\pi\)
0.0473542 + 0.998878i \(0.484921\pi\)
\(762\) 0 0
\(763\) 12.8371i 0.464734i
\(764\) 0 0
\(765\) −0.581449 + 2.34017i −0.0210223 + 0.0846091i
\(766\) 0 0
\(767\) 9.69878i 0.350202i
\(768\) 0 0
\(769\) 15.6742 0.565226 0.282613 0.959234i \(-0.408799\pi\)
0.282613 + 0.959234i \(0.408799\pi\)
\(770\) 0 0
\(771\) 5.07838 0.182893
\(772\) 0 0
\(773\) 5.81205i 0.209045i 0.994523 + 0.104522i \(0.0333314\pi\)
−0.994523 + 0.104522i \(0.966669\pi\)
\(774\) 0 0
\(775\) 34.2823 + 18.1568i 1.23146 + 0.652210i
\(776\) 0 0
\(777\) 10.8371i 0.388779i
\(778\) 0 0
\(779\) 20.0000 0.716574
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) 6.68035i 0.238736i
\(784\) 0 0
\(785\) 2.65368 10.6803i 0.0947140 0.381198i
\(786\) 0 0
\(787\) 39.3484i 1.40262i 0.712857 + 0.701310i \(0.247401\pi\)
−0.712857 + 0.701310i \(0.752599\pi\)
\(788\) 0 0
\(789\) −5.65983 −0.201495
\(790\) 0 0
\(791\) 5.23513 0.186140
\(792\) 0 0
\(793\) 3.83096i 0.136041i
\(794\) 0 0
\(795\) 8.15676 + 2.02666i 0.289290 + 0.0718783i
\(796\) 0 0
\(797\) 28.2823i 1.00181i −0.865502 0.500905i \(-0.833000\pi\)
0.865502 0.500905i \(-0.167000\pi\)
\(798\) 0 0
\(799\) 5.04718 0.178556
\(800\) 0 0
\(801\) 8.34017 0.294686
\(802\) 0 0