Properties

Label 1008.4.bt.d.593.4
Level $1008$
Weight $4$
Character 1008.593
Analytic conductor $59.474$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.bt (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 593.4
Character \(\chi\) \(=\) 1008.593
Dual form 1008.4.bt.d.17.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.89184 + 13.6691i) q^{5} +(-10.6185 + 15.1739i) q^{7} +O(q^{10})\) \(q+(-7.89184 + 13.6691i) q^{5} +(-10.6185 + 15.1739i) q^{7} +(28.2439 - 16.3066i) q^{11} -54.3118i q^{13} +(-12.3222 - 21.3427i) q^{17} +(-16.2989 - 9.41015i) q^{19} +(-46.7289 - 26.9789i) q^{23} +(-62.0622 - 107.495i) q^{25} -157.048i q^{29} +(-41.4452 + 23.9284i) q^{31} +(-123.614 - 264.895i) q^{35} +(-48.1973 + 83.4802i) q^{37} +263.002 q^{41} -258.982 q^{43} +(-62.5951 + 108.418i) q^{47} +(-117.497 - 322.248i) q^{49} +(471.579 - 272.266i) q^{53} +514.756i q^{55} +(-189.386 - 328.027i) q^{59} +(587.204 + 339.022i) q^{61} +(742.392 + 428.620i) q^{65} +(346.637 + 600.394i) q^{67} +238.831i q^{71} +(631.051 - 364.337i) q^{73} +(-52.4707 + 601.721i) q^{77} +(-439.845 + 761.833i) q^{79} +1222.11 q^{83} +388.979 q^{85} +(75.9540 - 131.556i) q^{89} +(824.125 + 576.708i) q^{91} +(257.256 - 148.527i) q^{95} -1591.43i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{7} + O(q^{10}) \) \( 48q + 24q^{7} - 540q^{19} - 924q^{25} - 648q^{31} - 132q^{37} + 792q^{43} + 672q^{49} + 12q^{67} + 2412q^{73} - 1680q^{79} + 480q^{85} - 1404q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −7.89184 + 13.6691i −0.705867 + 1.22260i 0.260510 + 0.965471i \(0.416109\pi\)
−0.966378 + 0.257127i \(0.917224\pi\)
\(6\) 0 0
\(7\) −10.6185 + 15.1739i −0.573343 + 0.819316i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 28.2439 16.3066i 0.774167 0.446966i −0.0601918 0.998187i \(-0.519171\pi\)
0.834359 + 0.551221i \(0.185838\pi\)
\(12\) 0 0
\(13\) 54.3118i 1.15872i −0.815071 0.579361i \(-0.803302\pi\)
0.815071 0.579361i \(-0.196698\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −12.3222 21.3427i −0.175798 0.304491i 0.764639 0.644459i \(-0.222917\pi\)
−0.940437 + 0.339967i \(0.889584\pi\)
\(18\) 0 0
\(19\) −16.2989 9.41015i −0.196801 0.113623i 0.398362 0.917228i \(-0.369579\pi\)
−0.595162 + 0.803606i \(0.702912\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −46.7289 26.9789i −0.423637 0.244587i 0.272995 0.962015i \(-0.411986\pi\)
−0.696632 + 0.717429i \(0.745319\pi\)
\(24\) 0 0
\(25\) −62.0622 107.495i −0.496498 0.859959i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 157.048i 1.00562i −0.864397 0.502811i \(-0.832299\pi\)
0.864397 0.502811i \(-0.167701\pi\)
\(30\) 0 0
\(31\) −41.4452 + 23.9284i −0.240122 + 0.138634i −0.615233 0.788345i \(-0.710938\pi\)
0.375111 + 0.926980i \(0.377605\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −123.614 264.895i −0.596990 1.27930i
\(36\) 0 0
\(37\) −48.1973 + 83.4802i −0.214151 + 0.370921i −0.953010 0.302940i \(-0.902032\pi\)
0.738858 + 0.673861i \(0.235365\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 263.002 1.00181 0.500903 0.865503i \(-0.333001\pi\)
0.500903 + 0.865503i \(0.333001\pi\)
\(42\) 0 0
\(43\) −258.982 −0.918474 −0.459237 0.888314i \(-0.651877\pi\)
−0.459237 + 0.888314i \(0.651877\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −62.5951 + 108.418i −0.194264 + 0.336476i −0.946659 0.322237i \(-0.895565\pi\)
0.752395 + 0.658713i \(0.228899\pi\)
\(48\) 0 0
\(49\) −117.497 322.248i −0.342557 0.939497i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 471.579 272.266i 1.22220 0.705635i 0.256810 0.966462i \(-0.417329\pi\)
0.965386 + 0.260827i \(0.0839952\pi\)
\(54\) 0 0
\(55\) 514.756i 1.26199i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −189.386 328.027i −0.417899 0.723822i 0.577829 0.816158i \(-0.303900\pi\)
−0.995728 + 0.0923360i \(0.970567\pi\)
\(60\) 0 0
\(61\) 587.204 + 339.022i 1.23252 + 0.711596i 0.967555 0.252662i \(-0.0813061\pi\)
0.264966 + 0.964258i \(0.414639\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 742.392 + 428.620i 1.41665 + 0.817905i
\(66\) 0 0
\(67\) 346.637 + 600.394i 0.632067 + 1.09477i 0.987128 + 0.159929i \(0.0511266\pi\)
−0.355061 + 0.934843i \(0.615540\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 238.831i 0.399212i 0.979876 + 0.199606i \(0.0639662\pi\)
−0.979876 + 0.199606i \(0.936034\pi\)
\(72\) 0 0
\(73\) 631.051 364.337i 1.01177 0.584143i 0.100058 0.994982i \(-0.468097\pi\)
0.911708 + 0.410838i \(0.134764\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −52.4707 + 601.721i −0.0776570 + 0.890552i
\(78\) 0 0
\(79\) −439.845 + 761.833i −0.626410 + 1.08497i 0.361856 + 0.932234i \(0.382143\pi\)
−0.988266 + 0.152740i \(0.951190\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1222.11 1.61619 0.808096 0.589050i \(-0.200498\pi\)
0.808096 + 0.589050i \(0.200498\pi\)
\(84\) 0 0
\(85\) 388.979 0.496361
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 75.9540 131.556i 0.0904619 0.156685i −0.817244 0.576292i \(-0.804499\pi\)
0.907706 + 0.419608i \(0.137832\pi\)
\(90\) 0 0
\(91\) 824.125 + 576.708i 0.949360 + 0.664345i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 257.256 148.527i 0.277830 0.160405i
\(96\) 0 0
\(97\) 1591.43i 1.66582i −0.553406 0.832912i \(-0.686672\pi\)
0.553406 0.832912i \(-0.313328\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −28.6940 49.6994i −0.0282689 0.0489631i 0.851545 0.524282i \(-0.175666\pi\)
−0.879814 + 0.475319i \(0.842333\pi\)
\(102\) 0 0
\(103\) 1674.25 + 966.626i 1.60163 + 0.924704i 0.991161 + 0.132667i \(0.0423541\pi\)
0.610473 + 0.792037i \(0.290979\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1729.67 998.625i −1.56274 0.902249i −0.996978 0.0776819i \(-0.975248\pi\)
−0.565764 0.824567i \(-0.691419\pi\)
\(108\) 0 0
\(109\) 698.958 + 1210.63i 0.614202 + 1.06383i 0.990524 + 0.137340i \(0.0438554\pi\)
−0.376322 + 0.926489i \(0.622811\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1636.31i 1.36222i −0.732181 0.681110i \(-0.761498\pi\)
0.732181 0.681110i \(-0.238502\pi\)
\(114\) 0 0
\(115\) 737.553 425.827i 0.598063 0.345292i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 454.695 + 39.6498i 0.350267 + 0.0305436i
\(120\) 0 0
\(121\) −133.690 + 231.558i −0.100443 + 0.173973i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −13.8192 −0.00988823
\(126\) 0 0
\(127\) −1729.20 −1.20820 −0.604101 0.796908i \(-0.706468\pi\)
−0.604101 + 0.796908i \(0.706468\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 89.9310 155.765i 0.0599795 0.103887i −0.834476 0.551044i \(-0.814230\pi\)
0.894456 + 0.447156i \(0.147563\pi\)
\(132\) 0 0
\(133\) 315.858 147.397i 0.205927 0.0960970i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2466.49 1424.03i 1.53815 0.888053i 0.539205 0.842174i \(-0.318725\pi\)
0.998947 0.0458784i \(-0.0146087\pi\)
\(138\) 0 0
\(139\) 58.4498i 0.0356665i 0.999841 + 0.0178333i \(0.00567680\pi\)
−0.999841 + 0.0178333i \(0.994323\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −885.641 1533.98i −0.517909 0.897045i
\(144\) 0 0
\(145\) 2146.70 + 1239.40i 1.22947 + 0.709836i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 701.675 + 405.112i 0.385795 + 0.222739i 0.680337 0.732900i \(-0.261834\pi\)
−0.294542 + 0.955639i \(0.595167\pi\)
\(150\) 0 0
\(151\) −1271.69 2202.64i −0.685357 1.18707i −0.973325 0.229433i \(-0.926313\pi\)
0.287968 0.957640i \(-0.407020\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 755.357i 0.391430i
\(156\) 0 0
\(157\) −2181.59 + 1259.54i −1.10898 + 0.640271i −0.938566 0.345101i \(-0.887845\pi\)
−0.170417 + 0.985372i \(0.554511\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 905.565 422.587i 0.443283 0.206860i
\(162\) 0 0
\(163\) −1072.18 + 1857.07i −0.515213 + 0.892375i 0.484631 + 0.874718i \(0.338954\pi\)
−0.999844 + 0.0176561i \(0.994380\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3381.59 1.56692 0.783458 0.621445i \(-0.213454\pi\)
0.783458 + 0.621445i \(0.213454\pi\)
\(168\) 0 0
\(169\) −752.775 −0.342638
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 98.9912 171.458i 0.0435038 0.0753509i −0.843454 0.537202i \(-0.819481\pi\)
0.886957 + 0.461851i \(0.152815\pi\)
\(174\) 0 0
\(175\) 2290.13 + 199.701i 0.989242 + 0.0862628i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3007.52 1736.40i 1.25583 0.725052i 0.283566 0.958953i \(-0.408482\pi\)
0.972260 + 0.233901i \(0.0751491\pi\)
\(180\) 0 0
\(181\) 2872.95i 1.17980i 0.807475 + 0.589902i \(0.200834\pi\)
−0.807475 + 0.589902i \(0.799166\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −760.731 1317.63i −0.302325 0.523642i
\(186\) 0 0
\(187\) −696.052 401.866i −0.272194 0.157152i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1075.20 + 620.765i 0.407322 + 0.235167i 0.689638 0.724154i \(-0.257770\pi\)
−0.282317 + 0.959321i \(0.591103\pi\)
\(192\) 0 0
\(193\) −1341.31 2323.21i −0.500256 0.866468i −1.00000 0.000295140i \(-0.999906\pi\)
0.499744 0.866173i \(-0.333427\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3056.57i 1.10544i −0.833367 0.552719i \(-0.813590\pi\)
0.833367 0.552719i \(-0.186410\pi\)
\(198\) 0 0
\(199\) 1864.33 1076.37i 0.664115 0.383427i −0.129728 0.991550i \(-0.541411\pi\)
0.793843 + 0.608123i \(0.208077\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2383.03 + 1667.60i 0.823922 + 0.576566i
\(204\) 0 0
\(205\) −2075.57 + 3595.00i −0.707143 + 1.22481i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −613.790 −0.203142
\(210\) 0 0
\(211\) 3912.38 1.27649 0.638245 0.769834i \(-0.279661\pi\)
0.638245 + 0.769834i \(0.279661\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2043.84 3540.04i 0.648321 1.12292i
\(216\) 0 0
\(217\) 76.9958 882.970i 0.0240867 0.276221i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1159.16 + 669.241i −0.352821 + 0.203701i
\(222\) 0 0
\(223\) 885.668i 0.265958i −0.991119 0.132979i \(-0.957546\pi\)
0.991119 0.132979i \(-0.0424544\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2687.02 + 4654.05i 0.785654 + 1.36079i 0.928607 + 0.371064i \(0.121007\pi\)
−0.142953 + 0.989729i \(0.545660\pi\)
\(228\) 0 0
\(229\) 5385.90 + 3109.55i 1.55419 + 0.897314i 0.997793 + 0.0663998i \(0.0211513\pi\)
0.556400 + 0.830914i \(0.312182\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5180.55 2990.99i −1.45661 0.840972i −0.457764 0.889074i \(-0.651350\pi\)
−0.998842 + 0.0481015i \(0.984683\pi\)
\(234\) 0 0
\(235\) −987.981 1711.23i −0.274250 0.475015i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3377.80i 0.914191i −0.889418 0.457095i \(-0.848890\pi\)
0.889418 0.457095i \(-0.151110\pi\)
\(240\) 0 0
\(241\) −1168.80 + 674.804i −0.312401 + 0.180365i −0.648001 0.761640i \(-0.724395\pi\)
0.335599 + 0.942005i \(0.391061\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5332.09 + 937.052i 1.39043 + 0.244351i
\(246\) 0 0
\(247\) −511.082 + 885.221i −0.131657 + 0.228037i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 731.129 0.183858 0.0919292 0.995766i \(-0.470697\pi\)
0.0919292 + 0.995766i \(0.470697\pi\)
\(252\) 0 0
\(253\) −1759.74 −0.437288
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2891.62 + 5008.43i −0.701845 + 1.21563i 0.265972 + 0.963981i \(0.414307\pi\)
−0.967818 + 0.251651i \(0.919026\pi\)
\(258\) 0 0
\(259\) −754.943 1617.77i −0.181119 0.388122i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1273.79 + 735.424i −0.298651 + 0.172426i −0.641837 0.766841i \(-0.721827\pi\)
0.343185 + 0.939268i \(0.388494\pi\)
\(264\) 0 0
\(265\) 8594.73i 1.99234i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2298.35 3980.86i −0.520941 0.902296i −0.999703 0.0243516i \(-0.992248\pi\)
0.478763 0.877944i \(-0.341085\pi\)
\(270\) 0 0
\(271\) 352.954 + 203.778i 0.0791160 + 0.0456777i 0.539036 0.842283i \(-0.318789\pi\)
−0.459920 + 0.887960i \(0.652122\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3505.75 2024.05i −0.768745 0.443835i
\(276\) 0 0
\(277\) −786.099 1361.56i −0.170513 0.295337i 0.768086 0.640346i \(-0.221209\pi\)
−0.938599 + 0.345009i \(0.887876\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 391.409i 0.0830943i 0.999137 + 0.0415471i \(0.0132287\pi\)
−0.999137 + 0.0415471i \(0.986771\pi\)
\(282\) 0 0
\(283\) 994.194 573.998i 0.208829 0.120568i −0.391938 0.919992i \(-0.628195\pi\)
0.600767 + 0.799424i \(0.294862\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2792.68 + 3990.78i −0.574378 + 0.820796i
\(288\) 0 0
\(289\) 2152.83 3728.81i 0.438190 0.758967i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7106.43 1.41694 0.708468 0.705743i \(-0.249387\pi\)
0.708468 + 0.705743i \(0.249387\pi\)
\(294\) 0 0
\(295\) 5978.43 1.17992
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1465.27 + 2537.93i −0.283408 + 0.490877i
\(300\) 0 0
\(301\) 2749.99 3929.78i 0.526600 0.752520i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −9268.23 + 5351.02i −1.73999 + 1.00458i
\(306\) 0 0
\(307\) 8035.73i 1.49389i −0.664887 0.746944i \(-0.731520\pi\)
0.664887 0.746944i \(-0.268480\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2093.96 + 3626.85i 0.381793 + 0.661285i 0.991319 0.131481i \(-0.0419733\pi\)
−0.609525 + 0.792767i \(0.708640\pi\)
\(312\) 0 0
\(313\) 6183.56 + 3570.08i 1.11666 + 0.644706i 0.940547 0.339663i \(-0.110313\pi\)
0.176117 + 0.984369i \(0.443646\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5241.84 + 3026.38i 0.928742 + 0.536210i 0.886414 0.462894i \(-0.153189\pi\)
0.0423286 + 0.999104i \(0.486522\pi\)
\(318\) 0 0
\(319\) −2560.91 4435.63i −0.449478 0.778519i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 463.814i 0.0798988i
\(324\) 0 0
\(325\) −5838.25 + 3370.71i −0.996454 + 0.575303i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −980.463 2101.04i −0.164300 0.352080i
\(330\) 0 0
\(331\) −5297.71 + 9175.90i −0.879724 + 1.52373i −0.0280795 + 0.999606i \(0.508939\pi\)
−0.851644 + 0.524120i \(0.824394\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −10942.4 −1.78462
\(336\) 0 0
\(337\) −629.759 −0.101796 −0.0508978 0.998704i \(-0.516208\pi\)
−0.0508978 + 0.998704i \(0.516208\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −780.382 + 1351.66i −0.123930 + 0.214653i
\(342\) 0 0
\(343\) 6137.40 + 1638.88i 0.966147 + 0.257992i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 355.046 204.986i 0.0549276 0.0317125i −0.472285 0.881446i \(-0.656571\pi\)
0.527212 + 0.849734i \(0.323237\pi\)
\(348\) 0 0
\(349\) 1777.77i 0.272670i −0.990663 0.136335i \(-0.956468\pi\)
0.990663 0.136335i \(-0.0435324\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4076.99 7061.56i −0.614721 1.06473i −0.990433 0.137991i \(-0.955935\pi\)
0.375713 0.926736i \(-0.377398\pi\)
\(354\) 0 0
\(355\) −3264.60 1884.82i −0.488076 0.281791i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 2451.26 + 1415.24i 0.360370 + 0.208060i 0.669243 0.743044i \(-0.266619\pi\)
−0.308873 + 0.951103i \(0.599952\pi\)
\(360\) 0 0
\(361\) −3252.40 5633.32i −0.474180 0.821303i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 11501.2i 1.64931i
\(366\) 0 0
\(367\) 233.258 134.671i 0.0331770 0.0191547i −0.483320 0.875444i \(-0.660569\pi\)
0.516497 + 0.856289i \(0.327236\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −876.087 + 10046.8i −0.122599 + 1.40593i
\(372\) 0 0
\(373\) 6119.60 10599.5i 0.849493 1.47136i −0.0321693 0.999482i \(-0.510242\pi\)
0.881662 0.471882i \(-0.156425\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8529.55 −1.16524
\(378\) 0 0
\(379\) −690.914 −0.0936409 −0.0468204 0.998903i \(-0.514909\pi\)
−0.0468204 + 0.998903i \(0.514909\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 4423.65 7661.98i 0.590177 1.02222i −0.404031 0.914745i \(-0.632391\pi\)
0.994208 0.107472i \(-0.0342755\pi\)
\(384\) 0 0
\(385\) −7810.88 5465.91i −1.03397 0.723555i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2808.67 1621.58i 0.366080 0.211356i −0.305665 0.952139i \(-0.598879\pi\)
0.671744 + 0.740783i \(0.265545\pi\)
\(390\) 0 0
\(391\) 1329.76i 0.171992i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6942.37 12024.5i −0.884325 1.53170i
\(396\) 0 0
\(397\) −9356.49 5401.97i −1.18284 0.682915i −0.226173 0.974087i \(-0.572621\pi\)
−0.956671 + 0.291172i \(0.905955\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −595.785 343.976i −0.0741947 0.0428363i 0.462444 0.886649i \(-0.346973\pi\)
−0.536638 + 0.843812i \(0.680306\pi\)
\(402\) 0 0
\(403\) 1299.60 + 2250.97i 0.160639 + 0.278235i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3143.74i 0.382873i
\(408\) 0 0
\(409\) 7348.56 4242.70i 0.888418 0.512929i 0.0149935 0.999888i \(-0.495227\pi\)
0.873425 + 0.486959i \(0.161894\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6988.45 + 609.400i 0.832638 + 0.0726068i
\(414\) 0 0
\(415\) −9644.69 + 16705.1i −1.14082 + 1.97595i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 11025.1 1.28547 0.642736 0.766088i \(-0.277799\pi\)
0.642736 + 0.766088i \(0.277799\pi\)
\(420\) 0 0
\(421\) −9636.91 −1.11562 −0.557808 0.829970i \(-0.688357\pi\)
−0.557808 + 0.829970i \(0.688357\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1529.48 + 2649.15i −0.174567 + 0.302359i
\(426\) 0 0
\(427\) −11379.5 + 5310.30i −1.28968 + 0.601835i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4664.33 + 2692.95i −0.521283 + 0.300963i −0.737459 0.675391i \(-0.763975\pi\)
0.216176 + 0.976354i \(0.430641\pi\)
\(432\) 0 0
\(433\) 4428.30i 0.491480i −0.969336 0.245740i \(-0.920969\pi\)
0.969336 0.245740i \(-0.0790309\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 507.751 + 879.451i 0.0555813 + 0.0962697i
\(438\) 0 0
\(439\) −14675.4 8472.85i −1.59549 0.921155i −0.992342 0.123523i \(-0.960581\pi\)
−0.603145 0.797632i \(-0.706086\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −15157.8 8751.39i −1.62567 0.938580i −0.985365 0.170458i \(-0.945475\pi\)
−0.640304 0.768122i \(-0.721191\pi\)
\(444\) 0 0
\(445\) 1198.83 + 2076.44i 0.127708 + 0.221197i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1975.26i 0.207614i 0.994597 + 0.103807i \(0.0331024\pi\)
−0.994597 + 0.103807i \(0.966898\pi\)
\(450\) 0 0
\(451\) 7428.20 4288.67i 0.775566 0.447773i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −14386.9 + 6713.73i −1.48235 + 0.691746i
\(456\) 0 0
\(457\) 6036.94 10456.3i 0.617935 1.07029i −0.371927 0.928262i \(-0.621303\pi\)
0.989862 0.142032i \(-0.0453637\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13447.2 1.35856 0.679281 0.733878i \(-0.262292\pi\)
0.679281 + 0.733878i \(0.262292\pi\)
\(462\) 0 0
\(463\) −15720.4 −1.57795 −0.788973 0.614428i \(-0.789387\pi\)
−0.788973 + 0.614428i \(0.789387\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 682.156 1181.53i 0.0675940 0.117076i −0.830248 0.557395i \(-0.811801\pi\)
0.897842 + 0.440318i \(0.145134\pi\)
\(468\) 0 0
\(469\) −12791.1 1115.40i −1.25936 0.109817i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −7314.65 + 4223.11i −0.711052 + 0.410526i
\(474\) 0 0
\(475\) 2336.06i 0.225654i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2078.39 + 3599.88i 0.198255 + 0.343388i 0.947963 0.318381i \(-0.103139\pi\)
−0.749708 + 0.661769i \(0.769806\pi\)
\(480\) 0 0
\(481\) 4533.96 + 2617.69i 0.429794 + 0.248142i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 21753.3 + 12559.3i 2.03663 + 1.17585i
\(486\) 0 0
\(487\) −6210.51 10756.9i −0.577875 1.00091i −0.995723 0.0923918i \(-0.970549\pi\)
0.417848 0.908517i \(-0.362785\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8234.71i 0.756879i 0.925626 + 0.378439i \(0.123539\pi\)
−0.925626 + 0.378439i \(0.876461\pi\)
\(492\) 0 0
\(493\) −3351.81 + 1935.17i −0.306203 + 0.176786i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3624.01 2536.02i −0.327081 0.228885i
\(498\) 0 0
\(499\) 1488.56 2578.26i 0.133541 0.231300i −0.791498 0.611172i \(-0.790698\pi\)
0.925039 + 0.379871i \(0.124032\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 537.349 0.0476327 0.0238163 0.999716i \(-0.492418\pi\)
0.0238163 + 0.999716i \(0.492418\pi\)
\(504\) 0 0
\(505\) 905.792 0.0798163
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4873.32 + 8440.83i −0.424373 + 0.735036i −0.996362 0.0852256i \(-0.972839\pi\)
0.571988 + 0.820262i \(0.306172\pi\)
\(510\) 0 0
\(511\) −1172.35 + 13444.2i −0.101491 + 1.16387i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −26425.8 + 15256.9i −2.26108 + 1.30544i
\(516\) 0 0
\(517\) 4082.85i 0.347318i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4831.31 8368.07i −0.406264 0.703670i 0.588204 0.808713i \(-0.299835\pi\)
−0.994468 + 0.105043i \(0.966502\pi\)
\(522\) 0 0
\(523\) −5153.64 2975.46i −0.430886 0.248772i 0.268838 0.963185i \(-0.413360\pi\)
−0.699724 + 0.714413i \(0.746694\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1021.39 + 589.701i 0.0844260 + 0.0487434i
\(528\) 0 0
\(529\) −4627.78 8015.54i −0.380355 0.658794i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 14284.1i 1.16082i
\(534\) 0 0
\(535\) 27300.5 15762.0i 2.20618 1.27374i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −8573.33 7185.54i −0.685119 0.574217i
\(540\) 0 0
\(541\) 4476.87 7754.17i 0.355778 0.616225i −0.631473 0.775398i \(-0.717549\pi\)
0.987251 + 0.159173i \(0.0508826\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −22064.3 −1.73418
\(546\) 0 0
\(547\) 20723.2 1.61985 0.809926 0.586532i \(-0.199507\pi\)
0.809926 + 0.586532i \(0.199507\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1477.84 + 2559.70i −0.114262 + 0.197907i
\(552\) 0 0
\(553\) −6889.54 14763.7i −0.529789 1.13529i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −11283.3 + 6514.43i −0.858330 + 0.495557i −0.863453 0.504430i \(-0.831703\pi\)
0.00512296 + 0.999987i \(0.498369\pi\)
\(558\) 0 0
\(559\) 14065.8i 1.06426i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −955.378 1654.76i −0.0715176 0.123872i 0.828049 0.560656i \(-0.189451\pi\)
−0.899567 + 0.436784i \(0.856118\pi\)
\(564\) 0 0
\(565\) 22366.8 + 12913.5i 1.66545 + 0.961546i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5509.88 + 3181.13i 0.405951 + 0.234376i 0.689049 0.724715i \(-0.258029\pi\)
−0.283098 + 0.959091i \(0.591362\pi\)
\(570\) 0 0
\(571\) 3394.59 + 5879.61i 0.248790 + 0.430918i 0.963190 0.268820i \(-0.0866336\pi\)
−0.714400 + 0.699737i \(0.753300\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6697.49i 0.485747i
\(576\) 0 0
\(577\) 6109.08 3527.08i 0.440770 0.254479i −0.263154 0.964754i \(-0.584763\pi\)
0.703924 + 0.710275i \(0.251429\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −12976.9 + 18544.2i −0.926632 + 1.32417i
\(582\) 0 0
\(583\) 8879.47 15379.7i 0.630789 1.09256i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 14742.1 1.03658 0.518290 0.855205i \(-0.326569\pi\)
0.518290 + 0.855205i \(0.326569\pi\)
\(588\) 0 0
\(589\) 900.679 0.0630082
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −6998.75 + 12122.2i −0.484662 + 0.839458i −0.999845 0.0176216i \(-0.994391\pi\)
0.515183 + 0.857080i \(0.327724\pi\)
\(594\) 0 0
\(595\) −4130.35 + 5902.34i −0.284585 + 0.406676i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 251.377 145.133i 0.0171469 0.00989977i −0.491402 0.870933i \(-0.663515\pi\)
0.508549 + 0.861033i \(0.330182\pi\)
\(600\) 0 0
\(601\) 3671.51i 0.249191i −0.992208 0.124596i \(-0.960237\pi\)
0.992208 0.124596i \(-0.0397634\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2110.12 3654.83i −0.141799 0.245603i
\(606\) 0 0
\(607\) −14231.9 8216.78i −0.951655 0.549438i −0.0580603 0.998313i \(-0.518492\pi\)
−0.893595 + 0.448875i \(0.851825\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5888.37 + 3399.65i 0.389882 + 0.225099i
\(612\) 0 0
\(613\) 11452.7 + 19836.6i 0.754599 + 1.30700i 0.945574 + 0.325408i \(0.105502\pi\)
−0.190975 + 0.981595i \(0.561165\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 10613.9i 0.692541i −0.938135 0.346271i \(-0.887448\pi\)
0.938135 0.346271i \(-0.112552\pi\)
\(618\) 0 0
\(619\) 5261.57 3037.77i 0.341648 0.197251i −0.319352 0.947636i \(-0.603465\pi\)
0.661001 + 0.750385i \(0.270132\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1189.71 + 2549.44i 0.0765085 + 0.163951i
\(624\) 0 0
\(625\) 7866.84 13625.8i 0.503478 0.872049i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2375.59 0.150590
\(630\) 0 0
\(631\) −16951.1 −1.06944 −0.534718 0.845031i \(-0.679582\pi\)
−0.534718 + 0.845031i \(0.679582\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 13646.6 23636.5i 0.852830 1.47715i
\(636\) 0 0
\(637\) −17501.9 + 6381.47i −1.08862 + 0.396928i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −10591.3 + 6114.91i −0.652625 + 0.376793i −0.789461 0.613800i \(-0.789640\pi\)
0.136836 + 0.990594i \(0.456307\pi\)
\(642\) 0 0
\(643\) 11251.9i 0.690095i −0.938585 0.345048i \(-0.887863\pi\)
0.938585 0.345048i \(-0.112137\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3237.83 + 5608.08i 0.196742 + 0.340767i 0.947470 0.319844i \(-0.103630\pi\)
−0.750728 + 0.660611i \(0.770297\pi\)
\(648\) 0 0
\(649\) −10698.0 6176.50i −0.647047 0.373573i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 16416.0 + 9477.77i 0.983778 + 0.567984i 0.903409 0.428781i \(-0.141057\pi\)
0.0803694 + 0.996765i \(0.474390\pi\)
\(654\) 0 0
\(655\) 1419.44 + 2458.55i 0.0846751 + 0.146662i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 22148.1i 1.30921i 0.755973 + 0.654603i \(0.227164\pi\)
−0.755973 + 0.654603i \(0.772836\pi\)
\(660\) 0 0
\(661\) −14010.5 + 8088.96i −0.824425 + 0.475982i −0.851940 0.523640i \(-0.824574\pi\)
0.0275153 + 0.999621i \(0.491240\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −477.923 + 5480.71i −0.0278693 + 0.319598i
\(666\) 0 0
\(667\) −4236.98 + 7338.66i −0.245962 + 0.426018i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 22113.2 1.27224
\(672\) 0 0
\(673\) 16420.1 0.940488 0.470244 0.882537i \(-0.344166\pi\)
0.470244 + 0.882537i \(0.344166\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11989.3 20766.0i 0.680627 1.17888i −0.294163 0.955755i \(-0.595041\pi\)
0.974790 0.223125i \(-0.0716258\pi\)
\(678\) 0 0
\(679\) 24148.2 + 16898.5i 1.36484 + 0.955088i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1924.00 + 1110.82i −0.107789 + 0.0622319i −0.552925 0.833231i \(-0.686488\pi\)
0.445136 + 0.895463i \(0.353155\pi\)
\(684\) 0 0
\(685\) 44952.9i 2.50739i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −14787.3 25612.3i −0.817635 1.41619i
\(690\) 0 0
\(691\) −20155.6 11636.9i −1.10963 0.640647i −0.170899 0.985289i \(-0.554667\pi\)
−0.938734 + 0.344642i \(0.888000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −798.954 461.276i −0.0436058 0.0251758i
\(696\) 0 0
\(697\) −3240.77 5613.17i −0.176116 0.305042i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 5003.94i 0.269610i −0.990872 0.134805i \(-0.956959\pi\)
0.990872 0.134805i \(-0.0430407\pi\)
\(702\) 0 0
\(703\) 1571.12 907.088i 0.0842902 0.0486650i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1058.82 + 92.3302i 0.0563240 + 0.00491151i
\(708\) 0 0
\(709\) −15002.2 + 25984.6i −0.794669 + 1.37641i 0.128381 + 0.991725i \(0.459022\pi\)
−0.923049 + 0.384682i \(0.874311\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2582.25 0.135633
\(714\) 0 0
\(715\) 27957.3 1.46230
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 7195.48 12462.9i 0.373221 0.646438i −0.616838 0.787090i \(-0.711587\pi\)
0.990059 + 0.140652i \(0.0449198\pi\)
\(720\) 0 0
\(721\) −32445.4 + 15140.8i −1.67591 + 0.782072i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −16881.8 + 9746.73i −0.864794 + 0.499289i
\(726\) 0 0
\(727\) 4931.70i 0.251591i 0.992056 + 0.125795i \(0.0401483\pi\)
−0.992056 + 0.125795i \(0.959852\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3191.22 + 5527.36i 0.161466 + 0.279667i
\(732\) 0 0
\(733\) 17813.2 + 10284.4i 0.897604 + 0.518232i 0.876422 0.481543i \(-0.159924\pi\)
0.0211822 + 0.999776i \(0.493257\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 19580.7 + 11305.0i 0.978652 + 0.565025i
\(738\) 0 0
\(739\) −15864.0 27477.2i −0.789669 1.36775i −0.926170 0.377106i \(-0.876919\pi\)
0.136501 0.990640i \(-0.456414\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 30966.4i 1.52900i −0.644623 0.764501i \(-0.722986\pi\)
0.644623 0.764501i \(-0.277014\pi\)
\(744\) 0 0
\(745\) −11075.0 + 6394.16i −0.544640 + 0.314448i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 33519.5 15642.0i 1.63521 0.763081i
\(750\) 0 0
\(751\) 17017.6 29475.4i 0.826873 1.43219i −0.0736070 0.997287i \(-0.523451\pi\)
0.900480 0.434898i \(-0.143216\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 40144.0 1.93508
\(756\) 0 0
\(757\) 1216.96 0.0584293 0.0292147 0.999573i \(-0.490699\pi\)
0.0292147 + 0.999573i \(0.490699\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 14359.4 24871.2i 0.684006 1.18473i −0.289742 0.957105i \(-0.593570\pi\)
0.973748 0.227628i \(-0.0730971\pi\)
\(762\) 0 0
\(763\) −25791.9 2249.08i −1.22376 0.106713i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −17815.7 + 10285.9i −0.838708 + 0.484229i
\(768\) 0 0
\(769\) 914.245i 0.0428719i −0.999770 0.0214360i \(-0.993176\pi\)
0.999770 0.0214360i \(-0.00682380\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −6138.69 10632.5i −0.285632 0.494729i 0.687131 0.726534i \(-0.258870\pi\)
−0.972762 + 0.231805i \(0.925537\pi\)
\(774\) 0 0
\(775\) 5144.37 + 2970.10i 0.238440 + 0.137663i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4286.64 2474.89i −0.197156 0.113828i
\(780\) 0 0
\(781\) 3894.52 + 6745.51i 0.178434 + 0.309057i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 39760.5i 1.80779i
\(786\) 0 0
\(787\) 16936.5 9778.31i 0.767119 0.442896i −0.0647271 0.997903i \(-0.520618\pi\)
0.831846 + 0.555007i \(0.187284\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 24829.2 + 17375.0i 1.11609 + 0.781018i
\(792\) 0 0
\(793\) 18412.9 31892.1i 0.824542 1.42815i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3319.70 0.147540 0.0737702 0.997275i \(-0.476497\pi\)
0.0737702 + 0.997275i \(0.476497\pi\)
\(798\) 0 0
\(799\) 3085.23 0.136605
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 11882.2 20580.6i 0.522184