Properties

Label 1520.2.d.g.609.2
Level $1520$
Weight $2$
Character 1520.609
Analytic conductor $12.137$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 760)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 609.2
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1520.609
Dual form 1520.2.d.g.609.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{3} +(1.00000 + 2.00000i) q^{5} +4.82843i q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.41421i q^{3} +(1.00000 + 2.00000i) q^{5} +4.82843i q^{7} +1.00000 q^{9} -4.82843 q^{11} +0.585786i q^{13} +(2.82843 - 1.41421i) q^{15} -2.82843i q^{17} -1.00000 q^{19} +6.82843 q^{21} +7.65685i q^{23} +(-3.00000 + 4.00000i) q^{25} -5.65685i q^{27} -3.65685 q^{29} -6.82843 q^{31} +6.82843i q^{33} +(-9.65685 + 4.82843i) q^{35} +0.585786i q^{37} +0.828427 q^{39} +0.828427 q^{41} -8.82843i q^{43} +(1.00000 + 2.00000i) q^{45} -0.828427i q^{47} -16.3137 q^{49} -4.00000 q^{51} +11.8995i q^{53} +(-4.82843 - 9.65685i) q^{55} +1.41421i q^{57} -6.82843 q^{59} -5.65685 q^{61} +4.82843i q^{63} +(-1.17157 + 0.585786i) q^{65} -9.89949i q^{67} +10.8284 q^{69} +8.48528 q^{71} +1.17157i q^{73} +(5.65685 + 4.24264i) q^{75} -23.3137i q^{77} +8.48528 q^{79} -5.00000 q^{81} +15.6569i q^{83} +(5.65685 - 2.82843i) q^{85} +5.17157i q^{87} +13.3137 q^{89} -2.82843 q^{91} +9.65685i q^{93} +(-1.00000 - 2.00000i) q^{95} +1.07107i q^{97} -4.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{5} + 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{5} + 4 q^{9} - 8 q^{11} - 4 q^{19} + 16 q^{21} - 12 q^{25} + 8 q^{29} - 16 q^{31} - 16 q^{35} - 8 q^{39} - 8 q^{41} + 4 q^{45} - 20 q^{49} - 16 q^{51} - 8 q^{55} - 16 q^{59} - 16 q^{65} + 32 q^{69} - 20 q^{81} + 8 q^{89} - 4 q^{95} - 8 q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.41421i 0.816497i −0.912871 0.408248i \(-0.866140\pi\)
0.912871 0.408248i \(-0.133860\pi\)
\(4\) 0 0
\(5\) 1.00000 + 2.00000i 0.447214 + 0.894427i
\(6\) 0 0
\(7\) 4.82843i 1.82497i 0.409106 + 0.912487i \(0.365841\pi\)
−0.409106 + 0.912487i \(0.634159\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.82843 −1.45583 −0.727913 0.685670i \(-0.759509\pi\)
−0.727913 + 0.685670i \(0.759509\pi\)
\(12\) 0 0
\(13\) 0.585786i 0.162468i 0.996695 + 0.0812340i \(0.0258861\pi\)
−0.996695 + 0.0812340i \(0.974114\pi\)
\(14\) 0 0
\(15\) 2.82843 1.41421i 0.730297 0.365148i
\(16\) 0 0
\(17\) 2.82843i 0.685994i −0.939336 0.342997i \(-0.888558\pi\)
0.939336 0.342997i \(-0.111442\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 6.82843 1.49008
\(22\) 0 0
\(23\) 7.65685i 1.59656i 0.602284 + 0.798282i \(0.294258\pi\)
−0.602284 + 0.798282i \(0.705742\pi\)
\(24\) 0 0
\(25\) −3.00000 + 4.00000i −0.600000 + 0.800000i
\(26\) 0 0
\(27\) 5.65685i 1.08866i
\(28\) 0 0
\(29\) −3.65685 −0.679061 −0.339530 0.940595i \(-0.610268\pi\)
−0.339530 + 0.940595i \(0.610268\pi\)
\(30\) 0 0
\(31\) −6.82843 −1.22642 −0.613211 0.789919i \(-0.710122\pi\)
−0.613211 + 0.789919i \(0.710122\pi\)
\(32\) 0 0
\(33\) 6.82843i 1.18868i
\(34\) 0 0
\(35\) −9.65685 + 4.82843i −1.63231 + 0.816153i
\(36\) 0 0
\(37\) 0.585786i 0.0963027i 0.998840 + 0.0481513i \(0.0153330\pi\)
−0.998840 + 0.0481513i \(0.984667\pi\)
\(38\) 0 0
\(39\) 0.828427 0.132655
\(40\) 0 0
\(41\) 0.828427 0.129379 0.0646893 0.997905i \(-0.479394\pi\)
0.0646893 + 0.997905i \(0.479394\pi\)
\(42\) 0 0
\(43\) 8.82843i 1.34632i −0.739496 0.673161i \(-0.764936\pi\)
0.739496 0.673161i \(-0.235064\pi\)
\(44\) 0 0
\(45\) 1.00000 + 2.00000i 0.149071 + 0.298142i
\(46\) 0 0
\(47\) 0.828427i 0.120839i −0.998173 0.0604193i \(-0.980756\pi\)
0.998173 0.0604193i \(-0.0192438\pi\)
\(48\) 0 0
\(49\) −16.3137 −2.33053
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 0 0
\(53\) 11.8995i 1.63452i 0.576268 + 0.817261i \(0.304508\pi\)
−0.576268 + 0.817261i \(0.695492\pi\)
\(54\) 0 0
\(55\) −4.82843 9.65685i −0.651065 1.30213i
\(56\) 0 0
\(57\) 1.41421i 0.187317i
\(58\) 0 0
\(59\) −6.82843 −0.888985 −0.444493 0.895782i \(-0.646616\pi\)
−0.444493 + 0.895782i \(0.646616\pi\)
\(60\) 0 0
\(61\) −5.65685 −0.724286 −0.362143 0.932123i \(-0.617955\pi\)
−0.362143 + 0.932123i \(0.617955\pi\)
\(62\) 0 0
\(63\) 4.82843i 0.608325i
\(64\) 0 0
\(65\) −1.17157 + 0.585786i −0.145316 + 0.0726579i
\(66\) 0 0
\(67\) 9.89949i 1.20942i −0.796447 0.604708i \(-0.793290\pi\)
0.796447 0.604708i \(-0.206710\pi\)
\(68\) 0 0
\(69\) 10.8284 1.30359
\(70\) 0 0
\(71\) 8.48528 1.00702 0.503509 0.863990i \(-0.332042\pi\)
0.503509 + 0.863990i \(0.332042\pi\)
\(72\) 0 0
\(73\) 1.17157i 0.137122i 0.997647 + 0.0685611i \(0.0218408\pi\)
−0.997647 + 0.0685611i \(0.978159\pi\)
\(74\) 0 0
\(75\) 5.65685 + 4.24264i 0.653197 + 0.489898i
\(76\) 0 0
\(77\) 23.3137i 2.65684i
\(78\) 0 0
\(79\) 8.48528 0.954669 0.477334 0.878722i \(-0.341603\pi\)
0.477334 + 0.878722i \(0.341603\pi\)
\(80\) 0 0
\(81\) −5.00000 −0.555556
\(82\) 0 0
\(83\) 15.6569i 1.71856i 0.511503 + 0.859282i \(0.329089\pi\)
−0.511503 + 0.859282i \(0.670911\pi\)
\(84\) 0 0
\(85\) 5.65685 2.82843i 0.613572 0.306786i
\(86\) 0 0
\(87\) 5.17157i 0.554451i
\(88\) 0 0
\(89\) 13.3137 1.41125 0.705625 0.708585i \(-0.250666\pi\)
0.705625 + 0.708585i \(0.250666\pi\)
\(90\) 0 0
\(91\) −2.82843 −0.296500
\(92\) 0 0
\(93\) 9.65685i 1.00137i
\(94\) 0 0
\(95\) −1.00000 2.00000i −0.102598 0.205196i
\(96\) 0 0
\(97\) 1.07107i 0.108750i 0.998521 + 0.0543752i \(0.0173167\pi\)
−0.998521 + 0.0543752i \(0.982683\pi\)
\(98\) 0 0
\(99\) −4.82843 −0.485275
\(100\) 0 0
\(101\) −8.00000 −0.796030 −0.398015 0.917379i \(-0.630301\pi\)
−0.398015 + 0.917379i \(0.630301\pi\)
\(102\) 0 0
\(103\) 9.89949i 0.975426i 0.873004 + 0.487713i \(0.162169\pi\)
−0.873004 + 0.487713i \(0.837831\pi\)
\(104\) 0 0
\(105\) 6.82843 + 13.6569i 0.666386 + 1.33277i
\(106\) 0 0
\(107\) 16.2426i 1.57024i 0.619347 + 0.785118i \(0.287398\pi\)
−0.619347 + 0.785118i \(0.712602\pi\)
\(108\) 0 0
\(109\) 10.4853 1.00431 0.502154 0.864778i \(-0.332541\pi\)
0.502154 + 0.864778i \(0.332541\pi\)
\(110\) 0 0
\(111\) 0.828427 0.0786308
\(112\) 0 0
\(113\) 11.4142i 1.07376i 0.843659 + 0.536879i \(0.180397\pi\)
−0.843659 + 0.536879i \(0.819603\pi\)
\(114\) 0 0
\(115\) −15.3137 + 7.65685i −1.42801 + 0.714005i
\(116\) 0 0
\(117\) 0.585786i 0.0541560i
\(118\) 0 0
\(119\) 13.6569 1.25192
\(120\) 0 0
\(121\) 12.3137 1.11943
\(122\) 0 0
\(123\) 1.17157i 0.105637i
\(124\) 0 0
\(125\) −11.0000 2.00000i −0.983870 0.178885i
\(126\) 0 0
\(127\) 12.7279i 1.12942i 0.825289 + 0.564710i \(0.191012\pi\)
−0.825289 + 0.564710i \(0.808988\pi\)
\(128\) 0 0
\(129\) −12.4853 −1.09927
\(130\) 0 0
\(131\) 17.6569 1.54269 0.771343 0.636419i \(-0.219585\pi\)
0.771343 + 0.636419i \(0.219585\pi\)
\(132\) 0 0
\(133\) 4.82843i 0.418678i
\(134\) 0 0
\(135\) 11.3137 5.65685i 0.973729 0.486864i
\(136\) 0 0
\(137\) 2.82843i 0.241649i −0.992674 0.120824i \(-0.961446\pi\)
0.992674 0.120824i \(-0.0385538\pi\)
\(138\) 0 0
\(139\) 15.1716 1.28684 0.643418 0.765515i \(-0.277516\pi\)
0.643418 + 0.765515i \(0.277516\pi\)
\(140\) 0 0
\(141\) −1.17157 −0.0986642
\(142\) 0 0
\(143\) 2.82843i 0.236525i
\(144\) 0 0
\(145\) −3.65685 7.31371i −0.303685 0.607370i
\(146\) 0 0
\(147\) 23.0711i 1.90287i
\(148\) 0 0
\(149\) −4.00000 −0.327693 −0.163846 0.986486i \(-0.552390\pi\)
−0.163846 + 0.986486i \(0.552390\pi\)
\(150\) 0 0
\(151\) 2.34315 0.190682 0.0953412 0.995445i \(-0.469606\pi\)
0.0953412 + 0.995445i \(0.469606\pi\)
\(152\) 0 0
\(153\) 2.82843i 0.228665i
\(154\) 0 0
\(155\) −6.82843 13.6569i −0.548472 1.09694i
\(156\) 0 0
\(157\) 4.48528i 0.357964i 0.983852 + 0.178982i \(0.0572805\pi\)
−0.983852 + 0.178982i \(0.942720\pi\)
\(158\) 0 0
\(159\) 16.8284 1.33458
\(160\) 0 0
\(161\) −36.9706 −2.91369
\(162\) 0 0
\(163\) 14.4853i 1.13457i −0.823520 0.567287i \(-0.807993\pi\)
0.823520 0.567287i \(-0.192007\pi\)
\(164\) 0 0
\(165\) −13.6569 + 6.82843i −1.06318 + 0.531592i
\(166\) 0 0
\(167\) 3.07107i 0.237646i −0.992915 0.118823i \(-0.962088\pi\)
0.992915 0.118823i \(-0.0379122\pi\)
\(168\) 0 0
\(169\) 12.6569 0.973604
\(170\) 0 0
\(171\) −1.00000 −0.0764719
\(172\) 0 0
\(173\) 8.58579i 0.652765i −0.945238 0.326383i \(-0.894170\pi\)
0.945238 0.326383i \(-0.105830\pi\)
\(174\) 0 0
\(175\) −19.3137 14.4853i −1.45998 1.09498i
\(176\) 0 0
\(177\) 9.65685i 0.725854i
\(178\) 0 0
\(179\) 22.8284 1.70628 0.853138 0.521685i \(-0.174696\pi\)
0.853138 + 0.521685i \(0.174696\pi\)
\(180\) 0 0
\(181\) 2.68629 0.199670 0.0998352 0.995004i \(-0.468168\pi\)
0.0998352 + 0.995004i \(0.468168\pi\)
\(182\) 0 0
\(183\) 8.00000i 0.591377i
\(184\) 0 0
\(185\) −1.17157 + 0.585786i −0.0861358 + 0.0430679i
\(186\) 0 0
\(187\) 13.6569i 0.998688i
\(188\) 0 0
\(189\) 27.3137 1.98678
\(190\) 0 0
\(191\) −19.3137 −1.39749 −0.698745 0.715370i \(-0.746258\pi\)
−0.698745 + 0.715370i \(0.746258\pi\)
\(192\) 0 0
\(193\) 1.07107i 0.0770971i −0.999257 0.0385486i \(-0.987727\pi\)
0.999257 0.0385486i \(-0.0122734\pi\)
\(194\) 0 0
\(195\) 0.828427 + 1.65685i 0.0593249 + 0.118650i
\(196\) 0 0
\(197\) 10.3431i 0.736919i −0.929644 0.368459i \(-0.879885\pi\)
0.929644 0.368459i \(-0.120115\pi\)
\(198\) 0 0
\(199\) −11.3137 −0.802008 −0.401004 0.916076i \(-0.631339\pi\)
−0.401004 + 0.916076i \(0.631339\pi\)
\(200\) 0 0
\(201\) −14.0000 −0.987484
\(202\) 0 0
\(203\) 17.6569i 1.23927i
\(204\) 0 0
\(205\) 0.828427 + 1.65685i 0.0578599 + 0.115720i
\(206\) 0 0
\(207\) 7.65685i 0.532188i
\(208\) 0 0
\(209\) 4.82843 0.333989
\(210\) 0 0
\(211\) 22.6274 1.55774 0.778868 0.627188i \(-0.215794\pi\)
0.778868 + 0.627188i \(0.215794\pi\)
\(212\) 0 0
\(213\) 12.0000i 0.822226i
\(214\) 0 0
\(215\) 17.6569 8.82843i 1.20419 0.602094i
\(216\) 0 0
\(217\) 32.9706i 2.23819i
\(218\) 0 0
\(219\) 1.65685 0.111960
\(220\) 0 0
\(221\) 1.65685 0.111452
\(222\) 0 0
\(223\) 9.89949i 0.662919i −0.943469 0.331460i \(-0.892459\pi\)
0.943469 0.331460i \(-0.107541\pi\)
\(224\) 0 0
\(225\) −3.00000 + 4.00000i −0.200000 + 0.266667i
\(226\) 0 0
\(227\) 4.92893i 0.327145i 0.986531 + 0.163572i \(0.0523017\pi\)
−0.986531 + 0.163572i \(0.947698\pi\)
\(228\) 0 0
\(229\) −3.31371 −0.218976 −0.109488 0.993988i \(-0.534921\pi\)
−0.109488 + 0.993988i \(0.534921\pi\)
\(230\) 0 0
\(231\) −32.9706 −2.16930
\(232\) 0 0
\(233\) 28.9706i 1.89792i 0.315389 + 0.948962i \(0.397865\pi\)
−0.315389 + 0.948962i \(0.602135\pi\)
\(234\) 0 0
\(235\) 1.65685 0.828427i 0.108081 0.0540406i
\(236\) 0 0
\(237\) 12.0000i 0.779484i
\(238\) 0 0
\(239\) −8.97056 −0.580257 −0.290129 0.956988i \(-0.593698\pi\)
−0.290129 + 0.956988i \(0.593698\pi\)
\(240\) 0 0
\(241\) 3.17157 0.204299 0.102149 0.994769i \(-0.467428\pi\)
0.102149 + 0.994769i \(0.467428\pi\)
\(242\) 0 0
\(243\) 9.89949i 0.635053i
\(244\) 0 0
\(245\) −16.3137 32.6274i −1.04224 2.08449i
\(246\) 0 0
\(247\) 0.585786i 0.0372727i
\(248\) 0 0
\(249\) 22.1421 1.40320
\(250\) 0 0
\(251\) −4.00000 −0.252478 −0.126239 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 0 0
\(253\) 36.9706i 2.32432i
\(254\) 0 0
\(255\) −4.00000 8.00000i −0.250490 0.500979i
\(256\) 0 0
\(257\) 10.2426i 0.638918i 0.947600 + 0.319459i \(0.103501\pi\)
−0.947600 + 0.319459i \(0.896499\pi\)
\(258\) 0 0
\(259\) −2.82843 −0.175750
\(260\) 0 0
\(261\) −3.65685 −0.226354
\(262\) 0 0
\(263\) 5.31371i 0.327657i 0.986489 + 0.163829i \(0.0523844\pi\)
−0.986489 + 0.163829i \(0.947616\pi\)
\(264\) 0 0
\(265\) −23.7990 + 11.8995i −1.46196 + 0.730980i
\(266\) 0 0
\(267\) 18.8284i 1.15228i
\(268\) 0 0
\(269\) −20.1421 −1.22809 −0.614044 0.789272i \(-0.710458\pi\)
−0.614044 + 0.789272i \(0.710458\pi\)
\(270\) 0 0
\(271\) −19.1716 −1.16459 −0.582295 0.812978i \(-0.697845\pi\)
−0.582295 + 0.812978i \(0.697845\pi\)
\(272\) 0 0
\(273\) 4.00000i 0.242091i
\(274\) 0 0
\(275\) 14.4853 19.3137i 0.873495 1.16466i
\(276\) 0 0
\(277\) 9.17157i 0.551066i −0.961292 0.275533i \(-0.911146\pi\)
0.961292 0.275533i \(-0.0888544\pi\)
\(278\) 0 0
\(279\) −6.82843 −0.408807
\(280\) 0 0
\(281\) −22.4853 −1.34136 −0.670680 0.741747i \(-0.733997\pi\)
−0.670680 + 0.741747i \(0.733997\pi\)
\(282\) 0 0
\(283\) 2.97056i 0.176582i 0.996095 + 0.0882908i \(0.0281405\pi\)
−0.996095 + 0.0882908i \(0.971860\pi\)
\(284\) 0 0
\(285\) −2.82843 + 1.41421i −0.167542 + 0.0837708i
\(286\) 0 0
\(287\) 4.00000i 0.236113i
\(288\) 0 0
\(289\) 9.00000 0.529412
\(290\) 0 0
\(291\) 1.51472 0.0887944
\(292\) 0 0
\(293\) 9.75736i 0.570031i −0.958523 0.285016i \(-0.908001\pi\)
0.958523 0.285016i \(-0.0919988\pi\)
\(294\) 0 0
\(295\) −6.82843 13.6569i −0.397566 0.795133i
\(296\) 0 0
\(297\) 27.3137i 1.58490i
\(298\) 0 0
\(299\) −4.48528 −0.259391
\(300\) 0 0
\(301\) 42.6274 2.45700
\(302\) 0 0
\(303\) 11.3137i 0.649956i
\(304\) 0 0
\(305\) −5.65685 11.3137i −0.323911 0.647821i
\(306\) 0 0
\(307\) 2.58579i 0.147579i 0.997274 + 0.0737893i \(0.0235092\pi\)
−0.997274 + 0.0737893i \(0.976491\pi\)
\(308\) 0 0
\(309\) 14.0000 0.796432
\(310\) 0 0
\(311\) 23.1716 1.31394 0.656970 0.753917i \(-0.271838\pi\)
0.656970 + 0.753917i \(0.271838\pi\)
\(312\) 0 0
\(313\) 20.9706i 1.18533i 0.805450 + 0.592663i \(0.201923\pi\)
−0.805450 + 0.592663i \(0.798077\pi\)
\(314\) 0 0
\(315\) −9.65685 + 4.82843i −0.544102 + 0.272051i
\(316\) 0 0
\(317\) 10.7279i 0.602540i 0.953539 + 0.301270i \(0.0974106\pi\)
−0.953539 + 0.301270i \(0.902589\pi\)
\(318\) 0 0
\(319\) 17.6569 0.988594
\(320\) 0 0
\(321\) 22.9706 1.28209
\(322\) 0 0
\(323\) 2.82843i 0.157378i
\(324\) 0 0
\(325\) −2.34315 1.75736i −0.129974 0.0974808i
\(326\) 0 0
\(327\) 14.8284i 0.820014i
\(328\) 0 0
\(329\) 4.00000 0.220527
\(330\) 0 0
\(331\) 13.6569 0.750649 0.375324 0.926894i \(-0.377531\pi\)
0.375324 + 0.926894i \(0.377531\pi\)
\(332\) 0 0
\(333\) 0.585786i 0.0321009i
\(334\) 0 0
\(335\) 19.7990 9.89949i 1.08173 0.540867i
\(336\) 0 0
\(337\) 15.8995i 0.866101i 0.901370 + 0.433050i \(0.142563\pi\)
−0.901370 + 0.433050i \(0.857437\pi\)
\(338\) 0 0
\(339\) 16.1421 0.876720
\(340\) 0 0
\(341\) 32.9706 1.78546
\(342\) 0 0
\(343\) 44.9706i 2.42818i
\(344\) 0 0
\(345\) 10.8284 + 21.6569i 0.582983 + 1.16597i
\(346\) 0 0
\(347\) 18.0000i 0.966291i −0.875540 0.483145i \(-0.839494\pi\)
0.875540 0.483145i \(-0.160506\pi\)
\(348\) 0 0
\(349\) −28.6274 −1.53239 −0.766195 0.642608i \(-0.777852\pi\)
−0.766195 + 0.642608i \(0.777852\pi\)
\(350\) 0 0
\(351\) 3.31371 0.176873
\(352\) 0 0
\(353\) 14.1421i 0.752710i −0.926476 0.376355i \(-0.877177\pi\)
0.926476 0.376355i \(-0.122823\pi\)
\(354\) 0 0
\(355\) 8.48528 + 16.9706i 0.450352 + 0.900704i
\(356\) 0 0
\(357\) 19.3137i 1.02219i
\(358\) 0 0
\(359\) −10.4853 −0.553392 −0.276696 0.960958i \(-0.589239\pi\)
−0.276696 + 0.960958i \(0.589239\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 17.4142i 0.914009i
\(364\) 0 0
\(365\) −2.34315 + 1.17157i −0.122646 + 0.0613229i
\(366\) 0 0
\(367\) 20.1421i 1.05141i 0.850667 + 0.525705i \(0.176199\pi\)
−0.850667 + 0.525705i \(0.823801\pi\)
\(368\) 0 0
\(369\) 0.828427 0.0431262
\(370\) 0 0
\(371\) −57.4558 −2.98296
\(372\) 0 0
\(373\) 27.8995i 1.44458i 0.691590 + 0.722291i \(0.256911\pi\)
−0.691590 + 0.722291i \(0.743089\pi\)
\(374\) 0 0
\(375\) −2.82843 + 15.5563i −0.146059 + 0.803326i
\(376\) 0 0
\(377\) 2.14214i 0.110326i
\(378\) 0 0
\(379\) −23.3137 −1.19754 −0.598772 0.800919i \(-0.704345\pi\)
−0.598772 + 0.800919i \(0.704345\pi\)
\(380\) 0 0
\(381\) 18.0000 0.922168
\(382\) 0 0
\(383\) 13.4142i 0.685434i 0.939439 + 0.342717i \(0.111347\pi\)
−0.939439 + 0.342717i \(0.888653\pi\)
\(384\) 0 0
\(385\) 46.6274 23.3137i 2.37635 1.18818i
\(386\) 0 0
\(387\) 8.82843i 0.448774i
\(388\) 0 0
\(389\) 9.31371 0.472224 0.236112 0.971726i \(-0.424127\pi\)
0.236112 + 0.971726i \(0.424127\pi\)
\(390\) 0 0
\(391\) 21.6569 1.09523
\(392\) 0 0
\(393\) 24.9706i 1.25960i
\(394\) 0 0
\(395\) 8.48528 + 16.9706i 0.426941 + 0.853882i
\(396\) 0 0
\(397\) 13.1716i 0.661062i −0.943795 0.330531i \(-0.892772\pi\)
0.943795 0.330531i \(-0.107228\pi\)
\(398\) 0 0
\(399\) −6.82843 −0.341849
\(400\) 0 0
\(401\) −26.9706 −1.34685 −0.673423 0.739258i \(-0.735177\pi\)
−0.673423 + 0.739258i \(0.735177\pi\)
\(402\) 0 0
\(403\) 4.00000i 0.199254i
\(404\) 0 0
\(405\) −5.00000 10.0000i −0.248452 0.496904i
\(406\) 0 0
\(407\) 2.82843i 0.140200i
\(408\) 0 0
\(409\) 36.8284 1.82105 0.910524 0.413456i \(-0.135678\pi\)
0.910524 + 0.413456i \(0.135678\pi\)
\(410\) 0 0
\(411\) −4.00000 −0.197305
\(412\) 0 0
\(413\) 32.9706i 1.62238i
\(414\) 0 0
\(415\) −31.3137 + 15.6569i −1.53713 + 0.768565i
\(416\) 0 0
\(417\) 21.4558i 1.05070i
\(418\) 0 0
\(419\) −10.6274 −0.519183 −0.259592 0.965718i \(-0.583588\pi\)
−0.259592 + 0.965718i \(0.583588\pi\)
\(420\) 0 0
\(421\) −1.79899 −0.0876774 −0.0438387 0.999039i \(-0.513959\pi\)
−0.0438387 + 0.999039i \(0.513959\pi\)
\(422\) 0 0
\(423\) 0.828427i 0.0402795i
\(424\) 0 0
\(425\) 11.3137 + 8.48528i 0.548795 + 0.411597i
\(426\) 0 0
\(427\) 27.3137i 1.32180i
\(428\) 0 0
\(429\) −4.00000 −0.193122
\(430\) 0 0
\(431\) 29.9411 1.44221 0.721107 0.692824i \(-0.243634\pi\)
0.721107 + 0.692824i \(0.243634\pi\)
\(432\) 0 0
\(433\) 37.5563i 1.80484i −0.430854 0.902421i \(-0.641788\pi\)
0.430854 0.902421i \(-0.358212\pi\)
\(434\) 0 0
\(435\) −10.3431 + 5.17157i −0.495916 + 0.247958i
\(436\) 0 0
\(437\) 7.65685i 0.366277i
\(438\) 0 0
\(439\) 28.4853 1.35953 0.679764 0.733431i \(-0.262082\pi\)
0.679764 + 0.733431i \(0.262082\pi\)
\(440\) 0 0
\(441\) −16.3137 −0.776843
\(442\) 0 0
\(443\) 16.6274i 0.789992i −0.918683 0.394996i \(-0.870746\pi\)
0.918683 0.394996i \(-0.129254\pi\)
\(444\) 0 0
\(445\) 13.3137 + 26.6274i 0.631130 + 1.26226i
\(446\) 0 0
\(447\) 5.65685i 0.267560i
\(448\) 0 0
\(449\) 26.4853 1.24992 0.624959 0.780658i \(-0.285116\pi\)
0.624959 + 0.780658i \(0.285116\pi\)
\(450\) 0 0
\(451\) −4.00000 −0.188353
\(452\) 0 0
\(453\) 3.31371i 0.155692i
\(454\) 0 0
\(455\) −2.82843 5.65685i −0.132599 0.265197i
\(456\) 0 0
\(457\) 8.97056i 0.419625i 0.977742 + 0.209813i \(0.0672854\pi\)
−0.977742 + 0.209813i \(0.932715\pi\)
\(458\) 0 0
\(459\) −16.0000 −0.746816
\(460\) 0 0
\(461\) −5.31371 −0.247484 −0.123742 0.992314i \(-0.539490\pi\)
−0.123742 + 0.992314i \(0.539490\pi\)
\(462\) 0 0
\(463\) 30.9706i 1.43932i −0.694325 0.719662i \(-0.744297\pi\)
0.694325 0.719662i \(-0.255703\pi\)
\(464\) 0 0
\(465\) −19.3137 + 9.65685i −0.895652 + 0.447826i
\(466\) 0 0
\(467\) 19.6569i 0.909611i 0.890591 + 0.454805i \(0.150291\pi\)
−0.890591 + 0.454805i \(0.849709\pi\)
\(468\) 0 0
\(469\) 47.7990 2.20715
\(470\) 0 0
\(471\) 6.34315 0.292277
\(472\) 0 0
\(473\) 42.6274i 1.96001i
\(474\) 0 0
\(475\) 3.00000 4.00000i 0.137649 0.183533i
\(476\) 0 0
\(477\) 11.8995i 0.544840i
\(478\) 0 0
\(479\) −12.8284 −0.586146 −0.293073 0.956090i \(-0.594678\pi\)
−0.293073 + 0.956090i \(0.594678\pi\)
\(480\) 0 0
\(481\) −0.343146 −0.0156461
\(482\) 0 0
\(483\) 52.2843i 2.37902i
\(484\) 0 0
\(485\) −2.14214 + 1.07107i −0.0972694 + 0.0486347i
\(486\) 0 0
\(487\) 7.27208i 0.329529i −0.986333 0.164765i \(-0.947314\pi\)
0.986333 0.164765i \(-0.0526865\pi\)
\(488\) 0 0
\(489\) −20.4853 −0.926376
\(490\) 0 0
\(491\) −6.34315 −0.286262 −0.143131 0.989704i \(-0.545717\pi\)
−0.143131 + 0.989704i \(0.545717\pi\)
\(492\) 0 0
\(493\) 10.3431i 0.465832i
\(494\) 0 0
\(495\) −4.82843 9.65685i −0.217022 0.434043i
\(496\) 0 0
\(497\) 40.9706i 1.83778i
\(498\) 0 0
\(499\) 15.4558 0.691899 0.345949 0.938253i \(-0.387557\pi\)
0.345949 + 0.938253i \(0.387557\pi\)
\(500\) 0 0
\(501\) −4.34315 −0.194037
\(502\) 0 0
\(503\) 26.0000i 1.15928i 0.814872 + 0.579641i \(0.196807\pi\)
−0.814872 + 0.579641i \(0.803193\pi\)
\(504\) 0 0
\(505\) −8.00000 16.0000i −0.355995 0.711991i
\(506\) 0 0
\(507\) 17.8995i 0.794944i
\(508\) 0 0
\(509\) 43.9411 1.94766 0.973828 0.227286i \(-0.0729852\pi\)
0.973828 + 0.227286i \(0.0729852\pi\)
\(510\) 0 0
\(511\) −5.65685 −0.250244
\(512\) 0 0
\(513\) 5.65685i 0.249756i
\(514\) 0 0
\(515\) −19.7990 + 9.89949i −0.872448 + 0.436224i
\(516\) 0 0
\(517\) 4.00000i 0.175920i
\(518\) 0 0
\(519\) −12.1421 −0.532981
\(520\) 0 0
\(521\) −24.3431 −1.06649 −0.533246 0.845960i \(-0.679028\pi\)
−0.533246 + 0.845960i \(0.679028\pi\)
\(522\) 0 0
\(523\) 34.5858i 1.51233i −0.654381 0.756165i \(-0.727071\pi\)
0.654381 0.756165i \(-0.272929\pi\)
\(524\) 0 0
\(525\) −20.4853 + 27.3137i −0.894051 + 1.19207i
\(526\) 0 0
\(527\) 19.3137i 0.841318i
\(528\) 0 0
\(529\) −35.6274 −1.54902
\(530\) 0 0
\(531\) −6.82843 −0.296328
\(532\) 0 0
\(533\) 0.485281i 0.0210199i
\(534\) 0 0
\(535\) −32.4853 + 16.2426i −1.40446 + 0.702231i
\(536\) 0 0
\(537\) 32.2843i 1.39317i
\(538\) 0 0
\(539\) 78.7696 3.39284
\(540\) 0 0
\(541\) 4.00000 0.171973 0.0859867 0.996296i \(-0.472596\pi\)
0.0859867 + 0.996296i \(0.472596\pi\)
\(542\) 0 0
\(543\) 3.79899i 0.163030i
\(544\) 0 0
\(545\) 10.4853 + 20.9706i 0.449140 + 0.898280i
\(546\) 0 0
\(547\) 8.24264i 0.352430i −0.984352 0.176215i \(-0.943615\pi\)
0.984352 0.176215i \(-0.0563854\pi\)
\(548\) 0 0
\(549\) −5.65685 −0.241429
\(550\) 0 0
\(551\) 3.65685 0.155787
\(552\) 0 0
\(553\) 40.9706i 1.74225i
\(554\) 0 0
\(555\) 0.828427 + 1.65685i 0.0351648 + 0.0703295i
\(556\) 0 0
\(557\) 14.8284i 0.628301i −0.949373 0.314150i \(-0.898280\pi\)
0.949373 0.314150i \(-0.101720\pi\)
\(558\) 0 0
\(559\) 5.17157 0.218734
\(560\) 0 0
\(561\) 19.3137 0.815425
\(562\) 0 0
\(563\) 45.4142i 1.91398i 0.290119 + 0.956990i \(0.406305\pi\)
−0.290119 + 0.956990i \(0.593695\pi\)
\(564\) 0 0
\(565\) −22.8284 + 11.4142i −0.960399 + 0.480200i
\(566\) 0 0
\(567\) 24.1421i 1.01387i
\(568\) 0 0
\(569\) −11.4558 −0.480254 −0.240127 0.970741i \(-0.577189\pi\)
−0.240127 + 0.970741i \(0.577189\pi\)
\(570\) 0 0
\(571\) 47.4558 1.98597 0.992983 0.118260i \(-0.0377317\pi\)
0.992983 + 0.118260i \(0.0377317\pi\)
\(572\) 0 0
\(573\) 27.3137i 1.14105i
\(574\) 0 0
\(575\) −30.6274 22.9706i −1.27725 0.957939i
\(576\) 0 0
\(577\) 6.34315i 0.264069i −0.991245 0.132034i \(-0.957849\pi\)
0.991245 0.132034i \(-0.0421509\pi\)
\(578\) 0 0
\(579\) −1.51472 −0.0629496
\(580\) 0 0
\(581\) −75.5980 −3.13633
\(582\) 0 0
\(583\) 57.4558i 2.37958i
\(584\) 0 0
\(585\) −1.17157 + 0.585786i −0.0484386 + 0.0242193i
\(586\) 0 0
\(587\) 18.0000i 0.742940i 0.928445 + 0.371470i \(0.121146\pi\)
−0.928445 + 0.371470i \(0.878854\pi\)
\(588\) 0 0
\(589\) 6.82843 0.281360
\(590\) 0 0
\(591\) −14.6274 −0.601692
\(592\) 0 0
\(593\) 14.6274i 0.600676i −0.953833 0.300338i \(-0.902901\pi\)
0.953833 0.300338i \(-0.0970995\pi\)
\(594\) 0 0
\(595\) 13.6569 + 27.3137i 0.559876 + 1.11975i
\(596\) 0 0
\(597\) 16.0000i 0.654836i
\(598\) 0 0
\(599\) 45.4558 1.85728 0.928638 0.370988i \(-0.120981\pi\)
0.928638 + 0.370988i \(0.120981\pi\)
\(600\) 0 0
\(601\) −11.8579 −0.483692 −0.241846 0.970315i \(-0.577753\pi\)
−0.241846 + 0.970315i \(0.577753\pi\)
\(602\) 0 0
\(603\) 9.89949i 0.403139i
\(604\) 0 0
\(605\) 12.3137 + 24.6274i 0.500623 + 1.00125i
\(606\) 0 0
\(607\) 41.2132i 1.67279i −0.548125 0.836396i \(-0.684658\pi\)
0.548125 0.836396i \(-0.315342\pi\)
\(608\) 0 0
\(609\) −24.9706 −1.01186
\(610\) 0 0
\(611\) 0.485281 0.0196324
\(612\) 0 0
\(613\) 24.4853i 0.988951i −0.869192 0.494476i \(-0.835360\pi\)
0.869192 0.494476i \(-0.164640\pi\)
\(614\) 0 0
\(615\) 2.34315 1.17157i 0.0944848 0.0472424i
\(616\) 0 0
\(617\) 6.82843i 0.274902i 0.990509 + 0.137451i \(0.0438910\pi\)
−0.990509 + 0.137451i \(0.956109\pi\)
\(618\) 0 0
\(619\) 31.1716 1.25289 0.626446 0.779465i \(-0.284509\pi\)
0.626446 + 0.779465i \(0.284509\pi\)
\(620\) 0 0
\(621\) 43.3137 1.73812
\(622\) 0 0
\(623\) 64.2843i 2.57549i
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 0 0
\(627\) 6.82843i 0.272701i
\(628\) 0 0
\(629\) 1.65685 0.0660631
\(630\) 0 0
\(631\) 21.7990 0.867804 0.433902 0.900960i \(-0.357136\pi\)
0.433902 + 0.900960i \(0.357136\pi\)
\(632\) 0 0
\(633\) 32.0000i 1.27189i
\(634\) 0 0
\(635\) −25.4558 + 12.7279i −1.01018 + 0.505092i
\(636\) 0 0
\(637\) 9.55635i 0.378636i
\(638\) 0 0
\(639\) 8.48528 0.335673
\(640\) 0 0
\(641\) −11.8579 −0.468357 −0.234179 0.972194i \(-0.575240\pi\)
−0.234179 + 0.972194i \(0.575240\pi\)
\(642\) 0 0
\(643\) 10.9706i 0.432637i −0.976323 0.216318i \(-0.930595\pi\)
0.976323 0.216318i \(-0.0694049\pi\)
\(644\) 0 0
\(645\) −12.4853 24.9706i −0.491607 0.983215i
\(646\) 0 0
\(647\) 10.2843i 0.404316i 0.979353 + 0.202158i \(0.0647955\pi\)
−0.979353 + 0.202158i \(0.935204\pi\)
\(648\) 0 0
\(649\) 32.9706 1.29421
\(650\) 0 0
\(651\) −46.6274 −1.82747
\(652\) 0 0
\(653\) 2.82843i 0.110685i −0.998467 0.0553425i \(-0.982375\pi\)
0.998467 0.0553425i \(-0.0176251\pi\)
\(654\) 0 0
\(655\) 17.6569 + 35.3137i 0.689910 + 1.37982i
\(656\) 0 0
\(657\) 1.17157i 0.0457074i
\(658\) 0 0
\(659\) −32.4853 −1.26545 −0.632723 0.774378i \(-0.718063\pi\)
−0.632723 + 0.774378i \(0.718063\pi\)
\(660\) 0 0
\(661\) 27.4558 1.06791 0.533954 0.845513i \(-0.320705\pi\)
0.533954 + 0.845513i \(0.320705\pi\)
\(662\) 0 0
\(663\) 2.34315i 0.0910002i
\(664\) 0 0
\(665\) 9.65685 4.82843i 0.374477 0.187238i
\(666\) 0 0
\(667\) 28.0000i 1.08416i
\(668\) 0 0
\(669\) −14.0000 −0.541271
\(670\) 0 0
\(671\) 27.3137 1.05443
\(672\) 0 0
\(673\) 21.7574i 0.838685i −0.907828 0.419342i \(-0.862261\pi\)
0.907828 0.419342i \(-0.137739\pi\)
\(674\) 0 0
\(675\) 22.6274 + 16.9706i 0.870930 + 0.653197i
\(676\) 0 0
\(677\) 12.1005i 0.465060i 0.972589 + 0.232530i \(0.0747004\pi\)
−0.972589 + 0.232530i \(0.925300\pi\)
\(678\) 0 0
\(679\) −5.17157 −0.198467
\(680\) 0 0
\(681\) 6.97056 0.267113
\(682\) 0 0
\(683\) 35.0711i 1.34196i 0.741477 + 0.670979i \(0.234126\pi\)
−0.741477 + 0.670979i \(0.765874\pi\)
\(684\) 0 0
\(685\) 5.65685 2.82843i 0.216137 0.108069i
\(686\) 0 0
\(687\) 4.68629i 0.178793i
\(688\) 0 0
\(689\) −6.97056 −0.265557
\(690\) 0 0
\(691\) −38.7696 −1.47486 −0.737432 0.675422i \(-0.763962\pi\)
−0.737432 + 0.675422i \(0.763962\pi\)
\(692\) 0 0
\(693\) 23.3137i 0.885615i
\(694\) 0 0
\(695\) 15.1716 + 30.3431i 0.575491 + 1.15098i
\(696\) 0 0
\(697\) 2.34315i 0.0887530i
\(698\) 0 0
\(699\) 40.9706 1.54965
\(700\) 0 0
\(701\) 31.3137 1.18270 0.591351 0.806414i \(-0.298595\pi\)
0.591351 + 0.806414i \(0.298595\pi\)
\(702\) 0 0
\(703\) 0.585786i 0.0220934i
\(704\) 0 0
\(705\) −1.17157 2.34315i −0.0441240 0.0882480i
\(706\) 0 0
\(707\) 38.6274i 1.45273i
\(708\) 0 0
\(709\) −33.3137 −1.25112 −0.625561 0.780175i \(-0.715130\pi\)
−0.625561 + 0.780175i \(0.715130\pi\)
\(710\) 0 0
\(711\) 8.48528 0.318223
\(712\) 0 0
\(713\) 52.2843i 1.95806i
\(714\) 0 0
\(715\) 5.65685 2.82843i 0.211554 0.105777i
\(716\) 0 0
\(717\) 12.6863i 0.473778i
\(718\) 0 0
\(719\) 2.48528 0.0926854 0.0463427 0.998926i \(-0.485243\pi\)
0.0463427 + 0.998926i \(0.485243\pi\)
\(720\) 0 0
\(721\) −47.7990 −1.78013
\(722\) 0 0
\(723\) 4.48528i 0.166809i
\(724\) 0 0
\(725\) 10.9706 14.6274i 0.407436 0.543249i
\(726\) 0 0
\(727\) 31.4558i 1.16663i 0.812245 + 0.583316i \(0.198245\pi\)
−0.812245 + 0.583316i \(0.801755\pi\)
\(728\) 0 0
\(729\) −29.0000 −1.07407
\(730\) 0 0
\(731\) −24.9706 −0.923570
\(732\) 0 0
\(733\) 12.6863i 0.468579i 0.972167 + 0.234289i \(0.0752763\pi\)
−0.972167 + 0.234289i \(0.924724\pi\)
\(734\) 0 0
\(735\) −46.1421 + 23.0711i −1.70198 + 0.850989i
\(736\) 0 0
\(737\) 47.7990i 1.76070i
\(738\) 0 0
\(739\) −12.0000 −0.441427 −0.220714 0.975339i \(-0.570839\pi\)
−0.220714 + 0.975339i \(0.570839\pi\)
\(740\) 0 0
\(741\) −0.828427 −0.0304330
\(742\) 0 0
\(743\) 2.10051i 0.0770601i −0.999257 0.0385300i \(-0.987732\pi\)
0.999257 0.0385300i \(-0.0122675\pi\)
\(744\) 0 0
\(745\) −4.00000 8.00000i −0.146549 0.293097i
\(746\) 0 0
\(747\) 15.6569i 0.572854i
\(748\) 0 0
\(749\) −78.4264 −2.86564
\(750\) 0 0
\(751\) −43.5980 −1.59091 −0.795456 0.606011i \(-0.792769\pi\)
−0.795456 + 0.606011i \(0.792769\pi\)
\(752\) 0 0
\(753\) 5.65685i 0.206147i
\(754\) 0 0
\(755\) 2.34315 + 4.68629i 0.0852758 + 0.170552i
\(756\) 0 0
\(757\) 38.6274i 1.40394i 0.712208 + 0.701969i \(0.247695\pi\)
−0.712208 + 0.701969i \(0.752305\pi\)
\(758\) 0 0
\(759\) −52.2843 −1.89780
\(760\) 0 0
\(761\) −24.2843 −0.880304 −0.440152 0.897923i \(-0.645075\pi\)
−0.440152 + 0.897923i \(0.645075\pi\)
\(762\) 0 0
\(763\) 50.6274i 1.83284i
\(764\) 0 0
\(765\) 5.65685 2.82843i 0.204524 0.102262i
\(766\) 0 0
\(767\) 4.00000i 0.144432i
\(768\) 0 0
\(769\) 36.2843 1.30844 0.654222 0.756302i \(-0.272996\pi\)
0.654222 + 0.756302i \(0.272996\pi\)
\(770\) 0 0
\(771\) 14.4853 0.521675
\(772\) 0 0
\(773\) 13.0711i 0.470134i −0.971979 0.235067i \(-0.924469\pi\)
0.971979 0.235067i \(-0.0755309\pi\)
\(774\) 0 0
\(775\) 20.4853 27.3137i 0.735853 0.981137i
\(776\) 0 0
\(777\) 4.00000i 0.143499i
\(778\) 0 0
\(779\) −0.828427 −0.0296815
\(780\) 0 0
\(781\) −40.9706 −1.46604
\(782\) 0 0
\(783\) 20.6863i 0.739268i
\(784\) 0 0
\(785\) −8.97056 + 4.48528i −0.320173 + 0.160087i
\(786\) 0 0
\(787\) 28.5269i 1.01687i −0.861099 0.508437i \(-0.830223\pi\)
0.861099 0.508437i \(-0.169777\pi\)
\(788\) 0 0
\(789\) 7.51472 0.267531
\(790\) 0 0
\(791\) −55.1127 −1.95958
\(792\) 0 0
\(793\) 3.31371i 0.117673i
\(794\) 0 0
\(795\) 16.8284 + 33.6569i 0.596843 + 1.19369i
\(796\) 0 0
\(797\) 38.0416i 1.34750i 0.738958 + 0.673752i \(0.235318\pi\)
−0.738958 + 0.673752i \(0.764682\pi\)
\(798\) 0 0
\(799\) −2.34315 −0.0828945
\(800\) 0 0
\(801\) 13.3137 0.470417
\(802\) 0