Properties

Label 1008.4.bt.d.17.10
Level $1008$
Weight $4$
Character 1008.17
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 17.10
Character \(\chi\) \(=\) 1008.17
Dual form 1008.4.bt.d.593.10

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.08296 - 3.60779i) q^{5} +(18.2790 + 2.97950i) q^{7} +O(q^{10})\) \(q+(-2.08296 - 3.60779i) q^{5} +(18.2790 + 2.97950i) q^{7} +(-33.1649 - 19.1477i) q^{11} +49.6184i q^{13} +(7.65240 - 13.2543i) q^{17} +(-122.914 + 70.9647i) q^{19} +(136.779 - 78.9695i) q^{23} +(53.8226 - 93.2234i) q^{25} -204.644i q^{29} +(90.5273 + 52.2660i) q^{31} +(-27.3250 - 72.1531i) q^{35} +(-194.054 - 336.111i) q^{37} -325.463 q^{41} -191.352 q^{43} +(249.874 + 432.795i) q^{47} +(325.245 + 108.925i) q^{49} +(-37.8772 - 21.8684i) q^{53} +159.536i q^{55} +(-86.5601 + 149.927i) q^{59} +(208.382 - 120.309i) q^{61} +(179.013 - 103.353i) q^{65} +(-440.624 + 763.183i) q^{67} -1017.80i q^{71} +(-361.028 - 208.439i) q^{73} +(-549.170 - 448.817i) q^{77} +(-237.361 - 411.121i) q^{79} +652.093 q^{83} -63.7586 q^{85} +(-298.995 - 517.874i) q^{89} +(-147.838 + 906.976i) q^{91} +(512.052 + 295.633i) q^{95} -1771.43i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 24q^{7} + O(q^{10}) \) \( 48q + 24q^{7} - 540q^{19} - 924q^{25} - 648q^{31} - 132q^{37} + 792q^{43} + 672q^{49} + 12q^{67} + 2412q^{73} - 1680q^{79} + 480q^{85} - 1404q^{91} + O(q^{100}) \)

Character values

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

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

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
\(5\) −2.08296 3.60779i −0.186306 0.322691i 0.757710 0.652591i \(-0.226318\pi\)
−0.944016 + 0.329901i \(0.892985\pi\)
\(6\) 0 0
\(7\) 18.2790 + 2.97950i 0.986974 + 0.160878i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −33.1649 19.1477i −0.909053 0.524842i −0.0289264 0.999582i \(-0.509209\pi\)
−0.880126 + 0.474740i \(0.842542\pi\)
\(12\) 0 0
\(13\) 49.6184i 1.05859i 0.848438 + 0.529295i \(0.177544\pi\)
−0.848438 + 0.529295i \(0.822456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.65240 13.2543i 0.109175 0.189097i −0.806261 0.591560i \(-0.798512\pi\)
0.915436 + 0.402463i \(0.131846\pi\)
\(18\) 0 0
\(19\) −122.914 + 70.9647i −1.48413 + 0.856864i −0.999837 0.0180413i \(-0.994257\pi\)
−0.484294 + 0.874905i \(0.660924\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 136.779 78.9695i 1.24002 0.715925i 0.270920 0.962602i \(-0.412672\pi\)
0.969098 + 0.246677i \(0.0793386\pi\)
\(24\) 0 0
\(25\) 53.8226 93.2234i 0.430580 0.745787i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 204.644i 1.31039i −0.755458 0.655197i \(-0.772586\pi\)
0.755458 0.655197i \(-0.227414\pi\)
\(30\) 0 0
\(31\) 90.5273 + 52.2660i 0.524490 + 0.302814i 0.738770 0.673958i \(-0.235407\pi\)
−0.214280 + 0.976772i \(0.568740\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −27.3250 72.1531i −0.131965 0.348460i
\(36\) 0 0
\(37\) −194.054 336.111i −0.862224 1.49341i −0.869778 0.493443i \(-0.835738\pi\)
0.00755433 0.999971i \(-0.497595\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −325.463 −1.23973 −0.619864 0.784709i \(-0.712812\pi\)
−0.619864 + 0.784709i \(0.712812\pi\)
\(42\) 0 0
\(43\) −191.352 −0.678626 −0.339313 0.940674i \(-0.610195\pi\)
−0.339313 + 0.940674i \(0.610195\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 249.874 + 432.795i 0.775487 + 1.34318i 0.934520 + 0.355910i \(0.115829\pi\)
−0.159033 + 0.987273i \(0.550838\pi\)
\(48\) 0 0
\(49\) 325.245 + 108.925i 0.948237 + 0.317565i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −37.8772 21.8684i −0.0981667 0.0566766i 0.450113 0.892972i \(-0.351384\pi\)
−0.548280 + 0.836295i \(0.684717\pi\)
\(54\) 0 0
\(55\) 159.536i 0.391124i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −86.5601 + 149.927i −0.191003 + 0.330827i −0.945583 0.325381i \(-0.894507\pi\)
0.754580 + 0.656208i \(0.227841\pi\)
\(60\) 0 0
\(61\) 208.382 120.309i 0.437386 0.252525i −0.265102 0.964220i \(-0.585406\pi\)
0.702488 + 0.711695i \(0.252072\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 179.013 103.353i 0.341597 0.197221i
\(66\) 0 0
\(67\) −440.624 + 763.183i −0.803445 + 1.39161i 0.113891 + 0.993493i \(0.463669\pi\)
−0.917336 + 0.398114i \(0.869665\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1017.80i 1.70128i −0.525746 0.850642i \(-0.676214\pi\)
0.525746 0.850642i \(-0.323786\pi\)
\(72\) 0 0
\(73\) −361.028 208.439i −0.578837 0.334192i 0.181834 0.983329i \(-0.441797\pi\)
−0.760671 + 0.649138i \(0.775130\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −549.170 448.817i −0.812776 0.664252i
\(78\) 0 0
\(79\) −237.361 411.121i −0.338041 0.585504i 0.646024 0.763318i \(-0.276431\pi\)
−0.984064 + 0.177814i \(0.943097\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 652.093 0.862368 0.431184 0.902264i \(-0.358096\pi\)
0.431184 + 0.902264i \(0.358096\pi\)
\(84\) 0 0
\(85\) −63.7586 −0.0813598
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −298.995 517.874i −0.356105 0.616793i 0.631201 0.775619i \(-0.282562\pi\)
−0.987307 + 0.158826i \(0.949229\pi\)
\(90\) 0 0
\(91\) −147.838 + 906.976i −0.170304 + 1.04480i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 512.052 + 295.633i 0.553004 + 0.319277i
\(96\) 0 0
\(97\) 1771.43i 1.85424i −0.374763 0.927121i \(-0.622276\pi\)
0.374763 0.927121i \(-0.377724\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 106.303 184.123i 0.104728 0.181395i −0.808899 0.587948i \(-0.799936\pi\)
0.913627 + 0.406553i \(0.133269\pi\)
\(102\) 0 0
\(103\) −1148.55 + 663.115i −1.09874 + 0.634356i −0.935889 0.352295i \(-0.885401\pi\)
−0.162848 + 0.986651i \(0.552068\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −106.629 + 61.5621i −0.0963382 + 0.0556209i −0.547395 0.836874i \(-0.684380\pi\)
0.451057 + 0.892495i \(0.351047\pi\)
\(108\) 0 0
\(109\) 8.14724 14.1114i 0.00715930 0.0124003i −0.862424 0.506187i \(-0.831054\pi\)
0.869583 + 0.493787i \(0.164388\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1537.79i 1.28020i −0.768291 0.640101i \(-0.778892\pi\)
0.768291 0.640101i \(-0.221108\pi\)
\(114\) 0 0
\(115\) −569.811 328.980i −0.462045 0.266762i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 179.370 219.476i 0.138175 0.169070i
\(120\) 0 0
\(121\) 67.7716 + 117.384i 0.0509178 + 0.0881922i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −969.181 −0.693489
\(126\) 0 0
\(127\) −1097.31 −0.766697 −0.383348 0.923604i \(-0.625229\pi\)
−0.383348 + 0.923604i \(0.625229\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1417.08 2454.45i −0.945119 1.63699i −0.755513 0.655134i \(-0.772612\pi\)
−0.189606 0.981860i \(-0.560721\pi\)
\(132\) 0 0
\(133\) −2458.19 + 930.941i −1.60265 + 0.606939i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −980.159 565.895i −0.611245 0.352903i 0.162207 0.986757i \(-0.448139\pi\)
−0.773453 + 0.633854i \(0.781472\pi\)
\(138\) 0 0
\(139\) 1088.19i 0.664020i −0.943276 0.332010i \(-0.892273\pi\)
0.943276 0.332010i \(-0.107727\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 950.080 1645.59i 0.555592 0.962314i
\(144\) 0 0
\(145\) −738.313 + 426.265i −0.422852 + 0.244134i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1485.18 857.470i 0.816583 0.471454i −0.0326539 0.999467i \(-0.510396\pi\)
0.849237 + 0.528012i \(0.177063\pi\)
\(150\) 0 0
\(151\) −128.682 + 222.885i −0.0693512 + 0.120120i −0.898616 0.438736i \(-0.855426\pi\)
0.829265 + 0.558856i \(0.188760\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 435.472i 0.225664i
\(156\) 0 0
\(157\) −644.785 372.267i −0.327767 0.189237i 0.327082 0.944996i \(-0.393935\pi\)
−0.654849 + 0.755759i \(0.727268\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2735.48 1035.95i 1.33904 0.507108i
\(162\) 0 0
\(163\) −218.407 378.292i −0.104951 0.181780i 0.808767 0.588129i \(-0.200135\pi\)
−0.913718 + 0.406349i \(0.866802\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1110.76 −0.514688 −0.257344 0.966320i \(-0.582847\pi\)
−0.257344 + 0.966320i \(0.582847\pi\)
\(168\) 0 0
\(169\) −264.987 −0.120613
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1967.21 3407.31i −0.864533 1.49741i −0.867510 0.497419i \(-0.834281\pi\)
0.00297733 0.999996i \(-0.499052\pi\)
\(174\) 0 0
\(175\) 1261.58 1543.67i 0.544953 0.666802i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −791.218 456.810i −0.330382 0.190746i 0.325628 0.945498i \(-0.394424\pi\)
−0.656011 + 0.754751i \(0.727757\pi\)
\(180\) 0 0
\(181\) 2909.50i 1.19482i 0.801938 + 0.597408i \(0.203803\pi\)
−0.801938 + 0.597408i \(0.796197\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −808.413 + 1400.21i −0.321274 + 0.556463i
\(186\) 0 0
\(187\) −507.581 + 293.052i −0.198492 + 0.114599i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1342.95 + 775.351i −0.508756 + 0.293730i −0.732322 0.680959i \(-0.761563\pi\)
0.223566 + 0.974689i \(0.428230\pi\)
\(192\) 0 0
\(193\) −840.304 + 1455.45i −0.313401 + 0.542827i −0.979096 0.203397i \(-0.934802\pi\)
0.665695 + 0.746224i \(0.268135\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3085.14i 1.11577i 0.829917 + 0.557887i \(0.188388\pi\)
−0.829917 + 0.557887i \(0.811612\pi\)
\(198\) 0 0
\(199\) 359.537 + 207.579i 0.128075 + 0.0739442i 0.562669 0.826682i \(-0.309775\pi\)
−0.434594 + 0.900627i \(0.643108\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 609.737 3740.69i 0.210813 1.29333i
\(204\) 0 0
\(205\) 677.927 + 1174.20i 0.230968 + 0.400049i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5435.25 1.79887
\(210\) 0 0
\(211\) 2166.75 0.706944 0.353472 0.935445i \(-0.385001\pi\)
0.353472 + 0.935445i \(0.385001\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 398.579 + 690.359i 0.126432 + 0.218986i
\(216\) 0 0
\(217\) 1499.02 + 1225.10i 0.468942 + 0.383249i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 657.660 + 379.700i 0.200176 + 0.115572i
\(222\) 0 0
\(223\) 2089.66i 0.627505i 0.949505 + 0.313753i \(0.101586\pi\)
−0.949505 + 0.313753i \(0.898414\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 137.016 237.319i 0.0400621 0.0693896i −0.845299 0.534293i \(-0.820578\pi\)
0.885361 + 0.464904i \(0.153911\pi\)
\(228\) 0 0
\(229\) 1942.69 1121.61i 0.560595 0.323660i −0.192789 0.981240i \(-0.561753\pi\)
0.753384 + 0.657580i \(0.228420\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −522.653 + 301.754i −0.146953 + 0.0848436i −0.571674 0.820481i \(-0.693706\pi\)
0.424720 + 0.905325i \(0.360372\pi\)
\(234\) 0 0
\(235\) 1040.96 1802.99i 0.288955 0.500485i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1504.81i 0.407273i −0.979047 0.203637i \(-0.934724\pi\)
0.979047 0.203637i \(-0.0652761\pi\)
\(240\) 0 0
\(241\) −4456.97 2573.23i −1.19128 0.687787i −0.232685 0.972552i \(-0.574751\pi\)
−0.958597 + 0.284765i \(0.908084\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −284.495 1400.30i −0.0741866 0.365151i
\(246\) 0 0
\(247\) −3521.15 6098.82i −0.907068 1.57109i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2852.49 0.717321 0.358661 0.933468i \(-0.383234\pi\)
0.358661 + 0.933468i \(0.383234\pi\)
\(252\) 0 0
\(253\) −6048.35 −1.50299
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1871.38 + 3241.33i 0.454216 + 0.786726i 0.998643 0.0520828i \(-0.0165860\pi\)
−0.544426 + 0.838809i \(0.683253\pi\)
\(258\) 0 0
\(259\) −2545.67 6721.97i −0.610735 1.61267i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6755.29 3900.17i −1.58384 0.914428i −0.994292 0.106691i \(-0.965974\pi\)
−0.589543 0.807737i \(-0.700692\pi\)
\(264\) 0 0
\(265\) 182.204i 0.0422366i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2102.33 3641.34i 0.476510 0.825340i −0.523128 0.852254i \(-0.675235\pi\)
0.999638 + 0.0269146i \(0.00856823\pi\)
\(270\) 0 0
\(271\) 1823.57 1052.84i 0.408761 0.235998i −0.281496 0.959562i \(-0.590831\pi\)
0.690257 + 0.723564i \(0.257497\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3570.03 + 2061.16i −0.782841 + 0.451973i
\(276\) 0 0
\(277\) −3935.66 + 6816.76i −0.853685 + 1.47863i 0.0241750 + 0.999708i \(0.492304\pi\)
−0.877860 + 0.478918i \(0.841029\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 826.499i 0.175462i −0.996144 0.0877310i \(-0.972038\pi\)
0.996144 0.0877310i \(-0.0279616\pi\)
\(282\) 0 0
\(283\) 3946.80 + 2278.68i 0.829020 + 0.478635i 0.853517 0.521065i \(-0.174465\pi\)
−0.0244968 + 0.999700i \(0.507798\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5949.15 969.718i −1.22358 0.199445i
\(288\) 0 0
\(289\) 2339.38 + 4051.93i 0.476162 + 0.824736i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7373.68 −1.47022 −0.735111 0.677947i \(-0.762870\pi\)
−0.735111 + 0.677947i \(0.762870\pi\)
\(294\) 0 0
\(295\) 721.205 0.142340
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3918.34 + 6786.76i 0.757871 + 1.31267i
\(300\) 0 0
\(301\) −3497.73 570.134i −0.669787 0.109176i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −868.101 501.198i −0.162975 0.0940936i
\(306\) 0 0
\(307\) 2406.09i 0.447306i 0.974669 + 0.223653i \(0.0717982\pi\)
−0.974669 + 0.223653i \(0.928202\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1437.77 2490.28i 0.262149 0.454055i −0.704664 0.709541i \(-0.748902\pi\)
0.966813 + 0.255486i \(0.0822356\pi\)
\(312\) 0 0
\(313\) 6586.58 3802.76i 1.18944 0.686725i 0.231263 0.972891i \(-0.425714\pi\)
0.958180 + 0.286166i \(0.0923809\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2360.31 1362.73i 0.418197 0.241446i −0.276109 0.961126i \(-0.589045\pi\)
0.694306 + 0.719680i \(0.255712\pi\)
\(318\) 0 0
\(319\) −3918.47 + 6786.99i −0.687750 + 1.19122i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2172.20i 0.374193i
\(324\) 0 0
\(325\) 4625.60 + 2670.59i 0.789483 + 0.455808i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3277.94 + 8655.57i 0.549298 + 1.45045i
\(330\) 0 0
\(331\) −2410.09 4174.40i −0.400214 0.693190i 0.593538 0.804806i \(-0.297731\pi\)
−0.993751 + 0.111616i \(0.964397\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3671.21 0.598745
\(336\) 0 0
\(337\) −3069.99 −0.496241 −0.248121 0.968729i \(-0.579813\pi\)
−0.248121 + 0.968729i \(0.579813\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2001.55 3466.79i −0.317859 0.550549i
\(342\) 0 0
\(343\) 5620.62 + 2960.10i 0.884796 + 0.465979i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3507.33 + 2024.96i 0.542603 + 0.313272i 0.746133 0.665797i \(-0.231908\pi\)
−0.203530 + 0.979069i \(0.565242\pi\)
\(348\) 0 0
\(349\) 4056.76i 0.622216i −0.950375 0.311108i \(-0.899300\pi\)
0.950375 0.311108i \(-0.100700\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4848.88 + 8398.51i −0.731105 + 1.26631i 0.225307 + 0.974288i \(0.427662\pi\)
−0.956411 + 0.292023i \(0.905672\pi\)
\(354\) 0 0
\(355\) −3672.03 + 2120.04i −0.548988 + 0.316959i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4481.02 2587.12i 0.658773 0.380343i −0.133036 0.991111i \(-0.542473\pi\)
0.791809 + 0.610769i \(0.209139\pi\)
\(360\) 0 0
\(361\) 6642.47 11505.1i 0.968431 1.67737i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1736.68i 0.249047i
\(366\) 0 0
\(367\) 8693.29 + 5019.07i 1.23647 + 0.713878i 0.968372 0.249512i \(-0.0802702\pi\)
0.268102 + 0.963391i \(0.413604\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −627.201 512.588i −0.0877700 0.0717312i
\(372\) 0 0
\(373\) 1372.10 + 2376.55i 0.190469 + 0.329901i 0.945406 0.325896i \(-0.105666\pi\)
−0.754937 + 0.655797i \(0.772333\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10154.1 1.38717
\(378\) 0 0
\(379\) −412.530 −0.0559109 −0.0279555 0.999609i \(-0.508900\pi\)
−0.0279555 + 0.999609i \(0.508900\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2792.64 + 4837.00i 0.372578 + 0.645324i 0.989961 0.141339i \(-0.0451406\pi\)
−0.617383 + 0.786662i \(0.711807\pi\)
\(384\) 0 0
\(385\) −475.337 + 2916.16i −0.0629232 + 0.386029i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −12438.4 7181.34i −1.62122 0.936011i −0.986595 0.163191i \(-0.947821\pi\)
−0.634625 0.772820i \(-0.718845\pi\)
\(390\) 0 0
\(391\) 2417.22i 0.312645i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −988.827 + 1712.70i −0.125958 + 0.218165i
\(396\) 0 0
\(397\) 9573.43 5527.22i 1.21027 0.698749i 0.247451 0.968900i \(-0.420407\pi\)
0.962818 + 0.270152i \(0.0870738\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 10385.2 5995.91i 1.29330 0.746686i 0.314061 0.949403i \(-0.398310\pi\)
0.979237 + 0.202716i \(0.0649770\pi\)
\(402\) 0 0
\(403\) −2593.36 + 4491.82i −0.320556 + 0.555220i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 14862.8i 1.81012i
\(408\) 0 0
\(409\) −1478.37 853.536i −0.178730 0.103190i 0.407966 0.912997i \(-0.366238\pi\)
−0.586696 + 0.809807i \(0.699572\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2028.94 + 2482.60i −0.241738 + 0.295789i
\(414\) 0 0
\(415\) −1358.28 2352.62i −0.160664 0.278278i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2025.17 0.236124 0.118062 0.993006i \(-0.462332\pi\)
0.118062 + 0.993006i \(0.462332\pi\)
\(420\) 0 0
\(421\) 16388.2 1.89718 0.948592 0.316503i \(-0.102509\pi\)
0.948592 + 0.316503i \(0.102509\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −823.744 1426.77i −0.0940175 0.162843i
\(426\) 0 0
\(427\) 4167.47 1578.26i 0.472314 0.178870i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 9721.77 + 5612.87i 1.08650 + 0.627290i 0.932642 0.360803i \(-0.117497\pi\)
0.153857 + 0.988093i \(0.450831\pi\)
\(432\) 0 0
\(433\) 15239.6i 1.69139i −0.533670 0.845693i \(-0.679187\pi\)
0.533670 0.845693i \(-0.320813\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −11208.1 + 19413.0i −1.22690 + 2.12505i
\(438\) 0 0
\(439\) −1650.32 + 952.810i −0.179420 + 0.103588i −0.587020 0.809572i \(-0.699699\pi\)
0.407600 + 0.913160i \(0.366366\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10032.5 + 5792.26i −1.07598 + 0.621215i −0.929808 0.368044i \(-0.880027\pi\)
−0.146168 + 0.989260i \(0.546694\pi\)
\(444\) 0 0
\(445\) −1245.59 + 2157.42i −0.132689 + 0.229824i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 16331.3i 1.71652i 0.513211 + 0.858262i \(0.328456\pi\)
−0.513211 + 0.858262i \(0.671544\pi\)
\(450\) 0 0
\(451\) 10793.9 + 6231.89i 1.12698 + 0.650661i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3580.12 1355.83i 0.368876 0.139697i
\(456\) 0 0
\(457\) 3320.32 + 5750.97i 0.339865 + 0.588663i 0.984407 0.175906i \(-0.0562853\pi\)
−0.644542 + 0.764569i \(0.722952\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6825.82 −0.689610 −0.344805 0.938674i \(-0.612055\pi\)
−0.344805 + 0.938674i \(0.612055\pi\)
\(462\) 0 0
\(463\) 3630.09 0.364373 0.182186 0.983264i \(-0.441683\pi\)
0.182186 + 0.983264i \(0.441683\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2775.83 + 4807.88i 0.275054 + 0.476407i 0.970149 0.242511i \(-0.0779711\pi\)
−0.695095 + 0.718918i \(0.744638\pi\)
\(468\) 0 0
\(469\) −10328.1 + 12637.4i −1.01686 + 1.24422i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6346.16 + 3663.96i 0.616907 + 0.356171i
\(474\) 0 0
\(475\) 15278.0i 1.47580i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8908.33 + 15429.7i −0.849753 + 1.47182i 0.0316748 + 0.999498i \(0.489916\pi\)
−0.881428 + 0.472318i \(0.843417\pi\)
\(480\) 0 0
\(481\) 16677.3 9628.65i 1.58091 0.912741i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6390.95 + 3689.82i −0.598346 + 0.345455i
\(486\) 0 0
\(487\) 532.969 923.130i 0.0495917 0.0858953i −0.840164 0.542332i \(-0.817541\pi\)
0.889756 + 0.456437i \(0.150875\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8952.43i 0.822846i −0.911444 0.411423i \(-0.865032\pi\)
0.911444 0.411423i \(-0.134968\pi\)
\(492\) 0 0
\(493\) −2712.42 1566.02i −0.247792 0.143063i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3032.55 18604.5i 0.273699 1.67912i
\(498\) 0 0
\(499\) −725.335 1256.32i −0.0650711 0.112706i 0.831654 0.555294i \(-0.187394\pi\)
−0.896726 + 0.442587i \(0.854061\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 10311.3 0.914032 0.457016 0.889458i \(-0.348918\pi\)
0.457016 + 0.889458i \(0.348918\pi\)
\(504\) 0 0
\(505\) −885.701 −0.0780459
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4844.36 8390.67i −0.421851 0.730668i 0.574269 0.818666i \(-0.305286\pi\)
−0.996121 + 0.0879987i \(0.971953\pi\)
\(510\) 0 0
\(511\) −5978.19 4885.75i −0.517533 0.422961i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4784.76 + 2762.48i 0.409402 + 0.236368i
\(516\) 0 0
\(517\) 19138.1i 1.62803i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9666.31 + 16742.5i −0.812838 + 1.40788i 0.0980312 + 0.995183i \(0.468746\pi\)
−0.910870 + 0.412694i \(0.864588\pi\)
\(522\) 0 0
\(523\) −19453.0 + 11231.2i −1.62643 + 0.939018i −0.641280 + 0.767307i \(0.721596\pi\)
−0.985147 + 0.171711i \(0.945070\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1385.50 799.920i 0.114523 0.0661197i
\(528\) 0 0
\(529\) 6388.85 11065.8i 0.525097 0.909494i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 16149.0i 1.31236i
\(534\) 0 0
\(535\) 444.206 + 256.463i 0.0358967 + 0.0207250i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −8701.05 9840.18i −0.695326 0.786357i
\(540\) 0 0
\(541\) 10846.0 + 18785.8i 0.861934 + 1.49291i 0.870060 + 0.492946i \(0.164080\pi\)
−0.00812568 + 0.999967i \(0.502587\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −67.8815 −0.00533527
\(546\) 0 0
\(547\) 22932.0 1.79251 0.896255 0.443538i \(-0.146277\pi\)
0.896255 + 0.443538i \(0.146277\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 14522.5 + 25153.7i 1.12283 + 1.94480i
\(552\) 0 0
\(553\) −3113.79 8222.11i −0.239443 0.632260i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4941.90 2853.21i −0.375934 0.217045i 0.300114 0.953903i \(-0.402975\pi\)
−0.676048 + 0.736858i \(0.736309\pi\)
\(558\) 0 0
\(559\) 9494.59i 0.718387i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 491.280 850.922i 0.0367762 0.0636982i −0.847051 0.531511i \(-0.821624\pi\)
0.883828 + 0.467813i \(0.154958\pi\)
\(564\) 0 0
\(565\) −5548.02 + 3203.15i −0.413109 + 0.238509i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 16337.6 9432.51i 1.20370 0.694958i 0.242326 0.970195i \(-0.422090\pi\)
0.961377 + 0.275237i \(0.0887562\pi\)
\(570\) 0 0
\(571\) 4441.37 7692.67i 0.325509 0.563797i −0.656107 0.754668i \(-0.727798\pi\)
0.981615 + 0.190871i \(0.0611312\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 17001.4i 1.23305i
\(576\) 0 0
\(577\) 3694.42 + 2132.98i 0.266553 + 0.153894i 0.627320 0.778762i \(-0.284152\pi\)
−0.360767 + 0.932656i \(0.617485\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 11919.6 + 1942.91i 0.851135 + 0.138736i
\(582\) 0 0
\(583\) 837.461 + 1450.53i 0.0594925 + 0.103044i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 19210.8 1.35079 0.675397 0.737454i \(-0.263972\pi\)
0.675397 + 0.737454i \(0.263972\pi\)
\(588\) 0 0
\(589\) −14836.2 −1.03788
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 10815.0 + 18732.1i 0.748934 + 1.29719i 0.948334 + 0.317274i \(0.102768\pi\)
−0.199399 + 0.979918i \(0.563899\pi\)
\(594\) 0 0
\(595\) −1165.44 189.969i −0.0803001 0.0130890i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −22218.7 12827.9i −1.51558 0.875018i −0.999833 0.0182745i \(-0.994183\pi\)
−0.515743 0.856744i \(-0.672484\pi\)
\(600\) 0 0
\(601\) 10757.1i 0.730099i 0.930988 + 0.365050i \(0.118948\pi\)
−0.930988 + 0.365050i \(0.881052\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 282.331 489.012i 0.0189725 0.0328614i
\(606\) 0 0
\(607\) −17158.2 + 9906.32i −1.14733 + 0.662414i −0.948236 0.317566i \(-0.897134\pi\)
−0.199098 + 0.979980i \(0.563801\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −21474.6 + 12398.4i −1.42188 + 0.820923i
\(612\) 0 0
\(613\) −8947.03 + 15496.7i −0.589506 + 1.02105i 0.404791 + 0.914409i \(0.367344\pi\)
−0.994297 + 0.106645i \(0.965989\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 26131.8i 1.70507i 0.522673 + 0.852533i \(0.324935\pi\)
−0.522673 + 0.852533i \(0.675065\pi\)
\(618\) 0 0
\(619\) 12114.7 + 6994.42i 0.786640 + 0.454167i 0.838778 0.544473i \(-0.183270\pi\)
−0.0521381 + 0.998640i \(0.516604\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3922.33 10357.1i −0.252239 0.666048i
\(624\) 0 0
\(625\) −4709.06 8156.32i −0.301380 0.522005i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −5939.91 −0.376534
\(630\) 0 0
\(631\) 1366.56 0.0862151 0.0431076 0.999070i \(-0.486274\pi\)
0.0431076 + 0.999070i \(0.486274\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2285.65 + 3958.86i 0.142840 + 0.247406i
\(636\) 0 0
\(637\) −5404.67 + 16138.2i −0.336171 + 1.00379i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2412.26 + 1392.72i 0.148641 + 0.0858177i 0.572476 0.819922i \(-0.305983\pi\)
−0.423835 + 0.905739i \(0.639316\pi\)
\(642\) 0 0
\(643\) 29078.1i 1.78340i −0.452623 0.891702i \(-0.649511\pi\)
0.452623 0.891702i \(-0.350489\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1249.03 2163.38i 0.0758955 0.131455i −0.825580 0.564285i \(-0.809152\pi\)
0.901475 + 0.432830i \(0.142485\pi\)
\(648\) 0 0
\(649\) 5741.51 3314.86i 0.347263 0.200493i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −11418.2 + 6592.32i −0.684272 + 0.395065i −0.801463 0.598045i \(-0.795945\pi\)
0.117191 + 0.993109i \(0.462611\pi\)
\(654\) 0 0
\(655\) −5903.43 + 10225.0i −0.352162 + 0.609962i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13405.1i 0.792398i 0.918165 + 0.396199i \(0.129671\pi\)
−0.918165 + 0.396199i \(0.870329\pi\)
\(660\) 0 0
\(661\) −6676.89 3854.91i −0.392891 0.226836i 0.290521 0.956869i \(-0.406171\pi\)
−0.683412 + 0.730033i \(0.739505\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 8478.96 + 6929.54i 0.494436 + 0.404084i
\(666\) 0 0
\(667\) −16160.6 27991.0i −0.938144 1.62491i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −9214.60 −0.530142
\(672\) 0 0
\(673\) 25045.3 1.43451 0.717255 0.696810i \(-0.245398\pi\)
0.717255 + 0.696810i \(0.245398\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3354.60 5810.33i −0.190440 0.329851i 0.754956 0.655775i \(-0.227658\pi\)
−0.945396 + 0.325924i \(0.894325\pi\)
\(678\) 0 0
\(679\) 5277.97 32380.0i 0.298306 1.83009i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −19735.9 11394.5i −1.10567 0.638361i −0.167968 0.985792i \(-0.553720\pi\)
−0.937705 + 0.347432i \(0.887054\pi\)
\(684\) 0 0
\(685\) 4714.94i 0.262991i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1085.08 1879.41i 0.0599973 0.103918i
\(690\) 0 0
\(691\) 17740.1 10242.2i 0.976650 0.563869i 0.0753929 0.997154i \(-0.475979\pi\)
0.901257 + 0.433285i \(0.142646\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3925.95 + 2266.65i −0.214273 + 0.123711i
\(696\) 0 0
\(697\) −2490.58 + 4313.80i −0.135348 + 0.234429i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 16624.7i 0.895731i −0.894101 0.447866i \(-0.852184\pi\)
0.894101 0.447866i \(-0.147816\pi\)
\(702\) 0 0
\(703\) 47704.1 + 27541.9i 2.55931 + 1.47762i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2491.71 3048.85i 0.132547 0.162184i
\(708\) 0 0
\(709\) 2183.47 + 3781.89i 0.115659 + 0.200327i 0.918043 0.396481i \(-0.129769\pi\)
−0.802384 + 0.596808i \(0.796435\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 16509.7 0.867170
\(714\) 0 0
\(715\) −7915.92 −0.414040
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2729.14 4727.01i −0.141557 0.245185i 0.786526 0.617557i \(-0.211878\pi\)
−0.928083 + 0.372373i \(0.878544\pi\)
\(720\) 0 0
\(721\) −22970.1 + 8698.99i −1.18648 + 0.449331i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −19077.6 11014.5i −0.977275 0.564230i
\(726\) 0 0
\(727\) 765.750i 0.0390648i −0.999809 0.0195324i \(-0.993782\pi\)
0.999809 0.0195324i \(-0.00621775\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1464.30 + 2536.25i −0.0740892 + 0.128326i
\(732\) 0 0
\(733\) −12534.5 + 7236.81i −0.631614 + 0.364662i −0.781377 0.624059i \(-0.785482\pi\)
0.149763 + 0.988722i \(0.452149\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 29226.5 16873.9i 1.46075 0.843363i
\(738\) 0 0
\(739\) −17644.2 + 30560.6i −0.878284 + 1.52123i −0.0250604 + 0.999686i \(0.507978\pi\)
−0.853223 + 0.521546i \(0.825356\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9060.44i 0.447369i −0.974662 0.223685i \(-0.928191\pi\)
0.974662 0.223685i \(-0.0718086\pi\)
\(744\) 0 0
\(745\) −6187.15 3572.15i −0.304268 0.175669i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2132.49 + 807.595i −0.104031 + 0.0393977i
\(750\) 0 0
\(751\) −14811.1 25653.7i −0.719662 1.24649i −0.961134 0.276084i \(-0.910963\pi\)
0.241471 0.970408i \(-0.422370\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1072.16 0.0516820
\(756\) 0 0
\(757\) −12661.2 −0.607900 −0.303950 0.952688i \(-0.598306\pi\)
−0.303950 + 0.952688i \(0.598306\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −613.595 1062.78i −0.0292284 0.0506250i 0.851041 0.525099i \(-0.175972\pi\)
−0.880270 + 0.474474i \(0.842638\pi\)
\(762\) 0 0
\(763\) 190.969 233.668i 0.00906098 0.0110870i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7439.12 4294.98i −0.350210 0.202194i
\(768\) 0 0
\(769\) 12271.0i 0.575428i −0.957716 0.287714i \(-0.907105\pi\)
0.957716 0.287714i \(-0.0928953\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −7280.79 + 12610.7i −0.338773 + 0.586773i −0.984202 0.177048i \(-0.943345\pi\)
0.645429 + 0.763820i \(0.276679\pi\)
\(774\) 0 0
\(775\) 9744.83 5626.18i 0.451670 0.260772i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 40004.1 23096.4i 1.83992 1.06228i
\(780\) 0 0
\(781\) −19488.6 + 33755.3i −0.892905 + 1.54656i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3101.67i 0.141023i
\(786\) 0 0
\(787\) −21263.2 12276.3i −0.963090 0.556040i −0.0659671 0.997822i \(-0.521013\pi\)
−0.897123 + 0.441782i \(0.854347\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 4581.84 28109.2i 0.205956 1.26353i
\(792\) 0 0
\(793\) 5969.55 + 10339.6i 0.267320 + 0.463012i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 20920.3 0.929781 0.464891 0.885368i \(-0.346094\pi\)
0.464891 + 0.885368i \(0.346094\pi\)
\(798\) 0 0
\(799\) 7648.55 0.338656
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 7982.29 +