Properties

Label 1840.2.e.e.369.4
Level $1840$
Weight $2$
Character 1840.369
Analytic conductor $14.692$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.11574317056.3
Defining polynomial: \(x^{8} + 45 x^{4} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.4
Root \(-1.83051 - 1.83051i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.e.369.5

$q$-expansion

\(f(q)\) \(=\) \(q-0.706585i q^{3} +(-1.83051 + 1.28422i) q^{5} -2.40815i q^{7} +2.50074 q^{9} +O(q^{10})\) \(q-0.706585i q^{3} +(-1.83051 + 1.28422i) q^{5} -2.40815i q^{7} +2.50074 q^{9} -4.95444 q^{11} +4.40815i q^{13} +(0.907411 + 1.29341i) q^{15} +0.200825i q^{17} +6.65600 q^{19} -1.70156 q^{21} -1.00000i q^{23} +(1.70156 - 4.70156i) q^{25} -3.88674i q^{27} -1.67942 q^{29} +1.82132 q^{31} +3.50074i q^{33} +(3.09259 + 4.40815i) q^{35} -8.47732i q^{37} +3.11473 q^{39} +11.0171 q^{41} +2.06268i q^{43} +(-4.57763 + 3.21149i) q^{45} -0.505760i q^{47} +1.20083 q^{49} +0.141900 q^{51} -5.84621i q^{53} +(9.06918 - 6.36259i) q^{55} -4.70304i q^{57} -4.41464 q^{59} -6.67815 q^{61} -6.02214i q^{63} +(-5.66103 - 8.06918i) q^{65} -12.6625i q^{67} -0.706585 q^{69} -3.61400 q^{71} -14.4589i q^{73} +(-3.32206 - 1.20230i) q^{75} +11.9310i q^{77} +9.95317 q^{79} +4.75590 q^{81} +13.3037i q^{83} +(-0.257904 - 0.367613i) q^{85} +1.18665i q^{87} +5.04576 q^{89} +10.6155 q^{91} -1.28692i q^{93} +(-12.1839 + 8.54777i) q^{95} +3.79917i q^{97} -12.3898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 14q^{9} + O(q^{10}) \) \( 8q - 14q^{9} - 10q^{11} + 16q^{15} - 2q^{19} + 12q^{21} - 12q^{25} - 4q^{29} - 10q^{31} + 16q^{35} + 46q^{41} - 26q^{45} + 18q^{49} - 14q^{51} + 18q^{55} + 32q^{59} + 18q^{61} - 16q^{65} - 6q^{69} - 38q^{71} + 32q^{75} - 12q^{79} + 32q^{81} - 24q^{85} - 60q^{89} + 26q^{91} - 18q^{95} - 54q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(3\) 0.706585i 0.407947i −0.978976 0.203974i \(-0.934614\pi\)
0.978976 0.203974i \(-0.0653857\pi\)
\(4\) 0 0
\(5\) −1.83051 + 1.28422i −0.818631 + 0.574320i
\(6\) 0 0
\(7\) 2.40815i 0.910194i −0.890442 0.455097i \(-0.849605\pi\)
0.890442 0.455097i \(-0.150395\pi\)
\(8\) 0 0
\(9\) 2.50074 0.833579
\(10\) 0 0
\(11\) −4.95444 −1.49382 −0.746910 0.664925i \(-0.768464\pi\)
−0.746910 + 0.664925i \(0.768464\pi\)
\(12\) 0 0
\(13\) 4.40815i 1.22260i 0.791399 + 0.611300i \(0.209353\pi\)
−0.791399 + 0.611300i \(0.790647\pi\)
\(14\) 0 0
\(15\) 0.907411 + 1.29341i 0.234292 + 0.333958i
\(16\) 0 0
\(17\) 0.200825i 0.0487073i 0.999703 + 0.0243536i \(0.00775277\pi\)
−0.999703 + 0.0243536i \(0.992247\pi\)
\(18\) 0 0
\(19\) 6.65600 1.52699 0.763496 0.645812i \(-0.223481\pi\)
0.763496 + 0.645812i \(0.223481\pi\)
\(20\) 0 0
\(21\) −1.70156 −0.371311
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) 1.70156 4.70156i 0.340312 0.940312i
\(26\) 0 0
\(27\) 3.88674i 0.748004i
\(28\) 0 0
\(29\) −1.67942 −0.311860 −0.155930 0.987768i \(-0.549837\pi\)
−0.155930 + 0.987768i \(0.549837\pi\)
\(30\) 0 0
\(31\) 1.82132 0.327118 0.163559 0.986534i \(-0.447703\pi\)
0.163559 + 0.986534i \(0.447703\pi\)
\(32\) 0 0
\(33\) 3.50074i 0.609400i
\(34\) 0 0
\(35\) 3.09259 + 4.40815i 0.522743 + 0.745113i
\(36\) 0 0
\(37\) 8.47732i 1.39366i −0.717235 0.696832i \(-0.754592\pi\)
0.717235 0.696832i \(-0.245408\pi\)
\(38\) 0 0
\(39\) 3.11473 0.498756
\(40\) 0 0
\(41\) 11.0171 1.72059 0.860293 0.509801i \(-0.170281\pi\)
0.860293 + 0.509801i \(0.170281\pi\)
\(42\) 0 0
\(43\) 2.06268i 0.314555i 0.987554 + 0.157278i \(0.0502718\pi\)
−0.987554 + 0.157278i \(0.949728\pi\)
\(44\) 0 0
\(45\) −4.57763 + 3.21149i −0.682393 + 0.478741i
\(46\) 0 0
\(47\) 0.505760i 0.0737727i −0.999319 0.0368864i \(-0.988256\pi\)
0.999319 0.0368864i \(-0.0117440\pi\)
\(48\) 0 0
\(49\) 1.20083 0.171546
\(50\) 0 0
\(51\) 0.141900 0.0198700
\(52\) 0 0
\(53\) 5.84621i 0.803038i −0.915851 0.401519i \(-0.868482\pi\)
0.915851 0.401519i \(-0.131518\pi\)
\(54\) 0 0
\(55\) 9.06918 6.36259i 1.22289 0.857931i
\(56\) 0 0
\(57\) 4.70304i 0.622932i
\(58\) 0 0
\(59\) −4.41464 −0.574738 −0.287369 0.957820i \(-0.592781\pi\)
−0.287369 + 0.957820i \(0.592781\pi\)
\(60\) 0 0
\(61\) −6.67815 −0.855049 −0.427525 0.904004i \(-0.640614\pi\)
−0.427525 + 0.904004i \(0.640614\pi\)
\(62\) 0 0
\(63\) 6.02214i 0.758719i
\(64\) 0 0
\(65\) −5.66103 8.06918i −0.702164 1.00086i
\(66\) 0 0
\(67\) 12.6625i 1.54697i −0.633814 0.773485i \(-0.718512\pi\)
0.633814 0.773485i \(-0.281488\pi\)
\(68\) 0 0
\(69\) −0.706585 −0.0850629
\(70\) 0 0
\(71\) −3.61400 −0.428902 −0.214451 0.976735i \(-0.568796\pi\)
−0.214451 + 0.976735i \(0.568796\pi\)
\(72\) 0 0
\(73\) 14.4589i 1.69229i −0.532953 0.846145i \(-0.678918\pi\)
0.532953 0.846145i \(-0.321082\pi\)
\(74\) 0 0
\(75\) −3.32206 1.20230i −0.383598 0.138830i
\(76\) 0 0
\(77\) 11.9310i 1.35967i
\(78\) 0 0
\(79\) 9.95317 1.11982 0.559910 0.828554i \(-0.310836\pi\)
0.559910 + 0.828554i \(0.310836\pi\)
\(80\) 0 0
\(81\) 4.75590 0.528433
\(82\) 0 0
\(83\) 13.3037i 1.46027i 0.683305 + 0.730133i \(0.260542\pi\)
−0.683305 + 0.730133i \(0.739458\pi\)
\(84\) 0 0
\(85\) −0.257904 0.367613i −0.0279736 0.0398733i
\(86\) 0 0
\(87\) 1.18665i 0.127223i
\(88\) 0 0
\(89\) 5.04576 0.534850 0.267425 0.963579i \(-0.413827\pi\)
0.267425 + 0.963579i \(0.413827\pi\)
\(90\) 0 0
\(91\) 10.6155 1.11280
\(92\) 0 0
\(93\) 1.28692i 0.133447i
\(94\) 0 0
\(95\) −12.1839 + 8.54777i −1.25004 + 0.876983i
\(96\) 0 0
\(97\) 3.79917i 0.385748i 0.981224 + 0.192874i \(0.0617808\pi\)
−0.981224 + 0.192874i \(0.938219\pi\)
\(98\) 0 0
\(99\) −12.3898 −1.24522
\(100\) 0 0
\(101\) 13.2410 1.31753 0.658764 0.752350i \(-0.271080\pi\)
0.658764 + 0.752350i \(0.271080\pi\)
\(102\) 0 0
\(103\) 10.4202i 1.02674i −0.858168 0.513369i \(-0.828397\pi\)
0.858168 0.513369i \(-0.171603\pi\)
\(104\) 0 0
\(105\) 3.11473 2.18518i 0.303967 0.213252i
\(106\) 0 0
\(107\) 9.98161i 0.964959i −0.875907 0.482479i \(-0.839736\pi\)
0.875907 0.482479i \(-0.160264\pi\)
\(108\) 0 0
\(109\) 13.8739 1.32888 0.664442 0.747340i \(-0.268669\pi\)
0.664442 + 0.747340i \(0.268669\pi\)
\(110\) 0 0
\(111\) −5.98995 −0.568541
\(112\) 0 0
\(113\) 18.4957i 1.73993i −0.493113 0.869965i \(-0.664141\pi\)
0.493113 0.869965i \(-0.335859\pi\)
\(114\) 0 0
\(115\) 1.28422 + 1.83051i 0.119754 + 0.170696i
\(116\) 0 0
\(117\) 11.0236i 1.01913i
\(118\) 0 0
\(119\) 0.483617 0.0443331
\(120\) 0 0
\(121\) 13.5465 1.23150
\(122\) 0 0
\(123\) 7.78454i 0.701908i
\(124\) 0 0
\(125\) 2.92310 + 10.7915i 0.261450 + 0.965217i
\(126\) 0 0
\(127\) 18.1384i 1.60952i 0.593601 + 0.804759i \(0.297706\pi\)
−0.593601 + 0.804759i \(0.702294\pi\)
\(128\) 0 0
\(129\) 1.45746 0.128322
\(130\) 0 0
\(131\) 1.98995 0.173863 0.0869315 0.996214i \(-0.472294\pi\)
0.0869315 + 0.996214i \(0.472294\pi\)
\(132\) 0 0
\(133\) 16.0286i 1.38986i
\(134\) 0 0
\(135\) 4.99143 + 7.11473i 0.429594 + 0.612339i
\(136\) 0 0
\(137\) 1.14337i 0.0976850i −0.998806 0.0488425i \(-0.984447\pi\)
0.998806 0.0488425i \(-0.0155532\pi\)
\(138\) 0 0
\(139\) 22.4489 1.90409 0.952045 0.305959i \(-0.0989769\pi\)
0.952045 + 0.305959i \(0.0989769\pi\)
\(140\) 0 0
\(141\) −0.357363 −0.0300954
\(142\) 0 0
\(143\) 21.8399i 1.82635i
\(144\) 0 0
\(145\) 3.07420 2.15674i 0.255298 0.179108i
\(146\) 0 0
\(147\) 0.848486i 0.0699819i
\(148\) 0 0
\(149\) −8.20458 −0.672145 −0.336073 0.941836i \(-0.609099\pi\)
−0.336073 + 0.941836i \(0.609099\pi\)
\(150\) 0 0
\(151\) −10.5244 −0.856460 −0.428230 0.903670i \(-0.640863\pi\)
−0.428230 + 0.903670i \(0.640863\pi\)
\(152\) 0 0
\(153\) 0.502211i 0.0406013i
\(154\) 0 0
\(155\) −3.33395 + 2.33897i −0.267789 + 0.187871i
\(156\) 0 0
\(157\) 1.02991i 0.0821959i 0.999155 + 0.0410979i \(0.0130856\pi\)
−0.999155 + 0.0410979i \(0.986914\pi\)
\(158\) 0 0
\(159\) −4.13084 −0.327597
\(160\) 0 0
\(161\) −2.40815 −0.189789
\(162\) 0 0
\(163\) 11.1802i 0.875697i −0.899049 0.437849i \(-0.855741\pi\)
0.899049 0.437849i \(-0.144259\pi\)
\(164\) 0 0
\(165\) −4.49571 6.40815i −0.349991 0.498874i
\(166\) 0 0
\(167\) 3.49424i 0.270392i −0.990819 0.135196i \(-0.956834\pi\)
0.990819 0.135196i \(-0.0431665\pi\)
\(168\) 0 0
\(169\) −6.43177 −0.494751
\(170\) 0 0
\(171\) 16.6449 1.27287
\(172\) 0 0
\(173\) 8.61547i 0.655022i −0.944847 0.327511i \(-0.893790\pi\)
0.944847 0.327511i \(-0.106210\pi\)
\(174\) 0 0
\(175\) −11.3221 4.09761i −0.855867 0.309750i
\(176\) 0 0
\(177\) 3.11932i 0.234463i
\(178\) 0 0
\(179\) −3.36634 −0.251612 −0.125806 0.992055i \(-0.540152\pi\)
−0.125806 + 0.992055i \(0.540152\pi\)
\(180\) 0 0
\(181\) −15.8970 −1.18161 −0.590807 0.806813i \(-0.701191\pi\)
−0.590807 + 0.806813i \(0.701191\pi\)
\(182\) 0 0
\(183\) 4.71868i 0.348815i
\(184\) 0 0
\(185\) 10.8867 + 15.5179i 0.800409 + 1.14090i
\(186\) 0 0
\(187\) 0.994977i 0.0727599i
\(188\) 0 0
\(189\) −9.35985 −0.680829
\(190\) 0 0
\(191\) 6.74527 0.488071 0.244035 0.969766i \(-0.421529\pi\)
0.244035 + 0.969766i \(0.421529\pi\)
\(192\) 0 0
\(193\) 4.81630i 0.346685i 0.984862 + 0.173342i \(0.0554567\pi\)
−0.984862 + 0.173342i \(0.944543\pi\)
\(194\) 0 0
\(195\) −5.70156 + 4.00000i −0.408297 + 0.286446i
\(196\) 0 0
\(197\) 12.8349i 0.914448i 0.889352 + 0.457224i \(0.151156\pi\)
−0.889352 + 0.457224i \(0.848844\pi\)
\(198\) 0 0
\(199\) −12.4957 −0.885798 −0.442899 0.896572i \(-0.646050\pi\)
−0.442899 + 0.896572i \(0.646050\pi\)
\(200\) 0 0
\(201\) −8.94714 −0.631083
\(202\) 0 0
\(203\) 4.04429i 0.283853i
\(204\) 0 0
\(205\) −20.1670 + 14.1484i −1.40852 + 0.988167i
\(206\) 0 0
\(207\) 2.50074i 0.173813i
\(208\) 0 0
\(209\) −32.9768 −2.28105
\(210\) 0 0
\(211\) 16.0130 1.10238 0.551190 0.834380i \(-0.314174\pi\)
0.551190 + 0.834380i \(0.314174\pi\)
\(212\) 0 0
\(213\) 2.55360i 0.174970i
\(214\) 0 0
\(215\) −2.64893 3.77576i −0.180656 0.257505i
\(216\) 0 0
\(217\) 4.38600i 0.297741i
\(218\) 0 0
\(219\) −10.2165 −0.690365
\(220\) 0 0
\(221\) −0.885267 −0.0595495
\(222\) 0 0
\(223\) 18.2094i 1.21939i 0.792636 + 0.609695i \(0.208708\pi\)
−0.792636 + 0.609695i \(0.791292\pi\)
\(224\) 0 0
\(225\) 4.25516 11.7574i 0.283677 0.783825i
\(226\) 0 0
\(227\) 19.5331i 1.29646i 0.761445 + 0.648230i \(0.224490\pi\)
−0.761445 + 0.648230i \(0.775510\pi\)
\(228\) 0 0
\(229\) 22.3419 1.47640 0.738198 0.674584i \(-0.235677\pi\)
0.738198 + 0.674584i \(0.235677\pi\)
\(230\) 0 0
\(231\) 8.43029 0.554672
\(232\) 0 0
\(233\) 6.42469i 0.420896i −0.977605 0.210448i \(-0.932508\pi\)
0.977605 0.210448i \(-0.0674922\pi\)
\(234\) 0 0
\(235\) 0.649507 + 0.925801i 0.0423692 + 0.0603926i
\(236\) 0 0
\(237\) 7.03277i 0.456827i
\(238\) 0 0
\(239\) −9.52848 −0.616346 −0.308173 0.951330i \(-0.599718\pi\)
−0.308173 + 0.951330i \(0.599718\pi\)
\(240\) 0 0
\(241\) −13.4842 −0.868593 −0.434297 0.900770i \(-0.643003\pi\)
−0.434297 + 0.900770i \(0.643003\pi\)
\(242\) 0 0
\(243\) 15.0207i 0.963576i
\(244\) 0 0
\(245\) −2.19813 + 1.54212i −0.140433 + 0.0985226i
\(246\) 0 0
\(247\) 29.3406i 1.86690i
\(248\) 0 0
\(249\) 9.40018 0.595712
\(250\) 0 0
\(251\) 10.1402 0.640044 0.320022 0.947410i \(-0.396310\pi\)
0.320022 + 0.947410i \(0.396310\pi\)
\(252\) 0 0
\(253\) 4.95444i 0.311483i
\(254\) 0 0
\(255\) −0.259750 + 0.182231i −0.0162662 + 0.0114117i
\(256\) 0 0
\(257\) 8.76196i 0.546556i −0.961935 0.273278i \(-0.911892\pi\)
0.961935 0.273278i \(-0.0881079\pi\)
\(258\) 0 0
\(259\) −20.4146 −1.26850
\(260\) 0 0
\(261\) −4.19978 −0.259960
\(262\) 0 0
\(263\) 15.7448i 0.970868i −0.874273 0.485434i \(-0.838662\pi\)
0.874273 0.485434i \(-0.161338\pi\)
\(264\) 0 0
\(265\) 7.50781 + 10.7016i 0.461201 + 0.657392i
\(266\) 0 0
\(267\) 3.56526i 0.218190i
\(268\) 0 0
\(269\) −23.5515 −1.43596 −0.717981 0.696063i \(-0.754933\pi\)
−0.717981 + 0.696063i \(0.754933\pi\)
\(270\) 0 0
\(271\) 1.62863 0.0989325 0.0494662 0.998776i \(-0.484248\pi\)
0.0494662 + 0.998776i \(0.484248\pi\)
\(272\) 0 0
\(273\) 7.50074i 0.453965i
\(274\) 0 0
\(275\) −8.43029 + 23.2936i −0.508366 + 1.40466i
\(276\) 0 0
\(277\) 21.9063i 1.31622i 0.752920 + 0.658112i \(0.228645\pi\)
−0.752920 + 0.658112i \(0.771355\pi\)
\(278\) 0 0
\(279\) 4.55464 0.272679
\(280\) 0 0
\(281\) −5.64264 −0.336612 −0.168306 0.985735i \(-0.553830\pi\)
−0.168306 + 0.985735i \(0.553830\pi\)
\(282\) 0 0
\(283\) 6.15674i 0.365980i −0.983115 0.182990i \(-0.941422\pi\)
0.983115 0.182990i \(-0.0585776\pi\)
\(284\) 0 0
\(285\) 6.03973 + 8.60897i 0.357763 + 0.509952i
\(286\) 0 0
\(287\) 26.5309i 1.56607i
\(288\) 0 0
\(289\) 16.9597 0.997628
\(290\) 0 0
\(291\) 2.68444 0.157365
\(292\) 0 0
\(293\) 21.4888i 1.25539i 0.778459 + 0.627696i \(0.216002\pi\)
−0.778459 + 0.627696i \(0.783998\pi\)
\(294\) 0 0
\(295\) 8.08107 5.66937i 0.470498 0.330084i
\(296\) 0 0
\(297\) 19.2566i 1.11738i
\(298\) 0 0
\(299\) 4.40815 0.254930
\(300\) 0 0
\(301\) 4.96723 0.286307
\(302\) 0 0
\(303\) 9.35589i 0.537482i
\(304\) 0 0
\(305\) 12.2244 8.57621i 0.699970 0.491072i
\(306\) 0 0
\(307\) 4.09672i 0.233812i 0.993143 + 0.116906i \(0.0372976\pi\)
−0.993143 + 0.116906i \(0.962702\pi\)
\(308\) 0 0
\(309\) −7.36279 −0.418855
\(310\) 0 0
\(311\) −24.0105 −1.36151 −0.680754 0.732512i \(-0.738348\pi\)
−0.680754 + 0.732512i \(0.738348\pi\)
\(312\) 0 0
\(313\) 10.8696i 0.614387i −0.951647 0.307194i \(-0.900610\pi\)
0.951647 0.307194i \(-0.0993899\pi\)
\(314\) 0 0
\(315\) 7.73375 + 11.0236i 0.435748 + 0.621110i
\(316\) 0 0
\(317\) 22.1661i 1.24497i −0.782631 0.622486i \(-0.786123\pi\)
0.782631 0.622486i \(-0.213877\pi\)
\(318\) 0 0
\(319\) 8.32058 0.465863
\(320\) 0 0
\(321\) −7.05286 −0.393652
\(322\) 0 0
\(323\) 1.33669i 0.0743756i
\(324\) 0 0
\(325\) 20.7252 + 7.50074i 1.14963 + 0.416066i
\(326\) 0 0
\(327\) 9.80313i 0.542114i
\(328\) 0 0
\(329\) −1.21795 −0.0671475
\(330\) 0 0
\(331\) 9.39308 0.516290 0.258145 0.966106i \(-0.416889\pi\)
0.258145 + 0.966106i \(0.416889\pi\)
\(332\) 0 0
\(333\) 21.1996i 1.16173i
\(334\) 0 0
\(335\) 16.2614 + 23.1789i 0.888457 + 1.26640i
\(336\) 0 0
\(337\) 19.8113i 1.07919i 0.841925 + 0.539594i \(0.181422\pi\)
−0.841925 + 0.539594i \(0.818578\pi\)
\(338\) 0 0
\(339\) −13.0688 −0.709800
\(340\) 0 0
\(341\) −9.02362 −0.488656
\(342\) 0 0
\(343\) 19.7488i 1.06633i
\(344\) 0 0
\(345\) 1.29341 0.907411i 0.0696351 0.0488533i
\(346\) 0 0
\(347\) 19.5128i 1.04750i 0.851871 + 0.523752i \(0.175468\pi\)
−0.851871 + 0.523752i \(0.824532\pi\)
\(348\) 0 0
\(349\) 22.7352 1.21699 0.608494 0.793558i \(-0.291774\pi\)
0.608494 + 0.793558i \(0.291774\pi\)
\(350\) 0 0
\(351\) 17.1333 0.914509
\(352\) 0 0
\(353\) 24.6471i 1.31183i 0.754835 + 0.655915i \(0.227717\pi\)
−0.754835 + 0.655915i \(0.772283\pi\)
\(354\) 0 0
\(355\) 6.61547 4.64116i 0.351113 0.246327i
\(356\) 0 0
\(357\) 0.341716i 0.0180856i
\(358\) 0 0
\(359\) 15.2778 0.806330 0.403165 0.915127i \(-0.367910\pi\)
0.403165 + 0.915127i \(0.367910\pi\)
\(360\) 0 0
\(361\) 25.3024 1.33170
\(362\) 0 0
\(363\) 9.57176i 0.502387i
\(364\) 0 0
\(365\) 18.5684 + 26.4673i 0.971916 + 1.38536i
\(366\) 0 0
\(367\) 9.59581i 0.500897i −0.968130 0.250449i \(-0.919422\pi\)
0.968130 0.250449i \(-0.0805781\pi\)
\(368\) 0 0
\(369\) 27.5509 1.43424
\(370\) 0 0
\(371\) −14.0785 −0.730921
\(372\) 0 0
\(373\) 17.2125i 0.891232i 0.895224 + 0.445616i \(0.147015\pi\)
−0.895224 + 0.445616i \(0.852985\pi\)
\(374\) 0 0
\(375\) 7.62508 2.06542i 0.393758 0.106658i
\(376\) 0 0
\(377\) 7.40312i 0.381280i
\(378\) 0 0
\(379\) −20.7354 −1.06511 −0.532554 0.846396i \(-0.678768\pi\)
−0.532554 + 0.846396i \(0.678768\pi\)
\(380\) 0 0
\(381\) 12.8163 0.656599
\(382\) 0 0
\(383\) 13.0115i 0.664858i 0.943128 + 0.332429i \(0.107868\pi\)
−0.943128 + 0.332429i \(0.892132\pi\)
\(384\) 0 0
\(385\) −15.3221 21.8399i −0.780884 1.11307i
\(386\) 0 0
\(387\) 5.15822i 0.262207i
\(388\) 0 0
\(389\) −6.55279 −0.332240 −0.166120 0.986106i \(-0.553124\pi\)
−0.166120 + 0.986106i \(0.553124\pi\)
\(390\) 0 0
\(391\) 0.200825 0.0101562
\(392\) 0 0
\(393\) 1.40607i 0.0709270i
\(394\) 0 0
\(395\) −18.2194 + 12.7821i −0.916718 + 0.643135i
\(396\) 0 0
\(397\) 6.79516i 0.341039i 0.985354 + 0.170520i \(0.0545446\pi\)
−0.985354 + 0.170520i \(0.945455\pi\)
\(398\) 0 0
\(399\) −11.3256 −0.566989
\(400\) 0 0
\(401\) −30.5660 −1.52639 −0.763196 0.646167i \(-0.776371\pi\)
−0.763196 + 0.646167i \(0.776371\pi\)
\(402\) 0 0
\(403\) 8.02864i 0.399935i
\(404\) 0 0
\(405\) −8.70573 + 6.10761i −0.432591 + 0.303490i
\(406\) 0 0
\(407\) 42.0004i 2.08188i
\(408\) 0 0
\(409\) −19.8610 −0.982066 −0.491033 0.871141i \(-0.663380\pi\)
−0.491033 + 0.871141i \(0.663380\pi\)
\(410\) 0 0
\(411\) −0.807892 −0.0398503
\(412\) 0 0
\(413\) 10.6311i 0.523123i
\(414\) 0 0
\(415\) −17.0848 24.3525i −0.838661 1.19542i
\(416\) 0 0
\(417\) 15.8621i 0.776768i
\(418\) 0 0
\(419\) 4.19057 0.204723 0.102361 0.994747i \(-0.467360\pi\)
0.102361 + 0.994747i \(0.467360\pi\)
\(420\) 0 0
\(421\) −32.2306 −1.57082 −0.785411 0.618975i \(-0.787548\pi\)
−0.785411 + 0.618975i \(0.787548\pi\)
\(422\) 0 0
\(423\) 1.26477i 0.0614954i
\(424\) 0 0
\(425\) 0.944192 + 0.341716i 0.0458000 + 0.0165757i
\(426\) 0 0
\(427\) 16.0820i 0.778261i
\(428\) 0 0
\(429\) −15.4318 −0.745053
\(430\) 0 0
\(431\) −18.7583 −0.903554 −0.451777 0.892131i \(-0.649210\pi\)
−0.451777 + 0.892131i \(0.649210\pi\)
\(432\) 0 0
\(433\) 28.3271i 1.36131i −0.732603 0.680656i \(-0.761695\pi\)
0.732603 0.680656i \(-0.238305\pi\)
\(434\) 0 0
\(435\) −1.52392 2.17218i −0.0730665 0.104148i
\(436\) 0 0
\(437\) 6.65600i 0.318400i
\(438\) 0 0
\(439\) 23.7532 1.13368 0.566840 0.823828i \(-0.308166\pi\)
0.566840 + 0.823828i \(0.308166\pi\)
\(440\) 0 0
\(441\) 3.00295 0.142998
\(442\) 0 0
\(443\) 9.91284i 0.470973i 0.971878 + 0.235487i \(0.0756684\pi\)
−0.971878 + 0.235487i \(0.924332\pi\)
\(444\) 0 0
\(445\) −9.23634 + 6.47986i −0.437844 + 0.307175i
\(446\) 0 0
\(447\) 5.79724i 0.274200i
\(448\) 0 0
\(449\) 39.3758 1.85826 0.929129 0.369755i \(-0.120558\pi\)
0.929129 + 0.369755i \(0.120558\pi\)
\(450\) 0 0
\(451\) −54.5837 −2.57025
\(452\) 0 0
\(453\) 7.43636i 0.349390i
\(454\) 0 0
\(455\) −19.4318 + 13.6326i −0.910975 + 0.639106i
\(456\) 0 0
\(457\) 15.1737i 0.709794i 0.934905 + 0.354897i \(0.115484\pi\)
−0.934905 + 0.354897i \(0.884516\pi\)
\(458\) 0 0
\(459\) 0.780555 0.0364332
\(460\) 0 0
\(461\) 8.44848 0.393485 0.196742 0.980455i \(-0.436964\pi\)
0.196742 + 0.980455i \(0.436964\pi\)
\(462\) 0 0
\(463\) 19.8888i 0.924311i 0.886799 + 0.462155i \(0.152924\pi\)
−0.886799 + 0.462155i \(0.847076\pi\)
\(464\) 0 0
\(465\) 1.65268 + 2.35572i 0.0766414 + 0.109244i
\(466\) 0 0
\(467\) 27.3066i 1.26360i 0.775132 + 0.631800i \(0.217683\pi\)
−0.775132 + 0.631800i \(0.782317\pi\)
\(468\) 0 0
\(469\) −30.4932 −1.40804
\(470\) 0 0
\(471\) 0.727720 0.0335316
\(472\) 0 0
\(473\) 10.2194i 0.469889i
\(474\) 0 0
\(475\) 11.3256 31.2936i 0.519654 1.43585i
\(476\) 0 0
\(477\) 14.6198i 0.669396i
\(478\) 0 0
\(479\) 21.0558 0.962064 0.481032 0.876703i \(-0.340262\pi\)
0.481032 + 0.876703i \(0.340262\pi\)
\(480\) 0 0
\(481\) 37.3693 1.70389
\(482\) 0 0
\(483\) 1.70156i 0.0774238i
\(484\) 0 0
\(485\) −4.87897 6.95444i −0.221543 0.315785i
\(486\) 0 0
\(487\) 22.5530i 1.02197i 0.859589 + 0.510987i \(0.170720\pi\)
−0.859589 + 0.510987i \(0.829280\pi\)
\(488\) 0 0
\(489\) −7.89974 −0.357238
\(490\) 0 0
\(491\) 17.1369 0.773376 0.386688 0.922211i \(-0.373619\pi\)
0.386688 + 0.922211i \(0.373619\pi\)
\(492\) 0 0
\(493\) 0.337269i 0.0151899i
\(494\) 0 0
\(495\) 22.6796 15.9112i 1.01937 0.715154i
\(496\) 0 0
\(497\) 8.70304i 0.390385i
\(498\) 0 0
\(499\) −12.1254 −0.542805 −0.271403 0.962466i \(-0.587488\pi\)
−0.271403 + 0.962466i \(0.587488\pi\)
\(500\) 0 0
\(501\) −2.46898 −0.110306
\(502\) 0 0
\(503\) 38.5026i 1.71675i 0.513025 + 0.858373i \(0.328525\pi\)
−0.513025 + 0.858373i \(0.671475\pi\)
\(504\) 0 0
\(505\) −24.2378 + 17.0043i −1.07857 + 0.756683i
\(506\) 0 0
\(507\) 4.54459i 0.201832i
\(508\) 0 0
\(509\) −11.8646 −0.525889 −0.262945 0.964811i \(-0.584694\pi\)
−0.262945 + 0.964811i \(0.584694\pi\)
\(510\) 0 0
\(511\) −34.8192 −1.54031
\(512\) 0 0
\(513\) 25.8702i 1.14220i
\(514\) 0 0
\(515\) 13.3819 + 19.0744i 0.589676 + 0.840519i
\(516\) 0 0
\(517\) 2.50576i 0.110203i
\(518\) 0 0
\(519\) −6.08757 −0.267214
\(520\) 0 0
\(521\) 0.876118 0.0383834 0.0191917 0.999816i \(-0.493891\pi\)
0.0191917 + 0.999816i \(0.493891\pi\)
\(522\) 0 0
\(523\) 35.9716i 1.57293i −0.617637 0.786463i \(-0.711910\pi\)
0.617637 0.786463i \(-0.288090\pi\)
\(524\) 0 0
\(525\) −2.89531 + 8.00000i −0.126362 + 0.349149i
\(526\) 0 0
\(527\) 0.365767i 0.0159330i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) −11.0399 −0.479089
\(532\) 0 0
\(533\) 48.5651i 2.10359i
\(534\) 0 0
\(535\) 12.8186 + 18.2715i 0.554195 + 0.789945i
\(536\) 0 0
\(537\) 2.37861i 0.102645i
\(538\) 0 0
\(539\) −5.94942 −0.256260
\(540\) 0 0
\(541\) −32.7051 −1.40610 −0.703051 0.711140i \(-0.748179\pi\)
−0.703051 + 0.711140i \(0.748179\pi\)
\(542\) 0 0
\(543\) 11.2326i 0.482036i
\(544\) 0 0
\(545\) −25.3965 + 17.8172i −1.08786 + 0.763205i
\(546\) 0 0
\(547\) 17.1463i 0.733124i −0.930394 0.366562i \(-0.880535\pi\)
0.930394 0.366562i \(-0.119465\pi\)
\(548\) 0 0
\(549\) −16.7003 −0.712751
\(550\) 0 0
\(551\) −11.1782 −0.476208
\(552\) 0 0
\(553\) 23.9687i 1.01925i
\(554\) 0 0
\(555\) 10.9647 7.69241i 0.465425 0.326525i
\(556\) 0 0
\(557\) 5.35049i 0.226708i −0.993555 0.113354i \(-0.963841\pi\)
0.993555 0.113354i \(-0.0361594\pi\)
\(558\) 0 0
\(559\) −9.09259 −0.384576
\(560\) 0 0
\(561\) −0.703036 −0.0296822
\(562\) 0 0
\(563\) 12.7511i 0.537394i −0.963225 0.268697i \(-0.913407\pi\)
0.963225 0.268697i \(-0.0865930\pi\)
\(564\) 0 0
\(565\) 23.7526 + 33.8567i 0.999277 + 1.42436i
\(566\) 0 0
\(567\) 11.4529i 0.480977i
\(568\) 0 0
\(569\) −38.8368 −1.62812 −0.814062 0.580779i \(-0.802748\pi\)
−0.814062 + 0.580779i \(0.802748\pi\)
\(570\) 0 0
\(571\) 8.80350 0.368415 0.184208 0.982887i \(-0.441028\pi\)
0.184208 + 0.982887i \(0.441028\pi\)
\(572\) 0 0
\(573\) 4.76611i 0.199107i
\(574\) 0 0
\(575\) −4.70156 1.70156i −0.196069 0.0709600i
\(576\) 0 0
\(577\) 16.5133i 0.687456i −0.939069 0.343728i \(-0.888310\pi\)
0.939069 0.343728i \(-0.111690\pi\)
\(578\) 0 0
\(579\) 3.40312 0.141429
\(580\) 0 0
\(581\) 32.0372 1.32913
\(582\) 0 0
\(583\) 28.9647i 1.19959i
\(584\) 0 0
\(585\) −14.1567 20.1789i −0.585309 0.834294i
\(586\) 0 0
\(587\) 31.0543i 1.28175i −0.767646 0.640874i \(-0.778572\pi\)
0.767646 0.640874i \(-0.221428\pi\)
\(588\) 0 0
\(589\) 12.1227 0.499507
\(590\) 0 0
\(591\) 9.06895 0.373047
\(592\) 0 0
\(593\) 10.6211i 0.436155i −0.975931 0.218078i \(-0.930021\pi\)
0.975931 0.218078i \(-0.0699786\pi\)
\(594\) 0 0
\(595\) −0.885267 + 0.621070i −0.0362924 + 0.0254614i
\(596\) 0 0
\(597\) 8.82929i 0.361359i
\(598\) 0 0
\(599\) 5.31351 0.217104 0.108552 0.994091i \(-0.465379\pi\)
0.108552 + 0.994091i \(0.465379\pi\)
\(600\) 0 0
\(601\) −15.6336 −0.637708 −0.318854 0.947804i \(-0.603298\pi\)
−0.318854 + 0.947804i \(0.603298\pi\)
\(602\) 0 0
\(603\) 31.6656i 1.28952i
\(604\) 0 0
\(605\) −24.7971 + 17.3967i −1.00814 + 0.707275i
\(606\) 0 0
\(607\) 15.0588i 0.611216i −0.952157 0.305608i \(-0.901140\pi\)
0.952157 0.305608i \(-0.0988597\pi\)
\(608\) 0 0
\(609\) 2.85763 0.115797
\(610\) 0 0
\(611\) 2.22947 0.0901945
\(612\) 0 0
\(613\) 44.1496i 1.78319i −0.452836 0.891594i \(-0.649588\pi\)
0.452836 0.891594i \(-0.350412\pi\)
\(614\) 0 0
\(615\) 9.99705 + 14.2497i 0.403120 + 0.574604i
\(616\) 0 0
\(617\) 10.1871i 0.410117i 0.978750 + 0.205058i \(0.0657384\pi\)
−0.978750 + 0.205058i \(0.934262\pi\)
\(618\) 0 0
\(619\) 2.48087 0.0997147 0.0498573 0.998756i \(-0.484123\pi\)
0.0498573 + 0.998756i \(0.484123\pi\)
\(620\) 0 0
\(621\) −3.88674 −0.155970
\(622\) 0 0
\(623\) 12.1509i 0.486817i
\(624\) 0 0
\(625\) −19.2094 16.0000i −0.768375 0.640000i
\(626\) 0 0
\(627\) 23.3009i 0.930549i
\(628\) 0 0
\(629\) 1.70246 0.0678815
\(630\) 0 0
\(631\) −14.0029 −0.557449 −0.278724 0.960371i \(-0.589912\pi\)
−0.278724 + 0.960371i \(0.589912\pi\)
\(632\) 0 0
\(633\) 11.3145i 0.449713i
\(634\) 0 0
\(635\) −23.2936 33.2025i −0.924379 1.31760i
\(636\) 0 0
\(637\) 5.29341i 0.209733i
\(638\) 0 0
\(639\) −9.03765 −0.357524
\(640\) 0 0
\(641\) 21.3592 0.843639 0.421820 0.906680i \(-0.361392\pi\)
0.421820 + 0.906680i \(0.361392\pi\)
\(642\) 0 0
\(643\) 7.65098i 0.301725i −0.988555 0.150863i \(-0.951795\pi\)
0.988555 0.150863i \(-0.0482051\pi\)
\(644\) 0 0
\(645\) −2.66790 + 1.87170i −0.105048 + 0.0736980i
\(646\) 0 0
\(647\) 9.66388i 0.379926i −0.981791 0.189963i \(-0.939163\pi\)
0.981791 0.189963i \(-0.0608369\pi\)
\(648\) 0 0
\(649\) 21.8721 0.858555
\(650\) 0 0
\(651\) −3.09909 −0.121463
\(652\) 0 0
\(653\) 7.76698i 0.303946i 0.988385 + 0.151973i \(0.0485626\pi\)
−0.988385 + 0.151973i \(0.951437\pi\)
\(654\) 0 0
\(655\) −3.64264 + 2.55554i −0.142330 + 0.0998531i
\(656\) 0 0
\(657\) 36.1580i 1.41066i
\(658\) 0 0
\(659\) 10.6157 0.413528 0.206764 0.978391i \(-0.433707\pi\)
0.206764 + 0.978391i \(0.433707\pi\)
\(660\) 0 0
\(661\) 24.7693 0.963413 0.481706 0.876333i \(-0.340017\pi\)
0.481706 + 0.876333i \(0.340017\pi\)
\(662\) 0 0
\(663\) 0.625517i 0.0242931i
\(664\) 0 0
\(665\) 20.5843 + 29.3406i 0.798224 + 1.13778i
\(666\) 0 0
\(667\) 1.67942i 0.0650273i
\(668\) 0 0
\(669\) 12.8665 0.497447
\(670\) 0 0
\(671\) 33.0865 1.27729
\(672\) 0 0
\(673\) 42.4961i 1.63811i 0.573719 + 0.819053i \(0.305500\pi\)
−0.573719 + 0.819053i \(0.694500\pi\)
\(674\) 0 0
\(675\) −18.2738 6.61353i −0.703357 0.254555i
\(676\) 0 0
\(677\) 42.9463i 1.65056i −0.564723 0.825280i \(-0.691017\pi\)
0.564723 0.825280i \(-0.308983\pi\)
\(678\) 0 0
\(679\) 9.14897 0.351105
\(680\) 0 0
\(681\) 13.8018 0.528887
\(682\) 0 0
\(683\) 42.2263i 1.61575i −0.589357 0.807873i \(-0.700619\pi\)
0.589357 0.807873i \(-0.299381\pi\)
\(684\) 0 0
\(685\) 1.46834 + 2.09296i 0.0561025 + 0.0799680i
\(686\) 0 0
\(687\) 15.7865i 0.602292i
\(688\) 0 0
\(689\) 25.7709 0.981795
\(690\) 0 0
\(691\) −47.6928 −1.81432 −0.907160 0.420785i \(-0.861755\pi\)
−0.907160 + 0.420785i \(0.861755\pi\)
\(692\) 0 0
\(693\) 29.8364i 1.13339i
\(694\) 0 0
\(695\) −41.0930 + 28.8293i −1.55875 + 1.09356i
\(696\) 0 0
\(697\) 2.21251i 0.0838050i
\(698\) 0 0
\(699\) −4.53959 −0.171703
\(700\) 0 0
\(701\) −4.52516 −0.170913 −0.0854565 0.996342i \(-0.527235\pi\)
−0.0854565 + 0.996342i \(0.527235\pi\)
\(702\) 0 0
\(703\) 56.4251i 2.12811i
\(704\) 0 0
\(705\) 0.654158 0.458932i 0.0246370 0.0172844i
\(706\) 0 0
\(707\) 31.8863i 1.19921i
\(708\) 0 0
\(709\) 21.5986 0.811151 0.405575 0.914062i \(-0.367071\pi\)
0.405575 + 0.914062i \(0.367071\pi\)
\(710\) 0 0
\(711\) 24.8903 0.933458
\(712\) 0 0
\(713\) 1.82132i 0.0682089i
\(714\) 0 0
\(715\) 28.0472 + 39.9783i 1.04891 + 1.49510i
\(716\) 0 0
\(717\) 6.73269i 0.251437i
\(718\) 0 0
\(719\) 16.8098 0.626900 0.313450 0.949605i \(-0.398515\pi\)
0.313450 + 0.949605i \(0.398515\pi\)
\(720\) 0 0
\(721\) −25.0935 −0.934530
\(722\) 0 0
\(723\) 9.52773i 0.354340i
\(724\) 0 0
\(725\) −2.85763 + 7.89589i −0.106130 + 0.293246i
\(726\) 0 0
\(727\) 5.65373i 0.209685i 0.994489 + 0.104843i \(0.0334339\pi\)
−0.994489 + 0.104843i \(0.966566\pi\)
\(728\) 0 0
\(729\) 3.65430 0.135345
\(730\) 0 0
\(731\) −0.414238 −0.0153211
\(732\) 0 0
\(733\) 40.2821i 1.48785i −0.668261 0.743927i \(-0.732961\pi\)
0.668261 0.743927i \(-0.267039\pi\)
\(734\) 0 0
\(735\) 1.08964 + 1.55316i 0.0401920 + 0.0572893i
\(736\) 0 0
\(737\) 62.7356i 2.31090i
\(738\) 0 0
\(739\) 1.97327 0.0725877 0.0362939 0.999341i \(-0.488445\pi\)
0.0362939 + 0.999341i \(0.488445\pi\)
\(740\) 0 0
\(741\) 20.7317 0.761597
\(742\) 0 0
\(743\) 24.8403i 0.911304i −0.890158 0.455652i \(-0.849406\pi\)
0.890158 0.455652i \(-0.150594\pi\)
\(744\) 0 0
\(745\) 15.0186 10.5365i 0.550239 0.386027i
\(746\) 0 0
\(747\) 33.2690i 1.21725i
\(748\) 0 0
\(749\) −24.0372 −0.878300
\(750\) 0 0
\(751\) −3.61665 −0.131973 −0.0659867 0.997821i \(-0.521019\pi\)
−0.0659867 + 0.997821i \(0.521019\pi\)
\(752\) 0 0
\(753\) 7.16492i 0.261104i
\(754\) 0 0
\(755\) 19.2650 13.5156i 0.701124 0.491882i
\(756\) 0 0
\(757\) 22.3992i 0.814113i −0.913403 0.407056i \(-0.866555\pi\)
0.913403 0.407056i \(-0.133445\pi\)
\(758\) 0 0
\(759\) 3.50074 0.127069
\(760\) 0 0
\(761\) 25.5137 0.924872 0.462436 0.886653i \(-0.346975\pi\)
0.462436 + 0.886653i \(0.346975\pi\)
\(762\) 0 0
\(763\) 33.4105i 1.20954i
\(764\) 0 0
\(765\) −0.644949 0.919304i −0.0233182 0.0332375i
\(766\) 0 0
\(767\) 19.4604i 0.702675i
\(768\) 0 0
\(769\) 13.8123 0.498084 0.249042 0.968493i \(-0.419884\pi\)
0.249042 + 0.968493i \(0.419884\pi\)
\(770\) 0 0
\(771\) −6.19107 −0.222966
\(772\) 0 0
\(773\) 3.36423i 0.121003i −0.998168 0.0605015i \(-0.980730\pi\)
0.998168 0.0605015i \(-0.0192700\pi\)
\(774\) 0 0
\(775\) 3.09909 8.56304i 0.111322 0.307594i
\(776\) 0 0
\(777\) 14.4247i 0.517483i
\(778\) 0 0
\(779\) 73.3300 2.62732
\(780\) 0 0
\(781\) 17.9053 0.640703
\(782\) 0 0
\(783\) 6.52746i 0.233273i
\(784\) 0 0
\(785\) −1.32263 1.88527i −0.0472068 0.0672881i
\(786\) 0 0
\(787\) 1.29067i 0.0460074i −0.999735 0.0230037i \(-0.992677\pi\)
0.999735 0.0230037i \(-0.00732296\pi\)
\(788\) 0 0
\(789\) −11.1251 −0.396063
\(790\) 0 0
\(791\) −44.5404 −1.58367
\(792\) 0 0
\(793\) 29.4383i 1.04538i
\(794\) 0 0
\(795\) 7.56157 5.30491i 0.268181 0.188146i
\(796\) 0 0
\(797\) 22.4673i 0.795832i −0.917422 0.397916i \(-0.869734\pi\)
0.917422 0.397916i \(-0.130266\pi\)
\(798\) 0 0
\(799\) 0.101569 0.00359327
\(800\) 0 0
\(801\) 12.6181 0.445839
\(802\) 0 0