Properties

Label 280.2.g.b.169.2
Level $280$
Weight $2$
Character 280.169
Analytic conductor $2.236$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5161984.1
Defining polynomial: \(x^{6} - 4 x^{3} + 25 x^{2} - 20 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 169.2
Root \(0.432320 - 0.432320i\) of defining polynomial
Character \(\chi\) \(=\) 280.169
Dual form 280.2.g.b.169.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.76156i q^{3} +(0.432320 - 2.19388i) q^{5} +1.00000i q^{7} -0.103084 q^{9} +O(q^{10})\) \(q-1.76156i q^{3} +(0.432320 - 2.19388i) q^{5} +1.00000i q^{7} -0.103084 q^{9} -0.626198 q^{11} -5.49084i q^{13} +(-3.86464 - 0.761557i) q^{15} +0.896916i q^{17} -6.38776 q^{19} +1.76156 q^{21} +3.72928i q^{23} +(-4.62620 - 1.89692i) q^{25} -5.10308i q^{27} +7.87859 q^{29} +7.52311 q^{31} +1.10308i q^{33} +(2.19388 + 0.432320i) q^{35} +6.00000i q^{37} -9.67243 q^{39} +7.72928 q^{41} -1.72928i q^{43} +(-0.0445652 + 0.226153i) q^{45} +5.87859i q^{47} -1.00000 q^{49} +1.57997 q^{51} +6.77551i q^{53} +(-0.270718 + 1.37380i) q^{55} +11.2524i q^{57} +0.593923 q^{59} +7.13536 q^{61} -0.103084i q^{63} +(-12.0462 - 2.37380i) q^{65} -5.79383i q^{67} +6.56934 q^{69} +5.52311 q^{71} +3.72928i q^{73} +(-3.34153 + 8.14931i) q^{75} -0.626198i q^{77} +5.67243 q^{79} -9.29862 q^{81} +17.4340i q^{83} +(1.96772 + 0.387755i) q^{85} -13.8786i q^{87} -14.2986 q^{89} +5.49084 q^{91} -13.2524i q^{93} +(-2.76156 + 14.0140i) q^{95} -10.1493i q^{97} +0.0645508 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 8q^{9} + O(q^{10}) \) \( 6q - 8q^{9} + 14q^{11} - 18q^{15} - 8q^{19} - 2q^{21} - 10q^{25} - 6q^{29} + 20q^{31} - 2q^{35} + 10q^{39} + 36q^{41} - 28q^{45} - 6q^{49} + 42q^{51} - 12q^{55} - 12q^{59} + 48q^{61} - 22q^{65} - 36q^{69} + 8q^{71} - 40q^{75} - 34q^{79} + 30q^{81} + 14q^{85} + 10q^{91} - 4q^{95} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(3\) 1.76156i 1.01704i −0.861052 0.508518i \(-0.830194\pi\)
0.861052 0.508518i \(-0.169806\pi\)
\(4\) 0 0
\(5\) 0.432320 2.19388i 0.193340 0.981132i
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) −0.103084 −0.0343612
\(10\) 0 0
\(11\) −0.626198 −0.188806 −0.0944029 0.995534i \(-0.530094\pi\)
−0.0944029 + 0.995534i \(0.530094\pi\)
\(12\) 0 0
\(13\) 5.49084i 1.52288i −0.648233 0.761442i \(-0.724492\pi\)
0.648233 0.761442i \(-0.275508\pi\)
\(14\) 0 0
\(15\) −3.86464 0.761557i −0.997846 0.196633i
\(16\) 0 0
\(17\) 0.896916i 0.217534i 0.994067 + 0.108767i \(0.0346903\pi\)
−0.994067 + 0.108767i \(0.965310\pi\)
\(18\) 0 0
\(19\) −6.38776 −1.46545 −0.732726 0.680524i \(-0.761752\pi\)
−0.732726 + 0.680524i \(0.761752\pi\)
\(20\) 0 0
\(21\) 1.76156 0.384403
\(22\) 0 0
\(23\) 3.72928i 0.777609i 0.921320 + 0.388805i \(0.127112\pi\)
−0.921320 + 0.388805i \(0.872888\pi\)
\(24\) 0 0
\(25\) −4.62620 1.89692i −0.925240 0.379383i
\(26\) 0 0
\(27\) 5.10308i 0.982089i
\(28\) 0 0
\(29\) 7.87859 1.46302 0.731509 0.681832i \(-0.238816\pi\)
0.731509 + 0.681832i \(0.238816\pi\)
\(30\) 0 0
\(31\) 7.52311 1.35119 0.675596 0.737272i \(-0.263887\pi\)
0.675596 + 0.737272i \(0.263887\pi\)
\(32\) 0 0
\(33\) 1.10308i 0.192022i
\(34\) 0 0
\(35\) 2.19388 + 0.432320i 0.370833 + 0.0730755i
\(36\) 0 0
\(37\) 6.00000i 0.986394i 0.869918 + 0.493197i \(0.164172\pi\)
−0.869918 + 0.493197i \(0.835828\pi\)
\(38\) 0 0
\(39\) −9.67243 −1.54883
\(40\) 0 0
\(41\) 7.72928 1.20711 0.603556 0.797321i \(-0.293750\pi\)
0.603556 + 0.797321i \(0.293750\pi\)
\(42\) 0 0
\(43\) 1.72928i 0.263713i −0.991269 0.131856i \(-0.957906\pi\)
0.991269 0.131856i \(-0.0420938\pi\)
\(44\) 0 0
\(45\) −0.0445652 + 0.226153i −0.00664339 + 0.0337129i
\(46\) 0 0
\(47\) 5.87859i 0.857481i 0.903428 + 0.428741i \(0.141043\pi\)
−0.903428 + 0.428741i \(0.858957\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 1.57997 0.221240
\(52\) 0 0
\(53\) 6.77551i 0.930688i 0.885130 + 0.465344i \(0.154069\pi\)
−0.885130 + 0.465344i \(0.845931\pi\)
\(54\) 0 0
\(55\) −0.270718 + 1.37380i −0.0365036 + 0.185243i
\(56\) 0 0
\(57\) 11.2524i 1.49042i
\(58\) 0 0
\(59\) 0.593923 0.0773221 0.0386611 0.999252i \(-0.487691\pi\)
0.0386611 + 0.999252i \(0.487691\pi\)
\(60\) 0 0
\(61\) 7.13536 0.913589 0.456795 0.889572i \(-0.348997\pi\)
0.456795 + 0.889572i \(0.348997\pi\)
\(62\) 0 0
\(63\) 0.103084i 0.0129873i
\(64\) 0 0
\(65\) −12.0462 2.37380i −1.49415 0.294434i
\(66\) 0 0
\(67\) 5.79383i 0.707829i −0.935278 0.353915i \(-0.884850\pi\)
0.935278 0.353915i \(-0.115150\pi\)
\(68\) 0 0
\(69\) 6.56934 0.790856
\(70\) 0 0
\(71\) 5.52311 0.655473 0.327737 0.944769i \(-0.393714\pi\)
0.327737 + 0.944769i \(0.393714\pi\)
\(72\) 0 0
\(73\) 3.72928i 0.436479i 0.975895 + 0.218240i \(0.0700315\pi\)
−0.975895 + 0.218240i \(0.929969\pi\)
\(74\) 0 0
\(75\) −3.34153 + 8.14931i −0.385846 + 0.941002i
\(76\) 0 0
\(77\) 0.626198i 0.0713619i
\(78\) 0 0
\(79\) 5.67243 0.638198 0.319099 0.947721i \(-0.396620\pi\)
0.319099 + 0.947721i \(0.396620\pi\)
\(80\) 0 0
\(81\) −9.29862 −1.03318
\(82\) 0 0
\(83\) 17.4340i 1.91363i 0.290700 + 0.956814i \(0.406112\pi\)
−0.290700 + 0.956814i \(0.593888\pi\)
\(84\) 0 0
\(85\) 1.96772 + 0.387755i 0.213430 + 0.0420580i
\(86\) 0 0
\(87\) 13.8786i 1.48794i
\(88\) 0 0
\(89\) −14.2986 −1.51565 −0.757826 0.652457i \(-0.773738\pi\)
−0.757826 + 0.652457i \(0.773738\pi\)
\(90\) 0 0
\(91\) 5.49084 0.575596
\(92\) 0 0
\(93\) 13.2524i 1.37421i
\(94\) 0 0
\(95\) −2.76156 + 14.0140i −0.283330 + 1.43780i
\(96\) 0 0
\(97\) 10.1493i 1.03051i −0.857038 0.515253i \(-0.827698\pi\)
0.857038 0.515253i \(-0.172302\pi\)
\(98\) 0 0
\(99\) 0.0645508 0.00648760
\(100\) 0 0
\(101\) 9.64015 0.959231 0.479615 0.877479i \(-0.340776\pi\)
0.479615 + 0.877479i \(0.340776\pi\)
\(102\) 0 0
\(103\) 0.626198i 0.0617011i 0.999524 + 0.0308506i \(0.00982160\pi\)
−0.999524 + 0.0308506i \(0.990178\pi\)
\(104\) 0 0
\(105\) 0.761557 3.86464i 0.0743204 0.377150i
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) −18.9248 −1.81267 −0.906335 0.422561i \(-0.861131\pi\)
−0.906335 + 0.422561i \(0.861131\pi\)
\(110\) 0 0
\(111\) 10.5693 1.00320
\(112\) 0 0
\(113\) 1.04623i 0.0984209i 0.998788 + 0.0492105i \(0.0156705\pi\)
−0.998788 + 0.0492105i \(0.984329\pi\)
\(114\) 0 0
\(115\) 8.18159 + 1.61224i 0.762937 + 0.150343i
\(116\) 0 0
\(117\) 0.566016i 0.0523282i
\(118\) 0 0
\(119\) −0.896916 −0.0822202
\(120\) 0 0
\(121\) −10.6079 −0.964352
\(122\) 0 0
\(123\) 13.6156i 1.22767i
\(124\) 0 0
\(125\) −6.16160 + 9.32924i −0.551110 + 0.834432i
\(126\) 0 0
\(127\) 21.2803i 1.88832i −0.329485 0.944161i \(-0.606875\pi\)
0.329485 0.944161i \(-0.393125\pi\)
\(128\) 0 0
\(129\) −3.04623 −0.268205
\(130\) 0 0
\(131\) −9.91087 −0.865917 −0.432958 0.901414i \(-0.642530\pi\)
−0.432958 + 0.901414i \(0.642530\pi\)
\(132\) 0 0
\(133\) 6.38776i 0.553889i
\(134\) 0 0
\(135\) −11.1955 2.20617i −0.963559 0.189877i
\(136\) 0 0
\(137\) 3.45856i 0.295485i 0.989026 + 0.147743i \(0.0472007\pi\)
−0.989026 + 0.147743i \(0.952799\pi\)
\(138\) 0 0
\(139\) 20.4157 1.73163 0.865817 0.500361i \(-0.166799\pi\)
0.865817 + 0.500361i \(0.166799\pi\)
\(140\) 0 0
\(141\) 10.3555 0.872089
\(142\) 0 0
\(143\) 3.43835i 0.287530i
\(144\) 0 0
\(145\) 3.40608 17.2847i 0.282859 1.43541i
\(146\) 0 0
\(147\) 1.76156i 0.145291i
\(148\) 0 0
\(149\) 17.0462 1.39648 0.698241 0.715863i \(-0.253967\pi\)
0.698241 + 0.715863i \(0.253967\pi\)
\(150\) 0 0
\(151\) 2.89692 0.235748 0.117874 0.993029i \(-0.462392\pi\)
0.117874 + 0.993029i \(0.462392\pi\)
\(152\) 0 0
\(153\) 0.0924575i 0.00747474i
\(154\) 0 0
\(155\) 3.25240 16.5048i 0.261239 1.32570i
\(156\) 0 0
\(157\) 10.1170i 0.807427i 0.914885 + 0.403714i \(0.132281\pi\)
−0.914885 + 0.403714i \(0.867719\pi\)
\(158\) 0 0
\(159\) 11.9354 0.946543
\(160\) 0 0
\(161\) −3.72928 −0.293909
\(162\) 0 0
\(163\) 0.476886i 0.0373526i −0.999826 0.0186763i \(-0.994055\pi\)
0.999826 0.0186763i \(-0.00594519\pi\)
\(164\) 0 0
\(165\) 2.42003 + 0.476886i 0.188399 + 0.0371255i
\(166\) 0 0
\(167\) 13.1676i 1.01894i −0.860488 0.509471i \(-0.829841\pi\)
0.860488 0.509471i \(-0.170159\pi\)
\(168\) 0 0
\(169\) −17.1493 −1.31918
\(170\) 0 0
\(171\) 0.658473 0.0503547
\(172\) 0 0
\(173\) 13.9677i 1.06195i −0.847389 0.530973i \(-0.821826\pi\)
0.847389 0.530973i \(-0.178174\pi\)
\(174\) 0 0
\(175\) 1.89692 4.62620i 0.143393 0.349708i
\(176\) 0 0
\(177\) 1.04623i 0.0786394i
\(178\) 0 0
\(179\) −7.45856 −0.557479 −0.278740 0.960367i \(-0.589917\pi\)
−0.278740 + 0.960367i \(0.589917\pi\)
\(180\) 0 0
\(181\) −14.1170 −1.04931 −0.524656 0.851315i \(-0.675806\pi\)
−0.524656 + 0.851315i \(0.675806\pi\)
\(182\) 0 0
\(183\) 12.5693i 0.929153i
\(184\) 0 0
\(185\) 13.1633 + 2.59392i 0.967783 + 0.190709i
\(186\) 0 0
\(187\) 0.561647i 0.0410717i
\(188\) 0 0
\(189\) 5.10308 0.371195
\(190\) 0 0
\(191\) −8.42003 −0.609252 −0.304626 0.952472i \(-0.598531\pi\)
−0.304626 + 0.952472i \(0.598531\pi\)
\(192\) 0 0
\(193\) 22.2986i 1.60509i 0.596591 + 0.802545i \(0.296521\pi\)
−0.596591 + 0.802545i \(0.703479\pi\)
\(194\) 0 0
\(195\) −4.18159 + 21.2201i −0.299450 + 1.51960i
\(196\) 0 0
\(197\) 26.3632i 1.87830i 0.343509 + 0.939149i \(0.388384\pi\)
−0.343509 + 0.939149i \(0.611616\pi\)
\(198\) 0 0
\(199\) −22.4402 −1.59075 −0.795373 0.606120i \(-0.792725\pi\)
−0.795373 + 0.606120i \(0.792725\pi\)
\(200\) 0 0
\(201\) −10.2062 −0.719888
\(202\) 0 0
\(203\) 7.87859i 0.552969i
\(204\) 0 0
\(205\) 3.34153 16.9571i 0.233382 1.18434i
\(206\) 0 0
\(207\) 0.384428i 0.0267196i
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) −15.1955 −1.04610 −0.523052 0.852301i \(-0.675207\pi\)
−0.523052 + 0.852301i \(0.675207\pi\)
\(212\) 0 0
\(213\) 9.72928i 0.666639i
\(214\) 0 0
\(215\) −3.79383 0.747604i −0.258737 0.0509862i
\(216\) 0 0
\(217\) 7.52311i 0.510702i
\(218\) 0 0
\(219\) 6.56934 0.443915
\(220\) 0 0
\(221\) 4.92482 0.331279
\(222\) 0 0
\(223\) 6.89692i 0.461852i 0.972971 + 0.230926i \(0.0741755\pi\)
−0.972971 + 0.230926i \(0.925825\pi\)
\(224\) 0 0
\(225\) 0.476886 + 0.195541i 0.0317924 + 0.0130361i
\(226\) 0 0
\(227\) 2.77988i 0.184507i −0.995736 0.0922535i \(-0.970593\pi\)
0.995736 0.0922535i \(-0.0294070\pi\)
\(228\) 0 0
\(229\) −18.6585 −1.23299 −0.616493 0.787360i \(-0.711447\pi\)
−0.616493 + 0.787360i \(0.711447\pi\)
\(230\) 0 0
\(231\) −1.10308 −0.0725776
\(232\) 0 0
\(233\) 11.0462i 0.723663i 0.932244 + 0.361831i \(0.117848\pi\)
−0.932244 + 0.361831i \(0.882152\pi\)
\(234\) 0 0
\(235\) 12.8969 + 2.54144i 0.841302 + 0.165785i
\(236\) 0 0
\(237\) 9.99230i 0.649070i
\(238\) 0 0
\(239\) 20.1493 1.30335 0.651675 0.758498i \(-0.274066\pi\)
0.651675 + 0.758498i \(0.274066\pi\)
\(240\) 0 0
\(241\) 3.72928 0.240224 0.120112 0.992760i \(-0.461675\pi\)
0.120112 + 0.992760i \(0.461675\pi\)
\(242\) 0 0
\(243\) 1.07081i 0.0686924i
\(244\) 0 0
\(245\) −0.432320 + 2.19388i −0.0276199 + 0.140162i
\(246\) 0 0
\(247\) 35.0741i 2.23171i
\(248\) 0 0
\(249\) 30.7110 1.94623
\(250\) 0 0
\(251\) −21.4985 −1.35698 −0.678488 0.734612i \(-0.737364\pi\)
−0.678488 + 0.734612i \(0.737364\pi\)
\(252\) 0 0
\(253\) 2.33527i 0.146817i
\(254\) 0 0
\(255\) 0.683053 3.46626i 0.0427744 0.217066i
\(256\) 0 0
\(257\) 4.27072i 0.266400i 0.991089 + 0.133200i \(0.0425253\pi\)
−0.991089 + 0.133200i \(0.957475\pi\)
\(258\) 0 0
\(259\) −6.00000 −0.372822
\(260\) 0 0
\(261\) −0.812155 −0.0502711
\(262\) 0 0
\(263\) 11.4586i 0.706565i 0.935517 + 0.353283i \(0.114935\pi\)
−0.935517 + 0.353283i \(0.885065\pi\)
\(264\) 0 0
\(265\) 14.8646 + 2.92919i 0.913128 + 0.179939i
\(266\) 0 0
\(267\) 25.1878i 1.54147i
\(268\) 0 0
\(269\) 7.07081 0.431115 0.215557 0.976491i \(-0.430843\pi\)
0.215557 + 0.976491i \(0.430843\pi\)
\(270\) 0 0
\(271\) 17.0096 1.03326 0.516629 0.856209i \(-0.327187\pi\)
0.516629 + 0.856209i \(0.327187\pi\)
\(272\) 0 0
\(273\) 9.67243i 0.585402i
\(274\) 0 0
\(275\) 2.89692 + 1.18785i 0.174691 + 0.0716298i
\(276\) 0 0
\(277\) 18.7755i 1.12811i −0.825737 0.564056i \(-0.809240\pi\)
0.825737 0.564056i \(-0.190760\pi\)
\(278\) 0 0
\(279\) −0.775511 −0.0464286
\(280\) 0 0
\(281\) −4.59829 −0.274311 −0.137156 0.990550i \(-0.543796\pi\)
−0.137156 + 0.990550i \(0.543796\pi\)
\(282\) 0 0
\(283\) 13.5833i 0.807443i 0.914882 + 0.403722i \(0.132284\pi\)
−0.914882 + 0.403722i \(0.867716\pi\)
\(284\) 0 0
\(285\) 24.6864 + 4.86464i 1.46229 + 0.288156i
\(286\) 0 0
\(287\) 7.72928i 0.456245i
\(288\) 0 0
\(289\) 16.1955 0.952679
\(290\) 0 0
\(291\) −17.8786 −1.04806
\(292\) 0 0
\(293\) 11.8261i 0.690889i −0.938439 0.345444i \(-0.887728\pi\)
0.938439 0.345444i \(-0.112272\pi\)
\(294\) 0 0
\(295\) 0.256765 1.30299i 0.0149494 0.0758632i
\(296\) 0 0
\(297\) 3.19554i 0.185424i
\(298\) 0 0
\(299\) 20.4769 1.18421
\(300\) 0 0
\(301\) 1.72928 0.0996741
\(302\) 0 0
\(303\) 16.9817i 0.975572i
\(304\) 0 0
\(305\) 3.08476 15.6541i 0.176633 0.896351i
\(306\) 0 0
\(307\) 20.9860i 1.19774i −0.800847 0.598868i \(-0.795617\pi\)
0.800847 0.598868i \(-0.204383\pi\)
\(308\) 0 0
\(309\) 1.10308 0.0627522
\(310\) 0 0
\(311\) −22.5048 −1.27613 −0.638065 0.769983i \(-0.720265\pi\)
−0.638065 + 0.769983i \(0.720265\pi\)
\(312\) 0 0
\(313\) 12.4846i 0.705670i 0.935686 + 0.352835i \(0.114782\pi\)
−0.935686 + 0.352835i \(0.885218\pi\)
\(314\) 0 0
\(315\) −0.226153 0.0445652i −0.0127423 0.00251096i
\(316\) 0 0
\(317\) 25.5231i 1.43352i 0.697319 + 0.716760i \(0.254376\pi\)
−0.697319 + 0.716760i \(0.745624\pi\)
\(318\) 0 0
\(319\) −4.93356 −0.276226
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5.72928i 0.318786i
\(324\) 0 0
\(325\) −10.4157 + 25.4017i −0.577757 + 1.40903i
\(326\) 0 0
\(327\) 33.3372i 1.84355i
\(328\) 0 0
\(329\) −5.87859 −0.324097
\(330\) 0 0
\(331\) −2.68305 −0.147474 −0.0737370 0.997278i \(-0.523493\pi\)
−0.0737370 + 0.997278i \(0.523493\pi\)
\(332\) 0 0
\(333\) 0.618502i 0.0338937i
\(334\) 0 0
\(335\) −12.7110 2.50479i −0.694474 0.136851i
\(336\) 0 0
\(337\) 12.5048i 0.681179i 0.940212 + 0.340590i \(0.110627\pi\)
−0.940212 + 0.340590i \(0.889373\pi\)
\(338\) 0 0
\(339\) 1.84299 0.100098
\(340\) 0 0
\(341\) −4.71096 −0.255113
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 2.84006 14.4123i 0.152904 0.775934i
\(346\) 0 0
\(347\) 28.9450i 1.55385i −0.629593 0.776925i \(-0.716778\pi\)
0.629593 0.776925i \(-0.283222\pi\)
\(348\) 0 0
\(349\) −32.1449 −1.72068 −0.860340 0.509721i \(-0.829749\pi\)
−0.860340 + 0.509721i \(0.829749\pi\)
\(350\) 0 0
\(351\) −28.0202 −1.49561
\(352\) 0 0
\(353\) 8.17722i 0.435229i −0.976035 0.217615i \(-0.930172\pi\)
0.976035 0.217615i \(-0.0698276\pi\)
\(354\) 0 0
\(355\) 2.38776 12.1170i 0.126729 0.643106i
\(356\) 0 0
\(357\) 1.57997i 0.0836208i
\(358\) 0 0
\(359\) −18.5048 −0.976646 −0.488323 0.872663i \(-0.662391\pi\)
−0.488323 + 0.872663i \(0.662391\pi\)
\(360\) 0 0
\(361\) 21.8034 1.14755
\(362\) 0 0
\(363\) 18.6864i 0.980781i
\(364\) 0 0
\(365\) 8.18159 + 1.61224i 0.428244 + 0.0843887i
\(366\) 0 0
\(367\) 27.4942i 1.43518i −0.696464 0.717592i \(-0.745244\pi\)
0.696464 0.717592i \(-0.254756\pi\)
\(368\) 0 0
\(369\) −0.796763 −0.0414778
\(370\) 0 0
\(371\) −6.77551 −0.351767
\(372\) 0 0
\(373\) 6.06455i 0.314011i −0.987598 0.157005i \(-0.949816\pi\)
0.987598 0.157005i \(-0.0501840\pi\)
\(374\) 0 0
\(375\) 16.4340 + 10.8540i 0.848647 + 0.560499i
\(376\) 0 0
\(377\) 43.2601i 2.22801i
\(378\) 0 0
\(379\) 5.72928 0.294293 0.147147 0.989115i \(-0.452991\pi\)
0.147147 + 0.989115i \(0.452991\pi\)
\(380\) 0 0
\(381\) −37.4865 −1.92049
\(382\) 0 0
\(383\) 1.72928i 0.0883622i 0.999024 + 0.0441811i \(0.0140679\pi\)
−0.999024 + 0.0441811i \(0.985932\pi\)
\(384\) 0 0
\(385\) −1.37380 0.270718i −0.0700154 0.0137971i
\(386\) 0 0
\(387\) 0.178261i 0.00906150i
\(388\) 0 0
\(389\) 36.7187 1.86171 0.930855 0.365389i \(-0.119064\pi\)
0.930855 + 0.365389i \(0.119064\pi\)
\(390\) 0 0
\(391\) −3.34485 −0.169157
\(392\) 0 0
\(393\) 17.4586i 0.880668i
\(394\) 0 0
\(395\) 2.45231 12.4446i 0.123389 0.626156i
\(396\) 0 0
\(397\) 2.03228i 0.101997i −0.998699 0.0509985i \(-0.983760\pi\)
0.998699 0.0509985i \(-0.0162404\pi\)
\(398\) 0 0
\(399\) −11.2524 −0.563324
\(400\) 0 0
\(401\) −1.64452 −0.0821234 −0.0410617 0.999157i \(-0.513074\pi\)
−0.0410617 + 0.999157i \(0.513074\pi\)
\(402\) 0 0
\(403\) 41.3082i 2.05771i
\(404\) 0 0
\(405\) −4.01999 + 20.4000i −0.199755 + 1.01369i
\(406\) 0 0
\(407\) 3.75719i 0.186237i
\(408\) 0 0
\(409\) 4.98168 0.246328 0.123164 0.992386i \(-0.460696\pi\)
0.123164 + 0.992386i \(0.460696\pi\)
\(410\) 0 0
\(411\) 6.09246 0.300519
\(412\) 0 0
\(413\) 0.593923i 0.0292250i
\(414\) 0 0
\(415\) 38.2480 + 7.53707i 1.87752 + 0.369980i
\(416\) 0 0
\(417\) 35.9634i 1.76113i
\(418\) 0 0
\(419\) −22.9205 −1.11974 −0.559869 0.828581i \(-0.689148\pi\)
−0.559869 + 0.828581i \(0.689148\pi\)
\(420\) 0 0
\(421\) −20.9527 −1.02117 −0.510587 0.859826i \(-0.670572\pi\)
−0.510587 + 0.859826i \(0.670572\pi\)
\(422\) 0 0
\(423\) 0.605987i 0.0294641i
\(424\) 0 0
\(425\) 1.70138 4.14931i 0.0825288 0.201271i
\(426\) 0 0
\(427\) 7.13536i 0.345304i
\(428\) 0 0
\(429\) 6.05685 0.292428
\(430\) 0 0
\(431\) 33.1589 1.59721 0.798604 0.601857i \(-0.205572\pi\)
0.798604 + 0.601857i \(0.205572\pi\)
\(432\) 0 0
\(433\) 18.5414i 0.891045i 0.895271 + 0.445522i \(0.146982\pi\)
−0.895271 + 0.445522i \(0.853018\pi\)
\(434\) 0 0
\(435\) −30.4479 6.00000i −1.45987 0.287678i
\(436\) 0 0
\(437\) 23.8217i 1.13955i
\(438\) 0 0
\(439\) 20.8401 0.994642 0.497321 0.867567i \(-0.334317\pi\)
0.497321 + 0.867567i \(0.334317\pi\)
\(440\) 0 0
\(441\) 0.103084 0.00490875
\(442\) 0 0
\(443\) 17.5510i 0.833874i −0.908935 0.416937i \(-0.863104\pi\)
0.908935 0.416937i \(-0.136896\pi\)
\(444\) 0 0
\(445\) −6.18159 + 31.3694i −0.293035 + 1.48705i
\(446\) 0 0
\(447\) 30.0279i 1.42027i
\(448\) 0 0
\(449\) 13.1955 0.622736 0.311368 0.950289i \(-0.399213\pi\)
0.311368 + 0.950289i \(0.399213\pi\)
\(450\) 0 0
\(451\) −4.84006 −0.227910
\(452\) 0 0
\(453\) 5.10308i 0.239764i
\(454\) 0 0
\(455\) 2.37380 12.0462i 0.111286 0.564736i
\(456\) 0 0
\(457\) 29.1020i 1.36134i −0.732592 0.680668i \(-0.761690\pi\)
0.732592 0.680668i \(-0.238310\pi\)
\(458\) 0 0
\(459\) 4.57704 0.213638
\(460\) 0 0
\(461\) −18.8280 −0.876907 −0.438454 0.898754i \(-0.644474\pi\)
−0.438454 + 0.898754i \(0.644474\pi\)
\(462\) 0 0
\(463\) 14.0925i 0.654932i 0.944863 + 0.327466i \(0.106195\pi\)
−0.944863 + 0.327466i \(0.893805\pi\)
\(464\) 0 0
\(465\) −29.0741 5.72928i −1.34828 0.265689i
\(466\) 0 0
\(467\) 12.2663i 0.567619i −0.958881 0.283809i \(-0.908402\pi\)
0.958881 0.283809i \(-0.0915983\pi\)
\(468\) 0 0
\(469\) 5.79383 0.267534
\(470\) 0 0
\(471\) 17.8217 0.821182
\(472\) 0 0
\(473\) 1.08287i 0.0497905i
\(474\) 0 0
\(475\) 29.5510 + 12.1170i 1.35589 + 0.555968i
\(476\) 0 0
\(477\) 0.698445i 0.0319796i
\(478\) 0 0
\(479\) 14.1570 0.646850 0.323425 0.946254i \(-0.395166\pi\)
0.323425 + 0.946254i \(0.395166\pi\)
\(480\) 0 0
\(481\) 32.9450 1.50216
\(482\) 0 0
\(483\) 6.56934i 0.298915i
\(484\) 0 0
\(485\) −22.2663 4.38776i −1.01106 0.199238i
\(486\) 0 0
\(487\) 30.2341i 1.37004i 0.728526 + 0.685018i \(0.240206\pi\)
−0.728526 + 0.685018i \(0.759794\pi\)
\(488\) 0 0
\(489\) −0.840061 −0.0379889
\(490\) 0 0
\(491\) 39.9065 1.80096 0.900478 0.434902i \(-0.143217\pi\)
0.900478 + 0.434902i \(0.143217\pi\)
\(492\) 0 0
\(493\) 7.06644i 0.318256i
\(494\) 0 0
\(495\) 0.0279066 0.141617i 0.00125431 0.00636519i
\(496\) 0 0
\(497\) 5.52311i 0.247746i
\(498\) 0 0
\(499\) −27.3246 −1.22322 −0.611610 0.791160i \(-0.709478\pi\)
−0.611610 + 0.791160i \(0.709478\pi\)
\(500\) 0 0
\(501\) −23.1955 −1.03630
\(502\) 0 0
\(503\) 1.40171i 0.0624991i −0.999512 0.0312495i \(-0.990051\pi\)
0.999512 0.0312495i \(-0.00994866\pi\)
\(504\) 0 0
\(505\) 4.16763 21.1493i 0.185457 0.941132i
\(506\) 0 0
\(507\) 30.2095i 1.34165i
\(508\) 0 0
\(509\) −18.6585 −0.827022 −0.413511 0.910499i \(-0.635698\pi\)
−0.413511 + 0.910499i \(0.635698\pi\)
\(510\) 0 0
\(511\) −3.72928 −0.164974
\(512\) 0 0
\(513\) 32.5972i 1.43920i
\(514\) 0 0
\(515\) 1.37380 + 0.270718i 0.0605369 + 0.0119293i
\(516\) 0 0
\(517\) 3.68116i 0.161897i
\(518\) 0 0
\(519\) −24.6049 −1.08004
\(520\) 0 0
\(521\) −4.02791 −0.176466 −0.0882329 0.996100i \(-0.528122\pi\)
−0.0882329 + 0.996100i \(0.528122\pi\)
\(522\) 0 0
\(523\) 38.4436i 1.68102i −0.541796 0.840510i \(-0.682256\pi\)
0.541796 0.840510i \(-0.317744\pi\)
\(524\) 0 0
\(525\) −8.14931 3.34153i −0.355665 0.145836i
\(526\) 0 0
\(527\) 6.74760i 0.293930i
\(528\) 0 0
\(529\) 9.09246 0.395324
\(530\) 0 0
\(531\) −0.0612237 −0.00265688
\(532\) 0 0
\(533\) 42.4402i 1.83829i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 13.1387i 0.566976i
\(538\) 0 0
\(539\) 0.626198 0.0269723
\(540\) 0 0
\(541\) 12.4846 0.536754 0.268377 0.963314i \(-0.413513\pi\)
0.268377 + 0.963314i \(0.413513\pi\)
\(542\) 0 0
\(543\) 24.8680i 1.06719i
\(544\) 0 0
\(545\) −8.18159 + 41.5187i −0.350461 + 1.77847i
\(546\) 0 0
\(547\) 37.7851i 1.61557i 0.589474 + 0.807787i \(0.299335\pi\)
−0.589474 + 0.807787i \(0.700665\pi\)
\(548\) 0 0
\(549\) −0.735539 −0.0313921
\(550\) 0 0
\(551\) −50.3265 −2.14398
\(552\) 0 0
\(553\) 5.67243i 0.241216i
\(554\) 0 0
\(555\) 4.56934 23.1878i 0.193958 0.984269i
\(556\) 0 0
\(557\) 1.93545i 0.0820076i 0.999159 + 0.0410038i \(0.0130556\pi\)
−0.999159 + 0.0410038i \(0.986944\pi\)
\(558\) 0 0
\(559\) −9.49521 −0.401604
\(560\) 0 0
\(561\) −0.989374 −0.0417714
\(562\) 0 0
\(563\) 29.8463i 1.25787i 0.777457 + 0.628936i \(0.216509\pi\)
−0.777457 + 0.628936i \(0.783491\pi\)
\(564\) 0 0
\(565\) 2.29530 + 0.452306i 0.0965639 + 0.0190287i
\(566\) 0 0
\(567\) 9.29862i 0.390506i
\(568\) 0 0
\(569\) −15.3449 −0.643290 −0.321645 0.946860i \(-0.604236\pi\)
−0.321645 + 0.946860i \(0.604236\pi\)
\(570\) 0 0
\(571\) 35.8217 1.49909 0.749547 0.661952i \(-0.230272\pi\)
0.749547 + 0.661952i \(0.230272\pi\)
\(572\) 0 0
\(573\) 14.8324i 0.619631i
\(574\) 0 0
\(575\) 7.07414 17.2524i 0.295012 0.719475i
\(576\) 0 0
\(577\) 2.92482i 0.121762i 0.998145 + 0.0608810i \(0.0193910\pi\)
−0.998145 + 0.0608810i \(0.980609\pi\)
\(578\) 0 0
\(579\) 39.2803 1.63243
\(580\) 0 0
\(581\) −17.4340 −0.723284
\(582\) 0 0
\(583\) 4.24281i 0.175719i
\(584\) 0 0
\(585\) 1.24177 + 0.244700i 0.0513409 + 0.0101171i
\(586\) 0 0
\(587\) 19.5756i 0.807972i 0.914765 + 0.403986i \(0.132375\pi\)
−0.914765 + 0.403986i \(0.867625\pi\)
\(588\) 0 0
\(589\) −48.0558 −1.98011
\(590\) 0 0
\(591\) 46.4402 1.91030
\(592\) 0 0
\(593\) 8.00770i 0.328837i −0.986391 0.164418i \(-0.947425\pi\)
0.986391 0.164418i \(-0.0525747\pi\)
\(594\) 0 0
\(595\) −0.387755 + 1.96772i −0.0158964 + 0.0806688i
\(596\) 0 0
\(597\) 39.5298i 1.61785i
\(598\) 0 0
\(599\) 29.3005 1.19719 0.598593 0.801053i \(-0.295727\pi\)
0.598593 + 0.801053i \(0.295727\pi\)
\(600\) 0 0
\(601\) 21.3449 0.870675 0.435337 0.900267i \(-0.356629\pi\)
0.435337 + 0.900267i \(0.356629\pi\)
\(602\) 0 0
\(603\) 0.597250i 0.0243219i
\(604\) 0 0
\(605\) −4.58600 + 23.2724i −0.186447 + 0.946157i
\(606\) 0 0
\(607\) 9.53081i 0.386844i 0.981116 + 0.193422i \(0.0619586\pi\)
−0.981116 + 0.193422i \(0.938041\pi\)
\(608\) 0 0
\(609\) 13.8786 0.562389
\(610\) 0 0
\(611\) 32.2784 1.30584
\(612\) 0 0
\(613\) 9.75719i 0.394089i 0.980395 + 0.197045i \(0.0631344\pi\)
−0.980395 + 0.197045i \(0.936866\pi\)
\(614\) 0 0
\(615\) −29.8709 5.88629i −1.20451 0.237358i
\(616\) 0 0
\(617\) 37.9267i 1.52687i −0.645884 0.763436i \(-0.723511\pi\)
0.645884 0.763436i \(-0.276489\pi\)
\(618\) 0 0
\(619\) −41.9109 −1.68454 −0.842270 0.539056i \(-0.818781\pi\)
−0.842270 + 0.539056i \(0.818781\pi\)
\(620\) 0 0
\(621\) 19.0308 0.763681
\(622\) 0 0
\(623\) 14.2986i 0.572862i
\(624\) 0 0
\(625\) 17.8034 + 17.5510i 0.712137 + 0.702041i
\(626\) 0 0
\(627\) 7.04623i 0.281399i
\(628\) 0 0
\(629\) −5.38150 −0.214574
\(630\) 0 0
\(631\) −8.42003 −0.335196 −0.167598 0.985855i \(-0.553601\pi\)
−0.167598 + 0.985855i \(0.553601\pi\)
\(632\) 0 0
\(633\) 26.7678i 1.06393i
\(634\) 0 0
\(635\) −46.6864 9.19991i −1.85269 0.365087i
\(636\) 0 0
\(637\) 5.49084i 0.217555i
\(638\) 0 0
\(639\) −0.569343 −0.0225229
\(640\) 0 0
\(641\) −2.07707 −0.0820392 −0.0410196 0.999158i \(-0.513061\pi\)
−0.0410196 + 0.999158i \(0.513061\pi\)
\(642\) 0 0
\(643\) 27.2480i 1.07456i 0.843405 + 0.537279i \(0.180548\pi\)
−0.843405 + 0.537279i \(0.819452\pi\)
\(644\) 0 0
\(645\) −1.31695 + 6.68305i −0.0518547 + 0.263145i
\(646\) 0 0
\(647\) 12.3632i 0.486047i 0.970020 + 0.243023i \(0.0781391\pi\)
−0.970020 + 0.243023i \(0.921861\pi\)
\(648\) 0 0
\(649\) −0.371913 −0.0145989
\(650\) 0 0
\(651\) 13.2524 0.519402
\(652\) 0 0
\(653\) 37.3449i 1.46142i −0.682690 0.730709i \(-0.739190\pi\)
0.682690 0.730709i \(-0.260810\pi\)
\(654\) 0 0
\(655\) −4.28467 + 21.7432i −0.167416 + 0.849578i
\(656\) 0 0
\(657\) 0.384428i 0.0149980i
\(658\) 0 0
\(659\) 14.1772 0.552266 0.276133 0.961119i \(-0.410947\pi\)
0.276133 + 0.961119i \(0.410947\pi\)
\(660\) 0 0
\(661\) −1.76925 −0.0688160 −0.0344080 0.999408i \(-0.510955\pi\)
−0.0344080 + 0.999408i \(0.510955\pi\)
\(662\) 0 0
\(663\) 8.67536i 0.336923i
\(664\) 0 0
\(665\) −14.0140 2.76156i −0.543438 0.107089i
\(666\) 0 0
\(667\) 29.3815i 1.13766i
\(668\) 0 0
\(669\) 12.1493 0.469720
\(670\) 0 0
\(671\) −4.46815 −0.172491
\(672\) 0 0
\(673\) 4.05581i 0.156340i −0.996940 0.0781701i \(-0.975092\pi\)
0.996940 0.0781701i \(-0.0249077\pi\)
\(674\) 0 0
\(675\) −9.68012 + 23.6079i −0.372588 + 0.908668i
\(676\) 0 0
\(677\) 9.37713i 0.360392i −0.983631 0.180196i \(-0.942327\pi\)
0.983631 0.180196i \(-0.0576733\pi\)
\(678\) 0 0
\(679\) 10.1493 0.389495
\(680\) 0 0
\(681\) −4.89692 −0.187650
\(682\) 0 0
\(683\) 5.49521i 0.210268i 0.994458 + 0.105134i \(0.0335272\pi\)
−0.994458 + 0.105134i \(0.966473\pi\)
\(684\) 0 0
\(685\) 7.58767 + 1.49521i 0.289910 + 0.0571290i
\(686\) 0 0
\(687\) 32.8680i 1.25399i
\(688\) 0 0
\(689\) 37.2032 1.41733
\(690\) 0 0
\(691\) −3.03416 −0.115425 −0.0577125 0.998333i \(-0.518381\pi\)
−0.0577125 + 0.998333i \(0.518381\pi\)
\(692\) 0 0
\(693\) 0.0645508i 0.00245208i
\(694\) 0 0
\(695\) 8.82611 44.7895i 0.334793 1.69896i
\(696\) 0 0
\(697\) 6.93252i 0.262588i
\(698\) 0 0
\(699\) 19.4586 0.735990
\(700\) 0 0
\(701\) 35.2234 1.33037 0.665186 0.746678i \(-0.268352\pi\)
0.665186 + 0.746678i \(0.268352\pi\)
\(702\) 0 0
\(703\) 38.3265i 1.44551i
\(704\) 0 0
\(705\) 4.47689 22.7187i 0.168609 0.855634i
\(706\) 0 0
\(707\) 9.64015i 0.362555i
\(708\) 0 0
\(709\) −28.7187 −1.07855 −0.539276 0.842129i \(-0.681302\pi\)
−0.539276 + 0.842129i \(0.681302\pi\)
\(710\) 0 0
\(711\) −0.584735 −0.0219293
\(712\) 0 0
\(713\) 28.0558i 1.05070i
\(714\) 0 0
\(715\) 7.54333 + 1.48647i 0.282104 + 0.0555908i
\(716\) 0 0
\(717\) 35.4942i 1.32555i
\(718\) 0 0
\(719\) 8.60599 0.320949 0.160475 0.987040i \(-0.448698\pi\)
0.160475 + 0.987040i \(0.448698\pi\)
\(720\) 0 0
\(721\) −0.626198 −0.0233208
\(722\) 0 0
\(723\) 6.56934i 0.244316i
\(724\) 0 0
\(725\) −36.4479 14.9450i −1.35364 0.555045i
\(726\) 0 0
\(727\) 15.2803i 0.566715i −0.959014 0.283358i \(-0.908552\pi\)
0.959014 0.283358i \(-0.0914483\pi\)
\(728\) 0 0
\(729\) −26.0096 −0.963318
\(730\) 0 0
\(731\) 1.55102 0.0573666
\(732\) 0 0
\(733\) 46.0235i 1.69992i 0.526849 + 0.849959i \(0.323373\pi\)
−0.526849 + 0.849959i \(0.676627\pi\)
\(734\) 0 0
\(735\) 3.86464 + 0.761557i 0.142549 + 0.0280905i
\(736\) 0 0
\(737\) 3.62809i 0.133642i
\(738\) 0 0
\(739\) −46.3467 −1.70489 −0.852446 0.522815i \(-0.824882\pi\)
−0.852446 + 0.522815i \(0.824882\pi\)
\(740\) 0 0
\(741\) 61.7851 2.26973
\(742\) 0 0
\(743\) 10.7755i 0.395315i −0.980271 0.197658i \(-0.936667\pi\)
0.980271 0.197658i \(-0.0633334\pi\)
\(744\) 0 0
\(745\) 7.36943 37.3973i 0.269995 1.37013i
\(746\) 0 0
\(747\) 1.79716i 0.0657546i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 2.76781 0.100999 0.0504995 0.998724i \(-0.483919\pi\)
0.0504995 + 0.998724i \(0.483919\pi\)
\(752\) 0 0
\(753\) 37.8709i 1.38009i
\(754\) 0 0
\(755\) 1.25240 6.35548i 0.0455794 0.231300i
\(756\) 0 0
\(757\) 14.8401i 0.539371i 0.962948 + 0.269686i \(0.0869198\pi\)
−0.962948 + 0.269686i \(0.913080\pi\)
\(758\) 0 0
\(759\) −4.11371 −0.149318
\(760\) 0 0
\(761\) 31.3169 1.13524 0.567619 0.823291i \(-0.307865\pi\)
0.567619 + 0.823291i \(0.307865\pi\)
\(762\) 0 0
\(763\) 18.9248i 0.685125i
\(764\) 0 0
\(765\) −0.202840 0.0399712i −0.00733371 0.00144516i
\(766\) 0 0
\(767\) 3.26113i 0.117753i
\(768\) 0 0
\(769\) −8.92586 −0.321875 −0.160937 0.986965i \(-0.551452\pi\)
−0.160937 + 0.986965i \(0.551452\pi\)
\(770\) 0 0
\(771\) 7.52311 0.270938
\(772\) 0 0
\(773\) 36.7711i 1.32257i −0.750136 0.661283i \(-0.770012\pi\)
0.750136 0.661283i \(-0.229988\pi\)
\(774\) 0 0
\(775\) −34.8034 14.2707i −1.25018 0.512619i
\(776\) 0 0
\(777\) 10.5693i 0.379173i
\(778\) 0 0
\(779\) −49.3728 −1.76896
\(780\) 0 0
\(781\) −3.45856 −0.123757
\(782\) 0 0
\(783\) 40.2051i 1.43681i
\(784\) 0 0
\(785\) 22.1955 + 4.37380i 0.792193 + 0.156108i
\(786\) 0 0
\(787\) 6.53707i 0.233021i 0.993189 + 0.116511i \(0.0371709\pi\)
−0.993189 + 0.116511i \(0.962829\pi\)
\(788\) 0 0
\(789\) 20.1849 0.718602
\(790\) 0 0
\(791\) −1.04623 −0.0371996
\(792\) 0 0
\(793\) 39.1791i 1.39129i
\(794\) 0 0
\(795\) 5.15994 26.1849i 0.183004 0.928683i
\(796\) 0 0
\(797\) 7.82611i 0.277215i 0.990347 + 0.138607i \(0.0442626\pi\)
−0.990347 + 0.138607i \(0.955737\pi\)
\(798\) 0 0
\(799\) −5.27261 −0.186531
\(800\) 0 0
\(801\) 1.47396 0.0520796
\(802\) 0 0