Properties

Label 2240.2.g.o.449.8
Level $2240$
Weight $2$
Character 2240.449
Analytic conductor $17.886$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2240.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.8864900528\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 13 x^{8} + 56 x^{6} + 97 x^{4} + 61 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 1120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 449.8
Root \(-2.52064i\) of defining polynomial
Character \(\chi\) \(=\) 2240.449
Dual form 2240.2.g.o.449.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.83297i q^{3} +(-1.86302 + 1.23660i) q^{5} -1.00000i q^{7} -0.359777 q^{9} +O(q^{10})\) \(q+1.83297i q^{3} +(-1.86302 + 1.23660i) q^{5} -1.00000i q^{7} -0.359777 q^{9} +4.40105 q^{11} +3.20830i q^{13} +(-2.26664 - 3.41485i) q^{15} -1.14821i q^{17} +1.72603 q^{19} +1.83297 q^{21} +3.25284i q^{23} +(1.94166 - 4.60760i) q^{25} +4.83945i q^{27} +4.18948 q^{29} -1.36952 q^{31} +8.06699i q^{33} +(1.23660 + 1.86302i) q^{35} +4.19923i q^{37} -5.88072 q^{39} +11.7485 q^{41} +2.64997i q^{43} +(0.670270 - 0.444899i) q^{45} -0.106937i q^{47} -1.00000 q^{49} +2.10463 q^{51} -7.86516i q^{53} +(-8.19923 + 5.44232i) q^{55} +3.16376i q^{57} -13.3029 q^{59} +10.0224 q^{61} +0.359777i q^{63} +(-3.96737 - 5.97712i) q^{65} +1.28045i q^{67} -5.96236 q^{69} -14.1616 q^{71} +11.8652i q^{73} +(8.44559 + 3.55900i) q^{75} -4.40105i q^{77} +5.48227 q^{79} -9.94989 q^{81} +17.1586i q^{83} +(1.41987 + 2.13913i) q^{85} +7.67919i q^{87} -4.31591 q^{89} +3.20830 q^{91} -2.51029i q^{93} +(-3.21563 + 2.13441i) q^{95} -7.65389i q^{97} -1.58340 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{5} - 14q^{9} + O(q^{10}) \) \( 10q + 2q^{5} - 14q^{9} + 8q^{11} - 4q^{15} - 24q^{19} + 4q^{21} + 6q^{25} - 24q^{29} - 24q^{31} + 64q^{39} - 4q^{41} - 10q^{45} - 10q^{49} + 24q^{51} - 16q^{55} - 32q^{59} + 20q^{61} - 8q^{65} + 8q^{69} - 8q^{71} + 64q^{75} + 64q^{79} + 2q^{81} + 12q^{85} - 4q^{89} - 60q^{95} - 80q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).

\(n\) \(897\) \(1471\) \(1541\) \(1921\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(3\) 1.83297i 1.05827i 0.848539 + 0.529133i \(0.177483\pi\)
−0.848539 + 0.529133i \(0.822517\pi\)
\(4\) 0 0
\(5\) −1.86302 + 1.23660i −0.833166 + 0.553023i
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) −0.359777 −0.119926
\(10\) 0 0
\(11\) 4.40105 1.32697 0.663483 0.748191i \(-0.269077\pi\)
0.663483 + 0.748191i \(0.269077\pi\)
\(12\) 0 0
\(13\) 3.20830i 0.889823i 0.895575 + 0.444911i \(0.146765\pi\)
−0.895575 + 0.444911i \(0.853235\pi\)
\(14\) 0 0
\(15\) −2.26664 3.41485i −0.585245 0.881711i
\(16\) 0 0
\(17\) 1.14821i 0.278482i −0.990259 0.139241i \(-0.955534\pi\)
0.990259 0.139241i \(-0.0444662\pi\)
\(18\) 0 0
\(19\) 1.72603 0.395979 0.197990 0.980204i \(-0.436559\pi\)
0.197990 + 0.980204i \(0.436559\pi\)
\(20\) 0 0
\(21\) 1.83297 0.399987
\(22\) 0 0
\(23\) 3.25284i 0.678264i 0.940739 + 0.339132i \(0.110133\pi\)
−0.940739 + 0.339132i \(0.889867\pi\)
\(24\) 0 0
\(25\) 1.94166 4.60760i 0.388332 0.921520i
\(26\) 0 0
\(27\) 4.83945i 0.931352i
\(28\) 0 0
\(29\) 4.18948 0.777967 0.388983 0.921245i \(-0.372826\pi\)
0.388983 + 0.921245i \(0.372826\pi\)
\(30\) 0 0
\(31\) −1.36952 −0.245973 −0.122987 0.992408i \(-0.539247\pi\)
−0.122987 + 0.992408i \(0.539247\pi\)
\(32\) 0 0
\(33\) 8.06699i 1.40428i
\(34\) 0 0
\(35\) 1.23660 + 1.86302i 0.209023 + 0.314907i
\(36\) 0 0
\(37\) 4.19923i 0.690348i 0.938539 + 0.345174i \(0.112180\pi\)
−0.938539 + 0.345174i \(0.887820\pi\)
\(38\) 0 0
\(39\) −5.88072 −0.941669
\(40\) 0 0
\(41\) 11.7485 1.83480 0.917402 0.397961i \(-0.130282\pi\)
0.917402 + 0.397961i \(0.130282\pi\)
\(42\) 0 0
\(43\) 2.64997i 0.404116i 0.979374 + 0.202058i \(0.0647630\pi\)
−0.979374 + 0.202058i \(0.935237\pi\)
\(44\) 0 0
\(45\) 0.670270 0.444899i 0.0999180 0.0663216i
\(46\) 0 0
\(47\) 0.106937i 0.0155983i −0.999970 0.00779917i \(-0.997517\pi\)
0.999970 0.00779917i \(-0.00248258\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 2.10463 0.294707
\(52\) 0 0
\(53\) 7.86516i 1.08036i −0.841548 0.540182i \(-0.818356\pi\)
0.841548 0.540182i \(-0.181644\pi\)
\(54\) 0 0
\(55\) −8.19923 + 5.44232i −1.10558 + 0.733842i
\(56\) 0 0
\(57\) 3.16376i 0.419051i
\(58\) 0 0
\(59\) −13.3029 −1.73189 −0.865945 0.500140i \(-0.833282\pi\)
−0.865945 + 0.500140i \(0.833282\pi\)
\(60\) 0 0
\(61\) 10.0224 1.28324 0.641622 0.767021i \(-0.278262\pi\)
0.641622 + 0.767021i \(0.278262\pi\)
\(62\) 0 0
\(63\) 0.359777i 0.0453276i
\(64\) 0 0
\(65\) −3.96737 5.97712i −0.492092 0.741370i
\(66\) 0 0
\(67\) 1.28045i 0.156431i 0.996936 + 0.0782157i \(0.0249223\pi\)
−0.996936 + 0.0782157i \(0.975078\pi\)
\(68\) 0 0
\(69\) −5.96236 −0.717783
\(70\) 0 0
\(71\) −14.1616 −1.68067 −0.840335 0.542067i \(-0.817642\pi\)
−0.840335 + 0.542067i \(0.817642\pi\)
\(72\) 0 0
\(73\) 11.8652i 1.38871i 0.719631 + 0.694356i \(0.244311\pi\)
−0.719631 + 0.694356i \(0.755689\pi\)
\(74\) 0 0
\(75\) 8.44559 + 3.55900i 0.975212 + 0.410958i
\(76\) 0 0
\(77\) 4.40105i 0.501546i
\(78\) 0 0
\(79\) 5.48227 0.616804 0.308402 0.951256i \(-0.400206\pi\)
0.308402 + 0.951256i \(0.400206\pi\)
\(80\) 0 0
\(81\) −9.94989 −1.10554
\(82\) 0 0
\(83\) 17.1586i 1.88340i 0.336451 + 0.941701i \(0.390773\pi\)
−0.336451 + 0.941701i \(0.609227\pi\)
\(84\) 0 0
\(85\) 1.41987 + 2.13913i 0.154007 + 0.232021i
\(86\) 0 0
\(87\) 7.67919i 0.823296i
\(88\) 0 0
\(89\) −4.31591 −0.457485 −0.228743 0.973487i \(-0.573461\pi\)
−0.228743 + 0.973487i \(0.573461\pi\)
\(90\) 0 0
\(91\) 3.20830 0.336321
\(92\) 0 0
\(93\) 2.51029i 0.260305i
\(94\) 0 0
\(95\) −3.21563 + 2.13441i −0.329916 + 0.218985i
\(96\) 0 0
\(97\) 7.65389i 0.777135i −0.921420 0.388567i \(-0.872970\pi\)
0.921420 0.388567i \(-0.127030\pi\)
\(98\) 0 0
\(99\) −1.58340 −0.159137
\(100\) 0 0
\(101\) 2.25581 0.224462 0.112231 0.993682i \(-0.464200\pi\)
0.112231 + 0.993682i \(0.464200\pi\)
\(102\) 0 0
\(103\) 6.61262i 0.651560i 0.945446 + 0.325780i \(0.105627\pi\)
−0.945446 + 0.325780i \(0.894373\pi\)
\(104\) 0 0
\(105\) −3.41485 + 2.26664i −0.333255 + 0.221202i
\(106\) 0 0
\(107\) 5.83756i 0.564338i 0.959365 + 0.282169i \(0.0910539\pi\)
−0.959365 + 0.282169i \(0.908946\pi\)
\(108\) 0 0
\(109\) −10.6952 −1.02441 −0.512205 0.858863i \(-0.671171\pi\)
−0.512205 + 0.858863i \(0.671171\pi\)
\(110\) 0 0
\(111\) −7.69705 −0.730572
\(112\) 0 0
\(113\) 0.867348i 0.0815932i −0.999167 0.0407966i \(-0.987010\pi\)
0.999167 0.0407966i \(-0.0129896\pi\)
\(114\) 0 0
\(115\) −4.02245 6.06009i −0.375095 0.565107i
\(116\) 0 0
\(117\) 1.15427i 0.106713i
\(118\) 0 0
\(119\) −1.14821 −0.105256
\(120\) 0 0
\(121\) 8.36923 0.760839
\(122\) 0 0
\(123\) 21.5346i 1.94171i
\(124\) 0 0
\(125\) 2.08040 + 10.9851i 0.186076 + 0.982535i
\(126\) 0 0
\(127\) 14.6158i 1.29695i −0.761238 0.648473i \(-0.775408\pi\)
0.761238 0.648473i \(-0.224592\pi\)
\(128\) 0 0
\(129\) −4.85731 −0.427662
\(130\) 0 0
\(131\) −17.8600 −1.56044 −0.780218 0.625508i \(-0.784892\pi\)
−0.780218 + 0.625508i \(0.784892\pi\)
\(132\) 0 0
\(133\) 1.72603i 0.149666i
\(134\) 0 0
\(135\) −5.98444 9.01597i −0.515059 0.775971i
\(136\) 0 0
\(137\) 5.22523i 0.446422i 0.974770 + 0.223211i \(0.0716539\pi\)
−0.974770 + 0.223211i \(0.928346\pi\)
\(138\) 0 0
\(139\) −5.25800 −0.445977 −0.222989 0.974821i \(-0.571581\pi\)
−0.222989 + 0.974821i \(0.571581\pi\)
\(140\) 0 0
\(141\) 0.196012 0.0165072
\(142\) 0 0
\(143\) 14.1199i 1.18076i
\(144\) 0 0
\(145\) −7.80507 + 5.18070i −0.648176 + 0.430233i
\(146\) 0 0
\(147\) 1.83297i 0.151181i
\(148\) 0 0
\(149\) −11.8928 −0.974294 −0.487147 0.873320i \(-0.661962\pi\)
−0.487147 + 0.873320i \(0.661962\pi\)
\(150\) 0 0
\(151\) −8.54534 −0.695410 −0.347705 0.937604i \(-0.613039\pi\)
−0.347705 + 0.937604i \(0.613039\pi\)
\(152\) 0 0
\(153\) 0.413099i 0.0333971i
\(154\) 0 0
\(155\) 2.55144 1.69355i 0.204937 0.136029i
\(156\) 0 0
\(157\) 3.36436i 0.268506i −0.990947 0.134253i \(-0.957137\pi\)
0.990947 0.134253i \(-0.0428634\pi\)
\(158\) 0 0
\(159\) 14.4166 1.14331
\(160\) 0 0
\(161\) 3.25284 0.256360
\(162\) 0 0
\(163\) 15.8310i 1.23998i −0.784609 0.619991i \(-0.787136\pi\)
0.784609 0.619991i \(-0.212864\pi\)
\(164\) 0 0
\(165\) −9.97561 15.0289i −0.776600 1.17000i
\(166\) 0 0
\(167\) 20.8843i 1.61608i 0.589128 + 0.808040i \(0.299471\pi\)
−0.589128 + 0.808040i \(0.700529\pi\)
\(168\) 0 0
\(169\) 2.70680 0.208215
\(170\) 0 0
\(171\) −0.620986 −0.0474880
\(172\) 0 0
\(173\) 5.94735i 0.452168i −0.974108 0.226084i \(-0.927408\pi\)
0.974108 0.226084i \(-0.0725924\pi\)
\(174\) 0 0
\(175\) −4.60760 1.94166i −0.348302 0.146776i
\(176\) 0 0
\(177\) 24.3838i 1.83280i
\(178\) 0 0
\(179\) −22.9041 −1.71194 −0.855968 0.517030i \(-0.827038\pi\)
−0.855968 + 0.517030i \(0.827038\pi\)
\(180\) 0 0
\(181\) 1.77746 0.132118 0.0660589 0.997816i \(-0.478957\pi\)
0.0660589 + 0.997816i \(0.478957\pi\)
\(182\) 0 0
\(183\) 18.3708i 1.35801i
\(184\) 0 0
\(185\) −5.19275 7.82322i −0.381778 0.575175i
\(186\) 0 0
\(187\) 5.05332i 0.369536i
\(188\) 0 0
\(189\) 4.83945 0.352018
\(190\) 0 0
\(191\) 19.7183 1.42676 0.713382 0.700775i \(-0.247162\pi\)
0.713382 + 0.700775i \(0.247162\pi\)
\(192\) 0 0
\(193\) 18.4956i 1.33135i −0.746244 0.665673i \(-0.768145\pi\)
0.746244 0.665673i \(-0.231855\pi\)
\(194\) 0 0
\(195\) 10.9559 7.27208i 0.784567 0.520764i
\(196\) 0 0
\(197\) 19.4179i 1.38347i 0.722151 + 0.691735i \(0.243153\pi\)
−0.722151 + 0.691735i \(0.756847\pi\)
\(198\) 0 0
\(199\) 21.7485 1.54171 0.770855 0.637011i \(-0.219830\pi\)
0.770855 + 0.637011i \(0.219830\pi\)
\(200\) 0 0
\(201\) −2.34702 −0.165546
\(202\) 0 0
\(203\) 4.18948i 0.294044i
\(204\) 0 0
\(205\) −21.8876 + 14.5281i −1.52870 + 1.01469i
\(206\) 0 0
\(207\) 1.17030i 0.0813412i
\(208\) 0 0
\(209\) 7.59635 0.525451
\(210\) 0 0
\(211\) 23.2091 1.59778 0.798890 0.601477i \(-0.205421\pi\)
0.798890 + 0.601477i \(0.205421\pi\)
\(212\) 0 0
\(213\) 25.9577i 1.77860i
\(214\) 0 0
\(215\) −3.27694 4.93693i −0.223485 0.336696i
\(216\) 0 0
\(217\) 1.36952i 0.0929692i
\(218\) 0 0
\(219\) −21.7485 −1.46963
\(220\) 0 0
\(221\) 3.68380 0.247799
\(222\) 0 0
\(223\) 0.784235i 0.0525163i −0.999655 0.0262581i \(-0.991641\pi\)
0.999655 0.0262581i \(-0.00835919\pi\)
\(224\) 0 0
\(225\) −0.698564 + 1.65771i −0.0465709 + 0.110514i
\(226\) 0 0
\(227\) 11.7257i 0.778265i −0.921182 0.389132i \(-0.872775\pi\)
0.921182 0.389132i \(-0.127225\pi\)
\(228\) 0 0
\(229\) −1.09555 −0.0723962 −0.0361981 0.999345i \(-0.511525\pi\)
−0.0361981 + 0.999345i \(0.511525\pi\)
\(230\) 0 0
\(231\) 8.06699 0.530769
\(232\) 0 0
\(233\) 25.3345i 1.65972i −0.557972 0.829860i \(-0.688420\pi\)
0.557972 0.829860i \(-0.311580\pi\)
\(234\) 0 0
\(235\) 0.132238 + 0.199225i 0.00862624 + 0.0129960i
\(236\) 0 0
\(237\) 10.0488i 0.652742i
\(238\) 0 0
\(239\) 28.8886 1.86865 0.934323 0.356427i \(-0.116005\pi\)
0.934323 + 0.356427i \(0.116005\pi\)
\(240\) 0 0
\(241\) 10.2542 0.660529 0.330264 0.943888i \(-0.392862\pi\)
0.330264 + 0.943888i \(0.392862\pi\)
\(242\) 0 0
\(243\) 3.71950i 0.238606i
\(244\) 0 0
\(245\) 1.86302 1.23660i 0.119024 0.0790032i
\(246\) 0 0
\(247\) 5.53763i 0.352351i
\(248\) 0 0
\(249\) −31.4512 −1.99314
\(250\) 0 0
\(251\) −27.5389 −1.73824 −0.869120 0.494601i \(-0.835314\pi\)
−0.869120 + 0.494601i \(0.835314\pi\)
\(252\) 0 0
\(253\) 14.3159i 0.900033i
\(254\) 0 0
\(255\) −3.92096 + 2.60258i −0.245540 + 0.162980i
\(256\) 0 0
\(257\) 12.2636i 0.764983i 0.923959 + 0.382492i \(0.124934\pi\)
−0.923959 + 0.382492i \(0.875066\pi\)
\(258\) 0 0
\(259\) 4.19923 0.260927
\(260\) 0 0
\(261\) −1.50728 −0.0932982
\(262\) 0 0
\(263\) 17.8928i 1.10332i 0.834071 + 0.551658i \(0.186005\pi\)
−0.834071 + 0.551658i \(0.813995\pi\)
\(264\) 0 0
\(265\) 9.72603 + 14.6529i 0.597465 + 0.900122i
\(266\) 0 0
\(267\) 7.91092i 0.484141i
\(268\) 0 0
\(269\) 25.2295 1.53827 0.769136 0.639085i \(-0.220687\pi\)
0.769136 + 0.639085i \(0.220687\pi\)
\(270\) 0 0
\(271\) −9.65999 −0.586803 −0.293401 0.955989i \(-0.594787\pi\)
−0.293401 + 0.955989i \(0.594787\pi\)
\(272\) 0 0
\(273\) 5.88072i 0.355917i
\(274\) 0 0
\(275\) 8.54534 20.2783i 0.515303 1.22283i
\(276\) 0 0
\(277\) 23.1970i 1.39378i −0.717180 0.696888i \(-0.754568\pi\)
0.717180 0.696888i \(-0.245432\pi\)
\(278\) 0 0
\(279\) 0.492722 0.0294985
\(280\) 0 0
\(281\) 26.9734 1.60910 0.804550 0.593885i \(-0.202407\pi\)
0.804550 + 0.593885i \(0.202407\pi\)
\(282\) 0 0
\(283\) 22.2119i 1.32036i 0.751106 + 0.660181i \(0.229520\pi\)
−0.751106 + 0.660181i \(0.770480\pi\)
\(284\) 0 0
\(285\) −3.91230 5.89415i −0.231745 0.349139i
\(286\) 0 0
\(287\) 11.7485i 0.693491i
\(288\) 0 0
\(289\) 15.6816 0.922448
\(290\) 0 0
\(291\) 14.0293 0.822415
\(292\) 0 0
\(293\) 20.8756i 1.21956i 0.792569 + 0.609782i \(0.208743\pi\)
−0.792569 + 0.609782i \(0.791257\pi\)
\(294\) 0 0
\(295\) 24.7835 16.4503i 1.44295 0.957774i
\(296\) 0 0
\(297\) 21.2986i 1.23587i
\(298\) 0 0
\(299\) −10.4361 −0.603535
\(300\) 0 0
\(301\) 2.64997 0.152742
\(302\) 0 0
\(303\) 4.13484i 0.237540i
\(304\) 0 0
\(305\) −18.6720 + 12.3937i −1.06915 + 0.709663i
\(306\) 0 0
\(307\) 2.97374i 0.169720i 0.996393 + 0.0848601i \(0.0270443\pi\)
−0.996393 + 0.0848601i \(0.972956\pi\)
\(308\) 0 0
\(309\) −12.1207 −0.689524
\(310\) 0 0
\(311\) −1.04007 −0.0589770 −0.0294885 0.999565i \(-0.509388\pi\)
−0.0294885 + 0.999565i \(0.509388\pi\)
\(312\) 0 0
\(313\) 9.12411i 0.515725i 0.966182 + 0.257863i \(0.0830182\pi\)
−0.966182 + 0.257863i \(0.916982\pi\)
\(314\) 0 0
\(315\) −0.444899 0.670270i −0.0250672 0.0377654i
\(316\) 0 0
\(317\) 4.74255i 0.266368i 0.991091 + 0.133184i \(0.0425201\pi\)
−0.991091 + 0.133184i \(0.957480\pi\)
\(318\) 0 0
\(319\) 18.4381 1.03234
\(320\) 0 0
\(321\) −10.7001 −0.597219
\(322\) 0 0
\(323\) 1.98185i 0.110273i
\(324\) 0 0
\(325\) 14.7826 + 6.22943i 0.819989 + 0.345547i
\(326\) 0 0
\(327\) 19.6039i 1.08410i
\(328\) 0 0
\(329\) −0.106937 −0.00589562
\(330\) 0 0
\(331\) 9.38114 0.515634 0.257817 0.966194i \(-0.416997\pi\)
0.257817 + 0.966194i \(0.416997\pi\)
\(332\) 0 0
\(333\) 1.51078i 0.0827904i
\(334\) 0 0
\(335\) −1.58340 2.38549i −0.0865101 0.130333i
\(336\) 0 0
\(337\) 17.4797i 0.952178i 0.879397 + 0.476089i \(0.157946\pi\)
−0.879397 + 0.476089i \(0.842054\pi\)
\(338\) 0 0
\(339\) 1.58982 0.0863472
\(340\) 0 0
\(341\) −6.02733 −0.326398
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 11.1080 7.37303i 0.598033 0.396950i
\(346\) 0 0
\(347\) 19.2623i 1.03405i −0.855969 0.517027i \(-0.827039\pi\)
0.855969 0.517027i \(-0.172961\pi\)
\(348\) 0 0
\(349\) 28.5730 1.52948 0.764740 0.644339i \(-0.222868\pi\)
0.764740 + 0.644339i \(0.222868\pi\)
\(350\) 0 0
\(351\) −15.5264 −0.828739
\(352\) 0 0
\(353\) 23.8293i 1.26831i 0.773208 + 0.634153i \(0.218651\pi\)
−0.773208 + 0.634153i \(0.781349\pi\)
\(354\) 0 0
\(355\) 26.3833 17.5122i 1.40028 0.929449i
\(356\) 0 0
\(357\) 2.10463i 0.111389i
\(358\) 0 0
\(359\) −2.03194 −0.107242 −0.0536209 0.998561i \(-0.517076\pi\)
−0.0536209 + 0.998561i \(0.517076\pi\)
\(360\) 0 0
\(361\) −16.0208 −0.843201
\(362\) 0 0
\(363\) 15.3405i 0.805170i
\(364\) 0 0
\(365\) −14.6724 22.1050i −0.767989 1.15703i
\(366\) 0 0
\(367\) 22.6965i 1.18475i −0.805663 0.592374i \(-0.798191\pi\)
0.805663 0.592374i \(-0.201809\pi\)
\(368\) 0 0
\(369\) −4.22683 −0.220040
\(370\) 0 0
\(371\) −7.86516 −0.408339
\(372\) 0 0
\(373\) 30.2909i 1.56841i 0.620505 + 0.784203i \(0.286928\pi\)
−0.620505 + 0.784203i \(0.713072\pi\)
\(374\) 0 0
\(375\) −20.1353 + 3.81330i −1.03978 + 0.196918i
\(376\) 0 0
\(377\) 13.4411i 0.692253i
\(378\) 0 0
\(379\) −14.9783 −0.769385 −0.384692 0.923045i \(-0.625693\pi\)
−0.384692 + 0.923045i \(0.625693\pi\)
\(380\) 0 0
\(381\) 26.7904 1.37251
\(382\) 0 0
\(383\) 5.37413i 0.274605i 0.990529 + 0.137303i \(0.0438433\pi\)
−0.990529 + 0.137303i \(0.956157\pi\)
\(384\) 0 0
\(385\) 5.44232 + 8.19923i 0.277366 + 0.417871i
\(386\) 0 0
\(387\) 0.953397i 0.0484639i
\(388\) 0 0
\(389\) −2.87331 −0.145683 −0.0728413 0.997344i \(-0.523207\pi\)
−0.0728413 + 0.997344i \(0.523207\pi\)
\(390\) 0 0
\(391\) 3.73494 0.188884
\(392\) 0 0
\(393\) 32.7368i 1.65136i
\(394\) 0 0
\(395\) −10.2136 + 6.77935i −0.513900 + 0.341106i
\(396\) 0 0
\(397\) 24.2887i 1.21901i −0.792781 0.609507i \(-0.791368\pi\)
0.792781 0.609507i \(-0.208632\pi\)
\(398\) 0 0
\(399\) 3.16376 0.158386
\(400\) 0 0
\(401\) 12.7274 0.635575 0.317787 0.948162i \(-0.397060\pi\)
0.317787 + 0.948162i \(0.397060\pi\)
\(402\) 0 0
\(403\) 4.39384i 0.218873i
\(404\) 0 0
\(405\) 18.5368 12.3040i 0.921101 0.611391i
\(406\) 0 0
\(407\) 18.4810i 0.916069i
\(408\) 0 0
\(409\) 10.0455 0.496717 0.248359 0.968668i \(-0.420109\pi\)
0.248359 + 0.968668i \(0.420109\pi\)
\(410\) 0 0
\(411\) −9.57769 −0.472433
\(412\) 0 0
\(413\) 13.3029i 0.654593i
\(414\) 0 0
\(415\) −21.2183 31.9668i −1.04156 1.56919i
\(416\) 0 0
\(417\) 9.63775i 0.471962i
\(418\) 0 0
\(419\) −16.2433 −0.793539 −0.396769 0.917918i \(-0.629869\pi\)
−0.396769 + 0.917918i \(0.629869\pi\)
\(420\) 0 0
\(421\) 31.8066 1.55016 0.775080 0.631863i \(-0.217709\pi\)
0.775080 + 0.631863i \(0.217709\pi\)
\(422\) 0 0
\(423\) 0.0384734i 0.00187064i
\(424\) 0 0
\(425\) −5.29048 2.22943i −0.256626 0.108143i
\(426\) 0 0
\(427\) 10.0224i 0.485020i
\(428\) 0 0
\(429\) −25.8813 −1.24956
\(430\) 0 0
\(431\) 18.8177 0.906414 0.453207 0.891405i \(-0.350280\pi\)
0.453207 + 0.891405i \(0.350280\pi\)
\(432\) 0 0
\(433\) 21.5825i 1.03719i −0.855020 0.518595i \(-0.826455\pi\)
0.855020 0.518595i \(-0.173545\pi\)
\(434\) 0 0
\(435\) −9.49606 14.3065i −0.455301 0.685942i
\(436\) 0 0
\(437\) 5.61451i 0.268578i
\(438\) 0 0
\(439\) −2.69487 −0.128619 −0.0643095 0.997930i \(-0.520484\pi\)
−0.0643095 + 0.997930i \(0.520484\pi\)
\(440\) 0 0
\(441\) 0.359777 0.0171322
\(442\) 0 0
\(443\) 18.5368i 0.880710i 0.897824 + 0.440355i \(0.145147\pi\)
−0.897824 + 0.440355i \(0.854853\pi\)
\(444\) 0 0
\(445\) 8.04060 5.33703i 0.381161 0.253000i
\(446\) 0 0
\(447\) 21.7991i 1.03106i
\(448\) 0 0
\(449\) 12.6816 0.598483 0.299241 0.954177i \(-0.403266\pi\)
0.299241 + 0.954177i \(0.403266\pi\)
\(450\) 0 0
\(451\) 51.7056 2.43472
\(452\) 0 0
\(453\) 15.6633i 0.735928i
\(454\) 0 0
\(455\) −5.97712 + 3.96737i −0.280212 + 0.185993i
\(456\) 0 0
\(457\) 19.5381i 0.913954i −0.889478 0.456977i \(-0.848932\pi\)
0.889478 0.456977i \(-0.151068\pi\)
\(458\) 0 0
\(459\) 5.55670 0.259364
\(460\) 0 0
\(461\) −14.9929 −0.698291 −0.349145 0.937069i \(-0.613528\pi\)
−0.349145 + 0.937069i \(0.613528\pi\)
\(462\) 0 0
\(463\) 24.9309i 1.15864i −0.815102 0.579318i \(-0.803319\pi\)
0.815102 0.579318i \(-0.196681\pi\)
\(464\) 0 0
\(465\) 3.10422 + 4.67671i 0.143955 + 0.216877i
\(466\) 0 0
\(467\) 30.4350i 1.40836i −0.710020 0.704181i \(-0.751314\pi\)
0.710020 0.704181i \(-0.248686\pi\)
\(468\) 0 0
\(469\) 1.28045 0.0591255
\(470\) 0 0
\(471\) 6.16678 0.284150
\(472\) 0 0
\(473\) 11.6626i 0.536249i
\(474\) 0 0
\(475\) 3.35137 7.95286i 0.153771 0.364902i
\(476\) 0 0
\(477\) 2.82970i 0.129563i
\(478\) 0 0
\(479\) −17.9694 −0.821041 −0.410521 0.911851i \(-0.634653\pi\)
−0.410521 + 0.911851i \(0.634653\pi\)
\(480\) 0 0
\(481\) −13.4724 −0.614288
\(482\) 0 0
\(483\) 5.96236i 0.271297i
\(484\) 0 0
\(485\) 9.46477 + 14.2593i 0.429773 + 0.647482i
\(486\) 0 0
\(487\) 9.51295i 0.431073i −0.976496 0.215536i \(-0.930850\pi\)
0.976496 0.215536i \(-0.0691500\pi\)
\(488\) 0 0
\(489\) 29.0178 1.31223
\(490\) 0 0
\(491\) 21.0466 0.949822 0.474911 0.880034i \(-0.342480\pi\)
0.474911 + 0.880034i \(0.342480\pi\)
\(492\) 0 0
\(493\) 4.81040i 0.216649i
\(494\) 0 0
\(495\) 2.94989 1.95802i 0.132588 0.0880065i
\(496\) 0 0
\(497\) 14.1616i 0.635234i
\(498\) 0 0
\(499\) 36.4408 1.63131 0.815656 0.578537i \(-0.196376\pi\)
0.815656 + 0.578537i \(0.196376\pi\)
\(500\) 0 0
\(501\) −38.2804 −1.71024
\(502\) 0 0
\(503\) 32.1783i 1.43476i 0.696681 + 0.717381i \(0.254659\pi\)
−0.696681 + 0.717381i \(0.745341\pi\)
\(504\) 0 0
\(505\) −4.20262 + 2.78953i −0.187014 + 0.124132i
\(506\) 0 0
\(507\) 4.96147i 0.220347i
\(508\) 0 0
\(509\) 2.06604 0.0915756 0.0457878 0.998951i \(-0.485420\pi\)
0.0457878 + 0.998951i \(0.485420\pi\)
\(510\) 0 0
\(511\) 11.8652 0.524884
\(512\) 0 0
\(513\) 8.35305i 0.368796i
\(514\) 0 0
\(515\) −8.17714 12.3194i −0.360328 0.542858i
\(516\) 0 0
\(517\) 0.470634i 0.0206985i
\(518\) 0 0
\(519\) 10.9013 0.478514
\(520\) 0 0
\(521\) −23.0609 −1.01032 −0.505158 0.863027i \(-0.668566\pi\)
−0.505158 + 0.863027i \(0.668566\pi\)
\(522\) 0 0
\(523\) 26.1602i 1.14391i 0.820286 + 0.571953i \(0.193814\pi\)
−0.820286 + 0.571953i \(0.806186\pi\)
\(524\) 0 0
\(525\) 3.55900 8.44559i 0.155328 0.368596i
\(526\) 0 0
\(527\) 1.57250i 0.0684990i
\(528\) 0 0
\(529\) 12.4190 0.539958
\(530\) 0 0
\(531\) 4.78607 0.207698
\(532\) 0 0
\(533\) 37.6927i 1.63265i
\(534\) 0 0
\(535\) −7.21870 10.8755i −0.312092 0.470187i
\(536\) 0 0
\(537\) 41.9826i 1.81168i
\(538\) 0 0
\(539\) −4.40105 −0.189567
\(540\) 0 0
\(541\) −41.2094 −1.77173 −0.885866 0.463941i \(-0.846435\pi\)
−0.885866 + 0.463941i \(0.846435\pi\)
\(542\) 0 0
\(543\) 3.25804i 0.139816i
\(544\) 0 0
\(545\) 19.9253 13.2256i 0.853504 0.566522i
\(546\) 0 0
\(547\) 7.67055i 0.327969i 0.986463 + 0.163985i \(0.0524347\pi\)
−0.986463 + 0.163985i \(0.947565\pi\)
\(548\) 0 0
\(549\) −3.60585 −0.153894
\(550\) 0 0
\(551\) 7.23118 0.308059
\(552\) 0 0
\(553\) 5.48227i 0.233130i
\(554\) 0 0
\(555\) 14.3397 9.51814i 0.608688 0.404023i
\(556\) 0 0
\(557\) 31.8600i 1.34995i −0.737841 0.674975i \(-0.764154\pi\)
0.737841 0.674975i \(-0.235846\pi\)
\(558\) 0 0
\(559\) −8.50190 −0.359592
\(560\) 0 0
\(561\) 9.26258 0.391067
\(562\) 0 0
\(563\) 9.20351i 0.387882i −0.981013 0.193941i \(-0.937873\pi\)
0.981013 0.193941i \(-0.0621270\pi\)
\(564\) 0 0
\(565\) 1.07256 + 1.61588i 0.0451229 + 0.0679807i
\(566\) 0 0
\(567\) 9.94989i 0.417856i
\(568\) 0 0
\(569\) −8.47615 −0.355339 −0.177669 0.984090i \(-0.556856\pi\)
−0.177669 + 0.984090i \(0.556856\pi\)
\(570\) 0 0
\(571\) 13.1245 0.549245 0.274622 0.961552i \(-0.411447\pi\)
0.274622 + 0.961552i \(0.411447\pi\)
\(572\) 0 0
\(573\) 36.1430i 1.50990i
\(574\) 0 0
\(575\) 14.9878 + 6.31591i 0.625034 + 0.263392i
\(576\) 0 0
\(577\) 16.5640i 0.689567i 0.938682 + 0.344783i \(0.112048\pi\)
−0.938682 + 0.344783i \(0.887952\pi\)
\(578\) 0 0
\(579\) 33.9019 1.40892
\(580\) 0 0
\(581\) 17.1586 0.711859
\(582\) 0 0
\(583\) 34.6150i 1.43361i
\(584\) 0 0
\(585\) 1.42737 + 2.15043i 0.0590145 + 0.0889093i
\(586\) 0 0
\(587\) 0.890659i 0.0367614i −0.999831 0.0183807i \(-0.994149\pi\)
0.999831 0.0183807i \(-0.00585109\pi\)
\(588\) 0 0
\(589\) −2.36384 −0.0974003
\(590\) 0 0
\(591\) −35.5925 −1.46408
\(592\) 0 0
\(593\) 8.12654i 0.333717i −0.985981 0.166858i \(-0.946638\pi\)
0.985981 0.166858i \(-0.0533623\pi\)
\(594\) 0 0
\(595\) 2.13913 1.41987i 0.0876958 0.0582090i
\(596\) 0 0
\(597\) 39.8643i 1.63154i
\(598\) 0 0
\(599\) 9.38288 0.383374 0.191687 0.981456i \(-0.438604\pi\)
0.191687 + 0.981456i \(0.438604\pi\)
\(600\) 0 0
\(601\) −5.44289 −0.222020 −0.111010 0.993819i \(-0.535409\pi\)
−0.111010 + 0.993819i \(0.535409\pi\)
\(602\) 0 0
\(603\) 0.460675i 0.0187601i
\(604\) 0 0
\(605\) −15.5920 + 10.3494i −0.633905 + 0.420761i
\(606\) 0 0
\(607\) 36.7479i 1.49155i −0.666197 0.745776i \(-0.732079\pi\)
0.666197 0.745776i \(-0.267921\pi\)
\(608\) 0 0
\(609\) 7.67919 0.311176
\(610\) 0 0
\(611\) 0.343086 0.0138798
\(612\) 0 0
\(613\) 16.8238i 0.679505i 0.940515 + 0.339753i \(0.110343\pi\)
−0.940515 + 0.339753i \(0.889657\pi\)
\(614\) 0 0
\(615\) −26.6296 40.1193i −1.07381 1.61777i
\(616\) 0 0
\(617\) 5.67406i 0.228429i 0.993456 + 0.114214i \(0.0364351\pi\)
−0.993456 + 0.114214i \(0.963565\pi\)
\(618\) 0 0
\(619\) 4.33702 0.174320 0.0871598 0.996194i \(-0.472221\pi\)
0.0871598 + 0.996194i \(0.472221\pi\)
\(620\) 0 0
\(621\) −15.7420 −0.631703
\(622\) 0 0
\(623\) 4.31591i 0.172913i
\(624\) 0 0
\(625\) −17.4599 17.8928i −0.698397 0.715711i
\(626\) 0 0
\(627\) 13.9239i 0.556066i
\(628\) 0 0
\(629\) 4.82159 0.192249
\(630\) 0 0
\(631\) −41.9784 −1.67113 −0.835567 0.549389i \(-0.814860\pi\)
−0.835567 + 0.549389i \(0.814860\pi\)
\(632\) 0 0
\(633\) 42.5416i 1.69088i
\(634\) 0 0
\(635\) 18.0739 + 27.2295i 0.717240 + 1.08057i
\(636\) 0 0
\(637\) 3.20830i 0.127118i
\(638\) 0 0
\(639\) 5.09501 0.201555
\(640\) 0 0
\(641\) −40.4035 −1.59584 −0.797922 0.602761i \(-0.794067\pi\)
−0.797922 + 0.602761i \(0.794067\pi\)
\(642\) 0 0
\(643\) 28.7826i 1.13507i −0.823348 0.567537i \(-0.807896\pi\)
0.823348 0.567537i \(-0.192104\pi\)
\(644\) 0 0
\(645\) 9.04925 6.00653i 0.356314 0.236507i
\(646\) 0 0
\(647\) 50.0475i 1.96757i −0.179346 0.983786i \(-0.557398\pi\)
0.179346 0.983786i \(-0.442602\pi\)
\(648\) 0 0
\(649\) −58.5467 −2.29816
\(650\) 0 0
\(651\) −2.51029 −0.0983861
\(652\) 0 0
\(653\) 39.5622i 1.54819i −0.633070 0.774095i \(-0.718205\pi\)
0.633070 0.774095i \(-0.281795\pi\)
\(654\) 0 0
\(655\) 33.2735 22.0856i 1.30010 0.862957i
\(656\) 0 0
\(657\) 4.26881i 0.166542i
\(658\) 0 0
\(659\) −10.0994 −0.393418 −0.196709 0.980462i \(-0.563025\pi\)
−0.196709 + 0.980462i \(0.563025\pi\)
\(660\) 0 0
\(661\) 4.51434 0.175588 0.0877938 0.996139i \(-0.472018\pi\)
0.0877938 + 0.996139i \(0.472018\pi\)
\(662\) 0 0
\(663\) 6.75229i 0.262237i
\(664\) 0 0
\(665\) 2.13441 + 3.21563i 0.0827687 + 0.124697i
\(666\) 0 0
\(667\) 13.6277i 0.527667i
\(668\) 0 0
\(669\) 1.43748 0.0555762
\(670\) 0 0
\(671\) 44.1093 1.70282
\(672\) 0 0
\(673\) 3.62104i 0.139581i −0.997562 0.0697904i \(-0.977767\pi\)
0.997562 0.0697904i \(-0.0222330\pi\)
\(674\) 0 0
\(675\) 22.2982 + 9.39656i 0.858259 + 0.361674i
\(676\) 0 0
\(677\) 35.1617i 1.35137i −0.737189 0.675687i \(-0.763847\pi\)
0.737189 0.675687i \(-0.236153\pi\)
\(678\) 0 0
\(679\) −7.65389 −0.293729
\(680\) 0 0
\(681\) 21.4929 0.823611
\(682\) 0 0
\(683\) 4.39058i 0.168001i −0.996466 0.0840005i \(-0.973230\pi\)
0.996466 0.0840005i \(-0.0267697\pi\)
\(684\) 0 0
\(685\) −6.46150 9.73470i −0.246881 0.371944i
\(686\) 0 0
\(687\) 2.00812i 0.0766144i
\(688\) 0 0
\(689\) 25.2338 0.961332
\(690\) 0 0
\(691\) −6.28314 −0.239022 −0.119511 0.992833i \(-0.538133\pi\)
−0.119511 + 0.992833i \(0.538133\pi\)
\(692\) 0 0
\(693\) 1.58340i 0.0601482i
\(694\) 0 0
\(695\) 9.79573 6.50202i 0.371573 0.246636i
\(696\) 0 0
\(697\) 13.4897i 0.510959i
\(698\) 0 0
\(699\) 46.4374 1.75642
\(700\) 0 0
\(701\) −5.41413 −0.204489 −0.102244 0.994759i \(-0.532602\pi\)
−0.102244 + 0.994759i \(0.532602\pi\)
\(702\) 0 0
\(703\) 7.24800i 0.273363i
\(704\) 0 0
\(705\) −0.365174 + 0.242388i −0.0137532 + 0.00912885i
\(706\) 0 0
\(707\) 2.25581i 0.0848386i
\(708\) 0 0
\(709\) 15.5284 0.583180 0.291590 0.956543i \(-0.405816\pi\)
0.291590 + 0.956543i \(0.405816\pi\)
\(710\) 0 0
\(711\) −1.97239 −0.0739705
\(712\) 0 0
\(713\) 4.45483i 0.166835i
\(714\) 0 0
\(715\) −17.4606 26.3056i −0.652990 0.983773i
\(716\) 0 0
\(717\) 52.9519i 1.97752i
\(718\) 0 0
\(719\) −19.9304 −0.743279 −0.371640 0.928377i \(-0.621204\pi\)
−0.371640 + 0.928377i \(0.621204\pi\)
\(720\) 0 0
\(721\) 6.61262 0.246267
\(722\) 0 0
\(723\) 18.7956i 0.699015i
\(724\) 0 0
\(725\) 8.13454 19.3034i 0.302109 0.716912i
\(726\) 0 0
\(727\) 24.0839i 0.893222i 0.894728 + 0.446611i \(0.147369\pi\)
−0.894728 + 0.446611i \(0.852631\pi\)
\(728\) 0 0
\(729\) −23.0319 −0.853035
\(730\) 0 0
\(731\) 3.04272 0.112539
\(732\) 0 0
\(733\) 35.8771i 1.32515i −0.748994 0.662576i \(-0.769463\pi\)
0.748994 0.662576i \(-0.230537\pi\)
\(734\) 0 0
\(735\) 2.26664 + 3.41485i 0.0836064 + 0.125959i
\(736\) 0 0
\(737\) 5.63531i 0.207579i
\(738\) 0 0
\(739\) 1.29734 0.0477233 0.0238617 0.999715i \(-0.492404\pi\)
0.0238617 + 0.999715i \(0.492404\pi\)
\(740\) 0 0
\(741\) −10.1503 −0.372881
\(742\) 0 0
\(743\) 8.53790i 0.313225i 0.987660 + 0.156613i \(0.0500574\pi\)
−0.987660 + 0.156613i \(0.949943\pi\)
\(744\) 0 0
\(745\) 22.1564 14.7066i 0.811749 0.538807i
\(746\) 0 0
\(747\) 6.17327i 0.225868i
\(748\) 0 0
\(749\) 5.83756 0.213300
\(750\) 0 0
\(751\) −17.5930 −0.641978 −0.320989 0.947083i \(-0.604015\pi\)
−0.320989 + 0.947083i \(0.604015\pi\)
\(752\) 0 0
\(753\) 50.4780i 1.83952i
\(754\) 0 0
\(755\) 15.9201 10.5671i 0.579392 0.384577i
\(756\) 0 0
\(757\) 33.5195i 1.21829i −0.793061 0.609143i \(-0.791514\pi\)
0.793061 0.609143i \(-0.208486\pi\)
\(758\) 0 0
\(759\) −26.2406 −0.952474
\(760\) 0 0
\(761\) −25.8063 −0.935479 −0.467740 0.883866i \(-0.654931\pi\)
−0.467740 + 0.883866i \(0.654931\pi\)
\(762\) 0 0
\(763\) 10.6952i 0.387191i
\(764\) 0 0
\(765\) −0.510837 0.769610i −0.0184693 0.0278253i
\(766\) 0 0
\(767\) 42.6797i 1.54108i
\(768\) 0 0
\(769\) 27.6616 0.997502 0.498751 0.866745i \(-0.333792\pi\)
0.498751 + 0.866745i \(0.333792\pi\)
\(770\) 0 0
\(771\) −22.4788 −0.809555
\(772\) 0 0
\(773\) 49.4294i 1.77785i −0.458050 0.888927i \(-0.651452\pi\)
0.458050 0.888927i \(-0.348548\pi\)
\(774\) 0 0
\(775\) −2.65914 + 6.31020i −0.0955193 + 0.226669i
\(776\) 0 0
\(777\) 7.69705i 0.276130i
\(778\) 0 0
\(779\) 20.2783 0.726544
\(780\) 0 0
\(781\) −62.3258 −2.23019
\(782\) 0 0
\(783\) 20.2748i 0.724561i
\(784\) 0 0
\(785\) 4.16036 + 6.26787i 0.148490 + 0.223710i
\(786\) 0 0
\(787\) 44.2790i 1.57837i −0.614153 0.789187i \(-0.710502\pi\)
0.614153 0.789187i \(-0.289498\pi\)
\(788\) 0 0
\(789\) −32.7969 −1.16760
\(790\) 0 0
\(791\) −0.867348 −0.0308393
\(792\) 0 0
\(793\) 32.1550i 1.14186i
\(794\) 0 0
\(795\) −26.8584 + 17.8275i −0.952568 + 0.632277i
\(796\) 0 0
\(797\) 17.7589i 0.629052i 0.949249 + 0.314526i \(0.101846\pi\)
−0.949249 + 0.314526i \(0.898154\pi\)
\(798\) 0 0
\(799\) −0.122786 −0.00434385
\(800\) 0 0
\(801\) 1.55276 0.0548642
\(802\) 0 0