Properties

Label 1728.3.q.j.1601.1
Level $1728$
Weight $3$
Character 1728.1601
Analytic conductor $47.085$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1728.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(47.0845896815\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.19269881856.9
Defining polynomial: \( x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1601.1
Root \(-1.41950 + 2.45865i\) of defining polynomial
Character \(\chi\) \(=\) 1728.1601
Dual form 1728.3.q.j.449.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-8.20800 + 4.73889i) q^{5} +(1.05671 - 1.83027i) q^{7} +O(q^{10})\) \(q+(-8.20800 + 4.73889i) q^{5} +(1.05671 - 1.83027i) q^{7} +(13.7064 + 7.91342i) q^{11} +(-4.70337 - 8.14648i) q^{13} -11.6027i q^{17} -12.9707 q^{19} +(5.27427 - 3.04510i) q^{23} +(32.4142 - 56.1431i) q^{25} +(-24.7667 - 14.2991i) q^{29} +(8.75365 + 15.1618i) q^{31} +20.0305i q^{35} +15.6207 q^{37} +(-14.8062 + 8.54836i) q^{41} +(21.7157 - 37.6127i) q^{43} +(-20.6696 - 11.9336i) q^{47} +(22.2667 + 38.5671i) q^{49} +14.1051i q^{53} -150.003 q^{55} +(38.5788 - 22.2735i) q^{59} +(1.86057 - 3.22260i) q^{61} +(77.2105 + 44.5775i) q^{65} +(-21.0090 - 36.3887i) q^{67} +120.440i q^{71} +5.48692 q^{73} +(28.9674 - 16.7243i) q^{77} +(60.5480 - 104.872i) q^{79} +(46.5861 + 26.8965i) q^{83} +(54.9840 + 95.2351i) q^{85} +102.195i q^{89} -19.8803 q^{91} +(106.463 - 61.4667i) q^{95} +(-58.9377 + 102.083i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{5} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 6 q^{5} + 6 q^{7} + 36 q^{11} - 14 q^{13} - 4 q^{19} + 102 q^{23} + 10 q^{25} - 114 q^{29} - 50 q^{31} - 120 q^{37} - 264 q^{41} + 28 q^{43} - 150 q^{47} + 94 q^{49} - 244 q^{55} - 108 q^{59} - 14 q^{61} + 198 q^{65} + 20 q^{67} - 76 q^{73} + 66 q^{77} + 26 q^{79} + 246 q^{83} + 224 q^{85} - 108 q^{91} + 456 q^{95} - 236 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(703\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(5\) −8.20800 + 4.73889i −1.64160 + 0.947779i −0.661336 + 0.750090i \(0.730010\pi\)
−0.980265 + 0.197688i \(0.936657\pi\)
\(6\) 0 0
\(7\) 1.05671 1.83027i 0.150958 0.261467i −0.780622 0.625004i \(-0.785097\pi\)
0.931580 + 0.363537i \(0.118431\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 13.7064 + 7.91342i 1.24604 + 0.719401i 0.970317 0.241836i \(-0.0777495\pi\)
0.275723 + 0.961237i \(0.411083\pi\)
\(12\) 0 0
\(13\) −4.70337 8.14648i −0.361798 0.626652i 0.626459 0.779454i \(-0.284504\pi\)
−0.988257 + 0.152802i \(0.951170\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 11.6027i 0.682513i −0.939970 0.341256i \(-0.889148\pi\)
0.939970 0.341256i \(-0.110852\pi\)
\(18\) 0 0
\(19\) −12.9707 −0.682667 −0.341334 0.939942i \(-0.610879\pi\)
−0.341334 + 0.939942i \(0.610879\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.27427 3.04510i 0.229316 0.132396i −0.380940 0.924600i \(-0.624400\pi\)
0.610256 + 0.792204i \(0.291066\pi\)
\(24\) 0 0
\(25\) 32.4142 56.1431i 1.29657 2.24572i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −24.7667 14.2991i −0.854026 0.493072i 0.00798151 0.999968i \(-0.497459\pi\)
−0.862007 + 0.506896i \(0.830793\pi\)
\(30\) 0 0
\(31\) 8.75365 + 15.1618i 0.282376 + 0.489089i 0.971969 0.235107i \(-0.0755442\pi\)
−0.689594 + 0.724196i \(0.742211\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 20.0305i 0.572299i
\(36\) 0 0
\(37\) 15.6207 0.422181 0.211091 0.977467i \(-0.432298\pi\)
0.211091 + 0.977467i \(0.432298\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −14.8062 + 8.54836i −0.361127 + 0.208497i −0.669575 0.742745i \(-0.733524\pi\)
0.308448 + 0.951241i \(0.400190\pi\)
\(42\) 0 0
\(43\) 21.7157 37.6127i 0.505016 0.874714i −0.494967 0.868912i \(-0.664820\pi\)
0.999983 0.00580217i \(-0.00184690\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −20.6696 11.9336i −0.439778 0.253906i 0.263726 0.964598i \(-0.415049\pi\)
−0.703503 + 0.710692i \(0.748382\pi\)
\(48\) 0 0
\(49\) 22.2667 + 38.5671i 0.454423 + 0.787084i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 14.1051i 0.266134i 0.991107 + 0.133067i \(0.0424825\pi\)
−0.991107 + 0.133067i \(0.957517\pi\)
\(54\) 0 0
\(55\) −150.003 −2.72733
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 38.5788 22.2735i 0.653877 0.377516i −0.136063 0.990700i \(-0.543445\pi\)
0.789940 + 0.613184i \(0.210112\pi\)
\(60\) 0 0
\(61\) 1.86057 3.22260i 0.0305012 0.0528296i −0.850372 0.526182i \(-0.823623\pi\)
0.880873 + 0.473353i \(0.156956\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 77.2105 + 44.5775i 1.18785 + 0.685808i
\(66\) 0 0
\(67\) −21.0090 36.3887i −0.313568 0.543115i 0.665564 0.746340i \(-0.268191\pi\)
−0.979132 + 0.203225i \(0.934858\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 120.440i 1.69634i 0.529724 + 0.848170i \(0.322295\pi\)
−0.529724 + 0.848170i \(0.677705\pi\)
\(72\) 0 0
\(73\) 5.48692 0.0751633 0.0375817 0.999294i \(-0.488035\pi\)
0.0375817 + 0.999294i \(0.488035\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 28.9674 16.7243i 0.376200 0.217199i
\(78\) 0 0
\(79\) 60.5480 104.872i 0.766430 1.32750i −0.173056 0.984912i \(-0.555364\pi\)
0.939487 0.342585i \(-0.111302\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 46.5861 + 26.8965i 0.561279 + 0.324054i 0.753659 0.657266i \(-0.228287\pi\)
−0.192380 + 0.981321i \(0.561621\pi\)
\(84\) 0 0
\(85\) 54.9840 + 95.2351i 0.646871 + 1.12041i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 102.195i 1.14825i 0.818766 + 0.574127i \(0.194658\pi\)
−0.818766 + 0.574127i \(0.805342\pi\)
\(90\) 0 0
\(91\) −19.8803 −0.218465
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 106.463 61.4667i 1.12067 0.647018i
\(96\) 0 0
\(97\) −58.9377 + 102.083i −0.607605 + 1.05240i 0.384029 + 0.923321i \(0.374536\pi\)
−0.991634 + 0.129081i \(0.958797\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 118.181 + 68.2317i 1.17011 + 0.675561i 0.953705 0.300743i \(-0.0972347\pi\)
0.216401 + 0.976304i \(0.430568\pi\)
\(102\) 0 0
\(103\) 60.8511 + 105.397i 0.590787 + 1.02327i 0.994127 + 0.108223i \(0.0345160\pi\)
−0.403340 + 0.915050i \(0.632151\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 82.1437i 0.767698i −0.923396 0.383849i \(-0.874598\pi\)
0.923396 0.383849i \(-0.125402\pi\)
\(108\) 0 0
\(109\) 165.603 1.51929 0.759646 0.650337i \(-0.225372\pi\)
0.759646 + 0.650337i \(0.225372\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −68.7460 + 39.6905i −0.608372 + 0.351244i −0.772328 0.635224i \(-0.780908\pi\)
0.163956 + 0.986468i \(0.447574\pi\)
\(114\) 0 0
\(115\) −28.8608 + 49.9884i −0.250964 + 0.434682i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −21.2361 12.2607i −0.178455 0.103031i
\(120\) 0 0
\(121\) 64.7443 + 112.140i 0.535077 + 0.926781i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 377.485i 3.01988i
\(126\) 0 0
\(127\) 147.235 1.15933 0.579666 0.814854i \(-0.303183\pi\)
0.579666 + 0.814854i \(0.303183\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −145.857 + 84.2103i −1.11341 + 0.642827i −0.939710 0.341972i \(-0.888905\pi\)
−0.173699 + 0.984799i \(0.555572\pi\)
\(132\) 0 0
\(133\) −13.7062 + 23.7398i −0.103054 + 0.178495i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 174.984 + 101.027i 1.27726 + 0.737426i 0.976343 0.216225i \(-0.0693746\pi\)
0.300915 + 0.953651i \(0.402708\pi\)
\(138\) 0 0
\(139\) 129.193 + 223.768i 0.929443 + 1.60984i 0.784255 + 0.620439i \(0.213046\pi\)
0.145189 + 0.989404i \(0.453621\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 148.879i 1.04111i
\(144\) 0 0
\(145\) 271.047 1.86929
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 68.6316 39.6245i 0.460615 0.265936i −0.251688 0.967808i \(-0.580986\pi\)
0.712303 + 0.701872i \(0.247652\pi\)
\(150\) 0 0
\(151\) 4.73094 8.19422i 0.0313307 0.0542664i −0.849935 0.526888i \(-0.823359\pi\)
0.881266 + 0.472621i \(0.156692\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −143.700 82.9652i −0.927096 0.535259i
\(156\) 0 0
\(157\) −34.3561 59.5066i −0.218829 0.379023i 0.735621 0.677393i \(-0.236890\pi\)
−0.954450 + 0.298370i \(0.903557\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 12.8711i 0.0799448i
\(162\) 0 0
\(163\) −209.391 −1.28461 −0.642304 0.766450i \(-0.722021\pi\)
−0.642304 + 0.766450i \(0.722021\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −21.3682 + 12.3369i −0.127953 + 0.0738739i −0.562610 0.826722i \(-0.690203\pi\)
0.434657 + 0.900596i \(0.356870\pi\)
\(168\) 0 0
\(169\) 40.2566 69.7265i 0.238205 0.412583i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 129.186 + 74.5855i 0.746739 + 0.431130i 0.824514 0.565841i \(-0.191448\pi\)
−0.0777754 + 0.996971i \(0.524782\pi\)
\(174\) 0 0
\(175\) −68.5046 118.654i −0.391455 0.678020i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 65.1600i 0.364022i 0.983296 + 0.182011i \(0.0582607\pi\)
−0.983296 + 0.182011i \(0.941739\pi\)
\(180\) 0 0
\(181\) 95.5019 0.527635 0.263817 0.964573i \(-0.415018\pi\)
0.263817 + 0.964573i \(0.415018\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −128.215 + 74.0248i −0.693053 + 0.400134i
\(186\) 0 0
\(187\) 91.8171 159.032i 0.491001 0.850438i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −160.947 92.9225i −0.842652 0.486505i 0.0155129 0.999880i \(-0.495062\pi\)
−0.858165 + 0.513374i \(0.828395\pi\)
\(192\) 0 0
\(193\) −48.1579 83.4119i −0.249523 0.432186i 0.713871 0.700277i \(-0.246940\pi\)
−0.963393 + 0.268091i \(0.913607\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 126.121i 0.640209i −0.947382 0.320105i \(-0.896282\pi\)
0.947382 0.320105i \(-0.103718\pi\)
\(198\) 0 0
\(199\) 131.718 0.661899 0.330950 0.943648i \(-0.392631\pi\)
0.330950 + 0.943648i \(0.392631\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −52.3424 + 30.2199i −0.257844 + 0.148866i
\(204\) 0 0
\(205\) 81.0195 140.330i 0.395217 0.684536i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −177.782 102.642i −0.850631 0.491112i
\(210\) 0 0
\(211\) 5.15331 + 8.92579i 0.0244233 + 0.0423023i 0.877979 0.478700i \(-0.158892\pi\)
−0.853555 + 0.521002i \(0.825558\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 411.634i 1.91457i
\(216\) 0 0
\(217\) 37.0001 0.170508
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −94.5212 + 54.5718i −0.427698 + 0.246931i
\(222\) 0 0
\(223\) −86.4202 + 149.684i −0.387535 + 0.671230i −0.992117 0.125313i \(-0.960007\pi\)
0.604583 + 0.796542i \(0.293340\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −173.974 100.444i −0.766403 0.442483i 0.0651869 0.997873i \(-0.479236\pi\)
−0.831590 + 0.555390i \(0.812569\pi\)
\(228\) 0 0
\(229\) 130.630 + 226.259i 0.570439 + 0.988029i 0.996521 + 0.0833443i \(0.0265601\pi\)
−0.426082 + 0.904684i \(0.640107\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 130.530i 0.560214i 0.959969 + 0.280107i \(0.0903700\pi\)
−0.959969 + 0.280107i \(0.909630\pi\)
\(234\) 0 0
\(235\) 226.208 0.962586
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 231.586 133.706i 0.968981 0.559441i 0.0700553 0.997543i \(-0.477682\pi\)
0.898925 + 0.438102i \(0.144349\pi\)
\(240\) 0 0
\(241\) −50.8188 + 88.0207i −0.210866 + 0.365231i −0.951986 0.306142i \(-0.900962\pi\)
0.741120 + 0.671373i \(0.234295\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −365.531 211.039i −1.49196 0.861385i
\(246\) 0 0
\(247\) 61.0059 + 105.665i 0.246987 + 0.427795i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 137.033i 0.545946i 0.962022 + 0.272973i \(0.0880070\pi\)
−0.962022 + 0.272973i \(0.911993\pi\)
\(252\) 0 0
\(253\) 96.3886 0.380983
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 217.737 125.711i 0.847226 0.489146i −0.0124876 0.999922i \(-0.503975\pi\)
0.859714 + 0.510776i \(0.170642\pi\)
\(258\) 0 0
\(259\) 16.5065 28.5901i 0.0637317 0.110387i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −416.538 240.488i −1.58379 0.914404i −0.994298 0.106633i \(-0.965993\pi\)
−0.589496 0.807771i \(-0.700674\pi\)
\(264\) 0 0
\(265\) −66.8425 115.775i −0.252236 0.436885i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 182.939i 0.680071i −0.940413 0.340036i \(-0.889561\pi\)
0.940413 0.340036i \(-0.110439\pi\)
\(270\) 0 0
\(271\) −31.0146 −0.114445 −0.0572225 0.998361i \(-0.518224\pi\)
−0.0572225 + 0.998361i \(0.518224\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 888.567 513.014i 3.23115 1.86551i
\(276\) 0 0
\(277\) 206.382 357.464i 0.745060 1.29048i −0.205106 0.978740i \(-0.565754\pi\)
0.950167 0.311743i \(-0.100913\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 107.255 + 61.9236i 0.381690 + 0.220369i 0.678553 0.734551i \(-0.262607\pi\)
−0.296863 + 0.954920i \(0.595941\pi\)
\(282\) 0 0
\(283\) 4.23689 + 7.33850i 0.0149713 + 0.0259311i 0.873414 0.486978i \(-0.161901\pi\)
−0.858443 + 0.512910i \(0.828568\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 36.1324i 0.125897i
\(288\) 0 0
\(289\) 154.377 0.534177
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −93.2120 + 53.8160i −0.318130 + 0.183672i −0.650559 0.759456i \(-0.725465\pi\)
0.332429 + 0.943128i \(0.392132\pi\)
\(294\) 0 0
\(295\) −211.103 + 365.641i −0.715604 + 1.23946i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −49.6137 28.6445i −0.165932 0.0958009i
\(300\) 0 0
\(301\) −45.8943 79.4912i −0.152473 0.264090i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 35.2682i 0.115633i
\(306\) 0 0
\(307\) 530.715 1.72871 0.864357 0.502878i \(-0.167726\pi\)
0.864357 + 0.502878i \(0.167726\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −142.535 + 82.2926i −0.458312 + 0.264606i −0.711334 0.702854i \(-0.751909\pi\)
0.253022 + 0.967460i \(0.418575\pi\)
\(312\) 0 0
\(313\) 273.833 474.293i 0.874866 1.51531i 0.0179611 0.999839i \(-0.494283\pi\)
0.856905 0.515474i \(-0.172384\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 67.7106 + 39.0928i 0.213598 + 0.123321i 0.602983 0.797754i \(-0.293979\pi\)
−0.389384 + 0.921075i \(0.627312\pi\)
\(318\) 0 0
\(319\) −226.309 391.979i −0.709433 1.22877i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 150.495i 0.465929i
\(324\) 0 0
\(325\) −609.824 −1.87638
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −43.6833 + 25.2206i −0.132776 + 0.0766583i
\(330\) 0 0
\(331\) −274.898 + 476.137i −0.830507 + 1.43848i 0.0671297 + 0.997744i \(0.478616\pi\)
−0.897637 + 0.440736i \(0.854717\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 344.884 + 199.119i 1.02951 + 0.594385i
\(336\) 0 0
\(337\) 36.8057 + 63.7494i 0.109216 + 0.189167i 0.915453 0.402425i \(-0.131833\pi\)
−0.806237 + 0.591593i \(0.798499\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 277.085i 0.812566i
\(342\) 0 0
\(343\) 197.675 0.576312
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −367.796 + 212.347i −1.05993 + 0.611951i −0.925413 0.378960i \(-0.876282\pi\)
−0.134517 + 0.990911i \(0.542948\pi\)
\(348\) 0 0
\(349\) −267.361 + 463.082i −0.766077 + 1.32688i 0.173599 + 0.984816i \(0.444460\pi\)
−0.939676 + 0.342067i \(0.888873\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 155.165 + 89.5845i 0.439561 + 0.253781i 0.703411 0.710783i \(-0.251659\pi\)
−0.263851 + 0.964564i \(0.584993\pi\)
\(354\) 0 0
\(355\) −570.753 988.573i −1.60775 2.78471i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 351.534i 0.979204i −0.871946 0.489602i \(-0.837142\pi\)
0.871946 0.489602i \(-0.162858\pi\)
\(360\) 0 0
\(361\) −192.761 −0.533965
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −45.0367 + 26.0019i −0.123388 + 0.0712382i
\(366\) 0 0
\(367\) 41.9855 72.7210i 0.114402 0.198150i −0.803139 0.595792i \(-0.796838\pi\)
0.917541 + 0.397642i \(0.130171\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 25.8161 + 14.9050i 0.0695853 + 0.0401751i
\(372\) 0 0
\(373\) 218.337 + 378.171i 0.585354 + 1.01386i 0.994831 + 0.101543i \(0.0323779\pi\)
−0.409477 + 0.912320i \(0.634289\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 269.016i 0.713569i
\(378\) 0 0
\(379\) −273.455 −0.721516 −0.360758 0.932659i \(-0.617482\pi\)
−0.360758 + 0.932659i \(0.617482\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 192.544 111.166i 0.502727 0.290249i −0.227112 0.973869i \(-0.572928\pi\)
0.729839 + 0.683619i \(0.239595\pi\)
\(384\) 0 0
\(385\) −158.510 + 274.547i −0.411713 + 0.713108i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 522.471 + 301.649i 1.34311 + 0.775447i 0.987263 0.159096i \(-0.0508578\pi\)
0.355851 + 0.934543i \(0.384191\pi\)
\(390\) 0 0
\(391\) −35.3314 61.1958i −0.0903617 0.156511i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1147.72i 2.90563i
\(396\) 0 0
\(397\) 138.804 0.349633 0.174816 0.984601i \(-0.444067\pi\)
0.174816 + 0.984601i \(0.444067\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 281.903 162.757i 0.702999 0.405877i −0.105464 0.994423i \(-0.533633\pi\)
0.808464 + 0.588546i \(0.200300\pi\)
\(402\) 0 0
\(403\) 82.3433 142.623i 0.204326 0.353903i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 214.104 + 123.613i 0.526055 + 0.303718i
\(408\) 0 0
\(409\) 257.442 + 445.903i 0.629443 + 1.09023i 0.987664 + 0.156591i \(0.0500504\pi\)
−0.358220 + 0.933637i \(0.616616\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 94.1461i 0.227957i
\(414\) 0 0
\(415\) −509.839 −1.22853
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 107.340 61.9726i 0.256181 0.147906i −0.366410 0.930453i \(-0.619413\pi\)
0.622591 + 0.782547i \(0.286080\pi\)
\(420\) 0 0
\(421\) −255.924 + 443.273i −0.607895 + 1.05291i 0.383691 + 0.923461i \(0.374653\pi\)
−0.991587 + 0.129444i \(0.958681\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −651.412 376.093i −1.53273 0.884924i
\(426\) 0 0
\(427\) −3.93216 6.81070i −0.00920880 0.0159501i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 650.840i 1.51007i 0.655684 + 0.755035i \(0.272380\pi\)
−0.655684 + 0.755035i \(0.727620\pi\)
\(432\) 0 0
\(433\) −432.455 −0.998742 −0.499371 0.866388i \(-0.666435\pi\)
−0.499371 + 0.866388i \(0.666435\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −68.4108 + 39.4970i −0.156547 + 0.0903822i
\(438\) 0 0
\(439\) 190.663 330.238i 0.434312 0.752251i −0.562927 0.826507i \(-0.690325\pi\)
0.997239 + 0.0742559i \(0.0236582\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −33.3781 19.2708i −0.0753455 0.0435007i 0.461854 0.886956i \(-0.347184\pi\)
−0.537199 + 0.843455i \(0.680518\pi\)
\(444\) 0 0
\(445\) −484.289 838.813i −1.08829 1.88497i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 373.577i 0.832019i −0.909360 0.416010i \(-0.863428\pi\)
0.909360 0.416010i \(-0.136572\pi\)
\(450\) 0 0
\(451\) −270.587 −0.599971
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 163.178 94.2108i 0.358633 0.207057i
\(456\) 0 0
\(457\) −121.482 + 210.414i −0.265826 + 0.460423i −0.967780 0.251799i \(-0.918978\pi\)
0.701954 + 0.712222i \(0.252311\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −116.211 67.0942i −0.252084 0.145541i 0.368634 0.929574i \(-0.379825\pi\)
−0.620718 + 0.784034i \(0.713159\pi\)
\(462\) 0 0
\(463\) −155.129 268.691i −0.335051 0.580326i 0.648443 0.761263i \(-0.275420\pi\)
−0.983495 + 0.180937i \(0.942087\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 765.680i 1.63957i −0.572670 0.819786i \(-0.694092\pi\)
0.572670 0.819786i \(-0.305908\pi\)
\(468\) 0 0
\(469\) −88.8015 −0.189342
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 595.290 343.691i 1.25854 0.726619i
\(474\) 0 0
\(475\) −420.434 + 728.214i −0.885125 + 1.53308i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −442.124 255.260i −0.923014 0.532902i −0.0384186 0.999262i \(-0.512232\pi\)
−0.884595 + 0.466359i \(0.845565\pi\)
\(480\) 0 0
\(481\) −73.4699 127.254i −0.152744 0.264561i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1117.20i 2.30350i
\(486\) 0 0
\(487\) 669.532 1.37481 0.687405 0.726274i \(-0.258750\pi\)
0.687405 + 0.726274i \(0.258750\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 640.537 369.814i 1.30456 0.753186i 0.323375 0.946271i \(-0.395183\pi\)
0.981182 + 0.193085i \(0.0618492\pi\)
\(492\) 0 0
\(493\) −165.908 + 287.361i −0.336528 + 0.582883i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 220.438 + 127.270i 0.443537 + 0.256076i
\(498\) 0 0
\(499\) 461.405 + 799.176i 0.924659 + 1.60156i 0.792109 + 0.610380i \(0.208983\pi\)
0.132550 + 0.991176i \(0.457684\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 223.098i 0.443534i 0.975100 + 0.221767i \(0.0711824\pi\)
−0.975100 + 0.221767i \(0.928818\pi\)
\(504\) 0 0
\(505\) −1293.37 −2.56113
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 125.233 72.3030i 0.246036 0.142049i −0.371912 0.928268i \(-0.621298\pi\)
0.617948 + 0.786219i \(0.287964\pi\)
\(510\) 0 0
\(511\) 5.79807 10.0425i 0.0113465 0.0196527i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −998.932 576.733i −1.93967 1.11987i
\(516\) 0 0
\(517\) −188.871 327.134i −0.365320 0.632753i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 452.382i 0.868296i −0.900842 0.434148i \(-0.857050\pi\)
0.900842 0.434148i \(-0.142950\pi\)
\(522\) 0 0
\(523\) 168.242 0.321686 0.160843 0.986980i \(-0.448579\pi\)
0.160843 + 0.986980i \(0.448579\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 175.918 101.566i 0.333809 0.192725i
\(528\) 0 0
\(529\) −245.955 + 426.006i −0.464943 + 0.805305i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 139.278 + 80.4122i 0.261309 + 0.150867i
\(534\) 0 0
\(535\) 389.270 + 674.235i 0.727607 + 1.26025i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 704.824i 1.30765i
\(540\) 0 0
\(541\) 809.693 1.49666 0.748330 0.663327i \(-0.230856\pi\)
0.748330 + 0.663327i \(0.230856\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1359.27 + 784.774i −2.49407 + 1.43995i
\(546\) 0 0
\(547\) 468.105 810.781i 0.855767 1.48223i −0.0201641 0.999797i \(-0.506419\pi\)
0.875931 0.482436i \(-0.160248\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 321.242 + 185.469i 0.583015 + 0.336604i
\(552\) 0 0
\(553\) −127.963 221.638i −0.231398 0.400793i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 318.572i 0.571942i −0.958238 0.285971i \(-0.907684\pi\)
0.958238 0.285971i \(-0.0923162\pi\)
\(558\) 0 0
\(559\) −408.548 −0.730855
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 700.038 404.167i 1.24341 0.717882i 0.273621 0.961838i \(-0.411779\pi\)
0.969786 + 0.243956i \(0.0784452\pi\)
\(564\) 0 0
\(565\) 376.178 651.560i 0.665802 1.15320i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −895.501 517.017i −1.57381 0.908642i −0.995695 0.0926904i \(-0.970453\pi\)
−0.578120 0.815952i \(-0.696213\pi\)
\(570\) 0 0
\(571\) −24.0163 41.5974i −0.0420600 0.0728500i 0.844229 0.535983i \(-0.180059\pi\)
−0.886289 + 0.463133i \(0.846725\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 394.818i 0.686640i
\(576\) 0 0
\(577\) 396.617 0.687378 0.343689 0.939084i \(-0.388323\pi\)
0.343689 + 0.939084i \(0.388323\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 98.4558 56.8435i 0.169459 0.0978373i
\(582\) 0 0
\(583\) −111.619 + 193.331i −0.191457 + 0.331613i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −560.569 323.645i −0.954973 0.551354i −0.0603509 0.998177i \(-0.519222\pi\)
−0.894622 + 0.446823i \(0.852555\pi\)
\(588\) 0 0
\(589\) −113.541 196.658i −0.192769 0.333885i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 322.360i 0.543609i −0.962352 0.271805i \(-0.912380\pi\)
0.962352 0.271805i \(-0.0876204\pi\)
\(594\) 0 0
\(595\) 232.408 0.390602
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 286.437 165.374i 0.478191 0.276084i −0.241471 0.970408i \(-0.577630\pi\)
0.719662 + 0.694324i \(0.244297\pi\)
\(600\) 0 0
\(601\) −2.29683 + 3.97823i −0.00382169 + 0.00661936i −0.867930 0.496687i \(-0.834550\pi\)
0.864108 + 0.503306i \(0.167883\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1062.84 613.633i −1.75677 1.01427i
\(606\) 0 0
\(607\) 100.896 + 174.756i 0.166220 + 0.287902i 0.937088 0.349093i \(-0.113510\pi\)
−0.770868 + 0.636995i \(0.780177\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 224.512i 0.367450i
\(612\) 0 0
\(613\) −594.531 −0.969871 −0.484936 0.874550i \(-0.661157\pi\)
−0.484936 + 0.874550i \(0.661157\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 562.741 324.899i 0.912060 0.526578i 0.0309665 0.999520i \(-0.490141\pi\)
0.881093 + 0.472942i \(0.156808\pi\)
\(618\) 0 0
\(619\) −114.275 + 197.931i −0.184613 + 0.319759i −0.943446 0.331526i \(-0.892436\pi\)
0.758833 + 0.651285i \(0.225770\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 187.044 + 107.990i 0.300231 + 0.173338i
\(624\) 0 0
\(625\) −978.507 1694.82i −1.56561 2.71172i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 181.243i 0.288144i
\(630\) 0 0
\(631\) −555.448 −0.880266 −0.440133 0.897933i \(-0.645069\pi\)
−0.440133 + 0.897933i \(0.645069\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1208.51 + 697.732i −1.90316 + 1.09879i
\(636\) 0 0
\(637\) 209.457 362.791i 0.328819 0.569530i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −374.507 216.222i −0.584254 0.337319i 0.178568 0.983928i \(-0.442853\pi\)
−0.762822 + 0.646608i \(0.776187\pi\)
\(642\) 0 0
\(643\) −170.831 295.888i −0.265678 0.460168i 0.702063 0.712115i \(-0.252262\pi\)
−0.967741 + 0.251947i \(0.918929\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1066.85i 1.64891i 0.565926 + 0.824456i \(0.308519\pi\)
−0.565926 + 0.824456i \(0.691481\pi\)
\(648\) 0 0
\(649\) 705.037 1.08634
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 576.545 332.868i 0.882917 0.509752i 0.0112977 0.999936i \(-0.496404\pi\)
0.871619 + 0.490184i \(0.163070\pi\)
\(654\) 0 0
\(655\) 798.128 1382.40i 1.21852 2.11053i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 795.462 + 459.260i 1.20707 + 0.696905i 0.962119 0.272630i \(-0.0878934\pi\)
0.244955 + 0.969534i \(0.421227\pi\)
\(660\) 0 0
\(661\) −385.777 668.185i −0.583626 1.01087i −0.995045 0.0994232i \(-0.968300\pi\)
0.411420 0.911446i \(-0.365033\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 259.809i 0.390690i
\(666\) 0 0
\(667\) −174.169 −0.261122
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 51.0036 29.4470i 0.0760114 0.0438852i
\(672\) 0 0
\(673\) 559.767 969.546i 0.831750 1.44063i −0.0649002 0.997892i \(-0.520673\pi\)
0.896650 0.442741i \(-0.145994\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −339.051 195.751i −0.500815 0.289145i 0.228235 0.973606i \(-0.426704\pi\)
−0.729050 + 0.684461i \(0.760038\pi\)
\(678\) 0 0
\(679\) 124.560 + 215.744i 0.183446 + 0.317737i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 661.278i 0.968196i −0.875014 0.484098i \(-0.839148\pi\)
0.875014 0.484098i \(-0.160852\pi\)
\(684\) 0 0
\(685\) −1915.03 −2.79566
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 114.907 66.3415i 0.166773 0.0962866i
\(690\) 0 0
\(691\) 412.836 715.053i 0.597447 1.03481i −0.395750 0.918358i \(-0.629515\pi\)
0.993197 0.116450i \(-0.0371515\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2120.83 1224.46i −3.05155 1.76181i
\(696\) 0 0
\(697\) 99.1841 + 171.792i 0.142301 + 0.246473i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 236.167i 0.336900i −0.985710 0.168450i \(-0.946124\pi\)
0.985710 0.168450i \(-0.0538761\pi\)
\(702\) 0 0
\(703\) −202.611 −0.288209
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 249.765 144.202i 0.353274 0.203963i
\(708\) 0 0
\(709\) 247.969 429.496i 0.349745 0.605777i −0.636459 0.771311i \(-0.719601\pi\)
0.986204 + 0.165534i \(0.0529348\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 92.3381 + 53.3115i 0.129507 + 0.0747706i
\(714\) 0 0
\(715\) 705.521 + 1222.00i 0.986743 + 1.70909i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1065.13i 1.48141i −0.671830 0.740705i \(-0.734492\pi\)
0.671830 0.740705i \(-0.265508\pi\)
\(720\) 0 0
\(721\) 257.207 0.356736
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1605.59 + 926.987i −2.21460 + 1.27860i
\(726\) 0 0
\(727\) −549.525 + 951.806i −0.755881 + 1.30922i 0.189054 + 0.981967i \(0.439458\pi\)
−0.944935 + 0.327257i \(0.893876\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −436.409 251.961i −0.597003 0.344680i
\(732\) 0 0
\(733\) 720.569 + 1248.06i 0.983041 + 1.70268i 0.650336 + 0.759647i \(0.274628\pi\)
0.332706 + 0.943031i \(0.392038\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 665.013i 0.902324i
\(738\) 0 0
\(739\) −1095.72 −1.48271 −0.741356 0.671112i \(-0.765817\pi\)
−0.741356 + 0.671112i \(0.765817\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −857.848 + 495.279i −1.15457 + 0.666593i −0.949997 0.312258i \(-0.898915\pi\)
−0.204575 + 0.978851i \(0.565581\pi\)
\(744\) 0 0
\(745\) −375.552 + 650.476i −0.504097 + 0.873122i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −150.345 86.8018i −0.200728 0.115890i
\(750\) 0 0
\(751\) 177.884 + 308.103i 0.236862 + 0.410258i 0.959812 0.280643i \(-0.0905476\pi\)
−0.722950 + 0.690900i \(0.757214\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 89.6776i 0.118778i
\(756\) 0 0
\(757\) 231.917 0.306364 0.153182 0.988198i \(-0.451048\pi\)
0.153182 + 0.988198i \(0.451048\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 368.325 212.653i 0.484002 0.279438i −0.238081 0.971245i \(-0.576518\pi\)
0.722083 + 0.691807i \(0.243185\pi\)
\(762\) 0 0
\(763\) 174.994 303.098i 0.229350 0.397245i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −362.900 209.521i −0.473143 0.273169i
\(768\) 0 0
\(769\) 422.147 + 731.179i 0.548955 + 0.950819i 0.998346 + 0.0574834i \(0.0183076\pi\)
−0.449391 + 0.893335i \(0.648359\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 816.503i 1.05628i 0.849158 + 0.528139i \(0.177110\pi\)
−0.849158 + 0.528139i \(0.822890\pi\)
\(774\) 0 0
\(775\) 1134.97 1.46448
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 192.046 110.878i 0.246529 0.142334i
\(780\) 0 0
\(781\) −953.093 + 1650.81i −1.22035 + 2.11371i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 563.991 + 325.620i 0.718459 + 0.414803i
\(786\) 0 0
\(787\) 178.111 + 308.497i 0.226316 + 0.391991i 0.956713 0.291031i \(-0.0939984\pi\)
−0.730397 + 0.683022i \(0.760665\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 167.765i 0.212092i
\(792\) 0 0
\(793\) −35.0038 −0.0441410
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 561.666 324.278i 0.704725 0.406873i −0.104380 0.994537i \(-0.533286\pi\)
0.809105 + 0.587664i \(0.199952\pi\)
\(798\) 0 0
\(799\) −138.462 + 239.823i −0.173294 + 0.300154i