Properties

Label 1728.3.q.f.449.1
Level $1728$
Weight $3$
Character 1728.449
Analytic conductor $47.085$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 449.1
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1728.449
Dual form 1728.3.q.f.1601.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.39898 - 1.96240i) q^{5} +(6.39898 + 11.0834i) q^{7} +O(q^{10})\) \(q+(-3.39898 - 1.96240i) q^{5} +(6.39898 + 11.0834i) q^{7} +(14.2980 - 8.25493i) q^{11} +(-1.39898 + 2.42310i) q^{13} +2.54270i q^{17} +21.5959 q^{19} +(2.60102 + 1.50170i) q^{23} +(-4.79796 - 8.31031i) q^{25} +(-13.1969 + 7.61926i) q^{29} +(-13.6010 + 23.5577i) q^{31} -50.2295i q^{35} +10.4041 q^{37} +(34.5000 + 19.9186i) q^{41} +(-17.0959 - 29.6110i) q^{43} +(58.1969 - 33.6000i) q^{47} +(-57.3939 + 99.4091i) q^{49} -100.680i q^{53} -64.7980 q^{55} +(-5.29796 - 3.05878i) q^{59} +(20.3990 + 35.3321i) q^{61} +(9.51021 - 5.49072i) q^{65} +(-54.4898 + 94.3791i) q^{67} +52.8829i q^{71} +68.7878 q^{73} +(182.985 + 105.646i) q^{77} +(-12.7929 - 22.1579i) q^{79} +(-52.0857 + 30.0717i) q^{83} +(4.98979 - 8.64258i) q^{85} +7.62809i q^{89} -35.8082 q^{91} +(-73.4041 - 42.3799i) q^{95} +(50.7020 + 87.8185i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{5} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{5} + 6 q^{7} + 18 q^{11} + 14 q^{13} + 8 q^{19} + 30 q^{23} + 20 q^{25} + 6 q^{29} - 74 q^{31} + 120 q^{37} + 138 q^{41} + 10 q^{43} + 174 q^{47} - 112 q^{49} - 220 q^{55} + 18 q^{59} + 62 q^{61} + 234 q^{65} - 22 q^{67} + 40 q^{73} + 438 q^{77} + 86 q^{79} + 66 q^{83} - 176 q^{85} - 300 q^{91} - 372 q^{95} + 242 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(325\) \(703\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(5\) −3.39898 1.96240i −0.679796 0.392480i 0.119982 0.992776i \(-0.461716\pi\)
−0.799778 + 0.600296i \(0.795050\pi\)
\(6\) 0 0
\(7\) 6.39898 + 11.0834i 0.914140 + 1.58334i 0.808156 + 0.588969i \(0.200466\pi\)
0.105984 + 0.994368i \(0.466201\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 14.2980 8.25493i 1.29981 0.750448i 0.319443 0.947606i \(-0.396504\pi\)
0.980372 + 0.197157i \(0.0631710\pi\)
\(12\) 0 0
\(13\) −1.39898 + 2.42310i −0.107614 + 0.186393i −0.914803 0.403900i \(-0.867654\pi\)
0.807189 + 0.590293i \(0.200988\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.54270i 0.149570i 0.997200 + 0.0747852i \(0.0238271\pi\)
−0.997200 + 0.0747852i \(0.976173\pi\)
\(18\) 0 0
\(19\) 21.5959 1.13663 0.568314 0.822812i \(-0.307596\pi\)
0.568314 + 0.822812i \(0.307596\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.60102 + 1.50170i 0.113088 + 0.0652913i 0.555477 0.831532i \(-0.312536\pi\)
−0.442389 + 0.896823i \(0.645869\pi\)
\(24\) 0 0
\(25\) −4.79796 8.31031i −0.191918 0.332412i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −13.1969 + 7.61926i −0.455067 + 0.262733i −0.709968 0.704234i \(-0.751290\pi\)
0.254901 + 0.966967i \(0.417957\pi\)
\(30\) 0 0
\(31\) −13.6010 + 23.5577i −0.438743 + 0.759924i −0.997593 0.0693442i \(-0.977909\pi\)
0.558850 + 0.829269i \(0.311243\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 50.2295i 1.43513i
\(36\) 0 0
\(37\) 10.4041 0.281191 0.140596 0.990067i \(-0.455098\pi\)
0.140596 + 0.990067i \(0.455098\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 34.5000 + 19.9186i 0.841463 + 0.485819i 0.857761 0.514048i \(-0.171855\pi\)
−0.0162980 + 0.999867i \(0.505188\pi\)
\(42\) 0 0
\(43\) −17.0959 29.6110i −0.397579 0.688628i 0.595847 0.803098i \(-0.296816\pi\)
−0.993427 + 0.114470i \(0.963483\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 58.1969 33.6000i 1.23823 0.714894i 0.269500 0.963000i \(-0.413142\pi\)
0.968733 + 0.248106i \(0.0798083\pi\)
\(48\) 0 0
\(49\) −57.3939 + 99.4091i −1.17130 + 2.02876i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 100.680i 1.89963i −0.312810 0.949816i \(-0.601270\pi\)
0.312810 0.949816i \(-0.398730\pi\)
\(54\) 0 0
\(55\) −64.7980 −1.17814
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.29796 3.05878i −0.0897959 0.0518437i 0.454430 0.890783i \(-0.349843\pi\)
−0.544226 + 0.838939i \(0.683176\pi\)
\(60\) 0 0
\(61\) 20.3990 + 35.3321i 0.334409 + 0.579214i 0.983371 0.181607i \(-0.0581298\pi\)
−0.648962 + 0.760821i \(0.724796\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 9.51021 5.49072i 0.146311 0.0844726i
\(66\) 0 0
\(67\) −54.4898 + 94.3791i −0.813281 + 1.40864i 0.0972755 + 0.995257i \(0.468987\pi\)
−0.910556 + 0.413386i \(0.864346\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 52.8829i 0.744830i 0.928066 + 0.372415i \(0.121470\pi\)
−0.928066 + 0.372415i \(0.878530\pi\)
\(72\) 0 0
\(73\) 68.7878 0.942298 0.471149 0.882054i \(-0.343839\pi\)
0.471149 + 0.882054i \(0.343839\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 182.985 + 105.646i 2.37642 + 1.37203i
\(78\) 0 0
\(79\) −12.7929 22.1579i −0.161935 0.280479i 0.773628 0.633640i \(-0.218440\pi\)
−0.935563 + 0.353161i \(0.885107\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −52.0857 + 30.0717i −0.627539 + 0.362310i −0.779798 0.626031i \(-0.784678\pi\)
0.152260 + 0.988341i \(0.451345\pi\)
\(84\) 0 0
\(85\) 4.98979 8.64258i 0.0587035 0.101677i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.62809i 0.0857089i 0.999081 + 0.0428545i \(0.0136452\pi\)
−0.999081 + 0.0428545i \(0.986355\pi\)
\(90\) 0 0
\(91\) −35.8082 −0.393496
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −73.4041 42.3799i −0.772675 0.446104i
\(96\) 0 0
\(97\) 50.7020 + 87.8185i 0.522701 + 0.905345i 0.999651 + 0.0264148i \(0.00840908\pi\)
−0.476950 + 0.878931i \(0.658258\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.19694 + 0.691053i −0.0118509 + 0.00684211i −0.505914 0.862584i \(-0.668845\pi\)
0.494063 + 0.869426i \(0.335511\pi\)
\(102\) 0 0
\(103\) −0.792856 + 1.37327i −0.00769763 + 0.0133327i −0.869849 0.493319i \(-0.835784\pi\)
0.862151 + 0.506652i \(0.169117\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 103.223i 0.964702i 0.875978 + 0.482351i \(0.160217\pi\)
−0.875978 + 0.482351i \(0.839783\pi\)
\(108\) 0 0
\(109\) −14.4041 −0.132148 −0.0660738 0.997815i \(-0.521047\pi\)
−0.0660738 + 0.997815i \(0.521047\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 92.0755 + 53.1598i 0.814828 + 0.470441i 0.848630 0.528988i \(-0.177428\pi\)
−0.0338020 + 0.999429i \(0.510762\pi\)
\(114\) 0 0
\(115\) −5.89388 10.2085i −0.0512511 0.0887695i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −28.1816 + 16.2707i −0.236820 + 0.136728i
\(120\) 0 0
\(121\) 75.7878 131.268i 0.626345 1.08486i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 135.782i 1.08626i
\(126\) 0 0
\(127\) 183.980 1.44866 0.724329 0.689454i \(-0.242150\pi\)
0.724329 + 0.689454i \(0.242150\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 91.6918 + 52.9383i 0.699938 + 0.404109i 0.807324 0.590108i \(-0.200915\pi\)
−0.107387 + 0.994217i \(0.534248\pi\)
\(132\) 0 0
\(133\) 138.192 + 239.355i 1.03904 + 1.79966i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 165.288 95.4289i 1.20648 0.696562i 0.244491 0.969651i \(-0.421379\pi\)
0.961989 + 0.273090i \(0.0880457\pi\)
\(138\) 0 0
\(139\) 47.4898 82.2547i 0.341653 0.591761i −0.643087 0.765793i \(-0.722347\pi\)
0.984740 + 0.174033i \(0.0556798\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 46.1939i 0.323034i
\(144\) 0 0
\(145\) 59.8082 0.412470
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 79.6112 + 45.9636i 0.534304 + 0.308480i 0.742767 0.669550i \(-0.233513\pi\)
−0.208464 + 0.978030i \(0.566846\pi\)
\(150\) 0 0
\(151\) −8.20714 14.2152i −0.0543519 0.0941403i 0.837569 0.546331i \(-0.183976\pi\)
−0.891921 + 0.452191i \(0.850643\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 92.4592 53.3813i 0.596511 0.344396i
\(156\) 0 0
\(157\) −105.985 + 183.571i −0.675062 + 1.16924i 0.301389 + 0.953501i \(0.402550\pi\)
−0.976451 + 0.215740i \(0.930784\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 38.4374i 0.238742i
\(162\) 0 0
\(163\) 172.788 1.06005 0.530024 0.847983i \(-0.322183\pi\)
0.530024 + 0.847983i \(0.322183\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −163.197 94.2218i −0.977227 0.564202i −0.0757953 0.997123i \(-0.524150\pi\)
−0.901432 + 0.432921i \(0.857483\pi\)
\(168\) 0 0
\(169\) 80.5857 + 139.579i 0.476839 + 0.825909i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 52.1969 30.1359i 0.301716 0.174196i −0.341497 0.939883i \(-0.610934\pi\)
0.643214 + 0.765687i \(0.277601\pi\)
\(174\) 0 0
\(175\) 61.4041 106.355i 0.350880 0.607743i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 72.7108i 0.406205i −0.979157 0.203103i \(-0.934897\pi\)
0.979157 0.203103i \(-0.0651025\pi\)
\(180\) 0 0
\(181\) 97.5959 0.539204 0.269602 0.962972i \(-0.413108\pi\)
0.269602 + 0.962972i \(0.413108\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −35.3633 20.4170i −0.191153 0.110362i
\(186\) 0 0
\(187\) 20.9898 + 36.3554i 0.112245 + 0.194414i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 282.560 163.136i 1.47937 0.854116i 0.479645 0.877462i \(-0.340765\pi\)
0.999727 + 0.0233462i \(0.00743200\pi\)
\(192\) 0 0
\(193\) −10.5102 + 18.2042i −0.0544570 + 0.0943223i −0.891969 0.452097i \(-0.850676\pi\)
0.837512 + 0.546419i \(0.184009\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 32.5413i 0.165184i 0.996583 + 0.0825922i \(0.0263199\pi\)
−0.996583 + 0.0825922i \(0.973680\pi\)
\(198\) 0 0
\(199\) 62.0000 0.311558 0.155779 0.987792i \(-0.450211\pi\)
0.155779 + 0.987792i \(0.450211\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −168.894 97.5109i −0.831990 0.480349i
\(204\) 0 0
\(205\) −78.1765 135.406i −0.381349 0.660516i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 308.778 178.273i 1.47740 0.852980i
\(210\) 0 0
\(211\) 84.2980 146.008i 0.399516 0.691983i −0.594150 0.804354i \(-0.702511\pi\)
0.993666 + 0.112372i \(0.0358447\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 134.196i 0.624169i
\(216\) 0 0
\(217\) −348.131 −1.60429
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6.16122 3.55718i −0.0278788 0.0160958i
\(222\) 0 0
\(223\) −78.1867 135.423i −0.350613 0.607280i 0.635744 0.771900i \(-0.280693\pi\)
−0.986357 + 0.164620i \(0.947360\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −86.6510 + 50.0280i −0.381723 + 0.220388i −0.678567 0.734538i \(-0.737399\pi\)
0.296845 + 0.954926i \(0.404066\pi\)
\(228\) 0 0
\(229\) −104.995 + 181.856i −0.458493 + 0.794133i −0.998882 0.0472824i \(-0.984944\pi\)
0.540389 + 0.841416i \(0.318277\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 307.127i 1.31814i 0.752081 + 0.659070i \(0.229050\pi\)
−0.752081 + 0.659070i \(0.770950\pi\)
\(234\) 0 0
\(235\) −263.747 −1.12233
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −70.3888 40.6390i −0.294514 0.170038i 0.345462 0.938433i \(-0.387722\pi\)
−0.639976 + 0.768395i \(0.721056\pi\)
\(240\) 0 0
\(241\) 180.096 + 311.935i 0.747286 + 1.29434i 0.949119 + 0.314917i \(0.101977\pi\)
−0.201833 + 0.979420i \(0.564690\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 390.161 225.260i 1.59249 0.919427i
\(246\) 0 0
\(247\) −30.2122 + 52.3291i −0.122317 + 0.211859i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 400.179i 1.59434i 0.603755 + 0.797170i \(0.293670\pi\)
−0.603755 + 0.797170i \(0.706330\pi\)
\(252\) 0 0
\(253\) 49.5857 0.195991
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −315.035 181.885i −1.22582 0.707725i −0.259664 0.965699i \(-0.583612\pi\)
−0.966152 + 0.257974i \(0.916945\pi\)
\(258\) 0 0
\(259\) 66.5755 + 115.312i 0.257048 + 0.445221i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −326.570 + 188.546i −1.24171 + 0.716903i −0.969443 0.245318i \(-0.921108\pi\)
−0.272270 + 0.962221i \(0.587774\pi\)
\(264\) 0 0
\(265\) −197.576 + 342.211i −0.745568 + 1.29136i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 170.849i 0.635125i −0.948237 0.317562i \(-0.897136\pi\)
0.948237 0.317562i \(-0.102864\pi\)
\(270\) 0 0
\(271\) 50.4041 0.185993 0.0929965 0.995666i \(-0.470355\pi\)
0.0929965 + 0.995666i \(0.470355\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −137.202 79.2136i −0.498917 0.288050i
\(276\) 0 0
\(277\) 12.8031 + 22.1756i 0.0462204 + 0.0800561i 0.888210 0.459438i \(-0.151949\pi\)
−0.841990 + 0.539494i \(0.818616\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −290.267 + 167.586i −1.03298 + 0.596391i −0.917837 0.396958i \(-0.870066\pi\)
−0.115143 + 0.993349i \(0.536733\pi\)
\(282\) 0 0
\(283\) 7.48979 12.9727i 0.0264657 0.0458399i −0.852489 0.522745i \(-0.824908\pi\)
0.878955 + 0.476905i \(0.158241\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 509.834i 1.77643i
\(288\) 0 0
\(289\) 282.535 0.977629
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −261.015 150.697i −0.890837 0.514325i −0.0166210 0.999862i \(-0.505291\pi\)
−0.874216 + 0.485537i \(0.838624\pi\)
\(294\) 0 0
\(295\) 12.0051 + 20.7934i 0.0406953 + 0.0704863i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −7.27755 + 4.20169i −0.0243396 + 0.0140525i
\(300\) 0 0
\(301\) 218.793 378.960i 0.726887 1.25900i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 160.124i 0.524997i
\(306\) 0 0
\(307\) −44.7469 −0.145755 −0.0728777 0.997341i \(-0.523218\pi\)
−0.0728777 + 0.997341i \(0.523218\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 281.348 + 162.436i 0.904656 + 0.522303i 0.878708 0.477360i \(-0.158406\pi\)
0.0259480 + 0.999663i \(0.491740\pi\)
\(312\) 0 0
\(313\) −156.894 271.748i −0.501258 0.868205i −0.999999 0.00145368i \(-0.999537\pi\)
0.498741 0.866751i \(-0.333796\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −47.9847 + 27.7040i −0.151371 + 0.0873942i −0.573773 0.819015i \(-0.694521\pi\)
0.422401 + 0.906409i \(0.361187\pi\)
\(318\) 0 0
\(319\) −125.793 + 217.880i −0.394335 + 0.683008i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 54.9119i 0.170006i
\(324\) 0 0
\(325\) 26.8490 0.0826123
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 744.802 + 430.012i 2.26384 + 1.30703i
\(330\) 0 0
\(331\) −7.70204 13.3403i −0.0232690 0.0403031i 0.854156 0.520016i \(-0.174074\pi\)
−0.877425 + 0.479713i \(0.840741\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 370.419 213.862i 1.10573 0.638393i
\(336\) 0 0
\(337\) −37.8837 + 65.6164i −0.112414 + 0.194708i −0.916743 0.399477i \(-0.869192\pi\)
0.804329 + 0.594184i \(0.202525\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 449.102i 1.31701i
\(342\) 0 0
\(343\) −841.949 −2.45466
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −578.651 334.084i −1.66758 0.962779i −0.968936 0.247312i \(-0.920453\pi\)
−0.698646 0.715467i \(-0.746214\pi\)
\(348\) 0 0
\(349\) −123.015 213.069i −0.352479 0.610512i 0.634204 0.773166i \(-0.281328\pi\)
−0.986683 + 0.162654i \(0.947995\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −156.510 + 90.3612i −0.443372 + 0.255981i −0.705027 0.709181i \(-0.749065\pi\)
0.261655 + 0.965161i \(0.415732\pi\)
\(354\) 0 0
\(355\) 103.778 179.748i 0.292331 0.506332i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 256.273i 0.713852i −0.934133 0.356926i \(-0.883825\pi\)
0.934133 0.356926i \(-0.116175\pi\)
\(360\) 0 0
\(361\) 105.384 0.291922
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −233.808 134.989i −0.640570 0.369833i
\(366\) 0 0
\(367\) 270.358 + 468.274i 0.736671 + 1.27595i 0.953986 + 0.299850i \(0.0969366\pi\)
−0.217316 + 0.976101i \(0.569730\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1115.88 644.252i 3.00776 1.73653i
\(372\) 0 0
\(373\) −85.9847 + 148.930i −0.230522 + 0.399276i −0.957962 0.286896i \(-0.907377\pi\)
0.727440 + 0.686171i \(0.240710\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 42.6367i 0.113095i
\(378\) 0 0
\(379\) −170.849 −0.450789 −0.225394 0.974268i \(-0.572367\pi\)
−0.225394 + 0.974268i \(0.572367\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −505.681 291.955i −1.32031 0.762284i −0.336536 0.941671i \(-0.609255\pi\)
−0.983779 + 0.179386i \(0.942589\pi\)
\(384\) 0 0
\(385\) −414.641 718.179i −1.07699 1.86540i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −384.752 + 222.137i −0.989080 + 0.571045i −0.904999 0.425413i \(-0.860129\pi\)
−0.0840807 + 0.996459i \(0.526795\pi\)
\(390\) 0 0
\(391\) −3.81837 + 6.61361i −0.00976565 + 0.0169146i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 100.419i 0.254225i
\(396\) 0 0
\(397\) 575.090 1.44859 0.724294 0.689491i \(-0.242166\pi\)
0.724294 + 0.689491i \(0.242166\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −141.318 81.5902i −0.352415 0.203467i 0.313333 0.949643i \(-0.398554\pi\)
−0.665748 + 0.746176i \(0.731888\pi\)
\(402\) 0 0
\(403\) −38.0551 65.9134i −0.0944295 0.163557i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 148.757 85.8850i 0.365497 0.211020i
\(408\) 0 0
\(409\) 300.641 520.725i 0.735063 1.27317i −0.219633 0.975583i \(-0.570486\pi\)
0.954696 0.297584i \(-0.0961808\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 78.2922i 0.189570i
\(414\) 0 0
\(415\) 236.051 0.568798
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 158.620 + 91.5795i 0.378569 + 0.218567i 0.677195 0.735803i \(-0.263195\pi\)
−0.298626 + 0.954370i \(0.596528\pi\)
\(420\) 0 0
\(421\) 83.7724 + 145.098i 0.198984 + 0.344651i 0.948199 0.317676i \(-0.102902\pi\)
−0.749215 + 0.662327i \(0.769569\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 21.1306 12.1998i 0.0497191 0.0287053i
\(426\) 0 0
\(427\) −261.065 + 452.178i −0.611394 + 1.05897i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 644.766i 1.49598i −0.663712 0.747988i \(-0.731020\pi\)
0.663712 0.747988i \(-0.268980\pi\)
\(432\) 0 0
\(433\) 133.514 0.308347 0.154174 0.988044i \(-0.450729\pi\)
0.154174 + 0.988044i \(0.450729\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 56.1714 + 32.4306i 0.128539 + 0.0742119i
\(438\) 0 0
\(439\) −46.2276 80.0685i −0.105302 0.182388i 0.808560 0.588414i \(-0.200248\pi\)
−0.913862 + 0.406026i \(0.866914\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 150.157 86.6933i 0.338955 0.195696i −0.320855 0.947128i \(-0.603970\pi\)
0.659810 + 0.751433i \(0.270637\pi\)
\(444\) 0 0
\(445\) 14.9694 25.9277i 0.0336391 0.0582646i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 430.692i 0.959224i −0.877481 0.479612i \(-0.840777\pi\)
0.877481 0.479612i \(-0.159223\pi\)
\(450\) 0 0
\(451\) 657.706 1.45833
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 121.711 + 70.2700i 0.267497 + 0.154440i
\(456\) 0 0
\(457\) 262.843 + 455.257i 0.575148 + 0.996186i 0.996025 + 0.0890687i \(0.0283891\pi\)
−0.420877 + 0.907118i \(0.638278\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.54999 0.894890i 0.00336224 0.00194119i −0.498318 0.866994i \(-0.666049\pi\)
0.501680 + 0.865053i \(0.332715\pi\)
\(462\) 0 0
\(463\) 263.166 455.817i 0.568394 0.984487i −0.428331 0.903622i \(-0.640898\pi\)
0.996725 0.0808651i \(-0.0257683\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 409.322i 0.876494i −0.898855 0.438247i \(-0.855600\pi\)
0.898855 0.438247i \(-0.144400\pi\)
\(468\) 0 0
\(469\) −1394.72 −2.97381
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −488.873 282.251i −1.03356 0.596726i
\(474\) 0 0
\(475\) −103.616 179.469i −0.218140 0.377829i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 525.207 303.228i 1.09647 0.633045i 0.161175 0.986926i \(-0.448472\pi\)
0.935290 + 0.353881i \(0.115138\pi\)
\(480\) 0 0
\(481\) −14.5551 + 25.2102i −0.0302601 + 0.0524120i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 397.991i 0.820600i
\(486\) 0 0
\(487\) 275.131 0.564950 0.282475 0.959275i \(-0.408845\pi\)
0.282475 + 0.959275i \(0.408845\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 127.469 + 73.5945i 0.259612 + 0.149887i 0.624157 0.781299i \(-0.285442\pi\)
−0.364546 + 0.931186i \(0.618776\pi\)
\(492\) 0 0
\(493\) −19.3735 33.5558i −0.0392971 0.0680646i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −586.120 + 338.397i −1.17932 + 0.680879i
\(498\) 0 0
\(499\) −226.308 + 391.977i −0.453523 + 0.785526i −0.998602 0.0528594i \(-0.983166\pi\)
0.545079 + 0.838385i \(0.316500\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 571.541i 1.13627i 0.822937 + 0.568133i \(0.192334\pi\)
−0.822937 + 0.568133i \(0.807666\pi\)
\(504\) 0 0
\(505\) 5.42449 0.0107416
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 394.136 + 227.554i 0.774333 + 0.447062i 0.834418 0.551132i \(-0.185804\pi\)
−0.0600849 + 0.998193i \(0.519137\pi\)
\(510\) 0 0
\(511\) 440.171 + 762.399i 0.861392 + 1.49198i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.38981 3.11181i 0.0104656 0.00604234i
\(516\) 0 0
\(517\) 554.732 960.823i 1.07298 1.85846i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 846.127i 1.62404i −0.583627 0.812022i \(-0.698367\pi\)
0.583627 0.812022i \(-0.301633\pi\)
\(522\) 0 0
\(523\) −487.616 −0.932345 −0.466172 0.884694i \(-0.654367\pi\)
−0.466172 + 0.884694i \(0.654367\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −59.9000 34.5833i −0.113662 0.0656229i
\(528\) 0 0
\(529\) −259.990 450.316i −0.491474 0.851258i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −96.5296 + 55.7314i −0.181106 + 0.104562i
\(534\) 0 0
\(535\) 202.565 350.853i 0.378627 0.655801i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1895.13i 3.51601i
\(540\) 0 0
\(541\) −608.302 −1.12440 −0.562202 0.827000i \(-0.690045\pi\)
−0.562202 + 0.827000i \(0.690045\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 48.9592 + 28.2666i 0.0898334 + 0.0518653i
\(546\) 0 0
\(547\) 431.671 + 747.677i 0.789162 + 1.36687i 0.926481 + 0.376341i \(0.122818\pi\)
−0.137319 + 0.990527i \(0.543849\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −285.000 + 164.545i −0.517241 + 0.298629i
\(552\) 0 0
\(553\) 163.722 283.576i 0.296062 0.512795i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 331.526i 0.595200i 0.954691 + 0.297600i \(0.0961861\pi\)
−0.954691 + 0.297600i \(0.903814\pi\)
\(558\) 0 0
\(559\) 95.6674 0.171140
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −514.024 296.772i −0.913010 0.527126i −0.0316114 0.999500i \(-0.510064\pi\)
−0.881398 + 0.472374i \(0.843397\pi\)
\(564\) 0 0
\(565\) −208.642 361.378i −0.369278 0.639608i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −889.155 + 513.354i −1.56266 + 0.902204i −0.565676 + 0.824627i \(0.691385\pi\)
−0.996986 + 0.0775764i \(0.975282\pi\)
\(570\) 0 0
\(571\) −191.843 + 332.282i −0.335977 + 0.581929i −0.983672 0.179971i \(-0.942400\pi\)
0.647695 + 0.761900i \(0.275733\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 28.8204i 0.0501224i
\(576\) 0 0
\(577\) −777.433 −1.34737 −0.673685 0.739019i \(-0.735290\pi\)
−0.673685 + 0.739019i \(0.735290\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −666.591 384.856i −1.14732 0.662403i
\(582\) 0 0
\(583\) −831.110 1439.53i −1.42557 2.46917i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −581.520 + 335.741i −0.990665 + 0.571961i −0.905473 0.424404i \(-0.860484\pi\)
−0.0851921 + 0.996365i \(0.527150\pi\)
\(588\) 0 0
\(589\) −293.727 + 508.749i −0.498687 + 0.863751i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 536.457i 0.904650i 0.891853 + 0.452325i \(0.149405\pi\)
−0.891853 + 0.452325i \(0.850595\pi\)
\(594\) 0 0
\(595\) 127.718 0.214653
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −735.438 424.605i −1.22778 0.708857i −0.261212 0.965282i \(-0.584122\pi\)
−0.966564 + 0.256425i \(0.917455\pi\)
\(600\) 0 0
\(601\) −330.692 572.775i −0.550236 0.953037i −0.998257 0.0590138i \(-0.981204\pi\)
0.448021 0.894023i \(-0.352129\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −515.202 + 297.452i −0.851574 + 0.491656i
\(606\) 0 0
\(607\) −10.9541 + 18.9730i −0.0180463 + 0.0312570i −0.874908 0.484290i \(-0.839078\pi\)
0.856861 + 0.515547i \(0.172411\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 188.023i 0.307730i
\(612\) 0 0
\(613\) 1164.75 1.90008 0.950038 0.312133i \(-0.101044\pi\)
0.950038 + 0.312133i \(0.101044\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −558.227 322.292i −0.904743 0.522354i −0.0260071 0.999662i \(-0.508279\pi\)
−0.878736 + 0.477308i \(0.841613\pi\)
\(618\) 0 0
\(619\) −564.469 977.690i −0.911905 1.57947i −0.811370 0.584533i \(-0.801278\pi\)
−0.100535 0.994933i \(-0.532056\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −84.5449 + 48.8120i −0.135706 + 0.0783499i
\(624\) 0 0
\(625\) 146.510 253.763i 0.234416 0.406021i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 26.4544i 0.0420579i
\(630\) 0 0
\(631\) −143.212 −0.226961 −0.113480 0.993540i \(-0.536200\pi\)
−0.113480 + 0.993540i \(0.536200\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −625.343 361.042i −0.984792 0.568570i
\(636\) 0 0
\(637\) −160.586 278.143i −0.252097 0.436645i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 198.418 114.557i 0.309545 0.178716i −0.337178 0.941441i \(-0.609472\pi\)
0.646723 + 0.762725i \(0.276139\pi\)
\(642\) 0 0
\(643\) 554.682 960.737i 0.862646 1.49415i −0.00671893 0.999977i \(-0.502139\pi\)
0.869365 0.494170i \(-0.164528\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1052.57i 1.62685i 0.581669 + 0.813426i \(0.302400\pi\)
−0.581669 + 0.813426i \(0.697600\pi\)
\(648\) 0 0
\(649\) −101.000 −0.155624
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −795.499 459.282i −1.21822 0.703341i −0.253685 0.967287i \(-0.581643\pi\)
−0.964537 + 0.263946i \(0.914976\pi\)
\(654\) 0 0
\(655\) −207.772 359.872i −0.317210 0.549424i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 207.288 119.678i 0.314549 0.181605i −0.334411 0.942427i \(-0.608537\pi\)
0.648960 + 0.760822i \(0.275204\pi\)
\(660\) 0 0
\(661\) 177.793 307.946i 0.268976 0.465879i −0.699622 0.714513i \(-0.746648\pi\)
0.968598 + 0.248634i \(0.0799816\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1084.75i 1.63121i
\(666\) 0 0
\(667\) −45.7673 −0.0686167
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 583.328 + 336.784i 0.869341 + 0.501914i
\(672\) 0 0
\(673\) 291.429 + 504.769i 0.433029 + 0.750028i 0.997132 0.0756758i \(-0.0241114\pi\)
−0.564103 + 0.825704i \(0.690778\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −154.450 + 89.1718i −0.228139 + 0.131716i −0.609713 0.792622i \(-0.708715\pi\)
0.381574 + 0.924338i \(0.375382\pi\)
\(678\) 0 0
\(679\) −648.883 + 1123.90i −0.955645 + 1.65522i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 660.510i 0.967072i −0.875325 0.483536i \(-0.839352\pi\)
0.875325 0.483536i \(-0.160648\pi\)
\(684\) 0 0
\(685\) −749.080 −1.09355
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 243.959 + 140.850i 0.354077 + 0.204427i
\(690\) 0 0
\(691\) −43.2571 74.9236i −0.0626008 0.108428i 0.833026 0.553233i \(-0.186606\pi\)
−0.895627 + 0.444805i \(0.853273\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −322.834 + 186.388i −0.464509 + 0.268184i
\(696\) 0 0
\(697\) −50.6469 + 87.7231i −0.0726642 + 0.125858i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1204.11i 1.71770i −0.512227 0.858850i \(-0.671179\pi\)
0.512227 0.858850i \(-0.328821\pi\)
\(702\) 0 0
\(703\) 224.686 0.319610
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −15.3184 8.84406i −0.0216667 0.0125093i
\(708\) 0 0
\(709\) −401.944 696.187i −0.566917 0.981928i −0.996869 0.0790766i \(-0.974803\pi\)
0.429952 0.902852i \(-0.358530\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −70.7531 + 40.8493i −0.0992329 + 0.0572921i
\(714\) 0 0
\(715\) 90.6510 157.012i 0.126785 0.219597i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 66.1101i 0.0919474i −0.998943 0.0459737i \(-0.985361\pi\)
0.998943 0.0459737i \(-0.0146390\pi\)
\(720\) 0 0
\(721\) −20.2939 −0.0281469
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 126.637 + 73.1138i 0.174671 + 0.100847i
\(726\) 0 0
\(727\) 259.834 + 450.045i 0.357405 + 0.619044i 0.987527 0.157453i \(-0.0503281\pi\)
−0.630121 + 0.776497i \(0.716995\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 75.2918 43.4698i 0.102998 0.0594662i
\(732\) 0 0
\(733\) −80.1459 + 138.817i −0.109340 + 0.189382i −0.915503 0.402311i \(-0.868207\pi\)
0.806163 + 0.591693i \(0.201540\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1799.24i 2.44130i
\(738\) 0 0
\(739\) −122.849 −0.166237 −0.0831184 0.996540i \(-0.526488\pi\)
−0.0831184 + 0.996540i \(0.526488\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −585.944 338.295i −0.788619 0.455309i 0.0508572 0.998706i \(-0.483805\pi\)
−0.839476 + 0.543397i \(0.817138\pi\)
\(744\) 0 0
\(745\) −180.398 312.458i −0.242145 0.419407i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1144.06 + 660.523i −1.52745 + 0.881873i
\(750\) 0 0
\(751\) 171.430 296.925i 0.228268 0.395373i −0.729027 0.684485i \(-0.760027\pi\)
0.957295 + 0.289113i \(0.0933603\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 64.4229i 0.0853283i
\(756\) 0 0
\(757\) 452.220 0.597385 0.298692 0.954349i \(-0.403450\pi\)
0.298692 + 0.954349i \(0.403450\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −203.520 117.503i −0.267438 0.154405i 0.360285 0.932842i \(-0.382680\pi\)
−0.627723 + 0.778437i \(0.716013\pi\)
\(762\) 0 0
\(763\) −92.1714 159.646i −0.120801 0.209234i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 14.8235 8.55834i 0.0193266 0.0111582i
\(768\) 0 0
\(769\) 318.439 551.552i 0.414095 0.717233i −0.581238 0.813733i \(-0.697432\pi\)
0.995333 + 0.0965005i \(0.0307649\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 592.885i 0.766992i 0.923543 + 0.383496i \(0.125280\pi\)
−0.923543 + 0.383496i \(0.874720\pi\)
\(774\) 0 0
\(775\) 261.029 0.336811
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 745.059 + 430.160i 0.956430 + 0.552195i
\(780\) 0 0
\(781\) 436.545 + 756.118i 0.558956 + 0.968141i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 720.480 415.969i 0.917808 0.529897i
\(786\) 0 0
\(787\) 666.904 1155.11i 0.847400 1.46774i −0.0361199 0.999347i \(-0.511500\pi\)
0.883520 0.468393i \(-0.155167\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1360.67i 1.72020i
\(792\) 0 0
\(793\) −114.151 −0.143948
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 638.540 + 368.661i 0.801179 + 0.462561i 0.843883 0.536527i \(-0.180264\pi\)
−0.0427041 + 0.999088i \(0.513597\pi\)
\(798\) 0 0
\(799\) 85.4347 + 147.977i 0.106927 + 0.185203i