Properties

Label 384.3.h.e.65.2
Level $384$
Weight $3$
Character 384.65
Analytic conductor $10.463$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 65.2
Root \(1.61803i\) of defining polynomial
Character \(\chi\) \(=\) 384.65
Dual form 384.3.h.e.65.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.23607 + 2.00000i) q^{3} -4.00000 q^{5} +8.94427 q^{7} +(1.00000 - 8.94427i) q^{9} +O(q^{10})\) \(q+(-2.23607 + 2.00000i) q^{3} -4.00000 q^{5} +8.94427 q^{7} +(1.00000 - 8.94427i) q^{9} +4.47214 q^{11} +17.8885i q^{13} +(8.94427 - 8.00000i) q^{15} +17.8885i q^{17} -20.0000i q^{19} +(-20.0000 + 17.8885i) q^{21} +16.0000i q^{23} -9.00000 q^{25} +(15.6525 + 22.0000i) q^{27} -52.0000 q^{29} -26.8328 q^{31} +(-10.0000 + 8.94427i) q^{33} -35.7771 q^{35} +53.6656i q^{37} +(-35.7771 - 40.0000i) q^{39} -35.7771i q^{41} +36.0000i q^{43} +(-4.00000 + 35.7771i) q^{45} +64.0000i q^{47} +31.0000 q^{49} +(-35.7771 - 40.0000i) q^{51} -20.0000 q^{53} -17.8885 q^{55} +(40.0000 + 44.7214i) q^{57} +102.859 q^{59} +17.8885i q^{61} +(8.94427 - 80.0000i) q^{63} -71.5542i q^{65} -44.0000i q^{67} +(-32.0000 - 35.7771i) q^{69} +80.0000i q^{71} -50.0000 q^{73} +(20.1246 - 18.0000i) q^{75} +40.0000 q^{77} +80.4984 q^{79} +(-79.0000 - 17.8885i) q^{81} -102.859 q^{83} -71.5542i q^{85} +(116.276 - 104.000i) q^{87} +160.997i q^{89} +160.000i q^{91} +(60.0000 - 53.6656i) q^{93} +80.0000i q^{95} +50.0000 q^{97} +(4.47214 - 40.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 16q^{5} + 4q^{9} + O(q^{10}) \) \( 4q - 16q^{5} + 4q^{9} - 80q^{21} - 36q^{25} - 208q^{29} - 40q^{33} - 16q^{45} + 124q^{49} - 80q^{53} + 160q^{57} - 128q^{69} - 200q^{73} + 160q^{77} - 316q^{81} + 240q^{93} + 200q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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
\(3\) −2.23607 + 2.00000i −0.745356 + 0.666667i
\(4\) 0 0
\(5\) −4.00000 −0.800000 −0.400000 0.916515i \(-0.630990\pi\)
−0.400000 + 0.916515i \(0.630990\pi\)
\(6\) 0 0
\(7\) 8.94427 1.27775 0.638877 0.769309i \(-0.279399\pi\)
0.638877 + 0.769309i \(0.279399\pi\)
\(8\) 0 0
\(9\) 1.00000 8.94427i 0.111111 0.993808i
\(10\) 0 0
\(11\) 4.47214 0.406558 0.203279 0.979121i \(-0.434840\pi\)
0.203279 + 0.979121i \(0.434840\pi\)
\(12\) 0 0
\(13\) 17.8885i 1.37604i 0.725691 + 0.688021i \(0.241520\pi\)
−0.725691 + 0.688021i \(0.758480\pi\)
\(14\) 0 0
\(15\) 8.94427 8.00000i 0.596285 0.533333i
\(16\) 0 0
\(17\) 17.8885i 1.05227i 0.850402 + 0.526134i \(0.176359\pi\)
−0.850402 + 0.526134i \(0.823641\pi\)
\(18\) 0 0
\(19\) 20.0000i 1.05263i −0.850289 0.526316i \(-0.823573\pi\)
0.850289 0.526316i \(-0.176427\pi\)
\(20\) 0 0
\(21\) −20.0000 + 17.8885i −0.952381 + 0.851835i
\(22\) 0 0
\(23\) 16.0000i 0.695652i 0.937559 + 0.347826i \(0.113080\pi\)
−0.937559 + 0.347826i \(0.886920\pi\)
\(24\) 0 0
\(25\) −9.00000 −0.360000
\(26\) 0 0
\(27\) 15.6525 + 22.0000i 0.579721 + 0.814815i
\(28\) 0 0
\(29\) −52.0000 −1.79310 −0.896552 0.442939i \(-0.853936\pi\)
−0.896552 + 0.442939i \(0.853936\pi\)
\(30\) 0 0
\(31\) −26.8328 −0.865575 −0.432787 0.901496i \(-0.642470\pi\)
−0.432787 + 0.901496i \(0.642470\pi\)
\(32\) 0 0
\(33\) −10.0000 + 8.94427i −0.303030 + 0.271039i
\(34\) 0 0
\(35\) −35.7771 −1.02220
\(36\) 0 0
\(37\) 53.6656i 1.45042i 0.688526 + 0.725211i \(0.258258\pi\)
−0.688526 + 0.725211i \(0.741742\pi\)
\(38\) 0 0
\(39\) −35.7771 40.0000i −0.917361 1.02564i
\(40\) 0 0
\(41\) 35.7771i 0.872612i −0.899798 0.436306i \(-0.856287\pi\)
0.899798 0.436306i \(-0.143713\pi\)
\(42\) 0 0
\(43\) 36.0000i 0.837209i 0.908169 + 0.418605i \(0.137481\pi\)
−0.908169 + 0.418605i \(0.862519\pi\)
\(44\) 0 0
\(45\) −4.00000 + 35.7771i −0.0888889 + 0.795046i
\(46\) 0 0
\(47\) 64.0000i 1.36170i 0.732422 + 0.680851i \(0.238390\pi\)
−0.732422 + 0.680851i \(0.761610\pi\)
\(48\) 0 0
\(49\) 31.0000 0.632653
\(50\) 0 0
\(51\) −35.7771 40.0000i −0.701512 0.784314i
\(52\) 0 0
\(53\) −20.0000 −0.377358 −0.188679 0.982039i \(-0.560421\pi\)
−0.188679 + 0.982039i \(0.560421\pi\)
\(54\) 0 0
\(55\) −17.8885 −0.325246
\(56\) 0 0
\(57\) 40.0000 + 44.7214i 0.701754 + 0.784585i
\(58\) 0 0
\(59\) 102.859 1.74338 0.871688 0.490062i \(-0.163026\pi\)
0.871688 + 0.490062i \(0.163026\pi\)
\(60\) 0 0
\(61\) 17.8885i 0.293255i 0.989192 + 0.146627i \(0.0468418\pi\)
−0.989192 + 0.146627i \(0.953158\pi\)
\(62\) 0 0
\(63\) 8.94427 80.0000i 0.141973 1.26984i
\(64\) 0 0
\(65\) 71.5542i 1.10083i
\(66\) 0 0
\(67\) 44.0000i 0.656716i −0.944553 0.328358i \(-0.893505\pi\)
0.944553 0.328358i \(-0.106495\pi\)
\(68\) 0 0
\(69\) −32.0000 35.7771i −0.463768 0.518509i
\(70\) 0 0
\(71\) 80.0000i 1.12676i 0.826198 + 0.563380i \(0.190499\pi\)
−0.826198 + 0.563380i \(0.809501\pi\)
\(72\) 0 0
\(73\) −50.0000 −0.684932 −0.342466 0.939530i \(-0.611262\pi\)
−0.342466 + 0.939530i \(0.611262\pi\)
\(74\) 0 0
\(75\) 20.1246 18.0000i 0.268328 0.240000i
\(76\) 0 0
\(77\) 40.0000 0.519481
\(78\) 0 0
\(79\) 80.4984 1.01897 0.509484 0.860480i \(-0.329836\pi\)
0.509484 + 0.860480i \(0.329836\pi\)
\(80\) 0 0
\(81\) −79.0000 17.8885i −0.975309 0.220846i
\(82\) 0 0
\(83\) −102.859 −1.23927 −0.619633 0.784891i \(-0.712719\pi\)
−0.619633 + 0.784891i \(0.712719\pi\)
\(84\) 0 0
\(85\) 71.5542i 0.841814i
\(86\) 0 0
\(87\) 116.276 104.000i 1.33650 1.19540i
\(88\) 0 0
\(89\) 160.997i 1.80895i 0.426523 + 0.904477i \(0.359738\pi\)
−0.426523 + 0.904477i \(0.640262\pi\)
\(90\) 0 0
\(91\) 160.000i 1.75824i
\(92\) 0 0
\(93\) 60.0000 53.6656i 0.645161 0.577050i
\(94\) 0 0
\(95\) 80.0000i 0.842105i
\(96\) 0 0
\(97\) 50.0000 0.515464 0.257732 0.966216i \(-0.417025\pi\)
0.257732 + 0.966216i \(0.417025\pi\)
\(98\) 0 0
\(99\) 4.47214 40.0000i 0.0451731 0.404040i
\(100\) 0 0
\(101\) 92.0000 0.910891 0.455446 0.890264i \(-0.349480\pi\)
0.455446 + 0.890264i \(0.349480\pi\)
\(102\) 0 0
\(103\) 44.7214 0.434188 0.217094 0.976151i \(-0.430342\pi\)
0.217094 + 0.976151i \(0.430342\pi\)
\(104\) 0 0
\(105\) 80.0000 71.5542i 0.761905 0.681468i
\(106\) 0 0
\(107\) −40.2492 −0.376161 −0.188080 0.982154i \(-0.560227\pi\)
−0.188080 + 0.982154i \(0.560227\pi\)
\(108\) 0 0
\(109\) 125.220i 1.14881i −0.818573 0.574403i \(-0.805234\pi\)
0.818573 0.574403i \(-0.194766\pi\)
\(110\) 0 0
\(111\) −107.331 120.000i −0.966948 1.08108i
\(112\) 0 0
\(113\) 35.7771i 0.316611i 0.987390 + 0.158306i \(0.0506031\pi\)
−0.987390 + 0.158306i \(0.949397\pi\)
\(114\) 0 0
\(115\) 64.0000i 0.556522i
\(116\) 0 0
\(117\) 160.000 + 17.8885i 1.36752 + 0.152894i
\(118\) 0 0
\(119\) 160.000i 1.34454i
\(120\) 0 0
\(121\) −101.000 −0.834711
\(122\) 0 0
\(123\) 71.5542 + 80.0000i 0.581741 + 0.650407i
\(124\) 0 0
\(125\) 136.000 1.08800
\(126\) 0 0
\(127\) −26.8328 −0.211282 −0.105641 0.994404i \(-0.533689\pi\)
−0.105641 + 0.994404i \(0.533689\pi\)
\(128\) 0 0
\(129\) −72.0000 80.4984i −0.558140 0.624019i
\(130\) 0 0
\(131\) 67.0820 0.512077 0.256038 0.966667i \(-0.417583\pi\)
0.256038 + 0.966667i \(0.417583\pi\)
\(132\) 0 0
\(133\) 178.885i 1.34500i
\(134\) 0 0
\(135\) −62.6099 88.0000i −0.463777 0.651852i
\(136\) 0 0
\(137\) 143.108i 1.04459i −0.852766 0.522293i \(-0.825077\pi\)
0.852766 0.522293i \(-0.174923\pi\)
\(138\) 0 0
\(139\) 260.000i 1.87050i −0.353983 0.935252i \(-0.615173\pi\)
0.353983 0.935252i \(-0.384827\pi\)
\(140\) 0 0
\(141\) −128.000 143.108i −0.907801 1.01495i
\(142\) 0 0
\(143\) 80.0000i 0.559441i
\(144\) 0 0
\(145\) 208.000 1.43448
\(146\) 0 0
\(147\) −69.3181 + 62.0000i −0.471552 + 0.421769i
\(148\) 0 0
\(149\) 28.0000 0.187919 0.0939597 0.995576i \(-0.470048\pi\)
0.0939597 + 0.995576i \(0.470048\pi\)
\(150\) 0 0
\(151\) −241.495 −1.59931 −0.799653 0.600462i \(-0.794983\pi\)
−0.799653 + 0.600462i \(0.794983\pi\)
\(152\) 0 0
\(153\) 160.000 + 17.8885i 1.04575 + 0.116919i
\(154\) 0 0
\(155\) 107.331 0.692460
\(156\) 0 0
\(157\) 53.6656i 0.341819i −0.985287 0.170910i \(-0.945329\pi\)
0.985287 0.170910i \(-0.0546706\pi\)
\(158\) 0 0
\(159\) 44.7214 40.0000i 0.281266 0.251572i
\(160\) 0 0
\(161\) 143.108i 0.888872i
\(162\) 0 0
\(163\) 124.000i 0.760736i 0.924835 + 0.380368i \(0.124203\pi\)
−0.924835 + 0.380368i \(0.875797\pi\)
\(164\) 0 0
\(165\) 40.0000 35.7771i 0.242424 0.216831i
\(166\) 0 0
\(167\) 16.0000i 0.0958084i −0.998852 0.0479042i \(-0.984746\pi\)
0.998852 0.0479042i \(-0.0152542\pi\)
\(168\) 0 0
\(169\) −151.000 −0.893491
\(170\) 0 0
\(171\) −178.885 20.0000i −1.04611 0.116959i
\(172\) 0 0
\(173\) 140.000 0.809249 0.404624 0.914483i \(-0.367402\pi\)
0.404624 + 0.914483i \(0.367402\pi\)
\(174\) 0 0
\(175\) −80.4984 −0.459991
\(176\) 0 0
\(177\) −230.000 + 205.718i −1.29944 + 1.16225i
\(178\) 0 0
\(179\) 67.0820 0.374760 0.187380 0.982288i \(-0.440000\pi\)
0.187380 + 0.982288i \(0.440000\pi\)
\(180\) 0 0
\(181\) 125.220i 0.691822i 0.938267 + 0.345911i \(0.112430\pi\)
−0.938267 + 0.345911i \(0.887570\pi\)
\(182\) 0 0
\(183\) −35.7771 40.0000i −0.195503 0.218579i
\(184\) 0 0
\(185\) 214.663i 1.16034i
\(186\) 0 0
\(187\) 80.0000i 0.427807i
\(188\) 0 0
\(189\) 140.000 + 196.774i 0.740741 + 1.04113i
\(190\) 0 0
\(191\) 160.000i 0.837696i 0.908056 + 0.418848i \(0.137566\pi\)
−0.908056 + 0.418848i \(0.862434\pi\)
\(192\) 0 0
\(193\) 30.0000 0.155440 0.0777202 0.996975i \(-0.475236\pi\)
0.0777202 + 0.996975i \(0.475236\pi\)
\(194\) 0 0
\(195\) 143.108 + 160.000i 0.733889 + 0.820513i
\(196\) 0 0
\(197\) −180.000 −0.913706 −0.456853 0.889542i \(-0.651023\pi\)
−0.456853 + 0.889542i \(0.651023\pi\)
\(198\) 0 0
\(199\) 259.384 1.30344 0.651718 0.758461i \(-0.274048\pi\)
0.651718 + 0.758461i \(0.274048\pi\)
\(200\) 0 0
\(201\) 88.0000 + 98.3870i 0.437811 + 0.489488i
\(202\) 0 0
\(203\) −465.102 −2.29114
\(204\) 0 0
\(205\) 143.108i 0.698090i
\(206\) 0 0
\(207\) 143.108 + 16.0000i 0.691345 + 0.0772947i
\(208\) 0 0
\(209\) 89.4427i 0.427956i
\(210\) 0 0
\(211\) 60.0000i 0.284360i −0.989841 0.142180i \(-0.954589\pi\)
0.989841 0.142180i \(-0.0454112\pi\)
\(212\) 0 0
\(213\) −160.000 178.885i −0.751174 0.839838i
\(214\) 0 0
\(215\) 144.000i 0.669767i
\(216\) 0 0
\(217\) −240.000 −1.10599
\(218\) 0 0
\(219\) 111.803 100.000i 0.510518 0.456621i
\(220\) 0 0
\(221\) −320.000 −1.44796
\(222\) 0 0
\(223\) 152.053 0.681850 0.340925 0.940090i \(-0.389260\pi\)
0.340925 + 0.940090i \(0.389260\pi\)
\(224\) 0 0
\(225\) −9.00000 + 80.4984i −0.0400000 + 0.357771i
\(226\) 0 0
\(227\) 254.912 1.12296 0.561480 0.827491i \(-0.310232\pi\)
0.561480 + 0.827491i \(0.310232\pi\)
\(228\) 0 0
\(229\) 196.774i 0.859275i 0.903001 + 0.429638i \(0.141359\pi\)
−0.903001 + 0.429638i \(0.858641\pi\)
\(230\) 0 0
\(231\) −89.4427 + 80.0000i −0.387198 + 0.346320i
\(232\) 0 0
\(233\) 160.997i 0.690974i 0.938424 + 0.345487i \(0.112286\pi\)
−0.938424 + 0.345487i \(0.887714\pi\)
\(234\) 0 0
\(235\) 256.000i 1.08936i
\(236\) 0 0
\(237\) −180.000 + 160.997i −0.759494 + 0.679312i
\(238\) 0 0
\(239\) 320.000i 1.33891i −0.742852 0.669456i \(-0.766527\pi\)
0.742852 0.669456i \(-0.233473\pi\)
\(240\) 0 0
\(241\) 318.000 1.31950 0.659751 0.751484i \(-0.270662\pi\)
0.659751 + 0.751484i \(0.270662\pi\)
\(242\) 0 0
\(243\) 212.426 118.000i 0.874183 0.485597i
\(244\) 0 0
\(245\) −124.000 −0.506122
\(246\) 0 0
\(247\) 357.771 1.44847
\(248\) 0 0
\(249\) 230.000 205.718i 0.923695 0.826178i
\(250\) 0 0
\(251\) 147.580 0.587970 0.293985 0.955810i \(-0.405018\pi\)
0.293985 + 0.955810i \(0.405018\pi\)
\(252\) 0 0
\(253\) 71.5542i 0.282823i
\(254\) 0 0
\(255\) 143.108 + 160.000i 0.561209 + 0.627451i
\(256\) 0 0
\(257\) 107.331i 0.417631i −0.977955 0.208816i \(-0.933039\pi\)
0.977955 0.208816i \(-0.0669609\pi\)
\(258\) 0 0
\(259\) 480.000i 1.85328i
\(260\) 0 0
\(261\) −52.0000 + 465.102i −0.199234 + 1.78200i
\(262\) 0 0
\(263\) 144.000i 0.547529i 0.961797 + 0.273764i \(0.0882688\pi\)
−0.961797 + 0.273764i \(0.911731\pi\)
\(264\) 0 0
\(265\) 80.0000 0.301887
\(266\) 0 0
\(267\) −321.994 360.000i −1.20597 1.34831i
\(268\) 0 0
\(269\) −132.000 −0.490706 −0.245353 0.969434i \(-0.578904\pi\)
−0.245353 + 0.969434i \(0.578904\pi\)
\(270\) 0 0
\(271\) −277.272 −1.02315 −0.511573 0.859240i \(-0.670937\pi\)
−0.511573 + 0.859240i \(0.670937\pi\)
\(272\) 0 0
\(273\) −320.000 357.771i −1.17216 1.31052i
\(274\) 0 0
\(275\) −40.2492 −0.146361
\(276\) 0 0
\(277\) 268.328i 0.968694i 0.874876 + 0.484347i \(0.160943\pi\)
−0.874876 + 0.484347i \(0.839057\pi\)
\(278\) 0 0
\(279\) −26.8328 + 240.000i −0.0961750 + 0.860215i
\(280\) 0 0
\(281\) 196.774i 0.700263i 0.936701 + 0.350132i \(0.113863\pi\)
−0.936701 + 0.350132i \(0.886137\pi\)
\(282\) 0 0
\(283\) 76.0000i 0.268551i 0.990944 + 0.134276i \(0.0428707\pi\)
−0.990944 + 0.134276i \(0.957129\pi\)
\(284\) 0 0
\(285\) −160.000 178.885i −0.561404 0.627668i
\(286\) 0 0
\(287\) 320.000i 1.11498i
\(288\) 0 0
\(289\) −31.0000 −0.107266
\(290\) 0 0
\(291\) −111.803 + 100.000i −0.384204 + 0.343643i
\(292\) 0 0
\(293\) 140.000 0.477816 0.238908 0.971042i \(-0.423211\pi\)
0.238908 + 0.971042i \(0.423211\pi\)
\(294\) 0 0
\(295\) −411.437 −1.39470
\(296\) 0 0
\(297\) 70.0000 + 98.3870i 0.235690 + 0.331269i
\(298\) 0 0
\(299\) −286.217 −0.957246
\(300\) 0 0
\(301\) 321.994i 1.06975i
\(302\) 0 0
\(303\) −205.718 + 184.000i −0.678938 + 0.607261i
\(304\) 0 0
\(305\) 71.5542i 0.234604i
\(306\) 0 0
\(307\) 244.000i 0.794788i 0.917648 + 0.397394i \(0.130085\pi\)
−0.917648 + 0.397394i \(0.869915\pi\)
\(308\) 0 0
\(309\) −100.000 + 89.4427i −0.323625 + 0.289459i
\(310\) 0 0
\(311\) 400.000i 1.28617i −0.765793 0.643087i \(-0.777653\pi\)
0.765793 0.643087i \(-0.222347\pi\)
\(312\) 0 0
\(313\) −290.000 −0.926518 −0.463259 0.886223i \(-0.653320\pi\)
−0.463259 + 0.886223i \(0.653320\pi\)
\(314\) 0 0
\(315\) −35.7771 + 320.000i −0.113578 + 1.01587i
\(316\) 0 0
\(317\) −420.000 −1.32492 −0.662461 0.749097i \(-0.730488\pi\)
−0.662461 + 0.749097i \(0.730488\pi\)
\(318\) 0 0
\(319\) −232.551 −0.729000
\(320\) 0 0
\(321\) 90.0000 80.4984i 0.280374 0.250774i
\(322\) 0 0
\(323\) 357.771 1.10765
\(324\) 0 0
\(325\) 160.997i 0.495375i
\(326\) 0 0
\(327\) 250.440 + 280.000i 0.765870 + 0.856269i
\(328\) 0 0
\(329\) 572.433i 1.73992i
\(330\) 0 0
\(331\) 340.000i 1.02719i −0.858033 0.513595i \(-0.828313\pi\)
0.858033 0.513595i \(-0.171687\pi\)
\(332\) 0 0
\(333\) 480.000 + 53.6656i 1.44144 + 0.161158i
\(334\) 0 0
\(335\) 176.000i 0.525373i
\(336\) 0 0
\(337\) 110.000 0.326409 0.163205 0.986592i \(-0.447817\pi\)
0.163205 + 0.986592i \(0.447817\pi\)
\(338\) 0 0
\(339\) −71.5542 80.0000i −0.211074 0.235988i
\(340\) 0 0
\(341\) −120.000 −0.351906
\(342\) 0 0
\(343\) −160.997 −0.469379
\(344\) 0 0
\(345\) 128.000 + 143.108i 0.371014 + 0.414807i
\(346\) 0 0
\(347\) 147.580 0.425304 0.212652 0.977128i \(-0.431790\pi\)
0.212652 + 0.977128i \(0.431790\pi\)
\(348\) 0 0
\(349\) 17.8885i 0.0512566i 0.999672 + 0.0256283i \(0.00815863\pi\)
−0.999672 + 0.0256283i \(0.991841\pi\)
\(350\) 0 0
\(351\) −393.548 + 280.000i −1.12122 + 0.797721i
\(352\) 0 0
\(353\) 214.663i 0.608109i 0.952655 + 0.304055i \(0.0983405\pi\)
−0.952655 + 0.304055i \(0.901659\pi\)
\(354\) 0 0
\(355\) 320.000i 0.901408i
\(356\) 0 0
\(357\) −320.000 357.771i −0.896359 1.00216i
\(358\) 0 0
\(359\) 560.000i 1.55989i −0.625849 0.779944i \(-0.715247\pi\)
0.625849 0.779944i \(-0.284753\pi\)
\(360\) 0 0
\(361\) −39.0000 −0.108033
\(362\) 0 0
\(363\) 225.843 202.000i 0.622157 0.556474i
\(364\) 0 0
\(365\) 200.000 0.547945
\(366\) 0 0
\(367\) 617.155 1.68162 0.840810 0.541330i \(-0.182079\pi\)
0.840810 + 0.541330i \(0.182079\pi\)
\(368\) 0 0
\(369\) −320.000 35.7771i −0.867209 0.0969569i
\(370\) 0 0
\(371\) −178.885 −0.482171
\(372\) 0 0
\(373\) 375.659i 1.00713i −0.863957 0.503565i \(-0.832021\pi\)
0.863957 0.503565i \(-0.167979\pi\)
\(374\) 0 0
\(375\) −304.105 + 272.000i −0.810947 + 0.725333i
\(376\) 0 0
\(377\) 930.204i 2.46739i
\(378\) 0 0
\(379\) 260.000i 0.686016i 0.939333 + 0.343008i \(0.111446\pi\)
−0.939333 + 0.343008i \(0.888554\pi\)
\(380\) 0 0
\(381\) 60.0000 53.6656i 0.157480 0.140855i
\(382\) 0 0
\(383\) 544.000i 1.42037i −0.704017 0.710183i \(-0.748612\pi\)
0.704017 0.710183i \(-0.251388\pi\)
\(384\) 0 0
\(385\) −160.000 −0.415584
\(386\) 0 0
\(387\) 321.994 + 36.0000i 0.832025 + 0.0930233i
\(388\) 0 0
\(389\) 332.000 0.853470 0.426735 0.904377i \(-0.359664\pi\)
0.426735 + 0.904377i \(0.359664\pi\)
\(390\) 0 0
\(391\) −286.217 −0.732012
\(392\) 0 0
\(393\) −150.000 + 134.164i −0.381679 + 0.341384i
\(394\) 0 0
\(395\) −321.994 −0.815174
\(396\) 0 0
\(397\) 268.328i 0.675890i −0.941166 0.337945i \(-0.890268\pi\)
0.941166 0.337945i \(-0.109732\pi\)
\(398\) 0 0
\(399\) 357.771 + 400.000i 0.896669 + 1.00251i
\(400\) 0 0
\(401\) 160.997i 0.401489i −0.979644 0.200744i \(-0.935664\pi\)
0.979644 0.200744i \(-0.0643360\pi\)
\(402\) 0 0
\(403\) 480.000i 1.19107i
\(404\) 0 0
\(405\) 316.000 + 71.5542i 0.780247 + 0.176677i
\(406\) 0 0
\(407\) 240.000i 0.589681i
\(408\) 0 0
\(409\) 178.000 0.435208 0.217604 0.976037i \(-0.430176\pi\)
0.217604 + 0.976037i \(0.430176\pi\)
\(410\) 0 0
\(411\) 286.217 + 320.000i 0.696391 + 0.778589i
\(412\) 0 0
\(413\) 920.000 2.22760
\(414\) 0 0
\(415\) 411.437 0.991413
\(416\) 0 0
\(417\) 520.000 + 581.378i 1.24700 + 1.39419i
\(418\) 0 0
\(419\) −245.967 −0.587035 −0.293517 0.955954i \(-0.594826\pi\)
−0.293517 + 0.955954i \(0.594826\pi\)
\(420\) 0 0
\(421\) 53.6656i 0.127472i 0.997967 + 0.0637359i \(0.0203015\pi\)
−0.997967 + 0.0637359i \(0.979698\pi\)
\(422\) 0 0
\(423\) 572.433 + 64.0000i 1.35327 + 0.151300i
\(424\) 0 0
\(425\) 160.997i 0.378816i
\(426\) 0 0
\(427\) 160.000i 0.374707i
\(428\) 0 0
\(429\) −160.000 178.885i −0.372960 0.416982i
\(430\) 0 0
\(431\) 320.000i 0.742459i −0.928541 0.371230i \(-0.878936\pi\)
0.928541 0.371230i \(-0.121064\pi\)
\(432\) 0 0
\(433\) 530.000 1.22402 0.612009 0.790851i \(-0.290362\pi\)
0.612009 + 0.790851i \(0.290362\pi\)
\(434\) 0 0
\(435\) −465.102 + 416.000i −1.06920 + 0.956322i
\(436\) 0 0
\(437\) 320.000 0.732265
\(438\) 0 0
\(439\) 474.046 1.07983 0.539916 0.841719i \(-0.318456\pi\)
0.539916 + 0.841719i \(0.318456\pi\)
\(440\) 0 0
\(441\) 31.0000 277.272i 0.0702948 0.628736i
\(442\) 0 0
\(443\) 505.351 1.14075 0.570374 0.821385i \(-0.306798\pi\)
0.570374 + 0.821385i \(0.306798\pi\)
\(444\) 0 0
\(445\) 643.988i 1.44716i
\(446\) 0 0
\(447\) −62.6099 + 56.0000i −0.140067 + 0.125280i
\(448\) 0 0
\(449\) 268.328i 0.597613i −0.954314 0.298806i \(-0.903412\pi\)
0.954314 0.298806i \(-0.0965885\pi\)
\(450\) 0 0
\(451\) 160.000i 0.354767i
\(452\) 0 0
\(453\) 540.000 482.991i 1.19205 1.06620i
\(454\) 0 0
\(455\) 640.000i 1.40659i
\(456\) 0 0
\(457\) 210.000 0.459519 0.229759 0.973247i \(-0.426206\pi\)
0.229759 + 0.973247i \(0.426206\pi\)
\(458\) 0 0
\(459\) −393.548 + 280.000i −0.857403 + 0.610022i
\(460\) 0 0
\(461\) −372.000 −0.806941 −0.403471 0.914993i \(-0.632196\pi\)
−0.403471 + 0.914993i \(0.632196\pi\)
\(462\) 0 0
\(463\) −169.941 −0.367044 −0.183522 0.983016i \(-0.558750\pi\)
−0.183522 + 0.983016i \(0.558750\pi\)
\(464\) 0 0
\(465\) −240.000 + 214.663i −0.516129 + 0.461640i
\(466\) 0 0
\(467\) −460.630 −0.986360 −0.493180 0.869927i \(-0.664166\pi\)
−0.493180 + 0.869927i \(0.664166\pi\)
\(468\) 0 0
\(469\) 393.548i 0.839121i
\(470\) 0 0
\(471\) 107.331 + 120.000i 0.227880 + 0.254777i
\(472\) 0 0
\(473\) 160.997i 0.340374i
\(474\) 0 0
\(475\) 180.000i 0.378947i
\(476\) 0 0
\(477\) −20.0000 + 178.885i −0.0419287 + 0.375022i
\(478\) 0 0
\(479\) 320.000i 0.668058i 0.942563 + 0.334029i \(0.108408\pi\)
−0.942563 + 0.334029i \(0.891592\pi\)
\(480\) 0 0
\(481\) −960.000 −1.99584
\(482\) 0 0
\(483\) −286.217 320.000i −0.592581 0.662526i
\(484\) 0 0
\(485\) −200.000 −0.412371
\(486\) 0 0
\(487\) −62.6099 −0.128562 −0.0642812 0.997932i \(-0.520475\pi\)
−0.0642812 + 0.997932i \(0.520475\pi\)
\(488\) 0 0
\(489\) −248.000 277.272i −0.507157 0.567019i
\(490\) 0 0
\(491\) 889.955 1.81254 0.906268 0.422704i \(-0.138919\pi\)
0.906268 + 0.422704i \(0.138919\pi\)
\(492\) 0 0
\(493\) 930.204i 1.88682i
\(494\) 0 0
\(495\) −17.8885 + 160.000i −0.0361385 + 0.323232i
\(496\) 0 0
\(497\) 715.542i 1.43972i
\(498\) 0 0
\(499\) 100.000i 0.200401i 0.994967 + 0.100200i \(0.0319484\pi\)
−0.994967 + 0.100200i \(0.968052\pi\)
\(500\) 0 0
\(501\) 32.0000 + 35.7771i 0.0638723 + 0.0714114i
\(502\) 0 0
\(503\) 16.0000i 0.0318091i −0.999874 0.0159046i \(-0.994937\pi\)
0.999874 0.0159046i \(-0.00506280\pi\)
\(504\) 0 0
\(505\) −368.000 −0.728713
\(506\) 0 0
\(507\) 337.646 302.000i 0.665969 0.595661i
\(508\) 0 0
\(509\) 332.000 0.652259 0.326130 0.945325i \(-0.394255\pi\)
0.326130 + 0.945325i \(0.394255\pi\)
\(510\) 0 0
\(511\) −447.214 −0.875173
\(512\) 0 0
\(513\) 440.000 313.050i 0.857700 0.610233i
\(514\) 0 0
\(515\) −178.885 −0.347350
\(516\) 0 0
\(517\) 286.217i 0.553611i
\(518\) 0 0
\(519\) −313.050 + 280.000i −0.603178 + 0.539499i
\(520\) 0 0
\(521\) 214.663i 0.412020i −0.978550 0.206010i \(-0.933952\pi\)
0.978550 0.206010i \(-0.0660480\pi\)
\(522\) 0 0
\(523\) 76.0000i 0.145315i −0.997357 0.0726577i \(-0.976852\pi\)
0.997357 0.0726577i \(-0.0231481\pi\)
\(524\) 0 0
\(525\) 180.000 160.997i 0.342857 0.306661i
\(526\) 0 0
\(527\) 480.000i 0.910816i
\(528\) 0 0
\(529\) 273.000 0.516068
\(530\) 0 0
\(531\) 102.859 920.000i 0.193708 1.73258i
\(532\) 0 0
\(533\) 640.000 1.20075
\(534\) 0 0
\(535\) 160.997 0.300929
\(536\) 0 0
\(537\) −150.000 + 134.164i −0.279330 + 0.249840i
\(538\) 0 0
\(539\) 138.636 0.257210
\(540\) 0 0
\(541\) 1019.65i 1.88474i 0.334566 + 0.942372i \(0.391410\pi\)
−0.334566 + 0.942372i \(0.608590\pi\)
\(542\) 0 0
\(543\) −250.440 280.000i −0.461215 0.515654i
\(544\) 0 0
\(545\) 500.879i 0.919044i
\(546\) 0 0
\(547\) 244.000i 0.446069i −0.974810 0.223035i \(-0.928404\pi\)
0.974810 0.223035i \(-0.0715963\pi\)
\(548\) 0 0
\(549\) 160.000 + 17.8885i 0.291439 + 0.0325839i
\(550\) 0 0
\(551\) 1040.00i 1.88748i
\(552\) 0 0
\(553\) 720.000 1.30199
\(554\) 0 0
\(555\) 429.325 + 480.000i 0.773559 + 0.864865i
\(556\) 0 0
\(557\) 60.0000 0.107720 0.0538600 0.998548i \(-0.482848\pi\)
0.0538600 + 0.998548i \(0.482848\pi\)
\(558\) 0 0
\(559\) −643.988 −1.15204
\(560\) 0 0
\(561\) −160.000 178.885i −0.285205 0.318869i
\(562\) 0 0
\(563\) 111.803 0.198585 0.0992925 0.995058i \(-0.468342\pi\)
0.0992925 + 0.995058i \(0.468342\pi\)
\(564\) 0 0
\(565\) 143.108i 0.253289i
\(566\) 0 0
\(567\) −706.597 160.000i −1.24620 0.282187i
\(568\) 0 0
\(569\) 858.650i 1.50905i 0.656271 + 0.754526i \(0.272133\pi\)
−0.656271 + 0.754526i \(0.727867\pi\)
\(570\) 0 0
\(571\) 940.000i 1.64623i 0.567871 + 0.823117i \(0.307767\pi\)
−0.567871 + 0.823117i \(0.692233\pi\)
\(572\) 0 0
\(573\) −320.000 357.771i −0.558464 0.624382i
\(574\) 0 0
\(575\) 144.000i 0.250435i
\(576\) 0 0
\(577\) −370.000 −0.641248 −0.320624 0.947207i \(-0.603893\pi\)
−0.320624 + 0.947207i \(0.603893\pi\)
\(578\) 0 0
\(579\) −67.0820 + 60.0000i −0.115858 + 0.103627i
\(580\) 0 0
\(581\) −920.000 −1.58348
\(582\) 0 0
\(583\) −89.4427 −0.153418
\(584\) 0 0
\(585\) −640.000 71.5542i −1.09402 0.122315i
\(586\) 0 0
\(587\) −469.574 −0.799956 −0.399978 0.916525i \(-0.630982\pi\)
−0.399978 + 0.916525i \(0.630982\pi\)
\(588\) 0 0
\(589\) 536.656i 0.911131i
\(590\) 0 0
\(591\) 402.492 360.000i 0.681036 0.609137i
\(592\) 0 0
\(593\) 572.433i 0.965318i −0.875808 0.482659i \(-0.839671\pi\)
0.875808 0.482659i \(-0.160329\pi\)
\(594\) 0 0
\(595\) 640.000i 1.07563i
\(596\) 0 0
\(597\) −580.000 + 518.768i −0.971524 + 0.868958i
\(598\) 0 0
\(599\) 560.000i 0.934891i −0.884022 0.467446i \(-0.845174\pi\)
0.884022 0.467446i \(-0.154826\pi\)
\(600\) 0 0
\(601\) 302.000 0.502496 0.251248 0.967923i \(-0.419159\pi\)
0.251248 + 0.967923i \(0.419159\pi\)
\(602\) 0 0
\(603\) −393.548 44.0000i −0.652650 0.0729685i
\(604\) 0 0
\(605\) 404.000 0.667769
\(606\) 0 0
\(607\) 44.7214 0.0736760 0.0368380 0.999321i \(-0.488271\pi\)
0.0368380 + 0.999321i \(0.488271\pi\)
\(608\) 0 0
\(609\) 1040.00 930.204i 1.70772 1.52743i
\(610\) 0 0
\(611\) −1144.87 −1.87376
\(612\) 0 0
\(613\) 447.214i 0.729549i −0.931096 0.364775i \(-0.881146\pi\)
0.931096 0.364775i \(-0.118854\pi\)
\(614\) 0 0
\(615\) −286.217 320.000i −0.465393 0.520325i
\(616\) 0 0
\(617\) 447.214i 0.724819i −0.932019 0.362410i \(-0.881954\pi\)
0.932019 0.362410i \(-0.118046\pi\)
\(618\) 0 0
\(619\) 780.000i 1.26010i 0.776556 + 0.630048i \(0.216965\pi\)
−0.776556 + 0.630048i \(0.783035\pi\)
\(620\) 0 0
\(621\) −352.000 + 250.440i −0.566828 + 0.403284i
\(622\) 0 0
\(623\) 1440.00i 2.31140i
\(624\) 0 0
\(625\) −319.000 −0.510400
\(626\) 0 0
\(627\) 178.885 + 200.000i 0.285304 + 0.318979i
\(628\) 0 0
\(629\) −960.000 −1.52623
\(630\) 0 0
\(631\) 80.4984 0.127573 0.0637864 0.997964i \(-0.479682\pi\)
0.0637864 + 0.997964i \(0.479682\pi\)
\(632\) 0 0
\(633\) 120.000 + 134.164i 0.189573 + 0.211950i
\(634\) 0 0
\(635\) 107.331 0.169026
\(636\) 0 0
\(637\) 554.545i 0.870557i
\(638\) 0 0
\(639\) 715.542 + 80.0000i 1.11978 + 0.125196i
\(640\) 0 0
\(641\) 661.876i 1.03257i −0.856417 0.516284i \(-0.827315\pi\)
0.856417 0.516284i \(-0.172685\pi\)
\(642\) 0 0
\(643\) 844.000i 1.31260i 0.754501 + 0.656299i \(0.227879\pi\)
−0.754501 + 0.656299i \(0.772121\pi\)
\(644\) 0 0
\(645\) 288.000 + 321.994i 0.446512 + 0.499215i
\(646\) 0 0
\(647\) 16.0000i 0.0247295i −0.999924 0.0123648i \(-0.996064\pi\)
0.999924 0.0123648i \(-0.00393593\pi\)
\(648\) 0 0
\(649\) 460.000 0.708783
\(650\) 0 0
\(651\) 536.656 480.000i 0.824357 0.737327i
\(652\) 0 0
\(653\) −660.000 −1.01072 −0.505360 0.862909i \(-0.668640\pi\)
−0.505360 + 0.862909i \(0.668640\pi\)
\(654\) 0 0
\(655\) −268.328 −0.409661
\(656\) 0 0
\(657\) −50.0000 + 447.214i −0.0761035 + 0.680690i
\(658\) 0 0
\(659\) 210.190 0.318954 0.159477 0.987202i \(-0.449019\pi\)
0.159477 + 0.987202i \(0.449019\pi\)
\(660\) 0 0
\(661\) 769.207i 1.16370i 0.813295 + 0.581851i \(0.197671\pi\)
−0.813295 + 0.581851i \(0.802329\pi\)
\(662\) 0 0
\(663\) 715.542 640.000i 1.07925 0.965309i
\(664\) 0 0
\(665\) 715.542i 1.07600i
\(666\) 0 0
\(667\) 832.000i 1.24738i
\(668\) 0 0
\(669\) −340.000 + 304.105i −0.508221 + 0.454567i
\(670\) 0 0
\(671\) 80.0000i 0.119225i
\(672\) 0 0
\(673\) −910.000 −1.35215 −0.676077 0.736831i \(-0.736321\pi\)
−0.676077 + 0.736831i \(0.736321\pi\)
\(674\) 0 0
\(675\) −140.872 198.000i −0.208700 0.293333i
\(676\) 0 0
\(677\) −260.000 −0.384047 −0.192024 0.981390i \(-0.561505\pi\)
−0.192024 + 0.981390i \(0.561505\pi\)
\(678\) 0 0
\(679\) 447.214 0.658636
\(680\) 0 0
\(681\) −570.000 + 509.823i −0.837004 + 0.748639i
\(682\) 0 0
\(683\) 934.676 1.36849 0.684243 0.729254i \(-0.260133\pi\)
0.684243 + 0.729254i \(0.260133\pi\)
\(684\) 0 0
\(685\) 572.433i 0.835669i
\(686\) 0 0
\(687\) −393.548 440.000i −0.572850 0.640466i
\(688\) 0 0
\(689\) 357.771i 0.519261i
\(690\) 0 0
\(691\) 100.000i 0.144718i −0.997379 0.0723589i \(-0.976947\pi\)
0.997379 0.0723589i \(-0.0230527\pi\)
\(692\) 0 0
\(693\) 40.0000 357.771i 0.0577201 0.516264i
\(694\) 0 0
\(695\) 1040.00i 1.49640i
\(696\) 0 0
\(697\) 640.000 0.918221
\(698\) 0 0
\(699\) −321.994 360.000i −0.460649 0.515021i
\(700\) 0 0
\(701\) −1028.00 −1.46648 −0.733238 0.679972i \(-0.761992\pi\)
−0.733238 + 0.679972i \(0.761992\pi\)
\(702\) 0 0
\(703\) 1073.31 1.52676
\(704\) 0 0
\(705\) 512.000 + 572.433i 0.726241 + 0.811962i
\(706\) 0 0
\(707\) 822.873 1.16389
\(708\) 0 0
\(709\) 912.316i 1.28676i 0.765545 + 0.643382i \(0.222469\pi\)
−0.765545 + 0.643382i \(0.777531\pi\)
\(710\) 0 0
\(711\) 80.4984 720.000i 0.113219 1.01266i
\(712\) 0 0
\(713\) 429.325i 0.602139i
\(714\) 0 0
\(715\) 320.000i 0.447552i
\(716\) 0 0
\(717\) 640.000 + 715.542i 0.892608 + 0.997966i
\(718\) 0 0
\(719\) 480.000i 0.667594i −0.942645 0.333797i \(-0.891670\pi\)
0.942645 0.333797i \(-0.108330\pi\)
\(720\) 0 0
\(721\) 400.000 0.554785
\(722\) 0 0
\(723\) −711.070 + 636.000i −0.983499 + 0.879668i
\(724\) 0 0
\(725\) 468.000 0.645517
\(726\) 0 0
\(727\) −241.495 −0.332181 −0.166090 0.986111i \(-0.553114\pi\)
−0.166090 + 0.986111i \(0.553114\pi\)
\(728\) 0 0
\(729\) −239.000 + 688.709i −0.327846 + 0.944731i
\(730\) 0 0
\(731\) −643.988 −0.880968
\(732\) 0 0
\(733\) 1126.98i 1.53749i −0.639557 0.768744i \(-0.720882\pi\)
0.639557 0.768744i \(-0.279118\pi\)
\(734\) 0 0
\(735\) 277.272 248.000i 0.377241 0.337415i
\(736\) 0 0
\(737\) 196.774i 0.266993i
\(738\) 0 0
\(739\) 1020.00i 1.38024i −0.723693 0.690122i \(-0.757557\pi\)
0.723693 0.690122i \(-0.242443\pi\)
\(740\) 0 0
\(741\) −800.000 + 715.542i −1.07962 + 0.965643i
\(742\) 0 0
\(743\) 176.000i 0.236878i 0.992961 + 0.118439i \(0.0377889\pi\)
−0.992961 + 0.118439i \(0.962211\pi\)
\(744\) 0 0
\(745\) −112.000 −0.150336
\(746\) 0 0
\(747\) −102.859 + 920.000i −0.137696 + 1.23159i
\(748\) 0 0
\(749\) −360.000 −0.480641
\(750\) 0 0
\(751\) 1296.92 1.72692 0.863462 0.504414i \(-0.168292\pi\)
0.863462 + 0.504414i \(0.168292\pi\)
\(752\) 0 0
\(753\) −330.000 + 295.161i −0.438247 + 0.391980i
\(754\) 0 0
\(755\) 965.981 1.27945
\(756\) 0 0
\(757\) 983.870i 1.29970i 0.760064 + 0.649848i \(0.225167\pi\)
−0.760064 + 0.649848i \(0.774833\pi\)
\(758\) 0 0
\(759\) −143.108 160.000i −0.188549 0.210804i
\(760\) 0 0
\(761\) 107.331i 0.141040i 0.997510 + 0.0705199i \(0.0224658\pi\)
−0.997510 + 0.0705199i \(0.977534\pi\)
\(762\) 0 0
\(763\) 1120.00i 1.46789i
\(764\) 0 0
\(765\) −640.000 71.5542i −0.836601 0.0935349i
\(766\) 0 0
\(767\) 1840.00i 2.39896i
\(768\) 0 0
\(769\) −1378.00 −1.79194 −0.895969 0.444117i \(-0.853517\pi\)
−0.895969 + 0.444117i \(0.853517\pi\)
\(770\) 0 0
\(771\) 214.663 + 240.000i 0.278421 + 0.311284i
\(772\) 0 0
\(773\) 1180.00 1.52652 0.763260 0.646091i \(-0.223598\pi\)
0.763260 + 0.646091i \(0.223598\pi\)
\(774\) 0 0
\(775\) 241.495 0.311607
\(776\) 0 0
\(777\) −960.000 1073.31i −1.23552 1.38135i
\(778\) 0 0
\(779\) −715.542 −0.918539
\(780\) 0 0
\(781\) 357.771i 0.458093i
\(782\) 0 0
\(783\) −813.929 1144.00i −1.03950 1.46105i
\(784\) 0 0
\(785\) 214.663i 0.273455i
\(786\) 0 0
\(787\) 1244.00i 1.58069i 0.612665 + 0.790343i \(0.290098\pi\)
−0.612665 + 0.790343i \(0.709902\pi\)
\(788\) 0 0
\(789\) −288.000 321.994i −0.365019 0.408104i
\(790\) 0 0
\(791\) 320.000i 0.404551i
\(792\) 0 0
\(793\) −320.000 −0.403531
\(794\) 0 0
\(795\) −178.885 + 160.000i −0.225013 + 0.201258i
\(796\) 0 0
\(797\) −580.000 −0.727729 −0.363864 0.931452i \(-0.618543\pi\)
−0.363864 + 0.931452i \(0.618543\pi\)
\(798\) 0 </