Properties

Label 2268.2.i.n.2053.7
Level $2268$
Weight $2$
Character 2268.2053
Analytic conductor $18.110$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 9 x^{14} + 31 x^{12} - 282 x^{10} + 1695 x^{8} - 3318 x^{6} + 4606 x^{4} - 4116 x^{2} + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2053.7
Root \(2.40332 + 0.123797i\) of defining polynomial
Character \(\chi\) \(=\) 2268.2053
Dual form 2268.2.i.n.865.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.15101 + 1.99360i) q^{5} +(2.41508 - 1.08045i) q^{7} +O(q^{10})\) \(q+(1.15101 + 1.99360i) q^{5} +(2.41508 - 1.08045i) q^{7} +(-2.23145 + 3.86499i) q^{11} +(1.42148 - 2.46208i) q^{13} +(-0.115312 - 0.199726i) q^{17} +(-1.49360 + 2.58700i) q^{19} +(0.400294 + 0.693329i) q^{23} +(-0.149635 + 0.259175i) q^{25} +(3.82751 + 6.62944i) q^{29} +5.28647 q^{31} +(4.93376 + 3.57112i) q^{35} +(-1.69333 + 2.93293i) q^{37} +(-0.899697 + 1.55832i) q^{41} +(4.85860 + 8.41533i) q^{43} +5.77636 q^{47} +(4.66527 - 5.21874i) q^{49} +(-4.31905 - 7.48081i) q^{53} -10.2737 q^{55} -8.35585 q^{59} -13.1735 q^{61} +6.54454 q^{65} -7.53090 q^{67} +8.59672 q^{71} +(-2.29287 - 3.97137i) q^{73} +(-1.21323 + 11.7453i) q^{77} +9.67313 q^{79} +(8.46521 + 14.6622i) q^{83} +(0.265450 - 0.459773i) q^{85} +(0.944450 - 1.63584i) q^{89} +(0.772852 - 7.48196i) q^{91} -6.87659 q^{95} +(7.70796 + 13.3506i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{7} + O(q^{10}) \) \( 16 q - 6 q^{7} + 10 q^{13} + 8 q^{19} + 16 q^{31} - 4 q^{37} - 10 q^{43} + 10 q^{49} - 32 q^{55} - 56 q^{61} - 36 q^{67} + 40 q^{79} - 38 q^{85} - 2 q^{91} + 42 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 1.15101 + 1.99360i 0.514746 + 0.891566i 0.999854 + 0.0171118i \(0.00544711\pi\)
−0.485108 + 0.874454i \(0.661220\pi\)
\(6\) 0 0
\(7\) 2.41508 1.08045i 0.912816 0.408371i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.23145 + 3.86499i −0.672809 + 1.16534i 0.304295 + 0.952578i \(0.401579\pi\)
−0.977104 + 0.212761i \(0.931754\pi\)
\(12\) 0 0
\(13\) 1.42148 2.46208i 0.394248 0.682858i −0.598757 0.800931i \(-0.704338\pi\)
0.993005 + 0.118073i \(0.0376717\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.115312 0.199726i −0.0279673 0.0484408i 0.851703 0.524025i \(-0.175570\pi\)
−0.879670 + 0.475584i \(0.842237\pi\)
\(18\) 0 0
\(19\) −1.49360 + 2.58700i −0.342656 + 0.593498i −0.984925 0.172982i \(-0.944660\pi\)
0.642269 + 0.766479i \(0.277993\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.400294 + 0.693329i 0.0834670 + 0.144569i 0.904737 0.425971i \(-0.140067\pi\)
−0.821270 + 0.570540i \(0.806734\pi\)
\(24\) 0 0
\(25\) −0.149635 + 0.259175i −0.0299269 + 0.0518349i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.82751 + 6.62944i 0.710750 + 1.23106i 0.964576 + 0.263806i \(0.0849778\pi\)
−0.253825 + 0.967250i \(0.581689\pi\)
\(30\) 0 0
\(31\) 5.28647 0.949479 0.474739 0.880126i \(-0.342542\pi\)
0.474739 + 0.880126i \(0.342542\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.93376 + 3.57112i 0.833958 + 0.603629i
\(36\) 0 0
\(37\) −1.69333 + 2.93293i −0.278382 + 0.482171i −0.970983 0.239150i \(-0.923131\pi\)
0.692601 + 0.721321i \(0.256465\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.899697 + 1.55832i −0.140509 + 0.243369i −0.927688 0.373355i \(-0.878207\pi\)
0.787179 + 0.616724i \(0.211541\pi\)
\(42\) 0 0
\(43\) 4.85860 + 8.41533i 0.740929 + 1.28333i 0.952073 + 0.305871i \(0.0989478\pi\)
−0.211144 + 0.977455i \(0.567719\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.77636 0.842569 0.421284 0.906929i \(-0.361579\pi\)
0.421284 + 0.906929i \(0.361579\pi\)
\(48\) 0 0
\(49\) 4.66527 5.21874i 0.666467 0.745535i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.31905 7.48081i −0.593267 1.02757i −0.993789 0.111281i \(-0.964505\pi\)
0.400522 0.916287i \(-0.368829\pi\)
\(54\) 0 0
\(55\) −10.2737 −1.38530
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.35585 −1.08784 −0.543920 0.839137i \(-0.683060\pi\)
−0.543920 + 0.839137i \(0.683060\pi\)
\(60\) 0 0
\(61\) −13.1735 −1.68669 −0.843347 0.537370i \(-0.819418\pi\)
−0.843347 + 0.537370i \(0.819418\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.54454 0.811751
\(66\) 0 0
\(67\) −7.53090 −0.920046 −0.460023 0.887907i \(-0.652159\pi\)
−0.460023 + 0.887907i \(0.652159\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.59672 1.02024 0.510122 0.860102i \(-0.329600\pi\)
0.510122 + 0.860102i \(0.329600\pi\)
\(72\) 0 0
\(73\) −2.29287 3.97137i −0.268360 0.464814i 0.700078 0.714066i \(-0.253148\pi\)
−0.968439 + 0.249252i \(0.919815\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.21323 + 11.7453i −0.138260 + 1.33850i
\(78\) 0 0
\(79\) 9.67313 1.08831 0.544156 0.838984i \(-0.316850\pi\)
0.544156 + 0.838984i \(0.316850\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 8.46521 + 14.6622i 0.929177 + 1.60938i 0.784701 + 0.619874i \(0.212816\pi\)
0.144476 + 0.989508i \(0.453850\pi\)
\(84\) 0 0
\(85\) 0.265450 0.459773i 0.0287921 0.0498694i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.944450 1.63584i 0.100111 0.173398i −0.811619 0.584187i \(-0.801413\pi\)
0.911730 + 0.410789i \(0.134747\pi\)
\(90\) 0 0
\(91\) 0.772852 7.48196i 0.0810169 0.784323i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −6.87659 −0.705523
\(96\) 0 0
\(97\) 7.70796 + 13.3506i 0.782624 + 1.35555i 0.930408 + 0.366525i \(0.119453\pi\)
−0.147784 + 0.989020i \(0.547214\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.40744 2.43775i 0.140045 0.242566i −0.787468 0.616355i \(-0.788609\pi\)
0.927513 + 0.373790i \(0.121942\pi\)
\(102\) 0 0
\(103\) −2.55832 4.43114i −0.252079 0.436614i 0.712019 0.702160i \(-0.247781\pi\)
−0.964098 + 0.265547i \(0.914448\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.29487 + 2.24278i −0.125180 + 0.216818i −0.921803 0.387658i \(-0.873284\pi\)
0.796623 + 0.604476i \(0.206617\pi\)
\(108\) 0 0
\(109\) −8.76728 15.1854i −0.839753 1.45450i −0.890101 0.455764i \(-0.849366\pi\)
0.0503474 0.998732i \(-0.483967\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −8.21711 + 14.2325i −0.773001 + 1.33888i 0.162910 + 0.986641i \(0.447912\pi\)
−0.935911 + 0.352236i \(0.885421\pi\)
\(114\) 0 0
\(115\) −0.921482 + 1.59605i −0.0859286 + 0.148833i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.494282 0.357767i −0.0453108 0.0327965i
\(120\) 0 0
\(121\) −4.45878 7.72283i −0.405344 0.702076i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 10.8211 0.967873
\(126\) 0 0
\(127\) 8.13145 0.721549 0.360775 0.932653i \(-0.382512\pi\)
0.360775 + 0.932653i \(0.382512\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.25591 + 10.8356i 0.546582 + 0.946707i 0.998506 + 0.0546508i \(0.0174046\pi\)
−0.451924 + 0.892057i \(0.649262\pi\)
\(132\) 0 0
\(133\) −0.812064 + 7.86157i −0.0704148 + 0.681685i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.09668 + 14.0239i −0.691746 + 1.19814i 0.279519 + 0.960140i \(0.409825\pi\)
−0.971265 + 0.237999i \(0.923508\pi\)
\(138\) 0 0
\(139\) 3.07212 5.32107i 0.260574 0.451327i −0.705821 0.708391i \(-0.749422\pi\)
0.966395 + 0.257063i \(0.0827549\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.34394 + 10.9880i 0.530507 + 0.918866i
\(144\) 0 0
\(145\) −8.81098 + 15.2611i −0.731712 + 1.26736i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.85927 6.68446i −0.316164 0.547612i 0.663520 0.748158i \(-0.269062\pi\)
−0.979684 + 0.200546i \(0.935728\pi\)
\(150\) 0 0
\(151\) 7.45878 12.9190i 0.606987 1.05133i −0.384747 0.923022i \(-0.625711\pi\)
0.991734 0.128310i \(-0.0409553\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.08477 + 10.5391i 0.488740 + 0.846523i
\(156\) 0 0
\(157\) −0.257220 −0.0205284 −0.0102642 0.999947i \(-0.503267\pi\)
−0.0102642 + 0.999947i \(0.503267\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.71585 + 1.24195i 0.135228 + 0.0978795i
\(162\) 0 0
\(163\) −6.28748 + 10.8902i −0.492473 + 0.852989i −0.999962 0.00866931i \(-0.997240\pi\)
0.507489 + 0.861658i \(0.330574\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.8470 18.7875i 0.839363 1.45382i −0.0510657 0.998695i \(-0.516262\pi\)
0.890428 0.455123i \(-0.150405\pi\)
\(168\) 0 0
\(169\) 2.45878 + 4.25873i 0.189137 + 0.327595i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 13.7605 1.04619 0.523095 0.852275i \(-0.324777\pi\)
0.523095 + 0.852275i \(0.324777\pi\)
\(174\) 0 0
\(175\) −0.0813555 + 0.787601i −0.00614990 + 0.0595370i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −0.448262 0.776412i −0.0335046 0.0580317i 0.848787 0.528735i \(-0.177334\pi\)
−0.882292 + 0.470703i \(0.844000\pi\)
\(180\) 0 0
\(181\) −17.4613 −1.29788 −0.648942 0.760838i \(-0.724788\pi\)
−0.648942 + 0.760838i \(0.724788\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −7.79613 −0.573183
\(186\) 0 0
\(187\) 1.02925 0.0752665
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.46902 −0.106295 −0.0531474 0.998587i \(-0.516925\pi\)
−0.0531474 + 0.998587i \(0.516925\pi\)
\(192\) 0 0
\(193\) 6.50330 0.468118 0.234059 0.972222i \(-0.424799\pi\)
0.234059 + 0.972222i \(0.424799\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −11.9521 −0.851552 −0.425776 0.904828i \(-0.639999\pi\)
−0.425776 + 0.904828i \(0.639999\pi\)
\(198\) 0 0
\(199\) 9.73886 + 16.8682i 0.690369 + 1.19575i 0.971717 + 0.236149i \(0.0758852\pi\)
−0.281348 + 0.959606i \(0.590781\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 16.4065 + 11.8752i 1.15151 + 0.833478i
\(204\) 0 0
\(205\) −4.14223 −0.289306
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −6.66581 11.5455i −0.461084 0.798621i
\(210\) 0 0
\(211\) 6.43611 11.1477i 0.443080 0.767437i −0.554836 0.831960i \(-0.687219\pi\)
0.997916 + 0.0645225i \(0.0205524\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −11.1846 + 19.3722i −0.762780 + 1.32117i
\(216\) 0 0
\(217\) 12.7673 5.71176i 0.866700 0.387739i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.655656 −0.0441042
\(222\) 0 0
\(223\) −4.92331 8.52743i −0.329690 0.571039i 0.652761 0.757564i \(-0.273611\pi\)
−0.982450 + 0.186525i \(0.940277\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −12.2254 + 21.1750i −0.811426 + 1.40543i 0.100439 + 0.994943i \(0.467975\pi\)
−0.911866 + 0.410489i \(0.865358\pi\)
\(228\) 0 0
\(229\) 11.0018 + 19.0557i 0.727022 + 1.25924i 0.958136 + 0.286312i \(0.0924293\pi\)
−0.231115 + 0.972926i \(0.574237\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.8179 18.7372i 0.708706 1.22752i −0.256631 0.966510i \(-0.582612\pi\)
0.965337 0.261006i \(-0.0840542\pi\)
\(234\) 0 0
\(235\) 6.64863 + 11.5158i 0.433709 + 0.751206i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.86360 + 15.3522i −0.573338 + 0.993051i 0.422882 + 0.906185i \(0.361019\pi\)
−0.996220 + 0.0868662i \(0.972315\pi\)
\(240\) 0 0
\(241\) −2.15887 + 3.73927i −0.139065 + 0.240868i −0.927143 0.374708i \(-0.877743\pi\)
0.788078 + 0.615575i \(0.211076\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 15.7739 + 3.29388i 1.00775 + 0.210438i
\(246\) 0 0
\(247\) 4.24626 + 7.35473i 0.270183 + 0.467971i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 10.2938 0.649741 0.324870 0.945759i \(-0.394679\pi\)
0.324870 + 0.945759i \(0.394679\pi\)
\(252\) 0 0
\(253\) −3.57295 −0.224629
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −5.89568 10.2116i −0.367763 0.636983i 0.621453 0.783452i \(-0.286543\pi\)
−0.989215 + 0.146468i \(0.953209\pi\)
\(258\) 0 0
\(259\) −0.920654 + 8.91283i −0.0572066 + 0.553816i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.59359 + 4.49223i −0.159928 + 0.277003i −0.934842 0.355063i \(-0.884459\pi\)
0.774915 + 0.632066i \(0.217793\pi\)
\(264\) 0 0
\(265\) 9.94251 17.2209i 0.610763 1.05787i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −14.6103 25.3058i −0.890805 1.54292i −0.838912 0.544268i \(-0.816808\pi\)
−0.0518936 0.998653i \(-0.516526\pi\)
\(270\) 0 0
\(271\) 10.2801 17.8056i 0.624470 1.08161i −0.364173 0.931331i \(-0.618648\pi\)
0.988643 0.150283i \(-0.0480184\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.667805 1.15667i −0.0402702 0.0697500i
\(276\) 0 0
\(277\) 5.97833 10.3548i 0.359203 0.622158i −0.628625 0.777709i \(-0.716382\pi\)
0.987828 + 0.155550i \(0.0497151\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −14.9166 25.8363i −0.889850 1.54126i −0.840052 0.542506i \(-0.817476\pi\)
−0.0497975 0.998759i \(-0.515858\pi\)
\(282\) 0 0
\(283\) −9.57094 −0.568933 −0.284467 0.958686i \(-0.591817\pi\)
−0.284467 + 0.958686i \(0.591817\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.489161 + 4.73555i −0.0288742 + 0.279531i
\(288\) 0 0
\(289\) 8.47341 14.6764i 0.498436 0.863316i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7.41014 12.8347i 0.432905 0.749813i −0.564217 0.825626i \(-0.690822\pi\)
0.997122 + 0.0758132i \(0.0241553\pi\)
\(294\) 0 0
\(295\) −9.61765 16.6583i −0.559961 0.969881i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.27604 0.131627
\(300\) 0 0
\(301\) 20.8262 + 15.0743i 1.20040 + 0.868867i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −15.1628 26.2627i −0.868219 1.50380i
\(306\) 0 0
\(307\) −5.88207 −0.335708 −0.167854 0.985812i \(-0.553684\pi\)
−0.167854 + 0.985812i \(0.553684\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 16.2351 0.920606 0.460303 0.887762i \(-0.347741\pi\)
0.460303 + 0.887762i \(0.347741\pi\)
\(312\) 0 0
\(313\) 17.6896 0.999875 0.499937 0.866062i \(-0.333356\pi\)
0.499937 + 0.866062i \(0.333356\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.28017 −0.296564 −0.148282 0.988945i \(-0.547374\pi\)
−0.148282 + 0.988945i \(0.547374\pi\)
\(318\) 0 0
\(319\) −34.1636 −1.91280
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.688922 0.0383326
\(324\) 0 0
\(325\) 0.425406 + 0.736824i 0.0235973 + 0.0408716i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 13.9504 6.24105i 0.769110 0.344080i
\(330\) 0 0
\(331\) −15.6072 −0.857847 −0.428923 0.903341i \(-0.641107\pi\)
−0.428923 + 0.903341i \(0.641107\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −8.66812 15.0136i −0.473590 0.820282i
\(336\) 0 0
\(337\) −3.77185 + 6.53303i −0.205466 + 0.355877i −0.950281 0.311394i \(-0.899204\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −11.7965 + 20.4322i −0.638818 + 1.10646i
\(342\) 0 0
\(343\) 5.62843 17.6443i 0.303907 0.952702i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −26.9003 −1.44408 −0.722042 0.691849i \(-0.756796\pi\)
−0.722042 + 0.691849i \(0.756796\pi\)
\(348\) 0 0
\(349\) 7.00100 + 12.1261i 0.374755 + 0.649095i 0.990290 0.139014i \(-0.0443934\pi\)
−0.615535 + 0.788109i \(0.711060\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 15.1655 26.2675i 0.807180 1.39808i −0.107630 0.994191i \(-0.534326\pi\)
0.914810 0.403885i \(-0.132341\pi\)
\(354\) 0 0
\(355\) 9.89489 + 17.1384i 0.525166 + 0.909614i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.99876 12.1222i 0.369381 0.639786i −0.620088 0.784532i \(-0.712903\pi\)
0.989469 + 0.144746i \(0.0462366\pi\)
\(360\) 0 0
\(361\) 5.03830 + 8.72659i 0.265174 + 0.459294i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.27822 9.14215i 0.276275 0.478522i
\(366\) 0 0
\(367\) 1.25165 2.16792i 0.0653356 0.113165i −0.831507 0.555514i \(-0.812522\pi\)
0.896843 + 0.442349i \(0.145855\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −18.5135 13.4003i −0.961172 0.695708i
\(372\) 0 0
\(373\) −8.80311 15.2474i −0.455808 0.789482i 0.542926 0.839780i \(-0.317316\pi\)
−0.998734 + 0.0502980i \(0.983983\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 21.7629 1.12085
\(378\) 0 0
\(379\) 10.5474 0.541781 0.270891 0.962610i \(-0.412682\pi\)
0.270891 + 0.962610i \(0.412682\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10.8418 + 18.7786i 0.553992 + 0.959542i 0.997981 + 0.0635100i \(0.0202295\pi\)
−0.443989 + 0.896032i \(0.646437\pi\)
\(384\) 0 0
\(385\) −24.8118 + 11.1002i −1.26453 + 0.565717i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.96652 12.0664i 0.353217 0.611790i −0.633594 0.773665i \(-0.718421\pi\)
0.986811 + 0.161876i \(0.0517545\pi\)
\(390\) 0 0
\(391\) 0.0923174 0.159898i 0.00466869 0.00808641i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 11.1338 + 19.2844i 0.560204 + 0.970303i
\(396\) 0 0
\(397\) 13.9542 24.1694i 0.700342 1.21303i −0.268004 0.963418i \(-0.586364\pi\)
0.968346 0.249610i \(-0.0803025\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −17.4525 30.2285i −0.871534 1.50954i −0.860410 0.509603i \(-0.829792\pi\)
−0.0111242 0.999938i \(-0.503541\pi\)
\(402\) 0 0
\(403\) 7.51463 13.0157i 0.374330 0.648359i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.55717 13.0894i −0.374595 0.648818i
\(408\) 0 0
\(409\) −20.6739 −1.02226 −0.511128 0.859504i \(-0.670772\pi\)
−0.511128 + 0.859504i \(0.670772\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −20.1801 + 9.02806i −0.992998 + 0.444242i
\(414\) 0 0
\(415\) −19.4870 + 33.7525i −0.956581 + 1.65685i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 19.9859 34.6166i 0.976376 1.69113i 0.301061 0.953605i \(-0.402659\pi\)
0.675316 0.737529i \(-0.264007\pi\)
\(420\) 0 0
\(421\) −12.5082 21.6649i −0.609614 1.05588i −0.991304 0.131592i \(-0.957991\pi\)
0.381690 0.924290i \(-0.375342\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.0690187 0.00334790
\(426\) 0 0
\(427\) −31.8151 + 14.2333i −1.53964 + 0.688796i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.05181 + 12.2141i 0.339674 + 0.588332i 0.984371 0.176106i \(-0.0563500\pi\)
−0.644698 + 0.764438i \(0.723017\pi\)
\(432\) 0 0
\(433\) 1.58941 0.0763821 0.0381911 0.999270i \(-0.487840\pi\)
0.0381911 + 0.999270i \(0.487840\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.39152 −0.114402
\(438\) 0 0
\(439\) −24.3768 −1.16344 −0.581721 0.813389i \(-0.697620\pi\)
−0.581721 + 0.813389i \(0.697620\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −18.5640 −0.882002 −0.441001 0.897507i \(-0.645376\pi\)
−0.441001 + 0.897507i \(0.645376\pi\)
\(444\) 0 0
\(445\) 4.34827 0.206128
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −21.4616 −1.01284 −0.506418 0.862288i \(-0.669031\pi\)
−0.506418 + 0.862288i \(0.669031\pi\)
\(450\) 0 0
\(451\) −4.01527 6.95465i −0.189072 0.327482i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 15.8056 7.07103i 0.740979 0.331495i
\(456\) 0 0
\(457\) 15.1274 0.707631 0.353816 0.935315i \(-0.384884\pi\)
0.353816 + 0.935315i \(0.384884\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −16.5385 28.6455i −0.770273 1.33415i −0.937413 0.348219i \(-0.886787\pi\)
0.167140 0.985933i \(-0.446547\pi\)
\(462\) 0 0
\(463\) −13.4223 + 23.2481i −0.623788 + 1.08043i 0.364986 + 0.931013i \(0.381074\pi\)
−0.988774 + 0.149419i \(0.952260\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.93579 + 10.2811i −0.274675 + 0.475752i −0.970053 0.242893i \(-0.921904\pi\)
0.695378 + 0.718644i \(0.255237\pi\)
\(468\) 0 0
\(469\) −18.1878 + 8.13674i −0.839833 + 0.375720i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −43.3669 −1.99401
\(474\) 0 0
\(475\) −0.446989 0.774208i −0.0205093 0.0355231i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −8.71973 + 15.1030i −0.398415 + 0.690075i −0.993531 0.113565i \(-0.963773\pi\)
0.595116 + 0.803640i \(0.297106\pi\)
\(480\) 0 0
\(481\) 4.81407 + 8.33822i 0.219503 + 0.380190i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −17.7438 + 30.7332i −0.805706 + 1.39552i
\(486\) 0 0
\(487\) 18.3889 + 31.8504i 0.833279 + 1.44328i 0.895424 + 0.445214i \(0.146872\pi\)
−0.0621458 + 0.998067i \(0.519794\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4.54050 7.86437i 0.204910 0.354914i −0.745194 0.666847i \(-0.767643\pi\)
0.950104 + 0.311933i \(0.100977\pi\)
\(492\) 0 0
\(493\) 0.882716 1.52891i 0.0397555 0.0688586i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20.7618 9.28831i 0.931294 0.416638i
\(498\) 0 0
\(499\) −3.41261 5.91082i −0.152769 0.264604i 0.779475 0.626433i \(-0.215486\pi\)
−0.932245 + 0.361829i \(0.882153\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.09211 0.182458 0.0912291 0.995830i \(-0.470920\pi\)
0.0912291 + 0.995830i \(0.470920\pi\)
\(504\) 0 0
\(505\) 6.47989 0.288351
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 14.3991 + 24.9400i 0.638228 + 1.10544i 0.985821 + 0.167798i \(0.0536658\pi\)
−0.347593 + 0.937646i \(0.613001\pi\)
\(510\) 0 0
\(511\) −9.82834 7.11387i −0.434780 0.314699i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.88929 10.2006i 0.259513 0.449490i
\(516\) 0 0
\(517\) −12.8897 + 22.3256i −0.566888 + 0.981878i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5.92170 10.2567i −0.259434 0.449353i 0.706656 0.707557i \(-0.250203\pi\)
−0.966090 + 0.258204i \(0.916869\pi\)
\(522\) 0 0
\(523\) 6.86664 11.8934i 0.300257 0.520061i −0.675937 0.736959i \(-0.736261\pi\)
0.976194 + 0.216899i \(0.0695942\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.609594 1.05585i −0.0265543 0.0459935i
\(528\) 0 0
\(529\) 11.1795 19.3635i 0.486067 0.841892i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.55781 + 4.43025i 0.110791 + 0.191896i
\(534\) 0 0
\(535\) −5.96162 −0.257743
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 9.76008 + 29.6766i 0.420396 + 1.27826i
\(540\) 0 0
\(541\) 21.7425 37.6592i 0.934784 1.61909i 0.159765 0.987155i \(-0.448926\pi\)
0.775019 0.631938i \(-0.217740\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 20.1824 34.9570i 0.864519 1.49739i
\(546\) 0 0
\(547\) −11.0307 19.1058i −0.471640 0.816904i 0.527834 0.849348i \(-0.323004\pi\)
−0.999474 + 0.0324437i \(0.989671\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −22.8671 −0.974171
\(552\) 0 0
\(553\) 23.3614 10.4513i 0.993429 0.444435i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −16.0925 27.8730i −0.681862 1.18102i −0.974412 0.224769i \(-0.927837\pi\)
0.292551 0.956250i \(-0.405496\pi\)
\(558\) 0 0
\(559\) 27.6256 1.16844
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.38738 0.142761 0.0713804 0.997449i \(-0.477260\pi\)
0.0713804 + 0.997449i \(0.477260\pi\)
\(564\) 0 0
\(565\) −37.8318 −1.59160
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −40.3474 −1.69145 −0.845726 0.533618i \(-0.820832\pi\)
−0.845726 + 0.533618i \(0.820832\pi\)
\(570\) 0 0
\(571\) −10.4386 −0.436840 −0.218420 0.975855i \(-0.570090\pi\)
−0.218420 + 0.975855i \(0.570090\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.239591 −0.00999164
\(576\) 0 0
\(577\) 5.55156 + 9.61559i 0.231114 + 0.400302i 0.958136 0.286312i \(-0.0924295\pi\)
−0.727022 + 0.686614i \(0.759096\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 36.2859 + 26.2642i 1.50539 + 1.08962i
\(582\) 0 0
\(583\) 38.5510 1.59662
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −20.3875 35.3122i −0.841482 1.45749i −0.888642 0.458602i \(-0.848350\pi\)
0.0471601 0.998887i \(-0.484983\pi\)
\(588\) 0 0
\(589\) −7.89589 + 13.6761i −0.325345 + 0.563513i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.7930 25.6221i 0.607474 1.05218i −0.384182 0.923258i \(-0.625516\pi\)
0.991655 0.128918i \(-0.0411503\pi\)
\(594\) 0 0
\(595\) 0.144324 1.39720i 0.00591669 0.0572794i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −18.3552 −0.749973 −0.374987 0.927030i \(-0.622353\pi\)
−0.374987 + 0.927030i \(0.622353\pi\)
\(600\) 0 0
\(601\) 15.9250 + 27.5828i 0.649593 + 1.12513i 0.983220 + 0.182423i \(0.0583939\pi\)
−0.333628 + 0.942705i \(0.608273\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 10.2642 17.7781i 0.417298 0.722781i
\(606\) 0 0
\(607\) −11.8452 20.5164i −0.480780 0.832736i 0.518977 0.854788i \(-0.326313\pi\)
−0.999757 + 0.0220527i \(0.992980\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8.21099 14.2219i 0.332181 0.575354i
\(612\) 0 0
\(613\) 13.3159 + 23.0638i 0.537824 + 0.931539i 0.999021 + 0.0442411i \(0.0140870\pi\)
−0.461197 + 0.887298i \(0.652580\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.72483 8.18364i 0.190214 0.329461i −0.755107 0.655602i \(-0.772415\pi\)
0.945321 + 0.326141i \(0.105748\pi\)
\(618\) 0 0
\(619\) 18.0474 31.2589i 0.725385 1.25640i −0.233431 0.972373i \(-0.574995\pi\)
0.958815 0.284030i \(-0.0916714\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.513492 4.97111i 0.0205726 0.199163i
\(624\) 0 0
\(625\) 13.2034 + 22.8689i 0.528136 + 0.914758i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.781045 0.0311423
\(630\) 0 0
\(631\) 0.0100579 0.000400401 0.000200200 1.00000i \(-0.499936\pi\)
0.000200200 1.00000i \(0.499936\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 9.35935 + 16.2109i 0.371415 + 0.643309i
\(636\) 0 0
\(637\) −6.21737 18.9046i −0.246341 0.749028i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.45227 4.24745i 0.0968587 0.167764i −0.813524 0.581531i \(-0.802454\pi\)
0.910383 + 0.413767i \(0.135787\pi\)
\(642\) 0 0
\(643\) 22.0655 38.2186i 0.870180 1.50720i 0.00837033 0.999965i \(-0.497336\pi\)
0.861810 0.507231i \(-0.169331\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −24.8813 43.0957i −0.978186 1.69427i −0.668993 0.743268i \(-0.733275\pi\)
−0.309192 0.950999i \(-0.600059\pi\)
\(648\) 0 0
\(649\) 18.6457 32.2953i 0.731908 1.26770i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6.98578 12.0997i −0.273375 0.473499i 0.696349 0.717703i \(-0.254807\pi\)
−0.969724 + 0.244205i \(0.921473\pi\)
\(654\) 0 0
\(655\) −14.4012 + 24.9436i −0.562702 + 0.974628i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 12.9827 + 22.4867i 0.505733 + 0.875956i 0.999978 + 0.00663317i \(0.00211142\pi\)
−0.494245 + 0.869323i \(0.664555\pi\)
\(660\) 0 0
\(661\) 25.5362 0.993244 0.496622 0.867967i \(-0.334574\pi\)
0.496622 + 0.867967i \(0.334574\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −16.6075 + 7.42979i −0.644013 + 0.288115i
\(666\) 0 0
\(667\) −3.06425 + 5.30744i −0.118648 + 0.205505i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 29.3961 50.9155i 1.13482 1.96557i
\(672\) 0 0
\(673\) 2.71472 + 4.70203i 0.104645 + 0.181250i 0.913593 0.406630i \(-0.133296\pi\)
−0.808948 + 0.587880i \(0.799963\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −14.1514 −0.543883 −0.271942 0.962314i \(-0.587666\pi\)
−0.271942 + 0.962314i \(0.587666\pi\)
\(678\) 0 0
\(679\) 33.0400 + 23.9147i 1.26796 + 0.917763i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.553330 0.958397i −0.0211726 0.0366720i 0.855245 0.518224i \(-0.173407\pi\)
−0.876418 + 0.481552i \(0.840073\pi\)
\(684\) 0 0
\(685\) −37.2773 −1.42429
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −24.5578 −0.935577
\(690\) 0 0
\(691\) 22.9077 0.871450 0.435725 0.900080i \(-0.356492\pi\)
0.435725 + 0.900080i \(0.356492\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 14.1441 0.536517
\(696\) 0 0
\(697\) 0.414984 0.0157186
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −11.4056 −0.430782 −0.215391 0.976528i \(-0.569103\pi\)
−0.215391 + 0.976528i \(0.569103\pi\)
\(702\) 0 0
\(703\) −5.05832 8.76127i −0.190778 0.330438i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0.765216 7.40805i 0.0287789 0.278608i
\(708\) 0 0
\(709\) −37.0671 −1.39208 −0.696042 0.718001i \(-0.745057\pi\)
−0.696042 + 0.718001i \(0.745057\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.11614 + 3.66527i 0.0792502 + 0.137265i
\(714\) 0 0
\(715\) −14.6038 + 25.2946i −0.546153 + 0.945965i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −0.459342 + 0.795604i −0.0171306 + 0.0296710i −0.874464 0.485091i \(-0.838786\pi\)
0.857333 + 0.514762i \(0.172120\pi\)
\(720\) 0 0
\(721\) −10.9662 7.93745i −0.408402 0.295606i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.29091 −0.0850822
\(726\) 0 0
\(727\) 7.34433 + 12.7208i 0.272386 + 0.471787i 0.969472 0.245201i \(-0.0788538\pi\)
−0.697086 + 0.716987i \(0.745521\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.12051 1.94078i 0.0414435 0.0717823i
\(732\) 0 0
\(733\) 11.4312 + 19.7994i 0.422220 + 0.731307i 0.996156 0.0875931i \(-0.0279175\pi\)
−0.573936 + 0.818900i \(0.694584\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 16.8049 29.1069i 0.619015 1.07217i
\(738\) 0 0
\(739\) 19.6692 + 34.0681i 0.723544 + 1.25321i 0.959571 + 0.281468i \(0.0908212\pi\)
−0.236027 + 0.971746i \(0.575845\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 10.8663 18.8210i 0.398647 0.690477i −0.594912 0.803791i \(-0.702813\pi\)
0.993559 + 0.113314i \(0.0361465\pi\)
\(744\) 0 0
\(745\) 8.88410 15.3877i 0.325488 0.563762i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −0.704014 + 6.81554i −0.0257241 + 0.249034i
\(750\) 0 0
\(751\) −10.3071 17.8525i −0.376113 0.651446i 0.614380 0.789010i \(-0.289406\pi\)
−0.990493 + 0.137564i \(0.956073\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 34.3404 1.24978
\(756\) 0 0
\(757\) 17.8453 0.648600 0.324300 0.945954i \(-0.394871\pi\)
0.324300 + 0.945954i \(0.394871\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 16.9714 + 29.3953i 0.615211 + 1.06558i 0.990347 + 0.138607i \(0.0442626\pi\)
−0.375136 + 0.926970i \(0.622404\pi\)
\(762\) 0 0
\(763\) −37.5807 27.2014i −1.36051 0.984756i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −11.8777 + 20.5728i −0.428879 + 0.742840i
\(768\) 0 0
\(769\) 20.3452 35.2389i 0.733665 1.27075i −0.221641 0.975128i \(-0.571141\pi\)
0.955306 0.295617i \(-0.0955253\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.17562 + 3.76829i 0.0782517 + 0.135536i 0.902496 0.430699i \(-0.141733\pi\)
−0.824244 + 0.566235i \(0.808400\pi\)
\(774\) 0 0
\(775\) −0.791039 + 1.37012i −0.0284150 + 0.0492162i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.68758 4.65503i −0.0962926 0.166784i
\(780\) 0 0
\(781\) −19.1832 + 33.2263i −0.686429 + 1.18893i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.296062 0.512795i −0.0105669 0.0183024i
\(786\) 0 0
\(787\) 37.6220 1.34108 0.670539 0.741874i \(-0.266063\pi\)
0.670539 + 0.741874i \(0.266063\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4.46760 + 43.2508i −0.158850 + 1.53782i
\(792\) 0 0
\(793\) −18.7259 + 32.4342i −0.664976 + 1.15177i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −22.1570 + 38.3771i −0.784842 + 1.35939i 0.144251 + 0.989541i \(0.453923\pi\)
−0.929093 + 0.369845i \(0.879411\pi\)
\(798\) 0 0
\(799\) −0.666084 1.15369i −0.0235644 0.0408147i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 20.4658 0.722221
\(804\) 0 0