Properties

Label 2160.2.q.k.1441.1
Level $2160$
Weight $2$
Character 2160.1441
Analytic conductor $17.248$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2160.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.2476868366\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.954288.1
Defining polynomial: \( x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1441.1
Root \(0.403374 + 1.68443i\) of defining polynomial
Character \(\chi\) \(=\) 2160.1441
Dual form 2160.2.q.k.721.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{5} +(-0.257068 - 0.445256i) q^{7} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{5} +(-0.257068 - 0.445256i) q^{7} +(1.66044 + 2.87597i) q^{11} +(0.660442 - 1.14392i) q^{13} +3.32088 q^{17} +1.32088 q^{19} +(-2.06382 + 3.57463i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.693252 - 1.20075i) q^{29} +(4.36783 - 7.56531i) q^{31} -0.514137 q^{35} +0.292611 q^{37} +(-5.67458 + 9.82866i) q^{41} +(5.17458 + 8.96263i) q^{43} +(2.43165 + 4.21174i) q^{47} +(3.36783 - 5.83326i) q^{49} +5.02827 q^{53} +3.32088 q^{55} +(2.51414 - 4.35461i) q^{59} +(-3.67458 - 6.36456i) q^{61} +(-0.660442 - 1.14392i) q^{65} +(4.72426 - 8.18266i) q^{67} +8.99093 q^{71} +6.05655 q^{73} +(0.853695 - 1.47864i) q^{77} +(-4.02827 - 6.97717i) q^{79} +(-0.771205 - 1.33577i) q^{83} +(1.66044 - 2.87597i) q^{85} +3.00000 q^{89} -0.679116 q^{91} +(0.660442 - 1.14392i) q^{95} +(6.12763 + 10.6134i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{5} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{5} + 5 q^{7} + 2 q^{11} - 4 q^{13} + 4 q^{17} - 8 q^{19} - 3 q^{23} - 3 q^{25} - 7 q^{29} + 8 q^{31} + 10 q^{35} + 12 q^{37} - 13 q^{41} + 10 q^{43} - 13 q^{47} + 2 q^{49} + 4 q^{53} + 4 q^{55} + 2 q^{59} - q^{61} + 4 q^{65} + 11 q^{67} - 20 q^{71} - 16 q^{73} + 2 q^{79} + 15 q^{83} + 2 q^{85} + 18 q^{89} - 20 q^{91} - 4 q^{95} + 18 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(1297\) \(1621\) \(2081\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −0.257068 0.445256i −0.0971627 0.168291i 0.813346 0.581780i \(-0.197643\pi\)
−0.910509 + 0.413489i \(0.864310\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.66044 + 2.87597i 0.500642 + 0.867138i 1.00000 0.000741679i \(0.000236084\pi\)
−0.499358 + 0.866396i \(0.666431\pi\)
\(12\) 0 0
\(13\) 0.660442 1.14392i 0.183174 0.317266i −0.759786 0.650173i \(-0.774696\pi\)
0.942960 + 0.332907i \(0.108030\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.32088 0.805433 0.402716 0.915325i \(-0.368066\pi\)
0.402716 + 0.915325i \(0.368066\pi\)
\(18\) 0 0
\(19\) 1.32088 0.303032 0.151516 0.988455i \(-0.451585\pi\)
0.151516 + 0.988455i \(0.451585\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.06382 + 3.57463i −0.430335 + 0.745363i −0.996902 0.0786532i \(-0.974938\pi\)
0.566567 + 0.824016i \(0.308271\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.693252 1.20075i −0.128734 0.222973i 0.794453 0.607326i \(-0.207758\pi\)
−0.923186 + 0.384353i \(0.874425\pi\)
\(30\) 0 0
\(31\) 4.36783 7.56531i 0.784486 1.35877i −0.144820 0.989458i \(-0.546260\pi\)
0.929306 0.369311i \(-0.120406\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.514137 −0.0869050
\(36\) 0 0
\(37\) 0.292611 0.0481049 0.0240524 0.999711i \(-0.492343\pi\)
0.0240524 + 0.999711i \(0.492343\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.67458 + 9.82866i −0.886220 + 1.53498i −0.0419119 + 0.999121i \(0.513345\pi\)
−0.844308 + 0.535857i \(0.819988\pi\)
\(42\) 0 0
\(43\) 5.17458 + 8.96263i 0.789116 + 1.36679i 0.926509 + 0.376272i \(0.122794\pi\)
−0.137393 + 0.990517i \(0.543872\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.43165 + 4.21174i 0.354692 + 0.614345i 0.987065 0.160319i \(-0.0512523\pi\)
−0.632373 + 0.774664i \(0.717919\pi\)
\(48\) 0 0
\(49\) 3.36783 5.83326i 0.481119 0.833322i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.02827 0.690687 0.345343 0.938476i \(-0.387762\pi\)
0.345343 + 0.938476i \(0.387762\pi\)
\(54\) 0 0
\(55\) 3.32088 0.447788
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.51414 4.35461i 0.327313 0.566922i −0.654665 0.755919i \(-0.727190\pi\)
0.981978 + 0.188997i \(0.0605236\pi\)
\(60\) 0 0
\(61\) −3.67458 6.36456i −0.470482 0.814898i 0.528948 0.848654i \(-0.322586\pi\)
−0.999430 + 0.0337558i \(0.989253\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.660442 1.14392i −0.0819178 0.141886i
\(66\) 0 0
\(67\) 4.72426 8.18266i 0.577160 0.999670i −0.418643 0.908151i \(-0.637494\pi\)
0.995803 0.0915197i \(-0.0291724\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.99093 1.06703 0.533513 0.845792i \(-0.320871\pi\)
0.533513 + 0.845792i \(0.320871\pi\)
\(72\) 0 0
\(73\) 6.05655 0.708865 0.354433 0.935082i \(-0.384674\pi\)
0.354433 + 0.935082i \(0.384674\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.853695 1.47864i 0.0972875 0.168507i
\(78\) 0 0
\(79\) −4.02827 6.97717i −0.453216 0.784994i 0.545367 0.838197i \(-0.316390\pi\)
−0.998584 + 0.0532036i \(0.983057\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.771205 1.33577i −0.0846508 0.146619i 0.820592 0.571515i \(-0.193644\pi\)
−0.905242 + 0.424896i \(0.860311\pi\)
\(84\) 0 0
\(85\) 1.66044 2.87597i 0.180100 0.311943i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.00000 0.317999 0.159000 0.987279i \(-0.449173\pi\)
0.159000 + 0.987279i \(0.449173\pi\)
\(90\) 0 0
\(91\) −0.679116 −0.0711906
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.660442 1.14392i 0.0677599 0.117364i
\(96\) 0 0
\(97\) 6.12763 + 10.6134i 0.622167 + 1.07762i 0.989081 + 0.147370i \(0.0470808\pi\)
−0.366915 + 0.930255i \(0.619586\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.83502 + 10.1066i 0.580606 + 1.00564i 0.995408 + 0.0957276i \(0.0305178\pi\)
−0.414801 + 0.909912i \(0.636149\pi\)
\(102\) 0 0
\(103\) 0.146305 0.253408i 0.0144159 0.0249691i −0.858727 0.512433i \(-0.828744\pi\)
0.873143 + 0.487464i \(0.162078\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.87237 0.181009 0.0905043 0.995896i \(-0.471152\pi\)
0.0905043 + 0.995896i \(0.471152\pi\)
\(108\) 0 0
\(109\) 5.54787 0.531390 0.265695 0.964057i \(-0.414399\pi\)
0.265695 + 0.964057i \(0.414399\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.90064 6.75611i 0.366942 0.635561i −0.622144 0.782903i \(-0.713738\pi\)
0.989086 + 0.147341i \(0.0470716\pi\)
\(114\) 0 0
\(115\) 2.06382 + 3.57463i 0.192452 + 0.333336i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.853695 1.47864i −0.0782581 0.135547i
\(120\) 0 0
\(121\) −0.0141369 + 0.0244859i −0.00128518 + 0.00222599i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −17.8916 −1.58762 −0.793810 0.608166i \(-0.791906\pi\)
−0.793810 + 0.608166i \(0.791906\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 0 0
\(133\) −0.339558 0.588131i −0.0294434 0.0509974i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.83502 + 4.91040i 0.242212 + 0.419524i 0.961344 0.275350i \(-0.0887936\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(138\) 0 0
\(139\) 4.00000 6.92820i 0.339276 0.587643i −0.645021 0.764165i \(-0.723151\pi\)
0.984297 + 0.176522i \(0.0564848\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.38650 0.366818
\(144\) 0 0
\(145\) −1.38650 −0.115143
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.83049 15.2948i 0.723422 1.25300i −0.236199 0.971705i \(-0.575902\pi\)
0.959620 0.281298i \(-0.0907650\pi\)
\(150\) 0 0
\(151\) 0.632168 + 1.09495i 0.0514451 + 0.0891056i 0.890601 0.454785i \(-0.150284\pi\)
−0.839156 + 0.543891i \(0.816951\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.36783 7.56531i −0.350833 0.607660i
\(156\) 0 0
\(157\) 7.83502 13.5707i 0.625303 1.08306i −0.363179 0.931719i \(-0.618309\pi\)
0.988482 0.151337i \(-0.0483579\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.12217 0.167250
\(162\) 0 0
\(163\) −15.7074 −1.23030 −0.615149 0.788411i \(-0.710904\pi\)
−0.615149 + 0.788411i \(0.710904\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.08249 + 5.33903i −0.238530 + 0.413146i −0.960293 0.278994i \(-0.909999\pi\)
0.721763 + 0.692141i \(0.243332\pi\)
\(168\) 0 0
\(169\) 5.62763 + 9.74734i 0.432895 + 0.749796i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.29261 + 7.43502i 0.326361 + 0.565274i 0.981787 0.189986i \(-0.0608441\pi\)
−0.655426 + 0.755260i \(0.727511\pi\)
\(174\) 0 0
\(175\) −0.257068 + 0.445256i −0.0194325 + 0.0336582i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.06562 −0.0796482 −0.0398241 0.999207i \(-0.512680\pi\)
−0.0398241 + 0.999207i \(0.512680\pi\)
\(180\) 0 0
\(181\) −12.6700 −0.941757 −0.470878 0.882198i \(-0.656063\pi\)
−0.470878 + 0.882198i \(0.656063\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.146305 0.253408i 0.0107566 0.0186309i
\(186\) 0 0
\(187\) 5.51414 + 9.55077i 0.403234 + 0.698421i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.46719 + 14.6656i 0.612664 + 1.06117i 0.990789 + 0.135411i \(0.0432356\pi\)
−0.378125 + 0.925754i \(0.623431\pi\)
\(192\) 0 0
\(193\) −13.3588 + 23.1380i −0.961585 + 1.66551i −0.243060 + 0.970011i \(0.578151\pi\)
−0.718524 + 0.695502i \(0.755182\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 14.2553 1.01565 0.507823 0.861462i \(-0.330450\pi\)
0.507823 + 0.861462i \(0.330450\pi\)
\(198\) 0 0
\(199\) 24.6610 1.74817 0.874085 0.485773i \(-0.161462\pi\)
0.874085 + 0.485773i \(0.161462\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.356427 + 0.617349i −0.0250162 + 0.0433294i
\(204\) 0 0
\(205\) 5.67458 + 9.82866i 0.396330 + 0.686463i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.19325 + 3.79882i 0.151710 + 0.262770i
\(210\) 0 0
\(211\) −2.68872 + 4.65699i −0.185099 + 0.320601i −0.943610 0.331060i \(-0.892594\pi\)
0.758511 + 0.651660i \(0.225927\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 10.3492 0.705807
\(216\) 0 0
\(217\) −4.49133 −0.304891
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.19325 3.79882i 0.147534 0.255537i
\(222\) 0 0
\(223\) 4.33229 + 7.50375i 0.290112 + 0.502488i 0.973836 0.227252i \(-0.0729743\pi\)
−0.683724 + 0.729740i \(0.739641\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.66044 2.87597i −0.110207 0.190885i 0.805646 0.592397i \(-0.201818\pi\)
−0.915854 + 0.401512i \(0.868485\pi\)
\(228\) 0 0
\(229\) 12.6559 21.9207i 0.836326 1.44856i −0.0566206 0.998396i \(-0.518033\pi\)
0.892946 0.450163i \(-0.148634\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −27.6327 −1.81028 −0.905139 0.425116i \(-0.860233\pi\)
−0.905139 + 0.425116i \(0.860233\pi\)
\(234\) 0 0
\(235\) 4.86330 0.317246
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.09936 3.63620i 0.135796 0.235206i −0.790105 0.612971i \(-0.789974\pi\)
0.925901 + 0.377765i \(0.123307\pi\)
\(240\) 0 0
\(241\) −1.80221 3.12152i −0.116091 0.201075i 0.802125 0.597157i \(-0.203703\pi\)
−0.918215 + 0.396082i \(0.870370\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.36783 5.83326i −0.215163 0.372673i
\(246\) 0 0
\(247\) 0.872368 1.51099i 0.0555074 0.0961417i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −6.87783 −0.434125 −0.217062 0.976158i \(-0.569648\pi\)
−0.217062 + 0.976158i \(0.569648\pi\)
\(252\) 0 0
\(253\) −13.7074 −0.861776
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 0 0
\(259\) −0.0752210 0.130287i −0.00467400 0.00809561i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.11803 5.40059i −0.192266 0.333015i 0.753735 0.657179i \(-0.228250\pi\)
−0.946001 + 0.324164i \(0.894917\pi\)
\(264\) 0 0
\(265\) 2.51414 4.35461i 0.154442 0.267502i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −9.92345 −0.605044 −0.302522 0.953142i \(-0.597828\pi\)
−0.302522 + 0.953142i \(0.597828\pi\)
\(270\) 0 0
\(271\) −6.60442 −0.401190 −0.200595 0.979674i \(-0.564288\pi\)
−0.200595 + 0.979674i \(0.564288\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.66044 2.87597i 0.100128 0.173428i
\(276\) 0 0
\(277\) −11.3305 19.6250i −0.680783 1.17915i −0.974742 0.223333i \(-0.928306\pi\)
0.293959 0.955818i \(-0.405027\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7.77394 13.4649i −0.463754 0.803246i 0.535390 0.844605i \(-0.320165\pi\)
−0.999144 + 0.0413590i \(0.986831\pi\)
\(282\) 0 0
\(283\) 0.322689 0.558913i 0.0191819 0.0332240i −0.856275 0.516520i \(-0.827227\pi\)
0.875457 + 0.483296i \(0.160561\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.83502 0.344430
\(288\) 0 0
\(289\) −5.97173 −0.351278
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −0.688716 + 1.19289i −0.0402352 + 0.0696895i −0.885442 0.464750i \(-0.846144\pi\)
0.845207 + 0.534440i \(0.179477\pi\)
\(294\) 0 0
\(295\) −2.51414 4.35461i −0.146379 0.253535i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.72606 + 4.72168i 0.157652 + 0.273062i
\(300\) 0 0
\(301\) 2.66044 4.60802i 0.153345 0.265602i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −7.34916 −0.420812
\(306\) 0 0
\(307\) 7.98546 0.455754 0.227877 0.973690i \(-0.426822\pi\)
0.227877 + 0.973690i \(0.426822\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4.81635 + 8.34216i −0.273110 + 0.473040i −0.969657 0.244471i \(-0.921386\pi\)
0.696547 + 0.717512i \(0.254719\pi\)
\(312\) 0 0
\(313\) 12.2685 + 21.2496i 0.693455 + 1.20110i 0.970699 + 0.240300i \(0.0772458\pi\)
−0.277244 + 0.960800i \(0.589421\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.1746 17.6229i −0.571461 0.989800i −0.996416 0.0845855i \(-0.973043\pi\)
0.424955 0.905215i \(-0.360290\pi\)
\(318\) 0 0
\(319\) 2.30221 3.98755i 0.128899 0.223260i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 4.38650 0.244072
\(324\) 0 0
\(325\) −1.32088 −0.0732695
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.25020 2.16541i 0.0689257 0.119383i
\(330\) 0 0
\(331\) 8.22153 + 14.2401i 0.451896 + 0.782707i 0.998504 0.0546819i \(-0.0174145\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −4.72426 8.18266i −0.258114 0.447066i
\(336\) 0 0
\(337\) −2.44852 + 4.24096i −0.133379 + 0.231020i −0.924977 0.380023i \(-0.875916\pi\)
0.791598 + 0.611042i \(0.209249\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 29.0101 1.57099
\(342\) 0 0
\(343\) −7.06201 −0.381313
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −11.1372 + 19.2903i −0.597878 + 1.03556i 0.395256 + 0.918571i \(0.370656\pi\)
−0.993134 + 0.116984i \(0.962677\pi\)
\(348\) 0 0
\(349\) 1.47173 + 2.54910i 0.0787797 + 0.136450i 0.902724 0.430221i \(-0.141564\pi\)
−0.823944 + 0.566671i \(0.808231\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9.41478 + 16.3069i 0.501098 + 0.867927i 0.999999 + 0.00126845i \(0.000403761\pi\)
−0.498901 + 0.866659i \(0.666263\pi\)
\(354\) 0 0
\(355\) 4.49546 7.78637i 0.238594 0.413258i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −31.8770 −1.68241 −0.841203 0.540720i \(-0.818152\pi\)
−0.841203 + 0.540720i \(0.818152\pi\)
\(360\) 0 0
\(361\) −17.2553 −0.908172
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3.02827 5.24512i 0.158507 0.274542i
\(366\) 0 0
\(367\) −9.17458 15.8908i −0.478909 0.829495i 0.520798 0.853680i \(-0.325634\pi\)
−0.999708 + 0.0241848i \(0.992301\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.29261 2.23887i −0.0671090 0.116236i
\(372\) 0 0
\(373\) 1.09936 1.90414i 0.0569226 0.0985929i −0.836160 0.548486i \(-0.815205\pi\)
0.893083 + 0.449893i \(0.148538\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.83141 −0.0943226
\(378\) 0 0
\(379\) −15.4713 −0.794709 −0.397354 0.917665i \(-0.630072\pi\)
−0.397354 + 0.917665i \(0.630072\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.85369 + 6.67479i −0.196915 + 0.341066i −0.947526 0.319677i \(-0.896426\pi\)
0.750612 + 0.660743i \(0.229759\pi\)
\(384\) 0 0
\(385\) −0.853695 1.47864i −0.0435083 0.0753586i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −12.3163 21.3325i −0.624464 1.08160i −0.988644 0.150274i \(-0.951984\pi\)
0.364181 0.931328i \(-0.381349\pi\)
\(390\) 0 0
\(391\) −6.85369 + 11.8709i −0.346606 + 0.600340i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.05655 −0.405369
\(396\) 0 0
\(397\) −6.77301 −0.339928 −0.169964 0.985450i \(-0.554365\pi\)
−0.169964 + 0.985450i \(0.554365\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.24980 + 16.0211i −0.461913 + 0.800057i −0.999056 0.0434343i \(-0.986170\pi\)
0.537143 + 0.843491i \(0.319503\pi\)
\(402\) 0 0
\(403\) −5.76940 9.99290i −0.287394 0.497782i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.485863 + 0.841540i 0.0240833 + 0.0417136i
\(408\) 0 0
\(409\) 6.70739 11.6175i 0.331659 0.574450i −0.651178 0.758925i \(-0.725725\pi\)
0.982837 + 0.184474i \(0.0590583\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.58522 −0.127210
\(414\) 0 0
\(415\) −1.54241 −0.0757140
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 16.5575 28.6784i 0.808886 1.40103i −0.104751 0.994499i \(-0.533404\pi\)
0.913636 0.406532i \(-0.133262\pi\)
\(420\) 0 0
\(421\) 7.34916 + 12.7291i 0.358176 + 0.620379i 0.987656 0.156637i \(-0.0500654\pi\)
−0.629480 + 0.777017i \(0.716732\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.66044 2.87597i −0.0805433 0.139505i
\(426\) 0 0
\(427\) −1.88924 + 3.27225i −0.0914266 + 0.158355i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −32.7549 −1.57775 −0.788873 0.614556i \(-0.789335\pi\)
−0.788873 + 0.614556i \(0.789335\pi\)
\(432\) 0 0
\(433\) −11.8314 −0.568581 −0.284291 0.958738i \(-0.591758\pi\)
−0.284291 + 0.958738i \(0.591758\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.72606 + 4.72168i −0.130405 + 0.225869i
\(438\) 0 0
\(439\) 4.15591 + 7.19824i 0.198351 + 0.343553i 0.947994 0.318289i \(-0.103108\pi\)
−0.749643 + 0.661842i \(0.769775\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14.5876 + 25.2664i 0.693076 + 1.20044i 0.970825 + 0.239789i \(0.0770781\pi\)
−0.277750 + 0.960654i \(0.589589\pi\)
\(444\) 0 0
\(445\) 1.50000 2.59808i 0.0711068 0.123161i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −18.9717 −0.895331 −0.447666 0.894201i \(-0.647744\pi\)
−0.447666 + 0.894201i \(0.647744\pi\)
\(450\) 0 0
\(451\) −37.6892 −1.77472
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.339558 + 0.588131i −0.0159187 + 0.0275720i
\(456\) 0 0
\(457\) 11.6176 + 20.1223i 0.543450 + 0.941283i 0.998703 + 0.0509206i \(0.0162155\pi\)
−0.455253 + 0.890362i \(0.650451\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.21285 + 3.83277i 0.103063 + 0.178510i 0.912945 0.408082i \(-0.133802\pi\)
−0.809882 + 0.586592i \(0.800469\pi\)
\(462\) 0 0
\(463\) −9.75434 + 16.8950i −0.453322 + 0.785178i −0.998590 0.0530845i \(-0.983095\pi\)
0.545268 + 0.838262i \(0.316428\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −24.5935 −1.13805 −0.569026 0.822320i \(-0.692679\pi\)
−0.569026 + 0.822320i \(0.692679\pi\)
\(468\) 0 0
\(469\) −4.85783 −0.224314
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −17.1842 + 29.7639i −0.790129 + 1.36854i
\(474\) 0 0
\(475\) −0.660442 1.14392i −0.0303032 0.0524866i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −16.3774 28.3665i −0.748304 1.29610i −0.948635 0.316372i \(-0.897535\pi\)
0.200331 0.979728i \(-0.435798\pi\)
\(480\) 0 0
\(481\) 0.193252 0.334723i 0.00881155 0.0152621i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.2553 0.556483
\(486\) 0 0
\(487\) 6.03735 0.273578 0.136789 0.990600i \(-0.456322\pi\)
0.136789 + 0.990600i \(0.456322\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.22153 + 12.5081i −0.325903 + 0.564480i −0.981695 0.190461i \(-0.939002\pi\)
0.655792 + 0.754942i \(0.272335\pi\)
\(492\) 0 0
\(493\) −2.30221 3.98755i −0.103686 0.179590i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.31128 4.00326i −0.103675 0.179571i
\(498\) 0 0
\(499\) 10.4859 18.1620i 0.469412 0.813045i −0.529977 0.848012i \(-0.677799\pi\)
0.999388 + 0.0349673i \(0.0111327\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −5.31728 −0.237086 −0.118543 0.992949i \(-0.537822\pi\)
−0.118543 + 0.992949i \(0.537822\pi\)
\(504\) 0 0
\(505\) 11.6700 0.519310
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9.11350 15.7850i 0.403949 0.699659i −0.590250 0.807221i \(-0.700971\pi\)
0.994198 + 0.107561i \(0.0343041\pi\)
\(510\) 0 0
\(511\) −1.55695 2.69671i −0.0688753 0.119296i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.146305 0.253408i −0.00644698 0.0111665i
\(516\) 0 0
\(517\) −8.07522 + 13.9867i −0.355148 + 0.615134i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −40.1232 −1.75783 −0.878915 0.476978i \(-0.841732\pi\)
−0.878915 + 0.476978i \(0.841732\pi\)
\(522\) 0 0
\(523\) −18.9873 −0.830257 −0.415129 0.909763i \(-0.636263\pi\)
−0.415129 + 0.909763i \(0.636263\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.5051 25.1235i 0.631851 1.09440i
\(528\) 0 0
\(529\) 2.98133 + 5.16381i 0.129623 + 0.224513i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 7.49546 + 12.9825i 0.324665 + 0.562336i
\(534\) 0 0
\(535\) 0.936184 1.62152i 0.0404748 0.0701043i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 22.3684 0.963473
\(540\) 0 0
\(541\) 16.5279 0.710589 0.355294 0.934754i \(-0.384381\pi\)
0.355294 + 0.934754i \(0.384381\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.77394 4.80460i 0.118822 0.205806i
\(546\) 0 0
\(547\) 8.83683 + 15.3058i 0.377835 + 0.654430i 0.990747 0.135721i \(-0.0433352\pi\)
−0.612912 + 0.790151i \(0.710002\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.915706 1.58605i −0.0390104 0.0675680i
\(552\) 0 0
\(553\) −2.07108 + 3.58722i −0.0880715 + 0.152544i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −17.3401 −0.734723 −0.367362 0.930078i \(-0.619739\pi\)
−0.367362 + 0.930078i \(0.619739\pi\)
\(558\) 0 0
\(559\) 13.6700 0.578181
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6.49727 + 11.2536i −0.273827 + 0.474283i −0.969839 0.243748i \(-0.921623\pi\)
0.696011 + 0.718031i \(0.254956\pi\)
\(564\) 0 0
\(565\) −3.90064 6.75611i −0.164101 0.284232i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.34009 14.4455i −0.349635 0.605585i 0.636550 0.771236i \(-0.280361\pi\)
−0.986184 + 0.165651i \(0.947028\pi\)
\(570\) 0 0
\(571\) 10.0000 17.3205i 0.418487 0.724841i −0.577301 0.816532i \(-0.695894\pi\)
0.995788 + 0.0916910i \(0.0292272\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4.12763 0.172134
\(576\) 0 0
\(577\) −23.5953 −0.982287 −0.491144 0.871079i \(-0.663421\pi\)
−0.491144 + 0.871079i \(0.663421\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.396505 + 0.686767i −0.0164498 + 0.0284919i
\(582\) 0 0
\(583\) 8.34916 + 14.4612i 0.345787 + 0.598920i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14.0638 24.3592i −0.580476 1.00541i −0.995423 0.0955681i \(-0.969533\pi\)
0.414947 0.909846i \(-0.363800\pi\)
\(588\) 0 0
\(589\) 5.76940 9.99290i 0.237724 0.411750i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9.17872 0.376925 0.188462 0.982080i \(-0.439650\pi\)
0.188462 + 0.982080i \(0.439650\pi\)
\(594\) 0 0
\(595\) −1.70739 −0.0699961
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 15.7357 27.2550i 0.642942 1.11361i −0.341831 0.939761i \(-0.611047\pi\)
0.984773 0.173846i \(-0.0556196\pi\)
\(600\) 0 0
\(601\) 14.6327 + 25.3446i 0.596880 + 1.03383i 0.993279 + 0.115748i \(0.0369265\pi\)
−0.396398 + 0.918079i \(0.629740\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.0141369 + 0.0244859i 0.000574748 + 0.000995493i
\(606\) 0 0
\(607\) −22.1017 + 38.2813i −0.897080 + 1.55379i −0.0658708 + 0.997828i \(0.520983\pi\)
−0.831209 + 0.555960i \(0.812351\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.42385 0.259881
\(612\) 0 0
\(613\) −35.1715 −1.42056 −0.710282 0.703918i \(-0.751432\pi\)
−0.710282 + 0.703918i \(0.751432\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.71285 + 6.43085i −0.149474 + 0.258896i −0.931033 0.364935i \(-0.881091\pi\)
0.781559 + 0.623831i \(0.214425\pi\)
\(618\) 0 0
\(619\) 4.27394 + 7.40268i 0.171784 + 0.297539i 0.939044 0.343798i \(-0.111714\pi\)
−0.767260 + 0.641337i \(0.778380\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.771205 1.33577i −0.0308977 0.0535164i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.971726 0.0387453
\(630\) 0 0
\(631\) 2.36836 0.0942829 0.0471415 0.998888i \(-0.484989\pi\)
0.0471415 + 0.998888i \(0.484989\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.94578 + 15.4946i −0.355003 + 0.614883i
\(636\) 0 0
\(637\) −4.44852 7.70506i −0.176257 0.305285i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.0665480 0.115265i −0.00262849 0.00455268i 0.864708 0.502275i \(-0.167503\pi\)
−0.867337 + 0.497722i \(0.834170\pi\)
\(642\) 0 0
\(643\) −11.3232 + 19.6124i −0.446544 + 0.773437i −0.998158 0.0606623i \(-0.980679\pi\)
0.551614 + 0.834099i \(0.314012\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 46.3912 1.82383 0.911913 0.410385i \(-0.134606\pi\)
0.911913 + 0.410385i \(0.134606\pi\)
\(648\) 0 0
\(649\) 16.6983 0.655466
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 18.2029 31.5283i 0.712333 1.23380i −0.251647 0.967819i \(-0.580972\pi\)
0.963979 0.265977i \(-0.0856946\pi\)
\(654\) 0 0
\(655\) −3.00000 5.19615i −0.117220 0.203030i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −9.57068 16.5769i −0.372821 0.645745i 0.617177 0.786824i \(-0.288276\pi\)
−0.989998 + 0.141079i \(0.954943\pi\)
\(660\) 0 0
\(661\) −19.9536 + 34.5606i −0.776104 + 1.34425i 0.158067 + 0.987428i \(0.449474\pi\)
−0.934172 + 0.356824i \(0.883860\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.679116 −0.0263350
\(666\) 0 0
\(667\) 5.72298 0.221595
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 12.2029 21.1360i 0.471086 0.815945i
\(672\) 0 0
\(673\) −11.8254 20.4822i −0.455836 0.789532i 0.542899 0.839798i \(-0.317326\pi\)
−0.998736 + 0.0502658i \(0.983993\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.40157 12.8199i −0.284465 0.492709i 0.688014 0.725697i \(-0.258483\pi\)
−0.972479 + 0.232989i \(0.925149\pi\)
\(678\) 0 0
\(679\) 3.15044 5.45673i 0.120903 0.209410i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −4.95252 −0.189503 −0.0947515 0.995501i \(-0.530206\pi\)
−0.0947515 + 0.995501i \(0.530206\pi\)
\(684\) 0 0
\(685\) 5.67004 0.216641
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.32088 5.75194i 0.126516 0.219131i
\(690\) 0 0
\(691\) −9.60442 16.6353i −0.365369 0.632838i 0.623466 0.781851i \(-0.285724\pi\)
−0.988835 + 0.149012i \(0.952391\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.00000 6.92820i −0.151729 0.262802i
\(696\) 0 0
\(697\) −18.8446 + 32.6398i −0.713791 + 1.23632i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 29.3492 1.10850 0.554251 0.832349i \(-0.313005\pi\)
0.554251 + 0.832349i \(0.313005\pi\)
\(702\) 0 0
\(703\) 0.386505 0.0145773
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.00000 5.19615i 0.112827 0.195421i
\(708\) 0 0
\(709\) −19.3633 33.5382i −0.727204 1.25955i −0.958060 0.286566i \(-0.907486\pi\)
0.230857 0.972988i \(-0.425847\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 18.0288 + 31.2268i 0.675184 + 1.16945i
\(714\) 0 0
\(715\) 2.19325 3.79882i 0.0820230 0.142068i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −15.0848 −0.562569 −0.281284 0.959624i \(-0.590760\pi\)
−0.281284 + 0.959624i \(0.590760\pi\)
\(720\) 0 0
\(721\) −0.150442 −0.00560275
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.693252 + 1.20075i −0.0257467 + 0.0445947i
\(726\) 0 0
\(727\) 6.17277 + 10.6916i 0.228936 + 0.396528i 0.957493 0.288457i \(-0.0931422\pi\)
−0.728557 + 0.684985i \(0.759809\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 17.1842 + 29.7639i 0.635580 + 1.10086i
\(732\) 0 0
\(733\) 11.0000 19.0526i 0.406294 0.703722i −0.588177 0.808732i \(-0.700154\pi\)
0.994471 + 0.105010i \(0.0334875\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 31.3774 1.15580
\(738\) 0 0
\(739\) −29.7266 −1.09351 −0.546755 0.837293i \(-0.684137\pi\)
−0.546755 + 0.837293i \(0.684137\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −24.1824 + 41.8851i −0.887165 + 1.53662i −0.0439537 + 0.999034i \(0.513995\pi\)
−0.843212 + 0.537582i \(0.819338\pi\)
\(744\) 0 0
\(745\) −8.83049 15.2948i −0.323524 0.560360i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −0.481327 0.833682i −0.0175873 0.0304621i
\(750\) 0 0
\(751\) −15.9102 + 27.5573i −0.580573 + 1.00558i 0.414838 + 0.909895i \(0.363838\pi\)
−0.995411 + 0.0956869i \(0.969495\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.26434 0.0460139
\(756\) 0 0
\(757\) 4.94531 0.179740 0.0898701 0.995953i \(-0.471355\pi\)
0.0898701 + 0.995953i \(0.471355\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17.7125 30.6789i 0.642076 1.11211i −0.342893 0.939375i \(-0.611407\pi\)
0.984969 0.172734i \(-0.0552600\pi\)
\(762\) 0 0
\(763\) −1.42618 2.47022i −0.0516313 0.0894281i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.32088 5.75194i −0.119910 0.207691i
\(768\) 0 0
\(769\) −24.7125 + 42.8032i −0.891154 + 1.54352i −0.0526602 + 0.998612i \(0.516770\pi\)
−0.838494 + 0.544911i \(0.816563\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.6599 −0.455345 −0.227673 0.973738i \(-0.573112\pi\)
−0.227673 + 0.973738i \(0.573112\pi\)
\(774\) 0 0
\(775\) −8.73566 −0.313794
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.49546 + 12.9825i −0.268553 + 0.465147i
\(780\) 0 0
\(781\) 14.9289 + 25.8576i 0.534199 + 0.925259i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7.83502 13.5707i −0.279644 0.484357i
\(786\) 0 0
\(787\) 15.4672 26.7900i 0.551346 0.954959i −0.446832 0.894618i \(-0.647448\pi\)
0.998178 0.0603410i \(-0.0192188\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4.01093 −0.142612
\(792\) 0 0
\(793\) −9.70739 −0.344720
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −15.2967 + 26.4947i −0.541839 + 0.938492i 0.456960 + 0.889487i \(0.348938\pi\)
−0.998799 + 0.0490047i \(0.984395\pi\)
\(798\) 0 0
\(799\) 8.07522 + 13.9867i 0.285681 + 0.494814i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0