Properties

Label 2340.2.q.a.2161.1
Level $2340$
Weight $2$
Character 2340.2161
Analytic conductor $18.685$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2340.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6849940730\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 260)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2161.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2340.2161
Dual form 2340.2.q.a.1621.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +O(q^{10})\) \(q-1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{11} +(1.00000 - 3.46410i) q^{13} +(-3.50000 + 6.06218i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-3.50000 - 6.06218i) q^{23} +1.00000 q^{25} +(-2.50000 - 4.33013i) q^{29} -4.00000 q^{31} +(1.50000 - 2.59808i) q^{35} +(1.50000 + 2.59808i) q^{37} +(3.50000 + 6.06218i) q^{41} +(4.50000 - 7.79423i) q^{43} -8.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} +6.00000 q^{53} +(-1.50000 - 2.59808i) q^{55} +(2.50000 - 4.33013i) q^{59} +(2.50000 - 4.33013i) q^{61} +(-1.00000 + 3.46410i) q^{65} +(-6.50000 - 11.2583i) q^{67} +(-1.50000 + 2.59808i) q^{71} -14.0000 q^{73} -9.00000 q^{77} -8.00000 q^{79} -12.0000 q^{83} +(3.50000 - 6.06218i) q^{85} +(3.50000 + 6.06218i) q^{89} +(7.50000 + 7.79423i) q^{91} +(0.500000 - 0.866025i) q^{95} +(5.50000 - 9.52628i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} - 3 q^{7} + O(q^{10}) \) \( 2 q - 2 q^{5} - 3 q^{7} + 3 q^{11} + 2 q^{13} - 7 q^{17} - q^{19} - 7 q^{23} + 2 q^{25} - 5 q^{29} - 8 q^{31} + 3 q^{35} + 3 q^{37} + 7 q^{41} + 9 q^{43} - 16 q^{47} - 2 q^{49} + 12 q^{53} - 3 q^{55} + 5 q^{59} + 5 q^{61} - 2 q^{65} - 13 q^{67} - 3 q^{71} - 28 q^{73} - 18 q^{77} - 16 q^{79} - 24 q^{83} + 7 q^{85} + 7 q^{89} + 15 q^{91} + q^{95} + 11 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2340\mathbb{Z}\right)^\times\).

\(n\) \(937\) \(1081\) \(1171\) \(2081\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.50000 + 2.59808i −0.566947 + 0.981981i 0.429919 + 0.902867i \(0.358542\pi\)
−0.996866 + 0.0791130i \(0.974791\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0 0
\(13\) 1.00000 3.46410i 0.277350 0.960769i
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.50000 + 6.06218i −0.848875 + 1.47029i 0.0333386 + 0.999444i \(0.489386\pi\)
−0.882213 + 0.470850i \(0.843947\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.50000 6.06218i −0.729800 1.26405i −0.956967 0.290196i \(-0.906280\pi\)
0.227167 0.973856i \(-0.427054\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i \(-0.320339\pi\)
−0.999167 + 0.0408130i \(0.987005\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.50000 2.59808i 0.253546 0.439155i
\(36\) 0 0
\(37\) 1.50000 + 2.59808i 0.246598 + 0.427121i 0.962580 0.270998i \(-0.0873538\pi\)
−0.715981 + 0.698119i \(0.754020\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.50000 + 6.06218i 0.546608 + 0.946753i 0.998504 + 0.0546823i \(0.0174146\pi\)
−0.451896 + 0.892071i \(0.649252\pi\)
\(42\) 0 0
\(43\) 4.50000 7.79423i 0.686244 1.18861i −0.286801 0.957990i \(-0.592592\pi\)
0.973044 0.230618i \(-0.0740749\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) −1.00000 1.73205i −0.142857 0.247436i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) −1.50000 2.59808i −0.202260 0.350325i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.50000 4.33013i 0.325472 0.563735i −0.656136 0.754643i \(-0.727810\pi\)
0.981608 + 0.190909i \(0.0611434\pi\)
\(60\) 0 0
\(61\) 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i \(-0.729619\pi\)
0.980507 + 0.196485i \(0.0629528\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.00000 + 3.46410i −0.124035 + 0.429669i
\(66\) 0 0
\(67\) −6.50000 11.2583i −0.794101 1.37542i −0.923408 0.383819i \(-0.874609\pi\)
0.129307 0.991605i \(-0.458725\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.50000 + 2.59808i −0.178017 + 0.308335i −0.941201 0.337846i \(-0.890302\pi\)
0.763184 + 0.646181i \(0.223635\pi\)
\(72\) 0 0
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.00000 −1.02565
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 3.50000 6.06218i 0.379628 0.657536i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.50000 + 6.06218i 0.370999 + 0.642590i 0.989720 0.143022i \(-0.0456819\pi\)
−0.618720 + 0.785611i \(0.712349\pi\)
\(90\) 0 0
\(91\) 7.50000 + 7.79423i 0.786214 + 0.817057i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) 0 0
\(97\) 5.50000 9.52628i 0.558440 0.967247i −0.439187 0.898396i \(-0.644733\pi\)
0.997627 0.0688512i \(-0.0219334\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i \(-0.314447\pi\)
−0.998240 + 0.0592978i \(0.981114\pi\)
\(102\) 0 0
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.50000 2.59808i −0.145010 0.251166i 0.784366 0.620298i \(-0.212988\pi\)
−0.929377 + 0.369132i \(0.879655\pi\)
\(108\) 0 0
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.50000 11.2583i 0.611469 1.05909i −0.379525 0.925182i \(-0.623912\pi\)
0.990993 0.133913i \(-0.0427543\pi\)
\(114\) 0 0
\(115\) 3.50000 + 6.06218i 0.326377 + 0.565301i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10.5000 18.1865i −0.962533 1.66716i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −0.500000 0.866025i −0.0443678 0.0768473i 0.842989 0.537931i \(-0.180794\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) −1.50000 2.59808i −0.130066 0.225282i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i \(-0.874238\pi\)
0.794808 + 0.606861i \(0.207572\pi\)
\(138\) 0 0
\(139\) −6.50000 + 11.2583i −0.551323 + 0.954919i 0.446857 + 0.894606i \(0.352543\pi\)
−0.998179 + 0.0603135i \(0.980790\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 10.5000 2.59808i 0.878054 0.217262i
\(144\) 0 0
\(145\) 2.50000 + 4.33013i 0.207614 + 0.359597i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i \(-0.794119\pi\)
0.920904 + 0.389789i \(0.127452\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) 6.00000 0.478852 0.239426 0.970915i \(-0.423041\pi\)
0.239426 + 0.970915i \(0.423041\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 21.0000 1.65503
\(162\) 0 0
\(163\) −5.50000 + 9.52628i −0.430793 + 0.746156i −0.996942 0.0781474i \(-0.975100\pi\)
0.566149 + 0.824303i \(0.308433\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.500000 + 0.866025i 0.0386912 + 0.0670151i 0.884723 0.466118i \(-0.154348\pi\)
−0.846031 + 0.533133i \(0.821014\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −7.50000 + 12.9904i −0.570214 + 0.987640i 0.426329 + 0.904568i \(0.359807\pi\)
−0.996544 + 0.0830722i \(0.973527\pi\)
\(174\) 0 0
\(175\) −1.50000 + 2.59808i −0.113389 + 0.196396i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 9.50000 + 16.4545i 0.710063 + 1.22987i 0.964833 + 0.262864i \(0.0846670\pi\)
−0.254770 + 0.967002i \(0.582000\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.50000 2.59808i −0.110282 0.191014i
\(186\) 0 0
\(187\) −21.0000 −1.53567
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i \(-0.867950\pi\)
0.806641 + 0.591041i \(0.201283\pi\)
\(192\) 0 0
\(193\) 7.50000 + 12.9904i 0.539862 + 0.935068i 0.998911 + 0.0466572i \(0.0148568\pi\)
−0.459049 + 0.888411i \(0.651810\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −11.5000 19.9186i −0.819341 1.41914i −0.906168 0.422917i \(-0.861006\pi\)
0.0868274 0.996223i \(-0.472327\pi\)
\(198\) 0 0
\(199\) −4.50000 + 7.79423i −0.318997 + 0.552518i −0.980279 0.197619i \(-0.936679\pi\)
0.661282 + 0.750137i \(0.270013\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 15.0000 1.05279
\(204\) 0 0
\(205\) −3.50000 6.06218i −0.244451 0.423401i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i \(-0.111609\pi\)
−0.767049 + 0.641588i \(0.778276\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.50000 + 7.79423i −0.306897 + 0.531562i
\(216\) 0 0
\(217\) 6.00000 10.3923i 0.407307 0.705476i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 17.5000 + 18.1865i 1.17718 + 1.22336i
\(222\) 0 0
\(223\) 11.5000 + 19.9186i 0.770097 + 1.33385i 0.937509 + 0.347960i \(0.113126\pi\)
−0.167412 + 0.985887i \(0.553541\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.500000 + 0.866025i −0.0331862 + 0.0574801i −0.882141 0.470985i \(-0.843899\pi\)
0.848955 + 0.528465i \(0.177232\pi\)
\(228\) 0 0
\(229\) 26.0000 1.71813 0.859064 0.511868i \(-0.171046\pi\)
0.859064 + 0.511868i \(0.171046\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) 8.00000 0.521862
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.00000 + 1.73205i 0.0638877 + 0.110657i
\(246\) 0 0
\(247\) 2.50000 + 2.59808i 0.159071 + 0.165312i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.50000 4.33013i 0.157799 0.273315i −0.776276 0.630393i \(-0.782894\pi\)
0.934075 + 0.357078i \(0.116227\pi\)
\(252\) 0 0
\(253\) 10.5000 18.1865i 0.660129 1.14338i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.50000 16.4545i −0.592594 1.02640i −0.993882 0.110450i \(-0.964771\pi\)
0.401288 0.915952i \(-0.368563\pi\)
\(258\) 0 0
\(259\) −9.00000 −0.559233
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.50000 6.06218i −0.215819 0.373810i 0.737706 0.675122i \(-0.235909\pi\)
−0.953526 + 0.301312i \(0.902576\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.50000 2.59808i 0.0914566 0.158408i −0.816668 0.577108i \(-0.804181\pi\)
0.908124 + 0.418701i \(0.137514\pi\)
\(270\) 0 0
\(271\) −11.5000 19.9186i −0.698575 1.20997i −0.968960 0.247216i \(-0.920484\pi\)
0.270385 0.962752i \(-0.412849\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) 0 0
\(277\) 11.5000 19.9186i 0.690968 1.19679i −0.280553 0.959839i \(-0.590518\pi\)
0.971521 0.236953i \(-0.0761488\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) −0.500000 0.866025i −0.0297219 0.0514799i 0.850782 0.525519i \(-0.176129\pi\)
−0.880504 + 0.474039i \(0.842796\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −21.0000 −1.23959
\(288\) 0 0
\(289\) −16.0000 27.7128i −0.941176 1.63017i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4.50000 7.79423i 0.262893 0.455344i −0.704117 0.710084i \(-0.748657\pi\)
0.967009 + 0.254741i \(0.0819901\pi\)
\(294\) 0 0
\(295\) −2.50000 + 4.33013i −0.145556 + 0.252110i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −24.5000 + 6.06218i −1.41687 + 0.350585i
\(300\) 0 0
\(301\) 13.5000 + 23.3827i 0.778127 + 1.34776i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.50000 + 4.33013i −0.143150 + 0.247942i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000 0.112331 0.0561656 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) 0 0
\(319\) 7.50000 12.9904i 0.419919 0.727322i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.50000 6.06218i −0.194745 0.337309i
\(324\) 0 0
\(325\) 1.00000 3.46410i 0.0554700 0.192154i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 12.0000 20.7846i 0.661581 1.14589i
\(330\) 0 0
\(331\) −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i \(-0.949627\pi\)
0.630232 + 0.776407i \(0.282960\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 6.50000 + 11.2583i 0.355133 + 0.615108i
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6.00000 10.3923i −0.324918 0.562775i
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.50000 + 11.2583i −0.348938 + 0.604379i −0.986061 0.166383i \(-0.946791\pi\)
0.637123 + 0.770762i \(0.280124\pi\)
\(348\) 0 0
\(349\) 12.5000 + 21.6506i 0.669110 + 1.15893i 0.978153 + 0.207884i \(0.0666577\pi\)
−0.309044 + 0.951048i \(0.600009\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.5000 + 18.1865i 0.558859 + 0.967972i 0.997592 + 0.0693543i \(0.0220939\pi\)
−0.438733 + 0.898617i \(0.644573\pi\)
\(354\) 0 0
\(355\) 1.50000 2.59808i 0.0796117 0.137892i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.00000 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 14.0000 0.732793
\(366\) 0 0
\(367\) −4.50000 7.79423i −0.234898 0.406855i 0.724345 0.689438i \(-0.242142\pi\)
−0.959243 + 0.282582i \(0.908809\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9.00000 + 15.5885i −0.467257 + 0.809312i
\(372\) 0 0
\(373\) 13.5000 23.3827i 0.699004 1.21071i −0.269809 0.962914i \(-0.586961\pi\)
0.968812 0.247796i \(-0.0797062\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −17.5000 + 4.33013i −0.901296 + 0.223013i
\(378\) 0 0
\(379\) 4.50000 + 7.79423i 0.231149 + 0.400363i 0.958147 0.286278i \(-0.0924180\pi\)
−0.726997 + 0.686640i \(0.759085\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.50000 + 11.2583i −0.332134 + 0.575274i −0.982930 0.183979i \(-0.941102\pi\)
0.650796 + 0.759253i \(0.274435\pi\)
\(384\) 0 0
\(385\) 9.00000 0.458682
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 0 0
\(391\) 49.0000 2.47804
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) −16.5000 + 28.5788i −0.828111 + 1.43433i 0.0714068 + 0.997447i \(0.477251\pi\)
−0.899518 + 0.436884i \(0.856082\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i \(-0.0444700\pi\)
−0.615725 + 0.787961i \(0.711137\pi\)
\(402\) 0 0
\(403\) −4.00000 + 13.8564i −0.199254 + 0.690237i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.50000 + 7.79423i −0.223057 + 0.386346i
\(408\) 0 0
\(409\) 0.500000 0.866025i 0.0247234 0.0428222i −0.853399 0.521258i \(-0.825463\pi\)
0.878122 + 0.478436i \(0.158796\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7.50000 + 12.9904i 0.369051 + 0.639215i
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −16.5000 28.5788i −0.806078 1.39617i −0.915561 0.402179i \(-0.868253\pi\)
0.109483 0.993989i \(-0.465080\pi\)
\(420\) 0 0
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.50000 + 6.06218i −0.169775 + 0.294059i
\(426\) 0 0
\(427\) 7.50000 + 12.9904i 0.362950 + 0.628649i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.50000 7.79423i −0.216757 0.375435i 0.737057 0.675830i \(-0.236215\pi\)
−0.953815 + 0.300395i \(0.902881\pi\)
\(432\) 0 0
\(433\) −0.500000 + 0.866025i −0.0240285 + 0.0416185i −0.877790 0.479046i \(-0.840983\pi\)
0.853761 + 0.520665i \(0.174316\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.00000 0.334855
\(438\) 0 0
\(439\) −1.50000 2.59808i −0.0715911 0.123999i 0.828008 0.560717i \(-0.189474\pi\)
−0.899599 + 0.436717i \(0.856141\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) 0 0
\(445\) −3.50000 6.06218i −0.165916 0.287375i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10.5000 + 18.1865i −0.495526 + 0.858276i −0.999987 0.00515887i \(-0.998358\pi\)
0.504461 + 0.863434i \(0.331691\pi\)
\(450\) 0 0
\(451\) −10.5000 + 18.1865i −0.494426 + 0.856370i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −7.50000 7.79423i −0.351605 0.365399i
\(456\) 0 0
\(457\) 11.5000 + 19.9186i 0.537947 + 0.931752i 0.999014 + 0.0443868i \(0.0141334\pi\)
−0.461067 + 0.887365i \(0.652533\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.50000 9.52628i 0.256161 0.443683i −0.709050 0.705159i \(-0.750876\pi\)
0.965210 + 0.261476i \(0.0842091\pi\)
\(462\) 0 0
\(463\) −28.0000 −1.30127 −0.650635 0.759390i \(-0.725497\pi\)
−0.650635 + 0.759390i \(0.725497\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −20.0000 −0.925490 −0.462745 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 0 0
\(469\) 39.0000 1.80085
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 27.0000 1.24146
\(474\) 0 0
\(475\) −0.500000 + 0.866025i −0.0229416 + 0.0397360i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.500000 0.866025i −0.0228456 0.0395697i 0.854377 0.519654i \(-0.173939\pi\)
−0.877222 + 0.480085i \(0.840606\pi\)
\(480\) 0 0
\(481\) 10.5000 2.59808i 0.478759 0.118462i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5.50000 + 9.52628i −0.249742 + 0.432566i
\(486\) 0 0
\(487\) 8.50000 14.7224i 0.385172 0.667137i −0.606621 0.794991i \(-0.707476\pi\)
0.991793 + 0.127854i \(0.0408089\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 11.5000 + 19.9186i 0.518988 + 0.898913i 0.999757 + 0.0220657i \(0.00702431\pi\)
−0.480769 + 0.876847i \(0.659642\pi\)
\(492\) 0 0
\(493\) 35.0000 1.57632
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.50000 7.79423i −0.201853 0.349619i
\(498\) 0 0
\(499\) −16.0000 −0.716258 −0.358129 0.933672i \(-0.616585\pi\)
−0.358129 + 0.933672i \(0.616585\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5.50000 9.52628i 0.245233 0.424756i −0.716964 0.697110i \(-0.754469\pi\)
0.962197 + 0.272354i \(0.0878022\pi\)
\(504\) 0 0
\(505\) 4.50000 + 7.79423i 0.200247 + 0.346839i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i \(-0.0587976\pi\)
−0.650556 + 0.759458i \(0.725464\pi\)
\(510\) 0 0
\(511\) 21.0000 36.3731i 0.928985 1.60905i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 16.0000 0.705044
\(516\) 0 0
\(517\) −12.0000 20.7846i −0.527759 0.914106i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 34.0000 1.48957 0.744784 0.667306i \(-0.232553\pi\)
0.744784 + 0.667306i \(0.232553\pi\)
\(522\) 0 0
\(523\) 11.5000 + 19.9186i 0.502860 + 0.870979i 0.999995 + 0.00330547i \(0.00105217\pi\)
−0.497135 + 0.867673i \(0.665615\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.0000 24.2487i 0.609850 1.05629i
\(528\) 0 0
\(529\) −13.0000 + 22.5167i −0.565217 + 0.978985i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 24.5000 6.06218i 1.06121 0.262582i
\(534\) 0 0
\(535\) 1.50000 + 2.59808i 0.0648507 + 0.112325i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3.00000 5.19615i 0.129219 0.223814i
\(540\) 0 0
\(541\) 10.0000 0.429934 0.214967 0.976621i \(-0.431036\pi\)
0.214967 + 0.976621i \(0.431036\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 14.0000 0.599694
\(546\) 0 0
\(547\) −16.0000 −0.684111 −0.342055 0.939680i \(-0.611123\pi\)
−0.342055 + 0.939680i \(0.611123\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 5.00000 0.213007
\(552\) 0 0
\(553\) 12.0000 20.7846i 0.510292 0.883852i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.50000 16.4545i −0.402528 0.697199i 0.591502 0.806303i \(-0.298535\pi\)
−0.994030 + 0.109104i \(0.965202\pi\)
\(558\) 0 0
\(559\) −22.5000 23.3827i −0.951649 0.988982i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −22.5000 + 38.9711i −0.948262 + 1.64244i −0.199177 + 0.979963i \(0.563827\pi\)
−0.749085 + 0.662474i \(0.769506\pi\)
\(564\) 0 0
\(565\) −6.50000 + 11.2583i −0.273457 + 0.473642i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 9.50000 + 16.4545i 0.398261 + 0.689808i 0.993511 0.113732i \(-0.0362806\pi\)
−0.595251 + 0.803540i \(0.702947\pi\)
\(570\) 0 0
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.50000 6.06218i −0.145960 0.252810i
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 18.0000 31.1769i 0.746766 1.29344i
\(582\) 0 0
\(583\) 9.00000 + 15.5885i 0.372742 + 0.645608i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18.5000 + 32.0429i 0.763577 + 1.32255i 0.940996 + 0.338418i \(0.109892\pi\)
−0.177419 + 0.984135i \(0.556775\pi\)
\(588\) 0 0
\(589\) 2.00000 3.46410i 0.0824086 0.142736i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −26.0000 −1.06769 −0.533846 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) 10.5000 + 18.1865i 0.430458 + 0.745575i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −8.00000 −0.326871 −0.163436 0.986554i \(-0.552258\pi\)
−0.163436 + 0.986554i \(0.552258\pi\)
\(600\) 0 0
\(601\) 6.50000 + 11.2583i 0.265141 + 0.459237i 0.967600 0.252486i \(-0.0812483\pi\)
−0.702460 + 0.711723i \(0.747915\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) 4.50000 7.79423i 0.182649 0.316358i −0.760133 0.649768i \(-0.774866\pi\)
0.942782 + 0.333410i \(0.108199\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −8.00000 + 27.7128i −0.323645 + 1.12114i
\(612\) 0 0
\(613\) 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.5000 25.1147i 0.583748 1.01108i −0.411282 0.911508i \(-0.634919\pi\)
0.995030 0.0995732i \(-0.0317477\pi\)
\(618\) 0 0
\(619\) 12.0000 0.482321 0.241160 0.970485i \(-0.422472\pi\)
0.241160 + 0.970485i \(0.422472\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −21.0000 −0.841347
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −21.0000 −0.837325
\(630\) 0 0
\(631\) 7.50000 12.9904i 0.298570 0.517139i −0.677239 0.735763i \(-0.736824\pi\)
0.975809 + 0.218624i \(0.0701569\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.500000 + 0.866025i 0.0198419 + 0.0343672i
\(636\) 0 0
\(637\) −7.00000 + 1.73205i −0.277350 + 0.0686264i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −10.5000 + 18.1865i −0.414725 + 0.718325i −0.995400 0.0958109i \(-0.969456\pi\)
0.580674 + 0.814136i \(0.302789\pi\)
\(642\) 0 0
\(643\) −3.50000 + 6.06218i −0.138027 + 0.239069i −0.926750 0.375680i \(-0.877409\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.50000 + 14.7224i 0.334169 + 0.578799i 0.983325 0.181857i \(-0.0582109\pi\)
−0.649155 + 0.760656i \(0.724878\pi\)
\(648\) 0 0
\(649\) 15.0000 0.588802
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5.50000 9.52628i −0.215232 0.372792i 0.738113 0.674678i \(-0.235717\pi\)
−0.953344 + 0.301885i \(0.902384\pi\)
\(654\) 0 0
\(655\) 4.00000 0.156293
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i \(-0.927707\pi\)
0.682161 + 0.731202i \(0.261040\pi\)
\(660\) 0 0
\(661\) 8.50000 + 14.7224i 0.330612 + 0.572636i 0.982632 0.185565i \(-0.0594116\pi\)
−0.652020 + 0.758202i \(0.726078\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.50000 + 2.59808i 0.0581675 + 0.100749i
\(666\) 0 0
\(667\) −17.5000 + 30.3109i −0.677603 + 1.17364i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15.0000 0.579069
\(672\) 0 0
\(673\) −6.50000 11.2583i −0.250557 0.433977i 0.713123 0.701039i \(-0.247280\pi\)
−0.963679 + 0.267063i \(0.913947\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −22.0000 −0.845529 −0.422764 0.906240i \(-0.638940\pi\)
−0.422764 + 0.906240i \(0.638940\pi\)
\(678\) 0 0
\(679\) 16.5000 + 28.5788i 0.633212 + 1.09676i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 15.5000 26.8468i 0.593091 1.02726i −0.400722 0.916200i \(-0.631241\pi\)
0.993813 0.111064i \(-0.0354259\pi\)
\(684\) 0 0
\(685\) 1.50000 2.59808i 0.0573121 0.0992674i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 6.00000 20.7846i 0.228582 0.791831i
\(690\) 0 0
\(691\) 12.5000 + 21.6506i 0.475522 + 0.823629i 0.999607 0.0280373i \(-0.00892572\pi\)
−0.524084 + 0.851666i \(0.675592\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.50000 11.2583i 0.246559 0.427053i
\(696\) 0 0
\(697\) −49.0000 −1.85601
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 0 0
\(703\) −3.00000 −0.113147
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 27.0000 1.01544
\(708\) 0 0
\(709\) −17.5000 + 30.3109i −0.657226 + 1.13835i 0.324104 + 0.946021i \(0.394937\pi\)
−0.981331 + 0.192328i \(0.938396\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 14.0000 + 24.2487i 0.524304 + 0.908121i
\(714\) 0 0
\(715\) −10.5000 + 2.59808i −0.392678 + 0.0971625i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.500000 0.866025i 0.0186469 0.0322973i −0.856551 0.516062i \(-0.827398\pi\)
0.875198 + 0.483764i \(0.160731\pi\)
\(720\) 0 0
\(721\) 24.0000 41.5692i 0.893807 1.54812i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.50000 4.33013i −0.0928477 0.160817i
\(726\) 0 0
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 31.5000 + 54.5596i 1.16507 + 2.01796i
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 19.5000 33.7750i 0.718292 1.24412i
\(738\) 0 0
\(739\) −19.5000 33.7750i −0.717319 1.24243i −0.962058 0.272844i \(-0.912036\pi\)
0.244739 0.969589i \(-0.421298\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.500000 + 0.866025i 0.0183432 + 0.0317714i 0.875051 0.484030i \(-0.160828\pi\)
−0.856708 + 0.515802i \(0.827494\pi\)
\(744\) 0 0
\(745\) −1.50000 + 2.59808i −0.0549557 + 0.0951861i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 9.00000 0.328853
\(750\) 0 0
\(751\) 6.50000 + 11.2583i 0.237188 + 0.410822i 0.959906 0.280321i \(-0.0904408\pi\)
−0.722718 + 0.691143i \(0.757107\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) −0.500000 0.866025i −0.0181728 0.0314762i 0.856796 0.515656i \(-0.172452\pi\)
−0.874969 + 0.484179i \(0.839118\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 25.5000 44.1673i 0.924374 1.60106i 0.131810 0.991275i \(-0.457921\pi\)
0.792564 0.609788i \(-0.208745\pi\)
\(762\) 0 0
\(763\) 21.0000 36.3731i 0.760251 1.31679i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −12.5000 12.9904i −0.451349 0.469055i
\(768\) 0 0
\(769\) 2.50000 + 4.33013i 0.0901523 + 0.156148i 0.907575 0.419890i \(-0.137931\pi\)
−0.817423 + 0.576038i \(0.804598\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 12.5000 21.6506i 0.449594 0.778719i −0.548766 0.835976i \(-0.684902\pi\)
0.998359 + 0.0572570i \(0.0182354\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.00000 −0.250801
\(780\) 0 0
\(781\) −9.00000 −0.322045
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.00000 −0.214149
\(786\) 0 0
\(787\) 0.500000 0.866025i 0.0178231 0.0308705i −0.856976 0.515356i \(-0.827660\pi\)
0.874799 + 0.484485i \(0.160993\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 19.5000 + 33.7750i 0.693340 + 1.20090i
\(792\) 0 0
\(793\) −12.5000 12.9904i −0.443888 0.461302i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3.50000 + 6.06218i −0.123976 + 0.214733i −0.921332 0.388776i \(-0.872898\pi\)
0.797356 + 0.603509i \(0.206231\pi\)
\(798\) 0 0
\(799\) 28.0000 48.4974i 0.990569 1.71572i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) &minus