Properties

Label 2592.2.s.g.1727.2
Level $2592$
Weight $2$
Character 2592.1727
Analytic conductor $20.697$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2592.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.6972242039\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 864)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1727.2
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 2592.1727
Dual form 2592.2.s.g.863.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.896575 + 0.517638i) q^{5} +(-0.232051 - 0.133975i) q^{7} +O(q^{10})\) \(q+(-0.896575 + 0.517638i) q^{5} +(-0.232051 - 0.133975i) q^{7} +(-1.93185 + 3.34607i) q^{11} +(1.23205 + 2.13397i) q^{13} -6.69213i q^{17} +1.73205i q^{19} +(-2.96713 - 5.13922i) q^{23} +(-1.96410 + 3.40192i) q^{25} +(1.79315 + 1.03528i) q^{29} +(-0.464102 + 0.267949i) q^{31} +0.277401 q^{35} -6.46410 q^{37} +(-1.79315 + 1.03528i) q^{41} +(6.46410 + 3.73205i) q^{43} +(-4.76028 + 8.24504i) q^{47} +(-3.46410 - 6.00000i) q^{49} -13.3843i q^{53} -4.00000i q^{55} +(-3.72500 - 6.45189i) q^{59} +(4.69615 - 8.13397i) q^{61} +(-2.20925 - 1.27551i) q^{65} +(8.42820 - 4.86603i) q^{67} -11.3137 q^{71} +9.92820 q^{73} +(0.896575 - 0.517638i) q^{77} +(-13.1603 - 7.59808i) q^{79} +(-3.86370 + 6.69213i) q^{83} +(3.46410 + 6.00000i) q^{85} -6.69213i q^{89} -0.660254i q^{91} +(-0.896575 - 1.55291i) q^{95} +(-3.50000 + 6.06218i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 12 q^{7} + O(q^{10}) \) \( 8 q + 12 q^{7} - 4 q^{13} + 12 q^{25} + 24 q^{31} - 24 q^{37} + 24 q^{43} - 4 q^{61} + 12 q^{67} + 24 q^{73} - 36 q^{79} - 28 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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
\(5\) −0.896575 + 0.517638i −0.400961 + 0.231495i −0.686898 0.726753i \(-0.741028\pi\)
0.285938 + 0.958248i \(0.407695\pi\)
\(6\) 0 0
\(7\) −0.232051 0.133975i −0.0877070 0.0506376i 0.455505 0.890233i \(-0.349459\pi\)
−0.543212 + 0.839596i \(0.682792\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.93185 + 3.34607i −0.582475 + 1.00888i 0.412710 + 0.910863i \(0.364582\pi\)
−0.995185 + 0.0980141i \(0.968751\pi\)
\(12\) 0 0
\(13\) 1.23205 + 2.13397i 0.341709 + 0.591858i 0.984750 0.173974i \(-0.0556608\pi\)
−0.643041 + 0.765832i \(0.722327\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.69213i 1.62308i −0.584297 0.811540i \(-0.698630\pi\)
0.584297 0.811540i \(-0.301370\pi\)
\(18\) 0 0
\(19\) 1.73205i 0.397360i 0.980064 + 0.198680i \(0.0636654\pi\)
−0.980064 + 0.198680i \(0.936335\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.96713 5.13922i −0.618689 1.07160i −0.989725 0.142982i \(-0.954331\pi\)
0.371036 0.928618i \(-0.379003\pi\)
\(24\) 0 0
\(25\) −1.96410 + 3.40192i −0.392820 + 0.680385i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.79315 + 1.03528i 0.332980 + 0.192246i 0.657163 0.753748i \(-0.271756\pi\)
−0.324184 + 0.945994i \(0.605090\pi\)
\(30\) 0 0
\(31\) −0.464102 + 0.267949i −0.0833551 + 0.0481251i −0.541098 0.840959i \(-0.681991\pi\)
0.457743 + 0.889085i \(0.348658\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.277401 0.0468894
\(36\) 0 0
\(37\) −6.46410 −1.06269 −0.531346 0.847155i \(-0.678314\pi\)
−0.531346 + 0.847155i \(0.678314\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.79315 + 1.03528i −0.280043 + 0.161683i −0.633443 0.773789i \(-0.718359\pi\)
0.353400 + 0.935472i \(0.385026\pi\)
\(42\) 0 0
\(43\) 6.46410 + 3.73205i 0.985766 + 0.569132i 0.904006 0.427520i \(-0.140613\pi\)
0.0817602 + 0.996652i \(0.473946\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.76028 + 8.24504i −0.694358 + 1.20266i 0.276039 + 0.961147i \(0.410978\pi\)
−0.970397 + 0.241517i \(0.922355\pi\)
\(48\) 0 0
\(49\) −3.46410 6.00000i −0.494872 0.857143i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 13.3843i 1.83847i −0.393710 0.919235i \(-0.628808\pi\)
0.393710 0.919235i \(-0.371192\pi\)
\(54\) 0 0
\(55\) 4.00000i 0.539360i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.72500 6.45189i −0.484954 0.839965i 0.514897 0.857252i \(-0.327830\pi\)
−0.999851 + 0.0172873i \(0.994497\pi\)
\(60\) 0 0
\(61\) 4.69615 8.13397i 0.601281 1.04145i −0.391347 0.920243i \(-0.627991\pi\)
0.992627 0.121205i \(-0.0386760\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.20925 1.27551i −0.274024 0.158208i
\(66\) 0 0
\(67\) 8.42820 4.86603i 1.02967 0.594480i 0.112779 0.993620i \(-0.464025\pi\)
0.916890 + 0.399140i \(0.130691\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −11.3137 −1.34269 −0.671345 0.741145i \(-0.734283\pi\)
−0.671345 + 0.741145i \(0.734283\pi\)
\(72\) 0 0
\(73\) 9.92820 1.16201 0.581004 0.813901i \(-0.302660\pi\)
0.581004 + 0.813901i \(0.302660\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.896575 0.517638i 0.102174 0.0589903i
\(78\) 0 0
\(79\) −13.1603 7.59808i −1.48064 0.854850i −0.480885 0.876784i \(-0.659684\pi\)
−0.999759 + 0.0219334i \(0.993018\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −3.86370 + 6.69213i −0.424097 + 0.734557i −0.996336 0.0855301i \(-0.972742\pi\)
0.572239 + 0.820087i \(0.306075\pi\)
\(84\) 0 0
\(85\) 3.46410 + 6.00000i 0.375735 + 0.650791i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.69213i 0.709364i −0.934987 0.354682i \(-0.884589\pi\)
0.934987 0.354682i \(-0.115411\pi\)
\(90\) 0 0
\(91\) 0.660254i 0.0692134i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −0.896575 1.55291i −0.0919867 0.159326i
\(96\) 0 0
\(97\) −3.50000 + 6.06218i −0.355371 + 0.615521i −0.987181 0.159602i \(-0.948979\pi\)
0.631810 + 0.775123i \(0.282312\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −13.3843 7.72741i −1.33178 0.768906i −0.346211 0.938157i \(-0.612532\pi\)
−0.985573 + 0.169251i \(0.945865\pi\)
\(102\) 0 0
\(103\) −15.2321 + 8.79423i −1.50086 + 0.866521i −0.500859 + 0.865529i \(0.666983\pi\)
−1.00000 0.000992235i \(0.999684\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −15.1774 −1.46726 −0.733628 0.679551i \(-0.762174\pi\)
−0.733628 + 0.679551i \(0.762174\pi\)
\(108\) 0 0
\(109\) −0.928203 −0.0889057 −0.0444529 0.999011i \(-0.514154\pi\)
−0.0444529 + 0.999011i \(0.514154\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.58871 4.38134i 0.713885 0.412162i −0.0986126 0.995126i \(-0.531440\pi\)
0.812498 + 0.582964i \(0.198107\pi\)
\(114\) 0 0
\(115\) 5.32051 + 3.07180i 0.496140 + 0.286447i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.896575 + 1.55291i −0.0821889 + 0.142355i
\(120\) 0 0
\(121\) −1.96410 3.40192i −0.178555 0.309266i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.24316i 0.826733i
\(126\) 0 0
\(127\) 3.46410i 0.307389i 0.988118 + 0.153695i \(0.0491172\pi\)
−0.988118 + 0.153695i \(0.950883\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.86370 + 6.69213i 0.337573 + 0.584694i 0.983976 0.178303i \(-0.0570606\pi\)
−0.646402 + 0.762997i \(0.723727\pi\)
\(132\) 0 0
\(133\) 0.232051 0.401924i 0.0201214 0.0348512i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.38186 5.41662i −0.801546 0.462773i 0.0424654 0.999098i \(-0.486479\pi\)
−0.844012 + 0.536325i \(0.819812\pi\)
\(138\) 0 0
\(139\) −1.03590 + 0.598076i −0.0878638 + 0.0507282i −0.543288 0.839546i \(-0.682821\pi\)
0.455424 + 0.890274i \(0.349488\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −9.52056 −0.796149
\(144\) 0 0
\(145\) −2.14359 −0.178016
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.79796 5.65685i 0.802680 0.463428i −0.0417274 0.999129i \(-0.513286\pi\)
0.844407 + 0.535701i \(0.179953\pi\)
\(150\) 0 0
\(151\) −7.16025 4.13397i −0.582693 0.336418i 0.179510 0.983756i \(-0.442549\pi\)
−0.762203 + 0.647338i \(0.775882\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.277401 0.480473i 0.0222814 0.0385925i
\(156\) 0 0
\(157\) 1.53590 + 2.66025i 0.122578 + 0.212311i 0.920784 0.390074i \(-0.127550\pi\)
−0.798206 + 0.602385i \(0.794217\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.59008i 0.125316i
\(162\) 0 0
\(163\) 15.5885i 1.22098i 0.792023 + 0.610491i \(0.209028\pi\)
−0.792023 + 0.610491i \(0.790972\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.17398 + 2.03339i 0.0908451 + 0.157348i 0.907867 0.419258i \(-0.137710\pi\)
−0.817022 + 0.576607i \(0.804377\pi\)
\(168\) 0 0
\(169\) 3.46410 6.00000i 0.266469 0.461538i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.00481 4.62158i −0.608594 0.351372i 0.163821 0.986490i \(-0.447618\pi\)
−0.772415 + 0.635118i \(0.780951\pi\)
\(174\) 0 0
\(175\) 0.911543 0.526279i 0.0689062 0.0397830i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −19.5959 −1.46467 −0.732334 0.680946i \(-0.761569\pi\)
−0.732334 + 0.680946i \(0.761569\pi\)
\(180\) 0 0
\(181\) −6.46410 −0.480473 −0.240236 0.970714i \(-0.577225\pi\)
−0.240236 + 0.970714i \(0.577225\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.79555 3.34607i 0.426098 0.246008i
\(186\) 0 0
\(187\) 22.3923 + 12.9282i 1.63749 + 0.945404i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.83083 11.8313i 0.494262 0.856086i −0.505717 0.862700i \(-0.668772\pi\)
0.999978 + 0.00661351i \(0.00210516\pi\)
\(192\) 0 0
\(193\) −0.0358984 0.0621778i −0.00258402 0.00447566i 0.864731 0.502236i \(-0.167489\pi\)
−0.867315 + 0.497761i \(0.834156\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 14.4195i 1.02735i 0.857985 + 0.513675i \(0.171716\pi\)
−0.857985 + 0.513675i \(0.828284\pi\)
\(198\) 0 0
\(199\) 25.5885i 1.81392i −0.421219 0.906959i \(-0.638398\pi\)
0.421219 0.906959i \(-0.361602\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.277401 0.480473i −0.0194698 0.0337226i
\(204\) 0 0
\(205\) 1.07180 1.85641i 0.0748575 0.129657i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.79555 3.34607i −0.400887 0.231452i
\(210\) 0 0
\(211\) 18.8205 10.8660i 1.29566 0.748048i 0.316006 0.948757i \(-0.397658\pi\)
0.979651 + 0.200709i \(0.0643246\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −7.72741 −0.527005
\(216\) 0 0
\(217\) 0.143594 0.00974776
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 14.2808 8.24504i 0.960633 0.554622i
\(222\) 0 0
\(223\) −20.3205 11.7321i −1.36076 0.785636i −0.371037 0.928618i \(-0.620998\pi\)
−0.989725 + 0.142982i \(0.954331\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.07055 3.58630i 0.137427 0.238031i −0.789095 0.614272i \(-0.789450\pi\)
0.926522 + 0.376240i \(0.122783\pi\)
\(228\) 0 0
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.3137i 0.741186i −0.928795 0.370593i \(-0.879155\pi\)
0.928795 0.370593i \(-0.120845\pi\)
\(234\) 0 0
\(235\) 9.85641i 0.642961i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.72741 + 13.3843i 0.499844 + 0.865756i 1.00000 0.000179684i \(-5.71951e-5\pi\)
−0.500156 + 0.865936i \(0.666724\pi\)
\(240\) 0 0
\(241\) −2.96410 + 5.13397i −0.190935 + 0.330708i −0.945560 0.325447i \(-0.894485\pi\)
0.754626 + 0.656156i \(0.227818\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.21166 + 3.58630i 0.396848 + 0.229120i
\(246\) 0 0
\(247\) −3.69615 + 2.13397i −0.235181 + 0.135782i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.58630 0.226365 0.113183 0.993574i \(-0.463895\pi\)
0.113183 + 0.993574i \(0.463895\pi\)
\(252\) 0 0
\(253\) 22.9282 1.44148
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.79315 1.03528i 0.111854 0.0645788i −0.443029 0.896507i \(-0.646096\pi\)
0.554883 + 0.831928i \(0.312763\pi\)
\(258\) 0 0
\(259\) 1.50000 + 0.866025i 0.0932055 + 0.0538122i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −7.72741 + 13.3843i −0.476492 + 0.825309i −0.999637 0.0269349i \(-0.991425\pi\)
0.523145 + 0.852244i \(0.324759\pi\)
\(264\) 0 0
\(265\) 6.92820 + 12.0000i 0.425596 + 0.737154i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.10583i 0.189366i 0.995507 + 0.0946829i \(0.0301837\pi\)
−0.995507 + 0.0946829i \(0.969816\pi\)
\(270\) 0 0
\(271\) 13.0526i 0.792886i 0.918059 + 0.396443i \(0.129756\pi\)
−0.918059 + 0.396443i \(0.870244\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7.58871 13.1440i −0.457616 0.792614i
\(276\) 0 0
\(277\) −10.4641 + 18.1244i −0.628727 + 1.08899i 0.359081 + 0.933307i \(0.383090\pi\)
−0.987807 + 0.155680i \(0.950243\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −15.1774 8.76268i −0.905408 0.522738i −0.0264575 0.999650i \(-0.508423\pi\)
−0.878951 + 0.476912i \(0.841756\pi\)
\(282\) 0 0
\(283\) 0.464102 0.267949i 0.0275880 0.0159279i −0.486143 0.873880i \(-0.661596\pi\)
0.513731 + 0.857952i \(0.328263\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.554803 0.0327490
\(288\) 0 0
\(289\) −27.7846 −1.63439
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −24.0788 + 13.9019i −1.40670 + 0.812158i −0.995068 0.0991934i \(-0.968374\pi\)
−0.411630 + 0.911351i \(0.635040\pi\)
\(294\) 0 0
\(295\) 6.67949 + 3.85641i 0.388895 + 0.224529i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7.31130 12.6636i 0.422824 0.732352i
\(300\) 0 0
\(301\) −1.00000 1.73205i −0.0576390 0.0998337i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 9.72363i 0.556773i
\(306\) 0 0
\(307\) 22.3923i 1.27800i 0.769208 + 0.638998i \(0.220651\pi\)
−0.769208 + 0.638998i \(0.779349\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5.03768 + 8.72552i 0.285661 + 0.494779i 0.972769 0.231776i \(-0.0744537\pi\)
−0.687109 + 0.726555i \(0.741120\pi\)
\(312\) 0 0
\(313\) 9.96410 17.2583i 0.563204 0.975499i −0.434010 0.900908i \(-0.642902\pi\)
0.997214 0.0745904i \(-0.0237649\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.79315 + 1.03528i 0.100713 + 0.0581469i 0.549511 0.835487i \(-0.314814\pi\)
−0.448797 + 0.893634i \(0.648147\pi\)
\(318\) 0 0
\(319\) −6.92820 + 4.00000i −0.387905 + 0.223957i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 11.5911 0.644947
\(324\) 0 0
\(325\) −9.67949 −0.536922
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2.20925 1.27551i 0.121800 0.0703213i
\(330\) 0 0
\(331\) 21.8205 + 12.5981i 1.19936 + 0.692453i 0.960413 0.278579i \(-0.0898634\pi\)
0.238950 + 0.971032i \(0.423197\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.03768 + 8.72552i −0.275238 + 0.476726i
\(336\) 0 0
\(337\) 7.42820 + 12.8660i 0.404640 + 0.700857i 0.994280 0.106809i \(-0.0340635\pi\)
−0.589639 + 0.807667i \(0.700730\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.07055i 0.112127i
\(342\) 0 0
\(343\) 3.73205i 0.201512i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.72741 + 13.3843i 0.414829 + 0.718505i 0.995410 0.0956973i \(-0.0305081\pi\)
−0.580582 + 0.814202i \(0.697175\pi\)
\(348\) 0 0
\(349\) −5.16025 + 8.93782i −0.276222 + 0.478431i −0.970443 0.241332i \(-0.922416\pi\)
0.694221 + 0.719762i \(0.255749\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 30.3548 + 17.5254i 1.61562 + 0.932781i 0.988034 + 0.154237i \(0.0492921\pi\)
0.627590 + 0.778544i \(0.284041\pi\)
\(354\) 0 0
\(355\) 10.1436 5.85641i 0.538366 0.310826i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 32.1480 1.69671 0.848353 0.529432i \(-0.177595\pi\)
0.848353 + 0.529432i \(0.177595\pi\)
\(360\) 0 0
\(361\) 16.0000 0.842105
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −8.90138 + 5.13922i −0.465920 + 0.268999i
\(366\) 0 0
\(367\) −14.7679 8.52628i −0.770881 0.445068i 0.0623080 0.998057i \(-0.480154\pi\)
−0.833189 + 0.552989i \(0.813487\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.79315 + 3.10583i −0.0930958 + 0.161247i
\(372\) 0 0
\(373\) −6.62436 11.4737i −0.342996 0.594087i 0.641991 0.766712i \(-0.278108\pi\)
−0.984988 + 0.172625i \(0.944775\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.10205i 0.262769i
\(378\) 0 0
\(379\) 9.19615i 0.472375i −0.971708 0.236187i \(-0.924102\pi\)
0.971708 0.236187i \(-0.0758979\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −17.5254 30.3548i −0.895504 1.55106i −0.833179 0.553003i \(-0.813482\pi\)
−0.0623252 0.998056i \(-0.519852\pi\)
\(384\) 0 0
\(385\) −0.535898 + 0.928203i −0.0273119 + 0.0473056i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 12.4877 + 7.20977i 0.633151 + 0.365550i 0.781971 0.623314i \(-0.214214\pi\)
−0.148821 + 0.988864i \(0.547548\pi\)
\(390\) 0 0
\(391\) −34.3923 + 19.8564i −1.73929 + 1.00418i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 15.7322 0.791574
\(396\) 0 0
\(397\) 26.7846 1.34428 0.672141 0.740424i \(-0.265375\pi\)
0.672141 + 0.740424i \(0.265375\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −19.5959 + 11.3137i −0.978573 + 0.564980i −0.901839 0.432072i \(-0.857783\pi\)
−0.0767343 + 0.997052i \(0.524449\pi\)
\(402\) 0 0
\(403\) −1.14359 0.660254i −0.0569665 0.0328896i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 12.4877 21.6293i 0.618992 1.07212i
\(408\) 0 0
\(409\) 6.50000 + 11.2583i 0.321404 + 0.556689i 0.980778 0.195127i \(-0.0625118\pi\)
−0.659374 + 0.751815i \(0.729178\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.99622i 0.0982277i
\(414\) 0 0
\(415\) 8.00000i 0.392705i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7.86611 13.6245i −0.384284 0.665600i 0.607385 0.794407i \(-0.292218\pi\)
−0.991670 + 0.128807i \(0.958885\pi\)
\(420\) 0 0
\(421\) −4.76795 + 8.25833i −0.232376 + 0.402486i −0.958507 0.285070i \(-0.907983\pi\)
0.726131 + 0.687556i \(0.241317\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 22.7661 + 13.1440i 1.10432 + 0.637579i
\(426\) 0 0
\(427\) −2.17949 + 1.25833i −0.105473 + 0.0608949i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.37945 0.259119 0.129560 0.991572i \(-0.458644\pi\)
0.129560 + 0.991572i \(0.458644\pi\)
\(432\) 0 0
\(433\) −26.7846 −1.28719 −0.643593 0.765368i \(-0.722557\pi\)
−0.643593 + 0.765368i \(0.722557\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 8.90138 5.13922i 0.425811 0.245842i
\(438\) 0 0
\(439\) −18.4641 10.6603i −0.881243 0.508786i −0.0101753 0.999948i \(-0.503239\pi\)
−0.871068 + 0.491162i \(0.836572\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13.6617 + 23.6627i −0.649085 + 1.12425i 0.334257 + 0.942482i \(0.391515\pi\)
−0.983342 + 0.181766i \(0.941819\pi\)
\(444\) 0 0
\(445\) 3.46410 + 6.00000i 0.164214 + 0.284427i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 12.9038i 0.608967i 0.952518 + 0.304484i \(0.0984839\pi\)
−0.952518 + 0.304484i \(0.901516\pi\)
\(450\) 0 0
\(451\) 8.00000i 0.376705i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.341773 + 0.591968i 0.0160225 + 0.0277519i
\(456\) 0 0
\(457\) 17.3923 30.1244i 0.813578 1.40916i −0.0967670 0.995307i \(-0.530850\pi\)
0.910345 0.413851i \(-0.135817\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 22.2856 + 12.8666i 1.03795 + 0.599258i 0.919251 0.393672i \(-0.128796\pi\)
0.118695 + 0.992931i \(0.462129\pi\)
\(462\) 0 0
\(463\) 27.0167 15.5981i 1.25557 0.724904i 0.283360 0.959013i \(-0.408551\pi\)
0.972210 + 0.234109i \(0.0752174\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 38.3596 1.77507 0.887536 0.460738i \(-0.152415\pi\)
0.887536 + 0.460738i \(0.152415\pi\)
\(468\) 0 0
\(469\) −2.60770 −0.120412
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −24.9754 + 14.4195i −1.14837 + 0.663011i
\(474\) 0 0
\(475\) −5.89230 3.40192i −0.270357 0.156091i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 7.45001 12.9038i 0.340399 0.589589i −0.644107 0.764935i \(-0.722771\pi\)
0.984507 + 0.175346i \(0.0561044\pi\)
\(480\) 0 0
\(481\) −7.96410 13.7942i −0.363132 0.628963i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.24693i 0.329066i
\(486\) 0 0
\(487\) 23.4449i 1.06239i −0.847250 0.531194i \(-0.821743\pi\)
0.847250 0.531194i \(-0.178257\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.86611 + 13.6245i 0.354992 + 0.614865i 0.987117 0.160002i \(-0.0511501\pi\)
−0.632124 + 0.774867i \(0.717817\pi\)
\(492\) 0 0
\(493\) 6.92820 12.0000i 0.312031 0.540453i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.62536 + 1.51575i 0.117763 + 0.0679907i
\(498\) 0 0
\(499\) 10.8564 6.26795i 0.485999 0.280592i −0.236914 0.971531i \(-0.576136\pi\)
0.722913 + 0.690939i \(0.242803\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 29.1165 1.29824 0.649120 0.760686i \(-0.275137\pi\)
0.649120 + 0.760686i \(0.275137\pi\)
\(504\) 0 0
\(505\) 16.0000 0.711991
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.0740 + 9.28032i −0.712467 + 0.411343i −0.811974 0.583694i \(-0.801607\pi\)
0.0995068 + 0.995037i \(0.468273\pi\)
\(510\) 0 0
\(511\) −2.30385 1.33013i −0.101916 0.0588414i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 9.10446 15.7694i 0.401190 0.694882i
\(516\) 0 0
\(517\) −18.3923 31.8564i −0.808893 1.40104i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 37.6018i 1.64736i 0.567053 + 0.823681i \(0.308084\pi\)
−0.567053 + 0.823681i \(0.691916\pi\)
\(522\) 0 0
\(523\) 10.8038i 0.472419i 0.971702 + 0.236210i \(0.0759052\pi\)
−0.971702 + 0.236210i \(0.924095\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.79315 + 3.10583i 0.0781109 + 0.135292i
\(528\) 0 0
\(529\) −6.10770 + 10.5788i −0.265552 + 0.459949i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.41851 2.55103i −0.191387 0.110497i
\(534\) 0 0
\(535\) 13.6077 7.85641i 0.588312 0.339662i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 26.7685 1.15300
\(540\) 0 0
\(541\) 14.6077 0.628034 0.314017 0.949417i \(-0.398325\pi\)
0.314017 + 0.949417i \(0.398325\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.832204 0.480473i 0.0356477 0.0205812i
\(546\) 0 0
\(547\) −4.96410 2.86603i −0.212250 0.122542i 0.390107 0.920770i \(-0.372438\pi\)
−0.602356 + 0.798227i \(0.705771\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.79315 + 3.10583i −0.0763908 + 0.132313i
\(552\) 0 0
\(553\) 2.03590 + 3.52628i 0.0865752 + 0.149953i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 10.2784i 0.435511i 0.976003 + 0.217756i \(0.0698736\pi\)
−0.976003 + 0.217756i \(0.930126\pi\)
\(558\) 0 0
\(559\) 18.3923i 0.777912i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9.52056 + 16.4901i 0.401244 + 0.694974i 0.993876 0.110498i \(-0.0352447\pi\)
−0.592633 + 0.805473i \(0.701911\pi\)
\(564\) 0 0
\(565\) −4.53590 + 7.85641i −0.190827 + 0.330522i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 33.3963 + 19.2814i 1.40004 + 0.808316i 0.994397 0.105713i \(-0.0337125\pi\)
0.405648 + 0.914029i \(0.367046\pi\)
\(570\) 0 0
\(571\) −19.9641 + 11.5263i −0.835472 + 0.482360i −0.855722 0.517435i \(-0.826887\pi\)
0.0202508 + 0.999795i \(0.493554\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 23.3110 0.972134
\(576\) 0 0
\(577\) −26.0718 −1.08538 −0.542692 0.839932i \(-0.682595\pi\)
−0.542692 + 0.839932i \(0.682595\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.79315 1.03528i 0.0743924 0.0429505i
\(582\) 0 0
\(583\) 44.7846 + 25.8564i 1.85479 + 1.07086i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0.138701 0.240237i 0.00572479 0.00991563i −0.863149 0.504950i \(-0.831511\pi\)
0.868874 + 0.495034i \(0.164844\pi\)
\(588\) 0 0
\(589\) −0.464102 0.803848i −0.0191230 0.0331220i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 25.8076i 1.05979i −0.848063 0.529895i \(-0.822231\pi\)
0.848063 0.529895i \(-0.177769\pi\)
\(594\) 0 0
\(595\) 1.85641i 0.0761052i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −5.93426 10.2784i −0.242467 0.419965i 0.718949 0.695062i \(-0.244623\pi\)
−0.961416 + 0.275097i \(0.911290\pi\)
\(600\) 0 0
\(601\) −3.39230 + 5.87564i −0.138375 + 0.239673i −0.926882 0.375354i \(-0.877521\pi\)
0.788507 + 0.615026i \(0.210855\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.52193 + 2.03339i 0.143187 + 0.0826690i
\(606\) 0 0
\(607\) −9.23205 + 5.33013i −0.374717 + 0.216343i −0.675517 0.737344i \(-0.736080\pi\)
0.300800 + 0.953687i \(0.402746\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −23.4596 −0.949075
\(612\) 0 0
\(613\) −37.3923 −1.51026 −0.755130 0.655575i \(-0.772427\pi\)
−0.755130 + 0.655575i \(0.772427\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.42091 + 4.86181i −0.339013 + 0.195729i −0.659836 0.751410i \(-0.729374\pi\)
0.320822 + 0.947139i \(0.396041\pi\)
\(618\) 0 0
\(619\) −0.571797 0.330127i −0.0229825 0.0132689i 0.488465 0.872584i \(-0.337557\pi\)
−0.511447 + 0.859315i \(0.670890\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.896575 + 1.55291i −0.0359205 + 0.0622162i
\(624\) 0 0
\(625\) −5.03590 8.72243i −0.201436 0.348897i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 43.2586i 1.72483i
\(630\) 0 0
\(631\) 19.9808i 0.795422i 0.917511 + 0.397711i \(0.130195\pi\)
−0.917511 + 0.397711i \(0.869805\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.79315 3.10583i −0.0711590 0.123251i
\(636\) 0 0
\(637\) 8.53590 14.7846i 0.338205 0.585788i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −36.5665 21.1117i −1.44429 0.833861i −0.446157 0.894955i \(-0.647208\pi\)
−0.998132 + 0.0610939i \(0.980541\pi\)
\(642\) 0 0
\(643\) −15.2487 + 8.80385i −0.601350 + 0.347190i −0.769573 0.638559i \(-0.779531\pi\)
0.168222 + 0.985749i \(0.446197\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −23.1822 −0.911387 −0.455694 0.890137i \(-0.650609\pi\)
−0.455694 + 0.890137i \(0.650609\pi\)
\(648\) 0 0
\(649\) 28.7846 1.12989
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.96575 + 5.17638i −0.350857 + 0.202567i −0.665063 0.746788i \(-0.731595\pi\)
0.314206 + 0.949355i \(0.398262\pi\)
\(654\) 0 0
\(655\) −6.92820 4.00000i −0.270707 0.156293i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 17.2480 29.8744i 0.671885 1.16374i −0.305484 0.952197i \(-0.598818\pi\)
0.977369 0.211542i \(-0.0678486\pi\)
\(660\) 0 0
\(661\) 21.6244 + 37.4545i 0.841090 + 1.45681i 0.888974 + 0.457958i \(0.151419\pi\)
−0.0478841 + 0.998853i \(0.515248\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.480473i 0.0186320i
\(666\) 0 0
\(667\) 12.2872i 0.475762i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 18.1445 + 31.4273i 0.700462 + 1.21324i
\(672\) 0 0
\(673\) −10.4282 + 18.0622i −0.401978 + 0.696246i −0.993965 0.109702i \(-0.965010\pi\)
0.591987 + 0.805948i \(0.298344\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 18.6993 + 10.7961i 0.718674 + 0.414927i 0.814264 0.580494i \(-0.197141\pi\)
−0.0955904 + 0.995421i \(0.530474\pi\)
\(678\) 0 0
\(679\) 1.62436 0.937822i 0.0623370 0.0359903i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 33.9411 1.29872 0.649361 0.760481i \(-0.275037\pi\)
0.649361 + 0.760481i \(0.275037\pi\)
\(684\) 0 0
\(685\) 11.2154 0.428518
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 28.5617 16.4901i 1.08811 0.628222i
\(690\) 0 0
\(691\) −26.3205 15.1962i −1.00128 0.578089i −0.0926528 0.995698i \(-0.529535\pi\)
−0.908627 + 0.417610i \(0.862868\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.619174 1.07244i 0.0234866 0.0406800i
\(696\) 0 0
\(697\) 6.92820 + 12.0000i 0.262424 + 0.454532i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 49.4703i 1.86847i 0.356663 + 0.934233i \(0.383914\pi\)
−0.356663 + 0.934233i \(0.616086\pi\)
\(702\) 0 0
\(703\) 11.1962i 0.422271i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.07055 + 3.58630i 0.0778711 + 0.134877i
\(708\) 0 0
\(709\) −6.08846 + 10.5455i −0.228657 + 0.396045i −0.957410 0.288731i \(-0.906767\pi\)
0.728753 + 0.684776i \(0.240100\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.75410 + 1.59008i 0.103142 + 0.0595489i
\(714\) 0 0
\(715\) 8.53590 4.92820i 0.319225 0.184304i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −3.58630 −0.133746 −0.0668732 0.997761i \(-0.521302\pi\)
−0.0668732 + 0.997761i \(0.521302\pi\)
\(720\) 0 0
\(721\) 4.71281 0.175514
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.04386 + 4.06678i −0.261602 + 0.151036i
\(726\) 0 0
\(727\) −18.4641 10.6603i −0.684796 0.395367i 0.116864 0.993148i \(-0.462716\pi\)
−0.801659 + 0.597781i \(0.796049\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 24.9754 43.2586i 0.923747 1.59998i
\(732\) 0 0
\(733\) 16.4641 + 28.5167i 0.608115 + 1.05329i 0.991551 + 0.129719i \(0.0414076\pi\)
−0.383435 + 0.923568i \(0.625259\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 37.6018i 1.38508i
\(738\) 0 0
\(739\) 14.3923i 0.529429i 0.964327 + 0.264715i \(0.0852778\pi\)
−0.964327 + 0.264715i \(0.914722\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 12.7651 + 22.1098i 0.468306 + 0.811129i 0.999344 0.0362187i \(-0.0115313\pi\)
−0.531038 + 0.847348i \(0.678198\pi\)
\(744\) 0 0
\(745\) −5.85641 + 10.1436i −0.214562 + 0.371633i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3.52193 + 2.03339i 0.128689 + 0.0742984i
\(750\) 0 0
\(751\) 2.76795 1.59808i 0.101004 0.0583146i −0.448647 0.893709i \(-0.648094\pi\)
0.549651 + 0.835394i \(0.314761\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.55961 0.311516
\(756\) 0 0
\(757\) −5.39230 −0.195987 −0.0979933 0.995187i \(-0.531242\pi\)
−0.0979933 + 0.995187i \(0.531242\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 37.9435 21.9067i 1.37545 0.794118i 0.383844 0.923398i \(-0.374600\pi\)
0.991608 + 0.129281i \(0.0412668\pi\)
\(762\) 0 0
\(763\) 0.215390 + 0.124356i 0.00779765 + 0.00450198i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.17878 15.8981i 0.331427 0.574048i
\(768\) 0 0
\(769\) −6.42820 11.1340i −0.231807 0.401501i 0.726533 0.687132i \(-0.241130\pi\)
−0.958340 + 0.285630i \(0.907797\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 20.5569i 0.739379i −0.929155 0.369690i \(-0.879464\pi\)
0.929155 0.369690i \(-0.120536\pi\)
\(774\) 0 0
\(775\) 2.10512i 0.0756181i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.79315 3.10583i −0.0642463 0.111278i
\(780\) 0 0
\(781\) 21.8564 37.8564i 0.782084 1.35461i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.75410 1.59008i −0.0982980 0.0567524i
\(786\) 0 0
\(787\) −26.2128 + 15.1340i −0.934386 + 0.539468i −0.888196 0.459465i \(-0.848041\pi\)
−0.0461899 + 0.998933i \(0.514708\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.34795 −0.0834836
\(792\) 0 0
\(793\) 23.1436 0.821853
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.62536 + 1.51575i −0.0929949 + 0.0536906i −0.545776 0.837931i \(-0.683765\pi\)
0.452781 + 0.891622i \(0.350432\pi\)
\(798\) 0 0
\(799\) 55.1769 + 31.8564i 1.95202 + 1.12700i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −19.1798 + 33.220