Properties

Label 1620.2.r.h.109.6
Level $1620$
Weight $2$
Character 1620.109
Analytic conductor $12.936$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1620.r (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.9357651274\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 3 x^{14} - 11 x^{12} - 90 x^{10} - 450 x^{8} - 2250 x^{6} - 6875 x^{4} + 46875 x^{2} + 390625\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 109.6
Root \(-1.02733 + 1.98610i\) of defining polynomial
Character \(\chi\) \(=\) 1620.109
Dual form 1620.2.r.h.1189.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.02733 + 1.98610i) q^{5} +(1.10979 - 0.640739i) q^{7} +O(q^{10})\) \(q+(1.02733 + 1.98610i) q^{5} +(1.10979 - 0.640739i) q^{7} +(-2.07237 - 3.58945i) q^{11} +(-5.64823 - 3.26101i) q^{13} +5.98507i q^{17} -7.17891 q^{19} +(-6.52202 - 3.76549i) q^{23} +(-2.88918 + 4.08076i) q^{25} +(2.59808 + 4.50000i) q^{29} +(-2.58945 + 4.48507i) q^{31} +(2.41269 + 1.54591i) q^{35} -5.24054i q^{37} +(-0.340322 + 0.589454i) q^{41} +(-1.10979 + 0.640739i) q^{43} +(4.59980 - 2.65570i) q^{47} +(-2.67891 + 4.64001i) q^{49} -2.21958i q^{53} +(5.00000 - 7.80350i) q^{55} +(-3.80442 + 6.58945i) q^{59} +(1.08945 + 1.88699i) q^{61} +(0.674082 - 14.5681i) q^{65} +(-13.5161 - 7.80350i) q^{67} +5.50603 q^{71} -7.80350i q^{73} +(-4.59980 - 2.65570i) q^{77} +(3.00000 + 5.19615i) q^{79} +(8.44423 - 4.87528i) q^{83} +(-11.8869 + 6.14865i) q^{85} +10.0215 q^{89} -8.35782 q^{91} +(-7.37512 - 14.2580i) q^{95} +(-12.4063 + 7.16276i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q - 24 q^{19} - 6 q^{25} + 4 q^{31} + 48 q^{49} + 80 q^{55} - 28 q^{61} + 48 q^{79} - 22 q^{85} + 48 q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 1.02733 + 1.98610i 0.459436 + 0.888211i
\(6\) 0 0
\(7\) 1.10979 0.640739i 0.419462 0.242176i −0.275385 0.961334i \(-0.588805\pi\)
0.694847 + 0.719158i \(0.255472\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.07237 3.58945i −0.624844 1.08226i −0.988571 0.150756i \(-0.951829\pi\)
0.363727 0.931505i \(-0.381504\pi\)
\(12\) 0 0
\(13\) −5.64823 3.26101i −1.56654 0.904441i −0.996568 0.0827757i \(-0.973621\pi\)
−0.569970 0.821666i \(-0.693045\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.98507i 1.45159i 0.687909 + 0.725797i \(0.258529\pi\)
−0.687909 + 0.725797i \(0.741471\pi\)
\(18\) 0 0
\(19\) −7.17891 −1.64695 −0.823477 0.567349i \(-0.807969\pi\)
−0.823477 + 0.567349i \(0.807969\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.52202 3.76549i −1.35993 0.785159i −0.370320 0.928904i \(-0.620752\pi\)
−0.989615 + 0.143745i \(0.954085\pi\)
\(24\) 0 0
\(25\) −2.88918 + 4.08076i −0.577836 + 0.816153i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.59808 + 4.50000i 0.482451 + 0.835629i 0.999797 0.0201471i \(-0.00641344\pi\)
−0.517346 + 0.855776i \(0.673080\pi\)
\(30\) 0 0
\(31\) −2.58945 + 4.48507i −0.465080 + 0.805542i −0.999205 0.0398636i \(-0.987308\pi\)
0.534125 + 0.845405i \(0.320641\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.41269 + 1.54591i 0.407820 + 0.261306i
\(36\) 0 0
\(37\) 5.24054i 0.861540i −0.902462 0.430770i \(-0.858242\pi\)
0.902462 0.430770i \(-0.141758\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.340322 + 0.589454i −0.0531493 + 0.0920573i −0.891376 0.453265i \(-0.850259\pi\)
0.838227 + 0.545322i \(0.183593\pi\)
\(42\) 0 0
\(43\) −1.10979 + 0.640739i −0.169242 + 0.0977117i −0.582228 0.813025i \(-0.697819\pi\)
0.412987 + 0.910737i \(0.364486\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.59980 2.65570i 0.670950 0.387373i −0.125486 0.992095i \(-0.540049\pi\)
0.796437 + 0.604722i \(0.206716\pi\)
\(48\) 0 0
\(49\) −2.67891 + 4.64001i −0.382701 + 0.662858i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.21958i 0.304883i −0.988312 0.152442i \(-0.951286\pi\)
0.988312 0.152442i \(-0.0487136\pi\)
\(54\) 0 0
\(55\) 5.00000 7.80350i 0.674200 1.05222i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.80442 + 6.58945i −0.495294 + 0.857874i −0.999985 0.00542586i \(-0.998273\pi\)
0.504692 + 0.863300i \(0.331606\pi\)
\(60\) 0 0
\(61\) 1.08945 + 1.88699i 0.139490 + 0.241604i 0.927304 0.374310i \(-0.122120\pi\)
−0.787813 + 0.615914i \(0.788787\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.674082 14.5681i 0.0836096 1.80695i
\(66\) 0 0
\(67\) −13.5161 7.80350i −1.65125 0.953349i −0.976560 0.215246i \(-0.930945\pi\)
−0.674689 0.738103i \(-0.735722\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.50603 0.653446 0.326723 0.945120i \(-0.394056\pi\)
0.326723 + 0.945120i \(0.394056\pi\)
\(72\) 0 0
\(73\) 7.80350i 0.913330i −0.889639 0.456665i \(-0.849044\pi\)
0.889639 0.456665i \(-0.150956\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.59980 2.65570i −0.524196 0.302645i
\(78\) 0 0
\(79\) 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i \(-0.0570765\pi\)
−0.646440 + 0.762964i \(0.723743\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 8.44423 4.87528i 0.926875 0.535132i 0.0410532 0.999157i \(-0.486929\pi\)
0.885822 + 0.464025i \(0.153595\pi\)
\(84\) 0 0
\(85\) −11.8869 + 6.14865i −1.28932 + 0.666915i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10.0215 1.06228 0.531141 0.847284i \(-0.321764\pi\)
0.531141 + 0.847284i \(0.321764\pi\)
\(90\) 0 0
\(91\) −8.35782 −0.876137
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −7.37512 14.2580i −0.756671 1.46284i
\(96\) 0 0
\(97\) −12.4063 + 7.16276i −1.25966 + 0.727268i −0.973009 0.230766i \(-0.925877\pi\)
−0.286655 + 0.958034i \(0.592543\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0.340322 + 0.589454i 0.0338633 + 0.0586529i 0.882460 0.470387i \(-0.155886\pi\)
−0.848597 + 0.529040i \(0.822552\pi\)
\(102\) 0 0
\(103\) 2.21958 + 1.28148i 0.218702 + 0.126268i 0.605349 0.795960i \(-0.293034\pi\)
−0.386647 + 0.922228i \(0.626367\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.86081 + 4.53844i 0.739483 + 0.426941i 0.821881 0.569659i \(-0.192925\pi\)
−0.0823983 + 0.996599i \(0.526258\pi\)
\(114\) 0 0
\(115\) 0.778363 16.8218i 0.0725827 1.56864i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.83487 + 6.64218i 0.351542 + 0.608888i
\(120\) 0 0
\(121\) −3.08945 + 5.35109i −0.280859 + 0.486463i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.0729 1.54591i −0.990395 0.138270i
\(126\) 0 0
\(127\) 1.28148i 0.113713i 0.998382 + 0.0568563i \(0.0181077\pi\)
−0.998382 + 0.0568563i \(0.981892\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.75302 + 4.76836i −0.240532 + 0.416614i −0.960866 0.277014i \(-0.910655\pi\)
0.720334 + 0.693627i \(0.243989\pi\)
\(132\) 0 0
\(133\) −7.96709 + 4.59980i −0.690835 + 0.398854i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.78303 + 5.64823i −0.835820 + 0.482561i −0.855841 0.517238i \(-0.826960\pi\)
0.0200209 + 0.999800i \(0.493627\pi\)
\(138\) 0 0
\(139\) 8.58945 14.8774i 0.728548 1.26188i −0.228949 0.973438i \(-0.573529\pi\)
0.957497 0.288444i \(-0.0931378\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 27.0321i 2.26054i
\(144\) 0 0
\(145\) −6.26836 + 9.78303i −0.520559 + 0.812436i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −9.86660 + 17.0895i −0.808303 + 1.40002i 0.105735 + 0.994394i \(0.466281\pi\)
−0.914038 + 0.405628i \(0.867053\pi\)
\(150\) 0 0
\(151\) −2.58945 4.48507i −0.210727 0.364990i 0.741215 0.671267i \(-0.234250\pi\)
−0.951942 + 0.306278i \(0.900916\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −11.5680 0.535265i −0.929165 0.0429935i
\(156\) 0 0
\(157\) −4.53844 2.62027i −0.362207 0.209120i 0.307841 0.951438i \(-0.400393\pi\)
−0.670049 + 0.742317i \(0.733727\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −9.65078 −0.760588
\(162\) 0 0
\(163\) 11.7626i 0.921315i −0.887578 0.460657i \(-0.847614\pi\)
0.887578 0.460657i \(-0.152386\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.92222 1.10979i −0.148746 0.0858783i 0.423780 0.905765i \(-0.360703\pi\)
−0.572526 + 0.819887i \(0.694036\pi\)
\(168\) 0 0
\(169\) 14.7684 + 25.5796i 1.13603 + 1.96766i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.583422 + 0.336839i −0.0443567 + 0.0256094i −0.522014 0.852937i \(-0.674819\pi\)
0.477658 + 0.878546i \(0.341486\pi\)
\(174\) 0 0
\(175\) −0.591687 + 6.38001i −0.0447273 + 0.482283i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 14.5370 1.08655 0.543275 0.839555i \(-0.317184\pi\)
0.543275 + 0.839555i \(0.317184\pi\)
\(180\) 0 0
\(181\) 15.1789 1.12824 0.564120 0.825693i \(-0.309216\pi\)
0.564120 + 0.825693i \(0.309216\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 10.4082 5.38377i 0.765229 0.395823i
\(186\) 0 0
\(187\) 21.4831 12.4033i 1.57100 0.907019i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −13.1453 22.7684i −0.951162 1.64746i −0.742916 0.669384i \(-0.766558\pi\)
−0.208246 0.978077i \(-0.566775\pi\)
\(192\) 0 0
\(193\) −11.1972 6.46470i −0.805992 0.465339i 0.0395704 0.999217i \(-0.487401\pi\)
−0.845562 + 0.533877i \(0.820734\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.20466i 0.584558i −0.956333 0.292279i \(-0.905586\pi\)
0.956333 0.292279i \(-0.0944135\pi\)
\(198\) 0 0
\(199\) 2.35782 0.167141 0.0835706 0.996502i \(-0.473368\pi\)
0.0835706 + 0.996502i \(0.473368\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.76665 + 3.32937i 0.404739 + 0.233676i
\(204\) 0 0
\(205\) −1.52034 0.0703477i −0.106185 0.00491330i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 14.8774 + 25.7684i 1.02909 + 1.78243i
\(210\) 0 0
\(211\) −2.41055 + 4.17519i −0.165949 + 0.287432i −0.936992 0.349351i \(-0.886402\pi\)
0.771043 + 0.636783i \(0.219735\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.41269 1.54591i −0.164544 0.105430i
\(216\) 0 0
\(217\) 6.63665i 0.450525i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 19.5174 33.8051i 1.31288 2.27398i
\(222\) 0 0
\(223\) 6.85730 3.95906i 0.459199 0.265119i −0.252508 0.967595i \(-0.581256\pi\)
0.711707 + 0.702476i \(0.247922\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 18.8107 10.8604i 1.24851 0.720827i 0.277697 0.960669i \(-0.410429\pi\)
0.970812 + 0.239842i \(0.0770956\pi\)
\(228\) 0 0
\(229\) 9.08945 15.7434i 0.600648 1.04035i −0.392075 0.919933i \(-0.628243\pi\)
0.992723 0.120420i \(-0.0384240\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 21.0470i 1.37884i −0.724363 0.689418i \(-0.757866\pi\)
0.724363 0.689418i \(-0.242134\pi\)
\(234\) 0 0
\(235\) 10.0000 + 6.40739i 0.652328 + 0.417972i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −11.0729 + 19.1789i −0.716249 + 1.24058i 0.246226 + 0.969212i \(0.420809\pi\)
−0.962476 + 0.271368i \(0.912524\pi\)
\(240\) 0 0
\(241\) −9.50000 16.4545i −0.611949 1.05993i −0.990912 0.134515i \(-0.957053\pi\)
0.378963 0.925412i \(-0.376281\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −11.9676 0.553756i −0.764584 0.0353782i
\(246\) 0 0
\(247\) 40.5482 + 23.4105i 2.58002 + 1.48957i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −17.3205 −1.09326 −0.546630 0.837374i \(-0.684090\pi\)
−0.546630 + 0.837374i \(0.684090\pi\)
\(252\) 0 0
\(253\) 31.2140i 1.96241i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.93860 + 3.42865i 0.370439 + 0.213873i 0.673650 0.739050i \(-0.264725\pi\)
−0.303211 + 0.952923i \(0.598059\pi\)
\(258\) 0 0
\(259\) −3.35782 5.81591i −0.208645 0.361383i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −13.0440 + 7.53098i −0.804330 + 0.464380i −0.844983 0.534793i \(-0.820389\pi\)
0.0406531 + 0.999173i \(0.487056\pi\)
\(264\) 0 0
\(265\) 4.40831 2.28025i 0.270801 0.140074i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −9.28001 −0.565812 −0.282906 0.959148i \(-0.591298\pi\)
−0.282906 + 0.959148i \(0.591298\pi\)
\(270\) 0 0
\(271\) 0.357817 0.0217358 0.0108679 0.999941i \(-0.496541\pi\)
0.0108679 + 0.999941i \(0.496541\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 20.6352 + 1.91372i 1.24435 + 0.115402i
\(276\) 0 0
\(277\) −10.1867 + 5.88128i −0.612058 + 0.353372i −0.773770 0.633466i \(-0.781632\pi\)
0.161712 + 0.986838i \(0.448298\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.61904 + 6.26836i 0.215894 + 0.373939i 0.953549 0.301239i \(-0.0974001\pi\)
−0.737655 + 0.675178i \(0.764067\pi\)
\(282\) 0 0
\(283\) 24.8125 + 14.3255i 1.47495 + 0.851563i 0.999601 0.0282335i \(-0.00898820\pi\)
0.475350 + 0.879797i \(0.342322\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0.872228i 0.0514860i
\(288\) 0 0
\(289\) −18.8211 −1.10712
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −15.5497 8.97761i −0.908422 0.524477i −0.0284987 0.999594i \(-0.509073\pi\)
−0.879923 + 0.475116i \(0.842406\pi\)
\(294\) 0 0
\(295\) −16.9957 0.786411i −0.989529 0.0457866i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 24.5586 + 42.5367i 1.42026 + 2.45996i
\(300\) 0 0
\(301\) −0.821092 + 1.42217i −0.0473269 + 0.0819727i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.62852 + 4.10233i −0.150509 + 0.234899i
\(306\) 0 0
\(307\) 16.8885i 0.963876i −0.876205 0.481938i \(-0.839933\pi\)
0.876205 0.481938i \(-0.160067\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4.48507 + 7.76836i −0.254325 + 0.440503i −0.964712 0.263308i \(-0.915187\pi\)
0.710387 + 0.703811i \(0.248520\pi\)
\(312\) 0 0
\(313\) 7.86782 4.54249i 0.444715 0.256757i −0.260880 0.965371i \(-0.584013\pi\)
0.705596 + 0.708615i \(0.250679\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.5384 + 6.08435i −0.591895 + 0.341731i −0.765847 0.643023i \(-0.777680\pi\)
0.173951 + 0.984754i \(0.444347\pi\)
\(318\) 0 0
\(319\) 10.7684 18.6514i 0.602913 1.04428i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 42.9663i 2.39071i
\(324\) 0 0
\(325\) 29.6262 13.6275i 1.64336 0.755915i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3.40322 5.89454i 0.187625 0.324977i
\(330\) 0 0
\(331\) −0.768363 1.33084i −0.0422330 0.0731497i 0.844136 0.536129i \(-0.180114\pi\)
−0.886369 + 0.462979i \(0.846781\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.61306 34.8610i 0.0881307 1.90466i
\(336\) 0 0
\(337\) 2.21958 + 1.28148i 0.120908 + 0.0698065i 0.559234 0.829010i \(-0.311095\pi\)
−0.438326 + 0.898816i \(0.644428\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 21.4653 1.16241
\(342\) 0 0
\(343\) 15.8363i 0.855078i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.92222 1.10979i −0.103190 0.0595767i 0.447517 0.894275i \(-0.352308\pi\)
−0.550707 + 0.834699i \(0.685642\pi\)
\(348\) 0 0
\(349\) 4.41055 + 7.63929i 0.236091 + 0.408922i 0.959589 0.281405i \(-0.0908003\pi\)
−0.723498 + 0.690326i \(0.757467\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −24.1659 + 13.9522i −1.28622 + 0.742599i −0.977978 0.208709i \(-0.933074\pi\)
−0.308241 + 0.951308i \(0.599740\pi\)
\(354\) 0 0
\(355\) 5.65652 + 10.9355i 0.300217 + 0.580397i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 19.3624 1.02191 0.510955 0.859607i \(-0.329292\pi\)
0.510955 + 0.859607i \(0.329292\pi\)
\(360\) 0 0
\(361\) 32.5367 1.71246
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 15.4985 8.01677i 0.811229 0.419617i
\(366\) 0 0
\(367\) −2.21958 + 1.28148i −0.115861 + 0.0668926i −0.556811 0.830639i \(-0.687975\pi\)
0.440949 + 0.897532i \(0.354642\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.42217 2.46327i −0.0738355 0.127887i
\(372\) 0 0
\(373\) 14.6258 + 8.44423i 0.757297 + 0.437226i 0.828325 0.560249i \(-0.189294\pi\)
−0.0710272 + 0.997474i \(0.522628\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 33.8894i 1.74539i
\(378\) 0 0
\(379\) −22.3578 −1.14844 −0.574222 0.818700i \(-0.694695\pi\)
−0.574222 + 0.818700i \(0.694695\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10.3664 + 5.98507i 0.529701 + 0.305823i 0.740895 0.671621i \(-0.234402\pi\)
−0.211194 + 0.977444i \(0.567735\pi\)
\(384\) 0 0
\(385\) 0.548958 11.8639i 0.0279775 0.604643i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.24756 + 10.8211i 0.316764 + 0.548651i 0.979811 0.199927i \(-0.0640704\pi\)
−0.663047 + 0.748578i \(0.730737\pi\)
\(390\) 0 0
\(391\) 22.5367 39.0348i 1.13973 1.97407i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7.23808 + 11.2965i −0.364187 + 0.568387i
\(396\) 0 0
\(397\) 24.6920i 1.23925i 0.784896 + 0.619627i \(0.212716\pi\)
−0.784896 + 0.619627i \(0.787284\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.03173 + 10.4473i −0.301210 + 0.521712i −0.976410 0.215923i \(-0.930724\pi\)
0.675200 + 0.737635i \(0.264057\pi\)
\(402\) 0 0
\(403\) 29.2517 16.8885i 1.45713 0.841275i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −18.8107 + 10.8604i −0.932411 + 0.538328i
\(408\) 0 0
\(409\) 9.08945 15.7434i 0.449445 0.778461i −0.548905 0.835885i \(-0.684955\pi\)
0.998350 + 0.0574237i \(0.0182886\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 9.75056i 0.479794i
\(414\) 0 0
\(415\) 18.3578 + 11.7626i 0.901150 + 0.577401i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.82539 8.35782i 0.235736 0.408306i −0.723751 0.690062i \(-0.757583\pi\)
0.959486 + 0.281756i \(0.0909167\pi\)
\(420\) 0 0
\(421\) 7.85782 + 13.6101i 0.382967 + 0.663318i 0.991485 0.130222i \(-0.0415691\pi\)
−0.608518 + 0.793540i \(0.708236\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −24.4237 17.2920i −1.18472 0.838783i
\(426\) 0 0
\(427\) 2.41813 + 1.39611i 0.117022 + 0.0675625i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −31.1160 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(432\) 0 0
\(433\) 16.7738i 0.806099i 0.915178 + 0.403050i \(0.132050\pi\)
−0.915178 + 0.403050i \(0.867950\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 46.8210 + 27.0321i 2.23975 + 1.29312i
\(438\) 0 0
\(439\) −7.76836 13.4552i −0.370764 0.642182i 0.618920 0.785454i \(-0.287571\pi\)
−0.989683 + 0.143273i \(0.954237\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.6438 10.1867i 0.838284 0.483984i −0.0183965 0.999831i \(-0.505856\pi\)
0.856681 + 0.515847i \(0.172523\pi\)
\(444\) 0 0
\(445\) 10.2954 + 19.9038i 0.488051 + 0.943529i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −33.8386 −1.59694 −0.798471 0.602033i \(-0.794358\pi\)
−0.798471 + 0.602033i \(0.794358\pi\)
\(450\) 0 0
\(451\) 2.82109 0.132840
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8.58625 16.5995i −0.402529 0.778194i
\(456\) 0 0
\(457\) 0.0992755 0.0573167i 0.00464391 0.00268116i −0.497676 0.867363i \(-0.665813\pi\)
0.502320 + 0.864682i \(0.332480\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.48507 + 7.76836i 0.208890 + 0.361809i 0.951365 0.308065i \(-0.0996815\pi\)
−0.742475 + 0.669874i \(0.766348\pi\)
\(462\) 0 0
\(463\) −6.65875 3.84443i −0.309458 0.178666i 0.337226 0.941424i \(-0.390511\pi\)
−0.646684 + 0.762758i \(0.723845\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 29.2517i 1.35361i 0.736164 + 0.676803i \(0.236635\pi\)
−0.736164 + 0.676803i \(0.763365\pi\)
\(468\) 0 0
\(469\) −20.0000 −0.923514
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.59980 + 2.65570i 0.211499 + 0.122109i
\(474\) 0 0
\(475\) 20.7412 29.2954i 0.951670 1.34417i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.9288 + 27.5895i 0.727804 + 1.26059i 0.957809 + 0.287405i \(0.0927925\pi\)
−0.230005 + 0.973190i \(0.573874\pi\)
\(480\) 0 0
\(481\) −17.0895 + 29.5998i −0.779212 + 1.34963i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −26.9713 17.2815i −1.22470 0.784714i
\(486\) 0 0
\(487\) 33.7769i 1.53058i 0.643686 + 0.765290i \(0.277404\pi\)
−0.643686 + 0.765290i \(0.722596\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 11.7231 20.3051i 0.529058 0.916356i −0.470367 0.882471i \(-0.655879\pi\)
0.999426 0.0338851i \(-0.0107880\pi\)
\(492\) 0 0
\(493\) −26.9328 + 15.5497i −1.21299 + 0.700322i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.11055 3.52793i 0.274095 0.158249i
\(498\) 0 0
\(499\) −3.58945 + 6.21712i −0.160686 + 0.278316i −0.935115 0.354345i \(-0.884704\pi\)
0.774429 + 0.632661i \(0.218037\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 40.7467i 1.81681i 0.418096 + 0.908403i \(0.362698\pi\)
−0.418096 + 0.908403i \(0.637302\pi\)
\(504\) 0 0
\(505\) −0.821092 + 1.28148i −0.0365381 + 0.0570250i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −15.8983 + 27.5367i −0.704681 + 1.22054i 0.262125 + 0.965034i \(0.415577\pi\)
−0.966806 + 0.255510i \(0.917757\pi\)
\(510\) 0 0
\(511\) −5.00000 8.66025i −0.221187 0.383107i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −0.264894 + 5.72481i −0.0116726 + 0.252265i
\(516\) 0 0
\(517\) −19.0650 11.0072i −0.838478 0.484096i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 22.1459 0.970229 0.485115 0.874451i \(-0.338778\pi\)
0.485115 + 0.874451i \(0.338778\pi\)
\(522\) 0 0
\(523\) 41.6951i 1.82320i −0.411081 0.911599i \(-0.634849\pi\)
0.411081 0.911599i \(-0.365151\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −26.8434 15.4981i −1.16932 0.675107i
\(528\) 0 0
\(529\) 16.8578 + 29.1986i 0.732949 + 1.26950i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.84443 2.21958i 0.166521 0.0961408i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 22.2068 0.956514
\(540\) 0 0
\(541\) −19.3578 −0.832258 −0.416129 0.909306i \(-0.636613\pi\)
−0.416129 + 0.909306i \(0.636613\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7.19132 13.9027i −0.308042 0.595526i
\(546\) 0 0
\(547\) 4.43917 2.56295i 0.189805 0.109584i −0.402086 0.915602i \(-0.631715\pi\)
0.591891 + 0.806018i \(0.298381\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −18.6514 32.3051i −0.794574 1.37624i
\(552\) 0 0
\(553\) 6.65875 + 3.84443i 0.283159 + 0.163482i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.41813i 0.102460i −0.998687 0.0512298i \(-0.983686\pi\)
0.998687 0.0512298i \(-0.0163141\pi\)
\(558\) 0 0
\(559\) 8.35782 0.353498
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4.59980 + 2.65570i 0.193859 + 0.111924i 0.593788 0.804622i \(-0.297632\pi\)
−0.399929 + 0.916546i \(0.630965\pi\)
\(564\) 0 0
\(565\) −0.938140 + 20.2748i −0.0394678 + 0.852969i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10.8876 + 18.8578i 0.456430 + 0.790561i 0.998769 0.0495991i \(-0.0157944\pi\)
−0.542339 + 0.840160i \(0.682461\pi\)
\(570\) 0 0
\(571\) 3.41055 5.90724i 0.142727 0.247210i −0.785796 0.618486i \(-0.787746\pi\)
0.928523 + 0.371276i \(0.121080\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 34.2094 15.7356i 1.42663 0.656221i
\(576\) 0 0
\(577\) 5.24054i 0.218167i −0.994033 0.109083i \(-0.965208\pi\)
0.994033 0.109083i \(-0.0347915\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 6.24756 10.8211i 0.259192 0.448935i
\(582\) 0 0
\(583\) −7.96709 + 4.59980i −0.329963 + 0.190504i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −41.0543 + 23.7027i −1.69449 + 0.978316i −0.743688 + 0.668527i \(0.766925\pi\)
−0.950805 + 0.309790i \(0.899741\pi\)
\(588\) 0 0
\(589\) 18.5895 32.1979i 0.765965 1.32669i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 11.2965i 0.463890i 0.972729 + 0.231945i \(0.0745090\pi\)
−0.972729 + 0.231945i \(0.925491\pi\)
\(594\) 0 0
\(595\) −9.25236 + 14.4401i −0.379310 + 0.591988i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −18.3415 + 31.7684i −0.749412 + 1.29802i 0.198692 + 0.980062i \(0.436331\pi\)
−0.948105 + 0.317958i \(0.897003\pi\)
\(600\) 0 0
\(601\) −9.67891 16.7644i −0.394811 0.683833i 0.598266 0.801297i \(-0.295857\pi\)
−0.993077 + 0.117465i \(0.962523\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −13.8017 0.638620i −0.561119 0.0259636i
\(606\) 0 0
\(607\) 1.10979 + 0.640739i 0.0450451 + 0.0260068i 0.522353 0.852729i \(-0.325054\pi\)
−0.477308 + 0.878736i \(0.658388\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −34.6410 −1.40143
\(612\) 0 0
\(613\) 38.9028i 1.57127i −0.618690 0.785636i \(-0.712336\pi\)
0.618690 0.785636i \(-0.287664\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −26.6715 15.3988i −1.07375 0.619932i −0.144549 0.989498i \(-0.546173\pi\)
−0.929205 + 0.369565i \(0.879507\pi\)
\(618\) 0 0
\(619\) 17.1789 + 29.7547i 0.690479 + 1.19594i 0.971681 + 0.236296i \(0.0759334\pi\)
−0.281203 + 0.959648i \(0.590733\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11.1218 6.42119i 0.445586 0.257259i
\(624\) 0 0
\(625\) −8.30526 23.5801i −0.332210 0.943205i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 31.3650 1.25061
\(630\) 0 0
\(631\) 11.5367 0.459270 0.229635 0.973277i \(-0.426247\pi\)
0.229635 + 0.973277i \(0.426247\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.54514 + 1.31650i −0.101001 + 0.0522438i
\(636\) 0 0
\(637\) 30.2622 17.4719i 1.19903 0.692261i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3.95936 6.85782i −0.156385 0.270867i 0.777177 0.629282i \(-0.216651\pi\)
−0.933563 + 0.358414i \(0.883318\pi\)
\(642\) 0 0
\(643\) −7.96709 4.59980i −0.314191 0.181399i 0.334609 0.942357i \(-0.391396\pi\)
−0.648801 + 0.760958i \(0.724729\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 13.7146i 0.539177i −0.962976 0.269588i \(-0.913112\pi\)
0.962976 0.269588i \(-0.0868876\pi\)
\(648\) 0 0
\(649\) 31.5367 1.23792
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 36.4545 + 21.0470i 1.42658 + 0.823634i 0.996849 0.0793250i \(-0.0252765\pi\)
0.429727 + 0.902959i \(0.358610\pi\)
\(654\) 0 0
\(655\) −12.2987 0.569075i −0.480550 0.0222356i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −12.0635 20.8945i −0.469926 0.813936i 0.529483 0.848321i \(-0.322386\pi\)
−0.999409 + 0.0343850i \(0.989053\pi\)
\(660\) 0 0
\(661\) −22.2156 + 38.4786i −0.864088 + 1.49664i 0.00386191 + 0.999993i \(0.498771\pi\)
−0.867950 + 0.496652i \(0.834563\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −17.3205 11.0979i −0.671660 0.430359i
\(666\) 0 0
\(667\) 39.1321i 1.51520i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.51551 7.82109i 0.174319 0.301930i
\(672\) 0 0
\(673\) −28.2412 + 16.3050i −1.08862 + 0.628513i −0.933208 0.359337i \(-0.883003\pi\)
−0.155409 + 0.987850i \(0.549670\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 44.1434 25.4862i 1.69657 0.979514i 0.747596 0.664154i \(-0.231208\pi\)
0.948972 0.315360i \(-0.102125\pi\)
\(678\) 0 0
\(679\) −9.17891 + 15.8983i −0.352254 + 0.610122i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 28.3795i 1.08591i −0.839762 0.542955i \(-0.817305\pi\)
0.839762 0.542955i \(-0.182695\pi\)
\(684\) 0 0
\(685\) −21.2684 13.6275i −0.812622 0.520678i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −7.23808 + 12.5367i −0.275749 + 0.477611i
\(690\) 0 0
\(691\) −7.35782 12.7441i −0.279905 0.484809i 0.691456 0.722418i \(-0.256969\pi\)
−0.971361 + 0.237609i \(0.923636\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 38.3722 + 1.77552i 1.45554 + 0.0673494i
\(696\) 0 0
\(697\) −3.52793 2.03685i −0.133630 0.0771512i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 14.2272 0.537353 0.268676 0.963230i \(-0.413414\pi\)
0.268676 + 0.963230i \(0.413414\pi\)
\(702\) 0 0
\(703\) 37.6214i 1.41892i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0.755372 + 0.436114i 0.0284087 + 0.0164018i
\(708\) 0 0
\(709\) −9.26836 16.0533i −0.348081 0.602893i 0.637828 0.770179i \(-0.279833\pi\)
−0.985908 + 0.167286i \(0.946500\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 33.7769 19.5011i 1.26496 0.730323i
\(714\) 0 0
\(715\) −53.6884 + 27.7709i −2.00783 + 1.03857i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 31.7358 1.18355 0.591773 0.806105i \(-0.298428\pi\)
0.591773 + 0.806105i \(0.298428\pi\)
\(720\) 0 0
\(721\) 3.28437 0.122316
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −25.8697 2.39918i −0.960778 0.0891034i
\(726\) 0 0
\(727\) −27.2307 + 15.7216i −1.00993 + 0.583083i −0.911171 0.412029i \(-0.864820\pi\)
−0.0987581 + 0.995111i \(0.531487\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.83487 6.64218i −0.141838 0.245670i
\(732\) 0 0
\(733\) −4.43917 2.56295i −0.163964 0.0946649i 0.415772 0.909469i \(-0.363511\pi\)
−0.579737 + 0.814804i \(0.696845\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 64.6870i 2.38278i
\(738\) 0 0
\(739\) −33.8945 −1.24683 −0.623415 0.781891i \(-0.714255\pi\)
−0.623415 + 0.781891i \(0.714255\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −33.0216 19.0650i −1.21144 0.699427i −0.248370 0.968665i \(-0.579895\pi\)
−0.963074 + 0.269238i \(0.913228\pi\)
\(744\) 0 0
\(745\) −44.0776 2.03952i −1.61488 0.0747223i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −8.17891 + 14.1663i −0.298453 + 0.516935i −0.975782 0.218745i \(-0.929804\pi\)
0.677330 + 0.735680i \(0.263137\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 6.24756 9.75056i 0.227372 0.354859i
\(756\) 0 0
\(757\) 28.6510i 1.04134i −0.853758 0.520670i \(-0.825682\pi\)
0.853758 0.520670i \(-0.174318\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.866025 + 1.50000i −0.0313934 + 0.0543750i −0.881295 0.472566i \(-0.843328\pi\)
0.849902 + 0.526941i \(0.176661\pi\)
\(762\) 0 0
\(763\) −7.76854 + 4.48517i −0.281240 + 0.162374i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 42.9765 24.8125i 1.55179 0.895928i
\(768\) 0 0
\(769\) −9.85782 + 17.0742i −0.355482 + 0.615713i −0.987200 0.159485i \(-0.949017\pi\)
0.631718 + 0.775198i \(0.282350\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.63772i 0.166807i −0.996516 0.0834036i \(-0.973421\pi\)
0.996516 0.0834036i \(-0.0265791\pi\)
\(774\) 0 0
\(775\) −10.8211 23.5251i −0.388705 0.845047i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.44314 4.23164i 0.0875345 0.151614i
\(780\) 0 0
\(781\) −11.4105 19.7636i −0.408301 0.707199i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.541635 11.7057i 0.0193318 0.417794i
\(786\) 0 0
\(787\) −39.6369 22.8844i −1.41290 0.815740i −0.417242 0.908795i \(-0.637003\pi\)
−0.995661 + 0.0930552i \(0.970337\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 11.6318 0.413580
\(792\) 0 0
\(793\) 14.2109i 0.504643i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −22.8271 13.1792i −0.808576 0.466832i 0.0378850 0.999282i \(-0.487938\pi\)
−0.846461 + 0.532450i \(0.821271\pi\)
\(798\) 0 0
\(799\) 15.8945 + 27.5302i 0.562308 + 0.973947i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −28.0103 + 16.1717i −0.988462 + 0.570689i