Properties

Label 3456.2.i.l.2305.3
Level $3456$
Weight $2$
Character 3456.2305
Analytic conductor $27.596$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3456 = 2^{7} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3456.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.5962989386\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} - 216 x^{3} + 243 x^{2} - 486 x + 729\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 1152)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.3
Root \(1.19051 + 1.25805i\) of defining polynomial
Character \(\chi\) \(=\) 3456.2305
Dual form 3456.2.i.l.1153.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.268104 + 0.464369i) q^{5} +(2.35014 + 4.07056i) q^{7} +O(q^{10})\) \(q+(-0.268104 + 0.464369i) q^{5} +(2.35014 + 4.07056i) q^{7} +(2.59922 + 4.50198i) q^{11} +(-0.778295 + 1.34805i) q^{13} -0.695781 q^{17} +5.80593 q^{19} +(-4.42809 + 7.66967i) q^{23} +(2.35624 + 4.08113i) q^{25} +(-1.92199 - 3.32898i) q^{29} +(2.77035 - 4.79840i) q^{31} -2.52033 q^{35} +4.09280 q^{37} +(-1.01019 + 1.74970i) q^{41} +(-3.71522 - 6.43494i) q^{43} +(0.186066 + 0.322275i) q^{47} +(-7.54633 + 13.0706i) q^{49} -5.30777 q^{53} -2.78744 q^{55} +(2.57152 - 4.45401i) q^{59} +(-0.921988 - 1.59693i) q^{61} +(-0.417328 - 0.722833i) q^{65} +(5.79316 - 10.0340i) q^{67} -10.6289 q^{71} +4.40840 q^{73} +(-12.2171 + 21.1606i) q^{77} +(3.32244 + 5.75464i) q^{79} +(-5.28055 - 9.14617i) q^{83} +(0.186541 - 0.323099i) q^{85} +7.30777 q^{89} -7.31642 q^{91} +(-1.55659 + 2.69609i) q^{95} +(-7.81612 - 13.5379i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{5} + 6 q^{7} + O(q^{10}) \) \( 12 q + 2 q^{5} + 6 q^{7} - 4 q^{11} + 10 q^{13} - 4 q^{17} + 4 q^{19} - 8 q^{23} - 14 q^{25} + 2 q^{29} + 8 q^{31} - 8 q^{35} + 2 q^{41} - 2 q^{43} + 14 q^{47} - 18 q^{49} - 24 q^{53} - 16 q^{55} - 6 q^{59} + 14 q^{61} + 8 q^{65} + 4 q^{67} + 28 q^{71} + 60 q^{73} - 2 q^{77} + 16 q^{79} - 24 q^{83} + 16 q^{85} + 48 q^{89} - 52 q^{91} + 20 q^{95} - 14 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times\).

\(n\) \(2053\) \(2431\) \(2945\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −0.268104 + 0.464369i −0.119900 + 0.207672i −0.919728 0.392557i \(-0.871591\pi\)
0.799828 + 0.600229i \(0.204924\pi\)
\(6\) 0 0
\(7\) 2.35014 + 4.07056i 0.888270 + 1.53853i 0.841919 + 0.539604i \(0.181426\pi\)
0.0463510 + 0.998925i \(0.485241\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.59922 + 4.50198i 0.783695 + 1.35740i 0.929776 + 0.368126i \(0.120001\pi\)
−0.146081 + 0.989273i \(0.546666\pi\)
\(12\) 0 0
\(13\) −0.778295 + 1.34805i −0.215860 + 0.373881i −0.953538 0.301272i \(-0.902589\pi\)
0.737678 + 0.675153i \(0.235922\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.695781 −0.168752 −0.0843759 0.996434i \(-0.526890\pi\)
−0.0843759 + 0.996434i \(0.526890\pi\)
\(18\) 0 0
\(19\) 5.80593 1.33197 0.665986 0.745965i \(-0.268011\pi\)
0.665986 + 0.745965i \(0.268011\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.42809 + 7.66967i −0.923320 + 1.59924i −0.129079 + 0.991634i \(0.541202\pi\)
−0.794241 + 0.607603i \(0.792131\pi\)
\(24\) 0 0
\(25\) 2.35624 + 4.08113i 0.471248 + 0.816226i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.92199 3.32898i −0.356904 0.618176i 0.630538 0.776159i \(-0.282834\pi\)
−0.987442 + 0.157982i \(0.949501\pi\)
\(30\) 0 0
\(31\) 2.77035 4.79840i 0.497570 0.861817i −0.502426 0.864620i \(-0.667559\pi\)
0.999996 + 0.00280317i \(0.000892278\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.52033 −0.426013
\(36\) 0 0
\(37\) 4.09280 0.672852 0.336426 0.941710i \(-0.390782\pi\)
0.336426 + 0.941710i \(0.390782\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.01019 + 1.74970i −0.157765 + 0.273258i −0.934063 0.357109i \(-0.883762\pi\)
0.776297 + 0.630367i \(0.217096\pi\)
\(42\) 0 0
\(43\) −3.71522 6.43494i −0.566565 0.981319i −0.996902 0.0786512i \(-0.974939\pi\)
0.430337 0.902668i \(-0.358395\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.186066 + 0.322275i 0.0271404 + 0.0470086i 0.879277 0.476311i \(-0.158027\pi\)
−0.852136 + 0.523320i \(0.824693\pi\)
\(48\) 0 0
\(49\) −7.54633 + 13.0706i −1.07805 + 1.86723i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −5.30777 −0.729078 −0.364539 0.931188i \(-0.618773\pi\)
−0.364539 + 0.931188i \(0.618773\pi\)
\(54\) 0 0
\(55\) −2.78744 −0.375859
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.57152 4.45401i 0.334784 0.579862i −0.648660 0.761079i \(-0.724670\pi\)
0.983443 + 0.181216i \(0.0580034\pi\)
\(60\) 0 0
\(61\) −0.921988 1.59693i −0.118049 0.204466i 0.800946 0.598737i \(-0.204330\pi\)
−0.918994 + 0.394271i \(0.870997\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.417328 0.722833i −0.0517631 0.0896564i
\(66\) 0 0
\(67\) 5.79316 10.0340i 0.707747 1.22585i −0.257944 0.966160i \(-0.583045\pi\)
0.965691 0.259694i \(-0.0836218\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −10.6289 −1.26142 −0.630708 0.776021i \(-0.717235\pi\)
−0.630708 + 0.776021i \(0.717235\pi\)
\(72\) 0 0
\(73\) 4.40840 0.515964 0.257982 0.966150i \(-0.416943\pi\)
0.257982 + 0.966150i \(0.416943\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −12.2171 + 21.1606i −1.39227 + 2.41147i
\(78\) 0 0
\(79\) 3.32244 + 5.75464i 0.373804 + 0.647448i 0.990147 0.140030i \(-0.0447199\pi\)
−0.616343 + 0.787478i \(0.711387\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.28055 9.14617i −0.579615 1.00392i −0.995523 0.0945164i \(-0.969870\pi\)
0.415908 0.909407i \(-0.363464\pi\)
\(84\) 0 0
\(85\) 0.186541 0.323099i 0.0202333 0.0350450i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.30777 0.774622 0.387311 0.921949i \(-0.373404\pi\)
0.387311 + 0.921949i \(0.373404\pi\)
\(90\) 0 0
\(91\) −7.31642 −0.766969
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.55659 + 2.69609i −0.159703 + 0.276613i
\(96\) 0 0
\(97\) −7.81612 13.5379i −0.793607 1.37457i −0.923720 0.383068i \(-0.874867\pi\)
0.130113 0.991499i \(-0.458466\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.43218 + 7.67676i 0.441018 + 0.763866i 0.997765 0.0668159i \(-0.0212840\pi\)
−0.556747 + 0.830682i \(0.687951\pi\)
\(102\) 0 0
\(103\) 1.64986 2.85764i 0.162565 0.281571i −0.773223 0.634135i \(-0.781356\pi\)
0.935788 + 0.352563i \(0.114690\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.12139 0.688451 0.344226 0.938887i \(-0.388142\pi\)
0.344226 + 0.938887i \(0.388142\pi\)
\(108\) 0 0
\(109\) 2.98862 0.286258 0.143129 0.989704i \(-0.454284\pi\)
0.143129 + 0.989704i \(0.454284\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.40833 + 5.90340i −0.320629 + 0.555345i −0.980618 0.195930i \(-0.937227\pi\)
0.659989 + 0.751275i \(0.270561\pi\)
\(114\) 0 0
\(115\) −2.37437 4.11253i −0.221411 0.383496i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.63518 2.83222i −0.149897 0.259629i
\(120\) 0 0
\(121\) −8.01190 + 13.8770i −0.728355 + 1.26155i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −5.20790 −0.465809
\(126\) 0 0
\(127\) −17.7567 −1.57565 −0.787826 0.615899i \(-0.788793\pi\)
−0.787826 + 0.615899i \(0.788793\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.51253 6.08389i 0.306892 0.531552i −0.670789 0.741648i \(-0.734044\pi\)
0.977681 + 0.210096i \(0.0673778\pi\)
\(132\) 0 0
\(133\) 13.6448 + 23.6334i 1.18315 + 2.04928i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −5.71048 9.89083i −0.487879 0.845031i 0.512024 0.858971i \(-0.328896\pi\)
−0.999903 + 0.0139402i \(0.995563\pi\)
\(138\) 0 0
\(139\) 3.10659 5.38078i 0.263498 0.456392i −0.703671 0.710526i \(-0.748457\pi\)
0.967169 + 0.254134i \(0.0817905\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −8.09185 −0.676674
\(144\) 0 0
\(145\) 2.06117 0.171171
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.47858 9.48918i 0.448823 0.777384i −0.549487 0.835502i \(-0.685177\pi\)
0.998310 + 0.0581186i \(0.0185102\pi\)
\(150\) 0 0
\(151\) 7.28439 + 12.6169i 0.592796 + 1.02675i 0.993854 + 0.110700i \(0.0353091\pi\)
−0.401058 + 0.916053i \(0.631358\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.48548 + 2.57293i 0.119317 + 0.206663i
\(156\) 0 0
\(157\) −7.66049 + 13.2684i −0.611373 + 1.05893i 0.379636 + 0.925136i \(0.376049\pi\)
−0.991009 + 0.133794i \(0.957284\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −41.6265 −3.28063
\(162\) 0 0
\(163\) −11.0724 −0.867258 −0.433629 0.901091i \(-0.642767\pi\)
−0.433629 + 0.901091i \(0.642767\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.15607 7.19852i 0.321606 0.557039i −0.659213 0.751956i \(-0.729111\pi\)
0.980820 + 0.194917i \(0.0624439\pi\)
\(168\) 0 0
\(169\) 5.28851 + 9.15997i 0.406809 + 0.704613i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.0396656 0.0687029i −0.00301572 0.00522338i 0.864514 0.502609i \(-0.167627\pi\)
−0.867529 + 0.497386i \(0.834293\pi\)
\(174\) 0 0
\(175\) −11.0750 + 19.1825i −0.837191 + 1.45006i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 20.8011 1.55475 0.777375 0.629038i \(-0.216551\pi\)
0.777375 + 0.629038i \(0.216551\pi\)
\(180\) 0 0
\(181\) −5.13118 −0.381397 −0.190699 0.981649i \(-0.561075\pi\)
−0.190699 + 0.981649i \(0.561075\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.09729 + 1.90057i −0.0806747 + 0.139733i
\(186\) 0 0
\(187\) −1.80849 3.13240i −0.132250 0.229063i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.89085 + 17.1315i 0.715677 + 1.23959i 0.962698 + 0.270579i \(0.0872150\pi\)
−0.247021 + 0.969010i \(0.579452\pi\)
\(192\) 0 0
\(193\) 1.79574 3.11031i 0.129260 0.223885i −0.794130 0.607748i \(-0.792073\pi\)
0.923390 + 0.383863i \(0.125407\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.71261 −0.122019 −0.0610093 0.998137i \(-0.519432\pi\)
−0.0610093 + 0.998137i \(0.519432\pi\)
\(198\) 0 0
\(199\) 18.1299 1.28520 0.642598 0.766203i \(-0.277856\pi\)
0.642598 + 0.766203i \(0.277856\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.03389 15.6472i 0.634055 1.09822i
\(204\) 0 0
\(205\) −0.541672 0.938204i −0.0378320 0.0655270i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 15.0909 + 26.1382i 1.04386 + 1.80802i
\(210\) 0 0
\(211\) 0.734306 1.27186i 0.0505517 0.0875581i −0.839642 0.543140i \(-0.817235\pi\)
0.890194 + 0.455582i \(0.150569\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.98425 0.271724
\(216\) 0 0
\(217\) 26.0429 1.76791
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.541523 0.937946i 0.0364268 0.0630931i
\(222\) 0 0
\(223\) 9.57845 + 16.5904i 0.641420 + 1.11097i 0.985116 + 0.171891i \(0.0549878\pi\)
−0.343696 + 0.939081i \(0.611679\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.92737 + 10.2665i 0.393414 + 0.681412i 0.992897 0.118975i \(-0.0379607\pi\)
−0.599484 + 0.800387i \(0.704627\pi\)
\(228\) 0 0
\(229\) −1.57219 + 2.72311i −0.103893 + 0.179948i −0.913285 0.407320i \(-0.866463\pi\)
0.809392 + 0.587268i \(0.199797\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.82935 0.185357 0.0926783 0.995696i \(-0.470457\pi\)
0.0926783 + 0.995696i \(0.470457\pi\)
\(234\) 0 0
\(235\) −0.199539 −0.0130165
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.58766 + 2.74991i −0.102697 + 0.177877i −0.912795 0.408418i \(-0.866081\pi\)
0.810098 + 0.586295i \(0.199414\pi\)
\(240\) 0 0
\(241\) 6.63053 + 11.4844i 0.427110 + 0.739776i 0.996615 0.0822117i \(-0.0261984\pi\)
−0.569505 + 0.821988i \(0.692865\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.04640 7.00857i −0.258515 0.447761i
\(246\) 0 0
\(247\) −4.51873 + 7.82666i −0.287520 + 0.497999i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.06394 0.193394 0.0966970 0.995314i \(-0.469172\pi\)
0.0966970 + 0.995314i \(0.469172\pi\)
\(252\) 0 0
\(253\) −46.0383 −2.89440
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.14120 + 14.1010i −0.507834 + 0.879595i 0.492125 + 0.870525i \(0.336220\pi\)
−0.999959 + 0.00907003i \(0.997113\pi\)
\(258\) 0 0
\(259\) 9.61866 + 16.6600i 0.597674 + 1.03520i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −11.0730 19.1790i −0.682789 1.18262i −0.974126 0.226005i \(-0.927434\pi\)
0.291337 0.956620i \(-0.405900\pi\)
\(264\) 0 0
\(265\) 1.42303 2.46476i 0.0874162 0.151409i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −31.7805 −1.93769 −0.968845 0.247667i \(-0.920336\pi\)
−0.968845 + 0.247667i \(0.920336\pi\)
\(270\) 0 0
\(271\) 0.794033 0.0482341 0.0241170 0.999709i \(-0.492323\pi\)
0.0241170 + 0.999709i \(0.492323\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −12.2488 + 21.2155i −0.738629 + 1.27934i
\(276\) 0 0
\(277\) 12.6085 + 21.8385i 0.757569 + 1.31215i 0.944087 + 0.329696i \(0.106946\pi\)
−0.186519 + 0.982451i \(0.559720\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.06672 + 8.77581i 0.302255 + 0.523521i 0.976646 0.214853i \(-0.0689273\pi\)
−0.674391 + 0.738374i \(0.735594\pi\)
\(282\) 0 0
\(283\) 11.6766 20.2245i 0.694102 1.20222i −0.276380 0.961048i \(-0.589135\pi\)
0.970482 0.241172i \(-0.0775319\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.49637 −0.560553
\(288\) 0 0
\(289\) −16.5159 −0.971523
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 13.1967 22.8573i 0.770959 1.33534i −0.166079 0.986112i \(-0.553111\pi\)
0.937038 0.349228i \(-0.113556\pi\)
\(294\) 0 0
\(295\) 1.37887 + 2.38827i 0.0802809 + 0.139051i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −6.89272 11.9385i −0.398616 0.690424i
\(300\) 0 0
\(301\) 17.4626 30.2461i 1.00653 1.74335i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.988754 0.0566159
\(306\) 0 0
\(307\) −21.6724 −1.23691 −0.618454 0.785821i \(-0.712241\pi\)
−0.618454 + 0.785821i \(0.712241\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −14.5448 + 25.1924i −0.824761 + 1.42853i 0.0773408 + 0.997005i \(0.475357\pi\)
−0.902102 + 0.431523i \(0.857976\pi\)
\(312\) 0 0
\(313\) 3.52393 + 6.10363i 0.199185 + 0.344998i 0.948264 0.317482i \(-0.102837\pi\)
−0.749080 + 0.662480i \(0.769504\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −0.444372 0.769675i −0.0249584 0.0432292i 0.853276 0.521459i \(-0.174612\pi\)
−0.878235 + 0.478230i \(0.841279\pi\)
\(318\) 0 0
\(319\) 9.99135 17.3055i 0.559408 0.968923i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.03966 −0.224772
\(324\) 0 0
\(325\) −7.33540 −0.406895
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −0.874561 + 1.51478i −0.0482161 + 0.0835127i
\(330\) 0 0
\(331\) 11.4513 + 19.8342i 0.629420 + 1.09019i 0.987668 + 0.156561i \(0.0500407\pi\)
−0.358249 + 0.933626i \(0.616626\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 3.10634 + 5.38033i 0.169717 + 0.293959i
\(336\) 0 0
\(337\) 0.415255 0.719243i 0.0226204 0.0391796i −0.854494 0.519462i \(-0.826132\pi\)
0.877114 + 0.480282i \(0.159466\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 28.8031 1.55977
\(342\) 0 0
\(343\) −38.0378 −2.05385
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8.53131 14.7767i 0.457985 0.793253i −0.540870 0.841106i \(-0.681905\pi\)
0.998854 + 0.0478537i \(0.0152381\pi\)
\(348\) 0 0
\(349\) 10.9443 + 18.9561i 0.585836 + 1.01470i 0.994771 + 0.102134i \(0.0325671\pi\)
−0.408935 + 0.912564i \(0.634100\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9.53407 16.5135i −0.507447 0.878924i −0.999963 0.00862082i \(-0.997256\pi\)
0.492516 0.870304i \(-0.336077\pi\)
\(354\) 0 0
\(355\) 2.84964 4.93572i 0.151243 0.261961i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 13.1482 0.693938 0.346969 0.937877i \(-0.387211\pi\)
0.346969 + 0.937877i \(0.387211\pi\)
\(360\) 0 0
\(361\) 14.7088 0.774147
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.18191 + 2.04712i −0.0618638 + 0.107151i
\(366\) 0 0
\(367\) −7.79061 13.4937i −0.406666 0.704367i 0.587848 0.808972i \(-0.299975\pi\)
−0.994514 + 0.104605i \(0.966642\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −12.4740 21.6056i −0.647618 1.12171i
\(372\) 0 0
\(373\) 9.92199 17.1854i 0.513741 0.889826i −0.486132 0.873885i \(-0.661593\pi\)
0.999873 0.0159402i \(-0.00507413\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.98350 0.308166
\(378\) 0 0
\(379\) −15.0470 −0.772914 −0.386457 0.922307i \(-0.626301\pi\)
−0.386457 + 0.922307i \(0.626301\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 16.4288 28.4556i 0.839474 1.45401i −0.0508616 0.998706i \(-0.516197\pi\)
0.890335 0.455305i \(-0.150470\pi\)
\(384\) 0 0
\(385\) −6.55089 11.3465i −0.333864 0.578270i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.87559 + 3.24862i 0.0950962 + 0.164711i 0.909649 0.415378i \(-0.136351\pi\)
−0.814553 + 0.580090i \(0.803017\pi\)
\(390\) 0 0
\(391\) 3.08098 5.33641i 0.155812 0.269874i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.56304 −0.179276
\(396\) 0 0
\(397\) −23.5495 −1.18192 −0.590958 0.806702i \(-0.701250\pi\)
−0.590958 + 0.806702i \(0.701250\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −7.28105 + 12.6111i −0.363598 + 0.629771i −0.988550 0.150893i \(-0.951785\pi\)
0.624952 + 0.780663i \(0.285119\pi\)
\(402\) 0 0
\(403\) 4.31231 + 7.46914i 0.214811 + 0.372064i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 10.6381 + 18.4257i 0.527310 + 0.913328i
\(408\) 0 0
\(409\) 3.23655 5.60586i 0.160037 0.277192i −0.774845 0.632152i \(-0.782172\pi\)
0.934882 + 0.354959i \(0.115505\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 24.1738 1.18951
\(414\) 0 0
\(415\) 5.66294 0.277983
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13.4378 23.2750i 0.656481 1.13706i −0.325040 0.945700i \(-0.605378\pi\)
0.981520 0.191357i \(-0.0612890\pi\)
\(420\) 0 0
\(421\) −3.85521 6.67742i −0.187892 0.325438i 0.756656 0.653814i \(-0.226832\pi\)
−0.944547 + 0.328376i \(0.893499\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.63943 2.83957i −0.0795239 0.137740i
\(426\) 0 0
\(427\) 4.33361 7.50603i 0.209718 0.363242i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −3.45993 −0.166659 −0.0833294 0.996522i \(-0.526555\pi\)
−0.0833294 + 0.996522i \(0.526555\pi\)
\(432\) 0 0
\(433\) −12.7863 −0.614471 −0.307236 0.951633i \(-0.599404\pi\)
−0.307236 + 0.951633i \(0.599404\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −25.7092 + 44.5296i −1.22984 + 2.13014i
\(438\) 0 0
\(439\) −2.76458 4.78840i −0.131946 0.228538i 0.792480 0.609897i \(-0.208789\pi\)
−0.924427 + 0.381359i \(0.875456\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13.2718 + 22.9874i 0.630563 + 1.09217i 0.987437 + 0.158014i \(0.0505091\pi\)
−0.356874 + 0.934152i \(0.616158\pi\)
\(444\) 0 0
\(445\) −1.95924 + 3.39350i −0.0928769 + 0.160867i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 29.9625 1.41402 0.707010 0.707204i \(-0.250044\pi\)
0.707010 + 0.707204i \(0.250044\pi\)
\(450\) 0 0
\(451\) −10.5028 −0.494560
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.96156 3.39752i 0.0919593 0.159278i
\(456\) 0 0
\(457\) −12.3904 21.4608i −0.579597 1.00389i −0.995525 0.0944945i \(-0.969877\pi\)
0.415928 0.909398i \(-0.363457\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.30632 + 9.19081i 0.247140 + 0.428059i 0.962731 0.270461i \(-0.0871760\pi\)
−0.715591 + 0.698519i \(0.753843\pi\)
\(462\) 0 0
\(463\) 5.31762 9.21040i 0.247131 0.428043i −0.715598 0.698513i \(-0.753846\pi\)
0.962729 + 0.270469i \(0.0871789\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 27.3831 1.26714 0.633569 0.773686i \(-0.281589\pi\)
0.633569 + 0.773686i \(0.281589\pi\)
\(468\) 0 0
\(469\) 54.4590 2.51468
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 19.3133 33.4517i 0.888028 1.53811i
\(474\) 0 0
\(475\) 13.6802 + 23.6947i 0.627689 + 1.08719i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −20.3026 35.1651i −0.927649 1.60674i −0.787245 0.616641i \(-0.788493\pi\)
−0.140404 0.990094i \(-0.544840\pi\)
\(480\) 0 0
\(481\) −3.18541 + 5.51728i −0.145242 + 0.251566i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.38212 0.380613
\(486\) 0 0
\(487\) −4.99658 −0.226417 −0.113208 0.993571i \(-0.536113\pi\)
−0.113208 + 0.993571i \(0.536113\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −19.2049 + 33.2639i −0.866705 + 1.50118i −0.00136059 + 0.999999i \(0.500433\pi\)
−0.865344 + 0.501178i \(0.832900\pi\)
\(492\) 0 0
\(493\) 1.33728 + 2.31624i 0.0602282 + 0.104318i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −24.9794 43.2655i −1.12048 1.94072i
\(498\) 0 0
\(499\) 11.3616 19.6788i 0.508614 0.880945i −0.491337 0.870970i \(-0.663491\pi\)
0.999950 0.00997497i \(-0.00317518\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 40.2323 1.79387 0.896935 0.442161i \(-0.145788\pi\)
0.896935 + 0.442161i \(0.145788\pi\)
\(504\) 0 0
\(505\) −4.75313 −0.211512
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.30968 + 7.46459i −0.191023 + 0.330862i −0.945590 0.325362i \(-0.894514\pi\)
0.754566 + 0.656224i \(0.227847\pi\)
\(510\) 0 0
\(511\) 10.3604 + 17.9447i 0.458315 + 0.793825i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.884666 + 1.53229i 0.0389830 + 0.0675206i
\(516\) 0 0
\(517\) −0.967251 + 1.67533i −0.0425396 + 0.0736808i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 20.5770 0.901496 0.450748 0.892651i \(-0.351157\pi\)
0.450748 + 0.892651i \(0.351157\pi\)
\(522\) 0 0
\(523\) −15.6990 −0.686470 −0.343235 0.939250i \(-0.611523\pi\)
−0.343235 + 0.939250i \(0.611523\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.92756 + 3.33863i −0.0839659 + 0.145433i
\(528\) 0 0
\(529\) −27.7159 48.0054i −1.20504 2.08719i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.57245 2.72357i −0.0681106 0.117971i
\(534\) 0 0
\(535\) −1.90927 + 3.30696i −0.0825450 + 0.142972i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −78.4584 −3.37944
\(540\) 0 0
\(541\) 4.79886 0.206319 0.103160 0.994665i \(-0.467105\pi\)
0.103160 + 0.994665i \(0.467105\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −0.801260 + 1.38782i −0.0343222 + 0.0594478i
\(546\) 0 0
\(547\) −8.26596 14.3171i −0.353427 0.612153i 0.633421 0.773808i \(-0.281650\pi\)
−0.986847 + 0.161654i \(0.948317\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −11.1589 19.3278i −0.475386 0.823393i
\(552\) 0 0
\(553\) −15.6164 + 27.0484i −0.664078 + 1.15022i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.2466 −0.603649 −0.301825 0.953363i \(-0.597596\pi\)
−0.301825 + 0.953363i \(0.597596\pi\)
\(558\) 0 0
\(559\) 11.5661 0.489196
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −13.4981 + 23.3794i −0.568876 + 0.985322i 0.427801 + 0.903873i \(0.359288\pi\)
−0.996677 + 0.0814497i \(0.974045\pi\)
\(564\) 0 0
\(565\) −1.82757 3.16545i −0.0768865 0.133171i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.82124 8.35063i −0.202117 0.350076i 0.747094 0.664719i \(-0.231449\pi\)
−0.949210 + 0.314643i \(0.898115\pi\)
\(570\) 0 0
\(571\) −15.0536 + 26.0736i −0.629973 + 1.09115i 0.357584 + 0.933881i \(0.383601\pi\)
−0.987557 + 0.157264i \(0.949733\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −41.7346 −1.74045
\(576\) 0 0
\(577\) 14.9642 0.622968 0.311484 0.950251i \(-0.399174\pi\)
0.311484 + 0.950251i \(0.399174\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 24.8201 42.9896i 1.02971 1.78351i
\(582\) 0 0
\(583\) −13.7961 23.8955i −0.571375 0.989650i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.0511 + 20.8731i 0.497401 + 0.861523i 0.999996 0.00299890i \(-0.000954581\pi\)
−0.502595 + 0.864522i \(0.667621\pi\)
\(588\) 0 0
\(589\) 16.0845 27.8591i 0.662749 1.14792i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −5.62882 −0.231148 −0.115574 0.993299i \(-0.536871\pi\)
−0.115574 + 0.993299i \(0.536871\pi\)
\(594\) 0 0
\(595\) 1.75360 0.0718904
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −9.75087 + 16.8890i −0.398410 + 0.690066i −0.993530 0.113571i \(-0.963771\pi\)
0.595120 + 0.803637i \(0.297104\pi\)
\(600\) 0 0
\(601\) −1.36834 2.37003i −0.0558158 0.0966757i 0.836767 0.547558i \(-0.184443\pi\)
−0.892583 + 0.450883i \(0.851109\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.29604 7.44096i −0.174659 0.302518i
\(606\) 0 0
\(607\) 23.6876 41.0282i 0.961452 1.66528i 0.242592 0.970128i \(-0.422002\pi\)
0.718860 0.695155i \(-0.244664\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.579256 −0.0234342
\(612\) 0 0
\(613\) −23.1963 −0.936891 −0.468446 0.883492i \(-0.655186\pi\)
−0.468446 + 0.883492i \(0.655186\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 19.8253 34.3384i 0.798137 1.38241i −0.122691 0.992445i \(-0.539152\pi\)
0.920828 0.389969i \(-0.127514\pi\)
\(618\) 0 0
\(619\) −0.813544 1.40910i −0.0326991 0.0566365i 0.849213 0.528051i \(-0.177077\pi\)
−0.881912 + 0.471414i \(0.843744\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 17.1743 + 29.7467i 0.688074 + 1.19178i
\(624\) 0 0
\(625\) −10.3849 + 17.9873i −0.415398 + 0.719490i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.84769 −0.113545
\(630\) 0 0
\(631\) −30.9685 −1.23283 −0.616417 0.787420i \(-0.711417\pi\)
−0.616417 + 0.787420i \(0.711417\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.76063 8.24566i 0.188920 0.327219i
\(636\) 0 0
\(637\) −11.7466 20.3456i −0.465415 0.806123i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 16.1499 + 27.9725i 0.637883 + 1.10485i 0.985897 + 0.167356i \(0.0535230\pi\)
−0.348014 + 0.937489i \(0.613144\pi\)
\(642\) 0 0
\(643\) 3.28376 5.68763i 0.129499 0.224298i −0.793984 0.607939i \(-0.791997\pi\)
0.923482 + 0.383641i \(0.125330\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 40.0823 1.57580 0.787899 0.615805i \(-0.211169\pi\)
0.787899 + 0.615805i \(0.211169\pi\)
\(648\) 0 0
\(649\) 26.7358 1.04947
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.62772 + 2.81929i −0.0636976 + 0.110327i −0.896116 0.443821i \(-0.853623\pi\)
0.832418 + 0.554148i \(0.186956\pi\)
\(654\) 0 0
\(655\) 1.88345 + 3.26223i 0.0735924 + 0.127466i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −7.58278 13.1338i −0.295383 0.511619i 0.679691 0.733499i \(-0.262114\pi\)
−0.975074 + 0.221880i \(0.928781\pi\)
\(660\) 0 0
\(661\) 10.1447 17.5711i 0.394582 0.683435i −0.598466 0.801148i \(-0.704223\pi\)
0.993048 + 0.117713i \(0.0375562\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −14.6328 −0.567437
\(666\) 0 0
\(667\) 34.0429 1.31815
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.79290 8.30155i 0.185028 0.320478i
\(672\) 0 0
\(673\) 11.6256 + 20.1361i 0.448134 + 0.776191i 0.998265 0.0588875i \(-0.0187553\pi\)
−0.550130 + 0.835079i \(0.685422\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15.6380 27.0859i −0.601018 1.04099i −0.992667 0.120879i \(-0.961429\pi\)
0.391649 0.920115i \(-0.371905\pi\)
\(678\) 0 0
\(679\) 36.7380 63.6320i 1.40987 2.44197i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −24.1812 −0.925269 −0.462635 0.886549i \(-0.653096\pi\)
−0.462635 + 0.886549i \(0.653096\pi\)
\(684\) 0 0
\(685\) 6.12400 0.233986
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4.13101 7.15512i 0.157379 0.272588i
\(690\) 0 0
\(691\) 9.03942 + 15.6567i 0.343876 + 0.595610i 0.985149 0.171702i \(-0.0549268\pi\)
−0.641273 + 0.767313i \(0.721593\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.66578 + 2.88521i 0.0631866 + 0.109442i
\(696\) 0 0
\(697\) 0.702872 1.21741i 0.0266232 0.0461127i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −17.2240 −0.650541 −0.325271 0.945621i \(-0.605455\pi\)
−0.325271 + 0.945621i \(0.605455\pi\)
\(702\) 0 0
\(703\) 23.7625 0.896219
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −20.8325 + 36.0830i −0.783487 + 1.35704i
\(708\) 0 0
\(709\) −13.3258 23.0809i −0.500459 0.866821i −1.00000 0.000530358i \(-0.999831\pi\)
0.499541 0.866290i \(-0.333502\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 24.5347 + 42.4954i 0.918833 + 1.59147i
\(714\) 0 0
\(715\) 2.16945 3.75760i 0.0811330 0.140526i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.4273 0.388875 0.194437 0.980915i \(-0.437712\pi\)
0.194437 + 0.980915i \(0.437712\pi\)
\(720\) 0 0
\(721\) 15.5096 0.577608
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 9.05733 15.6878i 0.336381 0.582629i
\(726\) 0 0
\(727\) 10.5682 + 18.3047i 0.391954 + 0.678884i 0.992707 0.120550i \(-0.0384659\pi\)
−0.600753 + 0.799434i \(0.705133\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.58498 + 4.47731i 0.0956088 + 0.165599i
\(732\) 0 0
\(733\) 15.6473 27.1020i 0.577948 1.00103i −0.417767 0.908554i \(-0.637187\pi\)
0.995714 0.0924806i \(-0.0294796\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 60.2308 2.21863
\(738\) 0 0
\(739\) 31.0455 1.14203 0.571014 0.820940i \(-0.306550\pi\)
0.571014 + 0.820940i \(0.306550\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 8.93131 15.4695i 0.327658 0.567520i −0.654389 0.756158i \(-0.727074\pi\)
0.982047 + 0.188638i \(0.0604073\pi\)
\(744\) 0 0
\(745\) 2.93765 + 5.08817i 0.107627 + 0.186416i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 16.7363 + 28.9881i 0.611530 + 1.05920i
\(750\) 0 0
\(751\) 4.70046 8.14144i 0.171522 0.297085i −0.767430 0.641133i \(-0.778465\pi\)
0.938952 + 0.344047i \(0.111798\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −7.81189 −0.284304
\(756\) 0 0
\(757\) −49.7959 −1.80986 −0.904931 0.425558i \(-0.860078\pi\)
−0.904931 + 0.425558i \(0.860078\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −5.42633 + 9.39868i −0.196704 + 0.340702i −0.947458 0.319880i \(-0.896357\pi\)
0.750754 + 0.660582i \(0.229691\pi\)
\(762\) 0 0
\(763\) 7.02368 + 12.1654i 0.254274 + 0.440416i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.00281 + 6.93307i 0.144533 + 0.250338i
\(768\) 0 0
\(769\) 2.93798 5.08873i 0.105946 0.183504i −0.808178 0.588938i \(-0.799546\pi\)
0.914124 + 0.405434i \(0.132880\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 26.2781 0.945159 0.472579 0.881288i \(-0.343323\pi\)
0.472579 + 0.881288i \(0.343323\pi\)
\(774\) 0 0
\(775\) 26.1105 0.937917
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.86510 + 10.1587i −0.210139 + 0.363971i
\(780\) 0 0
\(781\) −27.6268 47.8510i −0.988564 1.71224i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.10761 7.11459i −0.146607 0.253930i
\(786\) 0 0
\(787\) −16.3824 + 28.3752i −0.583970 + 1.01146i 0.411034 + 0.911620i \(0.365168\pi\)
−0.995003 + 0.0998447i \(0.968165\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −32.0402 −1.13922
\(792\) 0 0
\(793\) 2.87032 0.101928
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 26.8586 46.5205i 0.951382 1.64784i 0.208942 0.977928i \(-0.432998\pi\)
0.742440 0.669913i \(-0.233669\pi\)
\(798\) 0 0
\(799\) −0.129461 0.224233i −0.00458000 0.00793279i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 11.4584 + 19.8465i 0.404358 + 0.700368i
\(804\) 0 0