Properties

Label 1512.2.s.m.865.2
Level $1512$
Weight $2$
Character 1512.865
Analytic conductor $12.073$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.9391935744.3
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 12 x^{5} - 76 x^{4} + 84 x^{3} + 245 x^{2} - 1372 x + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.2
Root \(-2.47635 + 0.931486i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.m.1297.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 - 2.36603i) q^{5} +(0.431486 - 2.61033i) q^{7} +O(q^{10})\) \(q+(-1.36603 - 2.36603i) q^{5} +(0.431486 - 2.61033i) q^{7} +(-2.54487 + 4.40784i) q^{11} -3.48861 q^{13} +(-2.09808 + 3.63397i) q^{17} +(-3.16354 - 5.47941i) q^{19} +(3.04182 + 5.26858i) q^{23} +(-1.23205 + 2.13397i) q^{25} +6.45800 q^{29} +(-4.77692 + 8.27387i) q^{31} +(-6.76553 + 2.54487i) q^{35} +(0.118669 + 0.205541i) q^{37} -5.98332 q^{41} +12.6436 q^{43} +(4.31873 + 7.48027i) q^{47} +(-6.62764 - 2.25264i) q^{49} +(-2.30977 + 4.00063i) q^{53} +13.9054 q^{55} +(2.18718 - 3.78831i) q^{59} +(0.443740 + 0.768580i) q^{61} +(4.76553 + 8.25414i) q^{65} +(4.39559 - 7.61338i) q^{67} -2.55384 q^{71} +(-6.52122 + 11.2951i) q^{73} +(10.4078 + 8.54487i) q^{77} +(2.61338 + 4.52651i) q^{79} -5.73816 q^{83} +11.4641 q^{85} +(-1.50305 - 2.60336i) q^{89} +(-1.50529 + 9.10642i) q^{91} +(-8.64294 + 14.9700i) q^{95} -12.6436 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{5} - 2q^{7} + O(q^{10}) \) \( 8q - 4q^{5} - 2q^{7} - 2q^{11} - 8q^{13} + 4q^{17} - 6q^{19} + 2q^{23} + 4q^{25} + 16q^{29} - 6q^{31} - 2q^{35} - 16q^{41} - 20q^{47} - 6q^{49} - 10q^{53} + 16q^{55} + 22q^{59} + 2q^{61} - 14q^{65} + 2q^{67} + 44q^{71} - 10q^{73} + 54q^{77} + 8q^{79} - 40q^{83} + 64q^{85} - 16q^{89} - 24q^{91} - 30q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) −1.36603 2.36603i −0.610905 1.05812i −0.991088 0.133207i \(-0.957472\pi\)
0.380183 0.924911i \(-0.375861\pi\)
\(6\) 0 0
\(7\) 0.431486 2.61033i 0.163087 0.986612i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.54487 + 4.40784i −0.767307 + 1.32901i 0.171712 + 0.985147i \(0.445070\pi\)
−0.939018 + 0.343867i \(0.888263\pi\)
\(12\) 0 0
\(13\) −3.48861 −0.967566 −0.483783 0.875188i \(-0.660738\pi\)
−0.483783 + 0.875188i \(0.660738\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.09808 + 3.63397i −0.508858 + 0.881368i 0.491089 + 0.871109i \(0.336599\pi\)
−0.999947 + 0.0102590i \(0.996734\pi\)
\(18\) 0 0
\(19\) −3.16354 5.47941i −0.725765 1.25706i −0.958658 0.284560i \(-0.908153\pi\)
0.232893 0.972502i \(-0.425181\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.04182 + 5.26858i 0.634262 + 1.09857i 0.986671 + 0.162728i \(0.0520295\pi\)
−0.352408 + 0.935846i \(0.614637\pi\)
\(24\) 0 0
\(25\) −1.23205 + 2.13397i −0.246410 + 0.426795i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.45800 1.19922 0.599610 0.800292i \(-0.295322\pi\)
0.599610 + 0.800292i \(0.295322\pi\)
\(30\) 0 0
\(31\) −4.77692 + 8.27387i −0.857960 + 1.48603i 0.0159115 + 0.999873i \(0.494935\pi\)
−0.873872 + 0.486157i \(0.838398\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −6.76553 + 2.54487i −1.14358 + 0.430161i
\(36\) 0 0
\(37\) 0.118669 + 0.205541i 0.0195091 + 0.0337907i 0.875615 0.483010i \(-0.160456\pi\)
−0.856106 + 0.516800i \(0.827123\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.98332 −0.934438 −0.467219 0.884142i \(-0.654744\pi\)
−0.467219 + 0.884142i \(0.654744\pi\)
\(42\) 0 0
\(43\) 12.6436 1.92813 0.964064 0.265672i \(-0.0855937\pi\)
0.964064 + 0.265672i \(0.0855937\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.31873 + 7.48027i 0.629952 + 1.09111i 0.987561 + 0.157238i \(0.0502589\pi\)
−0.357609 + 0.933872i \(0.616408\pi\)
\(48\) 0 0
\(49\) −6.62764 2.25264i −0.946806 0.321806i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.30977 + 4.00063i −0.317271 + 0.549529i −0.979918 0.199403i \(-0.936100\pi\)
0.662647 + 0.748932i \(0.269433\pi\)
\(54\) 0 0
\(55\) 13.9054 1.87501
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.18718 3.78831i 0.284747 0.493196i −0.687801 0.725899i \(-0.741424\pi\)
0.972548 + 0.232703i \(0.0747571\pi\)
\(60\) 0 0
\(61\) 0.443740 + 0.768580i 0.0568150 + 0.0984065i 0.893034 0.449989i \(-0.148572\pi\)
−0.836219 + 0.548396i \(0.815239\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4.76553 + 8.25414i 0.591091 + 1.02380i
\(66\) 0 0
\(67\) 4.39559 7.61338i 0.537007 0.930123i −0.462057 0.886850i \(-0.652888\pi\)
0.999063 0.0432723i \(-0.0137783\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.55384 −0.303085 −0.151542 0.988451i \(-0.548424\pi\)
−0.151542 + 0.988451i \(0.548424\pi\)
\(72\) 0 0
\(73\) −6.52122 + 11.2951i −0.763251 + 1.32199i 0.177915 + 0.984046i \(0.443065\pi\)
−0.941166 + 0.337944i \(0.890268\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 10.4078 + 8.54487i 1.18608 + 0.973778i
\(78\) 0 0
\(79\) 2.61338 + 4.52651i 0.294028 + 0.509272i 0.974758 0.223262i \(-0.0716706\pi\)
−0.680730 + 0.732534i \(0.738337\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.73816 −0.629844 −0.314922 0.949117i \(-0.601978\pi\)
−0.314922 + 0.949117i \(0.601978\pi\)
\(84\) 0 0
\(85\) 11.4641 1.24346
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.50305 2.60336i −0.159323 0.275956i 0.775302 0.631591i \(-0.217598\pi\)
−0.934625 + 0.355635i \(0.884265\pi\)
\(90\) 0 0
\(91\) −1.50529 + 9.10642i −0.157797 + 0.954612i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8.64294 + 14.9700i −0.886747 + 1.53589i
\(96\) 0 0
\(97\) −12.6436 −1.28376 −0.641880 0.766805i \(-0.721845\pi\)
−0.641880 + 0.766805i \(0.721845\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −7.63460 + 13.2235i −0.759672 + 1.31579i 0.183347 + 0.983048i \(0.441307\pi\)
−0.943018 + 0.332741i \(0.892026\pi\)
\(102\) 0 0
\(103\) 2.20841 + 3.82507i 0.217601 + 0.376895i 0.954074 0.299571i \(-0.0968436\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.57834 14.8581i −0.829300 1.43639i −0.898588 0.438793i \(-0.855406\pi\)
0.0692884 0.997597i \(-0.477927\pi\)
\(108\) 0 0
\(109\) 1.55626 2.69552i 0.149063 0.258184i −0.781819 0.623506i \(-0.785708\pi\)
0.930881 + 0.365322i \(0.119041\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −15.7439 −1.48106 −0.740530 0.672023i \(-0.765426\pi\)
−0.740530 + 0.672023i \(0.765426\pi\)
\(114\) 0 0
\(115\) 8.31040 14.3940i 0.774948 1.34225i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 8.58058 + 7.04468i 0.786580 + 0.645785i
\(120\) 0 0
\(121\) −7.45271 12.9085i −0.677519 1.17350i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −6.92820 −0.619677
\(126\) 0 0
\(127\) −12.0897 −1.07279 −0.536395 0.843967i \(-0.680214\pi\)
−0.536395 + 0.843967i \(0.680214\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −0.446792 0.773867i −0.0390364 0.0676130i 0.845847 0.533425i \(-0.179095\pi\)
−0.884884 + 0.465812i \(0.845762\pi\)
\(132\) 0 0
\(133\) −15.6681 + 5.89358i −1.35859 + 0.511039i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.77997 + 11.7433i −0.579252 + 1.00329i 0.416313 + 0.909221i \(0.363322\pi\)
−0.995565 + 0.0940728i \(0.970011\pi\)
\(138\) 0 0
\(139\) 5.11424 0.433784 0.216892 0.976196i \(-0.430408\pi\)
0.216892 + 0.976196i \(0.430408\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.87805 15.3772i 0.742420 1.28591i
\(144\) 0 0
\(145\) −8.82179 15.2798i −0.732610 1.26892i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.36603 5.83013i −0.275756 0.477623i 0.694570 0.719425i \(-0.255595\pi\)
−0.970325 + 0.241803i \(0.922261\pi\)
\(150\) 0 0
\(151\) −1.31282 + 2.27387i −0.106836 + 0.185045i −0.914487 0.404616i \(-0.867405\pi\)
0.807651 + 0.589661i \(0.200739\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 26.1016 2.09653
\(156\) 0 0
\(157\) −3.10642 + 5.38047i −0.247919 + 0.429408i −0.962948 0.269686i \(-0.913080\pi\)
0.715029 + 0.699095i \(0.246413\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 15.0652 5.66682i 1.18731 0.446608i
\(162\) 0 0
\(163\) 3.63703 + 6.29952i 0.284874 + 0.493416i 0.972579 0.232574i \(-0.0747149\pi\)
−0.687705 + 0.725991i \(0.741382\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.01057 −0.232965 −0.116483 0.993193i \(-0.537162\pi\)
−0.116483 + 0.993193i \(0.537162\pi\)
\(168\) 0 0
\(169\) −0.829615 −0.0638165
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −6.08911 10.5466i −0.462946 0.801846i 0.536160 0.844116i \(-0.319874\pi\)
−0.999106 + 0.0422700i \(0.986541\pi\)
\(174\) 0 0
\(175\) 5.03876 + 4.13684i 0.380895 + 0.312716i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.22900 + 15.9851i −0.689808 + 1.19478i 0.282092 + 0.959387i \(0.408972\pi\)
−0.971900 + 0.235395i \(0.924362\pi\)
\(180\) 0 0
\(181\) −7.30429 −0.542924 −0.271462 0.962449i \(-0.587507\pi\)
−0.271462 + 0.962449i \(0.587507\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.324210 0.561547i 0.0238364 0.0412858i
\(186\) 0 0
\(187\) −10.6787 18.4960i −0.780901 1.35256i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.91986 + 17.1817i 0.717776 + 1.24322i 0.961879 + 0.273475i \(0.0881732\pi\)
−0.244103 + 0.969749i \(0.578493\pi\)
\(192\) 0 0
\(193\) 1.15825 2.00615i 0.0833727 0.144406i −0.821324 0.570462i \(-0.806764\pi\)
0.904697 + 0.426056i \(0.140097\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.29684 0.0923959 0.0461980 0.998932i \(-0.485289\pi\)
0.0461980 + 0.998932i \(0.485289\pi\)
\(198\) 0 0
\(199\) 12.7463 22.0773i 0.903562 1.56501i 0.0807256 0.996736i \(-0.474276\pi\)
0.822836 0.568279i \(-0.192390\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.78654 16.8575i 0.195577 1.18316i
\(204\) 0 0
\(205\) 8.17337 + 14.1567i 0.570853 + 0.988746i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 32.2031 2.22754
\(210\) 0 0
\(211\) 7.11825 0.490041 0.245020 0.969518i \(-0.421205\pi\)
0.245020 + 0.969518i \(0.421205\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −17.2714 29.9150i −1.17790 2.04019i
\(216\) 0 0
\(217\) 19.5363 + 16.0394i 1.32621 + 1.08882i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 7.31937 12.6775i 0.492354 0.852782i
\(222\) 0 0
\(223\) −0.261844 −0.0175344 −0.00876719 0.999962i \(-0.502791\pi\)
−0.00876719 + 0.999962i \(0.502791\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.04792 + 3.54710i −0.135925 + 0.235429i −0.925951 0.377645i \(-0.876734\pi\)
0.790025 + 0.613074i \(0.210067\pi\)
\(228\) 0 0
\(229\) −1.26553 2.19196i −0.0836284 0.144849i 0.821178 0.570673i \(-0.193318\pi\)
−0.904806 + 0.425824i \(0.859984\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −13.0843 22.6626i −0.857179 1.48468i −0.874609 0.484829i \(-0.838882\pi\)
0.0174307 0.999848i \(-0.494451\pi\)
\(234\) 0 0
\(235\) 11.7990 20.4365i 0.769682 1.33313i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.40898 0.414563 0.207281 0.978281i \(-0.433538\pi\)
0.207281 + 0.978281i \(0.433538\pi\)
\(240\) 0 0
\(241\) −9.44660 + 16.3620i −0.608509 + 1.05397i 0.382977 + 0.923758i \(0.374899\pi\)
−0.991486 + 0.130211i \(0.958434\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.72371 + 18.7583i 0.237899 + 1.19843i
\(246\) 0 0
\(247\) 11.0363 + 19.1155i 0.702226 + 1.21629i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −11.5477 −0.728886 −0.364443 0.931226i \(-0.618741\pi\)
−0.364443 + 0.931226i \(0.618741\pi\)
\(252\) 0 0
\(253\) −30.9641 −1.94670
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.86908 + 4.96939i 0.178968 + 0.309982i 0.941527 0.336936i \(-0.109391\pi\)
−0.762559 + 0.646918i \(0.776057\pi\)
\(258\) 0 0
\(259\) 0.587733 0.221077i 0.0365199 0.0137371i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.96168 12.0580i 0.429276 0.743527i −0.567533 0.823350i \(-0.692102\pi\)
0.996809 + 0.0798233i \(0.0254356\pi\)
\(264\) 0 0
\(265\) 12.6208 0.775289
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.98332 3.43521i 0.120925 0.209449i −0.799208 0.601055i \(-0.794747\pi\)
0.920133 + 0.391607i \(0.128081\pi\)
\(270\) 0 0
\(271\) 7.25942 + 12.5737i 0.440978 + 0.763797i 0.997762 0.0668603i \(-0.0212982\pi\)
−0.556784 + 0.830657i \(0.687965\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −6.27081 10.8614i −0.378144 0.654965i
\(276\) 0 0
\(277\) −5.13460 + 8.89340i −0.308509 + 0.534352i −0.978036 0.208435i \(-0.933163\pi\)
0.669528 + 0.742787i \(0.266496\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 17.1387 1.02241 0.511206 0.859458i \(-0.329199\pi\)
0.511206 + 0.859458i \(0.329199\pi\)
\(282\) 0 0
\(283\) −1.23205 + 2.13397i −0.0732378 + 0.126852i −0.900319 0.435231i \(-0.856667\pi\)
0.827081 + 0.562083i \(0.190000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.58172 + 15.6184i −0.152394 + 0.921927i
\(288\) 0 0
\(289\) −0.303848 0.526279i −0.0178734 0.0309576i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −18.2798 −1.06792 −0.533958 0.845511i \(-0.679296\pi\)
−0.533958 + 0.845511i \(0.679296\pi\)
\(294\) 0 0
\(295\) −11.9510 −0.695813
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −10.6117 18.3800i −0.613691 1.06294i
\(300\) 0 0
\(301\) 5.45553 33.0039i 0.314452 1.90231i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.21232 2.09980i 0.0694172 0.120234i
\(306\) 0 0
\(307\) 7.40451 0.422598 0.211299 0.977421i \(-0.432231\pi\)
0.211299 + 0.977421i \(0.432231\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 10.1705 17.6158i 0.576716 0.998902i −0.419136 0.907923i \(-0.637667\pi\)
0.995853 0.0909788i \(-0.0289995\pi\)
\(312\) 0 0
\(313\) 13.5803 + 23.5219i 0.767607 + 1.32953i 0.938857 + 0.344306i \(0.111886\pi\)
−0.171251 + 0.985227i \(0.554781\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.3360 19.6346i −0.636696 1.10279i −0.986153 0.165837i \(-0.946967\pi\)
0.349457 0.936952i \(-0.386366\pi\)
\(318\) 0 0
\(319\) −16.4348 + 28.4658i −0.920169 + 1.59378i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 26.5494 1.47725
\(324\) 0 0
\(325\) 4.29814 7.44460i 0.238418 0.412952i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 21.3894 8.04569i 1.17924 0.443573i
\(330\) 0 0
\(331\) −4.87280 8.43994i −0.267834 0.463901i 0.700469 0.713683i \(-0.252974\pi\)
−0.968302 + 0.249782i \(0.919641\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −24.0179 −1.31224
\(336\) 0 0
\(337\) 11.1492 0.607338 0.303669 0.952778i \(-0.401788\pi\)
0.303669 + 0.952778i \(0.401788\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −24.3133 42.1118i −1.31664 2.28048i
\(342\) 0 0
\(343\) −8.73988 + 16.3283i −0.471909 + 0.881647i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8.53590 + 14.7846i −0.458231 + 0.793679i −0.998868 0.0475768i \(-0.984850\pi\)
0.540637 + 0.841256i \(0.318183\pi\)
\(348\) 0 0
\(349\) 12.7317 0.681511 0.340755 0.940152i \(-0.389317\pi\)
0.340755 + 0.940152i \(0.389317\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 17.7272 30.7044i 0.943524 1.63423i 0.184844 0.982768i \(-0.440822\pi\)
0.758680 0.651464i \(-0.225845\pi\)
\(354\) 0 0
\(355\) 3.48861 + 6.04245i 0.185156 + 0.320700i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.57834 + 14.8581i 0.452748 + 0.784182i 0.998556 0.0537283i \(-0.0171105\pi\)
−0.545808 + 0.837910i \(0.683777\pi\)
\(360\) 0 0
\(361\) −10.5159 + 18.2141i −0.553470 + 0.958639i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 35.6326 1.86510
\(366\) 0 0
\(367\) 3.96738 6.87171i 0.207096 0.358700i −0.743703 0.668511i \(-0.766932\pi\)
0.950798 + 0.309810i \(0.100265\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 9.44633 + 7.75547i 0.490429 + 0.402644i
\(372\) 0 0
\(373\) −14.4188 24.9741i −0.746578 1.29311i −0.949454 0.313906i \(-0.898362\pi\)
0.202876 0.979204i \(-0.434971\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −22.5294 −1.16032
\(378\) 0 0
\(379\) −21.2659 −1.09235 −0.546177 0.837670i \(-0.683917\pi\)
−0.546177 + 0.837670i \(0.683917\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −9.50655 16.4658i −0.485762 0.841364i 0.514104 0.857728i \(-0.328124\pi\)
−0.999866 + 0.0163634i \(0.994791\pi\)
\(384\) 0 0
\(385\) 6.00000 36.2977i 0.305788 1.84990i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −13.8942 + 24.0655i −0.704465 + 1.22017i 0.262420 + 0.964954i \(0.415479\pi\)
−0.966884 + 0.255215i \(0.917854\pi\)
\(390\) 0 0
\(391\) −25.5278 −1.29100
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.13989 12.3667i 0.359247 0.622234i
\(396\) 0 0
\(397\) 9.64600 + 16.7074i 0.484119 + 0.838518i 0.999834 0.0182421i \(-0.00580695\pi\)
−0.515715 + 0.856760i \(0.672474\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.6346 23.6158i −0.680880 1.17932i −0.974713 0.223461i \(-0.928264\pi\)
0.293833 0.955857i \(-0.405069\pi\)
\(402\) 0 0
\(403\) 16.6648 28.8643i 0.830133 1.43783i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.20799 −0.0598777
\(408\) 0 0
\(409\) 6.72266 11.6440i 0.332414 0.575758i −0.650570 0.759446i \(-0.725470\pi\)
0.982985 + 0.183688i \(0.0588035\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.94500 7.34387i −0.440155 0.361368i
\(414\) 0 0
\(415\) 7.83847 + 13.5766i 0.384775 + 0.666450i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.38620 0.0677203 0.0338601 0.999427i \(-0.489220\pi\)
0.0338601 + 0.999427i \(0.489220\pi\)
\(420\) 0 0
\(421\) 20.0197 0.975699 0.487849 0.872928i \(-0.337782\pi\)
0.487849 + 0.872928i \(0.337782\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5.16987 8.95448i −0.250776 0.434356i
\(426\) 0 0
\(427\) 2.19771 0.826675i 0.106355 0.0400056i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.85526 6.67751i 0.185702 0.321644i −0.758111 0.652125i \(-0.773878\pi\)
0.943813 + 0.330481i \(0.107211\pi\)
\(432\) 0 0
\(433\) 9.16726 0.440551 0.220275 0.975438i \(-0.429304\pi\)
0.220275 + 0.975438i \(0.429304\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 19.2458 33.3347i 0.920651 1.59461i
\(438\) 0 0
\(439\) 5.43349 + 9.41108i 0.259326 + 0.449166i 0.966062 0.258312i \(-0.0831661\pi\)
−0.706735 + 0.707478i \(0.749833\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.8330 + 30.8876i 0.847271 + 1.46752i 0.883634 + 0.468178i \(0.155089\pi\)
−0.0363633 + 0.999339i \(0.511577\pi\)
\(444\) 0 0
\(445\) −4.10642 + 7.11252i −0.194663 + 0.337166i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3.39841 −0.160381 −0.0801904 0.996780i \(-0.525553\pi\)
−0.0801904 + 0.996780i \(0.525553\pi\)
\(450\) 0 0
\(451\) 15.2268 26.3735i 0.717000 1.24188i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 23.6023 8.87805i 1.10649 0.416209i
\(456\) 0 0
\(457\) −18.4115 31.8897i −0.861255 1.49174i −0.870718 0.491782i \(-0.836346\pi\)
0.00946370 0.999955i \(-0.496988\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 27.9356 1.30109 0.650545 0.759468i \(-0.274541\pi\)
0.650545 + 0.759468i \(0.274541\pi\)
\(462\) 0 0
\(463\) −24.5678 −1.14176 −0.570881 0.821033i \(-0.693398\pi\)
−0.570881 + 0.821033i \(0.693398\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10.6876 + 18.5115i 0.494564 + 0.856611i 0.999980 0.00626525i \(-0.00199431\pi\)
−0.505416 + 0.862876i \(0.668661\pi\)
\(468\) 0 0
\(469\) −17.9768 14.7590i −0.830091 0.681507i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −32.1762 + 55.7309i −1.47946 + 2.56251i
\(474\) 0 0
\(475\) 15.5906 0.715344
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.44966 9.43908i 0.249001 0.431283i −0.714248 0.699893i \(-0.753231\pi\)
0.963249 + 0.268610i \(0.0865644\pi\)
\(480\) 0 0
\(481\) −0.413989 0.717051i −0.0188763 0.0326947i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 17.2714 + 29.9150i 0.784256 + 1.35837i
\(486\) 0 0
\(487\) −10.3675 + 17.9571i −0.469797 + 0.813712i −0.999404 0.0345311i \(-0.989006\pi\)
0.529607 + 0.848243i \(0.322340\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −16.8670 −0.761196 −0.380598 0.924741i \(-0.624282\pi\)
−0.380598 + 0.924741i \(0.624282\pi\)
\(492\) 0 0
\(493\) −13.5494 + 23.4682i −0.610233 + 1.05695i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.10195 + 6.66636i −0.0494291 + 0.299027i
\(498\) 0 0
\(499\) −17.4054 30.1471i −0.779174 1.34957i −0.932419 0.361380i \(-0.882306\pi\)
0.153245 0.988188i \(-0.451028\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5.98561 0.266885 0.133442 0.991057i \(-0.457397\pi\)
0.133442 + 0.991057i \(0.457397\pi\)
\(504\) 0 0
\(505\) 41.7163 1.85635
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 13.9299 + 24.1273i 0.617433 + 1.06943i 0.989952 + 0.141401i \(0.0451607\pi\)
−0.372519 + 0.928024i \(0.621506\pi\)
\(510\) 0 0
\(511\) 26.6701 + 21.8962i 1.17982 + 0.968632i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.03348 10.4503i 0.265867 0.460495i
\(516\) 0 0
\(517\) −43.9624 −1.93347
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4.20398 + 7.28151i −0.184180 + 0.319009i −0.943300 0.331942i \(-0.892296\pi\)
0.759120 + 0.650951i \(0.225630\pi\)
\(522\) 0 0
\(523\) −9.50373 16.4609i −0.415569 0.719786i 0.579919 0.814674i \(-0.303084\pi\)
−0.995488 + 0.0948876i \(0.969751\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −20.0447 34.7184i −0.873160 1.51236i
\(528\) 0 0
\(529\) −7.00529 + 12.1335i −0.304578 + 0.527544i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 20.8735 0.904130
\(534\) 0 0
\(535\) −23.4365 + 40.5932i −1.01325 + 1.75500i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 26.7958 23.4809i 1.15418 1.01139i
\(540\) 0 0
\(541\) −5.80585 10.0560i −0.249613 0.432342i 0.713805 0.700344i \(-0.246970\pi\)
−0.963418 + 0.268002i \(0.913637\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8.50356 −0.364253
\(546\) 0 0
\(547\) −39.2855 −1.67973 −0.839864 0.542797i \(-0.817365\pi\)
−0.839864 + 0.542797i \(0.817365\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −20.4301 35.3860i −0.870352 1.50749i
\(552\) 0 0
\(553\) 12.9433 4.86866i 0.550406 0.207036i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.93654 3.35419i 0.0820540 0.142122i −0.822078 0.569375i \(-0.807185\pi\)
0.904132 + 0.427253i \(0.140519\pi\)
\(558\) 0 0
\(559\) −44.1085 −1.86559
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −0.863603 + 1.49580i −0.0363965 + 0.0630407i −0.883650 0.468148i \(-0.844921\pi\)
0.847253 + 0.531189i \(0.178255\pi\)
\(564\) 0 0
\(565\) 21.5065 + 37.2504i 0.904787 + 1.56714i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.05016 7.01507i −0.169791 0.294087i 0.768555 0.639784i \(-0.220976\pi\)
−0.938346 + 0.345696i \(0.887643\pi\)
\(570\) 0 0
\(571\) −9.47393 + 16.4093i −0.396472 + 0.686709i −0.993288 0.115669i \(-0.963099\pi\)
0.596816 + 0.802378i \(0.296432\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −14.9907 −0.625155
\(576\) 0 0
\(577\) 2.32379 4.02492i 0.0967407 0.167560i −0.813593 0.581435i \(-0.802492\pi\)
0.910334 + 0.413875i \(0.135825\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.47594 + 14.9785i −0.102719 + 0.621412i
\(582\) 0 0
\(583\) −11.7561 20.3622i −0.486888 0.843314i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −30.4939 −1.25862 −0.629308 0.777156i \(-0.716662\pi\)
−0.629308 + 0.777156i \(0.716662\pi\)
\(588\) 0 0
\(589\) 60.4478 2.49071
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.85400 3.21123i −0.0761348 0.131869i 0.825444 0.564483i \(-0.190925\pi\)
−0.901579 + 0.432614i \(0.857591\pi\)
\(594\) 0 0
\(595\) 4.94660 29.9251i 0.202791 1.22681i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −20.1070 + 34.8264i −0.821552 + 1.42297i 0.0829748 + 0.996552i \(0.473558\pi\)
−0.904526 + 0.426418i \(0.859775\pi\)
\(600\) 0 0
\(601\) −14.4852 −0.590866 −0.295433 0.955364i \(-0.595464\pi\)
−0.295433 + 0.955364i \(0.595464\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −20.3612 + 35.2666i −0.827800 + 1.43379i
\(606\) 0 0
\(607\) 8.93193 + 15.4706i 0.362536 + 0.627930i 0.988377 0.152020i \(-0.0485777\pi\)
−0.625842 + 0.779950i \(0.715244\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −15.0664 26.0957i −0.609520 1.05572i
\(612\) 0 0
\(613\) 18.2243 31.5655i 0.736074 1.27492i −0.218176 0.975909i \(-0.570011\pi\)
0.954250 0.299009i \(-0.0966559\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −22.8769 −0.920990 −0.460495 0.887662i \(-0.652328\pi\)
−0.460495 + 0.887662i \(0.652328\pi\)
\(618\) 0 0
\(619\) 9.46082 16.3866i 0.380262 0.658634i −0.610837 0.791756i \(-0.709167\pi\)
0.991100 + 0.133122i \(0.0425003\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7.44418 + 2.80015i −0.298245 + 0.112185i
\(624\) 0 0
\(625\) 15.6244 + 27.0622i 0.624974 + 1.08249i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −0.995906 −0.0397094
\(630\) 0 0
\(631\) −1.38657 −0.0551987 −0.0275993 0.999619i \(-0.508786\pi\)
−0.0275993 + 0.999619i \(0.508786\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 16.5149 + 28.6046i 0.655373 + 1.13514i
\(636\) 0 0
\(637\) 23.1212 + 7.85859i 0.916097 + 0.311369i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −13.6625 + 23.6641i −0.539636 + 0.934677i 0.459288 + 0.888288i \(0.348105\pi\)
−0.998923 + 0.0463891i \(0.985229\pi\)
\(642\) 0 0
\(643\) 29.1795 1.15073 0.575363 0.817898i \(-0.304861\pi\)
0.575363 + 0.817898i \(0.304861\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.55384 + 14.8157i −0.336286 + 0.582465i −0.983731 0.179648i \(-0.942504\pi\)
0.647445 + 0.762112i \(0.275838\pi\)
\(648\) 0 0
\(649\) 11.1322 + 19.2815i 0.436976 + 0.756865i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.26075 + 7.37984i 0.166736 + 0.288795i 0.937270 0.348603i \(-0.113344\pi\)
−0.770534 + 0.637398i \(0.780011\pi\)
\(654\) 0 0
\(655\) −1.22066 + 2.11424i −0.0476951 + 0.0826103i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 38.6253 1.50463 0.752313 0.658806i \(-0.228938\pi\)
0.752313 + 0.658806i \(0.228938\pi\)
\(660\) 0 0
\(661\) 14.0584 24.3498i 0.546808 0.947099i −0.451683 0.892178i \(-0.649176\pi\)
0.998491 0.0549202i \(-0.0174905\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 35.3474 + 29.0203i 1.37071 + 1.12536i
\(666\) 0 0
\(667\) 19.6440 + 34.0245i 0.760620 + 1.31743i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.51704 −0.174378
\(672\) 0 0
\(673\) 5.10115 0.196635 0.0983174 0.995155i \(-0.468654\pi\)
0.0983174 + 0.995155i \(0.468654\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −23.7561 41.1468i −0.913021 1.58140i −0.809773 0.586743i \(-0.800410\pi\)
−0.103248 0.994656i \(-0.532923\pi\)
\(678\) 0 0
\(679\) −5.45553 + 33.0039i −0.209364 + 1.26657i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −16.1639 + 27.9968i −0.618496 + 1.07127i 0.371264 + 0.928527i \(0.378924\pi\)
−0.989760 + 0.142739i \(0.954409\pi\)
\(684\) 0 0
\(685\) 37.0465 1.41547
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 8.05786 13.9566i 0.306980 0.531705i
\(690\) 0 0
\(691\) −3.99471 6.91905i −0.151966 0.263213i 0.779984 0.625799i \(-0.215227\pi\)
−0.931950 + 0.362586i \(0.881894\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −6.98619 12.1004i −0.265001 0.458995i
\(696\) 0 0
\(697\) 12.5535 21.7432i 0.475496 0.823584i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 31.9891 1.20821 0.604105 0.796905i \(-0.293531\pi\)
0.604105 + 0.796905i \(0.293531\pi\)
\(702\) 0 0
\(703\) 0.750827 1.30047i 0.0283180 0.0490482i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 31.2235 + 25.6346i 1.17428 + 0.964089i
\(708\) 0 0
\(709\) 12.9258 + 22.3881i 0.485438 + 0.840803i 0.999860 0.0167340i \(-0.00532685\pi\)
−0.514422 + 0.857537i \(0.671994\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −58.1220 −2.17669
\(714\) 0 0
\(715\) −48.5106 −1.81419
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 11.7362 + 20.3277i 0.437686 + 0.758094i 0.997511 0.0705173i \(-0.0224650\pi\)
−0.559825 + 0.828611i \(0.689132\pi\)
\(720\) 0 0
\(721\) 10.9376 4.11420i 0.407337 0.153221i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.95658 + 13.7812i −0.295500 + 0.511821i
\(726\) 0 0
\(727\) 9.63621 0.357387 0.178694 0.983905i \(-0.442813\pi\)
0.178694 + 0.983905i \(0.442813\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −26.5272 + 45.9464i −0.981143 + 1.69939i
\(732\) 0 0
\(733\) 14.5335 + 25.1727i 0.536806 + 0.929776i 0.999074 + 0.0430350i \(0.0137027\pi\)
−0.462267 + 0.886741i \(0.652964\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 22.3724 + 38.7501i 0.824097 + 1.42738i
\(738\) 0 0
\(739\) −10.4527 + 18.1046i −0.384509 + 0.665989i −0.991701 0.128566i \(-0.958963\pi\)
0.607192 + 0.794555i \(0.292296\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −22.6497 −0.830936 −0.415468 0.909608i \(-0.636382\pi\)
−0.415468 + 0.909608i \(0.636382\pi\)
\(744\) 0 0
\(745\) −9.19615 + 15.9282i −0.336921 + 0.583564i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −42.4860 + 15.9812i −1.55241 + 0.583941i
\(750\) 0 0
\(751\) 3.80757 + 6.59491i 0.138940 + 0.240652i 0.927096 0.374825i \(-0.122297\pi\)
−0.788155 + 0.615476i \(0.788964\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 7.17337 0.261066
\(756\) 0 0
\(757\) −2.38838 −0.0868073 −0.0434036 0.999058i \(-0.513820\pi\)
−0.0434036 + 0.999058i \(0.513820\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 5.02278 + 8.69972i 0.182076 + 0.315365i 0.942587 0.333960i \(-0.108385\pi\)
−0.760511 + 0.649325i \(0.775052\pi\)
\(762\) 0 0
\(763\) −6.36470 5.22543i −0.230417 0.189173i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7.63022 + 13.2159i −0.275511 + 0.477200i
\(768\) 0 0
\(769\) −18.9120 −0.681984 −0.340992 0.940066i \(-0.610763\pi\)
−0.340992 + 0.940066i \(0.610763\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −6.53042 + 11.3110i −0.234883 + 0.406829i −0.959239 0.282597i \(-0.908804\pi\)
0.724356 + 0.689426i \(0.242137\pi\)
\(774\) 0 0
\(775\) −11.7708 20.3876i −0.422820 0.732346i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 18.9285 + 32.7851i 0.678182 + 1.17465i
\(780\) 0 0
\(781\) 6.49918 11.2569i 0.232559 0.402804i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 16.9738 0.605820
\(786\) 0 0
\(787\) 16.4299 28.4575i 0.585664 1.01440i −0.409129 0.912477i \(-0.634167\pi\)
0.994792 0.101922i \(-0.0324994\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.79327 + 41.0967i −0.241541 + 1.46123i
\(792\) 0 0
\(793\) −1.54803 2.68127i −0.0549723 0.0952148i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −6.43559 −0.227960 −0.113980 0.993483i \(-0.536360\pi\)
−0.113980 + 0.993483i \(0.536360\pi\)
\(798\) 0 0
\(799\) −36.2441 −1.28223
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −33.1913 57.4890i −1.17130 2.02874i
\(804\) 0 0