Properties

Label 1512.2.s.p.865.4
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 865.4
Root \(-2.47635 + 0.931486i\) of defining polynomial
Character \(\chi\) \(=\) 1512.865
Dual form 1512.2.s.p.1297.4

$q$-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 \(0.0425277\pi\)
−0.380183 + 0.924911i \(0.624139\pi\)
\(6\) 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 \(-0.554930\pi\)
0.939018 0.343867i \(-0.111737\pi\)
\(12\) 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 \(-0.663401\pi\)
0.999947 0.0102590i \(-0.00326559\pi\)
\(18\) 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 \(-0.947971\pi\)
0.352408 0.935846i \(-0.385363\pi\)
\(24\) 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 \(-0.704678\pi\)
−0.599610 + 0.800292i \(0.704678\pi\)
\(30\) 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 \(-0.345256\pi\)
0.467219 + 0.884142i \(0.345256\pi\)
\(42\) 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 \(-0.949741\pi\)
0.357609 0.933872i \(-0.383592\pi\)
\(48\) 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 −0.662647 0.748932i \(-0.730567\pi\)
0.979918 + 0.199403i \(0.0639003\pi\)
\(54\) 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 −0.972548 0.232703i \(-0.925243\pi\)
0.687801 + 0.725899i \(0.258576\pi\)
\(60\) 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 \(-0.451576\pi\)
0.151542 + 0.988451i \(0.451576\pi\)
\(72\) 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 \(-0.398022\pi\)
0.314922 + 0.949117i \(0.398022\pi\)
\(84\) 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 0.934625 0.355635i \(-0.115735\pi\)
−0.775302 + 0.631591i \(0.782402\pi\)
\(90\) 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 \(-0.558693\pi\)
0.943018 0.332741i \(-0.107974\pi\)
\(102\) 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 \(0.144594\pi\)
−0.0692884 + 0.997597i \(0.522073\pi\)
\(108\) 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 \(-0.234574\pi\)
0.740530 + 0.672023i \(0.234574\pi\)
\(114\) 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 0.884884 0.465812i \(-0.154238\pi\)
−0.845847 + 0.533425i \(0.820905\pi\)
\(132\) 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 \(-0.636678\pi\)
0.995565 0.0940728i \(-0.0299886\pi\)
\(138\) 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 0.970325 0.241803i \(-0.0777386\pi\)
−0.694570 + 0.719425i \(0.744405\pi\)
\(150\) 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 \(-0.462838\pi\)
0.116483 + 0.993193i \(0.462838\pi\)
\(168\) 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 0.999106 0.0422700i \(-0.0134590\pi\)
−0.536160 + 0.844116i \(0.680126\pi\)
\(174\) 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 \(-0.591028\pi\)
0.971900 0.235395i \(-0.0756383\pi\)
\(180\) 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 \(-0.911827\pi\)
0.244103 0.969749i \(-0.421507\pi\)
\(192\) 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 \(-0.514711\pi\)
−0.0461980 + 0.998932i \(0.514711\pi\)
\(198\) 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 −0.790025 0.613074i \(-0.789933\pi\)
0.925951 + 0.377645i \(0.123266\pi\)
\(228\) 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 \(0.161118\pi\)
−0.0174307 + 0.999848i \(0.505549\pi\)
\(234\) 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 \(-0.566462\pi\)
−0.207281 + 0.978281i \(0.566462\pi\)
\(240\) 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 \(-0.381259\pi\)
0.364443 + 0.931226i \(0.381259\pi\)
\(252\) 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 0.762559 0.646918i \(-0.223943\pi\)
−0.941527 + 0.336936i \(0.890609\pi\)
\(258\) 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 −0.996809 0.0798233i \(-0.974564\pi\)
0.567533 + 0.823350i \(0.307898\pi\)
\(264\) 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 −0.920133 0.391607i \(-0.871919\pi\)
0.799208 + 0.601055i \(0.205253\pi\)
\(270\) 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 \(-0.670801\pi\)
−0.511206 + 0.859458i \(0.670801\pi\)
\(282\) 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 \(-0.320704\pi\)
0.533958 + 0.845511i \(0.320704\pi\)
\(294\) 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 \(0.362333\pi\)
−0.995853 + 0.0909788i \(0.971000\pi\)
\(312\) 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 \(0.0530326\pi\)
−0.349457 + 0.936952i \(0.613634\pi\)
\(318\) 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 −0.540637 0.841256i \(-0.681817\pi\)
0.998868 + 0.0475768i \(0.0151499\pi\)
\(348\) 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 \(0.559178\pi\)
−0.758680 + 0.651464i \(0.774155\pi\)
\(354\) 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 0.545808 0.837910i \(-0.316223\pi\)
−0.998556 + 0.0537283i \(0.982890\pi\)
\(360\) 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 0.999866 0.0163634i \(-0.00520888\pi\)
−0.514104 + 0.857728i \(0.671876\pi\)
\(384\) 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 \(-0.584521\pi\)
0.966884 0.255215i \(-0.0821462\pi\)
\(390\) 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 \(0.0717357\pi\)
−0.293833 + 0.955857i \(0.594931\pi\)
\(402\) 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 \(-0.510780\pi\)
−0.0338601 + 0.999427i \(0.510780\pi\)
\(420\) 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 −0.943813 0.330481i \(-0.892789\pi\)
0.758111 + 0.652125i \(0.226122\pi\)
\(432\) 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 \(-0.844911\pi\)
0.0363633 0.999339i \(-0.488423\pi\)
\(444\) 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 \(-0.474447\pi\)
0.0801904 + 0.996780i \(0.474447\pi\)
\(450\) 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 \(-0.725459\pi\)
−0.650545 + 0.759468i \(0.725459\pi\)
\(462\) 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 0.505416 0.862876i \(-0.331339\pi\)
−0.999980 + 0.00626525i \(0.998006\pi\)
\(468\) 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 −0.963249 0.268610i \(-0.913436\pi\)
0.714248 + 0.699893i \(0.246769\pi\)
\(480\) 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 \(-0.375718\pi\)
0.380598 + 0.924741i \(0.375718\pi\)
\(492\) 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 \(-0.542603\pi\)
−0.133442 + 0.991057i \(0.542603\pi\)
\(504\) 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 \(-0.954839\pi\)
0.372519 0.928024i \(-0.378494\pi\)
\(510\) 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 −0.759120 0.650951i \(-0.774370\pi\)
0.943300 + 0.331942i \(0.107704\pi\)
\(522\) 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 −0.904132 0.427253i \(-0.859481\pi\)
0.822078 + 0.569375i \(0.192815\pi\)
\(558\) 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 −0.847253 0.531189i \(-0.821745\pi\)
0.883650 + 0.468148i \(0.155079\pi\)
\(564\) 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 0.938346 0.345696i \(-0.112357\pi\)
−0.768555 + 0.639784i \(0.779024\pi\)
\(570\) 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 \(-0.283338\pi\)
0.629308 + 0.777156i \(0.283338\pi\)
\(588\) 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 0.901579 0.432614i \(-0.142409\pi\)
−0.825444 + 0.564483i \(0.809075\pi\)
\(594\) 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 \(-0.526442\pi\)
0.904526 0.426418i \(-0.140225\pi\)
\(600\) 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 \(-0.347672\pi\)
0.460495 + 0.887662i \(0.347672\pi\)
\(618\) 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 \(-0.651895\pi\)
0.998923 0.0463891i \(-0.0147714\pi\)
\(642\) 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 −0.647445 0.762112i \(-0.724162\pi\)
0.983731 + 0.179648i \(0.0574958\pi\)
\(648\) 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 0.770534 0.637398i \(-0.219989\pi\)
−0.937270 + 0.348603i \(0.886656\pi\)
\(654\) 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 \(-0.771062\pi\)
−0.752313 + 0.658806i \(0.771062\pi\)
\(660\) 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 \(0.199590\pi\)
0.103248 + 0.994656i \(0.467077\pi\)
\(678\) 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 \(-0.621076\pi\)
0.989760 0.142739i \(-0.0455910\pi\)
\(684\) 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 \(-0.706469\pi\)
−0.604105 + 0.796905i \(0.706469\pi\)
\(702\) 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 0.559825 0.828611i \(-0.310868\pi\)
−0.997511 + 0.0705173i \(0.977535\pi\)
\(720\) 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 \(-0.363618\pi\)
0.415468 + 0.909608i \(0.363618\pi\)
\(744\) 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 0.760511 0.649325i \(-0.224948\pi\)
−0.942587 + 0.333960i \(0.891615\pi\)
\(762\) 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 −0.724356 0.689426i \(-0.757863\pi\)
0.959239 + 0.282597i \(0.0911960\pi\)
\(774\) 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 \(-0.463640\pi\)
0.113980 + 0.993483i \(0.463640\pi\)
\(798\) 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
\(805\) −33.9873 27.9037i −1.19790 0.983476i
\(806\) 0 0