Properties

Label 1512.2.s.p.1297.4
Level $1512$
Weight $2$
Character 1512.1297
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 1297.4
Root \(-2.47635 - 0.931486i\) of defining polynomial
Character \(\chi\) \(=\) 1512.1297
Dual form 1512.2.s.p.865.4

$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

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

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 −0.380183 0.924911i \(-0.624139\pi\)
0.991088 0.133207i \(-0.0425277\pi\)
\(6\) 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 0.939018 + 0.343867i \(0.111737\pi\)
−0.171712 + 0.985147i \(0.554930\pi\)
\(12\) 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 0.999947 + 0.0102590i \(0.00326559\pi\)
−0.491089 + 0.871109i \(0.663401\pi\)
\(18\) 0 0
\(19\) −3.16354 + 5.47941i −0.725765 + 1.25706i 0.232893 + 0.972502i \(0.425181\pi\)
−0.958658 + 0.284560i \(0.908153\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.04182 + 5.26858i −0.634262 + 1.09857i 0.352408 + 0.935846i \(0.385363\pi\)
−0.986671 + 0.162728i \(0.947971\pi\)
\(24\) 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 −0.873872 0.486157i \(-0.838398\pi\)
0.0159115 0.999873i \(-0.494935\pi\)
\(32\) 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 −0.856106 0.516800i \(-0.827123\pi\)
0.875615 + 0.483010i \(0.160456\pi\)
\(38\) 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 0.357609 + 0.933872i \(0.383592\pi\)
−0.987561 + 0.157238i \(0.949741\pi\)
\(48\) 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 \(-0.0639003\pi\)
−0.662647 + 0.748932i \(0.730567\pi\)
\(54\) 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 \(-0.258576\pi\)
−0.972548 + 0.232703i \(0.925243\pi\)
\(60\) 0 0
\(61\) 0.443740 0.768580i 0.0568150 0.0984065i −0.836219 0.548396i \(-0.815239\pi\)
0.893034 + 0.449989i \(0.148572\pi\)
\(62\) 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 0.999063 + 0.0432723i \(0.0137783\pi\)
−0.462057 + 0.886850i \(0.652888\pi\)
\(68\) 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 −0.941166 0.337944i \(-0.890268\pi\)
0.177915 0.984046i \(-0.443065\pi\)
\(74\) 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 −0.680730 0.732534i \(-0.738337\pi\)
0.974758 + 0.223262i \(0.0716706\pi\)
\(80\) 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 −0.775302 0.631591i \(-0.782402\pi\)
0.934625 + 0.355635i \(0.115735\pi\)
\(90\) 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 0.943018 + 0.332741i \(0.107974\pi\)
−0.183347 + 0.983048i \(0.558693\pi\)
\(102\) 0 0
\(103\) 2.20841 3.82507i 0.217601 0.376895i −0.736473 0.676467i \(-0.763510\pi\)
0.954074 + 0.299571i \(0.0968436\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.57834 14.8581i 0.829300 1.43639i −0.0692884 0.997597i \(-0.522073\pi\)
0.898588 0.438793i \(-0.144594\pi\)
\(108\) 0 0
\(109\) 1.55626 + 2.69552i 0.149063 + 0.258184i 0.930881 0.365322i \(-0.119041\pi\)
−0.781819 + 0.623506i \(0.785708\pi\)
\(110\) 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 −0.845847 0.533425i \(-0.820905\pi\)
0.884884 + 0.465812i \(0.154238\pi\)
\(132\) 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 0.995565 + 0.0940728i \(0.0299886\pi\)
−0.416313 + 0.909221i \(0.636678\pi\)
\(138\) 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 \(-0.744405\pi\)
0.970325 + 0.241803i \(0.0777386\pi\)
\(150\) 0 0
\(151\) −1.31282 2.27387i −0.106836 0.185045i 0.807651 0.589661i \(-0.200739\pi\)
−0.914487 + 0.404616i \(0.867405\pi\)
\(152\) 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 0.715029 0.699095i \(-0.246413\pi\)
−0.962948 + 0.269686i \(0.913080\pi\)
\(158\) 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 −0.687705 0.725991i \(-0.741382\pi\)
0.972579 + 0.232574i \(0.0747149\pi\)
\(164\) 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 −0.536160 0.844116i \(-0.680126\pi\)
0.999106 + 0.0422700i \(0.0134590\pi\)
\(174\) 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 0.971900 + 0.235395i \(0.0756383\pi\)
−0.282092 + 0.959387i \(0.591028\pi\)
\(180\) 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 0.244103 + 0.969749i \(0.421507\pi\)
−0.961879 + 0.273475i \(0.911827\pi\)
\(192\) 0 0
\(193\) 1.15825 + 2.00615i 0.0833727 + 0.144406i 0.904697 0.426056i \(-0.140097\pi\)
−0.821324 + 0.570462i \(0.806764\pi\)
\(194\) 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 0.822836 + 0.568279i \(0.192390\pi\)
0.0807256 + 0.996736i \(0.474276\pi\)
\(200\) 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 \(-0.123266\pi\)
−0.790025 + 0.613074i \(0.789933\pi\)
\(228\) 0 0
\(229\) −1.26553 + 2.19196i −0.0836284 + 0.144849i −0.904806 0.425824i \(-0.859984\pi\)
0.821178 + 0.570673i \(0.193318\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.0843 22.6626i 0.857179 1.48468i −0.0174307 0.999848i \(-0.505549\pi\)
0.874609 0.484829i \(-0.161118\pi\)
\(234\) 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 −0.991486 0.130211i \(-0.958434\pi\)
0.382977 0.923758i \(-0.374899\pi\)
\(242\) 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 −0.941527 0.336936i \(-0.890609\pi\)
0.762559 + 0.646918i \(0.223943\pi\)
\(258\) 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 \(-0.307898\pi\)
−0.996809 + 0.0798233i \(0.974564\pi\)
\(264\) 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 \(-0.205253\pi\)
−0.920133 + 0.391607i \(0.871919\pi\)
\(270\) 0 0
\(271\) 7.25942 12.5737i 0.440978 0.763797i −0.556784 0.830657i \(-0.687965\pi\)
0.997762 + 0.0668603i \(0.0212982\pi\)
\(272\) 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 0.669528 0.742787i \(-0.266496\pi\)
−0.978036 + 0.208435i \(0.933163\pi\)
\(278\) 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 0.827081 0.562083i \(-0.190000\pi\)
−0.900319 + 0.435231i \(0.856667\pi\)
\(284\) 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 −0.995853 0.0909788i \(-0.971000\pi\)
0.419136 0.907923i \(-0.362333\pi\)
\(312\) 0 0
\(313\) 13.5803 23.5219i 0.767607 1.32953i −0.171251 0.985227i \(-0.554781\pi\)
0.938857 0.344306i \(-0.111886\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.3360 19.6346i 0.636696 1.10279i −0.349457 0.936952i \(-0.613634\pi\)
0.986153 0.165837i \(-0.0530326\pi\)
\(318\) 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 −0.968302 0.249782i \(-0.919641\pi\)
0.700469 + 0.713683i \(0.252974\pi\)
\(332\) 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 \(-0.0151499\pi\)
−0.540637 + 0.841256i \(0.681817\pi\)
\(348\) 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 −0.758680 0.651464i \(-0.774155\pi\)
−0.184844 0.982768i \(-0.559178\pi\)
\(354\) 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 \(-0.982890\pi\)
0.545808 + 0.837910i \(0.316223\pi\)
\(360\) 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 0.950798 0.309810i \(-0.100265\pi\)
−0.743703 + 0.668511i \(0.766932\pi\)
\(368\) 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 0.202876 + 0.979204i \(0.434971\pi\)
−0.949454 + 0.313906i \(0.898362\pi\)
\(374\) 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 \(-0.671876\pi\)
0.999866 + 0.0163634i \(0.00520888\pi\)
\(384\) 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 0.966884 + 0.255215i \(0.0821462\pi\)
−0.262420 + 0.964954i \(0.584521\pi\)
\(390\) 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 −0.515715 0.856760i \(-0.672474\pi\)
0.999834 + 0.0182421i \(0.00580695\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 13.6346 23.6158i 0.680880 1.17932i −0.293833 0.955857i \(-0.594931\pi\)
0.974713 0.223461i \(-0.0717357\pi\)
\(402\) 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 0.982985 0.183688i \(-0.0588035\pi\)
−0.650570 + 0.759446i \(0.725470\pi\)
\(410\) 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 0.758111 0.652125i \(-0.226122\pi\)
−0.943813 + 0.330481i \(0.892789\pi\)
\(432\) 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 −0.706735 0.707478i \(-0.749833\pi\)
0.966062 + 0.258312i \(0.0831661\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −17.8330 + 30.8876i −0.847271 + 1.46752i 0.0363633 + 0.999339i \(0.488423\pi\)
−0.883634 + 0.468178i \(0.844911\pi\)
\(444\) 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 0.00946370 + 0.999955i \(0.496988\pi\)
−0.870718 + 0.491782i \(0.836346\pi\)
\(458\) 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 −0.999980 0.00626525i \(-0.998006\pi\)
0.505416 + 0.862876i \(0.331339\pi\)
\(468\) 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 \(-0.246769\pi\)
−0.963249 + 0.268610i \(0.913436\pi\)
\(480\) 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 0.529607 0.848243i \(-0.322340\pi\)
−0.999404 + 0.0345311i \(0.989006\pi\)
\(488\) 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 0.153245 + 0.988188i \(0.451028\pi\)
−0.932419 + 0.361380i \(0.882306\pi\)
\(500\) 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 0.372519 + 0.928024i \(0.378494\pi\)
−0.989952 + 0.141401i \(0.954839\pi\)
\(510\) 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 \(-0.107704\pi\)
−0.759120 + 0.650951i \(0.774370\pi\)
\(522\) 0 0
\(523\) −9.50373 + 16.4609i −0.415569 + 0.719786i −0.995488 0.0948876i \(-0.969751\pi\)
0.579919 + 0.814674i \(0.303084\pi\)
\(524\) 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 −0.963418 0.268002i \(-0.913637\pi\)
0.713805 + 0.700344i \(0.246970\pi\)
\(542\) 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 \(-0.192815\pi\)
−0.904132 + 0.427253i \(0.859481\pi\)
\(558\) 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 \(-0.155079\pi\)
−0.847253 + 0.531189i \(0.821745\pi\)
\(564\) 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 \(-0.779024\pi\)
0.938346 + 0.345696i \(0.112357\pi\)
\(570\) 0 0
\(571\) −9.47393 16.4093i −0.396472 0.686709i 0.596816 0.802378i \(-0.296432\pi\)
−0.993288 + 0.115669i \(0.963099\pi\)
\(572\) 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 0.910334 0.413875i \(-0.135825\pi\)
−0.813593 + 0.581435i \(0.802492\pi\)
\(578\) 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 −0.825444 0.564483i \(-0.809075\pi\)
0.901579 + 0.432614i \(0.142409\pi\)
\(594\) 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 0.904526 + 0.426418i \(0.140225\pi\)
−0.0829748 + 0.996552i \(0.526442\pi\)
\(600\) 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 −0.625842 0.779950i \(-0.715244\pi\)
0.988377 + 0.152020i \(0.0485777\pi\)
\(608\) 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 0.954250 + 0.299009i \(0.0966559\pi\)
−0.218176 + 0.975909i \(0.570011\pi\)
\(614\) 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 0.991100 0.133122i \(-0.0425003\pi\)
−0.610837 + 0.791756i \(0.709167\pi\)
\(620\) 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 0.998923 + 0.0463891i \(0.0147714\pi\)
−0.459288 + 0.888288i \(0.651895\pi\)
\(642\) 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 \(-0.0574958\pi\)
−0.647445 + 0.762112i \(0.724162\pi\)
\(648\) 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 \(-0.886656\pi\)
0.770534 + 0.637398i \(0.219989\pi\)
\(654\) 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 0.998491 + 0.0549202i \(0.0174905\pi\)
−0.451683 + 0.892178i \(0.649176\pi\)
\(662\) 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 0.103248 0.994656i \(-0.467077\pi\)
0.809773 0.586743i \(-0.199590\pi\)
\(678\) 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 0.989760 + 0.142739i \(0.0455910\pi\)
−0.371264 + 0.928527i \(0.621076\pi\)
\(684\) 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 −0.931950 0.362586i \(-0.881894\pi\)
0.779984 + 0.625799i \(0.215227\pi\)
\(692\) 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 −0.514422 0.857537i \(-0.671994\pi\)
0.999860 + 0.0167340i \(0.00532685\pi\)
\(710\) 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 \(-0.977535\pi\)
0.559825 + 0.828611i \(0.310868\pi\)
\(720\) 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 −0.462267 0.886741i \(-0.652964\pi\)
0.999074 0.0430350i \(-0.0137027\pi\)
\(734\) 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 0.607192 0.794555i \(-0.292296\pi\)
−0.991701 + 0.128566i \(0.958963\pi\)
\(740\) 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 −0.788155 0.615476i \(-0.788964\pi\)
0.927096 + 0.374825i \(0.122297\pi\)
\(752\) 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 \(-0.891615\pi\)
0.760511 + 0.649325i \(0.224948\pi\)
\(762\) 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 \(-0.0911960\pi\)
−0.724356 + 0.689426i \(0.757863\pi\)
\(774\) 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 0.994792 + 0.101922i \(0.0324994\pi\)
−0.409129 + 0.912477i \(0.634167\pi\)
\(788\) 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