Properties

Label 3456.2.i.l.1153.2
Level $3456$
Weight $2$
Character 3456.1153
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 1153.2
Root \(1.73202 - 0.0102491i\) of defining polynomial
Character \(\chi\) \(=\) 3456.1153
Dual form 3456.2.i.l.2305.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.551563 - 0.955334i) q^{5} +(-1.62490 + 2.81442i) q^{7} +O(q^{10})\) \(q+(-0.551563 - 0.955334i) q^{5} +(-1.62490 + 2.81442i) q^{7} +(-1.28869 + 2.23208i) q^{11} +(1.58731 + 2.74930i) q^{13} -4.71601 q^{17} -5.75569 q^{19} +(-2.35397 - 4.07719i) q^{23} +(1.89156 - 3.27627i) q^{25} +(3.66250 - 6.34363i) q^{29} +(-2.93135 - 5.07724i) q^{31} +3.58494 q^{35} -0.0714979 q^{37} +(1.63887 + 2.83861i) q^{41} +(-2.12088 + 3.67347i) q^{43} +(4.72803 - 8.18919i) q^{47} +(-1.78062 - 3.08413i) q^{49} +6.42812 q^{53} +2.84317 q^{55} +(4.19606 + 7.26779i) q^{59} +(4.66250 - 8.07568i) q^{61} +(1.75100 - 3.03283i) q^{65} +(6.09975 + 10.5651i) q^{67} +0.335627 q^{71} +14.8664 q^{73} +(-4.18800 - 7.25382i) q^{77} +(4.85985 - 8.41750i) q^{79} +(3.07022 - 5.31778i) q^{83} +(2.60117 + 4.50537i) q^{85} -4.42812 q^{89} -10.3169 q^{91} +(3.17462 + 5.49861i) q^{95} +(6.39456 - 11.0757i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{5} + 6 q^{7} + O(q^{10}) \) \( 12 q + 2 q^{5} + 6 q^{7} - 4 q^{11} + 10 q^{13} - 4 q^{17} + 4 q^{19} - 8 q^{23} - 14 q^{25} + 2 q^{29} + 8 q^{31} - 8 q^{35} + 2 q^{41} - 2 q^{43} + 14 q^{47} - 18 q^{49} - 24 q^{53} - 16 q^{55} - 6 q^{59} + 14 q^{61} + 8 q^{65} + 4 q^{67} + 28 q^{71} + 60 q^{73} - 2 q^{77} + 16 q^{79} - 24 q^{83} + 16 q^{85} + 48 q^{89} - 52 q^{91} + 20 q^{95} - 14 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(2053\) \(2431\) \(2945\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) −0.551563 0.955334i −0.246666 0.427238i 0.715933 0.698169i \(-0.246002\pi\)
−0.962599 + 0.270931i \(0.912668\pi\)
\(6\) 0 0
\(7\) −1.62490 + 2.81442i −0.614156 + 1.06375i 0.376376 + 0.926467i \(0.377170\pi\)
−0.990532 + 0.137282i \(0.956163\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.28869 + 2.23208i −0.388555 + 0.672997i −0.992255 0.124215i \(-0.960359\pi\)
0.603701 + 0.797211i \(0.293692\pi\)
\(12\) 0 0
\(13\) 1.58731 + 2.74930i 0.440241 + 0.762520i 0.997707 0.0676799i \(-0.0215597\pi\)
−0.557466 + 0.830200i \(0.688226\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.71601 −1.14380 −0.571900 0.820323i \(-0.693794\pi\)
−0.571900 + 0.820323i \(0.693794\pi\)
\(18\) 0 0
\(19\) −5.75569 −1.32045 −0.660223 0.751070i \(-0.729538\pi\)
−0.660223 + 0.751070i \(0.729538\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.35397 4.07719i −0.490836 0.850152i 0.509109 0.860702i \(-0.329975\pi\)
−0.999944 + 0.0105499i \(0.996642\pi\)
\(24\) 0 0
\(25\) 1.89156 3.27627i 0.378312 0.655255i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.66250 6.34363i 0.680108 1.17798i −0.294839 0.955547i \(-0.595266\pi\)
0.974947 0.222435i \(-0.0714006\pi\)
\(30\) 0 0
\(31\) −2.93135 5.07724i −0.526485 0.911899i −0.999524 0.0308575i \(-0.990176\pi\)
0.473039 0.881042i \(-0.343157\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.58494 0.605966
\(36\) 0 0
\(37\) −0.0714979 −0.0117542 −0.00587709 0.999983i \(-0.501871\pi\)
−0.00587709 + 0.999983i \(0.501871\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.63887 + 2.83861i 0.255949 + 0.443317i 0.965153 0.261687i \(-0.0842787\pi\)
−0.709204 + 0.705004i \(0.750945\pi\)
\(42\) 0 0
\(43\) −2.12088 + 3.67347i −0.323431 + 0.560198i −0.981193 0.193027i \(-0.938170\pi\)
0.657763 + 0.753225i \(0.271503\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.72803 8.18919i 0.689654 1.19452i −0.282296 0.959327i \(-0.591096\pi\)
0.971950 0.235188i \(-0.0755706\pi\)
\(48\) 0 0
\(49\) −1.78062 3.08413i −0.254375 0.440590i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.42812 0.882970 0.441485 0.897269i \(-0.354452\pi\)
0.441485 + 0.897269i \(0.354452\pi\)
\(54\) 0 0
\(55\) 2.84317 0.383373
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.19606 + 7.26779i 0.546281 + 0.946186i 0.998525 + 0.0542918i \(0.0172901\pi\)
−0.452244 + 0.891894i \(0.649377\pi\)
\(60\) 0 0
\(61\) 4.66250 8.07568i 0.596971 1.03398i −0.396294 0.918124i \(-0.629704\pi\)
0.993265 0.115861i \(-0.0369628\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.75100 3.03283i 0.217185 0.376176i
\(66\) 0 0
\(67\) 6.09975 + 10.5651i 0.745203 + 1.29073i 0.950100 + 0.311945i \(0.100981\pi\)
−0.204897 + 0.978783i \(0.565686\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0.335627 0.0398316 0.0199158 0.999802i \(-0.493660\pi\)
0.0199158 + 0.999802i \(0.493660\pi\)
\(72\) 0 0
\(73\) 14.8664 1.73998 0.869989 0.493071i \(-0.164126\pi\)
0.869989 + 0.493071i \(0.164126\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.18800 7.25382i −0.477266 0.826650i
\(78\) 0 0
\(79\) 4.85985 8.41750i 0.546776 0.947043i −0.451717 0.892161i \(-0.649188\pi\)
0.998493 0.0548820i \(-0.0174783\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.07022 5.31778i 0.337000 0.583702i −0.646867 0.762603i \(-0.723921\pi\)
0.983867 + 0.178901i \(0.0572543\pi\)
\(84\) 0 0
\(85\) 2.60117 + 4.50537i 0.282137 + 0.488676i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.42812 −0.469379 −0.234690 0.972070i \(-0.575407\pi\)
−0.234690 + 0.972070i \(0.575407\pi\)
\(90\) 0 0
\(91\) −10.3169 −1.08151
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.17462 + 5.49861i 0.325709 + 0.564145i
\(96\) 0 0
\(97\) 6.39456 11.0757i 0.649270 1.12457i −0.334028 0.942563i \(-0.608408\pi\)
0.983298 0.182005i \(-0.0582586\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.80137 + 6.58417i −0.378250 + 0.655149i −0.990808 0.135277i \(-0.956808\pi\)
0.612557 + 0.790426i \(0.290141\pi\)
\(102\) 0 0
\(103\) 5.62490 + 9.74262i 0.554238 + 0.959969i 0.997962 + 0.0638053i \(0.0203237\pi\)
−0.443724 + 0.896163i \(0.646343\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.81493 0.272130 0.136065 0.990700i \(-0.456554\pi\)
0.136065 + 0.990700i \(0.456554\pi\)
\(108\) 0 0
\(109\) −15.6539 −1.49937 −0.749685 0.661795i \(-0.769795\pi\)
−0.749685 + 0.661795i \(0.769795\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −10.1828 17.6370i −0.957913 1.65915i −0.727557 0.686047i \(-0.759344\pi\)
−0.230355 0.973107i \(-0.573989\pi\)
\(114\) 0 0
\(115\) −2.59672 + 4.49765i −0.242145 + 0.419408i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.66306 13.2728i 0.702472 1.21672i
\(120\) 0 0
\(121\) 2.17855 + 3.77337i 0.198050 + 0.343033i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.68887 −0.866599
\(126\) 0 0
\(127\) 3.09888 0.274981 0.137491 0.990503i \(-0.456096\pi\)
0.137491 + 0.990503i \(0.456096\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −0.251085 0.434893i −0.0219374 0.0379968i 0.854848 0.518878i \(-0.173650\pi\)
−0.876786 + 0.480881i \(0.840317\pi\)
\(132\) 0 0
\(133\) 9.35244 16.1989i 0.810960 1.40462i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.88868 8.46744i 0.417668 0.723423i −0.578036 0.816011i \(-0.696181\pi\)
0.995704 + 0.0925885i \(0.0295141\pi\)
\(138\) 0 0
\(139\) −0.188498 0.326488i −0.0159882 0.0276924i 0.857921 0.513782i \(-0.171756\pi\)
−0.873909 + 0.486090i \(0.838423\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −8.18221 −0.684231
\(144\) 0 0
\(145\) −8.08038 −0.671039
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.83712 8.37814i −0.396272 0.686364i 0.596990 0.802248i \(-0.296363\pi\)
−0.993263 + 0.115885i \(0.963030\pi\)
\(150\) 0 0
\(151\) 8.42915 14.5997i 0.685954 1.18811i −0.287181 0.957876i \(-0.592718\pi\)
0.973136 0.230232i \(-0.0739484\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.23364 + 5.60083i −0.259732 + 0.449870i
\(156\) 0 0
\(157\) −4.36262 7.55628i −0.348175 0.603057i 0.637750 0.770243i \(-0.279865\pi\)
−0.985925 + 0.167187i \(0.946532\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 15.2999 1.20580
\(162\) 0 0
\(163\) −12.2063 −0.956067 −0.478034 0.878342i \(-0.658650\pi\)
−0.478034 + 0.878342i \(0.658650\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −11.3806 19.7118i −0.880657 1.52534i −0.850612 0.525794i \(-0.823768\pi\)
−0.0300447 0.999549i \(-0.509565\pi\)
\(168\) 0 0
\(169\) 1.46088 2.53033i 0.112376 0.194640i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 11.9797 20.7494i 0.910798 1.57755i 0.0978588 0.995200i \(-0.468801\pi\)
0.812939 0.582348i \(-0.197866\pi\)
\(174\) 0 0
\(175\) 6.14720 + 10.6473i 0.464684 + 0.804857i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −10.9992 −0.822121 −0.411061 0.911608i \(-0.634842\pi\)
−0.411061 + 0.911608i \(0.634842\pi\)
\(180\) 0 0
\(181\) 22.2168 1.65136 0.825679 0.564140i \(-0.190792\pi\)
0.825679 + 0.564140i \(0.190792\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.0394356 + 0.0683044i 0.00289936 + 0.00502184i
\(186\) 0 0
\(187\) 6.07748 10.5265i 0.444429 0.769774i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.48760 + 9.50479i −0.397068 + 0.687743i −0.993363 0.115023i \(-0.963306\pi\)
0.596294 + 0.802766i \(0.296639\pi\)
\(192\) 0 0
\(193\) −7.11682 12.3267i −0.512280 0.887294i −0.999899 0.0142378i \(-0.995468\pi\)
0.487619 0.873057i \(-0.337866\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.15037 −0.580690 −0.290345 0.956922i \(-0.593770\pi\)
−0.290345 + 0.956922i \(0.593770\pi\)
\(198\) 0 0
\(199\) 6.09200 0.431850 0.215925 0.976410i \(-0.430723\pi\)
0.215925 + 0.976410i \(0.430723\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 11.9024 + 20.6156i 0.835385 + 1.44693i
\(204\) 0 0
\(205\) 1.80788 3.13135i 0.126268 0.218703i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 7.41730 12.8471i 0.513066 0.888656i
\(210\) 0 0
\(211\) 3.01985 + 5.23054i 0.207895 + 0.360085i 0.951051 0.309033i \(-0.100005\pi\)
−0.743156 + 0.669118i \(0.766672\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.67918 0.319118
\(216\) 0 0
\(217\) 19.0526 1.29338
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −7.48578 12.9657i −0.503548 0.872170i
\(222\) 0 0
\(223\) 10.5391 18.2542i 0.705749 1.22239i −0.260671 0.965428i \(-0.583944\pi\)
0.966420 0.256966i \(-0.0827228\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.9946 + 25.9713i −0.995224 + 1.72378i −0.413069 + 0.910700i \(0.635543\pi\)
−0.582155 + 0.813078i \(0.697790\pi\)
\(228\) 0 0
\(229\) 9.53170 + 16.5094i 0.629873 + 1.09097i 0.987577 + 0.157136i \(0.0502262\pi\)
−0.357704 + 0.933835i \(0.616440\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.91098 −0.518266 −0.259133 0.965842i \(-0.583437\pi\)
−0.259133 + 0.965842i \(0.583437\pi\)
\(234\) 0 0
\(235\) −10.4312 −0.680457
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2.96685 5.13873i −0.191910 0.332397i 0.753973 0.656905i \(-0.228135\pi\)
−0.945883 + 0.324508i \(0.894801\pi\)
\(240\) 0 0
\(241\) −14.2494 + 24.6808i −0.917888 + 1.58983i −0.115270 + 0.993334i \(0.536773\pi\)
−0.802618 + 0.596494i \(0.796560\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.96425 + 3.40218i −0.125491 + 0.217357i
\(246\) 0 0
\(247\) −9.13607 15.8241i −0.581314 1.00687i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −15.6924 −0.990498 −0.495249 0.868751i \(-0.664923\pi\)
−0.495249 + 0.868751i \(0.664923\pi\)
\(252\) 0 0
\(253\) 12.1341 0.762866
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −11.5645 20.0304i −0.721377 1.24946i −0.960448 0.278459i \(-0.910176\pi\)
0.239071 0.971002i \(-0.423157\pi\)
\(258\) 0 0
\(259\) 0.116177 0.201225i 0.00721890 0.0125035i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −12.0737 + 20.9122i −0.744494 + 1.28950i 0.205937 + 0.978565i \(0.433976\pi\)
−0.950431 + 0.310936i \(0.899358\pi\)
\(264\) 0 0
\(265\) −3.54551 6.14100i −0.217799 0.377239i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 9.45599 0.576542 0.288271 0.957549i \(-0.406920\pi\)
0.288271 + 0.957549i \(0.406920\pi\)
\(270\) 0 0
\(271\) −15.5750 −0.946115 −0.473057 0.881032i \(-0.656850\pi\)
−0.473057 + 0.881032i \(0.656850\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 4.87526 + 8.44420i 0.293989 + 0.509205i
\(276\) 0 0
\(277\) 2.87862 4.98592i 0.172960 0.299575i −0.766494 0.642252i \(-0.778000\pi\)
0.939453 + 0.342677i \(0.111334\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5.99712 + 10.3873i −0.357758 + 0.619656i −0.987586 0.157079i \(-0.949792\pi\)
0.629828 + 0.776735i \(0.283126\pi\)
\(282\) 0 0
\(283\) −0.604018 1.04619i −0.0359051 0.0621895i 0.847514 0.530772i \(-0.178098\pi\)
−0.883420 + 0.468583i \(0.844765\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −10.6520 −0.628771
\(288\) 0 0
\(289\) 5.24075 0.308279
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 10.4657 + 18.1272i 0.611415 + 1.05900i 0.991002 + 0.133846i \(0.0427328\pi\)
−0.379587 + 0.925156i \(0.623934\pi\)
\(294\) 0 0
\(295\) 4.62878 8.01728i 0.269498 0.466784i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 7.47295 12.9435i 0.432172 0.748544i
\(300\) 0 0
\(301\) −6.89244 11.9381i −0.397274 0.688098i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −10.2866 −0.589011
\(306\) 0 0
\(307\) 5.12445 0.292468 0.146234 0.989250i \(-0.453285\pi\)
0.146234 + 0.989250i \(0.453285\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.70739 + 8.15344i 0.266931 + 0.462339i 0.968068 0.250688i \(-0.0806569\pi\)
−0.701136 + 0.713027i \(0.747324\pi\)
\(312\) 0 0
\(313\) −9.48986 + 16.4369i −0.536398 + 0.929069i 0.462696 + 0.886517i \(0.346882\pi\)
−0.999094 + 0.0425521i \(0.986451\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −14.2294 + 24.6461i −0.799205 + 1.38426i 0.120930 + 0.992661i \(0.461412\pi\)
−0.920135 + 0.391602i \(0.871921\pi\)
\(318\) 0 0
\(319\) 9.43965 + 16.3499i 0.528519 + 0.915421i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 27.1439 1.51033
\(324\) 0 0
\(325\) 12.0100 0.666193
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 15.3652 + 26.6133i 0.847110 + 1.46724i
\(330\) 0 0
\(331\) 0.837151 1.44999i 0.0460140 0.0796986i −0.842101 0.539320i \(-0.818681\pi\)
0.888115 + 0.459621i \(0.152015\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 6.72878 11.6546i 0.367633 0.636758i
\(336\) 0 0
\(337\) −15.1064 26.1651i −0.822899 1.42530i −0.903514 0.428558i \(-0.859022\pi\)
0.0806146 0.996745i \(-0.474312\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15.1104 0.818273
\(342\) 0 0
\(343\) −11.1753 −0.603408
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −8.46076 14.6545i −0.454197 0.786693i 0.544444 0.838797i \(-0.316741\pi\)
−0.998642 + 0.0521042i \(0.983407\pi\)
\(348\) 0 0
\(349\) 8.92436 15.4574i 0.477710 0.827418i −0.521964 0.852968i \(-0.674800\pi\)
0.999674 + 0.0255500i \(0.00813369\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6.93593 12.0134i 0.369162 0.639407i −0.620273 0.784386i \(-0.712978\pi\)
0.989435 + 0.144979i \(0.0463114\pi\)
\(354\) 0 0
\(355\) −0.185119 0.320636i −0.00982510 0.0170176i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.333139 0.0175824 0.00879120 0.999961i \(-0.497202\pi\)
0.00879120 + 0.999961i \(0.497202\pi\)
\(360\) 0 0
\(361\) 14.1280 0.743577
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −8.19974 14.2024i −0.429194 0.743386i
\(366\) 0 0
\(367\) 10.5763 18.3188i 0.552081 0.956232i −0.446043 0.895011i \(-0.647167\pi\)
0.998124 0.0612208i \(-0.0194994\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −10.4451 + 18.0914i −0.542281 + 0.939258i
\(372\) 0 0
\(373\) 4.33750 + 7.51278i 0.224587 + 0.388997i 0.956196 0.292729i \(-0.0945632\pi\)
−0.731608 + 0.681725i \(0.761230\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 23.2541 1.19765
\(378\) 0 0
\(379\) 14.2538 0.732168 0.366084 0.930582i \(-0.380698\pi\)
0.366084 + 0.930582i \(0.380698\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −5.11696 8.86283i −0.261464 0.452869i 0.705167 0.709041i \(-0.250872\pi\)
−0.966631 + 0.256172i \(0.917539\pi\)
\(384\) 0 0
\(385\) −4.61988 + 8.00187i −0.235451 + 0.407813i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.62675 + 2.81761i −0.0824793 + 0.142858i −0.904314 0.426867i \(-0.859617\pi\)
0.821835 + 0.569726i \(0.192951\pi\)
\(390\) 0 0
\(391\) 11.1013 + 19.2281i 0.561418 + 0.972405i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −10.7220 −0.539484
\(396\) 0 0
\(397\) −30.8709 −1.54936 −0.774682 0.632351i \(-0.782090\pi\)
−0.774682 + 0.632351i \(0.782090\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.01000 + 3.48143i 0.100375 + 0.173854i 0.911839 0.410548i \(-0.134662\pi\)
−0.811464 + 0.584402i \(0.801329\pi\)
\(402\) 0 0
\(403\) 9.30592 16.1183i 0.463561 0.802911i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.0921386 0.159589i 0.00456714 0.00791052i
\(408\) 0 0
\(409\) −3.33949 5.78416i −0.165127 0.286008i 0.771573 0.636140i \(-0.219470\pi\)
−0.936700 + 0.350132i \(0.886137\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −27.2728 −1.34201
\(414\) 0 0
\(415\) −6.77367 −0.332507
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −17.0507 29.5327i −0.832982 1.44277i −0.895663 0.444733i \(-0.853299\pi\)
0.0626815 0.998034i \(-0.480035\pi\)
\(420\) 0 0
\(421\) 9.34688 16.1893i 0.455539 0.789017i −0.543180 0.839616i \(-0.682780\pi\)
0.998719 + 0.0505996i \(0.0161132\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −8.92060 + 15.4509i −0.432713 + 0.749481i
\(426\) 0 0
\(427\) 15.1522 + 26.2444i 0.733267 + 1.27006i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.49967 0.313078 0.156539 0.987672i \(-0.449966\pi\)
0.156539 + 0.987672i \(0.449966\pi\)
\(432\) 0 0
\(433\) 28.3266 1.36129 0.680645 0.732613i \(-0.261700\pi\)
0.680645 + 0.732613i \(0.261700\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 13.5487 + 23.4670i 0.648122 + 1.12258i
\(438\) 0 0
\(439\) 3.82047 6.61724i 0.182341 0.315824i −0.760336 0.649530i \(-0.774966\pi\)
0.942677 + 0.333706i \(0.108299\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.94625 12.0313i 0.330026 0.571623i −0.652490 0.757797i \(-0.726276\pi\)
0.982517 + 0.186175i \(0.0596090\pi\)
\(444\) 0 0
\(445\) 2.44238 + 4.23033i 0.115780 + 0.200537i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −11.8869 −0.560976 −0.280488 0.959857i \(-0.590496\pi\)
−0.280488 + 0.959857i \(0.590496\pi\)
\(450\) 0 0
\(451\) −8.44800 −0.397801
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5.69042 + 9.85610i 0.266771 + 0.462061i
\(456\) 0 0
\(457\) 0.860741 1.49085i 0.0402638 0.0697389i −0.845191 0.534464i \(-0.820514\pi\)
0.885455 + 0.464725i \(0.153847\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15.8265 27.4123i 0.737113 1.27672i −0.216677 0.976243i \(-0.569522\pi\)
0.953790 0.300474i \(-0.0971447\pi\)
\(462\) 0 0
\(463\) 1.71702 + 2.97396i 0.0797966 + 0.138212i 0.903162 0.429300i \(-0.141240\pi\)
−0.823366 + 0.567511i \(0.807906\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15.5333 0.718797 0.359398 0.933184i \(-0.382982\pi\)
0.359398 + 0.933184i \(0.382982\pi\)
\(468\) 0 0
\(469\) −39.6460 −1.83068
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.46631 9.46792i −0.251341 0.435335i
\(474\) 0 0
\(475\) −10.8872 + 18.8572i −0.499540 + 0.865228i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 16.6927 28.9126i 0.762710 1.32105i −0.178739 0.983897i \(-0.557202\pi\)
0.941449 0.337156i \(-0.109465\pi\)
\(480\) 0 0
\(481\) −0.113489 0.196569i −0.00517467 0.00896280i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −14.1080 −0.640612
\(486\) 0 0
\(487\) −20.0794 −0.909883 −0.454941 0.890521i \(-0.650340\pi\)
−0.454941 + 0.890521i \(0.650340\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.10538 + 3.64663i 0.0950146 + 0.164570i 0.909615 0.415453i \(-0.136377\pi\)
−0.814600 + 0.580023i \(0.803044\pi\)
\(492\) 0 0
\(493\) −17.2724 + 29.9166i −0.777908 + 1.34738i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.545361 + 0.944593i −0.0244628 + 0.0423708i
\(498\) 0 0
\(499\) −5.24770 9.08928i −0.234919 0.406892i 0.724330 0.689453i \(-0.242149\pi\)
−0.959249 + 0.282561i \(0.908816\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 34.5118 1.53881 0.769403 0.638764i \(-0.220554\pi\)
0.769403 + 0.638764i \(0.220554\pi\)
\(504\) 0 0
\(505\) 8.38677 0.373206
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.62702 + 4.55013i 0.116440 + 0.201681i 0.918355 0.395758i \(-0.129518\pi\)
−0.801914 + 0.597439i \(0.796185\pi\)
\(510\) 0 0
\(511\) −24.1564 + 41.8402i −1.06862 + 1.85090i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.20497 10.7473i 0.273424 0.473584i
\(516\) 0 0
\(517\) 12.1859 + 21.1066i 0.535937 + 0.928269i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 12.9218 0.566113 0.283056 0.959103i \(-0.408652\pi\)
0.283056 + 0.959103i \(0.408652\pi\)
\(522\) 0 0
\(523\) 5.10475 0.223215 0.111607 0.993752i \(-0.464400\pi\)
0.111607 + 0.993752i \(0.464400\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 13.8243 + 23.9443i 0.602194 + 1.04303i
\(528\) 0 0
\(529\) 0.417694 0.723468i 0.0181606 0.0314551i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −5.20281 + 9.01153i −0.225359 + 0.390333i
\(534\) 0 0
\(535\) −1.55261 2.68920i −0.0671252 0.116264i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 9.17869 0.395354
\(540\) 0 0
\(541\) −37.9746 −1.63266 −0.816328 0.577589i \(-0.803994\pi\)
−0.816328 + 0.577589i \(0.803994\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 8.63410 + 14.9547i 0.369844 + 0.640589i
\(546\) 0 0
\(547\) 15.9350 27.6003i 0.681332 1.18010i −0.293243 0.956038i \(-0.594734\pi\)
0.974575 0.224063i \(-0.0719323\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −21.0802 + 36.5120i −0.898046 + 1.55546i
\(552\) 0 0
\(553\) 15.7936 + 27.3553i 0.671611 + 1.16326i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11.5906 0.491111 0.245555 0.969383i \(-0.421030\pi\)
0.245555 + 0.969383i \(0.421030\pi\)
\(558\) 0 0
\(559\) −13.4660 −0.569550
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.25138 2.16745i −0.0527392 0.0913470i 0.838451 0.544978i \(-0.183462\pi\)
−0.891190 + 0.453631i \(0.850129\pi\)
\(564\) 0 0
\(565\) −11.2328 + 19.4559i −0.472569 + 0.818514i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −12.9597 + 22.4469i −0.543301 + 0.941024i 0.455411 + 0.890281i \(0.349492\pi\)
−0.998712 + 0.0507432i \(0.983841\pi\)
\(570\) 0 0
\(571\) 5.03679 + 8.72398i 0.210783 + 0.365087i 0.951960 0.306223i \(-0.0990653\pi\)
−0.741177 + 0.671310i \(0.765732\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −17.8106 −0.742755
\(576\) 0 0
\(577\) −23.4726 −0.977177 −0.488588 0.872514i \(-0.662488\pi\)
−0.488588 + 0.872514i \(0.662488\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 9.97762 + 17.2818i 0.413942 + 0.716968i
\(582\) 0 0
\(583\) −8.28385 + 14.3481i −0.343082 + 0.594236i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.4138 21.5012i 0.512370 0.887451i −0.487527 0.873108i \(-0.662101\pi\)
0.999897 0.0143435i \(-0.00456582\pi\)
\(588\) 0 0
\(589\) 16.8719 + 29.2230i 0.695195 + 1.20411i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.70977 0.316602 0.158301 0.987391i \(-0.449398\pi\)
0.158301 + 0.987391i \(0.449398\pi\)
\(594\) 0 0
\(595\) −16.9066 −0.693104
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −14.7176 25.4916i −0.601344 1.04156i −0.992618 0.121284i \(-0.961299\pi\)
0.391274 0.920274i \(-0.372035\pi\)
\(600\) 0 0
\(601\) −1.76388 + 3.05514i −0.0719503 + 0.124622i −0.899756 0.436393i \(-0.856256\pi\)
0.827806 + 0.561015i \(0.189589\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.40322 4.16250i 0.0977047 0.169230i
\(606\) 0 0
\(607\) 13.3211 + 23.0728i 0.540687 + 0.936497i 0.998865 + 0.0476362i \(0.0151688\pi\)
−0.458178 + 0.888860i \(0.651498\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 30.0194 1.21446
\(612\) 0 0
\(613\) 0.706406 0.0285315 0.0142657 0.999898i \(-0.495459\pi\)
0.0142657 + 0.999898i \(0.495459\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8.58480 14.8693i −0.345611 0.598616i 0.639853 0.768497i \(-0.278995\pi\)
−0.985465 + 0.169881i \(0.945662\pi\)
\(618\) 0 0
\(619\) 4.17800 7.23651i 0.167928 0.290860i −0.769763 0.638330i \(-0.779626\pi\)
0.937691 + 0.347470i \(0.112959\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7.19526 12.4626i 0.288272 0.499302i
\(624\) 0 0
\(625\) −4.11377 7.12526i −0.164551 0.285010i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.337185 0.0134444
\(630\) 0 0
\(631\) −23.9865 −0.954889 −0.477444 0.878662i \(-0.658437\pi\)
−0.477444 + 0.878662i \(0.658437\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.70923 2.96047i −0.0678286 0.117483i
\(636\) 0 0
\(637\) 5.65281 9.79095i 0.223972 0.387932i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −6.58068 + 11.3981i −0.259921 + 0.450197i −0.966221 0.257716i \(-0.917030\pi\)
0.706299 + 0.707913i \(0.250363\pi\)
\(642\) 0 0
\(643\) −7.85931 13.6127i −0.309941 0.536834i 0.668408 0.743795i \(-0.266976\pi\)
−0.978349 + 0.206961i \(0.933643\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −23.5146 −0.924455 −0.462228 0.886761i \(-0.652950\pi\)
−0.462228 + 0.886761i \(0.652950\pi\)
\(648\) 0 0
\(649\) −21.6297 −0.849040
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.1340 + 22.7487i 0.513971 + 0.890224i 0.999869 + 0.0162084i \(0.00515952\pi\)
−0.485897 + 0.874016i \(0.661507\pi\)
\(654\) 0 0
\(655\) −0.276979 + 0.479741i −0.0108224 + 0.0187450i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13.2710 22.9860i 0.516963 0.895406i −0.482843 0.875707i \(-0.660396\pi\)
0.999806 0.0196993i \(-0.00627088\pi\)
\(660\) 0 0
\(661\) 0.981745 + 1.70043i 0.0381855 + 0.0661392i 0.884487 0.466566i \(-0.154509\pi\)
−0.846301 + 0.532705i \(0.821176\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −20.6338 −0.800145
\(666\) 0 0
\(667\) −34.4856 −1.33529
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 12.0170 + 20.8141i 0.463912 + 0.803519i
\(672\) 0 0
\(673\) −18.9859 + 32.8846i −0.731854 + 1.26761i 0.224236 + 0.974535i \(0.428011\pi\)
−0.956090 + 0.293073i \(0.905322\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 13.5894 23.5375i 0.522282 0.904619i −0.477382 0.878696i \(-0.658414\pi\)
0.999664 0.0259229i \(-0.00825242\pi\)
\(678\) 0 0
\(679\) 20.7811 + 35.9939i 0.797505 + 1.38132i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −46.9121 −1.79504 −0.897520 0.440974i \(-0.854633\pi\)
−0.897520 + 0.440974i \(0.854633\pi\)
\(684\) 0 0
\(685\) −10.7857 −0.412099
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 10.2034 + 17.6728i 0.388719 + 0.673282i
\(690\) 0 0
\(691\) 12.6750 21.9538i 0.482181 0.835161i −0.517610 0.855617i \(-0.673178\pi\)
0.999791 + 0.0204552i \(0.00651153\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.207937 + 0.360157i −0.00788750 + 0.0136616i
\(696\) 0 0
\(697\) −7.72895 13.3869i −0.292755 0.507066i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 44.2840 1.67258 0.836292 0.548284i \(-0.184719\pi\)
0.836292 + 0.548284i \(0.184719\pi\)
\(702\) 0 0
\(703\) 0.411520 0.0155208
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12.3537 21.3973i −0.464609 0.804727i
\(708\) 0 0
\(709\) −7.80457 + 13.5179i −0.293107 + 0.507676i −0.974543 0.224202i \(-0.928022\pi\)
0.681436 + 0.731878i \(0.261356\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −13.8006 + 23.9033i −0.516836 + 0.895185i
\(714\) 0 0
\(715\) 4.51300 + 7.81675i 0.168777 + 0.292330i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 21.1560 0.788985 0.394493 0.918899i \(-0.370920\pi\)
0.394493 + 0.918899i \(0.370920\pi\)
\(720\) 0 0
\(721\) −36.5597 −1.36155
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −13.8556 23.9987i −0.514586 0.891289i
\(726\) 0 0
\(727\) 12.9909 22.5009i 0.481805 0.834511i −0.517977 0.855395i \(-0.673315\pi\)
0.999782 + 0.0208834i \(0.00664789\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 10.0021 17.3241i 0.369940 0.640755i
\(732\) 0 0
\(733\) −5.41447 9.37814i −0.199988 0.346390i 0.748536 0.663094i \(-0.230757\pi\)
−0.948524 + 0.316704i \(0.897424\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −31.4427 −1.15821
\(738\) 0 0
\(739\) 11.4520 0.421270 0.210635 0.977565i \(-0.432447\pi\)
0.210635 + 0.977565i \(0.432447\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0077 + 41.5826i 0.880758 + 1.52552i 0.850500 + 0.525975i \(0.176299\pi\)
0.0302573 + 0.999542i \(0.490367\pi\)
\(744\) 0 0
\(745\) −5.33595 + 9.24213i −0.195494 + 0.338605i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4.57399 + 7.92239i −0.167130 + 0.289478i
\(750\) 0 0
\(751\) −22.5881 39.1238i −0.824253 1.42765i −0.902489 0.430713i \(-0.858262\pi\)
0.0782360 0.996935i \(-0.475071\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −18.5968 −0.676807
\(756\) 0 0
\(757\) −16.5457 −0.601365 −0.300682 0.953724i \(-0.597214\pi\)
−0.300682 + 0.953724i \(0.597214\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 20.6826 + 35.8234i 0.749745 + 1.29860i 0.947945 + 0.318435i \(0.103157\pi\)
−0.198200 + 0.980162i \(0.563509\pi\)
\(762\) 0 0
\(763\) 25.4361 44.0565i 0.920847 1.59495i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −13.3209 + 23.0725i −0.480990 + 0.833100i
\(768\) 0 0
\(769\) −3.22518 5.58617i −0.116303 0.201443i 0.801997 0.597328i \(-0.203771\pi\)
−0.918300 + 0.395886i \(0.870438\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −0.949001 −0.0341332 −0.0170666 0.999854i \(-0.505433\pi\)
−0.0170666 + 0.999854i \(0.505433\pi\)
\(774\) 0 0
\(775\) −22.1792 −0.796702
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9.43285 16.3382i −0.337967 0.585376i
\(780\) 0 0
\(781\) −0.432519 + 0.749145i −0.0154767 + 0.0268065i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.81251 + 8.33552i −0.171766 + 0.297507i
\(786\) 0 0
\(787\) 17.6992 + 30.6559i 0.630909 + 1.09277i 0.987366 + 0.158454i \(0.0506511\pi\)
−0.356458 + 0.934312i \(0.616016\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 66.1840 2.35323
\(792\) 0 0
\(793\) 29.6033 1.05125
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.42624 2.47032i −0.0505200 0.0875032i 0.839660 0.543113i \(-0.182755\pi\)
−0.890180 + 0.455610i \(0.849421\pi\)
\(798\) 0 0
\(799\) −22.2974 + 38.6203i −0.788826 + 1.36629i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −19.1582 + 33.1829i −0.676077 + 1.17100i
\(804\) 0 0 <