Properties

Label 1152.2.w.a.1007.7
Level $1152$
Weight $2$
Character 1152.1007
Analytic conductor $9.199$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.w (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 1007.7
Character \(\chi\) \(=\) 1152.1007
Dual form 1152.2.w.a.143.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.12344 + 2.71222i) q^{5} +(-3.03150 - 3.03150i) q^{7} +O(q^{10})\) \(q+(1.12344 + 2.71222i) q^{5} +(-3.03150 - 3.03150i) q^{7} +(0.616847 + 1.48920i) q^{11} +(3.35133 + 1.38816i) q^{13} -4.76709 q^{17} +(-1.13264 + 2.73444i) q^{19} +(4.11192 + 4.11192i) q^{23} +(-2.55851 + 2.55851i) q^{25} +(8.16664 + 3.38273i) q^{29} +6.16305i q^{31} +(4.81640 - 11.6278i) q^{35} +(-9.38963 + 3.88931i) q^{37} +(0.169917 - 0.169917i) q^{41} +(-7.57687 + 3.13844i) q^{43} +2.44049i q^{47} +11.3800i q^{49} +(-1.99073 + 0.824586i) q^{53} +(-3.34605 + 3.34605i) q^{55} +(1.21488 - 0.503218i) q^{59} +(1.04489 - 2.52258i) q^{61} +10.6491i q^{65} +(-3.91551 - 1.62186i) q^{67} +(-5.28919 + 5.28919i) q^{71} +(-1.57482 - 1.57482i) q^{73} +(2.64454 - 6.38449i) q^{77} +13.7711 q^{79} +(3.31934 + 1.37492i) q^{83} +(-5.35554 - 12.9294i) q^{85} +(-6.99010 - 6.99010i) q^{89} +(-5.95133 - 14.3678i) q^{91} -8.68886 q^{95} -13.5584 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{7}{8}\right)\)

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
\(5\) 1.12344 + 2.71222i 0.502418 + 1.21294i 0.948163 + 0.317784i \(0.102939\pi\)
−0.445745 + 0.895160i \(0.647061\pi\)
\(6\) 0 0
\(7\) −3.03150 3.03150i −1.14580 1.14580i −0.987370 0.158430i \(-0.949357\pi\)
−0.158430 0.987370i \(-0.550643\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.616847 + 1.48920i 0.185986 + 0.449011i 0.989180 0.146707i \(-0.0468676\pi\)
−0.803194 + 0.595718i \(0.796868\pi\)
\(12\) 0 0
\(13\) 3.35133 + 1.38816i 0.929490 + 0.385008i 0.795485 0.605973i \(-0.207216\pi\)
0.134005 + 0.990981i \(0.457216\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.76709 −1.15619 −0.578094 0.815970i \(-0.696203\pi\)
−0.578094 + 0.815970i \(0.696203\pi\)
\(18\) 0 0
\(19\) −1.13264 + 2.73444i −0.259846 + 0.627323i −0.998928 0.0462921i \(-0.985259\pi\)
0.739082 + 0.673615i \(0.235259\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.11192 + 4.11192i 0.857395 + 0.857395i 0.991031 0.133636i \(-0.0426652\pi\)
−0.133636 + 0.991031i \(0.542665\pi\)
\(24\) 0 0
\(25\) −2.55851 + 2.55851i −0.511702 + 0.511702i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8.16664 + 3.38273i 1.51651 + 0.628158i 0.976888 0.213751i \(-0.0685681\pi\)
0.539620 + 0.841909i \(0.318568\pi\)
\(30\) 0 0
\(31\) 6.16305i 1.10692i 0.832877 + 0.553458i \(0.186692\pi\)
−0.832877 + 0.553458i \(0.813308\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.81640 11.6278i 0.814121 1.96546i
\(36\) 0 0
\(37\) −9.38963 + 3.88931i −1.54365 + 0.639399i −0.982153 0.188083i \(-0.939773\pi\)
−0.561493 + 0.827482i \(0.689773\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.169917 0.169917i 0.0265365 0.0265365i −0.693714 0.720251i \(-0.744027\pi\)
0.720251 + 0.693714i \(0.244027\pi\)
\(42\) 0 0
\(43\) −7.57687 + 3.13844i −1.15546 + 0.478608i −0.876361 0.481654i \(-0.840036\pi\)
−0.279100 + 0.960262i \(0.590036\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.44049i 0.355981i 0.984032 + 0.177991i \(0.0569597\pi\)
−0.984032 + 0.177991i \(0.943040\pi\)
\(48\) 0 0
\(49\) 11.3800i 1.62572i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.99073 + 0.824586i −0.273447 + 0.113266i −0.515193 0.857074i \(-0.672280\pi\)
0.241746 + 0.970340i \(0.422280\pi\)
\(54\) 0 0
\(55\) −3.34605 + 3.34605i −0.451182 + 0.451182i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.21488 0.503218i 0.158163 0.0655134i −0.302197 0.953245i \(-0.597720\pi\)
0.460361 + 0.887732i \(0.347720\pi\)
\(60\) 0 0
\(61\) 1.04489 2.52258i 0.133784 0.322983i −0.842764 0.538283i \(-0.819073\pi\)
0.976548 + 0.215300i \(0.0690731\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.6491i 1.32085i
\(66\) 0 0
\(67\) −3.91551 1.62186i −0.478355 0.198141i 0.130459 0.991454i \(-0.458355\pi\)
−0.608815 + 0.793312i \(0.708355\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −5.28919 + 5.28919i −0.627711 + 0.627711i −0.947492 0.319781i \(-0.896391\pi\)
0.319781 + 0.947492i \(0.396391\pi\)
\(72\) 0 0
\(73\) −1.57482 1.57482i −0.184319 0.184319i 0.608916 0.793235i \(-0.291605\pi\)
−0.793235 + 0.608916i \(0.791605\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.64454 6.38449i 0.301373 0.727580i
\(78\) 0 0
\(79\) 13.7711 1.54937 0.774684 0.632348i \(-0.217909\pi\)
0.774684 + 0.632348i \(0.217909\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.31934 + 1.37492i 0.364345 + 0.150917i 0.557343 0.830282i \(-0.311821\pi\)
−0.192997 + 0.981199i \(0.561821\pi\)
\(84\) 0 0
\(85\) −5.35554 12.9294i −0.580890 1.40239i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.99010 6.99010i −0.740949 0.740949i 0.231811 0.972761i \(-0.425535\pi\)
−0.972761 + 0.231811i \(0.925535\pi\)
\(90\) 0 0
\(91\) −5.95133 14.3678i −0.623869 1.50615i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8.68886 −0.891459
\(96\) 0 0
\(97\) −13.5584 −1.37665 −0.688323 0.725404i \(-0.741653\pi\)
−0.688323 + 0.725404i \(0.741653\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.10479 + 2.66720i 0.109931 + 0.265396i 0.969265 0.246018i \(-0.0791221\pi\)
−0.859335 + 0.511413i \(0.829122\pi\)
\(102\) 0 0
\(103\) 12.8009 + 12.8009i 1.26131 + 1.26131i 0.950459 + 0.310851i \(0.100614\pi\)
0.310851 + 0.950459i \(0.399386\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.720677 1.73987i −0.0696704 0.168199i 0.885209 0.465194i \(-0.154016\pi\)
−0.954879 + 0.296995i \(0.904016\pi\)
\(108\) 0 0
\(109\) 4.45017 + 1.84332i 0.426249 + 0.176558i 0.585486 0.810682i \(-0.300904\pi\)
−0.159238 + 0.987240i \(0.550904\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 13.6612 1.28514 0.642568 0.766229i \(-0.277869\pi\)
0.642568 + 0.766229i \(0.277869\pi\)
\(114\) 0 0
\(115\) −6.53296 + 15.7720i −0.609201 + 1.47074i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 14.4514 + 14.4514i 1.32476 + 1.32476i
\(120\) 0 0
\(121\) 5.94096 5.94096i 0.540087 0.540087i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.74754 + 1.55228i 0.335190 + 0.138840i
\(126\) 0 0
\(127\) 13.2014i 1.17143i −0.810515 0.585717i \(-0.800813\pi\)
0.810515 0.585717i \(-0.199187\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.56553 + 6.19375i −0.224152 + 0.541150i −0.995446 0.0953287i \(-0.969610\pi\)
0.771294 + 0.636479i \(0.219610\pi\)
\(132\) 0 0
\(133\) 11.7231 4.85585i 1.01652 0.421056i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.77333 + 9.77333i −0.834992 + 0.834992i −0.988195 0.153203i \(-0.951041\pi\)
0.153203 + 0.988195i \(0.451041\pi\)
\(138\) 0 0
\(139\) 8.26616 3.42396i 0.701127 0.290416i −0.00350050 0.999994i \(-0.501114\pi\)
0.704627 + 0.709578i \(0.251114\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 5.84708i 0.488957i
\(144\) 0 0
\(145\) 25.9501i 2.15504i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 18.9803 7.86190i 1.55493 0.644072i 0.570729 0.821139i \(-0.306661\pi\)
0.984199 + 0.177066i \(0.0566607\pi\)
\(150\) 0 0
\(151\) −7.83326 + 7.83326i −0.637462 + 0.637462i −0.949929 0.312467i \(-0.898845\pi\)
0.312467 + 0.949929i \(0.398845\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −16.7156 + 6.92381i −1.34263 + 0.556134i
\(156\) 0 0
\(157\) 3.58014 8.64323i 0.285727 0.689805i −0.714222 0.699919i \(-0.753219\pi\)
0.999949 + 0.0101140i \(0.00321944\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 24.9306i 1.96481i
\(162\) 0 0
\(163\) 4.73693 + 1.96210i 0.371025 + 0.153684i 0.560402 0.828221i \(-0.310647\pi\)
−0.189377 + 0.981904i \(0.560647\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.55199 + 4.55199i −0.352244 + 0.352244i −0.860944 0.508700i \(-0.830126\pi\)
0.508700 + 0.860944i \(0.330126\pi\)
\(168\) 0 0
\(169\) 0.111994 + 0.111994i 0.00861490 + 0.00861490i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.28444 10.3436i 0.325740 0.786406i −0.673159 0.739498i \(-0.735063\pi\)
0.998899 0.0469083i \(-0.0149368\pi\)
\(174\) 0 0
\(175\) 15.5123 1.17262
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 10.2246 + 4.23519i 0.764226 + 0.316553i 0.730531 0.682880i \(-0.239273\pi\)
0.0336946 + 0.999432i \(0.489273\pi\)
\(180\) 0 0
\(181\) −1.33358 3.21956i −0.0991246 0.239308i 0.866536 0.499114i \(-0.166341\pi\)
−0.965661 + 0.259806i \(0.916341\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −21.0974 21.0974i −1.55111 1.55111i
\(186\) 0 0
\(187\) −2.94056 7.09915i −0.215035 0.519141i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.82446 0.349085 0.174543 0.984650i \(-0.444155\pi\)
0.174543 + 0.984650i \(0.444155\pi\)
\(192\) 0 0
\(193\) 0.222878 0.0160431 0.00802155 0.999968i \(-0.497447\pi\)
0.00802155 + 0.999968i \(0.497447\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.44160 + 22.7940i 0.672686 + 1.62401i 0.777028 + 0.629467i \(0.216727\pi\)
−0.104341 + 0.994542i \(0.533273\pi\)
\(198\) 0 0
\(199\) −14.8710 14.8710i −1.05418 1.05418i −0.998446 0.0557310i \(-0.982251\pi\)
−0.0557310 0.998446i \(-0.517749\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −14.5024 35.0120i −1.01787 2.45736i
\(204\) 0 0
\(205\) 0.651743 + 0.269961i 0.0455197 + 0.0188549i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4.77079 −0.330003
\(210\) 0 0
\(211\) 0.644000 1.55475i 0.0443348 0.107034i −0.900161 0.435558i \(-0.856551\pi\)
0.944496 + 0.328524i \(0.106551\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −17.0243 17.0243i −1.16105 1.16105i
\(216\) 0 0
\(217\) 18.6833 18.6833i 1.26830 1.26830i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −15.9761 6.61750i −1.07467 0.445141i
\(222\) 0 0
\(223\) 23.4280i 1.56885i −0.620221 0.784427i \(-0.712957\pi\)
0.620221 0.784427i \(-0.287043\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.10690 12.3292i 0.338957 0.818315i −0.658859 0.752266i \(-0.728961\pi\)
0.997816 0.0660486i \(-0.0210392\pi\)
\(228\) 0 0
\(229\) −7.82666 + 3.24191i −0.517200 + 0.214231i −0.625987 0.779834i \(-0.715304\pi\)
0.108786 + 0.994065i \(0.465304\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.66805 + 9.66805i −0.633375 + 0.633375i −0.948913 0.315538i \(-0.897815\pi\)
0.315538 + 0.948913i \(0.397815\pi\)
\(234\) 0 0
\(235\) −6.61915 + 2.74174i −0.431785 + 0.178851i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 25.8579i 1.67261i −0.548268 0.836303i \(-0.684713\pi\)
0.548268 0.836303i \(-0.315287\pi\)
\(240\) 0 0
\(241\) 24.9358i 1.60626i −0.595805 0.803129i \(-0.703167\pi\)
0.595805 0.803129i \(-0.296833\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −30.8652 + 12.7848i −1.97190 + 0.816789i
\(246\) 0 0
\(247\) −7.59170 + 7.59170i −0.483048 + 0.483048i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 11.5486 4.78358i 0.728939 0.301937i 0.0128233 0.999918i \(-0.495918\pi\)
0.716116 + 0.697981i \(0.245918\pi\)
\(252\) 0 0
\(253\) −3.58705 + 8.65990i −0.225516 + 0.544443i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 17.0780i 1.06530i 0.846337 + 0.532648i \(0.178803\pi\)
−0.846337 + 0.532648i \(0.821197\pi\)
\(258\) 0 0
\(259\) 40.2552 + 16.6742i 2.50133 + 1.03609i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −10.4595 + 10.4595i −0.644963 + 0.644963i −0.951771 0.306809i \(-0.900739\pi\)
0.306809 + 0.951771i \(0.400739\pi\)
\(264\) 0 0
\(265\) −4.47292 4.47292i −0.274770 0.274770i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.47587 8.39150i 0.211928 0.511639i −0.781792 0.623540i \(-0.785694\pi\)
0.993719 + 0.111901i \(0.0356939\pi\)
\(270\) 0 0
\(271\) 5.66173 0.343925 0.171963 0.985103i \(-0.444989\pi\)
0.171963 + 0.985103i \(0.444989\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.38834 2.23192i −0.324929 0.134590i
\(276\) 0 0
\(277\) −5.27625 12.7380i −0.317019 0.765352i −0.999409 0.0343637i \(-0.989060\pi\)
0.682390 0.730988i \(-0.260940\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.75892 + 5.75892i 0.343548 + 0.343548i 0.857700 0.514151i \(-0.171893\pi\)
−0.514151 + 0.857700i \(0.671893\pi\)
\(282\) 0 0
\(283\) −10.4136 25.1407i −0.619025 1.49446i −0.852837 0.522177i \(-0.825120\pi\)
0.233812 0.972282i \(-0.424880\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.03021 −0.0608111
\(288\) 0 0
\(289\) 5.72512 0.336772
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5.21345 12.5864i −0.304573 0.735304i −0.999863 0.0165743i \(-0.994724\pi\)
0.695290 0.718729i \(-0.255276\pi\)
\(294\) 0 0
\(295\) 2.72968 + 2.72968i 0.158928 + 0.158928i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 8.07236 + 19.4884i 0.466837 + 1.12704i
\(300\) 0 0
\(301\) 32.4835 + 13.4551i 1.87232 + 0.775539i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.01566 0.458975
\(306\) 0 0
\(307\) 8.98052 21.6809i 0.512545 1.23739i −0.429852 0.902899i \(-0.641434\pi\)
0.942398 0.334495i \(-0.108566\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 12.7177 + 12.7177i 0.721157 + 0.721157i 0.968841 0.247684i \(-0.0796695\pi\)
−0.247684 + 0.968841i \(0.579670\pi\)
\(312\) 0 0
\(313\) 10.1388 10.1388i 0.573081 0.573081i −0.359907 0.932988i \(-0.617192\pi\)
0.932988 + 0.359907i \(0.117192\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.52668 1.04659i −0.141913 0.0587822i 0.310597 0.950542i \(-0.399471\pi\)
−0.452509 + 0.891760i \(0.649471\pi\)
\(318\) 0 0
\(319\) 14.2484i 0.797757i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5.39940 13.0353i 0.300431 0.725304i
\(324\) 0 0
\(325\) −12.1260 + 5.02277i −0.672631 + 0.278613i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7.39834 7.39834i 0.407884 0.407884i
\(330\) 0 0
\(331\) 5.49794 2.27732i 0.302194 0.125173i −0.226434 0.974027i \(-0.572707\pi\)
0.528628 + 0.848854i \(0.322707\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 12.4418i 0.679768i
\(336\) 0 0
\(337\) 5.85273i 0.318818i 0.987213 + 0.159409i \(0.0509589\pi\)
−0.987213 + 0.159409i \(0.949041\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −9.17801 + 3.80166i −0.497017 + 0.205871i
\(342\) 0 0
\(343\) 13.2780 13.2780i 0.716946 0.716946i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −7.23994 + 2.99888i −0.388660 + 0.160988i −0.568452 0.822716i \(-0.692458\pi\)
0.179792 + 0.983705i \(0.442458\pi\)
\(348\) 0 0
\(349\) −4.01973 + 9.70449i −0.215171 + 0.519469i −0.994204 0.107515i \(-0.965711\pi\)
0.779032 + 0.626984i \(0.215711\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 16.6657i 0.887026i 0.896268 + 0.443513i \(0.146268\pi\)
−0.896268 + 0.443513i \(0.853732\pi\)
\(354\) 0 0
\(355\) −20.2875 8.40338i −1.07675 0.446005i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.54649 9.54649i 0.503845 0.503845i −0.408786 0.912630i \(-0.634048\pi\)
0.912630 + 0.408786i \(0.134048\pi\)
\(360\) 0 0
\(361\) 7.24075 + 7.24075i 0.381092 + 0.381092i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.50205 6.04049i 0.130963 0.316173i
\(366\) 0 0
\(367\) 6.31072 0.329417 0.164708 0.986342i \(-0.447332\pi\)
0.164708 + 0.986342i \(0.447332\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.53463 + 3.53516i 0.443096 + 0.183536i
\(372\) 0 0
\(373\) −3.06259 7.39375i −0.158575 0.382834i 0.824545 0.565797i \(-0.191431\pi\)
−0.983120 + 0.182963i \(0.941431\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 22.6733 + 22.6733i 1.16773 + 1.16773i
\(378\) 0 0
\(379\) 8.31838 + 20.0823i 0.427286 + 1.03156i 0.980144 + 0.198285i \(0.0635372\pi\)
−0.552858 + 0.833275i \(0.686463\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −7.95308 −0.406383 −0.203192 0.979139i \(-0.565131\pi\)
−0.203192 + 0.979139i \(0.565131\pi\)
\(384\) 0 0
\(385\) 20.2871 1.03393
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.38215 + 5.75102i 0.120780 + 0.291588i 0.972693 0.232094i \(-0.0745578\pi\)
−0.851913 + 0.523683i \(0.824558\pi\)
\(390\) 0 0
\(391\) −19.6019 19.6019i −0.991310 0.991310i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 15.4710 + 37.3503i 0.778430 + 1.87930i
\(396\) 0 0
\(397\) 25.3118 + 10.4845i 1.27036 + 0.526202i 0.913075 0.407792i \(-0.133701\pi\)
0.357288 + 0.933994i \(0.383701\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.81017 0.0903954 0.0451977 0.998978i \(-0.485608\pi\)
0.0451977 + 0.998978i \(0.485608\pi\)
\(402\) 0 0
\(403\) −8.55532 + 20.6544i −0.426171 + 1.02887i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −11.5839 11.5839i −0.574194 0.574194i
\(408\) 0 0
\(409\) −14.4331 + 14.4331i −0.713672 + 0.713672i −0.967301 0.253630i \(-0.918376\pi\)
0.253630 + 0.967301i \(0.418376\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −5.20841 2.15739i −0.256289 0.106158i
\(414\) 0 0
\(415\) 10.5474i 0.517754i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.33902 + 3.23269i −0.0654155 + 0.157927i −0.953207 0.302320i \(-0.902239\pi\)
0.887791 + 0.460247i \(0.152239\pi\)
\(420\) 0 0
\(421\) −10.5557 + 4.37232i −0.514454 + 0.213094i −0.624779 0.780802i \(-0.714811\pi\)
0.110325 + 0.993896i \(0.464811\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 12.1966 12.1966i 0.591624 0.591624i
\(426\) 0 0
\(427\) −10.8148 + 4.47963i −0.523364 + 0.216784i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.31967i 0.159903i −0.996799 0.0799513i \(-0.974524\pi\)
0.996799 0.0799513i \(-0.0254765\pi\)
\(432\) 0 0
\(433\) 4.53298i 0.217841i −0.994050 0.108921i \(-0.965261\pi\)
0.994050 0.108921i \(-0.0347394\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −15.9011 + 6.58646i −0.760654 + 0.315073i
\(438\) 0 0
\(439\) −20.9703 + 20.9703i −1.00086 + 1.00086i −0.000858061 1.00000i \(0.500273\pi\)
−1.00000 0.000858061i \(0.999727\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −31.9708 + 13.2427i −1.51898 + 0.629181i −0.977386 0.211462i \(-0.932178\pi\)
−0.541590 + 0.840643i \(0.682178\pi\)
\(444\) 0 0
\(445\) 11.1058 26.8117i 0.526464 1.27100i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 21.0485i 0.993340i −0.867940 0.496670i \(-0.834556\pi\)
0.867940 0.496670i \(-0.165444\pi\)
\(450\) 0 0
\(451\) 0.357852 + 0.148227i 0.0168506 + 0.00697975i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 32.2827 32.2827i 1.51344 1.51344i
\(456\) 0 0
\(457\) −4.62656 4.62656i −0.216421 0.216421i 0.590567 0.806988i \(-0.298904\pi\)
−0.806988 + 0.590567i \(0.798904\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.84388 + 11.6942i −0.225602 + 0.544652i −0.995633 0.0933550i \(-0.970241\pi\)
0.770031 + 0.638007i \(0.220241\pi\)
\(462\) 0 0
\(463\) −14.2219 −0.660950 −0.330475 0.943815i \(-0.607209\pi\)
−0.330475 + 0.943815i \(0.607209\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −34.5241 14.3003i −1.59758 0.661741i −0.606512 0.795074i \(-0.707432\pi\)
−0.991071 + 0.133333i \(0.957432\pi\)
\(468\) 0 0
\(469\) 6.95321 + 16.7865i 0.321069 + 0.775130i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −9.34754 9.34754i −0.429800 0.429800i
\(474\) 0 0
\(475\) −4.09821 9.89396i −0.188039 0.453966i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 13.4016 0.612333 0.306167 0.951978i \(-0.400954\pi\)
0.306167 + 0.951978i \(0.400954\pi\)
\(480\) 0 0
\(481\) −36.8667 −1.68098
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −15.2320 36.7734i −0.691652 1.66979i
\(486\) 0 0
\(487\) −1.26750 1.26750i −0.0574358 0.0574358i 0.677805 0.735241i \(-0.262931\pi\)
−0.735241 + 0.677805i \(0.762931\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8.81902 + 21.2910i 0.397997 + 0.960849i 0.988141 + 0.153551i \(0.0490710\pi\)
−0.590144 + 0.807298i \(0.700929\pi\)
\(492\) 0 0
\(493\) −38.9311 16.1258i −1.75337 0.726269i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 32.0684 1.43846
\(498\) 0 0
\(499\) 2.76574 6.67709i 0.123812 0.298908i −0.849805 0.527097i \(-0.823281\pi\)
0.973617 + 0.228189i \(0.0732805\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 17.1789 + 17.1789i 0.765968 + 0.765968i 0.977394 0.211426i \(-0.0678108\pi\)
−0.211426 + 0.977394i \(0.567811\pi\)
\(504\) 0 0
\(505\) −5.99287 + 5.99287i −0.266679 + 0.266679i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.432418 0.179113i −0.0191666 0.00793905i 0.373080 0.927799i \(-0.378302\pi\)
−0.392246 + 0.919860i \(0.628302\pi\)
\(510\) 0 0
\(511\) 9.54815i 0.422385i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −20.3379 + 49.0999i −0.896193 + 2.16360i
\(516\) 0 0
\(517\) −3.63437 + 1.50541i −0.159839 + 0.0662077i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 20.6495 20.6495i 0.904670 0.904670i −0.0911655 0.995836i \(-0.529059\pi\)
0.995836 + 0.0911655i \(0.0290592\pi\)
\(522\) 0 0
\(523\) 40.6453 16.8358i 1.77729 0.736180i 0.783974 0.620794i \(-0.213190\pi\)
0.993321 0.115386i \(-0.0368104\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 29.3798i 1.27980i
\(528\) 0 0
\(529\) 10.8158i 0.470252i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.805318 0.333574i 0.0348822 0.0144487i
\(534\) 0 0
\(535\) 3.90927 3.90927i 0.169013 0.169013i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −16.9471 + 7.01973i −0.729964 + 0.302361i
\(540\) 0 0
\(541\) −7.26862 + 17.5480i −0.312502 + 0.754447i 0.687109 + 0.726555i \(0.258880\pi\)
−0.999611 + 0.0278925i \(0.991120\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 14.1407i 0.605721i
\(546\) 0 0
\(547\) 5.22407 + 2.16388i 0.223365 + 0.0925208i 0.491560 0.870844i \(-0.336427\pi\)
−0.268195 + 0.963365i \(0.586427\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −18.4998 + 18.4998i −0.788116 + 0.788116i
\(552\) 0 0
\(553\) −41.7471 41.7471i −1.77527 1.77527i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7.20051 + 17.3836i −0.305095 + 0.736565i 0.694755 + 0.719247i \(0.255513\pi\)
−0.999850 + 0.0173184i \(0.994487\pi\)
\(558\) 0 0
\(559\) −29.7492 −1.25826
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 43.4445 + 17.9953i 1.83097 + 0.758411i 0.966959 + 0.254932i \(0.0820530\pi\)
0.864007 + 0.503479i \(0.167947\pi\)
\(564\) 0 0
\(565\) 15.3475 + 37.0522i 0.645675 + 1.55880i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.66061 + 5.66061i 0.237305 + 0.237305i 0.815733 0.578428i \(-0.196334\pi\)
−0.578428 + 0.815733i \(0.696334\pi\)
\(570\) 0 0
\(571\) 13.7365 + 33.1629i 0.574856 + 1.38783i 0.897378 + 0.441263i \(0.145469\pi\)
−0.322522 + 0.946562i \(0.604531\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −21.0408 −0.877461
\(576\) 0 0
\(577\) 4.38583 0.182584 0.0912922 0.995824i \(-0.470900\pi\)
0.0912922 + 0.995824i \(0.470900\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5.89454 14.2307i −0.244547 0.590388i
\(582\) 0 0
\(583\) −2.45595 2.45595i −0.101715 0.101715i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4.24918 10.2584i −0.175382 0.423411i 0.811605 0.584206i \(-0.198594\pi\)
−0.986988 + 0.160795i \(0.948594\pi\)
\(588\) 0 0
\(589\) −16.8525 6.98052i −0.694394 0.287627i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −5.76763 −0.236848 −0.118424 0.992963i \(-0.537784\pi\)
−0.118424 + 0.992963i \(0.537784\pi\)
\(594\) 0 0
\(595\) −22.9602 + 55.4309i −0.941277 + 2.27244i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −13.4401 13.4401i −0.549149 0.549149i 0.377045 0.926195i \(-0.376940\pi\)
−0.926195 + 0.377045i \(0.876940\pi\)
\(600\) 0 0
\(601\) 8.58677 8.58677i 0.350262 0.350262i −0.509945 0.860207i \(-0.670334\pi\)
0.860207 + 0.509945i \(0.170334\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 22.7875 + 9.43890i 0.926444 + 0.383746i
\(606\) 0 0
\(607\) 13.3743i 0.542847i 0.962460 + 0.271424i \(0.0874944\pi\)
−0.962460 + 0.271424i \(0.912506\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.38780 + 8.17886i −0.137056 + 0.330881i
\(612\) 0 0
\(613\) −10.6749 + 4.42168i −0.431154 + 0.178590i −0.587697 0.809081i \(-0.699965\pi\)
0.156542 + 0.987671i \(0.449965\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.8713 14.8713i 0.598695 0.598695i −0.341270 0.939965i \(-0.610857\pi\)
0.939965 + 0.341270i \(0.110857\pi\)
\(618\) 0 0
\(619\) 6.25062 2.58909i 0.251234 0.104064i −0.253513 0.967332i \(-0.581586\pi\)
0.504746 + 0.863268i \(0.331586\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 42.3810i 1.69796i
\(624\) 0 0
\(625\) 29.9995i 1.19998i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 44.7612 18.5407i 1.78475 0.739266i
\(630\) 0 0
\(631\) 5.78346 5.78346i 0.230236 0.230236i −0.582555 0.812791i \(-0.697947\pi\)
0.812791 + 0.582555i \(0.197947\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 35.8052 14.8310i 1.42088 0.588550i
\(636\) 0 0
\(637\) −15.7973 + 38.1381i −0.625913 + 1.51109i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 29.5203i 1.16598i 0.812479 + 0.582990i \(0.198117\pi\)
−0.812479 + 0.582990i \(0.801883\pi\)
\(642\) 0 0
\(643\) −10.0660 4.16947i −0.396964 0.164428i 0.175266 0.984521i \(-0.443921\pi\)
−0.572230 + 0.820093i \(0.693921\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 31.9256 31.9256i 1.25512 1.25512i 0.301730 0.953393i \(-0.402436\pi\)
0.953393 0.301730i \(-0.0975641\pi\)
\(648\) 0 0
\(649\) 1.49878 + 1.49878i 0.0588324 + 0.0588324i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6.05626 + 14.6211i −0.237000 + 0.572168i −0.996970 0.0777900i \(-0.975214\pi\)
0.759970 + 0.649958i \(0.225214\pi\)
\(654\) 0 0
\(655\) −19.6811 −0.769002
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 28.2612 + 11.7062i 1.10090 + 0.456008i 0.857795 0.513992i \(-0.171834\pi\)
0.243106 + 0.970000i \(0.421834\pi\)
\(660\) 0 0
\(661\) 6.64573 + 16.0442i 0.258489 + 0.624047i 0.998839 0.0481743i \(-0.0153403\pi\)
−0.740350 + 0.672221i \(0.765340\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 26.3403 + 26.3403i 1.02143 + 1.02143i
\(666\) 0 0
\(667\) 19.6711 + 47.4901i 0.761666 + 1.83883i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.40116 0.169905
\(672\) 0 0
\(673\) 34.2884 1.32172 0.660860 0.750509i \(-0.270192\pi\)
0.660860 + 0.750509i \(0.270192\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 16.6560 + 40.2112i 0.640142 + 1.54544i 0.826487 + 0.562956i \(0.190336\pi\)
−0.186345 + 0.982484i \(0.559664\pi\)
\(678\) 0 0
\(679\) 41.1023 + 41.1023i 1.57736 + 1.57736i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −5.35596 12.9304i −0.204940 0.494769i 0.787673 0.616094i \(-0.211286\pi\)
−0.992613 + 0.121325i \(0.961286\pi\)
\(684\) 0 0
\(685\) −37.4872 15.5277i −1.43231 0.593284i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −7.81623 −0.297775
\(690\) 0 0
\(691\) 19.9998 48.2837i 0.760826 1.83680i 0.279929 0.960021i \(-0.409689\pi\)
0.480898 0.876777i \(-0.340311\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 18.5731 + 18.5731i 0.704517 + 0.704517i
\(696\) 0 0
\(697\) −0.810008 + 0.810008i −0.0306812 + 0.0306812i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −22.6661 9.38859i −0.856085 0.354602i −0.0889098 0.996040i \(-0.528338\pi\)
−0.767175 + 0.641438i \(0.778338\pi\)
\(702\) 0 0
\(703\) 30.0806i 1.13451i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4.73644 11.4348i 0.178132 0.430049i
\(708\) 0 0
\(709\) −6.91323 + 2.86355i −0.259632 + 0.107543i −0.508703 0.860942i \(-0.669875\pi\)
0.249071 + 0.968485i \(0.419875\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −25.3420 + 25.3420i −0.949064 + 0.949064i
\(714\) 0 0
\(715\) −15.8586 + 6.56884i −0.593078 + 0.245661i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 32.1395i 1.19860i 0.800525 + 0.599300i \(0.204554\pi\)
−0.800525 + 0.599300i \(0.795446\pi\)
\(720\) 0 0
\(721\) 77.6119i 2.89042i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −29.5492 + 12.2397i −1.09743 + 0.454570i
\(726\) 0 0
\(727\) −24.0313 + 24.0313i −0.891271 + 0.891271i −0.994643 0.103372i \(-0.967037\pi\)
0.103372 + 0.994643i \(0.467037\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 36.1196 14.9612i 1.33593 0.553361i
\(732\) 0 0
\(733\) −3.28110 + 7.92127i −0.121190 + 0.292579i −0.972819 0.231566i \(-0.925615\pi\)
0.851629 + 0.524145i \(0.175615\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.83141i 0.251638i
\(738\) 0 0
\(739\) −4.01435 1.66280i −0.147670 0.0611671i 0.307624 0.951508i \(-0.400466\pi\)
−0.455295 + 0.890341i \(0.650466\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −20.6253 + 20.6253i −0.756669 + 0.756669i −0.975715 0.219046i \(-0.929706\pi\)
0.219046 + 0.975715i \(0.429706\pi\)
\(744\) 0 0
\(745\) 42.6465 + 42.6465i 1.56245 + 1.56245i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.08968 + 7.45915i −0.112894 + 0.272551i
\(750\) 0 0
\(751\) −13.6475 −0.498004 −0.249002 0.968503i \(-0.580103\pi\)
−0.249002 + 0.968503i \(0.580103\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −30.0458 12.4454i −1.09348 0.452933i
\(756\) 0 0
\(757\) 1.50145 + 3.62481i 0.0545710 + 0.131746i 0.948814 0.315836i \(-0.102285\pi\)
−0.894243 + 0.447582i \(0.852285\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 10.5824 + 10.5824i 0.383612 + 0.383612i 0.872402 0.488790i \(-0.162562\pi\)
−0.488790 + 0.872402i \(0.662562\pi\)
\(762\) 0 0
\(763\) −7.90266 19.0787i −0.286096 0.690696i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.76999 0.172234
\(768\) 0 0
\(769\) −42.6343 −1.53743 −0.768715 0.639591i \(-0.779104\pi\)
−0.768715 + 0.639591i \(0.779104\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −13.5374 32.6822i −0.486906 1.17550i −0.956268 0.292490i \(-0.905516\pi\)
0.469362 0.883006i \(-0.344484\pi\)
\(774\) 0 0
\(775\) −15.7682 15.7682i −0.566411 0.566411i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.272172 + 0.657081i 0.00975157 + 0.0235424i
\(780\) 0 0
\(781\) −11.1393 4.61404i −0.398595 0.165103i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 27.4645 0.980249
\(786\) 0 0
\(787\) 11.1547 26.9298i 0.397622 0.959945i −0.590606 0.806960i \(-0.701111\pi\)
0.988228 0.152985i \(-0.0488887\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −41.4139 41.4139i −1.47251 1.47251i
\(792\) 0 0
\(793\) 7.00350 7.00350i 0.248702 0.248702i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3.44606 1.42740i −0.122066 0.0505612i 0.320815 0.947142i \(-0.396043\pi\)
−0.442880 + 0.896581i \(0.646043\pi\)
\(798\) 0 0
\(799\) 11.6340i 0.411582i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.37380 3.31665i 0.0484804 0.117042i
\(804\) 0 0