Properties

Label 1152.2.w.b.143.2
Level $1152$
Weight $2$
Character 1152.143
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 143.2
Character \(\chi\) \(=\) 1152.143
Dual form 1152.2.w.b.1007.2

$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

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

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 0.445745 + 0.895160i \(0.352939\pi\)
−0.948163 + 0.317784i \(0.897061\pi\)
\(6\) 0 0
\(7\) −3.03150 + 3.03150i −1.14580 + 1.14580i −0.158430 + 0.987370i \(0.550643\pi\)
−0.987370 + 0.158430i \(0.949357\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.616847 + 1.48920i −0.185986 + 0.449011i −0.989180 0.146707i \(-0.953132\pi\)
0.803194 + 0.595718i \(0.203132\pi\)
\(12\) 0 0
\(13\) 3.35133 1.38816i 0.929490 0.385008i 0.134005 0.990981i \(-0.457216\pi\)
0.795485 + 0.605973i \(0.207216\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.76709 1.15619 0.578094 0.815970i \(-0.303797\pi\)
0.578094 + 0.815970i \(0.303797\pi\)
\(18\) 0 0
\(19\) −1.13264 2.73444i −0.259846 0.627323i 0.739082 0.673615i \(-0.235259\pi\)
−0.998928 + 0.0462921i \(0.985259\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.11192 + 4.11192i −0.857395 + 0.857395i −0.991031 0.133636i \(-0.957335\pi\)
0.133636 + 0.991031i \(0.457335\pi\)
\(24\) 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 \(-0.931432\pi\)
−0.539620 + 0.841909i \(0.681432\pi\)
\(30\) 0 0
\(31\) 6.16305i 1.10692i −0.832877 0.553458i \(-0.813308\pi\)
0.832877 0.553458i \(-0.186692\pi\)
\(32\) 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 −0.561493 0.827482i \(-0.689773\pi\)
−0.982153 + 0.188083i \(0.939773\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.169917 0.169917i −0.0265365 0.0265365i 0.693714 0.720251i \(-0.255973\pi\)
−0.720251 + 0.693714i \(0.755973\pi\)
\(42\) 0 0
\(43\) −7.57687 3.13844i −1.15546 0.478608i −0.279100 0.960262i \(-0.590036\pi\)
−0.876361 + 0.481654i \(0.840036\pi\)
\(44\) 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 \(-0.327720\pi\)
−0.241746 + 0.970340i \(0.577720\pi\)
\(54\) 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 \(-0.402280\pi\)
−0.460361 + 0.887732i \(0.652280\pi\)
\(60\) 0 0
\(61\) 1.04489 + 2.52258i 0.133784 + 0.322983i 0.976548 0.215300i \(-0.0690731\pi\)
−0.842764 + 0.538283i \(0.819073\pi\)
\(62\) 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 −0.608815 0.793312i \(-0.708355\pi\)
0.130459 + 0.991454i \(0.458355\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.28919 + 5.28919i 0.627711 + 0.627711i 0.947492 0.319781i \(-0.103609\pi\)
−0.319781 + 0.947492i \(0.603609\pi\)
\(72\) 0 0
\(73\) −1.57482 + 1.57482i −0.184319 + 0.184319i −0.793235 0.608916i \(-0.791605\pi\)
0.608916 + 0.793235i \(0.291605\pi\)
\(74\) 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 \(-0.688179\pi\)
0.192997 + 0.981199i \(0.438179\pi\)
\(84\) 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 \(-0.574465\pi\)
0.972761 + 0.231811i \(0.0744652\pi\)
\(90\) 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 \(-0.920878\pi\)
0.859335 + 0.511413i \(0.170878\pi\)
\(102\) 0 0
\(103\) 12.8009 12.8009i 1.26131 1.26131i 0.310851 0.950459i \(-0.399386\pi\)
0.950459 0.310851i \(-0.100614\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.720677 1.73987i 0.0696704 0.168199i −0.885209 0.465194i \(-0.845984\pi\)
0.954879 + 0.296995i \(0.0959845\pi\)
\(108\) 0 0
\(109\) 4.45017 1.84332i 0.426249 0.176558i −0.159238 0.987240i \(-0.550904\pi\)
0.585486 + 0.810682i \(0.300904\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −13.6612 −1.28514 −0.642568 0.766229i \(-0.722131\pi\)
−0.642568 + 0.766229i \(0.722131\pi\)
\(114\) 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 \(0.199187\pi\)
−0.810515 + 0.585717i \(0.800813\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.56553 + 6.19375i 0.224152 + 0.541150i 0.995446 0.0953287i \(-0.0303902\pi\)
−0.771294 + 0.636479i \(0.780390\pi\)
\(132\) 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 \(-0.0489587\pi\)
−0.153203 + 0.988195i \(0.548959\pi\)
\(138\) 0 0
\(139\) 8.26616 + 3.42396i 0.701127 + 0.290416i 0.704627 0.709578i \(-0.251114\pi\)
−0.00350050 + 0.999994i \(0.501114\pi\)
\(140\) 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 \(-0.693339\pi\)
−0.984199 + 0.177066i \(0.943339\pi\)
\(150\) 0 0
\(151\) −7.83326 7.83326i −0.637462 0.637462i 0.312467 0.949929i \(-0.398845\pi\)
−0.949929 + 0.312467i \(0.898845\pi\)
\(152\) 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 0.999949 0.0101140i \(-0.00321944\pi\)
−0.714222 + 0.699919i \(0.753219\pi\)
\(158\) 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 −0.189377 0.981904i \(-0.560647\pi\)
0.560402 + 0.828221i \(0.310647\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.55199 + 4.55199i 0.352244 + 0.352244i 0.860944 0.508700i \(-0.169874\pi\)
−0.508700 + 0.860944i \(0.669874\pi\)
\(168\) 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 −0.998899 0.0469083i \(-0.985063\pi\)
0.673159 0.739498i \(-0.264937\pi\)
\(174\) 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 \(-0.760727\pi\)
−0.0336946 + 0.999432i \(0.510727\pi\)
\(180\) 0 0
\(181\) −1.33358 + 3.21956i −0.0991246 + 0.239308i −0.965661 0.259806i \(-0.916341\pi\)
0.866536 + 0.499114i \(0.166341\pi\)
\(182\) 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 \(-0.555845\pi\)
−0.174543 + 0.984650i \(0.555845\pi\)
\(192\) 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 0.104341 + 0.994542i \(0.466727\pi\)
−0.777028 + 0.629467i \(0.783273\pi\)
\(198\) 0 0
\(199\) −14.8710 + 14.8710i −1.05418 + 1.05418i −0.0557310 + 0.998446i \(0.517749\pi\)
−0.998446 + 0.0557310i \(0.982251\pi\)
\(200\) 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 0.944496 0.328524i \(-0.106551\pi\)
−0.900161 + 0.435558i \(0.856551\pi\)
\(212\) 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 \(0.287043\pi\)
−0.620221 + 0.784427i \(0.712957\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.10690 12.3292i −0.338957 0.818315i −0.997816 0.0660486i \(-0.978961\pi\)
0.658859 0.752266i \(-0.271039\pi\)
\(228\) 0 0
\(229\) −7.82666 3.24191i −0.517200 0.214231i 0.108786 0.994065i \(-0.465304\pi\)
−0.625987 + 0.779834i \(0.715304\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.66805 + 9.66805i 0.633375 + 0.633375i 0.948913 0.315538i \(-0.102185\pi\)
−0.315538 + 0.948913i \(0.602185\pi\)
\(234\) 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 \(0.296833\pi\)
−0.595805 + 0.803129i \(0.703167\pi\)
\(242\) 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 \(-0.504082\pi\)
−0.716116 + 0.697981i \(0.754082\pi\)
\(252\) 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 \(-0.0992612\pi\)
−0.306809 + 0.951771i \(0.599261\pi\)
\(264\) 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 \(-0.214306\pi\)
−0.993719 + 0.111901i \(0.964306\pi\)
\(270\) 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 0.682390 + 0.730988i \(0.260940\pi\)
−0.999409 + 0.0343637i \(0.989060\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5.75892 + 5.75892i −0.343548 + 0.343548i −0.857700 0.514151i \(-0.828107\pi\)
0.514151 + 0.857700i \(0.328107\pi\)
\(282\) 0 0
\(283\) −10.4136 + 25.1407i −0.619025 + 1.49446i 0.233812 + 0.972282i \(0.424880\pi\)
−0.852837 + 0.522177i \(0.825120\pi\)
\(284\) 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 −0.695290 0.718729i \(-0.744724\pi\)
0.999863 0.0165743i \(-0.00527600\pi\)
\(294\) 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 0.942398 + 0.334495i \(0.108566\pi\)
−0.429852 + 0.902899i \(0.641434\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.7177 + 12.7177i −0.721157 + 0.721157i −0.968841 0.247684i \(-0.920330\pi\)
0.247684 + 0.968841i \(0.420330\pi\)
\(312\) 0 0
\(313\) 10.1388 + 10.1388i 0.573081 + 0.573081i 0.932988 0.359907i \(-0.117192\pi\)
−0.359907 + 0.932988i \(0.617192\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.52668 1.04659i 0.141913 0.0587822i −0.310597 0.950542i \(-0.600529\pi\)
0.452509 + 0.891760i \(0.350529\pi\)
\(318\) 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 0.528628 0.848854i \(-0.322707\pi\)
−0.226434 + 0.974027i \(0.572707\pi\)
\(332\) 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 \(-0.949041\pi\)
0.987213 0.159409i \(-0.0509589\pi\)
\(338\) 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 \(-0.307542\pi\)
−0.179792 + 0.983705i \(0.557542\pi\)
\(348\) 0 0
\(349\) −4.01973 9.70449i −0.215171 0.519469i 0.779032 0.626984i \(-0.215711\pi\)
−0.994204 + 0.107515i \(0.965711\pi\)
\(350\) 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 \(-0.365952\pi\)
−0.912630 + 0.408786i \(0.865952\pi\)
\(360\) 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 −0.983120 0.182963i \(-0.941431\pi\)
0.824545 + 0.565797i \(0.191431\pi\)
\(374\) 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 −0.552858 0.833275i \(-0.686463\pi\)
0.980144 0.198285i \(-0.0635372\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 7.95308 0.406383 0.203192 0.979139i \(-0.434869\pi\)
0.203192 + 0.979139i \(0.434869\pi\)
\(384\) 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 \(-0.925442\pi\)
0.851913 + 0.523683i \(0.175442\pi\)
\(390\) 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 0.357288 0.933994i \(-0.383701\pi\)
0.913075 + 0.407792i \(0.133701\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.81017 −0.0903954 −0.0451977 0.998978i \(-0.514392\pi\)
−0.0451977 + 0.998978i \(0.514392\pi\)
\(402\) 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 0.253630 0.967301i \(-0.418376\pi\)
−0.967301 + 0.253630i \(0.918376\pi\)
\(410\) 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 \(-0.0977610\pi\)
−0.887791 + 0.460247i \(0.847761\pi\)
\(420\) 0 0
\(421\) −10.5557 4.37232i −0.514454 0.213094i 0.110325 0.993896i \(-0.464811\pi\)
−0.624779 + 0.780802i \(0.714811\pi\)
\(422\) 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 \(0.0347394\pi\)
−0.994050 + 0.108921i \(0.965261\pi\)
\(434\) 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 −1.00000 0.000858061i \(-0.999727\pi\)
−0.000858061 1.00000i \(-0.500273\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 31.9708 + 13.2427i 1.51898 + 0.629181i 0.977386 0.211462i \(-0.0678225\pi\)
0.541590 + 0.840643i \(0.317822\pi\)
\(444\) 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 −0.806988 0.590567i \(-0.798904\pi\)
0.590567 + 0.806988i \(0.298904\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.84388 + 11.6942i 0.225602 + 0.544652i 0.995633 0.0933550i \(-0.0297592\pi\)
−0.770031 + 0.638007i \(0.779759\pi\)
\(462\) 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 \(-0.292568\pi\)
0.991071 + 0.133333i \(0.0425681\pi\)
\(468\) 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 \(-0.599046\pi\)
−0.306167 + 0.951978i \(0.599046\pi\)
\(480\) 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 −0.735241 0.677805i \(-0.762931\pi\)
0.677805 + 0.735241i \(0.262931\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −8.81902 + 21.2910i −0.397997 + 0.960849i 0.590144 + 0.807298i \(0.299071\pi\)
−0.988141 + 0.153551i \(0.950929\pi\)
\(492\) 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 0.973617 0.228189i \(-0.0732805\pi\)
−0.849805 + 0.527097i \(0.823281\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −17.1789 + 17.1789i −0.765968 + 0.765968i −0.977394 0.211426i \(-0.932189\pi\)
0.211426 + 0.977394i \(0.432189\pi\)
\(504\) 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 \(-0.621698\pi\)
0.392246 + 0.919860i \(0.371698\pi\)
\(510\) 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 \(-0.470941\pi\)
−0.995836 + 0.0911655i \(0.970941\pi\)
\(522\) 0 0
\(523\) 40.6453 + 16.8358i 1.77729 + 0.736180i 0.993321 + 0.115386i \(0.0368104\pi\)
0.783974 + 0.620794i \(0.213190\pi\)
\(524\) 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 −0.999611 0.0278925i \(-0.991120\pi\)
0.687109 0.726555i \(-0.258880\pi\)
\(542\) 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 −0.268195 0.963365i \(-0.586427\pi\)
0.491560 + 0.870844i \(0.336427\pi\)
\(548\) 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 0.999850 + 0.0173184i \(0.00551288\pi\)
−0.694755 + 0.719247i \(0.744487\pi\)
\(558\) 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 −0.864007 + 0.503479i \(0.832053\pi\)
−0.966959 + 0.254932i \(0.917947\pi\)
\(564\) 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 \(-0.803666\pi\)
0.578428 + 0.815733i \(0.303666\pi\)
\(570\) 0 0
\(571\) 13.7365 33.1629i 0.574856 1.38783i −0.322522 0.946562i \(-0.604531\pi\)
0.897378 0.441263i \(-0.145469\pi\)
\(572\) 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 \(-0.801406\pi\)
0.986988 + 0.160795i \(0.0514060\pi\)
\(588\) 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 \(-0.462216\pi\)
0.118424 + 0.992963i \(0.462216\pi\)
\(594\) 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 \(-0.623060\pi\)
0.926195 + 0.377045i \(0.123060\pi\)
\(600\) 0 0
\(601\) 8.58677 + 8.58677i 0.350262 + 0.350262i 0.860207 0.509945i \(-0.170334\pi\)
−0.509945 + 0.860207i \(0.670334\pi\)
\(602\) 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 \(-0.912506\pi\)
0.962460 0.271424i \(-0.0874944\pi\)
\(608\) 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 0.156542 0.987671i \(-0.449965\pi\)
−0.587697 + 0.809081i \(0.699965\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.8713 14.8713i −0.598695 0.598695i 0.341270 0.939965i \(-0.389143\pi\)
−0.939965 + 0.341270i \(0.889143\pi\)
\(618\) 0 0
\(619\) 6.25062 + 2.58909i 0.251234 + 0.104064i 0.504746 0.863268i \(-0.331586\pi\)
−0.253513 + 0.967332i \(0.581586\pi\)
\(620\) 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 0.812791 0.582555i \(-0.197947\pi\)
−0.582555 + 0.812791i \(0.697947\pi\)
\(632\) 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 −0.572230 0.820093i \(-0.693921\pi\)
0.175266 + 0.984521i \(0.443921\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −31.9256 31.9256i −1.25512 1.25512i −0.953393 0.301730i \(-0.902436\pi\)
−0.301730 0.953393i \(-0.597564\pi\)
\(648\) 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 \(-0.0247864\pi\)
−0.759970 + 0.649958i \(0.774786\pi\)
\(654\) 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 \(-0.828166\pi\)
−0.243106 + 0.970000i \(0.578166\pi\)
\(660\) 0 0
\(661\) 6.64573 16.0442i 0.258489 0.624047i −0.740350 0.672221i \(-0.765340\pi\)
0.998839 + 0.0481743i \(0.0153403\pi\)
\(662\) 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 0.186345 + 0.982484i \(0.440336\pi\)
−0.826487 + 0.562956i \(0.809664\pi\)
\(678\) 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 \(-0.788714\pi\)
0.992613 + 0.121325i \(0.0387142\pi\)
\(684\) 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 0.480898 + 0.876777i \(0.340311\pi\)
0.279929 + 0.960021i \(0.409689\pi\)
\(692\) 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 \(-0.471662\pi\)
0.767175 + 0.641438i \(0.221662\pi\)
\(702\) 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 0.249071 0.968485i \(-0.419875\pi\)
−0.508703 + 0.860942i \(0.669875\pi\)
\(710\) 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 0.103372 0.994643i \(-0.467037\pi\)
−0.994643 + 0.103372i \(0.967037\pi\)
\(728\) 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 0.851629 0.524145i \(-0.175615\pi\)
−0.972819 + 0.231566i \(0.925615\pi\)
\(734\) 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 −0.455295 0.890341i \(-0.650466\pi\)
0.307624 + 0.951508i \(0.400466\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 20.6253 + 20.6253i 0.756669 + 0.756669i 0.975715 0.219046i \(-0.0702944\pi\)
−0.219046 + 0.975715i \(0.570294\pi\)
\(744\) 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 −0.894243 0.447582i \(-0.852285\pi\)
0.948814 + 0.315836i \(0.102285\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −10.5824 + 10.5824i −0.383612 + 0.383612i −0.872402 0.488790i \(-0.837438\pi\)
0.488790 + 0.872402i \(0.337438\pi\)
\(762\) 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 −0.469362 0.883006i \(-0.655516\pi\)
0.956268 0.292490i \(-0.0944839\pi\)
\(774\) 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 0.988228 + 0.152985i \(0.0488887\pi\)
−0.590606 + 0.806960i \(0.701111\pi\)
\(788\) 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 \(-0.603957\pi\)
0.442880 + 0.896581i \(0.353957\pi\)
\(798\) 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