Properties

Label 864.2.i.c.289.2
Level $864$
Weight $2$
Character 864.289
Analytic conductor $6.899$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.2
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 864.289
Dual form 864.2.i.c.577.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{5} +(0.724745 - 1.25529i) q^{7} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{5} +(0.724745 - 1.25529i) q^{7} +(-1.72474 + 2.98735i) q^{11} +(1.94949 + 3.37662i) q^{13} +4.89898 q^{17} +4.00000 q^{19} +(-0.275255 - 0.476756i) q^{23} +(2.00000 - 3.46410i) q^{25} +(4.94949 - 8.57277i) q^{29} +(-3.72474 - 6.45145i) q^{31} -1.44949 q^{35} +8.89898 q^{37} +(-1.05051 - 1.81954i) q^{41} +(-6.17423 + 10.6941i) q^{43} +(4.17423 - 7.22999i) q^{47} +(2.44949 + 4.24264i) q^{49} +0.898979 q^{53} +3.44949 q^{55} +(-0.174235 - 0.301783i) q^{59} +(-0.949490 + 1.64456i) q^{61} +(1.94949 - 3.37662i) q^{65} +(1.17423 + 2.03383i) q^{67} +11.7980 q^{71} +4.89898 q^{73} +(2.50000 + 4.33013i) q^{77} +(-4.27526 + 7.40496i) q^{79} +(-2.72474 + 4.71940i) q^{83} +(-2.44949 - 4.24264i) q^{85} +3.10102 q^{89} +5.65153 q^{91} +(-2.00000 - 3.46410i) q^{95} +(-2.94949 + 5.10867i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{5} - 2 q^{7} - 2 q^{11} - 2 q^{13} + 16 q^{19} - 6 q^{23} + 8 q^{25} + 10 q^{29} - 10 q^{31} + 4 q^{35} + 16 q^{37} - 14 q^{41} - 10 q^{43} + 2 q^{47} - 16 q^{53} + 4 q^{55} + 14 q^{59} + 6 q^{61} - 2 q^{65} - 10 q^{67} + 8 q^{71} + 10 q^{77} - 22 q^{79} - 6 q^{83} + 32 q^{89} + 52 q^{91} - 8 q^{95} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 0 0
\(7\) 0.724745 1.25529i 0.273928 0.474457i −0.695936 0.718104i \(-0.745010\pi\)
0.969864 + 0.243647i \(0.0783437\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.72474 + 2.98735i −0.520030 + 0.900719i 0.479699 + 0.877433i \(0.340746\pi\)
−0.999729 + 0.0232854i \(0.992587\pi\)
\(12\) 0 0
\(13\) 1.94949 + 3.37662i 0.540691 + 0.936505i 0.998864 + 0.0476417i \(0.0151706\pi\)
−0.458173 + 0.888863i \(0.651496\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.89898 1.18818 0.594089 0.804400i \(-0.297513\pi\)
0.594089 + 0.804400i \(0.297513\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.275255 0.476756i −0.0573947 0.0994105i 0.835900 0.548881i \(-0.184946\pi\)
−0.893295 + 0.449471i \(0.851613\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.94949 8.57277i 0.919097 1.59192i 0.118308 0.992977i \(-0.462253\pi\)
0.800789 0.598946i \(-0.204414\pi\)
\(30\) 0 0
\(31\) −3.72474 6.45145i −0.668984 1.15871i −0.978189 0.207719i \(-0.933396\pi\)
0.309205 0.950996i \(-0.399937\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.44949 −0.245008
\(36\) 0 0
\(37\) 8.89898 1.46298 0.731492 0.681850i \(-0.238825\pi\)
0.731492 + 0.681850i \(0.238825\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.05051 1.81954i −0.164062 0.284164i 0.772260 0.635307i \(-0.219126\pi\)
−0.936322 + 0.351143i \(0.885793\pi\)
\(42\) 0 0
\(43\) −6.17423 + 10.6941i −0.941562 + 1.63083i −0.179069 + 0.983836i \(0.557309\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.17423 7.22999i 0.608875 1.05460i −0.382552 0.923934i \(-0.624955\pi\)
0.991426 0.130668i \(-0.0417121\pi\)
\(48\) 0 0
\(49\) 2.44949 + 4.24264i 0.349927 + 0.606092i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.898979 0.123484 0.0617422 0.998092i \(-0.480334\pi\)
0.0617422 + 0.998092i \(0.480334\pi\)
\(54\) 0 0
\(55\) 3.44949 0.465129
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.174235 0.301783i −0.0226834 0.0392888i 0.854461 0.519516i \(-0.173888\pi\)
−0.877144 + 0.480227i \(0.840554\pi\)
\(60\) 0 0
\(61\) −0.949490 + 1.64456i −0.121570 + 0.210565i −0.920387 0.391009i \(-0.872126\pi\)
0.798817 + 0.601574i \(0.205459\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.94949 3.37662i 0.241804 0.418818i
\(66\) 0 0
\(67\) 1.17423 + 2.03383i 0.143456 + 0.248472i 0.928796 0.370592i \(-0.120845\pi\)
−0.785340 + 0.619065i \(0.787512\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.7980 1.40016 0.700080 0.714064i \(-0.253148\pi\)
0.700080 + 0.714064i \(0.253148\pi\)
\(72\) 0 0
\(73\) 4.89898 0.573382 0.286691 0.958023i \(-0.407445\pi\)
0.286691 + 0.958023i \(0.407445\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.50000 + 4.33013i 0.284901 + 0.493464i
\(78\) 0 0
\(79\) −4.27526 + 7.40496i −0.481004 + 0.833123i −0.999762 0.0217978i \(-0.993061\pi\)
0.518759 + 0.854921i \(0.326394\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −2.72474 + 4.71940i −0.299080 + 0.518021i −0.975926 0.218104i \(-0.930013\pi\)
0.676846 + 0.736125i \(0.263346\pi\)
\(84\) 0 0
\(85\) −2.44949 4.24264i −0.265684 0.460179i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.10102 0.328708 0.164354 0.986401i \(-0.447446\pi\)
0.164354 + 0.986401i \(0.447446\pi\)
\(90\) 0 0
\(91\) 5.65153 0.592441
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.00000 3.46410i −0.205196 0.355409i
\(96\) 0 0
\(97\) −2.94949 + 5.10867i −0.299475 + 0.518706i −0.976016 0.217699i \(-0.930145\pi\)
0.676541 + 0.736405i \(0.263478\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.39898 + 5.88721i −0.338211 + 0.585799i −0.984096 0.177636i \(-0.943155\pi\)
0.645885 + 0.763435i \(0.276488\pi\)
\(102\) 0 0
\(103\) −8.72474 15.1117i −0.859675 1.48900i −0.872239 0.489079i \(-0.837333\pi\)
0.0125648 0.999921i \(-0.496000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.7980 −1.33390 −0.666950 0.745103i \(-0.732400\pi\)
−0.666950 + 0.745103i \(0.732400\pi\)
\(108\) 0 0
\(109\) −8.89898 −0.852368 −0.426184 0.904637i \(-0.640142\pi\)
−0.426184 + 0.904637i \(0.640142\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.39898 9.35131i −0.507893 0.879697i −0.999958 0.00913847i \(-0.997091\pi\)
0.492065 0.870558i \(-0.336242\pi\)
\(114\) 0 0
\(115\) −0.275255 + 0.476756i −0.0256677 + 0.0444577i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.55051 6.14966i 0.325475 0.563739i
\(120\) 0 0
\(121\) −0.449490 0.778539i −0.0408627 0.0707763i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 5.62372 + 9.74058i 0.491347 + 0.851038i 0.999950 0.00996288i \(-0.00317134\pi\)
−0.508603 + 0.861001i \(0.669838\pi\)
\(132\) 0 0
\(133\) 2.89898 5.02118i 0.251373 0.435392i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.94949 + 17.2330i −0.850042 + 1.47232i 0.0311270 + 0.999515i \(0.490090\pi\)
−0.881169 + 0.472801i \(0.843243\pi\)
\(138\) 0 0
\(139\) −0.724745 1.25529i −0.0614721 0.106473i 0.833652 0.552291i \(-0.186246\pi\)
−0.895124 + 0.445818i \(0.852913\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −13.4495 −1.12470
\(144\) 0 0
\(145\) −9.89898 −0.822066
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 6.94949 + 12.0369i 0.569324 + 0.986099i 0.996633 + 0.0819929i \(0.0261285\pi\)
−0.427309 + 0.904106i \(0.640538\pi\)
\(150\) 0 0
\(151\) 4.62372 8.00853i 0.376273 0.651725i −0.614243 0.789117i \(-0.710539\pi\)
0.990517 + 0.137392i \(0.0438720\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.72474 + 6.45145i −0.299179 + 0.518193i
\(156\) 0 0
\(157\) −4.39898 7.61926i −0.351077 0.608083i 0.635362 0.772215i \(-0.280851\pi\)
−0.986438 + 0.164132i \(0.947518\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.797959 −0.0628880
\(162\) 0 0
\(163\) 13.7980 1.08074 0.540370 0.841428i \(-0.318284\pi\)
0.540370 + 0.841428i \(0.318284\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.72474 + 8.18350i 0.365612 + 0.633258i 0.988874 0.148755i \(-0.0475265\pi\)
−0.623262 + 0.782013i \(0.714193\pi\)
\(168\) 0 0
\(169\) −1.10102 + 1.90702i −0.0846939 + 0.146694i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.50000 2.59808i 0.114043 0.197528i −0.803354 0.595502i \(-0.796953\pi\)
0.917397 + 0.397974i \(0.130287\pi\)
\(174\) 0 0
\(175\) −2.89898 5.02118i −0.219142 0.379566i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −18.6969 −1.38973 −0.694866 0.719139i \(-0.744536\pi\)
−0.694866 + 0.719139i \(0.744536\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.44949 7.70674i −0.327133 0.566611i
\(186\) 0 0
\(187\) −8.44949 + 14.6349i −0.617888 + 1.07021i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.72474 + 15.1117i −0.631300 + 1.09344i 0.355986 + 0.934491i \(0.384145\pi\)
−0.987286 + 0.158953i \(0.949188\pi\)
\(192\) 0 0
\(193\) −6.94949 12.0369i −0.500235 0.866433i −1.00000 0.000271627i \(-0.999914\pi\)
0.499765 0.866161i \(-0.333420\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −21.5959 −1.53865 −0.769323 0.638860i \(-0.779406\pi\)
−0.769323 + 0.638860i \(0.779406\pi\)
\(198\) 0 0
\(199\) 11.7980 0.836335 0.418168 0.908370i \(-0.362672\pi\)
0.418168 + 0.908370i \(0.362672\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.17423 12.4261i −0.503533 0.872144i
\(204\) 0 0
\(205\) −1.05051 + 1.81954i −0.0733708 + 0.127082i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −6.89898 + 11.9494i −0.477212 + 0.826556i
\(210\) 0 0
\(211\) −7.72474 13.3797i −0.531793 0.921093i −0.999311 0.0371095i \(-0.988185\pi\)
0.467518 0.883984i \(-0.345148\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 12.3485 0.842159
\(216\) 0 0
\(217\) −10.7980 −0.733013
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 9.55051 + 16.5420i 0.642437 + 1.11273i
\(222\) 0 0
\(223\) −9.07321 + 15.7153i −0.607587 + 1.05237i 0.384049 + 0.923313i \(0.374529\pi\)
−0.991637 + 0.129060i \(0.958804\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.1742 19.3543i 0.741660 1.28459i −0.210079 0.977684i \(-0.567372\pi\)
0.951739 0.306908i \(-0.0992945\pi\)
\(228\) 0 0
\(229\) 0.500000 + 0.866025i 0.0330409 + 0.0572286i 0.882073 0.471113i \(-0.156147\pi\)
−0.849032 + 0.528341i \(0.822814\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) −8.34847 −0.544594
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −10.0732 17.4473i −0.651582 1.12857i −0.982739 0.184998i \(-0.940772\pi\)
0.331157 0.943576i \(-0.392561\pi\)
\(240\) 0 0
\(241\) −3.50000 + 6.06218i −0.225455 + 0.390499i −0.956456 0.291877i \(-0.905720\pi\)
0.731001 + 0.682376i \(0.239053\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.44949 4.24264i 0.156492 0.271052i
\(246\) 0 0
\(247\) 7.79796 + 13.5065i 0.496172 + 0.859396i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −2.20204 −0.138992 −0.0694958 0.997582i \(-0.522139\pi\)
−0.0694958 + 0.997582i \(0.522139\pi\)
\(252\) 0 0
\(253\) 1.89898 0.119388
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.39898 + 7.61926i 0.274401 + 0.475276i 0.969984 0.243170i \(-0.0781872\pi\)
−0.695583 + 0.718446i \(0.744854\pi\)
\(258\) 0 0
\(259\) 6.44949 11.1708i 0.400752 0.694122i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.275255 0.476756i 0.0169730 0.0293980i −0.857414 0.514627i \(-0.827930\pi\)
0.874387 + 0.485229i \(0.161264\pi\)
\(264\) 0 0
\(265\) −0.449490 0.778539i −0.0276119 0.0478253i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −16.8990 −1.03035 −0.515174 0.857085i \(-0.672273\pi\)
−0.515174 + 0.857085i \(0.672273\pi\)
\(270\) 0 0
\(271\) −29.3939 −1.78555 −0.892775 0.450502i \(-0.851245\pi\)
−0.892775 + 0.450502i \(0.851245\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 6.89898 + 11.9494i 0.416024 + 0.720575i
\(276\) 0 0
\(277\) −2.39898 + 4.15515i −0.144141 + 0.249659i −0.929052 0.369949i \(-0.879375\pi\)
0.784911 + 0.619608i \(0.212708\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −9.94949 + 17.2330i −0.593537 + 1.02804i 0.400215 + 0.916421i \(0.368936\pi\)
−0.993752 + 0.111615i \(0.964398\pi\)
\(282\) 0 0
\(283\) −0.724745 1.25529i −0.0430816 0.0746195i 0.843681 0.536846i \(-0.180384\pi\)
−0.886762 + 0.462226i \(0.847051\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.04541 −0.179765
\(288\) 0 0
\(289\) 7.00000 0.411765
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −9.39898 16.2795i −0.549094 0.951059i −0.998337 0.0576493i \(-0.981639\pi\)
0.449243 0.893410i \(-0.351694\pi\)
\(294\) 0 0
\(295\) −0.174235 + 0.301783i −0.0101443 + 0.0175705i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.07321 1.85886i 0.0620656 0.107501i
\(300\) 0 0
\(301\) 8.94949 + 15.5010i 0.515840 + 0.893461i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.89898 0.108735
\(306\) 0 0
\(307\) −2.20204 −0.125677 −0.0628386 0.998024i \(-0.520015\pi\)
−0.0628386 + 0.998024i \(0.520015\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.62372 + 8.00853i 0.262187 + 0.454122i 0.966823 0.255448i \(-0.0822228\pi\)
−0.704636 + 0.709569i \(0.748889\pi\)
\(312\) 0 0
\(313\) 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i \(-0.673807\pi\)
0.999748 + 0.0224310i \(0.00714060\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8.05051 13.9439i 0.452162 0.783167i −0.546358 0.837552i \(-0.683986\pi\)
0.998520 + 0.0543845i \(0.0173197\pi\)
\(318\) 0 0
\(319\) 17.0732 + 29.5717i 0.955916 + 1.65570i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 19.5959 1.09035
\(324\) 0 0
\(325\) 15.5959 0.865106
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −6.05051 10.4798i −0.333575 0.577770i
\(330\) 0 0
\(331\) 6.62372 11.4726i 0.364073 0.630593i −0.624554 0.780982i \(-0.714719\pi\)
0.988627 + 0.150389i \(0.0480526\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.17423 2.03383i 0.0641553 0.111120i
\(336\) 0 0
\(337\) −4.39898 7.61926i −0.239628 0.415047i 0.720980 0.692956i \(-0.243692\pi\)
−0.960607 + 0.277909i \(0.910359\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 25.6969 1.39157
\(342\) 0 0
\(343\) 17.2474 0.931275
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −14.0732 24.3755i −0.755490 1.30855i −0.945130 0.326693i \(-0.894066\pi\)
0.189641 0.981854i \(-0.439268\pi\)
\(348\) 0 0
\(349\) −2.39898 + 4.15515i −0.128414 + 0.222420i −0.923062 0.384650i \(-0.874322\pi\)
0.794648 + 0.607070i \(0.207655\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7.84847 13.5939i 0.417732 0.723533i −0.577979 0.816052i \(-0.696158\pi\)
0.995711 + 0.0925188i \(0.0294918\pi\)
\(354\) 0 0
\(355\) −5.89898 10.2173i −0.313085 0.542280i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −17.7980 −0.939340 −0.469670 0.882842i \(-0.655627\pi\)
−0.469670 + 0.882842i \(0.655627\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.44949 4.24264i −0.128212 0.222070i
\(366\) 0 0
\(367\) −5.17423 + 8.96204i −0.270093 + 0.467815i −0.968885 0.247510i \(-0.920388\pi\)
0.698793 + 0.715324i \(0.253721\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.651531 1.12848i 0.0338258 0.0585880i
\(372\) 0 0
\(373\) −1.15153 1.99451i −0.0596240 0.103272i 0.834673 0.550746i \(-0.185657\pi\)
−0.894297 + 0.447475i \(0.852324\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 38.5959 1.98779
\(378\) 0 0
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 16.7247 + 28.9681i 0.854595 + 1.48020i 0.877021 + 0.480453i \(0.159528\pi\)
−0.0224261 + 0.999749i \(0.507139\pi\)
\(384\) 0 0
\(385\) 2.50000 4.33013i 0.127412 0.220684i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.39898 11.0834i 0.324441 0.561949i −0.656958 0.753927i \(-0.728157\pi\)
0.981399 + 0.191979i \(0.0614904\pi\)
\(390\) 0 0
\(391\) −1.34847 2.33562i −0.0681950 0.118117i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.55051 0.430223
\(396\) 0 0
\(397\) 18.6969 0.938372 0.469186 0.883099i \(-0.344547\pi\)
0.469186 + 0.883099i \(0.344547\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.84847 + 13.5939i 0.391934 + 0.678849i 0.992705 0.120572i \(-0.0384729\pi\)
−0.600771 + 0.799421i \(0.705140\pi\)
\(402\) 0 0
\(403\) 14.5227 25.1541i 0.723427 1.25301i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −15.3485 + 26.5843i −0.760795 + 1.31774i
\(408\) 0 0
\(409\) 6.29796 + 10.9084i 0.311414 + 0.539385i 0.978669 0.205445i \(-0.0658641\pi\)
−0.667255 + 0.744830i \(0.732531\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −0.505103 −0.0248545
\(414\) 0 0
\(415\) 5.44949 0.267505
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.37628 5.84788i −0.164942 0.285688i 0.771693 0.635995i \(-0.219410\pi\)
−0.936635 + 0.350308i \(0.886077\pi\)
\(420\) 0 0
\(421\) −4.94949 + 8.57277i −0.241223 + 0.417811i −0.961063 0.276329i \(-0.910882\pi\)
0.719840 + 0.694140i \(0.244215\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 9.79796 16.9706i 0.475271 0.823193i
\(426\) 0 0
\(427\) 1.37628 + 2.38378i 0.0666026 + 0.115359i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −33.7980 −1.62799 −0.813995 0.580872i \(-0.802712\pi\)
−0.813995 + 0.580872i \(0.802712\pi\)
\(432\) 0 0
\(433\) 40.4949 1.94606 0.973030 0.230677i \(-0.0740942\pi\)
0.973030 + 0.230677i \(0.0740942\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.10102 1.90702i −0.0526690 0.0912253i
\(438\) 0 0
\(439\) 10.8258 18.7508i 0.516686 0.894926i −0.483127 0.875550i \(-0.660499\pi\)
0.999812 0.0193752i \(-0.00616772\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9.27526 16.0652i 0.440681 0.763281i −0.557059 0.830473i \(-0.688070\pi\)
0.997740 + 0.0671913i \(0.0214038\pi\)
\(444\) 0 0
\(445\) −1.55051 2.68556i −0.0735012 0.127308i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −20.8990 −0.986284 −0.493142 0.869949i \(-0.664152\pi\)
−0.493142 + 0.869949i \(0.664152\pi\)
\(450\) 0 0
\(451\) 7.24745 0.341269
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.82577 4.89437i −0.132474 0.229452i
\(456\) 0 0
\(457\) −8.74745 + 15.1510i −0.409188 + 0.708735i −0.994799 0.101857i \(-0.967521\pi\)
0.585611 + 0.810593i \(0.300855\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.15153 5.45861i 0.146781 0.254233i −0.783255 0.621701i \(-0.786442\pi\)
0.930036 + 0.367468i \(0.119775\pi\)
\(462\) 0 0
\(463\) 3.37628 + 5.84788i 0.156909 + 0.271774i 0.933752 0.357920i \(-0.116514\pi\)
−0.776844 + 0.629694i \(0.783180\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −0.404082 −0.0186987 −0.00934934 0.999956i \(-0.502976\pi\)
−0.00934934 + 0.999956i \(0.502976\pi\)
\(468\) 0 0
\(469\) 3.40408 0.157186
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −21.2980 36.8891i −0.979281 1.69616i
\(474\) 0 0
\(475\) 8.00000 13.8564i 0.367065 0.635776i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9.52270 + 16.4938i −0.435103 + 0.753621i −0.997304 0.0733796i \(-0.976622\pi\)
0.562201 + 0.827001i \(0.309955\pi\)
\(480\) 0 0
\(481\) 17.3485 + 30.0484i 0.791022 + 1.37009i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.89898 0.267859
\(486\) 0 0
\(487\) 1.79796 0.0814733 0.0407366 0.999170i \(-0.487030\pi\)
0.0407366 + 0.999170i \(0.487030\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 17.6237 + 30.5252i 0.795348 + 1.37758i 0.922618 + 0.385714i \(0.126045\pi\)
−0.127271 + 0.991868i \(0.540622\pi\)
\(492\) 0 0
\(493\) 24.2474 41.9978i 1.09205 1.89149i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8.55051 14.8099i 0.383543 0.664316i
\(498\) 0 0
\(499\) 8.17423 + 14.1582i 0.365929 + 0.633808i 0.988925 0.148418i \(-0.0474180\pi\)
−0.622996 + 0.782225i \(0.714085\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 20.2020 0.900764 0.450382 0.892836i \(-0.351288\pi\)
0.450382 + 0.892836i \(0.351288\pi\)
\(504\) 0 0
\(505\) 6.79796 0.302505
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 16.7474 + 29.0074i 0.742318 + 1.28573i 0.951438 + 0.307842i \(0.0996068\pi\)
−0.209120 + 0.977890i \(0.567060\pi\)
\(510\) 0 0
\(511\) 3.55051 6.14966i 0.157065 0.272045i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.72474 + 15.1117i −0.384458 + 0.665901i
\(516\) 0 0
\(517\) 14.3990 + 24.9398i 0.633266 + 1.09685i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) −25.5959 −1.11923 −0.559616 0.828752i \(-0.689051\pi\)
−0.559616 + 0.828752i \(0.689051\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −18.2474 31.6055i −0.794871 1.37676i
\(528\) 0 0
\(529\) 11.3485 19.6561i 0.493412 0.854614i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 4.09592 7.09434i 0.177414 0.307290i
\(534\) 0 0
\(535\) 6.89898 + 11.9494i 0.298269 + 0.516617i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −16.8990 −0.727891
\(540\) 0 0
\(541\) −9.59592 −0.412561 −0.206280 0.978493i \(-0.566136\pi\)
−0.206280 + 0.978493i \(0.566136\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.44949 + 7.70674i 0.190595 + 0.330121i
\(546\) 0 0
\(547\) 5.72474 9.91555i 0.244772 0.423958i −0.717295 0.696769i \(-0.754620\pi\)
0.962068 + 0.272811i \(0.0879534\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 19.7980 34.2911i 0.843421 1.46085i
\(552\) 0 0
\(553\) 6.19694 + 10.7334i 0.263521 + 0.456431i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10.6969 −0.453244 −0.226622 0.973983i \(-0.572768\pi\)
−0.226622 + 0.973983i \(0.572768\pi\)
\(558\) 0 0
\(559\) −48.1464 −2.03638
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5.17423 8.96204i −0.218068 0.377705i 0.736149 0.676819i \(-0.236642\pi\)
−0.954217 + 0.299114i \(0.903309\pi\)
\(564\) 0 0
\(565\) −5.39898 + 9.35131i −0.227137 + 0.393412i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −0.500000 + 0.866025i −0.0209611 + 0.0363057i −0.876316 0.481737i \(-0.840006\pi\)
0.855355 + 0.518043i \(0.173339\pi\)
\(570\) 0 0
\(571\) 9.17423 + 15.8902i 0.383930 + 0.664986i 0.991620 0.129188i \(-0.0412371\pi\)
−0.607690 + 0.794174i \(0.707904\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2.20204 −0.0918315
\(576\) 0 0
\(577\) −28.8990 −1.20308 −0.601540 0.798843i \(-0.705446\pi\)
−0.601540 + 0.798843i \(0.705446\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.94949 + 6.84072i 0.163852 + 0.283801i
\(582\) 0 0
\(583\) −1.55051 + 2.68556i −0.0642156 + 0.111225i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.9722 20.7364i 0.494145 0.855885i −0.505832 0.862632i \(-0.668814\pi\)
0.999977 + 0.00674727i \(0.00214774\pi\)
\(588\) 0 0
\(589\) −14.8990 25.8058i −0.613902 1.06331i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −19.1010 −0.784385 −0.392192 0.919883i \(-0.628283\pi\)
−0.392192 + 0.919883i \(0.628283\pi\)
\(594\) 0 0
\(595\) −7.10102 −0.291113
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16.7247 + 28.9681i 0.683355 + 1.18360i 0.973951 + 0.226759i \(0.0728130\pi\)
−0.290596 + 0.956846i \(0.593854\pi\)
\(600\) 0 0
\(601\) −19.8485 + 34.3786i −0.809636 + 1.40233i 0.103480 + 0.994631i \(0.467002\pi\)
−0.913116 + 0.407699i \(0.866331\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.449490 + 0.778539i −0.0182744 + 0.0316521i
\(606\) 0 0
\(607\) 13.9722 + 24.2005i 0.567114 + 0.982270i 0.996850 + 0.0793153i \(0.0252734\pi\)
−0.429736 + 0.902955i \(0.641393\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 32.5505 1.31685
\(612\) 0 0
\(613\) 2.69694 0.108928 0.0544642 0.998516i \(-0.482655\pi\)
0.0544642 + 0.998516i \(0.482655\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2.84847 4.93369i −0.114675 0.198623i 0.802975 0.596013i \(-0.203249\pi\)
−0.917650 + 0.397390i \(0.869916\pi\)
\(618\) 0 0
\(619\) −4.07321 + 7.05501i −0.163716 + 0.283565i −0.936199 0.351471i \(-0.885681\pi\)
0.772482 + 0.635036i \(0.219015\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.24745 3.89270i 0.0900421 0.155958i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 43.5959 1.73828
\(630\) 0 0
\(631\) −25.7980 −1.02700 −0.513500 0.858089i \(-0.671651\pi\)
−0.513500 + 0.858089i \(0.671651\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.00000 6.92820i −0.158735 0.274937i
\(636\) 0 0
\(637\) −9.55051 + 16.5420i −0.378405 + 0.655417i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −6.29796 + 10.9084i −0.248754 + 0.430855i −0.963180 0.268856i \(-0.913355\pi\)
0.714426 + 0.699711i \(0.246688\pi\)
\(642\) 0 0
\(643\) 5.17423 + 8.96204i 0.204052 + 0.353428i 0.949830 0.312766i \(-0.101256\pi\)
−0.745778 + 0.666194i \(0.767922\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.79796 0.385198 0.192599 0.981278i \(-0.438308\pi\)
0.192599 + 0.981278i \(0.438308\pi\)
\(648\) 0 0
\(649\) 1.20204 0.0471842
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.50000 14.7224i −0.332631 0.576133i 0.650396 0.759595i \(-0.274603\pi\)
−0.983027 + 0.183462i \(0.941270\pi\)
\(654\) 0 0
\(655\) 5.62372 9.74058i 0.219737 0.380596i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 11.1742 19.3543i 0.435286 0.753938i −0.562033 0.827115i \(-0.689980\pi\)
0.997319 + 0.0731770i \(0.0233138\pi\)
\(660\) 0 0
\(661\) −14.1969 24.5898i −0.552197 0.956433i −0.998116 0.0613597i \(-0.980456\pi\)
0.445919 0.895073i \(-0.352877\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.79796 −0.224835
\(666\) 0 0
\(667\) −5.44949 −0.211005
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.27526 5.67291i −0.126440 0.219000i
\(672\) 0 0
\(673\) 20.6464 35.7607i 0.795861 1.37847i −0.126429 0.991976i \(-0.540352\pi\)
0.922291 0.386497i \(-0.126315\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −17.1969 + 29.7860i −0.660932 + 1.14477i 0.319439 + 0.947607i \(0.396506\pi\)
−0.980371 + 0.197161i \(0.936828\pi\)
\(678\) 0 0
\(679\) 4.27526 + 7.40496i 0.164069 + 0.284176i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −41.3939 −1.58389 −0.791946 0.610591i \(-0.790932\pi\)
−0.791946 + 0.610591i \(0.790932\pi\)
\(684\) 0 0
\(685\) 19.8990 0.760301
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.75255 + 3.03551i 0.0667669 + 0.115644i
\(690\) 0 0
\(691\) −7.97219 + 13.8082i −0.303277 + 0.525290i −0.976876 0.213806i \(-0.931414\pi\)
0.673600 + 0.739096i \(0.264747\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.724745 + 1.25529i −0.0274911 + 0.0476161i
\(696\) 0 0
\(697\) −5.14643 8.91388i −0.194935 0.337637i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −36.4949 −1.37839 −0.689197 0.724574i \(-0.742036\pi\)
−0.689197 + 0.724574i \(0.742036\pi\)
\(702\) 0 0
\(703\) 35.5959 1.34253
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4.92679 + 8.53344i 0.185291 + 0.320933i
\(708\) 0 0
\(709\) 2.50000 4.33013i 0.0938895 0.162621i −0.815255 0.579102i \(-0.803403\pi\)
0.909145 + 0.416481i \(0.136737\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.05051 + 3.55159i −0.0767922 + 0.133008i
\(714\) 0 0
\(715\) 6.72474 + 11.6476i 0.251491 + 0.435596i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 47.1918 1.75996 0.879979 0.475012i \(-0.157556\pi\)
0.879979 + 0.475012i \(0.157556\pi\)
\(720\) 0 0
\(721\) −25.2929 −0.941955
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −19.7980 34.2911i −0.735278 1.27354i
\(726\) 0 0
\(727\) 11.7247 20.3079i 0.434847 0.753177i −0.562436 0.826841i \(-0.690136\pi\)
0.997283 + 0.0736639i \(0.0234692\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −30.2474 + 52.3901i −1.11874 + 1.93772i
\(732\) 0 0
\(733\) 1.05051 + 1.81954i 0.0388015 + 0.0672061i 0.884774 0.466020i \(-0.154313\pi\)
−0.845972 + 0.533227i \(0.820979\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8.10102 −0.298405
\(738\) 0 0
\(739\) −14.0000 −0.514998 −0.257499 0.966279i \(-0.582898\pi\)
−0.257499 + 0.966279i \(0.582898\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −15.2753 26.4575i −0.560395 0.970632i −0.997462 0.0712033i \(-0.977316\pi\)
0.437067 0.899429i \(-0.356017\pi\)
\(744\) 0 0
\(745\) 6.94949 12.0369i 0.254610 0.440997i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −10.0000 + 17.3205i −0.365392 + 0.632878i
\(750\) 0 0
\(751\) −20.3207 35.1964i −0.741512 1.28434i −0.951807 0.306698i \(-0.900776\pi\)
0.210295 0.977638i \(-0.432557\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −9.24745 −0.336549
\(756\) 0 0
\(757\) −42.0000 −1.52652 −0.763258 0.646094i \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 21.6464 + 37.4927i 0.784682 + 1.35911i 0.929189 + 0.369606i \(0.120507\pi\)
−0.144506 + 0.989504i \(0.546159\pi\)
\(762\) 0 0
\(763\) −6.44949 + 11.1708i −0.233487 + 0.404412i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.679337 1.17665i 0.0245294 0.0424862i
\(768\) 0 0
\(769\) −1.29796 2.24813i −0.0468056 0.0810697i 0.841673 0.539987i \(-0.181571\pi\)
−0.888479 + 0.458917i \(0.848237\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.4949 −0.449410 −0.224705 0.974427i \(-0.572142\pi\)
−0.224705 + 0.974427i \(0.572142\pi\)
\(774\) 0 0
\(775\) −29.7980 −1.07037
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.20204 7.27815i −0.150554 0.260767i
\(780\) 0 0
\(781\) −20.3485 + 35.2446i −0.728125 + 1.26115i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −4.39898 + 7.61926i −0.157006 + 0.271943i
\(786\) 0 0
\(787\) −1.62372 2.81237i −0.0578795 0.100250i 0.835634 0.549287i \(-0.185101\pi\)
−0.893513 + 0.449037i \(0.851767\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −15.6515 −0.556504
\(792\) 0 0
\(793\) −7.40408 −0.262927
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 9.15153 + 15.8509i 0.324164 + 0.561468i 0.981343 0.192266i \(-0.0615838\pi\)
−0.657179 + 0.753735i \(0.728250\pi\)
\(798\) 0 0
\(799\) 20.4495 35.4196i 0.723451 1.25305i
\(800\) 0 0
\(801\) 0 0
\(802\)