Properties

Label 2592.2.s.h.863.3
Level $2592$
Weight $2$
Character 2592.863
Analytic conductor $20.697$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2592.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.6972242039\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 864)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 863.3
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 2592.863
Dual form 2592.2.s.h.1727.3

$q$-expansion

\(f(q)\) \(=\) \(q+(2.72474 + 1.57313i) q^{5} +(-2.98735 + 1.72474i) q^{7} +O(q^{10})\) \(q+(2.72474 + 1.57313i) q^{5} +(-2.98735 + 1.72474i) q^{7} +(-2.28024 - 3.94949i) q^{11} +(3.44949 - 5.97469i) q^{13} +3.46410i q^{17} -4.89898i q^{19} +(1.41421 - 2.44949i) q^{23} +(2.44949 + 4.24264i) q^{25} +(1.89898 - 1.09638i) q^{29} +(-2.20881 - 1.27526i) q^{31} -10.8530 q^{35} -4.89898 q^{37} +(-3.55051 - 2.04989i) q^{41} +(-2.51059 + 1.44949i) q^{43} +(-1.09638 - 1.89898i) q^{47} +(2.44949 - 4.24264i) q^{49} -12.9029i q^{53} -14.3485i q^{55} +(1.09638 - 1.89898i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(18.7980 - 10.8530i) q^{65} +(12.9029 + 7.44949i) q^{67} +13.2207 q^{71} -7.89898 q^{73} +(13.6237 + 7.86566i) q^{77} +(-1.73205 + 1.00000i) q^{79} +(-6.20504 - 10.7474i) q^{83} +(-5.44949 + 9.43879i) q^{85} -5.02118i q^{89} +23.7980i q^{91} +(7.70674 - 13.3485i) q^{95} +(2.50000 + 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 12 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 12 q^{5} + 8 q^{13} - 24 q^{29} - 48 q^{41} - 16 q^{61} + 72 q^{65} - 24 q^{73} + 60 q^{77} - 24 q^{85} + 20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(5\) 2.72474 + 1.57313i 1.21854 + 0.703526i 0.964606 0.263695i \(-0.0849412\pi\)
0.253937 + 0.967221i \(0.418274\pi\)
\(6\) 0 0
\(7\) −2.98735 + 1.72474i −1.12911 + 0.651892i −0.943711 0.330771i \(-0.892691\pi\)
−0.185399 + 0.982663i \(0.559358\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.28024 3.94949i −0.687518 1.19082i −0.972638 0.232324i \(-0.925367\pi\)
0.285120 0.958492i \(-0.407966\pi\)
\(12\) 0 0
\(13\) 3.44949 5.97469i 0.956716 1.65708i 0.226326 0.974052i \(-0.427329\pi\)
0.730391 0.683030i \(-0.239338\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.46410i 0.840168i 0.907485 + 0.420084i \(0.137999\pi\)
−0.907485 + 0.420084i \(0.862001\pi\)
\(18\) 0 0
\(19\) 4.89898i 1.12390i −0.827170 0.561951i \(-0.810051\pi\)
0.827170 0.561951i \(-0.189949\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.41421 2.44949i 0.294884 0.510754i −0.680074 0.733144i \(-0.738052\pi\)
0.974958 + 0.222390i \(0.0713857\pi\)
\(24\) 0 0
\(25\) 2.44949 + 4.24264i 0.489898 + 0.848528i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.89898 1.09638i 0.352632 0.203592i −0.313212 0.949683i \(-0.601405\pi\)
0.665844 + 0.746091i \(0.268072\pi\)
\(30\) 0 0
\(31\) −2.20881 1.27526i −0.396713 0.229043i 0.288352 0.957525i \(-0.406893\pi\)
−0.685065 + 0.728482i \(0.740226\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −10.8530 −1.83449
\(36\) 0 0
\(37\) −4.89898 −0.805387 −0.402694 0.915335i \(-0.631926\pi\)
−0.402694 + 0.915335i \(0.631926\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.55051 2.04989i −0.554497 0.320139i 0.196437 0.980516i \(-0.437063\pi\)
−0.750934 + 0.660378i \(0.770396\pi\)
\(42\) 0 0
\(43\) −2.51059 + 1.44949i −0.382861 + 0.221045i −0.679062 0.734080i \(-0.737613\pi\)
0.296201 + 0.955126i \(0.404280\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.09638 1.89898i −0.159923 0.276995i 0.774918 0.632062i \(-0.217791\pi\)
−0.934841 + 0.355067i \(0.884458\pi\)
\(48\) 0 0
\(49\) 2.44949 4.24264i 0.349927 0.606092i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 12.9029i 1.77235i −0.463352 0.886174i \(-0.653353\pi\)
0.463352 0.886174i \(-0.346647\pi\)
\(54\) 0 0
\(55\) 14.3485i 1.93475i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.09638 1.89898i 0.142736 0.247226i −0.785790 0.618493i \(-0.787743\pi\)
0.928526 + 0.371267i \(0.121077\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 18.7980 10.8530i 2.33160 1.34615i
\(66\) 0 0
\(67\) 12.9029 + 7.44949i 1.57634 + 0.910100i 0.995364 + 0.0961789i \(0.0306621\pi\)
0.580975 + 0.813921i \(0.302671\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.2207 1.56901 0.784506 0.620121i \(-0.212917\pi\)
0.784506 + 0.620121i \(0.212917\pi\)
\(72\) 0 0
\(73\) −7.89898 −0.924506 −0.462253 0.886748i \(-0.652959\pi\)
−0.462253 + 0.886748i \(0.652959\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 13.6237 + 7.86566i 1.55257 + 0.896375i
\(78\) 0 0
\(79\) −1.73205 + 1.00000i −0.194871 + 0.112509i −0.594261 0.804272i \(-0.702555\pi\)
0.399390 + 0.916781i \(0.369222\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.20504 10.7474i −0.681092 1.17969i −0.974648 0.223744i \(-0.928172\pi\)
0.293556 0.955942i \(-0.405161\pi\)
\(84\) 0 0
\(85\) −5.44949 + 9.43879i −0.591080 + 1.02378i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.02118i 0.532244i −0.963939 0.266122i \(-0.914258\pi\)
0.963939 0.266122i \(-0.0857424\pi\)
\(90\) 0 0
\(91\) 23.7980i 2.49470i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 7.70674 13.3485i 0.790695 1.36952i
\(96\) 0 0
\(97\) 2.50000 + 4.33013i 0.253837 + 0.439658i 0.964579 0.263795i \(-0.0849741\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.37628 + 0.794593i −0.136945 + 0.0790650i −0.566907 0.823782i \(-0.691860\pi\)
0.429962 + 0.902847i \(0.358527\pi\)
\(102\) 0 0
\(103\) −8.66025 5.00000i −0.853320 0.492665i 0.00844953 0.999964i \(-0.497310\pi\)
−0.861770 + 0.507300i \(0.830644\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.66025 0.837218 0.418609 0.908166i \(-0.362518\pi\)
0.418609 + 0.908166i \(0.362518\pi\)
\(108\) 0 0
\(109\) 4.89898 0.469237 0.234619 0.972088i \(-0.424616\pi\)
0.234619 + 0.972088i \(0.424616\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 12.2474 + 7.07107i 1.15214 + 0.665190i 0.949409 0.314044i \(-0.101684\pi\)
0.202735 + 0.979234i \(0.435017\pi\)
\(114\) 0 0
\(115\) 7.70674 4.44949i 0.718657 0.414917i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −5.97469 10.3485i −0.547699 0.948643i
\(120\) 0 0
\(121\) −4.89898 + 8.48528i −0.445362 + 0.771389i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0.317837i 0.0284282i
\(126\) 0 0
\(127\) 9.24745i 0.820578i 0.911955 + 0.410289i \(0.134572\pi\)
−0.911955 + 0.410289i \(0.865428\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.15855 12.3990i 0.625446 1.08330i −0.363009 0.931786i \(-0.618250\pi\)
0.988454 0.151518i \(-0.0484162\pi\)
\(132\) 0 0
\(133\) 8.44949 + 14.6349i 0.732664 + 1.26901i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 15.2474 8.80312i 1.30268 0.752101i 0.321815 0.946803i \(-0.395707\pi\)
0.980863 + 0.194701i \(0.0623738\pi\)
\(138\) 0 0
\(139\) 17.3205 + 10.0000i 1.46911 + 0.848189i 0.999400 0.0346338i \(-0.0110265\pi\)
0.469706 + 0.882823i \(0.344360\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −31.4626 −2.63104
\(144\) 0 0
\(145\) 6.89898 0.572929
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.72474 3.30518i −0.468989 0.270771i 0.246827 0.969060i \(-0.420612\pi\)
−0.715817 + 0.698288i \(0.753945\pi\)
\(150\) 0 0
\(151\) 6.27647 3.62372i 0.510772 0.294895i −0.222379 0.974960i \(-0.571382\pi\)
0.733151 + 0.680066i \(0.238049\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.01229 6.94949i −0.322275 0.558196i
\(156\) 0 0
\(157\) −2.89898 + 5.02118i −0.231364 + 0.400734i −0.958210 0.286067i \(-0.907652\pi\)
0.726846 + 0.686801i \(0.240985\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 9.75663i 0.768930i
\(162\) 0 0
\(163\) 6.00000i 0.469956i 0.972001 + 0.234978i \(0.0755019\pi\)
−0.972001 + 0.234978i \(0.924498\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.83183 + 10.1010i −0.451280 + 0.781640i −0.998466 0.0553709i \(-0.982366\pi\)
0.547186 + 0.837011i \(0.315699\pi\)
\(168\) 0 0
\(169\) −17.2980 29.9609i −1.33061 2.30469i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 7.62372 4.40156i 0.579621 0.334644i −0.181362 0.983416i \(-0.558050\pi\)
0.760983 + 0.648772i \(0.224717\pi\)
\(174\) 0 0
\(175\) −14.6349 8.44949i −1.10630 0.638721i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.66025 −0.647298 −0.323649 0.946177i \(-0.604910\pi\)
−0.323649 + 0.946177i \(0.604910\pi\)
\(180\) 0 0
\(181\) 9.79796 0.728277 0.364138 0.931345i \(-0.381364\pi\)
0.364138 + 0.931345i \(0.381364\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −13.3485 7.70674i −0.981399 0.566611i
\(186\) 0 0
\(187\) 13.6814 7.89898i 1.00049 0.577631i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.33902 9.24745i −0.386318 0.669122i 0.605633 0.795744i \(-0.292920\pi\)
−0.991951 + 0.126622i \(0.959586\pi\)
\(192\) 0 0
\(193\) −5.94949 + 10.3048i −0.428254 + 0.741757i −0.996718 0.0809508i \(-0.974204\pi\)
0.568464 + 0.822708i \(0.307538\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.87492i 0.133582i −0.997767 0.0667911i \(-0.978724\pi\)
0.997767 0.0667911i \(-0.0212761\pi\)
\(198\) 0 0
\(199\) 5.65153i 0.400626i −0.979732 0.200313i \(-0.935804\pi\)
0.979732 0.200313i \(-0.0641960\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.78194 + 6.55051i −0.265440 + 0.459756i
\(204\) 0 0
\(205\) −6.44949 11.1708i −0.450452 0.780206i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −19.3485 + 11.1708i −1.33836 + 0.772703i
\(210\) 0 0
\(211\) −17.7491 10.2474i −1.22190 0.705463i −0.256576 0.966524i \(-0.582594\pi\)
−0.965322 + 0.261061i \(0.915928\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −9.12096 −0.622044
\(216\) 0 0
\(217\) 8.79796 0.597244
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 20.6969 + 11.9494i 1.39223 + 0.803802i
\(222\) 0 0
\(223\) −17.1455 + 9.89898i −1.14815 + 0.662885i −0.948436 0.316969i \(-0.897335\pi\)
−0.199714 + 0.979854i \(0.564001\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.4887 + 19.8990i 0.762531 + 1.32074i 0.941542 + 0.336895i \(0.109377\pi\)
−0.179012 + 0.983847i \(0.557290\pi\)
\(228\) 0 0
\(229\) −1.00000 + 1.73205i −0.0660819 + 0.114457i −0.897173 0.441679i \(-0.854383\pi\)
0.831092 + 0.556136i \(0.187717\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.56388i 0.495526i −0.968821 0.247763i \(-0.920305\pi\)
0.968821 0.247763i \(-0.0796954\pi\)
\(234\) 0 0
\(235\) 6.89898i 0.450040i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −3.60697 + 6.24745i −0.233315 + 0.404114i −0.958782 0.284144i \(-0.908291\pi\)
0.725466 + 0.688258i \(0.241624\pi\)
\(240\) 0 0
\(241\) 0.101021 + 0.174973i 0.00650730 + 0.0112710i 0.869261 0.494354i \(-0.164595\pi\)
−0.862753 + 0.505625i \(0.831262\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 13.3485 7.70674i 0.852802 0.492366i
\(246\) 0 0
\(247\) −29.2699 16.8990i −1.86240 1.07526i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 17.3205 1.09326 0.546630 0.837374i \(-0.315910\pi\)
0.546630 + 0.837374i \(0.315910\pi\)
\(252\) 0 0
\(253\) −12.8990 −0.810952
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 19.8990 + 11.4887i 1.24126 + 0.716644i 0.969352 0.245678i \(-0.0790105\pi\)
0.271913 + 0.962322i \(0.412344\pi\)
\(258\) 0 0
\(259\) 14.6349 8.44949i 0.909371 0.525026i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −15.2706 26.4495i −0.941627 1.63095i −0.762368 0.647143i \(-0.775963\pi\)
−0.179258 0.983802i \(-0.557370\pi\)
\(264\) 0 0
\(265\) 20.2980 35.1571i 1.24689 2.15968i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 10.3923i 0.633630i 0.948487 + 0.316815i \(0.102613\pi\)
−0.948487 + 0.316815i \(0.897387\pi\)
\(270\) 0 0
\(271\) 17.4495i 1.05998i −0.848004 0.529991i \(-0.822195\pi\)
0.848004 0.529991i \(-0.177805\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 11.1708 19.3485i 0.673627 1.16676i
\(276\) 0 0
\(277\) −2.89898 5.02118i −0.174183 0.301693i 0.765695 0.643203i \(-0.222395\pi\)
−0.939878 + 0.341510i \(0.889062\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −18.7980 + 10.8530i −1.12139 + 0.647436i −0.941756 0.336297i \(-0.890825\pi\)
−0.179636 + 0.983733i \(0.557492\pi\)
\(282\) 0 0
\(283\) 11.1708 + 6.44949i 0.664038 + 0.383382i 0.793814 0.608161i \(-0.208092\pi\)
−0.129776 + 0.991543i \(0.541426\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 14.1421 0.834784
\(288\) 0 0
\(289\) 5.00000 0.294118
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −24.7980 14.3171i −1.44871 0.836414i −0.450307 0.892874i \(-0.648686\pi\)
−0.998405 + 0.0564592i \(0.982019\pi\)
\(294\) 0 0
\(295\) 5.97469 3.44949i 0.347860 0.200837i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −9.75663 16.8990i −0.564241 0.977293i
\(300\) 0 0
\(301\) 5.00000 8.66025i 0.288195 0.499169i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 12.5851i 0.720618i
\(306\) 0 0
\(307\) 18.0000i 1.02731i 0.857996 + 0.513657i \(0.171710\pi\)
−0.857996 + 0.513657i \(0.828290\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.87832 8.44949i 0.276624 0.479127i −0.693920 0.720052i \(-0.744118\pi\)
0.970544 + 0.240926i \(0.0774511\pi\)
\(312\) 0 0
\(313\) 9.74745 + 16.8831i 0.550958 + 0.954288i 0.998206 + 0.0598776i \(0.0190710\pi\)
−0.447247 + 0.894410i \(0.647596\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.3763 7.72280i 0.751286 0.433755i −0.0748721 0.997193i \(-0.523855\pi\)
0.826159 + 0.563438i \(0.190522\pi\)
\(318\) 0 0
\(319\) −8.66025 5.00000i −0.484881 0.279946i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 16.9706 0.944267
\(324\) 0 0
\(325\) 33.7980 1.87477
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.55051 + 3.78194i 0.361141 + 0.208505i
\(330\) 0 0
\(331\) −24.8523 + 14.3485i −1.36600 + 0.788663i −0.990415 0.138123i \(-0.955893\pi\)
−0.375590 + 0.926786i \(0.622560\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 23.4381 + 40.5959i 1.28056 + 2.21799i
\(336\) 0 0
\(337\) −11.8990 + 20.6096i −0.648179 + 1.12268i 0.335379 + 0.942083i \(0.391136\pi\)
−0.983558 + 0.180595i \(0.942198\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 11.6315i 0.629884i
\(342\) 0 0
\(343\) 7.24745i 0.391325i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −11.4012 + 19.7474i −0.612048 + 1.06010i 0.378847 + 0.925460i \(0.376321\pi\)
−0.990895 + 0.134639i \(0.957013\pi\)
\(348\) 0 0
\(349\) −7.55051 13.0779i −0.404170 0.700042i 0.590055 0.807363i \(-0.299106\pi\)
−0.994224 + 0.107321i \(0.965773\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.2474 7.07107i 0.651866 0.376355i −0.137305 0.990529i \(-0.543844\pi\)
0.789171 + 0.614174i \(0.210511\pi\)
\(354\) 0 0
\(355\) 36.0231 + 20.7980i 1.91191 + 1.10384i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.349945 0.0184694 0.00923470 0.999957i \(-0.497060\pi\)
0.00923470 + 0.999957i \(0.497060\pi\)
\(360\) 0 0
\(361\) −5.00000 −0.263158
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −21.5227 12.4261i −1.12655 0.650414i
\(366\) 0 0
\(367\) −11.6476 + 6.72474i −0.608000 + 0.351029i −0.772182 0.635401i \(-0.780835\pi\)
0.164182 + 0.986430i \(0.447501\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 22.2542 + 38.5454i 1.15538 + 2.00118i
\(372\) 0 0
\(373\) 7.24745 12.5529i 0.375259 0.649967i −0.615107 0.788444i \(-0.710887\pi\)
0.990366 + 0.138477i \(0.0442205\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 15.1278i 0.779119i
\(378\) 0 0
\(379\) 8.00000i 0.410932i 0.978664 + 0.205466i \(0.0658711\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.2672 21.2474i 0.626826 1.08569i −0.361359 0.932427i \(-0.617687\pi\)
0.988185 0.153267i \(-0.0489795\pi\)
\(384\) 0 0
\(385\) 24.7474 + 42.8638i 1.26125 + 2.18454i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −18.7702 + 10.8370i −0.951685 + 0.549455i −0.893604 0.448857i \(-0.851831\pi\)
−0.0580807 + 0.998312i \(0.518498\pi\)
\(390\) 0 0
\(391\) 8.48528 + 4.89898i 0.429119 + 0.247752i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6.29253 −0.316611
\(396\) 0 0
\(397\) −20.6969 −1.03875 −0.519375 0.854547i \(-0.673835\pi\)
−0.519375 + 0.854547i \(0.673835\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −19.5959 11.3137i −0.978573 0.564980i −0.0767343 0.997052i \(-0.524449\pi\)
−0.901839 + 0.432072i \(0.857783\pi\)
\(402\) 0 0
\(403\) −15.2385 + 8.79796i −0.759084 + 0.438258i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 11.1708 + 19.3485i 0.553718 + 0.959068i
\(408\) 0 0
\(409\) 3.50000 6.06218i 0.173064 0.299755i −0.766426 0.642333i \(-0.777967\pi\)
0.939490 + 0.342578i \(0.111300\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7.56388i 0.372194i
\(414\) 0 0
\(415\) 39.0454i 1.91666i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −9.58166 + 16.5959i −0.468095 + 0.810764i −0.999335 0.0364574i \(-0.988393\pi\)
0.531241 + 0.847221i \(0.321726\pi\)
\(420\) 0 0
\(421\) 5.10102 + 8.83523i 0.248609 + 0.430603i 0.963140 0.269001i \(-0.0866934\pi\)
−0.714531 + 0.699603i \(0.753360\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −14.6969 + 8.48528i −0.712906 + 0.411597i
\(426\) 0 0
\(427\) 11.9494 + 6.89898i 0.578271 + 0.333865i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.57826 0.316864 0.158432 0.987370i \(-0.449356\pi\)
0.158432 + 0.987370i \(0.449356\pi\)
\(432\) 0 0
\(433\) −26.3939 −1.26841 −0.634204 0.773165i \(-0.718672\pi\)
−0.634204 + 0.773165i \(0.718672\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −12.0000 6.92820i −0.574038 0.331421i
\(438\) 0 0
\(439\) −4.54442 + 2.62372i −0.216894 + 0.125224i −0.604511 0.796597i \(-0.706631\pi\)
0.387618 + 0.921820i \(0.373298\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.00340 5.20204i −0.142696 0.247156i 0.785815 0.618462i \(-0.212244\pi\)
−0.928511 + 0.371305i \(0.878910\pi\)
\(444\) 0 0
\(445\) 7.89898 13.6814i 0.374448 0.648562i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.37113i 0.253479i −0.991936 0.126740i \(-0.959549\pi\)
0.991936 0.126740i \(-0.0404512\pi\)
\(450\) 0 0
\(451\) 18.6969i 0.880404i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −37.4373 + 64.8434i −1.75509 + 3.03990i
\(456\) 0 0
\(457\) −12.5000 21.6506i −0.584725 1.01277i −0.994910 0.100771i \(-0.967869\pi\)
0.410184 0.912003i \(-0.365464\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.6237 + 6.13361i −0.494796 + 0.285671i −0.726562 0.687101i \(-0.758883\pi\)
0.231766 + 0.972772i \(0.425550\pi\)
\(462\) 0 0
\(463\) 14.7618 + 8.52270i 0.686037 + 0.396084i 0.802126 0.597155i \(-0.203702\pi\)
−0.116089 + 0.993239i \(0.537036\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.1455 −0.793401 −0.396700 0.917948i \(-0.629845\pi\)
−0.396700 + 0.917948i \(0.629845\pi\)
\(468\) 0 0
\(469\) −51.3939 −2.37315
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 11.4495 + 6.61037i 0.526448 + 0.303945i
\(474\) 0 0
\(475\) 20.7846 12.0000i 0.953663 0.550598i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9.58166 + 16.5959i 0.437797 + 0.758287i 0.997519 0.0703935i \(-0.0224255\pi\)
−0.559722 + 0.828680i \(0.689092\pi\)
\(480\) 0 0
\(481\) −16.8990 + 29.2699i −0.770527 + 1.33459i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 15.7313i 0.714323i
\(486\) 0 0
\(487\) 15.7980i 0.715874i 0.933746 + 0.357937i \(0.116520\pi\)
−0.933746 + 0.357937i \(0.883480\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.50170 + 2.60102i −0.0677708 + 0.117382i −0.897920 0.440159i \(-0.854922\pi\)
0.830149 + 0.557542i \(0.188255\pi\)
\(492\) 0 0
\(493\) 3.79796 + 6.57826i 0.171051 + 0.296270i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −39.4949 + 22.8024i −1.77159 + 1.02283i
\(498\) 0 0
\(499\) −4.41761 2.55051i −0.197760 0.114177i 0.397850 0.917450i \(-0.369756\pi\)
−0.595610 + 0.803274i \(0.703090\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 31.1127 1.38725 0.693623 0.720338i \(-0.256013\pi\)
0.693623 + 0.720338i \(0.256013\pi\)
\(504\) 0 0
\(505\) −5.00000 −0.222497
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −38.1186 22.0078i −1.68958 0.975478i −0.954837 0.297131i \(-0.903970\pi\)
−0.734742 0.678347i \(-0.762697\pi\)
\(510\) 0 0
\(511\) 23.5970 13.6237i 1.04387 0.602678i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −15.7313 27.2474i −0.693205 1.20067i
\(516\) 0 0
\(517\) −5.00000 + 8.66025i −0.219900 + 0.380878i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.921404i 0.0403674i −0.999796 0.0201837i \(-0.993575\pi\)
0.999796 0.0201837i \(-0.00642511\pi\)
\(522\) 0 0
\(523\) 31.3939i 1.37276i −0.727244 0.686379i \(-0.759199\pi\)
0.727244 0.686379i \(-0.240801\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.41761 7.65153i 0.192434 0.333306i
\(528\) 0 0
\(529\) 7.50000 + 12.9904i 0.326087 + 0.564799i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −24.4949 + 14.1421i −1.06099 + 0.612564i
\(534\) 0 0
\(535\) 23.5970 + 13.6237i 1.02019 + 0.589005i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −22.3417 −0.962325
\(540\) 0 0
\(541\) −20.0000 −0.859867 −0.429934 0.902861i \(-0.641463\pi\)
−0.429934 + 0.902861i \(0.641463\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 13.3485 + 7.70674i 0.571786 + 0.330121i
\(546\) 0 0
\(547\) −3.63907 + 2.10102i −0.155596 + 0.0898332i −0.575776 0.817607i \(-0.695300\pi\)
0.420181 + 0.907440i \(0.361967\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.37113 9.30306i −0.228818 0.396324i
\(552\) 0 0
\(553\) 3.44949 5.97469i 0.146687 0.254070i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 29.8735i 1.26578i 0.774242 + 0.632890i \(0.218131\pi\)
−0.774242 + 0.632890i \(0.781869\pi\)
\(558\) 0 0
\(559\) 20.0000i 0.845910i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2.74094 + 4.74745i −0.115517 + 0.200081i −0.917986 0.396612i \(-0.870186\pi\)
0.802469 + 0.596693i \(0.203519\pi\)
\(564\) 0 0
\(565\) 22.2474 + 38.5337i 0.935957 + 1.62113i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −16.8990 + 9.75663i −0.708442 + 0.409019i −0.810484 0.585761i \(-0.800796\pi\)
0.102042 + 0.994780i \(0.467462\pi\)
\(570\) 0 0
\(571\) 0.174973 + 0.101021i 0.00732238 + 0.00422758i 0.503657 0.863904i \(-0.331988\pi\)
−0.496334 + 0.868131i \(0.665321\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 13.8564 0.577852
\(576\) 0 0
\(577\) 15.7980 0.657678 0.328839 0.944386i \(-0.393343\pi\)
0.328839 + 0.944386i \(0.393343\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 37.0732 + 21.4042i 1.53806 + 0.887997i
\(582\) 0 0
\(583\) −50.9599 + 29.4217i −2.11054 + 1.21852i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 16.7402 + 28.9949i 0.690942 + 1.19675i 0.971529 + 0.236919i \(0.0761376\pi\)
−0.280587 + 0.959829i \(0.590529\pi\)
\(588\) 0 0
\(589\) −6.24745 + 10.8209i −0.257422 + 0.445867i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 42.7764i 1.75661i 0.478097 + 0.878307i \(0.341327\pi\)
−0.478097 + 0.878307i \(0.658673\pi\)
\(594\) 0 0
\(595\) 37.5959i 1.54128i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 18.4169 31.8990i 0.752493 1.30336i −0.194117 0.980978i \(-0.562184\pi\)
0.946611 0.322379i \(-0.104482\pi\)
\(600\) 0 0
\(601\) −19.8485 34.3786i −0.809636 1.40233i −0.913116 0.407699i \(-0.866331\pi\)
0.103480 0.994631i \(-0.467002\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −26.6969 + 15.4135i −1.08538 + 0.626647i
\(606\) 0 0
\(607\) 3.63907 + 2.10102i 0.147705 + 0.0852778i 0.572031 0.820232i \(-0.306156\pi\)
−0.424326 + 0.905510i \(0.639489\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −15.1278 −0.612003
\(612\) 0 0
\(613\) 30.0000 1.21169 0.605844 0.795583i \(-0.292835\pi\)
0.605844 + 0.795583i \(0.292835\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.247449 0.142865i −0.00996191 0.00575151i 0.495011 0.868887i \(-0.335164\pi\)
−0.504973 + 0.863135i \(0.668497\pi\)
\(618\) 0 0
\(619\) 15.2385 8.79796i 0.612488 0.353620i −0.161451 0.986881i \(-0.551617\pi\)
0.773938 + 0.633261i \(0.218284\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8.66025 + 15.0000i 0.346966 + 0.600962i
\(624\) 0 0
\(625\) 12.7474 22.0792i 0.509898 0.883169i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 16.9706i 0.676661i
\(630\) 0 0
\(631\) 27.7423i 1.10441i 0.833710 + 0.552203i \(0.186213\pi\)
−0.833710 + 0.552203i \(0.813787\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −14.5475 + 25.1969i −0.577298 + 0.999910i
\(636\) 0 0
\(637\) −16.8990 29.2699i −0.669562 1.15972i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 17.7526 10.2494i 0.701184 0.404829i −0.106604 0.994302i \(-0.533998\pi\)
0.807788 + 0.589473i \(0.200665\pi\)
\(642\) 0 0
\(643\) 18.5276 + 10.6969i 0.730659 + 0.421846i 0.818663 0.574274i \(-0.194716\pi\)
−0.0880043 + 0.996120i \(0.528049\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 20.7846 0.817127 0.408564 0.912730i \(-0.366030\pi\)
0.408564 + 0.912730i \(0.366030\pi\)
\(648\) 0 0
\(649\) −10.0000 −0.392534
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.07321 + 0.619620i 0.0419981 + 0.0242476i 0.520852 0.853647i \(-0.325614\pi\)
−0.478854 + 0.877895i \(0.658948\pi\)
\(654\) 0 0
\(655\) 39.0105 22.5227i 1.52427 0.880035i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 8.71563 + 15.0959i 0.339513 + 0.588053i 0.984341 0.176274i \(-0.0564045\pi\)
−0.644828 + 0.764327i \(0.723071\pi\)
\(660\) 0 0
\(661\) −22.2474 + 38.5337i −0.865325 + 1.49879i 0.00139818 + 0.999999i \(0.499555\pi\)
−0.866724 + 0.498789i \(0.833778\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 53.1687i 2.06179i
\(666\) 0 0
\(667\) 6.20204i 0.240144i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −9.12096 + 15.7980i −0.352111 + 0.609873i
\(672\) 0 0
\(673\) −1.29796 2.24813i −0.0500326 0.0866591i 0.839924 0.542703i \(-0.182599\pi\)
−0.889957 + 0.456044i \(0.849266\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 39.4949 22.8024i 1.51791 0.876367i 0.518134 0.855299i \(-0.326627\pi\)
0.999778 0.0210677i \(-0.00670654\pi\)
\(678\) 0 0
\(679\) −14.9367 8.62372i −0.573219 0.330948i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 10.3923 0.397650 0.198825 0.980035i \(-0.436287\pi\)
0.198825 + 0.980035i \(0.436287\pi\)
\(684\) 0 0
\(685\) 55.3939 2.11649
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −77.0908 44.5084i −2.93693 1.69564i
\(690\) 0 0
\(691\) −3.46410 + 2.00000i −0.131781 + 0.0760836i −0.564441 0.825473i \(-0.690908\pi\)
0.432660 + 0.901557i \(0.357575\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 31.4626 + 54.4949i 1.19345 + 2.06711i
\(696\) 0 0
\(697\) 7.10102 12.2993i 0.268970 0.465870i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 13.2528i 0.500553i −0.968174 0.250276i \(-0.919478\pi\)
0.968174 0.250276i \(-0.0805215\pi\)
\(702\) 0 0
\(703\) 24.0000i 0.905177i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.74094 4.74745i 0.103084 0.178546i
\(708\) 0 0
\(709\) 20.0000 + 34.6410i 0.751116 + 1.30097i 0.947282 + 0.320400i \(0.103817\pi\)
−0.196167 + 0.980571i \(0.562849\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6.24745 + 3.60697i −0.233969 + 0.135082i
\(714\) 0 0
\(715\) −85.7277 49.4949i −3.20603 1.85100i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −6.92820 −0.258378 −0.129189 0.991620i \(-0.541237\pi\)
−0.129189 + 0.991620i \(0.541237\pi\)
\(720\) 0 0
\(721\) 34.4949 1.28466
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 9.30306 + 5.37113i 0.345507 + 0.199479i
\(726\) 0 0
\(727\) −14.9367 + 8.62372i −0.553973 + 0.319836i −0.750723 0.660617i \(-0.770295\pi\)
0.196750 + 0.980454i \(0.436961\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −5.02118 8.69694i −0.185715 0.321668i
\(732\) 0 0
\(733\) 22.2474 38.5337i 0.821728 1.42328i −0.0826660 0.996577i \(-0.526343\pi\)
0.904394 0.426698i \(-0.140323\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 67.9465i 2.50284i
\(738\) 0 0
\(739\) 39.3939i 1.44913i 0.689208 + 0.724564i \(0.257959\pi\)
−0.689208 + 0.724564i \(0.742041\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.58919 + 2.75255i −0.0583016 + 0.100981i −0.893703 0.448659i \(-0.851902\pi\)
0.835402 + 0.549640i \(0.185235\pi\)
\(744\) 0 0
\(745\) −10.3990 18.0116i −0.380989 0.659893i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −25.8712 + 14.9367i −0.945312 + 0.545776i
\(750\) 0 0
\(751\) −22.2935 12.8712i −0.813502 0.469676i 0.0346683 0.999399i \(-0.488963\pi\)
−0.848171 + 0.529723i \(0.822296\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 22.8024 0.829864
\(756\) 0 0
\(757\) 19.3939 0.704882 0.352441 0.935834i \(-0.385352\pi\)
0.352441 + 0.935834i \(0.385352\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −26.2020 15.1278i −0.949823 0.548381i −0.0567972 0.998386i \(-0.518089\pi\)
−0.893026 + 0.450005i \(0.851422\pi\)
\(762\) 0 0
\(763\) −14.6349 + 8.44949i −0.529821 + 0.305892i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7.56388 13.1010i −0.273116 0.473050i
\(768\) 0 0
\(769\) 18.7474 32.4715i 0.676050 1.17095i −0.300110 0.953904i \(-0.597024\pi\)
0.976161 0.217049i \(-0.0696431\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.349945i 0.0125867i −0.999980 0.00629333i \(-0.997997\pi\)
0.999980 0.00629333i \(-0.00200324\pi\)
\(774\) 0 0
\(775\) 12.4949i 0.448830i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −10.0424 + 17.3939i −0.359805 + 0.623200i
\(780\) 0 0
\(781\) −30.1464 52.2151i −1.07872 1.86840i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −15.7980 + 9.12096i −0.563853 + 0.325541i
\(786\) 0 0
\(787\) −37.4052 21.5959i −1.33335 0.769811i −0.347540 0.937665i \(-0.612983\pi\)
−0.985812 + 0.167854i \(0.946316\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −48.7832 −1.73453
\(792\) 0 0
\(793\) −27.5959 −0.979960
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.72474 5.03723i −0.309046 0.178428i 0.337453 0.941342i \(-0.390434\pi\)
−0.646500 + 0.762914i \(0.723768\pi\)
\(798\) 0 0
\(799\) 6.57826 3.79796i 0.232722 0.134362i
\(800\) 0 0
\(801\) 0 0