Properties

Label 1600.2.q.b.49.1
Level $1600$
Weight $2$
Character 1600.49
Analytic conductor $12.776$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.q (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.7760643234\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 49.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1600.49
Dual form 1600.2.q.b.849.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{3} +2.00000 q^{7} -1.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{3} +2.00000 q^{7} -1.00000i q^{9} +(-1.00000 - 1.00000i) q^{11} +(-1.00000 - 1.00000i) q^{13} +2.00000i q^{17} +(3.00000 - 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} +6.00000 q^{23} +(4.00000 - 4.00000i) q^{27} +(-3.00000 + 3.00000i) q^{29} +8.00000 q^{31} -2.00000i q^{33} +(3.00000 - 3.00000i) q^{37} -2.00000i q^{39} +(5.00000 - 5.00000i) q^{43} +8.00000i q^{47} -3.00000 q^{49} +(-2.00000 + 2.00000i) q^{51} +(5.00000 - 5.00000i) q^{53} +6.00000 q^{57} +(-3.00000 - 3.00000i) q^{59} +(-9.00000 + 9.00000i) q^{61} -2.00000i q^{63} +(-5.00000 - 5.00000i) q^{67} +(6.00000 + 6.00000i) q^{69} +10.0000i q^{71} +4.00000 q^{73} +(-2.00000 - 2.00000i) q^{77} +5.00000 q^{81} +(1.00000 + 1.00000i) q^{83} -6.00000 q^{87} -4.00000i q^{89} +(-2.00000 - 2.00000i) q^{91} +(8.00000 + 8.00000i) q^{93} +2.00000i q^{97} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} + 4q^{7} + O(q^{10}) \) \( 2q + 2q^{3} + 4q^{7} - 2q^{11} - 2q^{13} + 6q^{19} + 4q^{21} + 12q^{23} + 8q^{27} - 6q^{29} + 16q^{31} + 6q^{37} + 10q^{43} - 6q^{49} - 4q^{51} + 10q^{53} + 12q^{57} - 6q^{59} - 18q^{61} - 10q^{67} + 12q^{69} + 8q^{73} - 4q^{77} + 10q^{81} + 2q^{83} - 12q^{87} - 4q^{91} + 16q^{93} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1151\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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
\(3\) 1.00000 + 1.00000i 0.577350 + 0.577350i 0.934172 0.356822i \(-0.116140\pi\)
−0.356822 + 0.934172i \(0.616140\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) −1.00000 1.00000i −0.301511 0.301511i 0.540094 0.841605i \(-0.318389\pi\)
−0.841605 + 0.540094i \(0.818389\pi\)
\(12\) 0 0
\(13\) −1.00000 1.00000i −0.277350 0.277350i 0.554700 0.832050i \(-0.312833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 0 0
\(19\) 3.00000 3.00000i 0.688247 0.688247i −0.273597 0.961844i \(-0.588214\pi\)
0.961844 + 0.273597i \(0.0882135\pi\)
\(20\) 0 0
\(21\) 2.00000 + 2.00000i 0.436436 + 0.436436i
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.00000 4.00000i 0.769800 0.769800i
\(28\) 0 0
\(29\) −3.00000 + 3.00000i −0.557086 + 0.557086i −0.928477 0.371391i \(-0.878881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0 0
\(33\) 2.00000i 0.348155i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 3.00000i 0.493197 0.493197i −0.416115 0.909312i \(-0.636609\pi\)
0.909312 + 0.416115i \(0.136609\pi\)
\(38\) 0 0
\(39\) 2.00000i 0.320256i
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 5.00000 5.00000i 0.762493 0.762493i −0.214280 0.976772i \(-0.568740\pi\)
0.976772 + 0.214280i \(0.0687403\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 0 0
\(51\) −2.00000 + 2.00000i −0.280056 + 0.280056i
\(52\) 0 0
\(53\) 5.00000 5.00000i 0.686803 0.686803i −0.274721 0.961524i \(-0.588586\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 6.00000 0.794719
\(58\) 0 0
\(59\) −3.00000 3.00000i −0.390567 0.390567i 0.484323 0.874889i \(-0.339066\pi\)
−0.874889 + 0.484323i \(0.839066\pi\)
\(60\) 0 0
\(61\) −9.00000 + 9.00000i −1.15233 + 1.15233i −0.166248 + 0.986084i \(0.553165\pi\)
−0.986084 + 0.166248i \(0.946835\pi\)
\(62\) 0 0
\(63\) 2.00000i 0.251976i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −5.00000 5.00000i −0.610847 0.610847i 0.332320 0.943167i \(-0.392169\pi\)
−0.943167 + 0.332320i \(0.892169\pi\)
\(68\) 0 0
\(69\) 6.00000 + 6.00000i 0.722315 + 0.722315i
\(70\) 0 0
\(71\) 10.0000i 1.18678i 0.804914 + 0.593391i \(0.202211\pi\)
−0.804914 + 0.593391i \(0.797789\pi\)
\(72\) 0 0
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.00000 2.00000i −0.227921 0.227921i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) 1.00000 + 1.00000i 0.109764 + 0.109764i 0.759856 0.650092i \(-0.225269\pi\)
−0.650092 + 0.759856i \(0.725269\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −6.00000 −0.643268
\(88\) 0 0
\(89\) 4.00000i 0.423999i −0.977270 0.212000i \(-0.932002\pi\)
0.977270 0.212000i \(-0.0679975\pi\)
\(90\) 0 0
\(91\) −2.00000 2.00000i −0.209657 0.209657i
\(92\) 0 0
\(93\) 8.00000 + 8.00000i 0.829561 + 0.829561i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000i 0.203069i 0.994832 + 0.101535i \(0.0323753\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) 0 0
\(99\) −1.00000 + 1.00000i −0.100504 + 0.100504i
\(100\) 0 0
\(101\) 11.0000 + 11.0000i 1.09454 + 1.09454i 0.995037 + 0.0995037i \(0.0317255\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 6.00000 0.591198 0.295599 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.00000 7.00000i 0.676716 0.676716i −0.282540 0.959256i \(-0.591177\pi\)
0.959256 + 0.282540i \(0.0911770\pi\)
\(108\) 0 0
\(109\) −3.00000 + 3.00000i −0.287348 + 0.287348i −0.836031 0.548683i \(-0.815129\pi\)
0.548683 + 0.836031i \(0.315129\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 + 1.00000i −0.0924500 + 0.0924500i
\(118\) 0 0
\(119\) 4.00000i 0.366679i
\(120\) 0 0
\(121\) 9.00000i 0.818182i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 8.00000i 0.709885i 0.934888 + 0.354943i \(0.115500\pi\)
−0.934888 + 0.354943i \(0.884500\pi\)
\(128\) 0 0
\(129\) 10.0000 0.880451
\(130\) 0 0
\(131\) −11.0000 + 11.0000i −0.961074 + 0.961074i −0.999270 0.0381958i \(-0.987839\pi\)
0.0381958 + 0.999270i \(0.487839\pi\)
\(132\) 0 0
\(133\) 6.00000 6.00000i 0.520266 0.520266i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.00000 0.683486 0.341743 0.939793i \(-0.388983\pi\)
0.341743 + 0.939793i \(0.388983\pi\)
\(138\) 0 0
\(139\) −3.00000 3.00000i −0.254457 0.254457i 0.568338 0.822795i \(-0.307586\pi\)
−0.822795 + 0.568338i \(0.807586\pi\)
\(140\) 0 0
\(141\) −8.00000 + 8.00000i −0.673722 + 0.673722i
\(142\) 0 0
\(143\) 2.00000i 0.167248i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −3.00000 3.00000i −0.247436 0.247436i
\(148\) 0 0
\(149\) −7.00000 7.00000i −0.573462 0.573462i 0.359632 0.933094i \(-0.382902\pi\)
−0.933094 + 0.359632i \(0.882902\pi\)
\(150\) 0 0
\(151\) 10.0000i 0.813788i 0.913475 + 0.406894i \(0.133388\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −15.0000 15.0000i −1.19713 1.19713i −0.975022 0.222108i \(-0.928706\pi\)
−0.222108 0.975022i \(-0.571294\pi\)
\(158\) 0 0
\(159\) 10.0000 0.793052
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) 0 0
\(163\) 1.00000 + 1.00000i 0.0783260 + 0.0783260i 0.745184 0.666858i \(-0.232361\pi\)
−0.666858 + 0.745184i \(0.732361\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.00000 0.154765 0.0773823 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) 0 0
\(171\) −3.00000 3.00000i −0.229416 0.229416i
\(172\) 0 0
\(173\) −1.00000 1.00000i −0.0760286 0.0760286i 0.668070 0.744099i \(-0.267121\pi\)
−0.744099 + 0.668070i \(0.767121\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 6.00000i 0.450988i
\(178\) 0 0
\(179\) −17.0000 + 17.0000i −1.27064 + 1.27064i −0.324887 + 0.945753i \(0.605326\pi\)
−0.945753 + 0.324887i \(0.894674\pi\)
\(180\) 0 0
\(181\) −9.00000 9.00000i −0.668965 0.668965i 0.288512 0.957476i \(-0.406840\pi\)
−0.957476 + 0.288512i \(0.906840\pi\)
\(182\) 0 0
\(183\) −18.0000 −1.33060
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.00000 2.00000i 0.146254 0.146254i
\(188\) 0 0
\(189\) 8.00000 8.00000i 0.581914 0.581914i
\(190\) 0 0
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) 14.0000i 1.00774i 0.863779 + 0.503871i \(0.168091\pi\)
−0.863779 + 0.503871i \(0.831909\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −17.0000 + 17.0000i −1.21120 + 1.21120i −0.240567 + 0.970632i \(0.577334\pi\)
−0.970632 + 0.240567i \(0.922666\pi\)
\(198\) 0 0
\(199\) 14.0000i 0.992434i 0.868199 + 0.496217i \(0.165278\pi\)
−0.868199 + 0.496217i \(0.834722\pi\)
\(200\) 0 0
\(201\) 10.0000i 0.705346i
\(202\) 0 0
\(203\) −6.00000 + 6.00000i −0.421117 + 0.421117i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.00000i 0.417029i
\(208\) 0 0
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) 9.00000 9.00000i 0.619586 0.619586i −0.325840 0.945425i \(-0.605647\pi\)
0.945425 + 0.325840i \(0.105647\pi\)
\(212\) 0 0
\(213\) −10.0000 + 10.0000i −0.685189 + 0.685189i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 16.0000 1.08615
\(218\) 0 0
\(219\) 4.00000 + 4.00000i 0.270295 + 0.270295i
\(220\) 0 0
\(221\) 2.00000 2.00000i 0.134535 0.134535i
\(222\) 0 0
\(223\) 24.0000i 1.60716i −0.595198 0.803579i \(-0.702926\pi\)
0.595198 0.803579i \(-0.297074\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 15.0000 + 15.0000i 0.995585 + 0.995585i 0.999990 0.00440533i \(-0.00140226\pi\)
−0.00440533 + 0.999990i \(0.501402\pi\)
\(228\) 0 0
\(229\) −7.00000 7.00000i −0.462573 0.462573i 0.436925 0.899498i \(-0.356068\pi\)
−0.899498 + 0.436925i \(0.856068\pi\)
\(230\) 0 0
\(231\) 4.00000i 0.263181i
\(232\) 0 0
\(233\) 4.00000 0.262049 0.131024 0.991379i \(-0.458173\pi\)
0.131024 + 0.991379i \(0.458173\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 0 0
\(243\) −7.00000 7.00000i −0.449050 0.449050i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.00000 −0.381771
\(248\) 0 0
\(249\) 2.00000i 0.126745i
\(250\) 0 0
\(251\) −21.0000 21.0000i −1.32551 1.32551i −0.909243 0.416265i \(-0.863339\pi\)
−0.416265 0.909243i \(-0.636661\pi\)
\(252\) 0 0
\(253\) −6.00000 6.00000i −0.377217 0.377217i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 22.0000i 1.37232i 0.727450 + 0.686161i \(0.240706\pi\)
−0.727450 + 0.686161i \(0.759294\pi\)
\(258\) 0 0
\(259\) 6.00000 6.00000i 0.372822 0.372822i
\(260\) 0 0
\(261\) 3.00000 + 3.00000i 0.185695 + 0.185695i
\(262\) 0 0
\(263\) 6.00000 0.369976 0.184988 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 4.00000 4.00000i 0.244796 0.244796i
\(268\) 0 0
\(269\) −3.00000 + 3.00000i −0.182913 + 0.182913i −0.792624 0.609711i \(-0.791286\pi\)
0.609711 + 0.792624i \(0.291286\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 0 0
\(273\) 4.00000i 0.242091i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 3.00000 3.00000i 0.180253 0.180253i −0.611213 0.791466i \(-0.709318\pi\)
0.791466 + 0.611213i \(0.209318\pi\)
\(278\) 0 0
\(279\) 8.00000i 0.478947i
\(280\) 0 0
\(281\) 20.0000i 1.19310i −0.802576 0.596550i \(-0.796538\pi\)
0.802576 0.596550i \(-0.203462\pi\)
\(282\) 0 0
\(283\) −15.0000 + 15.0000i −0.891657 + 0.891657i −0.994679 0.103022i \(-0.967149\pi\)
0.103022 + 0.994679i \(0.467149\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) −2.00000 + 2.00000i −0.117242 + 0.117242i
\(292\) 0 0
\(293\) −15.0000 + 15.0000i −0.876309 + 0.876309i −0.993151 0.116841i \(-0.962723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −8.00000 −0.464207
\(298\) 0 0
\(299\) −6.00000 6.00000i −0.346989 0.346989i
\(300\) 0 0
\(301\) 10.0000 10.0000i 0.576390 0.576390i
\(302\) 0 0
\(303\) 22.0000i 1.26387i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −5.00000 5.00000i −0.285365 0.285365i 0.549879 0.835244i \(-0.314674\pi\)
−0.835244 + 0.549879i \(0.814674\pi\)
\(308\) 0 0
\(309\) 6.00000 + 6.00000i 0.341328 + 0.341328i
\(310\) 0 0
\(311\) 30.0000i 1.70114i −0.525859 0.850572i \(-0.676256\pi\)
0.525859 0.850572i \(-0.323744\pi\)
\(312\) 0 0
\(313\) −16.0000 −0.904373 −0.452187 0.891923i \(-0.649356\pi\)
−0.452187 + 0.891923i \(0.649356\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.00000 + 5.00000i 0.280828 + 0.280828i 0.833439 0.552611i \(-0.186369\pi\)
−0.552611 + 0.833439i \(0.686369\pi\)
\(318\) 0 0
\(319\) 6.00000 0.335936
\(320\) 0 0
\(321\) 14.0000 0.781404
\(322\) 0 0
\(323\) 6.00000 + 6.00000i 0.333849 + 0.333849i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −6.00000 −0.331801
\(328\) 0 0
\(329\) 16.0000i 0.882109i
\(330\) 0 0
\(331\) −1.00000 1.00000i −0.0549650 0.0549650i 0.679090 0.734055i \(-0.262375\pi\)
−0.734055 + 0.679090i \(0.762375\pi\)
\(332\) 0 0
\(333\) −3.00000 3.00000i −0.164399 0.164399i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 18.0000i 0.980522i −0.871576 0.490261i \(-0.836901\pi\)
0.871576 0.490261i \(-0.163099\pi\)
\(338\) 0 0
\(339\) 6.00000 6.00000i 0.325875 0.325875i
\(340\) 0 0
\(341\) −8.00000 8.00000i −0.433224 0.433224i
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.0000 + 13.0000i −0.697877 + 0.697877i −0.963952 0.266076i \(-0.914273\pi\)
0.266076 + 0.963952i \(0.414273\pi\)
\(348\) 0 0
\(349\) −3.00000 + 3.00000i −0.160586 + 0.160586i −0.782826 0.622240i \(-0.786223\pi\)
0.622240 + 0.782826i \(0.286223\pi\)
\(350\) 0 0
\(351\) −8.00000 −0.427008
\(352\) 0 0
\(353\) 6.00000i 0.319348i −0.987170 0.159674i \(-0.948956\pi\)
0.987170 0.159674i \(-0.0510443\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −4.00000 + 4.00000i −0.211702 + 0.211702i
\(358\) 0 0
\(359\) 26.0000i 1.37223i −0.727494 0.686114i \(-0.759315\pi\)
0.727494 0.686114i \(-0.240685\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 0 0
\(363\) 9.00000 9.00000i 0.472377 0.472377i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 8.00000i 0.417597i 0.977959 + 0.208798i \(0.0669552\pi\)
−0.977959 + 0.208798i \(0.933045\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 10.0000 10.0000i 0.519174 0.519174i
\(372\) 0 0
\(373\) 5.00000 5.00000i 0.258890 0.258890i −0.565712 0.824603i \(-0.691399\pi\)
0.824603 + 0.565712i \(0.191399\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.00000 0.309016
\(378\) 0 0
\(379\) −3.00000 3.00000i −0.154100 0.154100i 0.625847 0.779946i \(-0.284754\pi\)
−0.779946 + 0.625847i \(0.784754\pi\)
\(380\) 0 0
\(381\) −8.00000 + 8.00000i −0.409852 + 0.409852i
\(382\) 0 0
\(383\) 16.0000i 0.817562i 0.912633 + 0.408781i \(0.134046\pi\)
−0.912633 + 0.408781i \(0.865954\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −5.00000 5.00000i −0.254164 0.254164i
\(388\) 0 0
\(389\) 13.0000 + 13.0000i 0.659126 + 0.659126i 0.955173 0.296047i \(-0.0956686\pi\)
−0.296047 + 0.955173i \(0.595669\pi\)
\(390\) 0 0
\(391\) 12.0000i 0.606866i
\(392\) 0 0
\(393\) −22.0000 −1.10975
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 5.00000 + 5.00000i 0.250943 + 0.250943i 0.821357 0.570414i \(-0.193217\pi\)
−0.570414 + 0.821357i \(0.693217\pi\)
\(398\) 0 0
\(399\) 12.0000 0.600751
\(400\) 0 0
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 0 0
\(403\) −8.00000 8.00000i −0.398508 0.398508i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6.00000 −0.297409
\(408\) 0 0
\(409\) 16.0000i 0.791149i 0.918434 + 0.395575i \(0.129455\pi\)
−0.918434 + 0.395575i \(0.870545\pi\)
\(410\) 0 0
\(411\) 8.00000 + 8.00000i 0.394611 + 0.394611i
\(412\) 0 0
\(413\) −6.00000 6.00000i −0.295241 0.295241i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 6.00000i 0.293821i
\(418\) 0 0
\(419\) 3.00000 3.00000i 0.146560 0.146560i −0.630020 0.776579i \(-0.716953\pi\)
0.776579 + 0.630020i \(0.216953\pi\)
\(420\) 0 0
\(421\) −9.00000 9.00000i −0.438633 0.438633i 0.452919 0.891552i \(-0.350383\pi\)
−0.891552 + 0.452919i \(0.850383\pi\)
\(422\) 0 0
\(423\) 8.00000 0.388973
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −18.0000 + 18.0000i −0.871081 + 0.871081i
\(428\) 0 0
\(429\) −2.00000 + 2.00000i −0.0965609 + 0.0965609i
\(430\) 0 0
\(431\) −32.0000 −1.54139 −0.770693 0.637207i \(-0.780090\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(432\) 0 0
\(433\) 14.0000i 0.672797i 0.941720 + 0.336399i \(0.109209\pi\)
−0.941720 + 0.336399i \(0.890791\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 18.0000 18.0000i 0.861057 0.861057i
\(438\) 0 0
\(439\) 14.0000i 0.668184i 0.942541 + 0.334092i \(0.108430\pi\)
−0.942541 + 0.334092i \(0.891570\pi\)
\(440\) 0 0
\(441\) 3.00000i 0.142857i
\(442\) 0 0
\(443\) −15.0000 + 15.0000i −0.712672 + 0.712672i −0.967093 0.254422i \(-0.918115\pi\)
0.254422 + 0.967093i \(0.418115\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 14.0000i 0.662177i
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −10.0000 + 10.0000i −0.469841 + 0.469841i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −32.0000 −1.49690 −0.748448 0.663193i \(-0.769201\pi\)
−0.748448 + 0.663193i \(0.769201\pi\)
\(458\) 0 0
\(459\) 8.00000 + 8.00000i 0.373408 + 0.373408i
\(460\) 0 0
\(461\) 11.0000 11.0000i 0.512321 0.512321i −0.402916 0.915237i \(-0.632003\pi\)
0.915237 + 0.402916i \(0.132003\pi\)
\(462\) 0 0
\(463\) 16.0000i 0.743583i 0.928316 + 0.371792i \(0.121256\pi\)
−0.928316 + 0.371792i \(0.878744\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.00000 5.00000i −0.231372 0.231372i 0.581893 0.813265i \(-0.302312\pi\)
−0.813265 + 0.581893i \(0.802312\pi\)
\(468\) 0 0
\(469\) −10.0000 10.0000i −0.461757 0.461757i
\(470\) 0 0
\(471\) 30.0000i 1.38233i
\(472\) 0 0
\(473\) −10.0000 −0.459800
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −5.00000 5.00000i −0.228934 0.228934i
\(478\) 0 0
\(479\) −40.0000 −1.82765 −0.913823 0.406112i \(-0.866884\pi\)
−0.913823 + 0.406112i \(0.866884\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 0 0
\(483\) 12.0000 + 12.0000i 0.546019 + 0.546019i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) 0 0
\(489\) 2.00000i 0.0904431i
\(490\) 0 0
\(491\) 19.0000 + 19.0000i 0.857458 + 0.857458i 0.991038 0.133580i \(-0.0426473\pi\)
−0.133580 + 0.991038i \(0.542647\pi\)
\(492\) 0 0
\(493\) −6.00000 6.00000i −0.270226 0.270226i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20.0000i 0.897123i
\(498\) 0 0
\(499\) 23.0000 23.0000i 1.02962 1.02962i 0.0300737 0.999548i \(-0.490426\pi\)
0.999548 0.0300737i \(-0.00957421\pi\)
\(500\) 0 0
\(501\) 2.00000 + 2.00000i 0.0893534 + 0.0893534i
\(502\) 0 0
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 11.0000 11.0000i 0.488527 0.488527i
\(508\) 0 0
\(509\) −23.0000 + 23.0000i −1.01946 + 1.01946i −0.0196502 + 0.999807i \(0.506255\pi\)
−0.999807 + 0.0196502i \(0.993745\pi\)
\(510\) 0 0
\(511\) 8.00000 0.353899
\(512\) 0 0
\(513\) 24.0000i 1.05963i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 8.00000 8.00000i 0.351840 0.351840i
\(518\) 0 0
\(519\) 2.00000i 0.0877903i
\(520\) 0 0
\(521\) 40.0000i 1.75243i 0.481919 + 0.876216i \(0.339940\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 0 0
\(523\) 25.0000 25.0000i 1.09317 1.09317i 0.0979859 0.995188i \(-0.468760\pi\)
0.995188 0.0979859i \(-0.0312400\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16.0000i 0.696971i
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) −3.00000 + 3.00000i −0.130189 + 0.130189i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −34.0000 −1.46721
\(538\) 0 0
\(539\) 3.00000 + 3.00000i 0.129219 + 0.129219i
\(540\) 0 0
\(541\) −9.00000 + 9.00000i −0.386940 + 0.386940i −0.873595 0.486654i \(-0.838217\pi\)
0.486654 + 0.873595i \(0.338217\pi\)
\(542\) 0 0
\(543\) 18.0000i 0.772454i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −5.00000 5.00000i −0.213785 0.213785i 0.592088 0.805873i \(-0.298304\pi\)
−0.805873 + 0.592088i \(0.798304\pi\)
\(548\) 0 0
\(549\) 9.00000 + 9.00000i 0.384111 + 0.384111i
\(550\) 0 0
\(551\) 18.0000i 0.766826i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 25.0000 + 25.0000i 1.05928 + 1.05928i 0.998128 + 0.0611558i \(0.0194786\pi\)
0.0611558 + 0.998128i \(0.480521\pi\)
\(558\) 0 0
\(559\) −10.0000 −0.422955
\(560\) 0 0
\(561\) 4.00000 0.168880
\(562\) 0 0
\(563\) −19.0000 19.0000i −0.800755 0.800755i 0.182459 0.983213i \(-0.441594\pi\)
−0.983213 + 0.182459i \(0.941594\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 10.0000 0.419961
\(568\) 0 0
\(569\) 24.0000i 1.00613i −0.864248 0.503066i \(-0.832205\pi\)
0.864248 0.503066i \(-0.167795\pi\)
\(570\) 0 0
\(571\) −1.00000 1.00000i −0.0418487 0.0418487i 0.685873 0.727721i \(-0.259421\pi\)
−0.727721 + 0.685873i \(0.759421\pi\)
\(572\) 0 0
\(573\) 8.00000 + 8.00000i 0.334205 + 0.334205i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 18.0000i 0.749350i −0.927156 0.374675i \(-0.877754\pi\)
0.927156 0.374675i \(-0.122246\pi\)
\(578\) 0 0
\(579\) −14.0000 + 14.0000i −0.581820 + 0.581820i
\(580\) 0 0
\(581\) 2.00000 + 2.00000i 0.0829740 + 0.0829740i
\(582\) 0 0
\(583\) −10.0000 −0.414158
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.00000 7.00000i 0.288921 0.288921i −0.547733 0.836653i \(-0.684509\pi\)
0.836653 + 0.547733i \(0.184509\pi\)
\(588\) 0 0
\(589\) 24.0000 24.0000i 0.988903 0.988903i
\(590\) 0 0
\(591\) −34.0000 −1.39857
\(592\) 0 0
\(593\) 34.0000i 1.39621i 0.715994 + 0.698106i \(0.245974\pi\)
−0.715994 + 0.698106i \(0.754026\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −14.0000 + 14.0000i −0.572982 + 0.572982i
\(598\) 0 0
\(599\) 14.0000i 0.572024i 0.958226 + 0.286012i \(0.0923298\pi\)
−0.958226 + 0.286012i \(0.907670\pi\)
\(600\) 0 0
\(601\) 20.0000i 0.815817i 0.913023 + 0.407909i \(0.133742\pi\)
−0.913023 + 0.407909i \(0.866258\pi\)
\(602\) 0 0
\(603\) −5.00000 + 5.00000i −0.203616 + 0.203616i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 32.0000i 1.29884i −0.760430 0.649420i \(-0.775012\pi\)
0.760430 0.649420i \(-0.224988\pi\)
\(608\) 0 0
\(609\) −12.0000 −0.486265
\(610\) 0 0
\(611\) 8.00000 8.00000i 0.323645 0.323645i
\(612\) 0 0
\(613\) 25.0000 25.0000i 1.00974 1.00974i 0.00978840 0.999952i \(-0.496884\pi\)
0.999952 0.00978840i \(-0.00311579\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −12.0000 −0.483102 −0.241551 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) 0 0
\(619\) 17.0000 + 17.0000i 0.683288 + 0.683288i 0.960740 0.277452i \(-0.0894899\pi\)
−0.277452 + 0.960740i \(0.589490\pi\)
\(620\) 0 0
\(621\) 24.0000 24.0000i 0.963087 0.963087i
\(622\) 0 0
\(623\) 8.00000i 0.320513i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −6.00000 6.00000i −0.239617 0.239617i
\(628\) 0 0
\(629\) 6.00000 + 6.00000i 0.239236 + 0.239236i
\(630\) 0 0
\(631\) 10.0000i 0.398094i 0.979990 + 0.199047i \(0.0637846\pi\)
−0.979990 + 0.199047i \(0.936215\pi\)
\(632\) 0 0
\(633\) 18.0000 0.715436
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 3.00000 + 3.00000i 0.118864 + 0.118864i
\(638\) 0 0
\(639\) 10.0000 0.395594
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) 21.0000 + 21.0000i 0.828159 + 0.828159i 0.987262 0.159103i \(-0.0508601\pi\)
−0.159103 + 0.987262i \(0.550860\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 42.0000 1.65119 0.825595 0.564263i \(-0.190840\pi\)
0.825595 + 0.564263i \(0.190840\pi\)
\(648\) 0 0
\(649\) 6.00000i 0.235521i
\(650\) 0 0
\(651\) 16.0000 + 16.0000i 0.627089 + 0.627089i
\(652\) 0 0
\(653\) 19.0000 + 19.0000i 0.743527 + 0.743527i 0.973255 0.229728i \(-0.0737835\pi\)
−0.229728 + 0.973255i \(0.573784\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 4.00000i 0.156055i
\(658\) 0 0
\(659\) −17.0000 + 17.0000i −0.662226 + 0.662226i −0.955904 0.293678i \(-0.905121\pi\)
0.293678 + 0.955904i \(0.405121\pi\)
\(660\) 0 0
\(661\) −9.00000 9.00000i −0.350059 0.350059i 0.510072 0.860132i \(-0.329619\pi\)
−0.860132 + 0.510072i \(0.829619\pi\)
\(662\) 0 0
\(663\) 4.00000 0.155347
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −18.0000 + 18.0000i −0.696963 + 0.696963i
\(668\) 0 0
\(669\) 24.0000 24.0000i 0.927894 0.927894i
\(670\) 0 0
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 14.0000i 0.539660i 0.962908 + 0.269830i \(0.0869676\pi\)
−0.962908 + 0.269830i \(0.913032\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.00000 3.00000i 0.115299 0.115299i −0.647103 0.762402i \(-0.724020\pi\)
0.762402 + 0.647103i \(0.224020\pi\)
\(678\) 0 0
\(679\) 4.00000i 0.153506i
\(680\) 0 0
\(681\) 30.0000i 1.14960i
\(682\) 0 0
\(683\) 5.00000 5.00000i 0.191320 0.191320i −0.604946 0.796266i \(-0.706805\pi\)
0.796266 + 0.604946i \(0.206805\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 14.0000i 0.534133i
\(688\) 0 0
\(689\) −10.0000 −0.380970
\(690\) 0 0
\(691\) 9.00000 9.00000i 0.342376 0.342376i −0.514884 0.857260i \(-0.672165\pi\)
0.857260 + 0.514884i \(0.172165\pi\)
\(692\) 0 0
\(693\) −2.00000 + 2.00000i −0.0759737 + 0.0759737i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 4.00000 + 4.00000i 0.151294 + 0.151294i
\(700\) 0 0
\(701\) 31.0000 31.0000i 1.17085 1.17085i 0.188847 0.982006i \(-0.439525\pi\)
0.982006 0.188847i \(-0.0604752\pi\)
\(702\) 0 0
\(703\) 18.0000i 0.678883i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 22.0000 + 22.0000i 0.827395 + 0.827395i
\(708\) 0 0
\(709\) −27.0000 27.0000i −1.01401 1.01401i −0.999901 0.0141058i \(-0.995510\pi\)
−0.0141058 0.999901i \(-0.504490\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 48.0000 1.79761
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) 0 0
\(723\) −18.0000 18.0000i −0.669427 0.669427i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.00000 0.0741759 0.0370879 0.999312i \(-0.488192\pi\)
0.0370879 + 0.999312i \(0.488192\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) 10.0000 + 10.0000i 0.369863 + 0.369863i
\(732\) 0 0
\(733\) −21.0000 21.0000i −0.775653 0.775653i 0.203436 0.979088i \(-0.434789\pi\)
−0.979088 + 0.203436i \(0.934789\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.0000i 0.368355i
\(738\) 0 0
\(739\) 23.0000 23.0000i 0.846069 0.846069i −0.143571 0.989640i \(-0.545859\pi\)
0.989640 + 0.143571i \(0.0458586\pi\)
\(740\) 0 0
\(741\) −6.00000 6.00000i −0.220416 0.220416i
\(742\) 0 0
\(743\) 46.0000 1.68758 0.843788 0.536676i \(-0.180320\pi\)
0.843788 + 0.536676i \(0.180320\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 1.00000 1.00000i 0.0365881 0.0365881i
\(748\) 0 0
\(749\) 14.0000 14.0000i 0.511549 0.511549i
\(750\) 0 0
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 0 0
\(753\) 42.0000i 1.53057i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 23.0000 23.0000i 0.835949 0.835949i −0.152374 0.988323i \(-0.548692\pi\)
0.988323 + 0.152374i \(0.0486917\pi\)
\(758\) 0 0
\(759\) 12.0000i 0.435572i
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) −6.00000 + 6.00000i −0.217215 + 0.217215i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 6.00000i 0.216647i
\(768\) 0 0
\(769\) 50.0000 1.80305 0.901523 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 0 0
\(771\) −22.0000 + 22.0000i −0.792311 + 0.792311i
\(772\) 0 0
\(773\) 5.00000 5.00000i 0.179838 0.179838i −0.611448 0.791285i \(-0.709412\pi\)
0.791285 + 0.611448i \(0.209412\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 12.0000 0.430498
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 10.0000 10.0000i 0.357828 0.357828i
\(782\) 0 0
\(783\) 24.0000i 0.857690i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 15.0000 + 15.0000i 0.534692 + 0.534692i 0.921965 0.387273i \(-0.126583\pi\)
−0.387273 + 0.921965i \(0.626583\pi\)
\(788\) 0 0
\(789\) 6.00000 + 6.00000i 0.213606 + 0.213606i
\(790\) 0 0
\(791\) 12.0000i 0.426671i
\(792\) 0 0
\(793\) 18.0000 0.639199
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 25.0000 + 25.0000i 0.885545 + 0.885545i 0.994091 0.108546i \(-0.0346195\pi\)
−0.108546 + 0.994091i \(0.534619\pi\)
\(798\) 0 0
\(799\) −16.0000 −0.566039
\(800\) 0 0
\(801\) −4.00000 −0.141333
\(802\) 0 0
\(803\) −4.00000