Properties

Label 1440.2.x.p.127.2
Level $1440$
Weight $2$
Character 1440.127
Analytic conductor $11.498$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.x (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.4984578911\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.2
Root \(-1.22474 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1440.127
Dual form 1440.2.x.p.703.2

$q$-expansion

\(f(q)\) \(=\) \(q+(2.22474 - 0.224745i) q^{5} +(-1.44949 + 1.44949i) q^{7} +O(q^{10})\) \(q+(2.22474 - 0.224745i) q^{5} +(-1.44949 + 1.44949i) q^{7} +2.44949i q^{11} +(2.00000 - 2.00000i) q^{13} +(0.449490 + 0.449490i) q^{17} +2.00000 q^{19} +(0.449490 + 0.449490i) q^{23} +(4.89898 - 1.00000i) q^{25} -0.449490i q^{29} +8.89898i q^{31} +(-2.89898 + 3.55051i) q^{35} +(2.89898 + 2.89898i) q^{37} -4.89898 q^{41} +(6.00000 + 6.00000i) q^{43} +(9.34847 - 9.34847i) q^{47} +2.79796i q^{49} +(-2.89898 + 2.89898i) q^{53} +(0.550510 + 5.44949i) q^{55} -11.3485 q^{59} +11.7980 q^{61} +(4.00000 - 4.89898i) q^{65} +(-6.89898 + 6.89898i) q^{67} -12.0000i q^{71} +(7.89898 - 7.89898i) q^{73} +(-3.55051 - 3.55051i) q^{77} +3.10102 q^{79} +(5.55051 + 5.55051i) q^{83} +(1.10102 + 0.898979i) q^{85} +12.0000i q^{89} +5.79796i q^{91} +(4.44949 - 0.449490i) q^{95} +(3.00000 + 3.00000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{5} + 4 q^{7} + O(q^{10}) \) \( 4 q + 4 q^{5} + 4 q^{7} + 8 q^{13} - 8 q^{17} + 8 q^{19} - 8 q^{23} + 8 q^{35} - 8 q^{37} + 24 q^{43} + 8 q^{47} + 8 q^{53} + 12 q^{55} - 16 q^{59} + 8 q^{61} + 16 q^{65} - 8 q^{67} + 12 q^{73} - 24 q^{77} + 32 q^{79} + 32 q^{83} + 24 q^{85} + 8 q^{95} + 12 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(991\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(-1\)

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
\(5\) 2.22474 0.224745i 0.994936 0.100509i
\(6\) 0 0
\(7\) −1.44949 + 1.44949i −0.547856 + 0.547856i −0.925820 0.377964i \(-0.876624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.44949i 0.738549i 0.929320 + 0.369274i \(0.120394\pi\)
−0.929320 + 0.369274i \(0.879606\pi\)
\(12\) 0 0
\(13\) 2.00000 2.00000i 0.554700 0.554700i −0.373094 0.927794i \(-0.621703\pi\)
0.927794 + 0.373094i \(0.121703\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.449490 + 0.449490i 0.109017 + 0.109017i 0.759511 0.650494i \(-0.225438\pi\)
−0.650494 + 0.759511i \(0.725438\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.449490 + 0.449490i 0.0937251 + 0.0937251i 0.752415 0.658690i \(-0.228889\pi\)
−0.658690 + 0.752415i \(0.728889\pi\)
\(24\) 0 0
\(25\) 4.89898 1.00000i 0.979796 0.200000i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.449490i 0.0834681i −0.999129 0.0417341i \(-0.986712\pi\)
0.999129 0.0417341i \(-0.0132882\pi\)
\(30\) 0 0
\(31\) 8.89898i 1.59830i 0.601129 + 0.799152i \(0.294718\pi\)
−0.601129 + 0.799152i \(0.705282\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.89898 + 3.55051i −0.490017 + 0.600146i
\(36\) 0 0
\(37\) 2.89898 + 2.89898i 0.476589 + 0.476589i 0.904039 0.427450i \(-0.140588\pi\)
−0.427450 + 0.904039i \(0.640588\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.89898 −0.765092 −0.382546 0.923936i \(-0.624953\pi\)
−0.382546 + 0.923936i \(0.624953\pi\)
\(42\) 0 0
\(43\) 6.00000 + 6.00000i 0.914991 + 0.914991i 0.996660 0.0816682i \(-0.0260248\pi\)
−0.0816682 + 0.996660i \(0.526025\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.34847 9.34847i 1.36361 1.36361i 0.494353 0.869261i \(-0.335405\pi\)
0.869261 0.494353i \(-0.164595\pi\)
\(48\) 0 0
\(49\) 2.79796i 0.399708i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.89898 + 2.89898i −0.398205 + 0.398205i −0.877600 0.479394i \(-0.840856\pi\)
0.479394 + 0.877600i \(0.340856\pi\)
\(54\) 0 0
\(55\) 0.550510 + 5.44949i 0.0742308 + 0.734809i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −11.3485 −1.47744 −0.738722 0.674010i \(-0.764571\pi\)
−0.738722 + 0.674010i \(0.764571\pi\)
\(60\) 0 0
\(61\) 11.7980 1.51057 0.755287 0.655394i \(-0.227498\pi\)
0.755287 + 0.655394i \(0.227498\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4.00000 4.89898i 0.496139 0.607644i
\(66\) 0 0
\(67\) −6.89898 + 6.89898i −0.842844 + 0.842844i −0.989228 0.146383i \(-0.953237\pi\)
0.146383 + 0.989228i \(0.453237\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000i 1.42414i −0.702109 0.712069i \(-0.747758\pi\)
0.702109 0.712069i \(-0.252242\pi\)
\(72\) 0 0
\(73\) 7.89898 7.89898i 0.924506 0.924506i −0.0728382 0.997344i \(-0.523206\pi\)
0.997344 + 0.0728382i \(0.0232057\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.55051 3.55051i −0.404618 0.404618i
\(78\) 0 0
\(79\) 3.10102 0.348892 0.174446 0.984667i \(-0.444187\pi\)
0.174446 + 0.984667i \(0.444187\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.55051 + 5.55051i 0.609248 + 0.609248i 0.942749 0.333502i \(-0.108230\pi\)
−0.333502 + 0.942749i \(0.608230\pi\)
\(84\) 0 0
\(85\) 1.10102 + 0.898979i 0.119422 + 0.0975080i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 12.0000i 1.27200i 0.771690 + 0.635999i \(0.219412\pi\)
−0.771690 + 0.635999i \(0.780588\pi\)
\(90\) 0 0
\(91\) 5.79796i 0.607791i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.44949 0.449490i 0.456508 0.0461167i
\(96\) 0 0
\(97\) 3.00000 + 3.00000i 0.304604 + 0.304604i 0.842812 0.538208i \(-0.180899\pi\)
−0.538208 + 0.842812i \(0.680899\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.44949 −0.840756 −0.420378 0.907349i \(-0.638102\pi\)
−0.420378 + 0.907349i \(0.638102\pi\)
\(102\) 0 0
\(103\) −0.550510 0.550510i −0.0542434 0.0542434i 0.679465 0.733708i \(-0.262212\pi\)
−0.733708 + 0.679465i \(0.762212\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.34847 + 7.34847i −0.710403 + 0.710403i −0.966620 0.256216i \(-0.917524\pi\)
0.256216 + 0.966620i \(0.417524\pi\)
\(108\) 0 0
\(109\) 11.7980i 1.13004i −0.825077 0.565020i \(-0.808869\pi\)
0.825077 0.565020i \(-0.191131\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.44949 8.44949i 0.794861 0.794861i −0.187419 0.982280i \(-0.560012\pi\)
0.982280 + 0.187419i \(0.0600122\pi\)
\(114\) 0 0
\(115\) 1.10102 + 0.898979i 0.102671 + 0.0838303i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.30306 −0.119451
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 10.6742 3.32577i 0.954733 0.297465i
\(126\) 0 0
\(127\) 7.44949 7.44949i 0.661035 0.661035i −0.294589 0.955624i \(-0.595183\pi\)
0.955624 + 0.294589i \(0.0951827\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.44949i 0.563495i 0.959489 + 0.281747i \(0.0909140\pi\)
−0.959489 + 0.281747i \(0.909086\pi\)
\(132\) 0 0
\(133\) −2.89898 + 2.89898i −0.251373 + 0.251373i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.44949 4.44949i −0.380146 0.380146i 0.491009 0.871155i \(-0.336628\pi\)
−0.871155 + 0.491009i \(0.836628\pi\)
\(138\) 0 0
\(139\) −15.7980 −1.33997 −0.669983 0.742377i \(-0.733698\pi\)
−0.669983 + 0.742377i \(0.733698\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.89898 + 4.89898i 0.409673 + 0.409673i
\(144\) 0 0
\(145\) −0.101021 1.00000i −0.00838930 0.0830455i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 20.4495i 1.67529i 0.546217 + 0.837644i \(0.316067\pi\)
−0.546217 + 0.837644i \(0.683933\pi\)
\(150\) 0 0
\(151\) 3.79796i 0.309074i −0.987987 0.154537i \(-0.950611\pi\)
0.987987 0.154537i \(-0.0493885\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00000 + 19.7980i 0.160644 + 1.59021i
\(156\) 0 0
\(157\) 4.89898 + 4.89898i 0.390981 + 0.390981i 0.875037 0.484056i \(-0.160837\pi\)
−0.484056 + 0.875037i \(0.660837\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.30306 −0.102696
\(162\) 0 0
\(163\) 8.89898 + 8.89898i 0.697022 + 0.697022i 0.963767 0.266745i \(-0.0859482\pi\)
−0.266745 + 0.963767i \(0.585948\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 11.5505 11.5505i 0.893805 0.893805i −0.101074 0.994879i \(-0.532228\pi\)
0.994879 + 0.101074i \(0.0322278\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 16.2474 16.2474i 1.23527 1.23527i 0.273358 0.961912i \(-0.411866\pi\)
0.961912 0.273358i \(-0.0881345\pi\)
\(174\) 0 0
\(175\) −5.65153 + 8.55051i −0.427216 + 0.646358i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −24.2474 −1.81234 −0.906170 0.422914i \(-0.861007\pi\)
−0.906170 + 0.422914i \(0.861007\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 7.10102 + 5.79796i 0.522077 + 0.426274i
\(186\) 0 0
\(187\) −1.10102 + 1.10102i −0.0805146 + 0.0805146i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 20.8990i 1.51220i −0.654458 0.756099i \(-0.727103\pi\)
0.654458 0.756099i \(-0.272897\pi\)
\(192\) 0 0
\(193\) −9.89898 + 9.89898i −0.712544 + 0.712544i −0.967067 0.254523i \(-0.918082\pi\)
0.254523 + 0.967067i \(0.418082\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −7.79796 7.79796i −0.555582 0.555582i 0.372465 0.928046i \(-0.378513\pi\)
−0.928046 + 0.372465i \(0.878513\pi\)
\(198\) 0 0
\(199\) 15.7980 1.11989 0.559944 0.828531i \(-0.310823\pi\)
0.559944 + 0.828531i \(0.310823\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0.651531 + 0.651531i 0.0457285 + 0.0457285i
\(204\) 0 0
\(205\) −10.8990 + 1.10102i −0.761218 + 0.0768986i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.89898i 0.338869i
\(210\) 0 0
\(211\) 17.5959i 1.21135i −0.795711 0.605676i \(-0.792903\pi\)
0.795711 0.605676i \(-0.207097\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 14.6969 + 12.0000i 1.00232 + 0.818393i
\(216\) 0 0
\(217\) −12.8990 12.8990i −0.875640 0.875640i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.79796 0.120944
\(222\) 0 0
\(223\) −18.3485 18.3485i −1.22870 1.22870i −0.964454 0.264250i \(-0.914876\pi\)
−0.264250 0.964454i \(-0.585124\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.10102 3.10102i 0.205822 0.205822i −0.596667 0.802489i \(-0.703509\pi\)
0.802489 + 0.596667i \(0.203509\pi\)
\(228\) 0 0
\(229\) 10.0000i 0.660819i 0.943838 + 0.330409i \(0.107187\pi\)
−0.943838 + 0.330409i \(0.892813\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.34847 + 9.34847i −0.612439 + 0.612439i −0.943581 0.331142i \(-0.892566\pi\)
0.331142 + 0.943581i \(0.392566\pi\)
\(234\) 0 0
\(235\) 18.6969 22.8990i 1.21965 1.49376i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −10.2020 −0.659915 −0.329958 0.943996i \(-0.607034\pi\)
−0.329958 + 0.943996i \(0.607034\pi\)
\(240\) 0 0
\(241\) −13.7980 −0.888805 −0.444402 0.895827i \(-0.646584\pi\)
−0.444402 + 0.895827i \(0.646584\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.628827 + 6.22474i 0.0401743 + 0.397684i
\(246\) 0 0
\(247\) 4.00000 4.00000i 0.254514 0.254514i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 17.1464i 1.08227i −0.840935 0.541136i \(-0.817994\pi\)
0.840935 0.541136i \(-0.182006\pi\)
\(252\) 0 0
\(253\) −1.10102 + 1.10102i −0.0692206 + 0.0692206i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −21.3485 21.3485i −1.33168 1.33168i −0.903867 0.427814i \(-0.859284\pi\)
−0.427814 0.903867i \(-0.640716\pi\)
\(258\) 0 0
\(259\) −8.40408 −0.522204
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6.24745 6.24745i −0.385234 0.385234i 0.487749 0.872984i \(-0.337818\pi\)
−0.872984 + 0.487749i \(0.837818\pi\)
\(264\) 0 0
\(265\) −5.79796 + 7.10102i −0.356166 + 0.436212i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.44949i 0.271290i 0.990757 + 0.135645i \(0.0433107\pi\)
−0.990757 + 0.135645i \(0.956689\pi\)
\(270\) 0 0
\(271\) 4.20204i 0.255256i −0.991822 0.127628i \(-0.959264\pi\)
0.991822 0.127628i \(-0.0407363\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.44949 + 12.0000i 0.147710 + 0.723627i
\(276\) 0 0
\(277\) −8.69694 8.69694i −0.522548 0.522548i 0.395792 0.918340i \(-0.370470\pi\)
−0.918340 + 0.395792i \(0.870470\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −18.6969 −1.11537 −0.557683 0.830054i \(-0.688309\pi\)
−0.557683 + 0.830054i \(0.688309\pi\)
\(282\) 0 0
\(283\) −8.69694 8.69694i −0.516979 0.516979i 0.399677 0.916656i \(-0.369122\pi\)
−0.916656 + 0.399677i \(0.869122\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 7.10102 7.10102i 0.419160 0.419160i
\(288\) 0 0
\(289\) 16.5959i 0.976230i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.89898 + 6.89898i −0.403043 + 0.403043i −0.879304 0.476261i \(-0.841992\pi\)
0.476261 + 0.879304i \(0.341992\pi\)
\(294\) 0 0
\(295\) −25.2474 + 2.55051i −1.46996 + 0.148496i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.79796 0.103979
\(300\) 0 0
\(301\) −17.3939 −1.00257
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 26.2474 2.65153i 1.50292 0.151826i
\(306\) 0 0
\(307\) 7.79796 7.79796i 0.445053 0.445053i −0.448653 0.893706i \(-0.648096\pi\)
0.893706 + 0.448653i \(0.148096\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5.79796i 0.328772i −0.986396 0.164386i \(-0.947436\pi\)
0.986396 0.164386i \(-0.0525643\pi\)
\(312\) 0 0
\(313\) −7.89898 + 7.89898i −0.446477 + 0.446477i −0.894181 0.447705i \(-0.852242\pi\)
0.447705 + 0.894181i \(0.352242\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.65153 8.65153i −0.485918 0.485918i 0.421097 0.907016i \(-0.361645\pi\)
−0.907016 + 0.421097i \(0.861645\pi\)
\(318\) 0 0
\(319\) 1.10102 0.0616453
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.898979 + 0.898979i 0.0500206 + 0.0500206i
\(324\) 0 0
\(325\) 7.79796 11.7980i 0.432553 0.654433i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 27.1010i 1.49413i
\(330\) 0 0
\(331\) 18.0000i 0.989369i −0.869072 0.494685i \(-0.835284\pi\)
0.869072 0.494685i \(-0.164716\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −13.7980 + 16.8990i −0.753863 + 0.923290i
\(336\) 0 0
\(337\) 8.10102 + 8.10102i 0.441291 + 0.441291i 0.892446 0.451155i \(-0.148988\pi\)
−0.451155 + 0.892446i \(0.648988\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −21.7980 −1.18043
\(342\) 0 0
\(343\) −14.2020 14.2020i −0.766838 0.766838i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.0000 12.0000i 0.644194 0.644194i −0.307390 0.951584i \(-0.599456\pi\)
0.951584 + 0.307390i \(0.0994556\pi\)
\(348\) 0 0
\(349\) 21.5959i 1.15600i 0.816036 + 0.578001i \(0.196167\pi\)
−0.816036 + 0.578001i \(0.803833\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 18.2474 18.2474i 0.971214 0.971214i −0.0283834 0.999597i \(-0.509036\pi\)
0.999597 + 0.0283834i \(0.00903593\pi\)
\(354\) 0 0
\(355\) −2.69694 26.6969i −0.143139 1.41693i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.6969 −0.564563 −0.282281 0.959332i \(-0.591091\pi\)
−0.282281 + 0.959332i \(0.591091\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 15.7980 19.3485i 0.826903 1.01275i
\(366\) 0 0
\(367\) 8.34847 8.34847i 0.435787 0.435787i −0.454805 0.890591i \(-0.650291\pi\)
0.890591 + 0.454805i \(0.150291\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.40408i 0.436318i
\(372\) 0 0
\(373\) −7.10102 + 7.10102i −0.367677 + 0.367677i −0.866629 0.498952i \(-0.833718\pi\)
0.498952 + 0.866629i \(0.333718\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.898979 0.898979i −0.0462998 0.0462998i
\(378\) 0 0
\(379\) −0.202041 −0.0103782 −0.00518908 0.999987i \(-0.501652\pi\)
−0.00518908 + 0.999987i \(0.501652\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.34847 + 9.34847i 0.477684 + 0.477684i 0.904390 0.426706i \(-0.140326\pi\)
−0.426706 + 0.904390i \(0.640326\pi\)
\(384\) 0 0
\(385\) −8.69694 7.10102i −0.443237 0.361902i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 35.1464i 1.78199i 0.454009 + 0.890997i \(0.349994\pi\)
−0.454009 + 0.890997i \(0.650006\pi\)
\(390\) 0 0
\(391\) 0.404082i 0.0204353i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 6.89898 0.696938i 0.347125 0.0350668i
\(396\) 0 0
\(397\) −27.5959 27.5959i −1.38500 1.38500i −0.835483 0.549517i \(-0.814812\pi\)
−0.549517 0.835483i \(-0.685188\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 23.5959 1.17832 0.589162 0.808015i \(-0.299458\pi\)
0.589162 + 0.808015i \(0.299458\pi\)
\(402\) 0 0
\(403\) 17.7980 + 17.7980i 0.886579 + 0.886579i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.10102 + 7.10102i −0.351985 + 0.351985i
\(408\) 0 0
\(409\) 20.0000i 0.988936i 0.869196 + 0.494468i \(0.164637\pi\)
−0.869196 + 0.494468i \(0.835363\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 16.4495 16.4495i 0.809426 0.809426i
\(414\) 0 0
\(415\) 13.5959 + 11.1010i 0.667397 + 0.544928i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −11.7526 −0.574150 −0.287075 0.957908i \(-0.592683\pi\)
−0.287075 + 0.957908i \(0.592683\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.65153 + 1.75255i 0.128618 + 0.0850112i
\(426\) 0 0
\(427\) −17.1010 + 17.1010i −0.827576 + 0.827576i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 20.4949i 0.987204i 0.869688 + 0.493602i \(0.164320\pi\)
−0.869688 + 0.493602i \(0.835680\pi\)
\(432\) 0 0
\(433\) 2.79796 2.79796i 0.134461 0.134461i −0.636673 0.771134i \(-0.719690\pi\)
0.771134 + 0.636673i \(0.219690\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.898979 + 0.898979i 0.0430040 + 0.0430040i
\(438\) 0 0
\(439\) 19.7980 0.944905 0.472453 0.881356i \(-0.343369\pi\)
0.472453 + 0.881356i \(0.343369\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.8990 + 12.8990i 0.612849 + 0.612849i 0.943687 0.330838i \(-0.107332\pi\)
−0.330838 + 0.943687i \(0.607332\pi\)
\(444\) 0 0
\(445\) 2.69694 + 26.6969i 0.127847 + 1.26556i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 20.4949i 0.967214i −0.875285 0.483607i \(-0.839326\pi\)
0.875285 0.483607i \(-0.160674\pi\)
\(450\) 0 0
\(451\) 12.0000i 0.565058i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.30306 + 12.8990i 0.0610885 + 0.604713i
\(456\) 0 0
\(457\) 0.797959 + 0.797959i 0.0373269 + 0.0373269i 0.725524 0.688197i \(-0.241598\pi\)
−0.688197 + 0.725524i \(0.741598\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.75255 −0.0816245 −0.0408122 0.999167i \(-0.512995\pi\)
−0.0408122 + 0.999167i \(0.512995\pi\)
\(462\) 0 0
\(463\) −23.2474 23.2474i −1.08040 1.08040i −0.996472 0.0839288i \(-0.973253\pi\)
−0.0839288 0.996472i \(-0.526747\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 21.1464 21.1464i 0.978540 0.978540i −0.0212345 0.999775i \(-0.506760\pi\)
0.999775 + 0.0212345i \(0.00675967\pi\)
\(468\) 0 0
\(469\) 20.0000i 0.923514i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −14.6969 + 14.6969i −0.675766 + 0.675766i
\(474\) 0 0
\(475\) 9.79796 2.00000i 0.449561 0.0917663i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −41.3939 −1.89133 −0.945667 0.325136i \(-0.894590\pi\)
−0.945667 + 0.325136i \(0.894590\pi\)
\(480\) 0 0
\(481\) 11.5959 0.528728
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.34847 + 6.00000i 0.333677 + 0.272446i
\(486\) 0 0
\(487\) 23.4495 23.4495i 1.06260 1.06260i 0.0646926 0.997905i \(-0.479393\pi\)
0.997905 0.0646926i \(-0.0206067\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.6515i 0.570956i −0.958385 0.285478i \(-0.907848\pi\)
0.958385 0.285478i \(-0.0921523\pi\)
\(492\) 0 0
\(493\) 0.202041 0.202041i 0.00909947 0.00909947i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 17.3939 + 17.3939i 0.780222 + 0.780222i
\(498\) 0 0
\(499\) −29.5959 −1.32490 −0.662448 0.749108i \(-0.730482\pi\)
−0.662448 + 0.749108i \(0.730482\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 26.2474 + 26.2474i 1.17032 + 1.17032i 0.982134 + 0.188182i \(0.0602594\pi\)
0.188182 + 0.982134i \(0.439741\pi\)
\(504\) 0 0
\(505\) −18.7980 + 1.89898i −0.836498 + 0.0845035i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 16.0454i 0.711200i −0.934638 0.355600i \(-0.884277\pi\)
0.934638 0.355600i \(-0.115723\pi\)
\(510\) 0 0
\(511\) 22.8990i 1.01299i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.34847 1.10102i −0.0594207 0.0485168i
\(516\) 0 0
\(517\) 22.8990 + 22.8990i 1.00710 + 1.00710i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −36.4949 −1.59887 −0.799435 0.600752i \(-0.794868\pi\)
−0.799435 + 0.600752i \(0.794868\pi\)
\(522\) 0 0
\(523\) 26.8990 + 26.8990i 1.17621 + 1.17621i 0.980702 + 0.195508i \(0.0626356\pi\)
0.195508 + 0.980702i \(0.437364\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.00000 + 4.00000i −0.174243 + 0.174243i
\(528\) 0 0
\(529\) 22.5959i 0.982431i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −9.79796 + 9.79796i −0.424397 + 0.424397i
\(534\) 0 0
\(535\) −14.6969 + 18.0000i −0.635404 + 0.778208i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −6.85357 −0.295204
\(540\) 0 0
\(541\) 15.7980 0.679207 0.339604 0.940569i \(-0.389707\pi\)
0.339604 + 0.940569i \(0.389707\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.65153 26.2474i −0.113579 1.12432i
\(546\) 0 0
\(547\) −25.5959 + 25.5959i −1.09440 + 1.09440i −0.0993499 + 0.995053i \(0.531676\pi\)
−0.995053 + 0.0993499i \(0.968324\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.898979i 0.0382978i
\(552\) 0 0
\(553\) −4.49490 + 4.49490i −0.191142 + 0.191142i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.10102 1.10102i −0.0466517 0.0466517i 0.683396 0.730048i \(-0.260502\pi\)
−0.730048 + 0.683396i \(0.760502\pi\)
\(558\) 0 0
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2.20204 2.20204i −0.0928050 0.0928050i 0.659180 0.751985i \(-0.270903\pi\)
−0.751985 + 0.659180i \(0.770903\pi\)
\(564\) 0 0
\(565\) 16.8990 20.6969i 0.710945 0.870727i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 33.3939i 1.39994i 0.714170 + 0.699972i \(0.246804\pi\)
−0.714170 + 0.699972i \(0.753196\pi\)
\(570\) 0 0
\(571\) 5.59592i 0.234182i 0.993121 + 0.117091i \(0.0373569\pi\)
−0.993121 + 0.117091i \(0.962643\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.65153 + 1.75255i 0.110576 + 0.0730864i
\(576\) 0 0
\(577\) 11.6969 + 11.6969i 0.486950 + 0.486950i 0.907342 0.420392i \(-0.138108\pi\)
−0.420392 + 0.907342i \(0.638108\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −16.0908 −0.667560
\(582\) 0 0
\(583\) −7.10102 7.10102i −0.294094 0.294094i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 25.1464 25.1464i 1.03790 1.03790i 0.0386514 0.999253i \(-0.487694\pi\)
0.999253 0.0386514i \(-0.0123062\pi\)
\(588\) 0 0
\(589\) 17.7980i 0.733352i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 19.5505 19.5505i 0.802843 0.802843i −0.180696 0.983539i \(-0.557835\pi\)
0.983539 + 0.180696i \(0.0578349\pi\)
\(594\) 0 0
\(595\) −2.89898 + 0.292856i −0.118847 + 0.0120059i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −28.4949 −1.16427 −0.582135 0.813092i \(-0.697782\pi\)
−0.582135 + 0.813092i \(0.697782\pi\)
\(600\) 0 0
\(601\) 34.0000 1.38689 0.693444 0.720510i \(-0.256092\pi\)
0.693444 + 0.720510i \(0.256092\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 11.1237 1.12372i 0.452244 0.0456859i
\(606\) 0 0
\(607\) 6.55051 6.55051i 0.265877 0.265877i −0.561559 0.827436i \(-0.689798\pi\)
0.827436 + 0.561559i \(0.189798\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 37.3939i 1.51279i
\(612\) 0 0
\(613\) 19.5959 19.5959i 0.791472 0.791472i −0.190262 0.981733i \(-0.560934\pi\)
0.981733 + 0.190262i \(0.0609337\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9.34847 9.34847i −0.376355 0.376355i 0.493430 0.869785i \(-0.335743\pi\)
−0.869785 + 0.493430i \(0.835743\pi\)
\(618\) 0 0
\(619\) −31.3939 −1.26183 −0.630913 0.775853i \(-0.717320\pi\)
−0.630913 + 0.775853i \(0.717320\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −17.3939 17.3939i −0.696871 0.696871i
\(624\) 0 0
\(625\) 23.0000 9.79796i 0.920000 0.391918i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.60612i 0.103913i
\(630\) 0 0
\(631\) 12.8990i 0.513500i 0.966478 + 0.256750i \(0.0826517\pi\)
−0.966478 + 0.256750i \(0.917348\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 14.8990 18.2474i 0.591248 0.724128i
\(636\) 0 0
\(637\) 5.59592 + 5.59592i 0.221718 + 0.221718i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −33.7980 −1.33494 −0.667470 0.744637i \(-0.732623\pi\)
−0.667470 + 0.744637i \(0.732623\pi\)
\(642\) 0 0
\(643\) 23.1010 + 23.1010i 0.911015 + 0.911015i 0.996352 0.0853368i \(-0.0271966\pi\)
−0.0853368 + 0.996352i \(0.527197\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.2474 + 10.2474i −0.402869 + 0.402869i −0.879243 0.476374i \(-0.841951\pi\)
0.476374 + 0.879243i \(0.341951\pi\)
\(648\) 0 0
\(649\) 27.7980i 1.09117i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.55051 1.55051i 0.0606762 0.0606762i −0.676118 0.736794i \(-0.736339\pi\)
0.736794 + 0.676118i \(0.236339\pi\)
\(654\) 0 0
\(655\) 1.44949 + 14.3485i 0.0566363 + 0.560641i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 40.2474 1.56782 0.783909 0.620876i \(-0.213223\pi\)
0.783909 + 0.620876i \(0.213223\pi\)
\(660\) 0 0
\(661\) 8.20204 0.319022 0.159511 0.987196i \(-0.449008\pi\)
0.159511 + 0.987196i \(0.449008\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.79796 + 7.10102i −0.224835 + 0.275366i
\(666\) 0 0
\(667\) 0.202041 0.202041i 0.00782306 0.00782306i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 28.8990i 1.11563i
\(672\) 0 0
\(673\) 8.79796 8.79796i 0.339136 0.339136i −0.516906 0.856042i \(-0.672916\pi\)
0.856042 + 0.516906i \(0.172916\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.65153 + 4.65153i 0.178773 + 0.178773i 0.790821 0.612048i \(-0.209654\pi\)
−0.612048 + 0.790821i \(0.709654\pi\)
\(678\) 0 0
\(679\) −8.69694 −0.333758
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −12.6515 12.6515i −0.484097 0.484097i 0.422340 0.906437i \(-0.361209\pi\)
−0.906437 + 0.422340i \(0.861209\pi\)
\(684\) 0 0
\(685\) −10.8990 8.89898i −0.416429 0.340013i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 11.5959i 0.441769i
\(690\) 0 0
\(691\) 7.79796i 0.296648i −0.988939 0.148324i \(-0.952612\pi\)
0.988939 0.148324i \(-0.0473879\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −35.1464 + 3.55051i −1.33318 + 0.134679i
\(696\) 0 0
\(697\) −2.20204 2.20204i −0.0834083 0.0834083i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 26.7423 1.01004 0.505022 0.863106i \(-0.331484\pi\)
0.505022 + 0.863106i \(0.331484\pi\)
\(702\) 0 0
\(703\) 5.79796 + 5.79796i 0.218674 + 0.218674i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 12.2474 12.2474i 0.460613 0.460613i
\(708\) 0 0
\(709\) 8.20204i 0.308034i −0.988068 0.154017i \(-0.950779\pi\)
0.988068 0.154017i \(-0.0492211\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4.00000 + 4.00000i −0.149801 + 0.149801i
\(714\) 0 0
\(715\) 12.0000 + 9.79796i 0.448775 + 0.366423i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 25.7980 0.962102 0.481051 0.876693i \(-0.340255\pi\)
0.481051 + 0.876693i \(0.340255\pi\)
\(720\) 0 0
\(721\) 1.59592 0.0594351
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.449490 2.20204i −0.0166936 0.0817818i
\(726\) 0 0
\(727\) −8.14643 + 8.14643i −0.302134 + 0.302134i −0.841848 0.539714i \(-0.818532\pi\)
0.539714 + 0.841848i \(0.318532\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5.39388i 0.199500i
\(732\) 0 0
\(733\) 13.1010 13.1010i 0.483897 0.483897i −0.422477 0.906374i \(-0.638839\pi\)
0.906374 + 0.422477i \(0.138839\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16.8990 16.8990i −0.622482 0.622482i
\(738\) 0 0
\(739\) 27.3939 1.00770 0.503850 0.863791i \(-0.331916\pi\)
0.503850 + 0.863791i \(0.331916\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −8.44949 8.44949i −0.309982 0.309982i 0.534921 0.844902i \(-0.320342\pi\)
−0.844902 + 0.534921i \(0.820342\pi\)
\(744\) 0 0
\(745\) 4.59592 + 45.4949i 0.168381 + 1.66680i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 21.3031i 0.778397i
\(750\) 0 0
\(751\) 42.6969i 1.55803i 0.627003 + 0.779017i \(0.284281\pi\)
−0.627003 + 0.779017i \(0.715719\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.853572 8.44949i −0.0310647 0.307508i
\(756\) 0 0
\(757\) 16.6969 + 16.6969i 0.606861 + 0.606861i 0.942124 0.335264i \(-0.108825\pi\)
−0.335264 + 0.942124i \(0.608825\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 34.6969 1.25776 0.628882 0.777501i \(-0.283513\pi\)
0.628882 + 0.777501i \(0.283513\pi\)
\(762\) 0 0
\(763\) 17.1010 + 17.1010i 0.619099 + 0.619099i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −22.6969 + 22.6969i −0.819539 + 0.819539i
\(768\) 0 0
\(769\) 25.1918i 0.908441i 0.890889 + 0.454220i \(0.150082\pi\)
−0.890889 + 0.454220i \(0.849918\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −23.3485 + 23.3485i −0.839786 + 0.839786i −0.988830 0.149044i \(-0.952380\pi\)
0.149044 + 0.988830i \(0.452380\pi\)
\(774\) 0 0
\(775\) 8.89898 + 43.5959i 0.319661 + 1.56601i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9.79796 −0.351048
\(780\) 0 0
\(781\) 29.3939 1.05180
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 12.0000 + 9.79796i 0.428298 + 0.349704i
\(786\) 0 0
\(787\) −25.1010 + 25.1010i −0.894755 + 0.894755i −0.994966 0.100211i \(-0.968048\pi\)
0.100211 + 0.994966i \(0.468048\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 24.4949i 0.870938i
\(792\) 0 0
\(793\) 23.5959 23.5959i 0.837916 0.837916i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −10.4495 10.4495i −0.370140 0.370140i 0.497388 0.867528i \(-0.334292\pi\)
−0.867528 + 0.497388i \(0.834292\pi\)
\(798\) 0 0
\(799\) 8.40408 0.297315
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 19.3485 + 19.3485i 0.682793 + 0.682793i