Properties

Label 2592.2.i.s.865.1
Level $2592$
Weight $2$
Character 2592.865
Analytic conductor $20.697$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(20.6972242039\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 864)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 865.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2592.865
Dual form 2592.2.i.s.1729.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{7} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{11} +(-0.500000 - 0.866025i) q^{13} -6.00000 q^{17} -5.00000 q^{19} +(-3.00000 - 5.19615i) q^{23} +(0.500000 - 0.866025i) q^{25} +(4.00000 - 6.92820i) q^{29} +(-4.00000 - 6.92820i) q^{31} -2.00000 q^{35} -5.00000 q^{37} +(4.00000 + 6.92820i) q^{41} +(2.00000 - 3.46410i) q^{43} +(5.00000 - 8.66025i) q^{47} +(3.00000 + 5.19615i) q^{49} -4.00000 q^{53} +4.00000 q^{55} +(-7.00000 - 12.1244i) q^{59} +(-1.50000 + 2.59808i) q^{61} +(1.00000 - 1.73205i) q^{65} +(6.50000 + 11.2583i) q^{67} -4.00000 q^{71} +9.00000 q^{73} +(1.00000 + 1.73205i) q^{77} +(-5.50000 + 9.52628i) q^{79} +(6.00000 - 10.3923i) q^{83} +(-6.00000 - 10.3923i) q^{85} +2.00000 q^{89} +1.00000 q^{91} +(-5.00000 - 8.66025i) q^{95} +(-0.500000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{5} - q^{7} + O(q^{10}) \) \( 2q + 2q^{5} - q^{7} + 2q^{11} - q^{13} - 12q^{17} - 10q^{19} - 6q^{23} + q^{25} + 8q^{29} - 8q^{31} - 4q^{35} - 10q^{37} + 8q^{41} + 4q^{43} + 10q^{47} + 6q^{49} - 8q^{53} + 8q^{55} - 14q^{59} - 3q^{61} + 2q^{65} + 13q^{67} - 8q^{71} + 18q^{73} + 2q^{77} - 11q^{79} + 12q^{83} - 12q^{85} + 4q^{89} + 2q^{91} - 10q^{95} - q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i \(-0.0190830\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i −0.944911 0.327327i \(-0.893852\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.00000 6.92820i 0.742781 1.28654i −0.208443 0.978035i \(-0.566840\pi\)
0.951224 0.308500i \(-0.0998271\pi\)
\(30\) 0 0
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.00000 −0.338062
\(36\) 0 0
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.00000 + 6.92820i 0.624695 + 1.08200i 0.988600 + 0.150567i \(0.0481100\pi\)
−0.363905 + 0.931436i \(0.618557\pi\)
\(42\) 0 0
\(43\) 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i \(-0.734678\pi\)
0.977261 + 0.212041i \(0.0680112\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.00000 8.66025i 0.729325 1.26323i −0.227844 0.973698i \(-0.573168\pi\)
0.957169 0.289530i \(-0.0934991\pi\)
\(48\) 0 0
\(49\) 3.00000 + 5.19615i 0.428571 + 0.742307i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.00000 12.1244i −0.911322 1.57846i −0.812198 0.583382i \(-0.801729\pi\)
−0.0991242 0.995075i \(-0.531604\pi\)
\(60\) 0 0
\(61\) −1.50000 + 2.59808i −0.192055 + 0.332650i −0.945931 0.324367i \(-0.894849\pi\)
0.753876 + 0.657017i \(0.228182\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.00000 1.73205i 0.124035 0.214834i
\(66\) 0 0
\(67\) 6.50000 + 11.2583i 0.794101 + 1.37542i 0.923408 + 0.383819i \(0.125391\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) 9.00000 1.05337 0.526685 0.850060i \(-0.323435\pi\)
0.526685 + 0.850060i \(0.323435\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.00000 + 1.73205i 0.113961 + 0.197386i
\(78\) 0 0
\(79\) −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 0 0
\(85\) −6.00000 10.3923i −0.650791 1.12720i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −5.00000 8.66025i −0.512989 0.888523i
\(96\) 0 0
\(97\) −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) 1.50000 + 2.59808i 0.147799 + 0.255996i 0.930414 0.366511i \(-0.119448\pi\)
−0.782614 + 0.622507i \(0.786114\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.00000 0.193347 0.0966736 0.995316i \(-0.469180\pi\)
0.0966736 + 0.995316i \(0.469180\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −5.00000 8.66025i −0.470360 0.814688i 0.529065 0.848581i \(-0.322543\pi\)
−0.999425 + 0.0338931i \(0.989209\pi\)
\(114\) 0 0
\(115\) 6.00000 10.3923i 0.559503 0.969087i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.00000 5.19615i 0.275010 0.476331i
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −8.00000 13.8564i −0.698963 1.21064i −0.968826 0.247741i \(-0.920312\pi\)
0.269863 0.962899i \(-0.413022\pi\)
\(132\) 0 0
\(133\) 2.50000 4.33013i 0.216777 0.375470i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 0 0
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.00000 −0.167248
\(144\) 0 0
\(145\) 16.0000 1.32873
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.00000 10.3923i −0.491539 0.851371i 0.508413 0.861113i \(-0.330232\pi\)
−0.999953 + 0.00974235i \(0.996899\pi\)
\(150\) 0 0
\(151\) 4.50000 7.79423i 0.366205 0.634285i −0.622764 0.782410i \(-0.713990\pi\)
0.988969 + 0.148124i \(0.0473236\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 8.00000 13.8564i 0.642575 1.11297i
\(156\) 0 0
\(157\) −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 0 0
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.00000 12.1244i −0.541676 0.938211i −0.998808 0.0488118i \(-0.984457\pi\)
0.457132 0.889399i \(-0.348877\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −12.0000 + 20.7846i −0.912343 + 1.58022i −0.101598 + 0.994826i \(0.532395\pi\)
−0.810745 + 0.585399i \(0.800938\pi\)
\(174\) 0 0
\(175\) 0.500000 + 0.866025i 0.0377964 + 0.0654654i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −19.0000 −1.41226 −0.706129 0.708083i \(-0.749560\pi\)
−0.706129 + 0.708083i \(0.749560\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.00000 8.66025i −0.367607 0.636715i
\(186\) 0 0
\(187\) −6.00000 + 10.3923i −0.438763 + 0.759961i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0 0
\(193\) 10.5000 + 18.1865i 0.755807 + 1.30910i 0.944972 + 0.327150i \(0.106088\pi\)
−0.189166 + 0.981945i \(0.560578\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) −19.0000 −1.34687 −0.673437 0.739244i \(-0.735183\pi\)
−0.673437 + 0.739244i \(0.735183\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.00000 + 6.92820i 0.280745 + 0.486265i
\(204\) 0 0
\(205\) −8.00000 + 13.8564i −0.558744 + 0.967773i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.00000 + 8.66025i −0.345857 + 0.599042i
\(210\) 0 0
\(211\) −0.500000 0.866025i −0.0344214 0.0596196i 0.848301 0.529514i \(-0.177626\pi\)
−0.882723 + 0.469894i \(0.844292\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 8.00000 0.545595
\(216\) 0 0
\(217\) 8.00000 0.543075
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3.00000 + 5.19615i 0.201802 + 0.349531i
\(222\) 0 0
\(223\) −8.00000 + 13.8564i −0.535720 + 0.927894i 0.463409 + 0.886145i \(0.346626\pi\)
−0.999128 + 0.0417488i \(0.986707\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i \(-0.963710\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(228\) 0 0
\(229\) −13.0000 22.5167i −0.859064 1.48794i −0.872823 0.488037i \(-0.837713\pi\)
0.0137585 0.999905i \(-0.495620\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 24.0000 1.57229 0.786146 0.618041i \(-0.212073\pi\)
0.786146 + 0.618041i \(0.212073\pi\)
\(234\) 0 0
\(235\) 20.0000 1.30466
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.00000 10.3923i −0.388108 0.672222i 0.604087 0.796918i \(-0.293538\pi\)
−0.992195 + 0.124696i \(0.960204\pi\)
\(240\) 0 0
\(241\) −6.50000 + 11.2583i −0.418702 + 0.725213i −0.995809 0.0914555i \(-0.970848\pi\)
0.577107 + 0.816668i \(0.304181\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.00000 + 10.3923i −0.383326 + 0.663940i
\(246\) 0 0
\(247\) 2.50000 + 4.33013i 0.159071 + 0.275519i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.00000 3.46410i −0.124757 0.216085i 0.796881 0.604136i \(-0.206482\pi\)
−0.921638 + 0.388051i \(0.873148\pi\)
\(258\) 0 0
\(259\) 2.50000 4.33013i 0.155342 0.269061i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i \(-0.712699\pi\)
0.989561 + 0.144112i \(0.0460326\pi\)
\(264\) 0 0
\(265\) −4.00000 6.92820i −0.245718 0.425596i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) −21.0000 −1.27566 −0.637830 0.770178i \(-0.720168\pi\)
−0.637830 + 0.770178i \(0.720168\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.00000 1.73205i −0.0603023 0.104447i
\(276\) 0 0
\(277\) 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.0000 20.7846i 0.715860 1.23991i −0.246767 0.969075i \(-0.579368\pi\)
0.962627 0.270831i \(-0.0872985\pi\)
\(282\) 0 0
\(283\) −10.0000 17.3205i −0.594438 1.02960i −0.993626 0.112728i \(-0.964041\pi\)
0.399188 0.916869i \(-0.369292\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.00000 −0.472225
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −9.00000 15.5885i −0.525786 0.910687i −0.999549 0.0300351i \(-0.990438\pi\)
0.473763 0.880652i \(-0.342895\pi\)
\(294\) 0 0
\(295\) 14.0000 24.2487i 0.815112 1.41181i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 0 0
\(301\) 2.00000 + 3.46410i 0.115278 + 0.199667i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −6.00000 −0.343559
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 15.0000 + 25.9808i 0.850572 + 1.47323i 0.880693 + 0.473688i \(0.157077\pi\)
−0.0301210 + 0.999546i \(0.509589\pi\)
\(312\) 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
\(317\) 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i \(-0.723923\pi\)
0.983866 + 0.178908i \(0.0572566\pi\)
\(318\) 0 0
\(319\) −8.00000 13.8564i −0.447914 0.775810i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 30.0000 1.66924
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5.00000 + 8.66025i 0.275659 + 0.477455i
\(330\) 0 0
\(331\) −14.5000 + 25.1147i −0.796992 + 1.38043i 0.124574 + 0.992210i \(0.460243\pi\)
−0.921567 + 0.388221i \(0.873090\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −13.0000 + 22.5167i −0.710266 + 1.23022i
\(336\) 0 0
\(337\) 15.5000 + 26.8468i 0.844339 + 1.46244i 0.886194 + 0.463314i \(0.153340\pi\)
−0.0418554 + 0.999124i \(0.513327\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −16.0000 −0.866449
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.00000 + 3.46410i 0.107366 + 0.185963i 0.914702 0.404128i \(-0.132425\pi\)
−0.807337 + 0.590091i \(0.799092\pi\)
\(348\) 0 0
\(349\) 2.50000 4.33013i 0.133822 0.231786i −0.791325 0.611396i \(-0.790608\pi\)
0.925147 + 0.379610i \(0.123942\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.00000 3.46410i 0.106449 0.184376i −0.807880 0.589347i \(-0.799385\pi\)
0.914329 + 0.404971i \(0.132718\pi\)
\(354\) 0 0
\(355\) −4.00000 6.92820i −0.212298 0.367711i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −14.0000 −0.738892 −0.369446 0.929252i \(-0.620452\pi\)
−0.369446 + 0.929252i \(0.620452\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9.00000 + 15.5885i 0.471082 + 0.815937i
\(366\) 0 0
\(367\) 7.50000 12.9904i 0.391497 0.678092i −0.601150 0.799136i \(-0.705291\pi\)
0.992647 + 0.121044i \(0.0386241\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.00000 3.46410i 0.103835 0.179847i
\(372\) 0 0
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8.00000 −0.412021
\(378\) 0 0
\(379\) 19.0000 0.975964 0.487982 0.872854i \(-0.337733\pi\)
0.487982 + 0.872854i \(0.337733\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8.00000 + 13.8564i 0.408781 + 0.708029i 0.994753 0.102302i \(-0.0326207\pi\)
−0.585973 + 0.810331i \(0.699287\pi\)
\(384\) 0 0
\(385\) −2.00000 + 3.46410i −0.101929 + 0.176547i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9.00000 15.5885i 0.456318 0.790366i −0.542445 0.840091i \(-0.682501\pi\)
0.998763 + 0.0497253i \(0.0158346\pi\)
\(390\) 0 0
\(391\) 18.0000 + 31.1769i 0.910299 + 1.57668i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −22.0000 −1.10694
\(396\) 0 0
\(397\) −14.0000 −0.702640 −0.351320 0.936255i \(-0.614267\pi\)
−0.351320 + 0.936255i \(0.614267\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 14.0000 + 24.2487i 0.699127 + 1.21092i 0.968770 + 0.247962i \(0.0797610\pi\)
−0.269643 + 0.962960i \(0.586906\pi\)
\(402\) 0 0
\(403\) −4.00000 + 6.92820i −0.199254 + 0.345118i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −5.00000 + 8.66025i −0.247841 + 0.429273i
\(408\) 0 0
\(409\) −6.50000 11.2583i −0.321404 0.556689i 0.659374 0.751815i \(-0.270822\pi\)
−0.980778 + 0.195127i \(0.937488\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 14.0000 0.688895
\(414\) 0 0
\(415\) 24.0000 1.17811
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13.0000 + 22.5167i 0.635092 + 1.10001i 0.986496 + 0.163787i \(0.0523710\pi\)
−0.351404 + 0.936224i \(0.614296\pi\)
\(420\) 0 0
\(421\) 9.50000 16.4545i 0.463002 0.801942i −0.536107 0.844150i \(-0.680106\pi\)
0.999109 + 0.0422075i \(0.0134391\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) 0 0
\(427\) −1.50000 2.59808i −0.0725901 0.125730i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 30.0000 1.44505 0.722525 0.691345i \(-0.242982\pi\)
0.722525 + 0.691345i \(0.242982\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 15.0000 + 25.9808i 0.717547 + 1.24283i
\(438\) 0 0
\(439\) 4.00000 6.92820i 0.190910 0.330665i −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) 0 0
\(445\) 2.00000 + 3.46410i 0.0948091 + 0.164214i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −34.0000 −1.60456 −0.802280 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 0 0
\(451\) 16.0000 0.753411
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.00000 + 1.73205i 0.0468807 + 0.0811998i
\(456\) 0 0
\(457\) −1.00000 + 1.73205i −0.0467780 + 0.0810219i −0.888466 0.458942i \(-0.848229\pi\)
0.841688 + 0.539964i \(0.181562\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 15.0000 25.9808i 0.698620 1.21004i −0.270326 0.962769i \(-0.587131\pi\)
0.968945 0.247276i \(-0.0795353\pi\)
\(462\) 0 0
\(463\) 9.50000 + 16.4545i 0.441502 + 0.764705i 0.997801 0.0662777i \(-0.0211123\pi\)
−0.556299 + 0.830982i \(0.687779\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.00000 −0.0925490 −0.0462745 0.998929i \(-0.514735\pi\)
−0.0462745 + 0.998929i \(0.514735\pi\)
\(468\) 0 0
\(469\) −13.0000 −0.600284
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.00000 6.92820i −0.183920 0.318559i
\(474\) 0 0
\(475\) −2.50000 + 4.33013i −0.114708 + 0.198680i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.00000 + 10.3923i −0.274147 + 0.474837i −0.969920 0.243426i \(-0.921729\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(480\) 0 0
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 0 0
\(487\) −11.0000 −0.498458 −0.249229 0.968445i \(-0.580177\pi\)
−0.249229 + 0.968445i \(0.580177\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.00000 + 12.1244i 0.315906 + 0.547165i 0.979630 0.200813i \(-0.0643584\pi\)
−0.663724 + 0.747978i \(0.731025\pi\)
\(492\) 0 0
\(493\) −24.0000 + 41.5692i −1.08091 + 1.87218i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.00000 3.46410i 0.0897123 0.155386i
\(498\) 0 0
\(499\) 12.0000 + 20.7846i 0.537194 + 0.930447i 0.999054 + 0.0434940i \(0.0138489\pi\)
−0.461860 + 0.886953i \(0.652818\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 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
\(507\) 0 0
\(508\) 0 0
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 0 0
\(511\) −4.50000 + 7.79423i −0.199068 + 0.344796i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −3.00000 + 5.19615i −0.132196 + 0.228970i
\(516\) 0 0
\(517\) −10.0000 17.3205i −0.439799 0.761755i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −42.0000 −1.84005 −0.920027 0.391856i \(-0.871833\pi\)
−0.920027 + 0.391856i \(0.871833\pi\)
\(522\) 0 0
\(523\) 15.0000 0.655904 0.327952 0.944694i \(-0.393642\pi\)
0.327952 + 0.944694i \(0.393642\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 24.0000 + 41.5692i 1.04546 + 1.81078i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 4.00000 6.92820i 0.173259 0.300094i
\(534\) 0 0
\(535\) 2.00000 + 3.46410i 0.0864675 + 0.149766i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) 37.0000 1.59075 0.795377 0.606115i \(-0.207273\pi\)
0.795377 + 0.606115i \(0.207273\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −10.0000 17.3205i −0.428353 0.741929i
\(546\) 0 0
\(547\) 7.50000 12.9904i 0.320677 0.555429i −0.659951 0.751309i \(-0.729423\pi\)
0.980628 + 0.195880i \(0.0627563\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −20.0000 + 34.6410i −0.852029 + 1.47576i
\(552\) 0 0
\(553\) −5.50000 9.52628i −0.233884 0.405099i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.0000 −0.593199 −0.296600 0.955002i \(-0.595853\pi\)
−0.296600 + 0.955002i \(0.595853\pi\)
\(558\) 0 0
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12.0000 + 20.7846i 0.505740 + 0.875967i 0.999978 + 0.00664037i \(0.00211371\pi\)
−0.494238 + 0.869326i \(0.664553\pi\)
\(564\) 0 0
\(565\) 10.0000 17.3205i 0.420703 0.728679i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.00000 + 8.66025i −0.209611 + 0.363057i −0.951592 0.307364i \(-0.900553\pi\)
0.741981 + 0.670421i \(0.233886\pi\)
\(570\) 0 0
\(571\) −9.50000 16.4545i −0.397563 0.688599i 0.595862 0.803087i \(-0.296811\pi\)
−0.993425 + 0.114488i \(0.963477\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) 0 0
\(577\) 3.00000 0.124892 0.0624458 0.998048i \(-0.480110\pi\)
0.0624458 + 0.998048i \(0.480110\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 6.00000 + 10.3923i 0.248922 + 0.431145i
\(582\) 0 0
\(583\) −4.00000 + 6.92820i −0.165663 + 0.286937i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3.00000 5.19615i 0.123823 0.214468i −0.797449 0.603386i \(-0.793818\pi\)
0.921272 + 0.388918i \(0.127151\pi\)
\(588\) 0 0
\(589\) 20.0000 + 34.6410i 0.824086 + 1.42736i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 36.0000 1.47834 0.739171 0.673517i \(-0.235217\pi\)
0.739171 + 0.673517i \(0.235217\pi\)
\(594\) 0 0
\(595\) 12.0000 0.491952
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4.00000 6.92820i −0.163436 0.283079i 0.772663 0.634816i \(-0.218924\pi\)
−0.936099 + 0.351738i \(0.885591\pi\)
\(600\) 0 0
\(601\) 13.0000 22.5167i 0.530281 0.918474i −0.469095 0.883148i \(-0.655420\pi\)
0.999376 0.0353259i \(-0.0112469\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.00000 + 12.1244i −0.284590 + 0.492925i
\(606\) 0 0
\(607\) −20.5000 35.5070i −0.832069 1.44119i −0.896394 0.443257i \(-0.853823\pi\)
0.0643251 0.997929i \(-0.479511\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −10.0000 −0.404557
\(612\) 0 0
\(613\) −9.00000 −0.363507 −0.181753 0.983344i \(-0.558177\pi\)
−0.181753 + 0.983344i \(0.558177\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21.0000 + 36.3731i 0.845428 + 1.46432i 0.885249 + 0.465118i \(0.153988\pi\)
−0.0398207 + 0.999207i \(0.512679\pi\)
\(618\) 0 0
\(619\) 4.50000 7.79423i 0.180870 0.313276i −0.761307 0.648392i \(-0.775442\pi\)
0.942177 + 0.335115i \(0.108775\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.00000 + 1.73205i −0.0400642 + 0.0693932i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 30.0000 1.19618
\(630\) 0 0
\(631\) −1.00000 −0.0398094 −0.0199047 0.999802i \(-0.506336\pi\)
−0.0199047 + 0.999802i \(0.506336\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 20.0000 + 34.6410i 0.793676 + 1.37469i
\(636\) 0 0
\(637\) 3.00000 5.19615i 0.118864 0.205879i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.00000 3.46410i 0.0789953 0.136824i −0.823821 0.566849i \(-0.808162\pi\)
0.902817 + 0.430026i \(0.141495\pi\)
\(642\) 0 0
\(643\) 6.00000 + 10.3923i 0.236617 + 0.409832i 0.959741 0.280885i \(-0.0906280\pi\)
−0.723124 + 0.690718i \(0.757295\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 24.0000 0.943537 0.471769 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 0 0
\(649\) −28.0000 −1.09910
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −22.0000 38.1051i −0.860927 1.49117i −0.871036 0.491220i \(-0.836551\pi\)
0.0101092 0.999949i \(-0.496782\pi\)
\(654\) 0 0
\(655\) 16.0000 27.7128i 0.625172 1.08283i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) 0 0
\(661\) −11.5000 19.9186i −0.447298 0.774743i 0.550911 0.834564i \(-0.314280\pi\)
−0.998209 + 0.0598209i \(0.980947\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 10.0000 0.387783
\(666\) 0 0
\(667\) −48.0000 −1.85857
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.00000 + 5.19615i 0.115814 + 0.200595i
\(672\) 0 0
\(673\) −11.5000 + 19.9186i −0.443292 + 0.767805i −0.997932 0.0642860i \(-0.979523\pi\)
0.554639 + 0.832091i \(0.312856\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.00000 + 12.1244i −0.269032 + 0.465977i −0.968612 0.248577i \(-0.920037\pi\)
0.699580 + 0.714554i \(0.253370\pi\)
\(678\) 0 0
\(679\) −0.500000 0.866025i −0.0191882 0.0332350i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 24.0000 0.918334 0.459167 0.888350i \(-0.348148\pi\)
0.459167 + 0.888350i \(0.348148\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.00000 + 3.46410i 0.0761939 + 0.131972i
\(690\) 0 0
\(691\) −2.00000 + 3.46410i −0.0760836 + 0.131781i −0.901557 0.432660i \(-0.857575\pi\)
0.825473 + 0.564441i \(0.190908\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.00000 8.66025i 0.189661 0.328502i
\(696\) 0 0
\(697\) −24.0000 41.5692i −0.909065 1.57455i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 25.0000 0.942893
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 11.5000 19.9186i 0.431892 0.748058i −0.565145 0.824992i \(-0.691180\pi\)
0.997036 + 0.0769337i \(0.0245130\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −24.0000 + 41.5692i −0.898807 + 1.55678i
\(714\) 0 0
\(715\) −2.00000 3.46410i −0.0747958 0.129550i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −52.0000 −1.93927 −0.969636 0.244551i \(-0.921359\pi\)
−0.969636 + 0.244551i \(0.921359\pi\)
\(720\) 0 0
\(721\) −3.00000 −0.111726
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.00000 6.92820i −0.148556 0.257307i
\(726\) 0 0
\(727\) −24.0000 + 41.5692i −0.890111 + 1.54172i −0.0503692 + 0.998731i \(0.516040\pi\)
−0.839742 + 0.542986i \(0.817294\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) 0 0
\(733\) 17.0000 + 29.4449i 0.627909 + 1.08757i 0.987971 + 0.154642i \(0.0494225\pi\)
−0.360061 + 0.932929i \(0.617244\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 26.0000 0.957722
\(738\) 0 0
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 21.0000 + 36.3731i 0.770415 + 1.33440i 0.937336 + 0.348428i \(0.113284\pi\)
−0.166920 + 0.985970i \(0.553382\pi\)
\(744\) 0 0
\(745\) 12.0000 20.7846i 0.439646 0.761489i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.00000 + 1.73205i −0.0365392 + 0.0632878i
\(750\) 0 0
\(751\) 12.5000 + 21.6506i 0.456131 + 0.790043i 0.998752 0.0499348i \(-0.0159013\pi\)
−0.542621 + 0.839978i \(0.682568\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 18.0000 0.655087
\(756\) 0 0
\(757\) 33.0000 1.19941 0.599703 0.800223i \(-0.295286\pi\)
0.599703 + 0.800223i \(0.295286\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −21.0000 36.3731i −0.761249 1.31852i −0.942207 0.335032i \(-0.891253\pi\)
0.180957 0.983491i \(-0.442080\pi\)
\(762\) 0 0
\(763\) 5.00000 8.66025i 0.181012 0.313522i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7.00000 + 12.1244i −0.252755 + 0.437785i
\(768\) 0 0
\(769\) 8.50000 + 14.7224i 0.306518 + 0.530904i 0.977598 0.210480i \(-0.0675028\pi\)
−0.671080 + 0.741385i \(0.734169\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 36.0000 1.29483 0.647415 0.762138i \(-0.275850\pi\)
0.647415 + 0.762138i \(0.275850\pi\)
\(774\) 0 0
\(775\) −8.00000 −0.287368
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −20.0000 34.6410i −0.716574 1.24114i
\(780\) 0 0
\(781\) −4.00000 + 6.92820i −0.143131 + 0.247911i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.00000 3.46410i 0.0713831 0.123639i
\(786\) 0 0
\(787\) −1.50000 2.59808i −0.0534692 0.0926114i 0.838052 0.545590i \(-0.183695\pi\)
−0.891521 + 0.452979i \(0.850361\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 10.0000 0.355559
\(792\) 0 0
\(793\) 3.00000 0.106533
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −12.0000 20.7846i −0.425062 0.736229i 0.571364 0.820696i \(-0.306414\pi\)
−0.996426 + 0.0844678i \(0.973081\pi\)
\(798\) 0 0
\(799\) −30.0000 + 51.9615i −1.06132 + 1.83827i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 9.00000 15.5885i 0.317603