Properties

Label 1512.2.s.j.1297.1
Level $1512$
Weight $2$
Character 1512.1297
Analytic conductor $12.073$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1297.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1512.1297
Dual form 1512.2.s.j.865.1

$q$-expansion

\(f(q)\) \(=\) \(q+(2.00000 - 3.46410i) q^{5} +(2.00000 + 1.73205i) q^{7} +O(q^{10})\) \(q+(2.00000 - 3.46410i) q^{5} +(2.00000 + 1.73205i) q^{7} +(-1.00000 - 1.73205i) q^{11} +5.00000 q^{13} +(-3.00000 - 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} +(-3.00000 + 5.19615i) q^{23} +(-5.50000 - 9.52628i) q^{25} +6.00000 q^{29} +(3.50000 + 6.06218i) q^{31} +(10.0000 - 3.46410i) q^{35} +(-3.50000 + 6.06218i) q^{37} +2.00000 q^{41} -7.00000 q^{43} +(1.00000 - 1.73205i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-3.00000 - 5.19615i) q^{53} -8.00000 q^{55} +(-3.00000 - 5.19615i) q^{59} +(4.50000 - 7.79423i) q^{61} +(10.0000 - 17.3205i) q^{65} +(3.50000 + 6.06218i) q^{67} -8.00000 q^{71} +(-5.00000 - 8.66025i) q^{73} +(1.00000 - 5.19615i) q^{77} +(-0.500000 + 0.866025i) q^{79} +14.0000 q^{83} -24.0000 q^{85} +(-6.00000 + 10.3923i) q^{89} +(10.0000 + 8.66025i) q^{91} +(-8.00000 - 13.8564i) q^{95} -15.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 4q^{5} + 4q^{7} + O(q^{10}) \) \( 2q + 4q^{5} + 4q^{7} - 2q^{11} + 10q^{13} - 6q^{17} + 4q^{19} - 6q^{23} - 11q^{25} + 12q^{29} + 7q^{31} + 20q^{35} - 7q^{37} + 4q^{41} - 14q^{43} + 2q^{47} + 2q^{49} - 6q^{53} - 16q^{55} - 6q^{59} + 9q^{61} + 20q^{65} + 7q^{67} - 16q^{71} - 10q^{73} + 2q^{77} - q^{79} + 28q^{83} - 48q^{85} - 12q^{89} + 20q^{91} - 16q^{95} - 30q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(5\) 2.00000 3.46410i 0.894427 1.54919i 0.0599153 0.998203i \(-0.480917\pi\)
0.834512 0.550990i \(-0.185750\pi\)
\(6\) 0 0
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0 0
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) −5.50000 9.52628i −1.10000 1.90526i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 3.50000 + 6.06218i 0.628619 + 1.08880i 0.987829 + 0.155543i \(0.0497126\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 10.0000 3.46410i 1.69031 0.585540i
\(36\) 0 0
\(37\) −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i \(0.361819\pi\)
−0.995998 + 0.0893706i \(0.971514\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −7.00000 −1.06749 −0.533745 0.845645i \(-0.679216\pi\)
−0.533745 + 0.845645i \(0.679216\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i \(-0.786737\pi\)
0.929695 + 0.368329i \(0.120070\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 0 0
\(55\) −8.00000 −1.07872
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 0 0
\(61\) 4.50000 7.79423i 0.576166 0.997949i −0.419748 0.907641i \(-0.637882\pi\)
0.995914 0.0903080i \(-0.0287851\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 10.0000 17.3205i 1.24035 2.14834i
\(66\) 0 0
\(67\) 3.50000 + 6.06218i 0.427593 + 0.740613i 0.996659 0.0816792i \(-0.0260283\pi\)
−0.569066 + 0.822292i \(0.692695\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −5.00000 8.66025i −0.585206 1.01361i −0.994850 0.101361i \(-0.967680\pi\)
0.409644 0.912245i \(-0.365653\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.00000 5.19615i 0.113961 0.592157i
\(78\) 0 0
\(79\) −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i \(-0.851249\pi\)
0.836527 + 0.547926i \(0.184582\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 14.0000 1.53670 0.768350 0.640030i \(-0.221078\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(84\) 0 0
\(85\) −24.0000 −2.60317
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 + 10.3923i −0.635999 + 1.10158i 0.350304 + 0.936636i \(0.386078\pi\)
−0.986303 + 0.164946i \(0.947255\pi\)
\(90\) 0 0
\(91\) 10.0000 + 8.66025i 1.04828 + 0.907841i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8.00000 13.8564i −0.820783 1.42164i
\(96\) 0 0
\(97\) −15.0000 −1.52302 −0.761510 0.648154i \(-0.775541\pi\)
−0.761510 + 0.648154i \(0.775541\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 8.00000 + 13.8564i 0.796030 + 1.37876i 0.922183 + 0.386753i \(0.126403\pi\)
−0.126153 + 0.992011i \(0.540263\pi\)
\(102\) 0 0
\(103\) 6.50000 11.2583i 0.640464 1.10932i −0.344865 0.938652i \(-0.612075\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.00000 5.19615i 0.290021 0.502331i −0.683793 0.729676i \(-0.739671\pi\)
0.973814 + 0.227345i \(0.0730044\pi\)
\(108\) 0 0
\(109\) −2.50000 4.33013i −0.239457 0.414751i 0.721102 0.692829i \(-0.243636\pi\)
−0.960558 + 0.278078i \(0.910303\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.00000 0.752577 0.376288 0.926503i \(-0.377200\pi\)
0.376288 + 0.926503i \(0.377200\pi\)
\(114\) 0 0
\(115\) 12.0000 + 20.7846i 1.11901 + 1.93817i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 3.00000 15.5885i 0.275010 1.42899i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) 13.0000 1.15356 0.576782 0.816898i \(-0.304308\pi\)
0.576782 + 0.816898i \(0.304308\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.00000 3.46410i 0.174741 0.302660i −0.765331 0.643637i \(-0.777425\pi\)
0.940072 + 0.340977i \(0.110758\pi\)
\(132\) 0 0
\(133\) 10.0000 3.46410i 0.867110 0.300376i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.00000 5.19615i −0.256307 0.443937i 0.708942 0.705266i \(-0.249173\pi\)
−0.965250 + 0.261329i \(0.915839\pi\)
\(138\) 0 0
\(139\) 7.00000 0.593732 0.296866 0.954919i \(-0.404058\pi\)
0.296866 + 0.954919i \(0.404058\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −5.00000 8.66025i −0.418121 0.724207i
\(144\) 0 0
\(145\) 12.0000 20.7846i 0.996546 1.72607i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) 0 0
\(151\) 4.50000 + 7.79423i 0.366205 + 0.634285i 0.988969 0.148124i \(-0.0473236\pi\)
−0.622764 + 0.782410i \(0.713990\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 28.0000 2.24901
\(156\) 0 0
\(157\) 3.00000 + 5.19615i 0.239426 + 0.414698i 0.960550 0.278108i \(-0.0897074\pi\)
−0.721124 + 0.692806i \(0.756374\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −15.0000 + 5.19615i −1.18217 + 0.409514i
\(162\) 0 0
\(163\) −10.5000 + 18.1865i −0.822423 + 1.42448i 0.0814491 + 0.996678i \(0.474045\pi\)
−0.903873 + 0.427802i \(0.859288\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.00000 −0.154765 −0.0773823 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 5.50000 28.5788i 0.415761 2.16036i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2.00000 + 3.46410i 0.149487 + 0.258919i 0.931038 0.364922i \(-0.118904\pi\)
−0.781551 + 0.623841i \(0.785571\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 14.0000 + 24.2487i 1.02930 + 1.78280i
\(186\) 0 0
\(187\) −6.00000 + 10.3923i −0.438763 + 0.759961i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −10.0000 + 17.3205i −0.723575 + 1.25327i 0.235983 + 0.971757i \(0.424169\pi\)
−0.959558 + 0.281511i \(0.909164\pi\)
\(192\) 0 0
\(193\) −3.50000 6.06218i −0.251936 0.436365i 0.712123 0.702055i \(-0.247734\pi\)
−0.964059 + 0.265689i \(0.914400\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 1.50000 + 2.59808i 0.106332 + 0.184173i 0.914282 0.405079i \(-0.132756\pi\)
−0.807950 + 0.589252i \(0.799423\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 12.0000 + 10.3923i 0.842235 + 0.729397i
\(204\) 0 0
\(205\) 4.00000 6.92820i 0.279372 0.483887i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) −27.0000 −1.85876 −0.929378 0.369129i \(-0.879656\pi\)
−0.929378 + 0.369129i \(0.879656\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −14.0000 + 24.2487i −0.954792 + 1.65375i
\(216\) 0 0
\(217\) −3.50000 + 18.1865i −0.237595 + 1.23458i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −15.0000 25.9808i −1.00901 1.74766i
\(222\) 0 0
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.00000 8.66025i −0.331862 0.574801i 0.651015 0.759065i \(-0.274343\pi\)
−0.982877 + 0.184263i \(0.941010\pi\)
\(228\) 0 0
\(229\) −6.50000 + 11.2583i −0.429532 + 0.743971i −0.996832 0.0795401i \(-0.974655\pi\)
0.567300 + 0.823511i \(0.307988\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.00000 + 6.92820i −0.262049 + 0.453882i −0.966786 0.255586i \(-0.917731\pi\)
0.704737 + 0.709468i \(0.251065\pi\)
\(234\) 0 0
\(235\) −4.00000 6.92820i −0.260931 0.451946i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 0 0
\(241\) −0.500000 0.866025i −0.0322078 0.0557856i 0.849472 0.527633i \(-0.176921\pi\)
−0.881680 + 0.471848i \(0.843587\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 26.0000 + 10.3923i 1.66108 + 0.663940i
\(246\) 0 0
\(247\) 10.0000 17.3205i 0.636285 1.10208i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −30.0000 −1.89358 −0.946792 0.321847i \(-0.895696\pi\)
−0.946792 + 0.321847i \(0.895696\pi\)
\(252\) 0 0
\(253\) 12.0000 0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −7.00000 + 12.1244i −0.436648 + 0.756297i −0.997429 0.0716680i \(-0.977168\pi\)
0.560781 + 0.827964i \(0.310501\pi\)
\(258\) 0 0
\(259\) −17.5000 + 6.06218i −1.08740 + 0.376685i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3.00000 + 5.19615i 0.184988 + 0.320408i 0.943572 0.331166i \(-0.107442\pi\)
−0.758585 + 0.651575i \(0.774109\pi\)
\(264\) 0 0
\(265\) −24.0000 −1.47431
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 16.0000 + 27.7128i 0.975537 + 1.68968i 0.678151 + 0.734923i \(0.262782\pi\)
0.297386 + 0.954757i \(0.403885\pi\)
\(270\) 0 0
\(271\) −7.50000 + 12.9904i −0.455593 + 0.789109i −0.998722 0.0505395i \(-0.983906\pi\)
0.543130 + 0.839649i \(0.317239\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −11.0000 + 19.0526i −0.663325 + 1.14891i
\(276\) 0 0
\(277\) −0.500000 0.866025i −0.0300421 0.0520344i 0.850613 0.525792i \(-0.176231\pi\)
−0.880656 + 0.473757i \(0.842897\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 24.0000 1.43172 0.715860 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) 0 0
\(283\) 5.50000 + 9.52628i 0.326941 + 0.566279i 0.981903 0.189383i \(-0.0606488\pi\)
−0.654962 + 0.755662i \(0.727315\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.00000 + 3.46410i 0.236113 + 0.204479i
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) 0 0
\(295\) −24.0000 −1.39733
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −15.0000 + 25.9808i −0.867472 + 1.50251i
\(300\) 0 0
\(301\) −14.0000 12.1244i −0.806947 0.698836i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −18.0000 31.1769i −1.03068 1.78518i
\(306\) 0 0
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 8.00000 + 13.8564i 0.453638 + 0.785725i 0.998609 0.0527306i \(-0.0167924\pi\)
−0.544970 + 0.838455i \(0.683459\pi\)
\(312\) 0 0
\(313\) −5.00000 + 8.66025i −0.282617 + 0.489506i −0.972028 0.234863i \(-0.924536\pi\)
0.689412 + 0.724370i \(0.257869\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) 0 0
\(319\) −6.00000 10.3923i −0.335936 0.581857i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −24.0000 −1.33540
\(324\) 0 0
\(325\) −27.5000 47.6314i −1.52543 2.64211i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5.00000 1.73205i 0.275659 0.0954911i
\(330\) 0 0
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 28.0000 1.52980
\(336\) 0 0
\(337\) 26.0000 1.41631 0.708155 0.706057i \(-0.249528\pi\)
0.708155 + 0.706057i \(0.249528\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 7.00000 12.1244i 0.379071 0.656571i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) 15.0000 0.802932 0.401466 0.915874i \(-0.368501\pi\)
0.401466 + 0.915874i \(0.368501\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −14.0000 24.2487i −0.745145 1.29063i −0.950127 0.311863i \(-0.899047\pi\)
0.204982 0.978766i \(-0.434286\pi\)
\(354\) 0 0
\(355\) −16.0000 + 27.7128i −0.849192 + 1.47084i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.00000 + 5.19615i −0.158334 + 0.274242i −0.934268 0.356572i \(-0.883946\pi\)
0.775934 + 0.630814i \(0.217279\pi\)
\(360\) 0 0
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −40.0000 −2.09370
\(366\) 0 0
\(367\) −14.0000 24.2487i −0.730794 1.26577i −0.956544 0.291587i \(-0.905817\pi\)
0.225750 0.974185i \(-0.427517\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.00000 15.5885i 0.155752 0.809312i
\(372\) 0 0
\(373\) −5.00000 + 8.66025i −0.258890 + 0.448411i −0.965945 0.258748i \(-0.916690\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 30.0000 1.54508
\(378\) 0 0
\(379\) 17.0000 0.873231 0.436616 0.899648i \(-0.356177\pi\)
0.436616 + 0.899648i \(0.356177\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −15.0000 + 25.9808i −0.766464 + 1.32755i 0.173005 + 0.984921i \(0.444652\pi\)
−0.939469 + 0.342634i \(0.888681\pi\)
\(384\) 0 0
\(385\) −16.0000 13.8564i −0.815436 0.706188i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 10.0000 + 17.3205i 0.507020 + 0.878185i 0.999967 + 0.00812520i \(0.00258636\pi\)
−0.492947 + 0.870059i \(0.664080\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.00000 + 3.46410i 0.100631 + 0.174298i
\(396\) 0 0
\(397\) 2.50000 4.33013i 0.125471 0.217323i −0.796446 0.604710i \(-0.793289\pi\)
0.921917 + 0.387387i \(0.126622\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 0 0
\(403\) 17.5000 + 30.3109i 0.871737 + 1.50989i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 14.0000 0.693954
\(408\) 0 0
\(409\) 17.5000 + 30.3109i 0.865319 + 1.49878i 0.866730 + 0.498778i \(0.166218\pi\)
−0.00141047 + 0.999999i \(0.500449\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 3.00000 15.5885i 0.147620 0.767058i
\(414\) 0 0
\(415\) 28.0000 48.4974i 1.37447 2.38064i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4.00000 −0.195413 −0.0977064 0.995215i \(-0.531151\pi\)
−0.0977064 + 0.995215i \(0.531151\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −33.0000 + 57.1577i −1.60074 + 2.77255i
\(426\) 0 0
\(427\) 22.5000 7.79423i 1.08885 0.377189i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.00000 8.66025i −0.240842 0.417150i 0.720113 0.693857i \(-0.244090\pi\)
−0.960954 + 0.276707i \(0.910757\pi\)
\(432\) 0 0
\(433\) 7.00000 0.336399 0.168199 0.985753i \(-0.446205\pi\)
0.168199 + 0.985753i \(0.446205\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 12.0000 + 20.7846i 0.574038 + 0.994263i
\(438\) 0 0
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.0000 + 20.7846i −0.570137 + 0.987507i 0.426414 + 0.904528i \(0.359777\pi\)
−0.996551 + 0.0829786i \(0.973557\pi\)
\(444\) 0 0
\(445\) 24.0000 + 41.5692i 1.13771 + 1.97057i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 28.0000 1.32140 0.660701 0.750649i \(-0.270259\pi\)
0.660701 + 0.750649i \(0.270259\pi\)
\(450\) 0 0
\(451\) −2.00000 3.46410i −0.0941763 0.163118i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 50.0000 17.3205i 2.34404 0.811998i
\(456\) 0 0
\(457\) 5.50000 9.52628i 0.257279 0.445621i −0.708233 0.705979i \(-0.750507\pi\)
0.965512 + 0.260358i \(0.0838407\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −20.0000 + 34.6410i −0.925490 + 1.60300i −0.134718 + 0.990884i \(0.543013\pi\)
−0.790772 + 0.612111i \(0.790321\pi\)
\(468\) 0 0
\(469\) −3.50000 + 18.1865i −0.161615 + 0.839776i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.00000 + 12.1244i 0.321860 + 0.557478i
\(474\) 0 0
\(475\) −44.0000 −2.01886
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 12.0000 + 20.7846i 0.548294 + 0.949673i 0.998392 + 0.0566937i \(0.0180558\pi\)
−0.450098 + 0.892979i \(0.648611\pi\)
\(480\) 0 0
\(481\) −17.5000 + 30.3109i −0.797931 + 1.38206i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −30.0000 + 51.9615i −1.36223 + 2.35945i
\(486\) 0 0
\(487\) −4.00000 6.92820i −0.181257 0.313947i 0.761052 0.648691i \(-0.224683\pi\)
−0.942309 + 0.334744i \(0.891350\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.00000 −0.270776 −0.135388 0.990793i \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) 0 0
\(493\) −18.0000 31.1769i −0.810679 1.40414i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.0000 13.8564i −0.717698 0.621545i
\(498\) 0 0
\(499\) 15.5000 26.8468i 0.693875 1.20183i −0.276683 0.960961i \(-0.589235\pi\)
0.970558 0.240866i \(-0.0774314\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −26.0000 −1.15928 −0.579641 0.814872i \(-0.696807\pi\)
−0.579641 + 0.814872i \(0.696807\pi\)
\(504\) 0 0
\(505\) 64.0000 2.84796
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 19.0000 32.9090i 0.842160 1.45866i −0.0459045 0.998946i \(-0.514617\pi\)
0.888065 0.459718i \(-0.152050\pi\)
\(510\) 0 0
\(511\) 5.00000 25.9808i 0.221187 1.14932i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −26.0000 45.0333i −1.14570 1.98441i
\(516\) 0 0
\(517\) −4.00000 −0.175920
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.00000 5.19615i −0.131432 0.227648i 0.792797 0.609486i \(-0.208624\pi\)
−0.924229 + 0.381839i \(0.875291\pi\)
\(522\) 0 0
\(523\) −12.5000 + 21.6506i −0.546587 + 0.946716i 0.451918 + 0.892059i \(0.350740\pi\)
−0.998505 + 0.0546569i \(0.982594\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 21.0000 36.3731i 0.914774 1.58444i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 10.0000 0.433148
\(534\) 0 0
\(535\) −12.0000 20.7846i −0.518805 0.898597i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 11.0000 8.66025i 0.473804 0.373024i
\(540\) 0 0
\(541\) −19.0000 + 32.9090i −0.816874 + 1.41487i 0.0911008 + 0.995842i \(0.470961\pi\)
−0.907975 + 0.419025i \(0.862372\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −20.0000 −0.856706
\(546\) 0 0
\(547\) −3.00000 −0.128271 −0.0641354 0.997941i \(-0.520429\pi\)
−0.0641354 + 0.997941i \(0.520429\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 12.0000 20.7846i 0.511217 0.885454i
\(552\) 0 0
\(553\) −2.50000 + 0.866025i −0.106311 + 0.0368271i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −10.0000 17.3205i −0.423714 0.733893i 0.572586 0.819845i \(-0.305940\pi\)
−0.996299 + 0.0859514i \(0.972607\pi\)
\(558\) 0 0
\(559\) −35.0000 −1.48034
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.00000 12.1244i −0.295015 0.510981i 0.679974 0.733237i \(-0.261991\pi\)
−0.974988 + 0.222256i \(0.928658\pi\)
\(564\) 0 0
\(565\) 16.0000 27.7128i 0.673125 1.16589i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 20.0000 34.6410i 0.838444 1.45223i −0.0527519 0.998608i \(-0.516799\pi\)
0.891196 0.453619i \(-0.149867\pi\)
\(570\) 0 0
\(571\) −8.00000 13.8564i −0.334790 0.579873i 0.648655 0.761083i \(-0.275332\pi\)
−0.983444 + 0.181210i \(0.941999\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 66.0000 2.75239
\(576\) 0 0
\(577\) −3.50000 6.06218i −0.145707 0.252372i 0.783930 0.620850i \(-0.213212\pi\)
−0.929636 + 0.368478i \(0.879879\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 28.0000 + 24.2487i 1.16164 + 1.00601i
\(582\) 0 0
\(583\) −6.00000 + 10.3923i −0.248495 + 0.430405i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −36.0000 −1.48588 −0.742940 0.669359i \(-0.766569\pi\)
−0.742940 + 0.669359i \(0.766569\pi\)
\(588\) 0 0
\(589\) 28.0000 1.15372
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −20.0000 + 34.6410i −0.821302 + 1.42254i 0.0834118 + 0.996515i \(0.473418\pi\)
−0.904713 + 0.426021i \(0.859915\pi\)
\(594\) 0 0
\(595\) −48.0000 41.5692i −1.96781 1.70417i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) 0 0
\(601\) 23.0000 0.938190 0.469095 0.883148i \(-0.344580\pi\)
0.469095 + 0.883148i \(0.344580\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −14.0000 24.2487i −0.569181 0.985850i
\(606\) 0 0
\(607\) −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i \(-0.885242\pi\)
0.773358 + 0.633970i \(0.218576\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.00000 8.66025i 0.202278 0.350356i
\(612\) 0 0
\(613\) 10.5000 + 18.1865i 0.424091 + 0.734547i 0.996335 0.0855362i \(-0.0272603\pi\)
−0.572244 + 0.820083i \(0.693927\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 34.0000 1.36879 0.684394 0.729112i \(-0.260067\pi\)
0.684394 + 0.729112i \(0.260067\pi\)
\(618\) 0 0
\(619\) 11.5000 + 19.9186i 0.462224 + 0.800595i 0.999071 0.0430838i \(-0.0137183\pi\)
−0.536847 + 0.843679i \(0.680385\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −30.0000 + 10.3923i −1.20192 + 0.416359i
\(624\) 0 0
\(625\) −20.5000 + 35.5070i −0.820000 + 1.42028i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 42.0000 1.67465
\(630\) 0 0
\(631\) −9.00000 −0.358284 −0.179142 0.983823i \(-0.557332\pi\)
−0.179142 + 0.983823i \(0.557332\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 26.0000 45.0333i 1.03178 1.78709i
\(636\) 0 0
\(637\) 5.00000 + 34.6410i 0.198107 + 1.37253i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3.00000 + 5.19615i 0.118493 + 0.205236i 0.919171 0.393860i \(-0.128860\pi\)
−0.800678 + 0.599095i \(0.795527\pi\)
\(642\) 0 0
\(643\) 1.00000 0.0394362 0.0197181 0.999806i \(-0.493723\pi\)
0.0197181 + 0.999806i \(0.493723\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −14.0000 24.2487i −0.550397 0.953315i −0.998246 0.0592060i \(-0.981143\pi\)
0.447849 0.894109i \(-0.352190\pi\)
\(648\) 0 0
\(649\) −6.00000 + 10.3923i −0.235521 + 0.407934i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5.00000 + 8.66025i −0.195665 + 0.338902i −0.947118 0.320884i \(-0.896020\pi\)
0.751453 + 0.659786i \(0.229353\pi\)
\(654\) 0 0
\(655\) −8.00000 13.8564i −0.312586 0.541415i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −1.00000 1.73205i −0.0388955 0.0673690i 0.845922 0.533306i \(-0.179051\pi\)
−0.884818 + 0.465937i \(0.845717\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 8.00000 41.5692i 0.310227 1.61199i
\(666\) 0 0
\(667\) −18.0000 + 31.1769i −0.696963 + 1.20717i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −18.0000 −0.694882
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −18.0000 + 31.1769i −0.691796 + 1.19823i 0.279453 + 0.960159i \(0.409847\pi\)
−0.971249 + 0.238067i \(0.923486\pi\)
\(678\) 0 0
\(679\) −30.0000 25.9808i −1.15129 0.997050i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −12.0000 20.7846i −0.459167 0.795301i 0.539750 0.841825i \(-0.318519\pi\)
−0.998917 + 0.0465244i \(0.985185\pi\)
\(684\) 0 0
\(685\) −24.0000 −0.916993
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −15.0000 25.9808i −0.571454 0.989788i
\(690\) 0 0
\(691\) −15.5000 + 26.8468i −0.589648 + 1.02130i 0.404631 + 0.914480i \(0.367400\pi\)
−0.994278 + 0.106820i \(0.965933\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 14.0000 24.2487i 0.531050 0.919806i
\(696\) 0 0
\(697\) −6.00000 10.3923i −0.227266 0.393637i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −24.0000 −0.906467 −0.453234 0.891392i \(-0.649730\pi\)
−0.453234 + 0.891392i \(0.649730\pi\)
\(702\) 0 0
\(703\) 14.0000 + 24.2487i 0.528020 + 0.914557i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.00000 + 41.5692i −0.300871 + 1.56337i
\(708\) 0 0
\(709\) −4.50000 + 7.79423i −0.169001 + 0.292718i −0.938069 0.346449i \(-0.887387\pi\)
0.769068 + 0.639167i \(0.220721\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −42.0000 −1.57291
\(714\) 0 0
\(715\) −40.0000 −1.49592
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 20.0000 34.6410i 0.745874 1.29189i −0.203911 0.978989i \(-0.565365\pi\)
0.949785 0.312903i \(-0.101301\pi\)
\(720\) 0 0
\(721\) 32.5000 11.2583i 1.21036 0.419282i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −33.0000 57.1577i −1.22559 2.12278i
\(726\) 0 0
\(727\) 19.0000 0.704671 0.352335 0.935874i \(-0.385388\pi\)
0.352335 + 0.935874i \(0.385388\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 21.0000 + 36.3731i 0.776713 + 1.34531i
\(732\) 0 0
\(733\) 15.5000 26.8468i 0.572506 0.991609i −0.423802 0.905755i \(-0.639305\pi\)
0.996308 0.0858539i \(-0.0273618\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 7.00000 12.1244i 0.257848 0.446606i
\(738\) 0 0
\(739\) 11.5000 + 19.9186i 0.423034 + 0.732717i 0.996235 0.0866983i \(-0.0276316\pi\)
−0.573200 + 0.819415i \(0.694298\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −34.0000 −1.24734 −0.623670 0.781688i \(-0.714359\pi\)
−0.623670 + 0.781688i \(0.714359\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 15.0000 5.19615i 0.548088 0.189863i
\(750\) 0 0
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 36.0000 1.31017
\(756\) 0 0
\(757\) −11.0000 −0.399802 −0.199901 0.979816i \(-0.564062\pi\)
−0.199901 + 0.979816i \(0.564062\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(762\) 0 0
\(763\) 2.50000 12.9904i 0.0905061 0.470283i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −15.0000 25.9808i −0.541619 0.938111i
\(768\) 0 0
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8.00000 + 13.8564i 0.287740 + 0.498380i 0.973270 0.229664i \(-0.0737628\pi\)
−0.685530 + 0.728044i \(0.740429\pi\)
\(774\) 0 0
\(775\) 38.5000 66.6840i 1.38296 2.39536i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.00000 6.92820i 0.143315 0.248229i
\(780\) 0 0
\(781\) 8.00000 + 13.8564i 0.286263 + 0.495821i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 24.0000 0.856597
\(786\) 0 0
\(787\) −11.5000 19.9186i −0.409931 0.710021i 0.584951 0.811069i \(-0.301114\pi\)
−0.994882 + 0.101048i \(0.967780\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 16.0000 + 13.8564i 0.568895 + 0.492677i
\(792\) 0 0
\(793\) 22.5000 38.9711i 0.798998 1.38391i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 42.0000 1.48772 0.743858 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −10.0000 + 17.3205i −0.352892 + 0.611227i
\(804\) 0 0
\(805\) −12.0000 + 62.3538i −0.422944 + 2.19768i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 5.00000 + 8.66025i 0.175791 + 0.304478i 0.940435 0.339975i \(-0.110418\pi\)
−0.764644 + 0.644453i \(0.777085\pi\)
\(810\) 0 0
\(811\) 16.0000 0.561836 0.280918 0.959732i \(-0.409361\pi\)
0.280918 + 0.959732i \(0.409361\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 42.0000 + 72.7461i 1.47120 + 2.54819i
\(816\) 0