Properties

Label 1216.2.i.d.961.1
Level $1216$
Weight $2$
Character 1216.961
Analytic conductor $9.710$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.70980888579\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1216.961
Dual form 1216.2.i.d.577.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +4.00000 q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +4.00000 q^{7} +(1.00000 + 1.73205i) q^{9} +3.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(3.00000 - 5.19615i) q^{17} +(-3.50000 - 2.59808i) q^{19} +(-2.00000 + 3.46410i) q^{21} +(-3.00000 - 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} -5.00000 q^{27} -2.00000 q^{31} +(-1.50000 + 2.59808i) q^{33} +10.0000 q^{37} -2.00000 q^{39} +(-4.50000 + 7.79423i) q^{41} +(2.00000 - 3.46410i) q^{43} +9.00000 q^{49} +(3.00000 + 5.19615i) q^{51} +(3.00000 + 5.19615i) q^{53} +(4.00000 - 1.73205i) q^{57} +(4.50000 - 7.79423i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(4.00000 + 6.92820i) q^{63} +(3.50000 + 6.06218i) q^{67} +6.00000 q^{69} +(-3.00000 + 5.19615i) q^{71} +(0.500000 - 0.866025i) q^{73} -5.00000 q^{75} +12.0000 q^{77} +(-2.00000 + 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.00000 q^{83} +(-3.00000 - 5.19615i) q^{89} +(4.00000 + 6.92820i) q^{91} +(1.00000 - 1.73205i) q^{93} +(-8.50000 + 14.7224i) q^{97} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} + 8q^{7} + 2q^{9} + O(q^{10}) \) \( 2q - q^{3} + 8q^{7} + 2q^{9} + 6q^{11} + 2q^{13} + 6q^{17} - 7q^{19} - 4q^{21} - 6q^{23} + 5q^{25} - 10q^{27} - 4q^{31} - 3q^{33} + 20q^{37} - 4q^{39} - 9q^{41} + 4q^{43} + 18q^{49} + 6q^{51} + 6q^{53} + 8q^{57} + 9q^{59} - 4q^{61} + 8q^{63} + 7q^{67} + 12q^{69} - 6q^{71} + q^{73} - 10q^{75} + 24q^{77} - 4q^{79} - q^{81} + 6q^{83} - 6q^{89} + 8q^{91} + 2q^{93} - 17q^{97} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(705\) \(837\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) 0 0
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0 0
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 0 0
\(19\) −3.50000 2.59808i −0.802955 0.596040i
\(20\) 0 0
\(21\) −2.00000 + 3.46410i −0.436436 + 0.755929i
\(22\) 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
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0 0
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 0 0
\(39\) −2.00000 −0.320256
\(40\) 0 0
\(41\) −4.50000 + 7.79423i −0.702782 + 1.21725i 0.264704 + 0.964330i \(0.414726\pi\)
−0.967486 + 0.252924i \(0.918608\pi\)
\(42\) 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
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 0 0
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.00000 1.73205i 0.529813 0.229416i
\(58\) 0 0
\(59\) 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i \(-0.634094\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 0 0
\(63\) 4.00000 + 6.92820i 0.503953 + 0.872872i
\(64\) 0 0
\(65\) 0 0
\(66\) 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
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 0 0
\(73\) 0.500000 0.866025i 0.0585206 0.101361i −0.835281 0.549823i \(-0.814695\pi\)
0.893801 + 0.448463i \(0.148028\pi\)
\(74\) 0 0
\(75\) −5.00000 −0.577350
\(76\) 0 0
\(77\) 12.0000 1.36753
\(78\) 0 0
\(79\) −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 3.00000 0.329293 0.164646 0.986353i \(-0.447352\pi\)
0.164646 + 0.986353i \(0.447352\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) 4.00000 + 6.92820i 0.419314 + 0.726273i
\(92\) 0 0
\(93\) 1.00000 1.73205i 0.103695 0.179605i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −8.50000 + 14.7224i −0.863044 + 1.49484i 0.00593185 + 0.999982i \(0.498112\pi\)
−0.868976 + 0.494854i \(0.835222\pi\)
\(98\) 0 0
\(99\) 3.00000 + 5.19615i 0.301511 + 0.522233i
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) −2.00000 −0.197066 −0.0985329 0.995134i \(-0.531415\pi\)
−0.0985329 + 0.995134i \(0.531415\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −8.00000 + 13.8564i −0.766261 + 1.32720i 0.173316 + 0.984866i \(0.444552\pi\)
−0.939577 + 0.342337i \(0.888782\pi\)
\(110\) 0 0
\(111\) −5.00000 + 8.66025i −0.474579 + 0.821995i
\(112\) 0 0
\(113\) 15.0000 1.41108 0.705541 0.708669i \(-0.250704\pi\)
0.705541 + 0.708669i \(0.250704\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −2.00000 + 3.46410i −0.184900 + 0.320256i
\(118\) 0 0
\(119\) 12.0000 20.7846i 1.10004 1.90532i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) −4.50000 7.79423i −0.405751 0.702782i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.00000 + 1.73205i 0.0887357 + 0.153695i 0.906977 0.421180i \(-0.138384\pi\)
−0.818241 + 0.574875i \(0.805051\pi\)
\(128\) 0 0
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) 0 0
\(131\) −4.50000 + 7.79423i −0.393167 + 0.680985i −0.992865 0.119241i \(-0.961954\pi\)
0.599699 + 0.800226i \(0.295287\pi\)
\(132\) 0 0
\(133\) −14.0000 10.3923i −1.21395 0.901127i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.50000 7.79423i −0.384461 0.665906i 0.607233 0.794524i \(-0.292279\pi\)
−0.991694 + 0.128618i \(0.958946\pi\)
\(138\) 0 0
\(139\) −5.50000 9.52628i −0.466504 0.808008i 0.532764 0.846264i \(-0.321153\pi\)
−0.999268 + 0.0382553i \(0.987820\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.00000 + 5.19615i 0.250873 + 0.434524i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −4.50000 + 7.79423i −0.371154 + 0.642857i
\(148\) 0 0
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 0 0
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) 0 0
\(153\) 12.0000 0.970143
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −8.00000 + 13.8564i −0.638470 + 1.10586i 0.347299 + 0.937754i \(0.387099\pi\)
−0.985769 + 0.168107i \(0.946235\pi\)
\(158\) 0 0
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) −12.0000 20.7846i −0.945732 1.63806i
\(162\) 0 0
\(163\) −19.0000 −1.48819 −0.744097 0.668071i \(-0.767120\pi\)
−0.744097 + 0.668071i \(0.767120\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.0000 20.7846i −0.928588 1.60836i −0.785687 0.618624i \(-0.787690\pi\)
−0.142901 0.989737i \(-0.545643\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) 1.00000 8.66025i 0.0764719 0.662266i
\(172\) 0 0
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 0 0
\(175\) 10.0000 + 17.3205i 0.755929 + 1.30931i
\(176\) 0 0
\(177\) 4.50000 + 7.79423i 0.338241 + 0.585850i
\(178\) 0 0
\(179\) 9.00000 0.672692 0.336346 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) 0 0
\(181\) 1.00000 + 1.73205i 0.0743294 + 0.128742i 0.900794 0.434246i \(-0.142985\pi\)
−0.826465 + 0.562988i \(0.809652\pi\)
\(182\) 0 0
\(183\) 4.00000 0.295689
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 9.00000 15.5885i 0.658145 1.13994i
\(188\) 0 0
\(189\) −20.0000 −1.45479
\(190\) 0 0
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 0 0
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −5.00000 8.66025i −0.354441 0.613909i 0.632581 0.774494i \(-0.281995\pi\)
−0.987022 + 0.160585i \(0.948662\pi\)
\(200\) 0 0
\(201\) −7.00000 −0.493742
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.00000 10.3923i 0.417029 0.722315i
\(208\) 0 0
\(209\) −10.5000 7.79423i −0.726300 0.539138i
\(210\) 0 0
\(211\) −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) 0 0
\(213\) −3.00000 5.19615i −0.205557 0.356034i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) 0 0
\(219\) 0.500000 + 0.866025i 0.0337869 + 0.0585206i
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 7.00000 12.1244i 0.468755 0.811907i −0.530607 0.847618i \(-0.678036\pi\)
0.999362 + 0.0357107i \(0.0113695\pi\)
\(224\) 0 0
\(225\) −5.00000 + 8.66025i −0.333333 + 0.577350i
\(226\) 0 0
\(227\) 3.00000 0.199117 0.0995585 0.995032i \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(228\) 0 0
\(229\) 16.0000 1.05731 0.528655 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) 0 0
\(231\) −6.00000 + 10.3923i −0.394771 + 0.683763i
\(232\) 0 0
\(233\) −1.50000 + 2.59808i −0.0982683 + 0.170206i −0.910968 0.412477i \(-0.864664\pi\)
0.812700 + 0.582683i \(0.197997\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −2.00000 3.46410i −0.129914 0.225018i
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −2.50000 4.33013i −0.161039 0.278928i 0.774202 0.632938i \(-0.218151\pi\)
−0.935242 + 0.354010i \(0.884818\pi\)
\(242\) 0 0
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.00000 8.66025i 0.0636285 0.551039i
\(248\) 0 0
\(249\) −1.50000 + 2.59808i −0.0950586 + 0.164646i
\(250\) 0 0
\(251\) 1.50000 + 2.59808i 0.0946792 + 0.163989i 0.909475 0.415759i \(-0.136484\pi\)
−0.814795 + 0.579748i \(0.803151\pi\)
\(252\) 0 0
\(253\) −9.00000 15.5885i −0.565825 0.980038i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) 0 0
\(259\) 40.0000 2.48548
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i \(-0.953967\pi\)
0.619586 + 0.784929i \(0.287301\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 0 0
\(269\) 6.00000 10.3923i 0.365826 0.633630i −0.623082 0.782157i \(-0.714120\pi\)
0.988908 + 0.148527i \(0.0474530\pi\)
\(270\) 0 0
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 0 0
\(273\) −8.00000 −0.484182
\(274\) 0 0
\(275\) 7.50000 + 12.9904i 0.452267 + 0.783349i
\(276\) 0 0
\(277\) −8.00000 −0.480673 −0.240337 0.970690i \(-0.577258\pi\)
−0.240337 + 0.970690i \(0.577258\pi\)
\(278\) 0 0
\(279\) −2.00000 3.46410i −0.119737 0.207390i
\(280\) 0 0
\(281\) −13.5000 23.3827i −0.805342 1.39489i −0.916060 0.401042i \(-0.868648\pi\)
0.110717 0.993852i \(-0.464685\pi\)
\(282\) 0 0
\(283\) −2.50000 + 4.33013i −0.148610 + 0.257399i −0.930714 0.365748i \(-0.880813\pi\)
0.782104 + 0.623148i \(0.214146\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −18.0000 + 31.1769i −1.06251 + 1.84032i
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 0 0
\(291\) −8.50000 14.7224i −0.498279 0.863044i
\(292\) 0 0
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −15.0000 −0.870388
\(298\) 0 0
\(299\) 6.00000 10.3923i 0.346989 0.601003i
\(300\) 0 0
\(301\) 8.00000 13.8564i 0.461112 0.798670i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 3.50000 6.06218i 0.199756 0.345987i −0.748694 0.662916i \(-0.769319\pi\)
0.948449 + 0.316929i \(0.102652\pi\)
\(308\) 0 0
\(309\) 1.00000 1.73205i 0.0568880 0.0985329i
\(310\) 0 0
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 0 0
\(313\) 9.50000 + 16.4545i 0.536972 + 0.930062i 0.999065 + 0.0432311i \(0.0137652\pi\)
−0.462093 + 0.886831i \(0.652902\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9.00000 15.5885i −0.505490 0.875535i −0.999980 0.00635137i \(-0.997978\pi\)
0.494489 0.869184i \(-0.335355\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −24.0000 + 10.3923i −1.33540 + 0.578243i
\(324\) 0 0
\(325\) −5.00000 + 8.66025i −0.277350 + 0.480384i
\(326\) 0 0
\(327\) −8.00000 13.8564i −0.442401 0.766261i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) 0 0
\(333\) 10.0000 + 17.3205i 0.547997 + 0.949158i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −5.50000 + 9.52628i −0.299604 + 0.518930i −0.976045 0.217567i \(-0.930188\pi\)
0.676441 + 0.736497i \(0.263521\pi\)
\(338\) 0 0
\(339\) −7.50000 + 12.9904i −0.407344 + 0.705541i
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) 8.00000 0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.50000 7.79423i 0.241573 0.418416i −0.719590 0.694399i \(-0.755670\pi\)
0.961162 + 0.275983i \(0.0890035\pi\)
\(348\) 0 0
\(349\) 4.00000 0.214115 0.107058 0.994253i \(-0.465857\pi\)
0.107058 + 0.994253i \(0.465857\pi\)
\(350\) 0 0
\(351\) −5.00000 8.66025i −0.266880 0.462250i
\(352\) 0 0
\(353\) 3.00000 0.159674 0.0798369 0.996808i \(-0.474560\pi\)
0.0798369 + 0.996808i \(0.474560\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 12.0000 + 20.7846i 0.635107 + 1.10004i
\(358\) 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
\(361\) 5.50000 + 18.1865i 0.289474 + 0.957186i
\(362\) 0 0
\(363\) 1.00000 1.73205i 0.0524864 0.0909091i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −11.0000 19.0526i −0.574195 0.994535i −0.996129 0.0879086i \(-0.971982\pi\)
0.421933 0.906627i \(-0.361352\pi\)
\(368\) 0 0
\(369\) −18.0000 −0.937043
\(370\) 0 0
\(371\) 12.0000 + 20.7846i 0.623009 + 1.07908i
\(372\) 0 0
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) −2.00000 −0.102463
\(382\) 0 0
\(383\) −18.0000 + 31.1769i −0.919757 + 1.59307i −0.119974 + 0.992777i \(0.538281\pi\)
−0.799783 + 0.600289i \(0.795052\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 8.00000 0.406663
\(388\) 0 0
\(389\) −18.0000 31.1769i −0.912636 1.58073i −0.810326 0.585980i \(-0.800710\pi\)
−0.102311 0.994753i \(-0.532624\pi\)
\(390\) 0 0
\(391\) −36.0000 −1.82060
\(392\) 0 0
\(393\) −4.50000 7.79423i −0.226995 0.393167i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −5.00000 + 8.66025i −0.250943 + 0.434646i −0.963786 0.266678i \(-0.914074\pi\)
0.712843 + 0.701324i \(0.247407\pi\)
\(398\) 0 0
\(399\) 16.0000 6.92820i 0.801002 0.346844i
\(400\) 0 0
\(401\) 13.5000 23.3827i 0.674158 1.16768i −0.302556 0.953131i \(-0.597840\pi\)
0.976714 0.214544i \(-0.0688266\pi\)
\(402\) 0 0
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 30.0000 1.48704
\(408\) 0 0
\(409\) −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) 0 0
\(413\) 18.0000 31.1769i 0.885722 1.53412i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 11.0000 0.538672
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −5.00000 + 8.66025i −0.243685 + 0.422075i −0.961761 0.273890i \(-0.911690\pi\)
0.718076 + 0.695965i \(0.245023\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 30.0000 1.45521
\(426\) 0 0
\(427\) −8.00000 13.8564i −0.387147 0.670559i
\(428\) 0 0
\(429\) −6.00000 −0.289683
\(430\) 0 0
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) 0 0
\(433\) −13.0000 22.5167i −0.624740 1.08208i −0.988591 0.150624i \(-0.951872\pi\)
0.363851 0.931457i \(-0.381462\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.00000 + 25.9808i −0.143509 + 1.24283i
\(438\) 0 0
\(439\) 7.00000 12.1244i 0.334092 0.578664i −0.649218 0.760602i \(-0.724904\pi\)
0.983310 + 0.181938i \(0.0582371\pi\)
\(440\) 0 0
\(441\) 9.00000 + 15.5885i 0.428571 + 0.742307i
\(442\) 0 0
\(443\) −4.50000 7.79423i −0.213801 0.370315i 0.739100 0.673596i \(-0.235251\pi\)
−0.952901 + 0.303281i \(0.901918\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 9.00000 + 15.5885i 0.425685 + 0.737309i
\(448\) 0 0
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) −13.5000 + 23.3827i −0.635690 + 1.10105i
\(452\) 0 0
\(453\) −5.00000 + 8.66025i −0.234920 + 0.406894i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 5.00000 0.233890 0.116945 0.993138i \(-0.462690\pi\)
0.116945 + 0.993138i \(0.462690\pi\)
\(458\) 0 0
\(459\) −15.0000 + 25.9808i −0.700140 + 1.21268i
\(460\) 0 0
\(461\) 3.00000 5.19615i 0.139724 0.242009i −0.787668 0.616100i \(-0.788712\pi\)
0.927392 + 0.374091i \(0.122045\pi\)
\(462\) 0 0
\(463\) 34.0000 1.58011 0.790057 0.613033i \(-0.210051\pi\)
0.790057 + 0.613033i \(0.210051\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −27.0000 −1.24941 −0.624705 0.780860i \(-0.714781\pi\)
−0.624705 + 0.780860i \(0.714781\pi\)
\(468\) 0 0
\(469\) 14.0000 + 24.2487i 0.646460 + 1.11970i
\(470\) 0 0
\(471\) −8.00000 13.8564i −0.368621 0.638470i
\(472\) 0 0
\(473\) 6.00000 10.3923i 0.275880 0.477839i
\(474\) 0 0
\(475\) 2.50000 21.6506i 0.114708 0.993399i
\(476\) 0 0
\(477\) −6.00000 + 10.3923i −0.274721 + 0.475831i
\(478\) 0 0
\(479\) 18.0000 + 31.1769i 0.822441 + 1.42451i 0.903859 + 0.427830i \(0.140722\pi\)
−0.0814184 + 0.996680i \(0.525945\pi\)
\(480\) 0 0
\(481\) 10.0000 + 17.3205i 0.455961 + 0.789747i
\(482\) 0 0
\(483\) 24.0000 1.09204
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 0 0
\(489\) 9.50000 16.4545i 0.429605 0.744097i
\(490\) 0 0
\(491\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −12.0000 + 20.7846i −0.538274 + 0.932317i
\(498\) 0 0
\(499\) 12.5000 21.6506i 0.559577 0.969216i −0.437955 0.898997i \(-0.644297\pi\)
0.997532 0.0702185i \(-0.0223697\pi\)
\(500\) 0 0
\(501\) 24.0000 1.07224
\(502\) 0 0
\(503\) 3.00000 + 5.19615i 0.133763 + 0.231685i 0.925124 0.379664i \(-0.123960\pi\)
−0.791361 + 0.611349i \(0.790627\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 4.50000 + 7.79423i 0.199852 + 0.346154i
\(508\) 0 0
\(509\) −12.0000 20.7846i −0.531891 0.921262i −0.999307 0.0372243i \(-0.988148\pi\)
0.467416 0.884037i \(-0.345185\pi\)
\(510\) 0 0
\(511\) 2.00000 3.46410i 0.0884748 0.153243i
\(512\) 0 0
\(513\) 17.5000 + 12.9904i 0.772644 + 0.573539i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 3.00000 + 5.19615i 0.131685 + 0.228086i
\(520\) 0 0
\(521\) 9.00000 0.394297 0.197149 0.980374i \(-0.436832\pi\)
0.197149 + 0.980374i \(0.436832\pi\)
\(522\) 0 0
\(523\) 14.0000 + 24.2487i 0.612177 + 1.06032i 0.990873 + 0.134801i \(0.0430394\pi\)
−0.378695 + 0.925521i \(0.623627\pi\)
\(524\) 0 0
\(525\) −20.0000 −0.872872
\(526\) 0 0
\(527\) −6.00000 + 10.3923i −0.261364 + 0.452696i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 18.0000 0.781133
\(532\) 0 0
\(533\) −18.0000 −0.779667
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −4.50000 + 7.79423i −0.194189 + 0.336346i
\(538\) 0 0
\(539\) 27.0000 1.16297
\(540\) 0 0
\(541\) 22.0000 + 38.1051i 0.945854 + 1.63827i 0.754032 + 0.656837i \(0.228106\pi\)
0.191821 + 0.981430i \(0.438561\pi\)
\(542\) 0 0
\(543\) −2.00000 −0.0858282
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 2.00000 + 3.46410i 0.0855138 + 0.148114i 0.905610 0.424111i \(-0.139413\pi\)
−0.820096 + 0.572226i \(0.806080\pi\)
\(548\) 0 0
\(549\) 4.00000 6.92820i 0.170716 0.295689i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −8.00000 + 13.8564i −0.340195 + 0.589234i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12.0000 + 20.7846i 0.508456 + 0.880672i 0.999952 + 0.00979220i \(0.00311700\pi\)
−0.491496 + 0.870880i \(0.663550\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 9.00000 + 15.5885i 0.379980 + 0.658145i
\(562\) 0 0
\(563\) −21.0000 −0.885044 −0.442522 0.896758i \(-0.645916\pi\)
−0.442522 + 0.896758i \(0.645916\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.00000 + 3.46410i −0.0839921 + 0.145479i
\(568\) 0 0
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) −7.00000 −0.292941 −0.146470 0.989215i \(-0.546791\pi\)
−0.146470 + 0.989215i \(0.546791\pi\)
\(572\) 0 0
\(573\) 6.00000 10.3923i 0.250654 0.434145i
\(574\) 0 0
\(575\) 15.0000 25.9808i 0.625543 1.08347i
\(576\) 0 0
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 0 0
\(579\) −1.00000 1.73205i −0.0415586 0.0719816i
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) 0 0
\(583\) 9.00000 + 15.5885i 0.372742 + 0.645608i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.00000 10.3923i 0.247647 0.428936i −0.715226 0.698893i \(-0.753676\pi\)
0.962872 + 0.269957i \(0.0870095\pi\)
\(588\) 0 0
\(589\) 7.00000 + 5.19615i 0.288430 + 0.214104i
\(590\) 0 0
\(591\) 9.00000 15.5885i 0.370211 0.641223i
\(592\) 0 0
\(593\) 10.5000 + 18.1865i 0.431183 + 0.746831i 0.996976 0.0777165i \(-0.0247629\pi\)
−0.565792 + 0.824548i \(0.691430\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 10.0000 0.409273
\(598\) 0 0
\(599\) −3.00000 5.19615i −0.122577 0.212309i 0.798206 0.602384i \(-0.205782\pi\)
−0.920783 + 0.390075i \(0.872449\pi\)
\(600\) 0 0
\(601\) −13.0000 −0.530281 −0.265141 0.964210i \(-0.585418\pi\)
−0.265141 + 0.964210i \(0.585418\pi\)
\(602\) 0 0
\(603\) −7.00000 + 12.1244i −0.285062 + 0.493742i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −20.0000 −0.811775 −0.405887 0.913923i \(-0.633038\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.00000 1.73205i 0.0403896 0.0699569i −0.845124 0.534570i \(-0.820473\pi\)
0.885514 + 0.464614i \(0.153807\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.50000 2.59808i −0.0603877 0.104595i 0.834251 0.551385i \(-0.185900\pi\)
−0.894639 + 0.446790i \(0.852567\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) 15.0000 + 25.9808i 0.601929 + 1.04257i
\(622\) 0 0
\(623\) −12.0000 20.7846i −0.480770 0.832718i
\(624\) 0 0
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) 12.0000 5.19615i 0.479234 0.207514i
\(628\) 0 0
\(629\) 30.0000 51.9615i 1.19618 2.07184i
\(630\) 0 0
\(631\) −14.0000 24.2487i −0.557331 0.965326i −0.997718 0.0675178i \(-0.978492\pi\)
0.440387 0.897808i \(-0.354841\pi\)
\(632\) 0 0
\(633\) −10.0000 17.3205i −0.397464 0.688428i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 9.00000 + 15.5885i 0.356593 + 0.617637i
\(638\) 0 0
\(639\) −12.0000 −0.474713
\(640\) 0 0
\(641\) 19.5000 33.7750i 0.770204 1.33403i −0.167247 0.985915i \(-0.553488\pi\)
0.937451 0.348117i \(-0.113179\pi\)
\(642\) 0 0
\(643\) 21.5000 37.2391i 0.847877 1.46857i −0.0352216 0.999380i \(-0.511214\pi\)
0.883099 0.469187i \(-0.155453\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.0000 −0.707653 −0.353827 0.935311i \(-0.615120\pi\)
−0.353827 + 0.935311i \(0.615120\pi\)
\(648\) 0 0
\(649\) 13.5000 23.3827i 0.529921 0.917851i
\(650\) 0 0
\(651\) 4.00000 6.92820i 0.156772 0.271538i
\(652\) 0 0
\(653\) 12.0000 0.469596 0.234798 0.972044i \(-0.424557\pi\)
0.234798 + 0.972044i \(0.424557\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) −18.0000 31.1769i −0.701180 1.21448i −0.968052 0.250748i \(-0.919323\pi\)
0.266872 0.963732i \(-0.414010\pi\)
\(660\) 0 0
\(661\) −20.0000 34.6410i −0.777910 1.34738i −0.933144 0.359502i \(-0.882947\pi\)
0.155235 0.987878i \(-0.450387\pi\)
\(662\) 0 0
\(663\) −6.00000 + 10.3923i −0.233021 + 0.403604i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 7.00000 + 12.1244i 0.270636 + 0.468755i
\(670\) 0 0
\(671\) −6.00000 10.3923i −0.231627 0.401190i
\(672\) 0 0
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 0 0
\(675\) −12.5000 21.6506i −0.481125 0.833333i
\(676\) 0 0
\(677\) 42.0000 1.61419 0.807096 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) 0 0
\(679\) −34.0000 + 58.8897i −1.30480 + 2.25998i
\(680\) 0 0
\(681\) −1.50000 + 2.59808i −0.0574801 + 0.0995585i
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −8.00000 + 13.8564i −0.305219 + 0.528655i
\(688\) 0 0
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 0 0
\(691\) 44.0000 1.67384 0.836919 0.547326i \(-0.184354\pi\)
0.836919 + 0.547326i \(0.184354\pi\)
\(692\) 0 0
\(693\) 12.0000 + 20.7846i 0.455842 + 0.789542i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 27.0000 + 46.7654i 1.02270 + 1.77136i
\(698\) 0 0
\(699\) −1.50000 2.59808i −0.0567352 0.0982683i
\(700\) 0 0
\(701\) −12.0000 + 20.7846i −0.453234 + 0.785024i −0.998585 0.0531839i \(-0.983063\pi\)
0.545351 + 0.838208i \(0.316396\pi\)
\(702\) 0 0
\(703\) −35.0000 25.9808i −1.32005 0.979883i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 7.00000 + 12.1244i 0.262891 + 0.455340i 0.967009 0.254743i \(-0.0819909\pi\)
−0.704118 + 0.710083i \(0.748658\pi\)
\(710\) 0 0
\(711\) −8.00000 −0.300023
\(712\) 0 0
\(713\) 6.00000 + 10.3923i 0.224702 + 0.389195i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.00000 + 10.3923i −0.224074 + 0.388108i
\(718\) 0 0
\(719\) 15.0000 25.9808i 0.559406 0.968919i −0.438141 0.898906i \(-0.644363\pi\)
0.997546 0.0700124i \(-0.0223039\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 0 0
\(723\) 5.00000 0.185952
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 16.0000 27.7128i 0.593407 1.02781i −0.400362 0.916357i \(-0.631116\pi\)
0.993770 0.111454i \(-0.0355509\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) 0 0
\(733\) 22.0000 0.812589 0.406294 0.913742i \(-0.366821\pi\)
0.406294 + 0.913742i \(0.366821\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.5000 + 18.1865i 0.386772 + 0.669910i
\(738\) 0 0
\(739\) −17.5000 + 30.3109i −0.643748 + 1.11500i 0.340841 + 0.940121i \(0.389288\pi\)
−0.984589 + 0.174883i \(0.944045\pi\)
\(740\) 0 0
\(741\) 7.00000 + 5.19615i 0.257151 + 0.190885i
\(742\) 0 0
\(743\) −9.00000 + 15.5885i −0.330178 + 0.571885i −0.982547 0.186017i \(-0.940442\pi\)
0.652369 + 0.757902i \(0.273775\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 3.00000 + 5.19615i 0.109764 + 0.190117i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 19.0000 + 32.9090i 0.693320 + 1.20087i 0.970744 + 0.240118i \(0.0771860\pi\)
−0.277424 + 0.960748i \(0.589481\pi\)
\(752\) 0 0
\(753\) −3.00000 −0.109326
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −5.00000 + 8.66025i −0.181728 + 0.314762i −0.942469 0.334293i \(-0.891502\pi\)
0.760741 + 0.649056i \(0.224836\pi\)
\(758\) 0 0
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) −39.0000 −1.41375 −0.706874 0.707339i \(-0.749895\pi\)
−0.706874 + 0.707339i \(0.749895\pi\)
\(762\) 0 0
\(763\) −32.0000 + 55.4256i −1.15848 + 2.00654i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 18.0000 0.649942
\(768\) 0 0
\(769\) −1.00000 1.73205i −0.0360609 0.0624593i 0.847432 0.530904i \(-0.178148\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) 0 0
\(773\) −24.0000 41.5692i −0.863220 1.49514i −0.868804 0.495156i \(-0.835111\pi\)
0.00558380 0.999984i \(-0.498223\pi\)
\(774\) 0 0
\(775\) −5.00000 8.66025i −0.179605 0.311086i
\(776\) 0 0
\(777\) −20.0000 + 34.6410i −0.717496 + 1.24274i
\(778\) 0 0
\(779\) 36.0000 15.5885i 1.28983 0.558514i
\(780\) 0 0
\(781\) −9.00000 + 15.5885i −0.322045 + 0.557799i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −7.00000 −0.249523 −0.124762 0.992187i \(-0.539817\pi\)
−0.124762 + 0.992187i \(0.539817\pi\)
\(788\) 0 0
\(789\) −6.00000 10.3923i −0.213606 0.369976i
\(790\) 0 0
\(791\) 60.0000 2.13335
\(792\) 0 0
\(793\) 4.00000 6.92820i 0.142044 0.246028i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −6.00000 −0.212531 −0.106265 0.994338i \(-0.533889\pi\)
−0.106265 + 0.994338i \(0.533889\pi\)
\(798\) 0 0
\(799\) 0 0