Properties

Label 2268.2.l.h.109.1
Level $2268$
Weight $2$
Character 2268.109
Analytic conductor $18.110$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.l (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
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 28)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2268.109
Dual form 2268.2.l.h.541.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00000 q^{5} +(2.50000 + 0.866025i) q^{7} +O(q^{10})\) \(q+3.00000 q^{5} +(2.50000 + 0.866025i) q^{7} -3.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(-1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{19} +3.00000 q^{23} +4.00000 q^{25} +(3.00000 + 5.19615i) q^{29} +(3.50000 + 6.06218i) q^{31} +(7.50000 + 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{43} +(4.50000 - 7.79423i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-1.50000 + 2.59808i) q^{53} -9.00000 q^{55} +(-4.50000 - 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-3.00000 + 5.19615i) q^{65} +(3.50000 + 6.06218i) q^{67} +(0.500000 - 0.866025i) q^{73} +(-7.50000 - 2.59808i) q^{77} +(6.50000 - 11.2583i) q^{79} +(-6.00000 - 10.3923i) q^{83} +(-4.50000 + 7.79423i) q^{85} +(-7.50000 - 12.9904i) q^{89} +(-4.00000 + 3.46410i) q^{91} +(1.50000 + 2.59808i) q^{95} +(5.00000 + 8.66025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 6q^{5} + 5q^{7} + O(q^{10}) \) \( 2q + 6q^{5} + 5q^{7} - 6q^{11} - 2q^{13} - 3q^{17} + q^{19} + 6q^{23} + 8q^{25} + 6q^{29} + 7q^{31} + 15q^{35} + q^{37} - 6q^{41} + 4q^{43} + 9q^{47} + 11q^{49} - 3q^{53} - 18q^{55} - 9q^{59} + q^{61} - 6q^{65} + 7q^{67} + q^{73} - 15q^{77} + 13q^{79} - 12q^{83} - 9q^{85} - 15q^{89} - 8q^{91} + 3q^{95} + 10q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) 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
\(35\) 7.50000 + 2.59808i 1.26773 + 0.439155i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) 0 0
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.50000 7.79423i 0.656392 1.13691i −0.325150 0.945662i \(-0.605415\pi\)
0.981543 0.191243i \(-0.0612518\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i \(-0.899391\pi\)
0.744423 + 0.667708i \(0.232725\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i \(-0.967427\pi\)
0.408919 0.912571i \(-0.365906\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) 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
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 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
\(75\) 0 0
\(76\) 0 0
\(77\) −7.50000 2.59808i −0.854704 0.296078i
\(78\) 0 0
\(79\) 6.50000 11.2583i 0.731307 1.26666i −0.225018 0.974355i \(-0.572244\pi\)
0.956325 0.292306i \(-0.0944227\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.00000 10.3923i −0.658586 1.14070i −0.980982 0.194099i \(-0.937822\pi\)
0.322396 0.946605i \(-0.395512\pi\)
\(84\) 0 0
\(85\) −4.50000 + 7.79423i −0.488094 + 0.845403i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.50000 12.9904i −0.794998 1.37698i −0.922840 0.385183i \(-0.874138\pi\)
0.127842 0.991795i \(-0.459195\pi\)
\(90\) 0 0
\(91\) −4.00000 + 3.46410i −0.419314 + 0.363137i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.50000 + 2.59808i 0.153897 + 0.266557i
\(96\) 0 0
\(97\) 5.00000 + 8.66025i 0.507673 + 0.879316i 0.999961 + 0.00888289i \(0.00282755\pi\)
−0.492287 + 0.870433i \(0.663839\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 15.0000 1.49256 0.746278 0.665635i \(-0.231839\pi\)
0.746278 + 0.665635i \(0.231839\pi\)
\(102\) 0 0
\(103\) 11.0000 1.08386 0.541931 0.840423i \(-0.317693\pi\)
0.541931 + 0.840423i \(0.317693\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.50000 12.9904i −0.725052 1.25583i −0.958952 0.283567i \(-0.908482\pi\)
0.233900 0.972261i \(-0.424851\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.00000 + 5.19615i −0.282216 + 0.488813i −0.971930 0.235269i \(-0.924403\pi\)
0.689714 + 0.724082i \(0.257736\pi\)
\(114\) 0 0
\(115\) 9.00000 0.839254
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −6.00000 + 5.19615i −0.550019 + 0.476331i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.00000 0.262111 0.131056 0.991375i \(-0.458163\pi\)
0.131056 + 0.991375i \(0.458163\pi\)
\(132\) 0 0
\(133\) 0.500000 + 2.59808i 0.0433555 + 0.225282i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −21.0000 −1.79415 −0.897076 0.441877i \(-0.854313\pi\)
−0.897076 + 0.441877i \(0.854313\pi\)
\(138\) 0 0
\(139\) −10.0000 + 17.3205i −0.848189 + 1.46911i 0.0346338 + 0.999400i \(0.488974\pi\)
−0.882823 + 0.469706i \(0.844360\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.00000 5.19615i 0.250873 0.434524i
\(144\) 0 0
\(145\) 9.00000 + 15.5885i 0.747409 + 1.29455i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 0 0
\(151\) 17.0000 1.38344 0.691720 0.722166i \(-0.256853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 10.5000 + 18.1865i 0.843380 + 1.46078i
\(156\) 0 0
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.50000 + 2.59808i 0.591083 + 0.204757i
\(162\) 0 0
\(163\) −5.50000 9.52628i −0.430793 0.746156i 0.566149 0.824303i \(-0.308433\pi\)
−0.996942 + 0.0781474i \(0.975100\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.00000 10.3923i 0.464294 0.804181i −0.534875 0.844931i \(-0.679641\pi\)
0.999169 + 0.0407502i \(0.0129748\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.50000 7.79423i 0.342129 0.592584i −0.642699 0.766119i \(-0.722185\pi\)
0.984828 + 0.173534i \(0.0555188\pi\)
\(174\) 0 0
\(175\) 10.0000 + 3.46410i 0.755929 + 0.261861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −10.5000 + 18.1865i −0.784807 + 1.35933i 0.144308 + 0.989533i \(0.453905\pi\)
−0.929114 + 0.369792i \(0.879429\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.50000 + 2.59808i 0.110282 + 0.191014i
\(186\) 0 0
\(187\) 4.50000 7.79423i 0.329073 0.569970i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.50000 7.79423i 0.325609 0.563971i −0.656027 0.754738i \(-0.727764\pi\)
0.981635 + 0.190767i \(0.0610975\pi\)
\(192\) 0 0
\(193\) −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i \(-0.296234\pi\)
−0.993215 + 0.116289i \(0.962900\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i \(-0.753524\pi\)
0.963001 + 0.269498i \(0.0868577\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3.00000 + 15.5885i 0.210559 + 1.09410i
\(204\) 0 0
\(205\) −9.00000 + 15.5885i −0.628587 + 1.08875i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.50000 2.59808i −0.103757 0.179713i
\(210\) 0 0
\(211\) 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i \(-0.789367\pi\)
0.926620 + 0.375999i \(0.122700\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.00000 + 10.3923i 0.409197 + 0.708749i
\(216\) 0 0
\(217\) 3.50000 + 18.1865i 0.237595 + 1.23458i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 0 0
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 0 0
\(229\) 11.0000 0.726900 0.363450 0.931614i \(-0.381599\pi\)
0.363450 + 0.931614i \(0.381599\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 10.5000 + 18.1865i 0.687878 + 1.19144i 0.972523 + 0.232806i \(0.0747909\pi\)
−0.284645 + 0.958633i \(0.591876\pi\)
\(234\) 0 0
\(235\) 13.5000 23.3827i 0.880643 1.52532i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.00000 10.3923i 0.388108 0.672222i −0.604087 0.796918i \(-0.706462\pi\)
0.992195 + 0.124696i \(0.0397955\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157 −0.0322078 0.999481i \(-0.510254\pi\)
−0.0322078 + 0.999481i \(0.510254\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 16.5000 + 12.9904i 1.05415 + 0.829925i
\(246\) 0 0
\(247\) −2.00000 −0.127257
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −9.00000 −0.565825
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.00000 0.187135 0.0935674 0.995613i \(-0.470173\pi\)
0.0935674 + 0.995613i \(0.470173\pi\)
\(258\) 0 0
\(259\) 0.500000 + 2.59808i 0.0310685 + 0.161437i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.00000 −0.184988 −0.0924940 0.995713i \(-0.529484\pi\)
−0.0924940 + 0.995713i \(0.529484\pi\)
\(264\) 0 0
\(265\) −4.50000 + 7.79423i −0.276433 + 0.478796i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.50000 + 2.59808i −0.0914566 + 0.158408i −0.908124 0.418701i \(-0.862486\pi\)
0.816668 + 0.577108i \(0.195819\pi\)
\(270\) 0 0
\(271\) −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i \(-0.275099\pi\)
−0.983312 + 0.181928i \(0.941766\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −12.0000 −0.723627
\(276\) 0 0
\(277\) −13.0000 −0.781094 −0.390547 0.920583i \(-0.627714\pi\)
−0.390547 + 0.920583i \(0.627714\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −15.0000 25.9808i −0.894825 1.54988i −0.834021 0.551733i \(-0.813967\pi\)
−0.0608039 0.998150i \(-0.519366\pi\)
\(282\) 0 0
\(283\) −14.5000 25.1147i −0.861936 1.49292i −0.870058 0.492949i \(-0.835919\pi\)
0.00812260 0.999967i \(-0.497414\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −12.0000 + 10.3923i −0.708338 + 0.613438i
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3.00000 + 5.19615i −0.175262 + 0.303562i −0.940252 0.340480i \(-0.889411\pi\)
0.764990 + 0.644042i \(0.222744\pi\)
\(294\) 0 0
\(295\) −13.5000 23.3827i −0.786000 1.36139i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 0 0
\(301\) 2.00000 + 10.3923i 0.115278 + 0.599002i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.50000 2.59808i 0.0858898 0.148765i
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 13.5000 + 23.3827i 0.765515 + 1.32591i 0.939974 + 0.341246i \(0.110849\pi\)
−0.174459 + 0.984664i \(0.555818\pi\)
\(312\) 0 0
\(313\) −11.5000 + 19.9186i −0.650018 + 1.12586i 0.333099 + 0.942892i \(0.391906\pi\)
−0.983118 + 0.182973i \(0.941428\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.50000 7.79423i 0.252745 0.437767i −0.711535 0.702650i \(-0.752000\pi\)
0.964281 + 0.264883i \(0.0853332\pi\)
\(318\) 0 0
\(319\) −9.00000 15.5885i −0.503903 0.872786i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.00000 −0.166924
\(324\) 0 0
\(325\) −4.00000 + 6.92820i −0.221880 + 0.384308i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 18.0000 15.5885i 0.992372 0.859419i
\(330\) 0 0
\(331\) 6.50000 11.2583i 0.357272 0.618814i −0.630232 0.776407i \(-0.717040\pi\)
0.987504 + 0.157593i \(0.0503735\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 10.5000 + 18.1865i 0.573676 + 0.993636i
\(336\) 0 0
\(337\) 17.0000 29.4449i 0.926049 1.60396i 0.136184 0.990684i \(-0.456516\pi\)
0.789865 0.613280i \(-0.210150\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −10.5000 18.1865i −0.568607 0.984856i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.50000 7.79423i −0.241573 0.418416i 0.719590 0.694399i \(-0.244330\pi\)
−0.961162 + 0.275983i \(0.910997\pi\)
\(348\) 0 0
\(349\) −13.0000 22.5167i −0.695874 1.20529i −0.969885 0.243563i \(-0.921684\pi\)
0.274011 0.961727i \(-0.411649\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −21.0000 −1.11772 −0.558859 0.829263i \(-0.688761\pi\)
−0.558859 + 0.829263i \(0.688761\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.50000 12.9904i −0.395835 0.685606i 0.597372 0.801964i \(-0.296211\pi\)
−0.993207 + 0.116358i \(0.962878\pi\)
\(360\) 0 0
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.50000 2.59808i 0.0785136 0.135990i
\(366\) 0 0
\(367\) 5.00000 0.260998 0.130499 0.991448i \(-0.458342\pi\)
0.130499 + 0.991448i \(0.458342\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6.00000 + 5.19615i −0.311504 + 0.269771i
\(372\) 0 0
\(373\) −25.0000 −1.29445 −0.647225 0.762299i \(-0.724071\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −33.0000 −1.68622 −0.843111 0.537740i \(-0.819278\pi\)
−0.843111 + 0.537740i \(0.819278\pi\)
\(384\) 0 0
\(385\) −22.5000 7.79423i −1.14671 0.397231i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 15.0000 0.760530 0.380265 0.924878i \(-0.375833\pi\)
0.380265 + 0.924878i \(0.375833\pi\)
\(390\) 0 0
\(391\) −4.50000 + 7.79423i −0.227575 + 0.394171i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 19.5000 33.7750i 0.981151 1.69940i
\(396\) 0 0
\(397\) 18.5000 + 32.0429i 0.928488 + 1.60819i 0.785853 + 0.618414i \(0.212224\pi\)
0.142636 + 0.989775i \(0.454442\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.00000 0.149813 0.0749064 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) 0 0
\(403\) −14.0000 −0.697390
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.50000 2.59808i −0.0743522 0.128782i
\(408\) 0 0
\(409\) −5.50000 9.52628i −0.271957 0.471044i 0.697406 0.716677i \(-0.254338\pi\)
−0.969363 + 0.245633i \(0.921004\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −4.50000 23.3827i −0.221431 1.15059i
\(414\) 0 0
\(415\) −18.0000 31.1769i −0.883585 1.53041i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 6.00000 10.3923i 0.293119 0.507697i −0.681426 0.731887i \(-0.738640\pi\)
0.974546 + 0.224189i \(0.0719734\pi\)
\(420\) 0 0
\(421\) 11.0000 + 19.0526i 0.536107 + 0.928565i 0.999109 + 0.0422075i \(0.0134391\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6.00000 + 10.3923i −0.291043 + 0.504101i
\(426\) 0 0
\(427\) 2.00000 1.73205i 0.0967868 0.0838198i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 7.50000 12.9904i 0.361262 0.625725i −0.626907 0.779094i \(-0.715679\pi\)
0.988169 + 0.153370i \(0.0490126\pi\)
\(432\) 0 0
\(433\) −10.0000 −0.480569 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.50000 + 2.59808i 0.0717547 + 0.124283i
\(438\) 0 0
\(439\) 0.500000 0.866025i 0.0238637 0.0413331i −0.853847 0.520524i \(-0.825737\pi\)
0.877711 + 0.479191i \(0.159070\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.50000 7.79423i 0.213801 0.370315i −0.739100 0.673596i \(-0.764749\pi\)
0.952901 + 0.303281i \(0.0980821\pi\)
\(444\) 0 0
\(445\) −22.5000 38.9711i −1.06660 1.84741i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −12.0000 + 10.3923i −0.562569 + 0.487199i
\(456\) 0 0
\(457\) −11.5000 + 19.9186i −0.537947 + 0.931752i 0.461067 + 0.887365i \(0.347467\pi\)
−0.999014 + 0.0443868i \(0.985867\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.00000 + 5.19615i 0.139724 + 0.242009i 0.927392 0.374091i \(-0.122045\pi\)
−0.787668 + 0.616100i \(0.788712\pi\)
\(462\) 0 0
\(463\) 8.00000 13.8564i 0.371792 0.643962i −0.618050 0.786139i \(-0.712077\pi\)
0.989841 + 0.142177i \(0.0454103\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10.5000 + 18.1865i 0.485882 + 0.841572i 0.999868 0.0162260i \(-0.00516512\pi\)
−0.513986 + 0.857798i \(0.671832\pi\)
\(468\) 0 0
\(469\) 3.50000 + 18.1865i 0.161615 + 0.839776i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.00000 10.3923i −0.275880 0.477839i
\(474\) 0 0
\(475\) 2.00000 + 3.46410i 0.0917663 + 0.158944i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −3.00000 −0.137073 −0.0685367 0.997649i \(-0.521833\pi\)
−0.0685367 + 0.997649i \(0.521833\pi\)
\(480\) 0 0
\(481\) −2.00000 −0.0911922
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 15.0000 + 25.9808i 0.681115 + 1.17973i
\(486\) 0 0
\(487\) 9.50000 16.4545i 0.430486 0.745624i −0.566429 0.824110i \(-0.691675\pi\)
0.996915 + 0.0784867i \(0.0250088\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −12.0000 + 20.7846i −0.541552 + 0.937996i 0.457263 + 0.889332i \(0.348830\pi\)
−0.998815 + 0.0486647i \(0.984503\pi\)
\(492\) 0 0
\(493\) −18.0000 −0.810679
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 11.0000 0.492428 0.246214 0.969216i \(-0.420813\pi\)
0.246214 + 0.969216i \(0.420813\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 45.0000 2.00247
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3.00000 0.132973 0.0664863 0.997787i \(-0.478821\pi\)
0.0664863 + 0.997787i \(0.478821\pi\)
\(510\) 0 0
\(511\) 2.00000 1.73205i 0.0884748 0.0766214i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 33.0000 1.45415
\(516\) 0 0
\(517\) −13.5000 + 23.3827i −0.593729 + 1.02837i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −19.5000 + 33.7750i −0.854311 + 1.47971i 0.0229727 + 0.999736i \(0.492687\pi\)
−0.877283 + 0.479973i \(0.840646\pi\)
\(522\) 0 0
\(523\) 0.500000 + 0.866025i 0.0218635 + 0.0378686i 0.876750 0.480946i \(-0.159707\pi\)
−0.854887 + 0.518815i \(0.826373\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −21.0000 −0.914774
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.00000 10.3923i −0.259889 0.450141i
\(534\) 0 0
\(535\) −22.5000 38.9711i −0.972760 1.68487i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −16.5000 12.9904i −0.710705 0.559535i
\(540\) 0 0
\(541\) −17.5000 30.3109i −0.752384 1.30317i −0.946664 0.322221i \(-0.895571\pi\)
0.194281 0.980946i \(-0.437763\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.50000 2.59808i 0.0642529 0.111289i
\(546\) 0 0
\(547\) −4.00000 6.92820i −0.171028 0.296229i 0.767752 0.640747i \(-0.221375\pi\)
−0.938779 + 0.344519i \(0.888042\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.00000 + 5.19615i −0.127804 + 0.221364i
\(552\) 0 0
\(553\) 26.0000 22.5167i 1.10563 0.957506i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.5000 28.5788i 0.699127 1.21092i −0.269642 0.962961i \(-0.586905\pi\)
0.968769 0.247964i \(-0.0797613\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.50000 7.79423i −0.189652 0.328488i 0.755482 0.655169i \(-0.227403\pi\)
−0.945134 + 0.326682i \(0.894069\pi\)
\(564\) 0 0
\(565\) −9.00000 + 15.5885i −0.378633 + 0.655811i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.50000 7.79423i 0.188650 0.326751i −0.756151 0.654398i \(-0.772922\pi\)
0.944800 + 0.327647i \(0.106256\pi\)
\(570\) 0 0
\(571\) −14.5000 25.1147i −0.606806 1.05102i −0.991763 0.128085i \(-0.959117\pi\)
0.384957 0.922934i \(-0.374216\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) 0.500000 0.866025i 0.0208153 0.0360531i −0.855430 0.517918i \(-0.826707\pi\)
0.876245 + 0.481865i \(0.160040\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6.00000 31.1769i −0.248922 1.29344i
\(582\) 0 0
\(583\) 4.50000 7.79423i 0.186371 0.322804i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6.00000 10.3923i −0.247647 0.428936i 0.715226 0.698893i \(-0.246324\pi\)
−0.962872 + 0.269957i \(0.912990\pi\)
\(588\) 0 0
\(589\) −3.50000 + 6.06218i −0.144215 + 0.249788i
\(590\) 0 0
\(591\) 0 0
\(592\) 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
\(595\) −18.0000 + 15.5885i −0.737928 + 0.639064i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 13.5000 + 23.3827i 0.551595 + 0.955391i 0.998160 + 0.0606393i \(0.0193139\pi\)
−0.446565 + 0.894751i \(0.647353\pi\)
\(600\) 0 0
\(601\) −7.00000 12.1244i −0.285536 0.494563i 0.687203 0.726465i \(-0.258838\pi\)
−0.972739 + 0.231903i \(0.925505\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −6.00000 −0.243935
\(606\) 0 0
\(607\) 47.0000 1.90767 0.953836 0.300329i \(-0.0970966\pi\)
0.953836 + 0.300329i \(0.0970966\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9.00000 + 15.5885i 0.364101 + 0.630641i
\(612\) 0 0
\(613\) 12.5000 21.6506i 0.504870 0.874461i −0.495114 0.868828i \(-0.664874\pi\)
0.999984 0.00563283i \(-0.00179300\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.00000 + 5.19615i −0.120775 + 0.209189i −0.920074 0.391745i \(-0.871871\pi\)
0.799298 + 0.600935i \(0.205205\pi\)
\(618\) 0 0
\(619\) −31.0000 −1.24600 −0.622998 0.782224i \(-0.714085\pi\)
−0.622998 + 0.782224i \(0.714085\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7.50000 38.9711i −0.300481 1.56135i
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3.00000 −0.119618
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 24.0000 0.952411
\(636\) 0 0
\(637\) −13.0000 + 5.19615i −0.515079 + 0.205879i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 15.0000 0.592464 0.296232 0.955116i \(-0.404270\pi\)
0.296232 + 0.955116i \(0.404270\pi\)
\(642\) 0 0
\(643\) −10.0000 + 17.3205i −0.394362 + 0.683054i −0.993019 0.117951i \(-0.962368\pi\)
0.598658 + 0.801005i \(0.295701\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.5000 + 18.1865i −0.412798 + 0.714986i −0.995194 0.0979182i \(-0.968782\pi\)
0.582397 + 0.812905i \(0.302115\pi\)
\(648\) 0 0
\(649\) 13.5000 + 23.3827i 0.529921 + 0.917851i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 39.0000 1.52619 0.763094 0.646288i \(-0.223679\pi\)
0.763094 + 0.646288i \(0.223679\pi\)
\(654\) 0 0
\(655\) 9.00000 0.351659
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −6.00000 10.3923i −0.233727 0.404827i 0.725175 0.688565i \(-0.241759\pi\)
−0.958902 + 0.283738i \(0.908425\pi\)
\(660\) 0 0
\(661\) −5.50000 9.52628i −0.213925 0.370529i 0.739014 0.673690i \(-0.235292\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.50000 + 7.79423i 0.0581675 + 0.302247i
\(666\) 0 0
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.50000 + 2.59808i −0.0579069 + 0.100298i
\(672\) 0 0
\(673\) −7.00000 12.1244i −0.269830 0.467360i 0.698988 0.715134i \(-0.253634\pi\)
−0.968818 + 0.247774i \(0.920301\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −13.5000 + 23.3827i −0.518847 + 0.898670i 0.480913 + 0.876768i \(0.340305\pi\)
−0.999760 + 0.0219013i \(0.993028\pi\)
\(678\) 0 0
\(679\) 5.00000 + 25.9808i 0.191882 + 0.997050i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −10.5000 + 18.1865i −0.401771 + 0.695888i −0.993940 0.109926i \(-0.964939\pi\)
0.592168 + 0.805814i \(0.298272\pi\)
\(684\) 0 0
\(685\) −63.0000 −2.40711
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) 0 0
\(691\) 6.50000 11.2583i 0.247272 0.428287i −0.715496 0.698617i \(-0.753799\pi\)
0.962768 + 0.270330i \(0.0871327\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −30.0000 + 51.9615i −1.13796 + 1.97101i
\(696\) 0 0
\(697\) −9.00000 15.5885i −0.340899 0.590455i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) −0.500000 + 0.866025i −0.0188579 + 0.0326628i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 37.5000 + 12.9904i 1.41033 + 0.488554i
\(708\) 0 0
\(709\) 0.500000 0.866025i 0.0187779 0.0325243i −0.856484 0.516174i \(-0.827356\pi\)
0.875262 + 0.483650i \(0.160689\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 10.5000 + 18.1865i 0.393228 + 0.681091i
\(714\) 0 0
\(715\) 9.00000 15.5885i 0.336581 0.582975i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.5000 + 18.1865i 0.391584 + 0.678243i 0.992659 0.120950i \(-0.0385939\pi\)
−0.601075 + 0.799193i \(0.705261\pi\)
\(720\) 0 0
\(721\) 27.5000 + 9.52628i 1.02415 + 0.354777i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 12.0000 + 20.7846i 0.445669 + 0.771921i
\(726\) 0 0
\(727\) −16.0000 27.7128i −0.593407 1.02781i −0.993770 0.111454i \(-0.964449\pi\)
0.400362 0.916357i \(-0.368884\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −12.0000 −0.443836
\(732\) 0 0
\(733\) −25.0000 −0.923396 −0.461698 0.887037i \(-0.652760\pi\)
−0.461698 + 0.887037i \(0.652760\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −10.5000 18.1865i −0.386772 0.669910i
\(738\) 0 0
\(739\) 9.50000 16.4545i 0.349463 0.605288i −0.636691 0.771119i \(-0.719697\pi\)
0.986154 + 0.165831i \(0.0530307\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000 41.5692i 0.880475 1.52503i 0.0296605 0.999560i \(-0.490557\pi\)
0.850814 0.525467i \(-0.176109\pi\)
\(744\) 0 0
\(745\) 9.00000 0.329734
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −7.50000 38.9711i −0.274044 1.42397i
\(750\) 0 0
\(751\) −25.0000 −0.912263 −0.456131 0.889912i \(-0.650765\pi\)
−0.456131 + 0.889912i \(0.650765\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 51.0000 1.85608
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 3.00000 0.108750 0.0543750 0.998521i \(-0.482683\pi\)
0.0543750 + 0.998521i \(0.482683\pi\)
\(762\) 0 0
\(763\) 2.00000 1.73205i 0.0724049 0.0627044i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 18.0000 0.649942
\(768\) 0 0
\(769\) 17.0000 29.4449i 0.613036 1.06181i −0.377690 0.925932i \(-0.623282\pi\)
0.990726 0.135877i \(-0.0433852\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 16.5000 28.5788i 0.593464 1.02791i −0.400298 0.916385i \(-0.631093\pi\)
0.993762 0.111524i \(-0.0355733\pi\)
\(774\) 0 0
\(775\) 14.0000 + 24.2487i 0.502895 + 0.871039i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.00000 −0.214972
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 19.5000 + 33.7750i 0.695985 + 1.20548i
\(786\) 0 0
\(787\) 15.5000 + 26.8468i 0.552515 + 0.956985i 0.998092 + 0.0617409i \(0.0196653\pi\)
−0.445577 + 0.895244i \(0.647001\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −12.0000 + 10.3923i −0.426671 + 0.369508i
\(792\) 0 0
\(793\) 1.00000 + 1.73205i 0.0355110 + 0.0615069i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −21.0000 + 36.3731i −0.743858 + 1.28840i 0.206868 + 0.978369i \(0.433673\pi\)
−0.950726 + 0.310031i \(0.899660\pi\)
\(798\) 0 0
\(799\) 13.5000 + 23.3827i 0.477596 + 0.827220i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0