Properties

Label 2646.2.h.h.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.h.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{8} +3.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{19} +(1.50000 + 2.59808i) q^{22} +6.00000 q^{23} -5.00000 q^{25} +(1.00000 - 1.73205i) q^{26} +(3.00000 - 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{34} +(2.00000 - 3.46410i) q^{37} +1.00000 q^{38} +(4.50000 + 7.79423i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(3.00000 + 5.19615i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-2.50000 - 4.33013i) q^{50} +2.00000 q^{52} +(6.00000 + 10.3923i) q^{53} +6.00000 q^{58} +(1.50000 - 2.59808i) q^{59} +(-4.00000 - 6.92820i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-2.50000 + 4.33013i) q^{67} +3.00000 q^{68} +12.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +4.00000 q^{74} +(0.500000 + 0.866025i) q^{76} +(2.00000 + 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{82} +(6.00000 - 10.3923i) q^{83} +1.00000 q^{86} -3.00000 q^{88} +(3.00000 - 5.19615i) q^{89} +(-3.00000 + 5.19615i) q^{92} +(3.00000 - 5.19615i) q^{94} +(-2.50000 + 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} - 2 q^{8} + O(q^{10}) \) \( 2 q + q^{2} - q^{4} - 2 q^{8} + 6 q^{11} - 2 q^{13} - q^{16} - 3 q^{17} + q^{19} + 3 q^{22} + 12 q^{23} - 10 q^{25} + 2 q^{26} + 6 q^{29} + 4 q^{31} + q^{32} + 3 q^{34} + 4 q^{37} + 2 q^{38} + 9 q^{41} + q^{43} - 3 q^{44} + 6 q^{46} - 6 q^{47} - 5 q^{50} + 4 q^{52} + 12 q^{53} + 12 q^{58} + 3 q^{59} - 8 q^{61} + 8 q^{62} + 2 q^{64} - 5 q^{67} + 6 q^{68} + 24 q^{71} - 11 q^{73} + 8 q^{74} + q^{76} + 4 q^{79} - 9 q^{82} + 12 q^{83} + 2 q^{86} - 6 q^{88} + 6 q^{89} - 6 q^{92} + 6 q^{94} - 5 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 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 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.50000 2.59808i 0.257248 0.445566i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) 1.00000 0.162221
\(39\) 0 0
\(40\) 0 0
\(41\) 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i \(0.0813924\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 0 0
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.50000 4.33013i −0.353553 0.612372i
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) 6.00000 + 10.3923i 0.824163 + 1.42749i 0.902557 + 0.430570i \(0.141688\pi\)
−0.0783936 + 0.996922i \(0.524979\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 6.00000 0.787839
\(59\) 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i \(-0.770771\pi\)
0.946993 + 0.321253i \(0.104104\pi\)
\(60\) 0 0
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −2.50000 + 4.33013i −0.305424 + 0.529009i −0.977356 0.211604i \(-0.932131\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) 3.00000 0.363803
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) 0.500000 + 0.866025i 0.0573539 + 0.0993399i
\(77\) 0 0
\(78\) 0 0
\(79\) 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −4.50000 + 7.79423i −0.496942 + 0.860729i
\(83\) 6.00000 10.3923i 0.658586 1.14070i −0.322396 0.946605i \(-0.604488\pi\)
0.980982 0.194099i \(-0.0621783\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.00000 0.107833
\(87\) 0 0
\(88\) −3.00000 −0.319801
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.00000 + 5.19615i −0.312772 + 0.541736i
\(93\) 0 0
\(94\) 3.00000 5.19615i 0.309426 0.535942i
\(95\) 0 0
\(96\) 0 0
\(97\) −2.50000 + 4.33013i −0.253837 + 0.439658i −0.964579 0.263795i \(-0.915026\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 1.00000 + 1.73205i 0.0980581 + 0.169842i
\(105\) 0 0
\(106\) −6.00000 + 10.3923i −0.582772 + 1.00939i
\(107\) 1.50000 2.59808i 0.145010 0.251166i −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) 0 0
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.00000 + 5.19615i 0.282216 + 0.488813i 0.971930 0.235269i \(-0.0755971\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 0 0
\(118\) 3.00000 0.276172
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 4.00000 6.92820i 0.362143 0.627250i
\(123\) 0 0
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) 0 0
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −5.00000 −0.431934
\(135\) 0 0
\(136\) 1.50000 + 2.59808i 0.128624 + 0.222783i
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 0 0
\(139\) 9.50000 + 16.4545i 0.805779 + 1.39565i 0.915764 + 0.401718i \(0.131587\pi\)
−0.109984 + 0.993933i \(0.535080\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 0 0
\(145\) 0 0
\(146\) 5.50000 9.52628i 0.455183 0.788400i
\(147\) 0 0
\(148\) 2.00000 + 3.46410i 0.164399 + 0.284747i
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −0.500000 + 0.866025i −0.0405554 + 0.0702439i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) −2.00000 + 3.46410i −0.159111 + 0.275589i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) −9.00000 −0.702782
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 0 0
\(178\) 6.00000 0.449719
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −6.00000 −0.442326
\(185\) 0 0
\(186\) 0 0
\(187\) −4.50000 7.79423i −0.329073 0.569970i
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) −9.00000 15.5885i −0.651217 1.12794i −0.982828 0.184525i \(-0.940925\pi\)
0.331611 0.943416i \(-0.392408\pi\)
\(192\) 0 0
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) −5.00000 −0.358979
\(195\) 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
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) 5.00000 0.353553
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) 0 0
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 1.50000 2.59808i 0.103757 0.179713i
\(210\) 0 0
\(211\) −10.0000 17.3205i −0.688428 1.19239i −0.972346 0.233544i \(-0.924968\pi\)
0.283918 0.958849i \(-0.408366\pi\)
\(212\) −12.0000 −0.824163
\(213\) 0 0
\(214\) 3.00000 0.205076
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −8.00000 + 13.8564i −0.541828 + 0.938474i
\(219\) 0 0
\(220\) 0 0
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 0 0
\(223\) −13.0000 + 22.5167i −0.870544 + 1.50783i −0.00910984 + 0.999959i \(0.502900\pi\)
−0.861435 + 0.507869i \(0.830434\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.00000 + 5.19615i −0.199557 + 0.345643i
\(227\) −21.0000 −1.39382 −0.696909 0.717159i \(-0.745442\pi\)
−0.696909 + 0.717159i \(0.745442\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.00000 + 5.19615i −0.196960 + 0.341144i
\(233\) 1.50000 2.59808i 0.0982683 0.170206i −0.812700 0.582683i \(-0.802003\pi\)
0.910968 + 0.412477i \(0.135336\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.50000 + 2.59808i 0.0976417 + 0.169120i
\(237\) 0 0
\(238\) 0 0
\(239\) 3.00000 + 5.19615i 0.194054 + 0.336111i 0.946590 0.322440i \(-0.104503\pi\)
−0.752536 + 0.658551i \(0.771170\pi\)
\(240\) 0 0
\(241\) −7.00000 −0.450910 −0.225455 0.974254i \(-0.572387\pi\)
−0.225455 + 0.974254i \(0.572387\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) 0 0
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 0 0
\(247\) −2.00000 −0.127257
\(248\) −2.00000 + 3.46410i −0.127000 + 0.219971i
\(249\) 0 0
\(250\) 0 0
\(251\) −21.0000 −1.32551 −0.662754 0.748837i \(-0.730613\pi\)
−0.662754 + 0.748837i \(0.730613\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) 1.00000 + 1.73205i 0.0627456 + 0.108679i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 21.0000 1.30994 0.654972 0.755653i \(-0.272680\pi\)
0.654972 + 0.755653i \(0.272680\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −18.0000 −1.10993 −0.554964 0.831875i \(-0.687268\pi\)
−0.554964 + 0.831875i \(0.687268\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −2.50000 4.33013i −0.152712 0.264505i
\(269\) −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i \(-0.905416\pi\)
0.224523 0.974469i \(-0.427917\pi\)
\(270\) 0 0
\(271\) −10.0000 + 17.3205i −0.607457 + 1.05215i 0.384201 + 0.923249i \(0.374477\pi\)
−0.991658 + 0.128897i \(0.958856\pi\)
\(272\) −1.50000 + 2.59808i −0.0909509 + 0.157532i
\(273\) 0 0
\(274\) 1.50000 + 2.59808i 0.0906183 + 0.156956i
\(275\) −15.0000 −0.904534
\(276\) 0 0
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) −9.50000 + 16.4545i −0.569772 + 0.986874i
\(279\) 0 0
\(280\) 0 0
\(281\) 3.00000 5.19615i 0.178965 0.309976i −0.762561 0.646916i \(-0.776058\pi\)
0.941526 + 0.336939i \(0.109392\pi\)
\(282\) 0 0
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) 0 0
\(286\) 3.00000 5.19615i 0.177394 0.307255i
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 0 0
\(292\) 11.0000 0.643726
\(293\) 15.0000 + 25.9808i 0.876309 + 1.51781i 0.855361 + 0.518032i \(0.173335\pi\)
0.0209480 + 0.999781i \(0.493332\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.00000 + 3.46410i −0.116248 + 0.201347i
\(297\) 0 0
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) −6.00000 10.3923i −0.346989 0.601003i
\(300\) 0 0
\(301\) 0 0
\(302\) −5.00000 8.66025i −0.287718 0.498342i
\(303\) 0 0
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) 0 0
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9.00000 + 15.5885i −0.510343 + 0.883940i 0.489585 + 0.871956i \(0.337148\pi\)
−0.999928 + 0.0119847i \(0.996185\pi\)
\(312\) 0 0
\(313\) −14.5000 25.1147i −0.819588 1.41957i −0.905986 0.423308i \(-0.860869\pi\)
0.0863973 0.996261i \(-0.472465\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) −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
\(319\) 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
\(325\) 5.00000 + 8.66025i 0.277350 + 0.480384i
\(326\) 4.00000 0.221540
\(327\) 0 0
\(328\) −4.50000 7.79423i −0.248471 0.430364i
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) 6.00000 + 10.3923i 0.329293 + 0.570352i
\(333\) 0 0
\(334\) 6.00000 10.3923i 0.328305 0.568642i
\(335\) 0 0
\(336\) 0 0
\(337\) 0.500000 + 0.866025i 0.0272367 + 0.0471754i 0.879322 0.476227i \(-0.157996\pi\)
−0.852086 + 0.523402i \(0.824663\pi\)
\(338\) 9.00000 0.489535
\(339\) 0 0
\(340\) 0 0
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 0 0
\(343\) 0 0
\(344\) −0.500000 + 0.866025i −0.0269582 + 0.0466930i
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) 16.5000 28.5788i 0.885766 1.53419i 0.0409337 0.999162i \(-0.486967\pi\)
0.844833 0.535031i \(-0.179700\pi\)
\(348\) 0 0
\(349\) 8.00000 13.8564i 0.428230 0.741716i −0.568486 0.822693i \(-0.692471\pi\)
0.996716 + 0.0809766i \(0.0258039\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) 21.0000 1.11772 0.558859 0.829263i \(-0.311239\pi\)
0.558859 + 0.829263i \(0.311239\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.00000 + 5.19615i 0.159000 + 0.275396i
\(357\) 0 0
\(358\) −6.00000 + 10.3923i −0.317110 + 0.549250i
\(359\) −9.00000 + 15.5885i −0.475002 + 0.822727i −0.999590 0.0286287i \(-0.990886\pi\)
0.524588 + 0.851356i \(0.324219\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 7.00000 + 12.1244i 0.367912 + 0.637242i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −28.0000 −1.46159 −0.730794 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) −3.00000 5.19615i −0.156386 0.270868i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −34.0000 −1.76045 −0.880227 0.474554i \(-0.842610\pi\)
−0.880227 + 0.474554i \(0.842610\pi\)
\(374\) 4.50000 7.79423i 0.232689 0.403030i
\(375\) 0 0
\(376\) 3.00000 + 5.19615i 0.154713 + 0.267971i
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 9.00000 15.5885i 0.460480 0.797575i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −5.00000 −0.254493
\(387\) 0 0
\(388\) −2.50000 4.33013i −0.126918 0.219829i
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 0 0
\(391\) −9.00000 15.5885i −0.455150 0.788342i
\(392\) 0 0
\(393\) 0 0
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) 0 0
\(396\) 0 0
\(397\) −10.0000 + 17.3205i −0.501886 + 0.869291i 0.498112 + 0.867113i \(0.334027\pi\)
−0.999998 + 0.00217869i \(0.999307\pi\)
\(398\) −5.00000 + 8.66025i −0.250627 + 0.434099i
\(399\) 0 0
\(400\) 2.50000 + 4.33013i 0.125000 + 0.216506i
\(401\) 27.0000 1.34832 0.674158 0.738587i \(-0.264507\pi\)
0.674158 + 0.738587i \(0.264507\pi\)
\(402\) 0 0
\(403\) −8.00000 −0.398508
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 6.00000 10.3923i 0.297409 0.515127i
\(408\) 0 0
\(409\) −8.50000 + 14.7224i −0.420298 + 0.727977i −0.995968 0.0897044i \(-0.971408\pi\)
0.575670 + 0.817682i \(0.304741\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −7.00000 + 12.1244i −0.344865 + 0.597324i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −2.00000 −0.0980581
\(417\) 0 0
\(418\) 3.00000 0.146735
\(419\) −6.00000 10.3923i −0.293119 0.507697i 0.681426 0.731887i \(-0.261360\pi\)
−0.974546 + 0.224189i \(0.928027\pi\)
\(420\) 0 0
\(421\) −10.0000 + 17.3205i −0.487370 + 0.844150i −0.999895 0.0145228i \(-0.995377\pi\)
0.512524 + 0.858673i \(0.328710\pi\)
\(422\) 10.0000 17.3205i 0.486792 0.843149i
\(423\) 0 0
\(424\) −6.00000 10.3923i −0.291386 0.504695i
\(425\) 7.50000 + 12.9904i 0.363803 + 0.630126i
\(426\) 0 0
\(427\) 0 0
\(428\) 1.50000 + 2.59808i 0.0725052 + 0.125583i
\(429\) 0 0
\(430\) 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
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) 3.00000 5.19615i 0.143509 0.248566i
\(438\) 0 0
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) 1.50000 + 2.59808i 0.0712672 + 0.123438i 0.899457 0.437009i \(-0.143962\pi\)
−0.828190 + 0.560448i \(0.810629\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −26.0000 −1.23114
\(447\) 0 0
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) 13.5000 + 23.3827i 0.635690 + 1.10105i
\(452\) −6.00000 −0.282216
\(453\) 0 0
\(454\) −10.5000 18.1865i −0.492789 0.853536i
\(455\) 0 0
\(456\) 0 0
\(457\) −8.50000 14.7224i −0.397613 0.688686i 0.595818 0.803120i \(-0.296828\pi\)
−0.993431 + 0.114433i \(0.963495\pi\)
\(458\) 7.00000 + 12.1244i 0.327089 + 0.566534i
\(459\) 0 0
\(460\) 0 0
\(461\) −15.0000 + 25.9808i −0.698620 + 1.21004i 0.270326 + 0.962769i \(0.412869\pi\)
−0.968945 + 0.247276i \(0.920465\pi\)
\(462\) 0 0
\(463\) −10.0000 17.3205i −0.464739 0.804952i 0.534450 0.845200i \(-0.320519\pi\)
−0.999190 + 0.0402476i \(0.987185\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) 3.00000 0.138972
\(467\) −7.50000 + 12.9904i −0.347059 + 0.601123i −0.985726 0.168360i \(-0.946153\pi\)
0.638667 + 0.769483i \(0.279486\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −1.50000 + 2.59808i −0.0690431 + 0.119586i
\(473\) 1.50000 2.59808i 0.0689701 0.119460i
\(474\) 0 0
\(475\) −2.50000 + 4.33013i −0.114708 + 0.198680i
\(476\) 0 0
\(477\) 0 0
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) 42.0000 1.91903 0.959514 0.281659i \(-0.0908848\pi\)
0.959514 + 0.281659i \(0.0908848\pi\)
\(480\) 0 0
\(481\) −8.00000 −0.364769
\(482\) −3.50000 6.06218i −0.159421 0.276125i
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 0 0
\(486\) 0 0
\(487\) −13.0000 22.5167i −0.589086 1.02033i −0.994352 0.106129i \(-0.966154\pi\)
0.405266 0.914199i \(-0.367179\pi\)
\(488\) 4.00000 + 6.92820i 0.181071 + 0.313625i
\(489\) 0 0
\(490\) 0 0
\(491\) −7.50000 12.9904i −0.338470 0.586248i 0.645675 0.763612i \(-0.276576\pi\)
−0.984145 + 0.177365i \(0.943243\pi\)
\(492\) 0 0
\(493\) −18.0000 −0.810679
\(494\) −1.00000 1.73205i −0.0449921 0.0779287i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) −13.0000 −0.581960 −0.290980 0.956729i \(-0.593981\pi\)
−0.290980 + 0.956729i \(0.593981\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −10.5000 18.1865i −0.468638 0.811705i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 9.00000 + 15.5885i 0.400099 + 0.692991i
\(507\) 0 0
\(508\) −1.00000 + 1.73205i −0.0443678 + 0.0768473i
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 10.5000 + 18.1865i 0.463135 + 0.802174i
\(515\) 0 0
\(516\) 0 0
\(517\) −9.00000 15.5885i −0.395820 0.685580i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.50000 2.59808i −0.0657162 0.113824i 0.831295 0.555831i \(-0.187600\pi\)
−0.897011 + 0.442007i \(0.854267\pi\)
\(522\) 0 0
\(523\) −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i \(-0.977388\pi\)
0.560208 + 0.828352i \(0.310721\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −9.00000 15.5885i −0.392419 0.679689i
\(527\) −12.0000 −0.522728
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 9.00000 15.5885i 0.389833 0.675211i
\(534\) 0 0
\(535\) 0 0
\(536\) 2.50000 4.33013i 0.107984 0.187033i
\(537\) 0 0
\(538\) 12.0000 20.7846i 0.517357 0.896088i
\(539\) 0 0
\(540\) 0 0
\(541\) 2.00000 3.46410i 0.0859867 0.148933i −0.819825 0.572615i \(-0.805929\pi\)
0.905811 + 0.423681i \(0.139262\pi\)
\(542\) −20.0000 −0.859074
\(543\) 0 0
\(544\) −3.00000 −0.128624
\(545\) 0 0
\(546\) 0 0
\(547\) 0.500000 0.866025i 0.0213785 0.0370286i −0.855138 0.518400i \(-0.826528\pi\)
0.876517 + 0.481371i \(0.159861\pi\)
\(548\) −1.50000 + 2.59808i −0.0640768 + 0.110984i
\(549\) 0 0
\(550\) −7.50000 12.9904i −0.319801 0.553912i
\(551\) −3.00000 5.19615i −0.127804 0.221364i
\(552\) 0 0
\(553\) 0 0
\(554\) −5.00000 8.66025i −0.212430 0.367939i
\(555\) 0 0
\(556\) −19.0000 −0.805779
\(557\) −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i \(-0.947432\pi\)
0.350824 0.936442i \(-0.385902\pi\)
\(558\) 0 0
\(559\) −2.00000 −0.0845910
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) −19.5000 + 33.7750i −0.821827 + 1.42345i 0.0824933 + 0.996592i \(0.473712\pi\)
−0.904320 + 0.426855i \(0.859622\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) 22.5000 + 38.9711i 0.943249 + 1.63376i 0.759220 + 0.650835i \(0.225581\pi\)
0.184030 + 0.982921i \(0.441086\pi\)
\(570\) 0 0
\(571\) 18.5000 32.0429i 0.774201 1.34096i −0.161042 0.986948i \(-0.551485\pi\)
0.935243 0.354008i \(-0.115181\pi\)
\(572\) 6.00000 0.250873
\(573\) 0 0
\(574\) 0 0
\(575\) −30.0000 −1.25109
\(576\) 0 0
\(577\) −5.50000 9.52628i −0.228968 0.396584i 0.728535 0.685009i \(-0.240202\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) 8.00000 0.332756
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 18.0000 + 31.1769i 0.745484 + 1.29122i
\(584\) 5.50000 + 9.52628i 0.227592 + 0.394200i
\(585\) 0 0
\(586\) −15.0000 + 25.9808i −0.619644 + 1.07326i
\(587\) −4.50000 + 7.79423i −0.185735 + 0.321702i −0.943824 0.330449i \(-0.892800\pi\)
0.758089 + 0.652151i \(0.226133\pi\)
\(588\) 0 0
\(589\) −2.00000 3.46410i −0.0824086 0.142736i
\(590\) 0 0
\(591\) 0 0
\(592\) −4.00000 −0.164399
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −3.00000 + 5.19615i −0.122885 + 0.212843i
\(597\) 0 0
\(598\) 6.00000 10.3923i 0.245358 0.424973i
\(599\) 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i \(-0.754495\pi\)
0.962175 + 0.272433i \(0.0878284\pi\)
\(600\) 0 0
\(601\) 18.5000 32.0429i 0.754631 1.30706i −0.190927 0.981604i \(-0.561149\pi\)
0.945558 0.325455i \(-0.105517\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 5.00000 8.66025i 0.203447 0.352381i
\(605\) 0 0
\(606\) 0 0
\(607\) −28.0000 −1.13648 −0.568242 0.822861i \(-0.692376\pi\)
−0.568242 + 0.822861i \(0.692376\pi\)
\(608\) −0.500000 0.866025i −0.0202777 0.0351220i
\(609\) 0 0
\(610\) 0 0
\(611\) −6.00000 + 10.3923i −0.242734 + 0.420428i
\(612\) 0 0
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) −3.50000 6.06218i −0.141249 0.244650i
\(615\) 0 0
\(616\) 0 0
\(617\) 13.5000 + 23.3827i 0.543490 + 0.941351i 0.998700 + 0.0509678i \(0.0162306\pi\)
−0.455211 + 0.890384i \(0.650436\pi\)
\(618\) 0 0
\(619\) 35.0000 1.40677 0.703384 0.710810i \(-0.251671\pi\)
0.703384 + 0.710810i \(0.251671\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −18.0000 −0.721734
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 14.5000 25.1147i 0.579537 1.00379i
\(627\) 0 0
\(628\) 2.00000 + 3.46410i 0.0798087 + 0.138233i
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) −2.00000 3.46410i −0.0795557 0.137795i
\(633\) 0 0
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 18.0000 0.712627
\(639\) 0 0
\(640\) 0 0
\(641\) 3.00000 0.118493 0.0592464 0.998243i \(-0.481130\pi\)
0.0592464 + 0.998243i \(0.481130\pi\)
\(642\) 0 0
\(643\) −11.5000 19.9186i −0.453516 0.785512i 0.545086 0.838380i \(-0.316497\pi\)
−0.998602 + 0.0528680i \(0.983164\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1.50000 2.59808i −0.0590167 0.102220i
\(647\) 9.00000 + 15.5885i 0.353827 + 0.612845i 0.986916 0.161233i \(-0.0515470\pi\)
−0.633090 + 0.774078i \(0.718214\pi\)
\(648\) 0 0
\(649\) 4.50000 7.79423i 0.176640 0.305950i
\(650\) −5.00000 + 8.66025i −0.196116 + 0.339683i
\(651\) 0 0
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.50000 7.79423i 0.175695 0.304314i
\(657\) 0 0
\(658\) 0 0
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) 0 0
\(661\) 2.00000 3.46410i 0.0777910 0.134738i −0.824506 0.565854i \(-0.808547\pi\)
0.902297 + 0.431116i \(0.141880\pi\)
\(662\) −2.00000 + 3.46410i −0.0777322 + 0.134636i
\(663\) 0 0
\(664\) −6.00000 + 10.3923i −0.232845 + 0.403300i
\(665\) 0 0
\(666\) 0 0
\(667\) 18.0000 31.1769i 0.696963 1.20717i
\(668\) 12.0000 0.464294
\(669\) 0 0
\(670\) 0 0
\(671\) −12.0000 20.7846i −0.463255 0.802381i
\(672\) 0 0
\(673\) 11.0000 19.0526i 0.424019 0.734422i −0.572309 0.820038i \(-0.693952\pi\)
0.996328 + 0.0856156i \(0.0272857\pi\)
\(674\) −0.500000 + 0.866025i −0.0192593 + 0.0333581i
\(675\) 0 0
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) 18.0000 + 31.1769i 0.691796 + 1.19823i 0.971249 + 0.238067i \(0.0765137\pi\)
−0.279453 + 0.960159i \(0.590153\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 12.0000 0.459504
\(683\) −4.50000 7.79423i −0.172188 0.298238i 0.766997 0.641651i \(-0.221750\pi\)
−0.939184 + 0.343413i \(0.888417\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −1.00000 −0.0381246
\(689\) 12.0000 20.7846i 0.457164 0.791831i
\(690\) 0 0
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 33.0000 1.25266
\(695\) 0 0
\(696\) 0 0
\(697\) 13.5000 23.3827i 0.511349 0.885682i
\(698\) 16.0000 0.605609
\(699\) 0 0
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) −2.00000 3.46410i −0.0754314 0.130651i
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) 10.5000 + 18.1865i 0.395173 + 0.684459i
\(707\) 0 0
\(708\) 0 0
\(709\) 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i \(-0.142735\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) 12.0000 20.7846i 0.449404 0.778390i
\(714\) 0 0
\(715\) 0 0
\(716\) −12.0000 −0.448461
\(717\) 0 0
\(718\) −18.0000 −0.671754
\(719\) −18.0000 + 31.1769i −0.671287 + 1.16270i 0.306253 + 0.951950i \(0.400925\pi\)
−0.977539 + 0.210752i \(0.932409\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −9.00000 + 15.5885i −0.334945 + 0.580142i
\(723\) 0 0
\(724\) −7.00000 + 12.1244i −0.260153 + 0.450598i
\(725\) −15.0000 + 25.9808i −0.557086 + 0.964901i
\(726\) 0 0
\(727\) −13.0000 + 22.5167i −0.482143 + 0.835097i −0.999790 0.0204978i \(-0.993475\pi\)
0.517647 + 0.855595i \(0.326808\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.00000 −0.110959
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) −14.0000 24.2487i −0.516749 0.895036i
\(735\) 0 0
\(736\) 3.00000 5.19615i 0.110581 0.191533i
\(737\) −7.50000 + 12.9904i −0.276266 + 0.478507i
\(738\) 0 0
\(739\) −23.5000 40.7032i −0.864461 1.49729i −0.867581 0.497296i \(-0.834326\pi\)
0.00311943 0.999995i \(-0.499007\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i \(-0.131563\pi\)
−0.805735 + 0.592277i \(0.798229\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −17.0000 29.4449i −0.622414 1.07805i
\(747\) 0 0
\(748\) 9.00000 0.329073
\(749\) 0 0
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) −3.00000 + 5.19615i −0.109399 + 0.189484i
\(753\) 0 0
\(754\) −6.00000 10.3923i −0.218507 0.378465i
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 11.5000 + 19.9186i 0.417699 + 0.723476i
\(759\) 0 0
\(760\) 0 0
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 18.0000 0.651217
\(765\) 0 0
\(766\) 0 0
\(767\) −6.00000 −0.216647
\(768\) 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
\(771\) 0 0
\(772\) −2.50000 4.33013i −0.0899770 0.155845i
\(773\) 9.00000 + 15.5885i 0.323708 + 0.560678i 0.981250 0.192740i \(-0.0617373\pi\)
−0.657542 + 0.753418i \(0.728404\pi\)
\(774\) 0 0
\(775\) −10.0000 + 17.3205i −0.359211 + 0.622171i
\(776\) 2.50000 4.33013i 0.0897448 0.155443i
\(777\) 0 0
\(778\) −9.00000 15.5885i −0.322666 0.558873i
\(779\) 9.00000 0.322458
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) 9.00000 15.5885i 0.321839 0.557442i
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 2.00000 3.46410i 0.0712923 0.123482i −0.828176 0.560469i \(-0.810621\pi\)
0.899468 + 0.436987i \(0.143954\pi\)
\(788\) −6.00000 + 10.3923i −0.213741 + 0.370211i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −8.00000 + 13.8564i −0.284088 + 0.492055i
\(794\) −20.0000 −0.709773
\(795\) 0 0
\(796\) −10.0000 −0.354441
\(797\) −6.00000 10.3923i −0.212531 0.368114i 0.739975 0.672634i \(-0.234837\pi\)
−0.952506 + 0.304520i \(0.901504\pi\)
\(798\) 0