Properties

Label 18.2.c.a.7.1
Level $18$
Weight $2$
Character 18.7
Analytic conductor $0.144$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 18.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.143730723638\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 7.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 18.7
Dual form 18.2.c.a.13.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} +1.73205i q^{12} +(-1.00000 - 1.73205i) q^{13} +(-1.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{17} -3.00000 q^{18} -1.00000 q^{19} +(3.00000 - 1.73205i) q^{21} +(1.50000 + 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} +2.00000 q^{26} -5.19615i q^{27} +2.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.50000 + 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} +(1.50000 - 2.59808i) q^{36} -4.00000 q^{37} +(0.500000 - 0.866025i) q^{38} +3.46410i q^{39} +(-4.50000 - 7.79423i) q^{41} +3.46410i q^{42} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} -6.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(1.50000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(2.50000 + 4.33013i) q^{50} +(4.50000 + 2.59808i) q^{51} +(-1.00000 + 1.73205i) q^{52} +12.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +(-1.00000 + 1.73205i) q^{56} +(1.50000 + 0.866025i) q^{57} +(-3.00000 - 5.19615i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-4.00000 + 6.92820i) q^{61} -4.00000 q^{62} -6.00000 q^{63} +1.00000 q^{64} -5.19615i q^{66} +(-2.50000 - 4.33013i) q^{67} +(1.50000 + 2.59808i) q^{68} -10.3923i q^{69} -12.0000 q^{71} +(1.50000 + 2.59808i) q^{72} +11.0000 q^{73} +(2.00000 - 3.46410i) q^{74} +(-7.50000 + 4.33013i) q^{75} +(0.500000 + 0.866025i) q^{76} +(3.00000 + 5.19615i) q^{77} +(-3.00000 - 1.73205i) q^{78} +(2.00000 - 3.46410i) q^{79} +(-4.50000 + 7.79423i) q^{81} +9.00000 q^{82} +(-6.00000 + 10.3923i) q^{83} +(-3.00000 - 1.73205i) q^{84} +(0.500000 + 0.866025i) q^{86} +(9.00000 - 5.19615i) q^{87} +(1.50000 - 2.59808i) q^{88} +6.00000 q^{89} +4.00000 q^{91} +(3.00000 - 5.19615i) q^{92} -6.92820i q^{93} +(3.00000 + 5.19615i) q^{94} +1.73205i q^{96} +(-2.50000 + 4.33013i) q^{97} -3.00000 q^{98} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} - 2 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} - 2 q^{7} + 2 q^{8} + 3 q^{9} + 3 q^{11} - 2 q^{13} - 2 q^{14} - q^{16} - 6 q^{17} - 6 q^{18} - 2 q^{19} + 6 q^{21} + 3 q^{22} + 6 q^{23} - 3 q^{24} + 5 q^{25} + 4 q^{26} + 4 q^{28} - 6 q^{29} + 4 q^{31} - q^{32} - 9 q^{33} + 3 q^{34} + 3 q^{36} - 8 q^{37} + q^{38} - 9 q^{41} + q^{43} - 6 q^{44} - 12 q^{46} + 6 q^{47} + 3 q^{48} + 3 q^{49} + 5 q^{50} + 9 q^{51} - 2 q^{52} + 24 q^{53} + 9 q^{54} - 2 q^{56} + 3 q^{57} - 6 q^{58} - 3 q^{59} - 8 q^{61} - 8 q^{62} - 12 q^{63} + 2 q^{64} - 5 q^{67} + 3 q^{68} - 24 q^{71} + 3 q^{72} + 22 q^{73} + 4 q^{74} - 15 q^{75} + q^{76} + 6 q^{77} - 6 q^{78} + 4 q^{79} - 9 q^{81} + 18 q^{82} - 12 q^{83} - 6 q^{84} + q^{86} + 18 q^{87} + 3 q^{88} + 12 q^{89} + 8 q^{91} + 6 q^{92} + 6 q^{94} - 5 q^{97} - 6 q^{98} + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/18\mathbb{Z}\right)^\times\).

\(n\) \(11\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −1.50000 0.866025i −0.866025 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 1.50000 0.866025i 0.612372 0.353553i
\(7\) −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 1.73205i 0.500000i
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −1.00000 1.73205i −0.267261 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) −3.00000 −0.707107
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 0 0
\(21\) 3.00000 1.73205i 0.654654 0.377964i
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) 2.00000 0.392232
\(27\) 5.19615i 1.00000i
\(28\) 2.00000 0.377964
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −4.50000 + 2.59808i −0.783349 + 0.452267i
\(34\) 1.50000 2.59808i 0.257248 0.445566i
\(35\) 0 0
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0.500000 0.866025i 0.0811107 0.140488i
\(39\) 3.46410i 0.554700i
\(40\) 0 0
\(41\) −4.50000 7.79423i −0.702782 1.21725i −0.967486 0.252924i \(-0.918608\pi\)
0.264704 0.964330i \(-0.414726\pi\)
\(42\) 3.46410i 0.534522i
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 1.50000 0.866025i 0.216506 0.125000i
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) 2.50000 + 4.33013i 0.353553 + 0.612372i
\(51\) 4.50000 + 2.59808i 0.630126 + 0.363803i
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 4.50000 + 2.59808i 0.612372 + 0.353553i
\(55\) 0 0
\(56\) −1.00000 + 1.73205i −0.133631 + 0.231455i
\(57\) 1.50000 + 0.866025i 0.198680 + 0.114708i
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) −4.00000 −0.508001
\(63\) −6.00000 −0.755929
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 5.19615i 0.639602i
\(67\) −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i \(-0.265465\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) 10.3923i 1.25109i
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 1.50000 + 2.59808i 0.176777 + 0.306186i
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) −7.50000 + 4.33013i −0.866025 + 0.500000i
\(76\) 0.500000 + 0.866025i 0.0573539 + 0.0993399i
\(77\) 3.00000 + 5.19615i 0.341882 + 0.592157i
\(78\) −3.00000 1.73205i −0.339683 0.196116i
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 9.00000 0.993884
\(83\) −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) −3.00000 1.73205i −0.327327 0.188982i
\(85\) 0 0
\(86\) 0.500000 + 0.866025i 0.0539164 + 0.0933859i
\(87\) 9.00000 5.19615i 0.964901 0.557086i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 3.00000 5.19615i 0.312772 0.541736i
\(93\) 6.92820i 0.718421i
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 0 0
\(96\) 1.73205i 0.176777i
\(97\) −2.50000 + 4.33013i −0.253837 + 0.439658i −0.964579 0.263795i \(-0.915026\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) −3.00000 −0.303046
\(99\) 9.00000 0.904534
\(100\) −5.00000 −0.500000
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) −4.50000 + 2.59808i −0.445566 + 0.257248i
\(103\) −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i \(-0.924396\pi\)
0.282194 0.959357i \(-0.408938\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) 0 0
\(106\) −6.00000 + 10.3923i −0.582772 + 1.00939i
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) −4.50000 + 2.59808i −0.433013 + 0.250000i
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) 6.00000 + 3.46410i 0.569495 + 0.328798i
\(112\) −1.00000 1.73205i −0.0944911 0.163663i
\(113\) −3.00000 5.19615i −0.282216 0.488813i 0.689714 0.724082i \(-0.257736\pi\)
−0.971930 + 0.235269i \(0.924403\pi\)
\(114\) −1.50000 + 0.866025i −0.140488 + 0.0811107i
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 3.00000 5.19615i 0.277350 0.480384i
\(118\) 3.00000 0.276172
\(119\) 3.00000 5.19615i 0.275010 0.476331i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −4.00000 6.92820i −0.362143 0.627250i
\(123\) 15.5885i 1.40556i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 0 0
\(126\) 3.00000 5.19615i 0.267261 0.462910i
\(127\) 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
\(129\) −1.50000 + 0.866025i −0.132068 + 0.0762493i
\(130\) 0 0
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 4.50000 + 2.59808i 0.391675 + 0.226134i
\(133\) 1.00000 1.73205i 0.0867110 0.150188i
\(134\) 5.00000 0.431934
\(135\) 0 0
\(136\) −3.00000 −0.257248
\(137\) 1.50000 2.59808i 0.128154 0.221969i −0.794808 0.606861i \(-0.792428\pi\)
0.922961 + 0.384893i \(0.125762\pi\)
\(138\) 9.00000 + 5.19615i 0.766131 + 0.442326i
\(139\) 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
\(141\) −9.00000 + 5.19615i −0.757937 + 0.437595i
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) −6.00000 −0.501745
\(144\) −3.00000 −0.250000
\(145\) 0 0
\(146\) −5.50000 + 9.52628i −0.455183 + 0.788400i
\(147\) 5.19615i 0.428571i
\(148\) 2.00000 + 3.46410i 0.164399 + 0.284747i
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 8.66025i 0.707107i
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −4.50000 7.79423i −0.363803 0.630126i
\(154\) −6.00000 −0.483494
\(155\) 0 0
\(156\) 3.00000 1.73205i 0.240192 0.138675i
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) 2.00000 + 3.46410i 0.159111 + 0.275589i
\(159\) −18.0000 10.3923i −1.42749 0.824163i
\(160\) 0 0
\(161\) −12.0000 −0.945732
\(162\) −4.50000 7.79423i −0.353553 0.612372i
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −4.50000 + 7.79423i −0.351391 + 0.608627i
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) 6.00000 + 10.3923i 0.464294 + 0.804181i 0.999169 0.0407502i \(-0.0129748\pi\)
−0.534875 + 0.844931i \(0.679641\pi\)
\(168\) 3.00000 1.73205i 0.231455 0.133631i
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) −1.50000 2.59808i −0.114708 0.198680i
\(172\) −1.00000 −0.0762493
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 10.3923i 0.787839i
\(175\) 5.00000 + 8.66025i 0.377964 + 0.654654i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 5.19615i 0.390567i
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) −2.00000 + 3.46410i −0.148250 + 0.256776i
\(183\) 12.0000 6.92820i 0.887066 0.512148i
\(184\) 3.00000 + 5.19615i 0.221163 + 0.383065i
\(185\) 0 0
\(186\) 6.00000 + 3.46410i 0.439941 + 0.254000i
\(187\) −4.50000 + 7.79423i −0.329073 + 0.569970i
\(188\) −6.00000 −0.437595
\(189\) 9.00000 + 5.19615i 0.654654 + 0.377964i
\(190\) 0 0
\(191\) 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i \(-0.607592\pi\)
0.982828 0.184525i \(-0.0590746\pi\)
\(192\) −1.50000 0.866025i −0.108253 0.0625000i
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) −2.50000 4.33013i −0.179490 0.310885i
\(195\) 0 0
\(196\) 1.50000 2.59808i 0.107143 0.185577i
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) −4.50000 + 7.79423i −0.319801 + 0.553912i
\(199\) −10.0000 −0.708881 −0.354441 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) 2.50000 4.33013i 0.176777 0.306186i
\(201\) 8.66025i 0.610847i
\(202\) 0 0
\(203\) −6.00000 10.3923i −0.421117 0.729397i
\(204\) 5.19615i 0.363803i
\(205\) 0 0
\(206\) 14.0000 0.975426
\(207\) −9.00000 + 15.5885i −0.625543 + 1.08347i
\(208\) 2.00000 0.138675
\(209\) −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 \(-0.408366\pi\)
\(212\) −6.00000 10.3923i −0.412082 0.713746i
\(213\) 18.0000 + 10.3923i 1.23334 + 0.712069i
\(214\) −1.50000 + 2.59808i −0.102538 + 0.177601i
\(215\) 0 0
\(216\) 5.19615i 0.353553i
\(217\) −8.00000 −0.543075
\(218\) 8.00000 13.8564i 0.541828 0.938474i
\(219\) −16.5000 9.52628i −1.11497 0.643726i
\(220\) 0 0
\(221\) 3.00000 + 5.19615i 0.201802 + 0.349531i
\(222\) −6.00000 + 3.46410i −0.402694 + 0.232495i
\(223\) −13.0000 + 22.5167i −0.870544 + 1.50783i −0.00910984 + 0.999959i \(0.502900\pi\)
−0.861435 + 0.507869i \(0.830434\pi\)
\(224\) 2.00000 0.133631
\(225\) 15.0000 1.00000
\(226\) 6.00000 0.399114
\(227\) −10.5000 + 18.1865i −0.696909 + 1.20708i 0.272623 + 0.962121i \(0.412109\pi\)
−0.969533 + 0.244962i \(0.921225\pi\)
\(228\) 1.73205i 0.114708i
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) 10.3923i 0.683763i
\(232\) −3.00000 + 5.19615i −0.196960 + 0.341144i
\(233\) 3.00000 0.196537 0.0982683 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) 3.00000 + 5.19615i 0.196116 + 0.339683i
\(235\) 0 0
\(236\) −1.50000 + 2.59808i −0.0976417 + 0.169120i
\(237\) −6.00000 + 3.46410i −0.389742 + 0.225018i
\(238\) 3.00000 + 5.19615i 0.194461 + 0.336817i
\(239\) −3.00000 5.19615i −0.194054 0.336111i 0.752536 0.658551i \(-0.228830\pi\)
−0.946590 + 0.322440i \(0.895497\pi\)
\(240\) 0 0
\(241\) 3.50000 6.06218i 0.225455 0.390499i −0.731001 0.682376i \(-0.760947\pi\)
0.956456 + 0.291877i \(0.0942799\pi\)
\(242\) −2.00000 −0.128565
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) −13.5000 7.79423i −0.860729 0.496942i
\(247\) 1.00000 + 1.73205i 0.0636285 + 0.110208i
\(248\) 2.00000 + 3.46410i 0.127000 + 0.219971i
\(249\) 18.0000 10.3923i 1.14070 0.658586i
\(250\) 0 0
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 3.00000 + 5.19615i 0.188982 + 0.327327i
\(253\) 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
\(257\) 10.5000 + 18.1865i 0.654972 + 1.13444i 0.981901 + 0.189396i \(0.0606529\pi\)
−0.326929 + 0.945049i \(0.606014\pi\)
\(258\) 1.73205i 0.107833i
\(259\) 4.00000 6.92820i 0.248548 0.430498i
\(260\) 0 0
\(261\) −18.0000 −1.11417
\(262\) 0 0
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) −4.50000 + 2.59808i −0.276956 + 0.159901i
\(265\) 0 0
\(266\) 1.00000 + 1.73205i 0.0613139 + 0.106199i
\(267\) −9.00000 5.19615i −0.550791 0.317999i
\(268\) −2.50000 + 4.33013i −0.152712 + 0.264505i
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 1.50000 2.59808i 0.0909509 0.157532i
\(273\) −6.00000 3.46410i −0.363137 0.209657i
\(274\) 1.50000 + 2.59808i 0.0906183 + 0.156956i
\(275\) −7.50000 12.9904i −0.452267 0.783349i
\(276\) −9.00000 + 5.19615i −0.541736 + 0.312772i
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) −19.0000 −1.13954
\(279\) −6.00000 + 10.3923i −0.359211 + 0.622171i
\(280\) 0 0
\(281\) −3.00000 + 5.19615i −0.178965 + 0.309976i −0.941526 0.336939i \(-0.890608\pi\)
0.762561 + 0.646916i \(0.223942\pi\)
\(282\) 10.3923i 0.618853i
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 0 0
\(286\) 3.00000 5.19615i 0.177394 0.307255i
\(287\) 18.0000 1.06251
\(288\) 1.50000 2.59808i 0.0883883 0.153093i
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 7.50000 4.33013i 0.439658 0.253837i
\(292\) −5.50000 9.52628i −0.321863 0.557483i
\(293\) −15.0000 25.9808i −0.876309 1.51781i −0.855361 0.518032i \(-0.826665\pi\)
−0.0209480 0.999781i \(-0.506668\pi\)
\(294\) 4.50000 + 2.59808i 0.262445 + 0.151523i
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) −13.5000 7.79423i −0.783349 0.452267i
\(298\) −6.00000 −0.347571
\(299\) 6.00000 10.3923i 0.346989 0.601003i
\(300\) 7.50000 + 4.33013i 0.433013 + 0.250000i
\(301\) 1.00000 + 1.73205i 0.0576390 + 0.0998337i
\(302\) 5.00000 + 8.66025i 0.287718 + 0.498342i
\(303\) 0 0
\(304\) 0.500000 0.866025i 0.0286770 0.0496700i
\(305\) 0 0
\(306\) 9.00000 0.514496
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 3.00000 5.19615i 0.170941 0.296078i
\(309\) 24.2487i 1.37946i
\(310\) 0 0
\(311\) 9.00000 + 15.5885i 0.510343 + 0.883940i 0.999928 + 0.0119847i \(0.00381495\pi\)
−0.489585 + 0.871956i \(0.662852\pi\)
\(312\) 3.46410i 0.196116i
\(313\) −14.5000 + 25.1147i −0.819588 + 1.41957i 0.0863973 + 0.996261i \(0.472465\pi\)
−0.905986 + 0.423308i \(0.860869\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 18.0000 10.3923i 1.00939 0.582772i
\(319\) 9.00000 + 15.5885i 0.503903 + 0.872786i
\(320\) 0 0
\(321\) −4.50000 2.59808i −0.251166 0.145010i
\(322\) 6.00000 10.3923i 0.334367 0.579141i
\(323\) 3.00000 0.166924
\(324\) 9.00000 0.500000
\(325\) −10.0000 −0.554700
\(326\) 2.00000 3.46410i 0.110770 0.191859i
\(327\) 24.0000 + 13.8564i 1.32720 + 0.766261i
\(328\) −4.50000 7.79423i −0.248471 0.430364i
\(329\) 6.00000 + 10.3923i 0.330791 + 0.572946i
\(330\) 0 0
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) 12.0000 0.658586
\(333\) −6.00000 10.3923i −0.328798 0.569495i
\(334\) −12.0000 −0.656611
\(335\) 0 0
\(336\) 3.46410i 0.188982i
\(337\) 0.500000 + 0.866025i 0.0272367 + 0.0471754i 0.879322 0.476227i \(-0.157996\pi\)
−0.852086 + 0.523402i \(0.824663\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) 10.3923i 0.564433i
\(340\) 0 0
\(341\) 12.0000 0.649836
\(342\) 3.00000 0.162221
\(343\) −20.0000 −1.07990
\(344\) 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 −0.844833 0.535031i \(-0.820300\pi\)
−0.0409337 0.999162i \(-0.513033\pi\)
\(348\) −9.00000 5.19615i −0.482451 0.278543i
\(349\) 8.00000 13.8564i 0.428230 0.741716i −0.568486 0.822693i \(-0.692471\pi\)
0.996716 + 0.0809766i \(0.0258039\pi\)
\(350\) −10.0000 −0.534522
\(351\) −9.00000 + 5.19615i −0.480384 + 0.277350i
\(352\) −3.00000 −0.159901
\(353\) 10.5000 18.1865i 0.558859 0.967972i −0.438733 0.898617i \(-0.644573\pi\)
0.997592 0.0693543i \(-0.0220939\pi\)
\(354\) −4.50000 2.59808i −0.239172 0.138086i
\(355\) 0 0
\(356\) −3.00000 5.19615i −0.159000 0.275396i
\(357\) −9.00000 + 5.19615i −0.476331 + 0.275010i
\(358\) −6.00000 + 10.3923i −0.317110 + 0.549250i
\(359\) −18.0000 −0.950004 −0.475002 0.879985i \(-0.657553\pi\)
−0.475002 + 0.879985i \(0.657553\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) −7.00000 + 12.1244i −0.367912 + 0.637242i
\(363\) 3.46410i 0.181818i
\(364\) −2.00000 3.46410i −0.104828 0.181568i
\(365\) 0 0
\(366\) 13.8564i 0.724286i
\(367\) 14.0000 24.2487i 0.730794 1.26577i −0.225750 0.974185i \(-0.572483\pi\)
0.956544 0.291587i \(-0.0941834\pi\)
\(368\) −6.00000 −0.312772
\(369\) 13.5000 23.3827i 0.702782 1.21725i
\(370\) 0 0
\(371\) −12.0000 + 20.7846i −0.623009 + 1.07908i
\(372\) −6.00000 + 3.46410i −0.311086 + 0.179605i
\(373\) 17.0000 + 29.4449i 0.880227 + 1.52460i 0.851089 + 0.525022i \(0.175943\pi\)
0.0291379 + 0.999575i \(0.490724\pi\)
\(374\) −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
\(378\) −9.00000 + 5.19615i −0.462910 + 0.267261i
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) 0 0
\(381\) −3.00000 1.73205i −0.153695 0.0887357i
\(382\) 9.00000 + 15.5885i 0.460480 + 0.797575i
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 1.50000 0.866025i 0.0765466 0.0441942i
\(385\) 0 0
\(386\) 5.00000 0.254493
\(387\) 3.00000 0.152499
\(388\) 5.00000 0.253837
\(389\) −9.00000 + 15.5885i −0.456318 + 0.790366i −0.998763 0.0497253i \(-0.984165\pi\)
0.542445 + 0.840091i \(0.317499\pi\)
\(390\) 0 0
\(391\) −9.00000 15.5885i −0.455150 0.788342i
\(392\) 1.50000 + 2.59808i 0.0757614 + 0.131223i
\(393\) 0 0
\(394\) 6.00000 10.3923i 0.302276 0.523557i
\(395\) 0 0
\(396\) −4.50000 7.79423i −0.226134 0.391675i
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) 5.00000 8.66025i 0.250627 0.434099i
\(399\) −3.00000 + 1.73205i −0.150188 + 0.0867110i
\(400\) 2.50000 + 4.33013i 0.125000 + 0.216506i
\(401\) 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i \(0.0688266\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) −7.50000 4.33013i −0.374066 0.215967i
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) 0 0
\(405\) 0 0
\(406\) 12.0000 0.595550
\(407\) −6.00000 + 10.3923i −0.297409 + 0.515127i
\(408\) 4.50000 + 2.59808i 0.222783 + 0.128624i
\(409\) −8.50000 14.7224i −0.420298 0.727977i 0.575670 0.817682i \(-0.304741\pi\)
−0.995968 + 0.0897044i \(0.971408\pi\)
\(410\) 0 0
\(411\) −4.50000 + 2.59808i −0.221969 + 0.128154i
\(412\) −7.00000 + 12.1244i −0.344865 + 0.597324i
\(413\) 6.00000 0.295241
\(414\) −9.00000 15.5885i −0.442326 0.766131i
\(415\) 0 0
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 32.9090i 1.61156i
\(418\) −1.50000 2.59808i −0.0733674 0.127076i
\(419\) 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 0 0
\(421\) −10.0000 + 17.3205i −0.487370 + 0.844150i −0.999895 0.0145228i \(-0.995377\pi\)
0.512524 + 0.858673i \(0.328710\pi\)
\(422\) 20.0000 0.973585
\(423\) 18.0000 0.875190
\(424\) 12.0000 0.582772
\(425\) −7.50000 + 12.9904i −0.363803 + 0.630126i
\(426\) −18.0000 + 10.3923i −0.872103 + 0.503509i
\(427\) −8.00000 13.8564i −0.387147 0.670559i
\(428\) −1.50000 2.59808i −0.0725052 0.125583i
\(429\) 9.00000 + 5.19615i 0.434524 + 0.250873i
\(430\) 0 0
\(431\) −30.0000 −1.44505 −0.722525 0.691345i \(-0.757018\pi\)
−0.722525 + 0.691345i \(0.757018\pi\)
\(432\) 4.50000 + 2.59808i 0.216506 + 0.125000i
\(433\) −7.00000 −0.336399 −0.168199 0.985753i \(-0.553795\pi\)
−0.168199 + 0.985753i \(0.553795\pi\)
\(434\) 4.00000 6.92820i 0.192006 0.332564i
\(435\) 0 0
\(436\) 8.00000 + 13.8564i 0.383131 + 0.663602i
\(437\) −3.00000 5.19615i −0.143509 0.248566i
\(438\) 16.5000 9.52628i 0.788400 0.455183i
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 0 0
\(441\) −4.50000 + 7.79423i −0.214286 + 0.371154i
\(442\) −6.00000 −0.285391
\(443\) −1.50000 + 2.59808i −0.0712672 + 0.123438i −0.899457 0.437009i \(-0.856038\pi\)
0.828190 + 0.560448i \(0.189371\pi\)
\(444\) 6.92820i 0.328798i
\(445\) 0 0
\(446\) −13.0000 22.5167i −0.615568 1.06619i
\(447\) 10.3923i 0.491539i
\(448\) −1.00000 + 1.73205i −0.0472456 + 0.0818317i
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) −7.50000 + 12.9904i −0.353553 + 0.612372i
\(451\) −27.0000 −1.27138
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) −15.0000 + 8.66025i −0.704761 + 0.406894i
\(454\) −10.5000 18.1865i −0.492789 0.853536i
\(455\) 0 0
\(456\) 1.50000 + 0.866025i 0.0702439 + 0.0405554i
\(457\) −8.50000 + 14.7224i −0.397613 + 0.688686i −0.993431 0.114433i \(-0.963495\pi\)
0.595818 + 0.803120i \(0.296828\pi\)
\(458\) 14.0000 0.654177
\(459\) 15.5885i 0.727607i
\(460\) 0 0
\(461\) 15.0000 25.9808i 0.698620 1.21004i −0.270326 0.962769i \(-0.587131\pi\)
0.968945 0.247276i \(-0.0795353\pi\)
\(462\) 9.00000 + 5.19615i 0.418718 + 0.241747i
\(463\) −10.0000 17.3205i −0.464739 0.804952i 0.534450 0.845200i \(-0.320519\pi\)
−0.999190 + 0.0402476i \(0.987185\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 0 0
\(466\) −1.50000 + 2.59808i −0.0694862 + 0.120354i
\(467\) −15.0000 −0.694117 −0.347059 0.937843i \(-0.612820\pi\)
−0.347059 + 0.937843i \(0.612820\pi\)
\(468\) −6.00000 −0.277350
\(469\) 10.0000 0.461757
\(470\) 0 0
\(471\) 6.92820i 0.319235i
\(472\) −1.50000 2.59808i −0.0690431 0.119586i
\(473\) −1.50000 2.59808i −0.0689701 0.119460i
\(474\) 6.92820i 0.318223i
\(475\) −2.50000 + 4.33013i −0.114708 + 0.198680i
\(476\) −6.00000 −0.275010
\(477\) 18.0000 + 31.1769i 0.824163 + 1.42749i
\(478\) 6.00000 0.274434
\(479\) 21.0000 36.3731i 0.959514 1.66193i 0.235833 0.971794i \(-0.424218\pi\)
0.723681 0.690134i \(-0.242449\pi\)
\(480\) 0 0
\(481\) 4.00000 + 6.92820i 0.182384 + 0.315899i
\(482\) 3.50000 + 6.06218i 0.159421 + 0.276125i
\(483\) 18.0000 + 10.3923i 0.819028 + 0.472866i
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 0 0
\(486\) 15.5885i 0.707107i
\(487\) 26.0000 1.17817 0.589086 0.808070i \(-0.299488\pi\)
0.589086 + 0.808070i \(0.299488\pi\)
\(488\) −4.00000 + 6.92820i −0.181071 + 0.313625i
\(489\) 6.00000 + 3.46410i 0.271329 + 0.156652i
\(490\) 0 0
\(491\) 7.50000 + 12.9904i 0.338470 + 0.586248i 0.984145 0.177365i \(-0.0567572\pi\)
−0.645675 + 0.763612i \(0.723424\pi\)
\(492\) 13.5000 7.79423i 0.608627 0.351391i
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) −2.00000 −0.0899843
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 12.0000 20.7846i 0.538274 0.932317i
\(498\) 20.7846i 0.931381i
\(499\) 6.50000 + 11.2583i 0.290980 + 0.503992i 0.974042 0.226369i \(-0.0726854\pi\)
−0.683062 + 0.730361i \(0.739352\pi\)
\(500\) 0 0
\(501\) 20.7846i 0.928588i
\(502\) −10.5000 + 18.1865i −0.468638 + 0.811705i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) −6.00000 −0.267261
\(505\) 0 0
\(506\) −9.00000 + 15.5885i −0.400099 + 0.692991i
\(507\) −13.5000 + 7.79423i −0.599556 + 0.346154i
\(508\) −1.00000 1.73205i −0.0443678 0.0768473i
\(509\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(510\) 0 0
\(511\) −11.0000 + 19.0526i −0.486611 + 0.842836i
\(512\) 1.00000 0.0441942
\(513\) 5.19615i 0.229416i
\(514\) −21.0000 −0.926270
\(515\) 0 0
\(516\) 1.50000 + 0.866025i 0.0660338 + 0.0381246i
\(517\) −9.00000 15.5885i −0.395820 0.685580i
\(518\) 4.00000 + 6.92820i 0.175750 + 0.304408i
\(519\) −9.00000 + 5.19615i −0.395056 + 0.228086i
\(520\) 0 0
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) 9.00000 15.5885i 0.393919 0.682288i
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 0 0
\(525\) 17.3205i 0.755929i
\(526\) −9.00000 15.5885i −0.392419 0.679689i
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) 5.19615i 0.226134i
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 4.50000 7.79423i 0.195283 0.338241i
\(532\) −2.00000 −0.0867110
\(533\) −9.00000 + 15.5885i −0.389833 + 0.675211i
\(534\) 9.00000 5.19615i 0.389468 0.224860i
\(535\) 0 0
\(536\) −2.50000 4.33013i −0.107984 0.187033i
\(537\) −18.0000 10.3923i −0.776757 0.448461i
\(538\) 12.0000 20.7846i 0.517357 0.896088i
\(539\) 9.00000 0.387657
\(540\) 0 0
\(541\) −4.00000 −0.171973 −0.0859867 0.996296i \(-0.527404\pi\)
−0.0859867 + 0.996296i \(0.527404\pi\)
\(542\) −10.0000 + 17.3205i −0.429537 + 0.743980i
\(543\) −21.0000 12.1244i −0.901196 0.520306i
\(544\) 1.50000 + 2.59808i 0.0643120 + 0.111392i
\(545\) 0 0
\(546\) 6.00000 3.46410i 0.256776 0.148250i
\(547\) 0.500000 0.866025i 0.0213785 0.0370286i −0.855138 0.518400i \(-0.826528\pi\)
0.876517 + 0.481371i \(0.159861\pi\)
\(548\) −3.00000 −0.128154
\(549\) −24.0000 −1.02430
\(550\) 15.0000 0.639602
\(551\) 3.00000 5.19615i 0.127804 0.221364i
\(552\) 10.3923i 0.442326i
\(553\) 4.00000 + 6.92820i 0.170097 + 0.294617i
\(554\) 5.00000 + 8.66025i 0.212430 + 0.367939i
\(555\) 0 0
\(556\) 9.50000 16.4545i 0.402890 0.697826i
\(557\) −30.0000 −1.27114 −0.635570 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) −6.00000 10.3923i −0.254000 0.439941i
\(559\) −2.00000 −0.0845910
\(560\) 0 0
\(561\) 13.5000 7.79423i 0.569970 0.329073i
\(562\) −3.00000 5.19615i −0.126547 0.219186i
\(563\) 19.5000 + 33.7750i 0.821827 + 1.42345i 0.904320 + 0.426855i \(0.140378\pi\)
−0.0824933 + 0.996592i \(0.526288\pi\)
\(564\) 9.00000 + 5.19615i 0.378968 + 0.218797i
\(565\) 0 0
\(566\) −4.00000 −0.168133
\(567\) −9.00000 15.5885i −0.377964 0.654654i
\(568\) −12.0000 −0.503509
\(569\) −22.5000 + 38.9711i −0.943249 + 1.63376i −0.184030 + 0.982921i \(0.558914\pi\)
−0.759220 + 0.650835i \(0.774419\pi\)
\(570\) 0 0
\(571\) 18.5000 + 32.0429i 0.774201 + 1.34096i 0.935243 + 0.354008i \(0.115181\pi\)
−0.161042 + 0.986948i \(0.551485\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) −27.0000 + 15.5885i −1.12794 + 0.651217i
\(574\) −9.00000 + 15.5885i −0.375653 + 0.650650i
\(575\) 30.0000 1.25109
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 8.66025i 0.359908i
\(580\) 0 0
\(581\) −12.0000 20.7846i −0.497844 0.862291i
\(582\) 8.66025i 0.358979i
\(583\) 18.0000 31.1769i 0.745484 1.29122i
\(584\) 11.0000 0.455183
\(585\) 0 0
\(586\) 30.0000 1.23929
\(587\) 4.50000 7.79423i 0.185735 0.321702i −0.758089 0.652151i \(-0.773867\pi\)
0.943824 + 0.330449i \(0.107200\pi\)
\(588\) −4.50000 + 2.59808i −0.185577 + 0.107143i
\(589\) −2.00000 3.46410i −0.0824086 0.142736i
\(590\) 0 0
\(591\) 18.0000 + 10.3923i 0.740421 + 0.427482i
\(592\) 2.00000 3.46410i 0.0821995 0.142374i
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 13.5000 7.79423i 0.553912 0.319801i
\(595\) 0 0
\(596\) 3.00000 5.19615i 0.122885 0.212843i
\(597\) 15.0000 + 8.66025i 0.613909 + 0.354441i
\(598\) 6.00000 + 10.3923i 0.245358 + 0.424973i
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) −7.50000 + 4.33013i −0.306186 + 0.176777i
\(601\) 18.5000 32.0429i 0.754631 1.30706i −0.190927 0.981604i \(-0.561149\pi\)
0.945558 0.325455i \(-0.105517\pi\)
\(602\) −2.00000 −0.0815139
\(603\) 7.50000 12.9904i 0.305424 0.529009i
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 0 0
\(607\) 14.0000 + 24.2487i 0.568242 + 0.984225i 0.996740 + 0.0806818i \(0.0257098\pi\)
−0.428497 + 0.903543i \(0.640957\pi\)
\(608\) 0.500000 + 0.866025i 0.0202777 + 0.0351220i
\(609\) 20.7846i 0.842235i
\(610\) 0 0
\(611\) −12.0000 −0.485468
\(612\) −4.50000 + 7.79423i −0.181902 + 0.315063i
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 3.50000 6.06218i 0.141249 0.244650i
\(615\) 0 0
\(616\) 3.00000 + 5.19615i 0.120873 + 0.209359i
\(617\) −13.5000 23.3827i −0.543490 0.941351i −0.998700 0.0509678i \(-0.983769\pi\)
0.455211 0.890384i \(-0.349564\pi\)
\(618\) −21.0000 12.1244i −0.844744 0.487713i
\(619\) −17.5000 + 30.3109i −0.703384 + 1.21830i 0.263887 + 0.964554i \(0.414995\pi\)
−0.967271 + 0.253744i \(0.918338\pi\)
\(620\) 0 0
\(621\) 27.0000 15.5885i 1.08347 0.625543i
\(622\) −18.0000 −0.721734
\(623\) −6.00000 + 10.3923i −0.240385 + 0.416359i
\(624\) −3.00000 1.73205i −0.120096 0.0693375i
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) −14.5000 25.1147i −0.579537 1.00379i
\(627\) 4.50000 2.59808i 0.179713 0.103757i
\(628\) 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
\(633\) 34.6410i 1.37686i
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) 0 0
\(636\) 20.7846i 0.824163i
\(637\) 3.00000 5.19615i 0.118864 0.205879i
\(638\) −18.0000 −0.712627
\(639\) −18.0000 31.1769i −0.712069 1.23334i
\(640\) 0 0
\(641\) 1.50000 2.59808i 0.0592464 0.102618i −0.834881 0.550431i \(-0.814464\pi\)
0.894127 + 0.447813i \(0.147797\pi\)
\(642\) 4.50000 2.59808i 0.177601 0.102538i
\(643\) −11.5000 19.9186i −0.453516 0.785512i 0.545086 0.838380i \(-0.316497\pi\)
−0.998602 + 0.0528680i \(0.983164\pi\)
\(644\) 6.00000 + 10.3923i 0.236433 + 0.409514i
\(645\) 0 0
\(646\) −1.50000 + 2.59808i −0.0590167 + 0.102220i
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) −4.50000 + 7.79423i −0.176777 + 0.306186i
\(649\) −9.00000 −0.353281
\(650\) 5.00000 8.66025i 0.196116 0.339683i
\(651\) 12.0000 + 6.92820i 0.470317 + 0.271538i
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i \(-0.129211\pi\)
−0.801337 + 0.598213i \(0.795878\pi\)
\(654\) −24.0000 + 13.8564i −0.938474 + 0.541828i
\(655\) 0 0
\(656\) 9.00000 0.351391
\(657\) 16.5000 + 28.5788i 0.643726 + 1.11497i
\(658\) −12.0000 −0.467809
\(659\) 18.0000 31.1769i 0.701180 1.21448i −0.266872 0.963732i \(-0.585990\pi\)
0.968052 0.250748i \(-0.0806766\pi\)
\(660\) 0 0
\(661\) 2.00000 + 3.46410i 0.0777910 + 0.134738i 0.902297 0.431116i \(-0.141880\pi\)
−0.824506 + 0.565854i \(0.808547\pi\)
\(662\) 2.00000 + 3.46410i 0.0777322 + 0.134636i
\(663\) 10.3923i 0.403604i
\(664\) −6.00000 + 10.3923i −0.232845 + 0.403300i
\(665\) 0 0
\(666\) 12.0000 0.464991
\(667\) −36.0000 −1.39393
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) 39.0000 22.5167i 1.50783 0.870544i
\(670\) 0 0
\(671\) 12.0000 + 20.7846i 0.463255 + 0.802381i
\(672\) −3.00000 1.73205i −0.115728 0.0668153i
\(673\) 11.0000 19.0526i 0.424019 0.734422i −0.572309 0.820038i \(-0.693952\pi\)
0.996328 + 0.0856156i \(0.0272857\pi\)
\(674\) −1.00000 −0.0385186
\(675\) −22.5000 12.9904i −0.866025 0.500000i
\(676\) −9.00000 −0.346154
\(677\) −18.0000 + 31.1769i −0.691796 + 1.19823i 0.279453 + 0.960159i \(0.409847\pi\)
−0.971249 + 0.238067i \(0.923486\pi\)
\(678\) −9.00000 5.19615i −0.345643 0.199557i
\(679\) −5.00000 8.66025i −0.191882 0.332350i
\(680\) 0 0
\(681\) 31.5000 18.1865i 1.20708 0.696909i
\(682\) −6.00000 + 10.3923i −0.229752 + 0.397942i
\(683\) −9.00000 −0.344375 −0.172188 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) −1.50000 + 2.59808i −0.0573539 + 0.0993399i
\(685\) 0 0
\(686\) 10.0000 17.3205i 0.381802 0.661300i
\(687\) 24.2487i 0.925146i
\(688\) 0.500000 + 0.866025i 0.0190623 + 0.0330169i
\(689\) −12.0000 20.7846i −0.457164 0.791831i
\(690\) 0 0
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) −6.00000 −0.228086
\(693\) −9.00000 + 15.5885i −0.341882 + 0.592157i
\(694\) 33.0000 1.25266
\(695\) 0 0
\(696\) 9.00000 5.19615i 0.341144 0.196960i
\(697\) 13.5000 + 23.3827i 0.511349 + 0.885682i
\(698\) 8.00000 + 13.8564i 0.302804 + 0.524473i
\(699\) −4.50000 2.59808i −0.170206 0.0982683i
\(700\) 5.00000 8.66025i 0.188982 0.327327i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 10.3923i 0.392232i
\(703\) 4.00000 0.150863
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 0 0
\(706\) 10.5000 + 18.1865i 0.395173 + 0.684459i
\(707\) 0 0
\(708\) 4.50000 2.59808i 0.169120 0.0976417i
\(709\) 2.00000 3.46410i 0.0751116 0.130097i −0.826023 0.563636i \(-0.809402\pi\)
0.901135 + 0.433539i \(0.142735\pi\)
\(710\) 0 0
\(711\) 12.0000 0.450035
\(712\) 6.00000 0.224860
\(713\) −12.0000 + 20.7846i −0.449404 + 0.778390i
\(714\) 10.3923i 0.388922i
\(715\) 0 0
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) 10.3923i 0.388108i
\(718\) 9.00000 15.5885i 0.335877 0.581756i
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) 0 0
\(721\) 28.0000 1.04277
\(722\) 9.00000 15.5885i 0.334945 0.580142i
\(723\) −10.5000 + 6.06218i −0.390499 + 0.225455i
\(724\) −7.00000 12.1244i −0.260153 0.450598i
\(725\) 15.0000 + 25.9808i 0.557086 + 0.964901i
\(726\) 3.00000 + 1.73205i 0.111340 + 0.0642824i
\(727\) −13.0000 + 22.5167i −0.482143 + 0.835097i −0.999790 0.0204978i \(-0.993475\pi\)
0.517647 + 0.855595i \(0.326808\pi\)
\(728\) 4.00000 0.148250
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −1.50000 + 2.59808i −0.0554795 + 0.0960933i
\(732\) −12.0000 6.92820i −0.443533 0.256074i
\(733\) −7.00000 12.1244i −0.258551 0.447823i 0.707303 0.706910i \(-0.249912\pi\)
−0.965854 + 0.259087i \(0.916578\pi\)
\(734\) 14.0000 + 24.2487i 0.516749 + 0.895036i
\(735\) 0 0
\(736\) 3.00000 5.19615i 0.110581 0.191533i
\(737\) −15.0000 −0.552532
\(738\) 13.5000 + 23.3827i 0.496942 + 0.860729i
\(739\) 47.0000 1.72892 0.864461 0.502699i \(-0.167660\pi\)
0.864461 + 0.502699i \(0.167660\pi\)
\(740\) 0 0
\(741\) 3.46410i 0.127257i
\(742\) −12.0000 20.7846i −0.440534 0.763027i
\(743\) −3.00000 5.19615i −0.110059 0.190628i 0.805735 0.592277i \(-0.201771\pi\)
−0.915794 + 0.401648i \(0.868437\pi\)
\(744\) 6.92820i 0.254000i
\(745\) 0 0
\(746\) −34.0000 −1.24483
\(747\) −36.0000 −1.31717
\(748\) 9.00000 0.329073
\(749\) −3.00000 + 5.19615i −0.109618 + 0.189863i
\(750\) 0 0
\(751\) −4.00000 6.92820i −0.145962 0.252814i 0.783769 0.621052i \(-0.213294\pi\)
−0.929731 + 0.368238i \(0.879961\pi\)
\(752\) 3.00000 + 5.19615i 0.109399 + 0.189484i
\(753\) −31.5000 18.1865i −1.14792 0.662754i
\(754\) −6.00000 + 10.3923i −0.218507 + 0.378465i
\(755\) 0 0
\(756\) 10.3923i 0.377964i
\(757\) 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
\(759\) −27.0000 15.5885i −0.980038 0.565825i
\(760\) 0 0
\(761\) −21.0000 36.3731i −0.761249 1.31852i −0.942207 0.335032i \(-0.891253\pi\)
0.180957 0.983491i \(-0.442080\pi\)
\(762\) 3.00000 1.73205i 0.108679 0.0627456i
\(763\) 16.0000 27.7128i 0.579239 1.00327i
\(764\) −18.0000 −0.651217
\(765\) 0 0
\(766\) 0 0
\(767\) −3.00000 + 5.19615i −0.108324 + 0.187622i
\(768\) 1.73205i 0.0625000i
\(769\) −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
\(771\) 36.3731i 1.30994i
\(772\) −2.50000 + 4.33013i −0.0899770 + 0.155845i
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) −1.50000 + 2.59808i −0.0539164 + 0.0933859i
\(775\) 20.0000 0.718421
\(776\) −2.50000 + 4.33013i −0.0897448 + 0.155443i
\(777\) −12.0000 + 6.92820i −0.430498 + 0.248548i
\(778\) −9.00000 15.5885i −0.322666 0.558873i
\(779\) 4.50000 + 7.79423i 0.161229 + 0.279257i
\(780\) 0 0
\(781\) −18.0000 + 31.1769i