Properties

Label 18.2.c.a.13.1
Level $18$
Weight $2$
Character 18.13
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 13.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 18.13
Dual form 18.2.c.a.7.1

$q$-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 \(\left(\mathbb{Z}/18\mathbb{Z}\right)^\times\).

\(n\) \(11\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 1.50000 + 0.866025i 0.612372 + 0.353553i
\(7\) −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) 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 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 1.73205i 0.500000i
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −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 −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) −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 −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 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
\(33\) −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 0.264704 + 0.964330i \(0.414726\pi\)
−0.967486 + 0.252924i \(0.918608\pi\)
\(42\) 3.46410i 0.534522i
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 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 −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) 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
\(63\) −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 −0.977356 0.211604i \(-0.932131\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) 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 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 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 −0.980982 0.194099i \(-0.937822\pi\)
0.322396 0.946605i \(-0.395512\pi\)
\(84\) −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 0.710742 0.703452i \(-0.248359\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) −3.00000 −0.303046
\(99\) 9.00000 0.904534
\(100\) −5.00000 −0.500000
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) −4.50000 2.59808i −0.445566 0.257248i
\(103\) −7.00000 + 12.1244i −0.689730 + 1.19465i 0.282194 + 0.959357i \(0.408938\pi\)
−0.971925 + 0.235291i \(0.924396\pi\)
\(104\) −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 −0.971930 0.235269i \(-0.924403\pi\)
0.689714 + 0.724082i \(0.257736\pi\)
\(114\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 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 0.922961 0.384893i \(-0.125762\pi\)
−0.794808 + 0.606861i \(0.792428\pi\)
\(138\) 9.00000 5.19615i 0.766131 0.442326i
\(139\) 9.50000 16.4545i 0.805779 1.39565i −0.109984 0.993933i \(-0.535080\pi\)
0.915764 0.401718i \(-0.131587\pi\)
\(140\) 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 −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 8.66025i 0.707107i
\(151\) 5.00000 + 8.66025i 0.406894 + 0.704761i 0.994540 0.104357i \(-0.0332784\pi\)
−0.587646 + 0.809118i \(0.699945\pi\)
\(152\) −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 −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) 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 −0.534875 0.844931i \(-0.679641\pi\)
0.999169 + 0.0407502i \(0.0129748\pi\)
\(168\) 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 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 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 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) −1.50000 + 0.866025i −0.108253 + 0.0625000i
\(193\) −2.50000 + 4.33013i −0.179954 + 0.311689i −0.941865 0.335993i \(-0.890928\pi\)
0.761911 + 0.647682i \(0.224262\pi\)
\(194\) −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 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) −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 −0.861435 0.507869i \(-0.830434\pi\)
−0.00910984 0.999959i \(-0.502900\pi\)
\(224\) 2.00000 0.133631
\(225\) 15.0000 1.00000
\(226\) 6.00000 0.399114
\(227\) −10.5000 18.1865i −0.696909 1.20708i −0.969533 0.244962i \(-0.921225\pi\)
0.272623 0.962121i \(-0.412109\pi\)
\(228\) 1.73205i 0.114708i
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 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 −0.946590 0.322440i \(-0.895497\pi\)
0.752536 + 0.658551i \(0.228830\pi\)
\(240\) 0 0
\(241\) 3.50000 + 6.06218i 0.225455 + 0.390499i 0.956456 0.291877i \(-0.0942799\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) −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 −0.326929 0.945049i \(-0.606014\pi\)
0.981901 0.189396i \(-0.0606529\pi\)
\(258\) 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 −0.997906 0.0646755i \(-0.979399\pi\)
0.442943 0.896550i \(-0.353935\pi\)
\(264\) −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 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) −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 0.762561 0.646916i \(-0.223942\pi\)
−0.941526 + 0.336939i \(0.890608\pi\)
\(282\) 10.3923i 0.618853i
\(283\) 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
\(287\) 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 −0.0209480 + 0.999781i \(0.506668\pi\)
−0.855361 + 0.518032i \(0.826665\pi\)
\(294\) 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 −0.489585 0.871956i \(-0.662852\pi\)
0.999928 0.0119847i \(-0.00381495\pi\)
\(312\) 3.46410i 0.196116i
\(313\) −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 \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 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 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) 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 −0.852086 0.523402i \(-0.824663\pi\)
0.879322 + 0.476227i \(0.157996\pi\)
\(338\) 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 −0.0409337 + 0.999162i \(0.513033\pi\)
−0.844833 + 0.535031i \(0.820300\pi\)
\(348\) −9.00000 + 5.19615i −0.482451 + 0.278543i
\(349\) 8.00000 + 13.8564i 0.428230 + 0.741716i 0.996716 0.0809766i \(-0.0258039\pi\)
−0.568486 + 0.822693i \(0.692471\pi\)
\(350\) −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 0.997592 + 0.0693543i \(0.0220939\pi\)
−0.438733 + 0.898617i \(0.644573\pi\)
\(354\) −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 0.956544 + 0.291587i \(0.0941834\pi\)
−0.225750 + 0.974185i \(0.572483\pi\)
\(368\) −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 0.0291379 0.999575i \(-0.490724\pi\)
0.851089 0.525022i \(-0.175943\pi\)
\(374\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 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 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) 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 −0.302556 0.953131i \(-0.597840\pi\)
0.976714 0.214544i \(-0.0688266\pi\)
\(402\) −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 −0.995968 0.0897044i \(-0.971408\pi\)
0.575670 + 0.817682i \(0.304741\pi\)
\(410\) 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 −0.681426 0.731887i \(-0.738640\pi\)
0.974546 + 0.224189i \(0.0719734\pi\)
\(420\) 0 0
\(421\) −10.0000 17.3205i −0.487370 0.844150i 0.512524 0.858673i \(-0.328710\pi\)
−0.999895 + 0.0145228i \(0.995377\pi\)
\(422\) 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 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 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 0.828190 0.560448i \(-0.189371\pi\)
−0.899457 + 0.437009i \(0.856038\pi\)
\(444\) 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 0.595818 0.803120i \(-0.296828\pi\)
−0.993431 + 0.114433i \(0.963495\pi\)
\(458\) 14.0000 0.654177
\(459\) 15.5885i 0.727607i
\(460\) 0 0
\(461\) 15.0000 + 25.9808i 0.698620 + 1.21004i 0.968945 + 0.247276i \(0.0795353\pi\)
−0.270326 + 0.962769i \(0.587131\pi\)
\(462\) 9.00000 5.19615i 0.418718 0.241747i
\(463\) −10.0000 + 17.3205i −0.464739 + 0.804952i −0.999190 0.0402476i \(-0.987185\pi\)
0.534450 + 0.845200i \(0.320519\pi\)
\(464\) −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 0.723681 + 0.690134i \(0.242449\pi\)
0.235833 + 0.971794i \(0.424218\pi\)
\(480\) 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 −0.645675 0.763612i \(-0.723424\pi\)
0.984145 + 0.177365i \(0.0567572\pi\)
\(492\) 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 −0.683062 0.730361i \(-0.739352\pi\)
0.974042 + 0.226369i \(0.0726854\pi\)
\(500\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(510\) 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 0.876517 0.481371i \(-0.159861\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) −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 −0.0824933 0.996592i \(-0.526288\pi\)
0.904320 0.426855i \(-0.140378\pi\)
\(564\) 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 −0.759220 0.650835i \(-0.774419\pi\)
−0.184030 0.982921i \(-0.558914\pi\)
\(570\) 0 0
\(571\) 18.5000 32.0429i 0.774201 1.34096i −0.161042 0.986948i \(-0.551485\pi\)
0.935243 0.354008i \(-0.115181\pi\)
\(572\) 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 0.943824 0.330449i \(-0.107200\pi\)
−0.758089 + 0.652151i \(0.773867\pi\)
\(588\) −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 −0.962175 0.272433i \(-0.912172\pi\)
0.717021 + 0.697051i \(0.245505\pi\)
\(600\) −7.50000 4.33013i −0.306186 0.176777i
\(601\) 18.5000 + 32.0429i 0.754631 + 1.30706i 0.945558 + 0.325455i \(0.105517\pi\)
−0.190927 + 0.981604i \(0.561149\pi\)
\(602\) −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 −0.428497 0.903543i \(-0.640957\pi\)
0.996740 0.0806818i \(-0.0257098\pi\)
\(608\) 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 0.455211 + 0.890384i \(0.349564\pi\)
−0.998700 + 0.0509678i \(0.983769\pi\)
\(618\) −21.0000 + 12.1244i −0.844744 + 0.487713i
\(619\) −17.5000 30.3109i −0.703384 1.21830i −0.967271 0.253744i \(-0.918338\pi\)
0.263887 0.964554i \(-0.414995\pi\)
\(620\) 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 0.894127 0.447813i \(-0.147797\pi\)
−0.834881 + 0.550431i \(0.814464\pi\)
\(642\) 4.50000 + 2.59808i 0.177601 + 0.102538i
\(643\) −11.5000 + 19.9186i −0.453516 + 0.785512i −0.998602 0.0528680i \(-0.983164\pi\)
0.545086 + 0.838380i \(0.316497\pi\)
\(644\) 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 −0.801337 0.598213i \(-0.795878\pi\)
0.918736 + 0.394872i \(0.129211\pi\)
\(654\) −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 0.968052 + 0.250748i \(0.0806766\pi\)
−0.266872 + 0.963732i \(0.585990\pi\)
\(660\) 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
\(663\) 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 0.996328 0.0856156i \(-0.0272857\pi\)
−0.572309 + 0.820038i \(0.693952\pi\)
\(674\) −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 −0.971249 0.238067i \(-0.923486\pi\)
0.279453 0.960159i \(-0.409847\pi\)
\(678\) −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 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) −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 0.901135 0.433539i \(-0.142735\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(710\) 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 0.517647 0.855595i \(-0.326808\pi\)
−0.999790 + 0.0204978i \(0.993475\pi\)
\(728\) 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 −0.965854 0.259087i \(-0.916578\pi\)
0.707303 + 0.706910i \(0.249912\pi\)
\(734\) 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 −0.915794 0.401648i \(-0.868437\pi\)
0.805735 + 0.592277i \(0.201771\pi\)
\(744\) 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 −0.929731 0.368238i \(-0.879961\pi\)
0.783769 + 0.621052i \(0.213294\pi\)
\(752\) 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 0.180957 + 0.983491i \(0.442080\pi\)
−0.942207 + 0.335032i \(0.891253\pi\)
\(762\) 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 −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) 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