Properties

Label 546.2.q.a.251.1
Level $546$
Weight $2$
Character 546.251
Analytic conductor $4.360$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 251.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.251
Dual form 546.2.q.a.335.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(3.00000 + 1.73205i) q^{10} +(1.50000 - 2.59808i) q^{11} +1.73205i q^{12} +(-3.50000 + 0.866025i) q^{13} +(2.00000 + 1.73205i) q^{14} +(-3.00000 + 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} -3.00000 q^{18} +(3.50000 + 6.06218i) q^{19} +(-3.00000 + 1.73205i) q^{20} +(-3.00000 + 3.46410i) q^{21} +(1.50000 + 2.59808i) q^{22} +(-6.00000 - 3.46410i) q^{23} +(-1.50000 - 0.866025i) q^{24} -7.00000 q^{25} +(1.00000 - 3.46410i) q^{26} -5.19615i q^{27} +(-2.50000 + 0.866025i) q^{28} +(1.50000 + 0.866025i) q^{29} +(-3.00000 - 5.19615i) q^{30} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.50000 + 2.59808i) q^{33} +3.00000 q^{34} +(-9.00000 - 1.73205i) q^{35} +(1.50000 - 2.59808i) q^{36} +(-6.00000 - 3.46410i) q^{37} -7.00000 q^{38} +(6.00000 + 1.73205i) q^{39} -3.46410i q^{40} +(-4.50000 - 2.59808i) q^{41} +(-1.50000 - 4.33013i) q^{42} +(4.00000 + 6.92820i) q^{43} -3.00000 q^{44} +(9.00000 - 5.19615i) q^{45} +(6.00000 - 3.46410i) q^{46} +8.66025i q^{47} +(1.50000 - 0.866025i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(3.50000 - 6.06218i) q^{50} +5.19615i q^{51} +(2.50000 + 2.59808i) q^{52} -8.66025i q^{53} +(4.50000 + 2.59808i) q^{54} +(-9.00000 - 5.19615i) q^{55} +(0.500000 - 2.59808i) q^{56} -12.1244i q^{57} +(-1.50000 + 0.866025i) q^{58} +(9.00000 - 5.19615i) q^{59} +6.00000 q^{60} +(-4.50000 + 2.59808i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(7.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(3.00000 + 12.1244i) q^{65} -5.19615i q^{66} +(-1.50000 + 2.59808i) q^{68} +(6.00000 + 10.3923i) q^{69} +(6.00000 - 6.92820i) q^{70} +(-3.00000 - 5.19615i) q^{71} +(1.50000 + 2.59808i) q^{72} +4.00000 q^{73} +(6.00000 - 3.46410i) q^{74} +(10.5000 + 6.06218i) q^{75} +(3.50000 - 6.06218i) q^{76} +(-6.00000 - 5.19615i) q^{77} +(-4.50000 + 4.33013i) q^{78} -11.0000 q^{79} +(3.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(4.50000 - 2.59808i) q^{82} +13.8564i q^{83} +(4.50000 + 0.866025i) q^{84} +(-9.00000 + 5.19615i) q^{85} -8.00000 q^{86} +(-1.50000 - 2.59808i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-7.50000 - 4.33013i) q^{89} +10.3923i q^{90} +(0.500000 + 9.52628i) q^{91} +6.92820i q^{92} +(-6.00000 - 3.46410i) q^{93} +(-7.50000 - 4.33013i) q^{94} +(21.0000 - 12.1244i) q^{95} +1.73205i q^{96} +(-1.00000 - 1.73205i) q^{97} +(5.50000 - 4.33013i) q^{98} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - 3q^{3} - q^{4} + 3q^{6} + q^{7} + 2q^{8} + 3q^{9} + O(q^{10}) \) \( 2q - q^{2} - 3q^{3} - q^{4} + 3q^{6} + q^{7} + 2q^{8} + 3q^{9} + 6q^{10} + 3q^{11} - 7q^{13} + 4q^{14} - 6q^{15} - q^{16} - 3q^{17} - 6q^{18} + 7q^{19} - 6q^{20} - 6q^{21} + 3q^{22} - 12q^{23} - 3q^{24} - 14q^{25} + 2q^{26} - 5q^{28} + 3q^{29} - 6q^{30} + 8q^{31} - q^{32} - 9q^{33} + 6q^{34} - 18q^{35} + 3q^{36} - 12q^{37} - 14q^{38} + 12q^{39} - 9q^{41} - 3q^{42} + 8q^{43} - 6q^{44} + 18q^{45} + 12q^{46} + 3q^{48} - 13q^{49} + 7q^{50} + 5q^{52} + 9q^{54} - 18q^{55} + q^{56} - 3q^{58} + 18q^{59} + 12q^{60} - 9q^{61} - 4q^{62} + 15q^{63} + 2q^{64} + 6q^{65} - 3q^{68} + 12q^{69} + 12q^{70} - 6q^{71} + 3q^{72} + 8q^{73} + 12q^{74} + 21q^{75} + 7q^{76} - 12q^{77} - 9q^{78} - 22q^{79} + 6q^{80} - 9q^{81} + 9q^{82} + 9q^{84} - 18q^{85} - 16q^{86} - 3q^{87} + 3q^{88} - 15q^{89} + q^{91} - 12q^{93} - 15q^{94} + 42q^{95} - 2q^{97} + 11q^{98} + 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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
\(5\) 3.46410i 1.54919i −0.632456 0.774597i \(-0.717953\pi\)
0.632456 0.774597i \(-0.282047\pi\)
\(6\) 1.50000 0.866025i 0.612372 0.353553i
\(7\) 0.500000 2.59808i 0.188982 0.981981i
\(8\) 1.00000 0.353553
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 3.00000 + 1.73205i 0.948683 + 0.547723i
\(11\) 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
\(13\) −3.50000 + 0.866025i −0.970725 + 0.240192i
\(14\) 2.00000 + 1.73205i 0.534522 + 0.462910i
\(15\) −3.00000 + 5.19615i −0.774597 + 1.34164i
\(16\) −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 \(0.951855\pi\)
\(18\) −3.00000 −0.707107
\(19\) 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i \(0.130073\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) −3.00000 + 1.73205i −0.670820 + 0.387298i
\(21\) −3.00000 + 3.46410i −0.654654 + 0.755929i
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) −6.00000 3.46410i −1.25109 0.722315i −0.279761 0.960070i \(-0.590255\pi\)
−0.971325 + 0.237754i \(0.923589\pi\)
\(24\) −1.50000 0.866025i −0.306186 0.176777i
\(25\) −7.00000 −1.40000
\(26\) 1.00000 3.46410i 0.196116 0.679366i
\(27\) 5.19615i 1.00000i
\(28\) −2.50000 + 0.866025i −0.472456 + 0.163663i
\(29\) 1.50000 + 0.866025i 0.278543 + 0.160817i 0.632764 0.774345i \(-0.281920\pi\)
−0.354221 + 0.935162i \(0.615254\pi\)
\(30\) −3.00000 5.19615i −0.547723 0.948683i
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −4.50000 + 2.59808i −0.783349 + 0.452267i
\(34\) 3.00000 0.514496
\(35\) −9.00000 1.73205i −1.52128 0.292770i
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) −6.00000 3.46410i −0.986394 0.569495i −0.0821995 0.996616i \(-0.526194\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) −7.00000 −1.13555
\(39\) 6.00000 + 1.73205i 0.960769 + 0.277350i
\(40\) 3.46410i 0.547723i
\(41\) −4.50000 2.59808i −0.702782 0.405751i 0.105601 0.994409i \(-0.466323\pi\)
−0.808383 + 0.588657i \(0.799657\pi\)
\(42\) −1.50000 4.33013i −0.231455 0.668153i
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) −3.00000 −0.452267
\(45\) 9.00000 5.19615i 1.34164 0.774597i
\(46\) 6.00000 3.46410i 0.884652 0.510754i
\(47\) 8.66025i 1.26323i 0.775283 + 0.631614i \(0.217607\pi\)
−0.775283 + 0.631614i \(0.782393\pi\)
\(48\) 1.50000 0.866025i 0.216506 0.125000i
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 3.50000 6.06218i 0.494975 0.857321i
\(51\) 5.19615i 0.727607i
\(52\) 2.50000 + 2.59808i 0.346688 + 0.360288i
\(53\) 8.66025i 1.18958i −0.803882 0.594789i \(-0.797236\pi\)
0.803882 0.594789i \(-0.202764\pi\)
\(54\) 4.50000 + 2.59808i 0.612372 + 0.353553i
\(55\) −9.00000 5.19615i −1.21356 0.700649i
\(56\) 0.500000 2.59808i 0.0668153 0.347183i
\(57\) 12.1244i 1.60591i
\(58\) −1.50000 + 0.866025i −0.196960 + 0.113715i
\(59\) 9.00000 5.19615i 1.17170 0.676481i 0.217620 0.976034i \(-0.430171\pi\)
0.954080 + 0.299552i \(0.0968372\pi\)
\(60\) 6.00000 0.774597
\(61\) −4.50000 + 2.59808i −0.576166 + 0.332650i −0.759608 0.650381i \(-0.774609\pi\)
0.183442 + 0.983030i \(0.441276\pi\)
\(62\) −2.00000 + 3.46410i −0.254000 + 0.439941i
\(63\) 7.50000 2.59808i 0.944911 0.327327i
\(64\) 1.00000 0.125000
\(65\) 3.00000 + 12.1244i 0.372104 + 1.50384i
\(66\) 5.19615i 0.639602i
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) −1.50000 + 2.59808i −0.181902 + 0.315063i
\(69\) 6.00000 + 10.3923i 0.722315 + 1.25109i
\(70\) 6.00000 6.92820i 0.717137 0.828079i
\(71\) −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) 1.50000 + 2.59808i 0.176777 + 0.306186i
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 6.00000 3.46410i 0.697486 0.402694i
\(75\) 10.5000 + 6.06218i 1.21244 + 0.700000i
\(76\) 3.50000 6.06218i 0.401478 0.695379i
\(77\) −6.00000 5.19615i −0.683763 0.592157i
\(78\) −4.50000 + 4.33013i −0.509525 + 0.490290i
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) 3.00000 + 1.73205i 0.335410 + 0.193649i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 4.50000 2.59808i 0.496942 0.286910i
\(83\) 13.8564i 1.52094i 0.649374 + 0.760469i \(0.275031\pi\)
−0.649374 + 0.760469i \(0.724969\pi\)
\(84\) 4.50000 + 0.866025i 0.490990 + 0.0944911i
\(85\) −9.00000 + 5.19615i −0.976187 + 0.563602i
\(86\) −8.00000 −0.862662
\(87\) −1.50000 2.59808i −0.160817 0.278543i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −7.50000 4.33013i −0.794998 0.458993i 0.0467209 0.998908i \(-0.485123\pi\)
−0.841719 + 0.539915i \(0.818456\pi\)
\(90\) 10.3923i 1.09545i
\(91\) 0.500000 + 9.52628i 0.0524142 + 0.998625i
\(92\) 6.92820i 0.722315i
\(93\) −6.00000 3.46410i −0.622171 0.359211i
\(94\) −7.50000 4.33013i −0.773566 0.446619i
\(95\) 21.0000 12.1244i 2.15455 1.24393i
\(96\) 1.73205i 0.176777i
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 5.50000 4.33013i 0.555584 0.437409i
\(99\) 9.00000 0.904534
\(100\) 3.50000 + 6.06218i 0.350000 + 0.606218i
\(101\) 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
\(103\) 3.46410i 0.341328i −0.985329 0.170664i \(-0.945409\pi\)
0.985329 0.170664i \(-0.0545913\pi\)
\(104\) −3.50000 + 0.866025i −0.343203 + 0.0849208i
\(105\) 12.0000 + 10.3923i 1.17108 + 1.01419i
\(106\) 7.50000 + 4.33013i 0.728464 + 0.420579i
\(107\) 4.50000 + 2.59808i 0.435031 + 0.251166i 0.701488 0.712681i \(-0.252519\pi\)
−0.266456 + 0.963847i \(0.585853\pi\)
\(108\) −4.50000 + 2.59808i −0.433013 + 0.250000i
\(109\) 3.46410i 0.331801i 0.986143 + 0.165900i \(0.0530530\pi\)
−0.986143 + 0.165900i \(0.946947\pi\)
\(110\) 9.00000 5.19615i 0.858116 0.495434i
\(111\) 6.00000 + 10.3923i 0.569495 + 0.986394i
\(112\) 2.00000 + 1.73205i 0.188982 + 0.163663i
\(113\) 12.0000 6.92820i 1.12887 0.651751i 0.185216 0.982698i \(-0.440702\pi\)
0.943649 + 0.330947i \(0.107368\pi\)
\(114\) 10.5000 + 6.06218i 0.983415 + 0.567775i
\(115\) −12.0000 + 20.7846i −1.11901 + 1.93817i
\(116\) 1.73205i 0.160817i
\(117\) −7.50000 7.79423i −0.693375 0.720577i
\(118\) 10.3923i 0.956689i
\(119\) −7.50000 + 2.59808i −0.687524 + 0.238165i
\(120\) −3.00000 + 5.19615i −0.273861 + 0.474342i
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 5.19615i 0.470438i
\(123\) 4.50000 + 7.79423i 0.405751 + 0.702782i
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) 6.92820i 0.619677i
\(126\) −1.50000 + 7.79423i −0.133631 + 0.694365i
\(127\) 4.00000 6.92820i 0.354943 0.614779i −0.632166 0.774833i \(-0.717834\pi\)
0.987108 + 0.160055i \(0.0511671\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 13.8564i 1.21999i
\(130\) −12.0000 3.46410i −1.05247 0.303822i
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 4.50000 + 2.59808i 0.391675 + 0.226134i
\(133\) 17.5000 6.06218i 1.51744 0.525657i
\(134\) 0 0
\(135\) −18.0000 −1.54919
\(136\) −1.50000 2.59808i −0.128624 0.222783i
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) −12.0000 −1.02151
\(139\) 4.50000 2.59808i 0.381685 0.220366i −0.296866 0.954919i \(-0.595942\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 3.00000 + 8.66025i 0.253546 + 0.731925i
\(141\) 7.50000 12.9904i 0.631614 1.09399i
\(142\) 6.00000 0.503509
\(143\) −3.00000 + 10.3923i −0.250873 + 0.869048i
\(144\) −3.00000 −0.250000
\(145\) 3.00000 5.19615i 0.249136 0.431517i
\(146\) −2.00000 + 3.46410i −0.165521 + 0.286691i
\(147\) 7.50000 + 9.52628i 0.618590 + 0.785714i
\(148\) 6.92820i 0.569495i
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) −10.5000 + 6.06218i −0.857321 + 0.494975i
\(151\) 8.66025i 0.704761i −0.935857 0.352381i \(-0.885372\pi\)
0.935857 0.352381i \(-0.114628\pi\)
\(152\) 3.50000 + 6.06218i 0.283887 + 0.491708i
\(153\) 4.50000 7.79423i 0.363803 0.630126i
\(154\) 7.50000 2.59808i 0.604367 0.209359i
\(155\) 13.8564i 1.11297i
\(156\) −1.50000 6.06218i −0.120096 0.485363i
\(157\) 13.8564i 1.10586i −0.833227 0.552931i \(-0.813509\pi\)
0.833227 0.552931i \(-0.186491\pi\)
\(158\) 5.50000 9.52628i 0.437557 0.757870i
\(159\) −7.50000 + 12.9904i −0.594789 + 1.03020i
\(160\) −3.00000 + 1.73205i −0.237171 + 0.136931i
\(161\) −12.0000 + 13.8564i −0.945732 + 1.09204i
\(162\) −4.50000 7.79423i −0.353553 0.612372i
\(163\) 21.0000 12.1244i 1.64485 0.949653i 0.665771 0.746156i \(-0.268103\pi\)
0.979076 0.203497i \(-0.0652307\pi\)
\(164\) 5.19615i 0.405751i
\(165\) 9.00000 + 15.5885i 0.700649 + 1.21356i
\(166\) −12.0000 6.92820i −0.931381 0.537733i
\(167\) −15.0000 8.66025i −1.16073 0.670151i −0.209255 0.977861i \(-0.567104\pi\)
−0.951480 + 0.307711i \(0.900437\pi\)
\(168\) −3.00000 + 3.46410i −0.231455 + 0.267261i
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) 10.3923i 0.797053i
\(171\) −10.5000 + 18.1865i −0.802955 + 1.39076i
\(172\) 4.00000 6.92820i 0.304997 0.528271i
\(173\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) 3.00000 0.227429
\(175\) −3.50000 + 18.1865i −0.264575 + 1.37477i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) −18.0000 −1.35296
\(178\) 7.50000 4.33013i 0.562149 0.324557i
\(179\) 21.0000 + 12.1244i 1.56961 + 0.906217i 0.996213 + 0.0869415i \(0.0277093\pi\)
0.573400 + 0.819275i \(0.305624\pi\)
\(180\) −9.00000 5.19615i −0.670820 0.387298i
\(181\) 1.73205i 0.128742i 0.997926 + 0.0643712i \(0.0205042\pi\)
−0.997926 + 0.0643712i \(0.979496\pi\)
\(182\) −8.50000 4.33013i −0.630062 0.320970i
\(183\) 9.00000 0.665299
\(184\) −6.00000 3.46410i −0.442326 0.255377i
\(185\) −12.0000 + 20.7846i −0.882258 + 1.52811i
\(186\) 6.00000 3.46410i 0.439941 0.254000i
\(187\) −9.00000 −0.658145
\(188\) 7.50000 4.33013i 0.546994 0.315807i
\(189\) −13.5000 2.59808i −0.981981 0.188982i
\(190\) 24.2487i 1.75919i
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) −1.50000 0.866025i −0.108253 0.0625000i
\(193\) −10.5000 6.06218i −0.755807 0.436365i 0.0719816 0.997406i \(-0.477068\pi\)
−0.827788 + 0.561041i \(0.810401\pi\)
\(194\) 2.00000 0.143592
\(195\) 6.00000 20.7846i 0.429669 1.48842i
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) −13.5000 + 23.3827i −0.961835 + 1.66595i −0.243947 + 0.969788i \(0.578442\pi\)
−0.717888 + 0.696159i \(0.754891\pi\)
\(198\) −4.50000 + 7.79423i −0.319801 + 0.553912i
\(199\) 9.00000 5.19615i 0.637993 0.368345i −0.145848 0.989307i \(-0.546591\pi\)
0.783841 + 0.620962i \(0.213258\pi\)
\(200\) −7.00000 −0.494975
\(201\) 0 0
\(202\) 0 0
\(203\) 3.00000 3.46410i 0.210559 0.243132i
\(204\) 4.50000 2.59808i 0.315063 0.181902i
\(205\) −9.00000 + 15.5885i −0.628587 + 1.08875i
\(206\) 3.00000 + 1.73205i 0.209020 + 0.120678i
\(207\) 20.7846i 1.44463i
\(208\) 1.00000 3.46410i 0.0693375 0.240192i
\(209\) 21.0000 1.45260
\(210\) −15.0000 + 5.19615i −1.03510 + 0.358569i
\(211\) 11.0000 19.0526i 0.757271 1.31163i −0.186966 0.982366i \(-0.559865\pi\)
0.944237 0.329266i \(-0.106801\pi\)
\(212\) −7.50000 + 4.33013i −0.515102 + 0.297394i
\(213\) 10.3923i 0.712069i
\(214\) −4.50000 + 2.59808i −0.307614 + 0.177601i
\(215\) 24.0000 13.8564i 1.63679 0.944999i
\(216\) 5.19615i 0.353553i
\(217\) 2.00000 10.3923i 0.135769 0.705476i
\(218\) −3.00000 1.73205i −0.203186 0.117309i
\(219\) −6.00000 3.46410i −0.405442 0.234082i
\(220\) 10.3923i 0.700649i
\(221\) 7.50000 + 7.79423i 0.504505 + 0.524297i
\(222\) −12.0000 −0.805387
\(223\) 8.00000 13.8564i 0.535720 0.927894i −0.463409 0.886145i \(-0.653374\pi\)
0.999128 0.0417488i \(-0.0132929\pi\)
\(224\) −2.50000 + 0.866025i −0.167038 + 0.0578638i
\(225\) −10.5000 18.1865i −0.700000 1.21244i
\(226\) 13.8564i 0.921714i
\(227\) 9.00000 5.19615i 0.597351 0.344881i −0.170648 0.985332i \(-0.554586\pi\)
0.767999 + 0.640451i \(0.221253\pi\)
\(228\) −10.5000 + 6.06218i −0.695379 + 0.401478i
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) −12.0000 20.7846i −0.791257 1.37050i
\(231\) 4.50000 + 12.9904i 0.296078 + 0.854704i
\(232\) 1.50000 + 0.866025i 0.0984798 + 0.0568574i
\(233\) 6.92820i 0.453882i −0.973909 0.226941i \(-0.927128\pi\)
0.973909 0.226941i \(-0.0728724\pi\)
\(234\) 10.5000 2.59808i 0.686406 0.169842i
\(235\) 30.0000 1.95698
\(236\) −9.00000 5.19615i −0.585850 0.338241i
\(237\) 16.5000 + 9.52628i 1.07179 + 0.618798i
\(238\) 1.50000 7.79423i 0.0972306 0.505225i
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) −3.00000 5.19615i −0.193649 0.335410i
\(241\) −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i \(-0.271048\pi\)
−0.980917 + 0.194429i \(0.937715\pi\)
\(242\) −2.00000 −0.128565
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) 4.50000 + 2.59808i 0.288083 + 0.166325i
\(245\) −9.00000 + 22.5167i −0.574989 + 1.43854i
\(246\) −9.00000 −0.573819
\(247\) −17.5000 18.1865i −1.11350 1.15718i
\(248\) 4.00000 0.254000
\(249\) 12.0000 20.7846i 0.760469 1.31717i
\(250\) −6.00000 3.46410i −0.379473 0.219089i
\(251\) −15.0000 25.9808i −0.946792 1.63989i −0.752124 0.659022i \(-0.770970\pi\)
−0.194668 0.980869i \(-0.562363\pi\)
\(252\) −6.00000 5.19615i −0.377964 0.327327i
\(253\) −18.0000 + 10.3923i −1.13165 + 0.653359i
\(254\) 4.00000 + 6.92820i 0.250982 + 0.434714i
\(255\) 18.0000 1.12720
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 13.5000 23.3827i 0.842107 1.45857i −0.0460033 0.998941i \(-0.514648\pi\)
0.888110 0.459631i \(-0.152018\pi\)
\(258\) 12.0000 + 6.92820i 0.747087 + 0.431331i
\(259\) −12.0000 + 13.8564i −0.745644 + 0.860995i
\(260\) 9.00000 8.66025i 0.558156 0.537086i
\(261\) 5.19615i 0.321634i
\(262\) −3.00000 + 5.19615i −0.185341 + 0.321019i
\(263\) −21.0000 12.1244i −1.29492 0.747620i −0.315394 0.948961i \(-0.602137\pi\)
−0.979521 + 0.201341i \(0.935470\pi\)
\(264\) −4.50000 + 2.59808i −0.276956 + 0.159901i
\(265\) −30.0000 −1.84289
\(266\) −3.50000 + 18.1865i −0.214599 + 1.11509i
\(267\) 7.50000 + 12.9904i 0.458993 + 0.794998i
\(268\) 0 0
\(269\) −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i \(-0.905416\pi\)
0.224523 0.974469i \(-0.427917\pi\)
\(270\) 9.00000 15.5885i 0.547723 0.948683i
\(271\) −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i \(-0.911459\pi\)
0.718580 + 0.695444i \(0.244792\pi\)
\(272\) 3.00000 0.181902
\(273\) 7.50000 14.7224i 0.453921 0.891042i
\(274\) 12.0000 0.724947
\(275\) −10.5000 + 18.1865i −0.633174 + 1.09669i
\(276\) 6.00000 10.3923i 0.361158 0.625543i
\(277\) 8.00000 + 13.8564i 0.480673 + 0.832551i 0.999754 0.0221745i \(-0.00705893\pi\)
−0.519081 + 0.854725i \(0.673726\pi\)
\(278\) 5.19615i 0.311645i
\(279\) 6.00000 + 10.3923i 0.359211 + 0.622171i
\(280\) −9.00000 1.73205i −0.537853 0.103510i
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 7.50000 + 12.9904i 0.446619 + 0.773566i
\(283\) −3.00000 1.73205i −0.178331 0.102960i 0.408177 0.912903i \(-0.366165\pi\)
−0.586509 + 0.809943i \(0.699498\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) −42.0000 −2.48787
\(286\) −7.50000 7.79423i −0.443484 0.460882i
\(287\) −9.00000 + 10.3923i −0.531253 + 0.613438i
\(288\) 1.50000 2.59808i 0.0883883 0.153093i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 3.00000 + 5.19615i 0.176166 + 0.305129i
\(291\) 3.46410i 0.203069i
\(292\) −2.00000 3.46410i −0.117041 0.202721i
\(293\) −6.00000 + 3.46410i −0.350524 + 0.202375i −0.664916 0.746918i \(-0.731533\pi\)
0.314392 + 0.949293i \(0.398199\pi\)
\(294\) −12.0000 + 1.73205i −0.699854 + 0.101015i
\(295\) −18.0000 31.1769i −1.04800 1.81519i
\(296\) −6.00000 3.46410i −0.348743 0.201347i
\(297\) −13.5000 7.79423i −0.783349 0.452267i
\(298\) −6.00000 −0.347571
\(299\) 24.0000 + 6.92820i 1.38796 + 0.400668i
\(300\) 12.1244i 0.700000i
\(301\) 20.0000 6.92820i 1.15278 0.399335i
\(302\) 7.50000 + 4.33013i 0.431577 + 0.249171i
\(303\) 0 0
\(304\) −7.00000 −0.401478
\(305\) 9.00000 + 15.5885i 0.515339 + 0.892592i
\(306\) 4.50000 + 7.79423i 0.257248 + 0.445566i
\(307\) 7.00000 0.399511 0.199756 0.979846i \(-0.435985\pi\)
0.199756 + 0.979846i \(0.435985\pi\)
\(308\) −1.50000 + 7.79423i −0.0854704 + 0.444117i
\(309\) −3.00000 + 5.19615i −0.170664 + 0.295599i
\(310\) 12.0000 + 6.92820i 0.681554 + 0.393496i
\(311\) −3.00000 −0.170114 −0.0850572 0.996376i \(-0.527107\pi\)
−0.0850572 + 0.996376i \(0.527107\pi\)
\(312\) 6.00000 + 1.73205i 0.339683 + 0.0980581i
\(313\) 20.7846i 1.17482i 0.809291 + 0.587408i \(0.199852\pi\)
−0.809291 + 0.587408i \(0.800148\pi\)
\(314\) 12.0000 + 6.92820i 0.677199 + 0.390981i
\(315\) −9.00000 25.9808i −0.507093 1.46385i
\(316\) 5.50000 + 9.52628i 0.309399 + 0.535895i
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) −7.50000 12.9904i −0.420579 0.728464i
\(319\) 4.50000 2.59808i 0.251952 0.145464i
\(320\) 3.46410i 0.193649i
\(321\) −4.50000 7.79423i −0.251166 0.435031i
\(322\) −6.00000 17.3205i −0.334367 0.965234i
\(323\) 10.5000 18.1865i 0.584236 1.01193i
\(324\) 9.00000 0.500000
\(325\) 24.5000 6.06218i 1.35902 0.336269i
\(326\) 24.2487i 1.34301i
\(327\) 3.00000 5.19615i 0.165900 0.287348i
\(328\) −4.50000 2.59808i −0.248471 0.143455i
\(329\) 22.5000 + 4.33013i 1.24047 + 0.238728i
\(330\) −18.0000 −0.990867
\(331\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(332\) 12.0000 6.92820i 0.658586 0.380235i
\(333\) 20.7846i 1.13899i
\(334\) 15.0000 8.66025i 0.820763 0.473868i
\(335\) 0 0
\(336\) −1.50000 4.33013i −0.0818317 0.236228i
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) −0.500000 + 12.9904i −0.0271964 + 0.706584i
\(339\) −24.0000 −1.30350
\(340\) 9.00000 + 5.19615i 0.488094 + 0.281801i
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) −10.5000 18.1865i −0.567775 0.983415i
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 4.00000 + 6.92820i 0.215666 + 0.373544i
\(345\) 36.0000 20.7846i 1.93817 1.11901i
\(346\) 0 0
\(347\) −13.5000 + 7.79423i −0.724718 + 0.418416i −0.816487 0.577364i \(-0.804081\pi\)
0.0917687 + 0.995780i \(0.470748\pi\)
\(348\) −1.50000 + 2.59808i −0.0804084 + 0.139272i
\(349\) 1.00000 1.73205i 0.0535288 0.0927146i −0.838019 0.545640i \(-0.816286\pi\)
0.891548 + 0.452926i \(0.149620\pi\)
\(350\) −14.0000 12.1244i −0.748331 0.648074i
\(351\) 4.50000 + 18.1865i 0.240192 + 0.970725i
\(352\) −3.00000 −0.159901
\(353\) 18.0000 + 10.3923i 0.958043 + 0.553127i 0.895570 0.444920i \(-0.146768\pi\)
0.0624731 + 0.998047i \(0.480101\pi\)
\(354\) 9.00000 15.5885i 0.478345 0.828517i
\(355\) −18.0000 + 10.3923i −0.955341 + 0.551566i
\(356\) 8.66025i 0.458993i
\(357\) 13.5000 + 2.59808i 0.714496 + 0.137505i
\(358\) −21.0000 + 12.1244i −1.10988 + 0.640792i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 9.00000 5.19615i 0.474342 0.273861i
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) −1.50000 0.866025i −0.0788382 0.0455173i
\(363\) 3.46410i 0.181818i
\(364\) 8.00000 5.19615i 0.419314 0.272352i
\(365\) 13.8564i 0.725277i
\(366\) −4.50000 + 7.79423i −0.235219 + 0.407411i
\(367\) 18.0000 + 10.3923i 0.939592 + 0.542474i 0.889833 0.456287i \(-0.150821\pi\)
0.0497598 + 0.998761i \(0.484154\pi\)
\(368\) 6.00000 3.46410i 0.312772 0.180579i
\(369\) 15.5885i 0.811503i
\(370\) −12.0000 20.7846i −0.623850 1.08054i
\(371\) −22.5000 4.33013i −1.16814 0.224809i
\(372\) 6.92820i 0.359211i
\(373\) 10.0000 + 17.3205i 0.517780 + 0.896822i 0.999787 + 0.0206542i \(0.00657489\pi\)
−0.482006 + 0.876168i \(0.660092\pi\)
\(374\) 4.50000 7.79423i 0.232689 0.403030i
\(375\) 6.00000 10.3923i 0.309839 0.536656i
\(376\) 8.66025i 0.446619i
\(377\) −6.00000 1.73205i −0.309016 0.0892052i
\(378\) 9.00000 10.3923i 0.462910 0.534522i
\(379\) −9.00000 5.19615i −0.462299 0.266908i 0.250711 0.968062i \(-0.419335\pi\)
−0.713010 + 0.701153i \(0.752669\pi\)
\(380\) −21.0000 12.1244i −1.07728 0.621966i
\(381\) −12.0000 + 6.92820i −0.614779 + 0.354943i
\(382\) 0 0
\(383\) −4.50000 + 2.59808i −0.229939 + 0.132755i −0.610544 0.791982i \(-0.709049\pi\)
0.380605 + 0.924738i \(0.375716\pi\)
\(384\) 1.50000 0.866025i 0.0765466 0.0441942i
\(385\) −18.0000 + 20.7846i −0.917365 + 1.05928i
\(386\) 10.5000 6.06218i 0.534436 0.308557i
\(387\) −12.0000 + 20.7846i −0.609994 + 1.05654i
\(388\) −1.00000 + 1.73205i −0.0507673 + 0.0879316i
\(389\) 20.7846i 1.05382i −0.849921 0.526911i \(-0.823350\pi\)
0.849921 0.526911i \(-0.176650\pi\)
\(390\) 15.0000 + 15.5885i 0.759555 + 0.789352i
\(391\) 20.7846i 1.05112i
\(392\) −6.50000 2.59808i −0.328300 0.131223i
\(393\) −9.00000 5.19615i −0.453990 0.262111i
\(394\) −13.5000 23.3827i −0.680120 1.17800i
\(395\) 38.1051i 1.91728i
\(396\) −4.50000 7.79423i −0.226134 0.391675i
\(397\) 3.50000 + 6.06218i 0.175660 + 0.304252i 0.940389 0.340099i \(-0.110461\pi\)
−0.764730 + 0.644351i \(0.777127\pi\)
\(398\) 10.3923i 0.520919i
\(399\) −31.5000 6.06218i −1.57697 0.303488i
\(400\) 3.50000 6.06218i 0.175000 0.303109i
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 0 0
\(403\) −14.0000 + 3.46410i −0.697390 + 0.172559i
\(404\) 0 0
\(405\) 27.0000 + 15.5885i 1.34164 + 0.774597i
\(406\) 1.50000 + 4.33013i 0.0744438 + 0.214901i
\(407\) −18.0000 + 10.3923i −0.892227 + 0.515127i
\(408\) 5.19615i 0.257248i
\(409\) 2.00000 + 3.46410i 0.0988936 + 0.171289i 0.911227 0.411905i \(-0.135136\pi\)
−0.812333 + 0.583193i \(0.801803\pi\)
\(410\) −9.00000 15.5885i −0.444478 0.769859i
\(411\) 20.7846i 1.02523i
\(412\) −3.00000 + 1.73205i −0.147799 + 0.0853320i
\(413\) −9.00000 25.9808i −0.442861 1.27843i
\(414\) 18.0000 + 10.3923i 0.884652 + 0.510754i
\(415\) 48.0000 2.35623
\(416\) 2.50000 + 2.59808i 0.122573 + 0.127381i
\(417\) −9.00000 −0.440732
\(418\) −10.5000 + 18.1865i −0.513572 + 0.889532i
\(419\) −6.00000 + 10.3923i −0.293119 + 0.507697i −0.974546 0.224189i \(-0.928027\pi\)
0.681426 + 0.731887i \(0.261360\pi\)
\(420\) 3.00000 15.5885i 0.146385 0.760639i
\(421\) 24.2487i 1.18181i −0.806741 0.590905i \(-0.798771\pi\)
0.806741 0.590905i \(-0.201229\pi\)
\(422\) 11.0000 + 19.0526i 0.535472 + 0.927464i
\(423\) −22.5000 + 12.9904i −1.09399 + 0.631614i
\(424\) 8.66025i 0.420579i
\(425\) 10.5000 + 18.1865i 0.509325 + 0.882176i
\(426\) −9.00000 5.19615i −0.436051 0.251754i
\(427\) 4.50000 + 12.9904i 0.217770 + 0.628649i
\(428\) 5.19615i 0.251166i
\(429\) 13.5000 12.9904i 0.651786 0.627182i
\(430\) 27.7128i 1.33643i
\(431\) −9.00000 + 15.5885i −0.433515 + 0.750870i −0.997173 0.0751385i \(-0.976060\pi\)
0.563658 + 0.826008i \(0.309393\pi\)
\(432\) 4.50000 + 2.59808i 0.216506 + 0.125000i
\(433\) 15.0000 8.66025i 0.720854 0.416185i −0.0942129 0.995552i \(-0.530033\pi\)
0.815067 + 0.579367i \(0.196700\pi\)
\(434\) 8.00000 + 6.92820i 0.384012 + 0.332564i
\(435\) −9.00000 + 5.19615i −0.431517 + 0.249136i
\(436\) 3.00000 1.73205i 0.143674 0.0829502i
\(437\) 48.4974i 2.31995i
\(438\) 6.00000 3.46410i 0.286691 0.165521i
\(439\) 3.00000 + 1.73205i 0.143182 + 0.0826663i 0.569880 0.821728i \(-0.306990\pi\)
−0.426698 + 0.904394i \(0.640323\pi\)
\(440\) −9.00000 5.19615i −0.429058 0.247717i
\(441\) −3.00000 20.7846i −0.142857 0.989743i
\(442\) −10.5000 + 2.59808i −0.499434 + 0.123578i
\(443\) 29.4449i 1.39897i 0.714648 + 0.699484i \(0.246587\pi\)
−0.714648 + 0.699484i \(0.753413\pi\)
\(444\) 6.00000 10.3923i 0.284747 0.493197i
\(445\) −15.0000 + 25.9808i −0.711068 + 1.23161i
\(446\) 8.00000 + 13.8564i 0.378811 + 0.656120i
\(447\) 10.3923i 0.491539i
\(448\) 0.500000 2.59808i 0.0236228 0.122748i
\(449\) 18.0000 + 31.1769i 0.849473 + 1.47133i 0.881680 + 0.471848i \(0.156413\pi\)
−0.0322072 + 0.999481i \(0.510254\pi\)
\(450\) 21.0000 0.989949
\(451\) −13.5000 + 7.79423i −0.635690 + 0.367016i
\(452\) −12.0000 6.92820i −0.564433 0.325875i
\(453\) −7.50000 + 12.9904i −0.352381 + 0.610341i
\(454\) 10.3923i 0.487735i
\(455\) 33.0000 1.73205i 1.54706 0.0811998i
\(456\) 12.1244i 0.567775i
\(457\) −6.00000 3.46410i −0.280668 0.162044i 0.353058 0.935602i \(-0.385142\pi\)
−0.633726 + 0.773558i \(0.718475\pi\)
\(458\) −6.50000 + 11.2583i −0.303725 + 0.526067i
\(459\) −13.5000 + 7.79423i −0.630126 + 0.363803i
\(460\) 24.0000 1.11901
\(461\) −27.0000 + 15.5885i −1.25752 + 0.726027i −0.972591 0.232523i \(-0.925302\pi\)
−0.284925 + 0.958550i \(0.591969\pi\)
\(462\) −13.5000 2.59808i −0.628077 0.120873i
\(463\) 36.3731i 1.69040i −0.534450 0.845200i \(-0.679481\pi\)
0.534450 0.845200i \(-0.320519\pi\)
\(464\) −1.50000 + 0.866025i −0.0696358 + 0.0402042i
\(465\) −12.0000 + 20.7846i −0.556487 + 0.963863i
\(466\) 6.00000 + 3.46410i 0.277945 + 0.160471i
\(467\) 6.00000 0.277647 0.138823 0.990317i \(-0.455668\pi\)
0.138823 + 0.990317i \(0.455668\pi\)
\(468\) −3.00000 + 10.3923i −0.138675 + 0.480384i
\(469\) 0 0
\(470\) −15.0000 + 25.9808i −0.691898 + 1.19840i
\(471\) −12.0000 + 20.7846i −0.552931 + 0.957704i
\(472\) 9.00000 5.19615i 0.414259 0.239172i
\(473\) 24.0000 1.10352
\(474\) −16.5000 + 9.52628i −0.757870 + 0.437557i
\(475\) −24.5000 42.4352i −1.12414 1.94706i
\(476\) 6.00000 + 5.19615i 0.275010 + 0.238165i
\(477\) 22.5000 12.9904i 1.03020 0.594789i
\(478\) 6.00000 10.3923i 0.274434 0.475333i
\(479\) 28.5000 + 16.4545i 1.30220 + 0.751825i 0.980781 0.195113i \(-0.0625074\pi\)
0.321417 + 0.946938i \(0.395841\pi\)
\(480\) 6.00000 0.273861
\(481\) 24.0000 + 6.92820i 1.09431 + 0.315899i
\(482\) 10.0000 0.455488
\(483\) 30.0000 10.3923i 1.36505 0.472866i
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) −6.00000 + 3.46410i −0.272446 + 0.157297i
\(486\) 15.5885i 0.707107i
\(487\) 7.50000 4.33013i 0.339857 0.196217i −0.320352 0.947299i \(-0.603801\pi\)
0.660209 + 0.751082i \(0.270468\pi\)
\(488\) −4.50000 + 2.59808i −0.203705 + 0.117609i
\(489\) −42.0000 −1.89931
\(490\) −15.0000 19.0526i −0.677631 0.860707i
\(491\) −9.00000 5.19615i −0.406164 0.234499i 0.282976 0.959127i \(-0.408678\pi\)
−0.689140 + 0.724628i \(0.742012\pi\)
\(492\) 4.50000 7.79423i 0.202876 0.351391i
\(493\) 5.19615i 0.234023i
\(494\) 24.5000 6.06218i 1.10231 0.272750i
\(495\) 31.1769i 1.40130i
\(496\) −2.00000 + 3.46410i −0.0898027 + 0.155543i
\(497\) −15.0000 + 5.19615i −0.672842 + 0.233079i
\(498\) 12.0000 + 20.7846i 0.537733 + 0.931381i
\(499\) 41.5692i 1.86089i 0.366427 + 0.930447i \(0.380581\pi\)
−0.366427 + 0.930447i \(0.619419\pi\)
\(500\) 6.00000 3.46410i 0.268328 0.154919i
\(501\) 15.0000 + 25.9808i 0.670151 + 1.16073i
\(502\) 30.0000 1.33897
\(503\) 6.00000 + 10.3923i 0.267527 + 0.463370i 0.968223 0.250090i \(-0.0804603\pi\)
−0.700696 + 0.713460i \(0.747127\pi\)
\(504\) 7.50000 2.59808i 0.334077 0.115728i
\(505\) 0 0
\(506\) 20.7846i 0.923989i
\(507\) −22.5000 0.866025i −0.999260 0.0384615i
\(508\) −8.00000 −0.354943
\(509\) 24.0000 + 13.8564i 1.06378 + 0.614174i 0.926476 0.376354i \(-0.122822\pi\)
0.137305 + 0.990529i \(0.456156\pi\)
\(510\) −9.00000 + 15.5885i −0.398527 + 0.690268i
\(511\) 2.00000 10.3923i 0.0884748 0.459728i
\(512\) 1.00000 0.0441942
\(513\) 31.5000 18.1865i 1.39076 0.802955i
\(514\) 13.5000 + 23.3827i 0.595459 + 1.03137i
\(515\) −12.0000 −0.528783
\(516\) −12.0000 + 6.92820i −0.528271 + 0.304997i
\(517\) 22.5000 + 12.9904i 0.989549 + 0.571316i
\(518\) −6.00000 17.3205i −0.263625 0.761019i
\(519\) 0 0
\(520\) 3.00000 + 12.1244i 0.131559 + 0.531688i
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) −4.50000 2.59808i −0.196960 0.113715i
\(523\) −28.5000 16.4545i −1.24622 0.719504i −0.275865 0.961196i \(-0.588964\pi\)
−0.970353 + 0.241692i \(0.922298\pi\)
\(524\) −3.00000 5.19615i −0.131056 0.226995i
\(525\) 21.0000 24.2487i 0.916515 1.05830i
\(526\) 21.0000 12.1244i 0.915644 0.528647i
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) 5.19615i 0.226134i
\(529\) 12.5000 + 21.6506i 0.543478 + 0.941332i
\(530\) 15.0000 25.9808i 0.651558 1.12853i
\(531\) 27.0000 + 15.5885i 1.17170 + 0.676481i
\(532\) −14.0000 12.1244i −0.606977 0.525657i
\(533\) 18.0000 + 5.19615i 0.779667 + 0.225070i
\(534\) −15.0000 −0.649113
\(535\) 9.00000 15.5885i 0.389104 0.673948i
\(536\) 0 0
\(537\) −21.0000 36.3731i −0.906217 1.56961i
\(538\) 24.0000 1.03471
\(539\) −16.5000 + 12.9904i −0.710705 + 0.559535i
\(540\) 9.00000 + 15.5885i 0.387298 + 0.670820i
\(541\) 31.1769i 1.34040i −0.742180 0.670200i \(-0.766208\pi\)
0.742180 0.670200i \(-0.233792\pi\)
\(542\) −4.00000 6.92820i −0.171815 0.297592i
\(543\) 1.50000 2.59808i 0.0643712 0.111494i
\(544\) −1.50000 + 2.59808i −0.0643120 + 0.111392i
\(545\) 12.0000 0.514024
\(546\) 9.00000 + 13.8564i 0.385164 + 0.592999i
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) −13.5000 7.79423i −0.576166 0.332650i
\(550\) −10.5000 18.1865i −0.447722 0.775476i
\(551\) 12.1244i 0.516515i
\(552\) 6.00000 + 10.3923i 0.255377 + 0.442326i
\(553\) −5.50000 + 28.5788i −0.233884 + 1.21530i
\(554\) −16.0000 −0.679775
\(555\) 36.0000 20.7846i 1.52811 0.882258i
\(556\) −4.50000 2.59808i −0.190843 0.110183i
\(557\) 1.50000 2.59808i 0.0635570 0.110084i −0.832496 0.554031i \(-0.813089\pi\)
0.896053 + 0.443947i \(0.146422\pi\)
\(558\) −12.0000 −0.508001
\(559\) −20.0000 20.7846i −0.845910 0.879095i
\(560\) 6.00000 6.92820i 0.253546 0.292770i
\(561\) 13.5000 + 7.79423i 0.569970 + 0.329073i
\(562\) 6.00000 10.3923i 0.253095 0.438373i
\(563\) −12.0000 20.7846i −0.505740 0.875967i −0.999978 0.00664037i \(-0.997886\pi\)
0.494238 0.869326i \(-0.335447\pi\)
\(564\) −15.0000 −0.631614
\(565\) −24.0000 41.5692i −1.00969 1.74883i
\(566\) 3.00000 1.73205i 0.126099 0.0728035i
\(567\) 18.0000 + 15.5885i 0.755929 + 0.654654i
\(568\) −3.00000 5.19615i −0.125877 0.218026i
\(569\) 15.0000 + 8.66025i 0.628833 + 0.363057i 0.780300 0.625406i \(-0.215066\pi\)
−0.151467 + 0.988462i \(0.548400\pi\)
\(570\) 21.0000 36.3731i 0.879593 1.52350i
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 10.5000 2.59808i 0.439027 0.108631i
\(573\) 0 0
\(574\) −4.50000 12.9904i −0.187826 0.542208i
\(575\) 42.0000 + 24.2487i 1.75152 + 1.01124i
\(576\) 1.50000 + 2.59808i 0.0625000 + 0.108253i
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 4.00000 + 6.92820i 0.166378 + 0.288175i
\(579\) 10.5000 + 18.1865i 0.436365 + 0.755807i
\(580\) −6.00000 −0.249136
\(581\) 36.0000 + 6.92820i 1.49353 + 0.287430i
\(582\) −3.00000 1.73205i −0.124354 0.0717958i
\(583\) −22.5000 12.9904i −0.931855 0.538007i
\(584\) 4.00000 0.165521
\(585\) −27.0000 + 25.9808i −1.11631 + 1.07417i
\(586\) 6.92820i 0.286201i
\(587\) −15.0000 8.66025i −0.619116 0.357447i 0.157409 0.987534i \(-0.449686\pi\)
−0.776525 + 0.630087i \(0.783019\pi\)
\(588\) 4.50000 11.2583i 0.185577 0.464286i
\(589\) 14.0000 + 24.2487i 0.576860 + 0.999151i
\(590\) 36.0000 1.48210
\(591\) 40.5000 23.3827i 1.66595 0.961835i
\(592\) 6.00000 3.46410i 0.246598 0.142374i
\(593\) 8.66025i 0.355634i 0.984064 + 0.177817i \(0.0569035\pi\)
−0.984064 + 0.177817i \(0.943096\pi\)
\(594\) 13.5000 7.79423i 0.553912 0.319801i
\(595\) 9.00000 + 25.9808i 0.368964 + 1.06511i
\(596\) 3.00000 5.19615i 0.122885 0.212843i
\(597\) −18.0000 −0.736691
\(598\) −18.0000 + 17.3205i −0.736075 + 0.708288i
\(599\) 3.46410i 0.141539i 0.997493 + 0.0707697i \(0.0225455\pi\)
−0.997493 + 0.0707697i \(0.977454\pi\)
\(600\) 10.5000 + 6.06218i 0.428661 + 0.247487i
\(601\) 27.0000 + 15.5885i 1.10135 + 0.635866i 0.936576 0.350464i \(-0.113976\pi\)
0.164777 + 0.986331i \(0.447310\pi\)
\(602\) −4.00000 + 20.7846i −0.163028 + 0.847117i
\(603\) 0 0
\(604\) −7.50000 + 4.33013i −0.305171 + 0.176190i
\(605\) 6.00000 3.46410i 0.243935 0.140836i
\(606\) 0 0
\(607\) 6.00000 3.46410i 0.243532 0.140604i −0.373267 0.927724i \(-0.621762\pi\)
0.616799 + 0.787121i \(0.288429\pi\)
\(608\) 3.50000 6.06218i 0.141944 0.245854i
\(609\) −7.50000 + 2.59808i −0.303915 + 0.105279i
\(610\) −18.0000 −0.728799
\(611\) −7.50000 30.3109i −0.303418 1.22625i
\(612\) −9.00000 −0.363803
\(613\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(614\) −3.50000 + 6.06218i −0.141249 + 0.244650i
\(615\) 27.0000 15.5885i 1.08875 0.628587i
\(616\) −6.00000 5.19615i −0.241747 0.209359i
\(617\) −3.00000 5.19615i −0.120775 0.209189i 0.799298 0.600935i \(-0.205205\pi\)
−0.920074 + 0.391745i \(0.871871\pi\)
\(618\) −3.00000 5.19615i −0.120678 0.209020i
\(619\) −31.0000 −1.24600 −0.622998 0.782224i \(-0.714085\pi\)
−0.622998 + 0.782224i \(0.714085\pi\)
\(620\) −12.0000 + 6.92820i −0.481932 + 0.278243i
\(621\) −18.0000 + 31.1769i −0.722315 + 1.25109i
\(622\) 1.50000 2.59808i 0.0601445 0.104173i
\(623\) −15.0000 + 17.3205i −0.600962 + 0.693932i
\(624\) −4.50000 + 4.33013i −0.180144 + 0.173344i
\(625\) −11.0000 −0.440000
\(626\) −18.0000 10.3923i −0.719425 0.415360i
\(627\) −31.5000 18.1865i −1.25799 0.726300i
\(628\) −12.0000 + 6.92820i −0.478852 + 0.276465i
\(629\) 20.7846i 0.828737i
\(630\) 27.0000 + 5.19615i 1.07571 + 0.207020i
\(631\) −40.5000 + 23.3827i −1.61228 + 0.930850i −0.623439 + 0.781872i \(0.714265\pi\)
−0.988841 + 0.148978i \(0.952402\pi\)
\(632\) −11.0000 −0.437557
\(633\) −33.0000 + 19.0526i −1.31163 + 0.757271i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) −24.0000 13.8564i −0.952411 0.549875i
\(636\) 15.0000 0.594789
\(637\) 25.0000 + 3.46410i 0.990536 + 0.137253i
\(638\) 5.19615i 0.205718i
\(639\) 9.00000 15.5885i 0.356034 0.616670i
\(640\) 3.00000 + 1.73205i 0.118585 + 0.0684653i
\(641\) −3.00000 + 1.73205i −0.118493 + 0.0684119i −0.558075 0.829790i \(-0.688460\pi\)
0.439582 + 0.898202i \(0.355127\pi\)
\(642\) 9.00000 0.355202
\(643\) 23.5000 + 40.7032i 0.926750 + 1.60518i 0.788723 + 0.614749i \(0.210743\pi\)
0.138027 + 0.990429i \(0.455924\pi\)
\(644\) 18.0000 + 3.46410i 0.709299 + 0.136505i
\(645\) −48.0000 −1.89000
\(646\) 10.5000 + 18.1865i 0.413117 + 0.715540i
\(647\) 10.5000 18.1865i 0.412798 0.714986i −0.582397 0.812905i \(-0.697885\pi\)
0.995194 + 0.0979182i \(0.0312184\pi\)
\(648\) −4.50000 + 7.79423i −0.176777 + 0.306186i
\(649\) 31.1769i 1.22380i
\(650\) −7.00000 + 24.2487i −0.274563 + 0.951113i
\(651\) −12.0000 + 13.8564i −0.470317 + 0.543075i
\(652\) −21.0000 12.1244i −0.822423 0.474826i
\(653\) 4.50000 + 2.59808i 0.176099 + 0.101671i 0.585458 0.810702i \(-0.300915\pi\)
−0.409360 + 0.912373i \(0.634248\pi\)
\(654\) 3.00000 + 5.19615i 0.117309 + 0.203186i
\(655\) 20.7846i 0.812122i
\(656\) 4.50000 2.59808i 0.175695 0.101438i
\(657\) 6.00000 + 10.3923i 0.234082 + 0.405442i
\(658\) −15.0000 + 17.3205i −0.584761 + 0.675224i
\(659\) 1.50000 0.866025i 0.0584317 0.0337356i −0.470500 0.882400i \(-0.655926\pi\)
0.528931 + 0.848665i \(0.322593\pi\)
\(660\) 9.00000 15.5885i 0.350325 0.606780i
\(661\) 7.00000 12.1244i 0.272268 0.471583i −0.697174 0.716902i \(-0.745559\pi\)
0.969442 + 0.245319i \(0.0788928\pi\)
\(662\) 0 0
\(663\) −4.50000 18.1865i −0.174766 0.706306i
\(664\) 13.8564i 0.537733i
\(665\) −21.0000 60.6218i −0.814345 2.35081i
\(666\) 18.0000 + 10.3923i 0.697486 + 0.402694i
\(667\) −6.00000 10.3923i −0.232321 0.402392i
\(668\) 17.3205i 0.670151i
\(669\) −24.0000 + 13.8564i −0.927894 + 0.535720i
\(670\) 0 0
\(671\) 15.5885i 0.601786i
\(672\) 4.50000 + 0.866025i 0.173591 + 0.0334077i
\(673\) 14.5000 25.1147i 0.558934 0.968102i −0.438652 0.898657i \(-0.644544\pi\)
0.997586 0.0694449i \(-0.0221228\pi\)
\(674\) 9.50000 16.4545i 0.365926 0.633803i
\(675\) 36.3731i 1.40000i
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 12.0000 20.7846i 0.460857 0.798228i
\(679\) −5.00000 + 1.73205i −0.191882 + 0.0664700i
\(680\) −9.00000 + 5.19615i −0.345134 + 0.199263i
\(681\) −18.0000 −0.689761
\(682\) 6.00000 + 10.3923i 0.229752 + 0.397942i
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 21.0000 0.802955
\(685\) −36.0000 + 20.7846i −1.37549 + 0.794139i
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) −19.5000 11.2583i −0.743971 0.429532i
\(688\) −8.00000 −0.304997
\(689\) 7.50000 + 30.3109i 0.285727 + 1.15475i
\(690\) 41.5692i 1.58251i
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) 0 0
\(693\) 4.50000 23.3827i 0.170941 0.888235i
\(694\) 15.5885i 0.591730i
\(695\) −9.00000 15.5885i −0.341389 0.591304i
\(696\) −1.50000 2.59808i −0.0568574 0.0984798i
\(697\) 15.5885i 0.590455i
\(698\) 1.00000 + 1.73205i 0.0378506 + 0.0655591i
\(699\) −6.00000 + 10.3923i −0.226941 + 0.393073i
\(700\) 17.5000 6.06218i 0.661438 0.229129i
\(701\) 12.1244i 0.457931i −0.973435 0.228965i \(-0.926466\pi\)
0.973435 0.228965i \(-0.0735342\pi\)
\(702\) −18.0000 5.19615i −0.679366 0.196116i
\(703\) 48.4974i 1.82911i
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) −45.0000 25.9808i −1.69480 0.978492i
\(706\) −18.0000 + 10.3923i −0.677439 + 0.391120i
\(707\) 0 0
\(708\) 9.00000 + 15.5885i 0.338241 + 0.585850i
\(709\) 21.0000 12.1244i 0.788672 0.455340i −0.0508231 0.998708i \(-0.516184\pi\)
0.839495 + 0.543368i \(0.182851\pi\)
\(710\) 20.7846i 0.780033i
\(711\) −16.5000 28.5788i −0.618798 1.07179i
\(712\) −7.50000 4.33013i −0.281074 0.162278i
\(713\) −24.0000 13.8564i −0.898807 0.518927i
\(714\) −9.00000 + 10.3923i −0.336817 + 0.388922i
\(715\) 36.0000 + 10.3923i 1.34632 + 0.388650i
\(716\) 24.2487i 0.906217i
\(717\) 18.0000 + 10.3923i 0.672222 + 0.388108i
\(718\) −12.0000 + 20.7846i −0.447836 + 0.775675i
\(719\) 10.5000 + 18.1865i 0.391584 + 0.678243i 0.992659 0.120950i \(-0.0385939\pi\)
−0.601075 + 0.799193i \(0.705261\pi\)
\(720\) 10.3923i 0.387298i
\(721\) −9.00000 1.73205i −0.335178 0.0645049i
\(722\) −15.0000 25.9808i −0.558242 0.966904i
\(723\) 17.3205i 0.644157i
\(724\) 1.50000 0.866025i 0.0557471 0.0321856i
\(725\) −10.5000 6.06218i −0.389960 0.225144i
\(726\) 3.00000 + 1.73205i 0.111340 + 0.0642824i
\(727\) 34.6410i 1.28476i −0.766385 0.642382i \(-0.777946\pi\)
0.766385 0.642382i \(-0.222054\pi\)
\(728\) 0.500000 + 9.52628i 0.0185312 + 0.353067i
\(729\) −27.0000 −1.00000
\(730\) 12.0000 + 6.92820i 0.444140 + 0.256424i
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) −4.50000 7.79423i −0.166325 0.288083i
\(733\) 13.0000 0.480166 0.240083 0.970752i \(-0.422825\pi\)
0.240083 + 0.970752i \(0.422825\pi\)
\(734\) −18.0000 + 10.3923i −0.664392 + 0.383587i
\(735\) 33.0000 25.9808i 1.21722 0.958315i
\(736\) 6.92820i 0.255377i
\(737\) 0 0
\(738\) 13.5000 + 7.79423i 0.496942 + 0.286910i
\(739\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(740\) 24.0000 0.882258
\(741\) 10.5000 + 42.4352i 0.385727 + 1.55890i
\(742\) 15.0000 17.3205i 0.550667 0.635856i
\(743\) −3.00000 + 5.19615i −0.110059 + 0.190628i −0.915794 0.401648i \(-0.868437\pi\)
0.805735 + 0.592277i \(0.201771\pi\)
\(744\) −6.00000 3.46410i −0.219971 0.127000i
\(745\) 18.0000 10.3923i 0.659469 0.380745i
\(746\) −20.0000 −0.732252
\(747\) −36.0000 + 20.7846i −1.31717 + 0.760469i
\(748\) 4.50000 + 7.79423i 0.164536 + 0.284985i
\(749\) 9.00000 10.3923i 0.328853 0.379727i
\(750\) 6.00000 + 10.3923i 0.219089 + 0.379473i
\(751\) −15.5000 + 26.8468i −0.565603 + 0.979653i 0.431390 + 0.902165i \(0.358023\pi\)
−0.996993 + 0.0774878i \(0.975310\pi\)
\(752\) −7.50000 4.33013i −0.273497 0.157903i
\(753\) 51.9615i 1.89358i
\(754\) 4.50000 4.33013i 0.163880 0.157694i
\(755\) −30.0000 −1.09181
\(756\) 4.50000 + 12.9904i 0.163663 + 0.472456i
\(757\) −10.0000 + 17.3205i −0.363456 + 0.629525i −0.988527 0.151043i \(-0.951737\pi\)
0.625071 + 0.780568i \(0.285070\pi\)
\(758\) 9.00000 5.19615i 0.326895 0.188733i
\(759\) 36.0000 1.30672
\(760\) 21.0000 12.1244i 0.761750 0.439797i
\(761\) 6.00000 3.46410i 0.217500 0.125574i −0.387292 0.921957i \(-0.626590\pi\)
0.604792 + 0.796383i \(0.293256\pi\)
\(762\) 13.8564i 0.501965i
\(763\) 9.00000 + 1.73205i 0.325822 + 0.0627044i
\(764\) 0 0
\(765\) −27.0000 15.5885i −0.976187 0.563602i
\(766\) 5.19615i 0.187745i
\(767\) −27.0000 + 25.9808i −0.974913 + 0.938111i
\(768\) 1.73205i 0.0625000i
\(769\) −20.0000 + 34.6410i −0.721218 + 1.24919i 0.239293 + 0.970947i \(0.423084\pi\)
−0.960512 + 0.278240i \(0.910249\pi\)
\(770\) −9.00000 25.9808i −0.324337 0.936282i
\(771\) −40.5000 + 23.3827i −1.45857 + 0.842107i
\(772\) 12.1244i 0.436365i
\(773\) 9.00000 5.19615i 0.323708 0.186893i −0.329336 0.944213i \(-0.606825\pi\)
0.653044 + 0.757320i \(0.273492\pi\)
\(774\) −12.0000 20.7846i −0.431331 0.747087i
\(775\) −28.0000