Properties

Label 546.2.q.d.335.1
Level $546$
Weight $2$
Character 546.335
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: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 335.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.335
Dual form 546.2.q.d.251.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.46410i q^{5} +(1.50000 + 0.866025i) q^{6} +(2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(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} +(2.50000 - 0.866025i) 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} +(-0.500000 + 2.59808i) 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} +(3.00000 + 8.66025i) 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} +(4.50000 + 0.866025i) 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} +(5.50000 - 4.33013i) 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} +(-2.50000 + 0.866025i) 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} +(1.50000 - 7.79423i) 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} +(1.50000 + 4.33013i) 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} +(9.50000 - 0.866025i) 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} +(6.50000 + 2.59808i) q^{98} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 3 q^{3} - q^{4} + 3 q^{6} + 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 3 q^{3} - q^{4} + 3 q^{6} + 5 q^{7} - 2 q^{8} + 3 q^{9} - 6 q^{10} - 3 q^{11} + 7 q^{13} + 4 q^{14} + 6 q^{15} - q^{16} - 3 q^{17} + 6 q^{18} - 7 q^{19} - 6 q^{20} + 6 q^{21} + 3 q^{22} + 12 q^{23} - 3 q^{24} - 14 q^{25} + 2 q^{26} - q^{28} - 3 q^{29} - 6 q^{30} - 8 q^{31} + q^{32} - 9 q^{33} - 6 q^{34} + 6 q^{35} + 3 q^{36} - 12 q^{37} - 14 q^{38} + 12 q^{39} - 9 q^{41} + 9 q^{42} + 8 q^{43} + 6 q^{44} + 18 q^{45} + 12 q^{46} - 3 q^{48} + 11 q^{49} - 7 q^{50} - 5 q^{52} + 9 q^{54} + 18 q^{55} - 5 q^{56} - 3 q^{58} + 18 q^{59} - 12 q^{60} + 9 q^{61} - 4 q^{62} + 3 q^{63} + 2 q^{64} - 6 q^{65} - 3 q^{68} + 12 q^{69} - 12 q^{70} + 6 q^{71} - 3 q^{72} - 8 q^{73} - 12 q^{74} - 21 q^{75} - 7 q^{76} - 12 q^{77} + 9 q^{78} - 22 q^{79} + 6 q^{80} - 9 q^{81} - 9 q^{82} + 3 q^{84} - 18 q^{85} + 16 q^{86} - 3 q^{87} + 3 q^{88} - 15 q^{89} + 19 q^{91} - 12 q^{93} + 15 q^{94} - 42 q^{95} + 2 q^{97} + 13 q^{98} - 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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 \(0.282047\pi\)
−0.632456 + 0.774597i \(0.717953\pi\)
\(6\) 1.50000 + 0.866025i 0.612372 + 0.353553i
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) −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 \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 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 −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 3.00000 0.707107
\(19\) −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i \(0.463407\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −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 \(-0.409745\pi\)
0.971325 + 0.237754i \(0.0764114\pi\)
\(24\) −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
\(28\) −0.500000 + 2.59808i −0.0944911 + 0.490990i
\(29\) −1.50000 + 0.866025i −0.278543 + 0.160817i −0.632764 0.774345i \(-0.718080\pi\)
0.354221 + 0.935162i \(0.384746\pi\)
\(30\) −3.00000 + 5.19615i −0.547723 + 0.948683i
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −4.50000 2.59808i −0.783349 0.452267i
\(34\) −3.00000 −0.514496
\(35\) 3.00000 + 8.66025i 0.507093 + 1.46385i
\(36\) 1.50000 + 2.59808i 0.250000 + 0.433013i
\(37\) −6.00000 + 3.46410i −0.986394 + 0.569495i −0.904194 0.427121i \(-0.859528\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) −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 −0.808383 0.588657i \(-0.799657\pi\)
0.105601 + 0.994409i \(0.466323\pi\)
\(42\) 4.50000 + 0.866025i 0.694365 + 0.133631i
\(43\) 4.00000 6.92820i 0.609994 1.05654i −0.381246 0.924473i \(-0.624505\pi\)
0.991241 0.132068i \(-0.0421616\pi\)
\(44\) 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 \(-0.782393\pi\)
0.775283 0.631614i \(-0.217607\pi\)
\(48\) −1.50000 0.866025i −0.216506 0.125000i
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) −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
\(56\) −2.50000 + 0.866025i −0.334077 + 0.115728i
\(57\) 12.1244i 1.60591i
\(58\) −1.50000 0.866025i −0.196960 0.113715i
\(59\) 9.00000 + 5.19615i 1.17170 + 0.676481i 0.954080 0.299552i \(-0.0968372\pi\)
0.217620 + 0.976034i \(0.430171\pi\)
\(60\) −6.00000 −0.774597
\(61\) 4.50000 + 2.59808i 0.576166 + 0.332650i 0.759608 0.650381i \(-0.225391\pi\)
−0.183442 + 0.983030i \(0.558724\pi\)
\(62\) −2.00000 3.46410i −0.254000 0.439941i
\(63\) 1.50000 7.79423i 0.188982 0.981981i
\(64\) 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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) −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 \(-0.717462\pi\)
0.987294 + 0.158901i \(0.0507952\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) −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 \(-0.724969\pi\)
0.649374 0.760469i \(-0.275031\pi\)
\(84\) 1.50000 + 4.33013i 0.163663 + 0.472456i
\(85\) −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 −0.841719 0.539915i \(-0.818456\pi\)
0.0467209 + 0.998908i \(0.485123\pi\)
\(90\) 10.3923i 1.09545i
\(91\) 9.50000 0.866025i 0.995871 0.0907841i
\(92\) 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 \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) 6.50000 + 2.59808i 0.656599 + 0.262445i
\(99\) −9.00000 −0.904534
\(100\) 3.50000 6.06218i 0.350000 0.606218i
\(101\) 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
\(103\) 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 \(-0.747481\pi\)
0.266456 + 0.963847i \(0.414147\pi\)
\(108\) 4.50000 + 2.59808i 0.433013 + 0.250000i
\(109\) 3.46410i 0.331801i −0.986143 0.165900i \(-0.946947\pi\)
0.986143 0.165900i \(-0.0530530\pi\)
\(110\) 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 \(-0.559298\pi\)
−0.943649 + 0.330947i \(0.892632\pi\)
\(114\) −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
\(119\) −1.50000 + 7.79423i −0.137505 + 0.714496i
\(120\) −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
\(126\) 7.50000 2.59808i 0.668153 0.231455i
\(127\) 4.00000 + 6.92820i 0.354943 + 0.614779i 0.987108 0.160055i \(-0.0511671\pi\)
−0.632166 + 0.774833i \(0.717834\pi\)
\(128\) 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
\(133\) −3.50000 + 18.1865i −0.303488 + 1.57697i
\(134\) 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 −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 12.0000 1.02151
\(139\) −4.50000 2.59808i −0.381685 0.220366i 0.296866 0.954919i \(-0.404058\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −9.00000 1.73205i −0.760639 0.146385i
\(141\) −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
\(147\) 4.50000 11.2583i 0.371154 0.928571i
\(148\) 6.92820i 0.569495i
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) −10.5000 6.06218i −0.857321 0.494975i
\(151\) 8.66025i 0.704761i 0.935857 + 0.352381i \(0.114628\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) 3.50000 6.06218i 0.283887 0.491708i
\(153\) 4.50000 + 7.79423i 0.363803 + 0.630126i
\(154\) 1.50000 7.79423i 0.120873 0.628077i
\(155\) 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 0.979076 + 0.203497i \(0.0652307\pi\)
0.665771 + 0.746156i \(0.268103\pi\)
\(164\) 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 −0.951480 0.307711i \(-0.900437\pi\)
−0.209255 + 0.977861i \(0.567104\pi\)
\(168\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) −3.00000 −0.227429
\(175\) −17.5000 + 6.06218i −1.32288 + 0.458258i
\(176\) −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 −0.573400 + 0.819275i \(0.694376\pi\)
−0.996213 + 0.0869415i \(0.972291\pi\)
\(180\) −9.00000 + 5.19615i −0.670820 + 0.387298i
\(181\) 1.73205i 0.128742i 0.997926 + 0.0643712i \(0.0205042\pi\)
−0.997926 + 0.0643712i \(0.979496\pi\)
\(182\) 5.50000 + 7.79423i 0.407687 + 0.577747i
\(183\) 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
\(189\) −4.50000 12.9904i −0.327327 0.944911i
\(190\) 24.2487i 1.75919i
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 1.50000 0.866025i 0.108253 0.0625000i
\(193\) −10.5000 + 6.06218i −0.755807 + 0.436365i −0.827788 0.561041i \(-0.810401\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 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 0.717888 + 0.696159i \(0.245109\pi\)
0.243947 + 0.969788i \(0.421558\pi\)
\(198\) −4.50000 7.79423i −0.319801 0.553912i
\(199\) −9.00000 5.19615i −0.637993 0.368345i 0.145848 0.989307i \(-0.453409\pi\)
−0.783841 + 0.620962i \(0.786742\pi\)
\(200\) 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
\(210\) −3.00000 + 15.5885i −0.207020 + 1.07571i
\(211\) 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i \(0.106801\pi\)
−0.186966 + 0.982366i \(0.559865\pi\)
\(212\) 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
\(217\) −10.0000 + 3.46410i −0.678844 + 0.235159i
\(218\) 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 −0.999128 0.0417488i \(-0.986707\pi\)
0.463409 0.886145i \(-0.346626\pi\)
\(224\) 0.500000 2.59808i 0.0334077 0.173591i
\(225\) −10.5000 + 18.1865i −0.700000 + 1.21244i
\(226\) 13.8564i 0.921714i
\(227\) 9.00000 + 5.19615i 0.597351 + 0.344881i 0.767999 0.640451i \(-0.221253\pi\)
−0.170648 + 0.985332i \(0.554586\pi\)
\(228\) −10.5000 6.06218i −0.695379 0.401478i
\(229\) −13.0000 −0.859064 −0.429532 0.903052i \(-0.641321\pi\)
−0.429532 + 0.903052i \(0.641321\pi\)
\(230\) −12.0000 + 20.7846i −0.791257 + 1.37050i
\(231\) −13.5000 2.59808i −0.888235 0.170941i
\(232\) 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
\(238\) −7.50000 + 2.59808i −0.486153 + 0.168408i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 3.00000 5.19615i 0.193649 0.335410i
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 2.00000 0.128565
\(243\) −13.5000 7.79423i −0.866025 0.500000i
\(244\) −4.50000 + 2.59808i −0.288083 + 0.166325i
\(245\) 15.0000 + 19.0526i 0.958315 + 1.21722i
\(246\) −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 −0.194668 + 0.980869i \(0.562363\pi\)
−0.752124 + 0.659022i \(0.770970\pi\)
\(252\) 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 0.888110 + 0.459631i \(0.152018\pi\)
−0.0460033 + 0.998941i \(0.514648\pi\)
\(258\) 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 \(-0.397863\pi\)
0.979521 + 0.201341i \(0.0645299\pi\)
\(264\) 4.50000 + 2.59808i 0.276956 + 0.159901i
\(265\) 30.0000 1.84289
\(266\) −17.5000 + 6.06218i −1.07299 + 0.371696i
\(267\) −7.50000 + 12.9904i −0.458993 + 0.794998i
\(268\) 0 0
\(269\) −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 9.00000 + 15.5885i 0.547723 + 0.948683i
\(271\) 4.00000 + 6.92820i 0.242983 + 0.420858i 0.961563 0.274586i \(-0.0885408\pi\)
−0.718580 + 0.695444i \(0.755208\pi\)
\(272\) 3.00000 0.181902
\(273\) 13.5000 9.52628i 0.817057 0.576557i
\(274\) 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 −0.519081 0.854725i \(-0.673726\pi\)
0.999754 + 0.0221745i \(0.00705893\pi\)
\(278\) 5.19615i 0.311645i
\(279\) −6.00000 + 10.3923i −0.359211 + 0.622171i
\(280\) −3.00000 8.66025i −0.179284 0.517549i
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 7.50000 12.9904i 0.446619 0.773566i
\(283\) 3.00000 1.73205i 0.178331 0.102960i −0.408177 0.912903i \(-0.633835\pi\)
0.586509 + 0.809943i \(0.300502\pi\)
\(284\) 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 0.314392 0.949293i \(-0.398199\pi\)
−0.664916 + 0.746918i \(0.731533\pi\)
\(294\) 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
\(301\) 4.00000 20.7846i 0.230556 1.19800i
\(302\) −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 \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 7.50000 2.59808i 0.427352 0.148039i
\(309\) −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
\(315\) 27.0000 + 5.19615i 1.52128 + 0.292770i
\(316\) 5.50000 9.52628i 0.309399 0.535895i
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 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
\(322\) 18.0000 + 3.46410i 1.00310 + 0.193047i
\(323\) −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
\(329\) −7.50000 21.6506i −0.413488 1.19364i
\(330\) 18.0000 0.990867
\(331\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 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
\(336\) −4.50000 0.866025i −0.245495 0.0472456i
\(337\) −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 \(-0.195919\pi\)
−0.0917687 + 0.995780i \(0.529252\pi\)
\(348\) −1.50000 2.59808i −0.0804084 0.139272i
\(349\) −1.00000 1.73205i −0.0535288 0.0927146i 0.838019 0.545640i \(-0.183714\pi\)
−0.891548 + 0.452926i \(0.850380\pi\)
\(350\) −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 0.0624731 0.998047i \(-0.480101\pi\)
0.895570 + 0.444920i \(0.146768\pi\)
\(354\) 9.00000 + 15.5885i 0.478345 + 0.828517i
\(355\) 18.0000 + 10.3923i 0.955341 + 0.551566i
\(356\) 8.66025i 0.458993i
\(357\) 4.50000 + 12.9904i 0.238165 + 0.687524i
\(358\) −21.0000 12.1244i −1.10988 0.640792i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) −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
\(364\) −4.00000 + 8.66025i −0.209657 + 0.453921i
\(365\) 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 \(-0.849179\pi\)
−0.0497598 + 0.998761i \(0.515846\pi\)
\(368\) −6.00000 3.46410i −0.312772 0.180579i
\(369\) 15.5885i 0.811503i
\(370\) 12.0000 20.7846i 0.623850 1.08054i
\(371\) −7.50000 21.6506i −0.389381 1.12404i
\(372\) 6.92820i 0.359211i
\(373\) 10.0000 17.3205i 0.517780 0.896822i −0.482006 0.876168i \(-0.660092\pi\)
0.999787 0.0206542i \(-0.00657489\pi\)
\(374\) 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 −0.713010 0.701153i \(-0.752669\pi\)
0.250711 + 0.968062i \(0.419335\pi\)
\(380\) 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 0.380605 0.924738i \(-0.375716\pi\)
−0.610544 + 0.791982i \(0.709049\pi\)
\(384\) 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
\(392\) −5.50000 + 4.33013i −0.277792 + 0.218704i
\(393\) 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 \(-0.889539\pi\)
0.764730 + 0.644351i \(0.222873\pi\)
\(398\) 10.3923i 0.520919i
\(399\) 10.5000 + 30.3109i 0.525657 + 1.51744i
\(400\) 3.50000 + 6.06218i 0.175000 + 0.303109i
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 0 0
\(403\) −14.0000 3.46410i −0.697390 0.172559i
\(404\) 0 0
\(405\) 27.0000 15.5885i 1.34164 0.774597i
\(406\) −4.50000 0.866025i −0.223331 0.0429801i
\(407\) 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 \(-0.864864\pi\)
0.812333 + 0.583193i \(0.198197\pi\)
\(410\) 9.00000 15.5885i 0.444478 0.769859i
\(411\) 20.7846i 1.02523i
\(412\) 3.00000 + 1.73205i 0.147799 + 0.0853320i
\(413\) 27.0000 + 5.19615i 1.32858 + 0.255686i
\(414\) 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 0.681426 0.731887i \(-0.261360\pi\)
−0.974546 + 0.224189i \(0.928027\pi\)
\(420\) −15.0000 + 5.19615i −0.731925 + 0.253546i
\(421\) 24.2487i 1.18181i 0.806741 + 0.590905i \(0.201229\pi\)
−0.806741 + 0.590905i \(0.798771\pi\)
\(422\) −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
\(427\) 13.5000 + 2.59808i 0.653311 + 0.125730i
\(428\) 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 \(-0.0239399\pi\)
−0.563658 + 0.826008i \(0.690607\pi\)
\(432\) −4.50000 + 2.59808i −0.216506 + 0.125000i
\(433\) −15.0000 8.66025i −0.720854 0.416185i 0.0942129 0.995552i \(-0.469967\pi\)
−0.815067 + 0.579367i \(0.803300\pi\)
\(434\) −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 \(-0.693010\pi\)
0.426698 + 0.904394i \(0.359677\pi\)
\(440\) −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
\(448\) 2.50000 0.866025i 0.118114 0.0409159i
\(449\) −18.0000 + 31.1769i −0.849473 + 1.47133i 0.0322072 + 0.999481i \(0.489746\pi\)
−0.881680 + 0.471848i \(0.843587\pi\)
\(450\) −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
\(455\) 3.00000 + 32.9090i 0.140642 + 1.54280i
\(456\) 12.1244i 0.567775i
\(457\) −6.00000 + 3.46410i −0.280668 + 0.162044i −0.633726 0.773558i \(-0.718475\pi\)
0.353058 + 0.935602i \(0.385142\pi\)
\(458\) −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 −0.284925 0.958550i \(-0.591969\pi\)
−0.972591 + 0.232523i \(0.925302\pi\)
\(462\) −4.50000 12.9904i −0.209359 0.604367i
\(463\) 36.3731i 1.69040i 0.534450 + 0.845200i \(0.320519\pi\)
−0.534450 + 0.845200i \(0.679481\pi\)
\(464\) 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 0.321417 0.946938i \(-0.395841\pi\)
0.980781 + 0.195113i \(0.0625074\pi\)
\(480\) 6.00000 0.273861
\(481\) −24.0000 + 6.92820i −1.09431 + 0.315899i
\(482\) 10.0000 0.455488
\(483\) 6.00000 31.1769i 0.273009 1.41860i
\(484\) 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 0.660209 0.751082i \(-0.270468\pi\)
−0.320352 + 0.947299i \(0.603801\pi\)
\(488\) −4.50000 2.59808i −0.203705 0.117609i
\(489\) 42.0000 1.89931
\(490\) −9.00000 + 22.5167i −0.406579 + 1.01720i
\(491\) 9.00000 5.19615i 0.406164 0.234499i −0.282976 0.959127i \(-0.591322\pi\)
0.689140 + 0.724628i \(0.257988\pi\)
\(492\) −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
\(497\) 3.00000 15.5885i 0.134568 0.699238i
\(498\) 12.0000 20.7846i 0.537733 0.931381i
\(499\) 41.5692i 1.86089i −0.366427 0.930447i \(-0.619419\pi\)
0.366427 0.930447i \(-0.380581\pi\)
\(500\) 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 −0.700696 0.713460i \(-0.747127\pi\)
0.968223 + 0.250090i \(0.0804603\pi\)
\(504\) −1.50000 + 7.79423i −0.0668153 + 0.347183i
\(505\) 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 0.137305 0.990529i \(-0.456156\pi\)
0.926476 + 0.376354i \(0.122822\pi\)
\(510\) −9.00000 15.5885i −0.398527 0.690268i
\(511\) −10.0000 + 3.46410i −0.442374 + 0.153243i
\(512\) −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
\(518\) −18.0000 3.46410i −0.790875 0.152204i
\(519\) 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 \(-0.411036\pi\)
0.970353 + 0.241692i \(0.0777024\pi\)
\(524\) −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
\(539\) −19.5000 7.79423i −0.839924 0.335721i
\(540\) −9.00000 + 15.5885i −0.387298 + 0.670820i
\(541\) 31.1769i 1.34040i 0.742180 + 0.670200i \(0.233792\pi\)
−0.742180 + 0.670200i \(0.766208\pi\)
\(542\) −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
\(546\) 15.0000 + 6.92820i 0.641941 + 0.296500i
\(547\) 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
\(553\) −27.5000 + 9.52628i −1.16942 + 0.405099i
\(554\) 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 \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) −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 0.494238 + 0.869326i \(0.335447\pi\)
−0.999978 + 0.00664037i \(0.997886\pi\)
\(564\) 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 \(-0.784934\pi\)
0.151467 + 0.988462i \(0.451600\pi\)
\(570\) −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
\(574\) −13.5000 2.59808i −0.563479 0.108442i
\(575\) −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 \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) −10.5000 + 18.1865i −0.436365 + 0.755807i
\(580\) 6.00000 0.249136
\(581\) −12.0000 34.6410i −0.497844 1.43715i
\(582\) 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 −0.776525 0.630087i \(-0.783019\pi\)
0.157409 + 0.987534i \(0.449686\pi\)
\(588\) 7.50000 + 9.52628i 0.309295 + 0.392857i
\(589\) 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 \(-0.943096\pi\)
0.984064 0.177817i \(-0.0569035\pi\)
\(594\) −13.5000 7.79423i −0.553912 0.319801i
\(595\) −27.0000 5.19615i −1.10689 0.213021i
\(596\) −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 \(-0.886024\pi\)
−0.164777 + 0.986331i \(0.552690\pi\)
\(602\) 20.0000 6.92820i 0.815139 0.282372i
\(603\) 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 \(-0.378238\pi\)
−0.616799 + 0.787121i \(0.711571\pi\)
\(608\) 3.50000 + 6.06218i 0.141944 + 0.245854i
\(609\) −1.50000 + 7.79423i −0.0607831 + 0.315838i
\(610\) −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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(614\) −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 \(-0.794795\pi\)
0.920074 + 0.391745i \(0.128129\pi\)
\(618\) 3.00000 5.19615i 0.120678 0.209020i
\(619\) 31.0000 1.24600 0.622998 0.782224i \(-0.285915\pi\)
0.622998 + 0.782224i \(0.285915\pi\)
\(620\) 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
\(630\) 9.00000 + 25.9808i 0.358569 + 1.03510i
\(631\) −40.5000 23.3827i −1.61228 0.930850i −0.988841 0.148978i \(-0.952402\pi\)
−0.623439 0.781872i \(-0.714265\pi\)
\(632\) 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
\(637\) 23.0000 10.3923i 0.911293 0.411758i
\(638\) 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 \(-0.311540\pi\)
−0.439582 + 0.898202i \(0.644873\pi\)
\(642\) −9.00000 −0.355202
\(643\) −23.5000 + 40.7032i −0.926750 + 1.60518i −0.138027 + 0.990429i \(0.544076\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) 6.00000 + 17.3205i 0.236433 + 0.682524i
\(645\) 48.0000 1.89000
\(646\) 10.5000 18.1865i 0.413117 0.715540i
\(647\) 10.5000 + 18.1865i 0.412798 + 0.714986i 0.995194 0.0979182i \(-0.0312184\pi\)
−0.582397 + 0.812905i \(0.697885\pi\)
\(648\) 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 \(-0.699085\pi\)
0.409360 + 0.912373i \(0.365752\pi\)
\(654\) 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 \(-0.344074\pi\)
−0.528931 + 0.848665i \(0.677407\pi\)
\(660\) 9.00000 + 15.5885i 0.350325 + 0.606780i
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) 0 0
\(663\) −4.50000 + 18.1865i −0.174766 + 0.706306i
\(664\) 13.8564i 0.537733i
\(665\) −63.0000 12.1244i −2.44304 0.470162i
\(666\) −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
\(672\) −1.50000 4.33013i −0.0578638 0.167038i
\(673\) 14.5000 + 25.1147i 0.558934 + 0.968102i 0.997586 + 0.0694449i \(0.0221228\pi\)
−0.438652 + 0.898657i \(0.644544\pi\)
\(674\) −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
\(679\) 1.00000 5.19615i 0.0383765 0.199410i
\(680\) 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 \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) −21.0000 −0.802955
\(685\) 36.0000 + 20.7846i 1.37549 + 0.794139i
\(686\) 18.5000 + 0.866025i 0.706333 + 0.0330650i
\(687\) −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 \(-0.118041\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) 0 0
\(693\) −22.5000 + 7.79423i −0.854704 + 0.296078i
\(694\) 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
\(700\) 3.50000 18.1865i 0.132288 0.687386i
\(701\) 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 0.839495 0.543368i \(-0.182851\pi\)
−0.0508231 + 0.998708i \(0.516184\pi\)
\(710\) 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 −0.601075 0.799193i \(-0.705261\pi\)
0.992659 + 0.120950i \(0.0385939\pi\)
\(720\) 10.3923i 0.387298i
\(721\) −3.00000 8.66025i −0.111726 0.322525i
\(722\) 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 \(-0.222054\pi\)
\(728\) −9.50000 + 0.866025i −0.352093 + 0.0320970i
\(729\) −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 \(-0.577175\pi\)
−0.240083 + 0.970752i \(0.577175\pi\)
\(734\) −18.0000 10.3923i −0.664392 0.383587i
\(735\) 39.0000 + 15.5885i 1.43854 + 0.574989i
\(736\) 6.92820i 0.255377i
\(737\) 0 0
\(738\) −13.5000 + 7.79423i −0.496942 + 0.286910i
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 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 \(-0.131563\pi\)
−0.805735 + 0.592277i \(0.798229\pi\)
\(744\) 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 −0.996993 0.0774878i \(-0.975310\pi\)
0.431390 0.902165i \(-0.358023\pi\)
\(752\) −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
\(756\) 13.5000 + 2.59808i 0.490990 + 0.0944911i
\(757\) −10.0000 17.3205i −0.363456 0.629525i 0.625071 0.780568i \(-0.285070\pi\)
−0.988527 + 0.151043i \(0.951737\pi\)
\(758\) −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 0.604792 0.796383i \(-0.293256\pi\)
−0.387292 + 0.921957i \(0.626590\pi\)
\(762\) 13.8564i 0.501965i
\(763\) −3.00000 8.66025i −0.108607 0.313522i
\(764\) 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 0.960512 + 0.278240i \(0.0897509\pi\)
−0.239293 + 0.970947i \(0.576916\pi\)
\(770\) 27.0000 + 5.19615i 0.973012 + 0.187256i
\(771\) 40.5000 + 23.3827i 1.45857 + 0.842107i
\(772\) 12.1244i 0.436365i
\(773\) 9.00000 + 5.19615i 0.323708 + 0.186893i 0.653044 0.757320i \(-0.273492\pi\)