Properties

Label 462.2.i.c.67.1
Level $462$
Weight $2$
Character 462.67
Analytic conductor $3.689$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
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: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 462.67
Dual form 462.2.i.c.331.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -1.00000 q^{6} +(2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +2.00000 q^{13} +(0.500000 + 2.59808i) q^{14} -3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} -3.00000 q^{20} +(-2.00000 + 1.73205i) q^{21} +1.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -6.00000 q^{29} +(-1.50000 - 2.59808i) q^{30} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} -3.00000 q^{34} +(1.50000 + 7.79423i) q^{35} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(-1.50000 - 2.59808i) q^{40} -3.00000 q^{41} +(-2.50000 - 0.866025i) q^{42} +2.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.50000 - 2.59808i) q^{45} +(1.50000 - 2.59808i) q^{46} +(4.50000 + 7.79423i) q^{47} +1.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -4.00000 q^{50} +(-1.50000 - 2.59808i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +3.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} +2.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(6.00000 - 10.3923i) q^{59} +(1.50000 - 2.59808i) q^{60} +(-2.50000 - 4.33013i) q^{61} +4.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-2.50000 + 4.33013i) q^{67} +(-1.50000 - 2.59808i) q^{68} +3.00000 q^{69} +(-6.00000 + 5.19615i) q^{70} +12.0000 q^{71} +(0.500000 + 0.866025i) q^{72} +(8.00000 - 13.8564i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-2.00000 - 3.46410i) q^{75} +2.00000 q^{76} +(2.00000 - 1.73205i) q^{77} -2.00000 q^{78} +(-8.50000 - 14.7224i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.50000 - 2.59808i) q^{82} +9.00000 q^{83} +(-0.500000 - 2.59808i) q^{84} -9.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(3.00000 - 5.19615i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +3.00000 q^{90} +(5.00000 + 1.73205i) q^{91} +3.00000 q^{92} +(2.00000 + 3.46410i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(3.00000 - 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{96} +17.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} + 3q^{5} - 2q^{6} + 5q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} + 3q^{5} - 2q^{6} + 5q^{7} - 2q^{8} - q^{9} - 3q^{10} + q^{11} - q^{12} + 4q^{13} + q^{14} - 6q^{15} - q^{16} - 3q^{17} + q^{18} - 2q^{19} - 6q^{20} - 4q^{21} + 2q^{22} - 3q^{23} + q^{24} - 4q^{25} + 2q^{26} + 2q^{27} - 4q^{28} - 12q^{29} - 3q^{30} + 4q^{31} + q^{32} + q^{33} - 6q^{34} + 3q^{35} + 2q^{36} - 2q^{37} + 2q^{38} - 2q^{39} - 3q^{40} - 6q^{41} - 5q^{42} + 4q^{43} + q^{44} + 3q^{45} + 3q^{46} + 9q^{47} + 2q^{48} + 11q^{49} - 8q^{50} - 3q^{51} - 2q^{52} - 6q^{53} + q^{54} + 6q^{55} - 5q^{56} + 4q^{57} - 6q^{58} + 12q^{59} + 3q^{60} - 5q^{61} + 8q^{62} - q^{63} + 2q^{64} + 6q^{65} - q^{66} - 5q^{67} - 3q^{68} + 6q^{69} - 12q^{70} + 24q^{71} + q^{72} + 16q^{73} + 2q^{74} - 4q^{75} + 4q^{76} + 4q^{77} - 4q^{78} - 17q^{79} + 3q^{80} - q^{81} - 3q^{82} + 18q^{83} - q^{84} - 18q^{85} + 2q^{86} + 6q^{87} - q^{88} + 6q^{89} + 6q^{90} + 10q^{91} + 6q^{92} + 4q^{93} - 9q^{94} + 6q^{95} + q^{96} + 34q^{97} - 2q^{98} - 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) −1.00000 −0.408248
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.50000 + 2.59808i −0.474342 + 0.821584i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0.500000 + 2.59808i 0.133631 + 0.694365i
\(15\) −3.00000 −0.774597
\(16\) −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 \(0.285189\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) −3.00000 −0.670820
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 1.00000 0.213201
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) 1.00000 + 1.73205i 0.196116 + 0.339683i
\(27\) 1.00000 0.192450
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −1.50000 2.59808i −0.273861 0.474342i
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0.500000 + 0.866025i 0.0870388 + 0.150756i
\(34\) −3.00000 −0.514496
\(35\) 1.50000 + 7.79423i 0.253546 + 1.31747i
\(36\) 1.00000 0.166667
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) −1.00000 + 1.73205i −0.160128 + 0.277350i
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) −2.50000 0.866025i −0.385758 0.133631i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 1.50000 2.59808i 0.223607 0.387298i
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) 4.50000 + 7.79423i 0.656392 + 1.13691i 0.981543 + 0.191243i \(0.0612518\pi\)
−0.325150 + 0.945662i \(0.605415\pi\)
\(48\) 1.00000 0.144338
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) −4.00000 −0.565685
\(51\) −1.50000 2.59808i −0.210042 0.363803i
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 3.00000 0.404520
\(56\) −2.50000 0.866025i −0.334077 0.115728i
\(57\) 2.00000 0.264906
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) 6.00000 10.3923i 0.781133 1.35296i −0.150148 0.988663i \(-0.547975\pi\)
0.931282 0.364299i \(-0.118692\pi\)
\(60\) 1.50000 2.59808i 0.193649 0.335410i
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) 4.00000 0.508001
\(63\) −0.500000 2.59808i −0.0629941 0.327327i
\(64\) 1.00000 0.125000
\(65\) 3.00000 + 5.19615i 0.372104 + 0.644503i
\(66\) −0.500000 + 0.866025i −0.0615457 + 0.106600i
\(67\) −2.50000 + 4.33013i −0.305424 + 0.529009i −0.977356 0.211604i \(-0.932131\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 3.00000 0.361158
\(70\) −6.00000 + 5.19615i −0.717137 + 0.621059i
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 8.00000 13.8564i 0.936329 1.62177i 0.164083 0.986447i \(-0.447534\pi\)
0.772246 0.635323i \(-0.219133\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) 2.00000 0.229416
\(77\) 2.00000 1.73205i 0.227921 0.197386i
\(78\) −2.00000 −0.226455
\(79\) −8.50000 14.7224i −0.956325 1.65640i −0.731307 0.682048i \(-0.761089\pi\)
−0.225018 0.974355i \(-0.572244\pi\)
\(80\) 1.50000 2.59808i 0.167705 0.290474i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) 9.00000 0.987878 0.493939 0.869496i \(-0.335557\pi\)
0.493939 + 0.869496i \(0.335557\pi\)
\(84\) −0.500000 2.59808i −0.0545545 0.283473i
\(85\) −9.00000 −0.976187
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) 3.00000 5.19615i 0.321634 0.557086i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 3.00000 0.316228
\(91\) 5.00000 + 1.73205i 0.524142 + 0.181568i
\(92\) 3.00000 0.312772
\(93\) 2.00000 + 3.46410i 0.207390 + 0.359211i
\(94\) −4.50000 + 7.79423i −0.464140 + 0.803913i
\(95\) 3.00000 5.19615i 0.307794 0.533114i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 17.0000 1.72609 0.863044 0.505128i \(-0.168555\pi\)
0.863044 + 0.505128i \(0.168555\pi\)
\(98\) −1.00000 + 6.92820i −0.101015 + 0.699854i
\(99\) −1.00000 −0.100504
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 1.50000 2.59808i 0.148522 0.257248i
\(103\) −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i \(-0.924396\pi\)
0.282194 0.959357i \(-0.408938\pi\)
\(104\) −2.00000 −0.196116
\(105\) −7.50000 2.59808i −0.731925 0.253546i
\(106\) −6.00000 −0.582772
\(107\) −1.50000 2.59808i −0.145010 0.251166i 0.784366 0.620298i \(-0.212988\pi\)
−0.929377 + 0.369132i \(0.879655\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −5.50000 + 9.52628i −0.526804 + 0.912452i 0.472708 + 0.881219i \(0.343277\pi\)
−0.999512 + 0.0312328i \(0.990057\pi\)
\(110\) 1.50000 + 2.59808i 0.143019 + 0.247717i
\(111\) 2.00000 0.189832
\(112\) −0.500000 2.59808i −0.0472456 0.245495i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) 4.50000 7.79423i 0.419627 0.726816i
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) −1.00000 1.73205i −0.0924500 0.160128i
\(118\) 12.0000 1.10469
\(119\) −6.00000 + 5.19615i −0.550019 + 0.476331i
\(120\) 3.00000 0.273861
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 2.50000 4.33013i 0.226339 0.392031i
\(123\) 1.50000 2.59808i 0.135250 0.234261i
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) 3.00000 0.268328
\(126\) 2.00000 1.73205i 0.178174 0.154303i
\(127\) 11.0000 0.976092 0.488046 0.872818i \(-0.337710\pi\)
0.488046 + 0.872818i \(0.337710\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −1.00000 + 1.73205i −0.0880451 + 0.152499i
\(130\) −3.00000 + 5.19615i −0.263117 + 0.455733i
\(131\) 6.00000 + 10.3923i 0.524222 + 0.907980i 0.999602 + 0.0281993i \(0.00897729\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −1.00000 5.19615i −0.0867110 0.450564i
\(134\) −5.00000 −0.431934
\(135\) 1.50000 + 2.59808i 0.129099 + 0.223607i
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) −9.00000 + 15.5885i −0.768922 + 1.33181i 0.169226 + 0.985577i \(0.445873\pi\)
−0.938148 + 0.346235i \(0.887460\pi\)
\(138\) 1.50000 + 2.59808i 0.127688 + 0.221163i
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) −7.50000 2.59808i −0.633866 0.219578i
\(141\) −9.00000 −0.757937
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) 1.00000 1.73205i 0.0836242 0.144841i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −9.00000 15.5885i −0.747409 1.29455i
\(146\) 16.0000 1.32417
\(147\) −6.50000 + 2.59808i −0.536111 + 0.214286i
\(148\) 2.00000 0.164399
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) 0.500000 0.866025i 0.0406894 0.0704761i −0.844963 0.534824i \(-0.820378\pi\)
0.885653 + 0.464348i \(0.153711\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) 3.00000 0.242536
\(154\) 2.50000 + 0.866025i 0.201456 + 0.0697863i
\(155\) 12.0000 0.963863
\(156\) −1.00000 1.73205i −0.0800641 0.138675i
\(157\) −10.0000 + 17.3205i −0.798087 + 1.38233i 0.122774 + 0.992435i \(0.460821\pi\)
−0.920860 + 0.389892i \(0.872512\pi\)
\(158\) 8.50000 14.7224i 0.676224 1.17125i
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) 3.00000 0.237171
\(161\) −1.50000 7.79423i −0.118217 0.614271i
\(162\) −1.00000 −0.0785674
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) 1.50000 2.59808i 0.117130 0.202876i
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) 4.50000 + 7.79423i 0.349268 + 0.604949i
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 2.00000 1.73205i 0.154303 0.133631i
\(169\) −9.00000 −0.692308
\(170\) −4.50000 7.79423i −0.345134 0.597790i
\(171\) −1.00000 + 1.73205i −0.0764719 + 0.132453i
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −6.00000 10.3923i −0.456172 0.790112i 0.542583 0.840002i \(-0.317446\pi\)
−0.998755 + 0.0498898i \(0.984113\pi\)
\(174\) 6.00000 0.454859
\(175\) −8.00000 + 6.92820i −0.604743 + 0.523723i
\(176\) −1.00000 −0.0753778
\(177\) 6.00000 + 10.3923i 0.450988 + 0.781133i
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 1.50000 + 2.59808i 0.111803 + 0.193649i
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 1.00000 + 5.19615i 0.0741249 + 0.385164i
\(183\) 5.00000 0.369611
\(184\) 1.50000 + 2.59808i 0.110581 + 0.191533i
\(185\) 3.00000 5.19615i 0.220564 0.382029i
\(186\) −2.00000 + 3.46410i −0.146647 + 0.254000i
\(187\) 1.50000 + 2.59808i 0.109691 + 0.189990i
\(188\) −9.00000 −0.656392
\(189\) 2.50000 + 0.866025i 0.181848 + 0.0629941i
\(190\) 6.00000 0.435286
\(191\) −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i \(-0.831886\pi\)
−0.00454614 0.999990i \(-0.501447\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i \(-0.856266\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 8.50000 + 14.7224i 0.610264 + 1.05701i
\(195\) −6.00000 −0.429669
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) −0.500000 0.866025i −0.0355335 0.0615457i
\(199\) −1.00000 + 1.73205i −0.0708881 + 0.122782i −0.899291 0.437351i \(-0.855917\pi\)
0.828403 + 0.560133i \(0.189250\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) −2.50000 4.33013i −0.176336 0.305424i
\(202\) −12.0000 −0.844317
\(203\) −15.0000 5.19615i −1.05279 0.364698i
\(204\) 3.00000 0.210042
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) −1.50000 + 2.59808i −0.104257 + 0.180579i
\(208\) −1.00000 1.73205i −0.0693375 0.120096i
\(209\) −2.00000 −0.138343
\(210\) −1.50000 7.79423i −0.103510 0.537853i
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) −6.00000 + 10.3923i −0.411113 + 0.712069i
\(214\) 1.50000 2.59808i 0.102538 0.177601i
\(215\) 3.00000 + 5.19615i 0.204598 + 0.354375i
\(216\) −1.00000 −0.0680414
\(217\) 8.00000 6.92820i 0.543075 0.470317i
\(218\) −11.0000 −0.745014
\(219\) 8.00000 + 13.8564i 0.540590 + 0.936329i
\(220\) −1.50000 + 2.59808i −0.101130 + 0.175162i
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 1.00000 + 1.73205i 0.0671156 + 0.116248i
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) 4.00000 0.266667
\(226\) −3.00000 5.19615i −0.199557 0.345643i
\(227\) 10.5000 18.1865i 0.696909 1.20708i −0.272623 0.962121i \(-0.587891\pi\)
0.969533 0.244962i \(-0.0787754\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) 9.00000 0.593442
\(231\) 0.500000 + 2.59808i 0.0328976 + 0.170941i
\(232\) 6.00000 0.393919
\(233\) −13.5000 23.3827i −0.884414 1.53185i −0.846383 0.532574i \(-0.821225\pi\)
−0.0380310 0.999277i \(-0.512109\pi\)
\(234\) 1.00000 1.73205i 0.0653720 0.113228i
\(235\) −13.5000 + 23.3827i −0.880643 + 1.52532i
\(236\) 6.00000 + 10.3923i 0.390567 + 0.676481i
\(237\) 17.0000 1.10427
\(238\) −7.50000 2.59808i −0.486153 0.168408i
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 1.50000 + 2.59808i 0.0968246 + 0.167705i
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 5.00000 0.320092
\(245\) −3.00000 + 20.7846i −0.191663 + 1.32788i
\(246\) 3.00000 0.191273
\(247\) −2.00000 3.46410i −0.127257 0.220416i
\(248\) −2.00000 + 3.46410i −0.127000 + 0.219971i
\(249\) −4.50000 + 7.79423i −0.285176 + 0.493939i
\(250\) 1.50000 + 2.59808i 0.0948683 + 0.164317i
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 2.50000 + 0.866025i 0.157485 + 0.0545545i
\(253\) −3.00000 −0.188608
\(254\) 5.50000 + 9.52628i 0.345101 + 0.597732i
\(255\) 4.50000 7.79423i 0.281801 0.488094i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i \(-0.226587\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(258\) −2.00000 −0.124515
\(259\) −1.00000 5.19615i −0.0621370 0.322873i
\(260\) −6.00000 −0.372104
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) −6.00000 + 10.3923i −0.370681 + 0.642039i
\(263\) 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i \(-0.712699\pi\)
0.989561 + 0.144112i \(0.0460326\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) −18.0000 −1.10573
\(266\) 4.00000 3.46410i 0.245256 0.212398i
\(267\) −6.00000 −0.367194
\(268\) −2.50000 4.33013i −0.152712 0.264505i
\(269\) −4.50000 + 7.79423i −0.274370 + 0.475223i −0.969976 0.243201i \(-0.921803\pi\)
0.695606 + 0.718423i \(0.255136\pi\)
\(270\) −1.50000 + 2.59808i −0.0912871 + 0.158114i
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 3.00000 0.181902
\(273\) −4.00000 + 3.46410i −0.242091 + 0.209657i
\(274\) −18.0000 −1.08742
\(275\) 2.00000 + 3.46410i 0.120605 + 0.208893i
\(276\) −1.50000 + 2.59808i −0.0902894 + 0.156386i
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) 7.00000 + 12.1244i 0.419832 + 0.727171i
\(279\) −4.00000 −0.239474
\(280\) −1.50000 7.79423i −0.0896421 0.465794i
\(281\) 3.00000 0.178965 0.0894825 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) −4.50000 7.79423i −0.267971 0.464140i
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) 3.00000 + 5.19615i 0.177705 + 0.307794i
\(286\) 2.00000 0.118262
\(287\) −7.50000 2.59808i −0.442711 0.153360i
\(288\) −1.00000 −0.0589256
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 9.00000 15.5885i 0.528498 0.915386i
\(291\) −8.50000 + 14.7224i −0.498279 + 0.863044i
\(292\) 8.00000 + 13.8564i 0.468165 + 0.810885i
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) −5.50000 4.33013i −0.320767 0.252538i
\(295\) 36.0000 2.09600
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) 0.500000 0.866025i 0.0290129 0.0502519i
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) −3.00000 5.19615i −0.173494 0.300501i
\(300\) 4.00000 0.230940
\(301\) 5.00000 + 1.73205i 0.288195 + 0.0998337i
\(302\) 1.00000 0.0575435
\(303\) −6.00000 10.3923i −0.344691 0.597022i
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) 7.50000 12.9904i 0.429449 0.743827i
\(306\) 1.50000 + 2.59808i 0.0857493 + 0.148522i
\(307\) −22.0000 −1.25561 −0.627803 0.778372i \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) 0.500000 + 2.59808i 0.0284901 + 0.148039i
\(309\) 14.0000 0.796432
\(310\) 6.00000 + 10.3923i 0.340777 + 0.590243i
\(311\) −10.5000 + 18.1865i −0.595400 + 1.03126i 0.398090 + 0.917346i \(0.369673\pi\)
−0.993490 + 0.113917i \(0.963660\pi\)
\(312\) 1.00000 1.73205i 0.0566139 0.0980581i
\(313\) −1.00000 1.73205i −0.0565233 0.0979013i 0.836379 0.548151i \(-0.184668\pi\)
−0.892903 + 0.450250i \(0.851335\pi\)
\(314\) −20.0000 −1.12867
\(315\) 6.00000 5.19615i 0.338062 0.292770i
\(316\) 17.0000 0.956325
\(317\) 16.5000 + 28.5788i 0.926732 + 1.60515i 0.788751 + 0.614713i \(0.210728\pi\)
0.137981 + 0.990435i \(0.455939\pi\)
\(318\) 3.00000 5.19615i 0.168232 0.291386i
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) 1.50000 + 2.59808i 0.0838525 + 0.145237i
\(321\) 3.00000 0.167444
\(322\) 6.00000 5.19615i 0.334367 0.289570i
\(323\) 6.00000 0.333849
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −4.00000 + 6.92820i −0.221880 + 0.384308i
\(326\) −0.500000 + 0.866025i −0.0276924 + 0.0479647i
\(327\) −5.50000 9.52628i −0.304151 0.526804i
\(328\) 3.00000 0.165647
\(329\) 4.50000 + 23.3827i 0.248093 + 1.28913i
\(330\) −3.00000 −0.165145
\(331\) −5.50000 9.52628i −0.302307 0.523612i 0.674351 0.738411i \(-0.264424\pi\)
−0.976658 + 0.214799i \(0.931090\pi\)
\(332\) −4.50000 + 7.79423i −0.246970 + 0.427764i
\(333\) −1.00000 + 1.73205i −0.0547997 + 0.0949158i
\(334\) −6.00000 10.3923i −0.328305 0.568642i
\(335\) −15.0000 −0.819538
\(336\) 2.50000 + 0.866025i 0.136386 + 0.0472456i
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) 4.50000 7.79423i 0.244047 0.422701i
\(341\) −2.00000 3.46410i −0.108306 0.187592i
\(342\) −2.00000 −0.108148
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −2.00000 −0.107833
\(345\) 4.50000 + 7.79423i 0.242272 + 0.419627i
\(346\) 6.00000 10.3923i 0.322562 0.558694i
\(347\) 16.5000 28.5788i 0.885766 1.53419i 0.0409337 0.999162i \(-0.486967\pi\)
0.844833 0.535031i \(-0.179700\pi\)
\(348\) 3.00000 + 5.19615i 0.160817 + 0.278543i
\(349\) 11.0000 0.588817 0.294408 0.955680i \(-0.404877\pi\)
0.294408 + 0.955680i \(0.404877\pi\)
\(350\) −10.0000 3.46410i −0.534522 0.185164i
\(351\) 2.00000 0.106752
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) 6.00000 10.3923i 0.319348 0.553127i −0.661004 0.750382i \(-0.729870\pi\)
0.980352 + 0.197256i \(0.0632029\pi\)
\(354\) −6.00000 + 10.3923i −0.318896 + 0.552345i
\(355\) 18.0000 + 31.1769i 0.955341 + 1.65470i
\(356\) −6.00000 −0.317999
\(357\) −1.50000 7.79423i −0.0793884 0.412514i
\(358\) −12.0000 −0.634220
\(359\) −15.0000 25.9808i −0.791670 1.37121i −0.924932 0.380131i \(-0.875879\pi\)
0.133263 0.991081i \(-0.457455\pi\)
\(360\) −1.50000 + 2.59808i −0.0790569 + 0.136931i
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) −5.00000 8.66025i −0.262794 0.455173i
\(363\) 1.00000 0.0524864
\(364\) −4.00000 + 3.46410i −0.209657 + 0.181568i
\(365\) 48.0000 2.51243
\(366\) 2.50000 + 4.33013i 0.130677 + 0.226339i
\(367\) 5.00000 8.66025i 0.260998 0.452062i −0.705509 0.708700i \(-0.749282\pi\)
0.966507 + 0.256639i \(0.0826151\pi\)
\(368\) −1.50000 + 2.59808i −0.0781929 + 0.135434i
\(369\) 1.50000 + 2.59808i 0.0780869 + 0.135250i
\(370\) 6.00000 0.311925
\(371\) −12.0000 + 10.3923i −0.623009 + 0.539542i
\(372\) −4.00000 −0.207390
\(373\) 0.500000 + 0.866025i 0.0258890 + 0.0448411i 0.878680 0.477412i \(-0.158425\pi\)
−0.852791 + 0.522253i \(0.825092\pi\)
\(374\) −1.50000 + 2.59808i −0.0775632 + 0.134343i
\(375\) −1.50000 + 2.59808i −0.0774597 + 0.134164i
\(376\) −4.50000 7.79423i −0.232070 0.401957i
\(377\) −12.0000 −0.618031
\(378\) 0.500000 + 2.59808i 0.0257172 + 0.133631i
\(379\) 29.0000 1.48963 0.744815 0.667271i \(-0.232538\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(380\) 3.00000 + 5.19615i 0.153897 + 0.266557i
\(381\) −5.50000 + 9.52628i −0.281774 + 0.488046i
\(382\) 12.0000 20.7846i 0.613973 1.06343i
\(383\) −12.0000 20.7846i −0.613171 1.06204i −0.990702 0.136047i \(-0.956560\pi\)
0.377531 0.925997i \(-0.376773\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 7.50000 + 2.59808i 0.382235 + 0.132410i
\(386\) −2.00000 −0.101797
\(387\) −1.00000 1.73205i −0.0508329 0.0880451i
\(388\) −8.50000 + 14.7224i −0.431522 + 0.747418i
\(389\) −10.5000 + 18.1865i −0.532371 + 0.922094i 0.466915 + 0.884302i \(0.345366\pi\)
−0.999286 + 0.0377914i \(0.987968\pi\)
\(390\) −3.00000 5.19615i −0.151911 0.263117i
\(391\) 9.00000 0.455150
\(392\) −5.50000 4.33013i −0.277792 0.218704i
\(393\) −12.0000 −0.605320
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) 25.5000 44.1673i 1.28304 2.22230i
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) −1.00000 1.73205i −0.0501886 0.0869291i 0.839840 0.542834i \(-0.182649\pi\)
−0.890028 + 0.455905i \(0.849316\pi\)
\(398\) −2.00000 −0.100251
\(399\) 5.00000 + 1.73205i 0.250313 + 0.0867110i
\(400\) 4.00000 0.200000
\(401\) −15.0000 25.9808i −0.749064 1.29742i −0.948272 0.317460i \(-0.897170\pi\)
0.199207 0.979957i \(-0.436163\pi\)
\(402\) 2.50000 4.33013i 0.124689 0.215967i
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) −6.00000 10.3923i −0.298511 0.517036i
\(405\) −3.00000 −0.149071
\(406\) −3.00000 15.5885i −0.148888 0.773642i
\(407\) −2.00000 −0.0991363
\(408\) 1.50000 + 2.59808i 0.0742611 + 0.128624i
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) 4.50000 7.79423i 0.222239 0.384930i
\(411\) −9.00000 15.5885i −0.443937 0.768922i
\(412\) 14.0000 0.689730
\(413\) 24.0000 20.7846i 1.18096 1.02274i
\(414\) −3.00000 −0.147442
\(415\) 13.5000 + 23.3827i 0.662689 + 1.14781i
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) −7.00000 + 12.1244i −0.342791 + 0.593732i
\(418\) −1.00000 1.73205i −0.0489116 0.0847174i
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 6.00000 5.19615i 0.292770 0.253546i
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) −11.0000 19.0526i −0.535472 0.927464i
\(423\) 4.50000 7.79423i 0.218797 0.378968i
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) −6.00000 10.3923i −0.291043 0.504101i
\(426\) −12.0000 −0.581402
\(427\) −2.50000 12.9904i −0.120983 0.628649i
\(428\) 3.00000 0.145010
\(429\) 1.00000 + 1.73205i 0.0482805 + 0.0836242i
\(430\) −3.00000 + 5.19615i −0.144673 + 0.250581i
\(431\) 3.00000 5.19615i 0.144505 0.250290i −0.784683 0.619897i \(-0.787174\pi\)
0.929188 + 0.369607i \(0.120508\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 35.0000 1.68199 0.840996 0.541041i \(-0.181970\pi\)
0.840996 + 0.541041i \(0.181970\pi\)
\(434\) 10.0000 + 3.46410i 0.480015 + 0.166282i
\(435\) 18.0000 0.863034
\(436\) −5.50000 9.52628i −0.263402 0.456226i
\(437\) −3.00000 + 5.19615i −0.143509 + 0.248566i
\(438\) −8.00000 + 13.8564i −0.382255 + 0.662085i
\(439\) 9.50000 + 16.4545i 0.453410 + 0.785330i 0.998595 0.0529862i \(-0.0168739\pi\)
−0.545185 + 0.838316i \(0.683541\pi\)
\(440\) −3.00000 −0.143019
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) −6.00000 −0.285391
\(443\) −9.00000 15.5885i −0.427603 0.740630i 0.569057 0.822298i \(-0.307309\pi\)
−0.996660 + 0.0816684i \(0.973975\pi\)
\(444\) −1.00000 + 1.73205i −0.0474579 + 0.0821995i
\(445\) −9.00000 + 15.5885i −0.426641 + 0.738964i
\(446\) 10.0000 + 17.3205i 0.473514 + 0.820150i
\(447\) 6.00000 0.283790
\(448\) 2.50000 + 0.866025i 0.118114 + 0.0409159i
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 2.00000 + 3.46410i 0.0942809 + 0.163299i
\(451\) −1.50000 + 2.59808i −0.0706322 + 0.122339i
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 0.500000 + 0.866025i 0.0234920 + 0.0406894i
\(454\) 21.0000 0.985579
\(455\) 3.00000 + 15.5885i 0.140642 + 0.730798i
\(456\) −2.00000 −0.0936586
\(457\) −19.0000 32.9090i −0.888783 1.53942i −0.841316 0.540544i \(-0.818219\pi\)
−0.0474665 0.998873i \(-0.515115\pi\)
\(458\) −5.00000 + 8.66025i −0.233635 + 0.404667i
\(459\) −1.50000 + 2.59808i −0.0700140 + 0.121268i
\(460\) 4.50000 + 7.79423i 0.209814 + 0.363408i
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) −2.00000 + 1.73205i −0.0930484 + 0.0805823i
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) −6.00000 + 10.3923i −0.278243 + 0.481932i
\(466\) 13.5000 23.3827i 0.625375 1.08318i
\(467\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) 2.00000 0.0924500
\(469\) −10.0000 + 8.66025i −0.461757 + 0.399893i
\(470\) −27.0000 −1.24542
\(471\) −10.0000 17.3205i −0.460776 0.798087i
\(472\) −6.00000 + 10.3923i −0.276172 + 0.478345i
\(473\) 1.00000 1.73205i 0.0459800 0.0796398i
\(474\) 8.50000 + 14.7224i 0.390418 + 0.676224i
\(475\) 8.00000 0.367065
\(476\) −1.50000 7.79423i −0.0687524 0.357248i
\(477\) 6.00000 0.274721
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) −1.50000 + 2.59808i −0.0684653 + 0.118585i
\(481\) −2.00000 3.46410i −0.0911922 0.157949i
\(482\) 10.0000 0.455488
\(483\) 7.50000 + 2.59808i 0.341262 + 0.118217i
\(484\) 1.00000 0.0454545
\(485\) 25.5000 + 44.1673i 1.15790 + 2.00553i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −4.00000 + 6.92820i −0.181257 + 0.313947i −0.942309 0.334744i \(-0.891350\pi\)
0.761052 + 0.648691i \(0.224683\pi\)
\(488\) 2.50000 + 4.33013i 0.113170 + 0.196016i
\(489\) −1.00000 −0.0452216
\(490\) −19.5000 + 7.79423i −0.880920 + 0.352107i
\(491\) −3.00000 −0.135388 −0.0676941 0.997706i \(-0.521564\pi\)
−0.0676941 + 0.997706i \(0.521564\pi\)
\(492\) 1.50000 + 2.59808i 0.0676252 + 0.117130i
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) 2.00000 3.46410i 0.0899843 0.155857i
\(495\) −1.50000 2.59808i −0.0674200 0.116775i
\(496\) −4.00000 −0.179605
\(497\) 30.0000 + 10.3923i 1.34568 + 0.466159i
\(498\) −9.00000 −0.403300
\(499\) 14.0000 + 24.2487i 0.626726 + 1.08552i 0.988204 + 0.153141i \(0.0489388\pi\)
−0.361478 + 0.932381i \(0.617728\pi\)
\(500\) −1.50000 + 2.59808i −0.0670820 + 0.116190i
\(501\) 6.00000 10.3923i 0.268060 0.464294i
\(502\) −12.0000 20.7846i −0.535586 0.927663i
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0.500000 + 2.59808i 0.0222718 + 0.115728i
\(505\) −36.0000 −1.60198
\(506\) −1.50000 2.59808i −0.0666831 0.115499i
\(507\) 4.50000 7.79423i 0.199852 0.346154i
\(508\) −5.50000 + 9.52628i −0.244023 + 0.422660i
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 9.00000 0.398527
\(511\) 32.0000 27.7128i 1.41560 1.22594i
\(512\) −1.00000 −0.0441942
\(513\) −1.00000 1.73205i −0.0441511 0.0764719i
\(514\) 3.00000 5.19615i 0.132324 0.229192i
\(515\) 21.0000 36.3731i 0.925371 1.60279i
\(516\) −1.00000 1.73205i −0.0440225 0.0762493i
\(517\) 9.00000 0.395820
\(518\) 4.00000 3.46410i 0.175750 0.152204i
\(519\) 12.0000 0.526742
\(520\) −3.00000 5.19615i −0.131559 0.227866i
\(521\) −9.00000 + 15.5885i −0.394297 + 0.682943i −0.993011 0.118020i \(-0.962345\pi\)
0.598714 + 0.800963i \(0.295679\pi\)
\(522\) −3.00000 + 5.19615i −0.131306 + 0.227429i
\(523\) −13.0000 22.5167i −0.568450 0.984585i −0.996719 0.0809336i \(-0.974210\pi\)
0.428269 0.903651i \(-0.359124\pi\)
\(524\) −12.0000 −0.524222
\(525\) −2.00000 10.3923i −0.0872872 0.453557i
\(526\) 12.0000 0.523225
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) 0.500000 0.866025i 0.0217597 0.0376889i
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) −9.00000 15.5885i −0.390935 0.677119i
\(531\) −12.0000 −0.520756
\(532\) 5.00000 + 1.73205i 0.216777 + 0.0750939i
\(533\) −6.00000 −0.259889
\(534\) −3.00000 5.19615i −0.129823 0.224860i
\(535\) 4.50000 7.79423i 0.194552 0.336974i
\(536\) 2.50000 4.33013i 0.107984 0.187033i
\(537\) −6.00000 10.3923i −0.258919 0.448461i
\(538\) −9.00000 −0.388018
\(539\) 6.50000 2.59808i 0.279975 0.111907i
\(540\) −3.00000 −0.129099
\(541\) −11.5000 19.9186i −0.494424 0.856367i 0.505556 0.862794i \(-0.331288\pi\)
−0.999979 + 0.00642713i \(0.997954\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) 5.00000 8.66025i 0.214571 0.371647i
\(544\) 1.50000 + 2.59808i 0.0643120 + 0.111392i
\(545\) −33.0000 −1.41356
\(546\) −5.00000 1.73205i −0.213980 0.0741249i
\(547\) −46.0000 −1.96682 −0.983409 0.181402i \(-0.941936\pi\)
−0.983409 + 0.181402i \(0.941936\pi\)
\(548\) −9.00000 15.5885i −0.384461 0.665906i
\(549\) −2.50000 + 4.33013i −0.106697 + 0.184805i
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) 6.00000 + 10.3923i 0.255609 + 0.442727i
\(552\) −3.00000 −0.127688
\(553\) −8.50000 44.1673i −0.361457 1.87818i
\(554\) 10.0000 0.424859
\(555\) 3.00000 + 5.19615i 0.127343 + 0.220564i
\(556\) −7.00000 + 12.1244i −0.296866 + 0.514187i
\(557\) 18.0000 31.1769i 0.762684 1.32101i −0.178778 0.983890i \(-0.557214\pi\)
0.941462 0.337119i \(-0.109452\pi\)
\(558\) −2.00000 3.46410i −0.0846668 0.146647i
\(559\) 4.00000 0.169182
\(560\) 6.00000 5.19615i 0.253546 0.219578i
\(561\) −3.00000 −0.126660
\(562\) 1.50000 + 2.59808i 0.0632737 + 0.109593i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 4.50000 7.79423i 0.189484 0.328196i
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) −14.0000 −0.588464
\(567\) −2.00000 + 1.73205i −0.0839921 + 0.0727393i
\(568\) −12.0000 −0.503509
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) −3.00000 + 5.19615i −0.125656 + 0.217643i
\(571\) −19.0000 + 32.9090i −0.795125 + 1.37720i 0.127634 + 0.991821i \(0.459262\pi\)
−0.922760 + 0.385376i \(0.874072\pi\)
\(572\) 1.00000 + 1.73205i 0.0418121 + 0.0724207i
\(573\) 24.0000 1.00261
\(574\) −1.50000 7.79423i −0.0626088 0.325325i
\(575\) 12.0000 0.500435
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −8.50000 + 14.7224i −0.353860 + 0.612903i −0.986922 0.161198i \(-0.948464\pi\)
0.633062 + 0.774101i \(0.281798\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) −1.00000 1.73205i −0.0415586 0.0719816i
\(580\) 18.0000 0.747409
\(581\) 22.5000 + 7.79423i 0.933457 + 0.323359i
\(582\) −17.0000 −0.704673
\(583\) 3.00000 + 5.19615i 0.124247 + 0.215203i
\(584\) −8.00000 + 13.8564i −0.331042 + 0.573382i
\(585\) 3.00000 5.19615i 0.124035 0.214834i
\(586\) −12.0000 20.7846i −0.495715 0.858604i
\(587\) 36.0000 1.48588 0.742940 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 1.00000 6.92820i 0.0412393 0.285714i
\(589\) −8.00000 −0.329634
\(590\) 18.0000 + 31.1769i 0.741048 + 1.28353i
\(591\) −6.00000 + 10.3923i −0.246807 + 0.427482i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) 1.00000 0.0410305
\(595\) −22.5000 7.79423i −0.922410 0.319532i
\(596\) 6.00000 0.245770
\(597\) −1.00000 1.73205i −0.0409273 0.0708881i
\(598\) 3.00000 5.19615i 0.122679 0.212486i
\(599\) −13.5000 + 23.3827i −0.551595 + 0.955391i 0.446565 + 0.894751i \(0.352647\pi\)
−0.998160 + 0.0606393i \(0.980686\pi\)
\(600\) 2.00000 + 3.46410i 0.0816497 + 0.141421i
\(601\) −28.0000 −1.14214 −0.571072 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) 1.00000 + 5.19615i 0.0407570 + 0.211779i
\(603\) 5.00000 0.203616
\(604\) 0.500000 + 0.866025i 0.0203447 + 0.0352381i
\(605\) 1.50000 2.59808i 0.0609837 0.105627i
\(606\) 6.00000 10.3923i 0.243733 0.422159i
\(607\) 0.500000 + 0.866025i 0.0202944 + 0.0351509i 0.875994 0.482322i \(-0.160206\pi\)
−0.855700 + 0.517472i \(0.826873\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 12.0000 10.3923i 0.486265 0.421117i
\(610\) 15.0000 0.607332
\(611\) 9.00000 + 15.5885i 0.364101 + 0.630641i
\(612\) −1.50000 + 2.59808i −0.0606339 + 0.105021i
\(613\) 15.5000 26.8468i 0.626039 1.08433i −0.362300 0.932062i \(-0.618008\pi\)
0.988339 0.152270i \(-0.0486583\pi\)
\(614\) −11.0000 19.0526i −0.443924 0.768899i
\(615\) 9.00000 0.362915
\(616\) −2.00000 + 1.73205i −0.0805823 + 0.0697863i
\(617\) 30.0000 1.20775 0.603877 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) 7.00000 + 12.1244i 0.281581 + 0.487713i
\(619\) −5.50000 + 9.52628i −0.221064 + 0.382893i −0.955131 0.296183i \(-0.904286\pi\)
0.734068 + 0.679076i \(0.237620\pi\)
\(620\) −6.00000 + 10.3923i −0.240966 + 0.417365i
\(621\) −1.50000 2.59808i −0.0601929 0.104257i
\(622\) −21.0000 −0.842023
\(623\) 3.00000 + 15.5885i 0.120192 + 0.624538i
\(624\) 2.00000 0.0800641
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 1.00000 1.73205i 0.0399680 0.0692267i
\(627\) 1.00000 1.73205i 0.0399362 0.0691714i
\(628\) −10.0000 17.3205i −0.399043 0.691164i
\(629\) 6.00000 0.239236
\(630\) 7.50000 + 2.59808i 0.298807 + 0.103510i
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 8.50000 + 14.7224i 0.338112 + 0.585627i
\(633\) 11.0000 19.0526i 0.437211 0.757271i
\(634\) −16.5000 + 28.5788i −0.655299 + 1.13501i
\(635\) 16.5000 + 28.5788i 0.654783 + 1.13412i
\(636\) 6.00000 0.237915
\(637\) 11.0000 + 8.66025i 0.435836 + 0.343132i
\(638\) −6.00000 −0.237542
\(639\) −6.00000 10.3923i −0.237356 0.411113i
\(640\) −1.50000 + 2.59808i −0.0592927 + 0.102698i
\(641\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) 1.50000 + 2.59808i 0.0592003 + 0.102538i
\(643\) −28.0000 −1.10421 −0.552106 0.833774i \(-0.686176\pi\)
−0.552106 + 0.833774i \(0.686176\pi\)
\(644\) 7.50000 + 2.59808i 0.295541 + 0.102379i
\(645\) −6.00000 −0.236250
\(646\) 3.00000 + 5.19615i 0.118033 + 0.204440i
\(647\) −19.5000 + 33.7750i −0.766624 + 1.32783i 0.172760 + 0.984964i \(0.444732\pi\)
−0.939384 + 0.342868i \(0.888602\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) −6.00000 10.3923i −0.235521 0.407934i
\(650\) −8.00000 −0.313786
\(651\) 2.00000 + 10.3923i 0.0783862 + 0.407307i
\(652\) −1.00000 −0.0391630
\(653\) 10.5000 + 18.1865i 0.410897 + 0.711694i 0.994988 0.0999939i \(-0.0318823\pi\)
−0.584091 + 0.811688i \(0.698549\pi\)
\(654\) 5.50000 9.52628i 0.215067 0.372507i
\(655\) −18.0000 + 31.1769i −0.703318 + 1.21818i
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) −16.0000 −0.624219
\(658\) −18.0000 + 15.5885i −0.701713 + 0.607701i
\(659\) −33.0000 −1.28550 −0.642749 0.766077i \(-0.722206\pi\)
−0.642749 + 0.766077i \(0.722206\pi\)
\(660\) −1.50000 2.59808i −0.0583874 0.101130i
\(661\) −16.0000 + 27.7128i −0.622328 + 1.07790i 0.366723 + 0.930330i \(0.380480\pi\)
−0.989051 + 0.147573i \(0.952854\pi\)
\(662\) 5.50000 9.52628i 0.213764 0.370249i
\(663\) −3.00000 5.19615i −0.116510 0.201802i
\(664\) −9.00000 −0.349268
\(665\) 12.0000 10.3923i 0.465340 0.402996i
\(666\) −2.00000 −0.0774984
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) −10.0000 + 17.3205i −0.386622 + 0.669650i
\(670\) −7.50000 12.9904i −0.289750 0.501862i
\(671\) −5.00000 −0.193023
\(672\) 0.500000 + 2.59808i 0.0192879 + 0.100223i
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) −11.0000 19.0526i −0.423704 0.733877i
\(675\) −2.00000 + 3.46410i −0.0769800 + 0.133333i
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) 15.0000 + 25.9808i 0.576497 + 0.998522i 0.995877 + 0.0907112i \(0.0289140\pi\)
−0.419380 + 0.907811i \(0.637753\pi\)
\(678\) 6.00000 0.230429
\(679\) 42.5000 + 14.7224i 1.63100 + 0.564995i
\(680\) 9.00000 0.345134
\(681\) 10.5000 + 18.1865i 0.402361 + 0.696909i
\(682\) 2.00000 3.46410i 0.0765840 0.132647i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) −1.00000 1.73205i −0.0382360 0.0662266i
\(685\) −54.0000 −2.06323
\(686\) −8.50000 + 16.4545i −0.324532 + 0.628235i
\(687\) −10.0000 −0.381524
\(688\) −1.00000 1.73205i −0.0381246 0.0660338i
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) −4.50000 + 7.79423i −0.171312 + 0.296721i
\(691\) 9.50000 + 16.4545i 0.361397 + 0.625958i 0.988191 0.153227i \(-0.0489666\pi\)
−0.626794 + 0.779185i \(0.715633\pi\)
\(692\) 12.0000 0.456172
\(693\) −2.50000 0.866025i −0.0949671 0.0328976i
\(694\) 33.0000 1.25266
\(695\) 21.0000 + 36.3731i 0.796575 + 1.37971i
\(696\) −3.00000 + 5.19615i −0.113715 + 0.196960i
\(697\) 4.50000 7.79423i 0.170450 0.295227i
\(698\) 5.50000 + 9.52628i 0.208178 + 0.360575i
\(699\) 27.0000 1.02123
\(700\) −2.00000 10.3923i −0.0755929 0.392792i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 1.00000 + 1.73205i 0.0377426 + 0.0653720i
\(703\) −2.00000 + 3.46410i −0.0754314 + 0.130651i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) −13.5000 23.3827i −0.508439 0.880643i
\(706\) 12.0000 0.451626
\(707\) −24.0000 + 20.7846i −0.902613 + 0.781686i
\(708\) −12.0000 −0.450988
\(709\) 14.0000 + 24.2487i 0.525781 + 0.910679i 0.999549 + 0.0300298i \(0.00956021\pi\)
−0.473768 + 0.880650i \(0.657106\pi\)
\(710\) −18.0000 + 31.1769i −0.675528 + 1.17005i
\(711\) −8.50000 + 14.7224i −0.318775 + 0.552134i
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) −12.0000 −0.449404
\(714\) 6.00000 5.19615i 0.224544 0.194461i
\(715\) 6.00000 0.224387
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) −3.00000 + 5.19615i −0.112037 + 0.194054i
\(718\) 15.0000 25.9808i 0.559795 0.969593i
\(719\) 10.5000 + 18.1865i 0.391584 + 0.678243i 0.992659 0.120950i \(-0.0385939\pi\)
−0.601075 + 0.799193i \(0.705261\pi\)
\(720\) −3.00000 −0.111803
\(721\) −7.00000 36.3731i −0.260694 1.35460i
\(722\) 15.0000 0.558242
\(723\) 5.00000 + 8.66025i 0.185952 + 0.322078i
\(724\) 5.00000 8.66025i 0.185824 0.321856i
\(725\) 12.0000 20.7846i 0.445669 0.771921i
\(726\) 0.500000 + 0.866025i 0.0185567 + 0.0321412i
\(727\) 14.0000 0.519231 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) −5.00000 1.73205i −0.185312 0.0641941i
\(729\) 1.00000 0.0370370
\(730\) 24.0000 + 41.5692i 0.888280 + 1.53855i
\(731\) −3.00000 + 5.19615i −0.110959 + 0.192187i
\(732\) −2.50000 + 4.33013i −0.0924027 + 0.160046i
\(733\) 24.5000 + 42.4352i 0.904928 + 1.56738i 0.821014 + 0.570909i \(0.193409\pi\)
0.0839145 + 0.996473i \(0.473258\pi\)
\(734\) 10.0000 0.369107
\(735\) −16.5000 12.9904i −0.608612 0.479157i
\(736\) −3.00000 −0.110581
\(737\) 2.50000 + 4.33013i 0.0920887 + 0.159502i
\(738\) −1.50000 + 2.59808i −0.0552158 + 0.0956365i
\(739\) −19.0000 + 32.9090i −0.698926 + 1.21058i 0.269913 + 0.962885i \(0.413005\pi\)
−0.968839 + 0.247691i \(0.920328\pi\)
\(740\) 3.00000 + 5.19615i 0.110282 + 0.191014i
\(741\) 4.00000 0.146944
\(742\) −15.0000 5.19615i −0.550667 0.190757i
\(743\) −30.0000 −1.10059 −0.550297 0.834969i \(-0.685485\pi\)
−0.550297 + 0.834969i \(0.685485\pi\)
\(744\) −2.00000 3.46410i −0.0733236 0.127000i
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) −0.500000 + 0.866025i −0.0183063 + 0.0317074i
\(747\) −4.50000 7.79423i −0.164646 0.285176i
\(748\) −3.00000 −0.109691
\(749\) −1.50000 7.79423i −0.0548088 0.284795i
\(750\) −3.00000 −0.109545
\(751\) −1.00000 1.73205i −0.0364905 0.0632034i 0.847203 0.531269i \(-0.178285\pi\)
−0.883694 + 0.468065i \(0.844951\pi\)
\(752\) 4.50000 7.79423i 0.164098 0.284226i
\(753\) 12.0000 20.7846i 0.437304 0.757433i
\(754\) −6.00000 10.3923i −0.218507 0.378465i
\(755\) 3.00000 0.109181
\(756\) −2.00000 + 1.73205i −0.0727393 + 0.0629941i
\(757\) 14.0000 0.508839 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(758\) 14.5000 + 25.1147i 0.526664 + 0.912208i
\(759\) 1.50000 2.59808i 0.0544466 0.0943042i
\(760\) −3.00000 + 5.19615i −0.108821 + 0.188484i
\(761\) −7.50000 12.9904i −0.271875 0.470901i 0.697467 0.716617i \(-0.254310\pi\)
−0.969342 + 0.245716i \(0.920977\pi\)
\(762\) −11.0000 −0.398488
\(763\) −22.0000 + 19.0526i −0.796453 + 0.689749i
\(764\) 24.0000 0.868290
\(765\) 4.50000 + 7.79423i 0.162698 + 0.281801i
\(766\) 12.0000 20.7846i 0.433578 0.750978i
\(767\) 12.0000 20.7846i 0.433295 0.750489i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) −46.0000 −1.65880 −0.829401 0.558653i \(-0.811318\pi\)
−0.829401 + 0.558653i \(0.811318\pi\)
\(770\) 1.50000 + 7.79423i 0.0540562 + 0.280885i
\(771\) 6.00000 0.216085
\(772\) −1.00000 1.73205i −0.0359908 0.0623379i
\(773\) 13.5000 23.3827i 0.485561 0.841017i −0.514301 0.857610i \(-0.671949\pi\)
0.999862 + 0.0165929i \(0.00528194\pi\)
\(774\) 1.00000 1.73205i 0.0359443 0.0622573i
\(775\) 8.00000 + 13.8564i 0.287368 + 0.497737i
\(776\) −17.0000 −0.610264