Properties

Label 462.2.i.c.331.1
Level $462$
Weight $2$
Character 462.331
Analytic conductor $3.689$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 331.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 462.331
Dual form 462.2.i.c.67.1

$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

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

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 −0.306851 0.951757i \(-0.599275\pi\)
0.977672 0.210138i \(-0.0673912\pi\)
\(6\) −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 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) −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 −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 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 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 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 −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 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 −0.325150 0.945662i \(-0.605415\pi\)
0.981543 0.191243i \(-0.0612518\pi\)
\(48\) 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 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 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 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 1.50000 + 2.59808i 0.193649 + 0.335410i
\(61\) −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i \(-0.937047\pi\)
0.660415 + 0.750901i \(0.270381\pi\)
\(62\) 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 0.671932 0.740613i \(-0.265465\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) −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 0.772246 + 0.635323i \(0.219133\pi\)
0.164083 + 0.986447i \(0.447534\pi\)
\(74\) 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 −0.225018 + 0.974355i \(0.572244\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 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 −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 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 −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) 1.50000 + 2.59808i 0.148522 + 0.257248i
\(103\) −7.00000 + 12.1244i −0.689730 + 1.19465i 0.282194 + 0.959357i \(0.408938\pi\)
−0.971925 + 0.235291i \(0.924396\pi\)
\(104\) −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 −0.929377 0.369132i \(-0.879655\pi\)
0.784366 + 0.620298i \(0.212988\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 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 −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) −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 −0.938148 0.346235i \(-0.887460\pi\)
0.169226 0.985577i \(-0.445873\pi\)
\(138\) 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 −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 2.00000 + 3.46410i 0.163299 + 0.282843i
\(151\) 0.500000 + 0.866025i 0.0406894 + 0.0704761i 0.885653 0.464348i \(-0.153711\pi\)
−0.844963 + 0.534824i \(0.820378\pi\)
\(152\) 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 −0.920860 0.389892i \(-0.872512\pi\)
0.122774 0.992435i \(-0.460821\pi\)
\(158\) 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 −0.845780 0.533533i \(-0.820864\pi\)
0.884943 + 0.465700i \(0.154198\pi\)
\(164\) 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 −0.998755 0.0498898i \(-0.984113\pi\)
0.542583 + 0.840002i \(0.317446\pi\)
\(174\) 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 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 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 −0.00454614 + 0.999990i \(0.501447\pi\)
−0.863743 + 0.503932i \(0.831886\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 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 0.828403 0.560133i \(-0.189250\pi\)
−0.899291 + 0.437351i \(0.855917\pi\)
\(200\) 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 0.969533 + 0.244962i \(0.0787754\pi\)
−0.272623 + 0.962121i \(0.587891\pi\)
\(228\) −1.00000 1.73205i −0.0662266 0.114708i
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 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 −0.0380310 + 0.999277i \(0.512109\pi\)
−0.846383 + 0.532574i \(0.821225\pi\)
\(234\) 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 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 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 −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) −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 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) −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 0.695606 0.718423i \(-0.255136\pi\)
−0.969976 + 0.243201i \(0.921803\pi\)
\(270\) −1.50000 2.59808i −0.0912871 0.158114i
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 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 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) 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 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) −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 −0.993490 0.113917i \(-0.963660\pi\)
0.398090 0.917346i \(-0.369673\pi\)
\(312\) 1.00000 + 1.73205i 0.0566139 + 0.0980581i
\(313\) −1.00000 + 1.73205i −0.0565233 + 0.0979013i −0.892903 0.450250i \(-0.851335\pi\)
0.836379 + 0.548151i \(0.184668\pi\)
\(314\) −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 0.137981 0.990435i \(-0.455939\pi\)
0.788751 0.614713i \(-0.210728\pi\)
\(318\) 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 −0.976658 0.214799i \(-0.931090\pi\)
0.674351 + 0.738411i \(0.264424\pi\)
\(332\) −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 0.844833 + 0.535031i \(0.179700\pi\)
0.0409337 + 0.999162i \(0.486967\pi\)
\(348\) 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 0.980352 0.197256i \(-0.0632029\pi\)
−0.661004 + 0.750382i \(0.729870\pi\)
\(354\) −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 0.133263 + 0.991081i \(0.457455\pi\)
−0.924932 + 0.380131i \(0.875879\pi\)
\(360\) −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 0.966507 0.256639i \(-0.0826151\pi\)
−0.705509 + 0.708700i \(0.749282\pi\)
\(368\) −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 −0.852791 0.522253i \(-0.825092\pi\)
0.878680 + 0.477412i \(0.158425\pi\)
\(374\) −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 0.377531 + 0.925997i \(0.376773\pi\)
−0.990702 + 0.136047i \(0.956560\pi\)
\(384\) −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 −0.999286 0.0377914i \(-0.987968\pi\)
0.466915 0.884302i \(-0.345366\pi\)
\(390\) −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 −0.890028 0.455905i \(-0.849316\pi\)
0.839840 + 0.542834i \(0.182649\pi\)
\(398\) −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 0.199207 + 0.979957i \(0.436163\pi\)
−0.948272 + 0.317460i \(0.897170\pi\)
\(402\) 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 0.639430 0.768849i \(-0.279170\pi\)
−0.985558 + 0.169338i \(0.945837\pi\)
\(410\) 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 0.929188 0.369607i \(-0.120508\pi\)
−0.784683 + 0.619897i \(0.787174\pi\)
\(432\) −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 −0.545185 0.838316i \(-0.683541\pi\)
0.998595 + 0.0529862i \(0.0168739\pi\)
\(440\) −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 −0.996660 0.0816684i \(-0.973975\pi\)
0.569057 + 0.822298i \(0.307309\pi\)
\(444\) −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 −0.0474665 + 0.998873i \(0.515115\pi\)
−0.841316 + 0.540544i \(0.818219\pi\)
\(458\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(468\) 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 −0.998392 0.0566937i \(-0.981944\pi\)
0.450098 0.892979i \(-0.351389\pi\)
\(480\) −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 0.761052 0.648691i \(-0.224683\pi\)
−0.942309 + 0.334744i \(0.891350\pi\)
\(488\) 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 −0.361478 0.932381i \(-0.617728\pi\)
0.988204 0.153141i \(-0.0489388\pi\)
\(500\) −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 −0.924821 0.380402i \(-0.875786\pi\)
0.791849 + 0.610718i \(0.209119\pi\)
\(510\) 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 0.598714 0.800963i \(-0.295679\pi\)
−0.993011 + 0.118020i \(0.962345\pi\)
\(522\) −3.00000 5.19615i −0.131306 0.227429i
\(523\) −13.0000 + 22.5167i −0.568450 + 0.984585i 0.428269 + 0.903651i \(0.359124\pi\)
−0.996719 + 0.0809336i \(0.974210\pi\)
\(524\) −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 −0.999979 0.00642713i \(-0.997954\pi\)
0.505556 + 0.862794i \(0.331288\pi\)
\(542\) −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 0.941462 + 0.337119i \(0.109452\pi\)
−0.178778 + 0.983890i \(0.557214\pi\)
\(558\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) 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 −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) −3.00000 5.19615i −0.125656 0.217643i
\(571\) −19.0000 32.9090i −0.795125 1.37720i −0.922760 0.385376i \(-0.874072\pi\)
0.127634 0.991821i \(-0.459262\pi\)
\(572\) 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 0.633062 0.774101i \(-0.281798\pi\)
−0.986922 + 0.161198i \(0.948464\pi\)
\(578\) −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 −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 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 −0.998160 0.0606393i \(-0.980686\pi\)
0.446565 0.894751i \(-0.352647\pi\)
\(600\) 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 −0.855700 0.517472i \(-0.826873\pi\)
0.875994 + 0.482322i \(0.160206\pi\)
\(608\) −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 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) −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 0.734068 0.679076i \(-0.237620\pi\)
−0.955131 + 0.296183i \(0.904286\pi\)
\(620\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) 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 −0.939384 0.342868i \(-0.888602\pi\)
0.172760 0.984964i \(-0.444732\pi\)
\(648\) 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 −0.584091 0.811688i \(-0.698549\pi\)
0.994988 + 0.0999939i \(0.0318823\pi\)
\(654\) 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 −0.989051 0.147573i \(-0.952854\pi\)
0.366723 0.930330i \(-0.380480\pi\)
\(662\) 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 −0.419380 0.907811i \(-0.637753\pi\)
0.995877 0.0907112i \(-0.0289140\pi\)
\(678\) 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 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) −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 −0.626794 0.779185i \(-0.715633\pi\)
0.988191 + 0.153227i \(0.0489666\pi\)
\(692\) 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 −0.473768 0.880650i \(-0.657106\pi\)
0.999549 0.0300298i \(-0.00956021\pi\)
\(710\) −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 −0.601075 0.799193i \(-0.705261\pi\)
0.992659 + 0.120950i \(0.0385939\pi\)
\(720\) −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 0.0839145 0.996473i \(-0.473258\pi\)
0.821014 0.570909i \(-0.193409\pi\)
\(734\) 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 −0.968839 0.247691i \(-0.920328\pi\)
0.269913 0.962885i \(-0.413005\pi\)
\(740\) 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 −0.883694 0.468065i \(-0.844951\pi\)
0.847203 + 0.531269i \(0.178285\pi\)
\(752\) 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 −0.969342 0.245716i \(-0.920977\pi\)
0.697467 + 0.716617i \(0.254310\pi\)
\(762\) −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 0.999862 0.0165929i \(-0.00528194\pi\)
−0.514301 + 0.857610i \(0.671949\pi\)
\(774\) 1.00000 + 1.73205i 0.0359443 + 0.0622573i
\(775\) 8.00000 13.8564i 0.287368 0.497737i
\(776\) −17.0000