Properties

Label 74.2.c.b.47.1
Level $74$
Weight $2$
Character 74.47
Analytic conductor $0.591$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 74.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.590892974957\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 47.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 74.47
Dual form 74.2.c.b.63.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +2.00000 q^{6} +(2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +2.00000 q^{6} +(2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -3.00000 q^{10} -6.00000 q^{11} +(1.00000 - 1.73205i) q^{12} +(-1.00000 - 1.73205i) q^{13} +4.00000 q^{14} +(3.00000 - 5.19615i) 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} +(-1.50000 + 2.59808i) q^{20} +(-4.00000 + 6.92820i) q^{21} +(-3.00000 + 5.19615i) q^{22} +6.00000 q^{23} +(-1.00000 - 1.73205i) q^{24} +(-2.00000 + 3.46410i) q^{25} -2.00000 q^{26} +4.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +3.00000 q^{29} +(-3.00000 - 5.19615i) q^{30} +2.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.00000 - 10.3923i) q^{33} +(1.50000 + 2.59808i) q^{34} +(6.00000 - 10.3923i) q^{35} +1.00000 q^{36} +(5.50000 + 2.59808i) q^{37} -2.00000 q^{38} +(2.00000 - 3.46410i) q^{39} +(1.50000 + 2.59808i) q^{40} +(-1.50000 - 2.59808i) q^{41} +(4.00000 + 6.92820i) q^{42} -4.00000 q^{43} +(3.00000 + 5.19615i) q^{44} +3.00000 q^{45} +(3.00000 - 5.19615i) q^{46} -6.00000 q^{47} -2.00000 q^{48} +(-4.50000 + 7.79423i) q^{49} +(2.00000 + 3.46410i) q^{50} -6.00000 q^{51} +(-1.00000 + 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(2.00000 - 3.46410i) q^{54} +(9.00000 + 15.5885i) q^{55} +(-2.00000 - 3.46410i) q^{56} +(2.00000 - 3.46410i) q^{57} +(1.50000 - 2.59808i) q^{58} -6.00000 q^{60} +(0.500000 + 0.866025i) q^{61} +(1.00000 - 1.73205i) q^{62} -4.00000 q^{63} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} -12.0000 q^{66} +(-1.00000 - 1.73205i) q^{67} +3.00000 q^{68} +(6.00000 + 10.3923i) q^{69} +(-6.00000 - 10.3923i) q^{70} +(6.00000 + 10.3923i) q^{71} +(0.500000 - 0.866025i) q^{72} -10.0000 q^{73} +(5.00000 - 3.46410i) q^{74} -8.00000 q^{75} +(-1.00000 + 1.73205i) q^{76} +(-12.0000 - 20.7846i) q^{77} +(-2.00000 - 3.46410i) q^{78} +(-7.00000 - 12.1244i) q^{79} +3.00000 q^{80} +(5.50000 + 9.52628i) q^{81} -3.00000 q^{82} +(-3.00000 + 5.19615i) q^{83} +8.00000 q^{84} +9.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(3.00000 + 5.19615i) q^{87} +6.00000 q^{88} +(-1.50000 + 2.59808i) q^{89} +(1.50000 - 2.59808i) q^{90} +(4.00000 - 6.92820i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(2.00000 + 3.46410i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(-1.00000 + 1.73205i) q^{96} -13.0000 q^{97} +(4.50000 + 7.79423i) q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} - 6 q^{10} - 12 q^{11} + 2 q^{12} - 2 q^{13} + 8 q^{14} + 6 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - 3 q^{20} - 8 q^{21} - 6 q^{22} + 12 q^{23} - 2 q^{24} - 4 q^{25} - 4 q^{26} + 8 q^{27} + 4 q^{28} + 6 q^{29} - 6 q^{30} + 4 q^{31} + q^{32} - 12 q^{33} + 3 q^{34} + 12 q^{35} + 2 q^{36} + 11 q^{37} - 4 q^{38} + 4 q^{39} + 3 q^{40} - 3 q^{41} + 8 q^{42} - 8 q^{43} + 6 q^{44} + 6 q^{45} + 6 q^{46} - 12 q^{47} - 4 q^{48} - 9 q^{49} + 4 q^{50} - 12 q^{51} - 2 q^{52} + 6 q^{53} + 4 q^{54} + 18 q^{55} - 4 q^{56} + 4 q^{57} + 3 q^{58} - 12 q^{60} + q^{61} + 2 q^{62} - 8 q^{63} + 2 q^{64} - 6 q^{65} - 24 q^{66} - 2 q^{67} + 6 q^{68} + 12 q^{69} - 12 q^{70} + 12 q^{71} + q^{72} - 20 q^{73} + 10 q^{74} - 16 q^{75} - 2 q^{76} - 24 q^{77} - 4 q^{78} - 14 q^{79} + 6 q^{80} + 11 q^{81} - 6 q^{82} - 6 q^{83} + 16 q^{84} + 18 q^{85} - 4 q^{86} + 6 q^{87} + 12 q^{88} - 3 q^{89} + 3 q^{90} + 8 q^{91} - 6 q^{92} + 4 q^{93} - 6 q^{94} - 6 q^{95} - 2 q^{96} - 26 q^{97} + 9 q^{98} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 1.00000 + 1.73205i 0.577350 + 1.00000i 0.995782 + 0.0917517i \(0.0292466\pi\)
−0.418432 + 0.908248i \(0.637420\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i \(-0.932609\pi\)
0.306851 0.951757i \(-0.400725\pi\)
\(6\) 2.00000 0.816497
\(7\) 2.00000 + 3.46410i 0.755929 + 1.30931i 0.944911 + 0.327327i \(0.106148\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −3.00000 −0.948683
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 1.00000 1.73205i 0.288675 0.500000i
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 4.00000 1.06904
\(15\) 3.00000 5.19615i 0.774597 1.34164i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 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 \(0.907015\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) −4.00000 + 6.92820i −0.872872 + 1.51186i
\(22\) −3.00000 + 5.19615i −0.639602 + 1.10782i
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) −1.00000 1.73205i −0.204124 0.353553i
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) −2.00000 −0.392232
\(27\) 4.00000 0.769800
\(28\) 2.00000 3.46410i 0.377964 0.654654i
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) −3.00000 5.19615i −0.547723 0.948683i
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −6.00000 10.3923i −1.04447 1.80907i
\(34\) 1.50000 + 2.59808i 0.257248 + 0.445566i
\(35\) 6.00000 10.3923i 1.01419 1.75662i
\(36\) 1.00000 0.166667
\(37\) 5.50000 + 2.59808i 0.904194 + 0.427121i
\(38\) −2.00000 −0.324443
\(39\) 2.00000 3.46410i 0.320256 0.554700i
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 4.00000 + 6.92820i 0.617213 + 1.06904i
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 3.00000 + 5.19615i 0.452267 + 0.783349i
\(45\) 3.00000 0.447214
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) −6.00000 −0.875190 −0.437595 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) −2.00000 −0.288675
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) −6.00000 −0.840168
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 2.00000 3.46410i 0.272166 0.471405i
\(55\) 9.00000 + 15.5885i 1.21356 + 2.10195i
\(56\) −2.00000 3.46410i −0.267261 0.462910i
\(57\) 2.00000 3.46410i 0.264906 0.458831i
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) −6.00000 −0.774597
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) 1.00000 1.73205i 0.127000 0.219971i
\(63\) −4.00000 −0.503953
\(64\) 1.00000 0.125000
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) −12.0000 −1.47710
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 3.00000 0.363803
\(69\) 6.00000 + 10.3923i 0.722315 + 1.25109i
\(70\) −6.00000 10.3923i −0.717137 1.24212i
\(71\) 6.00000 + 10.3923i 0.712069 + 1.23334i 0.964079 + 0.265615i \(0.0855750\pi\)
−0.252010 + 0.967725i \(0.581092\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 5.00000 3.46410i 0.581238 0.402694i
\(75\) −8.00000 −0.923760
\(76\) −1.00000 + 1.73205i −0.114708 + 0.198680i
\(77\) −12.0000 20.7846i −1.36753 2.36863i
\(78\) −2.00000 3.46410i −0.226455 0.392232i
\(79\) −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i \(-0.878010\pi\)
0.139895 0.990166i \(-0.455323\pi\)
\(80\) 3.00000 0.335410
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) −3.00000 −0.331295
\(83\) −3.00000 + 5.19615i −0.329293 + 0.570352i −0.982372 0.186938i \(-0.940144\pi\)
0.653079 + 0.757290i \(0.273477\pi\)
\(84\) 8.00000 0.872872
\(85\) 9.00000 0.976187
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 3.00000 + 5.19615i 0.321634 + 0.557086i
\(88\) 6.00000 0.639602
\(89\) −1.50000 + 2.59808i −0.159000 + 0.275396i −0.934508 0.355942i \(-0.884160\pi\)
0.775509 + 0.631337i \(0.217494\pi\)
\(90\) 1.50000 2.59808i 0.158114 0.273861i
\(91\) 4.00000 6.92820i 0.419314 0.726273i
\(92\) −3.00000 5.19615i −0.312772 0.541736i
\(93\) 2.00000 + 3.46410i 0.207390 + 0.359211i
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) −1.00000 + 1.73205i −0.102062 + 0.176777i
\(97\) −13.0000 −1.31995 −0.659975 0.751288i \(-0.729433\pi\)
−0.659975 + 0.751288i \(0.729433\pi\)
\(98\) 4.50000 + 7.79423i 0.454569 + 0.787336i
\(99\) 3.00000 5.19615i 0.301511 0.522233i
\(100\) 4.00000 0.400000
\(101\) 3.00000 0.298511 0.149256 0.988799i \(-0.452312\pi\)
0.149256 + 0.988799i \(0.452312\pi\)
\(102\) −3.00000 + 5.19615i −0.297044 + 0.514496i
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 1.00000 + 1.73205i 0.0980581 + 0.169842i
\(105\) 24.0000 2.34216
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) −2.00000 3.46410i −0.192450 0.333333i
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) 18.0000 1.71623
\(111\) 1.00000 + 12.1244i 0.0949158 + 1.15079i
\(112\) −4.00000 −0.377964
\(113\) 9.00000 15.5885i 0.846649 1.46644i −0.0375328 0.999295i \(-0.511950\pi\)
0.884182 0.467143i \(-0.154717\pi\)
\(114\) −2.00000 3.46410i −0.187317 0.324443i
\(115\) −9.00000 15.5885i −0.839254 1.45363i
\(116\) −1.50000 2.59808i −0.139272 0.241225i
\(117\) 2.00000 0.184900
\(118\) 0 0
\(119\) −12.0000 −1.10004
\(120\) −3.00000 + 5.19615i −0.273861 + 0.474342i
\(121\) 25.0000 2.27273
\(122\) 1.00000 0.0905357
\(123\) 3.00000 5.19615i 0.270501 0.468521i
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) −3.00000 −0.268328
\(126\) −2.00000 + 3.46410i −0.178174 + 0.308607i
\(127\) 5.00000 8.66025i 0.443678 0.768473i −0.554281 0.832330i \(-0.687007\pi\)
0.997959 + 0.0638564i \(0.0203400\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −4.00000 6.92820i −0.352180 0.609994i
\(130\) 3.00000 + 5.19615i 0.263117 + 0.455733i
\(131\) −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i \(0.454690\pi\)
−0.928199 + 0.372084i \(0.878643\pi\)
\(132\) −6.00000 + 10.3923i −0.522233 + 0.904534i
\(133\) 4.00000 6.92820i 0.346844 0.600751i
\(134\) −2.00000 −0.172774
\(135\) −6.00000 10.3923i −0.516398 0.894427i
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 12.0000 1.02151
\(139\) −1.00000 + 1.73205i −0.0848189 + 0.146911i −0.905314 0.424743i \(-0.860365\pi\)
0.820495 + 0.571654i \(0.193698\pi\)
\(140\) −12.0000 −1.01419
\(141\) −6.00000 10.3923i −0.505291 0.875190i
\(142\) 12.0000 1.00702
\(143\) 6.00000 + 10.3923i 0.501745 + 0.869048i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −4.50000 7.79423i −0.373705 0.647275i
\(146\) −5.00000 + 8.66025i −0.413803 + 0.716728i
\(147\) −18.0000 −1.48461
\(148\) −0.500000 6.06218i −0.0410997 0.498308i
\(149\) −21.0000 −1.72039 −0.860194 0.509968i \(-0.829657\pi\)
−0.860194 + 0.509968i \(0.829657\pi\)
\(150\) −4.00000 + 6.92820i −0.326599 + 0.565685i
\(151\) 11.0000 + 19.0526i 0.895167 + 1.55048i 0.833597 + 0.552372i \(0.186277\pi\)
0.0615699 + 0.998103i \(0.480389\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) −1.50000 2.59808i −0.121268 0.210042i
\(154\) −24.0000 −1.93398
\(155\) −3.00000 5.19615i −0.240966 0.417365i
\(156\) −4.00000 −0.320256
\(157\) −5.50000 + 9.52628i −0.438948 + 0.760280i −0.997609 0.0691164i \(-0.977982\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −14.0000 −1.11378
\(159\) 12.0000 0.951662
\(160\) 1.50000 2.59808i 0.118585 0.205396i
\(161\) 12.0000 + 20.7846i 0.945732 + 1.63806i
\(162\) 11.0000 0.864242
\(163\) 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) −1.50000 + 2.59808i −0.117130 + 0.202876i
\(165\) −18.0000 + 31.1769i −1.40130 + 2.42712i
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 4.00000 6.92820i 0.308607 0.534522i
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 4.50000 7.79423i 0.345134 0.597790i
\(171\) 2.00000 0.152944
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) 10.5000 18.1865i 0.798300 1.38270i −0.122422 0.992478i \(-0.539066\pi\)
0.920722 0.390218i \(-0.127601\pi\)
\(174\) 6.00000 0.454859
\(175\) −16.0000 −1.20949
\(176\) 3.00000 5.19615i 0.226134 0.391675i
\(177\) 0 0
\(178\) 1.50000 + 2.59808i 0.112430 + 0.194734i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −1.50000 2.59808i −0.111803 0.193649i
\(181\) 0.500000 + 0.866025i 0.0371647 + 0.0643712i 0.884009 0.467469i \(-0.154834\pi\)
−0.846845 + 0.531840i \(0.821501\pi\)
\(182\) −4.00000 6.92820i −0.296500 0.513553i
\(183\) −1.00000 + 1.73205i −0.0739221 + 0.128037i
\(184\) −6.00000 −0.442326
\(185\) −1.50000 18.1865i −0.110282 1.33710i
\(186\) 4.00000 0.293294
\(187\) 9.00000 15.5885i 0.658145 1.13994i
\(188\) 3.00000 + 5.19615i 0.218797 + 0.378968i
\(189\) 8.00000 + 13.8564i 0.581914 + 1.00791i
\(190\) 3.00000 + 5.19615i 0.217643 + 0.376969i
\(191\) −6.00000 −0.434145 −0.217072 0.976156i \(-0.569651\pi\)
−0.217072 + 0.976156i \(0.569651\pi\)
\(192\) 1.00000 + 1.73205i 0.0721688 + 0.125000i
\(193\) 11.0000 0.791797 0.395899 0.918294i \(-0.370433\pi\)
0.395899 + 0.918294i \(0.370433\pi\)
\(194\) −6.50000 + 11.2583i −0.466673 + 0.808301i
\(195\) −12.0000 −0.859338
\(196\) 9.00000 0.642857
\(197\) −1.50000 + 2.59808i −0.106871 + 0.185105i −0.914501 0.404584i \(-0.867416\pi\)
0.807630 + 0.589689i \(0.200750\pi\)
\(198\) −3.00000 5.19615i −0.213201 0.369274i
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) 2.00000 3.46410i 0.141069 0.244339i
\(202\) 1.50000 2.59808i 0.105540 0.182800i
\(203\) 6.00000 + 10.3923i 0.421117 + 0.729397i
\(204\) 3.00000 + 5.19615i 0.210042 + 0.363803i
\(205\) −4.50000 + 7.79423i −0.314294 + 0.544373i
\(206\) −2.00000 + 3.46410i −0.139347 + 0.241355i
\(207\) −3.00000 + 5.19615i −0.208514 + 0.361158i
\(208\) 2.00000 0.138675
\(209\) 6.00000 + 10.3923i 0.415029 + 0.718851i
\(210\) 12.0000 20.7846i 0.828079 1.43427i
\(211\) −16.0000 −1.10149 −0.550743 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −6.00000 −0.412082
\(213\) −12.0000 + 20.7846i −0.822226 + 1.42414i
\(214\) 12.0000 0.820303
\(215\) 6.00000 + 10.3923i 0.409197 + 0.708749i
\(216\) −4.00000 −0.272166
\(217\) 4.00000 + 6.92820i 0.271538 + 0.470317i
\(218\) −0.500000 0.866025i −0.0338643 0.0586546i
\(219\) −10.0000 17.3205i −0.675737 1.17041i
\(220\) 9.00000 15.5885i 0.606780 1.05097i
\(221\) 6.00000 0.403604
\(222\) 11.0000 + 5.19615i 0.738272 + 0.348743i
\(223\) 14.0000 0.937509 0.468755 0.883328i \(-0.344703\pi\)
0.468755 + 0.883328i \(0.344703\pi\)
\(224\) −2.00000 + 3.46410i −0.133631 + 0.231455i
\(225\) −2.00000 3.46410i −0.133333 0.230940i
\(226\) −9.00000 15.5885i −0.598671 1.03693i
\(227\) 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i \(0.0371134\pi\)
−0.395860 + 0.918311i \(0.629553\pi\)
\(228\) −4.00000 −0.264906
\(229\) −5.50000 9.52628i −0.363450 0.629514i 0.625076 0.780564i \(-0.285068\pi\)
−0.988526 + 0.151050i \(0.951735\pi\)
\(230\) −18.0000 −1.18688
\(231\) 24.0000 41.5692i 1.57908 2.73505i
\(232\) −3.00000 −0.196960
\(233\) −9.00000 −0.589610 −0.294805 0.955557i \(-0.595255\pi\)
−0.294805 + 0.955557i \(0.595255\pi\)
\(234\) 1.00000 1.73205i 0.0653720 0.113228i
\(235\) 9.00000 + 15.5885i 0.587095 + 1.01688i
\(236\) 0 0
\(237\) 14.0000 24.2487i 0.909398 1.57512i
\(238\) −6.00000 + 10.3923i −0.388922 + 0.673633i
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 3.00000 + 5.19615i 0.193649 + 0.335410i
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 12.5000 21.6506i 0.803530 1.39176i
\(243\) −5.00000 + 8.66025i −0.320750 + 0.555556i
\(244\) 0.500000 0.866025i 0.0320092 0.0554416i
\(245\) 27.0000 1.72497
\(246\) −3.00000 5.19615i −0.191273 0.331295i
\(247\) −2.00000 + 3.46410i −0.127257 + 0.220416i
\(248\) −2.00000 −0.127000
\(249\) −12.0000 −0.760469
\(250\) −1.50000 + 2.59808i −0.0948683 + 0.164317i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 2.00000 + 3.46410i 0.125988 + 0.218218i
\(253\) −36.0000 −2.26330
\(254\) −5.00000 8.66025i −0.313728 0.543393i
\(255\) 9.00000 + 15.5885i 0.563602 + 0.976187i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −13.5000 + 23.3827i −0.842107 + 1.45857i 0.0460033 + 0.998941i \(0.485352\pi\)
−0.888110 + 0.459631i \(0.847982\pi\)
\(258\) −8.00000 −0.498058
\(259\) 2.00000 + 24.2487i 0.124274 + 1.50674i
\(260\) 6.00000 0.372104
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) 9.00000 + 15.5885i 0.556022 + 0.963058i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 6.00000 + 10.3923i 0.369274 + 0.639602i
\(265\) −18.0000 −1.10573
\(266\) −4.00000 6.92820i −0.245256 0.424795i
\(267\) −6.00000 −0.367194
\(268\) −1.00000 + 1.73205i −0.0610847 + 0.105802i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) −12.0000 −0.730297
\(271\) 5.00000 8.66025i 0.303728 0.526073i −0.673249 0.739416i \(-0.735102\pi\)
0.976977 + 0.213343i \(0.0684351\pi\)
\(272\) −1.50000 2.59808i −0.0909509 0.157532i
\(273\) 16.0000 0.968364
\(274\) 1.50000 2.59808i 0.0906183 0.156956i
\(275\) 12.0000 20.7846i 0.723627 1.25336i
\(276\) 6.00000 10.3923i 0.361158 0.625543i
\(277\) 0.500000 + 0.866025i 0.0300421 + 0.0520344i 0.880656 0.473757i \(-0.157103\pi\)
−0.850613 + 0.525792i \(0.823769\pi\)
\(278\) 1.00000 + 1.73205i 0.0599760 + 0.103882i
\(279\) −1.00000 + 1.73205i −0.0598684 + 0.103695i
\(280\) −6.00000 + 10.3923i −0.358569 + 0.621059i
\(281\) −7.50000 + 12.9904i −0.447412 + 0.774941i −0.998217 0.0596933i \(-0.980988\pi\)
0.550804 + 0.834634i \(0.314321\pi\)
\(282\) −12.0000 −0.714590
\(283\) 8.00000 + 13.8564i 0.475551 + 0.823678i 0.999608 0.0280052i \(-0.00891551\pi\)
−0.524057 + 0.851683i \(0.675582\pi\)
\(284\) 6.00000 10.3923i 0.356034 0.616670i
\(285\) −12.0000 −0.710819
\(286\) 12.0000 0.709575
\(287\) 6.00000 10.3923i 0.354169 0.613438i
\(288\) −1.00000 −0.0589256
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) −9.00000 −0.528498
\(291\) −13.0000 22.5167i −0.762073 1.31995i
\(292\) 5.00000 + 8.66025i 0.292603 + 0.506803i
\(293\) −1.50000 2.59808i −0.0876309 0.151781i 0.818878 0.573967i \(-0.194596\pi\)
−0.906509 + 0.422186i \(0.861263\pi\)
\(294\) −9.00000 + 15.5885i −0.524891 + 0.909137i
\(295\) 0 0
\(296\) −5.50000 2.59808i −0.319681 0.151010i
\(297\) −24.0000 −1.39262
\(298\) −10.5000 + 18.1865i −0.608249 + 1.05352i
\(299\) −6.00000 10.3923i −0.346989 0.601003i
\(300\) 4.00000 + 6.92820i 0.230940 + 0.400000i
\(301\) −8.00000 13.8564i −0.461112 0.798670i
\(302\) 22.0000 1.26596
\(303\) 3.00000 + 5.19615i 0.172345 + 0.298511i
\(304\) 2.00000 0.114708
\(305\) 1.50000 2.59808i 0.0858898 0.148765i
\(306\) −3.00000 −0.171499
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) −12.0000 + 20.7846i −0.683763 + 1.18431i
\(309\) −4.00000 6.92820i −0.227552 0.394132i
\(310\) −6.00000 −0.340777
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) −2.00000 + 3.46410i −0.113228 + 0.196116i
\(313\) 6.50000 11.2583i 0.367402 0.636358i −0.621757 0.783210i \(-0.713581\pi\)
0.989158 + 0.146852i \(0.0469141\pi\)
\(314\) 5.50000 + 9.52628i 0.310383 + 0.537599i
\(315\) 6.00000 + 10.3923i 0.338062 + 0.585540i
\(316\) −7.00000 + 12.1244i −0.393781 + 0.682048i
\(317\) 10.5000 18.1865i 0.589739 1.02146i −0.404528 0.914526i \(-0.632564\pi\)
0.994266 0.106932i \(-0.0341026\pi\)
\(318\) 6.00000 10.3923i 0.336463 0.582772i
\(319\) −18.0000 −1.00781
\(320\) −1.50000 2.59808i −0.0838525 0.145237i
\(321\) −12.0000 + 20.7846i −0.669775 + 1.16008i
\(322\) 24.0000 1.33747
\(323\) 6.00000 0.333849
\(324\) 5.50000 9.52628i 0.305556 0.529238i
\(325\) 8.00000 0.443760
\(326\) −8.00000 13.8564i −0.443079 0.767435i
\(327\) 2.00000 0.110600
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) −12.0000 20.7846i −0.661581 1.14589i
\(330\) 18.0000 + 31.1769i 0.990867 + 1.71623i
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) 6.00000 0.329293
\(333\) −5.00000 + 3.46410i −0.273998 + 0.189832i
\(334\) −12.0000 −0.656611
\(335\) −3.00000 + 5.19615i −0.163908 + 0.283896i
\(336\) −4.00000 6.92820i −0.218218 0.377964i
\(337\) 12.5000 + 21.6506i 0.680918 + 1.17939i 0.974701 + 0.223513i \(0.0717525\pi\)
−0.293783 + 0.955872i \(0.594914\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) 36.0000 1.95525
\(340\) −4.50000 7.79423i −0.244047 0.422701i
\(341\) −12.0000 −0.649836
\(342\) 1.00000 1.73205i 0.0540738 0.0936586i
\(343\) −8.00000 −0.431959
\(344\) 4.00000 0.215666
\(345\) 18.0000 31.1769i 0.969087 1.67851i
\(346\) −10.5000 18.1865i −0.564483 0.977714i
\(347\) 6.00000 0.322097 0.161048 0.986947i \(-0.448512\pi\)
0.161048 + 0.986947i \(0.448512\pi\)
\(348\) 3.00000 5.19615i 0.160817 0.278543i
\(349\) 0.500000 0.866025i 0.0267644 0.0463573i −0.852333 0.523000i \(-0.824813\pi\)
0.879097 + 0.476642i \(0.158146\pi\)
\(350\) −8.00000 + 13.8564i −0.427618 + 0.740656i
\(351\) −4.00000 6.92820i −0.213504 0.369800i
\(352\) −3.00000 5.19615i −0.159901 0.276956i
\(353\) 10.5000 18.1865i 0.558859 0.967972i −0.438733 0.898617i \(-0.644573\pi\)
0.997592 0.0693543i \(-0.0220939\pi\)
\(354\) 0 0
\(355\) 18.0000 31.1769i 0.955341 1.65470i
\(356\) 3.00000 0.159000
\(357\) −12.0000 20.7846i −0.635107 1.10004i
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −3.00000 −0.158114
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 1.00000 0.0525588
\(363\) 25.0000 + 43.3013i 1.31216 + 2.27273i
\(364\) −8.00000 −0.419314
\(365\) 15.0000 + 25.9808i 0.785136 + 1.35990i
\(366\) 1.00000 + 1.73205i 0.0522708 + 0.0905357i
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) 3.00000 0.156174
\(370\) −16.5000 7.79423i −0.857794 0.405203i
\(371\) 24.0000 1.24602
\(372\) 2.00000 3.46410i 0.103695 0.179605i
\(373\) 12.5000 + 21.6506i 0.647225 + 1.12103i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) −9.00000 15.5885i −0.465379 0.806060i
\(375\) −3.00000 5.19615i −0.154919 0.268328i
\(376\) 6.00000 0.309426
\(377\) −3.00000 5.19615i −0.154508 0.267615i
\(378\) 16.0000 0.822951
\(379\) 8.00000 13.8564i 0.410932 0.711756i −0.584060 0.811711i \(-0.698537\pi\)
0.994992 + 0.0999550i \(0.0318699\pi\)
\(380\) 6.00000 0.307794
\(381\) 20.0000 1.02463
\(382\) −3.00000 + 5.19615i −0.153493 + 0.265858i
\(383\) −6.00000 10.3923i −0.306586 0.531022i 0.671027 0.741433i \(-0.265853\pi\)
−0.977613 + 0.210411i \(0.932520\pi\)
\(384\) 2.00000 0.102062
\(385\) −36.0000 + 62.3538i −1.83473 + 3.17785i
\(386\) 5.50000 9.52628i 0.279943 0.484875i
\(387\) 2.00000 3.46410i 0.101666 0.176090i
\(388\) 6.50000 + 11.2583i 0.329988 + 0.571555i
\(389\) 4.50000 + 7.79423i 0.228159 + 0.395183i 0.957263 0.289220i \(-0.0933960\pi\)
−0.729103 + 0.684403i \(0.760063\pi\)
\(390\) −6.00000 + 10.3923i −0.303822 + 0.526235i
\(391\) −9.00000 + 15.5885i −0.455150 + 0.788342i
\(392\) 4.50000 7.79423i 0.227284 0.393668i
\(393\) −36.0000 −1.81596
\(394\) 1.50000 + 2.59808i 0.0755689 + 0.130889i
\(395\) −21.0000 + 36.3731i −1.05662 + 1.83013i
\(396\) −6.00000 −0.301511
\(397\) 35.0000 1.75660 0.878300 0.478110i \(-0.158678\pi\)
0.878300 + 0.478110i \(0.158678\pi\)
\(398\) 4.00000 6.92820i 0.200502 0.347279i
\(399\) 16.0000 0.801002
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) −2.00000 3.46410i −0.0997509 0.172774i
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) −1.50000 2.59808i −0.0746278 0.129259i
\(405\) 16.5000 28.5788i 0.819892 1.42009i
\(406\) 12.0000 0.595550
\(407\) −33.0000 15.5885i −1.63575 0.772691i
\(408\) 6.00000 0.297044
\(409\) −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i \(-0.921004\pi\)
0.697406 + 0.716677i \(0.254338\pi\)
\(410\) 4.50000 + 7.79423i 0.222239 + 0.384930i
\(411\) 3.00000 + 5.19615i 0.147979 + 0.256307i
\(412\) 2.00000 + 3.46410i 0.0985329 + 0.170664i
\(413\) 0 0
\(414\) 3.00000 + 5.19615i 0.147442 + 0.255377i
\(415\) 18.0000 0.883585
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) −4.00000 −0.195881
\(418\) 12.0000 0.586939
\(419\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(420\) −12.0000 20.7846i −0.585540 1.01419i
\(421\) −37.0000 −1.80327 −0.901635 0.432498i \(-0.857632\pi\)
−0.901635 + 0.432498i \(0.857632\pi\)
\(422\) −8.00000 + 13.8564i −0.389434 + 0.674519i
\(423\) 3.00000 5.19615i 0.145865 0.252646i
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) −6.00000 10.3923i −0.291043 0.504101i
\(426\) 12.0000 + 20.7846i 0.581402 + 1.00702i
\(427\) −2.00000 + 3.46410i −0.0967868 + 0.167640i
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) −12.0000 + 20.7846i −0.579365 + 1.00349i
\(430\) 12.0000 0.578691
\(431\) −3.00000 5.19615i −0.144505 0.250290i 0.784683 0.619897i \(-0.212826\pi\)
−0.929188 + 0.369607i \(0.879492\pi\)
\(432\) −2.00000 + 3.46410i −0.0962250 + 0.166667i
\(433\) −25.0000 −1.20142 −0.600712 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) 8.00000 0.384012
\(435\) 9.00000 15.5885i 0.431517 0.747409i
\(436\) −1.00000 −0.0478913
\(437\) −6.00000 10.3923i −0.287019 0.497131i
\(438\) −20.0000 −0.955637
\(439\) −16.0000 27.7128i −0.763638 1.32266i −0.940963 0.338508i \(-0.890078\pi\)
0.177325 0.984152i \(-0.443256\pi\)
\(440\) −9.00000 15.5885i −0.429058 0.743151i
\(441\) −4.50000 7.79423i −0.214286 0.371154i
\(442\) 3.00000 5.19615i 0.142695 0.247156i
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) 10.0000 6.92820i 0.474579 0.328798i
\(445\) 9.00000 0.426641
\(446\) 7.00000 12.1244i 0.331460 0.574105i
\(447\) −21.0000 36.3731i −0.993266 1.72039i
\(448\) 2.00000 + 3.46410i 0.0944911 + 0.163663i
\(449\) −3.00000 5.19615i −0.141579 0.245222i 0.786513 0.617574i \(-0.211885\pi\)
−0.928091 + 0.372353i \(0.878551\pi\)
\(450\) −4.00000 −0.188562
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) −18.0000 −0.846649
\(453\) −22.0000 + 38.1051i −1.03365 + 1.79033i
\(454\) 18.0000 0.844782
\(455\) −24.0000 −1.12514
\(456\) −2.00000 + 3.46410i −0.0936586 + 0.162221i
\(457\) 18.5000 + 32.0429i 0.865393 + 1.49891i 0.866656 + 0.498906i \(0.166265\pi\)
−0.00126243 + 0.999999i \(0.500402\pi\)
\(458\) −11.0000 −0.513996
\(459\) −6.00000 + 10.3923i −0.280056 + 0.485071i
\(460\) −9.00000 + 15.5885i −0.419627 + 0.726816i
\(461\) 15.0000 25.9808i 0.698620 1.21004i −0.270326 0.962769i \(-0.587131\pi\)
0.968945 0.247276i \(-0.0795353\pi\)
\(462\) −24.0000 41.5692i −1.11658 1.93398i
\(463\) 8.00000 + 13.8564i 0.371792 + 0.643962i 0.989841 0.142177i \(-0.0454103\pi\)
−0.618050 + 0.786139i \(0.712077\pi\)
\(464\) −1.50000 + 2.59808i −0.0696358 + 0.120613i
\(465\) 6.00000 10.3923i 0.278243 0.481932i
\(466\) −4.50000 + 7.79423i −0.208458 + 0.361061i
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) −1.00000 1.73205i −0.0462250 0.0800641i
\(469\) 4.00000 6.92820i 0.184703 0.319915i
\(470\) 18.0000 0.830278
\(471\) −22.0000 −1.01371
\(472\) 0 0
\(473\) 24.0000 1.10352
\(474\) −14.0000 24.2487i −0.643041 1.11378i
\(475\) 8.00000 0.367065
\(476\) 6.00000 + 10.3923i 0.275010 + 0.476331i
\(477\) 3.00000 + 5.19615i 0.137361 + 0.237915i
\(478\) 0 0
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) 6.00000 0.273861
\(481\) −1.00000 12.1244i −0.0455961 0.552823i
\(482\) −14.0000 −0.637683
\(483\) −24.0000 + 41.5692i −1.09204 + 1.89146i
\(484\) −12.5000 21.6506i −0.568182 0.984120i
\(485\) 19.5000 + 33.7750i 0.885449 + 1.53364i
\(486\) 5.00000 + 8.66025i 0.226805 + 0.392837i
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) −0.500000 0.866025i −0.0226339 0.0392031i
\(489\) 32.0000 1.44709
\(490\) 13.5000 23.3827i 0.609868 1.05632i
\(491\) 6.00000 0.270776 0.135388 0.990793i \(-0.456772\pi\)
0.135388 + 0.990793i \(0.456772\pi\)
\(492\) −6.00000 −0.270501
\(493\) −4.50000 + 7.79423i −0.202670 + 0.351034i
\(494\) 2.00000 + 3.46410i 0.0899843 + 0.155857i
\(495\) −18.0000 −0.809040
\(496\) −1.00000 + 1.73205i −0.0449013 + 0.0777714i
\(497\) −24.0000 + 41.5692i −1.07655 + 1.86463i
\(498\) −6.00000 + 10.3923i −0.268866 + 0.465690i
\(499\) −7.00000 12.1244i −0.313363 0.542761i 0.665725 0.746197i \(-0.268122\pi\)
−0.979088 + 0.203436i \(0.934789\pi\)
\(500\) 1.50000 + 2.59808i 0.0670820 + 0.116190i
\(501\) 12.0000 20.7846i 0.536120 0.928588i
\(502\) 0 0
\(503\) −15.0000 + 25.9808i −0.668817 + 1.15842i 0.309418 + 0.950926i \(0.399866\pi\)
−0.978235 + 0.207499i \(0.933468\pi\)
\(504\) 4.00000 0.178174
\(505\) −4.50000 7.79423i −0.200247 0.346839i
\(506\) −18.0000 + 31.1769i −0.800198 + 1.38598i
\(507\) 18.0000 0.799408
\(508\) −10.0000 −0.443678
\(509\) −13.5000 + 23.3827i −0.598377 + 1.03642i 0.394684 + 0.918817i \(0.370854\pi\)
−0.993061 + 0.117602i \(0.962479\pi\)
\(510\) 18.0000 0.797053
\(511\) −20.0000 34.6410i −0.884748 1.53243i
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 6.92820i −0.176604 0.305888i
\(514\) 13.5000 + 23.3827i 0.595459 + 1.03137i
\(515\) 6.00000 + 10.3923i 0.264392 + 0.457940i
\(516\) −4.00000 + 6.92820i −0.176090 + 0.304997i
\(517\) 36.0000 1.58328
\(518\) 22.0000 + 10.3923i 0.966625 + 0.456612i
\(519\) 42.0000 1.84360
\(520\) 3.00000 5.19615i 0.131559 0.227866i
\(521\) −3.00000 5.19615i −0.131432 0.227648i 0.792797 0.609486i \(-0.208624\pi\)
−0.924229 + 0.381839i \(0.875291\pi\)
\(522\) 1.50000 + 2.59808i 0.0656532 + 0.113715i
\(523\) −13.0000 22.5167i −0.568450 0.984585i −0.996719 0.0809336i \(-0.974210\pi\)
0.428269 0.903651i \(-0.359124\pi\)
\(524\) 18.0000 0.786334
\(525\) −16.0000 27.7128i −0.698297 1.20949i
\(526\) 0 0
\(527\) −3.00000 + 5.19615i −0.130682 + 0.226348i
\(528\) 12.0000 0.522233
\(529\) 13.0000 0.565217
\(530\) −9.00000 + 15.5885i −0.390935 + 0.677119i
\(531\) 0 0
\(532\) −8.00000 −0.346844
\(533\) −3.00000 + 5.19615i −0.129944 + 0.225070i
\(534\) −3.00000 + 5.19615i −0.129823 + 0.224860i
\(535\) 18.0000 31.1769i 0.778208 1.34790i
\(536\) 1.00000 + 1.73205i 0.0431934 + 0.0748132i
\(537\) 0 0
\(538\) 9.00000 15.5885i 0.388018 0.672066i
\(539\) 27.0000 46.7654i 1.16297 2.01433i
\(540\) −6.00000 + 10.3923i −0.258199 + 0.447214i
\(541\) 35.0000 1.50477 0.752384 0.658725i \(-0.228904\pi\)
0.752384 + 0.658725i \(0.228904\pi\)
\(542\) −5.00000 8.66025i −0.214768 0.371990i
\(543\) −1.00000 + 1.73205i −0.0429141 + 0.0743294i
\(544\) −3.00000 −0.128624
\(545\) −3.00000 −0.128506
\(546\) 8.00000 13.8564i 0.342368 0.592999i
\(547\) −22.0000 −0.940652 −0.470326 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) −1.50000 2.59808i −0.0640768 0.110984i
\(549\) −1.00000 −0.0426790
\(550\) −12.0000 20.7846i −0.511682 0.886259i
\(551\) −3.00000 5.19615i −0.127804 0.221364i
\(552\) −6.00000 10.3923i −0.255377 0.442326i
\(553\) 28.0000 48.4974i 1.19068 2.06232i
\(554\) 1.00000 0.0424859
\(555\) 30.0000 20.7846i 1.27343 0.882258i
\(556\) 2.00000 0.0848189
\(557\) 16.5000 28.5788i 0.699127 1.21092i −0.269642 0.962961i \(-0.586905\pi\)
0.968769 0.247964i \(-0.0797613\pi\)
\(558\) 1.00000 + 1.73205i 0.0423334 + 0.0733236i
\(559\) 4.00000 + 6.92820i 0.169182 + 0.293032i
\(560\) 6.00000 + 10.3923i 0.253546 + 0.439155i
\(561\) 36.0000 1.51992
\(562\) 7.50000 + 12.9904i 0.316368 + 0.547966i
\(563\) 6.00000 0.252870 0.126435 0.991975i \(-0.459647\pi\)
0.126435 + 0.991975i \(0.459647\pi\)
\(564\) −6.00000 + 10.3923i −0.252646 + 0.437595i
\(565\) −54.0000 −2.27180
\(566\) 16.0000 0.672530
\(567\) −22.0000 + 38.1051i −0.923913 + 1.60026i
\(568\) −6.00000 10.3923i −0.251754 0.436051i
\(569\) 3.00000 0.125767 0.0628833 0.998021i \(-0.479970\pi\)
0.0628833 + 0.998021i \(0.479970\pi\)
\(570\) −6.00000 + 10.3923i −0.251312 + 0.435286i
\(571\) −19.0000 + 32.9090i −0.795125 + 1.37720i 0.127634 + 0.991821i \(0.459262\pi\)
−0.922760 + 0.385376i \(0.874072\pi\)
\(572\) 6.00000 10.3923i 0.250873 0.434524i
\(573\) −6.00000 10.3923i −0.250654 0.434145i
\(574\) −6.00000 10.3923i −0.250435 0.433766i
\(575\) −12.0000 + 20.7846i −0.500435 + 0.866778i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 17.0000 29.4449i 0.707719 1.22581i −0.257982 0.966150i \(-0.583058\pi\)
0.965701 0.259656i \(-0.0836092\pi\)
\(578\) 8.00000 0.332756
\(579\) 11.0000 + 19.0526i 0.457144 + 0.791797i
\(580\) −4.50000 + 7.79423i −0.186852 + 0.323638i
\(581\) −24.0000 −0.995688
\(582\) −26.0000 −1.07773
\(583\) −18.0000 + 31.1769i −0.745484 + 1.29122i
\(584\) 10.0000 0.413803
\(585\) −3.00000 5.19615i −0.124035 0.214834i
\(586\) −3.00000 −0.123929
\(587\) −9.00000 15.5885i −0.371470 0.643404i 0.618322 0.785925i \(-0.287813\pi\)
−0.989792 + 0.142520i \(0.954479\pi\)
\(588\) 9.00000 + 15.5885i 0.371154 + 0.642857i
\(589\) −2.00000 3.46410i −0.0824086 0.142736i
\(590\) 0 0
\(591\) −6.00000 −0.246807
\(592\) −5.00000 + 3.46410i −0.205499 + 0.142374i
\(593\) 27.0000 1.10876 0.554379 0.832265i \(-0.312956\pi\)
0.554379 + 0.832265i \(0.312956\pi\)
\(594\) −12.0000 + 20.7846i −0.492366 + 0.852803i
\(595\) 18.0000 + 31.1769i 0.737928 + 1.27813i
\(596\) 10.5000 + 18.1865i 0.430097 + 0.744949i
\(597\) 8.00000 + 13.8564i 0.327418 + 0.567105i
\(598\) −12.0000 −0.490716
\(599\) 3.00000 + 5.19615i 0.122577 + 0.212309i 0.920783 0.390075i \(-0.127551\pi\)
−0.798206 + 0.602384i \(0.794218\pi\)
\(600\) 8.00000 0.326599
\(601\) 6.50000 11.2583i 0.265141 0.459237i −0.702460 0.711723i \(-0.747915\pi\)
0.967600 + 0.252486i \(0.0812483\pi\)
\(602\) −16.0000 −0.652111
\(603\) 2.00000 0.0814463
\(604\) 11.0000 19.0526i 0.447584 0.775238i
\(605\) −37.5000 64.9519i −1.52459 2.64067i
\(606\) 6.00000 0.243733
\(607\) 11.0000 19.0526i 0.446476 0.773320i −0.551678 0.834058i \(-0.686012\pi\)
0.998154 + 0.0607380i \(0.0193454\pi\)
\(608\) 1.00000 1.73205i 0.0405554 0.0702439i
\(609\) −12.0000 + 20.7846i −0.486265 + 0.842235i
\(610\) −1.50000 2.59808i −0.0607332 0.105193i
\(611\) 6.00000 + 10.3923i 0.242734 + 0.420428i
\(612\) −1.50000 + 2.59808i −0.0606339 + 0.105021i
\(613\) 12.5000 21.6506i 0.504870 0.874461i −0.495114 0.868828i \(-0.664874\pi\)
0.999984 0.00563283i \(-0.00179300\pi\)
\(614\) −14.0000 + 24.2487i −0.564994 + 0.978598i
\(615\) −18.0000 −0.725830
\(616\) 12.0000 + 20.7846i 0.483494 + 0.837436i
\(617\) 9.00000 15.5885i 0.362326 0.627568i −0.626017 0.779809i \(-0.715316\pi\)
0.988343 + 0.152242i \(0.0486493\pi\)
\(618\) −8.00000 −0.321807
\(619\) −40.0000 −1.60774 −0.803868 0.594808i \(-0.797228\pi\)
−0.803868 + 0.594808i \(0.797228\pi\)
\(620\) −3.00000 + 5.19615i −0.120483 + 0.208683i
\(621\) 24.0000 0.963087
\(622\) 0 0
\(623\) −12.0000 −0.480770
\(624\) 2.00000 + 3.46410i 0.0800641 + 0.138675i
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −6.50000 11.2583i −0.259792 0.449973i
\(627\) −12.0000 + 20.7846i −0.479234 + 0.830057i
\(628\) 11.0000 0.438948
\(629\) −15.0000 + 10.3923i −0.598089 + 0.414368i
\(630\) 12.0000 0.478091
\(631\) 5.00000 8.66025i 0.199047 0.344759i −0.749173 0.662375i \(-0.769549\pi\)
0.948220 + 0.317615i \(0.102882\pi\)
\(632\) 7.00000 + 12.1244i 0.278445 + 0.482281i
\(633\) −16.0000 27.7128i −0.635943 1.10149i
\(634\) −10.5000 18.1865i −0.417008 0.722280i
\(635\) −30.0000 −1.19051
\(636\) −6.00000 10.3923i −0.237915 0.412082i
\(637\) 18.0000 0.713186
\(638\) −9.00000 + 15.5885i −0.356313 + 0.617153i
\(639\) −12.0000 −0.474713
\(640\) −3.00000 −0.118585
\(641\) 10.5000 18.1865i 0.414725 0.718325i −0.580674 0.814136i \(-0.697211\pi\)
0.995400 + 0.0958109i \(0.0305444\pi\)
\(642\) 12.0000 + 20.7846i 0.473602 + 0.820303i
\(643\) −34.0000 −1.34083 −0.670415 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) 12.0000 20.7846i 0.472866 0.819028i
\(645\) −12.0000 + 20.7846i −0.472500 + 0.818393i
\(646\) 3.00000 5.19615i 0.118033 0.204440i
\(647\) −12.0000 20.7846i −0.471769 0.817127i 0.527710 0.849425i \(-0.323051\pi\)
−0.999478 + 0.0322975i \(0.989718\pi\)
\(648\) −5.50000 9.52628i −0.216060 0.374228i
\(649\) 0 0
\(650\) 4.00000 6.92820i 0.156893 0.271746i
\(651\) −8.00000 + 13.8564i −0.313545 + 0.543075i
\(652\) −16.0000 −0.626608
\(653\) −1.50000 2.59808i −0.0586995 0.101671i 0.835182 0.549973i \(-0.185362\pi\)
−0.893882 + 0.448303i \(0.852029\pi\)
\(654\) 1.00000 1.73205i 0.0391031 0.0677285i
\(655\) 54.0000 2.10995
\(656\) 3.00000 0.117130
\(657\) 5.00000 8.66025i 0.195069 0.337869i
\(658\) −24.0000 −0.935617
\(659\) 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i \(0.0806766\pi\)
−0.266872 + 0.963732i \(0.585990\pi\)
\(660\) 36.0000 1.40130
\(661\) 12.5000 + 21.6506i 0.486194 + 0.842112i 0.999874 0.0158695i \(-0.00505163\pi\)
−0.513680 + 0.857982i \(0.671718\pi\)
\(662\) −2.00000 3.46410i −0.0777322 0.134636i
\(663\) 6.00000 + 10.3923i 0.233021 + 0.403604i
\(664\) 3.00000 5.19615i 0.116423 0.201650i
\(665\) −24.0000 −0.930680
\(666\) 0.500000 + 6.06218i 0.0193746 + 0.234905i
\(667\) 18.0000 0.696963
\(668\) −6.00000 + 10.3923i −0.232147 + 0.402090i
\(669\) 14.0000 + 24.2487i 0.541271 + 0.937509i
\(670\) 3.00000 + 5.19615i 0.115900 + 0.200745i
\(671\) −3.00000 5.19615i −0.115814 0.200595i
\(672\) −8.00000 −0.308607
\(673\) 5.00000 + 8.66025i 0.192736 + 0.333828i 0.946156 0.323711i \(-0.104931\pi\)
−0.753420 + 0.657539i \(0.771597\pi\)
\(674\) 25.0000 0.962964
\(675\) −8.00000 + 13.8564i −0.307920 + 0.533333i
\(676\) −9.00000 −0.346154
\(677\) 3.00000 0.115299 0.0576497 0.998337i \(-0.481639\pi\)
0.0576497 + 0.998337i \(0.481639\pi\)
\(678\) 18.0000 31.1769i 0.691286 1.19734i
\(679\) −26.0000 45.0333i −0.997788 1.72822i
\(680\) −9.00000 −0.345134
\(681\) −18.0000 + 31.1769i −0.689761 + 1.19470i
\(682\) −6.00000 + 10.3923i −0.229752 + 0.397942i
\(683\) −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
\(685\) −4.50000 7.79423i −0.171936 0.297802i
\(686\) −4.00000 + 6.92820i −0.152721 + 0.264520i
\(687\) 11.0000 19.0526i 0.419676 0.726900i
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) −12.0000 −0.457164
\(690\) −18.0000 31.1769i −0.685248 1.18688i
\(691\) −25.0000 + 43.3013i −0.951045 + 1.64726i −0.207875 + 0.978155i \(0.566655\pi\)
−0.743170 + 0.669102i \(0.766679\pi\)
\(692\) −21.0000 −0.798300
\(693\) 24.0000 0.911685
\(694\) 3.00000 5.19615i 0.113878 0.197243i
\(695\) 6.00000 0.227593
\(696\) −3.00000 5.19615i −0.113715 0.196960i
\(697\) 9.00000 0.340899
\(698\) −0.500000 0.866025i −0.0189253 0.0327795i
\(699\) −9.00000 15.5885i −0.340411 0.589610i
\(700\) 8.00000 + 13.8564i 0.302372 + 0.523723i
\(701\) −15.0000 + 25.9808i −0.566542 + 0.981280i 0.430362 + 0.902656i \(0.358386\pi\)
−0.996904 + 0.0786236i \(0.974947\pi\)
\(702\) −8.00000 −0.301941
\(703\) −1.00000 12.1244i −0.0377157 0.457279i
\(704\) −6.00000 −0.226134
\(705\) −18.0000 + 31.1769i −0.677919 + 1.17419i
\(706\) −10.5000 18.1865i −0.395173 0.684459i
\(707\) 6.00000 + 10.3923i 0.225653 + 0.390843i
\(708\) 0 0
\(709\) −22.0000 −0.826227 −0.413114 0.910679i \(-0.635559\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) −18.0000 31.1769i −0.675528 1.17005i
\(711\) 14.0000 0.525041
\(712\) 1.50000 2.59808i 0.0562149 0.0973670i
\(713\) 12.0000 0.449404
\(714\) −24.0000 −0.898177
\(715\) 18.0000 31.1769i 0.673162 1.16595i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 21.0000 36.3731i 0.783168 1.35649i −0.146920 0.989148i \(-0.546936\pi\)
0.930087 0.367338i \(-0.119731\pi\)
\(720\) −1.50000 + 2.59808i −0.0559017 + 0.0968246i
\(721\) −8.00000 13.8564i −0.297936 0.516040i
\(722\) −7.50000 12.9904i −0.279121 0.483452i
\(723\) 14.0000 24.2487i 0.520666 0.901819i
\(724\) 0.500000 0.866025i 0.0185824 0.0321856i
\(725\) −6.00000 + 10.3923i −0.222834 + 0.385961i
\(726\) 50.0000 1.85567
\(727\) 2.00000 + 3.46410i 0.0741759 + 0.128476i 0.900728 0.434384i \(-0.143034\pi\)
−0.826552 + 0.562861i \(0.809701\pi\)
\(728\) −4.00000 + 6.92820i −0.148250 + 0.256776i
\(729\) 13.0000 0.481481
\(730\) 30.0000 1.11035
\(731\) 6.00000 10.3923i 0.221918 0.384373i
\(732\) 2.00000 0.0739221
\(733\) −1.00000 1.73205i −0.0369358 0.0639748i 0.846967 0.531646i \(-0.178426\pi\)
−0.883902 + 0.467671i \(0.845093\pi\)
\(734\) 4.00000 0.147643
\(735\) 27.0000 + 46.7654i 0.995910 + 1.72497i
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) 6.00000 + 10.3923i 0.221013 + 0.382805i
\(738\) 1.50000 2.59808i 0.0552158 0.0956365i
\(739\) 38.0000 1.39785 0.698926 0.715194i \(-0.253662\pi\)
0.698926 + 0.715194i \(0.253662\pi\)
\(740\) −15.0000 + 10.3923i −0.551411 + 0.382029i
\(741\) −8.00000 −0.293887
\(742\) 12.0000 20.7846i 0.440534 0.763027i
\(743\) 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i \(-0.131563\pi\)
−0.805735 + 0.592277i \(0.798229\pi\)
\(744\) −2.00000 3.46410i −0.0733236 0.127000i
\(745\) 31.5000 + 54.5596i 1.15407 + 1.99891i
\(746\) 25.0000 0.915315
\(747\) −3.00000 5.19615i −0.109764 0.190117i
\(748\) −18.0000 −0.658145
\(749\) −24.0000 + 41.5692i −0.876941 + 1.51891i
\(750\) −6.00000 −0.219089
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) 3.00000 5.19615i 0.109399 0.189484i
\(753\) 0 0
\(754\) −6.00000 −0.218507
\(755\) 33.0000 57.1577i 1.20099 2.08018i
\(756\) 8.00000 13.8564i 0.290957 0.503953i
\(757\) −17.5000 + 30.3109i −0.636048 + 1.10167i 0.350244 + 0.936659i \(0.386099\pi\)
−0.986292 + 0.165009i \(0.947235\pi\)
\(758\) −8.00000 13.8564i −0.290573 0.503287i
\(759\) −36.0000 62.3538i −1.30672 2.26330i
\(760\) 3.00000 5.19615i 0.108821 0.188484i
\(761\) −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) 10.0000 17.3205i 0.362262 0.627456i
\(763\) 4.00000 0.144810
\(764\) 3.00000 + 5.19615i 0.108536 + 0.187990i
\(765\) −4.50000 + 7.79423i −0.162698 + 0.281801i
\(766\) −12.0000 −0.433578
\(767\) 0 0
\(768\) 1.00000 1.73205i 0.0360844 0.0625000i
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 36.0000 + 62.3538i 1.29735 + 2.24708i
\(771\) −54.0000 −1.94476
\(772\) −5.50000 9.52628i −0.197949 0.342858i
\(773\) 10.5000 + 18.1865i 0.377659 + 0.654124i 0.990721 0.135910i \(-0.0433959\pi\)
−0.613062 + 0.790034i \(0.710063\pi\)
\(774\) −2.00000 3.46410i −0.0718885 0.124515i
\(775\) −4.00000 + 6.92820i −0.143684 + 0.248868i
\(776\) 13.0000 0.466673