Properties

Label 546.2.l.h.295.1
Level $546$
Weight $2$
Character 546.295
Analytic conductor $4.360$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.295
Dual form 546.2.l.h.211.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +4.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +4.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{10} +(1.50000 - 2.59808i) q^{11} -1.00000 q^{12} +(-2.50000 + 2.59808i) q^{13} -1.00000 q^{14} +(2.00000 - 3.46410i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} -1.00000 q^{18} +(-1.50000 - 2.59808i) q^{19} +(-2.00000 - 3.46410i) q^{20} -1.00000 q^{21} +(-1.50000 - 2.59808i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{24} +11.0000 q^{25} +(1.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(4.50000 - 7.79423i) q^{29} +(-2.00000 - 3.46410i) q^{30} -4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +5.00000 q^{34} +(-2.00000 - 3.46410i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.00000 + 3.46410i) q^{37} -3.00000 q^{38} +(1.00000 + 3.46410i) q^{39} -4.00000 q^{40} +(-2.50000 + 4.33013i) q^{41} +(-0.500000 + 0.866025i) q^{42} -3.00000 q^{44} +(-2.00000 - 3.46410i) q^{45} +(3.00000 + 5.19615i) q^{46} -3.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(5.50000 - 9.52628i) q^{50} +5.00000 q^{51} +(3.50000 + 0.866025i) q^{52} -11.0000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(6.00000 - 10.3923i) q^{55} +(0.500000 + 0.866025i) q^{56} -3.00000 q^{57} +(-4.50000 - 7.79423i) q^{58} +(-1.00000 - 1.73205i) q^{59} -4.00000 q^{60} +(0.500000 + 0.866025i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(-10.0000 + 10.3923i) q^{65} -3.00000 q^{66} +(-1.00000 + 1.73205i) q^{67} +(2.50000 - 4.33013i) q^{68} +(3.00000 + 5.19615i) q^{69} -4.00000 q^{70} +(-3.00000 - 5.19615i) q^{71} +(0.500000 + 0.866025i) q^{72} +12.0000 q^{73} +(2.00000 + 3.46410i) q^{74} +(5.50000 - 9.52628i) q^{75} +(-1.50000 + 2.59808i) q^{76} -3.00000 q^{77} +(3.50000 + 0.866025i) q^{78} +11.0000 q^{79} +(-2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.50000 + 4.33013i) q^{82} +6.00000 q^{83} +(0.500000 + 0.866025i) q^{84} +(10.0000 + 17.3205i) q^{85} +(-4.50000 - 7.79423i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(-3.50000 + 6.06218i) q^{89} -4.00000 q^{90} +(3.50000 + 0.866025i) q^{91} +6.00000 q^{92} +(-2.00000 + 3.46410i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(-6.00000 - 10.3923i) q^{95} +1.00000 q^{96} +(6.00000 + 10.3923i) q^{97} +(0.500000 + 0.866025i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} + 8q^{5} - q^{6} - q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} + 8q^{5} - q^{6} - q^{7} - 2q^{8} - q^{9} + 4q^{10} + 3q^{11} - 2q^{12} - 5q^{13} - 2q^{14} + 4q^{15} - q^{16} + 5q^{17} - 2q^{18} - 3q^{19} - 4q^{20} - 2q^{21} - 3q^{22} - 6q^{23} - q^{24} + 22q^{25} + 2q^{26} - 2q^{27} - q^{28} + 9q^{29} - 4q^{30} - 8q^{31} + q^{32} - 3q^{33} + 10q^{34} - 4q^{35} - q^{36} - 4q^{37} - 6q^{38} + 2q^{39} - 8q^{40} - 5q^{41} - q^{42} - 6q^{44} - 4q^{45} + 6q^{46} - 6q^{47} + q^{48} - q^{49} + 11q^{50} + 10q^{51} + 7q^{52} - 22q^{53} - q^{54} + 12q^{55} + q^{56} - 6q^{57} - 9q^{58} - 2q^{59} - 8q^{60} + q^{61} - 4q^{62} - q^{63} + 2q^{64} - 20q^{65} - 6q^{66} - 2q^{67} + 5q^{68} + 6q^{69} - 8q^{70} - 6q^{71} + q^{72} + 24q^{73} + 4q^{74} + 11q^{75} - 3q^{76} - 6q^{77} + 7q^{78} + 22q^{79} - 4q^{80} - q^{81} + 5q^{82} + 12q^{83} + q^{84} + 20q^{85} - 9q^{87} - 3q^{88} - 7q^{89} - 8q^{90} + 7q^{91} + 12q^{92} - 4q^{93} - 3q^{94} - 12q^{95} + 2q^{96} + 12q^{97} + q^{98} - 6q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 4.00000 1.78885 0.894427 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) −0.500000 0.866025i −0.204124 0.353553i
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 2.00000 3.46410i 0.632456 1.09545i
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) −1.00000 −0.267261
\(15\) 2.00000 3.46410i 0.516398 0.894427i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.50000 + 4.33013i 0.606339 + 1.05021i 0.991838 + 0.127502i \(0.0406959\pi\)
−0.385499 + 0.922708i \(0.625971\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.50000 2.59808i −0.344124 0.596040i 0.641071 0.767482i \(-0.278491\pi\)
−0.985194 + 0.171442i \(0.945157\pi\)
\(20\) −2.00000 3.46410i −0.447214 0.774597i
\(21\) −1.00000 −0.218218
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 11.0000 2.20000
\(26\) 1.00000 + 3.46410i 0.196116 + 0.679366i
\(27\) −1.00000 −0.192450
\(28\) −0.500000 + 0.866025i −0.0944911 + 0.163663i
\(29\) 4.50000 7.79423i 0.835629 1.44735i −0.0578882 0.998323i \(-0.518437\pi\)
0.893517 0.449029i \(-0.148230\pi\)
\(30\) −2.00000 3.46410i −0.365148 0.632456i
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) 5.00000 0.857493
\(35\) −2.00000 3.46410i −0.338062 0.585540i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) −3.00000 −0.486664
\(39\) 1.00000 + 3.46410i 0.160128 + 0.554700i
\(40\) −4.00000 −0.632456
\(41\) −2.50000 + 4.33013i −0.390434 + 0.676252i −0.992507 0.122189i \(-0.961009\pi\)
0.602072 + 0.798441i \(0.294342\pi\)
\(42\) −0.500000 + 0.866025i −0.0771517 + 0.133631i
\(43\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(44\) −3.00000 −0.452267
\(45\) −2.00000 3.46410i −0.298142 0.516398i
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) −3.00000 −0.437595 −0.218797 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 5.50000 9.52628i 0.777817 1.34722i
\(51\) 5.00000 0.700140
\(52\) 3.50000 + 0.866025i 0.485363 + 0.120096i
\(53\) −11.0000 −1.51097 −0.755483 0.655168i \(-0.772598\pi\)
−0.755483 + 0.655168i \(0.772598\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 6.00000 10.3923i 0.809040 1.40130i
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) −3.00000 −0.397360
\(58\) −4.50000 7.79423i −0.590879 1.02343i
\(59\) −1.00000 1.73205i −0.130189 0.225494i 0.793560 0.608492i \(-0.208225\pi\)
−0.923749 + 0.382998i \(0.874892\pi\)
\(60\) −4.00000 −0.516398
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −2.00000 + 3.46410i −0.254000 + 0.439941i
\(63\) −0.500000 + 0.866025i −0.0629941 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) −10.0000 + 10.3923i −1.24035 + 1.28901i
\(66\) −3.00000 −0.369274
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) 2.50000 4.33013i 0.303170 0.525105i
\(69\) 3.00000 + 5.19615i 0.361158 + 0.625543i
\(70\) −4.00000 −0.478091
\(71\) −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 12.0000 1.40449 0.702247 0.711934i \(-0.252180\pi\)
0.702247 + 0.711934i \(0.252180\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) 5.50000 9.52628i 0.635085 1.10000i
\(76\) −1.50000 + 2.59808i −0.172062 + 0.298020i
\(77\) −3.00000 −0.341882
\(78\) 3.50000 + 0.866025i 0.396297 + 0.0980581i
\(79\) 11.0000 1.23760 0.618798 0.785550i \(-0.287620\pi\)
0.618798 + 0.785550i \(0.287620\pi\)
\(80\) −2.00000 + 3.46410i −0.223607 + 0.387298i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.50000 + 4.33013i 0.276079 + 0.478183i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0.500000 + 0.866025i 0.0545545 + 0.0944911i
\(85\) 10.0000 + 17.3205i 1.08465 + 1.87867i
\(86\) 0 0
\(87\) −4.50000 7.79423i −0.482451 0.835629i
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) −3.50000 + 6.06218i −0.370999 + 0.642590i −0.989720 0.143022i \(-0.954318\pi\)
0.618720 + 0.785611i \(0.287651\pi\)
\(90\) −4.00000 −0.421637
\(91\) 3.50000 + 0.866025i 0.366900 + 0.0907841i
\(92\) 6.00000 0.625543
\(93\) −2.00000 + 3.46410i −0.207390 + 0.359211i
\(94\) −1.50000 + 2.59808i −0.154713 + 0.267971i
\(95\) −6.00000 10.3923i −0.615587 1.06623i
\(96\) 1.00000 0.102062
\(97\) 6.00000 + 10.3923i 0.609208 + 1.05518i 0.991371 + 0.131084i \(0.0418458\pi\)
−0.382164 + 0.924095i \(0.624821\pi\)
\(98\) 0.500000 + 0.866025i 0.0505076 + 0.0874818i
\(99\) −3.00000 −0.301511
\(100\) −5.50000 9.52628i −0.550000 0.952628i
\(101\) −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i \(-0.999089\pi\)
0.502477 + 0.864590i \(0.332422\pi\)
\(102\) 2.50000 4.33013i 0.247537 0.428746i
\(103\) 20.0000 1.97066 0.985329 0.170664i \(-0.0545913\pi\)
0.985329 + 0.170664i \(0.0545913\pi\)
\(104\) 2.50000 2.59808i 0.245145 0.254762i
\(105\) −4.00000 −0.390360
\(106\) −5.50000 + 9.52628i −0.534207 + 0.925274i
\(107\) −8.50000 + 14.7224i −0.821726 + 1.42327i 0.0826699 + 0.996577i \(0.473655\pi\)
−0.904396 + 0.426694i \(0.859678\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −6.00000 10.3923i −0.572078 0.990867i
\(111\) 2.00000 + 3.46410i 0.189832 + 0.328798i
\(112\) 1.00000 0.0944911
\(113\) −6.00000 10.3923i −0.564433 0.977626i −0.997102 0.0760733i \(-0.975762\pi\)
0.432670 0.901553i \(-0.357572\pi\)
\(114\) −1.50000 + 2.59808i −0.140488 + 0.243332i
\(115\) −12.0000 + 20.7846i −1.11901 + 1.93817i
\(116\) −9.00000 −0.835629
\(117\) 3.50000 + 0.866025i 0.323575 + 0.0800641i
\(118\) −2.00000 −0.184115
\(119\) 2.50000 4.33013i 0.229175 0.396942i
\(120\) −2.00000 + 3.46410i −0.182574 + 0.316228i
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 1.00000 0.0905357
\(123\) 2.50000 + 4.33013i 0.225417 + 0.390434i
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) 24.0000 2.14663
\(126\) 0.500000 + 0.866025i 0.0445435 + 0.0771517i
\(127\) −4.00000 + 6.92820i −0.354943 + 0.614779i −0.987108 0.160055i \(-0.948833\pi\)
0.632166 + 0.774833i \(0.282166\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 4.00000 + 13.8564i 0.350823 + 1.21529i
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −1.50000 + 2.59808i −0.130558 + 0.226134i
\(133\) −1.50000 + 2.59808i −0.130066 + 0.225282i
\(134\) 1.00000 + 1.73205i 0.0863868 + 0.149626i
\(135\) −4.00000 −0.344265
\(136\) −2.50000 4.33013i −0.214373 0.371305i
\(137\) 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) 6.00000 0.510754
\(139\) −6.50000 11.2583i −0.551323 0.954919i −0.998179 0.0603135i \(-0.980790\pi\)
0.446857 0.894606i \(-0.352543\pi\)
\(140\) −2.00000 + 3.46410i −0.169031 + 0.292770i
\(141\) −1.50000 + 2.59808i −0.126323 + 0.218797i
\(142\) −6.00000 −0.503509
\(143\) 3.00000 + 10.3923i 0.250873 + 0.869048i
\(144\) 1.00000 0.0833333
\(145\) 18.0000 31.1769i 1.49482 2.58910i
\(146\) 6.00000 10.3923i 0.496564 0.860073i
\(147\) 0.500000 + 0.866025i 0.0412393 + 0.0714286i
\(148\) 4.00000 0.328798
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) −5.50000 9.52628i −0.449073 0.777817i
\(151\) −11.0000 −0.895167 −0.447584 0.894242i \(-0.647715\pi\)
−0.447584 + 0.894242i \(0.647715\pi\)
\(152\) 1.50000 + 2.59808i 0.121666 + 0.210732i
\(153\) 2.50000 4.33013i 0.202113 0.350070i
\(154\) −1.50000 + 2.59808i −0.120873 + 0.209359i
\(155\) −16.0000 −1.28515
\(156\) 2.50000 2.59808i 0.200160 0.208013i
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 5.50000 9.52628i 0.437557 0.757870i
\(159\) −5.50000 + 9.52628i −0.436178 + 0.755483i
\(160\) 2.00000 + 3.46410i 0.158114 + 0.273861i
\(161\) 6.00000 0.472866
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 5.00000 0.390434
\(165\) −6.00000 10.3923i −0.467099 0.809040i
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) 8.00000 13.8564i 0.619059 1.07224i −0.370599 0.928793i \(-0.620848\pi\)
0.989658 0.143448i \(-0.0458190\pi\)
\(168\) 1.00000 0.0771517
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 20.0000 1.53393
\(171\) −1.50000 + 2.59808i −0.114708 + 0.198680i
\(172\) 0 0
\(173\) 1.00000 + 1.73205i 0.0760286 + 0.131685i 0.901533 0.432710i \(-0.142443\pi\)
−0.825505 + 0.564396i \(0.809109\pi\)
\(174\) −9.00000 −0.682288
\(175\) −5.50000 9.52628i −0.415761 0.720119i
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) −2.00000 −0.150329
\(178\) 3.50000 + 6.06218i 0.262336 + 0.454379i
\(179\) −12.0000 + 20.7846i −0.896922 + 1.55351i −0.0655145 + 0.997852i \(0.520869\pi\)
−0.831408 + 0.555663i \(0.812464\pi\)
\(180\) −2.00000 + 3.46410i −0.149071 + 0.258199i
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) 2.50000 2.59808i 0.185312 0.192582i
\(183\) 1.00000 0.0739221
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) −8.00000 + 13.8564i −0.588172 + 1.01874i
\(186\) 2.00000 + 3.46410i 0.146647 + 0.254000i
\(187\) 15.0000 1.09691
\(188\) 1.50000 + 2.59808i 0.109399 + 0.189484i
\(189\) 0.500000 + 0.866025i 0.0363696 + 0.0629941i
\(190\) −12.0000 −0.870572
\(191\) 3.00000 + 5.19615i 0.217072 + 0.375980i 0.953912 0.300088i \(-0.0970159\pi\)
−0.736839 + 0.676068i \(0.763683\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −6.50000 + 11.2583i −0.467880 + 0.810392i −0.999326 0.0366998i \(-0.988315\pi\)
0.531446 + 0.847092i \(0.321649\pi\)
\(194\) 12.0000 0.861550
\(195\) 4.00000 + 13.8564i 0.286446 + 0.992278i
\(196\) 1.00000 0.0714286
\(197\) 9.50000 16.4545i 0.676847 1.17233i −0.299078 0.954229i \(-0.596679\pi\)
0.975925 0.218105i \(-0.0699875\pi\)
\(198\) −1.50000 + 2.59808i −0.106600 + 0.184637i
\(199\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(200\) −11.0000 −0.777817
\(201\) 1.00000 + 1.73205i 0.0705346 + 0.122169i
\(202\) 5.00000 + 8.66025i 0.351799 + 0.609333i
\(203\) −9.00000 −0.631676
\(204\) −2.50000 4.33013i −0.175035 0.303170i
\(205\) −10.0000 + 17.3205i −0.698430 + 1.20972i
\(206\) 10.0000 17.3205i 0.696733 1.20678i
\(207\) 6.00000 0.417029
\(208\) −1.00000 3.46410i −0.0693375 0.240192i
\(209\) −9.00000 −0.622543
\(210\) −2.00000 + 3.46410i −0.138013 + 0.239046i
\(211\) −7.00000 + 12.1244i −0.481900 + 0.834675i −0.999784 0.0207756i \(-0.993386\pi\)
0.517884 + 0.855451i \(0.326720\pi\)
\(212\) 5.50000 + 9.52628i 0.377742 + 0.654268i
\(213\) −6.00000 −0.411113
\(214\) 8.50000 + 14.7224i 0.581048 + 1.00640i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 2.00000 + 3.46410i 0.135769 + 0.235159i
\(218\) −1.00000 + 1.73205i −0.0677285 + 0.117309i
\(219\) 6.00000 10.3923i 0.405442 0.702247i
\(220\) −12.0000 −0.809040
\(221\) −17.5000 4.33013i −1.17718 0.291276i
\(222\) 4.00000 0.268462
\(223\) 8.00000 13.8564i 0.535720 0.927894i −0.463409 0.886145i \(-0.653374\pi\)
0.999128 0.0417488i \(-0.0132929\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) −5.50000 9.52628i −0.366667 0.635085i
\(226\) −12.0000 −0.798228
\(227\) −7.00000 12.1244i −0.464606 0.804722i 0.534577 0.845120i \(-0.320471\pi\)
−0.999184 + 0.0403978i \(0.987137\pi\)
\(228\) 1.50000 + 2.59808i 0.0993399 + 0.172062i
\(229\) −5.00000 −0.330409 −0.165205 0.986259i \(-0.552828\pi\)
−0.165205 + 0.986259i \(0.552828\pi\)
\(230\) 12.0000 + 20.7846i 0.791257 + 1.37050i
\(231\) −1.50000 + 2.59808i −0.0986928 + 0.170941i
\(232\) −4.50000 + 7.79423i −0.295439 + 0.511716i
\(233\) 4.00000 0.262049 0.131024 0.991379i \(-0.458173\pi\)
0.131024 + 0.991379i \(0.458173\pi\)
\(234\) 2.50000 2.59808i 0.163430 0.169842i
\(235\) −12.0000 −0.782794
\(236\) −1.00000 + 1.73205i −0.0650945 + 0.112747i
\(237\) 5.50000 9.52628i 0.357263 0.618798i
\(238\) −2.50000 4.33013i −0.162051 0.280680i
\(239\) −26.0000 −1.68180 −0.840900 0.541190i \(-0.817974\pi\)
−0.840900 + 0.541190i \(0.817974\pi\)
\(240\) 2.00000 + 3.46410i 0.129099 + 0.223607i
\(241\) −6.00000 10.3923i −0.386494 0.669427i 0.605481 0.795860i \(-0.292981\pi\)
−0.991975 + 0.126432i \(0.959647\pi\)
\(242\) 2.00000 0.128565
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0.500000 0.866025i 0.0320092 0.0554416i
\(245\) −2.00000 + 3.46410i −0.127775 + 0.221313i
\(246\) 5.00000 0.318788
\(247\) 10.5000 + 2.59808i 0.668099 + 0.165312i
\(248\) 4.00000 0.254000
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) 12.0000 20.7846i 0.758947 1.31453i
\(251\) −7.00000 12.1244i −0.441836 0.765283i 0.555990 0.831189i \(-0.312339\pi\)
−0.997826 + 0.0659066i \(0.979006\pi\)
\(252\) 1.00000 0.0629941
\(253\) 9.00000 + 15.5885i 0.565825 + 0.980038i
\(254\) 4.00000 + 6.92820i 0.250982 + 0.434714i
\(255\) 20.0000 1.25245
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.50000 + 6.06218i −0.218324 + 0.378148i −0.954296 0.298864i \(-0.903392\pi\)
0.735972 + 0.677012i \(0.236726\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) 14.0000 + 3.46410i 0.868243 + 0.214834i
\(261\) −9.00000 −0.557086
\(262\) 6.00000 10.3923i 0.370681 0.642039i
\(263\) 13.0000 22.5167i 0.801614 1.38844i −0.116939 0.993139i \(-0.537308\pi\)
0.918553 0.395298i \(-0.129359\pi\)
\(264\) 1.50000 + 2.59808i 0.0923186 + 0.159901i
\(265\) −44.0000 −2.70290
\(266\) 1.50000 + 2.59808i 0.0919709 + 0.159298i
\(267\) 3.50000 + 6.06218i 0.214197 + 0.370999i
\(268\) 2.00000 0.122169
\(269\) 12.0000 + 20.7846i 0.731653 + 1.26726i 0.956176 + 0.292791i \(0.0945841\pi\)
−0.224523 + 0.974469i \(0.572083\pi\)
\(270\) −2.00000 + 3.46410i −0.121716 + 0.210819i
\(271\) 6.00000 10.3923i 0.364474 0.631288i −0.624218 0.781251i \(-0.714582\pi\)
0.988692 + 0.149963i \(0.0479155\pi\)
\(272\) −5.00000 −0.303170
\(273\) 2.50000 2.59808i 0.151307 0.157243i
\(274\) 18.0000 1.08742
\(275\) 16.5000 28.5788i 0.994987 1.72337i
\(276\) 3.00000 5.19615i 0.180579 0.312772i
\(277\) −7.00000 12.1244i −0.420589 0.728482i 0.575408 0.817867i \(-0.304843\pi\)
−0.995997 + 0.0893846i \(0.971510\pi\)
\(278\) −13.0000 −0.779688
\(279\) 2.00000 + 3.46410i 0.119737 + 0.207390i
\(280\) 2.00000 + 3.46410i 0.119523 + 0.207020i
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 1.50000 + 2.59808i 0.0893237 + 0.154713i
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) −12.0000 −0.710819
\(286\) 10.5000 + 2.59808i 0.620878 + 0.153627i
\(287\) 5.00000 0.295141
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) −18.0000 31.1769i −1.05700 1.83077i
\(291\) 12.0000 0.703452
\(292\) −6.00000 10.3923i −0.351123 0.608164i
\(293\) −12.0000 20.7846i −0.701047 1.21425i −0.968099 0.250568i \(-0.919383\pi\)
0.267052 0.963682i \(-0.413951\pi\)
\(294\) 1.00000 0.0583212
\(295\) −4.00000 6.92820i −0.232889 0.403376i
\(296\) 2.00000 3.46410i 0.116248 0.201347i
\(297\) −1.50000 + 2.59808i −0.0870388 + 0.150756i
\(298\) −18.0000 −1.04271
\(299\) −6.00000 20.7846i −0.346989 1.20201i
\(300\) −11.0000 −0.635085
\(301\) 0 0
\(302\) −5.50000 + 9.52628i −0.316489 + 0.548176i
\(303\) 5.00000 + 8.66025i 0.287242 + 0.497519i
\(304\) 3.00000 0.172062
\(305\) 2.00000 + 3.46410i 0.114520 + 0.198354i
\(306\) −2.50000 4.33013i −0.142915 0.247537i
\(307\) 21.0000 1.19853 0.599267 0.800549i \(-0.295459\pi\)
0.599267 + 0.800549i \(0.295459\pi\)
\(308\) 1.50000 + 2.59808i 0.0854704 + 0.148039i
\(309\) 10.0000 17.3205i 0.568880 0.985329i
\(310\) −8.00000 + 13.8564i −0.454369 + 0.786991i
\(311\) −19.0000 −1.07739 −0.538696 0.842500i \(-0.681083\pi\)
−0.538696 + 0.842500i \(0.681083\pi\)
\(312\) −1.00000 3.46410i −0.0566139 0.196116i
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) −1.00000 + 1.73205i −0.0564333 + 0.0977453i
\(315\) −2.00000 + 3.46410i −0.112687 + 0.195180i
\(316\) −5.50000 9.52628i −0.309399 0.535895i
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 5.50000 + 9.52628i 0.308425 + 0.534207i
\(319\) −13.5000 23.3827i −0.755855 1.30918i
\(320\) 4.00000 0.223607
\(321\) 8.50000 + 14.7224i 0.474424 + 0.821726i
\(322\) 3.00000 5.19615i 0.167183 0.289570i
\(323\) 7.50000 12.9904i 0.417311 0.722804i
\(324\) 1.00000 0.0555556
\(325\) −27.5000 + 28.5788i −1.52543 + 1.58527i
\(326\) −20.0000 −1.10770
\(327\) −1.00000 + 1.73205i −0.0553001 + 0.0957826i
\(328\) 2.50000 4.33013i 0.138039 0.239091i
\(329\) 1.50000 + 2.59808i 0.0826977 + 0.143237i
\(330\) −12.0000 −0.660578
\(331\) −1.00000 1.73205i −0.0549650 0.0952021i 0.837234 0.546845i \(-0.184171\pi\)
−0.892199 + 0.451643i \(0.850838\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) 4.00000 0.219199
\(334\) −8.00000 13.8564i −0.437741 0.758189i
\(335\) −4.00000 + 6.92820i −0.218543 + 0.378528i
\(336\) 0.500000 0.866025i 0.0272772 0.0472456i
\(337\) 31.0000 1.68868 0.844339 0.535810i \(-0.179994\pi\)
0.844339 + 0.535810i \(0.179994\pi\)
\(338\) −11.5000 6.06218i −0.625518 0.329739i
\(339\) −12.0000 −0.651751
\(340\) 10.0000 17.3205i 0.542326 0.939336i
\(341\) −6.00000 + 10.3923i −0.324918 + 0.562775i
\(342\) 1.50000 + 2.59808i 0.0811107 + 0.140488i
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 12.0000 + 20.7846i 0.646058 + 1.11901i
\(346\) 2.00000 0.107521
\(347\) −5.50000 9.52628i −0.295255 0.511397i 0.679789 0.733408i \(-0.262071\pi\)
−0.975044 + 0.222010i \(0.928738\pi\)
\(348\) −4.50000 + 7.79423i −0.241225 + 0.417815i
\(349\) 17.0000 29.4449i 0.909989 1.57615i 0.0959126 0.995390i \(-0.469423\pi\)
0.814076 0.580758i \(-0.197244\pi\)
\(350\) −11.0000 −0.587975
\(351\) 2.50000 2.59808i 0.133440 0.138675i
\(352\) 3.00000 0.159901
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) −1.00000 + 1.73205i −0.0531494 + 0.0920575i
\(355\) −12.0000 20.7846i −0.636894 1.10313i
\(356\) 7.00000 0.370999
\(357\) −2.50000 4.33013i −0.132314 0.229175i
\(358\) 12.0000 + 20.7846i 0.634220 + 1.09850i
\(359\) −20.0000 −1.05556 −0.527780 0.849381i \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(360\) 2.00000 + 3.46410i 0.105409 + 0.182574i
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) −2.50000 + 4.33013i −0.131397 + 0.227586i
\(363\) 2.00000 0.104973
\(364\) −1.00000 3.46410i −0.0524142 0.181568i
\(365\) 48.0000 2.51243
\(366\) 0.500000 0.866025i 0.0261354 0.0452679i
\(367\) −9.00000 + 15.5885i −0.469796 + 0.813711i −0.999404 0.0345320i \(-0.989006\pi\)
0.529607 + 0.848243i \(0.322339\pi\)
\(368\) −3.00000 5.19615i −0.156386 0.270868i
\(369\) 5.00000 0.260290
\(370\) 8.00000 + 13.8564i 0.415900 + 0.720360i
\(371\) 5.50000 + 9.52628i 0.285546 + 0.494580i
\(372\) 4.00000 0.207390
\(373\) −17.0000 29.4449i −0.880227 1.52460i −0.851089 0.525022i \(-0.824057\pi\)
−0.0291379 0.999575i \(-0.509276\pi\)
\(374\) 7.50000 12.9904i 0.387816 0.671717i
\(375\) 12.0000 20.7846i 0.619677 1.07331i
\(376\) 3.00000 0.154713
\(377\) 9.00000 + 31.1769i 0.463524 + 1.60569i
\(378\) 1.00000 0.0514344
\(379\) 9.00000 15.5885i 0.462299 0.800725i −0.536776 0.843725i \(-0.680358\pi\)
0.999075 + 0.0429994i \(0.0136914\pi\)
\(380\) −6.00000 + 10.3923i −0.307794 + 0.533114i
\(381\) 4.00000 + 6.92820i 0.204926 + 0.354943i
\(382\) 6.00000 0.306987
\(383\) 5.50000 + 9.52628i 0.281037 + 0.486770i 0.971640 0.236463i \(-0.0759883\pi\)
−0.690604 + 0.723234i \(0.742655\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) −12.0000 −0.611577
\(386\) 6.50000 + 11.2583i 0.330841 + 0.573034i
\(387\) 0 0
\(388\) 6.00000 10.3923i 0.304604 0.527589i
\(389\) −26.0000 −1.31825 −0.659126 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) 14.0000 + 3.46410i 0.708918 + 0.175412i
\(391\) −30.0000 −1.51717
\(392\) 0.500000 0.866025i 0.0252538 0.0437409i
\(393\) 6.00000 10.3923i 0.302660 0.524222i
\(394\) −9.50000 16.4545i −0.478603 0.828965i
\(395\) 44.0000 2.21388
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) 11.5000 + 19.9186i 0.577168 + 0.999685i 0.995802 + 0.0915300i \(0.0291757\pi\)
−0.418634 + 0.908155i \(0.637491\pi\)
\(398\) 0 0
\(399\) 1.50000 + 2.59808i 0.0750939 + 0.130066i
\(400\) −5.50000 + 9.52628i −0.275000 + 0.476314i
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 2.00000 0.0997509
\(403\) 10.0000 10.3923i 0.498135 0.517678i
\(404\) 10.0000 0.497519
\(405\) −2.00000 + 3.46410i −0.0993808 + 0.172133i
\(406\) −4.50000 + 7.79423i −0.223331 + 0.386821i
\(407\) 6.00000 + 10.3923i 0.297409 + 0.515127i
\(408\) −5.00000 −0.247537
\(409\) 1.00000 + 1.73205i 0.0494468 + 0.0856444i 0.889689 0.456566i \(-0.150921\pi\)
−0.840243 + 0.542211i \(0.817588\pi\)
\(410\) 10.0000 + 17.3205i 0.493865 + 0.855399i
\(411\) 18.0000 0.887875
\(412\) −10.0000 17.3205i −0.492665 0.853320i
\(413\) −1.00000 + 1.73205i −0.0492068 + 0.0852286i
\(414\) 3.00000 5.19615i 0.147442 0.255377i
\(415\) 24.0000 1.17811
\(416\) −3.50000 0.866025i −0.171602 0.0424604i
\(417\) −13.0000 −0.636613
\(418\) −4.50000 + 7.79423i −0.220102 + 0.381228i
\(419\) −9.00000 + 15.5885i −0.439679 + 0.761546i −0.997665 0.0683046i \(-0.978241\pi\)
0.557986 + 0.829851i \(0.311574\pi\)
\(420\) 2.00000 + 3.46410i 0.0975900 + 0.169031i
\(421\) −18.0000 −0.877266 −0.438633 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(422\) 7.00000 + 12.1244i 0.340755 + 0.590204i
\(423\) 1.50000 + 2.59808i 0.0729325 + 0.126323i
\(424\) 11.0000 0.534207
\(425\) 27.5000 + 47.6314i 1.33395 + 2.31046i
\(426\) −3.00000 + 5.19615i −0.145350 + 0.251754i
\(427\) 0.500000 0.866025i 0.0241967 0.0419099i
\(428\) 17.0000 0.821726
\(429\) 10.5000 + 2.59808i 0.506945 + 0.125436i
\(430\) 0 0
\(431\) −19.0000 + 32.9090i −0.915198 + 1.58517i −0.108586 + 0.994087i \(0.534632\pi\)
−0.806611 + 0.591082i \(0.798701\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −17.0000 29.4449i −0.816968 1.41503i −0.907906 0.419173i \(-0.862320\pi\)
0.0909384 0.995857i \(-0.471013\pi\)
\(434\) 4.00000 0.192006
\(435\) −18.0000 31.1769i −0.863034 1.49482i
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) 18.0000 0.861057
\(438\) −6.00000 10.3923i −0.286691 0.496564i
\(439\) −20.0000 + 34.6410i −0.954548 + 1.65333i −0.219149 + 0.975691i \(0.570328\pi\)
−0.735399 + 0.677634i \(0.763005\pi\)
\(440\) −6.00000 + 10.3923i −0.286039 + 0.495434i
\(441\) 1.00000 0.0476190
\(442\) −12.5000 + 12.9904i −0.594564 + 0.617889i
\(443\) −15.0000 −0.712672 −0.356336 0.934358i \(-0.615974\pi\)
−0.356336 + 0.934358i \(0.615974\pi\)
\(444\) 2.00000 3.46410i 0.0949158 0.164399i
\(445\) −14.0000 + 24.2487i −0.663664 + 1.14950i
\(446\) −8.00000 13.8564i −0.378811 0.656120i
\(447\) −18.0000 −0.851371
\(448\) −0.500000 0.866025i −0.0236228 0.0409159i
\(449\) −10.0000 17.3205i −0.471929 0.817405i 0.527555 0.849521i \(-0.323109\pi\)
−0.999484 + 0.0321156i \(0.989776\pi\)
\(450\) −11.0000 −0.518545
\(451\) 7.50000 + 12.9904i 0.353161 + 0.611693i
\(452\) −6.00000 + 10.3923i −0.282216 + 0.488813i
\(453\) −5.50000 + 9.52628i −0.258413 + 0.447584i
\(454\) −14.0000 −0.657053
\(455\) 14.0000 + 3.46410i 0.656330 + 0.162400i
\(456\) 3.00000 0.140488
\(457\) 1.00000 1.73205i 0.0467780 0.0810219i −0.841688 0.539964i \(-0.818438\pi\)
0.888466 + 0.458942i \(0.151771\pi\)
\(458\) −2.50000 + 4.33013i −0.116817 + 0.202334i
\(459\) −2.50000 4.33013i −0.116690 0.202113i
\(460\) 24.0000 1.11901
\(461\) 16.0000 + 27.7128i 0.745194 + 1.29071i 0.950104 + 0.311933i \(0.100977\pi\)
−0.204910 + 0.978781i \(0.565690\pi\)
\(462\) 1.50000 + 2.59808i 0.0697863 + 0.120873i
\(463\) 1.00000 0.0464739 0.0232370 0.999730i \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) 4.50000 + 7.79423i 0.208907 + 0.361838i
\(465\) −8.00000 + 13.8564i −0.370991 + 0.642575i
\(466\) 2.00000 3.46410i 0.0926482 0.160471i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −1.00000 3.46410i −0.0462250 0.160128i
\(469\) 2.00000 0.0923514
\(470\) −6.00000 + 10.3923i −0.276759 + 0.479361i
\(471\) −1.00000 + 1.73205i −0.0460776 + 0.0798087i
\(472\) 1.00000 + 1.73205i 0.0460287 + 0.0797241i
\(473\) 0 0
\(474\) −5.50000 9.52628i −0.252623 0.437557i
\(475\) −16.5000 28.5788i −0.757072 1.31129i
\(476\) −5.00000 −0.229175
\(477\) 5.50000 + 9.52628i 0.251828 + 0.436178i
\(478\) −13.0000 + 22.5167i −0.594606 + 1.02989i
\(479\) 16.5000 28.5788i 0.753904 1.30580i −0.192013 0.981392i \(-0.561502\pi\)
0.945917 0.324408i \(-0.105165\pi\)
\(480\) 4.00000 0.182574
\(481\) −4.00000 13.8564i −0.182384 0.631798i
\(482\) −12.0000 −0.546585
\(483\) 3.00000 5.19615i 0.136505 0.236433i
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 24.0000 + 41.5692i 1.08978 + 1.88756i
\(486\) 1.00000 0.0453609
\(487\) 10.5000 + 18.1865i 0.475800 + 0.824110i 0.999616 0.0277214i \(-0.00882512\pi\)
−0.523815 + 0.851832i \(0.675492\pi\)
\(488\) −0.500000 0.866025i −0.0226339 0.0392031i
\(489\) −20.0000 −0.904431
\(490\) 2.00000 + 3.46410i 0.0903508 + 0.156492i
\(491\) 10.0000 17.3205i 0.451294 0.781664i −0.547173 0.837020i \(-0.684296\pi\)
0.998467 + 0.0553560i \(0.0176294\pi\)
\(492\) 2.50000 4.33013i 0.112709 0.195217i
\(493\) 45.0000 2.02670
\(494\) 7.50000 7.79423i 0.337441 0.350679i
\(495\) −12.0000 −0.539360
\(496\) 2.00000 3.46410i 0.0898027 0.155543i
\(497\) −3.00000 + 5.19615i −0.134568 + 0.233079i
\(498\) −3.00000 5.19615i −0.134433 0.232845i
\(499\) 40.0000 1.79065 0.895323 0.445418i \(-0.146945\pi\)
0.895323 + 0.445418i \(0.146945\pi\)
\(500\) −12.0000 20.7846i −0.536656 0.929516i
\(501\) −8.00000 13.8564i −0.357414 0.619059i
\(502\) −14.0000 −0.624851
\(503\) −8.00000 13.8564i −0.356702 0.617827i 0.630705 0.776022i \(-0.282766\pi\)
−0.987408 + 0.158196i \(0.949432\pi\)
\(504\) 0.500000 0.866025i 0.0222718 0.0385758i
\(505\) −20.0000 + 34.6410i −0.889988 + 1.54150i
\(506\) 18.0000 0.800198
\(507\) −11.5000 6.06218i −0.510733 0.269231i
\(508\) 8.00000 0.354943
\(509\) 15.0000 25.9808i 0.664863 1.15158i −0.314459 0.949271i \(-0.601823\pi\)
0.979322 0.202306i \(-0.0648436\pi\)
\(510\) 10.0000 17.3205i 0.442807 0.766965i
\(511\) −6.00000 10.3923i −0.265424 0.459728i
\(512\) −1.00000 −0.0441942
\(513\) 1.50000 + 2.59808i 0.0662266 + 0.114708i
\(514\) 3.50000 + 6.06218i 0.154378 + 0.267391i
\(515\) 80.0000 3.52522
\(516\) 0 0
\(517\) −4.50000 + 7.79423i −0.197910 + 0.342790i
\(518\) 2.00000 3.46410i 0.0878750 0.152204i
\(519\) 2.00000 0.0877903
\(520\) 10.0000 10.3923i 0.438529 0.455733i
\(521\) −5.00000 −0.219054 −0.109527 0.993984i \(-0.534934\pi\)
−0.109527 + 0.993984i \(0.534934\pi\)
\(522\) −4.50000 + 7.79423i −0.196960 + 0.341144i
\(523\) −13.5000 + 23.3827i −0.590314 + 1.02245i 0.403876 + 0.914814i \(0.367663\pi\)
−0.994190 + 0.107640i \(0.965671\pi\)
\(524\) −6.00000 10.3923i −0.262111 0.453990i
\(525\) −11.0000 −0.480079
\(526\) −13.0000 22.5167i −0.566827 0.981773i
\(527\) −10.0000 17.3205i −0.435607 0.754493i
\(528\) 3.00000 0.130558
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) −22.0000 + 38.1051i −0.955619 + 1.65518i
\(531\) −1.00000 + 1.73205i −0.0433963 + 0.0751646i
\(532\) 3.00000 0.130066
\(533\) −5.00000 17.3205i −0.216574 0.750234i
\(534\) 7.00000 0.302920
\(535\) −34.0000 + 58.8897i −1.46995 + 2.54602i
\(536\) 1.00000 1.73205i 0.0431934 0.0748132i
\(537\) 12.0000 + 20.7846i 0.517838 + 0.896922i
\(538\) 24.0000 1.03471
\(539\) 1.50000 + 2.59808i 0.0646096 + 0.111907i
\(540\) 2.00000 + 3.46410i 0.0860663 + 0.149071i
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) −6.00000 10.3923i −0.257722 0.446388i
\(543\) −2.50000 + 4.33013i −0.107285 + 0.185824i
\(544\) −2.50000 + 4.33013i −0.107187 + 0.185653i
\(545\) −8.00000 −0.342682
\(546\) −1.00000 3.46410i −0.0427960 0.148250i
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 9.00000 15.5885i 0.384461 0.665906i
\(549\) 0.500000 0.866025i 0.0213395 0.0369611i
\(550\) −16.5000 28.5788i −0.703562 1.21861i
\(551\) −27.0000 −1.15024
\(552\) −3.00000 5.19615i −0.127688 0.221163i
\(553\) −5.50000 9.52628i −0.233884 0.405099i
\(554\) −14.0000 −0.594803
\(555\) 8.00000 + 13.8564i 0.339581 + 0.588172i
\(556\) −6.50000 + 11.2583i −0.275661 + 0.477460i
\(557\) −5.50000 + 9.52628i −0.233042 + 0.403641i −0.958702 0.284413i \(-0.908201\pi\)
0.725660 + 0.688054i \(0.241535\pi\)
\(558\) 4.00000 0.169334
\(559\) 0 0
\(560\) 4.00000 0.169031
\(561\) 7.50000 12.9904i 0.316650 0.548454i
\(562\) 15.0000 25.9808i 0.632737 1.09593i
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) 3.00000 0.126323
\(565\) −24.0000 41.5692i −1.00969 1.74883i
\(566\) −2.00000 3.46410i −0.0840663 0.145607i
\(567\) 1.00000 0.0419961
\(568\) 3.00000 + 5.19615i 0.125877 + 0.218026i
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) −6.00000 + 10.3923i −0.251312 + 0.435286i
\(571\) 38.0000 1.59025 0.795125 0.606445i \(-0.207405\pi\)
0.795125 + 0.606445i \(0.207405\pi\)
\(572\) 7.50000 7.79423i 0.313591 0.325893i
\(573\) 6.00000 0.250654
\(574\) 2.50000 4.33013i 0.104348 0.180736i
\(575\) −33.0000 + 57.1577i −1.37620 + 2.38364i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) 4.00000 + 6.92820i 0.166378 + 0.288175i
\(579\) 6.50000 + 11.2583i 0.270131 + 0.467880i
\(580\) −36.0000 −1.49482
\(581\) −3.00000 5.19615i −0.124461 0.215573i
\(582\) 6.00000 10.3923i 0.248708 0.430775i
\(583\) −16.5000 + 28.5788i −0.683360 + 1.18361i
\(584\) −12.0000 −0.496564
\(585\) 14.0000 + 3.46410i 0.578829 + 0.143223i
\(586\) −24.0000 −0.991431
\(587\) 6.00000 10.3923i 0.247647 0.428936i −0.715226 0.698893i \(-0.753676\pi\)
0.962872 + 0.269957i \(0.0870095\pi\)
\(588\) 0.500000 0.866025i 0.0206197 0.0357143i
\(589\) 6.00000 + 10.3923i 0.247226 + 0.428207i
\(590\) −8.00000 −0.329355
\(591\) −9.50000 16.4545i −0.390778 0.676847i
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) 41.0000 1.68367 0.841834 0.539736i \(-0.181476\pi\)
0.841834 + 0.539736i \(0.181476\pi\)
\(594\) 1.50000 + 2.59808i 0.0615457 + 0.106600i
\(595\) 10.0000 17.3205i 0.409960 0.710072i
\(596\) −9.00000 + 15.5885i −0.368654 + 0.638528i
\(597\) 0 0
\(598\) −21.0000 5.19615i −0.858754 0.212486i
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) −5.50000 + 9.52628i −0.224537 + 0.388909i
\(601\) 22.0000 38.1051i 0.897399 1.55434i 0.0665912 0.997780i \(-0.478788\pi\)
0.830808 0.556560i \(-0.187879\pi\)
\(602\) 0 0
\(603\) 2.00000 0.0814463
\(604\) 5.50000 + 9.52628i 0.223792 + 0.387619i
\(605\) 4.00000 + 6.92820i 0.162623 + 0.281672i
\(606\) 10.0000 0.406222
\(607\) 4.00000 + 6.92820i 0.162355 + 0.281207i 0.935713 0.352763i \(-0.114758\pi\)
−0.773358 + 0.633970i \(0.781424\pi\)
\(608\) 1.50000 2.59808i 0.0608330 0.105366i
\(609\) −4.50000 + 7.79423i −0.182349 + 0.315838i
\(610\) 4.00000 0.161955
\(611\) 7.50000 7.79423i 0.303418 0.315321i
\(612\) −5.00000 −0.202113
\(613\) −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i \(-0.884985\pi\)
0.773869 + 0.633345i \(0.218319\pi\)
\(614\) 10.5000 18.1865i 0.423746 0.733949i
\(615\) 10.0000 + 17.3205i 0.403239 + 0.698430i
\(616\) 3.00000 0.120873
\(617\) −5.00000 8.66025i −0.201292 0.348649i 0.747653 0.664090i \(-0.231181\pi\)
−0.948945 + 0.315441i \(0.897847\pi\)
\(618\) −10.0000 17.3205i −0.402259 0.696733i
\(619\) 17.0000 0.683288 0.341644 0.939829i \(-0.389016\pi\)
0.341644 + 0.939829i \(0.389016\pi\)
\(620\) 8.00000 + 13.8564i 0.321288 + 0.556487i
\(621\) 3.00000 5.19615i 0.120386 0.208514i
\(622\) −9.50000 + 16.4545i −0.380915 + 0.659765i
\(623\) 7.00000 0.280449
\(624\) −3.50000 0.866025i −0.140112 0.0346688i
\(625\) 41.0000 1.64000
\(626\) −7.00000 + 12.1244i −0.279776 + 0.484587i
\(627\) −4.50000 + 7.79423i −0.179713 + 0.311272i
\(628\) 1.00000 + 1.73205i 0.0399043 + 0.0691164i
\(629\) −20.0000 −0.797452
\(630\) 2.00000 + 3.46410i 0.0796819 + 0.138013i
\(631\) 6.50000 + 11.2583i 0.258761 + 0.448187i 0.965910 0.258877i \(-0.0833525\pi\)
−0.707149 + 0.707064i \(0.750019\pi\)
\(632\) −11.0000 −0.437557
\(633\) 7.00000 + 12.1244i 0.278225 + 0.481900i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) −16.0000 + 27.7128i −0.634941 + 1.09975i
\(636\) 11.0000 0.436178
\(637\) −1.00000 3.46410i −0.0396214 0.137253i
\(638\) −27.0000 −1.06894
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 2.00000 3.46410i 0.0790569 0.136931i
\(641\) 15.0000 + 25.9808i 0.592464 + 1.02618i 0.993899 + 0.110291i \(0.0351782\pi\)
−0.401435 + 0.915888i \(0.631488\pi\)
\(642\) 17.0000 0.670936
\(643\) 8.50000 + 14.7224i 0.335207 + 0.580596i 0.983525 0.180774i \(-0.0578603\pi\)
−0.648317 + 0.761370i \(0.724527\pi\)
\(644\) −3.00000 5.19615i −0.118217 0.204757i
\(645\) 0 0
\(646\) −7.50000 12.9904i −0.295084 0.511100i
\(647\) −7.50000 + 12.9904i −0.294855 + 0.510705i −0.974951 0.222419i \(-0.928605\pi\)
0.680096 + 0.733123i \(0.261938\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) −6.00000 −0.235521
\(650\) 11.0000 + 38.1051i 0.431455 + 1.49461i
\(651\) 4.00000 0.156772
\(652\) −10.0000 + 17.3205i −0.391630 + 0.678323i
\(653\) 13.5000 23.3827i 0.528296 0.915035i −0.471160 0.882048i \(-0.656165\pi\)
0.999456 0.0329874i \(-0.0105021\pi\)
\(654\) 1.00000 + 1.73205i 0.0391031 + 0.0677285i
\(655\) 48.0000 1.87552
\(656\) −2.50000 4.33013i −0.0976086 0.169063i
\(657\) −6.00000 10.3923i −0.234082 0.405442i
\(658\) 3.00000 0.116952
\(659\) −19.5000 33.7750i −0.759612 1.31569i −0.943049 0.332655i \(-0.892055\pi\)
0.183436 0.983032i \(-0.441278\pi\)
\(660\) −6.00000 + 10.3923i −0.233550 + 0.404520i
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) −2.00000 −0.0777322
\(663\) −12.5000 + 12.9904i −0.485460 + 0.504505i
\(664\) −6.00000 −0.232845
\(665\) −6.00000 + 10.3923i −0.232670 + 0.402996i
\(666\) 2.00000 3.46410i 0.0774984 0.134231i
\(667\) 27.0000 + 46.7654i 1.04544 + 1.81076i
\(668\) −16.0000 −0.619059
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) 4.00000 + 6.92820i 0.154533 + 0.267660i
\(671\) 3.00000 0.115814
\(672\) −0.500000 0.866025i −0.0192879 0.0334077i
\(673\) −11.5000 + 19.9186i −0.443292 + 0.767805i −0.997932 0.0642860i \(-0.979523\pi\)
0.554639 + 0.832091i \(0.312856\pi\)
\(674\) 15.5000 26.8468i 0.597038 1.03410i
\(675\) −11.0000 −0.423390
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) −26.0000 −0.999261 −0.499631 0.866239i \(-0.666531\pi\)
−0.499631 + 0.866239i \(0.666531\pi\)
\(678\) −6.00000 + 10.3923i −0.230429 + 0.399114i
\(679\) 6.00000 10.3923i 0.230259 0.398820i
\(680\) −10.0000 17.3205i −0.383482 0.664211i
\(681\) −14.0000 −0.536481
\(682\) 6.00000 + 10.3923i 0.229752 + 0.397942i
\(683\) 10.0000 + 17.3205i 0.382639 + 0.662751i 0.991439 0.130573i \(-0.0416818\pi\)
−0.608799 + 0.793324i \(0.708349\pi\)
\(684\) 3.00000 0.114708
\(685\) 36.0000 + 62.3538i 1.37549 + 2.38242i
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) −2.50000 + 4.33013i −0.0953809 + 0.165205i
\(688\) 0 0
\(689\) 27.5000 28.5788i 1.04767 1.08877i
\(690\) 24.0000 0.913664
\(691\) −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i \(-0.881959\pi\)
0.779857 + 0.625958i \(0.215292\pi\)
\(692\) 1.00000 1.73205i 0.0380143 0.0658427i
\(693\) 1.50000 + 2.59808i 0.0569803 + 0.0986928i
\(694\) −11.0000 −0.417554
\(695\) −26.0000 45.0333i −0.986236 1.70821i
\(696\) 4.50000 + 7.79423i 0.170572 + 0.295439i
\(697\) −25.0000 −0.946943
\(698\) −17.0000 29.4449i −0.643459 1.11450i
\(699\) 2.00000 3.46410i 0.0756469 0.131024i
\(700\) −5.50000 + 9.52628i −0.207880 + 0.360060i
\(701\) −21.0000 −0.793159 −0.396580 0.918000i \(-0.629803\pi\)
−0.396580 + 0.918000i \(0.629803\pi\)
\(702\) −1.00000 3.46410i −0.0377426 0.130744i
\(703\) 12.0000 0.452589
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) −6.00000 + 10.3923i −0.225973 + 0.391397i
\(706\) −9.00000 15.5885i −0.338719 0.586679i
\(707\) 10.0000 0.376089
\(708\) 1.00000 + 1.73205i 0.0375823 + 0.0650945i
\(709\) −5.00000 8.66025i −0.187779 0.325243i 0.756730 0.653727i \(-0.226796\pi\)
−0.944509 + 0.328484i \(0.893462\pi\)
\(710\) −24.0000 −0.900704
\(711\) −5.50000 9.52628i −0.206266 0.357263i
\(712\) 3.50000 6.06218i 0.131168 0.227190i
\(713\) 12.0000 20.7846i 0.449404 0.778390i
\(714\) −5.00000 −0.187120
\(715\) 12.0000 + 41.5692i 0.448775 + 1.55460i
\(716\) 24.0000 0.896922
\(717\) −13.0000 + 22.5167i −0.485494 + 0.840900i
\(718\) −10.0000 + 17.3205i −0.373197 + 0.646396i
\(719\) 0.500000 + 0.866025i 0.0186469 + 0.0322973i 0.875198 0.483764i \(-0.160731\pi\)
−0.856551 + 0.516062i \(0.827398\pi\)
\(720\) 4.00000 0.149071
\(721\) −10.0000 17.3205i −0.372419 0.645049i
\(722\) −5.00000 8.66025i −0.186081 0.322301i
\(723\) −12.0000 −0.446285
\(724\) 2.50000 + 4.33013i 0.0929118 + 0.160928i
\(725\) 49.5000 85.7365i 1.83838 3.18417i
\(726\) 1.00000 1.73205i 0.0371135 0.0642824i
\(727\) 12.0000 0.445055 0.222528 0.974926i \(-0.428569\pi\)
0.222528 + 0.974926i \(0.428569\pi\)
\(728\) −3.50000 0.866025i −0.129719 0.0320970i
\(729\) 1.00000 0.0370370
\(730\) 24.0000 41.5692i 0.888280 1.53855i
\(731\) 0 0
\(732\) −0.500000 0.866025i −0.0184805 0.0320092i
\(733\) 13.0000 0.480166 0.240083 0.970752i \(-0.422825\pi\)
0.240083 + 0.970752i \(0.422825\pi\)
\(734\) 9.00000 + 15.5885i 0.332196 + 0.575380i
\(735\) 2.00000 + 3.46410i 0.0737711 + 0.127775i
\(736\) −6.00000 −0.221163
\(737\) 3.00000 + 5.19615i 0.110506 + 0.191403i
\(738\) 2.50000 4.33013i 0.0920263 0.159394i
\(739\) 27.0000 46.7654i 0.993211 1.72029i 0.395864 0.918309i \(-0.370445\pi\)
0.597347 0.801983i \(-0.296222\pi\)
\(740\) 16.0000 0.588172
\(741\) 7.50000 7.79423i 0.275519 0.286328i
\(742\) 11.0000 0.403823
\(743\) −14.0000 + 24.2487i −0.513610 + 0.889599i 0.486265 + 0.873811i \(0.338359\pi\)
−0.999875 + 0.0157876i \(0.994974\pi\)
\(744\) 2.00000 3.46410i 0.0733236 0.127000i
\(745\) −36.0000 62.3538i −1.31894 2.28447i
\(746\) −34.0000 −1.24483
\(747\) −3.00000 5.19615i −0.109764 0.190117i
\(748\) −7.50000 12.9904i −0.274227 0.474975i
\(749\) 17.0000 0.621166
\(750\) −12.0000 20.7846i −0.438178 0.758947i
\(751\) −15.5000 + 26.8468i −0.565603 + 0.979653i 0.431390 + 0.902165i \(0.358023\pi\)
−0.996993 + 0.0774878i \(0.975310\pi\)
\(752\) 1.50000 2.59808i 0.0546994 0.0947421i
\(753\) −14.0000 −0.510188
\(754\) 31.5000 + 7.79423i 1.14716 + 0.283849i
\(755\) −44.0000 −1.60132
\(756\) 0.500000 0.866025i 0.0181848 0.0314970i
\(757\) −11.0000 + 19.0526i −0.399802 + 0.692477i −0.993701 0.112062i \(-0.964254\pi\)
0.593899 + 0.804539i \(0.297588\pi\)
\(758\) −9.00000 15.5885i −0.326895 0.566198i
\(759\) 18.0000 0.653359
\(760\) 6.00000 + 10.3923i 0.217643 + 0.376969i
\(761\) 13.0000 + 22.5167i 0.471250 + 0.816228i 0.999459 0.0328858i \(-0.0104698\pi\)
−0.528209 + 0.849114i \(0.677136\pi\)
\(762\) 8.00000 0.289809
\(763\) 1.00000 + 1.73205i 0.0362024 + 0.0627044i
\(764\) 3.00000 5.19615i 0.108536 0.187990i
\(765\) 10.0000 17.3205i 0.361551 0.626224i
\(766\) 11.0000 0.397446
\(767\) 7.00000 + 1.73205i 0.252755 + 0.0625407i
\(768\) −1.00000 −0.0360844
\(769\) 2.00000 3.46410i 0.0721218 0.124919i −0.827709 0.561157i \(-0.810356\pi\)
0.899831 + 0.436239i \(0.143690\pi\)
\(770\) −6.00000 + 10.3923i −0.216225 + 0.374513i
\(771\) 3.50000 + 6.06218i 0.126049 + 0.218324i
\(772\) 13.0000 0.467880
\(773\) −9.00000 15.5885i −0.323708 0.560678i 0.657542 0.753418i \(-0.271596\pi\)
−0.981250 + 0.192740i \(0.938263\pi\)
\(774\) 0 0
\(775\) −44.0000 −1.58053
\(776\) −6.00000 10.3923i −0.215387 0.373062i
\(777\) 2.00000 3.46410i 0.0717496 0.124274i
\(778\) −13.0000 +