Properties

Label 63.2.g.a.4.1
Level $63$
Weight $2$
Character 63.4
Analytic conductor $0.503$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.g (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.503057532734\)
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 4.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 63.4
Dual form 63.2.g.a.16.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} -1.73205i q^{6} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} -1.73205i q^{6} +(0.500000 + 2.59808i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{10} +5.00000 q^{11} +(-1.50000 - 0.866025i) q^{12} +(2.50000 - 4.33013i) q^{13} +(-2.50000 - 0.866025i) q^{14} +(1.50000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-3.00000 - 3.46410i) q^{21} +(-2.50000 + 4.33013i) q^{22} +3.00000 q^{23} +(4.50000 - 2.59808i) q^{24} -4.00000 q^{25} +(2.50000 + 4.33013i) q^{26} +5.19615i q^{27} +(-2.00000 + 1.73205i) q^{28} +(0.500000 + 0.866025i) q^{29} +1.73205i q^{30} +(-2.50000 - 4.33013i) q^{32} +(-7.50000 + 4.33013i) q^{33} +(-1.50000 - 2.59808i) q^{34} +(-0.500000 - 2.59808i) q^{35} +3.00000 q^{36} +(-1.50000 - 2.59808i) q^{37} +1.00000 q^{38} +8.66025i q^{39} +3.00000 q^{40} +(2.50000 - 4.33013i) q^{41} +(4.50000 - 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(2.50000 + 4.33013i) q^{44} +(-1.50000 + 2.59808i) q^{45} +(-1.50000 + 2.59808i) q^{46} +1.73205i q^{48} +(-6.50000 + 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{50} -5.19615i q^{51} +5.00000 q^{52} +(4.50000 - 7.79423i) q^{53} +(-4.50000 - 2.59808i) q^{54} -5.00000 q^{55} +(-1.50000 - 7.79423i) q^{56} +(1.50000 + 0.866025i) q^{57} -1.00000 q^{58} +(1.50000 + 0.866025i) q^{60} +(7.00000 - 12.1244i) q^{61} +(7.50000 + 2.59808i) q^{63} +7.00000 q^{64} +(-2.50000 + 4.33013i) q^{65} -8.66025i q^{66} +(-2.00000 - 3.46410i) q^{67} -3.00000 q^{68} +(-4.50000 + 2.59808i) q^{69} +(2.50000 + 0.866025i) q^{70} -12.0000 q^{71} +(-4.50000 + 7.79423i) q^{72} +(-1.50000 + 2.59808i) q^{73} +3.00000 q^{74} +(6.00000 - 3.46410i) q^{75} +(0.500000 - 0.866025i) q^{76} +(2.50000 + 12.9904i) q^{77} +(-7.50000 - 4.33013i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.50000 + 4.33013i) q^{82} +(4.50000 + 7.79423i) q^{83} +(1.50000 - 4.33013i) q^{84} +(1.50000 - 2.59808i) q^{85} -1.00000 q^{86} +(-1.50000 - 0.866025i) q^{87} -15.0000 q^{88} +(6.50000 + 11.2583i) q^{89} +(-1.50000 - 2.59808i) q^{90} +(12.5000 + 4.33013i) q^{91} +(1.50000 + 2.59808i) q^{92} +(0.500000 + 0.866025i) q^{95} +(7.50000 + 4.33013i) q^{96} +(4.50000 + 7.79423i) q^{97} +(1.00000 - 6.92820i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - 3q^{3} + q^{4} - 2q^{5} + q^{7} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 2q - q^{2} - 3q^{3} + q^{4} - 2q^{5} + q^{7} - 6q^{8} + 3q^{9} + q^{10} + 10q^{11} - 3q^{12} + 5q^{13} - 5q^{14} + 3q^{15} + q^{16} - 3q^{17} + 3q^{18} - q^{19} - q^{20} - 6q^{21} - 5q^{22} + 6q^{23} + 9q^{24} - 8q^{25} + 5q^{26} - 4q^{28} + q^{29} - 5q^{32} - 15q^{33} - 3q^{34} - q^{35} + 6q^{36} - 3q^{37} + 2q^{38} + 6q^{40} + 5q^{41} + 9q^{42} + q^{43} + 5q^{44} - 3q^{45} - 3q^{46} - 13q^{49} + 4q^{50} + 10q^{52} + 9q^{53} - 9q^{54} - 10q^{55} - 3q^{56} + 3q^{57} - 2q^{58} + 3q^{60} + 14q^{61} + 15q^{63} + 14q^{64} - 5q^{65} - 4q^{67} - 6q^{68} - 9q^{69} + 5q^{70} - 24q^{71} - 9q^{72} - 3q^{73} + 6q^{74} + 12q^{75} + q^{76} + 5q^{77} - 15q^{78} - 8q^{79} - q^{80} - 9q^{81} + 5q^{82} + 9q^{83} + 3q^{84} + 3q^{85} - 2q^{86} - 3q^{87} - 30q^{88} + 13q^{89} - 3q^{90} + 25q^{91} + 3q^{92} + q^{95} + 15q^{96} + 9q^{97} + 2q^{98} + 15q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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 −0.986869 0.161521i \(-0.948360\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 1.73205i 0.707107i
\(7\) 0.500000 + 2.59808i 0.188982 + 0.981981i
\(8\) −3.00000 −1.06066
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) −1.50000 0.866025i −0.433013 0.250000i
\(13\) 2.50000 4.33013i 0.693375 1.20096i −0.277350 0.960769i \(-0.589456\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) −2.50000 0.866025i −0.668153 0.231455i
\(15\) 1.50000 0.866025i 0.387298 0.223607i
\(16\) 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 \(0.285189\pi\)
\(18\) 1.50000 + 2.59808i 0.353553 + 0.612372i
\(19\) −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i \(-0.203260\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) −3.00000 3.46410i −0.654654 0.755929i
\(22\) −2.50000 + 4.33013i −0.533002 + 0.923186i
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 4.50000 2.59808i 0.918559 0.530330i
\(25\) −4.00000 −0.800000
\(26\) 2.50000 + 4.33013i 0.490290 + 0.849208i
\(27\) 5.19615i 1.00000i
\(28\) −2.00000 + 1.73205i −0.377964 + 0.327327i
\(29\) 0.500000 + 0.866025i 0.0928477 + 0.160817i 0.908708 0.417432i \(-0.137070\pi\)
−0.815861 + 0.578249i \(0.803736\pi\)
\(30\) 1.73205i 0.316228i
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) −2.50000 4.33013i −0.441942 0.765466i
\(33\) −7.50000 + 4.33013i −1.30558 + 0.753778i
\(34\) −1.50000 2.59808i −0.257248 0.445566i
\(35\) −0.500000 2.59808i −0.0845154 0.439155i
\(36\) 3.00000 0.500000
\(37\) −1.50000 2.59808i −0.246598 0.427121i 0.715981 0.698119i \(-0.245980\pi\)
−0.962580 + 0.270998i \(0.912646\pi\)
\(38\) 1.00000 0.162221
\(39\) 8.66025i 1.38675i
\(40\) 3.00000 0.474342
\(41\) 2.50000 4.33013i 0.390434 0.676252i −0.602072 0.798441i \(-0.705658\pi\)
0.992507 + 0.122189i \(0.0389915\pi\)
\(42\) 4.50000 0.866025i 0.694365 0.133631i
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 2.50000 + 4.33013i 0.376889 + 0.652791i
\(45\) −1.50000 + 2.59808i −0.223607 + 0.387298i
\(46\) −1.50000 + 2.59808i −0.221163 + 0.383065i
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 1.73205i 0.250000i
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 2.00000 3.46410i 0.282843 0.489898i
\(51\) 5.19615i 0.727607i
\(52\) 5.00000 0.693375
\(53\) 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i \(-0.621227\pi\)
0.989828 0.142269i \(-0.0454398\pi\)
\(54\) −4.50000 2.59808i −0.612372 0.353553i
\(55\) −5.00000 −0.674200
\(56\) −1.50000 7.79423i −0.200446 1.04155i
\(57\) 1.50000 + 0.866025i 0.198680 + 0.114708i
\(58\) −1.00000 −0.131306
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 1.50000 + 0.866025i 0.193649 + 0.111803i
\(61\) 7.00000 12.1244i 0.896258 1.55236i 0.0640184 0.997949i \(-0.479608\pi\)
0.832240 0.554416i \(-0.187058\pi\)
\(62\) 0 0
\(63\) 7.50000 + 2.59808i 0.944911 + 0.327327i
\(64\) 7.00000 0.875000
\(65\) −2.50000 + 4.33013i −0.310087 + 0.537086i
\(66\) 8.66025i 1.06600i
\(67\) −2.00000 3.46410i −0.244339 0.423207i 0.717607 0.696449i \(-0.245238\pi\)
−0.961946 + 0.273241i \(0.911904\pi\)
\(68\) −3.00000 −0.363803
\(69\) −4.50000 + 2.59808i −0.541736 + 0.312772i
\(70\) 2.50000 + 0.866025i 0.298807 + 0.103510i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) −4.50000 + 7.79423i −0.530330 + 0.918559i
\(73\) −1.50000 + 2.59808i −0.175562 + 0.304082i −0.940356 0.340193i \(-0.889507\pi\)
0.764794 + 0.644275i \(0.222841\pi\)
\(74\) 3.00000 0.348743
\(75\) 6.00000 3.46410i 0.692820 0.400000i
\(76\) 0.500000 0.866025i 0.0573539 0.0993399i
\(77\) 2.50000 + 12.9904i 0.284901 + 1.48039i
\(78\) −7.50000 4.33013i −0.849208 0.490290i
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 2.50000 + 4.33013i 0.276079 + 0.478183i
\(83\) 4.50000 + 7.79423i 0.493939 + 0.855528i 0.999976 0.00698436i \(-0.00222321\pi\)
−0.506036 + 0.862512i \(0.668890\pi\)
\(84\) 1.50000 4.33013i 0.163663 0.472456i
\(85\) 1.50000 2.59808i 0.162698 0.281801i
\(86\) −1.00000 −0.107833
\(87\) −1.50000 0.866025i −0.160817 0.0928477i
\(88\) −15.0000 −1.59901
\(89\) 6.50000 + 11.2583i 0.688999 + 1.19338i 0.972162 + 0.234309i \(0.0752827\pi\)
−0.283164 + 0.959072i \(0.591384\pi\)
\(90\) −1.50000 2.59808i −0.158114 0.273861i
\(91\) 12.5000 + 4.33013i 1.31036 + 0.453921i
\(92\) 1.50000 + 2.59808i 0.156386 + 0.270868i
\(93\) 0 0
\(94\) 0 0
\(95\) 0.500000 + 0.866025i 0.0512989 + 0.0888523i
\(96\) 7.50000 + 4.33013i 0.765466 + 0.441942i
\(97\) 4.50000 + 7.79423i 0.456906 + 0.791384i 0.998796 0.0490655i \(-0.0156243\pi\)
−0.541890 + 0.840450i \(0.682291\pi\)
\(98\) 1.00000 6.92820i 0.101015 0.699854i
\(99\) 7.50000 12.9904i 0.753778 1.30558i
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) −17.0000 −1.69156 −0.845782 0.533529i \(-0.820865\pi\)
−0.845782 + 0.533529i \(0.820865\pi\)
\(102\) 4.50000 + 2.59808i 0.445566 + 0.257248i
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) −7.50000 + 12.9904i −0.735436 + 1.27381i
\(105\) 3.00000 + 3.46410i 0.292770 + 0.338062i
\(106\) 4.50000 + 7.79423i 0.437079 + 0.757042i
\(107\) −8.50000 14.7224i −0.821726 1.42327i −0.904396 0.426694i \(-0.859678\pi\)
0.0826699 0.996577i \(-0.473655\pi\)
\(108\) −4.50000 + 2.59808i −0.433013 + 0.250000i
\(109\) 4.50000 7.79423i 0.431022 0.746552i −0.565940 0.824447i \(-0.691487\pi\)
0.996962 + 0.0778949i \(0.0248199\pi\)
\(110\) 2.50000 4.33013i 0.238366 0.412861i
\(111\) 4.50000 + 2.59808i 0.427121 + 0.246598i
\(112\) 2.50000 + 0.866025i 0.236228 + 0.0818317i
\(113\) 0.500000 0.866025i 0.0470360 0.0814688i −0.841549 0.540181i \(-0.818356\pi\)
0.888585 + 0.458712i \(0.151689\pi\)
\(114\) −1.50000 + 0.866025i −0.140488 + 0.0811107i
\(115\) −3.00000 −0.279751
\(116\) −0.500000 + 0.866025i −0.0464238 + 0.0804084i
\(117\) −7.50000 12.9904i −0.693375 1.20096i
\(118\) 0 0
\(119\) −7.50000 2.59808i −0.687524 0.238165i
\(120\) −4.50000 + 2.59808i −0.410792 + 0.237171i
\(121\) 14.0000 1.27273
\(122\) 7.00000 + 12.1244i 0.633750 + 1.09769i
\(123\) 8.66025i 0.780869i
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) −6.00000 + 5.19615i −0.534522 + 0.462910i
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 1.50000 2.59808i 0.132583 0.229640i
\(129\) −1.50000 0.866025i −0.132068 0.0762493i
\(130\) −2.50000 4.33013i −0.219265 0.379777i
\(131\) −1.00000 −0.0873704 −0.0436852 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) −7.50000 4.33013i −0.652791 0.376889i
\(133\) 2.00000 1.73205i 0.173422 0.150188i
\(134\) 4.00000 0.345547
\(135\) 5.19615i 0.447214i
\(136\) 4.50000 7.79423i 0.385872 0.668350i
\(137\) −9.00000 −0.768922 −0.384461 0.923141i \(-0.625613\pi\)
−0.384461 + 0.923141i \(0.625613\pi\)
\(138\) 5.19615i 0.442326i
\(139\) −4.50000 + 7.79423i −0.381685 + 0.661098i −0.991303 0.131597i \(-0.957989\pi\)
0.609618 + 0.792695i \(0.291323\pi\)
\(140\) 2.00000 1.73205i 0.169031 0.146385i
\(141\) 0 0
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) 12.5000 21.6506i 1.04530 1.81052i
\(144\) −1.50000 2.59808i −0.125000 0.216506i
\(145\) −0.500000 0.866025i −0.0415227 0.0719195i
\(146\) −1.50000 2.59808i −0.124141 0.215018i
\(147\) 7.50000 9.52628i 0.618590 0.785714i
\(148\) 1.50000 2.59808i 0.123299 0.213561i
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 6.92820i 0.565685i
\(151\) 5.00000 0.406894 0.203447 0.979086i \(-0.434786\pi\)
0.203447 + 0.979086i \(0.434786\pi\)
\(152\) 1.50000 + 2.59808i 0.121666 + 0.210732i
\(153\) 4.50000 + 7.79423i 0.363803 + 0.630126i
\(154\) −12.5000 4.33013i −1.00728 0.348932i
\(155\) 0 0
\(156\) −7.50000 + 4.33013i −0.600481 + 0.346688i
\(157\) 7.00000 + 12.1244i 0.558661 + 0.967629i 0.997609 + 0.0691164i \(0.0220180\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) −4.00000 6.92820i −0.318223 0.551178i
\(159\) 15.5885i 1.23625i
\(160\) 2.50000 + 4.33013i 0.197642 + 0.342327i
\(161\) 1.50000 + 7.79423i 0.118217 + 0.614271i
\(162\) 9.00000 0.707107
\(163\) 5.50000 + 9.52628i 0.430793 + 0.746156i 0.996942 0.0781474i \(-0.0249005\pi\)
−0.566149 + 0.824303i \(0.691567\pi\)
\(164\) 5.00000 0.390434
\(165\) 7.50000 4.33013i 0.583874 0.337100i
\(166\) −9.00000 −0.698535
\(167\) 9.50000 16.4545i 0.735132 1.27329i −0.219533 0.975605i \(-0.570453\pi\)
0.954665 0.297681i \(-0.0962132\pi\)
\(168\) 9.00000 + 10.3923i 0.694365 + 0.801784i
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 1.50000 + 2.59808i 0.115045 + 0.199263i
\(171\) −3.00000 −0.229416
\(172\) −0.500000 + 0.866025i −0.0381246 + 0.0660338i
\(173\) 7.00000 12.1244i 0.532200 0.921798i −0.467093 0.884208i \(-0.654699\pi\)
0.999293 0.0375896i \(-0.0119679\pi\)
\(174\) 1.50000 0.866025i 0.113715 0.0656532i
\(175\) −2.00000 10.3923i −0.151186 0.785584i
\(176\) 2.50000 4.33013i 0.188445 0.326396i
\(177\) 0 0
\(178\) −13.0000 −0.974391
\(179\) −9.50000 + 16.4545i −0.710063 + 1.22987i 0.254770 + 0.967002i \(0.418000\pi\)
−0.964833 + 0.262864i \(0.915333\pi\)
\(180\) −3.00000 −0.223607
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) −10.0000 + 8.66025i −0.741249 + 0.641941i
\(183\) 24.2487i 1.79252i
\(184\) −9.00000 −0.663489
\(185\) 1.50000 + 2.59808i 0.110282 + 0.191014i
\(186\) 0 0
\(187\) −7.50000 + 12.9904i −0.548454 + 0.949951i
\(188\) 0 0
\(189\) −13.5000 + 2.59808i −0.981981 + 0.188982i
\(190\) −1.00000 −0.0725476
\(191\) −4.00000 + 6.92820i −0.289430 + 0.501307i −0.973674 0.227946i \(-0.926799\pi\)
0.684244 + 0.729253i \(0.260132\pi\)
\(192\) −10.5000 + 6.06218i −0.757772 + 0.437500i
\(193\) 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i \(-0.0494748\pi\)
−0.628037 + 0.778183i \(0.716141\pi\)
\(194\) −9.00000 −0.646162
\(195\) 8.66025i 0.620174i
\(196\) −5.50000 4.33013i −0.392857 0.309295i
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 7.50000 + 12.9904i 0.533002 + 0.923186i
\(199\) −1.50000 + 2.59808i −0.106332 + 0.184173i −0.914282 0.405079i \(-0.867244\pi\)
0.807950 + 0.589252i \(0.200577\pi\)
\(200\) 12.0000 0.848528
\(201\) 6.00000 + 3.46410i 0.423207 + 0.244339i
\(202\) 8.50000 14.7224i 0.598058 1.03587i
\(203\) −2.00000 + 1.73205i −0.140372 + 0.121566i
\(204\) 4.50000 2.59808i 0.315063 0.181902i
\(205\) −2.50000 + 4.33013i −0.174608 + 0.302429i
\(206\) 0.500000 0.866025i 0.0348367 0.0603388i
\(207\) 4.50000 7.79423i 0.312772 0.541736i
\(208\) −2.50000 4.33013i −0.173344 0.300240i
\(209\) −2.50000 4.33013i −0.172929 0.299521i
\(210\) −4.50000 + 0.866025i −0.310530 + 0.0597614i
\(211\) −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i \(-0.981011\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 9.00000 0.618123
\(213\) 18.0000 10.3923i 1.23334 0.712069i
\(214\) 17.0000 1.16210
\(215\) −0.500000 0.866025i −0.0340997 0.0590624i
\(216\) 15.5885i 1.06066i
\(217\) 0 0
\(218\) 4.50000 + 7.79423i 0.304778 + 0.527892i
\(219\) 5.19615i 0.351123i
\(220\) −2.50000 4.33013i −0.168550 0.291937i
\(221\) 7.50000 + 12.9904i 0.504505 + 0.873828i
\(222\) −4.50000 + 2.59808i −0.302020 + 0.174371i
\(223\) −9.50000 16.4545i −0.636167 1.10187i −0.986267 0.165161i \(-0.947186\pi\)
0.350100 0.936713i \(-0.386148\pi\)
\(224\) 10.0000 8.66025i 0.668153 0.578638i
\(225\) −6.00000 + 10.3923i −0.400000 + 0.692820i
\(226\) 0.500000 + 0.866025i 0.0332595 + 0.0576072i
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 1.73205i 0.114708i
\(229\) −1.00000 −0.0660819 −0.0330409 0.999454i \(-0.510519\pi\)
−0.0330409 + 0.999454i \(0.510519\pi\)
\(230\) 1.50000 2.59808i 0.0989071 0.171312i
\(231\) −15.0000 17.3205i −0.986928 1.13961i
\(232\) −1.50000 2.59808i −0.0984798 0.170572i
\(233\) −1.50000 2.59808i −0.0982683 0.170206i 0.812700 0.582683i \(-0.197997\pi\)
−0.910968 + 0.412477i \(0.864664\pi\)
\(234\) 15.0000 0.980581
\(235\) 0 0
\(236\) 0 0
\(237\) 13.8564i 0.900070i
\(238\) 6.00000 5.19615i 0.388922 0.336817i
\(239\) 7.50000 12.9904i 0.485135 0.840278i −0.514719 0.857359i \(-0.672104\pi\)
0.999854 + 0.0170808i \(0.00543724\pi\)
\(240\) 1.73205i 0.111803i
\(241\) 11.0000 0.708572 0.354286 0.935137i \(-0.384724\pi\)
0.354286 + 0.935137i \(0.384724\pi\)
\(242\) −7.00000 + 12.1244i −0.449977 + 0.779383i
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) 14.0000 0.896258
\(245\) 6.50000 2.59808i 0.415270 0.165985i
\(246\) −7.50000 4.33013i −0.478183 0.276079i
\(247\) −5.00000 −0.318142
\(248\) 0 0
\(249\) −13.5000 7.79423i −0.855528 0.493939i
\(250\) −4.50000 + 7.79423i −0.284605 + 0.492950i
\(251\) −28.0000 −1.76734 −0.883672 0.468106i \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 1.50000 + 7.79423i 0.0944911 + 0.490990i
\(253\) 15.0000 0.943042
\(254\) 6.00000 10.3923i 0.376473 0.652071i
\(255\) 5.19615i 0.325396i
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) −29.0000 −1.80897 −0.904485 0.426505i \(-0.859745\pi\)
−0.904485 + 0.426505i \(0.859745\pi\)
\(258\) 1.50000 0.866025i 0.0933859 0.0539164i
\(259\) 6.00000 5.19615i 0.372822 0.322873i
\(260\) −5.00000 −0.310087
\(261\) 3.00000 0.185695
\(262\) 0.500000 0.866025i 0.0308901 0.0535032i
\(263\) 5.00000 0.308313 0.154157 0.988046i \(-0.450734\pi\)
0.154157 + 0.988046i \(0.450734\pi\)
\(264\) 22.5000 12.9904i 1.38478 0.799503i
\(265\) −4.50000 + 7.79423i −0.276433 + 0.478796i
\(266\) 0.500000 + 2.59808i 0.0306570 + 0.159298i
\(267\) −19.5000 11.2583i −1.19338 0.688999i
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) −1.50000 + 2.59808i −0.0914566 + 0.158408i −0.908124 0.418701i \(-0.862486\pi\)
0.816668 + 0.577108i \(0.195819\pi\)
\(270\) 4.50000 + 2.59808i 0.273861 + 0.158114i
\(271\) −0.500000 0.866025i −0.0303728 0.0526073i 0.850439 0.526073i \(-0.176336\pi\)
−0.880812 + 0.473466i \(0.843003\pi\)
\(272\) 1.50000 + 2.59808i 0.0909509 + 0.157532i
\(273\) −22.5000 + 4.33013i −1.36176 + 0.262071i
\(274\) 4.50000 7.79423i 0.271855 0.470867i
\(275\) −20.0000 −1.20605
\(276\) −4.50000 2.59808i −0.270868 0.156386i
\(277\) 19.0000 1.14160 0.570800 0.821089i \(-0.306633\pi\)
0.570800 + 0.821089i \(0.306633\pi\)
\(278\) −4.50000 7.79423i −0.269892 0.467467i
\(279\) 0 0
\(280\) 1.50000 + 7.79423i 0.0896421 + 0.465794i
\(281\) 14.5000 + 25.1147i 0.864997 + 1.49822i 0.867050 + 0.498222i \(0.166013\pi\)
−0.00205220 + 0.999998i \(0.500653\pi\)
\(282\) 0 0
\(283\) −14.0000 24.2487i −0.832214 1.44144i −0.896279 0.443491i \(-0.853740\pi\)
0.0640654 0.997946i \(-0.479593\pi\)
\(284\) −6.00000 10.3923i −0.356034 0.616670i
\(285\) −1.50000 0.866025i −0.0888523 0.0512989i
\(286\) 12.5000 + 21.6506i 0.739140 + 1.28023i
\(287\) 12.5000 + 4.33013i 0.737852 + 0.255599i
\(288\) −15.0000 −0.883883
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 1.00000 0.0587220
\(291\) −13.5000 7.79423i −0.791384 0.456906i
\(292\) −3.00000 −0.175562
\(293\) 2.50000 4.33013i 0.146052 0.252969i −0.783713 0.621123i \(-0.786677\pi\)
0.929765 + 0.368154i \(0.120010\pi\)
\(294\) 4.50000 + 11.2583i 0.262445 + 0.656599i
\(295\) 0 0
\(296\) 4.50000 + 7.79423i 0.261557 + 0.453030i
\(297\) 25.9808i 1.50756i
\(298\) −1.50000 + 2.59808i −0.0868927 + 0.150503i
\(299\) 7.50000 12.9904i 0.433736 0.751253i
\(300\) 6.00000 + 3.46410i 0.346410 + 0.200000i
\(301\) −2.00000 + 1.73205i −0.115278 + 0.0998337i
\(302\) −2.50000 + 4.33013i −0.143859 + 0.249171i
\(303\) 25.5000 14.7224i 1.46494 0.845782i
\(304\) −1.00000 −0.0573539
\(305\) −7.00000 + 12.1244i −0.400819 + 0.694239i
\(306\) −9.00000 −0.514496
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) −10.0000 + 8.66025i −0.569803 + 0.493464i
\(309\) 1.50000 0.866025i 0.0853320 0.0492665i
\(310\) 0 0
\(311\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 25.9808i 1.47087i
\(313\) −7.00000 + 12.1244i −0.395663 + 0.685309i −0.993186 0.116543i \(-0.962819\pi\)
0.597522 + 0.801852i \(0.296152\pi\)
\(314\) −14.0000 −0.790066
\(315\) −7.50000 2.59808i −0.422577 0.146385i
\(316\) −8.00000 −0.450035
\(317\) 3.00000 5.19615i 0.168497 0.291845i −0.769395 0.638774i \(-0.779442\pi\)
0.937892 + 0.346929i \(0.112775\pi\)
\(318\) −13.5000 7.79423i −0.757042 0.437079i
\(319\) 2.50000 + 4.33013i 0.139973 + 0.242441i
\(320\) −7.00000 −0.391312
\(321\) 25.5000 + 14.7224i 1.42327 + 0.821726i
\(322\) −7.50000 2.59808i −0.417959 0.144785i
\(323\) 3.00000 0.166924
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) −10.0000 + 17.3205i −0.554700 + 0.960769i
\(326\) −11.0000 −0.609234
\(327\) 15.5885i 0.862044i
\(328\) −7.50000 + 12.9904i −0.414118 + 0.717274i
\(329\) 0 0
\(330\) 8.66025i 0.476731i
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) −4.50000 + 7.79423i −0.246970 + 0.427764i
\(333\) −9.00000 −0.493197
\(334\) 9.50000 + 16.4545i 0.519817 + 0.900349i
\(335\) 2.00000 + 3.46410i 0.109272 + 0.189264i
\(336\) −4.50000 + 0.866025i −0.245495 + 0.0472456i
\(337\) 14.5000 25.1147i 0.789865 1.36809i −0.136184 0.990684i \(-0.543484\pi\)
0.926049 0.377403i \(-0.123183\pi\)
\(338\) 12.0000 0.652714
\(339\) 1.73205i 0.0940721i
\(340\) 3.00000 0.162698
\(341\) 0 0
\(342\) 1.50000 2.59808i 0.0811107 0.140488i
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −1.50000 2.59808i −0.0808746 0.140079i
\(345\) 4.50000 2.59808i 0.242272 0.139876i
\(346\) 7.00000 + 12.1244i 0.376322 + 0.651809i
\(347\) −2.00000 3.46410i −0.107366 0.185963i 0.807337 0.590091i \(-0.200908\pi\)
−0.914702 + 0.404128i \(0.867575\pi\)
\(348\) 1.73205i 0.0928477i
\(349\) −9.50000 16.4545i −0.508523 0.880788i −0.999951 0.00987003i \(-0.996858\pi\)
0.491428 0.870918i \(-0.336475\pi\)
\(350\) 10.0000 + 3.46410i 0.534522 + 0.185164i
\(351\) 22.5000 + 12.9904i 1.20096 + 0.693375i
\(352\) −12.5000 21.6506i −0.666252 1.15398i
\(353\) 11.0000 0.585471 0.292735 0.956193i \(-0.405434\pi\)
0.292735 + 0.956193i \(0.405434\pi\)
\(354\) 0 0
\(355\) 12.0000 0.636894
\(356\) −6.50000 + 11.2583i −0.344499 + 0.596690i
\(357\) 13.5000 2.59808i 0.714496 0.137505i
\(358\) −9.50000 16.4545i −0.502091 0.869646i
\(359\) 5.50000 + 9.52628i 0.290279 + 0.502778i 0.973876 0.227082i \(-0.0729186\pi\)
−0.683597 + 0.729860i \(0.739585\pi\)
\(360\) 4.50000 7.79423i 0.237171 0.410792i
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) 7.00000 12.1244i 0.367912 0.637242i
\(363\) −21.0000 + 12.1244i −1.10221 + 0.636364i
\(364\) 2.50000 + 12.9904i 0.131036 + 0.680881i
\(365\) 1.50000 2.59808i 0.0785136 0.135990i
\(366\) −21.0000 12.1244i −1.09769 0.633750i
\(367\) −3.00000 −0.156599 −0.0782994 0.996930i \(-0.524949\pi\)
−0.0782994 + 0.996930i \(0.524949\pi\)
\(368\) 1.50000 2.59808i 0.0781929 0.135434i
\(369\) −7.50000 12.9904i −0.390434 0.676252i
\(370\) −3.00000 −0.155963
\(371\) 22.5000 + 7.79423i 1.16814 + 0.404656i
\(372\) 0 0
\(373\) −25.0000 −1.29445 −0.647225 0.762299i \(-0.724071\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) −7.50000 12.9904i −0.387816 0.671717i
\(375\) −13.5000 + 7.79423i −0.697137 + 0.402492i
\(376\) 0 0
\(377\) 5.00000 0.257513
\(378\) 4.50000 12.9904i 0.231455 0.668153i
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) −0.500000 + 0.866025i −0.0256495 + 0.0444262i
\(381\) 18.0000 10.3923i 0.922168 0.532414i
\(382\) −4.00000 6.92820i −0.204658 0.354478i
\(383\) 27.0000 1.37964 0.689818 0.723983i \(-0.257691\pi\)
0.689818 + 0.723983i \(0.257691\pi\)
\(384\) 5.19615i 0.265165i
\(385\) −2.50000 12.9904i −0.127412 0.662051i
\(386\) −10.0000 −0.508987
\(387\) 3.00000 0.152499
\(388\) −4.50000 + 7.79423i −0.228453 + 0.395692i
\(389\) −9.00000 −0.456318 −0.228159 0.973624i \(-0.573271\pi\)
−0.228159 + 0.973624i \(0.573271\pi\)
\(390\) 7.50000 + 4.33013i 0.379777 + 0.219265i
\(391\) −4.50000 + 7.79423i −0.227575 + 0.394171i
\(392\) 19.5000 7.79423i 0.984899 0.393668i
\(393\) 1.50000 0.866025i 0.0756650 0.0436852i
\(394\) −1.00000 + 1.73205i −0.0503793 + 0.0872595i
\(395\) 4.00000 6.92820i 0.201262 0.348596i
\(396\) 15.0000 0.753778
\(397\) −7.50000 12.9904i −0.376414 0.651969i 0.614123 0.789210i \(-0.289510\pi\)
−0.990538 + 0.137241i \(0.956176\pi\)
\(398\) −1.50000 2.59808i −0.0751882 0.130230i
\(399\) −1.50000 + 4.33013i −0.0750939 + 0.216777i
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) 3.00000 0.149813 0.0749064 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) −6.00000 + 3.46410i −0.299253 + 0.172774i
\(403\) 0 0
\(404\) −8.50000 14.7224i −0.422891 0.732468i
\(405\) 4.50000 + 7.79423i 0.223607 + 0.387298i
\(406\) −0.500000 2.59808i −0.0248146 0.128940i
\(407\) −7.50000 12.9904i −0.371761 0.643909i
\(408\) 15.5885i 0.771744i
\(409\) −7.00000 12.1244i −0.346128 0.599511i 0.639430 0.768849i \(-0.279170\pi\)
−0.985558 + 0.169338i \(0.945837\pi\)
\(410\) −2.50000 4.33013i −0.123466 0.213850i
\(411\) 13.5000 7.79423i 0.665906 0.384461i
\(412\) −0.500000 0.866025i −0.0246332 0.0426660i
\(413\) 0 0
\(414\) 4.50000 + 7.79423i 0.221163 + 0.383065i
\(415\) −4.50000 7.79423i −0.220896 0.382604i
\(416\) −25.0000 −1.22573
\(417\) 15.5885i 0.763370i
\(418\) 5.00000 0.244558
\(419\) −4.50000 + 7.79423i −0.219839 + 0.380773i −0.954759 0.297382i \(-0.903887\pi\)
0.734919 + 0.678155i \(0.237220\pi\)
\(420\) −1.50000 + 4.33013i −0.0731925 + 0.211289i
\(421\) 0.500000 + 0.866025i 0.0243685 + 0.0422075i 0.877952 0.478748i \(-0.158909\pi\)
−0.853584 + 0.520955i \(0.825576\pi\)
\(422\) −6.50000 11.2583i −0.316415 0.548047i
\(423\) 0 0
\(424\) −13.5000 + 23.3827i −0.655618 + 1.13556i
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) 20.7846i 1.00702i
\(427\) 35.0000 + 12.1244i 1.69377 + 0.586739i
\(428\) 8.50000 14.7224i 0.410863 0.711636i
\(429\) 43.3013i 2.09061i
\(430\) 1.00000 0.0482243
\(431\) 4.50000 7.79423i 0.216757 0.375435i −0.737057 0.675830i \(-0.763785\pi\)
0.953815 + 0.300395i \(0.0971186\pi\)
\(432\) 4.50000 + 2.59808i 0.216506 + 0.125000i
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 1.50000 + 0.866025i 0.0719195 + 0.0415227i
\(436\) 9.00000 0.431022
\(437\) −1.50000 2.59808i −0.0717547 0.124283i
\(438\) 4.50000 + 2.59808i 0.215018 + 0.124141i
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 15.0000 0.715097
\(441\) −3.00000 + 20.7846i −0.142857 + 0.989743i
\(442\) −15.0000 −0.713477
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) 5.19615i 0.246598i
\(445\) −6.50000 11.2583i −0.308130 0.533696i
\(446\) 19.0000 0.899676
\(447\) −4.50000 + 2.59808i −0.212843 + 0.122885i
\(448\) 3.50000 + 18.1865i 0.165359 + 0.859233i
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) −6.00000 10.3923i −0.282843 0.489898i
\(451\) 12.5000 21.6506i 0.588602 1.01949i
\(452\) 1.00000 0.0470360
\(453\) −7.50000 + 4.33013i −0.352381 + 0.203447i
\(454\) 1.50000 2.59808i 0.0703985 0.121934i
\(455\) −12.5000 4.33013i −0.586009 0.202999i
\(456\) −4.50000 2.59808i −0.210732 0.121666i
\(457\) −11.0000 + 19.0526i −0.514558 + 0.891241i 0.485299 + 0.874348i \(0.338711\pi\)
−0.999857 + 0.0168929i \(0.994623\pi\)
\(458\) 0.500000 0.866025i 0.0233635 0.0404667i
\(459\) −13.5000 7.79423i −0.630126 0.363803i
\(460\) −1.50000 2.59808i −0.0699379 0.121136i
\(461\) −9.50000 16.4545i −0.442459 0.766362i 0.555412 0.831575i \(-0.312560\pi\)
−0.997871 + 0.0652135i \(0.979227\pi\)
\(462\) 22.5000 4.33013i 1.04679 0.201456i
\(463\) −6.50000 + 11.2583i −0.302081 + 0.523219i −0.976607 0.215032i \(-0.931015\pi\)
0.674526 + 0.738251i \(0.264348\pi\)
\(464\) 1.00000 0.0464238
\(465\) 0 0
\(466\) 3.00000 0.138972
\(467\) 13.5000 + 23.3827i 0.624705 + 1.08202i 0.988598 + 0.150581i \(0.0481143\pi\)
−0.363892 + 0.931441i \(0.618552\pi\)
\(468\) 7.50000 12.9904i 0.346688 0.600481i
\(469\) 8.00000 6.92820i 0.369406 0.319915i
\(470\) 0 0
\(471\) −21.0000 12.1244i −0.967629 0.558661i
\(472\) 0 0
\(473\) 2.50000 + 4.33013i 0.114950 + 0.199099i
\(474\) 12.0000 + 6.92820i 0.551178 + 0.318223i
\(475\) 2.00000 + 3.46410i 0.0917663 + 0.158944i
\(476\) −1.50000 7.79423i −0.0687524 0.357248i
\(477\) −13.5000 23.3827i −0.618123 1.07062i
\(478\) 7.50000 + 12.9904i 0.343042 + 0.594166i
\(479\) 25.0000 1.14228 0.571140 0.820853i \(-0.306501\pi\)
0.571140 + 0.820853i \(0.306501\pi\)
\(480\) −7.50000 4.33013i −0.342327 0.197642i
\(481\) −15.0000 −0.683941
\(482\) −5.50000 + 9.52628i −0.250518 + 0.433910i
\(483\) −9.00000 10.3923i −0.409514 0.472866i
\(484\) 7.00000 + 12.1244i 0.318182 + 0.551107i
\(485\) −4.50000 7.79423i −0.204334 0.353918i
\(486\) −13.5000 + 7.79423i −0.612372 + 0.353553i
\(487\) −9.50000 + 16.4545i −0.430486 + 0.745624i −0.996915 0.0784867i \(-0.974991\pi\)
0.566429 + 0.824110i \(0.308325\pi\)
\(488\) −21.0000 + 36.3731i −0.950625 + 1.64653i
\(489\) −16.5000 9.52628i −0.746156 0.430793i
\(490\) −1.00000 + 6.92820i −0.0451754 + 0.312984i
\(491\) −6.50000 + 11.2583i −0.293341 + 0.508081i −0.974598 0.223963i \(-0.928100\pi\)
0.681257 + 0.732045i \(0.261434\pi\)
\(492\) −7.50000 + 4.33013i −0.338126 + 0.195217i
\(493\) −3.00000 −0.135113
\(494\) 2.50000 4.33013i 0.112480 0.194822i
\(495\) −7.50000 + 12.9904i −0.337100 + 0.583874i
\(496\) 0 0
\(497\) −6.00000 31.1769i −0.269137 1.39848i
\(498\) 13.5000 7.79423i 0.604949 0.349268i
\(499\) 31.0000 1.38775 0.693875 0.720095i \(-0.255902\pi\)
0.693875 + 0.720095i \(0.255902\pi\)
\(500\) 4.50000 + 7.79423i 0.201246 + 0.348569i
\(501\) 32.9090i 1.47026i
\(502\) 14.0000 24.2487i 0.624851 1.08227i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) −22.5000 7.79423i −1.00223 0.347183i
\(505\) 17.0000 0.756490
\(506\) −7.50000 + 12.9904i −0.333416 + 0.577493i
\(507\) 18.0000 + 10.3923i 0.799408 + 0.461538i
\(508\) −6.00000 10.3923i −0.266207 0.461084i
\(509\) −29.0000 −1.28540 −0.642701 0.766117i \(-0.722186\pi\)
−0.642701 + 0.766117i \(0.722186\pi\)
\(510\) −4.50000 2.59808i −0.199263 0.115045i
\(511\) −7.50000 2.59808i −0.331780 0.114932i
\(512\) −11.0000 −0.486136
\(513\) 4.50000 2.59808i 0.198680 0.114708i
\(514\) 14.5000 25.1147i 0.639568 1.10776i
\(515\) 1.00000 0.0440653
\(516\) 1.73205i 0.0762493i
\(517\) 0 0
\(518\) 1.50000 + 7.79423i 0.0659062 + 0.342459i
\(519\) 24.2487i 1.06440i
\(520\) 7.50000 12.9904i 0.328897 0.569666i
\(521\) −1.50000 + 2.59808i −0.0657162 + 0.113824i −0.897011 0.442007i \(-0.854267\pi\)
0.831295 + 0.555831i \(0.187600\pi\)
\(522\) −1.50000 + 2.59808i −0.0656532 + 0.113715i
\(523\) −0.500000 0.866025i −0.0218635 0.0378686i 0.854887 0.518815i \(-0.173627\pi\)
−0.876750 + 0.480946i \(0.840293\pi\)
\(524\) −0.500000 0.866025i −0.0218426 0.0378325i
\(525\) 12.0000 + 13.8564i 0.523723 + 0.604743i
\(526\) −2.50000 + 4.33013i −0.109005 + 0.188803i
\(527\) 0 0
\(528\) 8.66025i 0.376889i
\(529\) −14.0000 −0.608696
\(530\) −4.50000 7.79423i −0.195468 0.338560i
\(531\) 0 0
\(532\) 2.50000 + 0.866025i 0.108389 + 0.0375470i
\(533\) −12.5000 21.6506i −0.541435 0.937793i
\(534\) 19.5000 11.2583i 0.843848 0.487196i
\(535\) 8.50000 + 14.7224i 0.367487 + 0.636506i
\(536\) 6.00000 + 10.3923i 0.259161 + 0.448879i
\(537\) 32.9090i 1.42013i
\(538\) −1.50000 2.59808i −0.0646696 0.112011i
\(539\) −32.5000 + 12.9904i −1.39987 + 0.559535i
\(540\) 4.50000 2.59808i 0.193649 0.111803i
\(541\) 12.5000 + 21.6506i 0.537417 + 0.930834i 0.999042 + 0.0437584i \(0.0139332\pi\)
−0.461625 + 0.887075i \(0.652733\pi\)
\(542\) 1.00000 0.0429537
\(543\) 21.0000 12.1244i 0.901196 0.520306i
\(544\) 15.0000 0.643120
\(545\) −4.50000 + 7.79423i −0.192759 + 0.333868i
\(546\) 7.50000 21.6506i 0.320970 0.926562i
\(547\) 14.5000 + 25.1147i 0.619975 + 1.07383i 0.989490 + 0.144604i \(0.0461907\pi\)
−0.369514 + 0.929225i \(0.620476\pi\)
\(548\) −4.50000 7.79423i −0.192230 0.332953i
\(549\) −21.0000 36.3731i −0.896258 1.55236i
\(550\) 10.0000 17.3205i 0.426401 0.738549i
\(551\) 0.500000 0.866025i 0.0213007 0.0368939i
\(552\) 13.5000 7.79423i 0.574598 0.331744i
\(553\) −20.0000 6.92820i −0.850487 0.294617i
\(554\) −9.50000 + 16.4545i −0.403616 + 0.699084i
\(555\) −4.50000 2.59808i −0.191014 0.110282i
\(556\) −9.00000 −0.381685
\(557\) 18.5000 32.0429i 0.783870 1.35770i −0.145802 0.989314i \(-0.546576\pi\)
0.929672 0.368389i \(-0.120091\pi\)
\(558\) 0 0
\(559\) 5.00000 0.211477
\(560\) −2.50000 0.866025i −0.105644 0.0365963i
\(561\) 25.9808i 1.09691i
\(562\) −29.0000 −1.22329
\(563\) 14.0000 + 24.2487i 0.590030 + 1.02196i 0.994228 + 0.107290i \(0.0342173\pi\)
−0.404198 + 0.914671i \(0.632449\pi\)
\(564\) 0 0
\(565\) −0.500000 + 0.866025i −0.0210352 + 0.0364340i
\(566\) 28.0000 1.17693
\(567\) 18.0000 15.5885i 0.755929 0.654654i
\(568\) 36.0000 1.51053
\(569\) 17.0000 29.4449i 0.712677 1.23439i −0.251172 0.967943i \(-0.580816\pi\)
0.963849 0.266450i \(-0.0858508\pi\)
\(570\) 1.50000 0.866025i 0.0628281 0.0362738i
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 25.0000 1.04530
\(573\) 13.8564i 0.578860i
\(574\) −10.0000 + 8.66025i −0.417392 + 0.361472i
\(575\) −12.0000 −0.500435
\(576\) 10.5000 18.1865i 0.437500 0.757772i
\(577\) −15.5000 + 26.8468i −0.645273 + 1.11765i 0.338965 + 0.940799i \(0.389923\pi\)
−0.984238 + 0.176847i \(0.943410\pi\)
\(578\) −8.00000 −0.332756
\(579\) −15.0000 8.66025i −0.623379 0.359908i
\(580\) 0.500000 0.866025i 0.0207614 0.0359597i
\(581\) −18.0000 + 15.5885i −0.746766 + 0.646718i
\(582\) 13.5000 7.79423i 0.559593 0.323081i
\(583\) 22.5000 38.9711i 0.931855 1.61402i
\(584\) 4.50000 7.79423i 0.186211 0.322527i
\(585\) 7.50000 + 12.9904i 0.310087 + 0.537086i
\(586\) 2.50000 + 4.33013i 0.103274 + 0.178876i
\(587\) 18.5000 + 32.0429i 0.763577 + 1.32255i 0.940996 + 0.338418i \(0.109892\pi\)
−0.177419 + 0.984135i \(0.556775\pi\)
\(588\) 12.0000 + 1.73205i 0.494872 + 0.0714286i
\(589\) 0 0
\(590\) 0 0
\(591\) −3.00000 + 1.73205i −0.123404 + 0.0712470i
\(592\) −3.00000 −0.123299
\(593\) −7.50000 12.9904i −0.307988 0.533451i 0.669934 0.742421i \(-0.266322\pi\)
−0.977922 + 0.208970i \(0.932989\pi\)
\(594\) −22.5000 12.9904i −0.923186 0.533002i
\(595\) 7.50000 + 2.59808i 0.307470 + 0.106511i
\(596\) 1.50000 + 2.59808i 0.0614424 + 0.106421i
\(597\) 5.19615i 0.212664i
\(598\) 7.50000 + 12.9904i 0.306698 + 0.531216i
\(599\) 12.0000 + 20.7846i 0.490307 + 0.849236i 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) −18.0000 + 10.3923i −0.734847 + 0.424264i
\(601\) 4.50000 + 7.79423i 0.183559 + 0.317933i 0.943090 0.332538i \(-0.107905\pi\)
−0.759531 + 0.650471i \(0.774572\pi\)
\(602\) −0.500000 2.59808i −0.0203785 0.105890i
\(603\) −12.0000 −0.488678
\(604\) 2.50000 + 4.33013i 0.101724 + 0.176190i
\(605\) −14.0000 −0.569181
\(606\) 29.4449i 1.19612i
\(607\) −1.00000 −0.0405887 −0.0202944 0.999794i \(-0.506460\pi\)
−0.0202944 + 0.999794i \(0.506460\pi\)
\(608\) −2.50000 + 4.33013i −0.101388 + 0.175610i
\(609\) 1.50000 4.33013i 0.0607831 0.175466i
\(610\) −7.00000 12.1244i −0.283422 0.490901i
\(611\) 0 0
\(612\) −4.50000 + 7.79423i −0.181902 + 0.315063i
\(613\) −9.50000 + 16.4545i −0.383701 + 0.664590i −0.991588 0.129433i \(-0.958684\pi\)
0.607887 + 0.794024i \(0.292017\pi\)
\(614\) −14.0000 + 24.2487i −0.564994 + 0.978598i
\(615\) 8.66025i 0.349215i
\(616\) −7.50000 38.9711i −0.302184 1.57019i
\(617\) −13.5000 + 23.3827i −0.543490 + 0.941351i 0.455211 + 0.890384i \(0.349564\pi\)
−0.998700 + 0.0509678i \(0.983769\pi\)
\(618\) 1.73205i 0.0696733i
\(619\) 25.0000 1.00483 0.502417 0.864625i \(-0.332444\pi\)
0.502417 + 0.864625i \(0.332444\pi\)
\(620\) 0 0
\(621\) 15.5885i 0.625543i
\(622\) 0 0
\(623\) −26.0000 + 22.5167i −1.04167 + 0.902111i
\(624\) 7.50000 + 4.33013i 0.300240 + 0.173344i
\(625\) 11.0000 0.440000
\(626\) −7.00000 12.1244i −0.279776 0.484587i
\(627\) 7.50000 + 4.33013i 0.299521 + 0.172929i
\(628\) −7.00000 + 12.1244i −0.279330 + 0.483814i
\(629\) 9.00000 0.358854
\(630\) 6.00000 5.19615i 0.239046 0.207020i
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 12.0000 20.7846i 0.477334 0.826767i
\(633\) 22.5167i 0.894957i
\(634\) 3.00000 + 5.19615i 0.119145 + 0.206366i
\(635\) 12.0000 0.476205
\(636\) −13.5000 + 7.79423i −0.535310 + 0.309061i
\(637\) −5.00000 + 34.6410i −0.198107 + 1.37253i
\(638\) −5.00000 −0.197952
\(639\) −18.0000 + 31.1769i −0.712069 + 1.23334i
\(640\) −1.50000 + 2.59808i −0.0592927 + 0.102698i
\(641\) −9.00000 −0.355479 −0.177739 0.984078i \(-0.556878\pi\)
−0.177739 + 0.984078i \(0.556878\pi\)
\(642\) −25.5000 + 14.7224i −1.00640 + 0.581048i
\(643\) 9.50000 16.4545i 0.374643 0.648901i −0.615630 0.788035i \(-0.711098\pi\)
0.990274 + 0.139134i \(0.0444318\pi\)
\(644\) −6.00000 + 5.19615i −0.236433 + 0.204757i
\(645\) 1.50000 + 0.866025i 0.0590624 + 0.0340997i
\(646\) −1.50000 + 2.59808i −0.0590167 + 0.102220i
\(647\) −15.5000 + 26.8468i −0.609368 + 1.05546i 0.381977 + 0.924172i \(0.375243\pi\)
−0.991345 + 0.131284i \(0.958090\pi\)
\(648\) 13.5000 + 23.3827i 0.530330 + 0.918559i
\(649\) 0 0
\(650\) −10.0000 17.3205i −0.392232 0.679366i
\(651\) 0 0
\(652\) −5.50000 + 9.52628i −0.215397 + 0.373078i
\(653\) 3.00000 0.117399 0.0586995 0.998276i \(-0.481305\pi\)
0.0586995 + 0.998276i \(0.481305\pi\)
\(654\) −13.5000 7.79423i −0.527892 0.304778i
\(655\) 1.00000 0.0390732
\(656\) −2.50000 4.33013i −0.0976086 0.169063i
\(657\) 4.50000 + 7.79423i 0.175562 + 0.304082i
\(658\) 0 0
\(659\) −13.5000 23.3827i −0.525885 0.910860i −0.999545 0.0301523i \(-0.990401\pi\)
0.473660 0.880708i \(-0.342933\pi\)
\(660\) 7.50000 + 4.33013i 0.291937 + 0.168550i
\(661\) 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i \(-0.0788928\pi\)
−0.697174 + 0.716902i \(0.745559\pi\)
\(662\) −4.00000 6.92820i −0.155464 0.269272i
\(663\) −22.5000 12.9904i −0.873828 0.504505i
\(664\) −13.5000 23.3827i −0.523902 0.907424i
\(665\) −2.00000 + 1.73205i −0.0775567 + 0.0671660i
\(666\) 4.50000 7.79423i 0.174371 0.302020i
\(667\) 1.50000 + 2.59808i 0.0580802 + 0.100598i
\(668\) 19.0000 0.735132
\(669\) 28.5000 + 16.4545i 1.10187 + 0.636167i
\(670\) −4.00000 −0.154533
\(671\) 35.0000 60.6218i 1.35116 2.34028i
\(672\) −7.50000 + 21.6506i −0.289319 + 0.835191i
\(673\) 14.5000 + 25.1147i 0.558934 + 0.968102i 0.997586 + 0.0694449i \(0.0221228\pi\)
−0.438652 + 0.898657i \(0.644544\pi\)
\(674\) 14.5000 + 25.1147i 0.558519 + 0.967384i
\(675\) 20.7846i 0.800000i
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) −21.0000 + 36.3731i −0.807096 + 1.39793i 0.107772 + 0.994176i \(0.465628\pi\)
−0.914867 + 0.403755i \(0.867705\pi\)
\(678\) −1.50000 0.866025i −0.0576072 0.0332595i
\(679\) −18.0000 + 15.5885i −0.690777 + 0.598230i
\(680\) −4.50000 + 7.79423i −0.172567 + 0.298895i
\(681\) 4.50000 2.59808i 0.172440 0.0995585i
\(682\) 0 0
\(683\) 4.50000 7.79423i 0.172188 0.298238i −0.766997 0.641651i \(-0.778250\pi\)
0.939184 + 0.343413i \(0.111583\pi\)
\(684\) −1.50000 2.59808i −0.0573539 0.0993399i
\(685\) 9.00000 0.343872
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) 1.50000 0.866025i 0.0572286 0.0330409i
\(688\) 1.00000 0.0381246
\(689\) −22.5000 38.9711i −0.857182 1.48468i
\(690\) 5.19615i 0.197814i
\(691\) 14.0000 24.2487i 0.532585 0.922464i −0.466691 0.884420i \(-0.654554\pi\)
0.999276 0.0380440i \(-0.0121127\pi\)
\(692\) 14.0000 0.532200
\(693\) 37.5000 + 12.9904i 1.42451 + 0.493464i
\(694\) 4.00000 0.151838
\(695\) 4.50000 7.79423i 0.170695 0.295652i
\(696\) 4.50000 + 2.59808i 0.170572 + 0.0984798i
\(697\) 7.50000 + 12.9904i 0.284083 + 0.492046i
\(698\) 19.0000 0.719161
\(699\) 4.50000 + 2.59808i 0.170206 + 0.0982683i
\(700\) 8.00000 6.92820i 0.302372 0.261861i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) −22.5000 + 12.9904i −0.849208 + 0.490290i
\(703\) −1.50000 + 2.59808i −0.0565736 + 0.0979883i
\(704\) 35.0000 1.31911
\(705\) 0 0
\(706\) −5.50000 + 9.52628i −0.206995 + 0.358526i
\(707\) −8.50000 44.1673i −0.319675 1.66108i
\(708\) 0 0
\(709\) 3.00000 5.19615i 0.112667 0.195146i −0.804178 0.594389i \(-0.797394\pi\)
0.916845 + 0.399244i \(0.130727\pi\)
\(710\) −6.00000 + 10.3923i −0.225176 + 0.390016i
\(711\) 12.0000 + 20.7846i 0.450035 + 0.779484i
\(712\) −19.5000 33.7750i −0.730793 1.26577i
\(713\) 0 0
\(714\) −4.50000 + 12.9904i −0.168408 + 0.486153i
\(715\) −12.5000 + 21.6506i −0.467473 + 0.809688i
\(716\) −19.0000 −0.710063
\(717\) 25.9808i 0.970269i
\(718\) −11.0000 −0.410516
\(719\) 13.5000 + 23.3827i 0.503465 + 0.872027i 0.999992 + 0.00400572i \(0.00127506\pi\)
−0.496527 + 0.868021i \(0.665392\pi\)
\(720\) 1.50000 + 2.59808i 0.0559017 + 0.0968246i
\(721\) −0.500000 2.59808i −0.0186210 0.0967574i
\(722\) 9.00000 + 15.5885i 0.334945 + 0.580142i
\(723\) −16.5000 + 9.52628i −0.613642 + 0.354286i
\(724\) −7.00000 12.1244i −0.260153 0.450598i
\(725\) −2.00000 3.46410i −0.0742781 0.128654i
\(726\) 24.2487i 0.899954i
\(727\) −23.5000 40.7032i −0.871567 1.50960i −0.860376 0.509661i \(-0.829771\pi\)
−0.0111912 0.999937i \(-0.503562\pi\)
\(728\) −37.5000 12.9904i −1.38984 0.481456i
\(729\) −27.0000 −1.00000
\(730\) 1.50000 + 2.59808i 0.0555175 + 0.0961591i
\(731\) −3.00000 −0.110959
\(732\) −21.0000 + 12.1244i −0.776182 + 0.448129i
\(733\) 27.0000 0.997268 0.498634 0.866813i \(-0.333835\pi\)
0.498634 + 0.866813i \(0.333835\pi\)
\(734\) 1.50000 2.59808i 0.0553660 0.0958967i
\(735\) −7.50000 + 9.52628i −0.276642 + 0.351382i
\(736\) −7.50000 12.9904i −0.276454 0.478832i
\(737\) −10.0000 17.3205i −0.368355 0.638009i
\(738\) 15.0000 0.552158
\(739\) 4.50000 7.79423i 0.165535 0.286715i −0.771310 0.636460i \(-0.780398\pi\)
0.936845 + 0.349744i \(0.113732\pi\)
\(740\) −1.50000 + 2.59808i −0.0551411 + 0.0955072i
\(741\) 7.50000 4.33013i 0.275519 0.159071i
\(742\) −18.0000 + 15.5885i −0.660801 + 0.572270i
\(743\) 7.50000 12.9904i 0.275148 0.476571i −0.695024 0.718986i \(-0.744606\pi\)
0.970173 + 0.242415i \(0.0779397\pi\)
\(744\) 0 0
\(745\) −3.00000 −0.109911
\(746\) 12.5000 21.6506i 0.457658 0.792686i
\(747\) 27.0000 0.987878
\(748\) −15.0000 −0.548454
\(749\) 34.0000 29.4449i 1.24233 1.07589i
\(750\) 15.5885i 0.569210i
\(751\) 31.0000 1.13121 0.565603 0.824678i \(-0.308643\pi\)
0.565603 + 0.824678i \(0.308643\pi\)
\(752\) 0 0
\(753\) 42.0000 24.2487i 1.53057 0.883672i
\(754\) −2.50000 + 4.33013i −0.0910446 + 0.157694i
\(755\) −5.00000 −0.181969
\(756\) −9.00000 10.3923i −0.327327 0.377964i
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 6.00000 10.3923i 0.217930 0.377466i
\(759\) −22.5000 + 12.9904i −0.816698 + 0.471521i
\(760\) −1.50000 2.59808i −0.0544107 0.0942421i
\(761\) 27.0000 0.978749 0.489375 0.872074i \(-0.337225\pi\)
0.489375 + 0.872074i \(0.337225\pi\)
\(762\) 20.7846i 0.752947i
\(763\) 22.5000 + 7.79423i 0.814555 + 0.282170i
\(764\) −8.00000 −0.289430
\(765\) −4.50000 7.79423i −0.162698 0.281801i
\(766\) −13.5000 + 23.3827i −0.487775 + 0.844851i
\(767\) 0 0
\(768\) −25.5000 14.7224i −0.920152 0.531250i
\(769\) −11.5000 + 19.9186i −0.414701 + 0.718283i −0.995397 0.0958377i \(-0.969447\pi\)
0.580696 + 0.814120i \(0.302780\pi\)
\(770\) 12.5000 + 4.33013i 0.450469 + 0.156047i
\(771\) 43.5000 25.1147i 1.56661 0.904485i
\(772\) −5.00000 + 8.66025i −0.179954 + 0.311689i
\(773\) −15.5000 + 26.8468i −0.557496 + 0.965612i 0.440208 + 0.897896i \(0.354905\pi\)
−0.997705 + 0.0677162i \(0.978429\pi\)
\(774\) −1.50000 + 2.59808i −0.0539164 + 0.0933859i
\(775\) 0 0
\(776\) −13.5000 23.3827i −0.484622 0.839390i