Properties

Label 441.2.g.a.79.1
Level $441$
Weight $2$
Character 441.79
Analytic conductor $3.521$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
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: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.a.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} -1.73205i q^{6} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(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} -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} +(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} +(-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} +(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} +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} +(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} +(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 - 0.866025i) q^{57} -1.00000 q^{58} +(1.50000 - 0.866025i) q^{60} +(-7.00000 - 12.1244i) q^{61} +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} -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} +(-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 + 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} +(1.50000 - 2.59808i) q^{92} +(0.500000 - 0.866025i) q^{95} +(-7.50000 + 4.33013i) q^{96} +(-4.50000 + 7.79423i) q^{97} +(7.50000 + 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + 3q^{3} + q^{4} + 2q^{5} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 2q - q^{2} + 3q^{3} + q^{4} + 2q^{5} - 6q^{8} + 3q^{9} - q^{10} + 10q^{11} + 3q^{12} - 5q^{13} + 3q^{15} + q^{16} + 3q^{17} + 3q^{18} + q^{19} + q^{20} - 5q^{22} + 6q^{23} - 9q^{24} - 8q^{25} - 5q^{26} + q^{29} - 5q^{32} + 15q^{33} + 3q^{34} + 6q^{36} - 3q^{37} - 2q^{38} - 6q^{40} - 5q^{41} + q^{43} + 5q^{44} + 3q^{45} - 3q^{46} + 4q^{50} - 10q^{52} + 9q^{53} + 9q^{54} + 10q^{55} + 3q^{57} - 2q^{58} + 3q^{60} - 14q^{61} + 14q^{64} - 5q^{65} - 4q^{67} + 6q^{68} + 9q^{69} - 24q^{71} - 9q^{72} + 3q^{73} + 6q^{74} - 12q^{75} - q^{76} - 15q^{78} - 8q^{79} + q^{80} - 9q^{81} - 5q^{82} - 9q^{83} + 3q^{85} - 2q^{86} + 3q^{87} - 30q^{88} - 13q^{89} + 3q^{90} + 3q^{92} + q^{95} - 15q^{96} - 9q^{97} + 15q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) 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 \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 1.73205i 0.707107i
\(7\) 0 0
\(8\) −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 −0.970725 0.240192i \(-0.922790\pi\)
0.277350 0.960769i \(-0.410544\pi\)
\(14\) 0 0
\(15\) 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 \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 1.50000 2.59808i 0.353553 0.612372i
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 0 0
\(22\) −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
\(28\) 0 0
\(29\) 0.500000 0.866025i 0.0928477 0.160817i −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) 1.73205i 0.316228i
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −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 0
\(36\) 3.00000 0.500000
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) −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 \(-0.294342\pi\)
−0.992507 + 0.122189i \(0.961009\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 1.73205i 0.250000i
\(49\) 0 0
\(50\) 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 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 4.50000 2.59808i 0.612372 0.353553i
\(55\) 5.00000 0.674200
\(56\) 0 0
\(57\) 1.50000 0.866025i 0.198680 0.114708i
\(58\) −1.00000 −0.131306
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 1.50000 0.866025i 0.193649 0.111803i
\(61\) −7.00000 12.1244i −0.896258 1.55236i −0.832240 0.554416i \(-0.812942\pi\)
−0.0640184 0.997949i \(-0.520392\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 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 −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) 3.00000 0.363803
\(69\) 4.50000 + 2.59808i 0.541736 + 0.312772i
\(70\) 0 0
\(71\) −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 \(-0.110493\pi\)
−0.764794 + 0.644275i \(0.777159\pi\)
\(74\) 3.00000 0.348743
\(75\) −6.00000 3.46410i −0.692820 0.400000i
\(76\) −0.500000 0.866025i −0.0573539 0.0993399i
\(77\) 0 0
\(78\) −7.50000 + 4.33013i −0.849208 + 0.490290i
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 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 \(-0.997777\pi\)
0.506036 + 0.862512i \(0.331110\pi\)
\(84\) 0 0
\(85\) 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 0.283164 + 0.959072i \(0.408616\pi\)
−0.972162 + 0.234309i \(0.924717\pi\)
\(90\) 1.50000 2.59808i 0.158114 0.273861i
\(91\) 0 0
\(92\) 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 \(-0.984376\pi\)
0.541890 + 0.840450i \(0.317709\pi\)
\(98\) 0 0
\(99\) 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 \(-0.179135\pi\)
0.845782 + 0.533529i \(0.179135\pi\)
\(102\) 4.50000 2.59808i 0.445566 0.257248i
\(103\) 1.00000 0.0985329 0.0492665 0.998786i \(-0.484312\pi\)
0.0492665 + 0.998786i \(0.484312\pi\)
\(104\) 7.50000 + 12.9904i 0.735436 + 1.27381i
\(105\) 0 0
\(106\) 4.50000 7.79423i 0.437079 0.757042i
\(107\) −8.50000 + 14.7224i −0.821726 + 1.42327i 0.0826699 + 0.996577i \(0.473655\pi\)
−0.904396 + 0.426694i \(0.859678\pi\)
\(108\) 4.50000 + 2.59808i 0.433013 + 0.250000i
\(109\) 4.50000 + 7.79423i 0.431022 + 0.746552i 0.996962 0.0778949i \(-0.0248199\pi\)
−0.565940 + 0.824447i \(0.691487\pi\)
\(110\) −2.50000 4.33013i −0.238366 0.412861i
\(111\) −4.50000 + 2.59808i −0.427121 + 0.246598i
\(112\) 0 0
\(113\) 0.500000 + 0.866025i 0.0470360 + 0.0814688i 0.888585 0.458712i \(-0.151689\pi\)
−0.841549 + 0.540181i \(0.818356\pi\)
\(114\) −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
\(119\) 0 0
\(120\) −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
\(126\) 0 0
\(127\) −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 \(-0.486090\pi\)
0.0436852 + 0.999045i \(0.486090\pi\)
\(132\) 7.50000 4.33013i 0.652791 0.376889i
\(133\) 0 0
\(134\) 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 \(-0.0420106\pi\)
−0.609618 + 0.792695i \(0.708677\pi\)
\(140\) 0 0
\(141\) 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
\(147\) 0 0
\(148\) 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
\(154\) 0 0
\(155\) 0 0
\(156\) −7.50000 4.33013i −0.600481 0.346688i
\(157\) −7.00000 + 12.1244i −0.558661 + 0.967629i 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) −4.00000 + 6.92820i −0.318223 + 0.551178i
\(159\) 15.5885i 1.23625i
\(160\) −2.50000 + 4.33013i −0.197642 + 0.342327i
\(161\) 0 0
\(162\) 9.00000 0.707107
\(163\) 5.50000 9.52628i 0.430793 0.746156i −0.566149 0.824303i \(-0.691567\pi\)
0.996942 + 0.0781474i \(0.0249005\pi\)
\(164\) −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 −0.954665 0.297681i \(-0.903787\pi\)
0.219533 0.975605i \(-0.429547\pi\)
\(168\) 0 0
\(169\) −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 −0.999293 0.0375896i \(-0.988032\pi\)
0.467093 0.884208i \(-0.345301\pi\)
\(174\) −1.50000 0.866025i −0.113715 0.0656532i
\(175\) 0 0
\(176\) 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 −0.964833 0.262864i \(-0.915333\pi\)
0.254770 0.967002i \(-0.418000\pi\)
\(180\) 3.00000 0.223607
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 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
\(189\) 0 0
\(190\) −1.00000 −0.0725476
\(191\) −4.00000 6.92820i −0.289430 0.501307i 0.684244 0.729253i \(-0.260132\pi\)
−0.973674 + 0.227946i \(0.926799\pi\)
\(192\) 10.5000 + 6.06218i 0.757772 + 0.437500i
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) 9.00000 0.646162
\(195\) 8.66025i 0.620174i
\(196\) 0 0
\(197\) 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 \(-0.132756\pi\)
−0.807950 + 0.589252i \(0.799423\pi\)
\(200\) 12.0000 0.848528
\(201\) −6.00000 + 3.46410i −0.423207 + 0.244339i
\(202\) −8.50000 14.7224i −0.598058 1.03587i
\(203\) 0 0
\(204\) 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
\(210\) 0 0
\(211\) −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i \(-0.314345\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) 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 −0.350100 0.936713i \(-0.613852\pi\)
0.986267 0.165161i \(-0.0528144\pi\)
\(224\) 0 0
\(225\) −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 \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(228\) 1.73205i 0.114708i
\(229\) 1.00000 0.0660819 0.0330409 0.999454i \(-0.489481\pi\)
0.0330409 + 0.999454i \(0.489481\pi\)
\(230\) −1.50000 2.59808i −0.0989071 0.171312i
\(231\) 0 0
\(232\) −1.50000 + 2.59808i −0.0984798 + 0.170572i
\(233\) −1.50000 + 2.59808i −0.0982683 + 0.170206i −0.910968 0.412477i \(-0.864664\pi\)
0.812700 + 0.582683i \(0.197997\pi\)
\(234\) −15.0000 −0.980581
\(235\) 0 0
\(236\) 0 0
\(237\) 13.8564i 0.900070i
\(238\) 0 0
\(239\) 7.50000 + 12.9904i 0.485135 + 0.840278i 0.999854 0.0170808i \(-0.00543724\pi\)
−0.514719 + 0.857359i \(0.672104\pi\)
\(240\) 1.73205i 0.111803i
\(241\) −11.0000 −0.708572 −0.354286 0.935137i \(-0.615276\pi\)
−0.354286 + 0.935137i \(0.615276\pi\)
\(242\) −7.00000 12.1244i −0.449977 0.779383i
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) −14.0000 −0.896258
\(245\) 0 0
\(246\) −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 \(-0.155064\pi\)
0.883672 + 0.468106i \(0.155064\pi\)
\(252\) 0 0
\(253\) 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 \(-0.140255\pi\)
0.904485 + 0.426505i \(0.140255\pi\)
\(258\) −1.50000 0.866025i −0.0933859 0.0539164i
\(259\) 0 0
\(260\) −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 0
\(267\) −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 \(-0.137514\pi\)
−0.816668 + 0.577108i \(0.804181\pi\)
\(270\) 4.50000 2.59808i 0.273861 0.158114i
\(271\) 0.500000 0.866025i 0.0303728 0.0526073i −0.850439 0.526073i \(-0.823664\pi\)
0.880812 + 0.473466i \(0.156997\pi\)
\(272\) −1.50000 + 2.59808i −0.0909509 + 0.157532i
\(273\) 0 0
\(274\) 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
\(280\) 0 0
\(281\) 14.5000 25.1147i 0.864997 1.49822i −0.00205220 0.999998i \(-0.500653\pi\)
0.867050 0.498222i \(-0.166013\pi\)
\(282\) 0 0
\(283\) 14.0000 24.2487i 0.832214 1.44144i −0.0640654 0.997946i \(-0.520407\pi\)
0.896279 0.443491i \(-0.146260\pi\)
\(284\) −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
\(287\) 0 0
\(288\) −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 \(-0.213323\pi\)
−0.929765 + 0.368154i \(0.879990\pi\)
\(294\) 0 0
\(295\) 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
\(301\) 0 0
\(302\) −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 \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 1.50000 + 0.866025i 0.0853320 + 0.0492665i
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 25.9808i 1.47087i
\(313\) 7.00000 + 12.1244i 0.395663 + 0.685309i 0.993186 0.116543i \(-0.0371814\pi\)
−0.597522 + 0.801852i \(0.703848\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) 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
\(322\) 0 0
\(323\) 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 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) 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
\(336\) 0 0
\(337\) 14.5000 + 25.1147i 0.789865 + 1.36809i 0.926049 + 0.377403i \(0.123183\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) 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
\(343\) 0 0
\(344\) −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 −0.914702 0.404128i \(-0.867575\pi\)
0.807337 + 0.590091i \(0.200908\pi\)
\(348\) 1.73205i 0.0928477i
\(349\) 9.50000 16.4545i 0.508523 0.880788i −0.491428 0.870918i \(-0.663525\pi\)
0.999951 0.00987003i \(-0.00314178\pi\)
\(350\) 0 0
\(351\) 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 \(-0.594566\pi\)
−0.292735 + 0.956193i \(0.594566\pi\)
\(354\) 0 0
\(355\) −12.0000 −0.636894
\(356\) 6.50000 + 11.2583i 0.344499 + 0.596690i
\(357\) 0 0
\(358\) −9.50000 + 16.4545i −0.502091 + 0.869646i
\(359\) 5.50000 9.52628i 0.290279 0.502778i −0.683597 0.729860i \(-0.739585\pi\)
0.973876 + 0.227082i \(0.0729186\pi\)
\(360\) −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
\(364\) 0 0
\(365\) 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 \(-0.475051\pi\)
0.0782994 + 0.996930i \(0.475051\pi\)
\(368\) 1.50000 + 2.59808i 0.0781929 + 0.135434i
\(369\) 7.50000 12.9904i 0.390434 0.676252i
\(370\) 3.00000 0.155963
\(371\) 0 0
\(372\) 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
\(378\) 0 0
\(379\) −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 \(-0.742309\pi\)
−0.689818 + 0.723983i \(0.742309\pi\)
\(384\) 5.19615i 0.265165i
\(385\) 0 0
\(386\) −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
\(392\) 0 0
\(393\) 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 \(-0.710490\pi\)
0.990538 + 0.137241i \(0.0438236\pi\)
\(398\) 1.50000 2.59808i 0.0751882 0.130230i
\(399\) 0 0
\(400\) −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 0
\(407\) −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 \(-0.720830\pi\)
0.985558 + 0.169338i \(0.0541630\pi\)
\(410\) −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 \(-0.0961133\pi\)
−0.734919 + 0.678155i \(0.762780\pi\)
\(420\) 0 0
\(421\) 0.500000 0.866025i 0.0243685 0.0422075i −0.853584 0.520955i \(-0.825576\pi\)
0.877952 + 0.478748i \(0.158909\pi\)
\(422\) −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
\(427\) 0 0
\(428\) 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 0.953815 0.300395i \(-0.0971186\pi\)
−0.737057 + 0.675830i \(0.763785\pi\)
\(432\) −4.50000 + 2.59808i −0.216506 + 0.125000i
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) −15.0000 −0.715097
\(441\) 0 0
\(442\) −15.0000 −0.713477
\(443\) −18.0000 31.1769i −0.855206 1.48126i −0.876454 0.481486i \(-0.840097\pi\)
0.0212481 0.999774i \(-0.493236\pi\)
\(444\) 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
\(448\) 0 0
\(449\) 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
\(455\) 0 0
\(456\) −4.50000 + 2.59808i −0.210732 + 0.121666i
\(457\) −11.0000 19.0526i −0.514558 0.891241i −0.999857 0.0168929i \(-0.994623\pi\)
0.485299 0.874348i \(-0.338711\pi\)
\(458\) −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 \(-0.687440\pi\)
0.997871 + 0.0652135i \(0.0207728\pi\)
\(462\) 0 0
\(463\) −6.50000 11.2583i −0.302081 0.523219i 0.674526 0.738251i \(-0.264348\pi\)
−0.976607 + 0.215032i \(0.931015\pi\)
\(464\) 1.00000 0.0464238
\(465\) 0 0
\(466\) 3.00000 0.138972
\(467\) −13.5000 + 23.3827i −0.624705 + 1.08202i 0.363892 + 0.931441i \(0.381448\pi\)
−0.988598 + 0.150581i \(0.951886\pi\)
\(468\) −7.50000 12.9904i −0.346688 0.600481i
\(469\) 0 0
\(470\) 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
\(476\) 0 0
\(477\) −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 \(-0.693499\pi\)
−0.571140 + 0.820853i \(0.693499\pi\)
\(480\) −7.50000 + 4.33013i −0.342327 + 0.197642i
\(481\) 15.0000 0.683941
\(482\) 5.50000 + 9.52628i 0.250518 + 0.433910i
\(483\) 0 0
\(484\) 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 0.566429 0.824110i \(-0.308325\pi\)
−0.996915 + 0.0784867i \(0.974991\pi\)
\(488\) 21.0000 + 36.3731i 0.950625 + 1.64653i
\(489\) 16.5000 9.52628i 0.746156 0.430793i
\(490\) 0 0
\(491\) −6.50000 11.2583i −0.293341 0.508081i 0.681257 0.732045i \(-0.261434\pi\)
−0.974598 + 0.223963i \(0.928100\pi\)
\(492\) −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
\(497\) 0 0
\(498\) 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 \(0.5\pi\)
\(504\) 0 0
\(505\) 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 \(-0.277814\pi\)
0.642701 + 0.766117i \(0.277814\pi\)
\(510\) 4.50000 2.59808i 0.199263 0.115045i
\(511\) 0 0
\(512\) −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
\(518\) 0 0
\(519\) 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 \(-0.145733\pi\)
−0.831295 + 0.555831i \(0.812400\pi\)
\(522\) −1.50000 2.59808i −0.0656532 0.113715i
\(523\) 0.500000 0.866025i 0.0218635 0.0378686i −0.854887 0.518815i \(-0.826373\pi\)
0.876750 + 0.480946i \(0.159707\pi\)
\(524\) 0.500000 0.866025i 0.0218426 0.0378325i
\(525\) 0 0
\(526\) −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
\(532\) 0 0
\(533\) −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
\(539\) 0 0
\(540\) 4.50000 + 2.59808i 0.193649 + 0.111803i
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) −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
\(546\) 0 0
\(547\) 14.5000 25.1147i 0.619975 1.07383i −0.369514 0.929225i \(-0.620476\pi\)
0.989490 0.144604i \(-0.0461907\pi\)
\(548\) −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
\(553\) 0 0
\(554\) −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 0.929672 + 0.368389i \(0.120091\pi\)
−0.145802 + 0.989314i \(0.546576\pi\)
\(558\) 0 0
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) 25.9808i 1.09691i
\(562\) −29.0000 −1.22329
\(563\) −14.0000 + 24.2487i −0.590030 + 1.02196i 0.404198 + 0.914671i \(0.367551\pi\)
−0.994228 + 0.107290i \(0.965783\pi\)
\(564\) 0 0
\(565\) 0.500000 + 0.866025i 0.0210352 + 0.0364340i
\(566\) −28.0000 −1.17693
\(567\) 0 0
\(568\) 36.0000 1.51053
\(569\) 17.0000 + 29.4449i 0.712677 + 1.23439i 0.963849 + 0.266450i \(0.0858508\pi\)
−0.251172 + 0.967943i \(0.580816\pi\)
\(570\) −1.50000 0.866025i −0.0628281 0.0362738i
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) −25.0000 −1.04530
\(573\) 13.8564i 0.578860i
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 10.5000 + 18.1865i 0.437500 + 0.757772i
\(577\) 15.5000 + 26.8468i 0.645273 + 1.11765i 0.984238 + 0.176847i \(0.0565899\pi\)
−0.338965 + 0.940799i \(0.610077\pi\)
\(578\) −8.00000 −0.332756
\(579\) 15.0000 8.66025i 0.623379 0.359908i
\(580\) −0.500000 0.866025i −0.0207614 0.0359597i
\(581\) 0 0
\(582\) 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 0.177419 + 0.984135i \(0.443225\pi\)
−0.940996 + 0.338418i \(0.890108\pi\)
\(588\) 0 0
\(589\) 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 \(-0.733678\pi\)
0.977922 + 0.208970i \(0.0670110\pi\)
\(594\) 22.5000 12.9904i 0.923186 0.533002i
\(595\) 0 0
\(596\) 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 −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) 18.0000 + 10.3923i 0.734847 + 0.424264i
\(601\) −4.50000 + 7.79423i −0.183559 + 0.317933i −0.943090 0.332538i \(-0.892095\pi\)
0.759531 + 0.650471i \(0.225428\pi\)
\(602\) 0 0
\(603\) −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 \(-0.493540\pi\)
0.0202944 + 0.999794i \(0.493540\pi\)
\(608\) 2.50000 + 4.33013i 0.101388 + 0.175610i
\(609\) 0 0
\(610\) −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 0.607887 0.794024i \(-0.292017\pi\)
−0.991588 + 0.129433i \(0.958684\pi\)
\(614\) 14.0000 + 24.2487i 0.564994 + 0.978598i
\(615\) 8.66025i 0.349215i
\(616\) 0 0
\(617\) −13.5000 23.3827i −0.543490 0.941351i −0.998700 0.0509678i \(-0.983769\pi\)
0.455211 0.890384i \(-0.349564\pi\)
\(618\) 1.73205i 0.0696733i
\(619\) −25.0000 −1.00483 −0.502417 0.864625i \(-0.667556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(620\) 0 0
\(621\) 15.5885i 0.625543i
\(622\) 0 0
\(623\) 0 0
\(624\) 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
\(630\) 0 0
\(631\) −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
\(637\) 0 0
\(638\) −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 \(-0.288902\pi\)
−0.990274 + 0.139134i \(0.955568\pi\)
\(644\) 0 0
\(645\) 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 0.991345 + 0.131284i \(0.0419101\pi\)
−0.381977 + 0.924172i \(0.624757\pi\)
\(648\) 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 0.473660 + 0.880708i \(0.342933\pi\)
−0.999545 + 0.0301523i \(0.990401\pi\)
\(660\) 7.50000 4.33013i 0.291937 0.168550i
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) −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
\(665\) 0 0
\(666\) 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
\(672\) 0 0
\(673\) 14.5000 25.1147i 0.558934 0.968102i −0.438652 0.898657i \(-0.644544\pi\)
0.997586 0.0694449i \(-0.0221228\pi\)
\(674\) 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 0.914867 + 0.403755i \(0.132295\pi\)
−0.107772 + 0.994176i \(0.534372\pi\)
\(678\) 1.50000 0.866025i 0.0576072 0.0332595i
\(679\) 0 0
\(680\) −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 0.939184 0.343413i \(-0.111583\pi\)
−0.766997 + 0.641651i \(0.778250\pi\)
\(684\) 1.50000 2.59808i 0.0573539 0.0993399i
\(685\) −9.00000 −0.343872
\(686\) 0 0
\(687\) 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 −0.999276 0.0380440i \(-0.987887\pi\)
0.466691 0.884420i \(-0.345446\pi\)
\(692\) −14.0000 −0.532200
\(693\) 0 0
\(694\) 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
\(700\) 0 0
\(701\) 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
\(707\) 0 0
\(708\) 0 0
\(709\) 3.00000 + 5.19615i 0.112667 + 0.195146i 0.916845 0.399244i \(-0.130727\pi\)
−0.804178 + 0.594389i \(0.797394\pi\)
\(710\) 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
\(714\) 0 0
\(715\) −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 0.496527 + 0.868021i \(0.334608\pi\)
−0.999992 + 0.00400572i \(0.998725\pi\)
\(720\) −1.50000 + 2.59808i −0.0559017 + 0.0968246i
\(721\) 0 0
\(722\) 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 0.0111912 0.999937i \(-0.496438\pi\)
0.860376 0.509661i \(-0.170229\pi\)
\(728\) 0 0
\(729\) −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 \(-0.666165\pi\)
−0.498634 + 0.866813i \(0.666165\pi\)
\(734\) −1.50000 2.59808i −0.0553660 0.0958967i
\(735\) 0 0
\(736\) −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 0.936845 0.349744i \(-0.113732\pi\)
−0.771310 + 0.636460i \(0.780398\pi\)
\(740\) 1.50000 + 2.59808i 0.0551411 + 0.0955072i
\(741\) −7.50000 4.33013i −0.275519 0.159071i
\(742\) 0 0
\(743\) 7.50000 + 12.9904i 0.275148 + 0.476571i 0.970173 0.242415i \(-0.0779397\pi\)
−0.695024 + 0.718986i \(0.744606\pi\)
\(744\) 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
\(749\) 0 0
\(750\) 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
\(756\) 0 0
\(757\) 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 \(-0.662775\pi\)
−0.489375 + 0.872074i \(0.662775\pi\)
\(762\) 20.7846i 0.752947i
\(763\) 0 0
\(764\) −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 \(-0.0305530\pi\)
−0.580696 + 0.814120i \(0.697220\pi\)
\(770\) 0 0
\(771\) 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 0.997705 + 0.0677162i \(0.0215712\pi\)
−0.440208 + 0.897896i \(0.645095\pi\)
\(774\) −1.50000 2.59808i −0.0539164 0.0933859i
\(775\) 0 0
\(776\) 13.5000 23.3827i 0.484622 0.839390i
\(777\) 0 0
\(778\) 4.50000 + 7.79423i 0.161333 + 0.279437i
\(779\) −5.00000 −0.179144
\(780\) −7.50000 4.33013i −0.268543 0.155043i
\(781\) −60.0000 −2.14697
\(782\) 4.50000 7.79423i 0.160920 0.278721i
\(783\) 4.50000 + 2.59808i 0.160817 + 0.0928477i
\(784\) 0 0
\(785\) −7.00000 + 12.1244i −0.249841 + 0.432737i