Properties

Label 441.2.h.a.373.1
Level $441$
Weight $2$
Character 441.373
Analytic conductor $3.521$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.a.214.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.73205i q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +1.73205i q^{6} -3.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.73205i q^{3} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +1.73205i q^{6} -3.00000 q^{8} -3.00000 q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.50000 + 4.33013i) q^{11} -1.73205i q^{12} +(-2.50000 + 4.33013i) q^{13} +(1.50000 - 0.866025i) q^{15} -1.00000 q^{16} +(1.50000 + 2.59808i) q^{17} -3.00000 q^{18} +(0.500000 - 0.866025i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(-1.50000 - 2.59808i) q^{23} -5.19615i q^{24} +(2.00000 - 3.46410i) q^{25} +(-2.50000 + 4.33013i) q^{26} -5.19615i q^{27} +(0.500000 + 0.866025i) q^{29} +(1.50000 - 0.866025i) q^{30} +5.00000 q^{32} +(-7.50000 - 4.33013i) q^{33} +(1.50000 + 2.59808i) q^{34} +3.00000 q^{36} +(-1.50000 + 2.59808i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-7.50000 - 4.33013i) q^{39} +(1.50000 + 2.59808i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(0.500000 + 0.866025i) q^{43} +(2.50000 - 4.33013i) q^{44} +(1.50000 + 2.59808i) q^{45} +(-1.50000 - 2.59808i) q^{46} -1.73205i q^{48} +(2.00000 - 3.46410i) q^{50} +(-4.50000 + 2.59808i) q^{51} +(2.50000 - 4.33013i) q^{52} +(4.50000 + 7.79423i) q^{53} -5.19615i q^{54} +5.00000 q^{55} +(1.50000 + 0.866025i) q^{57} +(0.500000 + 0.866025i) q^{58} +(-1.50000 + 0.866025i) q^{60} +14.0000 q^{61} +7.00000 q^{64} +5.00000 q^{65} +(-7.50000 - 4.33013i) q^{66} +4.00000 q^{67} +(-1.50000 - 2.59808i) q^{68} +(4.50000 - 2.59808i) q^{69} -12.0000 q^{71} +9.00000 q^{72} +(1.50000 + 2.59808i) q^{73} +(-1.50000 + 2.59808i) q^{74} +(6.00000 + 3.46410i) q^{75} +(-0.500000 + 0.866025i) q^{76} +(-7.50000 - 4.33013i) q^{78} +8.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +9.00000 q^{81} +(-2.50000 + 4.33013i) q^{82} +(-4.50000 - 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(0.500000 + 0.866025i) q^{86} +(-1.50000 + 0.866025i) q^{87} +(7.50000 - 12.9904i) q^{88} +(-6.50000 + 11.2583i) q^{89} +(1.50000 + 2.59808i) q^{90} +(1.50000 + 2.59808i) q^{92} -1.00000 q^{95} +8.66025i q^{96} +(-4.50000 - 7.79423i) q^{97} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 2q^{4} - q^{5} - 6q^{8} - 6q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 2q^{4} - q^{5} - 6q^{8} - 6q^{9} - q^{10} - 5q^{11} - 5q^{13} + 3q^{15} - 2q^{16} + 3q^{17} - 6q^{18} + q^{19} + q^{20} - 5q^{22} - 3q^{23} + 4q^{25} - 5q^{26} + q^{29} + 3q^{30} + 10q^{32} - 15q^{33} + 3q^{34} + 6q^{36} - 3q^{37} + q^{38} - 15q^{39} + 3q^{40} - 5q^{41} + q^{43} + 5q^{44} + 3q^{45} - 3q^{46} + 4q^{50} - 9q^{51} + 5q^{52} + 9q^{53} + 10q^{55} + 3q^{57} + q^{58} - 3q^{60} + 28q^{61} + 14q^{64} + 10q^{65} - 15q^{66} + 8q^{67} - 3q^{68} + 9q^{69} - 24q^{71} + 18q^{72} + 3q^{73} - 3q^{74} + 12q^{75} - q^{76} - 15q^{78} + 16q^{79} + q^{80} + 18q^{81} - 5q^{82} - 9q^{83} + 3q^{85} + q^{86} - 3q^{87} + 15q^{88} - 13q^{89} + 3q^{90} + 3q^{92} - 2q^{95} - 9q^{97} + 15q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 1.73205i 1.00000i
\(4\) −1.00000 −0.500000
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 1.73205i 0.707107i
\(7\) 0 0
\(8\) −3.00000 −1.06066
\(9\) −3.00000 −1.00000
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 1.73205i 0.500000i
\(13\) −2.50000 + 4.33013i −0.693375 + 1.20096i 0.277350 + 0.960769i \(0.410544\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 1.50000 0.866025i 0.387298 0.223607i
\(16\) −1.00000 −0.250000
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) −3.00000 −0.707107
\(19\) 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
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 5.19615i 1.06066i
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) −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 0.908708 0.417432i \(-0.137070\pi\)
−0.815861 + 0.578249i \(0.803736\pi\)
\(30\) 1.50000 0.866025i 0.273861 0.158114i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 5.00000 0.883883
\(33\) −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 \(0.245980\pi\)
\(38\) 0.500000 0.866025i 0.0811107 0.140488i
\(39\) −7.50000 4.33013i −1.20096 0.693375i
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) −2.50000 + 4.33013i −0.390434 + 0.676252i −0.992507 0.122189i \(-0.961009\pi\)
0.602072 + 0.798441i \(0.294342\pi\)
\(42\) 0 0
\(43\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.73205i 0.250000i
\(49\) 0 0
\(50\) 2.00000 3.46410i 0.282843 0.489898i
\(51\) −4.50000 + 2.59808i −0.630126 + 0.363803i
\(52\) 2.50000 4.33013i 0.346688 0.600481i
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 5.19615i 0.707107i
\(55\) 5.00000 0.674200
\(56\) 0 0
\(57\) 1.50000 + 0.866025i 0.198680 + 0.114708i
\(58\) 0.500000 + 0.866025i 0.0656532 + 0.113715i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −1.50000 + 0.866025i −0.193649 + 0.111803i
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 5.00000 0.620174
\(66\) −7.50000 4.33013i −0.923186 0.533002i
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 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 \(0.752242\pi\)
\(72\) 9.00000 1.06066
\(73\) 1.50000 + 2.59808i 0.175562 + 0.304082i 0.940356 0.340193i \(-0.110493\pi\)
−0.764794 + 0.644275i \(0.777159\pi\)
\(74\) −1.50000 + 2.59808i −0.174371 + 0.302020i
\(75\) 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
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) 9.00000 1.00000
\(82\) −2.50000 + 4.33013i −0.276079 + 0.478183i
\(83\) −4.50000 7.79423i −0.493939 0.855528i 0.506036 0.862512i \(-0.331110\pi\)
−0.999976 + 0.00698436i \(0.997777\pi\)
\(84\) 0 0
\(85\) 1.50000 2.59808i 0.162698 0.281801i
\(86\) 0.500000 + 0.866025i 0.0539164 + 0.0933859i
\(87\) −1.50000 + 0.866025i −0.160817 + 0.0928477i
\(88\) 7.50000 12.9904i 0.799503 1.38478i
\(89\) −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
\(95\) −1.00000 −0.102598
\(96\) 8.66025i 0.883883i
\(97\) −4.50000 7.79423i −0.456906 0.791384i 0.541890 0.840450i \(-0.317709\pi\)
−0.998796 + 0.0490655i \(0.984376\pi\)
\(98\) 0 0
\(99\) 7.50000 12.9904i 0.753778 1.30558i
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −8.50000 + 14.7224i −0.845782 + 1.46494i 0.0391591 + 0.999233i \(0.487532\pi\)
−0.884941 + 0.465704i \(0.845801\pi\)
\(102\) −4.50000 + 2.59808i −0.445566 + 0.257248i
\(103\) −0.500000 0.866025i −0.0492665 0.0853320i 0.840341 0.542059i \(-0.182355\pi\)
−0.889607 + 0.456727i \(0.849022\pi\)
\(104\) 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 \(0.859678\pi\)
\(108\) 5.19615i 0.500000i
\(109\) 4.50000 + 7.79423i 0.431022 + 0.746552i 0.996962 0.0778949i \(-0.0248199\pi\)
−0.565940 + 0.824447i \(0.691487\pi\)
\(110\) 5.00000 0.476731
\(111\) −4.50000 2.59808i −0.427121 0.246598i
\(112\) 0 0
\(113\) 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
\(115\) −1.50000 + 2.59808i −0.139876 + 0.242272i
\(116\) −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
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 14.0000 1.26750
\(123\) −7.50000 4.33013i −0.676252 0.390434i
\(124\) 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 \(0.678715\pi\)
\(128\) −3.00000 −0.265165
\(129\) −1.50000 + 0.866025i −0.132068 + 0.0762493i
\(130\) 5.00000 0.438529
\(131\) −0.500000 0.866025i −0.0436852 0.0756650i 0.843356 0.537355i \(-0.180577\pi\)
−0.887041 + 0.461690i \(0.847243\pi\)
\(132\) 7.50000 + 4.33013i 0.652791 + 0.376889i
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) −4.50000 + 2.59808i −0.387298 + 0.223607i
\(136\) −4.50000 7.79423i −0.385872 0.668350i
\(137\) 4.50000 7.79423i 0.384461 0.665906i −0.607233 0.794524i \(-0.707721\pi\)
0.991694 + 0.128618i \(0.0410540\pi\)
\(138\) 4.50000 2.59808i 0.383065 0.221163i
\(139\) 4.50000 7.79423i 0.381685 0.661098i −0.609618 0.792695i \(-0.708677\pi\)
0.991303 + 0.131597i \(0.0420106\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −12.0000 −1.00702
\(143\) −12.5000 21.6506i −1.04530 1.81052i
\(144\) 3.00000 0.250000
\(145\) 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
\(149\) −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i \(-0.205881\pi\)
−0.920904 + 0.389789i \(0.872548\pi\)
\(150\) 6.00000 + 3.46410i 0.489898 + 0.282843i
\(151\) −2.50000 + 4.33013i −0.203447 + 0.352381i −0.949637 0.313353i \(-0.898548\pi\)
0.746190 + 0.665733i \(0.231881\pi\)
\(152\) −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
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 8.00000 0.636446
\(159\) −13.5000 + 7.79423i −1.07062 + 0.618123i
\(160\) −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 \(0.0249005\pi\)
\(164\) 2.50000 4.33013i 0.195217 0.338126i
\(165\) 8.66025i 0.674200i
\(166\) −4.50000 7.79423i −0.349268 0.604949i
\(167\) −9.50000 + 16.4545i −0.735132 + 1.27329i 0.219533 + 0.975605i \(0.429547\pi\)
−0.954665 + 0.297681i \(0.903787\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 1.50000 2.59808i 0.115045 0.199263i
\(171\) −1.50000 + 2.59808i −0.114708 + 0.198680i
\(172\) −0.500000 0.866025i −0.0381246 0.0660338i
\(173\) 14.0000 1.06440 0.532200 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) −1.50000 + 0.866025i −0.113715 + 0.0656532i
\(175\) 0 0
\(176\) 2.50000 4.33013i 0.188445 0.326396i
\(177\) 0 0
\(178\) −6.50000 + 11.2583i −0.487196 + 0.843848i
\(179\) −9.50000 16.4545i −0.710063 1.22987i −0.964833 0.262864i \(-0.915333\pi\)
0.254770 0.967002i \(-0.418000\pi\)
\(180\) −1.50000 2.59808i −0.111803 0.193649i
\(181\) 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
\(184\) 4.50000 + 7.79423i 0.331744 + 0.574598i
\(185\) 3.00000 0.220564
\(186\) 0 0
\(187\) −15.0000 −1.09691
\(188\) 0 0
\(189\) 0 0
\(190\) −1.00000 −0.0725476
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 12.1244i 0.875000i
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) −4.50000 7.79423i −0.323081 0.559593i
\(195\) 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 \(0.799423\pi\)
\(200\) −6.00000 + 10.3923i −0.424264 + 0.734847i
\(201\) 6.92820i 0.488678i
\(202\) −8.50000 + 14.7224i −0.598058 + 1.03587i
\(203\) 0 0
\(204\) 4.50000 2.59808i 0.315063 0.181902i
\(205\) 5.00000 0.349215
\(206\) −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 −0.998221 0.0596196i \(-0.981011\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) −4.50000 7.79423i −0.309061 0.535310i
\(213\) 20.7846i 1.42414i
\(214\) −8.50000 + 14.7224i −0.581048 + 1.00640i
\(215\) 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
\(219\) −4.50000 + 2.59808i −0.304082 + 0.175562i
\(220\) −5.00000 −0.337100
\(221\) −15.0000 −1.00901
\(222\) −4.50000 2.59808i −0.302020 0.174371i
\(223\) 9.50000 + 16.4545i 0.636167 + 1.10187i 0.986267 + 0.165161i \(0.0528144\pi\)
−0.350100 + 0.936713i \(0.613852\pi\)
\(224\) 0 0
\(225\) −6.00000 + 10.3923i −0.400000 + 0.692820i
\(226\) 0.500000 0.866025i 0.0332595 0.0576072i
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) −1.50000 0.866025i −0.0993399 0.0573539i
\(229\) −0.500000 0.866025i −0.0330409 0.0572286i 0.849032 0.528341i \(-0.177186\pi\)
−0.882073 + 0.471113i \(0.843853\pi\)
\(230\) −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 \(0.197997\pi\)
\(234\) 7.50000 12.9904i 0.490290 0.849208i
\(235\) 0 0
\(236\) 0 0
\(237\) 13.8564i 0.900070i
\(238\) 0 0
\(239\) 7.50000 12.9904i 0.485135 0.840278i −0.514719 0.857359i \(-0.672104\pi\)
0.999854 + 0.0170808i \(0.00543724\pi\)
\(240\) −1.50000 + 0.866025i −0.0968246 + 0.0559017i
\(241\) 5.50000 9.52628i 0.354286 0.613642i −0.632709 0.774389i \(-0.718057\pi\)
0.986996 + 0.160748i \(0.0513906\pi\)
\(242\) −7.00000 12.1244i −0.449977 0.779383i
\(243\) 15.5885i 1.00000i
\(244\) −14.0000 −0.896258
\(245\) 0 0
\(246\) −7.50000 4.33013i −0.478183 0.276079i
\(247\) 2.50000 + 4.33013i 0.159071 + 0.275519i
\(248\) 0 0
\(249\) 13.5000 7.79423i 0.855528 0.493939i
\(250\) −9.00000 −0.569210
\(251\) 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
\(254\) −12.0000 −0.752947
\(255\) 4.50000 + 2.59808i 0.281801 + 0.162698i
\(256\) −17.0000 −1.06250
\(257\) −14.5000 25.1147i −0.904485 1.56661i −0.821607 0.570055i \(-0.806922\pi\)
−0.0828783 0.996560i \(-0.526411\pi\)
\(258\) −1.50000 + 0.866025i −0.0933859 + 0.0539164i
\(259\) 0 0
\(260\) −5.00000 −0.310087
\(261\) −1.50000 2.59808i −0.0928477 0.160817i
\(262\) −0.500000 0.866025i −0.0308901 0.0535032i
\(263\) −2.50000 + 4.33013i −0.154157 + 0.267007i −0.932752 0.360520i \(-0.882599\pi\)
0.778595 + 0.627527i \(0.215933\pi\)
\(264\) 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
\(268\) −4.00000 −0.244339
\(269\) 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
\(275\) 10.0000 + 17.3205i 0.603023 + 1.04447i
\(276\) −4.50000 + 2.59808i −0.270868 + 0.156386i
\(277\) −9.50000 + 16.4545i −0.570800 + 0.988654i 0.425684 + 0.904872i \(0.360033\pi\)
−0.996484 + 0.0837823i \(0.973300\pi\)
\(278\) 4.50000 7.79423i 0.269892 0.467467i
\(279\) 0 0
\(280\) 0 0
\(281\) 14.5000 + 25.1147i 0.864997 + 1.49822i 0.867050 + 0.498222i \(0.166013\pi\)
−0.00205220 + 0.999998i \(0.500653\pi\)
\(282\) 0 0
\(283\) −28.0000 −1.66443 −0.832214 0.554455i \(-0.812927\pi\)
−0.832214 + 0.554455i \(0.812927\pi\)
\(284\) 12.0000 0.712069
\(285\) 1.73205i 0.102598i
\(286\) −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
\(290\) 0.500000 0.866025i 0.0293610 0.0508548i
\(291\) 13.5000 7.79423i 0.791384 0.456906i
\(292\) −1.50000 2.59808i −0.0877809 0.152041i
\(293\) −2.50000 + 4.33013i −0.146052 + 0.252969i −0.929765 0.368154i \(-0.879990\pi\)
0.783713 + 0.621123i \(0.213323\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4.50000 7.79423i 0.261557 0.453030i
\(297\) 22.5000 + 12.9904i 1.30558 + 0.753778i
\(298\) −1.50000 2.59808i −0.0868927 0.150503i
\(299\) 15.0000 0.867472
\(300\) −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
\(304\) −0.500000 + 0.866025i −0.0286770 + 0.0496700i
\(305\) −7.00000 12.1244i −0.400819 0.694239i
\(306\) −4.50000 7.79423i −0.257248 0.445566i
\(307\) −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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 22.5000 + 12.9904i 1.27381 + 0.735436i
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) −13.5000 + 7.79423i −0.757042 + 0.437079i
\(319\) −5.00000 −0.279946
\(320\) −3.50000 6.06218i −0.195656 0.338886i
\(321\) −25.5000 14.7224i −1.42327 0.821726i
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) −9.00000 −0.500000
\(325\) 10.0000 + 17.3205i 0.554700 + 0.960769i
\(326\) 5.50000 9.52628i 0.304617 0.527612i
\(327\) −13.5000 + 7.79423i −0.746552 + 0.431022i
\(328\) 7.50000 12.9904i 0.414118 0.717274i
\(329\) 0 0
\(330\) 8.66025i 0.476731i
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 4.50000 + 7.79423i 0.246970 + 0.427764i
\(333\) 4.50000 7.79423i 0.246598 0.427121i
\(334\) −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 −0.136184 0.990684i \(-0.543484\pi\)
0.926049 0.377403i \(-0.123183\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) 1.50000 + 0.866025i 0.0814688 + 0.0470360i
\(340\) −1.50000 + 2.59808i −0.0813489 + 0.140900i
\(341\) 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
\(346\) 14.0000 0.752645
\(347\) 4.00000 0.214731 0.107366 0.994220i \(-0.465758\pi\)
0.107366 + 0.994220i \(0.465758\pi\)
\(348\) 1.50000 0.866025i 0.0804084 0.0464238i
\(349\) 9.50000 + 16.4545i 0.508523 + 0.880788i 0.999951 + 0.00987003i \(0.00314178\pi\)
−0.491428 + 0.870918i \(0.663525\pi\)
\(350\) 0 0
\(351\) 22.5000 + 12.9904i 1.20096 + 0.693375i
\(352\) −12.5000 + 21.6506i −0.666252 + 1.15398i
\(353\) 5.50000 9.52628i 0.292735 0.507033i −0.681720 0.731613i \(-0.738768\pi\)
0.974456 + 0.224580i \(0.0721011\pi\)
\(354\) 0 0
\(355\) 6.00000 + 10.3923i 0.318447 + 0.551566i
\(356\) 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
\(362\) 14.0000 0.735824
\(363\) 21.0000 12.1244i 1.10221 0.636364i
\(364\) 0 0
\(365\) 1.50000 2.59808i 0.0785136 0.135990i
\(366\) 24.2487i 1.26750i
\(367\) −1.50000 + 2.59808i −0.0782994 + 0.135618i −0.902516 0.430656i \(-0.858282\pi\)
0.824217 + 0.566274i \(0.191616\pi\)
\(368\) 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
\(373\) 12.5000 + 21.6506i 0.647225 + 1.12103i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) −15.0000 −0.775632
\(375\) 15.5885i 0.804984i
\(376\) 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 \(0.599726\pi\)
\(380\) 1.00000 0.0512989
\(381\) 20.7846i 1.06483i
\(382\) 8.00000 0.409316
\(383\) 13.5000 + 23.3827i 0.689818 + 1.19480i 0.971897 + 0.235408i \(0.0756427\pi\)
−0.282079 + 0.959391i \(0.591024\pi\)
\(384\) 5.19615i 0.265165i
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) −1.50000 2.59808i −0.0762493 0.132068i
\(388\) 4.50000 + 7.79423i 0.228453 + 0.395692i
\(389\) 4.50000 7.79423i 0.228159 0.395183i −0.729103 0.684403i \(-0.760063\pi\)
0.957263 + 0.289220i \(0.0933960\pi\)
\(390\) 8.66025i 0.438529i
\(391\) 4.50000 7.79423i 0.227575 0.394171i
\(392\) 0 0
\(393\) 1.50000 0.866025i 0.0756650 0.0436852i
\(394\) 2.00000 0.100759
\(395\) −4.00000 6.92820i −0.201262 0.348596i
\(396\) −7.50000 + 12.9904i −0.376889 + 0.652791i
\(397\) 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
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 6.92820i 0.345547i
\(403\) 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
\(408\) 13.5000 7.79423i 0.668350 0.385872i
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 5.00000 0.246932
\(411\) 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
\(416\) −12.5000 + 21.6506i −0.612863 + 1.06151i
\(417\) 13.5000 + 7.79423i 0.661098 + 0.381685i
\(418\) 2.50000 + 4.33013i 0.122279 + 0.211793i
\(419\) 4.50000 7.79423i 0.219839 0.380773i −0.734919 0.678155i \(-0.762780\pi\)
0.954759 + 0.297382i \(0.0961133\pi\)
\(420\) 0 0
\(421\) 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
\(425\) 12.0000 0.582086
\(426\) 20.7846i 1.00702i
\(427\) 0 0
\(428\) 8.50000 14.7224i 0.410863 0.711636i
\(429\) 37.5000 21.6506i 1.81052 1.04530i
\(430\) 0.500000 0.866025i 0.0241121 0.0417635i
\(431\) 4.50000 + 7.79423i 0.216757 + 0.375435i 0.953815 0.300395i \(-0.0971186\pi\)
−0.737057 + 0.675830i \(0.763785\pi\)
\(432\) 5.19615i 0.250000i
\(433\) 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
\(436\) −4.50000 7.79423i −0.215511 0.373276i
\(437\) −3.00000 −0.143509
\(438\) −4.50000 + 2.59808i −0.215018 + 0.124141i
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) −15.0000 −0.715097
\(441\) 0 0
\(442\) −15.0000 −0.713477
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 4.50000 + 2.59808i 0.213561 + 0.123299i
\(445\) 13.0000 0.616259
\(446\) 9.50000 + 16.4545i 0.449838 + 0.779142i
\(447\) 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
\(452\) −0.500000 + 0.866025i −0.0235180 + 0.0407344i
\(453\) −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
\(457\) 22.0000 1.02912 0.514558 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) −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 0.997871 0.0652135i \(-0.0207728\pi\)
−0.555412 + 0.831575i \(0.687440\pi\)
\(462\) 0 0
\(463\) −6.50000 + 11.2583i −0.302081 + 0.523219i −0.976607 0.215032i \(-0.931015\pi\)
0.674526 + 0.738251i \(0.264348\pi\)
\(464\) −0.500000 0.866025i −0.0232119 0.0402042i
\(465\) 0 0
\(466\) −1.50000 + 2.59808i −0.0694862 + 0.120354i
\(467\) −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
\(471\) 24.2487i 1.11732i
\(472\) 0 0
\(473\) −5.00000 −0.229900
\(474\) 13.8564i 0.636446i
\(475\) −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
\(479\) 12.5000 21.6506i 0.571140 0.989243i −0.425310 0.905048i \(-0.639835\pi\)
0.996449 0.0841949i \(-0.0268318\pi\)
\(480\) 7.50000 4.33013i 0.342327 0.197642i
\(481\) −7.50000 12.9904i −0.341971 0.592310i
\(482\) 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
\(486\) 15.5885i 0.707107i
\(487\) −9.50000 16.4545i −0.430486 0.745624i 0.566429 0.824110i \(-0.308325\pi\)
−0.996915 + 0.0784867i \(0.974991\pi\)
\(488\) −42.0000 −1.90125
\(489\) 16.5000 + 9.52628i 0.746156 + 0.430793i
\(490\) 0 0
\(491\) −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
\(493\) −1.50000 + 2.59808i −0.0675566 + 0.117011i
\(494\) 2.50000 + 4.33013i 0.112480 + 0.194822i
\(495\) −15.0000 −0.674200
\(496\) 0 0
\(497\) 0 0
\(498\) 13.5000 7.79423i 0.604949 0.349268i
\(499\) −15.5000 26.8468i −0.693875 1.20183i −0.970558 0.240866i \(-0.922569\pi\)
0.276683 0.960961i \(-0.410765\pi\)
\(500\) 9.00000 0.402492
\(501\) −28.5000 16.4545i −1.27329 0.735132i
\(502\) 28.0000 1.24970
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 17.0000 0.756490
\(506\) 15.0000 0.666831
\(507\) 18.0000 10.3923i 0.799408 0.461538i
\(508\) 12.0000 0.532414
\(509\) −14.5000 25.1147i −0.642701 1.11319i −0.984827 0.173537i \(-0.944480\pi\)
0.342126 0.939654i \(-0.388853\pi\)
\(510\) 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
\(515\) −0.500000 + 0.866025i −0.0220326 + 0.0381616i
\(516\) 1.50000 0.866025i 0.0660338 0.0381246i
\(517\) 0 0
\(518\) 0 0
\(519\) 24.2487i 1.06440i
\(520\) −15.0000 −0.657794
\(521\) 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
\(528\) 7.50000 + 4.33013i 0.326396 + 0.188445i
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 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
\(535\) 17.0000 0.734974
\(536\) −12.0000 −0.518321
\(537\) 28.5000 16.4545i 1.22987 0.710063i
\(538\) 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 \(-0.0139332\pi\)
\(542\) 0.500000 0.866025i 0.0214768 0.0371990i
\(543\) 24.2487i 1.04061i
\(544\) 7.50000 + 12.9904i 0.321560 + 0.556958i
\(545\) 4.50000 7.79423i 0.192759 0.333868i
\(546\) 0 0
\(547\) 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
\(549\) −42.0000 −1.79252
\(550\) 10.0000 + 17.3205i 0.426401 + 0.738549i
\(551\) 1.00000 0.0426014
\(552\) −13.5000 + 7.79423i −0.574598 + 0.331744i
\(553\) 0 0
\(554\) −9.50000 + 16.4545i −0.403616 + 0.699084i
\(555\) 5.19615i 0.220564i
\(556\) −4.50000 + 7.79423i −0.190843 + 0.330549i
\(557\) 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
\(562\) 14.5000 + 25.1147i 0.611646 + 1.05940i
\(563\) 28.0000 1.18006 0.590030 0.807382i \(-0.299116\pi\)
0.590030 + 0.807382i \(0.299116\pi\)
\(564\) 0 0
\(565\) −1.00000 −0.0420703
\(566\) −28.0000 −1.17693
\(567\) 0 0
\(568\) 36.0000 1.51053
\(569\) −34.0000 −1.42535 −0.712677 0.701492i \(-0.752517\pi\)
−0.712677 + 0.701492i \(0.752517\pi\)
\(570\) 1.73205i 0.0725476i
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 12.5000 + 21.6506i 0.522651 + 0.905259i
\(573\) 13.8564i 0.578860i
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) −21.0000 −0.875000
\(577\) 15.5000 + 26.8468i 0.645273 + 1.11765i 0.984238 + 0.176847i \(0.0565899\pi\)
−0.338965 + 0.940799i \(0.610077\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 17.3205i 0.719816i
\(580\) −0.500000 + 0.866025i −0.0207614 + 0.0359597i
\(581\) 0 0
\(582\) 13.5000 7.79423i 0.559593 0.323081i
\(583\) −45.0000 −1.86371
\(584\) −4.50000 7.79423i −0.186211 0.322527i
\(585\) −15.0000 −0.620174
\(586\) −2.50000 + 4.33013i −0.103274 + 0.178876i
\(587\) −18.5000 32.0429i −0.763577 1.32255i −0.940996 0.338418i \(-0.890108\pi\)
0.177419 0.984135i \(-0.443225\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 3.46410i 0.142494i
\(592\) 1.50000 2.59808i 0.0616496 0.106780i
\(593\) 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
\(597\) −4.50000 + 2.59808i −0.184173 + 0.106332i
\(598\) 15.0000 0.613396
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) −18.0000 10.3923i −0.734847 0.424264i
\(601\) −4.50000 7.79423i −0.183559 0.317933i 0.759531 0.650471i \(-0.225428\pi\)
−0.943090 + 0.332538i \(0.892095\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 2.50000 4.33013i 0.101724 0.176190i
\(605\) −7.00000 + 12.1244i −0.284590 + 0.492925i
\(606\) −25.5000 14.7224i −1.03587 0.598058i
\(607\) −0.500000 0.866025i −0.0202944 0.0351509i 0.855700 0.517472i \(-0.173127\pi\)
−0.875994 + 0.482322i \(0.839794\pi\)
\(608\) 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 \(0.958684\pi\)
\(614\) −28.0000 −1.12999
\(615\) 8.66025i 0.349215i
\(616\) 0 0
\(617\) −13.5000 + 23.3827i −0.543490 + 0.941351i 0.455211 + 0.890384i \(0.349564\pi\)
−0.998700 + 0.0509678i \(0.983769\pi\)
\(618\) 1.50000 0.866025i 0.0603388 0.0348367i
\(619\) 12.5000 21.6506i 0.502417 0.870212i −0.497579 0.867419i \(-0.665777\pi\)
0.999996 0.00279365i \(-0.000889247\pi\)
\(620\) 0 0
\(621\) −13.5000 + 7.79423i −0.541736 + 0.312772i
\(622\) 0 0
\(623\) 0 0
\(624\) 7.50000 + 4.33013i 0.300240 + 0.173344i
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) −14.0000 −0.559553
\(627\) −7.50000 + 4.33013i −0.299521 + 0.172929i
\(628\) −14.0000 −0.558661
\(629\) −9.00000 −0.358854
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) −24.0000 −0.954669
\(633\) −19.5000 11.2583i −0.775055 0.447478i
\(634\) −6.00000 −0.238290
\(635\) 6.00000 + 10.3923i 0.238103 + 0.412406i
\(636\) 13.5000 7.79423i 0.535310 0.309061i
\(637\) 0 0
\(638\) −5.00000 −0.197952
\(639\) 36.0000 1.42414
\(640\) 1.50000 + 2.59808i 0.0592927 + 0.102698i
\(641\) 4.50000 7.79423i 0.177739 0.307854i −0.763367 0.645966i \(-0.776455\pi\)
0.941106 + 0.338112i \(0.109788\pi\)
\(642\) −25.5000 14.7224i −1.00640 0.581048i
\(643\) −9.50000 + 16.4545i −0.374643 + 0.648901i −0.990274 0.139134i \(-0.955568\pi\)
0.615630 + 0.788035i \(0.288902\pi\)
\(644\) 0 0
\(645\) 1.50000 + 0.866025i 0.0590624 + 0.0340997i
\(646\) 3.00000 0.118033
\(647\) 15.5000 + 26.8468i 0.609368 + 1.05546i 0.991345 + 0.131284i \(0.0419101\pi\)
−0.381977 + 0.924172i \(0.624757\pi\)
\(648\) −27.0000 −1.06066
\(649\) 0 0
\(650\) 10.0000 + 17.3205i 0.392232 + 0.679366i
\(651\) 0 0
\(652\) −5.50000 + 9.52628i −0.215397 + 0.373078i
\(653\) −1.50000 2.59808i −0.0586995 0.101671i 0.835182 0.549973i \(-0.185362\pi\)
−0.893882 + 0.448303i \(0.852029\pi\)
\(654\) −13.5000 + 7.79423i −0.527892 + 0.304778i
\(655\) −0.500000 + 0.866025i −0.0195366 + 0.0338384i
\(656\) 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 \(-0.342933\pi\)
\(660\) 8.66025i 0.337100i
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 8.00000 0.310929
\(663\) 25.9808i 1.00901i
\(664\) 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
\(668\) 9.50000 16.4545i 0.367566 0.636643i
\(669\) −28.5000 + 16.4545i −1.10187 + 0.636167i
\(670\) −2.00000 3.46410i −0.0772667 0.133830i
\(671\) −35.0000 + 60.6218i −1.35116 + 2.34028i
\(672\) 0 0
\(673\) 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
\(675\) −18.0000 10.3923i −0.692820 0.400000i
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 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
\(688\) −0.500000 0.866025i −0.0190623 0.0330169i
\(689\) −45.0000 −1.71436
\(690\) −4.50000 2.59808i −0.171312 0.0989071i
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) −14.0000 −0.532200
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) −9.00000 −0.341389
\(696\) 4.50000 2.59808i 0.170572 0.0984798i
\(697\) −15.0000 −0.568166
\(698\) 9.50000 + 16.4545i 0.359580 + 0.622811i
\(699\) −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
\(704\) −17.5000 + 30.3109i −0.659556 + 1.14238i
\(705\) 0 0
\(706\) 5.50000 9.52628i 0.206995 0.358526i
\(707\) 0 0
\(708\) 0 0
\(709\) −6.00000 −0.225335 −0.112667 0.993633i \(-0.535939\pi\)
−0.112667 + 0.993633i \(0.535939\pi\)
\(710\) 6.00000 + 10.3923i 0.225176 + 0.390016i
\(711\) −24.0000 −0.900070
\(712\) 19.5000 33.7750i 0.730793 1.26577i
\(713\) 0 0
\(714\) 0 0
\(715\) −12.5000 + 21.6506i −0.467473 + 0.809688i
\(716\) 9.50000 + 16.4545i 0.355032 + 0.614933i
\(717\) 22.5000 + 12.9904i 0.840278 + 0.485135i
\(718\) 5.50000 9.52628i 0.205258 0.355518i
\(719\) −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
\(724\) −14.0000 −0.520306
\(725\) 4.00000 0.148556
\(726\) 21.0000 12.1244i 0.779383 0.449977i
\(727\) 23.5000 + 40.7032i 0.871567 + 1.50960i 0.860376 + 0.509661i \(0.170229\pi\)
0.0111912 + 0.999937i \(0.496438\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 1.50000 2.59808i 0.0555175 0.0961591i
\(731\) −1.50000 + 2.59808i −0.0554795 + 0.0960933i
\(732\) 24.2487i 0.896258i
\(733\) 13.5000 + 23.3827i 0.498634 + 0.863659i 0.999999 0.00157675i \(-0.000501894\pi\)
−0.501365 + 0.865236i \(0.667169\pi\)
\(734\) −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
\(738\) 7.50000 12.9904i 0.276079 0.478183i
\(739\) 4.50000 + 7.79423i 0.165535 + 0.286715i 0.936845 0.349744i \(-0.113732\pi\)
−0.771310 + 0.636460i \(0.780398\pi\)
\(740\) −3.00000 −0.110282
\(741\) −7.50000 + 4.33013i −0.275519 + 0.159071i
\(742\) 0 0
\(743\) 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
\(745\) −1.50000 + 2.59808i −0.0549557 + 0.0951861i
\(746\) 12.5000 + 21.6506i 0.457658 + 0.792686i
\(747\) 13.5000 + 23.3827i 0.493939 + 0.855528i
\(748\) 15.0000 0.548454
\(749\) 0 0
\(750\) 15.5885i 0.569210i
\(751\) −15.5000 26.8468i −0.565603 0.979653i −0.996993 0.0774878i \(-0.975310\pi\)
0.431390 0.902165i \(-0.358023\pi\)
\(752\) 0 0
\(753\) 48.4974i 1.76734i
\(754\) −5.00000 −0.182089
\(755\) 5.00000 0.181969
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −12.0000 −0.435860
\(759\) 25.9808i 0.943042i
\(760\) 3.00000 0.108821
\(761\) 13.5000 + 23.3827i 0.489375 + 0.847622i 0.999925 0.0122260i \(-0.00389175\pi\)
−0.510551 + 0.859848i \(0.670558\pi\)
\(762\) 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
\(768\) 29.4449i 1.06250i
\(769\) 11.5000 19.9186i 0.414701 0.718283i −0.580696 0.814120i \(-0.697220\pi\)
0.995397 + 0.0958377i \(0.0305530\pi\)
\(770\) 0 0
\(771\) 43.5000 25.1147i 1.56661 0.904485i
\(772\) 10.0000 0.359908
\(773\) 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
\(779\) 2.50000 + 4.33013i 0.0895718 + 0.155143i
\(780\) 8.66025i 0.310087i
\(781\) 30.0000 51.9615i 1.07348 1.85933i
\(782\) 4.50000 7.79423i 0.160920 0.278721i
\(783\) 4.50000 2.59808i 0.160817 0.0928477i
\(784\) 0 0
\(785\)