Properties

Label 441.2.h.a.214.1
Level $441$
Weight $2$
Character 441.214
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.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 214.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.a.373.1

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 −0.955901 0.293691i \(-0.905116\pi\)
0.732294 + 0.680989i \(0.238450\pi\)
\(6\) 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 −0.945979 0.324227i \(-0.894896\pi\)
0.192201 0.981356i \(-0.438437\pi\)
\(12\) 1.73205i 0.500000i
\(13\) −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
\(16\) −1.00000 −0.250000
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) −3.00000 −0.707107
\(19\) 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i \(-0.130073\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 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 −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 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 −0.815861 0.578249i \(-0.803736\pi\)
0.908708 + 0.417432i \(0.137070\pi\)
\(30\) 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 0.715981 0.698119i \(-0.245980\pi\)
−0.962580 + 0.270998i \(0.912646\pi\)
\(38\) 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 0.602072 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 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 −0.371706 0.928351i \(-0.621227\pi\)
0.989828 0.142269i \(-0.0454398\pi\)
\(54\) 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 −0.764794 0.644275i \(-0.777159\pi\)
0.940356 + 0.340193i \(0.110493\pi\)
\(74\) −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 −0.999976 0.00698436i \(-0.997777\pi\)
0.506036 + 0.862512i \(0.331110\pi\)
\(84\) 0 0
\(85\) 1.50000 + 2.59808i 0.162698 + 0.281801i
\(86\) 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 −0.972162 0.234309i \(-0.924717\pi\)
0.283164 0.959072i \(-0.408616\pi\)
\(90\) 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 −0.998796 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
\(101\) −8.50000 14.7224i −0.845782 1.46494i −0.884941 0.465704i \(-0.845801\pi\)
0.0391591 0.999233i \(-0.487532\pi\)
\(102\) −4.50000 2.59808i −0.445566 0.257248i
\(103\) −0.500000 + 0.866025i −0.0492665 + 0.0853320i −0.889607 0.456727i \(-0.849022\pi\)
0.840341 + 0.542059i \(0.182355\pi\)
\(104\) 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 −0.904396 0.426694i \(-0.859678\pi\)
0.0826699 0.996577i \(-0.473655\pi\)
\(108\) 5.19615i 0.500000i
\(109\) 4.50000 7.79423i 0.431022 0.746552i −0.565940 0.824447i \(-0.691487\pi\)
0.996962 + 0.0778949i \(0.0248199\pi\)
\(110\) 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 0.888585 0.458712i \(-0.151689\pi\)
−0.841549 + 0.540181i \(0.818356\pi\)
\(114\) 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 −0.887041 0.461690i \(-0.847243\pi\)
0.843356 + 0.537355i \(0.180577\pi\)
\(132\) 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 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) 4.50000 + 2.59808i 0.383065 + 0.221163i
\(139\) 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
\(142\) −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 −0.920904 0.389789i \(-0.872548\pi\)
0.798019 + 0.602632i \(0.205881\pi\)
\(150\) 6.00000 3.46410i 0.489898 0.282843i
\(151\) −2.50000 4.33013i −0.203447 0.352381i 0.746190 0.665733i \(-0.231881\pi\)
−0.949637 + 0.313353i \(0.898548\pi\)
\(152\) −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 0.996942 0.0781474i \(-0.0249005\pi\)
−0.566149 + 0.824303i \(0.691567\pi\)
\(164\) 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 −0.954665 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
\(171\) −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 0.254770 + 0.967002i \(0.418000\pi\)
−0.964833 + 0.262864i \(0.915333\pi\)
\(180\) −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 −0.807950 0.589252i \(-0.799423\pi\)
0.914282 + 0.405079i \(0.132756\pi\)
\(200\) −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 0.550743 0.834675i \(-0.314345\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) −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 −0.350100 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
\(227\) −1.50000 2.59808i −0.0995585 0.172440i 0.811943 0.583736i \(-0.198410\pi\)
−0.911502 + 0.411296i \(0.865076\pi\)
\(228\) −1.50000 + 0.866025i −0.0993399 + 0.0573539i
\(229\) −0.500000 + 0.866025i −0.0330409 + 0.0572286i −0.882073 0.471113i \(-0.843853\pi\)
0.849032 + 0.528341i \(0.177186\pi\)
\(230\) −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 0.812700 0.582683i \(-0.197997\pi\)
−0.910968 + 0.412477i \(0.864664\pi\)
\(234\) 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 0.999854 0.0170808i \(-0.00543724\pi\)
−0.514719 + 0.857359i \(0.672104\pi\)
\(240\) −1.50000 0.866025i −0.0968246 0.0559017i
\(241\) 5.50000 + 9.52628i 0.354286 + 0.613642i 0.986996 0.160748i \(-0.0513906\pi\)
−0.632709 + 0.774389i \(0.718057\pi\)
\(242\) −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 −0.0828783 + 0.996560i \(0.526411\pi\)
−0.821607 + 0.570055i \(0.806922\pi\)
\(258\) −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 0.778595 0.627527i \(-0.215933\pi\)
−0.932752 + 0.360520i \(0.882599\pi\)
\(264\) 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 −0.816668 0.577108i \(-0.804181\pi\)
0.908124 + 0.418701i \(0.137514\pi\)
\(270\) −4.50000 2.59808i −0.273861 0.158114i
\(271\) 0.500000 + 0.866025i 0.0303728 + 0.0526073i 0.880812 0.473466i \(-0.156997\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −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 −0.996484 0.0837823i \(-0.973300\pi\)
0.425684 0.904872i \(-0.360033\pi\)
\(278\) 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
\(283\) −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 0.783713 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
\(297\) 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 0.926049 + 0.377403i \(0.123183\pi\)
−0.136184 + 0.990684i \(0.543484\pi\)
\(338\) −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 −0.491428 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
\(353\) 5.50000 + 9.52628i 0.292735 + 0.507033i 0.974456 0.224580i \(-0.0721011\pi\)
−0.681720 + 0.731613i \(0.738768\pi\)
\(354\) 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 0.973876 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
\(362\) 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 0.824217 0.566274i \(-0.191616\pi\)
−0.902516 + 0.430656i \(0.858282\pi\)
\(368\) 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 −0.336557 0.941663i \(-0.609263\pi\)
0.983783 0.179364i \(-0.0574041\pi\)
\(374\) −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 −0.282079 0.959391i \(-0.591024\pi\)
0.971897 0.235408i \(-0.0756427\pi\)
\(384\) 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 0.957263 0.289220i \(-0.0933960\pi\)
−0.729103 + 0.684403i \(0.760063\pi\)
\(390\) 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 0.990538 0.137241i \(-0.0438236\pi\)
−0.614123 + 0.789210i \(0.710490\pi\)
\(398\) 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 −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 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 0.954759 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
\(425\) 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 −0.737057 0.675830i \(-0.763785\pi\)
0.953815 + 0.300395i \(0.0971186\pi\)
\(432\) 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 −0.555412 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 \(0.931015\pi\)
\(464\) −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 −0.988598 0.150581i \(-0.951886\pi\)
0.363892 0.931441i \(-0.381448\pi\)
\(468\) −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 0.996449 + 0.0841949i \(0.0268318\pi\)
−0.425310 + 0.905048i \(0.639835\pi\)
\(480\) 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 −0.996915 0.0784867i \(-0.974991\pi\)
0.566429 + 0.824110i \(0.308325\pi\)
\(488\) −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 0.681257 0.732045i \(-0.261434\pi\)
−0.974598 + 0.223963i \(0.928100\pi\)
\(492\) 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 0.276683 + 0.960961i \(0.410765\pi\)
−0.970558 + 0.240866i \(0.922569\pi\)
\(500\) 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 0.342126 + 0.939654i \(0.388853\pi\)
−0.984827 + 0.173537i \(0.944480\pi\)
\(510\) 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 −0.831295 0.555831i \(-0.812400\pi\)
0.897011 + 0.442007i \(0.145733\pi\)
\(522\) −1.50000 + 2.59808i −0.0656532 + 0.113715i
\(523\) 0.500000 + 0.866025i 0.0218635 + 0.0378686i 0.876750 0.480946i \(-0.159707\pi\)
−0.854887 + 0.518815i \(0.826373\pi\)
\(524\) 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 0.999042 + 0.0437584i \(0.0139332\pi\)
−0.461625 + 0.887075i \(0.652733\pi\)
\(542\) 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 −0.369514 0.929225i \(-0.620476\pi\)
0.989490 0.144604i \(-0.0461907\pi\)
\(548\) −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 −0.145802 0.989314i \(-0.546576\pi\)
0.929672 0.368389i \(-0.120091\pi\)
\(558\) 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 −0.338965 0.940799i \(-0.610077\pi\)
0.984238 0.176847i \(-0.0565899\pi\)
\(578\) 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 0.177419 + 0.984135i \(0.443225\pi\)
−0.940996 + 0.338418i \(0.890108\pi\)
\(588\) 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 0.977922 0.208970i \(-0.0670110\pi\)
−0.669934 + 0.742421i \(0.733678\pi\)
\(594\) 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 −0.943090 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
\(605\) −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 −0.875994 0.482322i \(-0.839794\pi\)
0.855700 + 0.517472i \(0.173127\pi\)
\(608\) 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 −0.991588 0.129433i \(-0.958684\pi\)
0.607887 + 0.794024i \(0.292017\pi\)
\(614\) −28.0000 −1.12999
\(615\) 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 \(-0.349564\pi\)
\(618\) 1.50000 + 0.866025i 0.0603388 + 0.0348367i
\(619\) 12.5000 + 21.6506i 0.502417 + 0.870212i 0.999996 + 0.00279365i \(0.000889247\pi\)
−0.497579 + 0.867419i \(0.665777\pi\)
\(620\) 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 0.941106 0.338112i \(-0.109788\pi\)
−0.763367 + 0.645966i \(0.776455\pi\)
\(642\) −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
\(646\) 3.00000 0.118033
\(647\) 15.5000 26.8468i 0.609368 1.05546i −0.381977 0.924172i \(-0.624757\pi\)
0.991345 0.131284i \(-0.0419101\pi\)
\(648\) −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 −0.893882 0.448303i \(-0.852029\pi\)
0.835182 + 0.549973i \(0.185362\pi\)
\(654\) −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 0.473660 + 0.880708i \(0.342933\pi\)
−0.999545 + 0.0301523i \(0.990401\pi\)
\(660\) 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 −0.438652 0.898657i \(-0.644544\pi\)
0.997586 0.0694449i \(-0.0221228\pi\)
\(674\) 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 −0.766997 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
\(686\) 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 −0.999992 0.00400572i \(-0.998725\pi\)
0.496527 0.868021i \(-0.334608\pi\)
\(720\) −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 0.0111912 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
\(731\) −1.50000 2.59808i −0.0554795 0.0960933i
\(732\) 24.2487i 0.896258i
\(733\) 13.5000 23.3827i 0.498634 0.863659i −0.501365 0.865236i \(-0.667169\pi\)
0.999999 + 0.00157675i \(0.000501894\pi\)
\(734\) −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 −0.771310 0.636460i \(-0.780398\pi\)
0.936845 + 0.349744i \(0.113732\pi\)
\(740\) −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 0.970173 0.242415i \(-0.0779397\pi\)
−0.695024 + 0.718986i \(0.744606\pi\)
\(744\) 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 0.431390 + 0.902165i \(0.358023\pi\)
−0.996993 + 0.0774878i \(0.975310\pi\)
\(752\) 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 −0.510551 0.859848i \(-0.670558\pi\)
0.999925 + 0.0122260i \(0.00389175\pi\)
\(762\) 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 0.995397 0.0958377i \(-0.0305530\pi\)
−0.580696 + 0.814120i \(0.697220\pi\)
\(770\) 0 0
\(771\) 43.5000 + 25.1147i 1.56661 + 0.904485i
\(772\) 10.0000 0.359908
\(773\) 15.5000 26.8468i 0.557496 0.965612i −0.440208 0.897896i \(-0.645095\pi\)
0.997705 0.0677162i \(-0.0215712\pi\)
\(774\) −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