Properties

Label 441.2.f.a.148.1
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $1$
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.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(1\)
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 148.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.a.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.73205i q^{6} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.73205i q^{6} -3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +1.00000 q^{10} +(-2.50000 - 4.33013i) 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} -3.00000 q^{17} +(1.50000 - 2.59808i) q^{18} -1.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(4.50000 + 2.59808i) q^{24} +(2.00000 + 3.46410i) q^{25} +5.00000 q^{26} -5.19615i q^{27} +(0.500000 + 0.866025i) q^{29} +(-1.50000 - 0.866025i) q^{30} +(-2.50000 + 4.33013i) q^{32} +8.66025i q^{33} +(1.50000 + 2.59808i) q^{34} +3.00000 q^{36} +3.00000 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} -5.00000 q^{44} -3.00000 q^{45} +3.00000 q^{46} -1.73205i q^{48} +(2.00000 - 3.46410i) q^{50} +(4.50000 + 2.59808i) q^{51} +(2.50000 + 4.33013i) q^{52} -9.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +5.00000 q^{55} +(1.50000 + 0.866025i) q^{57} +(0.500000 - 0.866025i) q^{58} -1.73205i q^{60} +(-7.00000 - 12.1244i) q^{61} +7.00000 q^{64} +(-2.50000 - 4.33013i) q^{65} +(7.50000 - 4.33013i) q^{66} +(-2.00000 + 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(4.50000 - 2.59808i) q^{69} -12.0000 q^{71} +(-4.50000 - 7.79423i) q^{72} -3.00000 q^{73} +(-1.50000 - 2.59808i) q^{74} -6.92820i q^{75} +(-0.500000 + 0.866025i) q^{76} +(-7.50000 - 4.33013i) q^{78} +(-4.00000 - 6.92820i) q^{79} -1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} +5.00000 q^{82} +(-4.50000 - 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(0.500000 - 0.866025i) q^{86} -1.73205i q^{87} +(7.50000 + 12.9904i) q^{88} +13.0000 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - 3q^{3} + q^{4} - q^{5} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 2q - q^{2} - 3q^{3} + q^{4} - q^{5} - 6q^{8} + 3q^{9} + 2q^{10} - 5q^{11} - 3q^{12} - 5q^{13} + 3q^{15} + q^{16} - 6q^{17} + 3q^{18} - 2q^{19} + q^{20} - 5q^{22} - 3q^{23} + 9q^{24} + 4q^{25} + 10q^{26} + q^{29} - 3q^{30} - 5q^{32} + 3q^{34} + 6q^{36} + 6q^{37} + q^{38} + 15q^{39} + 3q^{40} - 5q^{41} + q^{43} - 10q^{44} - 6q^{45} + 6q^{46} + 4q^{50} + 9q^{51} + 5q^{52} - 18q^{53} - 9q^{54} + 10q^{55} + 3q^{57} + q^{58} - 14q^{61} + 14q^{64} - 5q^{65} + 15q^{66} - 4q^{67} - 3q^{68} + 9q^{69} - 24q^{71} - 9q^{72} - 6q^{73} - 3q^{74} - q^{76} - 15q^{78} - 8q^{79} - 2q^{80} - 9q^{81} + 10q^{82} - 9q^{83} + 3q^{85} + q^{86} + 15q^{88} + 26q^{89} + 3q^{90} + 3q^{92} + q^{95} + 15q^{96} - 9q^{97} + 15q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i 0.633316 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
\(5\) −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
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 1.00000 0.316228
\(11\) −2.50000 4.33013i −0.753778 1.30558i −0.945979 0.324227i \(-0.894896\pi\)
0.192201 0.981356i \(-0.438437\pi\)
\(12\) −1.50000 + 0.866025i −0.433013 + 0.250000i
\(13\) −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
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 1.50000 2.59808i 0.353553 0.612372i
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 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 \(0.267924\pi\)
\(24\) 4.50000 + 2.59808i 0.918559 + 0.530330i
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 5.00000 0.980581
\(27\) 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 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −2.50000 + 4.33013i −0.441942 + 0.765466i
\(33\) 8.66025i 1.50756i
\(34\) 1.50000 + 2.59808i 0.257248 + 0.445566i
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 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 \(0.809039\pi\)
\(44\) −5.00000 −0.753778
\(45\) −3.00000 −0.447214
\(46\) 3.00000 0.442326
\(47\) 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
\(51\) 4.50000 + 2.59808i 0.630126 + 0.363803i
\(52\) 2.50000 + 4.33013i 0.346688 + 0.600481i
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) −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
\(58\) 0.500000 0.866025i 0.0656532 0.113715i
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 1.73205i 0.223607i
\(61\) −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
\(66\) 7.50000 4.33013i 0.923186 0.533002i
\(67\) −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) −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 \(0.752242\pi\)
\(72\) −4.50000 7.79423i −0.530330 0.918559i
\(73\) −3.00000 −0.351123 −0.175562 0.984468i \(-0.556174\pi\)
−0.175562 + 0.984468i \(0.556174\pi\)
\(74\) −1.50000 2.59808i −0.174371 0.302020i
\(75\) 6.92820i 0.800000i
\(76\) −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 \(0.981922\pi\)
\(80\) −1.00000 −0.111803
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 5.00000 0.552158
\(83\) −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
\(87\) 1.73205i 0.185695i
\(88\) 7.50000 + 12.9904i 0.799503 + 1.38478i
\(89\) 13.0000 1.37800 0.688999 0.724763i \(-0.258051\pi\)
0.688999 + 0.724763i \(0.258051\pi\)
\(90\) 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 0.541890 0.840450i \(-0.317709\pi\)
−0.998796 + 0.0490655i \(0.984376\pi\)
\(98\) 0 0
\(99\) 7.50000 12.9904i 0.753778 1.30558i
\(100\) 4.00000 0.400000
\(101\) −8.50000 14.7224i −0.845782 1.46494i −0.884941 0.465704i \(-0.845801\pi\)
0.0391591 0.999233i \(-0.487532\pi\)
\(102\) 5.19615i 0.514496i
\(103\) −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
\(107\) 17.0000 1.64345 0.821726 0.569883i \(-0.193011\pi\)
0.821726 + 0.569883i \(0.193011\pi\)
\(108\) −4.50000 2.59808i −0.433013 0.250000i
\(109\) −9.00000 −0.862044 −0.431022 0.902342i \(-0.641847\pi\)
−0.431022 + 0.902342i \(0.641847\pi\)
\(110\) −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 −0.841549 0.540181i \(-0.818356\pi\)
0.888585 + 0.458712i \(0.151689\pi\)
\(114\) 1.73205i 0.162221i
\(115\) −1.50000 2.59808i −0.139876 0.242272i
\(116\) 1.00000 0.0928477
\(117\) −15.0000 −1.38675
\(118\) 0 0
\(119\) 0 0
\(120\) −4.50000 + 2.59808i −0.410792 + 0.237171i
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) −7.00000 + 12.1244i −0.633750 + 1.09769i
\(123\) 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 \(0.678715\pi\)
\(128\) 1.50000 + 2.59808i 0.132583 + 0.229640i
\(129\) 1.73205i 0.152499i
\(130\) −2.50000 + 4.33013i −0.219265 + 0.379777i
\(131\) −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
\(136\) 9.00000 0.771744
\(137\) 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 −0.609618 0.792695i \(-0.708677\pi\)
0.991303 + 0.131597i \(0.0420106\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) 25.0000 2.09061
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) −1.00000 −0.0830455
\(146\) 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 \(0.898548\pi\)
\(152\) 3.00000 0.243332
\(153\) −4.50000 7.79423i −0.363803 0.630126i
\(154\) 0 0
\(155\) 0 0
\(156\) 8.66025i 0.693375i
\(157\) −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
\(159\) 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
\(163\) −11.0000 −0.861586 −0.430793 0.902451i \(-0.641766\pi\)
−0.430793 + 0.902451i \(0.641766\pi\)
\(164\) 2.50000 + 4.33013i 0.195217 + 0.338126i
\(165\) −7.50000 4.33013i −0.583874 0.337100i
\(166\) −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
\(170\) −3.00000 −0.230089
\(171\) −1.50000 2.59808i −0.114708 0.198680i
\(172\) 1.00000 0.0762493
\(173\) −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
\(178\) −6.50000 11.2583i −0.487196 0.843848i
\(179\) 19.0000 1.42013 0.710063 0.704138i \(-0.248666\pi\)
0.710063 + 0.704138i \(0.248666\pi\)
\(180\) −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
\(185\) −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 \(0.0494748\pi\)
\(194\) −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 \(0.477302\pi\)
\(198\) −15.0000 −1.06600
\(199\) −3.00000 −0.212664 −0.106332 0.994331i \(-0.533911\pi\)
−0.106332 + 0.994331i \(0.533911\pi\)
\(200\) −6.00000 10.3923i −0.424264 0.734847i
\(201\) 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
\(206\) 1.00000 0.0696733
\(207\) −9.00000 −0.625543
\(208\) −5.00000 −0.346688
\(209\) 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
\(213\) 18.0000 + 10.3923i 1.23334 + 0.712069i
\(214\) −8.50000 14.7224i −0.581048 1.00640i
\(215\) −1.00000 −0.0681994
\(216\) 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
\(220\) 2.50000 4.33013i 0.168550 0.291937i
\(221\) 7.50000 12.9904i 0.504505 0.873828i
\(222\) 5.19615i 0.348743i
\(223\) 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
\(226\) −1.00000 −0.0665190
\(227\) −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
\(233\) 3.00000 0.196537 0.0982683 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) 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 0.986996 0.160748i \(-0.0513906\pi\)
−0.632709 + 0.774389i \(0.718057\pi\)
\(242\) 14.0000 0.899954
\(243\) 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
\(247\) 2.50000 4.33013i 0.159071 0.275519i
\(248\) 0 0
\(249\) 15.5885i 0.987878i
\(250\) 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
\(255\) −4.50000 + 2.59808i −0.281801 + 0.162698i
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −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
\(262\) 1.00000 0.0617802
\(263\) −2.50000 4.33013i −0.154157 0.267007i 0.778595 0.627527i \(-0.215933\pi\)
−0.932752 + 0.360520i \(0.882599\pi\)
\(264\) 25.9808i 1.59901i
\(265\) 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
\(269\) −3.00000 −0.182913 −0.0914566 0.995809i \(-0.529152\pi\)
−0.0914566 + 0.995809i \(0.529152\pi\)
\(270\) 5.19615i 0.316228i
\(271\) −1.00000 −0.0607457 −0.0303728 0.999539i \(-0.509669\pi\)
−0.0303728 + 0.999539i \(0.509669\pi\)
\(272\) −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
\(276\) 5.19615i 0.312772i
\(277\) −9.50000 16.4545i −0.570800 0.988654i −0.996484 0.0837823i \(-0.973300\pi\)
0.425684 0.904872i \(-0.360033\pi\)
\(278\) −9.00000 −0.539784
\(279\) 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
\(283\) 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
\(289\) −8.00000 −0.470588
\(290\) 0.500000 + 0.866025i 0.0293610 + 0.0508548i
\(291\) 15.5885i 0.913812i
\(292\) −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
\(296\) −9.00000 −0.523114
\(297\) −22.5000 + 12.9904i −1.30558 + 0.753778i
\(298\) 3.00000 0.173785
\(299\) −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
\(303\) 29.4449i 1.69156i
\(304\) −0.500000 0.866025i −0.0286770 0.0496700i
\(305\) 14.0000 0.801638
\(306\) −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 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) −22.5000 + 12.9904i −1.27381 + 0.735436i
\(313\) 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 \(0.779442\pi\)
\(318\) 15.5885i 0.874157i
\(319\) 2.50000 4.33013i 0.139973 0.242441i
\(320\) −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
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) −20.0000 −1.10940
\(326\) 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
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) −9.00000 −0.493939
\(333\) 4.50000 + 7.79423i 0.246598 + 0.427121i
\(334\) 19.0000 1.03963
\(335\) −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
\(345\) 5.19615i 0.279751i
\(346\) −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 \(0.200908\pi\)
\(348\) −1.50000 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
\(352\) 25.0000 1.33250
\(353\) 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
\(359\) −11.0000 −0.580558 −0.290279 0.956942i \(-0.593748\pi\)
−0.290279 + 0.956942i \(0.593748\pi\)
\(360\) 9.00000 0.474342
\(361\) −18.0000 −0.947368
\(362\) −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
\(367\) −1.50000 2.59808i −0.0782994 0.135618i 0.824217 0.566274i \(-0.191616\pi\)
−0.902516 + 0.430656i \(0.858282\pi\)
\(368\) −3.00000 −0.156386
\(369\) −15.0000 −0.780869
\(370\) 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 \(-0.0574041\pi\)
\(374\) 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
\(383\) 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
\(388\) −9.00000 −0.456906
\(389\) 4.50000 + 7.79423i 0.228159 + 0.395183i 0.957263 0.289220i \(-0.0933960\pi\)
−0.729103 + 0.684403i \(0.760063\pi\)
\(390\) 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
\(395\) 8.00000 0.402524
\(396\) −7.50000 12.9904i −0.376889 0.652791i
\(397\) −15.0000 −0.752828 −0.376414 0.926451i \(-0.622843\pi\)
−0.376414 + 0.926451i \(0.622843\pi\)
\(398\) 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 \(0.190532\pi\)
\(402\) −6.00000 3.46410i −0.299253 0.172774i
\(403\) 0 0
\(404\) −17.0000 −0.845782
\(405\) −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
\(409\) 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
\(411\) 15.5885i 0.768922i
\(412\) 0.500000 + 0.866025i 0.0246332 + 0.0426660i
\(413\) 0 0
\(414\) 4.50000 + 7.79423i 0.221163 + 0.383065i
\(415\) 9.00000 0.441793
\(416\) −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 \(0.825576\pi\)
\(422\) 13.0000 0.632830
\(423\) 0 0
\(424\) 27.0000 1.31124
\(425\) −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
\(429\) −37.5000 21.6506i −1.81052 1.04530i
\(430\) 0.500000 + 0.866025i 0.0241121 + 0.0417635i
\(431\) −9.00000 −0.433515 −0.216757 0.976226i \(-0.569548\pi\)
−0.216757 + 0.976226i \(0.569548\pi\)
\(432\) 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
\(436\) −4.50000 + 7.79423i −0.215511 + 0.373276i
\(437\) 1.50000 2.59808i 0.0717547 0.124283i
\(438\) 5.19615i 0.248282i
\(439\) 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 \(-0.493236\pi\)
\(444\) −4.50000 + 2.59808i −0.213561 + 0.123299i
\(445\) −6.50000 + 11.2583i −0.308130 + 0.533696i
\(446\) 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 \(0.249646\pi\)
\(450\) 12.0000 0.565685
\(451\) 25.0000 1.17720
\(452\) −0.500000 0.866025i −0.0235180 0.0407344i
\(453\) 8.66025i 0.406894i
\(454\) −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 \(-0.338711\pi\)
\(458\) 1.00000 0.0467269
\(459\) 15.5885i 0.727607i
\(460\) −3.00000 −0.139876
\(461\) 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
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) −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
\(478\) −15.0000 −0.686084
\(479\) 12.5000 + 21.6506i 0.571140 + 0.989243i 0.996449 + 0.0841949i \(0.0268318\pi\)
−0.425310 + 0.905048i \(0.639835\pi\)
\(480\) 8.66025i 0.395285i
\(481\) −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
\(485\) 9.00000 0.408669
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) 19.0000 0.860972 0.430486 0.902597i \(-0.358342\pi\)
0.430486 + 0.902597i \(0.358342\pi\)
\(488\) 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 −0.974598 0.223963i \(-0.928100\pi\)
0.681257 + 0.732045i \(0.261434\pi\)
\(492\) 8.66025i 0.390434i
\(493\) −1.50000 2.59808i −0.0675566 0.117011i
\(494\) −5.00000 −0.224961
\(495\) 7.50000 + 12.9904i 0.337100 + 0.583874i
\(496\) 0 0
\(497\) 0 0
\(498\) 13.5000 7.79423i 0.604949 0.349268i
\(499\) −15.5000 + 26.8468i −0.693875 + 1.20183i 0.276683 + 0.960961i \(0.410765\pi\)
−0.970558 + 0.240866i \(0.922569\pi\)
\(500\) −4.50000 + 7.79423i −0.201246 + 0.348569i
\(501\) 28.5000 16.4545i 1.27329 0.735132i
\(502\) −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
\(507\) 20.7846i 0.923077i
\(508\) −6.00000 + 10.3923i −0.266207 + 0.461084i
\(509\) −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
\(513\) 5.19615i 0.229416i
\(514\) 29.0000 1.27914
\(515\) −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
\(520\) 7.50000 + 12.9904i 0.328897 + 0.569666i
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) 3.00000 0.131306
\(523\) −1.00000 −0.0437269 −0.0218635 0.999761i \(-0.506960\pi\)
−0.0218635 + 0.999761i \(0.506960\pi\)
\(524\) 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
\(530\) −9.00000 −0.390935
\(531\) 0 0
\(532\) 0 0
\(533\) −12.5000 21.6506i −0.541435 0.937793i
\(534\) 22.5167i 0.974391i
\(535\) −8.50000 + 14.7224i −0.367487 + 0.636506i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) −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
\(541\) −25.0000 −1.07483 −0.537417 0.843317i \(-0.680600\pi\)
−0.537417 + 0.843317i \(0.680600\pi\)
\(542\) 0.500000 + 0.866025i 0.0214768 + 0.0371990i
\(543\) −21.0000 12.1244i −0.901196 0.520306i
\(544\) 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 \(0.620476\pi\)
\(548\) 9.00000 0.384461
\(549\) 21.0000 36.3731i 0.896258 1.55236i
\(550\) −20.0000 −0.852803
\(551\) −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
\(556\) −4.50000 7.79423i −0.190843 0.330549i
\(557\) −37.0000 −1.56774 −0.783870 0.620925i \(-0.786757\pi\)
−0.783870 + 0.620925i \(0.786757\pi\)
\(558\) 0 0
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) 25.9808i 1.09691i
\(562\) 14.5000 25.1147i 0.611646 1.05940i
\(563\) −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 \(0.933141\pi\)
\(572\) 12.5000 21.6506i 0.522651 0.905259i
\(573\) 13.8564i 0.578860i
\(574\) 0 0
\(575\) −12.0000 −0.500435
\(576\) 10.5000 + 18.1865i 0.437500 + 0.757772i
\(577\) −31.0000 −1.29055 −0.645273 0.763952i \(-0.723257\pi\)
−0.645273 + 0.763952i \(0.723257\pi\)
\(578\) 4.00000 + 6.92820i 0.166378 + 0.288175i
\(579\) −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
\(584\) 9.00000 0.372423
\(585\) 7.50000 12.9904i 0.310087 0.537086i
\(586\) 5.00000 0.206548
\(587\) −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
\(591\) −3.00000 1.73205i −0.123404 0.0712470i
\(592\) 1.50000 + 2.59808i 0.0616496 + 0.106780i
\(593\) −15.0000 −0.615976 −0.307988 0.951390i \(-0.599656\pi\)
−0.307988 + 0.951390i \(0.599656\pi\)
\(594\) 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
\(598\) −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 \(0.00355143\pi\)
\(600\) 20.7846i 0.848528i
\(601\) −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
\(604\) −5.00000 −0.203447
\(605\) −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
\(612\) −9.00000 −0.363803
\(613\) 19.0000 0.767403 0.383701 0.923457i \(-0.374649\pi\)
0.383701 + 0.923457i \(0.374649\pi\)
\(614\) 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 0.455211 + 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 0.999996 + 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
\(626\) 7.00000 12.1244i 0.279776 0.484587i
\(627\) 8.66025i 0.345857i
\(628\) 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
\(633\) 19.5000 11.2583i 0.775055 0.447478i
\(634\) 3.00000 5.19615i 0.119145 0.206366i
\(635\) 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
\(639\) −18.0000 31.1769i −0.712069 1.23334i
\(640\) −3.00000 −0.118585
\(641\) 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i \(-0.109788\pi\)
−0.763367 + 0.645966i \(0.776455\pi\)
\(642\) 29.4449i 1.16210i
\(643\) −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
\(646\) −1.50000 2.59808i −0.0590167 0.102220i
\(647\) −31.0000 −1.21874 −0.609368 0.792888i \(-0.708577\pi\)
−0.609368 + 0.792888i \(0.708577\pi\)
\(648\) 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
\(653\) −1.50000 + 2.59808i −0.0586995 + 0.101671i −0.893882 0.448303i \(-0.852029\pi\)
0.835182 + 0.549973i \(0.185362\pi\)
\(654\) 15.5885i 0.609557i
\(655\) −0.500000 0.866025i −0.0195366 0.0338384i
\(656\) −5.00000 −0.195217
\(657\) −4.50000 7.79423i −0.175562 0.304082i
\(658\) 0 0
\(659\) −13.5000 23.3827i −0.525885 0.910860i −0.999545 0.0301523i \(-0.990401\pi\)
0.473660 0.880708i \(-0.342933\pi\)
\(660\) −7.50000 + 4.33013i −0.291937 + 0.168550i
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
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
\(667\) −3.00000 −0.116160
\(668\) 9.50000 + 16.4545i 0.367566 + 0.636643i
\(669\) 32.9090i 1.27233i
\(670\) −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 \(0.644544\pi\)
\(674\) −29.0000 −1.11704
\(675\) 18.0000 10.3923i 0.692820 0.400000i
\(676\) −12.0000 −0.461538
\(677\) 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
\(681\) 5.19615i 0.199117i
\(682\) 0 0
\(683\) −9.00000 −0.344375 −0.172188 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) −3.00000 −0.114708
\(685\) −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
\(689\) 22.5000 38.9711i 0.857182 1.48468i
\(690\) 4.50000 2.59808i 0.171312 0.0989071i
\(691\) −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
\(696\) 5.19615i 0.196960i
\(697\) 7.50000 12.9904i 0.284083 0.492046i
\(698\) 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 \(0.308281\pi\)
\(702\) 25.9808i 0.980581i
\(703\) −3.00000 −0.113147
\(704\) −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
\(709\) 3.00000 + 5.19615i 0.112667 + 0.195146i 0.916845 0.399244i \(-0.130727\pi\)
−0.804178 + 0.594389i \(0.797394\pi\)
\(710\) −12.0000 −0.450352
\(711\) 12.0000 20.7846i 0.450035 0.779484i
\(712\) −39.0000 −1.46159
\(713\) 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
\(719\) 27.0000 1.00693 0.503465 0.864016i \(-0.332058\pi\)
0.503465 + 0.864016i \(0.332058\pi\)
\(720\) −1.50000 2.59808i −0.0559017 0.0968246i
\(721\) 0 0
\(722\) 9.00000 + 15.5885i 0.334945 + 0.580142i
\(723\) 19.0526i 0.708572i
\(724\) 7.00000 12.1244i 0.260153 0.450598i
\(725\) −2.00000 + 3.46410i −0.0742781 + 0.128654i
\(726\) −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
\(730\) −3.00000 −0.111035
\(731\) −1.50000 2.59808i −0.0554795 0.0960933i
\(732\) 21.0000 + 12.1244i 0.776182 + 0.448129i
\(733\) 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
\(737\) 20.0000 0.736709
\(738\) 7.50000 + 12.9904i 0.276079 + 0.478183i
\(739\) −9.00000 −0.331070 −0.165535 0.986204i \(-0.552935\pi\)
−0.165535 + 0.986204i \(0.552935\pi\)
\(740\) 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 −0.695024 0.718986i \(-0.744606\pi\)
0.970173 + 0.242415i \(0.0779397\pi\)
\(744\) 0 0
\(745\) −1.50000 2.59808i −0.0549557 0.0951861i
\(746\) −25.0000 −0.915315
\(747\) 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
\(753\) −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
\(761\) 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
\(765\) 9.00000 0.325396
\(766\) −27.0000 −0.975550
\(767\) 0 0
\(768\) −25.5000 + 14.7224i −0.920152 + 0.531250i
\(769\) 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
\(772\) −5.00000 8.66025i −0.179954 0.311689i
\(773\) −31.0000 −1.11499 −0.557496 0.830179i \(-0.688238\pi\)
−0.557496 + 0.830179i \(0.688238\pi\)
\(774\) 3.00000 0.107833
\(775\) 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
\(780\) 7.50000 + 4.33013i 0.268543 + 0.155043i
\(781\) 30.0000 + 51.9615i 1.07348 + 1.85933i
\(782\) −9.00000 −0.321839
\(783\) 4.50000 2.59808i 0.160817 0.0928477i
\(784\)