Properties

Label 441.2.f.b.148.1
Level $441$
Weight $2$
Character 441.148
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.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 148.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.b.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 −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 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 \(-0.589456\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 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 \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 1.50000 2.59808i 0.353553 0.612372i
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) −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 −0.602072 0.798441i \(-0.705658\pi\)
0.992507 + 0.122189i \(0.0389915\pi\)
\(42\) 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 \(0.187058\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 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 \(-0.443826\pi\)
0.175562 + 0.984468i \(0.443826\pi\)
\(74\) −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 0.999976 0.00698436i \(-0.00222321\pi\)
−0.506036 + 0.862512i \(0.668890\pi\)
\(84\) 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 \(-0.741949\pi\)
−0.688999 + 0.724763i \(0.741949\pi\)
\(90\) −1.50000 2.59808i −0.158114 0.273861i
\(91\) 0 0
\(92\) 1.50000 + 2.59808i 0.156386 + 0.270868i
\(93\) 0 0
\(94\) 0 0
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) −7.50000 + 4.33013i −0.765466 + 0.441942i
\(97\) 4.50000 + 7.79423i 0.456906 + 0.791384i 0.998796 0.0490655i \(-0.0156243\pi\)
−0.541890 + 0.840450i \(0.682291\pi\)
\(98\) 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 \(0.154199\pi\)
−0.0391591 + 0.999233i \(0.512468\pi\)
\(102\) 5.19615i 0.514496i
\(103\) 0.500000 0.866025i 0.0492665 0.0853320i −0.840341 0.542059i \(-0.817645\pi\)
0.889607 + 0.456727i \(0.150978\pi\)
\(104\) −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 −0.843356 0.537355i \(-0.819423\pi\)
0.887041 + 0.461690i \(0.152757\pi\)
\(132\) −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 −0.991303 0.131597i \(-0.957989\pi\)
0.609618 + 0.792695i \(0.291323\pi\)
\(140\) 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 \(-0.644649\pi\)
0.997609 0.0691164i \(-0.0220180\pi\)
\(158\) −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 \(-0.570453\pi\)
0.954665 0.297681i \(-0.0962132\pi\)
\(168\) 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 \(0.0119679\pi\)
−0.467093 + 0.884208i \(0.654699\pi\)
\(174\) 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 \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 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 \(-0.466089\pi\)
0.106332 + 0.994331i \(0.466089\pi\)
\(200\) −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 \(-0.947186\pi\)
0.350100 0.936713i \(-0.386148\pi\)
\(224\) 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 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) 1.50000 0.866025i 0.0993399 0.0573539i
\(229\) 0.500000 0.866025i 0.0330409 0.0572286i −0.849032 0.528341i \(-0.822814\pi\)
0.882073 + 0.471113i \(0.156147\pi\)
\(230\) 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 0.632709 0.774389i \(-0.281943\pi\)
−0.986996 + 0.160748i \(0.948609\pi\)
\(242\) 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 \(-0.844936\pi\)
−0.883672 + 0.468106i \(0.844936\pi\)
\(252\) 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 \(-0.473589\pi\)
0.821607 0.570055i \(-0.193078\pi\)
\(258\) 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 \(-0.470848\pi\)
0.0914566 + 0.995809i \(0.470848\pi\)
\(270\) 5.19615i 0.316228i
\(271\) 1.00000 0.0607457 0.0303728 0.999539i \(-0.490331\pi\)
0.0303728 + 0.999539i \(0.490331\pi\)
\(272\) 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 \(0.479593\pi\)
−0.896279 + 0.443491i \(0.853740\pi\)
\(284\) −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 −0.783713 0.621123i \(-0.786677\pi\)
0.929765 + 0.368154i \(0.120010\pi\)
\(294\) 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 \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 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 0.597522 0.801852i \(-0.296152\pi\)
−0.993186 + 0.116543i \(0.962819\pi\)
\(314\) −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 \(-0.996858\pi\)
0.491428 0.870918i \(-0.336475\pi\)
\(350\) 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 0.681720 0.731613i \(-0.261232\pi\)
−0.974456 + 0.224580i \(0.927899\pi\)
\(354\) 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 0.902516 0.430656i \(-0.141718\pi\)
−0.824217 + 0.566274i \(0.808384\pi\)
\(368\) −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 \(0.408976\pi\)
−0.971897 + 0.235408i \(0.924357\pi\)
\(384\) 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 \(-0.377157\pi\)
0.376414 + 0.926451i \(0.377157\pi\)
\(398\) −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 −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) −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 −0.954759 0.297382i \(-0.903887\pi\)
0.734919 + 0.678155i \(0.237220\pi\)
\(420\) 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 \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 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 0.555412 0.831575i \(-0.312560\pi\)
−0.997871 + 0.0652135i \(0.979227\pi\)
\(462\) 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 \(-0.714781\pi\)
−0.624705 + 0.780860i \(0.714781\pi\)
\(468\) 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 \(-0.973168\pi\)
0.425310 0.905048i \(-0.360165\pi\)
\(480\) 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 \(-0.611147\pi\)
0.984827 0.173537i \(-0.0555197\pi\)
\(510\) −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 \(-0.479067\pi\)
0.0657162 + 0.997838i \(0.479067\pi\)
\(522\) 3.00000 0.131306
\(523\) 1.00000 0.0437269 0.0218635 0.999761i \(-0.493040\pi\)
0.0218635 + 0.999761i \(0.493040\pi\)
\(524\) −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 \(-0.632449\pi\)
0.994228 0.107290i \(-0.0342173\pi\)
\(564\) 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 \(-0.276743\pi\)
0.645273 + 0.763952i \(0.276743\pi\)
\(578\) 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 \(0.109892\pi\)
−0.177419 + 0.984135i \(0.556775\pi\)
\(588\) 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 \(-0.400344\pi\)
0.307988 + 0.951390i \(0.400344\pi\)
\(594\) −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 0.943090 0.332538i \(-0.107905\pi\)
−0.759531 + 0.650471i \(0.774572\pi\)
\(602\) 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 −0.855700 0.517472i \(-0.826873\pi\)
0.875994 + 0.482322i \(0.160206\pi\)
\(608\) −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 \(-0.999111\pi\)
0.497579 0.867419i \(-0.334223\pi\)
\(620\) 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 −0.615630 0.788035i \(-0.711098\pi\)
0.990274 + 0.139134i \(0.0444318\pi\)
\(644\) 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 \(-0.291423\pi\)
0.609368 + 0.792888i \(0.291423\pi\)
\(648\) 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 −0.697174 0.716902i \(-0.745559\pi\)
0.969442 + 0.245319i \(0.0788928\pi\)
\(662\) −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 \(-0.867705\pi\)
0.107772 0.994176i \(-0.465628\pi\)
\(678\) −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 \(0.0121127\pi\)
−0.466691 + 0.884420i \(0.654554\pi\)
\(692\) 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 \(-0.667942\pi\)
−0.503465 + 0.864016i \(0.667942\pi\)
\(720\) 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 \(-0.829771\pi\)
−0.0111912 0.999937i \(-0.503562\pi\)
\(728\) 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 −0.999999 0.00157675i \(-0.999498\pi\)
0.501365 + 0.865236i \(0.332831\pi\)
\(734\) 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 −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) 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 −0.995397 0.0958377i \(-0.969447\pi\)
0.580696 + 0.814120i \(0.302780\pi\)
\(770\) 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 \(-0.311762\pi\)
0.557496 + 0.830179i \(0.311762\pi\)
\(774\) 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
\(784\) 0 0
\(785\) −7.00000 12.1244i