Properties

Label 43.2.c.a.6.1
Level 43
Weight 2
Character 43.6
Analytic conductor 0.343
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 43.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.343356728692\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 6.1
Root \(0.500000 + 0.866025i\) of \(x^{2} - x + 1\)
Character \(\chi\) \(=\) 43.6
Dual form 43.2.c.a.36.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{12} +(2.50000 + 4.33013i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{15} -1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +(1.00000 + 1.73205i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-0.500000 + 0.866025i) q^{20} +3.00000 q^{21} +(3.50000 - 6.06218i) q^{23} +(1.50000 - 2.59808i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.50000 + 4.33013i) q^{26} -5.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(0.500000 + 0.866025i) q^{30} +(-2.50000 + 4.33013i) q^{31} +5.00000 q^{32} +(-1.50000 - 2.59808i) q^{34} -3.00000 q^{35} +(-1.00000 - 1.73205i) q^{36} +(4.50000 - 7.79423i) q^{37} +(-0.500000 + 0.866025i) q^{38} -5.00000 q^{39} +(-1.50000 + 2.59808i) q^{40} -10.0000 q^{41} +3.00000 q^{42} +(-4.00000 + 5.19615i) q^{43} +2.00000 q^{45} +(3.50000 - 6.06218i) q^{46} -8.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(2.00000 + 3.46410i) q^{50} +3.00000 q^{51} +(-2.50000 - 4.33013i) q^{52} +(2.50000 - 4.33013i) q^{53} -5.00000 q^{54} +(4.50000 + 7.79423i) q^{56} +(-0.500000 - 0.866025i) q^{57} +(-1.50000 - 2.59808i) q^{58} +12.0000 q^{59} +(-0.500000 - 0.866025i) q^{60} +(6.50000 + 11.2583i) q^{61} +(-2.50000 + 4.33013i) q^{62} +(3.00000 - 5.19615i) q^{63} +7.00000 q^{64} +5.00000 q^{65} +(1.50000 - 2.59808i) q^{67} +(1.50000 + 2.59808i) q^{68} +(3.50000 + 6.06218i) q^{69} -3.00000 q^{70} +(0.500000 + 0.866025i) q^{71} +(-3.00000 - 5.19615i) q^{72} +(-5.50000 - 9.52628i) q^{73} +(4.50000 - 7.79423i) q^{74} -4.00000 q^{75} +(0.500000 - 0.866025i) q^{76} -5.00000 q^{78} +(2.50000 + 4.33013i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} -10.0000 q^{82} +(-4.50000 + 7.79423i) q^{83} -3.00000 q^{84} -3.00000 q^{85} +(-4.00000 + 5.19615i) q^{86} +3.00000 q^{87} +(0.500000 - 0.866025i) q^{89} +2.00000 q^{90} +(7.50000 - 12.9904i) q^{91} +(-3.50000 + 6.06218i) q^{92} +(-2.50000 - 4.33013i) q^{93} -8.00000 q^{94} +(0.500000 + 0.866025i) q^{95} +(-2.50000 + 4.33013i) q^{96} -2.00000 q^{97} +(-1.00000 + 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - q^{3} - 2q^{4} + q^{5} - q^{6} - 3q^{7} - 6q^{8} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - q^{3} - 2q^{4} + q^{5} - q^{6} - 3q^{7} - 6q^{8} + 2q^{9} + q^{10} + q^{12} + 5q^{13} - 3q^{14} + q^{15} - 2q^{16} - 3q^{17} + 2q^{18} - q^{19} - q^{20} + 6q^{21} + 7q^{23} + 3q^{24} + 4q^{25} + 5q^{26} - 10q^{27} + 3q^{28} - 3q^{29} + q^{30} - 5q^{31} + 10q^{32} - 3q^{34} - 6q^{35} - 2q^{36} + 9q^{37} - q^{38} - 10q^{39} - 3q^{40} - 20q^{41} + 6q^{42} - 8q^{43} + 4q^{45} + 7q^{46} - 16q^{47} + q^{48} - 2q^{49} + 4q^{50} + 6q^{51} - 5q^{52} + 5q^{53} - 10q^{54} + 9q^{56} - q^{57} - 3q^{58} + 24q^{59} - q^{60} + 13q^{61} - 5q^{62} + 6q^{63} + 14q^{64} + 10q^{65} + 3q^{67} + 3q^{68} + 7q^{69} - 6q^{70} + q^{71} - 6q^{72} - 11q^{73} + 9q^{74} - 8q^{75} + q^{76} - 10q^{78} + 5q^{79} - q^{80} - q^{81} - 20q^{82} - 9q^{83} - 6q^{84} - 6q^{85} - 8q^{86} + 6q^{87} + q^{89} + 4q^{90} + 15q^{91} - 7q^{92} - 5q^{93} - 16q^{94} + q^{95} - 5q^{96} - 4q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

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

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 \(0.384973\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) −1.00000 −0.500000
\(5\) 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −1.50000 2.59808i −0.566947 0.981981i −0.996866 0.0791130i \(-0.974791\pi\)
0.429919 0.902867i \(-0.358542\pi\)
\(8\) −3.00000 −1.06066
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 2.50000 + 4.33013i 0.693375 + 1.20096i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −1.50000 2.59808i −0.400892 0.694365i
\(15\) 0.500000 + 0.866025i 0.129099 + 0.223607i
\(16\) −1.00000 −0.250000
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 1.00000 + 1.73205i 0.235702 + 0.408248i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) −0.500000 + 0.866025i −0.111803 + 0.193649i
\(21\) 3.00000 0.654654
\(22\) 0 0
\(23\) 3.50000 6.06218i 0.729800 1.26405i −0.227167 0.973856i \(-0.572946\pi\)
0.956967 0.290196i \(-0.0937204\pi\)
\(24\) 1.50000 2.59808i 0.306186 0.530330i
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 2.50000 + 4.33013i 0.490290 + 0.849208i
\(27\) −5.00000 −0.962250
\(28\) 1.50000 + 2.59808i 0.283473 + 0.490990i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 0.500000 + 0.866025i 0.0912871 + 0.158114i
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) 5.00000 0.883883
\(33\) 0 0
\(34\) −1.50000 2.59808i −0.257248 0.445566i
\(35\) −3.00000 −0.507093
\(36\) −1.00000 1.73205i −0.166667 0.288675i
\(37\) 4.50000 7.79423i 0.739795 1.28136i −0.212792 0.977098i \(-0.568256\pi\)
0.952587 0.304266i \(-0.0984111\pi\)
\(38\) −0.500000 + 0.866025i −0.0811107 + 0.140488i
\(39\) −5.00000 −0.800641
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 3.00000 0.462910
\(43\) −4.00000 + 5.19615i −0.609994 + 0.792406i
\(44\) 0 0
\(45\) 2.00000 0.298142
\(46\) 3.50000 6.06218i 0.516047 0.893819i
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) 3.00000 0.420084
\(52\) −2.50000 4.33013i −0.346688 0.600481i
\(53\) 2.50000 4.33013i 0.343401 0.594789i −0.641661 0.766989i \(-0.721754\pi\)
0.985062 + 0.172200i \(0.0550875\pi\)
\(54\) −5.00000 −0.680414
\(55\) 0 0
\(56\) 4.50000 + 7.79423i 0.601338 + 1.04155i
\(57\) −0.500000 0.866025i −0.0662266 0.114708i
\(58\) −1.50000 2.59808i −0.196960 0.341144i
\(59\) 12.0000 1.56227 0.781133 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) −0.500000 0.866025i −0.0645497 0.111803i
\(61\) 6.50000 + 11.2583i 0.832240 + 1.44148i 0.896258 + 0.443533i \(0.146275\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) −2.50000 + 4.33013i −0.317500 + 0.549927i
\(63\) 3.00000 5.19615i 0.377964 0.654654i
\(64\) 7.00000 0.875000
\(65\) 5.00000 0.620174
\(66\) 0 0
\(67\) 1.50000 2.59808i 0.183254 0.317406i −0.759733 0.650236i \(-0.774670\pi\)
0.942987 + 0.332830i \(0.108004\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) 3.50000 + 6.06218i 0.421350 + 0.729800i
\(70\) −3.00000 −0.358569
\(71\) 0.500000 + 0.866025i 0.0593391 + 0.102778i 0.894169 0.447730i \(-0.147767\pi\)
−0.834830 + 0.550508i \(0.814434\pi\)
\(72\) −3.00000 5.19615i −0.353553 0.612372i
\(73\) −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) 4.50000 7.79423i 0.523114 0.906061i
\(75\) −4.00000 −0.461880
\(76\) 0.500000 0.866025i 0.0573539 0.0993399i
\(77\) 0 0
\(78\) −5.00000 −0.566139
\(79\) 2.50000 + 4.33013i 0.281272 + 0.487177i 0.971698 0.236225i \(-0.0759104\pi\)
−0.690426 + 0.723403i \(0.742577\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −10.0000 −1.10432
\(83\) −4.50000 + 7.79423i −0.493939 + 0.855528i −0.999976 0.00698436i \(-0.997777\pi\)
0.506036 + 0.862512i \(0.331110\pi\)
\(84\) −3.00000 −0.327327
\(85\) −3.00000 −0.325396
\(86\) −4.00000 + 5.19615i −0.431331 + 0.560316i
\(87\) 3.00000 0.321634
\(88\) 0 0
\(89\) 0.500000 0.866025i 0.0529999 0.0917985i −0.838308 0.545197i \(-0.816455\pi\)
0.891308 + 0.453398i \(0.149788\pi\)
\(90\) 2.00000 0.210819
\(91\) 7.50000 12.9904i 0.786214 1.36176i
\(92\) −3.50000 + 6.06218i −0.364900 + 0.632026i
\(93\) −2.50000 4.33013i −0.259238 0.449013i
\(94\) −8.00000 −0.825137
\(95\) 0.500000 + 0.866025i 0.0512989 + 0.0888523i
\(96\) −2.50000 + 4.33013i −0.255155 + 0.441942i
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) −1.00000 + 1.73205i −0.101015 + 0.174964i
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i \(-0.0188862\pi\)
−0.550474 + 0.834853i \(0.685553\pi\)
\(102\) 3.00000 0.297044
\(103\) −3.50000 6.06218i −0.344865 0.597324i 0.640464 0.767988i \(-0.278742\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) −7.50000 12.9904i −0.735436 1.27381i
\(105\) 1.50000 2.59808i 0.146385 0.253546i
\(106\) 2.50000 4.33013i 0.242821 0.420579i
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 5.00000 0.481125
\(109\) −3.50000 + 6.06218i −0.335239 + 0.580651i −0.983531 0.180741i \(-0.942150\pi\)
0.648292 + 0.761392i \(0.275484\pi\)
\(110\) 0 0
\(111\) 4.50000 + 7.79423i 0.427121 + 0.739795i
\(112\) 1.50000 + 2.59808i 0.141737 + 0.245495i
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) −0.500000 0.866025i −0.0468293 0.0811107i
\(115\) −3.50000 6.06218i −0.326377 0.565301i
\(116\) 1.50000 + 2.59808i 0.139272 + 0.241225i
\(117\) −5.00000 + 8.66025i −0.462250 + 0.800641i
\(118\) 12.0000 1.10469
\(119\) −4.50000 + 7.79423i −0.412514 + 0.714496i
\(120\) −1.50000 2.59808i −0.136931 0.237171i
\(121\) −11.0000 −1.00000
\(122\) 6.50000 + 11.2583i 0.588482 + 1.01928i
\(123\) 5.00000 8.66025i 0.450835 0.780869i
\(124\) 2.50000 4.33013i 0.224507 0.388857i
\(125\) 9.00000 0.804984
\(126\) 3.00000 5.19615i 0.267261 0.462910i
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −3.00000 −0.265165
\(129\) −2.50000 6.06218i −0.220113 0.533745i
\(130\) 5.00000 0.438529
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0 0
\(133\) 3.00000 0.260133
\(134\) 1.50000 2.59808i 0.129580 0.224440i
\(135\) −2.50000 + 4.33013i −0.215166 + 0.372678i
\(136\) 4.50000 + 7.79423i 0.385872 + 0.668350i
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 3.50000 + 6.06218i 0.297940 + 0.516047i
\(139\) −6.50000 + 11.2583i −0.551323 + 0.954919i 0.446857 + 0.894606i \(0.352543\pi\)
−0.998179 + 0.0603135i \(0.980790\pi\)
\(140\) 3.00000 0.253546
\(141\) 4.00000 6.92820i 0.336861 0.583460i
\(142\) 0.500000 + 0.866025i 0.0419591 + 0.0726752i
\(143\) 0 0
\(144\) −1.00000 1.73205i −0.0833333 0.144338i
\(145\) −3.00000 −0.249136
\(146\) −5.50000 9.52628i −0.455183 0.788400i
\(147\) −1.00000 1.73205i −0.0824786 0.142857i
\(148\) −4.50000 + 7.79423i −0.369898 + 0.640682i
\(149\) 10.5000 18.1865i 0.860194 1.48990i −0.0115483 0.999933i \(-0.503676\pi\)
0.871742 0.489966i \(-0.162991\pi\)
\(150\) −4.00000 −0.326599
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 1.50000 2.59808i 0.121666 0.210732i
\(153\) 3.00000 5.19615i 0.242536 0.420084i
\(154\) 0 0
\(155\) 2.50000 + 4.33013i 0.200805 + 0.347804i
\(156\) 5.00000 0.400320
\(157\) 0.500000 + 0.866025i 0.0399043 + 0.0691164i 0.885288 0.465044i \(-0.153961\pi\)
−0.845383 + 0.534160i \(0.820628\pi\)
\(158\) 2.50000 + 4.33013i 0.198889 + 0.344486i
\(159\) 2.50000 + 4.33013i 0.198263 + 0.343401i
\(160\) 2.50000 4.33013i 0.197642 0.342327i
\(161\) −21.0000 −1.65503
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) 10.0000 0.780869
\(165\) 0 0
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) 1.50000 2.59808i 0.116073 0.201045i −0.802135 0.597143i \(-0.796303\pi\)
0.918208 + 0.396098i \(0.129636\pi\)
\(168\) −9.00000 −0.694365
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) −3.00000 −0.230089
\(171\) −2.00000 −0.152944
\(172\) 4.00000 5.19615i 0.304997 0.396203i
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 3.00000 0.227429
\(175\) 6.00000 10.3923i 0.453557 0.785584i
\(176\) 0 0
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) 0.500000 0.866025i 0.0374766 0.0649113i
\(179\) 0.500000 + 0.866025i 0.0373718 + 0.0647298i 0.884106 0.467286i \(-0.154768\pi\)
−0.846735 + 0.532016i \(0.821435\pi\)
\(180\) −2.00000 −0.149071
\(181\) −3.50000 6.06218i −0.260153 0.450598i 0.706129 0.708083i \(-0.250440\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 7.50000 12.9904i 0.555937 0.962911i
\(183\) −13.0000 −0.960988
\(184\) −10.5000 + 18.1865i −0.774070 + 1.34073i
\(185\) −4.50000 7.79423i −0.330847 0.573043i
\(186\) −2.50000 4.33013i −0.183309 0.317500i
\(187\) 0 0
\(188\) 8.00000 0.583460
\(189\) 7.50000 + 12.9904i 0.545545 + 0.944911i
\(190\) 0.500000 + 0.866025i 0.0362738 + 0.0628281i
\(191\) 9.50000 16.4545i 0.687396 1.19060i −0.285282 0.958444i \(-0.592087\pi\)
0.972677 0.232161i \(-0.0745796\pi\)
\(192\) −3.50000 + 6.06218i −0.252591 + 0.437500i
\(193\) 6.00000 0.431889 0.215945 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) −2.00000 −0.143592
\(195\) −2.50000 + 4.33013i −0.179029 + 0.310087i
\(196\) 1.00000 1.73205i 0.0714286 0.123718i
\(197\) −5.50000 9.52628i −0.391859 0.678719i 0.600836 0.799372i \(-0.294834\pi\)
−0.992695 + 0.120653i \(0.961501\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −6.00000 10.3923i −0.424264 0.734847i
\(201\) 1.50000 + 2.59808i 0.105802 + 0.183254i
\(202\) 4.50000 + 7.79423i 0.316619 + 0.548400i
\(203\) −4.50000 + 7.79423i −0.315838 + 0.547048i
\(204\) −3.00000 −0.210042
\(205\) −5.00000 + 8.66025i −0.349215 + 0.604858i
\(206\) −3.50000 6.06218i −0.243857 0.422372i
\(207\) 14.0000 0.973067
\(208\) −2.50000 4.33013i −0.173344 0.300240i
\(209\) 0 0
\(210\) 1.50000 2.59808i 0.103510 0.179284i
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) −2.50000 + 4.33013i −0.171701 + 0.297394i
\(213\) −1.00000 −0.0685189
\(214\) 12.0000 0.820303
\(215\) 2.50000 + 6.06218i 0.170499 + 0.413437i
\(216\) 15.0000 1.02062
\(217\) 15.0000 1.01827
\(218\) −3.50000 + 6.06218i −0.237050 + 0.410582i
\(219\) 11.0000 0.743311
\(220\) 0 0
\(221\) 7.50000 12.9904i 0.504505 0.873828i
\(222\) 4.50000 + 7.79423i 0.302020 + 0.523114i
\(223\) 20.0000 1.33930 0.669650 0.742677i \(-0.266444\pi\)
0.669650 + 0.742677i \(0.266444\pi\)
\(224\) −7.50000 12.9904i −0.501115 0.867956i
\(225\) −4.00000 + 6.92820i −0.266667 + 0.461880i
\(226\) −2.00000 −0.133038
\(227\) 3.50000 6.06218i 0.232303 0.402361i −0.726182 0.687502i \(-0.758707\pi\)
0.958485 + 0.285141i \(0.0920405\pi\)
\(228\) 0.500000 + 0.866025i 0.0331133 + 0.0573539i
\(229\) 4.50000 + 7.79423i 0.297368 + 0.515057i 0.975533 0.219853i \(-0.0705577\pi\)
−0.678165 + 0.734910i \(0.737224\pi\)
\(230\) −3.50000 6.06218i −0.230783 0.399728i
\(231\) 0 0
\(232\) 4.50000 + 7.79423i 0.295439 + 0.511716i
\(233\) 4.50000 + 7.79423i 0.294805 + 0.510617i 0.974939 0.222470i \(-0.0714120\pi\)
−0.680135 + 0.733087i \(0.738079\pi\)
\(234\) −5.00000 + 8.66025i −0.326860 + 0.566139i
\(235\) −4.00000 + 6.92820i −0.260931 + 0.451946i
\(236\) −12.0000 −0.781133
\(237\) −5.00000 −0.324785
\(238\) −4.50000 + 7.79423i −0.291692 + 0.505225i
\(239\) −12.5000 + 21.6506i −0.808558 + 1.40046i 0.105305 + 0.994440i \(0.466418\pi\)
−0.913863 + 0.406023i \(0.866915\pi\)
\(240\) −0.500000 0.866025i −0.0322749 0.0559017i
\(241\) −7.50000 12.9904i −0.483117 0.836784i 0.516695 0.856170i \(-0.327162\pi\)
−0.999812 + 0.0193858i \(0.993829\pi\)
\(242\) −11.0000 −0.707107
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) −6.50000 11.2583i −0.416120 0.720741i
\(245\) 1.00000 + 1.73205i 0.0638877 + 0.110657i
\(246\) 5.00000 8.66025i 0.318788 0.552158i
\(247\) −5.00000 −0.318142
\(248\) 7.50000 12.9904i 0.476250 0.824890i
\(249\) −4.50000 7.79423i −0.285176 0.493939i
\(250\) 9.00000 0.569210
\(251\) −3.50000 6.06218i −0.220918 0.382641i 0.734169 0.678967i \(-0.237572\pi\)
−0.955087 + 0.296326i \(0.904239\pi\)
\(252\) −3.00000 + 5.19615i −0.188982 + 0.327327i
\(253\) 0 0
\(254\) 16.0000 1.00393
\(255\) 1.50000 2.59808i 0.0939336 0.162698i
\(256\) −17.0000 −1.06250
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) −2.50000 6.06218i −0.155643 0.377415i
\(259\) −27.0000 −1.67770
\(260\) −5.00000 −0.310087
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) −4.00000 −0.247121
\(263\) −10.5000 + 18.1865i −0.647458 + 1.12143i 0.336270 + 0.941766i \(0.390834\pi\)
−0.983728 + 0.179664i \(0.942499\pi\)
\(264\) 0 0
\(265\) −2.50000 4.33013i −0.153574 0.265998i
\(266\) 3.00000 0.183942
\(267\) 0.500000 + 0.866025i 0.0305995 + 0.0529999i
\(268\) −1.50000 + 2.59808i −0.0916271 + 0.158703i
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) −2.50000 + 4.33013i −0.152145 + 0.263523i
\(271\) −11.5000 19.9186i −0.698575 1.20997i −0.968960 0.247216i \(-0.920484\pi\)
0.270385 0.962752i \(-0.412849\pi\)
\(272\) 1.50000 + 2.59808i 0.0909509 + 0.157532i
\(273\) 7.50000 + 12.9904i 0.453921 + 0.786214i
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) −3.50000 6.06218i −0.210675 0.364900i
\(277\) −3.50000 + 6.06218i −0.210295 + 0.364241i −0.951807 0.306699i \(-0.900776\pi\)
0.741512 + 0.670940i \(0.234109\pi\)
\(278\) −6.50000 + 11.2583i −0.389844 + 0.675230i
\(279\) −10.0000 −0.598684
\(280\) 9.00000 0.537853
\(281\) 8.50000 14.7224i 0.507067 0.878267i −0.492899 0.870087i \(-0.664063\pi\)
0.999967 0.00818015i \(-0.00260385\pi\)
\(282\) 4.00000 6.92820i 0.238197 0.412568i
\(283\) −1.50000 2.59808i −0.0891657 0.154440i 0.817993 0.575228i \(-0.195087\pi\)
−0.907159 + 0.420789i \(0.861753\pi\)
\(284\) −0.500000 0.866025i −0.0296695 0.0513892i
\(285\) −1.00000 −0.0592349
\(286\) 0 0
\(287\) 15.0000 + 25.9808i 0.885422 + 1.53360i
\(288\) 5.00000 + 8.66025i 0.294628 + 0.510310i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) −3.00000 −0.176166
\(291\) 1.00000 1.73205i 0.0586210 0.101535i
\(292\) 5.50000 + 9.52628i 0.321863 + 0.557483i
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) −1.00000 1.73205i −0.0583212 0.101015i
\(295\) 6.00000 10.3923i 0.349334 0.605063i
\(296\) −13.5000 + 23.3827i −0.784672 + 1.35909i
\(297\) 0 0
\(298\) 10.5000 18.1865i 0.608249 1.05352i
\(299\) 35.0000 2.02410
\(300\) 4.00000 0.230940
\(301\) 19.5000 + 2.59808i 1.12396 + 0.149751i
\(302\) −8.00000 −0.460348
\(303\) −9.00000 −0.517036
\(304\) 0.500000 0.866025i 0.0286770 0.0496700i
\(305\) 13.0000 0.744378
\(306\) 3.00000 5.19615i 0.171499 0.297044i
\(307\) −2.50000 + 4.33013i −0.142683 + 0.247133i −0.928506 0.371318i \(-0.878906\pi\)
0.785823 + 0.618451i \(0.212239\pi\)
\(308\) 0 0
\(309\) 7.00000 0.398216
\(310\) 2.50000 + 4.33013i 0.141990 + 0.245935i
\(311\) 1.50000 2.59808i 0.0850572 0.147323i −0.820358 0.571850i \(-0.806226\pi\)
0.905416 + 0.424526i \(0.139559\pi\)
\(312\) 15.0000 0.849208
\(313\) 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i \(-0.673807\pi\)
0.999748 + 0.0224310i \(0.00714060\pi\)
\(314\) 0.500000 + 0.866025i 0.0282166 + 0.0488726i
\(315\) −3.00000 5.19615i −0.169031 0.292770i
\(316\) −2.50000 4.33013i −0.140636 0.243589i
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 2.50000 + 4.33013i 0.140193 + 0.242821i
\(319\) 0 0
\(320\) 3.50000 6.06218i 0.195656 0.338886i
\(321\) −6.00000 + 10.3923i −0.334887 + 0.580042i
\(322\) −21.0000 −1.17028
\(323\) 3.00000 0.166924
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −10.0000 + 17.3205i −0.554700 + 0.960769i
\(326\) 0.500000 + 0.866025i 0.0276924 + 0.0479647i
\(327\) −3.50000 6.06218i −0.193550 0.335239i
\(328\) 30.0000 1.65647
\(329\) 12.0000 + 20.7846i 0.661581 + 1.14589i
\(330\) 0 0
\(331\) −9.50000 16.4545i −0.522167 0.904420i −0.999667 0.0257885i \(-0.991790\pi\)
0.477500 0.878632i \(-0.341543\pi\)
\(332\) 4.50000 7.79423i 0.246970 0.427764i
\(333\) 18.0000 0.986394
\(334\) 1.50000 2.59808i 0.0820763 0.142160i
\(335\) −1.50000 2.59808i −0.0819538 0.141948i
\(336\) −3.00000 −0.163663
\(337\) −1.50000 2.59808i −0.0817102 0.141526i 0.822274 0.569091i \(-0.192705\pi\)
−0.903985 + 0.427565i \(0.859372\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) 1.00000 1.73205i 0.0543125 0.0940721i
\(340\) 3.00000 0.162698
\(341\) 0 0
\(342\) −2.00000 −0.108148
\(343\) −15.0000 −0.809924
\(344\) 12.0000 15.5885i 0.646997 0.840473i
\(345\) 7.00000 0.376867
\(346\) −6.00000 −0.322562
\(347\) −18.5000 + 32.0429i −0.993132 + 1.72016i −0.395242 + 0.918577i \(0.629339\pi\)
−0.597890 + 0.801578i \(0.703994\pi\)
\(348\) −3.00000 −0.160817
\(349\) 0.500000 0.866025i 0.0267644 0.0463573i −0.852333 0.523000i \(-0.824813\pi\)
0.879097 + 0.476642i \(0.158146\pi\)
\(350\) 6.00000 10.3923i 0.320713 0.555492i
\(351\) −12.5000 21.6506i −0.667201 1.15563i
\(352\) 0 0
\(353\) 12.5000 + 21.6506i 0.665308 + 1.15235i 0.979202 + 0.202889i \(0.0650330\pi\)
−0.313894 + 0.949458i \(0.601634\pi\)
\(354\) −6.00000 + 10.3923i −0.318896 + 0.552345i
\(355\) 1.00000 0.0530745
\(356\) −0.500000 + 0.866025i −0.0264999 + 0.0458993i
\(357\) −4.50000 7.79423i −0.238165 0.412514i
\(358\) 0.500000 + 0.866025i 0.0264258 + 0.0457709i
\(359\) −9.50000 16.4545i −0.501391 0.868434i −0.999999 0.00160673i \(-0.999489\pi\)
0.498608 0.866828i \(-0.333845\pi\)
\(360\) −6.00000 −0.316228
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −3.50000 6.06218i −0.183956 0.318621i
\(363\) 5.50000 9.52628i 0.288675 0.500000i
\(364\) −7.50000 + 12.9904i −0.393107 + 0.680881i
\(365\) −11.0000 −0.575766
\(366\) −13.0000 −0.679521
\(367\) −6.50000 + 11.2583i −0.339297 + 0.587680i −0.984301 0.176500i \(-0.943523\pi\)
0.645003 + 0.764180i \(0.276856\pi\)
\(368\) −3.50000 + 6.06218i −0.182450 + 0.316013i
\(369\) −10.0000 17.3205i −0.520579 0.901670i
\(370\) −4.50000 7.79423i −0.233944 0.405203i
\(371\) −15.0000 −0.778761
\(372\) 2.50000 + 4.33013i 0.129619 + 0.224507i
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) 0 0
\(375\) −4.50000 + 7.79423i −0.232379 + 0.402492i
\(376\) 24.0000 1.23771
\(377\) 7.50000 12.9904i 0.386270 0.669039i
\(378\) 7.50000 + 12.9904i 0.385758 + 0.668153i
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) −0.500000 0.866025i −0.0256495 0.0444262i
\(381\) −8.00000 + 13.8564i −0.409852 + 0.709885i
\(382\) 9.50000 16.4545i 0.486062 0.841885i
\(383\) 8.00000 0.408781 0.204390 0.978889i \(-0.434479\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(384\) 1.50000 2.59808i 0.0765466 0.132583i
\(385\) 0 0
\(386\) 6.00000 0.305392
\(387\) −13.0000 1.73205i −0.660827 0.0880451i
\(388\) 2.00000 0.101535
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) −2.50000 + 4.33013i −0.126592 + 0.219265i
\(391\) −21.0000 −1.06202
\(392\) 3.00000 5.19615i 0.151523 0.262445i
\(393\) 2.00000 3.46410i 0.100887 0.174741i
\(394\) −5.50000 9.52628i −0.277086 0.479927i
\(395\) 5.00000 0.251577
\(396\) 0 0
\(397\) 10.5000 18.1865i 0.526980 0.912756i −0.472526 0.881317i \(-0.656658\pi\)
0.999506 0.0314391i \(-0.0100090\pi\)
\(398\) 8.00000 0.401004
\(399\) −1.50000 + 2.59808i −0.0750939 + 0.130066i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 18.5000 + 32.0429i 0.923846 + 1.60015i 0.793407 + 0.608692i \(0.208305\pi\)
0.130439 + 0.991456i \(0.458361\pi\)
\(402\) 1.50000 + 2.59808i 0.0748132 + 0.129580i
\(403\) −25.0000 −1.24534
\(404\) −4.50000 7.79423i −0.223883 0.387777i
\(405\) 0.500000 + 0.866025i 0.0248452 + 0.0430331i
\(406\) −4.50000 + 7.79423i −0.223331 + 0.386821i
\(407\) 0 0
\(408\) −9.00000 −0.445566
\(409\) −18.0000 −0.890043 −0.445021 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) −5.00000 + 8.66025i −0.246932 + 0.427699i
\(411\) 9.00000 15.5885i 0.443937 0.768922i
\(412\) 3.50000 + 6.06218i 0.172433 + 0.298662i
\(413\) −18.0000 31.1769i −0.885722 1.53412i
\(414\) 14.0000 0.688062
\(415\) 4.50000 + 7.79423i 0.220896 + 0.382604i
\(416\) 12.5000 + 21.6506i 0.612863 + 1.06151i
\(417\) −6.50000 11.2583i −0.318306 0.551323i
\(418\) 0 0
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) −1.50000 + 2.59808i −0.0731925 + 0.126773i
\(421\) 18.5000 + 32.0429i 0.901635 + 1.56168i 0.825372 + 0.564590i \(0.190966\pi\)
0.0762630 + 0.997088i \(0.475701\pi\)
\(422\) 8.00000 0.389434
\(423\) −8.00000 13.8564i −0.388973 0.673722i
\(424\) −7.50000 + 12.9904i −0.364232 + 0.630869i
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) −1.00000 −0.0484502
\(427\) 19.5000 33.7750i 0.943671 1.63449i
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 2.50000 + 6.06218i 0.120561 + 0.292344i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 5.00000 0.240563
\(433\) −13.5000 + 23.3827i −0.648769 + 1.12370i 0.334649 + 0.942343i \(0.391382\pi\)
−0.983417 + 0.181357i \(0.941951\pi\)
\(434\) 15.0000 0.720023
\(435\) 1.50000 2.59808i 0.0719195 0.124568i
\(436\) 3.50000 6.06218i 0.167620 0.290326i
\(437\) 3.50000 + 6.06218i 0.167428 + 0.289993i
\(438\) 11.0000 0.525600
\(439\) 6.50000 + 11.2583i 0.310228 + 0.537331i 0.978412 0.206666i \(-0.0662612\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) −4.00000 −0.190476
\(442\) 7.50000 12.9904i 0.356739 0.617889i
\(443\) 18.5000 + 32.0429i 0.878962 + 1.52241i 0.852482 + 0.522757i \(0.175096\pi\)
0.0264796 + 0.999649i \(0.491570\pi\)
\(444\) −4.50000 7.79423i −0.213561 0.369898i
\(445\) −0.500000 0.866025i −0.0237023 0.0410535i
\(446\) 20.0000 0.947027
\(447\) 10.5000 + 18.1865i 0.496633 + 0.860194i
\(448\) −10.5000 18.1865i −0.496078 0.859233i
\(449\) 10.5000 18.1865i 0.495526 0.858276i −0.504461 0.863434i \(-0.668309\pi\)
0.999987 + 0.00515887i \(0.00164213\pi\)
\(450\) −4.00000 + 6.92820i −0.188562 + 0.326599i
\(451\) 0 0
\(452\) 2.00000 0.0940721
\(453\) 4.00000 6.92820i 0.187936 0.325515i
\(454\) 3.50000 6.06218i 0.164263 0.284512i
\(455\) −7.50000 12.9904i −0.351605 0.608998i
\(456\) 1.50000 + 2.59808i 0.0702439 + 0.121666i
\(457\) 6.00000 0.280668 0.140334 0.990104i \(-0.455182\pi\)
0.140334 + 0.990104i \(0.455182\pi\)
\(458\) 4.50000 + 7.79423i 0.210271 + 0.364200i
\(459\) 7.50000 + 12.9904i 0.350070 + 0.606339i
\(460\) 3.50000 + 6.06218i 0.163188 + 0.282650i
\(461\) −1.50000 + 2.59808i −0.0698620 + 0.121004i −0.898840 0.438276i \(-0.855589\pi\)
0.828978 + 0.559281i \(0.188923\pi\)
\(462\) 0 0
\(463\) 11.5000 19.9186i 0.534450 0.925695i −0.464739 0.885448i \(-0.653852\pi\)
0.999190 0.0402476i \(-0.0128147\pi\)
\(464\) 1.50000 + 2.59808i 0.0696358 + 0.120613i
\(465\) −5.00000 −0.231869
\(466\) 4.50000 + 7.79423i 0.208458 + 0.361061i
\(467\) −10.5000 + 18.1865i −0.485882 + 0.841572i −0.999868 0.0162260i \(-0.994835\pi\)
0.513986 + 0.857798i \(0.328168\pi\)
\(468\) 5.00000 8.66025i 0.231125 0.400320i
\(469\) −9.00000 −0.415581
\(470\) −4.00000 + 6.92820i −0.184506 + 0.319574i
\(471\) −1.00000 −0.0460776
\(472\) −36.0000 −1.65703
\(473\) 0 0
\(474\) −5.00000 −0.229658
\(475\) −4.00000 −0.183533
\(476\) 4.50000 7.79423i 0.206257 0.357248i
\(477\) 10.0000 0.457869
\(478\) −12.5000 + 21.6506i −0.571737 + 0.990277i
\(479\) 7.50000 12.9904i 0.342684 0.593546i −0.642246 0.766498i \(-0.721997\pi\)
0.984930 + 0.172953i \(0.0553307\pi\)
\(480\) 2.50000 + 4.33013i 0.114109 + 0.197642i
\(481\) 45.0000 2.05182
\(482\) −7.50000 12.9904i −0.341616 0.591696i
\(483\) 10.5000 18.1865i 0.477767 0.827516i
\(484\) 11.0000 0.500000
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) −8.00000 13.8564i −0.362887 0.628539i
\(487\) 4.50000 + 7.79423i 0.203914 + 0.353190i 0.949786 0.312899i \(-0.101300\pi\)
−0.745872 + 0.666089i \(0.767967\pi\)
\(488\) −19.5000 33.7750i −0.882724 1.52892i
\(489\) −1.00000 −0.0452216
\(490\) 1.00000 + 1.73205i 0.0451754 + 0.0782461i
\(491\) 4.50000 + 7.79423i 0.203082 + 0.351749i 0.949520 0.313707i \(-0.101571\pi\)
−0.746438 + 0.665455i \(0.768237\pi\)
\(492\) −5.00000 + 8.66025i −0.225417 + 0.390434i
\(493\) −4.50000 + 7.79423i −0.202670 + 0.351034i
\(494\) −5.00000 −0.224961
\(495\) 0 0
\(496\) 2.50000 4.33013i 0.112253 0.194428i
\(497\) 1.50000 2.59808i 0.0672842 0.116540i
\(498\) −4.50000 7.79423i −0.201650 0.349268i
\(499\) 8.50000 + 14.7224i 0.380512 + 0.659067i 0.991136 0.132855i \(-0.0424144\pi\)
−0.610623 + 0.791921i \(0.709081\pi\)
\(500\) −9.00000 −0.402492
\(501\) 1.50000 + 2.59808i 0.0670151 + 0.116073i
\(502\) −3.50000 6.06218i −0.156213 0.270568i
\(503\) 4.50000 + 7.79423i 0.200645 + 0.347527i 0.948736 0.316068i \(-0.102363\pi\)
−0.748091 + 0.663596i \(0.769030\pi\)
\(504\) −9.00000 + 15.5885i −0.400892 + 0.694365i
\(505\) 9.00000 0.400495
\(506\) 0 0
\(507\) −6.00000 10.3923i −0.266469 0.461538i
\(508\) −16.0000 −0.709885
\(509\) −13.5000 23.3827i −0.598377 1.03642i −0.993061 0.117602i \(-0.962479\pi\)
0.394684 0.918817i \(-0.370854\pi\)
\(510\) 1.50000 2.59808i 0.0664211 0.115045i
\(511\) −16.5000 + 28.5788i −0.729917 + 1.26425i
\(512\) −11.0000 −0.486136
\(513\) 2.50000 4.33013i 0.110378 0.191180i
\(514\) 6.00000 0.264649
\(515\) −7.00000 −0.308457
\(516\) 2.50000 + 6.06218i 0.110056 + 0.266872i
\(517\) 0 0
\(518\) −27.0000 −1.18631
\(519\) 3.00000 5.19615i 0.131685 0.228086i
\(520\) −15.0000 −0.657794
\(521\) −17.5000 + 30.3109i −0.766689 + 1.32794i 0.172660 + 0.984981i \(0.444764\pi\)
−0.939349 + 0.342963i \(0.888570\pi\)
\(522\) 3.00000 5.19615i 0.131306 0.227429i
\(523\) 10.5000 + 18.1865i 0.459133 + 0.795242i 0.998915 0.0465630i \(-0.0148268\pi\)
−0.539782 + 0.841805i \(0.681493\pi\)
\(524\) 4.00000 0.174741
\(525\) 6.00000 + 10.3923i 0.261861 + 0.453557i
\(526\) −10.5000 + 18.1865i −0.457822 + 0.792971i
\(527\) 15.0000 0.653410
\(528\) 0 0
\(529\) −13.0000 22.5167i −0.565217 0.978985i
\(530\) −2.50000 4.33013i −0.108593 0.188089i
\(531\) 12.0000 + 20.7846i 0.520756 + 0.901975i
\(532\) −3.00000 −0.130066
\(533\) −25.0000 43.3013i −1.08287 1.87559i
\(534\) 0.500000 + 0.866025i 0.0216371 + 0.0374766i
\(535\) 6.00000 10.3923i 0.259403 0.449299i
\(536\) −4.50000 + 7.79423i −0.194370 + 0.336659i
\(537\) −1.00000 −0.0431532
\(538\) 14.0000 0.603583
\(539\) 0 0
\(540\) 2.50000 4.33013i 0.107583 0.186339i
\(541\) −15.5000 26.8468i −0.666397 1.15423i −0.978905 0.204318i \(-0.934502\pi\)
0.312507 0.949915i \(-0.398831\pi\)
\(542\) −11.5000 19.9186i −0.493967 0.855576i
\(543\) 7.00000 0.300399
\(544\) −7.50000 12.9904i −0.321560 0.556958i
\(545\) 3.50000 + 6.06218i 0.149924 + 0.259675i
\(546\) 7.50000 + 12.9904i 0.320970 + 0.555937i
\(547\) −0.500000 + 0.866025i −0.0213785 + 0.0370286i −0.876517 0.481371i \(-0.840139\pi\)
0.855138 + 0.518400i \(0.173472\pi\)
\(548\) 18.0000 0.768922
\(549\) −13.0000 + 22.5167i −0.554826 + 0.960988i
\(550\) 0 0
\(551\) 3.00000 0.127804
\(552\) −10.5000 18.1865i −0.446910 0.774070i
\(553\) 7.50000 12.9904i 0.318932 0.552407i
\(554\) −3.50000 + 6.06218i −0.148701 + 0.257557i
\(555\) 9.00000 0.382029
\(556\) 6.50000 11.2583i 0.275661 0.477460i
\(557\) −6.00000 −0.254228 −0.127114 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(558\) −10.0000 −0.423334
\(559\) −32.5000 4.33013i −1.37460 0.183145i
\(560\) 3.00000 0.126773
\(561\) 0 0
\(562\) 8.50000 14.7224i 0.358551 0.621028i
\(563\) 4.00000 0.168580 0.0842900 0.996441i \(-0.473138\pi\)
0.0842900 + 0.996441i \(0.473138\pi\)
\(564\) −4.00000 + 6.92820i −0.168430 + 0.291730i
\(565\) −1.00000 + 1.73205i −0.0420703 + 0.0728679i
\(566\) −1.50000 2.59808i −0.0630497 0.109205i
\(567\) 3.00000 0.125988
\(568\) −1.50000 2.59808i −0.0629386 0.109013i
\(569\) 8.50000 14.7224i 0.356339 0.617196i −0.631008 0.775777i \(-0.717358\pi\)
0.987346 + 0.158580i \(0.0506917\pi\)
\(570\) −1.00000 −0.0418854
\(571\) −6.50000 + 11.2583i −0.272017 + 0.471146i −0.969378 0.245573i \(-0.921024\pi\)
0.697362 + 0.716720i \(0.254357\pi\)
\(572\) 0 0
\(573\) 9.50000 + 16.4545i 0.396868 + 0.687396i
\(574\) 15.0000 + 25.9808i 0.626088 + 1.08442i
\(575\) 28.0000 1.16768
\(576\) 7.00000 + 12.1244i 0.291667 + 0.505181i
\(577\) 2.50000 + 4.33013i 0.104076 + 0.180266i 0.913360 0.407152i \(-0.133478\pi\)
−0.809284 + 0.587417i \(0.800145\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) −3.00000 + 5.19615i −0.124676 + 0.215945i
\(580\) 3.00000 0.124568
\(581\) 27.0000 1.12015
\(582\) 1.00000 1.73205i 0.0414513 0.0717958i
\(583\) 0 0
\(584\) 16.5000 + 28.5788i 0.682775 + 1.18260i
\(585\) 5.00000 + 8.66025i 0.206725 + 0.358057i
\(586\) −14.0000 −0.578335
\(587\) 6.50000 + 11.2583i 0.268284 + 0.464681i 0.968419 0.249329i \(-0.0802102\pi\)
−0.700135 + 0.714010i \(0.746877\pi\)
\(588\) 1.00000 + 1.73205i 0.0412393 + 0.0714286i
\(589\) −2.50000 4.33013i −0.103011 0.178420i
\(590\) 6.00000 10.3923i 0.247016 0.427844i
\(591\) 11.0000 0.452480
\(592\) −4.50000 + 7.79423i −0.184949 + 0.320341i
\(593\) 0.500000 + 0.866025i 0.0205325 + 0.0355634i 0.876109 0.482113i \(-0.160130\pi\)
−0.855577 + 0.517676i \(0.826797\pi\)
\(594\) 0 0
\(595\) 4.50000 + 7.79423i 0.184482 + 0.319532i
\(596\) −10.5000 + 18.1865i −0.430097 + 0.744949i
\(597\) −4.00000 + 6.92820i −0.163709 + 0.283552i
\(598\) 35.0000 1.43126
\(599\) 15.5000 26.8468i 0.633313 1.09693i −0.353557 0.935413i \(-0.615028\pi\)
0.986870 0.161517i \(-0.0516387\pi\)
\(600\) 12.0000 0.489898
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 19.5000 + 2.59808i 0.794761 + 0.105890i
\(603\) 6.00000 0.244339
\(604\) 8.00000 0.325515
\(605\) −5.50000 + 9.52628i −0.223607 + 0.387298i
\(606\) −9.00000 −0.365600
\(607\) 21.5000 37.2391i 0.872658 1.51149i 0.0134214 0.999910i \(-0.495728\pi\)
0.859237 0.511578i \(-0.170939\pi\)
\(608\) −2.50000 + 4.33013i −0.101388 + 0.175610i
\(609\) −4.50000 7.79423i −0.182349 0.315838i
\(610\) 13.0000 0.526355
\(611\) −20.0000 34.6410i −0.809113 1.40143i
\(612\) −3.00000 + 5.19615i −0.121268 + 0.210042i
\(613\) −30.0000 −1.21169 −0.605844 0.795583i \(-0.707165\pi\)
−0.605844 + 0.795583i \(0.707165\pi\)
\(614\) −2.50000 + 4.33013i −0.100892 + 0.174750i
\(615\) −5.00000 8.66025i −0.201619 0.349215i
\(616\) 0 0
\(617\) −1.50000 2.59808i −0.0603877 0.104595i 0.834251 0.551385i \(-0.185900\pi\)
−0.894639 + 0.446790i \(0.852567\pi\)
\(618\) 7.00000 0.281581
\(619\) 10.5000 + 18.1865i 0.422031 + 0.730978i 0.996138 0.0878015i \(-0.0279841\pi\)
−0.574107 + 0.818780i \(0.694651\pi\)
\(620\) −2.50000 4.33013i −0.100402 0.173902i
\(621\) −17.5000 + 30.3109i −0.702251 + 1.21633i
\(622\) 1.50000 2.59808i 0.0601445 0.104173i
\(623\) −3.00000 −0.120192
\(624\) 5.00000 0.200160
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 8.50000 14.7224i 0.339728 0.588427i
\(627\) 0 0
\(628\) −0.500000 0.866025i −0.0199522 0.0345582i
\(629\) −27.0000 −1.07656
\(630\) −3.00000 5.19615i −0.119523 0.207020i
\(631\) 4.50000 + 7.79423i 0.179142 + 0.310283i 0.941587 0.336770i \(-0.109334\pi\)
−0.762445 + 0.647053i \(0.776001\pi\)
\(632\) −7.50000 12.9904i −0.298334 0.516730i
\(633\) −4.00000 + 6.92820i −0.158986 + 0.275371i
\(634\) −18.0000 −0.714871
\(635\) 8.00000 13.8564i 0.317470 0.549875i
\(636\) −2.50000 4.33013i −0.0991314 0.171701i
\(637\) −10.0000 −0.396214
\(638\) 0 0
\(639\) −1.00000 + 1.73205i −0.0395594 + 0.0685189i
\(640\) −1.50000 + 2.59808i −0.0592927 + 0.102698i
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) −6.00000 + 10.3923i −0.236801 + 0.410152i
\(643\) 12.0000 0.473234 0.236617 0.971603i \(-0.423961\pi\)
0.236617 + 0.971603i \(0.423961\pi\)
\(644\) 21.0000 0.827516
\(645\) −6.50000 0.866025i −0.255937 0.0340997i
\(646\) 3.00000 0.118033
\(647\) −12.0000 −0.471769 −0.235884 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) 1.50000 2.59808i 0.0589256 0.102062i
\(649\) 0 0
\(650\) −10.0000 + 17.3205i −0.392232 + 0.679366i
\(651\) −7.50000 + 12.9904i −0.293948 + 0.509133i
\(652\) −0.500000 0.866025i −0.0195815 0.0339162i
\(653\) −50.0000 −1.95665 −0.978326 0.207072i \(-0.933606\pi\)
−0.978326 + 0.207072i \(0.933606\pi\)
\(654\) −3.50000 6.06218i −0.136861 0.237050i
\(655\) −2.00000 + 3.46410i −0.0781465 + 0.135354i
\(656\) 10.0000 0.390434
\(657\) 11.0000 19.0526i 0.429151 0.743311i
\(658\) 12.0000 + 20.7846i 0.467809 + 0.810268i
\(659\) −11.5000 19.9186i −0.447976 0.775918i 0.550278 0.834982i \(-0.314522\pi\)
−0.998254 + 0.0590638i \(0.981188\pi\)
\(660\) 0 0
\(661\) −14.0000 −0.544537 −0.272268 0.962221i \(-0.587774\pi\)
−0.272268 + 0.962221i \(0.587774\pi\)
\(662\) −9.50000 16.4545i −0.369228 0.639522i
\(663\) 7.50000 + 12.9904i 0.291276 + 0.504505i
\(664\) 13.5000 23.3827i 0.523902 0.907424i
\(665\) 1.50000 2.59808i 0.0581675 0.100749i
\(666\) 18.0000 0.697486
\(667\) −21.0000 −0.813123
\(668\) −1.50000 + 2.59808i −0.0580367 + 0.100523i
\(669\) −10.0000 + 17.3205i −0.386622 + 0.669650i
\(670\) −1.50000 2.59808i −0.0579501 0.100372i
\(671\) 0 0
\(672\) 15.0000 0.578638
\(673\) −23.5000 40.7032i −0.905858 1.56899i −0.819761 0.572706i \(-0.805894\pi\)
−0.0860977 0.996287i \(-0.527440\pi\)
\(674\) −1.50000 2.59808i −0.0577778 0.100074i
\(675\) −10.0000 17.3205i −0.384900 0.666667i
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) −14.0000 −0.538064 −0.269032 0.963131i \(-0.586704\pi\)
−0.269032 + 0.963131i \(0.586704\pi\)
\(678\) 1.00000 1.73205i 0.0384048 0.0665190i
\(679\) 3.00000 + 5.19615i 0.115129 + 0.199410i
\(680\) 9.00000 0.345134
\(681\) 3.50000 + 6.06218i 0.134120 + 0.232303i
\(682\) 0 0
\(683\) −4.50000 + 7.79423i −0.172188 + 0.298238i −0.939184 0.343413i \(-0.888417\pi\)
0.766997 + 0.641651i \(0.221750\pi\)
\(684\) 2.00000 0.0764719
\(685\) −9.00000 + 15.5885i −0.343872 + 0.595604i
\(686\) −15.0000 −0.572703
\(687\) −9.00000 −0.343371
\(688\) 4.00000 5.19615i 0.152499 0.198101i
\(689\) 25.0000 0.952424
\(690\) 7.00000 0.266485
\(691\) −2.50000 + 4.33013i −0.0951045 + 0.164726i −0.909652 0.415371i \(-0.863652\pi\)
0.814548 + 0.580097i \(0.196985\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −18.5000 + 32.0429i −0.702250 + 1.21633i
\(695\) 6.50000 + 11.2583i 0.246559 + 0.427053i
\(696\) −9.00000 −0.341144
\(697\) 15.0000 + 25.9808i 0.568166 + 0.984092i
\(698\) 0.500000 0.866025i 0.0189253 0.0327795i
\(699\) −9.00000 −0.340411
\(700\) −6.00000 + 10.3923i −0.226779 + 0.392792i
\(701\) −3.50000 6.06218i −0.132193 0.228965i 0.792329 0.610095i \(-0.208869\pi\)
−0.924522 + 0.381129i \(0.875535\pi\)
\(702\) −12.5000 21.6506i −0.471782 0.817151i
\(703\) 4.50000 + 7.79423i 0.169721 + 0.293965i
\(704\) 0 0
\(705\) −4.00000 6.92820i −0.150649 0.260931i
\(706\) 12.5000 + 21.6506i 0.470444 + 0.814832i
\(707\) 13.5000 23.3827i 0.507720 0.879396i
\(708\) 6.00000 10.3923i 0.225494 0.390567i
\(709\) 26.0000 0.976450 0.488225 0.872718i \(-0.337644\pi\)
0.488225 + 0.872718i \(0.337644\pi\)
\(710\) 1.00000 0.0375293
\(711\) −5.00000 + 8.66025i −0.187515 + 0.324785i
\(712\) −1.50000 + 2.59808i −0.0562149 + 0.0973670i
\(713\) 17.5000 + 30.3109i 0.655380 + 1.13515i
\(714\) −4.50000 7.79423i −0.168408 0.291692i
\(715\) 0 0
\(716\) −0.500000 0.866025i −0.0186859 0.0323649i
\(717\) −12.5000 21.6506i −0.466821 0.808558i
\(718\) −9.50000 16.4545i −0.354537 0.614076i
\(719\) 15.5000 26.8468i 0.578052 1.00122i −0.417650 0.908608i \(-0.637146\pi\)
0.995703 0.0926083i \(-0.0295204\pi\)
\(720\) −2.00000 −0.0745356
\(721\) −10.5000 + 18.1865i −0.391040 + 0.677302i
\(722\) 9.00000 + 15.5885i 0.334945 + 0.580142i
\(723\) 15.0000 0.557856
\(724\) 3.50000 + 6.06218i 0.130076 + 0.225299i
\(725\) 6.00000 10.3923i 0.222834 0.385961i
\(726\) 5.50000 9.52628i 0.204124 0.353553i
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) −22.5000 + 38.9711i −0.833905 + 1.44437i
\(729\) 13.0000 0.481481
\(730\) −11.0000 −0.407128
\(731\) 19.5000 + 2.59808i 0.721234 + 0.0960933i
\(732\) 13.0000 0.480494
\(733\) 26.0000 0.960332 0.480166 0.877178i \(-0.340576\pi\)
0.480166 + 0.877178i \(0.340576\pi\)
\(734\) −6.50000 + 11.2583i −0.239919 + 0.415553i
\(735\) −2.00000 −0.0737711
\(736\) 17.5000 30.3109i 0.645059 1.11727i
\(737\) 0 0
\(738\) −10.0000 17.3205i −0.368105 0.637577i
\(739\) −4.00000 −0.147142 −0.0735712 0.997290i \(-0.523440\pi\)
−0.0735712 + 0.997290i \(0.523440\pi\)
\(740\) 4.50000 + 7.79423i 0.165423 + 0.286522i
\(741\) 2.50000 4.33013i 0.0918398 0.159071i
\(742\) −15.0000 −0.550667
\(743\) −10.5000 + 18.1865i −0.385208 + 0.667199i −0.991798 0.127815i \(-0.959204\pi\)
0.606590 + 0.795015i \(0.292537\pi\)
\(744\) 7.50000 + 12.9904i 0.274963 + 0.476250i
\(745\) −10.5000 18.1865i −0.384690 0.666303i
\(746\) −5.50000 9.52628i −0.201369 0.348782i
\(747\) −18.0000 −0.658586
\(748\) 0 0
\(749\) −18.0000 31.1769i −0.657706 1.13918i
\(750\) −4.50000 + 7.79423i −0.164317 + 0.284605i
\(751\) 13.5000 23.3827i 0.492622 0.853246i −0.507342 0.861745i \(-0.669372\pi\)
0.999964 + 0.00849853i \(0.00270520\pi\)
\(752\) 8.00000 0.291730
\(753\) 7.00000 0.255094
\(754\) 7.50000 12.9904i 0.273134 0.473082i
\(755\) −4.00000 + 6.92820i −0.145575 + 0.252143i
\(756\) −7.50000 12.9904i −0.272772 0.472456i
\(757\) 2.50000 + 4.33013i 0.0908640 + 0.157381i 0.907875 0.419241i \(-0.137704\pi\)
−0.817011 + 0.576622i \(0.804370\pi\)
\(758\) 20.0000 0.726433
\(759\) 0 0
\(760\) −1.50000 2.59808i −0.0544107 0.0942421i
\(761\) 18.5000 + 32.0429i 0.670624 + 1.16156i 0.977727 + 0.209879i \(0.0673071\pi\)
−0.307103 + 0.951676i \(0.599360\pi\)
\(762\) −8.00000 + 13.8564i −0.289809 + 0.501965i
\(763\) 21.0000 0.760251
\(764\) −9.50000 + 16.4545i −0.343698 + 0.595302i
\(765\) −3.00000 5.19615i −0.108465 0.187867i
\(766\) 8.00000 0.289052
\(767\) 30.0000 + 51.9615i 1.08324 + 1.87622i
\(768\) 8.50000 14.7224i 0.306717 0.531250i
\(769\) 16.5000 28.5788i 0.595005 1.03058i −0.398541 0.917151i \(-0.630483\pi\)
0.993546 0.113429i \(-0.0361834\pi\)
\(770\) 0 0
\(771\) −3.00000 + 5.19615i −0.108042 + 0.187135i
\(772\) −6.00000 −0.215945
\(773\) 26.0000 0.935155 0.467578 0.883952i \(-0.345127\pi\)
0.467578 + 0.883952i \(0.345127\pi\)
\(774\) −13.0000 1.73205i −0.467275 0.0622573i
\(775\) −20.0000 −0.718421
\(776\) 6.00000 0.215387
\(777\) 13.5000 23.3827i 0.484310 0.838849i
\(778\) −6.00000 −0.215110
\(779\) 5.00000 8.66025i 0.179144 0.310286i
\(780\) 2.50000 4.33013i 0.0895144 0.155043i
\(781\) 0 0
\(782\) −21.0000 −0.750958
\(783\) 7.50000 + 12.9904i 0.268028 + 0.464238i
\(784\) 1.00000 1.73205i 0.0357143 0.0618590i
\(785\) 1.00000 0.0356915
\(786\) 2.00000 3.46410i 0.0713376 0.123560i
\(787\) 2.50000 + 4.33013i 0.0891154 + 0.154352i 0.907137 0.420834i \(-0.138263\pi\)
−0.818022 + 0.575187i \(0.804929\pi\)
\(788\) 5.50000 + 9.52628i 0.195929 + 0.339360i
\(789\) −10.5000 18.1865i −0.373810 0.647458i
\(790\) 5.00000 0.177892
\(791\) 3.00000 + 5.19615i 0.106668 + 0.184754i
\(792\) 0 0
\(793\) −32.5000 + 56.2917i −1.15411 + 1.99898i
\(794\) 10.5000 18.1865i 0.372631 0.645416i