Properties

Label 78.2.e.a.55.1
Level $78$
Weight $2$
Character 78.55
Analytic conductor $0.623$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 78.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.622833135766\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 78.55
Dual form 78.2.e.a.61.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-3.00000 - 5.19615i) q^{11} +1.00000 q^{12} +(-3.50000 + 0.866025i) q^{13} -2.00000 q^{14} +(-1.50000 - 2.59808i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} -1.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +(-1.50000 + 2.59808i) q^{20} +2.00000 q^{21} +(3.00000 - 5.19615i) q^{22} +(3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +4.00000 q^{25} +(-2.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(1.50000 - 2.59808i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +3.00000 q^{34} +(-3.00000 + 5.19615i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.50000 + 6.06218i) q^{37} -2.00000 q^{38} +(2.50000 + 2.59808i) q^{39} -3.00000 q^{40} +(1.50000 + 2.59808i) q^{41} +(1.00000 + 1.73205i) q^{42} +(5.00000 - 8.66025i) q^{43} +6.00000 q^{44} +(-1.50000 + 2.59808i) q^{45} +(-3.00000 + 5.19615i) q^{46} +6.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} -3.00000 q^{51} +(1.00000 - 3.46410i) q^{52} +3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-9.00000 - 15.5885i) q^{55} +(1.00000 - 1.73205i) q^{56} +2.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +3.00000 q^{60} +(3.50000 - 6.06218i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-10.5000 + 2.59808i) q^{65} -6.00000 q^{66} +(5.00000 + 8.66025i) q^{67} +(1.50000 + 2.59808i) q^{68} +(3.00000 - 5.19615i) q^{69} -6.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(0.500000 - 0.866025i) q^{72} -13.0000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(-1.00000 - 1.73205i) q^{76} +12.0000 q^{77} +(-1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{82} -6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(4.50000 - 7.79423i) q^{85} +10.0000 q^{86} +(-1.50000 + 2.59808i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-9.00000 - 15.5885i) q^{89} -3.00000 q^{90} +(2.00000 - 6.92820i) q^{91} -6.00000 q^{92} +(2.00000 + 3.46410i) q^{93} +(3.00000 + 5.19615i) q^{94} +(-3.00000 + 5.19615i) q^{95} -1.00000 q^{96} +(-7.00000 + 12.1244i) q^{97} +(-1.50000 + 2.59808i) q^{98} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} + 6 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{3} - q^{4} + 6 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - q^{9} + 3 q^{10} - 6 q^{11} + 2 q^{12} - 7 q^{13} - 4 q^{14} - 3 q^{15} - q^{16} + 3 q^{17} - 2 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} + 6 q^{22} + 6 q^{23} + q^{24} + 8 q^{25} - 5 q^{26} + 2 q^{27} - 2 q^{28} - 3 q^{29} + 3 q^{30} - 8 q^{31} + q^{32} - 6 q^{33} + 6 q^{34} - 6 q^{35} - q^{36} + 7 q^{37} - 4 q^{38} + 5 q^{39} - 6 q^{40} + 3 q^{41} + 2 q^{42} + 10 q^{43} + 12 q^{44} - 3 q^{45} - 6 q^{46} + 12 q^{47} - q^{48} + 3 q^{49} + 4 q^{50} - 6 q^{51} + 2 q^{52} + 6 q^{53} + q^{54} - 18 q^{55} + 2 q^{56} + 4 q^{57} + 3 q^{58} + 6 q^{60} + 7 q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} - 21 q^{65} - 12 q^{66} + 10 q^{67} + 3 q^{68} + 6 q^{69} - 12 q^{70} - 6 q^{71} + q^{72} - 26 q^{73} - 7 q^{74} - 4 q^{75} - 2 q^{76} + 24 q^{77} - 2 q^{78} - 8 q^{79} - 3 q^{80} - q^{81} - 3 q^{82} - 12 q^{83} - 2 q^{84} + 9 q^{85} + 20 q^{86} - 3 q^{87} + 6 q^{88} - 18 q^{89} - 6 q^{90} + 4 q^{91} - 12 q^{92} + 4 q^{93} + 6 q^{94} - 6 q^{95} - 2 q^{96} - 14 q^{97} - 3 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.50000 + 2.59808i 0.474342 + 0.821584i
\(11\) −3.00000 5.19615i −0.904534 1.56670i −0.821541 0.570149i \(-0.806886\pi\)
−0.0829925 0.996550i \(-0.526448\pi\)
\(12\) 1.00000 0.288675
\(13\) −3.50000 + 0.866025i −0.970725 + 0.240192i
\(14\) −2.00000 −0.534522
\(15\) −1.50000 2.59808i −0.387298 0.670820i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) 2.00000 0.436436
\(22\) 3.00000 5.19615i 0.639602 1.10782i
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 4.00000 0.800000
\(26\) −2.50000 2.59808i −0.490290 0.509525i
\(27\) 1.00000 0.192450
\(28\) −1.00000 1.73205i −0.188982 0.327327i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 1.50000 2.59808i 0.273861 0.474342i
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −3.00000 + 5.19615i −0.522233 + 0.904534i
\(34\) 3.00000 0.514496
\(35\) −3.00000 + 5.19615i −0.507093 + 0.878310i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) −2.00000 −0.324443
\(39\) 2.50000 + 2.59808i 0.400320 + 0.416025i
\(40\) −3.00000 −0.474342
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 1.00000 + 1.73205i 0.154303 + 0.267261i
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) 6.00000 0.904534
\(45\) −1.50000 + 2.59808i −0.223607 + 0.387298i
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) −3.00000 −0.420084
\(52\) 1.00000 3.46410i 0.138675 0.480384i
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −9.00000 15.5885i −1.21356 2.10195i
\(56\) 1.00000 1.73205i 0.133631 0.231455i
\(57\) 2.00000 0.264906
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 3.00000 0.387298
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) −2.00000 3.46410i −0.254000 0.439941i
\(63\) −1.00000 1.73205i −0.125988 0.218218i
\(64\) 1.00000 0.125000
\(65\) −10.5000 + 2.59808i −1.30236 + 0.322252i
\(66\) −6.00000 −0.738549
\(67\) 5.00000 + 8.66025i 0.610847 + 1.05802i 0.991098 + 0.133135i \(0.0425044\pi\)
−0.380251 + 0.924883i \(0.624162\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) 3.00000 5.19615i 0.361158 0.625543i
\(70\) −6.00000 −0.717137
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −13.0000 −1.52153 −0.760767 0.649025i \(-0.775177\pi\)
−0.760767 + 0.649025i \(0.775177\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) 12.0000 1.36753
\(78\) −1.00000 + 3.46410i −0.113228 + 0.392232i
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) −1.50000 2.59808i −0.167705 0.290474i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.50000 + 2.59808i −0.165647 + 0.286910i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −1.00000 + 1.73205i −0.109109 + 0.188982i
\(85\) 4.50000 7.79423i 0.488094 0.845403i
\(86\) 10.0000 1.07833
\(87\) −1.50000 + 2.59808i −0.160817 + 0.278543i
\(88\) 3.00000 + 5.19615i 0.319801 + 0.553912i
\(89\) −9.00000 15.5885i −0.953998 1.65237i −0.736644 0.676280i \(-0.763591\pi\)
−0.217354 0.976093i \(-0.569742\pi\)
\(90\) −3.00000 −0.316228
\(91\) 2.00000 6.92820i 0.209657 0.726273i
\(92\) −6.00000 −0.625543
\(93\) 2.00000 + 3.46410i 0.207390 + 0.359211i
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) −1.00000 −0.102062
\(97\) −7.00000 + 12.1244i −0.710742 + 1.23104i 0.253837 + 0.967247i \(0.418307\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) −1.50000 + 2.59808i −0.151523 + 0.262445i
\(99\) 6.00000 0.603023
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) −1.50000 2.59808i −0.148522 0.257248i
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 3.50000 0.866025i 0.343203 0.0849208i
\(105\) 6.00000 0.585540
\(106\) 1.50000 + 2.59808i 0.145693 + 0.252347i
\(107\) 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 9.00000 15.5885i 0.858116 1.48630i
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) 2.00000 0.188982
\(113\) 1.50000 2.59808i 0.141108 0.244406i −0.786806 0.617200i \(-0.788267\pi\)
0.927914 + 0.372794i \(0.121600\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) 9.00000 + 15.5885i 0.839254 + 1.45363i
\(116\) 3.00000 0.278543
\(117\) 1.00000 3.46410i 0.0924500 0.320256i
\(118\) 0 0
\(119\) 3.00000 + 5.19615i 0.275010 + 0.476331i
\(120\) 1.50000 + 2.59808i 0.136931 + 0.237171i
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) 7.00000 0.633750
\(123\) 1.50000 2.59808i 0.135250 0.234261i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) −3.00000 −0.268328
\(126\) 1.00000 1.73205i 0.0890871 0.154303i
\(127\) 2.00000 + 3.46410i 0.177471 + 0.307389i 0.941014 0.338368i \(-0.109875\pi\)
−0.763542 + 0.645758i \(0.776542\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −10.0000 −0.880451
\(130\) −7.50000 7.79423i −0.657794 0.683599i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) −3.00000 5.19615i −0.261116 0.452267i
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) −5.00000 + 8.66025i −0.431934 + 0.748132i
\(135\) 3.00000 0.258199
\(136\) −1.50000 + 2.59808i −0.128624 + 0.222783i
\(137\) −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i \(-0.958946\pi\)
0.607233 + 0.794524i \(0.292279\pi\)
\(138\) 6.00000 0.510754
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) −3.00000 5.19615i −0.253546 0.439155i
\(141\) −3.00000 5.19615i −0.252646 0.437595i
\(142\) −6.00000 −0.503509
\(143\) 15.0000 + 15.5885i 1.25436 + 1.30357i
\(144\) 1.00000 0.0833333
\(145\) −4.50000 7.79423i −0.373705 0.647275i
\(146\) −6.50000 11.2583i −0.537944 0.931746i
\(147\) 1.50000 2.59808i 0.123718 0.214286i
\(148\) −7.00000 −0.575396
\(149\) 4.50000 7.79423i 0.368654 0.638528i −0.620701 0.784047i \(-0.713152\pi\)
0.989355 + 0.145519i \(0.0464853\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 1.00000 1.73205i 0.0811107 0.140488i
\(153\) 1.50000 + 2.59808i 0.121268 + 0.210042i
\(154\) 6.00000 + 10.3923i 0.483494 + 0.837436i
\(155\) −12.0000 −0.963863
\(156\) −3.50000 + 0.866025i −0.280224 + 0.0693375i
\(157\) 5.00000 0.399043 0.199522 0.979893i \(-0.436061\pi\)
0.199522 + 0.979893i \(0.436061\pi\)
\(158\) −2.00000 3.46410i −0.159111 0.275589i
\(159\) −1.50000 2.59808i −0.118958 0.206041i
\(160\) 1.50000 2.59808i 0.118585 0.205396i
\(161\) −12.0000 −0.945732
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) −3.00000 −0.234261
\(165\) −9.00000 + 15.5885i −0.700649 + 1.21356i
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) −2.00000 −0.154303
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) 9.00000 0.690268
\(171\) −1.00000 1.73205i −0.0764719 0.132453i
\(172\) 5.00000 + 8.66025i 0.381246 + 0.660338i
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) −3.00000 −0.227429
\(175\) −4.00000 + 6.92820i −0.302372 + 0.523723i
\(176\) −3.00000 + 5.19615i −0.226134 + 0.391675i
\(177\) 0 0
\(178\) 9.00000 15.5885i 0.674579 1.16840i
\(179\) −3.00000 5.19615i −0.224231 0.388379i 0.731858 0.681457i \(-0.238654\pi\)
−0.956088 + 0.293079i \(0.905320\pi\)
\(180\) −1.50000 2.59808i −0.111803 0.193649i
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 7.00000 1.73205i 0.518875 0.128388i
\(183\) −7.00000 −0.517455
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) 10.5000 + 18.1865i 0.771975 + 1.33710i
\(186\) −2.00000 + 3.46410i −0.146647 + 0.254000i
\(187\) −18.0000 −1.31629
\(188\) −3.00000 + 5.19615i −0.218797 + 0.378968i
\(189\) −1.00000 + 1.73205i −0.0727393 + 0.125988i
\(190\) −6.00000 −0.435286
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −11.5000 19.9186i −0.827788 1.43377i −0.899770 0.436365i \(-0.856266\pi\)
0.0719816 0.997406i \(-0.477068\pi\)
\(194\) −14.0000 −1.00514
\(195\) 7.50000 + 7.79423i 0.537086 + 0.558156i
\(196\) −3.00000 −0.214286
\(197\) −3.00000 5.19615i −0.213741 0.370211i 0.739141 0.673550i \(-0.235232\pi\)
−0.952882 + 0.303340i \(0.901898\pi\)
\(198\) 3.00000 + 5.19615i 0.213201 + 0.369274i
\(199\) 5.00000 8.66025i 0.354441 0.613909i −0.632581 0.774494i \(-0.718005\pi\)
0.987022 + 0.160585i \(0.0513380\pi\)
\(200\) −4.00000 −0.282843
\(201\) 5.00000 8.66025i 0.352673 0.610847i
\(202\) 7.50000 12.9904i 0.527698 0.914000i
\(203\) 6.00000 0.421117
\(204\) 1.50000 2.59808i 0.105021 0.181902i
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) −6.00000 −0.417029
\(208\) 2.50000 + 2.59808i 0.173344 + 0.180144i
\(209\) 12.0000 0.830057
\(210\) 3.00000 + 5.19615i 0.207020 + 0.358569i
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −1.50000 + 2.59808i −0.103020 + 0.178437i
\(213\) 6.00000 0.411113
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) 15.0000 25.9808i 1.02299 1.77187i
\(216\) −1.00000 −0.0680414
\(217\) 4.00000 6.92820i 0.271538 0.470317i
\(218\) 7.00000 + 12.1244i 0.474100 + 0.821165i
\(219\) 6.50000 + 11.2583i 0.439229 + 0.760767i
\(220\) 18.0000 1.21356
\(221\) −3.00000 + 10.3923i −0.201802 + 0.699062i
\(222\) 7.00000 0.469809
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) 1.00000 + 1.73205i 0.0668153 + 0.115728i
\(225\) −2.00000 + 3.46410i −0.133333 + 0.230940i
\(226\) 3.00000 0.199557
\(227\) −9.00000 + 15.5885i −0.597351 + 1.03464i 0.395860 + 0.918311i \(0.370447\pi\)
−0.993210 + 0.116331i \(0.962887\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) −9.00000 + 15.5885i −0.593442 + 1.02787i
\(231\) −6.00000 10.3923i −0.394771 0.683763i
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 3.50000 0.866025i 0.228802 0.0566139i
\(235\) 18.0000 1.17419
\(236\) 0 0
\(237\) 2.00000 + 3.46410i 0.129914 + 0.225018i
\(238\) −3.00000 + 5.19615i −0.194461 + 0.336817i
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −1.50000 + 2.59808i −0.0968246 + 0.167705i
\(241\) 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i \(-0.823079\pi\)
0.881680 + 0.471848i \(0.156413\pi\)
\(242\) −25.0000 −1.60706
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 3.50000 + 6.06218i 0.224065 + 0.388091i
\(245\) 4.50000 + 7.79423i 0.287494 + 0.497955i
\(246\) 3.00000 0.191273
\(247\) 2.00000 6.92820i 0.127257 0.440831i
\(248\) 4.00000 0.254000
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) −1.50000 2.59808i −0.0948683 0.164317i
\(251\) 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) 2.00000 0.125988
\(253\) 18.0000 31.1769i 1.13165 1.96008i
\(254\) −2.00000 + 3.46410i −0.125491 + 0.217357i
\(255\) −9.00000 −0.563602
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.50000 + 2.59808i 0.0935674 + 0.162064i 0.909010 0.416775i \(-0.136840\pi\)
−0.815442 + 0.578838i \(0.803506\pi\)
\(258\) −5.00000 8.66025i −0.311286 0.539164i
\(259\) −14.0000 −0.869918
\(260\) 3.00000 10.3923i 0.186052 0.644503i
\(261\) 3.00000 0.185695
\(262\) 0 0
\(263\) 3.00000 + 5.19615i 0.184988 + 0.320408i 0.943572 0.331166i \(-0.107442\pi\)
−0.758585 + 0.651575i \(0.774109\pi\)
\(264\) 3.00000 5.19615i 0.184637 0.319801i
\(265\) 9.00000 0.552866
\(266\) 2.00000 3.46410i 0.122628 0.212398i
\(267\) −9.00000 + 15.5885i −0.550791 + 0.953998i
\(268\) −10.0000 −0.610847
\(269\) −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) 1.50000 + 2.59808i 0.0912871 + 0.158114i
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) −3.00000 −0.181902
\(273\) −7.00000 + 1.73205i −0.423659 + 0.104828i
\(274\) −9.00000 −0.543710
\(275\) −12.0000 20.7846i −0.723627 1.25336i
\(276\) 3.00000 + 5.19615i 0.180579 + 0.312772i
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) 4.00000 0.239904
\(279\) 2.00000 3.46410i 0.119737 0.207390i
\(280\) 3.00000 5.19615i 0.179284 0.310530i
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 3.00000 5.19615i 0.178647 0.309426i
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 6.00000 0.355409
\(286\) −6.00000 + 20.7846i −0.354787 + 1.22902i
\(287\) −6.00000 −0.354169
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 4.50000 7.79423i 0.264249 0.457693i
\(291\) 14.0000 0.820695
\(292\) 6.50000 11.2583i 0.380384 0.658844i
\(293\) 10.5000 18.1865i 0.613417 1.06247i −0.377244 0.926114i \(-0.623128\pi\)
0.990660 0.136355i \(-0.0435386\pi\)
\(294\) 3.00000 0.174964
\(295\) 0 0
\(296\) −3.50000 6.06218i −0.203433 0.352357i
\(297\) −3.00000 5.19615i −0.174078 0.301511i
\(298\) 9.00000 0.521356
\(299\) −15.0000 15.5885i −0.867472 0.901504i
\(300\) 4.00000 0.230940
\(301\) 10.0000 + 17.3205i 0.576390 + 0.998337i
\(302\) −5.00000 8.66025i −0.287718 0.498342i
\(303\) −7.50000 + 12.9904i −0.430864 + 0.746278i
\(304\) 2.00000 0.114708
\(305\) 10.5000 18.1865i 0.601228 1.04136i
\(306\) −1.50000 + 2.59808i −0.0857493 + 0.148522i
\(307\) −10.0000 −0.570730 −0.285365 0.958419i \(-0.592115\pi\)
−0.285365 + 0.958419i \(0.592115\pi\)
\(308\) −6.00000 + 10.3923i −0.341882 + 0.592157i
\(309\) −7.00000 12.1244i −0.398216 0.689730i
\(310\) −6.00000 10.3923i −0.340777 0.590243i
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) −2.50000 2.59808i −0.141535 0.147087i
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 2.50000 + 4.33013i 0.141083 + 0.244363i
\(315\) −3.00000 5.19615i −0.169031 0.292770i
\(316\) 2.00000 3.46410i 0.112509 0.194871i
\(317\) 3.00000 0.168497 0.0842484 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) 1.50000 2.59808i 0.0841158 0.145693i
\(319\) −9.00000 + 15.5885i −0.503903 + 0.872786i
\(320\) 3.00000 0.167705
\(321\) 3.00000 5.19615i 0.167444 0.290021i
\(322\) −6.00000 10.3923i −0.334367 0.579141i
\(323\) 3.00000 + 5.19615i 0.166924 + 0.289122i
\(324\) 1.00000 0.0555556
\(325\) −14.0000 + 3.46410i −0.776580 + 0.192154i
\(326\) 4.00000 0.221540
\(327\) −7.00000 12.1244i −0.387101 0.670478i
\(328\) −1.50000 2.59808i −0.0828236 0.143455i
\(329\) −6.00000 + 10.3923i −0.330791 + 0.572946i
\(330\) −18.0000 −0.990867
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) −7.00000 −0.383598
\(334\) 0 0
\(335\) 15.0000 + 25.9808i 0.819538 + 1.41948i
\(336\) −1.00000 1.73205i −0.0545545 0.0944911i
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 11.0000 + 6.92820i 0.598321 + 0.376845i
\(339\) −3.00000 −0.162938
\(340\) 4.50000 + 7.79423i 0.244047 + 0.422701i
\(341\) 12.0000 + 20.7846i 0.649836 + 1.12555i
\(342\) 1.00000 1.73205i 0.0540738 0.0936586i
\(343\) −20.0000 −1.07990
\(344\) −5.00000 + 8.66025i −0.269582 + 0.466930i
\(345\) 9.00000 15.5885i 0.484544 0.839254i
\(346\) 6.00000 0.322562
\(347\) 15.0000 25.9808i 0.805242 1.39472i −0.110885 0.993833i \(-0.535369\pi\)
0.916127 0.400887i \(-0.131298\pi\)
\(348\) −1.50000 2.59808i −0.0804084 0.139272i
\(349\) 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i \(-0.0804216\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(350\) −8.00000 −0.427618
\(351\) −3.50000 + 0.866025i −0.186816 + 0.0462250i
\(352\) −6.00000 −0.319801
\(353\) 7.50000 + 12.9904i 0.399185 + 0.691408i 0.993626 0.112731i \(-0.0359599\pi\)
−0.594441 + 0.804139i \(0.702627\pi\)
\(354\) 0 0
\(355\) −9.00000 + 15.5885i −0.477670 + 0.827349i
\(356\) 18.0000 0.953998
\(357\) 3.00000 5.19615i 0.158777 0.275010i
\(358\) 3.00000 5.19615i 0.158555 0.274625i
\(359\) 6.00000 0.316668 0.158334 0.987386i \(-0.449388\pi\)
0.158334 + 0.987386i \(0.449388\pi\)
\(360\) 1.50000 2.59808i 0.0790569 0.136931i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −3.50000 6.06218i −0.183956 0.318621i
\(363\) 25.0000 1.31216
\(364\) 5.00000 + 5.19615i 0.262071 + 0.272352i
\(365\) −39.0000 −2.04135
\(366\) −3.50000 6.06218i −0.182948 0.316875i
\(367\) −1.00000 1.73205i −0.0521996 0.0904123i 0.838745 0.544524i \(-0.183290\pi\)
−0.890945 + 0.454112i \(0.849957\pi\)
\(368\) 3.00000 5.19615i 0.156386 0.270868i
\(369\) −3.00000 −0.156174
\(370\) −10.5000 + 18.1865i −0.545869 + 0.945473i
\(371\) −3.00000 + 5.19615i −0.155752 + 0.269771i
\(372\) −4.00000 −0.207390
\(373\) −14.5000 + 25.1147i −0.750782 + 1.30039i 0.196663 + 0.980471i \(0.436990\pi\)
−0.947444 + 0.319921i \(0.896344\pi\)
\(374\) −9.00000 15.5885i −0.465379 0.806060i
\(375\) 1.50000 + 2.59808i 0.0774597 + 0.134164i
\(376\) −6.00000 −0.309426
\(377\) 7.50000 + 7.79423i 0.386270 + 0.401423i
\(378\) −2.00000 −0.102869
\(379\) −10.0000 17.3205i −0.513665 0.889695i −0.999874 0.0158521i \(-0.994954\pi\)
0.486209 0.873843i \(-0.338379\pi\)
\(380\) −3.00000 5.19615i −0.153897 0.266557i
\(381\) 2.00000 3.46410i 0.102463 0.177471i
\(382\) 12.0000 0.613973
\(383\) −12.0000 + 20.7846i −0.613171 + 1.06204i 0.377531 + 0.925997i \(0.376773\pi\)
−0.990702 + 0.136047i \(0.956560\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 36.0000 1.83473
\(386\) 11.5000 19.9186i 0.585335 1.01383i
\(387\) 5.00000 + 8.66025i 0.254164 + 0.440225i
\(388\) −7.00000 12.1244i −0.355371 0.615521i
\(389\) 39.0000 1.97738 0.988689 0.149979i \(-0.0479205\pi\)
0.988689 + 0.149979i \(0.0479205\pi\)
\(390\) −3.00000 + 10.3923i −0.151911 + 0.526235i
\(391\) 18.0000 0.910299
\(392\) −1.50000 2.59808i −0.0757614 0.131223i
\(393\) 0 0
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) −12.0000 −0.603786
\(396\) −3.00000 + 5.19615i −0.150756 + 0.261116i
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) 10.0000 0.501255
\(399\) −2.00000 + 3.46410i −0.100125 + 0.173422i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) 1.50000 + 2.59808i 0.0749064 + 0.129742i 0.901046 0.433724i \(-0.142801\pi\)
−0.826139 + 0.563466i \(0.809468\pi\)
\(402\) 10.0000 0.498755
\(403\) 14.0000 3.46410i 0.697390 0.172559i
\(404\) 15.0000 0.746278
\(405\) −1.50000 2.59808i −0.0745356 0.129099i
\(406\) 3.00000 + 5.19615i 0.148888 + 0.257881i
\(407\) 21.0000 36.3731i 1.04093 1.80295i
\(408\) 3.00000 0.148522
\(409\) 0.500000 0.866025i 0.0247234 0.0428222i −0.853399 0.521258i \(-0.825463\pi\)
0.878122 + 0.478436i \(0.158796\pi\)
\(410\) −4.50000 + 7.79423i −0.222239 + 0.384930i
\(411\) 9.00000 0.443937
\(412\) −7.00000 + 12.1244i −0.344865 + 0.597324i
\(413\) 0 0
\(414\) −3.00000 5.19615i −0.147442 0.255377i
\(415\) −18.0000 −0.883585
\(416\) −1.00000 + 3.46410i −0.0490290 + 0.169842i
\(417\) −4.00000 −0.195881
\(418\) 6.00000 + 10.3923i 0.293470 + 0.508304i
\(419\) −12.0000 20.7846i −0.586238 1.01539i −0.994720 0.102628i \(-0.967275\pi\)
0.408481 0.912767i \(-0.366058\pi\)
\(420\) −3.00000 + 5.19615i −0.146385 + 0.253546i
\(421\) 29.0000 1.41337 0.706687 0.707527i \(-0.250189\pi\)
0.706687 + 0.707527i \(0.250189\pi\)
\(422\) −8.00000 + 13.8564i −0.389434 + 0.674519i
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) −3.00000 −0.145693
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) 3.00000 + 5.19615i 0.145350 + 0.251754i
\(427\) 7.00000 + 12.1244i 0.338754 + 0.586739i
\(428\) −6.00000 −0.290021
\(429\) 6.00000 20.7846i 0.289683 1.00349i
\(430\) 30.0000 1.44673
\(431\) 3.00000 + 5.19615i 0.144505 + 0.250290i 0.929188 0.369607i \(-0.120508\pi\)
−0.784683 + 0.619897i \(0.787174\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 6.50000 11.2583i 0.312370 0.541041i −0.666505 0.745501i \(-0.732210\pi\)
0.978875 + 0.204460i \(0.0655438\pi\)
\(434\) 8.00000 0.384012
\(435\) −4.50000 + 7.79423i −0.215758 + 0.373705i
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) −12.0000 −0.574038
\(438\) −6.50000 + 11.2583i −0.310582 + 0.537944i
\(439\) −7.00000 12.1244i −0.334092 0.578664i 0.649218 0.760602i \(-0.275096\pi\)
−0.983310 + 0.181938i \(0.941763\pi\)
\(440\) 9.00000 + 15.5885i 0.429058 + 0.743151i
\(441\) −3.00000 −0.142857
\(442\) −10.5000 + 2.59808i −0.499434 + 0.123578i
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 3.50000 + 6.06218i 0.166103 + 0.287698i
\(445\) −27.0000 46.7654i −1.27992 2.21689i
\(446\) 4.00000 6.92820i 0.189405 0.328060i
\(447\) −9.00000 −0.425685
\(448\) −1.00000 + 1.73205i −0.0472456 + 0.0818317i
\(449\) −9.00000 + 15.5885i −0.424736 + 0.735665i −0.996396 0.0848262i \(-0.972967\pi\)
0.571660 + 0.820491i \(0.306300\pi\)
\(450\) −4.00000 −0.188562
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) 1.50000 + 2.59808i 0.0705541 + 0.122203i
\(453\) 5.00000 + 8.66025i 0.234920 + 0.406894i
\(454\) −18.0000 −0.844782
\(455\) 6.00000 20.7846i 0.281284 0.974398i
\(456\) −2.00000 −0.0936586
\(457\) −5.50000 9.52628i −0.257279 0.445621i 0.708233 0.705979i \(-0.249493\pi\)
−0.965512 + 0.260358i \(0.916159\pi\)
\(458\) −11.0000 19.0526i −0.513996 0.890268i
\(459\) 1.50000 2.59808i 0.0700140 0.121268i
\(460\) −18.0000 −0.839254
\(461\) −7.50000 + 12.9904i −0.349310 + 0.605022i −0.986127 0.165992i \(-0.946917\pi\)
0.636817 + 0.771015i \(0.280251\pi\)
\(462\) 6.00000 10.3923i 0.279145 0.483494i
\(463\) 38.0000 1.76601 0.883005 0.469364i \(-0.155517\pi\)
0.883005 + 0.469364i \(0.155517\pi\)
\(464\) −1.50000 + 2.59808i −0.0696358 + 0.120613i
\(465\) 6.00000 + 10.3923i 0.278243 + 0.481932i
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) −18.0000 −0.832941 −0.416470 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) 2.50000 + 2.59808i 0.115563 + 0.120096i
\(469\) −20.0000 −0.923514
\(470\) 9.00000 + 15.5885i 0.415139 + 0.719042i
\(471\) −2.50000 4.33013i −0.115194 0.199522i
\(472\) 0 0
\(473\) −60.0000 −2.75880
\(474\) −2.00000 + 3.46410i −0.0918630 + 0.159111i
\(475\) −4.00000 + 6.92820i −0.183533 + 0.317888i
\(476\) −6.00000 −0.275010
\(477\) −1.50000 + 2.59808i −0.0686803 + 0.118958i
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) −3.00000 −0.136931
\(481\) −17.5000 18.1865i −0.797931 0.829235i
\(482\) 1.00000 0.0455488
\(483\) 6.00000 + 10.3923i 0.273009 + 0.472866i
\(484\) −12.5000 21.6506i −0.568182 0.984120i
\(485\) −21.0000 + 36.3731i −0.953561 + 1.65162i
\(486\) −1.00000 −0.0453609
\(487\) −1.00000 + 1.73205i −0.0453143 + 0.0784867i −0.887793 0.460243i \(-0.847762\pi\)
0.842479 + 0.538730i \(0.181096\pi\)
\(488\) −3.50000 + 6.06218i −0.158438 + 0.274422i
\(489\) −4.00000 −0.180886
\(490\) −4.50000 + 7.79423i −0.203289 + 0.352107i
\(491\) 9.00000 + 15.5885i 0.406164 + 0.703497i 0.994456 0.105151i \(-0.0335327\pi\)
−0.588292 + 0.808649i \(0.700199\pi\)
\(492\) 1.50000 + 2.59808i 0.0676252 + 0.117130i
\(493\) −9.00000 −0.405340
\(494\) 7.00000 1.73205i 0.314945 0.0779287i
\(495\) 18.0000 0.809040
\(496\) 2.00000 + 3.46410i 0.0898027 + 0.155543i
\(497\) −6.00000 10.3923i −0.269137 0.466159i
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 1.50000 2.59808i 0.0670820 0.116190i
\(501\) 0 0
\(502\) 12.0000 0.535586
\(503\) −3.00000 + 5.19615i −0.133763 + 0.231685i −0.925124 0.379664i \(-0.876040\pi\)
0.791361 + 0.611349i \(0.209373\pi\)
\(504\) 1.00000 + 1.73205i 0.0445435 + 0.0771517i
\(505\) −22.5000 38.9711i −1.00124 1.73419i
\(506\) 36.0000 1.60040
\(507\) −11.0000 6.92820i −0.488527 0.307692i
\(508\) −4.00000 −0.177471
\(509\) −1.50000 2.59808i −0.0664863 0.115158i 0.830866 0.556473i \(-0.187846\pi\)
−0.897352 + 0.441315i \(0.854512\pi\)
\(510\) −4.50000 7.79423i −0.199263 0.345134i
\(511\) 13.0000 22.5167i 0.575086 0.996078i
\(512\) −1.00000 −0.0441942
\(513\) −1.00000 + 1.73205i −0.0441511 + 0.0764719i
\(514\) −1.50000 + 2.59808i −0.0661622 + 0.114596i
\(515\) 42.0000 1.85074
\(516\) 5.00000 8.66025i 0.220113 0.381246i
\(517\) −18.0000 31.1769i −0.791639 1.37116i
\(518\) −7.00000 12.1244i −0.307562 0.532714i
\(519\) −6.00000 −0.263371
\(520\) 10.5000 2.59808i 0.460455 0.113933i
\(521\) 33.0000 1.44576 0.722878 0.690976i \(-0.242819\pi\)
0.722878 + 0.690976i \(0.242819\pi\)
\(522\) 1.50000 + 2.59808i 0.0656532 + 0.113715i
\(523\) 17.0000 + 29.4449i 0.743358 + 1.28753i 0.950958 + 0.309320i \(0.100101\pi\)
−0.207600 + 0.978214i \(0.566565\pi\)
\(524\) 0 0
\(525\) 8.00000 0.349149
\(526\) −3.00000 + 5.19615i −0.130806 + 0.226563i
\(527\) −6.00000 + 10.3923i −0.261364 + 0.452696i
\(528\) 6.00000 0.261116
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 4.50000 + 7.79423i 0.195468 + 0.338560i
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) −7.50000 7.79423i −0.324861 0.337606i
\(534\) −18.0000 −0.778936
\(535\) 9.00000 + 15.5885i 0.389104 + 0.673948i
\(536\) −5.00000 8.66025i −0.215967 0.374066i
\(537\) −3.00000 + 5.19615i −0.129460 + 0.224231i
\(538\) −18.0000 −0.776035
\(539\) 9.00000 15.5885i 0.387657 0.671442i
\(540\) −1.50000 + 2.59808i −0.0645497 + 0.111803i
\(541\) 29.0000 1.24681 0.623404 0.781900i \(-0.285749\pi\)
0.623404 + 0.781900i \(0.285749\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) 3.50000 + 6.06218i 0.150199 + 0.260153i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 42.0000 1.79908
\(546\) −5.00000 5.19615i −0.213980 0.222375i
\(547\) −34.0000 −1.45374 −0.726868 0.686778i \(-0.759025\pi\)
−0.726868 + 0.686778i \(0.759025\pi\)
\(548\) −4.50000 7.79423i −0.192230 0.332953i
\(549\) 3.50000 + 6.06218i 0.149376 + 0.258727i
\(550\) 12.0000 20.7846i 0.511682 0.886259i
\(551\) 6.00000 0.255609
\(552\) −3.00000 + 5.19615i −0.127688 + 0.221163i
\(553\) 4.00000 6.92820i 0.170097 0.294617i
\(554\) −17.0000 −0.722261
\(555\) 10.5000 18.1865i 0.445700 0.771975i
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −1.50000 2.59808i −0.0635570 0.110084i 0.832496 0.554031i \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) 4.00000 0.169334
\(559\) −10.0000 + 34.6410i −0.422955 + 1.46516i
\(560\) 6.00000 0.253546
\(561\) 9.00000 + 15.5885i 0.379980 + 0.658145i
\(562\) 4.50000 + 7.79423i 0.189821 + 0.328780i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 6.00000 0.252646
\(565\) 4.50000 7.79423i 0.189316 0.327906i
\(566\) 7.00000 12.1244i 0.294232 0.509625i
\(567\) 2.00000 0.0839921
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 3.00000 + 5.19615i 0.125656 + 0.217643i
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) −21.0000 + 5.19615i −0.878054 + 0.217262i
\(573\) −12.0000 −0.501307
\(574\) −3.00000 5.19615i −0.125218 0.216883i
\(575\) 12.0000 + 20.7846i 0.500435 + 0.866778i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) −11.5000 + 19.9186i −0.477924 + 0.827788i
\(580\) 9.00000 0.373705
\(581\) 6.00000 10.3923i 0.248922 0.431145i
\(582\) 7.00000 + 12.1244i 0.290159 + 0.502571i
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) 13.0000 0.537944
\(585\) 3.00000 10.3923i 0.124035 0.429669i
\(586\) 21.0000 0.867502
\(587\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) 1.50000 + 2.59808i 0.0618590 + 0.107143i
\(589\) 4.00000 6.92820i 0.164817 0.285472i
\(590\) 0 0
\(591\) −3.00000 + 5.19615i −0.123404 + 0.213741i
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) 9.00000 0.369586 0.184793 0.982777i \(-0.440839\pi\)
0.184793 + 0.982777i \(0.440839\pi\)
\(594\) 3.00000 5.19615i 0.123091 0.213201i
\(595\) 9.00000 + 15.5885i 0.368964 + 0.639064i
\(596\) 4.50000 + 7.79423i 0.184327 + 0.319264i
\(597\) −10.0000 −0.409273
\(598\) 6.00000 20.7846i 0.245358 0.849946i
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 2.00000 + 3.46410i 0.0816497 + 0.141421i
\(601\) 18.5000 + 32.0429i 0.754631 + 1.30706i 0.945558 + 0.325455i \(0.105517\pi\)
−0.190927 + 0.981604i \(0.561149\pi\)
\(602\) −10.0000 + 17.3205i −0.407570 + 0.705931i
\(603\) −10.0000 −0.407231
\(604\) 5.00000 8.66025i 0.203447 0.352381i
\(605\) −37.5000 + 64.9519i −1.52459 + 2.64067i
\(606\) −15.0000 −0.609333
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) 1.00000 + 1.73205i 0.0405554 + 0.0702439i
\(609\) −3.00000 5.19615i −0.121566 0.210559i
\(610\) 21.0000 0.850265
\(611\) −21.0000 + 5.19615i −0.849569 + 0.210214i
\(612\) −3.00000 −0.121268
\(613\) 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) −5.00000 8.66025i −0.201784 0.349499i
\(615\) 4.50000 7.79423i 0.181458 0.314294i
\(616\) −12.0000 −0.483494
\(617\) 7.50000 12.9904i 0.301939 0.522973i −0.674636 0.738150i \(-0.735700\pi\)
0.976575 + 0.215177i \(0.0690329\pi\)
\(618\) 7.00000 12.1244i 0.281581 0.487713i
\(619\) 8.00000 0.321547 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) 6.00000 10.3923i 0.240966 0.417365i
\(621\) 3.00000 + 5.19615i 0.120386 + 0.208514i
\(622\) −15.0000 25.9808i −0.601445 1.04173i
\(623\) 36.0000 1.44231
\(624\) 1.00000 3.46410i 0.0400320 0.138675i
\(625\) −29.0000 −1.16000
\(626\) −5.00000 8.66025i −0.199840 0.346133i
\(627\) −6.00000 10.3923i −0.239617 0.415029i
\(628\) −2.50000 + 4.33013i −0.0997609 + 0.172791i
\(629\) 21.0000 0.837325
\(630\) 3.00000 5.19615i 0.119523 0.207020i
\(631\) −10.0000 + 17.3205i −0.398094 + 0.689519i −0.993491 0.113913i \(-0.963661\pi\)
0.595397 + 0.803432i \(0.296995\pi\)
\(632\) 4.00000 0.159111
\(633\) 8.00000 13.8564i 0.317971 0.550743i
\(634\) 1.50000 + 2.59808i 0.0595726 + 0.103183i
\(635\) 6.00000 + 10.3923i 0.238103 + 0.412406i
\(636\) 3.00000 0.118958
\(637\) −7.50000 7.79423i −0.297161 0.308819i
\(638\) −18.0000 −0.712627
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) 1.50000 + 2.59808i 0.0592927 + 0.102698i
\(641\) 1.50000 2.59808i 0.0592464 0.102618i −0.834881 0.550431i \(-0.814464\pi\)
0.894127 + 0.447813i \(0.147797\pi\)
\(642\) 6.00000 0.236801
\(643\) 8.00000 13.8564i 0.315489 0.546443i −0.664052 0.747686i \(-0.731165\pi\)
0.979541 + 0.201243i \(0.0644981\pi\)
\(644\) 6.00000 10.3923i 0.236433 0.409514i
\(645\) −30.0000 −1.18125
\(646\) −3.00000 + 5.19615i −0.118033 + 0.204440i
\(647\) −12.0000 20.7846i −0.471769 0.817127i 0.527710 0.849425i \(-0.323051\pi\)
−0.999478 + 0.0322975i \(0.989718\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 0 0
\(650\) −10.0000 10.3923i −0.392232 0.407620i
\(651\) −8.00000 −0.313545
\(652\) 2.00000 + 3.46410i 0.0783260 + 0.135665i
\(653\) −21.0000 36.3731i −0.821794 1.42339i −0.904345 0.426801i \(-0.859640\pi\)
0.0825519 0.996587i \(-0.473693\pi\)
\(654\) 7.00000 12.1244i 0.273722 0.474100i
\(655\) 0 0
\(656\) 1.50000 2.59808i 0.0585652 0.101438i
\(657\) 6.50000 11.2583i 0.253589 0.439229i
\(658\) −12.0000 −0.467809
\(659\) −12.0000 + 20.7846i −0.467454 + 0.809653i −0.999309 0.0371821i \(-0.988162\pi\)
0.531855 + 0.846836i \(0.321495\pi\)
\(660\) −9.00000 15.5885i −0.350325 0.606780i
\(661\) −2.50000 4.33013i −0.0972387 0.168422i 0.813302 0.581842i \(-0.197668\pi\)
−0.910541 + 0.413419i \(0.864334\pi\)
\(662\) 4.00000 0.155464
\(663\) 10.5000 2.59808i 0.407786 0.100901i
\(664\) 6.00000 0.232845
\(665\) −6.00000 10.3923i −0.232670 0.402996i
\(666\) −3.50000 6.06218i −0.135622 0.234905i
\(667\) 9.00000 15.5885i 0.348481 0.603587i
\(668\) 0 0
\(669\) −4.00000 + 6.92820i −0.154649 + 0.267860i
\(670\) −15.0000 + 25.9808i −0.579501 + 1.00372i
\(671\) −42.0000 −1.62139
\(672\) 1.00000 1.73205i 0.0385758 0.0668153i
\(673\) 6.50000 + 11.2583i 0.250557 + 0.433977i 0.963679 0.267063i \(-0.0860531\pi\)
−0.713123 + 0.701039i \(0.752720\pi\)
\(674\) 11.5000 + 19.9186i 0.442963 + 0.767235i
\(675\) 4.00000 0.153960
\(676\) −0.500000 + 12.9904i −0.0192308 + 0.499630i
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −1.50000 2.59808i −0.0576072 0.0997785i
\(679\) −14.0000 24.2487i −0.537271 0.930580i
\(680\) −4.50000 + 7.79423i −0.172567 + 0.298895i
\(681\) 18.0000 0.689761
\(682\) −12.0000 + 20.7846i −0.459504 + 0.795884i
\(683\) 24.0000 41.5692i 0.918334 1.59060i 0.116390 0.993204i \(-0.462868\pi\)
0.801945 0.597398i \(-0.203799\pi\)
\(684\) 2.00000 0.0764719
\(685\) −13.5000 + 23.3827i −0.515808 + 0.893407i
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) 11.0000 + 19.0526i 0.419676 + 0.726900i
\(688\) −10.0000 −0.381246
\(689\) −10.5000 + 2.59808i −0.400018 + 0.0989788i
\(690\) 18.0000 0.685248
\(691\) −13.0000 22.5167i −0.494543 0.856574i 0.505437 0.862864i \(-0.331331\pi\)
−0.999980 + 0.00628943i \(0.997998\pi\)
\(692\) 3.00000 + 5.19615i 0.114043 + 0.197528i
\(693\) −6.00000 + 10.3923i −0.227921 + 0.394771i
\(694\) 30.0000 1.13878
\(695\) 6.00000 10.3923i 0.227593 0.394203i
\(696\) 1.50000 2.59808i 0.0568574 0.0984798i
\(697\) 9.00000 0.340899
\(698\) −5.00000 + 8.66025i −0.189253 + 0.327795i
\(699\) 3.00000 + 5.19615i 0.113470 + 0.196537i
\(700\) −4.00000 6.92820i −0.151186 0.261861i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) −2.50000 2.59808i −0.0943564 0.0980581i
\(703\) −14.0000 −0.528020
\(704\) −3.00000 5.19615i −0.113067 0.195837i
\(705\) −9.00000 15.5885i −0.338960 0.587095i
\(706\) −7.50000 + 12.9904i −0.282266 + 0.488899i
\(707\) 30.0000 1.12827
\(708\) 0 0
\(709\) −2.50000 + 4.33013i −0.0938895 + 0.162621i −0.909145 0.416481i \(-0.863263\pi\)
0.815255 + 0.579102i \(0.196597\pi\)
\(710\) −18.0000 −0.675528
\(711\) 2.00000 3.46410i 0.0750059 0.129914i
\(712\) 9.00000 + 15.5885i 0.337289 + 0.584202i
\(713\) −12.0000 20.7846i −0.449404 0.778390i
\(714\) 6.00000 0.224544
\(715\) 45.0000 + 46.7654i 1.68290 + 1.74893i
\(716\) 6.00000 0.224231
\(717\) −3.00000 5.19615i −0.112037 0.194054i
\(718\) 3.00000 + 5.19615i 0.111959 + 0.193919i
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 3.00000 0.111803
\(721\) −14.0000 + 24.2487i −0.521387 + 0.903069i
\(722\) −7.50000 + 12.9904i −0.279121 + 0.483452i
\(723\) −1.00000 −0.0371904
\(724\) 3.50000 6.06218i 0.130076 0.225299i
\(725\) −6.00000 10.3923i −0.222834 0.385961i
\(726\) 12.5000 + 21.6506i 0.463919 + 0.803530i
\(727\) 14.0000 0.519231 0.259616 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) −2.00000 + 6.92820i −0.0741249 + 0.256776i
\(729\) 1.00000 0.0370370
\(730\) −19.5000 33.7750i −0.721727 1.25007i
\(731\) −15.0000 25.9808i −0.554795 0.960933i
\(732\) 3.50000 6.06218i 0.129364 0.224065i
\(733\) −31.0000 −1.14501 −0.572506 0.819901i \(-0.694029\pi\)
−0.572506 + 0.819901i \(0.694029\pi\)
\(734\) 1.00000 1.73205i 0.0369107 0.0639312i
\(735\) 4.50000 7.79423i 0.165985 0.287494i
\(736\) 6.00000 0.221163
\(737\) 30.0000 51.9615i 1.10506 1.91403i
\(738\) −1.50000 2.59808i −0.0552158 0.0956365i
\(739\) 8.00000 + 13.8564i 0.294285 + 0.509716i 0.974818 0.223001i \(-0.0715853\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) −21.0000 −0.771975
\(741\) −7.00000 + 1.73205i −0.257151 + 0.0636285i
\(742\) −6.00000 −0.220267
\(743\) 18.0000 + 31.1769i 0.660356 + 1.14377i 0.980522 + 0.196409i \(0.0629279\pi\)
−0.320166 + 0.947361i \(0.603739\pi\)
\(744\) −2.00000 3.46410i −0.0733236 0.127000i
\(745\) 13.5000 23.3827i 0.494602 0.856675i
\(746\) −29.0000 −1.06177
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) 9.00000 15.5885i 0.329073 0.569970i
\(749\) −12.0000 −0.438470
\(750\) −1.50000 + 2.59808i −0.0547723 + 0.0948683i
\(751\) −7.00000 12.1244i −0.255434 0.442424i 0.709580 0.704625i \(-0.248885\pi\)
−0.965013 + 0.262201i \(0.915552\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) −12.0000 −0.437304
\(754\) −3.00000 + 10.3923i −0.109254 + 0.378465i
\(755\) −30.0000 −1.09181
\(756\) −1.00000 1.73205i −0.0363696 0.0629941i
\(757\) 17.0000 + 29.4449i 0.617876 + 1.07019i 0.989873 + 0.141958i \(0.0453398\pi\)
−0.371997 + 0.928234i \(0.621327\pi\)
\(758\) 10.0000 17.3205i 0.363216 0.629109i
\(759\) −36.0000 −1.30672
\(760\) 3.00000 5.19615i 0.108821 0.188484i
\(761\) 15.0000 25.9808i 0.543750 0.941802i −0.454935 0.890525i \(-0.650337\pi\)
0.998684 0.0512772i \(-0.0163292\pi\)
\(762\) 4.00000 0.144905
\(763\) −14.0000 + 24.2487i −0.506834 + 0.877862i
\(764\) 6.00000 + 10.3923i 0.217072 + 0.375980i
\(765\) 4.50000 + 7.79423i 0.162698 + 0.281801i
\(766\) −24.0000 −0.867155
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −7.00000 12.1244i −0.252426 0.437215i 0.711767 0.702416i \(-0.247895\pi\)
−0.964193 + 0.265200i \(0.914562\pi\)
\(770\) 18.0000 + 31.1769i 0.648675 + 1.12354i
\(771\) 1.50000 2.59808i 0.0540212 0.0935674i
\(772\) 23.0000 0.827788
\(773\) 15.0000 25.9808i 0.539513 0.934463i −0.459418 0.888220i \(-0.651942\pi\)
0.998930 0.0462427i \(-0.0147248\pi\)
\(774\) −5.00000 + 8.66025i −0.179721 + 0.311286i
\(775\) −16.0000 −0.574737