Properties

Label 546.2.l.e.211.1
Level $546$
Weight $2$
Character 546.211
Analytic conductor $4.360$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.e.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(2.50000 + 2.59808i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} -1.00000 q^{18} +(-2.50000 + 4.33013i) q^{19} +1.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} -5.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(4.50000 + 7.79423i) q^{29} +8.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +3.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-4.00000 - 6.92820i) q^{37} -5.00000 q^{38} +(1.00000 - 3.46410i) q^{39} +(-1.50000 - 2.59808i) q^{41} +(0.500000 + 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} -3.00000 q^{44} +(-3.00000 + 5.19615i) q^{46} +3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.50000 - 4.33013i) q^{50} -3.00000 q^{51} +(-3.50000 + 0.866025i) q^{52} -3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(0.500000 - 0.866025i) q^{56} +5.00000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(3.00000 - 5.19615i) q^{59} +(3.50000 - 6.06218i) q^{61} +(4.00000 + 6.92820i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(3.00000 - 5.19615i) q^{69} +(3.00000 - 5.19615i) q^{71} +(0.500000 - 0.866025i) q^{72} -16.0000 q^{73} +(4.00000 - 6.92820i) q^{74} +(2.50000 + 4.33013i) q^{75} +(-2.50000 - 4.33013i) q^{76} -3.00000 q^{77} +(3.50000 - 0.866025i) q^{78} -13.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} +18.0000 q^{83} +(-0.500000 + 0.866025i) q^{84} -8.00000 q^{86} +(4.50000 - 7.79423i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(7.50000 + 12.9904i) q^{89} +(-3.50000 + 0.866025i) q^{91} -6.00000 q^{92} +(-4.00000 - 6.92820i) q^{93} +(1.50000 + 2.59808i) q^{94} -1.00000 q^{96} +(8.00000 - 13.8564i) q^{97} +(0.500000 - 0.866025i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} + q^{6} - q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} + q^{6} - q^{7} - 2q^{8} - q^{9} + 3q^{11} + 2q^{12} + 5q^{13} - 2q^{14} - q^{16} + 3q^{17} - 2q^{18} - 5q^{19} + 2q^{21} - 3q^{22} + 6q^{23} + q^{24} - 10q^{25} - 2q^{26} + 2q^{27} - q^{28} + 9q^{29} + 16q^{31} + q^{32} + 3q^{33} + 6q^{34} - q^{36} - 8q^{37} - 10q^{38} + 2q^{39} - 3q^{41} + q^{42} - 8q^{43} - 6q^{44} - 6q^{46} + 6q^{47} - q^{48} - q^{49} - 5q^{50} - 6q^{51} - 7q^{52} - 6q^{53} + q^{54} + q^{56} + 10q^{57} - 9q^{58} + 6q^{59} + 7q^{61} + 8q^{62} - q^{63} + 2q^{64} + 6q^{66} - 2q^{67} + 3q^{68} + 6q^{69} + 6q^{71} + q^{72} - 32q^{73} + 8q^{74} + 5q^{75} - 5q^{76} - 6q^{77} + 7q^{78} - 26q^{79} - q^{81} + 3q^{82} + 36q^{83} - q^{84} - 16q^{86} + 9q^{87} - 3q^{88} + 15q^{89} - 7q^{91} - 12q^{92} - 8q^{93} + 3q^{94} - 2q^{96} + 16q^{97} + q^{98} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.50000 + 2.59808i 0.693375 + 0.720577i
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −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
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) 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
\(25\) −5.00000 −1.00000
\(26\) −1.00000 + 3.46410i −0.196116 + 0.679366i
\(27\) 1.00000 0.192450
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i \(0.148230\pi\)
−0.0578882 + 0.998323i \(0.518437\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i \(-0.938240\pi\)
0.323640 0.946180i \(-0.395093\pi\)
\(38\) −5.00000 −0.811107
\(39\) 1.00000 3.46410i 0.160128 0.554700i
\(40\) 0 0
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −2.50000 4.33013i −0.353553 0.612372i
\(51\) −3.00000 −0.420084
\(52\) −3.50000 + 0.866025i −0.485363 + 0.120096i
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 5.00000 0.662266
\(58\) −4.50000 + 7.79423i −0.590879 + 1.02343i
\(59\) 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0 0
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) 4.00000 + 6.92820i 0.508001 + 0.879883i
\(63\) −0.500000 0.866025i −0.0629941 0.109109i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.00000 0.369274
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) 3.00000 5.19615i 0.361158 0.625543i
\(70\) 0 0
\(71\) 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i \(-0.717462\pi\)
0.987294 + 0.158901i \(0.0507952\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −16.0000 −1.87266 −0.936329 0.351123i \(-0.885800\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) 4.00000 6.92820i 0.464991 0.805387i
\(75\) 2.50000 + 4.33013i 0.288675 + 0.500000i
\(76\) −2.50000 4.33013i −0.286770 0.496700i
\(77\) −3.00000 −0.341882
\(78\) 3.50000 0.866025i 0.396297 0.0980581i
\(79\) −13.0000 −1.46261 −0.731307 0.682048i \(-0.761089\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) 18.0000 1.97576 0.987878 0.155230i \(-0.0496119\pi\)
0.987878 + 0.155230i \(0.0496119\pi\)
\(84\) −0.500000 + 0.866025i −0.0545545 + 0.0944911i
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 4.50000 7.79423i 0.482451 0.835629i
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) 7.50000 + 12.9904i 0.794998 + 1.37698i 0.922840 + 0.385183i \(0.125862\pi\)
−0.127842 + 0.991795i \(0.540805\pi\)
\(90\) 0 0
\(91\) −3.50000 + 0.866025i −0.366900 + 0.0907841i
\(92\) −6.00000 −0.625543
\(93\) −4.00000 6.92820i −0.414781 0.718421i
\(94\) 1.50000 + 2.59808i 0.154713 + 0.267971i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 8.00000 13.8564i 0.812277 1.40690i −0.0989899 0.995088i \(-0.531561\pi\)
0.911267 0.411816i \(-0.135106\pi\)
\(98\) 0.500000 0.866025i 0.0505076 0.0874818i
\(99\) −3.00000 −0.301511
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) −9.00000 15.5885i −0.895533 1.55111i −0.833143 0.553058i \(-0.813461\pi\)
−0.0623905 0.998052i \(-0.519872\pi\)
\(102\) −1.50000 2.59808i −0.148522 0.257248i
\(103\) −4.00000 −0.394132 −0.197066 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) −2.50000 2.59808i −0.245145 0.254762i
\(105\) 0 0
\(106\) −1.50000 2.59808i −0.145693 0.252347i
\(107\) −4.50000 7.79423i −0.435031 0.753497i 0.562267 0.826956i \(-0.309929\pi\)
−0.997298 + 0.0734594i \(0.976596\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) −4.00000 + 6.92820i −0.379663 + 0.657596i
\(112\) 1.00000 0.0944911
\(113\) 6.00000 10.3923i 0.564433 0.977626i −0.432670 0.901553i \(-0.642428\pi\)
0.997102 0.0760733i \(-0.0242383\pi\)
\(114\) 2.50000 + 4.33013i 0.234146 + 0.405554i
\(115\) 0 0
\(116\) −9.00000 −0.835629
\(117\) −3.50000 + 0.866025i −0.323575 + 0.0800641i
\(118\) 6.00000 0.552345
\(119\) 1.50000 + 2.59808i 0.137505 + 0.238165i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 7.00000 0.633750
\(123\) −1.50000 + 2.59808i −0.135250 + 0.234261i
\(124\) −4.00000 + 6.92820i −0.359211 + 0.622171i
\(125\) 0 0
\(126\) 0.500000 0.866025i 0.0445435 0.0771517i
\(127\) 8.00000 + 13.8564i 0.709885 + 1.22956i 0.964899 + 0.262620i \(0.0845865\pi\)
−0.255014 + 0.966937i \(0.582080\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 8.00000 0.704361
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 1.50000 + 2.59808i 0.130558 + 0.226134i
\(133\) −2.50000 4.33013i −0.216777 0.375470i
\(134\) 1.00000 1.73205i 0.0863868 0.149626i
\(135\) 0 0
\(136\) −1.50000 + 2.59808i −0.128624 + 0.222783i
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 6.00000 0.510754
\(139\) −5.50000 + 9.52628i −0.466504 + 0.808008i −0.999268 0.0382553i \(-0.987820\pi\)
0.532764 + 0.846264i \(0.321153\pi\)
\(140\) 0 0
\(141\) −1.50000 2.59808i −0.126323 0.218797i
\(142\) 6.00000 0.503509
\(143\) −3.00000 + 10.3923i −0.250873 + 0.869048i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −8.00000 13.8564i −0.662085 1.14676i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) 8.00000 0.657596
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) −2.50000 + 4.33013i −0.204124 + 0.353553i
\(151\) −19.0000 −1.54620 −0.773099 0.634285i \(-0.781294\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) 2.50000 4.33013i 0.202777 0.351220i
\(153\) 1.50000 + 2.59808i 0.121268 + 0.210042i
\(154\) −1.50000 2.59808i −0.120873 0.209359i
\(155\) 0 0
\(156\) 2.50000 + 2.59808i 0.200160 + 0.208013i
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −6.50000 11.2583i −0.517112 0.895665i
\(159\) 1.50000 + 2.59808i 0.118958 + 0.206041i
\(160\) 0 0
\(161\) −6.00000 −0.472866
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) 3.00000 0.234261
\(165\) 0 0
\(166\) 9.00000 + 15.5885i 0.698535 + 1.20990i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) 0 0
\(171\) −2.50000 4.33013i −0.191180 0.331133i
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 9.00000 0.682288
\(175\) 2.50000 4.33013i 0.188982 0.327327i
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) −6.00000 −0.450988
\(178\) −7.50000 + 12.9904i −0.562149 + 0.973670i
\(179\) 12.0000 + 20.7846i 0.896922 + 1.55351i 0.831408 + 0.555663i \(0.187536\pi\)
0.0655145 + 0.997852i \(0.479131\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) −2.50000 2.59808i −0.185312 0.192582i
\(183\) −7.00000 −0.517455
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) 0 0
\(186\) 4.00000 6.92820i 0.293294 0.508001i
\(187\) 9.00000 0.658145
\(188\) −1.50000 + 2.59808i −0.109399 + 0.189484i
\(189\) −0.500000 + 0.866025i −0.0363696 + 0.0629941i
\(190\) 0 0
\(191\) −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) 16.0000 1.14873
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 1.50000 + 2.59808i 0.106871 + 0.185105i 0.914501 0.404584i \(-0.132584\pi\)
−0.807630 + 0.589689i \(0.799250\pi\)
\(198\) −1.50000 2.59808i −0.106600 0.184637i
\(199\) 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) 5.00000 0.353553
\(201\) −1.00000 + 1.73205i −0.0705346 + 0.122169i
\(202\) 9.00000 15.5885i 0.633238 1.09680i
\(203\) −9.00000 −0.631676
\(204\) 1.50000 2.59808i 0.105021 0.181902i
\(205\) 0 0
\(206\) −2.00000 3.46410i −0.139347 0.241355i
\(207\) −6.00000 −0.417029
\(208\) 1.00000 3.46410i 0.0693375 0.240192i
\(209\) −15.0000 −1.03757
\(210\) 0 0
\(211\) 11.0000 + 19.0526i 0.757271 + 1.31163i 0.944237 + 0.329266i \(0.106801\pi\)
−0.186966 + 0.982366i \(0.559865\pi\)
\(212\) 1.50000 2.59808i 0.103020 0.178437i
\(213\) −6.00000 −0.411113
\(214\) 4.50000 7.79423i 0.307614 0.532803i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −4.00000 + 6.92820i −0.271538 + 0.470317i
\(218\) 1.00000 + 1.73205i 0.0677285 + 0.117309i
\(219\) 8.00000 + 13.8564i 0.540590 + 0.936329i
\(220\) 0 0
\(221\) 10.5000 2.59808i 0.706306 0.174766i
\(222\) −8.00000 −0.536925
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 2.50000 4.33013i 0.166667 0.288675i
\(226\) 12.0000 0.798228
\(227\) 3.00000 5.19615i 0.199117 0.344881i −0.749125 0.662428i \(-0.769526\pi\)
0.948242 + 0.317547i \(0.102859\pi\)
\(228\) −2.50000 + 4.33013i −0.165567 + 0.286770i
\(229\) 5.00000 0.330409 0.165205 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) 0 0
\(231\) 1.50000 + 2.59808i 0.0986928 + 0.170941i
\(232\) −4.50000 7.79423i −0.295439 0.511716i
\(233\) −24.0000 −1.57229 −0.786146 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) −2.50000 2.59808i −0.163430 0.169842i
\(235\) 0 0
\(236\) 3.00000 + 5.19615i 0.195283 + 0.338241i
\(237\) 6.50000 + 11.2583i 0.422220 + 0.731307i
\(238\) −1.50000 + 2.59808i −0.0972306 + 0.168408i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) −4.00000 + 6.92820i −0.257663 + 0.446285i −0.965615 0.259975i \(-0.916286\pi\)
0.707953 + 0.706260i \(0.249619\pi\)
\(242\) 2.00000 0.128565
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 3.50000 + 6.06218i 0.224065 + 0.388091i
\(245\) 0 0
\(246\) −3.00000 −0.191273
\(247\) −17.5000 + 4.33013i −1.11350 + 0.275519i
\(248\) −8.00000 −0.508001
\(249\) −9.00000 15.5885i −0.570352 0.987878i
\(250\) 0 0
\(251\) −9.00000 + 15.5885i −0.568075 + 0.983935i 0.428681 + 0.903456i \(0.358978\pi\)
−0.996756 + 0.0804789i \(0.974355\pi\)
\(252\) 1.00000 0.0629941
\(253\) −9.00000 + 15.5885i −0.565825 + 0.980038i
\(254\) −8.00000 + 13.8564i −0.501965 + 0.869428i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.50000 + 12.9904i 0.467837 + 0.810318i 0.999325 0.0367485i \(-0.0117000\pi\)
−0.531487 + 0.847066i \(0.678367\pi\)
\(258\) 4.00000 + 6.92820i 0.249029 + 0.431331i
\(259\) 8.00000 0.497096
\(260\) 0 0
\(261\) −9.00000 −0.557086
\(262\) 6.00000 + 10.3923i 0.370681 + 0.642039i
\(263\) −3.00000 5.19615i −0.184988 0.320408i 0.758585 0.651575i \(-0.225891\pi\)
−0.943572 + 0.331166i \(0.892558\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) 0 0
\(266\) 2.50000 4.33013i 0.153285 0.265497i
\(267\) 7.50000 12.9904i 0.458993 0.794998i
\(268\) 2.00000 0.122169
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) −10.0000 17.3205i −0.607457 1.05215i −0.991658 0.128897i \(-0.958856\pi\)
0.384201 0.923249i \(-0.374477\pi\)
\(272\) −3.00000 −0.181902
\(273\) 2.50000 + 2.59808i 0.151307 + 0.157243i
\(274\) 6.00000 0.362473
\(275\) −7.50000 12.9904i −0.452267 0.783349i
\(276\) 3.00000 + 5.19615i 0.180579 + 0.312772i
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) −11.0000 −0.659736
\(279\) −4.00000 + 6.92820i −0.239474 + 0.414781i
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 1.50000 2.59808i 0.0893237 0.154713i
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 0 0
\(286\) −10.5000 + 2.59808i −0.620878 + 0.153627i
\(287\) 3.00000 0.177084
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) −16.0000 −0.937937
\(292\) 8.00000 13.8564i 0.468165 0.810885i
\(293\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 0 0
\(296\) 4.00000 + 6.92820i 0.232495 + 0.402694i
\(297\) 1.50000 + 2.59808i 0.0870388 + 0.150756i
\(298\) 6.00000 0.347571
\(299\) −6.00000 + 20.7846i −0.346989 + 1.20201i
\(300\) −5.00000 −0.288675
\(301\) −4.00000 6.92820i −0.230556 0.399335i
\(302\) −9.50000 16.4545i −0.546664 0.946849i
\(303\) −9.00000 + 15.5885i −0.517036 + 0.895533i
\(304\) 5.00000 0.286770
\(305\) 0 0
\(306\) −1.50000 + 2.59808i −0.0857493 + 0.148522i
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) 1.50000 2.59808i 0.0854704 0.148039i
\(309\) 2.00000 + 3.46410i 0.113776 + 0.197066i
\(310\) 0 0
\(311\) −21.0000 −1.19080 −0.595400 0.803429i \(-0.703007\pi\)
−0.595400 + 0.803429i \(0.703007\pi\)
\(312\) −1.00000 + 3.46410i −0.0566139 + 0.196116i
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) 1.00000 + 1.73205i 0.0564333 + 0.0977453i
\(315\) 0 0
\(316\) 6.50000 11.2583i 0.365654 0.633331i
\(317\) 30.0000 1.68497 0.842484 0.538721i \(-0.181092\pi\)
0.842484 + 0.538721i \(0.181092\pi\)
\(318\) −1.50000 + 2.59808i −0.0841158 + 0.145693i
\(319\) −13.5000 + 23.3827i −0.755855 + 1.30918i
\(320\) 0 0
\(321\) −4.50000 + 7.79423i −0.251166 + 0.435031i
\(322\) −3.00000 5.19615i −0.167183 0.289570i
\(323\) 7.50000 + 12.9904i 0.417311 + 0.722804i
\(324\) 1.00000 0.0555556
\(325\) −12.5000 12.9904i −0.693375 0.720577i
\(326\) 16.0000 0.886158
\(327\) −1.00000 1.73205i −0.0553001 0.0957826i
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) −1.50000 + 2.59808i −0.0826977 + 0.143237i
\(330\) 0 0
\(331\) 5.00000 8.66025i 0.274825 0.476011i −0.695266 0.718752i \(-0.744713\pi\)
0.970091 + 0.242742i \(0.0780468\pi\)
\(332\) −9.00000 + 15.5885i −0.493939 + 0.855528i
\(333\) 8.00000 0.438397
\(334\) 0 0
\(335\) 0 0
\(336\) −0.500000 0.866025i −0.0272772 0.0472456i
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) −11.5000 + 6.06218i −0.625518 + 0.329739i
\(339\) −12.0000 −0.651751
\(340\) 0 0
\(341\) 12.0000 + 20.7846i 0.649836 + 1.12555i
\(342\) 2.50000 4.33013i 0.135185 0.234146i
\(343\) 1.00000 0.0539949
\(344\) 4.00000 6.92820i 0.215666 0.373544i
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) −1.50000 + 2.59808i −0.0805242 + 0.139472i −0.903475 0.428640i \(-0.858993\pi\)
0.822951 + 0.568112i \(0.192326\pi\)
\(348\) 4.50000 + 7.79423i 0.241225 + 0.417815i
\(349\) −1.00000 1.73205i −0.0535288 0.0927146i 0.838019 0.545640i \(-0.183714\pi\)
−0.891548 + 0.452926i \(0.850380\pi\)
\(350\) 5.00000 0.267261
\(351\) 2.50000 + 2.59808i 0.133440 + 0.138675i
\(352\) 3.00000 0.159901
\(353\) −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i \(-0.325675\pi\)
−0.999711 + 0.0240566i \(0.992342\pi\)
\(354\) −3.00000 5.19615i −0.159448 0.276172i
\(355\) 0 0
\(356\) −15.0000 −0.794998
\(357\) 1.50000 2.59808i 0.0793884 0.137505i
\(358\) −12.0000 + 20.7846i −0.634220 + 1.09850i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 2.50000 + 4.33013i 0.131397 + 0.227586i
\(363\) −2.00000 −0.104973
\(364\) 1.00000 3.46410i 0.0524142 0.181568i
\(365\) 0 0
\(366\) −3.50000 6.06218i −0.182948 0.316875i
\(367\) 5.00000 + 8.66025i 0.260998 + 0.452062i 0.966507 0.256639i \(-0.0826151\pi\)
−0.705509 + 0.708700i \(0.749282\pi\)
\(368\) 3.00000 5.19615i 0.156386 0.270868i
\(369\) 3.00000 0.156174
\(370\) 0 0
\(371\) 1.50000 2.59808i 0.0778761 0.134885i
\(372\) 8.00000 0.414781
\(373\) 11.0000 19.0526i 0.569558 0.986504i −0.427051 0.904227i \(-0.640448\pi\)
0.996610 0.0822766i \(-0.0262191\pi\)
\(374\) 4.50000 + 7.79423i 0.232689 + 0.403030i
\(375\) 0 0
\(376\) −3.00000 −0.154713
\(377\) −9.00000 + 31.1769i −0.463524 + 1.60569i
\(378\) −1.00000 −0.0514344
\(379\) 5.00000 + 8.66025i 0.256833 + 0.444847i 0.965392 0.260804i \(-0.0839877\pi\)
−0.708559 + 0.705652i \(0.750654\pi\)
\(380\) 0 0
\(381\) 8.00000 13.8564i 0.409852 0.709885i
\(382\) −6.00000 −0.306987
\(383\) 10.5000 18.1865i 0.536525 0.929288i −0.462563 0.886586i \(-0.653070\pi\)
0.999088 0.0427020i \(-0.0135966\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 0 0
\(386\) 2.50000 4.33013i 0.127247 0.220398i
\(387\) −4.00000 6.92820i −0.203331 0.352180i
\(388\) 8.00000 + 13.8564i 0.406138 + 0.703452i
\(389\) −18.0000 −0.912636 −0.456318 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) −6.00000 10.3923i −0.302660 0.524222i
\(394\) −1.50000 + 2.59808i −0.0755689 + 0.130889i
\(395\) 0 0
\(396\) 1.50000 2.59808i 0.0753778 0.130558i
\(397\) 12.5000 21.6506i 0.627357 1.08661i −0.360723 0.932673i \(-0.617470\pi\)
0.988080 0.153941i \(-0.0491966\pi\)
\(398\) 4.00000 0.200502
\(399\) −2.50000 + 4.33013i −0.125157 + 0.216777i
\(400\) 2.50000 + 4.33013i 0.125000 + 0.216506i
\(401\) −3.00000 5.19615i −0.149813 0.259483i 0.781345 0.624099i \(-0.214534\pi\)
−0.931158 + 0.364615i \(0.881200\pi\)
\(402\) −2.00000 −0.0997509
\(403\) 20.0000 + 20.7846i 0.996271 + 1.03536i
\(404\) 18.0000 0.895533
\(405\) 0 0
\(406\) −4.50000 7.79423i −0.223331 0.386821i
\(407\) 12.0000 20.7846i 0.594818 1.03025i
\(408\) 3.00000 0.148522
\(409\) 11.0000 19.0526i 0.543915 0.942088i −0.454759 0.890614i \(-0.650275\pi\)
0.998674 0.0514740i \(-0.0163919\pi\)
\(410\) 0 0
\(411\) −6.00000 −0.295958
\(412\) 2.00000 3.46410i 0.0985329 0.170664i
\(413\) 3.00000 + 5.19615i 0.147620 + 0.255686i
\(414\) −3.00000 5.19615i −0.147442 0.255377i
\(415\) 0 0
\(416\) 3.50000 0.866025i 0.171602 0.0424604i
\(417\) 11.0000 0.538672
\(418\) −7.50000 12.9904i −0.366837 0.635380i
\(419\) 3.00000 + 5.19615i 0.146560 + 0.253849i 0.929954 0.367677i \(-0.119847\pi\)
−0.783394 + 0.621525i \(0.786513\pi\)
\(420\) 0 0
\(421\) 26.0000 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) −11.0000 + 19.0526i −0.535472 + 0.927464i
\(423\) −1.50000 + 2.59808i −0.0729325 + 0.126323i
\(424\) 3.00000 0.145693
\(425\) −7.50000 + 12.9904i −0.363803 + 0.630126i
\(426\) −3.00000 5.19615i −0.145350 0.251754i
\(427\) 3.50000 + 6.06218i 0.169377 + 0.293369i
\(428\) 9.00000 0.435031
\(429\) 10.5000 2.59808i 0.506945 0.125436i
\(430\) 0 0
\(431\) 9.00000 + 15.5885i 0.433515 + 0.750870i 0.997173 0.0751385i \(-0.0239399\pi\)
−0.563658 + 0.826008i \(0.690607\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −7.00000 + 12.1244i −0.336399 + 0.582659i −0.983752 0.179530i \(-0.942542\pi\)
0.647354 + 0.762190i \(0.275876\pi\)
\(434\) −8.00000 −0.384012
\(435\) 0 0
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) −30.0000 −1.43509
\(438\) −8.00000 + 13.8564i −0.382255 + 0.662085i
\(439\) −16.0000 27.7128i −0.763638 1.32266i −0.940963 0.338508i \(-0.890078\pi\)
0.177325 0.984152i \(-0.443256\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 7.50000 + 7.79423i 0.356739 + 0.370734i
\(443\) 33.0000 1.56788 0.783939 0.620838i \(-0.213208\pi\)
0.783939 + 0.620838i \(0.213208\pi\)
\(444\) −4.00000 6.92820i −0.189832 0.328798i
\(445\) 0 0
\(446\) 4.00000 6.92820i 0.189405 0.328060i
\(447\) −6.00000 −0.283790
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) −12.0000 + 20.7846i −0.566315 + 0.980886i 0.430611 + 0.902538i \(0.358298\pi\)
−0.996926 + 0.0783487i \(0.975035\pi\)
\(450\) 5.00000 0.235702
\(451\) 4.50000 7.79423i 0.211897 0.367016i
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) 9.50000 + 16.4545i 0.446349 + 0.773099i
\(454\) 6.00000 0.281594
\(455\) 0 0
\(456\) −5.00000 −0.234146
\(457\) −19.0000 32.9090i −0.888783 1.53942i −0.841316 0.540544i \(-0.818219\pi\)
−0.0474665 0.998873i \(-0.515115\pi\)
\(458\) 2.50000 + 4.33013i 0.116817 + 0.202334i
\(459\) 1.50000 2.59808i 0.0700140 0.121268i
\(460\) 0 0
\(461\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(462\) −1.50000 + 2.59808i −0.0697863 + 0.120873i
\(463\) −31.0000 −1.44069 −0.720346 0.693615i \(-0.756017\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 0 0
\(466\) −12.0000 20.7846i −0.555889 0.962828i
\(467\) −24.0000 −1.11059 −0.555294 0.831654i \(-0.687394\pi\)
−0.555294 + 0.831654i \(0.687394\pi\)
\(468\) 1.00000 3.46410i 0.0462250 0.160128i
\(469\) 2.00000 0.0923514
\(470\) 0 0
\(471\) −1.00000 1.73205i −0.0460776 0.0798087i
\(472\) −3.00000 + 5.19615i −0.138086 + 0.239172i
\(473\) −24.0000 −1.10352
\(474\) −6.50000 + 11.2583i −0.298555 + 0.517112i
\(475\) 12.5000 21.6506i 0.573539 0.993399i
\(476\) −3.00000 −0.137505
\(477\) 1.50000 2.59808i 0.0686803 0.118958i
\(478\) −3.00000 5.19615i −0.137217 0.237666i
\(479\) −4.50000 7.79423i −0.205610 0.356127i 0.744717 0.667381i \(-0.232585\pi\)
−0.950327 + 0.311253i \(0.899251\pi\)
\(480\) 0 0
\(481\) 8.00000 27.7128i 0.364769 1.26360i
\(482\) −8.00000 −0.364390
\(483\) 3.00000 + 5.19615i 0.136505 + 0.236433i
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 6.50000 11.2583i 0.294543 0.510164i −0.680335 0.732901i \(-0.738166\pi\)
0.974879 + 0.222737i \(0.0714992\pi\)
\(488\) −3.50000 + 6.06218i −0.158438 + 0.274422i
\(489\) −16.0000 −0.723545
\(490\) 0 0
\(491\) 6.00000 + 10.3923i 0.270776 + 0.468998i 0.969061 0.246822i \(-0.0793863\pi\)
−0.698285 + 0.715820i \(0.746053\pi\)
\(492\) −1.50000 2.59808i −0.0676252 0.117130i
\(493\) 27.0000 1.21602
\(494\) −12.5000 12.9904i −0.562402 0.584465i
\(495\) 0 0
\(496\) −4.00000 6.92820i −0.179605 0.311086i
\(497\) 3.00000 + 5.19615i 0.134568 + 0.233079i
\(498\) 9.00000 15.5885i 0.403300 0.698535i
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −18.0000 −0.803379
\(503\) 12.0000 20.7846i 0.535054 0.926740i −0.464107 0.885779i \(-0.653625\pi\)
0.999161 0.0409609i \(-0.0130419\pi\)
\(504\) 0.500000 + 0.866025i 0.0222718 + 0.0385758i
\(505\) 0 0
\(506\) −18.0000 −0.800198
\(507\) 11.5000 6.06218i 0.510733 0.269231i
\(508\) −16.0000 −0.709885
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 0 0
\(511\) 8.00000 13.8564i 0.353899 0.612971i
\(512\) −1.00000 −0.0441942
\(513\) −2.50000 + 4.33013i −0.110378 + 0.191180i
\(514\) −7.50000 + 12.9904i −0.330811 + 0.572981i
\(515\) 0 0
\(516\) −4.00000 + 6.92820i −0.176090 + 0.304997i
\(517\) 4.50000 + 7.79423i 0.197910 + 0.342790i
\(518\) 4.00000 + 6.92820i 0.175750 + 0.304408i
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 21.0000 0.920027 0.460013 0.887912i \(-0.347845\pi\)
0.460013 + 0.887912i \(0.347845\pi\)
\(522\) −4.50000 7.79423i −0.196960 0.341144i
\(523\) 9.50000 + 16.4545i 0.415406 + 0.719504i 0.995471 0.0950659i \(-0.0303062\pi\)
−0.580065 + 0.814570i \(0.696973\pi\)
\(524\) −6.00000 + 10.3923i −0.262111 + 0.453990i
\(525\) −5.00000 −0.218218
\(526\) 3.00000 5.19615i 0.130806 0.226563i
\(527\) 12.0000 20.7846i 0.522728 0.905392i
\(528\) −3.00000 −0.130558
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 3.00000 + 5.19615i 0.130189 + 0.225494i
\(532\) 5.00000 0.216777
\(533\) 3.00000 10.3923i 0.129944 0.450141i
\(534\) 15.0000 0.649113
\(535\) 0 0
\(536\) 1.00000 + 1.73205i 0.0431934 + 0.0748132i
\(537\) 12.0000 20.7846i 0.517838 0.896922i
\(538\) 0 0
\(539\) 1.50000 2.59808i 0.0646096 0.111907i
\(540\) 0 0
\(541\) −34.0000 −1.46177 −0.730887 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) 10.0000 17.3205i 0.429537 0.743980i
\(543\) −2.50000 4.33013i −0.107285 0.185824i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 0 0
\(546\) −1.00000 + 3.46410i −0.0427960 + 0.148250i
\(547\) −34.0000 −1.45374 −0.726868 0.686778i \(-0.759025\pi\)
−0.726868 + 0.686778i \(0.759025\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) 3.50000 + 6.06218i 0.149376 + 0.258727i
\(550\) 7.50000 12.9904i 0.319801 0.553912i
\(551\) −45.0000 −1.91706
\(552\) −3.00000 + 5.19615i −0.127688 + 0.221163i
\(553\) 6.50000 11.2583i 0.276408 0.478753i
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) −5.50000 9.52628i −0.233252 0.404004i
\(557\) −1.50000 2.59808i −0.0635570 0.110084i 0.832496 0.554031i \(-0.186911\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(558\) −8.00000 −0.338667
\(559\) −28.0000 + 6.92820i −1.18427 + 0.293032i
\(560\) 0 0
\(561\) −4.50000 7.79423i −0.189990 0.329073i
\(562\) −9.00000 15.5885i −0.379642 0.657559i
\(563\) 18.0000 31.1769i 0.758610 1.31395i −0.184950 0.982748i \(-0.559212\pi\)
0.943560 0.331202i \(-0.107454\pi\)
\(564\) 3.00000 0.126323
\(565\) 0 0
\(566\) −2.00000 + 3.46410i −0.0840663 + 0.145607i
\(567\) 1.00000 0.0419961
\(568\) −3.00000 + 5.19615i −0.125877 + 0.218026i
\(569\) 9.00000 + 15.5885i 0.377300 + 0.653502i 0.990668 0.136295i \(-0.0435194\pi\)
−0.613369 + 0.789797i \(0.710186\pi\)
\(570\) 0 0
\(571\) 26.0000 1.08807 0.544033 0.839064i \(-0.316897\pi\)
0.544033 + 0.839064i \(0.316897\pi\)
\(572\) −7.50000 7.79423i −0.313591 0.325893i
\(573\) 6.00000 0.250654
\(574\) 1.50000 + 2.59808i 0.0626088 + 0.108442i
\(575\) −15.0000 25.9808i −0.625543 1.08347i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) −2.50000 + 4.33013i −0.103896 + 0.179954i
\(580\) 0 0
\(581\) −9.00000 + 15.5885i −0.373383 + 0.646718i
\(582\) −8.00000 13.8564i −0.331611 0.574367i
\(583\) −4.50000 7.79423i −0.186371 0.322804i
\(584\) 16.0000 0.662085
\(585\) 0 0
\(586\) 0 0
\(587\) −12.0000 20.7846i −0.495293 0.857873i 0.504692 0.863299i \(-0.331606\pi\)
−0.999985 + 0.00542667i \(0.998273\pi\)
\(588\) −0.500000 0.866025i −0.0206197 0.0357143i
\(589\) −20.0000 + 34.6410i −0.824086 + 1.42736i
\(590\) 0 0
\(591\) 1.50000 2.59808i 0.0617018 0.106871i
\(592\) −4.00000 + 6.92820i −0.164399 + 0.284747i
\(593\) 15.0000 0.615976 0.307988 0.951390i \(-0.400344\pi\)
0.307988 + 0.951390i \(0.400344\pi\)
\(594\) −1.50000 + 2.59808i −0.0615457 + 0.106600i
\(595\) 0 0
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) −4.00000 −0.163709
\(598\) −21.0000 + 5.19615i −0.858754 + 0.212486i
\(599\) 6.00000 0.245153 0.122577 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) −2.50000 4.33013i −0.102062 0.176777i
\(601\) −4.00000 6.92820i −0.163163 0.282607i 0.772838 0.634603i \(-0.218836\pi\)
−0.936002 + 0.351996i \(0.885503\pi\)
\(602\) 4.00000 6.92820i 0.163028 0.282372i
\(603\) 2.00000 0.0814463
\(604\) 9.50000 16.4545i 0.386550 0.669523i
\(605\) 0 0
\(606\) −18.0000 −0.731200
\(607\) −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i \(-0.885242\pi\)
0.773358 + 0.633970i \(0.218576\pi\)
\(608\) 2.50000 + 4.33013i 0.101388 + 0.175610i
\(609\) 4.50000 + 7.79423i 0.182349 + 0.315838i
\(610\) 0 0
\(611\) 7.50000 + 7.79423i 0.303418 + 0.315321i
\(612\) −3.00000 −0.121268
\(613\) 20.0000 + 34.6410i 0.807792 + 1.39914i 0.914390 + 0.404835i \(0.132671\pi\)
−0.106597 + 0.994302i \(0.533996\pi\)
\(614\) −6.50000 11.2583i −0.262319 0.454349i
\(615\) 0 0
\(616\) 3.00000 0.120873
\(617\) 21.0000 36.3731i 0.845428 1.46432i −0.0398207 0.999207i \(-0.512679\pi\)
0.885249 0.465118i \(-0.153988\pi\)
\(618\) −2.00000 + 3.46410i −0.0804518 + 0.139347i
\(619\) −1.00000 −0.0401934 −0.0200967 0.999798i \(-0.506397\pi\)
−0.0200967 + 0.999798i \(0.506397\pi\)
\(620\) 0 0
\(621\) 3.00000 + 5.19615i 0.120386 + 0.208514i
\(622\) −10.5000 18.1865i −0.421012 0.729214i
\(623\) −15.0000 −0.600962
\(624\) −3.50000 + 0.866025i −0.140112 + 0.0346688i
\(625\) 25.0000 1.00000
\(626\) 13.0000 + 22.5167i 0.519584 + 0.899947i
\(627\) 7.50000 + 12.9904i 0.299521 + 0.518786i
\(628\) −1.00000 + 1.73205i −0.0399043 + 0.0691164i
\(629\) −24.0000 −0.956943
\(630\) 0 0
\(631\) 6.50000 11.2583i 0.258761 0.448187i −0.707149 0.707064i \(-0.750019\pi\)
0.965910 + 0.258877i \(0.0833525\pi\)
\(632\) 13.0000 0.517112
\(633\) 11.0000 19.0526i 0.437211 0.757271i
\(634\) 15.0000 + 25.9808i 0.595726 + 1.03183i
\(635\) 0 0
\(636\) −3.00000 −0.118958
\(637\) 1.00000 3.46410i 0.0396214 0.137253i
\(638\) −27.0000 −1.06894
\(639\) 3.00000 + 5.19615i 0.118678 + 0.205557i
\(640\) 0 0
\(641\) −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i \(-0.949015\pi\)
0.631721 + 0.775196i \(0.282349\pi\)
\(642\) −9.00000 −0.355202
\(643\) 15.5000 26.8468i 0.611260 1.05873i −0.379768 0.925082i \(-0.623996\pi\)
0.991028 0.133652i \(-0.0426705\pi\)
\(644\) 3.00000 5.19615i 0.118217 0.204757i
\(645\) 0 0
\(646\) −7.50000 + 12.9904i −0.295084 + 0.511100i
\(647\) −16.5000 28.5788i −0.648682 1.12355i −0.983438 0.181245i \(-0.941987\pi\)
0.334756 0.942305i \(-0.391346\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 18.0000 0.706562
\(650\) 5.00000 17.3205i 0.196116 0.679366i
\(651\) 8.00000 0.313545
\(652\) 8.00000 + 13.8564i 0.313304 + 0.542659i
\(653\) −10.5000 18.1865i −0.410897 0.711694i 0.584091 0.811688i \(-0.301451\pi\)
−0.994988 + 0.0999939i \(0.968118\pi\)
\(654\) 1.00000 1.73205i 0.0391031 0.0677285i
\(655\) 0 0
\(656\) −1.50000 + 2.59808i −0.0585652 + 0.101438i
\(657\) 8.00000 13.8564i 0.312110 0.540590i
\(658\) −3.00000 −0.116952
\(659\) 16.5000 28.5788i 0.642749 1.11327i −0.342068 0.939675i \(-0.611127\pi\)
0.984817 0.173598i \(-0.0555394\pi\)
\(660\) 0 0
\(661\) 11.0000 + 19.0526i 0.427850 + 0.741059i 0.996682 0.0813955i \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) 10.0000 0.388661
\(663\) −7.50000 7.79423i −0.291276 0.302703i
\(664\) −18.0000 −0.698535
\(665\) 0 0
\(666\) 4.00000 + 6.92820i 0.154997 + 0.268462i
\(667\) −27.0000 + 46.7654i −1.04544 + 1.81076i
\(668\) 0 0
\(669\) −4.00000 + 6.92820i −0.154649 + 0.267860i
\(670\) 0 0
\(671\) 21.0000 0.810696
\(672\) 0.500000 0.866025i 0.0192879 0.0334077i
\(673\) 0.500000 + 0.866025i 0.0192736 + 0.0333828i 0.875501 0.483216i \(-0.160531\pi\)
−0.856228 + 0.516599i \(0.827198\pi\)
\(674\) 11.5000 + 19.9186i 0.442963 + 0.767235i
\(675\) −5.00000 −0.192450
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) −6.00000 10.3923i −0.230429 0.399114i
\(679\) 8.00000 + 13.8564i 0.307012 + 0.531760i
\(680\) 0 0
\(681\) −6.00000 −0.229920
\(682\) −12.0000 + 20.7846i −0.459504 + 0.795884i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) 5.00000 0.191180
\(685\) 0 0
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) −2.50000 4.33013i −0.0953809 0.165205i
\(688\) 8.00000 0.304997
\(689\) −7.50000 7.79423i −0.285727 0.296936i
\(690\) 0 0
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 3.00000 + 5.19615i 0.114043 + 0.197528i
\(693\) 1.50000 2.59808i 0.0569803 0.0986928i
\(694\) −3.00000 −0.113878
\(695\) 0 0
\(696\) −4.50000 + 7.79423i −0.170572 + 0.295439i
\(697\) −9.00000 −0.340899
\(698\) 1.00000 1.73205i 0.0378506 0.0655591i
\(699\) 12.0000 + 20.7846i 0.453882 + 0.786146i
\(700\) 2.50000 + 4.33013i 0.0944911 + 0.163663i
\(701\) −21.0000 −0.793159 −0.396580 0.918000i \(-0.629803\pi\)
−0.396580 + 0.918000i \(0.629803\pi\)
\(702\) −1.00000 + 3.46410i −0.0377426 + 0.130744i
\(703\) 40.0000 1.50863
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) 9.00000 15.5885i 0.338719 0.586679i
\(707\) 18.0000 0.676960
\(708\) 3.00000 5.19615i 0.112747 0.195283i
\(709\) −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) 0 0
\(711\) 6.50000 11.2583i 0.243769 0.422220i
\(712\) −7.50000 12.9904i −0.281074 0.486835i
\(713\) 24.0000 + 41.5692i 0.898807 + 1.55678i
\(714\) 3.00000 0.112272
\(715\) 0 0
\(716\) −24.0000 −0.896922
\(717\) 3.00000 + 5.19615i 0.112037 + 0.194054i
\(718\) 12.0000 + 20.7846i 0.447836 + 0.775675i
\(719\) −4.50000 + 7.79423i −0.167822 + 0.290676i −0.937654 0.347571i \(-0.887007\pi\)
0.769832 + 0.638247i \(0.220340\pi\)
\(720\) 0 0
\(721\) 2.00000 3.46410i 0.0744839 0.129010i
\(722\) 3.00000 5.19615i 0.111648 0.193381i
\(723\) 8.00000 0.297523
\(724\) −2.50000 + 4.33013i −0.0929118 + 0.160928i
\(725\) −22.5000 38.9711i −0.835629 1.44735i
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) −16.0000 −0.593407 −0.296704 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 3.50000 0.866025i 0.129719 0.0320970i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) 3.50000 6.06218i 0.129364 0.224065i
\(733\) −37.0000 −1.36663 −0.683313 0.730125i \(-0.739462\pi\)
−0.683313 + 0.730125i \(0.739462\pi\)
\(734\) −5.00000 + 8.66025i −0.184553 + 0.319656i
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 3.00000 5.19615i 0.110506 0.191403i
\(738\) 1.50000 + 2.59808i 0.0552158 + 0.0956365i
\(739\) −1.00000 1.73205i −0.0367856 0.0637145i 0.847046 0.531519i \(-0.178379\pi\)
−0.883832 + 0.467804i \(0.845045\pi\)
\(740\) 0 0
\(741\) 12.5000 + 12.9904i 0.459199 + 0.477214i
\(742\) 3.00000 0.110133
\(743\) 6.00000 + 10.3923i 0.220119 + 0.381257i 0.954844 0.297108i \(-0.0960222\pi\)
−0.734725 + 0.678365i \(0.762689\pi\)
\(744\) 4.00000 + 6.92820i 0.146647 + 0.254000i
\(745\) 0 0
\(746\) 22.0000 0.805477
\(747\) −9.00000 + 15.5885i −0.329293 + 0.570352i
\(748\) −4.50000 + 7.79423i −0.164536 + 0.284985i
\(749\) 9.00000 0.328853
\(750\) 0 0
\(751\) 0.500000 + 0.866025i 0.0182453 + 0.0316017i 0.875004 0.484116i \(-0.160859\pi\)
−0.856759 + 0.515718i \(0.827525\pi\)
\(752\) −1.50000 2.59808i −0.0546994 0.0947421i
\(753\) 18.0000 0.655956
\(754\) −31.5000 + 7.79423i −1.14716 + 0.283849i
\(755\) 0 0
\(756\) −0.500000 0.866025i −0.0181848 0.0314970i
\(757\) 17.0000 + 29.4449i 0.617876 + 1.07019i 0.989873 + 0.141958i \(0.0453398\pi\)
−0.371997 + 0.928234i \(0.621327\pi\)
\(758\) −5.00000 + 8.66025i −0.181608 + 0.314555i
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) −21.0000 + 36.3731i −0.761249 + 1.31852i 0.180957 + 0.983491i \(0.442080\pi\)
−0.942207 + 0.335032i \(0.891253\pi\)
\(762\) 16.0000 0.579619
\(763\) −1.00000 + 1.73205i −0.0362024 + 0.0627044i
\(764\) −3.00000 5.19615i −0.108536 0.187990i
\(765\) 0 0
\(766\) 21.0000 0.758761
\(767\) 21.0000 5.19615i 0.758266 0.187622i
\(768\) 1.00000 0.0360844
\(769\) −4.00000 6.92820i −0.144244 0.249837i 0.784847 0.619690i \(-0.212742\pi\)
−0.929091 + 0.369852i \(0.879408\pi\)
\(770\) 0 0
\(771\) 7.50000 12.9904i 0.270106 0.467837i
\(772\) 5.00000 0.179954
\(773\) −21.0000 + 36.3731i −0.755318 + 1.30825i 0.189899 + 0.981804i \(0.439184\pi\)
−0.945216 + 0.326445i \(0.894149\pi\)
\(774\) 4.00000 6.92820i 0.143777 0.249029i
\(775\) −40.0000 −1.43684
\(776\) −8.00000 + 13.8564i −0.287183 + 0.497416i
\(777\) −4.00000 6.92820i −0.143499 0.248548i
\(778\) −9.00000 15.5885i −0.322666 0.558873i
\(779\) 15.0000 0.537431
\(780\) 0 0
\(781\) 18.0000 0.644091
\(782\) 9.00000 + 15.5885i 0.321839 + 0.557442i
\(783\) 4.50000 + 7.79423i 0.160817 + 0.278543i
\(784\) −0.500000 + 0.866025i −0.0178571 + 0.0309295i