Properties

Label 546.2.s.b.43.1
Level $546$
Weight $2$
Character 546.43
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
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.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 546.43
Dual form 546.2.s.b.127.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -2.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.36603 + 2.36603i) q^{10} +(4.50000 + 2.59808i) q^{11} -1.00000 q^{12} +(-0.866025 - 3.50000i) q^{13} +1.00000 q^{14} +(2.36603 + 1.36603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.86603 - 4.96410i) q^{17} +1.00000i q^{18} +(-5.59808 + 3.23205i) q^{19} +(2.36603 - 1.36603i) q^{20} -1.00000i q^{21} +(-2.59808 - 4.50000i) q^{22} +(-0.267949 + 0.464102i) q^{23} +(0.866025 + 0.500000i) q^{24} -2.46410 q^{25} +(-1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-0.866025 - 0.500000i) q^{28} +(5.23205 - 9.06218i) q^{29} +(-1.36603 - 2.36603i) q^{30} -6.73205i q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.50000 + 2.59808i) q^{33} +5.73205i q^{34} +(1.36603 + 2.36603i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.83013 - 1.63397i) q^{37} +6.46410 q^{38} +(3.46410 + 1.00000i) q^{39} -2.73205 q^{40} +(1.33013 + 0.767949i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-2.63397 - 4.56218i) q^{43} +5.19615i q^{44} +(-2.36603 + 1.36603i) q^{45} +(0.464102 - 0.267949i) q^{46} -9.92820i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.500000 - 0.866025i) q^{49} +(2.13397 + 1.23205i) q^{50} +5.73205 q^{51} +(2.59808 - 2.50000i) q^{52} +3.92820 q^{53} +(-0.866025 - 0.500000i) q^{54} +(7.09808 - 12.2942i) q^{55} +(0.500000 + 0.866025i) q^{56} -6.46410i q^{57} +(-9.06218 + 5.23205i) q^{58} +(4.26795 - 2.46410i) q^{59} +2.73205i q^{60} +(-0.133975 - 0.232051i) q^{61} +(-3.36603 + 5.83013i) q^{62} +(0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(-9.56218 + 2.36603i) q^{65} +5.19615 q^{66} +(-8.66025 - 5.00000i) q^{67} +(2.86603 - 4.96410i) q^{68} +(-0.267949 - 0.464102i) q^{69} -2.73205i q^{70} +(-9.29423 + 5.36603i) q^{71} +(-0.866025 + 0.500000i) q^{72} +5.46410i q^{73} +(1.63397 + 2.83013i) q^{74} +(1.23205 - 2.13397i) q^{75} +(-5.59808 - 3.23205i) q^{76} -5.19615 q^{77} +(-2.50000 - 2.59808i) q^{78} +9.00000 q^{79} +(2.36603 + 1.36603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.767949 - 1.33013i) q^{82} +12.7321i q^{83} +(0.866025 - 0.500000i) q^{84} +(-13.5622 + 7.83013i) q^{85} +5.26795i q^{86} +(5.23205 + 9.06218i) q^{87} +(2.59808 - 4.50000i) q^{88} +(-9.40192 - 5.42820i) q^{89} +2.73205 q^{90} +(2.50000 + 2.59808i) q^{91} -0.535898 q^{92} +(5.83013 + 3.36603i) q^{93} +(-4.96410 + 8.59808i) q^{94} +(8.83013 + 15.2942i) q^{95} +1.00000i q^{96} +(3.29423 - 1.90192i) q^{97} +(-0.866025 + 0.500000i) q^{98} -5.19615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} - 2q^{10} + 18q^{11} - 4q^{12} + 4q^{14} + 6q^{15} - 2q^{16} - 8q^{17} - 12q^{19} + 6q^{20} - 8q^{23} + 4q^{25} - 4q^{26} + 4q^{27} + 14q^{29} - 2q^{30} - 18q^{33} + 2q^{35} + 2q^{36} + 6q^{37} + 12q^{38} - 4q^{40} - 12q^{41} - 2q^{42} - 14q^{43} - 6q^{45} - 12q^{46} - 2q^{48} + 2q^{49} + 12q^{50} + 16q^{51} - 12q^{53} + 18q^{55} + 2q^{56} - 12q^{58} + 24q^{59} - 4q^{61} - 10q^{62} - 4q^{64} - 14q^{65} + 8q^{68} - 8q^{69} - 6q^{71} + 10q^{74} - 2q^{75} - 12q^{76} - 10q^{78} + 36q^{79} + 6q^{80} - 2q^{81} - 10q^{82} - 30q^{85} + 14q^{87} - 48q^{89} + 4q^{90} + 10q^{91} - 16q^{92} + 6q^{93} - 6q^{94} + 18q^{95} - 18q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 2.73205i 1.22181i −0.791704 0.610905i \(-0.790806\pi\)
0.791704 0.610905i \(-0.209194\pi\)
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.36603 + 2.36603i −0.431975 + 0.748203i
\(11\) 4.50000 + 2.59808i 1.35680 + 0.783349i 0.989191 0.146631i \(-0.0468429\pi\)
0.367610 + 0.929980i \(0.380176\pi\)
\(12\) −1.00000 −0.288675
\(13\) −0.866025 3.50000i −0.240192 0.970725i
\(14\) 1.00000 0.267261
\(15\) 2.36603 + 1.36603i 0.610905 + 0.352706i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.86603 4.96410i −0.695113 1.20397i −0.970143 0.242536i \(-0.922021\pi\)
0.275029 0.961436i \(-0.411312\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −5.59808 + 3.23205i −1.28429 + 0.741483i −0.977629 0.210337i \(-0.932544\pi\)
−0.306658 + 0.951820i \(0.599211\pi\)
\(20\) 2.36603 1.36603i 0.529059 0.305453i
\(21\) 1.00000i 0.218218i
\(22\) −2.59808 4.50000i −0.553912 0.959403i
\(23\) −0.267949 + 0.464102i −0.0558713 + 0.0967719i −0.892608 0.450833i \(-0.851127\pi\)
0.836737 + 0.547605i \(0.184460\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) −2.46410 −0.492820
\(26\) −1.00000 + 3.46410i −0.196116 + 0.679366i
\(27\) 1.00000 0.192450
\(28\) −0.866025 0.500000i −0.163663 0.0944911i
\(29\) 5.23205 9.06218i 0.971567 1.68280i 0.280741 0.959784i \(-0.409420\pi\)
0.690826 0.723021i \(-0.257247\pi\)
\(30\) −1.36603 2.36603i −0.249401 0.431975i
\(31\) 6.73205i 1.20911i −0.796563 0.604556i \(-0.793351\pi\)
0.796563 0.604556i \(-0.206649\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −4.50000 + 2.59808i −0.783349 + 0.452267i
\(34\) 5.73205i 0.983039i
\(35\) 1.36603 + 2.36603i 0.230900 + 0.399931i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −2.83013 1.63397i −0.465270 0.268624i 0.248988 0.968507i \(-0.419902\pi\)
−0.714258 + 0.699883i \(0.753235\pi\)
\(38\) 6.46410 1.04862
\(39\) 3.46410 + 1.00000i 0.554700 + 0.160128i
\(40\) −2.73205 −0.431975
\(41\) 1.33013 + 0.767949i 0.207731 + 0.119934i 0.600256 0.799808i \(-0.295065\pi\)
−0.392525 + 0.919741i \(0.628399\pi\)
\(42\) −0.500000 + 0.866025i −0.0771517 + 0.133631i
\(43\) −2.63397 4.56218i −0.401677 0.695726i 0.592251 0.805753i \(-0.298239\pi\)
−0.993929 + 0.110028i \(0.964906\pi\)
\(44\) 5.19615i 0.783349i
\(45\) −2.36603 + 1.36603i −0.352706 + 0.203635i
\(46\) 0.464102 0.267949i 0.0684280 0.0395070i
\(47\) 9.92820i 1.44818i −0.689707 0.724089i \(-0.742261\pi\)
0.689707 0.724089i \(-0.257739\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 2.13397 + 1.23205i 0.301790 + 0.174238i
\(51\) 5.73205 0.802648
\(52\) 2.59808 2.50000i 0.360288 0.346688i
\(53\) 3.92820 0.539580 0.269790 0.962919i \(-0.413046\pi\)
0.269790 + 0.962919i \(0.413046\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 7.09808 12.2942i 0.957104 1.65775i
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) 6.46410i 0.856191i
\(58\) −9.06218 + 5.23205i −1.18992 + 0.687002i
\(59\) 4.26795 2.46410i 0.555640 0.320799i −0.195754 0.980653i \(-0.562715\pi\)
0.751394 + 0.659854i \(0.229382\pi\)
\(60\) 2.73205i 0.352706i
\(61\) −0.133975 0.232051i −0.0171537 0.0297111i 0.857321 0.514782i \(-0.172127\pi\)
−0.874475 + 0.485071i \(0.838794\pi\)
\(62\) −3.36603 + 5.83013i −0.427486 + 0.740427i
\(63\) 0.866025 + 0.500000i 0.109109 + 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) −9.56218 + 2.36603i −1.18604 + 0.293469i
\(66\) 5.19615 0.639602
\(67\) −8.66025 5.00000i −1.05802 0.610847i −0.133135 0.991098i \(-0.542504\pi\)
−0.924883 + 0.380251i \(0.875838\pi\)
\(68\) 2.86603 4.96410i 0.347557 0.601986i
\(69\) −0.267949 0.464102i −0.0322573 0.0558713i
\(70\) 2.73205i 0.326543i
\(71\) −9.29423 + 5.36603i −1.10302 + 0.636830i −0.937013 0.349294i \(-0.886421\pi\)
−0.166009 + 0.986124i \(0.553088\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 5.46410i 0.639525i 0.947498 + 0.319762i \(0.103603\pi\)
−0.947498 + 0.319762i \(0.896397\pi\)
\(74\) 1.63397 + 2.83013i 0.189946 + 0.328996i
\(75\) 1.23205 2.13397i 0.142265 0.246410i
\(76\) −5.59808 3.23205i −0.642143 0.370742i
\(77\) −5.19615 −0.592157
\(78\) −2.50000 2.59808i −0.283069 0.294174i
\(79\) 9.00000 1.01258 0.506290 0.862364i \(-0.331017\pi\)
0.506290 + 0.862364i \(0.331017\pi\)
\(80\) 2.36603 + 1.36603i 0.264530 + 0.152726i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −0.767949 1.33013i −0.0848058 0.146888i
\(83\) 12.7321i 1.39752i 0.715354 + 0.698762i \(0.246265\pi\)
−0.715354 + 0.698762i \(0.753735\pi\)
\(84\) 0.866025 0.500000i 0.0944911 0.0545545i
\(85\) −13.5622 + 7.83013i −1.47102 + 0.849297i
\(86\) 5.26795i 0.568058i
\(87\) 5.23205 + 9.06218i 0.560935 + 0.971567i
\(88\) 2.59808 4.50000i 0.276956 0.479702i
\(89\) −9.40192 5.42820i −0.996602 0.575388i −0.0893608 0.995999i \(-0.528482\pi\)
−0.907241 + 0.420611i \(0.861816\pi\)
\(90\) 2.73205 0.287983
\(91\) 2.50000 + 2.59808i 0.262071 + 0.272352i
\(92\) −0.535898 −0.0558713
\(93\) 5.83013 + 3.36603i 0.604556 + 0.349041i
\(94\) −4.96410 + 8.59808i −0.512008 + 0.886824i
\(95\) 8.83013 + 15.2942i 0.905952 + 1.56915i
\(96\) 1.00000i 0.102062i
\(97\) 3.29423 1.90192i 0.334478 0.193111i −0.323349 0.946280i \(-0.604809\pi\)
0.657828 + 0.753169i \(0.271476\pi\)
\(98\) −0.866025 + 0.500000i −0.0874818 + 0.0505076i
\(99\) 5.19615i 0.522233i
\(100\) −1.23205 2.13397i −0.123205 0.213397i
\(101\) −4.46410 + 7.73205i −0.444195 + 0.769368i −0.997996 0.0632812i \(-0.979843\pi\)
0.553801 + 0.832649i \(0.313177\pi\)
\(102\) −4.96410 2.86603i −0.491519 0.283779i
\(103\) 5.80385 0.571870 0.285935 0.958249i \(-0.407696\pi\)
0.285935 + 0.958249i \(0.407696\pi\)
\(104\) −3.50000 + 0.866025i −0.343203 + 0.0849208i
\(105\) −2.73205 −0.266621
\(106\) −3.40192 1.96410i −0.330424 0.190770i
\(107\) 9.96410 17.2583i 0.963266 1.66843i 0.249063 0.968487i \(-0.419877\pi\)
0.714203 0.699938i \(-0.246789\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 14.7321i 1.41107i 0.708673 + 0.705537i \(0.249294\pi\)
−0.708673 + 0.705537i \(0.750706\pi\)
\(110\) −12.2942 + 7.09808i −1.17221 + 0.676775i
\(111\) 2.83013 1.63397i 0.268624 0.155090i
\(112\) 1.00000i 0.0944911i
\(113\) 4.83013 + 8.36603i 0.454380 + 0.787009i 0.998652 0.0518992i \(-0.0165275\pi\)
−0.544272 + 0.838909i \(0.683194\pi\)
\(114\) −3.23205 + 5.59808i −0.302709 + 0.524308i
\(115\) 1.26795 + 0.732051i 0.118237 + 0.0682641i
\(116\) 10.4641 0.971567
\(117\) −2.59808 + 2.50000i −0.240192 + 0.231125i
\(118\) −4.92820 −0.453678
\(119\) 4.96410 + 2.86603i 0.455058 + 0.262728i
\(120\) 1.36603 2.36603i 0.124700 0.215988i
\(121\) 8.00000 + 13.8564i 0.727273 + 1.25967i
\(122\) 0.267949i 0.0242590i
\(123\) −1.33013 + 0.767949i −0.119934 + 0.0692436i
\(124\) 5.83013 3.36603i 0.523561 0.302278i
\(125\) 6.92820i 0.619677i
\(126\) −0.500000 0.866025i −0.0445435 0.0771517i
\(127\) −3.19615 + 5.53590i −0.283613 + 0.491232i −0.972272 0.233854i \(-0.924866\pi\)
0.688659 + 0.725085i \(0.258200\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 5.26795 0.463817
\(130\) 9.46410 + 2.73205i 0.830057 + 0.239617i
\(131\) −1.07180 −0.0936433 −0.0468217 0.998903i \(-0.514909\pi\)
−0.0468217 + 0.998903i \(0.514909\pi\)
\(132\) −4.50000 2.59808i −0.391675 0.226134i
\(133\) 3.23205 5.59808i 0.280254 0.485415i
\(134\) 5.00000 + 8.66025i 0.431934 + 0.748132i
\(135\) 2.73205i 0.235137i
\(136\) −4.96410 + 2.86603i −0.425668 + 0.245760i
\(137\) 10.8564 6.26795i 0.927525 0.535507i 0.0414973 0.999139i \(-0.486787\pi\)
0.886028 + 0.463632i \(0.153454\pi\)
\(138\) 0.535898i 0.0456187i
\(139\) 10.5263 + 18.2321i 0.892827 + 1.54642i 0.836471 + 0.548012i \(0.184615\pi\)
0.0563567 + 0.998411i \(0.482052\pi\)
\(140\) −1.36603 + 2.36603i −0.115450 + 0.199966i
\(141\) 8.59808 + 4.96410i 0.724089 + 0.418053i
\(142\) 10.7321 0.900614
\(143\) 5.19615 18.0000i 0.434524 1.50524i
\(144\) 1.00000 0.0833333
\(145\) −24.7583 14.2942i −2.05607 1.18707i
\(146\) 2.73205 4.73205i 0.226106 0.391627i
\(147\) 0.500000 + 0.866025i 0.0412393 + 0.0714286i
\(148\) 3.26795i 0.268624i
\(149\) 6.92820 4.00000i 0.567581 0.327693i −0.188602 0.982054i \(-0.560396\pi\)
0.756182 + 0.654361i \(0.227062\pi\)
\(150\) −2.13397 + 1.23205i −0.174238 + 0.100597i
\(151\) 9.19615i 0.748372i 0.927354 + 0.374186i \(0.122078\pi\)
−0.927354 + 0.374186i \(0.877922\pi\)
\(152\) 3.23205 + 5.59808i 0.262154 + 0.454064i
\(153\) −2.86603 + 4.96410i −0.231704 + 0.401324i
\(154\) 4.50000 + 2.59808i 0.362620 + 0.209359i
\(155\) −18.3923 −1.47731
\(156\) 0.866025 + 3.50000i 0.0693375 + 0.280224i
\(157\) −4.53590 −0.362004 −0.181002 0.983483i \(-0.557934\pi\)
−0.181002 + 0.983483i \(0.557934\pi\)
\(158\) −7.79423 4.50000i −0.620076 0.358001i
\(159\) −1.96410 + 3.40192i −0.155763 + 0.269790i
\(160\) −1.36603 2.36603i −0.107994 0.187051i
\(161\) 0.535898i 0.0422347i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) −14.8301 + 8.56218i −1.16159 + 0.670642i −0.951683 0.307081i \(-0.900648\pi\)
−0.209902 + 0.977722i \(0.567314\pi\)
\(164\) 1.53590i 0.119934i
\(165\) 7.09808 + 12.2942i 0.552584 + 0.957104i
\(166\) 6.36603 11.0263i 0.494099 0.855805i
\(167\) 16.3923 + 9.46410i 1.26847 + 0.732354i 0.974699 0.223520i \(-0.0717549\pi\)
0.293775 + 0.955874i \(0.405088\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −11.5000 + 6.06218i −0.884615 + 0.466321i
\(170\) 15.6603 1.20109
\(171\) 5.59808 + 3.23205i 0.428096 + 0.247161i
\(172\) 2.63397 4.56218i 0.200839 0.347863i
\(173\) −4.09808 7.09808i −0.311571 0.539657i 0.667132 0.744940i \(-0.267522\pi\)
−0.978703 + 0.205283i \(0.934188\pi\)
\(174\) 10.4641i 0.793281i
\(175\) 2.13397 1.23205i 0.161313 0.0931343i
\(176\) −4.50000 + 2.59808i −0.339200 + 0.195837i
\(177\) 4.92820i 0.370426i
\(178\) 5.42820 + 9.40192i 0.406861 + 0.704704i
\(179\) 1.73205 3.00000i 0.129460 0.224231i −0.794008 0.607908i \(-0.792009\pi\)
0.923467 + 0.383677i \(0.125342\pi\)
\(180\) −2.36603 1.36603i −0.176353 0.101818i
\(181\) 17.7321 1.31801 0.659006 0.752137i \(-0.270977\pi\)
0.659006 + 0.752137i \(0.270977\pi\)
\(182\) −0.866025 3.50000i −0.0641941 0.259437i
\(183\) 0.267949 0.0198074
\(184\) 0.464102 + 0.267949i 0.0342140 + 0.0197535i
\(185\) −4.46410 + 7.73205i −0.328207 + 0.568472i
\(186\) −3.36603 5.83013i −0.246809 0.427486i
\(187\) 29.7846i 2.17807i
\(188\) 8.59808 4.96410i 0.627079 0.362044i
\(189\) −0.866025 + 0.500000i −0.0629941 + 0.0363696i
\(190\) 17.6603i 1.28121i
\(191\) −1.09808 1.90192i −0.0794540 0.137618i 0.823560 0.567228i \(-0.191984\pi\)
−0.903014 + 0.429610i \(0.858651\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 20.4282 + 11.7942i 1.47045 + 0.848967i 0.999450 0.0331638i \(-0.0105583\pi\)
0.471004 + 0.882131i \(0.343892\pi\)
\(194\) −3.80385 −0.273100
\(195\) 2.73205 9.46410i 0.195646 0.677738i
\(196\) 1.00000 0.0714286
\(197\) −3.23205 1.86603i −0.230274 0.132949i 0.380424 0.924812i \(-0.375778\pi\)
−0.610698 + 0.791863i \(0.709111\pi\)
\(198\) −2.59808 + 4.50000i −0.184637 + 0.319801i
\(199\) −3.29423 5.70577i −0.233522 0.404471i 0.725320 0.688412i \(-0.241692\pi\)
−0.958842 + 0.283940i \(0.908358\pi\)
\(200\) 2.46410i 0.174238i
\(201\) 8.66025 5.00000i 0.610847 0.352673i
\(202\) 7.73205 4.46410i 0.544025 0.314093i
\(203\) 10.4641i 0.734436i
\(204\) 2.86603 + 4.96410i 0.200662 + 0.347557i
\(205\) 2.09808 3.63397i 0.146536 0.253808i
\(206\) −5.02628 2.90192i −0.350197 0.202187i
\(207\) 0.535898 0.0372475
\(208\) 3.46410 + 1.00000i 0.240192 + 0.0693375i
\(209\) −33.5885 −2.32336
\(210\) 2.36603 + 1.36603i 0.163271 + 0.0942647i
\(211\) −5.53590 + 9.58846i −0.381107 + 0.660097i −0.991221 0.132217i \(-0.957790\pi\)
0.610114 + 0.792314i \(0.291124\pi\)
\(212\) 1.96410 + 3.40192i 0.134895 + 0.233645i
\(213\) 10.7321i 0.735348i
\(214\) −17.2583 + 9.96410i −1.17976 + 0.681132i
\(215\) −12.4641 + 7.19615i −0.850045 + 0.490774i
\(216\) 1.00000i 0.0680414i
\(217\) 3.36603 + 5.83013i 0.228501 + 0.395775i
\(218\) 7.36603 12.7583i 0.498890 0.864103i
\(219\) −4.73205 2.73205i −0.319762 0.184615i
\(220\) 14.1962 0.957104
\(221\) −14.8923 + 14.3301i −1.00176 + 0.963949i
\(222\) −3.26795 −0.219330
\(223\) −1.26795 0.732051i −0.0849082 0.0490217i 0.456945 0.889495i \(-0.348944\pi\)
−0.541853 + 0.840473i \(0.682277\pi\)
\(224\) −0.500000 + 0.866025i −0.0334077 + 0.0578638i
\(225\) 1.23205 + 2.13397i 0.0821367 + 0.142265i
\(226\) 9.66025i 0.642591i
\(227\) −18.4641 + 10.6603i −1.22551 + 0.707546i −0.966086 0.258219i \(-0.916864\pi\)
−0.259419 + 0.965765i \(0.583531\pi\)
\(228\) 5.59808 3.23205i 0.370742 0.214048i
\(229\) 3.39230i 0.224170i −0.993699 0.112085i \(-0.964247\pi\)
0.993699 0.112085i \(-0.0357529\pi\)
\(230\) −0.732051 1.26795i −0.0482700 0.0836061i
\(231\) 2.59808 4.50000i 0.170941 0.296078i
\(232\) −9.06218 5.23205i −0.594961 0.343501i
\(233\) −12.5885 −0.824697 −0.412349 0.911026i \(-0.635291\pi\)
−0.412349 + 0.911026i \(0.635291\pi\)
\(234\) 3.50000 0.866025i 0.228802 0.0566139i
\(235\) −27.1244 −1.76940
\(236\) 4.26795 + 2.46410i 0.277820 + 0.160399i
\(237\) −4.50000 + 7.79423i −0.292306 + 0.506290i
\(238\) −2.86603 4.96410i −0.185777 0.321775i
\(239\) 4.58846i 0.296803i −0.988927 0.148401i \(-0.952587\pi\)
0.988927 0.148401i \(-0.0474127\pi\)
\(240\) −2.36603 + 1.36603i −0.152726 + 0.0881766i
\(241\) 2.53590 1.46410i 0.163352 0.0943111i −0.416096 0.909321i \(-0.636602\pi\)
0.579447 + 0.815010i \(0.303269\pi\)
\(242\) 16.0000i 1.02852i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0.133975 0.232051i 0.00857684 0.0148555i
\(245\) −2.36603 1.36603i −0.151160 0.0872722i
\(246\) 1.53590 0.0979253
\(247\) 16.1603 + 16.7942i 1.02825 + 1.06859i
\(248\) −6.73205 −0.427486
\(249\) −11.0263 6.36603i −0.698762 0.403430i
\(250\) −3.46410 + 6.00000i −0.219089 + 0.379473i
\(251\) −13.7583 23.8301i −0.868418 1.50414i −0.863613 0.504156i \(-0.831804\pi\)
−0.00480540 0.999988i \(-0.501530\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) −2.41154 + 1.39230i −0.151612 + 0.0875335i
\(254\) 5.53590 3.19615i 0.347353 0.200544i
\(255\) 15.6603i 0.980683i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.52628 11.3038i 0.407098 0.705115i −0.587465 0.809250i \(-0.699874\pi\)
0.994563 + 0.104135i \(0.0332074\pi\)
\(258\) −4.56218 2.63397i −0.284029 0.163984i
\(259\) 3.26795 0.203060
\(260\) −6.83013 7.09808i −0.423586 0.440204i
\(261\) −10.4641 −0.647712
\(262\) 0.928203 + 0.535898i 0.0573446 + 0.0331079i
\(263\) 10.5622 18.2942i 0.651292 1.12807i −0.331518 0.943449i \(-0.607561\pi\)
0.982810 0.184622i \(-0.0591059\pi\)
\(264\) 2.59808 + 4.50000i 0.159901 + 0.276956i
\(265\) 10.7321i 0.659265i
\(266\) −5.59808 + 3.23205i −0.343240 + 0.198170i
\(267\) 9.40192 5.42820i 0.575388 0.332201i
\(268\) 10.0000i 0.610847i
\(269\) 2.00000 + 3.46410i 0.121942 + 0.211210i 0.920534 0.390664i \(-0.127754\pi\)
−0.798591 + 0.601874i \(0.794421\pi\)
\(270\) −1.36603 + 2.36603i −0.0831337 + 0.143992i
\(271\) 8.36603 + 4.83013i 0.508200 + 0.293409i 0.732093 0.681204i \(-0.238543\pi\)
−0.223894 + 0.974614i \(0.571877\pi\)
\(272\) 5.73205 0.347557
\(273\) −3.50000 + 0.866025i −0.211830 + 0.0524142i
\(274\) −12.5359 −0.757321
\(275\) −11.0885 6.40192i −0.668659 0.386051i
\(276\) 0.267949 0.464102i 0.0161286 0.0279356i
\(277\) 3.19615 + 5.53590i 0.192038 + 0.332620i 0.945926 0.324384i \(-0.105157\pi\)
−0.753887 + 0.657004i \(0.771824\pi\)
\(278\) 21.0526i 1.26265i
\(279\) −5.83013 + 3.36603i −0.349041 + 0.201519i
\(280\) 2.36603 1.36603i 0.141397 0.0816356i
\(281\) 9.26795i 0.552879i 0.961031 + 0.276440i \(0.0891546\pi\)
−0.961031 + 0.276440i \(0.910845\pi\)
\(282\) −4.96410 8.59808i −0.295608 0.512008i
\(283\) 4.92820 8.53590i 0.292951 0.507406i −0.681555 0.731767i \(-0.738696\pi\)
0.974506 + 0.224360i \(0.0720293\pi\)
\(284\) −9.29423 5.36603i −0.551511 0.318415i
\(285\) −17.6603 −1.04610
\(286\) −13.5000 + 12.9904i −0.798272 + 0.768137i
\(287\) −1.53590 −0.0906612
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) −7.92820 + 13.7321i −0.466365 + 0.807768i
\(290\) 14.2942 + 24.7583i 0.839386 + 1.45386i
\(291\) 3.80385i 0.222985i
\(292\) −4.73205 + 2.73205i −0.276922 + 0.159881i
\(293\) −12.9282 + 7.46410i −0.755274 + 0.436057i −0.827596 0.561324i \(-0.810292\pi\)
0.0723226 + 0.997381i \(0.476959\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) −6.73205 11.6603i −0.391955 0.678886i
\(296\) −1.63397 + 2.83013i −0.0949728 + 0.164498i
\(297\) 4.50000 + 2.59808i 0.261116 + 0.150756i
\(298\) −8.00000 −0.463428
\(299\) 1.85641 + 0.535898i 0.107359 + 0.0309918i
\(300\) 2.46410 0.142265
\(301\) 4.56218 + 2.63397i 0.262960 + 0.151820i
\(302\) 4.59808 7.96410i 0.264590 0.458283i
\(303\) −4.46410 7.73205i −0.256456 0.444195i
\(304\) 6.46410i 0.370742i
\(305\) −0.633975 + 0.366025i −0.0363013 + 0.0209586i
\(306\) 4.96410 2.86603i 0.283779 0.163840i
\(307\) 5.00000i 0.285365i −0.989769 0.142683i \(-0.954427\pi\)
0.989769 0.142683i \(-0.0455728\pi\)
\(308\) −2.59808 4.50000i −0.148039 0.256411i
\(309\) −2.90192 + 5.02628i −0.165085 + 0.285935i
\(310\) 15.9282 + 9.19615i 0.904661 + 0.522306i
\(311\) 25.1962 1.42874 0.714371 0.699767i \(-0.246713\pi\)
0.714371 + 0.699767i \(0.246713\pi\)
\(312\) 1.00000 3.46410i 0.0566139 0.196116i
\(313\) 31.1244 1.75925 0.879626 0.475665i \(-0.157793\pi\)
0.879626 + 0.475665i \(0.157793\pi\)
\(314\) 3.92820 + 2.26795i 0.221681 + 0.127988i
\(315\) 1.36603 2.36603i 0.0769668 0.133310i
\(316\) 4.50000 + 7.79423i 0.253145 + 0.438460i
\(317\) 26.7846i 1.50437i −0.658950 0.752187i \(-0.728999\pi\)
0.658950 0.752187i \(-0.271001\pi\)
\(318\) 3.40192 1.96410i 0.190770 0.110141i
\(319\) 47.0885 27.1865i 2.63645 1.52215i
\(320\) 2.73205i 0.152726i
\(321\) 9.96410 + 17.2583i 0.556142 + 0.963266i
\(322\) −0.267949 + 0.464102i −0.0149322 + 0.0258634i
\(323\) 32.0885 + 18.5263i 1.78545 + 1.03083i
\(324\) −1.00000 −0.0555556
\(325\) 2.13397 + 8.62436i 0.118372 + 0.478393i
\(326\) 17.1244 0.948430
\(327\) −12.7583 7.36603i −0.705537 0.407342i
\(328\) 0.767949 1.33013i 0.0424029 0.0734440i
\(329\) 4.96410 + 8.59808i 0.273680 + 0.474027i
\(330\) 14.1962i 0.781472i
\(331\) 30.1244 17.3923i 1.65578 0.955968i 0.681156 0.732138i \(-0.261478\pi\)
0.974628 0.223829i \(-0.0718558\pi\)
\(332\) −11.0263 + 6.36603i −0.605146 + 0.349381i
\(333\) 3.26795i 0.179083i
\(334\) −9.46410 16.3923i −0.517853 0.896947i
\(335\) −13.6603 + 23.6603i −0.746339 + 1.29270i
\(336\) 0.866025 + 0.500000i 0.0472456 + 0.0272772i
\(337\) −11.0000 −0.599208 −0.299604 0.954064i \(-0.596855\pi\)
−0.299604 + 0.954064i \(0.596855\pi\)
\(338\) 12.9904 + 0.500000i 0.706584 + 0.0271964i
\(339\) −9.66025 −0.524673
\(340\) −13.5622 7.83013i −0.735512 0.424648i
\(341\) 17.4904 30.2942i 0.947157 1.64052i
\(342\) −3.23205 5.59808i −0.174769 0.302709i
\(343\) 1.00000i 0.0539949i
\(344\) −4.56218 + 2.63397i −0.245976 + 0.142014i
\(345\) −1.26795 + 0.732051i −0.0682641 + 0.0394123i
\(346\) 8.19615i 0.440628i
\(347\) −0.232051 0.401924i −0.0124571 0.0215764i 0.859730 0.510749i \(-0.170632\pi\)
−0.872187 + 0.489173i \(0.837299\pi\)
\(348\) −5.23205 + 9.06218i −0.280467 + 0.485784i
\(349\) −29.3205 16.9282i −1.56949 0.906146i −0.996228 0.0867744i \(-0.972344\pi\)
−0.573263 0.819372i \(-0.694323\pi\)
\(350\) −2.46410 −0.131712
\(351\) −0.866025 3.50000i −0.0462250 0.186816i
\(352\) 5.19615 0.276956
\(353\) 2.87564 + 1.66025i 0.153055 + 0.0883664i 0.574572 0.818454i \(-0.305169\pi\)
−0.421516 + 0.906821i \(0.638502\pi\)
\(354\) 2.46410 4.26795i 0.130966 0.226839i
\(355\) 14.6603 + 25.3923i 0.778085 + 1.34768i
\(356\) 10.8564i 0.575388i
\(357\) −4.96410 + 2.86603i −0.262728 + 0.151686i
\(358\) −3.00000 + 1.73205i −0.158555 + 0.0915417i
\(359\) 24.4449i 1.29015i 0.764119 + 0.645075i \(0.223174\pi\)
−0.764119 + 0.645075i \(0.776826\pi\)
\(360\) 1.36603 + 2.36603i 0.0719959 + 0.124700i
\(361\) 11.3923 19.7321i 0.599595 1.03853i
\(362\) −15.3564 8.86603i −0.807115 0.465988i
\(363\) −16.0000 −0.839782
\(364\) −1.00000 + 3.46410i −0.0524142 + 0.181568i
\(365\) 14.9282 0.781378
\(366\) −0.232051 0.133975i −0.0121295 0.00700296i
\(367\) 10.6603 18.4641i 0.556461 0.963818i −0.441328 0.897346i \(-0.645492\pi\)
0.997788 0.0664722i \(-0.0211744\pi\)
\(368\) −0.267949 0.464102i −0.0139678 0.0241930i
\(369\) 1.53590i 0.0799557i
\(370\) 7.73205 4.46410i 0.401970 0.232078i
\(371\) −3.40192 + 1.96410i −0.176619 + 0.101971i
\(372\) 6.73205i 0.349041i
\(373\) −4.56218 7.90192i −0.236221 0.409146i 0.723406 0.690423i \(-0.242575\pi\)
−0.959627 + 0.281277i \(0.909242\pi\)
\(374\) −14.8923 + 25.7942i −0.770063 + 1.33379i
\(375\) 6.00000 + 3.46410i 0.309839 + 0.178885i
\(376\) −9.92820 −0.512008
\(377\) −36.2487 10.4641i −1.86690 0.538929i
\(378\) 1.00000 0.0514344
\(379\) −1.77757 1.02628i −0.0913075 0.0527164i 0.453651 0.891179i \(-0.350121\pi\)
−0.544959 + 0.838463i \(0.683455\pi\)
\(380\) −8.83013 + 15.2942i −0.452976 + 0.784577i
\(381\) −3.19615 5.53590i −0.163744 0.283613i
\(382\) 2.19615i 0.112365i
\(383\) −26.8468 + 15.5000i −1.37181 + 0.792013i −0.991155 0.132706i \(-0.957633\pi\)
−0.380651 + 0.924719i \(0.624300\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 14.1962i 0.723503i
\(386\) −11.7942 20.4282i −0.600310 1.03977i
\(387\) −2.63397 + 4.56218i −0.133892 + 0.231909i
\(388\) 3.29423 + 1.90192i 0.167239 + 0.0965556i
\(389\) 14.5359 0.736999 0.368500 0.929628i \(-0.379872\pi\)
0.368500 + 0.929628i \(0.379872\pi\)
\(390\) −7.09808 + 6.83013i −0.359425 + 0.345857i
\(391\) 3.07180 0.155347
\(392\) −0.866025 0.500000i −0.0437409 0.0252538i
\(393\) 0.535898 0.928203i 0.0270325 0.0468217i
\(394\) 1.86603 + 3.23205i 0.0940090 + 0.162828i
\(395\) 24.5885i 1.23718i
\(396\) 4.50000 2.59808i 0.226134 0.130558i
\(397\) 0.526279 0.303848i 0.0264132 0.0152497i −0.486735 0.873550i \(-0.661812\pi\)
0.513148 + 0.858300i \(0.328479\pi\)
\(398\) 6.58846i 0.330250i
\(399\) 3.23205 + 5.59808i 0.161805 + 0.280254i
\(400\) 1.23205 2.13397i 0.0616025 0.106699i
\(401\) 21.5885 + 12.4641i 1.07808 + 0.622428i 0.930377 0.366605i \(-0.119480\pi\)
0.147699 + 0.989032i \(0.452813\pi\)
\(402\) −10.0000 −0.498755
\(403\) −23.5622 + 5.83013i −1.17372 + 0.290419i
\(404\) −8.92820 −0.444195
\(405\) 2.36603 + 1.36603i 0.117569 + 0.0678783i
\(406\) 5.23205 9.06218i 0.259662 0.449748i
\(407\) −8.49038 14.7058i −0.420853 0.728938i
\(408\) 5.73205i 0.283779i
\(409\) −12.6340 + 7.29423i −0.624710 + 0.360676i −0.778700 0.627396i \(-0.784121\pi\)
0.153991 + 0.988072i \(0.450787\pi\)
\(410\) −3.63397 + 2.09808i −0.179469 + 0.103617i
\(411\) 12.5359i 0.618350i
\(412\) 2.90192 + 5.02628i 0.142968 + 0.247627i
\(413\) −2.46410 + 4.26795i −0.121251 + 0.210012i
\(414\) −0.464102 0.267949i −0.0228093 0.0131690i
\(415\) 34.7846 1.70751
\(416\) −2.50000 2.59808i −0.122573 0.127381i
\(417\) −21.0526 −1.03095
\(418\) 29.0885 + 16.7942i 1.42276 + 0.821433i
\(419\) −8.29423 + 14.3660i −0.405200 + 0.701826i −0.994345 0.106201i \(-0.966131\pi\)
0.589145 + 0.808027i \(0.299465\pi\)
\(420\) −1.36603 2.36603i −0.0666552 0.115450i
\(421\) 9.32051i 0.454254i −0.973865 0.227127i \(-0.927067\pi\)
0.973865 0.227127i \(-0.0729332\pi\)
\(422\) 9.58846 5.53590i 0.466759 0.269483i
\(423\) −8.59808 + 4.96410i −0.418053 + 0.241363i
\(424\) 3.92820i 0.190770i
\(425\) 7.06218 + 12.2321i 0.342566 + 0.593342i
\(426\) −5.36603 + 9.29423i −0.259985 + 0.450307i
\(427\) 0.232051 + 0.133975i 0.0112297 + 0.00648349i
\(428\) 19.9282 0.963266
\(429\) 12.9904 + 13.5000i 0.627182 + 0.651786i
\(430\) 14.3923 0.694059
\(431\) 9.63397 + 5.56218i 0.464052 + 0.267921i 0.713747 0.700404i \(-0.246997\pi\)
−0.249694 + 0.968325i \(0.580330\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 19.9282 + 34.5167i 0.957688 + 1.65876i 0.728093 + 0.685479i \(0.240407\pi\)
0.229596 + 0.973286i \(0.426260\pi\)
\(434\) 6.73205i 0.323149i
\(435\) 24.7583 14.2942i 1.18707 0.685356i
\(436\) −12.7583 + 7.36603i −0.611013 + 0.352769i
\(437\) 3.46410i 0.165710i
\(438\) 2.73205 + 4.73205i 0.130542 + 0.226106i
\(439\) −5.66025 + 9.80385i −0.270149 + 0.467912i −0.968900 0.247453i \(-0.920406\pi\)
0.698751 + 0.715365i \(0.253740\pi\)
\(440\) −12.2942 7.09808i −0.586104 0.338388i
\(441\) −1.00000 −0.0476190
\(442\) 20.0622 4.96410i 0.954260 0.236118i
\(443\) −25.0000 −1.18779 −0.593893 0.804544i \(-0.702410\pi\)
−0.593893 + 0.804544i \(0.702410\pi\)
\(444\) 2.83013 + 1.63397i 0.134312 + 0.0775450i
\(445\) −14.8301 + 25.6865i −0.703015 + 1.21766i
\(446\) 0.732051 + 1.26795i 0.0346636 + 0.0600391i
\(447\) 8.00000i 0.378387i
\(448\) 0.866025 0.500000i 0.0409159 0.0236228i
\(449\) 19.9019 11.4904i 0.939230 0.542265i 0.0495110 0.998774i \(-0.484234\pi\)
0.889719 + 0.456509i \(0.150900\pi\)
\(450\) 2.46410i 0.116159i
\(451\) 3.99038 + 6.91154i 0.187900 + 0.325452i
\(452\) −4.83013 + 8.36603i −0.227190 + 0.393505i
\(453\) −7.96410 4.59808i −0.374186 0.216036i
\(454\) 21.3205 1.00062
\(455\) 7.09808 6.83013i 0.332763 0.320201i
\(456\) −6.46410 −0.302709
\(457\) −22.2679 12.8564i −1.04165 0.601397i −0.121350 0.992610i \(-0.538722\pi\)
−0.920300 + 0.391212i \(0.872056\pi\)
\(458\) −1.69615 + 2.93782i −0.0792560 + 0.137275i
\(459\) −2.86603 4.96410i −0.133775 0.231704i
\(460\) 1.46410i 0.0682641i
\(461\) 6.00000 3.46410i 0.279448 0.161339i −0.353726 0.935349i \(-0.615085\pi\)
0.633173 + 0.774010i \(0.281752\pi\)
\(462\) −4.50000 + 2.59808i −0.209359 + 0.120873i
\(463\) 32.6603i 1.51785i 0.651178 + 0.758925i \(0.274275\pi\)
−0.651178 + 0.758925i \(0.725725\pi\)
\(464\) 5.23205 + 9.06218i 0.242892 + 0.420701i
\(465\) 9.19615 15.9282i 0.426461 0.738653i
\(466\) 10.9019 + 6.29423i 0.505022 + 0.291575i
\(467\) 5.07180 0.234695 0.117347 0.993091i \(-0.462561\pi\)
0.117347 + 0.993091i \(0.462561\pi\)
\(468\) −3.46410 1.00000i −0.160128 0.0462250i
\(469\) 10.0000 0.461757
\(470\) 23.4904 + 13.5622i 1.08353 + 0.625577i
\(471\) 2.26795 3.92820i 0.104502 0.181002i
\(472\) −2.46410 4.26795i −0.113419 0.196448i
\(473\) 27.3731i 1.25861i
\(474\) 7.79423 4.50000i 0.358001 0.206692i
\(475\) 13.7942 7.96410i 0.632923 0.365418i
\(476\) 5.73205i 0.262728i
\(477\) −1.96410 3.40192i −0.0899300 0.155763i
\(478\) −2.29423 + 3.97372i −0.104936 + 0.181754i
\(479\) 19.7942 + 11.4282i 0.904421 + 0.522168i 0.878632 0.477499i \(-0.158457\pi\)
0.0257894 + 0.999667i \(0.491790\pi\)
\(480\) 2.73205 0.124700
\(481\) −3.26795 + 11.3205i −0.149006 + 0.516171i
\(482\) −2.92820 −0.133376
\(483\) 0.464102 + 0.267949i 0.0211174 + 0.0121921i
\(484\) −8.00000 + 13.8564i −0.363636 + 0.629837i
\(485\) −5.19615 9.00000i −0.235945 0.408669i
\(486\) 1.00000i 0.0453609i
\(487\) −25.5000 + 14.7224i −1.15552 + 0.667137i −0.950225 0.311564i \(-0.899147\pi\)
−0.205290 + 0.978701i \(0.565814\pi\)
\(488\) −0.232051 + 0.133975i −0.0105044 + 0.00606475i
\(489\) 17.1244i 0.774390i
\(490\) 1.36603 + 2.36603i 0.0617107 + 0.106886i
\(491\) 7.19615 12.4641i 0.324758 0.562497i −0.656706 0.754147i \(-0.728051\pi\)
0.981463 + 0.191650i \(0.0613839\pi\)
\(492\) −1.33013 0.767949i −0.0599668 0.0346218i
\(493\) −59.9808 −2.70140
\(494\) −5.59808 22.6244i −0.251869 1.01792i
\(495\) −14.1962 −0.638070
\(496\) 5.83013 + 3.36603i 0.261780 + 0.151139i
\(497\) 5.36603 9.29423i 0.240699 0.416903i
\(498\) 6.36603 + 11.0263i 0.285268 + 0.494099i
\(499\) 10.5885i 0.474004i −0.971509 0.237002i \(-0.923835\pi\)
0.971509 0.237002i \(-0.0761649\pi\)
\(500\) 6.00000 3.46410i 0.268328 0.154919i
\(501\) −16.3923 + 9.46410i −0.732354 + 0.422825i
\(502\) 27.5167i 1.22813i
\(503\) 8.53590 + 14.7846i 0.380597 + 0.659213i 0.991148 0.132764i \(-0.0423852\pi\)
−0.610551 + 0.791977i \(0.709052\pi\)
\(504\) 0.500000 0.866025i 0.0222718 0.0385758i
\(505\) 21.1244 + 12.1962i 0.940021 + 0.542722i
\(506\) 2.78461 0.123791
\(507\) 0.500000 12.9904i 0.0222058 0.576923i
\(508\) −6.39230 −0.283613
\(509\) 10.6865 + 6.16987i 0.473672 + 0.273475i 0.717776 0.696274i \(-0.245160\pi\)
−0.244103 + 0.969749i \(0.578494\pi\)
\(510\) −7.83013 + 13.5622i −0.346724 + 0.600543i
\(511\) −2.73205 4.73205i −0.120859 0.209334i
\(512\) 1.00000i 0.0441942i
\(513\) −5.59808 + 3.23205i −0.247161 + 0.142699i
\(514\) −11.3038 + 6.52628i −0.498591 + 0.287862i
\(515\) 15.8564i 0.698717i
\(516\) 2.63397 + 4.56218i 0.115954 + 0.200839i
\(517\) 25.7942 44.6769i 1.13443 1.96489i
\(518\) −2.83013 1.63397i −0.124349 0.0717927i
\(519\) 8.19615 0.359771
\(520\) 2.36603 + 9.56218i 0.103757 + 0.419329i
\(521\) 9.58846 0.420078 0.210039 0.977693i \(-0.432641\pi\)
0.210039 + 0.977693i \(0.432641\pi\)
\(522\) 9.06218 + 5.23205i 0.396641 + 0.229001i
\(523\) 7.40192 12.8205i 0.323664 0.560602i −0.657577 0.753387i \(-0.728419\pi\)
0.981241 + 0.192785i \(0.0617521\pi\)
\(524\) −0.535898 0.928203i −0.0234108 0.0405487i
\(525\) 2.46410i 0.107542i
\(526\) −18.2942 + 10.5622i −0.797666 + 0.460533i
\(527\) −33.4186 + 19.2942i −1.45574 + 0.840470i
\(528\) 5.19615i 0.226134i
\(529\) 11.3564 + 19.6699i 0.493757 + 0.855212i
\(530\) −5.36603 + 9.29423i −0.233085 + 0.403715i
\(531\) −4.26795 2.46410i −0.185213 0.106933i
\(532\) 6.46410 0.280254
\(533\) 1.53590 5.32051i 0.0665271 0.230457i
\(534\) −10.8564 −0.469803
\(535\) −47.1506 27.2224i −2.03850 1.17693i
\(536\) −5.00000 + 8.66025i −0.215967 + 0.374066i
\(537\) 1.73205 + 3.00000i 0.0747435 + 0.129460i
\(538\) 4.00000i 0.172452i
\(539\) 4.50000 2.59808i 0.193829 0.111907i
\(540\) 2.36603 1.36603i 0.101818 0.0587844i
\(541\) 30.0526i 1.29206i −0.763312 0.646030i \(-0.776428\pi\)
0.763312 0.646030i \(-0.223572\pi\)
\(542\) −4.83013 8.36603i −0.207472 0.359352i
\(543\) −8.86603 + 15.3564i −0.380478 + 0.659006i
\(544\) −4.96410 2.86603i −0.212834 0.122880i
\(545\) 40.2487 1.72407
\(546\) 3.46410 + 1.00000i 0.148250 + 0.0427960i
\(547\) 6.19615 0.264928 0.132464 0.991188i \(-0.457711\pi\)
0.132464 + 0.991188i \(0.457711\pi\)
\(548\) 10.8564 + 6.26795i 0.463763 + 0.267754i
\(549\) −0.133975 + 0.232051i −0.00571790 + 0.00990369i
\(550\) 6.40192 + 11.0885i 0.272979 + 0.472813i
\(551\) 67.6410i 2.88160i
\(552\) −0.464102 + 0.267949i −0.0197535 + 0.0114047i
\(553\) −7.79423 + 4.50000i −0.331444 + 0.191359i
\(554\) 6.39230i 0.271583i
\(555\) −4.46410 7.73205i −0.189491 0.328207i
\(556\) −10.5263 + 18.2321i −0.446414 + 0.773211i
\(557\) −14.0885 8.13397i −0.596947 0.344648i 0.170893 0.985290i \(-0.445335\pi\)
−0.767840 + 0.640642i \(0.778668\pi\)
\(558\) 6.73205 0.284990
\(559\) −13.6865 + 13.1699i −0.578879 + 0.557026i
\(560\) −2.73205 −0.115450
\(561\) 25.7942 + 14.8923i 1.08903 + 0.628754i
\(562\) 4.63397 8.02628i 0.195472 0.338568i
\(563\) 1.83013 + 3.16987i 0.0771307 + 0.133594i 0.902011 0.431713i \(-0.142091\pi\)
−0.824880 + 0.565308i \(0.808757\pi\)
\(564\) 9.92820i 0.418053i
\(565\) 22.8564 13.1962i 0.961576 0.555166i
\(566\) −8.53590 + 4.92820i −0.358791 + 0.207148i
\(567\) 1.00000i 0.0419961i
\(568\) 5.36603 + 9.29423i 0.225153 + 0.389977i
\(569\) −7.83013 + 13.5622i −0.328256 + 0.568556i −0.982166 0.188016i \(-0.939794\pi\)
0.653910 + 0.756572i \(0.273128\pi\)
\(570\) 15.2942 + 8.83013i 0.640605 + 0.369853i
\(571\) −5.51666 −0.230865 −0.115433 0.993315i \(-0.536825\pi\)
−0.115433 + 0.993315i \(0.536825\pi\)
\(572\) 18.1865 4.50000i 0.760417 0.188154i
\(573\) 2.19615 0.0917456
\(574\) 1.33013 + 0.767949i 0.0555184 + 0.0320536i
\(575\) 0.660254 1.14359i 0.0275345 0.0476911i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 2.58846i 0.107759i 0.998547 + 0.0538794i \(0.0171587\pi\)
−0.998547 + 0.0538794i \(0.982841\pi\)
\(578\) 13.7321 7.92820i 0.571178 0.329770i
\(579\) −20.4282 + 11.7942i −0.848967 + 0.490151i
\(580\) 28.5885i 1.18707i
\(581\) −6.36603 11.0263i −0.264107 0.457447i
\(582\) 1.90192 3.29423i 0.0788373 0.136550i
\(583\) 17.6769 + 10.2058i 0.732103 + 0.422680i
\(584\) 5.46410 0.226106
\(585\) 6.83013 + 7.09808i 0.282391 + 0.293469i
\(586\) 14.9282 0.616678
\(587\) −16.5622 9.56218i −0.683594 0.394673i 0.117614 0.993059i \(-0.462476\pi\)
−0.801208 + 0.598386i \(0.795809\pi\)
\(588\) −0.500000 + 0.866025i −0.0206197 + 0.0357143i
\(589\) 21.7583 + 37.6865i 0.896536 + 1.55285i
\(590\) 13.4641i 0.554308i
\(591\) 3.23205 1.86603i 0.132949 0.0767580i
\(592\) 2.83013 1.63397i 0.116318 0.0671559i
\(593\) 37.0000i 1.51941i −0.650269 0.759704i \(-0.725344\pi\)
0.650269 0.759704i \(-0.274656\pi\)
\(594\) −2.59808 4.50000i −0.106600 0.184637i
\(595\) 7.83013 13.5622i 0.321004 0.555995i
\(596\) 6.92820 + 4.00000i 0.283790 + 0.163846i
\(597\) 6.58846 0.269648
\(598\) −1.33975 1.39230i −0.0547863 0.0569356i
\(599\) 35.5692 1.45332 0.726659 0.686998i \(-0.241072\pi\)
0.726659 + 0.686998i \(0.241072\pi\)
\(600\) −2.13397 1.23205i −0.0871191 0.0502983i
\(601\) −19.1506 + 33.1699i −0.781171 + 1.35303i 0.150089 + 0.988672i \(0.452044\pi\)
−0.931260 + 0.364355i \(0.881290\pi\)
\(602\) −2.63397 4.56218i −0.107353 0.185940i
\(603\) 10.0000i 0.407231i
\(604\) −7.96410 + 4.59808i −0.324055 + 0.187093i
\(605\) 37.8564 21.8564i 1.53908 0.888589i
\(606\) 8.92820i 0.362683i
\(607\) 4.16987 + 7.22243i 0.169250 + 0.293149i 0.938156 0.346212i \(-0.112532\pi\)
−0.768906 + 0.639361i \(0.779199\pi\)
\(608\) −3.23205 + 5.59808i −0.131077 + 0.227032i
\(609\) −9.06218 5.23205i −0.367218 0.212013i
\(610\) 0.732051 0.0296399
\(611\) −34.7487 + 8.59808i −1.40578 + 0.347841i
\(612\) −5.73205 −0.231704
\(613\) −6.67949 3.85641i −0.269782 0.155759i 0.359006 0.933335i \(-0.383116\pi\)
−0.628789 + 0.777576i \(0.716449\pi\)
\(614\) −2.50000 + 4.33013i −0.100892 + 0.174750i
\(615\) 2.09808 + 3.63397i 0.0846026 + 0.146536i
\(616\) 5.19615i 0.209359i
\(617\) −20.9545 + 12.0981i −0.843596 + 0.487050i −0.858485 0.512839i \(-0.828594\pi\)
0.0148891 + 0.999889i \(0.495260\pi\)
\(618\) 5.02628 2.90192i 0.202187 0.116732i
\(619\) 9.39230i 0.377509i −0.982024 0.188754i \(-0.939555\pi\)
0.982024 0.188754i \(-0.0604450\pi\)
\(620\) −9.19615 15.9282i −0.369326 0.639692i
\(621\) −0.267949 + 0.464102i −0.0107524 + 0.0186238i
\(622\) −21.8205 12.5981i −0.874923 0.505137i
\(623\) 10.8564 0.434953
\(624\) −2.59808 + 2.50000i −0.104006 + 0.100080i
\(625\) −31.2487 −1.24995
\(626\) −26.9545 15.5622i −1.07732 0.621990i
\(627\) 16.7942 29.0885i 0.670697 1.16168i
\(628\) −2.26795 3.92820i −0.0905010 0.156752i
\(629\) 18.7321i 0.746896i
\(630\) −2.36603 + 1.36603i −0.0942647 + 0.0544238i
\(631\) −22.6244 + 13.0622i −0.900661 + 0.519997i −0.877415 0.479733i \(-0.840734\pi\)
−0.0232467 + 0.999730i \(0.507400\pi\)
\(632\) 9.00000i 0.358001i
\(633\) −5.53590 9.58846i −0.220032 0.381107i
\(634\) −13.3923 + 23.1962i −0.531876 + 0.921237i
\(635\) 15.1244 + 8.73205i 0.600192 + 0.346521i
\(636\) −3.92820 −0.155763
\(637\) −3.46410 1.00000i −0.137253 0.0396214i
\(638\) −54.3731 −2.15265
\(639\) 9.29423 + 5.36603i 0.367674 + 0.212277i
\(640\) 1.36603 2.36603i 0.0539969 0.0935254i
\(641\) 8.66025 + 15.0000i 0.342059 + 0.592464i 0.984815 0.173607i \(-0.0555422\pi\)
−0.642756 + 0.766071i \(0.722209\pi\)
\(642\) 19.9282i 0.786503i
\(643\) 27.9904 16.1603i 1.10383 0.637298i 0.166608 0.986023i \(-0.446719\pi\)
0.937225 + 0.348725i \(0.113385\pi\)
\(644\) 0.464102 0.267949i 0.0182882 0.0105587i
\(645\) 14.3923i 0.566696i
\(646\) −18.5263 32.0885i −0.728907 1.26250i
\(647\) −10.1340 + 17.5526i −0.398408 + 0.690062i −0.993530 0.113573i \(-0.963770\pi\)
0.595122 + 0.803635i \(0.297104\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) 25.6077 1.00519
\(650\) 2.46410 8.53590i 0.0966500 0.334805i
\(651\) −6.73205 −0.263850
\(652\) −14.8301 8.56218i −0.580793 0.335321i
\(653\) −20.3564 + 35.2583i −0.796608 + 1.37977i 0.125206 + 0.992131i \(0.460041\pi\)
−0.921813 + 0.387634i \(0.873292\pi\)
\(654\) 7.36603 + 12.7583i 0.288034 + 0.498890i
\(655\) 2.92820i 0.114414i
\(656\) −1.33013 + 0.767949i −0.0519327 + 0.0299834i
\(657\) 4.73205 2.73205i 0.184615 0.106587i
\(658\) 9.92820i 0.387042i
\(659\) −17.6244 30.5263i −0.686547 1.18914i −0.972948 0.231025i \(-0.925792\pi\)
0.286400 0.958110i \(-0.407541\pi\)
\(660\) −7.09808 + 12.2942i −0.276292 + 0.478552i
\(661\) −25.5167 14.7321i −0.992483 0.573010i −0.0864675 0.996255i \(-0.527558\pi\)
−0.906016 + 0.423244i \(0.860891\pi\)
\(662\) −34.7846 −1.35194
\(663\) −4.96410 20.0622i −0.192790 0.779150i
\(664\) 12.7321 0.494099
\(665\) −15.2942 8.83013i −0.593085 0.342418i
\(666\) 1.63397 2.83013i 0.0633152 0.109665i
\(667\) 2.80385 + 4.85641i 0.108565 + 0.188041i
\(668\) 18.9282i 0.732354i
\(669\) 1.26795 0.732051i 0.0490217 0.0283027i
\(670\) 23.6603 13.6603i 0.914075 0.527742i
\(671\) 1.39230i 0.0537493i
\(672\) −0.500000 0.866025i −0.0192879 0.0334077i
\(673\) 12.8205 22.2058i 0.494194 0.855970i −0.505783 0.862661i \(-0.668796\pi\)
0.999978 + 0.00669096i \(0.00212981\pi\)
\(674\) 9.52628 + 5.50000i 0.366939 + 0.211852i
\(675\) −2.46410 −0.0948433
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) 46.7321 1.79606 0.898029 0.439936i \(-0.144999\pi\)
0.898029 + 0.439936i \(0.144999\pi\)
\(678\) 8.36603 + 4.83013i 0.321295 + 0.185500i
\(679\) −1.90192 + 3.29423i −0.0729891 + 0.126421i
\(680\) 7.83013 + 13.5622i 0.300272 + 0.520086i
\(681\) 21.3205i 0.817004i
\(682\) −30.2942 + 17.4904i −1.16003 + 0.669741i
\(683\) −15.0000 + 8.66025i −0.573959 + 0.331375i −0.758729 0.651406i \(-0.774179\pi\)
0.184770 + 0.982782i \(0.440846\pi\)
\(684\) 6.46410i 0.247161i
\(685\) −17.1244 29.6603i −0.654288 1.13326i
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) 2.93782 + 1.69615i 0.112085 + 0.0647123i
\(688\) 5.26795 0.200839
\(689\) −3.40192 13.7487i −0.129603 0.523784i
\(690\) 1.46410 0.0557374
\(691\) −44.1051 25.4641i −1.67784 0.968700i −0.963036 0.269373i \(-0.913184\pi\)
−0.714802 0.699327i \(-0.753483\pi\)
\(692\) 4.09808 7.09808i 0.155785 0.269828i
\(693\) 2.59808 + 4.50000i 0.0986928 + 0.170941i
\(694\) 0.464102i 0.0176171i
\(695\) 49.8109 28.7583i 1.88943 1.09087i
\(696\) 9.06218 5.23205i 0.343501 0.198320i
\(697\) 8.80385i 0.333470i
\(698\) 16.9282 + 29.3205i 0.640742 + 1.10980i
\(699\) 6.29423 10.9019i 0.238070 0.412349i
\(700\) 2.13397 + 1.23205i 0.0806567 + 0.0465671i
\(701\) 15.7846 0.596176 0.298088 0.954538i \(-0.403651\pi\)
0.298088 + 0.954538i \(0.403651\pi\)
\(702\) −1.00000 + 3.46410i −0.0377426 + 0.130744i
\(703\) 21.1244 0.796720
\(704\) −4.50000 2.59808i −0.169600 0.0979187i
\(705\) 13.5622 23.4904i 0.510781 0.884699i
\(706\) −1.66025 2.87564i −0.0624845 0.108226i
\(707\) 8.92820i 0.335780i
\(708\) −4.26795 + 2.46410i −0.160399 + 0.0926066i
\(709\) 18.5096 10.6865i 0.695143 0.401341i −0.110393 0.993888i \(-0.535211\pi\)
0.805536 + 0.592547i \(0.201878\pi\)
\(710\) 29.3205i 1.10038i
\(711\) −4.50000 7.79423i −0.168763 0.292306i
\(712\) −5.42820 + 9.40192i −0.203431 + 0.352352i
\(713\) 3.12436 + 1.80385i 0.117008 + 0.0675546i
\(714\) 5.73205 0.214517
\(715\) −49.1769 14.1962i −1.83911 0.530906i
\(716\) 3.46410 0.129460
\(717\) 3.97372 + 2.29423i 0.148401 + 0.0856795i
\(718\) 12.2224 21.1699i 0.456137 0.790053i
\(719\) −9.72243 16.8397i −0.362586 0.628017i 0.625800 0.779984i \(-0.284773\pi\)
−0.988386 + 0.151967i \(0.951439\pi\)
\(720\) 2.73205i 0.101818i
\(721\) −5.02628 + 2.90192i −0.187188 + 0.108073i
\(722\) −19.7321 + 11.3923i −0.734351 + 0.423978i
\(723\) 2.92820i 0.108901i
\(724\) 8.86603 + 15.3564i 0.329503 + 0.570716i
\(725\) −12.8923 + 22.3301i −0.478808 + 0.829320i
\(726\) 13.8564 + 8.00000i 0.514259 + 0.296908i
\(727\) 24.3923 0.904661 0.452330 0.891851i \(-0.350593\pi\)
0.452330 + 0.891851i \(0.350593\pi\)
\(728\) 2.59808 2.50000i 0.0962911 0.0926562i
\(729\) 1.00000 0.0370370
\(730\) −12.9282 7.46410i −0.478494 0.276259i
\(731\) −15.0981 + 26.1506i −0.558423 + 0.967216i
\(732\) 0.133975 + 0.232051i 0.00495184 + 0.00857684i
\(733\) 15.7846i 0.583018i 0.956568 + 0.291509i \(0.0941573\pi\)
−0.956568 + 0.291509i \(0.905843\pi\)
\(734\) −18.4641 + 10.6603i −0.681522 + 0.393477i
\(735\) 2.36603 1.36603i 0.0872722 0.0503866i
\(736\) 0.535898i 0.0197535i
\(737\) −25.9808 45.0000i −0.957014 1.65760i
\(738\) −0.767949 + 1.33013i −0.0282686 + 0.0489627i
\(739\) −20.0718 11.5885i −0.738353 0.426288i 0.0831172 0.996540i \(-0.473512\pi\)
−0.821470 + 0.570251i \(0.806846\pi\)
\(740\) −8.92820 −0.328207
\(741\) −22.6244 + 5.59808i −0.831126 + 0.205650i
\(742\) 3.92820 0.144209
\(743\) 20.8301 + 12.0263i 0.764183 + 0.441201i 0.830796 0.556578i \(-0.187886\pi\)
−0.0666124 + 0.997779i \(0.521219\pi\)
\(744\) 3.36603 5.83013i 0.123404 0.213743i
\(745\) −10.9282 18.9282i −0.400378 0.693476i
\(746\) 9.12436i 0.334066i
\(747\) 11.0263 6.36603i 0.403430 0.232921i
\(748\) 25.7942 14.8923i 0.943130 0.544517i
\(749\) 19.9282i 0.728161i
\(750\) −3.46410 6.00000i −0.126491 0.219089i
\(751\) 16.4282 28.4545i 0.599474 1.03832i −0.393425 0.919357i \(-0.628710\pi\)
0.992899 0.118962i \(-0.0379567\pi\)
\(752\) 8.59808 + 4.96410i 0.313540 + 0.181022i
\(753\) 27.5167 1.00276
\(754\) 26.1603 + 27.1865i 0.952700 + 0.990075i
\(755\) 25.1244 0.914369
\(756\) −0.866025 0.500000i −0.0314970 0.0181848i
\(757\) −2.90192 + 5.02628i −0.105472 + 0.182683i −0.913931 0.405870i \(-0.866969\pi\)
0.808459 + 0.588553i \(0.200302\pi\)
\(758\) 1.02628 + 1.77757i 0.0372761 + 0.0645642i
\(759\) 2.78461i 0.101075i
\(760\) 15.2942 8.83013i 0.554780 0.320302i
\(761\) −26.1962 + 15.1244i −0.949610 + 0.548257i −0.892960 0.450137i \(-0.851375\pi\)
−0.0566501 + 0.998394i \(0.518042\pi\)
\(762\) 6.39230i 0.231569i
\(763\) −7.36603 12.7583i −0.266668 0.461883i
\(764\) 1.09808 1.90192i 0.0397270 0.0688092i
\(765\) 13.5622 + 7.83013i 0.490342 + 0.283099i
\(766\) 31.0000 1.12008
\(767\) −12.3205 12.8038i −0.444868 0.462320i
\(768\) 1.00000 0.0360844
\(769\) 40.4711 + 23.3660i 1.45943 + 0.842600i 0.998983 0.0450885i \(-0.0143570\pi\)
0.460444 + 0.887689i \(0.347690\pi\)
\(770\) 7.09808 12.2942i 0.255797 0.443053i
\(771\) 6.52628 + 11.3038i 0.235038 + 0.407098i
\(772\) 23.5885i 0.848967i
\(773\) 37.3923 21.5885i 1.34491 0.776483i 0.357385 0.933957i \(-0.383669\pi\)
0.987523 + 0.157474i \(0.0503352\pi\)
\(774\) 4.56218 2.63397i 0.163984 0.0946763i