Properties

Label 546.2.s.b.127.1
Level $546$
Weight $2$
Character 546.127
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 127.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 546.127
Dual form 546.2.s.b.43.1

$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 \(0.209194\pi\)
−0.791704 + 0.610905i \(0.790806\pi\)
\(6\) 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 0.367610 0.929980i \(-0.380176\pi\)
0.989191 + 0.146631i \(0.0468429\pi\)
\(12\) −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 0.275029 + 0.961436i \(0.411312\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −5.59808 3.23205i −1.28429 0.741483i −0.306658 0.951820i \(-0.599211\pi\)
−0.977629 + 0.210337i \(0.932544\pi\)
\(20\) 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 0.836737 0.547605i \(-0.184460\pi\)
−0.892608 + 0.450833i \(0.851127\pi\)
\(24\) 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 0.690826 + 0.723021i \(0.257247\pi\)
0.280741 + 0.959784i \(0.409420\pi\)
\(30\) −1.36603 + 2.36603i −0.249401 + 0.431975i
\(31\) 6.73205i 1.20911i 0.796563 + 0.604556i \(0.206649\pi\)
−0.796563 + 0.604556i \(0.793351\pi\)
\(32\) 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 −0.714258 0.699883i \(-0.753235\pi\)
0.248988 + 0.968507i \(0.419902\pi\)
\(38\) 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 −0.392525 0.919741i \(-0.628399\pi\)
0.600256 + 0.799808i \(0.295065\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −2.63397 + 4.56218i −0.401677 + 0.695726i −0.993929 0.110028i \(-0.964906\pi\)
0.592251 + 0.805753i \(0.298239\pi\)
\(44\) 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 \(0.257739\pi\)
−0.689707 + 0.724089i \(0.742261\pi\)
\(48\) −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 0.751394 0.659854i \(-0.229382\pi\)
−0.195754 + 0.980653i \(0.562715\pi\)
\(60\) 2.73205i 0.352706i
\(61\) −0.133975 + 0.232051i −0.0171537 + 0.0297111i −0.874475 0.485071i \(-0.838794\pi\)
0.857321 + 0.514782i \(0.172127\pi\)
\(62\) −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 −0.924883 0.380251i \(-0.875838\pi\)
−0.133135 + 0.991098i \(0.542504\pi\)
\(68\) 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 −0.166009 0.986124i \(-0.553088\pi\)
−0.937013 + 0.349294i \(0.886421\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 5.46410i 0.639525i −0.947498 0.319762i \(-0.896397\pi\)
0.947498 0.319762i \(-0.103603\pi\)
\(74\) 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 \(-0.753735\pi\)
0.715354 0.698762i \(-0.246265\pi\)
\(84\) 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 −0.907241 0.420611i \(-0.861816\pi\)
−0.0893608 + 0.995999i \(0.528482\pi\)
\(90\) 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 0.657828 0.753169i \(-0.271476\pi\)
−0.323349 + 0.946280i \(0.604809\pi\)
\(98\) −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 0.553801 0.832649i \(-0.313177\pi\)
−0.997996 + 0.0632812i \(0.979843\pi\)
\(102\) −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 0.714203 + 0.699938i \(0.246789\pi\)
0.249063 + 0.968487i \(0.419877\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 14.7321i 1.41107i −0.708673 0.705537i \(-0.750706\pi\)
0.708673 0.705537i \(-0.249294\pi\)
\(110\) −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 −0.544272 0.838909i \(-0.683194\pi\)
0.998652 + 0.0518992i \(0.0165275\pi\)
\(114\) −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 0.688659 0.725085i \(-0.258200\pi\)
−0.972272 + 0.233854i \(0.924866\pi\)
\(128\) 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 0.886028 0.463632i \(-0.153454\pi\)
0.0414973 + 0.999139i \(0.486787\pi\)
\(138\) 0.535898i 0.0456187i
\(139\) 10.5263 18.2321i 0.892827 1.54642i 0.0563567 0.998411i \(-0.482052\pi\)
0.836471 0.548012i \(-0.184615\pi\)
\(140\) −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 0.756182 0.654361i \(-0.227062\pi\)
−0.188602 + 0.982054i \(0.560396\pi\)
\(150\) −2.13397 1.23205i −0.174238 0.100597i
\(151\) 9.19615i 0.748372i −0.927354 0.374186i \(-0.877922\pi\)
0.927354 0.374186i \(-0.122078\pi\)
\(152\) 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 −0.209902 0.977722i \(-0.567314\pi\)
−0.951683 + 0.307081i \(0.900648\pi\)
\(164\) 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 0.293775 0.955874i \(-0.405088\pi\)
0.974699 + 0.223520i \(0.0717549\pi\)
\(168\) −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 −0.978703 0.205283i \(-0.934188\pi\)
0.667132 + 0.744940i \(0.267522\pi\)
\(174\) 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 0.923467 0.383677i \(-0.125342\pi\)
−0.794008 + 0.607908i \(0.792009\pi\)
\(180\) −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 −0.903014 0.429610i \(-0.858651\pi\)
0.823560 + 0.567228i \(0.191984\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 20.4282 11.7942i 1.47045 0.848967i 0.471004 0.882131i \(-0.343892\pi\)
0.999450 + 0.0331638i \(0.0105583\pi\)
\(194\) −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 −0.610698 0.791863i \(-0.709111\pi\)
0.380424 + 0.924812i \(0.375778\pi\)
\(198\) −2.59808 4.50000i −0.184637 0.319801i
\(199\) −3.29423 + 5.70577i −0.233522 + 0.404471i −0.958842 0.283940i \(-0.908358\pi\)
0.725320 + 0.688412i \(0.241692\pi\)
\(200\) 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 0.610114 0.792314i \(-0.291124\pi\)
−0.991221 + 0.132217i \(0.957790\pi\)
\(212\) 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 −0.541853 0.840473i \(-0.682277\pi\)
0.456945 + 0.889495i \(0.348944\pi\)
\(224\) −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 −0.259419 0.965765i \(-0.583531\pi\)
−0.966086 + 0.258219i \(0.916864\pi\)
\(228\) 5.59808 + 3.23205i 0.370742 + 0.214048i
\(229\) 3.39230i 0.224170i 0.993699 + 0.112085i \(0.0357529\pi\)
−0.993699 + 0.112085i \(0.964247\pi\)
\(230\) −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 \(0.0474127\pi\)
−0.988927 + 0.148401i \(0.952587\pi\)
\(240\) −2.36603 1.36603i −0.152726 0.0881766i
\(241\) 2.53590 + 1.46410i 0.163352 + 0.0943111i 0.579447 0.815010i \(-0.303269\pi\)
−0.416096 + 0.909321i \(0.636602\pi\)
\(242\) 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 −0.00480540 + 0.999988i \(0.501530\pi\)
−0.863613 + 0.504156i \(0.831804\pi\)
\(252\) 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 0.994563 0.104135i \(-0.0332074\pi\)
−0.587465 + 0.809250i \(0.699874\pi\)
\(258\) −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 0.982810 + 0.184622i \(0.0591059\pi\)
−0.331518 + 0.943449i \(0.607561\pi\)
\(264\) 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 −0.798591 0.601874i \(-0.794421\pi\)
0.920534 + 0.390664i \(0.127754\pi\)
\(270\) −1.36603 2.36603i −0.0831337 0.143992i
\(271\) 8.36603 4.83013i 0.508200 0.293409i −0.223894 0.974614i \(-0.571877\pi\)
0.732093 + 0.681204i \(0.238543\pi\)
\(272\) 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 −0.753887 0.657004i \(-0.771824\pi\)
0.945926 + 0.324384i \(0.105157\pi\)
\(278\) 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 \(-0.910845\pi\)
0.961031 0.276440i \(-0.0891546\pi\)
\(282\) −4.96410 + 8.59808i −0.295608 + 0.512008i
\(283\) 4.92820 + 8.53590i 0.292951 + 0.507406i 0.974506 0.224360i \(-0.0720293\pi\)
−0.681555 + 0.731767i \(0.738696\pi\)
\(284\) −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 0.0723226 0.997381i \(-0.476959\pi\)
−0.827596 + 0.561324i \(0.810292\pi\)
\(294\) 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 \(0.0455728\pi\)
−0.989769 + 0.142683i \(0.954427\pi\)
\(308\) −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 \(0.271001\pi\)
−0.658950 + 0.752187i \(0.728999\pi\)
\(318\) 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 0.974628 + 0.223829i \(0.0718558\pi\)
0.681156 + 0.732138i \(0.261478\pi\)
\(332\) −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 −0.872187 0.489173i \(-0.837299\pi\)
0.859730 + 0.510749i \(0.170632\pi\)
\(348\) −5.23205 9.06218i −0.280467 0.485784i
\(349\) −29.3205 + 16.9282i −1.56949 + 0.906146i −0.573263 + 0.819372i \(0.694323\pi\)
−0.996228 + 0.0867744i \(0.972344\pi\)
\(350\) −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 −0.421516 0.906821i \(-0.638502\pi\)
0.574572 + 0.818454i \(0.305169\pi\)
\(354\) 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 \(-0.776826\pi\)
0.764119 0.645075i \(-0.223174\pi\)
\(360\) 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 0.997788 + 0.0664722i \(0.0211744\pi\)
−0.441328 + 0.897346i \(0.645492\pi\)
\(368\) −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 −0.959627 0.281277i \(-0.909242\pi\)
0.723406 + 0.690423i \(0.242575\pi\)
\(374\) −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 −0.544959 0.838463i \(-0.683455\pi\)
0.453651 + 0.891179i \(0.350121\pi\)
\(380\) −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 −0.380651 0.924719i \(-0.624300\pi\)
−0.991155 + 0.132706i \(0.957633\pi\)
\(384\) −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 0.513148 0.858300i \(-0.328479\pi\)
−0.486735 + 0.873550i \(0.661812\pi\)
\(398\) 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 0.147699 0.989032i \(-0.452813\pi\)
0.930377 + 0.366605i \(0.119480\pi\)
\(402\) −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 0.153991 0.988072i \(-0.450787\pi\)
−0.778700 + 0.627396i \(0.784121\pi\)
\(410\) −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 0.589145 0.808027i \(-0.299465\pi\)
−0.994345 + 0.106201i \(0.966131\pi\)
\(420\) −1.36603 + 2.36603i −0.0666552 + 0.115450i
\(421\) 9.32051i 0.454254i 0.973865 + 0.227127i \(0.0729332\pi\)
−0.973865 + 0.227127i \(0.927067\pi\)
\(422\) 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 −0.249694 0.968325i \(-0.580330\pi\)
0.713747 + 0.700404i \(0.246997\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 19.9282 34.5167i 0.957688 1.65876i 0.229596 0.973286i \(-0.426260\pi\)
0.728093 0.685479i \(-0.240407\pi\)
\(434\) 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 0.698751 0.715365i \(-0.253740\pi\)
−0.968900 + 0.247453i \(0.920406\pi\)
\(440\) −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 0.889719 0.456509i \(-0.150900\pi\)
0.0495110 + 0.998774i \(0.484234\pi\)
\(450\) 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 −0.920300 0.391212i \(-0.872056\pi\)
−0.121350 + 0.992610i \(0.538722\pi\)
\(458\) −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 0.633173 0.774010i \(-0.281752\pi\)
−0.353726 + 0.935349i \(0.615085\pi\)
\(462\) −4.50000 2.59808i −0.209359 0.120873i
\(463\) 32.6603i 1.51785i −0.651178 0.758925i \(-0.725725\pi\)
0.651178 0.758925i \(-0.274275\pi\)
\(464\) 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 0.0257894 0.999667i \(-0.491790\pi\)
0.878632 + 0.477499i \(0.158457\pi\)
\(480\) 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 −0.205290 0.978701i \(-0.565814\pi\)
−0.950225 + 0.311564i \(0.899147\pi\)
\(488\) −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 0.981463 0.191650i \(-0.0613839\pi\)
−0.656706 + 0.754147i \(0.728051\pi\)
\(492\) −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 \(0.0761649\pi\)
−0.971509 + 0.237002i \(0.923835\pi\)
\(500\) 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 −0.610551 0.791977i \(-0.709052\pi\)
0.991148 + 0.132764i \(0.0423852\pi\)
\(504\) 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 −0.244103 0.969749i \(-0.578494\pi\)
0.717776 + 0.696274i \(0.245160\pi\)
\(510\) −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 0.981241 0.192785i \(-0.0617521\pi\)
−0.657577 + 0.753387i \(0.728419\pi\)
\(524\) −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 \(0.223572\pi\)
−0.763312 + 0.646030i \(0.776428\pi\)
\(542\) −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 −0.767840 0.640642i \(-0.778668\pi\)
0.170893 + 0.985290i \(0.445335\pi\)
\(558\) 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 −0.824880 0.565308i \(-0.808757\pi\)
0.902011 + 0.431713i \(0.142091\pi\)
\(564\) 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 0.653910 0.756572i \(-0.273128\pi\)
−0.982166 + 0.188016i \(0.939794\pi\)
\(570\) 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 \(-0.982841\pi\)
0.998547 0.0538794i \(-0.0171587\pi\)
\(578\) 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 −0.801208 0.598386i \(-0.795809\pi\)
0.117614 + 0.993059i \(0.462476\pi\)
\(588\) −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 \(0.274656\pi\)
−0.650269 + 0.759704i \(0.725344\pi\)
\(594\) −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 −0.931260 0.364355i \(-0.881290\pi\)
0.150089 0.988672i \(-0.452044\pi\)
\(602\) −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 −0.768906 0.639361i \(-0.779199\pi\)
0.938156 + 0.346212i \(0.112532\pi\)
\(608\) −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 −0.628789 0.777576i \(-0.716449\pi\)
0.359006 + 0.933335i \(0.383116\pi\)
\(614\) −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 0.0148891 0.999889i \(-0.495260\pi\)
−0.858485 + 0.512839i \(0.828594\pi\)
\(618\) 5.02628 + 2.90192i 0.202187 + 0.116732i
\(619\) 9.39230i 0.377509i 0.982024 + 0.188754i \(0.0604450\pi\)
−0.982024 + 0.188754i \(0.939555\pi\)
\(620\) −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 −0.0232467 0.999730i \(-0.507400\pi\)
−0.877415 + 0.479733i \(0.840734\pi\)
\(632\) 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 −0.642756 0.766071i \(-0.722209\pi\)
0.984815 + 0.173607i \(0.0555422\pi\)
\(642\) 19.9282i 0.786503i
\(643\) 27.9904 + 16.1603i 1.10383 + 0.637298i 0.937225 0.348725i \(-0.113385\pi\)
0.166608 + 0.986023i \(0.446719\pi\)
\(644\) 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 0.595122 0.803635i \(-0.297104\pi\)
−0.993530 + 0.113573i \(0.963770\pi\)
\(648\) 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 −0.921813 0.387634i \(-0.873292\pi\)
0.125206 0.992131i \(-0.460041\pi\)
\(654\) 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 0.286400 + 0.958110i \(0.407541\pi\)
−0.972948 + 0.231025i \(0.925792\pi\)
\(660\) −7.09808 12.2942i −0.276292 0.478552i
\(661\) −25.5167 + 14.7321i −0.992483 + 0.573010i −0.906016 0.423244i \(-0.860891\pi\)
−0.0864675 + 0.996255i \(0.527558\pi\)
\(662\) −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 0.999978 0.00669096i \(-0.00212981\pi\)
−0.505783 + 0.862661i \(0.668796\pi\)
\(674\) 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 0.184770 0.982782i \(-0.440846\pi\)
−0.758729 + 0.651406i \(0.774179\pi\)
\(684\) 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 −0.714802 + 0.699327i \(0.753483\pi\)
−0.963036 + 0.269373i \(0.913184\pi\)
\(692\) 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 0.805536 0.592547i \(-0.201878\pi\)
−0.110393 + 0.993888i \(0.535211\pi\)
\(710\) 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 −0.988386 0.151967i \(-0.951439\pi\)
0.625800 + 0.779984i \(0.284773\pi\)
\(720\) 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 \(-0.905843\pi\)
0.956568 0.291509i \(-0.0941573\pi\)
\(734\) −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 −0.821470 0.570251i \(-0.806846\pi\)
0.0831172 + 0.996540i \(0.473512\pi\)
\(740\) −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 −0.0666124 0.997779i \(-0.521219\pi\)
0.830796 + 0.556578i \(0.187886\pi\)
\(744\) 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 0.992899 + 0.118962i \(0.0379567\pi\)
−0.393425 + 0.919357i \(0.628710\pi\)
\(752\) 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 0.808459 0.588553i \(-0.200302\pi\)
−0.913931 + 0.405870i \(0.866969\pi\)
\(758\) 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 −0.0566501 0.998394i \(-0.518042\pi\)
−0.892960 + 0.450137i \(0.851375\pi\)
\(762\) 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 0.460444 0.887689i \(-0.347690\pi\)
0.998983 + 0.0450885i \(0.0143570\pi\)
\(770\) 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 0.987523 0.157474i \(-0.0503352\pi\)
0.357385 + 0.933957i \(0.383669\pi\)
\(774\) 4.56218 + 2.63397i 0.163984 + 0.0946763i
\(775\)