Properties

Label 78.2.i.a.43.1
Level $78$
Weight $2$
Character 78.43
Analytic conductor $0.623$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 78.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.622833135766\)
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 \(\chi\) \(=\) 78.43
Dual form 78.2.i.a.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(2.36603 - 1.36603i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.73205i q^{5} +(0.866025 - 0.500000i) q^{6} +(2.36603 - 1.36603i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.86603 - 3.23205i) q^{10} +(1.09808 + 0.633975i) q^{11} -1.00000 q^{12} +(-2.59808 + 2.50000i) q^{13} -2.73205 q^{14} +(-3.23205 - 1.86603i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.86603 - 4.96410i) q^{17} +1.00000i q^{18} +(4.09808 - 2.36603i) q^{19} +(-3.23205 + 1.86603i) q^{20} +2.73205i q^{21} +(-0.633975 - 1.09808i) q^{22} +(2.09808 - 3.63397i) q^{23} +(0.866025 + 0.500000i) q^{24} -8.92820 q^{25} +(3.50000 - 0.866025i) q^{26} +1.00000 q^{27} +(2.36603 + 1.36603i) q^{28} +(2.23205 - 3.86603i) q^{29} +(1.86603 + 3.23205i) q^{30} +1.46410i q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.09808 + 0.633975i) q^{33} +5.73205i q^{34} +(5.09808 + 8.83013i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.06218 + 1.76795i) q^{37} -4.73205 q^{38} +(-0.866025 - 3.50000i) q^{39} +3.73205 q^{40} +(8.13397 + 4.69615i) q^{41} +(1.36603 - 2.36603i) q^{42} +(-4.83013 - 8.36603i) q^{43} +1.26795i q^{44} +(3.23205 - 1.86603i) q^{45} +(-3.63397 + 2.09808i) q^{46} -2.19615i q^{47} +(-0.500000 - 0.866025i) q^{48} +(0.232051 - 0.401924i) q^{49} +(7.73205 + 4.46410i) q^{50} +5.73205 q^{51} +(-3.46410 - 1.00000i) q^{52} -6.46410 q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.36603 + 4.09808i) q^{55} +(-1.36603 - 2.36603i) q^{56} +4.73205i q^{57} +(-3.86603 + 2.23205i) q^{58} +(-6.92820 + 4.00000i) q^{59} -3.73205i q^{60} +(4.59808 + 7.96410i) q^{61} +(0.732051 - 1.26795i) q^{62} +(-2.36603 - 1.36603i) q^{63} -1.00000 q^{64} +(-9.33013 - 9.69615i) q^{65} +1.26795 q^{66} +(-11.3660 - 6.56218i) q^{67} +(2.86603 - 4.96410i) q^{68} +(2.09808 + 3.63397i) q^{69} -10.1962i q^{70} +(4.09808 - 2.36603i) q^{71} +(-0.866025 + 0.500000i) q^{72} +6.26795i q^{73} +(-1.76795 - 3.06218i) q^{74} +(4.46410 - 7.73205i) q^{75} +(4.09808 + 2.36603i) q^{76} +3.46410 q^{77} +(-1.00000 + 3.46410i) q^{78} -2.53590 q^{79} +(-3.23205 - 1.86603i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.69615 - 8.13397i) q^{82} -0.196152i q^{83} +(-2.36603 + 1.36603i) q^{84} +(18.5263 - 10.6962i) q^{85} +9.66025i q^{86} +(2.23205 + 3.86603i) q^{87} +(0.633975 - 1.09808i) q^{88} +(-8.19615 - 4.73205i) q^{89} -3.73205 q^{90} +(-2.73205 + 9.46410i) q^{91} +4.19615 q^{92} +(-1.26795 - 0.732051i) q^{93} +(-1.09808 + 1.90192i) q^{94} +(8.83013 + 15.2942i) q^{95} +1.00000i q^{96} +(-5.19615 + 3.00000i) q^{97} +(-0.401924 + 0.232051i) q^{98} -1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{3} + 2 q^{4} + 6 q^{7} - 2 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} - 4 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} + 6 q^{19} - 6 q^{20} - 6 q^{22} - 2 q^{23} - 8 q^{25} + 14 q^{26} + 4 q^{27} + 6 q^{28} + 2 q^{29} + 4 q^{30} + 6 q^{33} + 10 q^{35} + 2 q^{36} - 12 q^{37} - 12 q^{38} + 8 q^{40} + 36 q^{41} + 2 q^{42} - 2 q^{43} + 6 q^{45} - 18 q^{46} - 2 q^{48} - 6 q^{49} + 24 q^{50} + 16 q^{51} - 12 q^{53} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 8 q^{61} - 4 q^{62} - 6 q^{63} - 4 q^{64} - 20 q^{65} + 12 q^{66} - 42 q^{67} + 8 q^{68} - 2 q^{69} + 6 q^{71} - 14 q^{74} + 4 q^{75} + 6 q^{76} - 4 q^{78} - 24 q^{79} - 6 q^{80} - 2 q^{81} + 2 q^{82} - 6 q^{84} + 36 q^{85} + 2 q^{87} + 6 q^{88} - 12 q^{89} - 8 q^{90} - 4 q^{91} - 4 q^{92} - 12 q^{93} + 6 q^{94} + 18 q^{95} - 12 q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(53\) \(67\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(5\) 3.73205i 1.66902i 0.550990 + 0.834512i \(0.314250\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) 2.36603 1.36603i 0.894274 0.516309i 0.0189356 0.999821i \(-0.493972\pi\)
0.875338 + 0.483512i \(0.160639\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.86603 3.23205i 0.590089 1.02206i
\(11\) 1.09808 + 0.633975i 0.331082 + 0.191151i 0.656322 0.754481i \(-0.272111\pi\)
−0.325239 + 0.945632i \(0.605445\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.59808 + 2.50000i −0.720577 + 0.693375i
\(14\) −2.73205 −0.730171
\(15\) −3.23205 1.86603i −0.834512 0.481806i
\(16\) −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
\(19\) 4.09808 2.36603i 0.940163 0.542803i 0.0501517 0.998742i \(-0.484030\pi\)
0.890011 + 0.455938i \(0.150696\pi\)
\(20\) −3.23205 + 1.86603i −0.722709 + 0.417256i
\(21\) 2.73205i 0.596182i
\(22\) −0.633975 1.09808i −0.135164 0.234111i
\(23\) 2.09808 3.63397i 0.437479 0.757736i −0.560015 0.828482i \(-0.689205\pi\)
0.997494 + 0.0707462i \(0.0225381\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) −8.92820 −1.78564
\(26\) 3.50000 0.866025i 0.686406 0.169842i
\(27\) 1.00000 0.192450
\(28\) 2.36603 + 1.36603i 0.447137 + 0.258155i
\(29\) 2.23205 3.86603i 0.414481 0.717903i −0.580892 0.813980i \(-0.697296\pi\)
0.995374 + 0.0960774i \(0.0306296\pi\)
\(30\) 1.86603 + 3.23205i 0.340688 + 0.590089i
\(31\) 1.46410i 0.262960i 0.991319 + 0.131480i \(0.0419730\pi\)
−0.991319 + 0.131480i \(0.958027\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) −1.09808 + 0.633975i −0.191151 + 0.110361i
\(34\) 5.73205i 0.983039i
\(35\) 5.09808 + 8.83013i 0.861732 + 1.49256i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 3.06218 + 1.76795i 0.503419 + 0.290649i 0.730124 0.683314i \(-0.239462\pi\)
−0.226705 + 0.973963i \(0.572795\pi\)
\(38\) −4.73205 −0.767640
\(39\) −0.866025 3.50000i −0.138675 0.560449i
\(40\) 3.73205 0.590089
\(41\) 8.13397 + 4.69615i 1.27031 + 0.733416i 0.975047 0.221999i \(-0.0712582\pi\)
0.295267 + 0.955415i \(0.404592\pi\)
\(42\) 1.36603 2.36603i 0.210782 0.365086i
\(43\) −4.83013 8.36603i −0.736587 1.27581i −0.954023 0.299732i \(-0.903103\pi\)
0.217436 0.976075i \(-0.430231\pi\)
\(44\) 1.26795i 0.191151i
\(45\) 3.23205 1.86603i 0.481806 0.278171i
\(46\) −3.63397 + 2.09808i −0.535800 + 0.309344i
\(47\) 2.19615i 0.320342i −0.987089 0.160171i \(-0.948795\pi\)
0.987089 0.160171i \(-0.0512045\pi\)
\(48\) −0.500000 0.866025i −0.0721688 0.125000i
\(49\) 0.232051 0.401924i 0.0331501 0.0574177i
\(50\) 7.73205 + 4.46410i 1.09348 + 0.631319i
\(51\) 5.73205 0.802648
\(52\) −3.46410 1.00000i −0.480384 0.138675i
\(53\) −6.46410 −0.887913 −0.443956 0.896048i \(-0.646425\pi\)
−0.443956 + 0.896048i \(0.646425\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) −2.36603 + 4.09808i −0.319035 + 0.552584i
\(56\) −1.36603 2.36603i −0.182543 0.316173i
\(57\) 4.73205i 0.626775i
\(58\) −3.86603 + 2.23205i −0.507634 + 0.293083i
\(59\) −6.92820 + 4.00000i −0.901975 + 0.520756i −0.877841 0.478953i \(-0.841016\pi\)
−0.0241347 + 0.999709i \(0.507683\pi\)
\(60\) 3.73205i 0.481806i
\(61\) 4.59808 + 7.96410i 0.588723 + 1.01970i 0.994400 + 0.105682i \(0.0337026\pi\)
−0.405677 + 0.914017i \(0.632964\pi\)
\(62\) 0.732051 1.26795i 0.0929705 0.161030i
\(63\) −2.36603 1.36603i −0.298091 0.172103i
\(64\) −1.00000 −0.125000
\(65\) −9.33013 9.69615i −1.15726 1.20266i
\(66\) 1.26795 0.156074
\(67\) −11.3660 6.56218i −1.38858 0.801698i −0.395426 0.918498i \(-0.629403\pi\)
−0.993155 + 0.116800i \(0.962736\pi\)
\(68\) 2.86603 4.96410i 0.347557 0.601986i
\(69\) 2.09808 + 3.63397i 0.252579 + 0.437479i
\(70\) 10.1962i 1.21867i
\(71\) 4.09808 2.36603i 0.486352 0.280796i −0.236708 0.971581i \(-0.576068\pi\)
0.723060 + 0.690785i \(0.242735\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 6.26795i 0.733608i 0.930298 + 0.366804i \(0.119548\pi\)
−0.930298 + 0.366804i \(0.880452\pi\)
\(74\) −1.76795 3.06218i −0.205520 0.355971i
\(75\) 4.46410 7.73205i 0.515470 0.892820i
\(76\) 4.09808 + 2.36603i 0.470082 + 0.271402i
\(77\) 3.46410 0.394771
\(78\) −1.00000 + 3.46410i −0.113228 + 0.392232i
\(79\) −2.53590 −0.285311 −0.142655 0.989772i \(-0.545564\pi\)
−0.142655 + 0.989772i \(0.545564\pi\)
\(80\) −3.23205 1.86603i −0.361354 0.208628i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −4.69615 8.13397i −0.518603 0.898247i
\(83\) 0.196152i 0.0215305i −0.999942 0.0107653i \(-0.996573\pi\)
0.999942 0.0107653i \(-0.00342676\pi\)
\(84\) −2.36603 + 1.36603i −0.258155 + 0.149046i
\(85\) 18.5263 10.6962i 2.00946 1.16016i
\(86\) 9.66025i 1.04169i
\(87\) 2.23205 + 3.86603i 0.239301 + 0.414481i
\(88\) 0.633975 1.09808i 0.0675819 0.117055i
\(89\) −8.19615 4.73205i −0.868790 0.501596i −0.00184433 0.999998i \(-0.500587\pi\)
−0.866946 + 0.498402i \(0.833920\pi\)
\(90\) −3.73205 −0.393393
\(91\) −2.73205 + 9.46410i −0.286397 + 0.992107i
\(92\) 4.19615 0.437479
\(93\) −1.26795 0.732051i −0.131480 0.0759101i
\(94\) −1.09808 + 1.90192i −0.113258 + 0.196168i
\(95\) 8.83013 + 15.2942i 0.905952 + 1.56915i
\(96\) 1.00000i 0.102062i
\(97\) −5.19615 + 3.00000i −0.527589 + 0.304604i −0.740034 0.672569i \(-0.765191\pi\)
0.212445 + 0.977173i \(0.431857\pi\)
\(98\) −0.401924 + 0.232051i −0.0406004 + 0.0234407i
\(99\) 1.26795i 0.127434i
\(100\) −4.46410 7.73205i −0.446410 0.773205i
\(101\) 0.964102 1.66987i 0.0959317 0.166159i −0.814065 0.580773i \(-0.802750\pi\)
0.909997 + 0.414615i \(0.136084\pi\)
\(102\) −4.96410 2.86603i −0.491519 0.283779i
\(103\) 15.2679 1.50440 0.752198 0.658937i \(-0.228994\pi\)
0.752198 + 0.658937i \(0.228994\pi\)
\(104\) 2.50000 + 2.59808i 0.245145 + 0.254762i
\(105\) −10.1962 −0.995043
\(106\) 5.59808 + 3.23205i 0.543733 + 0.313925i
\(107\) −5.09808 + 8.83013i −0.492850 + 0.853641i −0.999966 0.00823695i \(-0.997378\pi\)
0.507116 + 0.861878i \(0.330711\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 1.46410i 0.140236i 0.997539 + 0.0701178i \(0.0223375\pi\)
−0.997539 + 0.0701178i \(0.977662\pi\)
\(110\) 4.09808 2.36603i 0.390736 0.225592i
\(111\) −3.06218 + 1.76795i −0.290649 + 0.167806i
\(112\) 2.73205i 0.258155i
\(113\) 0.669873 + 1.16025i 0.0630163 + 0.109148i 0.895812 0.444432i \(-0.146595\pi\)
−0.832796 + 0.553580i \(0.813261\pi\)
\(114\) 2.36603 4.09808i 0.221599 0.383820i
\(115\) 13.5622 + 7.83013i 1.26468 + 0.730163i
\(116\) 4.46410 0.414481
\(117\) 3.46410 + 1.00000i 0.320256 + 0.0924500i
\(118\) 8.00000 0.736460
\(119\) −13.5622 7.83013i −1.24324 0.717787i
\(120\) −1.86603 + 3.23205i −0.170344 + 0.295045i
\(121\) −4.69615 8.13397i −0.426923 0.739452i
\(122\) 9.19615i 0.832581i
\(123\) −8.13397 + 4.69615i −0.733416 + 0.423438i
\(124\) −1.26795 + 0.732051i −0.113865 + 0.0657401i
\(125\) 14.6603i 1.31125i
\(126\) 1.36603 + 2.36603i 0.121695 + 0.210782i
\(127\) −4.92820 + 8.53590i −0.437307 + 0.757438i −0.997481 0.0709368i \(-0.977401\pi\)
0.560173 + 0.828375i \(0.310734\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 9.66025 0.850538
\(130\) 3.23205 + 13.0622i 0.283470 + 1.14563i
\(131\) 6.53590 0.571044 0.285522 0.958372i \(-0.407833\pi\)
0.285522 + 0.958372i \(0.407833\pi\)
\(132\) −1.09808 0.633975i −0.0955753 0.0551804i
\(133\) 6.46410 11.1962i 0.560509 0.970830i
\(134\) 6.56218 + 11.3660i 0.566886 + 0.981875i
\(135\) 3.73205i 0.321204i
\(136\) −4.96410 + 2.86603i −0.425668 + 0.245760i
\(137\) −10.3301 + 5.96410i −0.882562 + 0.509548i −0.871502 0.490391i \(-0.836854\pi\)
−0.0110599 + 0.999939i \(0.503521\pi\)
\(138\) 4.19615i 0.357200i
\(139\) −8.92820 15.4641i −0.757280 1.31165i −0.944233 0.329279i \(-0.893194\pi\)
0.186952 0.982369i \(-0.440139\pi\)
\(140\) −5.09808 + 8.83013i −0.430866 + 0.746282i
\(141\) 1.90192 + 1.09808i 0.160171 + 0.0924747i
\(142\) −4.73205 −0.397105
\(143\) −4.43782 + 1.09808i −0.371109 + 0.0918257i
\(144\) 1.00000 0.0833333
\(145\) 14.4282 + 8.33013i 1.19820 + 0.691779i
\(146\) 3.13397 5.42820i 0.259370 0.449241i
\(147\) 0.232051 + 0.401924i 0.0191392 + 0.0331501i
\(148\) 3.53590i 0.290649i
\(149\) 11.4282 6.59808i 0.936235 0.540535i 0.0474568 0.998873i \(-0.484888\pi\)
0.888778 + 0.458338i \(0.151555\pi\)
\(150\) −7.73205 + 4.46410i −0.631319 + 0.364492i
\(151\) 6.73205i 0.547847i −0.961752 0.273923i \(-0.911679\pi\)
0.961752 0.273923i \(-0.0883214\pi\)
\(152\) −2.36603 4.09808i −0.191910 0.332398i
\(153\) −2.86603 + 4.96410i −0.231704 + 0.401324i
\(154\) −3.00000 1.73205i −0.241747 0.139573i
\(155\) −5.46410 −0.438887
\(156\) 2.59808 2.50000i 0.208013 0.200160i
\(157\) 7.58846 0.605625 0.302812 0.953050i \(-0.402074\pi\)
0.302812 + 0.953050i \(0.402074\pi\)
\(158\) 2.19615 + 1.26795i 0.174717 + 0.100873i
\(159\) 3.23205 5.59808i 0.256318 0.443956i
\(160\) 1.86603 + 3.23205i 0.147522 + 0.255516i
\(161\) 11.4641i 0.903498i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) 11.6603 6.73205i 0.913302 0.527295i 0.0318096 0.999494i \(-0.489873\pi\)
0.881492 + 0.472199i \(0.156540\pi\)
\(164\) 9.39230i 0.733416i
\(165\) −2.36603 4.09808i −0.184195 0.319035i
\(166\) −0.0980762 + 0.169873i −0.00761219 + 0.0131847i
\(167\) −8.19615 4.73205i −0.634237 0.366177i 0.148154 0.988964i \(-0.452667\pi\)
−0.782391 + 0.622787i \(0.786000\pi\)
\(168\) 2.73205 0.210782
\(169\) 0.500000 12.9904i 0.0384615 0.999260i
\(170\) −21.3923 −1.64071
\(171\) −4.09808 2.36603i −0.313388 0.180934i
\(172\) 4.83013 8.36603i 0.368294 0.637903i
\(173\) 2.19615 + 3.80385i 0.166970 + 0.289201i 0.937353 0.348380i \(-0.113268\pi\)
−0.770383 + 0.637582i \(0.779935\pi\)
\(174\) 4.46410i 0.338423i
\(175\) −21.1244 + 12.1962i −1.59685 + 0.921942i
\(176\) −1.09808 + 0.633975i −0.0827706 + 0.0477876i
\(177\) 8.00000i 0.601317i
\(178\) 4.73205 + 8.19615i 0.354682 + 0.614328i
\(179\) −8.02628 + 13.9019i −0.599912 + 1.03908i 0.392921 + 0.919572i \(0.371465\pi\)
−0.992833 + 0.119506i \(0.961869\pi\)
\(180\) 3.23205 + 1.86603i 0.240903 + 0.139085i
\(181\) −19.1962 −1.42684 −0.713419 0.700737i \(-0.752855\pi\)
−0.713419 + 0.700737i \(0.752855\pi\)
\(182\) 7.09808 6.83013i 0.526144 0.506283i
\(183\) −9.19615 −0.679799
\(184\) −3.63397 2.09808i −0.267900 0.154672i
\(185\) −6.59808 + 11.4282i −0.485100 + 0.840218i
\(186\) 0.732051 + 1.26795i 0.0536766 + 0.0929705i
\(187\) 7.26795i 0.531485i
\(188\) 1.90192 1.09808i 0.138712 0.0800854i
\(189\) 2.36603 1.36603i 0.172103 0.0993637i
\(190\) 17.6603i 1.28121i
\(191\) 3.46410 + 6.00000i 0.250654 + 0.434145i 0.963706 0.266966i \(-0.0860212\pi\)
−0.713052 + 0.701111i \(0.752688\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −10.1603 5.86603i −0.731351 0.422246i 0.0875652 0.996159i \(-0.472091\pi\)
−0.818916 + 0.573913i \(0.805425\pi\)
\(194\) 6.00000 0.430775
\(195\) 13.0622 3.23205i 0.935402 0.231452i
\(196\) 0.464102 0.0331501
\(197\) 15.4641 + 8.92820i 1.10177 + 0.636108i 0.936686 0.350171i \(-0.113877\pi\)
0.165086 + 0.986279i \(0.447210\pi\)
\(198\) −0.633975 + 1.09808i −0.0450546 + 0.0780369i
\(199\) −7.09808 12.2942i −0.503169 0.871515i −0.999993 0.00366345i \(-0.998834\pi\)
0.496824 0.867851i \(-0.334499\pi\)
\(200\) 8.92820i 0.631319i
\(201\) 11.3660 6.56218i 0.801698 0.462860i
\(202\) −1.66987 + 0.964102i −0.117492 + 0.0678340i
\(203\) 12.1962i 0.856002i
\(204\) 2.86603 + 4.96410i 0.200662 + 0.347557i
\(205\) −17.5263 + 30.3564i −1.22409 + 2.12018i
\(206\) −13.2224 7.63397i −0.921250 0.531884i
\(207\) −4.19615 −0.291653
\(208\) −0.866025 3.50000i −0.0600481 0.242681i
\(209\) 6.00000 0.415029
\(210\) 8.83013 + 5.09808i 0.609337 + 0.351801i
\(211\) −8.19615 + 14.1962i −0.564246 + 0.977303i 0.432873 + 0.901455i \(0.357500\pi\)
−0.997119 + 0.0758485i \(0.975833\pi\)
\(212\) −3.23205 5.59808i −0.221978 0.384477i
\(213\) 4.73205i 0.324235i
\(214\) 8.83013 5.09808i 0.603615 0.348497i
\(215\) 31.2224 18.0263i 2.12935 1.22938i
\(216\) 1.00000i 0.0680414i
\(217\) 2.00000 + 3.46410i 0.135769 + 0.235159i
\(218\) 0.732051 1.26795i 0.0495807 0.0858764i
\(219\) −5.42820 3.13397i −0.366804 0.211774i
\(220\) −4.73205 −0.319035
\(221\) 19.8564 + 5.73205i 1.33569 + 0.385579i
\(222\) 3.53590 0.237314
\(223\) 23.3205 + 13.4641i 1.56166 + 0.901623i 0.997090 + 0.0762356i \(0.0242901\pi\)
0.564567 + 0.825387i \(0.309043\pi\)
\(224\) 1.36603 2.36603i 0.0912714 0.158087i
\(225\) 4.46410 + 7.73205i 0.297607 + 0.515470i
\(226\) 1.33975i 0.0891186i
\(227\) −10.5622 + 6.09808i −0.701036 + 0.404744i −0.807733 0.589548i \(-0.799306\pi\)
0.106697 + 0.994292i \(0.465973\pi\)
\(228\) −4.09808 + 2.36603i −0.271402 + 0.156694i
\(229\) 11.8564i 0.783493i 0.920073 + 0.391747i \(0.128129\pi\)
−0.920073 + 0.391747i \(0.871871\pi\)
\(230\) −7.83013 13.5622i −0.516303 0.894264i
\(231\) −1.73205 + 3.00000i −0.113961 + 0.197386i
\(232\) −3.86603 2.23205i −0.253817 0.146541i
\(233\) 7.85641 0.514690 0.257345 0.966320i \(-0.417152\pi\)
0.257345 + 0.966320i \(0.417152\pi\)
\(234\) −2.50000 2.59808i −0.163430 0.169842i
\(235\) 8.19615 0.534658
\(236\) −6.92820 4.00000i −0.450988 0.260378i
\(237\) 1.26795 2.19615i 0.0823622 0.142655i
\(238\) 7.83013 + 13.5622i 0.507552 + 0.879105i
\(239\) 7.66025i 0.495501i 0.968824 + 0.247750i \(0.0796913\pi\)
−0.968824 + 0.247750i \(0.920309\pi\)
\(240\) 3.23205 1.86603i 0.208628 0.120451i
\(241\) −11.7679 + 6.79423i −0.758040 + 0.437655i −0.828592 0.559853i \(-0.810857\pi\)
0.0705514 + 0.997508i \(0.477524\pi\)
\(242\) 9.39230i 0.603760i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −4.59808 + 7.96410i −0.294362 + 0.509849i
\(245\) 1.50000 + 0.866025i 0.0958315 + 0.0553283i
\(246\) 9.39230 0.598831
\(247\) −4.73205 + 16.3923i −0.301093 + 1.04302i
\(248\) 1.46410 0.0929705
\(249\) 0.169873 + 0.0980762i 0.0107653 + 0.00621533i
\(250\) −7.33013 + 12.6962i −0.463598 + 0.802975i
\(251\) 6.73205 + 11.6603i 0.424923 + 0.735989i 0.996413 0.0846203i \(-0.0269677\pi\)
−0.571490 + 0.820609i \(0.693634\pi\)
\(252\) 2.73205i 0.172103i
\(253\) 4.60770 2.66025i 0.289683 0.167249i
\(254\) 8.53590 4.92820i 0.535590 0.309223i
\(255\) 21.3923i 1.33964i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.66987 8.08846i 0.291299 0.504544i −0.682818 0.730588i \(-0.739246\pi\)
0.974117 + 0.226044i \(0.0725793\pi\)
\(258\) −8.36603 4.83013i −0.520846 0.300711i
\(259\) 9.66025 0.600259
\(260\) 3.73205 12.9282i 0.231452 0.801773i
\(261\) −4.46410 −0.276321
\(262\) −5.66025 3.26795i −0.349692 0.201895i
\(263\) 5.02628 8.70577i 0.309934 0.536821i −0.668414 0.743790i \(-0.733026\pi\)
0.978348 + 0.206969i \(0.0663598\pi\)
\(264\) 0.633975 + 1.09808i 0.0390184 + 0.0675819i
\(265\) 24.1244i 1.48195i
\(266\) −11.1962 + 6.46410i −0.686480 + 0.396339i
\(267\) 8.19615 4.73205i 0.501596 0.289597i
\(268\) 13.1244i 0.801698i
\(269\) −2.73205 4.73205i −0.166576 0.288518i 0.770638 0.637273i \(-0.219938\pi\)
−0.937214 + 0.348755i \(0.886604\pi\)
\(270\) 1.86603 3.23205i 0.113563 0.196696i
\(271\) −18.9282 10.9282i −1.14981 0.663841i −0.200966 0.979598i \(-0.564408\pi\)
−0.948840 + 0.315757i \(0.897742\pi\)
\(272\) 5.73205 0.347557
\(273\) −6.83013 7.09808i −0.413378 0.429595i
\(274\) 11.9282 0.720609
\(275\) −9.80385 5.66025i −0.591194 0.341326i
\(276\) −2.09808 + 3.63397i −0.126289 + 0.218740i
\(277\) −2.86603 4.96410i −0.172203 0.298264i 0.766987 0.641663i \(-0.221755\pi\)
−0.939190 + 0.343399i \(0.888422\pi\)
\(278\) 17.8564i 1.07096i
\(279\) 1.26795 0.732051i 0.0759101 0.0438267i
\(280\) 8.83013 5.09808i 0.527701 0.304668i
\(281\) 12.3205i 0.734980i −0.930027 0.367490i \(-0.880217\pi\)
0.930027 0.367490i \(-0.119783\pi\)
\(282\) −1.09808 1.90192i −0.0653895 0.113258i
\(283\) 12.8301 22.2224i 0.762672 1.32099i −0.178797 0.983886i \(-0.557220\pi\)
0.941469 0.337100i \(-0.109446\pi\)
\(284\) 4.09808 + 2.36603i 0.243176 + 0.140398i
\(285\) −17.6603 −1.04610
\(286\) 4.39230 + 1.26795i 0.259722 + 0.0749754i
\(287\) 25.6603 1.51468
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) −7.92820 + 13.7321i −0.466365 + 0.807768i
\(290\) −8.33013 14.4282i −0.489162 0.847253i
\(291\) 6.00000i 0.351726i
\(292\) −5.42820 + 3.13397i −0.317662 + 0.183402i
\(293\) −26.4282 + 15.2583i −1.54395 + 0.891401i −0.545368 + 0.838196i \(0.683610\pi\)
−0.998584 + 0.0532048i \(0.983056\pi\)
\(294\) 0.464102i 0.0270670i
\(295\) −14.9282 25.8564i −0.869154 1.50542i
\(296\) 1.76795 3.06218i 0.102760 0.177985i
\(297\) 1.09808 + 0.633975i 0.0637168 + 0.0367869i
\(298\) −13.1962 −0.764433
\(299\) 3.63397 + 14.6865i 0.210158 + 0.849344i
\(300\) 8.92820 0.515470
\(301\) −22.8564 13.1962i −1.31742 0.760614i
\(302\) −3.36603 + 5.83013i −0.193693 + 0.335486i
\(303\) 0.964102 + 1.66987i 0.0553862 + 0.0959317i
\(304\) 4.73205i 0.271402i
\(305\) −29.7224 + 17.1603i −1.70190 + 0.982593i
\(306\) 4.96410 2.86603i 0.283779 0.163840i
\(307\) 22.5885i 1.28919i 0.764524 + 0.644596i \(0.222974\pi\)
−0.764524 + 0.644596i \(0.777026\pi\)
\(308\) 1.73205 + 3.00000i 0.0986928 + 0.170941i
\(309\) −7.63397 + 13.2224i −0.434282 + 0.752198i
\(310\) 4.73205 + 2.73205i 0.268762 + 0.155170i
\(311\) 1.66025 0.0941444 0.0470722 0.998891i \(-0.485011\pi\)
0.0470722 + 0.998891i \(0.485011\pi\)
\(312\) −3.50000 + 0.866025i −0.198148 + 0.0490290i
\(313\) 6.53590 0.369431 0.184715 0.982792i \(-0.440864\pi\)
0.184715 + 0.982792i \(0.440864\pi\)
\(314\) −6.57180 3.79423i −0.370868 0.214121i
\(315\) 5.09808 8.83013i 0.287244 0.497521i
\(316\) −1.26795 2.19615i −0.0713277 0.123543i
\(317\) 20.6603i 1.16040i 0.814476 + 0.580198i \(0.197025\pi\)
−0.814476 + 0.580198i \(0.802975\pi\)
\(318\) −5.59808 + 3.23205i −0.313925 + 0.181244i
\(319\) 4.90192 2.83013i 0.274455 0.158457i
\(320\) 3.73205i 0.208628i
\(321\) −5.09808 8.83013i −0.284547 0.492850i
\(322\) −5.73205 + 9.92820i −0.319435 + 0.553277i
\(323\) −23.4904 13.5622i −1.30704 0.754620i
\(324\) −1.00000 −0.0555556
\(325\) 23.1962 22.3205i 1.28669 1.23812i
\(326\) −13.4641 −0.745708
\(327\) −1.26795 0.732051i −0.0701178 0.0404825i
\(328\) 4.69615 8.13397i 0.259302 0.449124i
\(329\) −3.00000 5.19615i −0.165395 0.286473i
\(330\) 4.73205i 0.260491i
\(331\) 17.3205 10.0000i 0.952021 0.549650i 0.0583130 0.998298i \(-0.481428\pi\)
0.893708 + 0.448649i \(0.148095\pi\)
\(332\) 0.169873 0.0980762i 0.00932299 0.00538263i
\(333\) 3.53590i 0.193766i
\(334\) 4.73205 + 8.19615i 0.258926 + 0.448474i
\(335\) 24.4904 42.4186i 1.33805 2.31757i
\(336\) −2.36603 1.36603i −0.129077 0.0745228i
\(337\) 20.8564 1.13612 0.568060 0.822987i \(-0.307694\pi\)
0.568060 + 0.822987i \(0.307694\pi\)
\(338\) −6.92820 + 11.0000i −0.376845 + 0.598321i
\(339\) −1.33975 −0.0727650
\(340\) 18.5263 + 10.6962i 1.00473 + 0.580080i
\(341\) −0.928203 + 1.60770i −0.0502650 + 0.0870616i
\(342\) 2.36603 + 4.09808i 0.127940 + 0.221599i
\(343\) 17.8564i 0.964155i
\(344\) −8.36603 + 4.83013i −0.451066 + 0.260423i
\(345\) −13.5622 + 7.83013i −0.730163 + 0.421560i
\(346\) 4.39230i 0.236132i
\(347\) −16.5622 28.6865i −0.889104 1.53997i −0.840936 0.541135i \(-0.817995\pi\)
−0.0481683 0.998839i \(-0.515338\pi\)
\(348\) −2.23205 + 3.86603i −0.119650 + 0.207241i
\(349\) 13.2679 + 7.66025i 0.710217 + 0.410044i 0.811141 0.584850i \(-0.198847\pi\)
−0.100924 + 0.994894i \(0.532180\pi\)
\(350\) 24.3923 1.30382
\(351\) −2.59808 + 2.50000i −0.138675 + 0.133440i
\(352\) 1.26795 0.0675819
\(353\) 18.8660 + 10.8923i 1.00414 + 0.579739i 0.909470 0.415770i \(-0.136488\pi\)
0.0946674 + 0.995509i \(0.469821\pi\)
\(354\) −4.00000 + 6.92820i −0.212598 + 0.368230i
\(355\) 8.83013 + 15.2942i 0.468654 + 0.811733i
\(356\) 9.46410i 0.501596i
\(357\) 13.5622 7.83013i 0.717787 0.414414i
\(358\) 13.9019 8.02628i 0.734740 0.424202i
\(359\) 1.12436i 0.0593412i 0.999560 + 0.0296706i \(0.00944584\pi\)
−0.999560 + 0.0296706i \(0.990554\pi\)
\(360\) −1.86603 3.23205i −0.0983482 0.170344i
\(361\) 1.69615 2.93782i 0.0892712 0.154622i
\(362\) 16.6244 + 9.59808i 0.873757 + 0.504464i
\(363\) 9.39230 0.492968
\(364\) −9.56218 + 2.36603i −0.501194 + 0.124013i
\(365\) −23.3923 −1.22441
\(366\) 7.96410 + 4.59808i 0.416290 + 0.240345i
\(367\) 5.63397 9.75833i 0.294091 0.509381i −0.680682 0.732579i \(-0.738316\pi\)
0.974773 + 0.223198i \(0.0716498\pi\)
\(368\) 2.09808 + 3.63397i 0.109370 + 0.189434i
\(369\) 9.39230i 0.488944i
\(370\) 11.4282 6.59808i 0.594124 0.343018i
\(371\) −15.2942 + 8.83013i −0.794037 + 0.458437i
\(372\) 1.46410i 0.0759101i
\(373\) 6.86603 + 11.8923i 0.355509 + 0.615760i 0.987205 0.159456i \(-0.0509741\pi\)
−0.631696 + 0.775216i \(0.717641\pi\)
\(374\) −3.63397 + 6.29423i −0.187908 + 0.325467i
\(375\) 12.6962 + 7.33013i 0.655626 + 0.378526i
\(376\) −2.19615 −0.113258
\(377\) 3.86603 + 15.6244i 0.199110 + 0.804695i
\(378\) −2.73205 −0.140522
\(379\) 4.73205 + 2.73205i 0.243069 + 0.140336i 0.616587 0.787287i \(-0.288515\pi\)
−0.373517 + 0.927623i \(0.621848\pi\)
\(380\) −8.83013 + 15.2942i −0.452976 + 0.784577i
\(381\) −4.92820 8.53590i −0.252479 0.437307i
\(382\) 6.92820i 0.354478i
\(383\) −1.26795 + 0.732051i −0.0647892 + 0.0374060i −0.532045 0.846716i \(-0.678576\pi\)
0.467255 + 0.884122i \(0.345243\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 12.9282i 0.658882i
\(386\) 5.86603 + 10.1603i 0.298573 + 0.517143i
\(387\) −4.83013 + 8.36603i −0.245529 + 0.425269i
\(388\) −5.19615 3.00000i −0.263795 0.152302i
\(389\) −11.7846 −0.597503 −0.298752 0.954331i \(-0.596570\pi\)
−0.298752 + 0.954331i \(0.596570\pi\)
\(390\) −12.9282 3.73205i −0.654645 0.188980i
\(391\) −24.0526 −1.21639
\(392\) −0.401924 0.232051i −0.0203002 0.0117203i
\(393\) −3.26795 + 5.66025i −0.164846 + 0.285522i
\(394\) −8.92820 15.4641i −0.449796 0.779070i
\(395\) 9.46410i 0.476191i
\(396\) 1.09808 0.633975i 0.0551804 0.0318584i
\(397\) −17.6603 + 10.1962i −0.886343 + 0.511730i −0.872744 0.488177i \(-0.837662\pi\)
−0.0135983 + 0.999908i \(0.504329\pi\)
\(398\) 14.1962i 0.711589i
\(399\) 6.46410 + 11.1962i 0.323610 + 0.560509i
\(400\) 4.46410 7.73205i 0.223205 0.386603i
\(401\) 6.99038 + 4.03590i 0.349083 + 0.201543i 0.664281 0.747483i \(-0.268738\pi\)
−0.315198 + 0.949026i \(0.602071\pi\)
\(402\) −13.1244 −0.654583
\(403\) −3.66025 3.80385i −0.182330 0.189483i
\(404\) 1.92820 0.0959317
\(405\) −3.23205 1.86603i −0.160602 0.0927235i
\(406\) −6.09808 + 10.5622i −0.302642 + 0.524192i
\(407\) 2.24167 + 3.88269i 0.111115 + 0.192458i
\(408\) 5.73205i 0.283779i
\(409\) 15.3564 8.86603i 0.759325 0.438397i −0.0697281 0.997566i \(-0.522213\pi\)
0.829053 + 0.559169i \(0.188880\pi\)
\(410\) 30.3564 17.5263i 1.49920 0.865561i
\(411\) 11.9282i 0.588375i
\(412\) 7.63397 + 13.2224i 0.376099 + 0.651422i
\(413\) −10.9282 + 18.9282i −0.537742 + 0.931396i
\(414\) 3.63397 + 2.09808i 0.178600 + 0.103115i
\(415\) 0.732051 0.0359350
\(416\) −1.00000 + 3.46410i −0.0490290 + 0.169842i
\(417\) 17.8564 0.874432
\(418\) −5.19615 3.00000i −0.254152 0.146735i
\(419\) 8.73205 15.1244i 0.426589 0.738873i −0.569979 0.821659i \(-0.693049\pi\)
0.996567 + 0.0827863i \(0.0263819\pi\)
\(420\) −5.09808 8.83013i −0.248761 0.430866i
\(421\) 22.7128i 1.10695i −0.832864 0.553477i \(-0.813301\pi\)
0.832864 0.553477i \(-0.186699\pi\)
\(422\) 14.1962 8.19615i 0.691058 0.398982i
\(423\) −1.90192 + 1.09808i −0.0924747 + 0.0533903i
\(424\) 6.46410i 0.313925i
\(425\) 25.5885 + 44.3205i 1.24122 + 2.14986i
\(426\) 2.36603 4.09808i 0.114634 0.198552i
\(427\) 21.7583 + 12.5622i 1.05296 + 0.607926i
\(428\) −10.1962 −0.492850
\(429\) 1.26795 4.39230i 0.0612172 0.212062i
\(430\) −36.0526 −1.73861
\(431\) −11.3660 6.56218i −0.547482 0.316089i 0.200624 0.979668i \(-0.435703\pi\)
−0.748106 + 0.663579i \(0.769036\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 6.42820 + 11.1340i 0.308920 + 0.535065i 0.978126 0.208012i \(-0.0666992\pi\)
−0.669207 + 0.743076i \(0.733366\pi\)
\(434\) 4.00000i 0.192006i
\(435\) −14.4282 + 8.33013i −0.691779 + 0.399399i
\(436\) −1.26795 + 0.732051i −0.0607238 + 0.0350589i
\(437\) 19.8564i 0.949861i
\(438\) 3.13397 + 5.42820i 0.149747 + 0.259370i
\(439\) −0.169873 + 0.294229i −0.00810760 + 0.0140428i −0.870051 0.492962i \(-0.835914\pi\)
0.861943 + 0.507005i \(0.169247\pi\)
\(440\) 4.09808 + 2.36603i 0.195368 + 0.112796i
\(441\) −0.464102 −0.0221001
\(442\) −14.3301 14.8923i −0.681615 0.708355i
\(443\) 15.6077 0.741544 0.370772 0.928724i \(-0.379093\pi\)
0.370772 + 0.928724i \(0.379093\pi\)
\(444\) −3.06218 1.76795i −0.145325 0.0839032i
\(445\) 17.6603 30.5885i 0.837176 1.45003i
\(446\) −13.4641 23.3205i −0.637544 1.10426i
\(447\) 13.1962i 0.624157i
\(448\) −2.36603 + 1.36603i −0.111784 + 0.0645386i
\(449\) −9.80385 + 5.66025i −0.462672 + 0.267124i −0.713167 0.700994i \(-0.752740\pi\)
0.250495 + 0.968118i \(0.419407\pi\)
\(450\) 8.92820i 0.420880i
\(451\) 5.95448 + 10.3135i 0.280386 + 0.485642i
\(452\) −0.669873 + 1.16025i −0.0315082 + 0.0545738i
\(453\) 5.83013 + 3.36603i 0.273923 + 0.158150i
\(454\) 12.1962 0.572394
\(455\) −35.3205 10.1962i −1.65585 0.478003i
\(456\) 4.73205 0.221599
\(457\) −1.16025 0.669873i −0.0542744 0.0313353i 0.472617 0.881268i \(-0.343309\pi\)
−0.526892 + 0.849932i \(0.676643\pi\)
\(458\) 5.92820 10.2679i 0.277007 0.479790i
\(459\) −2.86603 4.96410i −0.133775 0.231704i
\(460\) 15.6603i 0.730163i
\(461\) 19.2846 11.1340i 0.898174 0.518561i 0.0215666 0.999767i \(-0.493135\pi\)
0.876607 + 0.481207i \(0.159801\pi\)
\(462\) 3.00000 1.73205i 0.139573 0.0805823i
\(463\) 10.0526i 0.467182i −0.972335 0.233591i \(-0.924952\pi\)
0.972335 0.233591i \(-0.0750477\pi\)
\(464\) 2.23205 + 3.86603i 0.103620 + 0.179476i
\(465\) 2.73205 4.73205i 0.126696 0.219444i
\(466\) −6.80385 3.92820i −0.315182 0.181971i
\(467\) −18.5885 −0.860171 −0.430086 0.902788i \(-0.641517\pi\)
−0.430086 + 0.902788i \(0.641517\pi\)
\(468\) 0.866025 + 3.50000i 0.0400320 + 0.161788i
\(469\) −35.8564 −1.65570
\(470\) −7.09808 4.09808i −0.327410 0.189030i
\(471\) −3.79423 + 6.57180i −0.174829 + 0.302812i
\(472\) 4.00000 + 6.92820i 0.184115 + 0.318896i
\(473\) 12.2487i 0.563196i
\(474\) −2.19615 + 1.26795i −0.100873 + 0.0582388i
\(475\) −36.5885 + 21.1244i −1.67879 + 0.969252i
\(476\) 15.6603i 0.717787i
\(477\) 3.23205 + 5.59808i 0.147985 + 0.256318i
\(478\) 3.83013 6.63397i 0.175186 0.303431i
\(479\) 28.9808 + 16.7321i 1.32416 + 0.764507i 0.984390 0.176000i \(-0.0563159\pi\)
0.339775 + 0.940507i \(0.389649\pi\)
\(480\) −3.73205 −0.170344
\(481\) −12.3756 + 3.06218i −0.564281 + 0.139623i
\(482\) 13.5885 0.618937
\(483\) 9.92820 + 5.73205i 0.451749 + 0.260817i
\(484\) 4.69615 8.13397i 0.213461 0.369726i
\(485\) −11.1962 19.3923i −0.508391 0.880559i
\(486\) 1.00000i 0.0453609i
\(487\) −2.70577 + 1.56218i −0.122610 + 0.0707890i −0.560051 0.828458i \(-0.689218\pi\)
0.437441 + 0.899247i \(0.355885\pi\)
\(488\) 7.96410 4.59808i 0.360518 0.208145i
\(489\) 13.4641i 0.608868i
\(490\) −0.866025 1.50000i −0.0391230 0.0677631i
\(491\) 4.36603 7.56218i 0.197036 0.341276i −0.750530 0.660836i \(-0.770202\pi\)
0.947566 + 0.319560i \(0.103535\pi\)
\(492\) −8.13397 4.69615i −0.366708 0.211719i
\(493\) −25.5885 −1.15245
\(494\) 12.2942 11.8301i 0.553143 0.532263i
\(495\) 4.73205 0.212690
\(496\) −1.26795 0.732051i −0.0569326 0.0328701i
\(497\) 6.46410 11.1962i 0.289955 0.502216i
\(498\) −0.0980762 0.169873i −0.00439490 0.00761219i
\(499\) 32.0000i 1.43252i 0.697835 + 0.716258i \(0.254147\pi\)
−0.697835 + 0.716258i \(0.745853\pi\)
\(500\) 12.6962 7.33013i 0.567789 0.327813i
\(501\) 8.19615 4.73205i 0.366177 0.211412i
\(502\) 13.4641i 0.600932i
\(503\) −20.4904 35.4904i −0.913621 1.58244i −0.808908 0.587935i \(-0.799941\pi\)
−0.104713 0.994502i \(-0.533392\pi\)
\(504\) −1.36603 + 2.36603i −0.0608476 + 0.105391i
\(505\) 6.23205 + 3.59808i 0.277323 + 0.160112i
\(506\) −5.32051 −0.236525
\(507\) 11.0000 + 6.92820i 0.488527 + 0.307692i
\(508\) −9.85641 −0.437307
\(509\) −11.8923 6.86603i −0.527117 0.304331i 0.212725 0.977112i \(-0.431766\pi\)
−0.739842 + 0.672781i \(0.765100\pi\)
\(510\) 10.6962 18.5263i 0.473634 0.820357i
\(511\) 8.56218 + 14.8301i 0.378768 + 0.656046i
\(512\) 1.00000i 0.0441942i
\(513\) 4.09808 2.36603i 0.180934 0.104463i
\(514\) −8.08846 + 4.66987i −0.356767 + 0.205979i
\(515\) 56.9808i 2.51087i
\(516\) 4.83013 + 8.36603i 0.212634 + 0.368294i
\(517\) 1.39230 2.41154i 0.0612335 0.106060i
\(518\) −8.36603 4.83013i −0.367582 0.212224i
\(519\) −4.39230 −0.192801
\(520\) −9.69615 + 9.33013i −0.425204 + 0.409153i
\(521\) 41.4449 1.81573 0.907866 0.419260i \(-0.137710\pi\)
0.907866 + 0.419260i \(0.137710\pi\)
\(522\) 3.86603 + 2.23205i 0.169211 + 0.0976942i
\(523\) 11.2224 19.4378i 0.490723 0.849957i −0.509220 0.860636i \(-0.670066\pi\)
0.999943 + 0.0106796i \(0.00339949\pi\)
\(524\) 3.26795 + 5.66025i 0.142761 + 0.247269i
\(525\) 24.3923i 1.06457i
\(526\) −8.70577 + 5.02628i −0.379590 + 0.219156i
\(527\) 7.26795 4.19615i 0.316597 0.182787i
\(528\) 1.26795i 0.0551804i
\(529\) 2.69615 + 4.66987i 0.117224 + 0.203038i
\(530\) −12.0622 + 20.8923i −0.523948 + 0.907504i
\(531\) 6.92820 + 4.00000i 0.300658 + 0.173585i
\(532\) 12.9282 0.560509
\(533\) −32.8731 + 8.13397i −1.42389 + 0.352322i
\(534\) −9.46410 −0.409552
\(535\) −32.9545 19.0263i −1.42475 0.822578i
\(536\) −6.56218 + 11.3660i −0.283443 + 0.490938i
\(537\) −8.02628 13.9019i −0.346360 0.599912i
\(538\) 5.46410i 0.235574i
\(539\) 0.509619 0.294229i 0.0219508 0.0126733i
\(540\) −3.23205 + 1.86603i −0.139085 + 0.0803009i
\(541\) 5.67949i 0.244180i −0.992519 0.122090i \(-0.961040\pi\)
0.992519 0.122090i \(-0.0389597\pi\)
\(542\) 10.9282 + 18.9282i 0.469407 + 0.813036i
\(543\) 9.59808 16.6244i 0.411893 0.713419i
\(544\) −4.96410 2.86603i −0.212834 0.122880i
\(545\) −5.46410 −0.234056
\(546\) 2.36603 + 9.56218i 0.101257 + 0.409223i
\(547\) −4.19615 −0.179415 −0.0897073 0.995968i \(-0.528593\pi\)
−0.0897073 + 0.995968i \(0.528593\pi\)
\(548\) −10.3301 5.96410i −0.441281 0.254774i
\(549\) 4.59808 7.96410i 0.196241 0.339900i
\(550\) 5.66025 + 9.80385i 0.241354 + 0.418037i
\(551\) 21.1244i 0.899928i
\(552\) 3.63397 2.09808i 0.154672 0.0893001i
\(553\) −6.00000 + 3.46410i −0.255146 + 0.147309i
\(554\) 5.73205i 0.243532i
\(555\) −6.59808 11.4282i −0.280073 0.485100i
\(556\) 8.92820 15.4641i 0.378640 0.655824i
\(557\) 36.6962 + 21.1865i 1.55487 + 0.897702i 0.997734 + 0.0672780i \(0.0214314\pi\)
0.557132 + 0.830424i \(0.311902\pi\)
\(558\) −1.46410 −0.0619804
\(559\) 33.4641 + 9.66025i 1.41538 + 0.408585i
\(560\) −10.1962 −0.430866
\(561\) 6.29423 + 3.63397i 0.265743 + 0.153427i
\(562\) −6.16025 + 10.6699i −0.259855 + 0.450081i
\(563\) 17.4641 + 30.2487i 0.736024 + 1.27483i 0.954273 + 0.298938i \(0.0966324\pi\)
−0.218248 + 0.975893i \(0.570034\pi\)
\(564\) 2.19615i 0.0924747i
\(565\) −4.33013 + 2.50000i −0.182170 + 0.105176i
\(566\) −22.2224 + 12.8301i −0.934078 + 0.539290i
\(567\) 2.73205i 0.114735i
\(568\) −2.36603 4.09808i −0.0992762 0.171951i
\(569\) 15.3205 26.5359i 0.642269 1.11244i −0.342656 0.939461i \(-0.611326\pi\)
0.984925 0.172982i \(-0.0553402\pi\)
\(570\) 15.2942 + 8.83013i 0.640605 + 0.369853i
\(571\) −14.0526 −0.588081 −0.294041 0.955793i \(-0.595000\pi\)
−0.294041 + 0.955793i \(0.595000\pi\)
\(572\) −3.16987 3.29423i −0.132539 0.137739i
\(573\) −6.92820 −0.289430
\(574\) −22.2224 12.8301i −0.927546 0.535519i
\(575\) −18.7321 + 32.4449i −0.781181 + 1.35304i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 3.73205i 0.155367i 0.996978 + 0.0776837i \(0.0247524\pi\)
−0.996978 + 0.0776837i \(0.975248\pi\)
\(578\) 13.7321 7.92820i 0.571178 0.329770i
\(579\) 10.1603 5.86603i 0.422246 0.243784i
\(580\) 16.6603i 0.691779i
\(581\) −0.267949 0.464102i −0.0111164 0.0192542i
\(582\) −3.00000 + 5.19615i −0.124354 + 0.215387i
\(583\) −7.09808 4.09808i −0.293972 0.169725i
\(584\) 6.26795 0.259370
\(585\) −3.73205 + 12.9282i −0.154301 + 0.534515i
\(586\) 30.5167 1.26063
\(587\) −13.8564 8.00000i −0.571915 0.330195i 0.185999 0.982550i \(-0.440448\pi\)
−0.757914 + 0.652355i \(0.773781\pi\)
\(588\) −0.232051 + 0.401924i −0.00956961 + 0.0165751i
\(589\) 3.46410 + 6.00000i 0.142736 + 0.247226i
\(590\) 29.8564i 1.22917i
\(591\) −15.4641 + 8.92820i −0.636108 + 0.367257i
\(592\) −3.06218 + 1.76795i −0.125855 + 0.0726623i
\(593\) 9.14359i 0.375482i 0.982219 + 0.187741i \(0.0601166\pi\)
−0.982219 + 0.187741i \(0.939883\pi\)
\(594\) −0.633975 1.09808i −0.0260123 0.0450546i
\(595\) 29.2224 50.6147i 1.19800 2.07500i
\(596\) 11.4282 + 6.59808i 0.468117 + 0.270268i
\(597\) 14.1962 0.581010
\(598\) 4.19615 14.5359i 0.171593 0.594417i
\(599\) −2.53590 −0.103614 −0.0518070 0.998657i \(-0.516498\pi\)
−0.0518070 + 0.998657i \(0.516498\pi\)
\(600\) −7.73205 4.46410i −0.315660 0.182246i
\(601\) −3.96410 + 6.86603i −0.161699 + 0.280071i −0.935478 0.353385i \(-0.885031\pi\)
0.773779 + 0.633456i \(0.218364\pi\)
\(602\) 13.1962 + 22.8564i 0.537835 + 0.931558i
\(603\) 13.1244i 0.534465i
\(604\) 5.83013 3.36603i 0.237225 0.136962i
\(605\) 30.3564 17.5263i 1.23416 0.712545i
\(606\) 1.92820i 0.0783279i
\(607\) 20.3923 + 35.3205i 0.827698 + 1.43362i 0.899840 + 0.436221i \(0.143683\pi\)
−0.0721415 + 0.997394i \(0.522983\pi\)
\(608\) 2.36603 4.09808i 0.0959550 0.166199i
\(609\) 10.5622 + 6.09808i 0.428001 + 0.247107i
\(610\) 34.3205 1.38960
\(611\) 5.49038 + 5.70577i 0.222117 + 0.230831i
\(612\) −5.73205 −0.231704
\(613\) 8.13397 + 4.69615i 0.328528 + 0.189676i 0.655187 0.755466i \(-0.272590\pi\)
−0.326659 + 0.945142i \(0.605923\pi\)
\(614\) 11.2942 19.5622i 0.455798 0.789465i
\(615\) −17.5263 30.3564i −0.706728 1.22409i
\(616\) 3.46410i 0.139573i
\(617\) −11.4737 + 6.62436i −0.461915 + 0.266687i −0.712849 0.701318i \(-0.752596\pi\)
0.250934 + 0.968004i \(0.419262\pi\)
\(618\) 13.2224 7.63397i 0.531884 0.307083i
\(619\) 17.4641i 0.701942i −0.936386 0.350971i \(-0.885852\pi\)
0.936386 0.350971i \(-0.114148\pi\)
\(620\) −2.73205 4.73205i −0.109722 0.190044i
\(621\) 2.09808 3.63397i 0.0841929 0.145826i
\(622\) −1.43782 0.830127i −0.0576514 0.0332851i
\(623\) −25.8564 −1.03592
\(624\) 3.46410 + 1.00000i 0.138675 + 0.0400320i
\(625\) 10.0718 0.402872
\(626\) −5.66025 3.26795i −0.226229 0.130614i
\(627\) −3.00000 + 5.19615i −0.119808 + 0.207514i
\(628\) 3.79423 + 6.57180i 0.151406 + 0.262243i
\(629\) 20.2679i 0.808136i
\(630\) −8.83013 + 5.09808i −0.351801 + 0.203112i
\(631\) 6.67949 3.85641i 0.265906 0.153521i −0.361119 0.932520i \(-0.617605\pi\)
0.627026 + 0.778998i \(0.284272\pi\)
\(632\) 2.53590i 0.100873i
\(633\) −8.19615 14.1962i −0.325768 0.564246i
\(634\) 10.3301 17.8923i 0.410262 0.710594i
\(635\) −31.8564 18.3923i −1.26418 0.729876i
\(636\) 6.46410 0.256318
\(637\) 0.401924 + 1.62436i 0.0159248 + 0.0643593i
\(638\) −5.66025 −0.224092
\(639\) −4.09808 2.36603i −0.162117 0.0935985i
\(640\) −1.86603 + 3.23205i −0.0737611 + 0.127758i
\(641\) −12.9904 22.5000i −0.513089 0.888697i −0.999885 0.0151806i \(-0.995168\pi\)
0.486796 0.873516i \(-0.338166\pi\)
\(642\) 10.1962i 0.402410i
\(643\) −12.0000 + 6.92820i −0.473234 + 0.273222i −0.717592 0.696463i \(-0.754756\pi\)
0.244359 + 0.969685i \(0.421423\pi\)
\(644\) 9.92820 5.73205i 0.391226 0.225874i
\(645\) 36.0526i 1.41957i
\(646\) 13.5622 + 23.4904i 0.533597 + 0.924217i
\(647\) −11.1244 + 19.2679i −0.437344 + 0.757501i −0.997484 0.0708966i \(-0.977414\pi\)
0.560140 + 0.828398i \(0.310747\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −10.1436 −0.398171
\(650\) −31.2487 + 7.73205i −1.22568 + 0.303276i
\(651\) −4.00000 −0.156772
\(652\) 11.6603 + 6.73205i 0.456651 + 0.263647i
\(653\) 8.73205 15.1244i 0.341712 0.591862i −0.643039 0.765833i \(-0.722327\pi\)
0.984751 + 0.173972i \(0.0556601\pi\)
\(654\) 0.732051 + 1.26795i 0.0286255 + 0.0495807i
\(655\) 24.3923i 0.953086i
\(656\) −8.13397 + 4.69615i −0.317578 + 0.183354i
\(657\) 5.42820 3.13397i 0.211774 0.122268i
\(658\) 6.00000i 0.233904i
\(659\) 5.12436 + 8.87564i 0.199617 + 0.345746i 0.948404 0.317064i \(-0.102697\pi\)
−0.748788 + 0.662810i \(0.769364\pi\)
\(660\) 2.36603 4.09808i 0.0920974 0.159517i
\(661\) 9.86603 + 5.69615i 0.383744 + 0.221555i 0.679446 0.733726i \(-0.262220\pi\)
−0.295702 + 0.955280i \(0.595554\pi\)
\(662\) −20.0000 −0.777322
\(663\) −14.8923 + 14.3301i −0.578369 + 0.556536i
\(664\) −0.196152 −0.00761219
\(665\) 41.7846 + 24.1244i 1.62034 + 0.935502i
\(666\) −1.76795 + 3.06218i −0.0685066 + 0.118657i
\(667\) −9.36603 16.2224i −0.362654 0.628135i
\(668\) 9.46410i 0.366177i
\(669\) −23.3205 + 13.4641i −0.901623 + 0.520552i
\(670\) −42.4186 + 24.4904i −1.63877 + 0.946146i
\(671\) 11.6603i 0.450139i
\(672\) 1.36603 + 2.36603i 0.0526956 + 0.0912714i
\(673\) 13.9641 24.1865i 0.538277 0.932322i −0.460720 0.887545i \(-0.652409\pi\)
0.998997 0.0447770i \(-0.0142577\pi\)
\(674\) −18.0622 10.4282i −0.695729 0.401679i
\(675\) −8.92820 −0.343647
\(676\) 11.5000 6.06218i 0.442308 0.233161i
\(677\) −45.4641 −1.74733 −0.873664 0.486530i \(-0.838262\pi\)
−0.873664 + 0.486530i \(0.838262\pi\)
\(678\) 1.16025 + 0.669873i 0.0445593 + 0.0257263i
\(679\) −8.19615 + 14.1962i −0.314539 + 0.544798i
\(680\) −10.6962 18.5263i −0.410179 0.710450i
\(681\) 12.1962i 0.467358i
\(682\) 1.60770 0.928203i 0.0615618 0.0355427i
\(683\) 8.78461 5.07180i 0.336134 0.194067i −0.322427 0.946594i \(-0.604499\pi\)
0.658561 + 0.752527i \(0.271165\pi\)
\(684\) 4.73205i 0.180934i
\(685\) −22.2583 38.5526i −0.850447 1.47302i
\(686\) 8.92820 15.4641i 0.340880 0.590422i
\(687\) −10.2679 5.92820i −0.391747 0.226175i
\(688\) 9.66025 0.368294
\(689\) 16.7942 16.1603i 0.639809 0.615657i
\(690\) 15.6603 0.596176
\(691\) −37.8109 21.8301i −1.43839 0.830457i −0.440656 0.897676i \(-0.645254\pi\)
−0.997738 + 0.0672190i \(0.978587\pi\)
\(692\) −2.19615 + 3.80385i −0.0834852 + 0.144601i
\(693\) −1.73205 3.00000i −0.0657952 0.113961i
\(694\) 33.1244i 1.25738i
\(695\) 57.7128 33.3205i 2.18917 1.26392i
\(696\) 3.86603 2.23205i 0.146541 0.0846057i
\(697\) 53.8372i 2.03923i
\(698\) −7.66025 13.2679i −0.289945 0.502199i
\(699\) −3.92820 + 6.80385i −0.148578 + 0.257345i
\(700\) −21.1244 12.1962i −0.798426 0.460971i
\(701\) 3.32051 0.125414 0.0627069 0.998032i \(-0.480027\pi\)
0.0627069 + 0.998032i \(0.480027\pi\)
\(702\) 3.50000 0.866025i 0.132099 0.0326860i
\(703\) 16.7321 0.631061
\(704\) −1.09808 0.633975i −0.0413853 0.0238938i
\(705\) −4.09808 + 7.09808i −0.154342 + 0.267329i
\(706\) −10.8923 18.8660i −0.409937 0.710032i
\(707\) 5.26795i 0.198122i
\(708\) 6.92820 4.00000i 0.260378 0.150329i
\(709\) −11.3827 + 6.57180i −0.427486 + 0.246809i −0.698275 0.715830i \(-0.746049\pi\)
0.270789 + 0.962639i \(0.412715\pi\)
\(710\) 17.6603i 0.662778i
\(711\) 1.26795 + 2.19615i 0.0475518 + 0.0823622i
\(712\) −4.73205 + 8.19615i −0.177341 + 0.307164i
\(713\) 5.32051 + 3.07180i 0.199255 + 0.115040i
\(714\) −15.6603 −0.586070
\(715\) −4.09808 16.5622i −0.153259 0.619390i
\(716\) −16.0526 −0.599912
\(717\) −6.63397 3.83013i −0.247750 0.143039i
\(718\) 0.562178 0.973721i 0.0209803 0.0363389i
\(719\) −14.7321 25.5167i −0.549413 0.951611i −0.998315 0.0580299i \(-0.981518\pi\)
0.448902 0.893581i \(-0.351815\pi\)
\(720\) 3.73205i 0.139085i
\(721\) 36.1244 20.8564i 1.34534 0.776733i
\(722\) −2.93782 + 1.69615i −0.109334 + 0.0631243i
\(723\) 13.5885i 0.505360i
\(724\) −9.59808 16.6244i −0.356710 0.617839i
\(725\) −19.9282 + 34.5167i −0.740115 + 1.28192i
\(726\) −8.13397 4.69615i −0.301880 0.174291i
\(727\) 30.9808 1.14901 0.574506 0.818500i \(-0.305194\pi\)
0.574506 + 0.818500i \(0.305194\pi\)
\(728\) 9.46410 + 2.73205i 0.350763 + 0.101257i
\(729\) 1.00000 0.0370370
\(730\) 20.2583 + 11.6962i 0.749794 + 0.432894i
\(731\) −27.6865 + 47.9545i −1.02402 + 1.77366i
\(732\) −4.59808 7.96410i −0.169950 0.294362i
\(733\) 19.0000i 0.701781i 0.936416 + 0.350891i \(0.114121\pi\)
−0.936416 + 0.350891i \(0.885879\pi\)
\(734\) −9.75833 + 5.63397i −0.360187 + 0.207954i
\(735\) −1.50000 + 0.866025i −0.0553283 + 0.0319438i
\(736\) 4.19615i 0.154672i
\(737\) −8.32051 14.4115i −0.306490 0.530856i
\(738\) −4.69615 + 8.13397i −0.172868 + 0.299416i
\(739\) 2.53590 + 1.46410i 0.0932845 + 0.0538578i 0.545917 0.837840i \(-0.316182\pi\)
−0.452632 + 0.891697i \(0.649515\pi\)
\(740\) −13.1962 −0.485100
\(741\) −11.8301 12.2942i −0.434591 0.451640i
\(742\) 17.6603 0.648328
\(743\) 41.9090 + 24.1962i 1.53749 + 0.887671i 0.998985 + 0.0450491i \(0.0143444\pi\)
0.538506 + 0.842622i \(0.318989\pi\)
\(744\) −0.732051 + 1.26795i −0.0268383 + 0.0464853i
\(745\) 24.6244 + 42.6506i 0.902167 + 1.56260i
\(746\) 13.7321i 0.502766i
\(747\) −0.169873 + 0.0980762i −0.00621533 + 0.00358842i
\(748\) 6.29423 3.63397i 0.230140 0.132871i
\(749\) 27.8564i 1.01785i
\(750\) −7.33013 12.6962i −0.267658 0.463598i
\(751\) −24.9545 + 43.2224i −0.910602 + 1.57721i −0.0973862 + 0.995247i \(0.531048\pi\)
−0.813216 + 0.581962i \(0.802285\pi\)
\(752\) 1.90192 + 1.09808i 0.0693560 + 0.0400427i
\(753\) −13.4641 −0.490659
\(754\) 4.46410 15.4641i 0.162573 0.563169i
\(755\) 25.1244 0.914369
\(756\) 2.36603 + 1.36603i 0.0860515 + 0.0496819i
\(757\) −10.4641 + 18.1244i −0.380324 + 0.658741i −0.991109 0.133056i \(-0.957521\pi\)
0.610784 + 0.791797i \(0.290854\pi\)
\(758\) −2.73205 4.73205i −0.0992326 0.171876i
\(759\) 5.32051i 0.193122i
\(760\) 15.2942 8.83013i 0.554780 0.320302i
\(761\) −9.80385 + 5.66025i −0.355389 + 0.205184i −0.667056 0.745007i \(-0.732446\pi\)
0.311667 + 0.950191i \(0.399113\pi\)
\(762\) 9.85641i 0.357060i
\(763\) 2.00000 + 3.46410i 0.0724049 + 0.125409i
\(764\) −3.46410 + 6.00000i −0.125327 + 0.217072i
\(765\) −18.5263 10.6962i −0.669819 0.386720i
\(766\) 1.46410 0.0529001
\(767\) 8.00000 27.7128i 0.288863 1.00065i
\(768\) 1.00000 0.0360844
\(769\) 37.9808 + 21.9282i 1.36962 + 0.790751i 0.990879 0.134751i \(-0.0430235\pi\)
0.378742 + 0.925502i \(0.376357\pi\)
\(770\) 6.46410 11.1962i 0.232950 0.403481i
\(771\) 4.66987 + 8.08846i 0.168181 + 0.291299i
\(772\) 11.7321i 0.422246i
\(773\) −42.3731 + 24.4641i −1.52405 + 0.879913i −0.524459 + 0.851436i \(0.675732\pi\)
−0.999594 + 0.0284768i \(0.990934\pi\)
\(774\) 8.36603 4.83013i 0.300711 0.173615i
\(775\)