Properties

Label 546.2.s.a.127.2
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 127.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 546.127
Dual form 546.2.s.a.43.2

$q$-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} +(1.50000 - 0.866025i) q^{11} -1.00000 q^{12} +(-3.59808 + 0.232051i) q^{13} -1.00000 q^{14} +(-2.36603 + 1.36603i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.133975 - 0.232051i) q^{17} +1.00000i q^{18} +(-0.866025 - 0.500000i) q^{19} +(-2.36603 - 1.36603i) q^{20} +1.00000i q^{21} +(0.866025 - 1.50000i) q^{22} +(1.73205 + 3.00000i) q^{23} +(-0.866025 + 0.500000i) q^{24} -2.46410 q^{25} +(-3.00000 + 2.00000i) q^{26} +1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(0.232051 + 0.401924i) q^{29} +(-1.36603 + 2.36603i) q^{30} -8.19615i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.50000 - 0.866025i) q^{33} -0.267949i q^{34} +(-1.36603 + 2.36603i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-2.83013 + 1.63397i) q^{37} -1.00000 q^{38} +(2.00000 + 3.00000i) q^{39} -2.73205 q^{40} +(-2.59808 + 1.50000i) q^{41} +(0.500000 + 0.866025i) q^{42} +(3.36603 - 5.83013i) q^{43} -1.73205i q^{44} +(2.36603 + 1.36603i) q^{45} +(3.00000 + 1.73205i) q^{46} -4.46410i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-2.13397 + 1.23205i) q^{50} -0.267949 q^{51} +(-1.59808 + 3.23205i) q^{52} +7.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.36603 - 4.09808i) q^{55} +(-0.500000 + 0.866025i) q^{56} +1.00000i q^{57} +(0.401924 + 0.232051i) q^{58} +(11.1962 + 6.46410i) q^{59} +2.73205i q^{60} +(2.59808 - 4.50000i) q^{61} +(-4.09808 - 7.09808i) q^{62} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(0.633975 + 9.83013i) q^{65} -1.73205 q^{66} +(4.26795 - 2.46410i) q^{67} +(-0.133975 - 0.232051i) q^{68} +(1.73205 - 3.00000i) q^{69} +2.73205i q^{70} +(-7.09808 - 4.09808i) q^{71} +(0.866025 + 0.500000i) q^{72} +1.46410i q^{73} +(-1.63397 + 2.83013i) q^{74} +(1.23205 + 2.13397i) q^{75} +(-0.866025 + 0.500000i) q^{76} -1.73205 q^{77} +(3.23205 + 1.59808i) q^{78} +15.9282 q^{79} +(-2.36603 + 1.36603i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.50000 + 2.59808i) q^{82} -10.1962i q^{83} +(0.866025 + 0.500000i) q^{84} +(-0.633975 - 0.366025i) q^{85} -6.73205i q^{86} +(0.232051 - 0.401924i) q^{87} +(-0.866025 - 1.50000i) q^{88} +(3.06218 - 1.76795i) q^{89} +2.73205 q^{90} +(3.23205 + 1.59808i) q^{91} +3.46410 q^{92} +(-7.09808 + 4.09808i) q^{93} +(-2.23205 - 3.86603i) q^{94} +(-1.36603 + 2.36603i) q^{95} +1.00000i q^{96} +(1.43782 + 0.830127i) q^{97} +(0.866025 + 0.500000i) q^{98} +1.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} - 2q^{10} + 6q^{11} - 4q^{12} - 4q^{13} - 4q^{14} - 6q^{15} - 2q^{16} + 4q^{17} - 6q^{20} + 4q^{25} - 12q^{26} + 4q^{27} - 6q^{29} - 2q^{30} - 6q^{33} - 2q^{35} + 2q^{36} + 6q^{37} - 4q^{38} + 8q^{39} - 4q^{40} + 2q^{42} + 10q^{43} + 6q^{45} + 12q^{46} - 2q^{48} + 2q^{49} - 12q^{50} - 8q^{51} + 4q^{52} + 28q^{53} - 6q^{55} - 2q^{56} + 12q^{58} + 24q^{59} - 6q^{62} - 4q^{64} + 6q^{65} + 24q^{67} - 4q^{68} - 18q^{71} - 10q^{74} - 2q^{75} + 6q^{78} + 36q^{79} - 6q^{80} - 2q^{81} - 6q^{82} - 6q^{85} - 6q^{87} - 12q^{89} + 4q^{90} + 6q^{91} - 18q^{93} - 2q^{94} - 2q^{95} + 30q^{97} + O(q^{100}) \)

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 \(-0.790806\pi\)
0.791704 0.610905i \(-0.209194\pi\)
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) −0.866025 0.500000i −0.327327 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.36603 2.36603i −0.431975 0.748203i
\(11\) 1.50000 0.866025i 0.452267 0.261116i −0.256520 0.966539i \(-0.582576\pi\)
0.708787 + 0.705422i \(0.249243\pi\)
\(12\) −1.00000 −0.288675
\(13\) −3.59808 + 0.232051i −0.997927 + 0.0643593i
\(14\) −1.00000 −0.267261
\(15\) −2.36603 + 1.36603i −0.610905 + 0.352706i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.133975 0.232051i 0.0324936 0.0562806i −0.849321 0.527876i \(-0.822988\pi\)
0.881815 + 0.471596i \(0.156322\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −0.866025 0.500000i −0.198680 0.114708i 0.397360 0.917663i \(-0.369927\pi\)
−0.596040 + 0.802955i \(0.703260\pi\)
\(20\) −2.36603 1.36603i −0.529059 0.305453i
\(21\) 1.00000i 0.218218i
\(22\) 0.866025 1.50000i 0.184637 0.319801i
\(23\) 1.73205 + 3.00000i 0.361158 + 0.625543i 0.988152 0.153481i \(-0.0490483\pi\)
−0.626994 + 0.779024i \(0.715715\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) −2.46410 −0.492820
\(26\) −3.00000 + 2.00000i −0.588348 + 0.392232i
\(27\) 1.00000 0.192450
\(28\) −0.866025 + 0.500000i −0.163663 + 0.0944911i
\(29\) 0.232051 + 0.401924i 0.0430908 + 0.0746354i 0.886766 0.462218i \(-0.152946\pi\)
−0.843676 + 0.536853i \(0.819613\pi\)
\(30\) −1.36603 + 2.36603i −0.249401 + 0.431975i
\(31\) 8.19615i 1.47207i −0.676942 0.736036i \(-0.736695\pi\)
0.676942 0.736036i \(-0.263305\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −1.50000 0.866025i −0.261116 0.150756i
\(34\) 0.267949i 0.0459529i
\(35\) −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 \(0.419902\pi\)
\(38\) −1.00000 −0.162221
\(39\) 2.00000 + 3.00000i 0.320256 + 0.480384i
\(40\) −2.73205 −0.431975
\(41\) −2.59808 + 1.50000i −0.405751 + 0.234261i −0.688963 0.724797i \(-0.741934\pi\)
0.283211 + 0.959058i \(0.408600\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) 3.36603 5.83013i 0.513314 0.889086i −0.486567 0.873643i \(-0.661751\pi\)
0.999881 0.0154426i \(-0.00491573\pi\)
\(44\) 1.73205i 0.261116i
\(45\) 2.36603 + 1.36603i 0.352706 + 0.203635i
\(46\) 3.00000 + 1.73205i 0.442326 + 0.255377i
\(47\) 4.46410i 0.651156i −0.945515 0.325578i \(-0.894441\pi\)
0.945515 0.325578i \(-0.105559\pi\)
\(48\) −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
\(51\) −0.267949 −0.0375204
\(52\) −1.59808 + 3.23205i −0.221613 + 0.448205i
\(53\) 7.00000 0.961524 0.480762 0.876851i \(-0.340360\pi\)
0.480762 + 0.876851i \(0.340360\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) −2.36603 4.09808i −0.319035 0.552584i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 1.00000i 0.132453i
\(58\) 0.401924 + 0.232051i 0.0527752 + 0.0304698i
\(59\) 11.1962 + 6.46410i 1.45761 + 0.841554i 0.998894 0.0470259i \(-0.0149743\pi\)
0.458721 + 0.888580i \(0.348308\pi\)
\(60\) 2.73205i 0.352706i
\(61\) 2.59808 4.50000i 0.332650 0.576166i −0.650381 0.759608i \(-0.725391\pi\)
0.983030 + 0.183442i \(0.0587240\pi\)
\(62\) −4.09808 7.09808i −0.520456 0.901457i
\(63\) 0.866025 0.500000i 0.109109 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 0.633975 + 9.83013i 0.0786349 + 1.21928i
\(66\) −1.73205 −0.213201
\(67\) 4.26795 2.46410i 0.521413 0.301038i −0.216100 0.976371i \(-0.569334\pi\)
0.737513 + 0.675333i \(0.236000\pi\)
\(68\) −0.133975 0.232051i −0.0162468 0.0281403i
\(69\) 1.73205 3.00000i 0.208514 0.361158i
\(70\) 2.73205i 0.326543i
\(71\) −7.09808 4.09808i −0.842387 0.486352i 0.0156881 0.999877i \(-0.495006\pi\)
−0.858075 + 0.513525i \(0.828339\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 1.46410i 0.171360i 0.996323 + 0.0856801i \(0.0273063\pi\)
−0.996323 + 0.0856801i \(0.972694\pi\)
\(74\) −1.63397 + 2.83013i −0.189946 + 0.328996i
\(75\) 1.23205 + 2.13397i 0.142265 + 0.246410i
\(76\) −0.866025 + 0.500000i −0.0993399 + 0.0573539i
\(77\) −1.73205 −0.197386
\(78\) 3.23205 + 1.59808i 0.365958 + 0.180946i
\(79\) 15.9282 1.79206 0.896031 0.443991i \(-0.146438\pi\)
0.896031 + 0.443991i \(0.146438\pi\)
\(80\) −2.36603 + 1.36603i −0.264530 + 0.152726i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.50000 + 2.59808i −0.165647 + 0.286910i
\(83\) 10.1962i 1.11917i −0.828772 0.559587i \(-0.810960\pi\)
0.828772 0.559587i \(-0.189040\pi\)
\(84\) 0.866025 + 0.500000i 0.0944911 + 0.0545545i
\(85\) −0.633975 0.366025i −0.0687642 0.0397010i
\(86\) 6.73205i 0.725936i
\(87\) 0.232051 0.401924i 0.0248785 0.0430908i
\(88\) −0.866025 1.50000i −0.0923186 0.159901i
\(89\) 3.06218 1.76795i 0.324590 0.187402i −0.328847 0.944383i \(-0.606660\pi\)
0.653437 + 0.756981i \(0.273327\pi\)
\(90\) 2.73205 0.287983
\(91\) 3.23205 + 1.59808i 0.338811 + 0.167524i
\(92\) 3.46410 0.361158
\(93\) −7.09808 + 4.09808i −0.736036 + 0.424951i
\(94\) −2.23205 3.86603i −0.230218 0.398750i
\(95\) −1.36603 + 2.36603i −0.140151 + 0.242749i
\(96\) 1.00000i 0.102062i
\(97\) 1.43782 + 0.830127i 0.145989 + 0.0842866i 0.571215 0.820800i \(-0.306472\pi\)
−0.425226 + 0.905087i \(0.639806\pi\)
\(98\) 0.866025 + 0.500000i 0.0874818 + 0.0505076i
\(99\) 1.73205i 0.174078i
\(100\) −1.23205 + 2.13397i −0.123205 + 0.213397i
\(101\) 8.46410 + 14.6603i 0.842210 + 1.45875i 0.888023 + 0.459800i \(0.152079\pi\)
−0.0458130 + 0.998950i \(0.514588\pi\)
\(102\) −0.232051 + 0.133975i −0.0229765 + 0.0132655i
\(103\) −11.2679 −1.11026 −0.555132 0.831762i \(-0.687332\pi\)
−0.555132 + 0.831762i \(0.687332\pi\)
\(104\) 0.232051 + 3.59808i 0.0227545 + 0.352820i
\(105\) 2.73205 0.266621
\(106\) 6.06218 3.50000i 0.588811 0.339950i
\(107\) 8.42820 + 14.5981i 0.814785 + 1.41125i 0.909482 + 0.415743i \(0.136478\pi\)
−0.0946969 + 0.995506i \(0.530188\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 1.26795i 0.121448i 0.998155 + 0.0607238i \(0.0193409\pi\)
−0.998155 + 0.0607238i \(0.980659\pi\)
\(110\) −4.09808 2.36603i −0.390736 0.225592i
\(111\) 2.83013 + 1.63397i 0.268624 + 0.155090i
\(112\) 1.00000i 0.0944911i
\(113\) −9.36603 + 16.2224i −0.881082 + 1.52608i −0.0309416 + 0.999521i \(0.509851\pi\)
−0.850140 + 0.526557i \(0.823483\pi\)
\(114\) 0.500000 + 0.866025i 0.0468293 + 0.0811107i
\(115\) 8.19615 4.73205i 0.764295 0.441266i
\(116\) 0.464102 0.0430908
\(117\) 1.59808 3.23205i 0.147742 0.298803i
\(118\) 12.9282 1.19014
\(119\) −0.232051 + 0.133975i −0.0212721 + 0.0122814i
\(120\) 1.36603 + 2.36603i 0.124700 + 0.215988i
\(121\) −4.00000 + 6.92820i −0.363636 + 0.629837i
\(122\) 5.19615i 0.470438i
\(123\) 2.59808 + 1.50000i 0.234261 + 0.135250i
\(124\) −7.09808 4.09808i −0.637426 0.368018i
\(125\) 6.92820i 0.619677i
\(126\) 0.500000 0.866025i 0.0445435 0.0771517i
\(127\) −4.26795 7.39230i −0.378719 0.655961i 0.612157 0.790736i \(-0.290302\pi\)
−0.990876 + 0.134775i \(0.956969\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −6.73205 −0.592724
\(130\) 5.46410 + 8.19615i 0.479233 + 0.718850i
\(131\) 13.8564 1.21064 0.605320 0.795982i \(-0.293045\pi\)
0.605320 + 0.795982i \(0.293045\pi\)
\(132\) −1.50000 + 0.866025i −0.130558 + 0.0753778i
\(133\) 0.500000 + 0.866025i 0.0433555 + 0.0750939i
\(134\) 2.46410 4.26795i 0.212866 0.368695i
\(135\) 2.73205i 0.235137i
\(136\) −0.232051 0.133975i −0.0198982 0.0114882i
\(137\) 5.53590 + 3.19615i 0.472964 + 0.273066i 0.717480 0.696580i \(-0.245296\pi\)
−0.244516 + 0.969645i \(0.578629\pi\)
\(138\) 3.46410i 0.294884i
\(139\) 9.79423 16.9641i 0.830736 1.43888i −0.0667201 0.997772i \(-0.521253\pi\)
0.897456 0.441105i \(-0.145413\pi\)
\(140\) 1.36603 + 2.36603i 0.115450 + 0.199966i
\(141\) −3.86603 + 2.23205i −0.325578 + 0.187973i
\(142\) −8.19615 −0.687806
\(143\) −5.19615 + 3.46410i −0.434524 + 0.289683i
\(144\) 1.00000 0.0833333
\(145\) 1.09808 0.633975i 0.0911903 0.0526487i
\(146\) 0.732051 + 1.26795i 0.0605850 + 0.104936i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) 3.26795i 0.268624i
\(149\) 12.0000 + 6.92820i 0.983078 + 0.567581i 0.903198 0.429224i \(-0.141213\pi\)
0.0798802 + 0.996804i \(0.474546\pi\)
\(150\) 2.13397 + 1.23205i 0.174238 + 0.100597i
\(151\) 5.19615i 0.422857i −0.977393 0.211428i \(-0.932188\pi\)
0.977393 0.211428i \(-0.0678115\pi\)
\(152\) −0.500000 + 0.866025i −0.0405554 + 0.0702439i
\(153\) 0.133975 + 0.232051i 0.0108312 + 0.0187602i
\(154\) −1.50000 + 0.866025i −0.120873 + 0.0697863i
\(155\) −22.3923 −1.79859
\(156\) 3.59808 0.232051i 0.288077 0.0185789i
\(157\) −7.46410 −0.595700 −0.297850 0.954613i \(-0.596270\pi\)
−0.297850 + 0.954613i \(0.596270\pi\)
\(158\) 13.7942 7.96410i 1.09741 0.633590i
\(159\) −3.50000 6.06218i −0.277568 0.480762i
\(160\) −1.36603 + 2.36603i −0.107994 + 0.187051i
\(161\) 3.46410i 0.273009i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) 0.633975 + 0.366025i 0.0496567 + 0.0286693i 0.524623 0.851335i \(-0.324206\pi\)
−0.474966 + 0.880004i \(0.657540\pi\)
\(164\) 3.00000i 0.234261i
\(165\) −2.36603 + 4.09808i −0.184195 + 0.319035i
\(166\) −5.09808 8.83013i −0.395687 0.685351i
\(167\) −12.0000 + 6.92820i −0.928588 + 0.536120i −0.886365 0.462988i \(-0.846777\pi\)
−0.0422232 + 0.999108i \(0.513444\pi\)
\(168\) 1.00000 0.0771517
\(169\) 12.8923 1.66987i 0.991716 0.128452i
\(170\) −0.732051 −0.0561457
\(171\) 0.866025 0.500000i 0.0662266 0.0382360i
\(172\) −3.36603 5.83013i −0.256657 0.444543i
\(173\) 7.56218 13.0981i 0.574942 0.995828i −0.421106 0.907011i \(-0.638358\pi\)
0.996048 0.0888170i \(-0.0283086\pi\)
\(174\) 0.464102i 0.0351835i
\(175\) 2.13397 + 1.23205i 0.161313 + 0.0931343i
\(176\) −1.50000 0.866025i −0.113067 0.0652791i
\(177\) 12.9282i 0.971743i
\(178\) 1.76795 3.06218i 0.132513 0.229520i
\(179\) 2.26795 + 3.92820i 0.169514 + 0.293608i 0.938249 0.345960i \(-0.112447\pi\)
−0.768735 + 0.639568i \(0.779113\pi\)
\(180\) 2.36603 1.36603i 0.176353 0.101818i
\(181\) −14.6603 −1.08969 −0.544844 0.838537i \(-0.683411\pi\)
−0.544844 + 0.838537i \(0.683411\pi\)
\(182\) 3.59808 0.232051i 0.266707 0.0172008i
\(183\) −5.19615 −0.384111
\(184\) 3.00000 1.73205i 0.221163 0.127688i
\(185\) 4.46410 + 7.73205i 0.328207 + 0.568472i
\(186\) −4.09808 + 7.09808i −0.300486 + 0.520456i
\(187\) 0.464102i 0.0339385i
\(188\) −3.86603 2.23205i −0.281959 0.162789i
\(189\) −0.866025 0.500000i −0.0629941 0.0363696i
\(190\) 2.73205i 0.198204i
\(191\) 0.562178 0.973721i 0.0406778 0.0704559i −0.844970 0.534814i \(-0.820382\pi\)
0.885647 + 0.464358i \(0.153715\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −7.96410 + 4.59808i −0.573269 + 0.330977i −0.758454 0.651727i \(-0.774045\pi\)
0.185185 + 0.982704i \(0.440712\pi\)
\(194\) 1.66025 0.119199
\(195\) 8.19615 5.46410i 0.586939 0.391292i
\(196\) 1.00000 0.0714286
\(197\) −8.08846 + 4.66987i −0.576279 + 0.332715i −0.759653 0.650328i \(-0.774631\pi\)
0.183374 + 0.983043i \(0.441298\pi\)
\(198\) 0.866025 + 1.50000i 0.0615457 + 0.106600i
\(199\) −2.90192 + 5.02628i −0.205712 + 0.356304i −0.950359 0.311155i \(-0.899284\pi\)
0.744647 + 0.667458i \(0.232618\pi\)
\(200\) 2.46410i 0.174238i
\(201\) −4.26795 2.46410i −0.301038 0.173804i
\(202\) 14.6603 + 8.46410i 1.03149 + 0.595532i
\(203\) 0.464102i 0.0325735i
\(204\) −0.133975 + 0.232051i −0.00938010 + 0.0162468i
\(205\) 4.09808 + 7.09808i 0.286222 + 0.495751i
\(206\) −9.75833 + 5.63397i −0.679895 + 0.392538i
\(207\) −3.46410 −0.240772
\(208\) 2.00000 + 3.00000i 0.138675 + 0.208013i
\(209\) −1.73205 −0.119808
\(210\) 2.36603 1.36603i 0.163271 0.0942647i
\(211\) −13.0000 22.5167i −0.894957 1.55011i −0.833858 0.551979i \(-0.813873\pi\)
−0.0610990 0.998132i \(-0.519461\pi\)
\(212\) 3.50000 6.06218i 0.240381 0.416352i
\(213\) 8.19615i 0.561591i
\(214\) 14.5981 + 8.42820i 0.997904 + 0.576140i
\(215\) −15.9282 9.19615i −1.08629 0.627172i
\(216\) 1.00000i 0.0680414i
\(217\) −4.09808 + 7.09808i −0.278196 + 0.481849i
\(218\) 0.633975 + 1.09808i 0.0429382 + 0.0743711i
\(219\) 1.26795 0.732051i 0.0856801 0.0494674i
\(220\) −4.73205 −0.319035
\(221\) −0.428203 + 0.866025i −0.0288041 + 0.0582552i
\(222\) 3.26795 0.219330
\(223\) −3.12436 + 1.80385i −0.209222 + 0.120795i −0.600950 0.799287i \(-0.705211\pi\)
0.391728 + 0.920081i \(0.371878\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 1.23205 2.13397i 0.0821367 0.142265i
\(226\) 18.7321i 1.24604i
\(227\) 2.07180 + 1.19615i 0.137510 + 0.0793914i 0.567177 0.823596i \(-0.308036\pi\)
−0.429667 + 0.902988i \(0.641369\pi\)
\(228\) 0.866025 + 0.500000i 0.0573539 + 0.0331133i
\(229\) 6.07180i 0.401236i −0.979670 0.200618i \(-0.935705\pi\)
0.979670 0.200618i \(-0.0642949\pi\)
\(230\) 4.73205 8.19615i 0.312022 0.540438i
\(231\) 0.866025 + 1.50000i 0.0569803 + 0.0986928i
\(232\) 0.401924 0.232051i 0.0263876 0.0152349i
\(233\) −15.1244 −0.990829 −0.495415 0.868657i \(-0.664984\pi\)
−0.495415 + 0.868657i \(0.664984\pi\)
\(234\) −0.232051 3.59808i −0.0151696 0.235214i
\(235\) −12.1962 −0.795589
\(236\) 11.1962 6.46410i 0.728807 0.420777i
\(237\) −7.96410 13.7942i −0.517324 0.896031i
\(238\) −0.133975 + 0.232051i −0.00868428 + 0.0150416i
\(239\) 2.73205i 0.176722i −0.996089 0.0883608i \(-0.971837\pi\)
0.996089 0.0883608i \(-0.0281629\pi\)
\(240\) 2.36603 + 1.36603i 0.152726 + 0.0881766i
\(241\) 6.92820 + 4.00000i 0.446285 + 0.257663i 0.706260 0.707953i \(-0.250381\pi\)
−0.259975 + 0.965615i \(0.583714\pi\)
\(242\) 8.00000i 0.514259i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −2.59808 4.50000i −0.166325 0.288083i
\(245\) 2.36603 1.36603i 0.151160 0.0872722i
\(246\) 3.00000 0.191273
\(247\) 3.23205 + 1.59808i 0.205650 + 0.101683i
\(248\) −8.19615 −0.520456
\(249\) −8.83013 + 5.09808i −0.559587 + 0.323077i
\(250\) −3.46410 6.00000i −0.219089 0.379473i
\(251\) −5.56218 + 9.63397i −0.351082 + 0.608091i −0.986439 0.164127i \(-0.947519\pi\)
0.635358 + 0.772218i \(0.280853\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 5.19615 + 3.00000i 0.326679 + 0.188608i
\(254\) −7.39230 4.26795i −0.463834 0.267795i
\(255\) 0.732051i 0.0458428i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.66987 + 2.89230i 0.104164 + 0.180417i 0.913396 0.407072i \(-0.133450\pi\)
−0.809232 + 0.587489i \(0.800117\pi\)
\(258\) −5.83013 + 3.36603i −0.362968 + 0.209560i
\(259\) 3.26795 0.203060
\(260\) 8.83013 + 4.36603i 0.547621 + 0.270769i
\(261\) −0.464102 −0.0287272
\(262\) 12.0000 6.92820i 0.741362 0.428026i
\(263\) −4.56218 7.90192i −0.281316 0.487253i 0.690393 0.723434i \(-0.257438\pi\)
−0.971709 + 0.236181i \(0.924104\pi\)
\(264\) −0.866025 + 1.50000i −0.0533002 + 0.0923186i
\(265\) 19.1244i 1.17480i
\(266\) 0.866025 + 0.500000i 0.0530994 + 0.0306570i
\(267\) −3.06218 1.76795i −0.187402 0.108197i
\(268\) 4.92820i 0.301038i
\(269\) −8.92820 + 15.4641i −0.544362 + 0.942863i 0.454285 + 0.890857i \(0.349895\pi\)
−0.998647 + 0.0520063i \(0.983438\pi\)
\(270\) −1.36603 2.36603i −0.0831337 0.143992i
\(271\) −8.70577 + 5.02628i −0.528838 + 0.305325i −0.740543 0.672009i \(-0.765432\pi\)
0.211705 + 0.977334i \(0.432098\pi\)
\(272\) −0.267949 −0.0162468
\(273\) −0.232051 3.59808i −0.0140444 0.217765i
\(274\) 6.39230 0.386173
\(275\) −3.69615 + 2.13397i −0.222886 + 0.128684i
\(276\) −1.73205 3.00000i −0.104257 0.180579i
\(277\) −12.6603 + 21.9282i −0.760681 + 1.31754i 0.181819 + 0.983332i \(0.441801\pi\)
−0.942500 + 0.334206i \(0.891532\pi\)
\(278\) 19.5885i 1.17484i
\(279\) 7.09808 + 4.09808i 0.424951 + 0.245345i
\(280\) 2.36603 + 1.36603i 0.141397 + 0.0816356i
\(281\) 17.6603i 1.05352i −0.850013 0.526761i \(-0.823406\pi\)
0.850013 0.526761i \(-0.176594\pi\)
\(282\) −2.23205 + 3.86603i −0.132917 + 0.230218i
\(283\) 8.92820 + 15.4641i 0.530727 + 0.919245i 0.999357 + 0.0358512i \(0.0114142\pi\)
−0.468631 + 0.883394i \(0.655252\pi\)
\(284\) −7.09808 + 4.09808i −0.421193 + 0.243176i
\(285\) 2.73205 0.161833
\(286\) −2.76795 + 5.59808i −0.163672 + 0.331021i
\(287\) 3.00000 0.177084
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) 8.46410 + 14.6603i 0.497888 + 0.862368i
\(290\) 0.633975 1.09808i 0.0372283 0.0644813i
\(291\) 1.66025i 0.0973258i
\(292\) 1.26795 + 0.732051i 0.0742011 + 0.0428400i
\(293\) 26.7846 + 15.4641i 1.56477 + 0.903422i 0.996763 + 0.0804015i \(0.0256203\pi\)
0.568011 + 0.823021i \(0.307713\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) 17.6603 30.5885i 1.02822 1.78093i
\(296\) 1.63397 + 2.83013i 0.0949728 + 0.164498i
\(297\) 1.50000 0.866025i 0.0870388 0.0502519i
\(298\) 13.8564 0.802680
\(299\) −6.92820 10.3923i −0.400668 0.601003i
\(300\) 2.46410 0.142265
\(301\) −5.83013 + 3.36603i −0.336043 + 0.194014i
\(302\) −2.59808 4.50000i −0.149502 0.258946i
\(303\) 8.46410 14.6603i 0.486250 0.842210i
\(304\) 1.00000i 0.0573539i
\(305\) −12.2942 7.09808i −0.703965 0.406435i
\(306\) 0.232051 + 0.133975i 0.0132655 + 0.00765882i
\(307\) 29.3923i 1.67751i 0.544511 + 0.838754i \(0.316715\pi\)
−0.544511 + 0.838754i \(0.683285\pi\)
\(308\) −0.866025 + 1.50000i −0.0493464 + 0.0854704i
\(309\) 5.63397 + 9.75833i 0.320506 + 0.555132i
\(310\) −19.3923 + 11.1962i −1.10141 + 0.635899i
\(311\) −7.73205 −0.438444 −0.219222 0.975675i \(-0.570352\pi\)
−0.219222 + 0.975675i \(0.570352\pi\)
\(312\) 3.00000 2.00000i 0.169842 0.113228i
\(313\) −31.5167 −1.78143 −0.890713 0.454565i \(-0.849795\pi\)
−0.890713 + 0.454565i \(0.849795\pi\)
\(314\) −6.46410 + 3.73205i −0.364790 + 0.210612i
\(315\) −1.36603 2.36603i −0.0769668 0.133310i
\(316\) 7.96410 13.7942i 0.448016 0.775986i
\(317\) 15.8564i 0.890585i −0.895385 0.445292i \(-0.853100\pi\)
0.895385 0.445292i \(-0.146900\pi\)
\(318\) −6.06218 3.50000i −0.339950 0.196270i
\(319\) 0.696152 + 0.401924i 0.0389771 + 0.0225034i
\(320\) 2.73205i 0.152726i
\(321\) 8.42820 14.5981i 0.470416 0.814785i
\(322\) −1.73205 3.00000i −0.0965234 0.167183i
\(323\) −0.232051 + 0.133975i −0.0129117 + 0.00745455i
\(324\) −1.00000 −0.0555556
\(325\) 8.86603 0.571797i 0.491799 0.0317176i
\(326\) 0.732051 0.0405445
\(327\) 1.09808 0.633975i 0.0607238 0.0350589i
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) −2.23205 + 3.86603i −0.123057 + 0.213141i
\(330\) 4.73205i 0.260491i
\(331\) −0.124356 0.0717968i −0.00683520 0.00394631i 0.496579 0.867992i \(-0.334589\pi\)
−0.503414 + 0.864046i \(0.667923\pi\)
\(332\) −8.83013 5.09808i −0.484616 0.279793i
\(333\) 3.26795i 0.179083i
\(334\) −6.92820 + 12.0000i −0.379094 + 0.656611i
\(335\) −6.73205 11.6603i −0.367811 0.637068i
\(336\) 0.866025 0.500000i 0.0472456 0.0272772i
\(337\) −19.0000 −1.03500 −0.517498 0.855684i \(-0.673136\pi\)
−0.517498 + 0.855684i \(0.673136\pi\)
\(338\) 10.3301 7.89230i 0.561885 0.429285i
\(339\) 18.7321 1.01739
\(340\) −0.633975 + 0.366025i −0.0343821 + 0.0198505i
\(341\) −7.09808 12.2942i −0.384382 0.665770i
\(342\) 0.500000 0.866025i 0.0270369 0.0468293i
\(343\) 1.00000i 0.0539949i
\(344\) −5.83013 3.36603i −0.314339 0.181484i
\(345\) −8.19615 4.73205i −0.441266 0.254765i
\(346\) 15.1244i 0.813090i
\(347\) 7.69615 13.3301i 0.413151 0.715599i −0.582081 0.813131i \(-0.697761\pi\)
0.995232 + 0.0975319i \(0.0310948\pi\)
\(348\) −0.232051 0.401924i −0.0124392 0.0215454i
\(349\) −27.4641 + 15.8564i −1.47012 + 0.848774i −0.999438 0.0335290i \(-0.989325\pi\)
−0.470682 + 0.882303i \(0.655992\pi\)
\(350\) 2.46410 0.131712
\(351\) −3.59808 + 0.232051i −0.192051 + 0.0123860i
\(352\) −1.73205 −0.0923186
\(353\) 2.19615 1.26795i 0.116889 0.0674861i −0.440415 0.897794i \(-0.645169\pi\)
0.557305 + 0.830308i \(0.311835\pi\)
\(354\) −6.46410 11.1962i −0.343563 0.595069i
\(355\) −11.1962 + 19.3923i −0.594230 + 1.02924i
\(356\) 3.53590i 0.187402i
\(357\) 0.232051 + 0.133975i 0.0122814 + 0.00709069i
\(358\) 3.92820 + 2.26795i 0.207612 + 0.119865i
\(359\) 14.1962i 0.749244i −0.927178 0.374622i \(-0.877772\pi\)
0.927178 0.374622i \(-0.122228\pi\)
\(360\) 1.36603 2.36603i 0.0719959 0.124700i
\(361\) −9.00000 15.5885i −0.473684 0.820445i
\(362\) −12.6962 + 7.33013i −0.667295 + 0.385263i
\(363\) 8.00000 0.419891
\(364\) 3.00000 2.00000i 0.157243 0.104828i
\(365\) 4.00000 0.209370
\(366\) −4.50000 + 2.59808i −0.235219 + 0.135804i
\(367\) 4.66025 + 8.07180i 0.243263 + 0.421344i 0.961642 0.274308i \(-0.0884488\pi\)
−0.718379 + 0.695652i \(0.755115\pi\)
\(368\) 1.73205 3.00000i 0.0902894 0.156386i
\(369\) 3.00000i 0.156174i
\(370\) 7.73205 + 4.46410i 0.401970 + 0.232078i
\(371\) −6.06218 3.50000i −0.314733 0.181711i
\(372\) 8.19615i 0.424951i
\(373\) 3.83013 6.63397i 0.198316 0.343494i −0.749666 0.661816i \(-0.769786\pi\)
0.947983 + 0.318322i \(0.103119\pi\)
\(374\) −0.232051 0.401924i −0.0119991 0.0207830i
\(375\) −6.00000 + 3.46410i −0.309839 + 0.178885i
\(376\) −4.46410 −0.230218
\(377\) −0.928203 1.39230i −0.0478049 0.0717073i
\(378\) −1.00000 −0.0514344
\(379\) 26.3660 15.2224i 1.35433 0.781924i 0.365479 0.930820i \(-0.380905\pi\)
0.988853 + 0.148896i \(0.0475719\pi\)
\(380\) 1.36603 + 2.36603i 0.0700756 + 0.121375i
\(381\) −4.26795 + 7.39230i −0.218654 + 0.378719i
\(382\) 1.12436i 0.0575270i
\(383\) 10.7942 + 6.23205i 0.551559 + 0.318443i 0.749751 0.661720i \(-0.230173\pi\)
−0.198191 + 0.980163i \(0.563507\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 4.73205i 0.241168i
\(386\) −4.59808 + 7.96410i −0.234036 + 0.405362i
\(387\) 3.36603 + 5.83013i 0.171105 + 0.296362i
\(388\) 1.43782 0.830127i 0.0729944 0.0421433i
\(389\) 12.3923 0.628315 0.314157 0.949371i \(-0.398278\pi\)
0.314157 + 0.949371i \(0.398278\pi\)
\(390\) 4.36603 8.83013i 0.221082 0.447131i
\(391\) 0.928203 0.0469413
\(392\) 0.866025 0.500000i 0.0437409 0.0252538i
\(393\) −6.92820 12.0000i −0.349482 0.605320i
\(394\) −4.66987 + 8.08846i −0.235265 + 0.407491i
\(395\) 43.5167i 2.18956i
\(396\) 1.50000 + 0.866025i 0.0753778 + 0.0435194i
\(397\) −18.9904 10.9641i −0.953100 0.550272i −0.0590574 0.998255i \(-0.518809\pi\)
−0.894043 + 0.447982i \(0.852143\pi\)
\(398\) 5.80385i 0.290921i
\(399\) 0.500000 0.866025i 0.0250313 0.0433555i
\(400\) 1.23205 + 2.13397i 0.0616025 + 0.106699i
\(401\) −2.41154 + 1.39230i −0.120427 + 0.0695284i −0.559003 0.829165i \(-0.688816\pi\)
0.438577 + 0.898694i \(0.355483\pi\)
\(402\) −4.92820 −0.245796
\(403\) 1.90192 + 29.4904i 0.0947416 + 1.46902i
\(404\) 16.9282 0.842210
\(405\) −2.36603 + 1.36603i −0.117569 + 0.0678783i
\(406\) −0.232051 0.401924i −0.0115165 0.0199471i
\(407\) −2.83013 + 4.90192i −0.140284 + 0.242979i
\(408\) 0.267949i 0.0132655i
\(409\) 30.5429 + 17.6340i 1.51025 + 0.871944i 0.999928 + 0.0119609i \(0.00380738\pi\)
0.510323 + 0.859983i \(0.329526\pi\)
\(410\) 7.09808 + 4.09808i 0.350549 + 0.202390i
\(411\) 6.39230i 0.315309i
\(412\) −5.63397 + 9.75833i −0.277566 + 0.480758i
\(413\) −6.46410 11.1962i −0.318078 0.550927i
\(414\) −3.00000 + 1.73205i −0.147442 + 0.0851257i
\(415\) −27.8564 −1.36742
\(416\) 3.23205 + 1.59808i 0.158464 + 0.0783521i
\(417\) −19.5885 −0.959251
\(418\) −1.50000 + 0.866025i −0.0733674 + 0.0423587i
\(419\) 1.36603 + 2.36603i 0.0667347 + 0.115588i 0.897462 0.441091i \(-0.145409\pi\)
−0.830727 + 0.556679i \(0.812075\pi\)
\(420\) 1.36603 2.36603i 0.0666552 0.115450i
\(421\) 1.60770i 0.0783543i 0.999232 + 0.0391771i \(0.0124737\pi\)
−0.999232 + 0.0391771i \(0.987526\pi\)
\(422\) −22.5167 13.0000i −1.09609 0.632830i
\(423\) 3.86603 + 2.23205i 0.187973 + 0.108526i
\(424\) 7.00000i 0.339950i
\(425\) −0.330127 + 0.571797i −0.0160135 + 0.0277362i
\(426\) 4.09808 + 7.09808i 0.198552 + 0.343903i
\(427\) −4.50000 + 2.59808i −0.217770 + 0.125730i
\(428\) 16.8564 0.814785
\(429\) 5.59808 + 2.76795i 0.270278 + 0.133638i
\(430\) −18.3923 −0.886956
\(431\) 3.29423 1.90192i 0.158677 0.0916124i −0.418559 0.908190i \(-0.637465\pi\)
0.577236 + 0.816577i \(0.304131\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −20.4641 + 35.4449i −0.983442 + 1.70337i −0.334777 + 0.942297i \(0.608661\pi\)
−0.648665 + 0.761074i \(0.724672\pi\)
\(434\) 8.19615i 0.393428i
\(435\) −1.09808 0.633975i −0.0526487 0.0303968i
\(436\) 1.09808 + 0.633975i 0.0525883 + 0.0303619i
\(437\) 3.46410i 0.165710i
\(438\) 0.732051 1.26795i 0.0349787 0.0605850i
\(439\) 18.5885 + 32.1962i 0.887179 + 1.53664i 0.843196 + 0.537606i \(0.180671\pi\)
0.0439826 + 0.999032i \(0.485995\pi\)
\(440\) −4.09808 + 2.36603i −0.195368 + 0.112796i
\(441\) −1.00000 −0.0476190
\(442\) 0.0621778 + 0.964102i 0.00295750 + 0.0458576i
\(443\) 35.6410 1.69336 0.846678 0.532106i \(-0.178599\pi\)
0.846678 + 0.532106i \(0.178599\pi\)
\(444\) 2.83013 1.63397i 0.134312 0.0775450i
\(445\) −4.83013 8.36603i −0.228970 0.396588i
\(446\) −1.80385 + 3.12436i −0.0854147 + 0.147943i
\(447\) 13.8564i 0.655386i
\(448\) 0.866025 + 0.500000i 0.0409159 + 0.0236228i
\(449\) 9.16987 + 5.29423i 0.432753 + 0.249850i 0.700519 0.713634i \(-0.252952\pi\)
−0.267766 + 0.963484i \(0.586285\pi\)
\(450\) 2.46410i 0.116159i
\(451\) −2.59808 + 4.50000i −0.122339 + 0.211897i
\(452\) 9.36603 + 16.2224i 0.440541 + 0.763039i
\(453\) −4.50000 + 2.59808i −0.211428 + 0.122068i
\(454\) 2.39230 0.112276
\(455\) 4.36603 8.83013i 0.204682 0.413963i
\(456\) 1.00000 0.0468293
\(457\) 13.7321 7.92820i 0.642358 0.370866i −0.143164 0.989699i \(-0.545728\pi\)
0.785522 + 0.618833i \(0.212394\pi\)
\(458\) −3.03590 5.25833i −0.141858 0.245706i
\(459\) 0.133975 0.232051i 0.00625340 0.0108312i
\(460\) 9.46410i 0.441266i
\(461\) 11.3205 + 6.53590i 0.527249 + 0.304407i 0.739895 0.672722i \(-0.234875\pi\)
−0.212647 + 0.977129i \(0.568208\pi\)
\(462\) 1.50000 + 0.866025i 0.0697863 + 0.0402911i
\(463\) 9.73205i 0.452287i −0.974094 0.226143i \(-0.927388\pi\)
0.974094 0.226143i \(-0.0726118\pi\)
\(464\) 0.232051 0.401924i 0.0107727 0.0186588i
\(465\) 11.1962 + 19.3923i 0.519209 + 0.899297i
\(466\) −13.0981 + 7.56218i −0.606757 + 0.350311i
\(467\) −13.8564 −0.641198 −0.320599 0.947215i \(-0.603884\pi\)
−0.320599 + 0.947215i \(0.603884\pi\)
\(468\) −2.00000 3.00000i −0.0924500 0.138675i
\(469\) −4.92820 −0.227563
\(470\) −10.5622 + 6.09808i −0.487197 + 0.281283i
\(471\) 3.73205 + 6.46410i 0.171964 + 0.297850i
\(472\) 6.46410 11.1962i 0.297534 0.515345i
\(473\) 11.6603i 0.536139i
\(474\) −13.7942 7.96410i −0.633590 0.365803i
\(475\) 2.13397 + 1.23205i 0.0979135 + 0.0565304i
\(476\) 0.267949i 0.0122814i
\(477\) −3.50000 + 6.06218i −0.160254 + 0.277568i
\(478\) −1.36603 2.36603i −0.0624805 0.108219i
\(479\) 22.1147 12.7679i 1.01045 0.583382i 0.0991253 0.995075i \(-0.468396\pi\)
0.911323 + 0.411692i \(0.135062\pi\)
\(480\) 2.73205 0.124700
\(481\) 9.80385 6.53590i 0.447017 0.298011i
\(482\) 8.00000 0.364390
\(483\) −3.00000 + 1.73205i −0.136505 + 0.0788110i
\(484\) 4.00000 + 6.92820i 0.181818 + 0.314918i
\(485\) 2.26795 3.92820i 0.102982 0.178371i
\(486\) 1.00000i 0.0453609i
\(487\) −0.571797 0.330127i −0.0259106 0.0149595i 0.486989 0.873408i \(-0.338095\pi\)
−0.512899 + 0.858449i \(0.671429\pi\)
\(488\) −4.50000 2.59808i −0.203705 0.117609i
\(489\) 0.732051i 0.0331045i
\(490\) 1.36603 2.36603i 0.0617107 0.106886i
\(491\) 14.2679 + 24.7128i 0.643904 + 1.11527i 0.984554 + 0.175083i \(0.0560195\pi\)
−0.340650 + 0.940190i \(0.610647\pi\)
\(492\) 2.59808 1.50000i 0.117130 0.0676252i
\(493\) 0.124356 0.00560070
\(494\) 3.59808 0.232051i 0.161885 0.0104405i
\(495\) 4.73205 0.212690
\(496\) −7.09808 + 4.09808i −0.318713 + 0.184009i
\(497\) 4.09808 + 7.09808i 0.183824 + 0.318392i
\(498\) −5.09808 + 8.83013i −0.228450 + 0.395687i
\(499\) 33.5167i 1.50041i 0.661204 + 0.750206i \(0.270046\pi\)
−0.661204 + 0.750206i \(0.729954\pi\)
\(500\) −6.00000 3.46410i −0.268328 0.154919i
\(501\) 12.0000 + 6.92820i 0.536120 + 0.309529i
\(502\) 11.1244i 0.496504i
\(503\) 3.46410 6.00000i 0.154457 0.267527i −0.778404 0.627763i \(-0.783971\pi\)
0.932861 + 0.360236i \(0.117304\pi\)
\(504\) −0.500000 0.866025i −0.0222718 0.0385758i
\(505\) 40.0526 23.1244i 1.78232 1.02902i
\(506\) 6.00000 0.266733
\(507\) −7.89230 10.3301i −0.350510 0.458777i
\(508\) −8.53590 −0.378719
\(509\) 34.3468 19.8301i 1.52239 0.878955i 0.522745 0.852489i \(-0.324908\pi\)
0.999650 0.0264657i \(-0.00842529\pi\)
\(510\) 0.366025 + 0.633975i 0.0162079 + 0.0280729i
\(511\) 0.732051 1.26795i 0.0323840 0.0560908i
\(512\) 1.00000i 0.0441942i
\(513\) −0.866025 0.500000i −0.0382360 0.0220755i
\(514\) 2.89230 + 1.66987i 0.127574 + 0.0736549i
\(515\) 30.7846i 1.35653i
\(516\) −3.36603 + 5.83013i −0.148181 + 0.256657i
\(517\) −3.86603 6.69615i −0.170028 0.294496i
\(518\) 2.83013 1.63397i 0.124349 0.0717927i
\(519\) −15.1244 −0.663886
\(520\) 9.83013 0.633975i 0.431080 0.0278016i
\(521\) −31.0526 −1.36044 −0.680219 0.733009i \(-0.738115\pi\)
−0.680219 + 0.733009i \(0.738115\pi\)
\(522\) −0.401924 + 0.232051i −0.0175917 + 0.0101566i
\(523\) 19.0622 + 33.0167i 0.833531 + 1.44372i 0.895221 + 0.445622i \(0.147018\pi\)
−0.0616902 + 0.998095i \(0.519649\pi\)
\(524\) 6.92820 12.0000i 0.302660 0.524222i
\(525\) 2.46410i 0.107542i
\(526\) −7.90192 4.56218i −0.344540 0.198920i
\(527\) −1.90192 1.09808i −0.0828491 0.0478330i
\(528\) 1.73205i 0.0753778i
\(529\) 5.50000 9.52628i 0.239130 0.414186i
\(530\) −9.56218 16.5622i −0.415354 0.719415i
\(531\) −11.1962 + 6.46410i −0.485872 + 0.280518i
\(532\) 1.00000 0.0433555
\(533\) 9.00000 6.00000i 0.389833 0.259889i
\(534\) −3.53590 −0.153013
\(535\) 39.8827 23.0263i 1.72428 0.995513i
\(536\) −2.46410 4.26795i −0.106433 0.184347i
\(537\) 2.26795 3.92820i 0.0978692 0.169514i
\(538\) 17.8564i 0.769844i
\(539\) 1.50000 + 0.866025i 0.0646096 + 0.0373024i
\(540\) −2.36603 1.36603i −0.101818 0.0587844i
\(541\) 41.6603i 1.79111i −0.444947 0.895557i \(-0.646777\pi\)
0.444947 0.895557i \(-0.353223\pi\)
\(542\) −5.02628 + 8.70577i −0.215897 + 0.373945i
\(543\) 7.33013 + 12.6962i 0.314566 + 0.544844i
\(544\) −0.232051 + 0.133975i −0.00994910 + 0.00574411i
\(545\) 3.46410 0.148386
\(546\) −2.00000 3.00000i −0.0855921 0.128388i
\(547\) −4.73205 −0.202328 −0.101164 0.994870i \(-0.532257\pi\)
−0.101164 + 0.994870i \(0.532257\pi\)
\(548\) 5.53590 3.19615i 0.236482 0.136533i
\(549\) 2.59808 + 4.50000i 0.110883 + 0.192055i
\(550\) −2.13397 + 3.69615i −0.0909930 + 0.157604i
\(551\) 0.464102i 0.0197714i
\(552\) −3.00000 1.73205i −0.127688 0.0737210i
\(553\) −13.7942 7.96410i −0.586590 0.338668i
\(554\) 25.3205i 1.07577i
\(555\) 4.46410 7.73205i 0.189491 0.328207i
\(556\) −9.79423 16.9641i −0.415368 0.719438i
\(557\) 21.6962 12.5263i 0.919295 0.530755i 0.0358852 0.999356i \(-0.488575\pi\)
0.883410 + 0.468600i \(0.155242\pi\)
\(558\) 8.19615 0.346971
\(559\) −10.7583 + 21.7583i −0.455029 + 0.920279i
\(560\) 2.73205 0.115450
\(561\) −0.401924 + 0.232051i −0.0169692 + 0.00979719i
\(562\) −8.83013 15.2942i −0.372476 0.645148i
\(563\) −12.9019 + 22.3468i −0.543751 + 0.941805i 0.454933 + 0.890526i \(0.349663\pi\)
−0.998684 + 0.0512792i \(0.983670\pi\)
\(564\) 4.46410i 0.187973i
\(565\) 44.3205 + 25.5885i 1.86458 + 1.07651i
\(566\) 15.4641 + 8.92820i 0.650005 + 0.375280i
\(567\) 1.00000i 0.0419961i
\(568\) −4.09808 + 7.09808i −0.171951 + 0.297829i
\(569\) 10.2224 + 17.7058i 0.428547 + 0.742265i 0.996744 0.0806276i \(-0.0256924\pi\)
−0.568198 + 0.822892i \(0.692359\pi\)
\(570\) 2.36603 1.36603i 0.0991019 0.0572165i
\(571\) 34.9808 1.46390 0.731950 0.681359i \(-0.238611\pi\)
0.731950 + 0.681359i \(0.238611\pi\)
\(572\) 0.401924 + 6.23205i 0.0168053 + 0.260575i
\(573\) −1.12436 −0.0469706
\(574\) 2.59808 1.50000i 0.108442 0.0626088i
\(575\) −4.26795 7.39230i −0.177986 0.308280i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 27.6603i 1.15151i −0.817622 0.575756i \(-0.804708\pi\)
0.817622 0.575756i \(-0.195292\pi\)
\(578\) 14.6603 + 8.46410i 0.609786 + 0.352060i
\(579\) 7.96410 + 4.59808i 0.330977 + 0.191090i
\(580\) 1.26795i 0.0526487i
\(581\) −5.09808 + 8.83013i −0.211504 + 0.366335i
\(582\) −0.830127 1.43782i −0.0344099 0.0595996i
\(583\) 10.5000 6.06218i 0.434866 0.251070i
\(584\) 1.46410 0.0605850
\(585\) −8.83013 4.36603i −0.365081 0.180513i
\(586\) 30.9282 1.27763
\(587\) −25.6865 + 14.8301i −1.06020 + 0.612105i −0.925487 0.378780i \(-0.876344\pi\)
−0.134710 + 0.990885i \(0.543010\pi\)
\(588\) −0.500000 0.866025i −0.0206197 0.0357143i
\(589\) −4.09808 + 7.09808i −0.168858 + 0.292471i
\(590\) 35.3205i 1.45412i
\(591\) 8.08846 + 4.66987i 0.332715 + 0.192093i
\(592\) 2.83013 + 1.63397i 0.116318 + 0.0671559i
\(593\) 6.46410i 0.265449i −0.991153 0.132724i \(-0.957627\pi\)
0.991153 0.132724i \(-0.0423725\pi\)
\(594\) 0.866025 1.50000i 0.0355335 0.0615457i
\(595\) 0.366025 + 0.633975i 0.0150056 + 0.0259904i
\(596\) 12.0000 6.92820i 0.491539 0.283790i
\(597\) 5.80385 0.237536
\(598\) −11.1962 5.53590i −0.457845 0.226380i
\(599\) 40.6410 1.66055 0.830273 0.557356i \(-0.188184\pi\)
0.830273 + 0.557356i \(0.188184\pi\)
\(600\) 2.13397 1.23205i 0.0871191 0.0502983i
\(601\) 9.63397 + 16.6865i 0.392978 + 0.680658i 0.992841 0.119445i \(-0.0381115\pi\)
−0.599863 + 0.800103i \(0.704778\pi\)
\(602\) −3.36603 + 5.83013i −0.137189 + 0.237618i
\(603\) 4.92820i 0.200692i
\(604\) −4.50000 2.59808i −0.183102 0.105714i
\(605\) 18.9282 + 10.9282i 0.769541 + 0.444295i
\(606\) 16.9282i 0.687661i
\(607\) −6.75833 + 11.7058i −0.274312 + 0.475123i −0.969961 0.243259i \(-0.921783\pi\)
0.695649 + 0.718382i \(0.255117\pi\)
\(608\) 0.500000 + 0.866025i 0.0202777 + 0.0351220i
\(609\) −0.401924 + 0.232051i −0.0162868 + 0.00940317i
\(610\) −14.1962 −0.574785
\(611\) 1.03590 + 16.0622i 0.0419080 + 0.649806i
\(612\) 0.267949 0.0108312
\(613\) −3.46410 + 2.00000i −0.139914 + 0.0807792i −0.568323 0.822806i \(-0.692408\pi\)
0.428409 + 0.903585i \(0.359074\pi\)
\(614\) 14.6962 + 25.4545i 0.593088 + 1.02726i
\(615\) 4.09808 7.09808i 0.165250 0.286222i
\(616\) 1.73205i 0.0697863i
\(617\) 7.09808 + 4.09808i 0.285758 + 0.164982i 0.636027 0.771667i \(-0.280577\pi\)
−0.350269 + 0.936649i \(0.613910\pi\)
\(618\) 9.75833 + 5.63397i 0.392538 + 0.226632i
\(619\) 35.9282i 1.44408i 0.691853 + 0.722038i \(0.256795\pi\)
−0.691853 + 0.722038i \(0.743205\pi\)
\(620\) −11.1962 + 19.3923i −0.449648 + 0.778814i
\(621\) 1.73205 + 3.00000i 0.0695048 + 0.120386i
\(622\) −6.69615 + 3.86603i −0.268491 + 0.155013i
\(623\) −3.53590 −0.141663
\(624\) 1.59808 3.23205i 0.0639742 0.129386i
\(625\) −31.2487 −1.24995
\(626\) −27.2942 + 15.7583i −1.09090 + 0.629830i
\(627\) 0.866025 + 1.50000i 0.0345857 + 0.0599042i
\(628\) −3.73205 + 6.46410i −0.148925 + 0.257946i
\(629\) 0.875644i 0.0349142i
\(630\) −2.36603 1.36603i −0.0942647 0.0544238i
\(631\) −23.5526 13.5981i −0.937613 0.541331i −0.0484014 0.998828i \(-0.515413\pi\)
−0.889211 + 0.457497i \(0.848746\pi\)
\(632\) 15.9282i 0.633590i
\(633\) −13.0000 + 22.5167i −0.516704 + 0.894957i
\(634\) −7.92820 13.7321i −0.314869 0.545369i
\(635\) −20.1962 + 11.6603i −0.801460 + 0.462723i
\(636\) −7.00000 −0.277568
\(637\) −2.00000 3.00000i −0.0792429 0.118864i
\(638\) 0.803848 0.0318246
\(639\) 7.09808 4.09808i 0.280796 0.162117i
\(640\) 1.36603 + 2.36603i 0.0539969 + 0.0935254i
\(641\) −15.5885 + 27.0000i −0.615707 + 1.06644i 0.374553 + 0.927206i \(0.377796\pi\)
−0.990260 + 0.139230i \(0.955537\pi\)
\(642\) 16.8564i 0.665269i
\(643\) −4.45448 2.57180i −0.175668 0.101422i 0.409588 0.912271i \(-0.365672\pi\)
−0.585256 + 0.810849i \(0.699006\pi\)
\(644\) −3.00000 1.73205i −0.118217 0.0682524i
\(645\) 18.3923i 0.724196i
\(646\) −0.133975 + 0.232051i −0.00527116 + 0.00912992i
\(647\) −21.9186 37.9641i −0.861708 1.49252i −0.870279 0.492560i \(-0.836061\pi\)
0.00857027 0.999963i \(-0.497272\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 22.3923 0.878975
\(650\) 7.39230 4.92820i 0.289950 0.193300i
\(651\) 8.19615 0.321233
\(652\) 0.633975 0.366025i 0.0248284 0.0143347i
\(653\) 4.35641 + 7.54552i 0.170479 + 0.295279i 0.938588 0.345041i \(-0.112135\pi\)
−0.768108 + 0.640320i \(0.778802\pi\)
\(654\) 0.633975 1.09808i 0.0247904 0.0429382i
\(655\) 37.8564i 1.47917i
\(656\) 2.59808 + 1.50000i 0.101438 + 0.0585652i
\(657\) −1.26795 0.732051i −0.0494674 0.0285600i
\(658\) 4.46410i 0.174029i
\(659\) −19.6962 + 34.1147i −0.767253 + 1.32892i 0.171794 + 0.985133i \(0.445044\pi\)
−0.939047 + 0.343789i \(0.888290\pi\)
\(660\) 2.36603 + 4.09808i 0.0920974 + 0.159517i
\(661\) 7.26795 4.19615i 0.282690 0.163211i −0.351950 0.936019i \(-0.614481\pi\)
0.634641 + 0.772807i \(0.281148\pi\)
\(662\) −0.143594 −0.00558092
\(663\) 0.964102 0.0621778i 0.0374426 0.00241479i
\(664\) −10.1962 −0.395687
\(665\) 2.36603 1.36603i 0.0917505 0.0529722i
\(666\) −1.63397 2.83013i −0.0633152 0.109665i
\(667\) −0.803848 + 1.39230i −0.0311251 + 0.0539103i
\(668\) 13.8564i 0.536120i
\(669\) 3.12436 + 1.80385i 0.120795 + 0.0697408i
\(670\) −11.6603 6.73205i −0.450475 0.260082i
\(671\) 9.00000i 0.347441i
\(672\) 0.500000 0.866025i 0.0192879 0.0334077i
\(673\) 11.3564 + 19.6699i 0.437757 + 0.758218i 0.997516 0.0704376i \(-0.0224396\pi\)
−0.559759 + 0.828656i \(0.689106\pi\)
\(674\) −16.4545 + 9.50000i −0.633803 + 0.365926i
\(675\) −2.46410 −0.0948433
\(676\) 5.00000 12.0000i 0.192308 0.461538i
\(677\) 33.2679 1.27859 0.639296 0.768961i \(-0.279226\pi\)
0.639296 + 0.768961i \(0.279226\pi\)
\(678\) 16.2224 9.36603i 0.623019 0.359700i
\(679\) −0.830127 1.43782i −0.0318574 0.0551786i
\(680\) −0.366025 + 0.633975i −0.0140364 + 0.0243118i
\(681\) 2.39230i 0.0916733i
\(682\) −12.2942 7.09808i −0.470770 0.271799i
\(683\) −43.6410 25.1962i −1.66988 0.964104i −0.967701 0.252101i \(-0.918879\pi\)
−0.702176 0.712003i \(-0.747788\pi\)
\(684\) 1.00000i 0.0382360i
\(685\) 8.73205 15.1244i 0.333635 0.577872i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) −5.25833 + 3.03590i −0.200618 + 0.115827i
\(688\) −6.73205 −0.256657
\(689\) −25.1865 + 1.62436i −0.959531 + 0.0618830i
\(690\) −9.46410 −0.360292
\(691\) 10.1436 5.85641i 0.385880 0.222788i −0.294493 0.955654i \(-0.595151\pi\)
0.680374 + 0.732865i \(0.261817\pi\)
\(692\) −7.56218 13.0981i −0.287471 0.497914i
\(693\) 0.866025 1.50000i 0.0328976 0.0569803i
\(694\) 15.3923i 0.584284i
\(695\) −46.3468 26.7583i −1.75803 1.01500i
\(696\) −0.401924 0.232051i −0.0152349 0.00879586i
\(697\) 0.803848i 0.0304479i
\(698\) −15.8564 + 27.4641i −0.600174 + 1.03953i
\(699\) 7.56218 + 13.0981i 0.286028 + 0.495415i
\(700\) 2.13397 1.23205i 0.0806567 0.0465671i
\(701\) −28.8564 −1.08989 −0.544946 0.838471i \(-0.683450\pi\)
−0.544946 + 0.838471i \(0.683450\pi\)
\(702\) −3.00000 + 2.00000i −0.113228 + 0.0754851i
\(703\) 3.26795 0.123253
\(704\) −1.50000 + 0.866025i −0.0565334 + 0.0326396i
\(705\) 6.09808 + 10.5622i 0.229667 + 0.397795i
\(706\) 1.26795 2.19615i 0.0477199 0.0826533i
\(707\) 16.9282i 0.636651i
\(708\) −11.1962 6.46410i −0.420777 0.242936i
\(709\) −5.24167 3.02628i −0.196855 0.113654i 0.398333 0.917241i \(-0.369589\pi\)
−0.595188 + 0.803587i \(0.702922\pi\)
\(710\) 22.3923i 0.840368i
\(711\) −7.96410 + 13.7942i −0.298677 + 0.517324i
\(712\) −1.76795 3.06218i −0.0662567 0.114760i
\(713\) 24.5885 14.1962i 0.920845 0.531650i
\(714\) 0.267949 0.0100277
\(715\) 9.46410 + 14.1962i 0.353937 + 0.530906i
\(716\) 4.53590 0.169514
\(717\) −2.36603 + 1.36603i −0.0883608 + 0.0510152i
\(718\) −7.09808 12.2942i −0.264898 0.458817i
\(719\) −9.25833 + 16.0359i −0.345277 + 0.598038i −0.985404 0.170231i \(-0.945549\pi\)
0.640127 + 0.768269i \(0.278882\pi\)
\(720\) 2.73205i 0.101818i
\(721\) 9.75833 + 5.63397i 0.363419 + 0.209820i
\(722\) −15.5885 9.00000i −0.580142 0.334945i
\(723\) 8.00000i 0.297523i
\(724\) −7.33013 + 12.6962i −0.272422 + 0.471849i
\(725\) −0.571797 0.990381i −0.0212360 0.0367818i
\(726\) 6.92820 4.00000i 0.257130 0.148454i
\(727\) −15.3205 −0.568206 −0.284103 0.958794i \(-0.591696\pi\)
−0.284103 + 0.958794i \(0.591696\pi\)
\(728\) 1.59808 3.23205i 0.0592286 0.119788i
\(729\) 1.00000 0.0370370
\(730\) 3.46410 2.00000i 0.128212 0.0740233i
\(731\) −0.901924 1.56218i −0.0333589 0.0577792i
\(732\) −2.59808 + 4.50000i −0.0960277 + 0.166325i
\(733\) 14.1769i 0.523636i 0.965117 + 0.261818i \(0.0843221\pi\)
−0.965117 + 0.261818i \(0.915678\pi\)
\(734\) 8.07180 + 4.66025i 0.297935 + 0.172013i
\(735\) −2.36603 1.36603i −0.0872722 0.0503866i
\(736\) 3.46410i 0.127688i
\(737\) 4.26795 7.39230i 0.157212 0.272299i
\(738\) −1.50000 2.59808i −0.0552158 0.0956365i
\(739\) 40.8564 23.5885i 1.50293 0.867715i 0.502933 0.864325i \(-0.332254\pi\)
0.999994 0.00339000i \(-0.00107907\pi\)
\(740\) 8.92820 0.328207
\(741\) −0.232051 3.59808i −0.00852460 0.132179i
\(742\) −7.00000 −0.256978
\(743\) −20.8301 + 12.0263i −0.764183 + 0.441201i −0.830796 0.556578i \(-0.812114\pi\)
0.0666124 + 0.997779i \(0.478781\pi\)
\(744\) 4.09808 + 7.09808i 0.150243 + 0.260228i
\(745\) 18.9282 32.7846i 0.693476 1.20114i
\(746\) 7.66025i 0.280462i
\(747\) 8.83013 + 5.09808i 0.323077 + 0.186529i
\(748\) −0.401924 0.232051i −0.0146958 0.00848462i
\(749\) 16.8564i 0.615920i
\(750\) −3.46410 + 6.00000i −0.126491 + 0.219089i
\(751\) −23.4282 40.5788i −0.854907 1.48074i −0.876731 0.480981i \(-0.840281\pi\)
0.0218237 0.999762i \(-0.493053\pi\)
\(752\) −3.86603 + 2.23205i −0.140979 + 0.0813945i
\(753\) 11.1244 0.405394
\(754\) −1.50000 0.741670i −0.0546268 0.0270100i
\(755\) −14.1962 −0.516651
\(756\) −0.866025 + 0.500000i −0.0314970 + 0.0181848i
\(757\) −15.2942 26.4904i −0.555878 0.962809i −0.997835 0.0657728i \(-0.979049\pi\)
0.441956 0.897037i \(-0.354285\pi\)
\(758\) 15.2224 26.3660i 0.552904 0.957657i
\(759\) 6.00000i 0.217786i
\(760\) 2.36603 + 1.36603i 0.0858248 + 0.0495509i
\(761\) 16.7321 + 9.66025i 0.606536 + 0.350184i 0.771609 0.636098i \(-0.219452\pi\)
−0.165072 + 0.986281i \(0.552786\pi\)
\(762\) 8.53590i 0.309223i
\(763\) 0.633975 1.09808i 0.0229514 0.0397530i
\(764\) −0.562178 0.973721i −0.0203389 0.0352280i
\(765\) 0.633975 0.366025i 0.0229214 0.0132337i
\(766\) 12.4641 0.450346
\(767\) −41.7846 20.6603i −1.50875 0.745999i
\(768\) 1.00000 0.0360844
\(769\) 38.3660 22.1506i 1.38351 0.798772i 0.390940 0.920416i \(-0.372150\pi\)
0.992574 + 0.121644i \(0.0388165\pi\)
\(770\) 2.36603 + 4.09808i 0.0852656 + 0.147684i
\(771\) 1.66987 2.89230i 0.0601390 0.104164i
\(772\) 9.19615i 0.330977i
\(773\) −13.1436 7.58846i −0.472742 0.272938i 0.244645 0.969613i \(-0.421329\pi\)
−0.717387 + 0.696675i \(0.754662\pi\)
\(774\) 5.83013 + 3.36603i 0.209560 + 0.120989i
\(775\) 20.1962i