Properties

Label 546.2.s.b.127.2
Level $546$
Weight $2$
Character 546.127
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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.b.43.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.732051i q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.366025 + 0.633975i) q^{10} +(4.50000 - 2.59808i) q^{11} -1.00000 q^{12} +(0.866025 - 3.50000i) q^{13} +1.00000 q^{14} +(0.633975 - 0.366025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.13397 + 1.96410i) q^{17} +1.00000i q^{18} +(-0.401924 - 0.232051i) q^{19} +(0.633975 + 0.366025i) q^{20} -1.00000i q^{21} +(2.59808 - 4.50000i) q^{22} +(-3.73205 - 6.46410i) q^{23} +(-0.866025 + 0.500000i) q^{24} +4.46410 q^{25} +(-1.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(0.866025 - 0.500000i) q^{28} +(1.76795 + 3.06218i) q^{29} +(0.366025 - 0.633975i) q^{30} -3.26795i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-4.50000 - 2.59808i) q^{33} +2.26795i q^{34} +(-0.366025 + 0.633975i) q^{35} +(0.500000 + 0.866025i) q^{36} +(5.83013 - 3.36603i) q^{37} -0.464102 q^{38} +(-3.46410 + 1.00000i) q^{39} +0.732051 q^{40} +(-7.33013 + 4.23205i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.36603 + 7.56218i) q^{43} -5.19615i q^{44} +(-0.633975 - 0.366025i) q^{45} +(-6.46410 - 3.73205i) q^{46} +3.92820i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.86603 - 2.23205i) q^{50} +2.26795 q^{51} +(-2.59808 - 2.50000i) q^{52} -9.92820 q^{53} +(0.866025 - 0.500000i) q^{54} +(1.90192 + 3.29423i) q^{55} +(0.500000 - 0.866025i) q^{56} +0.464102i q^{57} +(3.06218 + 1.76795i) q^{58} +(7.73205 + 4.46410i) q^{59} -0.732051i q^{60} +(-1.86603 + 3.23205i) q^{61} +(-1.63397 - 2.83013i) q^{62} +(-0.866025 + 0.500000i) q^{63} -1.00000 q^{64} +(2.56218 + 0.633975i) q^{65} -5.19615 q^{66} +(8.66025 - 5.00000i) q^{67} +(1.13397 + 1.96410i) q^{68} +(-3.73205 + 6.46410i) q^{69} +0.732051i q^{70} +(6.29423 + 3.63397i) q^{71} +(0.866025 + 0.500000i) q^{72} -1.46410i q^{73} +(3.36603 - 5.83013i) q^{74} +(-2.23205 - 3.86603i) q^{75} +(-0.401924 + 0.232051i) q^{76} +5.19615 q^{77} +(-2.50000 + 2.59808i) q^{78} +9.00000 q^{79} +(0.633975 - 0.366025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.23205 + 7.33013i) q^{82} +9.26795i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-1.43782 - 0.830127i) q^{85} +8.73205i q^{86} +(1.76795 - 3.06218i) q^{87} +(-2.59808 - 4.50000i) q^{88} +(-14.5981 + 8.42820i) q^{89} -0.732051 q^{90} +(2.50000 - 2.59808i) q^{91} -7.46410 q^{92} +(-2.83013 + 1.63397i) q^{93} +(1.96410 + 3.40192i) q^{94} +(0.169873 - 0.294229i) q^{95} +1.00000i q^{96} +(-12.2942 - 7.09808i) q^{97} +(0.866025 + 0.500000i) q^{98} +5.19615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} + 2q^{4} - 2q^{9} - 2q^{10} + 18q^{11} - 4q^{12} + 4q^{14} + 6q^{15} - 2q^{16} - 8q^{17} - 12q^{19} + 6q^{20} - 8q^{23} + 4q^{25} - 4q^{26} + 4q^{27} + 14q^{29} - 2q^{30} - 18q^{33} + 2q^{35} + 2q^{36} + 6q^{37} + 12q^{38} - 4q^{40} - 12q^{41} - 2q^{42} - 14q^{43} - 6q^{45} - 12q^{46} - 2q^{48} + 2q^{49} + 12q^{50} + 16q^{51} - 12q^{53} + 18q^{55} + 2q^{56} - 12q^{58} + 24q^{59} - 4q^{61} - 10q^{62} - 4q^{64} - 14q^{65} + 8q^{68} - 8q^{69} - 6q^{71} + 10q^{74} - 2q^{75} - 12q^{76} - 10q^{78} + 36q^{79} + 6q^{80} - 2q^{81} - 10q^{82} - 30q^{85} + 14q^{87} - 48q^{89} + 4q^{90} + 10q^{91} - 16q^{92} + 6q^{93} - 6q^{94} + 18q^{95} - 18q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.732051i 0.327383i 0.986512 + 0.163692i \(0.0523402\pi\)
−0.986512 + 0.163692i \(0.947660\pi\)
\(6\) −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
\(10\) 0.366025 + 0.633975i 0.115747 + 0.200480i
\(11\) 4.50000 2.59808i 1.35680 0.783349i 0.367610 0.929980i \(-0.380176\pi\)
0.989191 + 0.146631i \(0.0468429\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0.866025 3.50000i 0.240192 0.970725i
\(14\) 1.00000 0.267261
\(15\) 0.633975 0.366025i 0.163692 0.0945074i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.13397 + 1.96410i −0.275029 + 0.476365i −0.970143 0.242536i \(-0.922021\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −0.401924 0.232051i −0.0922076 0.0532361i 0.453187 0.891415i \(-0.350287\pi\)
−0.545395 + 0.838179i \(0.683620\pi\)
\(20\) 0.633975 + 0.366025i 0.141761 + 0.0818458i
\(21\) 1.00000i 0.218218i
\(22\) 2.59808 4.50000i 0.553912 0.959403i
\(23\) −3.73205 6.46410i −0.778186 1.34786i −0.932986 0.359912i \(-0.882807\pi\)
0.154800 0.987946i \(-0.450527\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 4.46410 0.892820
\(26\) −1.00000 3.46410i −0.196116 0.679366i
\(27\) 1.00000 0.192450
\(28\) 0.866025 0.500000i 0.163663 0.0944911i
\(29\) 1.76795 + 3.06218i 0.328300 + 0.568632i 0.982175 0.187971i \(-0.0601910\pi\)
−0.653875 + 0.756603i \(0.726858\pi\)
\(30\) 0.366025 0.633975i 0.0668268 0.115747i
\(31\) 3.26795i 0.586941i −0.955968 0.293471i \(-0.905190\pi\)
0.955968 0.293471i \(-0.0948102\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −4.50000 2.59808i −0.783349 0.452267i
\(34\) 2.26795i 0.388950i
\(35\) −0.366025 + 0.633975i −0.0618696 + 0.107161i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 5.83013 3.36603i 0.958467 0.553371i 0.0627661 0.998028i \(-0.480008\pi\)
0.895701 + 0.444657i \(0.146674\pi\)
\(38\) −0.464102 −0.0752872
\(39\) −3.46410 + 1.00000i −0.554700 + 0.160128i
\(40\) 0.732051 0.115747
\(41\) −7.33013 + 4.23205i −1.14477 + 0.660935i −0.947608 0.319435i \(-0.896507\pi\)
−0.197165 + 0.980370i \(0.563174\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −4.36603 + 7.56218i −0.665813 + 1.15322i 0.313252 + 0.949670i \(0.398582\pi\)
−0.979064 + 0.203551i \(0.934752\pi\)
\(44\) 5.19615i 0.783349i
\(45\) −0.633975 0.366025i −0.0945074 0.0545638i
\(46\) −6.46410 3.73205i −0.953080 0.550261i
\(47\) 3.92820i 0.572987i 0.958082 + 0.286494i \(0.0924897\pi\)
−0.958082 + 0.286494i \(0.907510\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 3.86603 2.23205i 0.546739 0.315660i
\(51\) 2.26795 0.317576
\(52\) −2.59808 2.50000i −0.360288 0.346688i
\(53\) −9.92820 −1.36374 −0.681872 0.731472i \(-0.738834\pi\)
−0.681872 + 0.731472i \(0.738834\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 1.90192 + 3.29423i 0.256455 + 0.444194i
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 0.464102i 0.0614718i
\(58\) 3.06218 + 1.76795i 0.402084 + 0.232143i
\(59\) 7.73205 + 4.46410i 1.00663 + 0.581177i 0.910202 0.414164i \(-0.135926\pi\)
0.0964249 + 0.995340i \(0.469259\pi\)
\(60\) 0.732051i 0.0945074i
\(61\) −1.86603 + 3.23205i −0.238920 + 0.413822i −0.960405 0.278609i \(-0.910127\pi\)
0.721485 + 0.692430i \(0.243460\pi\)
\(62\) −1.63397 2.83013i −0.207515 0.359426i
\(63\) −0.866025 + 0.500000i −0.109109 + 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 2.56218 + 0.633975i 0.317799 + 0.0786349i
\(66\) −5.19615 −0.639602
\(67\) 8.66025 5.00000i 1.05802 0.610847i 0.133135 0.991098i \(-0.457496\pi\)
0.924883 + 0.380251i \(0.124162\pi\)
\(68\) 1.13397 + 1.96410i 0.137515 + 0.238182i
\(69\) −3.73205 + 6.46410i −0.449286 + 0.778186i
\(70\) 0.732051i 0.0874968i
\(71\) 6.29423 + 3.63397i 0.746988 + 0.431273i 0.824604 0.565710i \(-0.191398\pi\)
−0.0776169 + 0.996983i \(0.524731\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 1.46410i 0.171360i −0.996323 0.0856801i \(-0.972694\pi\)
0.996323 0.0856801i \(-0.0273063\pi\)
\(74\) 3.36603 5.83013i 0.391293 0.677738i
\(75\) −2.23205 3.86603i −0.257735 0.446410i
\(76\) −0.401924 + 0.232051i −0.0461038 + 0.0266181i
\(77\) 5.19615 0.592157
\(78\) −2.50000 + 2.59808i −0.283069 + 0.294174i
\(79\) 9.00000 1.01258 0.506290 0.862364i \(-0.331017\pi\)
0.506290 + 0.862364i \(0.331017\pi\)
\(80\) 0.633975 0.366025i 0.0708805 0.0409229i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −4.23205 + 7.33013i −0.467352 + 0.809477i
\(83\) 9.26795i 1.01729i 0.860976 + 0.508645i \(0.169853\pi\)
−0.860976 + 0.508645i \(0.830147\pi\)
\(84\) −0.866025 0.500000i −0.0944911 0.0545545i
\(85\) −1.43782 0.830127i −0.155954 0.0900399i
\(86\) 8.73205i 0.941601i
\(87\) 1.76795 3.06218i 0.189544 0.328300i
\(88\) −2.59808 4.50000i −0.276956 0.479702i
\(89\) −14.5981 + 8.42820i −1.54739 + 0.893388i −0.549053 + 0.835787i \(0.685012\pi\)
−0.998340 + 0.0576004i \(0.981655\pi\)
\(90\) −0.732051 −0.0771649
\(91\) 2.50000 2.59808i 0.262071 0.272352i
\(92\) −7.46410 −0.778186
\(93\) −2.83013 + 1.63397i −0.293471 + 0.169435i
\(94\) 1.96410 + 3.40192i 0.202582 + 0.350882i
\(95\) 0.169873 0.294229i 0.0174286 0.0301872i
\(96\) 1.00000i 0.102062i
\(97\) −12.2942 7.09808i −1.24829 0.720700i −0.277522 0.960719i \(-0.589513\pi\)
−0.970768 + 0.240019i \(0.922846\pi\)
\(98\) 0.866025 + 0.500000i 0.0874818 + 0.0505076i
\(99\) 5.19615i 0.522233i
\(100\) 2.23205 3.86603i 0.223205 0.386603i
\(101\) 2.46410 + 4.26795i 0.245187 + 0.424677i 0.962184 0.272399i \(-0.0878172\pi\)
−0.716997 + 0.697076i \(0.754484\pi\)
\(102\) 1.96410 1.13397i 0.194475 0.112280i
\(103\) 16.1962 1.59585 0.797927 0.602754i \(-0.205930\pi\)
0.797927 + 0.602754i \(0.205930\pi\)
\(104\) −3.50000 0.866025i −0.343203 0.0849208i
\(105\) 0.732051 0.0714408
\(106\) −8.59808 + 4.96410i −0.835119 + 0.482156i
\(107\) 3.03590 + 5.25833i 0.293491 + 0.508342i 0.974633 0.223810i \(-0.0718495\pi\)
−0.681141 + 0.732152i \(0.738516\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 11.2679i 1.07927i 0.841898 + 0.539637i \(0.181438\pi\)
−0.841898 + 0.539637i \(0.818562\pi\)
\(110\) 3.29423 + 1.90192i 0.314092 + 0.181341i
\(111\) −5.83013 3.36603i −0.553371 0.319489i
\(112\) 1.00000i 0.0944911i
\(113\) −3.83013 + 6.63397i −0.360308 + 0.624072i −0.988011 0.154381i \(-0.950662\pi\)
0.627703 + 0.778453i \(0.283995\pi\)
\(114\) 0.232051 + 0.401924i 0.0217335 + 0.0376436i
\(115\) 4.73205 2.73205i 0.441266 0.254765i
\(116\) 3.53590 0.328300
\(117\) 2.59808 + 2.50000i 0.240192 + 0.231125i
\(118\) 8.92820 0.821908
\(119\) −1.96410 + 1.13397i −0.180049 + 0.103951i
\(120\) −0.366025 0.633975i −0.0334134 0.0578737i
\(121\) 8.00000 13.8564i 0.727273 1.25967i
\(122\) 3.73205i 0.337884i
\(123\) 7.33013 + 4.23205i 0.660935 + 0.381591i
\(124\) −2.83013 1.63397i −0.254153 0.146735i
\(125\) 6.92820i 0.619677i
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) 7.19615 + 12.4641i 0.638555 + 1.10601i 0.985750 + 0.168217i \(0.0538010\pi\)
−0.347195 + 0.937793i \(0.612866\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 8.73205 0.768814
\(130\) 2.53590 0.732051i 0.222413 0.0642051i
\(131\) −14.9282 −1.30428 −0.652142 0.758097i \(-0.726129\pi\)
−0.652142 + 0.758097i \(0.726129\pi\)
\(132\) −4.50000 + 2.59808i −0.391675 + 0.226134i
\(133\) −0.232051 0.401924i −0.0201214 0.0348512i
\(134\) 5.00000 8.66025i 0.431934 0.748132i
\(135\) 0.732051i 0.0630049i
\(136\) 1.96410 + 1.13397i 0.168420 + 0.0972375i
\(137\) −16.8564 9.73205i −1.44014 0.831465i −0.442282 0.896876i \(-0.645831\pi\)
−0.997858 + 0.0654110i \(0.979164\pi\)
\(138\) 7.46410i 0.635387i
\(139\) −8.52628 + 14.7679i −0.723190 + 1.25260i 0.236525 + 0.971625i \(0.423991\pi\)
−0.959715 + 0.280976i \(0.909342\pi\)
\(140\) 0.366025 + 0.633975i 0.0309348 + 0.0535806i
\(141\) 3.40192 1.96410i 0.286494 0.165407i
\(142\) 7.26795 0.609913
\(143\) −5.19615 18.0000i −0.434524 1.50524i
\(144\) 1.00000 0.0833333
\(145\) −2.24167 + 1.29423i −0.186161 + 0.107480i
\(146\) −0.732051 1.26795i −0.0605850 0.104936i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) 6.73205i 0.553371i
\(149\) −6.92820 4.00000i −0.567581 0.327693i 0.188602 0.982054i \(-0.439604\pi\)
−0.756182 + 0.654361i \(0.772938\pi\)
\(150\) −3.86603 2.23205i −0.315660 0.182246i
\(151\) 1.19615i 0.0973415i −0.998815 0.0486708i \(-0.984501\pi\)
0.998815 0.0486708i \(-0.0154985\pi\)
\(152\) −0.232051 + 0.401924i −0.0188218 + 0.0326003i
\(153\) −1.13397 1.96410i −0.0916764 0.158788i
\(154\) 4.50000 2.59808i 0.362620 0.209359i
\(155\) 2.39230 0.192155
\(156\) −0.866025 + 3.50000i −0.0693375 + 0.280224i
\(157\) −11.4641 −0.914935 −0.457467 0.889226i \(-0.651243\pi\)
−0.457467 + 0.889226i \(0.651243\pi\)
\(158\) 7.79423 4.50000i 0.620076 0.358001i
\(159\) 4.96410 + 8.59808i 0.393679 + 0.681872i
\(160\) 0.366025 0.633975i 0.0289368 0.0501201i
\(161\) 7.46410i 0.588254i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) −6.16987 3.56218i −0.483262 0.279011i 0.238513 0.971139i \(-0.423340\pi\)
−0.721775 + 0.692128i \(0.756673\pi\)
\(164\) 8.46410i 0.660935i
\(165\) 1.90192 3.29423i 0.148065 0.256455i
\(166\) 4.63397 + 8.02628i 0.359666 + 0.622960i
\(167\) −4.39230 + 2.53590i −0.339887 + 0.196234i −0.660222 0.751071i \(-0.729538\pi\)
0.320335 + 0.947304i \(0.396204\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −11.5000 6.06218i −0.884615 0.466321i
\(170\) −1.66025 −0.127336
\(171\) 0.401924 0.232051i 0.0307359 0.0177454i
\(172\) 4.36603 + 7.56218i 0.332906 + 0.576611i
\(173\) 1.09808 1.90192i 0.0834852 0.144601i −0.821260 0.570555i \(-0.806728\pi\)
0.904745 + 0.425954i \(0.140062\pi\)
\(174\) 3.53590i 0.268056i
\(175\) 3.86603 + 2.23205i 0.292244 + 0.168727i
\(176\) −4.50000 2.59808i −0.339200 0.195837i
\(177\) 8.92820i 0.671085i
\(178\) −8.42820 + 14.5981i −0.631721 + 1.09417i
\(179\) −1.73205 3.00000i −0.129460 0.224231i 0.794008 0.607908i \(-0.207991\pi\)
−0.923467 + 0.383677i \(0.874658\pi\)
\(180\) −0.633975 + 0.366025i −0.0472537 + 0.0272819i
\(181\) 14.2679 1.06053 0.530264 0.847832i \(-0.322093\pi\)
0.530264 + 0.847832i \(0.322093\pi\)
\(182\) 0.866025 3.50000i 0.0641941 0.259437i
\(183\) 3.73205 0.275881
\(184\) −6.46410 + 3.73205i −0.476540 + 0.275130i
\(185\) 2.46410 + 4.26795i 0.181164 + 0.313786i
\(186\) −1.63397 + 2.83013i −0.119809 + 0.207515i
\(187\) 11.7846i 0.861776i
\(188\) 3.40192 + 1.96410i 0.248111 + 0.143247i
\(189\) 0.866025 + 0.500000i 0.0629941 + 0.0363696i
\(190\) 0.339746i 0.0246478i
\(191\) 4.09808 7.09808i 0.296526 0.513599i −0.678812 0.734312i \(-0.737505\pi\)
0.975339 + 0.220713i \(0.0708384\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 6.57180 3.79423i 0.473048 0.273115i −0.244467 0.969658i \(-0.578613\pi\)
0.717515 + 0.696543i \(0.245280\pi\)
\(194\) −14.1962 −1.01922
\(195\) −0.732051 2.53590i −0.0524232 0.181599i
\(196\) 1.00000 0.0714286
\(197\) 0.232051 0.133975i 0.0165329 0.00954529i −0.491711 0.870759i \(-0.663628\pi\)
0.508244 + 0.861213i \(0.330295\pi\)
\(198\) 2.59808 + 4.50000i 0.184637 + 0.319801i
\(199\) 12.2942 21.2942i 0.871515 1.50951i 0.0110851 0.999939i \(-0.496471\pi\)
0.860430 0.509569i \(-0.170195\pi\)
\(200\) 4.46410i 0.315660i
\(201\) −8.66025 5.00000i −0.610847 0.352673i
\(202\) 4.26795 + 2.46410i 0.300292 + 0.173374i
\(203\) 3.53590i 0.248171i
\(204\) 1.13397 1.96410i 0.0793941 0.137515i
\(205\) −3.09808 5.36603i −0.216379 0.374779i
\(206\) 14.0263 8.09808i 0.977257 0.564220i
\(207\) 7.46410 0.518791
\(208\) −3.46410 + 1.00000i −0.240192 + 0.0693375i
\(209\) −2.41154 −0.166810
\(210\) 0.633975 0.366025i 0.0437484 0.0252582i
\(211\) −12.4641 21.5885i −0.858064 1.48621i −0.873773 0.486334i \(-0.838334\pi\)
0.0157088 0.999877i \(-0.495000\pi\)
\(212\) −4.96410 + 8.59808i −0.340936 + 0.590518i
\(213\) 7.26795i 0.497992i
\(214\) 5.25833 + 3.03590i 0.359452 + 0.207530i
\(215\) −5.53590 3.19615i −0.377545 0.217976i
\(216\) 1.00000i 0.0680414i
\(217\) 1.63397 2.83013i 0.110921 0.192122i
\(218\) 5.63397 + 9.75833i 0.381581 + 0.660918i
\(219\) −1.26795 + 0.732051i −0.0856801 + 0.0494674i
\(220\) 3.80385 0.256455
\(221\) 5.89230 + 5.66987i 0.396359 + 0.381397i
\(222\) −6.73205 −0.451826
\(223\) −4.73205 + 2.73205i −0.316882 + 0.182952i −0.650002 0.759933i \(-0.725232\pi\)
0.333120 + 0.942884i \(0.391899\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) −2.23205 + 3.86603i −0.148803 + 0.257735i
\(226\) 7.66025i 0.509553i
\(227\) −11.5359 6.66025i −0.765664 0.442057i 0.0656613 0.997842i \(-0.479084\pi\)
−0.831326 + 0.555785i \(0.812418\pi\)
\(228\) 0.401924 + 0.232051i 0.0266181 + 0.0153679i
\(229\) 17.3923i 1.14932i 0.818394 + 0.574658i \(0.194865\pi\)
−0.818394 + 0.574658i \(0.805135\pi\)
\(230\) 2.73205 4.73205i 0.180146 0.312022i
\(231\) −2.59808 4.50000i −0.170941 0.296078i
\(232\) 3.06218 1.76795i 0.201042 0.116072i
\(233\) 18.5885 1.21777 0.608885 0.793258i \(-0.291617\pi\)
0.608885 + 0.793258i \(0.291617\pi\)
\(234\) 3.50000 + 0.866025i 0.228802 + 0.0566139i
\(235\) −2.87564 −0.187586
\(236\) 7.73205 4.46410i 0.503314 0.290588i
\(237\) −4.50000 7.79423i −0.292306 0.506290i
\(238\) −1.13397 + 1.96410i −0.0735047 + 0.127314i
\(239\) 26.5885i 1.71986i 0.510408 + 0.859932i \(0.329494\pi\)
−0.510408 + 0.859932i \(0.670506\pi\)
\(240\) −0.633975 0.366025i −0.0409229 0.0236268i
\(241\) 9.46410 + 5.46410i 0.609636 + 0.351974i 0.772823 0.634621i \(-0.218844\pi\)
−0.163187 + 0.986595i \(0.552177\pi\)
\(242\) 16.0000i 1.02852i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 1.86603 + 3.23205i 0.119460 + 0.206911i
\(245\) −0.633975 + 0.366025i −0.0405032 + 0.0233845i
\(246\) 8.46410 0.539651
\(247\) −1.16025 + 1.20577i −0.0738252 + 0.0767214i
\(248\) −3.26795 −0.207515
\(249\) 8.02628 4.63397i 0.508645 0.293666i
\(250\) 3.46410 + 6.00000i 0.219089 + 0.379473i
\(251\) 8.75833 15.1699i 0.552821 0.957514i −0.445249 0.895407i \(-0.646885\pi\)
0.998070 0.0621069i \(-0.0197820\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) −33.5885 19.3923i −2.11169 1.21918i
\(254\) 12.4641 + 7.19615i 0.782067 + 0.451527i
\(255\) 1.66025i 0.103969i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −12.5263 21.6962i −0.781368 1.35337i −0.931145 0.364649i \(-0.881189\pi\)
0.149777 0.988720i \(-0.452144\pi\)
\(258\) 7.56218 4.36603i 0.470801 0.271817i
\(259\) 6.73205 0.418309
\(260\) 1.83013 1.90192i 0.113500 0.117952i
\(261\) −3.53590 −0.218867
\(262\) −12.9282 + 7.46410i −0.798707 + 0.461134i
\(263\) −1.56218 2.70577i −0.0963280 0.166845i 0.813834 0.581097i \(-0.197376\pi\)
−0.910162 + 0.414252i \(0.864043\pi\)
\(264\) −2.59808 + 4.50000i −0.159901 + 0.276956i
\(265\) 7.26795i 0.446467i
\(266\) −0.401924 0.232051i −0.0246435 0.0142279i
\(267\) 14.5981 + 8.42820i 0.893388 + 0.515798i
\(268\) 10.0000i 0.610847i
\(269\) 2.00000 3.46410i 0.121942 0.211210i −0.798591 0.601874i \(-0.794421\pi\)
0.920534 + 0.390664i \(0.127754\pi\)
\(270\) 0.366025 + 0.633975i 0.0222756 + 0.0385825i
\(271\) 6.63397 3.83013i 0.402985 0.232664i −0.284786 0.958591i \(-0.591923\pi\)
0.687771 + 0.725927i \(0.258589\pi\)
\(272\) 2.26795 0.137515
\(273\) −3.50000 0.866025i −0.211830 0.0524142i
\(274\) −19.4641 −1.17587
\(275\) 20.0885 11.5981i 1.21138 0.699390i
\(276\) 3.73205 + 6.46410i 0.224643 + 0.389093i
\(277\) −7.19615 + 12.4641i −0.432375 + 0.748895i −0.997077 0.0763993i \(-0.975658\pi\)
0.564702 + 0.825295i \(0.308991\pi\)
\(278\) 17.0526i 1.02274i
\(279\) 2.83013 + 1.63397i 0.169435 + 0.0978235i
\(280\) 0.633975 + 0.366025i 0.0378872 + 0.0218742i
\(281\) 12.7321i 0.759530i 0.925083 + 0.379765i \(0.123995\pi\)
−0.925083 + 0.379765i \(0.876005\pi\)
\(282\) 1.96410 3.40192i 0.116961 0.202582i
\(283\) −8.92820 15.4641i −0.530727 0.919245i −0.999357 0.0358512i \(-0.988586\pi\)
0.468631 0.883394i \(-0.344748\pi\)
\(284\) 6.29423 3.63397i 0.373494 0.215637i
\(285\) −0.339746 −0.0201248
\(286\) −13.5000 12.9904i −0.798272 0.768137i
\(287\) −8.46410 −0.499620
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) 5.92820 + 10.2679i 0.348718 + 0.603997i
\(290\) −1.29423 + 2.24167i −0.0759997 + 0.131635i
\(291\) 14.1962i 0.832193i
\(292\) −1.26795 0.732051i −0.0742011 0.0428400i
\(293\) 0.928203 + 0.535898i 0.0542262 + 0.0313075i 0.526868 0.849947i \(-0.323366\pi\)
−0.472642 + 0.881255i \(0.656700\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) −3.26795 + 5.66025i −0.190267 + 0.329553i
\(296\) −3.36603 5.83013i −0.195646 0.338869i
\(297\) 4.50000 2.59808i 0.261116 0.150756i
\(298\) −8.00000 −0.463428
\(299\) −25.8564 + 7.46410i −1.49531 + 0.431660i
\(300\) −4.46410 −0.257735
\(301\) −7.56218 + 4.36603i −0.435877 + 0.251654i
\(302\) −0.598076 1.03590i −0.0344154 0.0596093i
\(303\) 2.46410 4.26795i 0.141559 0.245187i
\(304\) 0.464102i 0.0266181i
\(305\) −2.36603 1.36603i −0.135478 0.0782184i
\(306\) −1.96410 1.13397i −0.112280 0.0648250i
\(307\) 5.00000i 0.285365i −0.989769 0.142683i \(-0.954427\pi\)
0.989769 0.142683i \(-0.0455728\pi\)
\(308\) 2.59808 4.50000i 0.148039 0.256411i
\(309\) −8.09808 14.0263i −0.460683 0.797927i
\(310\) 2.07180 1.19615i 0.117670 0.0679369i
\(311\) 14.8038 0.839449 0.419725 0.907652i \(-0.362127\pi\)
0.419725 + 0.907652i \(0.362127\pi\)
\(312\) 1.00000 + 3.46410i 0.0566139 + 0.196116i
\(313\) 6.87564 0.388634 0.194317 0.980939i \(-0.437751\pi\)
0.194317 + 0.980939i \(0.437751\pi\)
\(314\) −9.92820 + 5.73205i −0.560281 + 0.323478i
\(315\) −0.366025 0.633975i −0.0206232 0.0357204i
\(316\) 4.50000 7.79423i 0.253145 0.438460i
\(317\) 14.7846i 0.830386i 0.909733 + 0.415193i \(0.136286\pi\)
−0.909733 + 0.415193i \(0.863714\pi\)
\(318\) 8.59808 + 4.96410i 0.482156 + 0.278373i
\(319\) 15.9115 + 9.18653i 0.890875 + 0.514347i
\(320\) 0.732051i 0.0409229i
\(321\) 3.03590 5.25833i 0.169447 0.293491i
\(322\) −3.73205 6.46410i −0.207979 0.360230i
\(323\) 0.911543 0.526279i 0.0507196 0.0292830i
\(324\) −1.00000 −0.0555556
\(325\) 3.86603 15.6244i 0.214449 0.866683i
\(326\) −7.12436 −0.394582
\(327\) 9.75833 5.63397i 0.539637 0.311560i
\(328\) 4.23205 + 7.33013i 0.233676 + 0.404739i
\(329\) −1.96410 + 3.40192i −0.108284 + 0.187554i
\(330\) 3.80385i 0.209395i
\(331\) 5.87564 + 3.39230i 0.322955 + 0.186458i 0.652709 0.757609i \(-0.273633\pi\)
−0.329754 + 0.944067i \(0.606966\pi\)
\(332\) 8.02628 + 4.63397i 0.440499 + 0.254322i
\(333\) 6.73205i 0.368914i
\(334\) −2.53590 + 4.39230i −0.138758 + 0.240336i
\(335\) 3.66025 + 6.33975i 0.199981 + 0.346377i
\(336\) −0.866025 + 0.500000i −0.0472456 + 0.0272772i
\(337\) −11.0000 −0.599208 −0.299604 0.954064i \(-0.596855\pi\)
−0.299604 + 0.954064i \(0.596855\pi\)
\(338\) −12.9904 + 0.500000i −0.706584 + 0.0271964i
\(339\) 7.66025 0.416048
\(340\) −1.43782 + 0.830127i −0.0779769 + 0.0450200i
\(341\) −8.49038 14.7058i −0.459780 0.796362i
\(342\) 0.232051 0.401924i 0.0125479 0.0217335i
\(343\) 1.00000i 0.0539949i
\(344\) 7.56218 + 4.36603i 0.407725 + 0.235400i
\(345\) −4.73205 2.73205i −0.254765 0.147089i
\(346\) 2.19615i 0.118066i
\(347\) 3.23205 5.59808i 0.173506 0.300520i −0.766138 0.642677i \(-0.777824\pi\)
0.939643 + 0.342156i \(0.111157\pi\)
\(348\) −1.76795 3.06218i −0.0947720 0.164150i
\(349\) 5.32051 3.07180i 0.284800 0.164430i −0.350794 0.936453i \(-0.614088\pi\)
0.635595 + 0.772023i \(0.280755\pi\)
\(350\) 4.46410 0.238616
\(351\) 0.866025 3.50000i 0.0462250 0.186816i
\(352\) −5.19615 −0.276956
\(353\) 27.1244 15.6603i 1.44368 0.833511i 0.445591 0.895237i \(-0.352994\pi\)
0.998093 + 0.0617256i \(0.0196604\pi\)
\(354\) −4.46410 7.73205i −0.237264 0.410954i
\(355\) −2.66025 + 4.60770i −0.141192 + 0.244551i
\(356\) 16.8564i 0.893388i
\(357\) 1.96410 + 1.13397i 0.103951 + 0.0600163i
\(358\) −3.00000 1.73205i −0.158555 0.0915417i
\(359\) 34.4449i 1.81793i −0.416872 0.908965i \(-0.636874\pi\)
0.416872 0.908965i \(-0.363126\pi\)
\(360\) −0.366025 + 0.633975i −0.0192912 + 0.0334134i
\(361\) −9.39230 16.2679i −0.494332 0.856208i
\(362\) 12.3564 7.13397i 0.649438 0.374953i
\(363\) −16.0000 −0.839782
\(364\) −1.00000 3.46410i −0.0524142 0.181568i
\(365\) 1.07180 0.0561004
\(366\) 3.23205 1.86603i 0.168942 0.0975387i
\(367\) −6.66025 11.5359i −0.347662 0.602169i 0.638171 0.769894i \(-0.279691\pi\)
−0.985834 + 0.167725i \(0.946358\pi\)
\(368\) −3.73205 + 6.46410i −0.194547 + 0.336965i
\(369\) 8.46410i 0.440624i
\(370\) 4.26795 + 2.46410i 0.221880 + 0.128103i
\(371\) −8.59808 4.96410i −0.446390 0.257723i
\(372\) 3.26795i 0.169435i
\(373\) 7.56218 13.0981i 0.391555 0.678193i −0.601100 0.799174i \(-0.705271\pi\)
0.992655 + 0.120981i \(0.0386040\pi\)
\(374\) 5.89230 + 10.2058i 0.304684 + 0.527728i
\(375\) 6.00000 3.46410i 0.309839 0.178885i
\(376\) 3.92820 0.202582
\(377\) 12.2487 3.53590i 0.630841 0.182108i
\(378\) 1.00000 0.0514344
\(379\) −31.2224 + 18.0263i −1.60379 + 0.925948i −0.613069 + 0.790030i \(0.710065\pi\)
−0.990720 + 0.135918i \(0.956602\pi\)
\(380\) −0.169873 0.294229i −0.00871430 0.0150936i
\(381\) 7.19615 12.4641i 0.368670 0.638555i
\(382\) 8.19615i 0.419352i
\(383\) 26.8468 + 15.5000i 1.37181 + 0.792013i 0.991155 0.132706i \(-0.0423665\pi\)
0.380651 + 0.924719i \(0.375700\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 3.80385i 0.193862i
\(386\) 3.79423 6.57180i 0.193121 0.334496i
\(387\) −4.36603 7.56218i −0.221938 0.384407i
\(388\) −12.2942 + 7.09808i −0.624145 + 0.360350i
\(389\) 21.4641 1.08827 0.544137 0.838997i \(-0.316857\pi\)
0.544137 + 0.838997i \(0.316857\pi\)
\(390\) −1.90192 1.83013i −0.0963077 0.0926721i
\(391\) 16.9282 0.856096
\(392\) 0.866025 0.500000i 0.0437409 0.0252538i
\(393\) 7.46410 + 12.9282i 0.376514 + 0.652142i
\(394\) 0.133975 0.232051i 0.00674954 0.0116906i
\(395\) 6.58846i 0.331501i
\(396\) 4.50000 + 2.59808i 0.226134 + 0.130558i
\(397\) −18.5263 10.6962i −0.929807 0.536825i −0.0430567 0.999073i \(-0.513710\pi\)
−0.886751 + 0.462248i \(0.847043\pi\)
\(398\) 24.5885i 1.23251i
\(399\) −0.232051 + 0.401924i −0.0116171 + 0.0201214i
\(400\) −2.23205 3.86603i −0.111603 0.193301i
\(401\) −9.58846 + 5.53590i −0.478825 + 0.276450i −0.719927 0.694050i \(-0.755825\pi\)
0.241102 + 0.970500i \(0.422491\pi\)
\(402\) −10.0000 −0.498755
\(403\) −11.4378 2.83013i −0.569759 0.140979i
\(404\) 4.92820 0.245187
\(405\) 0.633975 0.366025i 0.0315025 0.0181879i
\(406\) 1.76795 + 3.06218i 0.0877418 + 0.151973i
\(407\) 17.4904 30.2942i 0.866966 1.50163i
\(408\) 2.26795i 0.112280i
\(409\) −14.3660 8.29423i −0.710354 0.410123i 0.100838 0.994903i \(-0.467848\pi\)
−0.811192 + 0.584780i \(0.801181\pi\)
\(410\) −5.36603 3.09808i −0.265009 0.153003i
\(411\) 19.4641i 0.960093i
\(412\) 8.09808 14.0263i 0.398964 0.691025i
\(413\) 4.46410 + 7.73205i 0.219664 + 0.380469i
\(414\) 6.46410 3.73205i 0.317693 0.183420i
\(415\) −6.78461 −0.333043
\(416\) −2.50000 + 2.59808i −0.122573 + 0.127381i
\(417\) 17.0526 0.835067
\(418\) −2.08846 + 1.20577i −0.102150 + 0.0589762i
\(419\) 7.29423 + 12.6340i 0.356346 + 0.617210i 0.987347 0.158572i \(-0.0506890\pi\)
−0.631001 + 0.775782i \(0.717356\pi\)
\(420\) 0.366025 0.633975i 0.0178602 0.0309348i
\(421\) 25.3205i 1.23405i 0.786945 + 0.617023i \(0.211661\pi\)
−0.786945 + 0.617023i \(0.788339\pi\)
\(422\) −21.5885 12.4641i −1.05091 0.606743i
\(423\) −3.40192 1.96410i −0.165407 0.0954979i
\(424\) 9.92820i 0.482156i
\(425\) −5.06218 + 8.76795i −0.245552 + 0.425308i
\(426\) −3.63397 6.29423i −0.176067 0.304956i
\(427\) −3.23205 + 1.86603i −0.156410 + 0.0903033i
\(428\) 6.07180 0.293491
\(429\) −12.9904 + 13.5000i −0.627182 + 0.651786i
\(430\) −6.39230 −0.308264
\(431\) 11.3660 6.56218i 0.547482 0.316089i −0.200624 0.979668i \(-0.564297\pi\)
0.748106 + 0.663579i \(0.230964\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 6.07180 10.5167i 0.291792 0.505398i −0.682442 0.730940i \(-0.739082\pi\)
0.974234 + 0.225542i \(0.0724152\pi\)
\(434\) 3.26795i 0.156867i
\(435\) 2.24167 + 1.29423i 0.107480 + 0.0620535i
\(436\) 9.75833 + 5.63397i 0.467339 + 0.269818i
\(437\) 3.46410i 0.165710i
\(438\) −0.732051 + 1.26795i −0.0349787 + 0.0605850i
\(439\) 11.6603 + 20.1962i 0.556514 + 0.963910i 0.997784 + 0.0665356i \(0.0211946\pi\)
−0.441270 + 0.897374i \(0.645472\pi\)
\(440\) 3.29423 1.90192i 0.157046 0.0906707i
\(441\) −1.00000 −0.0476190
\(442\) 7.93782 + 1.96410i 0.377564 + 0.0934228i
\(443\) −25.0000 −1.18779 −0.593893 0.804544i \(-0.702410\pi\)
−0.593893 + 0.804544i \(0.702410\pi\)
\(444\) −5.83013 + 3.36603i −0.276686 + 0.159744i
\(445\) −6.16987 10.6865i −0.292480 0.506590i
\(446\) −2.73205 + 4.73205i −0.129366 + 0.224069i
\(447\) 8.00000i 0.378387i
\(448\) −0.866025 0.500000i −0.0409159 0.0236228i
\(449\) 25.0981 + 14.4904i 1.18445 + 0.683843i 0.957040 0.289955i \(-0.0936405\pi\)
0.227411 + 0.973799i \(0.426974\pi\)
\(450\) 4.46410i 0.210440i
\(451\) −21.9904 + 38.0885i −1.03549 + 1.79352i
\(452\) 3.83013 + 6.63397i 0.180154 + 0.312036i
\(453\) −1.03590 + 0.598076i −0.0486708 + 0.0281001i
\(454\) −13.3205 −0.625162
\(455\) 1.90192 + 1.83013i 0.0891636 + 0.0857977i
\(456\) 0.464102 0.0217335
\(457\) −25.7321 + 14.8564i −1.20369 + 0.694953i −0.961375 0.275243i \(-0.911242\pi\)
−0.242320 + 0.970196i \(0.577908\pi\)
\(458\) 8.69615 + 15.0622i 0.406345 + 0.703809i
\(459\) −1.13397 + 1.96410i −0.0529294 + 0.0916764i
\(460\) 5.46410i 0.254765i
\(461\) 6.00000 + 3.46410i 0.279448 + 0.161339i 0.633173 0.774010i \(-0.281752\pi\)
−0.353726 + 0.935349i \(0.615085\pi\)
\(462\) −4.50000 2.59808i −0.209359 0.120873i
\(463\) 15.3397i 0.712898i 0.934315 + 0.356449i \(0.116013\pi\)
−0.934315 + 0.356449i \(0.883987\pi\)
\(464\) 1.76795 3.06218i 0.0820750 0.142158i
\(465\) −1.19615 2.07180i −0.0554702 0.0960773i
\(466\) 16.0981 9.29423i 0.745729 0.430547i
\(467\) 18.9282 0.875893 0.437946 0.899001i \(-0.355706\pi\)
0.437946 + 0.899001i \(0.355706\pi\)
\(468\) 3.46410 1.00000i 0.160128 0.0462250i
\(469\) 10.0000 0.461757
\(470\) −2.49038 + 1.43782i −0.114873 + 0.0663218i
\(471\) 5.73205 + 9.92820i 0.264119 + 0.457467i
\(472\) 4.46410 7.73205i 0.205477 0.355896i
\(473\) 45.3731i 2.08626i
\(474\) −7.79423 4.50000i −0.358001 0.206692i
\(475\) −1.79423 1.03590i −0.0823249 0.0475303i
\(476\) 2.26795i 0.103951i
\(477\) 4.96410 8.59808i 0.227291 0.393679i
\(478\) 13.2942 + 23.0263i 0.608064 + 1.05320i
\(479\) 4.20577 2.42820i 0.192167 0.110947i −0.400830 0.916153i \(-0.631278\pi\)
0.592996 + 0.805205i \(0.297945\pi\)
\(480\) −0.732051 −0.0334134
\(481\) −6.73205 23.3205i −0.306955 1.06332i
\(482\) 10.9282 0.497766
\(483\) −6.46410 + 3.73205i −0.294127 + 0.169814i
\(484\) −8.00000 13.8564i −0.363636 0.629837i
\(485\) 5.19615 9.00000i 0.235945 0.408669i
\(486\) 1.00000i 0.0453609i
\(487\) −25.5000 14.7224i −1.15552 0.667137i −0.205290 0.978701i \(-0.565814\pi\)
−0.950225 + 0.311564i \(0.899147\pi\)
\(488\) 3.23205 + 1.86603i 0.146308 + 0.0844710i
\(489\) 7.12436i 0.322174i
\(490\) −0.366025 + 0.633975i −0.0165353 + 0.0286401i
\(491\) −3.19615 5.53590i −0.144240 0.249832i 0.784849 0.619687i \(-0.212741\pi\)
−0.929089 + 0.369856i \(0.879407\pi\)
\(492\) 7.33013 4.23205i 0.330468 0.190796i
\(493\) −8.01924 −0.361168
\(494\) −0.401924 + 1.62436i −0.0180834 + 0.0730832i
\(495\) −3.80385 −0.170970
\(496\) −2.83013 + 1.63397i −0.127076 + 0.0733676i
\(497\) 3.63397 + 6.29423i 0.163006 + 0.282335i
\(498\) 4.63397 8.02628i 0.207653 0.359666i
\(499\) 20.5885i 0.921666i 0.887487 + 0.460833i \(0.152449\pi\)
−0.887487 + 0.460833i \(0.847551\pi\)
\(500\) 6.00000 + 3.46410i 0.268328 + 0.154919i
\(501\) 4.39230 + 2.53590i 0.196234 + 0.113296i
\(502\) 17.5167i 0.781807i
\(503\) 15.4641 26.7846i 0.689510 1.19427i −0.282486 0.959271i \(-0.591159\pi\)
0.971996 0.234995i \(-0.0755075\pi\)
\(504\) 0.500000 + 0.866025i 0.0222718 + 0.0385758i
\(505\) −3.12436 + 1.80385i −0.139032 + 0.0802702i
\(506\) −38.7846 −1.72419
\(507\) 0.500000 + 12.9904i 0.0222058 + 0.576923i
\(508\) 14.3923 0.638555
\(509\) −25.6865 + 14.8301i −1.13854 + 0.657334i −0.946068 0.323969i \(-0.894983\pi\)
−0.192468 + 0.981303i \(0.561649\pi\)
\(510\) 0.830127 + 1.43782i 0.0367586 + 0.0636678i
\(511\) 0.732051 1.26795i 0.0323840 0.0560908i
\(512\) 1.00000i 0.0441942i
\(513\) −0.401924 0.232051i −0.0177454 0.0102453i
\(514\) −21.6962 12.5263i −0.956976 0.552511i
\(515\) 11.8564i 0.522456i
\(516\) 4.36603 7.56218i 0.192204 0.332906i
\(517\) 10.2058 + 17.6769i 0.448849 + 0.777430i
\(518\) 5.83013 3.36603i 0.256161 0.147895i
\(519\) −2.19615 −0.0964004
\(520\) 0.633975 2.56218i 0.0278016 0.112359i
\(521\) −21.5885 −0.945807 −0.472904 0.881114i \(-0.656794\pi\)
−0.472904 + 0.881114i \(0.656794\pi\)
\(522\) −3.06218 + 1.76795i −0.134028 + 0.0773810i
\(523\) 12.5981 + 21.8205i 0.550875 + 0.954144i 0.998212 + 0.0597784i \(0.0190394\pi\)
−0.447336 + 0.894366i \(0.647627\pi\)
\(524\) −7.46410 + 12.9282i −0.326071 + 0.564771i
\(525\) 4.46410i 0.194829i
\(526\) −2.70577 1.56218i −0.117977 0.0681142i
\(527\) 6.41858 + 3.70577i 0.279598 + 0.161426i
\(528\) 5.19615i 0.226134i
\(529\) −16.3564 + 28.3301i −0.711148 + 1.23174i
\(530\) −3.63397 6.29423i −0.157850 0.273404i
\(531\) −7.73205 + 4.46410i −0.335542 + 0.193726i
\(532\) −0.464102 −0.0201214
\(533\) 8.46410 + 29.3205i 0.366621 + 1.27001i
\(534\) 16.8564 0.729448
\(535\) −3.84936 + 2.22243i −0.166423 + 0.0960841i
\(536\) −5.00000 8.66025i −0.215967 0.374066i
\(537\) −1.73205 + 3.00000i −0.0747435 + 0.129460i
\(538\) 4.00000i 0.172452i
\(539\) 4.50000 + 2.59808i 0.193829 + 0.111907i
\(540\) 0.633975 + 0.366025i 0.0272819 + 0.0157512i
\(541\) 8.05256i 0.346207i 0.984904 + 0.173103i \(0.0553794\pi\)
−0.984904 + 0.173103i \(0.944621\pi\)
\(542\) 3.83013 6.63397i 0.164518 0.284954i
\(543\) −7.13397 12.3564i −0.306148 0.530264i
\(544\) 1.96410 1.13397i 0.0842102 0.0486188i
\(545\) −8.24871 −0.353336
\(546\) −3.46410 + 1.00000i −0.148250 + 0.0427960i
\(547\) −4.19615 −0.179415 −0.0897073 0.995968i \(-0.528593\pi\)
−0.0897073 + 0.995968i \(0.528593\pi\)
\(548\) −16.8564 + 9.73205i −0.720070 + 0.415733i
\(549\) −1.86603 3.23205i −0.0796400 0.137941i
\(550\) 11.5981 20.0885i 0.494544 0.856575i
\(551\) 1.64102i 0.0699096i
\(552\) 6.46410 + 3.73205i 0.275130 + 0.158847i
\(553\) 7.79423 + 4.50000i 0.331444 + 0.191359i
\(554\) 14.3923i 0.611470i
\(555\) 2.46410 4.26795i 0.104595 0.181164i
\(556\) 8.52628 + 14.7679i 0.361595 + 0.626301i
\(557\) 17.0885 9.86603i 0.724061 0.418037i −0.0921844 0.995742i \(-0.529385\pi\)
0.816246 + 0.577705i \(0.196052\pi\)
\(558\) 3.26795 0.138343
\(559\) 22.6865 + 21.8301i 0.959538 + 0.923316i
\(560\) 0.732051 0.0309348
\(561\) 10.2058 5.89230i 0.430888 0.248773i
\(562\) 6.36603 + 11.0263i 0.268535 + 0.465116i
\(563\) −6.83013 + 11.8301i −0.287856 + 0.498580i −0.973298 0.229547i \(-0.926276\pi\)
0.685442 + 0.728127i \(0.259609\pi\)
\(564\) 3.92820i 0.165407i
\(565\) −4.85641 2.80385i −0.204311 0.117959i
\(566\) −15.4641 8.92820i −0.650005 0.375280i
\(567\) 1.00000i 0.0419961i
\(568\) 3.63397 6.29423i 0.152478 0.264100i
\(569\) 0.830127 + 1.43782i 0.0348007 + 0.0602766i 0.882901 0.469559i \(-0.155587\pi\)
−0.848100 + 0.529835i \(0.822254\pi\)
\(570\) −0.294229 + 0.169873i −0.0123239 + 0.00711520i
\(571\) 39.5167 1.65372 0.826860 0.562407i \(-0.190125\pi\)
0.826860 + 0.562407i \(0.190125\pi\)
\(572\) −18.1865 4.50000i −0.760417 0.188154i
\(573\) −8.19615 −0.342399
\(574\) −7.33013 + 4.23205i −0.305954 + 0.176642i
\(575\) −16.6603 28.8564i −0.694781 1.20340i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 28.5885i 1.19015i −0.803669 0.595077i \(-0.797122\pi\)
0.803669 0.595077i \(-0.202878\pi\)
\(578\) 10.2679 + 5.92820i 0.427090 + 0.246581i
\(579\) −6.57180 3.79423i −0.273115 0.157683i
\(580\) 2.58846i 0.107480i
\(581\) −4.63397 + 8.02628i −0.192250 + 0.332986i
\(582\) 7.09808 + 12.2942i 0.294225 + 0.509612i
\(583\) −44.6769 + 25.7942i −1.85033 + 1.06829i
\(584\) −1.46410 −0.0605850
\(585\) −1.83013 + 1.90192i −0.0756664 + 0.0786349i
\(586\) 1.07180 0.0442755
\(587\) −4.43782 + 2.56218i −0.183169 + 0.105752i −0.588781 0.808293i \(-0.700392\pi\)
0.405612 + 0.914045i \(0.367058\pi\)
\(588\) −0.500000 0.866025i −0.0206197 0.0357143i
\(589\) −0.758330 + 1.31347i −0.0312465 + 0.0541204i
\(590\) 6.53590i 0.269079i
\(591\) −0.232051 0.133975i −0.00954529 0.00551098i
\(592\) −5.83013 3.36603i −0.239617 0.138343i
\(593\) 37.0000i 1.51941i −0.650269 0.759704i \(-0.725344\pi\)
0.650269 0.759704i \(-0.274656\pi\)
\(594\) 2.59808 4.50000i 0.106600 0.184637i
\(595\) −0.830127 1.43782i −0.0340319 0.0589450i
\(596\) −6.92820 + 4.00000i −0.283790 + 0.163846i
\(597\) −24.5885 −1.00634
\(598\) −18.6603 + 19.3923i −0.763075 + 0.793010i
\(599\) −47.5692 −1.94363 −0.971813 0.235754i \(-0.924244\pi\)
−0.971813 + 0.235754i \(0.924244\pi\)
\(600\) −3.86603 + 2.23205i −0.157830 + 0.0911231i
\(601\) 24.1506 + 41.8301i 0.985125 + 1.70629i 0.641380 + 0.767223i \(0.278362\pi\)
0.343745 + 0.939063i \(0.388304\pi\)
\(602\) −4.36603 + 7.56218i −0.177946 + 0.308211i
\(603\) 10.0000i 0.407231i
\(604\) −1.03590 0.598076i −0.0421501 0.0243354i
\(605\) 10.1436 + 5.85641i 0.412396 + 0.238097i
\(606\) 4.92820i 0.200195i
\(607\) 12.8301 22.2224i 0.520759 0.901981i −0.478950 0.877842i \(-0.658982\pi\)
0.999709 0.0241384i \(-0.00768424\pi\)
\(608\) 0.232051 + 0.401924i 0.00941090 + 0.0163002i
\(609\) 3.06218 1.76795i 0.124086 0.0716409i
\(610\) −2.73205 −0.110618
\(611\) 13.7487 + 3.40192i 0.556213 + 0.137627i
\(612\) −2.26795 −0.0916764
\(613\) −41.3205 + 23.8564i −1.66892 + 0.963551i −0.700698 + 0.713458i \(0.747128\pi\)
−0.968222 + 0.250093i \(0.919539\pi\)
\(614\) −2.50000 4.33013i −0.100892 0.174750i
\(615\) −3.09808 + 5.36603i −0.124926 + 0.216379i
\(616\) 5.19615i 0.209359i
\(617\) 11.9545 + 6.90192i 0.481269 + 0.277861i 0.720945 0.692992i \(-0.243708\pi\)
−0.239676 + 0.970853i \(0.577041\pi\)
\(618\) −14.0263 8.09808i −0.564220 0.325752i
\(619\) 11.3923i 0.457895i 0.973439 + 0.228948i \(0.0735285\pi\)
−0.973439 + 0.228948i \(0.926472\pi\)
\(620\) 1.19615 2.07180i 0.0480386 0.0832054i
\(621\) −3.73205 6.46410i −0.149762 0.259395i
\(622\) 12.8205 7.40192i 0.514056 0.296790i
\(623\) −16.8564 −0.675338
\(624\) 2.59808 + 2.50000i 0.104006 + 0.100080i
\(625\) 17.2487 0.689948
\(626\) 5.95448 3.43782i 0.237989 0.137403i
\(627\) 1.20577 + 2.08846i 0.0481539 + 0.0834049i
\(628\) −5.73205 + 9.92820i −0.228734 + 0.396178i
\(629\) 15.2679i 0.608773i
\(630\) −0.633975 0.366025i −0.0252582 0.0145828i
\(631\) 1.62436 + 0.937822i 0.0646646 + 0.0373341i 0.531984 0.846755i \(-0.321447\pi\)
−0.467319 + 0.884089i \(0.654780\pi\)
\(632\) 9.00000i 0.358001i
\(633\) −12.4641 + 21.5885i −0.495404 + 0.858064i
\(634\) 7.39230 + 12.8038i 0.293586 + 0.508506i
\(635\) −9.12436 + 5.26795i −0.362089 + 0.209052i
\(636\) 9.92820 0.393679
\(637\) 3.46410 1.00000i 0.137253 0.0396214i
\(638\) 18.3731 0.727397
\(639\) −6.29423 + 3.63397i −0.248996 + 0.143758i
\(640\) −0.366025 0.633975i −0.0144684 0.0250600i
\(641\) −8.66025 + 15.0000i −0.342059 + 0.592464i −0.984815 0.173607i \(-0.944458\pi\)
0.642756 + 0.766071i \(0.277791\pi\)
\(642\) 6.07180i 0.239635i
\(643\) 2.00962 + 1.16025i 0.0792516 + 0.0457560i 0.539102 0.842240i \(-0.318764\pi\)
−0.459851 + 0.887996i \(0.652097\pi\)
\(644\) −6.46410 3.73205i −0.254721 0.147063i
\(645\) 6.39230i 0.251697i
\(646\) 0.526279 0.911543i 0.0207062 0.0358642i
\(647\) −11.8660 20.5526i −0.466502 0.808004i 0.532766 0.846262i \(-0.321152\pi\)
−0.999268 + 0.0382579i \(0.987819\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 46.3923 1.82106
\(650\) −4.46410 15.4641i −0.175096 0.606552i
\(651\) −3.26795 −0.128081
\(652\) −6.16987 + 3.56218i −0.241631 + 0.139506i
\(653\) 7.35641 + 12.7417i 0.287878 + 0.498620i 0.973303 0.229523i \(-0.0737168\pi\)
−0.685425 + 0.728144i \(0.740383\pi\)
\(654\) 5.63397 9.75833i 0.220306 0.381581i
\(655\) 10.9282i 0.427000i
\(656\) 7.33013 + 4.23205i 0.286193 + 0.165234i
\(657\) 1.26795 + 0.732051i 0.0494674 + 0.0285600i
\(658\) 3.92820i 0.153137i
\(659\) 6.62436 11.4737i 0.258048 0.446953i −0.707671 0.706542i \(-0.750254\pi\)
0.965719 + 0.259590i \(0.0835873\pi\)
\(660\) −1.90192 3.29423i −0.0740323 0.128228i
\(661\) 19.5167 11.2679i 0.759110 0.438272i −0.0698660 0.997556i \(-0.522257\pi\)
0.828976 + 0.559284i \(0.188924\pi\)
\(662\) 6.78461 0.263691
\(663\) 1.96410 7.93782i 0.0762794 0.308279i
\(664\) 9.26795 0.359666
\(665\) 0.294229 0.169873i 0.0114097 0.00658739i
\(666\) 3.36603 + 5.83013i 0.130431 + 0.225913i
\(667\) 13.1962 22.8564i 0.510957 0.885004i
\(668\) 5.07180i 0.196234i
\(669\) 4.73205 + 2.73205i 0.182952 + 0.105627i
\(670\) 6.33975 + 3.66025i 0.244926 + 0.141408i
\(671\) 19.3923i 0.748632i
\(672\) −0.500000 + 0.866025i −0.0192879 + 0.0334077i
\(673\) −21.8205 37.7942i −0.841119 1.45686i −0.888950 0.458005i \(-0.848564\pi\)
0.0478308 0.998855i \(-0.484769\pi\)
\(674\) −9.52628 + 5.50000i −0.366939 + 0.211852i
\(675\) 4.46410 0.171823
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) 43.2679 1.66292 0.831461 0.555583i \(-0.187505\pi\)
0.831461 + 0.555583i \(0.187505\pi\)
\(678\) 6.63397 3.83013i 0.254776 0.147095i
\(679\) −7.09808 12.2942i −0.272399 0.471809i
\(680\) −0.830127 + 1.43782i −0.0318339 + 0.0551380i
\(681\) 13.3205i 0.510443i
\(682\) −14.7058 8.49038i −0.563113 0.325113i
\(683\) −15.0000 8.66025i −0.573959 0.331375i 0.184770 0.982782i \(-0.440846\pi\)
−0.758729 + 0.651406i \(0.774179\pi\)
\(684\) 0.464102i 0.0177454i
\(685\) 7.12436 12.3397i 0.272208 0.471477i
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) 15.0622 8.69615i 0.574658 0.331779i
\(688\) 8.73205 0.332906
\(689\) −8.59808 + 34.7487i −0.327561 + 1.32382i
\(690\) −5.46410 −0.208015
\(691\) 32.1051 18.5359i 1.22134 0.705139i 0.256133 0.966641i \(-0.417551\pi\)
0.965203 + 0.261503i \(0.0842180\pi\)
\(692\) −1.09808 1.90192i −0.0417426 0.0723003i
\(693\) −2.59808 + 4.50000i −0.0986928 + 0.170941i
\(694\) 6.46410i 0.245374i
\(695\) −10.8109 6.24167i −0.410080 0.236760i
\(696\) −3.06218 1.76795i −0.116072 0.0670139i
\(697\) 19.1962i 0.727106i
\(698\) 3.07180 5.32051i 0.116269 0.201384i
\(699\) −9.29423 16.0981i −0.351540 0.608885i
\(700\) 3.86603 2.23205i 0.146122 0.0843636i
\(701\) −25.7846 −0.973871 −0.486936 0.873438i \(-0.661885\pi\)
−0.486936 + 0.873438i \(0.661885\pi\)
\(702\) −1.00000 3.46410i −0.0377426 0.130744i
\(703\) −3.12436 −0.117837
\(704\) −4.50000 + 2.59808i −0.169600 + 0.0979187i
\(705\) 1.43782 + 2.49038i 0.0541515 + 0.0937932i
\(706\) 15.6603 27.1244i 0.589381 1.02084i
\(707\) 4.92820i 0.185344i
\(708\) −7.73205 4.46410i −0.290588 0.167771i
\(709\) 44.4904 + 25.6865i 1.67087 + 0.964678i 0.967152 + 0.254200i \(0.0818123\pi\)
0.703720 + 0.710478i \(0.251521\pi\)
\(710\) 5.32051i 0.199675i
\(711\) −4.50000 + 7.79423i −0.168763 + 0.292306i
\(712\) 8.42820 + 14.5981i 0.315860 + 0.547086i
\(713\) −21.1244 + 12.1962i −0.791113 + 0.456749i
\(714\) 2.26795 0.0848759
\(715\) 13.1769 3.80385i 0.492789 0.142256i
\(716\) −3.46410 −0.129460
\(717\) 23.0263 13.2942i 0.859932 0.496482i
\(718\) −17.2224 29.8301i −0.642735 1.11325i
\(719\) 19.7224 34.1603i 0.735523 1.27396i −0.218971 0.975731i \(-0.570270\pi\)
0.954494 0.298231i \(-0.0963966\pi\)
\(720\) 0.732051i 0.0272819i
\(721\) 14.0263 + 8.09808i 0.522366 + 0.301588i
\(722\) −16.2679 9.39230i −0.605430 0.349545i
\(723\) 10.9282i 0.406424i
\(724\) 7.13397 12.3564i 0.265132 0.459222i
\(725\) 7.89230 + 13.6699i 0.293113 + 0.507686i
\(726\) −13.8564 + 8.00000i −0.514259 + 0.296908i
\(727\) 3.60770 0.133802 0.0669010 0.997760i \(-0.478689\pi\)
0.0669010 + 0.997760i \(0.478689\pi\)
\(728\) −2.59808 2.50000i −0.0962911 0.0926562i
\(729\) 1.00000 0.0370370
\(730\) 0.928203 0.535898i 0.0343543 0.0198345i
\(731\) −9.90192 17.1506i −0.366236 0.634339i
\(732\) 1.86603 3.23205i 0.0689703 0.119460i
\(733\) 25.7846i 0.952376i −0.879343 0.476188i \(-0.842018\pi\)
0.879343 0.476188i \(-0.157982\pi\)
\(734\) −11.5359 6.66025i −0.425798 0.245834i
\(735\) 0.633975 + 0.366025i 0.0233845 + 0.0135011i
\(736\) 7.46410i 0.275130i
\(737\) 25.9808 45.0000i 0.957014 1.65760i
\(738\) −4.23205 7.33013i −0.155784 0.269826i
\(739\) −33.9282 + 19.5885i −1.24807 + 0.720573i −0.970724 0.240197i \(-0.922788\pi\)
−0.277345 + 0.960770i \(0.589455\pi\)
\(740\) 4.92820 0.181164
\(741\) 1.62436 + 0.401924i 0.0596722 + 0.0147650i
\(742\) −9.92820 −0.364476
\(743\) 12.1699 7.02628i 0.446469 0.257769i −0.259869 0.965644i \(-0.583679\pi\)
0.706338 + 0.707875i \(0.250346\pi\)
\(744\) 1.63397 + 2.83013i 0.0599044 + 0.103757i
\(745\) 2.92820 5.07180i 0.107281 0.185816i
\(746\) 15.1244i 0.553742i
\(747\) −8.02628 4.63397i −0.293666 0.169548i
\(748\) 10.2058 + 5.89230i 0.373160 + 0.215444i
\(749\) 6.07180i 0.221859i
\(750\) 3.46410 6.00000i 0.126491 0.219089i
\(751\) 2.57180 + 4.45448i 0.0938462 + 0.162546i 0.909126 0.416520i \(-0.136750\pi\)
−0.815280 + 0.579067i \(0.803417\pi\)
\(752\) 3.40192 1.96410i 0.124055 0.0716234i
\(753\) −17.5167 −0.638343
\(754\) 8.83975 9.18653i 0.321925 0.334554i
\(755\) 0.875644 0.0318680
\(756\) 0.866025 0.500000i 0.0314970 0.0181848i
\(757\) −8.09808 14.0263i −0.294330 0.509794i 0.680499 0.732749i \(-0.261763\pi\)
−0.974829 + 0.222955i \(0.928430\pi\)
\(758\) −18.0263 + 31.2224i −0.654744 + 1.13405i
\(759\) 38.7846i 1.40779i
\(760\) −0.294229 0.169873i −0.0106728 0.00616194i
\(761\) −15.8038 9.12436i −0.572889 0.330758i 0.185413 0.982661i \(-0.440638\pi\)
−0.758302 + 0.651903i \(0.773971\pi\)
\(762\) 14.3923i 0.521378i
\(763\) −5.63397 + 9.75833i −0.203964 + 0.353275i
\(764\) −4.09808 7.09808i −0.148263 0.256799i
\(765\) 1.43782 0.830127i 0.0519846 0.0300133i
\(766\) 31.0000 1.12008
\(767\) 22.3205 23.1962i 0.805947 0.837565i
\(768\) 1.00000 0.0360844
\(769\) −37.4711 + 21.6340i −1.35124 + 0.780141i −0.988424 0.151718i \(-0.951519\pi\)
−0.362820 + 0.931859i \(0.618186\pi\)
\(770\) 1.90192 + 3.29423i 0.0685406 + 0.118716i
\(771\) −12.5263 + 21.6962i −0.451123 + 0.781368i
\(772\) 7.58846i 0.273115i
\(773\) 16.6077 + 9.58846i 0.597337 + 0.344873i 0.767993 0.640458i \(-0.221255\pi\)
−0.170656 + 0.985331i \(0.554589\pi\)
\(774\) −7.56218 4.36603i −0.271817