Properties

Label 546.2.s.e.127.2
Level $546$
Weight $2$
Character 546.127
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
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: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.195105024.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 4 x^{5} - 20 x^{4} + 12 x^{3} + 45 x^{2} - 108 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 127.2
Root \(0.560908 - 1.63871i\) of defining polynomial
Character \(\chi\) \(=\) 546.127
Dual form 546.2.s.e.43.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -0.332808i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -0.332808i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.166404 + 0.288220i) q^{10} +(2.26053 - 1.30512i) q^{11} +1.00000 q^{12} +(3.41140 - 1.16719i) q^{13} +1.00000 q^{14} +(0.288220 - 0.166404i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.94383 + 3.36681i) q^{17} -1.00000i q^{18} +(4.85997 + 2.80591i) q^{19} +(-0.288220 - 0.166404i) q^{20} -1.00000i q^{21} +(-1.30512 + 2.26053i) q^{22} +(2.10628 + 3.64819i) q^{23} +(-0.866025 + 0.500000i) q^{24} +4.88924 q^{25} +(-2.37076 + 2.71652i) q^{26} -1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(0.593337 + 1.02769i) q^{29} +(-0.166404 + 0.288220i) q^{30} -7.07434i q^{31} +(0.866025 + 0.500000i) q^{32} +(2.26053 + 1.30512i) q^{33} -3.88766i q^{34} +(-0.166404 + 0.288220i) q^{35} +(0.500000 + 0.866025i) q^{36} +(0.499211 - 0.288220i) q^{37} -5.61181 q^{38} +(2.71652 + 2.37076i) q^{39} +0.332808 q^{40} +(0.451251 - 0.260530i) q^{41} +(0.500000 + 0.866025i) q^{42} +(1.53717 - 2.66245i) q^{43} -2.61023i q^{44} +(0.288220 + 0.166404i) q^{45} +(-3.64819 - 2.10628i) q^{46} +12.0528i q^{47} +(0.500000 - 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-4.23421 + 2.44462i) q^{50} -3.88766 q^{51} +(0.694883 - 3.53796i) q^{52} -9.71047 q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.434353 - 0.752321i) q^{55} +(0.500000 - 0.866025i) q^{56} +5.61181i q^{57} +(-1.02769 - 0.593337i) q^{58} +(9.07175 + 5.23758i) q^{59} -0.332808i q^{60} +(-3.71989 + 6.44304i) q^{61} +(3.53717 + 6.12656i) q^{62} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(-0.388451 - 1.13534i) q^{65} -2.61023 q^{66} +(10.3233 - 5.96015i) q^{67} +(1.94383 + 3.36681i) q^{68} +(-2.10628 + 3.64819i) q^{69} -0.332808i q^{70} +(-0.818065 - 0.472310i) q^{71} +(-0.866025 - 0.500000i) q^{72} +4.66562i q^{73} +(-0.288220 + 0.499211i) q^{74} +(2.44462 + 4.23421i) q^{75} +(4.85997 - 2.80591i) q^{76} -2.61023 q^{77} +(-3.53796 - 0.694883i) q^{78} -0.943042 q^{79} +(-0.288220 + 0.166404i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.260530 + 0.451251i) q^{82} -13.7172i q^{83} +(-0.866025 - 0.500000i) q^{84} +(1.12050 + 0.646922i) q^{85} +3.07434i q^{86} +(-0.593337 + 1.02769i) q^{87} +(1.30512 + 2.26053i) q^{88} +(2.92741 - 1.69014i) q^{89} -0.332808 q^{90} +(-3.53796 - 0.694883i) q^{91} +4.21257 q^{92} +(6.12656 - 3.53717i) q^{93} +(-6.02638 - 10.4380i) q^{94} +(0.933827 - 1.61744i) q^{95} +1.00000i q^{96} +(-5.03669 - 2.90793i) q^{97} +(-0.866025 - 0.500000i) q^{98} +2.61023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} + 6q^{10} + 6q^{11} + 8q^{12} + 12q^{13} + 8q^{14} + 6q^{15} - 4q^{16} + 2q^{17} - 12q^{19} - 6q^{20} - 4q^{22} + 8q^{23} - 24q^{25} + 6q^{26} - 8q^{27} + 2q^{29} - 6q^{30} + 6q^{33} - 6q^{35} + 4q^{36} + 18q^{37} - 4q^{38} + 12q^{40} + 12q^{41} + 4q^{42} - 8q^{43} + 6q^{45} + 18q^{46} + 4q^{48} + 4q^{49} + 12q^{50} + 4q^{51} + 12q^{52} - 12q^{53} - 22q^{55} + 4q^{56} - 24q^{58} + 18q^{59} - 8q^{61} + 8q^{62} - 8q^{64} + 46q^{65} - 8q^{66} + 18q^{67} - 2q^{68} - 8q^{69} + 6q^{71} - 6q^{74} - 12q^{75} - 12q^{76} - 8q^{77} + 6q^{78} - 4q^{79} - 6q^{80} - 4q^{81} + 10q^{82} - 54q^{85} - 2q^{87} + 4q^{88} - 18q^{89} - 12q^{90} + 6q^{91} + 16q^{92} + 30q^{93} - 2q^{94} - 50q^{95} - 54q^{97} + O(q^{100}) \)

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
\(5\) 0.332808i 0.148836i −0.997227 0.0744180i \(-0.976290\pi\)
0.997227 0.0744180i \(-0.0237099\pi\)
\(6\) −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
\(10\) 0.166404 + 0.288220i 0.0526215 + 0.0911431i
\(11\) 2.26053 1.30512i 0.681575 0.393508i −0.118873 0.992909i \(-0.537928\pi\)
0.800448 + 0.599402i \(0.204595\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.41140 1.16719i 0.946153 0.323721i
\(14\) 1.00000 0.267261
\(15\) 0.288220 0.166404i 0.0744180 0.0429653i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.94383 + 3.36681i −0.471448 + 0.816572i −0.999466 0.0326607i \(-0.989602\pi\)
0.528018 + 0.849233i \(0.322935\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.85997 + 2.80591i 1.11495 + 0.643719i 0.940108 0.340877i \(-0.110724\pi\)
0.174846 + 0.984596i \(0.444057\pi\)
\(20\) −0.288220 0.166404i −0.0644479 0.0372090i
\(21\) 1.00000i 0.218218i
\(22\) −1.30512 + 2.26053i −0.278252 + 0.481947i
\(23\) 2.10628 + 3.64819i 0.439191 + 0.760701i 0.997627 0.0688467i \(-0.0219319\pi\)
−0.558437 + 0.829547i \(0.688599\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 4.88924 0.977848
\(26\) −2.37076 + 2.71652i −0.464945 + 0.532753i
\(27\) −1.00000 −0.192450
\(28\) −0.866025 + 0.500000i −0.163663 + 0.0944911i
\(29\) 0.593337 + 1.02769i 0.110180 + 0.190837i 0.915843 0.401537i \(-0.131524\pi\)
−0.805663 + 0.592374i \(0.798191\pi\)
\(30\) −0.166404 + 0.288220i −0.0303810 + 0.0526215i
\(31\) 7.07434i 1.27059i −0.772270 0.635294i \(-0.780879\pi\)
0.772270 0.635294i \(-0.219121\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 2.26053 + 1.30512i 0.393508 + 0.227192i
\(34\) 3.88766i 0.666729i
\(35\) −0.166404 + 0.288220i −0.0281274 + 0.0487180i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 0.499211 0.288220i 0.0820699 0.0473831i −0.458403 0.888744i \(-0.651579\pi\)
0.540473 + 0.841361i \(0.318245\pi\)
\(38\) −5.61181 −0.910356
\(39\) 2.71652 + 2.37076i 0.434991 + 0.379626i
\(40\) 0.332808 0.0526215
\(41\) 0.451251 0.260530i 0.0704735 0.0406879i −0.464349 0.885652i \(-0.653712\pi\)
0.534823 + 0.844964i \(0.320378\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) 1.53717 2.66245i 0.234416 0.406020i −0.724687 0.689078i \(-0.758016\pi\)
0.959103 + 0.283058i \(0.0913489\pi\)
\(44\) 2.61023i 0.393508i
\(45\) 0.288220 + 0.166404i 0.0429653 + 0.0248060i
\(46\) −3.64819 2.10628i −0.537896 0.310555i
\(47\) 12.0528i 1.75807i 0.476753 + 0.879037i \(0.341814\pi\)
−0.476753 + 0.879037i \(0.658186\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) −4.23421 + 2.44462i −0.598807 + 0.345721i
\(51\) −3.88766 −0.544382
\(52\) 0.694883 3.53796i 0.0963629 0.490626i
\(53\) −9.71047 −1.33384 −0.666918 0.745132i \(-0.732387\pi\)
−0.666918 + 0.745132i \(0.732387\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) −0.434353 0.752321i −0.0585681 0.101443i
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 5.61181i 0.743303i
\(58\) −1.02769 0.593337i −0.134942 0.0779090i
\(59\) 9.07175 + 5.23758i 1.18104 + 0.681875i 0.956255 0.292533i \(-0.0944983\pi\)
0.224786 + 0.974408i \(0.427832\pi\)
\(60\) 0.332808i 0.0429653i
\(61\) −3.71989 + 6.44304i −0.476283 + 0.824947i −0.999631 0.0271724i \(-0.991350\pi\)
0.523347 + 0.852119i \(0.324683\pi\)
\(62\) 3.53717 + 6.12656i 0.449221 + 0.778073i
\(63\) 0.866025 0.500000i 0.109109 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) −0.388451 1.13534i −0.0481814 0.140822i
\(66\) −2.61023 −0.321298
\(67\) 10.3233 5.96015i 1.26119 0.728148i 0.287885 0.957665i \(-0.407048\pi\)
0.973305 + 0.229517i \(0.0737145\pi\)
\(68\) 1.94383 + 3.36681i 0.235724 + 0.408286i
\(69\) −2.10628 + 3.64819i −0.253567 + 0.439191i
\(70\) 0.332808i 0.0397781i
\(71\) −0.818065 0.472310i −0.0970864 0.0560529i 0.450671 0.892690i \(-0.351185\pi\)
−0.547757 + 0.836637i \(0.684518\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 4.66562i 0.546069i 0.962004 + 0.273034i \(0.0880273\pi\)
−0.962004 + 0.273034i \(0.911973\pi\)
\(74\) −0.288220 + 0.499211i −0.0335049 + 0.0580321i
\(75\) 2.44462 + 4.23421i 0.282280 + 0.488924i
\(76\) 4.85997 2.80591i 0.557477 0.321859i
\(77\) −2.61023 −0.297464
\(78\) −3.53796 0.694883i −0.400595 0.0786800i
\(79\) −0.943042 −0.106101 −0.0530503 0.998592i \(-0.516894\pi\)
−0.0530503 + 0.998592i \(0.516894\pi\)
\(80\) −0.288220 + 0.166404i −0.0322240 + 0.0186045i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −0.260530 + 0.451251i −0.0287707 + 0.0498323i
\(83\) 13.7172i 1.50566i −0.658215 0.752830i \(-0.728688\pi\)
0.658215 0.752830i \(-0.271312\pi\)
\(84\) −0.866025 0.500000i −0.0944911 0.0545545i
\(85\) 1.12050 + 0.646922i 0.121535 + 0.0701685i
\(86\) 3.07434i 0.331514i
\(87\) −0.593337 + 1.02769i −0.0636124 + 0.110180i
\(88\) 1.30512 + 2.26053i 0.139126 + 0.240973i
\(89\) 2.92741 1.69014i 0.310305 0.179155i −0.336758 0.941591i \(-0.609330\pi\)
0.647063 + 0.762436i \(0.275997\pi\)
\(90\) −0.332808 −0.0350810
\(91\) −3.53796 0.694883i −0.370879 0.0728435i
\(92\) 4.21257 0.439191
\(93\) 6.12656 3.53717i 0.635294 0.366787i
\(94\) −6.02638 10.4380i −0.621573 1.07660i
\(95\) 0.933827 1.61744i 0.0958086 0.165945i
\(96\) 1.00000i 0.102062i
\(97\) −5.03669 2.90793i −0.511398 0.295256i 0.222010 0.975044i \(-0.428738\pi\)
−0.733408 + 0.679789i \(0.762072\pi\)
\(98\) −0.866025 0.500000i −0.0874818 0.0505076i
\(99\) 2.61023i 0.262338i
\(100\) 2.44462 4.23421i 0.244462 0.423421i
\(101\) −7.98516 13.8307i −0.794553 1.37621i −0.923122 0.384506i \(-0.874372\pi\)
0.128569 0.991701i \(-0.458962\pi\)
\(102\) 3.36681 1.94383i 0.333364 0.192468i
\(103\) −7.50641 −0.739629 −0.369814 0.929106i \(-0.620579\pi\)
−0.369814 + 0.929106i \(0.620579\pi\)
\(104\) 1.16719 + 3.41140i 0.114453 + 0.334515i
\(105\) −0.332808 −0.0324787
\(106\) 8.40951 4.85523i 0.816804 0.471582i
\(107\) −4.32539 7.49179i −0.418151 0.724259i 0.577602 0.816318i \(-0.303988\pi\)
−0.995754 + 0.0920593i \(0.970655\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 18.6144i 1.78293i −0.453088 0.891466i \(-0.649678\pi\)
0.453088 0.891466i \(-0.350322\pi\)
\(110\) 0.752321 + 0.434353i 0.0717310 + 0.0414139i
\(111\) 0.499211 + 0.288220i 0.0473831 + 0.0273566i
\(112\) 1.00000i 0.0944911i
\(113\) −4.57512 + 7.92435i −0.430392 + 0.745460i −0.996907 0.0785911i \(-0.974958\pi\)
0.566515 + 0.824051i \(0.308291\pi\)
\(114\) −2.80591 4.85997i −0.262797 0.455178i
\(115\) 1.21415 0.700987i 0.113220 0.0653674i
\(116\) 1.18667 0.110180
\(117\) −0.694883 + 3.53796i −0.0642419 + 0.327084i
\(118\) −10.4752 −0.964316
\(119\) 3.36681 1.94383i 0.308635 0.178191i
\(120\) 0.166404 + 0.288220i 0.0151905 + 0.0263108i
\(121\) −2.09334 + 3.62577i −0.190303 + 0.329615i
\(122\) 7.43978i 0.673566i
\(123\) 0.451251 + 0.260530i 0.0406879 + 0.0234912i
\(124\) −6.12656 3.53717i −0.550181 0.317647i
\(125\) 3.29121i 0.294375i
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) 3.38977 + 5.87125i 0.300793 + 0.520989i 0.976316 0.216350i \(-0.0694153\pi\)
−0.675523 + 0.737339i \(0.736082\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 3.07434 0.270680
\(130\) 0.904078 + 0.789008i 0.0792929 + 0.0692006i
\(131\) 7.22879 0.631583 0.315791 0.948829i \(-0.397730\pi\)
0.315791 + 0.948829i \(0.397730\pi\)
\(132\) 2.26053 1.30512i 0.196754 0.113596i
\(133\) −2.80591 4.85997i −0.243303 0.421413i
\(134\) −5.96015 + 10.3233i −0.514879 + 0.891796i
\(135\) 0.332808i 0.0286435i
\(136\) −3.36681 1.94383i −0.288702 0.166682i
\(137\) −10.2964 5.94462i −0.879679 0.507883i −0.00912669 0.999958i \(-0.502905\pi\)
−0.870553 + 0.492075i \(0.836238\pi\)
\(138\) 4.21257i 0.358598i
\(139\) −7.16056 + 12.4025i −0.607351 + 1.05196i 0.384324 + 0.923198i \(0.374434\pi\)
−0.991675 + 0.128764i \(0.958899\pi\)
\(140\) 0.166404 + 0.288220i 0.0140637 + 0.0243590i
\(141\) −10.4380 + 6.02638i −0.879037 + 0.507512i
\(142\) 0.944620 0.0792707
\(143\) 6.18825 7.09075i 0.517488 0.592959i
\(144\) 1.00000 0.0833333
\(145\) 0.342023 0.197467i 0.0284035 0.0163988i
\(146\) −2.33281 4.04054i −0.193065 0.334398i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) 0.576440i 0.0473831i
\(149\) −5.24548 3.02848i −0.429726 0.248103i 0.269504 0.962999i \(-0.413140\pi\)
−0.699230 + 0.714897i \(0.746474\pi\)
\(150\) −4.23421 2.44462i −0.345721 0.199602i
\(151\) 21.4953i 1.74926i −0.484791 0.874630i \(-0.661104\pi\)
0.484791 0.874630i \(-0.338896\pi\)
\(152\) −2.80591 + 4.85997i −0.227589 + 0.394196i
\(153\) −1.94383 3.36681i −0.157149 0.272191i
\(154\) 2.26053 1.30512i 0.182159 0.105169i
\(155\) −2.35439 −0.189109
\(156\) 3.41140 1.16719i 0.273131 0.0934502i
\(157\) 2.29227 0.182943 0.0914714 0.995808i \(-0.470843\pi\)
0.0914714 + 0.995808i \(0.470843\pi\)
\(158\) 0.816699 0.471521i 0.0649731 0.0375122i
\(159\) −4.85523 8.40951i −0.385045 0.666918i
\(160\) 0.166404 0.288220i 0.0131554 0.0227858i
\(161\) 4.21257i 0.331997i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 2.89314 + 1.67035i 0.226608 + 0.130832i 0.609006 0.793165i \(-0.291568\pi\)
−0.382398 + 0.923998i \(0.624902\pi\)
\(164\) 0.521059i 0.0406879i
\(165\) 0.434353 0.752321i 0.0338143 0.0585681i
\(166\) 6.85861 + 11.8795i 0.532331 + 0.922024i
\(167\) 5.57802 3.22047i 0.431640 0.249207i −0.268405 0.963306i \(-0.586497\pi\)
0.700045 + 0.714099i \(0.253163\pi\)
\(168\) 1.00000 0.0771517
\(169\) 10.2753 7.96352i 0.790410 0.612579i
\(170\) −1.29384 −0.0992333
\(171\) −4.85997 + 2.80591i −0.371651 + 0.214573i
\(172\) −1.53717 2.66245i −0.117208 0.203010i
\(173\) −9.30718 + 16.1205i −0.707611 + 1.22562i 0.258129 + 0.966110i \(0.416894\pi\)
−0.965741 + 0.259509i \(0.916439\pi\)
\(174\) 1.18667i 0.0899616i
\(175\) −4.23421 2.44462i −0.320076 0.184796i
\(176\) −2.26053 1.30512i −0.170394 0.0983769i
\(177\) 10.4752i 0.787361i
\(178\) −1.69014 + 2.92741i −0.126682 + 0.219419i
\(179\) −11.1081 19.2398i −0.830261 1.43805i −0.897831 0.440339i \(-0.854858\pi\)
0.0675707 0.997714i \(-0.478475\pi\)
\(180\) 0.288220 0.166404i 0.0214826 0.0124030i
\(181\) −4.05853 −0.301669 −0.150834 0.988559i \(-0.548196\pi\)
−0.150834 + 0.988559i \(0.548196\pi\)
\(182\) 3.41140 1.16719i 0.252870 0.0865181i
\(183\) −7.43978 −0.549965
\(184\) −3.64819 + 2.10628i −0.268948 + 0.155277i
\(185\) −0.0959218 0.166141i −0.00705231 0.0122150i
\(186\) −3.53717 + 6.12656i −0.259358 + 0.449221i
\(187\) 10.1477i 0.742074i
\(188\) 10.4380 + 6.02638i 0.761269 + 0.439519i
\(189\) 0.866025 + 0.500000i 0.0629941 + 0.0363696i
\(190\) 1.86765i 0.135494i
\(191\) 5.86018 10.1501i 0.424028 0.734438i −0.572301 0.820044i \(-0.693949\pi\)
0.996329 + 0.0856056i \(0.0272825\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −20.6123 + 11.9005i −1.48371 + 0.856618i −0.999829 0.0185185i \(-0.994105\pi\)
−0.483877 + 0.875136i \(0.660772\pi\)
\(194\) 5.81587 0.417555
\(195\) 0.789008 0.904078i 0.0565021 0.0647424i
\(196\) 1.00000 0.0714286
\(197\) 8.73184 5.04133i 0.622118 0.359180i −0.155575 0.987824i \(-0.549723\pi\)
0.777693 + 0.628644i \(0.216390\pi\)
\(198\) −1.30512 2.26053i −0.0927507 0.160649i
\(199\) 6.92504 11.9945i 0.490903 0.850269i −0.509042 0.860742i \(-0.670000\pi\)
0.999945 + 0.0104725i \(0.00333355\pi\)
\(200\) 4.88924i 0.345721i
\(201\) 10.3233 + 5.96015i 0.728148 + 0.420397i
\(202\) 13.8307 + 7.98516i 0.973125 + 0.561834i
\(203\) 1.18667i 0.0832882i
\(204\) −1.94383 + 3.36681i −0.136095 + 0.235724i
\(205\) −0.0867062 0.150180i −0.00605583 0.0104890i
\(206\) 6.50074 3.75321i 0.452928 0.261498i
\(207\) −4.21257 −0.292794
\(208\) −2.71652 2.37076i −0.188357 0.164383i
\(209\) 14.6481 1.01323
\(210\) 0.288220 0.166404i 0.0198891 0.0114830i
\(211\) −2.27743 3.94462i −0.156785 0.271559i 0.776923 0.629596i \(-0.216779\pi\)
−0.933707 + 0.358037i \(0.883446\pi\)
\(212\) −4.85523 + 8.40951i −0.333459 + 0.577568i
\(213\) 0.944620i 0.0647243i
\(214\) 7.49179 + 4.32539i 0.512128 + 0.295677i
\(215\) −0.886085 0.511581i −0.0604305 0.0348896i
\(216\) 1.00000i 0.0680414i
\(217\) −3.53717 + 6.12656i −0.240119 + 0.415898i
\(218\) 9.30718 + 16.1205i 0.630361 + 1.09182i
\(219\) −4.04054 + 2.33281i −0.273034 + 0.157637i
\(220\) −0.868706 −0.0585681
\(221\) −2.70147 + 13.7544i −0.181720 + 0.925220i
\(222\) −0.576440 −0.0386881
\(223\) −7.30359 + 4.21673i −0.489085 + 0.282373i −0.724195 0.689596i \(-0.757788\pi\)
0.235110 + 0.971969i \(0.424455\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) −2.44462 + 4.23421i −0.162975 + 0.282280i
\(226\) 9.15025i 0.608666i
\(227\) 24.2394 + 13.9946i 1.60883 + 0.928857i 0.989633 + 0.143619i \(0.0458739\pi\)
0.619194 + 0.785238i \(0.287459\pi\)
\(228\) 4.85997 + 2.80591i 0.321859 + 0.185826i
\(229\) 28.7785i 1.90174i 0.309598 + 0.950868i \(0.399806\pi\)
−0.309598 + 0.950868i \(0.600194\pi\)
\(230\) −0.700987 + 1.21415i −0.0462217 + 0.0800584i
\(231\) −1.30512 2.26053i −0.0858704 0.148732i
\(232\) −1.02769 + 0.593337i −0.0674712 + 0.0389545i
\(233\) −18.8877 −1.23737 −0.618686 0.785638i \(-0.712335\pi\)
−0.618686 + 0.785638i \(0.712335\pi\)
\(234\) −1.16719 3.41140i −0.0763018 0.223010i
\(235\) 4.01125 0.261665
\(236\) 9.07175 5.23758i 0.590521 0.340937i
\(237\) −0.471521 0.816699i −0.0306286 0.0530503i
\(238\) −1.94383 + 3.36681i −0.126000 + 0.218238i
\(239\) 11.0933i 0.717565i −0.933421 0.358783i \(-0.883192\pi\)
0.933421 0.358783i \(-0.116808\pi\)
\(240\) −0.288220 0.166404i −0.0186045 0.0107413i
\(241\) −7.02686 4.05696i −0.452640 0.261332i 0.256305 0.966596i \(-0.417495\pi\)
−0.708944 + 0.705264i \(0.750828\pi\)
\(242\) 4.18667i 0.269130i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 3.71989 + 6.44304i 0.238142 + 0.412474i
\(245\) 0.288220 0.166404i 0.0184137 0.0106311i
\(246\) −0.521059 −0.0332215
\(247\) 19.8543 + 3.89955i 1.26330 + 0.248122i
\(248\) 7.07434 0.449221
\(249\) 11.8795 6.85861i 0.752830 0.434646i
\(250\) 1.64561 + 2.85027i 0.104077 + 0.180267i
\(251\) −1.58465 + 2.74469i −0.100022 + 0.173243i −0.911694 0.410871i \(-0.865225\pi\)
0.811671 + 0.584114i \(0.198558\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 9.52264 + 5.49790i 0.598683 + 0.345650i
\(254\) −5.87125 3.38977i −0.368395 0.212693i
\(255\) 1.29384i 0.0810236i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −0.0967103 0.167507i −0.00603263 0.0104488i 0.862993 0.505215i \(-0.168587\pi\)
−0.869026 + 0.494766i \(0.835254\pi\)
\(258\) −2.66245 + 1.53717i −0.165757 + 0.0956999i
\(259\) −0.576440 −0.0358182
\(260\) −1.17746 0.231262i −0.0730229 0.0143423i
\(261\) −1.18667 −0.0734533
\(262\) −6.26032 + 3.61440i −0.386764 + 0.223298i
\(263\) −6.02185 10.4301i −0.371323 0.643150i 0.618446 0.785827i \(-0.287762\pi\)
−0.989769 + 0.142677i \(0.954429\pi\)
\(264\) −1.30512 + 2.26053i −0.0803244 + 0.139126i
\(265\) 3.23172i 0.198523i
\(266\) 4.85997 + 2.80591i 0.297984 + 0.172041i
\(267\) 2.92741 + 1.69014i 0.179155 + 0.103435i
\(268\) 11.9203i 0.728148i
\(269\) −8.60487 + 14.9041i −0.524648 + 0.908718i 0.474940 + 0.880018i \(0.342470\pi\)
−0.999588 + 0.0286993i \(0.990863\pi\)
\(270\) −0.166404 0.288220i −0.0101270 0.0175405i
\(271\) −14.8453 + 8.57096i −0.901790 + 0.520649i −0.877781 0.479063i \(-0.840977\pi\)
−0.0240098 + 0.999712i \(0.507643\pi\)
\(272\) 3.88766 0.235724
\(273\) −1.16719 3.41140i −0.0706417 0.206467i
\(274\) 11.8892 0.718255
\(275\) 11.0523 6.38103i 0.666477 0.384791i
\(276\) 2.10628 + 3.64819i 0.126783 + 0.219595i
\(277\) −7.85660 + 13.6080i −0.472057 + 0.817627i −0.999489 0.0319704i \(-0.989822\pi\)
0.527432 + 0.849598i \(0.323155\pi\)
\(278\) 14.3211i 0.858924i
\(279\) 6.12656 + 3.53717i 0.366787 + 0.211765i
\(280\) −0.288220 0.166404i −0.0172244 0.00994453i
\(281\) 4.07337i 0.242997i 0.992592 + 0.121499i \(0.0387700\pi\)
−0.992592 + 0.121499i \(0.961230\pi\)
\(282\) 6.02638 10.4380i 0.358865 0.621573i
\(283\) 10.7674 + 18.6497i 0.640057 + 1.10861i 0.985420 + 0.170142i \(0.0544226\pi\)
−0.345363 + 0.938469i \(0.612244\pi\)
\(284\) −0.818065 + 0.472310i −0.0485432 + 0.0280264i
\(285\) 1.86765 0.110630
\(286\) −1.81381 + 9.23490i −0.107253 + 0.546071i
\(287\) −0.521059 −0.0307572
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 0.943042 + 1.63340i 0.0554731 + 0.0960822i
\(290\) −0.197467 + 0.342023i −0.0115957 + 0.0200843i
\(291\) 5.81587i 0.340932i
\(292\) 4.04054 + 2.33281i 0.236455 + 0.136517i
\(293\) 0.152457 + 0.0880210i 0.00890662 + 0.00514224i 0.504447 0.863443i \(-0.331697\pi\)
−0.495540 + 0.868585i \(0.665030\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) 1.74311 3.01915i 0.101488 0.175782i
\(296\) 0.288220 + 0.499211i 0.0167524 + 0.0290161i
\(297\) −2.26053 + 1.30512i −0.131169 + 0.0757306i
\(298\) 6.05696 0.350870
\(299\) 11.4435 + 9.98701i 0.661796 + 0.577564i
\(300\) 4.88924 0.282280
\(301\) −2.66245 + 1.53717i −0.153461 + 0.0886009i
\(302\) 10.7476 + 18.6154i 0.618457 + 1.07120i
\(303\) 7.98516 13.8307i 0.458736 0.794553i
\(304\) 5.61181i 0.321859i
\(305\) 2.14429 + 1.23801i 0.122782 + 0.0708882i
\(306\) 3.36681 + 1.94383i 0.192468 + 0.111121i
\(307\) 20.7405i 1.18372i 0.806040 + 0.591861i \(0.201606\pi\)
−0.806040 + 0.591861i \(0.798394\pi\)
\(308\) −1.30512 + 2.26053i −0.0743660 + 0.128806i
\(309\) −3.75321 6.50074i −0.213512 0.369814i
\(310\) 2.03896 1.17720i 0.115805 0.0668603i
\(311\) 10.9678 0.621926 0.310963 0.950422i \(-0.399348\pi\)
0.310963 + 0.950422i \(0.399348\pi\)
\(312\) −2.37076 + 2.71652i −0.134218 + 0.153793i
\(313\) 16.2189 0.916746 0.458373 0.888760i \(-0.348432\pi\)
0.458373 + 0.888760i \(0.348432\pi\)
\(314\) −1.98516 + 1.14613i −0.112029 + 0.0646800i
\(315\) −0.166404 0.288220i −0.00937579 0.0162393i
\(316\) −0.471521 + 0.816699i −0.0265251 + 0.0459429i
\(317\) 10.5358i 0.591750i −0.955227 0.295875i \(-0.904389\pi\)
0.955227 0.295875i \(-0.0956112\pi\)
\(318\) 8.40951 + 4.85523i 0.471582 + 0.272268i
\(319\) 2.68251 + 1.54875i 0.150192 + 0.0867133i
\(320\) 0.332808i 0.0186045i
\(321\) 4.32539 7.49179i 0.241420 0.418151i
\(322\) 2.10628 + 3.64819i 0.117379 + 0.203306i
\(323\) −18.8939 + 10.9084i −1.05129 + 0.606960i
\(324\) −1.00000 −0.0555556
\(325\) 16.6792 5.70668i 0.925193 0.316550i
\(326\) −3.34071 −0.185025
\(327\) 16.1205 9.30718i 0.891466 0.514688i
\(328\) 0.260530 + 0.451251i 0.0143853 + 0.0249161i
\(329\) 6.02638 10.4380i 0.332245 0.575465i
\(330\) 0.868706i 0.0478207i
\(331\) −13.9687 8.06486i −0.767792 0.443285i 0.0642946 0.997931i \(-0.479520\pi\)
−0.832086 + 0.554646i \(0.812854\pi\)
\(332\) −11.8795 6.85861i −0.651970 0.376415i
\(333\) 0.576440i 0.0315887i
\(334\) −3.22047 + 5.57802i −0.176216 + 0.305216i
\(335\) −1.98358 3.43567i −0.108375 0.187711i
\(336\) −0.866025 + 0.500000i −0.0472456 + 0.0272772i
\(337\) 1.78785 0.0973906 0.0486953 0.998814i \(-0.484494\pi\)
0.0486953 + 0.998814i \(0.484494\pi\)
\(338\) −4.91693 + 12.0343i −0.267446 + 0.654578i
\(339\) −9.15025 −0.496973
\(340\) 1.12050 0.646922i 0.0607677 0.0350843i
\(341\) −9.23284 15.9917i −0.499986 0.866002i
\(342\) 2.80591 4.85997i 0.151726 0.262797i
\(343\) 1.00000i 0.0539949i
\(344\) 2.66245 + 1.53717i 0.143550 + 0.0828786i
\(345\) 1.21415 + 0.700987i 0.0653674 + 0.0377399i
\(346\) 18.6144i 1.00071i
\(347\) −12.7030 + 22.0023i −0.681935 + 1.18115i 0.292454 + 0.956280i \(0.405528\pi\)
−0.974389 + 0.224867i \(0.927805\pi\)
\(348\) 0.593337 + 1.02769i 0.0318062 + 0.0550900i
\(349\) −24.5419 + 14.1693i −1.31370 + 0.758463i −0.982706 0.185172i \(-0.940716\pi\)
−0.330990 + 0.943634i \(0.607383\pi\)
\(350\) 4.88924 0.261341
\(351\) −3.41140 + 1.16719i −0.182087 + 0.0623001i
\(352\) 2.61023 0.139126
\(353\) −1.69146 + 0.976568i −0.0900276 + 0.0519774i −0.544338 0.838866i \(-0.683219\pi\)
0.454310 + 0.890843i \(0.349886\pi\)
\(354\) −5.23758 9.07175i −0.278374 0.482158i
\(355\) −0.157188 + 0.272258i −0.00834269 + 0.0144500i
\(356\) 3.38029i 0.179155i
\(357\) 3.36681 + 1.94383i 0.178191 + 0.102878i
\(358\) 19.2398 + 11.1081i 1.01686 + 0.587083i
\(359\) 27.6565i 1.45965i −0.683633 0.729826i \(-0.739601\pi\)
0.683633 0.729826i \(-0.260399\pi\)
\(360\) −0.166404 + 0.288220i −0.00877025 + 0.0151905i
\(361\) 6.24622 + 10.8188i 0.328748 + 0.569409i
\(362\) 3.51479 2.02927i 0.184733 0.106656i
\(363\) −4.18667 −0.219743
\(364\) −2.37076 + 2.71652i −0.124262 + 0.142384i
\(365\) 1.55275 0.0812748
\(366\) 6.44304 3.71989i 0.336783 0.194442i
\(367\) −2.87888 4.98636i −0.150276 0.260286i 0.781053 0.624465i \(-0.214683\pi\)
−0.931329 + 0.364179i \(0.881350\pi\)
\(368\) 2.10628 3.64819i 0.109798 0.190175i
\(369\) 0.521059i 0.0271253i
\(370\) 0.166141 + 0.0959218i 0.00863728 + 0.00498673i
\(371\) 8.40951 + 4.85523i 0.436600 + 0.252071i
\(372\) 7.07434i 0.366787i
\(373\) −13.9243 + 24.1177i −0.720975 + 1.24877i 0.239634 + 0.970863i \(0.422973\pi\)
−0.960609 + 0.277903i \(0.910361\pi\)
\(374\) −5.07386 8.78817i −0.262363 0.454426i
\(375\) 2.85027 1.64561i 0.147188 0.0849788i
\(376\) −12.0528 −0.621573
\(377\) 3.22362 + 2.81333i 0.166025 + 0.144894i
\(378\) −1.00000 −0.0514344
\(379\) −10.7836 + 6.22590i −0.553915 + 0.319803i −0.750700 0.660644i \(-0.770283\pi\)
0.196784 + 0.980447i \(0.436950\pi\)
\(380\) −0.933827 1.61744i −0.0479043 0.0829727i
\(381\) −3.38977 + 5.87125i −0.173663 + 0.300793i
\(382\) 11.7204i 0.599666i
\(383\) −8.42273 4.86286i −0.430381 0.248481i 0.269128 0.963104i \(-0.413265\pi\)
−0.699509 + 0.714624i \(0.746598\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0.868706i 0.0442734i
\(386\) 11.9005 20.6123i 0.605720 1.04914i
\(387\) 1.53717 + 2.66245i 0.0781387 + 0.135340i
\(388\) −5.03669 + 2.90793i −0.255699 + 0.147628i
\(389\) −13.8910 −0.704302 −0.352151 0.935943i \(-0.614550\pi\)
−0.352151 + 0.935943i \(0.614550\pi\)
\(390\) −0.231262 + 1.17746i −0.0117104 + 0.0596230i
\(391\) −16.3770 −0.828223
\(392\) −0.866025 + 0.500000i −0.0437409 + 0.0252538i
\(393\) 3.61440 + 6.26032i 0.182322 + 0.315791i
\(394\) −5.04133 + 8.73184i −0.253979 + 0.439904i
\(395\) 0.313852i 0.0157916i
\(396\) 2.26053 + 1.30512i 0.113596 + 0.0655846i
\(397\) 5.87033 + 3.38924i 0.294624 + 0.170101i 0.640025 0.768354i \(-0.278924\pi\)
−0.345401 + 0.938455i \(0.612257\pi\)
\(398\) 13.8501i 0.694242i
\(399\) 2.80591 4.85997i 0.140471 0.243303i
\(400\) −2.44462 4.23421i −0.122231 0.211710i
\(401\) 12.5254 7.23152i 0.625487 0.361125i −0.153515 0.988146i \(-0.549059\pi\)
0.779002 + 0.627021i \(0.215726\pi\)
\(402\) −11.9203 −0.594531
\(403\) −8.25711 24.1334i −0.411316 1.20217i
\(404\) −15.9703 −0.794553
\(405\) −0.288220 + 0.166404i −0.0143218 + 0.00826867i
\(406\) 0.593337 + 1.02769i 0.0294468 + 0.0510034i
\(407\) 0.752321 1.30306i 0.0372912 0.0645902i
\(408\) 3.88766i 0.192468i
\(409\) 20.2032 + 11.6643i 0.998982 + 0.576763i 0.907947 0.419085i \(-0.137649\pi\)
0.0910351 + 0.995848i \(0.470982\pi\)
\(410\) 0.150180 + 0.0867062i 0.00741684 + 0.00428212i
\(411\) 11.8892i 0.586453i
\(412\) −3.75321 + 6.50074i −0.184907 + 0.320269i
\(413\) −5.23758 9.07175i −0.257724 0.446392i
\(414\) 3.64819 2.10628i 0.179299 0.103518i
\(415\) −4.56519 −0.224096
\(416\) 3.53796 + 0.694883i 0.173463 + 0.0340694i
\(417\) −14.3211 −0.701308
\(418\) −12.6857 + 7.32407i −0.620476 + 0.358232i
\(419\) 11.2898 + 19.5544i 0.551540 + 0.955296i 0.998164 + 0.0605740i \(0.0192931\pi\)
−0.446623 + 0.894722i \(0.647374\pi\)
\(420\) −0.166404 + 0.288220i −0.00811967 + 0.0140637i
\(421\) 34.1708i 1.66538i −0.553738 0.832691i \(-0.686799\pi\)
0.553738 0.832691i \(-0.313201\pi\)
\(422\) 3.94462 + 2.27743i 0.192021 + 0.110863i
\(423\) −10.4380 6.02638i −0.507512 0.293012i
\(424\) 9.71047i 0.471582i
\(425\) −9.50385 + 16.4612i −0.461005 + 0.798483i
\(426\) 0.472310 + 0.818065i 0.0228835 + 0.0396354i
\(427\) 6.44304 3.71989i 0.311801 0.180018i
\(428\) −8.65078 −0.418151
\(429\) 9.23490 + 1.81381i 0.445865 + 0.0875714i
\(430\) 1.02316 0.0493413
\(431\) 4.53528 2.61844i 0.218457 0.126126i −0.386779 0.922173i \(-0.626412\pi\)
0.605235 + 0.796047i \(0.293079\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 8.41030 14.5671i 0.404173 0.700048i −0.590052 0.807365i \(-0.700893\pi\)
0.994225 + 0.107317i \(0.0342260\pi\)
\(434\) 7.07434i 0.339579i
\(435\) 0.342023 + 0.197467i 0.0163988 + 0.00946782i
\(436\) −16.1205 9.30718i −0.772032 0.445733i
\(437\) 23.6401i 1.13086i
\(438\) 2.33281 4.04054i 0.111466 0.193065i
\(439\) −7.36282 12.7528i −0.351408 0.608657i 0.635088 0.772440i \(-0.280964\pi\)
−0.986496 + 0.163783i \(0.947630\pi\)
\(440\) 0.752321 0.434353i 0.0358655 0.0207070i
\(441\) −1.00000 −0.0476190
\(442\) −4.53765 13.2624i −0.215834 0.630827i
\(443\) 36.2393 1.72178 0.860891 0.508789i \(-0.169907\pi\)
0.860891 + 0.508789i \(0.169907\pi\)
\(444\) 0.499211 0.288220i 0.0236915 0.0136783i
\(445\) −0.562493 0.974266i −0.0266647 0.0461846i
\(446\) 4.21673 7.30359i 0.199668 0.345835i
\(447\) 6.05696i 0.286484i
\(448\) 0.866025 + 0.500000i 0.0409159 + 0.0236228i
\(449\) −21.0351 12.1446i −0.992708 0.573140i −0.0866255 0.996241i \(-0.527608\pi\)
−0.906083 + 0.423101i \(0.860942\pi\)
\(450\) 4.88924i 0.230481i
\(451\) 0.680043 1.17787i 0.0320220 0.0554637i
\(452\) 4.57512 + 7.92435i 0.215196 + 0.372730i
\(453\) 18.6154 10.7476i 0.874630 0.504968i
\(454\) −27.9893 −1.31360
\(455\) −0.231262 + 1.17746i −0.0108417 + 0.0552001i
\(456\) −5.61181 −0.262797
\(457\) −28.8744 + 16.6706i −1.35069 + 0.779819i −0.988345 0.152227i \(-0.951355\pi\)
−0.362340 + 0.932046i \(0.618022\pi\)
\(458\) −14.3892 24.9229i −0.672365 1.16457i
\(459\) 1.94383 3.36681i 0.0907303 0.157149i
\(460\) 1.40197i 0.0653674i
\(461\) −25.6317 14.7985i −1.19379 0.689234i −0.234625 0.972086i \(-0.575386\pi\)
−0.959164 + 0.282852i \(0.908720\pi\)
\(462\) 2.26053 + 1.30512i 0.105169 + 0.0607196i
\(463\) 36.6027i 1.70107i −0.525918 0.850535i \(-0.676278\pi\)
0.525918 0.850535i \(-0.323722\pi\)
\(464\) 0.593337 1.02769i 0.0275450 0.0477093i
\(465\) −1.17720 2.03896i −0.0545912 0.0945547i
\(466\) 16.3572 9.44383i 0.757732 0.437477i
\(467\) −6.21635 −0.287658 −0.143829 0.989603i \(-0.545942\pi\)
−0.143829 + 0.989603i \(0.545942\pi\)
\(468\) 2.71652 + 2.37076i 0.125571 + 0.109589i
\(469\) −11.9203 −0.550428
\(470\) −3.47384 + 2.00562i −0.160236 + 0.0925125i
\(471\) 1.14613 + 1.98516i 0.0528110 + 0.0914714i
\(472\) −5.23758 + 9.07175i −0.241079 + 0.417561i
\(473\) 8.02474i 0.368978i
\(474\) 0.816699 + 0.471521i 0.0375122 + 0.0216577i
\(475\) 23.7616 + 13.7187i 1.09026 + 0.629459i
\(476\) 3.88766i 0.178191i
\(477\) 4.85523 8.40951i 0.222306 0.385045i
\(478\) 5.54665 + 9.60707i 0.253698 + 0.439417i
\(479\) −29.0757 + 16.7869i −1.32850 + 0.767011i −0.985068 0.172165i \(-0.944924\pi\)
−0.343434 + 0.939177i \(0.611590\pi\)
\(480\) 0.332808 0.0151905
\(481\) 1.36660 1.56591i 0.0623117 0.0713993i
\(482\) 8.11392 0.369579
\(483\) 3.64819 2.10628i 0.165998 0.0958393i
\(484\) 2.09334 + 3.62577i 0.0951517 + 0.164808i
\(485\) −0.967782 + 1.67625i −0.0439447 + 0.0761145i
\(486\) 1.00000i 0.0453609i
\(487\) 17.5020 + 10.1048i 0.793089 + 0.457890i 0.841049 0.540959i \(-0.181939\pi\)
−0.0479597 + 0.998849i \(0.515272\pi\)
\(488\) −6.44304 3.71989i −0.291663 0.168392i
\(489\) 3.34071i 0.151072i
\(490\) −0.166404 + 0.288220i −0.00751736 + 0.0130204i
\(491\) −3.38977 5.87125i −0.152978 0.264966i 0.779343 0.626598i \(-0.215553\pi\)
−0.932321 + 0.361632i \(0.882220\pi\)
\(492\) 0.451251 0.260530i 0.0203439 0.0117456i
\(493\) −4.61339 −0.207777
\(494\) −19.1441 + 6.55006i −0.861336 + 0.294701i
\(495\) 0.868706 0.0390454
\(496\) −6.12656 + 3.53717i −0.275090 + 0.158824i
\(497\) 0.472310 + 0.818065i 0.0211860 + 0.0366952i
\(498\) −6.85861 + 11.8795i −0.307341 + 0.532331i
\(499\) 11.0813i 0.496066i 0.968752 + 0.248033i \(0.0797841\pi\)
−0.968752 + 0.248033i \(0.920216\pi\)
\(500\) −2.85027 1.64561i −0.127468 0.0735938i
\(501\) 5.57802 + 3.22047i 0.249207 + 0.143880i
\(502\) 3.16930i 0.141453i
\(503\) 14.9958 25.9735i 0.668629 1.15810i −0.309658 0.950848i \(-0.600215\pi\)
0.978288 0.207252i \(-0.0664520\pi\)
\(504\) 0.500000 + 0.866025i 0.0222718 + 0.0385758i
\(505\) −4.60296 + 2.65752i −0.204829 + 0.118258i
\(506\) −10.9958 −0.488823
\(507\) 12.0343 + 4.91693i 0.534461 + 0.218368i
\(508\) 6.77953 0.300793
\(509\) 27.2629 15.7402i 1.20840 0.697673i 0.245994 0.969271i \(-0.420886\pi\)
0.962411 + 0.271599i \(0.0875523\pi\)
\(510\) −0.646922 1.12050i −0.0286462 0.0496166i
\(511\) 2.33281 4.04054i 0.103197 0.178743i
\(512\) 1.00000i 0.0441942i
\(513\) −4.85997 2.80591i −0.214573 0.123884i
\(514\) 0.167507 + 0.0967103i 0.00738843 + 0.00426571i
\(515\) 2.49819i 0.110083i
\(516\) 1.53717 2.66245i 0.0676701 0.117208i
\(517\) 15.7303 + 27.2456i 0.691816 + 1.19826i
\(518\) 0.499211 0.288220i 0.0219341 0.0126637i
\(519\) −18.6144 −0.817079
\(520\) 1.13534 0.388451i 0.0497880 0.0170347i
\(521\) 17.8010 0.779877 0.389939 0.920841i \(-0.372496\pi\)
0.389939 + 0.920841i \(0.372496\pi\)
\(522\) 1.02769 0.593337i 0.0449808 0.0259697i
\(523\) −16.4702 28.5272i −0.720192 1.24741i −0.960923 0.276817i \(-0.910720\pi\)
0.240731 0.970592i \(-0.422613\pi\)
\(524\) 3.61440 6.26032i 0.157896 0.273483i
\(525\) 4.88924i 0.213384i
\(526\) 10.4301 + 6.02185i 0.454776 + 0.262565i
\(527\) 23.8180 + 13.7513i 1.03753 + 0.599017i
\(528\) 2.61023i 0.113596i
\(529\) 2.62713 4.55033i 0.114223 0.197840i
\(530\) −1.61586 2.79875i −0.0701884 0.121570i
\(531\) −9.07175 + 5.23758i −0.393680 + 0.227292i
\(532\) −5.61181 −0.243303
\(533\) 1.23531 1.41547i 0.0535072 0.0613107i
\(534\) −3.38029 −0.146279
\(535\) −2.49333 + 1.43952i −0.107796 + 0.0622360i
\(536\) 5.96015 + 10.3233i 0.257439 + 0.445898i
\(537\) 11.1081 19.2398i 0.479351 0.830261i
\(538\) 17.2097i 0.741965i
\(539\) 2.26053 + 1.30512i 0.0973679 + 0.0562154i
\(540\) 0.288220 + 0.166404i 0.0124030 + 0.00716088i
\(541\) 15.5204i 0.667276i −0.942701 0.333638i \(-0.891724\pi\)
0.942701 0.333638i \(-0.108276\pi\)
\(542\) 8.57096 14.8453i 0.368154 0.637662i
\(543\) −2.02927 3.51479i −0.0870842 0.150834i
\(544\) −3.36681 + 1.94383i −0.144351 + 0.0833411i
\(545\) −6.19500 −0.265365
\(546\) 2.71652 + 2.37076i 0.116256 + 0.101459i
\(547\) 22.9529 0.981397 0.490698 0.871329i \(-0.336742\pi\)
0.490698 + 0.871329i \(0.336742\pi\)
\(548\) −10.2964 + 5.94462i −0.439840 + 0.253942i
\(549\) −3.71989 6.44304i −0.158761 0.274982i
\(550\) −6.38103 + 11.0523i −0.272088 + 0.471270i
\(551\) 6.65939i 0.283700i
\(552\) −3.64819 2.10628i −0.155277 0.0896494i
\(553\) 0.816699 + 0.471521i 0.0347296 + 0.0200511i
\(554\) 15.7132i 0.667590i
\(555\) 0.0959218 0.166141i 0.00407165 0.00705231i
\(556\) 7.16056 + 12.4025i 0.303675 + 0.525981i
\(557\) −20.8161 + 12.0182i −0.882005 + 0.509226i −0.871319 0.490717i \(-0.836735\pi\)
−0.0106863 + 0.999943i \(0.503402\pi\)
\(558\) −7.07434 −0.299481
\(559\) 2.13630 10.8769i 0.0903560 0.460043i
\(560\) 0.332808 0.0140637
\(561\) −8.78817 + 5.07386i −0.371037 + 0.214218i
\(562\) −2.03669 3.52765i −0.0859125 0.148805i
\(563\) −18.9379 + 32.8015i −0.798139 + 1.38242i 0.122687 + 0.992445i \(0.460849\pi\)
−0.920827 + 0.389972i \(0.872485\pi\)
\(564\) 12.0528i 0.507512i
\(565\) 2.63728 + 1.52264i 0.110951 + 0.0640578i
\(566\) −18.6497 10.7674i −0.783906 0.452589i
\(567\) 1.00000i 0.0419961i
\(568\) 0.472310 0.818065i 0.0198177 0.0343252i
\(569\) −13.6833 23.7001i −0.573632 0.993560i −0.996189 0.0872233i \(-0.972201\pi\)
0.422557 0.906336i \(-0.361133\pi\)
\(570\) −1.61744 + 0.933827i −0.0677469 + 0.0391137i
\(571\) 17.6639 0.739213 0.369607 0.929188i \(-0.379492\pi\)
0.369607 + 0.929188i \(0.379492\pi\)
\(572\) −3.04665 8.90456i −0.127387 0.372318i
\(573\) 11.7204 0.489625
\(574\) 0.451251 0.260530i 0.0188348 0.0108743i
\(575\) 10.2981 + 17.8369i 0.429462 + 0.743849i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 11.3804i 0.473772i 0.971537 + 0.236886i \(0.0761268\pi\)
−0.971537 + 0.236886i \(0.923873\pi\)
\(578\) −1.63340 0.943042i −0.0679404 0.0392254i
\(579\) −20.6123 11.9005i −0.856618 0.494568i
\(580\) 0.394934i 0.0163988i
\(581\) −6.85861 + 11.8795i −0.284543 + 0.492843i
\(582\) 2.90793 + 5.03669i 0.120538 + 0.208777i
\(583\) −21.9508 + 12.6733i −0.909109 + 0.524874i
\(584\) −4.66562 −0.193065
\(585\) 1.17746 + 0.231262i 0.0486819 + 0.00956152i
\(586\) −0.176042 −0.00727222
\(587\) 15.9949 9.23469i 0.660182 0.381156i −0.132164 0.991228i \(-0.542193\pi\)
0.792346 + 0.610072i \(0.208859\pi\)
\(588\) 0.500000 + 0.866025i 0.0206197 + 0.0357143i
\(589\) 19.8499 34.3811i 0.817902 1.41665i
\(590\) 3.48621i 0.143525i
\(591\) 8.73184 + 5.04133i 0.359180 + 0.207373i
\(592\) −0.499211 0.288220i −0.0205175 0.0118458i
\(593\) 19.3561i 0.794859i −0.917633 0.397429i \(-0.869902\pi\)
0.917633 0.397429i \(-0.130098\pi\)
\(594\) 1.30512 2.26053i 0.0535496 0.0927507i
\(595\) −0.646922 1.12050i −0.0265212 0.0459361i
\(596\) −5.24548 + 3.02848i −0.214863 + 0.124051i
\(597\) 13.8501 0.566846
\(598\) −14.9039 2.92724i −0.609465 0.119704i
\(599\) 21.1818 0.865466 0.432733 0.901522i \(-0.357549\pi\)
0.432733 + 0.901522i \(0.357549\pi\)
\(600\) −4.23421 + 2.44462i −0.172861 + 0.0998012i
\(601\) −11.0721 19.1774i −0.451639 0.782261i 0.546849 0.837231i \(-0.315827\pi\)
−0.998488 + 0.0549699i \(0.982494\pi\)
\(602\) 1.53717 2.66245i 0.0626503 0.108513i
\(603\) 11.9203i 0.485432i
\(604\) −18.6154 10.7476i −0.757452 0.437315i
\(605\) 1.20668 + 0.696679i 0.0490586 + 0.0283240i
\(606\) 15.9703i 0.648750i
\(607\) −17.1439 + 29.6942i −0.695851 + 1.20525i 0.274042 + 0.961718i \(0.411639\pi\)
−0.969893 + 0.243531i \(0.921694\pi\)
\(608\) 2.80591 + 4.85997i 0.113795 + 0.197098i
\(609\) 1.02769 0.593337i 0.0416441 0.0240432i
\(610\) −2.47602 −0.100251
\(611\) 14.0679 + 41.1168i 0.569125 + 1.66341i
\(612\) −3.88766 −0.157149
\(613\) 14.7308 8.50484i 0.594972 0.343507i −0.172089 0.985081i \(-0.555052\pi\)
0.767061 + 0.641574i \(0.221718\pi\)
\(614\) −10.3702 17.9618i −0.418509 0.724878i
\(615\) 0.0867062 0.150180i 0.00349633 0.00605583i
\(616\) 2.61023i 0.105169i
\(617\) 15.0005 + 8.66052i 0.603896 + 0.348659i 0.770573 0.637352i \(-0.219970\pi\)
−0.166677 + 0.986012i \(0.553304\pi\)
\(618\) 6.50074 + 3.75321i 0.261498 + 0.150976i
\(619\) 0.621482i 0.0249795i 0.999922 + 0.0124897i \(0.00397571\pi\)
−0.999922 + 0.0124897i \(0.996024\pi\)
\(620\) −1.17720 + 2.03896i −0.0472773 + 0.0818868i
\(621\) −2.10628 3.64819i −0.0845223 0.146397i
\(622\) −9.49838 + 5.48389i −0.380850 + 0.219884i
\(623\) −3.38029 −0.135428
\(624\) 0.694883 3.53796i 0.0278176 0.141632i
\(625\) 23.3509 0.934034
\(626\) −14.0460 + 8.10945i −0.561390 + 0.324119i
\(627\) 7.32407 + 12.6857i 0.292495 + 0.506617i
\(628\) 1.14613 1.98516i 0.0457357 0.0792165i
\(629\) 2.24100i 0.0893546i
\(630\) 0.288220 + 0.166404i 0.0114830 + 0.00662969i
\(631\) 11.7575 + 6.78817i 0.468057 + 0.270233i 0.715426 0.698688i \(-0.246233\pi\)
−0.247369 + 0.968921i \(0.579566\pi\)
\(632\) 0.943042i 0.0375122i
\(633\) 2.27743 3.94462i 0.0905196 0.156785i
\(634\) 5.26790 + 9.12428i 0.209215 + 0.362371i
\(635\) 1.95400 1.12814i 0.0775419 0.0447689i
\(636\) −9.71047 −0.385045
\(637\) 2.71652 + 2.37076i 0.107632 + 0.0939331i
\(638\) −3.09750 −0.122631
\(639\) 0.818065 0.472310i 0.0323621 0.0186843i
\(640\) −0.166404 0.288220i −0.00657769 0.0113929i
\(641\) −10.2558 + 17.7636i −0.405081 + 0.701622i −0.994331 0.106330i \(-0.966090\pi\)
0.589250 + 0.807951i \(0.299423\pi\)
\(642\) 8.65078i 0.341419i
\(643\) −37.0253 21.3766i −1.46013 0.843009i −0.461118 0.887339i \(-0.652552\pi\)
−0.999017 + 0.0443295i \(0.985885\pi\)
\(644\) −3.64819 2.10628i −0.143759 0.0829992i
\(645\) 1.02316i 0.0402870i
\(646\) 10.9084 18.8939i 0.429186 0.743372i
\(647\) −13.1115 22.7098i −0.515466 0.892814i −0.999839 0.0179521i \(-0.994285\pi\)
0.484372 0.874862i \(-0.339048\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) 27.3426 1.07329
\(650\) −11.5912 + 13.2817i −0.454646 + 0.520952i
\(651\) −7.07434 −0.277265
\(652\) 2.89314 1.67035i 0.113304 0.0654161i
\(653\) 4.36935 + 7.56794i 0.170986 + 0.296156i 0.938765 0.344558i \(-0.111971\pi\)
−0.767779 + 0.640715i \(0.778638\pi\)
\(654\) −9.30718 + 16.1205i −0.363939 + 0.630361i
\(655\) 2.40580i 0.0940023i
\(656\) −0.451251 0.260530i −0.0176184 0.0101720i
\(657\) −4.04054 2.33281i −0.157637 0.0910115i
\(658\) 12.0528i 0.469865i
\(659\) −0.251052 + 0.434834i −0.00977958 + 0.0169387i −0.870874 0.491507i \(-0.836446\pi\)
0.861094 + 0.508445i \(0.169780\pi\)
\(660\) −0.434353 0.752321i −0.0169072 0.0292841i
\(661\) 27.1062 15.6498i 1.05431 0.608705i 0.130456 0.991454i \(-0.458356\pi\)
0.923853 + 0.382749i \(0.125022\pi\)
\(662\) 16.1297 0.626899
\(663\) −13.2624 + 4.53765i −0.515068 + 0.176228i
\(664\) 13.7172 0.532331
\(665\) −1.61744 + 0.933827i −0.0627215 + 0.0362123i
\(666\) −0.288220 0.499211i −0.0111683 0.0193440i
\(667\) −2.49947 + 4.32922i −0.0967800 + 0.167628i
\(668\) 6.44094i 0.249207i
\(669\) −7.30359 4.21673i −0.282373 0.163028i
\(670\) 3.43567 + 1.98358i 0.132731 + 0.0766325i
\(671\) 19.4196i 0.749685i
\(672\) 0.500000 0.866025i 0.0192879 0.0334077i
\(673\) −11.8585 20.5395i −0.457112 0.791741i 0.541695 0.840575i \(-0.317783\pi\)
−0.998807 + 0.0488340i \(0.984449\pi\)
\(674\) −1.54833 + 0.893927i −0.0596393 + 0.0344328i
\(675\) −4.88924 −0.188187
\(676\) −1.75895 12.8805i −0.0676520 0.495402i
\(677\) 17.8136 0.684631 0.342315 0.939585i \(-0.388789\pi\)
0.342315 + 0.939585i \(0.388789\pi\)
\(678\) 7.92435 4.57512i 0.304333 0.175707i
\(679\) 2.90793 + 5.03669i 0.111596 + 0.193290i
\(680\) −0.646922 + 1.12050i −0.0248083 + 0.0429693i
\(681\) 27.9893i 1.07255i
\(682\) 15.9917 + 9.23284i 0.612356 + 0.353544i
\(683\) 10.3174 + 5.95673i 0.394783 + 0.227928i 0.684230 0.729266i \(-0.260138\pi\)
−0.289448 + 0.957194i \(0.593472\pi\)
\(684\) 5.61181i 0.214573i
\(685\) −1.97841 + 3.42671i −0.0755913 + 0.130928i
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) −24.9229 + 14.3892i −0.950868 + 0.548984i
\(688\) −3.07434 −0.117208
\(689\) −33.1263 + 11.3340i −1.26201 + 0.431790i
\(690\) −1.40197 −0.0533723
\(691\) −17.3085 + 9.99306i −0.658446 + 0.380154i −0.791685 0.610930i \(-0.790796\pi\)
0.133239 + 0.991084i \(0.457462\pi\)
\(692\) 9.30718 + 16.1205i 0.353806 + 0.612810i
\(693\) 1.30512 2.26053i 0.0495773 0.0858704i
\(694\) 25.4061i 0.964402i
\(695\) 4.12763 + 2.38309i 0.156570 + 0.0903957i
\(696\) −1.02769 0.593337i −0.0389545 0.0224904i
\(697\) 2.02570i 0.0767289i
\(698\) 14.1693 24.5419i 0.536314 0.928923i
\(699\) −9.44383 16.3572i −0.357198 0.618686i
\(700\) −4.23421 + 2.44462i −0.160038 + 0.0923979i
\(701\) −23.9244 −0.903613 −0.451806 0.892116i \(-0.649220\pi\)
−0.451806 + 0.892116i \(0.649220\pi\)
\(702\) 2.37076 2.71652i 0.0894787 0.102528i
\(703\) 3.23487 0.122005
\(704\) −2.26053 + 1.30512i −0.0851969 + 0.0491885i
\(705\) 2.00562 + 3.47384i 0.0755362 + 0.130832i
\(706\) 0.976568 1.69146i 0.0367536 0.0636591i
\(707\) 15.9703i 0.600626i
\(708\) 9.07175 + 5.23758i 0.340937 + 0.196840i
\(709\) 30.7406 + 17.7481i 1.15449 + 0.666544i 0.949977 0.312320i \(-0.101106\pi\)
0.204512 + 0.978864i \(0.434439\pi\)
\(710\) 0.314377i 0.0117983i
\(711\) 0.471521 0.816699i 0.0176834 0.0306286i
\(712\) 1.69014 + 2.92741i 0.0633408 + 0.109710i
\(713\) 25.8085 14.9006i 0.966537 0.558031i
\(714\) −3.88766 −0.145492
\(715\) −2.35986 2.05950i −0.0882536 0.0770208i
\(716\) −22.2163 −0.830261
\(717\) 9.60707 5.54665i 0.358783 0.207143i
\(718\) 13.8282 + 23.9512i 0.516065 + 0.893851i
\(719\) −3.09097 + 5.35372i −0.115274 + 0.199660i −0.917889 0.396837i \(-0.870108\pi\)
0.802615 + 0.596497i \(0.203441\pi\)
\(720\) 0.332808i 0.0124030i
\(721\) 6.50074 + 3.75321i 0.242100 + 0.139777i
\(722\) −10.8188 6.24622i −0.402633 0.232460i
\(723\) 8.11392i 0.301760i
\(724\) −2.02927 + 3.51479i −0.0754171 + 0.130626i
\(725\) 2.90097 + 5.02462i 0.107739 + 0.186610i
\(726\) 3.62577 2.09334i 0.134565 0.0776910i
\(727\) −43.2387 −1.60363 −0.801817 0.597569i \(-0.796133\pi\)
−0.801817 + 0.597569i \(0.796133\pi\)
\(728\) 0.694883 3.53796i 0.0257541 0.131125i
\(729\) 1.00000 0.0370370
\(730\) −1.34472 + 0.776376i −0.0497704 + 0.0287350i
\(731\) 5.97599 + 10.3507i 0.221030 + 0.382835i
\(732\) −3.71989 + 6.44304i −0.137491 + 0.238142i
\(733\) 32.0306i 1.18308i −0.806277 0.591538i \(-0.798521\pi\)
0.806277 0.591538i \(-0.201479\pi\)
\(734\) 4.98636 + 2.87888i 0.184050 + 0.106261i
\(735\) 0.288220 + 0.166404i 0.0106311 + 0.00613790i
\(736\) 4.21257i 0.155277i
\(737\) 15.5574 26.9462i 0.573064 0.992576i
\(738\) −0.260530 0.451251i −0.00959023 0.0166108i
\(739\) −22.0558 + 12.7339i −0.811334 + 0.468424i −0.847419 0.530925i \(-0.821845\pi\)
0.0360848 + 0.999349i \(0.488511\pi\)
\(740\) −0.191844 −0.00705231
\(741\) 6.55006 + 19.1441i 0.240623 + 0.703278i
\(742\) −9.71047 −0.356482
\(743\) −12.5533 + 7.24763i −0.460535 + 0.265890i −0.712269 0.701906i \(-0.752332\pi\)
0.251734 + 0.967796i \(0.418999\pi\)
\(744\) 3.53717 + 6.12656i 0.129679 + 0.224610i
\(745\) −1.00790 + 1.74574i −0.0369266 + 0.0639588i
\(746\) 27.8487i 1.01961i
\(747\) 11.8795 + 6.85861i 0.434646 + 0.250943i
\(748\) 8.78817 + 5.07386i 0.321327 + 0.185519i
\(749\) 8.65078i 0.316092i
\(750\) −1.64561 + 2.85027i −0.0600891 + 0.104077i
\(751\) 14.5632 + 25.2243i 0.531420 + 0.920447i 0.999327 + 0.0366690i \(0.0116747\pi\)
−0.467907 + 0.883777i \(0.654992\pi\)
\(752\) 10.4380 6.02638i 0.380634 0.219759i
\(753\) −3.16930 −0.115496
\(754\) −4.19840 0.824599i −0.152897 0.0300301i
\(755\) −7.15379 −0.260353
\(756\) 0.866025 0.500000i 0.0314970 0.0181848i
\(757\) 10.0230 + 17.3603i 0.364292 + 0.630973i 0.988662 0.150156i \(-0.0479776\pi\)
−0.624370 + 0.781129i \(0.714644\pi\)
\(758\) 6.22590 10.7836i 0.226135 0.391677i
\(759\) 10.9958i 0.399122i
\(760\) 1.61744 + 0.933827i 0.0586706 + 0.0338735i
\(761\) 16.4954 + 9.52360i 0.597956 + 0.345230i 0.768237 0.640165i \(-0.221134\pi\)
−0.170281 + 0.985396i \(0.554468\pi\)
\(762\) 6.77953i 0.245596i
\(763\) −9.30718 + 16.1205i −0.336942 + 0.583601i
\(764\) −5.86018 10.1501i −0.212014 0.367219i
\(765\) −1.12050 + 0.646922i −0.0405118 + 0.0233895i
\(766\) 9.72573 0.351405
\(767\) 37.0607 + 7.27900i 1.33818 + 0.262830i
\(768\) −1.00000 −0.0360844
\(769\) 13.2055 7.62418i 0.476201 0.274935i −0.242631 0.970119i \(-0.578010\pi\)
0.718832 + 0.695184i \(0.244677\pi\)
\(770\) −0.434353 0.752321i −0.0156530 0.0271118i
\(771\) 0.0967103 0.167507i 0.00348294 0.00603263i
\(772\) 23.8010i 0.856618i
\(773\) −5.77259 3.33281i −0.207626 0.119873i 0.392582 0.919717i \(-0.371582\pi\)
−0.600207 + 0.799844i \(0.704915\pi\)
\(774\) −2.66245 1.53717i −0.0956999 0.0552524i
\(775\) 34.5881i 1.24244i
\(776\) 2.90793 5.03669i 0.104389