Properties

Label 546.2.s.e.43.1
Level $546$
Weight $2$
Character 546.43
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 43.1
Root \(0.560908 + 1.63871i\) of defining polynomial
Character \(\chi\) \(=\) 546.43
Dual form 546.2.s.e.127.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.332808i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.332808i 0.148836i 0.997227 + 0.0744180i \(0.0237099\pi\)
−0.997227 + 0.0744180i \(0.976290\pi\)
\(6\) −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 0.800448 0.599402i \(-0.204595\pi\)
−0.118873 + 0.992909i \(0.537928\pi\)
\(12\) 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 0.528018 0.849233i \(-0.322935\pi\)
−0.999466 + 0.0326607i \(0.989602\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.85997 2.80591i 1.11495 0.643719i 0.174846 0.984596i \(-0.444057\pi\)
0.940108 + 0.340877i \(0.110724\pi\)
\(20\) −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 −0.558437 0.829547i \(-0.688599\pi\)
0.997627 + 0.0688467i \(0.0219319\pi\)
\(24\) −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 −0.805663 0.592374i \(-0.798191\pi\)
0.915843 + 0.401537i \(0.131524\pi\)
\(30\) −0.166404 0.288220i −0.0303810 0.0526215i
\(31\) 7.07434i 1.27059i 0.772270 + 0.635294i \(0.219121\pi\)
−0.772270 + 0.635294i \(0.780879\pi\)
\(32\) 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 0.540473 0.841361i \(-0.318245\pi\)
−0.458403 + 0.888744i \(0.651579\pi\)
\(38\) −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 0.534823 0.844964i \(-0.320378\pi\)
−0.464349 + 0.885652i \(0.653712\pi\)
\(42\) 0.500000 0.866025i 0.0771517 0.133631i
\(43\) 1.53717 + 2.66245i 0.234416 + 0.406020i 0.959103 0.283058i \(-0.0913489\pi\)
−0.724687 + 0.689078i \(0.758016\pi\)
\(44\) 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 \(-0.658186\pi\)
0.476753 0.879037i \(-0.341814\pi\)
\(48\) 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 0.224786 0.974408i \(-0.427832\pi\)
0.956255 + 0.292533i \(0.0944983\pi\)
\(60\) 0.332808i 0.0429653i
\(61\) −3.71989 6.44304i −0.476283 0.824947i 0.523347 0.852119i \(-0.324683\pi\)
−0.999631 + 0.0271724i \(0.991350\pi\)
\(62\) 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 0.973305 0.229517i \(-0.0737145\pi\)
0.287885 + 0.957665i \(0.407048\pi\)
\(68\) 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 −0.547757 0.836637i \(-0.684518\pi\)
0.450671 + 0.892690i \(0.351185\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 4.66562i 0.546069i −0.962004 0.273034i \(-0.911973\pi\)
0.962004 0.273034i \(-0.0880273\pi\)
\(74\) −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 \(0.271312\pi\)
−0.658215 + 0.752830i \(0.728688\pi\)
\(84\) −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 0.647063 0.762436i \(-0.275997\pi\)
−0.336758 + 0.941591i \(0.609330\pi\)
\(90\) −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 −0.733408 0.679789i \(-0.762072\pi\)
0.222010 + 0.975044i \(0.428738\pi\)
\(98\) −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 0.128569 + 0.991701i \(0.458962\pi\)
−0.923122 + 0.384506i \(0.874372\pi\)
\(102\) 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 −0.995754 0.0920593i \(-0.970655\pi\)
0.577602 + 0.816318i \(0.303988\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 18.6144i 1.78293i 0.453088 + 0.891466i \(0.350322\pi\)
−0.453088 + 0.891466i \(0.649678\pi\)
\(110\) 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 0.566515 0.824051i \(-0.308291\pi\)
−0.996907 + 0.0785911i \(0.974958\pi\)
\(114\) −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 −0.675523 0.737339i \(-0.736082\pi\)
0.976316 + 0.216350i \(0.0694153\pi\)
\(128\) 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 −0.870553 0.492075i \(-0.836238\pi\)
−0.00912669 + 0.999958i \(0.502905\pi\)
\(138\) 4.21257i 0.358598i
\(139\) −7.16056 12.4025i −0.607351 1.05196i −0.991675 0.128764i \(-0.958899\pi\)
0.384324 0.923198i \(-0.374434\pi\)
\(140\) 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 −0.699230 0.714897i \(-0.746474\pi\)
0.269504 + 0.962999i \(0.413140\pi\)
\(150\) −4.23421 + 2.44462i −0.345721 + 0.199602i
\(151\) 21.4953i 1.74926i 0.484791 + 0.874630i \(0.338896\pi\)
−0.484791 + 0.874630i \(0.661104\pi\)
\(152\) −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 −0.382398 0.923998i \(-0.624902\pi\)
0.609006 + 0.793165i \(0.291568\pi\)
\(164\) 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 0.700045 0.714099i \(-0.253163\pi\)
−0.268405 + 0.963306i \(0.586497\pi\)
\(168\) 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 −0.965741 0.259509i \(-0.916439\pi\)
0.258129 0.966110i \(-0.416894\pi\)
\(174\) 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 0.0675707 + 0.997714i \(0.478475\pi\)
−0.897831 + 0.440339i \(0.854858\pi\)
\(180\) 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 0.996329 0.0856056i \(-0.0272825\pi\)
−0.572301 + 0.820044i \(0.693949\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −20.6123 11.9005i −1.48371 0.856618i −0.483877 0.875136i \(-0.660772\pi\)
−0.999829 + 0.0185185i \(0.994105\pi\)
\(194\) 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 0.777693 0.628644i \(-0.216390\pi\)
−0.155575 + 0.987824i \(0.549723\pi\)
\(198\) −1.30512 + 2.26053i −0.0927507 + 0.160649i
\(199\) 6.92504 + 11.9945i 0.490903 + 0.850269i 0.999945 0.0104725i \(-0.00333355\pi\)
−0.509042 + 0.860742i \(0.670000\pi\)
\(200\) 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 −0.933707 0.358037i \(-0.883446\pi\)
0.776923 + 0.629596i \(0.216779\pi\)
\(212\) −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 0.235110 0.971969i \(-0.424455\pi\)
−0.724195 + 0.689596i \(0.757788\pi\)
\(224\) −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 0.619194 0.785238i \(-0.287459\pi\)
0.989633 0.143619i \(-0.0458739\pi\)
\(228\) 4.85997 2.80591i 0.321859 0.185826i
\(229\) 28.7785i 1.90174i −0.309598 0.950868i \(-0.600194\pi\)
0.309598 0.950868i \(-0.399806\pi\)
\(230\) −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 \(0.116808\pi\)
−0.933421 + 0.358783i \(0.883192\pi\)
\(240\) −0.288220 + 0.166404i −0.0186045 + 0.0107413i
\(241\) −7.02686 + 4.05696i −0.452640 + 0.261332i −0.708944 0.705264i \(-0.750828\pi\)
0.256305 + 0.966596i \(0.417495\pi\)
\(242\) 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 0.811671 0.584114i \(-0.198558\pi\)
−0.911694 + 0.410871i \(0.865225\pi\)
\(252\) 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 −0.869026 0.494766i \(-0.835254\pi\)
0.862993 + 0.505215i \(0.168587\pi\)
\(258\) −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 −0.989769 0.142677i \(-0.954429\pi\)
0.618446 + 0.785827i \(0.287762\pi\)
\(264\) −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 −0.999588 0.0286993i \(-0.990863\pi\)
0.474940 0.880018i \(-0.342470\pi\)
\(270\) −0.166404 + 0.288220i −0.0101270 + 0.0175405i
\(271\) −14.8453 8.57096i −0.901790 0.520649i −0.0240098 0.999712i \(-0.507643\pi\)
−0.877781 + 0.479063i \(0.840977\pi\)
\(272\) 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 0.527432 0.849598i \(-0.323155\pi\)
−0.999489 + 0.0319704i \(0.989822\pi\)
\(278\) 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 \(-0.961230\pi\)
0.992592 0.121499i \(-0.0387700\pi\)
\(282\) 6.02638 + 10.4380i 0.358865 + 0.621573i
\(283\) 10.7674 18.6497i 0.640057 1.10861i −0.345363 0.938469i \(-0.612244\pi\)
0.985420 0.170142i \(-0.0544226\pi\)
\(284\) −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 −0.495540 0.868585i \(-0.665030\pi\)
0.504447 + 0.863443i \(0.331697\pi\)
\(294\) 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 \(-0.798394\pi\)
0.806040 0.591861i \(-0.201606\pi\)
\(308\) −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 \(0.0956112\pi\)
−0.955227 + 0.295875i \(0.904389\pi\)
\(318\) 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 −0.832086 0.554646i \(-0.812854\pi\)
0.0642946 + 0.997931i \(0.479520\pi\)
\(332\) −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 −0.974389 0.224867i \(-0.927805\pi\)
0.292454 0.956280i \(-0.405528\pi\)
\(348\) 0.593337 1.02769i 0.0318062 0.0550900i
\(349\) −24.5419 14.1693i −1.31370 0.758463i −0.330990 0.943634i \(-0.607383\pi\)
−0.982706 + 0.185172i \(0.940716\pi\)
\(350\) 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 0.454310 0.890843i \(-0.349886\pi\)
−0.544338 + 0.838866i \(0.683219\pi\)
\(354\) −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 \(0.260399\pi\)
−0.683633 + 0.729826i \(0.739601\pi\)
\(360\) −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 −0.931329 0.364179i \(-0.881350\pi\)
0.781053 + 0.624465i \(0.214683\pi\)
\(368\) 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 −0.960609 0.277903i \(-0.910361\pi\)
0.239634 0.970863i \(-0.422973\pi\)
\(374\) −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 0.196784 0.980447i \(-0.436950\pi\)
−0.750700 + 0.660644i \(0.770283\pi\)
\(380\) −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 −0.699509 0.714624i \(-0.746598\pi\)
0.269128 + 0.963104i \(0.413265\pi\)
\(384\) 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 −0.345401 0.938455i \(-0.612257\pi\)
0.640025 + 0.768354i \(0.278924\pi\)
\(398\) 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 0.779002 0.627021i \(-0.215726\pi\)
−0.153515 + 0.988146i \(0.549059\pi\)
\(402\) −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 0.0910351 0.995848i \(-0.470982\pi\)
0.907947 + 0.419085i \(0.137649\pi\)
\(410\) 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 −0.446623 0.894722i \(-0.647374\pi\)
0.998164 0.0605740i \(-0.0192931\pi\)
\(420\) −0.166404 0.288220i −0.00811967 0.0140637i
\(421\) 34.1708i 1.66538i 0.553738 + 0.832691i \(0.313201\pi\)
−0.553738 + 0.832691i \(0.686799\pi\)
\(422\) 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 0.605235 0.796047i \(-0.293079\pi\)
−0.386779 + 0.922173i \(0.626412\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 8.41030 + 14.5671i 0.404173 + 0.700048i 0.994225 0.107317i \(-0.0342260\pi\)
−0.590052 + 0.807365i \(0.700893\pi\)
\(434\) 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 −0.986496 0.163783i \(-0.947630\pi\)
0.635088 + 0.772440i \(0.280964\pi\)
\(440\) 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 −0.906083 0.423101i \(-0.860942\pi\)
−0.0866255 + 0.996241i \(0.527608\pi\)
\(450\) 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 −0.362340 0.932046i \(-0.618022\pi\)
−0.988345 + 0.152227i \(0.951355\pi\)
\(458\) −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 −0.959164 0.282852i \(-0.908720\pi\)
−0.234625 + 0.972086i \(0.575386\pi\)
\(462\) 2.26053 1.30512i 0.105169 0.0607196i
\(463\) 36.6027i 1.70107i 0.525918 + 0.850535i \(0.323722\pi\)
−0.525918 + 0.850535i \(0.676278\pi\)
\(464\) 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 −0.343434 0.939177i \(-0.611590\pi\)
−0.985068 + 0.172165i \(0.944924\pi\)
\(480\) 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 −0.0479597 0.998849i \(-0.515272\pi\)
0.841049 + 0.540959i \(0.181939\pi\)
\(488\) −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 −0.932321 0.361632i \(-0.882220\pi\)
0.779343 + 0.626598i \(0.215553\pi\)
\(492\) 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 \(-0.920216\pi\)
0.968752 0.248033i \(-0.0797841\pi\)
\(500\) −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 0.978288 + 0.207252i \(0.0664520\pi\)
−0.309658 + 0.950848i \(0.600215\pi\)
\(504\) 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 0.962411 0.271599i \(-0.0875523\pi\)
0.245994 + 0.969271i \(0.420886\pi\)
\(510\) −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 0.240731 + 0.970592i \(0.422613\pi\)
−0.960923 + 0.276817i \(0.910720\pi\)
\(524\) 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 \(0.108276\pi\)
−0.942701 + 0.333638i \(0.891724\pi\)
\(542\) 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 −0.0106863 0.999943i \(-0.503402\pi\)
−0.871319 + 0.490717i \(0.836735\pi\)
\(558\) −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 −0.920827 0.389972i \(-0.872485\pi\)
0.122687 0.992445i \(-0.460849\pi\)
\(564\) 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 0.422557 + 0.906336i \(0.361133\pi\)
−0.996189 + 0.0872233i \(0.972201\pi\)
\(570\) −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 \(-0.923873\pi\)
0.971537 0.236886i \(-0.0761268\pi\)
\(578\) −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 0.792346 0.610072i \(-0.208859\pi\)
−0.132164 + 0.991228i \(0.542193\pi\)
\(588\) 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 \(0.130098\pi\)
−0.917633 + 0.397429i \(0.869902\pi\)
\(594\) 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 −0.998488 0.0549699i \(-0.982494\pi\)
0.546849 + 0.837231i \(0.315827\pi\)
\(602\) 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 −0.969893 0.243531i \(-0.921694\pi\)
0.274042 0.961718i \(-0.411639\pi\)
\(608\) 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 0.767061 0.641574i \(-0.221718\pi\)
−0.172089 + 0.985081i \(0.555052\pi\)
\(614\) −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 −0.166677 0.986012i \(-0.553304\pi\)
0.770573 + 0.637352i \(0.219970\pi\)
\(618\) 6.50074 3.75321i 0.261498 0.150976i
\(619\) 0.621482i 0.0249795i −0.999922 0.0124897i \(-0.996024\pi\)
0.999922 0.0124897i \(-0.00397571\pi\)
\(620\) −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 −0.247369 0.968921i \(-0.579566\pi\)
0.715426 + 0.698688i \(0.246233\pi\)
\(632\) 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 0.589250 0.807951i \(-0.299423\pi\)
−0.994331 + 0.106330i \(0.966090\pi\)
\(642\) 8.65078i 0.341419i
\(643\) −37.0253 + 21.3766i −1.46013 + 0.843009i −0.999017 0.0443295i \(-0.985885\pi\)
−0.461118 + 0.887339i \(0.652552\pi\)
\(644\) −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 0.484372 + 0.874862i \(0.339048\pi\)
−0.999839 + 0.0179521i \(0.994285\pi\)
\(648\) 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 −0.767779 0.640715i \(-0.778638\pi\)
0.938765 + 0.344558i \(0.111971\pi\)
\(654\) −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 0.861094 0.508445i \(-0.169780\pi\)
−0.870874 + 0.491507i \(0.836446\pi\)
\(660\) −0.434353 + 0.752321i −0.0169072 + 0.0292841i
\(661\) 27.1062 + 15.6498i 1.05431 + 0.608705i 0.923853 0.382749i \(-0.125022\pi\)
0.130456 + 0.991454i \(0.458356\pi\)
\(662\) 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 −0.998807 0.0488340i \(-0.984449\pi\)
0.541695 + 0.840575i \(0.317783\pi\)
\(674\) −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 −0.289448 0.957194i \(-0.593472\pi\)
0.684230 + 0.729266i \(0.260138\pi\)
\(684\) 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 0.133239 0.991084i \(-0.457462\pi\)
−0.791685 + 0.610930i \(0.790796\pi\)
\(692\) 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 0.204512 0.978864i \(-0.434439\pi\)
0.949977 + 0.312320i \(0.101106\pi\)
\(710\) 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 0.802615 0.596497i \(-0.203441\pi\)
−0.917889 + 0.396837i \(0.870108\pi\)
\(720\) 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 \(0.201479\pi\)
−0.806277 + 0.591538i \(0.798521\pi\)
\(734\) 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 0.0360848 0.999349i \(-0.488511\pi\)
−0.847419 + 0.530925i \(0.821845\pi\)
\(740\) −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 0.251734 0.967796i \(-0.418999\pi\)
−0.712269 + 0.701906i \(0.752332\pi\)
\(744\) 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 −0.467907 0.883777i \(-0.654992\pi\)
0.999327 0.0366690i \(-0.0116747\pi\)
\(752\) 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 −0.624370 0.781129i \(-0.714644\pi\)
0.988662 + 0.150156i \(0.0479776\pi\)
\(758\) 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 −0.170281 0.985396i \(-0.554468\pi\)
0.768237 + 0.640165i \(0.221134\pi\)
\(762\) 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 0.718832 0.695184i \(-0.244677\pi\)
−0.242631 + 0.970119i \(0.578010\pi\)
\(770\) −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 −0.600207 0.799844i \(-0.704915\pi\)
0.392582 + 0.919717i \(0.371582\pi\)
\(774\) −2.66245 + 1.53717i −0.0956999 + 0.0552524i
\(775\) 34.5881i 1.24244i
\(776\) 2.90793 + 5.03669i