Properties

Label 273.2.k.d.22.2
Level $273$
Weight $2$
Character 273.22
Analytic conductor $2.180$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.771147.1
Defining polynomial: \(x^{6} - x^{5} + 5 x^{4} + 6 x^{3} + 15 x^{2} + 4 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.2
Root \(-0.688601 + 1.19269i\) of defining polynomial
Character \(\chi\) \(=\) 273.22
Dual form 273.2.k.d.211.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.636945 - 1.10322i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.188601 + 0.326667i) q^{4} +1.10331 q^{5} +(-0.636945 - 1.10322i) q^{6} +(0.500000 + 0.866025i) q^{7} +3.02830 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.636945 - 1.10322i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.188601 + 0.326667i) q^{4} +1.10331 q^{5} +(-0.636945 - 1.10322i) q^{6} +(0.500000 + 0.866025i) q^{7} +3.02830 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.702750 - 1.21720i) q^{10} +(0.174453 - 0.302162i) q^{11} +0.377203 q^{12} +(-3.47664 + 0.955496i) q^{13} +1.27389 q^{14} +(0.551656 - 0.955496i) q^{15} +(1.55166 - 2.68755i) q^{16} +(-0.363055 - 0.628829i) q^{17} -1.27389 q^{18} +(-1.15109 - 1.99375i) q^{19} +(0.208086 + 0.360416i) q^{20} +1.00000 q^{21} +(-0.222234 - 0.384921i) q^{22} +(-0.0375080 + 0.0649658i) q^{23} +(1.51415 - 2.62258i) q^{24} -3.78270 q^{25} +(-1.16031 + 4.44410i) q^{26} -1.00000 q^{27} +(-0.188601 + 0.326667i) q^{28} +(-0.240258 + 0.416138i) q^{29} +(-0.702750 - 1.21720i) q^{30} -6.85772 q^{31} +(1.05166 + 1.82152i) q^{32} +(-0.174453 - 0.302162i) q^{33} -0.924984 q^{34} +(0.551656 + 0.955496i) q^{35} +(0.188601 - 0.326667i) q^{36} +(0.551656 - 0.955496i) q^{37} -2.93273 q^{38} +(-0.910836 + 3.48861i) q^{39} +3.34116 q^{40} +(-1.54778 + 2.68084i) q^{41} +(0.636945 - 1.10322i) q^{42} +(2.31140 + 4.00346i) q^{43} +0.131609 q^{44} +(-0.551656 - 0.955496i) q^{45} +(0.0477811 + 0.0827593i) q^{46} +4.70769 q^{47} +(-1.55166 - 2.68755i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.40937 + 4.17316i) q^{50} -0.726109 q^{51} +(-0.967829 - 0.955496i) q^{52} +5.54778 q^{53} +(-0.636945 + 1.10322i) q^{54} +(0.192476 - 0.333379i) q^{55} +(1.51415 + 2.62258i) q^{56} -2.30219 q^{57} +(0.306062 + 0.530115i) q^{58} +(1.96249 + 3.39914i) q^{59} +0.416173 q^{60} +(-2.77389 - 4.80452i) q^{61} +(-4.36799 + 7.56558i) q^{62} +(0.500000 - 0.866025i) q^{63} +8.88601 q^{64} +(-3.83582 + 1.05421i) q^{65} -0.444469 q^{66} +(-4.06193 + 7.03547i) q^{67} +(0.136945 - 0.237196i) q^{68} +(0.0375080 + 0.0649658i) q^{69} +1.40550 q^{70} +(4.76468 + 8.25267i) q^{71} +(-1.51415 - 2.62258i) q^{72} -10.4338 q^{73} +(-0.702750 - 1.21720i) q^{74} +(-1.89135 + 3.27592i) q^{75} +(0.434196 - 0.752049i) q^{76} +0.348907 q^{77} +(3.26855 + 3.22691i) q^{78} +17.1054 q^{79} +(1.71196 - 2.96520i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.97170 + 3.41509i) q^{82} -11.9143 q^{83} +(0.188601 + 0.326667i) q^{84} +(-0.400563 - 0.693795i) q^{85} +5.88894 q^{86} +(0.240258 + 0.416138i) q^{87} +(0.528296 - 0.915036i) q^{88} +(5.98052 - 10.3586i) q^{89} -1.40550 q^{90} +(-2.56580 - 2.53311i) q^{91} -0.0282963 q^{92} +(-3.42886 + 5.93896i) q^{93} +(2.99854 - 5.19362i) q^{94} +(-1.27002 - 2.19973i) q^{95} +2.10331 q^{96} +(-5.05166 - 8.74973i) q^{97} +(0.636945 + 1.10322i) q^{98} -0.348907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{2} + 3q^{3} - 4q^{4} - 2q^{6} + 3q^{7} - 6q^{8} - 3q^{9} + O(q^{10}) \) \( 6q + 2q^{2} + 3q^{3} - 4q^{4} - 2q^{6} + 3q^{7} - 6q^{8} - 3q^{9} - 13q^{10} + 8q^{11} - 8q^{12} + 4q^{14} + 6q^{16} - 4q^{17} - 4q^{18} + 7q^{19} + 13q^{20} + 6q^{21} - q^{22} - 9q^{23} - 3q^{24} + 22q^{25} - 26q^{26} - 6q^{27} + 4q^{28} + 7q^{29} + 13q^{30} - 14q^{31} + 3q^{32} - 8q^{33} + 12q^{34} - 4q^{36} - 8q^{38} + 26q^{40} - 2q^{41} + 2q^{42} + 19q^{43} - 30q^{44} - 7q^{46} - 34q^{47} - 6q^{48} - 3q^{49} + 16q^{50} - 8q^{51} - 26q^{52} + 26q^{53} - 2q^{54} - 3q^{56} + 14q^{57} - 22q^{58} + 3q^{59} + 26q^{60} - 13q^{61} + 17q^{62} + 3q^{63} + 2q^{64} - 2q^{66} - 5q^{67} - q^{68} + 9q^{69} - 26q^{70} - 8q^{71} + 3q^{72} - 4q^{73} + 13q^{74} + 11q^{75} + 18q^{76} + 16q^{77} - 13q^{78} - 2q^{79} + 26q^{80} - 3q^{81} + 36q^{82} + 4q^{83} - 4q^{84} - 13q^{85} + 34q^{86} - 7q^{87} - 21q^{88} + 19q^{89} + 26q^{90} + 24q^{92} - 7q^{93} - 7q^{94} + 6q^{96} - 27q^{97} + 2q^{98} - 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.636945 1.10322i 0.450388 0.780095i −0.548022 0.836464i \(-0.684619\pi\)
0.998410 + 0.0563687i \(0.0179522\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.188601 + 0.326667i 0.0943007 + 0.163334i
\(5\) 1.10331 0.493416 0.246708 0.969090i \(-0.420651\pi\)
0.246708 + 0.969090i \(0.420651\pi\)
\(6\) −0.636945 1.10322i −0.260032 0.450388i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 3.02830 1.07066
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.702750 1.21720i 0.222229 0.384912i
\(11\) 0.174453 0.302162i 0.0525996 0.0911053i −0.838527 0.544860i \(-0.816583\pi\)
0.891126 + 0.453755i \(0.149916\pi\)
\(12\) 0.377203 0.108889
\(13\) −3.47664 + 0.955496i −0.964246 + 0.265007i
\(14\) 1.27389 0.340462
\(15\) 0.551656 0.955496i 0.142437 0.246708i
\(16\) 1.55166 2.68755i 0.387914 0.671887i
\(17\) −0.363055 0.628829i −0.0880537 0.152513i 0.818635 0.574315i \(-0.194731\pi\)
−0.906688 + 0.421801i \(0.861398\pi\)
\(18\) −1.27389 −0.300259
\(19\) −1.15109 1.99375i −0.264079 0.457398i 0.703243 0.710950i \(-0.251735\pi\)
−0.967322 + 0.253551i \(0.918401\pi\)
\(20\) 0.208086 + 0.360416i 0.0465295 + 0.0805915i
\(21\) 1.00000 0.218218
\(22\) −0.222234 0.384921i −0.0473805 0.0820655i
\(23\) −0.0375080 + 0.0649658i −0.00782096 + 0.0135463i −0.869909 0.493212i \(-0.835823\pi\)
0.862088 + 0.506758i \(0.169156\pi\)
\(24\) 1.51415 2.62258i 0.309074 0.535332i
\(25\) −3.78270 −0.756540
\(26\) −1.16031 + 4.44410i −0.227555 + 0.871560i
\(27\) −1.00000 −0.192450
\(28\) −0.188601 + 0.326667i −0.0356423 + 0.0617343i
\(29\) −0.240258 + 0.416138i −0.0446147 + 0.0772749i −0.887470 0.460865i \(-0.847539\pi\)
0.842856 + 0.538140i \(0.180873\pi\)
\(30\) −0.702750 1.21720i −0.128304 0.222229i
\(31\) −6.85772 −1.23168 −0.615841 0.787870i \(-0.711184\pi\)
−0.615841 + 0.787870i \(0.711184\pi\)
\(32\) 1.05166 + 1.82152i 0.185908 + 0.322003i
\(33\) −0.174453 0.302162i −0.0303684 0.0525996i
\(34\) −0.924984 −0.158633
\(35\) 0.551656 + 0.955496i 0.0932469 + 0.161508i
\(36\) 0.188601 0.326667i 0.0314336 0.0544445i
\(37\) 0.551656 0.955496i 0.0906917 0.157083i −0.817111 0.576481i \(-0.804426\pi\)
0.907802 + 0.419398i \(0.137759\pi\)
\(38\) −2.93273 −0.475752
\(39\) −0.910836 + 3.48861i −0.145850 + 0.558624i
\(40\) 3.34116 0.528283
\(41\) −1.54778 + 2.68084i −0.241723 + 0.418676i −0.961205 0.275835i \(-0.911046\pi\)
0.719482 + 0.694511i \(0.244379\pi\)
\(42\) 0.636945 1.10322i 0.0982828 0.170231i
\(43\) 2.31140 + 4.00346i 0.352485 + 0.610522i 0.986684 0.162648i \(-0.0520034\pi\)
−0.634199 + 0.773170i \(0.718670\pi\)
\(44\) 0.131609 0.0198407
\(45\) −0.551656 0.955496i −0.0822360 0.142437i
\(46\) 0.0477811 + 0.0827593i 0.00704494 + 0.0122022i
\(47\) 4.70769 0.686687 0.343343 0.939210i \(-0.388441\pi\)
0.343343 + 0.939210i \(0.388441\pi\)
\(48\) −1.55166 2.68755i −0.223962 0.387914i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −2.40937 + 4.17316i −0.340737 + 0.590174i
\(51\) −0.726109 −0.101676
\(52\) −0.967829 0.955496i −0.134214 0.132504i
\(53\) 5.54778 0.762046 0.381023 0.924565i \(-0.375572\pi\)
0.381023 + 0.924565i \(0.375572\pi\)
\(54\) −0.636945 + 1.10322i −0.0866773 + 0.150129i
\(55\) 0.192476 0.333379i 0.0259535 0.0449528i
\(56\) 1.51415 + 2.62258i 0.202337 + 0.350457i
\(57\) −2.30219 −0.304932
\(58\) 0.306062 + 0.530115i 0.0401879 + 0.0696075i
\(59\) 1.96249 + 3.39914i 0.255495 + 0.442530i 0.965030 0.262140i \(-0.0844283\pi\)
−0.709535 + 0.704670i \(0.751095\pi\)
\(60\) 0.416173 0.0537276
\(61\) −2.77389 4.80452i −0.355160 0.615156i 0.631985 0.774981i \(-0.282240\pi\)
−0.987145 + 0.159825i \(0.948907\pi\)
\(62\) −4.36799 + 7.56558i −0.554735 + 0.960830i
\(63\) 0.500000 0.866025i 0.0629941 0.109109i
\(64\) 8.88601 1.11075
\(65\) −3.83582 + 1.05421i −0.475775 + 0.130759i
\(66\) −0.444469 −0.0547103
\(67\) −4.06193 + 7.03547i −0.496244 + 0.859519i −0.999991 0.00433206i \(-0.998621\pi\)
0.503747 + 0.863851i \(0.331954\pi\)
\(68\) 0.136945 0.237196i 0.0166071 0.0287643i
\(69\) 0.0375080 + 0.0649658i 0.00451543 + 0.00782096i
\(70\) 1.40550 0.167989
\(71\) 4.76468 + 8.25267i 0.565463 + 0.979411i 0.997006 + 0.0773189i \(0.0246360\pi\)
−0.431543 + 0.902092i \(0.642031\pi\)
\(72\) −1.51415 2.62258i −0.178444 0.309074i
\(73\) −10.4338 −1.22118 −0.610592 0.791946i \(-0.709068\pi\)
−0.610592 + 0.791946i \(0.709068\pi\)
\(74\) −0.702750 1.21720i −0.0816930 0.141496i
\(75\) −1.89135 + 3.27592i −0.218394 + 0.378270i
\(76\) 0.434196 0.752049i 0.0498057 0.0862659i
\(77\) 0.348907 0.0397616
\(78\) 3.26855 + 3.22691i 0.370091 + 0.365375i
\(79\) 17.1054 1.92451 0.962256 0.272146i \(-0.0877335\pi\)
0.962256 + 0.272146i \(0.0877335\pi\)
\(80\) 1.71196 2.96520i 0.191403 0.331520i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.97170 + 3.41509i 0.217738 + 0.377134i
\(83\) −11.9143 −1.30777 −0.653883 0.756596i \(-0.726861\pi\)
−0.653883 + 0.756596i \(0.726861\pi\)
\(84\) 0.188601 + 0.326667i 0.0205781 + 0.0356423i
\(85\) −0.400563 0.693795i −0.0434471 0.0752526i
\(86\) 5.88894 0.635020
\(87\) 0.240258 + 0.416138i 0.0257583 + 0.0446147i
\(88\) 0.528296 0.915036i 0.0563166 0.0975432i
\(89\) 5.98052 10.3586i 0.633933 1.09800i −0.352807 0.935696i \(-0.614773\pi\)
0.986740 0.162309i \(-0.0518940\pi\)
\(90\) −1.40550 −0.148153
\(91\) −2.56580 2.53311i −0.268969 0.265542i
\(92\) −0.0282963 −0.00295009
\(93\) −3.42886 + 5.93896i −0.355556 + 0.615841i
\(94\) 2.99854 5.19362i 0.309276 0.535681i
\(95\) −1.27002 2.19973i −0.130301 0.225688i
\(96\) 2.10331 0.214668
\(97\) −5.05166 8.74973i −0.512918 0.888400i −0.999888 0.0149812i \(-0.995231\pi\)
0.486970 0.873419i \(-0.338102\pi\)
\(98\) 0.636945 + 1.10322i 0.0643412 + 0.111442i
\(99\) −0.348907 −0.0350664
\(100\) −0.713423 1.23568i −0.0713423 0.123568i
\(101\) −2.03751 + 3.52907i −0.202740 + 0.351155i −0.949410 0.314039i \(-0.898318\pi\)
0.746671 + 0.665194i \(0.231651\pi\)
\(102\) −0.462492 + 0.801060i −0.0457935 + 0.0793167i
\(103\) −4.11106 −0.405075 −0.202538 0.979275i \(-0.564919\pi\)
−0.202538 + 0.979275i \(0.564919\pi\)
\(104\) −10.5283 + 2.89353i −1.03238 + 0.283734i
\(105\) 1.10331 0.107672
\(106\) 3.53363 6.12043i 0.343217 0.594469i
\(107\) 3.08529 5.34388i 0.298266 0.516612i −0.677473 0.735547i \(-0.736925\pi\)
0.975739 + 0.218935i \(0.0702584\pi\)
\(108\) −0.188601 0.326667i −0.0181482 0.0314336i
\(109\) −8.82167 −0.844963 −0.422481 0.906372i \(-0.638841\pi\)
−0.422481 + 0.906372i \(0.638841\pi\)
\(110\) −0.245194 0.424688i −0.0233783 0.0404924i
\(111\) −0.551656 0.955496i −0.0523609 0.0906917i
\(112\) 3.10331 0.293235
\(113\) −6.00494 10.4009i −0.564897 0.978430i −0.997059 0.0766343i \(-0.975583\pi\)
0.432162 0.901796i \(-0.357751\pi\)
\(114\) −1.46637 + 2.53982i −0.137338 + 0.237876i
\(115\) −0.0413831 + 0.0716776i −0.00385899 + 0.00668397i
\(116\) −0.181252 −0.0168288
\(117\) 2.56580 + 2.53311i 0.237209 + 0.234186i
\(118\) 5.00000 0.460287
\(119\) 0.363055 0.628829i 0.0332812 0.0576447i
\(120\) 1.67058 2.89353i 0.152502 0.264142i
\(121\) 5.43913 + 9.42085i 0.494467 + 0.856441i
\(122\) −7.06727 −0.639840
\(123\) 1.54778 + 2.68084i 0.139559 + 0.241723i
\(124\) −1.29338 2.24019i −0.116149 0.201175i
\(125\) −9.69006 −0.866706
\(126\) −0.636945 1.10322i −0.0567436 0.0982828i
\(127\) 2.92886 5.07293i 0.259894 0.450150i −0.706319 0.707894i \(-0.749646\pi\)
0.966213 + 0.257744i \(0.0829790\pi\)
\(128\) 3.55659 6.16020i 0.314361 0.544490i
\(129\) 4.62280 0.407015
\(130\) −1.28018 + 4.90323i −0.112279 + 0.430042i
\(131\) 22.4055 1.95758 0.978789 0.204872i \(-0.0656778\pi\)
0.978789 + 0.204872i \(0.0656778\pi\)
\(132\) 0.0658043 0.113976i 0.00572753 0.00992037i
\(133\) 1.15109 1.99375i 0.0998125 0.172880i
\(134\) 5.17445 + 8.96242i 0.447005 + 0.774235i
\(135\) −1.10331 −0.0949580
\(136\) −1.09944 1.90428i −0.0942760 0.163291i
\(137\) −10.1044 17.5013i −0.863275 1.49524i −0.868750 0.495251i \(-0.835076\pi\)
0.00547505 0.999985i \(-0.498257\pi\)
\(138\) 0.0955622 0.00813480
\(139\) −2.13695 3.70130i −0.181253 0.313940i 0.761054 0.648688i \(-0.224682\pi\)
−0.942308 + 0.334748i \(0.891349\pi\)
\(140\) −0.208086 + 0.360416i −0.0175865 + 0.0304607i
\(141\) 2.35384 4.07698i 0.198229 0.343343i
\(142\) 12.1394 1.01871
\(143\) −0.317797 + 1.21720i −0.0265755 + 0.101787i
\(144\) −3.10331 −0.258609
\(145\) −0.265079 + 0.459131i −0.0220136 + 0.0381287i
\(146\) −6.64576 + 11.5108i −0.550007 + 0.952640i
\(147\) 0.500000 + 0.866025i 0.0412393 + 0.0714286i
\(148\) 0.416173 0.0342092
\(149\) 2.44834 + 4.24066i 0.200576 + 0.347408i 0.948714 0.316135i \(-0.102385\pi\)
−0.748138 + 0.663543i \(0.769052\pi\)
\(150\) 2.40937 + 4.17316i 0.196725 + 0.340737i
\(151\) −8.94553 −0.727977 −0.363988 0.931403i \(-0.618585\pi\)
−0.363988 + 0.931403i \(0.618585\pi\)
\(152\) −3.48585 6.03767i −0.282740 0.489720i
\(153\) −0.363055 + 0.628829i −0.0293512 + 0.0508378i
\(154\) 0.222234 0.384921i 0.0179082 0.0310178i
\(155\) −7.56620 −0.607732
\(156\) −1.31140 + 0.360416i −0.104996 + 0.0288564i
\(157\) 6.59450 0.526298 0.263149 0.964755i \(-0.415239\pi\)
0.263149 + 0.964755i \(0.415239\pi\)
\(158\) 10.8952 18.8711i 0.866778 1.50130i
\(159\) 2.77389 4.80452i 0.219984 0.381023i
\(160\) 1.16031 + 2.00971i 0.0917302 + 0.158881i
\(161\) −0.0750160 −0.00591209
\(162\) 0.636945 + 1.10322i 0.0500431 + 0.0866773i
\(163\) 4.95222 + 8.57749i 0.387888 + 0.671841i 0.992165 0.124933i \(-0.0398715\pi\)
−0.604277 + 0.796774i \(0.706538\pi\)
\(164\) −1.16765 −0.0911785
\(165\) −0.192476 0.333379i −0.0149843 0.0259535i
\(166\) −7.58876 + 13.1441i −0.589002 + 1.02018i
\(167\) 8.37826 14.5116i 0.648330 1.12294i −0.335192 0.942150i \(-0.608801\pi\)
0.983522 0.180790i \(-0.0578654\pi\)
\(168\) 3.02830 0.233638
\(169\) 11.1741 6.64383i 0.859543 0.511064i
\(170\) −1.02055 −0.0782723
\(171\) −1.15109 + 1.99375i −0.0880263 + 0.152466i
\(172\) −0.871866 + 1.51012i −0.0664792 + 0.115145i
\(173\) −6.85918 11.8804i −0.521494 0.903254i −0.999687 0.0249993i \(-0.992042\pi\)
0.478194 0.878254i \(-0.341292\pi\)
\(174\) 0.612124 0.0464050
\(175\) −1.89135 3.27592i −0.142973 0.247636i
\(176\) −0.541383 0.937703i −0.0408083 0.0706820i
\(177\) 3.92498 0.295020
\(178\) −7.61852 13.1957i −0.571032 0.989057i
\(179\) 11.0152 19.0789i 0.823315 1.42602i −0.0798846 0.996804i \(-0.525455\pi\)
0.903200 0.429220i \(-0.141211\pi\)
\(180\) 0.208086 0.360416i 0.0155098 0.0268638i
\(181\) 9.43380 0.701208 0.350604 0.936524i \(-0.385976\pi\)
0.350604 + 0.936524i \(0.385976\pi\)
\(182\) −4.42886 + 1.21720i −0.328289 + 0.0902247i
\(183\) −5.54778 −0.410104
\(184\) −0.113585 + 0.196736i −0.00837363 + 0.0145035i
\(185\) 0.608649 1.05421i 0.0447488 0.0775071i
\(186\) 4.36799 + 7.56558i 0.320277 + 0.554735i
\(187\) −0.253344 −0.0185264
\(188\) 0.887876 + 1.53785i 0.0647550 + 0.112159i
\(189\) −0.500000 0.866025i −0.0363696 0.0629941i
\(190\) −3.23572 −0.234744
\(191\) 1.68860 + 2.92474i 0.122183 + 0.211627i 0.920628 0.390440i \(-0.127677\pi\)
−0.798445 + 0.602067i \(0.794344\pi\)
\(192\) 4.44301 7.69551i 0.320646 0.555376i
\(193\) −11.1614 + 19.3321i −0.803413 + 1.39155i 0.113945 + 0.993487i \(0.463651\pi\)
−0.917357 + 0.398065i \(0.869682\pi\)
\(194\) −12.8705 −0.924049
\(195\) −1.00494 + 3.84902i −0.0719650 + 0.275634i
\(196\) −0.377203 −0.0269431
\(197\) 12.7257 22.0416i 0.906669 1.57040i 0.0880085 0.996120i \(-0.471950\pi\)
0.818661 0.574277i \(-0.194717\pi\)
\(198\) −0.222234 + 0.384921i −0.0157935 + 0.0273552i
\(199\) 11.1702 + 19.3473i 0.791833 + 1.37149i 0.924831 + 0.380379i \(0.124206\pi\)
−0.132998 + 0.991116i \(0.542460\pi\)
\(200\) −11.4551 −0.810001
\(201\) 4.06193 + 7.03547i 0.286506 + 0.496244i
\(202\) 2.59556 + 4.49565i 0.182623 + 0.316313i
\(203\) −0.480515 −0.0337256
\(204\) −0.136945 0.237196i −0.00958809 0.0166071i
\(205\) −1.70769 + 2.95780i −0.119270 + 0.206582i
\(206\) −2.61852 + 4.53541i −0.182441 + 0.315997i
\(207\) 0.0750160 0.00521397
\(208\) −2.82661 + 10.8262i −0.195990 + 0.750664i
\(209\) −0.803248 −0.0555618
\(210\) 0.702750 1.21720i 0.0484943 0.0839946i
\(211\) −5.01908 + 8.69331i −0.345528 + 0.598472i −0.985450 0.169968i \(-0.945634\pi\)
0.639922 + 0.768440i \(0.278967\pi\)
\(212\) 1.04632 + 1.81228i 0.0718615 + 0.124468i
\(213\) 9.52936 0.652941
\(214\) −3.93032 6.80752i −0.268671 0.465352i
\(215\) 2.55019 + 4.41707i 0.173922 + 0.301241i
\(216\) −3.02830 −0.206049
\(217\) −3.42886 5.93896i −0.232766 0.403163i
\(218\) −5.61892 + 9.73226i −0.380561 + 0.659152i
\(219\) −5.21690 + 9.03593i −0.352525 + 0.610592i
\(220\) 0.145205 0.00978974
\(221\) 1.86305 + 1.83932i 0.125323 + 0.123726i
\(222\) −1.40550 −0.0943309
\(223\) 2.56727 4.44664i 0.171917 0.297769i −0.767173 0.641440i \(-0.778337\pi\)
0.939090 + 0.343671i \(0.111671\pi\)
\(224\) −1.05166 + 1.82152i −0.0702667 + 0.121706i
\(225\) 1.89135 + 3.27592i 0.126090 + 0.218394i
\(226\) −15.2993 −1.01769
\(227\) 14.4855 + 25.0895i 0.961433 + 1.66525i 0.718907 + 0.695106i \(0.244643\pi\)
0.242526 + 0.970145i \(0.422024\pi\)
\(228\) −0.434196 0.752049i −0.0287553 0.0498057i
\(229\) 0.679390 0.0448953 0.0224477 0.999748i \(-0.492854\pi\)
0.0224477 + 0.999748i \(0.492854\pi\)
\(230\) 0.0527175 + 0.0913094i 0.00347609 + 0.00602076i
\(231\) 0.174453 0.302162i 0.0114782 0.0198808i
\(232\) −0.727571 + 1.26019i −0.0477674 + 0.0827355i
\(233\) −18.3022 −1.19902 −0.599508 0.800369i \(-0.704637\pi\)
−0.599508 + 0.800369i \(0.704637\pi\)
\(234\) 4.42886 1.21720i 0.289524 0.0795707i
\(235\) 5.19405 0.338822
\(236\) −0.740258 + 1.28216i −0.0481867 + 0.0834618i
\(237\) 8.55272 14.8137i 0.555559 0.962256i
\(238\) −0.462492 0.801060i −0.0299789 0.0519250i
\(239\) −5.45222 −0.352675 −0.176337 0.984330i \(-0.556425\pi\)
−0.176337 + 0.984330i \(0.556425\pi\)
\(240\) −1.71196 2.96520i −0.110507 0.191403i
\(241\) 7.73105 + 13.3906i 0.498000 + 0.862562i 0.999997 0.00230736i \(-0.000734455\pi\)
−0.501997 + 0.864869i \(0.667401\pi\)
\(242\) 13.8577 0.890808
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 1.04632 1.81228i 0.0669837 0.116019i
\(245\) −0.551656 + 0.955496i −0.0352440 + 0.0610444i
\(246\) 3.94341 0.251422
\(247\) 5.90696 + 5.83169i 0.375851 + 0.371062i
\(248\) −20.7672 −1.31872
\(249\) −5.95716 + 10.3181i −0.377519 + 0.653883i
\(250\) −6.17204 + 10.6903i −0.390354 + 0.676113i
\(251\) 4.14722 + 7.18319i 0.261770 + 0.453399i 0.966712 0.255866i \(-0.0823604\pi\)
−0.704942 + 0.709265i \(0.749027\pi\)
\(252\) 0.377203 0.0237615
\(253\) 0.0130868 + 0.0226670i 0.000822760 + 0.00142506i
\(254\) −3.73105 6.46236i −0.234107 0.405485i
\(255\) −0.801125 −0.0501684
\(256\) 4.35530 + 7.54361i 0.272207 + 0.471476i
\(257\) 7.51908 13.0234i 0.469028 0.812380i −0.530346 0.847782i \(-0.677938\pi\)
0.999373 + 0.0354019i \(0.0112711\pi\)
\(258\) 2.94447 5.09997i 0.183315 0.317510i
\(259\) 1.10331 0.0685565
\(260\) −1.06782 1.05421i −0.0662232 0.0653794i
\(261\) 0.480515 0.0297431
\(262\) 14.2711 24.7182i 0.881670 1.52710i
\(263\) 8.62240 14.9344i 0.531680 0.920896i −0.467636 0.883921i \(-0.654894\pi\)
0.999316 0.0369754i \(-0.0117723\pi\)
\(264\) −0.528296 0.915036i −0.0325144 0.0563166i
\(265\) 6.12094 0.376006
\(266\) −1.46637 2.53982i −0.0899087 0.155726i
\(267\) −5.98052 10.3586i −0.366002 0.633933i
\(268\) −3.06434 −0.187185
\(269\) 12.1472 + 21.0396i 0.740629 + 1.28281i 0.952209 + 0.305446i \(0.0988057\pi\)
−0.211580 + 0.977361i \(0.567861\pi\)
\(270\) −0.702750 + 1.21720i −0.0427680 + 0.0740763i
\(271\) −9.16630 + 15.8765i −0.556813 + 0.964429i 0.440947 + 0.897533i \(0.354643\pi\)
−0.997760 + 0.0668956i \(0.978691\pi\)
\(272\) −2.25334 −0.136629
\(273\) −3.47664 + 0.955496i −0.210416 + 0.0578293i
\(274\) −25.7437 −1.55524
\(275\) −0.659905 + 1.14299i −0.0397938 + 0.0689248i
\(276\) −0.0141481 + 0.0245053i −0.000851617 + 0.00147504i
\(277\) −4.22717 7.32167i −0.253986 0.439917i 0.710634 0.703562i \(-0.248408\pi\)
−0.964620 + 0.263646i \(0.915075\pi\)
\(278\) −5.44447 −0.326538
\(279\) 3.42886 + 5.93896i 0.205280 + 0.355556i
\(280\) 1.67058 + 2.89353i 0.0998361 + 0.172921i
\(281\) −25.0120 −1.49209 −0.746045 0.665895i \(-0.768050\pi\)
−0.746045 + 0.665895i \(0.768050\pi\)
\(282\) −2.99854 5.19362i −0.178560 0.309276i
\(283\) −13.5707 + 23.5052i −0.806697 + 1.39724i 0.108443 + 0.994103i \(0.465414\pi\)
−0.915140 + 0.403137i \(0.867920\pi\)
\(284\) −1.79725 + 3.11293i −0.106647 + 0.184718i
\(285\) −2.54003 −0.150458
\(286\) 1.14042 + 1.12589i 0.0674344 + 0.0665752i
\(287\) −3.09556 −0.182725
\(288\) 1.05166 1.82152i 0.0619694 0.107334i
\(289\) 8.23638 14.2658i 0.484493 0.839167i
\(290\) 0.337682 + 0.584882i 0.0198294 + 0.0343455i
\(291\) −10.1033 −0.592267
\(292\) −1.96783 3.40838i −0.115158 0.199460i
\(293\) 5.27002 + 9.12793i 0.307878 + 0.533260i 0.977898 0.209083i \(-0.0670479\pi\)
−0.670020 + 0.742343i \(0.733715\pi\)
\(294\) 1.27389 0.0742948
\(295\) 2.16524 + 3.75031i 0.126065 + 0.218351i
\(296\) 1.67058 2.89353i 0.0971004 0.168183i
\(297\) −0.174453 + 0.302162i −0.0101228 + 0.0175332i
\(298\) 6.23784 0.361349
\(299\) 0.0683273 0.261701i 0.00395147 0.0151346i
\(300\) −1.42685 −0.0823790
\(301\) −2.31140 + 4.00346i −0.133227 + 0.230756i
\(302\) −5.69781 + 9.86890i −0.327872 + 0.567891i
\(303\) 2.03751 + 3.52907i 0.117052 + 0.202740i
\(304\) −7.14440 −0.409760
\(305\) −3.06047 5.30089i −0.175242 0.303528i
\(306\) 0.462492 + 0.801060i 0.0264389 + 0.0457935i
\(307\) −4.40842 −0.251602 −0.125801 0.992055i \(-0.540150\pi\)
−0.125801 + 0.992055i \(0.540150\pi\)
\(308\) 0.0658043 + 0.113976i 0.00374955 + 0.00649441i
\(309\) −2.05553 + 3.56028i −0.116935 + 0.202538i
\(310\) −4.81926 + 8.34720i −0.273715 + 0.474089i
\(311\) −2.32836 −0.132029 −0.0660146 0.997819i \(-0.521028\pi\)
−0.0660146 + 0.997819i \(0.521028\pi\)
\(312\) −2.75828 + 10.5645i −0.156157 + 0.598099i
\(313\) 12.6687 0.716078 0.358039 0.933707i \(-0.383445\pi\)
0.358039 + 0.933707i \(0.383445\pi\)
\(314\) 4.20034 7.27520i 0.237039 0.410563i
\(315\) 0.551656 0.955496i 0.0310823 0.0538361i
\(316\) 3.22611 + 5.58779i 0.181483 + 0.314337i
\(317\) −12.2915 −0.690360 −0.345180 0.938536i \(-0.612182\pi\)
−0.345180 + 0.938536i \(0.612182\pi\)
\(318\) −3.53363 6.12043i −0.198156 0.343217i
\(319\) 0.0838275 + 0.145193i 0.00469344 + 0.00812927i
\(320\) 9.80405 0.548063
\(321\) −3.08529 5.34388i −0.172204 0.298266i
\(322\) −0.0477811 + 0.0827593i −0.00266274 + 0.00461200i
\(323\) −0.835820 + 1.44768i −0.0465063 + 0.0805512i
\(324\) −0.377203 −0.0209557
\(325\) 13.1511 3.61436i 0.729491 0.200489i
\(326\) 12.6172 0.698800
\(327\) −4.41084 + 7.63979i −0.243920 + 0.422481i
\(328\) −4.68714 + 8.11836i −0.258804 + 0.448262i
\(329\) 2.35384 + 4.07698i 0.129772 + 0.224771i
\(330\) −0.490388 −0.0269950
\(331\) −6.64576 11.5108i −0.365284 0.632690i 0.623538 0.781793i \(-0.285695\pi\)
−0.988822 + 0.149103i \(0.952361\pi\)
\(332\) −2.24706 3.89202i −0.123323 0.213602i
\(333\) −1.10331 −0.0604611
\(334\) −10.6730 18.4862i −0.584000 1.01152i
\(335\) −4.48158 + 7.76232i −0.244855 + 0.424101i
\(336\) 1.55166 2.68755i 0.0846498 0.146618i
\(337\) −3.40550 −0.185509 −0.0927547 0.995689i \(-0.529567\pi\)
−0.0927547 + 0.995689i \(0.529567\pi\)
\(338\) −0.212362 16.5592i −0.0115510 0.900703i
\(339\) −12.0099 −0.652287
\(340\) 0.151093 0.261701i 0.00819419 0.0141928i
\(341\) −1.19635 + 2.07214i −0.0647861 + 0.112213i
\(342\) 1.46637 + 2.53982i 0.0792920 + 0.137338i
\(343\) −1.00000 −0.0539949
\(344\) 6.99960 + 12.1237i 0.377393 + 0.653664i
\(345\) 0.0413831 + 0.0716776i 0.00222799 + 0.00385899i
\(346\) −17.4757 −0.939499
\(347\) 16.7491 + 29.0102i 0.899137 + 1.55735i 0.828599 + 0.559842i \(0.189138\pi\)
0.0705378 + 0.997509i \(0.477528\pi\)
\(348\) −0.0906258 + 0.156969i −0.00485806 + 0.00841440i
\(349\) 14.0902 24.4050i 0.754232 1.30637i −0.191523 0.981488i \(-0.561342\pi\)
0.945755 0.324881i \(-0.105324\pi\)
\(350\) −4.81875 −0.257573
\(351\) 3.47664 0.955496i 0.185569 0.0510006i
\(352\) 0.733860 0.0391148
\(353\) 1.49612 2.59136i 0.0796307 0.137924i −0.823460 0.567374i \(-0.807959\pi\)
0.903091 + 0.429450i \(0.141293\pi\)
\(354\) 2.50000 4.33013i 0.132874 0.230144i
\(355\) 5.25693 + 9.10527i 0.279009 + 0.483257i
\(356\) 4.51173 0.239121
\(357\) −0.363055 0.628829i −0.0192149 0.0332812i
\(358\) −14.0322 24.3044i −0.741623 1.28453i
\(359\) 3.80888 0.201025 0.100512 0.994936i \(-0.467952\pi\)
0.100512 + 0.994936i \(0.467952\pi\)
\(360\) −1.67058 2.89353i −0.0880472 0.152502i
\(361\) 6.84997 11.8645i 0.360525 0.624447i
\(362\) 6.00881 10.4076i 0.315816 0.547010i
\(363\) 10.8783 0.570961
\(364\) 0.343570 1.31591i 0.0180080 0.0689726i
\(365\) −11.5117 −0.602552
\(366\) −3.53363 + 6.12043i −0.184706 + 0.319920i
\(367\) 13.2257 22.9076i 0.690376 1.19577i −0.281338 0.959609i \(-0.590778\pi\)
0.971715 0.236158i \(-0.0758884\pi\)
\(368\) 0.116399 + 0.201609i 0.00606772 + 0.0105096i
\(369\) 3.09556 0.161149
\(370\) −0.775352 1.34295i −0.0403086 0.0698166i
\(371\) 2.77389 + 4.80452i 0.144013 + 0.249438i
\(372\) −2.58675 −0.134117
\(373\) −1.06580 1.84603i −0.0551853 0.0955837i 0.837113 0.547030i \(-0.184242\pi\)
−0.892298 + 0.451446i \(0.850908\pi\)
\(374\) −0.161367 + 0.279495i −0.00834406 + 0.0144523i
\(375\) −4.84503 + 8.39184i −0.250196 + 0.433353i
\(376\) 14.2563 0.735211
\(377\) 0.437670 1.67633i 0.0225412 0.0863353i
\(378\) −1.27389 −0.0655219
\(379\) 6.97170 12.0753i 0.358112 0.620269i −0.629533 0.776974i \(-0.716754\pi\)
0.987645 + 0.156705i \(0.0500871\pi\)
\(380\) 0.479053 0.829745i 0.0245749 0.0425650i
\(381\) −2.92886 5.07293i −0.150050 0.259894i
\(382\) 4.30219 0.220119
\(383\) 9.30219 + 16.1119i 0.475320 + 0.823278i 0.999600 0.0282678i \(-0.00899913\pi\)
−0.524281 + 0.851545i \(0.675666\pi\)
\(384\) −3.55659 6.16020i −0.181497 0.314361i
\(385\) 0.384953 0.0196190
\(386\) 14.2184 + 24.6269i 0.723695 + 1.25348i
\(387\) 2.31140 4.00346i 0.117495 0.203507i
\(388\) 1.90550 3.30042i 0.0967371 0.167554i
\(389\) −1.23009 −0.0623682 −0.0311841 0.999514i \(-0.509928\pi\)
−0.0311841 + 0.999514i \(0.509928\pi\)
\(390\) 3.60624 + 3.56028i 0.182609 + 0.180282i
\(391\) 0.0544699 0.00275466
\(392\) −1.51415 + 2.62258i −0.0764760 + 0.132460i
\(393\) 11.2027 19.4037i 0.565104 0.978789i
\(394\) −16.2112 28.0786i −0.816706 1.41458i
\(395\) 18.8726 0.949585
\(396\) −0.0658043 0.113976i −0.00330679 0.00572753i
\(397\) −14.8071 25.6467i −0.743148 1.28717i −0.951055 0.309022i \(-0.899998\pi\)
0.207907 0.978149i \(-0.433335\pi\)
\(398\) 28.4592 1.42653
\(399\) −1.15109 1.99375i −0.0576267 0.0998125i
\(400\) −5.86945 + 10.1662i −0.293473 + 0.508310i
\(401\) −4.09023 + 7.08448i −0.204256 + 0.353782i −0.949895 0.312568i \(-0.898811\pi\)
0.745639 + 0.666350i \(0.232144\pi\)
\(402\) 10.3489 0.516157
\(403\) 23.8418 6.55253i 1.18765 0.326405i
\(404\) −1.53711 −0.0764740
\(405\) −0.551656 + 0.955496i −0.0274120 + 0.0474790i
\(406\) −0.306062 + 0.530115i −0.0151896 + 0.0263092i
\(407\) −0.192476 0.333379i −0.00954070 0.0165250i
\(408\) −2.19887 −0.108861
\(409\) −5.03363 8.71851i −0.248897 0.431102i 0.714323 0.699816i \(-0.246735\pi\)
−0.963220 + 0.268714i \(0.913401\pi\)
\(410\) 2.17540 + 3.76791i 0.107436 + 0.186084i
\(411\) −20.2087 −0.996824
\(412\) −0.775352 1.34295i −0.0381989 0.0661624i
\(413\) −1.96249 + 3.39914i −0.0965679 + 0.167261i
\(414\) 0.0477811 0.0827593i 0.00234831 0.00406740i
\(415\) −13.1452 −0.645273
\(416\) −5.39669 5.32792i −0.264594 0.261223i
\(417\) −4.27389 −0.209293
\(418\) −0.511625 + 0.886161i −0.0250244 + 0.0433435i
\(419\) −4.72998 + 8.19257i −0.231075 + 0.400233i −0.958125 0.286351i \(-0.907558\pi\)
0.727050 + 0.686585i \(0.240891\pi\)
\(420\) 0.208086 + 0.360416i 0.0101536 + 0.0175865i
\(421\) 31.0643 1.51398 0.756992 0.653424i \(-0.226668\pi\)
0.756992 + 0.653424i \(0.226668\pi\)
\(422\) 6.39376 + 11.0743i 0.311244 + 0.539090i
\(423\) −2.35384 4.07698i −0.114448 0.198229i
\(424\) 16.8003 0.815896
\(425\) 1.37333 + 2.37867i 0.0666162 + 0.115383i
\(426\) 6.06968 10.5130i 0.294077 0.509356i
\(427\) 2.77389 4.80452i 0.134238 0.232507i
\(428\) 2.32756 0.112507
\(429\) 0.895226 + 0.883819i 0.0432219 + 0.0426712i
\(430\) 6.49734 0.313329
\(431\) 12.6093 21.8400i 0.607369 1.05199i −0.384303 0.923207i \(-0.625558\pi\)
0.991672 0.128787i \(-0.0411084\pi\)
\(432\) −1.55166 + 2.68755i −0.0746541 + 0.129305i
\(433\) −1.88495 3.26483i −0.0905851 0.156898i 0.817172 0.576393i \(-0.195540\pi\)
−0.907757 + 0.419495i \(0.862207\pi\)
\(434\) −8.73598 −0.419341
\(435\) 0.265079 + 0.459131i 0.0127096 + 0.0220136i
\(436\) −1.66378 2.88175i −0.0796806 0.138011i
\(437\) 0.172701 0.00826141
\(438\) 6.64576 + 11.5108i 0.317547 + 0.550007i
\(439\) 11.3174 19.6023i 0.540150 0.935567i −0.458745 0.888568i \(-0.651701\pi\)
0.998895 0.0469991i \(-0.0149658\pi\)
\(440\) 0.582876 1.00957i 0.0277875 0.0481294i
\(441\) 1.00000 0.0476190
\(442\) 3.21584 0.883819i 0.152962 0.0420390i
\(443\) 4.64334 0.220612 0.110306 0.993898i \(-0.464817\pi\)
0.110306 + 0.993898i \(0.464817\pi\)
\(444\) 0.208086 0.360416i 0.00987534 0.0171046i
\(445\) 6.59838 11.4287i 0.312793 0.541773i
\(446\) −3.27042 5.66453i −0.154859 0.268223i
\(447\) 4.89669 0.231605
\(448\) 4.44301 + 7.69551i 0.209912 + 0.363579i
\(449\) −4.71156 8.16066i −0.222352 0.385125i 0.733170 0.680046i \(-0.238040\pi\)
−0.955522 + 0.294920i \(0.904707\pi\)
\(450\) 4.81875 0.227158
\(451\) 0.540031 + 0.935361i 0.0254291 + 0.0440444i
\(452\) 2.26508 3.92323i 0.106540 0.184533i
\(453\) −4.47277 + 7.74706i −0.210149 + 0.363988i
\(454\) 36.9058 1.73207
\(455\) −2.83088 2.79481i −0.132714 0.131023i
\(456\) −6.97170 −0.326480
\(457\) −6.35812 + 11.0126i −0.297420 + 0.515147i −0.975545 0.219800i \(-0.929460\pi\)
0.678125 + 0.734947i \(0.262793\pi\)
\(458\) 0.432734 0.749517i 0.0202203 0.0350226i
\(459\) 0.363055 + 0.628829i 0.0169459 + 0.0293512i
\(460\) −0.0312196 −0.00145562
\(461\) 14.8627 + 25.7429i 0.692223 + 1.19897i 0.971108 + 0.238641i \(0.0767018\pi\)
−0.278885 + 0.960324i \(0.589965\pi\)
\(462\) −0.222234 0.384921i −0.0103393 0.0179082i
\(463\) −15.2838 −0.710297 −0.355148 0.934810i \(-0.615570\pi\)
−0.355148 + 0.934810i \(0.615570\pi\)
\(464\) 0.745594 + 1.29141i 0.0346133 + 0.0599521i
\(465\) −3.78310 + 6.55253i −0.175437 + 0.303866i
\(466\) −11.6575 + 20.1914i −0.540023 + 0.935347i
\(467\) −26.6503 −1.23323 −0.616614 0.787265i \(-0.711496\pi\)
−0.616614 + 0.787265i \(0.711496\pi\)
\(468\) −0.343570 + 1.31591i −0.0158815 + 0.0608281i
\(469\) −8.12386 −0.375125
\(470\) 3.30832 5.73019i 0.152602 0.264314i
\(471\) 3.29725 5.71101i 0.151929 0.263149i
\(472\) 5.94301 + 10.2936i 0.273549 + 0.473801i
\(473\) 1.61292 0.0741623
\(474\) −10.8952 18.8711i −0.500434 0.866778i
\(475\) 4.35424 + 7.54177i 0.199786 + 0.346040i
\(476\) 0.273891 0.0125538
\(477\) −2.77389 4.80452i −0.127008 0.219984i
\(478\) −3.47277 + 6.01501i −0.158841 + 0.275120i
\(479\) 11.1058 19.2359i 0.507439 0.878909i −0.492524 0.870299i \(-0.663926\pi\)
0.999963 0.00861072i \(-0.00274091\pi\)
\(480\) 2.32061 0.105921
\(481\) −1.00494 + 3.84902i −0.0458212 + 0.175500i
\(482\) 19.6970 0.897174
\(483\) −0.0375080 + 0.0649658i −0.00170667 + 0.00295605i
\(484\) −2.05166 + 3.55357i −0.0932571 + 0.161526i
\(485\) −5.57355 9.65368i −0.253082 0.438351i
\(486\) 1.27389 0.0577848
\(487\) 0.485852 + 0.841520i 0.0220160 + 0.0381329i 0.876824 0.480812i \(-0.159658\pi\)
−0.854807 + 0.518945i \(0.826325\pi\)
\(488\) −8.40016 14.5495i −0.380257 0.658625i
\(489\) 9.90444 0.447894
\(490\) 0.702750 + 1.21720i 0.0317470 + 0.0549874i
\(491\) −13.4674 + 23.3263i −0.607777 + 1.05270i 0.383830 + 0.923404i \(0.374605\pi\)
−0.991606 + 0.129296i \(0.958728\pi\)
\(492\) −0.583827 + 1.01122i −0.0263210 + 0.0455893i
\(493\) 0.348907 0.0157140
\(494\) 10.1961 2.80222i 0.458742 0.126078i
\(495\) −0.384953 −0.0173023
\(496\) −10.6408 + 18.4304i −0.477787 + 0.827551i
\(497\) −4.76468 + 8.25267i −0.213725 + 0.370183i
\(498\) 7.58876 + 13.1441i 0.340061 + 0.589002i
\(499\) −21.1239 −0.945634 −0.472817 0.881161i \(-0.656763\pi\)
−0.472817 + 0.881161i \(0.656763\pi\)
\(500\) −1.82756 3.16543i −0.0817310 0.141562i
\(501\) −8.37826 14.5116i −0.374313 0.648330i
\(502\) 10.5662 0.471593
\(503\) −6.28270 10.8820i −0.280132 0.485203i 0.691285 0.722582i \(-0.257045\pi\)
−0.971417 + 0.237379i \(0.923712\pi\)
\(504\) 1.51415 2.62258i 0.0674455 0.116819i
\(505\) −2.24801 + 3.89366i −0.100035 + 0.173266i
\(506\) 0.0333423 0.00148225
\(507\) −0.166703 12.9989i −0.00740355 0.577303i
\(508\) 2.20955 0.0980328
\(509\) −13.8032 + 23.9079i −0.611818 + 1.05970i 0.379116 + 0.925349i \(0.376228\pi\)
−0.990934 + 0.134351i \(0.957105\pi\)
\(510\) −0.510273 + 0.883819i −0.0225953 + 0.0391362i
\(511\) −5.21690 9.03593i −0.230782 0.399726i
\(512\) 25.3227 1.11912
\(513\) 1.15109 + 1.99375i 0.0508220 + 0.0880263i
\(514\) −9.57849 16.5904i −0.422489 0.731773i
\(515\) −4.53579 −0.199871
\(516\) 0.871866 + 1.51012i 0.0383818 + 0.0664792i
\(517\) 0.821271 1.42248i 0.0361195 0.0625608i
\(518\) 0.702750 1.21720i 0.0308770 0.0534806i
\(519\) −13.7184 −0.602169
\(520\) −11.6160 + 3.19246i −0.509395 + 0.139999i
\(521\) −36.8783 −1.61567 −0.807833 0.589411i \(-0.799360\pi\)
−0.807833 + 0.589411i \(0.799360\pi\)
\(522\) 0.306062 0.530115i 0.0133960 0.0232025i
\(523\) −15.4027 + 26.6782i −0.673512 + 1.16656i 0.303389 + 0.952867i \(0.401882\pi\)
−0.976901 + 0.213691i \(0.931451\pi\)
\(524\) 4.22571 + 7.31914i 0.184601 + 0.319738i
\(525\) −3.78270 −0.165091
\(526\) −10.9840 19.0248i −0.478925 0.829522i
\(527\) 2.48973 + 4.31233i 0.108454 + 0.187848i
\(528\) −1.08277 −0.0471213
\(529\) 11.4972 + 19.9137i 0.499878 + 0.865814i
\(530\) 3.89870 6.75275i 0.169349 0.293321i
\(531\) 1.96249 3.39914i 0.0851649 0.147510i
\(532\) 0.868391 0.0376495
\(533\) 2.81955 10.7992i 0.122128 0.467765i
\(534\) −15.2370 −0.659371
\(535\) 3.40404 5.89597i 0.147169 0.254905i
\(536\) −12.3007 + 21.3055i −0.531310 + 0.920257i
\(537\) −11.0152 19.0789i −0.475341 0.823315i
\(538\) 30.9485 1.33428
\(539\) 0.174453 + 0.302162i 0.00751424 + 0.0130150i
\(540\) −0.208086 0.360416i −0.00895461 0.0155098i
\(541\) −41.4981 −1.78414 −0.892072 0.451893i \(-0.850749\pi\)
−0.892072 + 0.451893i \(0.850749\pi\)
\(542\) 11.6769 + 20.2249i 0.501564 + 0.868735i
\(543\) 4.71690 8.16991i 0.202421 0.350604i
\(544\) 0.763617 1.32262i 0.0327398 0.0567070i
\(545\) −9.73306 −0.416918
\(546\) −1.16031 + 4.44410i −0.0496565 + 0.190190i
\(547\) −41.3716 −1.76892 −0.884460 0.466615i \(-0.845473\pi\)
−0.884460 + 0.466615i \(0.845473\pi\)
\(548\) 3.81140 6.60154i 0.162815 0.282004i
\(549\) −2.77389 + 4.80452i −0.118387 + 0.205052i
\(550\) 0.840647 + 1.45604i 0.0358453 + 0.0620859i
\(551\) 1.10624 0.0471272
\(552\) 0.113585 + 0.196736i 0.00483452 + 0.00837363i
\(553\) 8.55272 + 14.8137i 0.363699 + 0.629944i
\(554\) −10.7699 −0.457569
\(555\) −0.608649 1.05421i −0.0258357 0.0447488i
\(556\) 0.806062 1.39614i 0.0341846 0.0592095i
\(557\) −15.0075 + 25.9937i −0.635886 + 1.10139i 0.350440 + 0.936585i \(0.386032\pi\)
−0.986327 + 0.164803i \(0.947301\pi\)
\(558\) 8.73598 0.369824
\(559\) −11.8612 11.7101i −0.501675 0.495283i
\(560\) 3.42392 0.144687
\(561\) −0.126672 + 0.219403i −0.00534810 + 0.00926319i
\(562\) −15.9313 + 27.5938i −0.672020 + 1.16397i
\(563\) −12.9674 22.4602i −0.546512 0.946586i −0.998510 0.0545676i \(-0.982622\pi\)
0.451998 0.892019i \(-0.350711\pi\)
\(564\) 1.77575 0.0747727
\(565\) −6.62532 11.4754i −0.278729 0.482773i
\(566\) 17.2876 + 29.9431i 0.726654 + 1.25860i
\(567\) −1.00000 −0.0419961
\(568\) 14.4289 + 24.9915i 0.605421 + 1.04862i
\(569\) 3.28310 5.68650i 0.137635 0.238390i −0.788966 0.614437i \(-0.789383\pi\)
0.926601 + 0.376046i \(0.122717\pi\)
\(570\) −1.61786 + 2.80222i −0.0677647 + 0.117372i
\(571\) −30.0539 −1.25772 −0.628858 0.777520i \(-0.716477\pi\)
−0.628858 + 0.777520i \(0.716477\pi\)
\(572\) −0.457556 + 0.125752i −0.0191314 + 0.00525794i
\(573\) 3.37720 0.141085
\(574\) −1.97170 + 3.41509i −0.0822973 + 0.142543i
\(575\) 0.141882 0.245746i 0.00591687 0.0102483i
\(576\) −4.44301 7.69551i −0.185125 0.320646i
\(577\) 21.1706 0.881343 0.440671 0.897669i \(-0.354740\pi\)
0.440671 + 0.897669i \(0.354740\pi\)
\(578\) −10.4922 18.1731i −0.436420 0.755902i
\(579\) 11.1614 + 19.3321i 0.463851 + 0.803413i
\(580\) −0.199977 −0.00830360
\(581\) −5.95716 10.3181i −0.247144 0.428067i
\(582\) −6.43526 + 11.1462i −0.266750 + 0.462025i
\(583\) 0.967829 1.67633i 0.0400834 0.0694264i
\(584\) −31.5966 −1.30748
\(585\) 2.83088 + 2.79481i 0.117043 + 0.115551i
\(586\) 13.4268 0.554658
\(587\) −0.0156098 + 0.0270370i −0.000644286 + 0.00111594i −0.866347 0.499442i \(-0.833538\pi\)
0.865703 + 0.500558i \(0.166872\pi\)
\(588\) −0.188601 + 0.326667i −0.00777779 + 0.0134715i
\(589\) 7.89387 + 13.6726i 0.325261 + 0.563369i
\(590\) 5.51656 0.227113
\(591\) −12.7257 22.0416i −0.523466 0.906669i
\(592\) −1.71196 2.96520i −0.0703612 0.121869i
\(593\) −10.3150 −0.423586 −0.211793 0.977315i \(-0.567930\pi\)
−0.211793 + 0.977315i \(0.567930\pi\)
\(594\) 0.222234 + 0.384921i 0.00911839 + 0.0157935i
\(595\) 0.400563 0.693795i 0.0164215 0.0284428i
\(596\) −0.923522 + 1.59959i −0.0378289 + 0.0655217i
\(597\) 22.3404 0.914330
\(598\) −0.245194 0.242070i −0.0100267 0.00989896i
\(599\) 44.0176 1.79851 0.899256 0.437423i \(-0.144109\pi\)
0.899256 + 0.437423i \(0.144109\pi\)
\(600\) −5.72757 + 9.92044i −0.233827 + 0.405000i
\(601\) −2.52336 + 4.37059i −0.102930 + 0.178280i −0.912891 0.408204i \(-0.866155\pi\)
0.809961 + 0.586484i \(0.199488\pi\)
\(602\) 2.94447 + 5.09997i 0.120008 + 0.207859i
\(603\) 8.12386 0.330829
\(604\) −1.68714 2.92221i −0.0686487 0.118903i
\(605\) 6.00106 + 10.3941i 0.243978 + 0.422582i
\(606\) 5.19112 0.210875
\(607\) −8.32409 14.4177i −0.337864 0.585198i 0.646167 0.763196i \(-0.276371\pi\)
−0.984031 + 0.177998i \(0.943038\pi\)
\(608\) 2.42111 4.19348i 0.0981889 0.170068i
\(609\) −0.240258 + 0.416138i −0.00973573 + 0.0168628i
\(610\) −7.79740 −0.315708
\(611\) −16.3669 + 4.49818i −0.662135 + 0.181977i
\(612\) −0.273891 −0.0110714
\(613\) −19.0060 + 32.9194i −0.767645 + 1.32960i 0.171192 + 0.985238i \(0.445238\pi\)
−0.938837 + 0.344362i \(0.888095\pi\)
\(614\) −2.80792 + 4.86347i −0.113319 + 0.196274i
\(615\) 1.70769 + 2.95780i 0.0688605 + 0.119270i
\(616\) 1.05659 0.0425713
\(617\) −7.83330 13.5677i −0.315357 0.546214i 0.664157 0.747593i \(-0.268791\pi\)
−0.979513 + 0.201380i \(0.935457\pi\)
\(618\) 2.61852 + 4.53541i 0.105332 + 0.182441i
\(619\) 3.26109 0.131074 0.0655372 0.997850i \(-0.479124\pi\)
0.0655372 + 0.997850i \(0.479124\pi\)
\(620\) −1.42700 2.47163i −0.0573096 0.0992631i
\(621\) 0.0375080 0.0649658i 0.00150514 0.00260699i
\(622\) −1.48304 + 2.56870i −0.0594644 + 0.102995i
\(623\) 11.9610 0.479209
\(624\) 7.96249 + 7.86103i 0.318755 + 0.314693i
\(625\) 8.22234 0.328894
\(626\) 8.06928 13.9764i 0.322513 0.558609i
\(627\) −0.401624 + 0.695633i −0.0160393 + 0.0277809i
\(628\) 1.24373 + 2.15421i 0.0496303 + 0.0859622i
\(629\) −0.801125 −0.0319430
\(630\) −0.702750 1.21720i −0.0279982 0.0484943i
\(631\) −0.799773 1.38525i −0.0318385 0.0551459i 0.849667 0.527319i \(-0.176803\pi\)
−0.881506 + 0.472174i \(0.843470\pi\)
\(632\) 51.8003 2.06051
\(633\) 5.01908 + 8.69331i 0.199491 + 0.345528i
\(634\) −7.82902 + 13.5603i −0.310930 + 0.538547i
\(635\) 3.23145 5.59703i 0.128236 0.222111i
\(636\) 2.09264 0.0829785
\(637\) 0.910836 3.48861i 0.0360886 0.138224i
\(638\) 0.213574 0.00845548
\(639\) 4.76468 8.25267i 0.188488 0.326470i
\(640\) 3.92403 6.79662i 0.155111 0.268660i
\(641\) −15.6779 27.1550i −0.619241 1.07256i −0.989625 0.143678i \(-0.954107\pi\)
0.370384 0.928879i \(-0.379226\pi\)
\(642\) −7.86064 −0.310235
\(643\) 9.33154 + 16.1627i 0.368000 + 0.637395i 0.989253 0.146215i \(-0.0467092\pi\)
−0.621253 + 0.783610i \(0.713376\pi\)
\(644\) −0.0141481 0.0245053i −0.000557514 0.000965643i
\(645\) 5.10039 0.200828
\(646\) 1.06474 + 1.84419i 0.0418918 + 0.0725586i
\(647\) −3.26855 + 5.66130i −0.128500 + 0.222569i −0.923096 0.384570i \(-0.874350\pi\)
0.794596 + 0.607139i \(0.207683\pi\)
\(648\) −1.51415 + 2.62258i −0.0594814 + 0.103025i
\(649\) 1.36945 0.0537557
\(650\) 4.38909 16.8107i 0.172154 0.659371i
\(651\) −6.85772 −0.268775
\(652\) −1.86799 + 3.23546i −0.0731562 + 0.126710i
\(653\) −7.92605 + 13.7283i −0.310170 + 0.537230i −0.978399 0.206725i \(-0.933719\pi\)
0.668229 + 0.743956i \(0.267053\pi\)
\(654\) 5.61892 + 9.73226i 0.219717 + 0.380561i
\(655\) 24.7203 0.965901
\(656\) 4.80325 + 8.31947i 0.187535 + 0.324821i
\(657\) 5.21690 + 9.03593i 0.203531 + 0.352525i
\(658\) 5.99708 0.233790
\(659\) 24.8987 + 43.1258i 0.969916 + 1.67994i 0.695784 + 0.718251i \(0.255057\pi\)
0.274132 + 0.961692i \(0.411610\pi\)
\(660\) 0.0726027 0.125752i 0.00282606 0.00489487i
\(661\) −1.78552 + 3.09260i −0.0694485 + 0.120288i −0.898659 0.438649i \(-0.855457\pi\)
0.829210 + 0.558937i \(0.188791\pi\)
\(662\) −16.9319 −0.658078
\(663\) 2.52442 0.693795i 0.0980404 0.0269448i
\(664\) −36.0801 −1.40018
\(665\) 1.27002 2.19973i 0.0492491 0.0853019i
\(666\) −0.702750 + 1.21720i −0.0272310 + 0.0471655i
\(667\) −0.0180232 0.0312170i −0.000697860 0.00120873i
\(668\) 6.32061 0.244552
\(669\) −2.56727 4.44664i −0.0992562 0.171917i
\(670\) 5.70904 + 9.88834i 0.220559 + 0.382020i
\(671\) −1.93566 −0.0747252
\(672\) 1.05166 + 1.82152i 0.0405685 + 0.0702667i
\(673\) −5.86693 + 10.1618i −0.226154 + 0.391709i −0.956665 0.291191i \(-0.905948\pi\)
0.730511 + 0.682901i \(0.239282\pi\)
\(674\) −2.16912 + 3.75702i −0.0835512 + 0.144715i
\(675\) 3.78270 0.145596
\(676\) 4.27777 + 2.39716i 0.164529 + 0.0921985i
\(677\) 17.3326 0.666146 0.333073 0.942901i \(-0.391914\pi\)
0.333073 + 0.942901i \(0.391914\pi\)
\(678\) −7.64963 + 13.2496i −0.293782 + 0.508846i
\(679\) 5.05166 8.74973i 0.193865 0.335784i
\(680\) −1.21302 2.10102i −0.0465173 0.0805703i
\(681\) 28.9709 1.11017
\(682\) 1.52402 + 2.63968i 0.0583578 + 0.101079i
\(683\) −8.48198 14.6912i −0.324554 0.562144i 0.656868 0.754005i \(-0.271881\pi\)
−0.981422 + 0.191862i \(0.938547\pi\)
\(684\) −0.868391 −0.0332038
\(685\) −11.1483 19.3094i −0.425954 0.737774i
\(686\) −0.636945 + 1.10322i −0.0243187 + 0.0421212i
\(687\) 0.339695 0.588369i 0.0129602 0.0224477i
\(688\) 14.3460 0.546935
\(689\) −19.2876 + 5.30089i −0.734801 + 0.201948i
\(690\) 0.105435 0.00401384
\(691\) −18.3213 + 31.7334i −0.696974 + 1.20719i 0.272537 + 0.962145i \(0.412137\pi\)
−0.969511 + 0.245049i \(0.921196\pi\)
\(692\) 2.58730 4.48134i 0.0983545 0.170355i
\(693\) −0.174453 0.302162i −0.00662693 0.0114782i
\(694\) 42.6730 1.61984
\(695\) −2.35772 4.08369i −0.0894333 0.154903i
\(696\) 0.727571 + 1.26019i 0.0275785 + 0.0477674i
\(697\) 2.24772 0.0851384
\(698\) −17.9494 31.0893i −0.679395 1.17675i
\(699\) −9.15109 + 15.8502i −0.346126 + 0.599508i
\(700\) 0.713423 1.23568i 0.0269649 0.0467045i
\(701\) −14.6092 −0.551782 −0.275891 0.961189i \(-0.588973\pi\)
−0.275891 + 0.961189i \(0.588973\pi\)
\(702\) 1.16031 4.44410i 0.0437929 0.167732i
\(703\) −2.54003 −0.0957991
\(704\) 1.55019 2.68502i 0.0584252 0.101195i
\(705\) 2.59702 4.49818i 0.0978096 0.169411i
\(706\) −1.90590 3.30111i −0.0717295 0.124239i
\(707\) −4.07502 −0.153257
\(708\) 0.740258 + 1.28216i 0.0278206 + 0.0481867i
\(709\) 11.7930 + 20.4260i 0.442894 + 0.767116i 0.997903 0.0647290i \(-0.0206183\pi\)
−0.555008 + 0.831845i \(0.687285\pi\)
\(710\) 13.3935 0.502649
\(711\) −8.55272 14.8137i −0.320752 0.555559i
\(712\) 18.1108 31.3688i 0.678730 1.17559i
\(713\) 0.257219 0.445517i 0.00963294 0.0166847i
\(714\) −0.924984 −0.0346167
\(715\) −0.350629 + 1.34295i −0.0131128 + 0.0502235i
\(716\) 8.30994 0.310557
\(717\) −2.72611 + 4.72176i −0.101808 + 0.176337i
\(718\) 2.42605 4.20203i 0.0905392 0.156819i
\(719\) −17.0669 29.5607i −0.636487 1.10243i −0.986198 0.165570i \(-0.947054\pi\)
0.349711 0.936857i \(-0.386280\pi\)
\(720\) −3.42392 −0.127602
\(721\) −2.05553 3.56028i −0.0765520 0.132592i
\(722\) −8.72611 15.1141i −0.324752 0.562487i
\(723\) 15.4621 0.575041
\(724\) 1.77923 + 3.08171i 0.0661245 + 0.114531i
\(725\) 0.908823 1.57413i 0.0337528 0.0584616i
\(726\) 6.92886 12.0011i 0.257154 0.445404i
\(727\) −15.3481 −0.569230 −0.284615 0.958642i \(-0.591866\pi\)
−0.284615 + 0.958642i \(0.591866\pi\)
\(728\) −7.77002 7.67101i −0.287976 0.284307i
\(729\) 1.00000 0.0370370
\(730\) −7.33235 + 12.7000i −0.271382 + 0.470048i
\(731\) 1.67833 2.90695i 0.0620752 0.107517i
\(732\) −1.04632 1.81228i −0.0386731 0.0669837i
\(733\) 23.2894 0.860213 0.430107 0.902778i \(-0.358476\pi\)
0.430107 + 0.902778i \(0.358476\pi\)
\(734\) −16.8481 29.1818i −0.621875 1.07712i
\(735\) 0.551656 + 0.955496i 0.0203481 + 0.0352440i
\(736\) −0.157782 −0.00581593
\(737\) 1.41723 + 2.45472i 0.0522045 + 0.0904208i
\(738\) 1.97170 3.41509i 0.0725794 0.125711i
\(739\) 5.13307 8.89074i 0.188823 0.327051i −0.756035 0.654531i \(-0.772866\pi\)
0.944858 + 0.327480i \(0.106199\pi\)
\(740\) 0.459168 0.0168794
\(741\) 8.00388 2.19973i 0.294030 0.0808092i
\(742\) 7.06727 0.259447
\(743\) 22.6741 39.2726i 0.831830 1.44077i −0.0647549 0.997901i \(-0.520627\pi\)
0.896585 0.442871i \(-0.146040\pi\)
\(744\) −10.3836 + 17.9849i −0.380681 + 0.659359i
\(745\) 2.70129 + 4.67877i 0.0989675 + 0.171417i
\(746\) −2.71544 −0.0994192
\(747\) 5.95716 + 10.3181i 0.217961 + 0.377519i
\(748\) −0.0477811 0.0827593i −0.00174705 0.00302598i
\(749\) 6.17058 0.225468
\(750\) 6.17204 + 10.6903i 0.225371 + 0.390354i
\(751\) 14.8057 25.6442i 0.540266 0.935769i −0.458622 0.888631i \(-0.651657\pi\)
0.998888 0.0471372i \(-0.0150098\pi\)
\(752\) 7.30471 12.6521i 0.266375 0.461376i
\(753\) 8.29444 0.302266
\(754\) −1.57059 1.55058i −0.0571975 0.0564687i
\(755\) −9.86971 −0.359196
\(756\) 0.188601 0.326667i 0.00685937 0.0118808i
\(757\) 12.9908 22.5007i 0.472158 0.817802i −0.527334 0.849658i \(-0.676808\pi\)
0.999492 + 0.0318559i \(0.0101418\pi\)
\(758\) −8.88119 15.3827i −0.322579 0.558724i
\(759\) 0.0261736 0.000950041
\(760\) −3.84598 6.66144i −0.139508 0.241636i
\(761\) 27.0332 + 46.8229i 0.979954 + 1.69733i 0.662510 + 0.749053i \(0.269491\pi\)
0.317444 + 0.948277i \(0.397176\pi\)
\(762\) −7.46209 −0.270323
\(763\) −4.41084 7.63979i −0.159683 0.276579i
\(764\) −0.636945 + 1.10322i −0.0230439 + 0.0399132i
\(765\) −0.400563 + 0.693795i −0.0144824 + 0.0250842i
\(766\) 23.6999 0.856313
\(767\) −10.0707 9.94242i −0.363633 0.359000i
\(768\) 8.71061 0.314317
\(769\) −12.8967 + 22.3377i −0.465066 + 0.805519i −0.999205 0.0398785i \(-0.987303\pi\)
0.534138 + 0.845397i \(0.320636\pi\)
\(770\) 0.245194 0.424688i 0.00883618 0.0153047i
\(771\) −7.51908 13.0234i −0.270793 0.469028i
\(772\) −8.42020 −0.303050
\(773\) 0.0608679 + 0.105426i 0.00218927 + 0.00379192i 0.867118 0.498103i \(-0.165970\pi\)
−0.864929 + 0.501895i \(0.832636\pi\)
\(774\) −2.94447 5.09997i −0.105837 0.183315i
\(775\) 25.9407 0.931818
\(776\) −15.2979 26.4968i −0.549163 0.951178i
\(777\) 0.551656 0.955496i 0.0197906 0.0342782i