Properties

Label 546.2.s.e.127.1
Level $546$
Weight $2$
Character 546.127
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.195105024.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 4 x^{5} - 20 x^{4} + 12 x^{3} + 45 x^{2} - 108 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 127.1
Root \(1.30512 + 1.13871i\) of defining polynomial
Character \(\chi\) \(=\) 546.127
Dual form 546.2.s.e.43.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.39924i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.39924i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.19962 + 3.80986i) q^{10} +(0.971521 - 0.560908i) q^{11} +1.00000 q^{12} +(-2.14345 + 2.89924i) q^{13} +1.00000 q^{14} +(3.80986 - 2.19962i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.57781 - 2.73284i) q^{17} -1.00000i q^{18} +(-6.99395 - 4.03796i) q^{19} +(-3.80986 - 2.19962i) q^{20} -1.00000i q^{21} +(-0.560908 + 0.971521i) q^{22} +(-2.70436 - 4.68409i) q^{23} +(-0.866025 + 0.500000i) q^{24} -14.3533 q^{25} +(0.406663 - 3.58254i) q^{26} -1.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(3.37076 + 5.83834i) q^{29} +(-2.19962 + 3.80986i) q^{30} -5.58592i q^{31} +(0.866025 + 0.500000i) q^{32} +(0.971521 + 0.560908i) q^{33} +3.15561i q^{34} +(-2.19962 + 3.80986i) q^{35} +(0.500000 + 0.866025i) q^{36} +(6.59886 - 3.80986i) q^{37} +8.07591 q^{38} +(-3.58254 - 0.406663i) q^{39} +4.39924 q^{40} +(-1.78138 + 1.02848i) q^{41} +(0.500000 + 0.866025i) q^{42} +(0.792959 - 1.37344i) q^{43} -1.12182i q^{44} +(3.80986 + 2.19962i) q^{45} +(4.68409 + 2.70436i) q^{46} -7.58865i q^{47} +(0.500000 - 0.866025i) q^{48} +(0.500000 + 0.866025i) q^{49} +(12.4304 - 7.17667i) q^{50} +3.15561 q^{51} +(1.43909 + 3.30591i) q^{52} +8.44252 q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.46757 - 4.27396i) q^{55} +(0.500000 - 0.866025i) q^{56} -8.07591i q^{57} +(-5.83834 - 3.37076i) q^{58} +(-6.30380 - 3.63950i) q^{59} -4.39924i q^{60} +(-5.20831 + 9.02106i) q^{61} +(2.79296 + 4.83755i) q^{62} +(0.866025 - 0.500000i) q^{63} -1.00000 q^{64} +(12.7545 + 9.42957i) q^{65} -1.12182 q^{66} +(4.56902 - 2.63792i) q^{67} +(-1.57781 - 2.73284i) q^{68} +(2.70436 - 4.68409i) q^{69} -4.39924i q^{70} +(7.51422 + 4.33834i) q^{71} +(-0.866025 - 0.500000i) q^{72} +12.7985i q^{73} +(-3.80986 + 6.59886i) q^{74} +(-7.17667 - 12.4304i) q^{75} +(-6.99395 + 4.03796i) q^{76} -1.12182 q^{77} +(3.30591 - 1.43909i) q^{78} -3.52106 q^{79} +(-3.80986 + 2.19962i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.02848 - 1.78138i) q^{82} -11.1392i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-12.0224 - 6.94115i) q^{85} +1.58592i q^{86} +(-3.37076 + 5.83834i) q^{87} +(0.560908 + 0.971521i) q^{88} +(9.02707 - 5.21178i) q^{89} -4.39924 q^{90} +(3.30591 - 1.43909i) q^{91} -5.40872 q^{92} +(4.83755 - 2.79296i) q^{93} +(3.79432 + 6.57196i) q^{94} +(-17.7640 + 30.7681i) q^{95} +1.00000i q^{96} +(1.06297 + 0.613704i) q^{97} +(-0.866025 - 0.500000i) q^{98} +1.12182i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} + 6q^{10} + 6q^{11} + 8q^{12} + 12q^{13} + 8q^{14} + 6q^{15} - 4q^{16} + 2q^{17} - 12q^{19} - 6q^{20} - 4q^{22} + 8q^{23} - 24q^{25} + 6q^{26} - 8q^{27} + 2q^{29} - 6q^{30} + 6q^{33} - 6q^{35} + 4q^{36} + 18q^{37} - 4q^{38} + 12q^{40} + 12q^{41} + 4q^{42} - 8q^{43} + 6q^{45} + 18q^{46} + 4q^{48} + 4q^{49} + 12q^{50} + 4q^{51} + 12q^{52} - 12q^{53} - 22q^{55} + 4q^{56} - 24q^{58} + 18q^{59} - 8q^{61} + 8q^{62} - 8q^{64} + 46q^{65} - 8q^{66} + 18q^{67} - 2q^{68} - 8q^{69} + 6q^{71} - 6q^{74} - 12q^{75} - 12q^{76} - 8q^{77} + 6q^{78} - 4q^{79} - 6q^{80} - 4q^{81} + 10q^{82} - 54q^{85} - 2q^{87} + 4q^{88} - 18q^{89} - 12q^{90} + 6q^{91} + 16q^{92} + 30q^{93} - 2q^{94} - 50q^{95} - 54q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 4.39924i 1.96740i −0.179814 0.983701i \(-0.557549\pi\)
0.179814 0.983701i \(-0.442451\pi\)
\(6\) −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
\(10\) 2.19962 + 3.80986i 0.695581 + 1.20478i
\(11\) 0.971521 0.560908i 0.292925 0.169120i −0.346335 0.938111i \(-0.612574\pi\)
0.639260 + 0.768991i \(0.279241\pi\)
\(12\) 1.00000 0.288675
\(13\) −2.14345 + 2.89924i −0.594487 + 0.804105i
\(14\) 1.00000 0.267261
\(15\) 3.80986 2.19962i 0.983701 0.567940i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.57781 2.73284i 0.382674 0.662811i −0.608769 0.793347i \(-0.708337\pi\)
0.991444 + 0.130536i \(0.0416699\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −6.99395 4.03796i −1.60452 0.926371i −0.990567 0.137029i \(-0.956245\pi\)
−0.613954 0.789342i \(-0.710422\pi\)
\(20\) −3.80986 2.19962i −0.851910 0.491850i
\(21\) 1.00000i 0.218218i
\(22\) −0.560908 + 0.971521i −0.119586 + 0.207129i
\(23\) −2.70436 4.68409i −0.563898 0.976700i −0.997151 0.0754280i \(-0.975968\pi\)
0.433253 0.901272i \(-0.357366\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) −14.3533 −2.87067
\(26\) 0.406663 3.58254i 0.0797531 0.702595i
\(27\) −1.00000 −0.192450
\(28\) −0.866025 + 0.500000i −0.163663 + 0.0944911i
\(29\) 3.37076 + 5.83834i 0.625935 + 1.08415i 0.988359 + 0.152138i \(0.0486159\pi\)
−0.362424 + 0.932013i \(0.618051\pi\)
\(30\) −2.19962 + 3.80986i −0.401594 + 0.695581i
\(31\) 5.58592i 1.00326i −0.865082 0.501630i \(-0.832734\pi\)
0.865082 0.501630i \(-0.167266\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0.971521 + 0.560908i 0.169120 + 0.0976416i
\(34\) 3.15561i 0.541183i
\(35\) −2.19962 + 3.80986i −0.371804 + 0.643983i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 6.59886 3.80986i 1.08485 0.626337i 0.152647 0.988281i \(-0.451220\pi\)
0.932200 + 0.361944i \(0.117887\pi\)
\(38\) 8.07591 1.31009
\(39\) −3.58254 0.406663i −0.573666 0.0651182i
\(40\) 4.39924 0.695581
\(41\) −1.78138 + 1.02848i −0.278204 + 0.160621i −0.632610 0.774470i \(-0.718016\pi\)
0.354406 + 0.935092i \(0.384683\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) 0.792959 1.37344i 0.120925 0.209448i −0.799208 0.601055i \(-0.794747\pi\)
0.920133 + 0.391607i \(0.128081\pi\)
\(44\) 1.12182i 0.169120i
\(45\) 3.80986 + 2.19962i 0.567940 + 0.327900i
\(46\) 4.68409 + 2.70436i 0.690631 + 0.398736i
\(47\) 7.58865i 1.10692i −0.832876 0.553459i \(-0.813308\pi\)
0.832876 0.553459i \(-0.186692\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 12.4304 7.17667i 1.75792 1.01493i
\(51\) 3.15561 0.441874
\(52\) 1.43909 + 3.30591i 0.199566 + 0.458447i
\(53\) 8.44252 1.15967 0.579834 0.814734i \(-0.303117\pi\)
0.579834 + 0.814734i \(0.303117\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) −2.46757 4.27396i −0.332727 0.576300i
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 8.07591i 1.06968i
\(58\) −5.83834 3.37076i −0.766611 0.442603i
\(59\) −6.30380 3.63950i −0.820685 0.473823i 0.0299675 0.999551i \(-0.490460\pi\)
−0.850653 + 0.525728i \(0.823793\pi\)
\(60\) 4.39924i 0.567940i
\(61\) −5.20831 + 9.02106i −0.666856 + 1.15503i 0.311923 + 0.950107i \(0.399027\pi\)
−0.978779 + 0.204921i \(0.934306\pi\)
\(62\) 2.79296 + 4.83755i 0.354706 + 0.614369i
\(63\) 0.866025 0.500000i 0.109109 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 12.7545 + 9.42957i 1.58200 + 1.16959i
\(66\) −1.12182 −0.138086
\(67\) 4.56902 2.63792i 0.558195 0.322274i −0.194226 0.980957i \(-0.562219\pi\)
0.752421 + 0.658683i \(0.228886\pi\)
\(68\) −1.57781 2.73284i −0.191337 0.331405i
\(69\) 2.70436 4.68409i 0.325567 0.563898i
\(70\) 4.39924i 0.525810i
\(71\) 7.51422 + 4.33834i 0.891773 + 0.514866i 0.874522 0.484986i \(-0.161175\pi\)
0.0172513 + 0.999851i \(0.494508\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 12.7985i 1.49795i 0.662599 + 0.748975i \(0.269454\pi\)
−0.662599 + 0.748975i \(0.730546\pi\)
\(74\) −3.80986 + 6.59886i −0.442887 + 0.767102i
\(75\) −7.17667 12.4304i −0.828691 1.43533i
\(76\) −6.99395 + 4.03796i −0.802261 + 0.463185i
\(77\) −1.12182 −0.127843
\(78\) 3.30591 1.43909i 0.374320 0.162945i
\(79\) −3.52106 −0.396150 −0.198075 0.980187i \(-0.563469\pi\)
−0.198075 + 0.980187i \(0.563469\pi\)
\(80\) −3.80986 + 2.19962i −0.425955 + 0.245925i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.02848 1.78138i 0.113576 0.196720i
\(83\) 11.1392i 1.22269i −0.791366 0.611343i \(-0.790630\pi\)
0.791366 0.611343i \(-0.209370\pi\)
\(84\) −0.866025 0.500000i −0.0944911 0.0545545i
\(85\) −12.0224 6.94115i −1.30402 0.752873i
\(86\) 1.58592i 0.171014i
\(87\) −3.37076 + 5.83834i −0.361384 + 0.625935i
\(88\) 0.560908 + 0.971521i 0.0597930 + 0.103565i
\(89\) 9.02707 5.21178i 0.956867 0.552448i 0.0616598 0.998097i \(-0.480361\pi\)
0.895207 + 0.445650i \(0.147027\pi\)
\(90\) −4.39924 −0.463721
\(91\) 3.30591 1.43909i 0.346553 0.150858i
\(92\) −5.40872 −0.563898
\(93\) 4.83755 2.79296i 0.501630 0.289616i
\(94\) 3.79432 + 6.57196i 0.391355 + 0.677846i
\(95\) −17.7640 + 30.7681i −1.82254 + 3.15674i
\(96\) 1.00000i 0.102062i
\(97\) 1.06297 + 0.613704i 0.107928 + 0.0623122i 0.552992 0.833186i \(-0.313486\pi\)
−0.445064 + 0.895499i \(0.646819\pi\)
\(98\) −0.866025 0.500000i −0.0874818 0.0505076i
\(99\) 1.12182i 0.112747i
\(100\) −7.17667 + 12.4304i −0.717667 + 1.24304i
\(101\) −5.40714 9.36545i −0.538031 0.931897i −0.999010 0.0444859i \(-0.985835\pi\)
0.460979 0.887411i \(-0.347498\pi\)
\(102\) −2.73284 + 1.57781i −0.270591 + 0.156226i
\(103\) 17.2910 1.70374 0.851868 0.523757i \(-0.175470\pi\)
0.851868 + 0.523757i \(0.175470\pi\)
\(104\) −2.89924 2.14345i −0.284294 0.210183i
\(105\) −4.39924 −0.429322
\(106\) −7.31143 + 4.22126i −0.710149 + 0.410005i
\(107\) −7.10282 12.3024i −0.686655 1.18932i −0.972914 0.231169i \(-0.925745\pi\)
0.286259 0.958152i \(-0.407588\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 3.43821i 0.329321i −0.986350 0.164660i \(-0.947347\pi\)
0.986350 0.164660i \(-0.0526528\pi\)
\(110\) 4.27396 + 2.46757i 0.407506 + 0.235274i
\(111\) 6.59886 + 3.80986i 0.626337 + 0.361616i
\(112\) 1.00000i 0.0944911i
\(113\) 3.01295 5.21858i 0.283434 0.490922i −0.688794 0.724957i \(-0.741860\pi\)
0.972228 + 0.234035i \(0.0751929\pi\)
\(114\) 4.03796 + 6.99395i 0.378189 + 0.655043i
\(115\) −20.6065 + 11.8971i −1.92156 + 1.10941i
\(116\) 6.74153 0.625935
\(117\) −1.43909 3.30591i −0.133044 0.305631i
\(118\) 7.27900 0.670087
\(119\) −2.73284 + 1.57781i −0.250519 + 0.144637i
\(120\) 2.19962 + 3.80986i 0.200797 + 0.347791i
\(121\) −4.87076 + 8.43641i −0.442797 + 0.766946i
\(122\) 10.4166i 0.943077i
\(123\) −1.78138 1.02848i −0.160621 0.0927348i
\(124\) −4.83755 2.79296i −0.434425 0.250815i
\(125\) 41.1476i 3.68036i
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) 4.87818 + 8.44926i 0.432869 + 0.749751i 0.997119 0.0758531i \(-0.0241680\pi\)
−0.564250 + 0.825604i \(0.690835\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 1.58592 0.139632
\(130\) −15.7605 1.78901i −1.38229 0.156906i
\(131\) 7.62761 0.666428 0.333214 0.942851i \(-0.391867\pi\)
0.333214 + 0.942851i \(0.391867\pi\)
\(132\) 0.971521 0.560908i 0.0845601 0.0488208i
\(133\) 4.03796 + 6.99395i 0.350135 + 0.606452i
\(134\) −2.63792 + 4.56902i −0.227882 + 0.394703i
\(135\) 4.39924i 0.378627i
\(136\) 2.73284 + 1.57781i 0.234339 + 0.135296i
\(137\) 6.36818 + 3.67667i 0.544070 + 0.314119i 0.746727 0.665131i \(-0.231624\pi\)
−0.202657 + 0.979250i \(0.564958\pi\)
\(138\) 5.40872i 0.460421i
\(139\) 4.29454 7.43835i 0.364258 0.630913i −0.624399 0.781106i \(-0.714656\pi\)
0.988657 + 0.150193i \(0.0479894\pi\)
\(140\) 2.19962 + 3.80986i 0.185902 + 0.321992i
\(141\) 6.57196 3.79432i 0.553459 0.319540i
\(142\) −8.67667 −0.728130
\(143\) −0.456201 + 4.01896i −0.0381494 + 0.336082i
\(144\) 1.00000 0.0833333
\(145\) 25.6843 14.8288i 2.13296 1.23147i
\(146\) −6.39924 11.0838i −0.529605 0.917303i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) 7.61971i 0.626337i
\(149\) −3.01285 1.73947i −0.246822 0.142503i 0.371486 0.928439i \(-0.378848\pi\)
−0.618308 + 0.785936i \(0.712182\pi\)
\(150\) 12.4304 + 7.17667i 1.01493 + 0.585973i
\(151\) 16.2991i 1.32640i 0.748441 + 0.663202i \(0.230803\pi\)
−0.748441 + 0.663202i \(0.769197\pi\)
\(152\) 4.03796 6.99395i 0.327522 0.567284i
\(153\) 1.57781 + 2.73284i 0.127558 + 0.220937i
\(154\) 0.971521 0.560908i 0.0782874 0.0451993i
\(155\) −24.5738 −1.97382
\(156\) −2.14345 + 2.89924i −0.171614 + 0.232125i
\(157\) −0.684571 −0.0546347 −0.0273174 0.999627i \(-0.508696\pi\)
−0.0273174 + 0.999627i \(0.508696\pi\)
\(158\) 3.04933 1.76053i 0.242591 0.140060i
\(159\) 4.22126 + 7.31143i 0.334768 + 0.579834i
\(160\) 2.19962 3.80986i 0.173895 0.301196i
\(161\) 5.40872i 0.426267i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 12.1690 + 7.02580i 0.953153 + 0.550303i 0.894059 0.447949i \(-0.147846\pi\)
0.0590938 + 0.998252i \(0.481179\pi\)
\(164\) 2.05696i 0.160621i
\(165\) 2.46757 4.27396i 0.192100 0.332727i
\(166\) 5.56960 + 9.64683i 0.432285 + 0.748739i
\(167\) 0.421983 0.243632i 0.0326540 0.0188528i −0.483584 0.875298i \(-0.660665\pi\)
0.516238 + 0.856445i \(0.327332\pi\)
\(168\) 1.00000 0.0771517
\(169\) −3.81122 12.4288i −0.293171 0.956060i
\(170\) 13.8823 1.06472
\(171\) 6.99395 4.03796i 0.534840 0.308790i
\(172\) −0.792959 1.37344i −0.0604625 0.104724i
\(173\) −1.71910 + 2.97757i −0.130701 + 0.226381i −0.923947 0.382521i \(-0.875056\pi\)
0.793246 + 0.608901i \(0.208389\pi\)
\(174\) 6.74153i 0.511074i
\(175\) 12.4304 + 7.17667i 0.939647 + 0.542505i
\(176\) −0.971521 0.560908i −0.0732312 0.0422800i
\(177\) 7.27900i 0.547123i
\(178\) −5.21178 + 9.02707i −0.390639 + 0.676607i
\(179\) −1.08802 1.88451i −0.0813225 0.140855i 0.822496 0.568771i \(-0.192581\pi\)
−0.903818 + 0.427917i \(0.859248\pi\)
\(180\) 3.80986 2.19962i 0.283970 0.163950i
\(181\) 10.7188 0.796721 0.398361 0.917229i \(-0.369579\pi\)
0.398361 + 0.917229i \(0.369579\pi\)
\(182\) −2.14345 + 2.89924i −0.158883 + 0.214906i
\(183\) −10.4166 −0.770019
\(184\) 4.68409 2.70436i 0.345316 0.199368i
\(185\) −16.7605 29.0300i −1.23226 2.13433i
\(186\) −2.79296 + 4.83755i −0.204790 + 0.354706i
\(187\) 3.54002i 0.258872i
\(188\) −6.57196 3.79432i −0.479310 0.276730i
\(189\) 0.866025 + 0.500000i 0.0629941 + 0.0363696i
\(190\) 35.5279i 2.57747i
\(191\) −7.62813 + 13.2123i −0.551952 + 0.956009i 0.446181 + 0.894943i \(0.352784\pi\)
−0.998134 + 0.0610668i \(0.980550\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −12.2800 + 7.08987i −0.883935 + 0.510340i −0.871954 0.489588i \(-0.837147\pi\)
−0.0119809 + 0.999928i \(0.503814\pi\)
\(194\) −1.22741 −0.0881228
\(195\) −1.78901 + 15.7605i −0.128114 + 1.12863i
\(196\) 1.00000 0.0714286
\(197\) 10.3662 5.98495i 0.738564 0.426410i −0.0829831 0.996551i \(-0.526445\pi\)
0.821547 + 0.570141i \(0.193111\pi\)
\(198\) −0.560908 0.971521i −0.0398620 0.0690430i
\(199\) −2.49684 + 4.32465i −0.176996 + 0.306566i −0.940850 0.338823i \(-0.889971\pi\)
0.763854 + 0.645389i \(0.223305\pi\)
\(200\) 14.3533i 1.01493i
\(201\) 4.56902 + 2.63792i 0.322274 + 0.186065i
\(202\) 9.36545 + 5.40714i 0.658951 + 0.380445i
\(203\) 6.74153i 0.473163i
\(204\) 1.57781 2.73284i 0.110468 0.191337i
\(205\) 4.52453 + 7.83671i 0.316007 + 0.547340i
\(206\) −14.9745 + 8.64551i −1.04332 + 0.602361i
\(207\) 5.40872 0.375932
\(208\) 3.58254 + 0.406663i 0.248405 + 0.0281970i
\(209\) −9.05969 −0.626672
\(210\) 3.80986 2.19962i 0.262905 0.151788i
\(211\) 3.27743 + 5.67667i 0.225627 + 0.390798i 0.956507 0.291708i \(-0.0942235\pi\)
−0.730880 + 0.682506i \(0.760890\pi\)
\(212\) 4.22126 7.31143i 0.289917 0.502151i
\(213\) 8.67667i 0.594516i
\(214\) 12.3024 + 7.10282i 0.840977 + 0.485538i
\(215\) −6.04212 3.48842i −0.412069 0.237908i
\(216\) 1.00000i 0.0680414i
\(217\) −2.79296 + 4.83755i −0.189598 + 0.328394i
\(218\) 1.71910 + 2.97757i 0.116432 + 0.201667i
\(219\) −11.0838 + 6.39924i −0.748975 + 0.432421i
\(220\) −4.93514 −0.332727
\(221\) 4.54121 + 10.4322i 0.305475 + 0.701743i
\(222\) −7.61971 −0.511402
\(223\) 6.43757 3.71673i 0.431091 0.248891i −0.268720 0.963218i \(-0.586601\pi\)
0.699811 + 0.714328i \(0.253267\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) 7.17667 12.4304i 0.478445 0.828691i
\(226\) 6.02589i 0.400837i
\(227\) 10.1529 + 5.86177i 0.673870 + 0.389059i 0.797542 0.603264i \(-0.206133\pi\)
−0.123671 + 0.992323i \(0.539467\pi\)
\(228\) −6.99395 4.03796i −0.463185 0.267420i
\(229\) 9.70668i 0.641436i −0.947175 0.320718i \(-0.896076\pi\)
0.947175 0.320718i \(-0.103924\pi\)
\(230\) 11.8971 20.6065i 0.784474 1.35875i
\(231\) −0.560908 0.971521i −0.0369050 0.0639214i
\(232\) −5.83834 + 3.37076i −0.383305 + 0.221302i
\(233\) −11.8444 −0.775952 −0.387976 0.921670i \(-0.626826\pi\)
−0.387976 + 0.921670i \(0.626826\pi\)
\(234\) 2.89924 + 2.14345i 0.189529 + 0.140122i
\(235\) −33.3843 −2.17775
\(236\) −6.30380 + 3.63950i −0.410343 + 0.236911i
\(237\) −1.76053 3.04933i −0.114359 0.198075i
\(238\) 1.57781 2.73284i 0.102274 0.177144i
\(239\) 1.50484i 0.0973397i 0.998815 + 0.0486698i \(0.0154982\pi\)
−0.998815 + 0.0486698i \(0.984502\pi\)
\(240\) −3.80986 2.19962i −0.245925 0.141985i
\(241\) −2.56160 1.47894i −0.165007 0.0952669i 0.415222 0.909720i \(-0.363704\pi\)
−0.580229 + 0.814453i \(0.697037\pi\)
\(242\) 9.74153i 0.626209i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 5.20831 + 9.02106i 0.333428 + 0.577514i
\(245\) 3.80986 2.19962i 0.243403 0.140529i
\(246\) 2.05696 0.131147
\(247\) 26.6982 11.6220i 1.69877 0.739489i
\(248\) 5.58592 0.354706
\(249\) 9.64683 5.56960i 0.611343 0.352959i
\(250\) −20.5738 35.6349i −1.30120 2.25375i
\(251\) −3.81728 + 6.61172i −0.240944 + 0.417328i −0.960984 0.276606i \(-0.910790\pi\)
0.720039 + 0.693933i \(0.244124\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) −5.25469 3.03380i −0.330359 0.190733i
\(254\) −8.44926 4.87818i −0.530154 0.306084i
\(255\) 13.8823i 0.869343i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −10.6616 18.4665i −0.665054 1.15191i −0.979271 0.202555i \(-0.935075\pi\)
0.314217 0.949351i \(-0.398258\pi\)
\(258\) −1.37344 + 0.792959i −0.0855069 + 0.0493675i
\(259\) −7.61971 −0.473466
\(260\) 14.5435 6.33092i 0.901949 0.392627i
\(261\) −6.74153 −0.417290
\(262\) −6.60571 + 3.81381i −0.408102 + 0.235618i
\(263\) 2.65582 + 4.60002i 0.163765 + 0.283649i 0.936216 0.351425i \(-0.114303\pi\)
−0.772451 + 0.635074i \(0.780969\pi\)
\(264\) −0.560908 + 0.971521i −0.0345215 + 0.0597930i
\(265\) 37.1407i 2.28153i
\(266\) −6.99395 4.03796i −0.428826 0.247583i
\(267\) 9.02707 + 5.21178i 0.552448 + 0.318956i
\(268\) 5.27585i 0.322274i
\(269\) 1.01642 1.76048i 0.0619720 0.107339i −0.833375 0.552708i \(-0.813594\pi\)
0.895347 + 0.445370i \(0.146928\pi\)
\(270\) −2.19962 3.80986i −0.133865 0.231860i
\(271\) 1.22099 0.704938i 0.0741698 0.0428219i −0.462456 0.886642i \(-0.653032\pi\)
0.536626 + 0.843820i \(0.319699\pi\)
\(272\) −3.15561 −0.191337
\(273\) 2.89924 + 2.14345i 0.175470 + 0.129728i
\(274\) −7.35334 −0.444232
\(275\) −13.9446 + 8.05090i −0.840889 + 0.485488i
\(276\) −2.70436 4.68409i −0.162783 0.281949i
\(277\) 11.7848 20.4119i 0.708080 1.22643i −0.257488 0.966281i \(-0.582895\pi\)
0.965568 0.260149i \(-0.0837718\pi\)
\(278\) 8.58907i 0.515138i
\(279\) 4.83755 + 2.79296i 0.289616 + 0.167210i
\(280\) −3.80986 2.19962i −0.227682 0.131453i
\(281\) 8.12593i 0.484753i −0.970182 0.242376i \(-0.922073\pi\)
0.970182 0.242376i \(-0.0779268\pi\)
\(282\) −3.79432 + 6.57196i −0.225949 + 0.391355i
\(283\) −9.96358 17.2574i −0.592273 1.02585i −0.993926 0.110055i \(-0.964897\pi\)
0.401652 0.915792i \(-0.368436\pi\)
\(284\) 7.51422 4.33834i 0.445887 0.257433i
\(285\) −35.5279 −2.10449
\(286\) −1.61440 3.70862i −0.0954613 0.219295i
\(287\) 2.05696 0.121418
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 3.52106 + 6.09865i 0.207121 + 0.358744i
\(290\) −14.8288 + 25.6843i −0.870778 + 1.50823i
\(291\) 1.22741i 0.0719519i
\(292\) 11.0838 + 6.39924i 0.648631 + 0.374487i
\(293\) 17.5078 + 10.1081i 1.02282 + 0.590523i 0.914918 0.403639i \(-0.132255\pi\)
0.107898 + 0.994162i \(0.465588\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) −16.0111 + 27.7320i −0.932200 + 1.61462i
\(296\) 3.80986 + 6.59886i 0.221443 + 0.383551i
\(297\) −0.971521 + 0.560908i −0.0563734 + 0.0325472i
\(298\) 3.47894 0.201530
\(299\) 19.3770 + 2.19953i 1.12060 + 0.127202i
\(300\) −14.3533 −0.828691
\(301\) −1.37344 + 0.792959i −0.0791641 + 0.0457054i
\(302\) −8.14956 14.1154i −0.468954 0.812253i
\(303\) 5.40714 9.36545i 0.310632 0.538031i
\(304\) 8.07591i 0.463185i
\(305\) 39.6858 + 22.9126i 2.27240 + 1.31197i
\(306\) −2.73284 1.57781i −0.156226 0.0901971i
\(307\) 26.2764i 1.49967i −0.661624 0.749836i \(-0.730132\pi\)
0.661624 0.749836i \(-0.269868\pi\)
\(308\) −0.560908 + 0.971521i −0.0319607 + 0.0553576i
\(309\) 8.64551 + 14.9745i 0.491826 + 0.851868i
\(310\) 21.2815 12.2869i 1.20871 0.697849i
\(311\) 7.30017 0.413954 0.206977 0.978346i \(-0.433637\pi\)
0.206977 + 0.978346i \(0.433637\pi\)
\(312\) 0.406663 3.58254i 0.0230227 0.202822i
\(313\) 25.4414 1.43803 0.719015 0.694994i \(-0.244593\pi\)
0.719015 + 0.694994i \(0.244593\pi\)
\(314\) 0.592856 0.342286i 0.0334568 0.0193163i
\(315\) −2.19962 3.80986i −0.123935 0.214661i
\(316\) −1.76053 + 3.04933i −0.0990375 + 0.171538i
\(317\) 20.2153i 1.13540i 0.823234 + 0.567702i \(0.192167\pi\)
−0.823234 + 0.567702i \(0.807833\pi\)
\(318\) −7.31143 4.22126i −0.410005 0.236716i
\(319\) 6.54954 + 3.78138i 0.366704 + 0.211716i
\(320\) 4.39924i 0.245925i
\(321\) 7.10282 12.3024i 0.396440 0.686655i
\(322\) −2.70436 4.68409i −0.150708 0.261034i
\(323\) −22.0702 + 12.7422i −1.22802 + 0.708996i
\(324\) −1.00000 −0.0555556
\(325\) 30.7657 41.6138i 1.70657 2.30832i
\(326\) −14.0516 −0.778246
\(327\) 2.97757 1.71910i 0.164660 0.0950666i
\(328\) −1.02848 1.78138i −0.0567882 0.0983601i
\(329\) −3.79432 + 6.57196i −0.209188 + 0.362324i
\(330\) 4.93514i 0.271671i
\(331\) −21.0120 12.1313i −1.15492 0.666796i −0.204842 0.978795i \(-0.565668\pi\)
−0.950083 + 0.311999i \(0.899002\pi\)
\(332\) −9.64683 5.56960i −0.529438 0.305671i
\(333\) 7.61971i 0.417558i
\(334\) −0.243632 + 0.421983i −0.0133310 + 0.0230899i
\(335\) −11.6049 20.1002i −0.634042 1.09819i
\(336\) −0.866025 + 0.500000i −0.0472456 + 0.0272772i
\(337\) 8.14035 0.443433 0.221717 0.975111i \(-0.428834\pi\)
0.221717 + 0.975111i \(0.428834\pi\)
\(338\) 9.51501 + 8.85803i 0.517548 + 0.481813i
\(339\) 6.02589 0.327282
\(340\) −12.0224 + 6.94115i −0.652008 + 0.376437i
\(341\) −3.13319 5.42684i −0.169672 0.293880i
\(342\) −4.03796 + 6.99395i −0.218348 + 0.378189i
\(343\) 1.00000i 0.0539949i
\(344\) 1.37344 + 0.792959i 0.0740512 + 0.0427535i
\(345\) −20.6065 11.8971i −1.10941 0.640520i
\(346\) 3.43821i 0.184839i
\(347\) 6.73894 11.6722i 0.361765 0.626596i −0.626486 0.779433i \(-0.715507\pi\)
0.988251 + 0.152836i \(0.0488408\pi\)
\(348\) 3.37076 + 5.83834i 0.180692 + 0.312968i
\(349\) −5.64467 + 3.25895i −0.302152 + 0.174448i −0.643409 0.765522i \(-0.722481\pi\)
0.341257 + 0.939970i \(0.389147\pi\)
\(350\) −14.3533 −0.767218
\(351\) 2.14345 2.89924i 0.114409 0.154750i
\(352\) 1.12182 0.0597930
\(353\) 20.7274 11.9669i 1.10321 0.636936i 0.166145 0.986101i \(-0.446868\pi\)
0.937061 + 0.349165i \(0.113535\pi\)
\(354\) 3.63950 + 6.30380i 0.193437 + 0.335043i
\(355\) 19.0854 33.0569i 1.01295 1.75448i
\(356\) 10.4236i 0.552448i
\(357\) −2.73284 1.57781i −0.144637 0.0835063i
\(358\) 1.88451 + 1.08802i 0.0995993 + 0.0575037i
\(359\) 7.32429i 0.386561i −0.981144 0.193281i \(-0.938087\pi\)
0.981144 0.193281i \(-0.0619128\pi\)
\(360\) −2.19962 + 3.80986i −0.115930 + 0.200797i
\(361\) 23.1102 + 40.0280i 1.21633 + 2.10674i
\(362\) −9.28274 + 5.35939i −0.487890 + 0.281684i
\(363\) −9.74153 −0.511298
\(364\) 0.406663 3.58254i 0.0213149 0.187776i
\(365\) 56.3037 2.94707
\(366\) 9.02106 5.20831i 0.471538 0.272243i
\(367\) −5.11150 8.85339i −0.266818 0.462143i 0.701220 0.712945i \(-0.252639\pi\)
−0.968038 + 0.250802i \(0.919306\pi\)
\(368\) −2.70436 + 4.68409i −0.140975 + 0.244175i
\(369\) 2.05696i 0.107081i
\(370\) 29.0300 + 16.7605i 1.50920 + 0.871336i
\(371\) −7.31143 4.22126i −0.379591 0.219157i
\(372\) 5.58592i 0.289616i
\(373\) −0.781422 + 1.35346i −0.0404605 + 0.0700797i −0.885547 0.464551i \(-0.846216\pi\)
0.845086 + 0.534630i \(0.179549\pi\)
\(374\) 1.77001 + 3.06574i 0.0915249 + 0.158526i
\(375\) −35.6349 + 20.5738i −1.84018 + 1.06243i
\(376\) 7.58865 0.391355
\(377\) −24.1518 2.74153i −1.24388 0.141196i
\(378\) −1.00000 −0.0514344
\(379\) −7.26194 + 4.19268i −0.373021 + 0.215364i −0.674777 0.738021i \(-0.735760\pi\)
0.301757 + 0.953385i \(0.402427\pi\)
\(380\) 17.7640 + 30.7681i 0.911272 + 1.57837i
\(381\) −4.87818 + 8.44926i −0.249917 + 0.432869i
\(382\) 15.2563i 0.780578i
\(383\) 7.89645 + 4.55902i 0.403490 + 0.232955i 0.687989 0.725722i \(-0.258494\pi\)
−0.284499 + 0.958676i \(0.591827\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 4.93514i 0.251518i
\(386\) 7.08987 12.2800i 0.360865 0.625036i
\(387\) 0.792959 + 1.37344i 0.0403084 + 0.0698161i
\(388\) 1.06297 0.613704i 0.0539639 0.0311561i
\(389\) 37.1923 1.88572 0.942862 0.333184i \(-0.108123\pi\)
0.942862 + 0.333184i \(0.108123\pi\)
\(390\) −6.33092 14.5435i −0.320578 0.736438i
\(391\) −17.0678 −0.863157
\(392\) −0.866025 + 0.500000i −0.0437409 + 0.0252538i
\(393\) 3.81381 + 6.60571i 0.192381 + 0.333214i
\(394\) −5.98495 + 10.3662i −0.301517 + 0.522243i
\(395\) 15.4900i 0.779386i
\(396\) 0.971521 + 0.560908i 0.0488208 + 0.0281867i
\(397\) −27.4588 15.8533i −1.37812 0.795656i −0.386184 0.922422i \(-0.626207\pi\)
−0.991933 + 0.126765i \(0.959541\pi\)
\(398\) 4.99368i 0.250310i
\(399\) −4.03796 + 6.99395i −0.202151 + 0.350135i
\(400\) 7.17667 + 12.4304i 0.358834 + 0.621518i
\(401\) −23.3818 + 13.4995i −1.16763 + 0.674132i −0.953121 0.302590i \(-0.902149\pi\)
−0.214509 + 0.976722i \(0.568815\pi\)
\(402\) −5.27585 −0.263135
\(403\) 16.1949 + 11.9731i 0.806727 + 0.596425i
\(404\) −10.8143 −0.538031
\(405\) −3.80986 + 2.19962i −0.189313 + 0.109300i
\(406\) 3.37076 + 5.83834i 0.167288 + 0.289752i
\(407\) 4.27396 7.40271i 0.211852 0.366939i
\(408\) 3.15561i 0.156226i
\(409\) 8.94747 + 5.16583i 0.442424 + 0.255434i 0.704625 0.709580i \(-0.251115\pi\)
−0.262201 + 0.965013i \(0.584448\pi\)
\(410\) −7.83671 4.52453i −0.387028 0.223451i
\(411\) 7.35334i 0.362714i
\(412\) 8.64551 14.9745i 0.425934 0.737739i
\(413\) 3.63950 + 6.30380i 0.179088 + 0.310190i
\(414\) −4.68409 + 2.70436i −0.230210 + 0.132912i
\(415\) −49.0040 −2.40551
\(416\) −3.30591 + 1.43909i −0.162085 + 0.0705573i
\(417\) 8.58907 0.420609
\(418\) 7.84592 4.52984i 0.383757 0.221562i
\(419\) −12.7635 22.1070i −0.623536 1.08000i −0.988822 0.149101i \(-0.952362\pi\)
0.365285 0.930896i \(-0.380971\pi\)
\(420\) −2.19962 + 3.80986i −0.107331 + 0.185902i
\(421\) 4.31438i 0.210270i 0.994458 + 0.105135i \(0.0335274\pi\)
−0.994458 + 0.105135i \(0.966473\pi\)
\(422\) −5.67667 3.27743i −0.276336 0.159543i
\(423\) 6.57196 + 3.79432i 0.319540 + 0.184486i
\(424\) 8.44252i 0.410005i
\(425\) −22.6468 + 39.2254i −1.09853 + 1.90271i
\(426\) −4.33834 7.51422i −0.210193 0.364065i
\(427\) 9.02106 5.20831i 0.436560 0.252048i
\(428\) −14.2056 −0.686655
\(429\) −3.70862 + 1.61440i −0.179054 + 0.0779438i
\(430\) 6.97684 0.336453
\(431\) −6.37502 + 3.68062i −0.307074 + 0.177289i −0.645616 0.763662i \(-0.723399\pi\)
0.338542 + 0.940951i \(0.390066\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −13.4103 + 23.2273i −0.644458 + 1.11623i 0.339969 + 0.940437i \(0.389584\pi\)
−0.984426 + 0.175797i \(0.943750\pi\)
\(434\) 5.58592i 0.268133i
\(435\) 25.6843 + 14.8288i 1.23147 + 0.710987i
\(436\) −2.97757 1.71910i −0.142600 0.0823301i
\(437\) 43.6804i 2.08952i
\(438\) 6.39924 11.0838i 0.305768 0.529605i
\(439\) 17.4346 + 30.1976i 0.832109 + 1.44125i 0.896363 + 0.443321i \(0.146200\pi\)
−0.0642541 + 0.997934i \(0.520467\pi\)
\(440\) 4.27396 2.46757i 0.203753 0.117637i
\(441\) −1.00000 −0.0476190
\(442\) −9.14888 6.76390i −0.435168 0.321726i
\(443\) −8.59832 −0.408518 −0.204259 0.978917i \(-0.565479\pi\)
−0.204259 + 0.978917i \(0.565479\pi\)
\(444\) 6.59886 3.80986i 0.313168 0.180808i
\(445\) −22.9279 39.7123i −1.08689 1.88254i
\(446\) −3.71673 + 6.43757i −0.175992 + 0.304828i
\(447\) 3.47894i 0.164548i
\(448\) 0.866025 + 0.500000i 0.0409159 + 0.0236228i
\(449\) −27.1348 15.6663i −1.28057 0.739337i −0.303616 0.952794i \(-0.598194\pi\)
−0.976952 + 0.213458i \(0.931527\pi\)
\(450\) 14.3533i 0.676623i
\(451\) −1.15376 + 1.99838i −0.0543286 + 0.0940999i
\(452\) −3.01295 5.21858i −0.141717 0.245461i
\(453\) −14.1154 + 8.14956i −0.663202 + 0.382900i
\(454\) −11.7235 −0.550213
\(455\) −6.33092 14.5435i −0.296798 0.681809i
\(456\) 8.07591 0.378189
\(457\) 8.32180 4.80459i 0.389277 0.224749i −0.292570 0.956244i \(-0.594510\pi\)
0.681847 + 0.731495i \(0.261177\pi\)
\(458\) 4.85334 + 8.40623i 0.226782 + 0.392797i
\(459\) −1.57781 + 2.73284i −0.0736457 + 0.127558i
\(460\) 23.7943i 1.10941i
\(461\) −11.5452 6.66562i −0.537713 0.310449i 0.206439 0.978460i \(-0.433813\pi\)
−0.744151 + 0.668011i \(0.767146\pi\)
\(462\) 0.971521 + 0.560908i 0.0451993 + 0.0260958i
\(463\) 5.55011i 0.257935i 0.991649 + 0.128968i \(0.0411664\pi\)
−0.991649 + 0.128968i \(0.958834\pi\)
\(464\) 3.37076 5.83834i 0.156484 0.271038i
\(465\) −12.2869 21.2815i −0.569792 0.986908i
\(466\) 10.2575 5.92219i 0.475171 0.274340i
\(467\) −16.9272 −0.783299 −0.391650 0.920114i \(-0.628095\pi\)
−0.391650 + 0.920114i \(0.628095\pi\)
\(468\) −3.58254 0.406663i −0.165603 0.0187980i
\(469\) −5.27585 −0.243616
\(470\) 28.9117 16.6922i 1.33360 0.769952i
\(471\) −0.342286 0.592856i −0.0157717 0.0273174i
\(472\) 3.63950 6.30380i 0.167522 0.290156i
\(473\) 1.77911i 0.0818035i
\(474\) 3.04933 + 1.76053i 0.140060 + 0.0808638i
\(475\) 100.386 + 57.9582i 4.60605 + 2.65930i
\(476\) 3.15561i 0.144637i
\(477\) −4.22126 + 7.31143i −0.193278 + 0.334768i
\(478\) −0.752418 1.30323i −0.0344148 0.0596081i
\(479\) 16.7981 9.69840i 0.767526 0.443131i −0.0644654 0.997920i \(-0.520534\pi\)
0.831991 + 0.554789i \(0.187201\pi\)
\(480\) 4.39924 0.200797
\(481\) −3.09865 + 27.2980i −0.141286 + 1.24468i
\(482\) 2.95788 0.134728
\(483\) −4.68409 + 2.70436i −0.213133 + 0.123053i
\(484\) 4.87076 + 8.43641i 0.221398 + 0.383473i
\(485\) 2.69983 4.67625i 0.122593 0.212337i
\(486\) 1.00000i 0.0453609i
\(487\) −13.3417 7.70283i −0.604570 0.349049i 0.166267 0.986081i \(-0.446829\pi\)
−0.770837 + 0.637032i \(0.780162\pi\)
\(488\) −9.02106 5.20831i −0.408364 0.235769i
\(489\) 14.0516i 0.635435i
\(490\) −2.19962 + 3.80986i −0.0993688 + 0.172112i
\(491\) −4.87818 8.44926i −0.220149 0.381310i 0.734704 0.678388i \(-0.237321\pi\)
−0.954853 + 0.297078i \(0.903988\pi\)
\(492\) −1.78138 + 1.02848i −0.0803107 + 0.0463674i
\(493\) 21.2736 0.958117
\(494\) −17.3103 + 23.4140i −0.778829 + 1.05345i
\(495\) 4.93514 0.221818
\(496\) −4.83755 + 2.79296i −0.217212 + 0.125408i
\(497\) −4.33834 7.51422i −0.194601 0.337059i
\(498\) −5.56960 + 9.64683i −0.249580 + 0.432285i
\(499\) 5.52642i 0.247397i 0.992320 + 0.123698i \(0.0394755\pi\)
−0.992320 + 0.123698i \(0.960525\pi\)
\(500\) 35.6349 + 20.5738i 1.59364 + 0.920089i
\(501\) 0.421983 + 0.243632i 0.0188528 + 0.0108847i
\(502\) 7.63455i 0.340747i
\(503\) −2.06759 + 3.58117i −0.0921893 + 0.159677i −0.908432 0.418032i \(-0.862720\pi\)
0.816243 + 0.577709i \(0.196053\pi\)
\(504\) 0.500000 + 0.866025i 0.0222718 + 0.0385758i
\(505\) −41.2009 + 23.7873i −1.83342 + 1.05852i
\(506\) 6.06759 0.269737
\(507\) 8.85803 9.51501i 0.393399 0.422576i
\(508\) 9.75637 0.432869
\(509\) −7.70067 + 4.44599i −0.341326 + 0.197065i −0.660858 0.750511i \(-0.729808\pi\)
0.319532 + 0.947575i \(0.396474\pi\)
\(510\) 6.94115 + 12.0224i 0.307359 + 0.532362i
\(511\) 6.39924 11.0838i 0.283086 0.490319i
\(512\) 1.00000i 0.0441942i
\(513\) 6.99395 + 4.03796i 0.308790 + 0.178280i
\(514\) 18.4665 + 10.6616i 0.814521 + 0.470264i
\(515\) 76.0674i 3.35193i
\(516\) 0.792959 1.37344i 0.0349081 0.0604625i
\(517\) −4.25653 7.37253i −0.187202 0.324244i
\(518\) 6.59886 3.80986i 0.289937 0.167395i
\(519\) −3.43821 −0.150921
\(520\) −9.42957 + 12.7545i −0.413514 + 0.559321i
\(521\) 8.17974 0.358361 0.179180 0.983816i \(-0.442655\pi\)
0.179180 + 0.983816i \(0.442655\pi\)
\(522\) 5.83834 3.37076i 0.255537 0.147534i
\(523\) −3.12787 5.41763i −0.136772 0.236896i 0.789501 0.613749i \(-0.210339\pi\)
−0.926273 + 0.376853i \(0.877006\pi\)
\(524\) 3.81381 6.60571i 0.166607 0.288572i
\(525\) 14.3533i 0.626431i
\(526\) −4.60002 2.65582i −0.200570 0.115799i
\(527\) −15.2654 8.81349i −0.664972 0.383922i
\(528\) 1.12182i 0.0488208i
\(529\) −3.12713 + 5.41635i −0.135962 + 0.235494i
\(530\) 18.5703 + 32.1648i 0.806644 + 1.39715i
\(531\) 6.30380 3.63950i 0.273562 0.157941i
\(532\) 8.07591 0.350135
\(533\) 0.836488 7.36914i 0.0362323 0.319193i
\(534\) −10.4236 −0.451072
\(535\) −54.1214 + 31.2470i −2.33987 + 1.35093i
\(536\) 2.63792 + 4.56902i 0.113941 + 0.197352i
\(537\) 1.08802 1.88451i 0.0469516 0.0813225i
\(538\) 2.03283i 0.0876416i
\(539\) 0.971521 + 0.560908i 0.0418464 + 0.0241600i
\(540\) 3.80986 + 2.19962i 0.163950 + 0.0946566i
\(541\) 35.8526i 1.54142i −0.637183 0.770712i \(-0.719901\pi\)
0.637183 0.770712i \(-0.280099\pi\)
\(542\) −0.704938 + 1.22099i −0.0302797 + 0.0524459i
\(543\) 5.35939 + 9.28274i 0.229994 + 0.398361i
\(544\) 2.73284 1.57781i 0.117170 0.0676479i
\(545\) −15.1255 −0.647906
\(546\) −3.58254 0.406663i −0.153319 0.0174036i
\(547\) 16.7073 0.714353 0.357177 0.934037i \(-0.383739\pi\)
0.357177 + 0.934037i \(0.383739\pi\)
\(548\) 6.36818 3.67667i 0.272035 0.157060i
\(549\) −5.20831 9.02106i −0.222285 0.385009i
\(550\) 8.05090 13.9446i 0.343292 0.594599i
\(551\) 54.4440i 2.31939i
\(552\) 4.68409 + 2.70436i 0.199368 + 0.115105i
\(553\) 3.04933 + 1.76053i 0.129671 + 0.0748653i
\(554\) 23.5696i 1.00138i
\(555\) 16.7605 29.0300i 0.711443 1.23226i
\(556\) −4.29454 7.43835i −0.182129 0.315456i
\(557\) −12.1384 + 7.00811i −0.514321 + 0.296943i −0.734608 0.678492i \(-0.762634\pi\)
0.220287 + 0.975435i \(0.429301\pi\)
\(558\) −5.58592 −0.236471
\(559\) 2.28228 + 5.24289i 0.0965302 + 0.221751i
\(560\) 4.39924 0.185902
\(561\) 3.06574 1.77001i 0.129436 0.0747298i
\(562\) 4.06297 + 7.03726i 0.171386 + 0.296849i
\(563\) 13.4476 23.2919i 0.566747 0.981635i −0.430138 0.902763i \(-0.641535\pi\)
0.996885 0.0788716i \(-0.0251317\pi\)
\(564\) 7.58865i 0.319540i
\(565\) −22.9578 13.2547i −0.965842 0.557629i
\(566\) 17.2574 + 9.96358i 0.725383 + 0.418800i
\(567\) 1.00000i 0.0419961i
\(568\) −4.33834 + 7.51422i −0.182033 + 0.315290i
\(569\) 3.92493 + 6.79817i 0.164541 + 0.284994i 0.936492 0.350688i \(-0.114052\pi\)
−0.771951 + 0.635682i \(0.780719\pi\)
\(570\) 30.7681 17.7640i 1.28873 0.744050i
\(571\) 7.24502 0.303195 0.151597 0.988442i \(-0.451558\pi\)
0.151597 + 0.988442i \(0.451558\pi\)
\(572\) 3.25242 + 2.40456i 0.135990 + 0.100540i
\(573\) −15.2563 −0.637340
\(574\) −1.78138 + 1.02848i −0.0743533 + 0.0429279i
\(575\) 38.8166 + 67.2323i 1.61876 + 2.80378i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 31.9688i 1.33088i −0.746451 0.665440i \(-0.768244\pi\)
0.746451 0.665440i \(-0.231756\pi\)
\(578\) −6.09865 3.52106i −0.253671 0.146457i
\(579\) −12.2800 7.08987i −0.510340 0.294645i
\(580\) 29.6576i 1.23147i
\(581\) −5.56960 + 9.64683i −0.231066 + 0.400218i
\(582\) −0.613704 1.06297i −0.0254388 0.0440614i
\(583\) 8.20208 4.73548i 0.339696 0.196123i
\(584\) −12.7985 −0.529605
\(585\) −14.5435 + 6.33092i −0.601299 + 0.261751i
\(586\) −20.2163 −0.835126
\(587\) −3.59302 + 2.07443i −0.148300 + 0.0856210i −0.572314 0.820035i \(-0.693954\pi\)
0.424014 + 0.905656i \(0.360621\pi\)
\(588\) 0.500000 + 0.866025i 0.0206197 + 0.0357143i
\(589\) −22.5557 + 39.0676i −0.929391 + 1.60975i
\(590\) 32.0221i 1.31833i
\(591\) 10.3662 + 5.98495i 0.426410 + 0.246188i
\(592\) −6.59886 3.80986i −0.271212 0.156584i
\(593\) 21.0163i 0.863037i 0.902104 + 0.431519i \(0.142022\pi\)
−0.902104 + 0.431519i \(0.857978\pi\)
\(594\) 0.560908 0.971521i 0.0230143 0.0398620i
\(595\) 6.94115 + 12.0224i 0.284559 + 0.492871i
\(596\) −3.01285 + 1.73947i −0.123411 + 0.0712515i
\(597\) −4.99368 −0.204378
\(598\) −17.8807 + 7.78365i −0.731197 + 0.318297i
\(599\) −35.0575 −1.43241 −0.716205 0.697890i \(-0.754122\pi\)
−0.716205 + 0.697890i \(0.754122\pi\)
\(600\) 12.4304 7.17667i 0.507467 0.292986i
\(601\) 15.7586 + 27.2947i 0.642806 + 1.11337i 0.984803 + 0.173672i \(0.0555634\pi\)
−0.341997 + 0.939701i \(0.611103\pi\)
\(602\) 0.792959 1.37344i 0.0323186 0.0559774i
\(603\) 5.27585i 0.214849i
\(604\) 14.1154 + 8.14956i 0.574349 + 0.331601i
\(605\) 37.1138 + 21.4277i 1.50889 + 0.871159i
\(606\) 10.8143i 0.439300i
\(607\) −16.9445 + 29.3488i −0.687757 + 1.19123i 0.284805 + 0.958586i \(0.408071\pi\)
−0.972562 + 0.232645i \(0.925262\pi\)
\(608\) −4.03796 6.99395i −0.163761 0.283642i
\(609\) 5.83834 3.37076i 0.236581 0.136590i
\(610\) −45.8253 −1.85541
\(611\) 22.0013 + 16.2659i 0.890079 + 0.658048i
\(612\) 3.15561 0.127558
\(613\) −7.08979 + 4.09329i −0.286354 + 0.165327i −0.636296 0.771445i \(-0.719534\pi\)
0.349942 + 0.936771i \(0.386201\pi\)
\(614\) 13.1382 + 22.7560i 0.530214 + 0.918358i
\(615\) −4.52453 + 7.83671i −0.182447 + 0.316007i
\(616\) 1.12182i 0.0451993i
\(617\) −31.4716 18.1701i −1.26700 0.731502i −0.292580 0.956241i \(-0.594514\pi\)
−0.974419 + 0.224739i \(0.927847\pi\)
\(618\) −14.9745 8.64551i −0.602361 0.347773i
\(619\) 38.2625i 1.53790i −0.639309 0.768950i \(-0.720780\pi\)
0.639309 0.768950i \(-0.279220\pi\)
\(620\) −12.2869 + 21.2815i −0.493454 + 0.854687i
\(621\) 2.70436 + 4.68409i 0.108522 + 0.187966i
\(622\) −6.32213 + 3.65008i −0.253494 + 0.146355i
\(623\) −10.4236 −0.417611
\(624\) 1.43909 + 3.30591i 0.0576098 + 0.132342i
\(625\) 109.252 4.37007
\(626\) −22.0329 + 12.7207i −0.880610 + 0.508421i
\(627\) −4.52984 7.84592i −0.180905 0.313336i
\(628\) −0.342286 + 0.592856i −0.0136587 + 0.0236575i
\(629\) 24.0449i 0.958731i
\(630\) 3.80986 + 2.19962i 0.151788 + 0.0876350i
\(631\) −8.77412 5.06574i −0.349292 0.201664i 0.315081 0.949065i \(-0.397968\pi\)
−0.664374 + 0.747401i \(0.731302\pi\)
\(632\) 3.52106i 0.140060i
\(633\) −3.27743 + 5.67667i −0.130266 + 0.225627i
\(634\) −10.1077 17.5070i −0.401426 0.695290i
\(635\) 37.1704 21.4603i 1.47506 0.851627i
\(636\) 8.44252 0.334768
\(637\) −3.58254 0.406663i −0.141946 0.0161126i
\(638\) −7.56276 −0.299412
\(639\) −7.51422 + 4.33834i −0.297258 + 0.171622i
\(640\) −2.19962 3.80986i −0.0869477 0.150598i
\(641\) 13.4520 23.2995i 0.531322 0.920276i −0.468010 0.883723i \(-0.655029\pi\)
0.999332 0.0365532i \(-0.0116378\pi\)
\(642\) 14.2056i 0.560652i
\(643\) −28.9459 16.7119i −1.14151 0.659053i −0.194708 0.980861i \(-0.562376\pi\)
−0.946805 + 0.321808i \(0.895709\pi\)
\(644\) 4.68409 + 2.70436i 0.184579 + 0.106567i
\(645\) 6.97684i 0.274713i
\(646\) 12.7422 22.0702i 0.501336 0.868339i
\(647\) −10.8789 18.8428i −0.427693 0.740786i 0.568975 0.822355i \(-0.307340\pi\)
−0.996668 + 0.0815693i \(0.974007\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −8.16570 −0.320532
\(650\) −5.83697 + 51.4215i −0.228945 + 2.01692i
\(651\) −5.58592 −0.218929
\(652\) 12.1690 7.02580i 0.476576 0.275151i
\(653\) −3.21872 5.57498i −0.125958 0.218166i 0.796149 0.605101i \(-0.206867\pi\)
−0.922107 + 0.386935i \(0.873534\pi\)
\(654\) −1.71910 + 2.97757i −0.0672223 + 0.116432i
\(655\) 33.5557i 1.31113i
\(656\) 1.78138 + 1.02848i 0.0695511 + 0.0401554i
\(657\) −11.0838 6.39924i −0.432421 0.249658i
\(658\) 7.58865i 0.295836i
\(659\) −4.51690 + 7.82350i −0.175953 + 0.304760i −0.940491 0.339819i \(-0.889634\pi\)
0.764537 + 0.644579i \(0.222967\pi\)
\(660\) −2.46757 4.27396i −0.0960501 0.166364i
\(661\) −8.45556 + 4.88182i −0.328883 + 0.189881i −0.655345 0.755330i \(-0.727477\pi\)
0.326462 + 0.945210i \(0.394143\pi\)
\(662\) 24.2626 0.942992
\(663\) −6.76390 + 9.14888i −0.262688 + 0.355313i
\(664\) 11.1392 0.432285
\(665\) 30.7681 17.7640i 1.19313 0.688857i
\(666\) −3.80986 6.59886i −0.147629 0.255701i
\(667\) 18.2315 31.5779i 0.705927 1.22270i
\(668\) 0.487264i 0.0188528i
\(669\) 6.43757 + 3.71673i 0.248891 + 0.143697i
\(670\) 20.1002 + 11.6049i 0.776540 + 0.448335i
\(671\) 11.6855i 0.451115i
\(672\) 0.500000 0.866025i 0.0192879 0.0334077i
\(673\) −20.3902 35.3169i −0.785985 1.36137i −0.928409 0.371559i \(-0.878823\pi\)
0.142425 0.989806i \(-0.454510\pi\)
\(674\) −7.04975 + 4.07017i −0.271546 + 0.156777i
\(675\) 14.3533 0.552460
\(676\) −12.6693 2.91377i −0.487279 0.112068i
\(677\) 28.6313 1.10039 0.550195 0.835036i \(-0.314553\pi\)
0.550195 + 0.835036i \(0.314553\pi\)
\(678\) −5.21858 + 3.01295i −0.200418 + 0.115712i
\(679\) −0.613704 1.06297i −0.0235518 0.0407929i
\(680\) 6.94115 12.0224i 0.266181 0.461039i
\(681\) 11.7235i 0.449247i
\(682\) 5.42684 + 3.13319i 0.207804 + 0.119976i
\(683\) 34.7160 + 20.0433i 1.32837 + 0.766935i 0.985047 0.172283i \(-0.0551144\pi\)
0.343322 + 0.939218i \(0.388448\pi\)
\(684\) 8.07591i 0.308790i
\(685\) 16.1746 28.0152i 0.617998 1.07040i
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) 8.40623 4.85334i 0.320718 0.185166i
\(688\) −1.58592 −0.0604625
\(689\) −18.0961 + 24.4769i −0.689408 + 0.932496i
\(690\) 23.7943 0.905833
\(691\) −24.3518 + 14.0595i −0.926385 + 0.534848i −0.885666 0.464322i \(-0.846298\pi\)
−0.0407184 + 0.999171i \(0.512965\pi\)
\(692\) 1.71910 + 2.97757i 0.0653505 + 0.113190i
\(693\) 0.560908 0.971521i 0.0213071 0.0369050i
\(694\) 13.4779i 0.511614i
\(695\) −32.7231 18.8927i −1.24126 0.716641i
\(696\) −5.83834 3.37076i −0.221302 0.127768i
\(697\) 6.49096i 0.245863i
\(698\) 3.25895 5.64467i 0.123353 0.213654i
\(699\) −5.92219 10.2575i −0.223998 0.387976i
\(700\) 12.4304 7.17667i 0.469823 0.271253i
\(701\) −3.59224 −0.135677 −0.0678385 0.997696i \(-0.521610\pi\)
−0.0678385 + 0.997696i \(0.521610\pi\)
\(702\) −0.406663 + 3.58254i −0.0153485 + 0.135214i
\(703\) −61.5361 −2.32088
\(704\) −0.971521 + 0.560908i −0.0366156 + 0.0211400i
\(705\) −16.6922 28.9117i −0.628663 1.08888i
\(706\) −11.9669 + 20.7274i −0.450382 + 0.780085i
\(707\) 10.8143i 0.406713i
\(708\) −6.30380 3.63950i −0.236911 0.136781i
\(709\) 7.28564 + 4.20637i 0.273618 + 0.157973i 0.630531 0.776164i \(-0.282837\pi\)
−0.356913 + 0.934138i \(0.616171\pi\)
\(710\) 38.1708i 1.43252i
\(711\) 1.76053 3.04933i 0.0660250 0.114359i
\(712\) 5.21178 + 9.02707i 0.195320 + 0.338304i
\(713\) −26.1649 + 15.1063i −0.979885 + 0.565737i
\(714\) 3.15561 0.118096
\(715\) 17.6804 + 2.00694i 0.661208 + 0.0750552i
\(716\) −2.17604 −0.0813225
\(717\) −1.30323 + 0.752418i −0.0486698 + 0.0280995i
\(718\) 3.66215 + 6.34302i 0.136670 + 0.236720i
\(719\) −24.1674 + 41.8591i −0.901290 + 1.56108i −0.0754696 + 0.997148i \(0.524046\pi\)
−0.825821 + 0.563933i \(0.809288\pi\)
\(720\) 4.39924i 0.163950i
\(721\) −14.9745 8.64551i −0.557678 0.321976i
\(722\) −40.0280 23.1102i −1.48969 0.860072i
\(723\) 2.95788i 0.110005i
\(724\) 5.35939 9.28274i 0.199180 0.344990i
\(725\) −48.3817 83.7996i −1.79685 3.11224i
\(726\) 8.43641 4.87076i 0.313105 0.180771i
\(727\) 46.3297 1.71827 0.859137 0.511745i \(-0.171001\pi\)
0.859137 + 0.511745i \(0.171001\pi\)
\(728\) 1.43909 + 3.30591i 0.0533363 + 0.122525i
\(729\) 1.00000 0.0370370
\(730\) −48.7604 + 28.1518i −1.80470 + 1.04195i
\(731\) −2.50227 4.33406i −0.0925498 0.160301i
\(732\) −5.20831 + 9.02106i −0.192505 + 0.333428i
\(733\) 17.1464i 0.633315i −0.948540 0.316658i \(-0.897439\pi\)
0.948540 0.316658i \(-0.102561\pi\)
\(734\) 8.85339 + 5.11150i 0.326784 + 0.188669i
\(735\) 3.80986 + 2.19962i 0.140529 + 0.0811343i
\(736\) 5.40872i 0.199368i
\(737\) 2.95927 5.12560i 0.109006 0.188804i
\(738\) 1.02848 + 1.78138i 0.0378588 + 0.0655734i
\(739\) −13.0327 + 7.52443i −0.479416 + 0.276791i −0.720173 0.693795i \(-0.755938\pi\)
0.240757 + 0.970585i \(0.422604\pi\)
\(740\) −33.5210 −1.23226
\(741\) 23.4140 + 17.3103i 0.860136 + 0.635911i
\(742\) 8.44252 0.309935
\(743\) 20.1776 11.6496i 0.740245 0.427381i −0.0819132 0.996639i \(-0.526103\pi\)
0.822158 + 0.569259i \(0.192770\pi\)
\(744\) 2.79296 + 4.83755i 0.102395 + 0.177353i
\(745\) −7.65235 + 13.2543i −0.280361 + 0.485599i
\(746\) 1.56284i 0.0572198i
\(747\) 9.64683 + 5.56960i 0.352959 + 0.203781i
\(748\) −3.06574 1.77001i −0.112095 0.0647179i
\(749\) 14.2056i 0.519062i
\(750\) 20.5738 35.6349i 0.751249 1.30120i
\(751\) 15.4534 + 26.7661i 0.563903 + 0.976709i 0.997151 + 0.0754344i \(0.0240343\pi\)
−0.433247 + 0.901275i \(0.642632\pi\)
\(752\) −6.57196 + 3.79432i −0.239655 + 0.138365i
\(753\) −7.63455 −0.278219
\(754\) 22.2869 9.70168i 0.811640 0.353314i
\(755\) 71.7038 2.60957
\(756\) 0.866025 0.500000i 0.0314970 0.0181848i
\(757\) −7.58518 13.1379i −0.275688 0.477506i 0.694620 0.719376i \(-0.255572\pi\)
−0.970308 + 0.241871i \(0.922239\pi\)
\(758\) 4.19268 7.26194i 0.152285 0.263766i
\(759\) 6.06759i 0.220240i
\(760\) −30.7681 17.7640i −1.11608 0.644366i
\(761\) 9.45208 + 5.45716i 0.342638 + 0.197822i 0.661438 0.750000i \(-0.269947\pi\)
−0.318800 + 0.947822i \(0.603280\pi\)
\(762\) 9.75637i 0.353436i
\(763\) −1.71910 + 2.97757i −0.0622357 + 0.107795i
\(764\) 7.62813 + 13.2123i 0.275976 + 0.478005i
\(765\) 12.0224 6.94115i 0.434672 0.250958i
\(766\) −9.11803 −0.329448
\(767\) 24.0637 10.4752i 0.868890 0.378236i
\(768\) −1.00000 −0.0360844
\(769\) −15.9112 + 9.18636i −0.573774 + 0.331269i −0.758655 0.651492i \(-0.774143\pi\)
0.184881 + 0.982761i \(0.440810\pi\)
\(770\) −2.46757 4.27396i −0.0889251 0.154023i
\(771\) 10.6616 18.4665i 0.383969 0.665054i
\(772\) 14.1797i 0.510340i
\(773\) −12.8159 7.39924i −0.460955 0.266132i 0.251491 0.967860i \(-0.419079\pi\)
−0.712446 + 0.701727i \(0.752412\pi\)
\(774\) −1.37344 0.792959i −0.0493675 0.0285023i
\(775\) 80.1766i 2.88003i
\(776\) −0.613704 + 1.06297i −0.0220307 + 0.0381583i