Properties

Label 731.2.e.a.307.10
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.10
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.10

$q$-expansion

\(f(q)\) \(=\) \(q-1.31896 q^{2} +(1.65592 - 2.86814i) q^{3} -0.260346 q^{4} +(-0.0483968 + 0.0838257i) q^{5} +(-2.18409 + 3.78296i) q^{6} +(-1.22618 - 2.12381i) q^{7} +2.98130 q^{8} +(-3.98416 - 6.90077i) q^{9} +O(q^{10})\) \(q-1.31896 q^{2} +(1.65592 - 2.86814i) q^{3} -0.260346 q^{4} +(-0.0483968 + 0.0838257i) q^{5} +(-2.18409 + 3.78296i) q^{6} +(-1.22618 - 2.12381i) q^{7} +2.98130 q^{8} +(-3.98416 - 6.90077i) q^{9} +(0.0638334 - 0.110563i) q^{10} +3.41685 q^{11} +(-0.431114 + 0.746711i) q^{12} +(-2.27375 - 3.93826i) q^{13} +(1.61728 + 2.80122i) q^{14} +(0.160283 + 0.277618i) q^{15} -3.41153 q^{16} +(0.500000 + 0.866025i) q^{17} +(5.25494 + 9.10183i) q^{18} +(-1.05890 + 1.83407i) q^{19} +(0.0125999 - 0.0218237i) q^{20} -8.12185 q^{21} -4.50669 q^{22} +(0.736015 - 1.27482i) q^{23} +(4.93681 - 8.55081i) q^{24} +(2.49532 + 4.32201i) q^{25} +(2.99899 + 5.19440i) q^{26} -16.4543 q^{27} +(0.319232 + 0.552926i) q^{28} +(-1.64169 - 2.84350i) q^{29} +(-0.211406 - 0.366166i) q^{30} +(1.52309 - 2.63808i) q^{31} -1.46294 q^{32} +(5.65804 - 9.80002i) q^{33} +(-0.659480 - 1.14225i) q^{34} +0.237373 q^{35} +(1.03726 + 1.79659i) q^{36} +(-0.131041 + 0.226970i) q^{37} +(1.39664 - 2.41906i) q^{38} -15.0606 q^{39} +(-0.144286 + 0.249910i) q^{40} +5.03275 q^{41} +10.7124 q^{42} +(-6.18746 - 2.17148i) q^{43} -0.889565 q^{44} +0.771282 q^{45} +(-0.970774 + 1.68143i) q^{46} +4.06549 q^{47} +(-5.64922 + 9.78474i) q^{48} +(0.492957 - 0.853827i) q^{49} +(-3.29122 - 5.70056i) q^{50} +3.31185 q^{51} +(0.591964 + 1.02531i) q^{52} +(-5.21765 + 9.03723i) q^{53} +21.7025 q^{54} +(-0.165365 + 0.286420i) q^{55} +(-3.65562 - 6.33172i) q^{56} +(3.50691 + 6.07414i) q^{57} +(2.16533 + 3.75045i) q^{58} -9.17786 q^{59} +(-0.0417290 - 0.0722768i) q^{60} +(4.01453 + 6.95338i) q^{61} +(-2.00890 + 3.47952i) q^{62} +(-9.77061 + 16.9232i) q^{63} +8.75262 q^{64} +0.440170 q^{65} +(-7.46273 + 12.9258i) q^{66} +(-4.99393 + 8.64974i) q^{67} +(-0.130173 - 0.225467i) q^{68} +(-2.43757 - 4.22199i) q^{69} -0.313085 q^{70} +(-2.11209 - 3.65824i) q^{71} +(-11.8780 - 20.5733i) q^{72} +(4.87124 + 8.43723i) q^{73} +(0.172838 - 0.299364i) q^{74} +16.5282 q^{75} +(0.275680 - 0.477492i) q^{76} +(-4.18968 - 7.25674i) q^{77} +19.8644 q^{78} +(-0.716526 - 1.24106i) q^{79} +(0.165107 - 0.285974i) q^{80} +(-15.2946 + 26.4910i) q^{81} -6.63800 q^{82} +(-2.19963 + 3.80987i) q^{83} +2.11449 q^{84} -0.0967936 q^{85} +(8.16101 + 2.86410i) q^{86} -10.8741 q^{87} +10.1867 q^{88} +(9.13187 - 15.8169i) q^{89} -1.01729 q^{90} +(-5.57607 + 9.65804i) q^{91} +(-0.191619 + 0.331894i) q^{92} +(-5.04425 - 8.73690i) q^{93} -5.36222 q^{94} +(-0.102495 - 0.177526i) q^{95} +(-2.42252 + 4.19593i) q^{96} +13.9407 q^{97} +(-0.650190 + 1.12616i) q^{98} +(-13.6133 - 23.5789i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31896 −0.932645 −0.466323 0.884615i \(-0.654421\pi\)
−0.466323 + 0.884615i \(0.654421\pi\)
\(3\) 1.65592 2.86814i 0.956047 1.65592i 0.224094 0.974567i \(-0.428058\pi\)
0.731953 0.681355i \(-0.238609\pi\)
\(4\) −0.260346 −0.130173
\(5\) −0.0483968 + 0.0838257i −0.0216437 + 0.0374880i −0.876644 0.481139i \(-0.840223\pi\)
0.855001 + 0.518627i \(0.173557\pi\)
\(6\) −2.18409 + 3.78296i −0.891653 + 1.54439i
\(7\) −1.22618 2.12381i −0.463453 0.802724i 0.535677 0.844423i \(-0.320056\pi\)
−0.999130 + 0.0416986i \(0.986723\pi\)
\(8\) 2.98130 1.05405
\(9\) −3.98416 6.90077i −1.32805 2.30026i
\(10\) 0.0638334 0.110563i 0.0201859 0.0349630i
\(11\) 3.41685 1.03022 0.515110 0.857124i \(-0.327751\pi\)
0.515110 + 0.857124i \(0.327751\pi\)
\(12\) −0.431114 + 0.746711i −0.124452 + 0.215557i
\(13\) −2.27375 3.93826i −0.630626 1.09228i −0.987424 0.158095i \(-0.949465\pi\)
0.356798 0.934182i \(-0.383868\pi\)
\(14\) 1.61728 + 2.80122i 0.432237 + 0.748657i
\(15\) 0.160283 + 0.277618i 0.0413848 + 0.0716806i
\(16\) −3.41153 −0.852882
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) 5.25494 + 9.10183i 1.23860 + 2.14532i
\(19\) −1.05890 + 1.83407i −0.242928 + 0.420763i −0.961547 0.274640i \(-0.911441\pi\)
0.718619 + 0.695404i \(0.244775\pi\)
\(20\) 0.0125999 0.0218237i 0.00281743 0.00487993i
\(21\) −8.12185 −1.77233
\(22\) −4.50669 −0.960829
\(23\) 0.736015 1.27482i 0.153470 0.265817i −0.779031 0.626985i \(-0.784289\pi\)
0.932501 + 0.361168i \(0.117622\pi\)
\(24\) 4.93681 8.55081i 1.00772 1.74543i
\(25\) 2.49532 + 4.32201i 0.499063 + 0.864403i
\(26\) 2.99899 + 5.19440i 0.588150 + 1.01871i
\(27\) −16.4543 −3.16663
\(28\) 0.319232 + 0.552926i 0.0603292 + 0.104493i
\(29\) −1.64169 2.84350i −0.304855 0.528024i 0.672374 0.740211i \(-0.265275\pi\)
−0.977229 + 0.212188i \(0.931941\pi\)
\(30\) −0.211406 0.366166i −0.0385973 0.0668525i
\(31\) 1.52309 2.63808i 0.273556 0.473813i −0.696214 0.717834i \(-0.745133\pi\)
0.969770 + 0.244022i \(0.0784668\pi\)
\(32\) −1.46294 −0.258615
\(33\) 5.65804 9.80002i 0.984939 1.70596i
\(34\) −0.659480 1.14225i −0.113100 0.195895i
\(35\) 0.237373 0.0401234
\(36\) 1.03726 + 1.79659i 0.172877 + 0.299432i
\(37\) −0.131041 + 0.226970i −0.0215430 + 0.0373136i −0.876596 0.481227i \(-0.840191\pi\)
0.855053 + 0.518541i \(0.173525\pi\)
\(38\) 1.39664 2.41906i 0.226565 0.392423i
\(39\) −15.0606 −2.41163
\(40\) −0.144286 + 0.249910i −0.0228136 + 0.0395142i
\(41\) 5.03275 0.785984 0.392992 0.919542i \(-0.371440\pi\)
0.392992 + 0.919542i \(0.371440\pi\)
\(42\) 10.7124 1.65296
\(43\) −6.18746 2.17148i −0.943579 0.331148i
\(44\) −0.889565 −0.134107
\(45\) 0.771282 0.114976
\(46\) −0.970774 + 1.68143i −0.143133 + 0.247913i
\(47\) 4.06549 0.593013 0.296507 0.955031i \(-0.404178\pi\)
0.296507 + 0.955031i \(0.404178\pi\)
\(48\) −5.64922 + 9.78474i −0.815395 + 1.41231i
\(49\) 0.492957 0.853827i 0.0704224 0.121975i
\(50\) −3.29122 5.70056i −0.465449 0.806181i
\(51\) 3.31185 0.463751
\(52\) 0.591964 + 1.02531i 0.0820906 + 0.142185i
\(53\) −5.21765 + 9.03723i −0.716699 + 1.24136i 0.245602 + 0.969371i \(0.421014\pi\)
−0.962301 + 0.271988i \(0.912319\pi\)
\(54\) 21.7025 2.95334
\(55\) −0.165365 + 0.286420i −0.0222978 + 0.0386209i
\(56\) −3.65562 6.33172i −0.488503 0.846112i
\(57\) 3.50691 + 6.07414i 0.464501 + 0.804539i
\(58\) 2.16533 + 3.75045i 0.284321 + 0.492459i
\(59\) −9.17786 −1.19486 −0.597428 0.801922i \(-0.703811\pi\)
−0.597428 + 0.801922i \(0.703811\pi\)
\(60\) −0.0417290 0.0722768i −0.00538719 0.00933089i
\(61\) 4.01453 + 6.95338i 0.514008 + 0.890289i 0.999868 + 0.0162518i \(0.00517332\pi\)
−0.485860 + 0.874037i \(0.661493\pi\)
\(62\) −2.00890 + 3.47952i −0.255131 + 0.441899i
\(63\) −9.77061 + 16.9232i −1.23098 + 2.13212i
\(64\) 8.75262 1.09408
\(65\) 0.440170 0.0545963
\(66\) −7.46273 + 12.9258i −0.918598 + 1.59106i
\(67\) −4.99393 + 8.64974i −0.610105 + 1.05673i 0.381117 + 0.924527i \(0.375540\pi\)
−0.991222 + 0.132207i \(0.957794\pi\)
\(68\) −0.130173 0.225467i −0.0157858 0.0273418i
\(69\) −2.43757 4.22199i −0.293449 0.508268i
\(70\) −0.313085 −0.0374209
\(71\) −2.11209 3.65824i −0.250659 0.434154i 0.713049 0.701115i \(-0.247314\pi\)
−0.963707 + 0.266961i \(0.913981\pi\)
\(72\) −11.8780 20.5733i −1.39983 2.42459i
\(73\) 4.87124 + 8.43723i 0.570135 + 0.987503i 0.996552 + 0.0829764i \(0.0264426\pi\)
−0.426416 + 0.904527i \(0.640224\pi\)
\(74\) 0.172838 0.299364i 0.0200920 0.0348003i
\(75\) 16.5282 1.90851
\(76\) 0.275680 0.477492i 0.0316227 0.0547721i
\(77\) −4.18968 7.25674i −0.477459 0.826982i
\(78\) 19.8644 2.24920
\(79\) −0.716526 1.24106i −0.0806154 0.139630i 0.822899 0.568188i \(-0.192355\pi\)
−0.903514 + 0.428558i \(0.859022\pi\)
\(80\) 0.165107 0.285974i 0.0184595 0.0319728i
\(81\) −15.2946 + 26.4910i −1.69940 + 2.94344i
\(82\) −6.63800 −0.733044
\(83\) −2.19963 + 3.80987i −0.241440 + 0.418187i −0.961125 0.276114i \(-0.910953\pi\)
0.719684 + 0.694301i \(0.244287\pi\)
\(84\) 2.11449 0.230710
\(85\) −0.0967936 −0.0104987
\(86\) 8.16101 + 2.86410i 0.880024 + 0.308843i
\(87\) −10.8741 −1.16582
\(88\) 10.1867 1.08590
\(89\) 9.13187 15.8169i 0.967977 1.67658i 0.266581 0.963813i \(-0.414106\pi\)
0.701396 0.712772i \(-0.252560\pi\)
\(90\) −1.01729 −0.107232
\(91\) −5.57607 + 9.65804i −0.584531 + 1.01244i
\(92\) −0.191619 + 0.331894i −0.0199777 + 0.0346023i
\(93\) −5.04425 8.73690i −0.523065 0.905975i
\(94\) −5.36222 −0.553071
\(95\) −0.102495 0.177526i −0.0105157 0.0182138i
\(96\) −2.42252 + 4.19593i −0.247248 + 0.428246i
\(97\) 13.9407 1.41546 0.707730 0.706483i \(-0.249719\pi\)
0.707730 + 0.706483i \(0.249719\pi\)
\(98\) −0.650190 + 1.12616i −0.0656791 + 0.113760i
\(99\) −13.6133 23.5789i −1.36819 2.36977i
\(100\) −0.649647 1.12522i −0.0649647 0.112522i
\(101\) −5.52837 9.57542i −0.550093 0.952790i −0.998267 0.0588432i \(-0.981259\pi\)
0.448174 0.893946i \(-0.352075\pi\)
\(102\) −4.36819 −0.432515
\(103\) −5.81736 10.0760i −0.573202 0.992814i −0.996234 0.0866999i \(-0.972368\pi\)
0.423033 0.906114i \(-0.360965\pi\)
\(104\) −6.77875 11.7411i −0.664712 1.15131i
\(105\) 0.393071 0.680820i 0.0383598 0.0664412i
\(106\) 6.88186 11.9197i 0.668425 1.15775i
\(107\) −8.64547 −0.835789 −0.417894 0.908496i \(-0.637232\pi\)
−0.417894 + 0.908496i \(0.637232\pi\)
\(108\) 4.28382 0.412211
\(109\) 4.44444 7.69800i 0.425700 0.737335i −0.570785 0.821099i \(-0.693361\pi\)
0.996486 + 0.0837648i \(0.0266944\pi\)
\(110\) 0.218109 0.377776i 0.0207959 0.0360196i
\(111\) 0.433988 + 0.751689i 0.0411923 + 0.0713471i
\(112\) 4.18315 + 7.24543i 0.395271 + 0.684629i
\(113\) 7.83955 0.737483 0.368741 0.929532i \(-0.379789\pi\)
0.368741 + 0.929532i \(0.379789\pi\)
\(114\) −4.62547 8.01154i −0.433215 0.750350i
\(115\) 0.0712415 + 0.123394i 0.00664331 + 0.0115065i
\(116\) 0.427409 + 0.740294i 0.0396839 + 0.0687346i
\(117\) −18.1180 + 31.3813i −1.67501 + 2.90120i
\(118\) 12.1052 1.11438
\(119\) 1.22618 2.12381i 0.112404 0.194689i
\(120\) 0.477852 + 0.827663i 0.0436217 + 0.0755550i
\(121\) 0.674881 0.0613528
\(122\) −5.29501 9.17122i −0.479387 0.830323i
\(123\) 8.33385 14.4347i 0.751438 1.30153i
\(124\) −0.396532 + 0.686814i −0.0356097 + 0.0616777i
\(125\) −0.967029 −0.0864937
\(126\) 12.8870 22.3210i 1.14807 1.98851i
\(127\) 6.42588 0.570205 0.285102 0.958497i \(-0.407972\pi\)
0.285102 + 0.958497i \(0.407972\pi\)
\(128\) −8.61846 −0.761771
\(129\) −16.4741 + 14.1507i −1.45046 + 1.24590i
\(130\) −0.580566 −0.0509190
\(131\) 5.57342 0.486952 0.243476 0.969907i \(-0.421712\pi\)
0.243476 + 0.969907i \(0.421712\pi\)
\(132\) −1.47305 + 2.55140i −0.128213 + 0.222071i
\(133\) 5.19361 0.450343
\(134\) 6.58679 11.4086i 0.569012 0.985557i
\(135\) 0.796335 1.37929i 0.0685376 0.118711i
\(136\) 1.49065 + 2.58189i 0.127822 + 0.221395i
\(137\) −20.5649 −1.75698 −0.878489 0.477762i \(-0.841448\pi\)
−0.878489 + 0.477762i \(0.841448\pi\)
\(138\) 3.21505 + 5.56863i 0.273683 + 0.474034i
\(139\) 10.3572 17.9392i 0.878487 1.52158i 0.0254862 0.999675i \(-0.491887\pi\)
0.853001 0.521909i \(-0.174780\pi\)
\(140\) −0.0617992 −0.00522299
\(141\) 6.73214 11.6604i 0.566949 0.981984i
\(142\) 2.78576 + 4.82507i 0.233776 + 0.404911i
\(143\) −7.76908 13.4564i −0.649683 1.12528i
\(144\) 13.5921 + 23.5421i 1.13267 + 1.96185i
\(145\) 0.317811 0.0263927
\(146\) −6.42497 11.1284i −0.531734 0.920990i
\(147\) −1.63260 2.82774i −0.134654 0.233228i
\(148\) 0.0341161 0.0590908i 0.00280432 0.00485723i
\(149\) 10.7483 18.6166i 0.880533 1.52513i 0.0297844 0.999556i \(-0.490518\pi\)
0.850749 0.525572i \(-0.176149\pi\)
\(150\) −21.8000 −1.77996
\(151\) 12.2700 0.998518 0.499259 0.866453i \(-0.333606\pi\)
0.499259 + 0.866453i \(0.333606\pi\)
\(152\) −3.15690 + 5.46791i −0.256058 + 0.443506i
\(153\) 3.98416 6.90077i 0.322100 0.557894i
\(154\) 5.52602 + 9.57135i 0.445299 + 0.771281i
\(155\) 0.147426 + 0.255349i 0.0118415 + 0.0205101i
\(156\) 3.92099 0.313930
\(157\) 8.77438 + 15.1977i 0.700271 + 1.21291i 0.968371 + 0.249515i \(0.0802710\pi\)
−0.268100 + 0.963391i \(0.586396\pi\)
\(158\) 0.945068 + 1.63691i 0.0751856 + 0.130225i
\(159\) 17.2800 + 29.9299i 1.37040 + 2.37359i
\(160\) 0.0708018 0.122632i 0.00559738 0.00969494i
\(161\) −3.60995 −0.284504
\(162\) 20.1729 34.9405i 1.58493 2.74519i
\(163\) 3.95361 + 6.84785i 0.309670 + 0.536365i 0.978290 0.207240i \(-0.0664480\pi\)
−0.668620 + 0.743604i \(0.733115\pi\)
\(164\) −1.31026 −0.102314
\(165\) 0.547662 + 0.948579i 0.0426354 + 0.0738468i
\(166\) 2.90122 5.02506i 0.225178 0.390020i
\(167\) 9.90428 17.1547i 0.766416 1.32747i −0.173079 0.984908i \(-0.555372\pi\)
0.939495 0.342563i \(-0.111295\pi\)
\(168\) −24.2137 −1.86813
\(169\) −3.83992 + 6.65093i −0.295378 + 0.511610i
\(170\) 0.127667 0.00979160
\(171\) 16.8753 1.29048
\(172\) 1.61088 + 0.565338i 0.122829 + 0.0431066i
\(173\) −8.69063 −0.660736 −0.330368 0.943852i \(-0.607173\pi\)
−0.330368 + 0.943852i \(0.607173\pi\)
\(174\) 14.3424 1.08730
\(175\) 6.11942 10.5991i 0.462585 0.801220i
\(176\) −11.6567 −0.878656
\(177\) −15.1978 + 26.3234i −1.14234 + 1.97859i
\(178\) −12.0446 + 20.8618i −0.902778 + 1.56366i
\(179\) 6.62568 + 11.4760i 0.495226 + 0.857757i 0.999985 0.00550353i \(-0.00175184\pi\)
−0.504759 + 0.863261i \(0.668419\pi\)
\(180\) −0.200801 −0.0149668
\(181\) −2.52685 4.37663i −0.187819 0.325312i 0.756704 0.653758i \(-0.226809\pi\)
−0.944523 + 0.328446i \(0.893475\pi\)
\(182\) 7.35461 12.7386i 0.545160 0.944245i
\(183\) 26.5910 1.96567
\(184\) 2.19429 3.80061i 0.161765 0.280185i
\(185\) −0.0126839 0.0219692i −0.000932541 0.00161521i
\(186\) 6.65317 + 11.5236i 0.487834 + 0.844953i
\(187\) 1.70843 + 2.95908i 0.124933 + 0.216389i
\(188\) −1.05844 −0.0771945
\(189\) 20.1760 + 34.9458i 1.46759 + 2.54193i
\(190\) 0.135186 + 0.234149i 0.00980743 + 0.0169870i
\(191\) 8.30880 14.3913i 0.601204 1.04132i −0.391435 0.920206i \(-0.628021\pi\)
0.992639 0.121110i \(-0.0386453\pi\)
\(192\) 14.4937 25.1038i 1.04599 1.81171i
\(193\) −5.50637 −0.396357 −0.198179 0.980166i \(-0.563503\pi\)
−0.198179 + 0.980166i \(0.563503\pi\)
\(194\) −18.3872 −1.32012
\(195\) 0.728887 1.26247i 0.0521967 0.0904073i
\(196\) −0.128340 + 0.222291i −0.00916712 + 0.0158779i
\(197\) 8.07567 + 13.9875i 0.575368 + 0.996566i 0.996002 + 0.0893355i \(0.0284743\pi\)
−0.420634 + 0.907230i \(0.638192\pi\)
\(198\) 17.9554 + 31.0996i 1.27603 + 2.21015i
\(199\) −2.41995 −0.171546 −0.0857728 0.996315i \(-0.527336\pi\)
−0.0857728 + 0.996315i \(0.527336\pi\)
\(200\) 7.43930 + 12.8852i 0.526038 + 0.911124i
\(201\) 16.5391 + 28.6466i 1.16658 + 2.02057i
\(202\) 7.29169 + 12.6296i 0.513042 + 0.888614i
\(203\) −4.02603 + 6.97328i −0.282572 + 0.489429i
\(204\) −0.862227 −0.0603680
\(205\) −0.243569 + 0.421874i −0.0170116 + 0.0294650i
\(206\) 7.67286 + 13.2898i 0.534594 + 0.925943i
\(207\) −11.7296 −0.815264
\(208\) 7.75697 + 13.4355i 0.537849 + 0.931582i
\(209\) −3.61810 + 6.26673i −0.250269 + 0.433479i
\(210\) −0.518445 + 0.897973i −0.0357761 + 0.0619660i
\(211\) 11.4955 0.791382 0.395691 0.918384i \(-0.370505\pi\)
0.395691 + 0.918384i \(0.370505\pi\)
\(212\) 1.35840 2.35281i 0.0932950 0.161592i
\(213\) −13.9898 −0.958567
\(214\) 11.4030 0.779494
\(215\) 0.481479 0.413575i 0.0328366 0.0282056i
\(216\) −49.0553 −3.33779
\(217\) −7.47036 −0.507121
\(218\) −5.86204 + 10.1533i −0.397027 + 0.687671i
\(219\) 32.2656 2.18031
\(220\) 0.0430521 0.0745685i 0.00290257 0.00502740i
\(221\) 2.27375 3.93826i 0.152949 0.264916i
\(222\) −0.572412 0.991447i −0.0384178 0.0665415i
\(223\) −5.84069 −0.391122 −0.195561 0.980692i \(-0.562653\pi\)
−0.195561 + 0.980692i \(0.562653\pi\)
\(224\) 1.79384 + 3.10702i 0.119856 + 0.207596i
\(225\) 19.8835 34.4392i 1.32556 2.29594i
\(226\) −10.3400 −0.687810
\(227\) 7.71357 13.3603i 0.511968 0.886754i −0.487936 0.872879i \(-0.662250\pi\)
0.999904 0.0138746i \(-0.00441655\pi\)
\(228\) −0.913011 1.58138i −0.0604656 0.104730i
\(229\) −9.66002 16.7317i −0.638352 1.10566i −0.985794 0.167957i \(-0.946283\pi\)
0.347442 0.937702i \(-0.387050\pi\)
\(230\) −0.0939647 0.162752i −0.00619585 0.0107315i
\(231\) −27.7512 −1.82589
\(232\) −4.89439 8.47733i −0.321332 0.556564i
\(233\) −8.93539 15.4766i −0.585377 1.01390i −0.994828 0.101571i \(-0.967613\pi\)
0.409451 0.912332i \(-0.365720\pi\)
\(234\) 23.8969 41.3906i 1.56219 2.70579i
\(235\) −0.196757 + 0.340793i −0.0128350 + 0.0222309i
\(236\) 2.38942 0.155538
\(237\) −4.74604 −0.308289
\(238\) −1.61728 + 2.80122i −0.104833 + 0.181576i
\(239\) 4.07631 7.06038i 0.263675 0.456698i −0.703541 0.710655i \(-0.748399\pi\)
0.967216 + 0.253957i \(0.0817322\pi\)
\(240\) −0.546809 0.947100i −0.0352963 0.0611351i
\(241\) −3.11039 5.38735i −0.200358 0.347030i 0.748286 0.663376i \(-0.230877\pi\)
−0.948644 + 0.316347i \(0.897544\pi\)
\(242\) −0.890141 −0.0572204
\(243\) 25.9718 + 44.9845i 1.66609 + 2.88575i
\(244\) −1.04517 1.81029i −0.0669101 0.115892i
\(245\) 0.0477151 + 0.0826449i 0.00304840 + 0.00527999i
\(246\) −10.9920 + 19.0387i −0.700825 + 1.21386i
\(247\) 9.63070 0.612786
\(248\) 4.54081 7.86491i 0.288342 0.499423i
\(249\) 7.28483 + 12.6177i 0.461657 + 0.799613i
\(250\) 1.27547 0.0806679
\(251\) −0.206976 0.358494i −0.0130642 0.0226279i 0.859419 0.511271i \(-0.170825\pi\)
−0.872484 + 0.488643i \(0.837492\pi\)
\(252\) 2.54374 4.40589i 0.160241 0.277545i
\(253\) 2.51485 4.35586i 0.158108 0.273850i
\(254\) −8.47548 −0.531799
\(255\) −0.160283 + 0.277618i −0.0100373 + 0.0173851i
\(256\) −6.13784 −0.383615
\(257\) 20.2345 1.26219 0.631097 0.775704i \(-0.282605\pi\)
0.631097 + 0.775704i \(0.282605\pi\)
\(258\) 21.7286 18.6642i 1.35277 1.16198i
\(259\) 0.642721 0.0399367
\(260\) −0.114597 −0.00710698
\(261\) −13.0815 + 22.6579i −0.809726 + 1.40249i
\(262\) −7.35111 −0.454153
\(263\) 5.03992 8.72940i 0.310775 0.538278i −0.667755 0.744381i \(-0.732745\pi\)
0.978530 + 0.206103i \(0.0660781\pi\)
\(264\) 16.8684 29.2168i 1.03818 1.79817i
\(265\) −0.505035 0.874746i −0.0310240 0.0537352i
\(266\) −6.85015 −0.420010
\(267\) −30.2433 52.3830i −1.85086 3.20579i
\(268\) 1.30015 2.25193i 0.0794194 0.137558i
\(269\) 21.7737 1.32757 0.663783 0.747925i \(-0.268950\pi\)
0.663783 + 0.747925i \(0.268950\pi\)
\(270\) −1.05033 + 1.81923i −0.0639213 + 0.110715i
\(271\) −11.8610 20.5439i −0.720505 1.24795i −0.960798 0.277250i \(-0.910577\pi\)
0.240293 0.970700i \(-0.422756\pi\)
\(272\) −1.70576 2.95447i −0.103427 0.179141i
\(273\) 18.4671 + 31.9859i 1.11768 + 1.93588i
\(274\) 27.1243 1.63864
\(275\) 8.52613 + 14.7677i 0.514145 + 0.890525i
\(276\) 0.634612 + 1.09918i 0.0381992 + 0.0661629i
\(277\) −14.1004 + 24.4227i −0.847213 + 1.46742i 0.0364721 + 0.999335i \(0.488388\pi\)
−0.883685 + 0.468082i \(0.844945\pi\)
\(278\) −13.6607 + 23.6611i −0.819317 + 1.41910i
\(279\) −24.2730 −1.45319
\(280\) 0.707681 0.0422921
\(281\) 9.97674 17.2802i 0.595162 1.03085i −0.398361 0.917229i \(-0.630421\pi\)
0.993524 0.113623i \(-0.0362456\pi\)
\(282\) −8.87942 + 15.3796i −0.528762 + 0.915843i
\(283\) 2.23591 + 3.87271i 0.132911 + 0.230209i 0.924798 0.380460i \(-0.124234\pi\)
−0.791886 + 0.610668i \(0.790901\pi\)
\(284\) 0.549875 + 0.952411i 0.0326291 + 0.0565152i
\(285\) −0.678892 −0.0402141
\(286\) 10.2471 + 17.7485i 0.605924 + 1.04949i
\(287\) −6.17107 10.6886i −0.364267 0.630929i
\(288\) 5.82861 + 10.0954i 0.343454 + 0.594880i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) −0.419179 −0.0246151
\(291\) 23.0847 39.9838i 1.35325 2.34389i
\(292\) −1.26821 2.19660i −0.0742164 0.128547i
\(293\) −27.9730 −1.63420 −0.817099 0.576498i \(-0.804419\pi\)
−0.817099 + 0.576498i \(0.804419\pi\)
\(294\) 2.15333 + 3.72968i 0.125585 + 0.217519i
\(295\) 0.444179 0.769341i 0.0258611 0.0447928i
\(296\) −0.390673 + 0.676666i −0.0227074 + 0.0393304i
\(297\) −56.2219 −3.26233
\(298\) −14.1765 + 24.5545i −0.821225 + 1.42240i
\(299\) −6.69407 −0.387128
\(300\) −4.30306 −0.248437
\(301\) 2.97514 + 15.8036i 0.171484 + 0.910905i
\(302\) −16.1836 −0.931263
\(303\) −36.6182 −2.10366
\(304\) 3.61246 6.25696i 0.207189 0.358861i
\(305\) −0.777162 −0.0445002
\(306\) −5.25494 + 9.10183i −0.300405 + 0.520317i
\(307\) −2.10155 + 3.64000i −0.119942 + 0.207746i −0.919744 0.392518i \(-0.871604\pi\)
0.799802 + 0.600263i \(0.204938\pi\)
\(308\) 1.09077 + 1.88927i 0.0621523 + 0.107651i
\(309\) −38.5324 −2.19203
\(310\) −0.194449 0.336795i −0.0110439 0.0191287i
\(311\) −7.80077 + 13.5113i −0.442341 + 0.766157i −0.997863 0.0653450i \(-0.979185\pi\)
0.555522 + 0.831502i \(0.312519\pi\)
\(312\) −44.9004 −2.54198
\(313\) −12.0401 + 20.8540i −0.680545 + 1.17874i 0.294270 + 0.955722i \(0.404923\pi\)
−0.974815 + 0.223016i \(0.928410\pi\)
\(314\) −11.5730 20.0451i −0.653105 1.13121i
\(315\) −0.945732 1.63806i −0.0532860 0.0922940i
\(316\) 0.186545 + 0.323105i 0.0104940 + 0.0181761i
\(317\) 26.5547 1.49146 0.745731 0.666248i \(-0.232101\pi\)
0.745731 + 0.666248i \(0.232101\pi\)
\(318\) −22.7917 39.4763i −1.27809 2.21372i
\(319\) −5.60942 9.71580i −0.314067 0.543981i
\(320\) −0.423599 + 0.733694i −0.0236799 + 0.0410148i
\(321\) −14.3162 + 24.7964i −0.799054 + 1.38400i
\(322\) 4.76138 0.265341
\(323\) −2.11780 −0.117837
\(324\) 3.98189 6.89683i 0.221216 0.383157i
\(325\) 11.3475 19.6544i 0.629444 1.09023i
\(326\) −5.21465 9.03203i −0.288812 0.500238i
\(327\) −14.7193 25.4946i −0.813979 1.40985i
\(328\) 15.0042 0.828467
\(329\) −4.98503 8.63433i −0.274834 0.476026i
\(330\) −0.722344 1.25114i −0.0397637 0.0688728i
\(331\) 14.1428 + 24.4960i 0.777357 + 1.34642i 0.933460 + 0.358681i \(0.116773\pi\)
−0.156103 + 0.987741i \(0.549893\pi\)
\(332\) 0.572665 0.991885i 0.0314291 0.0544368i
\(333\) 2.08835 0.114441
\(334\) −13.0633 + 22.6264i −0.714794 + 1.23806i
\(335\) −0.483380 0.837239i −0.0264099 0.0457433i
\(336\) 27.7079 1.51159
\(337\) 8.58519 + 14.8700i 0.467665 + 0.810020i 0.999317 0.0369428i \(-0.0117619\pi\)
−0.531652 + 0.846963i \(0.678429\pi\)
\(338\) 5.06469 8.77230i 0.275483 0.477150i
\(339\) 12.9817 22.4849i 0.705069 1.22121i
\(340\) 0.0251999 0.00136665
\(341\) 5.20419 9.01392i 0.281823 0.488131i
\(342\) −22.2578 −1.20356
\(343\) −19.5844 −1.05746
\(344\) −18.4467 6.47385i −0.994580 0.349047i
\(345\) 0.471882 0.0254053
\(346\) 11.4626 0.616232
\(347\) 8.56320 14.8319i 0.459697 0.796218i −0.539248 0.842147i \(-0.681291\pi\)
0.998945 + 0.0459290i \(0.0146248\pi\)
\(348\) 2.83102 0.151759
\(349\) 8.08138 13.9974i 0.432587 0.749262i −0.564509 0.825427i \(-0.690934\pi\)
0.997095 + 0.0761652i \(0.0242677\pi\)
\(350\) −8.07127 + 13.9798i −0.431427 + 0.747254i
\(351\) 37.4130 + 64.8013i 1.99696 + 3.45884i
\(352\) −4.99867 −0.266430
\(353\) 7.15534 + 12.3934i 0.380840 + 0.659635i 0.991183 0.132503i \(-0.0423014\pi\)
−0.610342 + 0.792138i \(0.708968\pi\)
\(354\) 20.0453 34.7195i 1.06540 1.84532i
\(355\) 0.408873 0.0217007
\(356\) −2.37745 + 4.11787i −0.126005 + 0.218246i
\(357\) −4.06092 7.03373i −0.214927 0.372264i
\(358\) −8.73900 15.1364i −0.461870 0.799983i
\(359\) 6.63765 + 11.4968i 0.350322 + 0.606775i 0.986306 0.164927i \(-0.0527388\pi\)
−0.635984 + 0.771702i \(0.719406\pi\)
\(360\) 2.29943 0.121190
\(361\) 7.25747 + 12.5703i 0.381972 + 0.661595i
\(362\) 3.33281 + 5.77259i 0.175168 + 0.303401i
\(363\) 1.11755 1.93565i 0.0586562 0.101596i
\(364\) 1.45171 2.51444i 0.0760903 0.131792i
\(365\) −0.943009 −0.0493594
\(366\) −35.0725 −1.83327
\(367\) 5.06693 8.77618i 0.264492 0.458113i −0.702939 0.711250i \(-0.748129\pi\)
0.967430 + 0.253138i \(0.0814626\pi\)
\(368\) −2.51093 + 4.34907i −0.130892 + 0.226711i
\(369\) −20.0513 34.7299i −1.04383 1.80796i
\(370\) 0.0167296 + 0.0289765i 0.000869730 + 0.00150642i
\(371\) 25.5911 1.32862
\(372\) 1.31325 + 2.27462i 0.0680890 + 0.117934i
\(373\) 7.61694 + 13.1929i 0.394390 + 0.683103i 0.993023 0.117920i \(-0.0376226\pi\)
−0.598633 + 0.801023i \(0.704289\pi\)
\(374\) −2.25334 3.90291i −0.116518 0.201815i
\(375\) −1.60133 + 2.77358i −0.0826921 + 0.143227i
\(376\) 12.1205 0.625066
\(377\) −7.46561 + 12.9308i −0.384499 + 0.665971i
\(378\) −26.6113 46.0921i −1.36874 2.37072i
\(379\) −14.1932 −0.729058 −0.364529 0.931192i \(-0.618770\pi\)
−0.364529 + 0.931192i \(0.618770\pi\)
\(380\) 0.0266841 + 0.0462182i 0.00136886 + 0.00237094i
\(381\) 10.6408 18.4303i 0.545143 0.944215i
\(382\) −10.9590 + 18.9815i −0.560710 + 0.971177i
\(383\) −30.7860 −1.57309 −0.786545 0.617533i \(-0.788132\pi\)
−0.786545 + 0.617533i \(0.788132\pi\)
\(384\) −14.2715 + 24.7190i −0.728289 + 1.26143i
\(385\) 0.811069 0.0413359
\(386\) 7.26267 0.369660
\(387\) 9.66694 + 51.3497i 0.491398 + 2.61025i
\(388\) −3.62941 −0.184255
\(389\) −5.73485 −0.290768 −0.145384 0.989375i \(-0.546442\pi\)
−0.145384 + 0.989375i \(0.546442\pi\)
\(390\) −0.961372 + 1.66515i −0.0486810 + 0.0843179i
\(391\) 1.47203 0.0744438
\(392\) 1.46966 2.54552i 0.0742288 0.128568i
\(393\) 9.22915 15.9854i 0.465549 0.806355i
\(394\) −10.6515 18.4489i −0.536614 0.929442i
\(395\) 0.138710 0.00697927
\(396\) 3.54417 + 6.13868i 0.178101 + 0.308480i
\(397\) 9.60460 16.6356i 0.482041 0.834919i −0.517747 0.855534i \(-0.673229\pi\)
0.999787 + 0.0206147i \(0.00656234\pi\)
\(398\) 3.19181 0.159991
\(399\) 8.60021 14.8960i 0.430549 0.745733i
\(400\) −8.51284 14.7447i −0.425642 0.737233i
\(401\) −1.60764 2.78452i −0.0802819 0.139052i 0.823089 0.567912i \(-0.192249\pi\)
−0.903371 + 0.428860i \(0.858915\pi\)
\(402\) −21.8144 37.7837i −1.08800 1.88448i
\(403\) −13.8526 −0.690046
\(404\) 1.43929 + 2.49293i 0.0716074 + 0.124028i
\(405\) −1.48042 2.56416i −0.0735625 0.127414i
\(406\) 5.31017 9.19748i 0.263539 0.456463i
\(407\) −0.447748 + 0.775522i −0.0221940 + 0.0384412i
\(408\) 9.87362 0.488817
\(409\) −14.0216 −0.693324 −0.346662 0.937990i \(-0.612685\pi\)
−0.346662 + 0.937990i \(0.612685\pi\)
\(410\) 0.321258 0.556435i 0.0158658 0.0274804i
\(411\) −34.0539 + 58.9831i −1.67975 + 2.90942i
\(412\) 1.51453 + 2.62324i 0.0746155 + 0.129238i
\(413\) 11.2537 + 19.4920i 0.553760 + 0.959140i
\(414\) 15.4709 0.760352
\(415\) −0.212910 0.368771i −0.0104513 0.0181022i
\(416\) 3.32638 + 5.76145i 0.163089 + 0.282479i
\(417\) −34.3015 59.4119i −1.67975 2.90941i
\(418\) 4.77212 8.26556i 0.233412 0.404282i
\(419\) 11.4938 0.561508 0.280754 0.959780i \(-0.409415\pi\)
0.280754 + 0.959780i \(0.409415\pi\)
\(420\) −0.102335 + 0.177249i −0.00499342 + 0.00864886i
\(421\) 14.1557 + 24.5184i 0.689907 + 1.19495i 0.971868 + 0.235528i \(0.0756818\pi\)
−0.281961 + 0.959426i \(0.590985\pi\)
\(422\) −15.1621 −0.738078
\(423\) −16.1976 28.0550i −0.787553 1.36408i
\(424\) −15.5554 + 26.9427i −0.755437 + 1.30845i
\(425\) −2.49532 + 4.32201i −0.121041 + 0.209648i
\(426\) 18.4520 0.894002
\(427\) 9.84510 17.0522i 0.476438 0.825214i
\(428\) 2.25082 0.108797
\(429\) −51.4600 −2.48451
\(430\) −0.635051 + 0.545489i −0.0306249 + 0.0263058i
\(431\) −34.9649 −1.68420 −0.842099 0.539323i \(-0.818680\pi\)
−0.842099 + 0.539323i \(0.818680\pi\)
\(432\) 56.1343 2.70076
\(433\) −3.82604 + 6.62690i −0.183868 + 0.318468i −0.943194 0.332241i \(-0.892195\pi\)
0.759327 + 0.650710i \(0.225528\pi\)
\(434\) 9.85311 0.472964
\(435\) 0.526270 0.911526i 0.0252327 0.0437043i
\(436\) −1.15709 + 2.00415i −0.0554148 + 0.0959812i
\(437\) 1.55873 + 2.69980i 0.0745642 + 0.129149i
\(438\) −42.5570 −2.03345
\(439\) −9.98969 17.3027i −0.476782 0.825811i 0.522864 0.852416i \(-0.324864\pi\)
−0.999646 + 0.0266054i \(0.991530\pi\)
\(440\) −0.493003 + 0.853906i −0.0235030 + 0.0407083i
\(441\) −7.85608 −0.374099
\(442\) −2.99899 + 5.19440i −0.142647 + 0.247072i
\(443\) 3.65243 + 6.32619i 0.173532 + 0.300566i 0.939652 0.342131i \(-0.111149\pi\)
−0.766120 + 0.642697i \(0.777815\pi\)
\(444\) −0.112987 0.195699i −0.00536213 0.00928749i
\(445\) 0.883907 + 1.53097i 0.0419012 + 0.0725750i
\(446\) 7.70363 0.364778
\(447\) −35.5966 61.6552i −1.68366 2.91619i
\(448\) −10.7323 18.5889i −0.507054 0.878242i
\(449\) −10.9954 + 19.0446i −0.518905 + 0.898769i 0.480854 + 0.876801i \(0.340327\pi\)
−0.999759 + 0.0219685i \(0.993007\pi\)
\(450\) −26.2255 + 45.4239i −1.23628 + 2.14130i
\(451\) 17.1962 0.809736
\(452\) −2.04100 −0.0960005
\(453\) 20.3182 35.1921i 0.954631 1.65347i
\(454\) −10.1739 + 17.6217i −0.477484 + 0.827027i
\(455\) −0.539728 0.934836i −0.0253028 0.0438258i
\(456\) 10.4552 + 18.1089i 0.489608 + 0.848025i
\(457\) 2.49152 0.116548 0.0582741 0.998301i \(-0.481440\pi\)
0.0582741 + 0.998301i \(0.481440\pi\)
\(458\) 12.7412 + 22.0684i 0.595356 + 1.03119i
\(459\) −8.22715 14.2498i −0.384010 0.665126i
\(460\) −0.0185475 0.0321252i −0.000864781 0.00149784i
\(461\) −4.08105 + 7.06859i −0.190074 + 0.329217i −0.945274 0.326276i \(-0.894206\pi\)
0.755201 + 0.655493i \(0.227539\pi\)
\(462\) 36.6026 1.70291
\(463\) 5.84972 10.1320i 0.271860 0.470875i −0.697478 0.716606i \(-0.745695\pi\)
0.969338 + 0.245731i \(0.0790280\pi\)
\(464\) 5.60068 + 9.70066i 0.260005 + 0.450342i
\(465\) 0.976503 0.0452842
\(466\) 11.7854 + 20.4129i 0.545949 + 0.945612i
\(467\) 19.0133 32.9320i 0.879829 1.52391i 0.0283014 0.999599i \(-0.490990\pi\)
0.851528 0.524309i \(-0.175676\pi\)
\(468\) 4.71696 8.17001i 0.218041 0.377659i
\(469\) 24.4939 1.13102
\(470\) 0.259514 0.449492i 0.0119705 0.0207335i
\(471\) 58.1187 2.67797
\(472\) −27.3620 −1.25944
\(473\) −21.1416 7.41963i −0.972094 0.341155i
\(474\) 6.25984 0.287524
\(475\) −10.5691 −0.484945
\(476\) −0.319232 + 0.552926i −0.0146320 + 0.0253433i
\(477\) 83.1517 3.80726
\(478\) −5.37649 + 9.31235i −0.245915 + 0.425937i
\(479\) −19.4996 + 33.7743i −0.890960 + 1.54319i −0.0522341 + 0.998635i \(0.516634\pi\)
−0.838726 + 0.544553i \(0.816699\pi\)
\(480\) −0.234485 0.406139i −0.0107027 0.0185376i
\(481\) 1.19182 0.0543423
\(482\) 4.10247 + 7.10569i 0.186863 + 0.323656i
\(483\) −5.97780 + 10.3539i −0.271999 + 0.471117i
\(484\) −0.175703 −0.00798650
\(485\) −0.674684 + 1.16859i −0.0306358 + 0.0530628i
\(486\) −34.2557 59.3327i −1.55387 2.69138i
\(487\) 9.86328 + 17.0837i 0.446948 + 0.774136i 0.998186 0.0602120i \(-0.0191777\pi\)
−0.551238 + 0.834348i \(0.685844\pi\)
\(488\) 11.9685 + 20.7301i 0.541791 + 0.938409i
\(489\) 26.1875 1.18424
\(490\) −0.0629342 0.109005i −0.00284308 0.00492436i
\(491\) 7.21017 + 12.4884i 0.325390 + 0.563593i 0.981591 0.190993i \(-0.0611709\pi\)
−0.656201 + 0.754586i \(0.727838\pi\)
\(492\) −2.16969 + 3.75801i −0.0978171 + 0.169424i
\(493\) 1.64169 2.84350i 0.0739381 0.128065i
\(494\) −12.7025 −0.571512
\(495\) 2.63536 0.118450
\(496\) −5.19608 + 8.99987i −0.233311 + 0.404106i
\(497\) −5.17961 + 8.97134i −0.232337 + 0.402420i
\(498\) −9.60839 16.6422i −0.430562 0.745756i
\(499\) 15.2988 + 26.4982i 0.684866 + 1.18622i 0.973479 + 0.228777i \(0.0734727\pi\)
−0.288613 + 0.957446i \(0.593194\pi\)
\(500\) 0.251763 0.0112592
\(501\) −32.8014 56.8137i −1.46546 2.53825i
\(502\) 0.272993 + 0.472839i 0.0121843 + 0.0211038i
\(503\) 5.28450 + 9.15302i 0.235624 + 0.408113i 0.959454 0.281866i \(-0.0909532\pi\)
−0.723830 + 0.689979i \(0.757620\pi\)
\(504\) −29.1292 + 50.4532i −1.29752 + 2.24736i
\(505\) 1.07022 0.0476242
\(506\) −3.31699 + 5.74520i −0.147458 + 0.255405i
\(507\) 12.7172 + 22.0268i 0.564791 + 0.978247i
\(508\) −1.67296 −0.0742254
\(509\) −4.43785 7.68659i −0.196704 0.340702i 0.750754 0.660582i \(-0.229691\pi\)
−0.947458 + 0.319880i \(0.896357\pi\)
\(510\) 0.211406 0.366166i 0.00936123 0.0162141i
\(511\) 11.9460 20.6912i 0.528462 0.915323i
\(512\) 25.3325 1.11955
\(513\) 17.4234 30.1783i 0.769263 1.33240i
\(514\) −26.6885 −1.17718
\(515\) 1.12617 0.0496248
\(516\) 4.28897 3.68409i 0.188811 0.162183i
\(517\) 13.8912 0.610934
\(518\) −0.847722 −0.0372468
\(519\) −14.3910 + 24.9260i −0.631695 + 1.09413i
\(520\) 1.31228 0.0575473
\(521\) −20.9386 + 36.2666i −0.917335 + 1.58887i −0.113888 + 0.993494i \(0.536330\pi\)
−0.803447 + 0.595376i \(0.797003\pi\)
\(522\) 17.2540 29.8848i 0.755187 1.30802i
\(523\) 17.5005 + 30.3117i 0.765243 + 1.32544i 0.940118 + 0.340849i \(0.110715\pi\)
−0.174875 + 0.984591i \(0.555952\pi\)
\(524\) −1.45102 −0.0633881
\(525\) −20.2666 35.1027i −0.884506 1.53201i
\(526\) −6.64745 + 11.5137i −0.289843 + 0.502022i
\(527\) 3.04619 0.132694
\(528\) −19.3026 + 33.4330i −0.840036 + 1.45499i
\(529\) 10.4166 + 18.0420i 0.452894 + 0.784436i
\(530\) 0.666120 + 1.15375i 0.0289344 + 0.0501159i
\(531\) 36.5661 + 63.3343i 1.58683 + 2.74847i
\(532\) −1.35214 −0.0586226
\(533\) −11.4432 19.8203i −0.495662 0.858512i
\(534\) 39.8897 + 69.0911i 1.72620 + 2.98986i
\(535\) 0.418413 0.724712i 0.0180896 0.0313320i
\(536\) −14.8884 + 25.7875i −0.643082 + 1.11385i
\(537\) 43.8864 1.89384
\(538\) −28.7186 −1.23815
\(539\) 1.68436 2.91740i 0.0725506 0.125661i
\(540\) −0.207323 + 0.359094i −0.00892176 + 0.0154529i
\(541\) −12.1266 21.0039i −0.521364 0.903030i −0.999691 0.0248478i \(-0.992090\pi\)
0.478327 0.878182i \(-0.341243\pi\)
\(542\) 15.6442 + 27.0965i 0.671975 + 1.16389i
\(543\) −16.7371 −0.718256
\(544\) −0.731472 1.26695i −0.0313616 0.0543199i
\(545\) 0.430193 + 0.745117i 0.0184275 + 0.0319173i
\(546\) −24.3573 42.1881i −1.04240 1.80549i
\(547\) 8.88087 15.3821i 0.379719 0.657692i −0.611303 0.791397i \(-0.709354\pi\)
0.991021 + 0.133705i \(0.0426875\pi\)
\(548\) 5.35400 0.228712
\(549\) 31.9891 55.4067i 1.36526 2.36470i
\(550\) −11.2456 19.4780i −0.479514 0.830543i
\(551\) 6.95354 0.296231
\(552\) −7.26713 12.5870i −0.309310 0.535740i
\(553\) −1.75718 + 3.04353i −0.0747229 + 0.129424i
\(554\) 18.5979 32.2125i 0.790149 1.36858i
\(555\) −0.0840144 −0.00356621
\(556\) −2.69646 + 4.67041i −0.114356 + 0.198070i
\(557\) −41.4501 −1.75630 −0.878148 0.478390i \(-0.841221\pi\)
−0.878148 + 0.478390i \(0.841221\pi\)
\(558\) 32.0151 1.35531
\(559\) 5.51691 + 29.3052i 0.233340 + 1.23948i
\(560\) −0.809804 −0.0342205
\(561\) 11.3161 0.477766
\(562\) −13.1589 + 22.7919i −0.555075 + 0.961419i
\(563\) 20.3733 0.858632 0.429316 0.903154i \(-0.358755\pi\)
0.429316 + 0.903154i \(0.358755\pi\)
\(564\) −1.75269 + 3.03575i −0.0738016 + 0.127828i
\(565\) −0.379409 + 0.657156i −0.0159619 + 0.0276468i
\(566\) −2.94908 5.10795i −0.123959 0.214703i
\(567\) 75.0157 3.15036
\(568\) −6.29678 10.9063i −0.264207 0.457620i
\(569\) −7.37103 + 12.7670i −0.309010 + 0.535220i −0.978146 0.207919i \(-0.933331\pi\)
0.669136 + 0.743140i \(0.266664\pi\)
\(570\) 0.895431 0.0375055
\(571\) 13.0130 22.5391i 0.544575 0.943232i −0.454058 0.890972i \(-0.650024\pi\)
0.998634 0.0522602i \(-0.0166425\pi\)
\(572\) 2.02265 + 3.50334i 0.0845714 + 0.146482i
\(573\) −27.5175 47.6616i −1.14956 1.99109i
\(574\) 8.13939 + 14.0978i 0.339732 + 0.588432i
\(575\) 7.34636 0.306364
\(576\) −34.8718 60.3998i −1.45299 2.51666i
\(577\) 17.5694 + 30.4310i 0.731423 + 1.26686i 0.956275 + 0.292468i \(0.0944766\pi\)
−0.224853 + 0.974393i \(0.572190\pi\)
\(578\) 0.659480 1.14225i 0.0274307 0.0475114i
\(579\) −9.11812 + 15.7930i −0.378936 + 0.656337i
\(580\) −0.0827409 −0.00343563
\(581\) 10.7886 0.447585
\(582\) −30.4477 + 52.7370i −1.26210 + 2.18602i
\(583\) −17.8279 + 30.8789i −0.738357 + 1.27887i
\(584\) 14.5226 + 25.1540i 0.600951 + 1.04088i
\(585\) −1.75371 3.03751i −0.0725068 0.125585i
\(586\) 36.8952 1.52413
\(587\) 17.6977 + 30.6534i 0.730464 + 1.26520i 0.956685 + 0.291125i \(0.0940294\pi\)
−0.226221 + 0.974076i \(0.572637\pi\)
\(588\) 0.425041 + 0.736193i 0.0175284 + 0.0303601i
\(589\) 3.22560 + 5.58691i 0.132909 + 0.230205i
\(590\) −0.585854 + 1.01473i −0.0241192 + 0.0417757i
\(591\) 53.4907 2.20031
\(592\) 0.447050 0.774313i 0.0183736 0.0318241i
\(593\) −7.87978 13.6482i −0.323584 0.560464i 0.657641 0.753332i \(-0.271554\pi\)
−0.981225 + 0.192868i \(0.938221\pi\)
\(594\) 74.1544 3.04259
\(595\) 0.118687 + 0.205571i 0.00486567 + 0.00842759i
\(596\) −2.79828 + 4.84676i −0.114622 + 0.198531i
\(597\) −4.00725 + 6.94076i −0.164006 + 0.284066i
\(598\) 8.82920 0.361053
\(599\) 20.3184 35.1924i 0.830185 1.43792i −0.0677056 0.997705i \(-0.521568\pi\)
0.897891 0.440218i \(-0.145099\pi\)
\(600\) 49.2756 2.01167
\(601\) −12.6482 −0.515929 −0.257965 0.966154i \(-0.583052\pi\)
−0.257965 + 0.966154i \(0.583052\pi\)
\(602\) −3.92409 20.8443i −0.159934 0.849551i
\(603\) 79.5864 3.24101
\(604\) −3.19445 −0.129980
\(605\) −0.0326621 + 0.0565724i −0.00132790 + 0.00229999i
\(606\) 48.2979 1.96197
\(607\) 17.0298 29.4965i 0.691219 1.19723i −0.280219 0.959936i \(-0.590407\pi\)
0.971439 0.237291i \(-0.0762595\pi\)
\(608\) 1.54911 2.68314i 0.0628247 0.108816i
\(609\) 13.3336 + 23.0944i 0.540304 + 0.935834i
\(610\) 1.02505 0.0415029
\(611\) −9.24393 16.0110i −0.373970 0.647734i
\(612\) −1.03726 + 1.79659i −0.0419288 + 0.0726228i
\(613\) −19.5136 −0.788149 −0.394074 0.919079i \(-0.628935\pi\)
−0.394074 + 0.919079i \(0.628935\pi\)
\(614\) 2.77186 4.80101i 0.111863 0.193753i
\(615\) 0.806663 + 1.39718i 0.0325278 + 0.0563398i
\(616\) −12.4907 21.6346i −0.503265 0.871681i
\(617\) −10.0889 17.4745i −0.406164 0.703497i 0.588292 0.808649i \(-0.299801\pi\)
−0.994456 + 0.105151i \(0.966467\pi\)
\(618\) 50.8227 2.04439
\(619\) 12.4435 + 21.5527i 0.500145 + 0.866276i 1.00000 0.000166979i \(5.31510e-5\pi\)
−0.499855 + 0.866109i \(0.666614\pi\)
\(620\) −0.0383818 0.0664792i −0.00154145 0.00266987i
\(621\) −12.1106 + 20.9762i −0.485982 + 0.841746i
\(622\) 10.2889 17.8209i 0.412547 0.714553i
\(623\) −44.7893 −1.79445
\(624\) 51.3798 2.05684
\(625\) −12.4298 + 21.5290i −0.497191 + 0.861160i
\(626\) 15.8804 27.5056i 0.634706 1.09934i
\(627\) 11.9826 + 20.7544i 0.478538 + 0.828853i
\(628\) −2.28438 3.95666i −0.0911566 0.157888i
\(629\) −0.262082 −0.0104499
\(630\) 1.24738 + 2.16053i 0.0496969 + 0.0860775i
\(631\) −20.4465 35.4144i −0.813963 1.40983i −0.910070 0.414454i \(-0.863972\pi\)
0.0961069 0.995371i \(-0.469361\pi\)
\(632\) −2.13618 3.69997i −0.0849727 0.147177i
\(633\) 19.0356 32.9707i 0.756599 1.31047i
\(634\) −35.0246 −1.39100
\(635\) −0.310992 + 0.538654i −0.0123413 + 0.0213758i
\(636\) −4.49880 7.79214i −0.178389 0.308979i
\(637\) −4.48345 −0.177641
\(638\) 7.39860 + 12.8148i 0.292913 + 0.507341i
\(639\) −16.8298 + 29.1501i −0.665776 + 1.15316i
\(640\) 0.417106 0.722448i 0.0164875 0.0285573i
\(641\) 28.8665 1.14016 0.570079 0.821590i \(-0.306912\pi\)
0.570079 + 0.821590i \(0.306912\pi\)
\(642\) 18.8825 32.7055i 0.745233 1.29078i
\(643\) −7.90891 −0.311897 −0.155949 0.987765i \(-0.549843\pi\)
−0.155949 + 0.987765i \(0.549843\pi\)
\(644\) 0.939838 0.0370348
\(645\) −0.388901 2.06580i −0.0153130 0.0813408i
\(646\) 2.79329 0.109900
\(647\) 15.4830 0.608701 0.304350 0.952560i \(-0.401561\pi\)
0.304350 + 0.952560i \(0.401561\pi\)
\(648\) −45.5978 + 78.9777i −1.79125 + 3.10254i
\(649\) −31.3594 −1.23096
\(650\) −14.9668 + 25.9233i −0.587048 + 1.01680i
\(651\) −12.3703 + 21.4261i −0.484832 + 0.839754i
\(652\) −1.02931 1.78281i −0.0403108 0.0698203i
\(653\) −22.8766 −0.895229 −0.447614 0.894227i \(-0.647726\pi\)
−0.447614 + 0.894227i \(0.647726\pi\)
\(654\) 19.4142 + 33.6263i 0.759154 + 1.31489i
\(655\) −0.269736 + 0.467196i −0.0105394 + 0.0182549i
\(656\) −17.1694 −0.670351
\(657\) 38.8156 67.2306i 1.51434 2.62291i
\(658\) 6.57506 + 11.3883i 0.256322 + 0.443963i
\(659\) −19.5644 33.8865i −0.762121 1.32003i −0.941756 0.336298i \(-0.890825\pi\)
0.179635 0.983733i \(-0.442508\pi\)
\(660\) −0.142582 0.246959i −0.00554999 0.00961287i
\(661\) −4.94941 −0.192510 −0.0962549 0.995357i \(-0.530686\pi\)
−0.0962549 + 0.995357i \(0.530686\pi\)
\(662\) −18.6537 32.3092i −0.724998 1.25573i
\(663\) −7.53032 13.0429i −0.292453 0.506544i
\(664\) −6.55776 + 11.3584i −0.254490 + 0.440790i
\(665\) −0.251354 + 0.435358i −0.00974708 + 0.0168824i
\(666\) −2.75445 −0.106733
\(667\) −4.83324 −0.187144
\(668\) −2.57854 + 4.46617i −0.0997668 + 0.172801i
\(669\) −9.67173 + 16.7519i −0.373931 + 0.647667i
\(670\) 0.637559 + 1.10428i 0.0246310 + 0.0426622i
\(671\) 13.7171 + 23.7587i 0.529542 + 0.917193i
\(672\) 11.8818 0.458351
\(673\) 1.76622 + 3.05919i 0.0680829 + 0.117923i 0.898057 0.439878i \(-0.144978\pi\)
−0.829975 + 0.557801i \(0.811645\pi\)
\(674\) −11.3235 19.6129i −0.436166 0.755461i
\(675\) −41.0587 71.1157i −1.58035 2.73724i
\(676\) 0.999708 1.73155i 0.0384503 0.0665979i
\(677\) −13.3754 −0.514057 −0.257029 0.966404i \(-0.582743\pi\)
−0.257029 + 0.966404i \(0.582743\pi\)
\(678\) −17.1223 + 29.6567i −0.657579 + 1.13896i
\(679\) −17.0938 29.6073i −0.656000 1.13622i
\(680\) −0.288571 −0.0110662
\(681\) −25.5461 44.2472i −0.978930 1.69556i
\(682\) −6.86412 + 11.8890i −0.262841 + 0.455253i
\(683\) −13.1975 + 22.8588i −0.504989 + 0.874667i 0.494994 + 0.868896i \(0.335170\pi\)
−0.999983 + 0.00577068i \(0.998163\pi\)
\(684\) −4.39342 −0.167987
\(685\) 0.995276 1.72387i 0.0380275 0.0658656i
\(686\) 25.8310 0.986231
\(687\) −63.9850 −2.44118
\(688\) 21.1087 + 7.40807i 0.804761 + 0.282430i
\(689\) 47.4546 1.80788
\(690\) −0.622393 −0.0236941
\(691\) −22.1400 + 38.3476i −0.842246 + 1.45881i 0.0457458 + 0.998953i \(0.485434\pi\)
−0.887992 + 0.459860i \(0.847900\pi\)
\(692\) 2.26257 0.0860102
\(693\) −33.3847 + 57.8240i −1.26818 + 2.19655i
\(694\) −11.2945 + 19.5627i −0.428734 + 0.742589i
\(695\) 1.00251 + 1.73640i 0.0380274 + 0.0658654i
\(696\) −32.4189 −1.22884
\(697\) 2.51638 + 4.35849i 0.0953146 + 0.165090i
\(698\) −10.6590 + 18.4620i −0.403450 + 0.698795i
\(699\) −59.1853 −2.23859
\(700\) −1.59317 + 2.75945i −0.0602161 + 0.104297i
\(701\) 4.38290 + 7.59141i 0.165540 + 0.286723i 0.936847 0.349740i \(-0.113730\pi\)
−0.771307 + 0.636463i \(0.780397\pi\)
\(702\) −49.3463 85.4702i −1.86245 3.22587i
\(703\) −0.277518 0.480676i −0.0104668 0.0181290i
\(704\) 29.9064 1.12714
\(705\) 0.651628 + 1.12865i 0.0245417 + 0.0425075i
\(706\) −9.43760 16.3464i −0.355189 0.615205i
\(707\) −13.5576 + 23.4824i −0.509885 + 0.883147i
\(708\) 3.95670 6.85321i 0.148702 0.257559i
\(709\) −27.3996 −1.02901 −0.514506 0.857487i \(-0.672025\pi\)
−0.514506 + 0.857487i \(0.672025\pi\)
\(710\) −0.539287 −0.0202391
\(711\) −5.70950 + 9.88915i −0.214123 + 0.370872i
\(712\) 27.2249 47.1549i 1.02030 1.76720i
\(713\) −2.24204 3.88333i −0.0839651 0.145432i
\(714\) 5.35619 + 9.27720i 0.200450 + 0.347190i
\(715\) 1.50399 0.0562462
\(716\) −1.72497 2.98774i −0.0644652 0.111657i
\(717\) −13.5001 23.3829i −0.504171 0.873249i
\(718\) −8.75479 15.1637i −0.326726 0.565906i
\(719\) 4.41778 7.65182i 0.164755 0.285365i −0.771813 0.635850i \(-0.780650\pi\)
0.936568 + 0.350485i \(0.113983\pi\)
\(720\) −2.63125 −0.0980609
\(721\) −14.2663 + 24.7099i −0.531304 + 0.920246i
\(722\) −9.57231 16.5797i −0.356244 0.617033i
\(723\) −20.6022 −0.766206
\(724\) 0.657856 + 1.13944i 0.0244490 + 0.0423469i
\(725\) 8.19308 14.1908i 0.304283 0.527034i
\(726\) −1.47400 + 2.55305i −0.0547054 + 0.0947526i
\(727\) −16.5783 −0.614854 −0.307427 0.951572i \(-0.599468\pi\)
−0.307427 + 0.951572i \(0.599468\pi\)
\(728\) −16.6240 + 28.7936i −0.616125 + 1.06716i
\(729\) 80.2617 2.97265
\(730\) 1.24379 0.0460348
\(731\) −1.21317 6.44424i −0.0448708 0.238349i
\(732\) −6.92288 −0.255877
\(733\) 51.4987 1.90215 0.951074 0.308964i \(-0.0999822\pi\)
0.951074 + 0.308964i \(0.0999822\pi\)
\(734\) −6.68307 + 11.5754i −0.246677 + 0.427257i
\(735\) 0.316050 0.0116577
\(736\) −1.07675 + 1.86498i −0.0396895 + 0.0687442i
\(737\) −17.0635 + 29.5549i −0.628543 + 1.08867i
\(738\) 26.4468 + 45.8073i 0.973522 + 1.68619i
\(739\) 4.68825 0.172460 0.0862301 0.996275i \(-0.472518\pi\)
0.0862301 + 0.996275i \(0.472518\pi\)
\(740\) 0.00330222 + 0.00571961i 0.000121392 + 0.000210257i
\(741\) 15.9477 27.6222i 0.585853 1.01473i
\(742\) −33.7536 −1.23914
\(743\) 9.12276 15.8011i 0.334682 0.579686i −0.648742 0.761008i \(-0.724705\pi\)
0.983424 + 0.181323i \(0.0580379\pi\)
\(744\) −15.0385 26.0474i −0.551337 0.954943i
\(745\) 1.04036 + 1.80196i 0.0381160 + 0.0660189i
\(746\) −10.0464 17.4009i −0.367826 0.637093i
\(747\) 35.0547 1.28258
\(748\) −0.444783 0.770386i −0.0162629 0.0281681i
\(749\) 10.6009 + 18.3613i 0.387349 + 0.670908i
\(750\) 2.11208 3.65823i 0.0771223 0.133580i
\(751\) 25.5279 44.2157i 0.931527 1.61345i 0.150815 0.988562i \(-0.451810\pi\)
0.780712 0.624891i \(-0.214857\pi\)
\(752\) −13.8695 −0.505770
\(753\) −1.37095 −0.0499601
\(754\) 9.84684 17.0552i 0.358601 0.621115i
\(755\) −0.593829 + 1.02854i −0.0216116 + 0.0374324i
\(756\) −5.25274 9.09801i −0.191040 0.330892i
\(757\) −8.71232 15.0902i −0.316655 0.548462i 0.663133 0.748501i \(-0.269226\pi\)
−0.979788 + 0.200040i \(0.935893\pi\)
\(758\) 18.7203 0.679952
\(759\) −8.32881 14.4259i −0.302317 0.523628i
\(760\) −0.305567 0.529258i −0.0110841 0.0191982i
\(761\) 0.592427 + 1.02611i 0.0214755 + 0.0371966i 0.876563 0.481286i \(-0.159830\pi\)
−0.855088 + 0.518483i \(0.826497\pi\)
\(762\) −14.0347 + 24.3089i −0.508425 + 0.880618i
\(763\) −21.7988 −0.789169
\(764\) −2.16317 + 3.74671i −0.0782606 + 0.135551i
\(765\) 0.385641 + 0.667950i 0.0139429 + 0.0241498i
\(766\) 40.6055 1.46714
\(767\) 20.8682 + 36.1448i 0.753507 + 1.30511i