Properties

Label 143.2.e.a.133.2
Level $143$
Weight $2$
Character 143.133
Analytic conductor $1.142$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 143.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14186074890\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1714608.1
Defining polynomial: \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 133.2
Root \(0.500000 + 1.75780i\) of defining polynomial
Character \(\chi\) \(=\) 143.133
Dual form 143.2.e.a.100.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.169938 + 0.294342i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.88448 q^{5} +(0.169938 - 0.294342i) q^{6} +(1.77230 - 3.06972i) q^{7} -3.00000 q^{8} +(1.44224 - 2.49804i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.169938 + 0.294342i) q^{3} +(0.500000 - 0.866025i) q^{4} -2.88448 q^{5} +(0.169938 - 0.294342i) q^{6} +(1.77230 - 3.06972i) q^{7} -3.00000 q^{8} +(1.44224 - 2.49804i) q^{9} +(1.44224 + 2.49804i) q^{10} +(-0.500000 - 0.866025i) q^{11} +0.339877 q^{12} +(1.66994 + 3.19551i) q^{13} -3.54461 q^{14} +(-0.490185 - 0.849025i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.61218 - 4.52443i) q^{17} -2.88448 q^{18} +(-3.11218 + 5.39045i) q^{19} +(-1.44224 + 2.49804i) q^{20} +1.20473 q^{21} +(-0.500000 + 0.866025i) q^{22} +(-0.339877 - 0.588684i) q^{23} +(-0.509815 - 0.883026i) q^{24} +3.32025 q^{25} +(1.93243 - 3.04397i) q^{26} +2.00000 q^{27} +(-1.77230 - 3.06972i) q^{28} +(4.21455 + 7.29981i) q^{29} +(-0.490185 + 0.849025i) q^{30} +8.40946 q^{31} +(-2.50000 + 4.33013i) q^{32} +(0.169938 - 0.294342i) q^{33} -5.22436 q^{34} +(-5.11218 + 8.85456i) q^{35} +(-1.44224 - 2.49804i) q^{36} +(-1.76249 - 3.05272i) q^{37} +6.22436 q^{38} +(-0.656787 + 1.03457i) q^{39} +8.65345 q^{40} +(2.87467 + 4.97907i) q^{41} +(-0.602365 - 1.04333i) q^{42} +(0.660123 - 1.14337i) q^{43} -1.00000 q^{44} +(-4.16012 + 7.20554i) q^{45} +(-0.339877 + 0.588684i) q^{46} +6.10884 q^{47} +(-0.169938 + 0.294342i) q^{48} +(-2.78212 - 4.81877i) q^{49} +(-1.66012 - 2.87542i) q^{50} +1.77564 q^{51} +(3.60236 + 0.151548i) q^{52} -6.08921 q^{53} +(-1.00000 - 1.73205i) q^{54} +(1.44224 + 2.49804i) q^{55} +(-5.31691 + 9.20916i) q^{56} -2.11552 q^{57} +(4.21455 - 7.29981i) q^{58} +(7.05442 - 12.2186i) q^{59} -0.980369 q^{60} +(-2.00982 + 3.48110i) q^{61} +(-4.20473 - 7.28281i) q^{62} +(-5.11218 - 8.85456i) q^{63} +7.00000 q^{64} +(-4.81691 - 9.21741i) q^{65} -0.339877 q^{66} +(-6.05442 - 10.4866i) q^{67} +(-2.61218 - 4.52443i) q^{68} +(0.115516 - 0.200080i) q^{69} +10.2244 q^{70} +(-3.00000 + 5.19615i) q^{71} +(-4.32673 + 7.49411i) q^{72} -16.0825 q^{73} +(-1.76249 + 3.05272i) q^{74} +(0.564237 + 0.977288i) q^{75} +(3.11218 + 5.39045i) q^{76} -3.54461 q^{77} +(1.22436 + 0.0515075i) q^{78} +0.904114 q^{79} +(-1.44224 - 2.49804i) q^{80} +(-3.98685 - 6.90542i) q^{81} +(2.87467 - 4.97907i) q^{82} +4.90411 q^{83} +(0.602365 - 1.04333i) q^{84} +(-7.53479 + 13.0506i) q^{85} -1.32025 q^{86} +(-1.43243 + 2.48104i) q^{87} +(1.50000 + 2.59808i) q^{88} +(2.82673 + 4.89603i) q^{89} +8.32025 q^{90} +(12.7690 + 0.537177i) q^{91} -0.679754 q^{92} +(1.42909 + 2.47526i) q^{93} +(-3.05442 - 5.29041i) q^{94} +(8.97703 - 15.5487i) q^{95} -1.69938 q^{96} +(-1.39764 + 2.42077i) q^{97} +(-2.78212 + 4.81877i) q^{98} -2.88448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9} - 3 q^{10} - 3 q^{11} + 9 q^{13} - 6 q^{15} + 3 q^{16} + 3 q^{17} + 6 q^{18} - 6 q^{19} + 3 q^{20} - 12 q^{21} - 3 q^{22} + 24 q^{25} + 3 q^{26} + 12 q^{27} + 3 q^{29} - 6 q^{30} + 12 q^{31} - 15 q^{32} - 6 q^{34} - 18 q^{35} + 3 q^{36} - 3 q^{37} + 12 q^{38} + 30 q^{39} - 18 q^{40} - 3 q^{41} + 6 q^{42} + 6 q^{43} - 6 q^{44} - 27 q^{45} - 12 q^{47} - 3 q^{49} - 12 q^{50} + 36 q^{51} + 12 q^{52} + 6 q^{53} - 6 q^{54} - 3 q^{55} - 36 q^{57} + 3 q^{58} + 18 q^{59} - 12 q^{60} - 9 q^{61} - 6 q^{62} - 18 q^{63} + 42 q^{64} + 3 q^{65} - 12 q^{67} - 3 q^{68} + 24 q^{69} + 36 q^{70} - 18 q^{71} + 9 q^{72} + 18 q^{73} - 3 q^{74} - 24 q^{75} + 6 q^{76} - 18 q^{78} - 24 q^{79} + 3 q^{80} + 9 q^{81} - 3 q^{82} - 6 q^{84} - 27 q^{85} - 12 q^{86} + 9 q^{88} - 18 q^{89} + 54 q^{90} + 30 q^{91} - 36 q^{93} + 6 q^{94} + 24 q^{95} - 18 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i 0.633316 0.773893i \(-0.281693\pi\)
−0.986869 + 0.161521i \(0.948360\pi\)
\(3\) 0.169938 + 0.294342i 0.0981140 + 0.169938i 0.910904 0.412618i \(-0.135386\pi\)
−0.812790 + 0.582557i \(0.802052\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −2.88448 −1.28998 −0.644990 0.764191i \(-0.723139\pi\)
−0.644990 + 0.764191i \(0.723139\pi\)
\(6\) 0.169938 0.294342i 0.0693771 0.120165i
\(7\) 1.77230 3.06972i 0.669868 1.16024i −0.308073 0.951363i \(-0.599684\pi\)
0.977941 0.208882i \(-0.0669825\pi\)
\(8\) −3.00000 −1.06066
\(9\) 1.44224 2.49804i 0.480747 0.832679i
\(10\) 1.44224 + 2.49804i 0.456077 + 0.789948i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 0.339877 0.0981140
\(13\) 1.66994 + 3.19551i 0.463158 + 0.886276i
\(14\) −3.54461 −0.947336
\(15\) −0.490185 0.849025i −0.126565 0.219217i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 2.61218 4.52443i 0.633547 1.09734i −0.353274 0.935520i \(-0.614932\pi\)
0.986821 0.161815i \(-0.0517349\pi\)
\(18\) −2.88448 −0.679879
\(19\) −3.11218 + 5.39045i −0.713983 + 1.23666i 0.249367 + 0.968409i \(0.419777\pi\)
−0.963350 + 0.268246i \(0.913556\pi\)
\(20\) −1.44224 + 2.49804i −0.322495 + 0.558578i
\(21\) 1.20473 0.262894
\(22\) −0.500000 + 0.866025i −0.106600 + 0.184637i
\(23\) −0.339877 0.588684i −0.0708692 0.122749i 0.828413 0.560117i \(-0.189244\pi\)
−0.899282 + 0.437368i \(0.855911\pi\)
\(24\) −0.509815 0.883026i −0.104066 0.180247i
\(25\) 3.32025 0.664049
\(26\) 1.93243 3.04397i 0.378980 0.596971i
\(27\) 2.00000 0.384900
\(28\) −1.77230 3.06972i −0.334934 0.580122i
\(29\) 4.21455 + 7.29981i 0.782621 + 1.35554i 0.930410 + 0.366521i \(0.119451\pi\)
−0.147788 + 0.989019i \(0.547215\pi\)
\(30\) −0.490185 + 0.849025i −0.0894951 + 0.155010i
\(31\) 8.40946 1.51038 0.755192 0.655504i \(-0.227544\pi\)
0.755192 + 0.655504i \(0.227544\pi\)
\(32\) −2.50000 + 4.33013i −0.441942 + 0.765466i
\(33\) 0.169938 0.294342i 0.0295825 0.0512384i
\(34\) −5.22436 −0.895970
\(35\) −5.11218 + 8.85456i −0.864116 + 1.49669i
\(36\) −1.44224 2.49804i −0.240374 0.416339i
\(37\) −1.76249 3.05272i −0.289751 0.501864i 0.683999 0.729483i \(-0.260239\pi\)
−0.973750 + 0.227619i \(0.926906\pi\)
\(38\) 6.22436 1.00972
\(39\) −0.656787 + 1.03457i −0.105170 + 0.165664i
\(40\) 8.65345 1.36823
\(41\) 2.87467 + 4.97907i 0.448948 + 0.777600i 0.998318 0.0579788i \(-0.0184656\pi\)
−0.549370 + 0.835579i \(0.685132\pi\)
\(42\) −0.602365 1.04333i −0.0929469 0.160989i
\(43\) 0.660123 1.14337i 0.100668 0.174362i −0.811292 0.584641i \(-0.801235\pi\)
0.911960 + 0.410279i \(0.134569\pi\)
\(44\) −1.00000 −0.150756
\(45\) −4.16012 + 7.20554i −0.620155 + 1.07414i
\(46\) −0.339877 + 0.588684i −0.0501121 + 0.0867967i
\(47\) 6.10884 0.891067 0.445533 0.895265i \(-0.353014\pi\)
0.445533 + 0.895265i \(0.353014\pi\)
\(48\) −0.169938 + 0.294342i −0.0245285 + 0.0424846i
\(49\) −2.78212 4.81877i −0.397446 0.688396i
\(50\) −1.66012 2.87542i −0.234777 0.406645i
\(51\) 1.77564 0.248639
\(52\) 3.60236 + 0.151548i 0.499558 + 0.0210159i
\(53\) −6.08921 −0.836418 −0.418209 0.908351i \(-0.637342\pi\)
−0.418209 + 0.908351i \(0.637342\pi\)
\(54\) −1.00000 1.73205i −0.136083 0.235702i
\(55\) 1.44224 + 2.49804i 0.194472 + 0.336835i
\(56\) −5.31691 + 9.20916i −0.710502 + 1.23063i
\(57\) −2.11552 −0.280207
\(58\) 4.21455 7.29981i 0.553397 0.958512i
\(59\) 7.05442 12.2186i 0.918408 1.59073i 0.116573 0.993182i \(-0.462809\pi\)
0.801834 0.597546i \(-0.203858\pi\)
\(60\) −0.980369 −0.126565
\(61\) −2.00982 + 3.48110i −0.257330 + 0.445709i −0.965526 0.260307i \(-0.916176\pi\)
0.708195 + 0.706016i \(0.249510\pi\)
\(62\) −4.20473 7.28281i −0.534001 0.924917i
\(63\) −5.11218 8.85456i −0.644074 1.11557i
\(64\) 7.00000 0.875000
\(65\) −4.81691 9.21741i −0.597464 1.14328i
\(66\) −0.339877 −0.0418360
\(67\) −6.05442 10.4866i −0.739665 1.28114i −0.952646 0.304082i \(-0.901650\pi\)
0.212981 0.977056i \(-0.431683\pi\)
\(68\) −2.61218 4.52443i −0.316773 0.548668i
\(69\) 0.115516 0.200080i 0.0139065 0.0240868i
\(70\) 10.2244 1.22204
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) −4.32673 + 7.49411i −0.509909 + 0.883189i
\(73\) −16.0825 −1.88232 −0.941160 0.337963i \(-0.890262\pi\)
−0.941160 + 0.337963i \(0.890262\pi\)
\(74\) −1.76249 + 3.05272i −0.204885 + 0.354871i
\(75\) 0.564237 + 0.977288i 0.0651525 + 0.112847i
\(76\) 3.11218 + 5.39045i 0.356992 + 0.618328i
\(77\) −3.54461 −0.403945
\(78\) 1.22436 + 0.0515075i 0.138632 + 0.00583208i
\(79\) 0.904114 0.101721 0.0508604 0.998706i \(-0.483804\pi\)
0.0508604 + 0.998706i \(0.483804\pi\)
\(80\) −1.44224 2.49804i −0.161248 0.279289i
\(81\) −3.98685 6.90542i −0.442983 0.767269i
\(82\) 2.87467 4.97907i 0.317454 0.549846i
\(83\) 4.90411 0.538296 0.269148 0.963099i \(-0.413258\pi\)
0.269148 + 0.963099i \(0.413258\pi\)
\(84\) 0.602365 1.04333i 0.0657234 0.113836i
\(85\) −7.53479 + 13.0506i −0.817263 + 1.41554i
\(86\) −1.32025 −0.142366
\(87\) −1.43243 + 2.48104i −0.153572 + 0.265995i
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) 2.82673 + 4.89603i 0.299632 + 0.518978i 0.976052 0.217538i \(-0.0698027\pi\)
−0.676420 + 0.736517i \(0.736469\pi\)
\(90\) 8.32025 0.877031
\(91\) 12.7690 + 0.537177i 1.33855 + 0.0563114i
\(92\) −0.679754 −0.0708692
\(93\) 1.42909 + 2.47526i 0.148190 + 0.256672i
\(94\) −3.05442 5.29041i −0.315040 0.545665i
\(95\) 8.97703 15.5487i 0.921024 1.59526i
\(96\) −1.69938 −0.173443
\(97\) −1.39764 + 2.42077i −0.141908 + 0.245792i −0.928215 0.372044i \(-0.878657\pi\)
0.786307 + 0.617836i \(0.211990\pi\)
\(98\) −2.78212 + 4.81877i −0.281036 + 0.486769i
\(99\) −2.88448 −0.289902
\(100\) 1.66012 2.87542i 0.166012 0.287542i
\(101\) 4.93243 + 8.54321i 0.490795 + 0.850081i 0.999944 0.0105969i \(-0.00337315\pi\)
−0.509149 + 0.860678i \(0.670040\pi\)
\(102\) −0.887820 1.53775i −0.0879073 0.152260i
\(103\) 5.35951 0.528088 0.264044 0.964511i \(-0.414944\pi\)
0.264044 + 0.964511i \(0.414944\pi\)
\(104\) −5.00982 9.58654i −0.491253 0.940038i
\(105\) −3.47502 −0.339128
\(106\) 3.04461 + 5.27341i 0.295718 + 0.512199i
\(107\) −1.65679 2.86964i −0.160168 0.277419i 0.774761 0.632254i \(-0.217870\pi\)
−0.934929 + 0.354836i \(0.884537\pi\)
\(108\) 1.00000 1.73205i 0.0962250 0.166667i
\(109\) 2.15478 0.206390 0.103195 0.994661i \(-0.467093\pi\)
0.103195 + 0.994661i \(0.467093\pi\)
\(110\) 1.44224 2.49804i 0.137512 0.238178i
\(111\) 0.599029 1.03755i 0.0568573 0.0984798i
\(112\) 3.54461 0.334934
\(113\) −1.89764 + 3.28680i −0.178514 + 0.309196i −0.941372 0.337371i \(-0.890462\pi\)
0.762857 + 0.646567i \(0.223796\pi\)
\(114\) 1.05776 + 1.83209i 0.0990681 + 0.171591i
\(115\) 0.980369 + 1.69805i 0.0914199 + 0.158344i
\(116\) 8.42909 0.782621
\(117\) 10.3910 + 0.437136i 0.960645 + 0.0404133i
\(118\) −14.1088 −1.29882
\(119\) −9.25915 16.0373i −0.848785 1.47014i
\(120\) 1.47055 + 2.54707i 0.134243 + 0.232515i
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 4.01963 0.363920
\(123\) −0.977033 + 1.69227i −0.0880961 + 0.152587i
\(124\) 4.20473 7.28281i 0.377596 0.654015i
\(125\) 4.84522 0.433370
\(126\) −5.11218 + 8.85456i −0.455429 + 0.788827i
\(127\) 8.08921 + 14.0109i 0.717802 + 1.24327i 0.961869 + 0.273511i \(0.0881849\pi\)
−0.244067 + 0.969758i \(0.578482\pi\)
\(128\) 1.50000 + 2.59808i 0.132583 + 0.229640i
\(129\) 0.448721 0.0395077
\(130\) −5.57405 + 8.78027i −0.488877 + 0.770081i
\(131\) −3.31357 −0.289508 −0.144754 0.989468i \(-0.546239\pi\)
−0.144754 + 0.989468i \(0.546239\pi\)
\(132\) −0.169938 0.294342i −0.0147912 0.0256192i
\(133\) 11.0315 + 19.1070i 0.956549 + 1.65679i
\(134\) −6.05442 + 10.4866i −0.523022 + 0.905901i
\(135\) −5.76897 −0.496514
\(136\) −7.83654 + 13.5733i −0.671978 + 1.16390i
\(137\) −6.87133 + 11.9015i −0.587058 + 1.01681i 0.407558 + 0.913179i \(0.366380\pi\)
−0.994615 + 0.103634i \(0.966953\pi\)
\(138\) −0.231033 −0.0196668
\(139\) −1.20473 + 2.08665i −0.102184 + 0.176988i −0.912584 0.408889i \(-0.865916\pi\)
0.810400 + 0.585877i \(0.199250\pi\)
\(140\) 5.11218 + 8.85456i 0.432058 + 0.748347i
\(141\) 1.03813 + 1.79809i 0.0874261 + 0.151426i
\(142\) 6.00000 0.503509
\(143\) 1.93243 3.04397i 0.161598 0.254549i
\(144\) 2.88448 0.240374
\(145\) −12.1568 21.0562i −1.00957 1.74862i
\(146\) 8.04127 + 13.9279i 0.665500 + 1.15268i
\(147\) 0.945578 1.63779i 0.0779899 0.135083i
\(148\) −3.52498 −0.289751
\(149\) 1.27230 2.20369i 0.104231 0.180534i −0.809193 0.587543i \(-0.800095\pi\)
0.913424 + 0.407010i \(0.133428\pi\)
\(150\) 0.564237 0.977288i 0.0460698 0.0797952i
\(151\) 8.44872 0.687547 0.343774 0.939053i \(-0.388295\pi\)
0.343774 + 0.939053i \(0.388295\pi\)
\(152\) 9.33654 16.1714i 0.757293 1.31167i
\(153\) −7.53479 13.0506i −0.609152 1.05508i
\(154\) 1.77230 + 3.06972i 0.142816 + 0.247365i
\(155\) −24.2569 −1.94837
\(156\) 0.567573 + 1.08608i 0.0454422 + 0.0869561i
\(157\) −16.3595 −1.30563 −0.652815 0.757517i \(-0.726412\pi\)
−0.652815 + 0.757517i \(0.726412\pi\)
\(158\) −0.452057 0.782986i −0.0359637 0.0622910i
\(159\) −1.03479 1.79231i −0.0820643 0.142140i
\(160\) 7.21121 12.4902i 0.570096 0.987435i
\(161\) −2.40946 −0.189892
\(162\) −3.98685 + 6.90542i −0.313236 + 0.542541i
\(163\) 5.39430 9.34320i 0.422514 0.731816i −0.573671 0.819086i \(-0.694481\pi\)
0.996185 + 0.0872702i \(0.0278144\pi\)
\(164\) 5.74934 0.448948
\(165\) −0.490185 + 0.849025i −0.0381608 + 0.0660965i
\(166\) −2.45206 4.24709i −0.190317 0.329638i
\(167\) −3.52498 6.10544i −0.272771 0.472453i 0.696799 0.717266i \(-0.254607\pi\)
−0.969570 + 0.244813i \(0.921273\pi\)
\(168\) −3.61419 −0.278841
\(169\) −7.42261 + 10.6726i −0.570970 + 0.820971i
\(170\) 15.0696 1.15578
\(171\) 8.97703 + 15.5487i 0.686491 + 1.18904i
\(172\) −0.660123 1.14337i −0.0503339 0.0871809i
\(173\) 0.922611 1.59801i 0.0701448 0.121494i −0.828820 0.559516i \(-0.810987\pi\)
0.898965 + 0.438021i \(0.144321\pi\)
\(174\) 2.86485 0.217184
\(175\) 5.88448 10.1922i 0.444825 0.770460i
\(176\) 0.500000 0.866025i 0.0376889 0.0652791i
\(177\) 4.79527 0.360435
\(178\) 2.82673 4.89603i 0.211872 0.366973i
\(179\) −2.71455 4.70173i −0.202895 0.351424i 0.746565 0.665312i \(-0.231702\pi\)
−0.949460 + 0.313888i \(0.898368\pi\)
\(180\) 4.16012 + 7.20554i 0.310077 + 0.537070i
\(181\) −4.47502 −0.332626 −0.166313 0.986073i \(-0.553186\pi\)
−0.166313 + 0.986073i \(0.553186\pi\)
\(182\) −5.91928 11.3268i −0.438766 0.839601i
\(183\) −1.36618 −0.100991
\(184\) 1.01963 + 1.76605i 0.0751682 + 0.130195i
\(185\) 5.08387 + 8.80552i 0.373773 + 0.647395i
\(186\) 1.42909 2.47526i 0.104786 0.181495i
\(187\) −5.22436 −0.382043
\(188\) 3.05442 5.29041i 0.222767 0.385843i
\(189\) 3.54461 6.13944i 0.257832 0.446578i
\(190\) −17.9541 −1.30252
\(191\) −4.94558 + 8.56599i −0.357849 + 0.619813i −0.987601 0.156983i \(-0.949823\pi\)
0.629752 + 0.776796i \(0.283157\pi\)
\(192\) 1.18957 + 2.06039i 0.0858498 + 0.148696i
\(193\) −2.55442 4.42439i −0.183871 0.318474i 0.759324 0.650712i \(-0.225530\pi\)
−0.943196 + 0.332238i \(0.892196\pi\)
\(194\) 2.79527 0.200689
\(195\) 1.89449 2.98421i 0.135667 0.213704i
\(196\) −5.56424 −0.397446
\(197\) −1.11552 1.93213i −0.0794772 0.137659i 0.823547 0.567248i \(-0.191992\pi\)
−0.903025 + 0.429589i \(0.858658\pi\)
\(198\) 1.44224 + 2.49804i 0.102496 + 0.177528i
\(199\) −8.93891 + 15.4826i −0.633662 + 1.09754i 0.353135 + 0.935573i \(0.385116\pi\)
−0.986797 + 0.161963i \(0.948218\pi\)
\(200\) −9.96074 −0.704331
\(201\) 2.05776 3.56414i 0.145143 0.251395i
\(202\) 4.93243 8.54321i 0.347044 0.601098i
\(203\) 29.8778 2.09701
\(204\) 0.887820 1.53775i 0.0621598 0.107664i
\(205\) −8.29193 14.3621i −0.579134 1.00309i
\(206\) −2.67975 4.64147i −0.186707 0.323387i
\(207\) −1.96074 −0.136281
\(208\) −1.93243 + 3.04397i −0.133990 + 0.211061i
\(209\) 6.22436 0.430548
\(210\) 1.73751 + 3.00946i 0.119900 + 0.207672i
\(211\) −5.45206 9.44324i −0.375335 0.650099i 0.615042 0.788494i \(-0.289139\pi\)
−0.990377 + 0.138395i \(0.955806\pi\)
\(212\) −3.04461 + 5.27341i −0.209104 + 0.362180i
\(213\) −2.03926 −0.139728
\(214\) −1.65679 + 2.86964i −0.113256 + 0.196165i
\(215\) −1.90411 + 3.29802i −0.129860 + 0.224923i
\(216\) −6.00000 −0.408248
\(217\) 14.9041 25.8147i 1.01176 1.75241i
\(218\) −1.07739 1.86609i −0.0729700 0.126388i
\(219\) −2.73304 4.73377i −0.184682 0.319878i
\(220\) 2.88448 0.194472
\(221\) 18.8201 + 0.791739i 1.26597 + 0.0532581i
\(222\) −1.19806 −0.0804084
\(223\) 9.71455 + 16.8261i 0.650534 + 1.12676i 0.982993 + 0.183640i \(0.0587882\pi\)
−0.332459 + 0.943118i \(0.607878\pi\)
\(224\) 8.86152 + 15.3486i 0.592085 + 1.02552i
\(225\) 4.78860 8.29410i 0.319240 0.552940i
\(226\) 3.79527 0.252458
\(227\) 3.66012 6.33952i 0.242931 0.420769i −0.718617 0.695406i \(-0.755225\pi\)
0.961548 + 0.274637i \(0.0885578\pi\)
\(228\) −1.05776 + 1.83209i −0.0700517 + 0.121333i
\(229\) 14.5642 0.962432 0.481216 0.876602i \(-0.340195\pi\)
0.481216 + 0.876602i \(0.340195\pi\)
\(230\) 0.980369 1.69805i 0.0646436 0.111966i
\(231\) −0.602365 1.04333i −0.0396327 0.0686459i
\(232\) −12.6436 21.8994i −0.830095 1.43777i
\(233\) 6.44872 0.422470 0.211235 0.977435i \(-0.432252\pi\)
0.211235 + 0.977435i \(0.432252\pi\)
\(234\) −4.81691 9.21741i −0.314891 0.602561i
\(235\) −17.6209 −1.14946
\(236\) −7.05442 12.2186i −0.459204 0.795364i
\(237\) 0.153644 + 0.266119i 0.00998024 + 0.0172863i
\(238\) −9.25915 + 16.0373i −0.600182 + 1.03955i
\(239\) −0.270294 −0.0174839 −0.00874193 0.999962i \(-0.502783\pi\)
−0.00874193 + 0.999962i \(0.502783\pi\)
\(240\) 0.490185 0.849025i 0.0316413 0.0548043i
\(241\) −15.2656 + 26.4408i −0.983346 + 1.70320i −0.334277 + 0.942475i \(0.608492\pi\)
−0.649068 + 0.760730i \(0.724841\pi\)
\(242\) 1.00000 0.0642824
\(243\) 4.35504 7.54315i 0.279376 0.483893i
\(244\) 2.00982 + 3.48110i 0.128665 + 0.222855i
\(245\) 8.02498 + 13.8997i 0.512697 + 0.888017i
\(246\) 1.95407 0.124587
\(247\) −22.4224 0.943287i −1.42670 0.0600199i
\(248\) −25.2284 −1.60200
\(249\) 0.833398 + 1.44349i 0.0528144 + 0.0914773i
\(250\) −2.42261 4.19609i −0.153219 0.265384i
\(251\) −5.23952 + 9.07512i −0.330716 + 0.572816i −0.982652 0.185457i \(-0.940623\pi\)
0.651937 + 0.758273i \(0.273957\pi\)
\(252\) −10.2244 −0.644074
\(253\) −0.339877 + 0.588684i −0.0213679 + 0.0370102i
\(254\) 8.08921 14.0109i 0.507562 0.879124i
\(255\) −5.12180 −0.320740
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −2.87800 4.98485i −0.179525 0.310946i 0.762193 0.647350i \(-0.224123\pi\)
−0.941718 + 0.336404i \(0.890789\pi\)
\(258\) −0.224361 0.388604i −0.0139681 0.0241934i
\(259\) −12.4947 −0.776380
\(260\) −10.3910 0.437136i −0.644420 0.0271101i
\(261\) 24.3136 1.50497
\(262\) 1.65679 + 2.86964i 0.102357 + 0.177287i
\(263\) −4.22436 7.31681i −0.260485 0.451174i 0.705886 0.708326i \(-0.250549\pi\)
−0.966371 + 0.257152i \(0.917216\pi\)
\(264\) −0.509815 + 0.883026i −0.0313770 + 0.0543465i
\(265\) 17.5642 1.07896
\(266\) 11.0315 19.1070i 0.676382 1.17153i
\(267\) −0.960739 + 1.66405i −0.0587963 + 0.101838i
\(268\) −12.1088 −0.739665
\(269\) −12.5446 + 21.7279i −0.764858 + 1.32477i 0.175463 + 0.984486i \(0.443858\pi\)
−0.940322 + 0.340287i \(0.889476\pi\)
\(270\) 2.88448 + 4.99607i 0.175544 + 0.304051i
\(271\) 5.22436 + 9.04886i 0.317357 + 0.549679i 0.979936 0.199314i \(-0.0638712\pi\)
−0.662578 + 0.748993i \(0.730538\pi\)
\(272\) 5.22436 0.316773
\(273\) 2.01182 + 3.84973i 0.121761 + 0.232996i
\(274\) 13.7427 0.830225
\(275\) −1.66012 2.87542i −0.100109 0.173394i
\(276\) −0.115516 0.200080i −0.00695326 0.0120434i
\(277\) −4.31043 + 7.46589i −0.258989 + 0.448582i −0.965971 0.258649i \(-0.916723\pi\)
0.706983 + 0.707231i \(0.250056\pi\)
\(278\) 2.40946 0.144510
\(279\) 12.1285 21.0071i 0.726113 1.25766i
\(280\) 15.3365 26.5637i 0.916534 1.58748i
\(281\) −1.98037 −0.118139 −0.0590695 0.998254i \(-0.518813\pi\)
−0.0590695 + 0.998254i \(0.518813\pi\)
\(282\) 1.03813 1.79809i 0.0618196 0.107075i
\(283\) −1.09255 1.89235i −0.0649453 0.112489i 0.831724 0.555189i \(-0.187354\pi\)
−0.896670 + 0.442700i \(0.854021\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 6.10217 0.361461
\(286\) −3.60236 0.151548i −0.213012 0.00896120i
\(287\) 20.3791 1.20294
\(288\) 7.21121 + 12.4902i 0.424925 + 0.735991i
\(289\) −5.14697 8.91482i −0.302763 0.524401i
\(290\) −12.1568 + 21.0562i −0.713871 + 1.23646i
\(291\) −0.950048 −0.0556928
\(292\) −8.04127 + 13.9279i −0.470580 + 0.815068i
\(293\) −3.06757 + 5.31319i −0.179210 + 0.310400i −0.941610 0.336705i \(-0.890687\pi\)
0.762400 + 0.647105i \(0.224021\pi\)
\(294\) −1.89116 −0.110294
\(295\) −20.3484 + 35.2444i −1.18473 + 2.05201i
\(296\) 5.28746 + 9.15816i 0.307328 + 0.532307i
\(297\) −1.00000 1.73205i −0.0580259 0.100504i
\(298\) −2.54461 −0.147405
\(299\) 1.31357 2.06915i 0.0759660 0.119662i
\(300\) 1.12847 0.0651525
\(301\) −2.33988 4.05279i −0.134868 0.233599i
\(302\) −4.22436 7.31681i −0.243085 0.421035i
\(303\) −1.67642 + 2.90364i −0.0963077 + 0.166810i
\(304\) −6.22436 −0.356992
\(305\) 5.79728 10.0412i 0.331951 0.574956i
\(306\) −7.53479 + 13.0506i −0.430735 + 0.746056i
\(307\) 6.18510 0.353002 0.176501 0.984300i \(-0.443522\pi\)
0.176501 + 0.984300i \(0.443522\pi\)
\(308\) −1.77230 + 3.06972i −0.100986 + 0.174914i
\(309\) 0.910786 + 1.57753i 0.0518128 + 0.0897424i
\(310\) 12.1285 + 21.0071i 0.688851 + 1.19313i
\(311\) −1.28992 −0.0731449 −0.0365725 0.999331i \(-0.511644\pi\)
−0.0365725 + 0.999331i \(0.511644\pi\)
\(312\) 1.97036 3.10372i 0.111550 0.175714i
\(313\) −0.293944 −0.0166147 −0.00830734 0.999965i \(-0.502644\pi\)
−0.00830734 + 0.999965i \(0.502644\pi\)
\(314\) 8.17975 + 14.1677i 0.461610 + 0.799532i
\(315\) 14.7460 + 25.5408i 0.830843 + 1.43906i
\(316\) 0.452057 0.782986i 0.0254302 0.0440464i
\(317\) −22.0522 −1.23858 −0.619288 0.785164i \(-0.712579\pi\)
−0.619288 + 0.785164i \(0.712579\pi\)
\(318\) −1.03479 + 1.79231i −0.0580282 + 0.100508i
\(319\) 4.21455 7.29981i 0.235969 0.408711i
\(320\) −20.1914 −1.12873
\(321\) 0.563104 0.975324i 0.0314294 0.0544373i
\(322\) 1.20473 + 2.08665i 0.0671370 + 0.116285i
\(323\) 16.2592 + 28.1617i 0.904683 + 1.56696i
\(324\) −7.97370 −0.442983
\(325\) 5.54461 + 10.6099i 0.307559 + 0.588531i
\(326\) −10.7886 −0.597525
\(327\) 0.366180 + 0.634242i 0.0202498 + 0.0350736i
\(328\) −8.62401 14.9372i −0.476181 0.824770i
\(329\) 10.8267 18.7524i 0.596897 1.03386i
\(330\) 0.980369 0.0539676
\(331\) 7.22436 12.5130i 0.397087 0.687774i −0.596278 0.802778i \(-0.703355\pi\)
0.993365 + 0.115003i \(0.0366879\pi\)
\(332\) 2.45206 4.24709i 0.134574 0.233089i
\(333\) −10.1677 −0.557189
\(334\) −3.52498 + 6.10544i −0.192878 + 0.334075i
\(335\) 17.4639 + 30.2483i 0.954154 + 1.65264i
\(336\) 0.602365 + 1.04333i 0.0328617 + 0.0569181i
\(337\) −18.5053 −1.00805 −0.504025 0.863689i \(-0.668148\pi\)
−0.504025 + 0.863689i \(0.668148\pi\)
\(338\) 12.9541 + 1.09186i 0.704608 + 0.0593893i
\(339\) −1.28992 −0.0700591
\(340\) 7.53479 + 13.0506i 0.408631 + 0.707770i
\(341\) −4.20473 7.28281i −0.227699 0.394386i
\(342\) 8.97703 15.5487i 0.485422 0.840776i
\(343\) 5.08921 0.274792
\(344\) −1.98037 + 3.43010i −0.106774 + 0.184939i
\(345\) −0.333205 + 0.577128i −0.0179391 + 0.0310715i
\(346\) −1.84522 −0.0991998
\(347\) 7.77230 13.4620i 0.417239 0.722679i −0.578422 0.815738i \(-0.696331\pi\)
0.995661 + 0.0930587i \(0.0296644\pi\)
\(348\) 1.43243 + 2.48104i 0.0767861 + 0.132997i
\(349\) −15.0000 25.9808i −0.802932 1.39072i −0.917679 0.397324i \(-0.869939\pi\)
0.114747 0.993395i \(-0.463394\pi\)
\(350\) −11.7690 −0.629078
\(351\) 3.33988 + 6.39103i 0.178269 + 0.341128i
\(352\) 5.00000 0.266501
\(353\) 2.16012 + 3.74144i 0.114972 + 0.199137i 0.917768 0.397116i \(-0.129989\pi\)
−0.802797 + 0.596253i \(0.796656\pi\)
\(354\) −2.39764 4.15283i −0.127433 0.220720i
\(355\) 8.65345 14.9882i 0.459277 0.795492i
\(356\) 5.65345 0.299632
\(357\) 3.14697 5.45072i 0.166555 0.288482i
\(358\) −2.71455 + 4.70173i −0.143468 + 0.248494i
\(359\) −0.231033 −0.0121934 −0.00609672 0.999981i \(-0.501941\pi\)
−0.00609672 + 0.999981i \(0.501941\pi\)
\(360\) 12.4804 21.6166i 0.657773 1.13930i
\(361\) −9.87133 17.0976i −0.519544 0.899876i
\(362\) 2.23751 + 3.87548i 0.117601 + 0.203691i
\(363\) −0.339877 −0.0178389
\(364\) 6.84969 10.7897i 0.359021 0.565532i
\(365\) 46.3898 2.42815
\(366\) 0.683090 + 1.18315i 0.0357057 + 0.0618440i
\(367\) −9.90411 17.1544i −0.516991 0.895454i −0.999805 0.0197314i \(-0.993719\pi\)
0.482815 0.875723i \(-0.339614\pi\)
\(368\) 0.339877 0.588684i 0.0177173 0.0306873i
\(369\) 16.5839 0.863322
\(370\) 5.08387 8.80552i 0.264298 0.457777i
\(371\) −10.7919 + 18.6922i −0.560289 + 0.970450i
\(372\) 2.85818 0.148190
\(373\) 7.45740 12.9166i 0.386130 0.668796i −0.605796 0.795620i \(-0.707145\pi\)
0.991925 + 0.126824i \(0.0404784\pi\)
\(374\) 2.61218 + 4.52443i 0.135073 + 0.233953i
\(375\) 0.823390 + 1.42615i 0.0425197 + 0.0736462i
\(376\) −18.3265 −0.945119
\(377\) −16.2886 + 25.6579i −0.838905 + 1.32145i
\(378\) −7.08921 −0.364630
\(379\) −3.32025 5.75084i −0.170550 0.295401i 0.768063 0.640375i \(-0.221221\pi\)
−0.938612 + 0.344974i \(0.887888\pi\)
\(380\) −8.97703 15.5487i −0.460512 0.797630i
\(381\) −2.74934 + 4.76199i −0.140853 + 0.243964i
\(382\) 9.89116 0.506076
\(383\) 2.57091 4.45295i 0.131367 0.227535i −0.792837 0.609434i \(-0.791397\pi\)
0.924204 + 0.381899i \(0.124730\pi\)
\(384\) −0.509815 + 0.883026i −0.0260164 + 0.0450617i
\(385\) 10.2244 0.521082
\(386\) −2.55442 + 4.42439i −0.130017 + 0.225195i
\(387\) −1.90411 3.29802i −0.0967916 0.167648i
\(388\) 1.39764 + 2.42077i 0.0709542 + 0.122896i
\(389\) −33.2806 −1.68739 −0.843697 0.536820i \(-0.819625\pi\)
−0.843697 + 0.536820i \(0.819625\pi\)
\(390\) −3.53165 0.148573i −0.178832 0.00752327i
\(391\) −3.55128 −0.179596
\(392\) 8.34636 + 14.4563i 0.421555 + 0.730154i
\(393\) −0.563104 0.975324i −0.0284048 0.0491986i
\(394\) −1.11552 + 1.93213i −0.0561989 + 0.0973393i
\(395\) −2.60790 −0.131218
\(396\) −1.44224 + 2.49804i −0.0724754 + 0.125531i
\(397\) −4.30175 + 7.45085i −0.215899 + 0.373947i −0.953550 0.301234i \(-0.902601\pi\)
0.737652 + 0.675182i \(0.235935\pi\)
\(398\) 17.8778 0.896134
\(399\) −3.74934 + 6.49404i −0.187702 + 0.325109i
\(400\) 1.66012 + 2.87542i 0.0830062 + 0.143771i
\(401\) 2.83988 + 4.91881i 0.141817 + 0.245634i 0.928181 0.372130i \(-0.121372\pi\)
−0.786364 + 0.617763i \(0.788039\pi\)
\(402\) −4.11552 −0.205263
\(403\) 14.0433 + 26.8725i 0.699546 + 1.33862i
\(404\) 9.86485 0.490795
\(405\) 11.5000 + 19.9186i 0.571440 + 0.989762i
\(406\) −14.9389 25.8749i −0.741405 1.28415i
\(407\) −1.76249 + 3.05272i −0.0873633 + 0.151318i
\(408\) −5.32692 −0.263722
\(409\) −11.4967 + 19.9128i −0.568473 + 0.984625i 0.428244 + 0.903663i \(0.359132\pi\)
−0.996717 + 0.0809616i \(0.974201\pi\)
\(410\) −8.29193 + 14.3621i −0.409509 + 0.709291i
\(411\) −4.67081 −0.230394
\(412\) 2.67975 4.64147i 0.132022 0.228669i
\(413\) −25.0052 43.3102i −1.23042 2.13116i
\(414\) 0.980369 + 1.69805i 0.0481825 + 0.0834546i
\(415\) −14.1458 −0.694392
\(416\) −18.0118 0.757738i −0.883102 0.0371512i
\(417\) −0.818920 −0.0401027
\(418\) −3.11218 5.39045i −0.152222 0.263656i
\(419\) −15.4291 26.7240i −0.753760 1.30555i −0.945988 0.324201i \(-0.894905\pi\)
0.192228 0.981350i \(-0.438429\pi\)
\(420\) −1.73751 + 3.00946i −0.0847819 + 0.146847i
\(421\) 23.6035 1.15036 0.575182 0.818025i \(-0.304931\pi\)
0.575182 + 0.818025i \(0.304931\pi\)
\(422\) −5.45206 + 9.44324i −0.265402 + 0.459690i
\(423\) 8.81043 15.2601i 0.428378 0.741972i
\(424\) 18.2676 0.887155
\(425\) 8.67308 15.0222i 0.420706 0.728685i
\(426\) 1.01963 + 1.76605i 0.0494013 + 0.0855655i
\(427\) 7.12401 + 12.3391i 0.344755 + 0.597133i
\(428\) −3.31357 −0.160168
\(429\) 1.22436 + 0.0515075i 0.0591127 + 0.00248681i
\(430\) 3.80823 0.183649
\(431\) −14.3169 24.7976i −0.689621 1.19446i −0.971960 0.235144i \(-0.924444\pi\)
0.282339 0.959315i \(-0.408890\pi\)
\(432\) 1.00000 + 1.73205i 0.0481125 + 0.0833333i
\(433\) 14.3267 24.8146i 0.688498 1.19251i −0.283825 0.958876i \(-0.591604\pi\)
0.972324 0.233638i \(-0.0750632\pi\)
\(434\) −29.8082 −1.43084
\(435\) 4.13181 7.15651i 0.198105 0.343128i
\(436\) 1.07739 1.86609i 0.0515976 0.0893696i
\(437\) 4.23103 0.202398
\(438\) −2.73304 + 4.73377i −0.130590 + 0.226188i
\(439\) 4.54794 + 7.87727i 0.217061 + 0.375961i 0.953908 0.300098i \(-0.0970195\pi\)
−0.736847 + 0.676060i \(0.763686\pi\)
\(440\) −4.32673 7.49411i −0.206269 0.357268i
\(441\) −16.0500 −0.764283
\(442\) −8.72436 16.6945i −0.414976 0.794077i
\(443\) 0.518304 0.0246254 0.0123127 0.999924i \(-0.496081\pi\)
0.0123127 + 0.999924i \(0.496081\pi\)
\(444\) −0.599029 1.03755i −0.0284287 0.0492399i
\(445\) −8.15364 14.1225i −0.386520 0.669472i
\(446\) 9.71455 16.8261i 0.459997 0.796738i
\(447\) 0.864853 0.0409061
\(448\) 12.4061 21.4880i 0.586134 1.01521i
\(449\) 16.5261 28.6241i 0.779915 1.35085i −0.152075 0.988369i \(-0.548595\pi\)
0.931990 0.362484i \(-0.118071\pi\)
\(450\) −9.57720 −0.451473
\(451\) 2.87467 4.97907i 0.135363 0.234455i
\(452\) 1.89764 + 3.28680i 0.0892572 + 0.154598i
\(453\) 1.43576 + 2.48681i 0.0674580 + 0.116841i
\(454\) −7.32025 −0.343556
\(455\) −36.8319 1.54948i −1.72671 0.0726406i
\(456\) 6.34655 0.297204
\(457\) 13.6633 + 23.6655i 0.639141 + 1.10702i 0.985622 + 0.168967i \(0.0540432\pi\)
−0.346481 + 0.938057i \(0.612624\pi\)
\(458\) −7.28212 12.6130i −0.340271 0.589367i
\(459\) 5.22436 9.04886i 0.243852 0.422365i
\(460\) 1.96074 0.0914199
\(461\) −6.64364 + 11.5071i −0.309425 + 0.535940i −0.978237 0.207492i \(-0.933470\pi\)
0.668812 + 0.743432i \(0.266803\pi\)
\(462\) −0.602365 + 1.04333i −0.0280246 + 0.0485400i
\(463\) 18.2480 0.848057 0.424028 0.905649i \(-0.360616\pi\)
0.424028 + 0.905649i \(0.360616\pi\)
\(464\) −4.21455 + 7.29981i −0.195655 + 0.338885i
\(465\) −4.12219 7.13984i −0.191162 0.331102i
\(466\) −3.22436 5.58476i −0.149366 0.258709i
\(467\) 28.2873 1.30898 0.654489 0.756071i \(-0.272884\pi\)
0.654489 + 0.756071i \(0.272884\pi\)
\(468\) 5.57405 8.78027i 0.257661 0.405868i
\(469\) −42.9211 −1.98191
\(470\) 8.81043 + 15.2601i 0.406395 + 0.703897i
\(471\) −2.78011 4.81529i −0.128101 0.221877i
\(472\) −21.1633 + 36.6559i −0.974118 + 1.68722i
\(473\) −1.32025 −0.0607050
\(474\) 0.153644 0.266119i 0.00705709 0.0122232i
\(475\) −10.3332 + 17.8976i −0.474120 + 0.821200i
\(476\) −18.5183 −0.848785
\(477\) −8.78212 + 15.2111i −0.402106 + 0.696467i
\(478\) 0.135147 + 0.234081i 0.00618148 + 0.0107066i
\(479\) −7.77230 13.4620i −0.355126 0.615096i 0.632014 0.774957i \(-0.282229\pi\)
−0.987139 + 0.159861i \(0.948895\pi\)
\(480\) 4.90185 0.223738
\(481\) 6.81176 10.7299i 0.310589 0.489242i
\(482\) 30.5313 1.39066
\(483\) −0.409460 0.709205i −0.0186311 0.0322700i
\(484\) 0.500000 + 0.866025i 0.0227273 + 0.0393648i
\(485\) 4.03146 6.98269i 0.183059 0.317067i
\(486\) −8.71008 −0.395097
\(487\) −16.1633 + 27.9956i −0.732428 + 1.26860i 0.223415 + 0.974723i \(0.428279\pi\)
−0.955843 + 0.293878i \(0.905054\pi\)
\(488\) 6.02945 10.4433i 0.272940 0.472746i
\(489\) 3.66680 0.165818
\(490\) 8.02498 13.8997i 0.362531 0.627923i
\(491\) −5.77230 9.99792i −0.260500 0.451200i 0.705875 0.708337i \(-0.250554\pi\)
−0.966375 + 0.257137i \(0.917221\pi\)
\(492\) 0.977033 + 1.69227i 0.0440481 + 0.0762935i
\(493\) 44.0366 1.98331
\(494\) 10.3943 + 19.8900i 0.467662 + 0.894895i
\(495\) 8.32025 0.373967
\(496\) 4.20473 + 7.28281i 0.188798 + 0.327008i
\(497\) 10.6338 + 18.4183i 0.476992 + 0.826174i
\(498\) 0.833398 1.44349i 0.0373454 0.0646842i
\(499\) −27.7859 −1.24387 −0.621935 0.783069i \(-0.713653\pi\)
−0.621935 + 0.783069i \(0.713653\pi\)
\(500\) 2.42261 4.19609i 0.108342 0.187655i
\(501\) 1.19806 2.07510i 0.0535253 0.0927085i
\(502\) 10.4790 0.467703
\(503\) 2.70272 4.68125i 0.120508 0.208727i −0.799460 0.600719i \(-0.794881\pi\)
0.919968 + 0.391993i \(0.128214\pi\)
\(504\) 15.3365 + 26.5637i 0.683144 + 1.18324i
\(505\) −14.2275 24.6428i −0.633116 1.09659i
\(506\) 0.679754 0.0302187
\(507\) −4.40279 0.371098i −0.195535 0.0164810i
\(508\) 16.1784 0.717802
\(509\) 12.7047 + 22.0052i 0.563127 + 0.975365i 0.997221 + 0.0744974i \(0.0237353\pi\)
−0.434094 + 0.900868i \(0.642931\pi\)
\(510\) 2.56090 + 4.43561i 0.113399 + 0.196412i
\(511\) −28.5031 + 49.3689i −1.26090 + 2.18395i
\(512\) −11.0000 −0.486136
\(513\) −6.22436 + 10.7809i −0.274812 + 0.475989i
\(514\) −2.87800 + 4.98485i −0.126943 + 0.219872i
\(515\) −15.4594 −0.681223
\(516\) 0.224361 0.388604i 0.00987692 0.0171073i
\(517\) −3.05442 5.29041i −0.134333 0.232672i
\(518\) 6.24733 + 10.8207i 0.274492 + 0.475434i
\(519\) 0.627148 0.0275288
\(520\) 14.4507 + 27.6522i 0.633706 + 1.21263i
\(521\) 33.1784 1.45357 0.726787 0.686863i \(-0.241013\pi\)
0.726787 + 0.686863i \(0.241013\pi\)
\(522\) −12.1568 21.0562i −0.532088 0.921604i
\(523\) 9.38649 + 16.2579i 0.410443 + 0.710908i 0.994938 0.100489i \(-0.0320409\pi\)
−0.584495 + 0.811397i \(0.698708\pi\)
\(524\) −1.65679 + 2.86964i −0.0723771 + 0.125361i
\(525\) 4.00000 0.174574
\(526\) −4.22436 + 7.31681i −0.184191 + 0.319028i
\(527\) 21.9670 38.0480i 0.956899 1.65740i
\(528\) 0.339877 0.0147912
\(529\) 11.2690 19.5184i 0.489955 0.848627i
\(530\) −8.78212 15.2111i −0.381471 0.660727i
\(531\) −20.3484 35.2444i −0.883044 1.52948i
\(532\) 22.0629 0.956549
\(533\) −11.1102 + 17.5008i −0.481235 + 0.758043i
\(534\) 1.92148 0.0831505
\(535\) 4.77898 + 8.27743i 0.206613 + 0.357864i
\(536\) 18.1633 + 31.4597i 0.784534 + 1.35885i
\(537\) 0.922611 1.59801i 0.0398136 0.0689592i
\(538\) 25.0892 1.08167
\(539\) −2.78212 + 4.81877i −0.119834 + 0.207559i
\(540\) −2.88448 + 4.99607i −0.124128 + 0.214997i
\(541\) 42.8016 1.84018 0.920091 0.391704i \(-0.128114\pi\)
0.920091 + 0.391704i \(0.128114\pi\)
\(542\) 5.22436 9.04886i 0.224406 0.388682i
\(543\) −0.760479 1.31719i −0.0326353 0.0565259i
\(544\) 13.0609 + 22.6221i 0.559982 + 0.969916i
\(545\) −6.21542 −0.266239
\(546\) 2.32805 3.66716i 0.0996314 0.156940i
\(547\) −33.7556 −1.44329 −0.721643 0.692265i \(-0.756613\pi\)
−0.721643 + 0.692265i \(0.756613\pi\)
\(548\) 6.87133 + 11.9015i 0.293529 + 0.508407i
\(549\) 5.79728 + 10.0412i 0.247422 + 0.428547i
\(550\) −1.66012 + 2.87542i −0.0707879 + 0.122608i
\(551\) −52.4657 −2.23511
\(552\) −0.346549 + 0.600240i −0.0147501 + 0.0255479i
\(553\) 1.60236 2.77538i 0.0681395 0.118021i
\(554\) 8.62086 0.366265
\(555\) −1.72789 + 2.99279i −0.0733448 + 0.127037i
\(556\) 1.20473 + 2.08665i 0.0510919 + 0.0884938i
\(557\) 0.894299 + 1.54897i 0.0378927 + 0.0656320i 0.884350 0.466825i \(-0.154602\pi\)
−0.846457 + 0.532457i \(0.821269\pi\)
\(558\) −24.2569 −1.02688
\(559\) 4.75601 + 0.200080i 0.201158 + 0.00846249i
\(560\) −10.2244 −0.432058
\(561\) −0.887820 1.53775i −0.0374838 0.0649238i
\(562\) 0.990185 + 1.71505i 0.0417684 + 0.0723450i
\(563\) 3.84189 6.65434i 0.161916 0.280447i −0.773640 0.633626i \(-0.781566\pi\)
0.935556 + 0.353179i \(0.114899\pi\)
\(564\) 2.07625 0.0874261
\(565\) 5.47370 9.48072i 0.230280 0.398857i
\(566\) −1.09255 + 1.89235i −0.0459233 + 0.0795415i
\(567\) −28.2636 −1.18696
\(568\) 9.00000 15.5885i 0.377632 0.654077i
\(569\) 13.0629 + 22.6256i 0.547626 + 0.948516i 0.998437 + 0.0558961i \(0.0178016\pi\)
−0.450811 + 0.892619i \(0.648865\pi\)
\(570\) −3.05109 5.28464i −0.127796 0.221349i
\(571\) −11.6624 −0.488056 −0.244028 0.969768i \(-0.578469\pi\)
−0.244028 + 0.969768i \(0.578469\pi\)
\(572\) −1.66994 3.19551i −0.0698236 0.133611i
\(573\) −3.36178 −0.140440
\(574\) −10.1896 17.6489i −0.425304 0.736649i
\(575\) −1.12847 1.95458i −0.0470607 0.0815115i
\(576\) 10.0957 17.4863i 0.420654 0.728594i
\(577\) 28.6008 1.19067 0.595334 0.803478i \(-0.297020\pi\)
0.595334 + 0.803478i \(0.297020\pi\)
\(578\) −5.14697 + 8.91482i −0.214086 + 0.370807i
\(579\) 0.868189 1.50375i 0.0360807 0.0624936i
\(580\) −24.3136 −1.00957
\(581\) 8.69158 15.0543i 0.360587 0.624556i
\(582\) 0.475024 + 0.822765i 0.0196904 + 0.0341047i
\(583\) 3.04461 + 5.27341i 0.126095 + 0.218402i
\(584\) 48.2476 1.99650
\(585\) −29.9726 1.26091i −1.23921 0.0521323i
\(586\) 6.13515 0.253441
\(587\) 17.5727 + 30.4369i 0.725304 + 1.25626i 0.958849 + 0.283917i \(0.0916341\pi\)
−0.233545 + 0.972346i \(0.575033\pi\)
\(588\) −0.945578 1.63779i −0.0389950 0.0675413i
\(589\) −26.1718 + 45.3308i −1.07839 + 1.86782i
\(590\) 40.6967 1.67546
\(591\) 0.379138 0.656687i 0.0155957 0.0270125i
\(592\) 1.76249 3.05272i 0.0724378 0.125466i
\(593\) −25.2087 −1.03520 −0.517600 0.855623i \(-0.673174\pi\)
−0.517600 + 0.855623i \(0.673174\pi\)
\(594\) −1.00000 + 1.73205i −0.0410305 + 0.0710669i
\(595\) 26.7079 + 46.2594i 1.09492 + 1.89645i
\(596\) −1.27230 2.20369i −0.0521156 0.0902668i
\(597\) −6.07625 −0.248685
\(598\) −2.44872 0.103015i −0.100136 0.00421260i
\(599\) 26.8582 1.09740 0.548698 0.836021i \(-0.315124\pi\)
0.548698 + 0.836021i \(0.315124\pi\)
\(600\) −1.69271 2.93186i −0.0691047 0.119693i
\(601\) −16.2841 28.2049i −0.664243 1.15050i −0.979490 0.201494i \(-0.935420\pi\)
0.315246 0.949010i \(-0.397913\pi\)
\(602\) −2.33988 + 4.05279i −0.0953663 + 0.165179i
\(603\) −34.9278 −1.42237
\(604\) 4.22436 7.31681i 0.171887 0.297717i
\(605\) 1.44224 2.49804i 0.0586355 0.101560i
\(606\) 3.35284 0.136200
\(607\) −20.3865 + 35.3104i −0.827462 + 1.43321i 0.0725607 + 0.997364i \(0.476883\pi\)
−0.900023 + 0.435843i \(0.856450\pi\)
\(608\) −15.5609 26.9523i −0.631078 1.09306i
\(609\) 5.07739 + 8.79430i 0.205746 + 0.356363i
\(610\) −11.5946 −0.469450
\(611\) 10.2014 + 19.5209i 0.412704 + 0.789731i
\(612\) −15.0696 −0.609152
\(613\) 11.6818 + 20.2334i 0.471822 + 0.817220i 0.999480 0.0322371i \(-0.0102632\pi\)
−0.527658 + 0.849457i \(0.676930\pi\)
\(614\) −3.09255 5.35645i −0.124805 0.216169i
\(615\) 2.81824 4.88133i 0.113642 0.196834i
\(616\) 10.6338 0.428449
\(617\) 9.70473 16.8091i 0.390698 0.676708i −0.601844 0.798614i \(-0.705567\pi\)
0.992542 + 0.121905i \(0.0389004\pi\)
\(618\) 0.910786 1.57753i 0.0366372 0.0634575i
\(619\) −0.941108 −0.0378263 −0.0189132 0.999821i \(-0.506021\pi\)
−0.0189132 + 0.999821i \(0.506021\pi\)
\(620\) −12.1285 + 21.0071i −0.487091 + 0.843667i
\(621\) −0.679754 1.17737i −0.0272776 0.0472462i
\(622\) 0.644962 + 1.11711i 0.0258606 + 0.0447919i
\(623\) 20.0393 0.802856
\(624\) −1.22436 0.0515075i −0.0490137 0.00206195i
\(625\) −30.5772 −1.22309
\(626\) 0.146972 + 0.254563i 0.00587417 + 0.0101744i
\(627\) 1.05776 + 1.83209i 0.0422428 + 0.0731667i
\(628\) −8.17975 + 14.1677i −0.326408 + 0.565355i
\(629\) −18.4157 −0.734284
\(630\) 14.7460 25.5408i 0.587495 1.01757i
\(631\) 10.7342 18.5921i 0.427321 0.740141i −0.569313 0.822121i \(-0.692791\pi\)
0.996634 + 0.0819794i \(0.0261242\pi\)
\(632\) −2.71234 −0.107891
\(633\) 1.85303 3.20954i 0.0736513 0.127568i
\(634\) 11.0261 + 19.0978i 0.437903 + 0.758470i
\(635\) −23.3332 40.4143i −0.925950 1.60379i
\(636\) −2.06958 −0.0820643
\(637\) 10.7525 16.9373i 0.426029 0.671082i
\(638\) −8.42909 −0.333711
\(639\) 8.65345 + 14.9882i 0.342325 + 0.592925i
\(640\) −4.32673 7.49411i −0.171029 0.296231i
\(641\) 12.2690 21.2505i 0.484595 0.839343i −0.515248 0.857041i \(-0.672300\pi\)
0.999843 + 0.0176977i \(0.00563363\pi\)
\(642\) −1.12621 −0.0444479
\(643\) 8.37467 14.5054i 0.330265 0.572035i −0.652299 0.757962i \(-0.726195\pi\)
0.982564 + 0.185927i \(0.0595287\pi\)
\(644\) −1.20473 + 2.08665i −0.0474730 + 0.0822257i
\(645\) −1.29433 −0.0509642
\(646\) 16.2592 28.1617i 0.639708 1.10801i
\(647\) −17.7993 30.8293i −0.699762 1.21202i −0.968549 0.248824i \(-0.919956\pi\)
0.268786 0.963200i \(-0.413377\pi\)
\(648\) 11.9605 + 20.7163i 0.469855 + 0.813812i
\(649\) −14.1088 −0.553821
\(650\) 6.41613 10.1067i 0.251661 0.396418i
\(651\) 10.1311 0.397070
\(652\) −5.39430 9.34320i −0.211257 0.365908i
\(653\) 3.51315 + 6.08496i 0.137480 + 0.238123i 0.926542 0.376191i \(-0.122766\pi\)
−0.789062 + 0.614314i \(0.789433\pi\)
\(654\) 0.366180 0.634242i 0.0143188 0.0248008i
\(655\) 9.55795 0.373460
\(656\) −2.87467 + 4.97907i −0.112237 + 0.194400i
\(657\) −23.1949 + 40.1748i −0.904920 + 1.56737i
\(658\) −21.6535 −0.844139
\(659\) −21.4454 + 37.1445i −0.835394 + 1.44694i 0.0583160 + 0.998298i \(0.481427\pi\)
−0.893710 + 0.448646i \(0.851906\pi\)
\(660\) 0.490185 + 0.849025i 0.0190804 + 0.0330482i
\(661\) −18.3267 31.7428i −0.712827 1.23465i −0.963792 0.266656i \(-0.914081\pi\)
0.250965 0.967996i \(-0.419252\pi\)
\(662\) −14.4487 −0.561565
\(663\) 2.96521 + 5.67408i 0.115159 + 0.220363i
\(664\) −14.7123 −0.570950
\(665\) −31.8201 55.1139i −1.23393 2.13723i
\(666\) 5.08387 + 8.80552i 0.196996 + 0.341207i
\(667\) 2.86485 4.96207i 0.110928 0.192132i
\(668\) −7.04995 −0.272771
\(669\) −3.30175 + 5.71880i −0.127653 + 0.221101i
\(670\) 17.4639 30.2483i 0.674689 1.16859i
\(671\) 4.01963 0.155176
\(672\) −3.01182 + 5.21663i −0.116184 + 0.201236i
\(673\) 1.36932 + 2.37174i 0.0527835 + 0.0914237i 0.891210 0.453591i \(-0.149857\pi\)
−0.838426 + 0.545015i \(0.816524\pi\)
\(674\) 9.25267 + 16.0261i 0.356400 + 0.617302i
\(675\) 6.64049 0.255593
\(676\) 5.53146 + 11.7645i 0.212748 + 0.452480i
\(677\) 17.3069 0.665158 0.332579 0.943075i \(-0.392081\pi\)
0.332579 + 0.943075i \(0.392081\pi\)
\(678\) 0.644962 + 1.11711i 0.0247696 + 0.0429023i
\(679\) 4.95407 + 8.58070i 0.190120 + 0.329297i
\(680\) 22.6044 39.1519i 0.866838 1.50141i
\(681\) 2.48798 0.0953397
\(682\) −4.20473 + 7.28281i −0.161007 + 0.278873i
\(683\) −23.3635 + 40.4668i −0.893980 + 1.54842i −0.0589192 + 0.998263i \(0.518765\pi\)
−0.835061 + 0.550157i \(0.814568\pi\)
\(684\) 17.9541 0.686491
\(685\) 19.8202 34.3297i 0.757293 1.31167i
\(686\) −2.54461 4.40739i −0.0971535 0.168275i
\(687\) 2.47502 + 4.28687i 0.0944280 + 0.163554i
\(688\) 1.32025 0.0503339
\(689\) −10.1686 19.4582i −0.387393 0.741297i
\(690\) 0.666410 0.0253698
\(691\) 5.97370 + 10.3467i 0.227250 + 0.393609i 0.956992 0.290114i \(-0.0936932\pi\)
−0.729742 + 0.683723i \(0.760360\pi\)
\(692\) −0.922611 1.59801i −0.0350724 0.0607472i
\(693\) −5.11218 + 8.85456i −0.194196 + 0.336357i
\(694\) −15.5446 −0.590065
\(695\) 3.47502 6.01892i 0.131815 0.228311i
\(696\) 4.29728 7.44311i 0.162888 0.282130i
\(697\) 30.0366 1.13772
\(698\) −15.0000 + 25.9808i −0.567758 + 0.983386i
\(699\) 1.09589 + 1.89813i 0.0414502 + 0.0717939i
\(700\) −5.88448 10.1922i −0.222413 0.385230i
\(701\) −19.2833 −0.728318 −0.364159 0.931337i \(-0.618644\pi\)
−0.364159 + 0.931337i \(0.618644\pi\)
\(702\) 3.86485 6.08793i 0.145869 0.229774i
\(703\) 21.9407 0.827510
\(704\) −3.50000 6.06218i −0.131911 0.228477i
\(705\) −2.99446 5.18656i −0.112778 0.195337i
\(706\) 2.16012 3.74144i 0.0812973 0.140811i
\(707\) 34.9670 1.31507
\(708\) 2.39764 4.15283i 0.0901086 0.156073i
\(709\) 20.8528 36.1182i 0.783145 1.35645i −0.146957 0.989143i \(-0.546948\pi\)
0.930101 0.367303i \(-0.119719\pi\)
\(710\) −17.3069 −0.649516
\(711\) 1.30395 2.25851i 0.0489020 0.0847008i
\(712\) −8.48018 14.6881i −0.317808 0.550460i
\(713\) −2.85818 4.95051i −0.107040 0.185398i
\(714\) −6.29394 −0.235545
\(715\) −5.57405 + 8.78027i −0.208458 + 0.328363i
\(716\) −5.42909 −0.202895
\(717\) −0.0459333 0.0795589i −0.00171541 0.00297118i
\(718\) 0.115516 + 0.200080i 0.00431103 + 0.00746692i
\(719\) 12.3136 21.3277i 0.459219 0.795390i −0.539701 0.841857i \(-0.681463\pi\)
0.998920 + 0.0464664i \(0.0147960\pi\)
\(720\) −8.32025 −0.310077
\(721\) 9.49867 16.4522i 0.353749 0.612711i
\(722\) −9.87133 + 17.0976i −0.367373 + 0.636309i
\(723\) −10.3769 −0.385920
\(724\) −2.23751 + 3.87548i −0.0831565 + 0.144031i
\(725\) 13.9933 + 24.2372i 0.519699 + 0.900145i
\(726\) 0.169938 + 0.294342i 0.00630701 + 0.0109241i
\(727\) 5.82157 0.215910 0.107955 0.994156i \(-0.465570\pi\)
0.107955 + 0.994156i \(0.465570\pi\)
\(728\) −38.3069 1.61153i −1.41975 0.0597273i
\(729\) −20.9607 −0.776324
\(730\) −23.1949 40.1748i −0.858482 1.48693i
\(731\) −3.44872 5.97336i −0.127556 0.220933i
\(732\) −0.683090 + 1.18315i −0.0252477 + 0.0437303i
\(733\) 32.1588 1.18781 0.593906 0.804534i \(-0.297585\pi\)
0.593906 + 0.804534i \(0.297585\pi\)
\(734\) −9.90411 + 17.1544i −0.365568 + 0.633182i
\(735\) −2.72750 + 4.72418i −0.100605 + 0.174254i
\(736\) 3.39877 0.125280
\(737\) −6.05442 + 10.4866i −0.223018 + 0.386278i
\(738\) −8.29193 14.3621i −0.305230 0.528674i
\(739\) 0.185099 + 0.320601i 0.00680899 + 0.0117935i 0.869410 0.494092i \(-0.164499\pi\)
−0.862601 + 0.505885i \(0.831166\pi\)
\(740\) 10.1677 0.373773
\(741\) −3.53278 6.76016i −0.129780 0.248341i
\(742\) 21.5839 0.792369
\(743\) −16.0466 27.7936i −0.588693 1.01965i −0.994404 0.105645i \(-0.966309\pi\)
0.405711 0.914002i \(-0.367024\pi\)
\(744\) −4.28727 7.42577i −0.157179 0.272242i
\(745\) −3.66994 + 6.35652i −0.134456 + 0.232885i
\(746\) −14.9148 −0.546070
\(747\) 7.07292 12.2507i 0.258785 0.448228i
\(748\) −2.61218 + 4.52443i −0.0955108 + 0.165430i
\(749\) −11.7453 −0.429165
\(750\) 0.823390 1.42615i 0.0300659 0.0520757i
\(751\) −5.38983 9.33546i −0.196678 0.340656i 0.750772 0.660562i \(-0.229682\pi\)
−0.947449 + 0.319906i \(0.896349\pi\)
\(752\) 3.05442 + 5.29041i 0.111383 + 0.192922i
\(753\) −3.56158 −0.129791
\(754\) 30.3647 + 1.27741i 1.10582 + 0.0465205i
\(755\) −24.3702 −0.886922
\(756\) −3.54461 6.13944i −0.128916 0.223289i
\(757\) 25.8397 + 44.7556i 0.939159 + 1.62667i 0.767044 + 0.641595i \(0.221727\pi\)
0.172116 + 0.985077i \(0.444940\pi\)
\(758\) −3.32025 + 5.75084i −0.120597 + 0.208880i
\(759\) −0.231033 −0.00838595
\(760\) −26.9311 + 46.6460i −0.976894 + 1.69203i
\(761\) 19.1392 33.1500i 0.693794 1.20169i −0.276791 0.960930i \(-0.589271\pi\)
0.970585 0.240757i \(-0.0773956\pi\)
\(762\) 5.49867 0.199196
\(763\) 3.81892 6.61456i 0.138254 0.239463i
\(764\) 4.94558 + 8.56599i 0.178925 + 0.309907i
\(765\) 21.7340 + 37.6444i 0.785794 + 1.36103i
\(766\) −5.14182 −0.185781
\(767\) 50.8252 + 2.13816i 1.83519 + 0.0772045i
\(768\) 5.77791 0.208492
\(769\) −23.2873 40.3347i −0.839760 1.45451i −0.890095 0.455775i \(-0.849362\pi\)
0.0503343 0.998732i \(-0.483971\pi\)
\(770\) −5.11218 8.85456i −0.184230 0.319096i
\(771\) 0.978167 1.69424i 0.0352278 0.0610164i
\(772\) −5.10884 −0.183871
\(773\) −11.3910 + 19.7297i −0.409704 + 0.709629i −0.994856 0.101295i \(-0.967702\pi\)
0.585152 + 0.810924i \(0.301035\pi\)
\(774\) −1.90411 + 3.29802i −0.0684420 + 0.118545i