Properties

Label 143.2.e.a.100.1
Level $143$
Weight $2$
Character 143.100
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 100.1
Root \(0.500000 + 0.385124i\) of defining polynomial
Character \(\chi\) \(=\) 143.100
Dual form 143.2.e.a.133.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.30084 + 2.25312i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.76873 q^{5} +(-1.30084 - 2.25312i) q^{6} +(-0.0835276 - 0.144674i) q^{7} -3.00000 q^{8} +(-1.88437 - 3.26382i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.30084 + 2.25312i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.76873 q^{5} +(-1.30084 - 2.25312i) q^{6} +(-0.0835276 - 0.144674i) q^{7} -3.00000 q^{8} +(-1.88437 - 3.26382i) q^{9} +(-1.88437 + 3.26382i) q^{10} +(-0.500000 + 0.866025i) q^{11} -2.60168 q^{12} +(0.199160 - 3.60005i) q^{13} +0.167055 q^{14} +(-4.90252 + 8.49141i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.18521 - 3.78489i) q^{17} +3.76873 q^{18} +(1.68521 + 2.91886i) q^{19} +(1.88437 + 3.26382i) q^{20} +0.434624 q^{21} +(-0.500000 - 0.866025i) q^{22} +(2.60168 - 4.50624i) q^{23} +(3.90252 - 6.75936i) q^{24} +9.20336 q^{25} +(3.01815 + 1.97250i) q^{26} +2.00000 q^{27} +(0.0835276 - 0.144674i) q^{28} +(-0.967895 + 1.67644i) q^{29} +(-4.90252 - 8.49141i) q^{30} +6.86925 q^{31} +(-2.50000 - 4.33013i) q^{32} +(-1.30084 - 2.25312i) q^{33} +4.37041 q^{34} +(-0.314793 - 0.545238i) q^{35} +(1.88437 - 3.26382i) q^{36} +(-4.31899 + 7.48071i) q^{37} -3.37041 q^{38} +(7.85226 + 5.13182i) q^{39} -11.3062 q^{40} +(0.633784 - 1.09775i) q^{41} +(-0.217312 + 0.376395i) q^{42} +(3.60168 + 6.23829i) q^{43} -1.00000 q^{44} +(-7.10168 - 12.3005i) q^{45} +(2.60168 + 4.50624i) q^{46} -10.1391 q^{47} +(1.30084 + 2.25312i) q^{48} +(3.48605 - 6.03801i) q^{49} +(-4.60168 + 7.97034i) q^{50} +11.3704 q^{51} +(3.21731 - 1.62755i) q^{52} +1.33411 q^{53} +(-1.00000 + 1.73205i) q^{54} +(-1.88437 + 3.26382i) q^{55} +(0.250583 + 0.434022i) q^{56} -8.76873 q^{57} +(-0.967895 - 1.67644i) q^{58} +(-1.06957 - 1.85256i) q^{59} -9.80504 q^{60} +(2.40252 + 4.16128i) q^{61} +(-3.43462 + 5.94894i) q^{62} +(-0.314793 + 0.545238i) q^{63} +7.00000 q^{64} +(0.750583 - 13.5676i) q^{65} +2.60168 q^{66} +(2.06957 - 3.58461i) q^{67} +(2.18521 - 3.78489i) q^{68} +(6.76873 + 11.7238i) q^{69} +0.629587 q^{70} +(-3.00000 - 5.19615i) q^{71} +(5.65310 + 9.79146i) q^{72} +14.2420 q^{73} +(-4.31899 - 7.48071i) q^{74} +(-11.9721 + 20.7363i) q^{75} +(-1.68521 + 2.91886i) q^{76} +0.167055 q^{77} +(-8.37041 + 4.23435i) q^{78} -14.5738 q^{79} +(1.88437 - 3.26382i) q^{80} +(3.05142 - 5.28522i) q^{81} +(0.633784 + 1.09775i) q^{82} -10.5738 q^{83} +(0.217312 + 0.376395i) q^{84} +(-8.23546 - 14.2642i) q^{85} -7.20336 q^{86} +(-2.51815 - 4.36157i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-7.15310 + 12.3895i) q^{89} +14.2034 q^{90} +(-0.537469 + 0.271890i) q^{91} +5.20336 q^{92} +(-8.93579 + 15.4772i) q^{93} +(5.06957 - 8.78076i) q^{94} +(6.35110 + 11.0004i) q^{95} +13.0084 q^{96} +(-1.78269 - 3.08771i) q^{97} +(3.48605 + 6.03801i) q^{98} +3.76873 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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i −0.986869 0.161521i \(-0.948360\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) −1.30084 + 2.25312i −0.751040 + 1.30084i 0.196279 + 0.980548i \(0.437114\pi\)
−0.947319 + 0.320291i \(0.896219\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 3.76873 1.68543 0.842715 0.538361i \(-0.180956\pi\)
0.842715 + 0.538361i \(0.180956\pi\)
\(6\) −1.30084 2.25312i −0.531066 0.919832i
\(7\) −0.0835276 0.144674i −0.0315705 0.0546816i 0.849808 0.527092i \(-0.176718\pi\)
−0.881379 + 0.472410i \(0.843384\pi\)
\(8\) −3.00000 −1.06066
\(9\) −1.88437 3.26382i −0.628122 1.08794i
\(10\) −1.88437 + 3.26382i −0.595889 + 1.03211i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) −2.60168 −0.751040
\(13\) 0.199160 3.60005i 0.0552372 0.998473i
\(14\) 0.167055 0.0446474
\(15\) −4.90252 + 8.49141i −1.26582 + 2.19247i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −2.18521 3.78489i −0.529990 0.917970i −0.999388 0.0349834i \(-0.988862\pi\)
0.469397 0.882987i \(-0.344471\pi\)
\(18\) 3.76873 0.888299
\(19\) 1.68521 + 2.91886i 0.386613 + 0.669633i 0.991992 0.126304i \(-0.0403116\pi\)
−0.605379 + 0.795938i \(0.706978\pi\)
\(20\) 1.88437 + 3.26382i 0.421357 + 0.729812i
\(21\) 0.434624 0.0948427
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) 2.60168 4.50624i 0.542488 0.939616i −0.456273 0.889840i \(-0.650816\pi\)
0.998760 0.0497761i \(-0.0158508\pi\)
\(24\) 3.90252 6.75936i 0.796598 1.37975i
\(25\) 9.20336 1.84067
\(26\) 3.01815 + 1.97250i 0.591908 + 0.386839i
\(27\) 2.00000 0.384900
\(28\) 0.0835276 0.144674i 0.0157852 0.0273408i
\(29\) −0.967895 + 1.67644i −0.179734 + 0.311308i −0.941789 0.336204i \(-0.890857\pi\)
0.762056 + 0.647511i \(0.224190\pi\)
\(30\) −4.90252 8.49141i −0.895073 1.55031i
\(31\) 6.86925 1.23375 0.616877 0.787060i \(-0.288398\pi\)
0.616877 + 0.787060i \(0.288398\pi\)
\(32\) −2.50000 4.33013i −0.441942 0.765466i
\(33\) −1.30084 2.25312i −0.226447 0.392218i
\(34\) 4.37041 0.749520
\(35\) −0.314793 0.545238i −0.0532098 0.0921620i
\(36\) 1.88437 3.26382i 0.314061 0.543970i
\(37\) −4.31899 + 7.48071i −0.710038 + 1.22982i 0.254805 + 0.966993i \(0.417989\pi\)
−0.964842 + 0.262829i \(0.915345\pi\)
\(38\) −3.37041 −0.546753
\(39\) 7.85226 + 5.13182i 1.25737 + 0.821748i
\(40\) −11.3062 −1.78767
\(41\) 0.633784 1.09775i 0.0989805 0.171439i −0.812282 0.583264i \(-0.801775\pi\)
0.911263 + 0.411825i \(0.135109\pi\)
\(42\) −0.217312 + 0.376395i −0.0335320 + 0.0580791i
\(43\) 3.60168 + 6.23829i 0.549251 + 0.951330i 0.998326 + 0.0578365i \(0.0184202\pi\)
−0.449075 + 0.893494i \(0.648246\pi\)
\(44\) −1.00000 −0.150756
\(45\) −7.10168 12.3005i −1.05866 1.83365i
\(46\) 2.60168 + 4.50624i 0.383597 + 0.664409i
\(47\) −10.1391 −1.47895 −0.739473 0.673186i \(-0.764925\pi\)
−0.739473 + 0.673186i \(0.764925\pi\)
\(48\) 1.30084 + 2.25312i 0.187760 + 0.325210i
\(49\) 3.48605 6.03801i 0.498007 0.862573i
\(50\) −4.60168 + 7.97034i −0.650776 + 1.12718i
\(51\) 11.3704 1.59218
\(52\) 3.21731 1.62755i 0.446161 0.225700i
\(53\) 1.33411 0.183254 0.0916271 0.995793i \(-0.470793\pi\)
0.0916271 + 0.995793i \(0.470793\pi\)
\(54\) −1.00000 + 1.73205i −0.136083 + 0.235702i
\(55\) −1.88437 + 3.26382i −0.254088 + 0.440093i
\(56\) 0.250583 + 0.434022i 0.0334855 + 0.0579986i
\(57\) −8.76873 −1.16145
\(58\) −0.967895 1.67644i −0.127091 0.220128i
\(59\) −1.06957 1.85256i −0.139247 0.241182i 0.787965 0.615720i \(-0.211135\pi\)
−0.927212 + 0.374538i \(0.877801\pi\)
\(60\) −9.80504 −1.26582
\(61\) 2.40252 + 4.16128i 0.307611 + 0.532798i 0.977839 0.209357i \(-0.0671371\pi\)
−0.670228 + 0.742155i \(0.733804\pi\)
\(62\) −3.43462 + 5.94894i −0.436198 + 0.755517i
\(63\) −0.314793 + 0.545238i −0.0396602 + 0.0686935i
\(64\) 7.00000 0.875000
\(65\) 0.750583 13.5676i 0.0930983 1.68286i
\(66\) 2.60168 0.320245
\(67\) 2.06957 3.58461i 0.252839 0.437929i −0.711468 0.702719i \(-0.751969\pi\)
0.964306 + 0.264789i \(0.0853025\pi\)
\(68\) 2.18521 3.78489i 0.264995 0.458985i
\(69\) 6.76873 + 11.7238i 0.814860 + 1.41138i
\(70\) 0.629587 0.0752500
\(71\) −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) 5.65310 + 9.79146i 0.666224 + 1.15393i
\(73\) 14.2420 1.66690 0.833450 0.552596i \(-0.186363\pi\)
0.833450 + 0.552596i \(0.186363\pi\)
\(74\) −4.31899 7.48071i −0.502073 0.869615i
\(75\) −11.9721 + 20.7363i −1.38242 + 2.39442i
\(76\) −1.68521 + 2.91886i −0.193306 + 0.334817i
\(77\) 0.167055 0.0190377
\(78\) −8.37041 + 4.23435i −0.947763 + 0.479446i
\(79\) −14.5738 −1.63968 −0.819839 0.572595i \(-0.805937\pi\)
−0.819839 + 0.572595i \(0.805937\pi\)
\(80\) 1.88437 3.26382i 0.210679 0.364906i
\(81\) 3.05142 5.28522i 0.339047 0.587247i
\(82\) 0.633784 + 1.09775i 0.0699898 + 0.121226i
\(83\) −10.5738 −1.16062 −0.580311 0.814395i \(-0.697069\pi\)
−0.580311 + 0.814395i \(0.697069\pi\)
\(84\) 0.217312 + 0.376395i 0.0237107 + 0.0410681i
\(85\) −8.23546 14.2642i −0.893261 1.54717i
\(86\) −7.20336 −0.776758
\(87\) −2.51815 4.36157i −0.269974 0.467609i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −7.15310 + 12.3895i −0.758227 + 1.31329i 0.185527 + 0.982639i \(0.440601\pi\)
−0.943754 + 0.330649i \(0.892732\pi\)
\(90\) 14.2034 1.49717
\(91\) −0.537469 + 0.271890i −0.0563420 + 0.0285018i
\(92\) 5.20336 0.542488
\(93\) −8.93579 + 15.4772i −0.926598 + 1.60492i
\(94\) 5.06957 8.78076i 0.522887 0.905666i
\(95\) 6.35110 + 11.0004i 0.651609 + 1.12862i
\(96\) 13.0084 1.32766
\(97\) −1.78269 3.08771i −0.181005 0.313509i 0.761218 0.648496i \(-0.224602\pi\)
−0.942223 + 0.334987i \(0.891268\pi\)
\(98\) 3.48605 + 6.03801i 0.352144 + 0.609931i
\(99\) 3.76873 0.378772
\(100\) 4.60168 + 7.97034i 0.460168 + 0.797034i
\(101\) 6.01815 10.4237i 0.598828 1.03720i −0.394166 0.919039i \(-0.628966\pi\)
0.992994 0.118162i \(-0.0377002\pi\)
\(102\) −5.68521 + 9.84707i −0.562919 + 0.975005i
\(103\) −6.40672 −0.631273 −0.315636 0.948880i \(-0.602218\pi\)
−0.315636 + 0.948880i \(0.602218\pi\)
\(104\) −0.597481 + 10.8001i −0.0585879 + 1.05904i
\(105\) 1.63798 0.159851
\(106\) −0.667055 + 1.15537i −0.0647901 + 0.112220i
\(107\) 6.85226 11.8685i 0.662433 1.14737i −0.317541 0.948244i \(-0.602857\pi\)
0.979974 0.199123i \(-0.0638095\pi\)
\(108\) 1.00000 + 1.73205i 0.0962250 + 0.166667i
\(109\) −8.84134 −0.846847 −0.423423 0.905932i \(-0.639172\pi\)
−0.423423 + 0.905932i \(0.639172\pi\)
\(110\) −1.88437 3.26382i −0.179667 0.311193i
\(111\) −11.2366 19.4624i −1.06653 1.84729i
\(112\) −0.167055 −0.0157852
\(113\) −2.28269 3.95373i −0.214737 0.371936i 0.738454 0.674304i \(-0.235556\pi\)
−0.953191 + 0.302368i \(0.902223\pi\)
\(114\) 4.38437 7.59395i 0.410634 0.711238i
\(115\) 9.80504 16.9828i 0.914324 1.58366i
\(116\) −1.93579 −0.179734
\(117\) −12.1252 + 6.13379i −1.12097 + 0.567069i
\(118\) 2.13915 0.196925
\(119\) −0.365050 + 0.632285i −0.0334641 + 0.0579615i
\(120\) 14.7076 25.4742i 1.34261 2.32547i
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −4.80504 −0.435028
\(123\) 1.64890 + 2.85598i 0.148677 + 0.257515i
\(124\) 3.43462 + 5.94894i 0.308438 + 0.534231i
\(125\) 15.8413 1.41689
\(126\) −0.314793 0.545238i −0.0280440 0.0485737i
\(127\) 0.665890 1.15335i 0.0590882 0.102344i −0.834968 0.550298i \(-0.814514\pi\)
0.894056 + 0.447955i \(0.147847\pi\)
\(128\) 1.50000 2.59808i 0.132583 0.229640i
\(129\) −18.7408 −1.65004
\(130\) 11.3746 + 7.43383i 0.997619 + 0.651990i
\(131\) 13.7045 1.19737 0.598685 0.800985i \(-0.295690\pi\)
0.598685 + 0.800985i \(0.295690\pi\)
\(132\) 1.30084 2.25312i 0.113224 0.196109i
\(133\) 0.281523 0.487611i 0.0244111 0.0422813i
\(134\) 2.06957 + 3.58461i 0.178784 + 0.309663i
\(135\) 7.53747 0.648722
\(136\) 6.55562 + 11.3547i 0.562140 + 0.973655i
\(137\) 6.82016 + 11.8129i 0.582685 + 1.00924i 0.995160 + 0.0982713i \(0.0313313\pi\)
−0.412474 + 0.910969i \(0.635335\pi\)
\(138\) −13.5375 −1.15239
\(139\) −0.434624 0.752791i −0.0368643 0.0638509i 0.847005 0.531586i \(-0.178404\pi\)
−0.883869 + 0.467735i \(0.845070\pi\)
\(140\) 0.314793 0.545238i 0.0266049 0.0460810i
\(141\) 13.1894 22.8447i 1.11075 1.92387i
\(142\) 6.00000 0.503509
\(143\) 3.01815 + 1.97250i 0.252391 + 0.164949i
\(144\) −3.76873 −0.314061
\(145\) −3.64774 + 6.31807i −0.302928 + 0.524687i
\(146\) −7.12100 + 12.3339i −0.589338 + 1.02076i
\(147\) 9.06957 + 15.7090i 0.748046 + 1.29565i
\(148\) −8.63798 −0.710038
\(149\) −0.583528 1.01070i −0.0478044 0.0827997i 0.841133 0.540828i \(-0.181889\pi\)
−0.888938 + 0.458028i \(0.848556\pi\)
\(150\) −11.9721 20.7363i −0.977517 1.69311i
\(151\) −10.7408 −0.874076 −0.437038 0.899443i \(-0.643972\pi\)
−0.437038 + 0.899443i \(0.643972\pi\)
\(152\) −5.05562 8.75659i −0.410065 0.710253i
\(153\) −8.23546 + 14.2642i −0.665798 + 1.15320i
\(154\) −0.0835276 + 0.144674i −0.00673084 + 0.0116582i
\(155\) 25.8884 2.07940
\(156\) −0.518152 + 9.36617i −0.0414853 + 0.749893i
\(157\) −4.59328 −0.366584 −0.183292 0.983059i \(-0.558675\pi\)
−0.183292 + 0.983059i \(0.558675\pi\)
\(158\) 7.28689 12.6213i 0.579714 1.00409i
\(159\) −1.73546 + 3.00591i −0.137631 + 0.238384i
\(160\) −9.42184 16.3191i −0.744862 1.29014i
\(161\) −0.869248 −0.0685063
\(162\) 3.05142 + 5.28522i 0.239742 + 0.415246i
\(163\) −5.67125 9.82290i −0.444207 0.769389i 0.553790 0.832657i \(-0.313181\pi\)
−0.997997 + 0.0632677i \(0.979848\pi\)
\(164\) 1.26757 0.0989805
\(165\) −4.90252 8.49141i −0.381661 0.661055i
\(166\) 5.28689 9.15715i 0.410342 0.710733i
\(167\) −8.63798 + 14.9614i −0.668427 + 1.15775i 0.309917 + 0.950764i \(0.399699\pi\)
−0.978344 + 0.206986i \(0.933635\pi\)
\(168\) −1.30387 −0.100596
\(169\) −12.9207 1.43397i −0.993898 0.110306i
\(170\) 16.4709 1.26326
\(171\) 6.35110 11.0004i 0.485680 0.841223i
\(172\) −3.60168 + 6.23829i −0.274625 + 0.475665i
\(173\) 6.42067 + 11.1209i 0.488155 + 0.845508i 0.999907 0.0136244i \(-0.00433691\pi\)
−0.511753 + 0.859133i \(0.671004\pi\)
\(174\) 5.03630 0.381801
\(175\) −0.768734 1.33149i −0.0581109 0.100651i
\(176\) 0.500000 + 0.866025i 0.0376889 + 0.0652791i
\(177\) 5.56538 0.418319
\(178\) −7.15310 12.3895i −0.536148 0.928635i
\(179\) 2.46789 4.27452i 0.184459 0.319493i −0.758935 0.651166i \(-0.774280\pi\)
0.943394 + 0.331674i \(0.107613\pi\)
\(180\) 7.10168 12.3005i 0.529328 0.916823i
\(181\) 0.637982 0.0474208 0.0237104 0.999719i \(-0.492452\pi\)
0.0237104 + 0.999719i \(0.492452\pi\)
\(182\) 0.0332708 0.601406i 0.00246619 0.0445792i
\(183\) −12.5012 −0.924113
\(184\) −7.80504 + 13.5187i −0.575395 + 0.996613i
\(185\) −16.2771 + 28.1928i −1.19672 + 2.07278i
\(186\) −8.93579 15.4772i −0.655204 1.13485i
\(187\) 4.37041 0.319596
\(188\) −5.06957 8.78076i −0.369737 0.640403i
\(189\) −0.167055 0.289348i −0.0121515 0.0210470i
\(190\) −12.7022 −0.921514
\(191\) −13.0696 22.6372i −0.945681 1.63797i −0.754382 0.656436i \(-0.772063\pi\)
−0.191300 0.981532i \(-0.561270\pi\)
\(192\) −9.10588 + 15.7718i −0.657160 + 1.13823i
\(193\) 5.56957 9.64678i 0.400907 0.694391i −0.592929 0.805255i \(-0.702028\pi\)
0.993836 + 0.110864i \(0.0353618\pi\)
\(194\) 3.56538 0.255979
\(195\) 29.5931 + 19.3404i 2.11921 + 1.38500i
\(196\) 6.97209 0.498007
\(197\) −7.76873 + 13.4558i −0.553499 + 0.958689i 0.444519 + 0.895769i \(0.353375\pi\)
−0.998019 + 0.0629198i \(0.979959\pi\)
\(198\) −1.88437 + 3.26382i −0.133916 + 0.231950i
\(199\) 5.83831 + 10.1122i 0.413867 + 0.716838i 0.995309 0.0967497i \(-0.0308446\pi\)
−0.581442 + 0.813588i \(0.697511\pi\)
\(200\) −27.6101 −1.95233
\(201\) 5.38437 + 9.32600i 0.379784 + 0.657805i
\(202\) 6.01815 + 10.4237i 0.423436 + 0.733412i
\(203\) 0.323384 0.0226971
\(204\) 5.68521 + 9.84707i 0.398044 + 0.689433i
\(205\) 2.38856 4.13712i 0.166825 0.288949i
\(206\) 3.20336 5.54838i 0.223189 0.386574i
\(207\) −19.6101 −1.36299
\(208\) −3.01815 1.97250i −0.209271 0.136768i
\(209\) −3.37041 −0.233136
\(210\) −0.818991 + 1.41853i −0.0565158 + 0.0978882i
\(211\) 2.28689 3.96100i 0.157436 0.272687i −0.776508 0.630108i \(-0.783011\pi\)
0.933943 + 0.357421i \(0.116344\pi\)
\(212\) 0.667055 + 1.15537i 0.0458135 + 0.0793514i
\(213\) 15.6101 1.06958
\(214\) 6.85226 + 11.8685i 0.468411 + 0.811312i
\(215\) 13.5738 + 23.5105i 0.925724 + 1.60340i
\(216\) −6.00000 −0.408248
\(217\) −0.573772 0.993802i −0.0389502 0.0674637i
\(218\) 4.42067 7.65683i 0.299406 0.518586i
\(219\) −18.5265 + 32.0889i −1.25191 + 2.16837i
\(220\) −3.76873 −0.254088
\(221\) −14.0610 + 7.11305i −0.945844 + 0.478475i
\(222\) 22.4733 1.50831
\(223\) 4.53211 7.84984i 0.303492 0.525664i −0.673432 0.739249i \(-0.735181\pi\)
0.976924 + 0.213585i \(0.0685140\pi\)
\(224\) −0.417638 + 0.723370i −0.0279046 + 0.0483322i
\(225\) −17.3425 30.0381i −1.15617 2.00254i
\(226\) 4.56538 0.303684
\(227\) 6.60168 + 11.4344i 0.438169 + 0.758931i 0.997548 0.0699810i \(-0.0222939\pi\)
−0.559379 + 0.828912i \(0.688961\pi\)
\(228\) −4.38437 7.59395i −0.290362 0.502921i
\(229\) 2.02791 0.134008 0.0670039 0.997753i \(-0.478656\pi\)
0.0670039 + 0.997753i \(0.478656\pi\)
\(230\) 9.80504 + 16.9828i 0.646525 + 1.11981i
\(231\) −0.217312 + 0.376395i −0.0142981 + 0.0247650i
\(232\) 2.90368 5.02933i 0.190636 0.330192i
\(233\) −12.7408 −0.834679 −0.417340 0.908751i \(-0.637037\pi\)
−0.417340 + 0.908751i \(0.637037\pi\)
\(234\) 0.750583 13.5676i 0.0490671 0.886943i
\(235\) −38.2118 −2.49266
\(236\) 1.06957 1.85256i 0.0696233 0.120591i
\(237\) 18.9581 32.8365i 1.23146 2.13296i
\(238\) −0.365050 0.632285i −0.0236627 0.0409850i
\(239\) 4.07261 0.263435 0.131717 0.991287i \(-0.457951\pi\)
0.131717 + 0.991287i \(0.457951\pi\)
\(240\) 4.90252 + 8.49141i 0.316456 + 0.548118i
\(241\) 9.49141 + 16.4396i 0.611395 + 1.05897i 0.991005 + 0.133821i \(0.0427248\pi\)
−0.379610 + 0.925147i \(0.623942\pi\)
\(242\) 1.00000 0.0642824
\(243\) 10.9388 + 18.9466i 0.701726 + 1.21542i
\(244\) −2.40252 + 4.16128i −0.153805 + 0.266399i
\(245\) 13.1380 22.7557i 0.839355 1.45381i
\(246\) −3.29781 −0.210261
\(247\) 10.8437 5.48550i 0.689966 0.349034i
\(248\) −20.6077 −1.30859
\(249\) 13.7548 23.8240i 0.871674 1.50978i
\(250\) −7.92067 + 13.7190i −0.500947 + 0.867666i
\(251\) −5.17009 8.95485i −0.326333 0.565225i 0.655448 0.755240i \(-0.272480\pi\)
−0.981781 + 0.190015i \(0.939146\pi\)
\(252\) −0.629587 −0.0396602
\(253\) 2.60168 + 4.50624i 0.163566 + 0.283305i
\(254\) 0.665890 + 1.15335i 0.0417816 + 0.0723679i
\(255\) 42.8521 2.68350
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) −12.0877 + 20.9366i −0.754012 + 1.30599i 0.191853 + 0.981424i \(0.438550\pi\)
−0.945864 + 0.324563i \(0.894783\pi\)
\(258\) 9.37041 16.2300i 0.583376 1.01044i
\(259\) 1.44302 0.0896649
\(260\) 12.1252 6.13379i 0.751973 0.380401i
\(261\) 7.29548 0.451579
\(262\) −6.85226 + 11.8685i −0.423334 + 0.733236i
\(263\) 5.37041 9.30183i 0.331154 0.573575i −0.651585 0.758576i \(-0.725895\pi\)
0.982738 + 0.185001i \(0.0592287\pi\)
\(264\) 3.90252 + 6.75936i 0.240183 + 0.416010i
\(265\) 5.02791 0.308862
\(266\) 0.281523 + 0.487611i 0.0172613 + 0.0298974i
\(267\) −18.6101 32.2336i −1.13892 1.97266i
\(268\) 4.13915 0.252839
\(269\) −8.83294 15.2991i −0.538554 0.932803i −0.998982 0.0451061i \(-0.985637\pi\)
0.460428 0.887697i \(-0.347696\pi\)
\(270\) −3.76873 + 6.52764i −0.229358 + 0.397259i
\(271\) −4.37041 + 7.56978i −0.265484 + 0.459831i −0.967690 0.252142i \(-0.918865\pi\)
0.702207 + 0.711973i \(0.252198\pi\)
\(272\) −4.37041 −0.264995
\(273\) 0.0865599 1.56467i 0.00523884 0.0946979i
\(274\) −13.6403 −0.824041
\(275\) −4.60168 + 7.97034i −0.277492 + 0.480630i
\(276\) −6.76873 + 11.7238i −0.407430 + 0.705689i
\(277\) −14.6059 25.2981i −0.877582 1.52002i −0.853986 0.520295i \(-0.825822\pi\)
−0.0235956 0.999722i \(-0.507511\pi\)
\(278\) 0.869248 0.0521340
\(279\) −12.9442 22.4200i −0.774948 1.34225i
\(280\) 0.944380 + 1.63571i 0.0564375 + 0.0977526i
\(281\) −10.8050 −0.644574 −0.322287 0.946642i \(-0.604452\pi\)
−0.322287 + 0.946642i \(0.604452\pi\)
\(282\) 13.1894 + 22.8447i 0.785418 + 1.36038i
\(283\) −5.11983 + 8.86781i −0.304342 + 0.527136i −0.977115 0.212713i \(-0.931770\pi\)
0.672772 + 0.739850i \(0.265103\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) −33.0470 −1.95754
\(286\) −3.21731 + 1.62755i −0.190244 + 0.0962388i
\(287\) −0.211754 −0.0124994
\(288\) −9.42184 + 16.3191i −0.555187 + 0.961612i
\(289\) −1.05026 + 1.81910i −0.0617798 + 0.107006i
\(290\) −3.64774 6.31807i −0.214203 0.371010i
\(291\) 9.27596 0.543767
\(292\) 7.12100 + 12.3339i 0.416725 + 0.721788i
\(293\) −1.98185 3.43266i −0.115781 0.200538i 0.802311 0.596907i \(-0.203604\pi\)
−0.918092 + 0.396368i \(0.870270\pi\)
\(294\) −18.1391 −1.05790
\(295\) −4.03094 6.98179i −0.234690 0.406496i
\(296\) 12.9570 22.4421i 0.753109 1.30442i
\(297\) −1.00000 + 1.73205i −0.0580259 + 0.100504i
\(298\) 1.16706 0.0676057
\(299\) −15.7045 10.2636i −0.908216 0.593561i
\(300\) −23.9442 −1.38242
\(301\) 0.601679 1.04214i 0.0346802 0.0600679i
\(302\) 5.37041 9.30183i 0.309033 0.535260i
\(303\) 15.6573 + 27.1192i 0.899488 + 1.55796i
\(304\) 3.37041 0.193306
\(305\) 9.05445 + 15.6828i 0.518457 + 0.897993i
\(306\) −8.23546 14.2642i −0.470790 0.815432i
\(307\) 14.2397 0.812700 0.406350 0.913717i \(-0.366801\pi\)
0.406350 + 0.913717i \(0.366801\pi\)
\(308\) 0.0835276 + 0.144674i 0.00475943 + 0.00824357i
\(309\) 8.33411 14.4351i 0.474111 0.821184i
\(310\) −12.9442 + 22.4200i −0.735180 + 1.27337i
\(311\) 11.8776 0.673519 0.336760 0.941591i \(-0.390669\pi\)
0.336760 + 0.941591i \(0.390669\pi\)
\(312\) −23.5568 15.3954i −1.33364 0.871596i
\(313\) 7.89949 0.446505 0.223253 0.974761i \(-0.428332\pi\)
0.223253 + 0.974761i \(0.428332\pi\)
\(314\) 2.29664 3.97790i 0.129607 0.224486i
\(315\) −1.18637 + 2.05486i −0.0668445 + 0.115778i
\(316\) −7.28689 12.6213i −0.409919 0.710001i
\(317\) 27.3230 1.53461 0.767306 0.641281i \(-0.221597\pi\)
0.767306 + 0.641281i \(0.221597\pi\)
\(318\) −1.73546 3.00591i −0.0973200 0.168563i
\(319\) −0.967895 1.67644i −0.0541917 0.0938628i
\(320\) 26.3811 1.47475
\(321\) 17.8274 + 30.8779i 0.995028 + 1.72344i
\(322\) 0.434624 0.752791i 0.0242206 0.0419514i
\(323\) 7.36505 12.7566i 0.409802 0.709798i
\(324\) 6.10284 0.339047
\(325\) 1.83294 33.1325i 0.101673 1.83786i
\(326\) 11.3425 0.628203
\(327\) 11.5012 19.9206i 0.636016 1.10161i
\(328\) −1.90135 + 3.29324i −0.104985 + 0.181839i
\(329\) 0.846899 + 1.46687i 0.0466910 + 0.0808712i
\(330\) 9.80504 0.539750
\(331\) −2.37041 4.10568i −0.130290 0.225668i 0.793499 0.608572i \(-0.208257\pi\)
−0.923788 + 0.382904i \(0.874924\pi\)
\(332\) −5.28689 9.15715i −0.290156 0.502564i
\(333\) 32.5543 1.78396
\(334\) −8.63798 14.9614i −0.472649 0.818653i
\(335\) 7.79967 13.5094i 0.426142 0.738099i
\(336\) 0.217312 0.376395i 0.0118553 0.0205341i
\(337\) −32.4430 −1.76728 −0.883642 0.468163i \(-0.844916\pi\)
−0.883642 + 0.468163i \(0.844916\pi\)
\(338\) 7.70219 10.4726i 0.418944 0.569637i
\(339\) 11.8776 0.645105
\(340\) 8.23546 14.2642i 0.446631 0.773587i
\(341\) −3.43462 + 5.94894i −0.185995 + 0.322153i
\(342\) 6.35110 + 11.0004i 0.343428 + 0.594835i
\(343\) −2.33411 −0.126030
\(344\) −10.8050 18.7149i −0.582569 1.00904i
\(345\) 25.5096 + 44.1839i 1.37339 + 2.37878i
\(346\) −12.8413 −0.690355
\(347\) 5.91647 + 10.2476i 0.317613 + 0.550122i 0.979989 0.199049i \(-0.0637854\pi\)
−0.662377 + 0.749171i \(0.730452\pi\)
\(348\) 2.51815 4.36157i 0.134987 0.233805i
\(349\) −15.0000 + 25.9808i −0.802932 + 1.39072i 0.114747 + 0.993395i \(0.463394\pi\)
−0.917679 + 0.397324i \(0.869939\pi\)
\(350\) 1.53747 0.0821812
\(351\) 0.398321 7.20009i 0.0212608 0.384313i
\(352\) 5.00000 0.266501
\(353\) 5.10168 8.83637i 0.271535 0.470312i −0.697720 0.716370i \(-0.745802\pi\)
0.969255 + 0.246058i \(0.0791354\pi\)
\(354\) −2.78269 + 4.81976i −0.147898 + 0.256167i
\(355\) −11.3062 19.5829i −0.600071 1.03935i
\(356\) −14.3062 −0.758227
\(357\) −0.949743 1.64500i −0.0502657 0.0870628i
\(358\) 2.46789 + 4.27452i 0.130432 + 0.225915i
\(359\) −13.5375 −0.714480 −0.357240 0.934013i \(-0.616282\pi\)
−0.357240 + 0.934013i \(0.616282\pi\)
\(360\) 21.3050 + 36.9014i 1.12287 + 1.94487i
\(361\) 3.82016 6.61671i 0.201061 0.348248i
\(362\) −0.318991 + 0.552509i −0.0167658 + 0.0290392i
\(363\) 2.60168 0.136553
\(364\) −0.504198 0.329517i −0.0264271 0.0172714i
\(365\) 53.6743 2.80944
\(366\) 6.25058 10.8263i 0.326723 0.565901i
\(367\) 5.57377 9.65406i 0.290949 0.503938i −0.683086 0.730338i \(-0.739362\pi\)
0.974034 + 0.226401i \(0.0726958\pi\)
\(368\) −2.60168 4.50624i −0.135622 0.234904i
\(369\) −4.77713 −0.248687
\(370\) −16.2771 28.1928i −0.846208 1.46567i
\(371\) −0.111435 0.193011i −0.00578542 0.0100206i
\(372\) −17.8716 −0.926598
\(373\) 13.6561 + 23.6531i 0.707088 + 1.22471i 0.965933 + 0.258793i \(0.0833248\pi\)
−0.258845 + 0.965919i \(0.583342\pi\)
\(374\) −2.18521 + 3.78489i −0.112994 + 0.195712i
\(375\) −20.6070 + 35.6924i −1.06414 + 1.84315i
\(376\) 30.4174 1.56866
\(377\) 5.84251 + 3.81835i 0.300904 + 0.196655i
\(378\) 0.334110 0.0171848
\(379\) −9.20336 + 15.9407i −0.472745 + 0.818818i −0.999513 0.0311907i \(-0.990070\pi\)
0.526769 + 0.850009i \(0.323403\pi\)
\(380\) −6.35110 + 11.0004i −0.325804 + 0.564310i
\(381\) 1.73243 + 3.00066i 0.0887551 + 0.153728i
\(382\) 26.1391 1.33740
\(383\) 12.9358 + 22.4054i 0.660988 + 1.14486i 0.980356 + 0.197234i \(0.0631959\pi\)
−0.319368 + 0.947631i \(0.603471\pi\)
\(384\) 3.90252 + 6.75936i 0.199150 + 0.344937i
\(385\) 0.629587 0.0320867
\(386\) 5.56957 + 9.64678i 0.283484 + 0.491008i
\(387\) 13.5738 23.5105i 0.689994 1.19510i
\(388\) 1.78269 3.08771i 0.0905023 0.156755i
\(389\) 20.7153 1.05030 0.525152 0.851008i \(-0.324008\pi\)
0.525152 + 0.851008i \(0.324008\pi\)
\(390\) −31.5459 + 15.9581i −1.59739 + 0.808072i
\(391\) −22.7408 −1.15005
\(392\) −10.4581 + 18.1140i −0.528216 + 0.914897i
\(393\) −17.8274 + 30.8779i −0.899273 + 1.55759i
\(394\) −7.76873 13.4558i −0.391383 0.677896i
\(395\) −54.9247 −2.76356
\(396\) 1.88437 + 3.26382i 0.0946930 + 0.164013i
\(397\) 10.7911 + 18.6907i 0.541589 + 0.938060i 0.998813 + 0.0487081i \(0.0155104\pi\)
−0.457224 + 0.889352i \(0.651156\pi\)
\(398\) −11.6766 −0.585296
\(399\) 0.732431 + 1.26861i 0.0366674 + 0.0635098i
\(400\) 4.60168 7.97034i 0.230084 0.398517i
\(401\) −0.101679 + 0.176113i −0.00507761 + 0.00879468i −0.868553 0.495596i \(-0.834950\pi\)
0.863475 + 0.504391i \(0.168283\pi\)
\(402\) −10.7687 −0.537096
\(403\) 1.36808 24.7296i 0.0681490 1.23187i
\(404\) 12.0363 0.598828
\(405\) 11.5000 19.9186i 0.571440 0.989762i
\(406\) −0.161692 + 0.280058i −0.00802463 + 0.0138991i
\(407\) −4.31899 7.48071i −0.214084 0.370805i
\(408\) −34.1112 −1.68876
\(409\) −0.0460590 0.0797765i −0.00227747 0.00394469i 0.864884 0.501971i \(-0.167392\pi\)
−0.867162 + 0.498026i \(0.834058\pi\)
\(410\) 2.38856 + 4.13712i 0.117963 + 0.204318i
\(411\) −35.4877 −1.75048
\(412\) −3.20336 5.54838i −0.157818 0.273349i
\(413\) −0.178678 + 0.309479i −0.00879216 + 0.0152285i
\(414\) 9.80504 16.9828i 0.481891 0.834660i
\(415\) −39.8497 −1.95615
\(416\) −16.0866 + 8.13773i −0.788708 + 0.398985i
\(417\) 2.26150 0.110746
\(418\) 1.68521 2.91886i 0.0824262 0.142766i
\(419\) −5.06421 + 8.77147i −0.247403 + 0.428514i −0.962804 0.270199i \(-0.912910\pi\)
0.715402 + 0.698714i \(0.246244\pi\)
\(420\) 0.818991 + 1.41853i 0.0399627 + 0.0692174i
\(421\) −6.58217 −0.320795 −0.160398 0.987052i \(-0.551278\pi\)
−0.160398 + 0.987052i \(0.551278\pi\)
\(422\) 2.28689 + 3.96100i 0.111324 + 0.192819i
\(423\) 19.1059 + 33.0923i 0.928960 + 1.60901i
\(424\) −4.00233 −0.194370
\(425\) −20.1112 34.8337i −0.975538 1.68968i
\(426\) −7.80504 + 13.5187i −0.378155 + 0.654984i
\(427\) 0.401353 0.695164i 0.0194228 0.0336413i
\(428\) 13.7045 0.662433
\(429\) −8.37041 + 4.23435i −0.404127 + 0.204436i
\(430\) −27.1475 −1.30917
\(431\) −8.74942 + 15.1544i −0.421445 + 0.729963i −0.996081 0.0884453i \(-0.971810\pi\)
0.574636 + 0.818409i \(0.305143\pi\)
\(432\) 1.00000 1.73205i 0.0481125 0.0833333i
\(433\) 4.34690 + 7.52905i 0.208899 + 0.361823i 0.951368 0.308057i \(-0.0996788\pi\)
−0.742469 + 0.669880i \(0.766345\pi\)
\(434\) 1.14754 0.0550838
\(435\) −9.49024 16.4376i −0.455022 0.788122i
\(436\) −4.42067 7.65683i −0.211712 0.366695i
\(437\) 17.5375 0.838931
\(438\) −18.5265 32.0889i −0.885233 1.53327i
\(439\) 12.2869 21.2815i 0.586421 1.01571i −0.408276 0.912859i \(-0.633870\pi\)
0.994697 0.102852i \(-0.0327969\pi\)
\(440\) 5.65310 9.79146i 0.269501 0.466789i
\(441\) −26.2760 −1.25124
\(442\) 0.870413 15.7337i 0.0414013 0.748375i
\(443\) −17.2699 −0.820518 −0.410259 0.911969i \(-0.634562\pi\)
−0.410259 + 0.911969i \(0.634562\pi\)
\(444\) 11.2366 19.4624i 0.533267 0.923645i
\(445\) −26.9581 + 46.6929i −1.27794 + 2.21345i
\(446\) 4.53211 + 7.84984i 0.214601 + 0.371701i
\(447\) 3.03630 0.143612
\(448\) −0.584693 1.01272i −0.0276242 0.0478464i
\(449\) −8.16150 14.1361i −0.385165 0.667125i 0.606627 0.794986i \(-0.292522\pi\)
−0.991792 + 0.127861i \(0.959189\pi\)
\(450\) 34.6850 1.63507
\(451\) 0.633784 + 1.09775i 0.0298437 + 0.0516909i
\(452\) 2.28269 3.95373i 0.107369 0.185968i
\(453\) 13.9721 24.2004i 0.656466 1.13703i
\(454\) −13.2034 −0.619664
\(455\) −2.02558 + 1.02468i −0.0949605 + 0.0480378i
\(456\) 26.3062 1.23190
\(457\) −10.7087 + 18.5480i −0.500933 + 0.867641i 0.499067 + 0.866564i \(0.333676\pi\)
−0.999999 + 0.00107752i \(0.999657\pi\)
\(458\) −1.01395 + 1.75622i −0.0473789 + 0.0820627i
\(459\) −4.37041 7.56978i −0.203993 0.353327i
\(460\) 19.6101 0.914324
\(461\) 8.90368 + 15.4216i 0.414686 + 0.718257i 0.995395 0.0958538i \(-0.0305581\pi\)
−0.580710 + 0.814111i \(0.697225\pi\)
\(462\) −0.217312 0.376395i −0.0101103 0.0175115i
\(463\) 4.80271 0.223201 0.111600 0.993753i \(-0.464402\pi\)
0.111600 + 0.993753i \(0.464402\pi\)
\(464\) 0.967895 + 1.67644i 0.0449334 + 0.0778269i
\(465\) −33.6766 + 58.3296i −1.56172 + 2.70497i
\(466\) 6.37041 11.0339i 0.295104 0.511135i
\(467\) −2.80737 −0.129910 −0.0649548 0.997888i \(-0.520690\pi\)
−0.0649548 + 0.997888i \(0.520690\pi\)
\(468\) −11.3746 7.43383i −0.525792 0.343629i
\(469\) −0.691466 −0.0319289
\(470\) 19.1059 33.0923i 0.881288 1.52644i
\(471\) 5.97512 10.3492i 0.275319 0.476867i
\(472\) 3.20872 + 5.55767i 0.147693 + 0.255812i
\(473\) −7.20336 −0.331211
\(474\) 18.9581 + 32.8365i 0.870776 + 1.50823i
\(475\) 15.5096 + 26.8633i 0.711627 + 1.23257i
\(476\) −0.730100 −0.0334641
\(477\) −2.51395 4.35430i −0.115106 0.199369i
\(478\) −2.03630 + 3.52698i −0.0931383 + 0.161320i
\(479\) −5.91647 + 10.2476i −0.270331 + 0.468226i −0.968946 0.247271i \(-0.920466\pi\)
0.698616 + 0.715497i \(0.253800\pi\)
\(480\) 49.0252 2.23768
\(481\) 26.0707 + 17.0384i 1.18872 + 0.776886i
\(482\) −18.9828 −0.864644
\(483\) 1.13075 1.95852i 0.0514510 0.0891157i
\(484\) 0.500000 0.866025i 0.0227273 0.0393648i
\(485\) −6.71848 11.6367i −0.305070 0.528397i
\(486\) −21.8776 −0.992390
\(487\) 8.20872 + 14.2179i 0.371973 + 0.644276i 0.989869 0.141984i \(-0.0453482\pi\)
−0.617896 + 0.786260i \(0.712015\pi\)
\(488\) −7.20756 12.4839i −0.326271 0.565117i
\(489\) 29.5096 1.33447
\(490\) 13.1380 + 22.7557i 0.593514 + 1.02800i
\(491\) −3.91647 + 6.78353i −0.176748 + 0.306136i −0.940765 0.339060i \(-0.889891\pi\)
0.764017 + 0.645196i \(0.223224\pi\)
\(492\) −1.64890 + 2.85598i −0.0743383 + 0.128758i
\(493\) 8.46020 0.381028
\(494\) −0.671253 + 12.1336i −0.0302011 + 0.545919i
\(495\) 14.2034 0.638393
\(496\) 3.43462 5.94894i 0.154219 0.267115i
\(497\) −0.501166 + 0.868044i −0.0224803 + 0.0389371i
\(498\) 13.7548 + 23.8240i 0.616366 + 1.06758i
\(499\) 12.2722 0.549381 0.274690 0.961533i \(-0.411425\pi\)
0.274690 + 0.961533i \(0.411425\pi\)
\(500\) 7.92067 + 13.7190i 0.354223 + 0.613532i
\(501\) −22.4733 38.9248i −1.00403 1.73903i
\(502\) 10.3402 0.461505
\(503\) −0.554455 0.960344i −0.0247219 0.0428196i 0.853400 0.521257i \(-0.174537\pi\)
−0.878122 + 0.478437i \(0.841203\pi\)
\(504\) 0.944380 1.63571i 0.0420660 0.0728605i
\(505\) 22.6808 39.2843i 1.00928 1.74813i
\(506\) −5.20336 −0.231317
\(507\) 20.0386 27.2465i 0.889947 1.21006i
\(508\) 1.33178 0.0590882
\(509\) 11.9346 20.6714i 0.528993 0.916243i −0.470435 0.882434i \(-0.655903\pi\)
0.999428 0.0338082i \(-0.0107635\pi\)
\(510\) −21.4260 + 37.1110i −0.948761 + 1.64330i
\(511\) −1.18960 2.06045i −0.0526248 0.0911488i
\(512\) −11.0000 −0.486136
\(513\) 3.37041 + 5.83773i 0.148807 + 0.257742i
\(514\) −12.0877 20.9366i −0.533167 0.923472i
\(515\) −24.1452 −1.06397
\(516\) −9.37041 16.2300i −0.412509 0.714487i
\(517\) 5.06957 8.78076i 0.222960 0.386177i
\(518\) −0.721510 + 1.24969i −0.0317013 + 0.0549083i
\(519\) −33.4090 −1.46649
\(520\) −2.25175 + 40.7029i −0.0987457 + 1.78494i
\(521\) 18.3318 0.803130 0.401565 0.915831i \(-0.368466\pi\)
0.401565 + 0.915831i \(0.368466\pi\)
\(522\) −3.64774 + 6.31807i −0.159657 + 0.276534i
\(523\) 5.22034 9.04190i 0.228270 0.395375i −0.729026 0.684486i \(-0.760027\pi\)
0.957295 + 0.289112i \(0.0933599\pi\)
\(524\) 6.85226 + 11.8685i 0.299342 + 0.518476i
\(525\) 4.00000 0.174574
\(526\) 5.37041 + 9.30183i 0.234161 + 0.405579i
\(527\) −15.0107 25.9993i −0.653878 1.13255i
\(528\) −2.60168 −0.113224
\(529\) −2.03747 3.52900i −0.0885856 0.153435i
\(530\) −2.51395 + 4.35430i −0.109199 + 0.189139i
\(531\) −4.03094 + 6.98179i −0.174928 + 0.302984i
\(532\) 0.563045 0.0244111
\(533\) −3.82571 2.50028i −0.165710 0.108299i
\(534\) 37.2201 1.61067
\(535\) 25.8244 44.7291i 1.11648 1.93381i
\(536\) −6.20872 + 10.7538i −0.268176 + 0.464494i
\(537\) 6.42067 + 11.1209i 0.277072 + 0.479903i
\(538\) 17.6659 0.761631
\(539\) 3.48605 + 6.03801i 0.150155 + 0.260075i
\(540\) 3.76873 + 6.52764i 0.162181 + 0.280905i
\(541\) −11.0554 −0.475310 −0.237655 0.971350i \(-0.576379\pi\)
−0.237655 + 0.971350i \(0.576379\pi\)
\(542\) −4.37041 7.56978i −0.187725 0.325150i
\(543\) −0.829913 + 1.43745i −0.0356150 + 0.0616869i
\(544\) −10.9260 + 18.9244i −0.468450 + 0.811379i
\(545\) −33.3207 −1.42730
\(546\) 1.31176 + 0.857296i 0.0561382 + 0.0366889i
\(547\) 25.3532 1.08403 0.542013 0.840370i \(-0.317662\pi\)
0.542013 + 0.840370i \(0.317662\pi\)
\(548\) −6.82016 + 11.8129i −0.291343 + 0.504620i
\(549\) 9.05445 15.6828i 0.386435 0.669325i
\(550\) −4.60168 7.97034i −0.196216 0.339857i
\(551\) −6.52441 −0.277949
\(552\) −20.3062 35.1714i −0.864289 1.49699i
\(553\) 1.21731 + 2.10845i 0.0517654 + 0.0896603i
\(554\) 29.2118 1.24109
\(555\) −42.3479 73.3487i −1.79757 3.11348i
\(556\) 0.434624 0.752791i 0.0184322 0.0319254i
\(557\) −10.1713 + 17.6171i −0.430970 + 0.746462i −0.996957 0.0779524i \(-0.975162\pi\)
0.565987 + 0.824414i \(0.308495\pi\)
\(558\) 25.8884 1.09594
\(559\) 23.1755 11.7238i 0.980217 0.495864i
\(560\) −0.629587 −0.0266049
\(561\) −5.68521 + 9.84707i −0.240030 + 0.415743i
\(562\) 5.40252 9.35744i 0.227891 0.394720i
\(563\) 3.38740 + 5.86715i 0.142762 + 0.247271i 0.928536 0.371243i \(-0.121068\pi\)
−0.785774 + 0.618514i \(0.787735\pi\)
\(564\) 26.3788 1.11075
\(565\) −8.60284 14.9006i −0.361924 0.626871i
\(566\) −5.11983 8.86781i −0.215203 0.372742i
\(567\) −1.01951 −0.0428155
\(568\) 9.00000 + 15.5885i 0.377632 + 0.654077i
\(569\) −8.43695 + 14.6132i −0.353696 + 0.612619i −0.986894 0.161371i \(-0.948408\pi\)
0.633198 + 0.773990i \(0.281742\pi\)
\(570\) 16.5235 28.6196i 0.692094 1.19874i
\(571\) 44.9973 1.88308 0.941539 0.336905i \(-0.109380\pi\)
0.941539 + 0.336905i \(0.109380\pi\)
\(572\) −0.199160 + 3.60005i −0.00832732 + 0.150526i
\(573\) 68.0057 2.84098
\(574\) 0.105877 0.183384i 0.00441922 0.00765431i
\(575\) 23.9442 41.4725i 0.998542 1.72952i
\(576\) −13.1906 22.8467i −0.549607 0.951947i
\(577\) −19.5119 −0.812291 −0.406145 0.913808i \(-0.633127\pi\)
−0.406145 + 0.913808i \(0.633127\pi\)
\(578\) −1.05026 1.81910i −0.0436849 0.0756645i
\(579\) 14.4902 + 25.0978i 0.602194 + 1.04303i
\(580\) −7.29548 −0.302928
\(581\) 0.883202 + 1.52975i 0.0366414 + 0.0634647i
\(582\) −4.63798 + 8.03322i −0.192251 + 0.332988i
\(583\) −0.667055 + 1.15537i −0.0276266 + 0.0478507i
\(584\) −42.7260 −1.76801
\(585\) −45.6966 + 23.1166i −1.88932 + 0.955754i
\(586\) 3.96370 0.163739
\(587\) −8.33947 + 14.4444i −0.344207 + 0.596184i −0.985209 0.171355i \(-0.945186\pi\)
0.641002 + 0.767539i \(0.278519\pi\)
\(588\) −9.06957 + 15.7090i −0.374023 + 0.647827i
\(589\) 11.5761 + 20.0504i 0.476985 + 0.826162i
\(590\) 8.06188 0.331902
\(591\) −20.2118 35.0078i −0.831400 1.44003i
\(592\) 4.31899 + 7.48071i 0.177509 + 0.307455i
\(593\) −29.4128 −1.20784 −0.603919 0.797046i \(-0.706395\pi\)
−0.603919 + 0.797046i \(0.706395\pi\)
\(594\) −1.00000 1.73205i −0.0410305 0.0710669i
\(595\) −1.37578 + 2.38292i −0.0564013 + 0.0976900i
\(596\) 0.583528 1.01070i 0.0239022 0.0413999i
\(597\) −30.3788 −1.24332
\(598\) 16.7408 8.46870i 0.684583 0.346311i
\(599\) 6.12842 0.250400 0.125200 0.992131i \(-0.460043\pi\)
0.125200 + 0.992131i \(0.460043\pi\)
\(600\) 35.9163 62.2088i 1.46628 2.53966i
\(601\) −12.5030 + 21.6559i −0.510009 + 0.883362i 0.489923 + 0.871765i \(0.337025\pi\)
−0.999933 + 0.0115966i \(0.996309\pi\)
\(602\) 0.601679 + 1.04214i 0.0245226 + 0.0424744i
\(603\) −15.5993 −0.635255
\(604\) −5.37041 9.30183i −0.218519 0.378486i
\(605\) −1.88437 3.26382i −0.0766104 0.132693i
\(606\) −31.3146 −1.27207
\(607\) −16.2203 28.0945i −0.658363 1.14032i −0.981039 0.193809i \(-0.937916\pi\)
0.322676 0.946510i \(-0.395418\pi\)
\(608\) 8.42603 14.5943i 0.341721 0.591878i
\(609\) −0.420670 + 0.728622i −0.0170464 + 0.0295253i
\(610\) −18.1089 −0.733208
\(611\) −2.01932 + 36.5014i −0.0816928 + 1.47669i
\(612\) −16.4709 −0.665798
\(613\) 8.28572 14.3513i 0.334657 0.579643i −0.648762 0.760992i \(-0.724713\pi\)
0.983419 + 0.181348i \(0.0580462\pi\)
\(614\) −7.11983 + 12.3319i −0.287333 + 0.497675i
\(615\) 6.21428 + 10.7634i 0.250584 + 0.434024i
\(616\) −0.501166 −0.0201925
\(617\) 8.93462 + 15.4752i 0.359694 + 0.623009i 0.987910 0.155031i \(-0.0495476\pi\)
−0.628215 + 0.778040i \(0.716214\pi\)
\(618\) 8.33411 + 14.4351i 0.335247 + 0.580665i
\(619\) −27.4151 −1.10191 −0.550953 0.834536i \(-0.685736\pi\)
−0.550953 + 0.834536i \(0.685736\pi\)
\(620\) 12.9442 + 22.4200i 0.519851 + 0.900408i
\(621\) 5.20336 9.01248i 0.208804 0.361658i
\(622\) −5.93882 + 10.2863i −0.238125 + 0.412445i
\(623\) 2.38993 0.0957503
\(624\) 8.37041 4.23435i 0.335085 0.169510i
\(625\) 13.6850 0.547400
\(626\) −3.94974 + 6.84116i −0.157863 + 0.273428i
\(627\) 4.38437 7.59395i 0.175095 0.303273i
\(628\) −2.29664 3.97790i −0.0916460 0.158735i
\(629\) 37.7516 1.50525
\(630\) −1.18637 2.05486i −0.0472662 0.0818675i
\(631\) −3.27293 5.66888i −0.130293 0.225675i 0.793496 0.608575i \(-0.208259\pi\)
−0.923790 + 0.382900i \(0.874925\pi\)
\(632\) 43.7213 1.73914
\(633\) 5.94974 + 10.3053i 0.236481 + 0.409597i
\(634\) −13.6615 + 23.6624i −0.542567 + 0.939754i
\(635\) 2.50956 4.34669i 0.0995889 0.172493i
\(636\) −3.47093 −0.137631
\(637\) −21.0428 13.7525i −0.833747 0.544892i
\(638\) 1.93579 0.0766386
\(639\) −11.3062 + 19.5829i −0.447266 + 0.774688i
\(640\) 5.65310 9.79146i 0.223458 0.387041i
\(641\) −1.03747 1.79695i −0.0409775 0.0709752i 0.844809 0.535068i \(-0.179714\pi\)
−0.885787 + 0.464092i \(0.846381\pi\)
\(642\) −35.6548 −1.40718
\(643\) 6.13378 + 10.6240i 0.241893 + 0.418971i 0.961253 0.275666i \(-0.0888984\pi\)
−0.719361 + 0.694637i \(0.755565\pi\)
\(644\) −0.434624 0.752791i −0.0171266 0.0296641i
\(645\) −70.6292 −2.78102
\(646\) 7.36505 + 12.7566i 0.289774 + 0.501903i
\(647\) −23.5435 + 40.7786i −0.925592 + 1.60317i −0.134985 + 0.990848i \(0.543099\pi\)
−0.790607 + 0.612324i \(0.790235\pi\)
\(648\) −9.15427 + 15.8557i −0.359614 + 0.622869i
\(649\) 2.13915 0.0839689
\(650\) 27.7771 + 18.1536i 1.08951 + 0.712044i
\(651\) 2.98554 0.117013
\(652\) 5.67125 9.82290i 0.222103 0.384694i
\(653\) 10.5514 18.2756i 0.412909 0.715179i −0.582297 0.812976i \(-0.697846\pi\)
0.995206 + 0.0977964i \(0.0311794\pi\)
\(654\) 11.5012 + 19.9206i 0.449731 + 0.778957i
\(655\) 51.6487 2.01808
\(656\) −0.633784 1.09775i −0.0247451 0.0428598i
\(657\) −26.8371 46.4833i −1.04702 1.81349i
\(658\) −1.69380 −0.0660311
\(659\) 9.19477 + 15.9258i 0.358177 + 0.620381i 0.987656 0.156636i \(-0.0500650\pi\)
−0.629479 + 0.777017i \(0.716732\pi\)
\(660\) 4.90252 8.49141i 0.190830 0.330528i
\(661\) −8.34690 + 14.4573i −0.324657 + 0.562322i −0.981443 0.191755i \(-0.938582\pi\)
0.656786 + 0.754077i \(0.271915\pi\)
\(662\) 4.74083 0.184257
\(663\) 2.26454 40.9340i 0.0879473 1.58975i
\(664\) 31.7213 1.23103
\(665\) 1.06098 1.83768i 0.0411432 0.0712621i
\(666\) −16.2771 + 28.1928i −0.630726 + 1.09245i
\(667\) 5.03630 + 8.72313i 0.195006 + 0.337761i
\(668\) −17.2760 −0.668427
\(669\) 11.7911 + 20.4228i 0.455870 + 0.789589i
\(670\) 7.79967 + 13.5094i 0.301328 + 0.521915i
\(671\) −4.80504 −0.185496
\(672\) −1.08656 1.88198i −0.0419150 0.0725988i
\(673\) −14.8092 + 25.6503i −0.570854 + 0.988748i 0.425624 + 0.904900i \(0.360054\pi\)
−0.996479 + 0.0838484i \(0.973279\pi\)
\(674\) 16.2215 28.0965i 0.624829 1.08224i
\(675\) 18.4067 0.708475
\(676\) −5.21848 11.9066i −0.200711 0.457947i
\(677\) −22.6124 −0.869065 −0.434533 0.900656i \(-0.643086\pi\)
−0.434533 + 0.900656i \(0.643086\pi\)
\(678\) −5.93882 + 10.2863i −0.228079 + 0.395045i
\(679\) −0.297807 + 0.515817i −0.0114288 + 0.0197953i
\(680\) 24.7064 + 42.7927i 0.947447 + 1.64103i
\(681\) −34.3509 −1.31633
\(682\) −3.43462 5.94894i −0.131519 0.227797i
\(683\) −16.5714 28.7026i −0.634089 1.09827i −0.986707 0.162507i \(-0.948042\pi\)
0.352619 0.935767i \(-0.385291\pi\)
\(684\) 12.7022 0.485680
\(685\) 25.7034 + 44.5195i 0.982075 + 1.70100i
\(686\) 1.16706 2.02140i 0.0445584 0.0771774i
\(687\) −2.63798 + 4.56912i −0.100645 + 0.174323i
\(688\) 7.20336 0.274625
\(689\) 0.265702 4.80286i 0.0101224 0.182974i
\(690\) −51.0191 −1.94226
\(691\) −8.10284 + 14.0345i −0.308247 + 0.533899i −0.977979 0.208704i \(-0.933076\pi\)
0.669732 + 0.742603i \(0.266409\pi\)
\(692\) −6.42067 + 11.1209i −0.244077 + 0.422754i
\(693\) −0.314793 0.545238i −0.0119580 0.0207119i
\(694\) −11.8329 −0.449172
\(695\) −1.63798 2.83707i −0.0621322 0.107616i
\(696\) 7.55445 + 13.0847i 0.286351 + 0.495974i
\(697\) −5.53980 −0.209835
\(698\) −15.0000 25.9808i −0.567758 0.983386i
\(699\) 16.5738 28.7066i 0.626878 1.08578i
\(700\) 0.768734 1.33149i 0.0290554 0.0503255i
\(701\) 16.7855 0.633981 0.316990 0.948429i \(-0.397328\pi\)
0.316990 + 0.948429i \(0.397328\pi\)
\(702\) 6.03630 + 3.94500i 0.227826 + 0.148895i
\(703\) −29.1136 −1.09804
\(704\) −3.50000 + 6.06218i −0.131911 + 0.228477i
\(705\) 49.7074 86.0957i 1.87209 3.24255i
\(706\) 5.10168 + 8.83637i 0.192004 + 0.332561i
\(707\) −2.01073 −0.0756212
\(708\) 2.78269 + 4.81976i 0.104580 + 0.181138i
\(709\) −13.8146 23.9276i −0.518818 0.898619i −0.999761 0.0218674i \(-0.993039\pi\)
0.480943 0.876752i \(-0.340294\pi\)
\(710\) 22.6124 0.848628
\(711\) 27.4623 + 47.5662i 1.02992 + 1.78387i
\(712\) 21.4593 37.1686i 0.804221 1.39295i
\(713\) 17.8716 30.9545i 0.669296 1.15925i
\(714\) 1.89949 0.0710865
\(715\) 11.3746 + 7.43383i 0.425386 + 0.278010i
\(716\) 4.93579 0.184459
\(717\) −5.29781 + 9.17607i −0.197850 + 0.342687i
\(718\) 6.76873 11.7238i 0.252607 0.437528i
\(719\) −4.70452 8.14847i −0.175449 0.303887i 0.764867 0.644188i \(-0.222804\pi\)
−0.940317 + 0.340301i \(0.889471\pi\)
\(720\) −14.2034 −0.529328
\(721\) 0.535138 + 0.926885i 0.0199296 + 0.0345190i
\(722\) 3.82016 + 6.61671i 0.142172 + 0.246248i
\(723\) −49.3872 −1.83673
\(724\) 0.318991 + 0.552509i 0.0118552 + 0.0205338i
\(725\) −8.90788 + 15.4289i −0.330830 + 0.573015i
\(726\) −1.30084 + 2.25312i −0.0482787 + 0.0836211i
\(727\) 20.6682 0.766542 0.383271 0.923636i \(-0.374798\pi\)
0.383271 + 0.923636i \(0.374798\pi\)
\(728\) 1.61241 0.815670i 0.0597597 0.0302307i
\(729\) −38.6101 −1.43000
\(730\) −26.8371 + 46.4833i −0.993287 + 1.72042i
\(731\) 15.7408 27.2639i 0.582196 1.00839i
\(732\) −6.25058 10.8263i −0.231028 0.400153i
\(733\) 26.1368 0.965385 0.482693 0.875790i \(-0.339659\pi\)
0.482693 + 0.875790i \(0.339659\pi\)
\(734\) 5.57377 + 9.65406i 0.205732 + 0.356338i
\(735\) 34.1808 + 59.2029i 1.26078 + 2.18373i
\(736\) −26.0168 −0.958992
\(737\) 2.06957 + 3.58461i 0.0762337 + 0.132041i
\(738\) 2.38856 4.13712i 0.0879243 0.152289i
\(739\) 8.23966 14.2715i 0.303101 0.524986i −0.673736 0.738972i \(-0.735311\pi\)
0.976837 + 0.213986i \(0.0686448\pi\)
\(740\) −32.5543 −1.19672
\(741\) −1.74638 + 31.5679i −0.0641551 + 1.15967i
\(742\) 0.222870 0.00818182
\(743\) −14.8220 + 25.6725i −0.543767 + 0.941833i 0.454916 + 0.890534i \(0.349669\pi\)
−0.998683 + 0.0512983i \(0.983664\pi\)
\(744\) 26.8074 46.4317i 0.982806 1.70227i
\(745\) −2.19916 3.80906i −0.0805710 0.139553i
\(746\) −27.3123 −0.999973
\(747\) 19.9249 + 34.5109i 0.729013 + 1.26269i
\(748\) 2.18521 + 3.78489i 0.0798991 + 0.138389i
\(749\) −2.28941 −0.0836533
\(750\) −20.6070 35.6924i −0.752463 1.30330i
\(751\) −12.6743 + 21.9525i −0.462491 + 0.801058i −0.999084 0.0427828i \(-0.986378\pi\)
0.536593 + 0.843841i \(0.319711\pi\)
\(752\) −5.06957 + 8.78076i −0.184868 + 0.320201i
\(753\) 26.9018 0.980357
\(754\) −6.22804 + 3.15059i −0.226812 + 0.114738i
\(755\) −40.4793 −1.47319
\(756\) 0.167055 0.289348i 0.00607574 0.0105235i
\(757\) −15.8660 + 27.4808i −0.576660 + 0.998805i 0.419199 + 0.907895i \(0.362311\pi\)
−0.995859 + 0.0909105i \(0.971022\pi\)
\(758\) −9.20336 15.9407i −0.334281 0.578992i
\(759\) −13.5375 −0.491379
\(760\) −19.0533 33.0013i −0.691135 1.19708i
\(761\) 21.9419 + 38.0044i 0.795392 + 1.37766i 0.922590 + 0.385781i \(0.126068\pi\)
−0.127199 + 0.991877i \(0.540599\pi\)
\(762\) −3.46486 −0.125519
\(763\) 0.738496 + 1.27911i 0.0267353 + 0.0463070i
\(764\) 13.0696 22.6372i 0.472841 0.818984i
\(765\) −31.0373 + 53.7581i −1.12216 + 1.94363i
\(766\) −25.8716 −0.934778
\(767\) −6.88231 + 3.48156i −0.248506 + 0.125712i
\(768\) −44.2285 −1.59596
\(769\) 7.80737 13.5228i 0.281541 0.487643i −0.690224 0.723596i \(-0.742488\pi\)
0.971764 + 0.235953i \(0.0758212\pi\)
\(770\) −0.314793 + 0.545238i −0.0113444 + 0.0196490i
\(771\) −31.4484 54.4702i −1.13259 1.96170i
\(772\) 11.1391 0.400907
\(773\) 11.1252 + 19.2694i 0.400145 + 0.693072i 0.993743 0.111690i \(-0.0356263\pi\)
−0.593598 + 0.804762i \(0.702293\pi\)
\(774\) 13.5738 + 23.5105i 0.487899 + 0.845066i
\(775\) 63.2201