Properties

Label 84.2.b.a.55.1
Level $84$
Weight $2$
Character 84.55
Analytic conductor $0.671$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 84.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.670743376979\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.2312.1
Defining polynomial: \(x^{4} - x^{3} - 2 x + 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.1
Root \(1.28078 + 0.599676i\) of defining polynomial
Character \(\chi\) \(=\) 84.55
Dual form 84.2.b.a.55.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.28078 - 0.599676i) q^{2} -1.00000 q^{3} +(1.28078 + 1.53610i) q^{4} -3.33513i q^{5} +(1.28078 + 0.599676i) q^{6} +(-1.56155 - 2.13578i) q^{7} +(-0.719224 - 2.73546i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.28078 - 0.599676i) q^{2} -1.00000 q^{3} +(1.28078 + 1.53610i) q^{4} -3.33513i q^{5} +(1.28078 + 0.599676i) q^{6} +(-1.56155 - 2.13578i) q^{7} +(-0.719224 - 2.73546i) q^{8} +1.00000 q^{9} +(-2.00000 + 4.27156i) q^{10} -0.936426i q^{11} +(-1.28078 - 1.53610i) q^{12} -1.87285i q^{13} +(0.719224 + 3.67188i) q^{14} +3.33513i q^{15} +(-0.719224 + 3.93481i) q^{16} +5.20798i q^{17} +(-1.28078 - 0.599676i) q^{18} +7.12311 q^{19} +(5.12311 - 4.27156i) q^{20} +(1.56155 + 2.13578i) q^{21} +(-0.561553 + 1.19935i) q^{22} +0.936426i q^{23} +(0.719224 + 2.73546i) q^{24} -6.12311 q^{25} +(-1.12311 + 2.39871i) q^{26} -1.00000 q^{27} +(1.28078 - 5.13416i) q^{28} -2.00000 q^{29} +(2.00000 - 4.27156i) q^{30} +(3.28078 - 4.60831i) q^{32} +0.936426i q^{33} +(3.12311 - 6.67026i) q^{34} +(-7.12311 + 5.20798i) q^{35} +(1.28078 + 1.53610i) q^{36} +1.12311 q^{37} +(-9.12311 - 4.27156i) q^{38} +1.87285i q^{39} +(-9.12311 + 2.39871i) q^{40} +1.46228i q^{41} +(-0.719224 - 3.67188i) q^{42} -9.06897i q^{43} +(1.43845 - 1.19935i) q^{44} -3.33513i q^{45} +(0.561553 - 1.19935i) q^{46} +6.24621 q^{47} +(0.719224 - 3.93481i) q^{48} +(-2.12311 + 6.67026i) q^{49} +(7.84233 + 3.67188i) q^{50} -5.20798i q^{51} +(2.87689 - 2.39871i) q^{52} +12.2462 q^{53} +(1.28078 + 0.599676i) q^{54} -3.12311 q^{55} +(-4.71922 + 5.80766i) q^{56} -7.12311 q^{57} +(2.56155 + 1.19935i) q^{58} +4.00000 q^{59} +(-5.12311 + 4.27156i) q^{60} -4.79741i q^{61} +(-1.56155 - 2.13578i) q^{63} +(-6.96543 + 3.93481i) q^{64} -6.24621 q^{65} +(0.561553 - 1.19935i) q^{66} +10.9418i q^{67} +(-8.00000 + 6.67026i) q^{68} -0.936426i q^{69} +(12.2462 - 2.39871i) q^{70} +3.86098i q^{71} +(-0.719224 - 2.73546i) q^{72} -6.67026i q^{73} +(-1.43845 - 0.673500i) q^{74} +6.12311 q^{75} +(9.12311 + 10.9418i) q^{76} +(-2.00000 + 1.46228i) q^{77} +(1.12311 - 2.39871i) q^{78} +2.39871i q^{79} +(13.1231 + 2.39871i) q^{80} +1.00000 q^{81} +(0.876894 - 1.87285i) q^{82} -10.2462 q^{83} +(-1.28078 + 5.13416i) q^{84} +17.3693 q^{85} +(-5.43845 + 11.6153i) q^{86} +2.00000 q^{87} +(-2.56155 + 0.673500i) q^{88} -1.46228i q^{89} +(-2.00000 + 4.27156i) q^{90} +(-4.00000 + 2.92456i) q^{91} +(-1.43845 + 1.19935i) q^{92} +(-8.00000 - 3.74571i) q^{94} -23.7565i q^{95} +(-3.28078 + 4.60831i) q^{96} +10.4160i q^{97} +(6.71922 - 7.26994i) q^{98} -0.936426i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{2} - 4q^{3} + q^{4} + q^{6} + 2q^{7} - 7q^{8} + 4q^{9} + O(q^{10}) \) \( 4q - q^{2} - 4q^{3} + q^{4} + q^{6} + 2q^{7} - 7q^{8} + 4q^{9} - 8q^{10} - q^{12} + 7q^{14} - 7q^{16} - q^{18} + 12q^{19} + 4q^{20} - 2q^{21} + 6q^{22} + 7q^{24} - 8q^{25} + 12q^{26} - 4q^{27} + q^{28} - 8q^{29} + 8q^{30} + 9q^{32} - 4q^{34} - 12q^{35} + q^{36} - 12q^{37} - 20q^{38} - 20q^{40} - 7q^{42} + 14q^{44} - 6q^{46} - 8q^{47} + 7q^{48} + 8q^{49} + 19q^{50} + 28q^{52} + 16q^{53} + q^{54} + 4q^{55} - 23q^{56} - 12q^{57} + 2q^{58} + 16q^{59} - 4q^{60} + 2q^{63} + q^{64} + 8q^{65} - 6q^{66} - 32q^{68} + 16q^{70} - 7q^{72} - 14q^{74} + 8q^{75} + 20q^{76} - 8q^{77} - 12q^{78} + 36q^{80} + 4q^{81} + 20q^{82} - 8q^{83} - q^{84} + 20q^{85} - 30q^{86} + 8q^{87} - 2q^{88} - 8q^{90} - 16q^{91} - 14q^{92} - 32q^{94} - 9q^{96} + 31q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28078 0.599676i −0.905646 0.424035i
\(3\) −1.00000 −0.577350
\(4\) 1.28078 + 1.53610i 0.640388 + 0.768051i
\(5\) 3.33513i 1.49152i −0.666217 0.745758i \(-0.732087\pi\)
0.666217 0.745758i \(-0.267913\pi\)
\(6\) 1.28078 + 0.599676i 0.522875 + 0.244817i
\(7\) −1.56155 2.13578i −0.590211 0.807249i
\(8\) −0.719224 2.73546i −0.254284 0.967130i
\(9\) 1.00000 0.333333
\(10\) −2.00000 + 4.27156i −0.632456 + 1.35079i
\(11\) 0.936426i 0.282343i −0.989985 0.141172i \(-0.954913\pi\)
0.989985 0.141172i \(-0.0450869\pi\)
\(12\) −1.28078 1.53610i −0.369728 0.443435i
\(13\) 1.87285i 0.519436i −0.965685 0.259718i \(-0.916370\pi\)
0.965685 0.259718i \(-0.0836296\pi\)
\(14\) 0.719224 + 3.67188i 0.192221 + 0.981352i
\(15\) 3.33513i 0.861127i
\(16\) −0.719224 + 3.93481i −0.179806 + 0.983702i
\(17\) 5.20798i 1.26312i 0.775326 + 0.631561i \(0.217585\pi\)
−0.775326 + 0.631561i \(0.782415\pi\)
\(18\) −1.28078 0.599676i −0.301882 0.141345i
\(19\) 7.12311 1.63415 0.817076 0.576530i \(-0.195593\pi\)
0.817076 + 0.576530i \(0.195593\pi\)
\(20\) 5.12311 4.27156i 1.14556 0.955149i
\(21\) 1.56155 + 2.13578i 0.340759 + 0.466065i
\(22\) −0.561553 + 1.19935i −0.119723 + 0.255703i
\(23\) 0.936426i 0.195258i 0.995223 + 0.0976292i \(0.0311259\pi\)
−0.995223 + 0.0976292i \(0.968874\pi\)
\(24\) 0.719224 + 2.73546i 0.146811 + 0.558373i
\(25\) −6.12311 −1.22462
\(26\) −1.12311 + 2.39871i −0.220259 + 0.470425i
\(27\) −1.00000 −0.192450
\(28\) 1.28078 5.13416i 0.242044 0.970265i
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 2.00000 4.27156i 0.365148 0.779876i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 3.28078 4.60831i 0.579965 0.814642i
\(33\) 0.936426i 0.163011i
\(34\) 3.12311 6.67026i 0.535608 1.14394i
\(35\) −7.12311 + 5.20798i −1.20402 + 0.880310i
\(36\) 1.28078 + 1.53610i 0.213463 + 0.256017i
\(37\) 1.12311 0.184637 0.0923187 0.995730i \(-0.470572\pi\)
0.0923187 + 0.995730i \(0.470572\pi\)
\(38\) −9.12311 4.27156i −1.47996 0.692938i
\(39\) 1.87285i 0.299896i
\(40\) −9.12311 + 2.39871i −1.44249 + 0.379269i
\(41\) 1.46228i 0.228370i 0.993460 + 0.114185i \(0.0364256\pi\)
−0.993460 + 0.114185i \(0.963574\pi\)
\(42\) −0.719224 3.67188i −0.110979 0.566584i
\(43\) 9.06897i 1.38300i −0.722374 0.691502i \(-0.756949\pi\)
0.722374 0.691502i \(-0.243051\pi\)
\(44\) 1.43845 1.19935i 0.216854 0.180809i
\(45\) 3.33513i 0.497172i
\(46\) 0.561553 1.19935i 0.0827964 0.176835i
\(47\) 6.24621 0.911104 0.455552 0.890209i \(-0.349442\pi\)
0.455552 + 0.890209i \(0.349442\pi\)
\(48\) 0.719224 3.93481i 0.103811 0.567941i
\(49\) −2.12311 + 6.67026i −0.303301 + 0.952895i
\(50\) 7.84233 + 3.67188i 1.10907 + 0.519283i
\(51\) 5.20798i 0.729264i
\(52\) 2.87689 2.39871i 0.398953 0.332641i
\(53\) 12.2462 1.68215 0.841073 0.540921i \(-0.181924\pi\)
0.841073 + 0.540921i \(0.181924\pi\)
\(54\) 1.28078 + 0.599676i 0.174292 + 0.0816056i
\(55\) −3.12311 −0.421119
\(56\) −4.71922 + 5.80766i −0.630633 + 0.776081i
\(57\) −7.12311 −0.943478
\(58\) 2.56155 + 1.19935i 0.336348 + 0.157483i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) −5.12311 + 4.27156i −0.661390 + 0.551456i
\(61\) 4.79741i 0.614246i −0.951670 0.307123i \(-0.900634\pi\)
0.951670 0.307123i \(-0.0993662\pi\)
\(62\) 0 0
\(63\) −1.56155 2.13578i −0.196737 0.269083i
\(64\) −6.96543 + 3.93481i −0.870679 + 0.491851i
\(65\) −6.24621 −0.774747
\(66\) 0.561553 1.19935i 0.0691224 0.147630i
\(67\) 10.9418i 1.33676i 0.743822 + 0.668378i \(0.233011\pi\)
−0.743822 + 0.668378i \(0.766989\pi\)
\(68\) −8.00000 + 6.67026i −0.970143 + 0.808888i
\(69\) 0.936426i 0.112732i
\(70\) 12.2462 2.39871i 1.46370 0.286700i
\(71\) 3.86098i 0.458215i 0.973401 + 0.229107i \(0.0735807\pi\)
−0.973401 + 0.229107i \(0.926419\pi\)
\(72\) −0.719224 2.73546i −0.0847613 0.322377i
\(73\) 6.67026i 0.780695i −0.920668 0.390348i \(-0.872355\pi\)
0.920668 0.390348i \(-0.127645\pi\)
\(74\) −1.43845 0.673500i −0.167216 0.0782928i
\(75\) 6.12311 0.707035
\(76\) 9.12311 + 10.9418i 1.04649 + 1.25511i
\(77\) −2.00000 + 1.46228i −0.227921 + 0.166642i
\(78\) 1.12311 2.39871i 0.127167 0.271600i
\(79\) 2.39871i 0.269875i 0.990854 + 0.134938i \(0.0430834\pi\)
−0.990854 + 0.134938i \(0.956917\pi\)
\(80\) 13.1231 + 2.39871i 1.46721 + 0.268183i
\(81\) 1.00000 0.111111
\(82\) 0.876894 1.87285i 0.0968368 0.206822i
\(83\) −10.2462 −1.12467 −0.562334 0.826910i \(-0.690096\pi\)
−0.562334 + 0.826910i \(0.690096\pi\)
\(84\) −1.28078 + 5.13416i −0.139744 + 0.560183i
\(85\) 17.3693 1.88397
\(86\) −5.43845 + 11.6153i −0.586443 + 1.25251i
\(87\) 2.00000 0.214423
\(88\) −2.56155 + 0.673500i −0.273062 + 0.0717953i
\(89\) 1.46228i 0.155001i −0.996992 0.0775006i \(-0.975306\pi\)
0.996992 0.0775006i \(-0.0246940\pi\)
\(90\) −2.00000 + 4.27156i −0.210819 + 0.450262i
\(91\) −4.00000 + 2.92456i −0.419314 + 0.306577i
\(92\) −1.43845 + 1.19935i −0.149968 + 0.125041i
\(93\) 0 0
\(94\) −8.00000 3.74571i −0.825137 0.386340i
\(95\) 23.7565i 2.43737i
\(96\) −3.28078 + 4.60831i −0.334843 + 0.470334i
\(97\) 10.4160i 1.05758i 0.848752 + 0.528791i \(0.177354\pi\)
−0.848752 + 0.528791i \(0.822646\pi\)
\(98\) 6.71922 7.26994i 0.678744 0.734375i
\(99\) 0.936426i 0.0941144i
\(100\) −7.84233 9.40572i −0.784233 0.940572i
\(101\) 13.7511i 1.36829i −0.729348 0.684143i \(-0.760176\pi\)
0.729348 0.684143i \(-0.239824\pi\)
\(102\) −3.12311 + 6.67026i −0.309234 + 0.660455i
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) −5.12311 + 1.34700i −0.502362 + 0.132084i
\(105\) 7.12311 5.20798i 0.695144 0.508247i
\(106\) −15.6847 7.34376i −1.52343 0.713289i
\(107\) 9.47954i 0.916422i 0.888843 + 0.458211i \(0.151510\pi\)
−0.888843 + 0.458211i \(0.848490\pi\)
\(108\) −1.28078 1.53610i −0.123243 0.147812i
\(109\) −8.24621 −0.789844 −0.394922 0.918715i \(-0.629228\pi\)
−0.394922 + 0.918715i \(0.629228\pi\)
\(110\) 4.00000 + 1.87285i 0.381385 + 0.178570i
\(111\) −1.12311 −0.106600
\(112\) 9.52699 4.60831i 0.900216 0.435444i
\(113\) −4.24621 −0.399450 −0.199725 0.979852i \(-0.564005\pi\)
−0.199725 + 0.979852i \(0.564005\pi\)
\(114\) 9.12311 + 4.27156i 0.854457 + 0.400068i
\(115\) 3.12311 0.291231
\(116\) −2.56155 3.07221i −0.237834 0.285247i
\(117\) 1.87285i 0.173145i
\(118\) −5.12311 2.39871i −0.471620 0.220819i
\(119\) 11.1231 8.13254i 1.01965 0.745509i
\(120\) 9.12311 2.39871i 0.832822 0.218971i
\(121\) 10.1231 0.920282
\(122\) −2.87689 + 6.14441i −0.260462 + 0.556289i
\(123\) 1.46228i 0.131849i
\(124\) 0 0
\(125\) 3.74571i 0.335026i
\(126\) 0.719224 + 3.67188i 0.0640735 + 0.327117i
\(127\) 9.89012i 0.877606i 0.898583 + 0.438803i \(0.144597\pi\)
−0.898583 + 0.438803i \(0.855403\pi\)
\(128\) 11.2808 0.862603i 0.997089 0.0762440i
\(129\) 9.06897i 0.798478i
\(130\) 8.00000 + 3.74571i 0.701646 + 0.328520i
\(131\) 5.75379 0.502711 0.251355 0.967895i \(-0.419124\pi\)
0.251355 + 0.967895i \(0.419124\pi\)
\(132\) −1.43845 + 1.19935i −0.125201 + 0.104390i
\(133\) −11.1231 15.2134i −0.964496 1.31917i
\(134\) 6.56155 14.0140i 0.566832 1.21063i
\(135\) 3.33513i 0.287042i
\(136\) 14.2462 3.74571i 1.22160 0.321192i
\(137\) 0.246211 0.0210352 0.0105176 0.999945i \(-0.496652\pi\)
0.0105176 + 0.999945i \(0.496652\pi\)
\(138\) −0.561553 + 1.19935i −0.0478025 + 0.102096i
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) −17.1231 4.27156i −1.44717 0.361013i
\(141\) −6.24621 −0.526026
\(142\) 2.31534 4.94506i 0.194299 0.414980i
\(143\) −1.75379 −0.146659
\(144\) −0.719224 + 3.93481i −0.0599353 + 0.327901i
\(145\) 6.67026i 0.553935i
\(146\) −4.00000 + 8.54312i −0.331042 + 0.707033i
\(147\) 2.12311 6.67026i 0.175111 0.550154i
\(148\) 1.43845 + 1.72521i 0.118240 + 0.141811i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) −7.84233 3.67188i −0.640323 0.299808i
\(151\) 9.06897i 0.738022i 0.929425 + 0.369011i \(0.120304\pi\)
−0.929425 + 0.369011i \(0.879696\pi\)
\(152\) −5.12311 19.4849i −0.415539 1.58044i
\(153\) 5.20798i 0.421041i
\(154\) 3.43845 0.673500i 0.277078 0.0542722i
\(155\) 0 0
\(156\) −2.87689 + 2.39871i −0.230336 + 0.192050i
\(157\) 21.8836i 1.74650i 0.487268 + 0.873252i \(0.337993\pi\)
−0.487268 + 0.873252i \(0.662007\pi\)
\(158\) 1.43845 3.07221i 0.114437 0.244412i
\(159\) −12.2462 −0.971188
\(160\) −15.3693 10.9418i −1.21505 0.865027i
\(161\) 2.00000 1.46228i 0.157622 0.115244i
\(162\) −1.28078 0.599676i −0.100627 0.0471150i
\(163\) 15.7392i 1.23279i −0.787436 0.616396i \(-0.788592\pi\)
0.787436 0.616396i \(-0.211408\pi\)
\(164\) −2.24621 + 1.87285i −0.175400 + 0.146245i
\(165\) 3.12311 0.243133
\(166\) 13.1231 + 6.14441i 1.01855 + 0.476899i
\(167\) 14.2462 1.10240 0.551202 0.834372i \(-0.314169\pi\)
0.551202 + 0.834372i \(0.314169\pi\)
\(168\) 4.71922 5.80766i 0.364096 0.448071i
\(169\) 9.49242 0.730186
\(170\) −22.2462 10.4160i −1.70621 0.798868i
\(171\) 7.12311 0.544718
\(172\) 13.9309 11.6153i 1.06222 0.885660i
\(173\) 16.6757i 1.26783i 0.773404 + 0.633913i \(0.218552\pi\)
−0.773404 + 0.633913i \(0.781448\pi\)
\(174\) −2.56155 1.19935i −0.194191 0.0909227i
\(175\) 9.56155 + 13.0776i 0.722785 + 0.988574i
\(176\) 3.68466 + 0.673500i 0.277742 + 0.0507670i
\(177\) −4.00000 −0.300658
\(178\) −0.876894 + 1.87285i −0.0657260 + 0.140376i
\(179\) 16.1498i 1.20709i 0.797328 + 0.603547i \(0.206246\pi\)
−0.797328 + 0.603547i \(0.793754\pi\)
\(180\) 5.12311 4.27156i 0.381854 0.318383i
\(181\) 1.87285i 0.139208i 0.997575 + 0.0696040i \(0.0221736\pi\)
−0.997575 + 0.0696040i \(0.977826\pi\)
\(182\) 6.87689 1.34700i 0.509749 0.0998463i
\(183\) 4.79741i 0.354635i
\(184\) 2.56155 0.673500i 0.188840 0.0496511i
\(185\) 3.74571i 0.275390i
\(186\) 0 0
\(187\) 4.87689 0.356634
\(188\) 8.00000 + 9.59482i 0.583460 + 0.699774i
\(189\) 1.56155 + 2.13578i 0.113586 + 0.155355i
\(190\) −14.2462 + 30.4268i −1.03353 + 2.20739i
\(191\) 2.80928i 0.203272i −0.994822 0.101636i \(-0.967592\pi\)
0.994822 0.101636i \(-0.0324078\pi\)
\(192\) 6.96543 3.93481i 0.502687 0.283970i
\(193\) −15.3693 −1.10631 −0.553154 0.833079i \(-0.686576\pi\)
−0.553154 + 0.833079i \(0.686576\pi\)
\(194\) 6.24621 13.3405i 0.448452 0.957794i
\(195\) 6.24621 0.447300
\(196\) −12.9654 + 5.28181i −0.926102 + 0.377272i
\(197\) −16.2462 −1.15749 −0.578747 0.815507i \(-0.696458\pi\)
−0.578747 + 0.815507i \(0.696458\pi\)
\(198\) −0.561553 + 1.19935i −0.0399078 + 0.0852343i
\(199\) −3.12311 −0.221391 −0.110696 0.993854i \(-0.535308\pi\)
−0.110696 + 0.993854i \(0.535308\pi\)
\(200\) 4.40388 + 16.7495i 0.311401 + 1.18437i
\(201\) 10.9418i 0.771777i
\(202\) −8.24621 + 17.6121i −0.580201 + 1.23918i
\(203\) 3.12311 + 4.27156i 0.219199 + 0.299805i
\(204\) 8.00000 6.67026i 0.560112 0.467012i
\(205\) 4.87689 0.340617
\(206\) 10.2462 + 4.79741i 0.713887 + 0.334251i
\(207\) 0.936426i 0.0650861i
\(208\) 7.36932 + 1.34700i 0.510970 + 0.0933976i
\(209\) 6.67026i 0.461392i
\(210\) −12.2462 + 2.39871i −0.845069 + 0.165526i
\(211\) 12.8147i 0.882199i −0.897458 0.441099i \(-0.854589\pi\)
0.897458 0.441099i \(-0.145411\pi\)
\(212\) 15.6847 + 18.8114i 1.07723 + 1.29197i
\(213\) 3.86098i 0.264550i
\(214\) 5.68466 12.1412i 0.388595 0.829954i
\(215\) −30.2462 −2.06277
\(216\) 0.719224 + 2.73546i 0.0489370 + 0.186124i
\(217\) 0 0
\(218\) 10.5616 + 4.94506i 0.715319 + 0.334922i
\(219\) 6.67026i 0.450735i
\(220\) −4.00000 4.79741i −0.269680 0.323441i
\(221\) 9.75379 0.656111
\(222\) 1.43845 + 0.673500i 0.0965423 + 0.0452024i
\(223\) 27.1231 1.81630 0.908149 0.418648i \(-0.137496\pi\)
0.908149 + 0.418648i \(0.137496\pi\)
\(224\) −14.9654 + 0.189103i −0.999920 + 0.0126350i
\(225\) −6.12311 −0.408207
\(226\) 5.43845 + 2.54635i 0.361760 + 0.169381i
\(227\) −16.4924 −1.09464 −0.547320 0.836923i \(-0.684352\pi\)
−0.547320 + 0.836923i \(0.684352\pi\)
\(228\) −9.12311 10.9418i −0.604192 0.724640i
\(229\) 5.61856i 0.371285i −0.982617 0.185642i \(-0.940563\pi\)
0.982617 0.185642i \(-0.0594366\pi\)
\(230\) −4.00000 1.87285i −0.263752 0.123492i
\(231\) 2.00000 1.46228i 0.131590 0.0962109i
\(232\) 1.43845 + 5.47091i 0.0944387 + 0.359183i
\(233\) 22.4924 1.47353 0.736764 0.676150i \(-0.236353\pi\)
0.736764 + 0.676150i \(0.236353\pi\)
\(234\) −1.12311 + 2.39871i −0.0734197 + 0.156808i
\(235\) 20.8319i 1.35893i
\(236\) 5.12311 + 6.14441i 0.333486 + 0.399967i
\(237\) 2.39871i 0.155813i
\(238\) −19.1231 + 3.74571i −1.23957 + 0.242798i
\(239\) 16.1498i 1.04464i −0.852748 0.522322i \(-0.825066\pi\)
0.852748 0.522322i \(-0.174934\pi\)
\(240\) −13.1231 2.39871i −0.847093 0.154836i
\(241\) 23.7565i 1.53029i −0.643858 0.765145i \(-0.722667\pi\)
0.643858 0.765145i \(-0.277333\pi\)
\(242\) −12.9654 6.07059i −0.833450 0.390232i
\(243\) −1.00000 −0.0641500
\(244\) 7.36932 6.14441i 0.471772 0.393356i
\(245\) 22.2462 + 7.08084i 1.42126 + 0.452378i
\(246\) −0.876894 + 1.87285i −0.0559087 + 0.119409i
\(247\) 13.3405i 0.848837i
\(248\) 0 0
\(249\) 10.2462 0.649327
\(250\) 2.24621 4.79741i 0.142063 0.303415i
\(251\) −5.75379 −0.363176 −0.181588 0.983375i \(-0.558124\pi\)
−0.181588 + 0.983375i \(0.558124\pi\)
\(252\) 1.28078 5.13416i 0.0806813 0.323422i
\(253\) 0.876894 0.0551299
\(254\) 5.93087 12.6670i 0.372136 0.794800i
\(255\) −17.3693 −1.08771
\(256\) −14.9654 5.66001i −0.935340 0.353751i
\(257\) 2.28343i 0.142436i −0.997461 0.0712181i \(-0.977311\pi\)
0.997461 0.0712181i \(-0.0226886\pi\)
\(258\) 5.43845 11.6153i 0.338583 0.723138i
\(259\) −1.75379 2.39871i −0.108975 0.149048i
\(260\) −8.00000 9.59482i −0.496139 0.595046i
\(261\) −2.00000 −0.123797
\(262\) −7.36932 3.45041i −0.455278 0.213167i
\(263\) 24.6929i 1.52263i 0.648382 + 0.761315i \(0.275446\pi\)
−0.648382 + 0.761315i \(0.724554\pi\)
\(264\) 2.56155 0.673500i 0.157653 0.0414511i
\(265\) 40.8427i 2.50895i
\(266\) 5.12311 + 26.1552i 0.314118 + 1.60368i
\(267\) 1.46228i 0.0894900i
\(268\) −16.8078 + 14.0140i −1.02670 + 0.856043i
\(269\) 10.8265i 0.660106i 0.943962 + 0.330053i \(0.107067\pi\)
−0.943962 + 0.330053i \(0.892933\pi\)
\(270\) 2.00000 4.27156i 0.121716 0.259959i
\(271\) −28.4924 −1.73079 −0.865396 0.501089i \(-0.832933\pi\)
−0.865396 + 0.501089i \(0.832933\pi\)
\(272\) −20.4924 3.74571i −1.24254 0.227117i
\(273\) 4.00000 2.92456i 0.242091 0.177002i
\(274\) −0.315342 0.147647i −0.0190505 0.00891969i
\(275\) 5.73384i 0.345763i
\(276\) 1.43845 1.19935i 0.0865843 0.0721926i
\(277\) −5.12311 −0.307818 −0.153909 0.988085i \(-0.549186\pi\)
−0.153909 + 0.988085i \(0.549186\pi\)
\(278\) 15.3693 + 7.19612i 0.921790 + 0.431594i
\(279\) 0 0
\(280\) 19.3693 + 15.7392i 1.15754 + 0.940599i
\(281\) 16.2462 0.969168 0.484584 0.874745i \(-0.338971\pi\)
0.484584 + 0.874745i \(0.338971\pi\)
\(282\) 8.00000 + 3.74571i 0.476393 + 0.223054i
\(283\) 8.87689 0.527677 0.263838 0.964567i \(-0.415011\pi\)
0.263838 + 0.964567i \(0.415011\pi\)
\(284\) −5.93087 + 4.94506i −0.351932 + 0.293435i
\(285\) 23.7565i 1.40721i
\(286\) 2.24621 + 1.05171i 0.132821 + 0.0621887i
\(287\) 3.12311 2.28343i 0.184351 0.134786i
\(288\) 3.28078 4.60831i 0.193322 0.271547i
\(289\) −10.1231 −0.595477
\(290\) 4.00000 8.54312i 0.234888 0.501669i
\(291\) 10.4160i 0.610595i
\(292\) 10.2462 8.54312i 0.599614 0.499948i
\(293\) 13.7511i 0.803348i −0.915783 0.401674i \(-0.868429\pi\)
0.915783 0.401674i \(-0.131571\pi\)
\(294\) −6.71922 + 7.26994i −0.391873 + 0.423992i
\(295\) 13.3405i 0.776716i
\(296\) −0.807764 3.07221i −0.0469503 0.178568i
\(297\) 0.936426i 0.0543370i
\(298\) 12.8078 + 5.99676i 0.741934 + 0.347383i
\(299\) 1.75379 0.101424
\(300\) 7.84233 + 9.40572i 0.452777 + 0.543039i
\(301\) −19.3693 + 14.1617i −1.11643 + 0.816265i
\(302\) 5.43845 11.6153i 0.312947 0.668387i
\(303\) 13.7511i 0.789980i
\(304\) −5.12311 + 28.0281i −0.293830 + 1.60752i
\(305\) −16.0000 −0.916157
\(306\) 3.12311 6.67026i 0.178536 0.381314i
\(307\) 19.6155 1.11952 0.559759 0.828656i \(-0.310894\pi\)
0.559759 + 0.828656i \(0.310894\pi\)
\(308\) −4.80776 1.19935i −0.273948 0.0683395i
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 5.12311 1.34700i 0.290039 0.0762589i
\(313\) 22.9354i 1.29638i 0.761478 + 0.648191i \(0.224474\pi\)
−0.761478 + 0.648191i \(0.775526\pi\)
\(314\) 13.1231 28.0281i 0.740580 1.58171i
\(315\) −7.12311 + 5.20798i −0.401342 + 0.293437i
\(316\) −3.68466 + 3.07221i −0.207278 + 0.172825i
\(317\) −14.4924 −0.813976 −0.406988 0.913434i \(-0.633421\pi\)
−0.406988 + 0.913434i \(0.633421\pi\)
\(318\) 15.6847 + 7.34376i 0.879552 + 0.411818i
\(319\) 1.87285i 0.104860i
\(320\) 13.1231 + 23.2306i 0.733604 + 1.29863i
\(321\) 9.47954i 0.529097i
\(322\) −3.43845 + 0.673500i −0.191617 + 0.0375327i
\(323\) 37.0970i 2.06413i
\(324\) 1.28078 + 1.53610i 0.0711542 + 0.0853390i
\(325\) 11.4677i 0.636112i
\(326\) −9.43845 + 20.1584i −0.522747 + 1.11647i
\(327\) 8.24621 0.456017
\(328\) 4.00000 1.05171i 0.220863 0.0580707i
\(329\) −9.75379 13.3405i −0.537744 0.735487i
\(330\) −4.00000 1.87285i −0.220193 0.103097i
\(331\) 17.6121i 0.968048i 0.875055 + 0.484024i \(0.160825\pi\)
−0.875055 + 0.484024i \(0.839175\pi\)
\(332\) −13.1231 15.7392i −0.720224 0.863803i
\(333\) 1.12311 0.0615458
\(334\) −18.2462 8.54312i −0.998388 0.467459i
\(335\) 36.4924 1.99379
\(336\) −9.52699 + 4.60831i −0.519740 + 0.251404i
\(337\) 8.24621 0.449200 0.224600 0.974451i \(-0.427892\pi\)
0.224600 + 0.974451i \(0.427892\pi\)
\(338\) −12.1577 5.69238i −0.661290 0.309625i
\(339\) 4.24621 0.230623
\(340\) 22.2462 + 26.6811i 1.20647 + 1.44698i
\(341\) 0 0
\(342\) −9.12311 4.27156i −0.493321 0.230979i
\(343\) 17.5616 5.88148i 0.948235 0.317570i
\(344\) −24.8078 + 6.52262i −1.33754 + 0.351676i
\(345\) −3.12311 −0.168142
\(346\) 10.0000 21.3578i 0.537603 1.14820i
\(347\) 20.1261i 1.08042i −0.841529 0.540212i \(-0.818344\pi\)
0.841529 0.540212i \(-0.181656\pi\)
\(348\) 2.56155 + 3.07221i 0.137314 + 0.164688i
\(349\) 21.8836i 1.17140i 0.810526 + 0.585702i \(0.199181\pi\)
−0.810526 + 0.585702i \(0.800819\pi\)
\(350\) −4.40388 22.4833i −0.235397 1.20178i
\(351\) 1.87285i 0.0999655i
\(352\) −4.31534 3.07221i −0.230008 0.163749i
\(353\) 28.9645i 1.54162i 0.637063 + 0.770812i \(0.280149\pi\)
−0.637063 + 0.770812i \(0.719851\pi\)
\(354\) 5.12311 + 2.39871i 0.272290 + 0.127490i
\(355\) 12.8769 0.683435
\(356\) 2.24621 1.87285i 0.119049 0.0992610i
\(357\) −11.1231 + 8.13254i −0.588697 + 0.430420i
\(358\) 9.68466 20.6843i 0.511850 1.09320i
\(359\) 22.8201i 1.20440i −0.798346 0.602199i \(-0.794292\pi\)
0.798346 0.602199i \(-0.205708\pi\)
\(360\) −9.12311 + 2.39871i −0.480830 + 0.126423i
\(361\) 31.7386 1.67045
\(362\) 1.12311 2.39871i 0.0590291 0.126073i
\(363\) −10.1231 −0.531325
\(364\) −9.61553 2.39871i −0.503991 0.125726i
\(365\) −22.2462 −1.16442
\(366\) 2.87689 6.14441i 0.150378 0.321174i
\(367\) −33.3693 −1.74186 −0.870932 0.491403i \(-0.836484\pi\)
−0.870932 + 0.491403i \(0.836484\pi\)
\(368\) −3.68466 0.673500i −0.192076 0.0351086i
\(369\) 1.46228i 0.0761232i
\(370\) −2.24621 + 4.79741i −0.116775 + 0.249406i
\(371\) −19.1231 26.1552i −0.992822 1.35791i
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) −6.24621 2.92456i −0.322984 0.151225i
\(375\) 3.74571i 0.193427i
\(376\) −4.49242 17.0862i −0.231679 0.881155i
\(377\) 3.74571i 0.192914i
\(378\) −0.719224 3.67188i −0.0369929 0.188861i
\(379\) 25.1035i 1.28948i 0.764402 + 0.644740i \(0.223034\pi\)
−0.764402 + 0.644740i \(0.776966\pi\)
\(380\) 36.4924 30.4268i 1.87202 1.56086i
\(381\) 9.89012i 0.506686i
\(382\) −1.68466 + 3.59806i −0.0861946 + 0.184093i
\(383\) −9.75379 −0.498395 −0.249198 0.968453i \(-0.580167\pi\)
−0.249198 + 0.968453i \(0.580167\pi\)
\(384\) −11.2808 + 0.862603i −0.575670 + 0.0440195i
\(385\) 4.87689 + 6.67026i 0.248550 + 0.339948i
\(386\) 19.6847 + 9.21662i 1.00192 + 0.469113i
\(387\) 9.06897i 0.461002i
\(388\) −16.0000 + 13.3405i −0.812277 + 0.677263i
\(389\) −16.2462 −0.823716 −0.411858 0.911248i \(-0.635120\pi\)
−0.411858 + 0.911248i \(0.635120\pi\)
\(390\) −8.00000 3.74571i −0.405096 0.189671i
\(391\) −4.87689 −0.246635
\(392\) 19.7732 + 1.01025i 0.998697 + 0.0510253i
\(393\) −5.75379 −0.290240
\(394\) 20.8078 + 9.74247i 1.04828 + 0.490819i
\(395\) 8.00000 0.402524
\(396\) 1.43845 1.19935i 0.0722847 0.0602697i
\(397\) 18.1379i 0.910317i −0.890410 0.455159i \(-0.849583\pi\)
0.890410 0.455159i \(-0.150417\pi\)
\(398\) 4.00000 + 1.87285i 0.200502 + 0.0938776i
\(399\) 11.1231 + 15.2134i 0.556852 + 0.761622i
\(400\) 4.40388 24.0932i 0.220194 1.20466i
\(401\) 8.24621 0.411796 0.205898 0.978573i \(-0.433988\pi\)
0.205898 + 0.978573i \(0.433988\pi\)
\(402\) −6.56155 + 14.0140i −0.327261 + 0.698956i
\(403\) 0 0
\(404\) 21.1231 17.6121i 1.05091 0.876234i
\(405\) 3.33513i 0.165724i
\(406\) −1.43845 7.34376i −0.0713889 0.364465i
\(407\) 1.05171i 0.0521311i
\(408\) −14.2462 + 3.74571i −0.705293 + 0.185440i
\(409\) 0.821147i 0.0406031i 0.999794 + 0.0203016i \(0.00646263\pi\)
−0.999794 + 0.0203016i \(0.993537\pi\)
\(410\) −6.24621 2.92456i −0.308478 0.144434i
\(411\) −0.246211 −0.0121447
\(412\) −10.2462 12.2888i −0.504795 0.605427i
\(413\) −6.24621 8.54312i −0.307356 0.420379i
\(414\) 0.561553 1.19935i 0.0275988 0.0589450i
\(415\) 34.1725i 1.67746i
\(416\) −8.63068 6.14441i −0.423154 0.301255i
\(417\) 12.0000 0.587643
\(418\) −4.00000 + 8.54312i −0.195646 + 0.417858i
\(419\) −16.4924 −0.805708 −0.402854 0.915264i \(-0.631982\pi\)
−0.402854 + 0.915264i \(0.631982\pi\)
\(420\) 17.1231 + 4.27156i 0.835522 + 0.208431i
\(421\) 10.8769 0.530107 0.265054 0.964234i \(-0.414610\pi\)
0.265054 + 0.964234i \(0.414610\pi\)
\(422\) −7.68466 + 16.4127i −0.374083 + 0.798959i
\(423\) 6.24621 0.303701
\(424\) −8.80776 33.4990i −0.427743 1.62685i
\(425\) 31.8890i 1.54685i
\(426\) −2.31534 + 4.94506i −0.112179 + 0.239589i
\(427\) −10.2462 + 7.49141i −0.495849 + 0.362535i
\(428\) −14.5616 + 12.1412i −0.703859 + 0.586866i
\(429\) 1.75379 0.0846737
\(430\) 38.7386 + 18.1379i 1.86814 + 0.874689i
\(431\) 4.68213i 0.225530i 0.993622 + 0.112765i \(0.0359708\pi\)
−0.993622 + 0.112765i \(0.964029\pi\)
\(432\) 0.719224 3.93481i 0.0346037 0.189314i
\(433\) 13.3405i 0.641105i 0.947231 + 0.320552i \(0.103869\pi\)
−0.947231 + 0.320552i \(0.896131\pi\)
\(434\) 0 0
\(435\) 6.67026i 0.319815i
\(436\) −10.5616 12.6670i −0.505807 0.606641i
\(437\) 6.67026i 0.319082i
\(438\) 4.00000 8.54312i 0.191127 0.408206i
\(439\) −6.63068 −0.316465 −0.158233 0.987402i \(-0.550580\pi\)
−0.158233 + 0.987402i \(0.550580\pi\)
\(440\) 2.24621 + 8.54312i 0.107084 + 0.407277i
\(441\) −2.12311 + 6.67026i −0.101100 + 0.317632i
\(442\) −12.4924 5.84912i −0.594204 0.278214i
\(443\) 18.8438i 0.895296i −0.894210 0.447648i \(-0.852262\pi\)
0.894210 0.447648i \(-0.147738\pi\)
\(444\) −1.43845 1.72521i −0.0682657 0.0818746i
\(445\) −4.87689 −0.231187
\(446\) −34.7386 16.2651i −1.64492 0.770174i
\(447\) 10.0000 0.472984
\(448\) 19.2808 + 8.73222i 0.910931 + 0.412559i
\(449\) 11.7538 0.554696 0.277348 0.960770i \(-0.410545\pi\)
0.277348 + 0.960770i \(0.410545\pi\)
\(450\) 7.84233 + 3.67188i 0.369691 + 0.173094i
\(451\) 1.36932 0.0644786
\(452\) −5.43845 6.52262i −0.255803 0.306798i
\(453\) 9.06897i 0.426097i
\(454\) 21.1231 + 9.89012i 0.991356 + 0.464166i
\(455\) 9.75379 + 13.3405i 0.457265 + 0.625414i
\(456\) 5.12311 + 19.4849i 0.239911 + 0.912466i
\(457\) 0.246211 0.0115173 0.00575864 0.999983i \(-0.498167\pi\)
0.00575864 + 0.999983i \(0.498167\pi\)
\(458\) −3.36932 + 7.19612i −0.157438 + 0.336252i
\(459\) 5.20798i 0.243088i
\(460\) 4.00000 + 4.79741i 0.186501 + 0.223680i
\(461\) 6.25969i 0.291543i 0.989318 + 0.145771i \(0.0465664\pi\)
−0.989318 + 0.145771i \(0.953434\pi\)
\(462\) −3.43845 + 0.673500i −0.159971 + 0.0313341i
\(463\) 39.2652i 1.82481i −0.409292 0.912404i \(-0.634224\pi\)
0.409292 0.912404i \(-0.365776\pi\)
\(464\) 1.43845 7.86962i 0.0667782 0.365338i
\(465\) 0 0
\(466\) −28.8078 13.4882i −1.33449 0.624828i
\(467\) 34.2462 1.58473 0.792363 0.610050i \(-0.208851\pi\)
0.792363 + 0.610050i \(0.208851\pi\)
\(468\) 2.87689 2.39871i 0.132984 0.110880i
\(469\) 23.3693 17.0862i 1.07909 0.788969i
\(470\) −12.4924 + 26.6811i −0.576232 + 1.23071i
\(471\) 21.8836i 1.00835i
\(472\) −2.87689 10.9418i −0.132420 0.503638i
\(473\) −8.49242 −0.390482
\(474\) −1.43845 + 3.07221i −0.0660701 + 0.141111i
\(475\) −43.6155 −2.00122
\(476\) 26.7386 + 6.67026i 1.22556 + 0.305731i
\(477\) 12.2462 0.560715
\(478\) −9.68466 + 20.6843i −0.442966 + 0.946077i
\(479\) 12.4924 0.570793 0.285397 0.958409i \(-0.407875\pi\)
0.285397 + 0.958409i \(0.407875\pi\)
\(480\) 15.3693 + 10.9418i 0.701510 + 0.499424i
\(481\) 2.10341i 0.0959073i
\(482\) −14.2462 + 30.4268i −0.648897 + 1.38590i
\(483\) −2.00000 + 1.46228i −0.0910032 + 0.0665360i
\(484\) 12.9654 + 15.5501i 0.589338 + 0.706824i
\(485\) 34.7386 1.57740
\(486\) 1.28078 + 0.599676i 0.0580972 + 0.0272019i
\(487\) 1.57756i 0.0714860i 0.999361 + 0.0357430i \(0.0113798\pi\)
−0.999361 + 0.0357430i \(0.988620\pi\)
\(488\) −13.1231 + 3.45041i −0.594055 + 0.156193i
\(489\) 15.7392i 0.711753i
\(490\) −24.2462 22.4095i −1.09533 1.01236i
\(491\) 11.3524i 0.512326i −0.966634 0.256163i \(-0.917542\pi\)
0.966634 0.256163i \(-0.0824585\pi\)
\(492\) 2.24621 1.87285i 0.101267 0.0844347i
\(493\) 10.4160i 0.469112i
\(494\) −8.00000 + 17.0862i −0.359937 + 0.768746i
\(495\) −3.12311 −0.140373
\(496\) 0 0
\(497\) 8.24621 6.02913i 0.369893 0.270444i
\(498\) −13.1231 6.14441i −0.588060 0.275338i
\(499\) 13.8664i 0.620744i 0.950615 + 0.310372i \(0.100454\pi\)
−0.950615 + 0.310372i \(0.899546\pi\)
\(500\) −5.75379 + 4.79741i −0.257317 + 0.214547i
\(501\) −14.2462 −0.636474
\(502\) 7.36932 + 3.45041i 0.328909 + 0.153999i
\(503\) −26.7386 −1.19222 −0.596108 0.802904i \(-0.703287\pi\)
−0.596108 + 0.802904i \(0.703287\pi\)
\(504\) −4.71922 + 5.80766i −0.210211 + 0.258694i
\(505\) −45.8617 −2.04082
\(506\) −1.12311 0.525853i −0.0499281 0.0233770i
\(507\) −9.49242 −0.421573
\(508\) −15.1922 + 12.6670i −0.674046 + 0.562008i
\(509\) 3.33513i 0.147827i 0.997265 + 0.0739136i \(0.0235489\pi\)
−0.997265 + 0.0739136i \(0.976451\pi\)
\(510\) 22.2462 + 10.4160i 0.985079 + 0.461227i
\(511\) −14.2462 + 10.4160i −0.630215 + 0.460775i
\(512\) 15.7732 + 16.2236i 0.697083 + 0.716990i
\(513\) −7.12311 −0.314493
\(514\) −1.36932 + 2.92456i −0.0603980 + 0.128997i
\(515\) 26.6811i 1.17571i
\(516\) −13.9309 + 11.6153i −0.613272 + 0.511336i
\(517\) 5.84912i 0.257244i
\(518\) 0.807764 + 4.12391i 0.0354911 + 0.181194i
\(519\) 16.6757i 0.731980i
\(520\) 4.49242 + 17.0862i 0.197006 + 0.749281i
\(521\) 29.7856i 1.30493i −0.757818 0.652466i \(-0.773734\pi\)
0.757818 0.652466i \(-0.226266\pi\)
\(522\) 2.56155 + 1.19935i 0.112116 + 0.0524942i
\(523\) 32.4924 1.42079 0.710397 0.703801i \(-0.248515\pi\)
0.710397 + 0.703801i \(0.248515\pi\)
\(524\) 7.36932 + 8.83841i 0.321930 + 0.386108i
\(525\) −9.56155 13.0776i −0.417300 0.570753i
\(526\) 14.8078 31.6261i 0.645649 1.37896i
\(527\) 0 0
\(528\) −3.68466 0.673500i −0.160354 0.0293103i
\(529\) 22.1231 0.961874
\(530\) −24.4924 + 52.3104i −1.06388 + 2.27222i
\(531\) 4.00000 0.173585
\(532\) 9.12311 36.5712i 0.395537 1.58556i
\(533\) 2.73863 0.118623
\(534\) 0.876894 1.87285i 0.0379469 0.0810463i
\(535\) 31.6155 1.36686
\(536\) 29.9309 7.86962i 1.29282 0.339916i
\(537\) 16.1498i 0.696916i
\(538\) 6.49242 13.8664i 0.279908 0.597822i
\(539\) 6.24621 + 1.98813i 0.269043 + 0.0856349i
\(540\) −5.12311 + 4.27156i −0.220463 + 0.183819i
\(541\) 2.87689 0.123687 0.0618437 0.998086i \(-0.480302\pi\)
0.0618437 + 0.998086i \(0.480302\pi\)
\(542\) 36.4924 + 17.0862i 1.56748 + 0.733917i
\(543\) 1.87285i 0.0803718i
\(544\) 24.0000 + 17.0862i 1.02899 + 0.732566i
\(545\) 27.5022i 1.17806i
\(546\) −6.87689 + 1.34700i −0.294304 + 0.0576463i
\(547\) 16.7909i 0.717929i 0.933351 + 0.358964i \(0.116870\pi\)
−0.933351 + 0.358964i \(0.883130\pi\)
\(548\) 0.315342 + 0.378206i 0.0134707 + 0.0161562i
\(549\) 4.79741i 0.204749i
\(550\) 3.43845 7.34376i 0.146616 0.313139i
\(551\) −14.2462 −0.606909
\(552\) −2.56155 + 0.673500i −0.109027 + 0.0286661i
\(553\) 5.12311 3.74571i 0.217857 0.159284i
\(554\) 6.56155 + 3.07221i 0.278774 + 0.130526i
\(555\) 3.74571i 0.158996i
\(556\) −15.3693 18.4332i −0.651804 0.781743i
\(557\) 14.0000 0.593199 0.296600 0.955002i \(-0.404147\pi\)
0.296600 + 0.955002i \(0.404147\pi\)
\(558\) 0 0
\(559\) −16.9848 −0.718382
\(560\) −15.3693 31.7738i −0.649472 1.34269i
\(561\) −4.87689 −0.205903
\(562\) −20.8078 9.74247i −0.877723 0.410961i
\(563\) 2.24621 0.0946665 0.0473333 0.998879i \(-0.484928\pi\)
0.0473333 + 0.998879i \(0.484928\pi\)
\(564\) −8.00000 9.59482i −0.336861 0.404015i
\(565\) 14.1617i 0.595786i
\(566\) −11.3693 5.32326i −0.477888 0.223753i
\(567\) −1.56155 2.13578i −0.0655791 0.0896943i
\(568\) 10.5616 2.77691i 0.443153 0.116517i
\(569\) −30.9848 −1.29895 −0.649476 0.760382i \(-0.725012\pi\)
−0.649476 + 0.760382i \(0.725012\pi\)
\(570\) 14.2462 30.4268i 0.596708 1.27444i
\(571\) 8.83841i 0.369876i 0.982750 + 0.184938i \(0.0592084\pi\)
−0.982750 + 0.184938i \(0.940792\pi\)
\(572\) −2.24621 2.69400i −0.0939188 0.112642i
\(573\) 2.80928i 0.117359i
\(574\) −5.36932 + 1.05171i −0.224111 + 0.0438973i
\(575\) 5.73384i 0.239118i
\(576\) −6.96543 + 3.93481i −0.290226 + 0.163950i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 12.9654 + 6.07059i 0.539291 + 0.252503i
\(579\) 15.3693 0.638727
\(580\) −10.2462 + 8.54312i −0.425451 + 0.354734i
\(581\) 16.0000 + 21.8836i 0.663792 + 0.907887i
\(582\) −6.24621 + 13.3405i −0.258914 + 0.552983i
\(583\) 11.4677i 0.474943i
\(584\) −18.2462 + 4.79741i −0.755034 + 0.198518i
\(585\) −6.24621 −0.258249
\(586\) −8.24621 + 17.6121i −0.340648 + 0.727549i
\(587\) −21.7538 −0.897875 −0.448937 0.893563i \(-0.648197\pi\)
−0.448937 + 0.893563i \(0.648197\pi\)
\(588\) 12.9654 5.28181i 0.534686 0.217818i
\(589\) 0 0
\(590\) −8.00000 + 17.0862i −0.329355 + 0.703429i
\(591\) 16.2462 0.668280
\(592\) −0.807764 + 4.41921i −0.0331989 + 0.181628i
\(593\) 26.0399i 1.06933i 0.845064 + 0.534666i \(0.179562\pi\)
−0.845064 + 0.534666i \(0.820438\pi\)
\(594\) 0.561553 1.19935i 0.0230408 0.0492100i
\(595\) −27.1231 37.0970i −1.11194 1.52083i
\(596\) −12.8078 15.3610i −0.524626 0.629212i
\(597\) 3.12311 0.127820
\(598\) −2.24621 1.05171i −0.0918544 0.0430074i
\(599\) 17.2015i 0.702835i 0.936219 + 0.351417i \(0.114300\pi\)
−0.936219 + 0.351417i \(0.885700\pi\)
\(600\) −4.40388 16.7495i −0.179788 0.683795i
\(601\) 17.0862i 0.696962i 0.937316 + 0.348481i \(0.113302\pi\)
−0.937316 + 0.348481i \(0.886698\pi\)
\(602\) 33.3002 6.52262i 1.35721 0.265842i
\(603\) 10.9418i 0.445585i
\(604\) −13.9309 + 11.6153i −0.566839 + 0.472621i
\(605\) 33.7619i 1.37262i
\(606\) 8.24621 17.6121i 0.334979 0.715442i
\(607\) 7.61553 0.309105 0.154552 0.987985i \(-0.450606\pi\)
0.154552 + 0.987985i \(0.450606\pi\)
\(608\) 23.3693 32.8255i 0.947751 1.33125i
\(609\) −3.12311 4.27156i −0.126555 0.173092i
\(610\) 20.4924 + 9.59482i 0.829714 + 0.388483i
\(611\) 11.6982i 0.473260i
\(612\) −8.00000 + 6.67026i −0.323381 + 0.269629i
\(613\) 8.73863 0.352950 0.176475 0.984305i \(-0.443531\pi\)
0.176475 + 0.984305i \(0.443531\pi\)
\(614\) −25.1231 11.7630i −1.01389 0.474715i
\(615\) −4.87689 −0.196655
\(616\) 5.43845 + 4.41921i 0.219121 + 0.178055i
\(617\) 32.2462 1.29818 0.649092 0.760710i \(-0.275149\pi\)
0.649092 + 0.760710i \(0.275149\pi\)
\(618\) −10.2462 4.79741i −0.412163 0.192980i
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) 0.936426i 0.0375775i
\(622\) −10.2462 4.79741i −0.410836 0.192359i
\(623\) −3.12311 + 2.28343i −0.125125 + 0.0914835i
\(624\) −7.36932 1.34700i −0.295009 0.0539232i
\(625\) −18.1231 −0.724924
\(626\) 13.7538 29.3751i 0.549712 1.17406i
\(627\) 6.67026i 0.266385i
\(628\) −33.6155 + 28.0281i −1.34141 + 1.11844i
\(629\) 5.84912i 0.233220i
\(630\) 12.2462 2.39871i 0.487901 0.0955667i
\(631\) 40.3169i 1.60499i 0.596659 + 0.802495i \(0.296494\pi\)
−0.596659 + 0.802495i \(0.703506\pi\)
\(632\) 6.56155 1.72521i 0.261005 0.0686250i
\(633\) 12.8147i 0.509338i
\(634\) 18.5616 + 8.69076i 0.737173 + 0.345154i
\(635\) 32.9848 1.30896
\(636\) −15.6847 18.8114i −0.621937 0.745922i
\(637\) 12.4924 + 3.97626i 0.494968 + 0.157545i
\(638\) 1.12311 2.39871i 0.0444642 0.0949657i
\(639\) 3.86098i 0.152738i
\(640\) −2.87689 37.6229i −0.113719 1.48717i
\(641\) −42.4924 −1.67835 −0.839175 0.543862i \(-0.816962\pi\)
−0.839175 + 0.543862i \(0.816962\pi\)
\(642\) −5.68466 + 12.1412i −0.224356 + 0.479174i
\(643\) −11.6155 −0.458072 −0.229036 0.973418i \(-0.573557\pi\)
−0.229036 + 0.973418i \(0.573557\pi\)
\(644\) 4.80776 + 1.19935i 0.189452 + 0.0472611i
\(645\) 30.2462 1.19094
\(646\) 22.2462 47.5130i 0.875265 1.86937i
\(647\) −32.9848 −1.29677 −0.648384 0.761313i \(-0.724555\pi\)
−0.648384 + 0.761313i \(0.724555\pi\)
\(648\) −0.719224 2.73546i −0.0282538 0.107459i
\(649\) 3.74571i 0.147032i
\(650\) 6.87689 14.6875i 0.269734 0.576092i
\(651\) 0 0
\(652\) 24.1771 20.1584i 0.946848 0.789465i
\(653\) 16.7386 0.655033 0.327517 0.944845i \(-0.393788\pi\)
0.327517 + 0.944845i \(0.393788\pi\)
\(654\) −10.5616 4.94506i −0.412989 0.193367i
\(655\) 19.1896i 0.749801i
\(656\) −5.75379 1.05171i −0.224648 0.0410622i
\(657\) 6.67026i 0.260232i
\(658\) 4.49242 + 22.9354i 0.175133 + 0.894113i
\(659\) 26.7963i 1.04384i −0.852995 0.521919i \(-0.825217\pi\)
0.852995 0.521919i \(-0.174783\pi\)
\(660\) 4.00000 + 4.79741i 0.155700 + 0.186739i
\(661\) 8.54312i 0.332289i −0.986101 0.166144i \(-0.946868\pi\)
0.986101 0.166144i \(-0.0531318\pi\)
\(662\) 10.5616 22.5571i 0.410486 0.876708i
\(663\) −9.75379 −0.378806
\(664\) 7.36932 + 28.0281i 0.285985 + 1.08770i
\(665\) −50.7386 + 37.0970i −1.96756 + 1.43856i
\(666\) −1.43845 0.673500i −0.0557387 0.0260976i
\(667\) 1.87285i 0.0725171i
\(668\) 18.2462 + 21.8836i 0.705967 + 0.846704i
\(669\) −27.1231 −1.04864
\(670\) −46.7386 21.8836i −1.80567 0.845439i
\(671\) −4.49242 −0.173428
\(672\) 14.9654 0.189103i 0.577304 0.00729480i
\(673\) −27.8617 −1.07399 −0.536996 0.843585i \(-0.680441\pi\)
−0.536996 + 0.843585i \(0.680441\pi\)
\(674\) −10.5616 4.94506i −0.406816 0.190477i
\(675\) 6.12311 0.235678
\(676\) 12.1577 + 14.5813i 0.467603 + 0.560821i
\(677\) 9.18425i 0.352979i −0.984302 0.176490i \(-0.943526\pi\)
0.984302 0.176490i \(-0.0564742\pi\)
\(678\) −5.43845 2.54635i −0.208862 0.0977921i
\(679\) 22.2462 16.2651i 0.853731 0.624197i
\(680\) −12.4924 47.5130i −0.479063 1.82204i
\(681\) 16.4924 0.631991
\(682\) 0 0
\(683\) 32.1843i 1.23150i −0.787942 0.615750i \(-0.788853\pi\)
0.787942 0.615750i \(-0.211147\pi\)
\(684\) 9.12311 + 10.9418i 0.348831 + 0.418371i
\(685\) 0.821147i 0.0313744i
\(686\) −26.0194 2.99838i −0.993426 0.114479i
\(687\) 5.61856i 0.214361i
\(688\) 35.6847 + 6.52262i 1.36046 + 0.248672i
\(689\) 22.9354i 0.873767i
\(690\) 4.00000 + 1.87285i 0.152277 + 0.0712983i
\(691\) 12.0000 0.456502 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) −25.6155 + 21.3578i −0.973756 + 0.811901i
\(693\) −2.00000 + 1.46228i −0.0759737 + 0.0555474i
\(694\) −12.0691 + 25.7770i −0.458138 + 0.978481i
\(695\) 40.0216i 1.51811i
\(696\) −1.43845 5.47091i −0.0545242 0.207374i
\(697\) −7.61553 −0.288459
\(698\) 13.1231 28.0281i 0.496717 1.06088i
\(699\) −22.4924 −0.850742
\(700\) −7.84233 + 31.4370i −0.296412 + 1.18821i
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) 1.12311 2.39871i 0.0423889 0.0905333i
\(703\) 8.00000 0.301726
\(704\) 3.68466 + 6.52262i 0.138871 + 0.245830i
\(705\) 20.8319i 0.784576i
\(706\) 17.3693 37.0970i 0.653703 1.39616i
\(707\) −29.3693 + 21.4731i −1.10455 + 0.807578i
\(708\) −5.12311 6.14441i −0.192538 0.230921i
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) −16.4924 7.72197i −0.618950 0.289800i
\(711\) 2.39871i 0.0899585i
\(712\) −4.00000 + 1.05171i −0.149906 + 0.0394143i
\(713\) 0 0
\(714\) 19.1231 3.74571i 0.715664 0.140180i
\(715\) 5.84912i 0.218745i
\(716\) −24.8078 + 20.6843i −0.927110 + 0.773008i
\(717\) 16.1498i 0.603126i
\(718\) −13.6847 + 29.2274i −0.510707 + 1.09076i
\(719\) 28.4924 1.06259 0.531294 0.847187i \(-0.321706\pi\)
0.531294 + 0.847187i \(0.321706\pi\)
\(720\) 13.1231 + 2.39871i 0.489069 + 0.0893945i
\(721\) 12.4924 + 17.0862i 0.465242 + 0.636325i
\(722\) −40.6501 19.0329i −1.51284 0.708332i
\(723\) 23.7565i 0.883514i
\(724\) −2.87689 + 2.39871i −0.106919 + 0.0891472i
\(725\) 12.2462 0.454813
\(726\) 12.9654 + 6.07059i 0.481192 + 0.225301i
\(727\) 32.9848 1.22334 0.611670 0.791113i \(-0.290498\pi\)
0.611670 + 0.791113i \(0.290498\pi\)
\(728\) 10.8769 + 8.83841i 0.403125 + 0.327573i
\(729\) 1.00000 0.0370370
\(730\) 28.4924 + 13.3405i 1.05455 + 0.493755i
\(731\) 47.2311 1.74690
\(732\) −7.36932 + 6.14441i −0.272378 + 0.227104i
\(733\) 36.0453i 1.33136i −0.746235 0.665682i \(-0.768141\pi\)
0.746235 0.665682i \(-0.231859\pi\)
\(734\) 42.7386 + 20.0108i 1.57751 + 0.738612i
\(735\) −22.2462 7.08084i −0.820564 0.261181i
\(736\) 4.31534 + 3.07221i 0.159066 + 0.113243i
\(737\) 10.2462 0.377424
\(738\) 0.876894 1.87285i 0.0322789 0.0689407i
\(739\) 36.5712i 1.34529i −0.739964 0.672646i \(-0.765158\pi\)
0.739964 0.672646i \(-0.234842\pi\)
\(740\) 5.75379 4.79741i 0.211513 0.176356i
\(741\) 13.3405i 0.490077i
\(742\) 8.80776 + 44.9666i 0.323343 + 1.65078i
\(743\) 35.1089i 1.28802i 0.765017 + 0.644010i \(0.222731\pi\)
−0.765017 + 0.644010i \(0.777269\pi\)
\(744\) 0 0
\(745\) 33.3513i 1.22190i
\(746\) 12.8078 + 5.99676i 0.468926 + 0.219557i
\(747\) −10.2462 −0.374889
\(748\) 6.24621 + 7.49141i 0.228384 + 0.273913i
\(749\) 20.2462 14.8028i 0.739780 0.540883i
\(750\) −2.24621 + 4.79741i −0.0820200 + 0.175177i
\(751\) 28.8492i 1.05272i −0.850261 0.526361i \(-0.823556\pi\)
0.850261 0.526361i \(-0.176444\pi\)
\(752\) −4.49242 + 24.5776i −0.163822 + 0.896254i
\(753\) 5.75379 0.209680
\(754\) 2.24621 4.79741i 0.0818022 0.174711i
\(755\) 30.2462 1.10077
\(756\) −1.28078 + 5.13416i −0.0465814 + 0.186728i
\(757\) −34.9848 −1.27155 −0.635773 0.771876i \(-0.719319\pi\)
−0.635773 + 0.771876i \(0.719319\pi\)
\(758\) 15.0540 32.1520i 0.546785 1.16781i
\(759\) −0.876894 −0.0318292
\(760\) −64.9848 + 17.0862i −2.35725 + 0.619783i
\(761\) 29.7856i 1.07973i 0.841752 + 0.539864i \(0.181524\pi\)
−0.841752 + 0.539864i \(0.818476\pi\)
\(762\) −5.93087 + 12.6670i −0.214853 + 0.458878i
\(763\) 12.8769 + 17.6121i 0.466175 + 0.637600i
\(764\) 4.31534 3.59806i 0.156124 0.130173i
\(765\) 17.3693 0.627989
\(766\) 12.4924 + 5.84912i 0.451370 + 0.211337i
\(767\) 7.49141i 0.270499i
\(768\) 14.9654 + 5.66001i 0.540019 + 0.204238i
\(769\) 32.5302i 1.17307i 0.809925 + 0.586534i \(0.199508\pi\)
−0.809925 + 0.586534i \(0.800492\pi\)
\(770\) −2.24621 11.4677i −0.0809478 0.413266i
\(771\) 2.28343i 0.0822356i
\(772\) −19.6847 23.6089i −0.708466 0.849701i
\(773\) 3.33513i 0.119956i −0.998200 0.0599782i \(-0.980897\pi\)
0.998200 0.0599782i \(-0.0191031\pi\)
\(774\) −5.43845 + 11.6153i −0.195481 + 0.417504i
\(775\) 0 0
\(776\) 28.4924 7.49141i 1.02282 0.268926i
\(777\) 1.75379 + 2.39871i 0.0629168 + 0.0860531i
\(778\) 20.8078 + 9.74247i 0.745994 + 0.349284i
\(779\) 10.4160i 0.373191i
\(780\) 8.00000 +