Properties

Label 105.3.t.b.86.9
Level 105
Weight 3
Character 105.86
Analytic conductor 2.861
Analytic rank 0
Dimension 36
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 86.9
Character \(\chi\) \(=\) 105.86
Dual form 105.3.t.b.11.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.644768 - 0.372257i) q^{2} +(-2.67627 - 1.35556i) q^{3} +(-1.72285 - 2.98406i) q^{4} +(1.93649 + 1.11803i) q^{5} +(1.22096 + 1.87029i) q^{6} +(-5.98242 + 3.63464i) q^{7} +5.54343i q^{8} +(5.32489 + 7.25573i) q^{9} +O(q^{10})\) \(q+(-0.644768 - 0.372257i) q^{2} +(-2.67627 - 1.35556i) q^{3} +(-1.72285 - 2.98406i) q^{4} +(1.93649 + 1.11803i) q^{5} +(1.22096 + 1.87029i) q^{6} +(-5.98242 + 3.63464i) q^{7} +5.54343i q^{8} +(5.32489 + 7.25573i) q^{9} +(-0.832392 - 1.44175i) q^{10} +(-8.35340 + 4.82284i) q^{11} +(0.565728 + 10.3216i) q^{12} -0.0661184 q^{13} +(5.21030 - 0.116499i) q^{14} +(-3.66702 - 5.61721i) q^{15} +(-4.82782 + 8.36202i) q^{16} +(-28.1197 + 16.2349i) q^{17} +(-0.732324 - 6.66049i) q^{18} +(12.7759 - 22.1286i) q^{19} -7.70482i q^{20} +(20.9376 - 1.61772i) q^{21} +7.18134 q^{22} +(-8.49789 - 4.90626i) q^{23} +(7.51448 - 14.8357i) q^{24} +(2.50000 + 4.33013i) q^{25} +(0.0426310 + 0.0246130i) q^{26} +(-4.41526 - 26.6365i) q^{27} +(21.1528 + 11.5900i) q^{28} +6.58972i q^{29} +(0.273330 + 4.98687i) q^{30} +(-16.4028 - 28.4105i) q^{31} +(25.4286 - 14.6812i) q^{32} +(28.8937 - 1.58366i) q^{33} +24.1742 q^{34} +(-15.6486 + 0.349891i) q^{35} +(12.4776 - 28.3903i) q^{36} +(-27.3632 + 47.3945i) q^{37} +(-16.4751 + 9.51187i) q^{38} +(0.176951 + 0.0896278i) q^{39} +(-6.19774 + 10.7348i) q^{40} -14.8128i q^{41} +(-14.1021 - 6.75111i) q^{42} -14.3286 q^{43} +(28.7833 + 16.6180i) q^{44} +(2.19945 + 20.0041i) q^{45} +(3.65278 + 6.32680i) q^{46} +(-63.7562 - 36.8097i) q^{47} +(24.2558 - 15.8347i) q^{48} +(22.5788 - 43.4879i) q^{49} -3.72257i q^{50} +(97.2635 - 5.33102i) q^{51} +(0.113912 + 0.197301i) q^{52} +(44.3287 - 25.5932i) q^{53} +(-7.06882 + 18.8180i) q^{54} -21.5684 q^{55} +(-20.1484 - 33.1631i) q^{56} +(-64.1887 + 41.9036i) q^{57} +(2.45307 - 4.24884i) q^{58} +(-75.2379 + 43.4386i) q^{59} +(-10.4444 + 20.6202i) q^{60} +(-12.5191 + 21.6838i) q^{61} +24.4242i q^{62} +(-58.2277 - 24.0528i) q^{63} +16.7618 q^{64} +(-0.128038 - 0.0739226i) q^{65} +(-19.2192 - 9.73477i) q^{66} +(24.0411 + 41.6403i) q^{67} +(96.8920 + 55.9406i) q^{68} +(16.0919 + 24.6499i) q^{69} +(10.2199 + 5.59969i) q^{70} +113.723i q^{71} +(-40.2216 + 29.5181i) q^{72} +(-21.2034 - 36.7253i) q^{73} +(35.2859 - 20.3723i) q^{74} +(-0.820919 - 14.9775i) q^{75} -88.0441 q^{76} +(32.4443 - 59.2138i) q^{77} +(-0.0807278 - 0.123660i) q^{78} +(9.49104 - 16.4390i) q^{79} +(-18.6981 + 10.7953i) q^{80} +(-24.2911 + 77.2719i) q^{81} +(-5.51416 + 9.55080i) q^{82} -46.8063i q^{83} +(-40.8997 - 59.6920i) q^{84} -72.6047 q^{85} +(9.23863 + 5.33393i) q^{86} +(8.93279 - 17.6359i) q^{87} +(-26.7350 - 46.3065i) q^{88} +(45.4566 + 26.2444i) q^{89} +(6.02851 - 13.7167i) q^{90} +(0.395548 - 0.240316i) q^{91} +33.8110i q^{92} +(5.38615 + 98.2693i) q^{93} +(27.4053 + 47.4674i) q^{94} +(49.4810 - 28.5679i) q^{95} +(-87.9554 + 4.82084i) q^{96} +147.764 q^{97} +(-30.7468 + 19.6345i) q^{98} +(-79.4741 - 34.9289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + O(q^{10}) \) \( 36q + 4q^{3} + 36q^{4} - 24q^{6} - 58q^{7} - 2q^{9} + 20q^{10} - 42q^{12} - 100q^{13} + 20q^{15} - 12q^{16} - 14q^{18} + 50q^{19} - 12q^{21} + 256q^{22} - 140q^{24} + 90q^{25} + 4q^{27} - 48q^{28} + 60q^{30} - 82q^{31} - 76q^{33} - 64q^{34} + 296q^{36} - 26q^{37} - 130q^{39} - 60q^{40} - 98q^{42} - 204q^{43} + 40q^{45} + 28q^{46} + 532q^{48} - 382q^{49} + 208q^{51} + 200q^{52} - 44q^{54} - 160q^{55} + 252q^{57} + 264q^{58} - 130q^{60} - 324q^{61} - 258q^{63} - 24q^{64} - 164q^{66} - 142q^{67} - 112q^{69} + 200q^{70} - 322q^{72} + 386q^{73} - 20q^{75} - 424q^{76} - 440q^{78} + 334q^{79} + 186q^{81} - 68q^{82} + 80q^{84} - 200q^{85} + 342q^{87} + 180q^{88} + 100q^{90} + 46q^{91} - 2q^{93} + 324q^{94} + 732q^{96} + 1616q^{97} + 384q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.644768 0.372257i −0.322384 0.186129i 0.330071 0.943956i \(-0.392927\pi\)
−0.652455 + 0.757828i \(0.726261\pi\)
\(3\) −2.67627 1.35556i −0.892091 0.451855i
\(4\) −1.72285 2.98406i −0.430712 0.746016i
\(5\) 1.93649 + 1.11803i 0.387298 + 0.223607i
\(6\) 1.22096 + 1.87029i 0.203493 + 0.311715i
\(7\) −5.98242 + 3.63464i −0.854632 + 0.519234i
\(8\) 5.54343i 0.692929i
\(9\) 5.32489 + 7.25573i 0.591654 + 0.806192i
\(10\) −0.832392 1.44175i −0.0832392 0.144175i
\(11\) −8.35340 + 4.82284i −0.759400 + 0.438440i −0.829080 0.559130i \(-0.811135\pi\)
0.0696804 + 0.997569i \(0.477802\pi\)
\(12\) 0.565728 + 10.3216i 0.0471440 + 0.860134i
\(13\) −0.0661184 −0.00508603 −0.00254302 0.999997i \(-0.500809\pi\)
−0.00254302 + 0.999997i \(0.500809\pi\)
\(14\) 5.21030 0.116499i 0.372164 0.00832133i
\(15\) −3.66702 5.61721i −0.244468 0.374480i
\(16\) −4.82782 + 8.36202i −0.301739 + 0.522627i
\(17\) −28.1197 + 16.2349i −1.65410 + 0.954995i −0.678739 + 0.734380i \(0.737473\pi\)
−0.975361 + 0.220615i \(0.929194\pi\)
\(18\) −0.732324 6.66049i −0.0406846 0.370027i
\(19\) 12.7759 22.1286i 0.672418 1.16466i −0.304798 0.952417i \(-0.598589\pi\)
0.977216 0.212246i \(-0.0680777\pi\)
\(20\) 7.70482i 0.385241i
\(21\) 20.9376 1.61772i 0.997028 0.0770345i
\(22\) 7.18134 0.326425
\(23\) −8.49789 4.90626i −0.369473 0.213316i 0.303755 0.952750i \(-0.401760\pi\)
−0.673228 + 0.739435i \(0.735093\pi\)
\(24\) 7.51448 14.8357i 0.313103 0.618156i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) 0.0426310 + 0.0246130i 0.00163966 + 0.000946655i
\(27\) −4.41526 26.6365i −0.163528 0.986539i
\(28\) 21.1528 + 11.5900i 0.755457 + 0.413928i
\(29\) 6.58972i 0.227232i 0.993525 + 0.113616i \(0.0362433\pi\)
−0.993525 + 0.113616i \(0.963757\pi\)
\(30\) 0.273330 + 4.98687i 0.00911102 + 0.166229i
\(31\) −16.4028 28.4105i −0.529123 0.916467i −0.999423 0.0339609i \(-0.989188\pi\)
0.470301 0.882506i \(-0.344146\pi\)
\(32\) 25.4286 14.6812i 0.794645 0.458789i
\(33\) 28.8937 1.58366i 0.875565 0.0479898i
\(34\) 24.1742 0.711007
\(35\) −15.6486 + 0.349891i −0.447102 + 0.00999689i
\(36\) 12.4776 28.3903i 0.346599 0.788620i
\(37\) −27.3632 + 47.3945i −0.739546 + 1.28093i 0.213154 + 0.977019i \(0.431627\pi\)
−0.952700 + 0.303913i \(0.901707\pi\)
\(38\) −16.4751 + 9.51187i −0.433554 + 0.250312i
\(39\) 0.176951 + 0.0896278i 0.00453720 + 0.00229815i
\(40\) −6.19774 + 10.7348i −0.154944 + 0.268370i
\(41\) 14.8128i 0.361287i −0.983549 0.180643i \(-0.942182\pi\)
0.983549 0.180643i \(-0.0578180\pi\)
\(42\) −14.1021 6.75111i −0.335764 0.160741i
\(43\) −14.3286 −0.333223 −0.166612 0.986023i \(-0.553283\pi\)
−0.166612 + 0.986023i \(0.553283\pi\)
\(44\) 28.7833 + 16.6180i 0.654166 + 0.377683i
\(45\) 2.19945 + 20.0041i 0.0488768 + 0.444535i
\(46\) 3.65278 + 6.32680i 0.0794082 + 0.137539i
\(47\) −63.7562 36.8097i −1.35652 0.783184i −0.367363 0.930078i \(-0.619739\pi\)
−0.989152 + 0.146893i \(0.953073\pi\)
\(48\) 24.2558 15.8347i 0.505330 0.329889i
\(49\) 22.5788 43.4879i 0.460792 0.887508i
\(50\) 3.72257i 0.0744514i
\(51\) 97.2635 5.33102i 1.90713 0.104530i
\(52\) 0.113912 + 0.197301i 0.00219062 + 0.00379426i
\(53\) 44.3287 25.5932i 0.836390 0.482890i −0.0196455 0.999807i \(-0.506254\pi\)
0.856036 + 0.516917i \(0.172920\pi\)
\(54\) −7.06882 + 18.8180i −0.130904 + 0.348482i
\(55\) −21.5684 −0.392152
\(56\) −20.1484 33.1631i −0.359792 0.592199i
\(57\) −64.1887 + 41.9036i −1.12612 + 0.735150i
\(58\) 2.45307 4.24884i 0.0422943 0.0732558i
\(59\) −75.2379 + 43.4386i −1.27522 + 0.736248i −0.975965 0.217926i \(-0.930071\pi\)
−0.299253 + 0.954174i \(0.596737\pi\)
\(60\) −10.4444 + 20.6202i −0.174073 + 0.343670i
\(61\) −12.5191 + 21.6838i −0.205232 + 0.355472i −0.950207 0.311621i \(-0.899128\pi\)
0.744975 + 0.667093i \(0.232461\pi\)
\(62\) 24.4242i 0.393939i
\(63\) −58.2277 24.0528i −0.924249 0.381790i
\(64\) 16.7618 0.261903
\(65\) −0.128038 0.0739226i −0.00196981 0.00113727i
\(66\) −19.2192 9.73477i −0.291201 0.147497i
\(67\) 24.0411 + 41.6403i 0.358822 + 0.621497i 0.987764 0.155954i \(-0.0498453\pi\)
−0.628943 + 0.777452i \(0.716512\pi\)
\(68\) 96.8920 + 55.9406i 1.42488 + 0.822656i
\(69\) 16.0919 + 24.6499i 0.233216 + 0.357245i
\(70\) 10.2199 + 5.59969i 0.145999 + 0.0799956i
\(71\) 113.723i 1.60173i 0.598842 + 0.800867i \(0.295628\pi\)
−0.598842 + 0.800867i \(0.704372\pi\)
\(72\) −40.2216 + 29.5181i −0.558633 + 0.409974i
\(73\) −21.2034 36.7253i −0.290457 0.503086i 0.683461 0.729987i \(-0.260474\pi\)
−0.973918 + 0.226901i \(0.927141\pi\)
\(74\) 35.2859 20.3723i 0.476836 0.275301i
\(75\) −0.820919 14.9775i −0.0109456 0.199700i
\(76\) −88.0441 −1.15848
\(77\) 32.4443 59.2138i 0.421355 0.769011i
\(78\) −0.0807278 0.123660i −0.00103497 0.00158539i
\(79\) 9.49104 16.4390i 0.120140 0.208088i −0.799683 0.600423i \(-0.794999\pi\)
0.919823 + 0.392334i \(0.128332\pi\)
\(80\) −18.6981 + 10.7953i −0.233726 + 0.134942i
\(81\) −24.2911 + 77.2719i −0.299890 + 0.953974i
\(82\) −5.51416 + 9.55080i −0.0672458 + 0.116473i
\(83\) 46.8063i 0.563932i −0.959424 0.281966i \(-0.909014\pi\)
0.959424 0.281966i \(-0.0909865\pi\)
\(84\) −40.8997 59.6920i −0.486901 0.710619i
\(85\) −72.6047 −0.854173
\(86\) 9.23863 + 5.33393i 0.107426 + 0.0620224i
\(87\) 8.93279 17.6359i 0.102676 0.202711i
\(88\) −26.7350 46.3065i −0.303807 0.526210i
\(89\) 45.4566 + 26.2444i 0.510748 + 0.294881i 0.733141 0.680077i \(-0.238053\pi\)
−0.222393 + 0.974957i \(0.571387\pi\)
\(90\) 6.02851 13.7167i 0.0669835 0.152408i
\(91\) 0.395548 0.240316i 0.00434668 0.00264084i
\(92\) 33.8110i 0.367511i
\(93\) 5.38615 + 98.2693i 0.0579155 + 1.05666i
\(94\) 27.4053 + 47.4674i 0.291546 + 0.504972i
\(95\) 49.4810 28.5679i 0.520853 0.300715i
\(96\) −87.9554 + 4.82084i −0.916202 + 0.0502171i
\(97\) 147.764 1.52334 0.761670 0.647965i \(-0.224380\pi\)
0.761670 + 0.647965i \(0.224380\pi\)
\(98\) −30.7468 + 19.6345i −0.313743 + 0.200352i
\(99\) −79.4741 34.9289i −0.802769 0.352817i
\(100\) 8.61425 14.9203i 0.0861425 0.149203i
\(101\) 55.1994 31.8694i 0.546529 0.315538i −0.201192 0.979552i \(-0.564482\pi\)
0.747721 + 0.664013i \(0.231148\pi\)
\(102\) −64.6969 32.7698i −0.634283 0.321272i
\(103\) 30.0287 52.0112i 0.291541 0.504964i −0.682633 0.730761i \(-0.739165\pi\)
0.974174 + 0.225797i \(0.0724987\pi\)
\(104\) 0.366523i 0.00352426i
\(105\) 42.3542 + 20.2762i 0.403373 + 0.193107i
\(106\) −38.1090 −0.359518
\(107\) −17.4895 10.0976i −0.163454 0.0943700i 0.416042 0.909345i \(-0.363417\pi\)
−0.579495 + 0.814976i \(0.696750\pi\)
\(108\) −71.8783 + 59.0662i −0.665540 + 0.546909i
\(109\) 10.9584 + 18.9805i 0.100536 + 0.174133i 0.911905 0.410400i \(-0.134611\pi\)
−0.811370 + 0.584533i \(0.801278\pi\)
\(110\) 13.9066 + 8.02898i 0.126424 + 0.0729908i
\(111\) 137.478 89.7480i 1.23854 0.808541i
\(112\) −1.51088 67.5725i −0.0134900 0.603326i
\(113\) 59.9095i 0.530172i −0.964225 0.265086i \(-0.914600\pi\)
0.964225 0.265086i \(-0.0854004\pi\)
\(114\) 56.9857 3.12339i 0.499875 0.0273982i
\(115\) −10.9707 19.0019i −0.0953976 0.165234i
\(116\) 19.6641 11.3531i 0.169518 0.0978714i
\(117\) −0.352073 0.479737i −0.00300917 0.00410032i
\(118\) 64.6813 0.548147
\(119\) 109.216 199.329i 0.917781 1.67503i
\(120\) 31.1386 20.3278i 0.259488 0.169399i
\(121\) −13.9805 + 24.2149i −0.115541 + 0.200123i
\(122\) 16.1439 9.32067i 0.132327 0.0763989i
\(123\) −20.0797 + 39.6430i −0.163249 + 0.322301i
\(124\) −56.5191 + 97.8940i −0.455799 + 0.789468i
\(125\) 11.1803i 0.0894427i
\(126\) 28.5895 + 37.1841i 0.226901 + 0.295112i
\(127\) 143.138 1.12707 0.563535 0.826092i \(-0.309441\pi\)
0.563535 + 0.826092i \(0.309441\pi\)
\(128\) −112.522 64.9646i −0.879078 0.507536i
\(129\) 38.3473 + 19.4234i 0.297266 + 0.150569i
\(130\) 0.0550364 + 0.0953259i 0.000423357 + 0.000733276i
\(131\) −90.7189 52.3766i −0.692511 0.399821i 0.112041 0.993704i \(-0.464261\pi\)
−0.804552 + 0.593882i \(0.797594\pi\)
\(132\) −54.5052 83.4921i −0.412918 0.632516i
\(133\) 3.99826 + 178.819i 0.0300621 + 1.34450i
\(134\) 35.7978i 0.267148i
\(135\) 21.2305 56.5179i 0.157263 0.418651i
\(136\) −89.9971 155.879i −0.661743 1.14617i
\(137\) 71.0097 40.9975i 0.518319 0.299252i −0.217928 0.975965i \(-0.569930\pi\)
0.736247 + 0.676713i \(0.236596\pi\)
\(138\) −1.19945 21.8838i −0.00869169 0.158578i
\(139\) 2.35082 0.0169124 0.00845618 0.999964i \(-0.497308\pi\)
0.00845618 + 0.999964i \(0.497308\pi\)
\(140\) 28.0042 + 46.0935i 0.200030 + 0.329239i
\(141\) 120.731 + 184.938i 0.856250 + 1.31162i
\(142\) 42.3342 73.3250i 0.298128 0.516374i
\(143\) 0.552313 0.318878i 0.00386233 0.00222992i
\(144\) −86.3801 + 9.49753i −0.599862 + 0.0659551i
\(145\) −7.36753 + 12.7609i −0.0508105 + 0.0880064i
\(146\) 31.5724i 0.216249i
\(147\) −119.378 + 85.7785i −0.812094 + 0.583527i
\(148\) 188.571 1.27413
\(149\) −37.8609 21.8590i −0.254100 0.146705i 0.367540 0.930008i \(-0.380200\pi\)
−0.621640 + 0.783303i \(0.713533\pi\)
\(150\) −5.04619 + 9.96262i −0.0336412 + 0.0664175i
\(151\) 5.05119 + 8.74891i 0.0334516 + 0.0579398i 0.882267 0.470750i \(-0.156017\pi\)
−0.848815 + 0.528690i \(0.822683\pi\)
\(152\) 122.668 + 70.8226i 0.807028 + 0.465938i
\(153\) −267.530 117.580i −1.74856 0.768495i
\(154\) −42.9618 + 26.1016i −0.278973 + 0.169491i
\(155\) 73.3556i 0.473262i
\(156\) −0.0374050 0.682448i −0.000239776 0.00437467i
\(157\) −44.2055 76.5661i −0.281564 0.487682i 0.690207 0.723612i \(-0.257520\pi\)
−0.971770 + 0.235930i \(0.924186\pi\)
\(158\) −12.2390 + 7.06621i −0.0774623 + 0.0447229i
\(159\) −153.329 + 8.40396i −0.964333 + 0.0528551i
\(160\) 65.6565 0.410353
\(161\) 68.6704 1.53542i 0.426524 0.00953679i
\(162\) 44.4271 40.7799i 0.274242 0.251728i
\(163\) −97.6632 + 169.158i −0.599161 + 1.03778i 0.393784 + 0.919203i \(0.371166\pi\)
−0.992945 + 0.118574i \(0.962168\pi\)
\(164\) −44.2022 + 25.5202i −0.269526 + 0.155611i
\(165\) 57.7229 + 29.2373i 0.349836 + 0.177196i
\(166\) −17.4240 + 30.1792i −0.104964 + 0.181803i
\(167\) 197.023i 1.17978i 0.807485 + 0.589888i \(0.200828\pi\)
−0.807485 + 0.589888i \(0.799172\pi\)
\(168\) 8.96773 + 116.066i 0.0533794 + 0.690869i
\(169\) −168.996 −0.999974
\(170\) 46.8132 + 27.0276i 0.275372 + 0.158986i
\(171\) 228.589 25.1335i 1.33678 0.146980i
\(172\) 24.6860 + 42.7575i 0.143523 + 0.248590i
\(173\) 68.0126 + 39.2671i 0.393136 + 0.226977i 0.683518 0.729934i \(-0.260449\pi\)
−0.290382 + 0.956911i \(0.593782\pi\)
\(174\) −12.3247 + 8.04577i −0.0708314 + 0.0462400i
\(175\) −30.6945 16.8181i −0.175397 0.0961032i
\(176\) 93.1351i 0.529177i
\(177\) 260.241 14.2638i 1.47029 0.0805866i
\(178\) −19.5393 33.8431i −0.109771 0.190130i
\(179\) −235.188 + 135.786i −1.31390 + 0.758581i −0.982740 0.184993i \(-0.940774\pi\)
−0.331162 + 0.943574i \(0.607441\pi\)
\(180\) 55.9040 41.0273i 0.310578 0.227929i
\(181\) −293.315 −1.62053 −0.810264 0.586065i \(-0.800676\pi\)
−0.810264 + 0.586065i \(0.800676\pi\)
\(182\) −0.344496 + 0.00770270i −0.00189284 + 4.23226e-5i
\(183\) 62.8984 41.0612i 0.343707 0.224378i
\(184\) 27.1975 47.1074i 0.147812 0.256019i
\(185\) −105.977 + 61.1860i −0.572850 + 0.330735i
\(186\) 33.1086 65.3660i 0.178003 0.351430i
\(187\) 156.597 271.233i 0.837415 1.45045i
\(188\) 253.670i 1.34931i
\(189\) 123.228 + 143.303i 0.652001 + 0.758218i
\(190\) −42.5384 −0.223886
\(191\) −164.055 94.7172i −0.858927 0.495902i 0.00472608 0.999989i \(-0.498496\pi\)
−0.863653 + 0.504087i \(0.831829\pi\)
\(192\) −44.8591 22.7216i −0.233641 0.118342i
\(193\) −107.937 186.952i −0.559259 0.968665i −0.997558 0.0698359i \(-0.977752\pi\)
0.438300 0.898829i \(-0.355581\pi\)
\(194\) −95.2736 55.0062i −0.491101 0.283537i
\(195\) 0.242457 + 0.371401i 0.00124337 + 0.00190462i
\(196\) −168.670 + 7.54649i −0.860564 + 0.0385025i
\(197\) 234.358i 1.18963i 0.803861 + 0.594817i \(0.202776\pi\)
−0.803861 + 0.594817i \(0.797224\pi\)
\(198\) 38.2398 + 52.1058i 0.193131 + 0.263161i
\(199\) 185.985 + 322.135i 0.934597 + 1.61877i 0.775351 + 0.631531i \(0.217573\pi\)
0.159246 + 0.987239i \(0.449094\pi\)
\(200\) −24.0037 + 13.8586i −0.120019 + 0.0692929i
\(201\) −7.89430 144.030i −0.0392751 0.716568i
\(202\) −47.4544 −0.234923
\(203\) −23.9512 39.4225i −0.117986 0.194199i
\(204\) −183.478 281.056i −0.899404 1.37772i
\(205\) 16.5612 28.6848i 0.0807862 0.139926i
\(206\) −38.7231 + 22.3568i −0.187976 + 0.108528i
\(207\) −9.65184 87.7836i −0.0466273 0.424075i
\(208\) 0.319207 0.552884i 0.00153465 0.00265809i
\(209\) 246.465i 1.17926i
\(210\) −19.7606 28.8401i −0.0940983 0.137334i
\(211\) 179.659 0.851463 0.425732 0.904850i \(-0.360017\pi\)
0.425732 + 0.904850i \(0.360017\pi\)
\(212\) −152.743 88.1864i −0.720487 0.415973i
\(213\) 154.159 304.354i 0.723751 1.42889i
\(214\) 7.51780 + 13.0212i 0.0351299 + 0.0608468i
\(215\) −27.7472 16.0199i −0.129057 0.0745110i
\(216\) 147.658 24.4757i 0.683601 0.113313i
\(217\) 201.390 + 110.345i 0.928066 + 0.508504i
\(218\) 16.3173i 0.0748502i
\(219\) 6.96250 + 127.030i 0.0317922 + 0.580044i
\(220\) 37.1591 + 64.3614i 0.168905 + 0.292552i
\(221\) 1.85923 1.07343i 0.00841280 0.00485713i
\(222\) −122.051 + 6.68960i −0.549778 + 0.0301333i
\(223\) −124.240 −0.557129 −0.278565 0.960418i \(-0.589859\pi\)
−0.278565 + 0.960418i \(0.589859\pi\)
\(224\) −98.7640 + 180.253i −0.440911 + 0.804702i
\(225\) −18.1060 + 41.1968i −0.0804711 + 0.183097i
\(226\) −22.3017 + 38.6277i −0.0986802 + 0.170919i
\(227\) 192.850 111.342i 0.849561 0.490494i −0.0109416 0.999940i \(-0.503483\pi\)
0.860503 + 0.509446i \(0.170150\pi\)
\(228\) 235.630 + 119.350i 1.03347 + 0.523463i
\(229\) −85.6244 + 148.306i −0.373906 + 0.647624i −0.990163 0.139921i \(-0.955315\pi\)
0.616257 + 0.787545i \(0.288648\pi\)
\(230\) 16.3357i 0.0710249i
\(231\) −167.098 + 114.492i −0.723368 + 0.495637i
\(232\) −36.5296 −0.157455
\(233\) −333.986 192.827i −1.43342 0.827583i −0.436037 0.899929i \(-0.643618\pi\)
−0.997380 + 0.0723454i \(0.976952\pi\)
\(234\) 0.0484201 + 0.440381i 0.000206923 + 0.00188197i
\(235\) −82.3089 142.563i −0.350251 0.606652i
\(236\) 259.247 + 149.676i 1.09850 + 0.634222i
\(237\) −47.6847 + 31.1294i −0.201201 + 0.131348i
\(238\) −144.621 + 87.8646i −0.607650 + 0.369179i
\(239\) 283.411i 1.18582i −0.805268 0.592911i \(-0.797979\pi\)
0.805268 0.592911i \(-0.202021\pi\)
\(240\) 64.6749 3.54483i 0.269479 0.0147701i
\(241\) 119.652 + 207.243i 0.496480 + 0.859928i 0.999992 0.00406029i \(-0.00129244\pi\)
−0.503512 + 0.863988i \(0.667959\pi\)
\(242\) 18.0284 10.4087i 0.0744973 0.0430111i
\(243\) 169.757 173.873i 0.698587 0.715525i
\(244\) 86.2743 0.353583
\(245\) 92.3446 58.9701i 0.376917 0.240694i
\(246\) 27.7041 18.0858i 0.112618 0.0735194i
\(247\) −0.844725 + 1.46311i −0.00341994 + 0.00592351i
\(248\) 157.491 90.9278i 0.635046 0.366644i
\(249\) −63.4490 + 125.267i −0.254815 + 0.503078i
\(250\) 4.16196 7.20873i 0.0166478 0.0288349i
\(251\) 355.767i 1.41740i 0.705510 + 0.708700i \(0.250718\pi\)
−0.705510 + 0.708700i \(0.749282\pi\)
\(252\) 28.5425 + 215.194i 0.113264 + 0.853946i
\(253\) 94.6483 0.374104
\(254\) −92.2907 53.2841i −0.363349 0.209780i
\(255\) 194.310 + 98.4204i 0.762001 + 0.385962i
\(256\) 14.8436 + 25.7098i 0.0579827 + 0.100429i
\(257\) −248.208 143.303i −0.965788 0.557598i −0.0678386 0.997696i \(-0.521610\pi\)
−0.897950 + 0.440098i \(0.854944\pi\)
\(258\) −17.4946 26.7986i −0.0678086 0.103871i
\(259\) −8.56338 382.989i −0.0330632 1.47872i
\(260\) 0.509430i 0.00195935i
\(261\) −47.8132 + 35.0895i −0.183192 + 0.134443i
\(262\) 38.9951 + 67.5415i 0.148836 + 0.257792i
\(263\) 2.82179 1.62916i 0.0107292 0.00619452i −0.494626 0.869106i \(-0.664695\pi\)
0.505355 + 0.862912i \(0.331362\pi\)
\(264\) 8.77892 + 160.170i 0.0332535 + 0.606704i
\(265\) 114.456 0.431910
\(266\) 63.9885 116.785i 0.240558 0.439041i
\(267\) −86.0783 131.856i −0.322391 0.493844i
\(268\) 82.8382 143.480i 0.309098 0.535373i
\(269\) 33.8538 19.5455i 0.125850 0.0726598i −0.435753 0.900066i \(-0.643518\pi\)
0.561604 + 0.827406i \(0.310185\pi\)
\(270\) −34.7279 + 28.5377i −0.128622 + 0.105695i
\(271\) 116.865 202.415i 0.431235 0.746921i −0.565745 0.824580i \(-0.691411\pi\)
0.996980 + 0.0776596i \(0.0247447\pi\)
\(272\) 313.517i 1.15264i
\(273\) −1.38436 + 0.106961i −0.00507092 + 0.000391800i
\(274\) −61.0464 −0.222797
\(275\) −41.7670 24.1142i −0.151880 0.0876879i
\(276\) 45.8330 90.4874i 0.166061 0.327853i
\(277\) 104.531 + 181.053i 0.377369 + 0.653623i 0.990679 0.136220i \(-0.0434954\pi\)
−0.613309 + 0.789843i \(0.710162\pi\)
\(278\) −1.51573 0.875109i −0.00545228 0.00314787i
\(279\) 118.796 270.297i 0.425791 0.968806i
\(280\) −1.93960 86.7467i −0.00692713 0.309810i
\(281\) 224.653i 0.799476i −0.916629 0.399738i \(-0.869101\pi\)
0.916629 0.399738i \(-0.130899\pi\)
\(282\) −8.99901 164.185i −0.0319114 0.582218i
\(283\) 2.60814 + 4.51743i 0.00921605 + 0.0159627i 0.870597 0.491997i \(-0.163733\pi\)
−0.861381 + 0.507960i \(0.830400\pi\)
\(284\) 339.357 195.928i 1.19492 0.689887i
\(285\) −171.150 + 9.38076i −0.600528 + 0.0329150i
\(286\) −0.474819 −0.00166021
\(287\) 53.8390 + 88.6162i 0.187592 + 0.308767i
\(288\) 241.928 + 106.327i 0.840027 + 0.369192i
\(289\) 382.645 662.760i 1.32403 2.29329i
\(290\) 9.50069 5.48523i 0.0327610 0.0189146i
\(291\) −395.457 200.304i −1.35896 0.688329i
\(292\) −73.0604 + 126.544i −0.250207 + 0.433371i
\(293\) 63.6178i 0.217126i −0.994090 0.108563i \(-0.965375\pi\)
0.994090 0.108563i \(-0.0346249\pi\)
\(294\) 108.903 10.8680i 0.370417 0.0369661i
\(295\) −194.263 −0.658520
\(296\) −262.728 151.686i −0.887594 0.512453i
\(297\) 165.346 + 201.212i 0.556721 + 0.677480i
\(298\) 16.2743 + 28.1879i 0.0546118 + 0.0945904i
\(299\) 0.561867 + 0.324394i 0.00187915 + 0.00108493i
\(300\) −43.2795 + 28.2537i −0.144265 + 0.0941789i
\(301\) 85.7198 52.0793i 0.284784 0.173021i
\(302\) 7.52136i 0.0249052i
\(303\) −190.930 + 10.4649i −0.630131 + 0.0345375i
\(304\) 123.360 + 213.666i 0.405789 + 0.702847i
\(305\) −48.4864 + 27.9936i −0.158972 + 0.0917824i
\(306\) 128.725 + 175.402i 0.420670 + 0.573208i
\(307\) −147.936 −0.481876 −0.240938 0.970541i \(-0.577455\pi\)
−0.240938 + 0.970541i \(0.577455\pi\)
\(308\) −232.594 + 5.20065i −0.755177 + 0.0168852i
\(309\) −150.870 + 98.4905i −0.488251 + 0.318740i
\(310\) −27.3071 + 47.2973i −0.0880875 + 0.152572i
\(311\) −79.3613 + 45.8193i −0.255181 + 0.147329i −0.622134 0.782911i \(-0.713734\pi\)
0.366953 + 0.930239i \(0.380401\pi\)
\(312\) −0.496845 + 0.980915i −0.00159245 + 0.00314396i
\(313\) −74.8604 + 129.662i −0.239170 + 0.414255i −0.960476 0.278361i \(-0.910209\pi\)
0.721306 + 0.692617i \(0.243542\pi\)
\(314\) 65.8232i 0.209628i
\(315\) −85.8656 111.679i −0.272589 0.354535i
\(316\) −65.4065 −0.206983
\(317\) −60.9909 35.2131i −0.192400 0.111082i 0.400705 0.916207i \(-0.368765\pi\)
−0.593106 + 0.805125i \(0.702098\pi\)
\(318\) 101.990 + 51.6592i 0.320723 + 0.162450i
\(319\) −31.7811 55.0465i −0.0996273 0.172560i
\(320\) 32.4590 + 18.7402i 0.101434 + 0.0585632i
\(321\) 33.1189 + 50.7321i 0.103174 + 0.158044i
\(322\) −44.8481 24.5731i −0.139280 0.0763139i
\(323\) 829.666i 2.56862i
\(324\) 272.434 60.6416i 0.840846 0.187165i
\(325\) −0.165296 0.286301i −0.000508603 0.000880926i
\(326\) 125.940 72.7116i 0.386320 0.223042i
\(327\) −3.59838 65.6518i −0.0110042 0.200770i
\(328\) 82.1135 0.250346
\(329\) 515.207 11.5197i 1.56598 0.0350142i
\(330\) −26.3341 40.3391i −0.0798003 0.122240i
\(331\) −246.435 + 426.839i −0.744518 + 1.28954i 0.205902 + 0.978573i \(0.433987\pi\)
−0.950420 + 0.310970i \(0.899346\pi\)
\(332\) −139.673 + 80.6402i −0.420702 + 0.242892i
\(333\) −489.587 + 53.8303i −1.47023 + 0.161653i
\(334\) 73.3430 127.034i 0.219590 0.380341i
\(335\) 107.515i 0.320940i
\(336\) −87.5554 + 182.891i −0.260582 + 0.544318i
\(337\) −321.869 −0.955102 −0.477551 0.878604i \(-0.658475\pi\)
−0.477551 + 0.878604i \(0.658475\pi\)
\(338\) 108.963 + 62.9098i 0.322376 + 0.186124i
\(339\) −81.2111 + 160.334i −0.239561 + 0.472962i
\(340\) 125.087 + 216.657i 0.367903 + 0.637227i
\(341\) 274.038 + 158.216i 0.803631 + 0.463977i
\(342\) −156.743 68.8888i −0.458314 0.201429i
\(343\) 22.9867 + 342.229i 0.0670165 + 0.997752i
\(344\) 79.4296i 0.230900i
\(345\) 3.60243 + 65.7257i 0.0104418 + 0.190509i
\(346\) −29.2349 50.6363i −0.0844939 0.146348i
\(347\) −56.0152 + 32.3404i −0.161427 + 0.0932000i −0.578537 0.815656i \(-0.696376\pi\)
0.417110 + 0.908856i \(0.363043\pi\)
\(348\) −68.0164 + 3.72798i −0.195450 + 0.0107126i
\(349\) −151.057 −0.432829 −0.216415 0.976302i \(-0.569436\pi\)
−0.216415 + 0.976302i \(0.569436\pi\)
\(350\) 13.5302 + 22.2700i 0.0386577 + 0.0636286i
\(351\) 0.291930 + 1.76117i 0.000831709 + 0.00501757i
\(352\) −141.610 + 245.276i −0.402302 + 0.696808i
\(353\) 302.998 174.936i 0.858350 0.495569i −0.00510945 0.999987i \(-0.501626\pi\)
0.863459 + 0.504418i \(0.168293\pi\)
\(354\) −173.105 87.6797i −0.488997 0.247683i
\(355\) −127.146 + 220.224i −0.358159 + 0.620349i
\(356\) 180.860i 0.508035i
\(357\) −562.495 + 385.410i −1.57562 + 1.07958i
\(358\) 202.189 0.564775
\(359\) 475.400 + 274.473i 1.32424 + 0.764548i 0.984401 0.175938i \(-0.0562958\pi\)
0.339834 + 0.940485i \(0.389629\pi\)
\(360\) −110.891 + 12.1925i −0.308031 + 0.0338681i
\(361\) −145.950 252.792i −0.404293 0.700256i
\(362\) 189.120 + 109.189i 0.522432 + 0.301626i
\(363\) 70.2405 45.8543i 0.193500 0.126320i
\(364\) −1.39859 0.766312i −0.00384228 0.00210525i
\(365\) 94.8243i 0.259793i
\(366\) −55.8402 + 3.06060i −0.152569 + 0.00836231i
\(367\) −186.447 322.935i −0.508030 0.879933i −0.999957 0.00929679i \(-0.997041\pi\)
0.491927 0.870636i \(-0.336293\pi\)
\(368\) 82.0525 47.3730i 0.222969 0.128731i
\(369\) 107.477 78.8763i 0.291267 0.213757i
\(370\) 91.1077 0.246237
\(371\) −172.171 + 314.228i −0.464073 + 0.846975i
\(372\) 283.962 185.376i 0.763339 0.498322i
\(373\) 122.029 211.361i 0.327156 0.566650i −0.654791 0.755810i \(-0.727243\pi\)
0.981946 + 0.189160i \(0.0605765\pi\)
\(374\) −201.937 + 116.588i −0.539939 + 0.311734i
\(375\) 15.1557 29.9217i 0.0404151 0.0797911i
\(376\) 204.052 353.428i 0.542691 0.939968i
\(377\) 0.435701i 0.00115571i
\(378\) −26.1079 138.270i −0.0690686 0.365793i
\(379\) −495.847 −1.30830 −0.654151 0.756364i \(-0.726974\pi\)
−0.654151 + 0.756364i \(0.726974\pi\)
\(380\) −170.497 98.4363i −0.448676 0.259043i
\(381\) −383.076 194.033i −1.00545 0.509272i
\(382\) 70.5183 + 122.141i 0.184603 + 0.319742i
\(383\) −305.600 176.438i −0.797912 0.460675i 0.0448283 0.998995i \(-0.485726\pi\)
−0.842741 + 0.538320i \(0.819059\pi\)
\(384\) 213.076 + 326.394i 0.554886 + 0.849984i
\(385\) 129.031 78.3933i 0.335146 0.203619i
\(386\) 160.721i 0.416376i
\(387\) −76.2983 103.964i −0.197153 0.268642i
\(388\) −254.575 440.937i −0.656122 1.13644i
\(389\) −94.6247 + 54.6316i −0.243251 + 0.140441i −0.616670 0.787222i \(-0.711519\pi\)
0.373419 + 0.927663i \(0.378185\pi\)
\(390\) −0.0180722 0.329724i −4.63389e−5 0.000845445i
\(391\) 318.611 0.814861
\(392\) 241.072 + 125.164i 0.614980 + 0.319296i
\(393\) 171.789 + 263.150i 0.437122 + 0.669592i
\(394\) 87.2414 151.107i 0.221425 0.383519i
\(395\) 36.7586 21.2226i 0.0930598 0.0537281i
\(396\) 32.6919 + 297.333i 0.0825552 + 0.750841i
\(397\) −320.446 + 555.029i −0.807170 + 1.39806i 0.107647 + 0.994189i \(0.465668\pi\)
−0.914816 + 0.403870i \(0.867665\pi\)
\(398\) 276.937i 0.695821i
\(399\) 231.700 483.987i 0.580701 1.21300i
\(400\) −48.2782 −0.120695
\(401\) 104.940 + 60.5871i 0.261695 + 0.151090i 0.625108 0.780538i \(-0.285055\pi\)
−0.363412 + 0.931628i \(0.618388\pi\)
\(402\) −48.5263 + 95.8048i −0.120712 + 0.238320i
\(403\) 1.08453 + 1.87846i 0.00269113 + 0.00466118i
\(404\) −190.200 109.812i −0.470793 0.271813i
\(405\) −133.432 + 122.478i −0.329462 + 0.302415i
\(406\) 0.767693 + 34.3344i 0.00189087 + 0.0845674i
\(407\) 527.873i 1.29699i
\(408\) 29.5521 + 539.173i 0.0724316 + 1.32150i
\(409\) 170.580 + 295.454i 0.417067 + 0.722381i 0.995643 0.0932474i \(-0.0297247\pi\)
−0.578576 + 0.815628i \(0.696391\pi\)
\(410\) −21.3562 + 12.3300i −0.0520884 + 0.0300732i
\(411\) −245.616 + 13.4622i −0.597606 + 0.0327548i
\(412\) −206.940 −0.502281
\(413\) 292.221 533.331i 0.707558 1.29136i
\(414\) −26.4549 + 60.1931i −0.0639007 + 0.145394i
\(415\) 52.3311 90.6400i 0.126099 0.218410i
\(416\) −1.68130 + 0.970700i −0.00404159 + 0.00233341i
\(417\) −6.29143 3.18669i −0.0150874 0.00764193i
\(418\) 91.7484 158.913i 0.219494 0.380175i
\(419\) 199.066i 0.475097i 0.971376 + 0.237549i \(0.0763439\pi\)
−0.971376 + 0.237549i \(0.923656\pi\)
\(420\) −12.4643 161.320i −0.0296768 0.384096i
\(421\) 620.416 1.47367 0.736837 0.676071i \(-0.236319\pi\)
0.736837 + 0.676071i \(0.236319\pi\)
\(422\) −115.838 66.8792i −0.274498 0.158482i
\(423\) −72.4139 658.605i −0.171191 1.55699i
\(424\) 141.874 + 245.733i 0.334608 + 0.579559i
\(425\) −140.598 81.1746i −0.330820 0.190999i
\(426\) −212.695 + 138.851i −0.499284 + 0.325942i
\(427\) −3.91789 175.224i −0.00917538 0.410361i
\(428\) 69.5865i 0.162585i
\(429\) −1.91040 + 0.104709i −0.00445315 + 0.000244077i
\(430\) 11.9270 + 20.6582i 0.0277373 + 0.0480423i
\(431\) 659.609 380.826i 1.53042 0.883586i 0.531074 0.847326i \(-0.321789\pi\)
0.999342 0.0362605i \(-0.0115446\pi\)
\(432\) 244.051 + 91.6759i 0.564934 + 0.212213i
\(433\) −74.9819 −0.173168 −0.0865842 0.996245i \(-0.527595\pi\)
−0.0865842 + 0.996245i \(0.527595\pi\)
\(434\) −88.7733 146.116i −0.204547 0.336673i
\(435\) 37.0158 24.1646i 0.0850938 0.0555508i
\(436\) 37.7593 65.4010i 0.0866039 0.150002i
\(437\) −217.137 + 125.364i −0.496881 + 0.286875i
\(438\) 42.7985 84.4964i 0.0977134 0.192914i
\(439\) 89.8008 155.539i 0.204558 0.354304i −0.745434 0.666579i \(-0.767758\pi\)
0.949992 + 0.312275i \(0.101091\pi\)
\(440\) 119.563i 0.271734i
\(441\) 435.766 67.7425i 0.988131 0.153611i
\(442\) −1.59836 −0.00361620
\(443\) 618.432 + 357.052i 1.39601 + 0.805986i 0.993972 0.109638i \(-0.0349692\pi\)
0.402036 + 0.915624i \(0.368302\pi\)
\(444\) −504.667 255.620i −1.13664 0.575720i
\(445\) 58.6842 + 101.644i 0.131875 + 0.228413i
\(446\) 80.1059 + 46.2491i 0.179610 + 0.103698i
\(447\) 71.6948 + 109.823i 0.160391 + 0.245690i
\(448\) −100.276 + 60.9229i −0.223830 + 0.135989i
\(449\) 183.881i 0.409534i −0.978811 0.204767i \(-0.934356\pi\)
0.978811 0.204767i \(-0.0656437\pi\)
\(450\) 27.0100 19.8223i 0.0600221 0.0440495i
\(451\) 71.4395 + 123.737i 0.158403 + 0.274361i
\(452\) −178.774 + 103.215i −0.395517 + 0.228352i
\(453\) −1.65865 30.2617i −0.00366147 0.0668029i
\(454\) −165.792 −0.365180
\(455\) 1.03466 0.0231342i 0.00227397 5.08445e-5i
\(456\) −232.289 355.825i −0.509406 0.780319i
\(457\) −352.168 + 609.973i −0.770608 + 1.33473i 0.166622 + 0.986021i \(0.446714\pi\)
−0.937230 + 0.348711i \(0.886619\pi\)
\(458\) 110.416 63.7486i 0.241083 0.139189i
\(459\) 556.598 + 677.330i 1.21263 + 1.47566i
\(460\) −37.8018 + 65.4747i −0.0821779 + 0.142336i
\(461\) 763.794i 1.65682i −0.560123 0.828410i \(-0.689246\pi\)
0.560123 0.828410i \(-0.310754\pi\)
\(462\) 150.360 11.6174i 0.325455 0.0251459i
\(463\) 707.653 1.52841 0.764204 0.644974i \(-0.223132\pi\)
0.764204 + 0.644974i \(0.223132\pi\)
\(464\) −55.1034 31.8139i −0.118757 0.0685645i
\(465\) −99.4382 + 196.320i −0.213846 + 0.422193i
\(466\) 143.562 + 248.657i 0.308074 + 0.533599i
\(467\) −14.6611 8.46457i −0.0313941 0.0181254i 0.484221 0.874946i \(-0.339103\pi\)
−0.515615 + 0.856820i \(0.672436\pi\)
\(468\) −0.824996 + 1.87712i −0.00176281 + 0.00401095i
\(469\) −295.171 161.730i −0.629363 0.344839i
\(470\) 122.560i 0.260767i
\(471\) 14.5156 + 264.835i 0.0308188 + 0.562283i
\(472\) −240.799 417.076i −0.510167 0.883635i
\(473\) 119.693 69.1045i 0.253050 0.146098i
\(474\) 42.3337 2.32031i 0.0893117 0.00489518i
\(475\) 127.759 0.268967
\(476\) −782.973 + 17.5067i −1.64490 + 0.0367789i
\(477\) 421.742 + 185.356i 0.884156 + 0.388587i
\(478\) −105.502 + 182.735i −0.220715 + 0.382290i
\(479\) −258.703 + 149.362i −0.540091 + 0.311821i −0.745116 0.666935i \(-0.767606\pi\)
0.205025 + 0.978757i \(0.434272\pi\)
\(480\) −175.715 89.0016i −0.366072 0.185420i
\(481\) 1.80921 3.13365i 0.00376135 0.00651486i
\(482\) 178.165i 0.369636i
\(483\) −185.862 88.9780i −0.384808 0.184219i
\(484\) 96.3451 0.199060
\(485\) 286.144 + 165.205i 0.589987 + 0.340629i
\(486\) −174.179 + 48.9143i −0.358393 + 0.100647i
\(487\) −165.123 286.002i −0.339062 0.587273i 0.645194 0.764019i \(-0.276776\pi\)
−0.984257 + 0.176745i \(0.943443\pi\)
\(488\) −120.202 69.3989i −0.246316 0.142211i
\(489\) 490.678 320.323i 1.00343 0.655058i
\(490\) −81.4929 + 3.64607i −0.166312 + 0.00744097i
\(491\) 356.915i 0.726914i 0.931611 + 0.363457i \(0.118404\pi\)
−0.931611 + 0.363457i \(0.881596\pi\)
\(492\) 152.891 8.37999i 0.310755 0.0170325i
\(493\) −106.983 185.301i −0.217005 0.375864i
\(494\) 1.08930 0.628910i 0.00220507 0.00127310i
\(495\) −114.849 156.494i −0.232019 0.316150i
\(496\) 316.759 0.638627
\(497\) −413.342 680.340i −0.831675 1.36889i
\(498\) 87.5412 57.1485i 0.175786 0.114756i
\(499\) −184.836 + 320.145i −0.370412 + 0.641573i −0.989629 0.143647i \(-0.954117\pi\)
0.619217 + 0.785220i \(0.287450\pi\)
\(500\) 33.3628 19.2620i 0.0667257 0.0385241i
\(501\) 267.077 527.286i 0.533087 1.05247i
\(502\) 132.437 229.387i 0.263819 0.456947i
\(503\) 85.3001i 0.169583i 0.996399 + 0.0847913i \(0.0270224\pi\)
−0.996399 + 0.0847913i \(0.972978\pi\)
\(504\) 133.335 322.781i 0.264553 0.640438i
\(505\) 142.524 0.282226
\(506\) −61.0262 35.2335i −0.120605 0.0696314i
\(507\) 452.279 + 229.085i 0.892068 + 0.451843i
\(508\) −246.605 427.132i −0.485443 0.840812i
\(509\) −261.852 151.180i −0.514443 0.297014i 0.220215 0.975451i \(-0.429324\pi\)
−0.734658 + 0.678437i \(0.762657\pi\)
\(510\) −88.6473 135.792i −0.173818 0.266258i
\(511\) 260.331 + 142.640i 0.509454 + 0.279139i
\(512\) 497.614i 0.971903i
\(513\) −645.838 242.604i −1.25894 0.472912i
\(514\) 106.691 + 184.794i 0.207570 + 0.359522i
\(515\) 116.301 67.1462i 0.225827 0.130381i
\(516\) −8.10609 147.894i −0.0157095 0.286617i
\(517\) 710.108 1.37352
\(518\) −137.049 + 250.127i −0.264573 + 0.482871i
\(519\) −128.791 197.285i −0.248153 0.380125i
\(520\) 0.409785 0.709768i 0.000788047 0.00136494i
\(521\) −412.783 + 238.320i −0.792289 + 0.457428i −0.840768 0.541396i \(-0.817896\pi\)
0.0484786 + 0.998824i \(0.484563\pi\)
\(522\) 43.8907 4.82580i 0.0840818 0.00924483i
\(523\) 17.4690 30.2571i 0.0334015 0.0578530i −0.848841 0.528648i \(-0.822699\pi\)
0.882243 + 0.470794i \(0.156033\pi\)
\(524\) 360.948i 0.688832i
\(525\) 59.3489 + 86.6181i 0.113046 + 0.164987i
\(526\) −2.42586 −0.00461191
\(527\) 922.483 + 532.596i 1.75044 + 1.01062i
\(528\) −126.251 + 249.255i −0.239111 + 0.472074i
\(529\) −216.357 374.742i −0.408993 0.708397i
\(530\) −73.7977 42.6071i −0.139241 0.0803908i
\(531\) −715.812 314.600i −1.34805 0.592466i
\(532\) 526.717 320.009i 0.990070 0.601520i
\(533\) 0.979396i 0.00183752i
\(534\) 6.41607 + 117.060i 0.0120151 + 0.219214i
\(535\) −22.5789 39.1078i −0.0422035 0.0730987i
\(536\) −230.830 + 133.270i −0.430653 + 0.248638i
\(537\) 813.495 44.5877i 1.51489 0.0830311i
\(538\) −29.1038 −0.0540963
\(539\) 21.1252 + 472.166i 0.0391932 + 0.876003i
\(540\) −205.230 + 34.0187i −0.380055 + 0.0629977i
\(541\) 255.386 442.342i 0.472063 0.817637i −0.527426 0.849601i \(-0.676843\pi\)
0.999489 + 0.0319640i \(0.0101762\pi\)
\(542\) −150.701 + 87.0074i −0.278046 + 0.160530i
\(543\) 784.993 + 397.608i 1.44566 + 0.732243i
\(544\) −476.697 + 825.664i −0.876281 + 1.51776i
\(545\) 49.0074i 0.0899218i
\(546\) 0.932409 + 0.446373i 0.00170771 + 0.000817532i
\(547\) −833.773 −1.52427 −0.762133 0.647421i \(-0.775848\pi\)
−0.762133 + 0.647421i \(0.775848\pi\)
\(548\) −244.678 141.265i −0.446493 0.257783i
\(549\) −223.994 + 24.6283i −0.408004 + 0.0448603i
\(550\) 17.9534 + 31.0961i 0.0326425 + 0.0565384i
\(551\) 145.821 + 84.1899i 0.264648 + 0.152795i
\(552\) −136.645 + 89.2044i −0.247545 + 0.161602i
\(553\) 2.97024 + 132.841i 0.00537114 + 0.240219i
\(554\) 155.650i 0.280957i
\(555\) 366.566 20.0915i 0.660479 0.0362009i
\(556\) −4.05011 7.01499i −0.00728436 0.0126169i
\(557\) −308.150 + 177.910i −0.553231 + 0.319408i −0.750424 0.660957i \(-0.770151\pi\)
0.197193 + 0.980365i \(0.436817\pi\)
\(558\) −177.216 + 130.056i −0.317591 + 0.233076i
\(559\) 0.947385 0.00169478
\(560\) 72.6226 132.543i 0.129683 0.236684i
\(561\) −786.770 + 513.618i −1.40244 + 0.915540i
\(562\) −83.6286 + 144.849i −0.148805 + 0.257738i
\(563\) −822.210 + 474.703i −1.46041 + 0.843167i −0.999030 0.0440357i \(-0.985978\pi\)
−0.461379 + 0.887203i \(0.652645\pi\)
\(564\) 343.866 678.891i 0.609692 1.20371i
\(565\) 66.9808 116.014i 0.118550 0.205335i
\(566\) 3.88360i 0.00686148i
\(567\) −135.535 550.563i −0.239040 0.971010i
\(568\) −630.416 −1.10989
\(569\) 3.80306 + 2.19570i 0.00668376 + 0.00385887i 0.503338 0.864090i \(-0.332105\pi\)
−0.496654 + 0.867948i \(0.665438\pi\)
\(570\) 113.844 + 57.6635i 0.199727 + 0.101164i
\(571\) 197.642 + 342.326i 0.346133 + 0.599520i 0.985559 0.169333i \(-0.0541612\pi\)
−0.639426 + 0.768853i \(0.720828\pi\)
\(572\) −1.90311 1.09876i −0.00332711 0.00192091i
\(573\) 310.661 + 475.876i 0.542166 + 0.830500i
\(574\) −1.72567 77.1789i −0.00300639 0.134458i
\(575\) 49.0626i 0.0853262i
\(576\) 89.2545 + 121.619i 0.154956 + 0.211144i
\(577\) −231.802 401.493i −0.401737 0.695829i 0.592199 0.805792i \(-0.298260\pi\)
−0.993936 + 0.109963i \(0.964927\pi\)
\(578\) −493.434 + 284.884i −0.853693 + 0.492880i
\(579\) 35.4430 + 646.651i 0.0612141 + 1.11684i
\(580\) 50.7725 0.0875389
\(581\) 170.124 + 280.015i 0.292812 + 0.481954i
\(582\) 180.414 + 276.361i 0.309989 + 0.474847i
\(583\) −246.863 + 427.580i −0.423436 + 0.733413i
\(584\) 203.584 117.539i 0.348603 0.201266i
\(585\) −0.145424 1.32264i −0.000248589 0.00226092i
\(586\) −23.6822 + 41.0187i −0.0404133 + 0.0699978i
\(587\) 641.429i 1.09272i 0.837549 + 0.546362i \(0.183988\pi\)
−0.837549 + 0.546362i \(0.816012\pi\)
\(588\) 461.638 + 208.447i 0.785099 + 0.354502i
\(589\) −838.245 −1.42317
\(590\) 125.255 + 72.3159i 0.212296 + 0.122569i
\(591\) 317.687 627.206i 0.537542 1.06126i
\(592\) −264.209 457.624i −0.446299 0.773013i
\(593\) 285.837 + 165.028i 0.482019 + 0.278294i 0.721257 0.692667i \(-0.243565\pi\)
−0.239239 + 0.970961i \(0.576898\pi\)
\(594\) −31.7075 191.286i −0.0533796 0.322030i
\(595\) 434.352 263.892i 0.730004 0.443516i
\(596\) 150.639i 0.252750i
\(597\) −61.0714 1114.24i −0.102297 1.86639i
\(598\) −0.241516 0.418318i −0.000403873 0.000699528i
\(599\) −408.273 + 235.716i −0.681590 + 0.393516i −0.800454 0.599394i \(-0.795408\pi\)
0.118864 + 0.992911i \(0.462075\pi\)
\(600\) 83.0268 4.55070i 0.138378 0.00758451i
\(601\) −92.4258 −0.153787 −0.0768933 0.997039i \(-0.524500\pi\)
−0.0768933 + 0.997039i \(0.524500\pi\)
\(602\) −74.6563 + 1.66926i −0.124014 + 0.00277286i
\(603\) −174.115 + 396.165i −0.288748 + 0.656991i
\(604\) 17.4049 30.1461i 0.0288160 0.0499108i
\(605\) −54.1462 + 31.2613i −0.0894979 + 0.0516716i
\(606\) 127.001 + 64.3275i 0.209573 + 0.106151i
\(607\) 144.614 250.479i 0.238244 0.412650i −0.721967 0.691928i \(-0.756762\pi\)
0.960210 + 0.279277i \(0.0900949\pi\)
\(608\) 750.267i 1.23399i
\(609\) 10.6603 + 137.973i 0.0175047 + 0.226556i
\(610\) 41.6833 0.0683333
\(611\) 4.21546 + 2.43380i 0.00689928 + 0.00398330i
\(612\) 110.049 + 1000.90i 0.179819 + 1.63546i
\(613\) 384.212 + 665.475i 0.626774 + 1.08560i 0.988195 + 0.153201i \(0.0489583\pi\)
−0.361421 + 0.932403i \(0.617708\pi\)
\(614\) 95.3844 + 55.0702i 0.155349 + 0.0896909i
\(615\) −83.2063 + 54.3186i −0.135295 + 0.0883230i
\(616\) 328.248 + 179.853i 0.532870 + 0.291969i
\(617\) 49.4273i 0.0801092i 0.999197 + 0.0400546i \(0.0127532\pi\)
−0.999197 + 0.0400546i \(0.987247\pi\)
\(618\) 133.940 7.34125i 0.216731 0.0118790i
\(619\) 141.832 + 245.660i 0.229131 + 0.396867i 0.957551 0.288265i \(-0.0930782\pi\)
−0.728420 + 0.685131i \(0.759745\pi\)
\(620\) −218.898 + 126.381i −0.353061 + 0.203840i
\(621\) −93.1654 + 248.017i −0.150025 + 0.399383i
\(622\) 68.2262 0.109688
\(623\) −367.329 + 8.21323i −0.589614 + 0.0131834i
\(624\) −1.60376 + 1.04696i −0.00257012 + 0.00167782i
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) 96.5352 55.7346i 0.154210 0.0890329i
\(627\) 334.100 659.609i 0.532854 1.05201i
\(628\) −152.319 + 263.824i −0.242546 + 0.420102i
\(629\) 1776.96i 2.82505i
\(630\) 13.7903 + 103.971i 0.0218893 + 0.165033i
\(631\) −129.777 −0.205668 −0.102834 0.994699i \(-0.532791\pi\)
−0.102834 + 0.994699i \(0.532791\pi\)
\(632\) 91.1282 + 52.6129i 0.144190 + 0.0832482i
\(633\) −480.816 243.539i −0.759583 0.384738i
\(634\) 26.2167 + 45.4086i 0.0413512 + 0.0716224i
\(635\) 277.185 + 160.033i 0.436512 + 0.252020i
\(636\) 289.241 + 443.064i 0.454781 + 0.696642i
\(637\) −1.49288 + 2.87535i −0.00234360 + 0.00451389i
\(638\) 47.3230i 0.0741740i
\(639\) −825.144 + 605.563i −1.29130 + 0.947673i
\(640\) −145.265 251.607i −0.226977 0.393136i
\(641\) −1054.68 + 608.920i −1.64537 + 0.949953i −0.666487 + 0.745517i \(0.732203\pi\)
−0.978880 + 0.204436i \(0.934464\pi\)
\(642\) −2.46860 45.0392i −0.00384517 0.0701545i
\(643\) −287.068 −0.446451 −0.223226 0.974767i \(-0.571659\pi\)
−0.223226 + 0.974767i \(0.571659\pi\)
\(644\) −122.891 202.272i −0.190824 0.314086i
\(645\) 52.5432 + 80.4867i 0.0814624 + 0.124786i
\(646\) 308.849 534.942i 0.478094 0.828084i
\(647\) 552.197 318.811i 0.853473 0.492753i −0.00834785 0.999965i \(-0.502657\pi\)
0.861821 + 0.507212i \(0.169324\pi\)
\(648\) −428.351 134.656i −0.661036 0.207803i
\(649\) 418.995 725.720i 0.645600 1.11821i
\(650\) 0.246130i 0.000378662i
\(651\) −389.396 568.312i −0.598150 0.872983i
\(652\) 673.036 1.03226
\(653\) −104.032 60.0629i −0.159314 0.0919799i 0.418223 0.908344i \(-0.362653\pi\)
−0.577537 + 0.816364i \(0.695986\pi\)
\(654\) −22.1192 + 43.6697i −0.0338214 + 0.0667732i
\(655\) −117.118 202.854i −0.178806 0.309700i
\(656\) 123.865 + 71.5133i 0.188818 + 0.109014i
\(657\) 153.563 349.404i 0.233734 0.531817i
\(658\) −336.477 184.362i −0.511363 0.280185i
\(659\) 254.620i 0.386373i 0.981162 + 0.193187i \(0.0618823\pi\)
−0.981162 + 0.193187i \(0.938118\pi\)
\(660\) −12.2018 222.620i −0.0184876 0.337303i
\(661\) −162.561 281.565i −0.245933 0.425968i 0.716461 0.697627i \(-0.245761\pi\)
−0.962393 + 0.271660i \(0.912428\pi\)
\(662\) 317.788 183.475i 0.480042 0.277152i
\(663\) −6.43091 + 0.352478i −0.00969971 + 0.000531641i
\(664\) 259.467 0.390764
\(665\) −192.183 + 350.751i −0.288996 + 0.527445i
\(666\) 335.709 + 147.544i 0.504068 + 0.221538i
\(667\) 32.3308 55.9987i 0.0484720 0.0839560i
\(668\) 587.928 339.440i 0.880131 0.508144i
\(669\) 332.500 + 168.415i 0.497010 + 0.251741i
\(670\) 40.0232 69.3222i 0.0597361 0.103466i
\(671\) 241.511i 0.359927i
\(672\) 508.665 348.526i 0.756941 0.518640i
\(673\) 184.479 0.274114 0.137057 0.990563i \(-0.456236\pi\)
0.137057 + 0.990563i \(0.456236\pi\)
\(674\) 207.531 + 119.818i 0.307910 + 0.177772i
\(675\) 104.301 85.7100i 0.154521 0.126978i
\(676\) 291.154 + 504.294i 0.430701 + 0.745996i
\(677\) 199.440 + 115.147i 0.294593 + 0.170084i 0.640011 0.768365i \(-0.278930\pi\)
−0.345418 + 0.938449i \(0.612263\pi\)
\(678\) 112.048 73.1469i 0.165262 0.107886i
\(679\) −883.987 + 537.069i −1.30190 + 0.790970i
\(680\) 402.479i 0.591881i
\(681\) −667.052 + 36.5612i −0.979518 + 0.0536875i
\(682\) −117.794 204.025i −0.172719 0.299157i
\(683\) 282.356 163.018i 0.413406 0.238680i −0.278846 0.960336i \(-0.589952\pi\)
0.692252 + 0.721656i \(0.256619\pi\)
\(684\) −468.825 638.824i −0.685417 0.933953i
\(685\) 183.346 0.267659
\(686\) 112.576 229.215i 0.164105 0.334133i
\(687\) 430.193 280.838i 0.626190 0.408789i
\(688\) 69.1759 119.816i 0.100546 0.174151i
\(689\) −2.93094 + 1.69218i −0.00425390 + 0.00245599i
\(690\) 22.1441 43.7189i 0.0320929 0.0633607i
\(691\) −497.886 + 862.363i −0.720529 + 1.24799i 0.240259 + 0.970709i \(0.422768\pi\)
−0.960788 + 0.277284i \(0.910566\pi\)
\(692\) 270.605i 0.391048i
\(693\) 602.402 79.9000i 0.869267 0.115296i
\(694\) 48.1558 0.0693887
\(695\) 4.55234 + 2.62829i 0.00655013 + 0.00378172i
\(696\) 97.7633 + 49.5183i 0.140464 + 0.0711469i
\(697\) 240.484 + 416.530i 0.345027 + 0.597605i
\(698\) 97.3970 + 56.2322i 0.139537 + 0.0805619i
\(699\) 632.449 + 968.797i 0.904791 + 1.38598i
\(700\) 2.69585 + 120.569i 0.00385121 + 0.172242i
\(701\) 1273.02i 1.81600i −0.418970 0.908000i \(-0.637609\pi\)
0.418970 0.908000i \(-0.362391\pi\)
\(702\) 0.467379 1.24422i 0.000665783 0.00177239i
\(703\) 699.182 + 1211.02i 0.994569 + 1.72264i
\(704\) −140.018 + 80.8392i −0.198889 + 0.114828i
\(705\) 27.0276 + 493.113i 0.0383370 + 0.699452i
\(706\) −260.484 −0.368958
\(707\) −214.393 + 391.286i −0.303243 + 0.553445i
\(708\) −490.920 752.001i −0.693390 1.06215i
\(709\) 480.408 832.091i 0.677585 1.17361i −0.298121 0.954528i \(-0.596360\pi\)
0.975706 0.219084i \(-0.0703069\pi\)
\(710\) 163.960 94.6622i 0.230929 0.133327i
\(711\) 169.815 18.6713i 0.238840 0.0262606i
\(712\) −145.484 + 251.985i −0.204331 + 0.353912i
\(713\) 321.905i 0.451480i
\(714\) 506.151 39.1072i 0.708894 0.0547721i
\(715\) 1.42607 0.00199450
\(716\) 810.388 + 467.878i 1.13183 + 0.653461i
\(717\) −384.182 + 758.486i −0.535819 + 1.05786i
\(718\) −204.349 353.942i −0.284608 0.492956i
\(719\) −548.388 316.612i −0.762710 0.440351i 0.0675581 0.997715i \(-0.478479\pi\)
−0.830268 + 0.557365i \(0.811813\pi\)
\(720\) −177.893 78.1840i −0.247074 0.108589i
\(721\) 9.39755 + 420.297i 0.0130340 + 0.582936i
\(722\) 217.323i 0.301002i
\(723\) −39.2897 716.834i −0.0543426 0.991471i
\(724\) 505.338 + 875.272i 0.697981 + 1.20894i
\(725\) −28.5343 + 16.4743i −0.0393577 + 0.0227232i
\(726\) −62.3585 + 3.41787i −0.0858932 + 0.00470781i
\(727\) 482.265 0.663363 0.331682 0.943391i \(-0.392384\pi\)
0.331682 + 0.943391i \(0.392384\pi\)
\(728\) 1.33218 + 2.19269i 0.00182991 + 0.00301194i
\(729\) −690.011 + 235.214i −0.946517 + 0.322654i
\(730\) −35.2990 + 61.1397i −0.0483548 + 0.0837530i
\(731\) 402.916 232.624i 0.551185 0.318227i
\(732\) −230.894 116.950i −0.315429 0.159768i
\(733\) 581.543 1007.26i 0.793374 1.37416i −0.130493 0.991449i \(-0.541656\pi\)
0.923867 0.382714i \(-0.125011\pi\)
\(734\) 277.625i 0.378235i
\(735\) −327.077 + 32.6409i −0.445003 + 0.0444094i
\(736\) −288.120 −0.391467
\(737\) −401.649 231.892i −0.544978 0.314643i
\(738\) −98.6602 + 10.8477i −0.133686 + 0.0146988i
\(739\) −28.8365 49.9463i −0.0390210 0.0675863i 0.845855 0.533412i \(-0.179091\pi\)
−0.884876 + 0.465826i \(0.845757\pi\)
\(740\) 365.166 + 210.829i 0.493467 + 0.284903i
\(741\) 4.24405 2.77060i 0.00572747 0.00373900i
\(742\) 227.984 138.512i 0.307256 0.186674i
\(743\) 1093.23i 1.47138i −0.677320 0.735689i \(-0.736859\pi\)
0.677320 0.735689i \(-0.263141\pi\)
\(744\) −544.749 + 29.8577i −0.732189 + 0.0401313i
\(745\) −48.8782 84.6595i −0.0656083 0.113637i
\(746\) −157.361 + 90.8524i −0.210940 + 0.121786i
\(747\) 339.614 249.238i 0.454637 0.333653i
\(748\) −1079.17 −1.44274
\(749\) 141.331 3.16006i 0.188693 0.00421904i
\(750\) −20.9104 + 13.6507i −0.0278806 + 0.0182010i
\(751\) −17.6663 + 30.5990i −0.0235237 + 0.0407443i −0.877548 0.479489i \(-0.840822\pi\)
0.854024 + 0.520234i \(0.174155\pi\)
\(752\) 615.607 355.421i 0.818626 0.472634i
\(753\) 482.266 952.131i 0.640459 1.26445i
\(754\) −0.162193 + 0.280926i −0.000215110 + 0.000372581i
\(755\) 22.5896i 0.0299200i
\(756\) 215.322 614.610i 0.284818 0.812977i
\(757\) 16.1191 0.0212934 0.0106467 0.999943i \(-0.496611\pi\)
0.0106467 + 0.999943i \(0.496611\pi\)
\(758\) 319.706 + 184.582i 0.421776 + 0.243513i
\(759\) −253.305 128.302i −0.333735 0.169041i
\(760\) 158.364 + 274.295i 0.208374 + 0.360914i
\(761\) −1015.70 586.417i −1.33470 0.770587i −0.348681 0.937242i \(-0.613370\pi\)
−0.986015 + 0.166654i \(0.946704\pi\)
\(762\) 174.765 + 267.709i 0.229351 + 0.351324i
\(763\) −134.545 73.7195i −0.176337 0.0966180i
\(764\) 652.734i 0.854364i
\(765\) −386.612 526.800i −0.505375 0.688628i
\(766\) 131.361 + 227.524i