Properties

Label 105.3.t.b.11.9
Level 105
Weight 3
Character 105.11
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 11.9
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.9

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.644768 + 0.372257i −0.322384 + 0.186129i −0.652455 0.757828i \(-0.726261\pi\)
0.330071 + 0.943956i \(0.392927\pi\)
\(3\) −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 0.0696804 0.997569i \(-0.477802\pi\)
−0.829080 + 0.559130i \(0.811135\pi\)
\(12\) 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 −0.975361 0.220615i \(-0.929194\pi\)
−0.678739 0.734380i \(-0.737473\pi\)
\(18\) −0.732324 + 6.66049i −0.0406846 + 0.370027i
\(19\) 12.7759 + 22.1286i 0.672418 + 1.16466i 0.977216 + 0.212246i \(0.0680777\pi\)
−0.304798 + 0.952417i \(0.598589\pi\)
\(20\) 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 −0.673228 0.739435i \(-0.735093\pi\)
0.303755 + 0.952750i \(0.401760\pi\)
\(24\) 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 \(-0.963757\pi\)
0.993525 0.113616i \(-0.0362433\pi\)
\(30\) 0.273330 4.98687i 0.00911102 0.166229i
\(31\) −16.4028 + 28.4105i −0.529123 + 0.916467i 0.470301 + 0.882506i \(0.344146\pi\)
−0.999423 + 0.0339609i \(0.989188\pi\)
\(32\) 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 −0.952700 0.303913i \(-0.901707\pi\)
0.213154 0.977019i \(-0.431627\pi\)
\(38\) −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 \(0.0578180\pi\)
−0.983549 + 0.180643i \(0.942182\pi\)
\(42\) −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 −0.989152 0.146893i \(-0.953073\pi\)
−0.367363 + 0.930078i \(0.619739\pi\)
\(48\) 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 0.856036 0.516917i \(-0.172920\pi\)
−0.0196455 + 0.999807i \(0.506254\pi\)
\(54\) −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 −0.299253 0.954174i \(-0.596737\pi\)
−0.975965 + 0.217926i \(0.930071\pi\)
\(60\) −10.4444 20.6202i −0.174073 0.343670i
\(61\) −12.5191 21.6838i −0.205232 0.355472i 0.744975 0.667093i \(-0.232461\pi\)
−0.950207 + 0.311621i \(0.899128\pi\)
\(62\) 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 −0.628943 0.777452i \(-0.716512\pi\)
0.987764 + 0.155954i \(0.0498453\pi\)
\(68\) 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 \(-0.704372\pi\)
0.598842 0.800867i \(-0.295628\pi\)
\(72\) −40.2216 29.5181i −0.558633 0.409974i
\(73\) −21.2034 + 36.7253i −0.290457 + 0.503086i −0.973918 0.226901i \(-0.927141\pi\)
0.683461 + 0.729987i \(0.260474\pi\)
\(74\) 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 0.919823 0.392334i \(-0.128332\pi\)
−0.799683 + 0.600423i \(0.794999\pi\)
\(80\) −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 \(0.0909865\pi\)
−0.959424 + 0.281966i \(0.909014\pi\)
\(84\) −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 −0.222393 0.974957i \(-0.571387\pi\)
0.733141 + 0.680077i \(0.238053\pi\)
\(90\) 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 0.747721 0.664013i \(-0.231148\pi\)
−0.201192 + 0.979552i \(0.564482\pi\)
\(102\) −64.6969 + 32.7698i −0.634283 + 0.321272i
\(103\) 30.0287 + 52.0112i 0.291541 + 0.504964i 0.974174 0.225797i \(-0.0724987\pi\)
−0.682633 + 0.730761i \(0.739165\pi\)
\(104\) 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 −0.579495 0.814976i \(-0.696750\pi\)
0.416042 + 0.909345i \(0.363417\pi\)
\(108\) −71.8783 59.0662i −0.665540 0.546909i
\(109\) 10.9584 18.9805i 0.100536 0.174133i −0.811370 0.584533i \(-0.801278\pi\)
0.911905 + 0.410400i \(0.134611\pi\)
\(110\) 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 \(0.0854004\pi\)
−0.964225 + 0.265086i \(0.914600\pi\)
\(114\) 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 −0.804552 0.593882i \(-0.797594\pi\)
0.112041 + 0.993704i \(0.464261\pi\)
\(132\) −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 0.736247 0.676713i \(-0.236596\pi\)
−0.217928 + 0.975965i \(0.569930\pi\)
\(138\) −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 −0.621640 0.783303i \(-0.713533\pi\)
0.367540 + 0.930008i \(0.380200\pi\)
\(150\) −5.04619 9.96262i −0.0336412 0.0664175i
\(151\) 5.05119 8.74891i 0.0334516 0.0579398i −0.848815 0.528690i \(-0.822683\pi\)
0.882267 + 0.470750i \(0.156017\pi\)
\(152\) 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 −0.971770 0.235930i \(-0.924186\pi\)
0.690207 + 0.723612i \(0.257520\pi\)
\(158\) −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 −0.992945 0.118574i \(-0.962168\pi\)
0.393784 0.919203i \(-0.371166\pi\)
\(164\) −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 \(-0.799172\pi\)
0.807485 0.589888i \(-0.200828\pi\)
\(168\) 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 −0.290382 0.956911i \(-0.593782\pi\)
0.683518 + 0.729934i \(0.260449\pi\)
\(174\) −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 −0.331162 0.943574i \(-0.607441\pi\)
−0.982740 + 0.184993i \(0.940774\pi\)
\(180\) 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 −0.863653 0.504087i \(-0.831829\pi\)
0.00472608 + 0.999989i \(0.498496\pi\)
\(192\) −44.8591 + 22.7216i −0.233641 + 0.118342i
\(193\) −107.937 + 186.952i −0.559259 + 0.968665i 0.438300 + 0.898829i \(0.355581\pi\)
−0.997558 + 0.0698359i \(0.977752\pi\)
\(194\) −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 \(-0.797224\pi\)
0.803861 0.594817i \(-0.202776\pi\)
\(198\) 38.2398 52.1058i 0.193131 0.263161i
\(199\) 185.985 322.135i 0.934597 1.61877i 0.159246 0.987239i \(-0.449094\pi\)
0.775351 0.631531i \(-0.217573\pi\)
\(200\) −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 0.860503 0.509446i \(-0.170150\pi\)
−0.0109416 + 0.999940i \(0.503483\pi\)
\(228\) 235.630 119.350i 1.03347 0.523463i
\(229\) −85.6244 148.306i −0.373906 0.647624i 0.616257 0.787545i \(-0.288648\pi\)
−0.990163 + 0.139921i \(0.955315\pi\)
\(230\) 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 −0.997380 0.0723454i \(-0.976952\pi\)
−0.436037 + 0.899929i \(0.643618\pi\)
\(234\) 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 \(0.202021\pi\)
−0.805268 + 0.592911i \(0.797979\pi\)
\(240\) 64.6749 + 3.54483i 0.269479 + 0.0147701i
\(241\) 119.652 207.243i 0.496480 0.859928i −0.503512 0.863988i \(-0.667959\pi\)
0.999992 + 0.00406029i \(0.00129244\pi\)
\(242\) 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 \(-0.749282\pi\)
0.705510 0.708700i \(-0.250718\pi\)
\(252\) 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 −0.897950 0.440098i \(-0.854944\pi\)
−0.0678386 + 0.997696i \(0.521610\pi\)
\(258\) −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 0.505355 0.862912i \(-0.331362\pi\)
−0.494626 + 0.869106i \(0.664695\pi\)
\(264\) 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 0.561604 0.827406i \(-0.310185\pi\)
−0.435753 + 0.900066i \(0.643518\pi\)
\(270\) −34.7279 28.5377i −0.128622 0.105695i
\(271\) 116.865 + 202.415i 0.431235 + 0.746921i 0.996980 0.0776596i \(-0.0247447\pi\)
−0.565745 + 0.824580i \(0.691411\pi\)
\(272\) 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 −0.613309 0.789843i \(-0.710162\pi\)
0.990679 + 0.136220i \(0.0434954\pi\)
\(278\) −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 \(0.130899\pi\)
−0.916629 + 0.399738i \(0.869101\pi\)
\(282\) −8.99901 + 164.185i −0.0319114 + 0.582218i
\(283\) 2.60814 4.51743i 0.00921605 0.0159627i −0.861381 0.507960i \(-0.830400\pi\)
0.870597 + 0.491997i \(0.163733\pi\)
\(284\) 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 \(0.0346249\pi\)
−0.994090 + 0.108563i \(0.965375\pi\)
\(294\) 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 0.366953 0.930239i \(-0.380401\pi\)
−0.622134 + 0.782911i \(0.713734\pi\)
\(312\) −0.496845 0.980915i −0.00159245 0.00314396i
\(313\) −74.8604 129.662i −0.239170 0.414255i 0.721306 0.692617i \(-0.243542\pi\)
−0.960476 + 0.278361i \(0.910209\pi\)
\(314\) 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 −0.593106 0.805125i \(-0.702098\pi\)
0.400705 + 0.916207i \(0.368765\pi\)
\(318\) 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 −0.950420 0.310970i \(-0.899346\pi\)
0.205902 0.978573i \(-0.433987\pi\)
\(332\) −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 0.417110 0.908856i \(-0.363043\pi\)
−0.578537 + 0.815656i \(0.696376\pi\)
\(348\) −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 0.863459 0.504418i \(-0.168293\pi\)
−0.00510945 + 0.999987i \(0.501626\pi\)
\(354\) −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 0.339834 0.940485i \(-0.389629\pi\)
0.984401 + 0.175938i \(0.0562958\pi\)
\(360\) −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 0.491927 + 0.870636i \(0.336293\pi\)
−0.999957 + 0.00929679i \(0.997041\pi\)
\(368\) 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 0.981946 0.189160i \(-0.0605765\pi\)
−0.654791 + 0.755810i \(0.727243\pi\)
\(374\) −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 −0.842741 0.538320i \(-0.819059\pi\)
0.0448283 + 0.998995i \(0.485726\pi\)
\(384\) 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 0.373419 0.927663i \(-0.378185\pi\)
−0.616670 + 0.787222i \(0.711519\pi\)
\(390\) −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 −0.914816 0.403870i \(-0.867665\pi\)
0.107647 0.994189i \(-0.465668\pi\)
\(398\) 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 −0.363412 0.931628i \(-0.618388\pi\)
0.625108 + 0.780538i \(0.285055\pi\)
\(402\) −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 −0.578576 0.815628i \(-0.696391\pi\)
0.995643 + 0.0932474i \(0.0297247\pi\)
\(410\) −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 \(-0.923656\pi\)
0.971376 0.237549i \(-0.0763439\pi\)
\(420\) −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 0.999342 + 0.0362605i \(0.0115446\pi\)
0.531074 + 0.847326i \(0.321789\pi\)
\(432\) 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 0.949992 0.312275i \(-0.101091\pi\)
−0.745434 + 0.666579i \(0.767758\pi\)
\(440\) 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 0.402036 0.915624i \(-0.368302\pi\)
0.993972 + 0.109638i \(0.0349692\pi\)
\(444\) −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 \(0.0656437\pi\)
−0.978811 + 0.204767i \(0.934356\pi\)
\(450\) 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 −0.937230 0.348711i \(-0.886619\pi\)
0.166622 0.986021i \(-0.446714\pi\)
\(458\) 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 \(0.310754\pi\)
−0.560123 + 0.828410i \(0.689246\pi\)
\(462\) 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 −0.515615 0.856820i \(-0.672436\pi\)
0.484221 + 0.874946i \(0.339103\pi\)
\(468\) −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 0.205025 0.978757i \(-0.434272\pi\)
−0.745116 + 0.666935i \(0.767606\pi\)
\(480\) −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 −0.984257 0.176745i \(-0.943443\pi\)
0.645194 + 0.764019i \(0.276776\pi\)
\(488\) −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 \(-0.881596\pi\)
0.931611 0.363457i \(-0.118404\pi\)
\(492\) 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 0.619217 0.785220i \(-0.287450\pi\)
−0.989629 + 0.143647i \(0.954117\pi\)
\(500\) 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 \(-0.972978\pi\)
0.996399 0.0847913i \(-0.0270224\pi\)
\(504\) 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 −0.734658 0.678437i \(-0.762657\pi\)
0.220215 + 0.975451i \(0.429324\pi\)
\(510\) −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 0.0484786 0.998824i \(-0.484563\pi\)
−0.840768 + 0.541396i \(0.817896\pi\)
\(522\) 43.8907 + 4.82580i 0.0840818 + 0.00924483i
\(523\) 17.4690 + 30.2571i 0.0334015 + 0.0578530i 0.882243 0.470794i \(-0.156033\pi\)
−0.848841 + 0.528648i \(0.822699\pi\)
\(524\) 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 0.999489 0.0319640i \(-0.0101762\pi\)
−0.527426 + 0.849601i \(0.676843\pi\)
\(542\) −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 0.197193 0.980365i \(-0.436817\pi\)
−0.750424 + 0.660957i \(0.770151\pi\)
\(558\) −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 −0.461379 0.887203i \(-0.652645\pi\)
−0.999030 + 0.0440357i \(0.985978\pi\)
\(564\) 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 −0.496654 0.867948i \(-0.665438\pi\)
0.503338 + 0.864090i \(0.332105\pi\)
\(570\) 113.844 57.6635i 0.199727 0.101164i
\(571\) 197.642 342.326i 0.346133 0.599520i −0.639426 0.768853i \(-0.720828\pi\)
0.985559 + 0.169333i \(0.0541612\pi\)
\(572\) −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 −0.993936 0.109963i \(-0.964927\pi\)
0.592199 + 0.805792i \(0.298260\pi\)
\(578\) −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 \(-0.816012\pi\)
0.837549 0.546362i \(-0.183988\pi\)
\(588\) 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 −0.239239 0.970961i \(-0.576898\pi\)
0.721257 + 0.692667i \(0.243565\pi\)
\(594\) −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 0.118864 0.992911i \(-0.462075\pi\)
−0.800454 + 0.599394i \(0.795408\pi\)
\(600\) 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 0.960210 0.279277i \(-0.0900949\pi\)
−0.721967 + 0.691928i \(0.756762\pi\)
\(608\) 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 −0.361421 0.932403i \(-0.617708\pi\)
0.988195 0.153201i \(-0.0489583\pi\)
\(614\) 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 \(-0.987247\pi\)
0.999197 0.0400546i \(-0.0127532\pi\)
\(618\) 133.940 + 7.34125i 0.216731 + 0.0118790i
\(619\) 141.832 245.660i 0.229131 0.396867i −0.728420 0.685131i \(-0.759745\pi\)
0.957551 + 0.288265i \(0.0930782\pi\)
\(620\) −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 −0.978880 0.204436i \(-0.934464\pi\)
−0.666487 0.745517i \(-0.732203\pi\)
\(642\) −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 0.861821 0.507212i \(-0.169324\pi\)
−0.00834785 + 0.999965i \(0.502657\pi\)
\(648\) −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 −0.577537 0.816364i \(-0.695986\pi\)
0.418223 + 0.908344i \(0.362653\pi\)
\(654\) −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 \(-0.938118\pi\)
0.981162 0.193187i \(-0.0618823\pi\)
\(660\) −12.2018 + 222.620i −0.0184876 + 0.337303i
\(661\) −162.561 + 281.565i −0.245933 + 0.425968i −0.962393 0.271660i \(-0.912428\pi\)
0.716461 + 0.697627i \(0.245761\pi\)
\(662\) 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 −0.345418 0.938449i \(-0.612263\pi\)
0.640011 + 0.768365i \(0.278930\pi\)
\(678\) 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 0.692252 0.721656i \(-0.256619\pi\)
−0.278846 + 0.960336i \(0.589952\pi\)
\(684\) −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 −0.960788 0.277284i \(-0.910566\pi\)
0.240259 0.970709i \(-0.422768\pi\)
\(692\) 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 \(0.362391\pi\)
−0.418970 + 0.908000i \(0.637609\pi\)
\(702\) 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 0.975706 + 0.219084i \(0.0703069\pi\)
−0.298121 + 0.954528i \(0.596360\pi\)
\(710\) 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 −0.830268 0.557365i \(-0.811813\pi\)
0.0675581 + 0.997715i \(0.478479\pi\)
\(720\) −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 0.923867 + 0.382714i \(0.125011\pi\)
−0.130493 + 0.991449i \(0.541656\pi\)
\(734\) 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 −0.884876 0.465826i \(-0.845757\pi\)
0.845855 + 0.533412i \(0.179091\pi\)
\(740\) 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 \(0.263141\pi\)
−0.677320 + 0.735689i \(0.736859\pi\)
\(744\) −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 0.854024 0.520234i \(-0.174155\pi\)
−0.877548 + 0.479489i \(0.840822\pi\)
\(752\) 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 −0.986015 0.166654i \(-0.946704\pi\)
−0.348681 + 0.937242i \(0.613370\pi\)
\(762\) 174.765 267.709i 0.229351 0.351324i
\(763\) −134.545 + 73.7195i −0.176337 + 0.0966180i
\(764\) 652.734i 0.854364i