Properties

Label 105.3.t.b.11.10
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 11.10
Character \(\chi\) \(=\) 105.11
Dual form 105.3.t.b.86.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.644768 - 0.372257i) q^{2} +(0.164184 + 2.99550i) q^{3} +(-1.72285 + 2.98406i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(1.22096 + 1.87029i) q^{6} +(-5.98242 - 3.63464i) q^{7} +5.54343i q^{8} +(-8.94609 + 0.983626i) q^{9} +O(q^{10})\) \(q+(0.644768 - 0.372257i) q^{2} +(0.164184 + 2.99550i) 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} +(-8.94609 + 0.983626i) q^{9} +(-0.832392 + 1.44175i) q^{10} +(8.35340 + 4.82284i) q^{11} +(-9.22163 - 4.67087i) 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} +(-5.40199 + 3.96446i) q^{18} +(12.7759 + 22.1286i) q^{19} -7.70482i q^{20} +(9.90535 - 18.5171i) q^{21} +7.18134 q^{22} +(8.49789 - 4.90626i) q^{23} +(-16.6054 + 0.910141i) 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} +(-4.45542 - 2.25672i) q^{30} +(-16.4028 + 28.4105i) q^{31} +(-25.4286 - 14.6812i) q^{32} +(-13.0753 + 25.8145i) 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} +(-0.0108556 - 0.198058i) q^{39} +(-6.19774 - 10.7348i) q^{40} -14.8128i q^{41} +(-0.506474 - 15.6266i) q^{42} -14.3286 q^{43} +(-28.7833 + 16.6180i) q^{44} +(16.2243 - 11.9068i) 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} +(-44.0149 + 86.8982i) q^{51} +(0.113912 - 0.197301i) q^{52} +(-44.3287 - 25.5932i) q^{53} +(-12.7625 - 15.5308i) 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} +(23.0798 - 1.26501i) q^{60} +(-12.5191 - 21.6838i) q^{61} +24.4242i q^{62} +(57.0944 + 26.6313i) q^{63} +16.7618 q^{64} +(0.128038 - 0.0739226i) q^{65} +(1.17906 + 21.5117i) 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} +(-5.45266 - 49.5920i) q^{72} +(-21.2034 + 36.7253i) q^{73} +(-35.2859 - 20.3723i) q^{74} +(13.3814 + 6.77782i) 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} +(79.0650 - 17.5992i) q^{81} +(-5.51416 - 9.55080i) q^{82} -46.8063i q^{83} +(38.1908 + 61.4604i) q^{84} -72.6047 q^{85} +(-9.23863 + 5.33393i) q^{86} +(-19.7395 + 1.08192i) 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} +(-87.7968 - 44.4701i) q^{93} +(27.4053 - 47.4674i) q^{94} +(-49.4810 - 28.5679i) q^{95} +(39.8027 - 78.5820i) 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 −0.330071 0.943956i \(-0.607073\pi\)
0.652455 + 0.757828i \(0.273739\pi\)
\(3\) 0.164184 + 2.99550i 0.0547279 + 0.998501i
\(4\) −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
\(9\) −8.94609 + 0.983626i −0.994010 + 0.109292i
\(10\) −0.832392 + 1.44175i −0.0832392 + 0.144175i
\(11\) 8.35340 + 4.82284i 0.759400 + 0.438440i 0.829080 0.559130i \(-0.188865\pi\)
−0.0696804 + 0.997569i \(0.522198\pi\)
\(12\) −9.22163 4.67087i −0.768470 0.389239i
\(13\) −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 \(0.0708064\pi\)
0.678739 + 0.734380i \(0.262527\pi\)
\(18\) −5.40199 + 3.96446i −0.300111 + 0.220248i
\(19\) 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
\(21\) 9.90535 18.5171i 0.471684 0.881768i
\(22\) 7.18134 0.326425
\(23\) 8.49789 4.90626i 0.369473 0.213316i −0.303755 0.952750i \(-0.598240\pi\)
0.673228 + 0.739435i \(0.264907\pi\)
\(24\) −16.6054 + 0.910141i −0.691890 + 0.0379225i
\(25\) 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 \(0.963757\pi\)
\(30\) −4.45542 2.25672i −0.148514 0.0752241i
\(31\) −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
\(33\) −13.0753 + 25.8145i −0.396222 + 0.782257i
\(34\) 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
\(39\) −0.0108556 0.198058i −0.000278348 0.00507841i
\(40\) −6.19774 10.7348i −0.154944 0.268370i
\(41\) 14.8128i 0.361287i −0.983549 0.180643i \(-0.942182\pi\)
0.983549 0.180643i \(-0.0578180\pi\)
\(42\) −0.506474 15.6266i −0.0120589 0.372062i
\(43\) −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
\(45\) 16.2243 11.9068i 0.360540 0.264596i
\(46\) 3.65278 6.32680i 0.0794082 0.137539i
\(47\) 63.7562 36.8097i 1.35652 0.783184i 0.367363 0.930078i \(-0.380261\pi\)
0.989152 + 0.146893i \(0.0469274\pi\)
\(48\) 24.2558 15.8347i 0.505330 0.329889i
\(49\) 22.5788 + 43.4879i 0.460792 + 0.887508i
\(50\) 3.72257i 0.0744514i
\(51\) −44.0149 + 86.8982i −0.863038 + 1.70389i
\(52\) 0.113912 0.197301i 0.00219062 0.00379426i
\(53\) −44.3287 25.5932i −0.836390 0.482890i 0.0196455 0.999807i \(-0.493746\pi\)
−0.856036 + 0.516917i \(0.827080\pi\)
\(54\) −12.7625 15.5308i −0.236342 0.287607i
\(55\) −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 \(-0.0699292\pi\)
0.299253 + 0.954174i \(0.403263\pi\)
\(60\) 23.0798 1.26501i 0.384663 0.0210834i
\(61\) −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
\(63\) 57.0944 + 26.6313i 0.906261 + 0.422719i
\(64\) 16.7618 0.261903
\(65\) 0.128038 0.0739226i 0.00196981 0.00113727i
\(66\) 1.17906 + 21.5117i 0.0178645 + 0.325935i
\(67\) 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 \(0.295628\pi\)
−0.598842 + 0.800867i \(0.704372\pi\)
\(72\) −5.45266 49.5920i −0.0757314 0.688778i
\(73\) −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
\(75\) 13.3814 + 6.77782i 0.178418 + 0.0903710i
\(76\) −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
\(81\) 79.0650 17.5992i 0.976111 0.217274i
\(82\) −5.51416 9.55080i −0.0672458 0.116473i
\(83\) 46.8063i 0.563932i −0.959424 0.281966i \(-0.909014\pi\)
0.959424 0.281966i \(-0.0909865\pi\)
\(84\) 38.1908 + 61.4604i 0.454653 + 0.731672i
\(85\) −72.6047 −0.854173
\(86\) −9.23863 + 5.33393i −0.107426 + 0.0620224i
\(87\) −19.7395 + 1.08192i −0.226891 + 0.0124359i
\(88\) −26.7350 + 46.3065i −0.303807 + 0.526210i
\(89\) −45.4566 + 26.2444i −0.510748 + 0.294881i −0.733141 0.680077i \(-0.761947\pi\)
0.222393 + 0.974957i \(0.428613\pi\)
\(90\) 6.02851 13.7167i 0.0669835 0.152408i
\(91\) 0.395548 + 0.240316i 0.00434668 + 0.00264084i
\(92\) 33.8110i 0.367511i
\(93\) −87.7968 44.4701i −0.944052 0.478173i
\(94\) 27.4053 47.4674i 0.291546 0.504972i
\(95\) −49.4810 28.5679i −0.520853 0.300715i
\(96\) 39.8027 78.5820i 0.414612 0.818563i
\(97\) 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 \(-0.435518\pi\)
−0.747721 + 0.664013i \(0.768852\pi\)
\(102\) 3.96902 + 72.4140i 0.0389119 + 0.709942i
\(103\) 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
\(105\) 1.52114 + 46.9328i 0.0144870 + 0.446979i
\(106\) −38.1090 −0.359518
\(107\) 17.4895 10.0976i 0.163454 0.0943700i −0.416042 0.909345i \(-0.636583\pi\)
0.579495 + 0.814976i \(0.303250\pi\)
\(108\) 87.0919 + 32.7153i 0.806407 + 0.302920i
\(109\) 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 \(-0.914600\pi\)
0.964225 0.265086i \(-0.0854004\pi\)
\(114\) −25.7879 + 50.9128i −0.226210 + 0.446603i
\(115\) −10.9707 + 19.0019i −0.0953976 + 0.165234i
\(116\) −19.6641 11.3531i −0.169518 0.0978714i
\(117\) 0.591501 0.0650358i 0.00505556 0.000555861i
\(118\) 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
\(123\) 44.3717 2.43201i 0.360745 0.0197725i
\(124\) −56.5191 97.8940i −0.455799 0.789468i
\(125\) 11.1803i 0.0894427i
\(126\) 46.7264 4.08278i 0.370844 0.0324030i
\(127\) 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
\(129\) −2.35252 42.9214i −0.0182366 0.332724i
\(130\) 0.0550364 0.0953259i 0.000423357 0.000733276i
\(131\) 90.7189 52.3766i 0.692511 0.399821i −0.112041 0.993704i \(-0.535739\pi\)
0.804552 + 0.593882i \(0.202406\pi\)
\(132\) −54.5052 83.4921i −0.412918 0.632516i
\(133\) 3.99826 178.819i 0.0300621 1.34450i
\(134\) 35.7978i 0.267148i
\(135\) 38.3307 + 46.6450i 0.283931 + 0.345519i
\(136\) −89.9971 + 155.879i −0.661743 + 1.14617i
\(137\) −71.0097 40.9975i −0.518319 0.299252i 0.217928 0.975965i \(-0.430070\pi\)
−0.736247 + 0.676713i \(0.763404\pi\)
\(138\) 19.5517 + 9.90315i 0.141679 + 0.0717620i
\(139\) 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
\(144\) 51.4152 + 70.0586i 0.357050 + 0.486518i
\(145\) −7.36753 12.7609i −0.0508105 0.0880064i
\(146\) 31.5724i 0.216249i
\(147\) −126.561 + 74.7749i −0.860960 + 0.508673i
\(148\) 188.571 1.27413
\(149\) 37.8609 21.8590i 0.254100 0.146705i −0.367540 0.930008i \(-0.619800\pi\)
0.621640 + 0.783303i \(0.286467\pi\)
\(150\) 11.1510 0.611186i 0.0743398 0.00407457i
\(151\) 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
\(156\) 0.609720 + 0.308830i 0.00390846 + 0.00197968i
\(157\) −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
\(159\) 69.3864 136.989i 0.436392 0.861564i
\(160\) 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
\(165\) −3.54118 64.6082i −0.0214617 0.391565i
\(166\) −17.4240 30.1792i −0.104964 0.181803i
\(167\) 197.023i 1.17978i 0.807485 + 0.589888i \(0.200828\pi\)
−0.807485 + 0.589888i \(0.799172\pi\)
\(168\) 102.648 + 54.9096i 0.611002 + 0.326843i
\(169\) −168.996 −0.999974
\(170\) −46.8132 + 27.0276i −0.275372 + 0.158986i
\(171\) −136.061 185.398i −0.795678 1.08420i
\(172\) 24.6860 42.7575i 0.143523 0.248590i
\(173\) −68.0126 + 39.2671i −0.393136 + 0.226977i −0.683518 0.729934i \(-0.739551\pi\)
0.290382 + 0.956911i \(0.406218\pi\)
\(174\) −12.3247 + 8.04577i −0.0708314 + 0.0462400i
\(175\) −30.6945 + 16.8181i −0.175397 + 0.0961032i
\(176\) 93.1351i 0.529177i
\(177\) −117.768 + 232.507i −0.665354 + 1.31360i
\(178\) −19.5393 + 33.8431i −0.109771 + 0.190130i
\(179\) 235.188 + 135.786i 1.31390 + 0.758581i 0.982740 0.184993i \(-0.0592261\pi\)
0.331162 + 0.943574i \(0.392559\pi\)
\(180\) 7.57866 + 68.9280i 0.0421037 + 0.382933i
\(181\) −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
\(186\) −73.1629 + 4.01006i −0.393349 + 0.0215595i
\(187\) 156.597 + 271.233i 0.837415 + 1.45045i
\(188\) 253.670i 1.34931i
\(189\) −70.4002 + 175.399i −0.372488 + 0.928037i
\(190\) −42.5384 −0.223886
\(191\) 164.055 94.7172i 0.858927 0.495902i −0.00472608 0.999989i \(-0.501504\pi\)
0.863653 + 0.504087i \(0.168171\pi\)
\(192\) 2.75201 + 50.2099i 0.0143334 + 0.261510i
\(193\) −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 \(0.202776\pi\)
−0.803861 + 0.594817i \(0.797224\pi\)
\(198\) −64.2449 + 7.06375i −0.324469 + 0.0356755i
\(199\) 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
\(201\) 128.681 + 65.1784i 0.640204 + 0.324271i
\(202\) −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
\(207\) −71.1969 + 52.2506i −0.343946 + 0.252418i
\(208\) 0.319207 + 0.552884i 0.00153465 + 0.00265809i
\(209\) 246.465i 1.17926i
\(210\) 18.4518 + 29.6945i 0.0878659 + 0.141402i
\(211\) 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
\(213\) −340.658 + 18.6715i −1.59933 + 0.0876595i
\(214\) 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
\(219\) −113.492 57.4851i −0.518229 0.262489i
\(220\) 37.1591 64.3614i 0.168905 0.292552i
\(221\) −1.85923 1.07343i −0.00841280 0.00485713i
\(222\) 55.2319 109.044i 0.248793 0.491188i
\(223\) −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 \(-0.496517\pi\)
−0.860503 + 0.509446i \(0.829850\pi\)
\(228\) −14.4554 263.737i −0.0634009 1.15674i
\(229\) −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
\(231\) 172.048 106.909i 0.744798 0.462810i
\(232\) −36.5296 −0.157455
\(233\) 333.986 192.827i 1.43342 0.827583i 0.436037 0.899929i \(-0.356382\pi\)
0.997380 + 0.0723454i \(0.0230484\pi\)
\(234\) 0.357171 0.262123i 0.00152637 0.00112019i
\(235\) −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 \(-0.202021\pi\)
\(240\) −29.2675 + 57.7825i −0.121948 + 0.240760i
\(241\) 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
\(243\) 65.6997 + 233.950i 0.270369 + 0.962757i
\(244\) 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
\(249\) 140.209 7.68484i 0.563086 0.0308628i
\(250\) 4.16196 + 7.20873i 0.0166478 + 0.0288349i
\(251\) 355.767i 1.41740i 0.705510 + 0.708700i \(0.250718\pi\)
−0.705510 + 0.708700i \(0.749282\pi\)
\(252\) −177.835 + 124.492i −0.705693 + 0.494014i
\(253\) 94.6483 0.374104
\(254\) 92.2907 53.2841i 0.363349 0.209780i
\(255\) −11.9205 217.488i −0.0467471 0.852893i
\(256\) 14.8436 25.7098i 0.0579827 0.100429i
\(257\) 248.208 143.303i 0.965788 0.557598i 0.0678386 0.997696i \(-0.478390\pi\)
0.897950 + 0.440098i \(0.145056\pi\)
\(258\) −17.4946 26.7986i −0.0678086 0.103871i
\(259\) −8.56338 + 382.989i −0.0330632 + 1.47872i
\(260\) 0.509430i 0.00195935i
\(261\) −6.48182 58.9522i −0.0248345 0.225870i
\(262\) 38.9951 67.5415i 0.148836 0.257792i
\(263\) −2.82179 1.62916i −0.0107292 0.00619452i 0.494626 0.869106i \(-0.335305\pi\)
−0.505355 + 0.862912i \(0.668638\pi\)
\(264\) −143.101 72.4822i −0.542048 0.274554i
\(265\) 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 \(-0.356482\pi\)
−0.561604 + 0.827406i \(0.689815\pi\)
\(270\) 42.0783 + 15.8064i 0.155846 + 0.0585421i
\(271\) 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
\(273\) −0.654926 + 1.22432i −0.00239900 + 0.00448470i
\(274\) −61.0464 −0.222797
\(275\) 41.7670 24.1142i 0.151880 0.0876879i
\(276\) −101.281 + 5.55121i −0.366960 + 0.0201131i
\(277\) 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 \(-0.869101\pi\)
0.916629 0.399738i \(-0.130899\pi\)
\(282\) 146.688 + 74.2994i 0.520171 + 0.263473i
\(283\) 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
\(285\) 77.4512 152.911i 0.271759 0.536530i
\(286\) −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
\(291\) 24.2605 + 442.628i 0.0833693 + 1.52106i
\(292\) −73.0604 126.544i −0.250207 0.433371i
\(293\) 63.6178i 0.217126i −0.994090 0.108563i \(-0.965375\pi\)
0.994090 0.108563i \(-0.0346249\pi\)
\(294\) −53.7671 + 95.3258i −0.182881 + 0.324237i
\(295\) −194.263 −0.658520
\(296\) 262.728 151.686i 0.887594 0.512453i
\(297\) 91.5813 243.800i 0.308355 0.820875i
\(298\) 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
\(303\) 86.4020 170.582i 0.285155 0.562978i
\(304\) 123.360 213.666i 0.405789 0.702847i
\(305\) 48.4864 + 27.9936i 0.158972 + 0.0917824i
\(306\) −216.265 + 23.7784i −0.706748 + 0.0777072i
\(307\) −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 \(-0.286266\pi\)
−0.366953 + 0.930239i \(0.619599\pi\)
\(312\) 1.09792 0.0601770i 0.00351897 0.000192875i
\(313\) −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
\(315\) −140.338 + 12.2622i −0.445516 + 0.0389275i
\(316\) −65.4065 −0.206983
\(317\) 60.9909 35.2131i 0.192400 0.111082i −0.400705 0.916207i \(-0.631235\pi\)
0.593106 + 0.805125i \(0.297902\pi\)
\(318\) −6.25687 114.156i −0.0196757 0.358980i
\(319\) −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
\(324\) −83.6999 + 266.256i −0.258333 + 0.821776i
\(325\) −0.165296 + 0.286301i −0.000508603 + 0.000880926i
\(326\) −125.940 72.7116i −0.386320 0.223042i
\(327\) 58.6553 + 29.7096i 0.179374 + 0.0908550i
\(328\) 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
\(333\) 291.412 + 397.080i 0.875111 + 1.19243i
\(334\) 73.3430 + 127.034i 0.219590 + 0.380341i
\(335\) 107.515i 0.320940i
\(336\) −202.662 + 6.56848i −0.603160 + 0.0195490i
\(337\) −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
\(339\) 179.459 9.83616i 0.529378 0.0290152i
\(340\) 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
\(345\) −58.7213 29.7431i −0.170207 0.0862118i
\(346\) −29.2349 + 50.6363i −0.0844939 + 0.146348i
\(347\) 56.0152 + 32.3404i 0.161427 + 0.0932000i 0.578537 0.815656i \(-0.303624\pi\)
−0.417110 + 0.908856i \(0.636957\pi\)
\(348\) 30.7797 60.7679i 0.0884474 0.174621i
\(349\) −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 \(-0.498374\pi\)
−0.863459 + 0.504418i \(0.831707\pi\)
\(354\) 10.6196 + 193.753i 0.0299989 + 0.547325i
\(355\) −127.146 220.224i −0.358159 0.620349i
\(356\) 180.860i 0.508035i
\(357\) 579.159 359.883i 1.62230 1.00808i
\(358\) 202.189 0.564775
\(359\) −475.400 + 274.473i −1.32424 + 0.764548i −0.984401 0.175938i \(-0.943704\pi\)
−0.339834 + 0.940485i \(0.610371\pi\)
\(360\) 66.0046 + 89.9382i 0.183346 + 0.249828i
\(361\) −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
\(366\) 25.2695 49.8893i 0.0690425 0.136310i
\(367\) −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
\(369\) 14.5702 + 132.516i 0.0394857 + 0.359123i
\(370\) 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
\(375\) −33.4908 + 1.83563i −0.0893087 + 0.00489501i
\(376\) 204.052 + 353.428i 0.542691 + 0.939968i
\(377\) 0.435701i 0.00115571i
\(378\) 19.9017 + 139.299i 0.0526499 + 0.368515i
\(379\) −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
\(381\) 23.5009 + 428.770i 0.0616822 + 1.12538i
\(382\) 70.5183 122.141i 0.184603 0.319742i
\(383\) 305.600 176.438i 0.797912 0.460675i −0.0448283 0.998995i \(-0.514274\pi\)
0.842741 + 0.538320i \(0.180941\pi\)
\(384\) 213.076 + 326.394i 0.554886 + 0.849984i
\(385\) 129.031 + 78.3933i 0.335146 + 0.203619i
\(386\) 160.721i 0.416376i
\(387\) 128.185 14.0940i 0.331227 0.0364186i
\(388\) −254.575 + 440.937i −0.656122 + 1.13644i
\(389\) 94.6247 + 54.6316i 0.243251 + 0.140441i 0.616670 0.787222i \(-0.288481\pi\)
−0.373419 + 0.927663i \(0.621815\pi\)
\(390\) 0.294585 + 0.149211i 0.000755347 + 0.000382592i
\(391\) 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
\(396\) 241.152 176.978i 0.608969 0.446915i
\(397\) −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
\(399\) 536.308 17.3823i 1.34413 0.0435647i
\(400\) −48.2782 −0.120695
\(401\) −104.940 + 60.5871i −0.261695 + 0.151090i −0.625108 0.780538i \(-0.714945\pi\)
0.363412 + 0.931628i \(0.381612\pi\)
\(402\) 107.232 5.87742i 0.266748 0.0146204i
\(403\) 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
\(408\) −481.714 243.994i −1.18067 0.598024i
\(409\) 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
\(411\) 111.149 219.441i 0.270437 0.533920i
\(412\) −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
\(417\) 0.385966 + 7.04188i 0.000925578 + 0.0168870i
\(418\) 91.7484 + 158.913i 0.219494 + 0.380175i
\(419\) 199.066i 0.475097i 0.971376 + 0.237549i \(0.0763439\pi\)
−0.971376 + 0.237549i \(0.923656\pi\)
\(420\) −142.671 76.3189i −0.339693 0.181712i
\(421\) 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
\(423\) −534.162 + 392.015i −1.26279 + 0.926749i
\(424\) 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
\(429\) 0.864520 1.70681i 0.00201520 0.00397858i
\(430\) 11.9270 20.6582i 0.0277373 0.0480423i
\(431\) −659.609 380.826i −1.53042 0.883586i −0.999342 0.0362605i \(-0.988455\pi\)
−0.531074 0.847326i \(-0.678211\pi\)
\(432\) −201.419 + 165.517i −0.466249 + 0.383141i
\(433\) −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
\(438\) −94.5753 + 5.18368i −0.215925 + 0.0118349i
\(439\) 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
\(441\) −244.768 366.837i −0.555029 0.831831i
\(442\) −1.59836 −0.00361620
\(443\) −618.432 + 357.052i −1.39601 + 0.805986i −0.993972 0.109638i \(-0.965031\pi\)
−0.402036 + 0.915624i \(0.631698\pi\)
\(444\) 30.9603 + 564.864i 0.0697303 + 1.27222i
\(445\) 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 \(-0.0656437\pi\)
\(450\) 3.66162 + 33.3024i 0.00813693 + 0.0740054i
\(451\) 71.4395 123.737i 0.158403 0.274361i
\(452\) 178.774 + 103.215i 0.395517 + 0.228352i
\(453\) 27.0367 + 13.6944i 0.0596837 + 0.0302305i
\(454\) −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
\(459\) 308.286 820.693i 0.671648 1.78800i
\(460\) −37.8018 65.4747i −0.0821779 0.142336i
\(461\) 763.794i 1.65682i −0.560123 0.828410i \(-0.689246\pi\)
0.560123 0.828410i \(-0.310754\pi\)
\(462\) 71.1337 132.978i 0.153969 0.287831i
\(463\) 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
\(465\) 219.737 12.0438i 0.472552 0.0259006i
\(466\) 143.562 248.657i 0.308074 0.533599i
\(467\) 14.6611 8.46457i 0.0313941 0.0181254i −0.484221 0.874946i \(-0.660897\pi\)
0.515615 + 0.856820i \(0.327564\pi\)
\(468\) −0.824996 + 1.87712i −0.00176281 + 0.00401095i
\(469\) −295.171 + 161.730i −0.629363 + 0.344839i
\(470\) 122.560i 0.260767i
\(471\) −236.612 119.847i −0.502361 0.254452i
\(472\) −240.799 + 417.076i −0.510167 + 0.883635i
\(473\) −119.693 69.1045i −0.253050 0.146098i
\(474\) −19.1574 + 37.8222i −0.0404165 + 0.0797938i
\(475\) 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 \(-0.232394\pi\)
−0.205025 + 0.978757i \(0.565728\pi\)
\(480\) 10.7797 + 196.674i 0.0224578 + 0.409738i
\(481\) 1.80921 + 3.13365i 0.00376135 + 0.00651486i
\(482\) 178.165i 0.369636i
\(483\) −6.67520 205.955i −0.0138203 0.426407i
\(484\) 96.3451 0.199060
\(485\) −286.144 + 165.205i −0.589987 + 0.340629i
\(486\) 129.451 + 126.386i 0.266359 + 0.260054i
\(487\) −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 \(0.118404\pi\)
−0.931611 + 0.363457i \(0.881596\pi\)
\(492\) −69.1885 + 136.598i −0.140627 + 0.277638i
\(493\) −106.983 + 185.301i −0.217005 + 0.375864i
\(494\) −1.08930 0.628910i −0.00220507 0.00127310i
\(495\) 192.953 21.2152i 0.389803 0.0428590i
\(496\) 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
\(501\) −590.182 + 32.3479i −1.17801 + 0.0645667i
\(502\) 132.437 + 229.387i 0.263819 + 0.456947i
\(503\) 85.3001i 0.169583i 0.996399 + 0.0847913i \(0.0270224\pi\)
−0.996399 + 0.0847913i \(0.972978\pi\)
\(504\) −147.629 + 316.499i −0.292914 + 0.627974i
\(505\) 142.524 0.282226
\(506\) 61.0262 35.2335i 0.120605 0.0696314i
\(507\) −27.7463 506.227i −0.0547265 0.998475i
\(508\) −246.605 + 427.132i −0.485443 + 0.840812i
\(509\) 261.852 151.180i 0.514443 0.297014i −0.220215 0.975451i \(-0.570676\pi\)
0.734658 + 0.678437i \(0.237343\pi\)
\(510\) −88.6473 135.792i −0.173818 0.266258i
\(511\) 260.331 142.640i 0.509454 0.279139i
\(512\) 497.614i 0.971903i
\(513\) 533.020 438.011i 1.03903 0.853822i
\(514\) 106.691 184.794i 0.207570 0.359522i
\(515\) −116.301 67.1462i −0.225827 0.130381i
\(516\) 132.133 + 66.9270i 0.256072 + 0.129704i
\(517\) 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 \(-0.182104\pi\)
−0.0484786 + 0.998824i \(0.515437\pi\)
\(522\) −26.1246 35.5976i −0.0500472 0.0681946i
\(523\) 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
\(525\) −55.4181 89.1843i −0.105558 0.169875i
\(526\) −2.42586 −0.00461191
\(527\) −922.483 + 532.596i −1.75044 + 1.01062i
\(528\) 278.987 15.2913i 0.528384 0.0289607i
\(529\) −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
\(534\) −104.585 52.9736i −0.195852 0.0992014i
\(535\) −22.5789 + 39.1078i −0.0422035 + 0.0730987i
\(536\) 230.830 + 133.270i 0.430653 + 0.248638i
\(537\) −368.134 + 726.802i −0.685537 + 1.35345i
\(538\) −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
\(543\) −48.1576 878.628i −0.0886881 1.61810i
\(544\) −476.697 825.664i −0.876281 1.51776i
\(545\) 49.0074i 0.0899218i
\(546\) 0.0334872 + 1.03321i 6.13319e−5 + 0.00189232i
\(547\) −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
\(549\) 133.326 + 181.671i 0.242852 + 0.330912i
\(550\) 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
\(555\) −165.883 + 327.501i −0.298889 + 0.590092i
\(556\) −4.05011 + 7.01499i −0.00728436 + 0.0126169i
\(557\) 308.150 + 177.910i 0.553231 + 0.319408i 0.750424 0.660957i \(-0.229849\pi\)
−0.197193 + 0.980365i \(0.563183\pi\)
\(558\) −24.0243 218.501i −0.0430543 0.391579i
\(559\) 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 \(-0.0140215\pi\)
0.461379 + 0.887203i \(0.347355\pi\)
\(564\) −759.870 + 41.6485i −1.34729 + 0.0738448i
\(565\) 66.9808 + 116.014i 0.118550 + 0.205335i
\(566\) 3.88360i 0.00686148i
\(567\) −536.967 182.087i −0.947032 0.321140i
\(568\) −630.416 −1.10989
\(569\) −3.80306 + 2.19570i −0.00668376 + 0.00385887i −0.503338 0.864090i \(-0.667895\pi\)
0.496654 + 0.867948i \(0.334562\pi\)
\(570\) −6.98411 127.424i −0.0122528 0.223551i
\(571\) 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
\(576\) −149.952 + 16.4873i −0.260334 + 0.0286238i
\(577\) −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
\(579\) −577.738 292.631i −0.997820 0.505408i
\(580\) 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
\(585\) −1.07272 + 0.787259i −0.00183372 + 0.00134574i
\(586\) −23.6822 41.0187i −0.0404133 0.0699978i
\(587\) 641.429i 1.09272i 0.837549 + 0.546362i \(0.183988\pi\)
−0.837549 + 0.546362i \(0.816012\pi\)
\(588\) −5.08742 506.492i −0.00865208 0.861381i
\(589\) −838.245 −1.42317
\(590\) −125.255 + 72.3159i −0.212296 + 0.122569i
\(591\) −702.020 + 38.4778i −1.18785 + 0.0651062i
\(592\) −264.209 + 457.624i −0.446299 + 0.773013i
\(593\) −285.837 + 165.028i −0.482019 + 0.278294i −0.721257 0.692667i \(-0.756435\pi\)
0.239239 + 0.970961i \(0.423102\pi\)
\(594\) −31.7075 191.286i −0.0533796 0.322030i
\(595\) 434.352 + 263.892i 0.730004 + 0.443516i
\(596\) 150.639i 0.252750i
\(597\) 995.493 + 504.229i 1.66749 + 0.844604i
\(598\) −0.241516 + 0.418318i −0.000403873 + 0.000699528i
\(599\) 408.273 + 235.716i 0.681590 + 0.393516i 0.800454 0.599394i \(-0.204592\pi\)
−0.118864 + 0.992911i \(0.537925\pi\)
\(600\) −37.5724 + 74.1787i −0.0626206 + 0.123631i
\(601\) −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
\(606\) −7.79124 142.150i −0.0128568 0.234571i
\(607\) 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
\(609\) 122.023 + 65.2735i 0.200365 + 0.107181i
\(610\) 41.6833 0.0683333
\(611\) −4.21546 + 2.43380i −0.00689928 + 0.00398330i
\(612\) 811.780 595.755i 1.32644 0.973456i
\(613\) 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 \(0.0127532\pi\)
−0.999197 + 0.0400546i \(0.987247\pi\)
\(618\) −60.6122 + 119.666i −0.0980780 + 0.193634i
\(619\) 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
\(621\) −168.206 204.692i −0.270863 0.329617i
\(622\) 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
\(627\) −738.288 + 40.4656i −1.17749 + 0.0645384i
\(628\) −152.319 263.824i −0.242546 0.420102i
\(629\) 1776.96i 2.82505i
\(630\) −85.9205 + 60.1479i −0.136382 + 0.0954729i
\(631\) −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
\(633\) 29.4970 + 538.168i 0.0465988 + 0.850187i
\(634\) 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
\(639\) −111.861 1017.38i −0.175056 1.59214i
\(640\) −145.265 + 251.607i −0.226977 + 0.393136i
\(641\) 1054.68 + 608.920i 1.64537 + 0.949953i 0.978880 + 0.204436i \(0.0655362\pi\)
0.666487 + 0.745517i \(0.267797\pi\)
\(642\) 40.2394 + 20.3817i 0.0626782 + 0.0317472i
\(643\) −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 \(-0.497343\pi\)
−0.861821 + 0.507212i \(0.830676\pi\)
\(648\) 97.5599 + 438.291i 0.150555 + 0.676375i
\(649\) 418.995 + 725.720i 0.645600 + 1.11821i
\(650\) 0.246130i 0.000378662i
\(651\) 363.605 + 585.149i 0.558533 + 0.898846i
\(652\) 673.036 1.03226
\(653\) 104.032 60.0629i 0.159314 0.0919799i −0.418223 0.908344i \(-0.637347\pi\)
0.577537 + 0.816364i \(0.304014\pi\)
\(654\) 48.8787 2.67904i 0.0747380 0.00409640i
\(655\) −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 \(0.938118\pi\)
\(660\) 198.896 + 100.743i 0.301357 + 0.152641i
\(661\) −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
\(663\) 2.91020 5.74557i 0.00438944 0.00866601i
\(664\) 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
\(669\) −20.3982 372.161i −0.0304905 0.556294i
\(670\) 40.0232 + 69.3222i 0.0597361 + 0.103466i
\(671\) 241.511i 0.359927i
\(672\) −523.734 + 325.443i −0.779366 + 0.484290i
\(673\) 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
\(675\) −126.378 47.4727i −0.187226 0.0703300i
\(676\) 291.154 504.294i 0.430701 0.745996i
\(677\) −199.440 + 115.147i −0.294593 + 0.170084i −0.640011 0.768365i \(-0.721070\pi\)
0.345418 + 0.938449i \(0.387737\pi\)
\(678\) 112.048 73.1469i 0.165262 0.107886i
\(679\) −883.987 537.069i −1.30190 0.790970i
\(680\) 402.479i 0.591881i
\(681\) 301.863 595.965i 0.443265 0.875132i
\(682\) −117.794 + 204.025i −0.172719 + 0.299157i
\(683\) −282.356 163.018i −0.413406 0.238680i 0.278846 0.960336i \(-0.410048\pi\)
−0.692252 + 0.721656i \(0.743381\pi\)
\(684\) 787.651 86.6025i 1.15154 0.126612i
\(685\) 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
\(690\) −48.9337 + 2.68206i −0.0709184 + 0.00388704i
\(691\) −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
\(693\) 348.494 + 497.819i 0.502877 + 0.718354i
\(694\) 48.1558 0.0693887
\(695\) −4.55234 + 2.62829i −0.00655013 + 0.00378172i
\(696\) −5.99757 109.425i −0.00861720 0.157219i
\(697\) 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 \(-0.362391\pi\)
\(702\) 0.843833 + 1.02687i 0.00120204 + 0.00146278i
\(703\) 699.182 1211.02i 0.994569 1.72264i
\(704\) 140.018 + 80.8392i 0.198889 + 0.114828i
\(705\) −440.562 223.150i −0.624911 0.316525i
\(706\) −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
\(711\) −101.077 137.729i −0.142162 0.193711i
\(712\) −145.484 251.985i −0.204331 0.353912i
\(713\) 321.905i 0.451480i
\(714\) 239.454 447.638i 0.335370 0.626943i
\(715\) 1.42607 0.00199450
\(716\) −810.388 + 467.878i −1.13183 + 0.653461i
\(717\) 848.960 46.5315i 1.18404 0.0648975i
\(718\) −204.349 + 353.942i −0.284608 + 0.492956i
\(719\) 548.388 316.612i 0.762710 0.440351i −0.0675581 0.997715i \(-0.521521\pi\)
0.830268 + 0.557365i \(0.188187\pi\)
\(720\) −177.893 78.1840i −0.247074 0.108589i
\(721\) 9.39755 420.297i 0.0130340 0.582936i
\(722\) 217.323i 0.301002i
\(723\) 640.441 + 324.391i 0.885810 + 0.448673i
\(724\) 505.338 875.272i 0.697981 1.20894i
\(725\) 28.5343 + 16.4743i 0.0393577 + 0.0227232i
\(726\) 28.2193 55.7129i 0.0388695 0.0767396i
\(727\) 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
\(732\) 14.1648 + 258.435i 0.0193509 + 0.353053i
\(733\) 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
\(735\) 161.484 286.301i 0.219706 0.389525i
\(736\) −288.120 −0.391467
\(737\) 401.649 231.892i 0.544978 0.314643i
\(738\) 58.7245 + 80.0184i 0.0795725 + 0.108426i
\(739\) −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 \(-0.736859\pi\)
0.677320 0.735689i \(-0.263141\pi\)
\(744\) 246.517 486.695i 0.331340 0.654160i
\(745\) −48.8782 + 84.6595i −0.0656083 + 0.113637i
\(746\) 157.361 + 90.8524i 0.210940 + 0.121786i
\(747\) 46.0399 + 418.733i 0.0616331 + 0.560553i
\(748\) −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
\(753\) −1065.70 + 58.4112i −1.41528 + 0.0775713i
\(754\) −0.162193 0.280926i −0.000215110 0.000372581i
\(755\) 22.5896i 0.0299200i
\(756\) −402.113 512.265i −0.531895 0.677599i
\(757\) 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
\(759\) 15.5397 + 283.519i 0.0204739 + 0.373543i
\(760\) 158.364 274.295i 0.208374 0.360914i
\(761\) 1015.70 586.417i 1.33470 0.770587i 0.348681 0.937242i \(-0.386630\pi\)
0.986015 + 0.166654i \(0.0532964\pi\)
\(762\) 174.765 + 267.709i 0.229351 + 0.351324i
\(763\) −134.545 + 73.7195i −0.176337 + 0.0966180i
\(764\) 652.734i 0.854364i
\(765\)