Properties

Label 731.2.e.a.307.19
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.19
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.19

$q$-expansion

\(f(q)\) \(=\) \(q+0.715873 q^{2} +(-1.27871 + 2.21478i) q^{3} -1.48753 q^{4} +(0.380045 - 0.658258i) q^{5} +(-0.915390 + 1.58550i) q^{6} +(-1.25160 - 2.16783i) q^{7} -2.49662 q^{8} +(-1.77018 - 3.06604i) q^{9} +O(q^{10})\) \(q+0.715873 q^{2} +(-1.27871 + 2.21478i) q^{3} -1.48753 q^{4} +(0.380045 - 0.658258i) q^{5} +(-0.915390 + 1.58550i) q^{6} +(-1.25160 - 2.16783i) q^{7} -2.49662 q^{8} +(-1.77018 - 3.06604i) q^{9} +(0.272064 - 0.471229i) q^{10} +3.64255 q^{11} +(1.90211 - 3.29455i) q^{12} +(-0.946091 - 1.63868i) q^{13} +(-0.895984 - 1.55189i) q^{14} +(0.971932 + 1.68344i) q^{15} +1.18779 q^{16} +(0.500000 + 0.866025i) q^{17} +(-1.26722 - 2.19489i) q^{18} +(3.30791 - 5.72947i) q^{19} +(-0.565328 + 0.979176i) q^{20} +6.40170 q^{21} +2.60761 q^{22} +(-1.37206 + 2.37648i) q^{23} +(3.19245 - 5.52948i) q^{24} +(2.21113 + 3.82979i) q^{25} +(-0.677281 - 1.17308i) q^{26} +1.38191 q^{27} +(1.86178 + 3.22470i) q^{28} +(-1.32854 - 2.30110i) q^{29} +(0.695780 + 1.20513i) q^{30} +(3.99769 - 6.92420i) q^{31} +5.84355 q^{32} +(-4.65776 + 8.06747i) q^{33} +(0.357936 + 0.619964i) q^{34} -1.90265 q^{35} +(2.63318 + 4.56081i) q^{36} +(0.162196 - 0.280931i) q^{37} +(2.36804 - 4.10157i) q^{38} +4.83909 q^{39} +(-0.948831 + 1.64342i) q^{40} +3.56122 q^{41} +4.58280 q^{42} +(5.24004 + 3.94234i) q^{43} -5.41840 q^{44} -2.69099 q^{45} +(-0.982221 + 1.70126i) q^{46} -1.45379 q^{47} +(-1.51883 + 2.63069i) q^{48} +(0.367011 - 0.635682i) q^{49} +(1.58289 + 2.74164i) q^{50} -2.55741 q^{51} +(1.40734 + 2.43758i) q^{52} +(4.87867 - 8.45010i) q^{53} +0.989269 q^{54} +(1.38434 - 2.39774i) q^{55} +(3.12477 + 5.41226i) q^{56} +(8.45969 + 14.6526i) q^{57} +(-0.951067 - 1.64730i) q^{58} -11.5260 q^{59} +(-1.44578 - 2.50416i) q^{60} +(-4.32567 - 7.49228i) q^{61} +(2.86184 - 4.95685i) q^{62} +(-4.43109 + 7.67488i) q^{63} +1.80767 q^{64} -1.43823 q^{65} +(-3.33436 + 5.77528i) q^{66} +(4.90932 - 8.50320i) q^{67} +(-0.743763 - 1.28824i) q^{68} +(-3.50892 - 6.07763i) q^{69} -1.36206 q^{70} +(-1.74234 - 3.01783i) q^{71} +(4.41947 + 7.65474i) q^{72} +(7.33800 + 12.7098i) q^{73} +(0.116111 - 0.201111i) q^{74} -11.3095 q^{75} +(-4.92060 + 8.52273i) q^{76} +(-4.55901 - 7.89644i) q^{77} +3.46417 q^{78} +(-4.69908 - 8.13904i) q^{79} +(0.451413 - 0.781870i) q^{80} +(3.54348 - 6.13749i) q^{81} +2.54938 q^{82} +(0.889198 - 1.54014i) q^{83} -9.52269 q^{84} +0.760091 q^{85} +(3.75120 + 2.82221i) q^{86} +6.79526 q^{87} -9.09409 q^{88} +(6.92596 - 11.9961i) q^{89} -1.92641 q^{90} +(-2.36825 + 4.10193i) q^{91} +(2.04098 - 3.53507i) q^{92} +(10.2237 + 17.7080i) q^{93} -1.04073 q^{94} +(-2.51431 - 4.35492i) q^{95} +(-7.47219 + 12.9422i) q^{96} +14.8714 q^{97} +(0.262733 - 0.455067i) q^{98} +(-6.44797 - 11.1682i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.715873 0.506198 0.253099 0.967440i \(-0.418550\pi\)
0.253099 + 0.967440i \(0.418550\pi\)
\(3\) −1.27871 + 2.21478i −0.738261 + 1.27871i 0.215017 + 0.976610i \(0.431019\pi\)
−0.953278 + 0.302095i \(0.902314\pi\)
\(4\) −1.48753 −0.743763
\(5\) 0.380045 0.658258i 0.169961 0.294382i −0.768445 0.639916i \(-0.778969\pi\)
0.938406 + 0.345534i \(0.112302\pi\)
\(6\) −0.915390 + 1.58550i −0.373707 + 0.647279i
\(7\) −1.25160 2.16783i −0.473059 0.819362i 0.526465 0.850197i \(-0.323517\pi\)
−0.999525 + 0.0308342i \(0.990184\pi\)
\(8\) −2.49662 −0.882690
\(9\) −1.77018 3.06604i −0.590059 1.02201i
\(10\) 0.272064 0.471229i 0.0860342 0.149016i
\(11\) 3.64255 1.09827 0.549136 0.835733i \(-0.314957\pi\)
0.549136 + 0.835733i \(0.314957\pi\)
\(12\) 1.90211 3.29455i 0.549091 0.951054i
\(13\) −0.946091 1.63868i −0.262398 0.454487i 0.704480 0.709724i \(-0.251180\pi\)
−0.966879 + 0.255236i \(0.917847\pi\)
\(14\) −0.895984 1.55189i −0.239462 0.414760i
\(15\) 0.971932 + 1.68344i 0.250952 + 0.434661i
\(16\) 1.18779 0.296947
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) −1.26722 2.19489i −0.298687 0.517341i
\(19\) 3.30791 5.72947i 0.758886 1.31443i −0.184532 0.982826i \(-0.559077\pi\)
0.943419 0.331603i \(-0.107590\pi\)
\(20\) −0.565328 + 0.979176i −0.126411 + 0.218950i
\(21\) 6.40170 1.39696
\(22\) 2.60761 0.555943
\(23\) −1.37206 + 2.37648i −0.286094 + 0.495530i −0.972874 0.231336i \(-0.925690\pi\)
0.686780 + 0.726866i \(0.259024\pi\)
\(24\) 3.19245 5.52948i 0.651656 1.12870i
\(25\) 2.21113 + 3.82979i 0.442226 + 0.765958i
\(26\) −0.677281 1.17308i −0.132826 0.230061i
\(27\) 1.38191 0.265948
\(28\) 1.86178 + 3.22470i 0.351844 + 0.609412i
\(29\) −1.32854 2.30110i −0.246704 0.427304i 0.715905 0.698198i \(-0.246014\pi\)
−0.962609 + 0.270893i \(0.912681\pi\)
\(30\) 0.695780 + 1.20513i 0.127031 + 0.220025i
\(31\) 3.99769 6.92420i 0.718006 1.24362i −0.243782 0.969830i \(-0.578388\pi\)
0.961789 0.273793i \(-0.0882785\pi\)
\(32\) 5.84355 1.03300
\(33\) −4.65776 + 8.06747i −0.810811 + 1.40437i
\(34\) 0.357936 + 0.619964i 0.0613856 + 0.106323i
\(35\) −1.90265 −0.321607
\(36\) 2.63318 + 4.56081i 0.438864 + 0.760135i
\(37\) 0.162196 0.280931i 0.0266648 0.0461848i −0.852385 0.522915i \(-0.824845\pi\)
0.879050 + 0.476730i \(0.158178\pi\)
\(38\) 2.36804 4.10157i 0.384147 0.665362i
\(39\) 4.83909 0.774874
\(40\) −0.948831 + 1.64342i −0.150023 + 0.259848i
\(41\) 3.56122 0.556169 0.278084 0.960557i \(-0.410300\pi\)
0.278084 + 0.960557i \(0.410300\pi\)
\(42\) 4.58280 0.707141
\(43\) 5.24004 + 3.94234i 0.799098 + 0.601201i
\(44\) −5.41840 −0.816854
\(45\) −2.69099 −0.401149
\(46\) −0.982221 + 1.70126i −0.144821 + 0.250837i
\(47\) −1.45379 −0.212057 −0.106028 0.994363i \(-0.533813\pi\)
−0.106028 + 0.994363i \(0.533813\pi\)
\(48\) −1.51883 + 2.63069i −0.219224 + 0.379708i
\(49\) 0.367011 0.635682i 0.0524302 0.0908117i
\(50\) 1.58289 + 2.74164i 0.223854 + 0.387727i
\(51\) −2.55741 −0.358109
\(52\) 1.40734 + 2.43758i 0.195162 + 0.338031i
\(53\) 4.87867 8.45010i 0.670137 1.16071i −0.307728 0.951474i \(-0.599569\pi\)
0.977865 0.209237i \(-0.0670979\pi\)
\(54\) 0.989269 0.134622
\(55\) 1.38434 2.39774i 0.186664 0.323311i
\(56\) 3.12477 + 5.41226i 0.417565 + 0.723243i
\(57\) 8.45969 + 14.6526i 1.12051 + 1.94078i
\(58\) −0.951067 1.64730i −0.124881 0.216301i
\(59\) −11.5260 −1.50056 −0.750278 0.661122i \(-0.770080\pi\)
−0.750278 + 0.661122i \(0.770080\pi\)
\(60\) −1.44578 2.50416i −0.186649 0.323285i
\(61\) −4.32567 7.49228i −0.553845 0.959289i −0.997992 0.0633345i \(-0.979826\pi\)
0.444147 0.895954i \(-0.353507\pi\)
\(62\) 2.86184 4.95685i 0.363454 0.629520i
\(63\) −4.43109 + 7.67488i −0.558265 + 0.966944i
\(64\) 1.80767 0.225958
\(65\) −1.43823 −0.178391
\(66\) −3.33436 + 5.77528i −0.410431 + 0.710888i
\(67\) 4.90932 8.50320i 0.599769 1.03883i −0.393085 0.919502i \(-0.628592\pi\)
0.992855 0.119329i \(-0.0380743\pi\)
\(68\) −0.743763 1.28824i −0.0901945 0.156222i
\(69\) −3.50892 6.07763i −0.422425 0.731661i
\(70\) −1.36206 −0.162797
\(71\) −1.74234 3.01783i −0.206778 0.358150i 0.743920 0.668269i \(-0.232964\pi\)
−0.950698 + 0.310119i \(0.899631\pi\)
\(72\) 4.41947 + 7.65474i 0.520839 + 0.902120i
\(73\) 7.33800 + 12.7098i 0.858848 + 1.48757i 0.873029 + 0.487668i \(0.162152\pi\)
−0.0141816 + 0.999899i \(0.504514\pi\)
\(74\) 0.116111 0.201111i 0.0134977 0.0233786i
\(75\) −11.3095 −1.30591
\(76\) −4.92060 + 8.52273i −0.564432 + 0.977625i
\(77\) −4.55901 7.89644i −0.519547 0.899882i
\(78\) 3.46417 0.392240
\(79\) −4.69908 8.13904i −0.528688 0.915714i −0.999440 0.0334488i \(-0.989351\pi\)
0.470753 0.882265i \(-0.343982\pi\)
\(80\) 0.451413 0.781870i 0.0504695 0.0874158i
\(81\) 3.54348 6.13749i 0.393720 0.681943i
\(82\) 2.54938 0.281532
\(83\) 0.889198 1.54014i 0.0976022 0.169052i −0.813089 0.582139i \(-0.802216\pi\)
0.910692 + 0.413087i \(0.135549\pi\)
\(84\) −9.52269 −1.03901
\(85\) 0.760091 0.0824434
\(86\) 3.75120 + 2.82221i 0.404502 + 0.304327i
\(87\) 6.79526 0.728528
\(88\) −9.09409 −0.969434
\(89\) 6.92596 11.9961i 0.734150 1.27158i −0.220945 0.975286i \(-0.570914\pi\)
0.955095 0.296299i \(-0.0957524\pi\)
\(90\) −1.92641 −0.203061
\(91\) −2.36825 + 4.10193i −0.248260 + 0.429999i
\(92\) 2.04098 3.53507i 0.212786 0.368557i
\(93\) 10.2237 + 17.7080i 1.06015 + 1.83624i
\(94\) −1.04073 −0.107343
\(95\) −2.51431 4.35492i −0.257963 0.446805i
\(96\) −7.47219 + 12.9422i −0.762627 + 1.32091i
\(97\) 14.8714 1.50996 0.754982 0.655745i \(-0.227645\pi\)
0.754982 + 0.655745i \(0.227645\pi\)
\(98\) 0.262733 0.455067i 0.0265401 0.0459688i
\(99\) −6.44797 11.1682i −0.648045 1.12245i
\(100\) −3.28912 5.69692i −0.328912 0.569692i
\(101\) 4.08019 + 7.06710i 0.405994 + 0.703202i 0.994437 0.105337i \(-0.0335920\pi\)
−0.588443 + 0.808539i \(0.700259\pi\)
\(102\) −1.83078 −0.181274
\(103\) −8.55020 14.8094i −0.842476 1.45921i −0.887795 0.460239i \(-0.847764\pi\)
0.0453191 0.998973i \(-0.485570\pi\)
\(104\) 2.36203 + 4.09116i 0.231617 + 0.401172i
\(105\) 2.43294 4.21397i 0.237430 0.411241i
\(106\) 3.49251 6.04920i 0.339222 0.587550i
\(107\) −7.75826 −0.750020 −0.375010 0.927021i \(-0.622361\pi\)
−0.375010 + 0.927021i \(0.622361\pi\)
\(108\) −2.05562 −0.197802
\(109\) −3.74818 + 6.49204i −0.359011 + 0.621825i −0.987796 0.155754i \(-0.950219\pi\)
0.628785 + 0.777579i \(0.283553\pi\)
\(110\) 0.991009 1.71648i 0.0944890 0.163660i
\(111\) 0.414801 + 0.718456i 0.0393711 + 0.0681928i
\(112\) −1.48663 2.57492i −0.140473 0.243307i
\(113\) −15.7319 −1.47993 −0.739967 0.672644i \(-0.765159\pi\)
−0.739967 + 0.672644i \(0.765159\pi\)
\(114\) 6.05606 + 10.4894i 0.567202 + 0.982422i
\(115\) 1.04289 + 1.80634i 0.0972501 + 0.168442i
\(116\) 1.97624 + 3.42295i 0.183489 + 0.317813i
\(117\) −3.34950 + 5.80150i −0.309661 + 0.536349i
\(118\) −8.25114 −0.759579
\(119\) 1.25160 2.16783i 0.114734 0.198725i
\(120\) −2.42655 4.20291i −0.221513 0.383671i
\(121\) 2.26821 0.206201
\(122\) −3.09663 5.36352i −0.280356 0.485590i
\(123\) −4.55375 + 7.88733i −0.410598 + 0.711176i
\(124\) −5.94667 + 10.2999i −0.534027 + 0.924961i
\(125\) 7.16177 0.640569
\(126\) −3.17210 + 5.49424i −0.282593 + 0.489466i
\(127\) −12.5597 −1.11449 −0.557246 0.830347i \(-0.688142\pi\)
−0.557246 + 0.830347i \(0.688142\pi\)
\(128\) −10.3930 −0.918624
\(129\) −15.4319 + 6.56445i −1.35870 + 0.577968i
\(130\) −1.02959 −0.0903010
\(131\) 3.30173 0.288473 0.144237 0.989543i \(-0.453927\pi\)
0.144237 + 0.989543i \(0.453927\pi\)
\(132\) 6.92853 12.0006i 0.603052 1.04452i
\(133\) −16.5607 −1.43599
\(134\) 3.51445 6.08721i 0.303602 0.525855i
\(135\) 0.525187 0.909651i 0.0452009 0.0782903i
\(136\) −1.24831 2.16214i −0.107042 0.185402i
\(137\) −0.977597 −0.0835218 −0.0417609 0.999128i \(-0.513297\pi\)
−0.0417609 + 0.999128i \(0.513297\pi\)
\(138\) −2.51194 4.35081i −0.213831 0.370366i
\(139\) 3.68381 6.38055i 0.312457 0.541191i −0.666437 0.745562i \(-0.732181\pi\)
0.978894 + 0.204370i \(0.0655147\pi\)
\(140\) 2.83025 0.239200
\(141\) 1.85897 3.21983i 0.156553 0.271158i
\(142\) −1.24730 2.16038i −0.104671 0.181295i
\(143\) −3.44619 5.96897i −0.288185 0.499151i
\(144\) −2.10259 3.64180i −0.175216 0.303483i
\(145\) −2.01963 −0.167721
\(146\) 5.25307 + 9.09859i 0.434747 + 0.753004i
\(147\) 0.938599 + 1.62570i 0.0774143 + 0.134086i
\(148\) −0.241270 + 0.417892i −0.0198323 + 0.0343505i
\(149\) −2.01327 + 3.48708i −0.164933 + 0.285673i −0.936632 0.350316i \(-0.886074\pi\)
0.771698 + 0.635989i \(0.219408\pi\)
\(150\) −8.09619 −0.661051
\(151\) −14.6830 −1.19488 −0.597441 0.801913i \(-0.703816\pi\)
−0.597441 + 0.801913i \(0.703816\pi\)
\(152\) −8.25861 + 14.3043i −0.669862 + 1.16023i
\(153\) 1.77018 3.06604i 0.143110 0.247874i
\(154\) −3.26367 5.65284i −0.262994 0.455519i
\(155\) −3.03861 5.26302i −0.244067 0.422736i
\(156\) −7.19827 −0.576323
\(157\) −1.97089 3.41369i −0.157294 0.272442i 0.776598 0.629997i \(-0.216944\pi\)
−0.933892 + 0.357555i \(0.883610\pi\)
\(158\) −3.36394 5.82652i −0.267621 0.463533i
\(159\) 12.4768 + 21.6104i 0.989472 + 1.71382i
\(160\) 2.22082 3.84657i 0.175571 0.304098i
\(161\) 6.86907 0.541358
\(162\) 2.53668 4.39366i 0.199300 0.345198i
\(163\) 4.12820 + 7.15026i 0.323346 + 0.560051i 0.981176 0.193115i \(-0.0618590\pi\)
−0.657830 + 0.753166i \(0.728526\pi\)
\(164\) −5.29741 −0.413658
\(165\) 3.54032 + 6.13201i 0.275613 + 0.477376i
\(166\) 0.636552 1.10254i 0.0494061 0.0855738i
\(167\) −3.61749 + 6.26568i −0.279930 + 0.484853i −0.971367 0.237584i \(-0.923645\pi\)
0.691437 + 0.722437i \(0.256978\pi\)
\(168\) −15.9826 −1.23309
\(169\) 4.70982 8.15765i 0.362294 0.627512i
\(170\) 0.544128 0.0417327
\(171\) −23.4223 −1.79115
\(172\) −7.79469 5.86433i −0.594340 0.447151i
\(173\) 12.1075 0.920518 0.460259 0.887785i \(-0.347756\pi\)
0.460259 + 0.887785i \(0.347756\pi\)
\(174\) 4.86454 0.368780
\(175\) 5.53489 9.58671i 0.418398 0.724687i
\(176\) 4.32658 0.326128
\(177\) 14.7383 25.5276i 1.10780 1.91877i
\(178\) 4.95810 8.58769i 0.371625 0.643674i
\(179\) 8.12878 + 14.0795i 0.607573 + 1.05235i 0.991639 + 0.129042i \(0.0411903\pi\)
−0.384066 + 0.923306i \(0.625476\pi\)
\(180\) 4.00292 0.298360
\(181\) 5.54624 + 9.60638i 0.412249 + 0.714036i 0.995135 0.0985174i \(-0.0314100\pi\)
−0.582886 + 0.812554i \(0.698077\pi\)
\(182\) −1.69536 + 2.93646i −0.125669 + 0.217665i
\(183\) 22.1250 1.63553
\(184\) 3.42552 5.93318i 0.252533 0.437399i
\(185\) −0.123283 0.213533i −0.00906397 0.0156993i
\(186\) 7.31889 + 12.6767i 0.536647 + 0.929501i
\(187\) 1.82128 + 3.15455i 0.133185 + 0.230683i
\(188\) 2.16255 0.157720
\(189\) −1.72959 2.99574i −0.125809 0.217908i
\(190\) −1.79993 3.11756i −0.130580 0.226172i
\(191\) −5.59162 + 9.68497i −0.404595 + 0.700780i −0.994274 0.106858i \(-0.965921\pi\)
0.589679 + 0.807638i \(0.299254\pi\)
\(192\) −2.31147 + 4.00359i −0.166816 + 0.288934i
\(193\) 17.3139 1.24629 0.623143 0.782108i \(-0.285856\pi\)
0.623143 + 0.782108i \(0.285856\pi\)
\(194\) 10.6460 0.764342
\(195\) 1.83907 3.18537i 0.131699 0.228109i
\(196\) −0.545939 + 0.945594i −0.0389956 + 0.0675424i
\(197\) 12.2009 + 21.1326i 0.869280 + 1.50564i 0.862733 + 0.505659i \(0.168751\pi\)
0.00654679 + 0.999979i \(0.497916\pi\)
\(198\) −4.61592 7.99501i −0.328039 0.568181i
\(199\) −10.6885 −0.757689 −0.378844 0.925460i \(-0.623678\pi\)
−0.378844 + 0.925460i \(0.623678\pi\)
\(200\) −5.52036 9.56155i −0.390349 0.676104i
\(201\) 12.5552 + 21.7462i 0.885573 + 1.53386i
\(202\) 2.92090 + 5.05914i 0.205514 + 0.355960i
\(203\) −3.32560 + 5.76011i −0.233411 + 0.404280i
\(204\) 3.80422 0.266348
\(205\) 1.35342 2.34420i 0.0945273 0.163726i
\(206\) −6.12085 10.6016i −0.426460 0.738650i
\(207\) 9.71516 0.675250
\(208\) −1.12376 1.94640i −0.0779184 0.134959i
\(209\) 12.0492 20.8699i 0.833463 1.44360i
\(210\) 1.74167 3.01666i 0.120187 0.208170i
\(211\) 1.58767 0.109300 0.0546499 0.998506i \(-0.482596\pi\)
0.0546499 + 0.998506i \(0.482596\pi\)
\(212\) −7.25715 + 12.5698i −0.498423 + 0.863294i
\(213\) 8.91177 0.610625
\(214\) −5.55393 −0.379659
\(215\) 4.58653 1.95103i 0.312799 0.133059i
\(216\) −3.45010 −0.234750
\(217\) −20.0140 −1.35864
\(218\) −2.68322 + 4.64748i −0.181731 + 0.314767i
\(219\) −37.5326 −2.53621
\(220\) −2.05924 + 3.56670i −0.138834 + 0.240467i
\(221\) 0.946091 1.63868i 0.0636410 0.110229i
\(222\) 0.296944 + 0.514323i 0.0199296 + 0.0345191i
\(223\) 14.1780 0.949428 0.474714 0.880140i \(-0.342551\pi\)
0.474714 + 0.880140i \(0.342551\pi\)
\(224\) −7.31377 12.6678i −0.488672 0.846405i
\(225\) 7.82819 13.5588i 0.521879 0.903921i
\(226\) −11.2620 −0.749140
\(227\) −8.35460 + 14.4706i −0.554514 + 0.960447i 0.443427 + 0.896310i \(0.353763\pi\)
−0.997941 + 0.0641362i \(0.979571\pi\)
\(228\) −12.5840 21.7961i −0.833396 1.44348i
\(229\) 2.57047 + 4.45219i 0.169862 + 0.294209i 0.938371 0.345630i \(-0.112335\pi\)
−0.768510 + 0.639838i \(0.779001\pi\)
\(230\) 0.746577 + 1.29311i 0.0492278 + 0.0852651i
\(231\) 23.3185 1.53425
\(232\) 3.31687 + 5.74499i 0.217763 + 0.377177i
\(233\) −3.94162 6.82709i −0.258224 0.447258i 0.707542 0.706671i \(-0.249804\pi\)
−0.965766 + 0.259414i \(0.916471\pi\)
\(234\) −2.39781 + 4.15313i −0.156750 + 0.271499i
\(235\) −0.552506 + 0.956968i −0.0360415 + 0.0624257i
\(236\) 17.1452 1.11606
\(237\) 24.0350 1.56124
\(238\) 0.895984 1.55189i 0.0580780 0.100594i
\(239\) 10.4912 18.1713i 0.678620 1.17540i −0.296776 0.954947i \(-0.595912\pi\)
0.975397 0.220458i \(-0.0707551\pi\)
\(240\) 1.15445 + 1.99956i 0.0745194 + 0.129071i
\(241\) 7.57065 + 13.1127i 0.487668 + 0.844666i 0.999899 0.0141814i \(-0.00451424\pi\)
−0.512231 + 0.858848i \(0.671181\pi\)
\(242\) 1.62375 0.104378
\(243\) 11.1350 + 19.2864i 0.714310 + 1.23722i
\(244\) 6.43455 + 11.1450i 0.411930 + 0.713483i
\(245\) −0.278962 0.483176i −0.0178222 0.0308690i
\(246\) −3.25991 + 5.64632i −0.207844 + 0.359996i
\(247\) −12.5183 −0.796523
\(248\) −9.98073 + 17.2871i −0.633777 + 1.09773i
\(249\) 2.27404 + 3.93876i 0.144112 + 0.249609i
\(250\) 5.12692 0.324255
\(251\) −5.74892 9.95742i −0.362868 0.628507i 0.625563 0.780173i \(-0.284869\pi\)
−0.988432 + 0.151667i \(0.951536\pi\)
\(252\) 6.59137 11.4166i 0.415217 0.719177i
\(253\) −4.99781 + 8.65645i −0.314209 + 0.544227i
\(254\) −8.99114 −0.564154
\(255\) −0.971932 + 1.68344i −0.0608648 + 0.105421i
\(256\) −11.0554 −0.690964
\(257\) 5.37055 0.335006 0.167503 0.985872i \(-0.446430\pi\)
0.167503 + 0.985872i \(0.446430\pi\)
\(258\) −11.0473 + 4.69931i −0.687773 + 0.292566i
\(259\) −0.812014 −0.0504561
\(260\) 2.13941 0.132680
\(261\) −4.70351 + 8.14672i −0.291140 + 0.504269i
\(262\) 2.36362 0.146025
\(263\) −6.48108 + 11.2256i −0.399640 + 0.692197i −0.993681 0.112237i \(-0.964198\pi\)
0.594041 + 0.804435i \(0.297532\pi\)
\(264\) 11.6287 20.1414i 0.715695 1.23962i
\(265\) −3.70823 6.42285i −0.227795 0.394552i
\(266\) −11.8553 −0.726897
\(267\) 17.7125 + 30.6790i 1.08399 + 1.87752i
\(268\) −7.30275 + 12.6487i −0.446086 + 0.772644i
\(269\) 14.5397 0.886498 0.443249 0.896398i \(-0.353826\pi\)
0.443249 + 0.896398i \(0.353826\pi\)
\(270\) 0.375967 0.651194i 0.0228806 0.0396304i
\(271\) −7.91602 13.7110i −0.480864 0.832881i 0.518895 0.854838i \(-0.326344\pi\)
−0.999759 + 0.0219570i \(0.993010\pi\)
\(272\) 0.593894 + 1.02865i 0.0360101 + 0.0623713i
\(273\) −6.05659 10.4903i −0.366561 0.634903i
\(274\) −0.699835 −0.0422786
\(275\) 8.05417 + 13.9502i 0.485684 + 0.841230i
\(276\) 5.21962 + 9.04064i 0.314184 + 0.544183i
\(277\) −12.5521 + 21.7409i −0.754184 + 1.30628i 0.191595 + 0.981474i \(0.438634\pi\)
−0.945779 + 0.324811i \(0.894699\pi\)
\(278\) 2.63714 4.56766i 0.158165 0.273950i
\(279\) −28.3065 −1.69466
\(280\) 4.75021 0.283880
\(281\) −2.81287 + 4.87204i −0.167802 + 0.290641i −0.937647 0.347590i \(-0.887000\pi\)
0.769845 + 0.638231i \(0.220334\pi\)
\(282\) 1.33078 2.30499i 0.0792471 0.137260i
\(283\) 0.417605 + 0.723314i 0.0248241 + 0.0429965i 0.878171 0.478348i \(-0.158764\pi\)
−0.853346 + 0.521344i \(0.825431\pi\)
\(284\) 2.59178 + 4.48910i 0.153794 + 0.266379i
\(285\) 12.8603 0.761776
\(286\) −2.46703 4.27303i −0.145879 0.252669i
\(287\) −4.45721 7.72011i −0.263101 0.455704i
\(288\) −10.3441 17.9165i −0.609533 1.05574i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) −1.44580 −0.0849000
\(291\) −19.0162 + 32.9370i −1.11475 + 1.93080i
\(292\) −10.9155 18.9061i −0.638779 1.10640i
\(293\) 12.7737 0.746249 0.373125 0.927781i \(-0.378286\pi\)
0.373125 + 0.927781i \(0.378286\pi\)
\(294\) 0.671917 + 1.16379i 0.0391870 + 0.0678739i
\(295\) −4.38040 + 7.58707i −0.255037 + 0.441737i
\(296\) −0.404941 + 0.701379i −0.0235367 + 0.0407668i
\(297\) 5.03367 0.292083
\(298\) −1.44124 + 2.49631i −0.0834890 + 0.144607i
\(299\) 5.19238 0.300283
\(300\) 16.8232 0.971290
\(301\) 1.98790 16.2937i 0.114581 0.939154i
\(302\) −10.5111 −0.604847
\(303\) −20.8694 −1.19892
\(304\) 3.92909 6.80539i 0.225349 0.390316i
\(305\) −6.57581 −0.376530
\(306\) 1.26722 2.19489i 0.0724422 0.125474i
\(307\) 15.9704 27.6616i 0.911482 1.57873i 0.0995089 0.995037i \(-0.468273\pi\)
0.811973 0.583696i \(-0.198394\pi\)
\(308\) 6.78165 + 11.7462i 0.386420 + 0.669299i
\(309\) 43.7327 2.48787
\(310\) −2.17526 3.76765i −0.123546 0.213988i
\(311\) −5.24146 + 9.07847i −0.297216 + 0.514793i −0.975498 0.220009i \(-0.929391\pi\)
0.678282 + 0.734802i \(0.262725\pi\)
\(312\) −12.0814 −0.683974
\(313\) 3.38555 5.86395i 0.191363 0.331450i −0.754339 0.656485i \(-0.772043\pi\)
0.945702 + 0.325035i \(0.105376\pi\)
\(314\) −1.41091 2.44377i −0.0796222 0.137910i
\(315\) 3.36803 + 5.83361i 0.189767 + 0.328687i
\(316\) 6.99000 + 12.1070i 0.393218 + 0.681074i
\(317\) −16.7433 −0.940400 −0.470200 0.882560i \(-0.655818\pi\)
−0.470200 + 0.882560i \(0.655818\pi\)
\(318\) 8.93178 + 15.4703i 0.500869 + 0.867531i
\(319\) −4.83929 8.38190i −0.270948 0.469296i
\(320\) 0.686995 1.18991i 0.0384042 0.0665180i
\(321\) 9.92053 17.1829i 0.553710 0.959054i
\(322\) 4.91738 0.274035
\(323\) 6.61582 0.368114
\(324\) −5.27102 + 9.12967i −0.292834 + 0.507204i
\(325\) 4.18386 7.24666i 0.232079 0.401973i
\(326\) 2.95527 + 5.11867i 0.163677 + 0.283497i
\(327\) −9.58564 16.6028i −0.530087 0.918138i
\(328\) −8.89103 −0.490925
\(329\) 1.81956 + 3.15157i 0.100315 + 0.173751i
\(330\) 2.53442 + 4.38974i 0.139515 + 0.241647i
\(331\) −6.67211 11.5564i −0.366733 0.635199i 0.622320 0.782763i \(-0.286190\pi\)
−0.989053 + 0.147563i \(0.952857\pi\)
\(332\) −1.32271 + 2.29099i −0.0725929 + 0.125735i
\(333\) −1.14846 −0.0629352
\(334\) −2.58967 + 4.48543i −0.141700 + 0.245432i
\(335\) −3.73153 6.46320i −0.203875 0.353122i
\(336\) 7.60385 0.414824
\(337\) 1.58319 + 2.74217i 0.0862418 + 0.149375i 0.905920 0.423449i \(-0.139181\pi\)
−0.819678 + 0.572825i \(0.805848\pi\)
\(338\) 3.37163 5.83984i 0.183393 0.317645i
\(339\) 20.1165 34.8428i 1.09258 1.89240i
\(340\) −1.13066 −0.0613184
\(341\) 14.5618 25.2218i 0.788566 1.36584i
\(342\) −16.7674 −0.906678
\(343\) −19.3598 −1.04533
\(344\) −13.0824 9.84254i −0.705356 0.530674i
\(345\) −5.33420 −0.287184
\(346\) 8.66745 0.465965
\(347\) 9.65269 16.7189i 0.518183 0.897520i −0.481593 0.876395i \(-0.659942\pi\)
0.999777 0.0211253i \(-0.00672489\pi\)
\(348\) −10.1081 −0.541853
\(349\) 8.73134 15.1231i 0.467378 0.809523i −0.531927 0.846790i \(-0.678532\pi\)
0.999305 + 0.0372675i \(0.0118654\pi\)
\(350\) 3.96228 6.86286i 0.211793 0.366835i
\(351\) −1.30741 2.26450i −0.0697843 0.120870i
\(352\) 21.2855 1.13452
\(353\) 10.5329 + 18.2436i 0.560612 + 0.971009i 0.997443 + 0.0714650i \(0.0227674\pi\)
−0.436831 + 0.899544i \(0.643899\pi\)
\(354\) 10.5508 18.2745i 0.560768 0.971278i
\(355\) −2.64868 −0.140577
\(356\) −10.3025 + 17.8445i −0.546034 + 0.945758i
\(357\) 3.20085 + 5.54403i 0.169407 + 0.293421i
\(358\) 5.81917 + 10.0791i 0.307553 + 0.532697i
\(359\) −14.0774 24.3828i −0.742977 1.28687i −0.951134 0.308779i \(-0.900080\pi\)
0.208157 0.978096i \(-0.433254\pi\)
\(360\) 6.71839 0.354090
\(361\) −12.3845 21.4506i −0.651817 1.12898i
\(362\) 3.97040 + 6.87694i 0.208680 + 0.361444i
\(363\) −2.90037 + 5.02359i −0.152230 + 0.263670i
\(364\) 3.52283 6.10173i 0.184647 0.319817i
\(365\) 11.1551 0.583884
\(366\) 15.8387 0.827903
\(367\) −16.0711 + 27.8359i −0.838903 + 1.45302i 0.0519103 + 0.998652i \(0.483469\pi\)
−0.890813 + 0.454370i \(0.849864\pi\)
\(368\) −1.62972 + 2.82275i −0.0849548 + 0.147146i
\(369\) −6.30399 10.9188i −0.328172 0.568411i
\(370\) −0.0882552 0.152862i −0.00458817 0.00794694i
\(371\) −24.4245 −1.26806
\(372\) −15.2081 26.3412i −0.788502 1.36573i
\(373\) −14.4614 25.0478i −0.748782 1.29693i −0.948407 0.317056i \(-0.897306\pi\)
0.199625 0.979872i \(-0.436028\pi\)
\(374\) 1.30380 + 2.25825i 0.0674180 + 0.116771i
\(375\) −9.15780 + 15.8618i −0.472907 + 0.819099i
\(376\) 3.62957 0.187181
\(377\) −2.51384 + 4.35411i −0.129470 + 0.224248i
\(378\) −1.23817 2.14457i −0.0636844 0.110305i
\(379\) 4.28489 0.220100 0.110050 0.993926i \(-0.464899\pi\)
0.110050 + 0.993926i \(0.464899\pi\)
\(380\) 3.74010 + 6.47805i 0.191863 + 0.332317i
\(381\) 16.0601 27.8170i 0.822786 1.42511i
\(382\) −4.00289 + 6.93321i −0.204806 + 0.354734i
\(383\) 19.4623 0.994478 0.497239 0.867614i \(-0.334347\pi\)
0.497239 + 0.867614i \(0.334347\pi\)
\(384\) 13.2897 23.0184i 0.678185 1.17465i
\(385\) −6.93052 −0.353212
\(386\) 12.3946 0.630868
\(387\) 2.81156 23.0448i 0.142920 1.17143i
\(388\) −22.1216 −1.12306
\(389\) −15.2120 −0.771279 −0.385640 0.922649i \(-0.626019\pi\)
−0.385640 + 0.922649i \(0.626019\pi\)
\(390\) 1.31654 2.28032i 0.0666657 0.115468i
\(391\) −2.74412 −0.138776
\(392\) −0.916289 + 1.58706i −0.0462796 + 0.0801586i
\(393\) −4.22194 + 7.31262i −0.212969 + 0.368873i
\(394\) 8.73431 + 15.1283i 0.440028 + 0.762151i
\(395\) −7.14345 −0.359426
\(396\) 9.59152 + 16.6130i 0.481992 + 0.834835i
\(397\) −8.05785 + 13.9566i −0.404412 + 0.700462i −0.994253 0.107058i \(-0.965857\pi\)
0.589841 + 0.807519i \(0.299190\pi\)
\(398\) −7.65162 −0.383541
\(399\) 21.1762 36.6783i 1.06014 1.83621i
\(400\) 2.62635 + 4.54898i 0.131318 + 0.227449i
\(401\) 19.2367 + 33.3190i 0.960635 + 1.66387i 0.720911 + 0.693028i \(0.243724\pi\)
0.239725 + 0.970841i \(0.422943\pi\)
\(402\) 8.98790 + 15.5675i 0.448276 + 0.776436i
\(403\) −15.1287 −0.753615
\(404\) −6.06939 10.5125i −0.301963 0.523016i
\(405\) −2.69337 4.66505i −0.133834 0.231808i
\(406\) −2.38071 + 4.12350i −0.118152 + 0.204646i
\(407\) 0.590806 1.02331i 0.0292852 0.0507234i
\(408\) 6.38490 0.316099
\(409\) −32.2260 −1.59347 −0.796736 0.604327i \(-0.793442\pi\)
−0.796736 + 0.604327i \(0.793442\pi\)
\(410\) 0.968880 1.67815i 0.0478496 0.0828779i
\(411\) 1.25006 2.16517i 0.0616609 0.106800i
\(412\) 12.7186 + 22.0293i 0.626603 + 1.08531i
\(413\) 14.4259 + 24.9864i 0.709852 + 1.22950i
\(414\) 6.95482 0.341811
\(415\) −0.675871 1.17064i −0.0331772 0.0574646i
\(416\) −5.52853 9.57570i −0.271059 0.469487i
\(417\) 9.42102 + 16.3177i 0.461349 + 0.799081i
\(418\) 8.62572 14.9402i 0.421898 0.730749i
\(419\) 10.1950 0.498059 0.249030 0.968496i \(-0.419888\pi\)
0.249030 + 0.968496i \(0.419888\pi\)
\(420\) −3.61906 + 6.26839i −0.176592 + 0.305866i
\(421\) −7.88602 13.6590i −0.384341 0.665699i 0.607336 0.794445i \(-0.292238\pi\)
−0.991678 + 0.128746i \(0.958905\pi\)
\(422\) 1.13657 0.0553273
\(423\) 2.57346 + 4.45737i 0.125126 + 0.216725i
\(424\) −12.1802 + 21.0967i −0.591523 + 1.02455i
\(425\) −2.21113 + 3.82979i −0.107256 + 0.185772i
\(426\) 6.37970 0.309097
\(427\) −10.8280 + 18.7546i −0.524003 + 0.907600i
\(428\) 11.5406 0.557837
\(429\) 17.6266 0.851023
\(430\) 3.28337 1.39669i 0.158338 0.0673542i
\(431\) 19.7859 0.953053 0.476527 0.879160i \(-0.341896\pi\)
0.476527 + 0.879160i \(0.341896\pi\)
\(432\) 1.64141 0.0789724
\(433\) 6.30712 10.9243i 0.303101 0.524986i −0.673736 0.738972i \(-0.735311\pi\)
0.976837 + 0.213986i \(0.0686447\pi\)
\(434\) −14.3275 −0.687740
\(435\) 2.58251 4.47303i 0.123822 0.214466i
\(436\) 5.57552 9.65708i 0.267019 0.462490i
\(437\) 9.07730 + 15.7224i 0.434226 + 0.752102i
\(438\) −26.8685 −1.28383
\(439\) 5.76511 + 9.98547i 0.275154 + 0.476580i 0.970174 0.242410i \(-0.0779379\pi\)
−0.695020 + 0.718990i \(0.744605\pi\)
\(440\) −3.45617 + 5.98626i −0.164766 + 0.285384i
\(441\) −2.59870 −0.123748
\(442\) 0.677281 1.17308i 0.0322150 0.0557979i
\(443\) 11.2179 + 19.4300i 0.532979 + 0.923147i 0.999258 + 0.0385092i \(0.0122609\pi\)
−0.466279 + 0.884638i \(0.654406\pi\)
\(444\) −0.617027 1.06872i −0.0292828 0.0507193i
\(445\) −5.26436 9.11813i −0.249554 0.432241i
\(446\) 10.1496 0.480599
\(447\) −5.14875 8.91790i −0.243528 0.421802i
\(448\) −2.26247 3.91871i −0.106892 0.185142i
\(449\) −18.8451 + 32.6407i −0.889357 + 1.54041i −0.0487194 + 0.998813i \(0.515514\pi\)
−0.840637 + 0.541598i \(0.817819\pi\)
\(450\) 5.60398 9.70638i 0.264174 0.457563i
\(451\) 12.9719 0.610824
\(452\) 23.4016 1.10072
\(453\) 18.7752 32.5196i 0.882135 1.52790i
\(454\) −5.98083 + 10.3591i −0.280694 + 0.486177i
\(455\) 1.80008 + 3.11784i 0.0843893 + 0.146166i
\(456\) −21.1207 36.5821i −0.989066 1.71311i
\(457\) −28.5256 −1.33437 −0.667186 0.744891i \(-0.732501\pi\)
−0.667186 + 0.744891i \(0.732501\pi\)
\(458\) 1.84013 + 3.18720i 0.0859836 + 0.148928i
\(459\) 0.690953 + 1.19677i 0.0322509 + 0.0558602i
\(460\) −1.55133 2.68698i −0.0723310 0.125281i
\(461\) −15.6485 + 27.1040i −0.728823 + 1.26236i 0.228559 + 0.973530i \(0.426599\pi\)
−0.957381 + 0.288827i \(0.906735\pi\)
\(462\) 16.6931 0.776633
\(463\) 12.0557 20.8810i 0.560275 0.970424i −0.437197 0.899366i \(-0.644029\pi\)
0.997472 0.0710588i \(-0.0226378\pi\)
\(464\) −1.57803 2.73322i −0.0732580 0.126887i
\(465\) 15.5419 0.720740
\(466\) −2.82170 4.88733i −0.130713 0.226401i
\(467\) 1.69581 2.93722i 0.0784725 0.135918i −0.824119 0.566417i \(-0.808329\pi\)
0.902591 + 0.430499i \(0.141662\pi\)
\(468\) 4.98247 8.62988i 0.230315 0.398916i
\(469\) −24.5780 −1.13491
\(470\) −0.395524 + 0.685067i −0.0182442 + 0.0315998i
\(471\) 10.0808 0.464497
\(472\) 28.7761 1.32453
\(473\) 19.0871 + 14.3602i 0.877627 + 0.660282i
\(474\) 17.2060 0.790296
\(475\) 29.2569 1.34240
\(476\) −1.86178 + 3.22470i −0.0853347 + 0.147804i
\(477\) −34.5444 −1.58168
\(478\) 7.51037 13.0083i 0.343516 0.594988i
\(479\) 17.0912 29.6029i 0.780919 1.35259i −0.150489 0.988612i \(-0.548085\pi\)
0.931407 0.363979i \(-0.118582\pi\)
\(480\) 5.67954 + 9.83725i 0.259234 + 0.449007i
\(481\) −0.613807 −0.0279872
\(482\) 5.41962 + 9.38706i 0.246857 + 0.427569i
\(483\) −8.78351 + 15.2135i −0.399664 + 0.692238i
\(484\) −3.37402 −0.153364
\(485\) 5.65182 9.78924i 0.256636 0.444506i
\(486\) 7.97124 + 13.8066i 0.361583 + 0.626280i
\(487\) −9.40789 16.2949i −0.426312 0.738394i 0.570230 0.821485i \(-0.306854\pi\)
−0.996542 + 0.0830909i \(0.973521\pi\)
\(488\) 10.7996 + 18.7054i 0.488874 + 0.846755i
\(489\) −21.1150 −0.954855
\(490\) −0.199701 0.345893i −0.00902158 0.0156258i
\(491\) 10.8434 + 18.7813i 0.489356 + 0.847589i 0.999925 0.0122475i \(-0.00389859\pi\)
−0.510569 + 0.859837i \(0.670565\pi\)
\(492\) 6.77382 11.7326i 0.305388 0.528947i
\(493\) 1.32854 2.30110i 0.0598346 0.103636i
\(494\) −8.96153 −0.403198
\(495\) −9.80208 −0.440571
\(496\) 4.74841 8.22448i 0.213210 0.369290i
\(497\) −4.36142 + 7.55420i −0.195636 + 0.338852i
\(498\) 1.62793 + 2.81965i 0.0729491 + 0.126352i
\(499\) −10.0596 17.4238i −0.450331 0.779996i 0.548075 0.836429i \(-0.315361\pi\)
−0.998406 + 0.0564329i \(0.982027\pi\)
\(500\) −10.6533 −0.476431
\(501\) −9.25142 16.0239i −0.413323 0.715897i
\(502\) −4.11549 7.12824i −0.183683 0.318149i
\(503\) −2.20467 3.81860i −0.0983014 0.170263i 0.812680 0.582710i \(-0.198008\pi\)
−0.910982 + 0.412447i \(0.864674\pi\)
\(504\) 11.0628 19.1613i 0.492775 0.853512i
\(505\) 6.20263 0.276013
\(506\) −3.57779 + 6.19692i −0.159052 + 0.275487i
\(507\) 12.0450 + 20.8625i 0.534935 + 0.926535i
\(508\) 18.6829 0.828918
\(509\) 4.01279 + 6.95036i 0.177864 + 0.308069i 0.941149 0.337993i \(-0.109748\pi\)
−0.763285 + 0.646062i \(0.776415\pi\)
\(510\) −0.695780 + 1.20513i −0.0308097 + 0.0533639i
\(511\) 18.3684 31.8150i 0.812571 1.40741i
\(512\) 12.8718 0.568859
\(513\) 4.57122 7.91759i 0.201824 0.349570i
\(514\) 3.84463 0.169579
\(515\) −12.9979 −0.572754
\(516\) 22.9553 9.76480i 1.01055 0.429871i
\(517\) −5.29551 −0.232896
\(518\) −0.581298 −0.0255408
\(519\) −15.4820 + 26.8156i −0.679583 + 1.17707i
\(520\) 3.59072 0.157464
\(521\) 20.5791 35.6440i 0.901586 1.56159i 0.0761516 0.997096i \(-0.475737\pi\)
0.825435 0.564497i \(-0.190930\pi\)
\(522\) −3.36711 + 5.83201i −0.147375 + 0.255260i
\(523\) 6.90801 + 11.9650i 0.302066 + 0.523194i 0.976604 0.215047i \(-0.0689903\pi\)
−0.674538 + 0.738240i \(0.735657\pi\)
\(524\) −4.91141 −0.214556
\(525\) 14.1550 + 24.5172i 0.617774 + 1.07002i
\(526\) −4.63963 + 8.03607i −0.202297 + 0.350389i
\(527\) 7.99538 0.348284
\(528\) −5.53242 + 9.58244i −0.240768 + 0.417022i
\(529\) 7.73490 + 13.3972i 0.336300 + 0.582489i
\(530\) −2.65462 4.59794i −0.115309 0.199722i
\(531\) 20.4030 + 35.3391i 0.885416 + 1.53359i
\(532\) 24.6344 1.06804
\(533\) −3.36924 5.83569i −0.145938 0.252772i
\(534\) 12.6799 + 21.9622i 0.548713 + 0.950399i
\(535\) −2.94849 + 5.10694i −0.127474 + 0.220792i
\(536\) −12.2567 + 21.2293i −0.529410 + 0.916966i
\(537\) −41.5773 −1.79419
\(538\) 10.4085 0.448744
\(539\) 1.33686 2.31551i 0.0575826 0.0997359i
\(540\) −0.781230 + 1.35313i −0.0336188 + 0.0582294i
\(541\) 2.58176 + 4.47174i 0.110999 + 0.192255i 0.916173 0.400783i \(-0.131262\pi\)
−0.805175 + 0.593038i \(0.797928\pi\)
\(542\) −5.66686 9.81530i −0.243413 0.421603i
\(543\) −28.3681 −1.21739
\(544\) 2.92178 + 5.06067i 0.125270 + 0.216974i
\(545\) 2.84896 + 4.93454i 0.122036 + 0.211373i
\(546\) −4.33575 7.50973i −0.185553 0.321387i
\(547\) −9.52713 + 16.5015i −0.407351 + 0.705552i −0.994592 0.103860i \(-0.966881\pi\)
0.587241 + 0.809412i \(0.300214\pi\)
\(548\) 1.45420 0.0621204
\(549\) −15.3144 + 26.5253i −0.653603 + 1.13207i
\(550\) 5.76576 + 9.98658i 0.245853 + 0.425829i
\(551\) −17.5788 −0.748882
\(552\) 8.76047 + 15.1736i 0.372870 + 0.645830i
\(553\) −11.7627 + 20.3736i −0.500201 + 0.866374i
\(554\) −8.98572 + 15.5637i −0.381767 + 0.661239i
\(555\) 0.630572 0.0267663
\(556\) −5.47977 + 9.49123i −0.232394 + 0.402518i
\(557\) 25.3072 1.07230 0.536150 0.844123i \(-0.319878\pi\)
0.536150 + 0.844123i \(0.319878\pi\)
\(558\) −20.2638 −0.857836
\(559\) 1.50267 12.3165i 0.0635562 0.520934i
\(560\) −2.25995 −0.0955003
\(561\) −9.31551 −0.393301
\(562\) −2.01366 + 3.48776i −0.0849411 + 0.147122i
\(563\) 25.0035 1.05377 0.526885 0.849936i \(-0.323360\pi\)
0.526885 + 0.849936i \(0.323360\pi\)
\(564\) −2.76526 + 4.78958i −0.116439 + 0.201678i
\(565\) −5.97884 + 10.3557i −0.251532 + 0.435666i
\(566\) 0.298952 + 0.517800i 0.0125659 + 0.0217648i
\(567\) −17.7400 −0.745011
\(568\) 4.34998 + 7.53438i 0.182521 + 0.316136i
\(569\) 0.394091 0.682585i 0.0165211 0.0286155i −0.857647 0.514239i \(-0.828074\pi\)
0.874168 + 0.485624i \(0.161408\pi\)
\(570\) 9.20631 0.385610
\(571\) 18.0687 31.2960i 0.756153 1.30970i −0.188646 0.982045i \(-0.560410\pi\)
0.944799 0.327651i \(-0.106257\pi\)
\(572\) 5.12630 + 8.87901i 0.214341 + 0.371250i
\(573\) −14.3001 24.7685i −0.597394 1.03472i
\(574\) −3.19079 5.52662i −0.133181 0.230677i
\(575\) −12.1352 −0.506074
\(576\) −3.19989 5.54237i −0.133329 0.230932i
\(577\) −12.4603 21.5820i −0.518731 0.898469i −0.999763 0.0217655i \(-0.993071\pi\)
0.481032 0.876703i \(-0.340262\pi\)
\(578\) −0.357936 + 0.619964i −0.0148882 + 0.0257871i
\(579\) −22.1394 + 38.3466i −0.920084 + 1.59363i
\(580\) 3.00425 0.124745
\(581\) −4.45167 −0.184686
\(582\) −13.6132 + 23.5787i −0.564284 + 0.977368i
\(583\) 17.7708 30.7800i 0.735992 1.27478i
\(584\) −18.3202 31.7316i −0.758096 1.31306i
\(585\) 2.54592 + 4.40967i 0.105261 + 0.182317i
\(586\) 9.14436 0.377750
\(587\) −0.417401 0.722960i −0.0172280 0.0298398i 0.857283 0.514846i \(-0.172151\pi\)
−0.874511 + 0.485006i \(0.838817\pi\)
\(588\) −1.39619 2.41827i −0.0575779 0.0997279i
\(589\) −26.4480 45.8093i −1.08977 1.88754i
\(590\) −3.13581 + 5.43138i −0.129099 + 0.223606i
\(591\) −62.4056 −2.56702
\(592\) 0.192654 0.333686i 0.00791802 0.0137144i
\(593\) −1.99330 3.45251i −0.0818552 0.141777i 0.822192 0.569211i \(-0.192751\pi\)
−0.904047 + 0.427433i \(0.859418\pi\)
\(594\) 3.60347 0.147852
\(595\) −0.951327 1.64775i −0.0390006 0.0675510i
\(596\) 2.99479 5.18713i 0.122671 0.212473i
\(597\) 13.6675 23.6727i 0.559372 0.968861i
\(598\) 3.71708 0.152003
\(599\) −14.7598 + 25.5648i −0.603071 + 1.04455i 0.389283 + 0.921118i \(0.372723\pi\)
−0.992353 + 0.123431i \(0.960610\pi\)
\(600\) 28.2357 1.15272
\(601\) 2.24560 0.0916000 0.0458000 0.998951i \(-0.485416\pi\)
0.0458000 + 0.998951i \(0.485416\pi\)
\(602\) 1.42309 11.6642i 0.0580007 0.475398i
\(603\) −34.7615 −1.41560
\(604\) 21.8413 0.888709
\(605\) 0.862022 1.49307i 0.0350462 0.0607017i
\(606\) −14.9399 −0.606891
\(607\) 1.60838 2.78580i 0.0652821 0.113072i −0.831537 0.555469i \(-0.812539\pi\)
0.896819 + 0.442397i \(0.145872\pi\)
\(608\) 19.3299 33.4805i 0.783933 1.35781i
\(609\) −8.50493 14.7310i −0.344637 0.596929i
\(610\) −4.70744 −0.190599
\(611\) 1.37542 + 2.38229i 0.0556434 + 0.0963772i
\(612\) −2.63318 + 4.56081i −0.106440 + 0.184360i
\(613\) −28.1969 −1.13886 −0.569430 0.822040i \(-0.692836\pi\)
−0.569430 + 0.822040i \(0.692836\pi\)
\(614\) 11.4328 19.8022i 0.461390 0.799152i
\(615\) 3.46126 + 5.99508i 0.139572 + 0.241745i
\(616\) 11.3821 + 19.7144i 0.458599 + 0.794317i
\(617\) 6.70101 + 11.6065i 0.269773 + 0.467260i 0.968803 0.247832i \(-0.0797181\pi\)
−0.699030 + 0.715092i \(0.746385\pi\)
\(618\) 31.3071 1.25936
\(619\) 8.17065 + 14.1520i 0.328406 + 0.568816i 0.982196 0.187860i \(-0.0601552\pi\)
−0.653790 + 0.756676i \(0.726822\pi\)
\(620\) 4.52001 + 7.82888i 0.181528 + 0.314416i
\(621\) −1.89606 + 3.28407i −0.0760862 + 0.131785i
\(622\) −3.75221 + 6.49903i −0.150450 + 0.260587i
\(623\) −34.6740 −1.38919
\(624\) 5.74781 0.230096
\(625\) −8.33386 + 14.4347i −0.333354 + 0.577386i
\(626\) 2.42362 4.19784i 0.0968675 0.167779i
\(627\) 30.8149 + 53.3729i 1.23063 + 2.13151i
\(628\) 2.93176 + 5.07795i 0.116990 + 0.202632i
\(629\) 0.324391 0.0129343
\(630\) 2.41108 + 4.17612i 0.0960599 + 0.166381i
\(631\) 6.37912 + 11.0490i 0.253949 + 0.439852i 0.964609 0.263683i \(-0.0849372\pi\)
−0.710661 + 0.703535i \(0.751604\pi\)
\(632\) 11.7318 + 20.3201i 0.466667 + 0.808292i
\(633\) −2.03016 + 3.51634i −0.0806917 + 0.139762i
\(634\) −11.9861 −0.476029
\(635\) −4.77325 + 8.26752i −0.189421 + 0.328086i
\(636\) −18.5595 32.1460i −0.735933 1.27467i
\(637\) −1.38890 −0.0550304
\(638\) −3.46432 6.00037i −0.137154 0.237557i
\(639\) −6.16851 + 10.6842i −0.244022 + 0.422659i
\(640\) −3.94983 + 6.84131i −0.156131 + 0.270426i
\(641\) 34.5437 1.36439 0.682197 0.731168i \(-0.261025\pi\)
0.682197 + 0.731168i \(0.261025\pi\)
\(642\) 7.10184 12.3007i 0.280287 0.485472i
\(643\) −6.53101 −0.257558 −0.128779 0.991673i \(-0.541106\pi\)
−0.128779 + 0.991673i \(0.541106\pi\)
\(644\) −10.2179 −0.402642
\(645\) −1.54372 + 12.6530i −0.0607837 + 0.498210i
\(646\) 4.73608 0.186339
\(647\) −35.2094 −1.38422 −0.692112 0.721790i \(-0.743320\pi\)
−0.692112 + 0.721790i \(0.743320\pi\)
\(648\) −8.84674 + 15.3230i −0.347533 + 0.601944i
\(649\) −41.9841 −1.64802
\(650\) 2.99511 5.18769i 0.117478 0.203478i
\(651\) 25.5920 44.3266i 1.00303 1.73730i
\(652\) −6.14081 10.6362i −0.240493 0.416546i
\(653\) −33.6405 −1.31645 −0.658227 0.752820i \(-0.728693\pi\)
−0.658227 + 0.752820i \(0.728693\pi\)
\(654\) −6.86210 11.8855i −0.268329 0.464760i
\(655\) 1.25481 2.17339i 0.0490294 0.0849214i
\(656\) 4.22997 0.165153
\(657\) 25.9791 44.9971i 1.01354 1.75550i
\(658\) 1.30257 + 2.25612i 0.0507795 + 0.0879527i
\(659\) 3.81676 + 6.61083i 0.148680 + 0.257521i 0.930740 0.365682i \(-0.119164\pi\)
−0.782060 + 0.623203i \(0.785831\pi\)
\(660\) −5.26632 9.12153i −0.204991 0.355055i
\(661\) 25.0604 0.974738 0.487369 0.873196i \(-0.337957\pi\)
0.487369 + 0.873196i \(0.337957\pi\)
\(662\) −4.77638 8.27294i −0.185639 0.321537i
\(663\) 2.41954 + 4.19077i 0.0939673 + 0.162756i
\(664\) −2.21999 + 3.84514i −0.0861525 + 0.149220i
\(665\) −6.29381 + 10.9012i −0.244063 + 0.422730i
\(666\) −0.822150 −0.0318577
\(667\) 7.29136 0.282323
\(668\) 5.38112 9.32037i 0.208202 0.360616i
\(669\) −18.1295 + 31.4012i −0.700926 + 1.21404i
\(670\) −2.67130 4.62683i −0.103201 0.178750i
\(671\) −15.7565 27.2911i −0.608273 1.05356i
\(672\) 37.4087 1.44307
\(673\) −21.9911 38.0897i −0.847695 1.46825i −0.883260 0.468884i \(-0.844656\pi\)
0.0355644 0.999367i \(-0.488677\pi\)
\(674\) 1.13336 + 1.96304i 0.0436555 + 0.0756135i
\(675\) 3.05558 + 5.29241i 0.117609 + 0.203705i
\(676\) −7.00599 + 12.1347i −0.269461 + 0.466720i
\(677\) 14.8738 0.571645 0.285822 0.958283i \(-0.407733\pi\)
0.285822 + 0.958283i \(0.407733\pi\)
\(678\) 14.4008 24.9430i 0.553061 0.957929i
\(679\) −18.6130 32.2387i −0.714303 1.23721i
\(680\) −1.89766 −0.0727720
\(681\) −21.3661 37.0072i −0.818752 1.41812i
\(682\) 10.4244 18.0556i 0.399171 0.691384i
\(683\) 3.03887 5.26348i 0.116279 0.201402i −0.802011 0.597309i \(-0.796237\pi\)
0.918290 + 0.395908i \(0.129570\pi\)
\(684\) 34.8413 1.33219
\(685\) −0.371531 + 0.643511i −0.0141955 + 0.0245873i
\(686\) −13.8591 −0.529144
\(687\) −13.1475 −0.501609
\(688\) 6.22405 + 4.68266i 0.237290 + 0.178525i
\(689\) −18.4627 −0.703371
\(690\) −3.81861 −0.145372
\(691\) −16.5272 + 28.6259i −0.628724 + 1.08898i 0.359084 + 0.933305i \(0.383089\pi\)
−0.987808 + 0.155677i \(0.950244\pi\)
\(692\) −18.0103 −0.684648
\(693\) −16.1405 + 27.9562i −0.613127 + 1.06197i
\(694\) 6.91010 11.9686i 0.262304 0.454323i
\(695\) −2.80003 4.84980i −0.106211 0.183963i
\(696\) −16.9652 −0.643065
\(697\) 1.78061 + 3.08411i 0.0674454 + 0.116819i
\(698\) 6.25053 10.8262i 0.236586 0.409779i
\(699\) 20.1607 0.762548
\(700\) −8.23329 + 14.2605i −0.311189 + 0.538996i
\(701\) 13.0361 + 22.5792i 0.492367 + 0.852805i 0.999961 0.00879148i \(-0.00279845\pi\)
−0.507594 + 0.861596i \(0.669465\pi\)
\(702\) −0.935938 1.62109i −0.0353247 0.0611842i
\(703\) −1.07306 1.85859i −0.0404711 0.0700980i
\(704\) 6.58452 0.248164
\(705\) −1.41298 2.44736i −0.0532161 0.0921730i
\(706\) 7.54025 + 13.0601i 0.283781 + 0.491523i
\(707\) 10.2135 17.6903i 0.384118 0.665312i
\(708\) −21.9237 + 37.9729i −0.823942 + 1.42711i
\(709\) 18.5267 0.695787 0.347893 0.937534i \(-0.386897\pi\)
0.347893 + 0.937534i \(0.386897\pi\)
\(710\) −1.89612 −0.0711600
\(711\) −16.6364 + 28.8151i −0.623914 + 1.08065i
\(712\) −17.2915 + 29.9498i −0.648027 + 1.12242i
\(713\) 10.9701 + 19.0009i 0.410835 + 0.711587i
\(714\) 2.29140 + 3.96882i 0.0857535 + 0.148529i
\(715\) −5.23883 −0.195921
\(716\) −12.0918 20.9436i −0.451891 0.782698i
\(717\) 26.8303 + 46.4715i 1.00200 + 1.73551i
\(718\) −10.0776 17.4550i −0.376094 0.651414i
\(719\) 17.2430 29.8657i 0.643054 1.11380i −0.341693 0.939812i \(-0.611000\pi\)
0.984747 0.173991i \(-0.0556665\pi\)
\(720\) −3.19632 −0.119120
\(721\) −21.4028 + 37.0707i −0.797082 + 1.38059i
\(722\) −8.86575 15.3559i −0.329949 0.571488i
\(723\) −38.7225 −1.44011
\(724\) −8.25018 14.2897i −0.306616 0.531074i
\(725\) 5.87516 10.1761i 0.218198 0.377930i
\(726\) −2.07629 + 3.59625i −0.0770585 + 0.133469i
\(727\) −40.8914 −1.51658 −0.758290 0.651918i \(-0.773965\pi\)
−0.758290 + 0.651918i \(0.773965\pi\)
\(728\) 5.91263 10.2410i 0.219137 0.379556i
\(729\) −35.6926 −1.32195
\(730\) 7.98562 0.295561
\(731\) −0.794147 + 6.50917i −0.0293726 + 0.240750i
\(732\) −32.9116 −1.21645
\(733\) 19.2856 0.712330 0.356165 0.934423i \(-0.384084\pi\)
0.356165 + 0.934423i \(0.384084\pi\)
\(734\) −11.5048 + 19.9270i −0.424651 + 0.735517i
\(735\) 1.42684 0.0526298
\(736\) −8.01771 + 13.8871i −0.295537 + 0.511885i
\(737\) 17.8825 30.9734i 0.658710 1.14092i
\(738\) −4.51285 7.81649i −0.166120 0.287729i
\(739\) −7.88800 −0.290165 −0.145082 0.989420i \(-0.546345\pi\)
−0.145082 + 0.989420i \(0.546345\pi\)
\(740\) 0.183387 + 0.317636i 0.00674145 + 0.0116765i
\(741\) 16.0073 27.7254i 0.588042 1.01852i
\(742\) −17.4848 −0.641889
\(743\) 13.4564 23.3072i 0.493669 0.855060i −0.506304 0.862355i \(-0.668989\pi\)
0.999973 + 0.00729512i \(0.00232213\pi\)
\(744\) −25.5248 44.2103i −0.935786 1.62083i
\(745\) 1.53027 + 2.65050i 0.0560646 + 0.0971068i
\(746\) −10.3525 17.9311i −0.379032 0.656503i
\(747\) −6.29615 −0.230364
\(748\) −2.70920 4.69247i −0.0990581 0.171574i
\(749\) 9.71022 + 16.8186i 0.354804 + 0.614538i
\(750\) −6.55582 + 11.3550i −0.239385 + 0.414626i
\(751\) −14.8378 + 25.6999i −0.541440 + 0.937801i 0.457382 + 0.889270i \(0.348787\pi\)
−0.998822 + 0.0485308i \(0.984546\pi\)
\(752\) −1.72679 −0.0629696
\(753\) 29.4047 1.07157
\(754\) −1.79959 + 3.11699i −0.0655373 + 0.113514i
\(755\) −5.58019 + 9.66517i −0.203084 + 0.351752i
\(756\) 2.57281 + 4.45624i 0.0935722 + 0.162072i
\(757\) 12.6905 + 21.9806i 0.461244 + 0.798898i 0.999023 0.0441880i \(-0.0140700\pi\)
−0.537780 + 0.843086i \(0.680737\pi\)
\(758\) 3.06744 0.111414
\(759\) −12.7814 22.1381i −0.463937 0.803563i
\(760\) 6.27729 + 10.8726i 0.227701 + 0.394390i
\(761\) 8.79880 + 15.2400i 0.318956 + 0.552448i 0.980271 0.197660i \(-0.0633344\pi\)
−0.661314 + 0.750109i \(0.730001\pi\)
\(762\) 11.4970 19.9134i 0.416493 0.721387i
\(763\) 18.7649 0.679333
\(764\) 8.31768 14.4066i 0.300923 0.521214i
\(765\) −1.34550 2.33047i −0.0486465 0.0842582i
\(766\) 13.9325 0.503403
\(767\) 10.9046 + 18.8874i 0.393744 + 0.681984i
\(768\) 14.1366