Properties

Label 392.3.k.j.67.2
Level 392
Weight 3
Character 392.67
Analytic conductor 10.681
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.796594176.2
Defining polynomial: \(x^{8} - 4 x^{7} + 18 x^{6} - 40 x^{5} + 83 x^{4} - 104 x^{3} + 22 x^{2} + 24 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 67.2
Root \(1.20711 + 2.54762i\) of defining polynomial
Character \(\chi\) \(=\) 392.67
Dual form 392.3.k.j.275.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.26663 + 1.54779i) q^{2} +(0.292893 - 0.507306i) q^{3} +(-0.791288 - 3.92095i) q^{4} +(7.82295 - 4.51658i) q^{5} +(0.414214 + 1.09591i) q^{6} +(7.07107 + 3.74166i) q^{8} +(4.32843 + 7.49706i) q^{9} +O(q^{10})\) \(q+(-1.26663 + 1.54779i) q^{2} +(0.292893 - 0.507306i) q^{3} +(-0.791288 - 3.92095i) q^{4} +(7.82295 - 4.51658i) q^{5} +(0.414214 + 1.09591i) q^{6} +(7.07107 + 3.74166i) q^{8} +(4.32843 + 7.49706i) q^{9} +(-2.91809 + 17.8291i) q^{10} +(-6.24264 + 10.8126i) q^{11} +(-2.22089 - 0.746995i) q^{12} -9.03316i q^{13} -5.29150i q^{15} +(-14.7477 + 6.20520i) q^{16} +(6.17157 - 10.6895i) q^{17} +(-17.0864 - 2.79653i) q^{18} +(14.4350 + 25.0022i) q^{19} +(-23.8995 - 27.0995i) q^{20} +(-8.82843 - 23.3578i) q^{22} +(21.3404 - 12.3209i) q^{23} +(3.96923 - 2.49129i) q^{24} +(28.2990 - 49.0153i) q^{25} +(13.9814 + 11.4417i) q^{26} +10.3431 q^{27} -22.4499i q^{29} +(8.19012 + 6.70239i) q^{30} +(14.5340 + 8.39119i) q^{31} +(9.07561 - 30.6860i) q^{32} +(3.65685 + 6.33386i) q^{33} +(8.72792 + 23.0919i) q^{34} +(25.9706 - 22.9039i) q^{36} +(-14.0734 + 8.12528i) q^{37} +(-56.9819 - 9.32624i) q^{38} +(-4.58258 - 2.64575i) q^{39} +(72.2161 - 2.66626i) q^{40} -6.97056 q^{41} -22.8284 q^{43} +(47.3353 + 15.9212i) q^{44} +(67.7221 + 39.0994i) q^{45} +(-7.96032 + 48.6364i) q^{46} +(-5.36882 + 3.09969i) q^{47} +(-1.17157 + 9.29907i) q^{48} +(40.0208 + 105.885i) q^{50} +(-3.61522 - 6.26175i) q^{51} +(-35.4186 + 7.14783i) q^{52} +(6.94131 + 4.00757i) q^{53} +(-13.1010 + 16.0090i) q^{54} +112.782i q^{55} +16.9117 q^{57} +(34.7477 + 28.4358i) q^{58} +(15.2218 - 26.3650i) q^{59} +(-20.7477 + 4.18710i) q^{60} +(-13.1918 + 7.61627i) q^{61} +(-31.3970 + 11.8669i) q^{62} +(36.0000 + 52.9150i) q^{64} +(-40.7990 - 70.6659i) q^{65} +(-14.4353 - 2.36263i) q^{66} +(39.3137 - 68.0933i) q^{67} +(-46.7964 - 15.7400i) q^{68} -14.4348i q^{69} +17.5345i q^{71} +(2.55519 + 69.2077i) q^{72} +(23.3431 - 40.4315i) q^{73} +(5.24961 - 32.0744i) q^{74} +(-16.5772 - 28.7125i) q^{75} +(86.6102 - 76.3830i) q^{76} +(9.89949 - 3.74166i) q^{78} +(70.1762 - 40.5163i) q^{79} +(-87.3444 + 115.152i) q^{80} +(-35.9264 + 62.2264i) q^{81} +(8.82914 - 10.7889i) q^{82} -40.3848 q^{83} -111.498i q^{85} +(28.9152 - 35.3335i) q^{86} +(-11.3890 - 6.57544i) q^{87} +(-84.5991 + 53.0986i) q^{88} +(55.9706 + 96.9439i) q^{89} +(-146.296 + 55.2949i) q^{90} +(-65.1960 - 73.9253i) q^{92} +(8.51380 - 4.91545i) q^{93} +(2.00266 - 12.2360i) q^{94} +(225.849 + 130.394i) q^{95} +(-12.9090 - 13.5918i) q^{96} +164.108 q^{97} -108.083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{3} + 12q^{4} - 8q^{6} + 12q^{9} + O(q^{10}) \) \( 8q + 8q^{3} + 12q^{4} - 8q^{6} + 12q^{9} - 28q^{10} - 16q^{11} - 24q^{12} - 8q^{16} + 72q^{17} - 16q^{18} + 8q^{19} - 112q^{20} - 48q^{22} - 40q^{24} + 68q^{25} + 28q^{26} + 128q^{27} - 16q^{33} - 32q^{34} + 72q^{36} - 76q^{38} + 56q^{40} + 80q^{41} - 160q^{43} + 48q^{44} - 224q^{46} - 32q^{48} + 224q^{50} - 176q^{51} - 56q^{52} - 16q^{54} - 272q^{57} + 168q^{58} + 184q^{59} - 56q^{60} + 224q^{62} + 288q^{64} - 168q^{65} - 32q^{66} + 224q^{67} - 216q^{68} + 160q^{72} + 232q^{73} + 280q^{74} + 88q^{75} + 48q^{76} - 336q^{80} + 52q^{81} - 48q^{82} - 176q^{83} - 8q^{86} - 240q^{88} + 312q^{89} - 616q^{90} + 112q^{92} - 112q^{94} + 176q^{96} + 272q^{97} - 480q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26663 + 1.54779i −0.633316 + 0.773893i
\(3\) 0.292893 0.507306i 0.0976311 0.169102i −0.813073 0.582162i \(-0.802207\pi\)
0.910704 + 0.413060i \(0.135540\pi\)
\(4\) −0.791288 3.92095i −0.197822 0.980238i
\(5\) 7.82295 4.51658i 1.56459 0.903316i 0.567807 0.823162i \(-0.307792\pi\)
0.996782 0.0801541i \(-0.0255412\pi\)
\(6\) 0.414214 + 1.09591i 0.0690356 + 0.182651i
\(7\) 0 0
\(8\) 7.07107 + 3.74166i 0.883883 + 0.467707i
\(9\) 4.32843 + 7.49706i 0.480936 + 0.833006i
\(10\) −2.91809 + 17.8291i −0.291809 + 1.78291i
\(11\) −6.24264 + 10.8126i −0.567513 + 0.982961i 0.429298 + 0.903163i \(0.358761\pi\)
−0.996811 + 0.0797982i \(0.974572\pi\)
\(12\) −2.22089 0.746995i −0.185074 0.0622496i
\(13\) 9.03316i 0.694858i −0.937706 0.347429i \(-0.887055\pi\)
0.937706 0.347429i \(-0.112945\pi\)
\(14\) 0 0
\(15\) 5.29150i 0.352767i
\(16\) −14.7477 + 6.20520i −0.921733 + 0.387825i
\(17\) 6.17157 10.6895i 0.363034 0.628793i −0.625425 0.780284i \(-0.715074\pi\)
0.988459 + 0.151492i \(0.0484076\pi\)
\(18\) −17.0864 2.79653i −0.949243 0.155363i
\(19\) 14.4350 + 25.0022i 0.759738 + 1.31591i 0.942984 + 0.332838i \(0.108006\pi\)
−0.183246 + 0.983067i \(0.558660\pi\)
\(20\) −23.8995 27.0995i −1.19497 1.35497i
\(21\) 0 0
\(22\) −8.82843 23.3578i −0.401292 1.06172i
\(23\) 21.3404 12.3209i 0.927843 0.535690i 0.0417142 0.999130i \(-0.486718\pi\)
0.886129 + 0.463439i \(0.153385\pi\)
\(24\) 3.96923 2.49129i 0.165385 0.103804i
\(25\) 28.2990 49.0153i 1.13196 1.96061i
\(26\) 13.9814 + 11.4417i 0.537746 + 0.440065i
\(27\) 10.3431 0.383079
\(28\) 0 0
\(29\) 22.4499i 0.774136i −0.922051 0.387068i \(-0.873488\pi\)
0.922051 0.387068i \(-0.126512\pi\)
\(30\) 8.19012 + 6.70239i 0.273004 + 0.223413i
\(31\) 14.5340 + 8.39119i 0.468838 + 0.270684i 0.715753 0.698353i \(-0.246084\pi\)
−0.246915 + 0.969037i \(0.579417\pi\)
\(32\) 9.07561 30.6860i 0.283613 0.958939i
\(33\) 3.65685 + 6.33386i 0.110814 + 0.191935i
\(34\) 8.72792 + 23.0919i 0.256704 + 0.679174i
\(35\) 0 0
\(36\) 25.9706 22.9039i 0.721405 0.636219i
\(37\) −14.0734 + 8.12528i −0.380362 + 0.219602i −0.677976 0.735084i \(-0.737143\pi\)
0.297614 + 0.954686i \(0.403809\pi\)
\(38\) −56.9819 9.32624i −1.49952 0.245427i
\(39\) −4.58258 2.64575i −0.117502 0.0678398i
\(40\) 72.2161 2.66626i 1.80540 0.0666565i
\(41\) −6.97056 −0.170014 −0.0850069 0.996380i \(-0.527091\pi\)
−0.0850069 + 0.996380i \(0.527091\pi\)
\(42\) 0 0
\(43\) −22.8284 −0.530894 −0.265447 0.964126i \(-0.585519\pi\)
−0.265447 + 0.964126i \(0.585519\pi\)
\(44\) 47.3353 + 15.9212i 1.07580 + 0.361846i
\(45\) 67.7221 + 39.0994i 1.50494 + 0.868875i
\(46\) −7.96032 + 48.6364i −0.173050 + 1.05731i
\(47\) −5.36882 + 3.09969i −0.114230 + 0.0659509i −0.556027 0.831165i \(-0.687675\pi\)
0.441796 + 0.897115i \(0.354341\pi\)
\(48\) −1.17157 + 9.29907i −0.0244078 + 0.193731i
\(49\) 0 0
\(50\) 40.0208 + 105.885i 0.800416 + 2.11770i
\(51\) −3.61522 6.26175i −0.0708867 0.122779i
\(52\) −35.4186 + 7.14783i −0.681127 + 0.137458i
\(53\) 6.94131 + 4.00757i 0.130968 + 0.0756145i 0.564053 0.825739i \(-0.309241\pi\)
−0.433084 + 0.901353i \(0.642575\pi\)
\(54\) −13.1010 + 16.0090i −0.242610 + 0.296463i
\(55\) 112.782i 2.05057i
\(56\) 0 0
\(57\) 16.9117 0.296696
\(58\) 34.7477 + 28.4358i 0.599099 + 0.490273i
\(59\) 15.2218 26.3650i 0.257997 0.446864i −0.707708 0.706505i \(-0.750271\pi\)
0.965705 + 0.259641i \(0.0836042\pi\)
\(60\) −20.7477 + 4.18710i −0.345795 + 0.0697850i
\(61\) −13.1918 + 7.61627i −0.216258 + 0.124857i −0.604217 0.796820i \(-0.706514\pi\)
0.387958 + 0.921677i \(0.373181\pi\)
\(62\) −31.3970 + 11.8669i −0.506403 + 0.191402i
\(63\) 0 0
\(64\) 36.0000 + 52.9150i 0.562500 + 0.826797i
\(65\) −40.7990 70.6659i −0.627677 1.08717i
\(66\) −14.4353 2.36263i −0.218717 0.0357975i
\(67\) 39.3137 68.0933i 0.586772 1.01632i −0.407880 0.913035i \(-0.633732\pi\)
0.994652 0.103283i \(-0.0329348\pi\)
\(68\) −46.7964 15.7400i −0.688183 0.231470i
\(69\) 14.4348i 0.209200i
\(70\) 0 0
\(71\) 17.5345i 0.246965i 0.992347 + 0.123482i \(0.0394062\pi\)
−0.992347 + 0.123482i \(0.960594\pi\)
\(72\) 2.55519 + 69.2077i 0.0354887 + 0.961218i
\(73\) 23.3431 40.4315i 0.319769 0.553856i −0.660671 0.750676i \(-0.729728\pi\)
0.980440 + 0.196820i \(0.0630613\pi\)
\(74\) 5.24961 32.0744i 0.0709407 0.433437i
\(75\) −16.5772 28.7125i −0.221029 0.382833i
\(76\) 86.6102 76.3830i 1.13961 1.00504i
\(77\) 0 0
\(78\) 9.89949 3.74166i 0.126917 0.0479700i
\(79\) 70.1762 40.5163i 0.888307 0.512864i 0.0149184 0.999889i \(-0.495251\pi\)
0.873388 + 0.487025i \(0.161918\pi\)
\(80\) −87.3444 + 115.152i −1.09180 + 1.43940i
\(81\) −35.9264 + 62.2264i −0.443536 + 0.768227i
\(82\) 8.82914 10.7889i 0.107672 0.131572i
\(83\) −40.3848 −0.486564 −0.243282 0.969956i \(-0.578224\pi\)
−0.243282 + 0.969956i \(0.578224\pi\)
\(84\) 0 0
\(85\) 111.498i 1.31174i
\(86\) 28.9152 35.3335i 0.336223 0.410855i
\(87\) −11.3890 6.57544i −0.130908 0.0755797i
\(88\) −84.5991 + 53.0986i −0.961353 + 0.603393i
\(89\) 55.9706 + 96.9439i 0.628883 + 1.08926i 0.987776 + 0.155878i \(0.0498208\pi\)
−0.358894 + 0.933379i \(0.616846\pi\)
\(90\) −146.296 + 55.2949i −1.62552 + 0.614387i
\(91\) 0 0
\(92\) −65.1960 73.9253i −0.708652 0.803536i
\(93\) 8.51380 4.91545i 0.0915463 0.0528543i
\(94\) 2.00266 12.2360i 0.0213049 0.130170i
\(95\) 225.849 + 130.394i 2.37736 + 1.37257i
\(96\) −12.9090 13.5918i −0.134469 0.141582i
\(97\) 164.108 1.69183 0.845916 0.533317i \(-0.179055\pi\)
0.845916 + 0.533317i \(0.179055\pi\)
\(98\) 0 0
\(99\) −108.083 −1.09175
\(100\) −214.579 72.1738i −2.14579 0.721738i
\(101\) −10.5074 6.06643i −0.104033 0.0600636i 0.447081 0.894494i \(-0.352464\pi\)
−0.551114 + 0.834430i \(0.685797\pi\)
\(102\) 14.2710 + 2.33574i 0.139912 + 0.0228994i
\(103\) −92.3029 + 53.2911i −0.896144 + 0.517389i −0.875947 0.482407i \(-0.839763\pi\)
−0.0201970 + 0.999796i \(0.506429\pi\)
\(104\) 33.7990 63.8741i 0.324990 0.614174i
\(105\) 0 0
\(106\) −14.9949 + 5.66756i −0.141462 + 0.0534675i
\(107\) 31.7990 + 55.0775i 0.297187 + 0.514743i 0.975491 0.220038i \(-0.0706182\pi\)
−0.678304 + 0.734781i \(0.737285\pi\)
\(108\) −8.18441 40.5550i −0.0757815 0.375509i
\(109\) −113.318 65.4239i −1.03961 0.600220i −0.119888 0.992787i \(-0.538253\pi\)
−0.919723 + 0.392568i \(0.871587\pi\)
\(110\) −174.562 142.853i −1.58693 1.29866i
\(111\) 9.51936i 0.0857600i
\(112\) 0 0
\(113\) −138.225 −1.22323 −0.611617 0.791154i \(-0.709481\pi\)
−0.611617 + 0.791154i \(0.709481\pi\)
\(114\) −21.4209 + 26.1757i −0.187902 + 0.229611i
\(115\) 111.296 192.771i 0.967795 1.67627i
\(116\) −88.0252 + 17.7644i −0.758838 + 0.153141i
\(117\) 67.7221 39.0994i 0.578821 0.334183i
\(118\) 21.5269 + 56.9549i 0.182431 + 0.482668i
\(119\) 0 0
\(120\) 19.7990 37.4166i 0.164992 0.311805i
\(121\) −17.4411 30.2089i −0.144142 0.249660i
\(122\) 4.92075 30.0651i 0.0403340 0.246435i
\(123\) −2.04163 + 3.53621i −0.0165986 + 0.0287497i
\(124\) 21.4009 63.6269i 0.172588 0.513120i
\(125\) 285.430i 2.28344i
\(126\) 0 0
\(127\) 114.442i 0.901114i 0.892748 + 0.450557i \(0.148775\pi\)
−0.892748 + 0.450557i \(0.851225\pi\)
\(128\) −127.500 11.3035i −0.996093 0.0883088i
\(129\) −6.68629 + 11.5810i −0.0518317 + 0.0897752i
\(130\) 161.053 + 26.3596i 1.23887 + 0.202766i
\(131\) −84.1751 145.796i −0.642558 1.11294i −0.984860 0.173353i \(-0.944540\pi\)
0.342301 0.939590i \(-0.388794\pi\)
\(132\) 21.9411 19.3503i 0.166221 0.146593i
\(133\) 0 0
\(134\) 55.5980 + 147.098i 0.414910 + 1.09775i
\(135\) 80.9139 46.7156i 0.599362 0.346042i
\(136\) 83.6360 52.4941i 0.614970 0.385986i
\(137\) −17.3431 + 30.0392i −0.126592 + 0.219264i −0.922354 0.386345i \(-0.873737\pi\)
0.795762 + 0.605610i \(0.207071\pi\)
\(138\) 22.3420 + 18.2836i 0.161899 + 0.132490i
\(139\) −107.664 −0.774561 −0.387281 0.921962i \(-0.626586\pi\)
−0.387281 + 0.921962i \(0.626586\pi\)
\(140\) 0 0
\(141\) 3.63151i 0.0257554i
\(142\) −27.1397 22.2098i −0.191124 0.156407i
\(143\) 97.6717 + 56.3908i 0.683019 + 0.394341i
\(144\) −110.355 83.7058i −0.766356 0.581290i
\(145\) −101.397 175.625i −0.699289 1.21120i
\(146\) 33.0122 + 87.3421i 0.226111 + 0.598233i
\(147\) 0 0
\(148\) 42.9949 + 48.7517i 0.290506 + 0.329403i
\(149\) −218.391 + 126.088i −1.46571 + 0.846229i −0.999266 0.0383198i \(-0.987799\pi\)
−0.466447 + 0.884549i \(0.654466\pi\)
\(150\) 65.4380 + 10.7102i 0.436253 + 0.0714016i
\(151\) −203.071 117.243i −1.34484 0.776444i −0.357327 0.933979i \(-0.616312\pi\)
−0.987513 + 0.157535i \(0.949645\pi\)
\(152\) 8.52139 + 230.803i 0.0560618 + 1.51844i
\(153\) 106.853 0.698384
\(154\) 0 0
\(155\) 151.598 0.978051
\(156\) −6.74773 + 20.0616i −0.0432547 + 0.128600i
\(157\) 8.74409 + 5.04840i 0.0556948 + 0.0321554i 0.527589 0.849500i \(-0.323096\pi\)
−0.471894 + 0.881655i \(0.656430\pi\)
\(158\) −26.1769 + 159.937i −0.165677 + 1.01226i
\(159\) 4.06613 2.34758i 0.0255731 0.0147647i
\(160\) −67.5980 281.046i −0.422487 1.75654i
\(161\) 0 0
\(162\) −50.8076 134.424i −0.313627 0.829780i
\(163\) −52.2670 90.5291i −0.320657 0.555394i 0.659967 0.751295i \(-0.270570\pi\)
−0.980624 + 0.195901i \(0.937237\pi\)
\(164\) 5.51572 + 27.3312i 0.0336324 + 0.166654i
\(165\) 57.2147 + 33.0329i 0.346756 + 0.200200i
\(166\) 51.1526 62.5070i 0.308148 0.376548i
\(167\) 296.765i 1.77703i 0.458843 + 0.888517i \(0.348264\pi\)
−0.458843 + 0.888517i \(0.651736\pi\)
\(168\) 0 0
\(169\) 87.4020 0.517172
\(170\) 172.575 + 141.226i 1.01514 + 0.830744i
\(171\) −124.962 + 216.440i −0.730772 + 1.26573i
\(172\) 18.0639 + 89.5092i 0.105022 + 0.520402i
\(173\) −34.6671 + 20.0150i −0.200388 + 0.115694i −0.596836 0.802363i \(-0.703576\pi\)
0.396449 + 0.918057i \(0.370242\pi\)
\(174\) 24.6030 9.29907i 0.141397 0.0534429i
\(175\) 0 0
\(176\) 24.9706 198.198i 0.141878 1.12612i
\(177\) −8.91674 15.4442i −0.0503771 0.0872556i
\(178\) −220.943 36.1617i −1.24125 0.203155i
\(179\) −147.397 + 255.299i −0.823447 + 1.42625i 0.0796538 + 0.996823i \(0.474619\pi\)
−0.903101 + 0.429429i \(0.858715\pi\)
\(180\) 99.7191 296.474i 0.553995 1.64708i
\(181\) 40.4706i 0.223595i −0.993731 0.111797i \(-0.964339\pi\)
0.993731 0.111797i \(-0.0356608\pi\)
\(182\) 0 0
\(183\) 8.92302i 0.0487596i
\(184\) 197.000 7.27335i 1.07065 0.0395291i
\(185\) −73.3970 + 127.127i −0.396740 + 0.687174i
\(186\) −3.17579 + 19.4036i −0.0170741 + 0.104321i
\(187\) 77.0538 + 133.461i 0.412053 + 0.713696i
\(188\) 16.4020 + 18.5981i 0.0872448 + 0.0989263i
\(189\) 0 0
\(190\) −487.889 + 184.405i −2.56784 + 0.970552i
\(191\) −135.905 + 78.4647i −0.711543 + 0.410810i −0.811632 0.584169i \(-0.801421\pi\)
0.100089 + 0.994979i \(0.468087\pi\)
\(192\) 37.3883 2.76456i 0.194731 0.0143988i
\(193\) 130.652 226.296i 0.676952 1.17252i −0.298942 0.954271i \(-0.596634\pi\)
0.975894 0.218245i \(-0.0700330\pi\)
\(194\) −207.864 + 254.004i −1.07146 + 1.30930i
\(195\) −47.7990 −0.245123
\(196\) 0 0
\(197\) 145.283i 0.737475i −0.929533 0.368738i \(-0.879790\pi\)
0.929533 0.368738i \(-0.120210\pi\)
\(198\) 136.902 167.290i 0.691423 0.844898i
\(199\) −338.189 195.254i −1.69944 0.981175i −0.946283 0.323339i \(-0.895195\pi\)
−0.753161 0.657836i \(1.22853\pi\)
\(200\) 383.502 240.705i 1.91751 1.20353i
\(201\) −23.0294 39.8882i −0.114574 0.198449i
\(202\) 22.6985 8.57922i 0.112369 0.0424714i
\(203\) 0 0
\(204\) −21.6913 + 19.1300i −0.106330 + 0.0937743i
\(205\) −54.5303 + 31.4831i −0.266002 + 0.153576i
\(206\) 34.4305 210.365i 0.167138 1.02119i
\(207\) 184.741 + 106.660i 0.892467 + 0.515266i
\(208\) 56.0526 + 133.219i 0.269484 + 0.640474i
\(209\) −360.451 −1.72464
\(210\) 0 0
\(211\) −164.049 −0.777482 −0.388741 0.921347i \(-0.627090\pi\)
−0.388741 + 0.921347i \(0.627090\pi\)
\(212\) 10.2209 30.3877i 0.0482118 0.143338i
\(213\) 8.89535 + 5.13574i 0.0417622 + 0.0241114i
\(214\) −125.526 20.5448i −0.586569 0.0960038i
\(215\) −178.586 + 103.106i −0.830630 + 0.479565i
\(216\) 73.1371 + 38.7005i 0.338598 + 0.179169i
\(217\) 0 0
\(218\) 244.794 92.5234i 1.12291 0.424419i
\(219\) −13.6741 23.6842i −0.0624388 0.108147i
\(220\) 442.211 89.2427i 2.01005 0.405648i
\(221\) −96.5598 55.7488i −0.436922 0.252257i
\(222\) −14.7339 12.0575i −0.0663691 0.0543132i
\(223\) 10.5830i 0.0474574i 0.999718 + 0.0237287i \(0.00755379\pi\)
−0.999718 + 0.0237287i \(0.992446\pi\)
\(224\) 0 0
\(225\) 489.960 2.17760
\(226\) 175.081 213.943i 0.774693 0.946652i
\(227\) −106.903 + 185.162i −0.470939 + 0.815690i −0.999447 0.0332382i \(-0.989418\pi\)
0.528509 + 0.848928i \(0.322751\pi\)
\(228\) −13.3820 66.3099i −0.0586930 0.290833i
\(229\) 200.942 116.014i 0.877478 0.506612i 0.00765200 0.999971i \(-0.497564\pi\)
0.869826 + 0.493359i \(0.164231\pi\)
\(230\) 157.397 + 416.433i 0.684335 + 1.81058i
\(231\) 0 0
\(232\) 84.0000 158.745i 0.362069 0.684246i
\(233\) 96.4315 + 167.024i 0.413869 + 0.716842i 0.995309 0.0967472i \(-0.0308439\pi\)
−0.581440 + 0.813589i \(0.697511\pi\)
\(234\) −25.2615 + 154.344i −0.107955 + 0.659589i
\(235\) −28.0000 + 48.4974i −0.119149 + 0.206372i
\(236\) −115.421 38.8218i −0.489071 0.164499i
\(237\) 47.4678i 0.200286i
\(238\) 0 0
\(239\) 327.917i 1.37204i 0.727583 + 0.686020i \(0.240644\pi\)
−0.727583 + 0.686020i \(0.759356\pi\)
\(240\) 32.8348 + 78.0376i 0.136812 + 0.325157i
\(241\) 35.9361 62.2431i 0.149112 0.258270i −0.781787 0.623545i \(-0.785692\pi\)
0.930900 + 0.365275i \(0.119025\pi\)
\(242\) 68.8484 + 11.2684i 0.284498 + 0.0465638i
\(243\) 67.5894 + 117.068i 0.278146 + 0.481762i
\(244\) 40.3015 + 45.6976i 0.165170 + 0.187285i
\(245\) 0 0
\(246\) −2.88730 7.63908i −0.0117370 0.0310532i
\(247\) 225.849 130.394i 0.914368 0.527911i
\(248\) 71.3737 + 113.716i 0.287797 + 0.458532i
\(249\) −11.8284 + 20.4874i −0.0475037 + 0.0822789i
\(250\) 441.784 + 361.534i 1.76714 + 1.44614i
\(251\) 256.919 1.02358 0.511790 0.859110i \(-0.328982\pi\)
0.511790 + 0.859110i \(0.328982\pi\)
\(252\) 0 0
\(253\) 307.659i 1.21604i
\(254\) −177.131 144.955i −0.697367 0.570690i
\(255\) −56.5634 32.6569i −0.221817 0.128066i
\(256\) 178.991 183.025i 0.699183 0.714943i
\(257\) 159.676 + 276.567i 0.621308 + 1.07614i 0.989242 + 0.146285i \(0.0467318\pi\)
−0.367934 + 0.929852i \(0.619935\pi\)
\(258\) −9.45584 25.0178i −0.0366506 0.0969683i
\(259\) 0 0
\(260\) −244.794 + 215.888i −0.941515 + 0.830338i
\(261\) 168.308 97.1729i 0.644860 0.372310i
\(262\) 332.279 + 54.3842i 1.26824 + 0.207573i
\(263\) −326.800 188.678i −1.24259 0.717408i −0.272967 0.962023i \(-0.588005\pi\)
−0.969620 + 0.244615i \(0.921338\pi\)
\(264\) 2.15874 + 58.4698i 0.00817705 + 0.221477i
\(265\) 72.4020 0.273215
\(266\) 0 0
\(267\) 65.5736 0.245594
\(268\) −298.099 100.266i −1.11231 0.374126i
\(269\) −24.3900 14.0816i −0.0906691 0.0523478i 0.453980 0.891012i \(-0.350004\pi\)
−0.544649 + 0.838664i \(0.683337\pi\)
\(270\) −30.1822 + 184.409i −0.111786 + 0.682996i
\(271\) 346.164 199.858i 1.27736 0.737482i 0.300995 0.953626i \(-0.402681\pi\)
0.976362 + 0.216143i \(0.0693479\pi\)
\(272\) −24.6863 + 195.941i −0.0907584 + 0.720373i
\(273\) 0 0
\(274\) −24.5269 64.8921i −0.0895143 0.236833i
\(275\) 353.321 + 611.970i 1.28480 + 2.22534i
\(276\) −56.5982 + 11.4221i −0.205066 + 0.0413844i
\(277\) −89.1579 51.4753i −0.321870 0.185831i 0.330356 0.943856i \(-0.392831\pi\)
−0.652226 + 0.758025i \(0.726165\pi\)
\(278\) 136.371 166.641i 0.490542 0.599428i
\(279\) 145.283i 0.520726i
\(280\) 0 0
\(281\) −150.235 −0.534646 −0.267323 0.963607i \(-0.586139\pi\)
−0.267323 + 0.963607i \(0.586139\pi\)
\(282\) −5.62081 4.59979i −0.0199319 0.0163113i
\(283\) −89.2807 + 154.639i −0.315480 + 0.546427i −0.979539 0.201253i \(-0.935499\pi\)
0.664060 + 0.747679i \(0.268832\pi\)
\(284\) 68.7519 13.8748i 0.242084 0.0488551i
\(285\) 132.299 76.3830i 0.464208 0.268011i
\(286\) −210.995 + 79.7486i −0.737745 + 0.278841i
\(287\) 0 0
\(288\) 269.338 64.7820i 0.935202 0.224937i
\(289\) 68.3234 + 118.340i 0.236413 + 0.409479i
\(290\) 400.262 + 65.5109i 1.38021 + 0.225900i
\(291\) 48.0660 83.2528i 0.165175 0.286092i
\(292\) −177.001 59.5344i −0.606168 0.203885i
\(293\) 219.189i 0.748085i −0.927411 0.374043i \(-0.877971\pi\)
0.927411 0.374043i \(-0.122029\pi\)
\(294\) 0 0
\(295\) 275.002i 0.932211i
\(296\) −129.916 + 4.79657i −0.438905 + 0.0162046i
\(297\) −64.5685 + 111.836i −0.217402 + 0.376552i
\(298\) 81.4635 497.730i 0.273368 1.67024i
\(299\) −111.296 192.771i −0.372229 0.644720i
\(300\) −99.4630 + 87.7181i −0.331543 + 0.292394i
\(301\) 0 0
\(302\) 438.683 165.807i 1.45259 0.549029i
\(303\) −6.15507 + 3.55363i −0.0203138 + 0.0117282i
\(304\) −368.028 279.153i −1.21062 0.918268i
\(305\) −68.7990 + 119.163i −0.225570 + 0.390699i
\(306\) −135.343 + 165.385i −0.442298 + 0.540475i
\(307\) −316.669 −1.03150 −0.515748 0.856741i \(-0.672486\pi\)
−0.515748 + 0.856741i \(0.672486\pi\)
\(308\) 0 0
\(309\) 62.4344i 0.202053i
\(310\) −192.019 + 234.641i −0.619416 + 0.756908i
\(311\) −62.5836 36.1326i −0.201233 0.116182i 0.395997 0.918252i \(-0.370399\pi\)
−0.597231 + 0.802070i \(0.703732\pi\)
\(312\) −22.5042 35.8547i −0.0721289 0.114919i
\(313\) 40.9756 + 70.9718i 0.130913 + 0.226747i 0.924029 0.382323i \(-0.124876\pi\)
−0.793116 + 0.609071i \(0.791543\pi\)
\(314\) −18.8894 + 7.13952i −0.0601573 + 0.0227373i
\(315\) 0 0
\(316\) −214.392 243.098i −0.678455 0.769296i
\(317\) 94.5267 54.5750i 0.298191 0.172161i −0.343439 0.939175i \(-0.611592\pi\)
0.641630 + 0.767014i \(0.278258\pi\)
\(318\) −1.51673 + 9.26702i −0.00476960 + 0.0291416i
\(319\) 242.742 + 140.147i 0.760945 + 0.439332i
\(320\) 520.621 + 251.355i 1.62694 + 0.785483i
\(321\) 37.2548 0.116059
\(322\) 0 0
\(323\) 356.347 1.10324
\(324\) 272.415 + 91.6267i 0.840786 + 0.282799i
\(325\) −442.763 255.629i −1.36235 0.786552i
\(326\) 206.323 + 33.7689i 0.632892 + 0.103586i
\(327\) −66.3799 + 38.3245i −0.202997 + 0.117200i
\(328\) −49.2893 26.0815i −0.150272 0.0795166i
\(329\) 0 0
\(330\) −123.598 + 46.7156i −0.374539 + 0.141563i
\(331\) −160.870 278.635i −0.486012 0.841798i 0.513858 0.857875i \(-0.328216\pi\)
−0.999871 + 0.0160770i \(0.994882\pi\)
\(332\) 31.9560 + 158.347i 0.0962530 + 0.476948i
\(333\) −121.831 70.3394i −0.365860 0.211229i
\(334\) −459.329 375.892i −1.37524 1.12542i
\(335\) 710.254i 2.12016i
\(336\) 0 0
\(337\) −164.049 −0.486792 −0.243396 0.969927i \(-0.578261\pi\)
−0.243396 + 0.969927i \(0.578261\pi\)
\(338\) −110.706 + 135.280i −0.327533 + 0.400236i
\(339\) −40.4853 + 70.1226i −0.119426 + 0.206851i
\(340\) −437.177 + 88.2267i −1.28581 + 0.259490i
\(341\) −181.461 + 104.766i −0.532143 + 0.307233i
\(342\) −176.723 467.565i −0.516734 1.36715i
\(343\) 0 0
\(344\) −161.421 85.4162i −0.469248 0.248303i
\(345\) −65.1960 112.923i −0.188974 0.327312i
\(346\) 12.9314 79.0089i 0.0373740 0.228349i
\(347\) 165.154 286.056i 0.475949 0.824368i −0.523671 0.851920i \(-0.675438\pi\)
0.999620 + 0.0275524i \(0.00877132\pi\)
\(348\) −16.7700 + 49.8587i −0.0481897 + 0.143272i
\(349\) 262.402i 0.751869i 0.926646 + 0.375934i \(0.122678\pi\)
−0.926646 + 0.375934i \(0.877322\pi\)
\(350\) 0 0
\(351\) 93.4313i 0.266186i
\(352\) 275.139 + 289.693i 0.781646 + 0.822990i
\(353\) −289.049 + 500.647i −0.818835 + 1.41826i 0.0877061 + 0.996146i \(0.472046\pi\)
−0.906541 + 0.422118i \(0.861287\pi\)
\(354\) 35.1986 + 5.76096i 0.0994311 + 0.0162739i
\(355\) 79.1960 + 137.171i 0.223087 + 0.386398i
\(356\) 335.823 296.168i 0.943324 0.831934i
\(357\) 0 0
\(358\) −208.451 551.509i −0.582265 1.54053i
\(359\) −316.198 + 182.557i −0.880774 + 0.508515i −0.870913 0.491437i \(-0.836472\pi\)
−0.00986020 + 0.999951i \(0.503139\pi\)
\(360\) 332.571 + 529.867i 0.923809 + 1.47185i
\(361\) −236.240 + 409.180i −0.654405 + 1.13346i
\(362\) 62.6399 + 51.2614i 0.173038 + 0.141606i
\(363\) −20.4335 −0.0562908
\(364\) 0 0
\(365\) 421.725i 1.15541i
\(366\) −13.8109 11.3022i −0.0377348 0.0308803i
\(367\) 450.395 + 260.036i 1.22723 + 0.708544i 0.966451 0.256853i \(-0.0826856\pi\)
0.260784 + 0.965397i \(0.416019\pi\)
\(368\) −238.269 + 314.126i −0.647469 + 0.853604i
\(369\) −30.1716 52.2587i −0.0817658 0.141622i
\(370\) −103.799 274.626i −0.280538 0.742233i
\(371\) 0 0
\(372\) −26.0101 29.4927i −0.0699196 0.0792814i
\(373\) −456.145 + 263.356i −1.22291 + 0.706048i −0.965537 0.260265i \(-0.916190\pi\)
−0.257373 + 0.966312i \(0.582857\pi\)
\(374\) −304.168 49.7832i −0.813284 0.133110i
\(375\) −144.800 83.6004i −0.386134 0.222934i
\(376\) −49.5613 + 1.82983i −0.131812 + 0.00486657i
\(377\) −202.794 −0.537915
\(378\) 0 0
\(379\) 121.976 0.321835 0.160918 0.986968i \(-0.448555\pi\)
0.160918 + 0.986968i \(0.448555\pi\)
\(380\) 332.557 988.722i 0.875150 2.60190i
\(381\) 58.0569 + 33.5191i 0.152380 + 0.0879768i
\(382\) 50.6947 309.737i 0.132709 0.810831i
\(383\) 274.033 158.213i 0.715492 0.413089i −0.0975993 0.995226i \(-0.531116\pi\)
0.813091 + 0.582136i \(0.197783\pi\)
\(384\) −43.0782 + 61.3707i −0.112183 + 0.159820i
\(385\) 0 0
\(386\) 184.770 + 488.854i 0.478678 + 1.26646i
\(387\) −98.8112 171.146i −0.255326 0.442238i
\(388\) −129.856 643.458i −0.334681 1.65840i
\(389\) −79.8020 46.0737i −0.205146 0.118441i 0.393907 0.919150i \(-0.371123\pi\)
−0.599054 + 0.800709i \(0.704456\pi\)
\(390\) 60.5437 73.9826i 0.155240 0.189699i
\(391\) 304.157i 0.777895i
\(392\) 0 0
\(393\) −98.6173 −0.250935
\(394\) 224.867 + 184.020i 0.570727 + 0.467055i
\(395\) 365.990 633.913i 0.926557 1.60484i
\(396\) 85.5250 + 423.789i 0.215972 + 1.07017i
\(397\) −486.937 + 281.133i −1.22654 + 0.708144i −0.966305 0.257400i \(-0.917134\pi\)
−0.260237 + 0.965545i \(0.583801\pi\)
\(398\) 730.573 276.131i 1.83561 0.693795i
\(399\) 0 0
\(400\) −113.196 + 898.465i −0.282990 + 2.24616i
\(401\) −40.6030 70.3265i −0.101254 0.175378i 0.810947 0.585119i \(-0.198952\pi\)
−0.912202 + 0.409741i \(0.865619\pi\)
\(402\) 90.9082 + 14.8789i 0.226140 + 0.0370123i
\(403\) 75.7990 131.288i 0.188087 0.325776i
\(404\) −15.4718 + 45.9991i −0.0382966 + 0.113859i
\(405\) 649.058i 1.60261i
\(406\) 0 0
\(407\) 202.893i 0.498508i
\(408\) −2.13416 57.8042i −0.00523080 0.141677i
\(409\) 225.368 390.348i 0.551021 0.954396i −0.447180 0.894444i \(-0.647572\pi\)
0.998201 0.0599523i \(-0.0190949\pi\)
\(410\) 20.3407 124.279i 0.0496115 0.303119i
\(411\) 10.1594 + 17.5966i 0.0247187 + 0.0428140i
\(412\) 281.990 + 319.746i 0.684442 + 0.776084i
\(413\) 0 0
\(414\) −399.085 + 150.840i −0.963974 + 0.364348i
\(415\) −315.928 + 182.401i −0.761272 + 0.439521i
\(416\) −277.192 81.9814i −0.666327 0.197071i
\(417\) −31.5341 + 54.6186i −0.0756212 + 0.130980i
\(418\) 456.558 557.901i 1.09225 1.33469i
\(419\) −624.988 −1.49162 −0.745809 0.666160i \(-0.767937\pi\)
−0.745809 + 0.666160i \(0.767937\pi\)
\(420\) 0 0
\(421\) 566.476i 1.34555i 0.739848 + 0.672774i \(0.234897\pi\)
−0.739848 + 0.672774i \(0.765103\pi\)
\(422\) 207.789 253.913i 0.492392 0.601688i
\(423\) −46.4771 26.8336i −0.109875 0.0634363i
\(424\) 34.0875 + 54.3098i 0.0803952 + 0.128089i
\(425\) −349.299 605.003i −0.821879 1.42354i
\(426\) −19.2162 + 7.26303i −0.0451084 + 0.0170494i
\(427\) 0 0
\(428\) 190.794 168.264i 0.445780 0.393141i
\(429\) 57.2147 33.0329i 0.133368 0.0769999i
\(430\) 66.6154 407.010i 0.154920 0.946535i
\(431\) −250.739 144.764i −0.581761 0.335880i 0.180072 0.983653i \(-0.442367\pi\)
−0.761833 + 0.647774i \(0.775700\pi\)
\(432\) −152.538 + 64.1813i −0.353097 + 0.148568i
\(433\) 597.696 1.38036 0.690180 0.723638i \(-0.257532\pi\)
0.690180 + 0.723638i \(0.257532\pi\)
\(434\) 0 0
\(435\) −118.794 −0.273090
\(436\) −166.857 + 496.082i −0.382700 + 1.13780i
\(437\) 616.098 + 355.704i 1.40984 + 0.813969i
\(438\) 53.9782 + 8.83461i 0.123238 + 0.0201704i
\(439\) 33.2458 19.1945i 0.0757308 0.0437232i −0.461656 0.887059i \(-0.652745\pi\)
0.537387 + 0.843336i \(0.319411\pi\)
\(440\) −421.990 + 797.486i −0.959068 + 1.81247i
\(441\) 0 0
\(442\) 208.593 78.8407i 0.471930 0.178373i
\(443\) −299.529 518.799i −0.676138 1.17110i −0.976135 0.217165i \(-0.930319\pi\)
0.299997 0.953940i \(-0.403014\pi\)
\(444\) 37.3250 7.53255i 0.0840652 0.0169652i
\(445\) 875.709 + 505.591i 1.96789 + 1.13616i
\(446\) −16.3802 13.4048i −0.0367270 0.0300555i
\(447\) 147.721i 0.330473i
\(448\) 0 0
\(449\) −460.039 −1.02459 −0.512293 0.858811i \(-0.671204\pi\)
−0.512293 + 0.858811i \(0.671204\pi\)
\(450\) −620.599 + 758.354i −1.37911 + 1.68523i
\(451\) 43.5147 75.3697i 0.0964850 0.167117i
\(452\) 109.376 + 541.975i 0.241982 + 1.19906i
\(453\) −118.956 + 68.6794i −0.262596 + 0.151610i
\(454\) −151.184 399.995i −0.333004 0.881045i
\(455\) 0 0
\(456\) 119.584 + 63.2777i 0.262245 + 0.138767i
\(457\) −133.161 230.642i −0.291382 0.504688i 0.682755 0.730647i \(-0.260782\pi\)
−0.974137 + 0.225959i \(0.927448\pi\)
\(458\) −74.9549 + 457.963i −0.163657 + 0.999920i
\(459\) 63.8335 110.563i 0.139071 0.240878i
\(460\) −843.914 283.851i −1.83460 0.617067i
\(461\) 763.123i 1.65537i 0.561196 + 0.827683i \(0.310341\pi\)
−0.561196 + 0.827683i \(0.689659\pi\)
\(462\) 0 0
\(463\) 123.988i 0.267792i 0.990995 + 0.133896i \(0.0427488\pi\)
−0.990995 + 0.133896i \(0.957251\pi\)
\(464\) 139.306 + 331.086i 0.300229 + 0.713547i
\(465\) 44.4020 76.9066i 0.0954882 0.165390i
\(466\) −380.661 62.3028i −0.816869 0.133697i
\(467\) −384.359 665.729i −0.823038 1.42554i −0.903409 0.428779i \(-0.858944\pi\)
0.0803710 0.996765i \(-0.474390\pi\)
\(468\) −206.894 234.596i −0.442082 0.501274i
\(469\) 0 0
\(470\) −39.5980 104.766i −0.0842510 0.222907i
\(471\) 5.12217 2.95729i 0.0108751 0.00627874i
\(472\) 206.283 129.474i 0.437041 0.274309i
\(473\) 142.510 246.834i 0.301289 0.521848i
\(474\) 73.4700 + 60.1242i 0.155000 + 0.126844i
\(475\) 1633.99 3.43997
\(476\) 0 0
\(477\) 69.3859i 0.145463i
\(478\) −507.546 415.351i −1.06181 0.868934i
\(479\) −103.041 59.4905i −0.215116 0.124197i 0.388571 0.921419i \(-0.372969\pi\)
−0.603687 + 0.797222i \(0.706302\pi\)
\(480\) −162.375 48.0236i −0.338282 0.100049i
\(481\) 73.3970 + 127.127i 0.152592 + 0.264298i
\(482\) 50.8213 + 134.460i 0.105438 + 0.278964i
\(483\) 0 0
\(484\) −104.647 + 92.2898i −0.216212 + 0.190681i
\(485\) 1283.81 741.205i 2.64702 1.52826i
\(486\) −266.807 43.6684i −0.548987 0.0898527i
\(487\) 244.719 + 141.288i 0.502503 + 0.290120i 0.729746 0.683718i \(-0.239638\pi\)
−0.227244 + 0.973838i \(0.572971\pi\)
\(488\) −121.777 + 4.49609i −0.249544 + 0.00921330i
\(489\) −61.2346 −0.125224
\(490\) 0 0
\(491\) −388.049 −0.790323 −0.395162 0.918612i \(-0.629311\pi\)
−0.395162 + 0.918612i \(0.629311\pi\)
\(492\) 15.4808 + 5.20698i 0.0314651 + 0.0105833i
\(493\) −239.978 138.551i −0.486771 0.281037i
\(494\) −84.2454 + 514.727i −0.170537 + 1.04196i
\(495\) −845.530 + 488.167i −1.70814 + 0.986195i
\(496\) −266.412 33.5648i −0.537121 0.0676709i
\(497\) 0 0
\(498\) −16.7279 44.2579i −0.0335902 0.0888713i
\(499\) 13.8579 + 24.0025i 0.0277713 + 0.0481013i 0.879577 0.475757i \(-0.157826\pi\)
−0.851806 + 0.523858i \(0.824492\pi\)
\(500\) −1119.16 + 225.857i −2.23831 + 0.451714i
\(501\) 150.551 + 86.9204i 0.300500 + 0.173494i
\(502\) −325.422 + 397.656i −0.648250 + 0.792143i
\(503\) 727.477i 1.44628i −0.690703 0.723138i \(-0.742699\pi\)
0.690703 0.723138i \(-0.257301\pi\)
\(504\) 0 0
\(505\) −109.598 −0.217026
\(506\) −476.191 389.691i −0.941089 0.770140i
\(507\) 25.5995 44.3396i 0.0504920 0.0874548i
\(508\) 448.720 90.5562i 0.883307 0.178260i
\(509\) 549.218 317.091i 1.07901 0.622969i 0.148384 0.988930i \(-0.452593\pi\)
0.930630 + 0.365961i \(0.119260\pi\)
\(510\) 122.191 46.1838i 0.239590 0.0905565i
\(511\) 0 0
\(512\) 56.5685 + 508.865i 0.110485 + 0.993878i
\(513\) 149.304 + 258.601i 0.291040 + 0.504096i
\(514\) −630.318 103.164i −1.22630 0.200709i
\(515\) −481.387 + 833.787i −0.934732 + 1.61900i
\(516\) 50.6993 + 17.0527i 0.0982545 + 0.0330479i
\(517\) 77.4010i 0.149712i
\(518\) 0 0
\(519\) 23.4491i 0.0451813i
\(520\) −24.0847 652.339i −0.0463168 1.25450i
\(521\) 416.563 721.509i 0.799546 1.38485i −0.120366 0.992730i \(-0.538407\pi\)
0.919912 0.392125i \(-0.128260\pi\)
\(522\) −62.7819 + 383.588i −0.120272 + 0.734843i
\(523\) 438.217 + 759.014i 0.837891 + 1.45127i 0.891655 + 0.452715i \(0.149545\pi\)
−0.0537645 + 0.998554i \(0.517122\pi\)
\(524\) −505.051 + 445.413i −0.963838 + 0.850025i
\(525\) 0 0
\(526\) 705.970 266.831i 1.34215 0.507284i
\(527\) 179.395 103.574i 0.340408 0.196535i
\(528\) −93.2332 70.7185i −0.176578 0.133937i
\(529\) 39.1081 67.7372i 0.0739283 0.128048i
\(530\) −91.7067 + 112.063i −0.173032 + 0.211439i
\(531\) 263.546 0.496321
\(532\) 0 0
\(533\) 62.9662i 0.118135i
\(534\) −83.0576 + 101.494i −0.155539 + 0.190064i
\(535\) 497.524 + 287.245i 0.929951 + 0.536907i
\(536\) 532.772 334.394i 0.993977 0.623870i
\(537\) 86.3431 + 149.551i 0.160788 + 0.278493i
\(538\) 52.6884 19.9143i 0.0979338 0.0370155i
\(539\) 0 0
\(540\) −247.196 280.294i −0.457770 0.519063i
\(541\) 351.532 202.957i 0.649783 0.375152i −0.138590 0.990350i \(-0.544257\pi\)
0.788373 + 0.615198i \(0.210924\pi\)
\(542\) −129.125 + 788.934i −0.238238 + 1.45560i
\(543\) −20.5310 11.8536i −0.0378103 0.0218298i
\(544\) −272.007 286.395i −0.500013 0.526461i
\(545\) −1181.97 −2.16875
\(546\) 0 0
\(547\) −606.024 −1.10791 −0.553953 0.832548i \(-0.686881\pi\)
−0.553953 + 0.832548i \(0.686881\pi\)
\(548\) 131.506 + 44.2320i 0.239974 + 0.0807153i
\(549\) −114.199 65.9329i −0.208013 0.120096i
\(550\) −1394.73 228.275i −2.53587 0.415045i
\(551\) 561.298 324.066i 1.01869 0.588141i
\(552\) 54.0101 102.069i 0.0978444 0.184909i
\(553\) 0 0
\(554\) 192.603 72.7971i 0.347659 0.131403i
\(555\) 42.9949 + 74.4694i 0.0774684 + 0.134179i
\(556\) 85.1932 + 422.145i 0.153225 + 0.759254i
\(557\) 31.5616 + 18.2221i 0.0566635 + 0.0327147i 0.528064 0.849204i \(-0.322918\pi\)
−0.471401 + 0.881919i \(0.656251\pi\)
\(558\) −224.867 184.020i −0.402987 0.329784i
\(559\) 206.213i 0.368896i
\(560\) 0 0
\(561\) 90.2742 0.160917
\(562\) 190.293 232.533i 0.338600 0.413759i
\(563\) −93.1945 + 161.418i −0.165532 + 0.286710i −0.936844 0.349747i \(-0.886267\pi\)
0.771312 + 0.636457i \(0.219601\pi\)
\(564\) 14.2390 2.87357i 0.0252464 0.00509499i
\(565\) −1081.33 + 624.306i −1.91386 + 1.10497i
\(566\) −126.262 334.058i −0.223078 0.590208i
\(567\) 0 0
\(568\) −65.6081 + 123.988i −0.115507 + 0.218288i
\(569\) 335.446 + 581.009i 0.589536 + 1.02111i 0.994293 + 0.106682i \(0.0340225\pi\)
−0.404758 + 0.914424i \(0.632644\pi\)
\(570\) −49.3498 + 301.520i −0.0865786 + 0.528983i
\(571\) 338.541 586.371i 0.592892 1.02692i −0.400949 0.916100i \(-0.631320\pi\)
0.993841 0.110818i \(-0.0353471\pi\)
\(572\) 143.819 427.587i 0.251432 0.747530i
\(573\) 91.9271i 0.160431i
\(574\) 0 0
\(575\) 1394.67i 2.42552i
\(576\) −240.884 + 498.933i −0.418201 + 0.866203i
\(577\) 463.950 803.586i 0.804073 1.39270i −0.112841 0.993613i \(-0.535995\pi\)
0.916915 0.399083i \(-0.130671\pi\)
\(578\) −269.705 44.1426i −0.466618 0.0763713i
\(579\) −76.5341 132.561i −0.132183 0.228948i
\(580\) −608.382 + 536.542i −1.04893 + 0.925073i
\(581\) 0 0
\(582\) 67.9756 + 179.847i 0.116797 + 0.309015i
\(583\) −86.6642 + 50.0356i −0.148652 + 0.0858244i
\(584\) 316.342 198.552i 0.541681 0.339986i
\(585\) 353.191 611.745i 0.603745 1.04572i
\(586\) 339.258 + 277.632i 0.578938 + 0.473774i
\(587\) 321.120 0.547053 0.273526 0.961865i \(-0.411810\pi\)
0.273526 + 0.961865i \(0.411810\pi\)
\(588\) 0 0
\(589\) 484.508i 0.822595i
\(590\) 425.645 + 348.327i 0.721432 + 0.590384i
\(591\) −73.7028 42.5523i −0.124709 0.0720005i
\(592\) 157.132 207.158i 0.265425 0.349929i
\(593\) −109.627 189.880i −0.184869 0.320203i 0.758663 0.651483i \(-0.225853\pi\)
−0.943532 + 0.331280i \(0.892519\pi\)
\(594\) −91.3137 241.593i −0.153727 0.406723i
\(595\) 0 0
\(596\) 667.196 + 756.529i 1.11946 + 1.26934i
\(597\) −198.107 + 114.377i −0.331837 + 0.191586i
\(598\) 439.340 + 71.9068i 0.734683 + 0.120246i
\(599\) 134.062 + 77.4010i 0.223811 + 0.129217i 0.607713 0.794156i \(-0.292087\pi\)
−0.383903 + 0.923373i \(0.625420\pi\)
\(600\) −9.78595 265.054i −0.0163099 0.441757i
\(601\) −205.862 −0.342533 −0.171266 0.985225i \(-0.554786\pi\)
−0.171266 + 0.985225i \(0.554786\pi\)
\(602\) 0 0
\(603\) 680.666 1.12880
\(604\) −299.017 + 889.004i −0.495061 + 1.47186i
\(605\) −272.882 157.548i −0.451045 0.260411i
\(606\) 2.29594 14.0279i 0.00378868 0.0231483i
\(607\) 684.735 395.332i 1.12806 0.651288i 0.184616 0.982811i \(-0.440896\pi\)
0.943447 + 0.331523i \(0.107562\pi\)
\(608\) 898.225 216.044i 1.47734 0.355335i
\(609\) 0 0
\(610\) −97.2965 257.422i −0.159502 0.422004i
\(611\) 28.0000 + 48.4974i 0.0458265 + 0.0793739i
\(612\) −84.5513 418.965i −0.138156 0.684583i
\(613\) 642.133 + 370.736i 1.04753 + 0.604789i 0.921955 0.387296i \(-0.126591\pi\)
0.125570 + 0.992085i \(0.459924\pi\)
\(614\) 401.103 490.136i 0.653262 0.798267i
\(615\) 36.8848i 0.0599752i
\(616\) 0 0
\(617\) 171.578 0.278084 0.139042 0.990286i \(-0.455598\pi\)
0.139042 + 0.990286i \(0.455598\pi\)
\(618\) −96.6351 79.0814i −0.156368 0.127963i
\(619\) −270.099 + 467.825i −0.436347 + 0.755776i −0.997405 0.0720012i \(-0.977061\pi\)
0.561057 + 0.827777i \(0.310395\pi\)
\(620\) −119.958 594.408i −0.193480 0.958723i
\(621\) 220.727 127.437i 0.355438 0.205212i
\(622\) 135.196 51.0993i 0.217357 0.0821532i
\(623\) 0 0
\(624\) 84.0000 + 10.5830i 0.134615 + 0.0169599i
\(625\) −581.691 1007.52i −0.930705 1.61203i
\(626\) −161.750 26.4737i −0.258387 0.0422902i
\(627\) −105.574 + 182.859i −0.168379 + 0.291641i
\(628\) 12.8755 38.2799i 0.0205023 0.0609552i
\(629\) 200.583i 0.318892i
\(630\) 0 0
\(631\) 269.399i 0.426940i −0.976950 0.213470i \(-0.931523\pi\)
0.976950 0.213470i \(-0.0684766\pi\)
\(632\) 647.819 23.9178i 1.02503 0.0378447i
\(633\) −48.0488 + 83.2229i −0.0759064 + 0.131474i
\(634\) −35.2600 + 215.434i −0.0556152 + 0.339801i
\(635\) 516.884 + 895.270i 0.813991 + 1.40987i
\(636\) −12.4222 14.0855i −0.0195318 0.0221470i
\(637\) 0 0
\(638\) −524.382 + 198.198i −0.821915 + 0.310655i
\(639\) −131.457 + 75.8968i −0.205723 + 0.118774i
\(640\) −1048.48 + 487.437i −1.63825 + 0.761620i
\(641\) −18.0934 + 31.3386i −0.0282268 + 0.0488902i −0.879794 0.475356i \(-0.842319\pi\)
0.851567 + 0.524246i \(0.175653\pi\)
\(642\) −47.1882 + 57.6625i −0.0735018 + 0.0898170i
\(643\) −266.297 −0.414148 −0.207074 0.978325i \(-0.566394\pi\)
−0.207074 + 0.978325i \(0.566394\pi\)
\(644\) 0 0
\(645\) 120.797i 0.187282i
\(646\) −451.361 + 551.550i −0.698701 + 0.853792i
\(647\) 940.708 + 543.118i 1.45395 + 0.839440i 0.998703 0.0509233i \(-0.0162164\pi\)
0.455250 + 0.890363i \(0.349550\pi\)
\(648\) −486.868 + 305.583i −0.751339 + 0.471578i
\(649\) 190.049 + 329.174i 0.292833 + 0.507202i
\(650\) 956.477 361.514i 1.47150 0.556176i
\(651\) 0 0
\(652\) −313.602 + 276.571i −0.480985 + 0.424189i
\(653\) −1035.20 + 597.674i −1.58530 + 0.915274i −0.591234 + 0.806500i \(0.701359\pi\)
−0.994066 + 0.108774i \(0.965307\pi\)
\(654\) 24.7608 151.285i 0.0378606 0.231322i
\(655\) −1317.00 760.368i −2.01068 1.16087i
\(656\) 102.800 43.2538i 0.156707 0.0659356i
\(657\) 404.156 0.615154
\(658\) 0 0
\(659\) −685.220 −1.03979 −0.519894 0.854231i \(-0.674029\pi\)
−0.519894 + 0.854231i \(0.674029\pi\)
\(660\) 84.2473 250.475i 0.127647 0.379507i
\(661\) 860.294 + 496.691i 1.30150 + 0.751423i 0.980662 0.195710i \(-0.0627010\pi\)
0.320842 + 0.947133i \(0.396034\pi\)
\(662\) 635.031 + 103.936i 0.959261 + 0.157002i
\(663\) −56.5634 + 32.6569i −0.0853143 + 0.0492563i
\(664\) −285.563 151.106i −0.430065 0.227569i
\(665\) 0 0
\(666\) 263.186 99.4749i 0.395174 0.149362i
\(667\) −276.603 479.091i −0.414697 0.718277i
\(668\) 1163.60 234.826i 1.74192 0.351536i
\(669\) 5.36882 + 3.09969i 0.00802514 + 0.00463332i
\(670\) 1099.32 + 899.630i 1.64078 + 1.34273i
\(671\) 190.183i 0.283432i
\(672\) 0 0
\(673\) 106.569 0.158349 0.0791743 0.996861i \(-0.474772\pi\)
0.0791743 + 0.996861i \(0.474772\pi\)
\(674\) 207.789 253.913i 0.308293 0.376725i
\(675\) 292.701 506.972i 0.433630 0.751070i
\(676\) −69.1602 342.699i −0.102308 0.506951i
\(677\) 869.650 502.092i 1.28456 0.741643i 0.306885 0.951747i \(-0.400713\pi\)
0.977679 + 0.210103i \(0.0673801\pi\)
\(678\) −57.2548 151.482i −0.0844467 0.223425i
\(679\) 0 0
\(680\) 417.186 788.407i 0.613509 1.15942i
\(681\) 62.6224 + 108.465i 0.0919565 + 0.159273i
\(682\) 67.6879 413.563i 0.0992491 0.606397i
\(683\) 339.113 587.360i 0.496505 0.859971i −0.503487 0.864003i \(-0.667950\pi\)
0.999992 + 0.00403135i \(0.00128322\pi\)
\(684\) 947.533 + 318.703i 1.38528 + 0.465940i
\(685\) 313.327i 0.457411i
\(686\) 0 0
\(687\) 135.919i 0.197844i
\(688\) 336.667 141.655i 0.489342 0.205894i
\(689\) 36.2010 62.7020i 0.0525414 0.0910043i
\(690\) 257.360 + 42.1221i 0.372985 + 0.0610465i
\(691\) −182.587 316.250i −0.264236 0.457671i 0.703127 0.711064i \(-0.251787\pi\)
−0.967363 + 0.253394i \(0.918453\pi\)
\(692\) 105.910 + 120.090i 0.153049 + 0.173541i
\(693\) 0 0
\(694\) 233.563 + 617.951i 0.336547 + 0.890419i
\(695\) −842.250 + 486.273i −1.21187 + 0.699673i
\(696\) −55.9293 89.1091i −0.0803582 0.128030i
\(697\) −43.0193 + 74.5117i −0.0617207 + 0.106903i
\(698\) −406.143 332.367i −0.581866 0.476170i
\(699\) 112.976 0.161626
\(700\) 0 0
\(701\) 940.292i 1.34136i −0.741748 0.670679i \(-0.766003\pi\)
0.741748 0.670679i \(-0.233997\pi\)
\(702\) 144.612 + 118.343i 0.206000 + 0.168580i
\(703\) −406.300 234.577i −0.577951 0.333680i
\(704\) −796.883 + 58.9231i −1.13194 + 0.0836975i
\(705\) 16.4020 + 28.4091i 0.0232653 + 0.0402966i
\(706\) −408.777 1081.52i −0.579004 1.53190i
\(707\) 0 0
\(708\) −53.5004 + 47.1829i −0.0755656 + 0.0666426i
\(709\) 915.785 528.729i 1.29166 0.745738i 0.312709 0.949849i \(-0.398764\pi\)
0.978948 + 0.204110i \(0.0654302\pi\)
\(710\) −312.624 51.1672i −0.440316 0.0720665i
\(711\) 607.505 + 350.743i 0.854438 + 0.493310i
\(712\) 33.0409 + 894.919i 0.0464058 + 1.25691i
\(713\) 413.547 0.580010
\(714\) 0 0
\(715\) 1018.77 1.42486
\(716\) 1117.65 + 375.921i 1.56096 + 0.525030i
\(717\) 166.354 + 96.0448i 0.232015 + 0.133954i
\(718\) 117.947 720.639i 0.164272 1.00368i
\(719\) −896.185 + 517.412i −1.24643 + 0.719628i −0.970396 0.241520i \(-0.922354\pi\)
−0.276036 + 0.961147i \(0.589021\pi\)
\(720\) −1241.37 156.397i −1.72412 0.217219i
\(721\) 0 0
\(722\) −334.094 883.930i −0.462734 1.22428i
\(723\) −21.0509 36.4612i −0.0291160 0.0504304i
\(724\) −158.683 + 32.0239i −0.219176 + 0.0442319i
\(725\) −1100.39 635.311i −1.51778 0.876291i
\(726\) 25.8818 31.6268i 0.0356498 0.0435631i
\(727\) 495.145i 0.681080i −0.940230 0.340540i \(-0.889390\pi\)
0.940230 0.340540i \(-0.110610\pi\)
\(728\) 0 0
\(729\) −567.489 −0.778449
\(730\) 652.740 + 534.170i 0.894164 + 0.731740i
\(731\) −140.887 + 244.024i −0.192732 + 0.333822i
\(732\) 34.9867 7.06067i 0.0477961 0.00964573i
\(733\) −491.464 + 283.747i −0.670483 + 0.387103i −0.796260 0.604955i \(-0.793191\pi\)
0.125777 + 0.992059i \(0.459858\pi\)
\(734\) −972.965 + 367.746i −1.32556 + 0.501016i
\(735\) 0 0
\(736\) −184.402 766.672i −0.250546 1.04167i
\(737\) 490.843 + 850.165i 0.666001 + 1.15355i
\(738\) 119.102 + 19.4934i 0.161384 + 0.0264138i
\(739\) 272.350 471.725i 0.368539 0.638328i −0.620798 0.783970i \(-0.713191\pi\)
0.989337 + 0.145642i \(0.0465248\pi\)
\(740\) 556.538 + 187.192i 0.752078 + 0.252962i
\(741\) 152.766i 0.206162i
\(742\) 0 0
\(743\) 731.264i 0.984205i 0.870537 + 0.492102i \(0.163771\pi\)
−0.870537 + 0.492102i \(0.836229\pi\)
\(744\) 78.5936 2.90172i 0.105637 0.00390016i
\(745\) −1138.97 + 1972.76i −1.52883 + 2.64800i
\(746\) 170.150 1039.59i 0.228083 1.39355i
\(747\) −174.803 302.767i −0.234006 0.405310i
\(748\) 462.323 407.731i 0.618079 0.545094i
\(749\) 0 0
\(750\) 312.804 118.229i 0.417072 0.157638i
\(751\) 577.000 333.131i 0.768309 0.443583i −0.0639622 0.997952i \(-0.520374\pi\)
0.832271 + 0.554369i \(0.187040\pi\)
\(752\) 59.9437 79.0280i 0.0797124 0.105090i
\(753\) 75.2498 130.336i 0.0999333 0.173090i
\(754\) 256.865 313.882i 0.340670 0.416289i
\(755\) −2118.15 −2.80550
\(756\) 0 0
\(757\) 238.623i 0.315222i −0.987501 0.157611i \(-0.949621\pi\)
0.987501 0.157611i \(-0.0503791\pi\)
\(758\) −154.498 + 188.792i −0.203823 + 0.249066i
\(759\) 156.077 + 90.1113i 0.205636 + 0.118724i
\(760\) 1109.10 + 1767.07i 1.45935 + 2.32510i
\(761\) 307.465 + 532.545i 0.404028 + 0.699797i 0.994208 0.107475i \(-0.0342766\pi\)
−0.590180 + 0.807272i \(0.700943\pi\)
\(762\) −125.417 + 47.4032i −0.164589 + 0.0622090i
\(763\) 0 0
\(764\) 415.196 + 470.788i 0.543450 + 0.616215i
\(765\) 835.904 482.609i 1.09268 0.630862i
\(766\) −102.219 + 624.543i −0.133445 + 0.815331i
\(767\) −238.159 137.501i −0.310507 0.179271i
\(768\) −40.4246 144.410i −0.0526362 0.188034i
\(769\) −178.950 −0.232705 −0.116353 0.993208i \(-0.537120\pi\)
−0.116353 + 0.993208i \(0.537120\pi\)
\(770\) 0 0
\(771\) 187.072 0.242636
\(772\) −990.677 333.215i −1.28326 0.431625i
\(773\) −546.994 315.807i −0.707625 0.408548i 0.102556 0.994727i \(-0.467298\pi\)
−0.810181 + 0.586180i \(0.800631\pi\)
\(774\) 390.055 + 63.8403i 0.503947 + 0.0824810i
\(775\) 822.593 474.925i 1.06141 0.612806i
\(776\) 1160.42 + 614.035i 1.49538 + 0.791282i
\(777\) 0 0
\(778\) 172.392 65.1580i 0.221583 0.0837507i
\(779\) −100.620 174.279i −0.129166 0.223722i
\(780\) 37.8228 + 187.418i 0.0484907