Properties

Label 507.2.e.d.22.1
Level $507$
Weight $2$
Character 507.22
Analytic conductor $4.048$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.d.484.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.20711 + 2.09077i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.91421 - 3.31552i) q^{4} -2.82843 q^{5} +(-1.20711 - 2.09077i) q^{6} +(-1.41421 - 2.44949i) q^{7} +4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.20711 + 2.09077i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.91421 - 3.31552i) q^{4} -2.82843 q^{5} +(-1.20711 - 2.09077i) q^{6} +(-1.41421 - 2.44949i) q^{7} +4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.41421 - 5.91359i) q^{10} +(-1.00000 + 1.73205i) q^{11} +3.82843 q^{12} +6.82843 q^{14} +(1.41421 - 2.44949i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(1.82843 + 3.16693i) q^{17} +2.41421 q^{18} +(1.41421 + 2.44949i) q^{19} +(5.41421 + 9.37769i) q^{20} +2.82843 q^{21} +(-2.41421 - 4.18154i) q^{22} +(2.00000 - 3.46410i) q^{23} +(-2.20711 + 3.82282i) q^{24} +3.00000 q^{25} +1.00000 q^{27} +(-5.41421 + 9.37769i) q^{28} +(-1.00000 + 1.73205i) q^{29} +(3.41421 + 5.91359i) q^{30} +6.82843 q^{31} +(0.792893 + 1.37333i) q^{32} +(-1.00000 - 1.73205i) q^{33} -8.82843 q^{34} +(4.00000 + 6.92820i) q^{35} +(-1.91421 + 3.31552i) q^{36} +(1.82843 - 3.16693i) q^{37} -6.82843 q^{38} -12.4853 q^{40} +(5.41421 - 9.37769i) q^{41} +(-3.41421 + 5.91359i) q^{42} +(-4.82843 - 8.36308i) q^{43} +7.65685 q^{44} +(1.41421 + 2.44949i) q^{45} +(4.82843 + 8.36308i) q^{46} +0.343146 q^{47} +(-1.50000 - 2.59808i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-3.62132 + 6.27231i) q^{50} -3.65685 q^{51} -2.00000 q^{53} +(-1.20711 + 2.09077i) q^{54} +(2.82843 - 4.89898i) q^{55} +(-6.24264 - 10.8126i) q^{56} -2.82843 q^{57} +(-2.41421 - 4.18154i) q^{58} +(-1.82843 - 3.16693i) q^{59} -10.8284 q^{60} +(4.65685 + 8.06591i) q^{61} +(-8.24264 + 14.2767i) q^{62} +(-1.41421 + 2.44949i) q^{63} -9.82843 q^{64} +4.82843 q^{66} +(0.585786 - 1.01461i) q^{67} +(7.00000 - 12.1244i) q^{68} +(2.00000 + 3.46410i) q^{69} -19.3137 q^{70} +(1.00000 + 1.73205i) q^{71} +(-2.20711 - 3.82282i) q^{72} -11.6569 q^{73} +(4.41421 + 7.64564i) q^{74} +(-1.50000 + 2.59808i) q^{75} +(5.41421 - 9.37769i) q^{76} +5.65685 q^{77} +11.3137 q^{79} +(4.24264 - 7.34847i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(13.0711 + 22.6398i) q^{82} +7.65685 q^{83} +(-5.41421 - 9.37769i) q^{84} +(-5.17157 - 8.95743i) q^{85} +23.3137 q^{86} +(-1.00000 - 1.73205i) q^{87} +(-4.41421 + 7.64564i) q^{88} +(4.58579 - 7.94282i) q^{89} -6.82843 q^{90} -15.3137 q^{92} +(-3.41421 + 5.91359i) q^{93} +(-0.414214 + 0.717439i) q^{94} +(-4.00000 - 6.92820i) q^{95} -1.58579 q^{96} +(-3.82843 - 6.63103i) q^{97} +(-1.20711 - 2.09077i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 2q^{6} + 12q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 2q^{6} + 12q^{8} - 2q^{9} + 8q^{10} - 4q^{11} + 4q^{12} + 16q^{14} - 6q^{16} - 4q^{17} + 4q^{18} + 16q^{20} - 4q^{22} + 8q^{23} - 6q^{24} + 12q^{25} + 4q^{27} - 16q^{28} - 4q^{29} + 8q^{30} + 16q^{31} + 6q^{32} - 4q^{33} - 24q^{34} + 16q^{35} - 2q^{36} - 4q^{37} - 16q^{38} - 16q^{40} + 16q^{41} - 8q^{42} - 8q^{43} + 8q^{44} + 8q^{46} + 24q^{47} - 6q^{48} - 2q^{49} - 6q^{50} + 8q^{51} - 8q^{53} - 2q^{54} - 8q^{56} - 4q^{58} + 4q^{59} - 32q^{60} - 4q^{61} - 16q^{62} - 28q^{64} + 8q^{66} + 8q^{67} + 28q^{68} + 8q^{69} - 32q^{70} + 4q^{71} - 6q^{72} - 24q^{73} + 12q^{74} - 6q^{75} + 16q^{76} - 2q^{81} + 24q^{82} + 8q^{83} - 16q^{84} - 32q^{85} + 48q^{86} - 4q^{87} - 12q^{88} + 24q^{89} - 16q^{90} - 16q^{92} - 8q^{93} + 4q^{94} - 16q^{95} - 12q^{96} - 4q^{97} - 2q^{98} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20711 + 2.09077i −0.853553 + 1.47840i 0.0244272 + 0.999702i \(0.492224\pi\)
−0.877981 + 0.478696i \(0.841110\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −1.91421 3.31552i −0.957107 1.65776i
\(5\) −2.82843 −1.26491 −0.632456 0.774597i \(-0.717953\pi\)
−0.632456 + 0.774597i \(0.717953\pi\)
\(6\) −1.20711 2.09077i −0.492799 0.853553i
\(7\) −1.41421 2.44949i −0.534522 0.925820i −0.999186 0.0403329i \(-0.987158\pi\)
0.464664 0.885487i \(-0.346175\pi\)
\(8\) 4.41421 1.56066
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 3.41421 5.91359i 1.07967 1.87004i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 3.82843 1.10517
\(13\) 0 0
\(14\) 6.82843 1.82497
\(15\) 1.41421 2.44949i 0.365148 0.632456i
\(16\) −1.50000 + 2.59808i −0.375000 + 0.649519i
\(17\) 1.82843 + 3.16693i 0.443459 + 0.768093i 0.997943 0.0641009i \(-0.0204179\pi\)
−0.554485 + 0.832194i \(0.687085\pi\)
\(18\) 2.41421 0.569036
\(19\) 1.41421 + 2.44949i 0.324443 + 0.561951i 0.981399 0.191977i \(-0.0614899\pi\)
−0.656957 + 0.753928i \(0.728157\pi\)
\(20\) 5.41421 + 9.37769i 1.21065 + 2.09692i
\(21\) 2.82843 0.617213
\(22\) −2.41421 4.18154i −0.514712 0.891507i
\(23\) 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) −2.20711 + 3.82282i −0.450524 + 0.780330i
\(25\) 3.00000 0.600000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −5.41421 + 9.37769i −1.02319 + 1.77222i
\(29\) −1.00000 + 1.73205i −0.185695 + 0.321634i −0.943811 0.330487i \(-0.892787\pi\)
0.758115 + 0.652121i \(0.226120\pi\)
\(30\) 3.41421 + 5.91359i 0.623347 + 1.07967i
\(31\) 6.82843 1.22642 0.613211 0.789919i \(-0.289878\pi\)
0.613211 + 0.789919i \(0.289878\pi\)
\(32\) 0.792893 + 1.37333i 0.140165 + 0.242773i
\(33\) −1.00000 1.73205i −0.174078 0.301511i
\(34\) −8.82843 −1.51406
\(35\) 4.00000 + 6.92820i 0.676123 + 1.17108i
\(36\) −1.91421 + 3.31552i −0.319036 + 0.552586i
\(37\) 1.82843 3.16693i 0.300592 0.520640i −0.675679 0.737196i \(-0.736149\pi\)
0.976270 + 0.216557i \(0.0694826\pi\)
\(38\) −6.82843 −1.10772
\(39\) 0 0
\(40\) −12.4853 −1.97410
\(41\) 5.41421 9.37769i 0.845558 1.46455i −0.0395775 0.999217i \(-0.512601\pi\)
0.885136 0.465333i \(-0.154065\pi\)
\(42\) −3.41421 + 5.91359i −0.526825 + 0.912487i
\(43\) −4.82843 8.36308i −0.736328 1.27536i −0.954138 0.299367i \(-0.903225\pi\)
0.217810 0.975991i \(-0.430109\pi\)
\(44\) 7.65685 1.15431
\(45\) 1.41421 + 2.44949i 0.210819 + 0.365148i
\(46\) 4.82843 + 8.36308i 0.711913 + 1.23307i
\(47\) 0.343146 0.0500530 0.0250265 0.999687i \(-0.492033\pi\)
0.0250265 + 0.999687i \(0.492033\pi\)
\(48\) −1.50000 2.59808i −0.216506 0.375000i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −3.62132 + 6.27231i −0.512132 + 0.887039i
\(51\) −3.65685 −0.512062
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) −1.20711 + 2.09077i −0.164266 + 0.284518i
\(55\) 2.82843 4.89898i 0.381385 0.660578i
\(56\) −6.24264 10.8126i −0.834208 1.44489i
\(57\) −2.82843 −0.374634
\(58\) −2.41421 4.18154i −0.317002 0.549063i
\(59\) −1.82843 3.16693i −0.238041 0.412299i 0.722111 0.691777i \(-0.243172\pi\)
−0.960152 + 0.279478i \(0.909839\pi\)
\(60\) −10.8284 −1.39794
\(61\) 4.65685 + 8.06591i 0.596249 + 1.03273i 0.993369 + 0.114967i \(0.0366763\pi\)
−0.397120 + 0.917767i \(0.629990\pi\)
\(62\) −8.24264 + 14.2767i −1.04682 + 1.81314i
\(63\) −1.41421 + 2.44949i −0.178174 + 0.308607i
\(64\) −9.82843 −1.22855
\(65\) 0 0
\(66\) 4.82843 0.594338
\(67\) 0.585786 1.01461i 0.0715652 0.123955i −0.828022 0.560695i \(-0.810534\pi\)
0.899587 + 0.436741i \(0.143867\pi\)
\(68\) 7.00000 12.1244i 0.848875 1.47029i
\(69\) 2.00000 + 3.46410i 0.240772 + 0.417029i
\(70\) −19.3137 −2.30843
\(71\) 1.00000 + 1.73205i 0.118678 + 0.205557i 0.919244 0.393688i \(-0.128801\pi\)
−0.800566 + 0.599245i \(0.795468\pi\)
\(72\) −2.20711 3.82282i −0.260110 0.450524i
\(73\) −11.6569 −1.36433 −0.682166 0.731198i \(-0.738962\pi\)
−0.682166 + 0.731198i \(0.738962\pi\)
\(74\) 4.41421 + 7.64564i 0.513142 + 0.888788i
\(75\) −1.50000 + 2.59808i −0.173205 + 0.300000i
\(76\) 5.41421 9.37769i 0.621053 1.07570i
\(77\) 5.65685 0.644658
\(78\) 0 0
\(79\) 11.3137 1.27289 0.636446 0.771321i \(-0.280404\pi\)
0.636446 + 0.771321i \(0.280404\pi\)
\(80\) 4.24264 7.34847i 0.474342 0.821584i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 13.0711 + 22.6398i 1.44346 + 2.50014i
\(83\) 7.65685 0.840449 0.420224 0.907420i \(-0.361951\pi\)
0.420224 + 0.907420i \(0.361951\pi\)
\(84\) −5.41421 9.37769i −0.590739 1.02319i
\(85\) −5.17157 8.95743i −0.560936 0.971569i
\(86\) 23.3137 2.51398
\(87\) −1.00000 1.73205i −0.107211 0.185695i
\(88\) −4.41421 + 7.64564i −0.470557 + 0.815028i
\(89\) 4.58579 7.94282i 0.486092 0.841937i −0.513780 0.857922i \(-0.671755\pi\)
0.999872 + 0.0159854i \(0.00508851\pi\)
\(90\) −6.82843 −0.719779
\(91\) 0 0
\(92\) −15.3137 −1.59656
\(93\) −3.41421 + 5.91359i −0.354037 + 0.613211i
\(94\) −0.414214 + 0.717439i −0.0427229 + 0.0739982i
\(95\) −4.00000 6.92820i −0.410391 0.710819i
\(96\) −1.58579 −0.161849
\(97\) −3.82843 6.63103i −0.388718 0.673279i 0.603559 0.797318i \(-0.293749\pi\)
−0.992277 + 0.124039i \(0.960415\pi\)
\(98\) −1.20711 2.09077i −0.121936 0.211200i
\(99\) 2.00000 0.201008
\(100\) −5.74264 9.94655i −0.574264 0.994655i
\(101\) 1.82843 3.16693i 0.181935 0.315121i −0.760604 0.649216i \(-0.775097\pi\)
0.942540 + 0.334095i \(0.108431\pi\)
\(102\) 4.41421 7.64564i 0.437072 0.757031i
\(103\) 13.6569 1.34565 0.672825 0.739802i \(-0.265081\pi\)
0.672825 + 0.739802i \(0.265081\pi\)
\(104\) 0 0
\(105\) −8.00000 −0.780720
\(106\) 2.41421 4.18154i 0.234489 0.406147i
\(107\) −5.65685 + 9.79796i −0.546869 + 0.947204i 0.451618 + 0.892211i \(0.350847\pi\)
−0.998487 + 0.0549930i \(0.982486\pi\)
\(108\) −1.91421 3.31552i −0.184195 0.319036i
\(109\) 17.3137 1.65835 0.829176 0.558987i \(-0.188810\pi\)
0.829176 + 0.558987i \(0.188810\pi\)
\(110\) 6.82843 + 11.8272i 0.651065 + 1.12768i
\(111\) 1.82843 + 3.16693i 0.173547 + 0.300592i
\(112\) 8.48528 0.801784
\(113\) −8.65685 14.9941i −0.814368 1.41053i −0.909781 0.415090i \(-0.863750\pi\)
0.0954122 0.995438i \(-0.469583\pi\)
\(114\) 3.41421 5.91359i 0.319770 0.553859i
\(115\) −5.65685 + 9.79796i −0.527504 + 0.913664i
\(116\) 7.65685 0.710921
\(117\) 0 0
\(118\) 8.82843 0.812723
\(119\) 5.17157 8.95743i 0.474077 0.821126i
\(120\) 6.24264 10.8126i 0.569873 0.987048i
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −22.4853 −2.03572
\(123\) 5.41421 + 9.37769i 0.488183 + 0.845558i
\(124\) −13.0711 22.6398i −1.17382 2.03311i
\(125\) 5.65685 0.505964
\(126\) −3.41421 5.91359i −0.304162 0.526825i
\(127\) 2.82843 4.89898i 0.250982 0.434714i −0.712814 0.701353i \(-0.752580\pi\)
0.963797 + 0.266639i \(0.0859131\pi\)
\(128\) 10.2782 17.8023i 0.908471 1.57352i
\(129\) 9.65685 0.850239
\(130\) 0 0
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) −3.82843 + 6.63103i −0.333222 + 0.577157i
\(133\) 4.00000 6.92820i 0.346844 0.600751i
\(134\) 1.41421 + 2.44949i 0.122169 + 0.211604i
\(135\) −2.82843 −0.243432
\(136\) 8.07107 + 13.9795i 0.692088 + 1.19873i
\(137\) −2.58579 4.47871i −0.220919 0.382642i 0.734169 0.678967i \(-0.237572\pi\)
−0.955087 + 0.296325i \(0.904239\pi\)
\(138\) −9.65685 −0.822046
\(139\) −7.65685 13.2621i −0.649446 1.12487i −0.983255 0.182233i \(-0.941668\pi\)
0.333810 0.942641i \(-0.391666\pi\)
\(140\) 15.3137 26.5241i 1.29424 2.24170i
\(141\) −0.171573 + 0.297173i −0.0144490 + 0.0250265i
\(142\) −4.82843 −0.405193
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) 2.82843 4.89898i 0.234888 0.406838i
\(146\) 14.0711 24.3718i 1.16453 2.01702i
\(147\) −0.500000 0.866025i −0.0412393 0.0714286i
\(148\) −14.0000 −1.15079
\(149\) −7.41421 12.8418i −0.607396 1.05204i −0.991668 0.128821i \(-0.958881\pi\)
0.384272 0.923220i \(-0.374453\pi\)
\(150\) −3.62132 6.27231i −0.295680 0.512132i
\(151\) 20.4853 1.66707 0.833534 0.552468i \(-0.186314\pi\)
0.833534 + 0.552468i \(0.186314\pi\)
\(152\) 6.24264 + 10.8126i 0.506345 + 0.877015i
\(153\) 1.82843 3.16693i 0.147820 0.256031i
\(154\) −6.82843 + 11.8272i −0.550250 + 0.953062i
\(155\) −19.3137 −1.55131
\(156\) 0 0
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) −13.6569 + 23.6544i −1.08648 + 1.88184i
\(159\) 1.00000 1.73205i 0.0793052 0.137361i
\(160\) −2.24264 3.88437i −0.177296 0.307086i
\(161\) −11.3137 −0.891645
\(162\) −1.20711 2.09077i −0.0948393 0.164266i
\(163\) 6.58579 + 11.4069i 0.515839 + 0.893459i 0.999831 + 0.0183864i \(0.00585292\pi\)
−0.483992 + 0.875072i \(0.660814\pi\)
\(164\) −41.4558 −3.23716
\(165\) 2.82843 + 4.89898i 0.220193 + 0.381385i
\(166\) −9.24264 + 16.0087i −0.717368 + 1.24252i
\(167\) 3.82843 6.63103i 0.296253 0.513125i −0.679023 0.734117i \(-0.737596\pi\)
0.975275 + 0.220993i \(0.0709296\pi\)
\(168\) 12.4853 0.963260
\(169\) 0 0
\(170\) 24.9706 1.91515
\(171\) 1.41421 2.44949i 0.108148 0.187317i
\(172\) −18.4853 + 32.0174i −1.40949 + 2.44131i
\(173\) 0.171573 + 0.297173i 0.0130444 + 0.0225936i 0.872474 0.488661i \(-0.162514\pi\)
−0.859429 + 0.511254i \(0.829181\pi\)
\(174\) 4.82843 0.366042
\(175\) −4.24264 7.34847i −0.320713 0.555492i
\(176\) −3.00000 5.19615i −0.226134 0.391675i
\(177\) 3.65685 0.274866
\(178\) 11.0711 + 19.1757i 0.829812 + 1.43728i
\(179\) 0.343146 0.594346i 0.0256479 0.0444235i −0.852917 0.522047i \(-0.825168\pi\)
0.878564 + 0.477624i \(0.158502\pi\)
\(180\) 5.41421 9.37769i 0.403552 0.698972i
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) −9.31371 −0.688489
\(184\) 8.82843 15.2913i 0.650840 1.12729i
\(185\) −5.17157 + 8.95743i −0.380222 + 0.658563i
\(186\) −8.24264 14.2767i −0.604380 1.04682i
\(187\) −7.31371 −0.534831
\(188\) −0.656854 1.13770i −0.0479060 0.0829757i
\(189\) −1.41421 2.44949i −0.102869 0.178174i
\(190\) 19.3137 1.40116
\(191\) 9.65685 + 16.7262i 0.698745 + 1.21026i 0.968902 + 0.247446i \(0.0795913\pi\)
−0.270156 + 0.962817i \(0.587075\pi\)
\(192\) 4.91421 8.51167i 0.354653 0.614277i
\(193\) −8.65685 + 14.9941i −0.623134 + 1.07930i 0.365765 + 0.930707i \(0.380808\pi\)
−0.988899 + 0.148592i \(0.952526\pi\)
\(194\) 18.4853 1.32717
\(195\) 0 0
\(196\) 3.82843 0.273459
\(197\) −8.24264 + 14.2767i −0.587264 + 1.01717i 0.407325 + 0.913283i \(0.366462\pi\)
−0.994589 + 0.103888i \(0.966872\pi\)
\(198\) −2.41421 + 4.18154i −0.171571 + 0.297169i
\(199\) −5.17157 8.95743i −0.366603 0.634975i 0.622429 0.782676i \(-0.286146\pi\)
−0.989032 + 0.147701i \(0.952813\pi\)
\(200\) 13.2426 0.936396
\(201\) 0.585786 + 1.01461i 0.0413182 + 0.0715652i
\(202\) 4.41421 + 7.64564i 0.310583 + 0.537946i
\(203\) 5.65685 0.397033
\(204\) 7.00000 + 12.1244i 0.490098 + 0.848875i
\(205\) −15.3137 + 26.5241i −1.06956 + 1.85252i
\(206\) −16.4853 + 28.5533i −1.14858 + 1.98941i
\(207\) −4.00000 −0.278019
\(208\) 0 0
\(209\) −5.65685 −0.391293
\(210\) 9.65685 16.7262i 0.666386 1.15421i
\(211\) 6.00000 10.3923i 0.413057 0.715436i −0.582165 0.813070i \(-0.697794\pi\)
0.995222 + 0.0976347i \(0.0311277\pi\)
\(212\) 3.82843 + 6.63103i 0.262937 + 0.455421i
\(213\) −2.00000 −0.137038
\(214\) −13.6569 23.6544i −0.933563 1.61698i
\(215\) 13.6569 + 23.6544i 0.931390 + 1.61321i
\(216\) 4.41421 0.300349
\(217\) −9.65685 16.7262i −0.655550 1.13545i
\(218\) −20.8995 + 36.1990i −1.41549 + 2.45170i
\(219\) 5.82843 10.0951i 0.393849 0.682166i
\(220\) −21.6569 −1.46010
\(221\) 0 0
\(222\) −8.82843 −0.592525
\(223\) 2.24264 3.88437i 0.150178 0.260116i −0.781115 0.624388i \(-0.785349\pi\)
0.931293 + 0.364271i \(0.118682\pi\)
\(224\) 2.24264 3.88437i 0.149843 0.259535i
\(225\) −1.50000 2.59808i −0.100000 0.173205i
\(226\) 41.7990 2.78043
\(227\) 2.65685 + 4.60181i 0.176342 + 0.305433i 0.940625 0.339448i \(-0.110240\pi\)
−0.764283 + 0.644881i \(0.776907\pi\)
\(228\) 5.41421 + 9.37769i 0.358565 + 0.621053i
\(229\) −21.3137 −1.40845 −0.704225 0.709977i \(-0.748705\pi\)
−0.704225 + 0.709977i \(0.748705\pi\)
\(230\) −13.6569 23.6544i −0.900506 1.55972i
\(231\) −2.82843 + 4.89898i −0.186097 + 0.322329i
\(232\) −4.41421 + 7.64564i −0.289807 + 0.501961i
\(233\) −26.9706 −1.76690 −0.883450 0.468525i \(-0.844786\pi\)
−0.883450 + 0.468525i \(0.844786\pi\)
\(234\) 0 0
\(235\) −0.970563 −0.0633125
\(236\) −7.00000 + 12.1244i −0.455661 + 0.789228i
\(237\) −5.65685 + 9.79796i −0.367452 + 0.636446i
\(238\) 12.4853 + 21.6251i 0.809301 + 1.40175i
\(239\) −2.00000 −0.129369 −0.0646846 0.997906i \(-0.520604\pi\)
−0.0646846 + 0.997906i \(0.520604\pi\)
\(240\) 4.24264 + 7.34847i 0.273861 + 0.474342i
\(241\) 5.82843 + 10.0951i 0.375442 + 0.650285i 0.990393 0.138281i \(-0.0441576\pi\)
−0.614951 + 0.788565i \(0.710824\pi\)
\(242\) −16.8995 −1.08634
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 17.8284 30.8797i 1.14135 1.97687i
\(245\) 1.41421 2.44949i 0.0903508 0.156492i
\(246\) −26.1421 −1.66676
\(247\) 0 0
\(248\) 30.1421 1.91403
\(249\) −3.82843 + 6.63103i −0.242617 + 0.420224i
\(250\) −6.82843 + 11.8272i −0.431868 + 0.748017i
\(251\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(252\) 10.8284 0.682127
\(253\) 4.00000 + 6.92820i 0.251478 + 0.435572i
\(254\) 6.82843 + 11.8272i 0.428454 + 0.742103i
\(255\) 10.3431 0.647713
\(256\) 14.9853 + 25.9553i 0.936580 + 1.62220i
\(257\) 7.82843 13.5592i 0.488324 0.845802i −0.511586 0.859232i \(-0.670942\pi\)
0.999910 + 0.0134304i \(0.00427515\pi\)
\(258\) −11.6569 + 20.1903i −0.725724 + 1.25699i
\(259\) −10.3431 −0.642692
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) 9.65685 16.7262i 0.596602 1.03335i
\(263\) −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i \(-0.953967\pi\)
0.619586 + 0.784929i \(0.287301\pi\)
\(264\) −4.41421 7.64564i −0.271676 0.470557i
\(265\) 5.65685 0.347498
\(266\) 9.65685 + 16.7262i 0.592100 + 1.02555i
\(267\) 4.58579 + 7.94282i 0.280646 + 0.486092i
\(268\) −4.48528 −0.273982
\(269\) −9.00000 15.5885i −0.548740 0.950445i −0.998361 0.0572259i \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) 3.41421 5.91359i 0.207782 0.359890i
\(271\) 5.89949 10.2182i 0.358369 0.620713i −0.629320 0.777147i \(-0.716666\pi\)
0.987688 + 0.156434i \(0.0499997\pi\)
\(272\) −10.9706 −0.665188
\(273\) 0 0
\(274\) 12.4853 0.754263
\(275\) −3.00000 + 5.19615i −0.180907 + 0.313340i
\(276\) 7.65685 13.2621i 0.460888 0.798282i
\(277\) 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i \(-0.147530\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(278\) 36.9706 2.21735
\(279\) −3.41421 5.91359i −0.204404 0.354037i
\(280\) 17.6569 + 30.5826i 1.05520 + 1.82766i
\(281\) −26.8284 −1.60045 −0.800225 0.599700i \(-0.795287\pi\)
−0.800225 + 0.599700i \(0.795287\pi\)
\(282\) −0.414214 0.717439i −0.0246661 0.0427229i
\(283\) 2.48528 4.30463i 0.147735 0.255884i −0.782655 0.622455i \(-0.786135\pi\)
0.930390 + 0.366572i \(0.119469\pi\)
\(284\) 3.82843 6.63103i 0.227175 0.393479i
\(285\) 8.00000 0.473879
\(286\) 0 0
\(287\) −30.6274 −1.80788
\(288\) 0.792893 1.37333i 0.0467217 0.0809243i
\(289\) 1.81371 3.14144i 0.106689 0.184790i
\(290\) 6.82843 + 11.8272i 0.400979 + 0.694516i
\(291\) 7.65685 0.448853
\(292\) 22.3137 + 38.6485i 1.30581 + 2.26173i
\(293\) −13.0711 22.6398i −0.763620 1.32263i −0.940973 0.338481i \(-0.890087\pi\)
0.177353 0.984147i \(-0.443247\pi\)
\(294\) 2.41421 0.140800
\(295\) 5.17157 + 8.95743i 0.301101 + 0.521522i
\(296\) 8.07107 13.9795i 0.469121 0.812542i
\(297\) −1.00000 + 1.73205i −0.0580259 + 0.100504i
\(298\) 35.7990 2.07378
\(299\) 0 0
\(300\) 11.4853 0.663103
\(301\) −13.6569 + 23.6544i −0.787168 + 1.36341i
\(302\) −24.7279 + 42.8300i −1.42293 + 2.46459i
\(303\) 1.82843 + 3.16693i 0.105040 + 0.181935i
\(304\) −8.48528 −0.486664
\(305\) −13.1716 22.8138i −0.754202 1.30632i
\(306\) 4.41421 + 7.64564i 0.252344 + 0.437072i
\(307\) 17.1716 0.980033 0.490017 0.871713i \(-0.336991\pi\)
0.490017 + 0.871713i \(0.336991\pi\)
\(308\) −10.8284 18.7554i −0.617007 1.06869i
\(309\) −6.82843 + 11.8272i −0.388456 + 0.672825i
\(310\) 23.3137 40.3805i 1.32413 2.29346i
\(311\) 34.6274 1.96354 0.981770 0.190071i \(-0.0608718\pi\)
0.981770 + 0.190071i \(0.0608718\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 12.0711 20.9077i 0.681210 1.17989i
\(315\) 4.00000 6.92820i 0.225374 0.390360i
\(316\) −21.6569 37.5108i −1.21829 2.11015i
\(317\) 8.48528 0.476581 0.238290 0.971194i \(-0.423413\pi\)
0.238290 + 0.971194i \(0.423413\pi\)
\(318\) 2.41421 + 4.18154i 0.135382 + 0.234489i
\(319\) −2.00000 3.46410i −0.111979 0.193952i
\(320\) 27.7990 1.55401
\(321\) −5.65685 9.79796i −0.315735 0.546869i
\(322\) 13.6569 23.6544i 0.761067 1.31821i
\(323\) −5.17157 + 8.95743i −0.287754 + 0.498405i
\(324\) 3.82843 0.212690
\(325\) 0 0
\(326\) −31.7990 −1.76118
\(327\) −8.65685 + 14.9941i −0.478725 + 0.829176i
\(328\) 23.8995 41.3951i 1.31963 2.28566i
\(329\) −0.485281 0.840532i −0.0267544 0.0463400i
\(330\) −13.6569 −0.751785
\(331\) −1.07107 1.85514i −0.0588712 0.101968i 0.835088 0.550117i \(-0.185417\pi\)
−0.893959 + 0.448149i \(0.852083\pi\)
\(332\) −14.6569 25.3864i −0.804399 1.39326i
\(333\) −3.65685 −0.200394
\(334\) 9.24264 + 16.0087i 0.505735 + 0.875958i
\(335\) −1.65685 + 2.86976i −0.0905236 + 0.156792i
\(336\) −4.24264 + 7.34847i −0.231455 + 0.400892i
\(337\) −13.3137 −0.725244 −0.362622 0.931936i \(-0.618118\pi\)
−0.362622 + 0.931936i \(0.618118\pi\)
\(338\) 0 0
\(339\) 17.3137 0.940352
\(340\) −19.7990 + 34.2929i −1.07375 + 1.85979i
\(341\) −6.82843 + 11.8272i −0.369780 + 0.640478i
\(342\) 3.41421 + 5.91359i 0.184620 + 0.319770i
\(343\) −16.9706 −0.916324
\(344\) −21.3137 36.9164i −1.14916 1.99040i
\(345\) −5.65685 9.79796i −0.304555 0.527504i
\(346\) −0.828427 −0.0445365
\(347\) 15.6569 + 27.1185i 0.840504 + 1.45580i 0.889469 + 0.456995i \(0.151074\pi\)
−0.0489652 + 0.998800i \(0.515592\pi\)
\(348\) −3.82843 + 6.63103i −0.205225 + 0.355461i
\(349\) −3.82843 + 6.63103i −0.204931 + 0.354951i −0.950111 0.311913i \(-0.899030\pi\)
0.745180 + 0.666864i \(0.232364\pi\)
\(350\) 20.4853 1.09498
\(351\) 0 0
\(352\) −3.17157 −0.169045
\(353\) 8.72792 15.1172i 0.464540 0.804608i −0.534640 0.845080i \(-0.679553\pi\)
0.999181 + 0.0404722i \(0.0128862\pi\)
\(354\) −4.41421 + 7.64564i −0.234613 + 0.406361i
\(355\) −2.82843 4.89898i −0.150117 0.260011i
\(356\) −35.1127 −1.86097
\(357\) 5.17157 + 8.95743i 0.273709 + 0.474077i
\(358\) 0.828427 + 1.43488i 0.0437837 + 0.0758357i
\(359\) −1.02944 −0.0543316 −0.0271658 0.999631i \(-0.508648\pi\)
−0.0271658 + 0.999631i \(0.508648\pi\)
\(360\) 6.24264 + 10.8126i 0.329016 + 0.569873i
\(361\) 5.50000 9.52628i 0.289474 0.501383i
\(362\) −16.8995 + 29.2708i −0.888218 + 1.53844i
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) 32.9706 1.72576
\(366\) 11.2426 19.4728i 0.587662 1.01786i
\(367\) 12.0000 20.7846i 0.626395 1.08495i −0.361874 0.932227i \(-0.617863\pi\)
0.988269 0.152721i \(-0.0488036\pi\)
\(368\) 6.00000 + 10.3923i 0.312772 + 0.541736i
\(369\) −10.8284 −0.563705
\(370\) −12.4853 21.6251i −0.649079 1.12424i
\(371\) 2.82843 + 4.89898i 0.146845 + 0.254342i
\(372\) 26.1421 1.35541
\(373\) −5.00000 8.66025i −0.258890 0.448411i 0.707055 0.707159i \(-0.250023\pi\)
−0.965945 + 0.258748i \(0.916690\pi\)
\(374\) 8.82843 15.2913i 0.456507 0.790693i
\(375\) −2.82843 + 4.89898i −0.146059 + 0.252982i
\(376\) 1.51472 0.0781156
\(377\) 0 0
\(378\) 6.82843 0.351216
\(379\) −8.24264 + 14.2767i −0.423396 + 0.733343i −0.996269 0.0863007i \(-0.972495\pi\)
0.572873 + 0.819644i \(0.305829\pi\)
\(380\) −15.3137 + 26.5241i −0.785577 + 1.36066i
\(381\) 2.82843 + 4.89898i 0.144905 + 0.250982i
\(382\) −46.6274 −2.38567
\(383\) −1.48528 2.57258i −0.0758943 0.131453i 0.825581 0.564284i \(-0.190848\pi\)
−0.901475 + 0.432832i \(0.857515\pi\)
\(384\) 10.2782 + 17.8023i 0.524506 + 0.908471i
\(385\) −16.0000 −0.815436
\(386\) −20.8995 36.1990i −1.06376 1.84248i
\(387\) −4.82843 + 8.36308i −0.245443 + 0.425119i
\(388\) −14.6569 + 25.3864i −0.744089 + 1.28880i
\(389\) 6.97056 0.353422 0.176711 0.984263i \(-0.443454\pi\)
0.176711 + 0.984263i \(0.443454\pi\)
\(390\) 0 0
\(391\) 14.6274 0.739740
\(392\) −2.20711 + 3.82282i −0.111476 + 0.193082i
\(393\) 4.00000 6.92820i 0.201773 0.349482i
\(394\) −19.8995 34.4669i −1.00252 1.73642i
\(395\) −32.0000 −1.61009
\(396\) −3.82843 6.63103i −0.192386 0.333222i
\(397\) −1.48528 2.57258i −0.0745441 0.129114i 0.826344 0.563166i \(-0.190417\pi\)
−0.900888 + 0.434052i \(0.857083\pi\)
\(398\) 24.9706 1.25166
\(399\) 4.00000 + 6.92820i 0.200250 + 0.346844i
\(400\) −4.50000 + 7.79423i −0.225000 + 0.389711i
\(401\) −1.07107 + 1.85514i −0.0534866 + 0.0926415i −0.891529 0.452964i \(-0.850367\pi\)
0.838042 + 0.545605i \(0.183700\pi\)
\(402\) −2.82843 −0.141069
\(403\) 0 0
\(404\) −14.0000 −0.696526
\(405\) 1.41421 2.44949i 0.0702728 0.121716i
\(406\) −6.82843 + 11.8272i −0.338889 + 0.586973i
\(407\) 3.65685 + 6.33386i 0.181264 + 0.313958i
\(408\) −16.1421 −0.799155
\(409\) −0.514719 0.891519i −0.0254512 0.0440828i 0.853019 0.521879i \(-0.174769\pi\)
−0.878470 + 0.477797i \(0.841436\pi\)
\(410\) −36.9706 64.0349i −1.82585 3.16246i
\(411\) 5.17157 0.255095
\(412\) −26.1421 45.2795i −1.28793 2.23076i
\(413\) −5.17157 + 8.95743i −0.254476 + 0.440766i
\(414\) 4.82843 8.36308i 0.237304 0.411023i
\(415\) −21.6569 −1.06309
\(416\) 0 0
\(417\) 15.3137 0.749916
\(418\) 6.82843 11.8272i 0.333989 0.578486i
\(419\) 15.3137 26.5241i 0.748124 1.29579i −0.200597 0.979674i \(-0.564288\pi\)
0.948721 0.316114i \(-0.102378\pi\)
\(420\) 15.3137 + 26.5241i 0.747232 + 1.29424i
\(421\) −14.6863 −0.715766 −0.357883 0.933766i \(-0.616501\pi\)
−0.357883 + 0.933766i \(0.616501\pi\)
\(422\) 14.4853 + 25.0892i 0.705132 + 1.22133i
\(423\) −0.171573 0.297173i −0.00834216 0.0144490i
\(424\) −8.82843 −0.428746
\(425\) 5.48528 + 9.50079i 0.266075 + 0.460856i
\(426\) 2.41421 4.18154i 0.116969 0.202596i
\(427\) 13.1716 22.8138i 0.637417 1.10404i
\(428\) 43.3137 2.09365
\(429\) 0 0
\(430\) −65.9411 −3.17996
\(431\) 9.82843 17.0233i 0.473419 0.819985i −0.526118 0.850411i \(-0.676353\pi\)
0.999537 + 0.0304262i \(0.00968644\pi\)
\(432\) −1.50000 + 2.59808i −0.0721688 + 0.125000i
\(433\) −0.656854 1.13770i −0.0315664 0.0546746i 0.849811 0.527088i \(-0.176716\pi\)
−0.881377 + 0.472414i \(0.843383\pi\)
\(434\) 46.6274 2.23819
\(435\) 2.82843 + 4.89898i 0.135613 + 0.234888i
\(436\) −33.1421 57.4039i −1.58722 2.74915i
\(437\) 11.3137 0.541208
\(438\) 14.0711 + 24.3718i 0.672342 + 1.16453i
\(439\) 8.48528 14.6969i 0.404980 0.701447i −0.589339 0.807886i \(-0.700612\pi\)
0.994319 + 0.106439i \(0.0339450\pi\)
\(440\) 12.4853 21.6251i 0.595212 1.03094i
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 41.9411 1.99268 0.996342 0.0854611i \(-0.0272364\pi\)
0.996342 + 0.0854611i \(0.0272364\pi\)
\(444\) 7.00000 12.1244i 0.332205 0.575396i
\(445\) −12.9706 + 22.4657i −0.614864 + 1.06498i
\(446\) 5.41421 + 9.37769i 0.256370 + 0.444047i
\(447\) 14.8284 0.701361
\(448\) 13.8995 + 24.0746i 0.656689 + 1.13742i
\(449\) 3.89949 + 6.75412i 0.184029 + 0.318747i 0.943249 0.332087i \(-0.107753\pi\)
−0.759220 + 0.650834i \(0.774419\pi\)
\(450\) 7.24264 0.341421
\(451\) 10.8284 + 18.7554i 0.509891 + 0.883157i
\(452\) −33.1421 + 57.4039i −1.55887 + 2.70005i
\(453\) −10.2426 + 17.7408i −0.481241 + 0.833534i
\(454\) −12.8284 −0.602068
\(455\) 0 0
\(456\) −12.4853 −0.584677
\(457\) 1.82843 3.16693i 0.0855302 0.148143i −0.820087 0.572239i \(-0.806075\pi\)
0.905617 + 0.424096i \(0.139408\pi\)
\(458\) 25.7279 44.5621i 1.20219 2.08225i
\(459\) 1.82843 + 3.16693i 0.0853437 + 0.147820i
\(460\) 43.3137 2.01951
\(461\) 5.41421 + 9.37769i 0.252165 + 0.436763i 0.964122 0.265461i \(-0.0855241\pi\)
−0.711957 + 0.702223i \(0.752191\pi\)
\(462\) −6.82843 11.8272i −0.317687 0.550250i
\(463\) 7.51472 0.349239 0.174619 0.984636i \(-0.444131\pi\)
0.174619 + 0.984636i \(0.444131\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 9.65685 16.7262i 0.447826 0.775657i
\(466\) 32.5563 56.3893i 1.50814 2.61218i
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 0 0
\(469\) −3.31371 −0.153013
\(470\) 1.17157 2.02922i 0.0540406 0.0936011i
\(471\) 5.00000 8.66025i 0.230388 0.399043i
\(472\) −8.07107 13.9795i −0.371501 0.643459i
\(473\) 19.3137 0.888045
\(474\) −13.6569 23.6544i −0.627280 1.08648i
\(475\) 4.24264 + 7.34847i 0.194666 + 0.337171i
\(476\) −39.5980 −1.81497
\(477\) 1.00000 + 1.73205i 0.0457869 + 0.0793052i
\(478\) 2.41421 4.18154i 0.110424 0.191259i
\(479\) 1.34315 2.32640i 0.0613699 0.106296i −0.833708 0.552205i \(-0.813786\pi\)
0.895078 + 0.445910i \(0.147120\pi\)
\(480\) 4.48528 0.204724
\(481\) 0 0
\(482\) −28.1421 −1.28184
\(483\) 5.65685 9.79796i 0.257396 0.445823i
\(484\) 13.3995 23.2086i 0.609068 1.05494i
\(485\) 10.8284 + 18.7554i 0.491694 + 0.851638i
\(486\) 2.41421 0.109511
\(487\) 15.8995 + 27.5387i 0.720475 + 1.24790i 0.960810 + 0.277209i \(0.0894095\pi\)
−0.240335 + 0.970690i \(0.577257\pi\)
\(488\) 20.5563 + 35.6046i 0.930542 + 1.61175i
\(489\) −13.1716 −0.595639
\(490\) 3.41421 + 5.91359i 0.154238 + 0.267149i
\(491\) 7.31371 12.6677i 0.330063 0.571686i −0.652461 0.757822i \(-0.726263\pi\)
0.982524 + 0.186136i \(0.0595967\pi\)
\(492\) 20.7279 35.9018i 0.934487 1.61858i
\(493\) −7.31371 −0.329393
\(494\) 0 0
\(495\) −5.65685 −0.254257
\(496\) −10.2426 + 17.7408i −0.459908 + 0.796584i
\(497\) 2.82843 4.89898i 0.126872 0.219749i
\(498\) −9.24264 16.0087i −0.414173 0.717368i
\(499\) 2.14214 0.0958952 0.0479476 0.998850i \(-0.484732\pi\)
0.0479476 + 0.998850i \(0.484732\pi\)
\(500\) −10.8284 18.7554i −0.484262 0.838766i
\(501\) 3.82843 + 6.63103i 0.171042 + 0.296253i
\(502\) 0 0
\(503\) −7.65685 13.2621i −0.341402 0.591326i 0.643291 0.765622i \(-0.277569\pi\)
−0.984693 + 0.174296i \(0.944235\pi\)
\(504\) −6.24264 + 10.8126i −0.278069 + 0.481630i
\(505\) −5.17157 + 8.95743i −0.230132 + 0.398600i
\(506\) −19.3137 −0.858599
\(507\) 0 0
\(508\) −21.6569 −0.960868
\(509\) −13.8995 + 24.0746i −0.616084 + 1.06709i 0.374109 + 0.927385i \(0.377949\pi\)
−0.990193 + 0.139705i \(0.955385\pi\)
\(510\) −12.4853 + 21.6251i −0.552858 + 0.957577i
\(511\) 16.4853 + 28.5533i 0.729266 + 1.26313i
\(512\) −31.2426 −1.38074
\(513\) 1.41421 + 2.44949i 0.0624391 + 0.108148i
\(514\) 18.8995 + 32.7349i 0.833621 + 1.44387i
\(515\) −38.6274 −1.70213
\(516\) −18.4853 32.0174i −0.813769 1.40949i
\(517\) −0.343146 + 0.594346i −0.0150915 + 0.0261393i
\(518\) 12.4853 21.6251i 0.548572 0.950154i
\(519\) −0.343146 −0.0150624
\(520\) 0 0
\(521\) 2.68629 0.117689 0.0588443 0.998267i \(-0.481258\pi\)
0.0588443 + 0.998267i \(0.481258\pi\)
\(522\) −2.41421 + 4.18154i −0.105667 + 0.183021i
\(523\) −3.65685 + 6.33386i −0.159903 + 0.276960i −0.934834 0.355086i \(-0.884452\pi\)
0.774930 + 0.632046i \(0.217785\pi\)
\(524\) 15.3137 + 26.5241i 0.668982 + 1.15871i
\(525\) 8.48528 0.370328
\(526\) −14.4853 25.0892i −0.631588 1.09394i
\(527\) 12.4853 + 21.6251i 0.543867 + 0.942006i
\(528\) 6.00000 0.261116
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) −6.82843 + 11.8272i −0.296608 + 0.513740i
\(531\) −1.82843 + 3.16693i −0.0793470 + 0.137433i
\(532\) −30.6274 −1.32787
\(533\) 0 0
\(534\) −22.1421 −0.958184
\(535\) 16.0000 27.7128i 0.691740 1.19813i
\(536\) 2.58579 4.47871i 0.111689 0.193451i
\(537\) 0.343146 + 0.594346i 0.0148078 + 0.0256479i
\(538\) 43.4558 1.87351
\(539\) −1.00000 1.73205i −0.0430730 0.0746047i
\(540\) 5.41421 + 9.37769i 0.232991 + 0.403552i
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 14.2426 + 24.6690i 0.611774 + 1.05962i
\(543\) −7.00000 + 12.1244i −0.300399 + 0.520306i
\(544\) −2.89949 + 5.02207i −0.124315 + 0.215320i
\(545\) −48.9706 −2.09767
\(546\) 0 0
\(547\) 0.686292 0.0293437 0.0146719 0.999892i \(-0.495330\pi\)
0.0146719 + 0.999892i \(0.495330\pi\)
\(548\) −9.89949 + 17.1464i −0.422885 + 0.732459i
\(549\) 4.65685 8.06591i 0.198750 0.344245i
\(550\) −7.24264 12.5446i −0.308827 0.534904i
\(551\) −5.65685 −0.240990
\(552\) 8.82843 + 15.2913i 0.375763 + 0.650840i
\(553\) −16.0000 27.7128i −0.680389 1.17847i
\(554\) −4.82843 −0.205140
\(555\) −5.17157 8.95743i −0.219521 0.380222i
\(556\) −29.3137 + 50.7728i −1.24318 + 2.15325i
\(557\) 15.8995 27.5387i 0.673683 1.16685i −0.303169 0.952937i \(-0.598045\pi\)
0.976852 0.213917i \(-0.0686221\pi\)
\(558\) 16.4853 0.697878
\(559\) 0 0
\(560\) −24.0000 −1.01419
\(561\) 3.65685 6.33386i 0.154393 0.267416i
\(562\) 32.3848 56.0921i 1.36607 2.36610i
\(563\) −2.00000 3.46410i −0.0842900 0.145994i 0.820798 0.571218i \(-0.193529\pi\)
−0.905088 + 0.425223i \(0.860196\pi\)
\(564\) 1.31371 0.0553171
\(565\) 24.4853 + 42.4098i 1.03010 + 1.78419i
\(566\) 6.00000 + 10.3923i 0.252199 + 0.436821i
\(567\) 2.82843 0.118783
\(568\) 4.41421 + 7.64564i 0.185216 + 0.320804i
\(569\) 4.51472 7.81972i 0.189267 0.327820i −0.755739 0.654873i \(-0.772722\pi\)
0.945006 + 0.327053i \(0.106056\pi\)
\(570\) −9.65685 + 16.7262i −0.404481 + 0.700582i
\(571\) 20.9706 0.877591 0.438795 0.898587i \(-0.355405\pi\)
0.438795 + 0.898587i \(0.355405\pi\)
\(572\) 0 0
\(573\) −19.3137 −0.806842
\(574\) 36.9706 64.0349i 1.54312 2.67276i
\(575\) 6.00000 10.3923i 0.250217 0.433389i
\(576\) 4.91421 + 8.51167i 0.204759 + 0.354653i
\(577\) −35.9411 −1.49625 −0.748124 0.663559i \(-0.769045\pi\)
−0.748124 + 0.663559i \(0.769045\pi\)
\(578\) 4.37868 + 7.58410i 0.182129 + 0.315457i
\(579\) −8.65685 14.9941i −0.359767 0.623134i
\(580\) −21.6569 −0.899252
\(581\) −10.8284 18.7554i −0.449239 0.778105i
\(582\) −9.24264 + 16.0087i −0.383120 + 0.663583i
\(583\) 2.00000 3.46410i 0.0828315 0.143468i
\(584\) −51.4558 −2.12926
\(585\) 0 0
\(586\) 63.1127 2.60716
\(587\) 11.4853 19.8931i 0.474048 0.821076i −0.525510 0.850787i \(-0.676126\pi\)
0.999559 + 0.0297116i \(0.00945887\pi\)
\(588\) −1.91421 + 3.31552i −0.0789408 + 0.136730i
\(589\) 9.65685 + 16.7262i 0.397904 + 0.689190i
\(590\) −24.9706 −1.02802
\(591\) −8.24264 14.2767i −0.339057 0.587264i
\(592\) 5.48528 + 9.50079i 0.225444 + 0.390480i
\(593\) 3.51472 0.144332 0.0721661 0.997393i \(-0.477009\pi\)
0.0721661 + 0.997393i \(0.477009\pi\)
\(594\) −2.41421 4.18154i −0.0990564 0.171571i
\(595\) −14.6274 + 25.3354i −0.599666 + 1.03865i
\(596\) −28.3848 + 49.1639i −1.16269 + 2.01383i
\(597\) 10.3431 0.423317
\(598\) 0 0
\(599\) −0.686292 −0.0280411 −0.0140206 0.999902i \(-0.504463\pi\)
−0.0140206 + 0.999902i \(0.504463\pi\)
\(600\) −6.62132 + 11.4685i −0.270314 + 0.468198i
\(601\) −22.3137 + 38.6485i −0.910195 + 1.57650i −0.0964075 + 0.995342i \(0.530735\pi\)
−0.813788 + 0.581162i \(0.802598\pi\)
\(602\) −32.9706 57.1067i −1.34378 2.32749i
\(603\) −1.17157 −0.0477101
\(604\) −39.2132 67.9193i −1.59556 2.76360i
\(605\) −9.89949 17.1464i −0.402472 0.697101i
\(606\) −8.82843 −0.358630
\(607\) 12.9706 + 22.4657i 0.526459 + 0.911854i 0.999525 + 0.0308265i \(0.00981393\pi\)
−0.473066 + 0.881027i \(0.656853\pi\)
\(608\) −2.24264 + 3.88437i −0.0909511 + 0.157532i
\(609\) −2.82843 + 4.89898i −0.114614 + 0.198517i
\(610\) 63.5980 2.57501
\(611\) 0 0
\(612\) −14.0000 −0.565916
\(613\) −18.1716 + 31.4741i −0.733943 + 1.27123i 0.221243 + 0.975219i \(0.428989\pi\)
−0.955186 + 0.296008i \(0.904345\pi\)
\(614\) −20.7279 + 35.9018i −0.836511 + 1.44888i
\(615\) −15.3137 26.5241i −0.617508 1.06956i
\(616\) 24.9706 1.00609
\(617\) −14.5858 25.2633i −0.587202 1.01706i −0.994597 0.103811i \(-0.966896\pi\)
0.407395 0.913252i \(-0.366437\pi\)
\(618\) −16.4853 28.5533i −0.663135 1.14858i
\(619\) 15.7990 0.635015 0.317508 0.948256i \(-0.397154\pi\)
0.317508 + 0.948256i \(0.397154\pi\)
\(620\) 36.9706 + 64.0349i 1.48477 + 2.57170i
\(621\) 2.00000 3.46410i 0.0802572 0.139010i
\(622\) −41.7990 + 72.3980i −1.67599 + 2.90289i
\(623\) −25.9411 −1.03931
\(624\) 0 0
\(625\) −31.0000 −1.24000
\(626\) −7.24264 + 12.5446i −0.289474 + 0.501384i
\(627\) 2.82843 4.89898i 0.112956 0.195646i
\(628\) 19.1421 + 33.1552i 0.763854 + 1.32303i
\(629\) 13.3726 0.533200
\(630\) 9.65685 + 16.7262i 0.384738 + 0.666386i
\(631\) −9.55635 16.5521i −0.380432 0.658928i 0.610692 0.791868i \(-0.290891\pi\)
−0.991124 + 0.132940i \(0.957558\pi\)
\(632\) 49.9411 1.98655
\(633\) 6.00000 + 10.3923i 0.238479 + 0.413057i
\(634\) −10.2426 + 17.7408i −0.406787 + 0.704576i
\(635\) −8.00000 + 13.8564i −0.317470 + 0.549875i
\(636\) −7.65685 −0.303614
\(637\) 0 0
\(638\) 9.65685 0.382319
\(639\) 1.00000 1.73205i 0.0395594 0.0685189i
\(640\) −29.0711 + 50.3526i −1.14913 + 1.99036i
\(641\) 13.1421 + 22.7628i 0.519083 + 0.899078i 0.999754 + 0.0221773i \(0.00705984\pi\)
−0.480671 + 0.876901i \(0.659607\pi\)
\(642\) 27.3137 1.07799
\(643\) 8.58579 + 14.8710i 0.338590 + 0.586456i 0.984168 0.177239i \(-0.0567166\pi\)
−0.645577 + 0.763695i \(0.723383\pi\)
\(644\) 21.6569 + 37.5108i 0.853400 + 1.47813i
\(645\) −27.3137 −1.07548
\(646\) −12.4853 21.6251i −0.491227 0.850830i
\(647\) 5.65685 9.79796i 0.222394 0.385198i −0.733140 0.680077i \(-0.761946\pi\)
0.955534 + 0.294880i \(0.0952796\pi\)
\(648\) −2.20711 + 3.82282i −0.0867033 + 0.150175i
\(649\) 7.31371 0.287088
\(650\) 0 0
\(651\) 19.3137 0.756964
\(652\) 25.2132 43.6705i 0.987425 1.71027i
\(653\) 1.34315 2.32640i 0.0525614 0.0910389i −0.838548 0.544828i \(-0.816595\pi\)
0.891109 + 0.453789i \(0.149928\pi\)
\(654\) −20.8995 36.1990i −0.817235 1.41549i
\(655\) 22.6274 0.884126
\(656\) 16.2426 + 28.1331i 0.634169 + 1.09841i
\(657\) 5.82843 + 10.0951i 0.227389 + 0.393849i
\(658\) 2.34315 0.0913453
\(659\) 12.3431 + 21.3790i 0.480821 + 0.832806i 0.999758 0.0220065i \(-0.00700546\pi\)
−0.518937 + 0.854812i \(0.673672\pi\)
\(660\) 10.8284 18.7554i 0.421496 0.730052i
\(661\) −0.514719 + 0.891519i −0.0200202 + 0.0346761i −0.875862 0.482562i \(-0.839706\pi\)
0.855842 + 0.517238i \(0.173040\pi\)
\(662\) 5.17157 0.200999
\(663\) 0 0
\(664\) 33.7990 1.31166
\(665\) −11.3137 + 19.5959i −0.438727 + 0.759897i
\(666\) 4.41421 7.64564i 0.171047 0.296263i
\(667\) 4.00000 + 6.92820i 0.154881 + 0.268261i
\(668\) −29.3137 −1.13418
\(669\) 2.24264 + 3.88437i 0.0867055 + 0.150178i
\(670\) −4.00000 6.92820i −0.154533 0.267660i
\(671\) −18.6274 −0.719103
\(672\) 2.24264 + 3.88437i 0.0865117 + 0.149843i
\(673\) 14.3137 24.7921i 0.551753 0.955664i −0.446395 0.894836i \(-0.647292\pi\)
0.998148 0.0608282i \(-0.0193742\pi\)
\(674\) 16.0711 27.8359i 0.619034 1.07220i
\(675\) 3.00000 0.115470
\(676\) 0 0
\(677\) 49.3137 1.89528 0.947640 0.319341i \(-0.103462\pi\)
0.947640 + 0.319341i \(0.103462\pi\)
\(678\) −20.8995 + 36.1990i −0.802640 + 1.39021i
\(679\) −10.8284 + 18.7554i −0.415557 + 0.719766i
\(680\) −22.8284 39.5400i −0.875430 1.51629i
\(681\) −5.31371 −0.203622
\(682\) −16.4853 28.5533i −0.631254 1.09336i
\(683\) −9.97056 17.2695i −0.381513 0.660800i 0.609766 0.792582i \(-0.291264\pi\)
−0.991279 + 0.131782i \(0.957930\pi\)
\(684\) −10.8284 −0.414035
\(685\) 7.31371 + 12.6677i 0.279442 + 0.484008i
\(686\) 20.4853 35.4815i 0.782132 1.35469i
\(687\) 10.6569 18.4582i 0.406584 0.704225i
\(688\) 28.9706 1.10449
\(689\) 0 0
\(690\) 27.3137 1.03982
\(691\) −17.0711 + 29.5680i −0.649414 + 1.12482i 0.333849 + 0.942627i \(0.391652\pi\)
−0.983263 + 0.182192i \(0.941681\pi\)
\(692\) 0.656854 1.13770i 0.0249699 0.0432491i
\(693\) −2.82843 4.89898i −0.107443 0.186097i
\(694\) −75.5980 −2.86966
\(695\) 21.6569 + 37.5108i 0.821491 + 1.42286i
\(696\) −4.41421 7.64564i −0.167320 0.289807i
\(697\) 39.5980 1.49988
\(698\) −9.24264 16.0087i −0.349839 0.605939i
\(699\) 13.4853 23.3572i 0.510060 0.883450i
\(700\) −16.2426 + 28.1331i −0.613914 + 1.06333i
\(701\) 38.9706 1.47190 0.735949 0.677037i \(-0.236736\pi\)
0.735949 + 0.677037i \(0.236736\pi\)
\(702\) 0 0
\(703\) 10.3431 0.390099
\(704\) 9.82843 17.0233i 0.370423 0.641591i
\(705\) 0.485281 0.840532i 0.0182768 0.0316563i
\(706\) 21.0711 + 36.4962i 0.793020 + 1.37355i
\(707\) −10.3431 −0.388994
\(708\) −7.00000 12.1244i −0.263076 0.455661i
\(709\) 20.3137 + 35.1844i 0.762897 + 1.32138i 0.941351 + 0.337429i \(0.109557\pi\)
−0.178454 + 0.983948i \(0.557109\pi\)
\(710\) 13.6569 0.512533
\(711\) −5.65685 9.79796i −0.212149 0.367452i
\(712\) 20.2426 35.0613i 0.758625 1.31398i
\(713\) 13.6569 23.6544i 0.511453 0.885863i
\(714\) −24.9706 −0.934500
\(715\) 0 0
\(716\) −2.62742 −0.0981912
\(717\) 1.00000 1.73205i 0.0373457 0.0646846i
\(718\) 1.24264 2.15232i 0.0463749 0.0803237i
\(719\) −18.9706 32.8580i −0.707483 1.22540i −0.965788 0.259333i \(-0.916497\pi\)
0.258305 0.966063i \(-0.416836\pi\)
\(720\) −8.48528 −0.316228
\(721\) −19.3137 33.4523i −0.719280 1.24583i
\(722\) 13.2782 + 22.9985i 0.494162 + 0.855915i
\(723\) −11.6569 −0.433523
\(724\) −26.7990 46.4172i −0.995977 1.72508i
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 8.44975 14.6354i 0.313600 0.543170i
\(727\) −21.6569 −0.803208 −0.401604 0.915813i \(-0.631547\pi\)
−0.401604 + 0.915813i \(0.631547\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −39.7990 + 68.9339i −1.47303 + 2.55136i
\(731\) 17.6569 30.5826i 0.653062 1.13114i
\(732\) 17.8284 + 30.8797i 0.658958 + 1.14135i
\(733\) −8.62742 −0.318661 −0.159330 0.987225i \(-0.550934\pi\)
−0.159330 + 0.987225i \(0.550934\pi\)
\(734\) 28.9706 + 50.1785i 1.06932 + 1.85212i
\(735\) 1.41421 + 2.44949i 0.0521641 + 0.0903508i
\(736\) 6.34315 0.233811
\(737\) 1.17157 + 2.02922i 0.0431554 + 0.0747474i
\(738\) 13.0711 22.6398i 0.481153 0.833381i
\(739\) 5.07107 8.78335i 0.186542 0.323101i −0.757553 0.652774i \(-0.773605\pi\)
0.944095 + 0.329673i \(0.106939\pi\)
\(740\) 39.5980 1.45565
\(741\) 0 0
\(742\) −13.6569 −0.501359
\(743\) 1.00000 1.73205i 0.0366864 0.0635428i −0.847099 0.531435i \(-0.821653\pi\)
0.883786 + 0.467892i \(0.154986\pi\)
\(744\) −15.0711 + 26.1039i −0.552532 + 0.957014i
\(745\) 20.9706 + 36.3221i 0.768302 + 1.33074i
\(746\) 24.1421 0.883906
\(747\) −3.82843 6.63103i −0.140075 0.242617i
\(748\) 14.0000 + 24.2487i 0.511891 + 0.886621i
\(749\) 32.0000 1.16925
\(750\) −6.82843 11.8272i −0.249339 0.431868i
\(751\) −16.4853 + 28.5533i −0.601556 + 1.04193i 0.391029 + 0.920378i \(0.372119\pi\)
−0.992586 + 0.121548i \(0.961214\pi\)
\(752\) −0.514719 + 0.891519i −0.0187699 + 0.0325103i
\(753\) 0 0
\(754\) 0 0
\(755\) −57.9411 −2.10869
\(756\) −5.41421 + 9.37769i −0.196913 + 0.341063i
\(757\) 7.97056 13.8054i 0.289695 0.501767i −0.684042 0.729443i \(-0.739779\pi\)
0.973737 + 0.227676i \(0.0731128\pi\)
\(758\) −19.8995 34.4669i −0.722782 1.25190i
\(759\) −8.00000 −0.290382
\(760\) −17.6569 30.5826i −0.640481 1.10935i
\(761\) 7.75736 + 13.4361i 0.281204 + 0.487060i 0.971682 0.236294i \(-0.0759329\pi\)
−0.690478 + 0.723354i \(0.742600\pi\)
\(762\) −13.6569 −0.494736
\(763\) −24.4853 42.4098i −0.886427 1.53534i
\(764\) 36.9706 64.0349i 1.33755 2.31670i
\(765\) −5.17157 + 8.95743i −0.186979 + 0.323856i
\(766\) 7.17157 0.259119
\(767\) 0 0
\(768\) −29.9706 −1.08147
\(769\) 21.0000 36.3731i 0.757279 1.31165i −0.186954 0.982369i \(-0.559861\pi\)
0.944233 0.329278i \(-0.106805\pi\)
\(770\) 19.3137 33.4523i 0.696018 1.20554i
\(771\) 7.82843 + 13.5592i 0.281934 + 0.488324i
\(772\) 66.2843 2.38562
\(773\) 2.92893 + 5.07306i 0.105346 + 0.182465i 0.913880 0.405985i \(-0.133072\pi\)
−0.808533 + 0.588450i \(0.799738\pi\)
\(774\) −11.6569 20.1903i −0.418997 0.725724i
\(775\) 20.4853 0.735853
\(776\) −16.8995 29.2708i −0.606657 1.05076i
\(777\) 5.17157 8.95743i 0.185529 0.321346i
\(778\) −8.41421 + 14.5738i −0.301664 + 0.522498i
\(779\) 30.6274 1.09734
\(780\) 0 0
\(781\) −4.00000