Properties

Label 441.2.g.f.67.2
Level $441$
Weight $2$
Character 441.67
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(-0.335166 + 0.580525i\) of defining polynomial
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.f.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.335166 + 0.580525i) q^{2} +(0.377302 + 1.69046i) q^{3} +(0.775327 + 1.34291i) q^{4} -1.42494 q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(-2.71529 + 1.27563i) q^{9} +O(q^{10})\) \(q+(-0.335166 + 0.580525i) q^{2} +(0.377302 + 1.69046i) q^{3} +(0.775327 + 1.34291i) q^{4} -1.42494 q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(-2.71529 + 1.27563i) q^{9} +(0.477591 - 0.827212i) q^{10} -4.93077 q^{11} +(-1.97759 + 1.81734i) q^{12} +(1.37730 - 2.38556i) q^{13} +(-0.537632 - 2.40879i) q^{15} +(-0.752918 + 1.30409i) q^{16} +(-0.559839 + 0.969670i) q^{17} +(0.169539 - 2.00384i) q^{18} +(2.00752 + 3.47713i) q^{19} +(-1.10479 - 1.91356i) q^{20} +(1.65263 - 2.86244i) q^{22} +5.43661 q^{23} +(-0.898025 - 4.02349i) q^{24} -2.96955 q^{25} +(0.923251 + 1.59912i) q^{26} +(-3.18087 - 4.10878i) q^{27} +(3.40555 + 5.89858i) q^{29} +(1.57856 + 0.495238i) q^{30} +(1.25292 + 2.17012i) q^{31} +(-2.88483 - 4.99666i) q^{32} +(-1.86039 - 8.33526i) q^{33} +(-0.375279 - 0.650002i) q^{34} +(-3.81828 - 2.65735i) q^{36} +(0.709787 + 1.22939i) q^{37} -2.69142 q^{38} +(4.55234 + 1.42819i) q^{39} +3.39152 q^{40} +(-0.124384 + 0.215440i) q^{41} +(-0.498313 - 0.863104i) q^{43} +(-3.82296 - 6.62156i) q^{44} +(3.86911 - 1.81769i) q^{45} +(-1.82217 + 3.15609i) q^{46} +(-4.73790 + 8.20628i) q^{47} +(-2.48859 - 0.780738i) q^{48} +(0.995294 - 1.72390i) q^{50} +(-1.85041 - 0.580525i) q^{51} +4.27144 q^{52} +(-0.410229 + 0.710537i) q^{53} +(3.45137 - 0.469454i) q^{54} +7.02604 q^{55} +(-5.12050 + 4.70556i) q^{57} -4.56570 q^{58} +(-3.29204 - 5.70197i) q^{59} +(2.81794 - 2.58959i) q^{60} +(0.0376322 - 0.0651809i) q^{61} -1.67974 q^{62} +0.855913 q^{64} +(-1.96257 + 3.39927i) q^{65} +(5.46237 + 1.71369i) q^{66} +(6.29385 + 10.9013i) q^{67} -1.73623 q^{68} +(2.05125 + 9.19035i) q^{69} +0.0804951 q^{71} +(6.46270 - 3.03614i) q^{72} +(-5.34551 + 9.25869i) q^{73} -0.951587 q^{74} +(-1.12042 - 5.01990i) q^{75} +(-3.11297 + 5.39183i) q^{76} +(-2.35489 + 2.16407i) q^{78} +(0.922457 - 1.59774i) q^{79} +(1.07286 - 1.85825i) q^{80} +(5.74555 - 6.92738i) q^{81} +(-0.0833788 - 0.144416i) q^{82} +(7.23583 + 12.5328i) q^{83} +(0.797736 - 1.38172i) q^{85} +0.668072 q^{86} +(-8.68637 + 7.98248i) q^{87} +11.7358 q^{88} +(-6.76292 - 11.7137i) q^{89} +(-0.241583 + 2.85534i) q^{90} +(4.21515 + 7.30085i) q^{92} +(-3.19576 + 2.93679i) q^{93} +(-3.17597 - 5.50094i) q^{94} +(-2.86059 - 4.95469i) q^{95} +(7.35819 - 6.76192i) q^{96} +(-2.70160 - 4.67930i) q^{97} +(13.3885 - 6.28982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{2} - 2q^{3} - 4q^{4} + 8q^{5} + 2q^{6} - 6q^{8} - 4q^{9} + O(q^{10}) \) \( 10q + 2q^{2} - 2q^{3} - 4q^{4} + 8q^{5} + 2q^{6} - 6q^{8} - 4q^{9} + 7q^{10} - 8q^{11} - 22q^{12} + 8q^{13} - 19q^{15} + 2q^{16} - 12q^{17} - 2q^{18} - q^{19} - 5q^{20} - q^{22} - 6q^{23} - 3q^{24} + 2q^{25} - 11q^{26} + 7q^{27} + 7q^{29} - 26q^{30} + 3q^{31} - 2q^{32} + q^{33} - 3q^{34} + 34q^{36} + 40q^{38} + 20q^{39} - 6q^{40} - 5q^{41} - 7q^{43} - 10q^{44} + q^{45} + 3q^{46} - 27q^{47} + 5q^{48} + 19q^{50} + 24q^{51} - 20q^{52} - 21q^{53} + 53q^{54} - 4q^{55} - 4q^{57} + 20q^{58} - 30q^{59} - 41q^{60} + 14q^{61} + 12q^{62} - 50q^{64} - 11q^{65} + 41q^{66} - 2q^{67} + 54q^{68} - 15q^{69} - 6q^{71} + 48q^{72} - 15q^{73} + 72q^{74} - 31q^{75} - 5q^{76} - 20q^{78} - 4q^{79} - 20q^{80} + 8q^{81} + 5q^{82} - 9q^{83} - 6q^{85} + 16q^{86} - 32q^{87} + 36q^{88} - 28q^{89} - 28q^{90} + 27q^{92} - 12q^{93} + 3q^{94} - 14q^{95} + q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.335166 + 0.580525i −0.236998 + 0.410493i −0.959852 0.280508i \(-0.909497\pi\)
0.722853 + 0.691002i \(0.242830\pi\)
\(3\) 0.377302 + 1.69046i 0.217836 + 0.975985i
\(4\) 0.775327 + 1.34291i 0.387664 + 0.671453i
\(5\) −1.42494 −0.637251 −0.318626 0.947881i \(-0.603221\pi\)
−0.318626 + 0.947881i \(0.603221\pi\)
\(6\) −1.10781 0.347551i −0.452262 0.141887i
\(7\) 0 0
\(8\) −2.38012 −0.841499
\(9\) −2.71529 + 1.27563i −0.905095 + 0.425209i
\(10\) 0.477591 0.827212i 0.151028 0.261587i
\(11\) −4.93077 −1.48668 −0.743342 0.668911i \(-0.766761\pi\)
−0.743342 + 0.668911i \(0.766761\pi\)
\(12\) −1.97759 + 1.81734i −0.570881 + 0.524620i
\(13\) 1.37730 2.38556i 0.381995 0.661635i −0.609352 0.792900i \(-0.708571\pi\)
0.991347 + 0.131265i \(0.0419038\pi\)
\(14\) 0 0
\(15\) −0.537632 2.40879i −0.138816 0.621948i
\(16\) −0.752918 + 1.30409i −0.188230 + 0.326023i
\(17\) −0.559839 + 0.969670i −0.135781 + 0.235180i −0.925896 0.377780i \(-0.876688\pi\)
0.790115 + 0.612959i \(0.210021\pi\)
\(18\) 0.169539 2.00384i 0.0399608 0.472309i
\(19\) 2.00752 + 3.47713i 0.460557 + 0.797709i 0.998989 0.0449606i \(-0.0143162\pi\)
−0.538431 + 0.842669i \(0.680983\pi\)
\(20\) −1.10479 1.91356i −0.247039 0.427884i
\(21\) 0 0
\(22\) 1.65263 2.86244i 0.352342 0.610274i
\(23\) 5.43661 1.13361 0.566806 0.823851i \(-0.308179\pi\)
0.566806 + 0.823851i \(0.308179\pi\)
\(24\) −0.898025 4.02349i −0.183309 0.821291i
\(25\) −2.96955 −0.593911
\(26\) 0.923251 + 1.59912i 0.181064 + 0.313613i
\(27\) −3.18087 4.10878i −0.612160 0.790734i
\(28\) 0 0
\(29\) 3.40555 + 5.89858i 0.632394 + 1.09534i 0.987061 + 0.160346i \(0.0512611\pi\)
−0.354667 + 0.934993i \(0.615406\pi\)
\(30\) 1.57856 + 0.495238i 0.288205 + 0.0904176i
\(31\) 1.25292 + 2.17012i 0.225031 + 0.389765i 0.956329 0.292294i \(-0.0944184\pi\)
−0.731298 + 0.682058i \(0.761085\pi\)
\(32\) −2.88483 4.99666i −0.509970 0.883294i
\(33\) −1.86039 8.33526i −0.323853 1.45098i
\(34\) −0.375279 0.650002i −0.0643597 0.111474i
\(35\) 0 0
\(36\) −3.81828 2.65735i −0.636380 0.442891i
\(37\) 0.709787 + 1.22939i 0.116688 + 0.202110i 0.918453 0.395529i \(-0.129439\pi\)
−0.801765 + 0.597639i \(0.796106\pi\)
\(38\) −2.69142 −0.436605
\(39\) 4.55234 + 1.42819i 0.728958 + 0.228694i
\(40\) 3.39152 0.536247
\(41\) −0.124384 + 0.215440i −0.0194256 + 0.0336460i −0.875575 0.483083i \(-0.839517\pi\)
0.856149 + 0.516729i \(0.172850\pi\)
\(42\) 0 0
\(43\) −0.498313 0.863104i −0.0759921 0.131622i 0.825525 0.564365i \(-0.190879\pi\)
−0.901517 + 0.432743i \(0.857546\pi\)
\(44\) −3.82296 6.62156i −0.576333 0.998238i
\(45\) 3.86911 1.81769i 0.576773 0.270965i
\(46\) −1.82217 + 3.15609i −0.268664 + 0.465340i
\(47\) −4.73790 + 8.20628i −0.691093 + 1.19701i 0.280387 + 0.959887i \(0.409537\pi\)
−0.971480 + 0.237122i \(0.923796\pi\)
\(48\) −2.48859 0.780738i −0.359197 0.112690i
\(49\) 0 0
\(50\) 0.995294 1.72390i 0.140756 0.243796i
\(51\) −1.85041 0.580525i −0.259110 0.0812898i
\(52\) 4.27144 0.592342
\(53\) −0.410229 + 0.710537i −0.0563493 + 0.0975998i −0.892824 0.450406i \(-0.851279\pi\)
0.836475 + 0.548005i \(0.184613\pi\)
\(54\) 3.45137 0.469454i 0.469672 0.0638846i
\(55\) 7.02604 0.947392
\(56\) 0 0
\(57\) −5.12050 + 4.70556i −0.678226 + 0.623267i
\(58\) −4.56570 −0.599506
\(59\) −3.29204 5.70197i −0.428586 0.742334i 0.568161 0.822917i \(-0.307655\pi\)
−0.996748 + 0.0805836i \(0.974322\pi\)
\(60\) 2.81794 2.58959i 0.363795 0.334315i
\(61\) 0.0376322 0.0651809i 0.00481831 0.00834556i −0.863606 0.504167i \(-0.831800\pi\)
0.868425 + 0.495821i \(0.165133\pi\)
\(62\) −1.67974 −0.213328
\(63\) 0 0
\(64\) 0.855913 0.106989
\(65\) −1.96257 + 3.39927i −0.243427 + 0.421628i
\(66\) 5.46237 + 1.71369i 0.672371 + 0.210941i
\(67\) 6.29385 + 10.9013i 0.768916 + 1.33180i 0.938151 + 0.346226i \(0.112537\pi\)
−0.169235 + 0.985576i \(0.554130\pi\)
\(68\) −1.73623 −0.210549
\(69\) 2.05125 + 9.19035i 0.246941 + 1.10639i
\(70\) 0 0
\(71\) 0.0804951 0.00955301 0.00477651 0.999989i \(-0.498480\pi\)
0.00477651 + 0.999989i \(0.498480\pi\)
\(72\) 6.46270 3.03614i 0.761637 0.357813i
\(73\) −5.34551 + 9.25869i −0.625644 + 1.08365i 0.362772 + 0.931878i \(0.381830\pi\)
−0.988416 + 0.151769i \(0.951503\pi\)
\(74\) −0.951587 −0.110620
\(75\) −1.12042 5.01990i −0.129375 0.579648i
\(76\) −3.11297 + 5.39183i −0.357083 + 0.618485i
\(77\) 0 0
\(78\) −2.35489 + 2.16407i −0.266639 + 0.245032i
\(79\) 0.922457 1.59774i 0.103785 0.179760i −0.809456 0.587180i \(-0.800238\pi\)
0.913241 + 0.407420i \(0.133571\pi\)
\(80\) 1.07286 1.85825i 0.119950 0.207759i
\(81\) 5.74555 6.92738i 0.638395 0.769709i
\(82\) −0.0833788 0.144416i −0.00920765 0.0159481i
\(83\) 7.23583 + 12.5328i 0.794236 + 1.37566i 0.923323 + 0.384023i \(0.125462\pi\)
−0.129088 + 0.991633i \(0.541205\pi\)
\(84\) 0 0
\(85\) 0.797736 1.38172i 0.0865266 0.149868i
\(86\) 0.668072 0.0720400
\(87\) −8.68637 + 7.98248i −0.931277 + 0.855811i
\(88\) 11.7358 1.25104
\(89\) −6.76292 11.7137i −0.716868 1.24165i −0.962235 0.272222i \(-0.912242\pi\)
0.245366 0.969430i \(-0.421092\pi\)
\(90\) −0.241583 + 2.85534i −0.0254651 + 0.300980i
\(91\) 0 0
\(92\) 4.21515 + 7.30085i 0.439460 + 0.761167i
\(93\) −3.19576 + 2.93679i −0.331385 + 0.304531i
\(94\) −3.17597 5.50094i −0.327576 0.567378i
\(95\) −2.86059 4.95469i −0.293491 0.508341i
\(96\) 7.35819 6.76192i 0.750992 0.690136i
\(97\) −2.70160 4.67930i −0.274306 0.475111i 0.695654 0.718377i \(-0.255115\pi\)
−0.969960 + 0.243266i \(0.921781\pi\)
\(98\) 0 0
\(99\) 13.3885 6.28982i 1.34559 0.632151i
\(100\) −2.30238 3.98783i −0.230238 0.398783i
\(101\) 5.13540 0.510991 0.255496 0.966810i \(-0.417761\pi\)
0.255496 + 0.966810i \(0.417761\pi\)
\(102\) 0.957206 0.879639i 0.0947775 0.0870973i
\(103\) 14.2112 1.40027 0.700137 0.714009i \(-0.253122\pi\)
0.700137 + 0.714009i \(0.253122\pi\)
\(104\) −3.27814 + 5.67791i −0.321448 + 0.556765i
\(105\) 0 0
\(106\) −0.274990 0.476296i −0.0267094 0.0462620i
\(107\) 3.83015 + 6.63401i 0.370274 + 0.641334i 0.989608 0.143794i \(-0.0459303\pi\)
−0.619333 + 0.785128i \(0.712597\pi\)
\(108\) 3.05148 7.45726i 0.293629 0.717575i
\(109\) −0.849394 + 1.47119i −0.0813572 + 0.140915i −0.903833 0.427885i \(-0.859259\pi\)
0.822476 + 0.568800i \(0.192592\pi\)
\(110\) −2.35489 + 4.07880i −0.224530 + 0.388898i
\(111\) −1.81042 + 1.66371i −0.171838 + 0.157913i
\(112\) 0 0
\(113\) −0.300351 + 0.520224i −0.0282547 + 0.0489385i −0.879807 0.475331i \(-0.842328\pi\)
0.851552 + 0.524270i \(0.175662\pi\)
\(114\) −1.01548 4.54972i −0.0951082 0.426121i
\(115\) −7.74683 −0.722395
\(116\) −5.28083 + 9.14666i −0.490312 + 0.849246i
\(117\) −0.696689 + 8.23439i −0.0644090 + 0.761270i
\(118\) 4.41352 0.406297
\(119\) 0 0
\(120\) 1.27963 + 5.73322i 0.116814 + 0.523369i
\(121\) 13.3125 1.21023
\(122\) 0.0252261 + 0.0436929i 0.00228386 + 0.00395577i
\(123\) −0.411122 0.128980i −0.0370696 0.0116298i
\(124\) −1.94284 + 3.36510i −0.174472 + 0.302195i
\(125\) 11.3561 1.01572
\(126\) 0 0
\(127\) 7.25977 0.644200 0.322100 0.946706i \(-0.395611\pi\)
0.322100 + 0.946706i \(0.395611\pi\)
\(128\) 5.48278 9.49645i 0.484614 0.839375i
\(129\) 1.27103 1.16803i 0.111908 0.102839i
\(130\) −1.31557 2.27864i −0.115384 0.199850i
\(131\) 20.4530 1.78698 0.893492 0.449079i \(-0.148248\pi\)
0.893492 + 0.449079i \(0.148248\pi\)
\(132\) 9.75105 8.96088i 0.848720 0.779945i
\(133\) 0 0
\(134\) −8.43794 −0.728927
\(135\) 4.53255 + 5.85475i 0.390100 + 0.503896i
\(136\) 1.33248 2.30793i 0.114260 0.197903i
\(137\) 12.2116 1.04331 0.521655 0.853157i \(-0.325315\pi\)
0.521655 + 0.853157i \(0.325315\pi\)
\(138\) −6.02274 1.88950i −0.512690 0.160845i
\(139\) 1.24092 2.14933i 0.105253 0.182304i −0.808588 0.588375i \(-0.799768\pi\)
0.913842 + 0.406071i \(0.133101\pi\)
\(140\) 0 0
\(141\) −15.6600 4.91296i −1.31881 0.413746i
\(142\) −0.0269793 + 0.0467294i −0.00226405 + 0.00392145i
\(143\) −6.79117 + 11.7626i −0.567906 + 0.983642i
\(144\) 0.380853 4.50143i 0.0317378 0.375119i
\(145\) −4.85269 8.40511i −0.402994 0.698006i
\(146\) −3.58327 6.20640i −0.296553 0.513645i
\(147\) 0 0
\(148\) −1.10063 + 1.90635i −0.0904715 + 0.156701i
\(149\) −8.55593 −0.700929 −0.350465 0.936576i \(-0.613976\pi\)
−0.350465 + 0.936576i \(0.613976\pi\)
\(150\) 3.28971 + 1.03207i 0.268603 + 0.0842682i
\(151\) −17.6592 −1.43709 −0.718544 0.695482i \(-0.755191\pi\)
−0.718544 + 0.695482i \(0.755191\pi\)
\(152\) −4.77814 8.27599i −0.387559 0.671271i
\(153\) 0.283187 3.34708i 0.0228943 0.270595i
\(154\) 0 0
\(155\) −1.78533 3.09228i −0.143401 0.248378i
\(156\) 1.61162 + 7.22068i 0.129033 + 0.578117i
\(157\) 3.16074 + 5.47457i 0.252255 + 0.436918i 0.964146 0.265371i \(-0.0854946\pi\)
−0.711891 + 0.702289i \(0.752161\pi\)
\(158\) 0.618353 + 1.07102i 0.0491936 + 0.0852057i
\(159\) −1.35591 0.425387i −0.107531 0.0337354i
\(160\) 4.11070 + 7.11993i 0.324979 + 0.562880i
\(161\) 0 0
\(162\) 2.09580 + 5.65726i 0.164662 + 0.444477i
\(163\) −4.01134 6.94784i −0.314192 0.544197i 0.665073 0.746778i \(-0.268400\pi\)
−0.979265 + 0.202581i \(0.935067\pi\)
\(164\) −0.385754 −0.0301223
\(165\) 2.65094 + 11.8772i 0.206376 + 0.924640i
\(166\) −9.70083 −0.752930
\(167\) −1.06038 + 1.83663i −0.0820545 + 0.142123i −0.904132 0.427253i \(-0.859482\pi\)
0.822078 + 0.569375i \(0.192815\pi\)
\(168\) 0 0
\(169\) 2.70608 + 4.68706i 0.208160 + 0.360543i
\(170\) 0.534749 + 0.926212i 0.0410133 + 0.0710372i
\(171\) −9.88652 6.88056i −0.756041 0.526169i
\(172\) 0.772712 1.33838i 0.0589187 0.102050i
\(173\) −9.14404 + 15.8379i −0.695208 + 1.20414i 0.274902 + 0.961472i \(0.411354\pi\)
−0.970110 + 0.242664i \(0.921979\pi\)
\(174\) −1.72265 7.71812i −0.130594 0.585109i
\(175\) 0 0
\(176\) 3.71247 6.43018i 0.279838 0.484693i
\(177\) 8.39684 7.71641i 0.631145 0.580001i
\(178\) 9.06681 0.679586
\(179\) 3.81276 6.60389i 0.284979 0.493598i −0.687625 0.726066i \(-0.741347\pi\)
0.972604 + 0.232468i \(0.0746801\pi\)
\(180\) 5.44081 + 3.78655i 0.405534 + 0.282233i
\(181\) −15.5305 −1.15438 −0.577188 0.816611i \(-0.695850\pi\)
−0.577188 + 0.816611i \(0.695850\pi\)
\(182\) 0 0
\(183\) 0.124384 + 0.0390227i 0.00919475 + 0.00288464i
\(184\) −12.9398 −0.953933
\(185\) −1.01140 1.75180i −0.0743597 0.128795i
\(186\) −0.633771 2.83953i −0.0464704 0.208205i
\(187\) 2.76044 4.78122i 0.201863 0.349638i
\(188\) −14.6937 −1.07165
\(189\) 0 0
\(190\) 3.83510 0.278227
\(191\) −7.41624 + 12.8453i −0.536620 + 0.929454i 0.462463 + 0.886639i \(0.346966\pi\)
−0.999083 + 0.0428150i \(0.986367\pi\)
\(192\) 0.322938 + 1.44688i 0.0233060 + 0.104420i
\(193\) −8.28387 14.3481i −0.596286 1.03280i −0.993364 0.115013i \(-0.963309\pi\)
0.397078 0.917785i \(-0.370024\pi\)
\(194\) 3.62194 0.260040
\(195\) −6.48680 2.03509i −0.464529 0.145736i
\(196\) 0 0
\(197\) −4.03740 −0.287653 −0.143826 0.989603i \(-0.545941\pi\)
−0.143826 + 0.989603i \(0.545941\pi\)
\(198\) −0.835960 + 9.88048i −0.0594091 + 0.702175i
\(199\) 12.6407 21.8943i 0.896076 1.55205i 0.0636081 0.997975i \(-0.479739\pi\)
0.832468 0.554074i \(-0.186927\pi\)
\(200\) 7.06789 0.499775
\(201\) −16.0534 + 14.7525i −1.13232 + 1.04056i
\(202\) −1.72121 + 2.98123i −0.121104 + 0.209758i
\(203\) 0 0
\(204\) −0.655085 2.93503i −0.0458651 0.205493i
\(205\) 0.177240 0.306988i 0.0123790 0.0214410i
\(206\) −4.76312 + 8.24997i −0.331862 + 0.574803i
\(207\) −14.7619 + 6.93508i −1.02603 + 0.482022i
\(208\) 2.07399 + 3.59226i 0.143805 + 0.249078i
\(209\) −9.89864 17.1449i −0.684703 1.18594i
\(210\) 0 0
\(211\) −3.76246 + 6.51678i −0.259019 + 0.448634i −0.965979 0.258619i \(-0.916732\pi\)
0.706961 + 0.707253i \(0.250066\pi\)
\(212\) −1.27225 −0.0873782
\(213\) 0.0303710 + 0.136073i 0.00208099 + 0.00932360i
\(214\) −5.13495 −0.351018
\(215\) 0.710065 + 1.22987i 0.0484261 + 0.0838764i
\(216\) 7.57086 + 9.77938i 0.515132 + 0.665402i
\(217\) 0 0
\(218\) −0.569377 0.986190i −0.0385631 0.0667932i
\(219\) −17.6683 5.54302i −1.19391 0.374563i
\(220\) 5.44748 + 9.43531i 0.367269 + 0.636129i
\(221\) 1.54214 + 2.67106i 0.103735 + 0.179675i
\(222\) −0.359036 1.60862i −0.0240969 0.107963i
\(223\) −6.49230 11.2450i −0.434757 0.753020i 0.562519 0.826784i \(-0.309832\pi\)
−0.997276 + 0.0737638i \(0.976499\pi\)
\(224\) 0 0
\(225\) 8.06319 3.78804i 0.537546 0.252536i
\(226\) −0.201335 0.348723i −0.0133926 0.0231967i
\(227\) 28.9665 1.92257 0.961286 0.275551i \(-0.0888603\pi\)
0.961286 + 0.275551i \(0.0888603\pi\)
\(228\) −10.2892 3.22800i −0.681418 0.213779i
\(229\) −15.4358 −1.02003 −0.510013 0.860167i \(-0.670360\pi\)
−0.510013 + 0.860167i \(0.670360\pi\)
\(230\) 2.59648 4.49723i 0.171207 0.296538i
\(231\) 0 0
\(232\) −8.10561 14.0393i −0.532159 0.921727i
\(233\) −2.47324 4.28378i −0.162027 0.280640i 0.773568 0.633713i \(-0.218470\pi\)
−0.935596 + 0.353073i \(0.885137\pi\)
\(234\) −4.54677 3.16434i −0.297231 0.206859i
\(235\) 6.75121 11.6934i 0.440400 0.762795i
\(236\) 5.10481 8.84179i 0.332295 0.575551i
\(237\) 3.04896 + 0.956542i 0.198051 + 0.0621341i
\(238\) 0 0
\(239\) 6.51732 11.2883i 0.421571 0.730182i −0.574523 0.818489i \(-0.694812\pi\)
0.996093 + 0.0883069i \(0.0281456\pi\)
\(240\) 3.54608 + 1.11250i 0.228899 + 0.0718118i
\(241\) −14.5825 −0.939339 −0.469670 0.882842i \(-0.655627\pi\)
−0.469670 + 0.882842i \(0.655627\pi\)
\(242\) −4.46191 + 7.72826i −0.286823 + 0.496791i
\(243\) 13.8782 + 7.09889i 0.890290 + 0.455394i
\(244\) 0.116709 0.00747154
\(245\) 0 0
\(246\) 0.212671 0.195437i 0.0135594 0.0124606i
\(247\) 11.0599 0.703722
\(248\) −2.98209 5.16514i −0.189363 0.327987i
\(249\) −18.4561 + 16.9605i −1.16961 + 1.07483i
\(250\) −3.80619 + 6.59251i −0.240724 + 0.416947i
\(251\) 14.0715 0.888187 0.444094 0.895980i \(-0.353526\pi\)
0.444094 + 0.895980i \(0.353526\pi\)
\(252\) 0 0
\(253\) −26.8067 −1.68532
\(254\) −2.43323 + 4.21448i −0.152674 + 0.264440i
\(255\) 2.63672 + 0.827212i 0.165118 + 0.0518020i
\(256\) 4.53120 + 7.84826i 0.283200 + 0.490517i
\(257\) 8.36215 0.521617 0.260808 0.965391i \(-0.416011\pi\)
0.260808 + 0.965391i \(0.416011\pi\)
\(258\) 0.252065 + 1.12935i 0.0156929 + 0.0703100i
\(259\) 0 0
\(260\) −6.08653 −0.377471
\(261\) −16.7714 11.6721i −1.03812 0.722487i
\(262\) −6.85515 + 11.8735i −0.423512 + 0.733545i
\(263\) 3.27066 0.201678 0.100839 0.994903i \(-0.467847\pi\)
0.100839 + 0.994903i \(0.467847\pi\)
\(264\) 4.42796 + 19.8389i 0.272522 + 1.22100i
\(265\) 0.584551 1.01247i 0.0359087 0.0621956i
\(266\) 0 0
\(267\) 17.2499 15.8520i 1.05568 0.970129i
\(268\) −9.75958 + 16.9041i −0.596161 + 1.03258i
\(269\) 7.69349 13.3255i 0.469081 0.812471i −0.530295 0.847813i \(-0.677919\pi\)
0.999375 + 0.0353420i \(0.0112521\pi\)
\(270\) −4.91799 + 0.668943i −0.299299 + 0.0407106i
\(271\) −4.06308 7.03747i −0.246815 0.427496i 0.715825 0.698279i \(-0.246051\pi\)
−0.962640 + 0.270783i \(0.912717\pi\)
\(272\) −0.843026 1.46016i −0.0511160 0.0885355i
\(273\) 0 0
\(274\) −4.09293 + 7.08915i −0.247263 + 0.428271i
\(275\) 14.6422 0.882958
\(276\) −10.7514 + 9.88016i −0.647158 + 0.594716i
\(277\) 12.8457 0.771826 0.385913 0.922535i \(-0.373887\pi\)
0.385913 + 0.922535i \(0.373887\pi\)
\(278\) 0.831826 + 1.44077i 0.0498896 + 0.0864114i
\(279\) −6.17029 4.29423i −0.369406 0.257089i
\(280\) 0 0
\(281\) −0.724081 1.25415i −0.0431951 0.0748161i 0.843620 0.536941i \(-0.180420\pi\)
−0.886815 + 0.462125i \(0.847087\pi\)
\(282\) 8.10079 7.44435i 0.482395 0.443305i
\(283\) −8.71926 15.1022i −0.518306 0.897732i −0.999774 0.0212686i \(-0.993229\pi\)
0.481468 0.876464i \(-0.340104\pi\)
\(284\) 0.0624100 + 0.108097i 0.00370335 + 0.00641440i
\(285\) 7.29639 6.70513i 0.432201 0.397178i
\(286\) −4.55234 7.88489i −0.269186 0.466243i
\(287\) 0 0
\(288\) 14.2070 + 9.88741i 0.837156 + 0.582621i
\(289\) 7.87316 + 13.6367i 0.463127 + 0.802160i
\(290\) 6.50584 0.382036
\(291\) 6.89084 6.33244i 0.403948 0.371214i
\(292\) −16.5781 −0.970158
\(293\) 0.900048 1.55893i 0.0525814 0.0910736i −0.838537 0.544845i \(-0.816588\pi\)
0.891118 + 0.453772i \(0.149922\pi\)
\(294\) 0 0
\(295\) 4.69094 + 8.12495i 0.273117 + 0.473053i
\(296\) −1.68938 2.92609i −0.0981931 0.170075i
\(297\) 15.6842 + 20.2594i 0.910088 + 1.17557i
\(298\) 2.86766 4.96693i 0.166119 0.287727i
\(299\) 7.48786 12.9693i 0.433034 0.750037i
\(300\) 5.87256 5.39668i 0.339053 0.311578i
\(301\) 0 0
\(302\) 5.91878 10.2516i 0.340588 0.589915i
\(303\) 1.93760 + 8.68117i 0.111312 + 0.498720i
\(304\) −6.04600 −0.346762
\(305\) −0.0536236 + 0.0928787i −0.00307048 + 0.00531822i
\(306\) 1.84815 + 1.28622i 0.105652 + 0.0735286i
\(307\) −1.06478 −0.0607699 −0.0303850 0.999538i \(-0.509673\pi\)
−0.0303850 + 0.999538i \(0.509673\pi\)
\(308\) 0 0
\(309\) 5.36193 + 24.0234i 0.305029 + 1.36665i
\(310\) 2.39353 0.135943
\(311\) −8.46463 14.6612i −0.479985 0.831359i 0.519751 0.854318i \(-0.326025\pi\)
−0.999736 + 0.0229591i \(0.992691\pi\)
\(312\) −10.8351 3.39927i −0.613418 0.192446i
\(313\) −4.13928 + 7.16944i −0.233966 + 0.405241i −0.958972 0.283502i \(-0.908504\pi\)
0.725006 + 0.688743i \(0.241837\pi\)
\(314\) −4.23750 −0.239136
\(315\) 0 0
\(316\) 2.86082 0.160934
\(317\) −3.27371 + 5.67023i −0.183870 + 0.318472i −0.943195 0.332239i \(-0.892196\pi\)
0.759325 + 0.650711i \(0.225529\pi\)
\(318\) 0.701404 0.644566i 0.0393328 0.0361455i
\(319\) −16.7920 29.0846i −0.940171 1.62842i
\(320\) −1.21962 −0.0681790
\(321\) −9.76938 + 8.97773i −0.545274 + 0.501088i
\(322\) 0 0
\(323\) −4.49556 −0.250140
\(324\) 13.7575 + 2.34475i 0.764306 + 0.130264i
\(325\) −4.08997 + 7.08404i −0.226871 + 0.392952i
\(326\) 5.37786 0.297852
\(327\) −2.80747 0.880779i −0.155253 0.0487072i
\(328\) 0.296049 0.512773i 0.0163466 0.0283131i
\(329\) 0 0
\(330\) −7.78353 2.44191i −0.428469 0.134422i
\(331\) 13.3629 23.1453i 0.734493 1.27218i −0.220453 0.975398i \(-0.570754\pi\)
0.954946 0.296781i \(-0.0959131\pi\)
\(332\) −11.2203 + 19.4341i −0.615792 + 1.06658i
\(333\) −3.49551 2.43271i −0.191553 0.133312i
\(334\) −0.710806 1.23115i −0.0388936 0.0673657i
\(335\) −8.96834 15.5336i −0.489993 0.848692i
\(336\) 0 0
\(337\) −4.76164 + 8.24740i −0.259383 + 0.449264i −0.966077 0.258255i \(-0.916853\pi\)
0.706694 + 0.707520i \(0.250186\pi\)
\(338\) −3.62794 −0.197334
\(339\) −0.992739 0.311449i −0.0539182 0.0169156i
\(340\) 2.47403 0.134173
\(341\) −6.17786 10.7004i −0.334550 0.579457i
\(342\) 7.30796 3.43324i 0.395169 0.185648i
\(343\) 0 0
\(344\) 1.18605 + 2.05429i 0.0639473 + 0.110760i
\(345\) −2.92290 13.0957i −0.157363 0.705048i
\(346\) −6.12955 10.6167i −0.329526 0.570757i
\(347\) 9.35156 + 16.1974i 0.502018 + 0.869521i 0.999997 + 0.00233189i \(0.000742265\pi\)
−0.497979 + 0.867189i \(0.665924\pi\)
\(348\) −17.4545 5.47595i −0.935659 0.293542i
\(349\) 15.0542 + 26.0747i 0.805834 + 1.39574i 0.915727 + 0.401801i \(0.131616\pi\)
−0.109893 + 0.993943i \(0.535051\pi\)
\(350\) 0 0
\(351\) −14.1827 + 1.92913i −0.757019 + 0.102970i
\(352\) 14.2244 + 24.6374i 0.758164 + 1.31318i
\(353\) −6.25933 −0.333150 −0.166575 0.986029i \(-0.553271\pi\)
−0.166575 + 0.986029i \(0.553271\pi\)
\(354\) 1.66523 + 7.46086i 0.0885060 + 0.396540i
\(355\) −0.114700 −0.00608767
\(356\) 10.4870 18.1639i 0.555807 0.962686i
\(357\) 0 0
\(358\) 2.55582 + 4.42680i 0.135079 + 0.233964i
\(359\) −5.09755 8.82921i −0.269038 0.465988i 0.699575 0.714559i \(-0.253372\pi\)
−0.968614 + 0.248571i \(0.920039\pi\)
\(360\) −9.20895 + 4.32631i −0.485354 + 0.228017i
\(361\) 1.43970 2.49364i 0.0757739 0.131244i
\(362\) 5.20532 9.01587i 0.273585 0.473864i
\(363\) 5.02285 + 22.5042i 0.263631 + 1.18117i
\(364\) 0 0
\(365\) 7.61701 13.1931i 0.398693 0.690556i
\(366\) −0.0643431 + 0.0591291i −0.00336327 + 0.00309073i
\(367\) 28.6557 1.49581 0.747906 0.663804i \(-0.231059\pi\)
0.747906 + 0.663804i \(0.231059\pi\)
\(368\) −4.09332 + 7.08984i −0.213379 + 0.369584i
\(369\) 0.0629181 0.743649i 0.00327538 0.0387128i
\(370\) 1.35595 0.0704926
\(371\) 0 0
\(372\) −6.42160 2.01463i −0.332944 0.104454i
\(373\) −16.0734 −0.832249 −0.416124 0.909308i \(-0.636612\pi\)
−0.416124 + 0.909308i \(0.636612\pi\)
\(374\) 1.85041 + 3.20501i 0.0956826 + 0.165727i
\(375\) 4.28469 + 19.1970i 0.221260 + 0.991330i
\(376\) 11.2768 19.5319i 0.581555 1.00728i
\(377\) 18.7619 0.966286
\(378\) 0 0
\(379\) −1.01893 −0.0523388 −0.0261694 0.999658i \(-0.508331\pi\)
−0.0261694 + 0.999658i \(0.508331\pi\)
\(380\) 4.43579 7.68302i 0.227551 0.394130i
\(381\) 2.73913 + 12.2723i 0.140330 + 0.628730i
\(382\) −4.97135 8.61063i −0.254356 0.440558i
\(383\) 11.5865 0.592044 0.296022 0.955181i \(-0.404340\pi\)
0.296022 + 0.955181i \(0.404340\pi\)
\(384\) 18.1220 + 5.68536i 0.924784 + 0.290130i
\(385\) 0 0
\(386\) 11.1059 0.565275
\(387\) 2.45406 + 1.70791i 0.124747 + 0.0868181i
\(388\) 4.18924 7.25598i 0.212677 0.368367i
\(389\) 17.8135 0.903181 0.451590 0.892225i \(-0.350857\pi\)
0.451590 + 0.892225i \(0.350857\pi\)
\(390\) 3.35558 3.08366i 0.169916 0.156147i
\(391\) −3.04363 + 5.27172i −0.153923 + 0.266602i
\(392\) 0 0
\(393\) 7.71695 + 34.5749i 0.389269 + 1.74407i
\(394\) 1.35320 2.34381i 0.0681732 0.118079i
\(395\) −1.31444 + 2.27668i −0.0661369 + 0.114552i
\(396\) 18.8271 + 13.1028i 0.946096 + 0.658439i
\(397\) 6.54229 + 11.3316i 0.328348 + 0.568715i 0.982184 0.187921i \(-0.0601748\pi\)
−0.653836 + 0.756636i \(0.726841\pi\)
\(398\) 8.47348 + 14.6765i 0.424737 + 0.735666i
\(399\) 0 0
\(400\) 2.23583 3.87257i 0.111792 0.193629i
\(401\) 14.1033 0.704285 0.352143 0.935946i \(-0.385453\pi\)
0.352143 + 0.935946i \(0.385453\pi\)
\(402\) −3.18366 14.2640i −0.158786 0.711423i
\(403\) 6.90259 0.343842
\(404\) 3.98161 + 6.89636i 0.198093 + 0.343107i
\(405\) −8.18706 + 9.87108i −0.406818 + 0.490498i
\(406\) 0 0
\(407\) −3.49980 6.06183i −0.173479 0.300474i
\(408\) 4.40421 + 1.38172i 0.218041 + 0.0684053i
\(409\) −1.32300 2.29150i −0.0654179 0.113307i 0.831461 0.555583i \(-0.187505\pi\)
−0.896879 + 0.442275i \(0.854171\pi\)
\(410\) 0.118810 + 0.205784i 0.00586759 + 0.0101630i
\(411\) 4.60747 + 20.6432i 0.227270 + 1.01825i
\(412\) 11.0183 + 19.0843i 0.542835 + 0.940217i
\(413\) 0 0
\(414\) 0.921719 10.8941i 0.0453000 0.535415i
\(415\) −10.3106 17.8585i −0.506128 0.876639i
\(416\) −15.8931 −0.779224
\(417\) 4.10155 + 1.28677i 0.200854 + 0.0630133i
\(418\) 13.2708 0.649094
\(419\) −16.7567 + 29.0235i −0.818619 + 1.41789i 0.0880816 + 0.996113i \(0.471926\pi\)
−0.906700 + 0.421776i \(0.861407\pi\)
\(420\) 0 0
\(421\) −2.41950 4.19071i −0.117919 0.204242i 0.801024 0.598633i \(-0.204289\pi\)
−0.918943 + 0.394390i \(0.870956\pi\)
\(422\) −2.52210 4.36841i −0.122774 0.212651i
\(423\) 2.39660 28.3262i 0.116527 1.37727i
\(424\) 0.976394 1.69116i 0.0474179 0.0821302i
\(425\) 1.66247 2.87949i 0.0806418 0.139676i
\(426\) −0.0891734 0.0279761i −0.00432047 0.00135545i
\(427\) 0 0
\(428\) −5.93923 + 10.2871i −0.287084 + 0.497244i
\(429\) −22.4466 7.04210i −1.08373 0.339996i
\(430\) −0.951960 −0.0459076
\(431\) 17.6643 30.5954i 0.850858 1.47373i −0.0295774 0.999562i \(-0.509416\pi\)
0.880435 0.474166i \(-0.157251\pi\)
\(432\) 7.75316 1.05458i 0.373024 0.0507386i
\(433\) −5.47404 −0.263066 −0.131533 0.991312i \(-0.541990\pi\)
−0.131533 + 0.991312i \(0.541990\pi\)
\(434\) 0 0
\(435\) 12.3775 11.3745i 0.593458 0.545367i
\(436\) −2.63423 −0.126157
\(437\) 10.9141 + 18.9038i 0.522093 + 0.904292i
\(438\) 9.13968 8.39905i 0.436711 0.401322i
\(439\) 3.19906 5.54093i 0.152683 0.264454i −0.779530 0.626365i \(-0.784542\pi\)
0.932213 + 0.361911i \(0.117875\pi\)
\(440\) −16.7228 −0.797229
\(441\) 0 0
\(442\) −2.06749 −0.0983404
\(443\) 3.19341 5.53115i 0.151723 0.262793i −0.780138 0.625608i \(-0.784851\pi\)
0.931861 + 0.362815i \(0.118184\pi\)
\(444\) −3.63788 1.14130i −0.172646 0.0541638i
\(445\) 9.63674 + 16.6913i 0.456825 + 0.791245i
\(446\) 8.70400 0.412146
\(447\) −3.22817 14.4634i −0.152687 0.684097i
\(448\) 0 0
\(449\) −11.7460 −0.554327 −0.277163 0.960823i \(-0.589394\pi\)
−0.277163 + 0.960823i \(0.589394\pi\)
\(450\) −0.503456 + 5.95051i −0.0237331 + 0.280510i
\(451\) 0.613311 1.06229i 0.0288797 0.0500210i
\(452\) −0.931482 −0.0438132
\(453\) −6.66287 29.8522i −0.313049 1.40258i
\(454\) −9.70859 + 16.8158i −0.455647 + 0.789203i
\(455\) 0 0
\(456\) 12.1874 11.1998i 0.570727 0.524478i
\(457\) −5.26120 + 9.11266i −0.246108 + 0.426272i −0.962443 0.271485i \(-0.912485\pi\)
0.716334 + 0.697757i \(0.245819\pi\)
\(458\) 5.17356 8.96087i 0.241745 0.418714i
\(459\) 5.76494 0.784145i 0.269084 0.0366007i
\(460\) −6.00633 10.4033i −0.280046 0.485055i
\(461\) 3.54278 + 6.13627i 0.165004 + 0.285794i 0.936657 0.350249i \(-0.113903\pi\)
−0.771653 + 0.636044i \(0.780570\pi\)
\(462\) 0 0
\(463\) 16.3760 28.3641i 0.761059 1.31819i −0.181246 0.983438i \(-0.558013\pi\)
0.942305 0.334755i \(-0.108654\pi\)
\(464\) −10.2564 −0.476141
\(465\) 4.55376 4.18475i 0.211176 0.194063i
\(466\) 3.31579 0.153601
\(467\) −1.96216 3.39856i −0.0907978 0.157266i 0.817049 0.576568i \(-0.195608\pi\)
−0.907847 + 0.419301i \(0.862275\pi\)
\(468\) −11.5982 + 5.44876i −0.536126 + 0.251869i
\(469\) 0 0
\(470\) 4.52555 + 7.83849i 0.208748 + 0.361563i
\(471\) −8.06196 + 7.40867i −0.371476 + 0.341373i
\(472\) 7.83544 + 13.5714i 0.360655 + 0.624673i
\(473\) 2.45707 + 4.25577i 0.112976 + 0.195681i
\(474\) −1.57721 + 1.44940i −0.0724434 + 0.0665730i
\(475\) −5.96145 10.3255i −0.273530 0.473768i
\(476\) 0 0
\(477\) 0.207509 2.45261i 0.00950117 0.112297i
\(478\) 4.36878 + 7.56694i 0.199823 + 0.346104i
\(479\) −16.0865 −0.735010 −0.367505 0.930022i \(-0.619788\pi\)
−0.367505 + 0.930022i \(0.619788\pi\)
\(480\) −10.4850 + 9.63532i −0.478571 + 0.439790i
\(481\) 3.91036 0.178297
\(482\) 4.88755 8.46549i 0.222622 0.385592i
\(483\) 0 0
\(484\) 10.3216 + 17.8775i 0.469162 + 0.812612i
\(485\) 3.84961 + 6.66771i 0.174802 + 0.302765i
\(486\) −8.77261 + 5.67736i −0.397934 + 0.257530i
\(487\) −1.75172 + 3.03407i −0.0793781 + 0.137487i −0.902982 0.429679i \(-0.858627\pi\)
0.823604 + 0.567166i \(0.191960\pi\)
\(488\) −0.0895692 + 0.155138i −0.00405461 + 0.00702279i
\(489\) 10.2315 9.40242i 0.462686 0.425192i
\(490\) 0 0
\(491\) −20.5546 + 35.6017i −0.927618 + 1.60668i −0.140321 + 0.990106i \(0.544814\pi\)
−0.787296 + 0.616575i \(0.788520\pi\)
\(492\) −0.145546 0.652100i −0.00656171 0.0293989i
\(493\) −7.62624 −0.343468
\(494\) −3.70689 + 6.42053i −0.166781 + 0.288873i
\(495\) −19.0777 + 8.96261i −0.857480 + 0.402839i
\(496\) −3.77338 −0.169430
\(497\) 0 0
\(498\) −3.66015 16.3988i −0.164015 0.734849i
\(499\) 11.8297 0.529571 0.264785 0.964307i \(-0.414699\pi\)
0.264785 + 0.964307i \(0.414699\pi\)
\(500\) 8.80470 + 15.2502i 0.393758 + 0.682009i
\(501\) −3.50482 1.09956i −0.156584 0.0491247i
\(502\) −4.71631 + 8.16888i −0.210499 + 0.364595i
\(503\) −21.8595 −0.974665 −0.487332 0.873217i \(-0.662030\pi\)
−0.487332 + 0.873217i \(0.662030\pi\)
\(504\) 0 0
\(505\) −7.31762 −0.325630
\(506\) 8.98470 15.5620i 0.399419 0.691813i
\(507\) −6.90226 + 6.34294i −0.306540 + 0.281700i
\(508\) 5.62869 + 9.74918i 0.249733 + 0.432550i
\(509\) −16.8966 −0.748930 −0.374465 0.927241i \(-0.622174\pi\)
−0.374465 + 0.927241i \(0.622174\pi\)
\(510\) −1.36396 + 1.25343i −0.0603971 + 0.0555029i
\(511\) 0 0
\(512\) 15.8563 0.700756
\(513\) 7.90108 19.3088i 0.348841 0.852503i
\(514\) −2.80271 + 4.85444i −0.123622 + 0.214120i
\(515\) −20.2501 −0.892326
\(516\) 2.55401 + 0.801263i 0.112434 + 0.0352736i
\(517\) 23.3615 40.4633i 1.02744 1.77957i
\(518\) 0 0
\(519\) −30.2234 9.48190i −1.32666 0.416209i
\(520\) 4.67115 8.09067i 0.204843 0.354799i
\(521\) 17.2466 29.8720i 0.755587 1.30872i −0.189495 0.981882i \(-0.560685\pi\)
0.945082 0.326834i \(-0.105982\pi\)
\(522\) 12.3972 5.82413i 0.542610 0.254915i
\(523\) −0.995615 1.72445i −0.0435352 0.0754051i 0.843437 0.537229i \(-0.180529\pi\)
−0.886972 + 0.461823i \(0.847195\pi\)
\(524\) 15.8577 + 27.4664i 0.692749 + 1.19988i
\(525\) 0 0
\(526\) −1.09622 + 1.89870i −0.0477972 + 0.0827873i
\(527\) −2.80573 −0.122220
\(528\) 12.2707 + 3.84964i 0.534012 + 0.167534i
\(529\) 6.55673 0.285075
\(530\) 0.391843 + 0.678693i 0.0170206 + 0.0294805i
\(531\) 16.2124 + 11.2831i 0.703558 + 0.489644i
\(532\) 0 0
\(533\) 0.342629 + 0.593452i 0.0148409 + 0.0257052i
\(534\) 3.42093 + 15.3271i 0.148038 + 0.663266i
\(535\) −5.45772 9.45305i −0.235958 0.408691i
\(536\) −14.9801 25.9463i −0.647042 1.12071i
\(537\) 12.6021 + 3.95364i 0.543823 + 0.170612i
\(538\) 5.15720 + 8.93253i 0.222343 + 0.385109i
\(539\) 0 0
\(540\) −4.34817 + 10.6261i −0.187115 + 0.457276i
\(541\) −15.0681 26.0988i −0.647830 1.12207i −0.983640 0.180145i \(-0.942343\pi\)
0.335810 0.941930i \(-0.390990\pi\)
\(542\) 5.44724 0.233979
\(543\) −5.85971 26.2537i −0.251464 1.12665i
\(544\) 6.46015 0.276977
\(545\) 1.21033 2.09636i 0.0518450 0.0897982i
\(546\) 0 0
\(547\) 7.68070 + 13.3034i 0.328403 + 0.568810i 0.982195 0.187864i \(-0.0601563\pi\)
−0.653792 + 0.756674i \(0.726823\pi\)
\(548\) 9.46800 + 16.3991i 0.404453 + 0.700533i
\(549\) −0.0190357 + 0.224990i −0.000812426 + 0.00960232i
\(550\) −4.90757 + 8.50016i −0.209260 + 0.362448i
\(551\) −13.6734 + 23.6831i −0.582508 + 1.00893i
\(552\) −4.88221 21.8741i −0.207801 0.931025i
\(553\) 0 0
\(554\) −4.30546 + 7.45728i −0.182921 + 0.316829i
\(555\) 2.57974 2.37069i 0.109504 0.100630i
\(556\) 3.84846 0.163211
\(557\) −11.6412 + 20.1631i −0.493252 + 0.854338i −0.999970 0.00777438i \(-0.997525\pi\)
0.506718 + 0.862112i \(0.330859\pi\)
\(558\) 4.56099 2.14273i 0.193082 0.0907088i
\(559\) −2.74531 −0.116114
\(560\) 0 0
\(561\) 9.12397 + 2.86244i 0.385214 + 0.120852i
\(562\) 0.970751 0.0409487
\(563\) 2.27942 + 3.94808i 0.0960663 + 0.166392i 0.910053 0.414492i \(-0.136041\pi\)
−0.813987 + 0.580883i \(0.802707\pi\)
\(564\) −5.54396 24.8390i −0.233443 1.04591i
\(565\) 0.427982 0.741286i 0.0180053 0.0311861i
\(566\) 11.6896 0.491351
\(567\) 0 0
\(568\) −0.191588 −0.00803885
\(569\) −9.09976 + 15.7612i −0.381482 + 0.660746i −0.991274 0.131815i \(-0.957919\pi\)
0.609793 + 0.792561i \(0.291253\pi\)
\(570\) 1.44699 + 6.48307i 0.0606078 + 0.271546i
\(571\) 8.52275 + 14.7618i 0.356666 + 0.617763i 0.987402 0.158234i \(-0.0505801\pi\)
−0.630736 + 0.775998i \(0.717247\pi\)
\(572\) −21.0615 −0.880625
\(573\) −24.5126 7.69027i −1.02403 0.321266i
\(574\) 0 0
\(575\) −16.1443 −0.673264
\(576\) −2.32405 + 1.09182i −0.0968353 + 0.0454927i
\(577\) 5.70473 9.88088i 0.237491 0.411346i −0.722503 0.691368i \(-0.757008\pi\)
0.959994 + 0.280022i \(0.0903417\pi\)
\(578\) −10.5553 −0.439041
\(579\) 21.1293 19.4171i 0.878103 0.806947i
\(580\) 7.52485 13.0334i 0.312452 0.541183i
\(581\) 0 0
\(582\) 1.36657 + 6.12273i 0.0566460 + 0.253795i
\(583\) 2.02275 3.50350i 0.0837736 0.145100i
\(584\) 12.7229 22.0368i 0.526479 0.911889i
\(585\) 0.992739 11.7335i 0.0410447 0.485120i
\(586\) 0.603332 + 1.04500i 0.0249234 + 0.0431686i
\(587\) −2.52544 4.37420i −0.104236 0.180543i 0.809190 0.587548i \(-0.199906\pi\)
−0.913426 + 0.407005i \(0.866573\pi\)
\(588\) 0 0
\(589\) −5.03052 + 8.71312i −0.207279 + 0.359018i
\(590\) −6.28899 −0.258913
\(591\) −1.52332 6.82504i −0.0626610 0.280745i
\(592\) −2.13765 −0.0878567
\(593\) 9.98892 + 17.3013i 0.410196 + 0.710480i 0.994911 0.100759i \(-0.0321271\pi\)
−0.584715 + 0.811239i \(0.698794\pi\)
\(594\) −17.0179 + 2.31477i −0.698254 + 0.0949763i
\(595\) 0 0
\(596\) −6.63365 11.4898i −0.271725 0.470641i
\(597\) 41.7808 + 13.1078i 1.70997 + 0.536465i
\(598\) 5.01935 + 8.69378i 0.205257 + 0.355515i
\(599\) −2.19660 3.80463i −0.0897508 0.155453i 0.817655 0.575709i \(-0.195274\pi\)
−0.907406 + 0.420256i \(0.861940\pi\)
\(600\) 2.66673 + 11.9480i 0.108869 + 0.487774i
\(601\) −12.1778 21.0926i −0.496743 0.860385i 0.503250 0.864141i \(-0.332138\pi\)
−0.999993 + 0.00375637i \(0.998804\pi\)
\(602\) 0 0
\(603\) −30.9955 21.5715i −1.26224 0.878457i
\(604\) −13.6917 23.7147i −0.557107 0.964937i
\(605\) −18.9695 −0.771221
\(606\) −5.68905 1.78481i −0.231102 0.0725030i
\(607\) −13.1256 −0.532752 −0.266376 0.963869i \(-0.585826\pi\)
−0.266376 + 0.963869i \(0.585826\pi\)
\(608\) 11.5827 20.0618i 0.469741 0.813615i
\(609\) 0 0
\(610\) −0.0359456 0.0622597i −0.00145540 0.00252082i
\(611\) 13.0510 + 22.6051i 0.527988 + 0.914502i
\(612\) 4.71437 2.21479i 0.190567 0.0895274i
\(613\) −23.2403 + 40.2534i −0.938667 + 1.62582i −0.170707 + 0.985322i \(0.554605\pi\)
−0.767960 + 0.640497i \(0.778728\pi\)
\(614\) 0.356877 0.618129i 0.0144024 0.0249456i
\(615\) 0.585823 + 0.183789i 0.0236227 + 0.00741108i
\(616\) 0 0
\(617\) 14.1948 24.5862i 0.571463 0.989803i −0.424953 0.905215i \(-0.639709\pi\)
0.996416 0.0845873i \(-0.0269572\pi\)
\(618\) −15.7434 4.93912i −0.633291 0.198680i
\(619\) −31.9212 −1.28302 −0.641511 0.767114i \(-0.721692\pi\)
−0.641511 + 0.767114i \(0.721692\pi\)
\(620\) 2.76843 4.79506i 0.111183 0.192574i
\(621\) −17.2932 22.3378i −0.693951 0.896385i
\(622\) 11.3482 0.455023
\(623\) 0 0
\(624\) −5.29004 + 4.86136i −0.211771 + 0.194610i
\(625\) −1.33399 −0.0533594
\(626\) −2.77469 4.80591i −0.110899 0.192083i
\(627\) 25.2480 23.2020i 1.00831 0.926601i
\(628\) −4.90122 + 8.48916i −0.195580 + 0.338754i
\(629\) −1.58947 −0.0633762
\(630\) 0 0
\(631\) 38.7184 1.54135 0.770677 0.637226i \(-0.219918\pi\)
0.770677 + 0.637226i \(0.219918\pi\)
\(632\) −2.19556 + 3.80282i −0.0873346 + 0.151268i
\(633\) −12.4359 3.90149i −0.494283 0.155070i
\(634\) −2.19447 3.80094i −0.0871537 0.150955i
\(635\) −10.3447 −0.410517
\(636\) −0.480022 2.15068i −0.0190341 0.0852799i
\(637\) 0 0
\(638\) 22.5124 0.891276
\(639\) −0.218567 + 0.102682i −0.00864639 + 0.00406202i
\(640\) −7.81261 + 13.5318i −0.308821 + 0.534893i
\(641\) −40.4001 −1.59571 −0.797854 0.602851i \(-0.794032\pi\)
−0.797854 + 0.602851i \(0.794032\pi\)
\(642\) −1.93743 8.68040i −0.0764642 0.342588i
\(643\) −6.27355 + 10.8661i −0.247405 + 0.428517i −0.962805 0.270198i \(-0.912911\pi\)
0.715400 + 0.698715i \(0.246244\pi\)
\(644\) 0 0
\(645\) −1.81113 + 1.66437i −0.0713132 + 0.0655344i
\(646\) 1.50676 2.60979i 0.0592827 0.102681i
\(647\) −17.2774 + 29.9253i −0.679245 + 1.17649i 0.295964 + 0.955199i \(0.404359\pi\)
−0.975209 + 0.221287i \(0.928974\pi\)
\(648\) −13.6751 + 16.4880i −0.537209 + 0.647710i
\(649\) 16.2323 + 28.1151i 0.637173 + 1.10362i
\(650\) −2.74164 4.74866i −0.107536 0.186258i
\(651\) 0 0
\(652\) 6.22019 10.7737i 0.243602 0.421930i
\(653\) −22.2944 −0.872446 −0.436223 0.899839i \(-0.643684\pi\)
−0.436223 + 0.899839i \(0.643684\pi\)
\(654\) 1.45228 1.33460i 0.0567888 0.0521869i
\(655\) −29.1442 −1.13876
\(656\) −0.187302 0.324417i −0.00731293 0.0126664i
\(657\) 2.70395 31.9589i 0.105491 1.24683i
\(658\) 0 0
\(659\) 3.57493 + 6.19196i 0.139259 + 0.241204i 0.927217 0.374526i \(-0.122194\pi\)
−0.787957 + 0.615730i \(0.788861\pi\)
\(660\) −13.8946 + 12.7687i −0.540848 + 0.497021i
\(661\) 21.4530 + 37.1577i 0.834425 + 1.44527i 0.894498 + 0.447072i \(0.147533\pi\)
−0.0600736 + 0.998194i \(0.519134\pi\)
\(662\) 8.95760 + 15.5150i 0.348147 + 0.603008i
\(663\) −3.93346 + 3.61471i −0.152763 + 0.140384i
\(664\) −17.2221 29.8296i −0.668349 1.15761i
\(665\) 0 0
\(666\) 2.58383 1.21387i 0.100121 0.0470365i
\(667\) 18.5146 + 32.0683i 0.716889 + 1.24169i
\(668\) −3.28856 −0.127238
\(669\) 16.5596 15.2177i 0.640232 0.588351i
\(670\) 12.0235 0.464510
\(671\) −0.185556 + 0.321392i −0.00716331 + 0.0124072i
\(672\) 0 0
\(673\) −18.8270 32.6094i −0.725729 1.25700i −0.958673 0.284510i \(-0.908169\pi\)
0.232944 0.972490i \(-0.425164\pi\)
\(674\) −3.19188 5.52850i −0.122947 0.212950i
\(675\) 9.44578 + 12.2012i 0.363568 + 0.469626i
\(676\) −4.19619 + 7.26801i −0.161392 + 0.279539i
\(677\) −13.1808 + 22.8298i −0.506580 + 0.877422i 0.493391 + 0.869808i \(0.335757\pi\)
−0.999971 + 0.00761453i \(0.997576\pi\)
\(678\) 0.513537 0.471923i 0.0197223 0.0181241i
\(679\) 0 0
\(680\) −1.89871 + 3.28866i −0.0728121 + 0.126114i
\(681\) 10.9291 + 48.9666i 0.418805 + 1.87640i
\(682\) 8.28244 0.317151
\(683\) 1.96588 3.40500i 0.0752222 0.130289i −0.825961 0.563728i \(-0.809367\pi\)
0.901183 + 0.433439i \(0.142700\pi\)
\(684\) 1.57465 18.6113i 0.0602084 0.711623i
\(685\) −17.4008 −0.664850
\(686\) 0 0
\(687\) −5.82396 26.0936i −0.222198 0.995531i
\(688\) 1.50076 0.0572158
\(689\) 1.13002 + 1.95725i 0.0430503 + 0.0745653i
\(690\) 8.58203 + 2.69241i 0.326712 + 0.102498i
\(691\) 9.95052 17.2348i 0.378536 0.655643i −0.612314 0.790615i \(-0.709761\pi\)
0.990849 + 0.134972i \(0.0430944\pi\)
\(692\) −28.3585 −1.07803
\(693\) 0 0
\(694\) −12.5373 −0.475910
\(695\) −1.76823 + 3.06266i −0.0670727 + 0.116173i
\(696\) 20.6746 18.9993i 0.783669 0.720165i
\(697\) −0.139270 0.241223i −0.00527524 0.00913699i
\(698\) −20.1827 −0.763925
\(699\) 6.30838 5.79718i 0.238605 0.219270i
\(700\) 0 0
\(701\) 43.7908 1.65396 0.826979 0.562234i \(-0.190058\pi\)
0.826979 + 0.562234i \(0.190058\pi\)
\(702\) 3.63367 8.88002i 0.137144 0.335155i
\(703\) −2.84983 + 4.93604i −0.107483 + 0.186166i
\(704\) −4.22031 −0.159059
\(705\) 22.3145 + 7.00066i 0.840412 + 0.263660i
\(706\) 2.09792 3.63370i 0.0789561 0.136756i
\(707\) 0 0
\(708\) 16.8727 + 5.29343i 0.634115 + 0.198939i
\(709\) −22.3172 + 38.6545i −0.838139 + 1.45170i 0.0533097 + 0.998578i \(0.483023\pi\)
−0.891449 + 0.453121i \(0.850310\pi\)
\(710\) 0.0384437 0.0665865i 0.00144277 0.00249895i
\(711\) −0.466612 + 5.51504i −0.0174993 + 0.206830i
\(712\) 16.0966 + 27.8801i 0.603244 + 1.04485i
\(713\) 6.81163 + 11.7981i 0.255097 + 0.441842i
\(714\) 0 0
\(715\) 9.67699 16.7610i 0.361899 0.626827i
\(716\) 11.8245 0.441904
\(717\) 21.5414 + 6.75814i 0.804480 + 0.252387i
\(718\) 6.83411 0.255047
\(719\) 19.5096 + 33.7917i 0.727586 + 1.26022i 0.957901 + 0.287100i \(0.0926912\pi\)
−0.230315 + 0.973116i \(0.573976\pi\)
\(720\) −0.542692 + 6.41425i −0.0202249 + 0.239045i
\(721\) 0 0
\(722\) 0.965081 + 1.67157i 0.0359166 + 0.0622094i
\(723\) −5.50200 24.6510i −0.204622 0.916781i
\(724\) −12.0413 20.8561i −0.447510 0.775109i
\(725\) −10.1130 17.5162i −0.375586 0.650534i
\(726\) −14.7478 4.62678i −0.547341 0.171716i
\(727\) 11.2554 + 19.4949i 0.417439 + 0.723025i 0.995681 0.0928402i \(-0.0295946\pi\)
−0.578242 + 0.815865i \(0.696261\pi\)
\(728\) 0 0
\(729\) −6.76407 + 26.1390i −0.250521 + 0.968111i
\(730\) 5.10593 + 8.84373i 0.188979 + 0.327321i
\(731\) 1.11590 0.0412731
\(732\) 0.0440346 + 0.197292i 0.00162757 + 0.00729211i
\(733\) 0.897039 0.0331329 0.0165664 0.999863i \(-0.494726\pi\)
0.0165664 + 0.999863i \(0.494726\pi\)
\(734\) −9.60441 + 16.6353i −0.354505 + 0.614021i
\(735\) 0 0
\(736\) −15.6837 27.1649i −0.578108 1.00131i
\(737\) −31.0335 53.7517i −1.14314 1.97997i
\(738\) 0.410619 + 0.285771i 0.0151151 + 0.0105194i
\(739\) 1.79032 3.10092i 0.0658578 0.114069i −0.831216 0.555949i \(-0.812355\pi\)
0.897074 + 0.441880i \(0.145688\pi\)
\(740\) 1.56833 2.71643i 0.0576531 0.0998581i
\(741\) 4.17291 + 18.6962i 0.153296 + 0.686823i
\(742\) 0 0
\(743\) −24.7964 + 42.9486i −0.909691 + 1.57563i −0.0951977 + 0.995458i \(0.530348\pi\)
−0.814493 + 0.580173i \(0.802985\pi\)
\(744\) 7.60629 6.98992i 0.278860 0.256263i
\(745\) 12.1917 0.446668
\(746\) 5.38726 9.33101i 0.197242 0.341633i
\(747\) −35.6346 24.8000i −1.30380 0.907384i
\(748\) 8.56098 0.313020
\(749\) 0 0
\(750\) −12.5804 3.94682i −0.459373 0.144118i
\(751\) −42.9030 −1.56555 −0.782776 0.622304i \(-0.786197\pi\)
−0.782776 + 0.622304i \(0.786197\pi\)
\(752\) −7.13450 12.3573i −0.260168 0.450625i
\(753\) 5.30922 + 23.7873i 0.193479 + 0.866858i
\(754\) −6.28835 + 10.8917i −0.229008 + 0.396654i
\(755\) 25.1633 0.915786
\(756\) 0 0
\(757\) 13.8029 0.501677 0.250838 0.968029i \(-0.419294\pi\)
0.250838 + 0.968029i \(0.419294\pi\)
\(758\) 0.341510 0.591513i 0.0124042 0.0214847i
\(759\) −10.1142 45.3155i −0.367123 1.64485i
\(760\) 6.80856 + 11.7928i 0.246972 + 0.427769i
\(761\) −40.7197 −1.47609 −0.738044 0.674752i \(-0.764251\pi\)
−0.738044 + 0.674752i \(0.764251\pi\)
\(762\) −8.04245 2.52314i −0.291347 0.0914036i
\(763\) 0 0
\(764\) −23.0001 −0.832113
\(765\) −0.403524 + 4.76938i −0.0145894 + 0.172437i
\(766\) −3.88342 + 6.72627i −0.140313 + 0.243030i
\(767\) −18.1365 −0.654871
\(768\) −11.5575 + 10.6210i −0.417046 + 0.383251i
\(769\) −5.57381 + 9.65413i −0.200997 + 0.348137i −0.948850 0.315728i \(-0.897751\pi\)
0.747853 + 0.663864i \(0.231085\pi\)
\(770\) 0 0
\(771\) 3.15506 + 14.1359i 0.113627 + 0.509090i
\(772\) 12.8454 22.2489i 0.462317 0.800756i
\(773\) 0.462831 0.801647i 0.0166469 0.0288332i −0.857582 0.514347i \(-0.828034\pi\)
0.874229 + 0.485514i \(0.161368\pi\)
\(774\) −1.81401 + 0.852210i −0.0652031 + 0.0306320i
\(775\) −3.72061 6.44428i −0.133648 0.231485i
\(776\) 6.43012 + 11.1373i 0.230828 + 0.399806i
\(777\) 0 0
\(778\) −5.97049 + 10.3412i −0.214052 + 0.370750i
\(779\) −0.998817 −0.0357863
\(780\) −2.29646 10.2890i −0.0822266 0.368406i
\(781\)