Properties

Label 154.2.e.f.23.1
Level $154$
Weight $2$
Character 154.23
Analytic conductor $1.230$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.22969619113\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 23.1
Root \(1.32288 - 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 154.23
Dual form 154.2.e.f.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.32288 - 2.29129i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.822876 - 1.42526i) q^{5} -2.64575 q^{6} +(-1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.32288 - 2.29129i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.822876 - 1.42526i) q^{5} -2.64575 q^{6} +(-1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 + 3.46410i) q^{9} +(-0.822876 - 1.42526i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.32288 + 2.29129i) q^{12} +5.00000 q^{13} +(1.32288 + 2.29129i) q^{14} -4.35425 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{18} +(2.82288 - 4.88936i) q^{19} -1.64575 q^{20} +7.00000 q^{21} -1.00000 q^{22} +(-0.822876 + 1.42526i) q^{23} +(1.32288 + 2.29129i) q^{24} +(1.14575 + 1.98450i) q^{25} +(2.50000 - 4.33013i) q^{26} +2.64575 q^{27} +2.64575 q^{28} +6.29150 q^{29} +(-2.17712 + 3.77089i) q^{30} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.32288 + 2.29129i) q^{33} -6.00000 q^{34} +(2.17712 + 3.77089i) q^{35} +4.00000 q^{36} +(-1.82288 + 3.15731i) q^{37} +(-2.82288 - 4.88936i) q^{38} +(-6.61438 - 11.4564i) q^{39} +(-0.822876 + 1.42526i) q^{40} +10.9373 q^{41} +(3.50000 - 6.06218i) q^{42} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(3.29150 + 5.70105i) q^{45} +(0.822876 + 1.42526i) q^{46} +(-1.35425 + 2.34563i) q^{47} +2.64575 q^{48} +(-3.50000 - 6.06218i) q^{49} +2.29150 q^{50} +(-7.93725 + 13.7477i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(-0.822876 - 1.42526i) q^{53} +(1.32288 - 2.29129i) q^{54} -1.64575 q^{55} +(1.32288 - 2.29129i) q^{56} -14.9373 q^{57} +(3.14575 - 5.44860i) q^{58} +(-2.32288 - 4.02334i) q^{59} +(2.17712 + 3.77089i) q^{60} +(-7.14575 + 12.3768i) q^{61} +4.00000 q^{62} +(-5.29150 - 9.16515i) q^{63} +1.00000 q^{64} +(4.11438 - 7.12631i) q^{65} +(1.32288 + 2.29129i) q^{66} +(5.96863 + 10.3380i) q^{67} +(-3.00000 + 5.19615i) q^{68} +4.35425 q^{69} +4.35425 q^{70} +4.35425 q^{71} +(2.00000 - 3.46410i) q^{72} +(-0.177124 - 0.306788i) q^{73} +(1.82288 + 3.15731i) q^{74} +(3.03137 - 5.25049i) q^{75} -5.64575 q^{76} +2.64575 q^{77} -13.2288 q^{78} +(1.32288 - 2.29129i) q^{79} +(0.822876 + 1.42526i) q^{80} +(2.50000 + 4.33013i) q^{81} +(5.46863 - 9.47194i) q^{82} +2.70850 q^{83} +(-3.50000 - 6.06218i) q^{84} -9.87451 q^{85} +(-2.00000 + 3.46410i) q^{86} +(-8.32288 - 14.4156i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-3.29150 + 5.70105i) q^{89} +6.58301 q^{90} +(-6.61438 + 11.4564i) q^{91} +1.64575 q^{92} +(5.29150 - 9.16515i) q^{93} +(1.35425 + 2.34563i) q^{94} +(-4.64575 - 8.04668i) q^{95} +(1.32288 - 2.29129i) q^{96} -16.2915 q^{97} -7.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 28 q^{15} - 2 q^{16} - 12 q^{17} + 8 q^{18} + 6 q^{19} + 4 q^{20} + 28 q^{21} - 4 q^{22} + 2 q^{23} - 6 q^{25} + 10 q^{26} + 4 q^{29} - 14 q^{30} + 8 q^{31} + 2 q^{32} - 24 q^{34} + 14 q^{35} + 16 q^{36} - 2 q^{37} - 6 q^{38} + 2 q^{40} + 12 q^{41} + 14 q^{42} - 16 q^{43} - 2 q^{44} - 8 q^{45} - 2 q^{46} - 16 q^{47} - 14 q^{49} - 12 q^{50} - 10 q^{52} + 2 q^{53} + 4 q^{55} - 28 q^{57} + 2 q^{58} - 4 q^{59} + 14 q^{60} - 18 q^{61} + 16 q^{62} + 4 q^{64} - 10 q^{65} + 8 q^{67} - 12 q^{68} + 28 q^{69} + 28 q^{70} + 28 q^{71} + 8 q^{72} - 6 q^{73} + 2 q^{74} + 28 q^{75} - 12 q^{76} - 2 q^{80} + 10 q^{81} + 6 q^{82} + 32 q^{83} - 14 q^{84} + 24 q^{85} - 8 q^{86} - 28 q^{87} + 2 q^{88} + 8 q^{89} - 16 q^{90} - 4 q^{92} + 16 q^{94} - 8 q^{95} - 44 q^{97} - 28 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −1.32288 2.29129i −0.763763 1.32288i −0.940898 0.338689i \(-0.890016\pi\)
0.177136 0.984186i \(-0.443317\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.822876 1.42526i 0.368001 0.637397i −0.621252 0.783611i \(-0.713376\pi\)
0.989253 + 0.146214i \(0.0467089\pi\)
\(6\) −2.64575 −1.08012
\(7\) −1.32288 + 2.29129i −0.500000 + 0.866025i
\(8\) −1.00000 −0.353553
\(9\) −2.00000 + 3.46410i −0.666667 + 1.15470i
\(10\) −0.822876 1.42526i −0.260216 0.450708i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) −1.32288 + 2.29129i −0.381881 + 0.661438i
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 1.32288 + 2.29129i 0.353553 + 0.612372i
\(15\) −4.35425 −1.12426
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 2.00000 + 3.46410i 0.471405 + 0.816497i
\(19\) 2.82288 4.88936i 0.647612 1.12170i −0.336080 0.941834i \(-0.609101\pi\)
0.983692 0.179863i \(-0.0575656\pi\)
\(20\) −1.64575 −0.368001
\(21\) 7.00000 1.52753
\(22\) −1.00000 −0.213201
\(23\) −0.822876 + 1.42526i −0.171581 + 0.297188i −0.938973 0.343991i \(-0.888221\pi\)
0.767391 + 0.641179i \(0.221554\pi\)
\(24\) 1.32288 + 2.29129i 0.270031 + 0.467707i
\(25\) 1.14575 + 1.98450i 0.229150 + 0.396900i
\(26\) 2.50000 4.33013i 0.490290 0.849208i
\(27\) 2.64575 0.509175
\(28\) 2.64575 0.500000
\(29\) 6.29150 1.16830 0.584151 0.811645i \(-0.301427\pi\)
0.584151 + 0.811645i \(0.301427\pi\)
\(30\) −2.17712 + 3.77089i −0.397487 + 0.688467i
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.32288 + 2.29129i −0.230283 + 0.398862i
\(34\) −6.00000 −1.02899
\(35\) 2.17712 + 3.77089i 0.368001 + 0.637397i
\(36\) 4.00000 0.666667
\(37\) −1.82288 + 3.15731i −0.299679 + 0.519059i −0.976062 0.217491i \(-0.930213\pi\)
0.676384 + 0.736550i \(0.263546\pi\)
\(38\) −2.82288 4.88936i −0.457931 0.793160i
\(39\) −6.61438 11.4564i −1.05915 1.83450i
\(40\) −0.822876 + 1.42526i −0.130108 + 0.225354i
\(41\) 10.9373 1.70811 0.854056 0.520181i \(-0.174136\pi\)
0.854056 + 0.520181i \(0.174136\pi\)
\(42\) 3.50000 6.06218i 0.540062 0.935414i
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 3.29150 + 5.70105i 0.490668 + 0.849862i
\(46\) 0.822876 + 1.42526i 0.121326 + 0.210143i
\(47\) −1.35425 + 2.34563i −0.197537 + 0.342145i −0.947729 0.319075i \(-0.896628\pi\)
0.750192 + 0.661220i \(0.229961\pi\)
\(48\) 2.64575 0.381881
\(49\) −3.50000 6.06218i −0.500000 0.866025i
\(50\) 2.29150 0.324067
\(51\) −7.93725 + 13.7477i −1.11144 + 1.92507i
\(52\) −2.50000 4.33013i −0.346688 0.600481i
\(53\) −0.822876 1.42526i −0.113031 0.195775i 0.803960 0.594683i \(-0.202722\pi\)
−0.916991 + 0.398908i \(0.869389\pi\)
\(54\) 1.32288 2.29129i 0.180021 0.311805i
\(55\) −1.64575 −0.221913
\(56\) 1.32288 2.29129i 0.176777 0.306186i
\(57\) −14.9373 −1.97849
\(58\) 3.14575 5.44860i 0.413057 0.715436i
\(59\) −2.32288 4.02334i −0.302413 0.523794i 0.674269 0.738486i \(-0.264459\pi\)
−0.976682 + 0.214692i \(0.931125\pi\)
\(60\) 2.17712 + 3.77089i 0.281066 + 0.486820i
\(61\) −7.14575 + 12.3768i −0.914920 + 1.58469i −0.107901 + 0.994162i \(0.534413\pi\)
−0.807019 + 0.590526i \(0.798920\pi\)
\(62\) 4.00000 0.508001
\(63\) −5.29150 9.16515i −0.666667 1.15470i
\(64\) 1.00000 0.125000
\(65\) 4.11438 7.12631i 0.510326 0.883910i
\(66\) 1.32288 + 2.29129i 0.162835 + 0.282038i
\(67\) 5.96863 + 10.3380i 0.729184 + 1.26298i 0.957229 + 0.289333i \(0.0934334\pi\)
−0.228045 + 0.973651i \(0.573233\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 4.35425 0.524190
\(70\) 4.35425 0.520432
\(71\) 4.35425 0.516754 0.258377 0.966044i \(-0.416812\pi\)
0.258377 + 0.966044i \(0.416812\pi\)
\(72\) 2.00000 3.46410i 0.235702 0.408248i
\(73\) −0.177124 0.306788i −0.0207308 0.0359069i 0.855474 0.517846i \(-0.173266\pi\)
−0.876205 + 0.481939i \(0.839933\pi\)
\(74\) 1.82288 + 3.15731i 0.211905 + 0.367030i
\(75\) 3.03137 5.25049i 0.350033 0.606275i
\(76\) −5.64575 −0.647612
\(77\) 2.64575 0.301511
\(78\) −13.2288 −1.49786
\(79\) 1.32288 2.29129i 0.148835 0.257790i −0.781962 0.623326i \(-0.785781\pi\)
0.930797 + 0.365536i \(0.119114\pi\)
\(80\) 0.822876 + 1.42526i 0.0920003 + 0.159349i
\(81\) 2.50000 + 4.33013i 0.277778 + 0.481125i
\(82\) 5.46863 9.47194i 0.603909 1.04600i
\(83\) 2.70850 0.297296 0.148648 0.988890i \(-0.452508\pi\)
0.148648 + 0.988890i \(0.452508\pi\)
\(84\) −3.50000 6.06218i −0.381881 0.661438i
\(85\) −9.87451 −1.07104
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) −8.32288 14.4156i −0.892306 1.54552i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) −3.29150 + 5.70105i −0.348899 + 0.604310i −0.986054 0.166425i \(-0.946778\pi\)
0.637156 + 0.770735i \(0.280111\pi\)
\(90\) 6.58301 0.693910
\(91\) −6.61438 + 11.4564i −0.693375 + 1.20096i
\(92\) 1.64575 0.171581
\(93\) 5.29150 9.16515i 0.548703 0.950382i
\(94\) 1.35425 + 2.34563i 0.139680 + 0.241933i
\(95\) −4.64575 8.04668i −0.476644 0.825572i
\(96\) 1.32288 2.29129i 0.135015 0.233854i
\(97\) −16.2915 −1.65415 −0.827076 0.562090i \(-0.809997\pi\)
−0.827076 + 0.562090i \(0.809997\pi\)
\(98\) −7.00000 −0.707107
\(99\) 4.00000 0.402015
\(100\) 1.14575 1.98450i 0.114575 0.198450i
\(101\) −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) 7.93725 + 13.7477i 0.785905 + 1.36123i
\(103\) 1.46863 2.54374i 0.144708 0.250642i −0.784556 0.620058i \(-0.787109\pi\)
0.929264 + 0.369416i \(0.120442\pi\)
\(104\) −5.00000 −0.490290
\(105\) 5.76013 9.97684i 0.562131 0.973640i
\(106\) −1.64575 −0.159849
\(107\) 5.46863 9.47194i 0.528672 0.915687i −0.470769 0.882257i \(-0.656023\pi\)
0.999441 0.0334304i \(-0.0106432\pi\)
\(108\) −1.32288 2.29129i −0.127294 0.220479i
\(109\) 5.29150 + 9.16515i 0.506834 + 0.877862i 0.999969 + 0.00790932i \(0.00251764\pi\)
−0.493135 + 0.869953i \(0.664149\pi\)
\(110\) −0.822876 + 1.42526i −0.0784581 + 0.135893i
\(111\) 9.64575 0.915534
\(112\) −1.32288 2.29129i −0.125000 0.216506i
\(113\) −18.2915 −1.72072 −0.860360 0.509687i \(-0.829761\pi\)
−0.860360 + 0.509687i \(0.829761\pi\)
\(114\) −7.46863 + 12.9360i −0.699501 + 1.21157i
\(115\) 1.35425 + 2.34563i 0.126284 + 0.218731i
\(116\) −3.14575 5.44860i −0.292076 0.505890i
\(117\) −10.0000 + 17.3205i −0.924500 + 1.60128i
\(118\) −4.64575 −0.427676
\(119\) 15.8745 1.45521
\(120\) 4.35425 0.397487
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 7.14575 + 12.3768i 0.646946 + 1.12054i
\(123\) −14.4686 25.0604i −1.30459 2.25962i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 12.0000 1.07331
\(126\) −10.5830 −0.942809
\(127\) 15.9373 1.41420 0.707101 0.707112i \(-0.250002\pi\)
0.707101 + 0.707112i \(0.250002\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 5.29150 + 9.16515i 0.465891 + 0.806947i
\(130\) −4.11438 7.12631i −0.360855 0.625019i
\(131\) −5.17712 + 8.96704i −0.452327 + 0.783454i −0.998530 0.0541989i \(-0.982739\pi\)
0.546203 + 0.837653i \(0.316073\pi\)
\(132\) 2.64575 0.230283
\(133\) 7.46863 + 12.9360i 0.647612 + 1.12170i
\(134\) 11.9373 1.03122
\(135\) 2.17712 3.77089i 0.187377 0.324547i
\(136\) 3.00000 + 5.19615i 0.257248 + 0.445566i
\(137\) 6.43725 + 11.1497i 0.549972 + 0.952579i 0.998276 + 0.0586978i \(0.0186948\pi\)
−0.448304 + 0.893881i \(0.647972\pi\)
\(138\) 2.17712 3.77089i 0.185329 0.320999i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 2.17712 3.77089i 0.184001 0.318698i
\(141\) 7.16601 0.603487
\(142\) 2.17712 3.77089i 0.182700 0.316446i
\(143\) −2.50000 4.33013i −0.209061 0.362103i
\(144\) −2.00000 3.46410i −0.166667 0.288675i
\(145\) 5.17712 8.96704i 0.429937 0.744672i
\(146\) −0.354249 −0.0293178
\(147\) −9.26013 + 16.0390i −0.763763 + 1.32288i
\(148\) 3.64575 0.299679
\(149\) 7.64575 13.2428i 0.626364 1.08489i −0.361911 0.932213i \(-0.617876\pi\)
0.988275 0.152682i \(-0.0487911\pi\)
\(150\) −3.03137 5.25049i −0.247511 0.428701i
\(151\) 4.32288 + 7.48744i 0.351791 + 0.609319i 0.986563 0.163380i \(-0.0522396\pi\)
−0.634773 + 0.772699i \(0.718906\pi\)
\(152\) −2.82288 + 4.88936i −0.228965 + 0.396580i
\(153\) 24.0000 1.94029
\(154\) 1.32288 2.29129i 0.106600 0.184637i
\(155\) 6.58301 0.528760
\(156\) −6.61438 + 11.4564i −0.529574 + 0.917249i
\(157\) −10.5830 18.3303i −0.844616 1.46292i −0.885954 0.463772i \(-0.846496\pi\)
0.0413387 0.999145i \(-0.486838\pi\)
\(158\) −1.32288 2.29129i −0.105242 0.182285i
\(159\) −2.17712 + 3.77089i −0.172657 + 0.299051i
\(160\) 1.64575 0.130108
\(161\) −2.17712 3.77089i −0.171581 0.297188i
\(162\) 5.00000 0.392837
\(163\) −0.322876 + 0.559237i −0.0252896 + 0.0438028i −0.878393 0.477939i \(-0.841384\pi\)
0.853104 + 0.521741i \(0.174717\pi\)
\(164\) −5.46863 9.47194i −0.427028 0.739634i
\(165\) 2.17712 + 3.77089i 0.169489 + 0.293563i
\(166\) 1.35425 2.34563i 0.105110 0.182056i
\(167\) −11.2288 −0.868907 −0.434454 0.900694i \(-0.643059\pi\)
−0.434454 + 0.900694i \(0.643059\pi\)
\(168\) −7.00000 −0.540062
\(169\) 12.0000 0.923077
\(170\) −4.93725 + 8.55157i −0.378670 + 0.655876i
\(171\) 11.2915 + 19.5575i 0.863483 + 1.49560i
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) 0.145751 0.252449i 0.0110813 0.0191933i −0.860432 0.509566i \(-0.829806\pi\)
0.871513 + 0.490373i \(0.163139\pi\)
\(174\) −16.6458 −1.26191
\(175\) −6.06275 −0.458301
\(176\) 1.00000 0.0753778
\(177\) −6.14575 + 10.6448i −0.461943 + 0.800109i
\(178\) 3.29150 + 5.70105i 0.246709 + 0.427312i
\(179\) 9.96863 + 17.2662i 0.745090 + 1.29053i 0.950153 + 0.311785i \(0.100927\pi\)
−0.205062 + 0.978749i \(0.565740\pi\)
\(180\) 3.29150 5.70105i 0.245334 0.424931i
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 6.61438 + 11.4564i 0.490290 + 0.849208i
\(183\) 37.8118 2.79513
\(184\) 0.822876 1.42526i 0.0606632 0.105072i
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) −5.29150 9.16515i −0.387992 0.672022i
\(187\) −3.00000 + 5.19615i −0.219382 + 0.379980i
\(188\) 2.70850 0.197537
\(189\) −3.50000 + 6.06218i −0.254588 + 0.440959i
\(190\) −9.29150 −0.674076
\(191\) 1.35425 2.34563i 0.0979900 0.169724i −0.812863 0.582456i \(-0.802092\pi\)
0.910853 + 0.412732i \(0.135425\pi\)
\(192\) −1.32288 2.29129i −0.0954703 0.165359i
\(193\) −12.7601 22.1012i −0.918494 1.59088i −0.801703 0.597722i \(-0.796073\pi\)
−0.116791 0.993157i \(-0.537261\pi\)
\(194\) −8.14575 + 14.1089i −0.584831 + 1.01296i
\(195\) −21.7712 −1.55907
\(196\) −3.50000 + 6.06218i −0.250000 + 0.433013i
\(197\) −12.8745 −0.917271 −0.458635 0.888625i \(-0.651662\pi\)
−0.458635 + 0.888625i \(0.651662\pi\)
\(198\) 2.00000 3.46410i 0.142134 0.246183i
\(199\) −2.11438 3.66221i −0.149884 0.259607i 0.781300 0.624155i \(-0.214557\pi\)
−0.931185 + 0.364548i \(0.881223\pi\)
\(200\) −1.14575 1.98450i −0.0810169 0.140325i
\(201\) 15.7915 27.3517i 1.11385 1.92924i
\(202\) −3.00000 −0.211079
\(203\) −8.32288 + 14.4156i −0.584151 + 1.01178i
\(204\) 15.8745 1.11144
\(205\) 9.00000 15.5885i 0.628587 1.08875i
\(206\) −1.46863 2.54374i −0.102324 0.177231i
\(207\) −3.29150 5.70105i −0.228775 0.396250i
\(208\) −2.50000 + 4.33013i −0.173344 + 0.300240i
\(209\) −5.64575 −0.390525
\(210\) −5.76013 9.97684i −0.397487 0.688467i
\(211\) 0.937254 0.0645232 0.0322616 0.999479i \(-0.489729\pi\)
0.0322616 + 0.999479i \(0.489729\pi\)
\(212\) −0.822876 + 1.42526i −0.0565153 + 0.0978874i
\(213\) −5.76013 9.97684i −0.394678 0.683602i
\(214\) −5.46863 9.47194i −0.373828 0.647488i
\(215\) −3.29150 + 5.70105i −0.224479 + 0.388808i
\(216\) −2.64575 −0.180021
\(217\) −10.5830 −0.718421
\(218\) 10.5830 0.716772
\(219\) −0.468627 + 0.811686i −0.0316669 + 0.0548486i
\(220\) 0.822876 + 1.42526i 0.0554783 + 0.0960912i
\(221\) −15.0000 25.9808i −1.00901 1.74766i
\(222\) 4.82288 8.35347i 0.323690 0.560648i
\(223\) −17.6458 −1.18165 −0.590823 0.806801i \(-0.701197\pi\)
−0.590823 + 0.806801i \(0.701197\pi\)
\(224\) −2.64575 −0.176777
\(225\) −9.16601 −0.611067
\(226\) −9.14575 + 15.8409i −0.608366 + 1.05372i
\(227\) 1.35425 + 2.34563i 0.0898846 + 0.155685i 0.907462 0.420134i \(-0.138017\pi\)
−0.817578 + 0.575818i \(0.804683\pi\)
\(228\) 7.46863 + 12.9360i 0.494622 + 0.856710i
\(229\) 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i \(-0.656030\pi\)
0.999442 0.0334101i \(-0.0106368\pi\)
\(230\) 2.70850 0.178593
\(231\) −3.50000 6.06218i −0.230283 0.398862i
\(232\) −6.29150 −0.413057
\(233\) −0.531373 + 0.920365i −0.0348114 + 0.0602951i −0.882906 0.469549i \(-0.844416\pi\)
0.848095 + 0.529845i \(0.177750\pi\)
\(234\) 10.0000 + 17.3205i 0.653720 + 1.13228i
\(235\) 2.22876 + 3.86032i 0.145388 + 0.251819i
\(236\) −2.32288 + 4.02334i −0.151206 + 0.261897i
\(237\) −7.00000 −0.454699
\(238\) 7.93725 13.7477i 0.514496 0.891133i
\(239\) −17.2288 −1.11444 −0.557218 0.830366i \(-0.688131\pi\)
−0.557218 + 0.830366i \(0.688131\pi\)
\(240\) 2.17712 3.77089i 0.140533 0.243410i
\(241\) 12.4059 + 21.4876i 0.799133 + 1.38414i 0.920181 + 0.391492i \(0.128041\pi\)
−0.121048 + 0.992647i \(0.538626\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 10.5830 18.3303i 0.678900 1.17589i
\(244\) 14.2915 0.914920
\(245\) −11.5203 −0.736002
\(246\) −28.9373 −1.84497
\(247\) 14.1144 24.4468i 0.898076 1.55551i
\(248\) −2.00000 3.46410i −0.127000 0.219971i
\(249\) −3.58301 6.20595i −0.227064 0.393286i
\(250\) 6.00000 10.3923i 0.379473 0.657267i
\(251\) −3.29150 −0.207758 −0.103879 0.994590i \(-0.533125\pi\)
−0.103879 + 0.994590i \(0.533125\pi\)
\(252\) −5.29150 + 9.16515i −0.333333 + 0.577350i
\(253\) 1.64575 0.103467
\(254\) 7.96863 13.8021i 0.499996 0.866019i
\(255\) 13.0627 + 22.6253i 0.818021 + 1.41685i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.7915 18.6914i 0.673155 1.16594i −0.303849 0.952720i \(-0.598272\pi\)
0.977004 0.213219i \(-0.0683948\pi\)
\(258\) 10.5830 0.658869
\(259\) −4.82288 8.35347i −0.299679 0.519059i
\(260\) −8.22876 −0.510326
\(261\) −12.5830 + 21.7944i −0.778868 + 1.34904i
\(262\) 5.17712 + 8.96704i 0.319844 + 0.553986i
\(263\) −9.96863 17.2662i −0.614692 1.06468i −0.990438 0.137955i \(-0.955947\pi\)
0.375747 0.926722i \(-0.377386\pi\)
\(264\) 1.32288 2.29129i 0.0814174 0.141019i
\(265\) −2.70850 −0.166382
\(266\) 14.9373 0.915862
\(267\) 17.4170 1.06590
\(268\) 5.96863 10.3380i 0.364592 0.631492i
\(269\) −2.70850 4.69126i −0.165140 0.286031i 0.771565 0.636151i \(-0.219474\pi\)
−0.936705 + 0.350120i \(0.886141\pi\)
\(270\) −2.17712 3.77089i −0.132496 0.229489i
\(271\) 1.03137 1.78639i 0.0626514 0.108515i −0.832998 0.553275i \(-0.813378\pi\)
0.895650 + 0.444760i \(0.146711\pi\)
\(272\) 6.00000 0.363803
\(273\) 35.0000 2.11830
\(274\) 12.8745 0.777777
\(275\) 1.14575 1.98450i 0.0690914 0.119670i
\(276\) −2.17712 3.77089i −0.131047 0.226981i
\(277\) 11.1458 + 19.3050i 0.669683 + 1.15993i 0.977993 + 0.208639i \(0.0669035\pi\)
−0.308309 + 0.951286i \(0.599763\pi\)
\(278\) −2.00000 + 3.46410i −0.119952 + 0.207763i
\(279\) −16.0000 −0.957895
\(280\) −2.17712 3.77089i −0.130108 0.225354i
\(281\) −22.9373 −1.36832 −0.684161 0.729331i \(-0.739831\pi\)
−0.684161 + 0.729331i \(0.739831\pi\)
\(282\) 3.58301 6.20595i 0.213365 0.369559i
\(283\) 1.17712 + 2.03884i 0.0699728 + 0.121196i 0.898889 0.438176i \(-0.144375\pi\)
−0.828916 + 0.559373i \(0.811042\pi\)
\(284\) −2.17712 3.77089i −0.129189 0.223761i
\(285\) −12.2915 + 21.2895i −0.728086 + 1.26108i
\(286\) −5.00000 −0.295656
\(287\) −14.4686 + 25.0604i −0.854056 + 1.47927i
\(288\) −4.00000 −0.235702
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) −5.17712 8.96704i −0.304011 0.526563i
\(291\) 21.5516 + 37.3285i 1.26338 + 2.18824i
\(292\) −0.177124 + 0.306788i −0.0103654 + 0.0179534i
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 9.26013 + 16.0390i 0.540062 + 0.935414i
\(295\) −7.64575 −0.445153
\(296\) 1.82288 3.15731i 0.105952 0.183515i
\(297\) −1.32288 2.29129i −0.0767610 0.132954i
\(298\) −7.64575 13.2428i −0.442906 0.767137i
\(299\) −4.11438 + 7.12631i −0.237941 + 0.412125i
\(300\) −6.06275 −0.350033
\(301\) 5.29150 9.16515i 0.304997 0.528271i
\(302\) 8.64575 0.497507
\(303\) −3.96863 + 6.87386i −0.227992 + 0.394893i
\(304\) 2.82288 + 4.88936i 0.161903 + 0.280424i
\(305\) 11.7601 + 20.3691i 0.673383 + 1.16633i
\(306\) 12.0000 20.7846i 0.685994 1.18818i
\(307\) 22.2288 1.26866 0.634331 0.773062i \(-0.281276\pi\)
0.634331 + 0.773062i \(0.281276\pi\)
\(308\) −1.32288 2.29129i −0.0753778 0.130558i
\(309\) −7.77124 −0.442091
\(310\) 3.29150 5.70105i 0.186945 0.323798i
\(311\) −0.531373 0.920365i −0.0301314 0.0521891i 0.850566 0.525868i \(-0.176259\pi\)
−0.880698 + 0.473678i \(0.842926\pi\)
\(312\) 6.61438 + 11.4564i 0.374465 + 0.648593i
\(313\) −11.7915 + 20.4235i −0.666495 + 1.15440i 0.312382 + 0.949956i \(0.398873\pi\)
−0.978878 + 0.204447i \(0.934460\pi\)
\(314\) −21.1660 −1.19447
\(315\) −17.4170 −0.981336
\(316\) −2.64575 −0.148835
\(317\) −6.00000 + 10.3923i −0.336994 + 0.583690i −0.983866 0.178908i \(-0.942743\pi\)
0.646872 + 0.762598i \(0.276077\pi\)
\(318\) 2.17712 + 3.77089i 0.122087 + 0.211461i
\(319\) −3.14575 5.44860i −0.176128 0.305063i
\(320\) 0.822876 1.42526i 0.0460001 0.0796746i
\(321\) −28.9373 −1.61512
\(322\) −4.35425 −0.242653
\(323\) −33.8745 −1.88483
\(324\) 2.50000 4.33013i 0.138889 0.240563i
\(325\) 5.72876 + 9.92250i 0.317774 + 0.550401i
\(326\) 0.322876 + 0.559237i 0.0178824 + 0.0309733i
\(327\) 14.0000 24.2487i 0.774202 1.34096i
\(328\) −10.9373 −0.603909
\(329\) −3.58301 6.20595i −0.197537 0.342145i
\(330\) 4.35425 0.239694
\(331\) 10.3229 17.8797i 0.567397 0.982760i −0.429426 0.903102i \(-0.641284\pi\)
0.996822 0.0796575i \(-0.0253827\pi\)
\(332\) −1.35425 2.34563i −0.0743241 0.128733i
\(333\) −7.29150 12.6293i −0.399572 0.692079i
\(334\) −5.61438 + 9.72439i −0.307205 + 0.532095i
\(335\) 19.6458 1.07336
\(336\) −3.50000 + 6.06218i −0.190941 + 0.330719i
\(337\) 9.06275 0.493679 0.246840 0.969056i \(-0.420608\pi\)
0.246840 + 0.969056i \(0.420608\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 24.1974 + 41.9111i 1.31422 + 2.27630i
\(340\) 4.93725 + 8.55157i 0.267760 + 0.463774i
\(341\) 2.00000 3.46410i 0.108306 0.187592i
\(342\) 22.5830 1.22115
\(343\) 18.5203 1.00000
\(344\) 4.00000 0.215666
\(345\) 3.58301 6.20595i 0.192903 0.334117i
\(346\) −0.145751 0.252449i −0.00783564 0.0135717i
\(347\) 10.4059 + 18.0235i 0.558617 + 0.967553i 0.997612 + 0.0690636i \(0.0220011\pi\)
−0.438995 + 0.898489i \(0.644666\pi\)
\(348\) −8.32288 + 14.4156i −0.446153 + 0.772760i
\(349\) −1.87451 −0.100340 −0.0501701 0.998741i \(-0.515976\pi\)
−0.0501701 + 0.998741i \(0.515976\pi\)
\(350\) −3.03137 + 5.25049i −0.162034 + 0.280651i
\(351\) 13.2288 0.706099
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) −3.58301 6.20595i −0.190704 0.330309i 0.754780 0.655978i \(-0.227744\pi\)
−0.945484 + 0.325669i \(0.894410\pi\)
\(354\) 6.14575 + 10.6448i 0.326643 + 0.565762i
\(355\) 3.58301 6.20595i 0.190166 0.329377i
\(356\) 6.58301 0.348899
\(357\) −21.0000 36.3731i −1.11144 1.92507i
\(358\) 19.9373 1.05372
\(359\) 12.9686 22.4623i 0.684458 1.18552i −0.289149 0.957284i \(-0.593372\pi\)
0.973607 0.228232i \(-0.0732944\pi\)
\(360\) −3.29150 5.70105i −0.173477 0.300472i
\(361\) −6.43725 11.1497i −0.338803 0.586824i
\(362\) −5.00000 + 8.66025i −0.262794 + 0.455173i
\(363\) 2.64575 0.138866
\(364\) 13.2288 0.693375
\(365\) −0.583005 −0.0305159
\(366\) 18.9059 32.7459i 0.988226 1.71166i
\(367\) 18.1144 + 31.3750i 0.945563 + 1.63776i 0.754620 + 0.656162i \(0.227821\pi\)
0.190943 + 0.981601i \(0.438846\pi\)
\(368\) −0.822876 1.42526i −0.0428954 0.0742969i
\(369\) −21.8745 + 37.8878i −1.13874 + 1.97236i
\(370\) 6.00000 0.311925
\(371\) 4.35425 0.226061
\(372\) −10.5830 −0.548703
\(373\) −10.4373 + 18.0779i −0.540421 + 0.936036i 0.458459 + 0.888715i \(0.348402\pi\)
−0.998880 + 0.0473204i \(0.984932\pi\)
\(374\) 3.00000 + 5.19615i 0.155126 + 0.268687i
\(375\) −15.8745 27.4955i −0.819756 1.41986i
\(376\) 1.35425 2.34563i 0.0698400 0.120967i
\(377\) 31.4575 1.62014
\(378\) 3.50000 + 6.06218i 0.180021 + 0.311805i
\(379\) 6.06275 0.311422 0.155711 0.987803i \(-0.450233\pi\)
0.155711 + 0.987803i \(0.450233\pi\)
\(380\) −4.64575 + 8.04668i −0.238322 + 0.412786i
\(381\) −21.0830 36.5168i −1.08012 1.87081i
\(382\) −1.35425 2.34563i −0.0692894 0.120013i
\(383\) −12.0516 + 20.8740i −0.615810 + 1.06661i 0.374432 + 0.927254i \(0.377838\pi\)
−0.990242 + 0.139359i \(0.955496\pi\)
\(384\) −2.64575 −0.135015
\(385\) 2.17712 3.77089i 0.110957 0.192182i
\(386\) −25.5203 −1.29895
\(387\) 8.00000 13.8564i 0.406663 0.704361i
\(388\) 8.14575 + 14.1089i 0.413538 + 0.716269i
\(389\) −13.4059 23.2197i −0.679705 1.17728i −0.975070 0.221899i \(-0.928774\pi\)
0.295364 0.955385i \(-0.404559\pi\)
\(390\) −10.8856 + 18.8544i −0.551215 + 0.954732i
\(391\) 9.87451 0.499375
\(392\) 3.50000 + 6.06218i 0.176777 + 0.306186i
\(393\) 27.3948 1.38188
\(394\) −6.43725 + 11.1497i −0.324304 + 0.561711i
\(395\) −2.17712 3.77089i −0.109543 0.189734i
\(396\) −2.00000 3.46410i −0.100504 0.174078i
\(397\) 5.58301 9.67005i 0.280203 0.485326i −0.691232 0.722633i \(-0.742932\pi\)
0.971435 + 0.237307i \(0.0762649\pi\)
\(398\) −4.22876 −0.211968
\(399\) 19.7601 34.2255i 0.989244 1.71342i
\(400\) −2.29150 −0.114575
\(401\) −10.7915 + 18.6914i −0.538902 + 0.933406i 0.460062 + 0.887887i \(0.347827\pi\)
−0.998963 + 0.0455185i \(0.985506\pi\)
\(402\) −15.7915 27.3517i −0.787609 1.36418i
\(403\) 10.0000 + 17.3205i 0.498135 + 0.862796i
\(404\) −1.50000 + 2.59808i −0.0746278 + 0.129259i
\(405\) 8.22876 0.408890
\(406\) 8.32288 + 14.4156i 0.413057 + 0.715436i
\(407\) 3.64575 0.180713
\(408\) 7.93725 13.7477i 0.392953 0.680614i
\(409\) −1.53137 2.65242i −0.0757215 0.131154i 0.825678 0.564141i \(-0.190793\pi\)
−0.901400 + 0.432988i \(0.857459\pi\)
\(410\) −9.00000 15.5885i −0.444478 0.769859i
\(411\) 17.0314 29.4992i 0.840096 1.45509i
\(412\) −2.93725 −0.144708
\(413\) 12.2915 0.604825
\(414\) −6.58301 −0.323537
\(415\) 2.22876 3.86032i 0.109405 0.189496i
\(416\) 2.50000 + 4.33013i 0.122573 + 0.212302i
\(417\) 5.29150 + 9.16515i 0.259126 + 0.448819i
\(418\) −2.82288 + 4.88936i −0.138071 + 0.239147i
\(419\) −9.87451 −0.482401 −0.241201 0.970475i \(-0.577541\pi\)
−0.241201 + 0.970475i \(0.577541\pi\)
\(420\) −11.5203 −0.562131
\(421\) 9.16601 0.446724 0.223362 0.974736i \(-0.428297\pi\)
0.223362 + 0.974736i \(0.428297\pi\)
\(422\) 0.468627 0.811686i 0.0228124 0.0395122i
\(423\) −5.41699 9.38251i −0.263383 0.456193i
\(424\) 0.822876 + 1.42526i 0.0399624 + 0.0692169i
\(425\) 6.87451 11.9070i 0.333463 0.577574i
\(426\) −11.5203 −0.558158
\(427\) −18.9059 32.7459i −0.914920 1.58469i
\(428\) −10.9373 −0.528672
\(429\) −6.61438 + 11.4564i −0.319345 + 0.553122i
\(430\) 3.29150 + 5.70105i 0.158730 + 0.274929i
\(431\) −14.6144 25.3128i −0.703950 1.21928i −0.967069 0.254514i \(-0.918085\pi\)
0.263119 0.964763i \(-0.415249\pi\)
\(432\) −1.32288 + 2.29129i −0.0636469 + 0.110240i
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −5.29150 + 9.16515i −0.254000 + 0.439941i
\(435\) −27.3948 −1.31348
\(436\) 5.29150 9.16515i 0.253417 0.438931i
\(437\) 4.64575 + 8.04668i 0.222236 + 0.384925i
\(438\) 0.468627 + 0.811686i 0.0223919 + 0.0387838i
\(439\) −1.96863 + 3.40976i −0.0939574 + 0.162739i −0.909173 0.416419i \(-0.863285\pi\)
0.815216 + 0.579158i \(0.196618\pi\)
\(440\) 1.64575 0.0784581
\(441\) 28.0000 1.33333
\(442\) −30.0000 −1.42695
\(443\) −17.2288 + 29.8411i −0.818563 + 1.41779i 0.0881781 + 0.996105i \(0.471896\pi\)
−0.906741 + 0.421688i \(0.861438\pi\)
\(444\) −4.82288 8.35347i −0.228884 0.396438i
\(445\) 5.41699 + 9.38251i 0.256790 + 0.444774i
\(446\) −8.82288 + 15.2817i −0.417775 + 0.723608i
\(447\) −40.4575 −1.91357
\(448\) −1.32288 + 2.29129i −0.0625000 + 0.108253i
\(449\) −21.8745 −1.03232 −0.516161 0.856492i \(-0.672639\pi\)
−0.516161 + 0.856492i \(0.672639\pi\)
\(450\) −4.58301 + 7.93800i −0.216045 + 0.374201i
\(451\) −5.46863 9.47194i −0.257508 0.446016i
\(452\) 9.14575 + 15.8409i 0.430180 + 0.745094i
\(453\) 11.4373 19.8099i 0.537369 0.930751i
\(454\) 2.70850 0.127116
\(455\) 10.8856 + 18.8544i 0.510326 + 0.883910i
\(456\) 14.9373 0.699501
\(457\) −1.58301 + 2.74185i −0.0740499 + 0.128258i −0.900673 0.434498i \(-0.856926\pi\)
0.826623 + 0.562756i \(0.190259\pi\)
\(458\) −8.00000 13.8564i −0.373815 0.647467i
\(459\) −7.93725 13.7477i −0.370479 0.641689i
\(460\) 1.35425 2.34563i 0.0631422 0.109365i
\(461\) 10.1660 0.473478 0.236739 0.971573i \(-0.423921\pi\)
0.236739 + 0.971573i \(0.423921\pi\)
\(462\) −7.00000 −0.325669
\(463\) 30.4575 1.41548 0.707740 0.706473i \(-0.249715\pi\)
0.707740 + 0.706473i \(0.249715\pi\)
\(464\) −3.14575 + 5.44860i −0.146038 + 0.252945i
\(465\) −8.70850 15.0836i −0.403847 0.699483i
\(466\) 0.531373 + 0.920365i 0.0246154 + 0.0426351i
\(467\) −10.6458 + 18.4390i −0.492627 + 0.853254i −0.999964 0.00849322i \(-0.997296\pi\)
0.507337 + 0.861748i \(0.330630\pi\)
\(468\) 20.0000 0.924500
\(469\) −31.5830 −1.45837
\(470\) 4.45751 0.205610
\(471\) −28.0000 + 48.4974i −1.29017 + 2.23464i
\(472\) 2.32288 + 4.02334i 0.106919 + 0.185189i
\(473\) 2.00000 + 3.46410i 0.0919601 + 0.159280i
\(474\) −3.50000 + 6.06218i −0.160760 + 0.278445i
\(475\) 12.9373 0.593602
\(476\) −7.93725 13.7477i −0.363803 0.630126i
\(477\) 6.58301 0.301415
\(478\) −8.61438 + 14.9205i −0.394012 + 0.682450i
\(479\) 5.03137 + 8.71459i 0.229889 + 0.398180i 0.957775 0.287518i \(-0.0928303\pi\)
−0.727886 + 0.685698i \(0.759497\pi\)
\(480\) −2.17712 3.77089i −0.0993717 0.172117i
\(481\) −9.11438 + 15.7866i −0.415580 + 0.719805i
\(482\) 24.8118 1.13014
\(483\) −5.76013 + 9.97684i −0.262095 + 0.453962i
\(484\) 1.00000 0.0454545
\(485\) −13.4059 + 23.2197i −0.608730 + 1.05435i
\(486\) −10.5830 18.3303i −0.480055 0.831479i
\(487\) 4.70850 + 8.15536i 0.213362 + 0.369554i 0.952765 0.303709i \(-0.0982252\pi\)
−0.739402 + 0.673264i \(0.764892\pi\)
\(488\) 7.14575 12.3768i 0.323473 0.560272i
\(489\) 1.70850 0.0772609
\(490\) −5.76013 + 9.97684i −0.260216 + 0.450708i
\(491\) 21.2915 0.960872 0.480436 0.877030i \(-0.340478\pi\)
0.480436 + 0.877030i \(0.340478\pi\)
\(492\) −14.4686 + 25.0604i −0.652296 + 1.12981i
\(493\) −18.8745 32.6916i −0.850065 1.47236i
\(494\) −14.1144 24.4468i −0.635036 1.09991i
\(495\) 3.29150 5.70105i 0.147942 0.256243i
\(496\) −4.00000 −0.179605
\(497\) −5.76013 + 9.97684i −0.258377 + 0.447522i
\(498\) −7.16601 −0.321117
\(499\) 6.93725 12.0157i 0.310554 0.537896i −0.667928 0.744226i \(-0.732819\pi\)
0.978482 + 0.206330i \(0.0661521\pi\)
\(500\) −6.00000 10.3923i −0.268328 0.464758i
\(501\) 14.8542 + 25.7283i 0.663639 + 1.14946i
\(502\) −1.64575 + 2.85052i −0.0734535 + 0.127225i
\(503\) −4.06275 −0.181149 −0.0905744 0.995890i \(-0.528870\pi\)
−0.0905744 + 0.995890i \(0.528870\pi\)
\(504\) 5.29150 + 9.16515i 0.235702 + 0.408248i
\(505\) −4.93725 −0.219705
\(506\) 0.822876 1.42526i 0.0365813 0.0633606i
\(507\) −15.8745 27.4955i −0.705012 1.22112i
\(508\) −7.96863 13.8021i −0.353551 0.612368i
\(509\) 0.291503 0.504897i 0.0129206 0.0223792i −0.859493 0.511148i \(-0.829220\pi\)
0.872413 + 0.488769i \(0.162554\pi\)
\(510\) 26.1255 1.15686
\(511\) 0.937254 0.0414617
\(512\) −1.00000 −0.0441942
\(513\) 7.46863 12.9360i 0.329748 0.571140i
\(514\) −10.7915 18.6914i −0.475993 0.824444i
\(515\) −2.41699 4.18636i −0.106506 0.184473i
\(516\) 5.29150 9.16515i 0.232945 0.403473i
\(517\) 2.70850 0.119120
\(518\) −9.64575 −0.423810
\(519\) −0.771243 −0.0338538
\(520\) −4.11438 + 7.12631i −0.180427 + 0.312509i
\(521\) 16.9373 + 29.3362i 0.742035 + 1.28524i 0.951567 + 0.307440i \(0.0994723\pi\)
−0.209533 + 0.977802i \(0.567194\pi\)
\(522\) 12.5830 + 21.7944i 0.550743 + 0.953915i
\(523\) 10.7601 18.6371i 0.470508 0.814943i −0.528923 0.848670i \(-0.677404\pi\)
0.999431 + 0.0337264i \(0.0107375\pi\)
\(524\) 10.3542 0.452327
\(525\) 8.02026 + 13.8915i 0.350033 + 0.606275i
\(526\) −19.9373 −0.869306
\(527\) 12.0000 20.7846i 0.522728 0.905392i
\(528\) −1.32288 2.29129i −0.0575708 0.0997155i
\(529\) 10.1458 + 17.5730i 0.441120 + 0.764042i
\(530\) −1.35425 + 2.34563i −0.0588248 + 0.101888i
\(531\) 18.5830 0.806434
\(532\) 7.46863 12.9360i 0.323806 0.560849i
\(533\) 54.6863 2.36873
\(534\) 8.70850 15.0836i 0.376854 0.652729i
\(535\) −9.00000 15.5885i −0.389104 0.673948i
\(536\) −5.96863 10.3380i −0.257805 0.446532i
\(537\) 26.3745 45.6820i 1.13814 1.97132i
\(538\) −5.41699 −0.233543
\(539\) −3.50000 + 6.06218i −0.150756 + 0.261116i
\(540\) −4.35425 −0.187377
\(541\) −1.14575 + 1.98450i −0.0492597 + 0.0853203i −0.889604 0.456733i \(-0.849020\pi\)
0.840344 + 0.542053i \(0.182353\pi\)
\(542\) −1.03137 1.78639i −0.0443013 0.0767320i
\(543\) 13.2288 + 22.9129i 0.567700 + 0.983286i
\(544\) 3.00000 5.19615i 0.128624 0.222783i
\(545\) 17.4170 0.746062
\(546\) 17.5000 30.3109i 0.748931 1.29719i
\(547\) −9.52026 −0.407057 −0.203528 0.979069i \(-0.565241\pi\)
−0.203528 + 0.979069i \(0.565241\pi\)
\(548\) 6.43725 11.1497i 0.274986 0.476289i
\(549\) −28.5830 49.5072i −1.21989 2.11292i
\(550\) −1.14575 1.98450i −0.0488550 0.0846193i
\(551\) 17.7601 30.7614i 0.756607 1.31048i
\(552\) −4.35425 −0.185329
\(553\) 3.50000 + 6.06218i 0.148835 + 0.257790i
\(554\) 22.2915 0.947075
\(555\) 7.93725 13.7477i 0.336918 0.583559i
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) 15.8745 + 27.4955i 0.672624 + 1.16502i 0.977157 + 0.212518i \(0.0681664\pi\)
−0.304533 + 0.952502i \(0.598500\pi\)
\(558\) −8.00000 + 13.8564i −0.338667 + 0.586588i
\(559\) −20.0000 −0.845910
\(560\) −4.35425 −0.184001
\(561\) 15.8745 0.670222
\(562\) −11.4686 + 19.8642i −0.483775 + 0.837923i
\(563\) −14.4686 25.0604i −0.609780 1.05617i −0.991276 0.131800i \(-0.957924\pi\)
0.381496 0.924370i \(-0.375409\pi\)
\(564\) −3.58301 6.20595i −0.150872 0.261318i
\(565\) −15.0516 + 26.0702i −0.633227 + 1.09678i
\(566\) 2.35425 0.0989565
\(567\) −13.2288 −0.555556
\(568\) −4.35425 −0.182700
\(569\) −0.583005 + 1.00979i −0.0244409 + 0.0423328i −0.877987 0.478684i \(-0.841114\pi\)
0.853546 + 0.521017i \(0.174447\pi\)
\(570\) 12.2915 + 21.2895i 0.514834 + 0.891719i
\(571\) 14.5314 + 25.1691i 0.608119 + 1.05329i 0.991550 + 0.129724i \(0.0414090\pi\)
−0.383431 + 0.923569i \(0.625258\pi\)
\(572\) −2.50000 + 4.33013i −0.104530 + 0.181052i
\(573\) −7.16601 −0.299364
\(574\) 14.4686 + 25.0604i 0.603909 + 1.04600i
\(575\) −3.77124 −0.157272
\(576\) −2.00000 + 3.46410i −0.0833333 + 0.144338i
\(577\) −13.7288 23.7789i −0.571536 0.989929i −0.996409 0.0846757i \(-0.973015\pi\)
0.424873 0.905253i \(-0.360319\pi\)
\(578\) 9.50000 + 16.4545i 0.395148 + 0.684416i
\(579\) −33.7601 + 58.4743i −1.40302 + 2.43011i
\(580\) −10.3542 −0.429937
\(581\) −3.58301 + 6.20595i −0.148648 + 0.257466i
\(582\) 43.1033 1.78669
\(583\) −0.822876 + 1.42526i −0.0340800 + 0.0590283i
\(584\) 0.177124 + 0.306788i 0.00732946 + 0.0126950i
\(585\) 16.4575 + 28.5052i 0.680434 + 1.17855i
\(586\) 6.00000 10.3923i 0.247858 0.429302i
\(587\) 7.93725 0.327606 0.163803 0.986493i \(-0.447624\pi\)
0.163803 + 0.986493i \(0.447624\pi\)
\(588\) 18.5203 0.763763
\(589\) 22.5830 0.930517
\(590\) −3.82288 + 6.62141i −0.157385 + 0.272599i
\(591\) 17.0314 + 29.4992i 0.700577 + 1.21344i
\(592\) −1.82288 3.15731i −0.0749197 0.129765i
\(593\) −3.53137 + 6.11652i −0.145016 + 0.251175i −0.929379 0.369127i \(-0.879657\pi\)
0.784363 + 0.620302i \(0.212990\pi\)
\(594\) −2.64575 −0.108556
\(595\) 13.0627 22.6253i 0.535520 0.927549i
\(596\) −15.2915 −0.626364
\(597\) −5.59412 + 9.68930i −0.228952 + 0.396557i
\(598\) 4.11438 + 7.12631i 0.168249 + 0.291417i
\(599\) −21.8745 37.8878i −0.893768 1.54805i −0.835322 0.549761i \(-0.814719\pi\)
−0.0584464 0.998291i \(-0.518615\pi\)
\(600\) −3.03137 + 5.25049i −0.123755 + 0.214350i
\(601\) −3.41699 −0.139382 −0.0696911 0.997569i \(-0.522201\pi\)
−0.0696911 + 0.997569i \(0.522201\pi\)
\(602\) −5.29150 9.16515i −0.215666 0.373544i
\(603\) −47.7490 −1.94449
\(604\) 4.32288 7.48744i 0.175895 0.304660i
\(605\) 0.822876 + 1.42526i 0.0334547 + 0.0579452i
\(606\) 3.96863 + 6.87386i 0.161214 + 0.279232i
\(607\) −5.35425 + 9.27383i −0.217322 + 0.376413i −0.953988 0.299843i \(-0.903066\pi\)
0.736666 + 0.676257i \(0.236399\pi\)
\(608\) 5.64575 0.228965
\(609\) 44.0405 1.78461
\(610\) 23.5203 0.952307
\(611\) −6.77124 + 11.7281i −0.273935 + 0.474470i
\(612\) −12.0000 20.7846i −0.485071 0.840168i
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) 11.1144 19.2507i 0.448540 0.776894i
\(615\) −47.6235 −1.92037
\(616\) −2.64575 −0.106600
\(617\) −5.70850 −0.229815 −0.114908 0.993376i \(-0.536657\pi\)
−0.114908 + 0.993376i \(0.536657\pi\)
\(618\) −3.88562 + 6.73009i −0.156303 + 0.270724i
\(619\) −6.70850 11.6195i −0.269637 0.467025i 0.699131 0.714994i \(-0.253570\pi\)
−0.968768 + 0.247968i \(0.920237\pi\)
\(620\) −3.29150 5.70105i −0.132190 0.228960i
\(621\) −2.17712 + 3.77089i −0.0873650 + 0.151321i
\(622\) −1.06275 −0.0426122
\(623\) −8.70850 15.0836i −0.348899 0.604310i
\(624\) 13.2288 0.529574
\(625\) 4.14575 7.18065i 0.165830 0.287226i
\(626\) 11.7915 + 20.4235i 0.471283 + 0.816286i
\(627\) 7.46863 + 12.9360i 0.298268 + 0.516616i
\(628\) −10.5830 + 18.3303i −0.422308 + 0.731459i
\(629\) 21.8745 0.872194
\(630\) −8.70850 + 15.0836i −0.346955 + 0.600943i
\(631\) −12.8118 −0.510028 −0.255014 0.966937i \(-0.582080\pi\)
−0.255014 + 0.966937i \(0.582080\pi\)
\(632\) −1.32288 + 2.29129i −0.0526212 + 0.0911425i
\(633\) −1.23987 2.14752i −0.0492804 0.0853562i
\(634\) 6.00000 + 10.3923i 0.238290 + 0.412731i
\(635\) 13.1144 22.7148i 0.520428 0.901408i
\(636\) 4.35425 0.172657
\(637\) −17.5000 30.3109i −0.693375 1.20096i
\(638\) −6.29150 −0.249083
\(639\) −8.70850 + 15.0836i −0.344503 + 0.596696i
\(640\) −0.822876 1.42526i −0.0325270 0.0563384i
\(641\) −6.43725 11.1497i −0.254256 0.440385i 0.710437 0.703761i \(-0.248497\pi\)
−0.964693 + 0.263376i \(0.915164\pi\)
\(642\) −14.4686 + 25.0604i −0.571031 + 0.989055i
\(643\) −30.5203 −1.20360 −0.601801 0.798646i \(-0.705550\pi\)
−0.601801 + 0.798646i \(0.705550\pi\)
\(644\) −2.17712 + 3.77089i −0.0857907 + 0.148594i
\(645\) 17.4170 0.685793
\(646\) −16.9373 + 29.3362i −0.666387 + 1.15422i
\(647\) 4.40588 + 7.63121i 0.173213 + 0.300014i 0.939541 0.342435i \(-0.111252\pi\)
−0.766328 + 0.642449i \(0.777918\pi\)
\(648\) −2.50000 4.33013i −0.0982093 0.170103i
\(649\) −2.32288 + 4.02334i −0.0911808 + 0.157930i
\(650\) 11.4575 0.449401
\(651\) 14.0000 + 24.2487i 0.548703 + 0.950382i
\(652\) 0.645751 0.0252896
\(653\) −3.82288 + 6.62141i −0.149601 + 0.259116i −0.931080 0.364815i \(-0.881132\pi\)
0.781479 + 0.623931i \(0.214465\pi\)
\(654\) −14.0000 24.2487i −0.547443 0.948200i
\(655\) 8.52026 + 14.7575i 0.332914 + 0.576624i
\(656\) −5.46863 + 9.47194i −0.213514 + 0.369817i
\(657\) 1.41699 0.0552822
\(658\) −7.16601 −0.279360
\(659\) −6.58301 −0.256437 −0.128219 0.991746i \(-0.540926\pi\)
−0.128219 + 0.991746i \(0.540926\pi\)
\(660\) 2.17712 3.77089i 0.0847445 0.146782i
\(661\) −3.70850 6.42331i −0.144244 0.249838i 0.784847 0.619690i \(-0.212742\pi\)
−0.929091 + 0.369852i \(0.879408\pi\)
\(662\) −10.3229 17.8797i −0.401210 0.694916i
\(663\) −39.6863 + 68.7386i −1.54129 + 2.66959i
\(664\) −2.70850 −0.105110
\(665\) 24.5830 0.953288
\(666\) −14.5830 −0.565080
\(667\) −5.17712 + 8.96704i −0.200459 + 0.347205i
\(668\) 5.61438 + 9.72439i 0.217227 + 0.376248i
\(669\) 23.3431 + 40.4315i 0.902498 + 1.56317i
\(670\) 9.82288 17.0137i 0.379491 0.657297i
\(671\) 14.2915 0.551717
\(672\) 3.50000 + 6.06218i 0.135015 + 0.233854i
\(673\) 0.937254 0.0361285 0.0180642 0.999837i \(-0.494250\pi\)
0.0180642 + 0.999837i \(0.494250\pi\)
\(674\) 4.53137 7.84857i 0.174542 0.302316i
\(675\) 3.03137 + 5.25049i 0.116678 + 0.202092i
\(676\) −6.00000 10.3923i −0.230769 0.399704i
\(677\) 16.9373 29.3362i 0.650952 1.12748i −0.331941 0.943300i \(-0.607703\pi\)
0.982892 0.184181i \(-0.0589632\pi\)
\(678\) 48.3948 1.85859
\(679\) 21.5516 37.3285i 0.827076 1.43254i
\(680\) 9.87451 0.378670
\(681\) 3.58301 6.20595i 0.137301 0.237812i
\(682\) −2.00000 3.46410i −0.0765840 0.132647i
\(683\) −0.968627 1.67771i −0.0370635 0.0641958i 0.846899 0.531754i \(-0.178467\pi\)
−0.883962 + 0.467559i \(0.845134\pi\)
\(684\) 11.2915 19.5575i 0.431741 0.747798i
\(685\) 21.1882 0.809561
\(686\) 9.26013 16.0390i 0.353553 0.612372i
\(687\) −42.3320 −1.61507
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) −4.11438 7.12631i −0.156745 0.271491i
\(690\) −3.58301 6.20595i −0.136403 0.236256i
\(691\) 22.6144 39.1693i 0.860291 1.49007i −0.0113561 0.999936i \(-0.503615\pi\)
0.871648 0.490133i \(-0.163052\pi\)
\(692\) −0.291503 −0.0110813
\(693\) −5.29150 + 9.16515i −0.201008 + 0.348155i
\(694\) 20.8118 0.790004
\(695\) −3.29150 + 5.70105i −0.124854 + 0.216253i
\(696\) 8.32288 + 14.4156i 0.315478 + 0.546424i
\(697\) −32.8118 56.8316i −1.24283 2.15265i
\(698\) −0.937254 + 1.62337i −0.0354756 + 0.0614455i
\(699\) 2.81176 0.106351
\(700\) 3.03137 + 5.25049i 0.114575 + 0.198450i
\(701\) 24.8745 0.939497 0.469749 0.882800i \(-0.344345\pi\)
0.469749 + 0.882800i \(0.344345\pi\)
\(702\) 6.61438 11.4564i 0.249644 0.432395i
\(703\) 10.2915 + 17.8254i 0.388151 + 0.672298i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 5.89674 10.2134i 0.222084 0.384661i
\(706\) −7.16601 −0.269696
\(707\) 7.93725 0.298511
\(708\) 12.2915 0.461943
\(709\) −20.4059 + 35.3440i −0.766359 + 1.32737i 0.173166 + 0.984893i \(0.444600\pi\)
−0.939525 + 0.342480i \(0.888733\pi\)
\(710\) −3.58301 6.20595i −0.134468 0.232905i
\(711\) 5.29150 + 9.16515i 0.198447 + 0.343720i
\(712\) 3.29150 5.70105i 0.123354 0.213656i
\(713\) −6.58301 −0.246535
\(714\) −42.0000 −1.57181
\(715\) −8.22876 −0.307738
\(716\) 9.96863 17.2662i 0.372545 0.645267i
\(717\) 22.7915 + 39.4760i 0.851164 + 1.47426i
\(718\) −12.9686 22.4623i −0.483985 0.838286i
\(719\) −13.9373 + 24.1400i −0.519772 + 0.900271i 0.479964 + 0.877288i \(0.340650\pi\)
−0.999736 + 0.0229831i \(0.992684\pi\)
\(720\) −6.58301 −0.245334
\(721\) 3.88562 + 6.73009i 0.144708 + 0.250642i
\(722\) −12.8745 −0.479140
\(723\) 32.8229 56.8509i 1.22070 2.11431i
\(724\) 5.00000 + 8.66025i 0.185824 + 0.321856i
\(725\) 7.20850 + 12.4855i 0.267717 + 0.463699i
\(726\) 1.32288 2.29129i 0.0490965 0.0850377i
\(727\) −6.70850 −0.248804 −0.124402 0.992232i \(-0.539701\pi\)
−0.124402 + 0.992232i \(0.539701\pi\)
\(728\) 6.61438 11.4564i 0.245145 0.424604i
\(729\) −41.0000 −1.51852
\(730\) −0.291503 + 0.504897i −0.0107890 + 0.0186871i
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) −18.9059 32.7459i −0.698781 1.21033i
\(733\) 5.72876 9.92250i 0.211596 0.366496i −0.740618 0.671926i \(-0.765467\pi\)
0.952214 + 0.305431i \(0.0988004\pi\)
\(734\) 36.2288 1.33723
\(735\) 15.2399 + 26.3962i 0.562131 + 0.973640i
\(736\) −1.64575 −0.0606632
\(737\) 5.96863 10.3380i 0.219857 0.380804i
\(738\) 21.8745 + 37.8878i 0.805212 + 1.39467i
\(739\) −11.9373 20.6759i −0.439119 0.760576i 0.558503 0.829503i \(-0.311376\pi\)
−0.997622 + 0.0689263i \(0.978043\pi\)
\(740\) 3.00000 5.19615i 0.110282 0.191014i
\(741\) −74.6863 −2.74367
\(742\) 2.17712 3.77089i 0.0799247 0.138434i
\(743\) −45.2915 −1.66158 −0.830792 0.556583i \(-0.812112\pi\)
−0.830792 + 0.556583i \(0.812112\pi\)
\(744\) −5.29150 + 9.16515i −0.193996 + 0.336011i
\(745\) −12.5830 21.7944i −0.461006 0.798485i
\(746\) 10.4373 + 18.0779i 0.382135 + 0.661877i
\(747\) −5.41699 + 9.38251i −0.198197 + 0.343288i
\(748\) 6.00000 0.219382
\(749\) 14.4686 + 25.0604i 0.528672 + 0.915687i
\(750\) −31.7490 −1.15931
\(751\) 8.00000 13.8564i 0.291924 0.505627i −0.682341 0.731034i \(-0.739038\pi\)
0.974265 + 0.225407i \(0.0723712\pi\)
\(752\) −1.35425 2.34563i −0.0493844 0.0855362i
\(753\) 4.35425 + 7.54178i 0.158678 + 0.274838i
\(754\) 15.7288 27.2430i 0.572808 0.992132i
\(755\) 14.2288 0.517837
\(756\) 7.00000 0.254588
\(757\) −23.1660 −0.841983 −0.420991 0.907065i \(-0.638318\pi\)
−0.420991 + 0.907065i \(0.638318\pi\)
\(758\) 3.03137 5.25049i 0.110104 0.190706i
\(759\) −2.17712 3.77089i −0.0790246 0.136875i
\(760\) 4.64575 + 8.04668i 0.168519 + 0.291884i
\(761\) 3.00000 5.19615i 0.108750 0.188360i −0.806514 0.591215i \(-0.798649\pi\)
0.915264 + 0.402854i \(0.131982\pi\)
\(762\) −42.1660 −1.52751
\(763\) −28.0000 −1.01367
\(764\) −2.70850 −0.0979900
\(765\) 19.7490 34.2063i 0.714027 1.23673i
\(766\) 12.0516 + 20.8740i 0.435443 + 0.754210i
\(767\) −11.6144 20.1167i −0.419371 0.726372i
\(768\) −1.32288 + 2.29129i −0.0477352 + 0.0826797i
\(769\) 27.1660 0.979631 0.489816 0.871826i \(-0.337064\pi\)
0.489816 + 0.871826i \(0.337064\pi\)
\(770\) −2.17712 3.77089i −0.0784581 0.135893i
\(771\) −57.1033 −2.05652
\(772\) −12.7601 + 22.1012i −0.459247 + 0.795439i
\(773\) 9.29150 + 16.0934i 0.334192 + 0.578838i 0.983329 0.181834i \(-0.0582032\pi\)
−0.649137 + 0.760671i \(0.724870\pi\)
\(774\) −8.00000 13.8564i −0.287554 0.498058i
\(775\) −4.58301 + 7.93800i −0.164626 + 0.285141i