Properties

Label 143.2.e.a.100.3
Level $143$
Weight $2$
Character 143.100
Analytic conductor $1.142$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 143.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14186074890\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1714608.1
Defining polynomial: \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 100.3
Root \(0.500000 + 2.23871i\) of defining polynomial
Character \(\chi\) \(=\) 143.100
Dual form 143.2.e.a.133.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.13090 - 1.95878i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.11575 q^{5} +(1.13090 + 1.95878i) q^{6} +(-1.68878 - 2.92505i) q^{7} -3.00000 q^{8} +(-1.05787 - 1.83229i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.13090 - 1.95878i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.11575 q^{5} +(1.13090 + 1.95878i) q^{6} +(-1.68878 - 2.92505i) q^{7} -3.00000 q^{8} +(-1.05787 - 1.83229i) q^{9} +(-1.05787 + 1.83229i) q^{10} +(-0.500000 + 0.866025i) q^{11} +2.26180 q^{12} +(2.63090 + 2.46543i) q^{13} +3.37755 q^{14} +(2.39270 - 4.14428i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.07303 + 1.85854i) q^{17} +2.11575 q^{18} +(-1.57303 - 2.72456i) q^{19} +(1.05787 + 1.83229i) q^{20} -7.63935 q^{21} +(-0.500000 - 0.866025i) q^{22} +(-2.26180 + 3.91756i) q^{23} +(-3.39270 + 5.87633i) q^{24} -0.523604 q^{25} +(-3.45058 + 1.04571i) q^{26} +2.00000 q^{27} +(1.68878 - 2.92505i) q^{28} +(-1.74665 + 3.02529i) q^{29} +(2.39270 + 4.14428i) q^{30} -9.27871 q^{31} +(-2.50000 - 4.33013i) q^{32} +(1.13090 + 1.95878i) q^{33} -2.14605 q^{34} +(-3.57303 - 6.18866i) q^{35} +(1.05787 - 1.83229i) q^{36} +(4.58148 - 7.93535i) q^{37} +3.14605 q^{38} +(7.80453 - 2.36519i) q^{39} -6.34725 q^{40} +(-5.00845 + 8.67489i) q^{41} +(3.81968 - 6.61587i) q^{42} +(-1.26180 - 2.18551i) q^{43} -1.00000 q^{44} +(-2.23820 - 3.87667i) q^{45} +(-2.26180 - 3.91756i) q^{46} -1.96970 q^{47} +(-1.13090 - 1.95878i) q^{48} +(-2.20393 + 3.81731i) q^{49} +(0.261802 - 0.453455i) q^{50} +4.85395 q^{51} +(-0.819677 + 3.51114i) q^{52} +7.75510 q^{53} +(-1.00000 + 1.73205i) q^{54} +(-1.05787 + 1.83229i) q^{55} +(5.06633 + 8.77514i) q^{56} -7.11575 q^{57} +(-1.74665 - 3.02529i) q^{58} +(3.01515 + 5.22240i) q^{59} +4.78541 q^{60} +(-4.89270 - 8.47441i) q^{61} +(4.63935 - 8.03560i) q^{62} +(-3.57303 + 6.18866i) q^{63} +7.00000 q^{64} +(5.56633 + 5.21624i) q^{65} -2.26180 q^{66} +(-2.01515 + 3.49035i) q^{67} +(-1.07303 + 1.85854i) q^{68} +(5.11575 + 8.86074i) q^{69} +7.14605 q^{70} +(-3.00000 - 5.19615i) q^{71} +(3.17362 + 5.49688i) q^{72} +10.8405 q^{73} +(4.58148 + 7.93535i) q^{74} +(-0.592145 + 1.02563i) q^{75} +(1.57303 - 2.72456i) q^{76} +3.37755 q^{77} +(-1.85395 + 7.94151i) q^{78} +1.66966 q^{79} +(1.05787 - 1.83229i) q^{80} +(5.43543 - 9.41443i) q^{81} +(-5.00845 - 8.67489i) q^{82} +5.66966 q^{83} +(-3.81968 - 6.61587i) q^{84} +(2.27026 + 3.93220i) q^{85} +2.52360 q^{86} +(3.95058 + 6.84260i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-4.67362 + 8.09495i) q^{89} +4.47640 q^{90} +(2.76850 - 11.8591i) q^{91} -4.52360 q^{92} +(-10.4933 + 18.1749i) q^{93} +(0.984848 - 1.70581i) q^{94} +(-3.32813 - 5.76449i) q^{95} -11.3090 q^{96} +(-5.81968 - 10.0800i) q^{97} +(-2.20393 - 3.81731i) q^{98} +2.11575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9} - 3 q^{10} - 3 q^{11} + 9 q^{13} - 6 q^{15} + 3 q^{16} + 3 q^{17} + 6 q^{18} - 6 q^{19} + 3 q^{20} - 12 q^{21} - 3 q^{22} + 24 q^{25} + 3 q^{26} + 12 q^{27} + 3 q^{29} - 6 q^{30} + 12 q^{31} - 15 q^{32} - 6 q^{34} - 18 q^{35} + 3 q^{36} - 3 q^{37} + 12 q^{38} + 30 q^{39} - 18 q^{40} - 3 q^{41} + 6 q^{42} + 6 q^{43} - 6 q^{44} - 27 q^{45} - 12 q^{47} - 3 q^{49} - 12 q^{50} + 36 q^{51} + 12 q^{52} + 6 q^{53} - 6 q^{54} - 3 q^{55} - 36 q^{57} + 3 q^{58} + 18 q^{59} - 12 q^{60} - 9 q^{61} - 6 q^{62} - 18 q^{63} + 42 q^{64} + 3 q^{65} - 12 q^{67} - 3 q^{68} + 24 q^{69} + 36 q^{70} - 18 q^{71} + 9 q^{72} + 18 q^{73} - 3 q^{74} - 24 q^{75} + 6 q^{76} - 18 q^{78} - 24 q^{79} + 3 q^{80} + 9 q^{81} - 3 q^{82} - 6 q^{84} - 27 q^{85} - 12 q^{86} + 9 q^{88} - 18 q^{89} + 54 q^{90} + 30 q^{91} - 36 q^{93} + 6 q^{94} + 24 q^{95} - 18 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.986869 0.161521i \(-0.948360\pi\)
0.633316 + 0.773893i \(0.281693\pi\)
\(3\) 1.13090 1.95878i 0.652926 1.13090i −0.329483 0.944161i \(-0.606875\pi\)
0.982409 0.186740i \(-0.0597921\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 2.11575 0.946192 0.473096 0.881011i \(-0.343136\pi\)
0.473096 + 0.881011i \(0.343136\pi\)
\(6\) 1.13090 + 1.95878i 0.461688 + 0.799668i
\(7\) −1.68878 2.92505i −0.638297 1.10556i −0.985806 0.167887i \(-0.946306\pi\)
0.347509 0.937677i \(-0.387028\pi\)
\(8\) −3.00000 −1.06066
\(9\) −1.05787 1.83229i −0.352625 0.610764i
\(10\) −1.05787 + 1.83229i −0.334529 + 0.579422i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) 2.26180 0.652926
\(13\) 2.63090 + 2.46543i 0.729681 + 0.683788i
\(14\) 3.37755 0.902689
\(15\) 2.39270 4.14428i 0.617793 1.07005i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 1.07303 + 1.85854i 0.260247 + 0.450761i 0.966308 0.257390i \(-0.0828626\pi\)
−0.706060 + 0.708152i \(0.749529\pi\)
\(18\) 2.11575 0.498687
\(19\) −1.57303 2.72456i −0.360877 0.625057i 0.627228 0.778835i \(-0.284189\pi\)
−0.988105 + 0.153778i \(0.950856\pi\)
\(20\) 1.05787 + 1.83229i 0.236548 + 0.409713i
\(21\) −7.63935 −1.66704
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) −2.26180 + 3.91756i −0.471618 + 0.816867i −0.999473 0.0324679i \(-0.989663\pi\)
0.527854 + 0.849335i \(0.322997\pi\)
\(24\) −3.39270 + 5.87633i −0.692533 + 1.19950i
\(25\) −0.523604 −0.104721
\(26\) −3.45058 + 1.04571i −0.676714 + 0.205081i
\(27\) 2.00000 0.384900
\(28\) 1.68878 2.92505i 0.319149 0.552782i
\(29\) −1.74665 + 3.02529i −0.324345 + 0.561782i −0.981380 0.192079i \(-0.938477\pi\)
0.657035 + 0.753860i \(0.271810\pi\)
\(30\) 2.39270 + 4.14428i 0.436846 + 0.756639i
\(31\) −9.27871 −1.66651 −0.833253 0.552893i \(-0.813524\pi\)
−0.833253 + 0.552893i \(0.813524\pi\)
\(32\) −2.50000 4.33013i −0.441942 0.765466i
\(33\) 1.13090 + 1.95878i 0.196865 + 0.340980i
\(34\) −2.14605 −0.368045
\(35\) −3.57303 6.18866i −0.603952 1.04608i
\(36\) 1.05787 1.83229i 0.176312 0.305382i
\(37\) 4.58148 7.93535i 0.753191 1.30456i −0.193078 0.981183i \(-0.561847\pi\)
0.946269 0.323381i \(-0.104820\pi\)
\(38\) 3.14605 0.510357
\(39\) 7.80453 2.36519i 1.24972 0.378734i
\(40\) −6.34725 −1.00359
\(41\) −5.00845 + 8.67489i −0.782189 + 1.35479i 0.148475 + 0.988916i \(0.452563\pi\)
−0.930664 + 0.365875i \(0.880770\pi\)
\(42\) 3.81968 6.61587i 0.589389 1.02085i
\(43\) −1.26180 2.18551i −0.192423 0.333286i 0.753630 0.657299i \(-0.228301\pi\)
−0.946053 + 0.324013i \(0.894968\pi\)
\(44\) −1.00000 −0.150756
\(45\) −2.23820 3.87667i −0.333651 0.577900i
\(46\) −2.26180 3.91756i −0.333485 0.577612i
\(47\) −1.96970 −0.287310 −0.143655 0.989628i \(-0.545886\pi\)
−0.143655 + 0.989628i \(0.545886\pi\)
\(48\) −1.13090 1.95878i −0.163232 0.282725i
\(49\) −2.20393 + 3.81731i −0.314847 + 0.545331i
\(50\) 0.261802 0.453455i 0.0370244 0.0641282i
\(51\) 4.85395 0.679689
\(52\) −0.819677 + 3.51114i −0.113669 + 0.486908i
\(53\) 7.75510 1.06525 0.532623 0.846353i \(-0.321206\pi\)
0.532623 + 0.846353i \(0.321206\pi\)
\(54\) −1.00000 + 1.73205i −0.136083 + 0.235702i
\(55\) −1.05787 + 1.83229i −0.142644 + 0.247066i
\(56\) 5.06633 + 8.77514i 0.677016 + 1.17263i
\(57\) −7.11575 −0.942504
\(58\) −1.74665 3.02529i −0.229346 0.397240i
\(59\) 3.01515 + 5.22240i 0.392539 + 0.679898i 0.992784 0.119919i \(-0.0382634\pi\)
−0.600244 + 0.799817i \(0.704930\pi\)
\(60\) 4.78541 0.617793
\(61\) −4.89270 8.47441i −0.626446 1.08504i −0.988259 0.152786i \(-0.951175\pi\)
0.361813 0.932251i \(-0.382158\pi\)
\(62\) 4.63935 8.03560i 0.589199 1.02052i
\(63\) −3.57303 + 6.18866i −0.450159 + 0.779698i
\(64\) 7.00000 0.875000
\(65\) 5.56633 + 5.21624i 0.690418 + 0.646995i
\(66\) −2.26180 −0.278409
\(67\) −2.01515 + 3.49035i −0.246190 + 0.426414i −0.962466 0.271404i \(-0.912512\pi\)
0.716276 + 0.697818i \(0.245845\pi\)
\(68\) −1.07303 + 1.85854i −0.130124 + 0.225381i
\(69\) 5.11575 + 8.86074i 0.615864 + 1.06671i
\(70\) 7.14605 0.854117
\(71\) −3.00000 5.19615i −0.356034 0.616670i 0.631260 0.775571i \(-0.282538\pi\)
−0.987294 + 0.158901i \(0.949205\pi\)
\(72\) 3.17362 + 5.49688i 0.374015 + 0.647813i
\(73\) 10.8405 1.26879 0.634395 0.773009i \(-0.281249\pi\)
0.634395 + 0.773009i \(0.281249\pi\)
\(74\) 4.58148 + 7.93535i 0.532586 + 0.922466i
\(75\) −0.592145 + 1.02563i −0.0683750 + 0.118429i
\(76\) 1.57303 2.72456i 0.180439 0.312529i
\(77\) 3.37755 0.384908
\(78\) −1.85395 + 7.94151i −0.209918 + 0.899199i
\(79\) 1.66966 0.187851 0.0939256 0.995579i \(-0.470058\pi\)
0.0939256 + 0.995579i \(0.470058\pi\)
\(80\) 1.05787 1.83229i 0.118274 0.204857i
\(81\) 5.43543 9.41443i 0.603936 1.04605i
\(82\) −5.00845 8.67489i −0.553091 0.957982i
\(83\) 5.66966 0.622326 0.311163 0.950357i \(-0.399282\pi\)
0.311163 + 0.950357i \(0.399282\pi\)
\(84\) −3.81968 6.61587i −0.416761 0.721851i
\(85\) 2.27026 + 3.93220i 0.246244 + 0.426507i
\(86\) 2.52360 0.272127
\(87\) 3.95058 + 6.84260i 0.423546 + 0.733604i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −4.67362 + 8.09495i −0.495403 + 0.858063i −0.999986 0.00529986i \(-0.998313\pi\)
0.504583 + 0.863363i \(0.331646\pi\)
\(90\) 4.47640 0.471854
\(91\) 2.76850 11.8591i 0.290218 1.24317i
\(92\) −4.52360 −0.471618
\(93\) −10.4933 + 18.1749i −1.08810 + 1.88465i
\(94\) 0.984848 1.70581i 0.101579 0.175941i
\(95\) −3.32813 5.76449i −0.341459 0.591424i
\(96\) −11.3090 −1.15422
\(97\) −5.81968 10.0800i −0.590899 1.02347i −0.994112 0.108360i \(-0.965440\pi\)
0.403213 0.915106i \(-0.367893\pi\)
\(98\) −2.20393 3.81731i −0.222630 0.385607i
\(99\) 2.11575 0.212641
\(100\) −0.261802 0.453455i −0.0261802 0.0453455i
\(101\) −0.450578 + 0.780424i −0.0448342 + 0.0776551i −0.887572 0.460670i \(-0.847609\pi\)
0.842737 + 0.538325i \(0.180943\pi\)
\(102\) −2.42697 + 4.20364i −0.240306 + 0.416223i
\(103\) 13.0472 1.28558 0.642790 0.766043i \(-0.277777\pi\)
0.642790 + 0.766043i \(0.277777\pi\)
\(104\) −7.89270 7.39630i −0.773943 0.725267i
\(105\) −16.1630 −1.57734
\(106\) −3.87755 + 6.71612i −0.376621 + 0.652327i
\(107\) 6.80453 11.7858i 0.657818 1.13937i −0.323361 0.946276i \(-0.604813\pi\)
0.981179 0.193099i \(-0.0618539\pi\)
\(108\) 1.00000 + 1.73205i 0.0962250 + 0.166667i
\(109\) 18.6866 1.78985 0.894924 0.446218i \(-0.147230\pi\)
0.894924 + 0.446218i \(0.147230\pi\)
\(110\) −1.05787 1.83229i −0.100864 0.174702i
\(111\) −10.3624 17.9482i −0.983555 1.70357i
\(112\) −3.37755 −0.319149
\(113\) −6.31968 10.9460i −0.594505 1.02971i −0.993616 0.112811i \(-0.964015\pi\)
0.399111 0.916902i \(-0.369319\pi\)
\(114\) 3.55787 6.16242i 0.333225 0.577163i
\(115\) −4.78541 + 8.28857i −0.446241 + 0.772913i
\(116\) −3.49330 −0.324345
\(117\) 1.73423 7.42870i 0.160330 0.686784i
\(118\) −6.03030 −0.555134
\(119\) 3.62420 6.27730i 0.332230 0.575439i
\(120\) −7.17811 + 12.4329i −0.655269 + 1.13496i
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 9.78541 0.885929
\(123\) 11.3281 + 19.6209i 1.02142 + 1.76916i
\(124\) −4.63935 8.03560i −0.416626 0.721618i
\(125\) −11.6866 −1.04528
\(126\) −3.57303 6.18866i −0.318310 0.551330i
\(127\) −5.75510 + 9.96813i −0.510683 + 0.884529i 0.489241 + 0.872149i \(0.337274\pi\)
−0.999923 + 0.0123797i \(0.996059\pi\)
\(128\) 1.50000 2.59808i 0.132583 0.229640i
\(129\) −5.70789 −0.502552
\(130\) −7.30056 + 2.21246i −0.640301 + 0.194046i
\(131\) 13.6091 1.18903 0.594514 0.804085i \(-0.297344\pi\)
0.594514 + 0.804085i \(0.297344\pi\)
\(132\) −1.13090 + 1.95878i −0.0984323 + 0.170490i
\(133\) −5.31298 + 9.20235i −0.460694 + 0.797945i
\(134\) −2.01515 3.49035i −0.174083 0.301520i
\(135\) 4.23150 0.364189
\(136\) −3.21908 5.57561i −0.276034 0.478105i
\(137\) 7.55118 + 13.0790i 0.645140 + 1.11742i 0.984269 + 0.176676i \(0.0565345\pi\)
−0.339129 + 0.940740i \(0.610132\pi\)
\(138\) −10.2315 −0.870963
\(139\) 7.63935 + 13.2317i 0.647962 + 1.12230i 0.983609 + 0.180315i \(0.0577116\pi\)
−0.335647 + 0.941988i \(0.608955\pi\)
\(140\) 3.57303 6.18866i 0.301976 0.523038i
\(141\) −2.22753 + 3.85820i −0.187592 + 0.324919i
\(142\) 6.00000 0.503509
\(143\) −3.45058 + 1.04571i −0.288552 + 0.0874467i
\(144\) −2.11575 −0.176312
\(145\) −3.69547 + 6.40075i −0.306892 + 0.531553i
\(146\) −5.42027 + 9.38819i −0.448585 + 0.776972i
\(147\) 4.98485 + 8.63401i 0.411143 + 0.712121i
\(148\) 9.16296 0.753191
\(149\) −2.18878 3.79107i −0.179312 0.310577i 0.762333 0.647184i \(-0.224054\pi\)
−0.941645 + 0.336608i \(0.890720\pi\)
\(150\) −0.592145 1.02563i −0.0483484 0.0837419i
\(151\) 2.29211 0.186529 0.0932645 0.995641i \(-0.470270\pi\)
0.0932645 + 0.995641i \(0.470270\pi\)
\(152\) 4.71908 + 8.17369i 0.382768 + 0.662973i
\(153\) 2.27026 3.93220i 0.183539 0.317899i
\(154\) −1.68878 + 2.92505i −0.136085 + 0.235707i
\(155\) −19.6314 −1.57683
\(156\) 5.95058 + 5.57632i 0.476428 + 0.446463i
\(157\) −24.0472 −1.91918 −0.959588 0.281408i \(-0.909198\pi\)
−0.959588 + 0.281408i \(0.909198\pi\)
\(158\) −0.834829 + 1.44597i −0.0664154 + 0.115035i
\(159\) 8.77026 15.1905i 0.695526 1.20469i
\(160\) −5.28937 9.16146i −0.418162 0.724277i
\(161\) 15.2787 1.20413
\(162\) 5.43543 + 9.41443i 0.427047 + 0.739668i
\(163\) 3.27695 + 5.67585i 0.256671 + 0.444567i 0.965348 0.260966i \(-0.0840410\pi\)
−0.708677 + 0.705533i \(0.750708\pi\)
\(164\) −10.0169 −0.782189
\(165\) 2.39270 + 4.14428i 0.186272 + 0.322632i
\(166\) −2.83483 + 4.91007i −0.220025 + 0.381095i
\(167\) 9.16296 15.8707i 0.709051 1.22811i −0.256159 0.966635i \(-0.582457\pi\)
0.965210 0.261478i \(-0.0842098\pi\)
\(168\) 22.9181 1.76817
\(169\) 0.843281 + 12.9726i 0.0648678 + 0.997894i
\(170\) −4.54051 −0.348241
\(171\) −3.32813 + 5.76449i −0.254508 + 0.440822i
\(172\) 1.26180 2.18551i 0.0962115 0.166643i
\(173\) −7.34328 12.7189i −0.558299 0.967003i −0.997639 0.0686816i \(-0.978121\pi\)
0.439339 0.898321i \(-0.355213\pi\)
\(174\) −7.90116 −0.598985
\(175\) 0.884251 + 1.53157i 0.0668431 + 0.115776i
\(176\) 0.500000 + 0.866025i 0.0376889 + 0.0652791i
\(177\) 13.6394 1.02520
\(178\) −4.67362 8.09495i −0.350303 0.606742i
\(179\) 3.24665 5.62336i 0.242666 0.420310i −0.718807 0.695210i \(-0.755311\pi\)
0.961473 + 0.274900i \(0.0886447\pi\)
\(180\) 2.23820 3.87667i 0.166825 0.288950i
\(181\) −17.1630 −1.27571 −0.637856 0.770155i \(-0.720179\pi\)
−0.637856 + 0.770155i \(0.720179\pi\)
\(182\) 8.88600 + 8.32713i 0.658674 + 0.617248i
\(183\) −22.1327 −1.63609
\(184\) 6.78541 11.7527i 0.500227 0.866418i
\(185\) 9.69326 16.7892i 0.712663 1.23437i
\(186\) −10.4933 18.1749i −0.769406 1.33265i
\(187\) −2.14605 −0.156935
\(188\) −0.984848 1.70581i −0.0718274 0.124409i
\(189\) −3.37755 5.85009i −0.245681 0.425532i
\(190\) 6.65626 0.482896
\(191\) −8.98485 15.5622i −0.650121 1.12604i −0.983093 0.183106i \(-0.941385\pi\)
0.332972 0.942937i \(-0.391948\pi\)
\(192\) 7.91631 13.7114i 0.571310 0.989538i
\(193\) 1.48485 2.57183i 0.106882 0.185125i −0.807624 0.589698i \(-0.799247\pi\)
0.914505 + 0.404574i \(0.132580\pi\)
\(194\) 11.6394 0.835657
\(195\) 16.5124 5.00415i 1.18248 0.358355i
\(196\) −4.40786 −0.314847
\(197\) −6.11575 + 10.5928i −0.435729 + 0.754705i −0.997355 0.0726865i \(-0.976843\pi\)
0.561626 + 0.827391i \(0.310176\pi\)
\(198\) −1.05787 + 1.83229i −0.0751799 + 0.130215i
\(199\) 0.100598 + 0.174240i 0.00713118 + 0.0123516i 0.869569 0.493812i \(-0.164397\pi\)
−0.862438 + 0.506163i \(0.831063\pi\)
\(200\) 1.57081 0.111073
\(201\) 4.55787 + 7.89447i 0.321488 + 0.556833i
\(202\) −0.450578 0.780424i −0.0317026 0.0549104i
\(203\) 11.7988 0.828114
\(204\) 2.42697 + 4.20364i 0.169922 + 0.294314i
\(205\) −10.5966 + 18.3539i −0.740101 + 1.28189i
\(206\) −6.52360 + 11.2992i −0.454521 + 0.787254i
\(207\) 9.57081 0.665218
\(208\) 3.45058 1.04571i 0.239255 0.0725070i
\(209\) 3.14605 0.217617
\(210\) 8.08148 13.9975i 0.557675 0.965922i
\(211\) −5.83483 + 10.1062i −0.401686 + 0.695741i −0.993930 0.110018i \(-0.964909\pi\)
0.592243 + 0.805759i \(0.298242\pi\)
\(212\) 3.87755 + 6.71612i 0.266311 + 0.461265i
\(213\) −13.5708 −0.929857
\(214\) 6.80453 + 11.7858i 0.465148 + 0.805660i
\(215\) −2.66966 4.62398i −0.182069 0.315353i
\(216\) −6.00000 −0.408248
\(217\) 15.6697 + 27.1406i 1.06373 + 1.84243i
\(218\) −9.34328 + 16.1830i −0.632807 + 1.09605i
\(219\) 12.2596 21.2342i 0.828426 1.43488i
\(220\) −2.11575 −0.142644
\(221\) −1.75907 + 7.53510i −0.118328 + 0.506866i
\(222\) 20.7248 1.39096
\(223\) 3.75335 6.50099i 0.251343 0.435339i −0.712553 0.701618i \(-0.752461\pi\)
0.963896 + 0.266280i \(0.0857945\pi\)
\(224\) −8.44388 + 14.6252i −0.564180 + 0.977189i
\(225\) 0.553908 + 0.959397i 0.0369272 + 0.0639598i
\(226\) 12.6394 0.840757
\(227\) 1.73820 + 3.01065i 0.115368 + 0.199824i 0.917927 0.396750i \(-0.129862\pi\)
−0.802559 + 0.596573i \(0.796529\pi\)
\(228\) −3.55787 6.16242i −0.235626 0.408116i
\(229\) 13.4079 0.886016 0.443008 0.896518i \(-0.353911\pi\)
0.443008 + 0.896518i \(0.353911\pi\)
\(230\) −4.78541 8.28857i −0.315540 0.546532i
\(231\) 3.81968 6.61587i 0.251316 0.435293i
\(232\) 5.23995 9.07586i 0.344020 0.595860i
\(233\) 0.292106 0.0191365 0.00956824 0.999954i \(-0.496954\pi\)
0.00956824 + 0.999954i \(0.496954\pi\)
\(234\) 5.56633 + 5.21624i 0.363882 + 0.340996i
\(235\) −4.16738 −0.271850
\(236\) −3.01515 + 5.22240i −0.196270 + 0.339949i
\(237\) 1.88822 3.27049i 0.122653 0.212441i
\(238\) 3.62420 + 6.27730i 0.234922 + 0.406897i
\(239\) −21.8023 −1.41027 −0.705137 0.709071i \(-0.749115\pi\)
−0.705137 + 0.709071i \(0.749115\pi\)
\(240\) −2.39270 4.14428i −0.154448 0.267512i
\(241\) 1.27422 + 2.20702i 0.0820798 + 0.142166i 0.904143 0.427230i \(-0.140510\pi\)
−0.822063 + 0.569396i \(0.807177\pi\)
\(242\) 1.00000 0.0642824
\(243\) −9.29386 16.0974i −0.596201 1.03265i
\(244\) 4.89270 8.47441i 0.313223 0.542519i
\(245\) −4.66296 + 8.07648i −0.297905 + 0.515987i
\(246\) −22.6563 −1.44451
\(247\) 2.57875 11.0462i 0.164082 0.702856i
\(248\) 27.8361 1.76760
\(249\) 6.41182 11.1056i 0.406333 0.703789i
\(250\) 5.84328 10.1209i 0.369562 0.640099i
\(251\) 13.4096 + 23.2261i 0.846407 + 1.46602i 0.884394 + 0.466742i \(0.154572\pi\)
−0.0379867 + 0.999278i \(0.512094\pi\)
\(252\) −7.14605 −0.450159
\(253\) −2.26180 3.91756i −0.142198 0.246295i
\(254\) −5.75510 9.96813i −0.361107 0.625456i
\(255\) 10.2697 0.643116
\(256\) 8.50000 + 14.7224i 0.531250 + 0.920152i
\(257\) −1.53427 + 2.65743i −0.0957051 + 0.165766i −0.909903 0.414822i \(-0.863844\pi\)
0.814198 + 0.580588i \(0.197177\pi\)
\(258\) 2.85395 4.94318i 0.177679 0.307749i
\(259\) −30.9484 −1.92304
\(260\) −1.73423 + 7.42870i −0.107552 + 0.460708i
\(261\) 7.39095 0.457488
\(262\) −6.80453 + 11.7858i −0.420385 + 0.728128i
\(263\) −1.14605 + 1.98502i −0.0706686 + 0.122402i −0.899195 0.437549i \(-0.855847\pi\)
0.828526 + 0.559951i \(0.189180\pi\)
\(264\) −3.39270 5.87633i −0.208806 0.361663i
\(265\) 16.4079 1.00793
\(266\) −5.31298 9.20235i −0.325760 0.564232i
\(267\) 10.5708 + 18.3092i 0.646923 + 1.12050i
\(268\) −4.03030 −0.246190
\(269\) −5.62245 9.73837i −0.342807 0.593759i 0.642146 0.766582i \(-0.278044\pi\)
−0.984953 + 0.172824i \(0.944711\pi\)
\(270\) −2.11575 + 3.66459i −0.128760 + 0.223020i
\(271\) 2.14605 3.71707i 0.130363 0.225796i −0.793453 0.608631i \(-0.791719\pi\)
0.923817 + 0.382835i \(0.125052\pi\)
\(272\) 2.14605 0.130124
\(273\) −20.0984 18.8343i −1.21641 1.13990i
\(274\) −15.1024 −0.912366
\(275\) 0.261802 0.453455i 0.0157873 0.0273444i
\(276\) −5.11575 + 8.86074i −0.307932 + 0.533354i
\(277\) 2.41631 + 4.18517i 0.145182 + 0.251462i 0.929441 0.368971i \(-0.120290\pi\)
−0.784259 + 0.620434i \(0.786957\pi\)
\(278\) −15.2787 −0.916356
\(279\) 9.81571 + 17.0013i 0.587651 + 1.01784i
\(280\) 10.7191 + 18.5660i 0.640588 + 1.10953i
\(281\) 3.78541 0.225818 0.112909 0.993605i \(-0.463983\pi\)
0.112909 + 0.993605i \(0.463983\pi\)
\(282\) −2.22753 3.85820i −0.132648 0.229752i
\(283\) 6.21238 10.7602i 0.369288 0.639625i −0.620167 0.784470i \(-0.712935\pi\)
0.989454 + 0.144845i \(0.0462684\pi\)
\(284\) 3.00000 5.19615i 0.178017 0.308335i
\(285\) −15.0551 −0.891790
\(286\) 0.819677 3.51114i 0.0484685 0.207618i
\(287\) 33.8326 1.99708
\(288\) −5.28937 + 9.16146i −0.311679 + 0.539844i
\(289\) 6.19723 10.7339i 0.364543 0.631407i
\(290\) −3.69547 6.40075i −0.217006 0.375865i
\(291\) −26.3259 −1.54325
\(292\) 5.42027 + 9.38819i 0.317198 + 0.549402i
\(293\) −8.45058 14.6368i −0.493688 0.855093i 0.506286 0.862366i \(-0.331018\pi\)
−0.999974 + 0.00727315i \(0.997685\pi\)
\(294\) −9.96970 −0.581445
\(295\) 6.37931 + 11.0493i 0.371418 + 0.643314i
\(296\) −13.7444 + 23.8061i −0.798879 + 1.38370i
\(297\) −1.00000 + 1.73205i −0.0580259 + 0.100504i
\(298\) 4.37755 0.253585
\(299\) −15.6091 + 4.73038i −0.902695 + 0.273565i
\(300\) −1.18429 −0.0683750
\(301\) −4.26180 + 7.38166i −0.245646 + 0.425472i
\(302\) −1.14605 + 1.98502i −0.0659479 + 0.114225i
\(303\) 1.01912 + 1.76516i 0.0585468 + 0.101406i
\(304\) −3.14605 −0.180439
\(305\) −10.3517 17.9297i −0.592739 1.02665i
\(306\) 2.27026 + 3.93220i 0.129782 + 0.224789i
\(307\) −8.42476 −0.480826 −0.240413 0.970671i \(-0.577283\pi\)
−0.240413 + 0.970671i \(0.577283\pi\)
\(308\) 1.68878 + 2.92505i 0.0962269 + 0.166670i
\(309\) 14.7551 25.5566i 0.839388 1.45386i
\(310\) 9.81571 17.0013i 0.557495 0.965609i
\(311\) −28.5877 −1.62106 −0.810530 0.585697i \(-0.800821\pi\)
−0.810530 + 0.585697i \(0.800821\pi\)
\(312\) −23.4136 + 7.09557i −1.32553 + 0.401708i
\(313\) 22.3945 1.26581 0.632905 0.774230i \(-0.281862\pi\)
0.632905 + 0.774230i \(0.281862\pi\)
\(314\) 12.0236 20.8255i 0.678531 1.17525i
\(315\) −7.55963 + 13.0937i −0.425937 + 0.737744i
\(316\) 0.834829 + 1.44597i 0.0469628 + 0.0813419i
\(317\) −26.2708 −1.47551 −0.737757 0.675067i \(-0.764115\pi\)
−0.737757 + 0.675067i \(0.764115\pi\)
\(318\) 8.77026 + 15.1905i 0.491811 + 0.851842i
\(319\) −1.74665 3.02529i −0.0977937 0.169384i
\(320\) 14.8102 0.827918
\(321\) −15.3905 26.6571i −0.859013 1.48785i
\(322\) −7.63935 + 13.2317i −0.425725 + 0.737377i
\(323\) 3.37580 5.84705i 0.187834 0.325339i
\(324\) 10.8709 0.603936
\(325\) −1.37755 1.29091i −0.0764128 0.0716069i
\(326\) −6.55391 −0.362987
\(327\) 21.1327 36.6028i 1.16864 2.02414i
\(328\) 15.0254 26.0247i 0.829637 1.43697i
\(329\) 3.32638 + 5.76145i 0.183389 + 0.317639i
\(330\) −4.78541 −0.263428
\(331\) 4.14605 + 7.18117i 0.227888 + 0.394713i 0.957182 0.289487i \(-0.0934848\pi\)
−0.729294 + 0.684200i \(0.760151\pi\)
\(332\) 2.83483 + 4.91007i 0.155581 + 0.269475i
\(333\) −19.3865 −1.06237
\(334\) 9.16296 + 15.8707i 0.501375 + 0.868407i
\(335\) −4.26356 + 7.38470i −0.232943 + 0.403469i
\(336\) −3.81968 + 6.61587i −0.208380 + 0.360926i
\(337\) −0.0516349 −0.00281273 −0.00140637 0.999999i \(-0.500448\pi\)
−0.00140637 + 0.999999i \(0.500448\pi\)
\(338\) −11.6563 5.75601i −0.634017 0.313086i
\(339\) −28.5877 −1.55267
\(340\) −2.27026 + 3.93220i −0.123122 + 0.213253i
\(341\) 4.63935 8.03560i 0.251235 0.435152i
\(342\) −3.32813 5.76449i −0.179965 0.311708i
\(343\) −8.75510 −0.472731
\(344\) 3.78541 + 6.55652i 0.204095 + 0.353504i
\(345\) 10.8236 + 18.7471i 0.582725 + 1.00931i
\(346\) 14.6866 0.789555
\(347\) 4.31122 + 7.46726i 0.231439 + 0.400863i 0.958232 0.285993i \(-0.0923234\pi\)
−0.726793 + 0.686856i \(0.758990\pi\)
\(348\) −3.95058 + 6.84260i −0.211773 + 0.366802i
\(349\) −15.0000 + 25.9808i −0.802932 + 1.39072i 0.114747 + 0.993395i \(0.463394\pi\)
−0.917679 + 0.397324i \(0.869939\pi\)
\(350\) −1.76850 −0.0945304
\(351\) 5.26180 + 4.93087i 0.280854 + 0.263190i
\(352\) 5.00000 0.266501
\(353\) 0.238198 0.412571i 0.0126780 0.0219589i −0.859617 0.510939i \(-0.829298\pi\)
0.872295 + 0.488980i \(0.162631\pi\)
\(354\) −6.81968 + 11.8120i −0.362462 + 0.627802i
\(355\) −6.34725 10.9938i −0.336877 0.583488i
\(356\) −9.34725 −0.495403
\(357\) −8.19723 14.1980i −0.433843 0.751439i
\(358\) 3.24665 + 5.62336i 0.171591 + 0.297204i
\(359\) −10.2315 −0.539998 −0.269999 0.962861i \(-0.587023\pi\)
−0.269999 + 0.962861i \(0.587023\pi\)
\(360\) 6.71459 + 11.6300i 0.353890 + 0.612956i
\(361\) 4.55118 7.88287i 0.239536 0.414888i
\(362\) 8.58148 14.8636i 0.451033 0.781211i
\(363\) −2.26180 −0.118714
\(364\) 11.6545 3.53194i 0.610862 0.185124i
\(365\) 22.9359 1.20052
\(366\) 11.0663 19.1674i 0.578446 1.00190i
\(367\) −10.6697 + 18.4804i −0.556952 + 0.964668i 0.440797 + 0.897607i \(0.354696\pi\)
−0.997749 + 0.0670617i \(0.978638\pi\)
\(368\) 2.26180 + 3.91756i 0.117905 + 0.204217i
\(369\) 21.1933 1.10328
\(370\) 9.69326 + 16.7892i 0.503929 + 0.872830i
\(371\) −13.0966 22.6840i −0.679943 1.17770i
\(372\) −20.9866 −1.08810
\(373\) −10.6135 18.3832i −0.549548 0.951845i −0.998305 0.0581916i \(-0.981467\pi\)
0.448757 0.893654i \(-0.351867\pi\)
\(374\) 1.07303 1.85854i 0.0554849 0.0961026i
\(375\) −13.2163 + 22.8914i −0.682489 + 1.18211i
\(376\) 5.90909 0.304738
\(377\) −12.0539 + 3.65298i −0.620808 + 0.188138i
\(378\) 6.75510 0.347445
\(379\) 0.523604 0.906910i 0.0268958 0.0465848i −0.852264 0.523112i \(-0.824771\pi\)
0.879160 + 0.476527i \(0.158104\pi\)
\(380\) 3.32813 5.76449i 0.170729 0.295712i
\(381\) 13.0169 + 22.5459i 0.666876 + 1.15506i
\(382\) 17.9697 0.919410
\(383\) 14.4933 + 25.1031i 0.740573 + 1.28271i 0.952235 + 0.305367i \(0.0987792\pi\)
−0.211662 + 0.977343i \(0.567887\pi\)
\(384\) −3.39270 5.87633i −0.173133 0.299875i
\(385\) 7.14605 0.364197
\(386\) 1.48485 + 2.57183i 0.0755768 + 0.130903i
\(387\) −2.66966 + 4.62398i −0.135706 + 0.235050i
\(388\) 5.81968 10.0800i 0.295449 0.511733i
\(389\) 15.5653 0.789195 0.394597 0.918854i \(-0.370884\pi\)
0.394597 + 0.918854i \(0.370884\pi\)
\(390\) −3.92249 + 16.8023i −0.198623 + 0.850815i
\(391\) −9.70789 −0.490949
\(392\) 6.61178 11.4519i 0.333945 0.578410i
\(393\) 15.3905 26.6571i 0.776348 1.34467i
\(394\) −6.11575 10.5928i −0.308107 0.533657i
\(395\) 3.53258 0.177743
\(396\) 1.05787 + 1.83229i 0.0531602 + 0.0920762i
\(397\) −9.48933 16.4360i −0.476256 0.824900i 0.523374 0.852103i \(-0.324673\pi\)
−0.999630 + 0.0272035i \(0.991340\pi\)
\(398\) −0.201195 −0.0100850
\(399\) 12.0169 + 20.8139i 0.601598 + 1.04200i
\(400\) −0.261802 + 0.453455i −0.0130901 + 0.0226727i
\(401\) 4.76180 8.24768i 0.237793 0.411870i −0.722288 0.691593i \(-0.756909\pi\)
0.960081 + 0.279723i \(0.0902427\pi\)
\(402\) −9.11575 −0.454652
\(403\) −24.4114 22.8760i −1.21602 1.13954i
\(404\) −0.901156 −0.0448342
\(405\) 11.5000 19.9186i 0.571440 0.989762i
\(406\) −5.89940 + 10.2181i −0.292782 + 0.507114i
\(407\) 4.58148 + 7.93535i 0.227095 + 0.393341i
\(408\) −14.5618 −0.720919
\(409\) −4.95728 8.58626i −0.245122 0.424563i 0.717044 0.697028i \(-0.245495\pi\)
−0.962166 + 0.272465i \(0.912161\pi\)
\(410\) −10.5966 18.3539i −0.523330 0.906435i
\(411\) 34.1585 1.68492
\(412\) 6.52360 + 11.2992i 0.321395 + 0.556672i
\(413\) 10.1838 17.6389i 0.501114 0.867954i
\(414\) −4.78541 + 8.28857i −0.235190 + 0.407361i
\(415\) 11.9956 0.588840
\(416\) 4.09838 17.5557i 0.200940 0.860740i
\(417\) 34.5574 1.69228
\(418\) −1.57303 + 2.72456i −0.0769392 + 0.133263i
\(419\) −3.50670 + 6.07378i −0.171313 + 0.296724i −0.938879 0.344246i \(-0.888134\pi\)
0.767566 + 0.640970i \(0.221468\pi\)
\(420\) −8.08148 13.9975i −0.394336 0.683010i
\(421\) 33.9787 1.65602 0.828009 0.560714i \(-0.189473\pi\)
0.828009 + 0.560714i \(0.189473\pi\)
\(422\) −5.83483 10.1062i −0.284035 0.491963i
\(423\) 2.08369 + 3.60906i 0.101313 + 0.175479i
\(424\) −23.2653 −1.12986
\(425\) −0.561841 0.973138i −0.0272533 0.0472041i
\(426\) 6.78541 11.7527i 0.328754 0.569419i
\(427\) −16.5254 + 28.6228i −0.799718 + 1.38515i
\(428\) 13.6091 0.657818
\(429\) −1.85395 + 7.94151i −0.0895094 + 0.383420i
\(430\) 5.33931 0.257485
\(431\) −3.93367 + 6.81332i −0.189478 + 0.328186i −0.945076 0.326849i \(-0.894013\pi\)
0.755598 + 0.655036i \(0.227346\pi\)
\(432\) 1.00000 1.73205i 0.0481125 0.0833333i
\(433\) 6.82638 + 11.8236i 0.328055 + 0.568207i 0.982126 0.188226i \(-0.0602736\pi\)
−0.654071 + 0.756433i \(0.726940\pi\)
\(434\) −31.3393 −1.50434
\(435\) 8.35843 + 14.4772i 0.400756 + 0.694130i
\(436\) 9.34328 + 16.1830i 0.447462 + 0.775027i
\(437\) 14.2315 0.680785
\(438\) 12.2596 + 21.2342i 0.585786 + 1.01461i
\(439\) 4.16517 7.21429i 0.198793 0.344319i −0.749344 0.662180i \(-0.769631\pi\)
0.948137 + 0.317861i \(0.102965\pi\)
\(440\) 3.17362 5.49688i 0.151297 0.262053i
\(441\) 9.32592 0.444091
\(442\) −5.64605 5.29095i −0.268555 0.251665i
\(443\) −25.2484 −1.19959 −0.599794 0.800154i \(-0.704751\pi\)
−0.599794 + 0.800154i \(0.704751\pi\)
\(444\) 10.3624 17.9482i 0.491778 0.851784i
\(445\) −9.88822 + 17.1269i −0.468746 + 0.811893i
\(446\) 3.75335 + 6.50099i 0.177726 + 0.307831i
\(447\) −9.90116 −0.468309
\(448\) −11.8214 20.4753i −0.558510 0.967368i
\(449\) 18.6354 + 32.2774i 0.879458 + 1.52327i 0.851936 + 0.523645i \(0.175428\pi\)
0.0275219 + 0.999621i \(0.491238\pi\)
\(450\) −1.10782 −0.0522229
\(451\) −5.00845 8.67489i −0.235839 0.408485i
\(452\) 6.31968 10.9460i 0.297253 0.514857i
\(453\) 2.59214 4.48973i 0.121790 0.210946i
\(454\) −3.47640 −0.163155
\(455\) 5.85745 25.0908i 0.274602 1.17628i
\(456\) 21.3472 0.999676
\(457\) 1.54546 2.67681i 0.0722933 0.125216i −0.827613 0.561300i \(-0.810302\pi\)
0.899906 + 0.436084i \(0.143635\pi\)
\(458\) −6.70393 + 11.6115i −0.313254 + 0.542572i
\(459\) 2.14605 + 3.71707i 0.100169 + 0.173498i
\(460\) −9.57081 −0.446241
\(461\) 11.2400 + 19.4682i 0.523497 + 0.906723i 0.999626 + 0.0273476i \(0.00870611\pi\)
−0.476129 + 0.879375i \(0.657961\pi\)
\(462\) 3.81968 + 6.61587i 0.177707 + 0.307798i
\(463\) −29.0507 −1.35010 −0.675051 0.737771i \(-0.735878\pi\)
−0.675051 + 0.737771i \(0.735878\pi\)
\(464\) 1.74665 + 3.02529i 0.0810862 + 0.140445i
\(465\) −22.2012 + 38.4536i −1.02956 + 1.78324i
\(466\) −0.146053 + 0.252971i −0.00676577 + 0.0117187i
\(467\) −7.47990 −0.346129 −0.173064 0.984911i \(-0.555367\pi\)
−0.173064 + 0.984911i \(0.555367\pi\)
\(468\) 7.30056 2.21246i 0.337468 0.102271i
\(469\) 13.6126 0.628570
\(470\) 2.08369 3.60906i 0.0961136 0.166474i
\(471\) −27.1950 + 47.1031i −1.25308 + 2.17040i
\(472\) −9.04546 15.6672i −0.416351 0.721141i
\(473\) 2.52360 0.116035
\(474\) 1.88822 + 3.27049i 0.0867287 + 0.150219i
\(475\) 0.823644 + 1.42659i 0.0377914 + 0.0654566i
\(476\) 7.24840 0.332230
\(477\) −8.20393 14.2096i −0.375632 0.650614i
\(478\) 10.9012 18.8814i 0.498607 0.863613i
\(479\) −4.31122 + 7.46726i −0.196985 + 0.341188i −0.947549 0.319609i \(-0.896448\pi\)
0.750565 + 0.660797i \(0.229782\pi\)
\(480\) −23.9270 −1.09211
\(481\) 31.6175 9.58180i 1.44163 0.436893i
\(482\) −2.54844 −0.116078
\(483\) 17.2787 29.9276i 0.786208 1.36175i
\(484\) 0.500000 0.866025i 0.0227273 0.0393648i
\(485\) −12.3130 21.3267i −0.559104 0.968396i
\(486\) 18.5877 0.843156
\(487\) −4.04546 7.00693i −0.183317 0.317514i 0.759691 0.650284i \(-0.225350\pi\)
−0.943008 + 0.332770i \(0.892017\pi\)
\(488\) 14.6781 + 25.4232i 0.664447 + 1.15086i
\(489\) 14.8236 0.670348
\(490\) −4.66296 8.07648i −0.210651 0.364858i
\(491\) −2.31122 + 4.00316i −0.104304 + 0.180660i −0.913454 0.406943i \(-0.866595\pi\)
0.809150 + 0.587603i \(0.199928\pi\)
\(492\) −11.3281 + 19.6209i −0.510712 + 0.884578i
\(493\) −7.49681 −0.337639
\(494\) 8.27695 + 7.75638i 0.372398 + 0.348976i
\(495\) 4.47640 0.201199
\(496\) −4.63935 + 8.03560i −0.208313 + 0.360809i
\(497\) −10.1327 + 17.5503i −0.454512 + 0.787237i
\(498\) 6.41182 + 11.1056i 0.287321 + 0.497654i
\(499\) 39.5137 1.76888 0.884438 0.466657i \(-0.154542\pi\)
0.884438 + 0.466657i \(0.154542\pi\)
\(500\) −5.84328 10.1209i −0.261319 0.452619i
\(501\) −20.7248 35.8964i −0.925916 1.60373i
\(502\) −26.8192 −1.19700
\(503\) 18.8517 + 32.6522i 0.840557 + 1.45589i 0.889424 + 0.457083i \(0.151106\pi\)
−0.0488670 + 0.998805i \(0.515561\pi\)
\(504\) 10.7191 18.5660i 0.477466 0.826995i
\(505\) −0.953310 + 1.65118i −0.0424218 + 0.0734766i
\(506\) 4.52360 0.201099
\(507\) 26.3642 + 13.0189i 1.17087 + 0.578192i
\(508\) −11.5102 −0.510683
\(509\) 3.86065 6.68684i 0.171120 0.296389i −0.767692 0.640819i \(-0.778595\pi\)
0.938812 + 0.344431i \(0.111928\pi\)
\(510\) −5.13487 + 8.89385i −0.227376 + 0.393826i
\(511\) −18.3073 31.7091i −0.809865 1.40273i
\(512\) −11.0000 −0.486136
\(513\) −3.14605 5.44912i −0.138902 0.240585i
\(514\) −1.53427 2.65743i −0.0676738 0.117214i
\(515\) 27.6046 1.21641
\(516\) −2.85395 4.94318i −0.125638 0.217611i
\(517\) 0.984848 1.70581i 0.0433136 0.0750213i
\(518\) 15.4742 26.8021i 0.679897 1.17762i
\(519\) −33.2181 −1.45811
\(520\) −16.6990 15.6487i −0.732299 0.686242i
\(521\) 5.48979 0.240512 0.120256 0.992743i \(-0.461628\pi\)
0.120256 + 0.992743i \(0.461628\pi\)
\(522\) −3.69547 + 6.40075i −0.161747 + 0.280153i
\(523\) −20.6068 + 35.6921i −0.901074 + 1.56071i −0.0749720 + 0.997186i \(0.523887\pi\)
−0.826102 + 0.563520i \(0.809447\pi\)
\(524\) 6.80453 + 11.7858i 0.297257 + 0.514864i
\(525\) 4.00000 0.174574
\(526\) −1.14605 1.98502i −0.0499703 0.0865511i
\(527\) −9.95630 17.2448i −0.433703 0.751196i
\(528\) 2.26180 0.0984323
\(529\) 1.26850 + 2.19711i 0.0551522 + 0.0955265i
\(530\) −8.20393 + 14.2096i −0.356356 + 0.617226i
\(531\) 6.37931 11.0493i 0.276838 0.479498i
\(532\) −10.6260 −0.460694
\(533\) −34.5641 + 10.4748i −1.49714 + 0.453713i
\(534\) −21.1416 −0.914888
\(535\) 14.3967 24.9358i 0.622422 1.07807i
\(536\) 6.04546 10.4710i 0.261124 0.452280i
\(537\) −7.34328 12.7189i −0.316886 0.548863i
\(538\) 11.2449 0.484802
\(539\) −2.20393 3.81731i −0.0949299 0.164423i
\(540\) 2.11575 + 3.66459i 0.0910474 + 0.157699i
\(541\) 31.2539 1.34371 0.671854 0.740683i \(-0.265498\pi\)
0.671854 + 0.740683i \(0.265498\pi\)
\(542\) 2.14605 + 3.71707i 0.0921809 + 0.159662i
\(543\) −19.4096 + 33.6184i −0.832946 + 1.44270i
\(544\) 5.36513 9.29268i 0.230028 0.398420i
\(545\) 39.5361 1.69354
\(546\) 26.3602 7.98855i 1.12811 0.341879i
\(547\) 2.40239 0.102719 0.0513594 0.998680i \(-0.483645\pi\)
0.0513594 + 0.998680i \(0.483645\pi\)
\(548\) −7.55118 + 13.0790i −0.322570 + 0.558708i
\(549\) −10.3517 + 17.9297i −0.441801 + 0.765222i
\(550\) 0.261802 + 0.453455i 0.0111633 + 0.0193354i
\(551\) 10.9901 0.468194
\(552\) −15.3472 26.5822i −0.653222 1.13141i
\(553\) −2.81968 4.88382i −0.119905 0.207681i
\(554\) −4.83262 −0.205318
\(555\) −21.9242 37.9739i −0.930632 1.61190i
\(556\) −7.63935 + 13.2317i −0.323981 + 0.561151i
\(557\) −1.22305 + 2.11838i −0.0518221 + 0.0897586i −0.890773 0.454449i \(-0.849836\pi\)
0.838951 + 0.544207i \(0.183170\pi\)
\(558\) −19.6314 −0.831064
\(559\) 2.06854 8.86074i 0.0874899 0.374769i
\(560\) −7.14605 −0.301976
\(561\) −2.42697 + 4.20364i −0.102467 + 0.177478i
\(562\) −1.89270 + 3.27826i −0.0798389 + 0.138285i
\(563\) −19.2293 33.3061i −0.810418 1.40368i −0.912572 0.408916i \(-0.865907\pi\)
0.102154 0.994769i \(-0.467426\pi\)
\(564\) −4.45506 −0.187592
\(565\) −13.3709 23.1590i −0.562516 0.974306i
\(566\) 6.21238 + 10.7602i 0.261126 + 0.452283i
\(567\) −36.7169 −1.54196
\(568\) 9.00000 + 15.5885i 0.377632 + 0.654077i
\(569\) −19.6260 + 33.9932i −0.822763 + 1.42507i 0.0808542 + 0.996726i \(0.474235\pi\)
−0.903617 + 0.428341i \(0.859098\pi\)
\(570\) 7.52757 13.0381i 0.315295 0.546107i
\(571\) −39.3349 −1.64611 −0.823057 0.567959i \(-0.807733\pi\)
−0.823057 + 0.567959i \(0.807733\pi\)
\(572\) −2.63090 2.46543i −0.110004 0.103085i
\(573\) −40.6439 −1.69792
\(574\) −16.9163 + 29.2999i −0.706073 + 1.22295i
\(575\) 1.18429 2.05125i 0.0493883 0.0855430i
\(576\) −7.40512 12.8260i −0.308547 0.534419i
\(577\) −24.0890 −1.00284 −0.501418 0.865205i \(-0.667188\pi\)
−0.501418 + 0.865205i \(0.667188\pi\)
\(578\) 6.19723 + 10.7339i 0.257771 + 0.446472i
\(579\) −3.35843 5.81698i −0.139572 0.241745i
\(580\) −7.39095 −0.306892
\(581\) −9.57478 16.5840i −0.397229 0.688020i
\(582\) 13.1630 22.7989i 0.545622 0.945045i
\(583\) −3.87755 + 6.71612i −0.160592 + 0.278153i
\(584\) −32.5216 −1.34576
\(585\) 3.66920 15.7173i 0.151703 0.649829i
\(586\) 16.9012 0.698180
\(587\) −12.2333 + 21.1886i −0.504920 + 0.874548i 0.495063 + 0.868857i \(0.335145\pi\)
−0.999984 + 0.00569090i \(0.998189\pi\)
\(588\) −4.98485 + 8.63401i −0.205572 + 0.356061i
\(589\) 14.5957 + 25.2804i 0.601403 + 1.04166i
\(590\) −12.7586 −0.525264
\(591\) 13.8326 + 23.9588i 0.568998 + 0.985533i
\(592\) −4.58148 7.93535i −0.188298 0.326141i
\(593\) 33.6215 1.38067 0.690335 0.723490i \(-0.257463\pi\)
0.690335 + 0.723490i \(0.257463\pi\)
\(594\) −1.00000 1.73205i −0.0410305 0.0710669i
\(595\) 7.66790 13.2812i 0.314353 0.544476i
\(596\) 2.18878 3.79107i 0.0896558 0.155288i
\(597\) 0.455064 0.0186245
\(598\) 3.70789 15.8830i 0.151627 0.649505i
\(599\) 3.01340 0.123124 0.0615621 0.998103i \(-0.480392\pi\)
0.0615621 + 0.998103i \(0.480392\pi\)
\(600\) 1.77643 3.07688i 0.0725226 0.125613i
\(601\) 9.28716 16.0858i 0.378831 0.656155i −0.612061 0.790810i \(-0.709659\pi\)
0.990892 + 0.134655i \(0.0429928\pi\)
\(602\) −4.26180 7.38166i −0.173698 0.300854i
\(603\) 8.52711 0.347251
\(604\) 1.14605 + 1.98502i 0.0466322 + 0.0807694i
\(605\) −1.05787 1.83229i −0.0430087 0.0744933i
\(606\) −2.03824 −0.0827977
\(607\) 9.60684 + 16.6395i 0.389930 + 0.675378i 0.992440 0.122733i \(-0.0391660\pi\)
−0.602510 + 0.798111i \(0.705833\pi\)
\(608\) −7.86513 + 13.6228i −0.318973 + 0.552478i
\(609\) 13.3433 23.1112i 0.540697 0.936515i
\(610\) 20.7035 0.838259
\(611\) −5.18208 4.85615i −0.209644 0.196459i
\(612\) 4.54051 0.183539
\(613\) −9.46748 + 16.3982i −0.382388 + 0.662316i −0.991403 0.130843i \(-0.958232\pi\)
0.609015 + 0.793159i \(0.291565\pi\)
\(614\) 4.21238 7.29606i 0.169998 0.294445i
\(615\) 23.9675 + 41.5129i 0.966462 + 1.67396i
\(616\) −10.1327 −0.408256
\(617\) 0.860646 + 1.49068i 0.0346483 + 0.0600126i 0.882830 0.469693i \(-0.155636\pi\)
−0.848181 + 0.529706i \(0.822302\pi\)
\(618\) 14.7551 + 25.5566i 0.593537 + 1.02804i
\(619\) 16.3562 0.657412 0.328706 0.944432i \(-0.393387\pi\)
0.328706 + 0.944432i \(0.393387\pi\)
\(620\) −9.81571 17.0013i −0.394208 0.682789i
\(621\) −4.52360 + 7.83511i −0.181526 + 0.314412i
\(622\) 14.2939 24.7577i 0.573132 0.992693i
\(623\) 31.5708 1.26486
\(624\) 1.85395 7.94151i 0.0742173 0.317915i
\(625\) −22.1078 −0.884313
\(626\) −11.1972 + 19.3942i −0.447531 + 0.775147i
\(627\) 3.55787 6.16242i 0.142088 0.246103i
\(628\) −12.0236 20.8255i −0.479794 0.831028i
\(629\) 19.6642 0.784063
\(630\) −7.55963 13.0937i −0.301183 0.521664i
\(631\) 10.5388 + 18.2537i 0.419541 + 0.726667i 0.995893 0.0905347i \(-0.0288576\pi\)
−0.576352 + 0.817202i \(0.695524\pi\)
\(632\) −5.00897 −0.199246
\(633\) 13.1972 + 22.8583i 0.524543 + 0.908535i
\(634\) 13.1354 22.7512i 0.521673 0.903564i
\(635\) −12.1764 + 21.0901i −0.483204 + 0.836934i
\(636\) 17.5405 0.695526
\(637\) −15.2096 + 4.60934i −0.602628 + 0.182629i
\(638\) 3.49330 0.138301
\(639\) −6.34725 + 10.9938i −0.251093 + 0.434906i
\(640\) 3.17362 5.49688i 0.125449 0.217283i
\(641\) 2.26850 + 3.92916i 0.0896004 + 0.155192i 0.907342 0.420393i \(-0.138108\pi\)
−0.817742 + 0.575585i \(0.804774\pi\)
\(642\) 30.7810 1.21483
\(643\) 0.491547 + 0.851385i 0.0193847 + 0.0335753i 0.875555 0.483118i \(-0.160496\pi\)
−0.856170 + 0.516694i \(0.827163\pi\)
\(644\) 7.63935 + 13.2317i 0.301033 + 0.521404i
\(645\) −12.0765 −0.475511
\(646\) 3.37580 + 5.84705i 0.132819 + 0.230049i
\(647\) 23.3428 40.4310i 0.917701 1.58950i 0.114803 0.993388i \(-0.463376\pi\)
0.802898 0.596117i \(-0.203290\pi\)
\(648\) −16.3063 + 28.2433i −0.640571 + 1.10950i
\(649\) −6.03030 −0.236710
\(650\) 1.80674 0.547539i 0.0708661 0.0214762i
\(651\) 70.8833 2.77814
\(652\) −3.27695 + 5.67585i −0.128335 + 0.222283i
\(653\) 12.9354 22.4048i 0.506202 0.876768i −0.493772 0.869591i \(-0.664382\pi\)
0.999974 0.00717672i \(-0.00228444\pi\)
\(654\) 21.1327 + 36.6028i 0.826352 + 1.43128i
\(655\) 28.7933 1.12505
\(656\) 5.00845 + 8.67489i 0.195547 + 0.338698i
\(657\) −11.4679 19.8631i −0.447407 0.774932i
\(658\) −6.65275 −0.259351
\(659\) −8.74938 15.1544i −0.340828 0.590331i 0.643759 0.765228i \(-0.277374\pi\)
−0.984587 + 0.174898i \(0.944041\pi\)
\(660\) −2.39270 + 4.14428i −0.0931359 + 0.161316i
\(661\) −10.8264 + 18.7518i −0.421097 + 0.729362i −0.996047 0.0888269i \(-0.971688\pi\)
0.574950 + 0.818189i \(0.305022\pi\)
\(662\) −8.29211 −0.322282
\(663\) 12.7703 + 11.9671i 0.495956 + 0.464763i
\(664\) −17.0090 −0.660076
\(665\) −11.2409 + 19.4699i −0.435905 + 0.755009i
\(666\) 9.69326 16.7892i 0.375606 0.650569i
\(667\) −7.90116 13.6852i −0.305934 0.529893i
\(668\) 18.3259 0.709051
\(669\) −8.48933 14.7040i −0.328217 0.568488i
\(670\) −4.26356 7.38470i −0.164716 0.285296i
\(671\) 9.78541 0.377761
\(672\) 19.0984 + 33.0794i 0.736736 + 1.27606i
\(673\) 11.9399 20.6805i 0.460250 0.797176i −0.538723 0.842483i \(-0.681093\pi\)
0.998973 + 0.0453067i \(0.0144265\pi\)
\(674\) 0.0258174 0.0447171i 0.000994451 0.00172244i
\(675\) −1.04721 −0.0403071
\(676\) −10.8130 + 7.21661i −0.415884 + 0.277562i
\(677\) −12.6945 −0.487889 −0.243945 0.969789i \(-0.578441\pi\)
−0.243945 + 0.969789i \(0.578441\pi\)
\(678\) 14.2939 24.7577i 0.548952 0.950813i
\(679\) −19.6563 + 34.0456i −0.754338 + 1.30655i
\(680\) −6.81077 11.7966i −0.261181 0.452379i
\(681\) 7.86292 0.301308
\(682\) 4.63935 + 8.03560i 0.177650 + 0.307699i
\(683\) 18.9350 + 32.7963i 0.724526 + 1.25492i 0.959169 + 0.282835i \(0.0912748\pi\)
−0.234642 + 0.972082i \(0.575392\pi\)
\(684\) −6.65626 −0.254508
\(685\) 15.9764 + 27.6719i 0.610427 + 1.05729i
\(686\) 4.37755 7.58214i 0.167136 0.289488i
\(687\) 15.1630 26.2630i 0.578503 1.00200i
\(688\) −2.52360 −0.0962115
\(689\) 20.4029 + 19.1197i 0.777289 + 0.728402i
\(690\) −21.6473 −0.824098
\(691\) −12.8709 + 22.2930i −0.489630 + 0.848065i −0.999929 0.0119328i \(-0.996202\pi\)
0.510298 + 0.859997i \(0.329535\pi\)
\(692\) 7.34328 12.7189i 0.279150 0.483501i
\(693\) −3.57303 6.18866i −0.135728 0.235088i
\(694\) −8.62245 −0.327304
\(695\) 16.1630 + 27.9951i 0.613096 + 1.06191i
\(696\) −11.8517 20.5278i −0.449239 0.778104i
\(697\) −21.4968 −0.814250
\(698\) −15.0000 25.9808i −0.567758 0.983386i
\(699\) 0.330343 0.572170i 0.0124947 0.0216415i
\(700\) −0.884251 + 1.53157i −0.0334215 + 0.0578878i
\(701\) −33.5023 −1.26536 −0.632682 0.774412i \(-0.718046\pi\)
−0.632682 + 0.774412i \(0.718046\pi\)
\(702\) −6.90116 + 2.09142i −0.260467 + 0.0789356i
\(703\) −28.8272 −1.08724
\(704\) −3.50000 + 6.06218i −0.131911 + 0.228477i
\(705\) −4.71290 + 8.16298i −0.177498 + 0.307436i
\(706\) 0.238198 + 0.412571i 0.00896469 + 0.0155273i
\(707\) 3.04370 0.114470
\(708\) 6.81968 + 11.8120i 0.256299 + 0.443923i
\(709\) 15.4618 + 26.7806i 0.580679 + 1.00577i 0.995399 + 0.0958161i \(0.0305461\pi\)
−0.414720 + 0.909949i \(0.636121\pi\)
\(710\) 12.6945 0.476416
\(711\) −1.76629 3.05930i −0.0662410 0.114733i
\(712\) 14.0209 24.2849i 0.525454 0.910114i
\(713\) 20.9866 36.3499i 0.785954 1.36131i
\(714\) 16.3945 0.613547
\(715\) −7.30056 + 2.21246i −0.273025 + 0.0827414i
\(716\) 6.49330 0.242666
\(717\) −24.6563 + 42.7059i −0.920805 + 1.59488i
\(718\) 5.11575 8.86074i 0.190918 0.330680i
\(719\) −4.60905 7.98311i −0.171889 0.297720i 0.767192 0.641418i \(-0.221654\pi\)
−0.939080 + 0.343698i \(0.888320\pi\)
\(720\) −4.47640 −0.166825
\(721\) −22.0338 38.1637i −0.820582 1.42129i
\(722\) 4.55118 + 7.88287i 0.169377 + 0.293370i
\(723\) 5.76408 0.214368
\(724\) −8.58148 14.8636i −0.318928 0.552400i
\(725\) 0.914554 1.58405i 0.0339657 0.0588303i
\(726\) 1.13090 1.95878i 0.0419717 0.0726971i
\(727\) 33.5102 1.24282 0.621412 0.783484i \(-0.286559\pi\)
0.621412 + 0.783484i \(0.286559\pi\)
\(728\) −8.30550 + 35.5772i −0.307822 + 1.31858i
\(729\) −9.42919 −0.349229
\(730\) −11.4679 + 19.8631i −0.424448 + 0.735165i
\(731\) 2.70789 4.69021i 0.100155 0.173474i
\(732\) −11.0663 19.1674i −0.409023 0.708449i
\(733\) −1.29561 −0.0478546 −0.0239273 0.999714i \(-0.507617\pi\)
−0.0239273 + 0.999714i \(0.507617\pi\)
\(734\) −10.6697 18.4804i −0.393824 0.682124i
\(735\) 10.5467 + 18.2674i 0.389021 + 0.673803i
\(736\) 22.6180 0.833711
\(737\) −2.01515 3.49035i −0.0742291 0.128569i
\(738\) −10.5966 + 18.3539i −0.390067 + 0.675617i
\(739\) −14.4248 + 24.9844i −0.530623 + 0.919067i 0.468738 + 0.883337i \(0.344709\pi\)
−0.999361 + 0.0357295i \(0.988625\pi\)
\(740\) 19.3865 0.712663
\(741\) −18.7208 17.5434i −0.687727 0.644473i
\(742\) 26.1933 0.961585
\(743\) 15.8686 27.4853i 0.582164 1.00834i −0.413059 0.910704i \(-0.635540\pi\)
0.995222 0.0976330i \(-0.0311271\pi\)
\(744\) 31.4799 54.5248i 1.15411 1.99898i
\(745\) −4.63090 8.02096i −0.169663 0.293865i
\(746\) 21.2271 0.777178
\(747\) −5.99779 10.3885i −0.219448 0.380094i
\(748\) −1.07303 1.85854i −0.0392337 0.0679548i
\(749\) −45.9653 −1.67953
\(750\) −13.2163 22.8914i −0.482593 0.835875i
\(751\) 18.0641 31.2880i 0.659169 1.14171i −0.321662 0.946854i \(-0.604242\pi\)
0.980831 0.194860i \(-0.0624251\pi\)
\(752\) −0.984848 + 1.70581i −0.0359137 + 0.0622044i
\(753\) 60.6598 2.21056
\(754\) 2.86338 12.2655i 0.104278 0.446682i
\(755\) 4.84952 0.176492
\(756\) 3.37755 5.85009i 0.122840 0.212766i
\(757\) 11.0263 19.0982i 0.400759 0.694135i −0.593059 0.805159i \(-0.702080\pi\)
0.993818 + 0.111024i \(0.0354131\pi\)
\(758\) 0.523604 + 0.906910i 0.0190182 + 0.0329404i
\(759\) −10.2315 −0.371380
\(760\) 9.98439 + 17.2935i 0.362172 + 0.627300i
\(761\) −20.0810 34.7813i −0.727936 1.26082i −0.957754 0.287589i \(-0.907146\pi\)
0.229817 0.973234i \(-0.426187\pi\)
\(762\) −26.0338 −0.943105
\(763\) −31.5574 54.6590i −1.14246 1.97879i
\(764\) 8.98485 15.5622i 0.325060 0.563021i
\(765\) 4.80329 8.31954i 0.173663 0.300794i
\(766\) −28.9866 −1.04733
\(767\) −4.94290 + 21.1733i −0.178478 + 0.764522i
\(768\) 38.4506 1.38747
\(769\) 12.4799 21.6158i 0.450037 0.779487i −0.548351 0.836248i \(-0.684744\pi\)
0.998388 + 0.0567617i \(0.0180775\pi\)
\(770\) −3.57303 + 6.18866i −0.128763 + 0.223024i
\(771\) 3.47022 + 6.01059i 0.124977 + 0.216466i
\(772\) 2.96970 0.106882
\(773\) −2.73423 4.73583i −0.0983435 0.170336i 0.812656 0.582744i \(-0.198021\pi\)
−0.910999 + 0.412408i \(0.864688\pi\)
\(774\) −2.66966 4.62398i −0.0959589 0.166206i
\(775\) 4.85837