Properties

Label 150.2.g.b.31.1
Level $150$
Weight $2$
Character 150.31
Analytic conductor $1.198$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 150.g (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.19775603032\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \(x^{4} - x^{3} + x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 31.1
Root \(-0.309017 + 0.951057i\) of defining polynomial
Character \(\chi\) \(=\) 150.31
Dual form 150.2.g.b.121.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-0.809017 - 0.587785i) q^{6} +2.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-0.809017 - 0.587785i) q^{6} +2.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.690983 - 2.12663i) q^{10} +(-1.61803 - 4.97980i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(-1.50000 + 4.61653i) q^{13} +(-0.618034 - 1.90211i) q^{14} +2.23607 q^{15} +(0.309017 - 0.951057i) q^{16} +(-6.35410 - 4.61653i) q^{17} -1.00000 q^{18} +(2.23607 + 1.62460i) q^{19} -2.23607 q^{20} +(1.61803 - 1.17557i) q^{21} +(-4.23607 + 3.07768i) q^{22} +(1.85410 + 5.70634i) q^{23} +1.00000 q^{24} +(1.54508 + 4.75528i) q^{25} +4.85410 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-1.61803 + 1.17557i) q^{28} +(1.11803 - 0.812299i) q^{29} +(-0.690983 - 2.12663i) q^{30} +(-3.00000 - 2.17963i) q^{31} -1.00000 q^{32} +(-4.23607 - 3.07768i) q^{33} +(-2.42705 + 7.46969i) q^{34} +(3.61803 + 2.62866i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-0.663119 + 2.04087i) q^{37} +(0.854102 - 2.62866i) q^{38} +(1.50000 + 4.61653i) q^{39} +(0.690983 + 2.12663i) q^{40} +(-1.88197 + 5.79210i) q^{41} +(-1.61803 - 1.17557i) q^{42} -1.23607 q^{43} +(4.23607 + 3.07768i) q^{44} +(1.80902 - 1.31433i) q^{45} +(4.85410 - 3.52671i) q^{46} +(-3.85410 + 2.80017i) q^{47} +(-0.309017 - 0.951057i) q^{48} -3.00000 q^{49} +(4.04508 - 2.93893i) q^{50} -7.85410 q^{51} +(-1.50000 - 4.61653i) q^{52} +(-6.92705 + 5.03280i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(3.61803 - 11.1352i) q^{55} +(1.61803 + 1.17557i) q^{56} +2.76393 q^{57} +(-1.11803 - 0.812299i) q^{58} +(2.76393 - 8.50651i) q^{59} +(-1.80902 + 1.31433i) q^{60} +(-2.73607 - 8.42075i) q^{61} +(-1.14590 + 3.52671i) q^{62} +(0.618034 - 1.90211i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-8.78115 + 6.37988i) q^{65} +(-1.61803 + 4.97980i) q^{66} +(7.85410 + 5.70634i) q^{67} +7.85410 q^{68} +(4.85410 + 3.52671i) q^{69} +(1.38197 - 4.25325i) q^{70} +(11.4721 - 8.33499i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-0.972136 - 2.99193i) q^{73} +2.14590 q^{74} +(4.04508 + 2.93893i) q^{75} -2.76393 q^{76} +(-3.23607 - 9.95959i) q^{77} +(3.92705 - 2.85317i) q^{78} +(1.80902 - 1.31433i) q^{80} +(-0.809017 - 0.587785i) q^{81} +6.09017 q^{82} +(-4.85410 - 3.52671i) q^{83} +(-0.618034 + 1.90211i) q^{84} +(-5.42705 - 16.7027i) q^{85} +(0.381966 + 1.17557i) q^{86} +(0.427051 - 1.31433i) q^{87} +(1.61803 - 4.97980i) q^{88} +(0.427051 + 1.31433i) q^{89} +(-1.80902 - 1.31433i) q^{90} +(-3.00000 + 9.23305i) q^{91} +(-4.85410 - 3.52671i) q^{92} -3.70820 q^{93} +(3.85410 + 2.80017i) q^{94} +(1.90983 + 5.87785i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(11.2082 - 8.14324i) q^{97} +(0.927051 + 2.85317i) q^{98} -5.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{2} + q^{3} - q^{4} + 5q^{5} - q^{6} + 8q^{7} + q^{8} - q^{9} + O(q^{10}) \) \( 4q + q^{2} + q^{3} - q^{4} + 5q^{5} - q^{6} + 8q^{7} + q^{8} - q^{9} + 5q^{10} - 2q^{11} + q^{12} - 6q^{13} + 2q^{14} - q^{16} - 12q^{17} - 4q^{18} + 2q^{21} - 8q^{22} - 6q^{23} + 4q^{24} - 5q^{25} + 6q^{26} + q^{27} - 2q^{28} - 5q^{30} - 12q^{31} - 4q^{32} - 8q^{33} - 3q^{34} + 10q^{35} - q^{36} + 13q^{37} - 10q^{38} + 6q^{39} + 5q^{40} - 12q^{41} - 2q^{42} + 4q^{43} + 8q^{44} + 5q^{45} + 6q^{46} - 2q^{47} + q^{48} - 12q^{49} + 5q^{50} - 18q^{51} - 6q^{52} - 21q^{53} - q^{54} + 10q^{55} + 2q^{56} + 20q^{57} + 20q^{59} - 5q^{60} - 2q^{61} - 18q^{62} - 2q^{63} - q^{64} - 15q^{65} - 2q^{66} + 18q^{67} + 18q^{68} + 6q^{69} + 10q^{70} + 28q^{71} + q^{72} + 14q^{73} + 22q^{74} + 5q^{75} - 20q^{76} - 4q^{77} + 9q^{78} + 5q^{80} - q^{81} + 2q^{82} - 6q^{83} + 2q^{84} - 15q^{85} + 6q^{86} - 5q^{87} + 2q^{88} - 5q^{89} - 5q^{90} - 12q^{91} - 6q^{92} + 12q^{93} + 2q^{94} + 30q^{95} - q^{96} + 18q^{97} - 3q^{98} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 0.951057i −0.218508 0.672499i
\(3\) 0.809017 0.587785i 0.467086 0.339358i
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) 1.80902 + 1.31433i 0.809017 + 0.587785i
\(6\) −0.809017 0.587785i −0.330280 0.239962i
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 0.809017 + 0.587785i 0.286031 + 0.207813i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) 0.690983 2.12663i 0.218508 0.672499i
\(11\) −1.61803 4.97980i −0.487856 1.50147i −0.827802 0.561020i \(-0.810409\pi\)
0.339946 0.940445i \(-0.389591\pi\)
\(12\) −0.309017 + 0.951057i −0.0892055 + 0.274546i
\(13\) −1.50000 + 4.61653i −0.416025 + 1.28039i 0.495306 + 0.868719i \(0.335056\pi\)
−0.911331 + 0.411675i \(0.864944\pi\)
\(14\) −0.618034 1.90211i −0.165177 0.508361i
\(15\) 2.23607 0.577350
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) −6.35410 4.61653i −1.54110 1.11967i −0.949644 0.313332i \(-0.898555\pi\)
−0.591452 0.806340i \(-0.701445\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.23607 + 1.62460i 0.512989 + 0.372708i 0.813956 0.580926i \(-0.197309\pi\)
−0.300967 + 0.953635i \(0.597309\pi\)
\(20\) −2.23607 −0.500000
\(21\) 1.61803 1.17557i 0.353084 0.256531i
\(22\) −4.23607 + 3.07768i −0.903133 + 0.656164i
\(23\) 1.85410 + 5.70634i 0.386607 + 1.18985i 0.935308 + 0.353835i \(0.115123\pi\)
−0.548701 + 0.836019i \(0.684877\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.54508 + 4.75528i 0.309017 + 0.951057i
\(26\) 4.85410 0.951968
\(27\) −0.309017 0.951057i −0.0594703 0.183031i
\(28\) −1.61803 + 1.17557i −0.305780 + 0.222162i
\(29\) 1.11803 0.812299i 0.207614 0.150840i −0.479120 0.877750i \(-0.659044\pi\)
0.686733 + 0.726909i \(0.259044\pi\)
\(30\) −0.690983 2.12663i −0.126156 0.388267i
\(31\) −3.00000 2.17963i −0.538816 0.391473i 0.284829 0.958578i \(-0.408063\pi\)
−0.823645 + 0.567106i \(0.808063\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.23607 3.07768i −0.737405 0.535756i
\(34\) −2.42705 + 7.46969i −0.416236 + 1.28104i
\(35\) 3.61803 + 2.62866i 0.611559 + 0.444324i
\(36\) 0.309017 + 0.951057i 0.0515028 + 0.158509i
\(37\) −0.663119 + 2.04087i −0.109016 + 0.335517i −0.990652 0.136413i \(-0.956443\pi\)
0.881636 + 0.471930i \(0.156443\pi\)
\(38\) 0.854102 2.62866i 0.138554 0.426424i
\(39\) 1.50000 + 4.61653i 0.240192 + 0.739236i
\(40\) 0.690983 + 2.12663i 0.109254 + 0.336249i
\(41\) −1.88197 + 5.79210i −0.293914 + 0.904573i 0.689670 + 0.724123i \(0.257755\pi\)
−0.983584 + 0.180450i \(0.942245\pi\)
\(42\) −1.61803 1.17557i −0.249668 0.181394i
\(43\) −1.23607 −0.188499 −0.0942493 0.995549i \(-0.530045\pi\)
−0.0942493 + 0.995549i \(0.530045\pi\)
\(44\) 4.23607 + 3.07768i 0.638611 + 0.463978i
\(45\) 1.80902 1.31433i 0.269672 0.195928i
\(46\) 4.85410 3.52671i 0.715698 0.519985i
\(47\) −3.85410 + 2.80017i −0.562179 + 0.408447i −0.832256 0.554392i \(-0.812951\pi\)
0.270077 + 0.962839i \(0.412951\pi\)
\(48\) −0.309017 0.951057i −0.0446028 0.137273i
\(49\) −3.00000 −0.428571
\(50\) 4.04508 2.93893i 0.572061 0.415627i
\(51\) −7.85410 −1.09979
\(52\) −1.50000 4.61653i −0.208013 0.640197i
\(53\) −6.92705 + 5.03280i −0.951504 + 0.691308i −0.951162 0.308692i \(-0.900109\pi\)
−0.000341607 1.00000i \(0.500109\pi\)
\(54\) −0.809017 + 0.587785i −0.110093 + 0.0799874i
\(55\) 3.61803 11.1352i 0.487856 1.50147i
\(56\) 1.61803 + 1.17557i 0.216219 + 0.157092i
\(57\) 2.76393 0.366092
\(58\) −1.11803 0.812299i −0.146805 0.106660i
\(59\) 2.76393 8.50651i 0.359833 1.10745i −0.593320 0.804966i \(-0.702183\pi\)
0.953154 0.302487i \(-0.0978167\pi\)
\(60\) −1.80902 + 1.31433i −0.233543 + 0.169679i
\(61\) −2.73607 8.42075i −0.350318 1.07817i −0.958675 0.284504i \(-0.908171\pi\)
0.608357 0.793663i \(-0.291829\pi\)
\(62\) −1.14590 + 3.52671i −0.145529 + 0.447893i
\(63\) 0.618034 1.90211i 0.0778650 0.239644i
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) −8.78115 + 6.37988i −1.08917 + 0.791327i
\(66\) −1.61803 + 4.97980i −0.199166 + 0.612971i
\(67\) 7.85410 + 5.70634i 0.959531 + 0.697140i 0.953042 0.302839i \(-0.0979343\pi\)
0.00648944 + 0.999979i \(0.497934\pi\)
\(68\) 7.85410 0.952450
\(69\) 4.85410 + 3.52671i 0.584365 + 0.424566i
\(70\) 1.38197 4.25325i 0.165177 0.508361i
\(71\) 11.4721 8.33499i 1.36149 0.989182i 0.363144 0.931733i \(-0.381703\pi\)
0.998348 0.0574487i \(-0.0182966\pi\)
\(72\) 0.809017 0.587785i 0.0953436 0.0692712i
\(73\) −0.972136 2.99193i −0.113780 0.350179i 0.877911 0.478824i \(-0.158937\pi\)
−0.991691 + 0.128646i \(0.958937\pi\)
\(74\) 2.14590 0.249456
\(75\) 4.04508 + 2.93893i 0.467086 + 0.339358i
\(76\) −2.76393 −0.317045
\(77\) −3.23607 9.95959i −0.368784 1.13500i
\(78\) 3.92705 2.85317i 0.444651 0.323058i
\(79\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(80\) 1.80902 1.31433i 0.202254 0.146946i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 6.09017 0.672547
\(83\) −4.85410 3.52671i −0.532807 0.387107i 0.288600 0.957450i \(-0.406810\pi\)
−0.821407 + 0.570343i \(0.806810\pi\)
\(84\) −0.618034 + 1.90211i −0.0674330 + 0.207538i
\(85\) −5.42705 16.7027i −0.588646 1.81167i
\(86\) 0.381966 + 1.17557i 0.0411885 + 0.126765i
\(87\) 0.427051 1.31433i 0.0457847 0.140911i
\(88\) 1.61803 4.97980i 0.172483 0.530848i
\(89\) 0.427051 + 1.31433i 0.0452673 + 0.139318i 0.971136 0.238528i \(-0.0766648\pi\)
−0.925868 + 0.377846i \(0.876665\pi\)
\(90\) −1.80902 1.31433i −0.190687 0.138542i
\(91\) −3.00000 + 9.23305i −0.314485 + 0.967887i
\(92\) −4.85410 3.52671i −0.506075 0.367685i
\(93\) −3.70820 −0.384523
\(94\) 3.85410 + 2.80017i 0.397520 + 0.288815i
\(95\) 1.90983 + 5.87785i 0.195944 + 0.603055i
\(96\) −0.809017 + 0.587785i −0.0825700 + 0.0599906i
\(97\) 11.2082 8.14324i 1.13802 0.826820i 0.151178 0.988506i \(-0.451693\pi\)
0.986842 + 0.161686i \(0.0516932\pi\)
\(98\) 0.927051 + 2.85317i 0.0936463 + 0.288214i
\(99\) −5.23607 −0.526245
\(100\) −4.04508 2.93893i −0.404508 0.293893i
\(101\) 1.67376 0.166546 0.0832728 0.996527i \(-0.473463\pi\)
0.0832728 + 0.996527i \(0.473463\pi\)
\(102\) 2.42705 + 7.46969i 0.240314 + 0.739610i
\(103\) 1.85410 1.34708i 0.182690 0.132732i −0.492682 0.870210i \(-0.663983\pi\)
0.675372 + 0.737478i \(0.263983\pi\)
\(104\) −3.92705 + 2.85317i −0.385079 + 0.279776i
\(105\) 4.47214 0.436436
\(106\) 6.92705 + 5.03280i 0.672815 + 0.488828i
\(107\) 10.9443 1.05802 0.529011 0.848615i \(-0.322563\pi\)
0.529011 + 0.848615i \(0.322563\pi\)
\(108\) 0.809017 + 0.587785i 0.0778477 + 0.0565597i
\(109\) 0.791796 2.43690i 0.0758403 0.233412i −0.905949 0.423388i \(-0.860841\pi\)
0.981789 + 0.189975i \(0.0608408\pi\)
\(110\) −11.7082 −1.11633
\(111\) 0.663119 + 2.04087i 0.0629405 + 0.193711i
\(112\) 0.618034 1.90211i 0.0583987 0.179733i
\(113\) −3.57295 + 10.9964i −0.336115 + 1.03445i 0.630056 + 0.776550i \(0.283032\pi\)
−0.966170 + 0.257905i \(0.916968\pi\)
\(114\) −0.854102 2.62866i −0.0799940 0.246196i
\(115\) −4.14590 + 12.7598i −0.386607 + 1.18985i
\(116\) −0.427051 + 1.31433i −0.0396507 + 0.122032i
\(117\) 3.92705 + 2.85317i 0.363056 + 0.263776i
\(118\) −8.94427 −0.823387
\(119\) −12.7082 9.23305i −1.16496 0.846392i
\(120\) 1.80902 + 1.31433i 0.165140 + 0.119981i
\(121\) −13.2812 + 9.64932i −1.20738 + 0.877211i
\(122\) −7.16312 + 5.20431i −0.648518 + 0.471176i
\(123\) 1.88197 + 5.79210i 0.169691 + 0.522256i
\(124\) 3.70820 0.333007
\(125\) −3.45492 + 10.6331i −0.309017 + 0.951057i
\(126\) −2.00000 −0.178174
\(127\) 0.0901699 + 0.277515i 0.00800129 + 0.0246254i 0.954977 0.296678i \(-0.0958789\pi\)
−0.946976 + 0.321304i \(0.895879\pi\)
\(128\) 0.809017 0.587785i 0.0715077 0.0519534i
\(129\) −1.00000 + 0.726543i −0.0880451 + 0.0639685i
\(130\) 8.78115 + 6.37988i 0.770158 + 0.559553i
\(131\) 0.618034 + 0.449028i 0.0539979 + 0.0392318i 0.614457 0.788950i \(-0.289375\pi\)
−0.560459 + 0.828182i \(0.689375\pi\)
\(132\) 5.23607 0.455741
\(133\) 4.47214 + 3.24920i 0.387783 + 0.281741i
\(134\) 3.00000 9.23305i 0.259161 0.797614i
\(135\) 0.690983 2.12663i 0.0594703 0.183031i
\(136\) −2.42705 7.46969i −0.208118 0.640521i
\(137\) −4.64590 + 14.2986i −0.396926 + 1.22161i 0.530526 + 0.847669i \(0.321995\pi\)
−0.927452 + 0.373943i \(0.878005\pi\)
\(138\) 1.85410 5.70634i 0.157832 0.485756i
\(139\) −4.14590 12.7598i −0.351650 1.08227i −0.957926 0.287014i \(-0.907337\pi\)
0.606276 0.795254i \(-0.292663\pi\)
\(140\) −4.47214 −0.377964
\(141\) −1.47214 + 4.53077i −0.123976 + 0.381560i
\(142\) −11.4721 8.33499i −0.962720 0.699457i
\(143\) 25.4164 2.12543
\(144\) −0.809017 0.587785i −0.0674181 0.0489821i
\(145\) 3.09017 0.256625
\(146\) −2.54508 + 1.84911i −0.210633 + 0.153034i
\(147\) −2.42705 + 1.76336i −0.200180 + 0.145439i
\(148\) −0.663119 2.04087i −0.0545080 0.167759i
\(149\) 7.03444 0.576284 0.288142 0.957588i \(-0.406962\pi\)
0.288142 + 0.957588i \(0.406962\pi\)
\(150\) 1.54508 4.75528i 0.126156 0.388267i
\(151\) −6.94427 −0.565117 −0.282558 0.959250i \(-0.591183\pi\)
−0.282558 + 0.959250i \(0.591183\pi\)
\(152\) 0.854102 + 2.62866i 0.0692768 + 0.213212i
\(153\) −6.35410 + 4.61653i −0.513699 + 0.373224i
\(154\) −8.47214 + 6.15537i −0.682704 + 0.496014i
\(155\) −2.56231 7.88597i −0.205809 0.633416i
\(156\) −3.92705 2.85317i −0.314416 0.228436i
\(157\) 17.8541 1.42491 0.712456 0.701717i \(-0.247583\pi\)
0.712456 + 0.701717i \(0.247583\pi\)
\(158\) 0 0
\(159\) −2.64590 + 8.14324i −0.209833 + 0.645801i
\(160\) −1.80902 1.31433i −0.143015 0.103907i
\(161\) 3.70820 + 11.4127i 0.292247 + 0.899445i
\(162\) −0.309017 + 0.951057i −0.0242787 + 0.0747221i
\(163\) 6.32624 19.4702i 0.495509 1.52502i −0.320652 0.947197i \(-0.603902\pi\)
0.816162 0.577824i \(-0.196098\pi\)
\(164\) −1.88197 5.79210i −0.146957 0.452287i
\(165\) −3.61803 11.1352i −0.281664 0.866871i
\(166\) −1.85410 + 5.70634i −0.143906 + 0.442898i
\(167\) −5.23607 3.80423i −0.405179 0.294380i 0.366468 0.930431i \(-0.380567\pi\)
−0.771647 + 0.636051i \(0.780567\pi\)
\(168\) 2.00000 0.154303
\(169\) −8.54508 6.20837i −0.657314 0.477567i
\(170\) −14.2082 + 10.3229i −1.08972 + 0.791728i
\(171\) 2.23607 1.62460i 0.170996 0.124236i
\(172\) 1.00000 0.726543i 0.0762493 0.0553983i
\(173\) −3.37132 10.3759i −0.256317 0.788862i −0.993567 0.113243i \(-0.963876\pi\)
0.737250 0.675620i \(-0.236124\pi\)
\(174\) −1.38197 −0.104767
\(175\) 3.09017 + 9.51057i 0.233595 + 0.718931i
\(176\) −5.23607 −0.394683
\(177\) −2.76393 8.50651i −0.207750 0.639388i
\(178\) 1.11803 0.812299i 0.0838002 0.0608844i
\(179\) 3.09017 2.24514i 0.230970 0.167810i −0.466281 0.884637i \(-0.654406\pi\)
0.697251 + 0.716827i \(0.254406\pi\)
\(180\) −0.690983 + 2.12663i −0.0515028 + 0.158509i
\(181\) 16.2082 + 11.7759i 1.20475 + 0.875299i 0.994743 0.102401i \(-0.0326526\pi\)
0.210003 + 0.977701i \(0.432653\pi\)
\(182\) 9.70820 0.719620
\(183\) −7.16312 5.20431i −0.529513 0.384714i
\(184\) −1.85410 + 5.70634i −0.136686 + 0.420677i
\(185\) −3.88197 + 2.82041i −0.285408 + 0.207361i
\(186\) 1.14590 + 3.52671i 0.0840213 + 0.258591i
\(187\) −12.7082 + 39.1118i −0.929316 + 2.86014i
\(188\) 1.47214 4.53077i 0.107367 0.330440i
\(189\) −0.618034 1.90211i −0.0449554 0.138358i
\(190\) 5.00000 3.63271i 0.362738 0.263545i
\(191\) −0.236068 + 0.726543i −0.0170813 + 0.0525708i −0.959234 0.282614i \(-0.908799\pi\)
0.942153 + 0.335184i \(0.108799\pi\)
\(192\) 0.809017 + 0.587785i 0.0583858 + 0.0424197i
\(193\) 2.38197 0.171458 0.0857288 0.996319i \(-0.472678\pi\)
0.0857288 + 0.996319i \(0.472678\pi\)
\(194\) −11.2082 8.14324i −0.804702 0.584650i
\(195\) −3.35410 + 10.3229i −0.240192 + 0.739236i
\(196\) 2.42705 1.76336i 0.173361 0.125954i
\(197\) 10.7812 7.83297i 0.768125 0.558076i −0.133266 0.991080i \(-0.542547\pi\)
0.901392 + 0.433005i \(0.142547\pi\)
\(198\) 1.61803 + 4.97980i 0.114989 + 0.353899i
\(199\) −6.18034 −0.438113 −0.219056 0.975712i \(-0.570298\pi\)
−0.219056 + 0.975712i \(0.570298\pi\)
\(200\) −1.54508 + 4.75528i −0.109254 + 0.336249i
\(201\) 9.70820 0.684764
\(202\) −0.517221 1.59184i −0.0363915 0.112002i
\(203\) 2.23607 1.62460i 0.156941 0.114024i
\(204\) 6.35410 4.61653i 0.444876 0.323221i
\(205\) −11.0172 + 8.00448i −0.769476 + 0.559057i
\(206\) −1.85410 1.34708i −0.129181 0.0938558i
\(207\) 6.00000 0.417029
\(208\) 3.92705 + 2.85317i 0.272292 + 0.197832i
\(209\) 4.47214 13.7638i 0.309344 0.952063i
\(210\) −1.38197 4.25325i −0.0953647 0.293502i
\(211\) −2.47214 7.60845i −0.170189 0.523787i 0.829192 0.558963i \(-0.188801\pi\)
−0.999381 + 0.0351760i \(0.988801\pi\)
\(212\) 2.64590 8.14324i 0.181721 0.559280i
\(213\) 4.38197 13.4863i 0.300247 0.924066i
\(214\) −3.38197 10.4086i −0.231186 0.711519i
\(215\) −2.23607 1.62460i −0.152499 0.110797i
\(216\) 0.309017 0.951057i 0.0210259 0.0647112i
\(217\) −6.00000 4.35926i −0.407307 0.295926i
\(218\) −2.56231 −0.173541
\(219\) −2.54508 1.84911i −0.171981 0.124951i
\(220\) 3.61803 + 11.1352i 0.243928 + 0.750733i
\(221\) 30.8435 22.4091i 2.07476 1.50740i
\(222\) 1.73607 1.26133i 0.116517 0.0846547i
\(223\) −0.708204 2.17963i −0.0474248 0.145959i 0.924540 0.381085i \(-0.124450\pi\)
−0.971965 + 0.235127i \(0.924450\pi\)
\(224\) −2.00000 −0.133631
\(225\) 5.00000 0.333333
\(226\) 11.5623 0.769113
\(227\) −5.23607 16.1150i −0.347530 1.06959i −0.960215 0.279261i \(-0.909911\pi\)
0.612685 0.790327i \(-0.290089\pi\)
\(228\) −2.23607 + 1.62460i −0.148087 + 0.107592i
\(229\) 19.6353 14.2658i 1.29753 0.942714i 0.297606 0.954689i \(-0.403812\pi\)
0.999928 + 0.0119751i \(0.00381187\pi\)
\(230\) 13.4164 0.884652
\(231\) −8.47214 6.15537i −0.557426 0.404993i
\(232\) 1.38197 0.0907305
\(233\) 17.8713 + 12.9843i 1.17079 + 0.850628i 0.991103 0.133096i \(-0.0424918\pi\)
0.179686 + 0.983724i \(0.442492\pi\)
\(234\) 1.50000 4.61653i 0.0980581 0.301792i
\(235\) −10.6525 −0.694891
\(236\) 2.76393 + 8.50651i 0.179917 + 0.553727i
\(237\) 0 0
\(238\) −4.85410 + 14.9394i −0.314645 + 0.968377i
\(239\) 8.29180 + 25.5195i 0.536352 + 1.65072i 0.740710 + 0.671825i \(0.234489\pi\)
−0.204358 + 0.978896i \(0.565511\pi\)
\(240\) 0.690983 2.12663i 0.0446028 0.137273i
\(241\) −4.28115 + 13.1760i −0.275773 + 0.848743i 0.713240 + 0.700919i \(0.247227\pi\)
−0.989014 + 0.147824i \(0.952773\pi\)
\(242\) 13.2812 + 9.64932i 0.853745 + 0.620282i
\(243\) −1.00000 −0.0641500
\(244\) 7.16312 + 5.20431i 0.458572 + 0.333172i
\(245\) −5.42705 3.94298i −0.346722 0.251908i
\(246\) 4.92705 3.57971i 0.314137 0.228234i
\(247\) −10.8541 + 7.88597i −0.690630 + 0.501772i
\(248\) −1.14590 3.52671i −0.0727646 0.223946i
\(249\) −6.00000 −0.380235
\(250\) 11.1803 0.707107
\(251\) −12.4721 −0.787234 −0.393617 0.919274i \(-0.628776\pi\)
−0.393617 + 0.919274i \(0.628776\pi\)
\(252\) 0.618034 + 1.90211i 0.0389325 + 0.119822i
\(253\) 25.4164 18.4661i 1.59792 1.16095i
\(254\) 0.236068 0.171513i 0.0148122 0.0107617i
\(255\) −14.2082 10.3229i −0.889752 0.646443i
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −11.6180 −0.724713 −0.362357 0.932040i \(-0.618028\pi\)
−0.362357 + 0.932040i \(0.618028\pi\)
\(258\) 1.00000 + 0.726543i 0.0622573 + 0.0452326i
\(259\) −1.32624 + 4.08174i −0.0824084 + 0.253627i
\(260\) 3.35410 10.3229i 0.208013 0.640197i
\(261\) −0.427051 1.31433i −0.0264338 0.0813548i
\(262\) 0.236068 0.726543i 0.0145843 0.0448859i
\(263\) 0.145898 0.449028i 0.00899646 0.0276883i −0.946458 0.322828i \(-0.895366\pi\)
0.955454 + 0.295140i \(0.0953663\pi\)
\(264\) −1.61803 4.97980i −0.0995831 0.306485i
\(265\) −19.1459 −1.17612
\(266\) 1.70820 5.25731i 0.104737 0.322346i
\(267\) 1.11803 + 0.812299i 0.0684226 + 0.0497119i
\(268\) −9.70820 −0.593023
\(269\) 1.54508 + 1.12257i 0.0942055 + 0.0684443i 0.633891 0.773422i \(-0.281457\pi\)
−0.539685 + 0.841867i \(0.681457\pi\)
\(270\) −2.23607 −0.136083
\(271\) −22.7984 + 16.5640i −1.38490 + 1.00619i −0.388500 + 0.921449i \(0.627007\pi\)
−0.996403 + 0.0847417i \(0.972993\pi\)
\(272\) −6.35410 + 4.61653i −0.385274 + 0.279918i
\(273\) 3.00000 + 9.23305i 0.181568 + 0.558810i
\(274\) 15.0344 0.908264
\(275\) 21.1803 15.3884i 1.27722 0.927957i
\(276\) −6.00000 −0.361158
\(277\) −6.84346 21.0620i −0.411184 1.26549i −0.915620 0.402044i \(-0.868300\pi\)
0.504437 0.863449i \(-0.331700\pi\)
\(278\) −10.8541 + 7.88597i −0.650986 + 0.472969i
\(279\) −3.00000 + 2.17963i −0.179605 + 0.130491i
\(280\) 1.38197 + 4.25325i 0.0825883 + 0.254181i
\(281\) 4.92705 + 3.57971i 0.293923 + 0.213548i 0.724968 0.688783i \(-0.241855\pi\)
−0.431044 + 0.902331i \(0.641855\pi\)
\(282\) 4.76393 0.283688
\(283\) −2.61803 1.90211i −0.155626 0.113069i 0.507247 0.861801i \(-0.330663\pi\)
−0.662873 + 0.748732i \(0.730663\pi\)
\(284\) −4.38197 + 13.4863i −0.260022 + 0.800265i
\(285\) 5.00000 + 3.63271i 0.296174 + 0.215183i
\(286\) −7.85410 24.1724i −0.464423 1.42935i
\(287\) −3.76393 + 11.5842i −0.222178 + 0.683793i
\(288\) −0.309017 + 0.951057i −0.0182090 + 0.0560415i
\(289\) 13.8090 + 42.4998i 0.812295 + 2.49999i
\(290\) −0.954915 2.93893i −0.0560745 0.172580i
\(291\) 4.28115 13.1760i 0.250966 0.772393i
\(292\) 2.54508 + 1.84911i 0.148940 + 0.108211i
\(293\) −28.7984 −1.68242 −0.841209 0.540709i \(-0.818156\pi\)
−0.841209 + 0.540709i \(0.818156\pi\)
\(294\) 2.42705 + 1.76336i 0.141548 + 0.102841i
\(295\) 16.1803 11.7557i 0.942056 0.684444i
\(296\) −1.73607 + 1.26133i −0.100907 + 0.0733132i
\(297\) −4.23607 + 3.07768i −0.245802 + 0.178585i
\(298\) −2.17376 6.69015i −0.125923 0.387550i
\(299\) −29.1246 −1.68432
\(300\) −5.00000 −0.288675
\(301\) −2.47214 −0.142492
\(302\) 2.14590 + 6.60440i 0.123483 + 0.380040i
\(303\) 1.35410 0.983813i 0.0777911 0.0565186i
\(304\) 2.23607 1.62460i 0.128247 0.0931771i
\(305\) 6.11803 18.8294i 0.350318 1.07817i
\(306\) 6.35410 + 4.61653i 0.363240 + 0.263909i
\(307\) −16.2918 −0.929822 −0.464911 0.885357i \(-0.653914\pi\)
−0.464911 + 0.885357i \(0.653914\pi\)
\(308\) 8.47214 + 6.15537i 0.482745 + 0.350735i
\(309\) 0.708204 2.17963i 0.0402883 0.123995i
\(310\) −6.70820 + 4.87380i −0.381000 + 0.276813i
\(311\) −5.76393 17.7396i −0.326843 1.00592i −0.970602 0.240690i \(-0.922626\pi\)
0.643759 0.765228i \(-0.277374\pi\)
\(312\) −1.50000 + 4.61653i −0.0849208 + 0.261359i
\(313\) −8.14590 + 25.0705i −0.460433 + 1.41707i 0.404203 + 0.914669i \(0.367549\pi\)
−0.864636 + 0.502399i \(0.832451\pi\)
\(314\) −5.51722 16.9803i −0.311355 0.958252i
\(315\) 3.61803 2.62866i 0.203853 0.148108i
\(316\) 0 0
\(317\) 5.61803 + 4.08174i 0.315540 + 0.229253i 0.734270 0.678857i \(-0.237525\pi\)
−0.418730 + 0.908111i \(0.637525\pi\)
\(318\) 8.56231 0.480150
\(319\) −5.85410 4.25325i −0.327767 0.238137i
\(320\) −0.690983 + 2.12663i −0.0386271 + 0.118882i
\(321\) 8.85410 6.43288i 0.494188 0.359048i
\(322\) 9.70820 7.05342i 0.541017 0.393072i
\(323\) −6.70820 20.6457i −0.373254 1.14876i
\(324\) 1.00000 0.0555556
\(325\) −24.2705 −1.34629
\(326\) −20.4721 −1.13385
\(327\) −0.791796 2.43690i −0.0437864 0.134761i
\(328\) −4.92705 + 3.57971i −0.272051 + 0.197657i
\(329\) −7.70820 + 5.60034i −0.424967 + 0.308757i
\(330\) −9.47214 + 6.88191i −0.521424 + 0.378837i
\(331\) 26.2705 + 19.0866i 1.44396 + 1.04910i 0.987197 + 0.159507i \(0.0509906\pi\)
0.456761 + 0.889589i \(0.349009\pi\)
\(332\) 6.00000 0.329293
\(333\) 1.73607 + 1.26133i 0.0951359 + 0.0691203i
\(334\) −2.00000 + 6.15537i −0.109435 + 0.336807i
\(335\) 6.70820 + 20.6457i 0.366508 + 1.12800i
\(336\) −0.618034 1.90211i −0.0337165 0.103769i
\(337\) 8.90983 27.4216i 0.485349 1.49375i −0.346125 0.938188i \(-0.612503\pi\)
0.831474 0.555563i \(-0.187497\pi\)
\(338\) −3.26393 + 10.0453i −0.177534 + 0.546395i
\(339\) 3.57295 + 10.9964i 0.194056 + 0.597243i
\(340\) 14.2082 + 10.3229i 0.770548 + 0.559836i
\(341\) −6.00000 + 18.4661i −0.324918 + 0.999995i
\(342\) −2.23607 1.62460i −0.120913 0.0878482i
\(343\) −20.0000 −1.07990
\(344\) −1.00000 0.726543i −0.0539164 0.0391725i
\(345\) 4.14590 + 12.7598i 0.223208 + 0.686963i
\(346\) −8.82624 + 6.41264i −0.474501 + 0.344746i
\(347\) 4.23607 3.07768i 0.227404 0.165219i −0.468249 0.883596i \(-0.655115\pi\)
0.695653 + 0.718378i \(0.255115\pi\)
\(348\) 0.427051 + 1.31433i 0.0228923 + 0.0704554i
\(349\) 14.7984 0.792139 0.396069 0.918221i \(-0.370374\pi\)
0.396069 + 0.918221i \(0.370374\pi\)
\(350\) 8.09017 5.87785i 0.432438 0.314184i
\(351\) 4.85410 0.259093
\(352\) 1.61803 + 4.97980i 0.0862415 + 0.265424i
\(353\) −16.5623 + 12.0332i −0.881523 + 0.640464i −0.933654 0.358177i \(-0.883399\pi\)
0.0521313 + 0.998640i \(0.483399\pi\)
\(354\) −7.23607 + 5.25731i −0.384593 + 0.279423i
\(355\) 31.7082 1.68290
\(356\) −1.11803 0.812299i −0.0592557 0.0430518i
\(357\) −15.7082 −0.831366
\(358\) −3.09017 2.24514i −0.163321 0.118659i
\(359\) −8.61803 + 26.5236i −0.454842 + 1.39986i 0.416478 + 0.909146i \(0.363264\pi\)
−0.871320 + 0.490715i \(0.836736\pi\)
\(360\) 2.23607 0.117851
\(361\) −3.51064 10.8046i −0.184771 0.568666i
\(362\) 6.19098 19.0539i 0.325391 1.00145i
\(363\) −5.07295 + 15.6129i −0.266261 + 0.819466i
\(364\) −3.00000 9.23305i −0.157243 0.483943i
\(365\) 2.17376 6.69015i 0.113780 0.350179i
\(366\) −2.73607 + 8.42075i −0.143017 + 0.440160i
\(367\) 10.0902 + 7.33094i 0.526703 + 0.382672i 0.819123 0.573618i \(-0.194461\pi\)
−0.292420 + 0.956290i \(0.594461\pi\)
\(368\) 6.00000 0.312772
\(369\) 4.92705 + 3.57971i 0.256492 + 0.186352i
\(370\) 3.88197 + 2.82041i 0.201814 + 0.146626i
\(371\) −13.8541 + 10.0656i −0.719269 + 0.522580i
\(372\) 3.00000 2.17963i 0.155543 0.113008i
\(373\) 0.798374 + 2.45714i 0.0413382 + 0.127226i 0.969596 0.244712i \(-0.0786934\pi\)
−0.928258 + 0.371938i \(0.878693\pi\)
\(374\) 41.1246 2.12650
\(375\) 3.45492 + 10.6331i 0.178411 + 0.549093i
\(376\) −4.76393 −0.245681
\(377\) 2.07295 + 6.37988i 0.106762 + 0.328581i
\(378\) −1.61803 + 1.17557i −0.0832227 + 0.0604648i
\(379\) 2.76393 2.00811i 0.141974 0.103150i −0.514531 0.857472i \(-0.672034\pi\)
0.656505 + 0.754322i \(0.272034\pi\)
\(380\) −5.00000 3.63271i −0.256495 0.186354i
\(381\) 0.236068 + 0.171513i 0.0120941 + 0.00878690i
\(382\) 0.763932 0.0390862
\(383\) −16.5623 12.0332i −0.846294 0.614869i 0.0778275 0.996967i \(-0.475202\pi\)
−0.924122 + 0.382098i \(0.875202\pi\)
\(384\) 0.309017 0.951057i 0.0157695 0.0485334i
\(385\) 7.23607 22.2703i 0.368784 1.13500i
\(386\) −0.736068 2.26538i −0.0374649 0.115305i
\(387\) −0.381966 + 1.17557i −0.0194164 + 0.0597576i
\(388\) −4.28115 + 13.1760i −0.217343 + 0.668912i
\(389\) 4.93769 + 15.1967i 0.250351 + 0.770501i 0.994710 + 0.102722i \(0.0327551\pi\)
−0.744359 + 0.667780i \(0.767245\pi\)
\(390\) 10.8541 0.549619
\(391\) 14.5623 44.8182i 0.736447 2.26655i
\(392\) −2.42705 1.76336i −0.122585 0.0890629i
\(393\) 0.763932 0.0385353
\(394\) −10.7812 7.83297i −0.543147 0.394619i
\(395\) 0 0
\(396\) 4.23607 3.07768i 0.212870 0.154659i
\(397\) −23.3262 + 16.9475i −1.17071 + 0.850571i −0.991094 0.133166i \(-0.957486\pi\)
−0.179617 + 0.983737i \(0.557486\pi\)
\(398\) 1.90983 + 5.87785i 0.0957311 + 0.294630i
\(399\) 5.52786 0.276739
\(400\) 5.00000 0.250000
\(401\) −26.0902 −1.30288 −0.651440 0.758700i \(-0.725835\pi\)
−0.651440 + 0.758700i \(0.725835\pi\)
\(402\) −3.00000 9.23305i −0.149626 0.460503i
\(403\) 14.5623 10.5801i 0.725400 0.527034i
\(404\) −1.35410 + 0.983813i −0.0673691 + 0.0489465i
\(405\) −0.690983 2.12663i −0.0343352 0.105673i
\(406\) −2.23607 1.62460i −0.110974 0.0806275i
\(407\) 11.2361 0.556951
\(408\) −6.35410 4.61653i −0.314575 0.228552i
\(409\) 6.48278 19.9519i 0.320553 0.986560i −0.652855 0.757483i \(-0.726429\pi\)
0.973408 0.229077i \(-0.0735709\pi\)
\(410\) 11.0172 + 8.00448i 0.544102 + 0.395313i
\(411\) 4.64590 + 14.2986i 0.229165 + 0.705298i
\(412\) −0.708204 + 2.17963i −0.0348907 + 0.107383i
\(413\) 5.52786 17.0130i 0.272008 0.837156i
\(414\) −1.85410 5.70634i −0.0911241 0.280451i
\(415\) −4.14590 12.7598i −0.203514 0.626352i
\(416\) 1.50000 4.61653i 0.0735436 0.226344i
\(417\) −10.8541 7.88597i −0.531528 0.386177i
\(418\) −14.4721 −0.707855
\(419\) 30.6525 + 22.2703i 1.49747 + 1.08798i 0.971375 + 0.237552i \(0.0763450\pi\)
0.526097 + 0.850425i \(0.323655\pi\)
\(420\) −3.61803 + 2.62866i −0.176542 + 0.128265i
\(421\) 8.97214 6.51864i 0.437275 0.317699i −0.347276 0.937763i \(-0.612893\pi\)
0.784551 + 0.620064i \(0.212893\pi\)
\(422\) −6.47214 + 4.70228i −0.315059 + 0.228904i
\(423\) 1.47214 + 4.53077i 0.0715777 + 0.220294i
\(424\) −8.56231 −0.415822
\(425\) 12.1353 37.3485i 0.588646 1.81167i
\(426\) −14.1803 −0.687040
\(427\) −5.47214 16.8415i −0.264815 0.815017i
\(428\) −8.85410 + 6.43288i −0.427979 + 0.310945i
\(429\) 20.5623 14.9394i 0.992757 0.721281i
\(430\) −0.854102 + 2.62866i −0.0411885 + 0.126765i
\(431\) −3.00000 2.17963i −0.144505 0.104989i 0.513184 0.858279i \(-0.328466\pi\)
−0.657689 + 0.753290i \(0.728466\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 18.7254 + 13.6048i 0.899886 + 0.653806i 0.938437 0.345451i \(-0.112274\pi\)
−0.0385504 + 0.999257i \(0.512274\pi\)
\(434\) −2.29180 + 7.05342i −0.110010 + 0.338575i
\(435\) 2.50000 1.81636i 0.119866 0.0870876i
\(436\) 0.791796 + 2.43690i 0.0379202 + 0.116706i
\(437\) −5.12461 + 15.7719i −0.245143 + 0.754474i
\(438\) −0.972136 + 2.99193i −0.0464505 + 0.142960i
\(439\) −7.76393 23.8949i −0.370552 1.14044i −0.946431 0.322907i \(-0.895340\pi\)
0.575878 0.817535i \(-0.304660\pi\)
\(440\) 9.47214 6.88191i 0.451566 0.328082i
\(441\) −0.927051 + 2.85317i −0.0441453 + 0.135865i
\(442\) −30.8435 22.4091i −1.46707 1.06589i
\(443\) 30.0689 1.42862 0.714308 0.699832i \(-0.246742\pi\)
0.714308 + 0.699832i \(0.246742\pi\)
\(444\) −1.73607 1.26133i −0.0823901 0.0598599i
\(445\) −0.954915 + 2.93893i −0.0452673 + 0.139318i
\(446\) −1.85410 + 1.34708i −0.0877943 + 0.0637863i
\(447\) 5.69098 4.13474i 0.269174 0.195567i
\(448\) 0.618034 + 1.90211i 0.0291994 + 0.0898664i
\(449\) 4.79837 0.226449 0.113225 0.993569i \(-0.463882\pi\)
0.113225 + 0.993569i \(0.463882\pi\)
\(450\) −1.54508 4.75528i −0.0728360 0.224166i
\(451\) 31.8885 1.50157
\(452\) −3.57295 10.9964i −0.168057 0.517227i
\(453\) −5.61803 + 4.08174i −0.263958 + 0.191777i
\(454\) −13.7082 + 9.95959i −0.643358 + 0.467427i
\(455\) −17.5623 + 12.7598i −0.823334 + 0.598187i
\(456\) 2.23607 + 1.62460i 0.104713 + 0.0760788i
\(457\) −12.4721 −0.583422 −0.291711 0.956507i \(-0.594225\pi\)
−0.291711 + 0.956507i \(0.594225\pi\)
\(458\) −19.6353 14.2658i −0.917495 0.666599i
\(459\) −2.42705 + 7.46969i −0.113285 + 0.348655i
\(460\) −4.14590 12.7598i −0.193303 0.594927i
\(461\) 7.75329 + 23.8622i 0.361107 + 1.11137i 0.952383 + 0.304903i \(0.0986241\pi\)
−0.591277 + 0.806469i \(0.701376\pi\)
\(462\) −3.23607 + 9.95959i −0.150556 + 0.463362i
\(463\) −3.79837 + 11.6902i −0.176525 + 0.543289i −0.999700 0.0244992i \(-0.992201\pi\)
0.823174 + 0.567789i \(0.192201\pi\)
\(464\) −0.427051 1.31433i −0.0198253 0.0610161i
\(465\) −6.70820 4.87380i −0.311086 0.226017i
\(466\) 6.82624 21.0090i 0.316219 0.973223i
\(467\) −12.7984 9.29856i −0.592238 0.430286i 0.250877 0.968019i \(-0.419281\pi\)
−0.843115 + 0.537733i \(0.819281\pi\)
\(468\) −4.85410 −0.224381
\(469\) 15.7082 + 11.4127i 0.725337 + 0.526989i
\(470\) 3.29180 + 10.1311i 0.151839 + 0.467313i
\(471\) 14.4443 10.4944i 0.665557 0.483555i
\(472\) 7.23607 5.25731i 0.333067 0.241987i
\(473\) 2.00000 + 6.15537i 0.0919601 + 0.283024i
\(474\) 0 0
\(475\) −4.27051 + 13.1433i −0.195944 + 0.603055i
\(476\) 15.7082 0.719984
\(477\) 2.64590 + 8.14324i 0.121147 + 0.372853i
\(478\) 21.7082 15.7719i 0.992910 0.721391i
\(479\) −3.61803 + 2.62866i −0.165312 + 0.120106i −0.667366 0.744730i \(-0.732578\pi\)
0.502053 + 0.864837i \(0.332578\pi\)
\(480\) −2.23607 −0.102062
\(481\) −8.42705 6.12261i −0.384240 0.279167i
\(482\) 13.8541 0.631037
\(483\) 9.70820 + 7.05342i 0.441739 + 0.320942i
\(484\) 5.07295 15.6129i 0.230589 0.709679i
\(485\) 30.9787 1.40667
\(486\) 0.309017 + 0.951057i 0.0140173 + 0.0431408i
\(487\) 3.18034 9.78808i 0.144115 0.443540i −0.852781 0.522268i \(-0.825086\pi\)
0.996896 + 0.0787282i \(0.0250859\pi\)
\(488\) 2.73607 8.42075i 0.123856 0.381190i
\(489\) −6.32624 19.4702i −0.286082 0.880471i
\(490\) −2.07295 + 6.37988i −0.0936463 + 0.288214i
\(491\) 9.23607 28.4257i 0.416818 1.28283i −0.493797 0.869577i \(-0.664391\pi\)
0.910615 0.413256i \(-0.135609\pi\)
\(492\) −4.92705 3.57971i −0.222129 0.161386i
\(493\) −10.8541 −0.488844
\(494\) 10.8541 + 7.88597i 0.488349 + 0.354806i
\(495\) −9.47214 6.88191i −0.425741 0.309319i
\(496\) −3.00000 + 2.17963i −0.134704 + 0.0978682i
\(497\) 22.9443 16.6700i 1.02919 0.747751i
\(498\) 1.85410 + 5.70634i 0.0830843 + 0.255707i
\(499\) −33.4164 −1.49592 −0.747962 0.663742i \(-0.768967\pi\)
−0.747962 + 0.663742i \(0.768967\pi\)
\(500\) −3.45492 10.6331i −0.154508 0.475528i
\(501\) −6.47214 −0.289154
\(502\) 3.85410 + 11.8617i 0.172017 + 0.529414i
\(503\) −17.4164 + 12.6538i −0.776559 + 0.564203i −0.903944 0.427650i \(-0.859342\pi\)
0.127385 + 0.991853i \(0.459342\pi\)
\(504\) 1.61803 1.17557i 0.0720730 0.0523641i
\(505\) 3.02786 + 2.19987i 0.134738 + 0.0978930i
\(506\) −25.4164 18.4661i −1.12990 0.820918i
\(507\) −10.5623 −0.469088
\(508\) −0.236068 0.171513i −0.0104738 0.00760968i
\(509\) −4.24671 + 13.0700i −0.188232 + 0.579319i −0.999989 0.00467647i \(-0.998511\pi\)
0.811757 + 0.583995i \(0.198511\pi\)
\(510\) −5.42705 + 16.7027i −0.240314 + 0.739610i
\(511\) −1.94427 5.98385i −0.0860095 0.264710i
\(512\) −0.309017 + 0.951057i −0.0136568 + 0.0420312i
\(513\) 0.854102 2.62866i 0.0377095 0.116058i
\(514\) 3.59017 + 11.0494i 0.158356 + 0.487368i
\(515\) 5.12461 0.225817
\(516\) 0.381966 1.17557i 0.0168151 0.0517516i
\(517\) 20.1803 + 14.6619i 0.887530 + 0.644829i
\(518\) 4.29180 0.188571
\(519\) −8.82624 6.41264i −0.387429 0.281484i
\(520\) −10.8541 −0.475984
\(521\) −5.07295 + 3.68571i −0.222250 + 0.161474i −0.693339 0.720612i \(-0.743861\pi\)
0.471089 + 0.882086i \(0.343861\pi\)
\(522\) −1.11803 + 0.812299i −0.0489350 + 0.0355534i
\(523\) −0.708204 2.17963i −0.0309676 0.0953085i 0.934378 0.356283i \(-0.115956\pi\)
−0.965346 + 0.260975i \(0.915956\pi\)
\(524\) −0.763932 −0.0333725
\(525\) 8.09017 + 5.87785i 0.353084 + 0.256531i
\(526\) −0.472136 −0.0205861
\(527\) 9.00000 + 27.6992i 0.392046 + 1.20659i
\(528\) −4.23607 + 3.07768i −0.184351 + 0.133939i
\(529\) −10.5172 + 7.64121i −0.457270 + 0.332226i
\(530\) 5.91641 + 18.2088i 0.256992 + 0.790941i
\(531\) −7.23607 5.25731i −0.314019 0.228148i
\(532\) −5.52786 −0.239663
\(533\) −23.9164 17.3763i −1.03593 0.752651i
\(534\) 0.427051 1.31433i 0.0184803 0.0568765i
\(535\) 19.7984 + 14.3844i 0.855958 + 0.621890i
\(536\) 3.00000 + 9.23305i 0.129580 + 0.398807i
\(537\) 1.18034 3.63271i 0.0509354 0.156763i
\(538\) 0.590170 1.81636i 0.0254440 0.0783087i
\(539\) 4.85410 + 14.9394i 0.209081 + 0.643485i
\(540\) 0.690983 + 2.12663i 0.0297352 + 0.0915155i
\(541\) 6.57295 20.2295i 0.282593 0.869732i −0.704517 0.709688i \(-0.748836\pi\)
0.987110 0.160045i \(-0.0511639\pi\)
\(542\) 22.7984 + 16.5640i 0.979274 + 0.711484i
\(543\) 20.0344 0.859760
\(544\) 6.35410 + 4.61653i 0.272430 + 0.197932i
\(545\) 4.63525 3.36771i 0.198553 0.144257i
\(546\) 7.85410 5.70634i 0.336125 0.244209i
\(547\) −1.61803 + 1.17557i −0.0691821 + 0.0502638i −0.621839 0.783145i \(-0.713614\pi\)
0.552657 + 0.833409i \(0.313614\pi\)
\(548\) −4.64590 14.2986i −0.198463 0.610806i
\(549\) −8.85410 −0.377884
\(550\) −21.1803 15.3884i −0.903133 0.656164i
\(551\) 3.81966 0.162723
\(552\) 1.85410 + 5.70634i 0.0789158 + 0.242878i
\(553\) 0 0
\(554\) −17.9164 + 13.0170i −0.761195 + 0.553041i
\(555\) −1.48278 + 4.56352i −0.0629405 + 0.193711i
\(556\) 10.8541 + 7.88597i 0.460316 + 0.334439i
\(557\) −27.2705 −1.15549 −0.577744 0.816218i \(-0.696067\pi\)
−0.577744 + 0.816218i \(0.696067\pi\)
\(558\) 3.00000 + 2.17963i 0.127000 + 0.0922710i
\(559\) 1.85410 5.70634i 0.0784202 0.241352i
\(560\) 3.61803 2.62866i 0.152890 0.111081i
\(561\) 12.7082 + 39.1118i 0.536541 + 1.65130i
\(562\) 1.88197 5.79210i 0.0793859 0.244325i
\(563\) 3.23607 9.95959i 0.136384 0.419747i −0.859419 0.511272i \(-0.829174\pi\)
0.995803 + 0.0915256i \(0.0291743\pi\)
\(564\) −1.47214 4.53077i −0.0619881 0.190780i
\(565\) −20.9164 + 15.1967i −0.879960 + 0.639328i
\(566\) −1.00000 + 3.07768i −0.0420331 + 0.129365i
\(567\) −1.61803 1.17557i −0.0679510 0.0493693i
\(568\) 14.1803 0.594994
\(569\) −17.2984 12.5680i −0.725186 0.526878i 0.162851 0.986651i \(-0.447931\pi\)
−0.888037 + 0.459772i \(0.847931\pi\)
\(570\) 1.90983 5.87785i 0.0799940 0.246196i
\(571\) −27.2705 + 19.8132i −1.14124 + 0.829156i −0.987291 0.158924i \(-0.949198\pi\)
−0.153944 + 0.988080i \(0.549198\pi\)
\(572\) −20.5623 + 14.9394i −0.859753 + 0.624647i
\(573\) 0.236068 + 0.726543i 0.00986188 + 0.0303517i
\(574\) 12.1803 0.508398
\(575\) −24.2705 + 17.6336i −1.01215 + 0.735370i
\(576\) 1.00000 0.0416667
\(577\) 8.90983 + 27.4216i 0.370921 + 1.14158i 0.946190 + 0.323613i \(0.104898\pi\)
−0.575268 + 0.817965i \(0.695102\pi\)
\(578\) 36.1525 26.2663i 1.50374 1.09253i
\(579\) 1.92705 1.40008i 0.0800855 0.0581855i
\(580\) −2.50000 + 1.81636i −0.103807 + 0.0754201i
\(581\) −9.70820 7.05342i −0.402764 0.292625i
\(582\) −13.8541 −0.574271
\(583\) 36.2705 + 26.3521i 1.50217 + 1.09139i
\(584\) 0.972136 2.99193i 0.0402273 0.123807i
\(585\) 3.35410 + 10.3229i 0.138675 + 0.426798i
\(586\) 8.89919 + 27.3889i 0.367622 + 1.13142i
\(587\) −4.90983 + 15.1109i −0.202650 + 0.623694i 0.797151 + 0.603780i \(0.206339\pi\)
−0.999802 + 0.0199141i \(0.993661\pi\)
\(588\) 0.927051 2.85317i 0.0382309 0.117663i
\(589\) −3.16718 9.74759i −0.130502 0.401642i
\(590\) −16.1803 11.7557i −0.666134 0.483975i
\(591\) 4.11803 12.6740i 0.169393 0.521339i
\(592\) 1.73607 + 1.26133i 0.0713520 + 0.0518402i
\(593\) −6.03444 −0.247805 −0.123902 0.992294i \(-0.539541\pi\)
−0.123902 + 0.992294i \(0.539541\pi\)
\(594\) 4.23607 + 3.07768i 0.173808 + 0.126279i
\(595\) −10.8541 33.4055i −0.444975 1.36949i
\(596\) −5.69098 + 4.13474i −0.233112 + 0.169366i
\(597\) −5.00000 + 3.63271i −0.204636 + 0.148677i
\(598\) 9.00000 + 27.6992i 0.368037 + 1.13270i
\(599\) 1.05573 0.0431359 0.0215679 0.999767i \(-0.493134\pi\)
0.0215679 + 0.999767i \(0.493134\pi\)
\(600\) 1.54508 + 4.75528i 0.0630778 + 0.194134i
\(601\) 7.32624 0.298843 0.149422 0.988774i \(-0.452259\pi\)
0.149422 + 0.988774i \(0.452259\pi\)
\(602\) 0.763932 + 2.35114i 0.0311355 + 0.0958254i
\(603\) 7.85410 5.70634i 0.319844 0.232380i
\(604\) 5.61803 4.08174i 0.228595 0.166084i
\(605\) −36.7082 −1.49240
\(606\) −1.35410 0.983813i −0.0550066 0.0399647i
\(607\) −1.81966 −0.0738577 −0.0369289 0.999318i \(-0.511757\pi\)
−0.0369289 + 0.999318i \(0.511757\pi\)
\(608\) −2.23607 1.62460i −0.0906845 0.0658862i
\(609\) 0.854102 2.62866i 0.0346100 0.106518i
\(610\) −19.7984 −0.801613
\(611\) −7.14590 21.9928i −0.289092 0.889734i
\(612\) 2.42705 7.46969i 0.0981077 0.301945i
\(613\) −6.66312 + 20.5070i −0.269121 + 0.828269i 0.721594 + 0.692316i \(0.243410\pi\)
−0.990715 + 0.135953i \(0.956590\pi\)
\(614\) 5.03444 + 15.4944i 0.203174 + 0.625304i
\(615\) −4.20820 + 12.9515i −0.169691 + 0.522256i
\(616\) 3.23607 9.95959i 0.130385 0.401283i
\(617\) −6.78115 4.92680i −0.272999 0.198345i 0.442859 0.896591i \(-0.353964\pi\)
−0.715858 + 0.698246i \(0.753964\pi\)
\(618\) −2.29180 −0.0921896
\(619\) −2.76393 2.00811i −0.111092 0.0807129i 0.530852 0.847464i \(-0.321872\pi\)
−0.641944 + 0.766751i \(0.721872\pi\)
\(620\) 6.70820 + 4.87380i 0.269408 + 0.195736i
\(621\) 4.85410 3.52671i 0.194788 0.141522i
\(622\) −15.0902 + 10.9637i −0.605061 + 0.439602i
\(623\) 0.854102 + 2.62866i 0.0342189 + 0.105315i
\(624\) 4.85410 0.194320
\(625\) −20.2254 + 14.6946i −0.809017 + 0.587785i
\(626\) 26.3607 1.05358
\(627\) −4.47214 13.7638i −0.178600 0.549674i
\(628\) −14.4443 + 10.4944i −0.576389 + 0.418771i
\(629\) 13.6353 9.90659i 0.543673 0.395002i
\(630\) −3.61803 2.62866i −0.144146 0.104728i
\(631\) 34.8885 + 25.3480i 1.38889 + 1.00909i 0.995986 + 0.0895093i \(0.0285299\pi\)
0.392905 + 0.919579i \(0.371470\pi\)
\(632\) 0 0
\(633\) −6.47214 4.70228i −0.257244 0.186899i
\(634\) 2.14590 6.60440i 0.0852245 0.262294i
\(635\) −0.201626 + 0.620541i −0.00800129 + 0.0246254i
\(636\) −2.64590 8.14324i −0.104917 0.322900i
\(637\) 4.50000 13.8496i 0.178296 0.548740i
\(638\) −2.23607 + 6.88191i −0.0885268 + 0.272457i
\(639\) −4.38197 13.4863i −0.173348 0.533510i
\(640\) 2.23607 0.0883883
\(641\) −8.32624 + 25.6255i −0.328867 + 1.01215i 0.640798 + 0.767709i \(0.278603\pi\)
−0.969665 + 0.244438i \(0.921397\pi\)
\(642\) −8.85410 6.43288i −0.349444 0.253886i
\(643\) −39.7771 −1.56866 −0.784328 0.620347i \(-0.786992\pi\)
−0.784328 + 0.620347i \(0.786992\pi\)
\(644\) −9.70820 7.05342i −0.382557 0.277944i
\(645\) −2.76393 −0.108830
\(646\) −17.5623 + 12.7598i −0.690980 + 0.502026i
\(647\) 29.0344 21.0948i 1.14146 0.829320i 0.154139 0.988049i \(-0.450739\pi\)
0.987322 + 0.158729i \(0.0507395\pi\)
\(648\) −0.309017 0.951057i −0.0121393 0.0373610i
\(649\) −46.8328 −1.83835
\(650\) 7.50000 + 23.0826i 0.294174 + 0.905375i
\(651\) −7.41641 −0.290672
\(652\) 6.32624 + 19.4702i 0.247755 + 0.762510i
\(653\) 26.0623 18.9354i 1.01990 0.740998i 0.0536351 0.998561i \(-0.482919\pi\)
0.966262 + 0.257562i \(0.0829192\pi\)
\(654\) −2.07295 + 1.50609i −0.0810587 + 0.0588926i
\(655\) 0.527864 + 1.62460i 0.0206254 + 0.0634783i
\(656\) 4.92705 + 3.57971i 0.192369 + 0.139764i
\(657\) −3.14590 −0.122733
\(658\) 7.70820 + 5.60034i 0.300497 + 0.218324i
\(659\) 12.0344 37.0382i 0.468795 1.44280i −0.385351 0.922770i \(-0.625920\pi\)
0.854146 0.520033i \(-0.174080\pi\)
\(660\) 9.47214 + 6.88191i 0.368702 + 0.267878i
\(661\) −7.27051 22.3763i −0.282790 0.870338i −0.987052 0.160398i \(-0.948722\pi\)
0.704262 0.709940i \(-0.251278\pi\)
\(662\) 10.0344 30.8828i 0.390000 1.20030i
\(663\) 11.7812 36.2587i 0.457542 1.40817i
\(664\) −1.85410 5.70634i −0.0719531 0.221449i
\(665\) 3.81966 + 11.7557i 0.148120 + 0.455867i
\(666\) 0.663119 2.04087i 0.0256953 0.0790821i
\(667\) 6.70820 + 4.87380i 0.259743 + 0.188714i
\(668\) 6.47214 0.250414
\(669\) −1.85410 1.34708i −0.0716837 0.0520813i
\(670\) 17.5623 12.7598i 0.678491 0.492953i
\(671\) −37.5066 + 27.2501i −1.44793 + 1.05198i
\(672\) −1.61803 + 1.17557i −0.0624170 + 0.0453486i
\(673\) −5.80902 17.8783i −0.223921 0.689158i −0.998399 0.0565578i \(-0.981987\pi\)
0.774478 0.632601i \(-0.218013\pi\)
\(674\) −28.8328 −1.11060
\(675\) 4.04508 2.93893i 0.155695 0.113119i
\(676\) 10.5623 0.406243
\(677\) 11.2705 + 34.6871i 0.433161 + 1.33313i 0.894960 + 0.446147i \(0.147204\pi\)
−0.461799 + 0.886985i \(0.652796\pi\)
\(678\) 9.35410 6.79615i 0.359242 0.261005i
\(679\) 22.4164 16.2865i 0.860263 0.625017i
\(680\) 5.42705 16.7027i 0.208118 0.640521i
\(681\) −13.7082 9.95959i −0.525300 0.381652i
\(682\) 19.4164 0.743493
\(683\) −15.7082 11.4127i −0.601058 0.436694i 0.245196 0.969473i \(-0.421148\pi\)
−0.846254 + 0.532779i \(0.821148\pi\)
\(684\) −0.854102 + 2.62866i −0.0326574 + 0.100509i
\(685\) −27.1976 + 19.7602i −1.03917 + 0.754998i
\(686\) 6.18034 + 19.0211i 0.235966 + 0.726230i
\(687\) 7.50000 23.0826i 0.286143 0.880657i
\(688\) −0.381966 + 1.17557i −0.0145623 + 0.0448182i
\(689\) −12.8435 39.5281i −0.489297 1.50590i
\(690\) 10.8541 7.88597i 0.413209 0.300214i
\(691\) −7.47214 + 22.9969i −0.284253 + 0.874842i 0.702368 + 0.711814i \(0.252126\pi\)
−0.986621 + 0.163028i \(0.947874\pi\)
\(692\) 8.82624 + 6.41264i 0.335523 + 0.243772i
\(693\) −10.4721 −0.397804
\(694\) −4.23607 3.07768i −0.160799 0.116827i
\(695\) 9.27051 28.5317i 0.351650 1.08227i
\(696\) 1.11803 0.812299i 0.0423790 0.0307901i
\(697\) 38.6976 28.1154i 1.46577 1.06495i
\(698\) −4.57295 14.0741i −0.173089 0.532712i
\(699\) 22.0902 0.835527
\(700\) −8.09017 5.87785i −0.305780 0.222162i
\(701\) −20.1591 −0.761397 −0.380698 0.924699i \(-0.624316\pi\)
−0.380698 + 0.924699i \(0.624316\pi\)
\(702\) −1.50000 4.61653i −0.0566139 0.174240i
\(703\) −4.79837 + 3.48622i −0.180974 + 0.131485i
\(704\) 4.23607 3.07768i 0.159653 0.115995i
\(705\) −8.61803 + 6.26137i −0.324574 + 0.235817i
\(706\) 16.5623 + 12.0332i 0.623331 + 0.452876i
\(707\) 3.34752 0.125897
\(708\) 7.23607 + 5.25731i 0.271948 + 0.197582i
\(709\) −9.20820 + 28.3399i −0.345821 + 1.06433i 0.615321 + 0.788276i \(0.289026\pi\)
−0.961143 + 0.276052i \(0.910974\pi\)
\(710\) −9.79837 30.1563i −0.367726 1.13175i
\(711\) 0 0
\(712\) −0.427051 + 1.31433i −0.0160044 + 0.0492565i
\(713\) 6.87539 21.1603i 0.257485 0.792458i
\(714\) 4.85410 + 14.9394i 0.181660 + 0.559093i
\(715\) 45.9787 + 33.4055i 1.71951 + 1.24929i
\(716\) −1.18034 + 3.63271i −0.0441114 + 0.135761i
\(717\) 21.7082 + 15.7719i 0.810708 + 0.589014i
\(718\) 27.8885 1.04079
\(719\) −18.0902 13.1433i −0.674649 0.490162i 0.196929 0.980418i \(-0.436903\pi\)
−0.871578 + 0.490256i \(0.836903\pi\)
\(720\) −0.690983 2.12663i −0.0257514 0.0792547i
\(721\) 3.70820 2.69417i 0.138101 0.100336i
\(722\) −9.19098 + 6.67764i −0.342053 + 0.248516i
\(723\) 4.28115 + 13.1760i 0.159218 + 0.490022i
\(724\) −20.0344 −0.744574
\(725\) 5.59017 + 4.06150i 0.207614 + 0.150840i
\(726\) 16.4164 0.609270
\(727\) 3.18034 + 9.78808i 0.117952 + 0.363020i 0.992551 0.121827i \(-0.0388753\pi\)
−0.874599 + 0.484847i \(0.838875\pi\)
\(728\) −7.85410 + 5.70634i −0.291092 + 0.211491i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) −7.03444 −0.260356
\(731\) 7.85410 + 5.70634i 0.290494 + 0.211057i
\(732\) 8.85410 0.327257
\(733\) 5.14590 + 3.73871i 0.190068 + 0.138093i 0.678750 0.734370i \(-0.262522\pi\)
−0.488682 + 0.872462i \(0.662522\pi\)
\(734\) 3.85410 11.8617i 0.142257 0.437824i
\(735\) −6.70820 −0.247436
\(736\) −1.85410 5.70634i −0.0683431 0.210338i
\(737\) 15.7082 48.3449i 0.578619 1.78081i
\(738\) 1.88197 5.79210i 0.0692761 0.213210i
\(739\) 2.56231 + 7.88597i 0.0942559 + 0.290090i 0.987059 0.160357i \(-0.0512646\pi\)
−0.892803 + 0.450447i \(0.851265\pi\)
\(740\) 1.48278 4.56352i 0.0545080 0.167759i
\(741\) −4.14590 + 12.7598i −0.152303 + 0.468742i
\(742\) 13.8541 + 10.0656i 0.508600 + 0.369520i
\(743\) 6.65248 0.244056 0.122028 0.992527i \(-0.461060\pi\)
0.122028 + 0.992527i \(0.461060\pi\)
\(744\) −3.00000 2.17963i −0.109985 0.0799090i
\(745\) 12.7254 + 9.24556i 0.466223 + 0.338731i
\(746\) 2.09017 1.51860i 0.0765266 0.0555998i
\(747\) −4.85410 + 3.52671i −0.177602 + 0.129036i
\(748\) −12.7082 39.1118i −0.464658 1.43007i
\(749\) 21.8885 0.799790
\(750\) 9.04508 6.57164i 0.330280 0.239962i
\(751\) 14.7639 0.538744 0.269372 0.963036i \(-0.413184\pi\)
0.269372 + 0.963036i \(0.413184\pi\)
\(752\) 1.47214 + 4.53077i 0.0536833 + 0.165220i
\(753\) −10.0902 + 7.33094i −0.367706 + 0.267154i
\(754\) 5.42705 3.94298i 0.197642 0.143595i
\(755\) −12.5623 9.12705i −0.457189 0.332167i
\(756\) 1.61803 + 1.17557i 0.0588473 + 0.0427551i
\(757\) −28.8541 −1.04872 −0.524360 0.851497i \(-0.675695\pi\)
−0.524360 + 0.851497i \(0.675695\pi\)
\(758\) −2.76393 2.00811i −0.100391 0.0729380i
\(759\) 9.70820 29.8788i 0.352385 1.08453i
\(760\) −1.90983 + 5.87785i −0.0692768 + 0.213212i
\(761\) 7.46556 + 22.9766i 0.270626 + 0.832902i 0.990344 + 0.138635i \(0.0442714\pi\)
−0.719717 + 0.694267i \(0.755729\pi\)
\(762\) 0.0901699 0.277515i 0.00326651 0.0100533i
\(763\) 1.58359 4.87380i 0.0573299 0.176443i
\(764\) −0.236068 0.726543i −0.00854064 0.0262854i
\(765\) −17.5623 −0.634967
\(766\) −6.32624 + 19.4702i −0.228576 + 0.703485i
\(767\) 35.1246 + 25.5195i 1.26828 + 0.921457i
\(768\) −1.00000 −0.0360844
\(769\) 1.90983 + 1.38757i 0.0688702 + 0.0500372i 0.621688 0.783265i \(-0.286447\pi\)
−0.552817 + 0.833302i \(0.686447\pi\)
\(770\) −23.4164 −0.843869
\(771\) −9.39919 + 6.82891i −0.338503 + 0.245937i
\(772\) −1.92705 + 1.40008i −0.0693561 + 0.0503901i
\(773\) 4.35410 + 13.4005i 0.156606 + 0.481984i 0.998320 0.0579395i \(-0.0184531\pi\)
−0.841714 + 0.539924i \(0.818453\pi\)
\(774\) 1.23607 0.0444295
\(775\)