Properties

Label 731.2.e.a.307.3
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.3
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.3

$q$-expansion

\(f(q)\) \(=\) \(q-2.32507 q^{2} +(1.39344 - 2.41351i) q^{3} +3.40595 q^{4} +(1.48534 - 2.57269i) q^{5} +(-3.23985 + 5.61158i) q^{6} +(1.79579 + 3.11040i) q^{7} -3.26893 q^{8} +(-2.38336 - 4.12809i) q^{9} +O(q^{10})\) \(q-2.32507 q^{2} +(1.39344 - 2.41351i) q^{3} +3.40595 q^{4} +(1.48534 - 2.57269i) q^{5} +(-3.23985 + 5.61158i) q^{6} +(1.79579 + 3.11040i) q^{7} -3.26893 q^{8} +(-2.38336 - 4.12809i) q^{9} +(-3.45353 + 5.98168i) q^{10} +0.503913 q^{11} +(4.74599 - 8.22030i) q^{12} +(1.43942 + 2.49315i) q^{13} +(-4.17534 - 7.23190i) q^{14} +(-4.13948 - 7.16978i) q^{15} +0.788599 q^{16} +(0.500000 + 0.866025i) q^{17} +(5.54147 + 9.59811i) q^{18} +(2.51253 - 4.35183i) q^{19} +(5.05901 - 8.76246i) q^{20} +10.0093 q^{21} -1.17163 q^{22} +(3.29078 - 5.69981i) q^{23} +(-4.55507 + 7.88961i) q^{24} +(-1.91249 - 3.31253i) q^{25} +(-3.34676 - 5.79676i) q^{26} -4.92362 q^{27} +(6.11638 + 10.5939i) q^{28} +(-2.23638 - 3.87352i) q^{29} +(9.62457 + 16.6702i) q^{30} +(-3.21859 + 5.57477i) q^{31} +4.70432 q^{32} +(0.702173 - 1.21620i) q^{33} +(-1.16254 - 2.01357i) q^{34} +10.6695 q^{35} +(-8.11759 - 14.0601i) q^{36} +(3.83987 - 6.65085i) q^{37} +(-5.84181 + 10.1183i) q^{38} +8.02301 q^{39} +(-4.85549 + 8.40995i) q^{40} +4.22141 q^{41} -23.2724 q^{42} +(-3.41951 + 5.59526i) q^{43} +1.71630 q^{44} -14.1604 q^{45} +(-7.65130 + 13.2524i) q^{46} -9.51331 q^{47} +(1.09887 - 1.90329i) q^{48} +(-2.94974 + 5.10909i) q^{49} +(4.44667 + 7.70186i) q^{50} +2.78688 q^{51} +(4.90260 + 8.49156i) q^{52} +(-2.74262 + 4.75036i) q^{53} +11.4478 q^{54} +(0.748484 - 1.29641i) q^{55} +(-5.87032 - 10.1677i) q^{56} +(-7.00213 - 12.1280i) q^{57} +(5.19973 + 9.00620i) q^{58} -2.40870 q^{59} +(-14.0989 - 24.4199i) q^{60} +(-2.28404 - 3.95607i) q^{61} +(7.48346 - 12.9617i) q^{62} +(8.56002 - 14.8264i) q^{63} -12.5151 q^{64} +8.55215 q^{65} +(-1.63260 + 2.82775i) q^{66} +(0.943401 - 1.63402i) q^{67} +(1.70298 + 2.94964i) q^{68} +(-9.17103 - 15.8847i) q^{69} -24.8073 q^{70} +(6.37565 + 11.0430i) q^{71} +(7.79103 + 13.4945i) q^{72} +(1.74386 + 3.02046i) q^{73} +(-8.92797 + 15.4637i) q^{74} -10.6598 q^{75} +(8.55755 - 14.8221i) q^{76} +(0.904923 + 1.56737i) q^{77} -18.6541 q^{78} +(2.32739 + 4.03115i) q^{79} +(1.17134 - 2.02882i) q^{80} +(0.289298 - 0.501079i) q^{81} -9.81508 q^{82} +(5.65525 - 9.79519i) q^{83} +34.0913 q^{84} +2.97069 q^{85} +(7.95060 - 13.0094i) q^{86} -12.4650 q^{87} -1.64726 q^{88} +(4.14612 - 7.18130i) q^{89} +32.9239 q^{90} +(-5.16981 + 8.95437i) q^{91} +(11.2082 - 19.4133i) q^{92} +(8.96984 + 15.5362i) q^{93} +22.1191 q^{94} +(-7.46394 - 12.9279i) q^{95} +(6.55519 - 11.3539i) q^{96} -10.2402 q^{97} +(6.85835 - 11.8790i) q^{98} +(-1.20100 - 2.08020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32507 −1.64407 −0.822036 0.569435i \(-0.807162\pi\)
−0.822036 + 0.569435i \(0.807162\pi\)
\(3\) 1.39344 2.41351i 0.804504 1.39344i −0.112122 0.993694i \(-0.535765\pi\)
0.916626 0.399747i \(-0.130902\pi\)
\(4\) 3.40595 1.70298
\(5\) 1.48534 2.57269i 0.664266 1.15054i −0.315218 0.949019i \(-0.602078\pi\)
0.979484 0.201523i \(-0.0645890\pi\)
\(6\) −3.23985 + 5.61158i −1.32266 + 2.29092i
\(7\) 1.79579 + 3.11040i 0.678746 + 1.17562i 0.975359 + 0.220624i \(0.0708094\pi\)
−0.296613 + 0.954998i \(0.595857\pi\)
\(8\) −3.26893 −1.15574
\(9\) −2.38336 4.12809i −0.794452 1.37603i
\(10\) −3.45353 + 5.98168i −1.09210 + 1.89157i
\(11\) 0.503913 0.151935 0.0759677 0.997110i \(-0.475795\pi\)
0.0759677 + 0.997110i \(0.475795\pi\)
\(12\) 4.74599 8.22030i 1.37005 2.37300i
\(13\) 1.43942 + 2.49315i 0.399224 + 0.691477i 0.993630 0.112688i \(-0.0359462\pi\)
−0.594406 + 0.804165i \(0.702613\pi\)
\(14\) −4.17534 7.23190i −1.11591 1.93281i
\(15\) −4.13948 7.16978i −1.06881 1.85123i
\(16\) 0.788599 0.197150
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) 5.54147 + 9.59811i 1.30614 + 2.26230i
\(19\) 2.51253 4.35183i 0.576414 0.998378i −0.419472 0.907768i \(-0.637785\pi\)
0.995886 0.0906103i \(-0.0288818\pi\)
\(20\) 5.05901 8.76246i 1.13123 1.95934i
\(21\) 10.0093 2.18421
\(22\) −1.17163 −0.249793
\(23\) 3.29078 5.69981i 0.686176 1.18849i −0.286890 0.957964i \(-0.592621\pi\)
0.973066 0.230528i \(-0.0740453\pi\)
\(24\) −4.55507 + 7.88961i −0.929799 + 1.61046i
\(25\) −1.91249 3.31253i −0.382498 0.662506i
\(26\) −3.34676 5.79676i −0.656354 1.13684i
\(27\) −4.92362 −0.947550
\(28\) 6.11638 + 10.5939i 1.15589 + 2.00205i
\(29\) −2.23638 3.87352i −0.415285 0.719294i 0.580174 0.814493i \(-0.302985\pi\)
−0.995458 + 0.0951986i \(0.969651\pi\)
\(30\) 9.62457 + 16.6702i 1.75720 + 3.04356i
\(31\) −3.21859 + 5.57477i −0.578077 + 1.00126i 0.417623 + 0.908620i \(0.362863\pi\)
−0.995700 + 0.0926378i \(0.970470\pi\)
\(32\) 4.70432 0.831614
\(33\) 0.702173 1.21620i 0.122233 0.211713i
\(34\) −1.16254 2.01357i −0.199373 0.345324i
\(35\) 10.6695 1.80347
\(36\) −8.11759 14.0601i −1.35293 2.34335i
\(37\) 3.83987 6.65085i 0.631271 1.09339i −0.356021 0.934478i \(-0.615867\pi\)
0.987292 0.158915i \(-0.0507997\pi\)
\(38\) −5.84181 + 10.1183i −0.947667 + 1.64141i
\(39\) 8.02301 1.28471
\(40\) −4.85549 + 8.40995i −0.767720 + 1.32973i
\(41\) 4.22141 0.659274 0.329637 0.944108i \(-0.393074\pi\)
0.329637 + 0.944108i \(0.393074\pi\)
\(42\) −23.2724 −3.59100
\(43\) −3.41951 + 5.59526i −0.521470 + 0.853270i
\(44\) 1.71630 0.258742
\(45\) −14.1604 −2.11091
\(46\) −7.65130 + 13.2524i −1.12812 + 1.95397i
\(47\) −9.51331 −1.38766 −0.693829 0.720140i \(-0.744078\pi\)
−0.693829 + 0.720140i \(0.744078\pi\)
\(48\) 1.09887 1.90329i 0.158608 0.274716i
\(49\) −2.94974 + 5.10909i −0.421391 + 0.729871i
\(50\) 4.44667 + 7.70186i 0.628854 + 1.08921i
\(51\) 2.78688 0.390242
\(52\) 4.90260 + 8.49156i 0.679869 + 1.17757i
\(53\) −2.74262 + 4.75036i −0.376728 + 0.652512i −0.990584 0.136906i \(-0.956284\pi\)
0.613856 + 0.789418i \(0.289618\pi\)
\(54\) 11.4478 1.55784
\(55\) 0.748484 1.29641i 0.100926 0.174808i
\(56\) −5.87032 10.1677i −0.784455 1.35872i
\(57\) −7.00213 12.1280i −0.927454 1.60640i
\(58\) 5.19973 + 9.00620i 0.682758 + 1.18257i
\(59\) −2.40870 −0.313585 −0.156793 0.987632i \(-0.550115\pi\)
−0.156793 + 0.987632i \(0.550115\pi\)
\(60\) −14.0989 24.4199i −1.82015 3.15260i
\(61\) −2.28404 3.95607i −0.292441 0.506522i 0.681946 0.731403i \(-0.261134\pi\)
−0.974386 + 0.224881i \(0.927801\pi\)
\(62\) 7.48346 12.9617i 0.950400 1.64614i
\(63\) 8.56002 14.8264i 1.07846 1.86795i
\(64\) −12.5151 −1.56438
\(65\) 8.55215 1.06076
\(66\) −1.63260 + 2.82775i −0.200959 + 0.348072i
\(67\) 0.943401 1.63402i 0.115255 0.199627i −0.802627 0.596482i \(-0.796565\pi\)
0.917882 + 0.396854i \(0.129898\pi\)
\(68\) 1.70298 + 2.94964i 0.206516 + 0.357696i
\(69\) −9.17103 15.8847i −1.10406 1.91229i
\(70\) −24.8073 −2.96504
\(71\) 6.37565 + 11.0430i 0.756651 + 1.31056i 0.944549 + 0.328369i \(0.106499\pi\)
−0.187899 + 0.982188i \(0.560168\pi\)
\(72\) 7.79103 + 13.4945i 0.918182 + 1.59034i
\(73\) 1.74386 + 3.02046i 0.204104 + 0.353518i 0.949847 0.312716i \(-0.101239\pi\)
−0.745743 + 0.666234i \(0.767905\pi\)
\(74\) −8.92797 + 15.4637i −1.03786 + 1.79762i
\(75\) −10.6598 −1.23088
\(76\) 8.55755 14.8221i 0.981619 1.70021i
\(77\) 0.904923 + 1.56737i 0.103126 + 0.178619i
\(78\) −18.6541 −2.11216
\(79\) 2.32739 + 4.03115i 0.261852 + 0.453540i 0.966734 0.255784i \(-0.0823336\pi\)
−0.704882 + 0.709324i \(0.749000\pi\)
\(80\) 1.17134 2.02882i 0.130960 0.226829i
\(81\) 0.289298 0.501079i 0.0321442 0.0556755i
\(82\) −9.81508 −1.08389
\(83\) 5.65525 9.79519i 0.620745 1.07516i −0.368602 0.929587i \(-0.620164\pi\)
0.989347 0.145574i \(-0.0465030\pi\)
\(84\) 34.0913 3.71966
\(85\) 2.97069 0.322216
\(86\) 7.95060 13.0094i 0.857335 1.40284i
\(87\) −12.4650 −1.33639
\(88\) −1.64726 −0.175598
\(89\) 4.14612 7.18130i 0.439488 0.761216i −0.558162 0.829732i \(-0.688493\pi\)
0.997650 + 0.0685162i \(0.0218265\pi\)
\(90\) 32.9239 3.47049
\(91\) −5.16981 + 8.95437i −0.541943 + 0.938673i
\(92\) 11.2082 19.4133i 1.16854 2.02397i
\(93\) 8.96984 + 15.5362i 0.930129 + 1.61103i
\(94\) 22.1191 2.28141
\(95\) −7.46394 12.9279i −0.765784 1.32638i
\(96\) 6.55519 11.3539i 0.669037 1.15881i
\(97\) −10.2402 −1.03973 −0.519867 0.854247i \(-0.674018\pi\)
−0.519867 + 0.854247i \(0.674018\pi\)
\(98\) 6.85835 11.8790i 0.692798 1.19996i
\(99\) −1.20100 2.08020i −0.120705 0.209068i
\(100\) −6.51384 11.2823i −0.651384 1.12823i
\(101\) 6.61995 + 11.4661i 0.658709 + 1.14092i 0.980950 + 0.194260i \(0.0622307\pi\)
−0.322241 + 0.946658i \(0.604436\pi\)
\(102\) −6.47970 −0.641585
\(103\) −7.17269 12.4235i −0.706746 1.22412i −0.966058 0.258327i \(-0.916829\pi\)
0.259311 0.965794i \(-0.416504\pi\)
\(104\) −4.70538 8.14996i −0.461400 0.799169i
\(105\) 14.8673 25.7509i 1.45090 2.51303i
\(106\) 6.37679 11.0449i 0.619368 1.07278i
\(107\) −12.0291 −1.16290 −0.581451 0.813582i \(-0.697515\pi\)
−0.581451 + 0.813582i \(0.697515\pi\)
\(108\) −16.7696 −1.61365
\(109\) −6.41856 + 11.1173i −0.614786 + 1.06484i 0.375635 + 0.926767i \(0.377424\pi\)
−0.990422 + 0.138074i \(0.955909\pi\)
\(110\) −1.74028 + 3.01425i −0.165929 + 0.287397i
\(111\) −10.7013 18.5351i −1.01572 1.75928i
\(112\) 1.41616 + 2.45286i 0.133814 + 0.231773i
\(113\) −4.82605 −0.453997 −0.226998 0.973895i \(-0.572891\pi\)
−0.226998 + 0.973895i \(0.572891\pi\)
\(114\) 16.2804 + 28.1985i 1.52480 + 2.64103i
\(115\) −9.77589 16.9323i −0.911606 1.57895i
\(116\) −7.61699 13.1930i −0.707220 1.22494i
\(117\) 6.86132 11.8841i 0.634329 1.09869i
\(118\) 5.60039 0.515557
\(119\) −1.79579 + 3.11040i −0.164620 + 0.285130i
\(120\) 13.5317 + 23.4375i 1.23527 + 2.13955i
\(121\) −10.7461 −0.976916
\(122\) 5.31054 + 9.19813i 0.480794 + 0.832759i
\(123\) 5.88229 10.1884i 0.530388 0.918660i
\(124\) −10.9624 + 18.9874i −0.984450 + 1.70512i
\(125\) 3.49062 0.312210
\(126\) −19.9027 + 34.4724i −1.77307 + 3.07105i
\(127\) 16.4456 1.45931 0.729654 0.683817i \(-0.239681\pi\)
0.729654 + 0.683817i \(0.239681\pi\)
\(128\) 19.6898 1.74035
\(129\) 8.73934 + 16.0497i 0.769456 + 1.41310i
\(130\) −19.8843 −1.74397
\(131\) −11.6217 −1.01539 −0.507697 0.861536i \(-0.669503\pi\)
−0.507697 + 0.861536i \(0.669503\pi\)
\(132\) 2.39157 4.14231i 0.208159 0.360542i
\(133\) 18.0479 1.56495
\(134\) −2.19347 + 3.79921i −0.189487 + 0.328202i
\(135\) −7.31326 + 12.6669i −0.629425 + 1.09020i
\(136\) −1.63447 2.83098i −0.140154 0.242755i
\(137\) −5.12027 −0.437455 −0.218727 0.975786i \(-0.570191\pi\)
−0.218727 + 0.975786i \(0.570191\pi\)
\(138\) 21.3233 + 36.9330i 1.81516 + 3.14395i
\(139\) −11.0870 + 19.2033i −0.940390 + 1.62880i −0.175661 + 0.984451i \(0.556206\pi\)
−0.764729 + 0.644352i \(0.777127\pi\)
\(140\) 36.3397 3.07126
\(141\) −13.2562 + 22.9605i −1.11638 + 1.93362i
\(142\) −14.8238 25.6756i −1.24399 2.15465i
\(143\) 0.725344 + 1.25633i 0.0606563 + 0.105060i
\(144\) −1.87951 3.25541i −0.156626 0.271284i
\(145\) −13.2871 −1.10344
\(146\) −4.05460 7.02278i −0.335561 0.581209i
\(147\) 8.22057 + 14.2384i 0.678021 + 1.17437i
\(148\) 13.0784 22.6525i 1.07504 1.86202i
\(149\) −8.58539 + 14.8703i −0.703343 + 1.21823i 0.263943 + 0.964538i \(0.414977\pi\)
−0.967286 + 0.253687i \(0.918357\pi\)
\(150\) 24.7847 2.02366
\(151\) −1.84274 −0.149960 −0.0749799 0.997185i \(-0.523889\pi\)
−0.0749799 + 0.997185i \(0.523889\pi\)
\(152\) −8.21330 + 14.2258i −0.666186 + 1.15387i
\(153\) 2.38336 4.12809i 0.192683 0.333737i
\(154\) −2.10401 3.64425i −0.169546 0.293662i
\(155\) 9.56144 + 16.5609i 0.767993 + 1.33020i
\(156\) 27.3260 2.18783
\(157\) 3.20156 + 5.54526i 0.255512 + 0.442560i 0.965035 0.262123i \(-0.0844226\pi\)
−0.709522 + 0.704683i \(0.751089\pi\)
\(158\) −5.41134 9.37271i −0.430503 0.745653i
\(159\) 7.64336 + 13.2387i 0.606158 + 1.04990i
\(160\) 6.98753 12.1028i 0.552413 0.956807i
\(161\) 23.6383 1.86296
\(162\) −0.672638 + 1.16504i −0.0528475 + 0.0915345i
\(163\) 10.5226 + 18.2258i 0.824197 + 1.42755i 0.902531 + 0.430624i \(0.141707\pi\)
−0.0783343 + 0.996927i \(0.524960\pi\)
\(164\) 14.3779 1.12273
\(165\) −2.08594 3.61295i −0.162390 0.281268i
\(166\) −13.1489 + 22.7745i −1.02055 + 1.76764i
\(167\) 4.65036 8.05466i 0.359856 0.623289i −0.628081 0.778148i \(-0.716159\pi\)
0.987936 + 0.154860i \(0.0494926\pi\)
\(168\) −32.7198 −2.52439
\(169\) 2.35612 4.08092i 0.181240 0.313917i
\(170\) −6.90705 −0.529747
\(171\) −23.9530 −1.83173
\(172\) −11.6467 + 19.0572i −0.888051 + 1.45310i
\(173\) 11.0411 0.839443 0.419721 0.907653i \(-0.362128\pi\)
0.419721 + 0.907653i \(0.362128\pi\)
\(174\) 28.9821 2.19713
\(175\) 6.86887 11.8972i 0.519237 0.899346i
\(176\) 0.397385 0.0299540
\(177\) −3.35638 + 5.81341i −0.252281 + 0.436963i
\(178\) −9.64003 + 16.6970i −0.722551 + 1.25149i
\(179\) 0.475587 + 0.823741i 0.0355470 + 0.0615693i 0.883252 0.468899i \(-0.155349\pi\)
−0.847705 + 0.530469i \(0.822016\pi\)
\(180\) −48.2296 −3.59483
\(181\) 11.2289 + 19.4491i 0.834640 + 1.44564i 0.894323 + 0.447422i \(0.147658\pi\)
−0.0596826 + 0.998217i \(0.519009\pi\)
\(182\) 12.0202 20.8195i 0.890994 1.54325i
\(183\) −12.7307 −0.941079
\(184\) −10.7574 + 18.6323i −0.793043 + 1.37359i
\(185\) −11.4071 19.7576i −0.838663 1.45261i
\(186\) −20.8555 36.1228i −1.52920 2.64865i
\(187\) 0.251956 + 0.436401i 0.0184249 + 0.0319128i
\(188\) −32.4019 −2.36315
\(189\) −8.84179 15.3144i −0.643146 1.11396i
\(190\) 17.3542 + 30.0583i 1.25900 + 2.18066i
\(191\) −9.97449 + 17.2763i −0.721729 + 1.25007i 0.238578 + 0.971123i \(0.423319\pi\)
−0.960306 + 0.278947i \(0.910014\pi\)
\(192\) −17.4390 + 30.2053i −1.25855 + 2.17988i
\(193\) −15.0663 −1.08449 −0.542247 0.840219i \(-0.682426\pi\)
−0.542247 + 0.840219i \(0.682426\pi\)
\(194\) 23.8092 1.70940
\(195\) 11.9169 20.6407i 0.853388 1.47811i
\(196\) −10.0467 + 17.4013i −0.717619 + 1.24295i
\(197\) −10.8742 18.8346i −0.774752 1.34191i −0.934934 0.354823i \(-0.884541\pi\)
0.160181 0.987088i \(-0.448792\pi\)
\(198\) 2.79242 + 4.83661i 0.198448 + 0.343723i
\(199\) 17.8288 1.26385 0.631927 0.775028i \(-0.282264\pi\)
0.631927 + 0.775028i \(0.282264\pi\)
\(200\) 6.25180 + 10.8284i 0.442069 + 0.765686i
\(201\) −2.62915 4.55382i −0.185446 0.321201i
\(202\) −15.3918 26.6595i −1.08297 1.87575i
\(203\) 8.03213 13.9121i 0.563745 0.976436i
\(204\) 9.49198 0.664572
\(205\) 6.27025 10.8604i 0.437933 0.758523i
\(206\) 16.6770 + 28.8854i 1.16194 + 2.01254i
\(207\) −31.3724 −2.18054
\(208\) 1.13513 + 1.96610i 0.0787069 + 0.136324i
\(209\) 1.26610 2.19294i 0.0875777 0.151689i
\(210\) −34.5675 + 59.8726i −2.38538 + 4.13160i
\(211\) −13.6092 −0.936896 −0.468448 0.883491i \(-0.655187\pi\)
−0.468448 + 0.883491i \(0.655187\pi\)
\(212\) −9.34123 + 16.1795i −0.641559 + 1.11121i
\(213\) 35.5364 2.43491
\(214\) 27.9686 1.91189
\(215\) 9.31573 + 17.1082i 0.635328 + 1.16677i
\(216\) 16.0950 1.09512
\(217\) −23.1197 −1.56947
\(218\) 14.9236 25.8484i 1.01075 1.75068i
\(219\) 9.71988 0.656809
\(220\) 2.54930 4.41551i 0.171874 0.297694i
\(221\) −1.43942 + 2.49315i −0.0968261 + 0.167708i
\(222\) 24.8812 + 43.0955i 1.66992 + 2.89238i
\(223\) 5.89939 0.395052 0.197526 0.980298i \(-0.436709\pi\)
0.197526 + 0.980298i \(0.436709\pi\)
\(224\) 8.44798 + 14.6323i 0.564454 + 0.977664i
\(225\) −9.11629 + 15.7899i −0.607752 + 1.05266i
\(226\) 11.2209 0.746403
\(227\) −8.20693 + 14.2148i −0.544713 + 0.943471i 0.453912 + 0.891047i \(0.350028\pi\)
−0.998625 + 0.0524241i \(0.983305\pi\)
\(228\) −23.8489 41.3075i −1.57943 2.73566i
\(229\) −1.06288 1.84097i −0.0702373 0.121655i 0.828768 0.559592i \(-0.189042\pi\)
−0.899005 + 0.437938i \(0.855709\pi\)
\(230\) 22.7296 + 39.3689i 1.49875 + 2.59591i
\(231\) 5.04383 0.331859
\(232\) 7.31057 + 12.6623i 0.479962 + 0.831319i
\(233\) −1.53910 2.66580i −0.100830 0.174643i 0.811197 0.584773i \(-0.198816\pi\)
−0.912027 + 0.410131i \(0.865483\pi\)
\(234\) −15.9530 + 27.6315i −1.04288 + 1.80633i
\(235\) −14.1305 + 24.4748i −0.921774 + 1.59656i
\(236\) −8.20390 −0.534028
\(237\) 12.9723 0.842642
\(238\) 4.17534 7.23190i 0.270647 0.468775i
\(239\) 14.5834 25.2592i 0.943322 1.63388i 0.184244 0.982880i \(-0.441016\pi\)
0.759077 0.651000i \(-0.225650\pi\)
\(240\) −3.26439 5.65408i −0.210715 0.364969i
\(241\) −7.66282 13.2724i −0.493606 0.854950i 0.506367 0.862318i \(-0.330988\pi\)
−0.999973 + 0.00736776i \(0.997655\pi\)
\(242\) 24.9854 1.60612
\(243\) −8.19166 14.1884i −0.525496 0.910185i
\(244\) −7.77931 13.4742i −0.498019 0.862595i
\(245\) 8.76275 + 15.1775i 0.559831 + 0.969656i
\(246\) −13.6767 + 23.6888i −0.871997 + 1.51034i
\(247\) 14.4664 0.920474
\(248\) 10.5214 18.2236i 0.668108 1.15720i
\(249\) −15.7605 27.2980i −0.998783 1.72994i
\(250\) −8.11593 −0.513297
\(251\) 8.69612 + 15.0621i 0.548895 + 0.950713i 0.998351 + 0.0574108i \(0.0182845\pi\)
−0.449456 + 0.893302i \(0.648382\pi\)
\(252\) 29.1550 50.4980i 1.83659 3.18107i
\(253\) 1.65827 2.87221i 0.104254 0.180574i
\(254\) −38.2371 −2.39921
\(255\) 4.13948 7.16978i 0.259224 0.448989i
\(256\) −20.7500 −1.29687
\(257\) 4.79336 0.299002 0.149501 0.988762i \(-0.452233\pi\)
0.149501 + 0.988762i \(0.452233\pi\)
\(258\) −20.3196 37.3166i −1.26504 2.32323i
\(259\) 27.5824 1.71389
\(260\) 29.1282 1.80645
\(261\) −10.6602 + 18.4639i −0.659847 + 1.14289i
\(262\) 27.0213 1.66938
\(263\) 1.15106 1.99370i 0.0709776 0.122937i −0.828352 0.560207i \(-0.810721\pi\)
0.899330 + 0.437271i \(0.144055\pi\)
\(264\) −2.29536 + 3.97567i −0.141269 + 0.244686i
\(265\) 8.14747 + 14.1118i 0.500495 + 0.866883i
\(266\) −41.9627 −2.57290
\(267\) −11.5548 20.0134i −0.707140 1.22480i
\(268\) 3.21318 5.56539i 0.196276 0.339960i
\(269\) 6.49631 0.396087 0.198044 0.980193i \(-0.436541\pi\)
0.198044 + 0.980193i \(0.436541\pi\)
\(270\) 17.0038 29.4515i 1.03482 1.79236i
\(271\) 5.26818 + 9.12476i 0.320019 + 0.554289i 0.980492 0.196561i \(-0.0629773\pi\)
−0.660472 + 0.750850i \(0.729644\pi\)
\(272\) 0.394299 + 0.682946i 0.0239079 + 0.0414097i
\(273\) 14.4076 + 24.9548i 0.871991 + 1.51033i
\(274\) 11.9050 0.719207
\(275\) −0.963728 1.66923i −0.0581150 0.100658i
\(276\) −31.2361 54.1025i −1.88019 3.25659i
\(277\) 13.4475 23.2917i 0.807980 1.39946i −0.106281 0.994336i \(-0.533894\pi\)
0.914261 0.405126i \(-0.132772\pi\)
\(278\) 25.7781 44.6490i 1.54607 2.67787i
\(279\) 30.6842 1.83702
\(280\) −34.8778 −2.08435
\(281\) 2.97549 5.15370i 0.177503 0.307444i −0.763522 0.645782i \(-0.776531\pi\)
0.941025 + 0.338338i \(0.109865\pi\)
\(282\) 30.8217 53.3847i 1.83540 3.17901i
\(283\) 9.49026 + 16.4376i 0.564138 + 0.977115i 0.997129 + 0.0757170i \(0.0241246\pi\)
−0.432992 + 0.901398i \(0.642542\pi\)
\(284\) 21.7152 + 37.6118i 1.28856 + 2.23185i
\(285\) −41.6022 −2.46430
\(286\) −1.68648 2.92106i −0.0997234 0.172726i
\(287\) 7.58078 + 13.1303i 0.447479 + 0.775057i
\(288\) −11.2121 19.4199i −0.660678 1.14433i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 30.8935 1.81413
\(291\) −14.2691 + 24.7148i −0.836469 + 1.44881i
\(292\) 5.93951 + 10.2875i 0.347584 + 0.602032i
\(293\) −4.11101 −0.240168 −0.120084 0.992764i \(-0.538316\pi\)
−0.120084 + 0.992764i \(0.538316\pi\)
\(294\) −19.1134 33.1054i −1.11472 1.93075i
\(295\) −3.57774 + 6.19683i −0.208304 + 0.360793i
\(296\) −12.5523 + 21.7412i −0.729587 + 1.26368i
\(297\) −2.48107 −0.143967
\(298\) 19.9616 34.5746i 1.15635 2.00285i
\(299\) 18.9473 1.09575
\(300\) −36.3066 −2.09616
\(301\) −23.5442 0.588121i −1.35707 0.0338988i
\(302\) 4.28449 0.246545
\(303\) 36.8980 2.11974
\(304\) 1.98138 3.43185i 0.113640 0.196830i
\(305\) −13.5703 −0.777034
\(306\) −5.54147 + 9.59811i −0.316785 + 0.548687i
\(307\) 7.22796 12.5192i 0.412521 0.714508i −0.582643 0.812728i \(-0.697982\pi\)
0.995165 + 0.0982201i \(0.0313149\pi\)
\(308\) 3.08212 + 5.33839i 0.175620 + 0.304183i
\(309\) −39.9789 −2.27432
\(310\) −22.2310 38.5052i −1.26264 2.18695i
\(311\) 5.40542 9.36246i 0.306513 0.530896i −0.671084 0.741381i \(-0.734171\pi\)
0.977597 + 0.210485i \(0.0675044\pi\)
\(312\) −26.2267 −1.48479
\(313\) 13.4845 23.3558i 0.762187 1.32015i −0.179534 0.983752i \(-0.557459\pi\)
0.941721 0.336395i \(-0.109208\pi\)
\(314\) −7.44385 12.8931i −0.420081 0.727601i
\(315\) −25.4291 44.0446i −1.43277 2.48163i
\(316\) 7.92697 + 13.7299i 0.445927 + 0.772368i
\(317\) −19.2227 −1.07965 −0.539826 0.841777i \(-0.681510\pi\)
−0.539826 + 0.841777i \(0.681510\pi\)
\(318\) −17.7714 30.7809i −0.996568 1.72611i
\(319\) −1.12694 1.95192i −0.0630965 0.109286i
\(320\) −18.5892 + 32.1974i −1.03917 + 1.79989i
\(321\) −16.7619 + 29.0325i −0.935558 + 1.62043i
\(322\) −54.9606 −3.06283
\(323\) 5.02506 0.279602
\(324\) 0.985335 1.70665i 0.0547408 0.0948139i
\(325\) 5.50576 9.53626i 0.305405 0.528977i
\(326\) −24.4659 42.3762i −1.35504 2.34700i
\(327\) 17.8878 + 30.9825i 0.989196 + 1.71334i
\(328\) −13.7995 −0.761951
\(329\) −17.0839 29.5902i −0.941867 1.63136i
\(330\) 4.84995 + 8.40035i 0.266981 + 0.462424i
\(331\) 15.9850 + 27.6868i 0.878613 + 1.52180i 0.852863 + 0.522135i \(0.174864\pi\)
0.0257503 + 0.999668i \(0.491803\pi\)
\(332\) 19.2615 33.3619i 1.05711 1.83097i
\(333\) −36.6071 −2.00606
\(334\) −10.8124 + 18.7277i −0.591629 + 1.02473i
\(335\) −2.80255 4.85416i −0.153120 0.265211i
\(336\) 7.89334 0.430617
\(337\) 13.6496 + 23.6418i 0.743541 + 1.28785i 0.950874 + 0.309580i \(0.100188\pi\)
−0.207333 + 0.978270i \(0.566478\pi\)
\(338\) −5.47815 + 9.48843i −0.297972 + 0.516102i
\(339\) −6.72482 + 11.6477i −0.365242 + 0.632618i
\(340\) 10.1180 0.548726
\(341\) −1.62189 + 2.80920i −0.0878303 + 0.152127i
\(342\) 55.6924 3.01150
\(343\) 3.95263 0.213422
\(344\) 11.1781 18.2905i 0.602685 0.986160i
\(345\) −54.4885 −2.93356
\(346\) −25.6714 −1.38011
\(347\) −2.25420 + 3.90439i −0.121012 + 0.209599i −0.920167 0.391526i \(-0.871947\pi\)
0.799155 + 0.601125i \(0.205281\pi\)
\(348\) −42.4553 −2.27584
\(349\) 0.902306 1.56284i 0.0482993 0.0836569i −0.840865 0.541245i \(-0.817953\pi\)
0.889164 + 0.457588i \(0.151287\pi\)
\(350\) −15.9706 + 27.6619i −0.853664 + 1.47859i
\(351\) −7.08717 12.2753i −0.378285 0.655209i
\(352\) 2.37057 0.126352
\(353\) −15.8692 27.4862i −0.844631 1.46294i −0.885942 0.463797i \(-0.846487\pi\)
0.0413108 0.999146i \(-0.486847\pi\)
\(354\) 7.80381 13.5166i 0.414768 0.718399i
\(355\) 37.8801 2.01047
\(356\) 14.1215 24.4591i 0.748438 1.29633i
\(357\) 5.00466 + 8.66833i 0.264875 + 0.458776i
\(358\) −1.10577 1.91525i −0.0584419 0.101224i
\(359\) 15.5614 + 26.9532i 0.821301 + 1.42253i 0.904714 + 0.426019i \(0.140085\pi\)
−0.0834133 + 0.996515i \(0.526582\pi\)
\(360\) 46.2894 2.43967
\(361\) −3.12562 5.41373i −0.164506 0.284933i
\(362\) −26.1081 45.2205i −1.37221 2.37674i
\(363\) −14.9740 + 25.9358i −0.785932 + 1.36127i
\(364\) −17.6081 + 30.4982i −0.922916 + 1.59854i
\(365\) 10.3609 0.542316
\(366\) 29.5997 1.54720
\(367\) 12.9247 22.3863i 0.674664 1.16855i −0.301903 0.953339i \(-0.597622\pi\)
0.976567 0.215214i \(-0.0690449\pi\)
\(368\) 2.59511 4.49486i 0.135279 0.234311i
\(369\) −10.0611 17.4264i −0.523762 0.907182i
\(370\) 26.5222 + 45.9378i 1.37882 + 2.38819i
\(371\) −19.7007 −1.02281
\(372\) 30.5508 + 52.9156i 1.58399 + 2.74355i
\(373\) 11.7173 + 20.2950i 0.606701 + 1.05084i 0.991780 + 0.127954i \(0.0408409\pi\)
−0.385079 + 0.922884i \(0.625826\pi\)
\(374\) −0.585816 1.01466i −0.0302918 0.0524670i
\(375\) 4.86397 8.42465i 0.251174 0.435047i
\(376\) 31.0984 1.60378
\(377\) 6.43819 11.1513i 0.331583 0.574319i
\(378\) 20.5578 + 35.6071i 1.05738 + 1.83143i
\(379\) 15.0200 0.771525 0.385762 0.922598i \(-0.373938\pi\)
0.385762 + 0.922598i \(0.373938\pi\)
\(380\) −25.4218 44.0319i −1.30411 2.25879i
\(381\) 22.9159 39.6915i 1.17402 2.03346i
\(382\) 23.1914 40.1687i 1.18657 2.05521i
\(383\) −13.4675 −0.688155 −0.344078 0.938941i \(-0.611808\pi\)
−0.344078 + 0.938941i \(0.611808\pi\)
\(384\) 27.4365 47.5215i 1.40012 2.42507i
\(385\) 5.37648 0.274011
\(386\) 35.0301 1.78299
\(387\) 31.2477 + 0.780548i 1.58841 + 0.0396775i
\(388\) −34.8776 −1.77064
\(389\) −33.1441 −1.68047 −0.840236 0.542221i \(-0.817583\pi\)
−0.840236 + 0.542221i \(0.817583\pi\)
\(390\) −27.7077 + 47.9911i −1.40303 + 2.43012i
\(391\) 6.58157 0.332844
\(392\) 9.64250 16.7013i 0.487020 0.843543i
\(393\) −16.1942 + 28.0491i −0.816888 + 1.41489i
\(394\) 25.2832 + 43.7918i 1.27375 + 2.20620i
\(395\) 13.8279 0.695756
\(396\) −4.09056 7.08506i −0.205558 0.356037i
\(397\) −6.22428 + 10.7808i −0.312388 + 0.541071i −0.978879 0.204442i \(-0.934462\pi\)
0.666491 + 0.745513i \(0.267795\pi\)
\(398\) −41.4533 −2.07787
\(399\) 25.1487 43.5589i 1.25901 2.18067i
\(400\) −1.50819 2.61226i −0.0754093 0.130613i
\(401\) −7.18772 12.4495i −0.358938 0.621699i 0.628846 0.777530i \(-0.283528\pi\)
−0.987784 + 0.155831i \(0.950194\pi\)
\(402\) 6.11295 + 10.5879i 0.304886 + 0.528079i
\(403\) −18.5317 −0.923129
\(404\) 22.5472 + 39.0529i 1.12177 + 1.94296i
\(405\) −0.859414 1.48855i −0.0427046 0.0739666i
\(406\) −18.6753 + 32.3465i −0.926838 + 1.60533i
\(407\) 1.93496 3.35145i 0.0959124 0.166125i
\(408\) −9.11013 −0.451019
\(409\) 12.2907 0.607738 0.303869 0.952714i \(-0.401722\pi\)
0.303869 + 0.952714i \(0.401722\pi\)
\(410\) −14.5788 + 25.2512i −0.719994 + 1.24707i
\(411\) −7.13480 + 12.3578i −0.351934 + 0.609567i
\(412\) −24.4298 42.3137i −1.20357 2.08465i
\(413\) −4.32552 7.49201i −0.212845 0.368658i
\(414\) 72.9431 3.58496
\(415\) −16.8000 29.0984i −0.824679 1.42839i
\(416\) 6.77151 + 11.7286i 0.332001 + 0.575042i
\(417\) 30.8983 + 53.5173i 1.51309 + 2.62076i
\(418\) −2.94376 + 5.09875i −0.143984 + 0.249388i
\(419\) −10.2081 −0.498696 −0.249348 0.968414i \(-0.580216\pi\)
−0.249348 + 0.968414i \(0.580216\pi\)
\(420\) 50.6372 87.7062i 2.47084 4.27963i
\(421\) −5.73239 9.92879i −0.279380 0.483900i 0.691851 0.722040i \(-0.256795\pi\)
−0.971231 + 0.238141i \(0.923462\pi\)
\(422\) 31.6423 1.54032
\(423\) 22.6736 + 39.2718i 1.10243 + 1.90946i
\(424\) 8.96545 15.5286i 0.435401 0.754136i
\(425\) 1.91249 3.31253i 0.0927694 0.160681i
\(426\) −82.6246 −4.00317
\(427\) 8.20330 14.2085i 0.396986 0.687599i
\(428\) −40.9707 −1.98039
\(429\) 4.04290 0.195193
\(430\) −21.6597 39.7778i −1.04452 1.91826i
\(431\) 12.6265 0.608196 0.304098 0.952641i \(-0.401645\pi\)
0.304098 + 0.952641i \(0.401645\pi\)
\(432\) −3.88276 −0.186809
\(433\) −4.74544 + 8.21934i −0.228051 + 0.394996i −0.957230 0.289326i \(-0.906569\pi\)
0.729179 + 0.684323i \(0.239902\pi\)
\(434\) 53.7549 2.58032
\(435\) −18.5149 + 32.0687i −0.887719 + 1.53758i
\(436\) −21.8613 + 37.8649i −1.04697 + 1.81340i
\(437\) −16.5364 28.6419i −0.791043 1.37013i
\(438\) −22.5994 −1.07984
\(439\) 7.16534 + 12.4107i 0.341983 + 0.592332i 0.984801 0.173687i \(-0.0555681\pi\)
−0.642818 + 0.766019i \(0.722235\pi\)
\(440\) −2.44674 + 4.23788i −0.116644 + 0.202033i
\(441\) 28.1211 1.33910
\(442\) 3.34676 5.79676i 0.159189 0.275724i
\(443\) −0.108587 0.188078i −0.00515913 0.00893587i 0.863434 0.504461i \(-0.168309\pi\)
−0.868593 + 0.495525i \(0.834976\pi\)
\(444\) −36.4480 63.1298i −1.72974 2.99601i
\(445\) −12.3168 21.3334i −0.583874 1.01130i
\(446\) −13.7165 −0.649495
\(447\) 23.9265 + 41.4419i 1.13168 + 1.96013i
\(448\) −22.4745 38.9269i −1.06182 1.83912i
\(449\) −20.0777 + 34.7756i −0.947526 + 1.64116i −0.196913 + 0.980421i \(0.563092\pi\)
−0.750613 + 0.660742i \(0.770242\pi\)
\(450\) 21.1960 36.7126i 0.999189 1.73065i
\(451\) 2.12722 0.100167
\(452\) −16.4373 −0.773145
\(453\) −2.56774 + 4.44746i −0.120643 + 0.208960i
\(454\) 19.0817 33.0504i 0.895548 1.55113i
\(455\) 15.3579 + 26.6006i 0.719989 + 1.24706i
\(456\) 22.8895 + 39.6458i 1.07190 + 1.85658i
\(457\) 20.9761 0.981222 0.490611 0.871379i \(-0.336774\pi\)
0.490611 + 0.871379i \(0.336774\pi\)
\(458\) 2.47128 + 4.28038i 0.115475 + 0.200009i
\(459\) −2.46181 4.26398i −0.114907 0.199025i
\(460\) −33.2962 57.6707i −1.55244 2.68891i
\(461\) 3.26361 5.65274i 0.152002 0.263274i −0.779962 0.625827i \(-0.784761\pi\)
0.931963 + 0.362553i \(0.118095\pi\)
\(462\) −11.7272 −0.545601
\(463\) 6.92572 11.9957i 0.321865 0.557487i −0.659008 0.752136i \(-0.729023\pi\)
0.980873 + 0.194649i \(0.0623568\pi\)
\(464\) −1.76360 3.05465i −0.0818732 0.141809i
\(465\) 53.2932 2.47141
\(466\) 3.57852 + 6.19818i 0.165772 + 0.287125i
\(467\) 1.81086 3.13651i 0.0837968 0.145140i −0.821081 0.570812i \(-0.806629\pi\)
0.904878 + 0.425671i \(0.139962\pi\)
\(468\) 23.3693 40.4768i 1.08025 1.87104i
\(469\) 6.77661 0.312915
\(470\) 32.8545 56.9056i 1.51546 2.62486i
\(471\) 17.8447 0.822242
\(472\) 7.87387 0.362424
\(473\) −1.72313 + 2.81952i −0.0792298 + 0.129642i
\(474\) −30.1615 −1.38536
\(475\) −19.2208 −0.881909
\(476\) −6.11638 + 10.5939i −0.280344 + 0.485570i
\(477\) 26.1466 1.19717
\(478\) −33.9074 + 58.7294i −1.55089 + 2.68622i
\(479\) −8.02385 + 13.8977i −0.366619 + 0.635003i −0.989035 0.147684i \(-0.952818\pi\)
0.622416 + 0.782687i \(0.286151\pi\)
\(480\) −19.4734 33.7290i −0.888836 1.53951i
\(481\) 22.1088 1.00807
\(482\) 17.8166 + 30.8593i 0.811524 + 1.40560i
\(483\) 32.9385 57.0512i 1.49875 2.59592i
\(484\) −36.6006 −1.66366
\(485\) −15.2102 + 26.3448i −0.690659 + 1.19626i
\(486\) 19.0462 + 32.9890i 0.863953 + 1.49641i
\(487\) 0.348282 + 0.603242i 0.0157822 + 0.0273355i 0.873809 0.486270i \(-0.161643\pi\)
−0.858026 + 0.513605i \(0.828310\pi\)
\(488\) 7.46636 + 12.9321i 0.337986 + 0.585409i
\(489\) 58.6507 2.65228
\(490\) −20.3740 35.2888i −0.920403 1.59419i
\(491\) 17.9222 + 31.0422i 0.808819 + 1.40092i 0.913682 + 0.406429i \(0.133226\pi\)
−0.104863 + 0.994487i \(0.533441\pi\)
\(492\) 20.0348 34.7013i 0.903238 1.56445i
\(493\) 2.23638 3.87352i 0.100721 0.174454i
\(494\) −33.6353 −1.51333
\(495\) −7.13561 −0.320722
\(496\) −2.53818 + 4.39625i −0.113968 + 0.197398i
\(497\) −22.8987 + 39.6617i −1.02715 + 1.77907i
\(498\) 36.6443 + 63.4698i 1.64207 + 2.84415i
\(499\) 0.985814 + 1.70748i 0.0441311 + 0.0764373i 0.887247 0.461294i \(-0.152615\pi\)
−0.843116 + 0.537732i \(0.819281\pi\)
\(500\) 11.8889 0.531687
\(501\) −12.9600 22.4474i −0.579011 1.00288i
\(502\) −20.2191 35.0205i −0.902423 1.56304i
\(503\) −5.79508 10.0374i −0.258390 0.447544i 0.707421 0.706792i \(-0.249859\pi\)
−0.965811 + 0.259248i \(0.916525\pi\)
\(504\) −27.9821 + 48.4665i −1.24642 + 2.15887i
\(505\) 39.3316 1.75023
\(506\) −3.85559 + 6.67808i −0.171402 + 0.296877i
\(507\) −6.56623 11.3730i −0.291617 0.505095i
\(508\) 56.0128 2.48516
\(509\) −20.1338 34.8727i −0.892414 1.54571i −0.836973 0.547244i \(-0.815677\pi\)
−0.0554402 0.998462i \(-0.517656\pi\)
\(510\) −9.62457 + 16.6702i −0.426183 + 0.738171i
\(511\) −6.26323 + 10.8482i −0.277069 + 0.479897i
\(512\) 8.86557 0.391807
\(513\) −12.3707 + 21.4267i −0.546181 + 0.946014i
\(514\) −11.1449 −0.491581
\(515\) −42.6156 −1.87787
\(516\) 29.7658 + 54.6644i 1.31036 + 2.40647i
\(517\) −4.79388 −0.210835
\(518\) −64.1311 −2.81776
\(519\) 15.3852 26.6479i 0.675335 1.16971i
\(520\) −27.9564 −1.22597
\(521\) −20.6123 + 35.7015i −0.903041 + 1.56411i −0.0795149 + 0.996834i \(0.525337\pi\)
−0.823526 + 0.567279i \(0.807996\pi\)
\(522\) 24.7856 42.9300i 1.08484 1.87899i
\(523\) 15.2683 + 26.4454i 0.667635 + 1.15638i 0.978564 + 0.205944i \(0.0660265\pi\)
−0.310929 + 0.950433i \(0.600640\pi\)
\(524\) −39.5830 −1.72919
\(525\) −19.1427 33.1562i −0.835457 1.44705i
\(526\) −2.67630 + 4.63550i −0.116692 + 0.202117i
\(527\) −6.43719 −0.280408
\(528\) 0.553733 0.959093i 0.0240981 0.0417392i
\(529\) −10.1585 17.5951i −0.441675 0.765003i
\(530\) −18.9434 32.8110i −0.822850 1.42522i
\(531\) 5.74078 + 9.94332i 0.249129 + 0.431503i
\(532\) 61.4703 2.66508
\(533\) 6.07640 + 10.5246i 0.263198 + 0.455873i
\(534\) 26.8656 + 46.5326i 1.16259 + 2.01366i
\(535\) −17.8674 + 30.9473i −0.772476 + 1.33797i
\(536\) −3.08392 + 5.34150i −0.133205 + 0.230718i
\(537\) 2.65081 0.114391
\(538\) −15.1044 −0.651196
\(539\) −1.48641 + 2.57454i −0.0640242 + 0.110893i
\(540\) −24.9086 + 43.1430i −1.07190 + 1.85658i
\(541\) −19.0950 33.0735i −0.820957 1.42194i −0.904970 0.425475i \(-0.860107\pi\)
0.0840131 0.996465i \(-0.473226\pi\)
\(542\) −12.2489 21.2157i −0.526135 0.911292i
\(543\) 62.5874 2.68588
\(544\) 2.35216 + 4.07406i 0.100848 + 0.174674i
\(545\) 19.0675 + 33.0259i 0.816763 + 1.41468i
\(546\) −33.4988 58.0216i −1.43362 2.48310i
\(547\) −19.3109 + 33.4474i −0.825674 + 1.43011i 0.0757291 + 0.997128i \(0.475872\pi\)
−0.901403 + 0.432981i \(0.857462\pi\)
\(548\) −17.4394 −0.744974
\(549\) −10.8873 + 18.8574i −0.464660 + 0.804815i
\(550\) 2.24074 + 3.88107i 0.0955453 + 0.165489i
\(551\) −22.4759 −0.957504
\(552\) 29.9795 + 51.9260i 1.27601 + 2.21012i
\(553\) −8.35901 + 14.4782i −0.355461 + 0.615677i
\(554\) −31.2663 + 54.1548i −1.32838 + 2.30082i
\(555\) −63.5802 −2.69883
\(556\) −37.7619 + 65.4055i −1.60146 + 2.77381i
\(557\) 23.3874 0.990956 0.495478 0.868621i \(-0.334993\pi\)
0.495478 + 0.868621i \(0.334993\pi\)
\(558\) −71.3430 −3.02019
\(559\) −18.8720 0.471411i −0.798199 0.0199386i
\(560\) 8.41393 0.355553
\(561\) 1.40435 0.0592915
\(562\) −6.91822 + 11.9827i −0.291827 + 0.505460i
\(563\) 1.78677 0.0753032 0.0376516 0.999291i \(-0.488012\pi\)
0.0376516 + 0.999291i \(0.488012\pi\)
\(564\) −45.1501 + 78.2022i −1.90116 + 3.29291i
\(565\) −7.16834 + 12.4159i −0.301574 + 0.522342i
\(566\) −22.0655 38.2186i −0.927483 1.60645i
\(567\) 2.07808 0.0872710
\(568\) −20.8416 36.0987i −0.874494 1.51467i
\(569\) 15.8375 27.4314i 0.663944 1.14998i −0.315627 0.948883i \(-0.602215\pi\)
0.979571 0.201101i \(-0.0644518\pi\)
\(570\) 96.7281 4.05150
\(571\) 1.82524 3.16141i 0.0763838 0.132301i −0.825303 0.564690i \(-0.808996\pi\)
0.901687 + 0.432389i \(0.142329\pi\)
\(572\) 2.47049 + 4.27901i 0.103296 + 0.178914i
\(573\) 27.7977 + 48.1471i 1.16127 + 2.01137i
\(574\) −17.6258 30.5289i −0.735689 1.27425i
\(575\) −25.1744 −1.04984
\(576\) 29.8279 + 51.6634i 1.24283 + 2.15264i
\(577\) −8.86014 15.3462i −0.368852 0.638871i 0.620534 0.784180i \(-0.286916\pi\)
−0.989386 + 0.145308i \(0.953583\pi\)
\(578\) 1.16254 2.01357i 0.0483551 0.0837535i
\(579\) −20.9939 + 36.3626i −0.872479 + 1.51118i
\(580\) −45.2554 −1.87913
\(581\) 40.6226 1.68531
\(582\) 33.1767 57.4636i 1.37522 2.38194i
\(583\) −1.38204 + 2.39377i −0.0572384 + 0.0991397i
\(584\) −5.70057 9.87368i −0.235891 0.408576i
\(585\) −20.3828 35.3041i −0.842726 1.45964i
\(586\) 9.55838 0.394853
\(587\) −9.08044 15.7278i −0.374790 0.649155i 0.615506 0.788132i \(-0.288952\pi\)
−0.990296 + 0.138977i \(0.955618\pi\)
\(588\) 27.9989 + 48.4954i 1.15465 + 1.99992i
\(589\) 16.1736 + 28.0136i 0.666423 + 1.15428i
\(590\) 8.31850 14.4081i 0.342467 0.593170i
\(591\) −60.6101 −2.49316
\(592\) 3.02812 5.24485i 0.124455 0.215562i
\(593\) −8.63919 14.9635i −0.354769 0.614478i 0.632309 0.774716i \(-0.282107\pi\)
−0.987078 + 0.160238i \(0.948774\pi\)
\(594\) 5.76867 0.236691
\(595\) 5.33474 + 9.24003i 0.218703 + 0.378804i
\(596\) −29.2414 + 50.6476i −1.19778 + 2.07461i
\(597\) 24.8434 43.0301i 1.01677 1.76110i
\(598\) −44.0539 −1.80150
\(599\) −0.129072 + 0.223559i −0.00527373 + 0.00913437i −0.868650 0.495426i \(-0.835012\pi\)
0.863376 + 0.504560i \(0.168345\pi\)
\(600\) 34.8461 1.42258
\(601\) −16.1648 −0.659375 −0.329687 0.944090i \(-0.606943\pi\)
−0.329687 + 0.944090i \(0.606943\pi\)
\(602\) 54.7420 + 1.36742i 2.23112 + 0.0557320i
\(603\) −8.99384 −0.366257
\(604\) −6.27627 −0.255378
\(605\) −15.9616 + 27.6463i −0.648932 + 1.12398i
\(606\) −85.7905 −3.48500
\(607\) −11.6809 + 20.2319i −0.474112 + 0.821186i −0.999561 0.0296392i \(-0.990564\pi\)
0.525449 + 0.850825i \(0.323897\pi\)
\(608\) 11.8197 20.4724i 0.479354 0.830266i
\(609\) −22.3846 38.7713i −0.907070 1.57109i
\(610\) 31.5519 1.27750
\(611\) −13.6937 23.7181i −0.553987 0.959533i
\(612\) 8.11759 14.0601i 0.328134 0.568345i
\(613\) −21.3899 −0.863931 −0.431965 0.901890i \(-0.642180\pi\)
−0.431965 + 0.901890i \(0.642180\pi\)
\(614\) −16.8055 + 29.1080i −0.678215 + 1.17470i
\(615\) −17.4744 30.2666i −0.704638 1.22047i
\(616\) −2.95813 5.12364i −0.119187 0.206437i
\(617\) −11.0481 19.1358i −0.444779 0.770380i 0.553258 0.833010i \(-0.313385\pi\)
−0.998037 + 0.0626300i \(0.980051\pi\)
\(618\) 92.9537 3.73915
\(619\) −9.14363 15.8372i −0.367513 0.636552i 0.621663 0.783285i \(-0.286457\pi\)
−0.989176 + 0.146733i \(0.953124\pi\)
\(620\) 32.5658 + 56.4056i 1.30787 + 2.26530i
\(621\) −16.2026 + 28.0637i −0.650186 + 1.12616i
\(622\) −12.5680 + 21.7684i −0.503930 + 0.872832i
\(623\) 29.7823 1.19320
\(624\) 6.32693 0.253280
\(625\) 14.7472 25.5429i 0.589889 1.02172i
\(626\) −31.3523 + 54.3038i −1.25309 + 2.17042i
\(627\) −3.52846 6.11147i −0.140913 0.244069i
\(628\) 10.9044 + 18.8869i 0.435131 + 0.753669i
\(629\) 7.67974 0.306211
\(630\) 59.1245 + 102.407i 2.35558 + 4.07998i
\(631\) −10.5426 18.2603i −0.419693 0.726930i 0.576215 0.817298i \(-0.304529\pi\)
−0.995908 + 0.0903679i \(0.971196\pi\)
\(632\) −7.60807 13.1776i −0.302633 0.524176i
\(633\) −18.9636 + 32.8459i −0.753736 + 1.30551i
\(634\) 44.6940 1.77503
\(635\) 24.4273 42.3093i 0.969368 1.67899i
\(636\) 26.0329 + 45.0903i 1.03227 + 1.78795i
\(637\) −16.9837 −0.672918
\(638\) 2.62021 + 4.53834i 0.103735 + 0.179675i
\(639\) 30.3909 52.6386i 1.20225 2.08235i
\(640\) 29.2461 50.6557i 1.15605 2.00234i
\(641\) 34.1434 1.34858 0.674291 0.738466i \(-0.264449\pi\)
0.674291 + 0.738466i \(0.264449\pi\)
\(642\) 38.9726 67.5025i 1.53813 2.66411i
\(643\) 28.8469 1.13761 0.568804 0.822473i \(-0.307406\pi\)
0.568804 + 0.822473i \(0.307406\pi\)
\(644\) 80.5107 3.17257
\(645\) 54.2718 + 1.35568i 2.13695 + 0.0533798i
\(646\) −11.6836 −0.459686
\(647\) 18.7741 0.738084 0.369042 0.929413i \(-0.379686\pi\)
0.369042 + 0.929413i \(0.379686\pi\)
\(648\) −0.945696 + 1.63799i −0.0371505 + 0.0643465i
\(649\) −1.21377 −0.0476448
\(650\) −12.8013 + 22.1725i −0.502108 + 0.869676i
\(651\) −32.2159 + 55.7997i −1.26264 + 2.18696i
\(652\) 35.8396 + 62.0760i 1.40359 + 2.43108i
\(653\) −43.6976 −1.71002 −0.855010 0.518612i \(-0.826449\pi\)
−0.855010 + 0.518612i \(0.826449\pi\)
\(654\) −41.5903 72.0365i −1.62631 2.81685i
\(655\) −17.2622 + 29.8991i −0.674491 + 1.16825i
\(656\) 3.32900 0.129976
\(657\) 8.31249 14.3977i 0.324301 0.561706i
\(658\) 39.7213 + 68.7993i 1.54850 + 2.68208i
\(659\) 9.68199 + 16.7697i 0.377157 + 0.653255i 0.990647 0.136447i \(-0.0435684\pi\)
−0.613490 + 0.789702i \(0.710235\pi\)
\(660\) −7.10459 12.3055i −0.276546 0.478992i
\(661\) −6.86779 −0.267126 −0.133563 0.991040i \(-0.542642\pi\)
−0.133563 + 0.991040i \(0.542642\pi\)
\(662\) −37.1662 64.3737i −1.44450 2.50195i
\(663\) 4.01150 + 6.94813i 0.155794 + 0.269843i
\(664\) −18.4867 + 32.0198i −0.717421 + 1.24261i
\(665\) 26.8074 46.4317i 1.03955 1.80054i
\(666\) 85.1141 3.29810
\(667\) −29.4377 −1.13983
\(668\) 15.8389 27.4338i 0.612826 1.06144i
\(669\) 8.22045 14.2382i 0.317821 0.550482i
\(670\) 6.51612 + 11.2863i 0.251740 + 0.436026i
\(671\) −1.15095 1.99351i −0.0444321 0.0769587i
\(672\) 47.0871 1.81642
\(673\) −16.0618 27.8199i −0.619138 1.07238i −0.989643 0.143548i \(-0.954149\pi\)
0.370505 0.928830i \(-0.379184\pi\)
\(674\) −31.7363 54.9688i −1.22243 2.11732i
\(675\) 9.41636 + 16.3096i 0.362436 + 0.627758i
\(676\) 8.02483 13.8994i 0.308647 0.534593i
\(677\) −4.98440 −0.191566 −0.0957831 0.995402i \(-0.530536\pi\)
−0.0957831 + 0.995402i \(0.530536\pi\)
\(678\) 15.6357 27.0818i 0.600484 1.04007i
\(679\) −18.3892 31.8511i −0.705714 1.22233i
\(680\) −9.71098 −0.372399
\(681\) 22.8717 + 39.6150i 0.876447 + 1.51805i
\(682\) 3.77101 6.53158i 0.144399 0.250107i
\(683\) −24.4049 + 42.2705i −0.933827 + 1.61743i −0.157113 + 0.987581i \(0.550219\pi\)
−0.776713 + 0.629854i \(0.783115\pi\)
\(684\) −81.5828 −3.11940
\(685\) −7.60537 + 13.1729i −0.290586 + 0.503310i
\(686\) −9.19014 −0.350881
\(687\) −5.92426 −0.226025
\(688\) −2.69662 + 4.41242i −0.102808 + 0.168222i
\(689\) −15.7912 −0.601596
\(690\) 126.690 4.82299
\(691\) 3.93880 6.82220i 0.149839 0.259529i −0.781329 0.624120i \(-0.785458\pi\)
0.931168 + 0.364591i \(0.118791\pi\)
\(692\) 37.6056 1.42955
\(693\) 4.31351 7.47121i 0.163857 0.283808i
\(694\) 5.24118 9.07799i 0.198952 0.344596i
\(695\) 32.9361 + 57.0470i 1.24934 + 2.16392i
\(696\) 40.7474 1.54453
\(697\) 2.11071 + 3.65585i 0.0799487 + 0.138475i
\(698\) −2.09793 + 3.63371i −0.0794076 + 0.137538i
\(699\) −8.57860 −0.324472
\(700\) 23.3950 40.5214i 0.884249 1.53156i
\(701\) −1.09638 1.89899i −0.0414097 0.0717237i 0.844578 0.535433i \(-0.179852\pi\)
−0.885987 + 0.463709i \(0.846518\pi\)
\(702\) 16.4782 + 28.5410i 0.621928 + 1.07721i
\(703\) −19.2956 33.4209i −0.727747 1.26049i
\(704\) −6.30651 −0.237685
\(705\) 39.3801 + 68.2084i 1.48314 + 2.56888i
\(706\) 36.8969 + 63.9074i 1.38863 + 2.40519i
\(707\) −23.7761 + 41.1814i −0.894192 + 1.54879i
\(708\) −11.4316 + 19.8002i −0.429628 + 0.744137i
\(709\) 13.0818 0.491298 0.245649 0.969359i \(-0.420999\pi\)
0.245649 + 0.969359i \(0.420999\pi\)
\(710\) −88.0740 −3.30536
\(711\) 11.0940 19.2153i 0.416057 0.720632i
\(712\) −13.5534 + 23.4752i −0.507935 + 0.879770i
\(713\) 21.1834 + 36.6907i 0.793325 + 1.37408i
\(714\) −11.6362 20.1545i −0.435473 0.754262i
\(715\) 4.30954 0.161168
\(716\) 1.61983 + 2.80562i 0.0605357 + 0.104851i
\(717\) −40.6422 70.3944i −1.51781 2.62893i
\(718\) −36.1814 62.6680i −1.35028 2.33875i
\(719\) 6.34936 10.9974i 0.236791 0.410134i −0.723000 0.690848i \(-0.757238\pi\)
0.959792 + 0.280713i \(0.0905709\pi\)
\(720\) −11.1669 −0.416165
\(721\) 25.7613 44.6199i 0.959402 1.66173i
\(722\) 7.26728 + 12.5873i 0.270460 + 0.468451i
\(723\) −42.7108 −1.58843
\(724\) 38.2452 + 66.2426i 1.42137 + 2.46189i
\(725\) −8.55409 + 14.8161i −0.317691 + 0.550257i
\(726\) 34.8156 60.3025i 1.29213 2.23803i
\(727\) −14.5455 −0.539464 −0.269732 0.962935i \(-0.586935\pi\)
−0.269732 + 0.962935i \(0.586935\pi\)
\(728\) 16.8998 29.2713i 0.626347 1.08486i
\(729\) −43.9226 −1.62676
\(730\) −24.0899 −0.891607
\(731\) −6.55539 0.163750i −0.242460 0.00605651i
\(732\) −43.3600 −1.60263
\(733\) 30.1939 1.11524 0.557619 0.830097i \(-0.311715\pi\)
0.557619 + 0.830097i \(0.311715\pi\)
\(734\) −30.0509 + 52.0496i −1.10920 + 1.92119i
\(735\) 48.8415 1.80154
\(736\) 15.4809 26.8137i 0.570634 0.988367i
\(737\) 0.475392 0.823403i 0.0175113 0.0303304i
\(738\) 23.3928 + 40.5176i 0.861102 + 1.49147i
\(739\) −4.33258 −0.159376 −0.0796882 0.996820i \(-0.525392\pi\)
−0.0796882 + 0.996820i \(0.525392\pi\)
\(740\) −38.8519 67.2934i −1.42822 2.47375i
\(741\) 20.1580 34.9148i 0.740524 1.28263i
\(742\) 45.8055 1.68157
\(743\) −2.05226 + 3.55461i −0.0752900 + 0.130406i −0.901212 0.433378i \(-0.857322\pi\)
0.825922 + 0.563784i \(0.190655\pi\)
\(744\) −29.3218 50.7869i −1.07499 1.86194i
\(745\) 25.5045 + 44.1751i 0.934413 + 1.61845i
\(746\) −27.2437 47.1874i −0.997461 1.72765i
\(747\) −53.9139 −1.97261
\(748\) 0.858151 + 1.48636i 0.0313771 + 0.0543468i
\(749\) −21.6018 37.4155i −0.789314 1.36713i
\(750\) −11.3091 + 19.5879i −0.412949 + 0.715249i
\(751\) 6.04133 10.4639i 0.220451 0.381833i −0.734494 0.678616i \(-0.762580\pi\)
0.954945 + 0.296782i \(0.0959136\pi\)
\(752\) −7.50218 −0.273576
\(753\) 48.4701 1.76635
\(754\) −14.9692 + 25.9275i −0.545147 + 0.944223i
\(755\) −2.73710 + 4.74079i −0.0996131 + 0.172535i
\(756\) −30.1147 52.1602i −1.09526 1.89705i
\(757\) −4.87313 8.44051i −0.177117 0.306775i 0.763775 0.645483i \(-0.223344\pi\)
−0.940892 + 0.338707i \(0.890010\pi\)
\(758\) −34.9225 −1.26844
\(759\) −4.62140 8.00450i −0.167746 0.290545i
\(760\) 24.3991 + 42.2605i 0.885049 + 1.53295i
\(761\) −9.68749 16.7792i −0.351171 0.608246i 0.635284 0.772279i \(-0.280883\pi\)
−0.986455 + 0.164032i \(0.947550\pi\)
\(762\) −53.2811 + 92.2856i −1.93017 + 3.34315i
\(763\) −46.1056 −1.66913
\(764\) −33.9726 + 58.8423i −1.22909 + 2.12884i
\(765\) −7.08020 12.2633i −0.255985 0.443380i
\(766\) 31.3128 1.13138
\(767\) −3.46713 6.00525i −0.125191 0.216837i
\(768\) −28.9139 + 50.0803i −1.04334 +