Properties

Label 750.2.l.b.107.3
Level $750$
Weight $2$
Character 750.107
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 107.3
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.b.743.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.891007 - 0.453990i) q^{2} +(-0.368756 - 1.69234i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.439743 + 1.67530i) q^{6} +(2.72680 + 2.72680i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.72804 + 1.24812i) q^{9} +O(q^{10})\) \(q+(-0.891007 - 0.453990i) q^{2} +(-0.368756 - 1.69234i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-0.439743 + 1.67530i) q^{6} +(2.72680 + 2.72680i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-2.72804 + 1.24812i) q^{9} +(-0.335657 + 0.109061i) q^{11} +(1.15238 - 1.29306i) q^{12} +(1.12512 + 2.20817i) q^{13} +(-1.19166 - 3.66754i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-3.49819 + 0.554059i) q^{17} +(2.99734 + 0.126420i) q^{18} +(-3.84926 + 5.29805i) q^{19} +(3.60915 - 5.62020i) q^{21} +(0.348585 + 0.0552105i) q^{22} +(-3.55825 + 6.98347i) q^{23} +(-1.61382 + 0.628956i) q^{24} -2.47829i q^{26} +(3.11823 + 4.15652i) q^{27} +(-0.603255 + 3.80880i) q^{28} +(-5.05137 + 3.67003i) q^{29} +(-3.39184 - 2.46432i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.308344 + 0.527829i) q^{33} +(3.36845 + 1.09448i) q^{34} +(-2.61325 - 1.47340i) q^{36} +(-4.33521 + 2.20890i) q^{37} +(5.83498 - 2.97307i) q^{38} +(3.32209 - 2.71836i) q^{39} +(8.06531 + 2.62058i) q^{41} +(-5.76730 + 3.36911i) q^{42} +(5.16349 - 5.16349i) q^{43} +(-0.285527 - 0.207447i) q^{44} +(6.34085 - 4.60690i) q^{46} +(0.668895 - 4.22323i) q^{47} +(1.72346 + 0.172255i) q^{48} +7.87088i q^{49} +(2.22763 + 5.71582i) q^{51} +(-1.12512 + 2.20817i) q^{52} +(4.34698 + 0.688494i) q^{53} +(-0.891339 - 5.11913i) q^{54} +(2.26666 - 3.11979i) q^{56} +(10.3855 + 4.56057i) q^{57} +(6.16696 - 0.976751i) q^{58} +(0.713107 - 2.19472i) q^{59} +(0.0451729 + 0.139028i) q^{61} +(1.90338 + 3.73559i) q^{62} +(-10.8422 - 4.03544i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-0.0351078 - 0.610284i) q^{66} +(-1.18445 - 7.47829i) q^{67} +(-2.50443 - 2.50443i) q^{68} +(13.1305 + 3.44659i) q^{69} +(3.62303 + 4.98667i) q^{71} +(1.65951 + 2.49920i) q^{72} +(9.30362 + 4.74043i) q^{73} +4.86552 q^{74} -6.54875 q^{76} +(-1.21266 - 0.617880i) q^{77} +(-4.19411 + 0.913883i) q^{78} +(0.803169 + 1.10547i) q^{79} +(5.88439 - 6.80984i) q^{81} +(-5.99652 - 5.99652i) q^{82} +(-0.915181 - 5.77823i) q^{83} +(6.66824 - 0.383604i) q^{84} +(-6.94488 + 2.25653i) q^{86} +(8.07367 + 7.19529i) q^{87} +(0.160227 + 0.314463i) q^{88} +(0.633239 + 1.94891i) q^{89} +(-2.95327 + 9.08922i) q^{91} +(-7.74123 + 1.22609i) q^{92} +(-2.91971 + 6.64888i) q^{93} +(-2.51330 + 3.45926i) q^{94} +(-1.45742 - 0.935916i) q^{96} +(-6.93926 - 1.09907i) q^{97} +(3.57330 - 7.01300i) q^{98} +(0.779562 - 0.716464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{3} - 4q^{7} + O(q^{10}) \) \( 80q - 4q^{3} - 4q^{7} + 4q^{12} + 20q^{16} + 8q^{18} - 40q^{19} + 36q^{22} - 4q^{27} + 16q^{28} - 4q^{33} - 40q^{34} + 24q^{37} - 40q^{39} + 4q^{42} + 24q^{43} + 4q^{48} + 64q^{57} - 20q^{58} - 64q^{63} - 96q^{67} + 140q^{69} - 8q^{72} - 100q^{73} - 100q^{78} + 80q^{79} - 40q^{81} - 96q^{82} + 60q^{84} - 80q^{87} - 4q^{88} - 12q^{93} + 32q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.891007 0.453990i −0.630037 0.321020i
\(3\) −0.368756 1.69234i −0.212901 0.977074i
\(4\) 0.587785 + 0.809017i 0.293893 + 0.404508i
\(5\) 0 0
\(6\) −0.439743 + 1.67530i −0.179524 + 0.683938i
\(7\) 2.72680 + 2.72680i 1.03063 + 1.03063i 0.999516 + 0.0311178i \(0.00990669\pi\)
0.0311178 + 0.999516i \(0.490093\pi\)
\(8\) −0.156434 0.987688i −0.0553079 0.349201i
\(9\) −2.72804 + 1.24812i −0.909346 + 0.416040i
\(10\) 0 0
\(11\) −0.335657 + 0.109061i −0.101204 + 0.0328833i −0.359181 0.933268i \(-0.616944\pi\)
0.257977 + 0.966151i \(0.416944\pi\)
\(12\) 1.15238 1.29306i 0.332665 0.373275i
\(13\) 1.12512 + 2.20817i 0.312052 + 0.612437i 0.992760 0.120119i \(-0.0383275\pi\)
−0.680707 + 0.732555i \(0.738327\pi\)
\(14\) −1.19166 3.66754i −0.318483 0.980191i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) −3.49819 + 0.554059i −0.848436 + 0.134379i −0.565488 0.824756i \(-0.691312\pi\)
−0.282948 + 0.959135i \(0.591312\pi\)
\(18\) 2.99734 + 0.126420i 0.706479 + 0.0297975i
\(19\) −3.84926 + 5.29805i −0.883080 + 1.21546i 0.0924780 + 0.995715i \(0.470521\pi\)
−0.975558 + 0.219741i \(0.929479\pi\)
\(20\) 0 0
\(21\) 3.60915 5.62020i 0.787582 1.22643i
\(22\) 0.348585 + 0.0552105i 0.0743186 + 0.0117709i
\(23\) −3.55825 + 6.98347i −0.741947 + 1.45615i 0.142638 + 0.989775i \(0.454441\pi\)
−0.884585 + 0.466378i \(0.845559\pi\)
\(24\) −1.61382 + 0.628956i −0.329420 + 0.128385i
\(25\) 0 0
\(26\) 2.47829i 0.486033i
\(27\) 3.11823 + 4.15652i 0.600103 + 0.799923i
\(28\) −0.603255 + 3.80880i −0.114004 + 0.719796i
\(29\) −5.05137 + 3.67003i −0.938015 + 0.681508i −0.947942 0.318443i \(-0.896840\pi\)
0.00992666 + 0.999951i \(0.496840\pi\)
\(30\) 0 0
\(31\) −3.39184 2.46432i −0.609193 0.442604i 0.239937 0.970788i \(-0.422873\pi\)
−0.849130 + 0.528184i \(0.822873\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0.308344 + 0.527829i 0.0536759 + 0.0918832i
\(34\) 3.36845 + 1.09448i 0.577684 + 0.187701i
\(35\) 0 0
\(36\) −2.61325 1.47340i −0.435542 0.245567i
\(37\) −4.33521 + 2.20890i −0.712704 + 0.363141i −0.772452 0.635073i \(-0.780970\pi\)
0.0597483 + 0.998213i \(0.480970\pi\)
\(38\) 5.83498 2.97307i 0.946558 0.482296i
\(39\) 3.32209 2.71836i 0.531960 0.435286i
\(40\) 0 0
\(41\) 8.06531 + 2.62058i 1.25959 + 0.409265i 0.861348 0.508015i \(-0.169621\pi\)
0.398241 + 0.917281i \(0.369621\pi\)
\(42\) −5.76730 + 3.36911i −0.889913 + 0.519865i
\(43\) 5.16349 5.16349i 0.787425 0.787425i −0.193647 0.981071i \(-0.562031\pi\)
0.981071 + 0.193647i \(0.0620315\pi\)
\(44\) −0.285527 0.207447i −0.0430448 0.0312738i
\(45\) 0 0
\(46\) 6.34085 4.60690i 0.934908 0.679250i
\(47\) 0.668895 4.22323i 0.0975683 0.616022i −0.889649 0.456644i \(-0.849051\pi\)
0.987218 0.159378i \(-0.0509488\pi\)
\(48\) 1.72346 + 0.172255i 0.248761 + 0.0248628i
\(49\) 7.87088i 1.12441i
\(50\) 0 0
\(51\) 2.22763 + 5.71582i 0.311931 + 0.800375i
\(52\) −1.12512 + 2.20817i −0.156026 + 0.306218i
\(53\) 4.34698 + 0.688494i 0.597103 + 0.0945719i 0.447668 0.894200i \(-0.352255\pi\)
0.149435 + 0.988772i \(0.452255\pi\)
\(54\) −0.891339 5.11913i −0.121296 0.696626i
\(55\) 0 0
\(56\) 2.26666 3.11979i 0.302896 0.416900i
\(57\) 10.3855 + 4.56057i 1.37560 + 0.604063i
\(58\) 6.16696 0.976751i 0.809762 0.128254i
\(59\) 0.713107 2.19472i 0.0928386 0.285728i −0.893846 0.448375i \(-0.852003\pi\)
0.986684 + 0.162647i \(0.0520031\pi\)
\(60\) 0 0
\(61\) 0.0451729 + 0.139028i 0.00578380 + 0.0178007i 0.953907 0.300103i \(-0.0970211\pi\)
−0.948123 + 0.317904i \(0.897021\pi\)
\(62\) 1.90338 + 3.73559i 0.241729 + 0.474420i
\(63\) −10.8422 4.03544i −1.36599 0.508418i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) −0.0351078 0.610284i −0.00432147 0.0751208i
\(67\) −1.18445 7.47829i −0.144703 0.913619i −0.948053 0.318112i \(-0.896951\pi\)
0.803350 0.595507i \(-0.203049\pi\)
\(68\) −2.50443 2.50443i −0.303707 0.303707i
\(69\) 13.1305 + 3.44659i 1.58073 + 0.414920i
\(70\) 0 0
\(71\) 3.62303 + 4.98667i 0.429974 + 0.591809i 0.967947 0.251153i \(-0.0808098\pi\)
−0.537973 + 0.842962i \(0.680810\pi\)
\(72\) 1.65951 + 2.49920i 0.195576 + 0.294534i
\(73\) 9.30362 + 4.74043i 1.08891 + 0.554825i 0.903827 0.427898i \(-0.140746\pi\)
0.185079 + 0.982724i \(0.440746\pi\)
\(74\) 4.86552 0.565605
\(75\) 0 0
\(76\) −6.54875 −0.751193
\(77\) −1.21266 0.617880i −0.138195 0.0704139i
\(78\) −4.19411 + 0.913883i −0.474890 + 0.103477i
\(79\) 0.803169 + 1.10547i 0.0903636 + 0.124375i 0.851805 0.523859i \(-0.175508\pi\)
−0.761442 + 0.648234i \(0.775508\pi\)
\(80\) 0 0
\(81\) 5.88439 6.80984i 0.653821 0.756649i
\(82\) −5.99652 5.99652i −0.662205 0.662205i
\(83\) −0.915181 5.77823i −0.100454 0.634243i −0.985621 0.168969i \(-0.945956\pi\)
0.885167 0.465273i \(-0.154044\pi\)
\(84\) 6.66824 0.383604i 0.727565 0.0418546i
\(85\) 0 0
\(86\) −6.94488 + 2.25653i −0.748886 + 0.243328i
\(87\) 8.07367 + 7.19529i 0.865588 + 0.771416i
\(88\) 0.160227 + 0.314463i 0.0170803 + 0.0335219i
\(89\) 0.633239 + 1.94891i 0.0671232 + 0.206584i 0.978992 0.203897i \(-0.0653608\pi\)
−0.911869 + 0.410481i \(0.865361\pi\)
\(90\) 0 0
\(91\) −2.95327 + 9.08922i −0.309587 + 0.952809i
\(92\) −7.74123 + 1.22609i −0.807079 + 0.127829i
\(93\) −2.91971 + 6.64888i −0.302759 + 0.689457i
\(94\) −2.51330 + 3.45926i −0.259227 + 0.356795i
\(95\) 0 0
\(96\) −1.45742 0.935916i −0.148747 0.0955216i
\(97\) −6.93926 1.09907i −0.704575 0.111594i −0.206142 0.978522i \(-0.566091\pi\)
−0.498433 + 0.866928i \(0.666091\pi\)
\(98\) 3.57330 7.01300i 0.360958 0.708420i
\(99\) 0.779562 0.716464i 0.0783490 0.0720073i
\(100\) 0 0
\(101\) 9.58679i 0.953921i 0.878925 + 0.476961i \(0.158262\pi\)
−0.878925 + 0.476961i \(0.841738\pi\)
\(102\) 0.610091 6.10416i 0.0604081 0.604402i
\(103\) −1.04075 + 6.57102i −0.102548 + 0.647462i 0.881853 + 0.471524i \(0.156296\pi\)
−0.984401 + 0.175938i \(0.943704\pi\)
\(104\) 2.00498 1.45670i 0.196604 0.142841i
\(105\) 0 0
\(106\) −3.56062 2.58694i −0.345838 0.251266i
\(107\) 10.4337 10.4337i 1.00866 1.00866i 0.00870186 0.999962i \(-0.497230\pi\)
0.999962 0.00870186i \(-0.00276992\pi\)
\(108\) −1.52985 + 4.96584i −0.147210 + 0.477838i
\(109\) −10.5722 3.43511i −1.01263 0.329024i −0.244729 0.969592i \(-0.578699\pi\)
−0.767902 + 0.640568i \(0.778699\pi\)
\(110\) 0 0
\(111\) 5.33685 + 6.52211i 0.506551 + 0.619051i
\(112\) −3.43597 + 1.75071i −0.324668 + 0.165427i
\(113\) 1.56816 0.799015i 0.147520 0.0751650i −0.378672 0.925531i \(-0.623619\pi\)
0.526192 + 0.850366i \(0.323619\pi\)
\(114\) −7.18313 8.77844i −0.672762 0.822176i
\(115\) 0 0
\(116\) −5.93824 1.92945i −0.551352 0.179145i
\(117\) −5.82544 4.61969i −0.538562 0.427091i
\(118\) −1.63176 + 1.63176i −0.150216 + 0.150216i
\(119\) −11.0497 8.02806i −1.01292 0.735931i
\(120\) 0 0
\(121\) −8.79842 + 6.39242i −0.799856 + 0.581129i
\(122\) 0.0228680 0.144383i 0.00207037 0.0130718i
\(123\) 1.46078 14.6156i 0.131714 1.31784i
\(124\) 4.19255i 0.376502i
\(125\) 0 0
\(126\) 7.82841 + 8.51786i 0.697410 + 0.758831i
\(127\) −2.44874 + 4.80592i −0.217290 + 0.426457i −0.973762 0.227571i \(-0.926922\pi\)
0.756471 + 0.654027i \(0.226922\pi\)
\(128\) 0.987688 + 0.156434i 0.0873001 + 0.0138270i
\(129\) −10.6425 6.83432i −0.937016 0.601728i
\(130\) 0 0
\(131\) 10.2354 14.0878i 0.894273 1.23086i −0.0779865 0.996954i \(-0.524849\pi\)
0.972259 0.233906i \(-0.0751509\pi\)
\(132\) −0.245782 + 0.559706i −0.0213926 + 0.0487161i
\(133\) −24.9429 + 3.95056i −2.16282 + 0.342557i
\(134\) −2.33973 + 7.20094i −0.202122 + 0.622066i
\(135\) 0 0
\(136\) 1.09448 + 3.36845i 0.0938505 + 0.288842i
\(137\) 8.13848 + 15.9727i 0.695317 + 1.36464i 0.920663 + 0.390358i \(0.127649\pi\)
−0.225346 + 0.974279i \(0.572351\pi\)
\(138\) −10.1347 9.03207i −0.862721 0.768861i
\(139\) 17.1405 5.56927i 1.45383 0.472379i 0.527654 0.849459i \(-0.323072\pi\)
0.926181 + 0.377080i \(0.123072\pi\)
\(140\) 0 0
\(141\) −7.39381 + 0.425343i −0.622671 + 0.0358204i
\(142\) −0.964240 6.08797i −0.0809172 0.510891i
\(143\) −0.618480 0.618480i −0.0517199 0.0517199i
\(144\) −0.344023 2.98021i −0.0286686 0.248351i
\(145\) 0 0
\(146\) −6.13747 8.44751i −0.507941 0.699121i
\(147\) 13.3202 2.90243i 1.09863 0.239388i
\(148\) −4.33521 2.20890i −0.356352 0.181570i
\(149\) 4.64891 0.380854 0.190427 0.981701i \(-0.439013\pi\)
0.190427 + 0.981701i \(0.439013\pi\)
\(150\) 0 0
\(151\) −14.6548 −1.19259 −0.596295 0.802765i \(-0.703361\pi\)
−0.596295 + 0.802765i \(0.703361\pi\)
\(152\) 5.83498 + 2.97307i 0.473279 + 0.241148i
\(153\) 8.85167 5.87766i 0.715615 0.475181i
\(154\) 0.799974 + 1.10107i 0.0644637 + 0.0887267i
\(155\) 0 0
\(156\) 4.15188 + 1.08981i 0.332416 + 0.0872547i
\(157\) −3.17235 3.17235i −0.253181 0.253181i 0.569093 0.822273i \(-0.307295\pi\)
−0.822273 + 0.569093i \(0.807295\pi\)
\(158\) −0.213757 1.34961i −0.0170056 0.107369i
\(159\) −0.437806 7.61046i −0.0347203 0.603548i
\(160\) 0 0
\(161\) −28.7452 + 9.33987i −2.26544 + 0.736085i
\(162\) −8.33463 + 3.39616i −0.654831 + 0.266827i
\(163\) 4.91227 + 9.64088i 0.384759 + 0.755132i 0.999434 0.0336487i \(-0.0107127\pi\)
−0.614675 + 0.788781i \(0.710713\pi\)
\(164\) 2.62058 + 8.06531i 0.204633 + 0.629795i
\(165\) 0 0
\(166\) −1.80783 + 5.56392i −0.140315 + 0.431844i
\(167\) −16.5871 + 2.62714i −1.28355 + 0.203295i −0.760686 0.649120i \(-0.775137\pi\)
−0.522866 + 0.852415i \(0.675137\pi\)
\(168\) −6.11560 2.68553i −0.471829 0.207193i
\(169\) 4.03108 5.54830i 0.310083 0.426793i
\(170\) 0 0
\(171\) 3.88832 19.2576i 0.297347 1.47267i
\(172\) 7.21237 + 1.14233i 0.549938 + 0.0871017i
\(173\) −7.90821 + 15.5207i −0.601250 + 1.18002i 0.367043 + 0.930204i \(0.380370\pi\)
−0.968293 + 0.249816i \(0.919630\pi\)
\(174\) −3.92710 10.0764i −0.297713 0.763892i
\(175\) 0 0
\(176\) 0.352930i 0.0266031i
\(177\) −3.97717 0.397506i −0.298943 0.0298784i
\(178\) 0.320566 2.02397i 0.0240274 0.151703i
\(179\) 5.94519 4.31943i 0.444364 0.322849i −0.343002 0.939334i \(-0.611444\pi\)
0.787367 + 0.616485i \(0.211444\pi\)
\(180\) 0 0
\(181\) −0.543117 0.394597i −0.0403695 0.0293302i 0.567418 0.823430i \(-0.307943\pi\)
−0.607787 + 0.794100i \(0.707943\pi\)
\(182\) 6.75780 6.75780i 0.500922 0.500922i
\(183\) 0.218625 0.127715i 0.0161612 0.00944098i
\(184\) 7.45412 + 2.42199i 0.549525 + 0.178552i
\(185\) 0 0
\(186\) 5.62001 4.59868i 0.412079 0.337192i
\(187\) 1.11376 0.567491i 0.0814465 0.0414991i
\(188\) 3.80983 1.94121i 0.277861 0.141577i
\(189\) −2.83122 + 19.8368i −0.205941 + 1.44291i
\(190\) 0 0
\(191\) 13.4008 + 4.35419i 0.969650 + 0.315058i 0.750675 0.660672i \(-0.229729\pi\)
0.218975 + 0.975730i \(0.429729\pi\)
\(192\) 0.873670 + 1.49556i 0.0630517 + 0.107933i
\(193\) 2.89340 2.89340i 0.208271 0.208271i −0.595261 0.803532i \(-0.702951\pi\)
0.803532 + 0.595261i \(0.202951\pi\)
\(194\) 5.68396 + 4.12964i 0.408085 + 0.296491i
\(195\) 0 0
\(196\) −6.36767 + 4.62638i −0.454834 + 0.330456i
\(197\) 3.55739 22.4605i 0.253454 1.60024i −0.452353 0.891839i \(-0.649415\pi\)
0.705806 0.708405i \(-0.250585\pi\)
\(198\) −1.01986 + 0.284460i −0.0724785 + 0.0202157i
\(199\) 6.31867i 0.447919i −0.974598 0.223959i \(-0.928102\pi\)
0.974598 0.223959i \(-0.0718983\pi\)
\(200\) 0 0
\(201\) −12.2191 + 4.76215i −0.861866 + 0.335896i
\(202\) 4.35231 8.54189i 0.306228 0.601006i
\(203\) −23.7815 3.76662i −1.66914 0.264365i
\(204\) −3.31483 + 5.16187i −0.232084 + 0.361403i
\(205\) 0 0
\(206\) 3.91049 5.38233i 0.272457 0.375005i
\(207\) 0.990845 23.4923i 0.0688685 1.63283i
\(208\) −2.44778 + 0.387690i −0.169723 + 0.0268815i
\(209\) 0.714216 2.19813i 0.0494033 0.152048i
\(210\) 0 0
\(211\) −1.28435 3.95283i −0.0884185 0.272124i 0.897064 0.441900i \(-0.145696\pi\)
−0.985483 + 0.169776i \(0.945696\pi\)
\(212\) 1.99809 + 3.92147i 0.137229 + 0.269327i
\(213\) 7.10313 7.97026i 0.486699 0.546113i
\(214\) −14.0333 + 4.55969i −0.959296 + 0.311694i
\(215\) 0 0
\(216\) 3.61755 3.73006i 0.246143 0.253798i
\(217\) −2.52917 15.9686i −0.171691 1.08402i
\(218\) 7.86037 + 7.86037i 0.532371 + 0.532371i
\(219\) 4.59166 17.4930i 0.310276 1.18206i
\(220\) 0 0
\(221\) −5.15934 7.10123i −0.347055 0.477680i
\(222\) −1.79419 8.23412i −0.120418 0.552638i
\(223\) −13.6942 6.97753i −0.917030 0.467250i −0.0692509 0.997599i \(-0.522061\pi\)
−0.847779 + 0.530349i \(0.822061\pi\)
\(224\) 3.85628 0.257658
\(225\) 0 0
\(226\) −1.75998 −0.117072
\(227\) −12.4969 6.36747i −0.829445 0.422624i −0.0129084 0.999917i \(-0.504109\pi\)
−0.816537 + 0.577293i \(0.804109\pi\)
\(228\) 2.41489 + 11.0827i 0.159930 + 0.733971i
\(229\) 10.1878 + 14.0224i 0.673232 + 0.926624i 0.999828 0.0185396i \(-0.00590167\pi\)
−0.326596 + 0.945164i \(0.605902\pi\)
\(230\) 0 0
\(231\) −0.598489 + 2.28008i −0.0393777 + 0.150018i
\(232\) 4.41506 + 4.41506i 0.289863 + 0.289863i
\(233\) 0.384884 + 2.43006i 0.0252146 + 0.159199i 0.997083 0.0763263i \(-0.0243191\pi\)
−0.971868 + 0.235525i \(0.924319\pi\)
\(234\) 3.09320 + 6.76087i 0.202209 + 0.441972i
\(235\) 0 0
\(236\) 2.19472 0.713107i 0.142864 0.0464193i
\(237\) 1.57466 1.76688i 0.102285 0.114771i
\(238\) 6.20067 + 12.1695i 0.401930 + 0.788831i
\(239\) 0.751883 + 2.31406i 0.0486352 + 0.149684i 0.972425 0.233217i \(-0.0749252\pi\)
−0.923790 + 0.382901i \(0.874925\pi\)
\(240\) 0 0
\(241\) 0.500207 1.53948i 0.0322212 0.0991666i −0.933653 0.358180i \(-0.883397\pi\)
0.965874 + 0.259013i \(0.0833974\pi\)
\(242\) 10.7415 1.70129i 0.690493 0.109363i
\(243\) −13.6945 7.44723i −0.878501 0.477740i
\(244\) −0.0859239 + 0.118264i −0.00550072 + 0.00757109i
\(245\) 0 0
\(246\) −7.93691 + 12.3594i −0.506039 + 0.788008i
\(247\) −16.0299 2.53888i −1.01996 0.161545i
\(248\) −1.90338 + 3.73559i −0.120865 + 0.237210i
\(249\) −9.44125 + 3.67955i −0.598315 + 0.233182i
\(250\) 0 0
\(251\) 24.7263i 1.56071i −0.625335 0.780357i \(-0.715038\pi\)
0.625335 0.780357i \(-0.284962\pi\)
\(252\) −3.10814 11.1435i −0.195794 0.701974i
\(253\) 0.432724 2.73211i 0.0272052 0.171767i
\(254\) 4.36369 3.17040i 0.273802 0.198929i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) −20.2470 + 20.2470i −1.26297 + 1.26297i −0.313326 + 0.949646i \(0.601443\pi\)
−0.949646 + 0.313326i \(0.898557\pi\)
\(258\) 6.37978 + 10.9210i 0.397188 + 0.679912i
\(259\) −17.8445 5.79802i −1.10880 0.360272i
\(260\) 0 0
\(261\) 9.19968 16.3167i 0.569446 1.00998i
\(262\) −15.5156 + 7.90558i −0.958555 + 0.488408i
\(263\) −2.68232 + 1.36671i −0.165399 + 0.0842750i −0.534730 0.845023i \(-0.679587\pi\)
0.369331 + 0.929298i \(0.379587\pi\)
\(264\) 0.473094 0.387119i 0.0291169 0.0238255i
\(265\) 0 0
\(266\) 24.0178 + 7.80385i 1.47262 + 0.478485i
\(267\) 3.06471 1.79033i 0.187557 0.109566i
\(268\) 5.35387 5.35387i 0.327039 0.327039i
\(269\) 10.4918 + 7.62274i 0.639697 + 0.464767i 0.859746 0.510722i \(-0.170622\pi\)
−0.220049 + 0.975489i \(0.570622\pi\)
\(270\) 0 0
\(271\) 13.7784 10.0106i 0.836981 0.608102i −0.0845447 0.996420i \(-0.526944\pi\)
0.921526 + 0.388317i \(0.126944\pi\)
\(272\) 0.554059 3.49819i 0.0335948 0.212109i
\(273\) 16.4711 + 1.64623i 0.996876 + 0.0996347i
\(274\) 17.9265i 1.08298i
\(275\) 0 0
\(276\) 4.92959 + 12.6487i 0.296726 + 0.761361i
\(277\) 4.82425 9.46812i 0.289861 0.568884i −0.699454 0.714677i \(-0.746573\pi\)
0.989315 + 0.145793i \(0.0465735\pi\)
\(278\) −17.8007 2.81935i −1.06761 0.169093i
\(279\) 12.3288 + 2.48932i 0.738108 + 0.149032i
\(280\) 0 0
\(281\) −16.4932 + 22.7009i −0.983902 + 1.35422i −0.0492011 + 0.998789i \(0.515668\pi\)
−0.934701 + 0.355436i \(0.884332\pi\)
\(282\) 6.78104 + 2.97774i 0.403805 + 0.177322i
\(283\) 25.3567 4.01611i 1.50730 0.238733i 0.652539 0.757755i \(-0.273704\pi\)
0.854761 + 0.519022i \(0.173704\pi\)
\(284\) −1.90474 + 5.86218i −0.113025 + 0.347856i
\(285\) 0 0
\(286\) 0.270286 + 0.831854i 0.0159823 + 0.0491886i
\(287\) 14.8467 + 29.1383i 0.876372 + 1.71998i
\(288\) −1.04646 + 2.81157i −0.0616632 + 0.165673i
\(289\) −4.23760 + 1.37688i −0.249271 + 0.0809930i
\(290\) 0 0
\(291\) 0.698888 + 12.1489i 0.0409696 + 0.712181i
\(292\) 1.63344 + 10.3131i 0.0955899 + 0.603531i
\(293\) 24.1559 + 24.1559i 1.41120 + 1.41120i 0.751709 + 0.659495i \(0.229230\pi\)
0.659495 + 0.751709i \(0.270770\pi\)
\(294\) −13.1861 3.46116i −0.769027 0.201859i
\(295\) 0 0
\(296\) 2.85988 + 3.93629i 0.166227 + 0.228792i
\(297\) −1.49997 1.05509i −0.0870370 0.0612223i
\(298\) −4.14221 2.11056i −0.239952 0.122262i
\(299\) −19.4242 −1.12333
\(300\) 0 0
\(301\) 28.1596 1.62309
\(302\) 13.0575 + 6.65314i 0.751376 + 0.382845i
\(303\) 16.2241 3.53518i 0.932051 0.203091i
\(304\) −3.84926 5.29805i −0.220770 0.303864i
\(305\) 0 0
\(306\) −10.5553 + 1.21846i −0.603406 + 0.0696547i
\(307\) 12.8970 + 12.8970i 0.736071 + 0.736071i 0.971815 0.235744i \(-0.0757527\pi\)
−0.235744 + 0.971815i \(0.575753\pi\)
\(308\) −0.212907 1.34424i −0.0121315 0.0765952i
\(309\) 11.5042 0.661801i 0.654451 0.0376485i
\(310\) 0 0
\(311\) −15.4255 + 5.01205i −0.874699 + 0.284207i −0.711755 0.702428i \(-0.752099\pi\)
−0.162945 + 0.986635i \(0.552099\pi\)
\(312\) −3.20458 2.85594i −0.181424 0.161686i
\(313\) −2.45198 4.81228i −0.138594 0.272006i 0.811269 0.584674i \(-0.198777\pi\)
−0.949863 + 0.312668i \(0.898777\pi\)
\(314\) 1.38637 + 4.26680i 0.0782372 + 0.240789i
\(315\) 0 0
\(316\) −0.422251 + 1.29956i −0.0237535 + 0.0731057i
\(317\) −8.47316 + 1.34202i −0.475900 + 0.0753752i −0.389777 0.920909i \(-0.627448\pi\)
−0.0861233 + 0.996284i \(0.527448\pi\)
\(318\) −3.06499 + 6.97973i −0.171876 + 0.391404i
\(319\) 1.29527 1.78278i 0.0725210 0.0998166i
\(320\) 0 0
\(321\) −21.5049 13.8099i −1.20028 0.770793i
\(322\) 29.8523 + 4.72815i 1.66361 + 0.263489i
\(323\) 10.5300 20.6663i 0.585905 1.14990i
\(324\) 8.96804 + 0.757846i 0.498224 + 0.0421025i
\(325\) 0 0
\(326\) 10.8202i 0.599276i
\(327\) −1.91483 + 19.1584i −0.105890 + 1.05946i
\(328\) 1.32662 8.37596i 0.0732504 0.462485i
\(329\) 13.3399 9.69197i 0.735450 0.534336i
\(330\) 0 0
\(331\) 22.9895 + 16.7029i 1.26362 + 0.918073i 0.998929 0.0462607i \(-0.0147305\pi\)
0.264690 + 0.964334i \(0.414731\pi\)
\(332\) 4.13675 4.13675i 0.227034 0.227034i
\(333\) 9.06965 11.4368i 0.497014 0.626734i
\(334\) 15.9719 + 5.18960i 0.873946 + 0.283962i
\(335\) 0 0
\(336\) 4.22984 + 5.16925i 0.230757 + 0.282005i
\(337\) 4.22871 2.15464i 0.230353 0.117371i −0.335005 0.942216i \(-0.608738\pi\)
0.565358 + 0.824846i \(0.308738\pi\)
\(338\) −6.11059 + 3.11350i −0.332372 + 0.169352i
\(339\) −1.93047 2.35921i −0.104849 0.128135i
\(340\) 0 0
\(341\) 1.40726 + 0.457245i 0.0762072 + 0.0247612i
\(342\) −12.2073 + 15.3934i −0.660095 + 0.832380i
\(343\) −2.37470 + 2.37470i −0.128222 + 0.128222i
\(344\) −5.90767 4.29217i −0.318520 0.231418i
\(345\) 0 0
\(346\) 14.0925 10.2388i 0.757620 0.550443i
\(347\) −1.25574 + 7.92843i −0.0674116 + 0.425620i 0.930784 + 0.365570i \(0.119126\pi\)
−0.998195 + 0.0600500i \(0.980874\pi\)
\(348\) −1.07553 + 10.7610i −0.0576545 + 0.576851i
\(349\) 18.9234i 1.01295i 0.862256 + 0.506474i \(0.169051\pi\)
−0.862256 + 0.506474i \(0.830949\pi\)
\(350\) 0 0
\(351\) −5.66994 + 11.5622i −0.302639 + 0.617143i
\(352\) −0.160227 + 0.314463i −0.00854013 + 0.0167609i
\(353\) 4.66620 + 0.739053i 0.248357 + 0.0393358i 0.279371 0.960183i \(-0.409874\pi\)
−0.0310149 + 0.999519i \(0.509874\pi\)
\(354\) 3.36322 + 2.15978i 0.178753 + 0.114791i
\(355\) 0 0
\(356\) −1.20449 + 1.65784i −0.0638379 + 0.0878654i
\(357\) −9.51159 + 21.6602i −0.503406 + 1.14638i
\(358\) −7.25818 + 1.14958i −0.383607 + 0.0607573i
\(359\) 4.67561 14.3900i 0.246769 0.759478i −0.748571 0.663054i \(-0.769260\pi\)
0.995340 0.0964232i \(-0.0307402\pi\)
\(360\) 0 0
\(361\) −7.38121 22.7170i −0.388485 1.19563i
\(362\) 0.304777 + 0.598158i 0.0160187 + 0.0314385i
\(363\) 14.0626 + 12.5327i 0.738097 + 0.657795i
\(364\) −9.08922 + 2.95327i −0.476405 + 0.154793i
\(365\) 0 0
\(366\) −0.252778 + 0.0145415i −0.0132129 + 0.000760098i
\(367\) 5.73021 + 36.1791i 0.299114 + 1.88853i 0.439193 + 0.898393i \(0.355265\pi\)
−0.140078 + 0.990140i \(0.544735\pi\)
\(368\) −5.54211 5.54211i −0.288902 0.288902i
\(369\) −25.2733 + 2.91744i −1.31567 + 0.151876i
\(370\) 0 0
\(371\) 9.97595 + 13.7307i 0.517926 + 0.712864i
\(372\) −7.09522 + 1.54603i −0.367870 + 0.0801577i
\(373\) 1.97517 + 1.00640i 0.102270 + 0.0521093i 0.504377 0.863483i \(-0.331722\pi\)
−0.402107 + 0.915593i \(0.631722\pi\)
\(374\) −1.25001 −0.0646363
\(375\) 0 0
\(376\) −4.27588 −0.220512
\(377\) −13.7875 7.02506i −0.710090 0.361809i
\(378\) 11.5283 16.3894i 0.592954 0.842977i
\(379\) 4.15559 + 5.71968i 0.213458 + 0.293800i 0.902297 0.431114i \(-0.141879\pi\)
−0.688839 + 0.724914i \(0.741879\pi\)
\(380\) 0 0
\(381\) 9.03625 + 2.37189i 0.462941 + 0.121516i
\(382\) −9.96347 9.96347i −0.509775 0.509775i
\(383\) −2.17700 13.7450i −0.111240 0.702339i −0.978771 0.204957i \(-0.934295\pi\)
0.867532 0.497382i \(-0.165705\pi\)
\(384\) −0.0994751 1.72919i −0.00507632 0.0882425i
\(385\) 0 0
\(386\) −3.89161 + 1.26446i −0.198078 + 0.0643593i
\(387\) −7.64154 + 20.5309i −0.388441 + 1.04364i
\(388\) −3.18963 6.26000i −0.161929 0.317803i
\(389\) −4.65972 14.3411i −0.236257 0.727125i −0.996952 0.0780155i \(-0.975142\pi\)
0.760695 0.649110i \(-0.224858\pi\)
\(390\) 0 0
\(391\) 8.57820 26.4010i 0.433818 1.33515i
\(392\) 7.77397 1.23128i 0.392645 0.0621888i
\(393\) −27.6158 12.1268i −1.39303 0.611719i
\(394\) −13.3665 + 18.3974i −0.673395 + 0.926849i
\(395\) 0 0
\(396\) 1.03785 + 0.209552i 0.0521538 + 0.0105304i
\(397\) 13.6256 + 2.15808i 0.683849 + 0.108311i 0.488686 0.872460i \(-0.337476\pi\)
0.195163 + 0.980771i \(0.437476\pi\)
\(398\) −2.86862 + 5.62998i −0.143791 + 0.282205i
\(399\) 15.8835 + 40.7551i 0.795171 + 2.04031i
\(400\) 0 0
\(401\) 15.8196i 0.789991i 0.918683 + 0.394995i \(0.129254\pi\)
−0.918683 + 0.394995i \(0.870746\pi\)
\(402\) 13.0492 + 1.30423i 0.650836 + 0.0650490i
\(403\) 1.62541 10.2624i 0.0809674 0.511208i
\(404\) −7.75588 + 5.63497i −0.385869 + 0.280350i
\(405\) 0 0
\(406\) 19.4795 + 14.1527i 0.966750 + 0.702385i
\(407\) 1.21424 1.21424i 0.0601875 0.0601875i
\(408\) 5.29697 3.09436i 0.262239 0.153194i
\(409\) −5.65867 1.83861i −0.279803 0.0909136i 0.165754 0.986167i \(-0.446994\pi\)
−0.445557 + 0.895254i \(0.646994\pi\)
\(410\) 0 0
\(411\) 24.0301 19.6631i 1.18532 0.969909i
\(412\) −5.92780 + 3.02037i −0.292042 + 0.148803i
\(413\) 7.92905 4.04005i 0.390163 0.198798i
\(414\) −11.5481 + 20.4820i −0.567559 + 1.00663i
\(415\) 0 0
\(416\) 2.35699 + 0.765834i 0.115561 + 0.0375481i
\(417\) −15.7457 26.9538i −0.771073 1.31993i
\(418\) −1.63430 + 1.63430i −0.0799363 + 0.0799363i
\(419\) −3.49605 2.54003i −0.170793 0.124088i 0.499105 0.866542i \(-0.333662\pi\)
−0.669898 + 0.742453i \(0.733662\pi\)
\(420\) 0 0
\(421\) −20.2471 + 14.7103i −0.986781 + 0.716939i −0.959214 0.282681i \(-0.908776\pi\)
−0.0275674 + 0.999620i \(0.508776\pi\)
\(422\) −0.650182 + 4.10508i −0.0316503 + 0.199832i
\(423\) 3.44634 + 12.3560i 0.167567 + 0.600770i
\(424\) 4.40116i 0.213739i
\(425\) 0 0
\(426\) −9.94736 + 3.87680i −0.481951 + 0.187831i
\(427\) −0.255924 + 0.502279i −0.0123850 + 0.0243070i
\(428\) 14.5738 + 2.30827i 0.704452 + 0.111574i
\(429\) −0.818612 + 1.27475i −0.0395230 + 0.0615454i
\(430\) 0 0
\(431\) 4.11469 5.66339i 0.198198 0.272796i −0.698337 0.715769i \(-0.746076\pi\)
0.896535 + 0.442973i \(0.146076\pi\)
\(432\) −4.91667 + 1.68117i −0.236553 + 0.0808855i
\(433\) 9.74698 1.54377i 0.468410 0.0741889i 0.0822322 0.996613i \(-0.473795\pi\)
0.386178 + 0.922424i \(0.373795\pi\)
\(434\) −4.99607 + 15.3763i −0.239819 + 0.738087i
\(435\) 0 0
\(436\) −3.43511 10.5722i −0.164512 0.506315i
\(437\) −23.3021 45.7330i −1.11469 2.18770i
\(438\) −12.0328 + 13.5018i −0.574951 + 0.645139i
\(439\) −0.555271 + 0.180419i −0.0265016 + 0.00861091i −0.322238 0.946659i \(-0.604435\pi\)
0.295736 + 0.955270i \(0.404435\pi\)
\(440\) 0 0
\(441\) −9.82380 21.4721i −0.467800 1.02248i
\(442\) 1.37312 + 8.66953i 0.0653126 + 0.412368i
\(443\) −6.33032 6.33032i −0.300763 0.300763i 0.540549 0.841312i \(-0.318216\pi\)
−0.841312 + 0.540549i \(0.818216\pi\)
\(444\) −2.13958 + 8.15120i −0.101540 + 0.386839i
\(445\) 0 0
\(446\) 9.03387 + 12.4341i 0.427766 + 0.588770i
\(447\) −1.71431 7.86754i −0.0810842 0.372122i
\(448\) −3.43597 1.75071i −0.162334 0.0827134i
\(449\) −18.3782 −0.867322 −0.433661 0.901076i \(-0.642779\pi\)
−0.433661 + 0.901076i \(0.642779\pi\)
\(450\) 0 0
\(451\) −2.99298 −0.140934
\(452\) 1.56816 + 0.799015i 0.0737598 + 0.0375825i
\(453\) 5.40404 + 24.8009i 0.253904 + 1.16525i
\(454\) 8.24401 + 11.3469i 0.386911 + 0.532537i
\(455\) 0 0
\(456\) 2.87977 10.9711i 0.134857 0.513769i
\(457\) 24.7918 + 24.7918i 1.15971 + 1.15971i 0.984537 + 0.175174i \(0.0560488\pi\)
0.175174 + 0.984537i \(0.443951\pi\)
\(458\) −2.71142 17.1192i −0.126696 0.799928i
\(459\) −13.2111 12.8126i −0.616642 0.598042i
\(460\) 0 0
\(461\) 0.133994 0.0435374i 0.00624074 0.00202774i −0.305895 0.952065i \(-0.598956\pi\)
0.312136 + 0.950038i \(0.398956\pi\)
\(462\) 1.56839 1.75985i 0.0729681 0.0818758i
\(463\) 4.02806 + 7.90552i 0.187200 + 0.367401i 0.965464 0.260537i \(-0.0838995\pi\)
−0.778264 + 0.627937i \(0.783899\pi\)
\(464\) −1.92945 5.93824i −0.0895725 0.275676i
\(465\) 0 0
\(466\) 0.760291 2.33993i 0.0352198 0.108395i
\(467\) 4.81480 0.762590i 0.222803 0.0352885i −0.0440349 0.999030i \(-0.514021\pi\)
0.266838 + 0.963742i \(0.414021\pi\)
\(468\) 0.313305 7.42827i 0.0144825 0.343372i
\(469\) 17.1621 23.6216i 0.792470 1.09074i
\(470\) 0 0
\(471\) −4.19887 + 6.53851i −0.193474 + 0.301279i
\(472\) −2.27925 0.360998i −0.104911 0.0166163i
\(473\) −1.17002 + 2.29630i −0.0537977 + 0.105584i
\(474\) −2.20518 + 0.859427i −0.101287 + 0.0394748i
\(475\) 0 0
\(476\) 13.6581i 0.626020i
\(477\) −12.7180 + 3.54732i −0.582319 + 0.162420i
\(478\) 0.380627 2.40319i 0.0174095 0.109919i
\(479\) −11.5308 + 8.37759i −0.526854 + 0.382782i −0.819180 0.573537i \(-0.805571\pi\)
0.292326 + 0.956319i \(0.405571\pi\)
\(480\) 0 0
\(481\) −9.75526 7.08761i −0.444802 0.323167i
\(482\) −1.14460 + 1.14460i −0.0521349 + 0.0521349i
\(483\) 26.4062 + 45.2025i 1.20152 + 2.05678i
\(484\) −10.3432 3.36070i −0.470144 0.152759i
\(485\) 0 0
\(486\) 8.82090 + 12.8527i 0.400124 + 0.583010i
\(487\) 31.0777 15.8349i 1.40827 0.717547i 0.425945 0.904749i \(-0.359942\pi\)
0.982321 + 0.187202i \(0.0599418\pi\)
\(488\) 0.130250 0.0663655i 0.00589612 0.00300422i
\(489\) 14.5042 11.8684i 0.655904 0.536706i
\(490\) 0 0
\(491\) −5.09165 1.65438i −0.229783 0.0746610i 0.191862 0.981422i \(-0.438547\pi\)
−0.421645 + 0.906761i \(0.638547\pi\)
\(492\) 12.6829 7.40904i 0.571789 0.334025i
\(493\) 15.6372 15.6372i 0.704266 0.704266i
\(494\) 13.1301 + 9.53958i 0.590751 + 0.429206i
\(495\) 0 0
\(496\) 3.39184 2.46432i 0.152298 0.110651i
\(497\) −3.71838 + 23.4769i −0.166792 + 1.05308i
\(498\) 10.0827 + 1.00773i 0.451817 + 0.0451576i
\(499\) 8.93736i 0.400091i −0.979787 0.200046i \(-0.935891\pi\)
0.979787 0.200046i \(-0.0641090\pi\)
\(500\) 0 0
\(501\) 10.5626 + 27.1023i 0.471903 + 1.21084i
\(502\) −11.2255 + 22.0313i −0.501020 + 0.983307i
\(503\) −2.88408 0.456793i −0.128595 0.0203674i 0.0918053 0.995777i \(-0.470736\pi\)
−0.220400 + 0.975410i \(0.570736\pi\)
\(504\) −2.28966 + 11.3400i −0.101990 + 0.505123i
\(505\) 0 0
\(506\) −1.62591 + 2.23788i −0.0722807 + 0.0994859i
\(507\) −10.8761 4.77599i −0.483025 0.212109i
\(508\) −5.32741 + 0.843778i −0.236365 + 0.0374366i
\(509\) −3.24395 + 9.98385i −0.143786 + 0.442527i −0.996853 0.0792745i \(-0.974740\pi\)
0.853067 + 0.521801i \(0.174740\pi\)
\(510\) 0 0
\(511\) 12.4429 + 38.2953i 0.550441 + 1.69408i
\(512\) 0.453990 + 0.891007i 0.0200637 + 0.0393773i
\(513\) −34.0243 + 0.520992i −1.50221 + 0.0230023i
\(514\) 27.2321 8.84825i 1.20116 0.390280i
\(515\) 0 0
\(516\) −0.726395 12.6270i −0.0319777 0.555874i
\(517\) 0.236073 + 1.49051i 0.0103825 + 0.0655524i
\(518\) 13.2673 + 13.2673i 0.582932 + 0.582932i
\(519\) 29.1826 + 7.66004i 1.28097 + 0.336238i
\(520\) 0 0
\(521\) 11.1471 + 15.3427i 0.488364 + 0.672175i 0.980085 0.198578i \(-0.0636322\pi\)
−0.491722 + 0.870753i \(0.663632\pi\)
\(522\) −15.6046 + 10.3617i −0.682995 + 0.453520i
\(523\) −21.7058 11.0596i −0.949127 0.483604i −0.0903250 0.995912i \(-0.528791\pi\)
−0.858802 + 0.512308i \(0.828791\pi\)
\(524\) 17.4135 0.760714
\(525\) 0 0
\(526\) 3.01044 0.131261
\(527\) 13.2307 + 6.74137i 0.576338 + 0.293659i
\(528\) −0.597278 + 0.130145i −0.0259932 + 0.00566383i
\(529\) −22.5886 31.0905i −0.982111 1.35176i
\(530\) 0 0
\(531\) 0.793889 + 6.87732i 0.0344518 + 0.298450i
\(532\) −17.8571 17.8571i −0.774205 0.774205i
\(533\) 3.28775 + 20.7580i 0.142408 + 0.899131i
\(534\) −3.54347 + 0.203845i −0.153341 + 0.00882122i
\(535\) 0 0
\(536\) −7.20094 + 2.33973i −0.311033 + 0.101061i
\(537\) −9.50227 8.46847i −0.410053 0.365441i
\(538\) −5.88761 11.5551i −0.253833 0.498175i
\(539\) −0.858409 2.64191i −0.0369743 0.113795i
\(540\) 0 0
\(541\) 8.94591 27.5327i 0.384615 1.18372i −0.552144 0.833749i \(-0.686190\pi\)
0.936759 0.349974i \(-0.113810\pi\)
\(542\) −16.8214 + 2.66425i −0.722542 + 0.114439i
\(543\) −0.467516 + 1.06465i −0.0200630 + 0.0456884i
\(544\) −2.08182 + 2.86537i −0.0892571 + 0.122852i
\(545\) 0 0
\(546\) −13.9285 8.94453i −0.596084 0.382790i
\(547\) −12.9801 2.05584i −0.554988 0.0879014i −0.127360 0.991857i \(-0.540650\pi\)
−0.427627 + 0.903955i \(0.640650\pi\)
\(548\) −8.13848 + 15.9727i −0.347659 + 0.682319i
\(549\) −0.296757 0.322892i −0.0126653 0.0137807i
\(550\) 0 0
\(551\) 40.8893i 1.74194i
\(552\) 1.35009 13.5080i 0.0574635 0.574940i
\(553\) −0.824307 + 5.20447i −0.0350531 + 0.221317i
\(554\) −8.59687 + 6.24599i −0.365246 + 0.265367i
\(555\) 0 0
\(556\) 14.5805 + 10.5934i 0.618353 + 0.449260i
\(557\) 24.6270 24.6270i 1.04348 1.04348i 0.0444707 0.999011i \(-0.485840\pi\)
0.999011 0.0444707i \(-0.0141601\pi\)
\(558\) −9.85495 7.81518i −0.417193 0.330843i
\(559\) 17.2114 + 5.59233i 0.727966 + 0.236530i
\(560\) 0 0
\(561\) −1.37110 1.67560i −0.0578877 0.0707441i
\(562\) 25.0016 12.7389i 1.05463 0.537359i
\(563\) 8.71723 4.44165i 0.367388 0.187193i −0.260544 0.965462i \(-0.583902\pi\)
0.627931 + 0.778269i \(0.283902\pi\)
\(564\) −4.69008 5.73171i −0.197488 0.241348i
\(565\) 0 0
\(566\) −24.4163 7.93332i −1.02629 0.333462i
\(567\) 34.6146 2.52353i 1.45368 0.105978i
\(568\) 4.35851 4.35851i 0.182879 0.182879i
\(569\) 8.66014 + 6.29196i 0.363052 + 0.263773i 0.754324 0.656502i \(-0.227965\pi\)
−0.391272 + 0.920275i \(0.627965\pi\)
\(570\) 0 0
\(571\) 12.5798 9.13980i 0.526450 0.382489i −0.292578 0.956242i \(-0.594513\pi\)
0.819028 + 0.573753i \(0.194513\pi\)
\(572\) 0.136828 0.863895i 0.00572105 0.0361213i
\(573\) 2.42715 24.2844i 0.101396 1.01450i
\(574\) 32.7026i 1.36498i
\(575\) 0 0
\(576\) 2.20883 2.03004i 0.0920345 0.0845852i
\(577\) 6.76199 13.2712i 0.281505 0.552485i −0.706350 0.707863i \(-0.749659\pi\)
0.987855 + 0.155378i \(0.0496594\pi\)
\(578\) 4.40082 + 0.697022i 0.183050 + 0.0289923i
\(579\) −5.96357 3.82966i −0.247837 0.159155i
\(580\) 0 0
\(581\) 13.2606 18.2516i 0.550140 0.757203i
\(582\) 4.89277 11.1420i 0.202812 0.461852i
\(583\) −1.53418 + 0.242990i −0.0635392 + 0.0100636i
\(584\) 3.22666 9.93064i 0.133520 0.410933i
\(585\) 0 0
\(586\) −10.5565 32.4896i −0.436086 1.34213i
\(587\) −11.6079 22.7817i −0.479108 0.940302i −0.996423 0.0845070i \(-0.973068\pi\)
0.517315 0.855795i \(-0.326932\pi\)
\(588\) 10.1775 + 9.07027i 0.419715 + 0.374052i
\(589\) 26.1121 8.48435i 1.07593 0.349592i
\(590\) 0 0
\(591\) −39.3226 + 2.26211i −1.61752 + 0.0930508i
\(592\) −0.761135 4.80562i −0.0312825 0.197510i
\(593\) 5.46116 + 5.46116i 0.224263 + 0.224263i 0.810291 0.586028i \(-0.199309\pi\)
−0.586028 + 0.810291i \(0.699309\pi\)
\(594\) 0.857484 + 1.62106i 0.0351830 + 0.0665129i
\(595\) 0 0
\(596\) 2.73256 + 3.76105i 0.111930 + 0.154058i
\(597\) −10.6933 + 2.33005i −0.437650 + 0.0953624i
\(598\) 17.3071 + 8.81838i 0.707738 + 0.360611i
\(599\) −20.6409 −0.843363 −0.421681 0.906744i \(-0.638560\pi\)
−0.421681 + 0.906744i \(0.638560\pi\)
\(600\) 0 0
\(601\) 17.9854 0.733642 0.366821 0.930292i \(-0.380446\pi\)
0.366821 + 0.930292i \(0.380446\pi\)
\(602\) −25.0904 12.7842i −1.02261 0.521045i
\(603\) 12.5650 + 18.9227i 0.511687 + 0.770594i
\(604\) −8.61387 11.8560i −0.350494 0.482413i
\(605\) 0 0
\(606\) −16.0607 4.21573i −0.652423 0.171252i
\(607\) −5.54524 5.54524i −0.225074 0.225074i 0.585557 0.810631i \(-0.300876\pi\)
−0.810631 + 0.585557i \(0.800876\pi\)
\(608\) 1.02445 + 6.46812i 0.0415469 + 0.262317i
\(609\) 2.39516 + 41.6354i 0.0970567 + 1.68715i
\(610\) 0 0
\(611\) 10.0782 3.27461i 0.407721 0.132477i
\(612\) 9.95800 + 3.70635i 0.402528 + 0.149820i
\(613\) 2.13588 + 4.19191i 0.0862676 + 0.169310i 0.930110 0.367282i \(-0.119712\pi\)
−0.843842 + 0.536592i \(0.819712\pi\)
\(614\) −5.63620 17.3464i −0.227459 0.700045i
\(615\) 0 0
\(616\) −0.420571 + 1.29439i −0.0169453 + 0.0521523i
\(617\) 40.5328 6.41977i 1.63179 0.258450i 0.727733 0.685861i \(-0.240574\pi\)
0.904058 + 0.427410i \(0.140574\pi\)
\(618\) −10.5508 4.63313i −0.424414 0.186372i
\(619\) −10.1486 + 13.9684i −0.407908 + 0.561438i −0.962707 0.270547i \(-0.912795\pi\)
0.554798 + 0.831985i \(0.312795\pi\)
\(620\) 0 0
\(621\) −40.1224 + 6.98607i −1.61005 + 0.280341i
\(622\) 16.0196 + 2.53726i 0.642329 + 0.101735i
\(623\) −3.58757 + 7.04100i −0.143733 + 0.282092i
\(624\) 1.55874 + 3.99951i 0.0623994 + 0.160109i
\(625\) 0 0
\(626\) 5.40095i 0.215865i
\(627\) −3.98336 0.398124i −0.159080 0.0158995i
\(628\) 0.701824 4.43114i 0.0280058 0.176822i
\(629\) 13.9415 10.1291i 0.555885 0.403874i
\(630\) 0 0
\(631\) −29.4746 21.4146i −1.17337 0.852501i −0.181959 0.983306i \(-0.558244\pi\)
−0.991408 + 0.130805i \(0.958244\pi\)
\(632\) 0.966214 0.966214i 0.0384339 0.0384339i
\(633\) −6.21593 + 3.63119i −0.247061 + 0.144327i
\(634\) 8.15891 + 2.65099i 0.324032 + 0.105284i
\(635\) 0 0
\(636\) 5.89965 4.82751i 0.233936 0.191423i
\(637\) −17.3803 + 8.85568i −0.688631 + 0.350875i
\(638\) −1.96346 + 1.00043i −0.0777340 + 0.0396074i
\(639\) −16.1077 9.08185i −0.637212 0.359272i
\(640\) 0 0
\(641\) 28.1775 + 9.15543i 1.11294 + 0.361618i 0.807071 0.590454i \(-0.201051\pi\)
0.305874 + 0.952072i \(0.401051\pi\)
\(642\) 12.8914 + 22.0677i 0.508784 + 0.870943i
\(643\) −16.2471 + 16.2471i −0.640721 + 0.640721i −0.950733 0.310012i \(-0.899667\pi\)
0.310012 + 0.950733i \(0.399667\pi\)
\(644\) −24.4521 17.7655i −0.963547 0.700058i
\(645\) 0 0
\(646\) −18.7646 + 13.6333i −0.738284 + 0.536394i
\(647\) −0.280589 + 1.77157i −0.0110311 + 0.0696477i −0.992590 0.121513i \(-0.961225\pi\)
0.981559 + 0.191161i \(0.0612253\pi\)
\(648\) −7.64652 4.74665i −0.300384 0.186466i
\(649\) 0.814444i 0.0319697i
\(650\) 0 0
\(651\) −26.0916 + 10.1687i −1.02261 + 0.398544i
\(652\) −4.91227 + 9.64088i −0.192379 + 0.377566i
\(653\) −26.3159 4.16803i −1.02982 0.163107i −0.381416 0.924404i \(-0.624563\pi\)
−0.648404 + 0.761296i \(0.724563\pi\)
\(654\) 10.4039 16.2010i 0.406824 0.633509i
\(655\) 0 0
\(656\) −4.98463 + 6.86076i −0.194617 + 0.267868i
\(657\) −31.2973 1.32004i −1.22102 0.0514996i
\(658\) −16.2860 + 2.57944i −0.634893 + 0.100557i
\(659\) −2.02081 + 6.21940i −0.0787195 + 0.242274i −0.982670 0.185363i \(-0.940654\pi\)
0.903951 + 0.427637i \(0.140654\pi\)
\(660\) 0 0
\(661\) 5.97584 + 18.3917i 0.232433 + 0.715356i 0.997452 + 0.0713473i \(0.0227299\pi\)
−0.765018 + 0.644008i \(0.777270\pi\)
\(662\) −12.9009 25.3194i −0.501407 0.984066i
\(663\) −10.1152 + 11.3500i −0.392840 + 0.440797i
\(664\) −5.56392 + 1.80783i −0.215922 + 0.0701573i
\(665\) 0 0
\(666\) −13.2733 + 6.07276i −0.514331 + 0.235315i
\(667\) −7.65551 48.3350i −0.296422 1.87154i
\(668\) −11.8751 11.8751i −0.459461 0.459461i
\(669\) −6.75856 + 25.7482i −0.261301 + 0.995484i
\(670\) 0 0
\(671\) −0.0303252 0.0417390i −0.00117069 0.00161132i
\(672\) −1.42202 6.52614i −0.0548558 0.251751i
\(673\) −39.1978 19.9723i −1.51096 0.769874i −0.514793 0.857315i \(-0.672131\pi\)
−0.996170 + 0.0874407i \(0.972131\pi\)
\(674\) −4.74599 −0.182809
\(675\) 0 0
\(676\) 6.85808 0.263772
\(677\) 33.3683 + 17.0020i 1.28245 + 0.653440i 0.956441 0.291927i \(-0.0942963\pi\)
0.326008 + 0.945367i \(0.394296\pi\)
\(678\) 0.649003 + 2.97849i 0.0249248 + 0.114388i
\(679\) −15.9250 21.9189i −0.611147 0.841171i
\(680\) 0 0
\(681\) −6.16764 + 23.4970i −0.236344 + 0.900406i
\(682\) −1.04629 1.04629i −0.0400645 0.0400645i
\(683\) −5.33840 33.7054i −0.204268 1.28970i −0.850263 0.526358i \(-0.823557\pi\)
0.645995 0.763342i \(-0.276443\pi\)
\(684\) 17.8652 8.17363i 0.683094 0.312526i
\(685\) 0 0
\(686\) 3.19397 1.03778i 0.121946 0.0396228i
\(687\) 19.9738 22.4121i 0.762049 0.855077i
\(688\) 3.31516 + 6.50638i 0.126389 + 0.248053i
\(689\) 3.37056 + 10.3735i 0.128408 + 0.395199i
\(690\) 0 0
\(691\) −9.75674 + 30.0282i −0.371164 + 1.14232i 0.574867 + 0.818247i \(0.305054\pi\)
−0.946030 + 0.324078i \(0.894946\pi\)
\(692\) −17.2049 + 2.72498i −0.654031 + 0.103588i
\(693\) 4.07936 + 0.172057i 0.154962 + 0.00653591i
\(694\) 4.71830 6.49419i 0.179104 0.246516i
\(695\) 0 0
\(696\) 5.84371 9.09986i 0.221505 0.344929i
\(697\) −29.6659 4.69862i −1.12368 0.177973i
\(698\) 8.59105 16.8609i 0.325176 0.638194i
\(699\) 3.97056 1.54745i 0.150181 0.0585301i
\(700\) 0 0
\(701\) 41.1349i 1.55364i −0.629720 0.776822i \(-0.716830\pi\)
0.629720 0.776822i \(-0.283170\pi\)
\(702\) 10.3011 7.72787i 0.388789 0.291670i
\(703\) 4.98448 31.4708i 0.187993 1.18694i
\(704\) 0.285527 0.207447i 0.0107612 0.00781846i
\(705\) 0 0
\(706\) −3.82209 2.77691i −0.143846 0.104510i
\(707\) −26.1413 + 26.1413i −0.983143 + 0.983143i
\(708\) −2.01613 3.45125i −0.0757710 0.129706i
\(709\) −48.5191 15.7648i −1.82217 0.592060i −0.999731 0.0232123i \(-0.992611\pi\)
−0.822443 0.568848i \(-0.807389\pi\)
\(710\) 0 0
\(711\) −3.57083 2.01331i −0.133917 0.0755049i
\(712\) 1.82585 0.930319i 0.0684268 0.0348652i
\(713\) 29.2785 14.9181i 1.09649 0.558689i
\(714\) 18.3084 14.9812i 0.685175 0.560658i
\(715\) 0 0
\(716\) 6.98899 + 2.27086i 0.261191 + 0.0848660i
\(717\) 3.63891 2.12576i 0.135898 0.0793881i
\(718\) −10.6989 + 10.6989i −0.399281 + 0.399281i
\(719\) 29.8994 + 21.7232i 1.11506 + 0.810138i 0.983453 0.181164i \(-0.0579866\pi\)
0.131606 + 0.991302i \(0.457987\pi\)
\(720\) 0 0
\(721\) −20.7558 + 15.0800i −0.772985 + 0.561607i
\(722\) −3.73661 + 23.5920i −0.139062 + 0.878004i
\(723\) −2.78978 0.278830i −0.103753 0.0103698i
\(724\) 0.671329i 0.0249497i
\(725\) 0 0
\(726\) −6.84017 17.5510i −0.253863 0.651379i
\(727\) −8.55075 + 16.7818i −0.317130 + 0.622402i −0.993458 0.114198i \(-0.963570\pi\)
0.676328 + 0.736600i \(0.263570\pi\)
\(728\) 9.43931 + 1.49504i 0.349844 + 0.0554099i
\(729\) −7.55333 + 25.9219i −0.279753 + 0.960072i
\(730\) 0 0
\(731\) −15.2020 + 20.9238i −0.562266 + 0.773893i
\(732\) 0.231828 + 0.101802i 0.00856862 + 0.00376271i
\(733\) −34.3095 + 5.43410i −1.26725 + 0.200713i −0.753627 0.657302i \(-0.771698\pi\)
−0.513625 + 0.858015i \(0.671698\pi\)
\(734\) 11.3193 34.8373i 0.417804 1.28587i
\(735\) 0 0
\(736\) 2.42199 + 7.45412i 0.0892758 + 0.274763i
\(737\) 1.21316 + 2.38096i 0.0446873 + 0.0877038i
\(738\) 23.8431 + 8.87436i 0.877678 + 0.326670i
\(739\) 2.70309 0.878288i 0.0994348 0.0323083i −0.258877 0.965910i \(-0.583352\pi\)
0.358312 + 0.933602i \(0.383352\pi\)
\(740\) 0 0
\(741\) 1.61445 + 28.0643i 0.0593083 + 1.03097i
\(742\) −2.65502 16.7632i −0.0974689 0.615395i
\(743\) −19.3245 19.3245i −0.708947 0.708947i 0.257367 0.966314i \(-0.417145\pi\)
−0.966314 + 0.257367i \(0.917145\pi\)
\(744\) 7.02377 + 1.84364i 0.257504 + 0.0675913i
\(745\) 0 0
\(746\) −1.30299 1.79341i −0.0477059 0.0656615i
\(747\) 9.70857 + 14.6210i 0.355218 + 0.534953i
\(748\) 1.11376 + 0.567491i 0.0407233 + 0.0207495i
\(749\) 56.9012 2.07913
\(750\) 0 0
\(751\) 13.6596 0.498445 0.249222 0.968446i \(-0.419825\pi\)
0.249222 + 0.968446i \(0.419825\pi\)
\(752\) 3.80983 + 1.94121i 0.138930 + 0.0707886i
\(753\) −41.8454 + 9.11798i −1.52493 + 0.332278i
\(754\) 9.09541 + 12.5188i 0.331235 + 0.455906i
\(755\) 0 0
\(756\) −17.7124 + 9.36926i −0.644195 + 0.340757i
\(757\) 11.1659 + 11.1659i 0.405833 + 0.405833i 0.880283 0.474450i \(-0.157353\pi\)
−0.474450 + 0.880283i \(0.657353\pi\)
\(758\) −1.10598 6.98287i −0.0401710 0.253629i
\(759\) −4.78324 + 0.275165i −0.173621 + 0.00998786i
\(760\) 0 0
\(761\) −13.3455 + 4.33621i −0.483774 + 0.157188i −0.540742 0.841188i \(-0.681857\pi\)
0.0569686 + 0.998376i \(0.481857\pi\)
\(762\) −6.97454 6.21574i −0.252661 0.225173i
\(763\) −19.4614 38.1951i −0.704548 1.38275i
\(764\) 4.35419 + 13.4008i 0.157529 + 0.484825i
\(765\) 0 0
\(766\) −4.30040 + 13.2353i −0.155380 + 0.478209i
\(767\) 5.64864 0.894657i 0.203961 0.0323042i
\(768\) −0.696404 + 1.58588i −0.0251293 + 0.0572256i
\(769\) 13.0082 17.9042i 0.469087 0.645643i −0.507275 0.861784i \(-0.669347\pi\)
0.976362 + 0.216141i \(0.0693471\pi\)
\(770\) 0 0
\(771\) 41.7310 + 26.7986i 1.50290 + 0.965128i
\(772\) 4.04150 + 0.640111i 0.145457 + 0.0230381i
\(773\) −19.2486 + 37.7774i −0.692323 + 1.35876i 0.230324 + 0.973114i \(0.426021\pi\)
−0.922647 + 0.385646i \(0.873979\pi\)
\(774\) 16.1295 14.8239i 0.579762 0.532836i
\(775\) 0 0
\(776\) 7.02576i 0.252210i
\(777\) −3.23198 + 32.3370i −0.115947 + 1.16008i
\(778\) −2.35890 + 14.8935i −0.0845708 + 0.533959i
\(779\) −44.9294 + 32.6431i −1.60976 + 1.16956i
\(780\) 0 0
\(781\) −1.75995 1.27868i −0.0629758 0.0457546i
\(782\) −19.6290 + 19.6290i −0.701932 + 0.701932i
\(783\)