Properties

Label 750.2.l.b.107.9
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 107.9
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.b.743.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.891007 + 0.453990i) q^{2} +(0.873670 - 1.49556i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.45742 - 0.935916i) q^{6} +(2.72680 + 2.72680i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.47340 - 2.61325i) q^{9} +O(q^{10})\) \(q+(0.891007 + 0.453990i) q^{2} +(0.873670 - 1.49556i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.45742 - 0.935916i) q^{6} +(2.72680 + 2.72680i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.47340 - 2.61325i) q^{9} +(0.335657 - 0.109061i) q^{11} +(1.72346 - 0.172255i) 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} +(-0.126420 - 2.99734i) q^{18} +(-3.84926 + 5.29805i) q^{19} +(6.46042 - 1.69577i) q^{21} +(0.348585 + 0.0552105i) q^{22} +(3.55825 - 6.98347i) q^{23} +(1.61382 + 0.628956i) q^{24} +2.47829i q^{26} +(-5.19554 - 0.0795559i) 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} +(0.130145 - 0.597278i) q^{33} +(3.36845 + 1.09448i) q^{34} +(1.24812 - 2.72804i) q^{36} +(-4.33521 + 2.20890i) q^{37} +(-5.83498 + 2.97307i) q^{38} +(4.28544 + 0.246528i) q^{39} +(-8.06531 - 2.62058i) q^{41} +(6.52614 + 1.42202i) 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} +(1.15238 + 1.29306i) q^{48} +7.87088i q^{49} +(2.22763 - 5.71582i) q^{51} +(-1.12512 + 2.20817i) q^{52} +(-4.34698 - 0.688494i) q^{53} +(-4.59315 - 2.42961i) q^{54} +(-2.26666 + 3.11979i) q^{56} +(4.56057 + 10.3855i) 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} +(3.10814 - 11.1435i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(0.387119 - 0.473094i) q^{66} +(-1.18445 - 7.47829i) q^{67} +(2.50443 + 2.50443i) q^{68} +(-7.33546 - 11.4228i) q^{69} +(-3.62303 - 4.98667i) q^{71} +(2.35059 - 1.86407i) q^{72} +(9.30362 + 4.74043i) q^{73} -4.86552 q^{74} -6.54875 q^{76} +(1.21266 + 0.617880i) q^{77} +(3.70643 + 2.16521i) q^{78} +(0.803169 + 1.10547i) q^{79} +(-4.65817 + 7.70074i) q^{81} +(-5.99652 - 5.99652i) q^{82} +(0.915181 + 5.77823i) q^{83} +(5.16925 + 4.22984i) q^{84} +(6.94488 - 2.25653i) q^{86} +(-1.07553 - 10.7610i) 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} +(-6.64888 + 2.91971i) q^{93} +(-2.51330 + 3.45926i) q^{94} +(0.439743 + 1.67530i) 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
\(3\) 0.873670 1.49556i 0.504413 0.863462i
\(4\) 0.587785 + 0.809017i 0.293893 + 0.404508i
\(5\) 0 0
\(6\) 1.45742 0.935916i 0.594987 0.382086i
\(7\) 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
\(9\) −1.47340 2.61325i −0.491134 0.871084i
\(10\) 0 0
\(11\) 0.335657 0.109061i 0.101204 0.0328833i −0.257977 0.966151i \(-0.583056\pi\)
0.359181 + 0.933268i \(0.383056\pi\)
\(12\) 1.72346 0.172255i 0.497521 0.0497257i
\(13\) 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 0.282948 0.959135i \(-0.408688\pi\)
0.565488 + 0.824756i \(0.308688\pi\)
\(18\) −0.126420 2.99734i −0.0297975 0.706479i
\(19\) −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
\(21\) 6.46042 1.69577i 1.40978 0.370048i
\(22\) 0.348585 + 0.0552105i 0.0743186 + 0.0117709i
\(23\) 3.55825 6.98347i 0.741947 1.45615i −0.142638 0.989775i \(-0.545559\pi\)
0.884585 0.466378i \(-0.154441\pi\)
\(24\) 1.61382 + 0.628956i 0.329420 + 0.128385i
\(25\) 0 0
\(26\) 2.47829i 0.486033i
\(27\) −5.19554 0.0795559i −0.999883 0.0153105i
\(28\) −0.603255 + 3.80880i −0.114004 + 0.719796i
\(29\) 5.05137 3.67003i 0.938015 0.681508i −0.00992666 0.999951i \(-0.503160\pi\)
0.947942 + 0.318443i \(0.103160\pi\)
\(30\) 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
\(33\) 0.130145 0.597278i 0.0226553 0.103973i
\(34\) 3.36845 + 1.09448i 0.577684 + 0.187701i
\(35\) 0 0
\(36\) 1.24812 2.72804i 0.208020 0.454673i
\(37\) −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
\(39\) 4.28544 + 0.246528i 0.686219 + 0.0394761i
\(40\) 0 0
\(41\) −8.06531 2.62058i −1.25959 0.409265i −0.398241 0.917281i \(-0.630379\pi\)
−0.861348 + 0.508015i \(0.830379\pi\)
\(42\) 6.52614 + 1.42202i 1.00700 + 0.219423i
\(43\) 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 \(0.150949\pi\)
−0.987218 + 0.159378i \(0.949051\pi\)
\(48\) 1.15238 + 1.29306i 0.166332 + 0.186638i
\(49\) 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 −0.149435 0.988772i \(-0.547745\pi\)
−0.447668 + 0.894200i \(0.647745\pi\)
\(54\) −4.59315 2.42961i −0.625048 0.330628i
\(55\) 0 0
\(56\) −2.26666 + 3.11979i −0.302896 + 0.416900i
\(57\) 4.56057 + 10.3855i 0.604063 + 1.37560i
\(58\) 6.16696 0.976751i 0.809762 0.128254i
\(59\) −0.713107 + 2.19472i −0.0928386 + 0.285728i −0.986684 0.162647i \(-0.947997\pi\)
0.893846 + 0.448375i \(0.147997\pi\)
\(60\) 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
\(63\) 3.10814 11.1435i 0.391589 1.40395i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) 0.387119 0.473094i 0.0476510 0.0582339i
\(67\) −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
\(69\) −7.33546 11.4228i −0.883085 1.37515i
\(70\) 0 0
\(71\) −3.62303 4.98667i −0.429974 0.591809i 0.537973 0.842962i \(-0.319190\pi\)
−0.967947 + 0.251153i \(0.919190\pi\)
\(72\) 2.35059 1.86407i 0.277019 0.219682i
\(73\) 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
\(78\) 3.70643 + 2.16521i 0.419671 + 0.245161i
\(79\) 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
\(81\) −4.65817 + 7.70074i −0.517574 + 0.855638i
\(82\) −5.99652 5.99652i −0.662205 0.662205i
\(83\) 0.915181 + 5.77823i 0.100454 + 0.634243i 0.985621 + 0.168969i \(0.0540439\pi\)
−0.885167 + 0.465273i \(0.845956\pi\)
\(84\) 5.16925 + 4.22984i 0.564011 + 0.461513i
\(85\) 0 0
\(86\) 6.94488 2.25653i 0.748886 0.243328i
\(87\) −1.07553 10.7610i −0.115309 1.15370i
\(88\) 0.160227 + 0.314463i 0.0170803 + 0.0335219i
\(89\) −0.633239 1.94891i −0.0671232 0.206584i 0.911869 0.410481i \(-0.134639\pi\)
−0.978992 + 0.203897i \(0.934639\pi\)
\(90\) 0 0
\(91\) −2.95327 + 9.08922i −0.309587 + 0.952809i
\(92\) 7.74123 1.22609i 0.807079 0.127829i
\(93\) −6.64888 + 2.91971i −0.689457 + 0.302759i
\(94\) −2.51330 + 3.45926i −0.259227 + 0.356795i
\(95\) 0 0
\(96\) 0.439743 + 1.67530i 0.0448811 + 0.170984i
\(97\) −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 \(-0.841738\pi\)
0.878925 0.476961i \(-0.158262\pi\)
\(102\) 4.57976 4.08151i 0.453464 0.404130i
\(103\) −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 \(0.502770\pi\)
−0.999962 + 0.00870186i \(0.997230\pi\)
\(108\) −2.98950 4.25004i −0.287665 0.408961i
\(109\) −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
\(111\) −0.483998 + 8.41342i −0.0459391 + 0.798566i
\(112\) −3.43597 + 1.75071i −0.324668 + 0.165427i
\(113\) −1.56816 + 0.799015i −0.147520 + 0.0751650i −0.526192 0.850366i \(-0.676381\pi\)
0.378672 + 0.925531i \(0.376381\pi\)
\(114\) −0.651437 + 11.3240i −0.0610127 + 1.06059i
\(115\) 0 0
\(116\) 5.93824 + 1.92945i 0.551352 + 0.179145i
\(117\) 4.11276 6.19375i 0.380224 0.572612i
\(118\) −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
\(123\) −10.9656 + 9.77263i −0.988739 + 0.881169i
\(124\) 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
\(129\) −3.21113 12.2335i −0.282724 1.07710i
\(130\) 0 0
\(131\) −10.2354 + 14.0878i −0.894273 + 1.23086i 0.0779865 + 0.996954i \(0.475151\pi\)
−0.972259 + 0.233906i \(0.924849\pi\)
\(132\) 0.559706 0.245782i 0.0487161 0.0213926i
\(133\) −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 \(-0.872351\pi\)
0.225346 0.974279i \(-0.427649\pi\)
\(138\) −1.35009 13.5080i −0.114927 1.14988i
\(139\) 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
\(141\) 5.73171 + 4.69008i 0.482697 + 0.394976i
\(142\) −0.964240 6.08797i −0.0809172 0.510891i
\(143\) 0.618480 + 0.618480i 0.0517199 + 0.0517199i
\(144\) 2.94066 0.593750i 0.245055 0.0494792i
\(145\) 0 0
\(146\) 6.13747 + 8.44751i 0.507941 + 0.699121i
\(147\) 11.7714 + 6.87655i 0.970886 + 0.567168i
\(148\) −4.33521 2.20890i −0.356352 0.181570i
\(149\) −4.64891 −0.380854 −0.190427 0.981701i \(-0.560987\pi\)
−0.190427 + 0.981701i \(0.560987\pi\)
\(150\) 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
\(153\) −6.60214 8.32530i −0.533751 0.673061i
\(154\) 0.799974 + 1.10107i 0.0644637 + 0.0887267i
\(155\) 0 0
\(156\) 2.31947 + 3.61190i 0.185706 + 0.289183i
\(157\) −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
\(159\) −4.82751 + 5.89965i −0.382846 + 0.467873i
\(160\) 0 0
\(161\) 28.7452 9.33987i 2.26544 0.736085i
\(162\) −7.64652 + 4.74665i −0.600768 + 0.372932i
\(163\) 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 0.522866 0.852415i \(-0.324863\pi\)
0.760686 + 0.649120i \(0.224863\pi\)
\(168\) 2.68553 + 6.11560i 0.207193 + 0.471829i
\(169\) 4.03108 5.54830i 0.310083 0.426793i
\(170\) 0 0
\(171\) 19.5166 + 2.25292i 1.49247 + 0.172285i
\(172\) 7.21237 + 1.14233i 0.549938 + 0.0871017i
\(173\) 7.90821 15.5207i 0.601250 1.18002i −0.367043 0.930204i \(-0.619630\pi\)
0.968293 0.249816i \(-0.0803702\pi\)
\(174\) 3.92710 10.0764i 0.297713 0.763892i
\(175\) 0 0
\(176\) 0.352930i 0.0266031i
\(177\) 2.65931 + 2.98395i 0.199886 + 0.224288i
\(178\) 0.320566 2.02397i 0.0240274 0.151703i
\(179\) −5.94519 + 4.31943i −0.444364 + 0.322849i −0.787367 0.616485i \(-0.788556\pi\)
0.343002 + 0.939334i \(0.388556\pi\)
\(180\) 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
\(183\) 0.247391 + 0.0539056i 0.0182877 + 0.00398482i
\(184\) 7.45412 + 2.42199i 0.549525 + 0.178552i
\(185\) 0 0
\(186\) −7.24972 0.417054i −0.531575 0.0305799i
\(187\) 1.11376 0.567491i 0.0814465 0.0414991i
\(188\) −3.80983 + 1.94121i −0.277861 + 0.141577i
\(189\) −13.9503 14.3841i −1.01473 1.04629i
\(190\) 0 0
\(191\) −13.4008 4.35419i −0.969650 0.315058i −0.218975 0.975730i \(-0.570271\pi\)
−0.750675 + 0.660672i \(0.770271\pi\)
\(192\) −0.368756 + 1.69234i −0.0266126 + 0.122134i
\(193\) 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 \(0.350585\pi\)
−0.705806 + 0.708405i \(0.749415\pi\)
\(198\) −0.369327 0.992288i −0.0262470 0.0705188i
\(199\) 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
\(204\) 5.93357 1.55748i 0.415433 0.109045i
\(205\) 0 0
\(206\) −3.91049 + 5.38233i −0.272457 + 0.375005i
\(207\) −23.4923 + 0.990845i −1.63283 + 0.0688685i
\(208\) −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
\(213\) −10.6232 + 1.06175i −0.727889 + 0.0727502i
\(214\) −14.0333 + 4.55969i −0.959296 + 0.311694i
\(215\) 0 0
\(216\) −0.734186 5.14402i −0.0499550 0.350006i
\(217\) −2.52917 15.9686i −0.171691 1.08402i
\(218\) −7.86037 7.86037i −0.532371 0.532371i
\(219\) 15.2179 9.77255i 1.02833 0.660368i
\(220\) 0 0
\(221\) 5.15934 + 7.10123i 0.347055 + 0.477680i
\(222\) −4.25086 + 7.27668i −0.285299 + 0.488379i
\(223\) −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 0.816537 0.577293i \(-0.195891\pi\)
0.0129084 + 0.999917i \(0.495891\pi\)
\(228\) −5.72144 + 9.79405i −0.378912 + 0.648627i
\(229\) 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
\(231\) 1.98354 1.27378i 0.130507 0.0838085i
\(232\) 4.41506 + 4.41506i 0.289863 + 0.289863i
\(233\) −0.384884 2.43006i −0.0252146 0.159199i 0.971868 0.235525i \(-0.0756809\pi\)
−0.997083 + 0.0763263i \(0.975681\pi\)
\(234\) 6.47640 3.65152i 0.423375 0.238707i
\(235\) 0 0
\(236\) −2.19472 + 0.713107i −0.142864 + 0.0464193i
\(237\) 2.35500 0.235375i 0.152974 0.0152892i
\(238\) 6.20067 + 12.1695i 0.401930 + 0.788831i
\(239\) −0.751883 2.31406i −0.0486352 0.149684i 0.923790 0.382901i \(-0.125075\pi\)
−0.972425 + 0.233217i \(0.925075\pi\)
\(240\) 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
\(243\) 7.44723 + 13.6945i 0.477740 + 0.878501i
\(244\) −0.0859239 + 0.118264i −0.00550072 + 0.00757109i
\(245\) 0 0
\(246\) −14.2071 + 3.72918i −0.905814 + 0.237764i
\(247\) −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 \(0.284962\pi\)
−0.625335 + 0.780357i \(0.715038\pi\)
\(252\) 10.8422 4.03544i 0.682994 0.254209i
\(253\) 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 \(-0.398557\pi\)
0.949646 0.313326i \(-0.101443\pi\)
\(258\) 2.69276 12.3579i 0.167644 0.769372i
\(259\) −17.8445 5.79802i −1.10880 0.360272i
\(260\) 0 0
\(261\) −17.0334 7.79306i −1.05434 0.482378i
\(262\) −15.5156 + 7.90558i −0.958555 + 0.488408i
\(263\) 2.68232 1.36671i 0.165399 0.0842750i −0.369331 0.929298i \(-0.620413\pi\)
0.534730 + 0.845023i \(0.320413\pi\)
\(264\) 0.610284 + 0.0351078i 0.0375604 + 0.00216073i
\(265\) 0 0
\(266\) −24.0178 7.80385i −1.47262 0.478485i
\(267\) −3.46795 0.755655i −0.212235 0.0462454i
\(268\) 5.35387 5.35387i 0.327039 0.327039i
\(269\) −10.4918 7.62274i −0.639697 0.464767i 0.220049 0.975489i \(-0.429378\pi\)
−0.859746 + 0.510722i \(0.829378\pi\)
\(270\) 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
\(273\) 11.0133 + 12.3578i 0.666555 + 0.747926i
\(274\) 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
\(279\) −1.44233 + 12.4947i −0.0863502 + 0.748036i
\(280\) 0 0
\(281\) 16.4932 22.7009i 0.983902 1.35422i 0.0492011 0.998789i \(-0.484332\pi\)
0.934701 0.355436i \(-0.115668\pi\)
\(282\) 2.97774 + 6.78104i 0.177322 + 0.403805i
\(283\) 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
\(288\) 2.88970 + 0.805995i 0.170277 + 0.0474937i
\(289\) −4.23760 + 1.37688i −0.249271 + 0.0809930i
\(290\) 0 0
\(291\) −7.70635 + 9.41786i −0.451754 + 0.552085i
\(292\) 1.63344 + 10.3131i 0.0955899 + 0.603531i
\(293\) −24.1559 24.1559i −1.41120 1.41120i −0.751709 0.659495i \(-0.770770\pi\)
−0.659495 0.751709i \(-0.729230\pi\)
\(294\) 7.36648 + 11.4711i 0.429622 + 0.669010i
\(295\) 0 0
\(296\) −2.85988 3.93629i −0.166227 0.228792i
\(297\) −1.75260 + 0.539930i −0.101696 + 0.0313299i
\(298\) −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
\(303\) −14.3376 8.37569i −0.823675 0.481171i
\(304\) −3.84926 5.29805i −0.220770 0.303864i
\(305\) 0 0
\(306\) −2.10294 10.4152i −0.120217 0.595398i
\(307\) 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
\(309\) 8.91809 + 7.29740i 0.507333 + 0.415135i
\(310\) 0 0
\(311\) 15.4255 5.01205i 0.874699 0.284207i 0.162945 0.986635i \(-0.447901\pi\)
0.711755 + 0.702428i \(0.247901\pi\)
\(312\) 0.426897 + 4.27124i 0.0241683 + 0.241812i
\(313\) −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 0.0861233 0.996284i \(-0.472552\pi\)
0.389777 + 0.920909i \(0.372552\pi\)
\(318\) −6.97973 + 3.06499i −0.391404 + 0.171876i
\(319\) 1.29527 1.78278i 0.0725210 0.0998166i
\(320\) 0 0
\(321\) 6.48862 + 24.7198i 0.362160 + 1.37973i
\(322\) 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
\(327\) −14.3740 + 12.8102i −0.794884 + 0.708404i
\(328\) 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
\(333\) 12.1599 + 8.07440i 0.666360 + 0.442474i
\(334\) 15.9719 + 5.18960i 0.873946 + 0.283962i
\(335\) 0 0
\(336\) −0.383604 + 6.66824i −0.0209273 + 0.363783i
\(337\) 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
\(339\) −0.175074 + 3.04335i −0.00950874 + 0.165292i
\(340\) 0 0
\(341\) −1.40726 0.457245i −0.0762072 0.0247612i
\(342\) 16.3666 + 10.8677i 0.885007 + 0.587660i
\(343\) −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 \(-0.880874\pi\)
0.998195 0.0600500i \(-0.0191260\pi\)
\(348\) 8.07367 7.19529i 0.432794 0.385708i
\(349\) 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 0.0310149 0.999519i \(-0.490126\pi\)
−0.279371 + 0.960183i \(0.590126\pi\)
\(354\) 1.01478 + 3.86602i 0.0539349 + 0.205477i
\(355\) 0 0
\(356\) 1.20449 1.65784i 0.0638379 0.0878654i
\(357\) 21.6602 9.51159i 1.14638 0.503406i
\(358\) −7.25818 + 1.14958i −0.383607 + 0.0607573i
\(359\) −4.67561 + 14.3900i −0.246769 + 0.759478i 0.748571 + 0.663054i \(0.230740\pi\)
−0.995340 + 0.0964232i \(0.969260\pi\)
\(360\) 0 0
\(361\) −7.38121 22.7170i −0.388485 1.19563i
\(362\) −0.304777 0.598158i −0.0160187 0.0314385i
\(363\) 1.87335 + 18.7434i 0.0983252 + 0.983775i
\(364\) −9.08922 + 2.95327i −0.476405 + 0.154793i
\(365\) 0 0
\(366\) 0.195954 + 0.160343i 0.0102427 + 0.00838128i
\(367\) 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
\(369\) 5.03522 + 24.9378i 0.262123 + 1.29821i
\(370\) 0 0
\(371\) −9.97595 13.7307i −0.517926 0.712864i
\(372\) −6.27021 3.66290i −0.325095 0.189913i
\(373\) 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
\(378\) −5.89952 19.1497i −0.303439 0.984952i
\(379\) 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
\(381\) 5.04816 + 7.86103i 0.258625 + 0.402733i
\(382\) −9.96347 9.96347i −0.509775 0.509775i
\(383\) 2.17700 + 13.7450i 0.111240 + 0.702339i 0.978771 + 0.204957i \(0.0657053\pi\)
−0.867532 + 0.497382i \(0.834295\pi\)
\(384\) −1.09687 + 1.34048i −0.0559744 + 0.0684059i
\(385\) 0 0
\(386\) 3.89161 1.26446i 0.198078 0.0643593i
\(387\) −21.1014 5.88560i −1.07264 0.299182i
\(388\) −3.18963 6.26000i −0.161929 0.317803i
\(389\) 4.65972 + 14.3411i 0.236257 + 0.727125i 0.996952 + 0.0780155i \(0.0248584\pi\)
−0.760695 + 0.649110i \(0.775142\pi\)
\(390\) 0 0
\(391\) 8.57820 26.4010i 0.433818 1.33515i
\(392\) −7.77397 + 1.23128i −0.392645 + 0.0621888i
\(393\) 12.1268 + 27.6158i 0.611719 + 1.39303i
\(394\) −13.3665 + 18.3974i −0.673395 + 0.926849i
\(395\) 0 0
\(396\) 0.121416 1.05181i 0.00610139 0.0528552i
\(397\) 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 \(-0.870746\pi\)
0.918683 0.394995i \(-0.129254\pi\)
\(402\) −8.72529 9.79044i −0.435178 0.488303i
\(403\) 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
\(408\) 5.99393 + 1.30606i 0.296744 + 0.0646595i
\(409\) −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
\(411\) −30.9984 1.78324i −1.52904 0.0879610i
\(412\) −5.92780 + 3.02037i −0.292042 + 0.148803i
\(413\) −7.92905 + 4.04005i −0.390163 + 0.198798i
\(414\) −21.3816 9.78243i −1.05085 0.480780i
\(415\) 0 0
\(416\) −2.35699 0.765834i −0.115561 0.0375481i
\(417\) 6.64591 30.5003i 0.325452 1.49361i
\(418\) −1.63430 + 1.63430i −0.0799363 + 0.0799363i
\(419\) 3.49605 + 2.54003i 0.170793 + 0.124088i 0.669898 0.742453i \(-0.266338\pi\)
−0.499105 + 0.866542i \(0.666338\pi\)
\(420\) 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
\(423\) 12.0219 4.47453i 0.584526 0.217559i
\(424\) 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
\(429\) 1.46532 0.384627i 0.0707464 0.0185700i
\(430\) 0 0
\(431\) −4.11469 + 5.66339i −0.198198 + 0.272796i −0.896535 0.442973i \(-0.853924\pi\)
0.698337 + 0.715769i \(0.253924\pi\)
\(432\) 1.68117 4.91667i 0.0808855 0.236553i
\(433\) 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
\(438\) 17.9959 1.79863i 0.859877 0.0859420i
\(439\) −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
\(441\) 20.5686 11.5970i 0.979456 0.552237i
\(442\) 1.37312 + 8.66953i 0.0653126 + 0.412368i
\(443\) 6.33032 + 6.33032i 0.300763 + 0.300763i 0.841312 0.540549i \(-0.181784\pi\)
−0.540549 + 0.841312i \(0.681784\pi\)
\(444\) −7.09108 + 4.55372i −0.336528 + 0.216110i
\(445\) 0 0
\(446\) −9.03387 12.4341i −0.427766 0.588770i
\(447\) −4.06161 + 6.95273i −0.192108 + 0.328853i
\(448\) −3.43597 1.75071i −0.162334 0.0827134i
\(449\) 18.3782 0.867322 0.433661 0.901076i \(-0.357221\pi\)
0.433661 + 0.901076i \(0.357221\pi\)
\(450\) 0 0
\(451\) −2.99298 −0.140934
\(452\) −1.56816 0.799015i −0.0737598 0.0375825i
\(453\) −12.8035 + 21.9171i −0.601559 + 1.02976i
\(454\) 8.24401 + 11.3469i 0.386911 + 0.532537i
\(455\) 0 0
\(456\) −9.54425 + 6.12908i −0.446950 + 0.287021i
\(457\) 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
\(459\) −18.2191 + 2.60034i −0.850394 + 0.121373i
\(460\) 0 0
\(461\) −0.133994 + 0.0435374i −0.00624074 + 0.00202774i −0.312136 0.950038i \(-0.601044\pi\)
0.305895 + 0.952065i \(0.401044\pi\)
\(462\) 2.34563 0.234438i 0.109129 0.0109071i
\(463\) 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 −0.266838 0.963742i \(-0.585979\pi\)
0.0440349 + 0.999030i \(0.485979\pi\)
\(468\) 7.42827 0.313305i 0.343372 0.0144825i
\(469\) 17.1621 23.6216i 0.792470 1.09074i
\(470\) 0 0
\(471\) −7.51602 + 1.97285i −0.346320 + 0.0909043i
\(472\) −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
\(477\) 4.60564 + 12.3742i 0.210878 + 0.566575i
\(478\) 0.380627 2.40319i 0.0174095 0.109919i
\(479\) 11.5308 8.37759i 0.526854 0.382782i −0.292326 0.956319i \(-0.594429\pi\)
0.819180 + 0.573537i \(0.194429\pi\)
\(480\) 0 0
\(481\) −9.75526 7.08761i −0.444802 0.323167i
\(482\) 1.14460 1.14460i 0.0521349 0.0521349i
\(483\) 11.1454 51.1501i 0.507135 2.32741i
\(484\) −10.3432 3.36070i −0.470144 0.152759i
\(485\) 0 0
\(486\) 0.418364 + 15.5828i 0.0189774 + 0.706852i
\(487\) 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
\(489\) 18.7102 + 1.07634i 0.846106 + 0.0486739i
\(490\) 0 0
\(491\) 5.09165 + 1.65438i 0.229783 + 0.0746610i 0.421645 0.906761i \(-0.361453\pi\)
−0.191862 + 0.981422i \(0.561453\pi\)
\(492\) −14.3517 3.12718i −0.647023 0.140984i
\(493\) 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
\(498\) 6.74174 + 7.56474i 0.302104 + 0.338984i
\(499\) 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 0.220400 0.975410i \(-0.429264\pi\)
−0.0918053 + 0.995777i \(0.529264\pi\)
\(504\) 11.4925 + 1.32665i 0.511917 + 0.0590936i
\(505\) 0 0
\(506\) 1.62591 2.23788i 0.0722807 0.0994859i
\(507\) −4.77599 10.8761i −0.212109 0.483025i
\(508\) −5.32741 + 0.843778i −0.236365 + 0.0374366i
\(509\) 3.24395 9.98385i 0.143786 0.442527i −0.853067 0.521801i \(-0.825260\pi\)
0.996853 + 0.0792745i \(0.0252604\pi\)
\(510\) 0 0
\(511\) 12.4429 + 38.2953i 0.550441 + 1.69408i
\(512\) −0.453990 0.891007i −0.0200637 0.0393773i
\(513\) 20.4205 27.2200i 0.901586 1.20179i
\(514\) 27.2321 8.84825i 1.20116 0.390280i
\(515\) 0 0
\(516\) 8.00965 9.78853i 0.352605 0.430916i
\(517\) 0.236073 + 1.49051i 0.0103825 + 0.0655524i
\(518\) −13.2673 13.2673i −0.582932 0.582932i
\(519\) −16.3030 25.3872i −0.715624 1.11437i
\(520\) 0 0
\(521\) −11.1471 15.3427i −0.488364 0.672175i 0.491722 0.870753i \(-0.336368\pi\)
−0.980085 + 0.198578i \(0.936368\pi\)
\(522\) −11.6389 14.6767i −0.509421 0.642381i
\(523\) −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
\(528\) 0.527829 + 0.308344i 0.0229708 + 0.0134190i
\(529\) −22.5886 31.0905i −0.982111 1.35176i
\(530\) 0 0
\(531\) 6.78604 1.37017i 0.294489 0.0594605i
\(532\) −17.8571 17.8571i −0.774205 0.774205i
\(533\) −3.28775 20.7580i −0.142408 0.899131i
\(534\) −2.74691 2.24771i −0.118870 0.0972680i
\(535\) 0 0
\(536\) 7.20094 2.33973i 0.311033 0.101061i
\(537\) 1.26584 + 12.6651i 0.0546251 + 0.546541i
\(538\) −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
\(543\) −1.06465 + 0.467516i −0.0456884 + 0.0200630i
\(544\) −2.08182 + 2.86537i −0.0892571 + 0.122852i
\(545\) 0 0
\(546\) 4.20261 + 16.0108i 0.179855 + 0.685198i
\(547\) −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
\(552\) 10.1347 9.03207i 0.431360 0.384430i
\(553\) −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 \(0.514160\pi\)
−0.999011 + 0.0444707i \(0.985840\pi\)
\(558\) −6.95759 + 10.4780i −0.294538 + 0.443570i
\(559\) 17.2114 + 5.59233i 0.727966 + 0.236530i
\(560\) 0 0
\(561\) 0.124345 2.16150i 0.00524983 0.0912587i
\(562\) 25.0016 12.7389i 1.05463 0.537359i
\(563\) −8.71723 + 4.44165i −0.367388 + 0.187193i −0.627931 0.778269i \(-0.716098\pi\)
0.260544 + 0.965462i \(0.416098\pi\)
\(564\) −0.425343 + 7.39381i −0.0179102 + 0.311336i
\(565\) 0 0
\(566\) 24.4163 + 7.93332i 1.02629 + 0.333462i
\(567\) −33.7003 + 8.29649i −1.41528 + 0.348420i
\(568\) 4.35851 4.35851i 0.182879 0.182879i
\(569\) −8.66014 6.29196i −0.363052 0.263773i 0.391272 0.920275i \(-0.372035\pi\)
−0.754324 + 0.656502i \(0.772035\pi\)
\(570\) 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
\(573\) −18.2199 + 16.2376i −0.761146 + 0.678337i
\(574\) 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
\(579\) −1.79938 6.85512i −0.0747795 0.284889i
\(580\) 0 0
\(581\) −13.2606 + 18.2516i −0.550140 + 0.757203i
\(582\) −11.1420 + 4.89277i −0.461852 + 0.202812i
\(583\) −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 \(0.0269315\pi\)
−0.517315 + 0.855795i \(0.673068\pi\)
\(588\) 1.35580 + 13.5652i 0.0559121 + 0.559418i
\(589\) 26.1121 8.48435i 1.07593 0.349592i
\(590\) 0 0
\(591\) 30.4830 + 24.9433i 1.25390 + 1.02603i
\(592\) −0.761135 4.80562i −0.0312825 0.197510i
\(593\) −5.46116 5.46116i −0.224263 0.224263i 0.586028 0.810291i \(-0.300691\pi\)
−0.810291 + 0.586028i \(0.800691\pi\)
\(594\) −1.80670 0.314580i −0.0741297 0.0129074i
\(595\) 0 0
\(596\) −2.73256 3.76105i −0.111930 0.154058i
\(597\) −9.44996 5.52043i −0.386761 0.225936i
\(598\) 17.3071 + 8.81838i 0.707738 + 0.360611i
\(599\) 20.6409 0.843363 0.421681 0.906744i \(-0.361440\pi\)
0.421681 + 0.906744i \(0.361440\pi\)
\(600\) 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
\(603\) −17.7975 + 14.1138i −0.724770 + 0.574758i
\(604\) −8.61387 11.8560i −0.350494 0.482413i
\(605\) 0 0
\(606\) −8.97244 13.9719i −0.364480 0.567571i
\(607\) −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
\(609\) 26.4104 32.2759i 1.07020 1.30789i
\(610\) 0 0
\(611\) −10.0782 + 3.27461i −0.407721 + 0.132477i
\(612\) 2.85467 10.2347i 0.115393 0.413715i
\(613\) 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 −0.904058 0.427410i \(-0.859426\pi\)
−0.727733 + 0.685861i \(0.759426\pi\)
\(618\) 4.63313 + 10.5508i 0.186372 + 0.424414i
\(619\) −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
\(621\) −19.0426 + 35.9998i −0.764155 + 1.44462i
\(622\) 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
\(627\) 2.66345 + 2.98859i 0.106368 + 0.119353i
\(628\) 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
\(633\) −7.03380 1.53264i −0.279569 0.0609171i
\(634\) 8.15891 + 2.65099i 0.324032 + 0.105284i
\(635\) 0 0
\(636\) −7.61046 0.437806i −0.301774 0.0173601i
\(637\) −17.3803 + 8.85568i −0.688631 + 0.350875i
\(638\) 1.96346 1.00043i 0.0777340 0.0396074i
\(639\) −7.69324 + 16.8152i −0.304340 + 0.665201i
\(640\) 0 0
\(641\) −28.1775 9.15543i −1.11294 0.361618i −0.305874 0.952072i \(-0.598949\pi\)
−0.807071 + 0.590454i \(0.798949\pi\)
\(642\) −5.44117 + 24.9713i −0.214746 + 0.985539i
\(643\) −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 −0.981559 0.191161i \(-0.938775\pi\)
0.992590 + 0.121513i \(0.0387747\pi\)
\(648\) −8.33463 3.39616i −0.327415 0.133414i
\(649\) 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 0.648404 0.761296i \(-0.275437\pi\)
0.381416 + 0.924404i \(0.375437\pi\)
\(654\) −18.6230 + 4.88829i −0.728218 + 0.191147i
\(655\) 0 0
\(656\) 4.98463 6.86076i 0.194617 0.267868i
\(657\) −1.32004 31.2973i −0.0514996 1.22102i
\(658\) −16.2860 + 2.57944i −0.634893 + 0.100557i
\(659\) 2.02081 6.21940i 0.0787195 0.242274i −0.903951 0.427637i \(-0.859346\pi\)
0.982670 + 0.185363i \(0.0593462\pi\)
\(660\) 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
\(663\) 15.1279 1.51198i 0.587518 0.0587206i
\(664\) −5.56392 + 1.80783i −0.215922 + 0.0701573i
\(665\) 0 0
\(666\) 7.16887 + 12.7148i 0.277788 + 0.492690i
\(667\) −7.65551 48.3350i −0.296422 1.87154i
\(668\) 11.8751 + 11.8751i 0.459461 + 0.459461i
\(669\) −22.3995 + 14.3844i −0.866015 + 0.556134i
\(670\) 0 0
\(671\) 0.0303252 + 0.0417390i 0.00117069 + 0.00161132i
\(672\) −3.36911 + 5.76730i −0.129966 + 0.222478i
\(673\) −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 −0.326008 0.945367i \(-0.605704\pi\)
−0.956441 + 0.291927i \(0.905704\pi\)
\(678\) −1.53764 + 2.63216i −0.0590528 + 0.101087i
\(679\) −15.9250 21.9189i −0.611147 0.841171i
\(680\) 0 0
\(681\) 20.4411 13.1267i 0.783303 0.503018i
\(682\) −1.04629 1.04629i −0.0400645 0.0400645i
\(683\) 5.33840 + 33.7054i 0.204268 + 1.28970i 0.850263 + 0.526358i \(0.176443\pi\)
−0.645995 + 0.763342i \(0.723557\pi\)
\(684\) 9.64894 + 17.1135i 0.368937 + 0.654352i
\(685\) 0 0
\(686\) −3.19397 + 1.03778i −0.121946 + 0.0396228i
\(687\) 29.8721 2.98562i 1.13969 0.113909i
\(688\) 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
\(693\) −0.172057 4.07936i −0.00653591 0.154962i
\(694\) 4.71830 6.49419i 0.179104 0.246516i
\(695\) 0 0
\(696\) 10.4603 2.74568i 0.396496 0.104075i
\(697\) −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 \(0.283170\pi\)
−0.629720 + 0.776822i \(0.716830\pi\)
\(702\) 0.197163 12.8761i 0.00744143 0.485976i
\(703\) 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
\(708\) −0.850963 + 3.90535i −0.0319812 + 0.146772i
\(709\) −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
\(711\) 1.70547 3.72768i 0.0639603 0.139799i
\(712\) 1.82585 0.930319i 0.0684268 0.0348652i
\(713\) −29.2785 + 14.9181i −1.09649 + 0.558689i
\(714\) 23.6176 + 1.35865i 0.883865 + 0.0508460i
\(715\) 0 0
\(716\) −6.98899 2.27086i −0.261191 0.0848660i
\(717\) −4.11771 0.897235i −0.153779 0.0335079i
\(718\) −10.6989 + 10.6989i −0.399281 + 0.399281i
\(719\) −29.8994 21.7232i −1.11506 0.810138i −0.131606 0.991302i \(-0.542013\pi\)
−0.983453 + 0.181164i \(0.942013\pi\)
\(720\) 0 0
\(721\) −20.7558 + 15.0800i −0.772985 + 0.561607i
\(722\) 3.73661 23.5920i 0.139062 0.878004i
\(723\) −1.86537 2.09309i −0.0693738 0.0778427i
\(724\) 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
\(729\) 26.9873 + 0.826673i 0.999531 + 0.0306175i
\(730\) 0 0
\(731\) 15.2020 20.9238i 0.562266 0.773893i
\(732\) 0.101802 + 0.231828i 0.00376271 + 0.00856862i
\(733\) −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
\(738\) −6.83513 + 24.5057i −0.251605 + 0.902068i
\(739\) 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
\(741\) −17.8019 + 21.7555i −0.653968 + 0.799209i
\(742\) −2.65502 16.7632i −0.0974689 0.615395i
\(743\) 19.3245 + 19.3245i 0.708947 + 0.708947i 0.966314 0.257367i \(-0.0828549\pi\)
−0.257367 + 0.966314i \(0.582855\pi\)
\(744\) −3.92387 6.11028i −0.143856 0.224014i
\(745\) 0 0
\(746\) 1.30299 + 1.79341i 0.0477059 + 0.0656615i
\(747\) 13.7515 10.9053i 0.503142 0.399002i
\(748\) 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
\(753\) 36.9797 + 21.6027i 1.34762 + 0.787245i
\(754\) 9.09541 + 12.5188i 0.331235 + 0.455906i
\(755\) 0 0
\(756\) 3.43725 19.7408i 0.125012 0.717966i
\(757\) 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
\(759\) −3.70798 3.03413i −0.134591 0.110132i
\(760\) 0 0
\(761\) 13.3455 4.33621i 0.483774 0.157188i −0.0569686 0.998376i \(-0.518143\pi\)
0.540742 + 0.841188i \(0.318143\pi\)
\(762\) 0.929110 + 9.29604i 0.0336581 + 0.336760i
\(763\) −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
\(768\) −1.58588 + 0.696404i −0.0572256 + 0.0251293i
\(769\) 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
\(771\) −12.5914 47.9697i −0.453468 1.72759i
\(772\) 4.04150 + 0.640111i 0.145457 + 0.0230381i
\(773\) 19.2486 37.7774i 0.692323 1.35876i −0.230324 0.973114i \(-0.573979\pi\)
0.922647 0.385646i \(-0.126021\pi\)
\(774\) −16.1295 14.8239i −0.579762 0.532836i
\(775\) 0 0
\(776\) 7.02576i 0.252210i
\(777\) −24.2615 + 21.6219i −0.870376 + 0.775683i
\(778\) −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