Properties

Label 1110.2.l.b.697.14
Level $1110$
Weight $2$
Character 1110.697
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 697.14
Character \(\chi\) \(=\) 1110.697
Dual form 1110.2.l.b.43.14

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(0.215025 - 2.22571i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.35684 - 1.35684i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(0.215025 - 2.22571i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.35684 - 1.35684i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(2.22571 + 0.215025i) q^{10} -0.0194198i q^{11} +(-0.707107 - 0.707107i) q^{12} +0.159054i q^{13} +(1.35684 - 1.35684i) q^{14} +(1.72586 - 1.42177i) q^{15} +1.00000 q^{16} -4.04014 q^{17} -1.00000 q^{18} +(-4.58811 - 4.58811i) q^{19} +(-0.215025 + 2.22571i) q^{20} -1.91886i q^{21} +0.0194198 q^{22} -2.53621i q^{23} +(0.707107 - 0.707107i) q^{24} +(-4.90753 - 0.957166i) q^{25} -0.159054 q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.35684 + 1.35684i) q^{28} +(-0.812030 + 0.812030i) q^{29} +(1.42177 + 1.72586i) q^{30} +(2.35628 + 2.35628i) q^{31} +1.00000i q^{32} +(0.0137318 - 0.0137318i) q^{33} -4.04014i q^{34} +(-3.31168 + 2.72817i) q^{35} -1.00000i q^{36} +(1.68369 - 5.84510i) q^{37} +(4.58811 - 4.58811i) q^{38} +(-0.112468 + 0.112468i) q^{39} +(-2.22571 - 0.215025i) q^{40} -8.21459i q^{41} +1.91886 q^{42} -4.36855i q^{43} +0.0194198i q^{44} +(2.22571 + 0.215025i) q^{45} +2.53621 q^{46} +(-5.16443 - 5.16443i) q^{47} +(0.707107 + 0.707107i) q^{48} -3.31797i q^{49} +(0.957166 - 4.90753i) q^{50} +(-2.85681 - 2.85681i) q^{51} -0.159054i q^{52} +(-4.20428 + 4.20428i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-0.0432227 - 0.00417574i) q^{55} +(-1.35684 + 1.35684i) q^{56} -6.48857i q^{57} +(-0.812030 - 0.812030i) q^{58} +(-3.16117 - 3.16117i) q^{59} +(-1.72586 + 1.42177i) q^{60} +(1.82280 + 1.82280i) q^{61} +(-2.35628 + 2.35628i) q^{62} +(1.35684 - 1.35684i) q^{63} -1.00000 q^{64} +(0.354008 + 0.0342007i) q^{65} +(0.0137318 + 0.0137318i) q^{66} +(-2.18514 + 2.18514i) q^{67} +4.04014 q^{68} +(1.79337 - 1.79337i) q^{69} +(-2.72817 - 3.31168i) q^{70} +4.70533 q^{71} +1.00000 q^{72} +(5.46673 + 5.46673i) q^{73} +(5.84510 + 1.68369i) q^{74} +(-2.79333 - 4.14696i) q^{75} +(4.58811 + 4.58811i) q^{76} +(-0.0263495 + 0.0263495i) q^{77} +(-0.112468 - 0.112468i) q^{78} +(4.93909 + 4.93909i) q^{79} +(0.215025 - 2.22571i) q^{80} -1.00000 q^{81} +8.21459 q^{82} +(6.36886 - 6.36886i) q^{83} +1.91886i q^{84} +(-0.868732 + 8.99216i) q^{85} +4.36855 q^{86} -1.14838 q^{87} -0.0194198 q^{88} +(-10.2334 + 10.2334i) q^{89} +(-0.215025 + 2.22571i) q^{90} +(0.215811 - 0.215811i) q^{91} +2.53621i q^{92} +3.33228i q^{93} +(5.16443 - 5.16443i) q^{94} +(-11.1983 + 9.22523i) q^{95} +(-0.707107 + 0.707107i) q^{96} +17.8376 q^{97} +3.31797 q^{98} +0.0194198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{4} - 4q^{7} + O(q^{10}) \) \( 40q - 40q^{4} - 4q^{7} + 4q^{14} + 40q^{16} + 24q^{17} - 40q^{18} + 4q^{19} + 8q^{22} + 8q^{25} + 8q^{26} + 4q^{28} + 28q^{31} - 4q^{33} + 20q^{35} + 20q^{37} - 4q^{38} + 4q^{39} + 16q^{42} - 16q^{47} + 16q^{51} + 20q^{53} + 16q^{55} - 4q^{56} - 4q^{59} - 8q^{61} - 28q^{62} + 4q^{63} - 40q^{64} - 4q^{65} - 4q^{66} + 16q^{67} - 24q^{68} - 8q^{69} + 12q^{70} + 40q^{71} + 40q^{72} + 8q^{73} - 8q^{74} + 16q^{75} - 4q^{76} - 24q^{77} + 4q^{78} - 12q^{79} - 40q^{81} - 24q^{82} - 8q^{83} - 8q^{85} + 8q^{87} - 8q^{88} + 12q^{89} - 24q^{91} + 16q^{94} - 28q^{95} + 40q^{97} - 56q^{98} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.707107 + 0.707107i 0.408248 + 0.408248i
\(4\) −1.00000 −0.500000
\(5\) 0.215025 2.22571i 0.0961622 0.995366i
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) −1.35684 1.35684i −0.512838 0.512838i 0.402557 0.915395i \(-0.368121\pi\)
−0.915395 + 0.402557i \(0.868121\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 1.00000i 0.333333i
\(10\) 2.22571 + 0.215025i 0.703830 + 0.0679969i
\(11\) 0.0194198i 0.00585528i −0.999996 0.00292764i \(-0.999068\pi\)
0.999996 0.00292764i \(-0.000931898\pi\)
\(12\) −0.707107 0.707107i −0.204124 0.204124i
\(13\) 0.159054i 0.0441137i 0.999757 + 0.0220569i \(0.00702148\pi\)
−0.999757 + 0.0220569i \(0.992979\pi\)
\(14\) 1.35684 1.35684i 0.362631 0.362631i
\(15\) 1.72586 1.42177i 0.445614 0.367098i
\(16\) 1.00000 0.250000
\(17\) −4.04014 −0.979877 −0.489939 0.871757i \(-0.662981\pi\)
−0.489939 + 0.871757i \(0.662981\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.58811 4.58811i −1.05259 1.05259i −0.998538 0.0540467i \(-0.982788\pi\)
−0.0540467 0.998538i \(-0.517212\pi\)
\(20\) −0.215025 + 2.22571i −0.0480811 + 0.497683i
\(21\) 1.91886i 0.418730i
\(22\) 0.0194198 0.00414031
\(23\) 2.53621i 0.528836i −0.964408 0.264418i \(-0.914820\pi\)
0.964408 0.264418i \(-0.0851799\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) −4.90753 0.957166i −0.981506 0.191433i
\(26\) −0.159054 −0.0311931
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) 1.35684 + 1.35684i 0.256419 + 0.256419i
\(29\) −0.812030 + 0.812030i −0.150790 + 0.150790i −0.778471 0.627681i \(-0.784004\pi\)
0.627681 + 0.778471i \(0.284004\pi\)
\(30\) 1.42177 + 1.72586i 0.259578 + 0.315097i
\(31\) 2.35628 + 2.35628i 0.423200 + 0.423200i 0.886304 0.463104i \(-0.153264\pi\)
−0.463104 + 0.886304i \(0.653264\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.0137318 0.0137318i 0.00239041 0.00239041i
\(34\) 4.04014i 0.692878i
\(35\) −3.31168 + 2.72817i −0.559777 + 0.461145i
\(36\) 1.00000i 0.166667i
\(37\) 1.68369 5.84510i 0.276797 0.960928i
\(38\) 4.58811 4.58811i 0.744290 0.744290i
\(39\) −0.112468 + 0.112468i −0.0180093 + 0.0180093i
\(40\) −2.22571 0.215025i −0.351915 0.0339985i
\(41\) 8.21459i 1.28290i −0.767164 0.641451i \(-0.778333\pi\)
0.767164 0.641451i \(-0.221667\pi\)
\(42\) 1.91886 0.296087
\(43\) 4.36855i 0.666197i −0.942892 0.333099i \(-0.891906\pi\)
0.942892 0.333099i \(-0.108094\pi\)
\(44\) 0.0194198i 0.00292764i
\(45\) 2.22571 + 0.215025i 0.331789 + 0.0320541i
\(46\) 2.53621 0.373944
\(47\) −5.16443 5.16443i −0.753309 0.753309i 0.221786 0.975095i \(-0.428811\pi\)
−0.975095 + 0.221786i \(0.928811\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 3.31797i 0.473995i
\(50\) 0.957166 4.90753i 0.135364 0.694029i
\(51\) −2.85681 2.85681i −0.400033 0.400033i
\(52\) 0.159054i 0.0220569i
\(53\) −4.20428 + 4.20428i −0.577502 + 0.577502i −0.934214 0.356712i \(-0.883898\pi\)
0.356712 + 0.934214i \(0.383898\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) −0.0432227 0.00417574i −0.00582814 0.000563057i
\(56\) −1.35684 + 1.35684i −0.181316 + 0.181316i
\(57\) 6.48857i 0.859432i
\(58\) −0.812030 0.812030i −0.106625 0.106625i
\(59\) −3.16117 3.16117i −0.411549 0.411549i 0.470729 0.882278i \(-0.343991\pi\)
−0.882278 + 0.470729i \(0.843991\pi\)
\(60\) −1.72586 + 1.42177i −0.222807 + 0.183549i
\(61\) 1.82280 + 1.82280i 0.233385 + 0.233385i 0.814104 0.580719i \(-0.197228\pi\)
−0.580719 + 0.814104i \(0.697228\pi\)
\(62\) −2.35628 + 2.35628i −0.299248 + 0.299248i
\(63\) 1.35684 1.35684i 0.170946 0.170946i
\(64\) −1.00000 −0.125000
\(65\) 0.354008 + 0.0342007i 0.0439093 + 0.00424207i
\(66\) 0.0137318 + 0.0137318i 0.00169027 + 0.00169027i
\(67\) −2.18514 + 2.18514i −0.266958 + 0.266958i −0.827873 0.560916i \(-0.810449\pi\)
0.560916 + 0.827873i \(0.310449\pi\)
\(68\) 4.04014 0.489939
\(69\) 1.79337 1.79337i 0.215896 0.215896i
\(70\) −2.72817 3.31168i −0.326079 0.395822i
\(71\) 4.70533 0.558420 0.279210 0.960230i \(-0.409927\pi\)
0.279210 + 0.960230i \(0.409927\pi\)
\(72\) 1.00000 0.117851
\(73\) 5.46673 + 5.46673i 0.639832 + 0.639832i 0.950514 0.310682i \(-0.100557\pi\)
−0.310682 + 0.950514i \(0.600557\pi\)
\(74\) 5.84510 + 1.68369i 0.679479 + 0.195725i
\(75\) −2.79333 4.14696i −0.322546 0.478850i
\(76\) 4.58811 + 4.58811i 0.526293 + 0.526293i
\(77\) −0.0263495 + 0.0263495i −0.00300281 + 0.00300281i
\(78\) −0.112468 0.112468i −0.0127345 0.0127345i
\(79\) 4.93909 + 4.93909i 0.555690 + 0.555690i 0.928078 0.372387i \(-0.121461\pi\)
−0.372387 + 0.928078i \(0.621461\pi\)
\(80\) 0.215025 2.22571i 0.0240406 0.248841i
\(81\) −1.00000 −0.111111
\(82\) 8.21459 0.907149
\(83\) 6.36886 6.36886i 0.699074 0.699074i −0.265137 0.964211i \(-0.585417\pi\)
0.964211 + 0.265137i \(0.0854172\pi\)
\(84\) 1.91886i 0.209365i
\(85\) −0.868732 + 8.99216i −0.0942272 + 0.975336i
\(86\) 4.36855 0.471073
\(87\) −1.14838 −0.123120
\(88\) −0.0194198 −0.00207015
\(89\) −10.2334 + 10.2334i −1.08474 + 1.08474i −0.0886823 + 0.996060i \(0.528266\pi\)
−0.996060 + 0.0886823i \(0.971734\pi\)
\(90\) −0.215025 + 2.22571i −0.0226656 + 0.234610i
\(91\) 0.215811 0.215811i 0.0226232 0.0226232i
\(92\) 2.53621i 0.264418i
\(93\) 3.33228i 0.345541i
\(94\) 5.16443 5.16443i 0.532670 0.532670i
\(95\) −11.1983 + 9.22523i −1.14893 + 0.946488i
\(96\) −0.707107 + 0.707107i −0.0721688 + 0.0721688i
\(97\) 17.8376 1.81114 0.905569 0.424198i \(-0.139444\pi\)
0.905569 + 0.424198i \(0.139444\pi\)
\(98\) 3.31797 0.335165
\(99\) 0.0194198 0.00195176
\(100\) 4.90753 + 0.957166i 0.490753 + 0.0957166i
\(101\) 0.190594i 0.0189648i 0.999955 + 0.00948241i \(0.00301839\pi\)
−0.999955 + 0.00948241i \(0.996982\pi\)
\(102\) 2.85681 2.85681i 0.282866 0.282866i
\(103\) −6.73625 −0.663743 −0.331871 0.943325i \(-0.607680\pi\)
−0.331871 + 0.943325i \(0.607680\pi\)
\(104\) 0.159054 0.0155966
\(105\) −4.27082 0.412604i −0.416790 0.0402660i
\(106\) −4.20428 4.20428i −0.408355 0.408355i
\(107\) −6.22156 6.22156i −0.601461 0.601461i 0.339239 0.940700i \(-0.389830\pi\)
−0.940700 + 0.339239i \(0.889830\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) 13.0168 + 13.0168i 1.24678 + 1.24678i 0.957132 + 0.289652i \(0.0935394\pi\)
0.289652 + 0.957132i \(0.406461\pi\)
\(110\) 0.00417574 0.0432227i 0.000398141 0.00412112i
\(111\) 5.32366 2.94256i 0.505299 0.279295i
\(112\) −1.35684 1.35684i −0.128209 0.128209i
\(113\) −9.74000 −0.916262 −0.458131 0.888885i \(-0.651481\pi\)
−0.458131 + 0.888885i \(0.651481\pi\)
\(114\) 6.48857 0.607710
\(115\) −5.64485 0.545349i −0.526385 0.0508541i
\(116\) 0.812030 0.812030i 0.0753951 0.0753951i
\(117\) −0.159054 −0.0147046
\(118\) 3.16117 3.16117i 0.291009 0.291009i
\(119\) 5.48182 + 5.48182i 0.502518 + 0.502518i
\(120\) −1.42177 1.72586i −0.129789 0.157548i
\(121\) 10.9996 0.999966
\(122\) −1.82280 + 1.82280i −0.165028 + 0.165028i
\(123\) 5.80859 5.80859i 0.523743 0.523743i
\(124\) −2.35628 2.35628i −0.211600 0.211600i
\(125\) −3.18561 + 10.7169i −0.284930 + 0.958548i
\(126\) 1.35684 + 1.35684i 0.120877 + 0.120877i
\(127\) −12.3217 12.3217i −1.09337 1.09337i −0.995166 0.0982049i \(-0.968690\pi\)
−0.0982049 0.995166i \(-0.531310\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 3.08903 3.08903i 0.271974 0.271974i
\(130\) −0.0342007 + 0.354008i −0.00299960 + 0.0310485i
\(131\) 2.08833 + 2.08833i 0.182458 + 0.182458i 0.792426 0.609968i \(-0.208818\pi\)
−0.609968 + 0.792426i \(0.708818\pi\)
\(132\) −0.0137318 + 0.0137318i −0.00119520 + 0.00119520i
\(133\) 12.4507i 1.07961i
\(134\) −2.18514 2.18514i −0.188767 0.188767i
\(135\) 1.42177 + 1.72586i 0.122366 + 0.148538i
\(136\) 4.04014i 0.346439i
\(137\) −3.35280 3.35280i −0.286449 0.286449i 0.549225 0.835674i \(-0.314923\pi\)
−0.835674 + 0.549225i \(0.814923\pi\)
\(138\) 1.79337 + 1.79337i 0.152662 + 0.152662i
\(139\) 20.9597 1.77778 0.888889 0.458123i \(-0.151478\pi\)
0.888889 + 0.458123i \(0.151478\pi\)
\(140\) 3.31168 2.72817i 0.279888 0.230573i
\(141\) 7.30360i 0.615074i
\(142\) 4.70533i 0.394862i
\(143\) 0.00308880 0.000258298
\(144\) 1.00000i 0.0833333i
\(145\) 1.63273 + 1.98195i 0.135591 + 0.164592i
\(146\) −5.46673 + 5.46673i −0.452429 + 0.452429i
\(147\) 2.34616 2.34616i 0.193508 0.193508i
\(148\) −1.68369 + 5.84510i −0.138399 + 0.480464i
\(149\) 6.54196i 0.535938i 0.963427 + 0.267969i \(0.0863525\pi\)
−0.963427 + 0.267969i \(0.913647\pi\)
\(150\) 4.14696 2.79333i 0.338598 0.228074i
\(151\) 14.2779i 1.16192i −0.813931 0.580961i \(-0.802677\pi\)
0.813931 0.580961i \(-0.197323\pi\)
\(152\) −4.58811 + 4.58811i −0.372145 + 0.372145i
\(153\) 4.04014i 0.326626i
\(154\) −0.0263495 0.0263495i −0.00212331 0.00212331i
\(155\) 5.75104 4.73772i 0.461935 0.380543i
\(156\) 0.112468 0.112468i 0.00900467 0.00900467i
\(157\) −0.0829263 0.0829263i −0.00661824 0.00661824i 0.703790 0.710408i \(-0.251490\pi\)
−0.710408 + 0.703790i \(0.751490\pi\)
\(158\) −4.93909 + 4.93909i −0.392933 + 0.392933i
\(159\) −5.94574 −0.471528
\(160\) 2.22571 + 0.215025i 0.175957 + 0.0169992i
\(161\) −3.44123 + 3.44123i −0.271207 + 0.271207i
\(162\) 1.00000i 0.0785674i
\(163\) −9.48615 −0.743012 −0.371506 0.928430i \(-0.621159\pi\)
−0.371506 + 0.928430i \(0.621159\pi\)
\(164\) 8.21459i 0.641451i
\(165\) −0.0276104 0.0335157i −0.00214946 0.00260920i
\(166\) 6.36886 + 6.36886i 0.494320 + 0.494320i
\(167\) −14.9171 −1.15432 −0.577161 0.816630i \(-0.695840\pi\)
−0.577161 + 0.816630i \(0.695840\pi\)
\(168\) −1.91886 −0.148043
\(169\) 12.9747 0.998054
\(170\) −8.99216 0.868732i −0.689667 0.0666287i
\(171\) 4.58811 4.58811i 0.350862 0.350862i
\(172\) 4.36855i 0.333099i
\(173\) −7.09005 7.09005i −0.539046 0.539046i 0.384203 0.923249i \(-0.374476\pi\)
−0.923249 + 0.384203i \(0.874476\pi\)
\(174\) 1.14838i 0.0870587i
\(175\) 5.36001 + 7.95746i 0.405179 + 0.601527i
\(176\) 0.0194198i 0.00146382i
\(177\) 4.47057i 0.336029i
\(178\) −10.2334 10.2334i −0.767029 0.767029i
\(179\) −12.4815 + 12.4815i −0.932912 + 0.932912i −0.997887 0.0649750i \(-0.979303\pi\)
0.0649750 + 0.997887i \(0.479303\pi\)
\(180\) −2.22571 0.215025i −0.165894 0.0160270i
\(181\) −3.65527 −0.271694 −0.135847 0.990730i \(-0.543376\pi\)
−0.135847 + 0.990730i \(0.543376\pi\)
\(182\) 0.215811 + 0.215811i 0.0159970 + 0.0159970i
\(183\) 2.57782i 0.190558i
\(184\) −2.53621 −0.186972
\(185\) −12.6474 5.00425i −0.929858 0.367919i
\(186\) −3.33228 −0.244335
\(187\) 0.0784585i 0.00573746i
\(188\) 5.16443 + 5.16443i 0.376655 + 0.376655i
\(189\) 1.91886 0.139577
\(190\) −9.22523 11.1983i −0.669268 0.812413i
\(191\) 6.33676 6.33676i 0.458512 0.458512i −0.439655 0.898167i \(-0.644899\pi\)
0.898167 + 0.439655i \(0.144899\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) 13.0970i 0.942746i 0.881934 + 0.471373i \(0.156241\pi\)
−0.881934 + 0.471373i \(0.843759\pi\)
\(194\) 17.8376i 1.28067i
\(195\) 0.226138 + 0.274505i 0.0161941 + 0.0196577i
\(196\) 3.31797i 0.236998i
\(197\) 0.639639 + 0.639639i 0.0455724 + 0.0455724i 0.729526 0.683953i \(-0.239741\pi\)
−0.683953 + 0.729526i \(0.739741\pi\)
\(198\) 0.0194198i 0.00138010i
\(199\) 9.39994 9.39994i 0.666344 0.666344i −0.290523 0.956868i \(-0.593829\pi\)
0.956868 + 0.290523i \(0.0938294\pi\)
\(200\) −0.957166 + 4.90753i −0.0676818 + 0.347015i
\(201\) −3.09026 −0.217970
\(202\) −0.190594 −0.0134102
\(203\) 2.20359 0.154662
\(204\) 2.85681 + 2.85681i 0.200017 + 0.200017i
\(205\) −18.2832 1.76634i −1.27696 0.123367i
\(206\) 6.73625i 0.469337i
\(207\) 2.53621 0.176279
\(208\) 0.159054i 0.0110284i
\(209\) −0.0891001 + 0.0891001i −0.00616318 + 0.00616318i
\(210\) 0.412604 4.27082i 0.0284724 0.294715i
\(211\) 2.64429 0.182041 0.0910203 0.995849i \(-0.470987\pi\)
0.0910203 + 0.995849i \(0.470987\pi\)
\(212\) 4.20428 4.20428i 0.288751 0.288751i
\(213\) 3.32717 + 3.32717i 0.227974 + 0.227974i
\(214\) 6.22156 6.22156i 0.425297 0.425297i
\(215\) −9.72310 0.939348i −0.663110 0.0640630i
\(216\) 0.707107 + 0.707107i 0.0481125 + 0.0481125i
\(217\) 6.39419i 0.434066i
\(218\) −13.0168 + 13.0168i −0.881609 + 0.881609i
\(219\) 7.73112i 0.522420i
\(220\) 0.0432227 + 0.00417574i 0.00291407 + 0.000281528i
\(221\) 0.642601i 0.0432260i
\(222\) 2.94256 + 5.32366i 0.197492 + 0.357301i
\(223\) −20.2192 + 20.2192i −1.35398 + 1.35398i −0.472813 + 0.881163i \(0.656761\pi\)
−0.881163 + 0.472813i \(0.843239\pi\)
\(224\) 1.35684 1.35684i 0.0906578 0.0906578i
\(225\) 0.957166 4.90753i 0.0638110 0.327169i
\(226\) 9.74000i 0.647895i
\(227\) 15.0931 1.00177 0.500884 0.865515i \(-0.333008\pi\)
0.500884 + 0.865515i \(0.333008\pi\)
\(228\) 6.48857i 0.429716i
\(229\) 4.42655i 0.292514i 0.989247 + 0.146257i \(0.0467227\pi\)
−0.989247 + 0.146257i \(0.953277\pi\)
\(230\) 0.545349 5.64485i 0.0359593 0.372211i
\(231\) −0.0372639 −0.00245178
\(232\) 0.812030 + 0.812030i 0.0533124 + 0.0533124i
\(233\) 0.899214 + 0.899214i 0.0589095 + 0.0589095i 0.735948 0.677038i \(-0.236737\pi\)
−0.677038 + 0.735948i \(0.736737\pi\)
\(234\) 0.159054i 0.0103977i
\(235\) −12.6050 + 10.3840i −0.822258 + 0.677378i
\(236\) 3.16117 + 3.16117i 0.205775 + 0.205775i
\(237\) 6.98492i 0.453719i
\(238\) −5.48182 + 5.48182i −0.355334 + 0.355334i
\(239\) 7.43447 + 7.43447i 0.480896 + 0.480896i 0.905418 0.424522i \(-0.139558\pi\)
−0.424522 + 0.905418i \(0.639558\pi\)
\(240\) 1.72586 1.42177i 0.111404 0.0917746i
\(241\) 18.1472 18.1472i 1.16897 1.16897i 0.186514 0.982452i \(-0.440281\pi\)
0.982452 0.186514i \(-0.0597190\pi\)
\(242\) 10.9996i 0.707083i
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) −1.82280 1.82280i −0.116693 0.116693i
\(245\) −7.38481 0.713446i −0.471798 0.0455804i
\(246\) 5.80859 + 5.80859i 0.370342 + 0.370342i
\(247\) 0.729759 0.729759i 0.0464334 0.0464334i
\(248\) 2.35628 2.35628i 0.149624 0.149624i
\(249\) 9.00693 0.570791
\(250\) −10.7169 3.18561i −0.677796 0.201476i
\(251\) −18.2937 18.2937i −1.15469 1.15469i −0.985601 0.169089i \(-0.945918\pi\)
−0.169089 0.985601i \(-0.554082\pi\)
\(252\) −1.35684 + 1.35684i −0.0854729 + 0.0854729i
\(253\) −0.0492526 −0.00309648
\(254\) 12.3217 12.3217i 0.773130 0.773130i
\(255\) −6.97270 + 5.74413i −0.436647 + 0.359711i
\(256\) 1.00000 0.0625000
\(257\) 7.10286 0.443064 0.221532 0.975153i \(-0.428894\pi\)
0.221532 + 0.975153i \(0.428894\pi\)
\(258\) 3.08903 + 3.08903i 0.192315 + 0.192315i
\(259\) −10.2154 + 5.64637i −0.634752 + 0.350848i
\(260\) −0.354008 0.0342007i −0.0219546 0.00212104i
\(261\) −0.812030 0.812030i −0.0502634 0.0502634i
\(262\) −2.08833 + 2.08833i −0.129017 + 0.129017i
\(263\) −15.7333 15.7333i −0.970154 0.970154i 0.0294131 0.999567i \(-0.490636\pi\)
−0.999567 + 0.0294131i \(0.990636\pi\)
\(264\) −0.0137318 0.0137318i −0.000845137 0.000845137i
\(265\) 8.45345 + 10.2615i 0.519292 + 0.630359i
\(266\) −12.4507 −0.763400
\(267\) −14.4723 −0.885688
\(268\) 2.18514 2.18514i 0.133479 0.133479i
\(269\) 8.36958i 0.510302i 0.966901 + 0.255151i \(0.0821252\pi\)
−0.966901 + 0.255151i \(0.917875\pi\)
\(270\) −1.72586 + 1.42177i −0.105032 + 0.0865259i
\(271\) 2.13823 0.129888 0.0649441 0.997889i \(-0.479313\pi\)
0.0649441 + 0.997889i \(0.479313\pi\)
\(272\) −4.04014 −0.244969
\(273\) 0.305203 0.0184717
\(274\) 3.35280 3.35280i 0.202550 0.202550i
\(275\) −0.0185879 + 0.0953031i −0.00112089 + 0.00574699i
\(276\) −1.79337 + 1.79337i −0.107948 + 0.107948i
\(277\) 8.76961i 0.526915i 0.964671 + 0.263457i \(0.0848628\pi\)
−0.964671 + 0.263457i \(0.915137\pi\)
\(278\) 20.9597i 1.25708i
\(279\) −2.35628 + 2.35628i −0.141067 + 0.141067i
\(280\) 2.72817 + 3.31168i 0.163040 + 0.197911i
\(281\) −1.22380 + 1.22380i −0.0730057 + 0.0730057i −0.742667 0.669661i \(-0.766439\pi\)
0.669661 + 0.742667i \(0.266439\pi\)
\(282\) 7.30360 0.434923
\(283\) 11.8050 0.701734 0.350867 0.936425i \(-0.385887\pi\)
0.350867 + 0.936425i \(0.385887\pi\)
\(284\) −4.70533 −0.279210
\(285\) −14.4416 1.39521i −0.855449 0.0826449i
\(286\) 0.00308880i 0.000182644i
\(287\) −11.1459 + 11.1459i −0.657921 + 0.657921i
\(288\) −1.00000 −0.0589256
\(289\) −0.677286 −0.0398403
\(290\) −1.98195 + 1.63273i −0.116384 + 0.0958773i
\(291\) 12.6131 + 12.6131i 0.739394 + 0.739394i
\(292\) −5.46673 5.46673i −0.319916 0.319916i
\(293\) 11.7733 11.7733i 0.687802 0.687802i −0.273944 0.961746i \(-0.588328\pi\)
0.961746 + 0.273944i \(0.0883283\pi\)
\(294\) 2.34616 + 2.34616i 0.136831 + 0.136831i
\(295\) −7.71556 + 6.35610i −0.449217 + 0.370067i
\(296\) −5.84510 1.68369i −0.339739 0.0978626i
\(297\) 0.0137318 + 0.0137318i 0.000796803 + 0.000796803i
\(298\) −6.54196 −0.378966
\(299\) 0.403395 0.0233289
\(300\) 2.79333 + 4.14696i 0.161273 + 0.239425i
\(301\) −5.92743 + 5.92743i −0.341651 + 0.341651i
\(302\) 14.2779 0.821604
\(303\) −0.134770 + 0.134770i −0.00774236 + 0.00774236i
\(304\) −4.58811 4.58811i −0.263146 0.263146i
\(305\) 4.44895 3.66506i 0.254746 0.209861i
\(306\) 4.04014 0.230959
\(307\) 5.74100 5.74100i 0.327656 0.327656i −0.524038 0.851695i \(-0.675575\pi\)
0.851695 + 0.524038i \(0.175575\pi\)
\(308\) 0.0263495 0.0263495i 0.00150140 0.00150140i
\(309\) −4.76325 4.76325i −0.270972 0.270972i
\(310\) 4.73772 + 5.75104i 0.269085 + 0.326637i
\(311\) 4.78072 + 4.78072i 0.271090 + 0.271090i 0.829539 0.558449i \(-0.188603\pi\)
−0.558449 + 0.829539i \(0.688603\pi\)
\(312\) 0.112468 + 0.112468i 0.00636727 + 0.00636727i
\(313\) 2.04383i 0.115524i 0.998330 + 0.0577621i \(0.0183965\pi\)
−0.998330 + 0.0577621i \(0.981604\pi\)
\(314\) 0.0829263 0.0829263i 0.00467980 0.00467980i
\(315\) −2.72817 3.31168i −0.153715 0.186592i
\(316\) −4.93909 4.93909i −0.277845 0.277845i
\(317\) −18.6699 + 18.6699i −1.04861 + 1.04861i −0.0498508 + 0.998757i \(0.515875\pi\)
−0.998757 + 0.0498508i \(0.984125\pi\)
\(318\) 5.94574i 0.333421i
\(319\) 0.0157694 + 0.0157694i 0.000882919 + 0.000882919i
\(320\) −0.215025 + 2.22571i −0.0120203 + 0.124421i
\(321\) 8.79861i 0.491091i
\(322\) −3.44123 3.44123i −0.191772 0.191772i
\(323\) 18.5366 + 18.5366i 1.03140 + 1.03140i
\(324\) 1.00000 0.0555556
\(325\) 0.152241 0.780563i 0.00844482 0.0432979i
\(326\) 9.48615i 0.525389i
\(327\) 18.4085i 1.01799i
\(328\) −8.21459 −0.453575
\(329\) 14.0146i 0.772651i
\(330\) 0.0335157 0.0276104i 0.00184498 0.00151990i
\(331\) 2.59788 2.59788i 0.142792 0.142792i −0.632097 0.774889i \(-0.717806\pi\)
0.774889 + 0.632097i \(0.217806\pi\)
\(332\) −6.36886 + 6.36886i −0.349537 + 0.349537i
\(333\) 5.84510 + 1.68369i 0.320309 + 0.0922657i
\(334\) 14.9171i 0.816229i
\(335\) 4.39362 + 5.33334i 0.240049 + 0.291392i
\(336\) 1.91886i 0.104683i
\(337\) 4.86472 4.86472i 0.264998 0.264998i −0.562083 0.827081i \(-0.690000\pi\)
0.827081 + 0.562083i \(0.190000\pi\)
\(338\) 12.9747i 0.705731i
\(339\) −6.88722 6.88722i −0.374062 0.374062i
\(340\) 0.868732 8.99216i 0.0471136 0.487668i
\(341\) 0.0457584 0.0457584i 0.00247796 0.00247796i
\(342\) 4.58811 + 4.58811i 0.248097 + 0.248097i
\(343\) −13.9998 + 13.9998i −0.755920 + 0.755920i
\(344\) −4.36855 −0.235536
\(345\) −3.60590 4.37714i −0.194135 0.235657i
\(346\) 7.09005 7.09005i 0.381163 0.381163i
\(347\) 3.00444i 0.161287i 0.996743 + 0.0806435i \(0.0256975\pi\)
−0.996743 + 0.0806435i \(0.974302\pi\)
\(348\) 1.14838 0.0615598
\(349\) 19.3862i 1.03772i −0.854860 0.518859i \(-0.826357\pi\)
0.854860 0.518859i \(-0.173643\pi\)
\(350\) −7.95746 + 5.36001i −0.425344 + 0.286505i
\(351\) −0.112468 0.112468i −0.00600312 0.00600312i
\(352\) 0.0194198 0.00103508
\(353\) 17.9551 0.955651 0.477826 0.878455i \(-0.341425\pi\)
0.477826 + 0.878455i \(0.341425\pi\)
\(354\) 4.47057 0.237608
\(355\) 1.01176 10.4727i 0.0536989 0.555832i
\(356\) 10.2334 10.2334i 0.542371 0.542371i
\(357\) 7.75247i 0.410304i
\(358\) −12.4815 12.4815i −0.659668 0.659668i
\(359\) 14.6602i 0.773734i −0.922136 0.386867i \(-0.873557\pi\)
0.922136 0.386867i \(-0.126443\pi\)
\(360\) 0.215025 2.22571i 0.0113328 0.117305i
\(361\) 23.1015i 1.21587i
\(362\) 3.65527i 0.192117i
\(363\) 7.77791 + 7.77791i 0.408234 + 0.408234i
\(364\) −0.215811 + 0.215811i −0.0113116 + 0.0113116i
\(365\) 13.3428 10.9918i 0.698394 0.575339i
\(366\) −2.57782 −0.134745
\(367\) −14.1413 14.1413i −0.738172 0.738172i 0.234052 0.972224i \(-0.424801\pi\)
−0.972224 + 0.234052i \(0.924801\pi\)
\(368\) 2.53621i 0.132209i
\(369\) 8.21459 0.427634
\(370\) 5.00425 12.6474i 0.260158 0.657509i
\(371\) 11.4091 0.592329
\(372\) 3.33228i 0.172771i
\(373\) 13.0549 + 13.0549i 0.675958 + 0.675958i 0.959083 0.283125i \(-0.0913713\pi\)
−0.283125 + 0.959083i \(0.591371\pi\)
\(374\) −0.0784585 −0.00405699
\(375\) −9.83056 + 5.32542i −0.507648 + 0.275004i
\(376\) −5.16443 + 5.16443i −0.266335 + 0.266335i
\(377\) −0.129157 0.129157i −0.00665191 0.00665191i
\(378\) 1.91886i 0.0986957i
\(379\) 23.0708i 1.18507i −0.805545 0.592534i \(-0.798128\pi\)
0.805545 0.592534i \(-0.201872\pi\)
\(380\) 11.1983 9.22523i 0.574463 0.473244i
\(381\) 17.4255i 0.892734i
\(382\) 6.33676 + 6.33676i 0.324217 + 0.324217i
\(383\) 12.0188i 0.614132i −0.951688 0.307066i \(-0.900653\pi\)
0.951688 0.307066i \(-0.0993472\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) 0.0529805 + 0.0643121i 0.00270014 + 0.00327765i
\(386\) −13.0970 −0.666622
\(387\) 4.36855 0.222066
\(388\) −17.8376 −0.905569
\(389\) −0.966160 0.966160i −0.0489862 0.0489862i 0.682189 0.731176i \(-0.261028\pi\)
−0.731176 + 0.682189i \(0.761028\pi\)
\(390\) −0.274505 + 0.226138i −0.0139001 + 0.0114509i
\(391\) 10.2466i 0.518195i
\(392\) −3.31797 −0.167583
\(393\) 2.95334i 0.148976i
\(394\) −0.639639 + 0.639639i −0.0322246 + 0.0322246i
\(395\) 12.0550 9.93092i 0.606552 0.499679i
\(396\) −0.0194198 −0.000975880
\(397\) −2.34748 + 2.34748i −0.117817 + 0.117817i −0.763557 0.645740i \(-0.776549\pi\)
0.645740 + 0.763557i \(0.276549\pi\)
\(398\) 9.39994 + 9.39994i 0.471177 + 0.471177i
\(399\) −8.80396 + 8.80396i −0.440749 + 0.440749i
\(400\) −4.90753 0.957166i −0.245376 0.0478583i
\(401\) 25.6841 + 25.6841i 1.28260 + 1.28260i 0.939181 + 0.343421i \(0.111586\pi\)
0.343421 + 0.939181i \(0.388414\pi\)
\(402\) 3.09026i 0.154128i
\(403\) −0.374776 + 0.374776i −0.0186689 + 0.0186689i
\(404\) 0.190594i 0.00948241i
\(405\) −0.215025 + 2.22571i −0.0106847 + 0.110596i
\(406\) 2.20359i 0.109362i
\(407\) −0.113510 0.0326969i −0.00562650 0.00162073i
\(408\) −2.85681 + 2.85681i −0.141433 + 0.141433i
\(409\) −2.09660 + 2.09660i −0.103670 + 0.103670i −0.757039 0.653369i \(-0.773355\pi\)
0.653369 + 0.757039i \(0.273355\pi\)
\(410\) 1.76634 18.2832i 0.0872335 0.902945i
\(411\) 4.74157i 0.233885i
\(412\) 6.73625 0.331871
\(413\) 8.57841i 0.422116i
\(414\) 2.53621i 0.124648i
\(415\) −12.8057 15.5447i −0.628609 0.763058i
\(416\) −0.159054 −0.00779828
\(417\) 14.8207 + 14.8207i 0.725775 + 0.725775i
\(418\) −0.0891001 0.0891001i −0.00435803 0.00435803i
\(419\) 24.3693i 1.19052i 0.803534 + 0.595259i \(0.202951\pi\)
−0.803534 + 0.595259i \(0.797049\pi\)
\(420\) 4.27082 + 0.412604i 0.208395 + 0.0201330i
\(421\) −20.8544 20.8544i −1.01638 1.01638i −0.999864 0.0165195i \(-0.994741\pi\)
−0.0165195 0.999864i \(-0.505259\pi\)
\(422\) 2.64429i 0.128722i
\(423\) 5.16443 5.16443i 0.251103 0.251103i
\(424\) 4.20428 + 4.20428i 0.204178 + 0.204178i
\(425\) 19.8271 + 3.86708i 0.961755 + 0.187581i
\(426\) −3.32717 + 3.32717i −0.161202 + 0.161202i
\(427\) 4.94649i 0.239377i
\(428\) 6.22156 + 6.22156i 0.300730 + 0.300730i
\(429\) 0.00218411 + 0.00218411i 0.000105450 + 0.000105450i
\(430\) 0.939348 9.72310i 0.0452994 0.468890i
\(431\) 15.2684 + 15.2684i 0.735455 + 0.735455i 0.971695 0.236240i \(-0.0759152\pi\)
−0.236240 + 0.971695i \(0.575915\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) 12.7638 12.7638i 0.613390 0.613390i −0.330438 0.943828i \(-0.607196\pi\)
0.943828 + 0.330438i \(0.107196\pi\)
\(434\) 6.39419 0.306931
\(435\) −0.246931 + 2.55596i −0.0118395 + 0.122549i
\(436\) −13.0168 13.0168i −0.623392 0.623392i
\(437\) −11.6364 + 11.6364i −0.556645 + 0.556645i
\(438\) −7.73112 −0.369407
\(439\) −11.8601 + 11.8601i −0.566050 + 0.566050i −0.931020 0.364969i \(-0.881080\pi\)
0.364969 + 0.931020i \(0.381080\pi\)
\(440\) −0.00417574 + 0.0432227i −0.000199071 + 0.00206056i
\(441\) 3.31797 0.157998
\(442\) 0.642601 0.0305654
\(443\) 1.27875 + 1.27875i 0.0607553 + 0.0607553i 0.736832 0.676076i \(-0.236321\pi\)
−0.676076 + 0.736832i \(0.736321\pi\)
\(444\) −5.32366 + 2.94256i −0.252650 + 0.139648i
\(445\) 20.5762 + 24.9771i 0.975404 + 1.18403i
\(446\) −20.2192 20.2192i −0.957405 0.957405i
\(447\) −4.62587 + 4.62587i −0.218796 + 0.218796i
\(448\) 1.35684 + 1.35684i 0.0641047 + 0.0641047i
\(449\) 8.61386 + 8.61386i 0.406513 + 0.406513i 0.880521 0.474008i \(-0.157193\pi\)
−0.474008 + 0.880521i \(0.657193\pi\)
\(450\) 4.90753 + 0.957166i 0.231343 + 0.0451212i
\(451\) −0.159525 −0.00751175
\(452\) 9.74000 0.458131
\(453\) 10.0960 10.0960i 0.474353 0.474353i
\(454\) 15.0931i 0.708357i
\(455\) −0.433927 0.526737i −0.0203428 0.0246938i
\(456\) −6.48857 −0.303855
\(457\) −22.6986 −1.06179 −0.530897 0.847436i \(-0.678145\pi\)
−0.530897 + 0.847436i \(0.678145\pi\)
\(458\) −4.42655 −0.206839
\(459\) 2.85681 2.85681i 0.133344 0.133344i
\(460\) 5.64485 + 0.545349i 0.263193 + 0.0254270i
\(461\) 0.105452 0.105452i 0.00491138 0.00491138i −0.704647 0.709558i \(-0.748895\pi\)
0.709558 + 0.704647i \(0.248895\pi\)
\(462\) 0.0372639i 0.00173367i
\(463\) 38.4038i 1.78478i 0.451270 + 0.892388i \(0.350971\pi\)
−0.451270 + 0.892388i \(0.649029\pi\)
\(464\) −0.812030 + 0.812030i −0.0376975 + 0.0376975i
\(465\) 7.41668 + 0.716525i 0.343940 + 0.0332280i
\(466\) −0.899214 + 0.899214i −0.0416553 + 0.0416553i
\(467\) −18.3192 −0.847713 −0.423857 0.905729i \(-0.639324\pi\)
−0.423857 + 0.905729i \(0.639324\pi\)
\(468\) 0.159054 0.00735228
\(469\) 5.92978 0.273812
\(470\) −10.3840 12.6050i −0.478979 0.581424i
\(471\) 0.117276i 0.00540377i
\(472\) −3.16117 + 3.16117i −0.145505 + 0.145505i
\(473\) −0.0848362 −0.00390077
\(474\) −6.98492 −0.320828
\(475\) 18.1247 + 26.9079i 0.831619 + 1.23462i
\(476\) −5.48182 5.48182i −0.251259 0.251259i
\(477\) −4.20428 4.20428i −0.192501 0.192501i
\(478\) −7.43447 + 7.43447i −0.340045 + 0.340045i
\(479\) −10.0271 10.0271i −0.458149 0.458149i 0.439899 0.898047i \(-0.355014\pi\)
−0.898047 + 0.439899i \(0.855014\pi\)
\(480\) 1.42177 + 1.72586i 0.0648944 + 0.0787742i
\(481\) 0.929688 + 0.267798i 0.0423901 + 0.0122106i
\(482\) 18.1472 + 18.1472i 0.826584 + 0.826584i
\(483\) −4.86664 −0.221440
\(484\) −10.9996 −0.499983
\(485\) 3.83554 39.7013i 0.174163 1.80275i
\(486\) 0.707107 0.707107i 0.0320750 0.0320750i
\(487\) 1.88010 0.0851955 0.0425977 0.999092i \(-0.486437\pi\)
0.0425977 + 0.999092i \(0.486437\pi\)
\(488\) 1.82280 1.82280i 0.0825141 0.0825141i
\(489\) −6.70772 6.70772i −0.303334 0.303334i
\(490\) 0.713446 7.38481i 0.0322302 0.333612i
\(491\) 3.90817 0.176373 0.0881867 0.996104i \(-0.471893\pi\)
0.0881867 + 0.996104i \(0.471893\pi\)
\(492\) −5.80859 + 5.80859i −0.261871 + 0.261871i
\(493\) 3.28071 3.28071i 0.147756 0.147756i
\(494\) 0.729759 + 0.729759i 0.0328334 + 0.0328334i
\(495\) 0.00417574 0.0432227i 0.000187686 0.00194271i
\(496\) 2.35628 + 2.35628i 0.105800 + 0.105800i
\(497\) −6.38438 6.38438i −0.286379 0.286379i
\(498\) 9.00693i 0.403610i
\(499\) 9.78694 9.78694i 0.438124 0.438124i −0.453257 0.891380i \(-0.649738\pi\)
0.891380 + 0.453257i \(0.149738\pi\)
\(500\) 3.18561 10.7169i 0.142465 0.479274i
\(501\) −10.5480 10.5480i −0.471250 0.471250i
\(502\) 18.2937 18.2937i 0.816489 0.816489i
\(503\) 29.6653i 1.32271i −0.750073 0.661355i \(-0.769982\pi\)
0.750073 0.661355i \(-0.230018\pi\)
\(504\) −1.35684 1.35684i −0.0604385 0.0604385i
\(505\) 0.424206 + 0.0409825i 0.0188769 + 0.00182370i
\(506\) 0.0492526i 0.00218954i
\(507\) 9.17450 + 9.17450i 0.407454 + 0.407454i
\(508\) 12.3217 + 12.3217i 0.546686 + 0.546686i
\(509\) 9.99725 0.443120 0.221560 0.975147i \(-0.428885\pi\)
0.221560 + 0.975147i \(0.428885\pi\)
\(510\) −5.74413 6.97270i −0.254354 0.308756i
\(511\) 14.8350i 0.656260i
\(512\) 1.00000i 0.0441942i
\(513\) 6.48857 0.286477
\(514\) 7.10286i 0.313294i
\(515\) −1.44846 + 14.9929i −0.0638269 + 0.660667i
\(516\) −3.08903 + 3.08903i −0.135987 + 0.135987i
\(517\) −0.100292 + 0.100292i −0.00441084 + 0.00441084i
\(518\) −5.64637 10.2154i −0.248087 0.448838i
\(519\) 10.0268i 0.440129i
\(520\) 0.0342007 0.354008i 0.00149980 0.0155243i
\(521\) 34.5888i 1.51536i −0.652625 0.757681i \(-0.726332\pi\)
0.652625 0.757681i \(-0.273668\pi\)
\(522\) 0.812030 0.812030i 0.0355416 0.0355416i
\(523\) 26.2205i 1.14654i −0.819366 0.573271i \(-0.805674\pi\)
0.819366 0.573271i \(-0.194326\pi\)
\(524\) −2.08833 2.08833i −0.0912291 0.0912291i
\(525\) −1.83667 + 9.41687i −0.0801588 + 0.410986i
\(526\) 15.7333 15.7333i 0.686003 0.686003i
\(527\) −9.51969 9.51969i −0.414684 0.414684i
\(528\) 0.0137318 0.0137318i 0.000597602 0.000597602i
\(529\) 16.5676 0.720332
\(530\) −10.2615 + 8.45345i −0.445731 + 0.367195i
\(531\) 3.16117 3.16117i 0.137183 0.137183i
\(532\) 12.4507i 0.539805i
\(533\) 1.30656 0.0565936
\(534\) 14.4723i 0.626276i
\(535\) −15.1851 + 12.5096i −0.656511 + 0.540836i
\(536\) 2.18514 + 2.18514i 0.0943837 + 0.0943837i
\(537\) −17.6515 −0.761719
\(538\) −8.36958 −0.360838
\(539\) −0.0644341 −0.00277537
\(540\) −1.42177 1.72586i −0.0611830 0.0742691i
\(541\) 30.0077 30.0077i 1.29013 1.29013i 0.355429 0.934703i \(-0.384335\pi\)
0.934703 0.355429i \(-0.115665\pi\)
\(542\) 2.13823i 0.0918449i
\(543\) −2.58467 2.58467i −0.110919 0.110919i
\(544\) 4.04014i 0.173219i
\(545\) 31.7705 26.1726i 1.36090 1.12111i
\(546\) 0.305203i 0.0130615i
\(547\) 22.2754i 0.952429i −0.879329 0.476214i \(-0.842009\pi\)
0.879329 0.476214i \(-0.157991\pi\)
\(548\) 3.35280 + 3.35280i 0.143225 + 0.143225i
\(549\) −1.82280 + 1.82280i −0.0777950 + 0.0777950i
\(550\) −0.0953031 0.0185879i −0.00406374 0.000792592i
\(551\) 7.45137 0.317439
\(552\) −1.79337 1.79337i −0.0763309 0.0763309i
\(553\) 13.4031i 0.569958i
\(554\) −8.76961 −0.372585
\(555\) −5.40455 12.4816i −0.229410 0.529815i
\(556\) −20.9597 −0.888889
\(557\) 6.61666i 0.280357i 0.990126 + 0.140178i \(0.0447676\pi\)
−0.990126 + 0.140178i \(0.955232\pi\)
\(558\) −2.35628 2.35628i −0.0997492 0.0997492i
\(559\) 0.694836 0.0293884
\(560\) −3.31168 + 2.72817i −0.139944 + 0.115286i
\(561\) −0.0554786 + 0.0554786i −0.00234231 + 0.00234231i
\(562\) −1.22380 1.22380i −0.0516228 0.0516228i
\(563\) 2.52225i 0.106300i −0.998587 0.0531501i \(-0.983074\pi\)
0.998587 0.0531501i \(-0.0169262\pi\)
\(564\) 7.30360i 0.307537i
\(565\) −2.09435 + 21.6784i −0.0881098 + 0.912016i
\(566\) 11.8050i 0.496201i
\(567\) 1.35684 + 1.35684i 0.0569820 + 0.0569820i
\(568\) 4.70533i 0.197431i
\(569\) 30.3659 30.3659i 1.27301 1.27301i 0.328503 0.944503i \(-0.393456\pi\)
0.944503 0.328503i \(-0.106544\pi\)
\(570\) 1.39521 14.4416i 0.0584388 0.604894i
\(571\) −18.8014 −0.786812 −0.393406 0.919365i \(-0.628703\pi\)
−0.393406 + 0.919365i \(0.628703\pi\)
\(572\) −0.00308880 −0.000129149
\(573\) 8.96153 0.374373
\(574\) −11.1459 11.1459i −0.465220 0.465220i
\(575\) −2.42757 + 12.4465i −0.101237 + 0.519056i
\(576\) 1.00000i 0.0416667i
\(577\) −24.0197 −0.999955 −0.499977 0.866039i \(-0.666658\pi\)
−0.499977 + 0.866039i \(0.666658\pi\)
\(578\) 0.677286i 0.0281714i
\(579\) −9.26101 + 9.26101i −0.384874 + 0.384874i
\(580\) −1.63273 1.98195i −0.0677955 0.0822958i
\(581\) −17.2831 −0.717023
\(582\) −12.6131 + 12.6131i −0.522831 + 0.522831i
\(583\) 0.0816461 + 0.0816461i 0.00338143 + 0.00338143i
\(584\) 5.46673 5.46673i 0.226215 0.226215i
\(585\) −0.0342007 + 0.354008i −0.00141402 + 0.0146364i
\(586\) 11.7733 + 11.7733i 0.486349 + 0.486349i
\(587\) 4.20338i 0.173492i 0.996230 + 0.0867461i \(0.0276469\pi\)
−0.996230 + 0.0867461i \(0.972353\pi\)
\(588\) −2.34616 + 2.34616i −0.0967538 + 0.0967538i
\(589\) 21.6217i 0.890908i
\(590\) −6.35610 7.71556i −0.261677 0.317645i
\(591\) 0.904587i 0.0372097i
\(592\) 1.68369 5.84510i 0.0691993 0.240232i
\(593\) 23.2834 23.2834i 0.956134 0.956134i −0.0429431 0.999078i \(-0.513673\pi\)
0.999078 + 0.0429431i \(0.0136734\pi\)
\(594\) −0.0137318 + 0.0137318i −0.000563425 + 0.000563425i
\(595\) 13.3797 11.0222i 0.548512 0.451866i
\(596\) 6.54196i 0.267969i
\(597\) 13.2935 0.544068
\(598\) 0.403395i 0.0164960i
\(599\) 16.5077i 0.674486i −0.941418 0.337243i \(-0.890506\pi\)
0.941418 0.337243i \(-0.109494\pi\)
\(600\) −4.14696 + 2.79333i −0.169299 + 0.114037i
\(601\) 35.4824 1.44736 0.723679 0.690137i \(-0.242450\pi\)
0.723679 + 0.690137i \(0.242450\pi\)
\(602\) −5.92743 5.92743i −0.241584 0.241584i
\(603\) −2.18514 2.18514i −0.0889858 0.0889858i
\(604\) 14.2779i 0.580961i
\(605\) 2.36520 24.4819i 0.0961589 0.995332i
\(606\) −0.134770 0.134770i −0.00547467 0.00547467i
\(607\) 3.25209i 0.131998i 0.997820 + 0.0659992i \(0.0210235\pi\)
−0.997820 + 0.0659992i \(0.978977\pi\)
\(608\) 4.58811 4.58811i 0.186073 0.186073i
\(609\) 1.55817 + 1.55817i 0.0631404 + 0.0631404i
\(610\) 3.66506 + 4.44895i 0.148394 + 0.180133i
\(611\) 0.821424 0.821424i 0.0332313 0.0332313i
\(612\) 4.04014i 0.163313i
\(613\) 17.6613 + 17.6613i 0.713332 + 0.713332i 0.967231 0.253898i \(-0.0817129\pi\)
−0.253898 + 0.967231i \(0.581713\pi\)
\(614\) 5.74100 + 5.74100i 0.231688 + 0.231688i
\(615\) −11.6792 14.1772i −0.470951 0.571680i
\(616\) 0.0263495 + 0.0263495i 0.00106165 + 0.00106165i
\(617\) 13.8113 13.8113i 0.556021 0.556021i −0.372151 0.928172i \(-0.621380\pi\)
0.928172 + 0.372151i \(0.121380\pi\)
\(618\) 4.76325 4.76325i 0.191606 0.191606i
\(619\) 3.58040 0.143909 0.0719543 0.997408i \(-0.477076\pi\)
0.0719543 + 0.997408i \(0.477076\pi\)
\(620\) −5.75104 + 4.73772i −0.230967 + 0.190272i
\(621\) 1.79337 + 1.79337i 0.0719655 + 0.0719655i
\(622\) −4.78072 + 4.78072i −0.191690 + 0.191690i
\(623\) 27.7703 1.11259
\(624\) −0.112468 + 0.112468i −0.00450234 + 0.00450234i
\(625\) 23.1677 + 9.39463i 0.926707 + 0.375785i
\(626\) −2.04383 −0.0816879
\(627\) −0.126007 −0.00503222
\(628\) 0.0829263 + 0.0829263i 0.00330912 + 0.00330912i
\(629\) −6.80235 + 23.6150i −0.271227 + 0.941592i
\(630\) 3.31168 2.72817i 0.131941 0.108693i
\(631\) 14.6097 + 14.6097i 0.581603 + 0.581603i 0.935344 0.353740i \(-0.115090\pi\)
−0.353740 + 0.935344i \(0.615090\pi\)
\(632\) 4.93909 4.93909i 0.196466 0.196466i
\(633\) 1.86980 + 1.86980i 0.0743177 + 0.0743177i
\(634\) −18.6699 18.6699i −0.741477 0.741477i
\(635\) −30.0739 + 24.7749i −1.19345 + 0.983163i
\(636\) 5.94574 0.235764
\(637\) 0.527736 0.0209097
\(638\) −0.0157694 + 0.0157694i −0.000624318 + 0.000624318i
\(639\) 4.70533i 0.186140i
\(640\) −2.22571 0.215025i −0.0879787 0.00849962i
\(641\) −0.439539 −0.0173607 −0.00868037 0.999962i \(-0.502763\pi\)
−0.00868037 + 0.999962i \(0.502763\pi\)
\(642\) 8.79861 0.347254
\(643\) −21.2554 −0.838230 −0.419115 0.907933i \(-0.637660\pi\)
−0.419115 + 0.907933i \(0.637660\pi\)
\(644\) 3.44123 3.44123i 0.135604 0.135604i
\(645\) −6.21105 7.53949i −0.244560 0.296867i
\(646\) −18.5366 + 18.5366i −0.729313 + 0.729313i
\(647\) 19.6315i 0.771793i −0.922542 0.385897i \(-0.873892\pi\)
0.922542 0.385897i \(-0.126108\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −0.0613892 + 0.0613892i −0.00240974 + 0.00240974i
\(650\) 0.780563 + 0.152241i 0.0306162 + 0.00597139i
\(651\) 4.52138 4.52138i 0.177207 0.177207i
\(652\) 9.48615 0.371506
\(653\) −6.65486 −0.260425 −0.130212 0.991486i \(-0.541566\pi\)
−0.130212 + 0.991486i \(0.541566\pi\)
\(654\) −18.4085 −0.719831
\(655\) 5.09705 4.19896i 0.199158 0.164067i
\(656\) 8.21459i 0.320726i
\(657\) −5.46673 + 5.46673i −0.213277 + 0.213277i
\(658\) −14.0146 −0.546347
\(659\) 12.4367 0.484467 0.242233 0.970218i \(-0.422120\pi\)
0.242233 + 0.970218i \(0.422120\pi\)
\(660\) 0.0276104 + 0.0335157i 0.00107473 + 0.00130460i
\(661\) 23.3713 + 23.3713i 0.909039 + 0.909039i 0.996195 0.0871559i \(-0.0277778\pi\)
−0.0871559 + 0.996195i \(0.527778\pi\)
\(662\) 2.59788 + 2.59788i 0.100969 + 0.100969i
\(663\) 0.454388 0.454388i 0.0176470 0.0176470i
\(664\) −6.36886 6.36886i −0.247160 0.247160i
\(665\) 27.7115 + 2.67721i 1.07461 + 0.103818i
\(666\) −1.68369 + 5.84510i −0.0652417 + 0.226493i
\(667\) 2.05948 + 2.05948i 0.0797433 + 0.0797433i
\(668\) 14.9171 0.577161
\(669\) −28.5942 −1.10552
\(670\) −5.33334 + 4.39362i −0.206045 + 0.169740i
\(671\) 0.0353983 0.0353983i 0.00136654 0.00136654i
\(672\) 1.91886 0.0740217
\(673\) 11.3601 11.3601i 0.437901 0.437901i −0.453404 0.891305i \(-0.649790\pi\)
0.891305 + 0.453404i \(0.149790\pi\)
\(674\) 4.86472 + 4.86472i 0.187382 + 0.187382i
\(675\) 4.14696 2.79333i 0.159617 0.107515i
\(676\) −12.9747 −0.499027
\(677\) 34.5887 34.5887i 1.32935 1.32935i 0.423417 0.905935i \(-0.360830\pi\)
0.905935 0.423417i \(-0.139170\pi\)
\(678\) 6.88722 6.88722i 0.264502 0.264502i
\(679\) −24.2028 24.2028i −0.928820 0.928820i
\(680\) 8.99216 + 0.868732i 0.344833 + 0.0333143i
\(681\) 10.6725 + 10.6725i 0.408970 + 0.408970i
\(682\) 0.0457584 + 0.0457584i 0.00175218 + 0.00175218i
\(683\) 14.2153i 0.543935i −0.962306 0.271967i \(-0.912326\pi\)
0.962306 0.271967i \(-0.0876743\pi\)
\(684\) −4.58811 + 4.58811i −0.175431 + 0.175431i
\(685\) −8.18328 + 6.74141i −0.312667 + 0.257576i
\(686\) −13.9998 13.9998i −0.534516 0.534516i
\(687\) −3.13004 + 3.13004i −0.119419 + 0.119419i
\(688\) 4.36855i 0.166549i
\(689\) −0.668708 0.668708i −0.0254757 0.0254757i
\(690\) 4.37714 3.60590i 0.166635 0.137274i
\(691\) 38.8851i 1.47926i −0.673015 0.739629i \(-0.735001\pi\)
0.673015 0.739629i \(-0.264999\pi\)
\(692\) 7.09005 + 7.09005i 0.269523 + 0.269523i
\(693\) −0.0263495 0.0263495i −0.00100094 0.00100094i
\(694\) −3.00444 −0.114047
\(695\) 4.50686 46.6501i 0.170955 1.76954i
\(696\) 1.14838i 0.0435294i
\(697\) 33.1881i 1.25709i
\(698\) 19.3862 0.733777
\(699\) 1.27168i 0.0480994i
\(700\) −5.36001 7.95746i −0.202589 0.300764i
\(701\) −26.6174 + 26.6174i −1.00532 + 1.00532i −0.00533868 + 0.999986i \(0.501699\pi\)
−0.999986 + 0.00533868i \(0.998301\pi\)
\(702\) 0.112468 0.112468i 0.00424484 0.00424484i
\(703\) −34.5429 + 19.0930i −1.30281 + 0.720106i
\(704\) 0.0194198i 0.000731910i
\(705\) −16.2557 1.57046i −0.612224 0.0591469i
\(706\) 17.9551i 0.675747i
\(707\) 0.258606 0.258606i 0.00972588 0.00972588i
\(708\) 4.47057i 0.168014i
\(709\) 15.4865 + 15.4865i 0.581609 + 0.581609i 0.935345 0.353736i \(-0.115089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(710\) 10.4727 + 1.01176i 0.393033 + 0.0379708i
\(711\) −4.93909 + 4.93909i −0.185230 + 0.185230i
\(712\) 10.2334 + 10.2334i 0.383514 + 0.383514i
\(713\) 5.97602 5.97602i 0.223804 0.223804i
\(714\) −7.75247 −0.290129
\(715\) 0.000664169 0.00687475i 2.48385e−5 0.000257101i
\(716\) 12.4815 12.4815i 0.466456 0.466456i
\(717\) 10.5139i 0.392650i
\(718\) 14.6602 0.547112
\(719\) 6.15628i 0.229591i −0.993389 0.114795i \(-0.963379\pi\)
0.993389 0.114795i \(-0.0366212\pi\)
\(720\) 2.22571 + 0.215025i 0.0829471 + 0.00801352i
\(721\) 9.14002 + 9.14002i 0.340392 + 0.340392i
\(722\) −23.1015 −0.859751
\(723\) 25.6641 0.954457
\(724\) 3.65527 0.135847
\(725\) 4.76231 3.20781i 0.176868 0.119135i
\(726\) −7.77791 + 7.77791i −0.288665 + 0.288665i
\(727\) 12.6971i 0.470911i 0.971885 + 0.235455i \(0.0756581\pi\)
−0.971885 + 0.235455i \(0.924342\pi\)
\(728\) −0.215811 0.215811i −0.00799850 0.00799850i
\(729\) 1.00000i 0.0370370i
\(730\) 10.9918 + 13.3428i 0.406826 + 0.493839i
\(731\) 17.6495i 0.652792i
\(732\) 2.57782i 0.0952791i
\(733\) −6.22173 6.22173i −0.229805 0.229805i 0.582806 0.812611i \(-0.301955\pi\)
−0.812611 + 0.582806i \(0.801955\pi\)
\(734\) 14.1413 14.1413i 0.521967 0.521967i
\(735\) −4.71737 5.72633i −0.174003 0.211219i
\(736\) 2.53621 0.0934859
\(737\) 0.0424349 + 0.0424349i 0.00156311 + 0.00156311i
\(738\) 8.21459i 0.302383i
\(739\) −12.1182 −0.445774 −0.222887 0.974844i \(-0.571548\pi\)
−0.222887 + 0.974844i \(0.571548\pi\)
\(740\) 12.6474 + 5.00425i 0.464929 + 0.183960i
\(741\) 1.03203 0.0379127
\(742\) 11.4091i 0.418840i
\(743\) 13.3639 + 13.3639i 0.490273 + 0.490273i 0.908392 0.418119i \(-0.137310\pi\)
−0.418119 + 0.908392i \(0.637310\pi\)
\(744\) 3.33228 0.122167
\(745\) 14.5605 + 1.40669i 0.533455 + 0.0515370i
\(746\) −13.0549 + 13.0549i −0.477974 + 0.477974i
\(747\) 6.36886 + 6.36886i 0.233025 + 0.233025i
\(748\) 0.0784585i 0.00286873i
\(749\) 16.8833i 0.616903i
\(750\) −5.32542 9.83056i −0.194457 0.358961i
\(751\) 28.9598i 1.05676i 0.849009 + 0.528379i \(0.177200\pi\)
−0.849009 + 0.528379i \(0.822800\pi\)
\(752\) −5.16443 5.16443i −0.188327 0.188327i
\(753\) 25.8712i 0.942800i
\(754\) 0.129157 0.129157i 0.00470361 0.00470361i
\(755\) −31.7785 3.07012i −1.15654 0.111733i
\(756\) −1.91886 −0.0697884
\(757\) −5.84398 −0.212403 −0.106202 0.994345i \(-0.533869\pi\)
−0.106202 + 0.994345i \(0.533869\pi\)
\(758\) 23.0708 0.837970
\(759\) −0.0348268 0.0348268i −0.00126413 0.00126413i
\(760\) 9.22523 + 11.1983i 0.334634 + 0.406207i
\(761\) 9.14339i 0.331448i −0.986172 0.165724i \(-0.947004\pi\)
0.986172 0.165724i \(-0.0529960\pi\)
\(762\) 17.4255 0.631258
\(763\) 35.3235i 1.27880i
\(764\) −6.33676 + 6.33676i −0.229256 + 0.229256i
\(765\) −8.99216 0.868732i −0.325112 0.0314091i
\(766\) 12.0188 0.434257
\(767\) 0.502797 0.502797i 0.0181550 0.0181550i
\(768\) 0.707107 + 0.707107i 0.0255155 + 0.0255155i
\(769\) −4.69206 + 4.69206i −0.169200 + 0.169200i −0.786628 0.617428i \(-0.788175\pi\)
0.617428 + 0.786628i \(0.288175\pi\)
\(770\) −0.0643121 + 0.0529805i −0.00231765 + 0.00190928i
\(771\) 5.02248 + 5.02248i 0.180880 + 0.180880i
\(772\) 13.0970i 0.471373i
\(773\) 9.03929 9.03929i 0.325121 0.325121i −0.525607 0.850728i \(-0.676162\pi\)
0.850728 + 0.525607i \(0.176162\pi\)
\(774\) 4.36855i 0.157024i
\(775\) −9.30816 13.8189i −0.334359 0.496388i
\(776\) 17.8376i 0.640334i
\(777\) −11.2159 3.23077i −0.402370 0.115903i
\(778\) 0.966160 0.966160i 0.0346385 0.0346385i
\(779\) −37.6894 + 37.6894i −1.35036 + 1.35036i