# 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

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 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