# Properties

 Label 300.2.j.c.7.3 Level $300$ Weight $2$ Character 300.7 Analytic conductor $2.396$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$300 = 2^{2} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 300.j (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.39551206064$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: $$\Q(\zeta_{24})$$ Defining polynomial: $$x^{8} - x^{4} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 7.3 Root $$-0.965926 + 0.258819i$$ of defining polynomial Character $$\chi$$ $$=$$ 300.7 Dual form 300.2.j.c.43.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.22474 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.36603 + 0.366025i) q^{6} +(1.74238 - 1.74238i) q^{7} -2.82843i q^{8} +1.00000i q^{9} +O(q^{10})$$ $$q+(1.22474 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.36603 + 0.366025i) q^{6} +(1.74238 - 1.74238i) q^{7} -2.82843i q^{8} +1.00000i q^{9} +2.00000i q^{11} +(1.93185 - 0.517638i) q^{12} +(-4.05317 + 4.05317i) q^{13} +(0.901924 - 3.36603i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-4.24264 - 4.24264i) q^{17} +(0.707107 + 1.22474i) q^{18} +7.19615 q^{19} +2.46410 q^{21} +(1.41421 + 2.44949i) q^{22} +(0.378937 + 0.378937i) q^{23} +(2.00000 - 2.00000i) q^{24} +(-2.09808 + 7.83013i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.27551 - 4.76028i) q^{28} +7.46410i q^{29} +0.267949i q^{31} +(-4.89898 - 2.82843i) q^{32} +(-1.41421 + 1.41421i) q^{33} +(-8.19615 - 2.19615i) q^{34} +(1.73205 + 1.00000i) q^{36} +(-2.07055 - 2.07055i) q^{37} +(8.81345 - 5.08845i) q^{38} -5.73205 q^{39} -5.46410 q^{41} +(3.01790 - 1.74238i) q^{42} +(-1.74238 - 1.74238i) q^{43} +(3.46410 + 2.00000i) q^{44} +(0.732051 + 0.196152i) q^{46} +(-9.14162 + 9.14162i) q^{47} +(1.03528 - 3.86370i) q^{48} +0.928203i q^{49} -6.00000i q^{51} +(2.96713 + 11.0735i) q^{52} +(-1.03528 + 1.03528i) q^{53} +(-0.366025 + 1.36603i) q^{54} +(-4.92820 - 4.92820i) q^{56} +(5.08845 + 5.08845i) q^{57} +(5.27792 + 9.14162i) q^{58} -4.53590 q^{59} +3.00000 q^{61} +(0.189469 + 0.328169i) q^{62} +(1.74238 + 1.74238i) q^{63} -8.00000 q^{64} +(-0.732051 + 2.73205i) q^{66} +(8.81345 - 8.81345i) q^{67} +(-11.5911 + 3.10583i) q^{68} +0.535898i q^{69} -9.46410i q^{71} +2.82843 q^{72} +(2.82843 - 2.82843i) q^{73} +(-4.00000 - 1.07180i) q^{74} +(7.19615 - 12.4641i) q^{76} +(3.48477 + 3.48477i) q^{77} +(-7.02030 + 4.05317i) q^{78} +0.535898 q^{79} -1.00000 q^{81} +(-6.69213 + 3.86370i) q^{82} +(0.656339 + 0.656339i) q^{83} +(2.46410 - 4.26795i) q^{84} +(-3.36603 - 0.901924i) q^{86} +(-5.27792 + 5.27792i) q^{87} +5.65685 q^{88} -6.92820i q^{89} +14.1244i q^{91} +(1.03528 - 0.277401i) q^{92} +(-0.189469 + 0.189469i) q^{93} +(-4.73205 + 17.6603i) q^{94} +(-1.46410 - 5.46410i) q^{96} +(4.43211 + 4.43211i) q^{97} +(0.656339 + 1.13681i) q^{98} -2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 8q^{4} + 4q^{6} + O(q^{10})$$ $$8q + 8q^{4} + 4q^{6} + 28q^{14} - 16q^{16} + 16q^{19} - 8q^{21} + 16q^{24} + 4q^{26} - 24q^{34} - 32q^{39} - 16q^{41} - 8q^{46} + 4q^{54} + 16q^{56} - 64q^{59} + 24q^{61} - 64q^{64} + 8q^{66} - 32q^{74} + 16q^{76} + 32q^{79} - 8q^{81} - 8q^{84} - 20q^{86} - 24q^{94} + 16q^{96} - 16q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$151$$ $$277$$ $$\chi(n)$$ $$1$$ $$-1$$ $$e\left(\frac{1}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.22474 0.707107i 0.866025 0.500000i
$$3$$ 0.707107 + 0.707107i 0.408248 + 0.408248i
$$4$$ 1.00000 1.73205i 0.500000 0.866025i
$$5$$ 0 0
$$6$$ 1.36603 + 0.366025i 0.557678 + 0.149429i
$$7$$ 1.74238 1.74238i 0.658559 0.658559i −0.296480 0.955039i $$-0.595813\pi$$
0.955039 + 0.296480i $$0.0958129\pi$$
$$8$$ 2.82843i 1.00000i
$$9$$ 1.00000i 0.333333i
$$10$$ 0 0
$$11$$ 2.00000i 0.603023i 0.953463 + 0.301511i $$0.0974911\pi$$
−0.953463 + 0.301511i $$0.902509\pi$$
$$12$$ 1.93185 0.517638i 0.557678 0.149429i
$$13$$ −4.05317 + 4.05317i −1.12415 + 1.12415i −0.133037 + 0.991111i $$0.542473\pi$$
−0.991111 + 0.133037i $$0.957527\pi$$
$$14$$ 0.901924 3.36603i 0.241049 0.899608i
$$15$$ 0 0
$$16$$ −2.00000 3.46410i −0.500000 0.866025i
$$17$$ −4.24264 4.24264i −1.02899 1.02899i −0.999567 0.0294245i $$-0.990633\pi$$
−0.0294245 0.999567i $$-0.509367\pi$$
$$18$$ 0.707107 + 1.22474i 0.166667 + 0.288675i
$$19$$ 7.19615 1.65091 0.825455 0.564467i $$-0.190918\pi$$
0.825455 + 0.564467i $$0.190918\pi$$
$$20$$ 0 0
$$21$$ 2.46410 0.537711
$$22$$ 1.41421 + 2.44949i 0.301511 + 0.522233i
$$23$$ 0.378937 + 0.378937i 0.0790139 + 0.0790139i 0.745509 0.666495i $$-0.232206\pi$$
−0.666495 + 0.745509i $$0.732206\pi$$
$$24$$ 2.00000 2.00000i 0.408248 0.408248i
$$25$$ 0 0
$$26$$ −2.09808 + 7.83013i −0.411467 + 1.53561i
$$27$$ −0.707107 + 0.707107i −0.136083 + 0.136083i
$$28$$ −1.27551 4.76028i −0.241049 0.899608i
$$29$$ 7.46410i 1.38605i 0.720914 + 0.693024i $$0.243722\pi$$
−0.720914 + 0.693024i $$0.756278\pi$$
$$30$$ 0 0
$$31$$ 0.267949i 0.0481251i 0.999710 + 0.0240625i $$0.00766009\pi$$
−0.999710 + 0.0240625i $$0.992340\pi$$
$$32$$ −4.89898 2.82843i −0.866025 0.500000i
$$33$$ −1.41421 + 1.41421i −0.246183 + 0.246183i
$$34$$ −8.19615 2.19615i −1.40563 0.376637i
$$35$$ 0 0
$$36$$ 1.73205 + 1.00000i 0.288675 + 0.166667i
$$37$$ −2.07055 2.07055i −0.340397 0.340397i 0.516120 0.856516i $$-0.327376\pi$$
−0.856516 + 0.516120i $$0.827376\pi$$
$$38$$ 8.81345 5.08845i 1.42973 0.825455i
$$39$$ −5.73205 −0.917863
$$40$$ 0 0
$$41$$ −5.46410 −0.853349 −0.426675 0.904405i $$-0.640315\pi$$
−0.426675 + 0.904405i $$0.640315\pi$$
$$42$$ 3.01790 1.74238i 0.465671 0.268856i
$$43$$ −1.74238 1.74238i −0.265711 0.265711i 0.561658 0.827369i $$-0.310164\pi$$
−0.827369 + 0.561658i $$0.810164\pi$$
$$44$$ 3.46410 + 2.00000i 0.522233 + 0.301511i
$$45$$ 0 0
$$46$$ 0.732051 + 0.196152i 0.107935 + 0.0289211i
$$47$$ −9.14162 + 9.14162i −1.33344 + 1.33344i −0.431173 + 0.902269i $$0.641900\pi$$
−0.902269 + 0.431173i $$0.858100\pi$$
$$48$$ 1.03528 3.86370i 0.149429 0.557678i
$$49$$ 0.928203i 0.132600i
$$50$$ 0 0
$$51$$ 6.00000i 0.840168i
$$52$$ 2.96713 + 11.0735i 0.411467 + 1.53561i
$$53$$ −1.03528 + 1.03528i −0.142206 + 0.142206i −0.774626 0.632420i $$-0.782062\pi$$
0.632420 + 0.774626i $$0.282062\pi$$
$$54$$ −0.366025 + 1.36603i −0.0498097 + 0.185893i
$$55$$ 0 0
$$56$$ −4.92820 4.92820i −0.658559 0.658559i
$$57$$ 5.08845 + 5.08845i 0.673981 + 0.673981i
$$58$$ 5.27792 + 9.14162i 0.693024 + 1.20035i
$$59$$ −4.53590 −0.590524 −0.295262 0.955416i $$-0.595407\pi$$
−0.295262 + 0.955416i $$0.595407\pi$$
$$60$$ 0 0
$$61$$ 3.00000 0.384111 0.192055 0.981384i $$-0.438485\pi$$
0.192055 + 0.981384i $$0.438485\pi$$
$$62$$ 0.189469 + 0.328169i 0.0240625 + 0.0416776i
$$63$$ 1.74238 + 1.74238i 0.219520 + 0.219520i
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ −0.732051 + 2.73205i −0.0901092 + 0.336292i
$$67$$ 8.81345 8.81345i 1.07673 1.07673i 0.0799342 0.996800i $$-0.474529\pi$$
0.996800 0.0799342i $$-0.0254710\pi$$
$$68$$ −11.5911 + 3.10583i −1.40563 + 0.376637i
$$69$$ 0.535898i 0.0645146i
$$70$$ 0 0
$$71$$ 9.46410i 1.12318i −0.827415 0.561591i $$-0.810189\pi$$
0.827415 0.561591i $$-0.189811\pi$$
$$72$$ 2.82843 0.333333
$$73$$ 2.82843 2.82843i 0.331042 0.331042i −0.521940 0.852982i $$-0.674791\pi$$
0.852982 + 0.521940i $$0.174791\pi$$
$$74$$ −4.00000 1.07180i −0.464991 0.124594i
$$75$$ 0 0
$$76$$ 7.19615 12.4641i 0.825455 1.42973i
$$77$$ 3.48477 + 3.48477i 0.397126 + 0.397126i
$$78$$ −7.02030 + 4.05317i −0.794892 + 0.458931i
$$79$$ 0.535898 0.0602933 0.0301466 0.999545i $$-0.490403\pi$$
0.0301466 + 0.999545i $$0.490403\pi$$
$$80$$ 0 0
$$81$$ −1.00000 −0.111111
$$82$$ −6.69213 + 3.86370i −0.739022 + 0.426675i
$$83$$ 0.656339 + 0.656339i 0.0720425 + 0.0720425i 0.742210 0.670167i $$-0.233778\pi$$
−0.670167 + 0.742210i $$0.733778\pi$$
$$84$$ 2.46410 4.26795i 0.268856 0.465671i
$$85$$ 0 0
$$86$$ −3.36603 0.901924i −0.362968 0.0972569i
$$87$$ −5.27792 + 5.27792i −0.565852 + 0.565852i
$$88$$ 5.65685 0.603023
$$89$$ 6.92820i 0.734388i −0.930144 0.367194i $$-0.880318\pi$$
0.930144 0.367194i $$-0.119682\pi$$
$$90$$ 0 0
$$91$$ 14.1244i 1.48063i
$$92$$ 1.03528 0.277401i 0.107935 0.0289211i
$$93$$ −0.189469 + 0.189469i −0.0196470 + 0.0196470i
$$94$$ −4.73205 + 17.6603i −0.488074 + 1.82152i
$$95$$ 0 0
$$96$$ −1.46410 5.46410i −0.149429 0.557678i
$$97$$ 4.43211 + 4.43211i 0.450013 + 0.450013i 0.895359 0.445346i $$-0.146919\pi$$
−0.445346 + 0.895359i $$0.646919\pi$$
$$98$$ 0.656339 + 1.13681i 0.0663002 + 0.114835i
$$99$$ −2.00000 −0.201008
$$100$$ 0 0
$$101$$ −1.46410 −0.145684 −0.0728418 0.997344i $$-0.523207\pi$$
−0.0728418 + 0.997344i $$0.523207\pi$$
$$102$$ −4.24264 7.34847i −0.420084 0.727607i
$$103$$ 4.89898 + 4.89898i 0.482711 + 0.482711i 0.905996 0.423286i $$-0.139123\pi$$
−0.423286 + 0.905996i $$0.639123\pi$$
$$104$$ 11.4641 + 11.4641i 1.12415 + 1.12415i
$$105$$ 0 0
$$106$$ −0.535898 + 2.00000i −0.0520511 + 0.194257i
$$107$$ 4.62158 4.62158i 0.446785 0.446785i −0.447499 0.894284i $$-0.647685\pi$$
0.894284 + 0.447499i $$0.147685\pi$$
$$108$$ 0.517638 + 1.93185i 0.0498097 + 0.185893i
$$109$$ 7.00000i 0.670478i −0.942133 0.335239i $$-0.891183\pi$$
0.942133 0.335239i $$-0.108817\pi$$
$$110$$ 0 0
$$111$$ 2.92820i 0.277933i
$$112$$ −9.52056 2.55103i −0.899608 0.241049i
$$113$$ 9.79796 9.79796i 0.921714 0.921714i −0.0754362 0.997151i $$-0.524035\pi$$
0.997151 + 0.0754362i $$0.0240349\pi$$
$$114$$ 9.83013 + 2.63397i 0.920676 + 0.246694i
$$115$$ 0 0
$$116$$ 12.9282 + 7.46410i 1.20035 + 0.693024i
$$117$$ −4.05317 4.05317i −0.374716 0.374716i
$$118$$ −5.55532 + 3.20736i −0.511409 + 0.295262i
$$119$$ −14.7846 −1.35530
$$120$$ 0 0
$$121$$ 7.00000 0.636364
$$122$$ 3.67423 2.12132i 0.332650 0.192055i
$$123$$ −3.86370 3.86370i −0.348378 0.348378i
$$124$$ 0.464102 + 0.267949i 0.0416776 + 0.0240625i
$$125$$ 0 0
$$126$$ 3.36603 + 0.901924i 0.299869 + 0.0803498i
$$127$$ 2.07055 2.07055i 0.183732 0.183732i −0.609248 0.792980i $$-0.708529\pi$$
0.792980 + 0.609248i $$0.208529\pi$$
$$128$$ −9.79796 + 5.65685i −0.866025 + 0.500000i
$$129$$ 2.46410i 0.216952i
$$130$$ 0 0
$$131$$ 9.46410i 0.826882i 0.910531 + 0.413441i $$0.135673\pi$$
−0.910531 + 0.413441i $$0.864327\pi$$
$$132$$ 1.03528 + 3.86370i 0.0901092 + 0.336292i
$$133$$ 12.5385 12.5385i 1.08722 1.08722i
$$134$$ 4.56218 17.0263i 0.394112 1.47085i
$$135$$ 0 0
$$136$$ −12.0000 + 12.0000i −1.02899 + 1.02899i
$$137$$ 6.03579 + 6.03579i 0.515672 + 0.515672i 0.916259 0.400586i $$-0.131194\pi$$
−0.400586 + 0.916259i $$0.631194\pi$$
$$138$$ 0.378937 + 0.656339i 0.0322573 + 0.0558713i
$$139$$ 19.4641 1.65092 0.825462 0.564458i $$-0.190915\pi$$
0.825462 + 0.564458i $$0.190915\pi$$
$$140$$ 0 0
$$141$$ −12.9282 −1.08875
$$142$$ −6.69213 11.5911i −0.561591 0.972704i
$$143$$ −8.10634 8.10634i −0.677887 0.677887i
$$144$$ 3.46410 2.00000i 0.288675 0.166667i
$$145$$ 0 0
$$146$$ 1.46410 5.46410i 0.121170 0.452212i
$$147$$ −0.656339 + 0.656339i −0.0541339 + 0.0541339i
$$148$$ −5.65685 + 1.51575i −0.464991 + 0.124594i
$$149$$ 15.8564i 1.29901i −0.760358 0.649504i $$-0.774977\pi$$
0.760358 0.649504i $$-0.225023\pi$$
$$150$$ 0 0
$$151$$ 4.26795i 0.347321i 0.984806 + 0.173660i $$0.0555595\pi$$
−0.984806 + 0.173660i $$0.944440\pi$$
$$152$$ 20.3538i 1.65091i
$$153$$ 4.24264 4.24264i 0.342997 0.342997i
$$154$$ 6.73205 + 1.80385i 0.542484 + 0.145358i
$$155$$ 0 0
$$156$$ −5.73205 + 9.92820i −0.458931 + 0.794892i
$$157$$ −6.88160 6.88160i −0.549211 0.549211i 0.377001 0.926213i $$-0.376955\pi$$
−0.926213 + 0.377001i $$0.876955\pi$$
$$158$$ 0.656339 0.378937i 0.0522155 0.0301466i
$$159$$ −1.46410 −0.116111
$$160$$ 0 0
$$161$$ 1.32051 0.104071
$$162$$ −1.22474 + 0.707107i −0.0962250 + 0.0555556i
$$163$$ −10.2277 10.2277i −0.801092 0.801092i 0.182174 0.983266i $$-0.441687\pi$$
−0.983266 + 0.182174i $$0.941687\pi$$
$$164$$ −5.46410 + 9.46410i −0.426675 + 0.739022i
$$165$$ 0 0
$$166$$ 1.26795 + 0.339746i 0.0984119 + 0.0263694i
$$167$$ 3.10583 3.10583i 0.240336 0.240336i −0.576653 0.816989i $$-0.695642\pi$$
0.816989 + 0.576653i $$0.195642\pi$$
$$168$$ 6.96953i 0.537711i
$$169$$ 19.8564i 1.52742i
$$170$$ 0 0
$$171$$ 7.19615i 0.550304i
$$172$$ −4.76028 + 1.27551i −0.362968 + 0.0972569i
$$173$$ −6.31319 + 6.31319i −0.479983 + 0.479983i −0.905126 0.425143i $$-0.860224\pi$$
0.425143 + 0.905126i $$0.360224\pi$$
$$174$$ −2.73205 + 10.1962i −0.207116 + 0.772968i
$$175$$ 0 0
$$176$$ 6.92820 4.00000i 0.522233 0.301511i
$$177$$ −3.20736 3.20736i −0.241080 0.241080i
$$178$$ −4.89898 8.48528i −0.367194 0.635999i
$$179$$ 25.3205 1.89254 0.946272 0.323372i $$-0.104817\pi$$
0.946272 + 0.323372i $$0.104817\pi$$
$$180$$ 0 0
$$181$$ −13.9282 −1.03528 −0.517638 0.855600i $$-0.673188\pi$$
−0.517638 + 0.855600i $$0.673188\pi$$
$$182$$ 9.98743 + 17.2987i 0.740317 + 1.28227i
$$183$$ 2.12132 + 2.12132i 0.156813 + 0.156813i
$$184$$ 1.07180 1.07180i 0.0790139 0.0790139i
$$185$$ 0 0
$$186$$ −0.0980762 + 0.366025i −0.00719130 + 0.0268383i
$$187$$ 8.48528 8.48528i 0.620505 0.620505i
$$188$$ 6.69213 + 24.9754i 0.488074 + 1.82152i
$$189$$ 2.46410i 0.179237i
$$190$$ 0 0
$$191$$ 16.9282i 1.22488i −0.790516 0.612441i $$-0.790188\pi$$
0.790516 0.612441i $$-0.209812\pi$$
$$192$$ −5.65685 5.65685i −0.408248 0.408248i
$$193$$ −9.71003 + 9.71003i −0.698943 + 0.698943i −0.964183 0.265240i $$-0.914549\pi$$
0.265240 + 0.964183i $$0.414549\pi$$
$$194$$ 8.56218 + 2.29423i 0.614729 + 0.164716i
$$195$$ 0 0
$$196$$ 1.60770 + 0.928203i 0.114835 + 0.0663002i
$$197$$ 10.1769 + 10.1769i 0.725074 + 0.725074i 0.969634 0.244560i $$-0.0786436\pi$$
−0.244560 + 0.969634i $$0.578644\pi$$
$$198$$ −2.44949 + 1.41421i −0.174078 + 0.100504i
$$199$$ −14.1244 −1.00125 −0.500625 0.865665i $$-0.666896\pi$$
−0.500625 + 0.865665i $$0.666896\pi$$
$$200$$ 0 0
$$201$$ 12.4641 0.879150
$$202$$ −1.79315 + 1.03528i −0.126166 + 0.0728418i
$$203$$ 13.0053 + 13.0053i 0.912795 + 0.912795i
$$204$$ −10.3923 6.00000i −0.727607 0.420084i
$$205$$ 0 0
$$206$$ 9.46410 + 2.53590i 0.659395 + 0.176684i
$$207$$ −0.378937 + 0.378937i −0.0263380 + 0.0263380i
$$208$$ 22.1469 + 5.93426i 1.53561 + 0.411467i
$$209$$ 14.3923i 0.995537i
$$210$$ 0 0
$$211$$ 7.19615i 0.495404i −0.968836 0.247702i $$-0.920325\pi$$
0.968836 0.247702i $$-0.0796753\pi$$
$$212$$ 0.757875 + 2.82843i 0.0520511 + 0.194257i
$$213$$ 6.69213 6.69213i 0.458537 0.458537i
$$214$$ 2.39230 8.92820i 0.163535 0.610319i
$$215$$ 0 0
$$216$$ 2.00000 + 2.00000i 0.136083 + 0.136083i
$$217$$ 0.466870 + 0.466870i 0.0316932 + 0.0316932i
$$218$$ −4.94975 8.57321i −0.335239 0.580651i
$$219$$ 4.00000 0.270295
$$220$$ 0 0
$$221$$ 34.3923 2.31348
$$222$$ −2.07055 3.58630i −0.138966 0.240697i
$$223$$ −8.05558 8.05558i −0.539441 0.539441i 0.383924 0.923365i $$-0.374573\pi$$
−0.923365 + 0.383924i $$0.874573\pi$$
$$224$$ −13.4641 + 3.60770i −0.899608 + 0.241049i
$$225$$ 0 0
$$226$$ 5.07180 18.9282i 0.337371 1.25909i
$$227$$ 8.76268 8.76268i 0.581600 0.581600i −0.353743 0.935343i $$-0.615091\pi$$
0.935343 + 0.353743i $$0.115091\pi$$
$$228$$ 13.9019 3.72500i 0.920676 0.246694i
$$229$$ 24.8564i 1.64256i 0.570527 + 0.821279i $$0.306739\pi$$
−0.570527 + 0.821279i $$0.693261\pi$$
$$230$$ 0 0
$$231$$ 4.92820i 0.324252i
$$232$$ 21.1117 1.38605
$$233$$ −8.76268 + 8.76268i −0.574062 + 0.574062i −0.933261 0.359199i $$-0.883050\pi$$
0.359199 + 0.933261i $$0.383050\pi$$
$$234$$ −7.83013 2.09808i −0.511871 0.137156i
$$235$$ 0 0
$$236$$ −4.53590 + 7.85641i −0.295262 + 0.511409i
$$237$$ 0.378937 + 0.378937i 0.0246146 + 0.0246146i
$$238$$ −18.1074 + 10.4543i −1.17373 + 0.677651i
$$239$$ −17.4641 −1.12966 −0.564829 0.825208i $$-0.691058\pi$$
−0.564829 + 0.825208i $$0.691058\pi$$
$$240$$ 0 0
$$241$$ −14.8564 −0.956985 −0.478493 0.878092i $$-0.658817\pi$$
−0.478493 + 0.878092i $$0.658817\pi$$
$$242$$ 8.57321 4.94975i 0.551107 0.318182i
$$243$$ −0.707107 0.707107i −0.0453609 0.0453609i
$$244$$ 3.00000 5.19615i 0.192055 0.332650i
$$245$$ 0 0
$$246$$ −7.46410 2.00000i −0.475894 0.127515i
$$247$$ −29.1672 + 29.1672i −1.85587 + 1.85587i
$$248$$ 0.757875 0.0481251
$$249$$ 0.928203i 0.0588225i
$$250$$ 0 0
$$251$$ 2.14359i 0.135302i −0.997709 0.0676512i $$-0.978449\pi$$
0.997709 0.0676512i $$-0.0215505\pi$$
$$252$$ 4.76028 1.27551i 0.299869 0.0803498i
$$253$$ −0.757875 + 0.757875i −0.0476472 + 0.0476472i
$$254$$ 1.07180 4.00000i 0.0672505 0.250982i
$$255$$ 0 0
$$256$$ −8.00000 + 13.8564i −0.500000 + 0.866025i
$$257$$ −9.04008 9.04008i −0.563905 0.563905i 0.366509 0.930414i $$-0.380553\pi$$
−0.930414 + 0.366509i $$0.880553\pi$$
$$258$$ −1.74238 3.01790i −0.108476 0.187886i
$$259$$ −7.21539 −0.448343
$$260$$ 0 0
$$261$$ −7.46410 −0.462016
$$262$$ 6.69213 + 11.5911i 0.413441 + 0.716101i
$$263$$ 15.1774 + 15.1774i 0.935879 + 0.935879i 0.998065 0.0621853i $$-0.0198070\pi$$
−0.0621853 + 0.998065i $$0.519807\pi$$
$$264$$ 4.00000 + 4.00000i 0.246183 + 0.246183i
$$265$$ 0 0
$$266$$ 6.49038 24.2224i 0.397951 1.48517i
$$267$$ 4.89898 4.89898i 0.299813 0.299813i
$$268$$ −6.45189 24.0788i −0.394112 1.47085i
$$269$$ 1.60770i 0.0980229i −0.998798 0.0490115i $$-0.984393\pi$$
0.998798 0.0490115i $$-0.0156071\pi$$
$$270$$ 0 0
$$271$$ 24.2487i 1.47300i −0.676435 0.736502i $$-0.736476\pi$$
0.676435 0.736502i $$-0.263524\pi$$
$$272$$ −6.21166 + 23.1822i −0.376637 + 1.40563i
$$273$$ −9.98743 + 9.98743i −0.604467 + 0.604467i
$$274$$ 11.6603 + 3.12436i 0.704422 + 0.188749i
$$275$$ 0 0
$$276$$ 0.928203 + 0.535898i 0.0558713 + 0.0322573i
$$277$$ −0.845807 0.845807i −0.0508196 0.0508196i 0.681240 0.732060i $$-0.261441\pi$$
−0.732060 + 0.681240i $$0.761441\pi$$
$$278$$ 23.8386 13.7632i 1.42974 0.825462i
$$279$$ −0.267949 −0.0160417
$$280$$ 0 0
$$281$$ −14.3923 −0.858573 −0.429286 0.903168i $$-0.641235\pi$$
−0.429286 + 0.903168i $$0.641235\pi$$
$$282$$ −15.8338 + 9.14162i −0.942886 + 0.544376i
$$283$$ 15.1266 + 15.1266i 0.899186 + 0.899186i 0.995364 0.0961785i $$-0.0306620\pi$$
−0.0961785 + 0.995364i $$0.530662\pi$$
$$284$$ −16.3923 9.46410i −0.972704 0.561591i
$$285$$ 0 0
$$286$$ −15.6603 4.19615i −0.926010 0.248124i
$$287$$ −9.52056 + 9.52056i −0.561981 + 0.561981i
$$288$$ 2.82843 4.89898i 0.166667 0.288675i
$$289$$ 19.0000i 1.11765i
$$290$$ 0 0
$$291$$ 6.26795i 0.367434i
$$292$$ −2.07055 7.72741i −0.121170 0.452212i
$$293$$ −8.86422 + 8.86422i −0.517853 + 0.517853i −0.916921 0.399068i $$-0.869334\pi$$
0.399068 + 0.916921i $$0.369334\pi$$
$$294$$ −0.339746 + 1.26795i −0.0198144 + 0.0739483i
$$295$$ 0 0
$$296$$ −5.85641 + 5.85641i −0.340397 + 0.340397i
$$297$$ −1.41421 1.41421i −0.0820610 0.0820610i
$$298$$ −11.2122 19.4201i −0.649504 1.12497i
$$299$$ −3.07180 −0.177647
$$300$$ 0 0
$$301$$ −6.07180 −0.349973
$$302$$ 3.01790 + 5.22715i 0.173660 + 0.300789i
$$303$$ −1.03528 1.03528i −0.0594751 0.0594751i
$$304$$ −14.3923 24.9282i −0.825455 1.42973i
$$305$$ 0 0
$$306$$ 2.19615 8.19615i 0.125546 0.468543i
$$307$$ −9.46979 + 9.46979i −0.540469 + 0.540469i −0.923667 0.383197i $$-0.874823\pi$$
0.383197 + 0.923667i $$0.374823\pi$$
$$308$$ 9.52056 2.55103i 0.542484 0.145358i
$$309$$ 6.92820i 0.394132i
$$310$$ 0 0
$$311$$ 27.4641i 1.55735i 0.627430 + 0.778673i $$0.284107\pi$$
−0.627430 + 0.778673i $$0.715893\pi$$
$$312$$ 16.2127i 0.917863i
$$313$$ −5.74479 + 5.74479i −0.324715 + 0.324715i −0.850572 0.525858i $$-0.823744\pi$$
0.525858 + 0.850572i $$0.323744\pi$$
$$314$$ −13.2942 3.56218i −0.750237 0.201025i
$$315$$ 0 0
$$316$$ 0.535898 0.928203i 0.0301466 0.0522155i
$$317$$ 4.89898 + 4.89898i 0.275154 + 0.275154i 0.831171 0.556017i $$-0.187671\pi$$
−0.556017 + 0.831171i $$0.687671\pi$$
$$318$$ −1.79315 + 1.03528i −0.100555 + 0.0580554i
$$319$$ −14.9282 −0.835819
$$320$$ 0 0
$$321$$ 6.53590 0.364798
$$322$$ 1.61729 0.933740i 0.0901278 0.0520353i
$$323$$ −30.5307 30.5307i −1.69877 1.69877i
$$324$$ −1.00000 + 1.73205i −0.0555556 + 0.0962250i
$$325$$ 0 0
$$326$$ −19.7583 5.29423i −1.09431 0.293220i
$$327$$ 4.94975 4.94975i 0.273722 0.273722i
$$328$$ 15.4548i 0.853349i
$$329$$ 31.8564i 1.75630i
$$330$$ 0 0
$$331$$ 2.39230i 0.131493i 0.997836 + 0.0657465i $$0.0209429\pi$$
−0.997836 + 0.0657465i $$0.979057\pi$$
$$332$$ 1.79315 0.480473i 0.0984119 0.0263694i
$$333$$ 2.07055 2.07055i 0.113466 0.113466i
$$334$$ 1.60770 6.00000i 0.0879692 0.328305i
$$335$$ 0 0
$$336$$ −4.92820 8.53590i −0.268856 0.465671i
$$337$$ −8.01841 8.01841i −0.436791 0.436791i 0.454140 0.890930i $$-0.349947\pi$$
−0.890930 + 0.454140i $$0.849947\pi$$
$$338$$ −14.0406 24.3190i −0.763708 1.32278i
$$339$$ 13.8564 0.752577
$$340$$ 0 0
$$341$$ −0.535898 −0.0290205
$$342$$ 5.08845 + 8.81345i 0.275152 + 0.476577i
$$343$$ 13.8140 + 13.8140i 0.745884 + 0.745884i
$$344$$ −4.92820 + 4.92820i −0.265711 + 0.265711i
$$345$$ 0 0
$$346$$ −3.26795 + 12.1962i −0.175686 + 0.655669i
$$347$$ 7.82894 7.82894i 0.420280 0.420280i −0.465020 0.885300i $$-0.653953\pi$$
0.885300 + 0.465020i $$0.153953\pi$$
$$348$$ 3.86370 + 14.4195i 0.207116 + 0.772968i
$$349$$ 3.85641i 0.206429i −0.994659 0.103214i $$-0.967087\pi$$
0.994659 0.103214i $$-0.0329128\pi$$
$$350$$ 0 0
$$351$$ 5.73205i 0.305954i
$$352$$ 5.65685 9.79796i 0.301511 0.522233i
$$353$$ 11.2122 11.2122i 0.596764 0.596764i −0.342686 0.939450i $$-0.611337\pi$$
0.939450 + 0.342686i $$0.111337\pi$$
$$354$$ −6.19615 1.66025i −0.329322 0.0882415i
$$355$$ 0 0
$$356$$ −12.0000 6.92820i −0.635999 0.367194i
$$357$$ −10.4543 10.4543i −0.553300 0.553300i
$$358$$ 31.0112 17.9043i 1.63899 0.946272i
$$359$$ 24.3923 1.28738 0.643688 0.765288i $$-0.277403\pi$$
0.643688 + 0.765288i $$0.277403\pi$$
$$360$$ 0 0
$$361$$ 32.7846 1.72551
$$362$$ −17.0585 + 9.84873i −0.896575 + 0.517638i
$$363$$ 4.94975 + 4.94975i 0.259794 + 0.259794i
$$364$$ 24.4641 + 14.1244i 1.28227 + 0.740317i
$$365$$ 0 0
$$366$$ 4.09808 + 1.09808i 0.214210 + 0.0573974i
$$367$$ −7.50077 + 7.50077i −0.391537 + 0.391537i −0.875235 0.483698i $$-0.839293\pi$$
0.483698 + 0.875235i $$0.339293\pi$$
$$368$$ 0.554803 2.07055i 0.0289211 0.107935i
$$369$$ 5.46410i 0.284450i
$$370$$ 0 0
$$371$$ 3.60770i 0.187302i
$$372$$ 0.138701 + 0.517638i 0.00719130 + 0.0268383i
$$373$$ −13.6753 + 13.6753i −0.708078 + 0.708078i −0.966131 0.258052i $$-0.916919\pi$$
0.258052 + 0.966131i $$0.416919\pi$$
$$374$$ 4.39230 16.3923i 0.227121 0.847626i
$$375$$ 0 0
$$376$$ 25.8564 + 25.8564i 1.33344 + 1.33344i
$$377$$ −30.2533 30.2533i −1.55812 1.55812i
$$378$$ 1.74238 + 3.01790i 0.0896185 + 0.155224i
$$379$$ −15.7321 −0.808101 −0.404051 0.914737i $$-0.632398\pi$$
−0.404051 + 0.914737i $$0.632398\pi$$
$$380$$ 0 0
$$381$$ 2.92820 0.150016
$$382$$ −11.9700 20.7327i −0.612441 1.06078i
$$383$$ 11.8685 + 11.8685i 0.606453 + 0.606453i 0.942017 0.335565i $$-0.108927\pi$$
−0.335565 + 0.942017i $$0.608927\pi$$
$$384$$ −10.9282 2.92820i −0.557678 0.149429i
$$385$$ 0 0
$$386$$ −5.02628 + 18.7583i −0.255831 + 0.954774i
$$387$$ 1.74238 1.74238i 0.0885703 0.0885703i
$$388$$ 12.1087 3.24453i 0.614729 0.164716i
$$389$$ 14.5359i 0.736999i −0.929628 0.368500i $$-0.879872\pi$$
0.929628 0.368500i $$-0.120128\pi$$
$$390$$ 0 0
$$391$$ 3.21539i 0.162609i
$$392$$ 2.62536 0.132600
$$393$$ −6.69213 + 6.69213i −0.337573 + 0.337573i
$$394$$ 19.6603 + 5.26795i 0.990469 + 0.265395i
$$395$$ 0 0
$$396$$ −2.00000 + 3.46410i −0.100504 + 0.174078i
$$397$$ 13.8511 + 13.8511i 0.695168 + 0.695168i 0.963364 0.268196i $$-0.0864275\pi$$
−0.268196 + 0.963364i $$0.586427\pi$$
$$398$$ −17.2987 + 9.98743i −0.867107 + 0.500625i
$$399$$ 17.7321 0.887713
$$400$$ 0 0
$$401$$ −33.1769 −1.65678 −0.828388 0.560155i $$-0.810742\pi$$
−0.828388 + 0.560155i $$0.810742\pi$$
$$402$$ 15.2653 8.81345i 0.761366 0.439575i
$$403$$ −1.08604 1.08604i −0.0540997 0.0540997i
$$404$$ −1.46410 + 2.53590i −0.0728418 + 0.126166i
$$405$$ 0 0
$$406$$ 25.1244 + 6.73205i 1.24690 + 0.334106i
$$407$$ 4.14110 4.14110i 0.205267 0.205267i
$$408$$ −16.9706 −0.840168
$$409$$ 27.7846i 1.37386i 0.726723 + 0.686930i $$0.241042\pi$$
−0.726723 + 0.686930i $$0.758958\pi$$
$$410$$ 0 0
$$411$$ 8.53590i 0.421045i
$$412$$ 13.3843 3.58630i 0.659395 0.176684i
$$413$$ −7.90327 + 7.90327i −0.388895 + 0.388895i
$$414$$ −0.196152 + 0.732051i −0.00964037 + 0.0359783i
$$415$$ 0 0
$$416$$ 31.3205 8.39230i 1.53561 0.411467i
$$417$$ 13.7632 + 13.7632i 0.673987 + 0.673987i
$$418$$ 10.1769 + 17.6269i 0.497768 + 0.862160i
$$419$$ 26.5359 1.29636 0.648182 0.761486i $$-0.275530\pi$$
0.648182 + 0.761486i $$0.275530\pi$$
$$420$$ 0 0
$$421$$ 6.78461 0.330662 0.165331 0.986238i $$-0.447131\pi$$
0.165331 + 0.986238i $$0.447131\pi$$
$$422$$ −5.08845 8.81345i −0.247702 0.429032i
$$423$$ −9.14162 9.14162i −0.444481 0.444481i
$$424$$ 2.92820 + 2.92820i 0.142206 + 0.142206i
$$425$$ 0 0
$$426$$ 3.46410 12.9282i 0.167836 0.626373i
$$427$$ 5.22715 5.22715i 0.252959 0.252959i
$$428$$ −3.38323 12.6264i −0.163535 0.610319i
$$429$$ 11.4641i 0.553492i
$$430$$ 0 0
$$431$$ 25.7128i 1.23854i −0.785177 0.619271i $$-0.787428\pi$$
0.785177 0.619271i $$-0.212572\pi$$
$$432$$ 3.86370 + 1.03528i 0.185893 + 0.0498097i
$$433$$ 3.11943 3.11943i 0.149910 0.149910i −0.628168 0.778078i $$-0.716195\pi$$
0.778078 + 0.628168i $$0.216195\pi$$
$$434$$ 0.901924 + 0.241670i 0.0432937 + 0.0116005i
$$435$$ 0 0
$$436$$ −12.1244 7.00000i −0.580651 0.335239i
$$437$$ 2.72689 + 2.72689i 0.130445 + 0.130445i
$$438$$ 4.89898 2.82843i 0.234082 0.135147i
$$439$$ −27.9808 −1.33545 −0.667724 0.744409i $$-0.732732\pi$$
−0.667724 + 0.744409i $$0.732732\pi$$
$$440$$ 0 0
$$441$$ −0.928203 −0.0442002
$$442$$ 42.1218 24.3190i 2.00353 1.15674i
$$443$$ −9.04008 9.04008i −0.429507 0.429507i 0.458953 0.888460i $$-0.348225\pi$$
−0.888460 + 0.458953i $$0.848225\pi$$
$$444$$ −5.07180 2.92820i −0.240697 0.138966i
$$445$$ 0 0
$$446$$ −15.5622 4.16987i −0.736890 0.197449i
$$447$$ 11.2122 11.2122i 0.530318 0.530318i
$$448$$ −13.9391 + 13.9391i −0.658559 + 0.658559i
$$449$$ 33.8564i 1.59778i −0.601475 0.798891i $$-0.705420\pi$$
0.601475 0.798891i $$-0.294580\pi$$
$$450$$ 0 0
$$451$$ 10.9282i 0.514589i
$$452$$ −7.17260 26.7685i −0.337371 1.25909i
$$453$$ −3.01790 + 3.01790i −0.141793 + 0.141793i
$$454$$ 4.53590 16.9282i 0.212880 0.794480i
$$455$$ 0 0
$$456$$ 14.3923 14.3923i 0.673981 0.673981i
$$457$$ 25.2528 + 25.2528i 1.18127 + 1.18127i 0.979414 + 0.201861i $$0.0646988\pi$$
0.201861 + 0.979414i $$0.435301\pi$$
$$458$$ 17.5761 + 30.4428i 0.821279 + 1.42250i
$$459$$ 6.00000 0.280056
$$460$$ 0 0
$$461$$ 15.6077 0.726923 0.363461 0.931609i $$-0.381595\pi$$
0.363461 + 0.931609i $$0.381595\pi$$
$$462$$ 3.48477 + 6.03579i 0.162126 + 0.280810i
$$463$$ −9.24316 9.24316i −0.429566 0.429566i 0.458915 0.888480i $$-0.348238\pi$$
−0.888480 + 0.458915i $$0.848238\pi$$
$$464$$ 25.8564 14.9282i 1.20035 0.693024i
$$465$$ 0 0
$$466$$ −4.53590 + 16.9282i −0.210121 + 0.784184i
$$467$$ 2.44949 2.44949i 0.113349 0.113349i −0.648157 0.761506i $$-0.724460\pi$$
0.761506 + 0.648157i $$0.224460\pi$$
$$468$$ −11.0735 + 2.96713i −0.511871 + 0.137156i
$$469$$ 30.7128i 1.41819i
$$470$$ 0 0
$$471$$ 9.73205i 0.448429i
$$472$$ 12.8295i 0.590524i
$$473$$ 3.48477 3.48477i 0.160230 0.160230i
$$474$$ 0.732051 + 0.196152i 0.0336242 + 0.00900958i
$$475$$ 0 0
$$476$$ −14.7846 + 25.6077i −0.677651 + 1.17373i
$$477$$ −1.03528 1.03528i −0.0474020 0.0474020i
$$478$$ −21.3891 + 12.3490i −0.978313 + 0.564829i
$$479$$ 13.3205 0.608630 0.304315 0.952572i $$-0.401573\pi$$
0.304315 + 0.952572i $$0.401573\pi$$
$$480$$ 0 0
$$481$$ 16.7846 0.765312
$$482$$ −18.1953 + 10.5051i −0.828774 + 0.478493i
$$483$$ 0.933740 + 0.933740i 0.0424867 + 0.0424867i
$$484$$ 7.00000 12.1244i 0.318182 0.551107i
$$485$$ 0 0
$$486$$ −1.36603 0.366025i −0.0619642 0.0166032i
$$487$$ 15.2282 15.2282i 0.690055 0.690055i −0.272189 0.962244i $$-0.587748\pi$$
0.962244 + 0.272189i $$0.0877476\pi$$
$$488$$ 8.48528i 0.384111i
$$489$$ 14.4641i 0.654089i
$$490$$ 0 0
$$491$$ 34.6410i 1.56333i 0.623700 + 0.781664i $$0.285629\pi$$
−0.623700 + 0.781664i $$0.714371\pi$$
$$492$$ −10.5558 + 2.82843i −0.475894 + 0.127515i
$$493$$ 31.6675 31.6675i 1.42623 1.42623i
$$494$$ −15.0981 + 56.3468i −0.679295 + 2.53516i
$$495$$ 0 0
$$496$$ 0.928203 0.535898i 0.0416776 0.0240625i
$$497$$ −16.4901 16.4901i −0.739682 0.739682i
$$498$$ 0.656339 + 1.13681i 0.0294112 + 0.0509418i
$$499$$ 5.87564 0.263030 0.131515 0.991314i $$-0.458016\pi$$
0.131515 + 0.991314i $$0.458016\pi$$
$$500$$ 0 0
$$501$$ 4.39230 0.196234
$$502$$ −1.51575 2.62536i −0.0676512 0.117175i
$$503$$ −14.4195 14.4195i −0.642935 0.642935i 0.308341 0.951276i $$-0.400226\pi$$
−0.951276 + 0.308341i $$0.900226\pi$$
$$504$$ 4.92820 4.92820i 0.219520 0.219520i
$$505$$ 0 0
$$506$$ −0.392305 + 1.46410i −0.0174401 + 0.0650873i
$$507$$ 14.0406 14.0406i 0.623565 0.623565i
$$508$$ −1.51575 5.65685i −0.0672505 0.250982i
$$509$$ 11.0718i 0.490749i 0.969428 + 0.245374i $$0.0789109\pi$$
−0.969428 + 0.245374i $$0.921089\pi$$
$$510$$ 0 0
$$511$$ 9.85641i 0.436022i
$$512$$ 22.6274i 1.00000i
$$513$$ −5.08845 + 5.08845i −0.224660 + 0.224660i
$$514$$ −17.4641 4.67949i −0.770309 0.206404i
$$515$$ 0 0
$$516$$ −4.26795 2.46410i −0.187886 0.108476i
$$517$$ −18.2832 18.2832i −0.804096 0.804096i
$$518$$ −8.83701 + 5.10205i −0.388276 + 0.224171i
$$519$$ −8.92820 −0.391905
$$520$$ 0 0
$$521$$ −17.6077 −0.771407 −0.385704 0.922623i $$-0.626041\pi$$
−0.385704 + 0.922623i $$0.626041\pi$$
$$522$$ −9.14162 + 5.27792i −0.400118 + 0.231008i
$$523$$ 13.7124 + 13.7124i 0.599603 + 0.599603i 0.940207 0.340604i $$-0.110632\pi$$
−0.340604 + 0.940207i $$0.610632\pi$$
$$524$$ 16.3923 + 9.46410i 0.716101 + 0.413441i
$$525$$ 0 0
$$526$$ 29.3205 + 7.85641i 1.27843 + 0.342556i
$$527$$ 1.13681 1.13681i 0.0495203 0.0495203i
$$528$$ 7.72741 + 2.07055i 0.336292 + 0.0901092i
$$529$$ 22.7128i 0.987514i
$$530$$ 0 0
$$531$$ 4.53590i 0.196841i
$$532$$ −9.17878 34.2557i −0.397951 1.48517i
$$533$$ 22.1469 22.1469i 0.959291 0.959291i
$$534$$ 2.53590 9.46410i 0.109739 0.409552i
$$535$$ 0 0
$$536$$ −24.9282 24.9282i −1.07673 1.07673i
$$537$$ 17.9043 + 17.9043i 0.772628 + 0.772628i
$$538$$ −1.13681 1.96902i −0.0490115 0.0848903i
$$539$$ −1.85641 −0.0799611
$$540$$ 0 0
$$541$$ −33.7846 −1.45251 −0.726257 0.687423i $$-0.758742\pi$$
−0.726257 + 0.687423i $$0.758742\pi$$
$$542$$ −17.1464 29.6985i −0.736502 1.27566i
$$543$$ −9.84873 9.84873i −0.422649 0.422649i
$$544$$ 8.78461 + 32.7846i 0.376637 + 1.40563i
$$545$$ 0 0
$$546$$ −5.16987 + 19.2942i −0.221250 + 0.825717i
$$547$$ −17.5254 + 17.5254i −0.749331 + 0.749331i −0.974353 0.225023i $$-0.927754\pi$$
0.225023 + 0.974353i $$0.427754\pi$$
$$548$$ 16.4901 4.41851i 0.704422 0.188749i
$$549$$ 3.00000i 0.128037i
$$550$$ 0 0
$$551$$ 53.7128i 2.28824i
$$552$$ 1.51575 0.0645146
$$553$$ 0.933740 0.933740i 0.0397067 0.0397067i
$$554$$ −1.63397 0.437822i −0.0694209 0.0186013i
$$555$$ 0 0
$$556$$ 19.4641 33.7128i 0.825462 1.42974i
$$557$$ 25.6317 + 25.6317i 1.08605 + 1.08605i 0.995931 + 0.0901194i $$0.0287249\pi$$
0.0901194 + 0.995931i $$0.471275\pi$$
$$558$$ −0.328169 + 0.189469i −0.0138925 + 0.00802085i
$$559$$ 14.1244 0.597397
$$560$$ 0 0
$$561$$ 12.0000 0.506640
$$562$$ −17.6269 + 10.1769i −0.743546 + 0.429286i
$$563$$ 16.3886 + 16.3886i 0.690695 + 0.690695i 0.962385 0.271690i $$-0.0875824\pi$$
−0.271690 + 0.962385i $$0.587582\pi$$
$$564$$ −12.9282 + 22.3923i −0.544376 + 0.942886i
$$565$$ 0 0
$$566$$ 29.2224 + 7.83013i 1.22831 + 0.329125i
$$567$$ −1.74238 + 1.74238i −0.0731732 + 0.0731732i
$$568$$ −26.7685 −1.12318
$$569$$ 17.3205i 0.726113i −0.931767 0.363057i $$-0.881733\pi$$
0.931767 0.363057i $$-0.118267\pi$$
$$570$$ 0 0
$$571$$ 16.8038i 0.703219i 0.936147 + 0.351610i $$0.114366\pi$$
−0.936147 + 0.351610i $$0.885634\pi$$
$$572$$ −22.1469 + 5.93426i −0.926010 + 0.248124i
$$573$$ 11.9700 11.9700i 0.500056 0.500056i
$$574$$ −4.92820 + 18.3923i −0.205699 + 0.767680i
$$575$$ 0 0
$$576$$ 8.00000i 0.333333i
$$577$$ 10.8468 + 10.8468i 0.451560 + 0.451560i 0.895872 0.444312i $$-0.146552\pi$$
−0.444312 + 0.895872i $$0.646552\pi$$
$$578$$ 13.4350 + 23.2702i 0.558824 + 0.967911i
$$579$$ −13.7321 −0.570685
$$580$$ 0 0
$$581$$ 2.28719 0.0948885
$$582$$ 4.43211 + 7.67664i 0.183717 + 0.318207i
$$583$$ −2.07055 2.07055i −0.0857535 0.0857535i
$$584$$ −8.00000 8.00000i −0.331042 0.331042i
$$585$$ 0 0
$$586$$ −4.58846 + 17.1244i −0.189547 + 0.707401i
$$587$$ −13.6617 + 13.6617i −0.563877 + 0.563877i −0.930406 0.366529i $$-0.880546\pi$$
0.366529 + 0.930406i $$0.380546\pi$$
$$588$$ 0.480473 + 1.79315i 0.0198144 + 0.0739483i
$$589$$ 1.92820i 0.0794502i
$$590$$ 0 0
$$591$$ 14.3923i 0.592020i
$$592$$ −3.03150 + 11.3137i −0.124594 + 0.464991i
$$593$$ 22.9048 22.9048i 0.940588 0.940588i −0.0577433 0.998331i $$-0.518390\pi$$
0.998331 + 0.0577433i $$0.0183905\pi$$
$$594$$ −2.73205 0.732051i −0.112097 0.0300364i
$$595$$ 0 0
$$596$$ −27.4641 15.8564i −1.12497 0.649504i
$$597$$ −9.98743 9.98743i −0.408758 0.408758i
$$598$$ −3.76217 + 2.17209i −0.153846 + 0.0888233i
$$599$$ −46.6410 −1.90570 −0.952850 0.303441i $$-0.901864\pi$$
−0.952850 + 0.303441i $$0.901864\pi$$
$$600$$ 0 0
$$601$$ −19.7846 −0.807031 −0.403516 0.914973i $$-0.632212\pi$$
−0.403516 + 0.914973i $$0.632212\pi$$
$$602$$ −7.43640 + 4.29341i −0.303085 + 0.174986i
$$603$$ 8.81345 + 8.81345i 0.358911 + 0.358911i
$$604$$ 7.39230 + 4.26795i 0.300789 + 0.173660i
$$605$$ 0 0
$$606$$ −2.00000 0.535898i −0.0812444 0.0217694i
$$607$$ −13.9391 + 13.9391i −0.565769 + 0.565769i −0.930940 0.365171i $$-0.881010\pi$$
0.365171 + 0.930940i $$0.381010\pi$$
$$608$$ −35.2538 20.3538i −1.42973 0.825455i
$$609$$ 18.3923i 0.745294i
$$610$$ 0 0
$$611$$ 74.1051i 2.99797i
$$612$$ −3.10583 11.5911i −0.125546 0.468543i
$$613$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$614$$ −4.90192 + 18.2942i −0.197826 + 0.738295i
$$615$$ 0 0
$$616$$ 9.85641 9.85641i 0.397126 0.397126i
$$617$$ −10.0754 10.0754i −0.405619 0.405619i 0.474589 0.880208i $$-0.342597\pi$$
−0.880208 + 0.474589i $$0.842597\pi$$
$$618$$ 4.89898 + 8.48528i 0.197066 + 0.341328i
$$619$$ −35.9808 −1.44619 −0.723094 0.690749i $$-0.757281\pi$$
−0.723094 + 0.690749i $$0.757281\pi$$
$$620$$ 0 0
$$621$$ −0.535898 −0.0215049
$$622$$ 19.4201 + 33.6365i 0.778673 + 1.34870i
$$623$$ −12.0716 12.0716i −0.483638 0.483638i
$$624$$ 11.4641 + 19.8564i 0.458931 + 0.794892i
$$625$$ 0 0
$$626$$ −2.97372 + 11.0981i −0.118854 + 0.443568i
$$627$$ −10.1769 + 10.1769i −0.406426 + 0.406426i
$$628$$ −18.8009 + 5.03768i −0.750237 + 0.201025i
$$629$$ 17.5692i 0.700531i
$$630$$ 0 0
$$631$$ 1.58846i 0.0632355i 0.999500 + 0.0316177i $$0.0100659\pi$$
−0.999500 + 0.0316177i $$0.989934\pi$$
$$632$$ 1.51575i 0.0602933i
$$633$$ 5.08845 5.08845i 0.202248 0.202248i
$$634$$ 9.46410 + 2.53590i 0.375867 + 0.100713i
$$635$$ 0 0
$$636$$ −1.46410 + 2.53590i −0.0580554 + 0.100555i
$$637$$ −3.76217 3.76217i −0.149062 0.149062i
$$638$$ −18.2832 + 10.5558i −0.723840 + 0.417909i
$$639$$ 9.46410 0.374394
$$640$$ 0 0
$$641$$ −3.21539 −0.127000 −0.0635001 0.997982i $$-0.520226\pi$$
−0.0635001 + 0.997982i $$0.520226\pi$$
$$642$$ 8.00481 4.62158i 0.315925 0.182399i
$$643$$ −12.0716 12.0716i −0.476057 0.476057i 0.427811 0.903868i $$-0.359285\pi$$
−0.903868 + 0.427811i $$0.859285\pi$$
$$644$$ 1.32051 2.28719i 0.0520353 0.0901278i
$$645$$ 0 0
$$646$$ −58.9808 15.8038i −2.32057 0.621794i
$$647$$ 3.58630 3.58630i 0.140992 0.140992i −0.633088 0.774080i $$-0.718213\pi$$
0.774080 + 0.633088i $$0.218213\pi$$
$$648$$ 2.82843i 0.111111i
$$649$$ 9.07180i 0.356099i
$$650$$ 0 0
$$651$$ 0.660254i 0.0258774i
$$652$$ −27.9425 + 7.48717i −1.09431 + 0.293220i
$$653$$ −7.34847 + 7.34847i −0.287568 + 0.287568i −0.836118 0.548550i $$-0.815180\pi$$
0.548550 + 0.836118i $$0.315180\pi$$
$$654$$ 2.56218 9.56218i 0.100189 0.373911i
$$655$$ 0 0
$$656$$ 10.9282 + 18.9282i 0.426675 + 0.739022i
$$657$$ 2.82843 + 2.82843i 0.110347 + 0.110347i
$$658$$ 22.5259 + 39.0160i 0.878150 + 1.52100i
$$659$$ −14.5359 −0.566238 −0.283119 0.959085i $$-0.591369\pi$$
−0.283119 + 0.959085i $$0.591369\pi$$
$$660$$ 0 0
$$661$$ −7.85641 −0.305579 −0.152789 0.988259i $$-0.548826\pi$$
−0.152789 + 0.988259i $$0.548826\pi$$
$$662$$ 1.69161 + 2.92996i 0.0657465 + 0.113876i
$$663$$ 24.3190 + 24.3190i 0.944473 + 0.944473i
$$664$$ 1.85641 1.85641i 0.0720425 0.0720425i
$$665$$ 0 0
$$666$$ 1.07180 4.00000i 0.0415313 0.154997i
$$667$$ −2.82843 + 2.82843i −0.109517 + 0.109517i
$$668$$ −2.27362 8.48528i −0.0879692 0.328305i
$$669$$ 11.3923i 0.440452i
$$670$$ 0 0
$$671$$ 6.00000i 0.231627i
$$672$$ −12.0716 6.96953i −0.465671 0.268856i
$$673$$ −2.82843 + 2.82843i −0.109028 + 0.109028i −0.759516 0.650488i $$-0.774564\pi$$
0.650488 + 0.759516i $$0.274564\pi$$
$$674$$ −15.4904 4.15064i −0.596667 0.159876i
$$675$$ 0 0
$$676$$ −34.3923 19.8564i −1.32278 0.763708i
$$677$$ 25.9091 + 25.9091i 0.995768 + 0.995768i 0.999991 0.00422306i $$-0.00134424\pi$$
−0.00422306 + 0.999991i $$0.501344\pi$$
$$678$$ 16.9706 9.79796i 0.651751 0.376288i
$$679$$ 15.4449 0.592719
$$680$$ 0 0
$$681$$ 12.3923 0.474874
$$682$$ −0.656339 + 0.378937i −0.0251325 + 0.0145103i
$$683$$ 3.58630 + 3.58630i 0.137226 + 0.137226i 0.772383 0.635157i $$-0.219065\pi$$
−0.635157 + 0.772383i $$0.719065\pi$$
$$684$$ 12.4641 + 7.19615i 0.476577 + 0.275152i
$$685$$ 0 0
$$686$$ 26.6865 + 7.15064i 1.01890 + 0.273013i
$$687$$ −17.5761 + 17.5761i −0.670571 + 0.670571i
$$688$$ −2.55103 + 9.52056i −0.0972569 + 0.362968i
$$689$$ 8.39230i 0.319721i
$$690$$ 0 0
$$691$$ 25.3205i 0.963238i −0.876381 0.481619i $$-0.840049\pi$$
0.876381 0.481619i $$-0.159951\pi$$
$$692$$ 4.62158 + 17.2480i 0.175686 + 0.655669i
$$693$$ −3.48477 + 3.48477i −0.132375 + 0.132375i
$$694$$ 4.05256 15.1244i 0.153833 0.574113i
$$695$$ 0 0
$$696$$ 14.9282 + 14.9282i 0.565852 + 0.565852i
$$697$$ 23.1822 + 23.1822i 0.878089 + 0.878089i
$$698$$ −2.72689 4.72311i −0.103214 0.178773i
$$699$$ −12.3923 −0.468720
$$700$$ 0 0
$$701$$ −15.4641 −0.584071 −0.292036 0.956407i $$-0.594333\pi$$
−0.292036 + 0.956407i $$0.594333\pi$$
$$702$$ −4.05317 7.02030i −0.152977 0.264964i
$$703$$ −14.9000 14.9000i −0.561965 0.561965i
$$704$$ 16.0000i 0.603023i
$$705$$ 0 0
$$706$$ 5.80385 21.6603i 0.218431 0.815194i
$$707$$ −2.55103 + 2.55103i −0.0959412 + 0.0959412i
$$708$$ −8.76268 + 2.34795i −0.329322 + 0.0882415i
$$709$$ 24.8564i 0.933502i 0.884389 + 0.466751i $$0.154576\pi$$
−0.884389 + 0.466751i $$0.845424\pi$$
$$710$$ 0 0
$$711$$ 0.535898i 0.0200978i
$$712$$ −19.5959 −0.734388
$$713$$ −0.101536 + 0.101536i −0.00380255 + 0.00380255i
$$714$$ −20.1962 5.41154i −0.755822 0.202522i
$$715$$ 0 0
$$716$$ 25.3205 43.8564i 0.946272 1.63899i
$$717$$ −12.3490 12.3490i −0.461181 0.461181i
$$718$$ 29.8744 17.2480i 1.11490 0.643688i
$$719$$ 12.9282 0.482141 0.241070 0.970508i $$-0.422502\pi$$
0.241070 + 0.970508i $$0.422502\pi$$
$$720$$ 0 0
$$721$$ 17.0718 0.635787
$$722$$ 40.1528 23.1822i 1.49433 0.862753i
$$723$$ −10.5051 10.5051i −0.390688 0.390688i
$$724$$ −13.9282 + 24.1244i −0.517638 + 0.896575i
$$725$$ 0 0
$$726$$ 9.56218 + 2.56218i 0.354886 + 0.0950913i
$$727$$ 33.3083 33.3083i 1.23534 1.23534i 0.273453 0.961885i $$-0.411834\pi$$
0.961885 0.273453i $$-0.0881658\pi$$
$$728$$ 39.9497 1.48063
$$729$$ 1.00000i 0.0370370i
$$730$$ 0 0
$$731$$ 14.7846i 0.546829i
$$732$$ 5.79555 1.55291i 0.214210 0.0573974i
$$733$$ −13.9391 + 13.9391i −0.514851 + 0.514851i −0.916009 0.401158i $$-0.868608\pi$$
0.401158 + 0.916009i $$0.368608\pi$$
$$734$$ −3.88269 + 14.4904i −0.143313 + 0.534850i
$$735$$ 0 0
$$736$$ −0.784610 2.92820i −0.0289211 0.107935i
$$737$$ 17.6269 + 17.6269i 0.649295 + 0.649295i
$$738$$ −3.86370 6.69213i −0.142225 0.246341i
$$739$$ 14.3923 0.529429 0.264715 0.964327i $$-0.414722\pi$$
0.264715 + 0.964327i $$0.414722\pi$$
$$740$$ 0 0
$$741$$ −41.2487 −1.51531
$$742$$ 2.55103 + 4.41851i 0.0936511 + 0.162208i
$$743$$ 21.8695 + 21.8695i 0.802316 + 0.802316i 0.983457 0.181141i $$-0.0579792\pi$$
−0.181141 + 0.983457i $$0.557979\pi$$
$$744$$ 0.535898 + 0.535898i 0.0196470 + 0.0196470i
$$745$$ 0 0
$$746$$ −7.07884 + 26.4186i −0.259175 + 0.967253i
$$747$$ −0.656339 + 0.656339i −0.0240142 + 0.0240142i
$$748$$ −6.21166 23.1822i −0.227121 0.847626i
$$749$$ 16.1051i 0.588468i
$$750$$ 0 0
$$751$$ 11.4641i 0.418331i −0.977880 0.209166i $$-0.932925\pi$$
0.977880 0.209166i $$-0.0670747\pi$$
$$752$$ 49.9507 + 13.3843i 1.82152 + 0.488074i
$$753$$ 1.51575 1.51575i 0.0552370 0.0552370i
$$754$$ −58.4449 15.6603i −2.12844 0.570313i
$$755$$ 0 0
$$756$$ 4.26795 + 2.46410i 0.155224 + 0.0896185i
$$757$$ −20.6448 20.6448i −0.750348 0.750348i 0.224196 0.974544i $$-0.428024\pi$$
−0.974544 + 0.224196i $$0.928024\pi$$
$$758$$ −19.2677 + 11.1242i −0.699836 + 0.404051i
$$759$$ −1.07180 −0.0389038
$$760$$ 0 0
$$761$$ 46.6410 1.69074 0.845368 0.534185i $$-0.179381\pi$$
0.845368 + 0.534185i $$0.179381\pi$$
$$762$$ 3.58630 2.07055i 0.129918 0.0750082i
$$763$$ −12.1967 12.1967i −0.441549 0.441549i
$$764$$ −29.3205 16.9282i −1.06078 0.612441i
$$765$$ 0 0
$$766$$ 22.9282 + 6.14359i 0.828430 + 0.221977i
$$767$$ 18.3848 18.3848i 0.663836 0.663836i
$$768$$ −15.4548 + 4.14110i −0.557678 + 0.149429i
$$769$$ 29.9282i 1.07924i −0.841909 0.539619i $$-0.818568\pi$$
0.841909 0.539619i $$-0.181432\pi$$
$$770$$ 0 0
$$771$$ 12.7846i 0.460426i
$$772$$ 7.10823 + 26.5283i 0.255831 + 0.954774i
$$773$$ −23.4596 + 23.4596i −0.843784 + 0.843784i −0.989349 0.145565i $$-0.953500\pi$$
0.145565 + 0.989349i $$0.453500\pi$$
$$774$$ 0.901924 3.36603i 0.0324190 0.120989i
$$775$$ 0 0
$$776$$ 12.5359 12.5359i 0.450013 0.450013i
$$777$$ −5.10205 5.10205i −0.183035 0.183035i
$$778$$ −10.2784 17.8028i −0.368500 0.638260i
$$779$$ −39.3205 −1.40880
$$780$$ 0 0
$$781$$ 18.9282 0.677304
$$782$$ −2.27362 3.93803i −0.0813046 0.140824i
$$783$$ −5.27792 5.27792i −0.188617 0.188617i