# Properties

 Label 1170.2.bs.e.361.1 Level $1170$ Weight $2$ Character 1170.361 Analytic conductor $9.342$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1170.bs (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.34249703649$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 361.1 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1170.361 Dual form 1170.2.bs.e.901.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{10} +(-0.401924 + 0.232051i) q^{11} +(1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.464102 - 0.267949i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(0.232051 - 0.401924i) q^{22} +(0.133975 + 0.232051i) q^{23} -1.00000 q^{25} +(-2.59808 - 2.50000i) q^{26} +(1.73205 - 1.00000i) q^{28} +(1.86603 + 3.23205i) q^{29} +1.73205i q^{31} +(0.866025 + 0.500000i) q^{32} -4.00000i q^{34} +(1.00000 - 1.73205i) q^{35} +(1.03590 - 0.598076i) q^{37} +0.535898 q^{38} +1.00000 q^{40} +(1.73205 - 1.00000i) q^{41} +(0.964102 - 1.66987i) q^{43} +0.464102i q^{44} +(-0.232051 - 0.133975i) q^{46} +10.4641i q^{47} +(-1.50000 - 2.59808i) q^{49} +(0.866025 - 0.500000i) q^{50} +(3.50000 + 0.866025i) q^{52} +12.9282 q^{53} +(0.232051 + 0.401924i) q^{55} +(-1.00000 + 1.73205i) q^{56} +(-3.23205 - 1.86603i) q^{58} +(1.33013 + 0.767949i) q^{59} +(-5.19615 + 9.00000i) q^{61} +(-0.866025 - 1.50000i) q^{62} -1.00000 q^{64} +(3.46410 - 1.00000i) q^{65} +(3.92820 - 2.26795i) q^{67} +(2.00000 + 3.46410i) q^{68} +2.00000i q^{70} +(7.26795 + 4.19615i) q^{71} +2.00000i q^{73} +(-0.598076 + 1.03590i) q^{74} +(-0.464102 + 0.267949i) q^{76} -0.928203 q^{77} -0.0717968 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-1.00000 + 1.73205i) q^{82} +4.92820i q^{83} +(3.46410 + 2.00000i) q^{85} +1.92820i q^{86} +(-0.232051 - 0.401924i) q^{88} +(-6.46410 + 3.73205i) q^{89} +(-1.73205 + 7.00000i) q^{91} +0.267949 q^{92} +(-5.23205 - 9.06218i) q^{94} +(-0.267949 + 0.464102i) q^{95} +(-6.46410 - 3.73205i) q^{97} +(2.59808 + 1.50000i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{4} + O(q^{10})$$ $$4q + 2q^{4} + 2q^{10} - 12q^{11} + 4q^{13} - 8q^{14} - 2q^{16} - 8q^{17} + 12q^{19} - 6q^{22} + 4q^{23} - 4q^{25} + 4q^{29} + 4q^{35} + 18q^{37} + 16q^{38} + 4q^{40} - 10q^{43} + 6q^{46} - 6q^{49} + 14q^{52} + 24q^{53} - 6q^{55} - 4q^{56} - 6q^{58} - 12q^{59} - 4q^{64} - 12q^{67} + 8q^{68} + 36q^{71} + 8q^{74} + 12q^{76} + 24q^{77} - 28q^{79} - 4q^{82} + 6q^{88} - 12q^{89} + 8q^{92} - 14q^{94} - 8q^{95} - 12q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$$.

 $$n$$ $$911$$ $$937$$ $$1081$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 + 0.500000i −0.612372 + 0.353553i
$$3$$ 0 0
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 1.00000i 0.447214i
$$6$$ 0 0
$$7$$ 1.73205 + 1.00000i 0.654654 + 0.377964i 0.790237 0.612801i $$-0.209957\pi$$
−0.135583 + 0.990766i $$0.543291\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 0.500000 + 0.866025i 0.158114 + 0.273861i
$$11$$ −0.401924 + 0.232051i −0.121185 + 0.0699660i −0.559367 0.828920i $$-0.688956\pi$$
0.438182 + 0.898886i $$0.355622\pi$$
$$12$$ 0 0
$$13$$ 1.00000 + 3.46410i 0.277350 + 0.960769i
$$14$$ −2.00000 −0.534522
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i $$-0.994540\pi$$
0.514782 + 0.857321i $$0.327873\pi$$
$$18$$ 0 0
$$19$$ −0.464102 0.267949i −0.106472 0.0614718i 0.445818 0.895123i $$-0.352913\pi$$
−0.552291 + 0.833652i $$0.686246\pi$$
$$20$$ −0.866025 0.500000i −0.193649 0.111803i
$$21$$ 0 0
$$22$$ 0.232051 0.401924i 0.0494734 0.0856904i
$$23$$ 0.133975 + 0.232051i 0.0279356 + 0.0483859i 0.879655 0.475612i $$-0.157773\pi$$
−0.851720 + 0.523998i $$0.824440\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ −2.59808 2.50000i −0.509525 0.490290i
$$27$$ 0 0
$$28$$ 1.73205 1.00000i 0.327327 0.188982i
$$29$$ 1.86603 + 3.23205i 0.346512 + 0.600177i 0.985627 0.168934i $$-0.0540326\pi$$
−0.639115 + 0.769111i $$0.720699\pi$$
$$30$$ 0 0
$$31$$ 1.73205i 0.311086i 0.987829 + 0.155543i $$0.0497126\pi$$
−0.987829 + 0.155543i $$0.950287\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ 0 0
$$34$$ 4.00000i 0.685994i
$$35$$ 1.00000 1.73205i 0.169031 0.292770i
$$36$$ 0 0
$$37$$ 1.03590 0.598076i 0.170301 0.0983231i −0.412427 0.910991i $$-0.635319\pi$$
0.582728 + 0.812668i $$0.301985\pi$$
$$38$$ 0.535898 0.0869342
$$39$$ 0 0
$$40$$ 1.00000 0.158114
$$41$$ 1.73205 1.00000i 0.270501 0.156174i −0.358614 0.933486i $$-0.616751\pi$$
0.629115 + 0.777312i $$0.283417\pi$$
$$42$$ 0 0
$$43$$ 0.964102 1.66987i 0.147024 0.254653i −0.783102 0.621893i $$-0.786364\pi$$
0.930126 + 0.367240i $$0.119697\pi$$
$$44$$ 0.464102i 0.0699660i
$$45$$ 0 0
$$46$$ −0.232051 0.133975i −0.0342140 0.0197535i
$$47$$ 10.4641i 1.52635i 0.646194 + 0.763173i $$0.276360\pi$$
−0.646194 + 0.763173i $$0.723640\pi$$
$$48$$ 0 0
$$49$$ −1.50000 2.59808i −0.214286 0.371154i
$$50$$ 0.866025 0.500000i 0.122474 0.0707107i
$$51$$ 0 0
$$52$$ 3.50000 + 0.866025i 0.485363 + 0.120096i
$$53$$ 12.9282 1.77583 0.887913 0.460012i $$-0.152155\pi$$
0.887913 + 0.460012i $$0.152155\pi$$
$$54$$ 0 0
$$55$$ 0.232051 + 0.401924i 0.0312897 + 0.0541954i
$$56$$ −1.00000 + 1.73205i −0.133631 + 0.231455i
$$57$$ 0 0
$$58$$ −3.23205 1.86603i −0.424389 0.245021i
$$59$$ 1.33013 + 0.767949i 0.173168 + 0.0999785i 0.584079 0.811697i $$-0.301456\pi$$
−0.410911 + 0.911676i $$0.634789\pi$$
$$60$$ 0 0
$$61$$ −5.19615 + 9.00000i −0.665299 + 1.15233i 0.313905 + 0.949454i $$0.398363\pi$$
−0.979204 + 0.202878i $$0.934971\pi$$
$$62$$ −0.866025 1.50000i −0.109985 0.190500i
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 3.46410 1.00000i 0.429669 0.124035i
$$66$$ 0 0
$$67$$ 3.92820 2.26795i 0.479906 0.277074i −0.240471 0.970656i $$-0.577302\pi$$
0.720377 + 0.693582i $$0.243969\pi$$
$$68$$ 2.00000 + 3.46410i 0.242536 + 0.420084i
$$69$$ 0 0
$$70$$ 2.00000i 0.239046i
$$71$$ 7.26795 + 4.19615i 0.862547 + 0.497992i 0.864864 0.502006i $$-0.167404\pi$$
−0.00231747 + 0.999997i $$0.500738\pi$$
$$72$$ 0 0
$$73$$ 2.00000i 0.234082i 0.993127 + 0.117041i $$0.0373409\pi$$
−0.993127 + 0.117041i $$0.962659\pi$$
$$74$$ −0.598076 + 1.03590i −0.0695249 + 0.120421i
$$75$$ 0 0
$$76$$ −0.464102 + 0.267949i −0.0532361 + 0.0307359i
$$77$$ −0.928203 −0.105779
$$78$$ 0 0
$$79$$ −0.0717968 −0.00807777 −0.00403888 0.999992i $$-0.501286\pi$$
−0.00403888 + 0.999992i $$0.501286\pi$$
$$80$$ −0.866025 + 0.500000i −0.0968246 + 0.0559017i
$$81$$ 0 0
$$82$$ −1.00000 + 1.73205i −0.110432 + 0.191273i
$$83$$ 4.92820i 0.540941i 0.962728 + 0.270470i $$0.0871792\pi$$
−0.962728 + 0.270470i $$0.912821\pi$$
$$84$$ 0 0
$$85$$ 3.46410 + 2.00000i 0.375735 + 0.216930i
$$86$$ 1.92820i 0.207924i
$$87$$ 0 0
$$88$$ −0.232051 0.401924i −0.0247367 0.0428452i
$$89$$ −6.46410 + 3.73205i −0.685193 + 0.395597i −0.801809 0.597581i $$-0.796129\pi$$
0.116615 + 0.993177i $$0.462795\pi$$
$$90$$ 0 0
$$91$$ −1.73205 + 7.00000i −0.181568 + 0.733799i
$$92$$ 0.267949 0.0279356
$$93$$ 0 0
$$94$$ −5.23205 9.06218i −0.539645 0.934692i
$$95$$ −0.267949 + 0.464102i −0.0274910 + 0.0476158i
$$96$$ 0 0
$$97$$ −6.46410 3.73205i −0.656330 0.378932i 0.134547 0.990907i $$-0.457042\pi$$
−0.790877 + 0.611975i $$0.790375\pi$$
$$98$$ 2.59808 + 1.50000i 0.262445 + 0.151523i
$$99$$ 0 0
$$100$$ −0.500000 + 0.866025i −0.0500000 + 0.0866025i
$$101$$ −5.46410 9.46410i −0.543698 0.941713i −0.998688 0.0512163i $$-0.983690\pi$$
0.454989 0.890497i $$-0.349643\pi$$
$$102$$ 0 0
$$103$$ 15.8564 1.56238 0.781189 0.624295i $$-0.214613\pi$$
0.781189 + 0.624295i $$0.214613\pi$$
$$104$$ −3.46410 + 1.00000i −0.339683 + 0.0980581i
$$105$$ 0 0
$$106$$ −11.1962 + 6.46410i −1.08747 + 0.627849i
$$107$$ 9.92820 + 17.1962i 0.959796 + 1.66241i 0.722991 + 0.690858i $$0.242767\pi$$
0.236805 + 0.971557i $$0.423900\pi$$
$$108$$ 0 0
$$109$$ 11.8564i 1.13564i 0.823154 + 0.567819i $$0.192213\pi$$
−0.823154 + 0.567819i $$0.807787\pi$$
$$110$$ −0.401924 0.232051i −0.0383219 0.0221252i
$$111$$ 0 0
$$112$$ 2.00000i 0.188982i
$$113$$ 5.59808 9.69615i 0.526623 0.912137i −0.472896 0.881118i $$-0.656791\pi$$
0.999519 0.0310191i $$-0.00987527\pi$$
$$114$$ 0 0
$$115$$ 0.232051 0.133975i 0.0216388 0.0124932i
$$116$$ 3.73205 0.346512
$$117$$ 0 0
$$118$$ −1.53590 −0.141391
$$119$$ −6.92820 + 4.00000i −0.635107 + 0.366679i
$$120$$ 0 0
$$121$$ −5.39230 + 9.33975i −0.490210 + 0.849068i
$$122$$ 10.3923i 0.940875i
$$123$$ 0 0
$$124$$ 1.50000 + 0.866025i 0.134704 + 0.0777714i
$$125$$ 1.00000i 0.0894427i
$$126$$ 0 0
$$127$$ −4.46410 7.73205i −0.396125 0.686109i 0.597119 0.802153i $$-0.296312\pi$$
−0.993244 + 0.116044i $$0.962979\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ 0 0
$$130$$ −2.50000 + 2.59808i −0.219265 + 0.227866i
$$131$$ 1.33975 0.117054 0.0585271 0.998286i $$-0.481360\pi$$
0.0585271 + 0.998286i $$0.481360\pi$$
$$132$$ 0 0
$$133$$ −0.535898 0.928203i −0.0464683 0.0804854i
$$134$$ −2.26795 + 3.92820i −0.195921 + 0.339345i
$$135$$ 0 0
$$136$$ −3.46410 2.00000i −0.297044 0.171499i
$$137$$ 3.86603 + 2.23205i 0.330297 + 0.190697i 0.655973 0.754784i $$-0.272259\pi$$
−0.325676 + 0.945481i $$0.605592\pi$$
$$138$$ 0 0
$$139$$ −0.464102 + 0.803848i −0.0393646 + 0.0681815i −0.885036 0.465522i $$-0.845867\pi$$
0.845672 + 0.533703i $$0.179200\pi$$
$$140$$ −1.00000 1.73205i −0.0845154 0.146385i
$$141$$ 0 0
$$142$$ −8.39230 −0.704267
$$143$$ −1.20577 1.16025i −0.100832 0.0970253i
$$144$$ 0 0
$$145$$ 3.23205 1.86603i 0.268407 0.154965i
$$146$$ −1.00000 1.73205i −0.0827606 0.143346i
$$147$$ 0 0
$$148$$ 1.19615i 0.0983231i
$$149$$ −17.7224 10.2321i −1.45188 0.838242i −0.453290 0.891363i $$-0.649750\pi$$
−0.998588 + 0.0531208i $$0.983083\pi$$
$$150$$ 0 0
$$151$$ 10.3923i 0.845714i 0.906196 + 0.422857i $$0.138973\pi$$
−0.906196 + 0.422857i $$0.861027\pi$$
$$152$$ 0.267949 0.464102i 0.0217335 0.0376436i
$$153$$ 0 0
$$154$$ 0.803848 0.464102i 0.0647759 0.0373984i
$$155$$ 1.73205 0.139122
$$156$$ 0 0
$$157$$ −5.00000 −0.399043 −0.199522 0.979893i $$-0.563939\pi$$
−0.199522 + 0.979893i $$0.563939\pi$$
$$158$$ 0.0621778 0.0358984i 0.00494660 0.00285592i
$$159$$ 0 0
$$160$$ 0.500000 0.866025i 0.0395285 0.0684653i
$$161$$ 0.535898i 0.0422347i
$$162$$ 0 0
$$163$$ 19.9641 + 11.5263i 1.56371 + 0.902808i 0.996877 + 0.0789748i $$0.0251647\pi$$
0.566833 + 0.823833i $$0.308169\pi$$
$$164$$ 2.00000i 0.156174i
$$165$$ 0 0
$$166$$ −2.46410 4.26795i −0.191251 0.331257i
$$167$$ −15.8660 + 9.16025i −1.22775 + 0.708842i −0.966559 0.256445i $$-0.917449\pi$$
−0.261191 + 0.965287i $$0.584115\pi$$
$$168$$ 0 0
$$169$$ −11.0000 + 6.92820i −0.846154 + 0.532939i
$$170$$ −4.00000 −0.306786
$$171$$ 0 0
$$172$$ −0.964102 1.66987i −0.0735121 0.127327i
$$173$$ −1.46410 + 2.53590i −0.111314 + 0.192801i −0.916300 0.400492i $$-0.868839\pi$$
0.804987 + 0.593293i $$0.202172\pi$$
$$174$$ 0 0
$$175$$ −1.73205 1.00000i −0.130931 0.0755929i
$$176$$ 0.401924 + 0.232051i 0.0302961 + 0.0174915i
$$177$$ 0 0
$$178$$ 3.73205 6.46410i 0.279729 0.484505i
$$179$$ −8.13397 14.0885i −0.607962 1.05302i −0.991576 0.129527i $$-0.958654\pi$$
0.383614 0.923494i $$-0.374679\pi$$
$$180$$ 0 0
$$181$$ 10.9282 0.812287 0.406143 0.913809i $$-0.366873\pi$$
0.406143 + 0.913809i $$0.366873\pi$$
$$182$$ −2.00000 6.92820i −0.148250 0.513553i
$$183$$ 0 0
$$184$$ −0.232051 + 0.133975i −0.0171070 + 0.00987674i
$$185$$ −0.598076 1.03590i −0.0439714 0.0761608i
$$186$$ 0 0
$$187$$ 1.85641i 0.135754i
$$188$$ 9.06218 + 5.23205i 0.660927 + 0.381587i
$$189$$ 0 0
$$190$$ 0.535898i 0.0388782i
$$191$$ 7.26795 12.5885i 0.525890 0.910869i −0.473655 0.880711i $$-0.657066\pi$$
0.999545 0.0301582i $$-0.00960111\pi$$
$$192$$ 0 0
$$193$$ 20.1962 11.6603i 1.45375 0.839323i 0.455059 0.890461i $$-0.349618\pi$$
0.998692 + 0.0511377i $$0.0162847\pi$$
$$194$$ 7.46410 0.535891
$$195$$ 0 0
$$196$$ −3.00000 −0.214286
$$197$$ −14.1962 + 8.19615i −1.01143 + 0.583952i −0.911611 0.411054i $$-0.865161\pi$$
−0.0998228 + 0.995005i $$0.531828\pi$$
$$198$$ 0 0
$$199$$ 9.46410 16.3923i 0.670892 1.16202i −0.306759 0.951787i $$-0.599245\pi$$
0.977651 0.210232i $$-0.0674221\pi$$
$$200$$ 1.00000i 0.0707107i
$$201$$ 0 0
$$202$$ 9.46410 + 5.46410i 0.665892 + 0.384453i
$$203$$ 7.46410i 0.523877i
$$204$$ 0 0
$$205$$ −1.00000 1.73205i −0.0698430 0.120972i
$$206$$ −13.7321 + 7.92820i −0.956757 + 0.552384i
$$207$$ 0 0
$$208$$ 2.50000 2.59808i 0.173344 0.180144i
$$209$$ 0.248711 0.0172037
$$210$$ 0 0
$$211$$ −11.6603 20.1962i −0.802725 1.39036i −0.917816 0.397006i $$-0.870049\pi$$
0.115091 0.993355i $$-0.463284\pi$$
$$212$$ 6.46410 11.1962i 0.443956 0.768955i
$$213$$ 0 0
$$214$$ −17.1962 9.92820i −1.17550 0.678678i
$$215$$ −1.66987 0.964102i −0.113884 0.0657512i
$$216$$ 0 0
$$217$$ −1.73205 + 3.00000i −0.117579 + 0.203653i
$$218$$ −5.92820 10.2679i −0.401509 0.695433i
$$219$$ 0 0
$$220$$ 0.464102 0.0312897
$$221$$ −14.0000 3.46410i −0.941742 0.233021i
$$222$$ 0 0
$$223$$ 23.7846 13.7321i 1.59274 0.919566i 0.599900 0.800075i $$-0.295207\pi$$
0.992835 0.119491i $$-0.0381263\pi$$
$$224$$ 1.00000 + 1.73205i 0.0668153 + 0.115728i
$$225$$ 0 0
$$226$$ 11.1962i 0.744757i
$$227$$ 3.80385 + 2.19615i 0.252470 + 0.145764i 0.620895 0.783894i $$-0.286769\pi$$
−0.368425 + 0.929658i $$0.620103\pi$$
$$228$$ 0 0
$$229$$ 19.8564i 1.31215i 0.754696 + 0.656074i $$0.227784\pi$$
−0.754696 + 0.656074i $$0.772216\pi$$
$$230$$ −0.133975 + 0.232051i −0.00883402 + 0.0153010i
$$231$$ 0 0
$$232$$ −3.23205 + 1.86603i −0.212195 + 0.122511i
$$233$$ 18.1244 1.18737 0.593683 0.804699i $$-0.297673\pi$$
0.593683 + 0.804699i $$0.297673\pi$$
$$234$$ 0 0
$$235$$ 10.4641 0.682603
$$236$$ 1.33013 0.767949i 0.0865839 0.0499892i
$$237$$ 0 0
$$238$$ 4.00000 6.92820i 0.259281 0.449089i
$$239$$ 4.39230i 0.284115i −0.989858 0.142057i $$-0.954628\pi$$
0.989858 0.142057i $$-0.0453717\pi$$
$$240$$ 0 0
$$241$$ −12.3564 7.13397i −0.795946 0.459540i 0.0461056 0.998937i $$-0.485319\pi$$
−0.842052 + 0.539397i $$0.818652\pi$$
$$242$$ 10.7846i 0.693261i
$$243$$ 0 0
$$244$$ 5.19615 + 9.00000i 0.332650 + 0.576166i
$$245$$ −2.59808 + 1.50000i −0.165985 + 0.0958315i
$$246$$ 0 0
$$247$$ 0.464102 1.87564i 0.0295301 0.119344i
$$248$$ −1.73205 −0.109985
$$249$$ 0 0
$$250$$ −0.500000 0.866025i −0.0316228 0.0547723i
$$251$$ 6.13397 10.6244i 0.387173 0.670603i −0.604895 0.796305i $$-0.706785\pi$$
0.992068 + 0.125702i $$0.0401183\pi$$
$$252$$ 0 0
$$253$$ −0.107695 0.0621778i −0.00677074 0.00390909i
$$254$$ 7.73205 + 4.46410i 0.485152 + 0.280103i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −11.3301 19.6244i −0.706754 1.22413i −0.966055 0.258337i $$-0.916825\pi$$
0.259301 0.965797i $$-0.416508\pi$$
$$258$$ 0 0
$$259$$ 2.39230 0.148651
$$260$$ 0.866025 3.50000i 0.0537086 0.217061i
$$261$$ 0 0
$$262$$ −1.16025 + 0.669873i −0.0716807 + 0.0413849i
$$263$$ −9.06218 15.6962i −0.558798 0.967866i −0.997597 0.0692812i $$-0.977929\pi$$
0.438799 0.898585i $$-0.355404\pi$$
$$264$$ 0 0
$$265$$ 12.9282i 0.794173i
$$266$$ 0.928203 + 0.535898i 0.0569118 + 0.0328580i
$$267$$ 0 0
$$268$$ 4.53590i 0.277074i
$$269$$ 6.00000 10.3923i 0.365826 0.633630i −0.623082 0.782157i $$-0.714120\pi$$
0.988908 + 0.148527i $$0.0474530\pi$$
$$270$$ 0 0
$$271$$ 7.96410 4.59808i 0.483785 0.279313i −0.238208 0.971214i $$-0.576560\pi$$
0.721992 + 0.691901i $$0.243227\pi$$
$$272$$ 4.00000 0.242536
$$273$$ 0 0
$$274$$ −4.46410 −0.269686
$$275$$ 0.401924 0.232051i 0.0242369 0.0139932i
$$276$$ 0 0
$$277$$ −4.96410 + 8.59808i −0.298264 + 0.516608i −0.975739 0.218938i $$-0.929741\pi$$
0.677475 + 0.735546i $$0.263074\pi$$
$$278$$ 0.928203i 0.0556699i
$$279$$ 0 0
$$280$$ 1.73205 + 1.00000i 0.103510 + 0.0597614i
$$281$$ 4.92820i 0.293992i −0.989137 0.146996i $$-0.953040\pi$$
0.989137 0.146996i $$-0.0469604\pi$$
$$282$$ 0 0
$$283$$ −1.96410 3.40192i −0.116754 0.202223i 0.801726 0.597692i $$-0.203915\pi$$
−0.918479 + 0.395469i $$0.870582\pi$$
$$284$$ 7.26795 4.19615i 0.431273 0.248996i
$$285$$ 0 0
$$286$$ 1.62436 + 0.401924i 0.0960502 + 0.0237663i
$$287$$ 4.00000 0.236113
$$288$$ 0 0
$$289$$ 0.500000 + 0.866025i 0.0294118 + 0.0509427i
$$290$$ −1.86603 + 3.23205i −0.109577 + 0.189793i
$$291$$ 0 0
$$292$$ 1.73205 + 1.00000i 0.101361 + 0.0585206i
$$293$$ −3.58846 2.07180i −0.209640 0.121036i 0.391504 0.920176i $$-0.371955\pi$$
−0.601144 + 0.799141i $$0.705288\pi$$
$$294$$ 0 0
$$295$$ 0.767949 1.33013i 0.0447117 0.0774430i
$$296$$ 0.598076 + 1.03590i 0.0347625 + 0.0602104i
$$297$$ 0 0
$$298$$ 20.4641 1.18545
$$299$$ −0.669873 + 0.696152i −0.0387398 + 0.0402595i
$$300$$ 0 0
$$301$$ 3.33975 1.92820i 0.192500 0.111140i
$$302$$ −5.19615 9.00000i −0.299005 0.517892i
$$303$$ 0 0
$$304$$ 0.535898i 0.0307359i
$$305$$ 9.00000 + 5.19615i 0.515339 + 0.297531i
$$306$$ 0 0
$$307$$ 12.5359i 0.715462i 0.933825 + 0.357731i $$0.116449\pi$$
−0.933825 + 0.357731i $$0.883551\pi$$
$$308$$ −0.464102 + 0.803848i −0.0264446 + 0.0458035i
$$309$$ 0 0
$$310$$ −1.50000 + 0.866025i −0.0851943 + 0.0491869i
$$311$$ 7.60770 0.431393 0.215696 0.976460i $$-0.430798\pi$$
0.215696 + 0.976460i $$0.430798\pi$$
$$312$$ 0 0
$$313$$ −28.0000 −1.58265 −0.791327 0.611393i $$-0.790609\pi$$
−0.791327 + 0.611393i $$0.790609\pi$$
$$314$$ 4.33013 2.50000i 0.244363 0.141083i
$$315$$ 0 0
$$316$$ −0.0358984 + 0.0621778i −0.00201944 + 0.00349778i
$$317$$ 21.4641i 1.20554i −0.797913 0.602772i $$-0.794063\pi$$
0.797913 0.602772i $$-0.205937\pi$$
$$318$$ 0 0
$$319$$ −1.50000 0.866025i −0.0839839 0.0484881i
$$320$$ 1.00000i 0.0559017i
$$321$$ 0 0
$$322$$ −0.267949 0.464102i −0.0149322 0.0258634i
$$323$$ 1.85641 1.07180i 0.103293 0.0596364i
$$324$$ 0 0
$$325$$ −1.00000 3.46410i −0.0554700 0.192154i
$$326$$ −23.0526 −1.27676
$$327$$ 0 0
$$328$$ 1.00000 + 1.73205i 0.0552158 + 0.0956365i
$$329$$ −10.4641 + 18.1244i −0.576905 + 0.999228i
$$330$$ 0 0
$$331$$ −21.4641 12.3923i −1.17977 0.681143i −0.223812 0.974632i $$-0.571850\pi$$
−0.955962 + 0.293490i $$0.905183\pi$$
$$332$$ 4.26795 + 2.46410i 0.234234 + 0.135235i
$$333$$ 0 0
$$334$$ 9.16025 15.8660i 0.501227 0.868150i
$$335$$ −2.26795 3.92820i −0.123911 0.214621i
$$336$$ 0 0
$$337$$ −25.3205 −1.37930 −0.689648 0.724145i $$-0.742235\pi$$
−0.689648 + 0.724145i $$0.742235\pi$$
$$338$$ 6.06218 11.5000i 0.329739 0.625518i
$$339$$ 0 0
$$340$$ 3.46410 2.00000i 0.187867 0.108465i
$$341$$ −0.401924 0.696152i −0.0217654 0.0376988i
$$342$$ 0 0
$$343$$ 20.0000i 1.07990i
$$344$$ 1.66987 + 0.964102i 0.0900335 + 0.0519809i
$$345$$ 0 0
$$346$$ 2.92820i 0.157421i
$$347$$ 11.1962 19.3923i 0.601041 1.04103i −0.391623 0.920126i $$-0.628086\pi$$
0.992664 0.120908i $$-0.0385805\pi$$
$$348$$ 0 0
$$349$$ −12.5885 + 7.26795i −0.673845 + 0.389044i −0.797532 0.603277i $$-0.793861\pi$$
0.123687 + 0.992321i $$0.460528\pi$$
$$350$$ 2.00000 0.106904
$$351$$ 0 0
$$352$$ −0.464102 −0.0247367
$$353$$ 1.73205 1.00000i 0.0921878 0.0532246i −0.453197 0.891410i $$-0.649717\pi$$
0.545385 + 0.838186i $$0.316383\pi$$
$$354$$ 0 0
$$355$$ 4.19615 7.26795i 0.222709 0.385743i
$$356$$ 7.46410i 0.395597i
$$357$$ 0 0
$$358$$ 14.0885 + 8.13397i 0.744598 + 0.429894i
$$359$$ 18.9282i 0.998992i −0.866316 0.499496i $$-0.833518\pi$$
0.866316 0.499496i $$-0.166482\pi$$
$$360$$ 0 0
$$361$$ −9.35641 16.2058i −0.492442 0.852935i
$$362$$ −9.46410 + 5.46410i −0.497422 + 0.287187i
$$363$$ 0 0
$$364$$ 5.19615 + 5.00000i 0.272352 + 0.262071i
$$365$$ 2.00000 0.104685
$$366$$ 0 0
$$367$$ −18.1962 31.5167i −0.949831 1.64516i −0.745776 0.666197i $$-0.767921\pi$$
−0.204056 0.978959i $$-0.565412\pi$$
$$368$$ 0.133975 0.232051i 0.00698391 0.0120965i
$$369$$ 0 0
$$370$$ 1.03590 + 0.598076i 0.0538538 + 0.0310925i
$$371$$ 22.3923 + 12.9282i 1.16255 + 0.671199i
$$372$$ 0 0
$$373$$ −12.8923 + 22.3301i −0.667538 + 1.15621i 0.311052 + 0.950393i $$0.399319\pi$$
−0.978590 + 0.205817i $$0.934015\pi$$
$$374$$ 0.928203 + 1.60770i 0.0479962 + 0.0831319i
$$375$$ 0 0
$$376$$ −10.4641 −0.539645
$$377$$ −9.33013 + 9.69615i −0.480526 + 0.499377i
$$378$$ 0 0
$$379$$ −0.124356 + 0.0717968i −0.00638772 + 0.00368795i −0.503190 0.864176i $$-0.667841\pi$$
0.496803 + 0.867863i $$0.334507\pi$$
$$380$$ 0.267949 + 0.464102i 0.0137455 + 0.0238079i
$$381$$ 0 0
$$382$$ 14.5359i 0.743721i
$$383$$ 3.99038 + 2.30385i 0.203899 + 0.117721i 0.598473 0.801143i $$-0.295774\pi$$
−0.394574 + 0.918864i $$0.629108\pi$$
$$384$$ 0 0
$$385$$ 0.928203i 0.0473056i
$$386$$ −11.6603 + 20.1962i −0.593491 + 1.02796i
$$387$$ 0 0
$$388$$ −6.46410 + 3.73205i −0.328165 + 0.189466i
$$389$$ 20.2679 1.02763 0.513813 0.857902i $$-0.328233\pi$$
0.513813 + 0.857902i $$0.328233\pi$$
$$390$$ 0 0
$$391$$ −1.07180 −0.0542031
$$392$$ 2.59808 1.50000i 0.131223 0.0757614i
$$393$$ 0 0
$$394$$ 8.19615 14.1962i 0.412916 0.715192i
$$395$$ 0.0717968i 0.00361249i
$$396$$ 0 0
$$397$$ 10.5000 + 6.06218i 0.526980 + 0.304252i 0.739786 0.672843i $$-0.234927\pi$$
−0.212806 + 0.977095i $$0.568260\pi$$
$$398$$ 18.9282i 0.948785i
$$399$$ 0 0
$$400$$ 0.500000 + 0.866025i 0.0250000 + 0.0433013i
$$401$$ −27.7128 + 16.0000i −1.38391 + 0.799002i −0.992620 0.121265i $$-0.961305\pi$$
−0.391292 + 0.920267i $$0.627972\pi$$
$$402$$ 0 0
$$403$$ −6.00000 + 1.73205i −0.298881 + 0.0862796i
$$404$$ −10.9282 −0.543698
$$405$$ 0 0
$$406$$ −3.73205 6.46410i −0.185219 0.320808i
$$407$$ −0.277568 + 0.480762i −0.0137585 + 0.0238305i
$$408$$ 0 0
$$409$$ −3.46410 2.00000i −0.171289 0.0988936i 0.411905 0.911227i $$-0.364864\pi$$
−0.583193 + 0.812333i $$0.698197\pi$$
$$410$$ 1.73205 + 1.00000i 0.0855399 + 0.0493865i
$$411$$ 0 0
$$412$$ 7.92820 13.7321i 0.390595 0.676530i
$$413$$ 1.53590 + 2.66025i 0.0755766 + 0.130903i
$$414$$ 0 0
$$415$$ 4.92820 0.241916
$$416$$ −0.866025 + 3.50000i −0.0424604 + 0.171602i
$$417$$ 0 0
$$418$$ −0.215390 + 0.124356i −0.0105351 + 0.00608243i
$$419$$ 0.803848 + 1.39230i 0.0392705 + 0.0680185i 0.884993 0.465605i $$-0.154163\pi$$
−0.845722 + 0.533624i $$0.820830\pi$$
$$420$$ 0 0
$$421$$ 16.3923i 0.798912i −0.916752 0.399456i $$-0.869199\pi$$
0.916752 0.399456i $$-0.130801\pi$$
$$422$$ 20.1962 + 11.6603i 0.983133 + 0.567612i
$$423$$ 0 0
$$424$$ 12.9282i 0.627849i
$$425$$ 2.00000 3.46410i 0.0970143 0.168034i
$$426$$ 0 0
$$427$$ −18.0000 + 10.3923i −0.871081 + 0.502919i
$$428$$ 19.8564 0.959796
$$429$$ 0 0
$$430$$ 1.92820 0.0929862
$$431$$ 6.58846 3.80385i 0.317355 0.183225i −0.332858 0.942977i $$-0.608013\pi$$
0.650213 + 0.759752i $$0.274680\pi$$
$$432$$ 0 0
$$433$$ 7.66025 13.2679i 0.368128 0.637617i −0.621145 0.783696i $$-0.713332\pi$$
0.989273 + 0.146079i $$0.0466654\pi$$
$$434$$ 3.46410i 0.166282i
$$435$$ 0 0
$$436$$ 10.2679 + 5.92820i 0.491746 + 0.283909i
$$437$$ 0.143594i 0.00686901i
$$438$$ 0 0
$$439$$ −4.92820 8.53590i −0.235210 0.407396i 0.724123 0.689670i $$-0.242245\pi$$
−0.959334 + 0.282274i $$0.908911\pi$$
$$440$$ −0.401924 + 0.232051i −0.0191610 + 0.0110626i
$$441$$ 0 0
$$442$$ 13.8564 4.00000i 0.659082 0.190261i
$$443$$ 4.39230 0.208685 0.104342 0.994541i $$-0.466726\pi$$
0.104342 + 0.994541i $$0.466726\pi$$
$$444$$ 0 0
$$445$$ 3.73205 + 6.46410i 0.176916 + 0.306428i
$$446$$ −13.7321 + 23.7846i −0.650231 + 1.12623i
$$447$$ 0 0
$$448$$ −1.73205 1.00000i −0.0818317 0.0472456i
$$449$$ 34.3923 + 19.8564i 1.62307 + 0.937082i 0.986092 + 0.166203i $$0.0531506\pi$$
0.636982 + 0.770879i $$0.280183\pi$$
$$450$$ 0 0
$$451$$ −0.464102 + 0.803848i −0.0218537 + 0.0378517i
$$452$$ −5.59808 9.69615i −0.263311 0.456069i
$$453$$ 0 0
$$454$$ −4.39230 −0.206141
$$455$$ 7.00000 + 1.73205i 0.328165 + 0.0811998i
$$456$$ 0 0
$$457$$ −27.2487 + 15.7321i −1.27464 + 0.735914i −0.975858 0.218407i $$-0.929914\pi$$
−0.298783 + 0.954321i $$0.596581\pi$$
$$458$$ −9.92820 17.1962i −0.463914 0.803523i
$$459$$ 0 0
$$460$$ 0.267949i 0.0124932i
$$461$$ −5.59808 3.23205i −0.260728 0.150532i 0.363938 0.931423i $$-0.381432\pi$$
−0.624667 + 0.780891i $$0.714765\pi$$
$$462$$ 0 0
$$463$$ 20.9282i 0.972616i 0.873787 + 0.486308i $$0.161657\pi$$
−0.873787 + 0.486308i $$0.838343\pi$$
$$464$$ 1.86603 3.23205i 0.0866281 0.150044i
$$465$$ 0 0
$$466$$ −15.6962 + 9.06218i −0.727110 + 0.419797i
$$467$$ −11.8564 −0.548649 −0.274325 0.961637i $$-0.588454\pi$$
−0.274325 + 0.961637i $$0.588454\pi$$
$$468$$ 0 0
$$469$$ 9.07180 0.418897
$$470$$ −9.06218 + 5.23205i −0.418007 + 0.241337i
$$471$$ 0 0
$$472$$ −0.767949 + 1.33013i −0.0353477 + 0.0612241i
$$473$$ 0.894882i 0.0411467i
$$474$$ 0 0
$$475$$ 0.464102 + 0.267949i 0.0212944 + 0.0122944i
$$476$$ 8.00000i 0.366679i
$$477$$ 0 0
$$478$$ 2.19615 + 3.80385i 0.100450 + 0.173984i
$$479$$ −1.26795 + 0.732051i −0.0579341 + 0.0334483i −0.528687 0.848817i $$-0.677316\pi$$
0.470753 + 0.882265i $$0.343982\pi$$
$$480$$ 0 0
$$481$$ 3.10770 + 2.99038i 0.141699 + 0.136350i
$$482$$ 14.2679 0.649887
$$483$$ 0 0
$$484$$ 5.39230 + 9.33975i 0.245105 + 0.424534i
$$485$$ −3.73205 + 6.46410i −0.169464 + 0.293520i
$$486$$ 0 0
$$487$$ 33.9282 + 19.5885i 1.53743 + 0.887638i 0.998988 + 0.0449775i $$0.0143216\pi$$
0.538446 + 0.842660i $$0.319012\pi$$
$$488$$ −9.00000 5.19615i −0.407411 0.235219i
$$489$$ 0 0
$$490$$ 1.50000 2.59808i 0.0677631 0.117369i
$$491$$ 8.66025 + 15.0000i 0.390832 + 0.676941i 0.992559 0.121761i $$-0.0388541\pi$$
−0.601728 + 0.798701i $$0.705521\pi$$
$$492$$ 0 0
$$493$$ −14.9282 −0.672332
$$494$$ 0.535898 + 1.85641i 0.0241112 + 0.0835237i
$$495$$ 0 0
$$496$$ 1.50000 0.866025i 0.0673520 0.0388857i
$$497$$ 8.39230 + 14.5359i 0.376446 + 0.652024i
$$498$$ 0 0
$$499$$ 13.4641i 0.602736i 0.953508 + 0.301368i $$0.0974433\pi$$
−0.953508 + 0.301368i $$0.902557\pi$$
$$500$$ 0.866025 + 0.500000i 0.0387298 + 0.0223607i
$$501$$ 0 0
$$502$$ 12.2679i 0.547545i
$$503$$ 15.5885 27.0000i 0.695055 1.20387i −0.275107 0.961414i $$-0.588713\pi$$
0.970162 0.242457i $$-0.0779533\pi$$
$$504$$ 0 0
$$505$$ −9.46410 + 5.46410i −0.421147 + 0.243149i
$$506$$ 0.124356 0.00552828
$$507$$ 0 0
$$508$$ −8.92820 −0.396125
$$509$$ −16.7942 + 9.69615i −0.744391 + 0.429774i −0.823664 0.567079i $$-0.808074\pi$$
0.0792726 + 0.996853i $$0.474740\pi$$
$$510$$ 0 0
$$511$$ −2.00000 + 3.46410i −0.0884748 + 0.153243i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 19.6244 + 11.3301i 0.865593 + 0.499750i
$$515$$ 15.8564i 0.698717i
$$516$$ 0 0
$$517$$ −2.42820 4.20577i −0.106792 0.184970i
$$518$$ −2.07180 + 1.19615i −0.0910295 + 0.0525559i
$$519$$ 0 0
$$520$$ 1.00000 + 3.46410i 0.0438529 + 0.151911i
$$521$$ −17.3205 −0.758825 −0.379413 0.925228i $$-0.623874\pi$$
−0.379413 + 0.925228i $$0.623874\pi$$
$$522$$ 0 0
$$523$$ 14.8923 + 25.7942i 0.651195 + 1.12790i 0.982833 + 0.184496i $$0.0590653\pi$$
−0.331638 + 0.943407i $$0.607601\pi$$
$$524$$ 0.669873 1.16025i 0.0292635 0.0506859i
$$525$$ 0 0
$$526$$ 15.6962 + 9.06218i 0.684385 + 0.395130i
$$527$$ −6.00000 3.46410i −0.261364 0.150899i
$$528$$ 0 0
$$529$$ 11.4641 19.8564i 0.498439 0.863322i
$$530$$ 6.46410 + 11.1962i 0.280783 + 0.486330i
$$531$$ 0 0
$$532$$ −1.07180 −0.0464683
$$533$$ 5.19615 + 5.00000i 0.225070 + 0.216574i
$$534$$ 0 0
$$535$$ 17.1962 9.92820i 0.743455 0.429234i
$$536$$ 2.26795 + 3.92820i 0.0979605 + 0.169673i
$$537$$ 0 0
$$538$$ 12.0000i 0.517357i
$$539$$ 1.20577 + 0.696152i 0.0519362 + 0.0299854i
$$540$$ 0 0
$$541$$ 13.0718i 0.562000i 0.959708 + 0.281000i $$0.0906662\pi$$
−0.959708 + 0.281000i $$0.909334\pi$$
$$542$$ −4.59808 + 7.96410i −0.197504 + 0.342087i
$$543$$ 0 0
$$544$$ −3.46410 + 2.00000i −0.148522 + 0.0857493i
$$545$$ 11.8564 0.507873
$$546$$ 0 0
$$547$$ 9.07180 0.387882 0.193941 0.981013i $$-0.437873\pi$$
0.193941 + 0.981013i $$0.437873\pi$$
$$548$$ 3.86603 2.23205i 0.165148 0.0953485i
$$549$$ 0 0
$$550$$ −0.232051 + 0.401924i −0.00989468 + 0.0171381i
$$551$$ 2.00000i 0.0852029i
$$552$$ 0 0
$$553$$ −0.124356 0.0717968i −0.00528814 0.00305311i
$$554$$ 9.92820i 0.421809i
$$555$$ 0 0
$$556$$ 0.464102 + 0.803848i 0.0196823 + 0.0340907i
$$557$$ −32.6603 + 18.8564i −1.38386 + 0.798972i −0.992614 0.121315i $$-0.961289\pi$$
−0.391245 + 0.920286i $$0.627956\pi$$
$$558$$ 0 0
$$559$$ 6.74871 + 1.66987i 0.285440 + 0.0706281i
$$560$$ −2.00000 −0.0845154
$$561$$ 0 0
$$562$$ 2.46410 + 4.26795i 0.103942 + 0.180033i
$$563$$ −19.6603 + 34.0526i −0.828581 + 1.43514i 0.0705706 + 0.997507i $$0.477518\pi$$
−0.899152 + 0.437637i $$0.855815\pi$$
$$564$$ 0 0
$$565$$ −9.69615 5.59808i −0.407920 0.235513i
$$566$$ 3.40192 + 1.96410i 0.142994 + 0.0825573i
$$567$$ 0 0
$$568$$ −4.19615 + 7.26795i −0.176067 + 0.304956i
$$569$$ −2.66025 4.60770i −0.111524 0.193165i 0.804861 0.593463i $$-0.202240\pi$$
−0.916385 + 0.400299i $$0.868906\pi$$
$$570$$ 0 0
$$571$$ 45.1769 1.89060 0.945298 0.326209i $$-0.105771\pi$$
0.945298 + 0.326209i $$0.105771\pi$$
$$572$$ −1.60770 + 0.464102i −0.0672211 + 0.0194051i
$$573$$ 0 0
$$574$$ −3.46410 + 2.00000i −0.144589 + 0.0834784i
$$575$$ −0.133975 0.232051i −0.00558713 0.00967719i
$$576$$ 0 0
$$577$$ 10.0000i 0.416305i −0.978096 0.208153i $$-0.933255\pi$$
0.978096 0.208153i $$-0.0667451\pi$$
$$578$$ −0.866025 0.500000i −0.0360219 0.0207973i
$$579$$ 0 0
$$580$$ 3.73205i 0.154965i
$$581$$ −4.92820 + 8.53590i −0.204456 + 0.354129i
$$582$$ 0 0
$$583$$ −5.19615 + 3.00000i −0.215203 + 0.124247i
$$584$$ −2.00000 −0.0827606
$$585$$ 0 0
$$586$$ 4.14359 0.171170
$$587$$ 15.9282 9.19615i 0.657427 0.379566i −0.133869 0.990999i $$-0.542740\pi$$
0.791296 + 0.611433i $$0.209407\pi$$
$$588$$ 0 0
$$589$$ 0.464102 0.803848i 0.0191230 0.0331220i
$$590$$ 1.53590i 0.0632319i
$$591$$ 0 0
$$592$$ −1.03590 0.598076i −0.0425752 0.0245808i
$$593$$ 31.1051i 1.27733i 0.769483 + 0.638667i $$0.220514\pi$$
−0.769483 + 0.638667i $$0.779486\pi$$
$$594$$ 0 0
$$595$$ 4.00000 + 6.92820i 0.163984 + 0.284029i
$$596$$ −17.7224 + 10.2321i −0.725939 + 0.419121i
$$597$$ 0 0
$$598$$ 0.232051 0.937822i 0.00948926 0.0383504i
$$599$$ −10.3923 −0.424618 −0.212309 0.977203i $$-0.568098\pi$$
−0.212309 + 0.977203i $$0.568098\pi$$
$$600$$ 0 0
$$601$$ −10.8923 18.8660i −0.444306 0.769561i 0.553697 0.832718i $$-0.313216\pi$$
−0.998004 + 0.0631568i $$0.979883\pi$$
$$602$$ −1.92820 + 3.33975i −0.0785877 + 0.136118i
$$603$$ 0 0
$$604$$ 9.00000 + 5.19615i 0.366205 + 0.211428i
$$605$$ 9.33975 + 5.39230i 0.379715 + 0.219228i
$$606$$ 0 0
$$607$$ −21.5885 + 37.3923i −0.876248 + 1.51771i −0.0208216 + 0.999783i $$0.506628\pi$$
−0.855427 + 0.517924i $$0.826705\pi$$
$$608$$ −0.267949 0.464102i −0.0108668 0.0188218i
$$609$$ 0 0
$$610$$ −10.3923 −0.420772
$$611$$ −36.2487 + 10.4641i −1.46647 + 0.423332i
$$612$$ 0 0
$$613$$ 0.820508 0.473721i 0.0331400 0.0191334i −0.483338 0.875434i $$-0.660576\pi$$
0.516478 + 0.856300i $$0.327243\pi$$
$$614$$ −6.26795 10.8564i −0.252954 0.438129i
$$615$$ 0 0
$$616$$ 0.928203i 0.0373984i
$$617$$ −13.4545 7.76795i −0.541657 0.312726i 0.204093 0.978951i $$-0.434575\pi$$
−0.745750 + 0.666226i $$0.767909\pi$$
$$618$$ 0 0
$$619$$ 24.2487i 0.974638i 0.873224 + 0.487319i $$0.162025\pi$$
−0.873224 + 0.487319i $$0.837975\pi$$
$$620$$ 0.866025 1.50000i 0.0347804 0.0602414i
$$621$$ 0 0
$$622$$ −6.58846 + 3.80385i −0.264173 + 0.152520i
$$623$$ −14.9282 −0.598086
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 24.2487 14.0000i 0.969173 0.559553i
$$627$$ 0 0
$$628$$ −2.50000 + 4.33013i −0.0997609 + 0.172791i
$$629$$ 4.78461i 0.190775i
$$630$$ 0 0
$$631$$ −21.2487 12.2679i −0.845898 0.488379i 0.0133668 0.999911i $$-0.495745\pi$$
−0.859265 + 0.511531i $$0.829078\pi$$
$$632$$ 0.0717968i 0.00285592i
$$633$$ 0 0
$$634$$ 10.7321 + 18.5885i 0.426224 + 0.738242i
$$635$$ −7.73205 + 4.46410i −0.306837 + 0.177152i
$$636$$ 0 0
$$637$$ 7.50000 7.79423i 0.297161 0.308819i
$$638$$ 1.73205 0.0685725
$$639$$ 0 0
$$640$$ −0.500000 0.866025i −0.0197642 0.0342327i
$$641$$ 13.9282 24.1244i 0.550131 0.952855i −0.448134 0.893967i $$-0.647911\pi$$
0.998265 0.0588882i $$-0.0187555\pi$$
$$642$$ 0 0
$$643$$ 23.7846 + 13.7321i 0.937973 + 0.541539i 0.889324 0.457277i $$-0.151175\pi$$
0.0486490 + 0.998816i $$0.484508\pi$$
$$644$$ 0.464102 + 0.267949i 0.0182882 + 0.0105587i
$$645$$ 0 0
$$646$$ −1.07180 + 1.85641i −0.0421693 + 0.0730393i
$$647$$ 10.6603 + 18.4641i 0.419098 + 0.725899i 0.995849 0.0910212i $$-0.0290131\pi$$
−0.576751 + 0.816920i $$0.695680\pi$$
$$648$$ 0 0
$$649$$ −0.712813 −0.0279804
$$650$$ 2.59808 + 2.50000i 0.101905 + 0.0980581i
$$651$$ 0 0
$$652$$ 19.9641 11.5263i 0.781855 0.451404i
$$653$$ −22.1244 38.3205i −0.865793 1.49960i −0.866258 0.499597i $$-0.833481\pi$$
0.000464739 1.00000i $$-0.499852\pi$$
$$654$$ 0 0
$$655$$ 1.33975i 0.0523482i
$$656$$ −1.73205 1.00000i −0.0676252 0.0390434i
$$657$$ 0 0
$$658$$ 20.9282i 0.815866i
$$659$$ −1.86603 + 3.23205i −0.0726900 + 0.125903i −0.900079 0.435726i $$-0.856492\pi$$
0.827389 + 0.561629i $$0.189825\pi$$
$$660$$ 0 0
$$661$$ 37.5167 21.6603i 1.45923 0.842486i 0.460256 0.887786i $$-0.347758\pi$$
0.998973 + 0.0453002i $$0.0144244\pi$$
$$662$$ 24.7846 0.963281
$$663$$ 0 0
$$664$$ −4.92820 −0.191251
$$665$$ −0.928203 + 0.535898i −0.0359942 + 0.0207812i
$$666$$ 0 0
$$667$$ −0.500000 + 0.866025i −0.0193601 + 0.0335326i
$$668$$ 18.3205i 0.708842i
$$669$$ 0 0
$$670$$ 3.92820 + 2.26795i 0.151760 + 0.0876185i
$$671$$ 4.82309i 0.186193i
$$672$$ 0 0
$$673$$ −16.0000 27.7128i −0.616755 1.06825i −0.990074 0.140548i $$-0.955114\pi$$
0.373319 0.927703i $$-0.378220\pi$$
$$674$$ 21.9282 12.6603i 0.844643 0.487655i
$$675$$ 0 0
$$676$$ 0.500000 + 12.9904i 0.0192308 + 0.499630i
$$677$$ −11.6077 −0.446120 −0.223060 0.974805i $$-0.571605\pi$$
−0.223060 + 0.974805i $$0.571605\pi$$
$$678$$ 0 0
$$679$$ −7.46410 12.9282i −0.286446 0.496139i
$$680$$ −2.00000 + 3.46410i −0.0766965 + 0.132842i
$$681$$ 0 0
$$682$$ 0.696152 + 0.401924i 0.0266571 + 0.0153905i
$$683$$ 0.679492 + 0.392305i 0.0260000 + 0.0150111i 0.512944 0.858422i $$-0.328555\pi$$
−0.486944 + 0.873433i $$0.661888\pi$$
$$684$$ 0 0
$$685$$ 2.23205 3.86603i 0.0852823 0.147713i
$$686$$ 10.0000 + 17.3205i 0.381802 + 0.661300i
$$687$$ 0 0
$$688$$ −1.92820 −0.0735121
$$689$$ 12.9282 + 44.7846i 0.492525 + 1.70616i
$$690$$ 0 0
$$691$$ −30.4641 + 17.5885i −1.15891 + 0.669096i −0.951042 0.309061i $$-0.899985\pi$$
−0.207867 + 0.978157i $$0.566652\pi$$
$$692$$ 1.46410 + 2.53590i 0.0556568 + 0.0964004i
$$693$$ 0 0
$$694$$ 22.3923i 0.850000i
$$695$$ 0.803848 + 0.464102i 0.0304917 + 0.0176044i
$$696$$ 0 0
$$697$$ 8.00000i 0.303022i
$$698$$ 7.26795 12.5885i 0.275096 0.476480i
$$699$$ 0 0
$$700$$ −1.73205 + 1.00000i −0.0654654 + 0.0377964i
$$701$$ 3.73205 0.140958 0.0704788 0.997513i $$-0.477547\pi$$
0.0704788 + 0.997513i $$0.477547\pi$$
$$702$$ 0 0
$$703$$ −0.641016 −0.0241764
$$704$$ 0.401924 0.232051i 0.0151481 0.00874574i
$$705$$ 0 0
$$706$$ −1.00000 + 1.73205i −0.0376355 + 0.0651866i
$$707$$ 21.8564i 0.821995i
$$708$$ 0 0
$$709$$ 7.85641 + 4.53590i 0.295054 + 0.170349i 0.640219 0.768193i $$-0.278844\pi$$
−0.345165 + 0.938542i $$0.612177\pi$$
$$710$$ 8.39230i 0.314958i
$$711$$ 0 0
$$712$$ −3.73205 6.46410i −0.139865 0.242252i
$$713$$ −0.401924 + 0.232051i −0.0150522 + 0.00869037i
$$714$$ 0 0
$$715$$ −1.16025 + 1.20577i −0.0433910 + 0.0450933i
$$716$$ −16.2679 −0.607962
$$717$$ 0 0
$$718$$ 9.46410 + 16.3923i 0.353197 + 0.611755i
$$719$$ 17.3205 30.0000i 0.645946 1.11881i −0.338136 0.941097i $$-0.609796\pi$$
0.984082 0.177714i $$-0.0568702\pi$$
$$720$$ 0 0
$$721$$ 27.4641 + 15.8564i 1.02282 + 0.590523i
$$722$$ 16.2058 + 9.35641i 0.603116 + 0.348209i
$$723$$ 0 0
$$724$$ 5.46410 9.46410i 0.203072 0.351731i
$$725$$ −1.86603 3.23205i −0.0693024 0.120035i
$$726$$ 0 0
$$727$$ 23.7128 0.879460 0.439730 0.898130i $$-0.355074\pi$$
0.439730 + 0.898130i $$0.355074\pi$$
$$728$$ −7.00000 1.73205i −0.259437 0.0641941i
$$729$$ 0 0
$$730$$ −1.73205 + 1.00000i −0.0641061 + 0.0370117i
$$731$$ 3.85641 + 6.67949i 0.142634 + 0.247050i
$$732$$ 0 0
$$733$$ 37.0718i 1.36928i −0.728882 0.684639i $$-0.759960\pi$$
0.728882 0.684639i $$-0.240040\pi$$
$$734$$ 31.5167 + 18.1962i 1.16330 + 0.671632i
$$735$$ 0 0
$$736$$ 0.267949i 0.00987674i
$$737$$ −1.05256 + 1.82309i −0.0387715 + 0.0671542i
$$738$$ 0 0
$$739$$ −13.2679 + 7.66025i −0.488069 + 0.281787i −0.723773 0.690038i $$-0.757594\pi$$
0.235704 + 0.971825i $$0.424260\pi$$
$$740$$ −1.19615 −0.0439714
$$741$$ 0 0
$$742$$ −25.8564 −0.949219
$$743$$ −29.0429 + 16.7679i −1.06548 + 0.615156i −0.926944 0.375201i $$-0.877574\pi$$
−0.138539 + 0.990357i $$0.544240\pi$$
$$744$$ 0 0
$$745$$ −10.2321 + 17.7224i −0.374873 + 0.649300i
$$746$$ 25.7846i 0.944042i
$$747$$ 0 0
$$748$$ −1.60770 0.928203i −0.0587832 0.0339385i
$$749$$ 39.7128i 1.45107i
$$750$$ 0 0
$$751$$ −13.9641 24.1865i −0.509557 0.882579i −0.999939 0.0110712i $$-0.996476\pi$$
0.490381 0.871508i $$-0.336857\pi$$
$$752$$ 9.06218 5.23205i 0.330464 0.190793i
$$753$$ 0 0
$$754$$ 3.23205 13.0622i 0.117704 0.475696i
$$755$$ 10.3923 0.378215
$$756$$ 0 0
$$757$$ 9.00000 + 15.5885i 0.327111 + 0.566572i 0.981937 0.189207i $$-0.0605917\pi$$
−0.654827 + 0.755779i $$0.727258\pi$$
$$758$$ 0.0717968 0.124356i 0.00260778 0.00451680i
$$759$$ 0 0
$$760$$ −0.464102 0.267949i −0.0168347 0.00971954i
$$761$$ 16.3923 + 9.46410i 0.594221 + 0.343073i 0.766765 0.641928i $$-0.221865\pi$$
−0.172544 + 0.985002i $$0.555199\pi$$
$$762$$ 0 0
$$763$$ −11.8564 + 20.5359i −0.429231 + 0.743449i
$$764$$ −7.26795 12.5885i −0.262945 0.455434i
$$765$$ 0 0
$$766$$ −4.60770 −0.166483
$$767$$ −1.33013 + 5.37564i −0.0480281 + 0.194103i
$$768$$ 0 0
$$769$$ −16.9641 + 9.79423i −0.611741 + 0.353189i −0.773647 0.633617i $$-0.781569\pi$$
0.161905 + 0.986806i $$0.448236\pi$$
$$770$$ −0.464102 0.803848i −0.0167251 0.0289687i
$$771$$ 0 0
$$772$$ 23.3205i 0.839323i
$$773$$ −24.0000 13.8564i −0.863220 0.498380i 0.00186926 0.999998i $$-0.499405\pi$$
−0.865089 + 0.501618i $$0.832738\pi$$
$$774$$ 0 0
$$775$$ 1.73205i 0.0622171i
$$776$$ 3.73205 6.46410i 0.133973 0.232048i
$$777$$ 0 0
$$778$$ −17.5526 + 10.1340i −0.629290 + 0.363321i
$$779$$ −1.07180 −0.0384011
$$780$$ 0 0
$$781$$ −3.89488 −0.139370
$$782$$ 0.928203 0.535898i 0.0331925 0.0191637i
$$783$$ 0 0
$$784$$ −1.50000 + 2.59808i −0.0535714 + 0.0927884i
$$785$$ 5.00000i 0.178458i
$$786$$ 0 0
$$787$$ 1.50000 + 0.866025i 0.0534692 + 0.0308705i 0.526496 0.850177i $$-0.323505\pi$$
−0.473027 + 0.881048i $$0.656839\pi$$
$$788$$ 16.3923i 0.583952i