# Properties

 Label 1050.2.o.f.949.2 Level $1050$ Weight $2$ Character 1050.949 Analytic conductor $8.384$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1050.o (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.38429221223$$ 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: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 949.2 Root $$-0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1050.949 Dual form 1050.2.o.f.499.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-0.866025 + 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +(-0.866025 + 0.500000i) q^{12} -4.00000i q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.33013 - 2.50000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(2.00000 - 1.73205i) q^{21} -2.00000i q^{22} +(4.33013 - 2.50000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -1.00000i q^{27} +(1.73205 + 2.00000i) q^{28} +6.00000 q^{29} +(5.50000 - 9.52628i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.73205 + 1.00000i) q^{33} -5.00000 q^{34} +1.00000 q^{36} +(-6.92820 + 4.00000i) q^{37} +(-3.46410 - 2.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} +5.00000 q^{41} +(0.866025 - 2.50000i) q^{42} +(-1.00000 - 1.73205i) q^{44} +(2.50000 - 4.33013i) q^{46} +(0.866025 - 0.500000i) q^{47} +1.00000i q^{48} +(-5.50000 - 4.33013i) q^{49} +(2.50000 + 4.33013i) q^{51} +(-3.46410 - 2.00000i) q^{52} +(-10.3923 - 6.00000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(2.50000 + 0.866025i) q^{56} +4.00000i q^{57} +(5.19615 - 3.00000i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(-5.00000 - 8.66025i) q^{61} -11.0000i q^{62} +(-2.59808 + 0.500000i) q^{63} -1.00000 q^{64} +(-1.00000 + 1.73205i) q^{66} +(-4.33013 + 2.50000i) q^{68} -5.00000 q^{69} -1.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-1.73205 - 1.00000i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(3.46410 + 4.00000i) q^{77} +4.00000i q^{78} +(4.50000 + 7.79423i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.33013 - 2.50000i) q^{82} +6.00000i q^{83} +(-0.500000 - 2.59808i) q^{84} +(-5.19615 - 3.00000i) q^{87} +(-1.73205 - 1.00000i) q^{88} +(5.50000 + 9.52628i) q^{89} +(10.0000 + 3.46410i) q^{91} -5.00000i q^{92} +(-9.52628 + 5.50000i) q^{93} +(0.500000 - 0.866025i) q^{94} +(0.500000 + 0.866025i) q^{96} +1.00000i q^{97} +(-6.92820 - 1.00000i) q^{98} +2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{4} - 4q^{6} + 2q^{9} + O(q^{10})$$ $$4q + 2q^{4} - 4q^{6} + 2q^{9} + 4q^{11} + 2q^{14} - 2q^{16} - 8q^{19} + 8q^{21} - 2q^{24} - 8q^{26} + 24q^{29} + 22q^{31} - 20q^{34} + 4q^{36} - 8q^{39} + 20q^{41} - 4q^{44} + 10q^{46} - 22q^{49} + 10q^{51} - 2q^{54} + 10q^{56} - 4q^{59} - 20q^{61} - 4q^{64} - 4q^{66} - 20q^{69} - 4q^{71} - 16q^{74} - 16q^{76} + 18q^{79} - 2q^{81} - 2q^{84} + 22q^{89} + 40q^{91} + 2q^{94} + 2q^{96} + 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$701$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 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
$$3$$ −0.866025 0.500000i −0.500000 0.288675i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 0 0
$$6$$ −1.00000 −0.408248
$$7$$ −0.866025 + 2.50000i −0.327327 + 0.944911i
$$8$$ 1.00000i 0.353553i
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i $$-0.735842\pi$$
0.976478 + 0.215615i $$0.0691756\pi$$
$$12$$ −0.866025 + 0.500000i −0.250000 + 0.144338i
$$13$$ 4.00000i 1.10940i −0.832050 0.554700i $$-0.812833\pi$$
0.832050 0.554700i $$-0.187167\pi$$
$$14$$ 0.500000 + 2.59808i 0.133631 + 0.694365i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −4.33013 2.50000i −1.05021 0.606339i −0.127502 0.991838i $$-0.540696\pi$$
−0.922708 + 0.385499i $$0.874029\pi$$
$$18$$ 0.866025 + 0.500000i 0.204124 + 0.117851i
$$19$$ −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i $$-0.318398\pi$$
−0.998899 + 0.0469020i $$0.985065\pi$$
$$20$$ 0 0
$$21$$ 2.00000 1.73205i 0.436436 0.377964i
$$22$$ 2.00000i 0.426401i
$$23$$ 4.33013 2.50000i 0.902894 0.521286i 0.0247559 0.999694i $$-0.492119\pi$$
0.878138 + 0.478407i $$0.158786\pi$$
$$24$$ −0.500000 + 0.866025i −0.102062 + 0.176777i
$$25$$ 0 0
$$26$$ −2.00000 3.46410i −0.392232 0.679366i
$$27$$ 1.00000i 0.192450i
$$28$$ 1.73205 + 2.00000i 0.327327 + 0.377964i
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 0 0
$$31$$ 5.50000 9.52628i 0.987829 1.71097i 0.359211 0.933257i $$-0.383046\pi$$
0.628619 0.777714i $$-0.283621\pi$$
$$32$$ −0.866025 0.500000i −0.153093 0.0883883i
$$33$$ −1.73205 + 1.00000i −0.301511 + 0.174078i
$$34$$ −5.00000 −0.857493
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −6.92820 + 4.00000i −1.13899 + 0.657596i −0.946180 0.323640i $$-0.895093\pi$$
−0.192809 + 0.981236i $$0.561760\pi$$
$$38$$ −3.46410 2.00000i −0.561951 0.324443i
$$39$$ −2.00000 + 3.46410i −0.320256 + 0.554700i
$$40$$ 0 0
$$41$$ 5.00000 0.780869 0.390434 0.920631i $$-0.372325\pi$$
0.390434 + 0.920631i $$0.372325\pi$$
$$42$$ 0.866025 2.50000i 0.133631 0.385758i
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ −1.00000 1.73205i −0.150756 0.261116i
$$45$$ 0 0
$$46$$ 2.50000 4.33013i 0.368605 0.638442i
$$47$$ 0.866025 0.500000i 0.126323 0.0729325i −0.435507 0.900185i $$-0.643431\pi$$
0.561830 + 0.827253i $$0.310098\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ −5.50000 4.33013i −0.785714 0.618590i
$$50$$ 0 0
$$51$$ 2.50000 + 4.33013i 0.350070 + 0.606339i
$$52$$ −3.46410 2.00000i −0.480384 0.277350i
$$53$$ −10.3923 6.00000i −1.42749 0.824163i −0.430570 0.902557i $$-0.641688\pi$$
−0.996922 + 0.0783936i $$0.975021\pi$$
$$54$$ −0.500000 0.866025i −0.0680414 0.117851i
$$55$$ 0 0
$$56$$ 2.50000 + 0.866025i 0.334077 + 0.115728i
$$57$$ 4.00000i 0.529813i
$$58$$ 5.19615 3.00000i 0.682288 0.393919i
$$59$$ −1.00000 + 1.73205i −0.130189 + 0.225494i −0.923749 0.382998i $$-0.874892\pi$$
0.793560 + 0.608492i $$0.208225\pi$$
$$60$$ 0 0
$$61$$ −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i $$-0.945525\pi$$
0.345207 0.938527i $$-0.387809\pi$$
$$62$$ 11.0000i 1.39700i
$$63$$ −2.59808 + 0.500000i −0.327327 + 0.0629941i
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ −1.00000 + 1.73205i −0.123091 + 0.213201i
$$67$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$68$$ −4.33013 + 2.50000i −0.525105 + 0.303170i
$$69$$ −5.00000 −0.601929
$$70$$ 0 0
$$71$$ −1.00000 −0.118678 −0.0593391 0.998238i $$-0.518899\pi$$
−0.0593391 + 0.998238i $$0.518899\pi$$
$$72$$ 0.866025 0.500000i 0.102062 0.0589256i
$$73$$ −1.73205 1.00000i −0.202721 0.117041i 0.395203 0.918594i $$-0.370674\pi$$
−0.597924 + 0.801553i $$0.704008\pi$$
$$74$$ −4.00000 + 6.92820i −0.464991 + 0.805387i
$$75$$ 0 0
$$76$$ −4.00000 −0.458831
$$77$$ 3.46410 + 4.00000i 0.394771 + 0.455842i
$$78$$ 4.00000i 0.452911i
$$79$$ 4.50000 + 7.79423i 0.506290 + 0.876919i 0.999974 + 0.00727784i $$0.00231663\pi$$
−0.493684 + 0.869641i $$0.664350\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 4.33013 2.50000i 0.478183 0.276079i
$$83$$ 6.00000i 0.658586i 0.944228 + 0.329293i $$0.106810\pi$$
−0.944228 + 0.329293i $$0.893190\pi$$
$$84$$ −0.500000 2.59808i −0.0545545 0.283473i
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −5.19615 3.00000i −0.557086 0.321634i
$$88$$ −1.73205 1.00000i −0.184637 0.106600i
$$89$$ 5.50000 + 9.52628i 0.582999 + 1.00978i 0.995122 + 0.0986553i $$0.0314541\pi$$
−0.412123 + 0.911128i $$0.635213\pi$$
$$90$$ 0 0
$$91$$ 10.0000 + 3.46410i 1.04828 + 0.363137i
$$92$$ 5.00000i 0.521286i
$$93$$ −9.52628 + 5.50000i −0.987829 + 0.570323i
$$94$$ 0.500000 0.866025i 0.0515711 0.0893237i
$$95$$ 0 0
$$96$$ 0.500000 + 0.866025i 0.0510310 + 0.0883883i
$$97$$ 1.00000i 0.101535i 0.998711 + 0.0507673i $$0.0161667\pi$$
−0.998711 + 0.0507673i $$0.983833\pi$$
$$98$$ −6.92820 1.00000i −0.699854 0.101015i
$$99$$ 2.00000 0.201008
$$100$$ 0 0
$$101$$ −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i $$0.370316\pi$$
−0.993258 + 0.115924i $$0.963017\pi$$
$$102$$ 4.33013 + 2.50000i 0.428746 + 0.247537i
$$103$$ 11.2583 6.50000i 1.10932 0.640464i 0.170664 0.985329i $$-0.445409\pi$$
0.938652 + 0.344865i $$0.112075\pi$$
$$104$$ −4.00000 −0.392232
$$105$$ 0 0
$$106$$ −12.0000 −1.16554
$$107$$ −1.73205 + 1.00000i −0.167444 + 0.0966736i −0.581380 0.813632i $$-0.697487\pi$$
0.413936 + 0.910306i $$0.364154\pi$$
$$108$$ −0.866025 0.500000i −0.0833333 0.0481125i
$$109$$ 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i $$-0.771977\pi$$
0.945769 + 0.324840i $$0.105310\pi$$
$$110$$ 0 0
$$111$$ 8.00000 0.759326
$$112$$ 2.59808 0.500000i 0.245495 0.0472456i
$$113$$ 5.00000i 0.470360i 0.971952 + 0.235180i $$0.0755680\pi$$
−0.971952 + 0.235180i $$0.924432\pi$$
$$114$$ 2.00000 + 3.46410i 0.187317 + 0.324443i
$$115$$ 0 0
$$116$$ 3.00000 5.19615i 0.278543 0.482451i
$$117$$ 3.46410 2.00000i 0.320256 0.184900i
$$118$$ 2.00000i 0.184115i
$$119$$ 10.0000 8.66025i 0.916698 0.793884i
$$120$$ 0 0
$$121$$ 3.50000 + 6.06218i 0.318182 + 0.551107i
$$122$$ −8.66025 5.00000i −0.784063 0.452679i
$$123$$ −4.33013 2.50000i −0.390434 0.225417i
$$124$$ −5.50000 9.52628i −0.493915 0.855485i
$$125$$ 0 0
$$126$$ −2.00000 + 1.73205i −0.178174 + 0.154303i
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ −0.866025 + 0.500000i −0.0765466 + 0.0441942i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i $$-0.251085\pi$$
−0.966803 + 0.255524i $$0.917752\pi$$
$$132$$ 2.00000i 0.174078i
$$133$$ 10.3923 2.00000i 0.901127 0.173422i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ −2.50000 + 4.33013i −0.214373 + 0.371305i
$$137$$ 19.9186 + 11.5000i 1.70176 + 0.982511i 0.943981 + 0.329999i $$0.107048\pi$$
0.757778 + 0.652512i $$0.226285\pi$$
$$138$$ −4.33013 + 2.50000i −0.368605 + 0.212814i
$$139$$ −2.00000 −0.169638 −0.0848189 0.996396i $$-0.527031\pi$$
−0.0848189 + 0.996396i $$0.527031\pi$$
$$140$$ 0 0
$$141$$ −1.00000 −0.0842152
$$142$$ −0.866025 + 0.500000i −0.0726752 + 0.0419591i
$$143$$ −6.92820 4.00000i −0.579365 0.334497i
$$144$$ 0.500000 0.866025i 0.0416667 0.0721688i
$$145$$ 0 0
$$146$$ −2.00000 −0.165521
$$147$$ 2.59808 + 6.50000i 0.214286 + 0.536111i
$$148$$ 8.00000i 0.657596i
$$149$$ 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i $$0.0972370\pi$$
−0.216394 + 0.976306i $$0.569430\pi$$
$$150$$ 0 0
$$151$$ 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i $$-0.607670\pi$$
0.982873 0.184284i $$-0.0589965\pi$$
$$152$$ −3.46410 + 2.00000i −0.280976 + 0.162221i
$$153$$ 5.00000i 0.404226i
$$154$$ 5.00000 + 1.73205i 0.402911 + 0.139573i
$$155$$ 0 0
$$156$$ 2.00000 + 3.46410i 0.160128 + 0.277350i
$$157$$ −12.1244 7.00000i −0.967629 0.558661i −0.0691164 0.997609i $$-0.522018\pi$$
−0.898513 + 0.438948i $$0.855351\pi$$
$$158$$ 7.79423 + 4.50000i 0.620076 + 0.358001i
$$159$$ 6.00000 + 10.3923i 0.475831 + 0.824163i
$$160$$ 0 0
$$161$$ 2.50000 + 12.9904i 0.197028 + 1.02379i
$$162$$ 1.00000i 0.0785674i
$$163$$ 20.7846 12.0000i 1.62798 0.939913i 0.643280 0.765631i $$-0.277573\pi$$
0.984696 0.174282i $$-0.0557604\pi$$
$$164$$ 2.50000 4.33013i 0.195217 0.338126i
$$165$$ 0 0
$$166$$ 3.00000 + 5.19615i 0.232845 + 0.403300i
$$167$$ 16.0000i 1.23812i −0.785345 0.619059i $$-0.787514\pi$$
0.785345 0.619059i $$-0.212486\pi$$
$$168$$ −1.73205 2.00000i −0.133631 0.154303i
$$169$$ −3.00000 −0.230769
$$170$$ 0 0
$$171$$ 2.00000 3.46410i 0.152944 0.264906i
$$172$$ 0 0
$$173$$ −1.73205 + 1.00000i −0.131685 + 0.0760286i −0.564396 0.825505i $$-0.690891\pi$$
0.432710 + 0.901533i $$0.357557\pi$$
$$174$$ −6.00000 −0.454859
$$175$$ 0 0
$$176$$ −2.00000 −0.150756
$$177$$ 1.73205 1.00000i 0.130189 0.0751646i
$$178$$ 9.52628 + 5.50000i 0.714025 + 0.412242i
$$179$$ 11.0000 19.0526i 0.822179 1.42406i −0.0818780 0.996642i $$-0.526092\pi$$
0.904057 0.427413i $$-0.140575\pi$$
$$180$$ 0 0
$$181$$ −22.0000 −1.63525 −0.817624 0.575753i $$-0.804709\pi$$
−0.817624 + 0.575753i $$0.804709\pi$$
$$182$$ 10.3923 2.00000i 0.770329 0.148250i
$$183$$ 10.0000i 0.739221i
$$184$$ −2.50000 4.33013i −0.184302 0.319221i
$$185$$ 0 0
$$186$$ −5.50000 + 9.52628i −0.403280 + 0.698501i
$$187$$ −8.66025 + 5.00000i −0.633300 + 0.365636i
$$188$$ 1.00000i 0.0729325i
$$189$$ 2.50000 + 0.866025i 0.181848 + 0.0629941i
$$190$$ 0 0
$$191$$ 12.5000 + 21.6506i 0.904468 + 1.56658i 0.821629 + 0.570022i $$0.193065\pi$$
0.0828388 + 0.996563i $$0.473601\pi$$
$$192$$ 0.866025 + 0.500000i 0.0625000 + 0.0360844i
$$193$$ −9.52628 5.50000i −0.685717 0.395899i 0.116289 0.993215i $$-0.462900\pi$$
−0.802005 + 0.597317i $$0.796234\pi$$
$$194$$ 0.500000 + 0.866025i 0.0358979 + 0.0621770i
$$195$$ 0 0
$$196$$ −6.50000 + 2.59808i −0.464286 + 0.185577i
$$197$$ 24.0000i 1.70993i 0.518686 + 0.854965i $$0.326421\pi$$
−0.518686 + 0.854965i $$0.673579\pi$$
$$198$$ 1.73205 1.00000i 0.123091 0.0710669i
$$199$$ 2.50000 4.33013i 0.177220 0.306955i −0.763707 0.645563i $$-0.776623\pi$$
0.940927 + 0.338608i $$0.109956\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 12.0000i 0.844317i
$$203$$ −5.19615 + 15.0000i −0.364698 + 1.05279i
$$204$$ 5.00000 0.350070
$$205$$ 0 0
$$206$$ 6.50000 11.2583i 0.452876 0.784405i
$$207$$ 4.33013 + 2.50000i 0.300965 + 0.173762i
$$208$$ −3.46410 + 2.00000i −0.240192 + 0.138675i
$$209$$ −8.00000 −0.553372
$$210$$ 0 0
$$211$$ −16.0000 −1.10149 −0.550743 0.834675i $$-0.685655\pi$$
−0.550743 + 0.834675i $$0.685655\pi$$
$$212$$ −10.3923 + 6.00000i −0.713746 + 0.412082i
$$213$$ 0.866025 + 0.500000i 0.0593391 + 0.0342594i
$$214$$ −1.00000 + 1.73205i −0.0683586 + 0.118401i
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ 19.0526 + 22.0000i 1.29337 + 1.49346i
$$218$$ 4.00000i 0.270914i
$$219$$ 1.00000 + 1.73205i 0.0675737 + 0.117041i
$$220$$ 0 0
$$221$$ −10.0000 + 17.3205i −0.672673 + 1.16510i
$$222$$ 6.92820 4.00000i 0.464991 0.268462i
$$223$$ 21.0000i 1.40626i 0.711059 + 0.703132i $$0.248216\pi$$
−0.711059 + 0.703132i $$0.751784\pi$$
$$224$$ 2.00000 1.73205i 0.133631 0.115728i
$$225$$ 0 0
$$226$$ 2.50000 + 4.33013i 0.166298 + 0.288036i
$$227$$ 15.5885 + 9.00000i 1.03464 + 0.597351i 0.918311 0.395860i $$-0.129553\pi$$
0.116331 + 0.993210i $$0.462887\pi$$
$$228$$ 3.46410 + 2.00000i 0.229416 + 0.132453i
$$229$$ −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i $$-0.319740\pi$$
−0.999088 + 0.0426906i $$0.986407\pi$$
$$230$$ 0 0
$$231$$ −1.00000 5.19615i −0.0657952 0.341882i
$$232$$ 6.00000i 0.393919i
$$233$$ 22.5167 13.0000i 1.47512 0.851658i 0.475509 0.879711i $$-0.342264\pi$$
0.999606 + 0.0280525i $$0.00893057\pi$$
$$234$$ 2.00000 3.46410i 0.130744 0.226455i
$$235$$ 0 0
$$236$$ 1.00000 + 1.73205i 0.0650945 + 0.112747i
$$237$$ 9.00000i 0.584613i
$$238$$ 4.33013 12.5000i 0.280680 0.810255i
$$239$$ −11.0000 −0.711531 −0.355765 0.934575i $$-0.615780\pi$$
−0.355765 + 0.934575i $$0.615780\pi$$
$$240$$ 0 0
$$241$$ 3.00000 5.19615i 0.193247 0.334714i −0.753077 0.657932i $$-0.771431\pi$$
0.946324 + 0.323218i $$0.104765\pi$$
$$242$$ 6.06218 + 3.50000i 0.389692 + 0.224989i
$$243$$ 0.866025 0.500000i 0.0555556 0.0320750i
$$244$$ −10.0000 −0.640184
$$245$$ 0 0
$$246$$ −5.00000 −0.318788
$$247$$ −13.8564 + 8.00000i −0.881662 + 0.509028i
$$248$$ −9.52628 5.50000i −0.604919 0.349250i
$$249$$ 3.00000 5.19615i 0.190117 0.329293i
$$250$$ 0 0
$$251$$ −8.00000 −0.504956 −0.252478 0.967603i $$-0.581245\pi$$
−0.252478 + 0.967603i $$0.581245\pi$$
$$252$$ −0.866025 + 2.50000i −0.0545545 + 0.157485i
$$253$$ 10.0000i 0.628695i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 12.1244 7.00000i 0.756297 0.436648i −0.0716680 0.997429i $$-0.522832\pi$$
0.827964 + 0.560781i $$0.189499\pi$$
$$258$$ 0 0
$$259$$ −4.00000 20.7846i −0.248548 1.29149i
$$260$$ 0 0
$$261$$ 3.00000 + 5.19615i 0.185695 + 0.321634i
$$262$$ −5.19615 3.00000i −0.321019 0.185341i
$$263$$ 18.1865 + 10.5000i 1.12143 + 0.647458i 0.941766 0.336270i $$-0.109166\pi$$
0.179664 + 0.983728i $$0.442499\pi$$
$$264$$ 1.00000 + 1.73205i 0.0615457 + 0.106600i
$$265$$ 0 0
$$266$$ 8.00000 6.92820i 0.490511 0.424795i
$$267$$ 11.0000i 0.673189i
$$268$$ 0 0
$$269$$ −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i $$0.427917\pi$$
−0.956176 + 0.292791i $$0.905416\pi$$
$$270$$ 0 0
$$271$$ 4.50000 + 7.79423i 0.273356 + 0.473466i 0.969719 0.244224i $$-0.0785331\pi$$
−0.696363 + 0.717689i $$0.745200\pi$$
$$272$$ 5.00000i 0.303170i
$$273$$ −6.92820 8.00000i −0.419314 0.484182i
$$274$$ 23.0000 1.38948
$$275$$ 0 0
$$276$$ −2.50000 + 4.33013i −0.150482 + 0.260643i
$$277$$ −1.73205 1.00000i −0.104069 0.0600842i 0.447062 0.894503i $$-0.352470\pi$$
−0.551131 + 0.834419i $$0.685804\pi$$
$$278$$ −1.73205 + 1.00000i −0.103882 + 0.0599760i
$$279$$ 11.0000 0.658553
$$280$$ 0 0
$$281$$ −29.0000 −1.72999 −0.864997 0.501776i $$-0.832680\pi$$
−0.864997 + 0.501776i $$0.832680\pi$$
$$282$$ −0.866025 + 0.500000i −0.0515711 + 0.0297746i
$$283$$ 22.5167 + 13.0000i 1.33848 + 0.772770i 0.986581 0.163270i $$-0.0522041\pi$$
0.351895 + 0.936039i $$0.385537\pi$$
$$284$$ −0.500000 + 0.866025i −0.0296695 + 0.0513892i
$$285$$ 0 0
$$286$$ −8.00000 −0.473050
$$287$$ −4.33013 + 12.5000i −0.255599 + 0.737852i
$$288$$ 1.00000i 0.0589256i
$$289$$ 4.00000 + 6.92820i 0.235294 + 0.407541i
$$290$$ 0 0
$$291$$ 0.500000 0.866025i 0.0293105 0.0507673i
$$292$$ −1.73205 + 1.00000i −0.101361 + 0.0585206i
$$293$$ 18.0000i 1.05157i 0.850617 + 0.525786i $$0.176229\pi$$
−0.850617 + 0.525786i $$0.823771\pi$$
$$294$$ 5.50000 + 4.33013i 0.320767 + 0.252538i
$$295$$ 0 0
$$296$$ 4.00000 + 6.92820i 0.232495 + 0.402694i
$$297$$ −1.73205 1.00000i −0.100504 0.0580259i
$$298$$ 15.5885 + 9.00000i 0.903015 + 0.521356i
$$299$$ −10.0000 17.3205i −0.578315 1.00167i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 16.0000i 0.920697i
$$303$$ 10.3923 6.00000i 0.597022 0.344691i
$$304$$ −2.00000 + 3.46410i −0.114708 + 0.198680i
$$305$$ 0 0
$$306$$ −2.50000 4.33013i −0.142915 0.247537i
$$307$$ 28.0000i 1.59804i −0.601302 0.799022i $$-0.705351\pi$$
0.601302 0.799022i $$-0.294649\pi$$
$$308$$ 5.19615 1.00000i 0.296078 0.0569803i
$$309$$ −13.0000 −0.739544
$$310$$ 0 0
$$311$$ −14.5000 + 25.1147i −0.822220 + 1.42413i 0.0818063 + 0.996648i $$0.473931\pi$$
−0.904026 + 0.427478i $$0.859402\pi$$
$$312$$ 3.46410 + 2.00000i 0.196116 + 0.113228i
$$313$$ −0.866025 + 0.500000i −0.0489506 + 0.0282617i −0.524276 0.851549i $$-0.675664\pi$$
0.475325 + 0.879810i $$0.342331\pi$$
$$314$$ −14.0000 −0.790066
$$315$$ 0 0
$$316$$ 9.00000 0.506290
$$317$$ −3.46410 + 2.00000i −0.194563 + 0.112331i −0.594117 0.804379i $$-0.702498\pi$$
0.399554 + 0.916710i $$0.369165\pi$$
$$318$$ 10.3923 + 6.00000i 0.582772 + 0.336463i
$$319$$ 6.00000 10.3923i 0.335936 0.581857i
$$320$$ 0 0
$$321$$ 2.00000 0.111629
$$322$$ 8.66025 + 10.0000i 0.482617 + 0.557278i
$$323$$ 20.0000i 1.11283i
$$324$$ 0.500000 + 0.866025i 0.0277778 + 0.0481125i
$$325$$ 0 0
$$326$$ 12.0000 20.7846i 0.664619 1.15115i
$$327$$ −3.46410 + 2.00000i −0.191565 + 0.110600i
$$328$$ 5.00000i 0.276079i
$$329$$ 0.500000 + 2.59808i 0.0275659 + 0.143237i
$$330$$ 0 0
$$331$$ −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i $$-0.255287\pi$$
−0.970091 + 0.242742i $$0.921953\pi$$
$$332$$ 5.19615 + 3.00000i 0.285176 + 0.164646i
$$333$$ −6.92820 4.00000i −0.379663 0.219199i
$$334$$ −8.00000 13.8564i −0.437741 0.758189i
$$335$$ 0 0
$$336$$ −2.50000 0.866025i −0.136386 0.0472456i
$$337$$ 13.0000i 0.708155i −0.935216 0.354078i $$-0.884795\pi$$
0.935216 0.354078i $$-0.115205\pi$$
$$338$$ −2.59808 + 1.50000i −0.141317 + 0.0815892i
$$339$$ 2.50000 4.33013i 0.135781 0.235180i
$$340$$ 0 0
$$341$$ −11.0000 19.0526i −0.595683 1.03175i
$$342$$ 4.00000i 0.216295i
$$343$$ 15.5885 10.0000i 0.841698 0.539949i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −1.00000 + 1.73205i −0.0537603 + 0.0931156i
$$347$$ −15.5885 9.00000i −0.836832 0.483145i 0.0193540 0.999813i $$-0.493839\pi$$
−0.856186 + 0.516667i $$0.827172\pi$$
$$348$$ −5.19615 + 3.00000i −0.278543 + 0.160817i
$$349$$ 4.00000 0.214115 0.107058 0.994253i $$-0.465857\pi$$
0.107058 + 0.994253i $$0.465857\pi$$
$$350$$ 0 0
$$351$$ −4.00000 −0.213504
$$352$$ −1.73205 + 1.00000i −0.0923186 + 0.0533002i
$$353$$ −7.79423 4.50000i −0.414845 0.239511i 0.278024 0.960574i $$-0.410320\pi$$
−0.692869 + 0.721063i $$0.743654\pi$$
$$354$$ 1.00000 1.73205i 0.0531494 0.0920575i
$$355$$ 0 0
$$356$$ 11.0000 0.582999
$$357$$ −12.9904 + 2.50000i −0.687524 + 0.132314i
$$358$$ 22.0000i 1.16274i
$$359$$ −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i $$-0.989691\pi$$
0.471696 0.881761i $$-0.343642\pi$$
$$360$$ 0 0
$$361$$ 1.50000 2.59808i 0.0789474 0.136741i
$$362$$ −19.0526 + 11.0000i −1.00138 + 0.578147i
$$363$$ 7.00000i 0.367405i
$$364$$ 8.00000 6.92820i 0.419314 0.363137i
$$365$$ 0 0
$$366$$ 5.00000 + 8.66025i 0.261354 + 0.452679i
$$367$$ −3.46410 2.00000i −0.180825 0.104399i 0.406855 0.913493i $$-0.366625\pi$$
−0.587680 + 0.809093i $$0.699959\pi$$
$$368$$ −4.33013 2.50000i −0.225723 0.130322i
$$369$$ 2.50000 + 4.33013i 0.130145 + 0.225417i
$$370$$ 0 0
$$371$$ 24.0000 20.7846i 1.24602 1.07908i
$$372$$ 11.0000i 0.570323i
$$373$$ −27.7128 + 16.0000i −1.43492 + 0.828449i −0.997490 0.0708063i $$-0.977443\pi$$
−0.437425 + 0.899255i $$0.644109\pi$$
$$374$$ −5.00000 + 8.66025i −0.258544 + 0.447811i
$$375$$ 0 0
$$376$$ −0.500000 0.866025i −0.0257855 0.0446619i
$$377$$ 24.0000i 1.23606i
$$378$$ 2.59808 0.500000i 0.133631 0.0257172i
$$379$$ 2.00000 0.102733 0.0513665 0.998680i $$-0.483642\pi$$
0.0513665 + 0.998680i $$0.483642\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 21.6506 + 12.5000i 1.10774 + 0.639556i
$$383$$ 2.59808 1.50000i 0.132755 0.0766464i −0.432151 0.901801i $$-0.642245\pi$$
0.564907 + 0.825155i $$0.308912\pi$$
$$384$$ 1.00000 0.0510310
$$385$$ 0 0
$$386$$ −11.0000 −0.559885
$$387$$ 0 0
$$388$$ 0.866025 + 0.500000i 0.0439658 + 0.0253837i
$$389$$ 12.0000 20.7846i 0.608424 1.05382i −0.383076 0.923717i $$-0.625135\pi$$
0.991500 0.130105i $$-0.0415314\pi$$
$$390$$ 0 0
$$391$$ −25.0000 −1.26430
$$392$$ −4.33013 + 5.50000i −0.218704 + 0.277792i
$$393$$ 6.00000i 0.302660i
$$394$$ 12.0000 + 20.7846i 0.604551 + 1.04711i
$$395$$ 0 0
$$396$$ 1.00000 1.73205i 0.0502519 0.0870388i
$$397$$ 29.4449 17.0000i 1.47780 0.853206i 0.478110 0.878300i $$-0.341322\pi$$
0.999685 + 0.0250943i $$0.00798860\pi$$
$$398$$ 5.00000i 0.250627i
$$399$$ −10.0000 3.46410i −0.500626 0.173422i
$$400$$ 0 0
$$401$$ 3.00000 + 5.19615i 0.149813 + 0.259483i 0.931158 0.364615i $$-0.118800\pi$$
−0.781345 + 0.624099i $$0.785466\pi$$
$$402$$ 0 0
$$403$$ −38.1051 22.0000i −1.89815 1.09590i
$$404$$ 6.00000 + 10.3923i 0.298511 + 0.517036i
$$405$$ 0 0
$$406$$ 3.00000 + 15.5885i 0.148888 + 0.773642i
$$407$$ 16.0000i 0.793091i
$$408$$ 4.33013 2.50000i 0.214373 0.123768i
$$409$$ −17.5000 + 30.3109i −0.865319 + 1.49878i 0.00141047 + 0.999999i $$0.499551\pi$$
−0.866730 + 0.498778i $$0.833782\pi$$
$$410$$ 0 0
$$411$$ −11.5000 19.9186i −0.567253 0.982511i
$$412$$ 13.0000i 0.640464i
$$413$$ −3.46410 4.00000i −0.170457 0.196827i
$$414$$ 5.00000 0.245737
$$415$$ 0 0
$$416$$ −2.00000 + 3.46410i −0.0980581 + 0.169842i
$$417$$ 1.73205 + 1.00000i 0.0848189 + 0.0489702i
$$418$$ −6.92820 + 4.00000i −0.338869 + 0.195646i
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 0 0
$$421$$ 28.0000 1.36464 0.682318 0.731055i $$-0.260972\pi$$
0.682318 + 0.731055i $$0.260972\pi$$
$$422$$ −13.8564 + 8.00000i −0.674519 + 0.389434i
$$423$$ 0.866025 + 0.500000i 0.0421076 + 0.0243108i
$$424$$ −6.00000 + 10.3923i −0.291386 + 0.504695i
$$425$$ 0 0
$$426$$ 1.00000 0.0484502
$$427$$ 25.9808 5.00000i 1.25730 0.241967i
$$428$$ 2.00000i 0.0966736i
$$429$$ 4.00000 + 6.92820i 0.193122 + 0.334497i
$$430$$ 0 0
$$431$$ 1.50000 2.59808i 0.0722525 0.125145i −0.827636 0.561266i $$-0.810315\pi$$
0.899888 + 0.436121i $$0.143648\pi$$
$$432$$ −0.866025 + 0.500000i −0.0416667 + 0.0240563i
$$433$$ 9.00000i 0.432512i −0.976337 0.216256i $$-0.930615\pi$$
0.976337 0.216256i $$-0.0693846\pi$$
$$434$$ 27.5000 + 9.52628i 1.32004 + 0.457276i
$$435$$ 0 0
$$436$$ −2.00000 3.46410i −0.0957826 0.165900i
$$437$$ −17.3205 10.0000i −0.828552 0.478365i
$$438$$ 1.73205 + 1.00000i 0.0827606 + 0.0477818i
$$439$$ 17.5000 + 30.3109i 0.835229 + 1.44666i 0.893843 + 0.448379i $$0.147999\pi$$
−0.0586141 + 0.998281i $$0.518668\pi$$
$$440$$ 0 0
$$441$$ 1.00000 6.92820i 0.0476190 0.329914i
$$442$$ 20.0000i 0.951303i
$$443$$ −6.92820 + 4.00000i −0.329169 + 0.190046i −0.655472 0.755219i $$-0.727530\pi$$
0.326303 + 0.945265i $$0.394197\pi$$
$$444$$ 4.00000 6.92820i 0.189832 0.328798i
$$445$$ 0 0
$$446$$ 10.5000 + 18.1865i 0.497189 + 0.861157i
$$447$$ 18.0000i 0.851371i
$$448$$ 0.866025 2.50000i 0.0409159 0.118114i
$$449$$ −37.0000 −1.74614 −0.873069 0.487597i $$-0.837874\pi$$
−0.873069 + 0.487597i $$0.837874\pi$$
$$450$$ 0 0
$$451$$ 5.00000 8.66025i 0.235441 0.407795i
$$452$$ 4.33013 + 2.50000i 0.203672 + 0.117590i
$$453$$ −13.8564 + 8.00000i −0.651031 + 0.375873i
$$454$$ 18.0000 0.844782
$$455$$ 0 0
$$456$$ 4.00000 0.187317
$$457$$ −12.1244 + 7.00000i −0.567153 + 0.327446i −0.756012 0.654558i $$-0.772855\pi$$
0.188858 + 0.982004i $$0.439521\pi$$
$$458$$ −12.1244 7.00000i −0.566534 0.327089i
$$459$$ −2.50000 + 4.33013i −0.116690 + 0.202113i
$$460$$ 0 0
$$461$$ 20.0000 0.931493 0.465746 0.884918i $$-0.345786\pi$$
0.465746 + 0.884918i $$0.345786\pi$$
$$462$$ −3.46410 4.00000i −0.161165 0.186097i
$$463$$ 13.0000i 0.604161i 0.953282 + 0.302081i $$0.0976812\pi$$
−0.953282 + 0.302081i $$0.902319\pi$$
$$464$$ −3.00000 5.19615i −0.139272 0.241225i
$$465$$ 0 0
$$466$$ 13.0000 22.5167i 0.602213 1.04306i
$$467$$ 29.4449 17.0000i 1.36255 0.786666i 0.372584 0.927999i $$-0.378472\pi$$
0.989962 + 0.141332i $$0.0451386\pi$$
$$468$$ 4.00000i 0.184900i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 7.00000 + 12.1244i 0.322543 + 0.558661i
$$472$$ 1.73205 + 1.00000i 0.0797241 + 0.0460287i
$$473$$ 0 0
$$474$$ −4.50000 7.79423i −0.206692 0.358001i
$$475$$ 0 0
$$476$$ −2.50000 12.9904i −0.114587 0.595413i
$$477$$ 12.0000i 0.549442i
$$478$$ −9.52628 + 5.50000i −0.435722 + 0.251564i
$$479$$ −1.50000 + 2.59808i −0.0685367 + 0.118709i −0.898257 0.439470i $$-0.855166\pi$$
0.829721 + 0.558179i $$0.188500\pi$$
$$480$$ 0 0
$$481$$ 16.0000 + 27.7128i 0.729537 + 1.26360i
$$482$$ 6.00000i 0.273293i
$$483$$ 4.33013 12.5000i 0.197028 0.568770i
$$484$$ 7.00000 0.318182
$$485$$ 0 0
$$486$$ 0.500000 0.866025i 0.0226805 0.0392837i
$$487$$ −33.7750 19.5000i −1.53049 0.883629i −0.999339 0.0363527i $$-0.988426\pi$$
−0.531152 0.847277i $$-0.678241\pi$$
$$488$$ −8.66025 + 5.00000i −0.392031 + 0.226339i
$$489$$ −24.0000 −1.08532
$$490$$ 0 0
$$491$$ 12.0000 0.541552 0.270776 0.962642i $$-0.412720\pi$$
0.270776 + 0.962642i $$0.412720\pi$$
$$492$$ −4.33013 + 2.50000i −0.195217 + 0.112709i
$$493$$ −25.9808 15.0000i −1.17011 0.675566i
$$494$$ −8.00000 + 13.8564i −0.359937 + 0.623429i
$$495$$ 0 0
$$496$$ −11.0000 −0.493915
$$497$$ 0.866025 2.50000i 0.0388465 0.112140i
$$498$$ 6.00000i 0.268866i
$$499$$ 11.0000 + 19.0526i 0.492428 + 0.852910i 0.999962 0.00872186i $$-0.00277629\pi$$
−0.507534 + 0.861632i $$0.669443\pi$$
$$500$$ 0 0
$$501$$ −8.00000 + 13.8564i −0.357414 + 0.619059i
$$502$$ −6.92820 + 4.00000i −0.309221 + 0.178529i
$$503$$ 8.00000i 0.356702i 0.983967 + 0.178351i $$0.0570763\pi$$
−0.983967 + 0.178351i $$0.942924\pi$$
$$504$$ 0.500000 + 2.59808i 0.0222718 + 0.115728i
$$505$$ 0 0
$$506$$ −5.00000 8.66025i −0.222277 0.384995i
$$507$$ 2.59808 + 1.50000i 0.115385 + 0.0666173i
$$508$$ 0 0
$$509$$ 1.00000 + 1.73205i 0.0443242 + 0.0767718i 0.887336 0.461123i $$-0.152553\pi$$
−0.843012 + 0.537895i $$0.819220\pi$$
$$510$$ 0 0
$$511$$ 4.00000 3.46410i 0.176950 0.153243i
$$512$$ 1.00000i 0.0441942i
$$513$$ −3.46410 + 2.00000i −0.152944 + 0.0883022i
$$514$$ 7.00000 12.1244i 0.308757 0.534782i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 2.00000i 0.0879599i
$$518$$ −13.8564 16.0000i −0.608816 0.703000i
$$519$$ 2.00000 0.0877903
$$520$$ 0 0
$$521$$ 1.50000 2.59808i 0.0657162 0.113824i −0.831295 0.555831i $$-0.812400\pi$$
0.897011 + 0.442007i $$0.145733\pi$$
$$522$$ 5.19615 + 3.00000i 0.227429 + 0.131306i
$$523$$ −12.1244 + 7.00000i −0.530161 + 0.306089i −0.741082 0.671414i $$-0.765687\pi$$
0.210921 + 0.977503i $$0.432354\pi$$
$$524$$ −6.00000 −0.262111
$$525$$ 0 0
$$526$$ 21.0000 0.915644
$$527$$ −47.6314 + 27.5000i −2.07486 + 1.19792i
$$528$$ 1.73205 + 1.00000i 0.0753778 + 0.0435194i
$$529$$ 1.00000 1.73205i 0.0434783 0.0753066i
$$530$$ 0 0
$$531$$ −2.00000 −0.0867926
$$532$$ 3.46410 10.0000i 0.150188 0.433555i
$$533$$ 20.0000i 0.866296i
$$534$$ −5.50000 9.52628i −0.238008 0.412242i
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −19.0526 + 11.0000i −0.822179 + 0.474685i
$$538$$ 24.0000i 1.03471i
$$539$$ −13.0000 + 5.19615i −0.559950 + 0.223814i
$$540$$ 0 0
$$541$$ 2.00000 + 3.46410i 0.0859867 + 0.148933i 0.905811 0.423681i $$-0.139262\pi$$
−0.819825 + 0.572615i $$0.805929\pi$$
$$542$$ 7.79423 + 4.50000i 0.334791 + 0.193292i
$$543$$ 19.0526 + 11.0000i 0.817624 + 0.472055i
$$544$$ 2.50000 + 4.33013i 0.107187 + 0.185653i
$$545$$ 0 0
$$546$$ −10.0000 3.46410i −0.427960 0.148250i
$$547$$ 8.00000i 0.342055i −0.985266 0.171028i $$-0.945291\pi$$
0.985266 0.171028i $$-0.0547087\pi$$
$$548$$ 19.9186 11.5000i 0.850880 0.491256i
$$549$$ 5.00000 8.66025i 0.213395 0.369611i
$$550$$ 0 0
$$551$$ −12.0000 20.7846i −0.511217 0.885454i
$$552$$ 5.00000i 0.212814i
$$553$$ −23.3827 + 4.50000i −0.994333 + 0.191359i
$$554$$ −2.00000 −0.0849719
$$555$$ 0 0
$$556$$ −1.00000 + 1.73205i −0.0424094 + 0.0734553i
$$557$$ 32.9090 + 19.0000i 1.39440 + 0.805056i 0.993798 0.111198i $$-0.0354686\pi$$
0.400599 + 0.916253i $$0.368802\pi$$
$$558$$ 9.52628 5.50000i 0.403280 0.232834i
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 10.0000 0.422200
$$562$$ −25.1147 + 14.5000i −1.05940 + 0.611646i
$$563$$ 31.1769 + 18.0000i 1.31395 + 0.758610i 0.982748 0.184950i $$-0.0592124\pi$$
0.331202 + 0.943560i $$0.392546\pi$$
$$564$$ −0.500000 + 0.866025i −0.0210538 + 0.0364662i
$$565$$ 0 0
$$566$$ 26.0000 1.09286
$$567$$ −1.73205 2.00000i −0.0727393 0.0839921i
$$568$$ 1.00000i 0.0419591i
$$569$$ 4.50000 + 7.79423i 0.188650 + 0.326751i 0.944800 0.327647i $$-0.106256\pi$$
−0.756151 + 0.654398i $$0.772922\pi$$
$$570$$ 0 0
$$571$$ 22.0000 38.1051i 0.920671 1.59465i 0.122292 0.992494i $$-0.460975\pi$$
0.798379 0.602155i $$-0.205691\pi$$
$$572$$ −6.92820 + 4.00000i −0.289683 + 0.167248i
$$573$$ 25.0000i 1.04439i
$$574$$ 2.50000 + 12.9904i 0.104348 + 0.542208i
$$575$$ 0 0
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ −1.73205 1.00000i −0.0721062 0.0416305i 0.463513 0.886090i $$-0.346589\pi$$
−0.535620 + 0.844459i $$0.679922\pi$$
$$578$$ 6.92820 + 4.00000i 0.288175 + 0.166378i
$$579$$ 5.50000 + 9.52628i 0.228572 + 0.395899i
$$580$$ 0 0
$$581$$ −15.0000 5.19615i −0.622305 0.215573i
$$582$$ 1.00000i 0.0414513i
$$583$$ −20.7846 + 12.0000i −0.860811 + 0.496989i
$$584$$ −1.00000 + 1.73205i −0.0413803 + 0.0716728i
$$585$$ 0 0
$$586$$ 9.00000 + 15.5885i 0.371787 + 0.643953i
$$587$$ 6.00000i 0.247647i −0.992304 0.123823i $$-0.960484\pi$$
0.992304 0.123823i $$-0.0395156\pi$$
$$588$$ 6.92820 + 1.00000i 0.285714 + 0.0412393i
$$589$$ −44.0000 −1.81299
$$590$$ 0 0
$$591$$ 12.0000 20.7846i 0.493614 0.854965i
$$592$$ 6.92820 + 4.00000i 0.284747 + 0.164399i
$$593$$ 7.79423 4.50000i 0.320071 0.184793i −0.331353 0.943507i $$-0.607505\pi$$
0.651424 + 0.758714i $$0.274172\pi$$
$$594$$ −2.00000 −0.0820610
$$595$$ 0 0
$$596$$ 18.0000 0.737309
$$597$$ −4.33013 + 2.50000i −0.177220 + 0.102318i
$$598$$ −17.3205 10.0000i −0.708288 0.408930i
$$599$$ 8.50000 14.7224i 0.347301 0.601542i −0.638468 0.769648i $$-0.720432\pi$$
0.985769 + 0.168106i $$0.0537650\pi$$
$$600$$ 0 0
$$601$$ −34.0000 −1.38689 −0.693444 0.720510i $$-0.743908\pi$$
−0.693444 + 0.720510i $$0.743908\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −8.00000 13.8564i −0.325515 0.563809i
$$605$$ 0 0
$$606$$ 6.00000 10.3923i 0.243733 0.422159i
$$607$$ 23.3827 13.5000i 0.949074 0.547948i 0.0562808 0.998415i $$-0.482076\pi$$
0.892793 + 0.450467i $$0.148742\pi$$
$$608$$ 4.00000i 0.162221i
$$609$$ 12.0000 10.3923i 0.486265 0.421117i
$$610$$ 0 0
$$611$$ −2.00000 3.46410i −0.0809113 0.140143i
$$612$$ −4.33013 2.50000i −0.175035 0.101057i
$$613$$ −29.4449 17.0000i −1.18927 0.686624i −0.231127 0.972924i $$-0.574241\pi$$
−0.958140 + 0.286300i $$0.907575\pi$$
$$614$$ −14.0000 24.2487i −0.564994 0.978598i
$$615$$ 0 0
$$616$$ 4.00000 3.46410i 0.161165 0.139573i
$$617$$ 29.0000i 1.16750i −0.811935 0.583748i $$-0.801586\pi$$
0.811935 0.583748i $$-0.198414\pi$$
$$618$$ −11.2583 + 6.50000i −0.452876 + 0.261468i
$$619$$ −7.00000 + 12.1244i −0.281354 + 0.487319i −0.971718 0.236143i $$-0.924117\pi$$
0.690365 + 0.723462i $$0.257450\pi$$
$$620$$ 0 0
$$621$$ −2.50000 4.33013i −0.100322 0.173762i
$$622$$ 29.0000i 1.16279i
$$623$$ −28.5788 + 5.50000i −1.14499 + 0.220353i
$$624$$ 4.00000 0.160128
$$625$$ 0 0
$$626$$ −0.500000 + 0.866025i −0.0199840 + 0.0346133i
$$627$$ 6.92820 + 4.00000i 0.276686 + 0.159745i
$$628$$ −12.1244 + 7.00000i −0.483814 + 0.279330i
$$629$$ 40.0000 1.59490
$$630$$ 0 0
$$631$$ 33.0000 1.31371 0.656855 0.754017i $$-0.271887\pi$$
0.656855 + 0.754017i $$0.271887\pi$$
$$632$$ 7.79423 4.50000i 0.310038 0.179000i
$$633$$ 13.8564 + 8.00000i 0.550743 + 0.317971i
$$634$$ −2.00000 + 3.46410i −0.0794301 + 0.137577i
$$635$$ 0 0
$$636$$ 12.0000 0.475831
$$637$$ −17.3205 + 22.0000i −0.686264 + 0.871672i
$$638$$ 12.0000i 0.475085i
$$639$$ −0.500000 0.866025i −0.0197797 0.0342594i
$$640$$ 0 0
$$641$$ 7.50000 12.9904i 0.296232 0.513089i −0.679039 0.734103i $$-0.737603\pi$$
0.975271 + 0.221013i $$0.0709364\pi$$
$$642$$ 1.73205 1.00000i 0.0683586 0.0394669i
$$643$$ 26.0000i 1.02534i 0.858586 + 0.512670i $$0.171344\pi$$
−0.858586 + 0.512670i $$0.828656\pi$$
$$644$$ 12.5000 + 4.33013i 0.492569 + 0.170631i
$$645$$ 0 0
$$646$$ 10.0000 + 17.3205i 0.393445 + 0.681466i
$$647$$ −24.2487 14.0000i −0.953315 0.550397i −0.0592060 0.998246i $$-0.518857\pi$$
−0.894109 + 0.447849i $$0.852190\pi$$
$$648$$ 0.866025 + 0.500000i 0.0340207 + 0.0196419i
$$649$$ 2.00000 + 3.46410i 0.0785069 + 0.135978i
$$650$$ 0 0
$$651$$ −5.50000 28.5788i −0.215562 1.12009i
$$652$$ 24.0000i 0.939913i
$$653$$ 24.2487 14.0000i 0.948925 0.547862i 0.0561784 0.998421i $$-0.482108\pi$$
0.892747 + 0.450558i $$0.148775\pi$$
$$654$$ −2.00000 + 3.46410i −0.0782062 + 0.135457i
$$655$$ 0 0
$$656$$ −2.50000 4.33013i −0.0976086 0.169063i
$$657$$ 2.00000i 0.0780274i
$$658$$ 1.73205 + 2.00000i 0.0675224 + 0.0779681i
$$659$$ 14.0000 0.545363 0.272681 0.962104i $$-0.412090\pi$$
0.272681 + 0.962104i $$0.412090\pi$$
$$660$$ 0 0
$$661$$ −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i $$-0.921107\pi$$
0.697174 + 0.716902i $$0.254441\pi$$
$$662$$ −8.66025 5.00000i −0.336590 0.194331i
$$663$$ 17.3205 10.0000i 0.672673 0.388368i
$$664$$ 6.00000 0.232845
$$665$$ 0 0
$$666$$ −8.00000 −0.309994
$$667$$ 25.9808 15.0000i 1.00598 0.580802i
$$668$$ −13.8564 8.00000i −0.536120 0.309529i
$$669$$ 10.5000 18.1865i 0.405953 0.703132i
$$670$$ 0 0
$$671$$ −20.0000 −0.772091
$$672$$ −2.59808 + 0.500000i −0.100223 + 0.0192879i
$$673$$ 19.0000i 0.732396i 0.930537 + 0.366198i $$0.119341\pi$$
−0.930537 + 0.366198i $$0.880659\pi$$
$$674$$ −6.50000 11.2583i −0.250371 0.433655i
$$675$$ 0 0
$$676$$ −1.50000 + 2.59808i −0.0576923 + 0.0999260i
$$677$$ 15.5885 9.00000i 0.599113 0.345898i −0.169580 0.985517i $$-0.554241\pi$$
0.768693 + 0.639618i $$0.220908\pi$$
$$678$$ 5.00000i 0.192024i
$$679$$ −2.50000 0.866025i −0.0959412 0.0332350i
$$680$$ 0 0
$$681$$ −9.00000 15.5885i −0.344881 0.597351i
$$682$$ −19.0526 11.0000i −0.729560 0.421212i
$$683$$ 1.73205 + 1.00000i 0.0662751 + 0.0382639i 0.532771 0.846259i $$-0.321151\pi$$
−0.466496 + 0.884523i $$0.654484\pi$$
$$684$$ −2.00000 3.46410i −0.0764719 0.132453i
$$685$$ 0 0
$$686$$ 8.50000 16.4545i 0.324532 0.628235i
$$687$$ 14.0000i 0.534133i
$$688$$ 0 0
$$689$$ −24.0000 + 41.5692i −0.914327 + 1.58366i
$$690$$ 0 0
$$691$$ 1.00000 + 1.73205i 0.0380418 + 0.0658903i 0.884419 0.466693i $$-0.154555\pi$$
−0.846378 + 0.532583i $$0.821221\pi$$
$$692$$ 2.00000i 0.0760286i
$$693$$ −1.73205 + 5.00000i −0.0657952 + 0.189934i
$$694$$ −18.0000 −0.683271
$$695$$ 0 0
$$696$$ −3.00000 + 5.19615i −0.113715 + 0.196960i
$$697$$ −21.6506 12.5000i −0.820076 0.473471i
$$698$$ 3.46410 2.00000i 0.131118 0.0757011i
$$699$$ −26.0000 −0.983410
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ −3.46410 + 2.00000i −0.130744 + 0.0754851i
$$703$$ 27.7128 + 16.0000i 1.04521 + 0.603451i
$$704$$ −1.00000 + 1.73205i −0.0376889 + 0.0652791i
$$705$$ 0 0
$$706$$ −9.00000 −0.338719
$$707$$ −20.7846 24.0000i −0.781686 0.902613i
$$708$$ 2.00000i 0.0751646i
$$709$$ 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i $$-0.106538\pi$$
−0.756730 + 0.653727i $$0.773204\pi$$
$$710$$ 0 0
$$711$$ −4.50000 + 7.79423i −0.168763 + 0.292306i
$$712$$ 9.52628 5.50000i 0.357012 0.206121i
$$713$$ 55.0000i 2.05977i
$$714$$ −10.0000 + 8.66025i −0.374241 + 0.324102i
$$715$$ 0 0
$$716$$ −11.0000 19.0526i −0.411089 0.712028i
$$717$$ 9.52628 + 5.50000i 0.355765 + 0.205401i
$$718$$ −17.3205 10.0000i −0.646396 0.373197i
$$719$$ −1.50000 2.59808i −0.0559406 0.0968919i 0.836699 0.547663i $$-0.184482\pi$$
−0.892640 + 0.450771i $$0.851149\pi$$
$$720$$ 0 0
$$721$$ 6.50000 + 33.7750i 0.242073 + 1.25785i
$$722$$ 3.00000i 0.111648i
$$723$$ −5.19615 + 3.00000i −0.193247 + 0.111571i
$$724$$ −11.0000 + 19.0526i −0.408812 + 0.708083i
$$725$$ 0 0
$$726$$ −3.50000 6.06218i −0.129897 0.224989i
$$727$$ 33.0000i 1.22390i 0.790896 + 0.611951i $$0.209615\pi$$
−0.790896 + 0.611951i $$0.790385\pi$$
$$728$$ 3.46410 10.0000i 0.128388 0.370625i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 8.66025 + 5.00000i 0.320092 + 0.184805i
$$733$$ 25.9808 15.0000i 0.959621 0.554038i 0.0635649 0.997978i $$-0.479753\pi$$
0.896056 + 0.443940i $$0.146420\pi$$
$$734$$ −4.00000 −0.147643
$$735$$ 0 0
$$736$$ −5.00000 −0.184302
$$737$$ 0 0
$$738$$ 4.33013 + 2.50000i 0.159394 + 0.0920263i
$$739$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$740$$ 0 0
$$741$$ 16.0000 0.587775
$$742$$ 10.3923 30.0000i 0.381514 1.10133i
$$743$$ 33.0000i 1.21065i −0.795977 0.605326i $$-0.793043\pi$$
0.795977 0.605326i $$-0.206957\pi$$
$$744$$ 5.50000 + 9.52628i 0.201640 + 0.349250i
$$745$$ 0 0
$$746$$ −16.0000 + 27.7128i −0.585802 + 1.01464i
$$747$$ −5.19615 + 3.00000i −0.190117 + 0.109764i
$$748$$ 10.0000i 0.365636i
$$749$$ −1.00000 5.19615i −0.0365392 0.189863i
$$750$$ 0 0
$$751$$ 16.0000 + 27.7128i 0.583848 + 1.01125i 0.995018 + 0.0996961i $$0.0317870\pi$$
−0.411170 + 0.911559i $$0.634880\pi$$
$$752$$ −0.866025 0.500000i −0.0315807 0.0182331i
$$753$$ 6.92820 + 4.00000i 0.252478 + 0.145768i
$$754$$ −12.0000 20.7846i −0.437014 0.756931i
$$755$$ 0 0
$$756$$ 2.00000 1.73205i 0.0727393 0.0629941i
$$757$$ 28.0000i 1.01768i −0.860862 0.508839i $$-0.830075\pi$$
0.860862 0.508839i $$-0.169925\pi$$
$$758$$ 1.73205 1.00000i 0.0629109 0.0363216i
$$759$$ −5.00000 + 8.66025i −0.181489 + 0.314347i
$$760$$ 0 0
$$761$$ −8.50000 14.7224i −0.308125 0.533688i 0.669827 0.742517i $$-0.266368\pi$$
−0.977952 + 0.208829i $$0.933035\pi$$
$$762$$ 0 0
$$763$$ 6.92820 + 8.00000i 0.250818 + 0.289619i
$$764$$ 25.0000 0.904468
$$765$$ 0 0
$$766$$ 1.50000 2.59808i 0.0541972 0.0938723i
$$767$$ 6.92820 + 4.00000i 0.250163 + 0.144432i
$$768$$ 0.866025 0.500000i 0.0312500 0.0180422i
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ −14.0000 −0.504198
$$772$$ −9.52628 + 5.50000i −0.342858 + 0.197949i
$$773$$ 3.46410 + 2.00000i 0.124595 + 0.0719350i 0.561002 0.827814i $$-0.310416\pi$$
−0.436407 + 0.899749i $$0.643749\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 1.00000 0.0358979
$$777$$ −6.92820 + 20.0000i −0.248548 + 0.717496i
$$778$$ 24.0000i 0.860442i
$$779$$ −10.0000 17.3205i −0.358287 0.620572i
$$780$$ 0 0
$$781$$ −1.00000 + 1.73205i −0.0357828 + 0.0619777i
$$782$$ −21.6506 + 12.5000i −0.774225 + 0.446999i
$$783$$ 6.00000i 0.214423i
$$784$$ −1.00000 + 6.92820i −0.0357143 + 0.247436i
$$785$$ 0 0
$$786$$ 3.00000