# Properties

 Label 576.2.bb.a.529.1 Level $576$ Weight $2$ Character 576.529 Analytic conductor $4.599$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$576 = 2^{6} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 576.bb (of order $$12$$, degree $$4$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.59938315643$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 144) Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 529.1 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 576.529 Dual form 576.2.bb.a.49.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.73205 q^{3} +(-1.86603 - 0.500000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +3.00000 q^{9} +O(q^{10})$$ $$q-1.73205 q^{3} +(-1.86603 - 0.500000i) q^{5} +(-3.86603 - 2.23205i) q^{7} +3.00000 q^{9} +(0.500000 + 1.86603i) q^{11} +(-0.598076 + 2.23205i) q^{13} +(3.23205 + 0.866025i) q^{15} +4.00000 q^{17} +(3.00000 + 3.00000i) q^{19} +(6.69615 + 3.86603i) q^{21} +(5.59808 - 3.23205i) q^{23} +(-1.09808 - 0.633975i) q^{25} -5.19615 q^{27} +(-0.866025 + 0.232051i) q^{29} +(4.59808 + 7.96410i) q^{31} +(-0.866025 - 3.23205i) q^{33} +(6.09808 + 6.09808i) q^{35} +(-4.26795 + 4.26795i) q^{37} +(1.03590 - 3.86603i) q^{39} +(0.696152 - 0.401924i) q^{41} +(1.69615 + 6.33013i) q^{43} +(-5.59808 - 1.50000i) q^{45} +(0.598076 - 1.03590i) q^{47} +(6.46410 + 11.1962i) q^{49} -6.92820 q^{51} +(5.73205 - 5.73205i) q^{53} -3.73205i q^{55} +(-5.19615 - 5.19615i) q^{57} +(1.50000 + 0.401924i) q^{59} +(-2.13397 + 0.571797i) q^{61} +(-11.5981 - 6.69615i) q^{63} +(2.23205 - 3.86603i) q^{65} +(2.23205 - 8.33013i) q^{67} +(-9.69615 + 5.59808i) q^{69} +2.92820i q^{71} +7.46410i q^{73} +(1.90192 + 1.09808i) q^{75} +(2.23205 - 8.33013i) q^{77} +(0.866025 - 1.50000i) q^{79} +9.00000 q^{81} +(14.1603 - 3.79423i) q^{83} +(-7.46410 - 2.00000i) q^{85} +(1.50000 - 0.401924i) q^{87} +15.8564i q^{89} +(7.29423 - 7.29423i) q^{91} +(-7.96410 - 13.7942i) q^{93} +(-4.09808 - 7.09808i) q^{95} +(-0.500000 + 0.866025i) q^{97} +(1.50000 + 5.59808i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{5} - 12q^{7} + 12q^{9} + O(q^{10})$$ $$4q - 4q^{5} - 12q^{7} + 12q^{9} + 2q^{11} + 8q^{13} + 6q^{15} + 16q^{17} + 12q^{19} + 6q^{21} + 12q^{23} + 6q^{25} + 8q^{31} + 14q^{35} - 24q^{37} + 18q^{39} - 18q^{41} - 14q^{43} - 12q^{45} - 8q^{47} + 12q^{49} + 16q^{53} + 6q^{59} - 12q^{61} - 36q^{63} + 2q^{65} + 2q^{67} - 18q^{69} + 18q^{75} + 2q^{77} + 36q^{81} + 22q^{83} - 16q^{85} + 6q^{87} - 2q^{91} - 18q^{93} - 6q^{95} - 2q^{97} + 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$$.

 $$n$$ $$65$$ $$127$$ $$325$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.73205 −1.00000
$$4$$ 0 0
$$5$$ −1.86603 0.500000i −0.834512 0.223607i −0.183831 0.982958i $$-0.558850\pi$$
−0.650681 + 0.759351i $$0.725517\pi$$
$$6$$ 0 0
$$7$$ −3.86603 2.23205i −1.46122 0.843636i −0.462152 0.886801i $$-0.652923\pi$$
−0.999068 + 0.0431647i $$0.986256\pi$$
$$8$$ 0 0
$$9$$ 3.00000 1.00000
$$10$$ 0 0
$$11$$ 0.500000 + 1.86603i 0.150756 + 0.562628i 0.999432 + 0.0337145i $$0.0107337\pi$$
−0.848676 + 0.528913i $$0.822600\pi$$
$$12$$ 0 0
$$13$$ −0.598076 + 2.23205i −0.165876 + 0.619060i 0.832050 + 0.554700i $$0.187167\pi$$
−0.997927 + 0.0643593i $$0.979500\pi$$
$$14$$ 0 0
$$15$$ 3.23205 + 0.866025i 0.834512 + 0.223607i
$$16$$ 0 0
$$17$$ 4.00000 0.970143 0.485071 0.874475i $$-0.338794\pi$$
0.485071 + 0.874475i $$0.338794\pi$$
$$18$$ 0 0
$$19$$ 3.00000 + 3.00000i 0.688247 + 0.688247i 0.961844 0.273597i $$-0.0882135\pi$$
−0.273597 + 0.961844i $$0.588214\pi$$
$$20$$ 0 0
$$21$$ 6.69615 + 3.86603i 1.46122 + 0.843636i
$$22$$ 0 0
$$23$$ 5.59808 3.23205i 1.16728 0.673929i 0.214242 0.976781i $$-0.431272\pi$$
0.953038 + 0.302851i $$0.0979386\pi$$
$$24$$ 0 0
$$25$$ −1.09808 0.633975i −0.219615 0.126795i
$$26$$ 0 0
$$27$$ −5.19615 −1.00000
$$28$$ 0 0
$$29$$ −0.866025 + 0.232051i −0.160817 + 0.0430908i −0.338329 0.941028i $$-0.609862\pi$$
0.177512 + 0.984119i $$0.443195\pi$$
$$30$$ 0 0
$$31$$ 4.59808 + 7.96410i 0.825839 + 1.43039i 0.901277 + 0.433244i $$0.142631\pi$$
−0.0754376 + 0.997151i $$0.524035\pi$$
$$32$$ 0 0
$$33$$ −0.866025 3.23205i −0.150756 0.562628i
$$34$$ 0 0
$$35$$ 6.09808 + 6.09808i 1.03076 + 1.03076i
$$36$$ 0 0
$$37$$ −4.26795 + 4.26795i −0.701647 + 0.701647i −0.964764 0.263117i $$-0.915249\pi$$
0.263117 + 0.964764i $$0.415249\pi$$
$$38$$ 0 0
$$39$$ 1.03590 3.86603i 0.165876 0.619060i
$$40$$ 0 0
$$41$$ 0.696152 0.401924i 0.108721 0.0627700i −0.444654 0.895703i $$-0.646673\pi$$
0.553374 + 0.832933i $$0.313340\pi$$
$$42$$ 0 0
$$43$$ 1.69615 + 6.33013i 0.258661 + 0.965335i 0.966017 + 0.258478i $$0.0832210\pi$$
−0.707356 + 0.706857i $$0.750112\pi$$
$$44$$ 0 0
$$45$$ −5.59808 1.50000i −0.834512 0.223607i
$$46$$ 0 0
$$47$$ 0.598076 1.03590i 0.0872384 0.151101i −0.819104 0.573644i $$-0.805529\pi$$
0.906343 + 0.422543i $$0.138862\pi$$
$$48$$ 0 0
$$49$$ 6.46410 + 11.1962i 0.923443 + 1.59945i
$$50$$ 0 0
$$51$$ −6.92820 −0.970143
$$52$$ 0 0
$$53$$ 5.73205 5.73205i 0.787358 0.787358i −0.193703 0.981060i $$-0.562050\pi$$
0.981060 + 0.193703i $$0.0620497\pi$$
$$54$$ 0 0
$$55$$ 3.73205i 0.503230i
$$56$$ 0 0
$$57$$ −5.19615 5.19615i −0.688247 0.688247i
$$58$$ 0 0
$$59$$ 1.50000 + 0.401924i 0.195283 + 0.0523260i 0.355135 0.934815i $$-0.384435\pi$$
−0.159852 + 0.987141i $$0.551102\pi$$
$$60$$ 0 0
$$61$$ −2.13397 + 0.571797i −0.273227 + 0.0732111i −0.392831 0.919611i $$-0.628504\pi$$
0.119604 + 0.992822i $$0.461838\pi$$
$$62$$ 0 0
$$63$$ −11.5981 6.69615i −1.46122 0.843636i
$$64$$ 0 0
$$65$$ 2.23205 3.86603i 0.276852 0.479521i
$$66$$ 0 0
$$67$$ 2.23205 8.33013i 0.272688 1.01769i −0.684686 0.728838i $$-0.740061\pi$$
0.957375 0.288849i $$-0.0932726\pi$$
$$68$$ 0 0
$$69$$ −9.69615 + 5.59808i −1.16728 + 0.673929i
$$70$$ 0 0
$$71$$ 2.92820i 0.347514i 0.984789 + 0.173757i $$0.0555907\pi$$
−0.984789 + 0.173757i $$0.944409\pi$$
$$72$$ 0 0
$$73$$ 7.46410i 0.873607i 0.899557 + 0.436804i $$0.143889\pi$$
−0.899557 + 0.436804i $$0.856111\pi$$
$$74$$ 0 0
$$75$$ 1.90192 + 1.09808i 0.219615 + 0.126795i
$$76$$ 0 0
$$77$$ 2.23205 8.33013i 0.254366 0.949306i
$$78$$ 0 0
$$79$$ 0.866025 1.50000i 0.0974355 0.168763i −0.813187 0.582003i $$-0.802269\pi$$
0.910622 + 0.413239i $$0.135603\pi$$
$$80$$ 0 0
$$81$$ 9.00000 1.00000
$$82$$ 0 0
$$83$$ 14.1603 3.79423i 1.55429 0.416471i 0.623440 0.781872i $$-0.285735\pi$$
0.930850 + 0.365401i $$0.119068\pi$$
$$84$$ 0 0
$$85$$ −7.46410 2.00000i −0.809595 0.216930i
$$86$$ 0 0
$$87$$ 1.50000 0.401924i 0.160817 0.0430908i
$$88$$ 0 0
$$89$$ 15.8564i 1.68078i 0.541985 + 0.840388i $$0.317673\pi$$
−0.541985 + 0.840388i $$0.682327\pi$$
$$90$$ 0 0
$$91$$ 7.29423 7.29423i 0.764643 0.764643i
$$92$$ 0 0
$$93$$ −7.96410 13.7942i −0.825839 1.43039i
$$94$$ 0 0
$$95$$ −4.09808 7.09808i −0.420454 0.728247i
$$96$$ 0 0
$$97$$ −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i $$-0.849500\pi$$
0.839525 + 0.543321i $$0.182833\pi$$
$$98$$ 0 0
$$99$$ 1.50000 + 5.59808i 0.150756 + 0.562628i
$$100$$ 0 0
$$101$$ −0.133975 0.500000i −0.0133310 0.0497519i 0.958940 0.283609i $$-0.0915318\pi$$
−0.972271 + 0.233857i $$0.924865\pi$$
$$102$$ 0 0
$$103$$ −13.7942 + 7.96410i −1.35919 + 0.784726i −0.989514 0.144436i $$-0.953863\pi$$
−0.369672 + 0.929162i $$0.620530\pi$$
$$104$$ 0 0
$$105$$ −10.5622 10.5622i −1.03076 1.03076i
$$106$$ 0 0
$$107$$ −9.39230 + 9.39230i −0.907988 + 0.907988i −0.996110 0.0881214i $$-0.971914\pi$$
0.0881214 + 0.996110i $$0.471914\pi$$
$$108$$ 0 0
$$109$$ −1.73205 1.73205i −0.165900 0.165900i 0.619274 0.785175i $$-0.287427\pi$$
−0.785175 + 0.619274i $$0.787427\pi$$
$$110$$ 0 0
$$111$$ 7.39230 7.39230i 0.701647 0.701647i
$$112$$ 0 0
$$113$$ −6.23205 10.7942i −0.586262 1.01544i −0.994717 0.102657i $$-0.967266\pi$$
0.408455 0.912779i $$-0.366068\pi$$
$$114$$ 0 0
$$115$$ −12.0622 + 3.23205i −1.12480 + 0.301390i
$$116$$ 0 0
$$117$$ −1.79423 + 6.69615i −0.165876 + 0.619060i
$$118$$ 0 0
$$119$$ −15.4641 8.92820i −1.41759 0.818447i
$$120$$ 0 0
$$121$$ 6.29423 3.63397i 0.572203 0.330361i
$$122$$ 0 0
$$123$$ −1.20577 + 0.696152i −0.108721 + 0.0627700i
$$124$$ 0 0
$$125$$ 8.56218 + 8.56218i 0.765824 + 0.765824i
$$126$$ 0 0
$$127$$ −0.392305 −0.0348114 −0.0174057 0.999849i $$-0.505541\pi$$
−0.0174057 + 0.999849i $$0.505541\pi$$
$$128$$ 0 0
$$129$$ −2.93782 10.9641i −0.258661 0.965335i
$$130$$ 0 0
$$131$$ −1.30385 + 4.86603i −0.113918 + 0.425147i −0.999204 0.0399004i $$-0.987296\pi$$
0.885286 + 0.465047i $$0.153963\pi$$
$$132$$ 0 0
$$133$$ −4.90192 18.2942i −0.425051 1.58631i
$$134$$ 0 0
$$135$$ 9.69615 + 2.59808i 0.834512 + 0.223607i
$$136$$ 0 0
$$137$$ −0.571797 0.330127i −0.0488519 0.0282047i 0.475375 0.879783i $$-0.342312\pi$$
−0.524227 + 0.851579i $$0.675646\pi$$
$$138$$ 0 0
$$139$$ −16.1603 4.33013i −1.37069 0.367277i −0.502962 0.864308i $$-0.667757\pi$$
−0.867732 + 0.497032i $$0.834423\pi$$
$$140$$ 0 0
$$141$$ −1.03590 + 1.79423i −0.0872384 + 0.151101i
$$142$$ 0 0
$$143$$ −4.46410 −0.373307
$$144$$ 0 0
$$145$$ 1.73205 0.143839
$$146$$ 0 0
$$147$$ −11.1962 19.3923i −0.923443 1.59945i
$$148$$ 0 0
$$149$$ 16.0622 + 4.30385i 1.31586 + 0.352585i 0.847427 0.530912i $$-0.178150\pi$$
0.468438 + 0.883497i $$0.344817\pi$$
$$150$$ 0 0
$$151$$ 6.06218 + 3.50000i 0.493333 + 0.284826i 0.725956 0.687741i $$-0.241398\pi$$
−0.232623 + 0.972567i $$0.574731\pi$$
$$152$$ 0 0
$$153$$ 12.0000 0.970143
$$154$$ 0 0
$$155$$ −4.59808 17.1603i −0.369326 1.37834i
$$156$$ 0 0
$$157$$ −0.866025 + 3.23205i −0.0691164 + 0.257946i −0.991835 0.127529i $$-0.959296\pi$$
0.922719 + 0.385474i $$0.125962\pi$$
$$158$$ 0 0
$$159$$ −9.92820 + 9.92820i −0.787358 + 0.787358i
$$160$$ 0 0
$$161$$ −28.8564 −2.27420
$$162$$ 0 0
$$163$$ 1.92820 + 1.92820i 0.151029 + 0.151029i 0.778577 0.627549i $$-0.215942\pi$$
−0.627549 + 0.778577i $$0.715942\pi$$
$$164$$ 0 0
$$165$$ 6.46410i 0.503230i
$$166$$ 0 0
$$167$$ 14.2583 8.23205i 1.10334 0.637015i 0.166246 0.986084i $$-0.446835\pi$$
0.937097 + 0.349069i $$0.113502\pi$$
$$168$$ 0 0
$$169$$ 6.63397 + 3.83013i 0.510306 + 0.294625i
$$170$$ 0 0
$$171$$ 9.00000 + 9.00000i 0.688247 + 0.688247i
$$172$$ 0 0
$$173$$ 7.59808 2.03590i 0.577671 0.154786i 0.0418586 0.999124i $$-0.486672\pi$$
0.535812 + 0.844337i $$0.320005\pi$$
$$174$$ 0 0
$$175$$ 2.83013 + 4.90192i 0.213937 + 0.370551i
$$176$$ 0 0
$$177$$ −2.59808 0.696152i −0.195283 0.0523260i
$$178$$ 0 0
$$179$$ 5.92820 + 5.92820i 0.443095 + 0.443095i 0.893051 0.449956i $$-0.148560\pi$$
−0.449956 + 0.893051i $$0.648560\pi$$
$$180$$ 0 0
$$181$$ −7.73205 + 7.73205i −0.574719 + 0.574719i −0.933443 0.358725i $$-0.883212\pi$$
0.358725 + 0.933443i $$0.383212\pi$$
$$182$$ 0 0
$$183$$ 3.69615 0.990381i 0.273227 0.0732111i
$$184$$ 0 0
$$185$$ 10.0981 5.83013i 0.742425 0.428639i
$$186$$ 0 0
$$187$$ 2.00000 + 7.46410i 0.146254 + 0.545829i
$$188$$ 0 0
$$189$$ 20.0885 + 11.5981i 1.46122 + 0.843636i
$$190$$ 0 0
$$191$$ −1.40192 + 2.42820i −0.101440 + 0.175699i −0.912278 0.409572i $$-0.865678\pi$$
0.810838 + 0.585270i $$0.199012\pi$$
$$192$$ 0 0
$$193$$ 2.23205 + 3.86603i 0.160667 + 0.278283i 0.935108 0.354363i $$-0.115302\pi$$
−0.774441 + 0.632646i $$0.781969\pi$$
$$194$$ 0 0
$$195$$ −3.86603 + 6.69615i −0.276852 + 0.479521i
$$196$$ 0 0
$$197$$ 3.53590 3.53590i 0.251922 0.251922i −0.569836 0.821758i $$-0.692993\pi$$
0.821758 + 0.569836i $$0.192993\pi$$
$$198$$ 0 0
$$199$$ 21.8564i 1.54936i 0.632354 + 0.774680i $$0.282089\pi$$
−0.632354 + 0.774680i $$0.717911\pi$$
$$200$$ 0 0
$$201$$ −3.86603 + 14.4282i −0.272688 + 1.01769i
$$202$$ 0 0
$$203$$ 3.86603 + 1.03590i 0.271342 + 0.0727058i
$$204$$ 0 0
$$205$$ −1.50000 + 0.401924i −0.104765 + 0.0280716i
$$206$$ 0 0
$$207$$ 16.7942 9.69615i 1.16728 0.673929i
$$208$$ 0 0
$$209$$ −4.09808 + 7.09808i −0.283470 + 0.490984i
$$210$$ 0 0
$$211$$ 4.96410 18.5263i 0.341743 1.27540i −0.554629 0.832098i $$-0.687140\pi$$
0.896371 0.443304i $$-0.146194\pi$$
$$212$$ 0 0
$$213$$ 5.07180i 0.347514i
$$214$$ 0 0
$$215$$ 12.6603i 0.863422i
$$216$$ 0 0
$$217$$ 41.0526i 2.78683i
$$218$$ 0 0
$$219$$ 12.9282i 0.873607i
$$220$$ 0 0
$$221$$ −2.39230 + 8.92820i −0.160924 + 0.600576i
$$222$$ 0 0
$$223$$ −7.79423 + 13.5000i −0.521940 + 0.904027i 0.477734 + 0.878504i $$0.341458\pi$$
−0.999674 + 0.0255224i $$0.991875\pi$$
$$224$$ 0 0
$$225$$ −3.29423 1.90192i −0.219615 0.126795i
$$226$$ 0 0
$$227$$ −19.6244 + 5.25833i −1.30251 + 0.349008i −0.842400 0.538852i $$-0.818858\pi$$
−0.460114 + 0.887860i $$0.652191\pi$$
$$228$$ 0 0
$$229$$ 16.5263 + 4.42820i 1.09209 + 0.292624i 0.759539 0.650462i $$-0.225425\pi$$
0.332549 + 0.943086i $$0.392091\pi$$
$$230$$ 0 0
$$231$$ −3.86603 + 14.4282i −0.254366 + 0.949306i
$$232$$ 0 0
$$233$$ 9.07180i 0.594313i 0.954829 + 0.297157i $$0.0960383\pi$$
−0.954829 + 0.297157i $$0.903962\pi$$
$$234$$ 0 0
$$235$$ −1.63397 + 1.63397i −0.106589 + 0.106589i
$$236$$ 0 0
$$237$$ −1.50000 + 2.59808i −0.0974355 + 0.168763i
$$238$$ 0 0
$$239$$ 0.401924 + 0.696152i 0.0259983 + 0.0450304i 0.878732 0.477316i $$-0.158390\pi$$
−0.852734 + 0.522346i $$0.825057\pi$$
$$240$$ 0 0
$$241$$ −2.76795 + 4.79423i −0.178299 + 0.308823i −0.941298 0.337576i $$-0.890393\pi$$
0.762999 + 0.646400i $$0.223726\pi$$
$$242$$ 0 0
$$243$$ −15.5885 −1.00000
$$244$$ 0 0
$$245$$ −6.46410 24.1244i −0.412976 1.54125i
$$246$$ 0 0
$$247$$ −8.49038 + 4.90192i −0.540230 + 0.311902i
$$248$$ 0 0
$$249$$ −24.5263 + 6.57180i −1.55429 + 0.416471i
$$250$$ 0 0
$$251$$ 13.3923 13.3923i 0.845315 0.845315i −0.144229 0.989544i $$-0.546070\pi$$
0.989544 + 0.144229i $$0.0460703\pi$$
$$252$$ 0 0
$$253$$ 8.83013 + 8.83013i 0.555145 + 0.555145i
$$254$$ 0 0
$$255$$ 12.9282 + 3.46410i 0.809595 + 0.216930i
$$256$$ 0 0
$$257$$ 12.1603 + 21.0622i 0.758536 + 1.31382i 0.943597 + 0.331096i $$0.107418\pi$$
−0.185061 + 0.982727i $$0.559248\pi$$
$$258$$ 0 0
$$259$$ 26.0263 6.97372i 1.61719 0.433326i
$$260$$ 0 0
$$261$$ −2.59808 + 0.696152i −0.160817 + 0.0430908i
$$262$$ 0 0
$$263$$ 8.59808 + 4.96410i 0.530180 + 0.306100i 0.741090 0.671406i $$-0.234309\pi$$
−0.210910 + 0.977506i $$0.567643\pi$$
$$264$$ 0 0
$$265$$ −13.5622 + 7.83013i −0.833118 + 0.481001i
$$266$$ 0 0
$$267$$ 27.4641i 1.68078i
$$268$$ 0 0
$$269$$ 4.26795 + 4.26795i 0.260221 + 0.260221i 0.825144 0.564923i $$-0.191094\pi$$
−0.564923 + 0.825144i $$0.691094\pi$$
$$270$$ 0 0
$$271$$ 1.07180 0.0651070 0.0325535 0.999470i $$-0.489636\pi$$
0.0325535 + 0.999470i $$0.489636\pi$$
$$272$$ 0 0
$$273$$ −12.6340 + 12.6340i −0.764643 + 0.764643i
$$274$$ 0 0
$$275$$ 0.633975 2.36603i 0.0382301 0.142677i
$$276$$ 0 0
$$277$$ −1.79423 6.69615i −0.107805 0.402333i 0.890844 0.454310i $$-0.150114\pi$$
−0.998648 + 0.0519775i $$0.983448\pi$$
$$278$$ 0 0
$$279$$ 13.7942 + 23.8923i 0.825839 + 1.43039i
$$280$$ 0 0
$$281$$ −10.0359 5.79423i −0.598692 0.345655i 0.169835 0.985472i $$-0.445676\pi$$
−0.768527 + 0.639818i $$0.779010\pi$$
$$282$$ 0 0
$$283$$ 13.1603 + 3.52628i 0.782296 + 0.209616i 0.627797 0.778377i $$-0.283957\pi$$
0.154499 + 0.987993i $$0.450624\pi$$
$$284$$ 0 0
$$285$$ 7.09808 + 12.2942i 0.420454 + 0.728247i
$$286$$ 0 0
$$287$$ −3.58846 −0.211820
$$288$$ 0 0
$$289$$ −1.00000 −0.0588235
$$290$$ 0 0
$$291$$ 0.866025 1.50000i 0.0507673 0.0879316i
$$292$$ 0 0
$$293$$ 2.13397 + 0.571797i 0.124668 + 0.0334047i 0.320614 0.947210i $$-0.396111\pi$$
−0.195945 + 0.980615i $$0.562778\pi$$
$$294$$ 0 0
$$295$$ −2.59808 1.50000i −0.151266 0.0873334i
$$296$$ 0 0
$$297$$ −2.59808 9.69615i −0.150756 0.562628i
$$298$$ 0 0
$$299$$ 3.86603 + 14.4282i 0.223578 + 0.834405i
$$300$$ 0 0
$$301$$ 7.57180 28.2583i 0.436431 1.62878i
$$302$$ 0 0
$$303$$ 0.232051 + 0.866025i 0.0133310 + 0.0497519i
$$304$$ 0 0
$$305$$ 4.26795 0.244382
$$306$$ 0 0
$$307$$ −7.92820 7.92820i −0.452486 0.452486i 0.443693 0.896179i $$-0.353668\pi$$
−0.896179 + 0.443693i $$0.853668\pi$$
$$308$$ 0 0
$$309$$ 23.8923 13.7942i 1.35919 0.784726i
$$310$$ 0 0
$$311$$ −9.18653 + 5.30385i −0.520921 + 0.300754i −0.737311 0.675553i $$-0.763905\pi$$
0.216391 + 0.976307i $$0.430572\pi$$
$$312$$ 0 0
$$313$$ 25.1603 + 14.5263i 1.42214 + 0.821074i 0.996482 0.0838094i $$-0.0267087\pi$$
0.425660 + 0.904883i $$0.360042\pi$$
$$314$$ 0 0
$$315$$ 18.2942 + 18.2942i 1.03076 + 1.03076i
$$316$$ 0 0
$$317$$ −33.4545 + 8.96410i −1.87899 + 0.503474i −0.879364 + 0.476150i $$0.842032\pi$$
−0.999627 + 0.0273246i $$0.991301\pi$$
$$318$$ 0 0
$$319$$ −0.866025 1.50000i −0.0484881 0.0839839i
$$320$$ 0 0
$$321$$ 16.2679 16.2679i 0.907988 0.907988i
$$322$$ 0 0
$$323$$ 12.0000 + 12.0000i 0.667698 + 0.667698i
$$324$$ 0 0
$$325$$ 2.07180 2.07180i 0.114923 0.114923i
$$326$$ 0 0
$$327$$ 3.00000 + 3.00000i 0.165900 + 0.165900i
$$328$$ 0 0
$$329$$ −4.62436 + 2.66987i −0.254949 + 0.147195i
$$330$$ 0 0
$$331$$ −1.35641 5.06218i −0.0745548 0.278242i 0.918577 0.395242i $$-0.129339\pi$$
−0.993132 + 0.116999i $$0.962672\pi$$
$$332$$ 0 0
$$333$$ −12.8038 + 12.8038i −0.701647 + 0.701647i
$$334$$ 0 0
$$335$$ −8.33013 + 14.4282i −0.455123 + 0.788297i
$$336$$ 0 0
$$337$$ −9.69615 16.7942i −0.528183 0.914840i −0.999460 0.0328547i $$-0.989540\pi$$
0.471277 0.881985i $$-0.343793\pi$$
$$338$$ 0 0
$$339$$ 10.7942 + 18.6962i 0.586262 + 1.01544i
$$340$$ 0 0
$$341$$ −12.5622 + 12.5622i −0.680280 + 0.680280i
$$342$$ 0 0
$$343$$ 26.4641i 1.42893i
$$344$$ 0 0
$$345$$ 20.8923 5.59808i 1.12480 0.301390i
$$346$$ 0 0
$$347$$ 1.76795 + 0.473721i 0.0949085 + 0.0254307i 0.305961 0.952044i $$-0.401022\pi$$
−0.211052 + 0.977475i $$0.567689\pi$$
$$348$$ 0 0
$$349$$ −3.86603 + 1.03590i −0.206944 + 0.0554504i −0.360802 0.932643i $$-0.617497\pi$$
0.153858 + 0.988093i $$0.450830\pi$$
$$350$$ 0 0
$$351$$ 3.10770 11.5981i 0.165876 0.619060i
$$352$$ 0 0
$$353$$ −11.7679 + 20.3827i −0.626345 + 1.08486i 0.361934 + 0.932204i $$0.382116\pi$$
−0.988279 + 0.152657i $$0.951217\pi$$
$$354$$ 0 0
$$355$$ 1.46410 5.46410i 0.0777064 0.290004i
$$356$$ 0 0
$$357$$ 26.7846 + 15.4641i 1.41759 + 0.818447i
$$358$$ 0 0
$$359$$ 28.9282i 1.52677i 0.645942 + 0.763386i $$0.276465\pi$$
−0.645942 + 0.763386i $$0.723535\pi$$
$$360$$ 0 0
$$361$$ 1.00000i 0.0526316i
$$362$$ 0 0
$$363$$ −10.9019 + 6.29423i −0.572203 + 0.330361i
$$364$$ 0 0
$$365$$ 3.73205 13.9282i 0.195344 0.729035i
$$366$$ 0 0
$$367$$ 17.4545 30.2321i 0.911117 1.57810i 0.0986270 0.995124i $$-0.468555\pi$$
0.812490 0.582976i $$-0.198112\pi$$
$$368$$ 0 0
$$369$$ 2.08846 1.20577i 0.108721 0.0627700i
$$370$$ 0 0
$$371$$ −34.9545 + 9.36603i −1.81475 + 0.486260i
$$372$$ 0 0
$$373$$ −1.59808 0.428203i −0.0827452 0.0221715i 0.217209 0.976125i $$-0.430305\pi$$
−0.299954 + 0.953954i $$0.596971\pi$$
$$374$$ 0 0
$$375$$ −14.8301 14.8301i −0.765824 0.765824i
$$376$$ 0 0
$$377$$ 2.07180i 0.106703i
$$378$$ 0 0
$$379$$ 15.5885 15.5885i 0.800725 0.800725i −0.182484 0.983209i $$-0.558414\pi$$
0.983209 + 0.182484i $$0.0584137\pi$$
$$380$$ 0 0
$$381$$ 0.679492 0.0348114
$$382$$ 0 0
$$383$$ −3.66987 6.35641i −0.187522 0.324797i 0.756902 0.653529i $$-0.226712\pi$$
−0.944423 + 0.328732i $$0.893379\pi$$
$$384$$ 0 0
$$385$$ −8.33013 + 14.4282i −0.424543 + 0.735329i
$$386$$ 0 0
$$387$$ 5.08846 + 18.9904i 0.258661 + 0.965335i
$$388$$ 0 0
$$389$$ 2.40192 + 8.96410i 0.121782 + 0.454498i 0.999705 0.0243053i $$-0.00773738\pi$$
−0.877922 + 0.478803i $$0.841071\pi$$
$$390$$ 0 0
$$391$$ 22.3923 12.9282i 1.13243 0.653807i
$$392$$ 0 0
$$393$$ 2.25833 8.42820i 0.113918 0.425147i
$$394$$ 0 0
$$395$$ −2.36603 + 2.36603i −0.119048 + 0.119048i
$$396$$ 0 0
$$397$$ 17.0526 + 17.0526i 0.855843 + 0.855843i 0.990845 0.135002i $$-0.0431041\pi$$
−0.135002 + 0.990845i $$0.543104\pi$$
$$398$$ 0 0
$$399$$ 8.49038 + 31.6865i 0.425051 + 1.58631i
$$400$$ 0 0
$$401$$ −16.1603 27.9904i −0.807005 1.39777i −0.914929 0.403614i $$-0.867754\pi$$
0.107925 0.994159i $$-0.465579\pi$$
$$402$$ 0 0
$$403$$ −20.5263 + 5.50000i −1.02249 + 0.273975i
$$404$$ 0 0
$$405$$ −16.7942 4.50000i −0.834512 0.223607i
$$406$$ 0 0
$$407$$ −10.0981 5.83013i −0.500543 0.288989i
$$408$$ 0 0
$$409$$ −19.6244 + 11.3301i −0.970362 + 0.560239i −0.899347 0.437236i $$-0.855957\pi$$
−0.0710154 + 0.997475i $$0.522624\pi$$
$$410$$ 0 0
$$411$$ 0.990381 + 0.571797i 0.0488519 + 0.0282047i
$$412$$ 0 0
$$413$$ −4.90192 4.90192i −0.241208 0.241208i
$$414$$ 0 0
$$415$$ −28.3205 −1.39020
$$416$$ 0 0
$$417$$ 27.9904 + 7.50000i 1.37069 + 0.367277i
$$418$$ 0 0
$$419$$ 4.96410 18.5263i 0.242512 0.905068i −0.732105 0.681191i $$-0.761462\pi$$
0.974618 0.223876i $$-0.0718712\pi$$
$$420$$ 0 0
$$421$$ −4.79423 17.8923i −0.233656 0.872018i −0.978750 0.205058i $$-0.934262\pi$$
0.745094 0.666960i $$-0.232405\pi$$
$$422$$ 0 0
$$423$$ 1.79423 3.10770i 0.0872384 0.151101i
$$424$$ 0 0
$$425$$ −4.39230 2.53590i −0.213058 0.123009i
$$426$$ 0 0
$$427$$ 9.52628 + 2.55256i 0.461009 + 0.123527i
$$428$$ 0 0
$$429$$ 7.73205 0.373307
$$430$$ 0 0
$$431$$ 3.32051 0.159943 0.0799716 0.996797i $$-0.474517\pi$$
0.0799716 + 0.996797i $$0.474517\pi$$
$$432$$ 0 0
$$433$$ 3.60770 0.173375 0.0866874 0.996236i $$-0.472372\pi$$
0.0866874 + 0.996236i $$0.472372\pi$$
$$434$$ 0 0
$$435$$ −3.00000 −0.143839
$$436$$ 0 0
$$437$$ 26.4904 + 7.09808i 1.26721 + 0.339547i
$$438$$ 0 0
$$439$$ −5.93782 3.42820i −0.283397 0.163619i 0.351563 0.936164i $$-0.385650\pi$$
−0.634960 + 0.772545i $$0.718984\pi$$
$$440$$ 0 0
$$441$$ 19.3923 + 33.5885i 0.923443 + 1.59945i
$$442$$ 0 0
$$443$$ 1.16025 + 4.33013i 0.0551253 + 0.205731i 0.987996 0.154482i $$-0.0493708\pi$$
−0.932870 + 0.360213i $$0.882704\pi$$
$$444$$ 0 0
$$445$$ 7.92820 29.5885i 0.375833 1.40263i
$$446$$ 0 0
$$447$$ −27.8205 7.45448i −1.31586 0.352585i
$$448$$ 0 0
$$449$$ 35.3205 1.66688 0.833439 0.552612i $$-0.186369\pi$$
0.833439 + 0.552612i $$0.186369\pi$$
$$450$$ 0 0
$$451$$ 1.09808 + 1.09808i 0.0517064 + 0.0517064i
$$452$$ 0 0
$$453$$ −10.5000 6.06218i −0.493333 0.284826i
$$454$$ 0 0
$$455$$ −17.2583 + 9.96410i −0.809083 + 0.467124i
$$456$$ 0 0
$$457$$ 25.9641 + 14.9904i 1.21455 + 0.701220i 0.963747 0.266818i $$-0.0859722\pi$$
0.250802 + 0.968038i $$0.419306\pi$$
$$458$$ 0 0
$$459$$ −20.7846 −0.970143
$$460$$ 0 0
$$461$$ 4.59808 1.23205i 0.214154 0.0573823i −0.150147 0.988664i $$-0.547975\pi$$
0.364301 + 0.931281i $$0.381308\pi$$
$$462$$ 0 0
$$463$$ 5.33013 + 9.23205i 0.247712 + 0.429050i 0.962891 0.269892i $$-0.0869880\pi$$
−0.715179 + 0.698942i $$0.753655\pi$$
$$464$$ 0 0
$$465$$ 7.96410 + 29.7224i 0.369326 + 1.37834i
$$466$$ 0 0
$$467$$ −21.7846 21.7846i −1.00807 1.00807i −0.999967 0.00810436i $$-0.997420\pi$$
−0.00810436 0.999967i $$-0.502580\pi$$
$$468$$ 0 0
$$469$$ −27.2224 + 27.2224i −1.25702 + 1.25702i
$$470$$ 0 0
$$471$$ 1.50000 5.59808i 0.0691164 0.257946i
$$472$$ 0 0
$$473$$ −10.9641 + 6.33013i −0.504130 + 0.291060i
$$474$$ 0 0
$$475$$ −1.39230 5.19615i −0.0638833 0.238416i
$$476$$ 0 0
$$477$$ 17.1962 17.1962i 0.787358 0.787358i
$$478$$ 0 0
$$479$$ −9.33013 + 16.1603i −0.426304 + 0.738381i −0.996541 0.0830995i $$-0.973518\pi$$
0.570237 + 0.821480i $$0.306851\pi$$
$$480$$ 0 0
$$481$$ −6.97372 12.0788i −0.317974 0.550748i
$$482$$ 0 0
$$483$$ 49.9808 2.27420
$$484$$ 0 0
$$485$$ 1.36603 1.36603i 0.0620280 0.0620280i
$$486$$ 0 0
$$487$$ 6.78461i 0.307440i 0.988114 + 0.153720i $$0.0491254\pi$$
−0.988114 + 0.153720i $$0.950875\pi$$
$$488$$ 0 0
$$489$$ −3.33975 3.33975i −0.151029 0.151029i
$$490$$ 0 0
$$491$$ −0.500000 0.133975i −0.0225647 0.00604619i 0.247519 0.968883i $$-0.420385\pi$$
−0.270084 + 0.962837i $$0.587051\pi$$
$$492$$ 0 0
$$493$$ −3.46410 + 0.928203i −0.156015 + 0.0418042i
$$494$$ 0 0
$$495$$ 11.1962i 0.503230i
$$496$$ 0 0
$$497$$ 6.53590 11.3205i 0.293175 0.507794i
$$498$$ 0 0
$$499$$ 2.50000 9.33013i 0.111915 0.417674i −0.887122 0.461534i $$-0.847299\pi$$
0.999038 + 0.0438606i $$0.0139657\pi$$
$$500$$ 0 0
$$501$$ −24.6962 + 14.2583i −1.10334 + 0.637015i
$$502$$ 0 0
$$503$$ 13.8564i 0.617827i −0.951090 0.308913i $$-0.900035\pi$$
0.951090 0.308913i $$-0.0999653\pi$$
$$504$$ 0 0
$$505$$ 1.00000i 0.0444994i
$$506$$ 0 0
$$507$$ −11.4904 6.63397i −0.510306 0.294625i
$$508$$ 0 0
$$509$$ 1.25833 4.69615i 0.0557745 0.208153i −0.932415 0.361389i $$-0.882303\pi$$
0.988190 + 0.153236i $$0.0489693\pi$$
$$510$$ 0 0
$$511$$ 16.6603 28.8564i 0.737006 1.27653i
$$512$$ 0 0
$$513$$ −15.5885 15.5885i −0.688247 0.688247i
$$514$$ 0 0
$$515$$ 29.7224 7.96410i 1.30973 0.350940i
$$516$$ 0 0
$$517$$ 2.23205 + 0.598076i 0.0981655 + 0.0263034i
$$518$$ 0 0
$$519$$ −13.1603 + 3.52628i −0.577671 + 0.154786i
$$520$$ 0 0
$$521$$ 41.8564i 1.83376i −0.399160 0.916881i $$-0.630698\pi$$
0.399160 0.916881i $$-0.369302\pi$$
$$522$$ 0 0
$$523$$ −22.1244 + 22.1244i −0.967431 + 0.967431i −0.999486 0.0320556i $$-0.989795\pi$$
0.0320556 + 0.999486i $$0.489795\pi$$
$$524$$ 0 0
$$525$$ −4.90192 8.49038i −0.213937 0.370551i
$$526$$ 0 0
$$527$$ 18.3923 + 31.8564i 0.801181 + 1.38769i
$$528$$ 0 0
$$529$$ 9.39230 16.2679i 0.408361 0.707302i
$$530$$ 0 0
$$531$$ 4.50000 + 1.20577i 0.195283 + 0.0523260i
$$532$$ 0 0
$$533$$ 0.480762 + 1.79423i 0.0208241 + 0.0777167i
$$534$$ 0 0
$$535$$ 22.2224 12.8301i 0.960760 0.554695i
$$536$$ 0 0
$$537$$ −10.2679 10.2679i −0.443095 0.443095i
$$538$$ 0 0
$$539$$ −17.6603 + 17.6603i −0.760681 + 0.760681i
$$540$$ 0 0
$$541$$ −15.0000 15.0000i −0.644900 0.644900i 0.306856 0.951756i $$-0.400723\pi$$
−0.951756 + 0.306856i $$0.900723\pi$$
$$542$$ 0 0
$$543$$ 13.3923 13.3923i 0.574719 0.574719i
$$544$$ 0 0
$$545$$ 2.36603 + 4.09808i 0.101349 + 0.175542i
$$546$$ 0 0
$$547$$ −21.4282 + 5.74167i −0.916204 + 0.245496i −0.685962 0.727637i $$-0.740618\pi$$
−0.230242 + 0.973133i $$0.573952\pi$$
$$548$$ 0 0
$$549$$ −6.40192 + 1.71539i −0.273227 + 0.0732111i
$$550$$ 0 0
$$551$$ −3.29423 1.90192i −0.140339 0.0810247i
$$552$$ 0 0
$$553$$ −6.69615 + 3.86603i −0.284749 + 0.164400i
$$554$$ 0 0
$$555$$ −17.4904 + 10.0981i −0.742425 + 0.428639i
$$556$$ 0 0
$$557$$ −23.9808 23.9808i −1.01610 1.01610i −0.999868 0.0162292i $$-0.994834\pi$$
−0.0162292 0.999868i $$-0.505166\pi$$
$$558$$ 0 0
$$559$$ −15.1436 −0.640506
$$560$$ 0 0
$$561$$ −3.46410 12.9282i −0.146254 0.545829i
$$562$$ 0 0
$$563$$ 1.64359 6.13397i 0.0692692 0.258516i −0.922604 0.385749i $$-0.873943\pi$$
0.991873 + 0.127233i $$0.0406096\pi$$
$$564$$ 0 0
$$565$$ 6.23205 + 23.2583i 0.262184 + 0.978485i
$$566$$ 0 0
$$567$$ −34.7942 20.0885i −1.46122 0.843636i
$$568$$ 0 0
$$569$$ −27.4808 15.8660i −1.15205 0.665138i −0.202667 0.979248i $$-0.564961\pi$$
−0.949387 + 0.314109i $$0.898294\pi$$
$$570$$ 0 0
$$571$$ −39.5526 10.5981i −1.65522 0.443516i −0.694155 0.719826i $$-0.744222\pi$$
−0.961068 + 0.276310i $$0.910888\pi$$
$$572$$ 0 0
$$573$$ 2.42820 4.20577i 0.101440 0.175699i
$$574$$ 0 0
$$575$$ −8.19615 −0.341803
$$576$$ 0 0
$$577$$ −25.1769 −1.04813 −0.524064 0.851679i $$-0.675585\pi$$
−0.524064 + 0.851679i $$0.675585\pi$$
$$578$$ 0 0
$$579$$ −3.86603 6.69615i −0.160667 0.278283i
$$580$$ 0 0
$$581$$ −63.2128 16.9378i −2.62251 0.702699i
$$582$$ 0 0
$$583$$ 13.5622 + 7.83013i 0.561688 + 0.324291i
$$584$$ 0 0
$$585$$ 6.69615 11.5981i 0.276852 0.479521i
$$586$$ 0 0
$$587$$ −3.96410 14.7942i −0.163616 0.610623i −0.998213 0.0597617i $$-0.980966\pi$$
0.834597 0.550861i $$-0.185701\pi$$
$$588$$ 0 0
$$589$$ −10.0981 + 37.6865i −0.416084 + 1.55285i
$$590$$ 0 0
$$591$$ −6.12436 + 6.12436i −0.251922 + 0.251922i
$$592$$ 0 0
$$593$$ −5.46410 −0.224384 −0.112192 0.993687i $$-0.535787\pi$$
−0.112192 + 0.993687i $$0.535787\pi$$
$$594$$ 0 0
$$595$$ 24.3923 + 24.3923i 0.999987 + 0.999987i
$$596$$ 0 0
$$597$$ 37.8564i 1.54936i
$$598$$ 0 0
$$599$$ 30.3109 17.5000i 1.23847 0.715031i 0.269688 0.962948i $$-0.413079\pi$$
0.968781 + 0.247917i $$0.0797461\pi$$
$$600$$ 0 0
$$601$$ −26.7679 15.4545i −1.09189 0.630401i −0.157809 0.987470i $$-0.550443\pi$$
−0.934078 + 0.357068i $$0.883776\pi$$
$$602$$ 0 0
$$603$$ 6.69615 24.9904i 0.272688 1.01769i
$$604$$ 0 0
$$605$$ −13.5622 + 3.63397i −0.551381 + 0.147742i
$$606$$ 0 0
$$607$$ −0.598076 1.03590i −0.0242752 0.0420458i 0.853633 0.520876i $$-0.174394\pi$$
−0.877908 + 0.478830i $$0.841061\pi$$
$$608$$ 0 0
$$609$$ −6.69615 1.79423i −0.271342 0.0727058i
$$610$$ 0 0
$$611$$ 1.95448 + 1.95448i 0.0790699 + 0.0790699i
$$612$$ 0 0
$$613$$ 23.5885 23.5885i 0.952729 0.952729i −0.0462032 0.998932i $$-0.514712\pi$$
0.998932 + 0.0462032i $$0.0147122\pi$$
$$614$$ 0 0
$$615$$ 2.59808 0.696152i 0.104765 0.0280716i
$$616$$ 0 0
$$617$$ 23.0885 13.3301i 0.929506 0.536651i 0.0428509 0.999081i $$-0.486356\pi$$
0.886655 + 0.462431i $$0.153023\pi$$
$$618$$ 0 0
$$619$$ 1.91154 + 7.13397i 0.0768314 + 0.286739i 0.993642 0.112583i $$-0.0359124\pi$$
−0.916811 + 0.399322i $$0.869246\pi$$
$$620$$ 0 0
$$621$$ −29.0885 + 16.7942i −1.16728 + 0.673929i
$$622$$ 0 0
$$623$$ 35.3923 61.3013i 1.41796 2.45598i
$$624$$ 0 0
$$625$$ −8.52628 14.7679i −0.341051 0.590718i
$$626$$ 0 0
$$627$$ 7.09808 12.2942i 0.283470 0.490984i
$$628$$ 0 0
$$629$$ −17.0718 + 17.0718i −0.680697 + 0.680697i
$$630$$ 0 0
$$631$$ 16.2487i 0.646851i −0.946254 0.323425i $$-0.895165\pi$$
0.946254 0.323425i $$-0.104835\pi$$
$$632$$ 0 0
$$633$$ −8.59808 + 32.0885i −0.341743 + 1.27540i
$$634$$ 0 0
$$635$$ 0.732051 + 0.196152i 0.0290506 + 0.00778407i
$$636$$ 0 0
$$637$$ −28.8564 + 7.73205i −1.14333 + 0.306355i
$$638$$ 0 0
$$639$$ 8.78461i 0.347514i
$$640$$ 0 0
$$641$$ 9.23205 15.9904i 0.364644 0.631582i −0.624075 0.781365i $$-0.714524\pi$$
0.988719 + 0.149782i $$0.0478573\pi$$
$$642$$ 0 0
$$643$$ −7.96410 + 29.7224i −0.314074 + 1.17214i 0.610776 + 0.791804i $$0.290858\pi$$
−0.924849 + 0.380334i $$0.875809\pi$$
$$644$$ 0 0
$$645$$ 21.9282i 0.863422i
$$646$$ 0 0
$$647$$ 25.6077i 1.00674i −0.864070 0.503371i $$-0.832093\pi$$
0.864070 0.503371i $$-0.167907\pi$$
$$648$$ 0 0
$$649$$ 3.00000i 0.117760i
$$650$$ 0 0
$$651$$ 71.1051i 2.78683i
$$652$$ 0 0
$$653$$ −12.6699 + 47.2846i −0.495810 + 1.85039i 0.0296324 + 0.999561i $$0.490566\pi$$
−0.525443 + 0.850829i $$0.676100\pi$$
$$654$$ 0 0
$$655$$ 4.86603 8.42820i 0.190131 0.329317i
$$656$$ 0 0
$$657$$ 22.3923i 0.873607i
$$658$$ 0 0
$$659$$ −1.23205 + 0.330127i −0.0479939 + 0.0128599i −0.282736 0.959198i $$-0.591242\pi$$
0.234742 + 0.972058i $$0.424575\pi$$
$$660$$ 0 0
$$661$$ 19.7942 + 5.30385i 0.769906 + 0.206296i 0.622330 0.782755i $$-0.286186\pi$$
0.147576 + 0.989051i $$0.452853\pi$$
$$662$$ 0 0
$$663$$ 4.14359 15.4641i 0.160924 0.600576i
$$664$$ 0 0
$$665$$ 36.5885i 1.41884i
$$666$$ 0 0
$$667$$ −4.09808 + 4.09808i −0.158678 + 0.158678i
$$668$$ 0 0
$$669$$ 13.5000 23.3827i 0.521940 0.904027i
$$670$$ 0 0
$$671$$ −2.13397 3.69615i −0.0823812 0.142688i
$$672$$ 0 0
$$673$$ 21.1603 36.6506i 0.815668 1.41278i −0.0931795 0.995649i $$-0.529703\pi$$
0.908847 0.417129i $$-0.136964\pi$$
$$674$$ 0 0
$$675$$ 5.70577 + 3.29423i 0.219615 + 0.126795i
$$676$$ 0 0
$$677$$ 2.34936 + 8.76795i 0.0902934 + 0.336980i 0.996264 0.0863612i $$-0.0275239\pi$$
−0.905970 + 0.423341i $$0.860857\pi$$
$$678$$ 0 0
$$679$$ 3.86603 2.23205i 0.148364 0.0856582i
$$680$$ 0 0
$$681$$ 33.9904 9.10770i 1.30251 0.349008i
$$682$$ 0 0
$$683$$ −15.3923 + 15.3923i −0.588970 + 0.588970i −0.937353 0.348382i $$-0.886731\pi$$
0.348382 + 0.937353i $$0.386731\pi$$
$$684$$ 0 0
$$685$$ 0.901924 + 0.901924i 0.0344607 + 0.0344607i
$$686$$ 0 0
$$687$$ −28.6244 7.66987i −1.09209 0.292624i
$$688$$ 0 0
$$689$$ 9.36603 + 16.2224i 0.356817 + 0.618025i
$$690$$ 0 0
$$691$$ 1.96410 0.526279i 0.0747179 0.0200206i −0.221266 0.975213i $$-0.571019\pi$$
0.295984 + 0.955193i $$0.404352\pi$$
$$692$$ 0 0
$$693$$ 6.69615 24.9904i 0.254366 0.949306i
$$694$$ 0 0
$$695$$ 27.9904 + 16.1603i 1.06174 + 0.612993i
$$696$$ 0 0
$$697$$ 2.78461 1.60770i 0.105475 0.0608958i
$$698$$ 0 0
$$699$$ 15.7128i 0.594313i
$$700$$ 0 0
$$701$$ 17.0526 + 17.0526i 0.644066 + 0.644066i 0.951553 0.307486i $$-0.0994878\pi$$
−0.307486 + 0.951553i $$0.599488\pi$$
$$702$$ 0 0
$$703$$ −25.6077 −0.965813
$$704$$ 0 0
$$705$$ 2.83013 2.83013i 0.106589 0.106589i
$$706$$ 0 0
$$707$$ −0.598076 + 2.23205i −0.0224930 + 0.0839449i
$$708$$ 0 0
$$709$$ 10.1147 + 37.7487i 0.379867 + 1.41768i 0.846102 + 0.533022i $$0.178944\pi$$
−0.466235 + 0.884661i $$0.654390\pi$$
$$710$$ 0 0
$$711$$ 2.59808 4.50000i 0.0974355 0.168763i
$$712$$ 0 0
$$713$$ 51.4808 + 29.7224i 1.92797 + 1.11311i
$$714$$ 0 0
$$715$$ 8.33013 + 2.23205i 0.311529 + 0.0834740i
$$716$$ 0 0
$$717$$ −0.696152 1.20577i −0.0259983 0.0450304i
$$718$$ 0 0
$$719$$ 11.3205 0.422184 0.211092 0.977466i $$-0.432298\pi$$
0.211092 + 0.977466i $$0.432298\pi$$
$$720$$ 0 0
$$721$$ 71.1051 2.64809
$$722$$ 0 0
$$723$$ 4.79423 8.30385i 0.178299 0.308823i
$$724$$ 0 0
$$725$$ 1.09808 + 0.294229i 0.0407815 + 0.0109274i
$$726$$ 0 0
$$727$$ −3.06218 1.76795i −0.113570 0.0655696i 0.442139 0.896947i $$-0.354220\pi$$
−0.555709 + 0.831377i $$0.687553\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ 6.78461 + 25.3205i 0.250938 + 0.936513i
$$732$$ 0 0
$$733$$ 8.47372 31.6244i 0.312984 1.16807i −0.612868 0.790185i $$-0.709984\pi$$
0.925852 0.377887i $$-0.123349\pi$$
$$734$$ 0 0
$$735$$ 11.1962 + 41.7846i 0.412976 + 1.54125i
$$736$$ 0 0
$$737$$ 16.6603 0.613688
$$738$$ 0 0
$$739$$ 26.2679 + 26.2679i 0.966282 + 0.966282i 0.999450 0.0331677i $$-0.0105595\pi$$
−0.0331677 + 0.999450i $$0.510560\pi$$
$$740$$ 0 0
$$741$$ 14.7058 8.49038i 0.540230 0.311902i
$$742$$ 0 0
$$743$$ −25.1147 + 14.5000i −0.921370 + 0.531953i −0.884072 0.467351i $$-0.845209\pi$$
−0.0372984 + 0.999304i $$0.511875\pi$$
$$744$$ 0 0
$$745$$ −27.8205 16.0622i −1.01926 0.588473i
$$746$$ 0 0
$$747$$ 42.4808 11.3827i 1.55429 0.416471i
$$748$$ 0 0
$$749$$ 57.2750 15.3468i 2.09278 0.560759i
$$750$$ 0 0
$$751$$ 24.7224 + 42.8205i 0.902134 + 1.56254i 0.824718 + 0.565544i $$0.191334\pi$$
0.0774160 + 0.996999i $$0.475333\pi$$
$$752$$ 0 0
$$753$$ −23.1962 + 23.1962i −0.845315 + 0.845315i
$$754$$ 0 0
$$755$$ −9.56218 9.56218i −0.348003 0.348003i
$$756$$ 0 0
$$757$$ 1.53590 1.53590i 0.0558232 0.0558232i −0.678644 0.734467i $$-0.737432\pi$$
0.734467 + 0.678644i $$0.237432\pi$$
$$758$$ 0 0
$$759$$ −15.2942 15.2942i −0.555145 0.555145i
$$760$$ 0 0
$$761$$ −16.2846 + 9.40192i −0.590317 + 0.340819i −0.765223 0.643766i $$-0.777371\pi$$
0.174906 + 0.984585i $$0.444038\pi$$
$$762$$ 0 0
$$763$$ 2.83013 + 10.5622i 0.102457 + 0.382377i
$$764$$ 0 0
$$765$$ −22.3923 6.00000i −0.809595 0.216930i
$$766$$ 0 0
$$767$$ −1.79423 + 3.10770i −0.0647858 + 0.112212i
$$768$$ 0 0
$$769$$ −3.50000 6.06218i −0.126213 0.218608i 0.795993 0.605305i $$-0.206949\pi$$
−0.922207 + 0.386698i $$0.873616\pi$$
$$770$$ 0 0
$$771$$ −21.0622 36.4808i −0.758536 1.31382i
$$772$$ 0 0
$$773$$ −23.5885 + 23.5885i −0.848418 + 0.848418i −0.989936 0.141518i $$-0.954802\pi$$
0.141518 + 0.989936i $$0.454802\pi$$
$$774$$ 0 0
$$775$$ 11.6603i 0.418849i
$$776$$ 0 0
$$777$$ −45.0788 + 12.0788i −1.61719 + 0.433326i
$$778$$ 0 0
$$779$$ 3.29423 + 0.882686i 0.118028 + 0.0316255i
$$780$$ 0 0
$$781$$ −5.46410 + 1.46410i −0.195521 + 0.0523897i
$$782$$ 0 0
$$783$$ 4.50000 1.20577i 0.160817 0.0430908i
$$784$$ 0 0
$$785$$ 3.23205 5.59808i 0.115357 0.199804i
$$786$$ 0 0
$$787$$ −0.820508 + 3.06218i −0.0292480 + 0.109155i −0.979007 0.203828i $$-0.934662\pi$$
0.949759 + 0.312983i $$0.101328\pi$$
$$788$$ 0 0
$$789$$ −14.8923 8.59808i −0.530180 0.306100i
$$790$$ 0 0
$$791$$ 55.6410i 1.97837i
$$792$$ 0 0
$$793$$