# Properties

 Label 570.2.c.b.569.3 Level $570$ Weight $2$ Character 570.569 Analytic conductor $4.551$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 569.3 Root $$-0.707107 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.569 Dual form 570.2.c.b.569.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000 q^{4} +(-2.12132 - 0.707107i) q^{5} +(-1.00000 - 1.41421i) q^{6} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$$ $$q+1.00000i q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000 q^{4} +(-2.12132 - 0.707107i) q^{5} +(-1.00000 - 1.41421i) q^{6} -1.00000i q^{8} +(1.00000 - 2.82843i) q^{9} +(0.707107 - 2.12132i) q^{10} -2.82843i q^{11} +(1.41421 - 1.00000i) q^{12} +4.24264 q^{13} +(3.70711 - 1.12132i) q^{15} +1.00000 q^{16} +(2.82843 + 1.00000i) q^{18} +(1.00000 + 4.24264i) q^{19} +(2.12132 + 0.707107i) q^{20} +2.82843 q^{22} -4.24264 q^{23} +(1.00000 + 1.41421i) q^{24} +(4.00000 + 3.00000i) q^{25} +4.24264i q^{26} +(1.41421 + 5.00000i) q^{27} +6.00000 q^{29} +(1.12132 + 3.70711i) q^{30} -4.24264i q^{31} +1.00000i q^{32} +(2.82843 + 4.00000i) q^{33} +(-1.00000 + 2.82843i) q^{36} +4.24264 q^{37} +(-4.24264 + 1.00000i) q^{38} +(-6.00000 + 4.24264i) q^{39} +(-0.707107 + 2.12132i) q^{40} -6.00000 q^{41} -12.0000i q^{43} +2.82843i q^{44} +(-4.12132 + 5.29289i) q^{45} -4.24264i q^{46} +12.7279 q^{47} +(-1.41421 + 1.00000i) q^{48} +7.00000 q^{49} +(-3.00000 + 4.00000i) q^{50} -4.24264 q^{52} -6.00000i q^{53} +(-5.00000 + 1.41421i) q^{54} +(-2.00000 + 6.00000i) q^{55} +(-5.65685 - 5.00000i) q^{57} +6.00000i q^{58} +6.00000 q^{59} +(-3.70711 + 1.12132i) q^{60} +10.0000 q^{61} +4.24264 q^{62} -1.00000 q^{64} +(-9.00000 - 3.00000i) q^{65} +(-4.00000 + 2.82843i) q^{66} +(6.00000 - 4.24264i) q^{69} -12.0000 q^{71} +(-2.82843 - 1.00000i) q^{72} -6.00000i q^{73} +4.24264i q^{74} +(-8.65685 - 0.242641i) q^{75} +(-1.00000 - 4.24264i) q^{76} +(-4.24264 - 6.00000i) q^{78} +12.7279i q^{79} +(-2.12132 - 0.707107i) q^{80} +(-7.00000 - 5.65685i) q^{81} -6.00000i q^{82} +12.0000 q^{86} +(-8.48528 + 6.00000i) q^{87} -2.82843 q^{88} +12.0000 q^{89} +(-5.29289 - 4.12132i) q^{90} +4.24264 q^{92} +(4.24264 + 6.00000i) q^{93} +12.7279i q^{94} +(0.878680 - 9.70711i) q^{95} +(-1.00000 - 1.41421i) q^{96} +7.00000i q^{98} +(-8.00000 - 2.82843i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{4} - 4q^{6} + 4q^{9} + O(q^{10})$$ $$4q - 4q^{4} - 4q^{6} + 4q^{9} + 12q^{15} + 4q^{16} + 4q^{19} + 4q^{24} + 16q^{25} + 24q^{29} - 4q^{30} - 4q^{36} - 24q^{39} - 24q^{41} - 8q^{45} + 28q^{49} - 12q^{50} - 20q^{54} - 8q^{55} + 24q^{59} - 12q^{60} + 40q^{61} - 4q^{64} - 36q^{65} - 16q^{66} + 24q^{69} - 48q^{71} - 12q^{75} - 4q^{76} - 28q^{81} + 48q^{86} + 48q^{89} - 24q^{90} + 12q^{95} - 4q^{96} - 32q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ −1.41421 + 1.00000i −0.816497 + 0.577350i
$$4$$ −1.00000 −0.500000
$$5$$ −2.12132 0.707107i −0.948683 0.316228i
$$6$$ −1.00000 1.41421i −0.408248 0.577350i
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 1.00000 2.82843i 0.333333 0.942809i
$$10$$ 0.707107 2.12132i 0.223607 0.670820i
$$11$$ 2.82843i 0.852803i −0.904534 0.426401i $$-0.859781\pi$$
0.904534 0.426401i $$-0.140219\pi$$
$$12$$ 1.41421 1.00000i 0.408248 0.288675i
$$13$$ 4.24264 1.17670 0.588348 0.808608i $$-0.299778\pi$$
0.588348 + 0.808608i $$0.299778\pi$$
$$14$$ 0 0
$$15$$ 3.70711 1.12132i 0.957171 0.289524i
$$16$$ 1.00000 0.250000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 2.82843 + 1.00000i 0.666667 + 0.235702i
$$19$$ 1.00000 + 4.24264i 0.229416 + 0.973329i
$$20$$ 2.12132 + 0.707107i 0.474342 + 0.158114i
$$21$$ 0 0
$$22$$ 2.82843 0.603023
$$23$$ −4.24264 −0.884652 −0.442326 0.896854i $$-0.645847\pi$$
−0.442326 + 0.896854i $$0.645847\pi$$
$$24$$ 1.00000 + 1.41421i 0.204124 + 0.288675i
$$25$$ 4.00000 + 3.00000i 0.800000 + 0.600000i
$$26$$ 4.24264i 0.832050i
$$27$$ 1.41421 + 5.00000i 0.272166 + 0.962250i
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 1.12132 + 3.70711i 0.204724 + 0.676822i
$$31$$ 4.24264i 0.762001i −0.924575 0.381000i $$-0.875580\pi$$
0.924575 0.381000i $$-0.124420\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 2.82843 + 4.00000i 0.492366 + 0.696311i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ −1.00000 + 2.82843i −0.166667 + 0.471405i
$$37$$ 4.24264 0.697486 0.348743 0.937218i $$-0.386609\pi$$
0.348743 + 0.937218i $$0.386609\pi$$
$$38$$ −4.24264 + 1.00000i −0.688247 + 0.162221i
$$39$$ −6.00000 + 4.24264i −0.960769 + 0.679366i
$$40$$ −0.707107 + 2.12132i −0.111803 + 0.335410i
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 12.0000i 1.82998i −0.403473 0.914991i $$-0.632197\pi$$
0.403473 0.914991i $$-0.367803\pi$$
$$44$$ 2.82843i 0.426401i
$$45$$ −4.12132 + 5.29289i −0.614370 + 0.789018i
$$46$$ 4.24264i 0.625543i
$$47$$ 12.7279 1.85656 0.928279 0.371884i $$-0.121288\pi$$
0.928279 + 0.371884i $$0.121288\pi$$
$$48$$ −1.41421 + 1.00000i −0.204124 + 0.144338i
$$49$$ 7.00000 1.00000
$$50$$ −3.00000 + 4.00000i −0.424264 + 0.565685i
$$51$$ 0 0
$$52$$ −4.24264 −0.588348
$$53$$ 6.00000i 0.824163i −0.911147 0.412082i $$-0.864802\pi$$
0.911147 0.412082i $$-0.135198\pi$$
$$54$$ −5.00000 + 1.41421i −0.680414 + 0.192450i
$$55$$ −2.00000 + 6.00000i −0.269680 + 0.809040i
$$56$$ 0 0
$$57$$ −5.65685 5.00000i −0.749269 0.662266i
$$58$$ 6.00000i 0.787839i
$$59$$ 6.00000 0.781133 0.390567 0.920575i $$-0.372279\pi$$
0.390567 + 0.920575i $$0.372279\pi$$
$$60$$ −3.70711 + 1.12132i −0.478585 + 0.144762i
$$61$$ 10.0000 1.28037 0.640184 0.768221i $$-0.278858\pi$$
0.640184 + 0.768221i $$0.278858\pi$$
$$62$$ 4.24264 0.538816
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ −9.00000 3.00000i −1.11631 0.372104i
$$66$$ −4.00000 + 2.82843i −0.492366 + 0.348155i
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 0 0
$$69$$ 6.00000 4.24264i 0.722315 0.510754i
$$70$$ 0 0
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ −2.82843 1.00000i −0.333333 0.117851i
$$73$$ 6.00000i 0.702247i −0.936329 0.351123i $$-0.885800\pi$$
0.936329 0.351123i $$-0.114200\pi$$
$$74$$ 4.24264i 0.493197i
$$75$$ −8.65685 0.242641i −0.999607 0.0280177i
$$76$$ −1.00000 4.24264i −0.114708 0.486664i
$$77$$ 0 0
$$78$$ −4.24264 6.00000i −0.480384 0.679366i
$$79$$ 12.7279i 1.43200i 0.698099 + 0.716002i $$0.254030\pi$$
−0.698099 + 0.716002i $$0.745970\pi$$
$$80$$ −2.12132 0.707107i −0.237171 0.0790569i
$$81$$ −7.00000 5.65685i −0.777778 0.628539i
$$82$$ 6.00000i 0.662589i
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 12.0000 1.29399
$$87$$ −8.48528 + 6.00000i −0.909718 + 0.643268i
$$88$$ −2.82843 −0.301511
$$89$$ 12.0000 1.27200 0.635999 0.771690i $$-0.280588\pi$$
0.635999 + 0.771690i $$0.280588\pi$$
$$90$$ −5.29289 4.12132i −0.557920 0.434425i
$$91$$ 0 0
$$92$$ 4.24264 0.442326
$$93$$ 4.24264 + 6.00000i 0.439941 + 0.622171i
$$94$$ 12.7279i 1.31278i
$$95$$ 0.878680 9.70711i 0.0901506 0.995928i
$$96$$ −1.00000 1.41421i −0.102062 0.144338i
$$97$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$98$$ 7.00000i 0.707107i
$$99$$ −8.00000 2.82843i −0.804030 0.284268i
$$100$$ −4.00000 3.00000i −0.400000 0.300000i
$$101$$ 15.5563i 1.54791i −0.633238 0.773957i $$-0.718274\pi$$
0.633238 0.773957i $$-0.281726\pi$$
$$102$$ 0 0
$$103$$ −4.24264 −0.418040 −0.209020 0.977911i $$-0.567027\pi$$
−0.209020 + 0.977911i $$0.567027\pi$$
$$104$$ 4.24264i 0.416025i
$$105$$ 0 0
$$106$$ 6.00000 0.582772
$$107$$ 12.0000i 1.16008i −0.814587 0.580042i $$-0.803036\pi$$
0.814587 0.580042i $$-0.196964\pi$$
$$108$$ −1.41421 5.00000i −0.136083 0.481125i
$$109$$ 4.24264i 0.406371i −0.979140 0.203186i $$-0.934871\pi$$
0.979140 0.203186i $$-0.0651295\pi$$
$$110$$ −6.00000 2.00000i −0.572078 0.190693i
$$111$$ −6.00000 + 4.24264i −0.569495 + 0.402694i
$$112$$ 0 0
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 5.00000 5.65685i 0.468293 0.529813i
$$115$$ 9.00000 + 3.00000i 0.839254 + 0.279751i
$$116$$ −6.00000 −0.557086
$$117$$ 4.24264 12.0000i 0.392232 1.10940i
$$118$$ 6.00000i 0.552345i
$$119$$ 0 0
$$120$$ −1.12132 3.70711i −0.102362 0.338411i
$$121$$ 3.00000 0.272727
$$122$$ 10.0000i 0.905357i
$$123$$ 8.48528 6.00000i 0.765092 0.541002i
$$124$$ 4.24264i 0.381000i
$$125$$ −6.36396 9.19239i −0.569210 0.822192i
$$126$$ 0 0
$$127$$ −12.7279 −1.12942 −0.564710 0.825289i $$-0.691012\pi$$
−0.564710 + 0.825289i $$0.691012\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 12.0000 + 16.9706i 1.05654 + 1.49417i
$$130$$ 3.00000 9.00000i 0.263117 0.789352i
$$131$$ 11.3137i 0.988483i 0.869325 + 0.494242i $$0.164554\pi$$
−0.869325 + 0.494242i $$0.835446\pi$$
$$132$$ −2.82843 4.00000i −0.246183 0.348155i
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0.535534 11.6066i 0.0460914 0.998937i
$$136$$ 0 0
$$137$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ 4.24264 + 6.00000i 0.361158 + 0.510754i
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ −18.0000 + 12.7279i −1.51587 + 1.07188i
$$142$$ 12.0000i 1.00702i
$$143$$ 12.0000i 1.00349i
$$144$$ 1.00000 2.82843i 0.0833333 0.235702i
$$145$$ −12.7279 4.24264i −1.05700 0.352332i
$$146$$ 6.00000 0.496564
$$147$$ −9.89949 + 7.00000i −0.816497 + 0.577350i
$$148$$ −4.24264 −0.348743
$$149$$ 1.41421i 0.115857i 0.998321 + 0.0579284i $$0.0184495\pi$$
−0.998321 + 0.0579284i $$0.981550\pi$$
$$150$$ 0.242641 8.65685i 0.0198115 0.706829i
$$151$$ 4.24264i 0.345261i 0.984987 + 0.172631i $$0.0552267\pi$$
−0.984987 + 0.172631i $$0.944773\pi$$
$$152$$ 4.24264 1.00000i 0.344124 0.0811107i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −3.00000 + 9.00000i −0.240966 + 0.722897i
$$156$$ 6.00000 4.24264i 0.480384 0.339683i
$$157$$ 18.0000i 1.43656i −0.695756 0.718278i $$-0.744931\pi$$
0.695756 0.718278i $$-0.255069\pi$$
$$158$$ −12.7279 −1.01258
$$159$$ 6.00000 + 8.48528i 0.475831 + 0.672927i
$$160$$ 0.707107 2.12132i 0.0559017 0.167705i
$$161$$ 0 0
$$162$$ 5.65685 7.00000i 0.444444 0.549972i
$$163$$ 6.00000i 0.469956i 0.972001 + 0.234978i $$0.0755019\pi$$
−0.972001 + 0.234978i $$0.924498\pi$$
$$164$$ 6.00000 0.468521
$$165$$ −3.17157 10.4853i −0.246907 0.816278i
$$166$$ 0 0
$$167$$ 12.0000i 0.928588i 0.885681 + 0.464294i $$0.153692\pi$$
−0.885681 + 0.464294i $$0.846308\pi$$
$$168$$ 0 0
$$169$$ 5.00000 0.384615
$$170$$ 0 0
$$171$$ 13.0000 + 1.41421i 0.994135 + 0.108148i
$$172$$ 12.0000i 0.914991i
$$173$$ 6.00000i 0.456172i 0.973641 + 0.228086i $$0.0732467\pi$$
−0.973641 + 0.228086i $$0.926753\pi$$
$$174$$ −6.00000 8.48528i −0.454859 0.643268i
$$175$$ 0 0
$$176$$ 2.82843i 0.213201i
$$177$$ −8.48528 + 6.00000i −0.637793 + 0.450988i
$$178$$ 12.0000i 0.899438i
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 4.12132 5.29289i 0.307185 0.394509i
$$181$$ 4.24264i 0.315353i −0.987491 0.157676i $$-0.949600\pi$$
0.987491 0.157676i $$-0.0504003\pi$$
$$182$$ 0 0
$$183$$ −14.1421 + 10.0000i −1.04542 + 0.739221i
$$184$$ 4.24264i 0.312772i
$$185$$ −9.00000 3.00000i −0.661693 0.220564i
$$186$$ −6.00000 + 4.24264i −0.439941 + 0.311086i
$$187$$ 0 0
$$188$$ −12.7279 −0.928279
$$189$$ 0 0
$$190$$ 9.70711 + 0.878680i 0.704228 + 0.0637461i
$$191$$ 15.5563i 1.12562i 0.826587 + 0.562809i $$0.190279\pi$$
−0.826587 + 0.562809i $$0.809721\pi$$
$$192$$ 1.41421 1.00000i 0.102062 0.0721688i
$$193$$ −16.9706 −1.22157 −0.610784 0.791797i $$-0.709146\pi$$
−0.610784 + 0.791797i $$0.709146\pi$$
$$194$$ 0 0
$$195$$ 15.7279 4.75736i 1.12630 0.340682i
$$196$$ −7.00000 −0.500000
$$197$$ 12.7279 0.906827 0.453413 0.891300i $$-0.350206\pi$$
0.453413 + 0.891300i $$0.350206\pi$$
$$198$$ 2.82843 8.00000i 0.201008 0.568535i
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ 3.00000 4.00000i 0.212132 0.282843i
$$201$$ 0 0
$$202$$ 15.5563 1.09454
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 12.7279 + 4.24264i 0.888957 + 0.296319i
$$206$$ 4.24264i 0.295599i
$$207$$ −4.24264 + 12.0000i −0.294884 + 0.834058i
$$208$$ 4.24264 0.294174
$$209$$ 12.0000 2.82843i 0.830057 0.195646i
$$210$$ 0 0
$$211$$ 8.48528i 0.584151i −0.956395 0.292075i $$-0.905654\pi$$
0.956395 0.292075i $$-0.0943458\pi$$
$$212$$ 6.00000i 0.412082i
$$213$$ 16.9706 12.0000i 1.16280 0.822226i
$$214$$ 12.0000 0.820303
$$215$$ −8.48528 + 25.4558i −0.578691 + 1.73607i
$$216$$ 5.00000 1.41421i 0.340207 0.0962250i
$$217$$ 0 0
$$218$$ 4.24264 0.287348
$$219$$ 6.00000 + 8.48528i 0.405442 + 0.573382i
$$220$$ 2.00000 6.00000i 0.134840 0.404520i
$$221$$ 0 0
$$222$$ −4.24264 6.00000i −0.284747 0.402694i
$$223$$ 21.2132 1.42054 0.710271 0.703929i $$-0.248573\pi$$
0.710271 + 0.703929i $$0.248573\pi$$
$$224$$ 0 0
$$225$$ 12.4853 8.31371i 0.832352 0.554247i
$$226$$ 0 0
$$227$$ 18.0000i 1.19470i −0.801980 0.597351i $$-0.796220\pi$$
0.801980 0.597351i $$-0.203780\pi$$
$$228$$ 5.65685 + 5.00000i 0.374634 + 0.331133i
$$229$$ −14.0000 −0.925146 −0.462573 0.886581i $$-0.653074\pi$$
−0.462573 + 0.886581i $$0.653074\pi$$
$$230$$ −3.00000 + 9.00000i −0.197814 + 0.593442i
$$231$$ 0 0
$$232$$ 6.00000i 0.393919i
$$233$$ 8.48528 0.555889 0.277945 0.960597i $$-0.410347\pi$$
0.277945 + 0.960597i $$0.410347\pi$$
$$234$$ 12.0000 + 4.24264i 0.784465 + 0.277350i
$$235$$ −27.0000 9.00000i −1.76129 0.587095i
$$236$$ −6.00000 −0.390567
$$237$$ −12.7279 18.0000i −0.826767 1.16923i
$$238$$ 0 0
$$239$$ 24.0416i 1.55512i 0.628806 + 0.777562i $$0.283544\pi$$
−0.628806 + 0.777562i $$0.716456\pi$$
$$240$$ 3.70711 1.12132i 0.239293 0.0723809i
$$241$$ 8.48528i 0.546585i −0.961931 0.273293i $$-0.911887\pi$$
0.961931 0.273293i $$-0.0881127\pi$$
$$242$$ 3.00000i 0.192847i
$$243$$ 15.5563 + 1.00000i 0.997940 + 0.0641500i
$$244$$ −10.0000 −0.640184
$$245$$ −14.8492 4.94975i −0.948683 0.316228i
$$246$$ 6.00000 + 8.48528i 0.382546 + 0.541002i
$$247$$ 4.24264 + 18.0000i 0.269953 + 1.14531i
$$248$$ −4.24264 −0.269408
$$249$$ 0 0
$$250$$ 9.19239 6.36396i 0.581378 0.402492i
$$251$$ 5.65685i 0.357057i −0.983935 0.178529i $$-0.942866\pi$$
0.983935 0.178529i $$-0.0571337\pi$$
$$252$$ 0 0
$$253$$ 12.0000i 0.754434i
$$254$$ 12.7279i 0.798621i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 18.0000i 1.12281i 0.827541 + 0.561405i $$0.189739\pi$$
−0.827541 + 0.561405i $$0.810261\pi$$
$$258$$ −16.9706 + 12.0000i −1.05654 + 0.747087i
$$259$$ 0 0
$$260$$ 9.00000 + 3.00000i 0.558156 + 0.186052i
$$261$$ 6.00000 16.9706i 0.371391 1.05045i
$$262$$ −11.3137 −0.698963
$$263$$ 21.2132 1.30806 0.654031 0.756468i $$-0.273077\pi$$
0.654031 + 0.756468i $$0.273077\pi$$
$$264$$ 4.00000 2.82843i 0.246183 0.174078i
$$265$$ −4.24264 + 12.7279i −0.260623 + 0.781870i
$$266$$ 0 0
$$267$$ −16.9706 + 12.0000i −1.03858 + 0.734388i
$$268$$ 0 0
$$269$$ 6.00000 0.365826 0.182913 0.983129i $$-0.441447\pi$$
0.182913 + 0.983129i $$0.441447\pi$$
$$270$$ 11.6066 + 0.535534i 0.706355 + 0.0325916i
$$271$$ −20.0000 −1.21491 −0.607457 0.794353i $$-0.707810\pi$$
−0.607457 + 0.794353i $$0.707810\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 8.48528 11.3137i 0.511682 0.682242i
$$276$$ −6.00000 + 4.24264i −0.361158 + 0.255377i
$$277$$ 18.0000i 1.08152i 0.841178 + 0.540758i $$0.181862\pi$$
−0.841178 + 0.540758i $$0.818138\pi$$
$$278$$ 4.00000i 0.239904i
$$279$$ −12.0000 4.24264i −0.718421 0.254000i
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ −12.7279 18.0000i −0.757937 1.07188i
$$283$$ 18.0000i 1.06999i 0.844856 + 0.534994i $$0.179686\pi$$
−0.844856 + 0.534994i $$0.820314\pi$$
$$284$$ 12.0000 0.712069
$$285$$ 8.46447 + 14.6066i 0.501392 + 0.865220i
$$286$$ 12.0000 0.709575
$$287$$ 0 0
$$288$$ 2.82843 + 1.00000i 0.166667 + 0.0589256i
$$289$$ −17.0000 −1.00000
$$290$$ 4.24264 12.7279i 0.249136 0.747409i
$$291$$ 0 0
$$292$$ 6.00000i 0.351123i
$$293$$ 18.0000i 1.05157i 0.850617 + 0.525786i $$0.176229\pi$$
−0.850617 + 0.525786i $$0.823771\pi$$
$$294$$ −7.00000 9.89949i −0.408248 0.577350i
$$295$$ −12.7279 4.24264i −0.741048 0.247016i
$$296$$ 4.24264i 0.246598i
$$297$$ 14.1421 4.00000i 0.820610 0.232104i
$$298$$ −1.41421 −0.0819232
$$299$$ −18.0000 −1.04097
$$300$$ 8.65685 + 0.242641i 0.499804 + 0.0140089i
$$301$$ 0 0
$$302$$ −4.24264 −0.244137
$$303$$ 15.5563 + 22.0000i 0.893689 + 1.26387i
$$304$$ 1.00000 + 4.24264i 0.0573539 + 0.243332i
$$305$$ −21.2132 7.07107i −1.21466 0.404888i
$$306$$ 0 0
$$307$$ 33.9411 1.93712 0.968561 0.248776i $$-0.0800281\pi$$
0.968561 + 0.248776i $$0.0800281\pi$$
$$308$$ 0 0
$$309$$ 6.00000 4.24264i 0.341328 0.241355i
$$310$$ −9.00000 3.00000i −0.511166 0.170389i
$$311$$ 1.41421i 0.0801927i 0.999196 + 0.0400963i $$0.0127665\pi$$
−0.999196 + 0.0400963i $$0.987234\pi$$
$$312$$ 4.24264 + 6.00000i 0.240192 + 0.339683i
$$313$$ 30.0000i 1.69570i −0.530236 0.847850i $$-0.677897\pi$$
0.530236 0.847850i $$-0.322103\pi$$
$$314$$ 18.0000 1.01580
$$315$$ 0 0
$$316$$ 12.7279i 0.716002i
$$317$$ 18.0000i 1.01098i 0.862832 + 0.505490i $$0.168688\pi$$
−0.862832 + 0.505490i $$0.831312\pi$$
$$318$$ −8.48528 + 6.00000i −0.475831 + 0.336463i
$$319$$ 16.9706i 0.950169i
$$320$$ 2.12132 + 0.707107i 0.118585 + 0.0395285i
$$321$$ 12.0000 + 16.9706i 0.669775 + 0.947204i
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 7.00000 + 5.65685i 0.388889 + 0.314270i
$$325$$ 16.9706 + 12.7279i 0.941357 + 0.706018i
$$326$$ −6.00000 −0.332309
$$327$$ 4.24264 + 6.00000i 0.234619 + 0.331801i
$$328$$ 6.00000i 0.331295i
$$329$$ 0 0
$$330$$ 10.4853 3.17157i 0.577196 0.174589i
$$331$$ 33.9411i 1.86557i −0.360429 0.932786i $$-0.617370\pi$$
0.360429 0.932786i $$-0.382630\pi$$
$$332$$ 0 0
$$333$$ 4.24264 12.0000i 0.232495 0.657596i
$$334$$ −12.0000 −0.656611
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −25.4558 −1.38667 −0.693334 0.720616i $$-0.743859\pi$$
−0.693334 + 0.720616i $$0.743859\pi$$
$$338$$ 5.00000i 0.271964i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −12.0000 −0.649836
$$342$$ −1.41421 + 13.0000i −0.0764719 + 0.702959i
$$343$$ 0 0
$$344$$ −12.0000 −0.646997
$$345$$ −15.7279 + 4.75736i −0.846763 + 0.256128i
$$346$$ −6.00000 −0.322562
$$347$$ 8.48528 0.455514 0.227757 0.973718i $$-0.426861\pi$$
0.227757 + 0.973718i $$0.426861\pi$$
$$348$$ 8.48528 6.00000i 0.454859 0.321634i
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 0 0
$$351$$ 6.00000 + 21.2132i 0.320256 + 1.13228i
$$352$$ 2.82843 0.150756
$$353$$ −8.48528 −0.451626 −0.225813 0.974171i $$-0.572504\pi$$
−0.225813 + 0.974171i $$0.572504\pi$$
$$354$$ −6.00000 8.48528i −0.318896 0.450988i
$$355$$ 25.4558 + 8.48528i 1.35106 + 0.450352i
$$356$$ −12.0000 −0.635999
$$357$$ 0 0
$$358$$ 12.0000i 0.634220i
$$359$$ 7.07107i 0.373197i −0.982436 0.186598i $$-0.940254\pi$$
0.982436 0.186598i $$-0.0597463\pi$$
$$360$$ 5.29289 + 4.12132i 0.278960 + 0.217213i
$$361$$ −17.0000 + 8.48528i −0.894737 + 0.446594i
$$362$$ 4.24264 0.222988
$$363$$ −4.24264 + 3.00000i −0.222681 + 0.157459i
$$364$$ 0 0
$$365$$ −4.24264 + 12.7279i −0.222070 + 0.666210i
$$366$$ −10.0000 14.1421i −0.522708 0.739221i
$$367$$ 24.0000i 1.25279i 0.779506 + 0.626395i $$0.215470\pi$$
−0.779506 + 0.626395i $$0.784530\pi$$
$$368$$ −4.24264 −0.221163
$$369$$ −6.00000 + 16.9706i −0.312348 + 0.883452i
$$370$$ 3.00000 9.00000i 0.155963 0.467888i
$$371$$ 0 0
$$372$$ −4.24264 6.00000i −0.219971 0.311086i
$$373$$ 21.2132 1.09838 0.549189 0.835698i $$-0.314937\pi$$
0.549189 + 0.835698i $$0.314937\pi$$
$$374$$ 0 0
$$375$$ 18.1924 + 6.63604i 0.939451 + 0.342684i
$$376$$ 12.7279i 0.656392i
$$377$$ 25.4558 1.31104
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ −0.878680 + 9.70711i −0.0450753 + 0.497964i
$$381$$ 18.0000 12.7279i 0.922168 0.652071i
$$382$$ −15.5563 −0.795932
$$383$$ 12.0000i 0.613171i −0.951843 0.306586i $$-0.900813\pi$$
0.951843 0.306586i $$-0.0991866\pi$$
$$384$$ 1.00000 + 1.41421i 0.0510310 + 0.0721688i
$$385$$ 0 0
$$386$$ 16.9706i 0.863779i
$$387$$ −33.9411 12.0000i −1.72532 0.609994i
$$388$$ 0 0
$$389$$ 9.89949i 0.501924i −0.967997 0.250962i $$-0.919253\pi$$
0.967997 0.250962i $$-0.0807470\pi$$
$$390$$ 4.75736 + 15.7279i 0.240898 + 0.796414i
$$391$$ 0 0
$$392$$ 7.00000i 0.353553i
$$393$$ −11.3137 16.0000i −0.570701 0.807093i
$$394$$ 12.7279i 0.641223i
$$395$$ 9.00000 27.0000i 0.452839 1.35852i
$$396$$ 8.00000 + 2.82843i 0.402015 + 0.142134i
$$397$$ 30.0000i 1.50566i 0.658217 + 0.752828i $$0.271311\pi$$
−0.658217 + 0.752828i $$0.728689\pi$$
$$398$$ 16.0000i 0.802008i
$$399$$ 0 0
$$400$$ 4.00000 + 3.00000i 0.200000 + 0.150000i
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 0 0
$$403$$ 18.0000i 0.896644i
$$404$$ 15.5563i 0.773957i
$$405$$ 10.8492 + 16.9497i 0.539103 + 0.842240i
$$406$$ 0 0
$$407$$ 12.0000i 0.594818i
$$408$$ 0 0
$$409$$ 25.4558i 1.25871i −0.777118 0.629355i $$-0.783319\pi$$
0.777118 0.629355i $$-0.216681\pi$$
$$410$$ −4.24264 + 12.7279i −0.209529 + 0.628587i
$$411$$ 0 0
$$412$$ 4.24264 0.209020
$$413$$ 0 0
$$414$$ −12.0000 4.24264i −0.589768 0.208514i
$$415$$ 0 0
$$416$$ 4.24264i 0.208013i
$$417$$ −5.65685 + 4.00000i −0.277017 + 0.195881i
$$418$$ 2.82843 + 12.0000i 0.138343 + 0.586939i
$$419$$ 14.1421i 0.690889i −0.938439 0.345444i $$-0.887728\pi$$
0.938439 0.345444i $$-0.112272\pi$$
$$420$$ 0 0
$$421$$ 29.6985i 1.44742i 0.690107 + 0.723708i $$0.257564\pi$$
−0.690107 + 0.723708i $$0.742436\pi$$
$$422$$ 8.48528 0.413057
$$423$$ 12.7279 36.0000i 0.618853 1.75038i
$$424$$ −6.00000 −0.291386
$$425$$ 0 0
$$426$$ 12.0000 + 16.9706i 0.581402 + 0.822226i
$$427$$ 0 0
$$428$$ 12.0000i 0.580042i
$$429$$ 12.0000 + 16.9706i 0.579365 + 0.819346i
$$430$$ −25.4558 8.48528i −1.22759 0.409197i
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ 1.41421 + 5.00000i 0.0680414 + 0.240563i
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 22.2426 6.72792i 1.06645 0.322579i
$$436$$ 4.24264i 0.203186i
$$437$$ −4.24264 18.0000i −0.202953 0.861057i
$$438$$ −8.48528 + 6.00000i −0.405442 + 0.286691i
$$439$$ 4.24264i 0.202490i 0.994862 + 0.101245i $$0.0322826\pi$$
−0.994862 + 0.101245i $$0.967717\pi$$
$$440$$ 6.00000 + 2.00000i 0.286039 + 0.0953463i
$$441$$ 7.00000 19.7990i 0.333333 0.942809i
$$442$$ 0 0
$$443$$ 8.48528 0.403148 0.201574 0.979473i $$-0.435394\pi$$
0.201574 + 0.979473i $$0.435394\pi$$
$$444$$ 6.00000 4.24264i 0.284747 0.201347i
$$445$$ −25.4558 8.48528i −1.20672 0.402241i
$$446$$ 21.2132i 1.00447i
$$447$$ −1.41421 2.00000i −0.0668900 0.0945968i
$$448$$ 0 0
$$449$$ −24.0000 −1.13263 −0.566315 0.824189i $$-0.691631\pi$$
−0.566315 + 0.824189i $$0.691631\pi$$
$$450$$ 8.31371 + 12.4853i 0.391912 + 0.588562i
$$451$$ 16.9706i 0.799113i
$$452$$ 0 0
$$453$$ −4.24264 6.00000i −0.199337 0.281905i
$$454$$ 18.0000 0.844782
$$455$$ 0 0
$$456$$ −5.00000 + 5.65685i −0.234146 + 0.264906i
$$457$$ 12.0000i 0.561336i −0.959805 0.280668i $$-0.909444\pi$$
0.959805 0.280668i $$-0.0905560\pi$$
$$458$$ 14.0000i 0.654177i
$$459$$ 0 0
$$460$$ −9.00000 3.00000i −0.419627 0.139876i
$$461$$ 15.5563i 0.724531i 0.932075 + 0.362266i $$0.117997\pi$$
−0.932075 + 0.362266i $$0.882003\pi$$
$$462$$ 0 0
$$463$$ 36.0000i 1.67306i −0.547920 0.836531i $$-0.684580\pi$$
0.547920 0.836531i $$-0.315420\pi$$
$$464$$ 6.00000 0.278543
$$465$$ −4.75736 15.7279i −0.220617 0.729365i
$$466$$ 8.48528i 0.393073i
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ −4.24264 + 12.0000i −0.196116 + 0.554700i
$$469$$ 0 0
$$470$$ 9.00000 27.0000i 0.415139 1.24542i
$$471$$ 18.0000 + 25.4558i 0.829396 + 1.17294i
$$472$$ 6.00000i 0.276172i
$$473$$ −33.9411 −1.56061
$$474$$ 18.0000 12.7279i 0.826767 0.584613i
$$475$$ −8.72792 + 19.9706i −0.400465 + 0.916312i
$$476$$ 0 0
$$477$$ −16.9706 6.00000i −0.777029 0.274721i
$$478$$ −24.0416 −1.09964
$$479$$ 9.89949i 0.452319i 0.974090 + 0.226160i $$0.0726171\pi$$
−0.974090 + 0.226160i $$0.927383\pi$$
$$480$$ 1.12132 + 3.70711i 0.0511810 + 0.169206i
$$481$$ 18.0000 0.820729
$$482$$ 8.48528 0.386494
$$483$$ 0 0
$$484$$ −3.00000 −0.136364
$$485$$ 0 0
$$486$$ −1.00000 + 15.5563i −0.0453609 + 0.705650i
$$487$$ −12.7279 −0.576757 −0.288379 0.957516i $$-0.593116\pi$$
−0.288379 + 0.957516i $$0.593116\pi$$
$$488$$ 10.0000i 0.452679i
$$489$$ −6.00000 8.48528i −0.271329 0.383718i
$$490$$ 4.94975 14.8492i 0.223607 0.670820i
$$491$$ 39.5980i 1.78703i −0.449032 0.893516i $$-0.648231\pi$$
0.449032 0.893516i $$-0.351769\pi$$
$$492$$ −8.48528 + 6.00000i −0.382546 + 0.270501i
$$493$$ 0 0
$$494$$ −18.0000 + 4.24264i −0.809858 + 0.190885i
$$495$$ 14.9706 + 11.6569i 0.672877 + 0.523937i
$$496$$ 4.24264i 0.190500i
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −14.0000 −0.626726 −0.313363 0.949633i $$-0.601456\pi$$
−0.313363 + 0.949633i $$0.601456\pi$$
$$500$$ 6.36396 + 9.19239i 0.284605 + 0.411096i
$$501$$ −12.0000 16.9706i −0.536120 0.758189i
$$502$$ 5.65685 0.252478
$$503$$ 21.2132 0.945850 0.472925 0.881103i $$-0.343198\pi$$
0.472925 + 0.881103i $$0.343198\pi$$
$$504$$ 0 0
$$505$$ −11.0000 + 33.0000i −0.489494 + 1.46848i
$$506$$ −12.0000 −0.533465
$$507$$ −7.07107 + 5.00000i −0.314037 + 0.222058i
$$508$$ 12.7279 0.564710
$$509$$ 18.0000 0.797836 0.398918 0.916987i $$-0.369386\pi$$
0.398918 + 0.916987i $$0.369386\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000i 0.0441942i
$$513$$ −19.7990 + 11.0000i −0.874147 + 0.485662i
$$514$$ −18.0000 −0.793946
$$515$$ 9.00000 + 3.00000i 0.396587 + 0.132196i
$$516$$ −12.0000 16.9706i −0.528271 0.747087i
$$517$$ 36.0000i 1.58328i
$$518$$ 0 0
$$519$$ −6.00000 8.48528i −0.263371 0.372463i
$$520$$ −3.00000 + 9.00000i −0.131559 + 0.394676i
$$521$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$522$$ 16.9706 + 6.00000i 0.742781 + 0.262613i
$$523$$ −16.9706 −0.742071 −0.371035 0.928619i $$-0.620997\pi$$
−0.371035 + 0.928619i $$0.620997\pi$$
$$524$$ 11.3137i 0.494242i
$$525$$ 0 0
$$526$$ 21.2132i 0.924940i
$$527$$ 0 0
$$528$$ 2.82843 + 4.00000i 0.123091 + 0.174078i
$$529$$ −5.00000 −0.217391
$$530$$ −12.7279 4.24264i −0.552866 0.184289i
$$531$$ 6.00000 16.9706i 0.260378 0.736460i
$$532$$ 0 0
$$533$$ −25.4558 −1.10262
$$534$$ −12.0000 16.9706i −0.519291 0.734388i
$$535$$ −8.48528 + 25.4558i −0.366851 + 1.10055i
$$536$$ 0 0
$$537$$ 16.9706 12.0000i 0.732334 0.517838i
$$538$$ 6.00000i 0.258678i
$$539$$ 19.7990i 0.852803i
$$540$$ −0.535534 + 11.6066i −0.0230457 + 0.499469i
$$541$$ −38.0000 −1.63375 −0.816874 0.576816i $$-0.804295\pi$$
−0.816874 + 0.576816i $$0.804295\pi$$
$$542$$ 20.0000i 0.859074i
$$543$$ 4.24264 + 6.00000i 0.182069 + 0.257485i
$$544$$ 0 0
$$545$$ −3.00000 + 9.00000i −0.128506 + 0.385518i
$$546$$ 0 0
$$547$$ −33.9411 −1.45122 −0.725609 0.688107i $$-0.758442\pi$$
−0.725609 + 0.688107i $$0.758442\pi$$
$$548$$ 0 0
$$549$$ 10.0000 28.2843i 0.426790 1.20714i
$$550$$ 11.3137 + 8.48528i 0.482418 + 0.361814i
$$551$$ 6.00000 + 25.4558i 0.255609 + 1.08446i
$$552$$ −4.24264 6.00000i −0.180579 0.255377i
$$553$$ 0 0
$$554$$ −18.0000 −0.764747
$$555$$ 15.7279 4.75736i 0.667613 0.201939i
$$556$$ −4.00000 −0.169638
$$557$$ 21.2132 0.898832 0.449416 0.893323i $$-0.351632\pi$$
0.449416 + 0.893323i $$0.351632\pi$$
$$558$$ 4.24264 12.0000i 0.179605 0.508001i
$$559$$ 50.9117i 2.15333i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 18.0000i 0.759284i
$$563$$ 12.0000i 0.505740i −0.967500 0.252870i $$-0.918626\pi$$
0.967500 0.252870i $$-0.0813744\pi$$
$$564$$ 18.0000 12.7279i 0.757937 0.535942i
$$565$$ 0 0
$$566$$ −18.0000 −0.756596
$$567$$ 0 0
$$568$$ 12.0000i 0.503509i
$$569$$ −24.0000 −1.00613 −0.503066 0.864248i $$-0.667795\pi$$
−0.503066 + 0.864248i $$0.667795\pi$$
$$570$$ −14.6066 + 8.46447i −0.611803 + 0.354537i
$$571$$ 22.0000 0.920671 0.460336 0.887745i $$-0.347729\pi$$
0.460336 + 0.887745i $$0.347729\pi$$
$$572$$ 12.0000i 0.501745i
$$573$$ −15.5563 22.0000i −0.649876 0.919063i
$$574$$ 0 0
$$575$$ −16.9706 12.7279i −0.707721 0.530791i
$$576$$ −1.00000 + 2.82843i −0.0416667 + 0.117851i
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 17.0000i 0.707107i
$$579$$ 24.0000 16.9706i 0.997406 0.705273i
$$580$$ 12.7279 + 4.24264i 0.528498 + 0.176166i
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −16.9706 −0.702849
$$584$$ −6.00000 −0.248282
$$585$$ −17.4853 + 22.4558i −0.722927 + 0.928435i
$$586$$ −18.0000 −0.743573
$$587$$ −42.4264 −1.75113 −0.875563 0.483105i $$-0.839509\pi$$
−0.875563 + 0.483105i $$0.839509\pi$$
$$588$$ 9.89949 7.00000i 0.408248 0.288675i
$$589$$ 18.0000 4.24264i 0.741677 0.174815i
$$590$$ 4.24264 12.7279i 0.174667 0.524000i
$$591$$ −18.0000 + 12.7279i −0.740421 + 0.523557i
$$592$$ 4.24264 0.174371
$$593$$ −8.48528 −0.348449 −0.174224 0.984706i $$-0.555742\pi$$
−0.174224 + 0.984706i $$0.555742\pi$$
$$594$$ 4.00000 + 14.1421i 0.164122 + 0.580259i
$$595$$ 0 0
$$596$$ 1.41421i 0.0579284i
$$597$$ 22.6274 16.0000i 0.926079 0.654836i
$$598$$ 18.0000i 0.736075i
$$599$$ −48.0000 −1.96123 −0.980613 0.195952i $$-0.937220\pi$$
−0.980613 + 0.195952i $$0.937220\pi$$
$$600$$ −0.242641 + 8.65685i −0.00990576 + 0.353415i
$$601$$ 16.9706i 0.692244i 0.938190 + 0.346122i $$0.112502\pi$$
−0.938190 + 0.346122i $$0.887498\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 4.24264i 0.172631i
$$605$$ −6.36396 2.12132i −0.258732 0.0862439i
$$606$$ −22.0000 + 15.5563i −0.893689 + 0.631933i
$$607$$ 4.24264 0.172203 0.0861017 0.996286i $$-0.472559\pi$$
0.0861017 + 0.996286i $$0.472559\pi$$
$$608$$ −4.24264 + 1.00000i −0.172062 + 0.0405554i
$$609$$ 0 0
$$610$$ 7.07107 21.2132i 0.286299 0.858898i
$$611$$ 54.0000 2.18461
$$612$$ 0 0
$$613$$ 6.00000i 0.242338i −0.992632 0.121169i $$-0.961336\pi$$
0.992632 0.121169i $$-0.0386643\pi$$
$$614$$ 33.9411i 1.36975i
$$615$$ −22.2426 + 6.72792i −0.896910 + 0.271296i
$$616$$ 0 0
$$617$$ 42.4264 1.70802 0.854011 0.520254i $$-0.174163\pi$$
0.854011 + 0.520254i $$0.174163\pi$$
$$618$$ 4.24264 + 6.00000i 0.170664 + 0.241355i
$$619$$ 10.0000 0.401934 0.200967 0.979598i $$-0.435592\pi$$
0.200967 + 0.979598i $$0.435592\pi$$
$$620$$ 3.00000 9.00000i 0.120483 0.361449i
$$621$$ −6.00000 21.2132i −0.240772 0.851257i
$$622$$ −1.41421 −0.0567048
$$623$$ 0 0
$$624$$ −6.00000 + 4.24264i −0.240192 + 0.169842i
$$625$$ 7.00000 + 24.0000i 0.280000 + 0.960000i
$$626$$ 30.0000 1.19904
$$627$$ −14.1421 + 16.0000i −0.564782 + 0.638978i
$$628$$ 18.0000i 0.718278i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −20.0000 −0.796187 −0.398094 0.917345i $$-0.630328\pi$$
−0.398094 + 0.917345i $$0.630328\pi$$
$$632$$ 12.7279 0.506290
$$633$$ 8.48528 + 12.0000i 0.337260 + 0.476957i
$$634$$ −18.0000 −0.714871
$$635$$ 27.0000 + 9.00000i 1.07146 + 0.357154i
$$636$$ −6.00000 8.48528i −0.237915 0.336463i
$$637$$ 29.6985 1.17670
$$638$$ 16.9706 0.671871
$$639$$ −12.0000 + 33.9411i −0.474713 + 1.34269i
$$640$$ −0.707107 + 2.12132i −0.0279508 + 0.0838525i
$$641$$ 24.0000 0.947943 0.473972 0.880540i $$-0.342820\pi$$
0.473972 + 0.880540i $$0.342820\pi$$
$$642$$ −16.9706 + 12.0000i −0.669775 + 0.473602i
$$643$$ 6.00000i 0.236617i −0.992977 0.118308i $$-0.962253\pi$$
0.992977 0.118308i $$-0.0377472\pi$$
$$644$$ 0 0
$$645$$ −13.4558 44.4853i −0.529823 1.75161i
$$646$$ 0 0
$$647$$ −4.24264 −0.166795 −0.0833977 0.996516i $$-0.526577\pi$$
−0.0833977 + 0.996516i $$0.526577\pi$$
$$648$$ −5.65685 + 7.00000i −0.222222 + 0.274986i
$$649$$ 16.9706i 0.666153i
$$650$$ −12.7279 + 16.9706i −0.499230 + 0.665640i
$$651$$ 0 0
$$652$$ 6.00000i 0.234978i
$$653$$ 21.2132 0.830137 0.415068 0.909790i $$-0.363758\pi$$
0.415068 + 0.909790i $$0.363758\pi$$
$$654$$ −6.00000 + 4.24264i −0.234619 + 0.165900i
$$655$$ 8.00000 24.0000i 0.312586 0.937758i
$$656$$ −6.00000 −0.234261
$$657$$ −16.9706 6.00000i −0.662085 0.234082i
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 3.17157 + 10.4853i 0.123453 + 0.408139i
$$661$$ 4.24264i 0.165020i 0.996590 + 0.0825098i $$0.0262936\pi$$
−0.996590 + 0.0825098i $$0.973706\pi$$
$$662$$ 33.9411 1.31916
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 12.0000 + 4.24264i 0.464991 + 0.164399i
$$667$$ −25.4558 −0.985654
$$668$$ 12.0000i 0.464294i
$$669$$ −30.0000 + 21.2132i −1.15987 + 0.820150i
$$670$$ 0 0
$$671$$ 28.2843i 1.09190i
$$672$$ 0 0
$$673$$ −16.9706 −0.654167 −0.327084 0.944995i $$-0.606066\pi$$
−0.327084 + 0.944995i $$0.606066\pi$$
$$674$$ 25.4558i 0.980522i
$$675$$ −9.34315 + 24.2426i −0.359618 + 0.933100i
$$676$$ −5.00000 −0.192308
$$677$$ 42.0000i 1.61419i 0.590421 + 0.807096i $$0.298962\pi$$
−0.590421 + 0.807096i $$0.701038\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 18.0000 + 25.4558i 0.689761 + 0.975470i
$$682$$ 12.0000i 0.459504i
$$683$$ 18.0000i 0.688751i 0.938832 + 0.344375i $$0.111909\pi$$
−0.938832 + 0.344375i $$0.888091\pi$$
$$684$$ −13.0000 1.41421i −0.497067 0.0540738i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 19.7990 14.0000i 0.755379 0.534133i
$$688$$ 12.0000i 0.457496i
$$689$$ 25.4558i 0.969790i
$$690$$ −4.75736 15.7279i −0.181110 0.598752i
$$691$$ 46.0000 1.74992 0.874961 0.484193i $$-0.160887\pi$$
0.874961 + 0.484193i $$0.160887\pi$$
$$692$$ 6.00000i 0.228086i
$$693$$ 0 0
$$694$$ 8.48528i 0.322097i
$$695$$ −8.48528 2.82843i −0.321865 0.107288i
$$696$$ 6.00000 + 8.48528i 0.227429 + 0.321634i
$$697$$ 0 0
$$698$$ 26.0000i 0.984115i
$$699$$ −12.0000 + 8.48528i −0.453882 + 0.320943i
$$700$$ 0 0
$$701$$ 43.8406i 1.65584i 0.560848 + 0.827919i $$0.310475\pi$$
−0.560848 + 0.827919i $$0.689525\pi$$
$$702$$ −21.2132 + 6.00000i −0.800641 + 0.226455i
$$703$$ 4.24264 + 18.0000i 0.160014 + 0.678883i
$$704$$ 2.82843i 0.106600i
$$705$$ 47.1838 14.2721i 1.77704 0.537518i
$$706$$ 8.48528i 0.319348i
$$707$$ 0 0
$$708$$ 8.48528 6.00000i 0.318896 0.225494i
$$709$$ −10.0000 −0.375558 −0.187779 0.982211i $$-0.560129\pi$$
−0.187779 + 0.982211i $$0.560129\pi$$
$$710$$ −8.48528 + 25.4558i −0.318447 + 0.955341i
$$711$$ 36.0000 + 12.7279i 1.35011 + 0.477334i
$$712$$ 12.0000i 0.449719i
$$713$$ 18.0000i 0.674105i
$$714$$ 0 0
$$715$$ −8.48528 + 25.4558i −0.317332 + 0.951995i
$$716$$ 12.0000 0.448461
$$717$$ −24.0416 34.0000i −0.897851 1.26975i
$$718$$ 7.07107 0.263890
$$719$$ 18.3848i 0.685636i 0.939402 + 0.342818i $$0.111381\pi$$
−0.939402 + 0.342818i $$0.888619\pi$$
$$720$$ −4.12132 + 5.29289i −0.153593 + 0.197254i
$$721$$ 0 0
$$722$$ −8.48528 17.0000i −0.315789 0.632674i
$$723$$ 8.48528 + 12.0000i 0.315571 + 0.446285i
$$724$$ 4.24264i 0.157676i
$$725$$ 24.0000 + 18.0000i 0.891338 + 0.668503i
$$726$$ −3.00000 4.24264i −0.111340 0.157459i
$$727$$ 12.0000i 0.445055i −0.974926 0.222528i $$-0.928569\pi$$
0.974926 0.222528i $$-0.0714308\pi$$
$$728$$ 0 0
$$729$$ −23.0000 + 14.1421i −0.851852 + 0.523783i
$$730$$ −12.7279 4.24264i −0.471082 0.157027i
$$731$$ 0 0
$$732$$ 14.1421 10.0000i 0.522708 0.369611i
$$733$$ 42.0000i 1.55131i 0.631160 + 0.775653i $$0.282579\pi$$
−0.631160 + 0.775653i $$0.717421\pi$$
$$734$$ −24.0000 −0.885856
$$735$$ 25.9497 7.84924i 0.957171 0.289524i
$$736$$ 4.24264i 0.156386i
$$737$$ 0 0
$$738$$ −16.9706 6.00000i −0.624695 0.220863i
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ 9.00000 + 3.00000i 0.330847 + 0.110282i
$$741$$ −24.0000 21.2132i −0.881662 0.779287i
$$742$$ 0 0
$$743$$ 24.0000i 0.880475i −0.897881 0.440237i $$-0.854894\pi$$
0.897881 0.440237i $$-0.145106\pi$$
$$744$$ 6.00000 4.24264i 0.219971 0.155543i
$$745$$ 1.00000 3.00000i 0.0366372 0.109911i
$$746$$ 21.2132i 0.776671i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ −6.63604 + 18.1924i −0.242314 + 0.664292i
$$751$$ 12.7279i 0.464448i −0.972662 0.232224i $$-0.925400\pi$$
0.972662 0.232224i $$-0.0746003\pi$$
$$752$$ 12.7279 0.464140
$$753$$ 5.65685 + 8.00000i 0.206147 + 0.291536i
$$754$$ 25.4558i 0.927047i
$$755$$ 3.00000 9.00000i 0.109181 0.327544i
$$756$$ 0 0
$$757$$ 42.0000i 1.52652i −0.646094 0.763258i $$-0.723599\pi$$
0.646094 0.763258i $$-0.276401\pi$$
$$758$$ 0 0
$$759$$ −12.0000 16.9706i −0.435572 0.615992i
$$760$$ −9.70711 0.878680i −0.352114 0.0318731i
$$761$$ 14.1421i 0.512652i 0.966590 + 0.256326i $$0.0825121\pi$$
−0.966590 + 0.256326i $$0.917488\pi$$
$$762$$ 12.7279 + 18.0000i 0.461084 + 0.652071i
$$763$$ 0 0
$$764$$ 15.5563i 0.562809i
$$765$$ 0 0
$$766$$ 12.0000 0.433578
$$767$$ 25.4558 0.919157
$$768$$ −1.41421 + 1.00000i −0.0510310 + 0.0360844i
$$769$$ 40.0000 1.44244 0.721218 0.692708i $$-0.243582\pi$$
0.721218 + 0.692708i $$0.243582\pi$$
$$770$$ 0 0
$$771$$ −18.0000 25.4558i −0.648254 0.916770i
$$772$$ 16.9706 0.610784
$$773$$ 6.00000i 0.215805i 0.994161 + 0.107903i $$0.0344134\pi$$
−0.994161 + 0.107903i $$0.965587\pi$$
$$774$$ 12.0000 33.9411i 0.431331 1.21999i
$$775$$ 12.7279 16.9706i 0.457200 0.609601i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 9.89949 0.354914
$$779$$ −6.00000 25.4558i −0.214972 0.912050i
$$780$$ −15.7279 + 4.75736i −0.563150 + 0.170341i
$$781$$ 33.9411i 1.21451i
$$782$$ 0 0
$$783$$ 8.48528 + 30.0000i 0.303239 + 1.07211i
$$784$$ 7.00000 0.250000
$$785$$ −12.7279 + 38.1838i −0.454279 + 1.36284i
$$786$$ 16.0000 11.3137i 0.570701 0.403547i
$$787$$ 25.4558 0.907403 0.453701 0.891154i $$-0.350103\pi$$
0.453701 + 0.891154i $$0.350103\pi$$
$$788$$ −12.7279 −0.453413
$$789$$ −30.0000 + 21.2132i −1.06803 + 0.755210i