# Properties

 Label 805.2.c.a.484.2 Level $805$ Weight $2$ Character 805.484 Analytic conductor $6.428$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$805 = 5 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 805.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.42795736271$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 484.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 805.484 Dual form 805.2.c.a.484.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{3} +2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000i q^{7} +2.00000 q^{9} +O(q^{10})$$ $$q+1.00000i q^{3} +2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000i q^{7} +2.00000 q^{9} -1.00000 q^{11} +2.00000i q^{12} +1.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +4.00000 q^{16} -1.00000i q^{17} -2.00000 q^{19} +(4.00000 - 2.00000i) q^{20} -1.00000 q^{21} +1.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +5.00000i q^{27} +2.00000i q^{28} -7.00000 q^{29} +4.00000 q^{31} -1.00000i q^{33} +(1.00000 + 2.00000i) q^{35} +4.00000 q^{36} -8.00000i q^{37} -1.00000 q^{39} -6.00000 q^{41} -8.00000i q^{43} -2.00000 q^{44} +(4.00000 - 2.00000i) q^{45} +7.00000i q^{47} +4.00000i q^{48} -1.00000 q^{49} +1.00000 q^{51} +2.00000i q^{52} +4.00000i q^{53} +(-2.00000 + 1.00000i) q^{55} -2.00000i q^{57} +4.00000 q^{59} +(2.00000 + 4.00000i) q^{60} -10.0000 q^{61} +2.00000i q^{63} +8.00000 q^{64} +(1.00000 + 2.00000i) q^{65} +14.0000i q^{67} -2.00000i q^{68} -1.00000 q^{69} +2.00000i q^{73} +(4.00000 + 3.00000i) q^{75} -4.00000 q^{76} -1.00000i q^{77} +15.0000 q^{79} +(8.00000 - 4.00000i) q^{80} +1.00000 q^{81} -8.00000i q^{83} -2.00000 q^{84} +(-1.00000 - 2.00000i) q^{85} -7.00000i q^{87} -6.00000 q^{89} -1.00000 q^{91} +2.00000i q^{92} +4.00000i q^{93} +(-4.00000 + 2.00000i) q^{95} +7.00000i q^{97} -2.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 4 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10})$$ 2 * q + 4 * q^4 + 4 * q^5 + 4 * q^9 $$2 q + 4 q^{4} + 4 q^{5} + 4 q^{9} - 2 q^{11} + 2 q^{15} + 8 q^{16} - 4 q^{19} + 8 q^{20} - 2 q^{21} + 6 q^{25} - 14 q^{29} + 8 q^{31} + 2 q^{35} + 8 q^{36} - 2 q^{39} - 12 q^{41} - 4 q^{44} + 8 q^{45} - 2 q^{49} + 2 q^{51} - 4 q^{55} + 8 q^{59} + 4 q^{60} - 20 q^{61} + 16 q^{64} + 2 q^{65} - 2 q^{69} + 8 q^{75} - 8 q^{76} + 30 q^{79} + 16 q^{80} + 2 q^{81} - 4 q^{84} - 2 q^{85} - 12 q^{89} - 2 q^{91} - 8 q^{95} - 4 q^{99}+O(q^{100})$$ 2 * q + 4 * q^4 + 4 * q^5 + 4 * q^9 - 2 * q^11 + 2 * q^15 + 8 * q^16 - 4 * q^19 + 8 * q^20 - 2 * q^21 + 6 * q^25 - 14 * q^29 + 8 * q^31 + 2 * q^35 + 8 * q^36 - 2 * q^39 - 12 * q^41 - 4 * q^44 + 8 * q^45 - 2 * q^49 + 2 * q^51 - 4 * q^55 + 8 * q^59 + 4 * q^60 - 20 * q^61 + 16 * q^64 + 2 * q^65 - 2 * q^69 + 8 * q^75 - 8 * q^76 + 30 * q^79 + 16 * q^80 + 2 * q^81 - 4 * q^84 - 2 * q^85 - 12 * q^89 - 2 * q^91 - 8 * q^95 - 4 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$$.

 $$n$$ $$162$$ $$281$$ $$346$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$3$$ 1.00000i 0.577350i 0.957427 + 0.288675i $$0.0932147\pi$$
−0.957427 + 0.288675i $$0.906785\pi$$
$$4$$ 2.00000 1.00000
$$5$$ 2.00000 1.00000i 0.894427 0.447214i
$$6$$ 0 0
$$7$$ 1.00000i 0.377964i
$$8$$ 0 0
$$9$$ 2.00000 0.666667
$$10$$ 0 0
$$11$$ −1.00000 −0.301511 −0.150756 0.988571i $$-0.548171\pi$$
−0.150756 + 0.988571i $$0.548171\pi$$
$$12$$ 2.00000i 0.577350i
$$13$$ 1.00000i 0.277350i 0.990338 + 0.138675i $$0.0442844\pi$$
−0.990338 + 0.138675i $$0.955716\pi$$
$$14$$ 0 0
$$15$$ 1.00000 + 2.00000i 0.258199 + 0.516398i
$$16$$ 4.00000 1.00000
$$17$$ 1.00000i 0.242536i −0.992620 0.121268i $$-0.961304\pi$$
0.992620 0.121268i $$-0.0386960\pi$$
$$18$$ 0 0
$$19$$ −2.00000 −0.458831 −0.229416 0.973329i $$-0.573682\pi$$
−0.229416 + 0.973329i $$0.573682\pi$$
$$20$$ 4.00000 2.00000i 0.894427 0.447214i
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ 1.00000i 0.208514i
$$24$$ 0 0
$$25$$ 3.00000 4.00000i 0.600000 0.800000i
$$26$$ 0 0
$$27$$ 5.00000i 0.962250i
$$28$$ 2.00000i 0.377964i
$$29$$ −7.00000 −1.29987 −0.649934 0.759991i $$-0.725203\pi$$
−0.649934 + 0.759991i $$0.725203\pi$$
$$30$$ 0 0
$$31$$ 4.00000 0.718421 0.359211 0.933257i $$-0.383046\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 0 0
$$33$$ 1.00000i 0.174078i
$$34$$ 0 0
$$35$$ 1.00000 + 2.00000i 0.169031 + 0.338062i
$$36$$ 4.00000 0.666667
$$37$$ 8.00000i 1.31519i −0.753371 0.657596i $$-0.771573\pi$$
0.753371 0.657596i $$-0.228427\pi$$
$$38$$ 0 0
$$39$$ −1.00000 −0.160128
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 8.00000i 1.21999i −0.792406 0.609994i $$-0.791172\pi$$
0.792406 0.609994i $$-0.208828\pi$$
$$44$$ −2.00000 −0.301511
$$45$$ 4.00000 2.00000i 0.596285 0.298142i
$$46$$ 0 0
$$47$$ 7.00000i 1.02105i 0.859861 + 0.510527i $$0.170550\pi$$
−0.859861 + 0.510527i $$0.829450\pi$$
$$48$$ 4.00000i 0.577350i
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ 1.00000 0.140028
$$52$$ 2.00000i 0.277350i
$$53$$ 4.00000i 0.549442i 0.961524 + 0.274721i $$0.0885855\pi$$
−0.961524 + 0.274721i $$0.911414\pi$$
$$54$$ 0 0
$$55$$ −2.00000 + 1.00000i −0.269680 + 0.134840i
$$56$$ 0 0
$$57$$ 2.00000i 0.264906i
$$58$$ 0 0
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 2.00000 + 4.00000i 0.258199 + 0.516398i
$$61$$ −10.0000 −1.28037 −0.640184 0.768221i $$-0.721142\pi$$
−0.640184 + 0.768221i $$0.721142\pi$$
$$62$$ 0 0
$$63$$ 2.00000i 0.251976i
$$64$$ 8.00000 1.00000
$$65$$ 1.00000 + 2.00000i 0.124035 + 0.248069i
$$66$$ 0 0
$$67$$ 14.0000i 1.71037i 0.518321 + 0.855186i $$0.326557\pi$$
−0.518321 + 0.855186i $$0.673443\pi$$
$$68$$ 2.00000i 0.242536i
$$69$$ −1.00000 −0.120386
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 2.00000i 0.234082i 0.993127 + 0.117041i $$0.0373409\pi$$
−0.993127 + 0.117041i $$0.962659\pi$$
$$74$$ 0 0
$$75$$ 4.00000 + 3.00000i 0.461880 + 0.346410i
$$76$$ −4.00000 −0.458831
$$77$$ 1.00000i 0.113961i
$$78$$ 0 0
$$79$$ 15.0000 1.68763 0.843816 0.536633i $$-0.180304\pi$$
0.843816 + 0.536633i $$0.180304\pi$$
$$80$$ 8.00000 4.00000i 0.894427 0.447214i
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 8.00000i 0.878114i −0.898459 0.439057i $$-0.855313\pi$$
0.898459 0.439057i $$-0.144687\pi$$
$$84$$ −2.00000 −0.218218
$$85$$ −1.00000 2.00000i −0.108465 0.216930i
$$86$$ 0 0
$$87$$ 7.00000i 0.750479i
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ −1.00000 −0.104828
$$92$$ 2.00000i 0.208514i
$$93$$ 4.00000i 0.414781i
$$94$$ 0 0
$$95$$ −4.00000 + 2.00000i −0.410391 + 0.205196i
$$96$$ 0 0
$$97$$ 7.00000i 0.710742i 0.934725 + 0.355371i $$0.115646\pi$$
−0.934725 + 0.355371i $$0.884354\pi$$
$$98$$ 0 0
$$99$$ −2.00000 −0.201008
$$100$$ 6.00000 8.00000i 0.600000 0.800000i
$$101$$ −4.00000 −0.398015 −0.199007 0.979998i $$-0.563772\pi$$
−0.199007 + 0.979998i $$0.563772\pi$$
$$102$$ 0 0
$$103$$ 7.00000i 0.689730i 0.938652 + 0.344865i $$0.112075\pi$$
−0.938652 + 0.344865i $$0.887925\pi$$
$$104$$ 0 0
$$105$$ −2.00000 + 1.00000i −0.195180 + 0.0975900i
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 10.0000i 0.962250i
$$109$$ 5.00000 0.478913 0.239457 0.970907i $$-0.423031\pi$$
0.239457 + 0.970907i $$0.423031\pi$$
$$110$$ 0 0
$$111$$ 8.00000 0.759326
$$112$$ 4.00000i 0.377964i
$$113$$ 18.0000i 1.69330i −0.532152 0.846649i $$-0.678617\pi$$
0.532152 0.846649i $$-0.321383\pi$$
$$114$$ 0 0
$$115$$ 1.00000 + 2.00000i 0.0932505 + 0.186501i
$$116$$ −14.0000 −1.29987
$$117$$ 2.00000i 0.184900i
$$118$$ 0 0
$$119$$ 1.00000 0.0916698
$$120$$ 0 0
$$121$$ −10.0000 −0.909091
$$122$$ 0 0
$$123$$ 6.00000i 0.541002i
$$124$$ 8.00000 0.718421
$$125$$ 2.00000 11.0000i 0.178885 0.983870i
$$126$$ 0 0
$$127$$ 2.00000i 0.177471i −0.996055 0.0887357i $$-0.971717\pi$$
0.996055 0.0887357i $$-0.0282826\pi$$
$$128$$ 0 0
$$129$$ 8.00000 0.704361
$$130$$ 0 0
$$131$$ −20.0000 −1.74741 −0.873704 0.486458i $$-0.838289\pi$$
−0.873704 + 0.486458i $$0.838289\pi$$
$$132$$ 2.00000i 0.174078i
$$133$$ 2.00000i 0.173422i
$$134$$ 0 0
$$135$$ 5.00000 + 10.0000i 0.430331 + 0.860663i
$$136$$ 0 0
$$137$$ 10.0000i 0.854358i −0.904167 0.427179i $$-0.859507\pi$$
0.904167 0.427179i $$-0.140493\pi$$
$$138$$ 0 0
$$139$$ −4.00000 −0.339276 −0.169638 0.985506i $$-0.554260\pi$$
−0.169638 + 0.985506i $$0.554260\pi$$
$$140$$ 2.00000 + 4.00000i 0.169031 + 0.338062i
$$141$$ −7.00000 −0.589506
$$142$$ 0 0
$$143$$ 1.00000i 0.0836242i
$$144$$ 8.00000 0.666667
$$145$$ −14.0000 + 7.00000i −1.16264 + 0.581318i
$$146$$ 0 0
$$147$$ 1.00000i 0.0824786i
$$148$$ 16.0000i 1.31519i
$$149$$ −14.0000 −1.14692 −0.573462 0.819232i $$-0.694400\pi$$
−0.573462 + 0.819232i $$0.694400\pi$$
$$150$$ 0 0
$$151$$ −1.00000 −0.0813788 −0.0406894 0.999172i $$-0.512955\pi$$
−0.0406894 + 0.999172i $$0.512955\pi$$
$$152$$ 0 0
$$153$$ 2.00000i 0.161690i
$$154$$ 0 0
$$155$$ 8.00000 4.00000i 0.642575 0.321288i
$$156$$ −2.00000 −0.160128
$$157$$ 18.0000i 1.43656i −0.695756 0.718278i $$-0.744931\pi$$
0.695756 0.718278i $$-0.255069\pi$$
$$158$$ 0 0
$$159$$ −4.00000 −0.317221
$$160$$ 0 0
$$161$$ −1.00000 −0.0788110
$$162$$ 0 0
$$163$$ 4.00000i 0.313304i −0.987654 0.156652i $$-0.949930\pi$$
0.987654 0.156652i $$-0.0500701\pi$$
$$164$$ −12.0000 −0.937043
$$165$$ −1.00000 2.00000i −0.0778499 0.155700i
$$166$$ 0 0
$$167$$ 3.00000i 0.232147i 0.993241 + 0.116073i $$0.0370308\pi$$
−0.993241 + 0.116073i $$0.962969\pi$$
$$168$$ 0 0
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ −4.00000 −0.305888
$$172$$ 16.0000i 1.21999i
$$173$$ 7.00000i 0.532200i 0.963945 + 0.266100i $$0.0857352\pi$$
−0.963945 + 0.266100i $$0.914265\pi$$
$$174$$ 0 0
$$175$$ 4.00000 + 3.00000i 0.302372 + 0.226779i
$$176$$ −4.00000 −0.301511
$$177$$ 4.00000i 0.300658i
$$178$$ 0 0
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 8.00000 4.00000i 0.596285 0.298142i
$$181$$ −16.0000 −1.18927 −0.594635 0.803996i $$-0.702704\pi$$
−0.594635 + 0.803996i $$0.702704\pi$$
$$182$$ 0 0
$$183$$ 10.0000i 0.739221i
$$184$$ 0 0
$$185$$ −8.00000 16.0000i −0.588172 1.17634i
$$186$$ 0 0
$$187$$ 1.00000i 0.0731272i
$$188$$ 14.0000i 1.02105i
$$189$$ −5.00000 −0.363696
$$190$$ 0 0
$$191$$ −25.0000 −1.80894 −0.904468 0.426541i $$-0.859732\pi$$
−0.904468 + 0.426541i $$0.859732\pi$$
$$192$$ 8.00000i 0.577350i
$$193$$ 14.0000i 1.00774i −0.863779 0.503871i $$-0.831909\pi$$
0.863779 0.503871i $$-0.168091\pi$$
$$194$$ 0 0
$$195$$ −2.00000 + 1.00000i −0.143223 + 0.0716115i
$$196$$ −2.00000 −0.142857
$$197$$ 18.0000i 1.28245i −0.767354 0.641223i $$-0.778427\pi$$
0.767354 0.641223i $$-0.221573\pi$$
$$198$$ 0 0
$$199$$ −12.0000 −0.850657 −0.425329 0.905039i $$-0.639842\pi$$
−0.425329 + 0.905039i $$0.639842\pi$$
$$200$$ 0 0
$$201$$ −14.0000 −0.987484
$$202$$ 0 0
$$203$$ 7.00000i 0.491304i
$$204$$ 2.00000 0.140028
$$205$$ −12.0000 + 6.00000i −0.838116 + 0.419058i
$$206$$ 0 0
$$207$$ 2.00000i 0.139010i
$$208$$ 4.00000i 0.277350i
$$209$$ 2.00000 0.138343
$$210$$ 0 0
$$211$$ −5.00000 −0.344214 −0.172107 0.985078i $$-0.555058\pi$$
−0.172107 + 0.985078i $$0.555058\pi$$
$$212$$ 8.00000i 0.549442i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −8.00000 16.0000i −0.545595 1.09119i
$$216$$ 0 0
$$217$$ 4.00000i 0.271538i
$$218$$ 0 0
$$219$$ −2.00000 −0.135147
$$220$$ −4.00000 + 2.00000i −0.269680 + 0.134840i
$$221$$ 1.00000 0.0672673
$$222$$ 0 0
$$223$$ 25.0000i 1.67412i 0.547108 + 0.837062i $$0.315729\pi$$
−0.547108 + 0.837062i $$0.684271\pi$$
$$224$$ 0 0
$$225$$ 6.00000 8.00000i 0.400000 0.533333i
$$226$$ 0 0
$$227$$ 15.0000i 0.995585i −0.867296 0.497792i $$-0.834144\pi$$
0.867296 0.497792i $$-0.165856\pi$$
$$228$$ 4.00000i 0.264906i
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 0 0
$$231$$ 1.00000 0.0657952
$$232$$ 0 0
$$233$$ 10.0000i 0.655122i 0.944830 + 0.327561i $$0.106227\pi$$
−0.944830 + 0.327561i $$0.893773\pi$$
$$234$$ 0 0
$$235$$ 7.00000 + 14.0000i 0.456630 + 0.913259i
$$236$$ 8.00000 0.520756
$$237$$ 15.0000i 0.974355i
$$238$$ 0 0
$$239$$ 9.00000 0.582162 0.291081 0.956698i $$-0.405985\pi$$
0.291081 + 0.956698i $$0.405985\pi$$
$$240$$ 4.00000 + 8.00000i 0.258199 + 0.516398i
$$241$$ 10.0000 0.644157 0.322078 0.946713i $$-0.395619\pi$$
0.322078 + 0.946713i $$0.395619\pi$$
$$242$$ 0 0
$$243$$ 16.0000i 1.02640i
$$244$$ −20.0000 −1.28037
$$245$$ −2.00000 + 1.00000i −0.127775 + 0.0638877i
$$246$$ 0 0
$$247$$ 2.00000i 0.127257i
$$248$$ 0 0
$$249$$ 8.00000 0.506979
$$250$$ 0 0
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 4.00000i 0.251976i
$$253$$ 1.00000i 0.0628695i
$$254$$ 0 0
$$255$$ 2.00000 1.00000i 0.125245 0.0626224i
$$256$$ 16.0000 1.00000
$$257$$ 18.0000i 1.12281i 0.827541 + 0.561405i $$0.189739\pi$$
−0.827541 + 0.561405i $$0.810261\pi$$
$$258$$ 0 0
$$259$$ 8.00000 0.497096
$$260$$ 2.00000 + 4.00000i 0.124035 + 0.248069i
$$261$$ −14.0000 −0.866578
$$262$$ 0 0
$$263$$ 2.00000i 0.123325i 0.998097 + 0.0616626i $$0.0196403\pi$$
−0.998097 + 0.0616626i $$0.980360\pi$$
$$264$$ 0 0
$$265$$ 4.00000 + 8.00000i 0.245718 + 0.491436i
$$266$$ 0 0
$$267$$ 6.00000i 0.367194i
$$268$$ 28.0000i 1.71037i
$$269$$ 6.00000 0.365826 0.182913 0.983129i $$-0.441447\pi$$
0.182913 + 0.983129i $$0.441447\pi$$
$$270$$ 0 0
$$271$$ 10.0000 0.607457 0.303728 0.952759i $$-0.401768\pi$$
0.303728 + 0.952759i $$0.401768\pi$$
$$272$$ 4.00000i 0.242536i
$$273$$ 1.00000i 0.0605228i
$$274$$ 0 0
$$275$$ −3.00000 + 4.00000i −0.180907 + 0.241209i
$$276$$ −2.00000 −0.120386
$$277$$ 24.0000i 1.44202i −0.692925 0.721010i $$-0.743678\pi$$
0.692925 0.721010i $$-0.256322\pi$$
$$278$$ 0 0
$$279$$ 8.00000 0.478947
$$280$$ 0 0
$$281$$ 9.00000 0.536895 0.268447 0.963294i $$-0.413489\pi$$
0.268447 + 0.963294i $$0.413489\pi$$
$$282$$ 0 0
$$283$$ 17.0000i 1.01055i 0.862960 + 0.505273i $$0.168608\pi$$
−0.862960 + 0.505273i $$0.831392\pi$$
$$284$$ 0 0
$$285$$ −2.00000 4.00000i −0.118470 0.236940i
$$286$$ 0 0
$$287$$ 6.00000i 0.354169i
$$288$$ 0 0
$$289$$ 16.0000 0.941176
$$290$$ 0 0
$$291$$ −7.00000 −0.410347
$$292$$ 4.00000i 0.234082i
$$293$$ 27.0000i 1.57736i −0.614806 0.788678i $$-0.710766\pi$$
0.614806 0.788678i $$-0.289234\pi$$
$$294$$ 0 0
$$295$$ 8.00000 4.00000i 0.465778 0.232889i
$$296$$ 0 0
$$297$$ 5.00000i 0.290129i
$$298$$ 0 0
$$299$$ −1.00000 −0.0578315
$$300$$ 8.00000 + 6.00000i 0.461880 + 0.346410i
$$301$$ 8.00000 0.461112
$$302$$ 0 0
$$303$$ 4.00000i 0.229794i
$$304$$ −8.00000 −0.458831
$$305$$ −20.0000 + 10.0000i −1.14520 + 0.572598i
$$306$$ 0 0
$$307$$ 9.00000i 0.513657i 0.966457 + 0.256829i $$0.0826776\pi$$
−0.966457 + 0.256829i $$0.917322\pi$$
$$308$$ 2.00000i 0.113961i
$$309$$ −7.00000 −0.398216
$$310$$ 0 0
$$311$$ −18.0000 −1.02069 −0.510343 0.859971i $$-0.670482\pi$$
−0.510343 + 0.859971i $$0.670482\pi$$
$$312$$ 0 0
$$313$$ 9.00000i 0.508710i −0.967111 0.254355i $$-0.918137\pi$$
0.967111 0.254355i $$-0.0818632\pi$$
$$314$$ 0 0
$$315$$ 2.00000 + 4.00000i 0.112687 + 0.225374i
$$316$$ 30.0000 1.68763
$$317$$ 6.00000i 0.336994i 0.985702 + 0.168497i $$0.0538913\pi$$
−0.985702 + 0.168497i $$0.946109\pi$$
$$318$$ 0 0
$$319$$ 7.00000 0.391925
$$320$$ 16.0000 8.00000i 0.894427 0.447214i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 2.00000i 0.111283i
$$324$$ 2.00000 0.111111
$$325$$ 4.00000 + 3.00000i 0.221880 + 0.166410i
$$326$$ 0 0
$$327$$ 5.00000i 0.276501i
$$328$$ 0 0
$$329$$ −7.00000 −0.385922
$$330$$ 0 0
$$331$$ −4.00000 −0.219860 −0.109930 0.993939i $$-0.535063\pi$$
−0.109930 + 0.993939i $$0.535063\pi$$
$$332$$ 16.0000i 0.878114i
$$333$$ 16.0000i 0.876795i
$$334$$ 0 0
$$335$$ 14.0000 + 28.0000i 0.764902 + 1.52980i
$$336$$ −4.00000 −0.218218
$$337$$ 10.0000i 0.544735i 0.962193 + 0.272367i $$0.0878066\pi$$
−0.962193 + 0.272367i $$0.912193\pi$$
$$338$$ 0 0
$$339$$ 18.0000 0.977626
$$340$$ −2.00000 4.00000i −0.108465 0.216930i
$$341$$ −4.00000 −0.216612
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 0 0
$$345$$ −2.00000 + 1.00000i −0.107676 + 0.0538382i
$$346$$ 0 0
$$347$$ 8.00000i 0.429463i −0.976673 0.214731i $$-0.931112\pi$$
0.976673 0.214731i $$-0.0688876\pi$$
$$348$$ 14.0000i 0.750479i
$$349$$ 10.0000 0.535288 0.267644 0.963518i $$-0.413755\pi$$
0.267644 + 0.963518i $$0.413755\pi$$
$$350$$ 0 0
$$351$$ −5.00000 −0.266880
$$352$$ 0 0
$$353$$ 9.00000i 0.479022i −0.970894 0.239511i $$-0.923013\pi$$
0.970894 0.239511i $$-0.0769871\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −12.0000 −0.635999
$$357$$ 1.00000i 0.0529256i
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 0 0
$$363$$ 10.0000i 0.524864i
$$364$$ −2.00000 −0.104828
$$365$$ 2.00000 + 4.00000i 0.104685 + 0.209370i
$$366$$ 0 0
$$367$$ 23.0000i 1.20059i −0.799779 0.600295i $$-0.795050\pi$$
0.799779 0.600295i $$-0.204950\pi$$
$$368$$ 4.00000i 0.208514i
$$369$$ −12.0000 −0.624695
$$370$$ 0 0
$$371$$ −4.00000 −0.207670
$$372$$ 8.00000i 0.414781i
$$373$$ 14.0000i 0.724893i 0.932005 + 0.362446i $$0.118058\pi$$
−0.932005 + 0.362446i $$0.881942\pi$$
$$374$$ 0 0
$$375$$ 11.0000 + 2.00000i 0.568038 + 0.103280i
$$376$$ 0 0
$$377$$ 7.00000i 0.360518i
$$378$$ 0 0
$$379$$ 28.0000 1.43826 0.719132 0.694874i $$-0.244540\pi$$
0.719132 + 0.694874i $$0.244540\pi$$
$$380$$ −8.00000 + 4.00000i −0.410391 + 0.205196i
$$381$$ 2.00000 0.102463
$$382$$ 0 0
$$383$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$384$$ 0 0
$$385$$ −1.00000 2.00000i −0.0509647 0.101929i
$$386$$ 0 0
$$387$$ 16.0000i 0.813326i
$$388$$ 14.0000i 0.710742i
$$389$$ 29.0000 1.47036 0.735179 0.677873i $$-0.237098\pi$$
0.735179 + 0.677873i $$0.237098\pi$$
$$390$$ 0 0
$$391$$ 1.00000 0.0505722
$$392$$ 0 0
$$393$$ 20.0000i 1.00887i
$$394$$ 0 0
$$395$$ 30.0000 15.0000i 1.50946 0.754732i
$$396$$ −4.00000 −0.201008
$$397$$ 33.0000i 1.65622i 0.560564 + 0.828111i $$0.310584\pi$$
−0.560564 + 0.828111i $$0.689416\pi$$
$$398$$ 0 0
$$399$$ 2.00000 0.100125
$$400$$ 12.0000 16.0000i 0.600000 0.800000i
$$401$$ −5.00000 −0.249688 −0.124844 0.992176i $$-0.539843\pi$$
−0.124844 + 0.992176i $$0.539843\pi$$
$$402$$ 0 0
$$403$$ 4.00000i 0.199254i
$$404$$ −8.00000 −0.398015
$$405$$ 2.00000 1.00000i 0.0993808 0.0496904i
$$406$$ 0 0
$$407$$ 8.00000i 0.396545i
$$408$$ 0 0
$$409$$ −4.00000 −0.197787 −0.0988936 0.995098i $$-0.531530\pi$$
−0.0988936 + 0.995098i $$0.531530\pi$$
$$410$$ 0 0
$$411$$ 10.0000 0.493264
$$412$$ 14.0000i 0.689730i
$$413$$ 4.00000i 0.196827i
$$414$$ 0 0
$$415$$ −8.00000 16.0000i −0.392705 0.785409i
$$416$$ 0 0
$$417$$ 4.00000i 0.195881i
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ −4.00000 + 2.00000i −0.195180 + 0.0975900i
$$421$$ −5.00000 −0.243685 −0.121843 0.992549i $$-0.538880\pi$$
−0.121843 + 0.992549i $$0.538880\pi$$
$$422$$ 0 0
$$423$$ 14.0000i 0.680703i
$$424$$ 0 0
$$425$$ −4.00000 3.00000i −0.194029 0.145521i
$$426$$ 0 0
$$427$$ 10.0000i 0.483934i
$$428$$ 0 0
$$429$$ 1.00000 0.0482805
$$430$$ 0 0
$$431$$ 11.0000 0.529851 0.264926 0.964269i $$-0.414653\pi$$
0.264926 + 0.964269i $$0.414653\pi$$
$$432$$ 20.0000i 0.962250i
$$433$$ 30.0000i 1.44171i 0.693087 + 0.720854i $$0.256250\pi$$
−0.693087 + 0.720854i $$0.743750\pi$$
$$434$$ 0 0
$$435$$ −7.00000 14.0000i −0.335624 0.671249i
$$436$$ 10.0000 0.478913
$$437$$ 2.00000i 0.0956730i
$$438$$ 0 0
$$439$$ 34.0000 1.62273 0.811366 0.584539i $$-0.198725\pi$$
0.811366 + 0.584539i $$0.198725\pi$$
$$440$$ 0 0
$$441$$ −2.00000 −0.0952381
$$442$$ 0 0
$$443$$ 40.0000i 1.90046i 0.311553 + 0.950229i $$0.399151\pi$$
−0.311553 + 0.950229i $$0.600849\pi$$
$$444$$ 16.0000 0.759326
$$445$$ −12.0000 + 6.00000i −0.568855 + 0.284427i
$$446$$ 0 0
$$447$$ 14.0000i 0.662177i
$$448$$ 8.00000i 0.377964i
$$449$$ −15.0000 −0.707894 −0.353947 0.935266i $$-0.615161\pi$$
−0.353947 + 0.935266i $$0.615161\pi$$
$$450$$ 0 0
$$451$$ 6.00000 0.282529
$$452$$ 36.0000i 1.69330i
$$453$$ 1.00000i 0.0469841i
$$454$$ 0 0
$$455$$ −2.00000 + 1.00000i −0.0937614 + 0.0468807i
$$456$$ 0 0
$$457$$ 2.00000i 0.0935561i −0.998905 0.0467780i $$-0.985105\pi$$
0.998905 0.0467780i $$-0.0148953\pi$$
$$458$$ 0 0
$$459$$ 5.00000 0.233380
$$460$$ 2.00000 + 4.00000i 0.0932505 + 0.186501i
$$461$$ 28.0000 1.30409 0.652045 0.758180i $$-0.273911\pi$$
0.652045 + 0.758180i $$0.273911\pi$$
$$462$$ 0 0
$$463$$ 30.0000i 1.39422i −0.716965 0.697109i $$-0.754469\pi$$
0.716965 0.697109i $$-0.245531\pi$$
$$464$$ −28.0000 −1.29987
$$465$$ 4.00000 + 8.00000i 0.185496 + 0.370991i
$$466$$ 0 0
$$467$$ 27.0000i 1.24941i 0.780860 + 0.624705i $$0.214781\pi$$
−0.780860 + 0.624705i $$0.785219\pi$$
$$468$$ 4.00000i 0.184900i
$$469$$ −14.0000 −0.646460
$$470$$ 0 0
$$471$$ 18.0000 0.829396
$$472$$ 0 0
$$473$$ 8.00000i 0.367840i
$$474$$ 0 0
$$475$$ −6.00000 + 8.00000i −0.275299 + 0.367065i
$$476$$ 2.00000 0.0916698
$$477$$ 8.00000i 0.366295i
$$478$$ 0 0
$$479$$ 10.0000 0.456912 0.228456 0.973554i $$-0.426632\pi$$
0.228456 + 0.973554i $$0.426632\pi$$
$$480$$ 0 0
$$481$$ 8.00000 0.364769
$$482$$ 0 0
$$483$$ 1.00000i 0.0455016i
$$484$$ −20.0000 −0.909091
$$485$$ 7.00000 + 14.0000i 0.317854 + 0.635707i
$$486$$ 0 0
$$487$$ 14.0000i 0.634401i 0.948359 + 0.317200i $$0.102743\pi$$
−0.948359 + 0.317200i $$0.897257\pi$$
$$488$$ 0 0
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ 15.0000 0.676941 0.338470 0.940977i $$-0.390091\pi$$
0.338470 + 0.940977i $$0.390091\pi$$
$$492$$ 12.0000i 0.541002i
$$493$$ 7.00000i 0.315264i
$$494$$ 0 0
$$495$$ −4.00000 + 2.00000i −0.179787 + 0.0898933i
$$496$$ 16.0000 0.718421
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −25.0000 −1.11915 −0.559577 0.828778i $$-0.689036\pi$$
−0.559577 + 0.828778i $$0.689036\pi$$
$$500$$ 4.00000 22.0000i 0.178885 0.983870i
$$501$$ −3.00000 −0.134030
$$502$$ 0 0
$$503$$ 5.00000i 0.222939i 0.993768 + 0.111469i $$0.0355557\pi$$
−0.993768 + 0.111469i $$0.964444\pi$$
$$504$$ 0 0
$$505$$ −8.00000 + 4.00000i −0.355995 + 0.177998i
$$506$$ 0 0
$$507$$ 12.0000i 0.532939i
$$508$$ 4.00000i 0.177471i
$$509$$ 8.00000 0.354594 0.177297 0.984157i $$-0.443265\pi$$
0.177297 + 0.984157i $$0.443265\pi$$
$$510$$ 0 0
$$511$$ −2.00000 −0.0884748
$$512$$ 0 0
$$513$$ 10.0000i 0.441511i
$$514$$ 0 0
$$515$$ 7.00000 + 14.0000i 0.308457 + 0.616914i
$$516$$ 16.0000 0.704361
$$517$$ 7.00000i 0.307860i
$$518$$ 0 0
$$519$$ −7.00000 −0.307266
$$520$$ 0 0
$$521$$ 12.0000 0.525730 0.262865 0.964833i $$-0.415333\pi$$
0.262865 + 0.964833i $$0.415333\pi$$
$$522$$ 0 0
$$523$$ 24.0000i 1.04945i −0.851273 0.524723i $$-0.824169\pi$$
0.851273 0.524723i $$-0.175831\pi$$
$$524$$ −40.0000 −1.74741
$$525$$ −3.00000 + 4.00000i −0.130931 + 0.174574i
$$526$$ 0 0
$$527$$ 4.00000i 0.174243i
$$528$$ 4.00000i 0.174078i
$$529$$ −1.00000 −0.0434783
$$530$$ 0 0
$$531$$ 8.00000 0.347170
$$532$$ 4.00000i 0.173422i
$$533$$ 6.00000i 0.259889i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 4.00000i 0.172613i
$$538$$ 0 0
$$539$$ 1.00000 0.0430730
$$540$$ 10.0000 + 20.0000i 0.430331 + 0.860663i
$$541$$ 43.0000 1.84871 0.924357 0.381528i $$-0.124602\pi$$
0.924357 + 0.381528i $$0.124602\pi$$
$$542$$ 0 0
$$543$$ 16.0000i 0.686626i
$$544$$ 0 0
$$545$$ 10.0000 5.00000i 0.428353 0.214176i
$$546$$ 0 0
$$547$$ 38.0000i 1.62476i 0.583127 + 0.812381i $$0.301829\pi$$
−0.583127 + 0.812381i $$0.698171\pi$$
$$548$$ 20.0000i 0.854358i
$$549$$ −20.0000 −0.853579
$$550$$ 0 0
$$551$$ 14.0000 0.596420
$$552$$ 0 0
$$553$$ 15.0000i 0.637865i
$$554$$ 0 0
$$555$$ 16.0000 8.00000i 0.679162 0.339581i
$$556$$ −8.00000 −0.339276
$$557$$ 42.0000i 1.77960i 0.456354 + 0.889799i $$0.349155\pi$$
−0.456354 + 0.889799i $$0.650845\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 4.00000 + 8.00000i 0.169031 + 0.338062i
$$561$$ −1.00000 −0.0422200
$$562$$ 0 0
$$563$$ 4.00000i 0.168580i −0.996441 0.0842900i $$-0.973138\pi$$
0.996441 0.0842900i $$-0.0268622\pi$$
$$564$$ −14.0000 −0.589506
$$565$$ −18.0000 36.0000i −0.757266 1.51453i
$$566$$ 0 0
$$567$$ 1.00000i 0.0419961i
$$568$$ 0 0
$$569$$ 10.0000 0.419222 0.209611 0.977785i $$-0.432780\pi$$
0.209611 + 0.977785i $$0.432780\pi$$
$$570$$ 0 0
$$571$$ −36.0000 −1.50655 −0.753277 0.657704i $$-0.771528\pi$$
−0.753277 + 0.657704i $$0.771528\pi$$
$$572$$ 2.00000i 0.0836242i
$$573$$ 25.0000i 1.04439i
$$574$$ 0 0
$$575$$ 4.00000 + 3.00000i 0.166812 + 0.125109i
$$576$$ 16.0000 0.666667
$$577$$ 3.00000i 0.124892i 0.998048 + 0.0624458i $$0.0198901\pi$$
−0.998048 + 0.0624458i $$0.980110\pi$$
$$578$$ 0 0
$$579$$ 14.0000 0.581820
$$580$$ −28.0000 + 14.0000i −1.16264 + 0.581318i
$$581$$ 8.00000 0.331896
$$582$$ 0 0
$$583$$ 4.00000i 0.165663i
$$584$$ 0 0
$$585$$ 2.00000 + 4.00000i 0.0826898 + 0.165380i
$$586$$ 0 0
$$587$$ 28.0000i 1.15568i 0.816149 + 0.577842i $$0.196105\pi$$
−0.816149 + 0.577842i $$0.803895\pi$$
$$588$$ 2.00000i 0.0824786i
$$589$$ −8.00000 −0.329634
$$590$$ 0 0
$$591$$ 18.0000 0.740421
$$592$$ 32.0000i 1.31519i
$$593$$ 37.0000i 1.51941i 0.650269 + 0.759704i $$0.274656\pi$$
−0.650269 + 0.759704i $$0.725344\pi$$
$$594$$ 0 0
$$595$$ 2.00000 1.00000i 0.0819920 0.0409960i
$$596$$ −28.0000 −1.14692
$$597$$ 12.0000i 0.491127i
$$598$$ 0 0
$$599$$ −25.0000 −1.02147 −0.510736 0.859738i $$-0.670627\pi$$
−0.510736 + 0.859738i $$0.670627\pi$$
$$600$$ 0 0
$$601$$ 10.0000 0.407909 0.203954 0.978980i $$-0.434621\pi$$
0.203954 + 0.978980i $$0.434621\pi$$
$$602$$ 0 0
$$603$$ 28.0000i 1.14025i
$$604$$ −2.00000 −0.0813788
$$605$$ −20.0000 + 10.0000i −0.813116 + 0.406558i
$$606$$ 0 0
$$607$$ 25.0000i 1.01472i 0.861735 + 0.507359i $$0.169378\pi$$
−0.861735 + 0.507359i $$0.830622\pi$$
$$608$$ 0 0
$$609$$ 7.00000 0.283654
$$610$$ 0 0
$$611$$ −7.00000 −0.283190
$$612$$ 4.00000i 0.161690i
$$613$$ 46.0000i 1.85792i 0.370177 + 0.928961i $$0.379297\pi$$
−0.370177 + 0.928961i $$0.620703\pi$$
$$614$$ 0 0
$$615$$ −6.00000 12.0000i −0.241943 0.483887i
$$616$$ 0 0
$$617$$ 28.0000i 1.12724i −0.826035 0.563619i $$-0.809409\pi$$
0.826035 0.563619i $$-0.190591\pi$$
$$618$$ 0 0
$$619$$ −22.0000 −0.884255 −0.442127 0.896952i $$-0.645776\pi$$
−0.442127 + 0.896952i $$0.645776\pi$$
$$620$$ 16.0000 8.00000i 0.642575 0.321288i
$$621$$ −5.00000 −0.200643
$$622$$ 0 0
$$623$$ 6.00000i 0.240385i
$$624$$ −4.00000 −0.160128
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ 0 0
$$627$$ 2.00000i 0.0798723i
$$628$$ 36.0000i 1.43656i
$$629$$ −8.00000 −0.318981
$$630$$ 0 0
$$631$$ 7.00000 0.278666 0.139333 0.990246i $$-0.455504\pi$$
0.139333 + 0.990246i $$0.455504\pi$$
$$632$$ 0 0
$$633$$ 5.00000i 0.198732i
$$634$$ 0 0
$$635$$ −2.00000 4.00000i −0.0793676 0.158735i
$$636$$ −8.00000 −0.317221
$$637$$ 1.00000i 0.0396214i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −18.0000 −0.710957 −0.355479 0.934684i $$-0.615682\pi$$
−0.355479 + 0.934684i $$0.615682\pi$$
$$642$$ 0 0
$$643$$ 49.0000i 1.93237i −0.257847 0.966186i $$-0.583013\pi$$
0.257847 0.966186i $$-0.416987\pi$$
$$644$$ −2.00000 −0.0788110
$$645$$ 16.0000 8.00000i 0.629999 0.315000i
$$646$$ 0 0
$$647$$ 48.0000i 1.88707i −0.331266 0.943537i $$-0.607476\pi$$
0.331266 0.943537i $$-0.392524\pi$$
$$648$$ 0 0
$$649$$ −4.00000 −0.157014
$$650$$ 0 0
$$651$$ −4.00000 −0.156772
$$652$$ 8.00000i 0.313304i
$$653$$ 6.00000i 0.234798i 0.993085 + 0.117399i $$0.0374557\pi$$
−0.993085 + 0.117399i $$0.962544\pi$$
$$654$$ 0 0
$$655$$ −40.0000 + 20.0000i −1.56293 + 0.781465i
$$656$$ −24.0000 −0.937043
$$657$$ 4.00000i 0.156055i
$$658$$ 0 0
$$659$$ 41.0000 1.59713 0.798567 0.601906i $$-0.205592\pi$$
0.798567 + 0.601906i $$0.205592\pi$$
$$660$$ −2.00000 4.00000i −0.0778499 0.155700i
$$661$$ 20.0000 0.777910 0.388955 0.921257i $$-0.372836\pi$$
0.388955 + 0.921257i $$0.372836\pi$$
$$662$$ 0 0
$$663$$ 1.00000i 0.0388368i
$$664$$ 0 0
$$665$$ −2.00000 4.00000i −0.0775567 0.155113i
$$666$$ 0 0
$$667$$ 7.00000i 0.271041i
$$668$$ 6.00000i 0.232147i
$$669$$ −25.0000 −0.966556
$$670$$ 0 0
$$671$$ 10.0000 0.386046
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 20.0000 + 15.0000i 0.769800 + 0.577350i
$$676$$ 24.0000 0.923077
$$677$$ 21.0000i 0.807096i 0.914959 + 0.403548i $$0.132223\pi$$
−0.914959 + 0.403548i $$0.867777\pi$$
$$678$$ 0 0
$$679$$ −7.00000 −0.268635
$$680$$ 0 0
$$681$$ 15.0000 0.574801
$$682$$ 0 0
$$683$$ 12.0000i 0.459167i 0.973289 + 0.229584i $$0.0737364\pi$$
−0.973289 + 0.229584i $$0.926264\pi$$
$$684$$ −8.00000 −0.305888
$$685$$ −10.0000 20.0000i −0.382080 0.764161i
$$686$$ 0 0
$$687$$ 14.0000i 0.534133i
$$688$$ 32.0000i 1.21999i
$$689$$ −4.00000 −0.152388
$$690$$ 0 0
$$691$$ 18.0000 0.684752 0.342376 0.939563i $$-0.388768\pi$$
0.342376 + 0.939563i $$0.388768\pi$$
$$692$$ 14.0000i 0.532200i
$$693$$ 2.00000i 0.0759737i
$$694$$ 0 0
$$695$$ −8.00000 + 4.00000i −0.303457 + 0.151729i
$$696$$ 0 0
$$697$$ 6.00000i 0.227266i
$$698$$ 0 0
$$699$$ −10.0000 −0.378235
$$700$$ 8.00000 + 6.00000i 0.302372 + 0.226779i
$$701$$ −15.0000 −0.566542 −0.283271 0.959040i $$-0.591420\pi$$
−0.283271 + 0.959040i $$0.591420\pi$$
$$702$$ 0 0
$$703$$ 16.0000i 0.603451i
$$704$$ −8.00000 −0.301511
$$705$$ −14.0000 + 7.00000i −0.527271 + 0.263635i
$$706$$ 0 0
$$707$$ 4.00000i 0.150435i
$$708$$ 8.00000i 0.300658i
$$709$$ 19.0000 0.713560 0.356780 0.934188i $$-0.383875\pi$$
0.356780 + 0.934188i $$0.383875\pi$$
$$710$$ 0 0
$$711$$ 30.0000 1.12509
$$712$$ 0 0
$$713$$ 4.00000i 0.149801i
$$714$$ 0 0
$$715$$ −1.00000 2.00000i −0.0373979 0.0747958i
$$716$$ 8.00000 0.298974
$$717$$ 9.00000i 0.336111i
$$718$$ 0 0
$$719$$ −30.0000 −1.11881 −0.559406 0.828894i $$-0.688971\pi$$
−0.559406 + 0.828894i $$0.688971\pi$$
$$720$$ 16.0000 8.00000i 0.596285 0.298142i
$$721$$ −7.00000 −0.260694
$$722$$ 0 0
$$723$$ 10.0000i 0.371904i
$$724$$ −32.0000 −1.18927
$$725$$ −21.0000 + 28.0000i −0.779920 + 1.03989i
$$726$$ 0 0
$$727$$ 8.00000i 0.296704i 0.988935 + 0.148352i $$0.0473968\pi$$
−0.988935 + 0.148352i $$0.952603\pi$$
$$728$$ 0 0
$$729$$ −13.0000 −0.481481
$$730$$ 0 0
$$731$$ −8.00000 −0.295891
$$732$$ 20.0000i 0.739221i
$$733$$ 3.00000i 0.110808i 0.998464 + 0.0554038i $$0.0176446\pi$$
−0.998464 + 0.0554038i $$0.982355\pi$$
$$734$$ 0 0
$$735$$ −1.00000 2.00000i −0.0368856 0.0737711i
$$736$$ 0 0
$$737$$ 14.0000i 0.515697i
$$738$$ 0 0
$$739$$ 43.0000 1.58178 0.790890 0.611958i $$-0.209618\pi$$
0.790890 + 0.611958i $$0.209618\pi$$
$$740$$ −16.0000 32.0000i −0.588172 1.17634i
$$741$$ 2.00000 0.0734718
$$742$$ 0 0
$$743$$ 24.0000i 0.880475i −0.897881 0.440237i $$-0.854894\pi$$
0.897881 0.440237i $$-0.145106\pi$$
$$744$$ 0 0
$$745$$ −28.0000 + 14.0000i −1.02584 + 0.512920i
$$746$$ 0 0
$$747$$ 16.0000i 0.585409i
$$748$$ 2.00000i 0.0731272i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −7.00000 −0.255434 −0.127717 0.991811i $$-0.540765\pi$$
−0.127717 + 0.991811i $$0.540765\pi$$
$$752$$ 28.0000i 1.02105i
$$753$$ 12.0000i 0.437304i
$$754$$ 0 0
$$755$$ −2.00000 + 1.00000i −0.0727875 + 0.0363937i
$$756$$ −10.0000 −0.363696
$$757$$ 8.00000i 0.290765i 0.989376 + 0.145382i $$0.0464413\pi$$
−0.989376 + 0.145382i $$0.953559\pi$$
$$758$$ 0 0
$$759$$ 1.00000 0.0362977
$$760$$ 0 0
$$761$$ −28.0000 −1.01500 −0.507500 0.861652i $$-0.669430\pi$$
−0.507500 + 0.861652i $$0.669430\pi$$
$$762$$ 0 0
$$763$$ 5.00000i 0.181012i
$$764$$ −50.0000 −1.80894
$$765$$ −2.00000 4.00000i −0.0723102 0.144620i
$$766$$ 0 0
$$767$$ 4.00000i 0.144432i
$$768$$ 16.0000i 0.577350i
$$769$$ 2.00000 0.0721218 0.0360609 0.999350i $$-0.488519\pi$$
0.0360609 + 0.999350i $$0.488519\pi$$
$$770$$ 0 0
$$771$$ −18.0000 −0.648254
$$772$$ 28.0000i 1.00774i
$$773$$ 49.0000i 1.76241i −0.472737 0.881204i $$-0.656734\pi$$
0.472737 0.881204i $$-0.343266\pi$$
$$774$$ 0 0
$$775$$ 12.0000 16.0000i 0.431053 0.574737i
$$776$$ 0 0
$$777$$ 8.00000i 0.286998i
$$778$$ 0 0
$$779$$ 12.0000 0.429945
$$780$$ −4.00000 + 2.00000i −0.143223 + 0.0716115i
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 35.0000i 1.25080i
$$784$$ −4.00000 −0.142857
$$785$$ −18.0000 36.0000i −0.642448 1.28490i
$$786$$ 0 0
$$787$$ 35.0000i 1.24762i −0.781578 0.623808i $$-0.785585\pi$$
0.781578 0.623808i $$-0.214415\pi$$
$$788$$ 36.0000i 1.28245i
$$789$$ −2.00000 −0.0712019
$$790$$ 0 0
$$791$$ 18.0000 0.640006
$$792$$ 0 0
$$793$$ 10.0000i 0.355110i
$$794$$ 0 0
$$795$$ −8.00000 + 4.00000i −0.283731 +