# Properties

 Label 912.2.f.e.113.2 Level $912$ Weight $2$ Character 912.113 Analytic conductor $7.282$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 912.f (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.28235666434$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 114) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 113.2 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 912.113 Dual form 912.2.f.e.113.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.50000 + 0.866025i) q^{3} -3.46410i q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(1.50000 + 0.866025i) q^{3} -3.46410i q^{5} -1.00000 q^{7} +(1.50000 + 2.59808i) q^{9} -3.46410i q^{11} +1.73205i q^{13} +(3.00000 - 5.19615i) q^{15} -1.73205i q^{17} +(4.00000 + 1.73205i) q^{19} +(-1.50000 - 0.866025i) q^{21} -5.19615i q^{23} -7.00000 q^{25} +5.19615i q^{27} +9.00000 q^{29} -10.3923i q^{31} +(3.00000 - 5.19615i) q^{33} +3.46410i q^{35} -6.92820i q^{37} +(-1.50000 + 2.59808i) q^{39} -2.00000 q^{43} +(9.00000 - 5.19615i) q^{45} +3.46410i q^{47} -6.00000 q^{49} +(1.50000 - 2.59808i) q^{51} -9.00000 q^{53} -12.0000 q^{55} +(4.50000 + 6.06218i) q^{57} +3.00000 q^{59} -8.00000 q^{61} +(-1.50000 - 2.59808i) q^{63} +6.00000 q^{65} +8.66025i q^{67} +(4.50000 - 7.79423i) q^{69} +12.0000 q^{71} +11.0000 q^{73} +(-10.5000 - 6.06218i) q^{75} +3.46410i q^{77} +6.92820i q^{79} +(-4.50000 + 7.79423i) q^{81} +10.3923i q^{83} -6.00000 q^{85} +(13.5000 + 7.79423i) q^{87} +6.00000 q^{89} -1.73205i q^{91} +(9.00000 - 15.5885i) q^{93} +(6.00000 - 13.8564i) q^{95} +13.8564i q^{97} +(9.00000 - 5.19615i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 3 q^{3} - 2 q^{7} + 3 q^{9}+O(q^{10})$$ 2 * q + 3 * q^3 - 2 * q^7 + 3 * q^9 $$2 q + 3 q^{3} - 2 q^{7} + 3 q^{9} + 6 q^{15} + 8 q^{19} - 3 q^{21} - 14 q^{25} + 18 q^{29} + 6 q^{33} - 3 q^{39} - 4 q^{43} + 18 q^{45} - 12 q^{49} + 3 q^{51} - 18 q^{53} - 24 q^{55} + 9 q^{57} + 6 q^{59} - 16 q^{61} - 3 q^{63} + 12 q^{65} + 9 q^{69} + 24 q^{71} + 22 q^{73} - 21 q^{75} - 9 q^{81} - 12 q^{85} + 27 q^{87} + 12 q^{89} + 18 q^{93} + 12 q^{95} + 18 q^{99}+O(q^{100})$$ 2 * q + 3 * q^3 - 2 * q^7 + 3 * q^9 + 6 * q^15 + 8 * q^19 - 3 * q^21 - 14 * q^25 + 18 * q^29 + 6 * q^33 - 3 * q^39 - 4 * q^43 + 18 * q^45 - 12 * q^49 + 3 * q^51 - 18 * q^53 - 24 * q^55 + 9 * q^57 + 6 * q^59 - 16 * q^61 - 3 * q^63 + 12 * q^65 + 9 * q^69 + 24 * q^71 + 22 * q^73 - 21 * q^75 - 9 * q^81 - 12 * q^85 + 27 * q^87 + 12 * q^89 + 18 * q^93 + 12 * q^95 + 18 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$$.

 $$n$$ $$97$$ $$229$$ $$305$$ $$799$$ $$\chi(n)$$ $$-1$$ $$1$$ $$-1$$ $$1$$

## 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
$$3$$ 1.50000 + 0.866025i 0.866025 + 0.500000i
$$4$$ 0 0
$$5$$ 3.46410i 1.54919i −0.632456 0.774597i $$-0.717953\pi$$
0.632456 0.774597i $$-0.282047\pi$$
$$6$$ 0 0
$$7$$ −1.00000 −0.377964 −0.188982 0.981981i $$-0.560519\pi$$
−0.188982 + 0.981981i $$0.560519\pi$$
$$8$$ 0 0
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ 0 0
$$11$$ 3.46410i 1.04447i −0.852803 0.522233i $$-0.825099\pi$$
0.852803 0.522233i $$-0.174901\pi$$
$$12$$ 0 0
$$13$$ 1.73205i 0.480384i 0.970725 + 0.240192i $$0.0772105\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ 0 0
$$15$$ 3.00000 5.19615i 0.774597 1.34164i
$$16$$ 0 0
$$17$$ 1.73205i 0.420084i −0.977692 0.210042i $$-0.932640\pi$$
0.977692 0.210042i $$-0.0673601\pi$$
$$18$$ 0 0
$$19$$ 4.00000 + 1.73205i 0.917663 + 0.397360i
$$20$$ 0 0
$$21$$ −1.50000 0.866025i −0.327327 0.188982i
$$22$$ 0 0
$$23$$ 5.19615i 1.08347i −0.840548 0.541736i $$-0.817767\pi$$
0.840548 0.541736i $$-0.182233\pi$$
$$24$$ 0 0
$$25$$ −7.00000 −1.40000
$$26$$ 0 0
$$27$$ 5.19615i 1.00000i
$$28$$ 0 0
$$29$$ 9.00000 1.67126 0.835629 0.549294i $$-0.185103\pi$$
0.835629 + 0.549294i $$0.185103\pi$$
$$30$$ 0 0
$$31$$ 10.3923i 1.86651i −0.359211 0.933257i $$-0.616954\pi$$
0.359211 0.933257i $$-0.383046\pi$$
$$32$$ 0 0
$$33$$ 3.00000 5.19615i 0.522233 0.904534i
$$34$$ 0 0
$$35$$ 3.46410i 0.585540i
$$36$$ 0 0
$$37$$ 6.92820i 1.13899i −0.821995 0.569495i $$-0.807139\pi$$
0.821995 0.569495i $$-0.192861\pi$$
$$38$$ 0 0
$$39$$ −1.50000 + 2.59808i −0.240192 + 0.416025i
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −2.00000 −0.304997 −0.152499 0.988304i $$-0.548732\pi$$
−0.152499 + 0.988304i $$0.548732\pi$$
$$44$$ 0 0
$$45$$ 9.00000 5.19615i 1.34164 0.774597i
$$46$$ 0 0
$$47$$ 3.46410i 0.505291i 0.967559 + 0.252646i $$0.0813007\pi$$
−0.967559 + 0.252646i $$0.918699\pi$$
$$48$$ 0 0
$$49$$ −6.00000 −0.857143
$$50$$ 0 0
$$51$$ 1.50000 2.59808i 0.210042 0.363803i
$$52$$ 0 0
$$53$$ −9.00000 −1.23625 −0.618123 0.786082i $$-0.712106\pi$$
−0.618123 + 0.786082i $$0.712106\pi$$
$$54$$ 0 0
$$55$$ −12.0000 −1.61808
$$56$$ 0 0
$$57$$ 4.50000 + 6.06218i 0.596040 + 0.802955i
$$58$$ 0 0
$$59$$ 3.00000 0.390567 0.195283 0.980747i $$-0.437437\pi$$
0.195283 + 0.980747i $$0.437437\pi$$
$$60$$ 0 0
$$61$$ −8.00000 −1.02430 −0.512148 0.858898i $$-0.671150\pi$$
−0.512148 + 0.858898i $$0.671150\pi$$
$$62$$ 0 0
$$63$$ −1.50000 2.59808i −0.188982 0.327327i
$$64$$ 0 0
$$65$$ 6.00000 0.744208
$$66$$ 0 0
$$67$$ 8.66025i 1.05802i 0.848616 + 0.529009i $$0.177436\pi$$
−0.848616 + 0.529009i $$0.822564\pi$$
$$68$$ 0 0
$$69$$ 4.50000 7.79423i 0.541736 0.938315i
$$70$$ 0 0
$$71$$ 12.0000 1.42414 0.712069 0.702109i $$-0.247758\pi$$
0.712069 + 0.702109i $$0.247758\pi$$
$$72$$ 0 0
$$73$$ 11.0000 1.28745 0.643726 0.765256i $$-0.277388\pi$$
0.643726 + 0.765256i $$0.277388\pi$$
$$74$$ 0 0
$$75$$ −10.5000 6.06218i −1.21244 0.700000i
$$76$$ 0 0
$$77$$ 3.46410i 0.394771i
$$78$$ 0 0
$$79$$ 6.92820i 0.779484i 0.920924 + 0.389742i $$0.127436\pi$$
−0.920924 + 0.389742i $$0.872564\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 10.3923i 1.14070i 0.821401 + 0.570352i $$0.193193\pi$$
−0.821401 + 0.570352i $$0.806807\pi$$
$$84$$ 0 0
$$85$$ −6.00000 −0.650791
$$86$$ 0 0
$$87$$ 13.5000 + 7.79423i 1.44735 + 0.835629i
$$88$$ 0 0
$$89$$ 6.00000 0.635999 0.317999 0.948091i $$-0.396989\pi$$
0.317999 + 0.948091i $$0.396989\pi$$
$$90$$ 0 0
$$91$$ 1.73205i 0.181568i
$$92$$ 0 0
$$93$$ 9.00000 15.5885i 0.933257 1.61645i
$$94$$ 0 0
$$95$$ 6.00000 13.8564i 0.615587 1.42164i
$$96$$ 0 0
$$97$$ 13.8564i 1.40690i 0.710742 + 0.703452i $$0.248359\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ 9.00000 5.19615i 0.904534 0.522233i
$$100$$ 0 0
$$101$$ 10.3923i 1.03407i 0.855963 + 0.517036i $$0.172965\pi$$
−0.855963 + 0.517036i $$0.827035\pi$$
$$102$$ 0 0
$$103$$ 3.46410i 0.341328i 0.985329 + 0.170664i $$0.0545913\pi$$
−0.985329 + 0.170664i $$0.945409\pi$$
$$104$$ 0 0
$$105$$ −3.00000 + 5.19615i −0.292770 + 0.507093i
$$106$$ 0 0
$$107$$ −3.00000 −0.290021 −0.145010 0.989430i $$-0.546322\pi$$
−0.145010 + 0.989430i $$0.546322\pi$$
$$108$$ 0 0
$$109$$ 15.5885i 1.49310i 0.665327 + 0.746552i $$0.268292\pi$$
−0.665327 + 0.746552i $$0.731708\pi$$
$$110$$ 0 0
$$111$$ 6.00000 10.3923i 0.569495 0.986394i
$$112$$ 0 0
$$113$$ −12.0000 −1.12887 −0.564433 0.825479i $$-0.690905\pi$$
−0.564433 + 0.825479i $$0.690905\pi$$
$$114$$ 0 0
$$115$$ −18.0000 −1.67851
$$116$$ 0 0
$$117$$ −4.50000 + 2.59808i −0.416025 + 0.240192i
$$118$$ 0 0
$$119$$ 1.73205i 0.158777i
$$120$$ 0 0
$$121$$ −1.00000 −0.0909091
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 6.92820i 0.619677i
$$126$$ 0 0
$$127$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$128$$ 0 0
$$129$$ −3.00000 1.73205i −0.264135 0.152499i
$$130$$ 0 0
$$131$$ 3.46410i 0.302660i 0.988483 + 0.151330i $$0.0483556\pi$$
−0.988483 + 0.151330i $$0.951644\pi$$
$$132$$ 0 0
$$133$$ −4.00000 1.73205i −0.346844 0.150188i
$$134$$ 0 0
$$135$$ 18.0000 1.54919
$$136$$ 0 0
$$137$$ 8.66025i 0.739895i −0.929053 0.369948i $$-0.879376\pi$$
0.929053 0.369948i $$-0.120624\pi$$
$$138$$ 0 0
$$139$$ 14.0000 1.18746 0.593732 0.804663i $$-0.297654\pi$$
0.593732 + 0.804663i $$0.297654\pi$$
$$140$$ 0 0
$$141$$ −3.00000 + 5.19615i −0.252646 + 0.437595i
$$142$$ 0 0
$$143$$ 6.00000 0.501745
$$144$$ 0 0
$$145$$ 31.1769i 2.58910i
$$146$$ 0 0
$$147$$ −9.00000 5.19615i −0.742307 0.428571i
$$148$$ 0 0
$$149$$ 6.92820i 0.567581i −0.958886 0.283790i $$-0.908408\pi$$
0.958886 0.283790i $$-0.0915919\pi$$
$$150$$ 0 0
$$151$$ 3.46410i 0.281905i −0.990016 0.140952i $$-0.954984\pi$$
0.990016 0.140952i $$-0.0450164\pi$$
$$152$$ 0 0
$$153$$ 4.50000 2.59808i 0.363803 0.210042i
$$154$$ 0 0
$$155$$ −36.0000 −2.89159
$$156$$ 0 0
$$157$$ 4.00000 0.319235 0.159617 0.987179i $$-0.448974\pi$$
0.159617 + 0.987179i $$0.448974\pi$$
$$158$$ 0 0
$$159$$ −13.5000 7.79423i −1.07062 0.618123i
$$160$$ 0 0
$$161$$ 5.19615i 0.409514i
$$162$$ 0 0
$$163$$ −10.0000 −0.783260 −0.391630 0.920123i $$-0.628089\pi$$
−0.391630 + 0.920123i $$0.628089\pi$$
$$164$$ 0 0
$$165$$ −18.0000 10.3923i −1.40130 0.809040i
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 10.0000 0.769231
$$170$$ 0 0
$$171$$ 1.50000 + 12.9904i 0.114708 + 0.993399i
$$172$$ 0 0
$$173$$ 6.00000 0.456172 0.228086 0.973641i $$-0.426753\pi$$
0.228086 + 0.973641i $$0.426753\pi$$
$$174$$ 0 0
$$175$$ 7.00000 0.529150
$$176$$ 0 0
$$177$$ 4.50000 + 2.59808i 0.338241 + 0.195283i
$$178$$ 0 0
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ 0 0
$$181$$ 13.8564i 1.02994i 0.857209 + 0.514969i $$0.172197\pi$$
−0.857209 + 0.514969i $$0.827803\pi$$
$$182$$ 0 0
$$183$$ −12.0000 6.92820i −0.887066 0.512148i
$$184$$ 0 0
$$185$$ −24.0000 −1.76452
$$186$$ 0 0
$$187$$ −6.00000 −0.438763
$$188$$ 0 0
$$189$$ 5.19615i 0.377964i
$$190$$ 0 0
$$191$$ 19.0526i 1.37859i 0.724479 + 0.689297i $$0.242081\pi$$
−0.724479 + 0.689297i $$0.757919\pi$$
$$192$$ 0 0
$$193$$ 3.46410i 0.249351i 0.992198 + 0.124676i $$0.0397891\pi$$
−0.992198 + 0.124676i $$0.960211\pi$$
$$194$$ 0 0
$$195$$ 9.00000 + 5.19615i 0.644503 + 0.372104i
$$196$$ 0 0
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ −11.0000 −0.779769 −0.389885 0.920864i $$-0.627485\pi$$
−0.389885 + 0.920864i $$0.627485\pi$$
$$200$$ 0 0
$$201$$ −7.50000 + 12.9904i −0.529009 + 0.916271i
$$202$$ 0 0
$$203$$ −9.00000 −0.631676
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 13.5000 7.79423i 0.938315 0.541736i
$$208$$ 0 0
$$209$$ 6.00000 13.8564i 0.415029 0.958468i
$$210$$ 0 0
$$211$$ 12.1244i 0.834675i 0.908752 + 0.417338i $$0.137037\pi$$
−0.908752 + 0.417338i $$0.862963\pi$$
$$212$$ 0 0
$$213$$ 18.0000 + 10.3923i 1.23334 + 0.712069i
$$214$$ 0 0
$$215$$ 6.92820i 0.472500i
$$216$$ 0 0
$$217$$ 10.3923i 0.705476i
$$218$$ 0 0
$$219$$ 16.5000 + 9.52628i 1.11497 + 0.643726i
$$220$$ 0 0
$$221$$ 3.00000 0.201802
$$222$$ 0 0
$$223$$ 10.3923i 0.695920i 0.937509 + 0.347960i $$0.113126\pi$$
−0.937509 + 0.347960i $$0.886874\pi$$
$$224$$ 0 0
$$225$$ −10.5000 18.1865i −0.700000 1.21244i
$$226$$ 0 0
$$227$$ 3.00000 0.199117 0.0995585 0.995032i $$-0.468257\pi$$
0.0995585 + 0.995032i $$0.468257\pi$$
$$228$$ 0 0
$$229$$ −8.00000 −0.528655 −0.264327 0.964433i $$-0.585150\pi$$
−0.264327 + 0.964433i $$0.585150\pi$$
$$230$$ 0 0
$$231$$ −3.00000 + 5.19615i −0.197386 + 0.341882i
$$232$$ 0 0
$$233$$ 6.92820i 0.453882i −0.973909 0.226941i $$-0.927128\pi$$
0.973909 0.226941i $$-0.0728724\pi$$
$$234$$ 0 0
$$235$$ 12.0000 0.782794
$$236$$ 0 0
$$237$$ −6.00000 + 10.3923i −0.389742 + 0.675053i
$$238$$ 0 0
$$239$$ 12.1244i 0.784259i −0.919910 0.392130i $$-0.871738\pi$$
0.919910 0.392130i $$-0.128262\pi$$
$$240$$ 0 0
$$241$$ 13.8564i 0.892570i −0.894891 0.446285i $$-0.852747\pi$$
0.894891 0.446285i $$-0.147253\pi$$
$$242$$ 0 0
$$243$$ −13.5000 + 7.79423i −0.866025 + 0.500000i
$$244$$ 0 0
$$245$$ 20.7846i 1.32788i
$$246$$ 0 0
$$247$$ −3.00000 + 6.92820i −0.190885 + 0.440831i
$$248$$ 0 0
$$249$$ −9.00000 + 15.5885i −0.570352 + 0.987878i
$$250$$ 0 0
$$251$$ 13.8564i 0.874609i −0.899314 0.437304i $$-0.855933\pi$$
0.899314 0.437304i $$-0.144067\pi$$
$$252$$ 0 0
$$253$$ −18.0000 −1.13165
$$254$$ 0 0
$$255$$ −9.00000 5.19615i −0.563602 0.325396i
$$256$$ 0 0
$$257$$ 6.00000 0.374270 0.187135 0.982334i $$-0.440080\pi$$
0.187135 + 0.982334i $$0.440080\pi$$
$$258$$ 0 0
$$259$$ 6.92820i 0.430498i
$$260$$ 0 0
$$261$$ 13.5000 + 23.3827i 0.835629 + 1.44735i
$$262$$ 0 0
$$263$$ 3.46410i 0.213606i −0.994280 0.106803i $$-0.965939\pi$$
0.994280 0.106803i $$-0.0340614\pi$$
$$264$$ 0 0
$$265$$ 31.1769i 1.91518i
$$266$$ 0 0
$$267$$ 9.00000 + 5.19615i 0.550791 + 0.317999i
$$268$$ 0 0
$$269$$ 18.0000 1.09748 0.548740 0.835993i $$-0.315108\pi$$
0.548740 + 0.835993i $$0.315108\pi$$
$$270$$ 0 0
$$271$$ 1.00000 0.0607457 0.0303728 0.999539i $$-0.490331\pi$$
0.0303728 + 0.999539i $$0.490331\pi$$
$$272$$ 0 0
$$273$$ 1.50000 2.59808i 0.0907841 0.157243i
$$274$$ 0 0
$$275$$ 24.2487i 1.46225i
$$276$$ 0 0
$$277$$ −2.00000 −0.120168 −0.0600842 0.998193i $$-0.519137\pi$$
−0.0600842 + 0.998193i $$0.519137\pi$$
$$278$$ 0 0
$$279$$ 27.0000 15.5885i 1.61645 0.933257i
$$280$$ 0 0
$$281$$ −12.0000 −0.715860 −0.357930 0.933748i $$-0.616517\pi$$
−0.357930 + 0.933748i $$0.616517\pi$$
$$282$$ 0 0
$$283$$ 10.0000 0.594438 0.297219 0.954809i $$-0.403941\pi$$
0.297219 + 0.954809i $$0.403941\pi$$
$$284$$ 0 0
$$285$$ 21.0000 15.5885i 1.24393 0.923381i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 14.0000 0.823529
$$290$$ 0 0
$$291$$ −12.0000 + 20.7846i −0.703452 + 1.21842i
$$292$$ 0 0
$$293$$ −21.0000 −1.22683 −0.613417 0.789760i $$-0.710205\pi$$
−0.613417 + 0.789760i $$0.710205\pi$$
$$294$$ 0 0
$$295$$ 10.3923i 0.605063i
$$296$$ 0 0
$$297$$ 18.0000 1.04447
$$298$$ 0 0
$$299$$ 9.00000 0.520483
$$300$$ 0 0
$$301$$ 2.00000 0.115278
$$302$$ 0 0
$$303$$ −9.00000 + 15.5885i −0.517036 + 0.895533i
$$304$$ 0 0
$$305$$ 27.7128i 1.58683i
$$306$$ 0 0
$$307$$ 10.3923i 0.593120i 0.955014 + 0.296560i $$0.0958395\pi$$
−0.955014 + 0.296560i $$0.904160\pi$$
$$308$$ 0 0
$$309$$ −3.00000 + 5.19615i −0.170664 + 0.295599i
$$310$$ 0 0
$$311$$ 22.5167i 1.27680i −0.769704 0.638401i $$-0.779596\pi$$
0.769704 0.638401i $$-0.220404\pi$$
$$312$$ 0 0
$$313$$ 13.0000 0.734803 0.367402 0.930062i $$-0.380247\pi$$
0.367402 + 0.930062i $$0.380247\pi$$
$$314$$ 0 0
$$315$$ −9.00000 + 5.19615i −0.507093 + 0.292770i
$$316$$ 0 0
$$317$$ 3.00000 0.168497 0.0842484 0.996445i $$-0.473151\pi$$
0.0842484 + 0.996445i $$0.473151\pi$$
$$318$$ 0 0
$$319$$ 31.1769i 1.74557i
$$320$$ 0 0
$$321$$ −4.50000 2.59808i −0.251166 0.145010i
$$322$$ 0 0
$$323$$ 3.00000 6.92820i 0.166924 0.385496i
$$324$$ 0 0
$$325$$ 12.1244i 0.672538i
$$326$$ 0 0
$$327$$ −13.5000 + 23.3827i −0.746552 + 1.29307i
$$328$$ 0 0
$$329$$ 3.46410i 0.190982i
$$330$$ 0 0
$$331$$ 19.0526i 1.04722i 0.851957 + 0.523612i $$0.175416\pi$$
−0.851957 + 0.523612i $$0.824584\pi$$
$$332$$ 0 0
$$333$$ 18.0000 10.3923i 0.986394 0.569495i
$$334$$ 0 0
$$335$$ 30.0000 1.63908
$$336$$ 0 0
$$337$$ 24.2487i 1.32091i −0.750865 0.660456i $$-0.770363\pi$$
0.750865 0.660456i $$-0.229637\pi$$
$$338$$ 0 0
$$339$$ −18.0000 10.3923i −0.977626 0.564433i
$$340$$ 0 0
$$341$$ −36.0000 −1.94951
$$342$$ 0 0
$$343$$ 13.0000 0.701934
$$344$$ 0 0
$$345$$ −27.0000 15.5885i −1.45363 0.839254i
$$346$$ 0 0
$$347$$ 27.7128i 1.48770i −0.668346 0.743851i $$-0.732997\pi$$
0.668346 0.743851i $$-0.267003\pi$$
$$348$$ 0 0
$$349$$ −28.0000 −1.49881 −0.749403 0.662114i $$-0.769659\pi$$
−0.749403 + 0.662114i $$0.769659\pi$$
$$350$$ 0 0
$$351$$ −9.00000 −0.480384
$$352$$ 0 0
$$353$$ 25.9808i 1.38282i −0.722464 0.691408i $$-0.756991\pi$$
0.722464 0.691408i $$-0.243009\pi$$
$$354$$ 0 0
$$355$$ 41.5692i 2.20627i
$$356$$ 0 0
$$357$$ −1.50000 + 2.59808i −0.0793884 + 0.137505i
$$358$$ 0 0
$$359$$ 19.0526i 1.00556i 0.864416 + 0.502778i $$0.167689\pi$$
−0.864416 + 0.502778i $$0.832311\pi$$
$$360$$ 0 0
$$361$$ 13.0000 + 13.8564i 0.684211 + 0.729285i
$$362$$ 0 0
$$363$$ −1.50000 0.866025i −0.0787296 0.0454545i
$$364$$ 0 0
$$365$$ 38.1051i 1.99451i
$$366$$ 0 0
$$367$$ −32.0000 −1.67039 −0.835193 0.549957i $$-0.814644\pi$$
−0.835193 + 0.549957i $$0.814644\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 9.00000 0.467257
$$372$$ 0 0
$$373$$ 29.4449i 1.52460i 0.647225 + 0.762299i $$0.275929\pi$$
−0.647225 + 0.762299i $$0.724071\pi$$
$$374$$ 0 0
$$375$$ −6.00000 + 10.3923i −0.309839 + 0.536656i
$$376$$ 0 0
$$377$$ 15.5885i 0.802846i
$$378$$ 0 0
$$379$$ 12.1244i 0.622786i 0.950281 + 0.311393i $$0.100796\pi$$
−0.950281 + 0.311393i $$0.899204\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −6.00000 −0.306586 −0.153293 0.988181i $$-0.548988\pi$$
−0.153293 + 0.988181i $$0.548988\pi$$
$$384$$ 0 0
$$385$$ 12.0000 0.611577
$$386$$ 0 0
$$387$$ −3.00000 5.19615i −0.152499 0.264135i
$$388$$ 0 0
$$389$$ 3.46410i 0.175637i 0.996136 + 0.0878185i $$0.0279895\pi$$
−0.996136 + 0.0878185i $$0.972010\pi$$
$$390$$ 0 0
$$391$$ −9.00000 −0.455150
$$392$$ 0 0
$$393$$ −3.00000 + 5.19615i −0.151330 + 0.262111i
$$394$$ 0 0
$$395$$ 24.0000 1.20757
$$396$$ 0 0
$$397$$ −22.0000 −1.10415 −0.552074 0.833795i $$-0.686163\pi$$
−0.552074 + 0.833795i $$0.686163\pi$$
$$398$$ 0 0
$$399$$ −4.50000 6.06218i −0.225282 0.303488i
$$400$$ 0 0
$$401$$ 24.0000 1.19850 0.599251 0.800561i $$-0.295465\pi$$
0.599251 + 0.800561i $$0.295465\pi$$
$$402$$ 0 0
$$403$$ 18.0000 0.896644
$$404$$ 0 0
$$405$$ 27.0000 + 15.5885i 1.34164 + 0.774597i
$$406$$ 0 0
$$407$$ −24.0000 −1.18964
$$408$$ 0 0
$$409$$ 38.1051i 1.88418i −0.335365 0.942088i $$-0.608860\pi$$
0.335365 0.942088i $$-0.391140\pi$$
$$410$$ 0 0
$$411$$ 7.50000 12.9904i 0.369948 0.640768i
$$412$$ 0 0
$$413$$ −3.00000 −0.147620
$$414$$ 0 0
$$415$$ 36.0000 1.76717
$$416$$ 0 0
$$417$$ 21.0000 + 12.1244i 1.02837 + 0.593732i
$$418$$ 0 0
$$419$$ 10.3923i 0.507697i 0.967244 + 0.253849i $$0.0816965\pi$$
−0.967244 + 0.253849i $$0.918303\pi$$
$$420$$ 0 0
$$421$$ 12.1244i 0.590905i 0.955357 + 0.295452i $$0.0954704\pi$$
−0.955357 + 0.295452i $$0.904530\pi$$
$$422$$ 0 0
$$423$$ −9.00000 + 5.19615i −0.437595 + 0.252646i
$$424$$ 0 0
$$425$$ 12.1244i 0.588118i
$$426$$ 0 0
$$427$$ 8.00000 0.387147
$$428$$ 0 0
$$429$$ 9.00000 + 5.19615i 0.434524 + 0.250873i
$$430$$ 0 0
$$431$$ −12.0000 −0.578020 −0.289010 0.957326i $$-0.593326\pi$$
−0.289010 + 0.957326i $$0.593326\pi$$
$$432$$ 0 0
$$433$$ 10.3923i 0.499422i −0.968320 0.249711i $$-0.919664\pi$$
0.968320 0.249711i $$-0.0803357\pi$$
$$434$$ 0 0
$$435$$ 27.0000 46.7654i 1.29455 2.24223i
$$436$$ 0 0
$$437$$ 9.00000 20.7846i 0.430528 0.994263i
$$438$$ 0 0
$$439$$ 20.7846i 0.991995i −0.868324 0.495998i $$-0.834802\pi$$
0.868324 0.495998i $$-0.165198\pi$$
$$440$$ 0 0
$$441$$ −9.00000 15.5885i −0.428571 0.742307i
$$442$$ 0 0
$$443$$ 17.3205i 0.822922i −0.911427 0.411461i $$-0.865019\pi$$
0.911427 0.411461i $$-0.134981\pi$$
$$444$$ 0 0
$$445$$ 20.7846i 0.985285i
$$446$$ 0 0
$$447$$ 6.00000 10.3923i 0.283790 0.491539i
$$448$$ 0 0
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 3.00000 5.19615i 0.140952 0.244137i
$$454$$ 0 0
$$455$$ −6.00000 −0.281284
$$456$$ 0 0
$$457$$ −25.0000 −1.16945 −0.584725 0.811231i $$-0.698798\pi$$
−0.584725 + 0.811231i $$0.698798\pi$$
$$458$$ 0 0
$$459$$ 9.00000 0.420084
$$460$$ 0 0
$$461$$ 13.8564i 0.645357i 0.946509 + 0.322679i $$0.104583\pi$$
−0.946509 + 0.322679i $$0.895417\pi$$
$$462$$ 0 0
$$463$$ 40.0000 1.85896 0.929479 0.368875i $$-0.120257\pi$$
0.929479 + 0.368875i $$0.120257\pi$$
$$464$$ 0 0
$$465$$ −54.0000 31.1769i −2.50419 1.44579i
$$466$$ 0 0
$$467$$ 27.7128i 1.28240i 0.767375 + 0.641198i $$0.221562\pi$$
−0.767375 + 0.641198i $$0.778438\pi$$
$$468$$ 0 0
$$469$$ 8.66025i 0.399893i
$$470$$ 0 0
$$471$$ 6.00000 + 3.46410i 0.276465 + 0.159617i
$$472$$ 0 0
$$473$$ 6.92820i 0.318559i
$$474$$ 0 0
$$475$$ −28.0000 12.1244i −1.28473 0.556304i
$$476$$ 0 0
$$477$$ −13.5000 23.3827i −0.618123 1.07062i
$$478$$ 0 0
$$479$$ 10.3923i 0.474837i −0.971408 0.237418i $$-0.923699\pi$$
0.971408 0.237418i $$-0.0763012\pi$$
$$480$$ 0 0
$$481$$ 12.0000 0.547153
$$482$$ 0 0
$$483$$ −4.50000 + 7.79423i −0.204757 + 0.354650i
$$484$$ 0 0
$$485$$ 48.0000 2.17957
$$486$$ 0 0
$$487$$ 3.46410i 0.156973i −0.996915 0.0784867i $$-0.974991\pi$$
0.996915 0.0784867i $$-0.0250088\pi$$
$$488$$ 0 0
$$489$$ −15.0000 8.66025i −0.678323 0.391630i
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 15.5885i 0.702069i
$$494$$ 0 0
$$495$$ −18.0000 31.1769i −0.809040 1.40130i
$$496$$ 0 0
$$497$$ −12.0000 −0.538274
$$498$$ 0 0
$$499$$ −10.0000 −0.447661 −0.223831 0.974628i $$-0.571856\pi$$
−0.223831 + 0.974628i $$0.571856\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 25.9808i 1.15842i −0.815177 0.579212i $$-0.803360\pi$$
0.815177 0.579212i $$-0.196640\pi$$
$$504$$ 0 0
$$505$$ 36.0000 1.60198
$$506$$ 0 0
$$507$$ 15.0000 + 8.66025i 0.666173 + 0.384615i
$$508$$ 0 0
$$509$$ 6.00000 0.265945 0.132973 0.991120i $$-0.457548\pi$$
0.132973 + 0.991120i $$0.457548\pi$$
$$510$$ 0 0
$$511$$ −11.0000 −0.486611
$$512$$ 0 0
$$513$$ −9.00000 + 20.7846i −0.397360 + 0.917663i
$$514$$ 0 0
$$515$$ 12.0000 0.528783
$$516$$ 0 0
$$517$$ 12.0000 0.527759
$$518$$ 0 0
$$519$$ 9.00000 + 5.19615i 0.395056 + 0.228086i
$$520$$ 0 0
$$521$$ −24.0000 −1.05146 −0.525730 0.850652i $$-0.676208\pi$$
−0.525730 + 0.850652i $$0.676208\pi$$
$$522$$ 0 0
$$523$$ 32.9090i 1.43901i −0.694488 0.719504i $$-0.744369\pi$$
0.694488 0.719504i $$-0.255631\pi$$
$$524$$ 0 0
$$525$$ 10.5000 + 6.06218i 0.458258 + 0.264575i
$$526$$ 0 0
$$527$$ −18.0000 −0.784092
$$528$$ 0 0
$$529$$ −4.00000 −0.173913
$$530$$ 0 0
$$531$$ 4.50000 + 7.79423i 0.195283 + 0.338241i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 10.3923i 0.449299i
$$536$$ 0 0
$$537$$ −18.0000 10.3923i −0.776757 0.448461i
$$538$$ 0 0
$$539$$ 20.7846i 0.895257i
$$540$$ 0 0
$$541$$ 38.0000 1.63375 0.816874 0.576816i $$-0.195705\pi$$
0.816874 + 0.576816i $$0.195705\pi$$
$$542$$ 0 0
$$543$$ −12.0000 + 20.7846i −0.514969 + 0.891953i
$$544$$ 0 0
$$545$$ 54.0000 2.31311
$$546$$ 0 0
$$547$$ 24.2487i 1.03680i 0.855138 + 0.518400i $$0.173472\pi$$
−0.855138 + 0.518400i $$0.826528\pi$$
$$548$$ 0 0
$$549$$ −12.0000 20.7846i −0.512148 0.887066i
$$550$$ 0 0
$$551$$ 36.0000 + 15.5885i 1.53365 + 0.664091i
$$552$$ 0 0
$$553$$ 6.92820i 0.294617i
$$554$$ 0 0
$$555$$ −36.0000 20.7846i −1.52811 0.882258i
$$556$$ 0 0
$$557$$ 45.0333i 1.90812i −0.299611 0.954062i $$-0.596857\pi$$
0.299611 0.954062i $$-0.403143\pi$$
$$558$$ 0 0
$$559$$ 3.46410i 0.146516i
$$560$$ 0 0
$$561$$ −9.00000 5.19615i −0.379980 0.219382i
$$562$$ 0 0
$$563$$ 24.0000 1.01148 0.505740 0.862686i $$-0.331220\pi$$
0.505740 + 0.862686i $$0.331220\pi$$
$$564$$ 0 0
$$565$$ 41.5692i 1.74883i
$$566$$ 0 0
$$567$$ 4.50000 7.79423i 0.188982 0.327327i
$$568$$ 0 0
$$569$$ 24.0000 1.00613 0.503066 0.864248i $$-0.332205\pi$$
0.503066 + 0.864248i $$0.332205\pi$$
$$570$$ 0 0
$$571$$ 16.0000 0.669579 0.334790 0.942293i $$-0.391335\pi$$
0.334790 + 0.942293i $$0.391335\pi$$
$$572$$ 0 0
$$573$$ −16.5000 + 28.5788i −0.689297 + 1.19390i
$$574$$ 0 0
$$575$$ 36.3731i 1.51686i
$$576$$ 0 0
$$577$$ 25.0000 1.04076 0.520382 0.853934i $$-0.325790\pi$$
0.520382 + 0.853934i $$0.325790\pi$$
$$578$$ 0 0
$$579$$ −3.00000 + 5.19615i −0.124676 + 0.215945i
$$580$$ 0 0
$$581$$ 10.3923i 0.431145i
$$582$$ 0 0
$$583$$ 31.1769i 1.29122i
$$584$$ 0 0
$$585$$ 9.00000 + 15.5885i 0.372104 + 0.644503i
$$586$$ 0 0
$$587$$ 13.8564i 0.571915i −0.958242 0.285958i $$-0.907688\pi$$
0.958242 0.285958i $$-0.0923116\pi$$
$$588$$ 0 0
$$589$$ 18.0000 41.5692i 0.741677 1.71283i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 20.7846i 0.853522i 0.904365 + 0.426761i $$0.140345\pi$$
−0.904365 + 0.426761i $$0.859655\pi$$
$$594$$ 0 0
$$595$$ 6.00000 0.245976
$$596$$ 0 0
$$597$$ −16.5000 9.52628i −0.675300 0.389885i
$$598$$ 0 0
$$599$$ −12.0000 −0.490307 −0.245153 0.969484i $$-0.578838\pi$$
−0.245153 + 0.969484i $$0.578838\pi$$
$$600$$ 0 0
$$601$$ 10.3923i 0.423911i −0.977279 0.211955i $$-0.932017\pi$$
0.977279 0.211955i $$-0.0679832\pi$$
$$602$$ 0 0
$$603$$ −22.5000 + 12.9904i −0.916271 + 0.529009i
$$604$$ 0 0
$$605$$ 3.46410i 0.140836i
$$606$$ 0 0
$$607$$ 27.7128i 1.12483i 0.826856 + 0.562414i $$0.190127\pi$$
−0.826856 + 0.562414i $$0.809873\pi$$
$$608$$ 0 0
$$609$$ −13.5000 7.79423i −0.547048 0.315838i
$$610$$ 0 0
$$611$$ −6.00000 −0.242734
$$612$$ 0 0
$$613$$ −2.00000 −0.0807792 −0.0403896 0.999184i $$-0.512860\pi$$
−0.0403896 + 0.999184i $$0.512860\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 48.4974i 1.95243i 0.216799 + 0.976216i $$0.430439\pi$$
−0.216799 + 0.976216i $$0.569561\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ 0 0
$$621$$ 27.0000 1.08347
$$622$$ 0 0
$$623$$ −6.00000 −0.240385
$$624$$ 0 0
$$625$$ −11.0000 −0.440000
$$626$$ 0 0
$$627$$ 21.0000 15.5885i 0.838659 0.622543i
$$628$$ 0 0
$$629$$ −12.0000 −0.478471
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 0 0
$$633$$ −10.5000 + 18.1865i −0.417338 + 0.722850i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 10.3923i 0.411758i
$$638$$ 0 0
$$639$$ 18.0000 + 31.1769i 0.712069 + 1.23334i
$$640$$ 0 0
$$641$$ −30.0000 −1.18493 −0.592464 0.805597i $$-0.701845\pi$$
−0.592464 + 0.805597i $$0.701845\pi$$
$$642$$ 0 0
$$643$$ 28.0000 1.10421 0.552106 0.833774i $$-0.313824\pi$$
0.552106 + 0.833774i $$0.313824\pi$$
$$644$$ 0 0
$$645$$ −6.00000 + 10.3923i −0.236250 + 0.409197i
$$646$$ 0 0
$$647$$ 1.73205i 0.0680939i 0.999420 + 0.0340470i $$0.0108396\pi$$
−0.999420 + 0.0340470i $$0.989160\pi$$
$$648$$ 0 0
$$649$$ 10.3923i 0.407934i
$$650$$ 0 0
$$651$$ −9.00000 + 15.5885i −0.352738 + 0.610960i
$$652$$ 0 0
$$653$$ 17.3205i 0.677804i 0.940822 + 0.338902i $$0.110055\pi$$
−0.940822 + 0.338902i $$0.889945\pi$$
$$654$$ 0 0
$$655$$ 12.0000 0.468879
$$656$$ 0 0
$$657$$ 16.5000 + 28.5788i 0.643726 + 1.11497i
$$658$$ 0 0
$$659$$ 33.0000 1.28550 0.642749 0.766077i $$-0.277794\pi$$
0.642749 + 0.766077i $$0.277794\pi$$
$$660$$ 0 0
$$661$$ 22.5167i 0.875797i 0.899025 + 0.437898i $$0.144277\pi$$
−0.899025 + 0.437898i $$0.855723\pi$$
$$662$$ 0 0
$$663$$ 4.50000 + 2.59808i 0.174766 + 0.100901i
$$664$$ 0 0
$$665$$ −6.00000 + 13.8564i −0.232670 + 0.537328i
$$666$$ 0 0
$$667$$ 46.7654i 1.81076i
$$668$$ 0 0
$$669$$ −9.00000 + 15.5885i −0.347960 + 0.602685i
$$670$$ 0 0
$$671$$ 27.7128i 1.06984i
$$672$$ 0 0
$$673$$ 48.4974i 1.86944i 0.355387 + 0.934719i $$0.384349\pi$$
−0.355387 + 0.934719i $$0.615651\pi$$
$$674$$ 0 0
$$675$$ 36.3731i 1.40000i
$$676$$ 0 0
$$677$$ −15.0000 −0.576497 −0.288248 0.957556i $$-0.593073\pi$$
−0.288248 + 0.957556i $$0.593073\pi$$
$$678$$ 0 0
$$679$$ 13.8564i 0.531760i
$$680$$ 0 0
$$681$$ 4.50000 + 2.59808i 0.172440 + 0.0995585i
$$682$$ 0 0
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 0 0
$$685$$ −30.0000 −1.14624
$$686$$ 0 0
$$687$$ −12.0000 6.92820i −0.457829 0.264327i
$$688$$ 0 0
$$689$$ 15.5885i 0.593873i
$$690$$ 0 0
$$691$$ −20.0000 −0.760836 −0.380418 0.924815i $$-0.624220\pi$$
−0.380418 + 0.924815i $$0.624220\pi$$
$$692$$ 0 0
$$693$$ −9.00000 + 5.19615i −0.341882 + 0.197386i
$$694$$ 0 0
$$695$$ 48.4974i 1.83961i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 6.00000 10.3923i 0.226941 0.393073i
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 12.0000 27.7128i 0.452589 1.04521i
$$704$$ 0 0
$$705$$ 18.0000 + 10.3923i 0.677919 + 0.391397i
$$706$$ 0 0
$$707$$ 10.3923i 0.390843i
$$708$$ 0 0
$$709$$ −4.00000 −0.150223 −0.0751116 0.997175i $$-0.523931\pi$$
−0.0751116 + 0.997175i $$0.523931\pi$$
$$710$$ 0 0
$$711$$ −18.0000 + 10.3923i −0.675053 + 0.389742i
$$712$$ 0 0
$$713$$ −54.0000 −2.02232
$$714$$ 0 0
$$715$$ 20.7846i 0.777300i
$$716$$ 0 0
$$717$$ 10.5000 18.1865i 0.392130 0.679189i
$$718$$ 0 0
$$719$$ 8.66025i 0.322973i −0.986875 0.161486i $$-0.948371\pi$$
0.986875 0.161486i $$-0.0516288\pi$$
$$720$$ 0 0
$$721$$ 3.46410i 0.129010i
$$722$$ 0 0
$$723$$ 12.0000 20.7846i 0.446285 0.772988i
$$724$$ 0 0
$$725$$ −63.0000 −2.33976
$$726$$ 0 0
$$727$$ 7.00000 0.259616 0.129808 0.991539i $$-0.458564\pi$$
0.129808 + 0.991539i $$0.458564\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 3.46410i 0.128124i
$$732$$ 0 0
$$733$$ −22.0000 −0.812589 −0.406294 0.913742i $$-0.633179\pi$$
−0.406294 + 0.913742i $$0.633179\pi$$
$$734$$ 0 0
$$735$$ −18.0000 + 31.1769i −0.663940 + 1.14998i
$$736$$ 0 0
$$737$$ 30.0000 1.10506
$$738$$ 0 0
$$739$$ −40.0000 −1.47142 −0.735712 0.677295i $$-0.763152\pi$$
−0.735712 + 0.677295i $$0.763152\pi$$
$$740$$ 0 0
$$741$$ −10.5000 + 7.79423i −0.385727 + 0.286328i
$$742$$ 0 0
$$743$$ −30.0000 −1.10059 −0.550297 0.834969i $$-0.685485\pi$$
−0.550297 + 0.834969i $$0.685485\pi$$
$$744$$ 0 0
$$745$$ −24.0000 −0.879292
$$746$$ 0 0
$$747$$ −27.0000 + 15.5885i −0.987878 + 0.570352i
$$748$$ 0 0
$$749$$ 3.00000 0.109618
$$750$$ 0 0
$$751$$ 6.92820i 0.252814i 0.991978 + 0.126407i $$0.0403445\pi$$
−0.991978 + 0.126407i $$0.959656\pi$$
$$752$$ 0 0
$$753$$ 12.0000 20.7846i 0.437304 0.757433i
$$754$$ 0 0
$$755$$ −12.0000 −0.436725
$$756$$ 0 0
$$757$$ 16.0000 0.581530 0.290765 0.956795i $$-0.406090\pi$$
0.290765 + 0.956795i $$0.406090\pi$$
$$758$$ 0 0
$$759$$ −27.0000 15.5885i −0.980038 0.565825i
$$760$$ 0 0
$$761$$ 8.66025i 0.313934i 0.987604 + 0.156967i $$0.0501716\pi$$
−0.987604 + 0.156967i $$0.949828\pi$$
$$762$$ 0 0
$$763$$ 15.5885i 0.564340i
$$764$$ 0 0
$$765$$ −9.00000 15.5885i −0.325396 0.563602i
$$766$$ 0 0
$$767$$ 5.19615i 0.187622i
$$768$$ 0 0
$$769$$ 49.0000 1.76699 0.883493 0.468445i $$-0.155186\pi$$
0.883493 + 0.468445i $$0.155186\pi$$
$$770$$ 0 0
$$771$$ 9.00000 + 5.19615i 0.324127 + 0.187135i
$$772$$ 0 0
$$773$$ −3.00000 −0.107903 −0.0539513 0.998544i $$-0.517182\pi$$
−0.0539513 + 0.998544i $$0.517182\pi$$
$$774$$ 0 0
$$775$$ 72.7461i 2.61312i
$$776$$ 0 0
$$777$$ −6.00000 + 10.3923i −0.215249 + 0.372822i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 41.5692i 1.48746i
$$782$$ 0 0
$$783$$ 46.7654i 1.67126i
$$784$$ 0 0
$$785$$ 13.8564i 0.494556i
$$786$$ 0 0
$$787$$ 22.5167i 0.802632i −0.915940 0.401316i $$-0.868553\pi$$
0.915940 0.401316i $$-0.131447\pi$$
$$788$$ 0 0
$$789$$ 3.00000 5.19615i 0.106803 0.184988i
$$790$$ 0 0
$$791$$ 12.0000 0.426671
$$792$$ 0 0
$$793$$ 13.8564i 0.492055i
$$794$$ 0 0
$$795$$ −27.0000 + 46.7654i −0.957591 + 1.65860i
$$796$$ 0 0
$$797$$ −21.0000 −0.743858 −0.371929 0.928261i $$-0.621304\pi$$
−0.371929 + 0.928261i $$0.621304\pi$$
$$798$$ 0 0
$$799$$ 6.00000 0.212265