# Properties

 Label 2394.2.b.e.1709.1 Level $2394$ Weight $2$ Character 2394.1709 Analytic conductor $19.116$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2394.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$19.1161862439$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-2})$$ Defining polynomial: $$x^{2} + 2$$ x^2 + 2 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1709.1 Root $$-1.41421i$$ of defining polynomial Character $$\chi$$ $$=$$ 2394.1709 Dual form 2394.2.b.e.1709.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} +1.00000 q^{4} -2.82843i q^{5} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+1.00000 q^{2} +1.00000 q^{4} -2.82843i q^{5} +1.00000 q^{7} +1.00000 q^{8} -2.82843i q^{10} +5.65685i q^{11} +4.24264i q^{13} +1.00000 q^{14} +1.00000 q^{16} +5.65685i q^{17} +(1.00000 + 4.24264i) q^{19} -2.82843i q^{20} +5.65685i q^{22} +5.65685i q^{23} -3.00000 q^{25} +4.24264i q^{26} +1.00000 q^{28} -6.00000 q^{29} -8.48528i q^{31} +1.00000 q^{32} +5.65685i q^{34} -2.82843i q^{35} +(1.00000 + 4.24264i) q^{38} -2.82843i q^{40} -4.00000 q^{43} +5.65685i q^{44} +5.65685i q^{46} +9.89949i q^{47} +1.00000 q^{49} -3.00000 q^{50} +4.24264i q^{52} -6.00000 q^{53} +16.0000 q^{55} +1.00000 q^{56} -6.00000 q^{58} +12.0000 q^{59} +2.00000 q^{61} -8.48528i q^{62} +1.00000 q^{64} +12.0000 q^{65} -12.7279i q^{67} +5.65685i q^{68} -2.82843i q^{70} +6.00000 q^{71} +14.0000 q^{73} +(1.00000 + 4.24264i) q^{76} +5.65685i q^{77} -12.7279i q^{79} -2.82843i q^{80} -15.5563i q^{83} +16.0000 q^{85} -4.00000 q^{86} +5.65685i q^{88} -6.00000 q^{89} +4.24264i q^{91} +5.65685i q^{92} +9.89949i q^{94} +(12.0000 - 2.82843i) q^{95} +4.24264i q^{97} +1.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 2 q^{2} + 2 q^{4} + 2 q^{7} + 2 q^{8}+O(q^{10})$$ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^7 + 2 * q^8 $$2 q + 2 q^{2} + 2 q^{4} + 2 q^{7} + 2 q^{8} + 2 q^{14} + 2 q^{16} + 2 q^{19} - 6 q^{25} + 2 q^{28} - 12 q^{29} + 2 q^{32} + 2 q^{38} - 8 q^{43} + 2 q^{49} - 6 q^{50} - 12 q^{53} + 32 q^{55} + 2 q^{56} - 12 q^{58} + 24 q^{59} + 4 q^{61} + 2 q^{64} + 24 q^{65} + 12 q^{71} + 28 q^{73} + 2 q^{76} + 32 q^{85} - 8 q^{86} - 12 q^{89} + 24 q^{95} + 2 q^{98}+O(q^{100})$$ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^7 + 2 * q^8 + 2 * q^14 + 2 * q^16 + 2 * q^19 - 6 * q^25 + 2 * q^28 - 12 * q^29 + 2 * q^32 + 2 * q^38 - 8 * q^43 + 2 * q^49 - 6 * q^50 - 12 * q^53 + 32 * q^55 + 2 * q^56 - 12 * q^58 + 24 * q^59 + 4 * q^61 + 2 * q^64 + 24 * q^65 + 12 * q^71 + 28 * q^73 + 2 * q^76 + 32 * q^85 - 8 * q^86 - 12 * q^89 + 24 * q^95 + 2 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times$$.

 $$n$$ $$533$$ $$1009$$ $$1711$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ 2.82843i 1.26491i −0.774597 0.632456i $$-0.782047\pi$$
0.774597 0.632456i $$-0.217953\pi$$
$$6$$ 0 0
$$7$$ 1.00000 0.377964
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 2.82843i 0.894427i
$$11$$ 5.65685i 1.70561i 0.522233 + 0.852803i $$0.325099\pi$$
−0.522233 + 0.852803i $$0.674901\pi$$
$$12$$ 0 0
$$13$$ 4.24264i 1.17670i 0.808608 + 0.588348i $$0.200222\pi$$
−0.808608 + 0.588348i $$0.799778\pi$$
$$14$$ 1.00000 0.267261
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 5.65685i 1.37199i 0.727607 + 0.685994i $$0.240633\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 0 0
$$19$$ 1.00000 + 4.24264i 0.229416 + 0.973329i
$$20$$ 2.82843i 0.632456i
$$21$$ 0 0
$$22$$ 5.65685i 1.20605i
$$23$$ 5.65685i 1.17954i 0.807573 + 0.589768i $$0.200781\pi$$
−0.807573 + 0.589768i $$0.799219\pi$$
$$24$$ 0 0
$$25$$ −3.00000 −0.600000
$$26$$ 4.24264i 0.832050i
$$27$$ 0 0
$$28$$ 1.00000 0.188982
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 8.48528i 1.52400i −0.647576 0.762001i $$-0.724217\pi$$
0.647576 0.762001i $$-0.275783\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 5.65685i 0.970143i
$$35$$ 2.82843i 0.478091i
$$36$$ 0 0
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 1.00000 + 4.24264i 0.162221 + 0.688247i
$$39$$ 0 0
$$40$$ 2.82843i 0.447214i
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 5.65685i 0.852803i
$$45$$ 0 0
$$46$$ 5.65685i 0.834058i
$$47$$ 9.89949i 1.44399i 0.691898 + 0.721995i $$0.256775\pi$$
−0.691898 + 0.721995i $$0.743225\pi$$
$$48$$ 0 0
$$49$$ 1.00000 0.142857
$$50$$ −3.00000 −0.424264
$$51$$ 0 0
$$52$$ 4.24264i 0.588348i
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ 16.0000 2.15744
$$56$$ 1.00000 0.133631
$$57$$ 0 0
$$58$$ −6.00000 −0.787839
$$59$$ 12.0000 1.56227 0.781133 0.624364i $$-0.214642\pi$$
0.781133 + 0.624364i $$0.214642\pi$$
$$60$$ 0 0
$$61$$ 2.00000 0.256074 0.128037 0.991769i $$-0.459132\pi$$
0.128037 + 0.991769i $$0.459132\pi$$
$$62$$ 8.48528i 1.07763i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 12.0000 1.48842
$$66$$ 0 0
$$67$$ 12.7279i 1.55496i −0.628906 0.777482i $$-0.716497\pi$$
0.628906 0.777482i $$-0.283503\pi$$
$$68$$ 5.65685i 0.685994i
$$69$$ 0 0
$$70$$ 2.82843i 0.338062i
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 0 0
$$73$$ 14.0000 1.63858 0.819288 0.573382i $$-0.194369\pi$$
0.819288 + 0.573382i $$0.194369\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 1.00000 + 4.24264i 0.114708 + 0.486664i
$$77$$ 5.65685i 0.644658i
$$78$$ 0 0
$$79$$ 12.7279i 1.43200i −0.698099 0.716002i $$-0.745970\pi$$
0.698099 0.716002i $$-0.254030\pi$$
$$80$$ 2.82843i 0.316228i
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 15.5563i 1.70753i −0.520658 0.853766i $$-0.674313\pi$$
0.520658 0.853766i $$-0.325687\pi$$
$$84$$ 0 0
$$85$$ 16.0000 1.73544
$$86$$ −4.00000 −0.431331
$$87$$ 0 0
$$88$$ 5.65685i 0.603023i
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ 0 0
$$91$$ 4.24264i 0.444750i
$$92$$ 5.65685i 0.589768i
$$93$$ 0 0
$$94$$ 9.89949i 1.02105i
$$95$$ 12.0000 2.82843i 1.23117 0.290191i
$$96$$ 0 0
$$97$$ 4.24264i 0.430775i 0.976529 + 0.215387i $$0.0691014\pi$$
−0.976529 + 0.215387i $$0.930899\pi$$
$$98$$ 1.00000 0.101015
$$99$$ 0 0
$$100$$ −3.00000 −0.300000
$$101$$ 11.3137i 1.12576i −0.826540 0.562878i $$-0.809694\pi$$
0.826540 0.562878i $$-0.190306\pi$$
$$102$$ 0 0
$$103$$ 16.9706i 1.67216i 0.548608 + 0.836080i $$0.315158\pi$$
−0.548608 + 0.836080i $$0.684842\pi$$
$$104$$ 4.24264i 0.416025i
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ −18.0000 −1.74013 −0.870063 0.492941i $$-0.835922\pi$$
−0.870063 + 0.492941i $$0.835922\pi$$
$$108$$ 0 0
$$109$$ 8.48528i 0.812743i 0.913708 + 0.406371i $$0.133206\pi$$
−0.913708 + 0.406371i $$0.866794\pi$$
$$110$$ 16.0000 1.52554
$$111$$ 0 0
$$112$$ 1.00000 0.0944911
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ 16.0000 1.49201
$$116$$ −6.00000 −0.557086
$$117$$ 0 0
$$118$$ 12.0000 1.10469
$$119$$ 5.65685i 0.518563i
$$120$$ 0 0
$$121$$ −21.0000 −1.90909
$$122$$ 2.00000 0.181071
$$123$$ 0 0
$$124$$ 8.48528i 0.762001i
$$125$$ 5.65685i 0.505964i
$$126$$ 0 0
$$127$$ 12.7279i 1.12942i −0.825289 0.564710i $$-0.808988\pi$$
0.825289 0.564710i $$-0.191012\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 0 0
$$130$$ 12.0000 1.05247
$$131$$ 1.41421i 0.123560i 0.998090 + 0.0617802i $$0.0196778\pi$$
−0.998090 + 0.0617802i $$0.980322\pi$$
$$132$$ 0 0
$$133$$ 1.00000 + 4.24264i 0.0867110 + 0.367884i
$$134$$ 12.7279i 1.09952i
$$135$$ 0 0
$$136$$ 5.65685i 0.485071i
$$137$$ 9.89949i 0.845771i 0.906183 + 0.422885i $$0.138983\pi$$
−0.906183 + 0.422885i $$0.861017\pi$$
$$138$$ 0 0
$$139$$ 2.00000 0.169638 0.0848189 0.996396i $$-0.472969\pi$$
0.0848189 + 0.996396i $$0.472969\pi$$
$$140$$ 2.82843i 0.239046i
$$141$$ 0 0
$$142$$ 6.00000 0.503509
$$143$$ −24.0000 −2.00698
$$144$$ 0 0
$$145$$ 16.9706i 1.40933i
$$146$$ 14.0000 1.15865
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 7.07107i 0.579284i −0.957135 0.289642i $$-0.906464\pi$$
0.957135 0.289642i $$-0.0935363\pi$$
$$150$$ 0 0
$$151$$ 12.7279i 1.03578i −0.855446 0.517892i $$-0.826717\pi$$
0.855446 0.517892i $$-0.173283\pi$$
$$152$$ 1.00000 + 4.24264i 0.0811107 + 0.344124i
$$153$$ 0 0
$$154$$ 5.65685i 0.455842i
$$155$$ −24.0000 −1.92773
$$156$$ 0 0
$$157$$ 14.0000 1.11732 0.558661 0.829396i $$-0.311315\pi$$
0.558661 + 0.829396i $$0.311315\pi$$
$$158$$ 12.7279i 1.01258i
$$159$$ 0 0
$$160$$ 2.82843i 0.223607i
$$161$$ 5.65685i 0.445823i
$$162$$ 0 0
$$163$$ 8.00000 0.626608 0.313304 0.949653i $$-0.398564\pi$$
0.313304 + 0.949653i $$0.398564\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 15.5563i 1.20741i
$$167$$ 12.0000 0.928588 0.464294 0.885681i $$-0.346308\pi$$
0.464294 + 0.885681i $$0.346308\pi$$
$$168$$ 0 0
$$169$$ −5.00000 −0.384615
$$170$$ 16.0000 1.22714
$$171$$ 0 0
$$172$$ −4.00000 −0.304997
$$173$$ −6.00000 −0.456172 −0.228086 0.973641i $$-0.573247\pi$$
−0.228086 + 0.973641i $$0.573247\pi$$
$$174$$ 0 0
$$175$$ −3.00000 −0.226779
$$176$$ 5.65685i 0.426401i
$$177$$ 0 0
$$178$$ −6.00000 −0.449719
$$179$$ 18.0000 1.34538 0.672692 0.739923i $$-0.265138\pi$$
0.672692 + 0.739923i $$0.265138\pi$$
$$180$$ 0 0
$$181$$ 4.24264i 0.315353i −0.987491 0.157676i $$-0.949600\pi$$
0.987491 0.157676i $$-0.0504003\pi$$
$$182$$ 4.24264i 0.314485i
$$183$$ 0 0
$$184$$ 5.65685i 0.417029i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −32.0000 −2.34007
$$188$$ 9.89949i 0.721995i
$$189$$ 0 0
$$190$$ 12.0000 2.82843i 0.870572 0.205196i
$$191$$ 14.1421i 1.02329i 0.859197 + 0.511645i $$0.170964\pi$$
−0.859197 + 0.511645i $$0.829036\pi$$
$$192$$ 0 0
$$193$$ 16.9706i 1.22157i 0.791797 + 0.610784i $$0.209146\pi$$
−0.791797 + 0.610784i $$0.790854\pi$$
$$194$$ 4.24264i 0.304604i
$$195$$ 0 0
$$196$$ 1.00000 0.0714286
$$197$$ 18.3848i 1.30986i 0.755689 + 0.654931i $$0.227302\pi$$
−0.755689 + 0.654931i $$0.772698\pi$$
$$198$$ 0 0
$$199$$ 8.00000 0.567105 0.283552 0.958957i $$-0.408487\pi$$
0.283552 + 0.958957i $$0.408487\pi$$
$$200$$ −3.00000 −0.212132
$$201$$ 0 0
$$202$$ 11.3137i 0.796030i
$$203$$ −6.00000 −0.421117
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 16.9706i 1.18240i
$$207$$ 0 0
$$208$$ 4.24264i 0.294174i
$$209$$ −24.0000 + 5.65685i −1.66011 + 0.391293i
$$210$$ 0 0
$$211$$ 4.24264i 0.292075i −0.989279 0.146038i $$-0.953348\pi$$
0.989279 0.146038i $$-0.0466521\pi$$
$$212$$ −6.00000 −0.412082
$$213$$ 0 0
$$214$$ −18.0000 −1.23045
$$215$$ 11.3137i 0.771589i
$$216$$ 0 0
$$217$$ 8.48528i 0.576018i
$$218$$ 8.48528i 0.574696i
$$219$$ 0 0
$$220$$ 16.0000 1.07872
$$221$$ −24.0000 −1.61441
$$222$$ 0 0
$$223$$ 25.4558i 1.70465i −0.523013 0.852325i $$-0.675192\pi$$
0.523013 0.852325i $$-0.324808\pi$$
$$224$$ 1.00000 0.0668153
$$225$$ 0 0
$$226$$ −6.00000 −0.399114
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ 0 0
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 16.0000 1.05501
$$231$$ 0 0
$$232$$ −6.00000 −0.393919
$$233$$ 7.07107i 0.463241i −0.972806 0.231621i $$-0.925597\pi$$
0.972806 0.231621i $$-0.0744028\pi$$
$$234$$ 0 0
$$235$$ 28.0000 1.82652
$$236$$ 12.0000 0.781133
$$237$$ 0 0
$$238$$ 5.65685i 0.366679i
$$239$$ 14.1421i 0.914779i 0.889267 + 0.457389i $$0.151215\pi$$
−0.889267 + 0.457389i $$0.848785\pi$$
$$240$$ 0 0
$$241$$ 12.7279i 0.819878i −0.912113 0.409939i $$-0.865550\pi$$
0.912113 0.409939i $$-0.134450\pi$$
$$242$$ −21.0000 −1.34993
$$243$$ 0 0
$$244$$ 2.00000 0.128037
$$245$$ 2.82843i 0.180702i
$$246$$ 0 0
$$247$$ −18.0000 + 4.24264i −1.14531 + 0.269953i
$$248$$ 8.48528i 0.538816i
$$249$$ 0 0
$$250$$ 5.65685i 0.357771i
$$251$$ 1.41421i 0.0892644i 0.999003 + 0.0446322i $$0.0142116\pi$$
−0.999003 + 0.0446322i $$0.985788\pi$$
$$252$$ 0 0
$$253$$ −32.0000 −2.01182
$$254$$ 12.7279i 0.798621i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −18.0000 −1.12281 −0.561405 0.827541i $$-0.689739\pi$$
−0.561405 + 0.827541i $$0.689739\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 12.0000 0.744208
$$261$$ 0 0
$$262$$ 1.41421i 0.0873704i
$$263$$ 28.2843i 1.74408i −0.489432 0.872041i $$-0.662796\pi$$
0.489432 0.872041i $$-0.337204\pi$$
$$264$$ 0 0
$$265$$ 16.9706i 1.04249i
$$266$$ 1.00000 + 4.24264i 0.0613139 + 0.260133i
$$267$$ 0 0
$$268$$ 12.7279i 0.777482i
$$269$$ 12.0000 0.731653 0.365826 0.930683i $$-0.380786\pi$$
0.365826 + 0.930683i $$0.380786\pi$$
$$270$$ 0 0
$$271$$ 26.0000 1.57939 0.789694 0.613501i $$-0.210239\pi$$
0.789694 + 0.613501i $$0.210239\pi$$
$$272$$ 5.65685i 0.342997i
$$273$$ 0 0
$$274$$ 9.89949i 0.598050i
$$275$$ 16.9706i 1.02336i
$$276$$ 0 0
$$277$$ 8.00000 0.480673 0.240337 0.970690i $$-0.422742\pi$$
0.240337 + 0.970690i $$0.422742\pi$$
$$278$$ 2.00000 0.119952
$$279$$ 0 0
$$280$$ 2.82843i 0.169031i
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ −4.00000 −0.237775 −0.118888 0.992908i $$-0.537933\pi$$
−0.118888 + 0.992908i $$0.537933\pi$$
$$284$$ 6.00000 0.356034
$$285$$ 0 0
$$286$$ −24.0000 −1.41915
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −15.0000 −0.882353
$$290$$ 16.9706i 0.996546i
$$291$$ 0 0
$$292$$ 14.0000 0.819288
$$293$$ 24.0000 1.40209 0.701047 0.713115i $$-0.252716\pi$$
0.701047 + 0.713115i $$0.252716\pi$$
$$294$$ 0 0
$$295$$ 33.9411i 1.97613i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 7.07107i 0.409616i
$$299$$ −24.0000 −1.38796
$$300$$ 0 0
$$301$$ −4.00000 −0.230556
$$302$$ 12.7279i 0.732410i
$$303$$ 0 0
$$304$$ 1.00000 + 4.24264i 0.0573539 + 0.243332i
$$305$$ 5.65685i 0.323911i
$$306$$ 0 0
$$307$$ 25.4558i 1.45284i 0.687250 + 0.726421i $$0.258818\pi$$
−0.687250 + 0.726421i $$0.741182\pi$$
$$308$$ 5.65685i 0.322329i
$$309$$ 0 0
$$310$$ −24.0000 −1.36311
$$311$$ 1.41421i 0.0801927i 0.999196 + 0.0400963i $$0.0127665\pi$$
−0.999196 + 0.0400963i $$0.987234\pi$$
$$312$$ 0 0
$$313$$ 14.0000 0.791327 0.395663 0.918396i $$-0.370515\pi$$
0.395663 + 0.918396i $$0.370515\pi$$
$$314$$ 14.0000 0.790066
$$315$$ 0 0
$$316$$ 12.7279i 0.716002i
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 0 0
$$319$$ 33.9411i 1.90034i
$$320$$ 2.82843i 0.158114i
$$321$$ 0 0
$$322$$ 5.65685i 0.315244i
$$323$$ −24.0000 + 5.65685i −1.33540 + 0.314756i
$$324$$ 0 0
$$325$$ 12.7279i 0.706018i
$$326$$ 8.00000 0.443079
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 9.89949i 0.545777i
$$330$$ 0 0
$$331$$ 29.6985i 1.63238i 0.577786 + 0.816188i $$0.303917\pi$$
−0.577786 + 0.816188i $$0.696083\pi$$
$$332$$ 15.5563i 0.853766i
$$333$$ 0 0
$$334$$ 12.0000 0.656611
$$335$$ −36.0000 −1.96689
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ −5.00000 −0.271964
$$339$$ 0 0
$$340$$ 16.0000 0.867722
$$341$$ 48.0000 2.59935
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ −4.00000 −0.215666
$$345$$ 0 0
$$346$$ −6.00000 −0.322562
$$347$$ 2.82843i 0.151838i −0.997114 0.0759190i $$-0.975811\pi$$
0.997114 0.0759190i $$-0.0241890\pi$$
$$348$$ 0 0
$$349$$ −10.0000 −0.535288 −0.267644 0.963518i $$-0.586245\pi$$
−0.267644 + 0.963518i $$0.586245\pi$$
$$350$$ −3.00000 −0.160357
$$351$$ 0 0
$$352$$ 5.65685i 0.301511i
$$353$$ 22.6274i 1.20434i 0.798369 + 0.602168i $$0.205696\pi$$
−0.798369 + 0.602168i $$0.794304\pi$$
$$354$$ 0 0
$$355$$ 16.9706i 0.900704i
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ 18.0000 0.951330
$$359$$ 28.2843i 1.49279i −0.665505 0.746393i $$-0.731784\pi$$
0.665505 0.746393i $$-0.268216\pi$$
$$360$$ 0 0
$$361$$ −17.0000 + 8.48528i −0.894737 + 0.446594i
$$362$$ 4.24264i 0.222988i
$$363$$ 0 0
$$364$$ 4.24264i 0.222375i
$$365$$ 39.5980i 2.07265i
$$366$$ 0 0
$$367$$ −10.0000 −0.521996 −0.260998 0.965339i $$-0.584052\pi$$
−0.260998 + 0.965339i $$0.584052\pi$$
$$368$$ 5.65685i 0.294884i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −6.00000 −0.311504
$$372$$ 0 0
$$373$$ 25.4558i 1.31805i −0.752119 0.659027i $$-0.770968\pi$$
0.752119 0.659027i $$-0.229032\pi$$
$$374$$ −32.0000 −1.65468
$$375$$ 0 0
$$376$$ 9.89949i 0.510527i
$$377$$ 25.4558i 1.31104i
$$378$$ 0 0
$$379$$ 4.24264i 0.217930i 0.994046 + 0.108965i $$0.0347536\pi$$
−0.994046 + 0.108965i $$0.965246\pi$$
$$380$$ 12.0000 2.82843i 0.615587 0.145095i
$$381$$ 0 0
$$382$$ 14.1421i 0.723575i
$$383$$ 24.0000 1.22634 0.613171 0.789950i $$-0.289894\pi$$
0.613171 + 0.789950i $$0.289894\pi$$
$$384$$ 0 0
$$385$$ 16.0000 0.815436
$$386$$ 16.9706i 0.863779i
$$387$$ 0 0
$$388$$ 4.24264i 0.215387i
$$389$$ 9.89949i 0.501924i 0.967997 + 0.250962i $$0.0807470\pi$$
−0.967997 + 0.250962i $$0.919253\pi$$
$$390$$ 0 0
$$391$$ −32.0000 −1.61831
$$392$$ 1.00000 0.0505076
$$393$$ 0 0
$$394$$ 18.3848i 0.926212i
$$395$$ −36.0000 −1.81136
$$396$$ 0 0
$$397$$ 2.00000 0.100377 0.0501886 0.998740i $$-0.484018\pi$$
0.0501886 + 0.998740i $$0.484018\pi$$
$$398$$ 8.00000 0.401004
$$399$$ 0 0
$$400$$ −3.00000 −0.150000
$$401$$ −6.00000 −0.299626 −0.149813 0.988714i $$-0.547867\pi$$
−0.149813 + 0.988714i $$0.547867\pi$$
$$402$$ 0 0
$$403$$ 36.0000 1.79329
$$404$$ 11.3137i 0.562878i
$$405$$ 0 0
$$406$$ −6.00000 −0.297775
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 12.7279i 0.629355i 0.949199 + 0.314678i $$0.101896\pi$$
−0.949199 + 0.314678i $$0.898104\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 16.9706i 0.836080i
$$413$$ 12.0000 0.590481
$$414$$ 0 0
$$415$$ −44.0000 −2.15988
$$416$$ 4.24264i 0.208013i
$$417$$ 0 0
$$418$$ −24.0000 + 5.65685i −1.17388 + 0.276686i
$$419$$ 15.5563i 0.759977i −0.924991 0.379989i $$-0.875928\pi$$
0.924991 0.379989i $$-0.124072\pi$$
$$420$$ 0 0
$$421$$ 16.9706i 0.827095i −0.910483 0.413547i $$-0.864290\pi$$
0.910483 0.413547i $$-0.135710\pi$$
$$422$$ 4.24264i 0.206529i
$$423$$ 0 0
$$424$$ −6.00000 −0.291386
$$425$$ 16.9706i 0.823193i
$$426$$ 0 0
$$427$$ 2.00000 0.0967868
$$428$$ −18.0000 −0.870063
$$429$$ 0 0
$$430$$ 11.3137i 0.545595i
$$431$$ 6.00000 0.289010 0.144505 0.989504i $$-0.453841\pi$$
0.144505 + 0.989504i $$0.453841\pi$$
$$432$$ 0 0
$$433$$ 4.24264i 0.203888i −0.994790 0.101944i $$-0.967494\pi$$
0.994790 0.101944i $$-0.0325063\pi$$
$$434$$ 8.48528i 0.407307i
$$435$$ 0 0
$$436$$ 8.48528i 0.406371i
$$437$$ −24.0000 + 5.65685i −1.14808 + 0.270604i
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 16.0000 0.762770
$$441$$ 0 0
$$442$$ −24.0000 −1.14156
$$443$$ 28.2843i 1.34383i −0.740630 0.671913i $$-0.765473\pi$$
0.740630 0.671913i $$-0.234527\pi$$
$$444$$ 0 0
$$445$$ 16.9706i 0.804482i
$$446$$ 25.4558i 1.20537i
$$447$$ 0 0
$$448$$ 1.00000 0.0472456
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ −6.00000 −0.282216
$$453$$ 0 0
$$454$$ −12.0000 −0.563188
$$455$$ 12.0000 0.562569
$$456$$ 0 0
$$457$$ 32.0000 1.49690 0.748448 0.663193i $$-0.230799\pi$$
0.748448 + 0.663193i $$0.230799\pi$$
$$458$$ 14.0000 0.654177
$$459$$ 0 0
$$460$$ 16.0000 0.746004
$$461$$ 22.6274i 1.05386i 0.849907 + 0.526932i $$0.176658\pi$$
−0.849907 + 0.526932i $$0.823342\pi$$
$$462$$ 0 0
$$463$$ 32.0000 1.48717 0.743583 0.668644i $$-0.233125\pi$$
0.743583 + 0.668644i $$0.233125\pi$$
$$464$$ −6.00000 −0.278543
$$465$$ 0 0
$$466$$ 7.07107i 0.327561i
$$467$$ 18.3848i 0.850746i 0.905018 + 0.425373i $$0.139857\pi$$
−0.905018 + 0.425373i $$0.860143\pi$$
$$468$$ 0 0
$$469$$ 12.7279i 0.587721i
$$470$$ 28.0000 1.29154
$$471$$ 0 0
$$472$$ 12.0000 0.552345
$$473$$ 22.6274i 1.04041i
$$474$$ 0 0
$$475$$ −3.00000 12.7279i −0.137649 0.583997i
$$476$$ 5.65685i 0.259281i
$$477$$ 0 0
$$478$$ 14.1421i 0.646846i
$$479$$ 18.3848i 0.840022i 0.907519 + 0.420011i $$0.137974\pi$$
−0.907519 + 0.420011i $$0.862026\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 12.7279i 0.579741i
$$483$$ 0 0
$$484$$ −21.0000 −0.954545
$$485$$ 12.0000 0.544892
$$486$$ 0 0
$$487$$ 12.7279i 0.576757i 0.957516 + 0.288379i $$0.0931162\pi$$
−0.957516 + 0.288379i $$0.906884\pi$$
$$488$$ 2.00000 0.0905357
$$489$$ 0 0
$$490$$ 2.82843i 0.127775i
$$491$$ 36.7696i 1.65939i −0.558219 0.829693i $$-0.688515\pi$$
0.558219 0.829693i $$-0.311485\pi$$
$$492$$ 0 0
$$493$$ 33.9411i 1.52863i
$$494$$ −18.0000 + 4.24264i −0.809858 + 0.190885i
$$495$$ 0 0
$$496$$ 8.48528i 0.381000i
$$497$$ 6.00000 0.269137
$$498$$ 0 0
$$499$$ −16.0000 −0.716258 −0.358129 0.933672i $$-0.616585\pi$$
−0.358129 + 0.933672i $$0.616585\pi$$
$$500$$ 5.65685i 0.252982i
$$501$$ 0 0
$$502$$ 1.41421i 0.0631194i
$$503$$ 9.89949i 0.441397i 0.975342 + 0.220698i $$0.0708336\pi$$
−0.975342 + 0.220698i $$0.929166\pi$$
$$504$$ 0 0
$$505$$ −32.0000 −1.42398
$$506$$ −32.0000 −1.42257
$$507$$ 0 0
$$508$$ 12.7279i 0.564710i
$$509$$ 18.0000 0.797836 0.398918 0.916987i $$-0.369386\pi$$
0.398918 + 0.916987i $$0.369386\pi$$
$$510$$ 0 0
$$511$$ 14.0000 0.619324
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ −18.0000 −0.793946
$$515$$ 48.0000 2.11513
$$516$$ 0 0
$$517$$ −56.0000 −2.46288
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 12.0000 0.526235
$$521$$ −12.0000 −0.525730 −0.262865 0.964833i $$-0.584667\pi$$
−0.262865 + 0.964833i $$0.584667\pi$$
$$522$$ 0 0
$$523$$ 16.9706i 0.742071i −0.928619 0.371035i $$-0.879003\pi$$
0.928619 0.371035i $$-0.120997\pi$$
$$524$$ 1.41421i 0.0617802i
$$525$$ 0 0
$$526$$ 28.2843i 1.23325i
$$527$$ 48.0000 2.09091
$$528$$ 0 0
$$529$$ −9.00000 −0.391304
$$530$$ 16.9706i 0.737154i
$$531$$ 0 0
$$532$$ 1.00000 + 4.24264i 0.0433555 + 0.183942i
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 50.9117i 2.20110i
$$536$$ 12.7279i 0.549762i
$$537$$ 0 0
$$538$$ 12.0000 0.517357
$$539$$ 5.65685i 0.243658i
$$540$$ 0 0
$$541$$ −40.0000 −1.71973 −0.859867 0.510518i $$-0.829454\pi$$
−0.859867 + 0.510518i $$0.829454\pi$$
$$542$$ 26.0000 1.11680
$$543$$ 0 0
$$544$$ 5.65685i 0.242536i
$$545$$ 24.0000 1.02805
$$546$$ 0 0
$$547$$ 12.7279i 0.544207i −0.962268 0.272103i $$-0.912281\pi$$
0.962268 0.272103i $$-0.0877193\pi$$
$$548$$ 9.89949i 0.422885i
$$549$$ 0 0
$$550$$ 16.9706i 0.723627i
$$551$$ −6.00000 25.4558i −0.255609 1.08446i
$$552$$ 0 0
$$553$$ 12.7279i 0.541246i
$$554$$ 8.00000 0.339887
$$555$$ 0 0
$$556$$ 2.00000 0.0848189
$$557$$ 35.3553i 1.49805i 0.662540 + 0.749027i $$0.269479\pi$$
−0.662540 + 0.749027i $$0.730521\pi$$
$$558$$ 0 0
$$559$$ 16.9706i 0.717778i
$$560$$ 2.82843i 0.119523i
$$561$$ 0 0
$$562$$ −18.0000 −0.759284
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 16.9706i 0.713957i
$$566$$ −4.00000 −0.168133
$$567$$ 0 0
$$568$$ 6.00000 0.251754
$$569$$ 42.0000 1.76073 0.880366 0.474295i $$-0.157297\pi$$
0.880366 + 0.474295i $$0.157297\pi$$
$$570$$ 0 0
$$571$$ −28.0000 −1.17176 −0.585882 0.810397i $$-0.699252\pi$$
−0.585882 + 0.810397i $$0.699252\pi$$
$$572$$ −24.0000 −1.00349
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 16.9706i 0.707721i
$$576$$ 0 0
$$577$$ 2.00000 0.0832611 0.0416305 0.999133i $$-0.486745\pi$$
0.0416305 + 0.999133i $$0.486745\pi$$
$$578$$ −15.0000 −0.623918
$$579$$ 0 0
$$580$$ 16.9706i 0.704664i
$$581$$ 15.5563i 0.645386i
$$582$$ 0 0
$$583$$ 33.9411i 1.40570i
$$584$$ 14.0000 0.579324
$$585$$ 0 0
$$586$$ 24.0000 0.991431
$$587$$ 15.5563i 0.642079i −0.947066 0.321040i $$-0.895968\pi$$
0.947066 0.321040i $$-0.104032\pi$$
$$588$$ 0 0
$$589$$ 36.0000 8.48528i 1.48335 0.349630i
$$590$$ 33.9411i 1.39733i
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 39.5980i 1.62609i 0.582198 + 0.813047i $$0.302193\pi$$
−0.582198 + 0.813047i $$0.697807\pi$$
$$594$$ 0 0
$$595$$ 16.0000 0.655936
$$596$$ 7.07107i 0.289642i
$$597$$ 0 0
$$598$$ −24.0000 −0.981433
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 0 0
$$601$$ 4.24264i 0.173061i −0.996249 0.0865305i $$-0.972422\pi$$
0.996249 0.0865305i $$-0.0275780\pi$$
$$602$$ −4.00000 −0.163028
$$603$$ 0 0
$$604$$ 12.7279i 0.517892i
$$605$$ 59.3970i 2.41483i
$$606$$ 0 0
$$607$$ 33.9411i 1.37763i 0.724938 + 0.688814i $$0.241868\pi$$
−0.724938 + 0.688814i $$0.758132\pi$$
$$608$$ 1.00000 + 4.24264i 0.0405554 + 0.172062i
$$609$$ 0 0
$$610$$ 5.65685i 0.229039i
$$611$$ −42.0000 −1.69914
$$612$$ 0 0
$$613$$ −16.0000 −0.646234 −0.323117 0.946359i $$-0.604731\pi$$
−0.323117 + 0.946359i $$0.604731\pi$$
$$614$$ 25.4558i 1.02731i
$$615$$ 0 0
$$616$$ 5.65685i 0.227921i
$$617$$ 32.5269i 1.30948i −0.755852 0.654742i $$-0.772777\pi$$
0.755852 0.654742i $$-0.227223\pi$$
$$618$$ 0 0
$$619$$ −4.00000 −0.160774 −0.0803868 0.996764i $$-0.525616\pi$$
−0.0803868 + 0.996764i $$0.525616\pi$$
$$620$$ −24.0000 −0.963863
$$621$$ 0 0
$$622$$ 1.41421i 0.0567048i
$$623$$ −6.00000 −0.240385
$$624$$ 0 0
$$625$$ −31.0000 −1.24000
$$626$$ 14.0000 0.559553
$$627$$ 0 0
$$628$$ 14.0000 0.558661
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −28.0000 −1.11466 −0.557331 0.830290i $$-0.688175\pi$$
−0.557331 + 0.830290i $$0.688175\pi$$
$$632$$ 12.7279i 0.506290i
$$633$$ 0 0
$$634$$ 18.0000 0.714871
$$635$$ −36.0000 −1.42862
$$636$$ 0 0
$$637$$ 4.24264i 0.168100i
$$638$$ 33.9411i 1.34374i
$$639$$ 0 0
$$640$$ 2.82843i 0.111803i
$$641$$ 18.0000 0.710957 0.355479 0.934684i $$-0.384318\pi$$
0.355479 + 0.934684i $$0.384318\pi$$
$$642$$ 0 0
$$643$$ −22.0000 −0.867595 −0.433798 0.901010i $$-0.642827\pi$$
−0.433798 + 0.901010i $$0.642827\pi$$
$$644$$ 5.65685i 0.222911i
$$645$$ 0 0
$$646$$ −24.0000 + 5.65685i −0.944267 + 0.222566i
$$647$$ 15.5563i 0.611583i −0.952098 0.305792i $$-0.901079\pi$$
0.952098 0.305792i $$-0.0989211\pi$$
$$648$$ 0 0
$$649$$ 67.8823i 2.66461i
$$650$$ 12.7279i 0.499230i
$$651$$ 0 0
$$652$$ 8.00000 0.313304
$$653$$ 24.0416i 0.940822i −0.882448 0.470411i $$-0.844106\pi$$
0.882448 0.470411i $$-0.155894\pi$$
$$654$$ 0 0
$$655$$ 4.00000 0.156293
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 9.89949i 0.385922i
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ 38.1838i 1.48518i −0.669748 0.742588i $$-0.733598\pi$$
0.669748 0.742588i $$-0.266402\pi$$
$$662$$ 29.6985i 1.15426i
$$663$$ 0 0
$$664$$ 15.5563i 0.603703i
$$665$$ 12.0000 2.82843i 0.465340 0.109682i
$$666$$ 0 0
$$667$$ 33.9411i 1.31421i
$$668$$ 12.0000 0.464294
$$669$$ 0 0
$$670$$ −36.0000 −1.39080
$$671$$ 11.3137i 0.436761i
$$672$$ 0 0
$$673$$ 42.4264i 1.63542i 0.575632 + 0.817709i $$0.304756\pi$$
−0.575632 + 0.817709i $$0.695244\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ −5.00000 −0.192308
$$677$$ 30.0000 1.15299 0.576497 0.817099i $$-0.304419\pi$$
0.576497 + 0.817099i $$0.304419\pi$$
$$678$$ 0 0
$$679$$ 4.24264i 0.162818i
$$680$$ 16.0000 0.613572
$$681$$ 0 0
$$682$$ 48.0000 1.83801
$$683$$ −12.0000 −0.459167 −0.229584 0.973289i $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 0 0
$$685$$ 28.0000 1.06983
$$686$$ 1.00000 0.0381802
$$687$$ 0 0
$$688$$ −4.00000 −0.152499
$$689$$ 25.4558i 0.969790i
$$690$$ 0 0
$$691$$ −28.0000 −1.06517 −0.532585 0.846376i $$-0.678779\pi$$
−0.532585 + 0.846376i $$0.678779\pi$$
$$692$$ −6.00000 −0.228086
$$693$$ 0 0
$$694$$ 2.82843i 0.107366i
$$695$$ 5.65685i 0.214577i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −10.0000 −0.378506
$$699$$ 0 0
$$700$$ −3.00000 −0.113389
$$701$$ 7.07107i 0.267071i −0.991044 0.133535i $$-0.957367\pi$$
0.991044 0.133535i $$-0.0426329\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 5.65685i 0.213201i
$$705$$ 0 0
$$706$$ 22.6274i 0.851594i
$$707$$ 11.3137i 0.425496i
$$708$$ 0 0
$$709$$ −4.00000 −0.150223 −0.0751116 0.997175i $$-0.523931\pi$$
−0.0751116 + 0.997175i $$0.523931\pi$$
$$710$$ 16.9706i 0.636894i
$$711$$ 0 0
$$712$$ −6.00000 −0.224860
$$713$$ 48.0000 1.79761
$$714$$ 0 0
$$715$$ 67.8823i 2.53865i
$$716$$ 18.0000 0.672692
$$717$$ 0 0
$$718$$ 28.2843i 1.05556i
$$719$$ 7.07107i 0.263706i −0.991269 0.131853i $$-0.957907\pi$$
0.991269 0.131853i $$-0.0420927\pi$$
$$720$$ 0 0
$$721$$ 16.9706i 0.632017i
$$722$$ −17.0000 + 8.48528i −0.632674 + 0.315789i
$$723$$ 0 0
$$724$$ 4.24264i 0.157676i
$$725$$ 18.0000 0.668503
$$726$$ 0 0
$$727$$ 2.00000 0.0741759 0.0370879 0.999312i $$-0.488192\pi$$
0.0370879 + 0.999312i $$0.488192\pi$$
$$728$$ 4.24264i 0.157243i
$$729$$ 0 0
$$730$$ 39.5980i 1.46559i
$$731$$ 22.6274i 0.836905i
$$732$$ 0 0
$$733$$ 14.0000 0.517102 0.258551 0.965998i $$-0.416755\pi$$
0.258551 + 0.965998i $$0.416755\pi$$
$$734$$ −10.0000 −0.369107
$$735$$ 0 0
$$736$$ 5.65685i 0.208514i
$$737$$ 72.0000 2.65215
$$738$$ 0 0
$$739$$ −16.0000 −0.588570 −0.294285 0.955718i $$-0.595081\pi$$
−0.294285 + 0.955718i $$0.595081\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −6.00000 −0.220267
$$743$$ −48.0000 −1.76095 −0.880475 0.474093i $$-0.842776\pi$$
−0.880475 + 0.474093i $$0.842776\pi$$
$$744$$ 0 0
$$745$$ −20.0000 −0.732743
$$746$$ 25.4558i 0.932005i
$$747$$ 0 0
$$748$$ −32.0000 −1.17004
$$749$$ −18.0000 −0.657706
$$750$$ 0 0
$$751$$ 12.7279i 0.464448i 0.972662 + 0.232224i $$0.0746003\pi$$
−0.972662 + 0.232224i $$0.925400\pi$$
$$752$$ 9.89949i 0.360997i
$$753$$ 0 0
$$754$$ 25.4558i 0.927047i
$$755$$ −36.0000 −1.31017
$$756$$ 0 0
$$757$$ 44.0000 1.59921 0.799604 0.600528i $$-0.205043\pi$$
0.799604 + 0.600528i $$0.205043\pi$$
$$758$$ 4.24264i 0.154100i
$$759$$ 0 0
$$760$$ 12.0000 2.82843i 0.435286 0.102598i
$$761$$ 2.82843i 0.102530i −0.998685 0.0512652i $$-0.983675\pi$$
0.998685 0.0512652i $$-0.0163254\pi$$
$$762$$ 0 0
$$763$$ 8.48528i 0.307188i
$$764$$ 14.1421i 0.511645i
$$765$$ 0 0
$$766$$ 24.0000 0.867155
$$767$$ 50.9117i 1.83831i
$$768$$ 0 0
$$769$$ −22.0000 −0.793340 −0.396670 0.917961i $$-0.629834\pi$$
−0.396670 + 0.917961i $$0.629834\pi$$
$$770$$ 16.0000 0.576600
$$771$$ 0 0
$$772$$ 16.9706i 0.610784i
$$773$$ 6.00000 0.215805 0.107903 0.994161i $$-0.465587\pi$$
0.107903 + 0.994161i $$0.465587\pi$$
$$774$$ 0 0
$$775$$ 25.4558i 0.914401i
$$776$$ 4.24264i 0.152302i
$$777$$ 0 0
$$778$$ 9.89949i 0.354914i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 33.9411i 1.21451i
$$782$$ −32.0000 −1.14432
$$783$$ 0 0
$$784$$ 1.00000 0.0357143
$$785$$ 39.5980i 1.41331i
$$786$$ 0 0
$$787$$ 33.9411i 1.20987i −0.796275 0.604935i $$-0.793199\pi$$
0.796275 0.604935i $$-0.206801\pi$$
$$788$$ 18.3848i 0.654931i
$$789$$ 0 0
$$790$$ −36.0000 −1.28082
$$791$$ −6.00000 −0.213335
$$792$$ 0 0
$$793$$ 8.48528i 0.301321i
$$794$$ 2.00000 0.0709773
$$795$$ 0 0
$$796$$ 8.00000 0.283552
$$797$$ −48.0000 −1.70025 −0.850124 0.526583i $$-0.823473\pi$$
−0.850124 + 0.526583i $$0.823473\pi$$
$$798$$ 0 0
$$799$$ −56.0000 −1.98114