# Properties

 Label 60.2.h.a.59.1 Level $60$ Weight $2$ Character 60.59 Analytic conductor $0.479$ Analytic rank $0$ Dimension $4$ CM discriminant -20 Inner twists $8$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$60 = 2^{2} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 60.h (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.479102412128$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{-5})$$ Defining polynomial: $$x^{4} - 4 x^{2} + 9$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

## Embedding invariants

 Embedding label 59.1 Root $$1.58114 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 60.59 Dual form 60.2.h.a.59.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.41421i q^{2} +(-1.58114 - 0.707107i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-1.00000 + 2.23607i) q^{6} +3.16228 q^{7} +2.82843i q^{8} +(2.00000 + 2.23607i) q^{9} +O(q^{10})$$ $$q-1.41421i q^{2} +(-1.58114 - 0.707107i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-1.00000 + 2.23607i) q^{6} +3.16228 q^{7} +2.82843i q^{8} +(2.00000 + 2.23607i) q^{9} -3.16228 q^{10} +(3.16228 + 1.41421i) q^{12} -4.47214i q^{14} +(-1.58114 + 3.53553i) q^{15} +4.00000 q^{16} +(3.16228 - 2.82843i) q^{18} +4.47214i q^{20} +(-5.00000 - 2.23607i) q^{21} +1.41421i q^{23} +(2.00000 - 4.47214i) q^{24} -5.00000 q^{25} +(-1.58114 - 4.94975i) q^{27} -6.32456 q^{28} +8.94427i q^{29} +(5.00000 + 2.23607i) q^{30} -5.65685i q^{32} -7.07107i q^{35} +(-4.00000 - 4.47214i) q^{36} +6.32456 q^{40} -4.47214i q^{41} +(-3.16228 + 7.07107i) q^{42} +3.16228 q^{43} +(5.00000 - 4.47214i) q^{45} +2.00000 q^{46} +9.89949i q^{47} +(-6.32456 - 2.82843i) q^{48} +3.00000 q^{49} +7.07107i q^{50} +(-7.00000 + 2.23607i) q^{54} +8.94427i q^{56} +12.6491 q^{58} +(3.16228 - 7.07107i) q^{60} +8.00000 q^{61} +(6.32456 + 7.07107i) q^{63} -8.00000 q^{64} -15.8114 q^{67} +(1.00000 - 2.23607i) q^{69} -10.0000 q^{70} +(-6.32456 + 5.65685i) q^{72} +(7.90569 + 3.53553i) q^{75} -8.94427i q^{80} +(-1.00000 + 8.94427i) q^{81} -6.32456 q^{82} -15.5563i q^{83} +(10.0000 + 4.47214i) q^{84} -4.47214i q^{86} +(6.32456 - 14.1421i) q^{87} -17.8885i q^{89} +(-6.32456 - 7.07107i) q^{90} -2.82843i q^{92} +14.0000 q^{94} +(-4.00000 + 8.94427i) q^{96} -4.24264i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 8q^{4} - 4q^{6} + 8q^{9} + O(q^{10})$$ $$4q - 8q^{4} - 4q^{6} + 8q^{9} + 16q^{16} - 20q^{21} + 8q^{24} - 20q^{25} + 20q^{30} - 16q^{36} + 20q^{45} + 8q^{46} + 12q^{49} - 28q^{54} + 32q^{61} - 32q^{64} + 4q^{69} - 40q^{70} - 4q^{81} + 40q^{84} + 56q^{94} - 16q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$37$$ $$41$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.41421i 1.00000i
$$3$$ −1.58114 0.707107i −0.912871 0.408248i
$$4$$ −2.00000 −1.00000
$$5$$ 2.23607i 1.00000i
$$6$$ −1.00000 + 2.23607i −0.408248 + 0.912871i
$$7$$ 3.16228 1.19523 0.597614 0.801784i $$-0.296115\pi$$
0.597614 + 0.801784i $$0.296115\pi$$
$$8$$ 2.82843i 1.00000i
$$9$$ 2.00000 + 2.23607i 0.666667 + 0.745356i
$$10$$ −3.16228 −1.00000
$$11$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$12$$ 3.16228 + 1.41421i 0.912871 + 0.408248i
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 4.47214i 1.19523i
$$15$$ −1.58114 + 3.53553i −0.408248 + 0.912871i
$$16$$ 4.00000 1.00000
$$17$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$18$$ 3.16228 2.82843i 0.745356 0.666667i
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 4.47214i 1.00000i
$$21$$ −5.00000 2.23607i −1.09109 0.487950i
$$22$$ 0 0
$$23$$ 1.41421i 0.294884i 0.989071 + 0.147442i $$0.0471040\pi$$
−0.989071 + 0.147442i $$0.952896\pi$$
$$24$$ 2.00000 4.47214i 0.408248 0.912871i
$$25$$ −5.00000 −1.00000
$$26$$ 0 0
$$27$$ −1.58114 4.94975i −0.304290 0.952579i
$$28$$ −6.32456 −1.19523
$$29$$ 8.94427i 1.66091i 0.557086 + 0.830455i $$0.311919\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 5.00000 + 2.23607i 0.912871 + 0.408248i
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 5.65685i 1.00000i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 7.07107i 1.19523i
$$36$$ −4.00000 4.47214i −0.666667 0.745356i
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 6.32456 1.00000
$$41$$ 4.47214i 0.698430i −0.937043 0.349215i $$-0.886448\pi$$
0.937043 0.349215i $$-0.113552\pi$$
$$42$$ −3.16228 + 7.07107i −0.487950 + 1.09109i
$$43$$ 3.16228 0.482243 0.241121 0.970495i $$-0.422485\pi$$
0.241121 + 0.970495i $$0.422485\pi$$
$$44$$ 0 0
$$45$$ 5.00000 4.47214i 0.745356 0.666667i
$$46$$ 2.00000 0.294884
$$47$$ 9.89949i 1.44399i 0.691898 + 0.721995i $$0.256775\pi$$
−0.691898 + 0.721995i $$0.743225\pi$$
$$48$$ −6.32456 2.82843i −0.912871 0.408248i
$$49$$ 3.00000 0.428571
$$50$$ 7.07107i 1.00000i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ −7.00000 + 2.23607i −0.952579 + 0.304290i
$$55$$ 0 0
$$56$$ 8.94427i 1.19523i
$$57$$ 0 0
$$58$$ 12.6491 1.66091
$$59$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$60$$ 3.16228 7.07107i 0.408248 0.912871i
$$61$$ 8.00000 1.02430 0.512148 0.858898i $$-0.328850\pi$$
0.512148 + 0.858898i $$0.328850\pi$$
$$62$$ 0 0
$$63$$ 6.32456 + 7.07107i 0.796819 + 0.890871i
$$64$$ −8.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −15.8114 −1.93167 −0.965834 0.259161i $$-0.916554\pi$$
−0.965834 + 0.259161i $$0.916554\pi$$
$$68$$ 0 0
$$69$$ 1.00000 2.23607i 0.120386 0.269191i
$$70$$ −10.0000 −1.19523
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ −6.32456 + 5.65685i −0.745356 + 0.666667i
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 7.90569 + 3.53553i 0.912871 + 0.408248i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 8.94427i 1.00000i
$$81$$ −1.00000 + 8.94427i −0.111111 + 0.993808i
$$82$$ −6.32456 −0.698430
$$83$$ 15.5563i 1.70753i −0.520658 0.853766i $$-0.674313\pi$$
0.520658 0.853766i $$-0.325687\pi$$
$$84$$ 10.0000 + 4.47214i 1.09109 + 0.487950i
$$85$$ 0 0
$$86$$ 4.47214i 0.482243i
$$87$$ 6.32456 14.1421i 0.678064 1.51620i
$$88$$ 0 0
$$89$$ 17.8885i 1.89618i −0.317999 0.948091i $$-0.603011\pi$$
0.317999 0.948091i $$-0.396989\pi$$
$$90$$ −6.32456 7.07107i −0.666667 0.745356i
$$91$$ 0 0
$$92$$ 2.82843i 0.294884i
$$93$$ 0 0
$$94$$ 14.0000 1.44399
$$95$$ 0 0
$$96$$ −4.00000 + 8.94427i −0.408248 + 0.912871i
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 4.24264i 0.428571i
$$99$$ 0 0
$$100$$ 10.0000 1.00000
$$101$$ 8.94427i 0.889988i 0.895533 + 0.444994i $$0.146794\pi$$
−0.895533 + 0.444994i $$0.853206\pi$$
$$102$$ 0 0
$$103$$ −15.8114 −1.55794 −0.778971 0.627060i $$-0.784258\pi$$
−0.778971 + 0.627060i $$0.784258\pi$$
$$104$$ 0 0
$$105$$ −5.00000 + 11.1803i −0.487950 + 1.09109i
$$106$$ 0 0
$$107$$ 18.3848i 1.77732i 0.458563 + 0.888662i $$0.348364\pi$$
−0.458563 + 0.888662i $$0.651636\pi$$
$$108$$ 3.16228 + 9.89949i 0.304290 + 0.952579i
$$109$$ −16.0000 −1.53252 −0.766261 0.642529i $$-0.777885\pi$$
−0.766261 + 0.642529i $$0.777885\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 12.6491 1.19523
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 3.16228 0.294884
$$116$$ 17.8885i 1.66091i
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ −10.0000 4.47214i −0.912871 0.408248i
$$121$$ −11.0000 −1.00000
$$122$$ 11.3137i 1.02430i
$$123$$ −3.16228 + 7.07107i −0.285133 + 0.637577i
$$124$$ 0 0
$$125$$ 11.1803i 1.00000i
$$126$$ 10.0000 8.94427i 0.890871 0.796819i
$$127$$ 22.1359 1.96425 0.982124 0.188237i $$-0.0602772\pi$$
0.982124 + 0.188237i $$0.0602772\pi$$
$$128$$ 11.3137i 1.00000i
$$129$$ −5.00000 2.23607i −0.440225 0.196875i
$$130$$ 0 0
$$131$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 22.3607i 1.93167i
$$135$$ −11.0680 + 3.53553i −0.952579 + 0.304290i
$$136$$ 0 0
$$137$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$138$$ −3.16228 1.41421i −0.269191 0.120386i
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 14.1421i 1.19523i
$$141$$ 7.00000 15.6525i 0.589506 1.31818i
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 8.00000 + 8.94427i 0.666667 + 0.745356i
$$145$$ 20.0000 1.66091
$$146$$ 0 0
$$147$$ −4.74342 2.12132i −0.391230 0.174964i
$$148$$ 0 0
$$149$$ 4.47214i 0.366372i −0.983078 0.183186i $$-0.941359\pi$$
0.983078 0.183186i $$-0.0586410\pi$$
$$150$$ 5.00000 11.1803i 0.408248 0.912871i
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ −12.6491 −1.00000
$$161$$ 4.47214i 0.352454i
$$162$$ 12.6491 + 1.41421i 0.993808 + 0.111111i
$$163$$ 22.1359 1.73382 0.866910 0.498464i $$-0.166102\pi$$
0.866910 + 0.498464i $$0.166102\pi$$
$$164$$ 8.94427i 0.698430i
$$165$$ 0 0
$$166$$ −22.0000 −1.70753
$$167$$ 24.0416i 1.86040i −0.367057 0.930199i $$-0.619634\pi$$
0.367057 0.930199i $$-0.380366\pi$$
$$168$$ 6.32456 14.1421i 0.487950 1.09109i
$$169$$ 13.0000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −6.32456 −0.482243
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ −20.0000 8.94427i −1.51620 0.678064i
$$175$$ −15.8114 −1.19523
$$176$$ 0 0
$$177$$ 0 0
$$178$$ −25.2982 −1.89618
$$179$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$180$$ −10.0000 + 8.94427i −0.745356 + 0.666667i
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ −12.6491 5.65685i −0.935049 0.418167i
$$184$$ −4.00000 −0.294884
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 19.7990i 1.44399i
$$189$$ −5.00000 15.6525i −0.363696 1.13855i
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 12.6491 + 5.65685i 0.912871 + 0.408248i
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −6.00000 −0.428571
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 14.1421i 1.00000i
$$201$$ 25.0000 + 11.1803i 1.76336 + 0.788600i
$$202$$ 12.6491 0.889988
$$203$$ 28.2843i 1.98517i
$$204$$ 0 0
$$205$$ −10.0000 −0.698430
$$206$$ 22.3607i 1.55794i
$$207$$ −3.16228 + 2.82843i −0.219793 + 0.196589i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 15.8114 + 7.07107i 1.09109 + 0.487950i
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 26.0000 1.77732
$$215$$ 7.07107i 0.482243i
$$216$$ 14.0000 4.47214i 0.952579 0.304290i
$$217$$ 0 0
$$218$$ 22.6274i 1.53252i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 3.16228 0.211762 0.105881 0.994379i $$-0.466234\pi$$
0.105881 + 0.994379i $$0.466234\pi$$
$$224$$ 17.8885i 1.19523i
$$225$$ −10.0000 11.1803i −0.666667 0.745356i
$$226$$ 0 0
$$227$$ 9.89949i 0.657053i 0.944495 + 0.328526i $$0.106552\pi$$
−0.944495 + 0.328526i $$0.893448\pi$$
$$228$$ 0 0
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ 4.47214i 0.294884i
$$231$$ 0 0
$$232$$ −25.2982 −1.66091
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ 0 0
$$235$$ 22.1359 1.44399
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ −6.32456 + 14.1421i −0.408248 + 0.912871i
$$241$$ −28.0000 −1.80364 −0.901819 0.432113i $$-0.857768\pi$$
−0.901819 + 0.432113i $$0.857768\pi$$
$$242$$ 15.5563i 1.00000i
$$243$$ 7.90569 13.4350i 0.507151 0.861858i
$$244$$ −16.0000 −1.02430
$$245$$ 6.70820i 0.428571i
$$246$$ 10.0000 + 4.47214i 0.637577 + 0.285133i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −11.0000 + 24.5967i −0.697097 + 1.55876i
$$250$$ 15.8114 1.00000
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ −12.6491 14.1421i −0.796819 0.890871i
$$253$$ 0 0
$$254$$ 31.3050i 1.96425i
$$255$$ 0 0
$$256$$ 16.0000 1.00000
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ −3.16228 + 7.07107i −0.196875 + 0.440225i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −20.0000 + 17.8885i −1.23797 + 1.10727i
$$262$$ 0 0
$$263$$ 15.5563i 0.959246i −0.877475 0.479623i $$-0.840774\pi$$
0.877475 0.479623i $$-0.159226\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −12.6491 + 28.2843i −0.774113 + 1.73097i
$$268$$ 31.6228 1.93167
$$269$$ 22.3607i 1.36335i 0.731653 + 0.681677i $$0.238749\pi$$
−0.731653 + 0.681677i $$0.761251\pi$$
$$270$$ 5.00000 + 15.6525i 0.304290 + 0.952579i
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ −2.00000 + 4.47214i −0.120386 + 0.269191i
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 20.0000 1.19523
$$281$$ 31.3050i 1.86750i −0.357930 0.933748i $$-0.616517\pi$$
0.357930 0.933748i $$-0.383483\pi$$
$$282$$ −22.1359 9.89949i −1.31818 0.589506i
$$283$$ −15.8114 −0.939889 −0.469945 0.882696i $$-0.655726\pi$$
−0.469945 + 0.882696i $$0.655726\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 14.1421i 0.834784i
$$288$$ 12.6491 11.3137i 0.745356 0.666667i
$$289$$ −17.0000 −1.00000
$$290$$ 28.2843i 1.66091i
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ −3.00000 + 6.70820i −0.174964 + 0.391230i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ −6.32456 −0.366372
$$299$$ 0 0
$$300$$ −15.8114 7.07107i −0.912871 0.408248i
$$301$$ 10.0000 0.576390
$$302$$ 0 0
$$303$$ 6.32456 14.1421i 0.363336 0.812444i
$$304$$ 0 0
$$305$$ 17.8885i 1.02430i
$$306$$ 0 0
$$307$$ −34.7851 −1.98529 −0.992644 0.121070i $$-0.961367\pi$$
−0.992644 + 0.121070i $$0.961367\pi$$
$$308$$ 0 0
$$309$$ 25.0000 + 11.1803i 1.42220 + 0.636027i
$$310$$ 0 0
$$311$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 15.8114 14.1421i 0.890871 0.796819i
$$316$$ 0 0
$$317$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 17.8885i 1.00000i
$$321$$ 13.0000 29.0689i 0.725589 1.62247i
$$322$$ 6.32456 0.352454
$$323$$ 0 0
$$324$$ 2.00000 17.8885i 0.111111 0.993808i
$$325$$ 0 0
$$326$$ 31.3050i 1.73382i
$$327$$ 25.2982 + 11.3137i 1.39899 + 0.625650i
$$328$$ 12.6491 0.698430
$$329$$ 31.3050i 1.72590i
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 31.1127i 1.70753i
$$333$$ 0 0
$$334$$ −34.0000 −1.86040
$$335$$ 35.3553i 1.93167i
$$336$$ −20.0000 8.94427i −1.09109 0.487950i
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 18.3848i 1.00000i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −12.6491 −0.682988
$$344$$ 8.94427i 0.482243i
$$345$$ −5.00000 2.23607i −0.269191 0.120386i
$$346$$ 0 0
$$347$$ 24.0416i 1.29062i −0.763920 0.645311i $$-0.776728\pi$$
0.763920 0.645311i $$-0.223272\pi$$
$$348$$ −12.6491 + 28.2843i −0.678064 + 1.51620i
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 22.3607i 1.19523i
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 35.7771i 1.89618i
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$360$$ 12.6491 + 14.1421i 0.666667 + 0.745356i
$$361$$ 19.0000 1.00000
$$362$$ 2.82843i 0.148659i
$$363$$ 17.3925 + 7.77817i 0.912871 + 0.408248i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −8.00000 + 17.8885i −0.418167 + 0.935049i
$$367$$ 3.16228 0.165070 0.0825348 0.996588i $$-0.473698\pi$$
0.0825348 + 0.996588i $$0.473698\pi$$
$$368$$ 5.65685i 0.294884i
$$369$$ 10.0000 8.94427i 0.520579 0.465620i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 7.90569 17.6777i 0.408248 0.912871i
$$376$$ −28.0000 −1.44399
$$377$$ 0 0
$$378$$ −22.1359 + 7.07107i −1.13855 + 0.363696i
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ −35.0000 15.6525i −1.79310 0.801901i
$$382$$ 0 0
$$383$$ 26.8701i 1.37300i 0.727132 + 0.686498i $$0.240853\pi$$
−0.727132 + 0.686498i $$0.759147\pi$$
$$384$$ 8.00000 17.8885i 0.408248 0.912871i
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 6.32456 + 7.07107i 0.321495 + 0.359443i
$$388$$ 0 0
$$389$$ 31.3050i 1.58722i −0.608424 0.793612i $$-0.708198\pi$$
0.608424 0.793612i $$-0.291802\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 8.48528i 0.428571i
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −20.0000 −1.00000
$$401$$ 35.7771i 1.78662i 0.449439 + 0.893311i $$0.351624\pi$$
−0.449439 + 0.893311i $$0.648376\pi$$
$$402$$ 15.8114 35.3553i 0.788600 1.76336i
$$403$$ 0 0
$$404$$ 17.8885i 0.889988i
$$405$$ 20.0000 + 2.23607i 0.993808 + 0.111111i
$$406$$ 40.0000 1.98517
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −4.00000 −0.197787 −0.0988936 0.995098i $$-0.531530\pi$$
−0.0988936 + 0.995098i $$0.531530\pi$$
$$410$$ 14.1421i 0.698430i
$$411$$ 0 0
$$412$$ 31.6228 1.55794
$$413$$ 0 0
$$414$$ 4.00000 + 4.47214i 0.196589 + 0.219793i
$$415$$ −34.7851 −1.70753
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$420$$ 10.0000 22.3607i 0.487950 1.09109i
$$421$$ 8.00000 0.389896 0.194948 0.980814i $$-0.437546\pi$$
0.194948 + 0.980814i $$0.437546\pi$$
$$422$$ 0 0
$$423$$ −22.1359 + 19.7990i −1.07629 + 0.962660i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 25.2982 1.22427
$$428$$ 36.7696i 1.77732i
$$429$$ 0 0
$$430$$ −10.0000 −0.482243
$$431$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$432$$ −6.32456 19.7990i −0.304290 0.952579i
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 0 0
$$435$$ −31.6228 14.1421i −1.51620 0.678064i
$$436$$ 32.0000 1.53252
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 6.00000 + 6.70820i 0.285714 + 0.319438i
$$442$$ 0 0
$$443$$ 41.0122i 1.94855i −0.225367 0.974274i $$-0.572358\pi$$
0.225367 0.974274i $$-0.427642\pi$$
$$444$$ 0 0
$$445$$ −40.0000 −1.89618
$$446$$ 4.47214i 0.211762i
$$447$$ −3.16228 + 7.07107i −0.149571 + 0.334450i
$$448$$ −25.2982 −1.19523
$$449$$ 22.3607i 1.05527i 0.849473 + 0.527633i $$0.176920\pi$$
−0.849473 + 0.527633i $$0.823080\pi$$
$$450$$ −15.8114 + 14.1421i −0.745356 + 0.666667i
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 14.0000 0.657053
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ 19.7990i 0.925146i
$$459$$ 0 0
$$460$$ −6.32456 −0.294884
$$461$$ 8.94427i 0.416576i 0.978068 + 0.208288i $$0.0667892\pi$$
−0.978068 + 0.208288i $$0.933211\pi$$
$$462$$ 0 0
$$463$$ 41.1096 1.91053 0.955263 0.295758i $$-0.0955723\pi$$
0.955263 + 0.295758i $$0.0955723\pi$$
$$464$$ 35.7771i 1.66091i
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 32.5269i 1.50517i −0.658497 0.752583i $$-0.728808\pi$$
0.658497 0.752583i $$-0.271192\pi$$
$$468$$ 0 0
$$469$$ −50.0000 −2.30879
$$470$$ 31.3050i 1.44399i
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$480$$ 20.0000 + 8.94427i 0.912871 + 0.408248i
$$481$$ 0 0
$$482$$ 39.5980i 1.80364i
$$483$$ 3.16228 7.07107i 0.143889 0.321745i
$$484$$ 22.0000 1.00000
$$485$$ 0 0
$$486$$ −19.0000 11.1803i −0.861858 0.507151i
$$487$$ 22.1359 1.00308 0.501538 0.865136i $$-0.332768\pi$$
0.501538 + 0.865136i $$0.332768\pi$$
$$488$$ 22.6274i 1.02430i
$$489$$ −35.0000 15.6525i −1.58275 0.707829i
$$490$$ −9.48683 −0.428571
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 6.32456 14.1421i 0.285133 0.637577i
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 34.7851 + 15.5563i 1.55876 + 0.697097i
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ 22.3607i 1.00000i
$$501$$ −17.0000 + 38.0132i −0.759504 + 1.69830i
$$502$$ 0 0
$$503$$ 43.8406i 1.95476i 0.211498 + 0.977378i $$0.432166\pi$$
−0.211498 + 0.977378i $$0.567834\pi$$
$$504$$ −20.0000 + 17.8885i −0.890871 + 0.796819i
$$505$$ 20.0000 0.889988
$$506$$ 0 0
$$507$$ −20.5548 9.19239i −0.912871 0.408248i
$$508$$ −44.2719 −1.96425
$$509$$ 44.7214i 1.98224i −0.132973 0.991120i $$-0.542452\pi$$
0.132973 0.991120i $$-0.457548\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 22.6274i 1.00000i
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 35.3553i 1.55794i
$$516$$ 10.0000 + 4.47214i 0.440225 + 0.196875i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 17.8885i 0.783711i −0.920027 0.391856i $$-0.871833\pi$$
0.920027 0.391856i $$-0.128167\pi$$
$$522$$ 25.2982 + 28.2843i 1.10727 + 1.23797i
$$523$$ −34.7851 −1.52104 −0.760522 0.649312i $$-0.775057\pi$$
−0.760522 + 0.649312i $$0.775057\pi$$
$$524$$ 0 0
$$525$$ 25.0000 + 11.1803i 1.09109 + 0.487950i
$$526$$ −22.0000 −0.959246
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 21.0000 0.913043
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 40.0000 + 17.8885i 1.73097 + 0.774113i
$$535$$ 41.1096 1.77732
$$536$$ 44.7214i 1.93167i
$$537$$ 0 0
$$538$$ 31.6228 1.36335
$$539$$ 0 0
$$540$$ 22.1359 7.07107i 0.952579 0.304290i
$$541$$ 38.0000 1.63375 0.816874 0.576816i $$-0.195705\pi$$
0.816874 + 0.576816i $$0.195705\pi$$
$$542$$ 0 0
$$543$$ −3.16228 1.41421i −0.135706 0.0606897i
$$544$$ 0 0
$$545$$ 35.7771i 1.53252i
$$546$$ 0 0
$$547$$ 3.16228 0.135209 0.0676046 0.997712i $$-0.478464\pi$$
0.0676046 + 0.997712i $$0.478464\pi$$
$$548$$ 0 0
$$549$$ 16.0000 + 17.8885i 0.682863 + 0.763464i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 6.32456 + 2.82843i 0.269191 + 0.120386i
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 28.2843i 1.19523i
$$561$$ 0 0
$$562$$ −44.2719 −1.86750
$$563$$ 1.41421i 0.0596020i 0.999556 + 0.0298010i $$0.00948736\pi$$
−0.999556 + 0.0298010i $$0.990513\pi$$
$$564$$ −14.0000 + 31.3050i −0.589506 + 1.31818i
$$565$$ 0 0
$$566$$ 22.3607i 0.939889i
$$567$$ −3.16228 + 28.2843i −0.132803 + 1.18783i
$$568$$ 0 0
$$569$$ 31.3050i 1.31237i −0.754599 0.656186i $$-0.772169\pi$$
0.754599 0.656186i $$-0.227831\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −20.0000 −0.834784
$$575$$ 7.07107i 0.294884i
$$576$$ −16.0000 17.8885i −0.666667 0.745356i
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ 24.0416i 1.00000i
$$579$$ 0 0
$$580$$ −40.0000 −1.66091
$$581$$ 49.1935i 2.04089i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 9.89949i 0.408596i 0.978909 + 0.204298i $$0.0654911\pi$$
−0.978909 + 0.204298i $$0.934509\pi$$
$$588$$ 9.48683 + 4.24264i 0.391230 + 0.174964i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 8.94427i 0.366372i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ −10.0000 + 22.3607i −0.408248 + 0.912871i
$$601$$ −28.0000 −1.14214 −0.571072 0.820900i $$-0.693472\pi$$
−0.571072 + 0.820900i $$0.693472\pi$$
$$602$$ 14.1421i 0.576390i
$$603$$ −31.6228 35.3553i −1.28778 1.43978i
$$604$$ 0 0
$$605$$ 24.5967i 1.00000i
$$606$$ −20.0000 8.94427i −0.812444 0.363336i
$$607$$ −15.8114 −0.641764 −0.320882 0.947119i $$-0.603979\pi$$
−0.320882 + 0.947119i $$0.603979\pi$$
$$608$$ 0 0
$$609$$ 20.0000 44.7214i 0.810441 1.81220i
$$610$$ −25.2982 −1.02430
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 49.1935i 1.98529i
$$615$$ 15.8114 + 7.07107i 0.637577 + 0.285133i
$$616$$ 0 0
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 15.8114 35.3553i 0.636027 1.42220i
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 7.00000 2.23607i 0.280900 0.0897303i
$$622$$ 0 0
$$623$$ 56.5685i 2.26637i
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ −20.0000 22.3607i −0.796819 0.890871i
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 49.4975i 1.96425i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 25.2982 1.00000
$$641$$ 49.1935i 1.94303i 0.236986 + 0.971513i $$0.423841\pi$$
−0.236986 + 0.971513i $$0.576159\pi$$
$$642$$ −41.1096 18.3848i −1.62247 0.725589i
$$643$$ 41.1096 1.62120 0.810602 0.585597i $$-0.199140\pi$$
0.810602 + 0.585597i $$0.199140\pi$$
$$644$$ 8.94427i 0.352454i
$$645$$ −5.00000 + 11.1803i −0.196875 + 0.440225i
$$646$$ 0 0
$$647$$ 18.3848i 0.722780i 0.932415 + 0.361390i $$0.117698\pi$$
−0.932415 + 0.361390i $$0.882302\pi$$
$$648$$ −25.2982 2.82843i −0.993808 0.111111i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −44.2719 −1.73382
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 16.0000 35.7771i 0.625650 1.39899i
$$655$$ 0 0
$$656$$ 17.8885i 0.698430i
$$657$$ 0 0
$$658$$ 44.2719 1.72590
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 32.0000 1.24466 0.622328 0.782757i $$-0.286187\pi$$
0.622328 + 0.782757i $$0.286187\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 44.0000 1.70753
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −12.6491 −0.489776
$$668$$ 48.0833i 1.86040i
$$669$$ −5.00000 2.23607i −0.193311 0.0864514i
$$670$$ 50.0000 1.93167
$$671$$ 0 0
$$672$$ −12.6491 + 28.2843i −0.487950 + 1.09109i
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 7.90569 + 24.7487i 0.304290 + 0.952579i
$$676$$ −26.0000 −1.00000
$$677$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 7.00000 15.6525i 0.268241 0.599804i
$$682$$ 0 0
$$683$$ 43.8406i 1.67751i 0.544505 + 0.838757i $$0.316717\pi$$
−0.544505 + 0.838757i $$0.683283\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 17.8885i 0.682988i
$$687$$ −22.1359 9.89949i −0.844539 0.377689i
$$688$$ 12.6491 0.482243
$$689$$ 0 0
$$690$$ −3.16228 + 7.07107i −0.120386 + 0.269191i
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −34.0000 −1.29062
$$695$$ 0 0
$$696$$ 40.0000 + 17.8885i 1.51620 + 0.678064i
$$697$$ 0 0
$$698$$ 36.7696i 1.39175i
$$699$$ 0 0
$$700$$ 31.6228 1.19523
$$701$$ 22.3607i 0.844551i 0.906467 + 0.422276i $$0.138769\pi$$
−0.906467 + 0.422276i $$0.861231\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ −35.0000 15.6525i −1.31818 0.589506i
$$706$$ 0 0
$$707$$ 28.2843i 1.06374i
$$708$$ 0 0
$$709$$ −46.0000 −1.72757 −0.863783 0.503864i $$-0.831911\pi$$
−0.863783 + 0.503864i $$0.831911\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 50.5964 1.89618
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$720$$ 20.0000 17.8885i 0.745356 0.666667i
$$721$$ −50.0000 −1.86210
$$722$$ 26.8701i 1.00000i
$$723$$ 44.2719 + 19.7990i 1.64649 + 0.736332i
$$724$$ −4.00000 −0.148659
$$725$$ 44.7214i 1.66091i
$$726$$ 11.0000 24.5967i 0.408248 0.912871i
$$727$$ −53.7587 −1.99380 −0.996900 0.0786754i $$-0.974931\pi$$
−0.996900 + 0.0786754i $$0.974931\pi$$
$$728$$ 0 0
$$729$$ −22.0000 + 15.6525i −0.814815 + 0.579721i
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 25.2982 + 11.3137i 0.935049 + 0.418167i
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 4.47214i 0.165070i
$$735$$ −4.74342 + 10.6066i −0.174964 + 0.391230i
$$736$$ 8.00000 0.294884
$$737$$ 0 0
$$738$$ −12.6491 14.1421i −0.465620 0.520579i
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 26.8701i 0.985767i 0.870095 + 0.492883i $$0.164057\pi$$
−0.870095 + 0.492883i $$0.835943\pi$$
$$744$$ 0 0
$$745$$ −10.0000 −0.366372
$$746$$ 0 0
$$747$$ 34.7851 31.1127i 1.27272 1.13835i
$$748$$ 0 0
$$749$$ 58.1378i 2.12431i
$$750$$ −25.0000 11.1803i −0.912871 0.408248i
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 39.5980i 1.44399i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 10.0000 + 31.3050i 0.363696 + 1.13855i
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 35.7771i 1.29692i 0.761249 + 0.648459i $$0.224586\pi$$
−0.761249 + 0.648459i $$0.775414\pi$$
$$762$$ −22.1359 + 49.4975i −0.801901 + 1.79310i
$$763$$ −50.5964 −1.83171
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 38.0000 1.37300
$$767$$ 0 0
$$768$$ −25.2982 11.3137i −0.912871 0.408248i
$$769$$ 14.0000 0.504853 0.252426 0.967616i $$-0.418771\pi$$
0.252426 + 0.967616i $$0.418771\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$774$$ 10.0000 8.94427i 0.359443 0.321495i
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −44.2719 −1.58722
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 44.2719 14.1421i 1.58215 0.505399i
$$784$$ 12.0000 0.428571
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 41.1096 1.46540 0.732700 0.680552i $$-0.238260\pi$$
0.732700 + 0.680552i $$0.238260\pi$$
$$788$$ 0 0
$$789$$ −11.0000 + 24.5967i −0.391610 + 0.875667i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 28.2843i 1.00000i
$$801$$ 40.0000 35.7771i 1.41333 1.26412i
$$802$$ 50.5964 1.78662
$$803$$ 0 0