Properties

 Label 3120.2.l.i.1249.2 Level $3120$ Weight $2$ Character 3120.1249 Analytic conductor $24.913$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3120.l (of order $$2$$, degree $$1$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$24.9133254306$$ 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: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

 Embedding label 1249.2 Root $$1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 3120.1249 Dual form 3120.2.l.i.1249.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{3} +(2.00000 - 1.00000i) q^{5} +4.00000i q^{7} -1.00000 q^{9} +O(q^{10})$$ $$q+1.00000i q^{3} +(2.00000 - 1.00000i) q^{5} +4.00000i q^{7} -1.00000 q^{9} +6.00000 q^{11} -1.00000i q^{13} +(1.00000 + 2.00000i) q^{15} -4.00000i q^{17} +2.00000 q^{19} -4.00000 q^{21} -6.00000i q^{23} +(3.00000 - 4.00000i) q^{25} -1.00000i q^{27} +10.0000 q^{29} -4.00000 q^{31} +6.00000i q^{33} +(4.00000 + 8.00000i) q^{35} -6.00000i q^{37} +1.00000 q^{39} +10.0000 q^{41} +(-2.00000 + 1.00000i) q^{45} -8.00000i q^{47} -9.00000 q^{49} +4.00000 q^{51} +6.00000i q^{53} +(12.0000 - 6.00000i) q^{55} +2.00000i q^{57} -6.00000 q^{59} -6.00000 q^{61} -4.00000i q^{63} +(-1.00000 - 2.00000i) q^{65} +12.0000i q^{67} +6.00000 q^{69} -2.00000i q^{73} +(4.00000 + 3.00000i) q^{75} +24.0000i q^{77} -8.00000 q^{79} +1.00000 q^{81} -4.00000i q^{83} +(-4.00000 - 8.00000i) q^{85} +10.0000i q^{87} -14.0000 q^{89} +4.00000 q^{91} -4.00000i q^{93} +(4.00000 - 2.00000i) q^{95} +14.0000i q^{97} -6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 4 q^{5} - 2 q^{9}+O(q^{10})$$ 2 * q + 4 * q^5 - 2 * q^9 $$2 q + 4 q^{5} - 2 q^{9} + 12 q^{11} + 2 q^{15} + 4 q^{19} - 8 q^{21} + 6 q^{25} + 20 q^{29} - 8 q^{31} + 8 q^{35} + 2 q^{39} + 20 q^{41} - 4 q^{45} - 18 q^{49} + 8 q^{51} + 24 q^{55} - 12 q^{59} - 12 q^{61} - 2 q^{65} + 12 q^{69} + 8 q^{75} - 16 q^{79} + 2 q^{81} - 8 q^{85} - 28 q^{89} + 8 q^{91} + 8 q^{95} - 12 q^{99}+O(q^{100})$$ 2 * q + 4 * q^5 - 2 * q^9 + 12 * q^11 + 2 * q^15 + 4 * q^19 - 8 * q^21 + 6 * q^25 + 20 * q^29 - 8 * q^31 + 8 * q^35 + 2 * q^39 + 20 * q^41 - 4 * q^45 - 18 * q^49 + 8 * q^51 + 24 * q^55 - 12 * q^59 - 12 * q^61 - 2 * q^65 + 12 * q^69 + 8 * q^75 - 16 * q^79 + 2 * q^81 - 8 * q^85 - 28 * q^89 + 8 * q^91 + 8 * q^95 - 12 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3120\mathbb{Z}\right)^\times$$.

 $$n$$ $$1951$$ $$2081$$ $$2341$$ $$2497$$ $$2641$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$

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
$$3$$ 1.00000i 0.577350i
$$4$$ 0 0
$$5$$ 2.00000 1.00000i 0.894427 0.447214i
$$6$$ 0 0
$$7$$ 4.00000i 1.51186i 0.654654 + 0.755929i $$0.272814\pi$$
−0.654654 + 0.755929i $$0.727186\pi$$
$$8$$ 0 0
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ 6.00000 1.80907 0.904534 0.426401i $$-0.140219\pi$$
0.904534 + 0.426401i $$0.140219\pi$$
$$12$$ 0 0
$$13$$ 1.00000i 0.277350i
$$14$$ 0 0
$$15$$ 1.00000 + 2.00000i 0.258199 + 0.516398i
$$16$$ 0 0
$$17$$ 4.00000i 0.970143i −0.874475 0.485071i $$-0.838794\pi$$
0.874475 0.485071i $$-0.161206\pi$$
$$18$$ 0 0
$$19$$ 2.00000 0.458831 0.229416 0.973329i $$-0.426318\pi$$
0.229416 + 0.973329i $$0.426318\pi$$
$$20$$ 0 0
$$21$$ −4.00000 −0.872872
$$22$$ 0 0
$$23$$ 6.00000i 1.25109i −0.780189 0.625543i $$-0.784877\pi$$
0.780189 0.625543i $$-0.215123\pi$$
$$24$$ 0 0
$$25$$ 3.00000 4.00000i 0.600000 0.800000i
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ 10.0000 1.85695 0.928477 0.371391i $$-0.121119\pi$$
0.928477 + 0.371391i $$0.121119\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ 6.00000i 1.04447i
$$34$$ 0 0
$$35$$ 4.00000 + 8.00000i 0.676123 + 1.35225i
$$36$$ 0 0
$$37$$ 6.00000i 0.986394i −0.869918 0.493197i $$-0.835828\pi$$
0.869918 0.493197i $$-0.164172\pi$$
$$38$$ 0 0
$$39$$ 1.00000 0.160128
$$40$$ 0 0
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 0 0
$$45$$ −2.00000 + 1.00000i −0.298142 + 0.149071i
$$46$$ 0 0
$$47$$ 8.00000i 1.16692i −0.812142 0.583460i $$-0.801699\pi$$
0.812142 0.583460i $$-0.198301\pi$$
$$48$$ 0 0
$$49$$ −9.00000 −1.28571
$$50$$ 0 0
$$51$$ 4.00000 0.560112
$$52$$ 0 0
$$53$$ 6.00000i 0.824163i 0.911147 + 0.412082i $$0.135198\pi$$
−0.911147 + 0.412082i $$0.864802\pi$$
$$54$$ 0 0
$$55$$ 12.0000 6.00000i 1.61808 0.809040i
$$56$$ 0 0
$$57$$ 2.00000i 0.264906i
$$58$$ 0 0
$$59$$ −6.00000 −0.781133 −0.390567 0.920575i $$-0.627721\pi$$
−0.390567 + 0.920575i $$0.627721\pi$$
$$60$$ 0 0
$$61$$ −6.00000 −0.768221 −0.384111 0.923287i $$-0.625492\pi$$
−0.384111 + 0.923287i $$0.625492\pi$$
$$62$$ 0 0
$$63$$ 4.00000i 0.503953i
$$64$$ 0 0
$$65$$ −1.00000 2.00000i −0.124035 0.248069i
$$66$$ 0 0
$$67$$ 12.0000i 1.46603i 0.680211 + 0.733017i $$0.261888\pi$$
−0.680211 + 0.733017i $$0.738112\pi$$
$$68$$ 0 0
$$69$$ 6.00000 0.722315
$$70$$ 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 $$-0.962659\pi$$
0.993127 0.117041i $$-0.0373409\pi$$
$$74$$ 0 0
$$75$$ 4.00000 + 3.00000i 0.461880 + 0.346410i
$$76$$ 0 0
$$77$$ 24.0000i 2.73505i
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 4.00000i 0.439057i −0.975606 0.219529i $$-0.929548\pi$$
0.975606 0.219529i $$-0.0704519\pi$$
$$84$$ 0 0
$$85$$ −4.00000 8.00000i −0.433861 0.867722i
$$86$$ 0 0
$$87$$ 10.0000i 1.07211i
$$88$$ 0 0
$$89$$ −14.0000 −1.48400 −0.741999 0.670402i $$-0.766122\pi$$
−0.741999 + 0.670402i $$0.766122\pi$$
$$90$$ 0 0
$$91$$ 4.00000 0.419314
$$92$$ 0 0
$$93$$ 4.00000i 0.414781i
$$94$$ 0 0
$$95$$ 4.00000 2.00000i 0.410391 0.205196i
$$96$$ 0 0
$$97$$ 14.0000i 1.42148i 0.703452 + 0.710742i $$0.251641\pi$$
−0.703452 + 0.710742i $$0.748359\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ 10.0000 0.995037 0.497519 0.867453i $$-0.334245\pi$$
0.497519 + 0.867453i $$0.334245\pi$$
$$102$$ 0 0
$$103$$ 2.00000i 0.197066i −0.995134 0.0985329i $$-0.968585\pi$$
0.995134 0.0985329i $$-0.0314150\pi$$
$$104$$ 0 0
$$105$$ −8.00000 + 4.00000i −0.780720 + 0.390360i
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ −4.00000 −0.383131 −0.191565 0.981480i $$-0.561356\pi$$
−0.191565 + 0.981480i $$0.561356\pi$$
$$110$$ 0 0
$$111$$ 6.00000 0.569495
$$112$$ 0 0
$$113$$ 4.00000i 0.376288i 0.982141 + 0.188144i $$0.0602472\pi$$
−0.982141 + 0.188144i $$0.939753\pi$$
$$114$$ 0 0
$$115$$ −6.00000 12.0000i −0.559503 1.11901i
$$116$$ 0 0
$$117$$ 1.00000i 0.0924500i
$$118$$ 0 0
$$119$$ 16.0000 1.46672
$$120$$ 0 0
$$121$$ 25.0000 2.27273
$$122$$ 0 0
$$123$$ 10.0000i 0.901670i
$$124$$ 0 0
$$125$$ 2.00000 11.0000i 0.178885 0.983870i
$$126$$ 0 0
$$127$$ 10.0000i 0.887357i 0.896186 + 0.443678i $$0.146327\pi$$
−0.896186 + 0.443678i $$0.853673\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 8.00000 0.698963 0.349482 0.936943i $$-0.386358\pi$$
0.349482 + 0.936943i $$0.386358\pi$$
$$132$$ 0 0
$$133$$ 8.00000i 0.693688i
$$134$$ 0 0
$$135$$ −1.00000 2.00000i −0.0860663 0.172133i
$$136$$ 0 0
$$137$$ 14.0000i 1.19610i −0.801459 0.598050i $$-0.795942\pi$$
0.801459 0.598050i $$-0.204058\pi$$
$$138$$ 0 0
$$139$$ 16.0000 1.35710 0.678551 0.734553i $$-0.262608\pi$$
0.678551 + 0.734553i $$0.262608\pi$$
$$140$$ 0 0
$$141$$ 8.00000 0.673722
$$142$$ 0 0
$$143$$ 6.00000i 0.501745i
$$144$$ 0 0
$$145$$ 20.0000 10.0000i 1.66091 0.830455i
$$146$$ 0 0
$$147$$ 9.00000i 0.742307i
$$148$$ 0 0
$$149$$ −16.0000 −1.31077 −0.655386 0.755295i $$-0.727494\pi$$
−0.655386 + 0.755295i $$0.727494\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 0 0
$$153$$ 4.00000i 0.323381i
$$154$$ 0 0
$$155$$ −8.00000 + 4.00000i −0.642575 + 0.321288i
$$156$$ 0 0
$$157$$ 6.00000i 0.478852i 0.970915 + 0.239426i $$0.0769593\pi$$
−0.970915 + 0.239426i $$0.923041\pi$$
$$158$$ 0 0
$$159$$ −6.00000 −0.475831
$$160$$ 0 0
$$161$$ 24.0000 1.89146
$$162$$ 0 0
$$163$$ 4.00000i 0.313304i −0.987654 0.156652i $$-0.949930\pi$$
0.987654 0.156652i $$-0.0500701\pi$$
$$164$$ 0 0
$$165$$ 6.00000 + 12.0000i 0.467099 + 0.934199i
$$166$$ 0 0
$$167$$ 16.0000i 1.23812i 0.785345 + 0.619059i $$0.212486\pi$$
−0.785345 + 0.619059i $$0.787514\pi$$
$$168$$ 0 0
$$169$$ −1.00000 −0.0769231
$$170$$ 0 0
$$171$$ −2.00000 −0.152944
$$172$$ 0 0
$$173$$ 22.0000i 1.67263i 0.548250 + 0.836315i $$0.315294\pi$$
−0.548250 + 0.836315i $$0.684706\pi$$
$$174$$ 0 0
$$175$$ 16.0000 + 12.0000i 1.20949 + 0.907115i
$$176$$ 0 0
$$177$$ 6.00000i 0.450988i
$$178$$ 0 0
$$179$$ −24.0000 −1.79384 −0.896922 0.442189i $$-0.854202\pi$$
−0.896922 + 0.442189i $$0.854202\pi$$
$$180$$ 0 0
$$181$$ 6.00000 0.445976 0.222988 0.974821i $$-0.428419\pi$$
0.222988 + 0.974821i $$0.428419\pi$$
$$182$$ 0 0
$$183$$ 6.00000i 0.443533i
$$184$$ 0 0
$$185$$ −6.00000 12.0000i −0.441129 0.882258i
$$186$$ 0 0
$$187$$ 24.0000i 1.75505i
$$188$$ 0 0
$$189$$ 4.00000 0.290957
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 0 0
$$193$$ 2.00000i 0.143963i 0.997406 + 0.0719816i $$0.0229323\pi$$
−0.997406 + 0.0719816i $$0.977068\pi$$
$$194$$ 0 0
$$195$$ 2.00000 1.00000i 0.143223 0.0716115i
$$196$$ 0 0
$$197$$ 6.00000i 0.427482i −0.976890 0.213741i $$-0.931435\pi$$
0.976890 0.213741i $$-0.0685649\pi$$
$$198$$ 0 0
$$199$$ −8.00000 −0.567105 −0.283552 0.958957i $$-0.591513\pi$$
−0.283552 + 0.958957i $$0.591513\pi$$
$$200$$ 0 0
$$201$$ −12.0000 −0.846415
$$202$$ 0 0
$$203$$ 40.0000i 2.80745i
$$204$$ 0 0
$$205$$ 20.0000 10.0000i 1.39686 0.698430i
$$206$$ 0 0
$$207$$ 6.00000i 0.417029i
$$208$$ 0 0
$$209$$ 12.0000 0.830057
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 16.0000i 1.08615i
$$218$$ 0 0
$$219$$ 2.00000 0.135147
$$220$$ 0 0
$$221$$ −4.00000 −0.269069
$$222$$ 0 0
$$223$$ 8.00000i 0.535720i 0.963458 + 0.267860i $$0.0863164\pi$$
−0.963458 + 0.267860i $$0.913684\pi$$
$$224$$ 0 0
$$225$$ −3.00000 + 4.00000i −0.200000 + 0.266667i
$$226$$ 0 0
$$227$$ 4.00000i 0.265489i 0.991150 + 0.132745i $$0.0423790\pi$$
−0.991150 + 0.132745i $$0.957621\pi$$
$$228$$ 0 0
$$229$$ −8.00000 −0.528655 −0.264327 0.964433i $$-0.585150\pi$$
−0.264327 + 0.964433i $$0.585150\pi$$
$$230$$ 0 0
$$231$$ −24.0000 −1.57908
$$232$$ 0 0
$$233$$ 12.0000i 0.786146i 0.919507 + 0.393073i $$0.128588\pi$$
−0.919507 + 0.393073i $$0.871412\pi$$
$$234$$ 0 0
$$235$$ −8.00000 16.0000i −0.521862 1.04372i
$$236$$ 0 0
$$237$$ 8.00000i 0.519656i
$$238$$ 0 0
$$239$$ −4.00000 −0.258738 −0.129369 0.991596i $$-0.541295\pi$$
−0.129369 + 0.991596i $$0.541295\pi$$
$$240$$ 0 0
$$241$$ 18.0000 1.15948 0.579741 0.814801i $$-0.303154\pi$$
0.579741 + 0.814801i $$0.303154\pi$$
$$242$$ 0 0
$$243$$ 1.00000i 0.0641500i
$$244$$ 0 0
$$245$$ −18.0000 + 9.00000i −1.14998 + 0.574989i
$$246$$ 0 0
$$247$$ 2.00000i 0.127257i
$$248$$ 0 0
$$249$$ 4.00000 0.253490
$$250$$ 0 0
$$251$$ 20.0000 1.26239 0.631194 0.775625i $$-0.282565\pi$$
0.631194 + 0.775625i $$0.282565\pi$$
$$252$$ 0 0
$$253$$ 36.0000i 2.26330i
$$254$$ 0 0
$$255$$ 8.00000 4.00000i 0.500979 0.250490i
$$256$$ 0 0
$$257$$ 28.0000i 1.74659i 0.487190 + 0.873296i $$0.338022\pi$$
−0.487190 + 0.873296i $$0.661978\pi$$
$$258$$ 0 0
$$259$$ 24.0000 1.49129
$$260$$ 0 0
$$261$$ −10.0000 −0.618984
$$262$$ 0 0
$$263$$ 10.0000i 0.616626i −0.951285 0.308313i $$-0.900236\pi$$
0.951285 0.308313i $$-0.0997645\pi$$
$$264$$ 0 0
$$265$$ 6.00000 + 12.0000i 0.368577 + 0.737154i
$$266$$ 0 0
$$267$$ 14.0000i 0.856786i
$$268$$ 0 0
$$269$$ −10.0000 −0.609711 −0.304855 0.952399i $$-0.598608\pi$$
−0.304855 + 0.952399i $$0.598608\pi$$
$$270$$ 0 0
$$271$$ 8.00000 0.485965 0.242983 0.970031i $$-0.421874\pi$$
0.242983 + 0.970031i $$0.421874\pi$$
$$272$$ 0 0
$$273$$ 4.00000i 0.242091i
$$274$$ 0 0
$$275$$ 18.0000 24.0000i 1.08544 1.44725i
$$276$$ 0 0
$$277$$ 14.0000i 0.841178i −0.907251 0.420589i $$-0.861823\pi$$
0.907251 0.420589i $$-0.138177\pi$$
$$278$$ 0 0
$$279$$ 4.00000 0.239474
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ 0 0
$$283$$ 12.0000i 0.713326i −0.934233 0.356663i $$-0.883914\pi$$
0.934233 0.356663i $$-0.116086\pi$$
$$284$$ 0 0
$$285$$ 2.00000 + 4.00000i 0.118470 + 0.236940i
$$286$$ 0 0
$$287$$ 40.0000i 2.36113i
$$288$$ 0 0
$$289$$ 1.00000 0.0588235
$$290$$ 0 0
$$291$$ −14.0000 −0.820695
$$292$$ 0 0
$$293$$ 18.0000i 1.05157i −0.850617 0.525786i $$-0.823771\pi$$
0.850617 0.525786i $$-0.176229\pi$$
$$294$$ 0 0
$$295$$ −12.0000 + 6.00000i −0.698667 + 0.349334i
$$296$$ 0 0
$$297$$ 6.00000i 0.348155i
$$298$$ 0 0
$$299$$ −6.00000 −0.346989
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 10.0000i 0.574485i
$$304$$ 0 0
$$305$$ −12.0000 + 6.00000i −0.687118 + 0.343559i
$$306$$ 0 0
$$307$$ 4.00000i 0.228292i 0.993464 + 0.114146i $$0.0364132\pi$$
−0.993464 + 0.114146i $$0.963587\pi$$
$$308$$ 0 0
$$309$$ 2.00000 0.113776
$$310$$ 0 0
$$311$$ 8.00000 0.453638 0.226819 0.973937i $$-0.427167\pi$$
0.226819 + 0.973937i $$0.427167\pi$$
$$312$$ 0 0
$$313$$ 8.00000i 0.452187i 0.974106 + 0.226093i $$0.0725954\pi$$
−0.974106 + 0.226093i $$0.927405\pi$$
$$314$$ 0 0
$$315$$ −4.00000 8.00000i −0.225374 0.450749i
$$316$$ 0 0
$$317$$ 2.00000i 0.112331i 0.998421 + 0.0561656i $$0.0178875\pi$$
−0.998421 + 0.0561656i $$0.982113\pi$$
$$318$$ 0 0
$$319$$ 60.0000 3.35936
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.00000i 0.445132i
$$324$$ 0 0
$$325$$ −4.00000 3.00000i −0.221880 0.166410i
$$326$$ 0 0
$$327$$ 4.00000i 0.221201i
$$328$$ 0 0
$$329$$ 32.0000 1.76422
$$330$$ 0 0
$$331$$ −2.00000 −0.109930 −0.0549650 0.998488i $$-0.517505\pi$$
−0.0549650 + 0.998488i $$0.517505\pi$$
$$332$$ 0 0
$$333$$ 6.00000i 0.328798i
$$334$$ 0 0
$$335$$ 12.0000 + 24.0000i 0.655630 + 1.31126i
$$336$$ 0 0
$$337$$ 16.0000i 0.871576i 0.900049 + 0.435788i $$0.143530\pi$$
−0.900049 + 0.435788i $$0.856470\pi$$
$$338$$ 0 0
$$339$$ −4.00000 −0.217250
$$340$$ 0 0
$$341$$ −24.0000 −1.29967
$$342$$ 0 0
$$343$$ 8.00000i 0.431959i
$$344$$ 0 0
$$345$$ 12.0000 6.00000i 0.646058 0.323029i
$$346$$ 0 0
$$347$$ 16.0000i 0.858925i −0.903085 0.429463i $$-0.858703\pi$$
0.903085 0.429463i $$-0.141297\pi$$
$$348$$ 0 0
$$349$$ 4.00000 0.214115 0.107058 0.994253i $$-0.465857\pi$$
0.107058 + 0.994253i $$0.465857\pi$$
$$350$$ 0 0
$$351$$ −1.00000 −0.0533761
$$352$$ 0 0
$$353$$ 26.0000i 1.38384i 0.721974 + 0.691920i $$0.243235\pi$$
−0.721974 + 0.691920i $$0.756765\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 16.0000i 0.846810i
$$358$$ 0 0
$$359$$ −20.0000 −1.05556 −0.527780 0.849381i $$-0.676975\pi$$
−0.527780 + 0.849381i $$0.676975\pi$$
$$360$$ 0 0
$$361$$ −15.0000 −0.789474
$$362$$ 0 0
$$363$$ 25.0000i 1.31216i
$$364$$ 0 0
$$365$$ −2.00000 4.00000i −0.104685 0.209370i
$$366$$ 0 0
$$367$$ 18.0000i 0.939592i 0.882775 + 0.469796i $$0.155673\pi$$
−0.882775 + 0.469796i $$0.844327\pi$$
$$368$$ 0 0
$$369$$ −10.0000 −0.520579
$$370$$ 0 0
$$371$$ −24.0000 −1.24602
$$372$$ 0 0
$$373$$ 18.0000i 0.932005i 0.884783 + 0.466002i $$0.154306\pi$$
−0.884783 + 0.466002i $$0.845694\pi$$
$$374$$ 0 0
$$375$$ 11.0000 + 2.00000i 0.568038 + 0.103280i
$$376$$ 0 0
$$377$$ 10.0000i 0.515026i
$$378$$ 0 0
$$379$$ 10.0000 0.513665 0.256833 0.966456i $$-0.417321\pi$$
0.256833 + 0.966456i $$0.417321\pi$$
$$380$$ 0 0
$$381$$ −10.0000 −0.512316
$$382$$ 0 0
$$383$$ 20.0000i 1.02195i 0.859595 + 0.510976i $$0.170716\pi$$
−0.859595 + 0.510976i $$0.829284\pi$$
$$384$$ 0 0
$$385$$ 24.0000 + 48.0000i 1.22315 + 2.44631i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −30.0000 −1.52106 −0.760530 0.649303i $$-0.775061\pi$$
−0.760530 + 0.649303i $$0.775061\pi$$
$$390$$ 0 0
$$391$$ −24.0000 −1.21373
$$392$$ 0 0
$$393$$ 8.00000i 0.403547i
$$394$$ 0 0
$$395$$ −16.0000 + 8.00000i −0.805047 + 0.402524i
$$396$$ 0 0
$$397$$ 10.0000i 0.501886i −0.968002 0.250943i $$-0.919259\pi$$
0.968002 0.250943i $$-0.0807406\pi$$
$$398$$ 0 0
$$399$$ −8.00000 −0.400501
$$400$$ 0 0
$$401$$ 30.0000 1.49813 0.749064 0.662497i $$-0.230503\pi$$
0.749064 + 0.662497i $$0.230503\pi$$
$$402$$ 0 0
$$403$$ 4.00000i 0.199254i
$$404$$ 0 0
$$405$$ 2.00000 1.00000i 0.0993808 0.0496904i
$$406$$ 0 0
$$407$$ 36.0000i 1.78445i
$$408$$ 0 0
$$409$$ 34.0000 1.68119 0.840596 0.541663i $$-0.182205\pi$$
0.840596 + 0.541663i $$0.182205\pi$$
$$410$$ 0 0
$$411$$ 14.0000 0.690569
$$412$$ 0 0
$$413$$ 24.0000i 1.18096i
$$414$$ 0 0
$$415$$ −4.00000 8.00000i −0.196352 0.392705i
$$416$$ 0 0
$$417$$ 16.0000i 0.783523i
$$418$$ 0 0
$$419$$ 8.00000 0.390826 0.195413 0.980721i $$-0.437395\pi$$
0.195413 + 0.980721i $$0.437395\pi$$
$$420$$ 0 0
$$421$$ 4.00000 0.194948 0.0974740 0.995238i $$-0.468924\pi$$
0.0974740 + 0.995238i $$0.468924\pi$$
$$422$$ 0 0
$$423$$ 8.00000i 0.388973i
$$424$$ 0 0
$$425$$ −16.0000 12.0000i −0.776114 0.582086i
$$426$$ 0 0
$$427$$ 24.0000i 1.16144i
$$428$$ 0 0
$$429$$ 6.00000 0.289683
$$430$$ 0 0
$$431$$ 16.0000 0.770693 0.385346 0.922772i $$-0.374082\pi$$
0.385346 + 0.922772i $$0.374082\pi$$
$$432$$ 0 0
$$433$$ 16.0000i 0.768911i −0.923144 0.384455i $$-0.874389\pi$$
0.923144 0.384455i $$-0.125611\pi$$
$$434$$ 0 0
$$435$$ 10.0000 + 20.0000i 0.479463 + 0.958927i
$$436$$ 0 0
$$437$$ 12.0000i 0.574038i
$$438$$ 0 0
$$439$$ −32.0000 −1.52728 −0.763638 0.645644i $$-0.776589\pi$$
−0.763638 + 0.645644i $$0.776589\pi$$
$$440$$ 0 0
$$441$$ 9.00000 0.428571
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ −28.0000 + 14.0000i −1.32733 + 0.663664i
$$446$$ 0 0
$$447$$ 16.0000i 0.756774i
$$448$$ 0 0
$$449$$ −38.0000 −1.79333 −0.896665 0.442709i $$-0.854018\pi$$
−0.896665 + 0.442709i $$0.854018\pi$$
$$450$$ 0 0
$$451$$ 60.0000 2.82529
$$452$$ 0 0
$$453$$ 16.0000i 0.751746i
$$454$$ 0 0
$$455$$ 8.00000 4.00000i 0.375046 0.187523i
$$456$$ 0 0
$$457$$ 14.0000i 0.654892i 0.944870 + 0.327446i $$0.106188\pi$$
−0.944870 + 0.327446i $$0.893812\pi$$
$$458$$ 0 0
$$459$$ −4.00000 −0.186704
$$460$$ 0 0
$$461$$ −4.00000 −0.186299 −0.0931493 0.995652i $$-0.529693\pi$$
−0.0931493 + 0.995652i $$0.529693\pi$$
$$462$$ 0 0
$$463$$ 4.00000i 0.185896i 0.995671 + 0.0929479i $$0.0296290\pi$$
−0.995671 + 0.0929479i $$0.970371\pi$$
$$464$$ 0 0
$$465$$ −4.00000 8.00000i −0.185496 0.370991i
$$466$$ 0 0
$$467$$ 8.00000i 0.370196i −0.982720 0.185098i $$-0.940740\pi$$
0.982720 0.185098i $$-0.0592602\pi$$
$$468$$ 0 0
$$469$$ −48.0000 −2.21643
$$470$$ 0 0
$$471$$ −6.00000 −0.276465
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 6.00000 8.00000i 0.275299 0.367065i
$$476$$ 0 0
$$477$$ 6.00000i 0.274721i
$$478$$ 0 0
$$479$$ −20.0000 −0.913823 −0.456912 0.889512i $$-0.651044\pi$$
−0.456912 + 0.889512i $$0.651044\pi$$
$$480$$ 0 0
$$481$$ −6.00000 −0.273576
$$482$$ 0 0
$$483$$ 24.0000i 1.09204i
$$484$$ 0 0
$$485$$ 14.0000 + 28.0000i 0.635707 + 1.27141i
$$486$$ 0 0
$$487$$ 32.0000i 1.45006i −0.688718 0.725029i $$-0.741826\pi$$
0.688718 0.725029i $$-0.258174\pi$$
$$488$$ 0 0
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$492$$ 0 0
$$493$$ 40.0000i 1.80151i
$$494$$ 0 0
$$495$$ −12.0000 + 6.00000i −0.539360 + 0.269680i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −18.0000 −0.805791 −0.402895 0.915246i $$-0.631996\pi$$
−0.402895 + 0.915246i $$0.631996\pi$$
$$500$$ 0 0
$$501$$ −16.0000 −0.714827
$$502$$ 0 0
$$503$$ 14.0000i 0.624229i −0.950044 0.312115i $$-0.898963\pi$$
0.950044 0.312115i $$-0.101037\pi$$
$$504$$ 0 0
$$505$$ 20.0000 10.0000i 0.889988 0.444994i
$$506$$ 0 0
$$507$$ 1.00000i 0.0444116i
$$508$$ 0 0
$$509$$ −16.0000 −0.709188 −0.354594 0.935020i $$-0.615381\pi$$
−0.354594 + 0.935020i $$0.615381\pi$$
$$510$$ 0 0
$$511$$ 8.00000 0.353899
$$512$$ 0 0
$$513$$ 2.00000i 0.0883022i
$$514$$ 0 0
$$515$$ −2.00000 4.00000i −0.0881305 0.176261i
$$516$$ 0 0
$$517$$ 48.0000i 2.11104i
$$518$$ 0 0
$$519$$ −22.0000 −0.965693
$$520$$ 0 0
$$521$$ 6.00000 0.262865 0.131432 0.991325i $$-0.458042\pi$$
0.131432 + 0.991325i $$0.458042\pi$$
$$522$$ 0 0
$$523$$ 16.0000i 0.699631i 0.936819 + 0.349816i $$0.113756\pi$$
−0.936819 + 0.349816i $$0.886244\pi$$
$$524$$ 0 0
$$525$$ −12.0000 + 16.0000i −0.523723 + 0.698297i
$$526$$ 0 0
$$527$$ 16.0000i 0.696971i
$$528$$ 0 0
$$529$$ −13.0000 −0.565217
$$530$$ 0 0
$$531$$ 6.00000 0.260378
$$532$$ 0 0
$$533$$ 10.0000i 0.433148i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 24.0000i 1.03568i
$$538$$ 0 0
$$539$$ −54.0000 −2.32594
$$540$$ 0 0
$$541$$ −32.0000 −1.37579 −0.687894 0.725811i $$-0.741464\pi$$
−0.687894 + 0.725811i $$0.741464\pi$$
$$542$$ 0 0
$$543$$ 6.00000i 0.257485i
$$544$$ 0 0
$$545$$ −8.00000 + 4.00000i −0.342682 + 0.171341i
$$546$$ 0 0
$$547$$ 36.0000i 1.53925i −0.638497 0.769624i $$-0.720443\pi$$
0.638497 0.769624i $$-0.279557\pi$$
$$548$$ 0 0
$$549$$ 6.00000 0.256074
$$550$$ 0 0
$$551$$ 20.0000 0.852029
$$552$$ 0 0
$$553$$ 32.0000i 1.36078i
$$554$$ 0 0
$$555$$ 12.0000 6.00000i 0.509372 0.254686i
$$556$$ 0 0
$$557$$ 18.0000i 0.762684i −0.924434 0.381342i $$-0.875462\pi$$
0.924434 0.381342i $$-0.124538\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 24.0000 1.01328
$$562$$ 0 0
$$563$$ 24.0000i 1.01148i 0.862686 + 0.505740i $$0.168780\pi$$
−0.862686 + 0.505740i $$0.831220\pi$$
$$564$$ 0 0
$$565$$ 4.00000 + 8.00000i 0.168281 + 0.336563i
$$566$$ 0 0
$$567$$ 4.00000i 0.167984i
$$568$$ 0 0
$$569$$ 42.0000 1.76073 0.880366 0.474295i $$-0.157297\pi$$
0.880366 + 0.474295i $$0.157297\pi$$
$$570$$ 0 0
$$571$$ −12.0000 −0.502184 −0.251092 0.967963i $$-0.580790\pi$$
−0.251092 + 0.967963i $$0.580790\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −24.0000 18.0000i −1.00087 0.750652i
$$576$$ 0 0
$$577$$ 2.00000i 0.0832611i 0.999133 + 0.0416305i $$0.0132552\pi$$
−0.999133 + 0.0416305i $$0.986745\pi$$
$$578$$ 0 0
$$579$$ −2.00000 −0.0831172
$$580$$ 0 0
$$581$$ 16.0000 0.663792
$$582$$ 0 0
$$583$$ 36.0000i 1.49097i
$$584$$ 0 0
$$585$$ 1.00000 + 2.00000i 0.0413449 + 0.0826898i
$$586$$ 0 0
$$587$$ 28.0000i 1.15568i 0.816149 + 0.577842i $$0.196105\pi$$
−0.816149 + 0.577842i $$0.803895\pi$$
$$588$$ 0 0
$$589$$ −8.00000 −0.329634
$$590$$ 0 0
$$591$$ 6.00000 0.246807
$$592$$ 0 0
$$593$$ 14.0000i 0.574911i −0.957794 0.287456i $$-0.907191\pi$$
0.957794 0.287456i $$-0.0928094\pi$$
$$594$$ 0 0
$$595$$ 32.0000 16.0000i 1.31187 0.655936i
$$596$$ 0 0
$$597$$ 8.00000i 0.327418i
$$598$$ 0 0
$$599$$ −32.0000 −1.30748 −0.653742 0.756717i $$-0.726802\pi$$
−0.653742 + 0.756717i $$0.726802\pi$$
$$600$$ 0 0
$$601$$ 22.0000 0.897399 0.448699 0.893683i $$-0.351887\pi$$
0.448699 + 0.893683i $$0.351887\pi$$
$$602$$ 0 0
$$603$$ 12.0000i 0.488678i
$$604$$ 0 0
$$605$$ 50.0000 25.0000i 2.03279 1.01639i
$$606$$ 0 0
$$607$$ 42.0000i 1.70473i −0.522949 0.852364i $$-0.675168\pi$$
0.522949 0.852364i $$-0.324832\pi$$
$$608$$ 0 0
$$609$$ −40.0000 −1.62088
$$610$$ 0 0
$$611$$ −8.00000 −0.323645
$$612$$ 0 0
$$613$$ 38.0000i 1.53481i 0.641165 + 0.767403i $$0.278451\pi$$
−0.641165 + 0.767403i $$0.721549\pi$$
$$614$$ 0 0
$$615$$ 10.0000 + 20.0000i 0.403239 + 0.806478i
$$616$$ 0 0
$$617$$ 18.0000i 0.724653i −0.932051 0.362326i $$-0.881983\pi$$
0.932051 0.362326i $$-0.118017\pi$$
$$618$$ 0 0
$$619$$ −22.0000 −0.884255 −0.442127 0.896952i $$-0.645776\pi$$
−0.442127 + 0.896952i $$0.645776\pi$$
$$620$$ 0 0
$$621$$ −6.00000 −0.240772
$$622$$ 0 0
$$623$$ 56.0000i 2.24359i
$$624$$ 0 0
$$625$$ −7.00000 24.0000i −0.280000 0.960000i
$$626$$ 0 0
$$627$$ 12.0000i 0.479234i
$$628$$ 0 0
$$629$$ −24.0000 −0.956943
$$630$$ 0 0
$$631$$ −40.0000 −1.59237 −0.796187 0.605050i $$-0.793153\pi$$
−0.796187 + 0.605050i $$0.793153\pi$$
$$632$$ 0 0
$$633$$ 4.00000i 0.158986i
$$634$$ 0 0
$$635$$ 10.0000 + 20.0000i 0.396838 + 0.793676i
$$636$$ 0 0
$$637$$ 9.00000i 0.356593i
$$638$$ 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
$$643$$ 20.0000i 0.788723i −0.918955 0.394362i $$-0.870966\pi$$
0.918955 0.394362i $$-0.129034\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 6.00000i 0.235884i 0.993020 + 0.117942i $$0.0376297\pi$$
−0.993020 + 0.117942i $$0.962370\pi$$
$$648$$ 0 0
$$649$$ −36.0000 −1.41312
$$650$$ 0 0
$$651$$ 16.0000 0.627089
$$652$$ 0 0
$$653$$ 10.0000i 0.391330i 0.980671 + 0.195665i $$0.0626866\pi$$
−0.980671 + 0.195665i $$0.937313\pi$$
$$654$$ 0 0
$$655$$ 16.0000 8.00000i 0.625172 0.312586i
$$656$$ 0 0
$$657$$ 2.00000i 0.0780274i
$$658$$ 0 0
$$659$$ −32.0000 −1.24654 −0.623272 0.782006i $$-0.714197\pi$$
−0.623272 + 0.782006i $$0.714197\pi$$
$$660$$ 0 0
$$661$$ −32.0000 −1.24466 −0.622328 0.782757i $$-0.713813\pi$$
−0.622328 + 0.782757i $$0.713813\pi$$
$$662$$ 0 0
$$663$$ 4.00000i 0.155347i
$$664$$ 0 0
$$665$$ 8.00000 + 16.0000i 0.310227 + 0.620453i
$$666$$ 0 0
$$667$$ 60.0000i 2.32321i
$$668$$ 0 0
$$669$$ −8.00000 −0.309298
$$670$$ 0 0
$$671$$ −36.0000 −1.38976
$$672$$ 0 0
$$673$$ 44.0000i 1.69608i −0.529936 0.848038i $$-0.677784\pi$$
0.529936 0.848038i $$-0.322216\pi$$
$$674$$ 0 0
$$675$$ −4.00000 3.00000i −0.153960 0.115470i
$$676$$ 0 0
$$677$$ 6.00000i 0.230599i 0.993331 + 0.115299i $$0.0367827\pi$$
−0.993331 + 0.115299i $$0.963217\pi$$
$$678$$ 0 0
$$679$$ −56.0000 −2.14908
$$680$$ 0 0
$$681$$ −4.00000 −0.153280
$$682$$ 0 0
$$683$$ 20.0000i 0.765279i −0.923898 0.382639i $$-0.875015\pi$$
0.923898 0.382639i $$-0.124985\pi$$
$$684$$ 0 0
$$685$$ −14.0000 28.0000i −0.534913 1.06983i
$$686$$ 0 0
$$687$$ 8.00000i 0.305219i
$$688$$ 0 0
$$689$$ 6.00000 0.228582
$$690$$ 0 0
$$691$$ −18.0000 −0.684752 −0.342376 0.939563i $$-0.611232\pi$$
−0.342376 + 0.939563i $$0.611232\pi$$
$$692$$ 0 0
$$693$$ 24.0000i 0.911685i
$$694$$ 0 0
$$695$$ 32.0000 16.0000i 1.21383 0.606915i
$$696$$ 0 0
$$697$$ 40.0000i 1.51511i
$$698$$ 0 0
$$699$$ −12.0000 −0.453882
$$700$$ 0 0
$$701$$ −6.00000 −0.226617 −0.113308 0.993560i $$-0.536145\pi$$
−0.113308 + 0.993560i $$0.536145\pi$$
$$702$$ 0 0
$$703$$ 12.0000i 0.452589i
$$704$$ 0 0
$$705$$ 16.0000 8.00000i 0.602595 0.301297i
$$706$$ 0 0
$$707$$ 40.0000i 1.50435i
$$708$$ 0 0
$$709$$ 8.00000 0.300446 0.150223 0.988652i $$-0.452001\pi$$
0.150223 + 0.988652i $$0.452001\pi$$
$$710$$ 0 0
$$711$$ 8.00000 0.300023
$$712$$ 0 0
$$713$$ 24.0000i 0.898807i
$$714$$ 0 0
$$715$$ −6.00000 12.0000i −0.224387 0.448775i
$$716$$ 0 0
$$717$$ 4.00000i 0.149383i
$$718$$ 0 0
$$719$$ 8.00000 0.298350 0.149175 0.988811i $$-0.452338\pi$$
0.149175 + 0.988811i $$0.452338\pi$$
$$720$$ 0 0
$$721$$ 8.00000 0.297936
$$722$$ 0 0
$$723$$ 18.0000i 0.669427i
$$724$$ 0 0
$$725$$ 30.0000 40.0000i 1.11417 1.48556i
$$726$$ 0 0
$$727$$ 38.0000i 1.40934i −0.709534 0.704671i $$-0.751095\pi$$
0.709534 0.704671i $$-0.248905\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 18.0000i 0.664845i 0.943131 + 0.332423i $$0.107866\pi$$
−0.943131 + 0.332423i $$0.892134\pi$$
$$734$$ 0 0
$$735$$ −9.00000 18.0000i −0.331970 0.663940i
$$736$$ 0 0
$$737$$ 72.0000i 2.65215i
$$738$$ 0 0
$$739$$ −2.00000 −0.0735712 −0.0367856 0.999323i $$-0.511712\pi$$
−0.0367856 + 0.999323i $$0.511712\pi$$
$$740$$ 0 0
$$741$$ 2.00000 0.0734718
$$742$$ 0 0
$$743$$ 36.0000i 1.32071i −0.750953 0.660356i $$-0.770405\pi$$
0.750953 0.660356i $$-0.229595\pi$$
$$744$$ 0 0
$$745$$ −32.0000 + 16.0000i −1.17239 + 0.586195i
$$746$$ 0 0
$$747$$ 4.00000i 0.146352i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 48.0000 1.75154 0.875772 0.482724i $$-0.160353\pi$$
0.875772 + 0.482724i $$0.160353\pi$$
$$752$$ 0 0
$$753$$ 20.0000i 0.728841i
$$754$$ 0 0
$$755$$ −32.0000 + 16.0000i −1.16460 + 0.582300i
$$756$$ 0 0
$$757$$ 22.0000i 0.799604i −0.916602 0.399802i $$-0.869079\pi$$
0.916602 0.399802i $$-0.130921\pi$$
$$758$$ 0 0
$$759$$ 36.0000 1.30672
$$760$$ 0 0
$$761$$ 30.0000 1.08750 0.543750 0.839248i $$-0.317004\pi$$
0.543750 + 0.839248i $$0.317004\pi$$
$$762$$ 0 0
$$763$$ 16.0000i 0.579239i
$$764$$ 0 0
$$765$$ 4.00000 + 8.00000i 0.144620 + 0.289241i
$$766$$ 0 0
$$767$$ 6.00000i 0.216647i
$$768$$ 0 0
$$769$$ −10.0000 −0.360609 −0.180305 0.983611i $$-0.557708\pi$$
−0.180305 + 0.983611i $$0.557708\pi$$
$$770$$ 0 0
$$771$$ −28.0000 −1.00840
$$772$$ 0 0
$$773$$ 18.0000i 0.647415i 0.946157 + 0.323708i $$0.104929\pi$$
−0.946157 + 0.323708i $$0.895071\pi$$
$$774$$ 0 0
$$775$$ −12.0000 + 16.0000i −0.431053 + 0.574737i
$$776$$ 0 0
$$777$$ 24.0000i 0.860995i
$$778$$ 0 0
$$779$$ 20.0000 0.716574
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 10.0000i 0.357371i
$$784$$ 0 0
$$785$$ 6.00000 + 12.0000i 0.214149 + 0.428298i
$$786$$ 0 0
$$787$$ 12.0000i 0.427754i 0.976861 + 0.213877i $$0.0686091\pi$$
−0.976861 + 0.213877i $$0.931391\pi$$
$$788$$ 0 0
$$789$$ 10.0000 0.356009
$$790$$ 0 0
$$791$$ −16.0000 −0.568895
$$792$$ 0 0
$$793$$ 6.00000i 0.213066i
$$794$$ 0 0
$$795$$ −12.0000 + 6.00000i −0.425596 + 0.212798i
$$796$$ 0 0
$$797$$ 30.0000i 1.06265i −0.847167 0.531327i $$-0.821693\pi$$
0.847167 0.531327i $$-0.178307\pi$$
$$798$$ 0 0
$$799$$ −32.0000 −1.13208
$$800$$ 0