# Properties

 Label 336.2.bl.d.31.1 Level $336$ Weight $2$ Character 336.31 Analytic conductor $2.683$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$336 = 2^{4} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 336.bl (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.68297350792$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 31.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 336.31 Dual form 336.2.bl.d.271.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} +(3.00000 - 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} +(3.00000 - 1.73205i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-3.00000 - 1.73205i) q^{11} -1.73205i q^{13} +3.46410i q^{15} +(2.50000 + 4.33013i) q^{19} +(2.00000 + 1.73205i) q^{21} +(6.00000 - 3.46410i) q^{23} +(3.50000 - 6.06218i) q^{25} +1.00000 q^{27} +(-2.50000 + 4.33013i) q^{31} +(3.00000 - 1.73205i) q^{33} +(-3.00000 - 8.66025i) q^{35} +(5.50000 + 9.52628i) q^{37} +(1.50000 + 0.866025i) q^{39} -3.46410i q^{41} +8.66025i q^{43} +(-3.00000 - 1.73205i) q^{45} +(-3.00000 - 5.19615i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-6.00000 + 10.3923i) q^{53} -12.0000 q^{55} -5.00000 q^{57} +(6.00000 - 10.3923i) q^{59} +(-12.0000 + 6.92820i) q^{61} +(-2.50000 + 0.866025i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(7.50000 + 4.33013i) q^{67} +6.92820i q^{69} +3.46410i q^{71} +(-4.50000 - 2.59808i) q^{73} +(3.50000 + 6.06218i) q^{75} +(-6.00000 + 6.92820i) q^{77} +(10.5000 - 6.06218i) q^{79} +(-0.500000 + 0.866025i) q^{81} -18.0000 q^{83} +(6.00000 - 3.46410i) q^{89} +(-4.50000 - 0.866025i) q^{91} +(-2.50000 - 4.33013i) q^{93} +(15.0000 + 8.66025i) q^{95} +6.92820i q^{97} +3.46410i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} + 6q^{5} + q^{7} - q^{9} + O(q^{10})$$ $$2q - q^{3} + 6q^{5} + q^{7} - q^{9} - 6q^{11} + 5q^{19} + 4q^{21} + 12q^{23} + 7q^{25} + 2q^{27} - 5q^{31} + 6q^{33} - 6q^{35} + 11q^{37} + 3q^{39} - 6q^{45} - 6q^{47} - 13q^{49} - 12q^{53} - 24q^{55} - 10q^{57} + 12q^{59} - 24q^{61} - 5q^{63} - 6q^{65} + 15q^{67} - 9q^{73} + 7q^{75} - 12q^{77} + 21q^{79} - q^{81} - 36q^{83} + 12q^{89} - 9q^{91} - 5q^{93} + 30q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$$.

 $$n$$ $$85$$ $$113$$ $$127$$ $$241$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ 0 0
$$5$$ 3.00000 1.73205i 1.34164 0.774597i 0.354593 0.935021i $$-0.384620\pi$$
0.987048 + 0.160424i $$0.0512862\pi$$
$$6$$ 0 0
$$7$$ 0.500000 2.59808i 0.188982 0.981981i
$$8$$ 0 0
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ 0 0
$$11$$ −3.00000 1.73205i −0.904534 0.522233i −0.0258656 0.999665i $$-0.508234\pi$$
−0.878668 + 0.477432i $$0.841568\pi$$
$$12$$ 0 0
$$13$$ 1.73205i 0.480384i −0.970725 0.240192i $$-0.922790\pi$$
0.970725 0.240192i $$-0.0772105\pi$$
$$14$$ 0 0
$$15$$ 3.46410i 0.894427i
$$16$$ 0 0
$$17$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$18$$ 0 0
$$19$$ 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i $$0.0277634\pi$$
−0.422659 + 0.906289i $$0.638903\pi$$
$$20$$ 0 0
$$21$$ 2.00000 + 1.73205i 0.436436 + 0.377964i
$$22$$ 0 0
$$23$$ 6.00000 3.46410i 1.25109 0.722315i 0.279761 0.960070i $$-0.409745\pi$$
0.971325 + 0.237754i $$0.0764114\pi$$
$$24$$ 0 0
$$25$$ 3.50000 6.06218i 0.700000 1.21244i
$$26$$ 0 0
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$30$$ 0 0
$$31$$ −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i $$-0.981558\pi$$
0.549309 + 0.835619i $$0.314891\pi$$
$$32$$ 0 0
$$33$$ 3.00000 1.73205i 0.522233 0.301511i
$$34$$ 0 0
$$35$$ −3.00000 8.66025i −0.507093 1.46385i
$$36$$ 0 0
$$37$$ 5.50000 + 9.52628i 0.904194 + 1.56611i 0.821995 + 0.569495i $$0.192861\pi$$
0.0821995 + 0.996616i $$0.473806\pi$$
$$38$$ 0 0
$$39$$ 1.50000 + 0.866025i 0.240192 + 0.138675i
$$40$$ 0 0
$$41$$ 3.46410i 0.541002i −0.962720 0.270501i $$-0.912811\pi$$
0.962720 0.270501i $$-0.0871893\pi$$
$$42$$ 0 0
$$43$$ 8.66025i 1.32068i 0.750968 + 0.660338i $$0.229587\pi$$
−0.750968 + 0.660338i $$0.770413\pi$$
$$44$$ 0 0
$$45$$ −3.00000 1.73205i −0.447214 0.258199i
$$46$$ 0 0
$$47$$ −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i $$-0.310836\pi$$
−0.997503 + 0.0706177i $$0.977503\pi$$
$$48$$ 0 0
$$49$$ −6.50000 2.59808i −0.928571 0.371154i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i $$0.475021\pi$$
−0.902557 + 0.430570i $$0.858312\pi$$
$$54$$ 0 0
$$55$$ −12.0000 −1.61808
$$56$$ 0 0
$$57$$ −5.00000 −0.662266
$$58$$ 0 0
$$59$$ 6.00000 10.3923i 0.781133 1.35296i −0.150148 0.988663i $$-0.547975\pi$$
0.931282 0.364299i $$-0.118692\pi$$
$$60$$ 0 0
$$61$$ −12.0000 + 6.92820i −1.53644 + 0.887066i −0.537400 + 0.843328i $$0.680593\pi$$
−0.999043 + 0.0437377i $$0.986073\pi$$
$$62$$ 0 0
$$63$$ −2.50000 + 0.866025i −0.314970 + 0.109109i
$$64$$ 0 0
$$65$$ −3.00000 5.19615i −0.372104 0.644503i
$$66$$ 0 0
$$67$$ 7.50000 + 4.33013i 0.916271 + 0.529009i 0.882443 0.470418i $$-0.155897\pi$$
0.0338274 + 0.999428i $$0.489230\pi$$
$$68$$ 0 0
$$69$$ 6.92820i 0.834058i
$$70$$ 0 0
$$71$$ 3.46410i 0.411113i 0.978645 + 0.205557i $$0.0659005\pi$$
−0.978645 + 0.205557i $$0.934100\pi$$
$$72$$ 0 0
$$73$$ −4.50000 2.59808i −0.526685 0.304082i 0.212980 0.977056i $$-0.431683\pi$$
−0.739666 + 0.672975i $$0.765016\pi$$
$$74$$ 0 0
$$75$$ 3.50000 + 6.06218i 0.404145 + 0.700000i
$$76$$ 0 0
$$77$$ −6.00000 + 6.92820i −0.683763 + 0.789542i
$$78$$ 0 0
$$79$$ 10.5000 6.06218i 1.18134 0.682048i 0.225018 0.974355i $$-0.427756\pi$$
0.956325 + 0.292306i $$0.0944227\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ −18.0000 −1.97576 −0.987878 0.155230i $$-0.950388\pi$$
−0.987878 + 0.155230i $$0.950388\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 6.00000 3.46410i 0.635999 0.367194i −0.147073 0.989126i $$-0.546985\pi$$
0.783072 + 0.621932i $$0.213652\pi$$
$$90$$ 0 0
$$91$$ −4.50000 0.866025i −0.471728 0.0907841i
$$92$$ 0 0
$$93$$ −2.50000 4.33013i −0.259238 0.449013i
$$94$$ 0 0
$$95$$ 15.0000 + 8.66025i 1.53897 + 0.888523i
$$96$$ 0 0
$$97$$ 6.92820i 0.703452i 0.936103 + 0.351726i $$0.114405\pi$$
−0.936103 + 0.351726i $$0.885595\pi$$
$$98$$ 0 0
$$99$$ 3.46410i 0.348155i
$$100$$ 0 0
$$101$$ 9.00000 + 5.19615i 0.895533 + 0.517036i 0.875748 0.482768i $$-0.160368\pi$$
0.0197851 + 0.999804i $$0.493702\pi$$
$$102$$ 0 0
$$103$$ −2.50000 4.33013i −0.246332 0.426660i 0.716173 0.697923i $$-0.245892\pi$$
−0.962505 + 0.271263i $$0.912559\pi$$
$$104$$ 0 0
$$105$$ 9.00000 + 1.73205i 0.878310 + 0.169031i
$$106$$ 0 0
$$107$$ 0 0 −0.500000 0.866025i $$-0.666667\pi$$
0.500000 + 0.866025i $$0.333333\pi$$
$$108$$ 0 0
$$109$$ 3.50000 6.06218i 0.335239 0.580651i −0.648292 0.761392i $$-0.724516\pi$$
0.983531 + 0.180741i $$0.0578495\pi$$
$$110$$ 0 0
$$111$$ −11.0000 −1.04407
$$112$$ 0 0
$$113$$ −6.00000 −0.564433 −0.282216 0.959351i $$-0.591070\pi$$
−0.282216 + 0.959351i $$0.591070\pi$$
$$114$$ 0 0
$$115$$ 12.0000 20.7846i 1.11901 1.93817i
$$116$$ 0 0
$$117$$ −1.50000 + 0.866025i −0.138675 + 0.0800641i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 0.500000 + 0.866025i 0.0454545 + 0.0787296i
$$122$$ 0 0
$$123$$ 3.00000 + 1.73205i 0.270501 + 0.156174i
$$124$$ 0 0
$$125$$ 6.92820i 0.619677i
$$126$$ 0 0
$$127$$ 12.1244i 1.07586i 0.842989 + 0.537931i $$0.180794\pi$$
−0.842989 + 0.537931i $$0.819206\pi$$
$$128$$ 0 0
$$129$$ −7.50000 4.33013i −0.660338 0.381246i
$$130$$ 0 0
$$131$$ 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i $$-0.0822479\pi$$
−0.704692 + 0.709514i $$0.748915\pi$$
$$132$$ 0 0
$$133$$ 12.5000 4.33013i 1.08389 0.375470i
$$134$$ 0 0
$$135$$ 3.00000 1.73205i 0.258199 0.149071i
$$136$$ 0 0
$$137$$ −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i $$0.337990\pi$$
−0.999893 + 0.0146279i $$0.995344\pi$$
$$138$$ 0 0
$$139$$ −7.00000 −0.593732 −0.296866 0.954919i $$-0.595942\pi$$
−0.296866 + 0.954919i $$0.595942\pi$$
$$140$$ 0 0
$$141$$ 6.00000 0.505291
$$142$$ 0 0
$$143$$ −3.00000 + 5.19615i −0.250873 + 0.434524i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 5.50000 4.33013i 0.453632 0.357143i
$$148$$ 0 0
$$149$$ −6.00000 10.3923i −0.491539 0.851371i 0.508413 0.861113i $$-0.330232\pi$$
−0.999953 + 0.00974235i $$0.996899\pi$$
$$150$$ 0 0
$$151$$ 3.00000 + 1.73205i 0.244137 + 0.140952i 0.617076 0.786903i $$-0.288317\pi$$
−0.372940 + 0.927855i $$0.621650\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 17.3205i 1.39122i
$$156$$ 0 0
$$157$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$158$$ 0 0
$$159$$ −6.00000 10.3923i −0.475831 0.824163i
$$160$$ 0 0
$$161$$ −6.00000 17.3205i −0.472866 1.36505i
$$162$$ 0 0
$$163$$ −3.00000 + 1.73205i −0.234978 + 0.135665i −0.612866 0.790186i $$-0.709984\pi$$
0.377888 + 0.925851i $$0.376650\pi$$
$$164$$ 0 0
$$165$$ 6.00000 10.3923i 0.467099 0.809040i
$$166$$ 0 0
$$167$$ −6.00000 −0.464294 −0.232147 0.972681i $$-0.574575\pi$$
−0.232147 + 0.972681i $$0.574575\pi$$
$$168$$ 0 0
$$169$$ 10.0000 0.769231
$$170$$ 0 0
$$171$$ 2.50000 4.33013i 0.191180 0.331133i
$$172$$ 0 0
$$173$$ 6.00000 3.46410i 0.456172 0.263371i −0.254262 0.967135i $$-0.581832\pi$$
0.710433 + 0.703765i $$0.248499\pi$$
$$174$$ 0 0
$$175$$ −14.0000 12.1244i −1.05830 0.916515i
$$176$$ 0 0
$$177$$ 6.00000 + 10.3923i 0.450988 + 0.781133i
$$178$$ 0 0
$$179$$ −9.00000 5.19615i −0.672692 0.388379i 0.124404 0.992232i $$-0.460298\pi$$
−0.797096 + 0.603853i $$0.793631\pi$$
$$180$$ 0 0
$$181$$ 5.19615i 0.386227i −0.981176 0.193113i $$-0.938141\pi$$
0.981176 0.193113i $$-0.0618586\pi$$
$$182$$ 0 0
$$183$$ 13.8564i 1.02430i
$$184$$ 0 0
$$185$$ 33.0000 + 19.0526i 2.42621 + 1.40077i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0.500000 2.59808i 0.0363696 0.188982i
$$190$$ 0 0
$$191$$ 15.0000 8.66025i 1.08536 0.626634i 0.153024 0.988222i $$-0.451099\pi$$
0.932338 + 0.361588i $$0.117765\pi$$
$$192$$ 0 0
$$193$$ 5.50000 9.52628i 0.395899 0.685717i −0.597317 0.802005i $$-0.703766\pi$$
0.993215 + 0.116289i $$0.0370998\pi$$
$$194$$ 0 0
$$195$$ 6.00000 0.429669
$$196$$ 0 0
$$197$$ 24.0000 1.70993 0.854965 0.518686i $$-0.173579\pi$$
0.854965 + 0.518686i $$0.173579\pi$$
$$198$$ 0 0
$$199$$ −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i $$0.358603\pi$$
−0.996850 + 0.0793045i $$0.974730\pi$$
$$200$$ 0 0
$$201$$ −7.50000 + 4.33013i −0.529009 + 0.305424i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −6.00000 10.3923i −0.419058 0.725830i
$$206$$ 0 0
$$207$$ −6.00000 3.46410i −0.417029 0.240772i
$$208$$ 0 0
$$209$$ 17.3205i 1.19808i
$$210$$ 0 0
$$211$$ 3.46410i 0.238479i 0.992866 + 0.119239i $$0.0380456\pi$$
−0.992866 + 0.119239i $$0.961954\pi$$
$$212$$ 0 0
$$213$$ −3.00000 1.73205i −0.205557 0.118678i
$$214$$ 0 0
$$215$$ 15.0000 + 25.9808i 1.02299 + 1.77187i
$$216$$ 0 0
$$217$$ 10.0000 + 8.66025i 0.678844 + 0.587896i
$$218$$ 0 0
$$219$$ 4.50000 2.59808i 0.304082 0.175562i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 0 0
$$225$$ −7.00000 −0.466667
$$226$$ 0 0
$$227$$ −9.00000 + 15.5885i −0.597351 + 1.03464i 0.395860 + 0.918311i $$0.370447\pi$$
−0.993210 + 0.116331i $$0.962887\pi$$
$$228$$ 0 0
$$229$$ 7.50000 4.33013i 0.495614 0.286143i −0.231287 0.972886i $$-0.574293\pi$$
0.726900 + 0.686743i $$0.240960\pi$$
$$230$$ 0 0
$$231$$ −3.00000 8.66025i −0.197386 0.569803i
$$232$$ 0 0
$$233$$ 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i $$-0.103697\pi$$
−0.750867 + 0.660454i $$0.770364\pi$$
$$234$$ 0 0
$$235$$ −18.0000 10.3923i −1.17419 0.677919i
$$236$$ 0 0
$$237$$ 12.1244i 0.787562i
$$238$$ 0 0
$$239$$ 10.3923i 0.672222i 0.941822 + 0.336111i $$0.109112\pi$$
−0.941822 + 0.336111i $$0.890888\pi$$
$$240$$ 0 0
$$241$$ −12.0000 6.92820i −0.772988 0.446285i 0.0609515 0.998141i $$-0.480586\pi$$
−0.833939 + 0.551856i $$0.813920\pi$$
$$242$$ 0 0
$$243$$ −0.500000 0.866025i −0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ −24.0000 + 3.46410i −1.53330 + 0.221313i
$$246$$ 0 0
$$247$$ 7.50000 4.33013i 0.477214 0.275519i
$$248$$ 0 0
$$249$$ 9.00000 15.5885i 0.570352 0.987878i
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ −24.0000 −1.50887
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −15.0000 + 8.66025i −0.935674 + 0.540212i −0.888602 0.458680i $$-0.848323\pi$$
−0.0470726 + 0.998891i $$0.514989\pi$$
$$258$$ 0 0
$$259$$ 27.5000 9.52628i 1.70877 0.591934i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 12.0000 + 6.92820i 0.739952 + 0.427211i 0.822052 0.569413i $$-0.192829\pi$$
−0.0821001 + 0.996624i $$0.526163\pi$$
$$264$$ 0 0
$$265$$ 41.5692i 2.55358i
$$266$$ 0 0
$$267$$ 6.92820i 0.423999i
$$268$$ 0 0
$$269$$ −15.0000 8.66025i −0.914566 0.528025i −0.0326687 0.999466i $$-0.510401\pi$$
−0.881897 + 0.471441i $$0.843734\pi$$
$$270$$ 0 0
$$271$$ −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i $$-0.244792\pi$$
−0.961563 + 0.274586i $$0.911459\pi$$
$$272$$ 0 0
$$273$$ 3.00000 3.46410i 0.181568 0.209657i
$$274$$ 0 0
$$275$$ −21.0000 + 12.1244i −1.26635 + 0.731126i
$$276$$ 0 0
$$277$$ −9.50000 + 16.4545i −0.570800 + 0.988654i 0.425684 + 0.904872i $$0.360033\pi$$
−0.996484 + 0.0837823i $$0.973300\pi$$
$$278$$ 0 0
$$279$$ 5.00000 0.299342
$$280$$ 0 0
$$281$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$282$$ 0 0
$$283$$ −3.50000 + 6.06218i −0.208053 + 0.360359i −0.951101 0.308879i $$-0.900046\pi$$
0.743048 + 0.669238i $$0.233379\pi$$
$$284$$ 0 0
$$285$$ −15.0000 + 8.66025i −0.888523 + 0.512989i
$$286$$ 0 0
$$287$$ −9.00000 1.73205i −0.531253 0.102240i
$$288$$ 0 0
$$289$$ −8.50000 14.7224i −0.500000 0.866025i
$$290$$ 0 0
$$291$$ −6.00000 3.46410i −0.351726 0.203069i
$$292$$ 0 0
$$293$$ 20.7846i 1.21425i −0.794606 0.607125i $$-0.792323\pi$$
0.794606 0.607125i $$-0.207677\pi$$
$$294$$ 0 0
$$295$$ 41.5692i 2.42025i
$$296$$ 0 0
$$297$$ −3.00000 1.73205i −0.174078 0.100504i
$$298$$ 0 0
$$299$$ −6.00000 10.3923i −0.346989 0.601003i
$$300$$ 0 0
$$301$$ 22.5000 + 4.33013i 1.29688 + 0.249584i
$$302$$ 0 0
$$303$$ −9.00000 + 5.19615i −0.517036 + 0.298511i
$$304$$ 0 0
$$305$$ −24.0000 + 41.5692i −1.37424 + 2.38025i
$$306$$ 0 0
$$307$$ −11.0000 −0.627803 −0.313902 0.949456i $$-0.601636\pi$$
−0.313902 + 0.949456i $$0.601636\pi$$
$$308$$ 0 0
$$309$$ 5.00000 0.284440
$$310$$ 0 0
$$311$$ −9.00000 + 15.5885i −0.510343 + 0.883940i 0.489585 + 0.871956i $$0.337148\pi$$
−0.999928 + 0.0119847i $$0.996185\pi$$
$$312$$ 0 0
$$313$$ 13.5000 7.79423i 0.763065 0.440556i −0.0673300 0.997731i $$-0.521448\pi$$
0.830395 + 0.557175i $$0.188115\pi$$
$$314$$ 0 0
$$315$$ −6.00000 + 6.92820i −0.338062 + 0.390360i
$$316$$ 0 0
$$317$$ 6.00000 + 10.3923i 0.336994 + 0.583690i 0.983866 0.178908i $$-0.0572566\pi$$
−0.646872 + 0.762598i $$0.723923\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −10.5000 6.06218i −0.582435 0.336269i
$$326$$ 0 0
$$327$$ 3.50000 + 6.06218i 0.193550 + 0.335239i
$$328$$ 0 0
$$329$$ −15.0000 + 5.19615i −0.826977 + 0.286473i
$$330$$ 0 0
$$331$$ 13.5000 7.79423i 0.742027 0.428410i −0.0807788 0.996732i $$-0.525741\pi$$
0.822806 + 0.568323i $$0.192407\pi$$
$$332$$ 0 0
$$333$$ 5.50000 9.52628i 0.301398 0.522037i
$$334$$ 0 0
$$335$$ 30.0000 1.63908
$$336$$ 0 0
$$337$$ −19.0000 −1.03500 −0.517498 0.855684i $$-0.673136\pi$$
−0.517498 + 0.855684i $$0.673136\pi$$
$$338$$ 0 0
$$339$$ 3.00000 5.19615i 0.162938 0.282216i
$$340$$ 0 0
$$341$$ 15.0000 8.66025i 0.812296 0.468979i
$$342$$ 0 0
$$343$$ −10.0000 + 15.5885i −0.539949 + 0.841698i
$$344$$ 0 0
$$345$$ 12.0000 + 20.7846i 0.646058 + 1.11901i
$$346$$ 0 0
$$347$$ −24.0000 13.8564i −1.28839 0.743851i −0.310021 0.950730i $$-0.600336\pi$$
−0.978367 + 0.206879i $$0.933669\pi$$
$$348$$ 0 0
$$349$$ 13.8564i 0.741716i −0.928689 0.370858i $$-0.879064\pi$$
0.928689 0.370858i $$-0.120936\pi$$
$$350$$ 0 0
$$351$$ 1.73205i 0.0924500i
$$352$$ 0 0
$$353$$ 21.0000 + 12.1244i 1.11772 + 0.645314i 0.940817 0.338914i $$-0.110060\pi$$
0.176900 + 0.984229i $$0.443393\pi$$
$$354$$ 0 0
$$355$$ 6.00000 + 10.3923i 0.318447 + 0.551566i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −18.0000 + 10.3923i −0.950004 + 0.548485i −0.893082 0.449894i $$-0.851462\pi$$
−0.0569216 + 0.998379i $$0.518129\pi$$
$$360$$ 0 0
$$361$$ −3.00000 + 5.19615i −0.157895 + 0.273482i
$$362$$ 0 0
$$363$$ −1.00000 −0.0524864
$$364$$ 0 0
$$365$$ −18.0000 −0.942163
$$366$$ 0 0
$$367$$ 5.50000 9.52628i 0.287098 0.497268i −0.686018 0.727585i $$-0.740643\pi$$
0.973116 + 0.230317i $$0.0739762\pi$$
$$368$$ 0 0
$$369$$ −3.00000 + 1.73205i −0.156174 + 0.0901670i
$$370$$ 0 0
$$371$$ 24.0000 + 20.7846i 1.24602 + 1.07908i
$$372$$ 0 0
$$373$$ 0.500000 + 0.866025i 0.0258890 + 0.0448411i 0.878680 0.477412i $$-0.158425\pi$$
−0.852791 + 0.522253i $$0.825092\pi$$
$$374$$ 0 0
$$375$$ 6.00000 + 3.46410i 0.309839 + 0.178885i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 8.66025i 0.444847i 0.974950 + 0.222424i $$0.0713968\pi$$
−0.974950 + 0.222424i $$0.928603\pi$$
$$380$$ 0 0
$$381$$ −10.5000 6.06218i −0.537931 0.310575i
$$382$$ 0 0
$$383$$ −12.0000 20.7846i −0.613171 1.06204i −0.990702 0.136047i $$-0.956560\pi$$
0.377531 0.925997i $$1.62323\pi$$
$$384$$ 0 0
$$385$$ −6.00000 + 31.1769i −0.305788 + 1.58892i
$$386$$ 0 0
$$387$$ 7.50000 4.33013i 0.381246 0.220113i
$$388$$ 0 0
$$389$$ 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i $$-0.784728\pi$$
0.932002 + 0.362454i $$0.118061\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ −6.00000 −0.302660
$$394$$ 0 0
$$395$$ 21.0000 36.3731i 1.05662 1.83013i
$$396$$ 0 0
$$397$$ −1.50000 + 0.866025i −0.0752828 + 0.0434646i −0.537169 0.843475i $$-0.680506\pi$$
0.461886 + 0.886939i $$0.347173\pi$$
$$398$$ 0 0
$$399$$ −2.50000 + 12.9904i −0.125157 + 0.650332i
$$400$$ 0 0
$$401$$ −6.00000 10.3923i −0.299626 0.518967i 0.676425 0.736512i $$-0.263528\pi$$
−0.976050 + 0.217545i $$0.930195\pi$$
$$402$$ 0 0
$$403$$ 7.50000 + 4.33013i 0.373602 + 0.215699i
$$404$$ 0 0
$$405$$ 3.46410i 0.172133i
$$406$$ 0 0
$$407$$ 38.1051i 1.88880i
$$408$$ 0 0
$$409$$ −19.5000 11.2583i −0.964213 0.556689i −0.0667458 0.997770i $$-0.521262\pi$$
−0.897467 + 0.441081i $$0.854595\pi$$
$$410$$ 0 0
$$411$$ −6.00000 10.3923i −0.295958 0.512615i
$$412$$ 0 0
$$413$$ −24.0000 20.7846i −1.18096 1.02274i
$$414$$ 0 0
$$415$$ −54.0000 + 31.1769i −2.65076 + 1.53041i
$$416$$ 0 0
$$417$$ 3.50000 6.06218i 0.171396 0.296866i
$$418$$ 0 0
$$419$$ −6.00000 −0.293119 −0.146560 0.989202i $$-0.546820\pi$$
−0.146560 + 0.989202i $$0.546820\pi$$
$$420$$ 0 0
$$421$$ 7.00000 0.341159 0.170580 0.985344i $$-0.445436\pi$$
0.170580 + 0.985344i $$0.445436\pi$$
$$422$$ 0 0
$$423$$ −3.00000 + 5.19615i −0.145865 + 0.252646i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 12.0000 + 34.6410i 0.580721 + 1.67640i
$$428$$ 0 0
$$429$$ −3.00000 5.19615i −0.144841 0.250873i
$$430$$ 0 0
$$431$$ 21.0000 + 12.1244i 1.01153 + 0.584010i 0.911641 0.410988i $$-0.134816\pi$$
0.0998939 + 0.994998i $$0.468150\pi$$
$$432$$ 0 0
$$433$$ 1.73205i 0.0832370i −0.999134 0.0416185i $$-0.986749\pi$$
0.999134 0.0416185i $$-0.0132514\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 30.0000 + 17.3205i 1.43509 + 0.828552i
$$438$$ 0 0
$$439$$ 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i $$-0.105523\pi$$
−0.754642 + 0.656136i $$0.772190\pi$$
$$440$$ 0 0
$$441$$ 1.00000 + 6.92820i 0.0476190 + 0.329914i
$$442$$ 0 0
$$443$$ 12.0000 6.92820i 0.570137 0.329169i −0.187067 0.982347i $$-0.559898\pi$$
0.757204 + 0.653178i $$0.226565\pi$$
$$444$$ 0 0
$$445$$ 12.0000 20.7846i 0.568855 0.985285i
$$446$$ 0 0
$$447$$ 12.0000 0.567581
$$448$$ 0 0
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ −6.00000 + 10.3923i −0.282529 + 0.489355i
$$452$$ 0 0
$$453$$ −3.00000 + 1.73205i −0.140952 + 0.0813788i
$$454$$ 0 0
$$455$$ −15.0000 + 5.19615i −0.703211 + 0.243599i
$$456$$ 0 0
$$457$$ 9.50000 + 16.4545i 0.444391 + 0.769708i 0.998010 0.0630623i $$-0.0200867\pi$$
−0.553618 + 0.832771i $$0.686753\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 13.8564i 0.645357i −0.946509 0.322679i $$-0.895417\pi$$
0.946509 0.322679i $$-0.104583\pi$$
$$462$$ 0 0
$$463$$ 15.5885i 0.724457i −0.932089 0.362229i $$-0.882016\pi$$
0.932089 0.362229i $$-0.117984\pi$$
$$464$$ 0 0
$$465$$ −15.0000 8.66025i −0.695608 0.401610i
$$466$$ 0 0
$$467$$ −15.0000 25.9808i −0.694117 1.20225i −0.970477 0.241192i $$-0.922462\pi$$
0.276360 0.961054i $$1.58913\pi$$
$$468$$ 0 0
$$469$$ 15.0000 17.3205i 0.692636 0.799787i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 15.0000 25.9808i 0.689701 1.19460i
$$474$$ 0 0
$$475$$ 35.0000 1.60591
$$476$$ 0 0
$$477$$ 12.0000 0.549442
$$478$$ 0 0
$$479$$ 6.00000 10.3923i 0.274147 0.474837i −0.695773 0.718262i $$-0.744938\pi$$
0.969920 + 0.243426i $$0.0782712\pi$$
$$480$$ 0 0
$$481$$ 16.5000 9.52628i 0.752335 0.434361i
$$482$$ 0 0
$$483$$ 18.0000 + 3.46410i 0.819028 + 0.157622i
$$484$$ 0 0
$$485$$ 12.0000 + 20.7846i 0.544892 + 0.943781i
$$486$$ 0 0
$$487$$ 22.5000 + 12.9904i 1.01957 + 0.588650i 0.913980 0.405759i $$-0.132993\pi$$
0.105592 + 0.994410i $$0.466326\pi$$
$$488$$ 0 0
$$489$$ 3.46410i 0.156652i
$$490$$ 0 0
$$491$$ 34.6410i 1.56333i −0.623700 0.781664i $$-0.714371\pi$$
0.623700 0.781664i $$-0.285629\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 6.00000 + 10.3923i 0.269680 + 0.467099i
$$496$$ 0 0
$$497$$ 9.00000 + 1.73205i 0.403705 + 0.0776931i
$$498$$ 0 0
$$499$$ −28.5000 + 16.4545i −1.27584 + 0.736604i −0.976080 0.217412i $$-0.930238\pi$$
−0.299755 + 0.954016i $$0.596905\pi$$
$$500$$ 0 0
$$501$$ 3.00000 5.19615i 0.134030 0.232147i
$$502$$ 0 0
$$503$$ −6.00000 −0.267527 −0.133763 0.991013i $$-0.542706\pi$$
−0.133763 + 0.991013i $$0.542706\pi$$
$$504$$ 0 0
$$505$$ 36.0000 1.60198
$$506$$ 0 0
$$507$$ −5.00000 + 8.66025i −0.222058 + 0.384615i
$$508$$ 0 0
$$509$$ 27.0000 15.5885i 1.19675 0.690946i 0.236924 0.971528i $$-0.423861\pi$$
0.959830 + 0.280582i $$0.0905275\pi$$
$$510$$ 0 0
$$511$$ −9.00000 + 10.3923i −0.398137 + 0.459728i
$$512$$ 0 0
$$513$$ 2.50000 + 4.33013i 0.110378 + 0.191180i
$$514$$ 0 0
$$515$$ −15.0000 8.66025i −0.660979 0.381616i
$$516$$ 0 0
$$517$$ 20.7846i 0.914106i
$$518$$ 0 0
$$519$$ 6.92820i 0.304114i
$$520$$ 0 0
$$521$$ −12.0000 6.92820i −0.525730 0.303530i 0.213546 0.976933i $$-0.431499\pi$$
−0.739276 + 0.673403i $$0.764832\pi$$
$$522$$ 0 0
$$523$$ −5.50000 9.52628i −0.240498 0.416555i 0.720358 0.693602i $$-0.243977\pi$$
−0.960856 + 0.277047i $$0.910644\pi$$
$$524$$ 0 0
$$525$$ 17.5000 6.06218i 0.763763 0.264575i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 12.5000 21.6506i 0.543478 0.941332i
$$530$$ 0 0
$$531$$ −12.0000 −0.520756
$$532$$ 0 0
$$533$$ −6.00000 −0.259889
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 9.00000 5.19615i 0.388379 0.224231i
$$538$$ 0 0
$$539$$ 15.0000 + 19.0526i 0.646096 + 0.820652i
$$540$$ 0 0
$$541$$ 2.50000 + 4.33013i 0.107483 + 0.186167i 0.914750 0.404020i $$-0.132387\pi$$
−0.807267 + 0.590187i $$0.799054\pi$$
$$542$$ 0 0
$$543$$ 4.50000 + 2.59808i 0.193113 + 0.111494i
$$544$$ 0 0
$$545$$ 24.2487i 1.03870i
$$546$$ 0 0
$$547$$ 3.46410i 0.148114i −0.997254 0.0740571i $$-0.976405\pi$$
0.997254 0.0740571i $$-0.0235947\pi$$
$$548$$ 0 0
$$549$$ 12.0000 + 6.92820i 0.512148 + 0.295689i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −10.5000 30.3109i −0.446505 1.28895i
$$554$$ 0 0
$$555$$ −33.0000 + 19.0526i −1.40077 + 0.808736i
$$556$$ 0 0
$$557$$ −21.0000 + 36.3731i −0.889799 + 1.54118i −0.0496855 + 0.998765i $$0.515822\pi$$
−0.840113 + 0.542411i $$0.817511\pi$$
$$558$$ 0 0
$$559$$ 15.0000 0.634432
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −3.00000 + 5.19615i −0.126435 + 0.218992i −0.922293 0.386492i $$-0.873687\pi$$
0.795858 + 0.605483i $$0.207020\pi$$
$$564$$ 0 0
$$565$$ −18.0000 + 10.3923i −0.757266 + 0.437208i
$$566$$ 0 0
$$567$$ 2.00000 + 1.73205i 0.0839921 + 0.0727393i
$$568$$ 0 0
$$569$$ −21.0000 36.3731i −0.880366 1.52484i −0.850935 0.525271i $$-0.823964\pi$$
−0.0294311 0.999567i $$-0.509370\pi$$
$$570$$ 0 0
$$571$$ −40.5000 23.3827i −1.69487 0.978535i −0.950477 0.310796i $$-0.899404\pi$$
−0.744396 0.667739i $$1.23274\pi$$
$$572$$ 0 0
$$573$$ 17.3205i 0.723575i
$$574$$ 0 0
$$575$$ 48.4974i 2.02248i
$$576$$ 0 0
$$577$$ 10.5000 + 6.06218i 0.437121 + 0.252372i 0.702376 0.711807i $$-0.252123\pi$$
−0.265255 + 0.964178i $$0.585456\pi$$
$$578$$ 0 0
$$579$$ 5.50000 + 9.52628i 0.228572 + 0.395899i
$$580$$ 0 0
$$581$$ −9.00000 + 46.7654i −0.373383 + 1.94015i
$$582$$ 0 0
$$583$$ 36.0000 20.7846i 1.49097 0.860811i
$$584$$ 0 0
$$585$$ −3.00000 + 5.19615i −0.124035 + 0.214834i
$$586$$ 0 0
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ −25.0000 −1.03011
$$590$$ 0 0
$$591$$ −12.0000 + 20.7846i −0.493614 + 0.854965i
$$592$$ 0 0
$$593$$ 3.00000 1.73205i 0.123195 0.0711268i −0.437136 0.899395i $$-0.644007\pi$$
0.560331 + 0.828269i $$0.310674\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −8.00000 13.8564i −0.327418 0.567105i
$$598$$ 0 0
$$599$$ −42.0000 24.2487i −1.71607 0.990775i −0.925794 0.378030i $$-0.876602\pi$$
−0.790280 0.612746i $$1.20994\pi$$
$$600$$ 0 0
$$601$$ 39.8372i 1.62499i −0.582967 0.812496i $$-0.698108\pi$$
0.582967 0.812496i $$-0.301892\pi$$
$$602$$ 0 0
$$603$$ 8.66025i 0.352673i
$$604$$ 0 0
$$605$$ 3.00000 + 1.73205i 0.121967 + 0.0704179i
$$606$$ 0 0
$$607$$ −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i $$-0.251651\pi$$
−0.967256 + 0.253804i $$0.918318\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −9.00000 + 5.19615i −0.364101 + 0.210214i
$$612$$ 0 0
$$613$$ −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i $$-0.846193\pi$$
0.845124 + 0.534570i $$0.179527\pi$$
$$614$$ 0 0
$$615$$ 12.0000 0.483887
$$616$$ 0 0
$$617$$ −18.0000 −0.724653 −0.362326 0.932051i $$-0.618017\pi$$
−0.362326 + 0.932051i $$0.618017\pi$$
$$618$$ 0 0
$$619$$ 0.500000 0.866025i 0.0200967 0.0348085i −0.855802 0.517303i $$-0.826936\pi$$
0.875899 + 0.482495i $$0.160269\pi$$
$$620$$ 0 0
$$621$$ 6.00000 3.46410i 0.240772 0.139010i
$$622$$ 0 0
$$623$$ −6.00000 17.3205i −0.240385 0.693932i
$$624$$ 0 0
$$625$$ 5.50000 + 9.52628i 0.220000 + 0.381051i
$$626$$ 0 0
$$627$$ 15.0000 + 8.66025i 0.599042 + 0.345857i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 3.46410i 0.137904i 0.997620 + 0.0689519i $$0.0219655\pi$$
−0.997620 + 0.0689519i $$0.978035\pi$$
$$632$$ 0 0
$$633$$ −3.00000 1.73205i −0.119239 0.0688428i
$$634$$ 0 0
$$635$$ 21.0000 + 36.3731i 0.833360 + 1.44342i
$$636$$ 0 0
$$637$$ −4.50000 + 11.2583i −0.178296 + 0.446071i
$$638$$ 0 0
$$639$$ 3.00000 1.73205i 0.118678 0.0685189i
$$640$$ 0 0
$$641$$ −12.0000 + 20.7846i −0.473972 + 0.820943i −0.999556 0.0297987i $$-0.990513\pi$$
0.525584 + 0.850741i $$0.323847\pi$$
$$642$$ 0 0
$$643$$ 31.0000 1.22252 0.611260 0.791430i $$-0.290663\pi$$
0.611260 + 0.791430i $$0.290663\pi$$
$$644$$ 0 0
$$645$$ −30.0000 −1.18125
$$646$$ 0 0
$$647$$ −15.0000 + 25.9808i −0.589711 + 1.02141i 0.404559 + 0.914512i $$0.367425\pi$$
−0.994270 + 0.106897i $$0.965908\pi$$
$$648$$ 0 0
$$649$$ −36.0000 + 20.7846i −1.41312 + 0.815867i
$$650$$ 0 0
$$651$$ −12.5000 + 4.33013i −0.489914 + 0.169711i
$$652$$ 0 0
$$653$$ −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i $$-0.204122\pi$$
−0.918736 + 0.394872i $$0.870789\pi$$
$$654$$ 0 0
$$655$$ 18.0000 + 10.3923i 0.703318 + 0.406061i
$$656$$ 0 0
$$657$$ 5.19615i 0.202721i
$$658$$ 0 0
$$659$$ 13.8564i 0.539769i 0.962893 + 0.269884i $$0.0869855\pi$$
−0.962893 + 0.269884i $$0.913014\pi$$
$$660$$ 0 0
$$661$$ 22.5000 + 12.9904i 0.875149 + 0.505267i 0.869056 0.494714i $$-0.164727\pi$$
0.00609283 + 0.999981i $$0.498061\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 30.0000 34.6410i 1.16335 1.34332i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ −8.00000 + 13.8564i −0.309298 + 0.535720i
$$670$$ 0 0
$$671$$ 48.0000 1.85302
$$672$$ 0 0
$$673$$ 1.00000 0.0385472 0.0192736 0.999814i $$-0.493865\pi$$
0.0192736 + 0.999814i $$0.493865\pi$$
$$674$$ 0 0
$$675$$ 3.50000 6.06218i 0.134715 0.233333i
$$676$$ 0 0
$$677$$ −6.00000 + 3.46410i −0.230599 + 0.133136i −0.610848 0.791748i $$-0.709171\pi$$
0.380250 + 0.924884i $$0.375838\pi$$
$$678$$ 0 0
$$679$$ 18.0000 + 3.46410i 0.690777 + 0.132940i
$$680$$ 0 0
$$681$$ −9.00000 15.5885i −0.344881 0.597351i
$$682$$ 0 0
$$683$$ 6.00000 + 3.46410i 0.229584 + 0.132550i 0.610380 0.792109i $$-0.291017\pi$$
−0.380796 + 0.924659i $$0.624350\pi$$
$$684$$ 0 0
$$685$$ 41.5692i 1.58828i
$$686$$ 0 0
$$687$$ 8.66025i 0.330409i
$$688$$ 0 0
$$689$$ 18.0000 + 10.3923i 0.685745 + 0.395915i
$$690$$ 0 0
$$691$$ −11.5000 19.9186i −0.437481 0.757739i 0.560014 0.828483i $$-0.310796\pi$$
−0.997494 + 0.0707446i $$0.977462\pi$$
$$692$$ 0 0
$$693$$ 9.00000 + 1.73205i 0.341882 + 0.0657952i
$$694$$ 0 0
$$695$$ −21.0000 + 12.1244i −0.796575 + 0.459903i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ −6.00000 −0.226941
$$700$$ 0 0
$$701$$ 12.0000 0.453234 0.226617 0.973984i $$-0.427233\pi$$
0.226617 + 0.973984i $$0.427233\pi$$
$$702$$ 0 0
$$703$$ −27.5000 + 47.6314i −1.03718 + 1.79645i
$$704$$ 0 0
$$705$$ 18.0000 10.3923i 0.677919 0.391397i
$$706$$ 0 0
$$707$$ 18.0000 20.7846i 0.676960 0.781686i
$$708$$ 0 0
$$709$$ 5.00000 + 8.66025i 0.187779 + 0.325243i 0.944509 0.328484i $$-0.106538\pi$$
−0.756730 + 0.653727i $$0.773204\pi$$
$$710$$ 0 0
$$711$$ −10.5000 6.06218i −0.393781 0.227349i
$$712$$ 0 0
$$713$$ 34.6410i 1.29732i
$$714$$ 0 0
$$715$$ 20.7846i 0.777300i
$$716$$ 0 0
$$717$$ −9.00000 5.19615i −0.336111 0.194054i
$$718$$ 0 0
$$719$$ −15.0000 25.9808i −0.559406 0.968919i −0.997546 0.0700124i $$-0.977696\pi$$
0.438141 0.898906i $$1.64436\pi$$
$$720$$ 0 0
$$721$$ −12.5000 + 4.33013i −0.465524 + 0.161262i
$$722$$ 0 0
$$723$$ 12.0000 6.92820i 0.446285 0.257663i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 23.0000 0.853023 0.426511 0.904482i $$-0.359742\pi$$
0.426511 + 0.904482i $$0.359742\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −25.5000 + 14.7224i −0.941864 + 0.543785i −0.890544 0.454897i $$-0.849676\pi$$
−0.0513199 + 0.998682i $$0.516343\pi$$
$$734$$ 0 0
$$735$$ 9.00000 22.5167i 0.331970 0.830540i
$$736$$ 0 0
$$737$$ −15.0000 25.9808i −0.552532 0.957014i
$$738$$ 0 0
$$739$$ −46.5000 26.8468i −1.71053 0.987575i −0.933839 0.357693i $$-0.883563\pi$$
−0.776691 0.629882i $$1.21690\pi$$
$$740$$ 0 0
$$741$$ 8.66025i 0.318142i
$$742$$ 0 0
$$743$$ 3.46410i 0.127086i 0.997979 + 0.0635428i $$0.0202399\pi$$
−0.997979 + 0.0635428i $$0.979760\pi$$
$$744$$ 0 0
$$745$$ −36.0000 20.7846i −1.31894 0.761489i
$$746$$ 0 0
$$747$$ 9.00000 + 15.5885i 0.329293 + 0.570352i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −4.50000 + 2.59808i −0.164207 + 0.0948051i −0.579852 0.814722i $$-0.696889\pi$$
0.415644 + 0.909527i $$0.363556\pi$$
$$752$$ 0 0
$$753$$ −6.00000 + 10.3923i −0.218652 + 0.378717i
$$754$$ 0 0
$$755$$ 12.0000 0.436725
$$756$$ 0 0
$$757$$ 26.0000 0.944986 0.472493 0.881334i $$-0.343354\pi$$
0.472493 + 0.881334i $$0.343354\pi$$
$$758$$ 0 0
$$759$$ 12.0000 20.7846i 0.435572 0.754434i
$$760$$ 0 0
$$761$$ −36.0000 + 20.7846i −1.30500 + 0.753442i −0.981257 0.192704i $$-0.938274\pi$$
−0.323742 + 0.946145i $$0.604941\pi$$
$$762$$ 0 0
$$763$$ −14.0000 12.1244i −0.506834 0.438931i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −18.0000 10.3923i −0.649942 0.375244i
$$768$$ 0 0
$$769$$ 15.5885i 0.562134i −0.959688 0.281067i $$-0.909312\pi$$
0.959688 0.281067i $$-0.0906883\pi$$
$$770$$ 0 0
$$771$$ 17.3205i 0.623783i
$$772$$ 0 0
$$773$$ −39.0000 22.5167i −1.40273 0.809868i −0.408060 0.912955i $$-0.633795\pi$$
−0.994672 + 0.103087i $$0.967128\pi$$
$$774$$ 0 0
$$775$$ 17.5000 + 30.3109i 0.628619 + 1.08880i
$$776$$ 0 0
$$777$$ −5.50000 + 28.5788i −0.197311 + 1.02526i
$$778$$ 0 0
$$779$$ 15.0000 8.66025i 0.537431 0.310286i
$$780$$ 0 0
$$781$$ 6.00000 10.3923i 0.214697 0.371866i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 8.00000 13.8564i 0.285169 0.493928i −0.687481 0.726202i $$-0.741284\pi$$
0.972650 + 0.232275i $$0.0746169\pi$$
$$788$$ 0 0
$$789$$ −12.0000 + 6.92820i −0.427211 + 0.246651i
$$790$$ 0 0
$$791$$ −3.00000 + 15.5885i −0.106668 + 0.554262i
$$792$$ 0 0
$$793$$ 12.0000 + 20.7846i 0.426132 + 0.738083i
$$794$$ 0 0
$$795$$ −36.0000 20.7846i −1.27679 0.737154i
$$796$$ 0 0
$$797$$ 34.6410i 1.22705i