# Properties

 Label 784.2.i.d.177.1 Level $784$ Weight $2$ Character 784.177 Analytic conductor $6.260$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$784 = 2^{4} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 784.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.26027151847$$ 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: no (minimal twist has level 28) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 177.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 784.177 Dual form 784.2.i.d.753.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} -2.00000 q^{13} -3.00000 q^{15} +(1.50000 + 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{19} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.00000 q^{27} -6.00000 q^{29} +(3.50000 + 6.06218i) q^{31} +(-1.50000 + 2.59808i) q^{33} +(0.500000 - 0.866025i) q^{37} +(1.00000 + 1.73205i) q^{39} -6.00000 q^{41} +4.00000 q^{43} +(-3.00000 - 5.19615i) q^{45} +(4.50000 - 7.79423i) q^{47} +(1.50000 - 2.59808i) q^{51} +(-1.50000 - 2.59808i) q^{53} -9.00000 q^{55} -1.00000 q^{57} +(-4.50000 - 7.79423i) q^{59} +(-0.500000 + 0.866025i) q^{61} +(-3.00000 + 5.19615i) q^{65} +(-3.50000 - 6.06218i) q^{67} -3.00000 q^{69} +(-0.500000 - 0.866025i) q^{73} +(-2.00000 + 3.46410i) q^{75} +(-6.50000 + 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +9.00000 q^{85} +(3.00000 + 5.19615i) q^{87} +(7.50000 - 12.9904i) q^{89} +(3.50000 - 6.06218i) q^{93} +(-1.50000 - 2.59808i) q^{95} +10.0000 q^{97} -6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} + 3q^{5} + 2q^{9} + O(q^{10})$$ $$2q - q^{3} + 3q^{5} + 2q^{9} - 3q^{11} - 4q^{13} - 6q^{15} + 3q^{17} + q^{19} + 3q^{23} - 4q^{25} - 10q^{27} - 12q^{29} + 7q^{31} - 3q^{33} + q^{37} + 2q^{39} - 12q^{41} + 8q^{43} - 6q^{45} + 9q^{47} + 3q^{51} - 3q^{53} - 18q^{55} - 2q^{57} - 9q^{59} - q^{61} - 6q^{65} - 7q^{67} - 6q^{69} - q^{73} - 4q^{75} - 13q^{79} - q^{81} + 24q^{83} + 18q^{85} + 6q^{87} + 15q^{89} + 7q^{93} - 3q^{95} + 20q^{97} - 12q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$687$$ $$689$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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 0.684819 0.728714i $$-0.259881\pi$$
−0.973494 + 0.228714i $$0.926548\pi$$
$$4$$ 0 0
$$5$$ 1.50000 2.59808i 0.670820 1.16190i −0.306851 0.951757i $$-0.599275\pi$$
0.977672 0.210138i $$-0.0673912\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 1.00000 1.73205i 0.333333 0.577350i
$$10$$ 0 0
$$11$$ −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i $$-0.316051\pi$$
−0.998526 + 0.0542666i $$0.982718\pi$$
$$12$$ 0 0
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ −3.00000 −0.774597
$$16$$ 0 0
$$17$$ 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i $$-0.0481447\pi$$
−0.624780 + 0.780801i $$0.714811\pi$$
$$18$$ 0 0
$$19$$ 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i $$-0.796740\pi$$
0.917663 + 0.397360i $$0.130073\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i $$-0.732076\pi$$
0.978961 + 0.204046i $$0.0654092\pi$$
$$24$$ 0 0
$$25$$ −2.00000 3.46410i −0.400000 0.692820i
$$26$$ 0 0
$$27$$ −5.00000 −0.962250
$$28$$ 0 0
$$29$$ −6.00000 −1.11417 −0.557086 0.830455i $$-0.688081\pi$$
−0.557086 + 0.830455i $$0.688081\pi$$
$$30$$ 0 0
$$31$$ 3.50000 + 6.06218i 0.628619 + 1.08880i 0.987829 + 0.155543i $$0.0497126\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ −1.50000 + 2.59808i −0.261116 + 0.452267i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i $$-0.807139\pi$$
0.904194 + 0.427121i $$0.140472\pi$$
$$38$$ 0 0
$$39$$ 1.00000 + 1.73205i 0.160128 + 0.277350i
$$40$$ 0 0
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ 0 0
$$45$$ −3.00000 5.19615i −0.447214 0.774597i
$$46$$ 0 0
$$47$$ 4.50000 7.79423i 0.656392 1.13691i −0.325150 0.945662i $$-0.605415\pi$$
0.981543 0.191243i $$-0.0612518\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 1.50000 2.59808i 0.210042 0.363803i
$$52$$ 0 0
$$53$$ −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i $$-0.232725\pi$$
−0.950464 + 0.310835i $$0.899391\pi$$
$$54$$ 0 0
$$55$$ −9.00000 −1.21356
$$56$$ 0 0
$$57$$ −1.00000 −0.132453
$$58$$ 0 0
$$59$$ −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i $$-0.967427\pi$$
0.408919 0.912571i $$-0.365906\pi$$
$$60$$ 0 0
$$61$$ −0.500000 + 0.866025i −0.0640184 + 0.110883i −0.896258 0.443533i $$-0.853725\pi$$
0.832240 + 0.554416i $$0.187058\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −3.00000 + 5.19615i −0.372104 + 0.644503i
$$66$$ 0 0
$$67$$ −3.50000 6.06218i −0.427593 0.740613i 0.569066 0.822292i $$-0.307305\pi$$
−0.996659 + 0.0816792i $$0.973972\pi$$
$$68$$ 0 0
$$69$$ −3.00000 −0.361158
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −0.500000 0.866025i −0.0585206 0.101361i 0.835281 0.549823i $$-0.185305\pi$$
−0.893801 + 0.448463i $$0.851972\pi$$
$$74$$ 0 0
$$75$$ −2.00000 + 3.46410i −0.230940 + 0.400000i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −6.50000 + 11.2583i −0.731307 + 1.26666i 0.225018 + 0.974355i $$0.427756\pi$$
−0.956325 + 0.292306i $$0.905577\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ 9.00000 0.976187
$$86$$ 0 0
$$87$$ 3.00000 + 5.19615i 0.321634 + 0.557086i
$$88$$ 0 0
$$89$$ 7.50000 12.9904i 0.794998 1.37698i −0.127842 0.991795i $$-0.540805\pi$$
0.922840 0.385183i $$-0.125862\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 3.50000 6.06218i 0.362933 0.628619i
$$94$$ 0 0
$$95$$ −1.50000 2.59808i −0.153897 0.266557i
$$96$$ 0 0
$$97$$ 10.0000 1.01535 0.507673 0.861550i $$-0.330506\pi$$
0.507673 + 0.861550i $$0.330506\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ 7.50000 + 12.9904i 0.746278 + 1.29259i 0.949595 + 0.313478i $$0.101494\pi$$
−0.203317 + 0.979113i $$0.565172\pi$$
$$102$$ 0 0
$$103$$ −5.50000 + 9.52628i −0.541931 + 0.938652i 0.456862 + 0.889538i $$0.348973\pi$$
−0.998793 + 0.0491146i $$0.984360\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 7.50000 12.9904i 0.725052 1.25583i −0.233900 0.972261i $$-0.575149\pi$$
0.958952 0.283567i $$-0.0915178\pi$$
$$108$$ 0 0
$$109$$ 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i $$-0.151417\pi$$
−0.841086 + 0.540901i $$0.818083\pi$$
$$110$$ 0 0
$$111$$ −1.00000 −0.0949158
$$112$$ 0 0
$$113$$ 6.00000 0.564433 0.282216 0.959351i $$-0.408930\pi$$
0.282216 + 0.959351i $$0.408930\pi$$
$$114$$ 0 0
$$115$$ −4.50000 7.79423i −0.419627 0.726816i
$$116$$ 0 0
$$117$$ −2.00000 + 3.46410i −0.184900 + 0.320256i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ 0 0
$$123$$ 3.00000 + 5.19615i 0.270501 + 0.468521i
$$124$$ 0 0
$$125$$ 3.00000 0.268328
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ 0 0
$$129$$ −2.00000 3.46410i −0.176090 0.304997i
$$130$$ 0 0
$$131$$ −1.50000 + 2.59808i −0.131056 + 0.226995i −0.924084 0.382190i $$-0.875170\pi$$
0.793028 + 0.609185i $$0.208503\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −7.50000 + 12.9904i −0.645497 + 1.11803i
$$136$$ 0 0
$$137$$ 10.5000 + 18.1865i 0.897076 + 1.55378i 0.831215 + 0.555952i $$0.187646\pi$$
0.0658609 + 0.997829i $$0.479021\pi$$
$$138$$ 0 0
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ 0 0
$$141$$ −9.00000 −0.757937
$$142$$ 0 0
$$143$$ 3.00000 + 5.19615i 0.250873 + 0.434524i
$$144$$ 0 0
$$145$$ −9.00000 + 15.5885i −0.747409 + 1.29455i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1.50000 + 2.59808i −0.122885 + 0.212843i −0.920904 0.389789i $$-0.872548\pi$$
0.798019 + 0.602632i $$0.205881\pi$$
$$150$$ 0 0
$$151$$ 8.50000 + 14.7224i 0.691720 + 1.19809i 0.971274 + 0.237964i $$0.0764802\pi$$
−0.279554 + 0.960130i $$0.590186\pi$$
$$152$$ 0 0
$$153$$ 6.00000 0.485071
$$154$$ 0 0
$$155$$ 21.0000 1.68676
$$156$$ 0 0
$$157$$ −6.50000 11.2583i −0.518756 0.898513i −0.999762 0.0217953i $$-0.993062\pi$$
0.481006 0.876717i $$-0.340272\pi$$
$$158$$ 0 0
$$159$$ −1.50000 + 2.59808i −0.118958 + 0.206041i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 5.50000 9.52628i 0.430793 0.746156i −0.566149 0.824303i $$-0.691567\pi$$
0.996942 + 0.0781474i $$0.0249005\pi$$
$$164$$ 0 0
$$165$$ 4.50000 + 7.79423i 0.350325 + 0.606780i
$$166$$ 0 0
$$167$$ −12.0000 −0.928588 −0.464294 0.885681i $$-0.653692\pi$$
−0.464294 + 0.885681i $$0.653692\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 0 0
$$171$$ −1.00000 1.73205i −0.0764719 0.132453i
$$172$$ 0 0
$$173$$ −4.50000 + 7.79423i −0.342129 + 0.592584i −0.984828 0.173534i $$-0.944481\pi$$
0.642699 + 0.766119i $$0.277815\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −4.50000 + 7.79423i −0.338241 + 0.585850i
$$178$$ 0 0
$$179$$ 10.5000 + 18.1865i 0.784807 + 1.35933i 0.929114 + 0.369792i $$0.120571\pi$$
−0.144308 + 0.989533i $$0.546095\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 0 0
$$183$$ 1.00000 0.0739221
$$184$$ 0 0
$$185$$ −1.50000 2.59808i −0.110282 0.191014i
$$186$$ 0 0
$$187$$ 4.50000 7.79423i 0.329073 0.569970i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −4.50000 + 7.79423i −0.325609 + 0.563971i −0.981635 0.190767i $$-0.938902\pi$$
0.656027 + 0.754738i $$0.272236\pi$$
$$192$$ 0 0
$$193$$ −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i $$-0.296234\pi$$
−0.993215 + 0.116289i $$0.962900\pi$$
$$194$$ 0 0
$$195$$ 6.00000 0.429669
$$196$$ 0 0
$$197$$ 18.0000 1.28245 0.641223 0.767354i $$-0.278427\pi$$
0.641223 + 0.767354i $$0.278427\pi$$
$$198$$ 0 0
$$199$$ 3.50000 + 6.06218i 0.248108 + 0.429736i 0.963001 0.269498i $$-0.0868577\pi$$
−0.714893 + 0.699234i $$0.753524\pi$$
$$200$$ 0 0
$$201$$ −3.50000 + 6.06218i −0.246871 + 0.427593i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −9.00000 + 15.5885i −0.628587 + 1.08875i
$$206$$ 0 0
$$207$$ −3.00000 5.19615i −0.208514 0.361158i
$$208$$ 0 0
$$209$$ −3.00000 −0.207514
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 6.00000 10.3923i 0.409197 0.708749i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −0.500000 + 0.866025i −0.0337869 + 0.0585206i
$$220$$ 0 0
$$221$$ −3.00000 5.19615i −0.201802 0.349531i
$$222$$ 0 0
$$223$$ 8.00000 0.535720 0.267860 0.963458i $$-0.413684\pi$$
0.267860 + 0.963458i $$0.413684\pi$$
$$224$$ 0 0
$$225$$ −8.00000 −0.533333
$$226$$ 0 0
$$227$$ 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i $$-0.134924\pi$$
−0.811943 + 0.583736i $$0.801590\pi$$
$$228$$ 0 0
$$229$$ 5.50000 9.52628i 0.363450 0.629514i −0.625076 0.780564i $$-0.714932\pi$$
0.988526 + 0.151050i $$0.0482653\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 10.5000 18.1865i 0.687878 1.19144i −0.284645 0.958633i $$-0.591876\pi$$
0.972523 0.232806i $$-0.0747909\pi$$
$$234$$ 0 0
$$235$$ −13.5000 23.3827i −0.880643 1.52532i
$$236$$ 0 0
$$237$$ 13.0000 0.844441
$$238$$ 0 0
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −0.500000 0.866025i −0.0322078 0.0557856i 0.849472 0.527633i $$-0.176921\pi$$
−0.881680 + 0.471848i $$0.843587\pi$$
$$242$$ 0 0
$$243$$ −8.00000 + 13.8564i −0.513200 + 0.888889i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −1.00000 + 1.73205i −0.0636285 + 0.110208i
$$248$$ 0 0
$$249$$ −6.00000 10.3923i −0.380235 0.658586i
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ −9.00000 −0.565825
$$254$$ 0 0
$$255$$ −4.50000 7.79423i −0.281801 0.488094i
$$256$$ 0 0
$$257$$ 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i $$-0.803506\pi$$
0.909010 + 0.416775i $$0.136840\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −6.00000 + 10.3923i −0.371391 + 0.643268i
$$262$$ 0 0
$$263$$ −1.50000 2.59808i −0.0924940 0.160204i 0.816066 0.577959i $$-0.196151\pi$$
−0.908560 + 0.417755i $$0.862817\pi$$
$$264$$ 0 0
$$265$$ −9.00000 −0.552866
$$266$$ 0 0
$$267$$ −15.0000 −0.917985
$$268$$ 0 0
$$269$$ 1.50000 + 2.59808i 0.0914566 + 0.158408i 0.908124 0.418701i $$-0.137514\pi$$
−0.816668 + 0.577108i $$0.804181\pi$$
$$270$$ 0 0
$$271$$ −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i $$-0.941766\pi$$
0.649211 + 0.760609i $$0.275099\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −6.00000 + 10.3923i −0.361814 + 0.626680i
$$276$$ 0 0
$$277$$ 6.50000 + 11.2583i 0.390547 + 0.676448i 0.992522 0.122068i $$-0.0389525\pi$$
−0.601975 + 0.798515i $$0.705619\pi$$
$$278$$ 0 0
$$279$$ 14.0000 0.838158
$$280$$ 0 0
$$281$$ 30.0000 1.78965 0.894825 0.446417i $$-0.147300\pi$$
0.894825 + 0.446417i $$0.147300\pi$$
$$282$$ 0 0
$$283$$ −14.5000 25.1147i −0.861936 1.49292i −0.870058 0.492949i $$-0.835919\pi$$
0.00812260 0.999967i $$-0.497414\pi$$
$$284$$ 0 0
$$285$$ −1.50000 + 2.59808i −0.0888523 + 0.153897i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 4.00000 6.92820i 0.235294 0.407541i
$$290$$ 0 0
$$291$$ −5.00000 8.66025i −0.293105 0.507673i
$$292$$ 0 0
$$293$$ −6.00000 −0.350524 −0.175262 0.984522i $$-0.556077\pi$$
−0.175262 + 0.984522i $$0.556077\pi$$
$$294$$ 0 0
$$295$$ −27.0000 −1.57200
$$296$$ 0 0
$$297$$ 7.50000 + 12.9904i 0.435194 + 0.753778i
$$298$$ 0 0
$$299$$ −3.00000 + 5.19615i −0.173494 + 0.300501i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 7.50000 12.9904i 0.430864 0.746278i
$$304$$ 0 0
$$305$$ 1.50000 + 2.59808i 0.0858898 + 0.148765i
$$306$$ 0 0
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 0 0
$$309$$ 11.0000 0.625768
$$310$$ 0 0
$$311$$ 13.5000 + 23.3827i 0.765515 + 1.32591i 0.939974 + 0.341246i $$0.110849\pi$$
−0.174459 + 0.984664i $$0.555818\pi$$
$$312$$ 0 0
$$313$$ 11.5000 19.9186i 0.650018 1.12586i −0.333099 0.942892i $$-0.608094\pi$$
0.983118 0.182973i $$-0.0585722\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 4.50000 7.79423i 0.252745 0.437767i −0.711535 0.702650i $$-0.752000\pi$$
0.964281 + 0.264883i $$0.0853332\pi$$
$$318$$ 0 0
$$319$$ 9.00000 + 15.5885i 0.503903 + 0.872786i
$$320$$ 0 0
$$321$$ −15.0000 −0.837218
$$322$$ 0 0
$$323$$ 3.00000 0.166924
$$324$$ 0 0
$$325$$ 4.00000 + 6.92820i 0.221880 + 0.384308i
$$326$$ 0 0
$$327$$ 0.500000 0.866025i 0.0276501 0.0478913i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −6.50000 + 11.2583i −0.357272 + 0.618814i −0.987504 0.157593i $$-0.949627\pi$$
0.630232 + 0.776407i $$0.282960\pi$$
$$332$$ 0 0
$$333$$ −1.00000 1.73205i −0.0547997 0.0949158i
$$334$$ 0 0
$$335$$ −21.0000 −1.14735
$$336$$ 0 0
$$337$$ −34.0000 −1.85210 −0.926049 0.377403i $$-0.876817\pi$$
−0.926049 + 0.377403i $$0.876817\pi$$
$$338$$ 0 0
$$339$$ −3.00000 5.19615i −0.162938 0.282216i
$$340$$ 0 0
$$341$$ 10.5000 18.1865i 0.568607 0.984856i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −4.50000 + 7.79423i −0.242272 + 0.419627i
$$346$$ 0 0
$$347$$ 4.50000 + 7.79423i 0.241573 + 0.418416i 0.961162 0.275983i $$-0.0890035\pi$$
−0.719590 + 0.694399i $$0.755670\pi$$
$$348$$ 0 0
$$349$$ −26.0000 −1.39175 −0.695874 0.718164i $$-0.744983\pi$$
−0.695874 + 0.718164i $$0.744983\pi$$
$$350$$ 0 0
$$351$$ 10.0000 0.533761
$$352$$ 0 0
$$353$$ −10.5000 18.1865i −0.558859 0.967972i −0.997592 0.0693543i $$-0.977906\pi$$
0.438733 0.898617i $$-0.355427\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 7.50000 12.9904i 0.395835 0.685606i −0.597372 0.801964i $$-0.703789\pi$$
0.993207 + 0.116358i $$0.0371219\pi$$
$$360$$ 0 0
$$361$$ 9.00000 + 15.5885i 0.473684 + 0.820445i
$$362$$ 0 0
$$363$$ −2.00000 −0.104973
$$364$$ 0 0
$$365$$ −3.00000 −0.157027
$$366$$ 0 0
$$367$$ −2.50000 4.33013i −0.130499 0.226031i 0.793370 0.608740i $$-0.208325\pi$$
−0.923869 + 0.382709i $$0.874991\pi$$
$$368$$ 0 0
$$369$$ −6.00000 + 10.3923i −0.312348 + 0.541002i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 12.5000 21.6506i 0.647225 1.12103i −0.336557 0.941663i $$-0.609263\pi$$
0.983783 0.179364i $$-0.0574041\pi$$
$$374$$ 0 0
$$375$$ −1.50000 2.59808i −0.0774597 0.134164i
$$376$$ 0 0
$$377$$ 12.0000 0.618031
$$378$$ 0 0
$$379$$ −8.00000 −0.410932 −0.205466 0.978664i $$-0.565871\pi$$
−0.205466 + 0.978664i $$0.565871\pi$$
$$380$$ 0 0
$$381$$ 4.00000 + 6.92820i 0.204926 + 0.354943i
$$382$$ 0 0
$$383$$ 16.5000 28.5788i 0.843111 1.46031i −0.0441413 0.999025i $$-0.514055\pi$$
0.887252 0.461285i $$-0.152611\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 4.00000 6.92820i 0.203331 0.352180i
$$388$$ 0 0
$$389$$ −7.50000 12.9904i −0.380265 0.658638i 0.610835 0.791758i $$-0.290834\pi$$
−0.991100 + 0.133120i $$0.957501\pi$$
$$390$$ 0 0
$$391$$ 9.00000 0.455150
$$392$$ 0 0
$$393$$ 3.00000 0.151330
$$394$$ 0 0
$$395$$ 19.5000 + 33.7750i 0.981151 + 1.69940i
$$396$$ 0 0
$$397$$ −18.5000 + 32.0429i −0.928488 + 1.60819i −0.142636 + 0.989775i $$0.545558\pi$$
−0.785853 + 0.618414i $$0.787776\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i $$-0.857199\pi$$
0.826139 + 0.563466i $$0.190532\pi$$
$$402$$ 0 0
$$403$$ −7.00000 12.1244i −0.348695 0.603957i
$$404$$ 0 0
$$405$$ −3.00000 −0.149071
$$406$$ 0 0
$$407$$ −3.00000 −0.148704
$$408$$ 0 0
$$409$$ 5.50000 + 9.52628i 0.271957 + 0.471044i 0.969363 0.245633i $$-0.0789957\pi$$
−0.697406 + 0.716677i $$0.745662\pi$$
$$410$$ 0 0
$$411$$ 10.5000 18.1865i 0.517927 0.897076i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 18.0000 31.1769i 0.883585 1.53041i
$$416$$ 0 0
$$417$$ −10.0000 17.3205i −0.489702 0.848189i
$$418$$ 0 0
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ −22.0000 −1.07221 −0.536107 0.844150i $$-0.680106\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ 0 0
$$423$$ −9.00000 15.5885i −0.437595 0.757937i
$$424$$ 0 0
$$425$$ 6.00000 10.3923i 0.291043 0.504101i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 3.00000 5.19615i 0.144841 0.250873i
$$430$$ 0 0
$$431$$ −7.50000 12.9904i −0.361262 0.625725i 0.626907 0.779094i $$-0.284321\pi$$
−0.988169 + 0.153370i $$0.950987\pi$$
$$432$$ 0 0
$$433$$ 10.0000 0.480569 0.240285 0.970702i $$-0.422759\pi$$
0.240285 + 0.970702i $$0.422759\pi$$
$$434$$ 0 0
$$435$$ 18.0000 0.863034
$$436$$ 0 0
$$437$$ −1.50000 2.59808i −0.0717547 0.124283i
$$438$$ 0 0
$$439$$ 0.500000 0.866025i 0.0238637 0.0413331i −0.853847 0.520524i $$-0.825737\pi$$
0.877711 + 0.479191i $$0.159070\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −4.50000 + 7.79423i −0.213801 + 0.370315i −0.952901 0.303281i $$-0.901918\pi$$
0.739100 + 0.673596i $$0.235251\pi$$
$$444$$ 0 0
$$445$$ −22.5000 38.9711i −1.06660 1.84741i
$$446$$ 0 0
$$447$$ 3.00000 0.141895
$$448$$ 0 0
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 0 0
$$451$$ 9.00000 + 15.5885i 0.423793 + 0.734032i
$$452$$ 0 0
$$453$$ 8.50000 14.7224i 0.399365 0.691720i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −11.5000 + 19.9186i −0.537947 + 0.931752i 0.461067 + 0.887365i $$0.347467\pi$$
−0.999014 + 0.0443868i $$0.985867\pi$$
$$458$$ 0 0
$$459$$ −7.50000 12.9904i −0.350070 0.606339i
$$460$$ 0 0
$$461$$ 6.00000 0.279448 0.139724 0.990190i $$-0.455378\pi$$
0.139724 + 0.990190i $$0.455378\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ 0 0
$$465$$ −10.5000 18.1865i −0.486926 0.843380i
$$466$$ 0 0
$$467$$ 10.5000 18.1865i 0.485882 0.841572i −0.513986 0.857798i $$-0.671832\pi$$
0.999868 + 0.0162260i $$0.00516512\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −6.50000 + 11.2583i −0.299504 + 0.518756i
$$472$$ 0 0
$$473$$ −6.00000 10.3923i −0.275880 0.477839i
$$474$$ 0 0
$$475$$ −4.00000 −0.183533
$$476$$ 0 0
$$477$$ −6.00000 −0.274721
$$478$$ 0 0
$$479$$ 1.50000 + 2.59808i 0.0685367 + 0.118709i 0.898257 0.439470i $$-0.144834\pi$$
−0.829721 + 0.558179i $$0.811500\pi$$
$$480$$ 0 0
$$481$$ −1.00000 + 1.73205i −0.0455961 + 0.0789747i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 15.0000 25.9808i 0.681115 1.17973i
$$486$$ 0 0
$$487$$ −9.50000 16.4545i −0.430486 0.745624i 0.566429 0.824110i $$-0.308325\pi$$
−0.996915 + 0.0784867i $$0.974991\pi$$
$$488$$ 0 0
$$489$$ −11.0000 −0.497437
$$490$$ 0 0
$$491$$ −24.0000 −1.08310 −0.541552 0.840667i $$-0.682163\pi$$
−0.541552 + 0.840667i $$0.682163\pi$$
$$492$$ 0 0
$$493$$ −9.00000 15.5885i −0.405340 0.702069i
$$494$$ 0 0
$$495$$ −9.00000 + 15.5885i −0.404520 + 0.700649i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 5.50000 9.52628i 0.246214 0.426455i −0.716258 0.697835i $$-0.754147\pi$$
0.962472 + 0.271380i $$0.0874801\pi$$
$$500$$ 0 0
$$501$$ 6.00000 + 10.3923i 0.268060 + 0.464294i
$$502$$ 0 0
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 45.0000 2.00247
$$506$$ 0 0
$$507$$ 4.50000 + 7.79423i 0.199852 + 0.346154i
$$508$$ 0 0
$$509$$ 1.50000 2.59808i 0.0664863 0.115158i −0.830866 0.556473i $$-0.812154\pi$$
0.897352 + 0.441315i $$0.145488\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ −2.50000 + 4.33013i −0.110378 + 0.191180i
$$514$$ 0 0
$$515$$ 16.5000 + 28.5788i 0.727077 + 1.25933i
$$516$$ 0 0
$$517$$ −27.0000 −1.18746
$$518$$ 0 0
$$519$$ 9.00000 0.395056
$$520$$ 0 0
$$521$$ 19.5000 + 33.7750i 0.854311 + 1.47971i 0.877283 + 0.479973i $$0.159354\pi$$
−0.0229727 + 0.999736i $$0.507313\pi$$
$$522$$ 0 0
$$523$$ 0.500000 0.866025i 0.0218635 0.0378686i −0.854887 0.518815i $$-0.826373\pi$$
0.876750 + 0.480946i $$0.159707\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −10.5000 + 18.1865i −0.457387 + 0.792218i
$$528$$ 0 0
$$529$$ 7.00000 + 12.1244i 0.304348 + 0.527146i
$$530$$ 0 0
$$531$$ −18.0000 −0.781133
$$532$$ 0 0
$$533$$ 12.0000 0.519778
$$534$$ 0 0
$$535$$ −22.5000 38.9711i −0.972760 1.68487i
$$536$$ 0 0
$$537$$ 10.5000 18.1865i 0.453108 0.784807i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −17.5000 + 30.3109i −0.752384 + 1.30317i 0.194281 + 0.980946i $$0.437763\pi$$
−0.946664 + 0.322221i $$0.895571\pi$$
$$542$$ 0 0
$$543$$ −5.00000 8.66025i −0.214571 0.371647i
$$544$$ 0 0
$$545$$ 3.00000 0.128506
$$546$$ 0 0
$$547$$ −8.00000 −0.342055 −0.171028 0.985266i $$-0.554709\pi$$
−0.171028 + 0.985266i $$0.554709\pi$$
$$548$$ 0 0
$$549$$ 1.00000 + 1.73205i 0.0426790 + 0.0739221i
$$550$$ 0 0
$$551$$ −3.00000 + 5.19615i −0.127804 + 0.221364i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −1.50000 + 2.59808i −0.0636715 + 0.110282i
$$556$$ 0 0
$$557$$ 16.5000 + 28.5788i 0.699127 + 1.21092i 0.968769 + 0.247964i $$0.0797613\pi$$
−0.269642 + 0.962961i $$0.586905\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ −9.00000 −0.379980
$$562$$ 0 0
$$563$$ −4.50000 7.79423i −0.189652 0.328488i 0.755482 0.655169i $$-0.227403\pi$$
−0.945134 + 0.326682i $$0.894069\pi$$
$$564$$ 0 0
$$565$$ 9.00000 15.5885i 0.378633 0.655811i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 4.50000 7.79423i 0.188650 0.326751i −0.756151 0.654398i $$-0.772922\pi$$
0.944800 + 0.327647i $$0.106256\pi$$
$$570$$ 0 0
$$571$$ 14.5000 + 25.1147i 0.606806 + 1.05102i 0.991763 + 0.128085i $$0.0408829\pi$$
−0.384957 + 0.922934i $$0.625784\pi$$
$$572$$ 0 0
$$573$$ 9.00000 0.375980
$$574$$ 0 0
$$575$$ −12.0000 −0.500435
$$576$$ 0 0
$$577$$ −0.500000 0.866025i −0.0208153 0.0360531i 0.855430 0.517918i $$-0.173293\pi$$
−0.876245 + 0.481865i $$0.839960\pi$$
$$578$$ 0 0
$$579$$ −5.50000 + 9.52628i −0.228572 + 0.395899i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −4.50000 + 7.79423i −0.186371 + 0.322804i
$$584$$ 0 0
$$585$$ 6.00000 + 10.3923i 0.248069 + 0.429669i
$$586$$ 0 0
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ 7.00000 0.288430
$$590$$ 0 0
$$591$$ −9.00000 15.5885i −0.370211 0.641223i
$$592$$ 0 0
$$593$$ −10.5000 + 18.1865i −0.431183 + 0.746831i −0.996976 0.0777165i $$-0.975237\pi$$
0.565792 + 0.824548i $$0.308570\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 3.50000 6.06218i 0.143245 0.248108i
$$598$$ 0 0
$$599$$ −13.5000 23.3827i −0.551595 0.955391i −0.998160 0.0606393i $$-0.980686\pi$$
0.446565 0.894751i $$-0.352647\pi$$
$$600$$ 0 0
$$601$$ −14.0000 −0.571072 −0.285536 0.958368i $$-0.592172\pi$$
−0.285536 + 0.958368i $$0.592172\pi$$
$$602$$ 0 0
$$603$$ −14.0000 −0.570124
$$604$$ 0 0
$$605$$ −3.00000 5.19615i −0.121967 0.211254i
$$606$$ 0 0
$$607$$ −23.5000 + 40.7032i −0.953836 + 1.65209i −0.216825 + 0.976210i $$0.569570\pi$$
−0.737011 + 0.675881i $$0.763763\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −9.00000 + 15.5885i −0.364101 + 0.630641i
$$612$$ 0 0
$$613$$ 12.5000 + 21.6506i 0.504870 + 0.874461i 0.999984 + 0.00563283i $$0.00179300\pi$$
−0.495114 + 0.868828i $$0.664874\pi$$
$$614$$ 0 0
$$615$$ 18.0000 0.725830
$$616$$ 0 0
$$617$$ 6.00000 0.241551 0.120775 0.992680i $$-0.461462\pi$$
0.120775 + 0.992680i $$0.461462\pi$$
$$618$$ 0 0
$$619$$ 15.5000 + 26.8468i 0.622998 + 1.07906i 0.988924 + 0.148420i $$0.0474187\pi$$
−0.365927 + 0.930644i $$0.619248\pi$$
$$620$$ 0 0
$$621$$ −7.50000 + 12.9904i −0.300965 + 0.521286i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 14.5000 25.1147i 0.580000 1.00459i
$$626$$ 0 0
$$627$$ 1.50000 + 2.59808i 0.0599042 + 0.103757i
$$628$$ 0 0
$$629$$ 3.00000 0.119618
$$630$$ 0 0
$$631$$ 16.0000 0.636950 0.318475 0.947931i $$-0.396829\pi$$
0.318475 + 0.947931i $$0.396829\pi$$
$$632$$ 0 0
$$633$$ −2.00000 3.46410i −0.0794929 0.137686i
$$634$$ 0 0
$$635$$ −12.0000 + 20.7846i −0.476205 + 0.824812i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −7.50000 12.9904i −0.296232 0.513089i 0.679039 0.734103i $$-0.262397\pi$$
−0.975271 + 0.221013i $$0.929064\pi$$
$$642$$ 0 0
$$643$$ 20.0000 0.788723 0.394362 0.918955i $$-0.370966\pi$$
0.394362 + 0.918955i $$0.370966\pi$$
$$644$$ 0 0
$$645$$ −12.0000 −0.472500
$$646$$ 0 0
$$647$$ −10.5000 18.1865i −0.412798 0.714986i 0.582397 0.812905i $$-0.302115\pi$$
−0.995194 + 0.0979182i $$0.968782\pi$$
$$648$$ 0 0
$$649$$ −13.5000 + 23.3827i −0.529921 + 0.917851i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −19.5000 + 33.7750i −0.763094 + 1.32172i 0.178154 + 0.984003i $$0.442987\pi$$
−0.941248 + 0.337715i $$0.890346\pi$$
$$654$$ 0 0
$$655$$ 4.50000 + 7.79423i 0.175830 + 0.304546i
$$656$$ 0 0
$$657$$ −2.00000 −0.0780274
$$658$$ 0 0
$$659$$ −12.0000 −0.467454 −0.233727 0.972302i $$-0.575092\pi$$
−0.233727 + 0.972302i $$0.575092\pi$$
$$660$$ 0 0
$$661$$ 5.50000 + 9.52628i 0.213925 + 0.370529i 0.952940 0.303160i $$-0.0980418\pi$$
−0.739014 + 0.673690i $$0.764708\pi$$
$$662$$ 0 0
$$663$$ −3.00000 + 5.19615i −0.116510 + 0.201802i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −9.00000 + 15.5885i −0.348481 + 0.603587i
$$668$$ 0 0
$$669$$ −4.00000 6.92820i −0.154649 0.267860i
$$670$$ 0 0
$$671$$ 3.00000 0.115814
$$672$$ 0 0
$$673$$ 14.0000 0.539660 0.269830 0.962908i $$-0.413032\pi$$
0.269830 + 0.962908i $$0.413032\pi$$
$$674$$ 0 0
$$675$$ 10.0000 + 17.3205i 0.384900 + 0.666667i
$$676$$ 0 0
$$677$$ 13.5000 23.3827i 0.518847 0.898670i −0.480913 0.876768i $$-0.659695\pi$$
0.999760 0.0219013i $$-0.00697196\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 1.50000 2.59808i 0.0574801 0.0995585i
$$682$$ 0 0
$$683$$ 10.5000 + 18.1865i 0.401771 + 0.695888i 0.993940 0.109926i $$-0.0350613\pi$$
−0.592168 + 0.805814i $$0.701728\pi$$
$$684$$ 0 0
$$685$$ 63.0000 2.40711
$$686$$ 0 0
$$687$$ −11.0000 −0.419676
$$688$$ 0 0
$$689$$ 3.00000 + 5.19615i 0.114291 + 0.197958i
$$690$$ 0 0
$$691$$ 6.50000 11.2583i 0.247272 0.428287i −0.715496 0.698617i $$-0.753799\pi$$
0.962768 + 0.270330i $$0.0871327\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 30.0000 51.9615i 1.13796 1.97101i
$$696$$ 0 0
$$697$$ −9.00000 15.5885i −0.340899 0.590455i
$$698$$ 0 0
$$699$$ −21.0000 −0.794293
$$700$$ 0 0
$$701$$ −18.0000 −0.679851 −0.339925 0.940452i $$-0.610402\pi$$
−0.339925 + 0.940452i $$0.610402\pi$$
$$702$$ 0 0
$$703$$ −0.500000 0.866025i −0.0188579 0.0326628i
$$704$$ 0 0
$$705$$ −13.5000 + 23.3827i −0.508439 + 0.880643i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0.500000 0.866025i 0.0187779 0.0325243i −0.856484 0.516174i $$-0.827356\pi$$
0.875262 + 0.483650i $$0.160689\pi$$
$$710$$ 0 0
$$711$$ 13.0000 + 22.5167i 0.487538 + 0.844441i
$$712$$ 0 0
$$713$$ 21.0000 0.786456
$$714$$ 0 0
$$715$$ 18.0000 0.673162
$$716$$ 0 0
$$717$$ −6.00000 10.3923i −0.224074 0.388108i
$$718$$ 0 0
$$719$$ 10.5000 18.1865i 0.391584 0.678243i −0.601075 0.799193i $$-0.705261\pi$$
0.992659 + 0.120950i $$0.0385939\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ −0.500000 + 0.866025i −0.0185952 + 0.0322078i
$$724$$ 0 0
$$725$$ 12.0000 + 20.7846i 0.445669 + 0.771921i
$$726$$ 0 0
$$727$$ 32.0000 1.18681 0.593407 0.804902i $$-0.297782\pi$$
0.593407 + 0.804902i $$0.297782\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 6.00000 + 10.3923i 0.221918 + 0.384373i
$$732$$ 0 0
$$733$$ −12.5000 + 21.6506i −0.461698 + 0.799684i −0.999046 0.0436764i $$-0.986093\pi$$
0.537348 + 0.843361i $$0.319426\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −10.5000 + 18.1865i −0.386772 + 0.669910i
$$738$$ 0 0
$$739$$ −9.50000 16.4545i −0.349463 0.605288i 0.636691 0.771119i $$-0.280303\pi$$
−0.986154 + 0.165831i $$0.946969\pi$$
$$740$$ 0 0
$$741$$ 2.00000 0.0734718
$$742$$ 0 0
$$743$$ 48.0000 1.76095 0.880475 0.474093i $$-0.157224\pi$$
0.880475 + 0.474093i $$0.157224\pi$$
$$744$$ 0 0
$$745$$ 4.50000 + 7.79423i 0.164867 + 0.285558i
$$746$$ 0 0
$$747$$ 12.0000 20.7846i 0.439057 0.760469i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −12.5000 + 21.6506i −0.456131 + 0.790043i −0.998752 0.0499348i $$-0.984099\pi$$
0.542621 + 0.839978i $$0.317432\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 51.0000 1.85608
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 0 0
$$759$$ 4.50000 + 7.79423i 0.163340 + 0.282913i
$$760$$ 0 0
$$761$$ 1.50000 2.59808i 0.0543750 0.0941802i −0.837557 0.546350i $$-0.816017\pi$$
0.891932 + 0.452170i $$0.149350\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 9.00000 15.5885i 0.325396 0.563602i
$$766$$ 0 0
$$767$$ 9.00000 + 15.5885i 0.324971 + 0.562867i
$$768$$ 0 0
$$769$$ 34.0000 1.22607 0.613036 0.790055i $$-0.289948\pi$$
0.613036 + 0.790055i $$0.289948\pi$$
$$770$$ 0 0
$$771$$ −3.00000 −0.108042
$$772$$ 0 0
$$773$$ −16.5000 28.5788i −0.593464 1.02791i −0.993762 0.111524i $$-0.964427\pi$$
0.400298 0.916385i $$-0.368907\pi$$
$$774$$ 0 0
$$775$$ 14.0000 24.2487i 0.502895 0.871039i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −3.00000 + 5.19615i −0.107486 + 0.186171i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 30.0000 1.07211
$$784$$ 0 0
$$785$$ −39.0000 −1.39197
$$786$$ 0 0
$$787$$ 15.5000 + 26.8468i 0.552515 + 0.956985i 0.998092 + 0.0617409i $$0.0196653\pi$$
−0.445577 + 0.895244i $$0.647001\pi$$
$$788$$ 0 0
$$789$$ −1.50000 + 2.59808i −0.0534014 + 0.0924940i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 1.00000 1.73205i 0.0355110 0.0615069i
$$794$$ 0 0
$$795$$ 4.50000 + 7.79423i 0.159599 + 0.276433i
$$796$$ 0 0
$$797$$ −42.0000 −1.48772 −0.743858 0.668338i $$-0.767006\pi$$
−0.743858 + 0.668338i $$0.767006\pi$$
$$798$$ 0 0
$$799$$ 27.0000 0.955191
$$800$$