# Properties

 Label 700.2.r.b.149.1 Level $700$ Weight $2$ Character 700.149 Analytic conductor $5.590$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$700 = 2^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 700.r (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.58952814149$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 28) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 149.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 700.149 Dual form 700.2.r.b.249.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{3} +(1.73205 - 2.00000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{3} +(1.73205 - 2.00000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{11} -2.00000i q^{13} +(2.59808 - 1.50000i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-0.500000 + 2.59808i) q^{21} +(2.59808 + 1.50000i) q^{23} -5.00000i q^{27} +6.00000 q^{29} +(3.50000 + 6.06218i) q^{31} +(-2.59808 - 1.50000i) q^{33} +(0.866025 + 0.500000i) q^{37} +(1.00000 + 1.73205i) q^{39} +6.00000 q^{41} +4.00000i q^{43} +(7.79423 + 4.50000i) q^{47} +(-1.00000 - 6.92820i) q^{49} +(-1.50000 + 2.59808i) q^{51} +(-2.59808 + 1.50000i) q^{53} -1.00000i q^{57} +(4.50000 + 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{61} +(1.73205 + 5.00000i) q^{63} +(-6.06218 + 3.50000i) q^{67} -3.00000 q^{69} +(0.866025 - 0.500000i) q^{73} +(7.79423 + 1.50000i) q^{77} +(-6.50000 + 11.2583i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000i q^{83} +(-5.19615 + 3.00000i) q^{87} +(7.50000 - 12.9904i) q^{89} +(-4.00000 - 3.46410i) q^{91} +(-6.06218 - 3.50000i) q^{93} -10.0000i q^{97} -6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 4q^{9} + O(q^{10})$$ $$4q - 4q^{9} + 6q^{11} - 2q^{19} - 2q^{21} + 24q^{29} + 14q^{31} + 4q^{39} + 24q^{41} - 4q^{49} - 6q^{51} + 18q^{59} + 2q^{61} - 12q^{69} - 26q^{79} - 2q^{81} + 30q^{89} - 16q^{91} - 24q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$351$$ $$477$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$-1$$

## 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
$$3$$ −0.866025 + 0.500000i −0.500000 + 0.288675i −0.728714 0.684819i $$-0.759881\pi$$
0.228714 + 0.973494i $$0.426548\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 1.73205 2.00000i 0.654654 0.755929i
$$8$$ 0 0
$$9$$ −1.00000 + 1.73205i −0.333333 + 0.577350i
$$10$$ 0 0
$$11$$ 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i $$-0.0172821\pi$$
−0.546259 + 0.837616i $$0.683949\pi$$
$$12$$ 0 0
$$13$$ 2.00000i 0.554700i −0.960769 0.277350i $$-0.910544\pi$$
0.960769 0.277350i $$-0.0894562\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.59808 1.50000i 0.630126 0.363803i −0.150675 0.988583i $$-0.548145\pi$$
0.780801 + 0.624780i $$0.214811\pi$$
$$18$$ 0 0
$$19$$ −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i $$-0.869927\pi$$
0.802955 + 0.596040i $$0.203260\pi$$
$$20$$ 0 0
$$21$$ −0.500000 + 2.59808i −0.109109 + 0.566947i
$$22$$ 0 0
$$23$$ 2.59808 + 1.50000i 0.541736 + 0.312772i 0.745782 0.666190i $$-0.232076\pi$$
−0.204046 + 0.978961i $$0.565409\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 5.00000i 0.962250i
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 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
$$33$$ −2.59808 1.50000i −0.452267 0.261116i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0.866025 + 0.500000i 0.142374 + 0.0821995i 0.569495 0.821995i $$-0.307139\pi$$
−0.427121 + 0.904194i $$0.640472\pi$$
$$38$$ 0 0
$$39$$ 1.00000 + 1.73205i 0.160128 + 0.277350i
$$40$$ 0 0
$$41$$ 6.00000 0.937043 0.468521 0.883452i $$-0.344787\pi$$
0.468521 + 0.883452i $$0.344787\pi$$
$$42$$ 0 0
$$43$$ 4.00000i 0.609994i 0.952353 + 0.304997i $$0.0986555\pi$$
−0.952353 + 0.304997i $$0.901344\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 7.79423 + 4.50000i 1.13691 + 0.656392i 0.945662 0.325150i $$-0.105415\pi$$
0.191243 + 0.981543i $$0.438748\pi$$
$$48$$ 0 0
$$49$$ −1.00000 6.92820i −0.142857 0.989743i
$$50$$ 0 0
$$51$$ −1.50000 + 2.59808i −0.210042 + 0.363803i
$$52$$ 0 0
$$53$$ −2.59808 + 1.50000i −0.356873 + 0.206041i −0.667708 0.744423i $$-0.732725\pi$$
0.310835 + 0.950464i $$0.399391\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 1.00000i 0.132453i
$$58$$ 0 0
$$59$$ 4.50000 + 7.79423i 0.585850 + 1.01472i 0.994769 + 0.102151i $$0.0325726\pi$$
−0.408919 + 0.912571i $$0.634094\pi$$
$$60$$ 0 0
$$61$$ 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i $$-0.812942\pi$$
0.896258 + 0.443533i $$0.146275\pi$$
$$62$$ 0 0
$$63$$ 1.73205 + 5.00000i 0.218218 + 0.629941i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −6.06218 + 3.50000i −0.740613 + 0.427593i −0.822292 0.569066i $$-0.807305\pi$$
0.0816792 + 0.996659i $$0.473972\pi$$
$$68$$ 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
$$73$$ 0.866025 0.500000i 0.101361 0.0585206i −0.448463 0.893801i $$-0.648028\pi$$
0.549823 + 0.835281i $$0.314695\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 7.79423 + 1.50000i 0.888235 + 0.170941i
$$78$$ 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
$$83$$ 12.0000i 1.31717i −0.752506 0.658586i $$-0.771155\pi$$
0.752506 0.658586i $$-0.228845\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −5.19615 + 3.00000i −0.557086 + 0.321634i
$$88$$ 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
$$91$$ −4.00000 3.46410i −0.419314 0.363137i
$$92$$ 0 0
$$93$$ −6.06218 3.50000i −0.628619 0.362933i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 10.0000i 1.01535i −0.861550 0.507673i $$-0.830506\pi$$
0.861550 0.507673i $$-0.169494\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i $$-0.898506\pi$$
0.203317 0.979113i $$-0.434828\pi$$
$$102$$ 0 0
$$103$$ 9.52628 + 5.50000i 0.938652 + 0.541931i 0.889538 0.456862i $$-0.151027\pi$$
0.0491146 + 0.998793i $$0.484360\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −12.9904 7.50000i −1.25583 0.725052i −0.283567 0.958952i $$-0.591518\pi$$
−0.972261 + 0.233900i $$0.924851\pi$$
$$108$$ 0 0
$$109$$ −0.500000 0.866025i −0.0478913 0.0829502i 0.841086 0.540901i $$-0.181917\pi$$
−0.888977 + 0.457951i $$0.848583\pi$$
$$110$$ 0 0
$$111$$ −1.00000 −0.0949158
$$112$$ 0 0
$$113$$ 6.00000i 0.564433i −0.959351 0.282216i $$-0.908930\pi$$
0.959351 0.282216i $$-0.0910696\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 3.46410 + 2.00000i 0.320256 + 0.184900i
$$118$$ 0 0
$$119$$ 1.50000 7.79423i 0.137505 0.714496i
$$120$$ 0 0
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ 0 0
$$123$$ −5.19615 + 3.00000i −0.468521 + 0.270501i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 8.00000i 0.709885i 0.934888 + 0.354943i $$0.115500\pi$$
−0.934888 + 0.354943i $$0.884500\pi$$
$$128$$ 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
$$133$$ 0.866025 + 2.50000i 0.0750939 + 0.216777i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −18.1865 + 10.5000i −1.55378 + 0.897076i −0.555952 + 0.831215i $$0.687646\pi$$
−0.997829 + 0.0658609i $$0.979021\pi$$
$$138$$ 0 0
$$139$$ −20.0000 −1.69638 −0.848189 0.529694i $$-0.822307\pi$$
−0.848189 + 0.529694i $$0.822307\pi$$
$$140$$ 0 0
$$141$$ −9.00000 −0.757937
$$142$$ 0 0
$$143$$ 5.19615 3.00000i 0.434524 0.250873i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 4.33013 + 5.50000i 0.357143 + 0.453632i
$$148$$ 0 0
$$149$$ 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i $$-0.794119\pi$$
0.920904 + 0.389789i $$0.127452\pi$$
$$150$$ 0 0
$$151$$ −8.50000 14.7224i −0.691720 1.19809i −0.971274 0.237964i $$-0.923520\pi$$
0.279554 0.960130i $$-0.409814\pi$$
$$152$$ 0 0
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −11.2583 + 6.50000i −0.898513 + 0.518756i −0.876717 0.481006i $$-0.840272\pi$$
−0.0217953 + 0.999762i $$0.506938\pi$$
$$158$$ 0 0
$$159$$ 1.50000 2.59808i 0.118958 0.206041i
$$160$$ 0 0
$$161$$ 7.50000 2.59808i 0.591083 0.204757i
$$162$$ 0 0
$$163$$ 9.52628 + 5.50000i 0.746156 + 0.430793i 0.824303 0.566149i $$-0.191567\pi$$
−0.0781474 + 0.996942i $$0.524900\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 12.0000i 0.928588i −0.885681 0.464294i $$-0.846308\pi$$
0.885681 0.464294i $$-0.153692\pi$$
$$168$$ 0 0
$$169$$ 9.00000 0.692308
$$170$$ 0 0
$$171$$ −1.00000 1.73205i −0.0764719 0.132453i
$$172$$ 0 0
$$173$$ −7.79423 4.50000i −0.592584 0.342129i 0.173534 0.984828i $$-0.444481\pi$$
−0.766119 + 0.642699i $$0.777815\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −7.79423 4.50000i −0.585850 0.338241i
$$178$$ 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 $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ 1.00000i 0.0739221i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 7.79423 + 4.50000i 0.569970 + 0.329073i
$$188$$ 0 0
$$189$$ −10.0000 8.66025i −0.727393 0.629941i
$$190$$ 0 0
$$191$$ 4.50000 7.79423i 0.325609 0.563971i −0.656027 0.754738i $$-0.727764\pi$$
0.981635 + 0.190767i $$0.0610975\pi$$
$$192$$ 0 0
$$193$$ −9.52628 + 5.50000i −0.685717 + 0.395899i −0.802005 0.597317i $$-0.796234\pi$$
0.116289 + 0.993215i $$0.462900\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 18.0000i 1.28245i 0.767354 + 0.641223i $$0.221573\pi$$
−0.767354 + 0.641223i $$0.778427\pi$$
$$198$$ 0 0
$$199$$ −3.50000 6.06218i −0.248108 0.429736i 0.714893 0.699234i $$-0.246476\pi$$
−0.963001 + 0.269498i $$0.913142\pi$$
$$200$$ 0 0
$$201$$ 3.50000 6.06218i 0.246871 0.427593i
$$202$$ 0 0
$$203$$ 10.3923 12.0000i 0.729397 0.842235i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −5.19615 + 3.00000i −0.361158 + 0.208514i
$$208$$ 0 0
$$209$$ −3.00000 −0.207514
$$210$$ 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
$$217$$ 18.1865 + 3.50000i 1.23458 + 0.237595i
$$218$$ 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
$$223$$ 8.00000i 0.535720i −0.963458 0.267860i $$-0.913684\pi$$
0.963458 0.267860i $$-0.0863164\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −2.59808 + 1.50000i −0.172440 + 0.0995585i −0.583736 0.811943i $$-0.698410\pi$$
0.411296 + 0.911502i $$0.365076\pi$$
$$228$$ 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
$$231$$ −7.50000 + 2.59808i −0.493464 + 0.170941i
$$232$$ 0 0
$$233$$ −18.1865 10.5000i −1.19144 0.687878i −0.232806 0.972523i $$-0.574791\pi$$
−0.958633 + 0.284645i $$0.908124\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 13.0000i 0.844441i
$$238$$ 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 0.881680 0.471848i $$-0.156413\pi$$
−0.849472 + 0.527633i $$0.823079\pi$$
$$242$$ 0 0
$$243$$ 13.8564 + 8.00000i 0.888889 + 0.513200i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1.73205 + 1.00000i 0.110208 + 0.0636285i
$$248$$ 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
$$253$$ 9.00000i 0.565825i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −2.59808 1.50000i −0.162064 0.0935674i 0.416775 0.909010i $$-0.363160\pi$$
−0.578838 + 0.815442i $$0.696494\pi$$
$$258$$ 0 0
$$259$$ 2.50000 0.866025i 0.155342 0.0538122i
$$260$$ 0 0
$$261$$ −6.00000 + 10.3923i −0.371391 + 0.643268i
$$262$$ 0 0
$$263$$ 2.59808 1.50000i 0.160204 0.0924940i −0.417755 0.908560i $$-0.637183\pi$$
0.577959 + 0.816066i $$0.303849\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 15.0000i 0.917985i
$$268$$ 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
$$273$$ 5.19615 + 1.00000i 0.314485 + 0.0605228i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −11.2583 + 6.50000i −0.676448 + 0.390547i −0.798515 0.601975i $$-0.794381\pi$$
0.122068 + 0.992522i $$0.461047\pi$$
$$278$$ 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
$$283$$ −25.1147 + 14.5000i −1.49292 + 0.861936i −0.999967 0.00812260i $$-0.997414\pi$$
−0.492949 + 0.870058i $$0.664081\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 10.3923 12.0000i 0.613438 0.708338i
$$288$$ 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
$$293$$ 6.00000i 0.350524i −0.984522 0.175262i $$-0.943923\pi$$
0.984522 0.175262i $$-0.0560772\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 12.9904 7.50000i 0.753778 0.435194i
$$298$$ 0 0
$$299$$ 3.00000 5.19615i 0.173494 0.300501i
$$300$$ 0 0
$$301$$ 8.00000 + 6.92820i 0.461112 + 0.399335i
$$302$$ 0 0
$$303$$ 12.9904 + 7.50000i 0.746278 + 0.430864i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 28.0000i 1.59804i −0.601302 0.799022i $$-0.705351\pi$$
0.601302 0.799022i $$-0.294649\pi$$
$$308$$ 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
$$313$$ 19.9186 + 11.5000i 1.12586 + 0.650018i 0.942892 0.333099i $$-0.108094\pi$$
0.182973 + 0.983118i $$0.441428\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 7.79423 + 4.50000i 0.437767 + 0.252745i 0.702650 0.711535i $$-0.252000\pi$$
−0.264883 + 0.964281i $$0.585333\pi$$
$$318$$ 0 0
$$319$$ 9.00000 + 15.5885i 0.503903 + 0.872786i
$$320$$ 0 0
$$321$$ 15.0000 0.837218
$$322$$ 0 0
$$323$$ 3.00000i 0.166924i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0.866025 + 0.500000i 0.0478913 + 0.0276501i
$$328$$ 0 0
$$329$$ 22.5000 7.79423i 1.24047 0.429710i
$$330$$ 0 0
$$331$$ 6.50000 11.2583i 0.357272 0.618814i −0.630232 0.776407i $$-0.717040\pi$$
0.987504 + 0.157593i $$0.0503735\pi$$
$$332$$ 0 0
$$333$$ −1.73205 + 1.00000i −0.0949158 + 0.0547997i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 34.0000i 1.85210i −0.377403 0.926049i $$-0.623183\pi$$
0.377403 0.926049i $$-0.376817\pi$$
$$338$$ 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
$$343$$ −15.5885 10.0000i −0.841698 0.539949i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 7.79423 4.50000i 0.418416 0.241573i −0.275983 0.961162i $$-0.589003\pi$$
0.694399 + 0.719590i $$0.255670\pi$$
$$348$$ 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
$$353$$ 18.1865 10.5000i 0.967972 0.558859i 0.0693543 0.997592i $$-0.477906\pi$$
0.898617 + 0.438733i $$0.144573\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 2.59808 + 7.50000i 0.137505 + 0.396942i
$$358$$ 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
$$363$$ 2.00000i 0.104973i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 4.33013 2.50000i 0.226031 0.130499i −0.382709 0.923869i $$-0.625009\pi$$
0.608740 + 0.793370i $$0.291675\pi$$
$$368$$ 0 0
$$369$$ −6.00000 + 10.3923i −0.312348 + 0.541002i
$$370$$ 0 0
$$371$$ −1.50000 + 7.79423i −0.0778761 + 0.404656i
$$372$$ 0 0
$$373$$ −21.6506 12.5000i −1.12103 0.647225i −0.179364 0.983783i $$-0.557404\pi$$
−0.941663 + 0.336557i $$0.890737\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 12.0000i 0.618031i
$$378$$ 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
$$383$$ −28.5788 16.5000i −1.46031 0.843111i −0.461285 0.887252i $$-0.652611\pi$$
−0.999025 + 0.0441413i $$0.985945\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −6.92820 4.00000i −0.352180 0.203331i
$$388$$ 0 0
$$389$$ 7.50000 + 12.9904i 0.380265 + 0.658638i 0.991100 0.133120i $$-0.0424994\pi$$
−0.610835 + 0.791758i $$0.709166\pi$$
$$390$$ 0 0
$$391$$ 9.00000 0.455150
$$392$$ 0 0
$$393$$ 3.00000i 0.151330i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 32.0429 + 18.5000i 1.60819 + 0.928488i 0.989775 + 0.142636i $$0.0455577\pi$$
0.618414 + 0.785853i $$0.287776\pi$$
$$398$$ 0 0
$$399$$ −2.00000 1.73205i −0.100125 0.0867110i
$$400$$ 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
$$403$$ 12.1244 7.00000i 0.603957 0.348695i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 3.00000i 0.148704i
$$408$$ 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
$$413$$ 23.3827 + 4.50000i 1.15059 + 0.221431i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 17.3205 10.0000i 0.848189 0.489702i
$$418$$ 0 0
$$419$$ 12.0000 0.586238 0.293119 0.956076i $$-0.405307\pi$$
0.293119 + 0.956076i $$0.405307\pi$$
$$420$$ 0 0
$$421$$ −22.0000 −1.07221 −0.536107 0.844150i $$-0.680106\pi$$
−0.536107 + 0.844150i $$0.680106\pi$$
$$422$$ 0 0
$$423$$ −15.5885 + 9.00000i −0.757937 + 0.437595i
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −0.866025 2.50000i −0.0419099 0.120983i
$$428$$ 0 0
$$429$$ −3.00000 + 5.19615i −0.144841 + 0.250873i
$$430$$ 0 0
$$431$$ 7.50000 + 12.9904i 0.361262 + 0.625725i 0.988169 0.153370i $$-0.0490126\pi$$
−0.626907 + 0.779094i $$0.715679\pi$$
$$432$$ 0 0
$$433$$ 10.0000i 0.480569i 0.970702 + 0.240285i $$0.0772408\pi$$
−0.970702 + 0.240285i $$0.922759\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −2.59808 + 1.50000i −0.124283 + 0.0717547i
$$438$$ 0 0
$$439$$ −0.500000 + 0.866025i −0.0238637 + 0.0413331i −0.877711 0.479191i $$-0.840930\pi$$
0.853847 + 0.520524i $$0.174263\pi$$
$$440$$ 0 0
$$441$$ 13.0000 + 5.19615i 0.619048 + 0.247436i
$$442$$ 0 0
$$443$$ −7.79423 4.50000i −0.370315 0.213801i 0.303281 0.952901i $$-0.401918\pi$$
−0.673596 + 0.739100i $$0.735251\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 3.00000i 0.141895i
$$448$$ 0 0
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 0 0
$$451$$ 9.00000 + 15.5885i 0.423793 + 0.734032i
$$452$$ 0 0
$$453$$ 14.7224 + 8.50000i 0.691720 + 0.399365i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −19.9186 11.5000i −0.931752 0.537947i −0.0443868 0.999014i $$-0.514133\pi$$
−0.887365 + 0.461067i $$0.847467\pi$$
$$458$$ 0 0
$$459$$ −7.50000 12.9904i −0.350070 0.606339i
$$460$$ 0 0
$$461$$ −6.00000 −0.279448 −0.139724 0.990190i $$-0.544622\pi$$
−0.139724 + 0.990190i $$0.544622\pi$$
$$462$$ 0 0
$$463$$ 16.0000i 0.743583i 0.928316 + 0.371792i $$0.121256\pi$$
−0.928316 + 0.371792i $$0.878744\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 18.1865 + 10.5000i 0.841572 + 0.485882i 0.857798 0.513986i $$-0.171832\pi$$
−0.0162260 + 0.999868i $$0.505165\pi$$
$$468$$ 0 0
$$469$$ −3.50000 + 18.1865i −0.161615 + 0.839776i
$$470$$ 0 0
$$471$$ 6.50000 11.2583i 0.299504 0.518756i
$$472$$ 0 0
$$473$$ −10.3923 + 6.00000i −0.477839 + 0.275880i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 6.00000i 0.274721i
$$478$$ 0 0
$$479$$ −1.50000 2.59808i −0.0685367 0.118709i 0.829721 0.558179i $$-0.188500\pi$$
−0.898257 + 0.439470i $$0.855166\pi$$
$$480$$ 0 0
$$481$$ 1.00000 1.73205i 0.0455961 0.0789747i
$$482$$ 0 0
$$483$$ −5.19615 + 6.00000i −0.236433 + 0.273009i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −16.4545 + 9.50000i −0.745624 + 0.430486i −0.824110 0.566429i $$-0.808325\pi$$
0.0784867 + 0.996915i $$0.474991\pi$$
$$488$$ 0 0
$$489$$ −11.0000 −0.497437
$$490$$ 0 0
$$491$$ 24.0000 1.08310 0.541552 0.840667i $$-0.317837\pi$$
0.541552 + 0.840667i $$0.317837\pi$$
$$492$$ 0 0
$$493$$ 15.5885 9.00000i 0.702069 0.405340i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 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 1.00000 $$0$$
−1.00000 $$\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −7.79423 + 4.50000i −0.346154 + 0.199852i
$$508$$ 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
$$511$$ 0.500000 2.59808i 0.0221187 0.114932i
$$512$$ 0 0
$$513$$ 4.33013 + 2.50000i 0.191180 + 0.110378i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 27.0000i 1.18746i
$$518$$ 0 0
$$519$$ 9.00000 0.395056
$$520$$ 0 0
$$521$$ −19.5000 33.7750i −0.854311 1.47971i −0.877283 0.479973i $$-0.840646\pi$$
0.0229727 0.999736i $$-0.492687\pi$$
$$522$$ 0 0
$$523$$ −0.866025 0.500000i −0.0378686 0.0218635i 0.480946 0.876750i $$-0.340293\pi$$
−0.518815 + 0.854887i $$0.673627\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 18.1865 + 10.5000i 0.792218 + 0.457387i
$$528$$ 0 0
$$529$$ −7.00000 12.1244i −0.304348 0.527146i
$$530$$ 0 0
$$531$$ −18.0000 −0.781133
$$532$$ 0 0
$$533$$ 12.0000i 0.519778i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −18.1865 10.5000i −0.784807 0.453108i
$$538$$ 0 0
$$539$$ 16.5000 12.9904i 0.710705 0.559535i
$$540$$ 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
$$543$$ 8.66025 5.00000i 0.371647 0.214571i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 8.00000i 0.342055i 0.985266 + 0.171028i $$0.0547087\pi$$
−0.985266 + 0.171028i $$0.945291\pi$$
$$548$$ 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
$$553$$ 11.2583 + 32.5000i 0.478753 + 1.38204i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −28.5788 + 16.5000i −1.21092 + 0.699127i −0.962961 0.269642i $$-0.913095\pi$$
−0.247964 + 0.968769i $$0.579761\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ −9.00000 −0.379980
$$562$$ 0 0
$$563$$ −7.79423 + 4.50000i −0.328488 + 0.189652i −0.655169 0.755482i $$-0.727403\pi$$
0.326682 + 0.945134i $$0.394069\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −2.59808 0.500000i −0.109109 0.0209980i
$$568$$ 0 0
$$569$$ −4.50000 + 7.79423i −0.188650 + 0.326751i −0.944800 0.327647i $$-0.893744\pi$$
0.756151 + 0.654398i $$0.227078\pi$$
$$570$$ 0 0
$$571$$ −14.5000 25.1147i −0.606806 1.05102i −0.991763 0.128085i $$-0.959117\pi$$
0.384957 0.922934i $$-0.374216\pi$$
$$572$$ 0 0
$$573$$ 9.00000i 0.375980i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −0.866025 + 0.500000i −0.0360531 + 0.0208153i −0.517918 0.855430i $$-0.673293\pi$$
0.481865 + 0.876245i $$0.339960\pi$$
$$578$$ 0 0
$$579$$ 5.50000 9.52628i 0.228572 0.395899i
$$580$$ 0 0
$$581$$ −24.0000 20.7846i −0.995688 0.862291i
$$582$$ 0 0
$$583$$ −7.79423 4.50000i −0.322804 0.186371i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 12.0000i 0.495293i 0.968850 + 0.247647i $$0.0796572\pi$$
−0.968850 + 0.247647i $$0.920343\pi$$
$$588$$ 0 0
$$589$$ −7.00000 −0.288430
$$590$$ 0 0
$$591$$ −9.00000 15.5885i −0.370211 0.641223i
$$592$$ 0 0
$$593$$ −18.1865 10.5000i −0.746831 0.431183i 0.0777165 0.996976i $$-0.475237\pi$$
−0.824548 + 0.565792i $$0.808570\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 6.06218 + 3.50000i 0.248108 + 0.143245i
$$598$$ 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 $$-0.407828\pi$$
0.285536 + 0.958368i $$0.407828\pi$$
$$602$$ 0 0
$$603$$ 14.0000i 0.570124i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −40.7032 23.5000i −1.65209 0.953836i −0.976210 0.216825i $$-0.930430\pi$$
−0.675881 0.737011i $$-0.736237\pi$$
$$608$$ 0 0
$$609$$ −3.00000 + 15.5885i −0.121566 + 0.631676i
$$610$$ 0 0
$$611$$ 9.00000 15.5885i 0.364101 0.630641i
$$612$$ 0 0
$$613$$ 21.6506 12.5000i 0.874461 0.504870i 0.00563283 0.999984i $$-0.498207\pi$$
0.868828 + 0.495114i $$0.164874\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 6.00000i 0.241551i 0.992680 + 0.120775i $$0.0385381\pi$$
−0.992680 + 0.120775i $$0.961462\pi$$
$$618$$ 0 0
$$619$$ −15.5000 26.8468i −0.622998 1.07906i −0.988924 0.148420i $$-0.952581\pi$$
0.365927 0.930644i $$-0.380752\pi$$
$$620$$ 0 0
$$621$$ 7.50000 12.9904i 0.300965 0.521286i
$$622$$ 0 0
$$623$$ −12.9904 37.5000i −0.520449 1.50241i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 2.59808 1.50000i 0.103757 0.0599042i
$$628$$ 0 0
$$629$$ 3.00000 0.119618
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 0 0
$$633$$ 3.46410 2.00000i 0.137686 0.0794929i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −13.8564 + 2.00000i −0.549011 + 0.0792429i
$$638$$ 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
$$643$$ 20.0000i 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
$$647$$ 18.1865 10.5000i 0.714986 0.412798i −0.0979182 0.995194i $$-0.531218\pi$$
0.812905 + 0.582397i $$0.197885\pi$$
$$648$$ 0 0
$$649$$ −13.5000 + 23.3827i −0.529921 + 0.917851i
$$650$$ 0 0
$$651$$ −17.5000 + 6.06218i −0.685879 + 0.237595i
$$652$$ 0 0
$$653$$ 33.7750 + 19.5000i 1.32172 + 0.763094i 0.984003 0.178154i $$-0.0570127\pi$$
0.337715 + 0.941248i $$0.390346\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 2.00000i 0.0780274i
$$658$$ 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 0.739014 0.673690i $$-0.235292\pi$$
−0.952940 + 0.303160i $$0.901958\pi$$
$$662$$ 0 0
$$663$$ 5.19615 + 3.00000i 0.201802 + 0.116510i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 15.5885 + 9.00000i 0.603587 + 0.348481i
$$668$$ 0 0
$$669$$ 4.00000 + 6.92820i 0.154649 + 0.267860i
$$670$$ 0 0
$$671$$ 3.00000 0.115814
$$672$$ 0 0
$$673$$ 14.0000i 0.539660i −0.962908 0.269830i $$-0.913032\pi$$
0.962908 0.269830i $$-0.0869676\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −23.3827 13.5000i −0.898670 0.518847i −0.0219013 0.999760i $$-0.506972\pi$$
−0.876768 + 0.480913i $$0.840305\pi$$
$$678$$ 0 0
$$679$$ −20.0000 17.3205i −0.767530 0.664700i
$$680$$ 0 0
$$681$$ 1.50000 2.59808i 0.0574801 0.0995585i
$$682$$ 0 0
$$683$$ −18.1865 + 10.5000i −0.695888 + 0.401771i −0.805814 0.592168i $$-0.798272\pi$$
0.109926 + 0.993940i $$0.464939\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 11.0000i 0.419676i
$$688$$ 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
$$693$$ −10.3923 + 12.0000i −0.394771 + 0.455842i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 15.5885 9.00000i 0.590455 0.340899i
$$698$$ 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
$$703$$ −0.866025 + 0.500000i −0.0326628 + 0.0188579i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −38.9711 7.50000i −1.46566 0.282067i
$$708$$ 0 0
$$709$$ −0.500000 + 0.866025i −0.0187779 + 0.0325243i −0.875262 0.483650i $$-0.839311\pi$$
0.856484 + 0.516174i $$0.172644\pi$$
$$710$$ 0 0
$$711$$ −13.0000 22.5167i −0.487538 0.844441i
$$712$$ 0 0
$$713$$ 21.0000i 0.786456i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ −10.3923 + 6.00000i −0.388108 + 0.224074i
$$718$$ 0 0
$$719$$ −10.5000 + 18.1865i −0.391584 + 0.678243i −0.992659 0.120950i $$-0.961406\pi$$
0.601075 + 0.799193i $$0.294739\pi$$
$$720$$ 0 0
$$721$$ 27.5000 9.52628i 1.02415 0.354777i
$$722$$ 0 0
$$723$$ −0.866025 0.500000i −0.0322078 0.0185952i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 32.0000i 1.18681i 0.804902 + 0.593407i $$0.202218\pi$$
−0.804902 + 0.593407i $$0.797782\pi$$
$$728$$ 0 0
$$729$$ −13.0000 −0.481481
$$730$$ 0 0
$$731$$ 6.00000 + 10.3923i 0.221918 + 0.384373i
$$732$$ 0 0
$$733$$ −21.6506 12.5000i −0.799684 0.461698i 0.0436764 0.999046i $$-0.486093\pi$$
−0.843361 + 0.537348i $$0.819426\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −18.1865 10.5000i −0.669910 0.386772i
$$738$$ 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
$$743$$ 48.0000i 1.76095i 0.474093 + 0.880475i $$0.342776\pi$$
−0.474093 + 0.880475i $$0.657224\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 20.7846 + 12.0000i 0.760469 + 0.439057i
$$748$$ 0 0
$$749$$ −37.5000 + 12.9904i −1.37022 + 0.474658i
$$750$$ 0 0
$$751$$ 12.5000 21.6506i 0.456131 0.790043i −0.542621 0.839978i $$-0.682568\pi$$
0.998752 + 0.0499348i $$0.0159013\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 2.00000i 0.0726912i 0.999339 + 0.0363456i $$0.0115717\pi$$
−0.999339 + 0.0363456i $$0.988428\pi$$
$$758$$ 0 0
$$759$$ −4.50000 7.79423i −0.163340 0.282913i
$$760$$ 0 0
$$761$$ −1.50000 + 2.59808i −0.0543750 + 0.0941802i −0.891932 0.452170i $$-0.850650\pi$$
0.837557 + 0.546350i $$0.183983\pi$$
$$762$$ 0 0
$$763$$ −2.59808 0.500000i −0.0940567 0.0181012i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 15.5885 9.00000i 0.562867 0.324971i
$$768$$ 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
$$773$$ 28.5788 16.5000i 1.02791 0.593464i 0.111524 0.993762i $$-0.464427\pi$$
0.916385 + 0.400298i $$0.131093\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ −1.73205 + 2.00000i −0.0621370 + 0.0717496i
$$778$$ 0 0
$$779$$ −3.00000 + 5.19615i −0.107486 + 0.186171i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 30.0000i 1.07211i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −26.8468 + 15.5000i −0.956985 + 0.552515i −0.895244 0.445577i $$-0.852999\pi$$
−0.0617409 + 0.998092i $$0.519665\pi$$
$$788$$ 0 0
$$789$$ −1.50000 + 2.59808i −0.0534014 + 0.0924940i
$$790$$ 0 0
$$791$$ −12.0000 10.3923i −0.426671 0.369508i
$$792$$ 0 0
$$793$$ −1.73205 1.00000i −0.0615069 0.0355110i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 42.0000i 1.48772i 0.668338 + 0.743858i $$0.267006\pi$$
−0.668338 + 0.743858i $$0.732994\pi$$
$$798$$ 0 0
$$799$$ 27.0000 0.955191
$$800$$ 0 0