# Properties

 Label 28.2.e.a.25.1 Level $28$ Weight $2$ Character 28.25 Analytic conductor $0.224$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$28 = 2^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 28.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.223581125660$$ 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: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 25.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 28.25 Dual form 28.2.e.a.9.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{3} +(-1.50000 - 2.59808i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{11} +2.00000 q^{13} +3.00000 q^{15} +(-1.50000 + 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{19} +(-0.500000 - 2.59808i) q^{21} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} -5.00000 q^{27} -6.00000 q^{29} +(3.50000 - 6.06218i) q^{31} +(1.50000 + 2.59808i) q^{33} +(7.50000 + 2.59808i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-1.00000 + 1.73205i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(3.00000 - 5.19615i) q^{45} +(4.50000 + 7.79423i) q^{47} +(1.00000 - 6.92820i) q^{49} +(-1.50000 - 2.59808i) q^{51} +(-1.50000 + 2.59808i) q^{53} -9.00000 q^{55} -1.00000 q^{57} +(-4.50000 + 7.79423i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-5.00000 - 1.73205i) q^{63} +(-3.00000 - 5.19615i) q^{65} +(3.50000 - 6.06218i) q^{67} +3.00000 q^{69} +(0.500000 - 0.866025i) q^{73} +(-2.00000 - 3.46410i) q^{75} +(1.50000 + 7.79423i) q^{77} +(6.50000 + 11.2583i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +9.00000 q^{85} +(3.00000 - 5.19615i) q^{87} +(-7.50000 - 12.9904i) q^{89} +(-4.00000 + 3.46410i) q^{91} +(3.50000 + 6.06218i) q^{93} +(1.50000 - 2.59808i) q^{95} -10.0000 q^{97} +6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{3} - 3q^{5} - 4q^{7} + 2q^{9} + O(q^{10})$$ $$2q - q^{3} - 3q^{5} - 4q^{7} + 2q^{9} + 3q^{11} + 4q^{13} + 6q^{15} - 3q^{17} + q^{19} - q^{21} - 3q^{23} - 4q^{25} - 10q^{27} - 12q^{29} + 7q^{31} + 3q^{33} + 15q^{35} + q^{37} - 2q^{39} + 12q^{41} - 8q^{43} + 6q^{45} + 9q^{47} + 2q^{49} - 3q^{51} - 3q^{53} - 18q^{55} - 2q^{57} - 9q^{59} + q^{61} - 10q^{63} - 6q^{65} + 7q^{67} + 6q^{69} + q^{73} - 4q^{75} + 3q^{77} + 13q^{79} - q^{81} + 24q^{83} + 18q^{85} + 6q^{87} - 15q^{89} - 8q^{91} + 7q^{93} + 3q^{95} - 20q^{97} + 12q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$$.

 $$n$$ $$15$$ $$17$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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 −0.973494 0.228714i $$-0.926548\pi$$
0.684819 + 0.728714i $$0.259881\pi$$
$$4$$ 0 0
$$5$$ −1.50000 2.59808i −0.670820 1.16190i −0.977672 0.210138i $$-0.932609\pi$$
0.306851 0.951757i $$-0.400725\pi$$
$$6$$ 0 0
$$7$$ −2.00000 + 1.73205i −0.755929 + 0.654654i
$$8$$ 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 $$-0.683949\pi$$
0.998526 + 0.0542666i $$0.0172821\pi$$
$$12$$ 0 0
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 0 0
$$15$$ 3.00000 0.774597
$$16$$ 0 0
$$17$$ −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i $$-0.951855\pi$$
0.624780 + 0.780801i $$0.285189\pi$$
$$18$$ 0 0
$$19$$ 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i $$-0.130073\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ 0 0
$$21$$ −0.500000 2.59808i −0.109109 0.566947i
$$22$$ 0 0
$$23$$ −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i $$-0.267924\pi$$
−0.978961 + 0.204046i $$0.934591\pi$$
$$24$$ 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 −0.359211 0.933257i $$-0.616954\pi$$
0.987829 0.155543i $$-0.0497126\pi$$
$$32$$ 0 0
$$33$$ 1.50000 + 2.59808i 0.261116 + 0.452267i
$$34$$ 0 0
$$35$$ 7.50000 + 2.59808i 1.26773 + 0.439155i
$$36$$ 0 0
$$37$$ 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i $$-0.140472\pi$$
−0.821995 + 0.569495i $$0.807139\pi$$
$$38$$ 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
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 0 0
$$45$$ 3.00000 5.19615i 0.447214 0.774597i
$$46$$ 0 0
$$47$$ 4.50000 + 7.79423i 0.656392 + 1.13691i 0.981543 + 0.191243i $$0.0612518\pi$$
−0.325150 + 0.945662i $$0.605415\pi$$
$$48$$ 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
$$53$$ −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i $$-0.899391\pi$$
0.744423 + 0.667708i $$0.232725\pi$$
$$54$$ 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 0.408919 + 0.912571i $$0.365906\pi$$
−0.994769 + 0.102151i $$0.967427\pi$$
$$60$$ 0 0
$$61$$ 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i $$-0.146275\pi$$
−0.832240 + 0.554416i $$0.812942\pi$$
$$62$$ 0 0
$$63$$ −5.00000 1.73205i −0.629941 0.218218i
$$64$$ 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 $$-0.692695\pi$$
0.996659 + 0.0816792i $$0.0260283\pi$$
$$68$$ 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 $$-0.814695\pi$$
0.893801 + 0.448463i $$0.148028\pi$$
$$74$$ 0 0
$$75$$ −2.00000 3.46410i −0.230940 0.400000i
$$76$$ 0 0
$$77$$ 1.50000 + 7.79423i 0.170941 + 0.888235i
$$78$$ 0 0
$$79$$ 6.50000 + 11.2583i 0.731307 + 1.26666i 0.956325 + 0.292306i $$0.0944227\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 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 −0.922840 0.385183i $$-0.874138\pi$$
0.127842 0.991795i $$-0.459195\pi$$
$$90$$ 0 0
$$91$$ −4.00000 + 3.46410i −0.419314 + 0.363137i
$$92$$ 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 $$-0.669494\pi$$
−0.507673 + 0.861550i $$0.669494\pi$$
$$98$$ 0 0
$$99$$ 6.00000 0.603023
$$100$$ 0 0
$$101$$ −7.50000 + 12.9904i −0.746278 + 1.29259i 0.203317 + 0.979113i $$0.434828\pi$$
−0.949595 + 0.313478i $$0.898506\pi$$
$$102$$ 0 0
$$103$$ −5.50000 9.52628i −0.541931 0.938652i −0.998793 0.0491146i $$-0.984360\pi$$
0.456862 0.889538i $$-0.348973\pi$$
$$104$$ 0 0
$$105$$ −6.00000 + 5.19615i −0.585540 + 0.507093i
$$106$$ 0 0
$$107$$ −7.50000 12.9904i −0.725052 1.25583i −0.958952 0.283567i $$-0.908482\pi$$
0.233900 0.972261i $$-0.424851\pi$$
$$108$$ 0 0
$$109$$ 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i $$-0.818083\pi$$
0.888977 + 0.457951i $$0.151417\pi$$
$$110$$ 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
$$119$$ −1.50000 7.79423i −0.137505 0.714496i
$$120$$ 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 $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 0 0
$$129$$ 2.00000 3.46410i 0.176090 0.304997i
$$130$$ 0 0
$$131$$ −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i $$-0.208503\pi$$
−0.924084 + 0.382190i $$0.875170\pi$$
$$132$$ 0 0
$$133$$ −2.50000 0.866025i −0.216777 0.0750939i
$$134$$ 0 0
$$135$$ 7.50000 + 12.9904i 0.645497 + 1.11803i
$$136$$ 0 0
$$137$$ 10.5000 18.1865i 0.897076 1.55378i 0.0658609 0.997829i $$-0.479021\pi$$
0.831215 0.555952i $$-0.187646\pi$$
$$138$$ 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
$$147$$ 5.50000 + 4.33013i 0.453632 + 0.357143i
$$148$$ 0 0
$$149$$ −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i $$-0.205881\pi$$
−0.920904 + 0.389789i $$0.872548\pi$$
$$150$$ 0 0
$$151$$ −8.50000 + 14.7224i −0.691720 + 1.19809i 0.279554 + 0.960130i $$0.409814\pi$$
−0.971274 + 0.237964i $$0.923520\pi$$
$$152$$ 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 −0.481006 0.876717i $$-0.659728\pi$$
0.999762 0.0217953i $$-0.00693820\pi$$
$$158$$ 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
$$163$$ −5.50000 9.52628i −0.430793 0.746156i 0.566149 0.824303i $$-0.308433\pi$$
−0.996942 + 0.0781474i $$0.975100\pi$$
$$164$$ 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 $$-0.0555188\pi$$
−0.642699 + 0.766119i $$0.722185\pi$$
$$174$$ 0 0
$$175$$ −2.00000 10.3923i −0.151186 0.785584i
$$176$$ 0 0
$$177$$ −4.50000 7.79423i −0.338241 0.585850i
$$178$$ 0 0
$$179$$ −10.5000 + 18.1865i −0.784807 + 1.35933i 0.144308 + 0.989533i $$0.453905\pi$$
−0.929114 + 0.369792i $$0.879429\pi$$
$$180$$ 0 0
$$181$$ −10.0000 −0.743294 −0.371647 0.928374i $$-0.621207\pi$$
−0.371647 + 0.928374i $$0.621207\pi$$
$$182$$ 0 0
$$183$$ −1.00000 −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
$$189$$ 10.0000 8.66025i 0.727393 0.629941i
$$190$$ 0 0
$$191$$ 4.50000 + 7.79423i 0.325609 + 0.563971i 0.981635 0.190767i $$-0.0610975\pi$$
−0.656027 + 0.754738i $$0.727764\pi$$
$$192$$ 0 0
$$193$$ −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i $$-0.962900\pi$$
0.597317 + 0.802005i $$0.296234\pi$$
$$194$$ 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 −0.714893 0.699234i $$-0.753524\pi$$
0.963001 + 0.269498i $$0.0868577\pi$$
$$200$$ 0 0
$$201$$ 3.50000 + 6.06218i 0.246871 + 0.427593i
$$202$$ 0 0
$$203$$ 12.0000 10.3923i 0.842235 0.729397i
$$204$$ 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 $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 6.00000 + 10.3923i 0.409197 + 0.708749i
$$216$$ 0 0
$$217$$ 3.50000 + 18.1865i 0.237595 + 1.23458i
$$218$$ 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 −0.811943 0.583736i $$-0.801590\pi$$
0.911502 + 0.411296i $$0.134924\pi$$
$$228$$ 0 0
$$229$$ −5.50000 9.52628i −0.363450 0.629514i 0.625076 0.780564i $$-0.285068\pi$$
−0.988526 + 0.151050i $$0.951735\pi$$
$$230$$ 0 0
$$231$$ −7.50000 2.59808i −0.493464 0.170941i
$$232$$ 0 0
$$233$$ 10.5000 + 18.1865i 0.687878 + 1.19144i 0.972523 + 0.232806i $$0.0747909\pi$$
−0.284645 + 0.958633i $$0.591876\pi$$
$$234$$ 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 $$-0.626871\pi$$
−0.388108 + 0.921614i $$0.626871\pi$$
$$240$$ 0 0
$$241$$ 0.500000 0.866025i 0.0322078 0.0557856i −0.849472 0.527633i $$-0.823079\pi$$
0.881680 + 0.471848i $$0.156413\pi$$
$$242$$ 0 0
$$243$$ −8.00000 13.8564i −0.513200 0.888889i
$$244$$ 0 0
$$245$$ −19.5000 + 7.79423i −1.24581 + 0.497955i
$$246$$ 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 $$-0.196494\pi$$
−0.909010 + 0.416775i $$0.863160\pi$$
$$258$$ 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
$$263$$ 1.50000 2.59808i 0.0924940 0.160204i −0.816066 0.577959i $$-0.803849\pi$$
0.908560 + 0.417755i $$0.137183\pi$$
$$264$$ 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 $$-0.862486\pi$$
0.816668 + 0.577108i $$0.195819\pi$$
$$270$$ 0 0
$$271$$ −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i $$-0.275099\pi$$
−0.983312 + 0.181928i $$0.941766\pi$$
$$272$$ 0 0
$$273$$ −1.00000 5.19615i −0.0605228 0.314485i
$$274$$ 0 0
$$275$$ 6.00000 + 10.3923i 0.361814 + 0.626680i
$$276$$ 0 0
$$277$$ 6.50000 11.2583i 0.390547 0.676448i −0.601975 0.798515i $$-0.705619\pi$$
0.992522 + 0.122068i $$0.0389525\pi$$
$$278$$ 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 0.00812260 + 0.999967i $$0.497414\pi$$
−0.870058 + 0.492949i $$0.835919\pi$$
$$284$$ 0 0
$$285$$ 1.50000 + 2.59808i 0.0888523 + 0.153897i
$$286$$ 0 0
$$287$$ −12.0000 + 10.3923i −0.708338 + 0.613438i
$$288$$ 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 $$-0.443923\pi$$
0.175262 + 0.984522i $$0.443923\pi$$
$$294$$ 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
$$301$$ 8.00000 6.92820i 0.461112 0.399335i
$$302$$ 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 −0.174459 0.984664i $$-0.555818\pi$$
0.939974 0.341246i $$-0.110849\pi$$
$$312$$ 0 0
$$313$$ −11.5000 19.9186i −0.650018 1.12586i −0.983118 0.182973i $$-0.941428\pi$$
0.333099 0.942892i $$-0.391906\pi$$
$$314$$ 0 0
$$315$$ 3.00000 + 15.5885i 0.169031 + 0.878310i
$$316$$ 0 0
$$317$$ 4.50000 + 7.79423i 0.252745 + 0.437767i 0.964281 0.264883i $$-0.0853332\pi$$
−0.711535 + 0.702650i $$0.752000\pi$$
$$318$$ 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
$$329$$ −22.5000 7.79423i −1.24047 0.429710i
$$330$$ 0 0
$$331$$ 6.50000 + 11.2583i 0.357272 + 0.618814i 0.987504 0.157593i $$-0.0503735\pi$$
−0.630232 + 0.776407i $$0.717040\pi$$
$$332$$ 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
$$343$$ 10.0000 + 15.5885i 0.539949 + 0.841698i
$$344$$ 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 $$-0.910997\pi$$
0.719590 + 0.694399i $$0.244330\pi$$
$$348$$ 0 0
$$349$$ 26.0000 1.39175 0.695874 0.718164i $$-0.255017\pi$$
0.695874 + 0.718164i $$0.255017\pi$$
$$350$$ 0 0
$$351$$ −10.0000 −0.533761
$$352$$ 0 0
$$353$$ 10.5000 18.1865i 0.558859 0.967972i −0.438733 0.898617i $$-0.644573\pi$$
0.997592 0.0693543i $$-0.0220939\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 7.50000 + 2.59808i 0.396942 + 0.137505i
$$358$$ 0 0
$$359$$ −7.50000 12.9904i −0.395835 0.685606i 0.597372 0.801964i $$-0.296211\pi$$
−0.993207 + 0.116358i $$0.962878\pi$$
$$360$$ 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 −0.923869 0.382709i $$-0.874991\pi$$
0.793370 + 0.608740i $$0.208325\pi$$
$$368$$ 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
$$373$$ 12.5000 + 21.6506i 0.647225 + 1.12103i 0.983783 + 0.179364i $$0.0574041\pi$$
−0.336557 + 0.941663i $$0.609263\pi$$
$$374$$ 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 $$-0.434129\pi$$
0.205466 + 0.978664i $$0.434129\pi$$
$$380$$ 0 0
$$381$$ −4.00000 + 6.92820i −0.204926 + 0.354943i
$$382$$ 0 0
$$383$$ 16.5000 + 28.5788i 0.843111 + 1.46031i 0.887252 + 0.461285i $$0.152611\pi$$
−0.0441413 + 0.999025i $$0.514055\pi$$
$$384$$ 0 0
$$385$$ 18.0000 15.5885i 0.917365 0.794461i
$$386$$ 0 0
$$387$$ −4.00000 6.92820i −0.203331 0.352180i
$$388$$ 0 0
$$389$$ −7.50000 + 12.9904i −0.380265 + 0.658638i −0.991100 0.133120i $$-0.957501\pi$$
0.610835 + 0.791758i $$0.290834\pi$$
$$390$$ 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 0.785853 + 0.618414i $$0.212224\pi$$
0.142636 + 0.989775i $$0.454442\pi$$
$$398$$ 0 0
$$399$$ 2.00000 1.73205i 0.100125 0.0867110i
$$400$$ 0 0
$$401$$ −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i $$-0.190532\pi$$
−0.901046 + 0.433724i $$0.857199\pi$$
$$402$$ 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 $$-0.921004\pi$$
0.697406 + 0.716677i $$0.254338\pi$$
$$410$$ 0 0
$$411$$ 10.5000 + 18.1865i 0.517927 + 0.897076i
$$412$$ 0 0
$$413$$ −4.50000 23.3827i −0.221431 1.15059i
$$414$$ 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
$$427$$ −2.50000 0.866025i −0.120983 0.0419099i
$$428$$ 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 $$-0.715679\pi$$
0.988169 + 0.153370i $$0.0490126\pi$$
$$432$$ 0 0
$$433$$ −10.0000 −0.480569 −0.240285 0.970702i $$-0.577241\pi$$
−0.240285 + 0.970702i $$0.577241\pi$$
$$434$$ 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 0.877711 0.479191i $$-0.159070\pi$$
−0.853847 + 0.520524i $$0.825737\pi$$
$$440$$ 0 0
$$441$$ 13.0000 5.19615i 0.619048 0.247436i
$$442$$ 0 0
$$443$$ 4.50000 + 7.79423i 0.213801 + 0.370315i 0.952901 0.303281i $$-0.0980821\pi$$
−0.739100 + 0.673596i $$0.764749\pi$$
$$444$$ 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
$$455$$ 15.0000 + 5.19615i 0.703211 + 0.243599i
$$456$$ 0 0
$$457$$ −11.5000 19.9186i −0.537947 0.931752i −0.999014 0.0443868i $$-0.985867\pi$$
0.461067 0.887365i $$-0.347467\pi$$
$$458$$ 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
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ 10.5000 18.1865i 0.486926 0.843380i
$$466$$ 0 0
$$467$$ 10.5000 + 18.1865i 0.485882 + 0.841572i 0.999868 0.0162260i $$-0.00516512\pi$$
−0.513986 + 0.857798i $$0.671832\pi$$
$$468$$ 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
$$473$$ −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 −0.829721 0.558179i $$-0.811500\pi$$
0.898257 + 0.439470i $$0.144834\pi$$
$$480$$ 0 0
$$481$$ 1.00000 + 1.73205i 0.0455961 + 0.0789747i
$$482$$ 0 0
$$483$$ −6.00000 + 5.19615i −0.273009 + 0.236433i
$$484$$ 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 $$-0.691675\pi$$
0.996915 + 0.0784867i $$0.0250088\pi$$
$$488$$ 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
$$493$$ 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 $$-0.245853\pi$$
−0.962472 + 0.271380i $$0.912520\pi$$
$$500$$ 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 $$-0.187846\pi$$
−0.897352 + 0.441315i $$0.854512\pi$$
$$510$$ 0 0
$$511$$ 0.500000 + 2.59808i 0.0221187 + 0.114932i
$$512$$ 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 0.0229727 + 0.999736i $$0.492687\pi$$
−0.877283 + 0.479973i $$0.840646\pi$$
$$522$$ 0 0
$$523$$ 0.500000 + 0.866025i 0.0218635 + 0.0378686i 0.876750 0.480946i $$-0.159707\pi$$
−0.854887 + 0.518815i $$0.826373\pi$$
$$524$$ 0 0
$$525$$ 10.0000 + 3.46410i 0.436436 + 0.151186i
$$526$$ 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
$$539$$ −16.5000 12.9904i −0.710705 0.559535i
$$540$$ 0 0
$$541$$ −17.5000 30.3109i −0.752384 1.30317i −0.946664 0.322221i $$-0.895571\pi$$
0.194281 0.980946i $$-0.437763\pi$$
$$542$$ 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 $$-0.445291\pi$$
0.171028 + 0.985266i $$0.445291\pi$$
$$548$$ 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
$$553$$ −32.5000 11.2583i −1.38204 0.478753i
$$554$$ 0 0
$$555$$ 1.50000 + 2.59808i 0.0636715 + 0.110282i
$$556$$ 0 0
$$557$$ 16.5000 28.5788i 0.699127 1.21092i −0.269642 0.962961i $$-0.586905\pi$$
0.968769 0.247964i $$-0.0797613\pi$$
$$558$$ 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 −0.945134 0.326682i $$-0.894069\pi$$
0.755482 + 0.655169i $$0.227403\pi$$
$$564$$ 0 0
$$565$$ −9.00000 15.5885i −0.378633 0.655811i
$$566$$ 0 0
$$567$$ −0.500000 2.59808i −0.0209980 0.109109i
$$568$$ 0 0
$$569$$ 4.50000 + 7.79423i 0.188650 + 0.326751i 0.944800 0.327647i $$-0.106256\pi$$
−0.756151 + 0.654398i $$0.772922\pi$$
$$570$$ 0 0
$$571$$ −14.5000 + 25.1147i −0.606806 + 1.05102i 0.384957 + 0.922934i $$0.374216\pi$$
−0.991763 + 0.128085i $$0.959117\pi$$
$$572$$ 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 $$-0.826707\pi$$
0.876245 + 0.481865i $$0.160040\pi$$
$$578$$ 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
$$583$$ 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 $$-0.0247629\pi$$
−0.565792 + 0.824548i $$0.691430\pi$$
$$594$$ 0 0
$$595$$ −18.0000 + 15.5885i −0.737928 + 0.639064i
$$596$$ 0 0
$$597$$ 3.50000 + 6.06218i 0.143245 + 0.248108i
$$598$$ 0 0
$$599$$ 13.5000 23.3827i 0.551595 0.955391i −0.446565 0.894751i $$-0.647353\pi$$
0.998160 0.0606393i $$-0.0193139\pi$$
$$600$$ 0 0
$$601$$ 14.0000 0.571072 0.285536 0.958368i $$-0.407828\pi$$
0.285536 + 0.958368i $$0.407828\pi$$
$$602$$ 0 0
$$603$$ 14.0000 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 −0.737011 0.675881i $$-0.763763\pi$$
−0.216825 0.976210i $$-0.569570\pi$$
$$608$$ 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
$$613$$ 12.5000 21.6506i 0.504870 0.874461i −0.495114 0.868828i $$-0.664874\pi$$
0.999984 0.00563283i $$-0.00179300\pi$$
$$614$$ 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 −0.365927 0.930644i $$-0.619248\pi$$
0.988924 0.148420i $$-0.0474187\pi$$
$$620$$ 0 0
$$621$$ 7.50000 + 12.9904i 0.300965 + 0.521286i
$$622$$ 0 0
$$623$$ 37.5000 + 12.9904i 1.50241 + 0.520449i
$$624$$ 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 $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 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
$$637$$ 2.00000 13.8564i 0.0792429 0.549011i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −7.50000 + 12.9904i −0.296232 + 0.513089i −0.975271 0.221013i $$-0.929064\pi$$
0.679039 + 0.734103i $$0.262397\pi$$
$$642$$ 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 −0.995194 0.0979182i $$-0.968782\pi$$
0.582397 + 0.812905i $$0.302115\pi$$
$$648$$ 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
$$653$$ −19.5000 33.7750i −0.763094 1.32172i −0.941248 0.337715i $$-0.890346\pi$$
0.178154 0.984003i $$-0.442987\pi$$
$$654$$ 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 $$-0.424908\pi$$
0.233727 + 0.972302i $$0.424908\pi$$
$$660$$ 0 0
$$661$$ −5.50000 + 9.52628i −0.213925 + 0.370529i −0.952940 0.303160i $$-0.901958\pi$$
0.739014 + 0.673690i $$0.235292\pi$$
$$662$$ 0 0
$$663$$ −3.00000 5.19615i −0.116510 0.201802i
$$664$$ 0 0
$$665$$ 1.50000 + 7.79423i 0.0581675 + 0.302247i
$$666$$ 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 −0.999760 0.0219013i $$-0.993028\pi$$
0.480913 0.876768i $$-0.340305\pi$$
$$678$$ 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
$$683$$ −10.5000 + 18.1865i −0.401771 + 0.695888i −0.993940 0.109926i $$-0.964939\pi$$
0.592168 + 0.805814i $$0.298272\pi$$
$$684$$ 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 0.962768 0.270330i $$-0.0871327\pi$$
−0.715496 + 0.698617i $$0.753799\pi$$
$$692$$ 0 0
$$693$$ −12.0000 + 10.3923i −0.455842 + 0.394771i
$$694$$ 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
$$707$$ −7.50000 38.9711i −0.282067 1.46566i
$$708$$ 0 0
$$709$$ 0.500000 + 0.866025i 0.0187779 + 0.0325243i 0.875262 0.483650i $$-0.160689\pi$$
−0.856484 + 0.516174i $$0.827356\pi$$
$$710$$ 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 0.992659 0.120950i $$-0.0385939\pi$$
−0.601075 + 0.799193i $$0.705261\pi$$
$$720$$ 0 0
$$721$$ 27.5000 + 9.52628i 1.02415 + 0.354777i
$$722$$ 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 $$-0.0139070\pi$$
−0.537348 + 0.843361i $$0.680574\pi$$
$$734$$ 0 0
$$735$$ 3.00000 20.7846i 0.110657 0.766652i
$$736$$ 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 $$-0.719697\pi$$
0.986154 + 0.165831i $$0.0530307\pi$$
$$740$$ 0 0
$$741$$ −2.00000 −0.0734718
$$742$$ 0 0
$$743$$ −48.0000 −1.76095 −0.880475 0.474093i $$-0.842776\pi$$
−0.880475 + 0.474093i $$0.842776\pi$$
$$744$$ 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
$$749$$ 37.5000 + 12.9904i 1.37022 + 0.474658i
$$750$$ 0 0
$$751$$ 12.5000 + 21.6506i 0.456131 + 0.790043i 0.998752 0.0499348i $$-0.0159013\pi$$
−0.542621 + 0.839978i $$0.682568\pi$$
$$752$$ 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 $$-0.183983\pi$$
−0.891932 + 0.452170i $$0.850650\pi$$
$$762$$ 0 0
$$763$$ 0.500000 + 2.59808i 0.0181012 + 0.0940567i
$$764$$ 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 $$-0.710052\pi$$
−0.613036 + 0.790055i $$0.710052\pi$$
$$770$$ 0 0
$$771$$ 3.00000 0.108042
$$772$$ 0 0
$$773$$ 16.5000 28.5788i 0.593464 1.02791i −0.400298 0.916385i $$-0.631093\pi$$
0.993762 0.111524i $$-0.0355733\pi$$
$$774$$ 0 0
$$775$$ 14.0000 + 24.2487i 0.502895 + 0.871039i
$$776$$ 0 0
$$777$$ 2.00000 1.73205i 0.0717496 0.0621370i
$$778$$ 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 −0.445577 0.895244i $$-0.647001\pi$$
0.998092 0.0617409i $$-0.0196653\pi$$
$$788$$ 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
$$793$$ 1.00000 + 1.73205i 0.0355110 + 0.0615069i
$$794$$ 0 0
$$795$$ −4.50000 + 7.79423i −0.159599 + 0.276433i
$$796$$ 0 0