# Properties

 Label 567.2.g.f.109.1 Level $567$ Weight $2$ Character 567.109 Analytic conductor $4.528$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 567.g (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.52751779461$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 21) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 109.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 567.109 Dual form 567.2.g.f.541.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 - 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})$$ $$q+(1.00000 - 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} +2.00000 q^{5} +(0.500000 + 2.59808i) q^{7} +(2.00000 - 3.46410i) q^{10} +2.00000 q^{11} +(-0.500000 + 0.866025i) q^{13} +(5.00000 + 1.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-0.500000 - 0.866025i) q^{19} +(-2.00000 - 3.46410i) q^{20} +(2.00000 - 3.46410i) q^{22} -1.00000 q^{25} +(1.00000 + 1.73205i) q^{26} +(4.00000 - 3.46410i) q^{28} +(2.00000 + 3.46410i) q^{29} +(-4.50000 - 7.79423i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(1.00000 + 5.19615i) q^{35} +(-1.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(-5.00000 + 8.66025i) q^{41} +(-2.50000 - 4.33013i) q^{43} +(-2.00000 - 3.46410i) q^{44} +(-3.00000 + 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-1.00000 + 1.73205i) q^{50} +2.00000 q^{52} +(6.00000 - 10.3923i) q^{53} +4.00000 q^{55} +8.00000 q^{58} +(-6.00000 - 10.3923i) q^{59} +(-5.00000 + 8.66025i) q^{61} -18.0000 q^{62} -8.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(2.50000 + 4.33013i) q^{67} +(10.0000 + 3.46410i) q^{70} +6.00000 q^{71} +(1.50000 - 2.59808i) q^{73} -6.00000 q^{74} +(-1.00000 + 1.73205i) q^{76} +(1.00000 + 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(4.00000 - 6.92820i) q^{80} +(10.0000 + 17.3205i) q^{82} +(3.00000 + 5.19615i) q^{83} -10.0000 q^{86} +(8.00000 + 13.8564i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(6.00000 + 10.3923i) q^{94} +(-1.00000 - 1.73205i) q^{95} +(3.00000 + 5.19615i) q^{97} +(-2.00000 + 13.8564i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 2q^{2} - 2q^{4} + 4q^{5} + q^{7} + O(q^{10})$$ $$2q + 2q^{2} - 2q^{4} + 4q^{5} + q^{7} + 4q^{10} + 4q^{11} - q^{13} + 10q^{14} + 4q^{16} - q^{19} - 4q^{20} + 4q^{22} - 2q^{25} + 2q^{26} + 8q^{28} + 4q^{29} - 9q^{31} - 8q^{32} + 2q^{35} - 3q^{37} - 4q^{38} - 10q^{41} - 5q^{43} - 4q^{44} - 6q^{47} - 13q^{49} - 2q^{50} + 4q^{52} + 12q^{53} + 8q^{55} + 16q^{58} - 12q^{59} - 10q^{61} - 36q^{62} - 16q^{64} - 2q^{65} + 5q^{67} + 20q^{70} + 12q^{71} + 3q^{73} - 12q^{74} - 2q^{76} + 2q^{77} + q^{79} + 8q^{80} + 20q^{82} + 6q^{83} - 20q^{86} + 16q^{89} - 5q^{91} + 12q^{94} - 2q^{95} + 6q^{97} - 4q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 1.73205i 0.707107 1.22474i −0.258819 0.965926i $$-0.583333\pi$$
0.965926 0.258819i $$-0.0833333\pi$$
$$3$$ 0 0
$$4$$ −1.00000 1.73205i −0.500000 0.866025i
$$5$$ 2.00000 0.894427 0.447214 0.894427i $$-0.352416\pi$$
0.447214 + 0.894427i $$0.352416\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 2.59808i 0.188982 + 0.981981i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 2.00000 3.46410i 0.632456 1.09545i
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 0 0
$$13$$ −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i $$-0.877618\pi$$
0.788320 + 0.615265i $$0.210951\pi$$
$$14$$ 5.00000 + 1.73205i 1.33631 + 0.462910i
$$15$$ 0 0
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$18$$ 0 0
$$19$$ −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i $$-0.203260\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ −2.00000 3.46410i −0.447214 0.774597i
$$21$$ 0 0
$$22$$ 2.00000 3.46410i 0.426401 0.738549i
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 1.00000 + 1.73205i 0.196116 + 0.339683i
$$27$$ 0 0
$$28$$ 4.00000 3.46410i 0.755929 0.654654i
$$29$$ 2.00000 + 3.46410i 0.371391 + 0.643268i 0.989780 0.142605i $$-0.0455477\pi$$
−0.618389 + 0.785872i $$0.712214\pi$$
$$30$$ 0 0
$$31$$ −4.50000 7.79423i −0.808224 1.39988i −0.914093 0.405505i $$-0.867096\pi$$
0.105869 0.994380i $$-0.466238\pi$$
$$32$$ −4.00000 6.92820i −0.707107 1.22474i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 1.00000 + 5.19615i 0.169031 + 0.878310i
$$36$$ 0 0
$$37$$ −1.50000 2.59808i −0.246598 0.427121i 0.715981 0.698119i $$-0.245980\pi$$
−0.962580 + 0.270998i $$0.912646\pi$$
$$38$$ −2.00000 −0.324443
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −5.00000 + 8.66025i −0.780869 + 1.35250i 0.150567 + 0.988600i $$0.451890\pi$$
−0.931436 + 0.363905i $$0.881443\pi$$
$$42$$ 0 0
$$43$$ −2.50000 4.33013i −0.381246 0.660338i 0.609994 0.792406i $$-0.291172\pi$$
−0.991241 + 0.132068i $$0.957838\pi$$
$$44$$ −2.00000 3.46410i −0.301511 0.522233i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i $$-0.977503\pi$$
0.559908 + 0.828554i $$0.310836\pi$$
$$48$$ 0 0
$$49$$ −6.50000 + 2.59808i −0.928571 + 0.371154i
$$50$$ −1.00000 + 1.73205i −0.141421 + 0.244949i
$$51$$ 0 0
$$52$$ 2.00000 0.277350
$$53$$ 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i $$-0.524979\pi$$
0.902557 0.430570i $$-0.141688\pi$$
$$54$$ 0 0
$$55$$ 4.00000 0.539360
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 8.00000 1.05045
$$59$$ −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i $$-0.881308\pi$$
0.150148 0.988663i $$-0.452025\pi$$
$$60$$ 0 0
$$61$$ −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i $$0.387809\pi$$
−0.985391 + 0.170305i $$0.945525\pi$$
$$62$$ −18.0000 −2.28600
$$63$$ 0 0
$$64$$ −8.00000 −1.00000
$$65$$ −1.00000 + 1.73205i −0.124035 + 0.214834i
$$66$$ 0 0
$$67$$ 2.50000 + 4.33013i 0.305424 + 0.529009i 0.977356 0.211604i $$-0.0678686\pi$$
−0.671932 + 0.740613i $$0.734535\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 10.0000 + 3.46410i 1.19523 + 0.414039i
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 0 0
$$73$$ 1.50000 2.59808i 0.175562 0.304082i −0.764794 0.644275i $$-0.777159\pi$$
0.940356 + 0.340193i $$0.110493\pi$$
$$74$$ −6.00000 −0.697486
$$75$$ 0 0
$$76$$ −1.00000 + 1.73205i −0.114708 + 0.198680i
$$77$$ 1.00000 + 5.19615i 0.113961 + 0.592157i
$$78$$ 0 0
$$79$$ 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i $$-0.815418\pi$$
0.892781 + 0.450490i $$0.148751\pi$$
$$80$$ 4.00000 6.92820i 0.447214 0.774597i
$$81$$ 0 0
$$82$$ 10.0000 + 17.3205i 1.10432 + 1.91273i
$$83$$ 3.00000 + 5.19615i 0.329293 + 0.570352i 0.982372 0.186938i $$-0.0598564\pi$$
−0.653079 + 0.757290i $$0.726523\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −10.0000 −1.07833
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 8.00000 + 13.8564i 0.847998 + 1.46878i 0.882992 + 0.469389i $$0.155526\pi$$
−0.0349934 + 0.999388i $$0.511141\pi$$
$$90$$ 0 0
$$91$$ −2.50000 0.866025i −0.262071 0.0907841i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 6.00000 + 10.3923i 0.618853 + 1.07188i
$$95$$ −1.00000 1.73205i −0.102598 0.177705i
$$96$$ 0 0
$$97$$ 3.00000 + 5.19615i 0.304604 + 0.527589i 0.977173 0.212445i $$-0.0681426\pi$$
−0.672569 + 0.740034i $$0.734809\pi$$
$$98$$ −2.00000 + 13.8564i −0.202031 + 1.39971i
$$99$$ 0 0
$$100$$ 1.00000 + 1.73205i 0.100000 + 0.173205i
$$101$$ −2.00000 −0.199007 −0.0995037 0.995037i $$-0.531726\pi$$
−0.0995037 + 0.995037i $$0.531726\pi$$
$$102$$ 0 0
$$103$$ −7.00000 −0.689730 −0.344865 0.938652i $$-0.612075\pi$$
−0.344865 + 0.938652i $$0.612075\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ −12.0000 20.7846i −1.16554 2.01878i
$$107$$ −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i $$-0.293050\pi$$
−0.992003 + 0.126217i $$0.959717\pi$$
$$108$$ 0 0
$$109$$ −4.50000 + 7.79423i −0.431022 + 0.746552i −0.996962 0.0778949i $$-0.975180\pi$$
0.565940 + 0.824447i $$0.308513\pi$$
$$110$$ 4.00000 6.92820i 0.381385 0.660578i
$$111$$ 0 0
$$112$$ 10.0000 + 3.46410i 0.944911 + 0.327327i
$$113$$ 5.00000 8.66025i 0.470360 0.814688i −0.529065 0.848581i $$-0.677457\pi$$
0.999425 + 0.0338931i $$0.0107906\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 4.00000 6.92820i 0.371391 0.643268i
$$117$$ 0 0
$$118$$ −24.0000 −2.20938
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −7.00000 −0.636364
$$122$$ 10.0000 + 17.3205i 0.905357 + 1.56813i
$$123$$ 0 0
$$124$$ −9.00000 + 15.5885i −0.808224 + 1.39988i
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ −15.0000 −1.33103 −0.665517 0.746382i $$-0.731789\pi$$
−0.665517 + 0.746382i $$0.731789\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 2.00000 + 3.46410i 0.175412 + 0.303822i
$$131$$ 14.0000 1.22319 0.611593 0.791173i $$-0.290529\pi$$
0.611593 + 0.791173i $$0.290529\pi$$
$$132$$ 0 0
$$133$$ 2.00000 1.73205i 0.173422 0.150188i
$$134$$ 10.0000 0.863868
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 12.0000 1.02523 0.512615 0.858619i $$-0.328677\pi$$
0.512615 + 0.858619i $$0.328677\pi$$
$$138$$ 0 0
$$139$$ 1.50000 2.59808i 0.127228 0.220366i −0.795373 0.606120i $$-0.792725\pi$$
0.922602 + 0.385754i $$0.126059\pi$$
$$140$$ 8.00000 6.92820i 0.676123 0.585540i
$$141$$ 0 0
$$142$$ 6.00000 10.3923i 0.503509 0.872103i
$$143$$ −1.00000 + 1.73205i −0.0836242 + 0.144841i
$$144$$ 0 0
$$145$$ 4.00000 + 6.92820i 0.332182 + 0.575356i
$$146$$ −3.00000 5.19615i −0.248282 0.430037i
$$147$$ 0 0
$$148$$ −3.00000 + 5.19615i −0.246598 + 0.427121i
$$149$$ 12.0000 0.983078 0.491539 0.870855i $$-0.336434\pi$$
0.491539 + 0.870855i $$0.336434\pi$$
$$150$$ 0 0
$$151$$ −16.0000 −1.30206 −0.651031 0.759051i $$-0.725663\pi$$
−0.651031 + 0.759051i $$0.725663\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 10.0000 + 3.46410i 0.805823 + 0.279145i
$$155$$ −9.00000 15.5885i −0.722897 1.25210i
$$156$$ 0 0
$$157$$ 7.00000 + 12.1244i 0.558661 + 0.967629i 0.997609 + 0.0691164i $$0.0220180\pi$$
−0.438948 + 0.898513i $$0.644649\pi$$
$$158$$ −1.00000 1.73205i −0.0795557 0.137795i
$$159$$ 0 0
$$160$$ −8.00000 13.8564i −0.632456 1.09545i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i $$-0.216737\pi$$
−0.933659 + 0.358162i $$0.883403\pi$$
$$164$$ 20.0000 1.56174
$$165$$ 0 0
$$166$$ 12.0000 0.931381
$$167$$ −7.00000 + 12.1244i −0.541676 + 0.938211i 0.457132 + 0.889399i $$0.348877\pi$$
−0.998808 + 0.0488118i $$0.984457\pi$$
$$168$$ 0 0
$$169$$ 6.00000 + 10.3923i 0.461538 + 0.799408i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −5.00000 + 8.66025i −0.381246 + 0.660338i
$$173$$ 4.00000 6.92820i 0.304114 0.526742i −0.672949 0.739689i $$-0.734973\pi$$
0.977064 + 0.212947i $$0.0683062\pi$$
$$174$$ 0 0
$$175$$ −0.500000 2.59808i −0.0377964 0.196396i
$$176$$ 4.00000 6.92820i 0.301511 0.522233i
$$177$$ 0 0
$$178$$ 32.0000 2.39850
$$179$$ 1.00000 1.73205i 0.0747435 0.129460i −0.826231 0.563331i $$-0.809520\pi$$
0.900975 + 0.433872i $$0.142853\pi$$
$$180$$ 0 0
$$181$$ 13.0000 0.966282 0.483141 0.875542i $$-0.339496\pi$$
0.483141 + 0.875542i $$0.339496\pi$$
$$182$$ −4.00000 + 3.46410i −0.296500 + 0.256776i
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −3.00000 5.19615i −0.220564 0.382029i
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 12.0000 0.875190
$$189$$ 0 0
$$190$$ −4.00000 −0.290191
$$191$$ 5.00000 8.66025i 0.361787 0.626634i −0.626468 0.779447i $$-0.715500\pi$$
0.988255 + 0.152813i $$0.0488333\pi$$
$$192$$ 0 0
$$193$$ −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i $$-0.296234\pi$$
−0.993215 + 0.116289i $$0.962900\pi$$
$$194$$ 12.0000 0.861550
$$195$$ 0 0
$$196$$ 11.0000 + 8.66025i 0.785714 + 0.618590i
$$197$$ −16.0000 −1.13995 −0.569976 0.821661i $$-0.693048\pi$$
−0.569976 + 0.821661i $$0.693048\pi$$
$$198$$ 0 0
$$199$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −2.00000 + 3.46410i −0.140720 + 0.243733i
$$203$$ −8.00000 + 6.92820i −0.561490 + 0.486265i
$$204$$ 0 0
$$205$$ −10.0000 + 17.3205i −0.698430 + 1.20972i
$$206$$ −7.00000 + 12.1244i −0.487713 + 0.844744i
$$207$$ 0 0
$$208$$ 2.00000 + 3.46410i 0.138675 + 0.240192i
$$209$$ −1.00000 1.73205i −0.0691714 0.119808i
$$210$$ 0 0
$$211$$ −2.00000 + 3.46410i −0.137686 + 0.238479i −0.926620 0.375999i $$-0.877300\pi$$
0.788935 + 0.614477i $$0.210633\pi$$
$$212$$ −24.0000 −1.64833
$$213$$ 0 0
$$214$$ −16.0000 −1.09374
$$215$$ −5.00000 8.66025i −0.340997 0.590624i
$$216$$ 0 0
$$217$$ 18.0000 15.5885i 1.22192 1.05821i
$$218$$ 9.00000 + 15.5885i 0.609557 + 1.05578i
$$219$$ 0 0
$$220$$ −4.00000 6.92820i −0.269680 0.467099i
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −8.00000 13.8564i −0.535720 0.927894i −0.999128 0.0417488i $$-0.986707\pi$$
0.463409 0.886145i $$-0.346626\pi$$
$$224$$ 16.0000 13.8564i 1.06904 0.925820i
$$225$$ 0 0
$$226$$ −10.0000 17.3205i −0.665190 1.15214i
$$227$$ −18.0000 −1.19470 −0.597351 0.801980i $$-0.703780\pi$$
−0.597351 + 0.801980i $$0.703780\pi$$
$$228$$ 0 0
$$229$$ −19.0000 −1.25556 −0.627778 0.778393i $$-0.716035\pi$$
−0.627778 + 0.778393i $$0.716035\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i $$-0.103697\pi$$
−0.750867 + 0.660454i $$0.770364\pi$$
$$234$$ 0 0
$$235$$ −6.00000 + 10.3923i −0.391397 + 0.677919i
$$236$$ −12.0000 + 20.7846i −0.781133 + 1.35296i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 3.00000 5.19615i 0.194054 0.336111i −0.752536 0.658551i $$-0.771170\pi$$
0.946590 + 0.322440i $$0.104503\pi$$
$$240$$ 0 0
$$241$$ 14.0000 0.901819 0.450910 0.892570i $$-0.351100\pi$$
0.450910 + 0.892570i $$0.351100\pi$$
$$242$$ −7.00000 + 12.1244i −0.449977 + 0.779383i
$$243$$ 0 0
$$244$$ 20.0000 1.28037
$$245$$ −13.0000 + 5.19615i −0.830540 + 0.331970i
$$246$$ 0 0
$$247$$ 1.00000 0.0636285
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −12.0000 + 20.7846i −0.758947 + 1.31453i
$$251$$ 8.00000 0.504956 0.252478 0.967603i $$-0.418755\pi$$
0.252478 + 0.967603i $$0.418755\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −15.0000 + 25.9808i −0.941184 + 1.63018i
$$255$$ 0 0
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ −26.0000 −1.62184 −0.810918 0.585160i $$-0.801032\pi$$
−0.810918 + 0.585160i $$0.801032\pi$$
$$258$$ 0 0
$$259$$ 6.00000 5.19615i 0.372822 0.322873i
$$260$$ 4.00000 0.248069
$$261$$ 0 0
$$262$$ 14.0000 24.2487i 0.864923 1.49809i
$$263$$ −4.00000 −0.246651 −0.123325 0.992366i $$-0.539356\pi$$
−0.123325 + 0.992366i $$0.539356\pi$$
$$264$$ 0 0
$$265$$ 12.0000 20.7846i 0.737154 1.27679i
$$266$$ −1.00000 5.19615i −0.0613139 0.318597i
$$267$$ 0 0
$$268$$ 5.00000 8.66025i 0.305424 0.529009i
$$269$$ 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i $$-0.774781\pi$$
0.942871 + 0.333157i $$0.108114\pi$$
$$270$$ 0 0
$$271$$ −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i $$-0.328199\pi$$
−0.999870 + 0.0161307i $$0.994865\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 12.0000 20.7846i 0.724947 1.25564i
$$275$$ −2.00000 −0.120605
$$276$$ 0 0
$$277$$ 13.0000 0.781094 0.390547 0.920583i $$-0.372286\pi$$
0.390547 + 0.920583i $$0.372286\pi$$
$$278$$ −3.00000 5.19615i −0.179928 0.311645i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −2.00000 3.46410i −0.119310 0.206651i 0.800184 0.599754i $$-0.204735\pi$$
−0.919494 + 0.393103i $$0.871402\pi$$
$$282$$ 0 0
$$283$$ 5.50000 + 9.52628i 0.326941 + 0.566279i 0.981903 0.189383i $$-0.0606488\pi$$
−0.654962 + 0.755662i $$0.727315\pi$$
$$284$$ −6.00000 10.3923i −0.356034 0.616670i
$$285$$ 0 0
$$286$$ 2.00000 + 3.46410i 0.118262 + 0.204837i
$$287$$ −25.0000 8.66025i −1.47570 0.511199i
$$288$$ 0 0
$$289$$ 8.50000 + 14.7224i 0.500000 + 0.866025i
$$290$$ 16.0000 0.939552
$$291$$ 0 0
$$292$$ −6.00000 −0.351123
$$293$$ 4.00000 6.92820i 0.233682 0.404750i −0.725206 0.688531i $$-0.758256\pi$$
0.958889 + 0.283782i $$0.0915890\pi$$
$$294$$ 0 0
$$295$$ −12.0000 20.7846i −0.698667 1.21013i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 12.0000 20.7846i 0.695141 1.20402i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 10.0000 8.66025i 0.576390 0.499169i
$$302$$ −16.0000 + 27.7128i −0.920697 + 1.59469i
$$303$$ 0 0
$$304$$ −4.00000 −0.229416
$$305$$ −10.0000 + 17.3205i −0.572598 + 0.991769i
$$306$$ 0 0
$$307$$ −17.0000 −0.970241 −0.485121 0.874447i $$-0.661224\pi$$
−0.485121 + 0.874447i $$0.661224\pi$$
$$308$$ 8.00000 6.92820i 0.455842 0.394771i
$$309$$ 0 0
$$310$$ −36.0000 −2.04466
$$311$$ −3.00000 5.19615i −0.170114 0.294647i 0.768345 0.640036i $$-0.221080\pi$$
−0.938460 + 0.345389i $$0.887747\pi$$
$$312$$ 0 0
$$313$$ 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i $$-0.824336\pi$$
0.879810 + 0.475325i $$0.157669\pi$$
$$314$$ 28.0000 1.58013
$$315$$ 0 0
$$316$$ −2.00000 −0.112509
$$317$$ 12.0000 20.7846i 0.673987 1.16738i −0.302777 0.953062i $$-0.597914\pi$$
0.976764 0.214318i $$-0.0687530\pi$$
$$318$$ 0 0
$$319$$ 4.00000 + 6.92820i 0.223957 + 0.387905i
$$320$$ −16.0000 −0.894427
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0.500000 0.866025i 0.0277350 0.0480384i
$$326$$ −8.00000 −0.443079
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −15.0000 5.19615i −0.826977 0.286473i
$$330$$ 0 0
$$331$$ 12.5000 21.6506i 0.687062 1.19003i −0.285722 0.958313i $$-0.592233\pi$$
0.972784 0.231714i $$-0.0744333\pi$$
$$332$$ 6.00000 10.3923i 0.329293 0.570352i
$$333$$ 0 0
$$334$$ 14.0000 + 24.2487i 0.766046 + 1.32683i
$$335$$ 5.00000 + 8.66025i 0.273179 + 0.473160i
$$336$$ 0 0
$$337$$ −6.50000 + 11.2583i −0.354078 + 0.613280i −0.986960 0.160968i $$-0.948538\pi$$
0.632882 + 0.774248i $$0.281872\pi$$
$$338$$ 24.0000 1.30543
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −9.00000 15.5885i −0.487377 0.844162i
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ −8.00000 13.8564i −0.430083 0.744925i
$$347$$ 16.0000 + 27.7128i 0.858925 + 1.48770i 0.872955 + 0.487800i $$0.162201\pi$$
−0.0140303 + 0.999902i $$0.504466\pi$$
$$348$$ 0 0
$$349$$ 7.00000 + 12.1244i 0.374701 + 0.649002i 0.990282 0.139072i $$-0.0444119\pi$$
−0.615581 + 0.788074i $$0.711079\pi$$
$$350$$ −5.00000 1.73205i −0.267261 0.0925820i
$$351$$ 0 0
$$352$$ −8.00000 13.8564i −0.426401 0.738549i
$$353$$ −34.0000 −1.80964 −0.904819 0.425797i $$-0.859994\pi$$
−0.904819 + 0.425797i $$0.859994\pi$$
$$354$$ 0 0
$$355$$ 12.0000 0.636894
$$356$$ 16.0000 27.7128i 0.847998 1.46878i
$$357$$ 0 0
$$358$$ −2.00000 3.46410i −0.105703 0.183083i
$$359$$ 10.0000 + 17.3205i 0.527780 + 0.914141i 0.999476 + 0.0323801i $$0.0103087\pi$$
−0.471696 + 0.881761i $$0.656358\pi$$
$$360$$ 0 0
$$361$$ 9.00000 15.5885i 0.473684 0.820445i
$$362$$ 13.0000 22.5167i 0.683265 1.18345i
$$363$$ 0 0
$$364$$ 1.00000 + 5.19615i 0.0524142 + 0.272352i
$$365$$ 3.00000 5.19615i 0.157027 0.271979i
$$366$$ 0 0
$$367$$ −9.00000 −0.469796 −0.234898 0.972020i $$-0.575476\pi$$
−0.234898 + 0.972020i $$0.575476\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ −12.0000 −0.623850
$$371$$ 30.0000 + 10.3923i 1.55752 + 0.539542i
$$372$$ 0 0
$$373$$ 23.0000 1.19089 0.595447 0.803394i $$-0.296975\pi$$
0.595447 + 0.803394i $$0.296975\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4.00000 −0.206010
$$378$$ 0 0
$$379$$ 3.00000 0.154100 0.0770498 0.997027i $$-0.475450\pi$$
0.0770498 + 0.997027i $$0.475450\pi$$
$$380$$ −2.00000 + 3.46410i −0.102598 + 0.177705i
$$381$$ 0 0
$$382$$ −10.0000 17.3205i −0.511645 0.886194i
$$383$$ 12.0000 0.613171 0.306586 0.951843i $$-0.400813\pi$$
0.306586 + 0.951843i $$0.400813\pi$$
$$384$$ 0 0
$$385$$ 2.00000 + 10.3923i 0.101929 + 0.529641i
$$386$$ −22.0000 −1.11977
$$387$$ 0 0
$$388$$ 6.00000 10.3923i 0.304604 0.527589i
$$389$$ 6.00000 0.304212 0.152106 0.988364i $$-0.451394\pi$$
0.152106 + 0.988364i $$0.451394\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −16.0000 + 27.7128i −0.806068 + 1.39615i
$$395$$ 1.00000 1.73205i 0.0503155 0.0871489i
$$396$$ 0 0
$$397$$ 4.50000 + 7.79423i 0.225849 + 0.391181i 0.956574 0.291491i $$-0.0941512\pi$$
−0.730725 + 0.682672i $$0.760818\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ −2.00000 + 3.46410i −0.100000 + 0.173205i
$$401$$ 36.0000 1.79775 0.898877 0.438201i $$-0.144384\pi$$
0.898877 + 0.438201i $$0.144384\pi$$
$$402$$ 0 0
$$403$$ 9.00000 0.448322
$$404$$ 2.00000 + 3.46410i 0.0995037 + 0.172345i
$$405$$ 0 0
$$406$$ 4.00000 + 20.7846i 0.198517 + 1.03152i
$$407$$ −3.00000 5.19615i −0.148704 0.257564i
$$408$$ 0 0
$$409$$ −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i $$-0.206116\pi$$
−0.921192 + 0.389109i $$0.872783\pi$$
$$410$$ 20.0000 + 34.6410i 0.987730 + 1.71080i
$$411$$ 0 0
$$412$$ 7.00000 + 12.1244i 0.344865 + 0.597324i
$$413$$ 24.0000 20.7846i 1.18096 1.02274i
$$414$$ 0 0
$$415$$ 6.00000 + 10.3923i 0.294528 + 0.510138i
$$416$$ 8.00000 0.392232
$$417$$ 0 0
$$418$$ −4.00000 −0.195646
$$419$$ 15.0000 25.9808i 0.732798 1.26924i −0.222885 0.974845i $$-0.571547\pi$$
0.955683 0.294398i $$-0.0951193\pi$$
$$420$$ 0 0
$$421$$ 3.50000 + 6.06218i 0.170580 + 0.295452i 0.938623 0.344946i $$-0.112103\pi$$
−0.768043 + 0.640398i $$0.778769\pi$$
$$422$$ 4.00000 + 6.92820i 0.194717 + 0.337260i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −25.0000 8.66025i −1.20983 0.419099i
$$428$$ −8.00000 + 13.8564i −0.386695 + 0.669775i
$$429$$ 0 0
$$430$$ −20.0000 −0.964486
$$431$$ −9.00000 + 15.5885i −0.433515 + 0.750870i −0.997173 0.0751385i $$-0.976060\pi$$
0.563658 + 0.826008i $$0.309393\pi$$
$$432$$ 0 0
$$433$$ 31.0000 1.48976 0.744882 0.667196i $$-0.232506\pi$$
0.744882 + 0.667196i $$0.232506\pi$$
$$434$$ −9.00000 46.7654i −0.432014 2.24481i
$$435$$ 0 0
$$436$$ 18.0000 0.862044
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i $$-0.741317\pi$$
0.972626 + 0.232377i $$0.0746503\pi$$
$$444$$ 0 0
$$445$$ 16.0000 + 27.7128i 0.758473 + 1.31371i
$$446$$ −32.0000 −1.51524
$$447$$ 0 0
$$448$$ −4.00000 20.7846i −0.188982 0.981981i
$$449$$ 18.0000 0.849473 0.424736 0.905317i $$-0.360367\pi$$
0.424736 + 0.905317i $$0.360367\pi$$
$$450$$ 0 0
$$451$$ −10.0000 + 17.3205i −0.470882 + 0.815591i
$$452$$ −20.0000 −0.940721
$$453$$ 0 0
$$454$$ −18.0000 + 31.1769i −0.844782 + 1.46321i
$$455$$ −5.00000 1.73205i −0.234404 0.0811998i
$$456$$ 0 0
$$457$$ 5.50000 9.52628i 0.257279 0.445621i −0.708233 0.705979i $$-0.750507\pi$$
0.965512 + 0.260358i $$0.0838407\pi$$
$$458$$ −19.0000 + 32.9090i −0.887812 + 1.53773i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 10.0000 + 17.3205i 0.465746 + 0.806696i 0.999235 0.0391109i $$-0.0124526\pi$$
−0.533488 + 0.845807i $$0.679119\pi$$
$$462$$ 0 0
$$463$$ 8.50000 14.7224i 0.395029 0.684209i −0.598076 0.801439i $$-0.704068\pi$$
0.993105 + 0.117230i $$0.0374014\pi$$
$$464$$ 16.0000 0.742781
$$465$$ 0 0
$$466$$ 12.0000 0.555889
$$467$$ 3.00000 + 5.19615i 0.138823 + 0.240449i 0.927052 0.374934i $$-0.122335\pi$$
−0.788228 + 0.615383i $$0.789001\pi$$
$$468$$ 0 0
$$469$$ −10.0000 + 8.66025i −0.461757 + 0.399893i
$$470$$ 12.0000 + 20.7846i 0.553519 + 0.958723i
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −5.00000 8.66025i −0.229900 0.398199i
$$474$$ 0 0
$$475$$ 0.500000 + 0.866025i 0.0229416 + 0.0397360i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −6.00000 10.3923i −0.274434 0.475333i
$$479$$ 28.0000 1.27935 0.639676 0.768644i $$-0.279068\pi$$
0.639676 + 0.768644i $$0.279068\pi$$
$$480$$ 0 0
$$481$$ 3.00000 0.136788
$$482$$ 14.0000 24.2487i 0.637683 1.10450i
$$483$$ 0 0
$$484$$ 7.00000 + 12.1244i 0.318182 + 0.551107i
$$485$$ 6.00000 + 10.3923i 0.272446 + 0.471890i
$$486$$ 0 0
$$487$$ −15.5000 + 26.8468i −0.702372 + 1.21654i 0.265260 + 0.964177i $$0.414542\pi$$
−0.967632 + 0.252367i $$0.918791\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ −4.00000 + 27.7128i −0.180702 + 1.25194i
$$491$$ −14.0000 + 24.2487i −0.631811 + 1.09433i 0.355370 + 0.934726i $$0.384355\pi$$
−0.987181 + 0.159603i $$0.948978\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 1.00000 1.73205i 0.0449921 0.0779287i
$$495$$ 0 0
$$496$$ −36.0000 −1.61645
$$497$$ 3.00000 + 15.5885i 0.134568 + 0.699238i
$$498$$ 0 0
$$499$$ 37.0000 1.65635 0.828174 0.560471i $$-0.189380\pi$$
0.828174 + 0.560471i $$0.189380\pi$$
$$500$$ 12.0000 + 20.7846i 0.536656 + 0.929516i
$$501$$ 0 0
$$502$$ 8.00000 13.8564i 0.357057 0.618442i
$$503$$ 42.0000 1.87269 0.936344 0.351085i $$-0.114187\pi$$
0.936344 + 0.351085i $$0.114187\pi$$
$$504$$ 0 0
$$505$$ −4.00000 −0.177998
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 15.0000 + 25.9808i 0.665517 + 1.15271i
$$509$$ −2.00000 −0.0886484 −0.0443242 0.999017i $$-0.514113\pi$$
−0.0443242 + 0.999017i $$0.514113\pi$$
$$510$$ 0 0
$$511$$ 7.50000 + 2.59808i 0.331780 + 0.114932i
$$512$$ −32.0000 −1.41421
$$513$$ 0 0
$$514$$ −26.0000 + 45.0333i −1.14681 + 1.98633i
$$515$$ −14.0000 −0.616914
$$516$$ 0 0
$$517$$ −6.00000 + 10.3923i −0.263880 + 0.457053i
$$518$$ −3.00000 15.5885i −0.131812 0.684917i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 6.00000 10.3923i 0.262865 0.455295i −0.704137 0.710064i $$-0.748666\pi$$
0.967002 + 0.254769i $$0.0819994\pi$$
$$522$$ 0 0
$$523$$ −15.5000 26.8468i −0.677768 1.17393i −0.975652 0.219326i $$-0.929614\pi$$
0.297884 0.954602i $$-0.403719\pi$$
$$524$$ −14.0000 24.2487i −0.611593 1.05931i
$$525$$ 0 0
$$526$$ −4.00000 + 6.92820i −0.174408 + 0.302084i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −23.0000 −1.00000
$$530$$ −24.0000 41.5692i −1.04249 1.80565i
$$531$$ 0 0
$$532$$ −5.00000 1.73205i −0.216777 0.0750939i
$$533$$ −5.00000 8.66025i −0.216574 0.375117i
$$534$$ 0 0
$$535$$ −8.00000 13.8564i −0.345870 0.599065i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −6.00000 10.3923i −0.258678 0.448044i
$$539$$ −13.0000 + 5.19615i −0.559950 + 0.223814i
$$540$$ 0 0
$$541$$ 9.50000 + 16.4545i 0.408437 + 0.707433i 0.994715 0.102677i $$-0.0327407\pi$$
−0.586278 + 0.810110i $$0.699407\pi$$
$$542$$ −32.0000 −1.37452
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −9.00000 + 15.5885i −0.385518 + 0.667736i
$$546$$ 0 0
$$547$$ −14.0000 24.2487i −0.598597 1.03680i −0.993028 0.117875i $$-0.962392\pi$$
0.394432 0.918925i $$-0.370941\pi$$
$$548$$ −12.0000 20.7846i −0.512615 0.887875i
$$549$$ 0 0
$$550$$ −2.00000 + 3.46410i −0.0852803 + 0.147710i
$$551$$ 2.00000 3.46410i 0.0852029 0.147576i
$$552$$ 0 0
$$553$$ 2.50000 + 0.866025i 0.106311 + 0.0368271i
$$554$$ 13.0000 22.5167i 0.552317 0.956641i
$$555$$ 0 0
$$556$$ −6.00000 −0.254457
$$557$$ −1.00000 + 1.73205i −0.0423714 + 0.0733893i −0.886433 0.462856i $$-0.846825\pi$$
0.844062 + 0.536246i $$0.180158\pi$$
$$558$$ 0 0
$$559$$ 5.00000 0.211477
$$560$$ 20.0000 + 6.92820i 0.845154 + 0.292770i
$$561$$ 0 0
$$562$$ −8.00000 −0.337460
$$563$$ −13.0000 22.5167i −0.547885 0.948964i −0.998419 0.0562051i $$-0.982100\pi$$
0.450535 0.892759i $$-0.351233\pi$$
$$564$$ 0 0
$$565$$ 10.0000 17.3205i 0.420703 0.728679i
$$566$$ 22.0000 0.924729
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −13.0000 + 22.5167i −0.544988 + 0.943948i 0.453619 + 0.891196i $$0.350133\pi$$
−0.998608 + 0.0527519i $$0.983201\pi$$
$$570$$ 0 0
$$571$$ 9.50000 + 16.4545i 0.397563 + 0.688599i 0.993425 0.114488i $$-0.0365228\pi$$
−0.595862 + 0.803087i $$0.703189\pi$$
$$572$$ 4.00000 0.167248
$$573$$ 0 0
$$574$$ −40.0000 + 34.6410i −1.66957 + 1.44589i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 8.50000 14.7224i 0.353860 0.612903i −0.633062 0.774101i $$-0.718202\pi$$
0.986922 + 0.161198i $$0.0515357\pi$$
$$578$$ 34.0000 1.41421
$$579$$ 0 0
$$580$$ 8.00000 13.8564i 0.332182 0.575356i
$$581$$ −12.0000 + 10.3923i −0.497844 + 0.431145i
$$582$$ 0 0
$$583$$ 12.0000 20.7846i 0.496989 0.860811i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ −8.00000 13.8564i −0.330477 0.572403i
$$587$$ 8.00000 + 13.8564i 0.330195 + 0.571915i 0.982550 0.185999i $$-0.0595520\pi$$
−0.652355 + 0.757914i $$0.726219\pi$$
$$588$$ 0 0
$$589$$ −4.50000 + 7.79423i −0.185419 + 0.321156i
$$590$$ −48.0000 −1.97613
$$591$$ 0 0
$$592$$ −12.0000 −0.493197
$$593$$ −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i $$-0.205981\pi$$
−0.921026 + 0.389501i $$0.872647\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −12.0000 20.7846i −0.491539 0.851371i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 6.00000 + 10.3923i 0.245153 + 0.424618i 0.962175 0.272433i $$-0.0878284\pi$$
−0.717021 + 0.697051i $$0.754495\pi$$
$$600$$ 0 0
$$601$$ 4.50000 + 7.79423i 0.183559 + 0.317933i 0.943090 0.332538i $$-0.107905\pi$$
−0.759531 + 0.650471i $$0.774572\pi$$
$$602$$ −5.00000 25.9808i −0.203785 1.05890i
$$603$$ 0 0
$$604$$ 16.0000 + 27.7128i 0.651031 + 1.12762i
$$605$$ −14.0000 −0.569181
$$606$$ 0 0
$$607$$ 23.0000 0.933541 0.466771 0.884378i $$-0.345417\pi$$
0.466771 + 0.884378i $$0.345417\pi$$
$$608$$ −4.00000 + 6.92820i −0.162221 + 0.280976i
$$609$$ 0 0
$$610$$ 20.0000 + 34.6410i 0.809776 + 1.40257i
$$611$$ −3.00000 5.19615i −0.121367 0.210214i
$$612$$ 0 0
$$613$$ −17.0000 + 29.4449i −0.686624 + 1.18927i 0.286300 + 0.958140i $$0.407575\pi$$
−0.972924 + 0.231127i $$0.925759\pi$$
$$614$$ −17.0000 + 29.4449i −0.686064 + 1.18830i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −3.00000 + 5.19615i −0.120775 + 0.209189i −0.920074 0.391745i $$-0.871871\pi$$
0.799298 + 0.600935i $$0.205205\pi$$
$$618$$ 0 0
$$619$$ −29.0000 −1.16561 −0.582804 0.812613i $$-0.698045\pi$$
−0.582804 + 0.812613i $$0.698045\pi$$
$$620$$ −18.0000 + 31.1769i −0.722897 + 1.25210i
$$621$$ 0 0
$$622$$ −12.0000 −0.481156
$$623$$ −32.0000 + 27.7128i −1.28205 + 1.11029i
$$624$$ 0 0
$$625$$ −19.0000 −0.760000
$$626$$ −1.00000 1.73205i −0.0399680 0.0692267i
$$627$$ 0 0
$$628$$ 14.0000 24.2487i 0.558661 0.967629i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 8.00000 0.318475 0.159237 0.987240i $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −24.0000 41.5692i −0.953162 1.65092i
$$635$$ −30.0000 −1.19051
$$636$$ 0 0
$$637$$ 1.00000 6.92820i 0.0396214 0.274505i
$$638$$ 16.0000 0.633446
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$642$$ 0 0
$$643$$ 9.50000 16.4545i 0.374643 0.648901i −0.615630 0.788035i $$-0.711098\pi$$
0.990274 + 0.139134i $$0.0444318\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.00000 1.73205i 0.0393141 0.0680939i −0.845699 0.533660i $$-0.820816\pi$$
0.885013 + 0.465566i $$0.154149\pi$$
$$648$$ 0 0
$$649$$ −12.0000 20.7846i −0.471041 0.815867i
$$650$$ −1.00000 1.73205i −0.0392232 0.0679366i
$$651$$ 0 0
$$652$$ −4.00000 + 6.92820i −0.156652 + 0.271329i
$$653$$ −18.0000 −0.704394 −0.352197 0.935926i $$-0.614565\pi$$
−0.352197 + 0.935926i $$0.614565\pi$$
$$654$$ 0 0
$$655$$ 28.0000 1.09405
$$656$$ 20.0000 + 34.6410i 0.780869 + 1.35250i
$$657$$ 0 0
$$658$$ −24.0000 + 20.7846i −0.935617 + 0.810268i
$$659$$ 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i $$0.0806766\pi$$
−0.266872 + 0.963732i $$0.585990\pi$$
$$660$$ 0 0
$$661$$ 20.5000 + 35.5070i 0.797358 + 1.38106i 0.921331 + 0.388778i $$0.127103\pi$$
−0.123974 + 0.992286i $$0.539564\pi$$
$$662$$ −25.0000 43.3013i −0.971653 1.68295i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 4.00000 3.46410i 0.155113 0.134332i
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 28.0000 1.08335
$$669$$ 0 0
$$670$$ 20.0000 0.772667
$$671$$ −10.0000 + 17.3205i −0.386046 + 0.668651i
$$672$$ 0 0
$$673$$ 20.5000 + 35.5070i 0.790217 + 1.36870i 0.925832 + 0.377934i $$0.123365\pi$$
−0.135615 + 0.990762i $$0.543301\pi$$
$$674$$ 13.0000 + 22.5167i 0.500741 + 0.867309i
$$675$$ 0 0
$$676$$ 12.0000 20.7846i 0.461538 0.799408i
$$677$$ 6.00000 10.3923i 0.230599 0.399409i −0.727386 0.686229i $$-0.759265\pi$$
0.957984 + 0.286820i $$0.0925982\pi$$
$$678$$ 0 0
$$679$$ −12.0000 + 10.3923i −0.460518 + 0.398820i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −36.0000 −1.37851
$$683$$ −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i $$-0.907070\pi$$
0.728101 + 0.685470i $$0.240403\pi$$
$$684$$ 0 0
$$685$$ 24.0000 0.916993
$$686$$ −37.0000 + 1.73205i −1.41267 + 0.0661300i
$$687$$ 0 0
$$688$$ −20.0000 −0.762493
$$689$$ 6.00000 + 10.3923i 0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ 18.5000 32.0429i 0.703773 1.21897i −0.263359 0.964698i $$-0.584830\pi$$
0.967132 0.254273i $$-0.0818362\pi$$
$$692$$ −16.0000 −0.608229
$$693$$ 0 0
$$694$$ 64.0000 2.42941
$$695$$ 3.00000 5.19615i 0.113796 0.197101i
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 28.0000 1.05982
$$699$$ 0 0
$$700$$ −4.00000 + 3.46410i −0.151186 + 0.130931i
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ −1.50000 + 2.59808i −0.0565736 + 0.0979883i
$$704$$ −16.0000 −0.603023
$$705$$ 0 0
$$706$$ −34.0000 + 58.8897i −1.27961 + 2.21634i
$$707$$ −1.00000 5.19615i −0.0376089 0.195421i
$$708$$ 0 0
$$709$$ −15.0000 + 25.9808i −0.563337 + 0.975728i 0.433865 + 0.900978i $$0.357149\pi$$
−0.997202 + 0.0747503i $$0.976184\pi$$
$$710$$ 12.0000 20.7846i 0.450352 0.780033i
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −2.00000 + 3.46410i −0.0747958 + 0.129550i
$$716$$ −4.00000 −0.149487
$$717$$ 0 0
$$718$$ 40.0000 1.49279
$$719$$ −9.00000 15.5885i −0.335643 0.581351i 0.647965 0.761670i $$-0.275620\pi$$
−0.983608 + 0.180319i $$0.942287\pi$$
$$720$$ 0 0
$$721$$ −3.50000 18.1865i −0.130347 0.677302i
$$722$$ −18.0000 31.1769i −0.669891 1.16028i
$$723$$ 0 0
$$724$$ −13.0000 22.5167i −0.483141 0.836825i
$$725$$ −2.00000 3.46410i −0.0742781 0.128654i
$$726$$ 0 0
$$727$$ 6.50000 + 11.2583i 0.241072 + 0.417548i 0.961020 0.276479i $$-0.0891678\pi$$
−0.719948 + 0.694028i $$0.755834\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −6.00000 10.3923i −0.222070 0.384636i
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −15.0000 −0.554038 −0.277019 0.960864i $$-0.589346\pi$$
−0.277019 + 0.960864i $$0.589346\pi$$
$$734$$ −9.00000 + 15.5885i −0.332196 + 0.575380i
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 5.00000 + 8.66025i 0.184177 + 0.319005i
$$738$$ 0 0
$$739$$ 7.50000 12.9904i 0.275892 0.477859i −0.694468 0.719524i $$-0.744360\pi$$
0.970360 + 0.241665i $$0.0776935\pi$$
$$740$$ −6.00000 + 10.3923i −0.220564 + 0.382029i
$$741$$ 0 0
$$742$$ 48.0000 41.5692i 1.76214 1.52605i
$$743$$ 21.0000 36.3731i 0.770415 1.33440i −0.166920 0.985970i $$-0.553382\pi$$
0.937336 0.348428i $$-0.113284\pi$$
$$744$$ 0 0
$$745$$ 24.0000 0.879292
$$746$$ 23.0000 39.8372i 0.842090 1.45854i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 16.0000 13.8564i 0.584627 0.506302i
$$750$$ 0 0
$$751$$ 13.0000 0.474377 0.237188 0.971464i $$-0.423774\pi$$
0.237188 + 0.971464i $$0.423774\pi$$
$$752$$ 12.0000 + 20.7846i 0.437595 + 0.757937i
$$753$$ 0 0
$$754$$ −4.00000 + 6.92820i −0.145671 + 0.252310i
$$755$$ −32.0000 −1.16460
$$756$$ 0 0
$$757$$ −22.0000 −0.799604 −0.399802 0.916602i $$-0.630921\pi$$
−0.399802 + 0.916602i $$0.630921\pi$$
$$758$$ 3.00000 5.19615i 0.108965 0.188733i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 48.0000 1.74000 0.869999 0.493053i $$-0.164119\pi$$
0.869999 + 0.493053i $$0.164119\pi$$
$$762$$ 0 0
$$763$$ −22.5000 7.79423i −0.814555 0.282170i
$$764$$ −20.0000 −0.723575
$$765$$ 0 0
$$766$$ 12.0000 20.7846i 0.433578 0.750978i
$$767$$ 12.0000 0.433295
$$768$$ 0 0
$$769$$ 24.5000 42.4352i 0.883493 1.53025i 0.0360609 0.999350i $$-0.488519\pi$$
0.847432 0.530904i $$-0.178148\pi$$
$$770$$ 20.0000 + 6.92820i 0.720750 + 0.249675i
$$771$$ 0 0
$$772$$ −11.0000 + 19.0526i −0.395899 + 0.685717i
$$773$$ −17.0000 + 29.4449i −0.611448 + 1.05906i 0.379549 + 0.925172i $$0.376079\pi$$
−0.990997 + 0.133887i $$0.957254\pi$$
$$774$$ 0 0
$$775$$ 4.50000 + 7.79423i 0.161645 + 0.279977i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 6.00000 10.3923i 0.215110 0.372582i
$$779$$ 10.0000 0.358287
$$780$$ 0 0
$$781$$ 12.0000 0.429394
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −4.00000 + 27.7128i −0.142857 + 0.989743i
$$785$$ 14.0000 + 24.2487i 0.499681 + 0.865474i
$$786$$ 0 0
$$787$$ −20.0000 34.6410i −0.712923 1.23482i −0.963755 0.266788i $$-0.914038\pi$$
0.250832 0.968031i $$-0.419296\pi$$
$$788$$ 16.0000 + 27.7128i 0.569976 + 0.987228i
$$789$$ 0 0
$$790$$ −2.00000 3.46410i −0.0711568 0.123247i
$$791$$ 25.0000 + 8.66025i 0.888898 + 0.307923i
$$792$$ 0 0
$$793$$ −5.00000 8.66025i −0.177555 0.307535i
$$794$$ 18.0000