# Properties

 Label 567.2.f.b.190.1 Level $567$ Weight $2$ Character 567.190 Analytic conductor $4.528$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 567.f (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: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 21) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 190.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 567.190 Dual form 567.2.f.b.379.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +2.00000 q^{10} +(2.00000 + 3.46410i) q^{11} +(1.00000 - 1.73205i) q^{13} +(0.500000 - 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +6.00000 q^{17} +4.00000 q^{19} +(1.00000 + 1.73205i) q^{20} +(2.00000 - 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{25} -2.00000 q^{26} +1.00000 q^{28} +(-1.00000 - 1.73205i) q^{29} +(-2.50000 + 4.33013i) q^{32} +(-3.00000 - 5.19615i) q^{34} -2.00000 q^{35} +6.00000 q^{37} +(-2.00000 - 3.46410i) q^{38} +(3.00000 - 5.19615i) q^{40} +(1.00000 - 1.73205i) q^{41} +(2.00000 + 3.46410i) q^{43} +4.00000 q^{44} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-1.00000 - 1.73205i) q^{52} -6.00000 q^{53} -8.00000 q^{55} +(-1.50000 - 2.59808i) q^{56} +(-1.00000 + 1.73205i) q^{58} +(6.00000 - 10.3923i) q^{59} +(1.00000 + 1.73205i) q^{61} +7.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{68} +(1.00000 + 1.73205i) q^{70} -6.00000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-2.00000 + 3.46410i) q^{77} +(8.00000 + 13.8564i) q^{79} -2.00000 q^{80} -2.00000 q^{82} +(-6.00000 - 10.3923i) q^{83} +(-6.00000 + 10.3923i) q^{85} +(2.00000 - 3.46410i) q^{86} +(-6.00000 - 10.3923i) q^{88} +14.0000 q^{89} +2.00000 q^{91} +(-4.00000 + 6.92820i) q^{95} +(-9.00000 - 15.5885i) q^{97} +1.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} + q^{4} - 2q^{5} + q^{7} - 6q^{8} + O(q^{10})$$ $$2q - q^{2} + q^{4} - 2q^{5} + q^{7} - 6q^{8} + 4q^{10} + 4q^{11} + 2q^{13} + q^{14} + q^{16} + 12q^{17} + 8q^{19} + 2q^{20} + 4q^{22} + q^{25} - 4q^{26} + 2q^{28} - 2q^{29} - 5q^{32} - 6q^{34} - 4q^{35} + 12q^{37} - 4q^{38} + 6q^{40} + 2q^{41} + 4q^{43} + 8q^{44} - q^{49} + q^{50} - 2q^{52} - 12q^{53} - 16q^{55} - 3q^{56} - 2q^{58} + 12q^{59} + 2q^{61} + 14q^{64} + 4q^{65} - 4q^{67} + 6q^{68} + 2q^{70} - 12q^{73} - 6q^{74} + 4q^{76} - 4q^{77} + 16q^{79} - 4q^{80} - 4q^{82} - 12q^{83} - 12q^{85} + 4q^{86} - 12q^{88} + 28q^{89} + 4q^{91} - 8q^{95} - 18q^{97} + 2q^{98} + O(q^{100})$$

## Character values

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

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

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 0.866025i −0.353553 0.612372i 0.633316 0.773893i $$-0.281693\pi$$
−0.986869 + 0.161521i $$0.948360\pi$$
$$3$$ 0 0
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i $$-0.980917\pi$$
0.550990 + 0.834512i $$0.314250\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 0.866025i 0.188982 + 0.327327i
$$8$$ −3.00000 −1.06066
$$9$$ 0 0
$$10$$ 2.00000 0.632456
$$11$$ 2.00000 + 3.46410i 0.603023 + 1.04447i 0.992361 + 0.123371i $$0.0393705\pi$$
−0.389338 + 0.921095i $$0.627296\pi$$
$$12$$ 0 0
$$13$$ 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i $$-0.743877\pi$$
0.970725 + 0.240192i $$0.0772105\pi$$
$$14$$ 0.500000 0.866025i 0.133631 0.231455i
$$15$$ 0 0
$$16$$ 0.500000 + 0.866025i 0.125000 + 0.216506i
$$17$$ 6.00000 1.45521 0.727607 0.685994i $$-0.240633\pi$$
0.727607 + 0.685994i $$0.240633\pi$$
$$18$$ 0 0
$$19$$ 4.00000 0.917663 0.458831 0.888523i $$-0.348268\pi$$
0.458831 + 0.888523i $$0.348268\pi$$
$$20$$ 1.00000 + 1.73205i 0.223607 + 0.387298i
$$21$$ 0 0
$$22$$ 2.00000 3.46410i 0.426401 0.738549i
$$23$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ 0 0
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ −2.00000 −0.392232
$$27$$ 0 0
$$28$$ 1.00000 0.188982
$$29$$ −1.00000 1.73205i −0.185695 0.321634i 0.758115 0.652121i $$-0.226120\pi$$
−0.943811 + 0.330487i $$0.892787\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$32$$ −2.50000 + 4.33013i −0.441942 + 0.765466i
$$33$$ 0 0
$$34$$ −3.00000 5.19615i −0.514496 0.891133i
$$35$$ −2.00000 −0.338062
$$36$$ 0 0
$$37$$ 6.00000 0.986394 0.493197 0.869918i $$-0.335828\pi$$
0.493197 + 0.869918i $$0.335828\pi$$
$$38$$ −2.00000 3.46410i −0.324443 0.561951i
$$39$$ 0 0
$$40$$ 3.00000 5.19615i 0.474342 0.821584i
$$41$$ 1.00000 1.73205i 0.156174 0.270501i −0.777312 0.629115i $$-0.783417\pi$$
0.933486 + 0.358614i $$0.116751\pi$$
$$42$$ 0 0
$$43$$ 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i $$-0.0680112\pi$$
−0.672264 + 0.740312i $$0.734678\pi$$
$$44$$ 4.00000 0.603023
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$48$$ 0 0
$$49$$ −0.500000 + 0.866025i −0.0714286 + 0.123718i
$$50$$ 0.500000 0.866025i 0.0707107 0.122474i
$$51$$ 0 0
$$52$$ −1.00000 1.73205i −0.138675 0.240192i
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ 0 0
$$55$$ −8.00000 −1.07872
$$56$$ −1.50000 2.59808i −0.200446 0.347183i
$$57$$ 0 0
$$58$$ −1.00000 + 1.73205i −0.131306 + 0.227429i
$$59$$ 6.00000 10.3923i 0.781133 1.35296i −0.150148 0.988663i $$-0.547975\pi$$
0.931282 0.364299i $$-0.118692\pi$$
$$60$$ 0 0
$$61$$ 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i $$-0.125799\pi$$
−0.794879 + 0.606768i $$0.792466\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ 2.00000 + 3.46410i 0.248069 + 0.429669i
$$66$$ 0 0
$$67$$ −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i $$-0.911904\pi$$
0.717607 + 0.696449i $$0.245238\pi$$
$$68$$ 3.00000 5.19615i 0.363803 0.630126i
$$69$$ 0 0
$$70$$ 1.00000 + 1.73205i 0.119523 + 0.207020i
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ −6.00000 −0.702247 −0.351123 0.936329i $$-0.614200\pi$$
−0.351123 + 0.936329i $$0.614200\pi$$
$$74$$ −3.00000 5.19615i −0.348743 0.604040i
$$75$$ 0 0
$$76$$ 2.00000 3.46410i 0.229416 0.397360i
$$77$$ −2.00000 + 3.46410i −0.227921 + 0.394771i
$$78$$ 0 0
$$79$$ 8.00000 + 13.8564i 0.900070 + 1.55897i 0.827401 + 0.561611i $$0.189818\pi$$
0.0726692 + 0.997356i $$0.476848\pi$$
$$80$$ −2.00000 −0.223607
$$81$$ 0 0
$$82$$ −2.00000 −0.220863
$$83$$ −6.00000 10.3923i −0.658586 1.14070i −0.980982 0.194099i $$-0.937822\pi$$
0.322396 0.946605i $$-0.395512\pi$$
$$84$$ 0 0
$$85$$ −6.00000 + 10.3923i −0.650791 + 1.12720i
$$86$$ 2.00000 3.46410i 0.215666 0.373544i
$$87$$ 0 0
$$88$$ −6.00000 10.3923i −0.639602 1.10782i
$$89$$ 14.0000 1.48400 0.741999 0.670402i $$-0.233878\pi$$
0.741999 + 0.670402i $$0.233878\pi$$
$$90$$ 0 0
$$91$$ 2.00000 0.209657
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −4.00000 + 6.92820i −0.410391 + 0.710819i
$$96$$ 0 0
$$97$$ −9.00000 15.5885i −0.913812 1.58277i −0.808632 0.588315i $$-0.799792\pi$$
−0.105180 0.994453i $$-0.533542\pi$$
$$98$$ 1.00000 0.101015
$$99$$ 0 0
$$100$$ 1.00000 0.100000
$$101$$ 7.00000 + 12.1244i 0.696526 + 1.20642i 0.969664 + 0.244443i $$0.0786053\pi$$
−0.273138 + 0.961975i $$0.588061\pi$$
$$102$$ 0 0
$$103$$ −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i $$-0.962288\pi$$
0.598858 + 0.800855i $$0.295621\pi$$
$$104$$ −3.00000 + 5.19615i −0.294174 + 0.509525i
$$105$$ 0 0
$$106$$ 3.00000 + 5.19615i 0.291386 + 0.504695i
$$107$$ −4.00000 −0.386695 −0.193347 0.981130i $$-0.561934\pi$$
−0.193347 + 0.981130i $$0.561934\pi$$
$$108$$ 0 0
$$109$$ −18.0000 −1.72409 −0.862044 0.506834i $$-0.830816\pi$$
−0.862044 + 0.506834i $$0.830816\pi$$
$$110$$ 4.00000 + 6.92820i 0.381385 + 0.660578i
$$111$$ 0 0
$$112$$ −0.500000 + 0.866025i −0.0472456 + 0.0818317i
$$113$$ −7.00000 + 12.1244i −0.658505 + 1.14056i 0.322498 + 0.946570i $$0.395477\pi$$
−0.981003 + 0.193993i $$0.937856\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −2.00000 −0.185695
$$117$$ 0 0
$$118$$ −12.0000 −1.10469
$$119$$ 3.00000 + 5.19615i 0.275010 + 0.476331i
$$120$$ 0 0
$$121$$ −2.50000 + 4.33013i −0.227273 + 0.393648i
$$122$$ 1.00000 1.73205i 0.0905357 0.156813i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 1.50000 + 2.59808i 0.132583 + 0.229640i
$$129$$ 0 0
$$130$$ 2.00000 3.46410i 0.175412 0.303822i
$$131$$ 2.00000 3.46410i 0.174741 0.302660i −0.765331 0.643637i $$-0.777425\pi$$
0.940072 + 0.340977i $$0.110758\pi$$
$$132$$ 0 0
$$133$$ 2.00000 + 3.46410i 0.173422 + 0.300376i
$$134$$ 4.00000 0.345547
$$135$$ 0 0
$$136$$ −18.0000 −1.54349
$$137$$ −3.00000 5.19615i −0.256307 0.443937i 0.708942 0.705266i $$-0.249173\pi$$
−0.965250 + 0.261329i $$0.915839\pi$$
$$138$$ 0 0
$$139$$ −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i $$0.336619\pi$$
−0.999947 + 0.0103230i $$0.996714\pi$$
$$140$$ −1.00000 + 1.73205i −0.0845154 + 0.146385i
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 8.00000 0.668994
$$144$$ 0 0
$$145$$ 4.00000 0.332182
$$146$$ 3.00000 + 5.19615i 0.248282 + 0.430037i
$$147$$ 0 0
$$148$$ 3.00000 5.19615i 0.246598 0.427121i
$$149$$ 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i $$-0.754293\pi$$
0.962348 + 0.271821i $$0.0876260\pi$$
$$150$$ 0 0
$$151$$ −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i $$-0.272204\pi$$
−0.981617 + 0.190864i $$0.938871\pi$$
$$152$$ −12.0000 −0.973329
$$153$$ 0 0
$$154$$ 4.00000 0.322329
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 1.00000 1.73205i 0.0798087 0.138233i −0.823359 0.567521i $$-0.807902\pi$$
0.903167 + 0.429289i $$0.141236\pi$$
$$158$$ 8.00000 13.8564i 0.636446 1.10236i
$$159$$ 0 0
$$160$$ −5.00000 8.66025i −0.395285 0.684653i
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 4.00000 0.313304 0.156652 0.987654i $$-0.449930\pi$$
0.156652 + 0.987654i $$0.449930\pi$$
$$164$$ −1.00000 1.73205i −0.0780869 0.135250i
$$165$$ 0 0
$$166$$ −6.00000 + 10.3923i −0.465690 + 0.806599i
$$167$$ −4.00000 + 6.92820i −0.309529 + 0.536120i −0.978259 0.207385i $$-0.933505\pi$$
0.668730 + 0.743505i $$0.266838\pi$$
$$168$$ 0 0
$$169$$ 4.50000 + 7.79423i 0.346154 + 0.599556i
$$170$$ 12.0000 0.920358
$$171$$ 0 0
$$172$$ 4.00000 0.304997
$$173$$ −5.00000 8.66025i −0.380143 0.658427i 0.610939 0.791677i $$-0.290792\pi$$
−0.991082 + 0.133250i $$0.957459\pi$$
$$174$$ 0 0
$$175$$ −0.500000 + 0.866025i −0.0377964 + 0.0654654i
$$176$$ −2.00000 + 3.46410i −0.150756 + 0.261116i
$$177$$ 0 0
$$178$$ −7.00000 12.1244i −0.524672 0.908759i
$$179$$ 4.00000 0.298974 0.149487 0.988764i $$-0.452238\pi$$
0.149487 + 0.988764i $$0.452238\pi$$
$$180$$ 0 0
$$181$$ −26.0000 −1.93256 −0.966282 0.257485i $$-0.917106\pi$$
−0.966282 + 0.257485i $$0.917106\pi$$
$$182$$ −1.00000 1.73205i −0.0741249 0.128388i
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −6.00000 + 10.3923i −0.441129 + 0.764057i
$$186$$ 0 0
$$187$$ 12.0000 + 20.7846i 0.877527 + 1.51992i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 8.00000 0.580381
$$191$$ −4.00000 6.92820i −0.289430 0.501307i 0.684244 0.729253i $$-0.260132\pi$$
−0.973674 + 0.227946i $$0.926799\pi$$
$$192$$ 0 0
$$193$$ −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i $$-0.856266\pi$$
0.827788 + 0.561041i $$0.189599\pi$$
$$194$$ −9.00000 + 15.5885i −0.646162 + 1.11919i
$$195$$ 0 0
$$196$$ 0.500000 + 0.866025i 0.0357143 + 0.0618590i
$$197$$ −22.0000 −1.56744 −0.783718 0.621117i $$-0.786679\pi$$
−0.783718 + 0.621117i $$0.786679\pi$$
$$198$$ 0 0
$$199$$ 24.0000 1.70131 0.850657 0.525720i $$-0.176204\pi$$
0.850657 + 0.525720i $$0.176204\pi$$
$$200$$ −1.50000 2.59808i −0.106066 0.183712i
$$201$$ 0 0
$$202$$ 7.00000 12.1244i 0.492518 0.853067i
$$203$$ 1.00000 1.73205i 0.0701862 0.121566i
$$204$$ 0 0
$$205$$ 2.00000 + 3.46410i 0.139686 + 0.241943i
$$206$$ 8.00000 0.557386
$$207$$ 0 0
$$208$$ 2.00000 0.138675
$$209$$ 8.00000 + 13.8564i 0.553372 + 0.958468i
$$210$$ 0 0
$$211$$ −2.00000 + 3.46410i −0.137686 + 0.238479i −0.926620 0.375999i $$-0.877300\pi$$
0.788935 + 0.614477i $$0.210633\pi$$
$$212$$ −3.00000 + 5.19615i −0.206041 + 0.356873i
$$213$$ 0 0
$$214$$ 2.00000 + 3.46410i 0.136717 + 0.236801i
$$215$$ −8.00000 −0.545595
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 9.00000 + 15.5885i 0.609557 + 1.05578i
$$219$$ 0 0
$$220$$ −4.00000 + 6.92820i −0.269680 + 0.467099i
$$221$$ 6.00000 10.3923i 0.403604 0.699062i
$$222$$ 0 0
$$223$$ −8.00000 13.8564i −0.535720 0.927894i −0.999128 0.0417488i $$-0.986707\pi$$
0.463409 0.886145i $$-0.346626\pi$$
$$224$$ −5.00000 −0.334077
$$225$$ 0 0
$$226$$ 14.0000 0.931266
$$227$$ −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i $$-0.297043\pi$$
−0.993508 + 0.113761i $$0.963710\pi$$
$$228$$ 0 0
$$229$$ 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i $$-0.726147\pi$$
0.982592 + 0.185776i $$0.0594799\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 3.00000 + 5.19615i 0.196960 + 0.341144i
$$233$$ 6.00000 0.393073 0.196537 0.980497i $$-0.437031\pi$$
0.196537 + 0.980497i $$0.437031\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −6.00000 10.3923i −0.390567 0.676481i
$$237$$ 0 0
$$238$$ 3.00000 5.19615i 0.194461 0.336817i
$$239$$ 12.0000 20.7846i 0.776215 1.34444i −0.157893 0.987456i $$-0.550470\pi$$
0.934109 0.356988i $$-0.116196\pi$$
$$240$$ 0 0
$$241$$ −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i $$-0.187185\pi$$
−0.896435 + 0.443176i $$0.853852\pi$$
$$242$$ 5.00000 0.321412
$$243$$ 0 0
$$244$$ 2.00000 0.128037
$$245$$ −1.00000 1.73205i −0.0638877 0.110657i
$$246$$ 0 0
$$247$$ 4.00000 6.92820i 0.254514 0.440831i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 6.00000 + 10.3923i 0.379473 + 0.657267i
$$251$$ 20.0000 1.26239 0.631194 0.775625i $$-0.282565\pi$$
0.631194 + 0.775625i $$0.282565\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 8.50000 14.7224i 0.531250 0.920152i
$$257$$ 13.0000 22.5167i 0.810918 1.40455i −0.101305 0.994855i $$-0.532302\pi$$
0.912222 0.409695i $$-0.134365\pi$$
$$258$$ 0 0
$$259$$ 3.00000 + 5.19615i 0.186411 + 0.322873i
$$260$$ 4.00000 0.248069
$$261$$ 0 0
$$262$$ −4.00000 −0.247121
$$263$$ 8.00000 + 13.8564i 0.493301 + 0.854423i 0.999970 0.00771799i $$-0.00245674\pi$$
−0.506669 + 0.862141i $$0.669123\pi$$
$$264$$ 0 0
$$265$$ 6.00000 10.3923i 0.368577 0.638394i
$$266$$ 2.00000 3.46410i 0.122628 0.212398i
$$267$$ 0 0
$$268$$ 2.00000 + 3.46410i 0.122169 + 0.211604i
$$269$$ −6.00000 −0.365826 −0.182913 0.983129i $$-0.558553\pi$$
−0.182913 + 0.983129i $$0.558553\pi$$
$$270$$ 0 0
$$271$$ 16.0000 0.971931 0.485965 0.873978i $$-0.338468\pi$$
0.485965 + 0.873978i $$0.338468\pi$$
$$272$$ 3.00000 + 5.19615i 0.181902 + 0.315063i
$$273$$ 0 0
$$274$$ −3.00000 + 5.19615i −0.181237 + 0.313911i
$$275$$ −2.00000 + 3.46410i −0.120605 + 0.208893i
$$276$$ 0 0
$$277$$ −11.0000 19.0526i −0.660926 1.14476i −0.980373 0.197153i $$-0.936830\pi$$
0.319447 0.947604i $$-0.396503\pi$$
$$278$$ 12.0000 0.719712
$$279$$ 0 0
$$280$$ 6.00000 0.358569
$$281$$ −11.0000 19.0526i −0.656205 1.13658i −0.981590 0.190999i $$-0.938827\pi$$
0.325385 0.945582i $$-0.394506\pi$$
$$282$$ 0 0
$$283$$ 10.0000 17.3205i 0.594438 1.02960i −0.399188 0.916869i $$-0.630708\pi$$
0.993626 0.112728i $$-0.0359589\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ −4.00000 6.92820i −0.236525 0.409673i
$$287$$ 2.00000 0.118056
$$288$$ 0 0
$$289$$ 19.0000 1.11765
$$290$$ −2.00000 3.46410i −0.117444 0.203419i
$$291$$ 0 0
$$292$$ −3.00000 + 5.19615i −0.175562 + 0.304082i
$$293$$ 7.00000 12.1244i 0.408944 0.708312i −0.585827 0.810436i $$-0.699230\pi$$
0.994772 + 0.102123i $$0.0325637\pi$$
$$294$$ 0 0
$$295$$ 12.0000 + 20.7846i 0.698667 + 1.21013i
$$296$$ −18.0000 −1.04623
$$297$$ 0 0
$$298$$ −6.00000 −0.347571
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −2.00000 + 3.46410i −0.115278 + 0.199667i
$$302$$ −4.00000 + 6.92820i −0.230174 + 0.398673i
$$303$$ 0 0
$$304$$ 2.00000 + 3.46410i 0.114708 + 0.198680i
$$305$$ −4.00000 −0.229039
$$306$$ 0 0
$$307$$ 4.00000 0.228292 0.114146 0.993464i $$-0.463587\pi$$
0.114146 + 0.993464i $$0.463587\pi$$
$$308$$ 2.00000 + 3.46410i 0.113961 + 0.197386i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i $$0.404886\pi$$
−0.974841 + 0.222900i $$0.928448\pi$$
$$312$$ 0 0
$$313$$ −13.0000 22.5167i −0.734803 1.27272i −0.954810 0.297218i $$-0.903941\pi$$
0.220006 0.975499i $$-0.429392\pi$$
$$314$$ −2.00000 −0.112867
$$315$$ 0 0
$$316$$ 16.0000 0.900070
$$317$$ −9.00000 15.5885i −0.505490 0.875535i −0.999980 0.00635137i $$-0.997978\pi$$
0.494489 0.869184i $$-0.335355\pi$$
$$318$$ 0 0
$$319$$ 4.00000 6.92820i 0.223957 0.387905i
$$320$$ −7.00000 + 12.1244i −0.391312 + 0.677772i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 24.0000 1.33540
$$324$$ 0 0
$$325$$ 2.00000 0.110940
$$326$$ −2.00000 3.46410i −0.110770 0.191859i
$$327$$ 0 0
$$328$$ −3.00000 + 5.19615i −0.165647 + 0.286910i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i $$-0.131604\pi$$
−0.805812 + 0.592172i $$0.798271\pi$$
$$332$$ −12.0000 −0.658586
$$333$$ 0 0
$$334$$ 8.00000 0.437741
$$335$$ −4.00000 6.92820i −0.218543 0.378528i
$$336$$ 0 0
$$337$$ 7.00000 12.1244i 0.381314 0.660456i −0.609936 0.792451i $$-0.708805\pi$$
0.991250 + 0.131995i $$0.0421382\pi$$
$$338$$ 4.50000 7.79423i 0.244768 0.423950i
$$339$$ 0 0
$$340$$ 6.00000 + 10.3923i 0.325396 + 0.563602i
$$341$$ 0 0
$$342$$ 0 0
$$343$$ −1.00000 −0.0539949
$$344$$ −6.00000 10.3923i −0.323498 0.560316i
$$345$$ 0 0
$$346$$ −5.00000 + 8.66025i −0.268802 + 0.465578i
$$347$$ −14.0000 + 24.2487i −0.751559 + 1.30174i 0.195507 + 0.980702i $$0.437365\pi$$
−0.947067 + 0.321037i $$0.895969\pi$$
$$348$$ 0 0
$$349$$ 1.00000 + 1.73205i 0.0535288 + 0.0927146i 0.891548 0.452926i $$-0.149620\pi$$
−0.838019 + 0.545640i $$0.816286\pi$$
$$350$$ 1.00000 0.0534522
$$351$$ 0 0
$$352$$ −20.0000 −1.06600
$$353$$ 5.00000 + 8.66025i 0.266123 + 0.460939i 0.967857 0.251500i $$-0.0809239\pi$$
−0.701734 + 0.712439i $$0.747591\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 7.00000 12.1244i 0.370999 0.642590i
$$357$$ 0 0
$$358$$ −2.00000 3.46410i −0.105703 0.183083i
$$359$$ −32.0000 −1.68890 −0.844448 0.535638i $$-0.820071\pi$$
−0.844448 + 0.535638i $$0.820071\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 13.0000 + 22.5167i 0.683265 + 1.18345i
$$363$$ 0 0
$$364$$ 1.00000 1.73205i 0.0524142 0.0907841i
$$365$$ 6.00000 10.3923i 0.314054 0.543958i
$$366$$ 0 0
$$367$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 12.0000 0.623850
$$371$$ −3.00000 5.19615i −0.155752 0.269771i
$$372$$ 0 0
$$373$$ 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i $$-0.749977\pi$$
0.965945 + 0.258748i $$0.0833099\pi$$
$$374$$ 12.0000 20.7846i 0.620505 1.07475i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −4.00000 −0.206010
$$378$$ 0 0
$$379$$ 12.0000 0.616399 0.308199 0.951322i $$-0.400274\pi$$
0.308199 + 0.951322i $$0.400274\pi$$
$$380$$ 4.00000 + 6.92820i 0.205196 + 0.355409i
$$381$$ 0 0
$$382$$ −4.00000 + 6.92820i −0.204658 + 0.354478i
$$383$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$384$$ 0 0
$$385$$ −4.00000 6.92820i −0.203859 0.353094i
$$386$$ 2.00000 0.101797
$$387$$ 0 0
$$388$$ −18.0000 −0.913812
$$389$$ 3.00000 + 5.19615i 0.152106 + 0.263455i 0.932002 0.362454i $$-0.118061\pi$$
−0.779895 + 0.625910i $$0.784728\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 1.50000 2.59808i 0.0757614 0.131223i
$$393$$ 0 0
$$394$$ 11.0000 + 19.0526i 0.554172 + 0.959854i
$$395$$ −32.0000 −1.61009
$$396$$ 0 0
$$397$$ −18.0000 −0.903394 −0.451697 0.892171i $$-0.649181\pi$$
−0.451697 + 0.892171i $$0.649181\pi$$
$$398$$ −12.0000 20.7846i −0.601506 1.04184i
$$399$$ 0 0
$$400$$ −0.500000 + 0.866025i −0.0250000 + 0.0433013i
$$401$$ −15.0000 + 25.9808i −0.749064 + 1.29742i 0.199207 + 0.979957i $$0.436163\pi$$
−0.948272 + 0.317460i $$0.897170\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 14.0000 0.696526
$$405$$ 0 0
$$406$$ −2.00000 −0.0992583
$$407$$ 12.0000 + 20.7846i 0.594818 + 1.03025i
$$408$$ 0 0
$$409$$ 11.0000 19.0526i 0.543915 0.942088i −0.454759 0.890614i $$-0.650275\pi$$
0.998674 0.0514740i $$-0.0163919\pi$$
$$410$$ 2.00000 3.46410i 0.0987730 0.171080i
$$411$$ 0 0
$$412$$ 4.00000 + 6.92820i 0.197066 + 0.341328i
$$413$$ 12.0000 0.590481
$$414$$ 0 0
$$415$$ 24.0000 1.17811
$$416$$ 5.00000 + 8.66025i 0.245145 + 0.424604i
$$417$$ 0 0
$$418$$ 8.00000 13.8564i 0.391293 0.677739i
$$419$$ −6.00000 + 10.3923i −0.293119 + 0.507697i −0.974546 0.224189i $$-0.928027\pi$$
0.681426 + 0.731887i $$0.261360\pi$$
$$420$$ 0 0
$$421$$ −19.0000 32.9090i −0.926003 1.60388i −0.789940 0.613185i $$-0.789888\pi$$
−0.136064 0.990700i $$-0.543445\pi$$
$$422$$ 4.00000 0.194717
$$423$$ 0 0
$$424$$ 18.0000 0.874157
$$425$$ 3.00000 + 5.19615i 0.145521 + 0.252050i
$$426$$ 0 0
$$427$$ −1.00000 + 1.73205i −0.0483934 + 0.0838198i
$$428$$ −2.00000 + 3.46410i −0.0966736 + 0.167444i
$$429$$ 0 0
$$430$$ 4.00000 + 6.92820i 0.192897 + 0.334108i
$$431$$ 24.0000 1.15604 0.578020 0.816023i $$-0.303826\pi$$
0.578020 + 0.816023i $$0.303826\pi$$
$$432$$ 0 0
$$433$$ −14.0000 −0.672797 −0.336399 0.941720i $$-0.609209\pi$$
−0.336399 + 0.941720i $$0.609209\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −9.00000 + 15.5885i −0.431022 + 0.746552i
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 12.0000 + 20.7846i 0.572729 + 0.991995i 0.996284 + 0.0861252i $$0.0274485\pi$$
−0.423556 + 0.905870i $$0.639218\pi$$
$$440$$ 24.0000 1.14416
$$441$$ 0 0
$$442$$ −12.0000 −0.570782
$$443$$ 18.0000 + 31.1769i 0.855206 + 1.48126i 0.876454 + 0.481486i $$0.159903\pi$$
−0.0212481 + 0.999774i $$0.506764\pi$$
$$444$$ 0 0
$$445$$ −14.0000 + 24.2487i −0.663664 + 1.14950i
$$446$$ −8.00000 + 13.8564i −0.378811 + 0.656120i
$$447$$ 0 0
$$448$$ 3.50000 + 6.06218i 0.165359 + 0.286411i
$$449$$ 30.0000 1.41579 0.707894 0.706319i $$-0.249646\pi$$
0.707894 + 0.706319i $$0.249646\pi$$
$$450$$ 0 0
$$451$$ 8.00000 0.376705
$$452$$ 7.00000 + 12.1244i 0.329252 + 0.570282i
$$453$$ 0 0
$$454$$ −6.00000 + 10.3923i −0.281594 + 0.487735i
$$455$$ −2.00000 + 3.46410i −0.0937614 + 0.162400i
$$456$$ 0 0
$$457$$ −5.00000 8.66025i −0.233890 0.405110i 0.725059 0.688686i $$-0.241812\pi$$
−0.958950 + 0.283577i $$0.908479\pi$$
$$458$$ −10.0000 −0.467269
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −5.00000 8.66025i −0.232873 0.403348i 0.725779 0.687928i $$-0.241479\pi$$
−0.958652 + 0.284579i $$0.908146\pi$$
$$462$$ 0 0
$$463$$ −8.00000 + 13.8564i −0.371792 + 0.643962i −0.989841 0.142177i $$-0.954590\pi$$
0.618050 + 0.786139i $$0.287923\pi$$
$$464$$ 1.00000 1.73205i 0.0464238 0.0804084i
$$465$$ 0 0
$$466$$ −3.00000 5.19615i −0.138972 0.240707i
$$467$$ −36.0000 −1.66588 −0.832941 0.553362i $$-0.813345\pi$$
−0.832941 + 0.553362i $$0.813345\pi$$
$$468$$ 0 0
$$469$$ −4.00000 −0.184703
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −18.0000 + 31.1769i −0.828517 + 1.43503i
$$473$$ −8.00000 + 13.8564i −0.367840 + 0.637118i
$$474$$ 0 0
$$475$$ 2.00000 + 3.46410i 0.0917663 + 0.158944i
$$476$$ 6.00000 0.275010
$$477$$ 0 0
$$478$$ −24.0000 −1.09773
$$479$$ −8.00000 13.8564i −0.365529 0.633115i 0.623332 0.781958i $$-0.285779\pi$$
−0.988861 + 0.148842i $$0.952445\pi$$
$$480$$ 0 0
$$481$$ 6.00000 10.3923i 0.273576 0.473848i
$$482$$ −1.00000 + 1.73205i −0.0455488 + 0.0788928i
$$483$$ 0 0
$$484$$ 2.50000 + 4.33013i 0.113636 + 0.196824i
$$485$$ 36.0000 1.63468
$$486$$ 0 0
$$487$$ −8.00000 −0.362515 −0.181257 0.983436i $$-0.558017\pi$$
−0.181257 + 0.983436i $$0.558017\pi$$
$$488$$ −3.00000 5.19615i −0.135804 0.235219i
$$489$$ 0 0
$$490$$ −1.00000 + 1.73205i −0.0451754 + 0.0782461i
$$491$$ 10.0000 17.3205i 0.451294 0.781664i −0.547173 0.837020i $$-0.684296\pi$$
0.998467 + 0.0553560i $$0.0176294\pi$$
$$492$$ 0 0
$$493$$ −6.00000 10.3923i −0.270226 0.468046i
$$494$$ −8.00000 −0.359937
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ −2.00000 + 3.46410i −0.0895323 + 0.155074i −0.907314 0.420455i $$-0.861871\pi$$
0.817781 + 0.575529i $$0.195204\pi$$
$$500$$ −6.00000 + 10.3923i −0.268328 + 0.464758i
$$501$$ 0 0
$$502$$ −10.0000 17.3205i −0.446322 0.773052i
$$503$$ −24.0000 −1.07011 −0.535054 0.844818i $$-0.679709\pi$$
−0.535054 + 0.844818i $$0.679709\pi$$
$$504$$ 0 0
$$505$$ −28.0000 −1.24598
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −5.00000 + 8.66025i −0.221621 + 0.383859i −0.955300 0.295637i $$-0.904468\pi$$
0.733679 + 0.679496i $$0.237801\pi$$
$$510$$ 0 0
$$511$$ −3.00000 5.19615i −0.132712 0.229864i
$$512$$ −11.0000 −0.486136
$$513$$ 0 0
$$514$$ −26.0000 −1.14681
$$515$$ −8.00000 13.8564i −0.352522 0.610586i
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 3.00000 5.19615i 0.131812 0.228306i
$$519$$ 0 0
$$520$$ −6.00000 10.3923i −0.263117 0.455733i
$$521$$ −18.0000 −0.788594 −0.394297 0.918983i $$-0.629012\pi$$
−0.394297 + 0.918983i $$0.629012\pi$$
$$522$$ 0 0
$$523$$ −20.0000 −0.874539 −0.437269 0.899331i $$-0.644054\pi$$
−0.437269 + 0.899331i $$0.644054\pi$$
$$524$$ −2.00000 3.46410i −0.0873704 0.151330i
$$525$$ 0 0
$$526$$ 8.00000 13.8564i 0.348817 0.604168i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 11.5000 + 19.9186i 0.500000 + 0.866025i
$$530$$ −12.0000 −0.521247
$$531$$ 0 0
$$532$$ 4.00000 0.173422
$$533$$ −2.00000 3.46410i −0.0866296 0.150047i
$$534$$ 0 0
$$535$$ 4.00000 6.92820i 0.172935 0.299532i
$$536$$ 6.00000 10.3923i 0.259161 0.448879i
$$537$$ 0 0
$$538$$ 3.00000 + 5.19615i 0.129339 + 0.224022i
$$539$$ −4.00000 −0.172292
$$540$$ 0 0
$$541$$ −34.0000 −1.46177 −0.730887 0.682498i $$-0.760893\pi$$
−0.730887 + 0.682498i $$0.760893\pi$$
$$542$$ −8.00000 13.8564i −0.343629 0.595184i
$$543$$ 0 0
$$544$$ −15.0000 + 25.9808i −0.643120 + 1.11392i
$$545$$ 18.0000 31.1769i 0.771035 1.33547i
$$546$$ 0 0
$$547$$ −2.00000 3.46410i −0.0855138 0.148114i 0.820096 0.572226i $$-0.193920\pi$$
−0.905610 + 0.424111i $$0.860587\pi$$
$$548$$ −6.00000 −0.256307
$$549$$ 0 0
$$550$$ 4.00000 0.170561
$$551$$ −4.00000 6.92820i −0.170406 0.295151i
$$552$$ 0 0
$$553$$ −8.00000 + 13.8564i −0.340195 + 0.589234i
$$554$$ −11.0000 + 19.0526i −0.467345 + 0.809466i
$$555$$ 0 0
$$556$$ 6.00000 + 10.3923i 0.254457 + 0.440732i
$$557$$ 2.00000 0.0847427 0.0423714 0.999102i $$-0.486509\pi$$
0.0423714 + 0.999102i $$0.486509\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ −1.00000 1.73205i −0.0422577 0.0731925i
$$561$$ 0 0
$$562$$ −11.0000 + 19.0526i −0.464007 + 0.803684i
$$563$$ 2.00000 3.46410i 0.0842900 0.145994i −0.820798 0.571218i $$-0.806471\pi$$
0.905088 + 0.425223i $$0.139804\pi$$
$$564$$ 0 0
$$565$$ −14.0000 24.2487i −0.588984 1.02015i
$$566$$ −20.0000 −0.840663
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 5.00000 + 8.66025i 0.209611 + 0.363057i 0.951592 0.307364i $$-0.0994469\pi$$
−0.741981 + 0.670421i $$0.766114\pi$$
$$570$$ 0 0
$$571$$ 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i $$-0.806660\pi$$
0.904835 + 0.425762i $$0.139994\pi$$
$$572$$ 4.00000 6.92820i 0.167248 0.289683i
$$573$$ 0 0
$$574$$ −1.00000 1.73205i −0.0417392 0.0722944i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 34.0000 1.41544 0.707719 0.706494i $$-0.249724\pi$$
0.707719 + 0.706494i $$0.249724\pi$$
$$578$$ −9.50000 16.4545i −0.395148 0.684416i
$$579$$ 0 0
$$580$$ 2.00000 3.46410i 0.0830455 0.143839i
$$581$$ 6.00000 10.3923i 0.248922 0.431145i
$$582$$ 0 0
$$583$$ −12.0000 20.7846i −0.496989 0.860811i
$$584$$ 18.0000 0.744845
$$585$$ 0 0
$$586$$ −14.0000 −0.578335
$$587$$ 14.0000 + 24.2487i 0.577842 + 1.00085i 0.995726 + 0.0923513i $$0.0294383\pi$$
−0.417885 + 0.908500i $$0.637228\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 12.0000 20.7846i 0.494032 0.855689i
$$591$$ 0 0
$$592$$ 3.00000 + 5.19615i 0.123299 + 0.213561i
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ 0 0
$$595$$ −12.0000 −0.491952
$$596$$ −3.00000 5.19615i −0.122885 0.212843i
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 24.0000 41.5692i 0.980613 1.69847i 0.320607 0.947212i $$-0.396113\pi$$
0.660006 0.751260i $$-0.270554\pi$$
$$600$$ 0 0
$$601$$ 3.00000 + 5.19615i 0.122373 + 0.211955i 0.920703 0.390264i $$-0.127616\pi$$
−0.798330 + 0.602220i $$0.794283\pi$$
$$602$$ 4.00000 0.163028
$$603$$ 0 0
$$604$$ −8.00000 −0.325515
$$605$$ −5.00000 8.66025i −0.203279 0.352089i
$$606$$ 0 0
$$607$$ 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i $$-0.728067\pi$$
0.981454 + 0.191700i $$0.0614000\pi$$
$$608$$ −10.0000 + 17.3205i −0.405554 + 0.702439i
$$609$$ 0 0
$$610$$ 2.00000 + 3.46410i 0.0809776 + 0.140257i
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −26.0000 −1.05013 −0.525065 0.851062i $$-0.675959\pi$$
−0.525065 + 0.851062i $$0.675959\pi$$
$$614$$ −2.00000 3.46410i −0.0807134 0.139800i
$$615$$ 0 0
$$616$$ 6.00000 10.3923i 0.241747 0.418718i
$$617$$ −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
$$619$$ 10.0000 + 17.3205i 0.401934 + 0.696170i 0.993959 0.109749i $$-0.0350048\pi$$
−0.592025 + 0.805919i $$0.701671\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 24.0000 0.962312
$$623$$ 7.00000 + 12.1244i 0.280449 + 0.485752i
$$624$$ 0 0
$$625$$ 9.50000 16.4545i 0.380000 0.658179i
$$626$$ −13.0000 + 22.5167i −0.519584 + 0.899947i
$$627$$ 0 0
$$628$$ −1.00000 1.73205i −0.0399043 0.0691164i
$$629$$ 36.0000 1.43541
$$630$$ 0 0
$$631$$ −40.0000 −1.59237 −0.796187 0.605050i $$-0.793153\pi$$
−0.796187 + 0.605050i $$0.793153\pi$$
$$632$$ −24.0000 41.5692i −0.954669 1.65353i
$$633$$ 0 0
$$634$$ −9.00000 + 15.5885i −0.357436 + 0.619097i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 1.00000 + 1.73205i 0.0396214 + 0.0686264i
$$638$$ −8.00000 −0.316723
$$639$$ 0 0
$$640$$ −6.00000 −0.237171
$$641$$ 9.00000 + 15.5885i 0.355479 + 0.615707i 0.987200 0.159489i $$-0.0509845\pi$$
−0.631721 + 0.775196i $$0.717651\pi$$
$$642$$ 0 0
$$643$$ −10.0000 + 17.3205i −0.394362 + 0.683054i −0.993019 0.117951i $$-0.962368\pi$$
0.598658 + 0.801005i $$0.295701\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −12.0000 20.7846i −0.472134 0.817760i
$$647$$ 40.0000 1.57256 0.786281 0.617869i $$-0.212004\pi$$
0.786281 + 0.617869i $$0.212004\pi$$
$$648$$ 0 0
$$649$$ 48.0000 1.88416
$$650$$ −1.00000 1.73205i −0.0392232 0.0679366i
$$651$$ 0 0
$$652$$ 2.00000 3.46410i 0.0783260 0.135665i
$$653$$ −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i $$-0.947899\pi$$
0.634437 + 0.772975i $$0.281232\pi$$
$$654$$ 0 0
$$655$$ 4.00000 + 6.92820i 0.156293 + 0.270707i
$$656$$ 2.00000 0.0780869
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 6.00000 + 10.3923i 0.233727 + 0.404827i 0.958902 0.283738i $$-0.0915745\pi$$
−0.725175 + 0.688565i $$0.758241\pi$$
$$660$$ 0 0
$$661$$ −11.0000 + 19.0526i −0.427850 + 0.741059i −0.996682 0.0813955i $$-0.974062\pi$$
0.568831 + 0.822454i $$0.307396\pi$$
$$662$$ 2.00000 3.46410i 0.0777322 0.134636i
$$663$$ 0 0
$$664$$ 18.0000 + 31.1769i 0.698535 + 1.20990i
$$665$$ −8.00000 −0.310227
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 4.00000 + 6.92820i 0.154765 + 0.268060i
$$669$$ 0 0
$$670$$ −4.00000 + 6.92820i −0.154533 + 0.267660i
$$671$$ −4.00000 + 6.92820i −0.154418 + 0.267460i
$$672$$ 0 0
$$673$$ −17.0000 29.4449i −0.655302 1.13502i −0.981818 0.189824i $$-0.939208\pi$$
0.326516 0.945192i $$-0.394125\pi$$
$$674$$ −14.0000 −0.539260
$$675$$ 0 0
$$676$$ 9.00000 0.346154
$$677$$ −9.00000 15.5885i −0.345898 0.599113i 0.639618 0.768693i $$-0.279092\pi$$
−0.985517 + 0.169580i $$0.945759\pi$$
$$678$$ 0 0
$$679$$ 9.00000 15.5885i 0.345388 0.598230i
$$680$$ 18.0000 31.1769i 0.690268 1.19558i
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ 0 0
$$685$$ 12.0000 0.458496
$$686$$ 0.500000 + 0.866025i 0.0190901 + 0.0330650i
$$687$$ 0 0
$$688$$ −2.00000 + 3.46410i −0.0762493 + 0.132068i
$$689$$ −6.00000 + 10.3923i −0.228582 + 0.395915i
$$690$$ 0 0
$$691$$ −10.0000 17.3205i −0.380418 0.658903i 0.610704 0.791859i $$-0.290887\pi$$
−0.991122 + 0.132956i $$0.957553\pi$$
$$692$$ −10.0000 −0.380143
$$693$$ 0 0
$$694$$ 28.0000 1.06287
$$695$$ −12.0000 20.7846i −0.455186 0.788405i
$$696$$ 0 0
$$697$$ 6.00000 10.3923i 0.227266 0.393637i
$$698$$ 1.00000 1.73205i 0.0378506 0.0655591i
$$699$$ 0 0
$$700$$ 0.500000 + 0.866025i 0.0188982 + 0.0327327i
$$701$$ −30.0000 −1.13308 −0.566542 0.824033i $$-0.691719\pi$$
−0.566542 + 0.824033i $$0.691719\pi$$
$$702$$ 0 0
$$703$$ 24.0000 0.905177
$$704$$ 14.0000 + 24.2487i 0.527645 + 0.913908i
$$705$$ 0 0
$$706$$ 5.00000 8.66025i 0.188177 0.325933i
$$707$$ −7.00000 + 12.1244i −0.263262 + 0.455983i
$$708$$ 0 0
$$709$$ −3.00000 5.19615i −0.112667 0.195146i 0.804178 0.594389i $$-0.202606\pi$$
−0.916845 + 0.399244i $$0.869273\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −42.0000 −1.57402
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −8.00000 + 13.8564i −0.299183 + 0.518200i
$$716$$ 2.00000 3.46410i 0.0747435 0.129460i
$$717$$ 0 0
$$718$$ 16.0000 + 27.7128i 0.597115 + 1.03423i
$$719$$ 48.0000 1.79010 0.895049 0.445968i $$-0.147140\pi$$
0.895049 + 0.445968i $$0.147140\pi$$
$$720$$ 0 0
$$721$$ −8.00000 −0.297936
$$722$$ 1.50000 + 2.59808i 0.0558242 + 0.0966904i
$$723$$ 0 0
$$724$$ −13.0000 + 22.5167i −0.483141 + 0.836825i
$$725$$ 1.00000 1.73205i 0.0371391 0.0643268i
$$726$$ 0 0
$$727$$ 20.0000 + 34.6410i 0.741759 + 1.28476i 0.951694 + 0.307049i $$0.0993415\pi$$
−0.209935 + 0.977715i $$0.567325\pi$$
$$728$$ −6.00000 −0.222375
$$729$$ 0 0
$$730$$ −12.0000 −0.444140
$$731$$ 12.0000 + 20.7846i 0.443836 + 0.768747i
$$732$$ 0 0
$$733$$ 9.00000 15.5885i 0.332423 0.575773i −0.650564 0.759452i $$-0.725467\pi$$
0.982986 + 0.183679i $$0.0588007\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −16.0000 −0.589368
$$738$$ 0 0
$$739$$ 36.0000 1.32428 0.662141 0.749380i $$-0.269648\pi$$
0.662141 + 0.749380i $$0.269648\pi$$
$$740$$ 6.00000 + 10.3923i 0.220564 + 0.382029i
$$741$$ 0 0
$$742$$ −3.00000 + 5.19615i −0.110133 + 0.190757i
$$743$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$744$$ 0 0
$$745$$ 6.00000 + 10.3923i 0.219823 + 0.380745i
$$746$$ −10.0000 −0.366126
$$747$$ 0 0
$$748$$ 24.0000 0.877527
$$749$$ −2.00000 3.46410i −0.0730784 0.126576i
$$750$$ 0 0
$$751$$ 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i $$-0.634880\pi$$
0.995018 0.0996961i $$-0.0317870\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 2.00000 + 3.46410i 0.0728357 + 0.126155i
$$755$$ 16.0000 0.582300
$$756$$ 0 0
$$757$$ −10.0000 −0.363456 −0.181728 0.983349i $$-0.558169\pi$$
−0.181728 + 0.983349i $$0.558169\pi$$
$$758$$ −6.00000 10.3923i −0.217930 0.377466i
$$759$$ 0 0
$$760$$ 12.0000 20.7846i 0.435286 0.753937i
$$761$$ 9.00000 15.5885i 0.326250 0.565081i −0.655515 0.755182i $$-0.727548\pi$$
0.981764 + 0.190101i $$0.0608816\pi$$
$$762$$ 0 0
$$763$$ −9.00000 15.5885i −0.325822 0.564340i
$$764$$ −8.00000 −0.289430
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −12.0000 20.7846i −0.433295 0.750489i
$$768$$ 0 0
$$769$$ −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i $$-0.844814\pi$$
0.847432 + 0.530904i $$0.178148\pi$$
$$770$$ −4.00000 + 6.92820i −0.144150 + 0.249675i
$$771$$ 0 0
$$772$$ 1.00000 + 1.73205i 0.0359908 + 0.0623379i
$$773$$ −14.0000 −0.503545 −0.251773 0.967786i $$-0.581013\pi$$
−0.251773 + 0.967786i $$0.581013\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 27.0000 + 46.7654i 0.969244 + 1.67878i
$$777$$ 0 0
$$778$$ 3.00000 5.19615i 0.107555 0.186291i
$$779$$ 4.00000 6.92820i 0.143315 0.248229i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −1.00000 −0.0357143
$$785$$ 2.00000 + 3.46410i 0.0713831 + 0.123639i
$$786$$ 0 0
$$787$$ 22.0000 38.1051i 0.784215 1.35830i −0.145251 0.989395i $$-0.546399\pi$$
0.929467 0.368906i $$-0.120268\pi$$
$$788$$ −11.0000 + 19.0526i −0.391859 + 0.678719i
$$789$$ 0 0
$$790$$ 16.0000 + 27.7128i 0.569254 + 0.985978i
$$791$$ −14.0000 −0.497783
$$792$$ 0 0
$$793$$ 4.00000 0.142044
$$794$$