# Properties

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

# Learn more about

## 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.g.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 0.986869 0.161521i $$-0.0516399\pi$$
−0.633316 + 0.773893i $$0.718307\pi$$
$$3$$ 0 0
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i $$-0.685750\pi$$
0.998203 + 0.0599153i $$0.0190830\pi$$
$$6$$ 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 $$-0.960630\pi$$
0.389338 0.921095i $$-0.372704\pi$$
$$12$$ 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 $$-0.759367\pi$$
−0.727607 + 0.685994i $$0.759367\pi$$
$$18$$ 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 0.943811 0.330487i $$-0.107213\pi$$
−0.758115 + 0.652121i $$0.773880\pi$$
$$30$$ 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 −0.933486 0.358614i $$-0.883249\pi$$
0.777312 + 0.629115i $$0.216583\pi$$
$$42$$ 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 $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 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 $$0.452025\pi$$
−0.931282 + 0.364299i $$0.881308\pi$$
$$60$$ 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 $$0.0621783\pi$$
−0.322396 + 0.946605i $$0.604488\pi$$
$$84$$ 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 $$-0.766122\pi$$
−0.741999 + 0.670402i $$0.766122\pi$$
$$90$$ 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 $$-0.921395\pi$$
0.273138 0.961975i $$-0.411939\pi$$
$$102$$ 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 $$-0.438066\pi$$
0.193347 + 0.981130i $$0.438066\pi$$
$$108$$ 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 $$-0.604523\pi$$
0.981003 0.193993i $$-0.0621440\pi$$
$$114$$ 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 −0.940072 0.340977i $$-0.889242\pi$$
0.765331 + 0.643637i $$0.222575\pi$$
$$132$$ 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 0.965250 0.261329i $$-0.0841608\pi$$
−0.708942 + 0.705266i $$0.750827\pi$$
$$138$$ 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 −0.962348 0.271821i $$-0.912374\pi$$
0.716578 + 0.697507i $$0.245707\pi$$
$$150$$ 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 −0.668730 0.743505i $$-0.733162\pi$$
0.978259 + 0.207385i $$0.0664952\pi$$
$$168$$ 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 0.991082 0.133250i $$-0.0425415\pi$$
−0.610939 + 0.791677i $$0.709208\pi$$
$$174$$ 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 $$-0.547762\pi$$
−0.149487 + 0.988764i $$0.547762\pi$$
$$180$$ 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 0.973674 0.227946i $$-0.0732010\pi$$
−0.684244 + 0.729253i $$0.739868\pi$$
$$192$$ 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 $$-0.213321\pi$$
0.783718 + 0.621117i $$0.213321\pi$$
$$198$$ 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 0.993508 0.113761i $$-0.0362899\pi$$
−0.595274 + 0.803523i $$0.702957\pi$$
$$228$$ 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 $$-0.562969\pi$$
−0.196537 + 0.980497i $$0.562969\pi$$
$$234$$ 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 $$0.449530\pi$$
−0.934109 + 0.356988i $$0.883804\pi$$
$$240$$ 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 $$-0.717435\pi$$
−0.631194 + 0.775625i $$0.717435\pi$$
$$252$$ 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 $$0.467698\pi$$
−0.912222 + 0.409695i $$0.865635\pi$$
$$258$$ 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 0.506669 0.862141i $$-0.330877\pi$$
−0.999970 + 0.00771799i $$0.997543\pi$$
$$264$$ 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 $$-0.441447\pi$$
0.182913 + 0.983129i $$0.441447\pi$$
$$270$$ 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 $$0.0611727\pi$$
−0.325385 + 0.945582i $$0.605494\pi$$
$$282$$ 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 −0.994772 0.102123i $$-0.967436\pi$$
0.585827 + 0.810436i $$0.300770\pi$$
$$294$$ 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 $$-0.595114\pi$$
0.974841 0.222900i $$-0.0715523\pi$$
$$312$$ 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 $$0.00202172\pi$$
−0.494489 + 0.869184i $$0.664645\pi$$
$$318$$ 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 $$-0.562635\pi$$
0.947067 0.321037i $$-0.104031\pi$$
$$348$$ 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 0.701734 0.712439i $$-0.252409\pi$$
−0.967857 + 0.251500i $$0.919076\pi$$
$$354$$ 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 $$-0.179929\pi$$
0.844448 + 0.535638i $$0.179929\pi$$
$$360$$ 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 0.779895 0.625910i $$-0.215272\pi$$
−0.932002 + 0.362454i $$0.881939\pi$$
$$390$$ 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 $$-0.563837\pi$$
0.948272 0.317460i $$-0.102830\pi$$
$$402$$ 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 −0.681426 0.731887i $$-0.738640\pi$$
0.974546 + 0.224189i $$0.0719734\pi$$
$$420$$ 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 $$-0.696174\pi$$
−0.578020 + 0.816023i $$0.696174\pi$$
$$432$$ 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 $$-0.840097\pi$$
0.0212481 0.999774i $$-0.493236\pi$$
$$444$$ 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 $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ 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 0.958652 0.284579i $$-0.0918539\pi$$
−0.725779 + 0.687928i $$0.758521\pi$$
$$462$$ 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 $$-0.186655\pi$$
0.832941 + 0.553362i $$0.186655\pi$$
$$468$$ 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 0.988861 0.148842i $$-0.0475547\pi$$
−0.623332 + 0.781958i $$0.714221\pi$$
$$480$$ 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 −0.998467 0.0553560i $$-0.982371\pi$$
0.547173 + 0.837020i $$0.315704\pi$$
$$492$$ 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 $$-0.320291\pi$$
0.535054 + 0.844818i $$0.320291\pi$$
$$504$$ 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 −0.733679 0.679496i $$-0.762199\pi$$
0.955300 + 0.295637i $$0.0955319\pi$$
$$510$$ 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 $$-0.370988\pi$$
0.394297 + 0.918983i $$0.370988\pi$$
$$522$$ 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 $$-0.513491\pi$$
−0.0423714 + 0.999102i $$0.513491\pi$$
$$558$$ 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 −0.905088 0.425223i $$-0.860196\pi$$
0.820798 + 0.571218i $$0.193529\pi$$
$$564$$ 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 0.741981 0.670421i $$-0.233886\pi$$
−0.951592 + 0.307364i $$0.900553\pi$$
$$570$$ 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 $$-0.970562\pi$$
0.417885 0.908500i $$-0.362772\pi$$
$$588$$ 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 $$-0.539314\pi$$
−0.123195 + 0.992382i $$0.539314\pi$$
$$594$$ 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 $$0.603887\pi$$
−0.660006 + 0.751260i $$0.729446\pi$$
$$600$$ 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 −0.799298 0.600935i $$-0.794795\pi$$
0.920074 + 0.391745i $$0.128129\pi$$
$$618$$ 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 0.631721 0.775196i $$-0.282349\pi$$
−0.987200 + 0.159489i $$0.949015\pi$$
$$642$$ 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 $$-0.787996\pi$$
−0.786281 + 0.617869i $$0.787996\pi$$
$$648$$ 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 −0.634437 0.772975i $$-0.718768\pi$$
0.986634 + 0.162951i $$0.0521013\pi$$
$$654$$ 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 0.725175 0.688565i $$-0.241759\pi$$
−0.958902 + 0.283738i $$0.908425\pi$$
$$660$$ 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 0.985517 0.169580i $$-0.0542410\pi$$
−0.639618 + 0.768693i $$0.720908\pi$$
$$678$$ 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 $$-0.573736\pi$$
−0.229584 + 0.973289i $$0.573736\pi$$
$$684$$ 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 $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 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 $$-0.852860\pi$$
−0.895049 + 0.445968i $$0.852860\pi$$
$$720$$ 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 −0.981764 0.190101i $$-0.939118\pi$$
0.655515 + 0.755182i $$0.272452\pi$$
$$762$$ 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 $$-0.418987\pi$$
0.251773 + 0.967786i $$0.418987\pi$$
$$774$$ 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
$$794$$ −9.00000 15.5885i −0.319398 0.553214i
$$795$$ 0 0
$$796$$ 12.0000 20.7846i 0.425329 0.736691i
$$797$$ 13.0000 22.5167i 0.460484 0.797581i −0.538501 0.842625i $$-0.681009\pi$$
0.998985 + 0.0450436i $$0.0143427\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 5.00000 0.176777
$$801$$ 0 0
$$802$$ 30.0000 1.05934
$$803$$ 12.0000 + 20.7846i 0.423471 + 0.733473i
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ −21.0000 36.3731i −0.738777 1.27960i