# Properties

 Label 147.2.e.b.79.1 Level $147$ Weight $2$ Character 147.79 Analytic conductor $1.174$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$147 = 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 147.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.17380090971$$ 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 79.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 147.79 Dual form 147.2.e.b.67.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(-2.00000 - 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{12} -2.00000 q^{13} -2.00000 q^{15} +(0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} +2.00000 q^{20} -4.00000 q^{22} +(-1.50000 - 2.59808i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(2.50000 + 4.33013i) q^{32} +(-2.00000 + 3.46410i) q^{33} +6.00000 q^{34} -1.00000 q^{36} +(-3.00000 + 5.19615i) q^{37} +(2.00000 + 3.46410i) q^{38} +(1.00000 + 1.73205i) q^{39} +(3.00000 - 5.19615i) q^{40} +2.00000 q^{41} -4.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(1.00000 + 1.73205i) q^{45} -1.00000 q^{48} +1.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(0.500000 - 0.866025i) q^{54} -8.00000 q^{55} +4.00000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(1.00000 - 1.73205i) q^{61} +7.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(2.00000 + 3.46410i) q^{66} +(-2.00000 - 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{72} +(3.00000 + 5.19615i) q^{73} +(3.00000 + 5.19615i) q^{74} +(0.500000 - 0.866025i) q^{75} -4.00000 q^{76} +2.00000 q^{78} +(8.00000 - 13.8564i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} -12.0000 q^{83} +12.0000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(1.00000 + 1.73205i) q^{87} +(-6.00000 - 10.3923i) q^{88} +(7.00000 - 12.1244i) q^{89} +2.00000 q^{90} +(4.00000 + 6.92820i) q^{95} +(2.50000 - 4.33013i) q^{96} +18.0000 q^{97} +4.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + q^{2} - q^{3} + q^{4} + 2q^{5} - 2q^{6} + 6q^{8} - q^{9} + O(q^{10})$$ $$2q + q^{2} - q^{3} + q^{4} + 2q^{5} - 2q^{6} + 6q^{8} - q^{9} - 2q^{10} - 4q^{11} + q^{12} - 4q^{13} - 4q^{15} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + 4q^{20} - 8q^{22} - 3q^{24} + q^{25} - 2q^{26} + 2q^{27} - 4q^{29} - 2q^{30} + 5q^{32} - 4q^{33} + 12q^{34} - 2q^{36} - 6q^{37} + 4q^{38} + 2q^{39} + 6q^{40} + 4q^{41} - 8q^{43} + 4q^{44} + 2q^{45} - 2q^{48} + 2q^{50} + 6q^{51} - 2q^{52} - 6q^{53} + q^{54} - 16q^{55} + 8q^{57} - 2q^{58} - 12q^{59} - 2q^{60} + 2q^{61} + 14q^{64} - 4q^{65} + 4q^{66} - 4q^{67} - 6q^{68} - 3q^{72} + 6q^{73} + 6q^{74} + q^{75} - 8q^{76} + 4q^{78} + 16q^{79} - 2q^{80} - q^{81} + 2q^{82} - 24q^{83} + 24q^{85} - 4q^{86} + 2q^{87} - 12q^{88} + 14q^{89} + 4q^{90} + 8q^{95} + 5q^{96} + 36q^{97} + 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$$.

 $$n$$ $$50$$ $$52$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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 $$-0.718307\pi$$
0.986869 + 0.161521i $$0.0516399\pi$$
$$3$$ −0.500000 0.866025i −0.288675 0.500000i
$$4$$ 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 $$0.0190830\pi$$
$$6$$ −1.00000 −0.408248
$$7$$ 0 0
$$8$$ 3.00000 1.06066
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ −1.00000 1.73205i −0.316228 0.547723i
$$11$$ −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i $$-0.960630\pi$$
0.389338 0.921095i $$-0.372704\pi$$
$$12$$ 0.500000 0.866025i 0.144338 0.250000i
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ −2.00000 −0.516398
$$16$$ 0.500000 0.866025i 0.125000 0.216506i
$$17$$ 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i $$0.0927008\pi$$
−0.230285 + 0.973123i $$0.573966\pi$$
$$18$$ 0.500000 + 0.866025i 0.117851 + 0.204124i
$$19$$ −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i $$-0.985065\pi$$
0.540068 + 0.841621i $$0.318398\pi$$
$$20$$ 2.00000 0.447214
$$21$$ 0 0
$$22$$ −4.00000 −0.852803
$$23$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$24$$ −1.50000 2.59808i −0.306186 0.530330i
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ −1.00000 + 1.73205i −0.196116 + 0.339683i
$$27$$ 1.00000 0.192450
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ −1.00000 + 1.73205i −0.182574 + 0.316228i
$$31$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$32$$ 2.50000 + 4.33013i 0.441942 + 0.765466i
$$33$$ −2.00000 + 3.46410i −0.348155 + 0.603023i
$$34$$ 6.00000 1.02899
$$35$$ 0 0
$$36$$ −1.00000 −0.166667
$$37$$ −3.00000 + 5.19615i −0.493197 + 0.854242i −0.999969 0.00783774i $$-0.997505\pi$$
0.506772 + 0.862080i $$0.330838\pi$$
$$38$$ 2.00000 + 3.46410i 0.324443 + 0.561951i
$$39$$ 1.00000 + 1.73205i 0.160128 + 0.277350i
$$40$$ 3.00000 5.19615i 0.474342 0.821584i
$$41$$ 2.00000 0.312348 0.156174 0.987730i $$-0.450084\pi$$
0.156174 + 0.987730i $$0.450084\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ 2.00000 3.46410i 0.301511 0.522233i
$$45$$ 1.00000 + 1.73205i 0.149071 + 0.258199i
$$46$$ 0 0
$$47$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 0 0
$$50$$ 1.00000 0.141421
$$51$$ 3.00000 5.19615i 0.420084 0.727607i
$$52$$ −1.00000 1.73205i −0.138675 0.240192i
$$53$$ −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i $$-0.301865\pi$$
−0.995117 + 0.0987002i $$0.968532\pi$$
$$54$$ 0.500000 0.866025i 0.0680414 0.117851i
$$55$$ −8.00000 −1.07872
$$56$$ 0 0
$$57$$ 4.00000 0.529813
$$58$$ −1.00000 + 1.73205i −0.131306 + 0.227429i
$$59$$ −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i $$-0.881308\pi$$
0.150148 0.988663i $$-0.452025\pi$$
$$60$$ −1.00000 1.73205i −0.129099 0.223607i
$$61$$ 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i $$-0.792466\pi$$
0.922916 + 0.385002i $$0.125799\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ −2.00000 + 3.46410i −0.248069 + 0.429669i
$$66$$ 2.00000 + 3.46410i 0.246183 + 0.426401i
$$67$$ −2.00000 3.46410i −0.244339 0.423207i 0.717607 0.696449i $$-0.245238\pi$$
−0.961946 + 0.273241i $$0.911904\pi$$
$$68$$ −3.00000 + 5.19615i −0.363803 + 0.630126i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ −1.50000 + 2.59808i −0.176777 + 0.306186i
$$73$$ 3.00000 + 5.19615i 0.351123 + 0.608164i 0.986447 0.164083i $$-0.0524664\pi$$
−0.635323 + 0.772246i $$0.719133\pi$$
$$74$$ 3.00000 + 5.19615i 0.348743 + 0.604040i
$$75$$ 0.500000 0.866025i 0.0577350 0.100000i
$$76$$ −4.00000 −0.458831
$$77$$ 0 0
$$78$$ 2.00000 0.226455
$$79$$ 8.00000 13.8564i 0.900070 1.55897i 0.0726692 0.997356i $$-0.476848\pi$$
0.827401 0.561611i $$-0.189818\pi$$
$$80$$ −1.00000 1.73205i −0.111803 0.193649i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 1.00000 1.73205i 0.110432 0.191273i
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 12.0000 1.30158
$$86$$ −2.00000 + 3.46410i −0.215666 + 0.373544i
$$87$$ 1.00000 + 1.73205i 0.107211 + 0.185695i
$$88$$ −6.00000 10.3923i −0.639602 1.10782i
$$89$$ 7.00000 12.1244i 0.741999 1.28518i −0.209585 0.977790i $$-0.567211\pi$$
0.951584 0.307389i $$-0.0994552\pi$$
$$90$$ 2.00000 0.210819
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 4.00000 + 6.92820i 0.410391 + 0.710819i
$$96$$ 2.50000 4.33013i 0.255155 0.441942i
$$97$$ 18.0000 1.82762 0.913812 0.406138i $$-0.133125\pi$$
0.913812 + 0.406138i $$0.133125\pi$$
$$98$$ 0 0
$$99$$ 4.00000 0.402015
$$100$$ −0.500000 + 0.866025i −0.0500000 + 0.0866025i
$$101$$ −7.00000 12.1244i −0.696526 1.20642i −0.969664 0.244443i $$-0.921395\pi$$
0.273138 0.961975i $$-0.411939\pi$$
$$102$$ −3.00000 5.19615i −0.297044 0.514496i
$$103$$ −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i $$-0.962288\pi$$
0.598858 + 0.800855i $$0.295621\pi$$
$$104$$ −6.00000 −0.588348
$$105$$ 0 0
$$106$$ −6.00000 −0.582772
$$107$$ −2.00000 + 3.46410i −0.193347 + 0.334887i −0.946357 0.323122i $$-0.895268\pi$$
0.753010 + 0.658009i $$0.228601\pi$$
$$108$$ 0.500000 + 0.866025i 0.0481125 + 0.0833333i
$$109$$ 9.00000 + 15.5885i 0.862044 + 1.49310i 0.869953 + 0.493135i $$0.164149\pi$$
−0.00790932 + 0.999969i $$0.502518\pi$$
$$110$$ −4.00000 + 6.92820i −0.381385 + 0.660578i
$$111$$ 6.00000 0.569495
$$112$$ 0 0
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 2.00000 3.46410i 0.187317 0.324443i
$$115$$ 0 0
$$116$$ −1.00000 1.73205i −0.0928477 0.160817i
$$117$$ 1.00000 1.73205i 0.0924500 0.160128i
$$118$$ −12.0000 −1.10469
$$119$$ 0 0
$$120$$ −6.00000 −0.547723
$$121$$ −2.50000 + 4.33013i −0.227273 + 0.393648i
$$122$$ −1.00000 1.73205i −0.0905357 0.156813i
$$123$$ −1.00000 1.73205i −0.0901670 0.156174i
$$124$$ 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
$$129$$ 2.00000 + 3.46410i 0.176090 + 0.304997i
$$130$$ 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 $$0.222575\pi$$
$$132$$ −4.00000 −0.348155
$$133$$ 0 0
$$134$$ −4.00000 −0.345547
$$135$$ 1.00000 1.73205i 0.0860663 0.149071i
$$136$$ 9.00000 + 15.5885i 0.771744 + 1.33670i
$$137$$ 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
$$139$$ 12.0000 1.01783 0.508913 0.860818i $$-0.330047\pi$$
0.508913 + 0.860818i $$0.330047\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 4.00000 + 6.92820i 0.334497 + 0.579365i
$$144$$ 0.500000 + 0.866025i 0.0416667 + 0.0721688i
$$145$$ −2.00000 + 3.46410i −0.166091 + 0.287678i
$$146$$ 6.00000 0.496564
$$147$$ 0 0
$$148$$ −6.00000 −0.493197
$$149$$ −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i $$-0.912374\pi$$
0.716578 + 0.697507i $$0.245707\pi$$
$$150$$ −0.500000 0.866025i −0.0408248 0.0707107i
$$151$$ −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i $$-0.272204\pi$$
−0.981617 + 0.190864i $$0.938871\pi$$
$$152$$ −6.00000 + 10.3923i −0.486664 + 0.842927i
$$153$$ −6.00000 −0.485071
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −1.00000 + 1.73205i −0.0800641 + 0.138675i
$$157$$ 1.00000 + 1.73205i 0.0798087 + 0.138233i 0.903167 0.429289i $$-0.141236\pi$$
−0.823359 + 0.567521i $$0.807902\pi$$
$$158$$ −8.00000 13.8564i −0.636446 1.10236i
$$159$$ −3.00000 + 5.19615i −0.237915 + 0.412082i
$$160$$ 10.0000 0.790569
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i $$-0.883403\pi$$
0.777007 + 0.629492i $$0.216737\pi$$
$$164$$ 1.00000 + 1.73205i 0.0780869 + 0.135250i
$$165$$ 4.00000 + 6.92820i 0.311400 + 0.539360i
$$166$$ −6.00000 + 10.3923i −0.465690 + 0.806599i
$$167$$ −8.00000 −0.619059 −0.309529 0.950890i $$-0.600171\pi$$
−0.309529 + 0.950890i $$0.600171\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 6.00000 10.3923i 0.460179 0.797053i
$$171$$ −2.00000 3.46410i −0.152944 0.264906i
$$172$$ −2.00000 3.46410i −0.152499 0.264135i
$$173$$ 5.00000 8.66025i 0.380143 0.658427i −0.610939 0.791677i $$-0.709208\pi$$
0.991082 + 0.133250i $$0.0425415\pi$$
$$174$$ 2.00000 0.151620
$$175$$ 0 0
$$176$$ −4.00000 −0.301511
$$177$$ −6.00000 + 10.3923i −0.450988 + 0.781133i
$$178$$ −7.00000 12.1244i −0.524672 0.908759i
$$179$$ 2.00000 + 3.46410i 0.149487 + 0.258919i 0.931038 0.364922i $$-0.118904\pi$$
−0.781551 + 0.623841i $$0.785571\pi$$
$$180$$ −1.00000 + 1.73205i −0.0745356 + 0.129099i
$$181$$ −26.0000 −1.93256 −0.966282 0.257485i $$-0.917106\pi$$
−0.966282 + 0.257485i $$0.917106\pi$$
$$182$$ 0 0
$$183$$ −2.00000 −0.147844
$$184$$ 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 $$-0.739868\pi$$
0.973674 + 0.227946i $$0.0732010\pi$$
$$192$$ −3.50000 6.06218i −0.252591 0.437500i
$$193$$ −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i $$-0.189599\pi$$
−0.899770 + 0.436365i $$0.856266\pi$$
$$194$$ 9.00000 15.5885i 0.646162 1.11919i
$$195$$ 4.00000 0.286446
$$196$$ 0 0
$$197$$ 22.0000 1.56744 0.783718 0.621117i $$-0.213321\pi$$
0.783718 + 0.621117i $$0.213321\pi$$
$$198$$ 2.00000 3.46410i 0.142134 0.246183i
$$199$$ −12.0000 20.7846i −0.850657 1.47338i −0.880616 0.473831i $$-0.842871\pi$$
0.0299585 0.999551i $$-0.490462\pi$$
$$200$$ 1.50000 + 2.59808i 0.106066 + 0.183712i
$$201$$ −2.00000 + 3.46410i −0.141069 + 0.244339i
$$202$$ −14.0000 −0.985037
$$203$$ 0 0
$$204$$ 6.00000 0.420084
$$205$$ 2.00000 3.46410i 0.139686 0.241943i
$$206$$ 4.00000 + 6.92820i 0.278693 + 0.482711i
$$207$$ 0 0
$$208$$ −1.00000 + 1.73205i −0.0693375 + 0.120096i
$$209$$ 16.0000 1.10674
$$210$$ 0 0
$$211$$ 4.00000 0.275371 0.137686 0.990476i $$-0.456034\pi$$
0.137686 + 0.990476i $$0.456034\pi$$
$$212$$ 3.00000 5.19615i 0.206041 0.356873i
$$213$$ 0 0
$$214$$ 2.00000 + 3.46410i 0.136717 + 0.236801i
$$215$$ −4.00000 + 6.92820i −0.272798 + 0.472500i
$$216$$ 3.00000 0.204124
$$217$$ 0 0
$$218$$ 18.0000 1.21911
$$219$$ 3.00000 5.19615i 0.202721 0.351123i
$$220$$ −4.00000 6.92820i −0.269680 0.467099i
$$221$$ −6.00000 10.3923i −0.403604 0.699062i
$$222$$ 3.00000 5.19615i 0.201347 0.348743i
$$223$$ 16.0000 1.07144 0.535720 0.844396i $$-0.320040\pi$$
0.535720 + 0.844396i $$0.320040\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −0.0666667
$$226$$ −7.00000 + 12.1244i −0.465633 + 0.806500i
$$227$$ 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i $$-0.0362899\pi$$
−0.595274 + 0.803523i $$0.702957\pi$$
$$228$$ 2.00000 + 3.46410i 0.132453 + 0.229416i
$$229$$ 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
$$232$$ −6.00000 −0.393919
$$233$$ 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i $$-0.770364\pi$$
0.947403 + 0.320043i $$0.103697\pi$$
$$234$$ −1.00000 1.73205i −0.0653720 0.113228i
$$235$$ 0 0
$$236$$ 6.00000 10.3923i 0.390567 0.676481i
$$237$$ −16.0000 −1.03931
$$238$$ 0 0
$$239$$ 24.0000 1.55243 0.776215 0.630468i $$-0.217137\pi$$
0.776215 + 0.630468i $$0.217137\pi$$
$$240$$ −1.00000 + 1.73205i −0.0645497 + 0.111803i
$$241$$ −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i $$-0.187185\pi$$
−0.896435 + 0.443176i $$0.853852\pi$$
$$242$$ 2.50000 + 4.33013i 0.160706 + 0.278351i
$$243$$ −0.500000 + 0.866025i −0.0320750 + 0.0555556i
$$244$$ 2.00000 0.128037
$$245$$ 0 0
$$246$$ −2.00000 −0.127515
$$247$$ 4.00000 6.92820i 0.254514 0.440831i
$$248$$ 0 0
$$249$$ 6.00000 + 10.3923i 0.380235 + 0.658586i
$$250$$ 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
$$255$$ −6.00000 10.3923i −0.375735 0.650791i
$$256$$ 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 $$0.865635\pi$$
$$258$$ 4.00000 0.249029
$$259$$ 0 0
$$260$$ −4.00000 −0.248069
$$261$$ 1.00000 1.73205i 0.0618984 0.107211i
$$262$$ 2.00000 + 3.46410i 0.123560 + 0.214013i
$$263$$ −8.00000 13.8564i −0.493301 0.854423i 0.506669 0.862141i $$-0.330877\pi$$
−0.999970 + 0.00771799i $$0.997543\pi$$
$$264$$ −6.00000 + 10.3923i −0.369274 + 0.639602i
$$265$$ −12.0000 −0.737154
$$266$$ 0 0
$$267$$ −14.0000 −0.856786
$$268$$ 2.00000 3.46410i 0.122169 0.211604i
$$269$$ −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i $$-0.225219\pi$$
−0.942871 + 0.333157i $$0.891886\pi$$
$$270$$ −1.00000 1.73205i −0.0608581 0.105409i
$$271$$ −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i $$-0.994865\pi$$
0.513905 + 0.857847i $$0.328199\pi$$
$$272$$ 6.00000 0.363803
$$273$$ 0 0
$$274$$ 6.00000 0.362473
$$275$$ 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 $$-0.396503\pi$$
$$278$$ 6.00000 10.3923i 0.359856 0.623289i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −22.0000 −1.31241 −0.656205 0.754583i $$-0.727839\pi$$
−0.656205 + 0.754583i $$0.727839\pi$$
$$282$$ 0 0
$$283$$ 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i $$0.0359589\pi$$
−0.399188 + 0.916869i $$0.630708\pi$$
$$284$$ 0 0
$$285$$ 4.00000 6.92820i 0.236940 0.410391i
$$286$$ 8.00000 0.473050
$$287$$ 0 0
$$288$$ −5.00000 −0.294628
$$289$$ −9.50000 + 16.4545i −0.558824 + 0.967911i
$$290$$ 2.00000 + 3.46410i 0.117444 + 0.203419i
$$291$$ −9.00000 15.5885i −0.527589 0.913812i
$$292$$ −3.00000 + 5.19615i −0.175562 + 0.304082i
$$293$$ 14.0000 0.817889 0.408944 0.912559i $$-0.365897\pi$$
0.408944 + 0.912559i $$0.365897\pi$$
$$294$$ 0 0
$$295$$ −24.0000 −1.39733
$$296$$ −9.00000 + 15.5885i −0.523114 + 0.906061i
$$297$$ −2.00000 3.46410i −0.116052 0.201008i
$$298$$ 3.00000 + 5.19615i 0.173785 + 0.301005i
$$299$$ 0 0
$$300$$ 1.00000 0.0577350
$$301$$ 0 0
$$302$$ −8.00000 −0.460348
$$303$$ −7.00000 + 12.1244i −0.402139 + 0.696526i
$$304$$ 2.00000 + 3.46410i 0.114708 + 0.198680i
$$305$$ −2.00000 3.46410i −0.114520 0.198354i
$$306$$ −3.00000 + 5.19615i −0.171499 + 0.297044i
$$307$$ 4.00000 0.228292 0.114146 0.993464i $$-0.463587\pi$$
0.114146 + 0.993464i $$0.463587\pi$$
$$308$$ 0 0
$$309$$ 8.00000 0.455104
$$310$$ 0 0
$$311$$ 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i $$0.0715523\pi$$
−0.294384 + 0.955687i $$0.595114\pi$$
$$312$$ 3.00000 + 5.19615i 0.169842 + 0.294174i
$$313$$ −13.0000 + 22.5167i −0.734803 + 1.27272i 0.220006 + 0.975499i $$0.429392\pi$$
−0.954810 + 0.297218i $$0.903941\pi$$
$$314$$ 2.00000 0.112867
$$315$$ 0 0
$$316$$ 16.0000 0.900070
$$317$$ 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i $$-0.664645\pi$$
0.999980 0.00635137i $$-0.00202172\pi$$
$$318$$ 3.00000 + 5.19615i 0.168232 + 0.291386i
$$319$$ 4.00000 + 6.92820i 0.223957 + 0.387905i
$$320$$ 7.00000 12.1244i 0.391312 0.677772i
$$321$$ 4.00000 0.223258
$$322$$ 0 0
$$323$$ −24.0000 −1.33540
$$324$$ 0.500000 0.866025i 0.0277778 0.0481125i
$$325$$ −1.00000 1.73205i −0.0554700 0.0960769i
$$326$$ 2.00000 + 3.46410i 0.110770 + 0.191859i
$$327$$ 9.00000 15.5885i 0.497701 0.862044i
$$328$$ 6.00000 0.331295
$$329$$ 0 0
$$330$$ 8.00000 0.440386
$$331$$ 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i $$-0.798271\pi$$
0.915742 + 0.401768i $$0.131604\pi$$
$$332$$ −6.00000 10.3923i −0.329293 0.570352i
$$333$$ −3.00000 5.19615i −0.164399 0.284747i
$$334$$ −4.00000 + 6.92820i −0.218870 + 0.379094i
$$335$$ −8.00000 −0.437087
$$336$$ 0 0
$$337$$ −14.0000 −0.762629 −0.381314 0.924445i $$-0.624528\pi$$
−0.381314 + 0.924445i $$0.624528\pi$$
$$338$$ −4.50000 + 7.79423i −0.244768 + 0.423950i
$$339$$ 7.00000 + 12.1244i 0.380188 + 0.658505i
$$340$$ 6.00000 + 10.3923i 0.325396 + 0.563602i
$$341$$ 0 0
$$342$$ −4.00000 −0.216295
$$343$$ 0 0
$$344$$ −12.0000 −0.646997
$$345$$ 0 0
$$346$$ −5.00000 8.66025i −0.268802 0.465578i
$$347$$ 14.0000 + 24.2487i 0.751559 + 1.30174i 0.947067 + 0.321037i $$0.104031\pi$$
−0.195507 + 0.980702i $$0.562635\pi$$
$$348$$ −1.00000 + 1.73205i −0.0536056 + 0.0928477i
$$349$$ −2.00000 −0.107058 −0.0535288 0.998566i $$-0.517047\pi$$
−0.0535288 + 0.998566i $$0.517047\pi$$
$$350$$ 0 0
$$351$$ −2.00000 −0.106752
$$352$$ 10.0000 17.3205i 0.533002 0.923186i
$$353$$ −5.00000 8.66025i −0.266123 0.460939i 0.701734 0.712439i $$-0.252409\pi$$
−0.967857 + 0.251500i $$0.919076\pi$$
$$354$$ 6.00000 + 10.3923i 0.318896 + 0.552345i
$$355$$ 0 0
$$356$$ 14.0000 0.741999
$$357$$ 0 0
$$358$$ 4.00000 0.211407
$$359$$ −16.0000 + 27.7128i −0.844448 + 1.46263i 0.0416523 + 0.999132i $$0.486738\pi$$
−0.886100 + 0.463494i $$0.846596\pi$$
$$360$$ 3.00000 + 5.19615i 0.158114 + 0.273861i
$$361$$ 1.50000 + 2.59808i 0.0789474 + 0.136741i
$$362$$ −13.0000 + 22.5167i −0.683265 + 1.18345i
$$363$$ 5.00000 0.262432
$$364$$ 0 0
$$365$$ 12.0000 0.628109
$$366$$ −1.00000 + 1.73205i −0.0522708 + 0.0905357i
$$367$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$368$$ 0 0
$$369$$ −1.00000 + 1.73205i −0.0520579 + 0.0901670i
$$370$$ 12.0000 0.623850
$$371$$ 0 0
$$372$$ 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
$$375$$ −6.00000 10.3923i −0.309839 0.536656i
$$376$$ 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 $$0.166667\pi$$
$$384$$ 3.00000 0.153093
$$385$$ 0 0
$$386$$ −2.00000 −0.101797
$$387$$ 2.00000 3.46410i 0.101666 0.176090i
$$388$$ 9.00000 + 15.5885i 0.456906 + 0.791384i
$$389$$ −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i $$-0.215272\pi$$
−0.932002 + 0.362454i $$0.881939\pi$$
$$390$$ 2.00000 3.46410i 0.101274 0.175412i
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 4.00000 0.201773
$$394$$ 11.0000 19.0526i 0.554172 0.959854i
$$395$$ −16.0000 27.7128i −0.805047 1.39438i
$$396$$ 2.00000 + 3.46410i 0.100504 + 0.174078i
$$397$$ 9.00000 15.5885i 0.451697 0.782362i −0.546795 0.837267i $$-0.684152\pi$$
0.998492 + 0.0549046i $$0.0174855\pi$$
$$398$$ −24.0000 −1.20301
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ 15.0000 25.9808i 0.749064 1.29742i −0.199207 0.979957i $$-0.563837\pi$$
0.948272 0.317460i $$-0.102830\pi$$
$$402$$ 2.00000 + 3.46410i 0.0997509 + 0.172774i
$$403$$ 0 0
$$404$$ 7.00000 12.1244i 0.348263 0.603209i
$$405$$ −2.00000 −0.0993808
$$406$$ 0 0
$$407$$ 24.0000 1.18964
$$408$$ 9.00000 15.5885i 0.445566 0.771744i
$$409$$ 11.0000 + 19.0526i 0.543915 + 0.942088i 0.998674 + 0.0514740i $$0.0163919\pi$$
−0.454759 + 0.890614i $$0.650275\pi$$
$$410$$ −2.00000 3.46410i −0.0987730 0.171080i
$$411$$ 3.00000 5.19615i 0.147979 0.256307i
$$412$$ −8.00000 −0.394132
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −12.0000 + 20.7846i −0.589057 + 1.02028i
$$416$$ −5.00000 8.66025i −0.245145 0.424604i
$$417$$ −6.00000 10.3923i −0.293821 0.508913i
$$418$$ 8.00000 13.8564i 0.391293 0.677739i
$$419$$ −12.0000 −0.586238 −0.293119 0.956076i $$-0.594693\pi$$
−0.293119 + 0.956076i $$0.594693\pi$$
$$420$$ 0 0
$$421$$ 38.0000 1.85201 0.926003 0.377515i $$-0.123221\pi$$
0.926003 + 0.377515i $$0.123221\pi$$
$$422$$ 2.00000 3.46410i 0.0973585 0.168630i
$$423$$ 0 0
$$424$$ −9.00000 15.5885i −0.437079 0.757042i
$$425$$ −3.00000 + 5.19615i −0.145521 + 0.252050i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −4.00000 −0.193347
$$429$$ 4.00000 6.92820i 0.193122 0.334497i
$$430$$ 4.00000 + 6.92820i 0.192897 + 0.334108i
$$431$$ 12.0000 + 20.7846i 0.578020 + 1.00116i 0.995706 + 0.0925683i $$0.0295076\pi$$
−0.417687 + 0.908591i $$0.637159\pi$$
$$432$$ 0.500000 0.866025i 0.0240563 0.0416667i
$$433$$ −14.0000 −0.672797 −0.336399 0.941720i $$-0.609209\pi$$
−0.336399 + 0.941720i $$0.609209\pi$$
$$434$$ 0 0
$$435$$ 4.00000 0.191785
$$436$$ −9.00000 + 15.5885i −0.431022 + 0.746552i
$$437$$ 0 0
$$438$$ −3.00000 5.19615i −0.143346 0.248282i
$$439$$ 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i $$-0.639218\pi$$
0.996284 0.0861252i $$-0.0274485\pi$$
$$440$$ −24.0000 −1.14416
$$441$$ 0 0
$$442$$ −12.0000 −0.570782
$$443$$ −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i $$0.493236\pi$$
−0.876454 + 0.481486i $$0.840097\pi$$
$$444$$ 3.00000 + 5.19615i 0.142374 + 0.246598i
$$445$$ −14.0000 24.2487i −0.663664 1.14950i
$$446$$ 8.00000 13.8564i 0.378811 0.656120i
$$447$$ 6.00000 0.283790
$$448$$ 0 0
$$449$$ −30.0000 −1.41579 −0.707894 0.706319i $$-0.750354\pi$$
−0.707894 + 0.706319i $$0.750354\pi$$
$$450$$ −0.500000 + 0.866025i −0.0235702 + 0.0408248i
$$451$$ −4.00000 6.92820i −0.188353 0.326236i
$$452$$ −7.00000 12.1244i −0.329252 0.570282i
$$453$$ −4.00000 + 6.92820i −0.187936 + 0.325515i
$$454$$ 12.0000 0.563188
$$455$$ 0 0
$$456$$ 12.0000 0.561951
$$457$$ −5.00000 + 8.66025i −0.233890 + 0.405110i −0.958950 0.283577i $$-0.908479\pi$$
0.725059 + 0.688686i $$0.241812\pi$$
$$458$$ −5.00000 8.66025i −0.233635 0.404667i
$$459$$ 3.00000 + 5.19615i 0.140028 + 0.242536i
$$460$$ 0 0
$$461$$ −10.0000 −0.465746 −0.232873 0.972507i $$-0.574813\pi$$
−0.232873 + 0.972507i $$0.574813\pi$$
$$462$$ 0 0
$$463$$ 16.0000 0.743583 0.371792 0.928316i $$-0.378744\pi$$
0.371792 + 0.928316i $$0.378744\pi$$
$$464$$ −1.00000 + 1.73205i −0.0464238 + 0.0804084i
$$465$$ 0 0
$$466$$ −3.00000 5.19615i −0.138972 0.240707i
$$467$$ −18.0000 + 31.1769i −0.832941 + 1.44270i 0.0627555 + 0.998029i $$0.480011\pi$$
−0.895696 + 0.444667i $$0.853322\pi$$
$$468$$ 2.00000 0.0924500
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 1.00000 1.73205i 0.0460776 0.0798087i
$$472$$ −18.0000 31.1769i −0.828517 1.43503i
$$473$$ 8.00000 + 13.8564i 0.367840 + 0.637118i
$$474$$ −8.00000 + 13.8564i −0.367452 + 0.636446i
$$475$$ −4.00000 −0.183533
$$476$$ 0 0
$$477$$ 6.00000 0.274721
$$478$$ 12.0000 20.7846i 0.548867 0.950666i
$$479$$ 8.00000 + 13.8564i 0.365529 + 0.633115i 0.988861 0.148842i $$-0.0475547\pi$$
−0.623332 + 0.781958i $$0.714221\pi$$
$$480$$ −5.00000 8.66025i −0.228218 0.395285i
$$481$$ 6.00000 10.3923i 0.273576 0.473848i
$$482$$ −2.00000 −0.0910975
$$483$$ 0 0
$$484$$ −5.00000 −0.227273
$$485$$ 18.0000 31.1769i 0.817338 1.41567i
$$486$$ 0.500000 + 0.866025i 0.0226805 + 0.0392837i
$$487$$ 4.00000 + 6.92820i 0.181257 + 0.313947i 0.942309 0.334744i $$-0.108650\pi$$
−0.761052 + 0.648691i $$0.775317\pi$$
$$488$$ 3.00000 5.19615i 0.135804 0.235219i
$$489$$ 4.00000 0.180886
$$490$$ 0 0
$$491$$ 20.0000 0.902587 0.451294 0.892375i $$-0.350963\pi$$
0.451294 + 0.892375i $$0.350963\pi$$
$$492$$ 1.00000 1.73205i 0.0450835 0.0780869i
$$493$$ −6.00000 10.3923i −0.270226 0.468046i
$$494$$ −4.00000 6.92820i −0.179969 0.311715i
$$495$$ 4.00000 6.92820i 0.179787 0.311400i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 12.0000 0.537733
$$499$$ −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
$$501$$ 4.00000 + 6.92820i 0.178707 + 0.309529i
$$502$$ −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
$$507$$ 4.50000 + 7.79423i 0.199852 + 0.346154i
$$508$$ 0 0
$$509$$ 5.00000 8.66025i 0.221621 0.383859i −0.733679 0.679496i $$-0.762199\pi$$
0.955300 + 0.295637i $$0.0955319\pi$$
$$510$$ −12.0000 −0.531369
$$511$$ 0 0
$$512$$ 11.0000 0.486136
$$513$$ −2.00000 + 3.46410i −0.0883022 + 0.152944i
$$514$$ 13.0000 + 22.5167i 0.573405 + 0.993167i
$$515$$ 8.00000 + 13.8564i 0.352522 + 0.610586i
$$516$$ −2.00000 + 3.46410i −0.0880451 + 0.152499i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −10.0000 −0.438951
$$520$$ −6.00000 + 10.3923i −0.263117 + 0.455733i
$$521$$ −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i $$-0.295679\pi$$
−0.993011 + 0.118020i $$0.962345\pi$$
$$522$$ −1.00000 1.73205i −0.0437688 0.0758098i
$$523$$ 10.0000 17.3205i 0.437269 0.757373i −0.560208 0.828352i $$-0.689279\pi$$
0.997478 + 0.0709788i $$0.0226123\pi$$
$$524$$ −4.00000 −0.174741
$$525$$ 0 0
$$526$$ −16.0000 −0.697633
$$527$$ 0 0
$$528$$ 2.00000 + 3.46410i 0.0870388 + 0.150756i
$$529$$ 11.5000 + 19.9186i 0.500000 + 0.866025i
$$530$$ −6.00000 + 10.3923i −0.260623 + 0.451413i
$$531$$ 12.0000 0.520756
$$532$$ 0 0
$$533$$ −4.00000 −0.173259
$$534$$ −7.00000 + 12.1244i −0.302920 + 0.524672i
$$535$$ 4.00000 + 6.92820i 0.172935 + 0.299532i
$$536$$ −6.00000 10.3923i −0.259161 0.448879i
$$537$$ 2.00000 3.46410i 0.0863064 0.149487i
$$538$$ −6.00000 −0.258678
$$539$$ 0 0
$$540$$ 2.00000 0.0860663
$$541$$ 17.0000 29.4449i 0.730887 1.26593i −0.225617 0.974216i $$-0.572440\pi$$
0.956504 0.291718i $$-0.0942267\pi$$
$$542$$ 8.00000 + 13.8564i 0.343629 + 0.595184i
$$543$$ 13.0000 + 22.5167i 0.557883 + 0.966282i
$$544$$ −15.0000 + 25.9808i −0.643120 + 1.11392i
$$545$$ 36.0000 1.54207
$$546$$ 0 0
$$547$$ 4.00000 0.171028 0.0855138 0.996337i $$-0.472747\pi$$
0.0855138 + 0.996337i $$0.472747\pi$$
$$548$$ −3.00000 + 5.19615i −0.128154 + 0.221969i
$$549$$ 1.00000 + 1.73205i 0.0426790 + 0.0739221i
$$550$$ −2.00000 3.46410i −0.0852803 0.147710i
$$551$$ 4.00000 6.92820i 0.170406 0.295151i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −22.0000 −0.934690
$$555$$ 6.00000 10.3923i 0.254686 0.441129i
$$556$$ 6.00000 + 10.3923i 0.254457 + 0.440732i
$$557$$ 1.00000 + 1.73205i 0.0423714 + 0.0733893i 0.886433 0.462856i $$-0.153175\pi$$
−0.844062 + 0.536246i $$0.819842\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ −24.0000 −1.01328
$$562$$ −11.0000 + 19.0526i −0.464007 + 0.803684i
$$563$$ −2.00000 3.46410i −0.0842900 0.145994i 0.820798 0.571218i $$-0.193529\pi$$
−0.905088 + 0.425223i $$0.860196\pi$$
$$564$$ 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 $$-0.900553\pi$$
0.741981 + 0.670421i $$0.233886\pi$$
$$570$$ −4.00000 6.92820i −0.167542 0.290191i
$$571$$ 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i $$-0.139994\pi$$
−0.821138 + 0.570730i $$0.806660\pi$$
$$572$$ −4.00000 + 6.92820i −0.167248 + 0.289683i
$$573$$ −8.00000 −0.334205
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −3.50000 + 6.06218i −0.145833 + 0.252591i
$$577$$ −17.0000 29.4449i −0.707719 1.22581i −0.965701 0.259656i $$-0.916391\pi$$
0.257982 0.966150i $$-0.416942\pi$$
$$578$$ 9.50000 + 16.4545i 0.395148 + 0.684416i
$$579$$ −1.00000 + 1.73205i −0.0415586 + 0.0719816i
$$580$$ −4.00000 −0.166091
$$581$$ 0 0
$$582$$ −18.0000 −0.746124
$$583$$ −12.0000 + 20.7846i −0.496989 + 0.860811i
$$584$$ 9.00000 + 15.5885i 0.372423 + 0.645055i
$$585$$ −2.00000 3.46410i −0.0826898 0.143223i
$$586$$ 7.00000 12.1244i 0.289167 0.500853i
$$587$$ 28.0000 1.15568 0.577842 0.816149i $$-0.303895\pi$$
0.577842 + 0.816149i $$0.303895\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −12.0000 + 20.7846i −0.494032 + 0.855689i
$$591$$ −11.0000 19.0526i −0.452480 0.783718i
$$592$$ 3.00000 + 5.19615i 0.123299 + 0.213561i
$$593$$ 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i $$-0.794019\pi$$
0.921026 + 0.389501i $$0.127353\pi$$
$$594$$ −4.00000 −0.164122
$$595$$ 0 0
$$596$$ −6.00000 −0.245770
$$597$$ −12.0000 + 20.7846i −0.491127 + 0.850657i
$$598$$ 0 0
$$599$$ −24.0000 41.5692i −0.980613 1.69847i −0.660006 0.751260i $$-0.729446\pi$$
−0.320607 0.947212i $$-0.603887\pi$$
$$600$$ 1.50000 2.59808i 0.0612372 0.106066i
$$601$$ −6.00000 −0.244745 −0.122373 0.992484i $$-0.539050\pi$$
−0.122373 + 0.992484i $$0.539050\pi$$
$$602$$ 0 0
$$603$$ 4.00000 0.162893
$$604$$ 4.00000 6.92820i 0.162758 0.281905i
$$605$$ 5.00000 + 8.66025i 0.203279 + 0.352089i
$$606$$ 7.00000 + 12.1244i 0.284356 + 0.492518i
$$607$$ 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i $$-0.728067\pi$$
0.981454 + 0.191700i $$0.0614000\pi$$
$$608$$ −20.0000 −0.811107
$$609$$ 0 0
$$610$$ −4.00000 −0.161955
$$611$$ 0 0
$$612$$ −3.00000 5.19615i −0.121268 0.210042i
$$613$$ 13.0000 + 22.5167i 0.525065 + 0.909439i 0.999574 + 0.0291886i $$0.00929235\pi$$
−0.474509 + 0.880251i $$0.657374\pi$$
$$614$$ 2.00000 3.46410i 0.0807134 0.139800i
$$615$$ −4.00000 −0.161296
$$616$$ 0 0
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ 4.00000 6.92820i 0.160904 0.278693i
$$619$$ 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
$$623$$ 0 0
$$624$$ 2.00000 0.0800641
$$625$$ 9.50000 16.4545i 0.380000 0.658179i
$$626$$ 13.0000 + 22.5167i 0.519584 + 0.899947i
$$627$$ −8.00000 13.8564i −0.319489 0.553372i
$$628$$ −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
$$633$$ −2.00000 3.46410i −0.0794929 0.137686i
$$634$$ −9.00000 15.5885i −0.357436 0.619097i
$$635$$ 0 0
$$636$$ −6.00000 −0.237915
$$637$$ 0 0
$$638$$ 8.00000 0.316723
$$639$$ 0 0
$$640$$ 3.00000 + 5.19615i 0.118585 + 0.205396i
$$641$$ −9.00000 15.5885i −0.355479 0.615707i 0.631721 0.775196i $$-0.282349\pi$$
−0.987200 + 0.159489i $$0.949015\pi$$
$$642$$ 2.00000 3.46410i 0.0789337 0.136717i
$$643$$ 20.0000 0.788723 0.394362 0.918955i $$-0.370966\pi$$
0.394362 + 0.918955i $$0.370966\pi$$
$$644$$ 0 0
$$645$$ 8.00000 0.315000
$$646$$ −12.0000 + 20.7846i −0.472134 + 0.817760i
$$647$$ 20.0000 + 34.6410i 0.786281 + 1.36188i 0.928231 + 0.372005i $$0.121330\pi$$
−0.141950 + 0.989874i $$0.545337\pi$$
$$648$$ −1.50000 2.59808i −0.0589256 0.102062i
$$649$$ −24.0000 + 41.5692i −0.942082 + 1.63173i
$$650$$ −2.00000 −0.0784465
$$651$$ 0 0
$$652$$ −4.00000 −0.156652
$$653$$ 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i $$-0.718768\pi$$
0.986634 + 0.162951i $$0.0521013\pi$$
$$654$$ −9.00000 15.5885i −0.351928 0.609557i
$$655$$ 4.00000 + 6.92820i 0.156293 + 0.270707i
$$656$$ 1.00000 1.73205i 0.0390434 0.0676252i
$$657$$ −6.00000 −0.234082
$$658$$ 0 0
$$659$$ 12.0000 0.467454 0.233727 0.972302i $$-0.424908\pi$$
0.233727 + 0.972302i $$0.424908\pi$$
$$660$$ −4.00000 + 6.92820i −0.155700 + 0.269680i
$$661$$ −11.0000 19.0526i −0.427850 0.741059i 0.568831 0.822454i $$-0.307396\pi$$
−0.996682 + 0.0813955i $$0.974062\pi$$
$$662$$ −2.00000 3.46410i −0.0777322 0.134636i
$$663$$ −6.00000 + 10.3923i −0.233021 + 0.403604i
$$664$$ −36.0000 −1.39707
$$665$$ 0 0
$$666$$ −6.00000 −0.232495
$$667$$ 0 0
$$668$$ −4.00000 6.92820i −0.154765 0.268060i
$$669$$ −8.00000 13.8564i −0.309298 0.535720i
$$670$$ −4.00000 + 6.92820i −0.154533 + 0.267660i
$$671$$ −8.00000 −0.308837
$$672$$ 0 0
$$673$$ 34.0000 1.31060 0.655302 0.755367i $$-0.272541\pi$$
0.655302 + 0.755367i $$0.272541\pi$$
$$674$$ −7.00000 + 12.1244i −0.269630 + 0.467013i
$$675$$ 0.500000 + 0.866025i 0.0192450 + 0.0333333i
$$676$$ −4.50000 7.79423i −0.173077 0.299778i
$$677$$ 9.00000 15.5885i 0.345898 0.599113i −0.639618 0.768693i $$-0.720908\pi$$
0.985517 + 0.169580i $$0.0542410\pi$$
$$678$$ 14.0000 0.537667
$$679$$ 0 0
$$680$$ 36.0000 1.38054
$$681$$ 6.00000 10.3923i 0.229920 0.398234i
$$682$$ 0 0
$$683$$ 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i $$-0.0929302\pi$$
−0.728101 + 0.685470i $$0.759597\pi$$
$$684$$ 2.00000 3.46410i 0.0764719 0.132453i
$$685$$ 12.0000 0.458496
$$686$$ 0 0
$$687$$ −10.0000 −0.381524
$$688$$ −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 −0.991122 0.132956i $$-0.957553\pi$$
0.610704 + 0.791859i $$0.290887\pi$$
$$692$$ 10.0000 0.380143
$$693$$ 0 0
$$694$$ 28.0000 1.06287
$$695$$ 12.0000 20.7846i 0.455186 0.788405i
$$696$$ 3.00000 + 5.19615i 0.113715 + 0.196960i
$$697$$ 6.00000 + 10.3923i 0.227266 + 0.393637i
$$698$$ −1.00000 + 1.73205i −0.0378506 + 0.0655591i
$$699$$ −6.00000 −0.226941
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ −1.00000 + 1.73205i −0.0377426 + 0.0653720i
$$703$$ −12.0000 20.7846i −0.452589 0.783906i
$$704$$ −14.0000 24.2487i −0.527645 0.913908i
$$705$$ 0 0
$$706$$ −10.0000 −0.376355
$$707$$ 0 0
$$708$$ −12.0000 −0.450988
$$709$$ −3.00000 + 5.19615i −0.112667 + 0.195146i −0.916845 0.399244i $$-0.869273\pi$$
0.804178 + 0.594389i $$0.202606\pi$$
$$710$$ 0 0
$$711$$ 8.00000 + 13.8564i 0.300023 + 0.519656i
$$712$$ 21.0000 36.3731i 0.787008 1.36314i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 16.0000 0.598366
$$716$$ −2.00000 + 3.46410i −0.0747435 + 0.129460i
$$717$$ −12.0000 20.7846i −0.448148 0.776215i
$$718$$ 16.0000 + 27.7128i 0.597115 + 1.03423i
$$719$$ 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i $$-0.480474\pi$$
0.833744 0.552151i $$-0.186193\pi$$
$$720$$ 2.00000 0.0745356
$$721$$ 0 0
$$722$$ 3.00000 0.111648
$$723$$ −1.00000 + 1.73205i −0.0371904 + 0.0644157i
$$724$$ −13.0000 22.5167i −0.483141 0.836825i
$$725$$ −1.00000 1.73205i −0.0371391 0.0643268i
$$726$$ 2.50000 4.33013i 0.0927837 0.160706i
$$727$$ −40.0000 −1.48352 −0.741759 0.670667i $$-0.766008\pi$$
−0.741759 + 0.670667i $$0.766008\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 6.00000 10.3923i 0.222070 0.384636i
$$731$$ −12.0000 20.7846i −0.443836 0.768747i
$$732$$ −1.00000 1.73205i −0.0369611 0.0640184i
$$733$$ 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
$$737$$ −8.00000 + 13.8564i −0.294684 + 0.510407i
$$738$$ 1.00000 + 1.73205i 0.0368105 + 0.0637577i
$$739$$ −18.0000 31.1769i −0.662141 1.14686i −0.980052 0.198741i $$-0.936315\pi$$
0.317911 0.948120i $$-0.397019\pi$$
$$740$$ −6.00000 + 10.3923i −0.220564 + 0.382029i
$$741$$ −8.00000 −0.293887
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 6.00000 + 10.3923i 0.219823 + 0.380745i
$$746$$ −5.00000 8.66025i −0.183063 0.317074i
$$747$$ 6.00000 10.3923i 0.219529 0.380235i
$$748$$ 24.0000 0.877527
$$749$$ 0 0
$$750$$ −12.0000 −0.438178
$$751$$ 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
$$753$$ 10.0000 + 17.3205i 0.364420 + 0.631194i
$$754$$ 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
$$763$$ 0 0
$$764$$ 8.00000 0.289430
$$765$$ −6.00000 + 10.3923i −0.216930 + 0.375735i
$$766$$ 0 0
$$767$$ 12.0000 + 20.7846i 0.433295 + 0.750489i
$$768$$ 8.50000 14.7224i 0.306717 0.531250i
$$769$$ 2.00000 0.0721218 0.0360609 0.999350i $$-0.488519\pi$$
0.0360609 + 0.999350i $$0.488519\pi$$
$$770$$ 0 0
$$771$$ 26.0000 0.936367
$$772$$ 1.00000 1.73205i 0.0359908 0.0623379i
$$773$$ −7.00000 12.1244i −0.251773 0.436083i 0.712241 0.701935i $$-0.247680\pi$$
−0.964014 + 0.265852i $$0.914347\pi$$
$$774$$ −2.00000 3.46410i −0.0718885 0.124515i
$$775$$ 0 0
$$776$$ 54.0000 1.93849
$$777$$ 0 0
$$778$$ −6.00000 −0.215110
$$779$$ −4.00000 + 6.92820i −0.143315 + 0.248229i
$$780$$ 2.00000 + 3.46410i 0.0716115 + 0.124035i
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −2.00000 −0.0714742
$$784$$ 0 0
$$785$$ 4.00000 0.142766
$$786$$ 2.00000 3.46410i 0.0713376 0.123560i
$$787$$ 22.0000 + 38.1051i 0.784215 + 1.35830i 0.929467 + 0.368906i