# Properties

 Label 1078.2.e.h.177.1 Level $1078$ Weight $2$ Character 1078.177 Analytic conductor $8.608$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1078 = 2 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1078.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.60787333789$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 154) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 177.1 Root $$0.500000 - 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1078.177 Dual form 1078.2.e.h.67.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.00000 + 1.73205i) q^{12} -4.00000 q^{13} +4.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} +2.00000 q^{20} -1.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(1.00000 + 1.73205i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-2.00000 + 3.46410i) q^{26} -4.00000 q^{27} +2.00000 q^{29} +(2.00000 - 3.46410i) q^{30} +(5.00000 + 8.66025i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +1.00000 q^{36} +(3.00000 - 5.19615i) q^{37} +(2.00000 + 3.46410i) q^{38} +(4.00000 + 6.92820i) q^{39} +(1.00000 - 1.73205i) q^{40} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(2.00000 + 3.46410i) q^{46} +(-5.00000 + 8.66025i) q^{47} +2.00000 q^{48} +1.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(7.00000 + 12.1244i) q^{53} +(-2.00000 + 3.46410i) q^{54} +2.00000 q^{55} +8.00000 q^{57} +(1.00000 - 1.73205i) q^{58} +(-5.00000 - 8.66025i) q^{59} +(-2.00000 - 3.46410i) q^{60} +(4.00000 - 6.92820i) q^{61} +10.0000 q^{62} +1.00000 q^{64} +(4.00000 - 6.92820i) q^{65} +(1.00000 + 1.73205i) q^{66} +(-4.00000 - 6.92820i) q^{67} +8.00000 q^{69} -4.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(-3.00000 - 5.19615i) q^{74} +(1.00000 - 1.73205i) q^{75} +4.00000 q^{76} +8.00000 q^{78} +(-8.00000 + 13.8564i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(5.50000 + 9.52628i) q^{81} +4.00000 q^{83} +(-2.00000 + 3.46410i) q^{86} +(-2.00000 - 3.46410i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} -2.00000 q^{90} +4.00000 q^{92} +(10.0000 - 17.3205i) q^{93} +(5.00000 + 8.66025i) q^{94} +(-4.00000 - 6.92820i) q^{95} +(1.00000 - 1.73205i) q^{96} +6.00000 q^{97} +1.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10})$$ 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 4 * q^6 - 2 * q^8 - q^9 $$2 q + q^{2} - 2 q^{3} - q^{4} - 2 q^{5} - 4 q^{6} - 2 q^{8} - q^{9} + 2 q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 8 q^{15} - q^{16} + q^{18} - 4 q^{19} + 4 q^{20} - 2 q^{22} - 4 q^{23} + 2 q^{24} + q^{25} - 4 q^{26} - 8 q^{27} + 4 q^{29} + 4 q^{30} + 10 q^{31} + q^{32} - 2 q^{33} + 2 q^{36} + 6 q^{37} + 4 q^{38} + 8 q^{39} + 2 q^{40} - 8 q^{43} - q^{44} - 2 q^{45} + 4 q^{46} - 10 q^{47} + 4 q^{48} + 2 q^{50} + 4 q^{52} + 14 q^{53} - 4 q^{54} + 4 q^{55} + 16 q^{57} + 2 q^{58} - 10 q^{59} - 4 q^{60} + 8 q^{61} + 20 q^{62} + 2 q^{64} + 8 q^{65} + 2 q^{66} - 8 q^{67} + 16 q^{69} - 8 q^{71} + q^{72} - 4 q^{73} - 6 q^{74} + 2 q^{75} + 8 q^{76} + 16 q^{78} - 16 q^{79} - 2 q^{80} + 11 q^{81} + 8 q^{83} - 4 q^{86} - 4 q^{87} + q^{88} - 10 q^{89} - 4 q^{90} + 8 q^{92} + 20 q^{93} + 10 q^{94} - 8 q^{95} + 2 q^{96} + 12 q^{97} + 2 q^{99}+O(q^{100})$$ 2 * q + q^2 - 2 * q^3 - q^4 - 2 * q^5 - 4 * q^6 - 2 * q^8 - q^9 + 2 * q^10 - q^11 - 2 * q^12 - 8 * q^13 + 8 * q^15 - q^16 + q^18 - 4 * q^19 + 4 * q^20 - 2 * q^22 - 4 * q^23 + 2 * q^24 + q^25 - 4 * q^26 - 8 * q^27 + 4 * q^29 + 4 * q^30 + 10 * q^31 + q^32 - 2 * q^33 + 2 * q^36 + 6 * q^37 + 4 * q^38 + 8 * q^39 + 2 * q^40 - 8 * q^43 - q^44 - 2 * q^45 + 4 * q^46 - 10 * q^47 + 4 * q^48 + 2 * q^50 + 4 * q^52 + 14 * q^53 - 4 * q^54 + 4 * q^55 + 16 * q^57 + 2 * q^58 - 10 * q^59 - 4 * q^60 + 8 * q^61 + 20 * q^62 + 2 * q^64 + 8 * q^65 + 2 * q^66 - 8 * q^67 + 16 * q^69 - 8 * q^71 + q^72 - 4 * q^73 - 6 * q^74 + 2 * q^75 + 8 * q^76 + 16 * q^78 - 16 * q^79 - 2 * q^80 + 11 * q^81 + 8 * q^83 - 4 * q^86 - 4 * q^87 + q^88 - 10 * q^89 - 4 * q^90 + 8 * q^92 + 20 * q^93 + 10 * q^94 - 8 * q^95 + 2 * q^96 + 12 * q^97 + 2 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$981$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$3$$ −1.00000 1.73205i −0.577350 1.00000i −0.995782 0.0917517i $$-0.970753\pi$$
0.418432 0.908248i $$-0.362580\pi$$
$$4$$ −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 $$0.314250\pi$$
$$6$$ −2.00000 −0.816497
$$7$$ 0 0
$$8$$ −1.00000 −0.353553
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 1.00000 + 1.73205i 0.316228 + 0.547723i
$$11$$ −0.500000 0.866025i −0.150756 0.261116i
$$12$$ −1.00000 + 1.73205i −0.288675 + 0.500000i
$$13$$ −4.00000 −1.10940 −0.554700 0.832050i $$-0.687167\pi$$
−0.554700 + 0.832050i $$0.687167\pi$$
$$14$$ 0 0
$$15$$ 4.00000 1.03280
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ 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
$$22$$ −1.00000 −0.213201
$$23$$ −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i $$-0.970262\pi$$
0.578610 + 0.815604i $$0.303595\pi$$
$$24$$ 1.00000 + 1.73205i 0.204124 + 0.353553i
$$25$$ 0.500000 + 0.866025i 0.100000 + 0.173205i
$$26$$ −2.00000 + 3.46410i −0.392232 + 0.679366i
$$27$$ −4.00000 −0.769800
$$28$$ 0 0
$$29$$ 2.00000 0.371391 0.185695 0.982607i $$-0.440546\pi$$
0.185695 + 0.982607i $$0.440546\pi$$
$$30$$ 2.00000 3.46410i 0.365148 0.632456i
$$31$$ 5.00000 + 8.66025i 0.898027 + 1.55543i 0.830014 + 0.557743i $$0.188333\pi$$
0.0680129 + 0.997684i $$0.478334\pi$$
$$32$$ 0.500000 + 0.866025i 0.0883883 + 0.153093i
$$33$$ −1.00000 + 1.73205i −0.174078 + 0.301511i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 3.00000 5.19615i 0.493197 0.854242i −0.506772 0.862080i $$-0.669162\pi$$
0.999969 + 0.00783774i $$0.00249486\pi$$
$$38$$ 2.00000 + 3.46410i 0.324443 + 0.561951i
$$39$$ 4.00000 + 6.92820i 0.640513 + 1.10940i
$$40$$ 1.00000 1.73205i 0.158114 0.273861i
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −4.00000 −0.609994 −0.304997 0.952353i $$-0.598656\pi$$
−0.304997 + 0.952353i $$0.598656\pi$$
$$44$$ −0.500000 + 0.866025i −0.0753778 + 0.130558i
$$45$$ −1.00000 1.73205i −0.149071 0.258199i
$$46$$ 2.00000 + 3.46410i 0.294884 + 0.510754i
$$47$$ −5.00000 + 8.66025i −0.729325 + 1.26323i 0.227844 + 0.973698i $$0.426832\pi$$
−0.957169 + 0.289530i $$0.906501\pi$$
$$48$$ 2.00000 0.288675
$$49$$ 0 0
$$50$$ 1.00000 0.141421
$$51$$ 0 0
$$52$$ 2.00000 + 3.46410i 0.277350 + 0.480384i
$$53$$ 7.00000 + 12.1244i 0.961524 + 1.66541i 0.718677 + 0.695344i $$0.244748\pi$$
0.242846 + 0.970065i $$0.421919\pi$$
$$54$$ −2.00000 + 3.46410i −0.272166 + 0.471405i
$$55$$ 2.00000 0.269680
$$56$$ 0 0
$$57$$ 8.00000 1.05963
$$58$$ 1.00000 1.73205i 0.131306 0.227429i
$$59$$ −5.00000 8.66025i −0.650945 1.12747i −0.982894 0.184172i $$-0.941040\pi$$
0.331949 0.943297i $$-0.392294\pi$$
$$60$$ −2.00000 3.46410i −0.258199 0.447214i
$$61$$ 4.00000 6.92820i 0.512148 0.887066i −0.487753 0.872982i $$-0.662183\pi$$
0.999901 0.0140840i $$-0.00448323\pi$$
$$62$$ 10.0000 1.27000
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 4.00000 6.92820i 0.496139 0.859338i
$$66$$ 1.00000 + 1.73205i 0.123091 + 0.213201i
$$67$$ −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i $$-0.329187\pi$$
−0.999915 + 0.0130248i $$0.995854\pi$$
$$68$$ 0 0
$$69$$ 8.00000 0.963087
$$70$$ 0 0
$$71$$ −4.00000 −0.474713 −0.237356 0.971423i $$-0.576281\pi$$
−0.237356 + 0.971423i $$0.576281\pi$$
$$72$$ 0.500000 0.866025i 0.0589256 0.102062i
$$73$$ −2.00000 3.46410i −0.234082 0.405442i 0.724923 0.688830i $$-0.241875\pi$$
−0.959006 + 0.283387i $$0.908542\pi$$
$$74$$ −3.00000 5.19615i −0.348743 0.604040i
$$75$$ 1.00000 1.73205i 0.115470 0.200000i
$$76$$ 4.00000 0.458831
$$77$$ 0 0
$$78$$ 8.00000 0.905822
$$79$$ −8.00000 + 13.8564i −0.900070 + 1.55897i −0.0726692 + 0.997356i $$0.523152\pi$$
−0.827401 + 0.561611i $$0.810182\pi$$
$$80$$ −1.00000 1.73205i −0.111803 0.193649i
$$81$$ 5.50000 + 9.52628i 0.611111 + 1.05848i
$$82$$ 0 0
$$83$$ 4.00000 0.439057 0.219529 0.975606i $$-0.429548\pi$$
0.219529 + 0.975606i $$0.429548\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −2.00000 + 3.46410i −0.215666 + 0.373544i
$$87$$ −2.00000 3.46410i −0.214423 0.371391i
$$88$$ 0.500000 + 0.866025i 0.0533002 + 0.0923186i
$$89$$ −5.00000 + 8.66025i −0.529999 + 0.917985i 0.469389 + 0.882992i $$0.344474\pi$$
−0.999388 + 0.0349934i $$0.988859\pi$$
$$90$$ −2.00000 −0.210819
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ 10.0000 17.3205i 1.03695 1.79605i
$$94$$ 5.00000 + 8.66025i 0.515711 + 0.893237i
$$95$$ −4.00000 6.92820i −0.410391 0.710819i
$$96$$ 1.00000 1.73205i 0.102062 0.176777i
$$97$$ 6.00000 0.609208 0.304604 0.952479i $$-0.401476\pi$$
0.304604 + 0.952479i $$0.401476\pi$$
$$98$$ 0 0
$$99$$ 1.00000 0.100504
$$100$$ 0.500000 0.866025i 0.0500000 0.0866025i
$$101$$ −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i $$-0.963017\pi$$
0.396236 0.918149i $$-0.370316\pi$$
$$102$$ 0 0
$$103$$ −1.00000 + 1.73205i −0.0985329 + 0.170664i −0.911078 0.412235i $$-0.864748\pi$$
0.812545 + 0.582899i $$0.198082\pi$$
$$104$$ 4.00000 0.392232
$$105$$ 0 0
$$106$$ 14.0000 1.35980
$$107$$ 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i $$-0.636370\pi$$
0.995474 0.0950377i $$-0.0302972\pi$$
$$108$$ 2.00000 + 3.46410i 0.192450 + 0.333333i
$$109$$ 7.00000 + 12.1244i 0.670478 + 1.16130i 0.977769 + 0.209687i $$0.0672444\pi$$
−0.307290 + 0.951616i $$0.599422\pi$$
$$110$$ 1.00000 1.73205i 0.0953463 0.165145i
$$111$$ −12.0000 −1.13899
$$112$$ 0 0
$$113$$ −14.0000 −1.31701 −0.658505 0.752577i $$-0.728811\pi$$
−0.658505 + 0.752577i $$0.728811\pi$$
$$114$$ 4.00000 6.92820i 0.374634 0.648886i
$$115$$ −4.00000 6.92820i −0.373002 0.646058i
$$116$$ −1.00000 1.73205i −0.0928477 0.160817i
$$117$$ 2.00000 3.46410i 0.184900 0.320256i
$$118$$ −10.0000 −0.920575
$$119$$ 0 0
$$120$$ −4.00000 −0.365148
$$121$$ −0.500000 + 0.866025i −0.0454545 + 0.0787296i
$$122$$ −4.00000 6.92820i −0.362143 0.627250i
$$123$$ 0 0
$$124$$ 5.00000 8.66025i 0.449013 0.777714i
$$125$$ −12.0000 −1.07331
$$126$$ 0 0
$$127$$ −16.0000 −1.41977 −0.709885 0.704317i $$-0.751253\pi$$
−0.709885 + 0.704317i $$0.751253\pi$$
$$128$$ 0.500000 0.866025i 0.0441942 0.0765466i
$$129$$ 4.00000 + 6.92820i 0.352180 + 0.609994i
$$130$$ −4.00000 6.92820i −0.350823 0.607644i
$$131$$ −4.00000 + 6.92820i −0.349482 + 0.605320i −0.986157 0.165812i $$-0.946976\pi$$
0.636676 + 0.771132i $$0.280309\pi$$
$$132$$ 2.00000 0.174078
$$133$$ 0 0
$$134$$ −8.00000 −0.691095
$$135$$ 4.00000 6.92820i 0.344265 0.596285i
$$136$$ 0 0
$$137$$ −3.00000 5.19615i −0.256307 0.443937i 0.708942 0.705266i $$-0.249173\pi$$
−0.965250 + 0.261329i $$0.915839\pi$$
$$138$$ 4.00000 6.92820i 0.340503 0.589768i
$$139$$ 20.0000 1.69638 0.848189 0.529694i $$-0.177693\pi$$
0.848189 + 0.529694i $$0.177693\pi$$
$$140$$ 0 0
$$141$$ 20.0000 1.68430
$$142$$ −2.00000 + 3.46410i −0.167836 + 0.290701i
$$143$$ 2.00000 + 3.46410i 0.167248 + 0.289683i
$$144$$ −0.500000 0.866025i −0.0416667 0.0721688i
$$145$$ −2.00000 + 3.46410i −0.166091 + 0.287678i
$$146$$ −4.00000 −0.331042
$$147$$ 0 0
$$148$$ −6.00000 −0.493197
$$149$$ −11.0000 + 19.0526i −0.901155 + 1.56085i −0.0751583 + 0.997172i $$0.523946\pi$$
−0.825997 + 0.563675i $$0.809387\pi$$
$$150$$ −1.00000 1.73205i −0.0816497 0.141421i
$$151$$ −8.00000 13.8564i −0.651031 1.12762i −0.982873 0.184284i $$-0.941004\pi$$
0.331842 0.943335i $$-0.392330\pi$$
$$152$$ 2.00000 3.46410i 0.162221 0.280976i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −20.0000 −1.60644
$$156$$ 4.00000 6.92820i 0.320256 0.554700i
$$157$$ −5.00000 8.66025i −0.399043 0.691164i 0.594565 0.804048i $$-0.297324\pi$$
−0.993608 + 0.112884i $$0.963991\pi$$
$$158$$ 8.00000 + 13.8564i 0.636446 + 1.10236i
$$159$$ 14.0000 24.2487i 1.11027 1.92305i
$$160$$ −2.00000 −0.158114
$$161$$ 0 0
$$162$$ 11.0000 0.864242
$$163$$ −12.0000 + 20.7846i −0.939913 + 1.62798i −0.174282 + 0.984696i $$0.555760\pi$$
−0.765631 + 0.643280i $$0.777573\pi$$
$$164$$ 0 0
$$165$$ −2.00000 3.46410i −0.155700 0.269680i
$$166$$ 2.00000 3.46410i 0.155230 0.268866i
$$167$$ −8.00000 −0.619059 −0.309529 0.950890i $$-0.600171\pi$$
−0.309529 + 0.950890i $$0.600171\pi$$
$$168$$ 0 0
$$169$$ 3.00000 0.230769
$$170$$ 0 0
$$171$$ −2.00000 3.46410i −0.152944 0.264906i
$$172$$ 2.00000 + 3.46410i 0.152499 + 0.264135i
$$173$$ −2.00000 + 3.46410i −0.152057 + 0.263371i −0.931984 0.362500i $$-0.881923\pi$$
0.779926 + 0.625871i $$0.215256\pi$$
$$174$$ −4.00000 −0.303239
$$175$$ 0 0
$$176$$ 1.00000 0.0753778
$$177$$ −10.0000 + 17.3205i −0.751646 + 1.30189i
$$178$$ 5.00000 + 8.66025i 0.374766 + 0.649113i
$$179$$ −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i $$-0.314694\pi$$
−0.998286 + 0.0585225i $$0.981361\pi$$
$$180$$ −1.00000 + 1.73205i −0.0745356 + 0.129099i
$$181$$ 14.0000 1.04061 0.520306 0.853980i $$-0.325818\pi$$
0.520306 + 0.853980i $$0.325818\pi$$
$$182$$ 0 0
$$183$$ −16.0000 −1.18275
$$184$$ 2.00000 3.46410i 0.147442 0.255377i
$$185$$ 6.00000 + 10.3923i 0.441129 + 0.764057i
$$186$$ −10.0000 17.3205i −0.733236 1.27000i
$$187$$ 0 0
$$188$$ 10.0000 0.729325
$$189$$ 0 0
$$190$$ −8.00000 −0.580381
$$191$$ −4.00000 + 6.92820i −0.289430 + 0.501307i −0.973674 0.227946i $$-0.926799\pi$$
0.684244 + 0.729253i $$0.260132\pi$$
$$192$$ −1.00000 1.73205i −0.0721688 0.125000i
$$193$$ 3.00000 + 5.19615i 0.215945 + 0.374027i 0.953564 0.301189i $$-0.0973836\pi$$
−0.737620 + 0.675216i $$0.764050\pi$$
$$194$$ 3.00000 5.19615i 0.215387 0.373062i
$$195$$ −16.0000 −1.14578
$$196$$ 0 0
$$197$$ −18.0000 −1.28245 −0.641223 0.767354i $$-0.721573\pi$$
−0.641223 + 0.767354i $$0.721573\pi$$
$$198$$ 0.500000 0.866025i 0.0355335 0.0615457i
$$199$$ 7.00000 + 12.1244i 0.496217 + 0.859473i 0.999990 0.00436292i $$-0.00138876\pi$$
−0.503774 + 0.863836i $$0.668055\pi$$
$$200$$ −0.500000 0.866025i −0.0353553 0.0612372i
$$201$$ −8.00000 + 13.8564i −0.564276 + 0.977356i
$$202$$ −12.0000 −0.844317
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 1.00000 + 1.73205i 0.0696733 + 0.120678i
$$207$$ −2.00000 3.46410i −0.139010 0.240772i
$$208$$ 2.00000 3.46410i 0.138675 0.240192i
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ −4.00000 −0.275371 −0.137686 0.990476i $$-0.543966\pi$$
−0.137686 + 0.990476i $$0.543966\pi$$
$$212$$ 7.00000 12.1244i 0.480762 0.832704i
$$213$$ 4.00000 + 6.92820i 0.274075 + 0.474713i
$$214$$ −6.00000 10.3923i −0.410152 0.710403i
$$215$$ 4.00000 6.92820i 0.272798 0.472500i
$$216$$ 4.00000 0.272166
$$217$$ 0 0
$$218$$ 14.0000 0.948200
$$219$$ −4.00000 + 6.92820i −0.270295 + 0.468165i
$$220$$ −1.00000 1.73205i −0.0674200 0.116775i
$$221$$ 0 0
$$222$$ −6.00000 + 10.3923i −0.402694 + 0.697486i
$$223$$ −14.0000 −0.937509 −0.468755 0.883328i $$-0.655297\pi$$
−0.468755 + 0.883328i $$0.655297\pi$$
$$224$$ 0 0
$$225$$ −1.00000 −0.0666667
$$226$$ −7.00000 + 12.1244i −0.465633 + 0.806500i
$$227$$ −4.00000 6.92820i −0.265489 0.459841i 0.702202 0.711977i $$-0.252200\pi$$
−0.967692 + 0.252136i $$0.918867\pi$$
$$228$$ −4.00000 6.92820i −0.264906 0.458831i
$$229$$ 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i $$-0.726147\pi$$
0.982592 + 0.185776i $$0.0594799\pi$$
$$230$$ −8.00000 −0.527504
$$231$$ 0 0
$$232$$ −2.00000 −0.131306
$$233$$ −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i $$-0.896303\pi$$
0.750867 + 0.660454i $$0.229636\pi$$
$$234$$ −2.00000 3.46410i −0.130744 0.226455i
$$235$$ −10.0000 17.3205i −0.652328 1.12987i
$$236$$ −5.00000 + 8.66025i −0.325472 + 0.563735i
$$237$$ 32.0000 2.07862
$$238$$ 0 0
$$239$$ −8.00000 −0.517477 −0.258738 0.965947i $$-0.583307\pi$$
−0.258738 + 0.965947i $$0.583307\pi$$
$$240$$ −2.00000 + 3.46410i −0.129099 + 0.223607i
$$241$$ −4.00000 6.92820i −0.257663 0.446285i 0.707953 0.706260i $$-0.249619\pi$$
−0.965615 + 0.259975i $$0.916286\pi$$
$$242$$ 0.500000 + 0.866025i 0.0321412 + 0.0556702i
$$243$$ 5.00000 8.66025i 0.320750 0.555556i
$$244$$ −8.00000 −0.512148
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 8.00000 13.8564i 0.509028 0.881662i
$$248$$ −5.00000 8.66025i −0.317500 0.549927i
$$249$$ −4.00000 6.92820i −0.253490 0.439057i
$$250$$ −6.00000 + 10.3923i −0.379473 + 0.657267i
$$251$$ −26.0000 −1.64111 −0.820553 0.571571i $$-0.806334\pi$$
−0.820553 + 0.571571i $$0.806334\pi$$
$$252$$ 0 0
$$253$$ 4.00000 0.251478
$$254$$ −8.00000 + 13.8564i −0.501965 + 0.869428i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −1.00000 + 1.73205i −0.0623783 + 0.108042i −0.895528 0.445005i $$-0.853202\pi$$
0.833150 + 0.553047i $$0.186535\pi$$
$$258$$ 8.00000 0.498058
$$259$$ 0 0
$$260$$ −8.00000 −0.496139
$$261$$ −1.00000 + 1.73205i −0.0618984 + 0.107211i
$$262$$ 4.00000 + 6.92820i 0.247121 + 0.428026i
$$263$$ 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i $$0.0984850\pi$$
−0.212565 + 0.977147i $$0.568182\pi$$
$$264$$ 1.00000 1.73205i 0.0615457 0.106600i
$$265$$ −28.0000 −1.72003
$$266$$ 0 0
$$267$$ 20.0000 1.22398
$$268$$ −4.00000 + 6.92820i −0.244339 + 0.423207i
$$269$$ −7.00000 12.1244i −0.426798 0.739235i 0.569789 0.821791i $$-0.307025\pi$$
−0.996586 + 0.0825561i $$0.973692\pi$$
$$270$$ −4.00000 6.92820i −0.243432 0.421637i
$$271$$ 14.0000 24.2487i 0.850439 1.47300i −0.0303728 0.999539i $$-0.509669\pi$$
0.880812 0.473466i $$-0.156997\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ −6.00000 −0.362473
$$275$$ 0.500000 0.866025i 0.0301511 0.0522233i
$$276$$ −4.00000 6.92820i −0.240772 0.417029i
$$277$$ −3.00000 5.19615i −0.180253 0.312207i 0.761714 0.647913i $$-0.224358\pi$$
−0.941966 + 0.335707i $$0.891025\pi$$
$$278$$ 10.0000 17.3205i 0.599760 1.03882i
$$279$$ −10.0000 −0.598684
$$280$$ 0 0
$$281$$ 30.0000 1.78965 0.894825 0.446417i $$-0.147300\pi$$
0.894825 + 0.446417i $$0.147300\pi$$
$$282$$ 10.0000 17.3205i 0.595491 1.03142i
$$283$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$284$$ 2.00000 + 3.46410i 0.118678 + 0.205557i
$$285$$ −8.00000 + 13.8564i −0.473879 + 0.820783i
$$286$$ 4.00000 0.236525
$$287$$ 0 0
$$288$$ −1.00000 −0.0589256
$$289$$ 8.50000 14.7224i 0.500000 0.866025i
$$290$$ 2.00000 + 3.46410i 0.117444 + 0.203419i
$$291$$ −6.00000 10.3923i −0.351726 0.609208i
$$292$$ −2.00000 + 3.46410i −0.117041 + 0.202721i
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 20.0000 1.16445
$$296$$ −3.00000 + 5.19615i −0.174371 + 0.302020i
$$297$$ 2.00000 + 3.46410i 0.116052 + 0.201008i
$$298$$ 11.0000 + 19.0526i 0.637213 + 1.10369i
$$299$$ 8.00000 13.8564i 0.462652 0.801337i
$$300$$ −2.00000 −0.115470
$$301$$ 0 0
$$302$$ −16.0000 −0.920697
$$303$$ −12.0000 + 20.7846i −0.689382 + 1.19404i
$$304$$ −2.00000 3.46410i −0.114708 0.198680i
$$305$$ 8.00000 + 13.8564i 0.458079 + 0.793416i
$$306$$ 0 0
$$307$$ 16.0000 0.913168 0.456584 0.889680i $$-0.349073\pi$$
0.456584 + 0.889680i $$0.349073\pi$$
$$308$$ 0 0
$$309$$ 4.00000 0.227552
$$310$$ −10.0000 + 17.3205i −0.567962 + 0.983739i
$$311$$ 3.00000 + 5.19615i 0.170114 + 0.294647i 0.938460 0.345389i $$-0.112253\pi$$
−0.768345 + 0.640036i $$0.778920\pi$$
$$312$$ −4.00000 6.92820i −0.226455 0.392232i
$$313$$ 3.00000 5.19615i 0.169570 0.293704i −0.768699 0.639611i $$-0.779095\pi$$
0.938269 + 0.345907i $$0.112429\pi$$
$$314$$ −10.0000 −0.564333
$$315$$ 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 $$-0.00202172\pi$$
$$318$$ −14.0000 24.2487i −0.785081 1.35980i
$$319$$ −1.00000 1.73205i −0.0559893 0.0969762i
$$320$$ −1.00000 + 1.73205i −0.0559017 + 0.0968246i
$$321$$ −24.0000 −1.33955
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 5.50000 9.52628i 0.305556 0.529238i
$$325$$ −2.00000 3.46410i −0.110940 0.192154i
$$326$$ 12.0000 + 20.7846i 0.664619 + 1.15115i
$$327$$ 14.0000 24.2487i 0.774202 1.34096i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ −4.00000 −0.220193
$$331$$ 10.0000 17.3205i 0.549650 0.952021i −0.448649 0.893708i $$-0.648095\pi$$
0.998298 0.0583130i $$-0.0185721\pi$$
$$332$$ −2.00000 3.46410i −0.109764 0.190117i
$$333$$ 3.00000 + 5.19615i 0.164399 + 0.284747i
$$334$$ −4.00000 + 6.92820i −0.218870 + 0.379094i
$$335$$ 16.0000 0.874173
$$336$$ 0 0
$$337$$ −34.0000 −1.85210 −0.926049 0.377403i $$-0.876817\pi$$
−0.926049 + 0.377403i $$0.876817\pi$$
$$338$$ 1.50000 2.59808i 0.0815892 0.141317i
$$339$$ 14.0000 + 24.2487i 0.760376 + 1.31701i
$$340$$ 0 0
$$341$$ 5.00000 8.66025i 0.270765 0.468979i
$$342$$ −4.00000 −0.216295
$$343$$ 0 0
$$344$$ 4.00000 0.215666
$$345$$ −8.00000 + 13.8564i −0.430706 + 0.746004i
$$346$$ 2.00000 + 3.46410i 0.107521 + 0.186231i
$$347$$ 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i $$-0.0622790\pi$$
−0.658824 + 0.752297i $$0.728946\pi$$
$$348$$ −2.00000 + 3.46410i −0.107211 + 0.185695i
$$349$$ 32.0000 1.71292 0.856460 0.516213i $$-0.172659\pi$$
0.856460 + 0.516213i $$0.172659\pi$$
$$350$$ 0 0
$$351$$ 16.0000 0.854017
$$352$$ 0.500000 0.866025i 0.0266501 0.0461593i
$$353$$ −1.00000 1.73205i −0.0532246 0.0921878i 0.838186 0.545385i $$-0.183617\pi$$
−0.891410 + 0.453197i $$0.850283\pi$$
$$354$$ 10.0000 + 17.3205i 0.531494 + 0.920575i
$$355$$ 4.00000 6.92820i 0.212298 0.367711i
$$356$$ 10.0000 0.529999
$$357$$ 0 0
$$358$$ −12.0000 −0.634220
$$359$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$360$$ 1.00000 + 1.73205i 0.0527046 + 0.0912871i
$$361$$ 1.50000 + 2.59808i 0.0789474 + 0.136741i
$$362$$ 7.00000 12.1244i 0.367912 0.637242i
$$363$$ 2.00000 0.104973
$$364$$ 0 0
$$365$$ 8.00000 0.418739
$$366$$ −8.00000 + 13.8564i −0.418167 + 0.724286i
$$367$$ −9.00000 15.5885i −0.469796 0.813711i 0.529607 0.848243i $$-0.322339\pi$$
−0.999404 + 0.0345320i $$0.989006\pi$$
$$368$$ −2.00000 3.46410i −0.104257 0.180579i
$$369$$ 0 0
$$370$$ 12.0000 0.623850
$$371$$ 0 0
$$372$$ −20.0000 −1.03695
$$373$$ 17.0000 29.4449i 0.880227 1.52460i 0.0291379 0.999575i $$-0.490724\pi$$
0.851089 0.525022i $$-0.175943\pi$$
$$374$$ 0 0
$$375$$ 12.0000 + 20.7846i 0.619677 + 1.07331i
$$376$$ 5.00000 8.66025i 0.257855 0.446619i
$$377$$ −8.00000 −0.412021
$$378$$ 0 0
$$379$$ 8.00000 0.410932 0.205466 0.978664i $$-0.434129\pi$$
0.205466 + 0.978664i $$0.434129\pi$$
$$380$$ −4.00000 + 6.92820i −0.205196 + 0.355409i
$$381$$ 16.0000 + 27.7128i 0.819705 + 1.41977i
$$382$$ 4.00000 + 6.92820i 0.204658 + 0.354478i
$$383$$ −7.00000 + 12.1244i −0.357683 + 0.619526i −0.987573 0.157159i $$-0.949767\pi$$
0.629890 + 0.776684i $$0.283100\pi$$
$$384$$ −2.00000 −0.102062
$$385$$ 0 0
$$386$$ 6.00000 0.305392
$$387$$ 2.00000 3.46410i 0.101666 0.176090i
$$388$$ −3.00000 5.19615i −0.152302 0.263795i
$$389$$ 9.00000 + 15.5885i 0.456318 + 0.790366i 0.998763 0.0497253i $$-0.0158346\pi$$
−0.542445 + 0.840091i $$0.682501\pi$$
$$390$$ −8.00000 + 13.8564i −0.405096 + 0.701646i
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 16.0000 0.807093
$$394$$ −9.00000 + 15.5885i −0.453413 + 0.785335i
$$395$$ −16.0000 27.7128i −0.805047 1.39438i
$$396$$ −0.500000 0.866025i −0.0251259 0.0435194i
$$397$$ −9.00000 + 15.5885i −0.451697 + 0.782362i −0.998492 0.0549046i $$-0.982515\pi$$
0.546795 + 0.837267i $$0.315848\pi$$
$$398$$ 14.0000 0.701757
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ −5.00000 + 8.66025i −0.249688 + 0.432472i −0.963439 0.267927i $$-0.913661\pi$$
0.713751 + 0.700399i $$0.246995\pi$$
$$402$$ 8.00000 + 13.8564i 0.399004 + 0.691095i
$$403$$ −20.0000 34.6410i −0.996271 1.72559i
$$404$$ −6.00000 + 10.3923i −0.298511 + 0.517036i
$$405$$ −22.0000 −1.09319
$$406$$ 0 0
$$407$$ −6.00000 −0.297409
$$408$$ 0 0
$$409$$ 2.00000 + 3.46410i 0.0988936 + 0.171289i 0.911227 0.411905i $$-0.135136\pi$$
−0.812333 + 0.583193i $$0.801803\pi$$
$$410$$ 0 0
$$411$$ −6.00000 + 10.3923i −0.295958 + 0.512615i
$$412$$ 2.00000 0.0985329
$$413$$ 0 0
$$414$$ −4.00000 −0.196589
$$415$$ −4.00000 + 6.92820i −0.196352 + 0.340092i
$$416$$ −2.00000 3.46410i −0.0980581 0.169842i
$$417$$ −20.0000 34.6410i −0.979404 1.69638i
$$418$$ 2.00000 3.46410i 0.0978232 0.169435i
$$419$$ −30.0000 −1.46560 −0.732798 0.680446i $$-0.761786\pi$$
−0.732798 + 0.680446i $$0.761786\pi$$
$$420$$ 0 0
$$421$$ 10.0000 0.487370 0.243685 0.969854i $$-0.421644\pi$$
0.243685 + 0.969854i $$0.421644\pi$$
$$422$$ −2.00000 + 3.46410i −0.0973585 + 0.168630i
$$423$$ −5.00000 8.66025i −0.243108 0.421076i
$$424$$ −7.00000 12.1244i −0.339950 0.588811i
$$425$$ 0 0
$$426$$ 8.00000 0.387601
$$427$$ 0 0
$$428$$ −12.0000 −0.580042
$$429$$ 4.00000 6.92820i 0.193122 0.334497i
$$430$$ −4.00000 6.92820i −0.192897 0.334108i
$$431$$ 8.00000 + 13.8564i 0.385346 + 0.667440i 0.991817 0.127666i $$-0.0407486\pi$$
−0.606471 + 0.795106i $$0.707415\pi$$
$$432$$ 2.00000 3.46410i 0.0962250 0.166667i
$$433$$ −10.0000 −0.480569 −0.240285 0.970702i $$-0.577241\pi$$
−0.240285 + 0.970702i $$0.577241\pi$$
$$434$$ 0 0
$$435$$ 8.00000 0.383571
$$436$$ 7.00000 12.1244i 0.335239 0.580651i
$$437$$ −8.00000 13.8564i −0.382692 0.662842i
$$438$$ 4.00000 + 6.92820i 0.191127 + 0.331042i
$$439$$ 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i $$-0.600405\pi$$
0.978412 0.206666i $$-0.0662612\pi$$
$$440$$ −2.00000 −0.0953463
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −2.00000 + 3.46410i −0.0950229 + 0.164584i −0.909618 0.415445i $$-0.863626\pi$$
0.814595 + 0.580030i $$0.196959\pi$$
$$444$$ 6.00000 + 10.3923i 0.284747 + 0.493197i
$$445$$ −10.0000 17.3205i −0.474045 0.821071i
$$446$$ −7.00000 + 12.1244i −0.331460 + 0.574105i
$$447$$ 44.0000 2.08113
$$448$$ 0 0
$$449$$ 6.00000 0.283158 0.141579 0.989927i $$-0.454782\pi$$
0.141579 + 0.989927i $$0.454782\pi$$
$$450$$ −0.500000 + 0.866025i −0.0235702 + 0.0408248i
$$451$$ 0 0
$$452$$ 7.00000 + 12.1244i 0.329252 + 0.570282i
$$453$$ −16.0000 + 27.7128i −0.751746 + 1.30206i
$$454$$ −8.00000 −0.375459
$$455$$ 0 0
$$456$$ −8.00000 −0.374634
$$457$$ 19.0000 32.9090i 0.888783 1.53942i 0.0474665 0.998873i $$-0.484885\pi$$
0.841316 0.540544i $$-0.181781\pi$$
$$458$$ −5.00000 8.66025i −0.233635 0.404667i
$$459$$ 0 0
$$460$$ −4.00000 + 6.92820i −0.186501 + 0.323029i
$$461$$ 32.0000 1.49039 0.745194 0.666847i $$-0.232357\pi$$
0.745194 + 0.666847i $$0.232357\pi$$
$$462$$ 0 0
$$463$$ 12.0000 0.557687 0.278844 0.960337i $$-0.410049\pi$$
0.278844 + 0.960337i $$0.410049\pi$$
$$464$$ −1.00000 + 1.73205i −0.0464238 + 0.0804084i
$$465$$ 20.0000 + 34.6410i 0.927478 + 1.60644i
$$466$$ 3.00000 + 5.19615i 0.138972 + 0.240707i
$$467$$ −7.00000 + 12.1244i −0.323921 + 0.561048i −0.981293 0.192518i $$-0.938335\pi$$
0.657372 + 0.753566i $$0.271668\pi$$
$$468$$ −4.00000 −0.184900
$$469$$ 0 0
$$470$$ −20.0000 −0.922531
$$471$$ −10.0000 + 17.3205i −0.460776 + 0.798087i
$$472$$ 5.00000 + 8.66025i 0.230144 + 0.398621i
$$473$$ 2.00000 + 3.46410i 0.0919601 + 0.159280i
$$474$$ 16.0000 27.7128i 0.734904 1.27289i
$$475$$ −4.00000 −0.183533
$$476$$ 0 0
$$477$$ −14.0000 −0.641016
$$478$$ −4.00000 + 6.92820i −0.182956 + 0.316889i
$$479$$ −6.00000 10.3923i −0.274147 0.474837i 0.695773 0.718262i $$-0.255062\pi$$
−0.969920 + 0.243426i $$0.921729\pi$$
$$480$$ 2.00000 + 3.46410i 0.0912871 + 0.158114i
$$481$$ −12.0000 + 20.7846i −0.547153 + 0.947697i
$$482$$ −8.00000 −0.364390
$$483$$ 0 0
$$484$$ 1.00000 0.0454545
$$485$$ −6.00000 + 10.3923i −0.272446 + 0.471890i
$$486$$ −5.00000 8.66025i −0.226805 0.392837i
$$487$$ −6.00000 10.3923i −0.271886 0.470920i 0.697459 0.716625i $$-0.254314\pi$$
−0.969345 + 0.245705i $$0.920981\pi$$
$$488$$ −4.00000 + 6.92820i −0.181071 + 0.313625i
$$489$$ 48.0000 2.17064
$$490$$ 0 0
$$491$$ −28.0000 −1.26362 −0.631811 0.775122i $$-0.717688\pi$$
−0.631811 + 0.775122i $$0.717688\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ −8.00000 13.8564i −0.359937 0.623429i
$$495$$ −1.00000 + 1.73205i −0.0449467 + 0.0778499i
$$496$$ −10.0000 −0.449013
$$497$$ 0 0
$$498$$ −8.00000 −0.358489
$$499$$ 8.00000 13.8564i 0.358129 0.620298i −0.629519 0.776985i $$-0.716748\pi$$
0.987648 + 0.156687i $$0.0500814\pi$$
$$500$$ 6.00000 + 10.3923i 0.268328 + 0.464758i
$$501$$ 8.00000 + 13.8564i 0.357414 + 0.619059i
$$502$$ −13.0000 + 22.5167i −0.580218 + 1.00497i
$$503$$ 12.0000 0.535054 0.267527 0.963550i $$-0.413794\pi$$
0.267527 + 0.963550i $$0.413794\pi$$
$$504$$ 0 0
$$505$$ 24.0000 1.06799
$$506$$ 2.00000 3.46410i 0.0889108 0.153998i
$$507$$ −3.00000 5.19615i −0.133235 0.230769i
$$508$$ 8.00000 + 13.8564i 0.354943 + 0.614779i
$$509$$ −19.0000 + 32.9090i −0.842160 + 1.45866i 0.0459045 + 0.998946i $$0.485383\pi$$
−0.888065 + 0.459718i $$0.847950\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −0.0441942
$$513$$ 8.00000 13.8564i 0.353209 0.611775i
$$514$$ 1.00000 + 1.73205i 0.0441081 + 0.0763975i
$$515$$ −2.00000 3.46410i −0.0881305 0.152647i
$$516$$ 4.00000 6.92820i 0.176090 0.304997i
$$517$$ 10.0000 0.439799
$$518$$ 0 0
$$519$$ 8.00000 0.351161
$$520$$ −4.00000 + 6.92820i −0.175412 + 0.303822i
$$521$$ 21.0000 + 36.3731i 0.920027 + 1.59353i 0.799370 + 0.600839i $$0.205167\pi$$
0.120656 + 0.992694i $$0.461500\pi$$
$$522$$ 1.00000 + 1.73205i 0.0437688 + 0.0758098i
$$523$$ −8.00000 + 13.8564i −0.349816 + 0.605898i −0.986216 0.165460i $$-0.947089\pi$$
0.636401 + 0.771358i $$0.280422\pi$$
$$524$$ 8.00000 0.349482
$$525$$ 0 0
$$526$$ 24.0000 1.04645
$$527$$ 0 0
$$528$$ −1.00000 1.73205i −0.0435194 0.0753778i
$$529$$ 3.50000 + 6.06218i 0.152174 + 0.263573i
$$530$$ −14.0000 + 24.2487i −0.608121 + 1.05330i
$$531$$ 10.0000 0.433963
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 10.0000 17.3205i 0.432742 0.749532i
$$535$$ 12.0000 + 20.7846i 0.518805 + 0.898597i
$$536$$ 4.00000 + 6.92820i 0.172774 + 0.299253i
$$537$$ −12.0000 + 20.7846i −0.517838 + 0.896922i
$$538$$ −14.0000 −0.603583
$$539$$ 0 0
$$540$$ −8.00000 −0.344265
$$541$$ 1.00000 1.73205i 0.0429934 0.0744667i −0.843728 0.536771i $$-0.819644\pi$$
0.886721 + 0.462304i $$0.152977\pi$$
$$542$$ −14.0000 24.2487i −0.601351 1.04157i
$$543$$ −14.0000 24.2487i −0.600798 1.04061i
$$544$$ 0 0
$$545$$ −28.0000 −1.19939
$$546$$ 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
$$549$$ 4.00000 + 6.92820i 0.170716 + 0.295689i
$$550$$ −0.500000 0.866025i −0.0213201 0.0369274i
$$551$$ −4.00000 + 6.92820i −0.170406 + 0.295151i
$$552$$ −8.00000 −0.340503
$$553$$ 0 0
$$554$$ −6.00000 −0.254916
$$555$$ 12.0000 20.7846i 0.509372 0.882258i
$$556$$ −10.0000 17.3205i −0.424094 0.734553i
$$557$$ −15.0000 25.9808i −0.635570 1.10084i −0.986394 0.164399i $$-0.947432\pi$$
0.350824 0.936442i $$-0.385902\pi$$
$$558$$ −5.00000 + 8.66025i −0.211667 + 0.366618i
$$559$$ 16.0000 0.676728
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 15.0000 25.9808i 0.632737 1.09593i
$$563$$ −6.00000 10.3923i −0.252870 0.437983i 0.711445 0.702742i $$-0.248041\pi$$
−0.964315 + 0.264758i $$0.914708\pi$$
$$564$$ −10.0000 17.3205i −0.421076 0.729325i
$$565$$ 14.0000 24.2487i 0.588984 1.02015i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 4.00000 0.167836
$$569$$ −7.00000 + 12.1244i −0.293455 + 0.508279i −0.974624 0.223847i $$-0.928139\pi$$
0.681169 + 0.732126i $$0.261472\pi$$
$$570$$ 8.00000 + 13.8564i 0.335083 + 0.580381i
$$571$$ 14.0000 + 24.2487i 0.585882 + 1.01478i 0.994765 + 0.102190i $$0.0325850\pi$$
−0.408883 + 0.912587i $$0.634082\pi$$
$$572$$ 2.00000 3.46410i 0.0836242 0.144841i
$$573$$ 16.0000 0.668410
$$574$$ 0 0
$$575$$ −4.00000 −0.166812
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 21.0000 + 36.3731i 0.874241 + 1.51423i 0.857569 + 0.514370i $$0.171974\pi$$
0.0166728 + 0.999861i $$0.494693\pi$$
$$578$$ −8.50000 14.7224i −0.353553 0.612372i
$$579$$ 6.00000 10.3923i 0.249351 0.431889i
$$580$$ 4.00000 0.166091
$$581$$ 0 0
$$582$$ −12.0000 −0.497416
$$583$$ 7.00000 12.1244i 0.289910 0.502140i
$$584$$ 2.00000 + 3.46410i 0.0827606 + 0.143346i
$$585$$ 4.00000 + 6.92820i 0.165380 + 0.286446i
$$586$$ 0 0
$$587$$ −42.0000 −1.73353 −0.866763 0.498721i $$-0.833803\pi$$
−0.866763 + 0.498721i $$0.833803\pi$$
$$588$$ 0 0
$$589$$ −40.0000 −1.64817
$$590$$ 10.0000 17.3205i 0.411693 0.713074i
$$591$$ 18.0000 + 31.1769i 0.740421 + 1.28245i
$$592$$ 3.00000 + 5.19615i 0.123299 + 0.213561i
$$593$$ −6.00000 + 10.3923i −0.246390 + 0.426761i −0.962522 0.271205i $$-0.912578\pi$$
0.716131 + 0.697966i $$0.245911\pi$$
$$594$$ 4.00000 0.164122
$$595$$ 0 0
$$596$$ 22.0000 0.901155
$$597$$ 14.0000 24.2487i 0.572982 0.992434i
$$598$$ −8.00000 13.8564i −0.327144 0.566631i
$$599$$ 6.00000 + 10.3923i 0.245153 + 0.424618i 0.962175 0.272433i $$-0.0878284\pi$$
−0.717021 + 0.697051i $$0.754495\pi$$
$$600$$ −1.00000 + 1.73205i −0.0408248 + 0.0707107i
$$601$$ −24.0000 −0.978980 −0.489490 0.872009i $$-0.662817\pi$$
−0.489490 + 0.872009i $$0.662817\pi$$
$$602$$ 0 0
$$603$$ 8.00000 0.325785
$$604$$ −8.00000 + 13.8564i −0.325515 + 0.563809i
$$605$$ −1.00000 1.73205i −0.0406558 0.0704179i
$$606$$ 12.0000 + 20.7846i 0.487467 + 0.844317i
$$607$$ 12.0000 20.7846i 0.487065 0.843621i −0.512824 0.858494i $$-0.671401\pi$$
0.999889 + 0.0148722i $$0.00473415\pi$$
$$608$$ −4.00000 −0.162221
$$609$$ 0 0
$$610$$ 16.0000 0.647821
$$611$$ 20.0000 34.6410i 0.809113 1.40143i
$$612$$ 0 0
$$613$$ −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i $$-0.179527\pi$$
−0.885514 + 0.464614i $$0.846193\pi$$
$$614$$ 8.00000 13.8564i 0.322854 0.559199i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 38.0000 1.52982 0.764911 0.644136i $$-0.222783\pi$$
0.764911 + 0.644136i $$0.222783\pi$$
$$618$$ 2.00000 3.46410i 0.0804518 0.139347i
$$619$$ 1.00000 + 1.73205i 0.0401934 + 0.0696170i 0.885422 0.464787i $$-0.153869\pi$$
−0.845229 + 0.534404i $$0.820536\pi$$
$$620$$ 10.0000 + 17.3205i 0.401610 + 0.695608i
$$621$$ 8.00000 13.8564i 0.321029 0.556038i
$$622$$ 6.00000 0.240578
$$623$$ 0 0
$$624$$ −8.00000 −0.320256
$$625$$ 9.50000 16.4545i 0.380000 0.658179i
$$626$$ −3.00000 5.19615i −0.119904 0.207680i
$$627$$ −4.00000 6.92820i −0.159745 0.276686i
$$628$$ −5.00000 + 8.66025i −0.199522 + 0.345582i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 8.00000 0.318475 0.159237 0.987240i $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ 8.00000 13.8564i 0.318223 0.551178i
$$633$$ 4.00000 + 6.92820i 0.158986 + 0.275371i
$$634$$ −9.00000 15.5885i −0.357436 0.619097i
$$635$$ 16.0000 27.7128i 0.634941 1.09975i
$$636$$ −28.0000 −1.11027
$$637$$ 0 0
$$638$$ −2.00000 −0.0791808
$$639$$ 2.00000 3.46410i 0.0791188 0.137038i
$$640$$ 1.00000 + 1.73205i 0.0395285 + 0.0684653i
$$641$$ 9.00000 + 15.5885i 0.355479 + 0.615707i 0.987200 0.159489i $$-0.0509845\pi$$
−0.631721 + 0.775196i $$0.717651\pi$$
$$642$$ −12.0000 + 20.7846i −0.473602 + 0.820303i
$$643$$ 22.0000 0.867595 0.433798 0.901010i $$-0.357173\pi$$
0.433798 + 0.901010i $$0.357173\pi$$
$$644$$ 0 0
$$645$$ −16.0000 −0.629999
$$646$$ 0 0
$$647$$ −3.00000 5.19615i −0.117942 0.204282i 0.801010 0.598651i $$-0.204296\pi$$
−0.918952 + 0.394369i $$0.870963\pi$$
$$648$$ −5.50000 9.52628i −0.216060 0.374228i
$$649$$ −5.00000 + 8.66025i −0.196267 + 0.339945i
$$650$$ −4.00000 −0.156893
$$651$$ 0 0
$$652$$ 24.0000 0.939913
$$653$$ −23.0000 + 39.8372i −0.900060 + 1.55895i −0.0726446 + 0.997358i $$0.523144\pi$$
−0.827415 + 0.561591i $$0.810189\pi$$
$$654$$ −14.0000 24.2487i −0.547443 0.948200i
$$655$$ −8.00000 13.8564i −0.312586 0.541415i
$$656$$ 0 0
$$657$$ 4.00000 0.156055
$$658$$ 0 0
$$659$$ 20.0000 0.779089 0.389545 0.921008i $$-0.372632\pi$$
0.389545 + 0.921008i $$0.372632\pi$$
$$660$$ −2.00000 + 3.46410i −0.0778499 + 0.134840i
$$661$$ 19.0000 + 32.9090i 0.739014 + 1.28001i 0.952940 + 0.303160i $$0.0980418\pi$$
−0.213925 + 0.976850i $$0.568625\pi$$
$$662$$ −10.0000 17.3205i −0.388661 0.673181i
$$663$$ 0 0
$$664$$ −4.00000 −0.155230
$$665$$ 0 0
$$666$$ 6.00000 0.232495
$$667$$ −4.00000 + 6.92820i −0.154881 + 0.268261i
$$668$$ 4.00000 + 6.92820i 0.154765 + 0.268060i
$$669$$ 14.0000 + 24.2487i 0.541271 + 0.937509i
$$670$$ 8.00000 13.8564i 0.309067 0.535320i
$$671$$ −8.00000 −0.308837
$$672$$ 0 0
$$673$$ −10.0000 −0.385472 −0.192736 0.981251i $$-0.561736\pi$$
−0.192736 + 0.981251i $$0.561736\pi$$
$$674$$ −17.0000 + 29.4449i −0.654816 + 1.13417i
$$675$$ −2.00000 3.46410i −0.0769800 0.133333i
$$676$$ −1.50000 2.59808i −0.0576923 0.0999260i
$$677$$ −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i $$-0.907402\pi$$
0.727386 + 0.686229i $$0.240735\pi$$
$$678$$ 28.0000 1.07533
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −8.00000 + 13.8564i −0.306561 + 0.530979i
$$682$$ −5.00000 8.66025i −0.191460 0.331618i
$$683$$ −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i $$-0.240403\pi$$
−0.957685 + 0.287819i $$0.907070\pi$$
$$684$$ −2.00000 + 3.46410i −0.0764719 + 0.132453i
$$685$$ 12.0000 0.458496
$$686$$ 0 0
$$687$$ −20.0000 −0.763048
$$688$$ 2.00000 3.46410i 0.0762493 0.132068i
$$689$$ −28.0000 48.4974i −1.06672 1.84760i
$$690$$ 8.00000 + 13.8564i 0.304555 + 0.527504i
$$691$$ −21.0000 + 36.3731i −0.798878 + 1.38370i 0.121470 + 0.992595i $$0.461239\pi$$
−0.920348 + 0.391102i $$0.872094\pi$$
$$692$$ 4.00000 0.152057
$$693$$ 0 0
$$694$$ 12.0000 0.455514
$$695$$ −20.0000 + 34.6410i −0.758643 + 1.31401i
$$696$$ 2.00000 + 3.46410i 0.0758098 + 0.131306i
$$697$$ 0 0
$$698$$ 16.0000 27.7128i 0.605609 1.04895i
$$699$$ 12.0000 0.453882
$$700$$ 0 0
$$701$$ −6.00000 −0.226617 −0.113308 0.993560i $$-0.536145\pi$$
−0.113308 + 0.993560i $$0.536145\pi$$
$$702$$ 8.00000 13.8564i 0.301941 0.522976i
$$703$$ 12.0000 + 20.7846i 0.452589 + 0.783906i
$$704$$ −0.500000 0.866025i −0.0188445 0.0326396i
$$705$$ −20.0000 + 34.6410i −0.753244 + 1.30466i
$$706$$ −2.00000 −0.0752710
$$707$$ 0 0
$$708$$ 20.0000 0.751646
$$709$$ 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i $$-0.773204\pi$$
0.944509 + 0.328484i $$0.106538\pi$$
$$710$$ −4.00000 6.92820i −0.150117 0.260011i
$$711$$ −8.00000 13.8564i −0.300023 0.519656i
$$712$$ 5.00000 8.66025i 0.187383 0.324557i
$$713$$ −40.0000 −1.49801
$$714$$ 0 0
$$715$$ −8.00000 −0.299183
$$716$$ −6.00000 + 10.3923i −0.224231 + 0.388379i
$$717$$ 8.00000 + 13.8564i 0.298765 + 0.517477i
$$718$$ 0 0
$$719$$ −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i $$-0.869021\pi$$
0.804648 + 0.593753i $$0.202354\pi$$
$$720$$ 2.00000 0.0745356
$$721$$ 0 0
$$722$$ 3.00000 0.111648
$$723$$ −8.00000 + 13.8564i −0.297523 + 0.515325i
$$724$$ −7.00000 12.1244i −0.260153 0.450598i
$$725$$ 1.00000 + 1.73205i 0.0371391 + 0.0643268i
$$726$$ 1.00000 1.73205i 0.0371135 0.0642824i
$$727$$ 46.0000 1.70605 0.853023 0.521874i $$-0.174767\pi$$
0.853023 + 0.521874i $$0.174767\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 4.00000 6.92820i 0.148047 0.256424i
$$731$$ 0 0
$$732$$ 8.00000 + 13.8564i 0.295689 + 0.512148i
$$733$$ 4.00000 6.92820i 0.147743 0.255899i −0.782650 0.622462i $$-0.786132\pi$$
0.930393 + 0.366563i $$0.119466\pi$$
$$734$$ −18.0000 −0.664392
$$735$$ 0 0
$$736$$ −4.00000 −0.147442
$$737$$ −4.00000 + 6.92820i −0.147342 + 0.255204i
$$738$$ 0 0
$$739$$ 26.0000 + 45.0333i 0.956425 + 1.65658i 0.731072 + 0.682300i $$0.239020\pi$$
0.225354 + 0.974277i $$0.427646\pi$$
$$740$$ 6.00000 10.3923i 0.220564 0.382029i
$$741$$ −32.0000 −1.17555
$$742$$ 0 0
$$743$$ 16.0000 0.586983 0.293492 0.955962i $$-0.405183\pi$$
0.293492 + 0.955962i $$0.405183\pi$$
$$744$$ −10.0000 + 17.3205i −0.366618 + 0.635001i
$$745$$ −22.0000 38.1051i −0.806018 1.39606i
$$746$$ −17.0000 29.4449i −0.622414 1.07805i
$$747$$ −2.00000 + 3.46410i −0.0731762 + 0.126745i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 24.0000 0.876356
$$751$$ −10.0000 + 17.3205i −0.364905 + 0.632034i −0.988761 0.149505i $$-0.952232\pi$$
0.623856 + 0.781540i $$0.285565\pi$$
$$752$$ −5.00000 8.66025i −0.182331 0.315807i
$$753$$ 26.0000 + 45.0333i 0.947493 + 1.64111i
$$754$$ −4.00000 + 6.92820i −0.145671 + 0.252310i
$$755$$ 32.0000 1.16460
$$756$$ 0 0
$$757$$ 30.0000 1.09037 0.545184 0.838316i $$-0.316460\pi$$
0.545184 + 0.838316i $$0.316460\pi$$
$$758$$ 4.00000 6.92820i 0.145287 0.251644i
$$759$$ −4.00000 6.92820i −0.145191 0.251478i
$$760$$ 4.00000 + 6.92820i 0.145095 + 0.251312i
$$761$$ 6.00000 10.3923i 0.217500 0.376721i −0.736543 0.676391i $$-0.763543\pi$$
0.954043 + 0.299670i $$0.0968765\pi$$
$$762$$ 32.0000 1.15924
$$763$$ 0 0
$$764$$ 8.00000 0.289430
$$765$$ 0 0
$$766$$ 7.00000 + 12.1244i 0.252920 + 0.438071i
$$767$$ 20.0000 + 34.6410i 0.722158 + 1.25081i
$$768$$ −1.00000 + 1.73205i −0.0360844 + 0.0625000i
$$769$$ 4.00000 0.144244 0.0721218 0.997396i $$-0.477023\pi$$
0.0721218 + 0.997396i $$0.477023\pi$$
$$770$$ 0 0
$$771$$ 4.00000 0.144056
$$772$$ 3.00000 5.19615i 0.107972 0.187014i
$$773$$ 17.0000 + 29.4449i 0.611448 + 1.05906i 0.990997 + 0.133887i $$0.0427458\pi$$
−0.379549 + 0.925172i $$0.623921\pi$$
$$774$$ −2.00000 3.46410i −0.0718885 0.124515i
$$775$$ −5.00000 + 8.66025i −0.179605 + 0.311086i
$$776$$ −6.00000 −0.215387
$$777$$ 0 0
$$778$$ 18.0000 0.645331
$$779$$ 0 0
$$780$$ 8.00000 + 13.8564i 0.286446 + 0.496139i
$$781$$ 2.00000 + 3.46410i 0.0715656 + 0.123955i
$$782$$ 0 0
$$783$$ −8.00000