# Properties

 Label 735.2.i.d.361.1 Level $735$ Weight $2$ Character 735.361 Analytic conductor $5.869$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$735 = 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 735.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.86900454856$$ 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 15) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 735.361 Dual form 735.2.i.d.226.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(2.00000 - 3.46410i) q^{11} +(0.500000 + 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(0.500000 - 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +1.00000 q^{20} +4.00000 q^{22} +(-1.50000 + 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(2.50000 - 4.33013i) q^{32} +(2.00000 + 3.46410i) q^{33} +2.00000 q^{34} -1.00000 q^{36} +(5.00000 + 8.66025i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(1.50000 + 2.59808i) q^{40} -10.0000 q^{41} +4.00000 q^{43} +(-2.00000 - 3.46410i) q^{44} +(0.500000 - 0.866025i) q^{45} +(4.00000 + 6.92820i) q^{47} -1.00000 q^{48} -1.00000 q^{50} +(1.00000 + 1.73205i) q^{51} +(1.00000 - 1.73205i) q^{52} +(5.00000 - 8.66025i) q^{53} +(0.500000 + 0.866025i) q^{54} +4.00000 q^{55} -4.00000 q^{57} +(-1.00000 - 1.73205i) q^{58} +(-2.00000 + 3.46410i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-1.00000 - 1.73205i) q^{61} +7.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(-2.00000 + 3.46410i) q^{66} +(-6.00000 + 10.3923i) q^{67} +(-1.00000 - 1.73205i) q^{68} -8.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +(5.00000 - 8.66025i) q^{73} +(-5.00000 + 8.66025i) q^{74} +(-0.500000 - 0.866025i) q^{75} +4.00000 q^{76} -2.00000 q^{78} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.00000 - 8.66025i) q^{82} -12.0000 q^{83} +2.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(1.00000 - 1.73205i) q^{87} +(6.00000 - 10.3923i) q^{88} +(-3.00000 - 5.19615i) q^{89} +1.00000 q^{90} +(-4.00000 + 6.92820i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(2.50000 + 4.33013i) q^{96} -2.00000 q^{97} -4.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{2} - q^{3} + q^{4} + q^{5} - 2 q^{6} + 6 q^{8} - q^{9}+O(q^{10})$$ 2 * q + q^2 - q^3 + q^4 + q^5 - 2 * q^6 + 6 * q^8 - q^9 $$2 q + q^{2} - q^{3} + q^{4} + q^{5} - 2 q^{6} + 6 q^{8} - q^{9} - q^{10} + 4 q^{11} + q^{12} + 4 q^{13} - 2 q^{15} + q^{16} + 2 q^{17} + q^{18} + 4 q^{19} + 2 q^{20} + 8 q^{22} - 3 q^{24} - q^{25} + 2 q^{26} + 2 q^{27} - 4 q^{29} - q^{30} + 5 q^{32} + 4 q^{33} + 4 q^{34} - 2 q^{36} + 10 q^{37} - 4 q^{38} - 2 q^{39} + 3 q^{40} - 20 q^{41} + 8 q^{43} - 4 q^{44} + q^{45} + 8 q^{47} - 2 q^{48} - 2 q^{50} + 2 q^{51} + 2 q^{52} + 10 q^{53} + q^{54} + 8 q^{55} - 8 q^{57} - 2 q^{58} - 4 q^{59} - q^{60} - 2 q^{61} + 14 q^{64} + 2 q^{65} - 4 q^{66} - 12 q^{67} - 2 q^{68} - 16 q^{71} - 3 q^{72} + 10 q^{73} - 10 q^{74} - q^{75} + 8 q^{76} - 4 q^{78} - q^{80} - q^{81} - 10 q^{82} - 24 q^{83} + 4 q^{85} + 4 q^{86} + 2 q^{87} + 12 q^{88} - 6 q^{89} + 2 q^{90} - 8 q^{94} - 4 q^{95} + 5 q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100})$$ 2 * q + q^2 - q^3 + q^4 + q^5 - 2 * q^6 + 6 * q^8 - q^9 - q^10 + 4 * q^11 + q^12 + 4 * q^13 - 2 * q^15 + q^16 + 2 * q^17 + q^18 + 4 * q^19 + 2 * q^20 + 8 * q^22 - 3 * q^24 - q^25 + 2 * q^26 + 2 * q^27 - 4 * q^29 - q^30 + 5 * q^32 + 4 * q^33 + 4 * q^34 - 2 * q^36 + 10 * q^37 - 4 * q^38 - 2 * q^39 + 3 * q^40 - 20 * q^41 + 8 * q^43 - 4 * q^44 + q^45 + 8 * q^47 - 2 * q^48 - 2 * q^50 + 2 * q^51 + 2 * q^52 + 10 * q^53 + q^54 + 8 * q^55 - 8 * q^57 - 2 * q^58 - 4 * q^59 - q^60 - 2 * q^61 + 14 * q^64 + 2 * q^65 - 4 * q^66 - 12 * q^67 - 2 * q^68 - 16 * q^71 - 3 * q^72 + 10 * q^73 - 10 * q^74 - q^75 + 8 * q^76 - 4 * q^78 - q^80 - q^81 - 10 * q^82 - 24 * q^83 + 4 * q^85 + 4 * q^86 + 2 * q^87 + 12 * q^88 - 6 * q^89 + 2 * q^90 - 8 * q^94 - 4 * q^95 + 5 * q^96 - 4 * q^97 - 8 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$$.

 $$n$$ $$346$$ $$442$$ $$491$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

## 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 0.986869 0.161521i $$-0.0516399\pi$$
−0.633316 + 0.773893i $$0.718307\pi$$
$$3$$ −0.500000 + 0.866025i −0.288675 + 0.500000i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 0.500000 + 0.866025i 0.223607 + 0.387298i
$$6$$ −1.00000 −0.408248
$$7$$ 0 0
$$8$$ 3.00000 1.06066
$$9$$ −0.500000 0.866025i −0.166667 0.288675i
$$10$$ −0.500000 + 0.866025i −0.158114 + 0.273861i
$$11$$ 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i $$-0.627296\pi$$
0.992361 0.123371i $$-0.0393705\pi$$
$$12$$ 0.500000 + 0.866025i 0.144338 + 0.250000i
$$13$$ 2.00000 0.554700 0.277350 0.960769i $$-0.410544\pi$$
0.277350 + 0.960769i $$0.410544\pi$$
$$14$$ 0 0
$$15$$ −1.00000 −0.258199
$$16$$ 0.500000 + 0.866025i 0.125000 + 0.216506i
$$17$$ 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i $$-0.755354\pi$$
0.961436 + 0.275029i $$0.0886875\pi$$
$$18$$ 0.500000 0.866025i 0.117851 0.204124i
$$19$$ 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i $$-0.0149348\pi$$
−0.540068 + 0.841621i $$0.681602\pi$$
$$20$$ 1.00000 0.223607
$$21$$ 0 0
$$22$$ 4.00000 0.852803
$$23$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$24$$ −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 $$0.559454\pi$$
$$30$$ −0.500000 0.866025i −0.0912871 0.158114i
$$31$$ 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
$$33$$ 2.00000 + 3.46410i 0.348155 + 0.603023i
$$34$$ 2.00000 0.342997
$$35$$ 0 0
$$36$$ −1.00000 −0.166667
$$37$$ 5.00000 + 8.66025i 0.821995 + 1.42374i 0.904194 + 0.427121i $$0.140472\pi$$
−0.0821995 + 0.996616i $$0.526194\pi$$
$$38$$ −2.00000 + 3.46410i −0.324443 + 0.561951i
$$39$$ −1.00000 + 1.73205i −0.160128 + 0.277350i
$$40$$ 1.50000 + 2.59808i 0.237171 + 0.410792i
$$41$$ −10.0000 −1.56174 −0.780869 0.624695i $$-0.785223\pi$$
−0.780869 + 0.624695i $$0.785223\pi$$
$$42$$ 0 0
$$43$$ 4.00000 0.609994 0.304997 0.952353i $$-0.401344\pi$$
0.304997 + 0.952353i $$0.401344\pi$$
$$44$$ −2.00000 3.46410i −0.301511 0.522233i
$$45$$ 0.500000 0.866025i 0.0745356 0.129099i
$$46$$ 0 0
$$47$$ 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i $$0.0316348\pi$$
−0.411606 + 0.911362i $$0.635032\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ 0 0
$$50$$ −1.00000 −0.141421
$$51$$ 1.00000 + 1.73205i 0.140028 + 0.242536i
$$52$$ 1.00000 1.73205i 0.138675 0.240192i
$$53$$ 5.00000 8.66025i 0.686803 1.18958i −0.286064 0.958211i $$-0.592347\pi$$
0.972867 0.231367i $$-0.0743197\pi$$
$$54$$ 0.500000 + 0.866025i 0.0680414 + 0.117851i
$$55$$ 4.00000 0.539360
$$56$$ 0 0
$$57$$ −4.00000 −0.529813
$$58$$ −1.00000 1.73205i −0.131306 0.227429i
$$59$$ −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i $$-0.917180\pi$$
0.705965 + 0.708247i $$0.250514\pi$$
$$60$$ −0.500000 + 0.866025i −0.0645497 + 0.111803i
$$61$$ −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i $$-0.207534\pi$$
−0.922916 + 0.385002i $$0.874201\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 7.00000 0.875000
$$65$$ 1.00000 + 1.73205i 0.124035 + 0.214834i
$$66$$ −2.00000 + 3.46410i −0.246183 + 0.426401i
$$67$$ −6.00000 + 10.3923i −0.733017 + 1.26962i 0.222571 + 0.974916i $$0.428555\pi$$
−0.955588 + 0.294706i $$0.904778\pi$$
$$68$$ −1.00000 1.73205i −0.121268 0.210042i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −8.00000 −0.949425 −0.474713 0.880141i $$-0.657448\pi$$
−0.474713 + 0.880141i $$0.657448\pi$$
$$72$$ −1.50000 2.59808i −0.176777 0.306186i
$$73$$ 5.00000 8.66025i 0.585206 1.01361i −0.409644 0.912245i $$-0.634347\pi$$
0.994850 0.101361i $$-0.0323196\pi$$
$$74$$ −5.00000 + 8.66025i −0.581238 + 1.00673i
$$75$$ −0.500000 0.866025i −0.0577350 0.100000i
$$76$$ 4.00000 0.458831
$$77$$ 0 0
$$78$$ −2.00000 −0.226455
$$79$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$80$$ −0.500000 + 0.866025i −0.0559017 + 0.0968246i
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ −5.00000 8.66025i −0.552158 0.956365i
$$83$$ −12.0000 −1.31717 −0.658586 0.752506i $$-0.728845\pi$$
−0.658586 + 0.752506i $$0.728845\pi$$
$$84$$ 0 0
$$85$$ 2.00000 0.216930
$$86$$ 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
$$89$$ −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i $$-0.269678\pi$$
−0.980071 + 0.198650i $$0.936344\pi$$
$$90$$ 1.00000 0.105409
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −4.00000 + 6.92820i −0.412568 + 0.714590i
$$95$$ −2.00000 + 3.46410i −0.205196 + 0.355409i
$$96$$ 2.50000 + 4.33013i 0.255155 + 0.441942i
$$97$$ −2.00000 −0.203069 −0.101535 0.994832i $$-0.532375\pi$$
−0.101535 + 0.994832i $$0.532375\pi$$
$$98$$ 0 0
$$99$$ −4.00000 −0.402015
$$100$$ 0.500000 + 0.866025i 0.0500000 + 0.0866025i
$$101$$ 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i $$-0.736843\pi$$
0.975796 + 0.218685i $$0.0701767\pi$$
$$102$$ −1.00000 + 1.73205i −0.0990148 + 0.171499i
$$103$$ −8.00000 13.8564i −0.788263 1.36531i −0.927030 0.374987i $$-0.877647\pi$$
0.138767 0.990325i $$-0.455686\pi$$
$$104$$ 6.00000 0.588348
$$105$$ 0 0
$$106$$ 10.0000 0.971286
$$107$$ 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i $$0.0302972\pi$$
−0.415432 + 0.909624i $$0.636370\pi$$
$$108$$ 0.500000 0.866025i 0.0481125 0.0833333i
$$109$$ −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i $$0.400578\pi$$
−0.977769 + 0.209687i $$0.932756\pi$$
$$110$$ 2.00000 + 3.46410i 0.190693 + 0.330289i
$$111$$ −10.0000 −0.949158
$$112$$ 0 0
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ −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
$$118$$ −4.00000 −0.368230
$$119$$ 0 0
$$120$$ −3.00000 −0.273861
$$121$$ −2.50000 4.33013i −0.227273 0.393648i
$$122$$ 1.00000 1.73205i 0.0905357 0.156813i
$$123$$ 5.00000 8.66025i 0.450835 0.780869i
$$124$$ 0 0
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ −8.00000 −0.709885 −0.354943 0.934888i $$-0.615500\pi$$
−0.354943 + 0.934888i $$0.615500\pi$$
$$128$$ −1.50000 2.59808i −0.132583 0.229640i
$$129$$ −2.00000 + 3.46410i −0.176090 + 0.304997i
$$130$$ −1.00000 + 1.73205i −0.0877058 + 0.151911i
$$131$$ −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i $$-0.991023\pi$$
0.475380 0.879781i $$-0.342311\pi$$
$$132$$ 4.00000 0.348155
$$133$$ 0 0
$$134$$ −12.0000 −1.03664
$$135$$ 0.500000 + 0.866025i 0.0430331 + 0.0745356i
$$136$$ 3.00000 5.19615i 0.257248 0.445566i
$$137$$ 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i $$-0.750827\pi$$
0.965250 + 0.261329i $$0.0841608\pi$$
$$138$$ 0 0
$$139$$ 4.00000 0.339276 0.169638 0.985506i $$-0.445740\pi$$
0.169638 + 0.985506i $$0.445740\pi$$
$$140$$ 0 0
$$141$$ −8.00000 −0.673722
$$142$$ −4.00000 6.92820i −0.335673 0.581402i
$$143$$ 4.00000 6.92820i 0.334497 0.579365i
$$144$$ 0.500000 0.866025i 0.0416667 0.0721688i
$$145$$ −1.00000 1.73205i −0.0830455 0.143839i
$$146$$ 10.0000 0.827606
$$147$$ 0 0
$$148$$ 10.0000 0.821995
$$149$$ −11.0000 19.0526i −0.901155 1.56085i −0.825997 0.563675i $$-0.809387\pi$$
−0.0751583 0.997172i $$-0.523946\pi$$
$$150$$ 0.500000 0.866025i 0.0408248 0.0707107i
$$151$$ 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i $$-0.727796\pi$$
0.981617 + 0.190864i $$0.0611289\pi$$
$$152$$ 6.00000 + 10.3923i 0.486664 + 0.842927i
$$153$$ −2.00000 −0.161690
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 1.00000 + 1.73205i 0.0800641 + 0.138675i
$$157$$ 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i $$-0.644649\pi$$
0.997609 0.0691164i $$-0.0220180\pi$$
$$158$$ 0 0
$$159$$ 5.00000 + 8.66025i 0.396526 + 0.686803i
$$160$$ 5.00000 0.395285
$$161$$ 0 0
$$162$$ −1.00000 −0.0785674
$$163$$ 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i $$-0.116597\pi$$
−0.777007 + 0.629492i $$0.783263\pi$$
$$164$$ −5.00000 + 8.66025i −0.390434 + 0.676252i
$$165$$ −2.00000 + 3.46410i −0.155700 + 0.269680i
$$166$$ −6.00000 10.3923i −0.465690 0.806599i
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ 1.00000 + 1.73205i 0.0766965 + 0.132842i
$$171$$ 2.00000 3.46410i 0.152944 0.264906i
$$172$$ 2.00000 3.46410i 0.152499 0.264135i
$$173$$ −9.00000 15.5885i −0.684257 1.18517i −0.973670 0.227964i $$-0.926793\pi$$
0.289412 0.957205i $$-0.406540\pi$$
$$174$$ 2.00000 0.151620
$$175$$ 0 0
$$176$$ 4.00000 0.301511
$$177$$ −2.00000 3.46410i −0.150329 0.260378i
$$178$$ 3.00000 5.19615i 0.224860 0.389468i
$$179$$ −10.0000 + 17.3205i −0.747435 + 1.29460i 0.201613 + 0.979465i $$0.435382\pi$$
−0.949048 + 0.315130i $$0.897952\pi$$
$$180$$ −0.500000 0.866025i −0.0372678 0.0645497i
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 0 0
$$183$$ 2.00000 0.147844
$$184$$ 0 0
$$185$$ −5.00000 + 8.66025i −0.367607 + 0.636715i
$$186$$ 0 0
$$187$$ −4.00000 6.92820i −0.292509 0.506640i
$$188$$ 8.00000 0.583460
$$189$$ 0 0
$$190$$ −4.00000 −0.290191
$$191$$ −8.00000 13.8564i −0.578860 1.00261i −0.995610 0.0935936i $$-0.970165\pi$$
0.416751 0.909021i $$-0.363169\pi$$
$$192$$ −3.50000 + 6.06218i −0.252591 + 0.437500i
$$193$$ −1.00000 + 1.73205i −0.0719816 + 0.124676i −0.899770 0.436365i $$-0.856266\pi$$
0.827788 + 0.561041i $$0.189599\pi$$
$$194$$ −1.00000 1.73205i −0.0717958 0.124354i
$$195$$ −2.00000 −0.143223
$$196$$ 0 0
$$197$$ 6.00000 0.427482 0.213741 0.976890i $$-0.431435\pi$$
0.213741 + 0.976890i $$0.431435\pi$$
$$198$$ −2.00000 3.46410i −0.142134 0.246183i
$$199$$ −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i $$-0.924846\pi$$
0.688705 + 0.725042i $$0.258180\pi$$
$$200$$ −1.50000 + 2.59808i −0.106066 + 0.183712i
$$201$$ −6.00000 10.3923i −0.423207 0.733017i
$$202$$ 6.00000 0.422159
$$203$$ 0 0
$$204$$ 2.00000 0.140028
$$205$$ −5.00000 8.66025i −0.349215 0.604858i
$$206$$ 8.00000 13.8564i 0.557386 0.965422i
$$207$$ 0 0
$$208$$ 1.00000 + 1.73205i 0.0693375 + 0.120096i
$$209$$ 16.0000 1.10674
$$210$$ 0 0
$$211$$ 20.0000 1.37686 0.688428 0.725304i $$-0.258301\pi$$
0.688428 + 0.725304i $$0.258301\pi$$
$$212$$ −5.00000 8.66025i −0.343401 0.594789i
$$213$$ 4.00000 6.92820i 0.274075 0.474713i
$$214$$ −6.00000 + 10.3923i −0.410152 + 0.710403i
$$215$$ 2.00000 + 3.46410i 0.136399 + 0.236250i
$$216$$ 3.00000 0.204124
$$217$$ 0 0
$$218$$ −14.0000 −0.948200
$$219$$ 5.00000 + 8.66025i 0.337869 + 0.585206i
$$220$$ 2.00000 3.46410i 0.134840 0.233550i
$$221$$ 2.00000 3.46410i 0.134535 0.233021i
$$222$$ −5.00000 8.66025i −0.335578 0.581238i
$$223$$ −8.00000 −0.535720 −0.267860 0.963458i $$-0.586316\pi$$
−0.267860 + 0.963458i $$0.586316\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 1.00000 + 1.73205i 0.0665190 + 0.115214i
$$227$$ −10.0000 + 17.3205i −0.663723 + 1.14960i 0.315906 + 0.948790i $$0.397691\pi$$
−0.979630 + 0.200812i $$0.935642\pi$$
$$228$$ −2.00000 + 3.46410i −0.132453 + 0.229416i
$$229$$ 3.00000 + 5.19615i 0.198246 + 0.343371i 0.947960 0.318390i $$-0.103142\pi$$
−0.749714 + 0.661762i $$0.769809\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ −6.00000 −0.393919
$$233$$ 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i $$-0.103697\pi$$
−0.750867 + 0.660454i $$0.770364\pi$$
$$234$$ 1.00000 1.73205i 0.0653720 0.113228i
$$235$$ −4.00000 + 6.92820i −0.260931 + 0.451946i
$$236$$ 2.00000 + 3.46410i 0.130189 + 0.225494i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −16.0000 −1.03495 −0.517477 0.855697i $$-0.673129\pi$$
−0.517477 + 0.855697i $$0.673129\pi$$
$$240$$ −0.500000 0.866025i −0.0322749 0.0559017i
$$241$$ −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i $$-0.982234\pi$$
0.547533 + 0.836784i $$0.315567\pi$$
$$242$$ 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
$$246$$ 10.0000 0.637577
$$247$$ 4.00000 + 6.92820i 0.254514 + 0.440831i
$$248$$ 0 0
$$249$$ 6.00000 10.3923i 0.380235 0.658586i
$$250$$ −0.500000 0.866025i −0.0316228 0.0547723i
$$251$$ −12.0000 −0.757433 −0.378717 0.925513i $$-0.623635\pi$$
−0.378717 + 0.925513i $$0.623635\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −4.00000 6.92820i −0.250982 0.434714i
$$255$$ −1.00000 + 1.73205i −0.0626224 + 0.108465i
$$256$$ 8.50000 14.7224i 0.531250 0.920152i
$$257$$ 9.00000 + 15.5885i 0.561405 + 0.972381i 0.997374 + 0.0724199i $$0.0230722\pi$$
−0.435970 + 0.899961i $$0.643595\pi$$
$$258$$ −4.00000 −0.249029
$$259$$ 0 0
$$260$$ 2.00000 0.124035
$$261$$ 1.00000 + 1.73205i 0.0618984 + 0.107211i
$$262$$ 6.00000 10.3923i 0.370681 0.642039i
$$263$$ −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i $$-0.997543\pi$$
0.506669 + 0.862141i $$0.330877\pi$$
$$264$$ 6.00000 + 10.3923i 0.369274 + 0.639602i
$$265$$ 10.0000 0.614295
$$266$$ 0 0
$$267$$ 6.00000 0.367194
$$268$$ 6.00000 + 10.3923i 0.366508 + 0.634811i
$$269$$ 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i $$-0.692975\pi$$
0.996586 + 0.0825561i $$0.0263084\pi$$
$$270$$ −0.500000 + 0.866025i −0.0304290 + 0.0527046i
$$271$$ 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i $$-0.00513477\pi$$
−0.513905 + 0.857847i $$0.671801\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ 6.00000 0.362473
$$275$$ 2.00000 + 3.46410i 0.120605 + 0.208893i
$$276$$ 0 0
$$277$$ −3.00000 + 5.19615i −0.180253 + 0.312207i −0.941966 0.335707i $$-0.891025\pi$$
0.761714 + 0.647913i $$0.224358\pi$$
$$278$$ 2.00000 + 3.46410i 0.119952 + 0.207763i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −6.00000 −0.357930 −0.178965 0.983855i $$-0.557275\pi$$
−0.178965 + 0.983855i $$0.557275\pi$$
$$282$$ −4.00000 6.92820i −0.238197 0.412568i
$$283$$ −6.00000 + 10.3923i −0.356663 + 0.617758i −0.987401 0.158237i $$-0.949419\pi$$
0.630738 + 0.775996i $$0.282752\pi$$
$$284$$ −4.00000 + 6.92820i −0.237356 + 0.411113i
$$285$$ −2.00000 3.46410i −0.118470 0.205196i
$$286$$ 8.00000 0.473050
$$287$$ 0 0
$$288$$ −5.00000 −0.294628
$$289$$ 6.50000 + 11.2583i 0.382353 + 0.662255i
$$290$$ 1.00000 1.73205i 0.0587220 0.101710i
$$291$$ 1.00000 1.73205i 0.0586210 0.101535i
$$292$$ −5.00000 8.66025i −0.292603 0.506803i
$$293$$ −6.00000 −0.350524 −0.175262 0.984522i $$-0.556077\pi$$
−0.175262 + 0.984522i $$0.556077\pi$$
$$294$$ 0 0
$$295$$ −4.00000 −0.232889
$$296$$ 15.0000 + 25.9808i 0.871857 + 1.51010i
$$297$$ 2.00000 3.46410i 0.116052 0.201008i
$$298$$ 11.0000 19.0526i 0.637213 1.10369i
$$299$$ 0 0
$$300$$ −1.00000 −0.0577350
$$301$$ 0 0
$$302$$ 8.00000 0.460348
$$303$$ 3.00000 + 5.19615i 0.172345 + 0.298511i
$$304$$ −2.00000 + 3.46410i −0.114708 + 0.198680i
$$305$$ 1.00000 1.73205i 0.0572598 0.0991769i
$$306$$ −1.00000 1.73205i −0.0571662 0.0990148i
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 0 0
$$309$$ 16.0000 0.910208
$$310$$ 0 0
$$311$$ −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i $$0.404886\pi$$
−0.974841 + 0.222900i $$0.928448\pi$$
$$312$$ −3.00000 + 5.19615i −0.169842 + 0.294174i
$$313$$ 13.0000 + 22.5167i 0.734803 + 1.27272i 0.954810 + 0.297218i $$0.0960589\pi$$
−0.220006 + 0.975499i $$0.570608\pi$$
$$314$$ 14.0000 0.790066
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1.00000 + 1.73205i 0.0561656 + 0.0972817i 0.892741 0.450570i $$-0.148779\pi$$
−0.836576 + 0.547852i $$0.815446\pi$$
$$318$$ −5.00000 + 8.66025i −0.280386 + 0.485643i
$$319$$ −4.00000 + 6.92820i −0.223957 + 0.387905i
$$320$$ 3.50000 + 6.06218i 0.195656 + 0.338886i
$$321$$ −12.0000 −0.669775
$$322$$ 0 0
$$323$$ 8.00000 0.445132
$$324$$ 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
$$327$$ −7.00000 12.1244i −0.387101 0.670478i
$$328$$ −30.0000 −1.65647
$$329$$ 0 0
$$330$$ −4.00000 −0.220193
$$331$$ −6.00000 10.3923i −0.329790 0.571213i 0.652680 0.757634i $$-0.273645\pi$$
−0.982470 + 0.186421i $$0.940311\pi$$
$$332$$ −6.00000 + 10.3923i −0.329293 + 0.570352i
$$333$$ 5.00000 8.66025i 0.273998 0.474579i
$$334$$ 0 0
$$335$$ −12.0000 −0.655630
$$336$$ 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
$$339$$ −1.00000 + 1.73205i −0.0543125 + 0.0940721i
$$340$$ 1.00000 1.73205i 0.0542326 0.0939336i
$$341$$ 0 0
$$342$$ 4.00000 0.216295
$$343$$ 0 0
$$344$$ 12.0000 0.646997
$$345$$ 0 0
$$346$$ 9.00000 15.5885i 0.483843 0.838041i
$$347$$ 14.0000 24.2487i 0.751559 1.30174i −0.195507 0.980702i $$-0.562635\pi$$
0.947067 0.321037i $$-0.104031\pi$$
$$348$$ −1.00000 1.73205i −0.0536056 0.0928477i
$$349$$ 2.00000 0.107058 0.0535288 0.998566i $$-0.482953\pi$$
0.0535288 + 0.998566i $$0.482953\pi$$
$$350$$ 0 0
$$351$$ 2.00000 0.106752
$$352$$ −10.0000 17.3205i −0.533002 0.923186i
$$353$$ 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i $$-0.674325\pi$$
0.999711 + 0.0240566i $$0.00765819\pi$$
$$354$$ 2.00000 3.46410i 0.106299 0.184115i
$$355$$ −4.00000 6.92820i −0.212298 0.367711i
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ −20.0000 −1.05703
$$359$$ 12.0000 + 20.7846i 0.633336 + 1.09697i 0.986865 + 0.161546i $$0.0516481\pi$$
−0.353529 + 0.935423i $$0.615019\pi$$
$$360$$ 1.50000 2.59808i 0.0790569 0.136931i
$$361$$ 1.50000 2.59808i 0.0789474 0.136741i
$$362$$ 5.00000 + 8.66025i 0.262794 + 0.455173i
$$363$$ 5.00000 0.262432
$$364$$ 0 0
$$365$$ 10.0000 0.523424
$$366$$ 1.00000 + 1.73205i 0.0522708 + 0.0905357i
$$367$$ −12.0000 + 20.7846i −0.626395 + 1.08495i 0.361874 + 0.932227i $$0.382137\pi$$
−0.988269 + 0.152721i $$0.951196\pi$$
$$368$$ 0 0
$$369$$ 5.00000 + 8.66025i 0.260290 + 0.450835i
$$370$$ −10.0000 −0.519875
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 13.0000 + 22.5167i 0.673114 + 1.16587i 0.977016 + 0.213165i $$0.0683772\pi$$
−0.303902 + 0.952703i $$0.598289\pi$$
$$374$$ 4.00000 6.92820i 0.206835 0.358249i
$$375$$ 0.500000 0.866025i 0.0258199 0.0447214i
$$376$$ 12.0000 + 20.7846i 0.618853 + 1.07188i
$$377$$ −4.00000 −0.206010
$$378$$ 0 0
$$379$$ −20.0000 −1.02733 −0.513665 0.857991i $$-0.671713\pi$$
−0.513665 + 0.857991i $$0.671713\pi$$
$$380$$ 2.00000 + 3.46410i 0.102598 + 0.177705i
$$381$$ 4.00000 6.92820i 0.204926 0.354943i
$$382$$ 8.00000 13.8564i 0.409316 0.708955i
$$383$$ −12.0000 20.7846i −0.613171 1.06204i −0.990702 0.136047i $$-0.956560\pi$$
0.377531 0.925997i $$-0.376773\pi$$
$$384$$ 3.00000 0.153093
$$385$$ 0 0
$$386$$ −2.00000 −0.101797
$$387$$ −2.00000 3.46410i −0.101666 0.176090i
$$388$$ −1.00000 + 1.73205i −0.0507673 + 0.0879316i
$$389$$ −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i $$-0.881939\pi$$
0.779895 + 0.625910i $$0.215272\pi$$
$$390$$ −1.00000 1.73205i −0.0506370 0.0877058i
$$391$$ 0 0
$$392$$ 0 0
$$393$$ 12.0000 0.605320
$$394$$ 3.00000 + 5.19615i 0.151138 + 0.261778i
$$395$$ 0 0
$$396$$ −2.00000 + 3.46410i −0.100504 + 0.174078i
$$397$$ −1.00000 1.73205i −0.0501886 0.0869291i 0.839840 0.542834i $$-0.182649\pi$$
−0.890028 + 0.455905i $$0.849316\pi$$
$$398$$ −8.00000 −0.401004
$$399$$ 0 0
$$400$$ −1.00000 −0.0500000
$$401$$ −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i $$-0.315043\pi$$
−0.998350 + 0.0574304i $$0.981709\pi$$
$$402$$ 6.00000 10.3923i 0.299253 0.518321i
$$403$$ 0 0
$$404$$ −3.00000 5.19615i −0.149256 0.258518i
$$405$$ −1.00000 −0.0496904
$$406$$ 0 0
$$407$$ 40.0000 1.98273
$$408$$ 3.00000 + 5.19615i 0.148522 + 0.257248i
$$409$$ 13.0000 22.5167i 0.642809 1.11338i −0.341994 0.939702i $$-0.611102\pi$$
0.984803 0.173675i $$-0.0555643\pi$$
$$410$$ 5.00000 8.66025i 0.246932 0.427699i
$$411$$ 3.00000 + 5.19615i 0.147979 + 0.256307i
$$412$$ −16.0000 −0.788263
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −6.00000 10.3923i −0.294528 0.510138i
$$416$$ 5.00000 8.66025i 0.245145 0.424604i
$$417$$ −2.00000 + 3.46410i −0.0979404 + 0.169638i
$$418$$ 8.00000 + 13.8564i 0.391293 + 0.677739i
$$419$$ −4.00000 −0.195413 −0.0977064 0.995215i $$-0.531151\pi$$
−0.0977064 + 0.995215i $$0.531151\pi$$
$$420$$ 0 0
$$421$$ −26.0000 −1.26716 −0.633581 0.773676i $$-0.718416\pi$$
−0.633581 + 0.773676i $$0.718416\pi$$
$$422$$ 10.0000 + 17.3205i 0.486792 + 0.843149i
$$423$$ 4.00000 6.92820i 0.194487 0.336861i
$$424$$ 15.0000 25.9808i 0.728464 1.26174i
$$425$$ 1.00000 + 1.73205i 0.0485071 + 0.0840168i
$$426$$ 8.00000 0.387601
$$427$$ 0 0
$$428$$ 12.0000 0.580042
$$429$$ 4.00000 + 6.92820i 0.193122 + 0.334497i
$$430$$ −2.00000 + 3.46410i −0.0964486 + 0.167054i
$$431$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$432$$ 0.500000 + 0.866025i 0.0240563 + 0.0416667i
$$433$$ 14.0000 0.672797 0.336399 0.941720i $$-0.390791\pi$$
0.336399 + 0.941720i $$0.390791\pi$$
$$434$$ 0 0
$$435$$ 2.00000 0.0958927
$$436$$ 7.00000 + 12.1244i 0.335239 + 0.580651i
$$437$$ 0 0
$$438$$ −5.00000 + 8.66025i −0.238909 + 0.413803i
$$439$$ 20.0000 + 34.6410i 0.954548 + 1.65333i 0.735399 + 0.677634i $$0.236995\pi$$
0.219149 + 0.975691i $$0.429672\pi$$
$$440$$ 12.0000 0.572078
$$441$$ 0 0
$$442$$ 4.00000 0.190261
$$443$$ 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i $$-0.0746503\pi$$
−0.687557 + 0.726130i $$0.741317\pi$$
$$444$$ −5.00000 + 8.66025i −0.237289 + 0.410997i
$$445$$ 3.00000 5.19615i 0.142214 0.246321i
$$446$$ −4.00000 6.92820i −0.189405 0.328060i
$$447$$ 22.0000 1.04056
$$448$$ 0 0
$$449$$ 2.00000 0.0943858 0.0471929 0.998886i $$-0.484972\pi$$
0.0471929 + 0.998886i $$0.484972\pi$$
$$450$$ 0.500000 + 0.866025i 0.0235702 + 0.0408248i
$$451$$ −20.0000 + 34.6410i −0.941763 + 1.63118i
$$452$$ 1.00000 1.73205i 0.0470360 0.0814688i
$$453$$ 4.00000 + 6.92820i 0.187936 + 0.325515i
$$454$$ −20.0000 −0.938647
$$455$$ 0 0
$$456$$ −12.0000 −0.561951
$$457$$ −5.00000 8.66025i −0.233890 0.405110i 0.725059 0.688686i $$-0.241812\pi$$
−0.958950 + 0.283577i $$0.908479\pi$$
$$458$$ −3.00000 + 5.19615i −0.140181 + 0.242800i
$$459$$ 1.00000 1.73205i 0.0466760 0.0808452i
$$460$$ 0 0
$$461$$ 18.0000 0.838344 0.419172 0.907907i $$-0.362320\pi$$
0.419172 + 0.907907i $$0.362320\pi$$
$$462$$ 0 0
$$463$$ 24.0000 1.11537 0.557687 0.830051i $$-0.311689\pi$$
0.557687 + 0.830051i $$0.311689\pi$$
$$464$$ −1.00000 1.73205i −0.0464238 0.0804084i
$$465$$ 0 0
$$466$$ −3.00000 + 5.19615i −0.138972 + 0.240707i
$$467$$ 14.0000 + 24.2487i 0.647843 + 1.12210i 0.983637 + 0.180161i $$0.0576619\pi$$
−0.335794 + 0.941935i $$0.609005\pi$$
$$468$$ −2.00000 −0.0924500
$$469$$ 0 0
$$470$$ −8.00000 −0.369012
$$471$$ 7.00000 + 12.1244i 0.322543 + 0.558661i
$$472$$ −6.00000 + 10.3923i −0.276172 + 0.478345i
$$473$$ 8.00000 13.8564i 0.367840 0.637118i
$$474$$ 0 0
$$475$$ −4.00000 −0.183533
$$476$$ 0 0
$$477$$ −10.0000 −0.457869
$$478$$ −8.00000 13.8564i −0.365911 0.633777i
$$479$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$480$$ −2.50000 + 4.33013i −0.114109 + 0.197642i
$$481$$ 10.0000 + 17.3205i 0.455961 + 0.789747i
$$482$$ −14.0000 −0.637683
$$483$$ 0 0
$$484$$ −5.00000 −0.227273
$$485$$ −1.00000 1.73205i −0.0454077 0.0786484i
$$486$$ 0.500000 0.866025i 0.0226805 0.0392837i
$$487$$ −16.0000 + 27.7128i −0.725029 + 1.25579i 0.233933 + 0.972253i $$0.424840\pi$$
−0.958962 + 0.283535i $$0.908493\pi$$
$$488$$ −3.00000 5.19615i −0.135804 0.235219i
$$489$$ −4.00000 −0.180886
$$490$$ 0 0
$$491$$ 28.0000 1.26362 0.631811 0.775122i $$-0.282312\pi$$
0.631811 + 0.775122i $$0.282312\pi$$
$$492$$ −5.00000 8.66025i −0.225417 0.390434i
$$493$$ −2.00000 + 3.46410i −0.0900755 + 0.156015i
$$494$$ −4.00000 + 6.92820i −0.179969 + 0.311715i
$$495$$ −2.00000 3.46410i −0.0898933 0.155700i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 12.0000 0.537733
$$499$$ −2.00000 3.46410i −0.0895323 0.155074i 0.817781 0.575529i $$-0.195204\pi$$
−0.907314 + 0.420455i $$0.861871\pi$$
$$500$$ −0.500000 + 0.866025i −0.0223607 + 0.0387298i
$$501$$ 0 0
$$502$$ −6.00000 10.3923i −0.267793 0.463831i
$$503$$ 32.0000 1.42681 0.713405 0.700752i $$-0.247152\pi$$
0.713405 + 0.700752i $$0.247152\pi$$
$$504$$ 0 0
$$505$$ 6.00000 0.266996
$$506$$ 0 0
$$507$$ 4.50000 7.79423i 0.199852 0.346154i
$$508$$ −4.00000 + 6.92820i −0.177471 + 0.307389i
$$509$$ −17.0000 29.4449i −0.753512 1.30512i −0.946111 0.323843i $$-0.895025\pi$$
0.192599 0.981278i $$-0.438308\pi$$
$$510$$ −2.00000 −0.0885615
$$511$$ 0 0
$$512$$ 11.0000 0.486136
$$513$$ 2.00000 + 3.46410i 0.0883022 + 0.152944i
$$514$$ −9.00000 + 15.5885i −0.396973 + 0.687577i
$$515$$ 8.00000 13.8564i 0.352522 0.610586i
$$516$$ 2.00000 + 3.46410i 0.0880451 + 0.152499i
$$517$$ 32.0000 1.40736
$$518$$ 0 0
$$519$$ 18.0000 0.790112
$$520$$ 3.00000 + 5.19615i 0.131559 + 0.227866i
$$521$$ 5.00000 8.66025i 0.219054 0.379413i −0.735465 0.677563i $$-0.763036\pi$$
0.954519 + 0.298150i $$0.0963696\pi$$
$$522$$ −1.00000 + 1.73205i −0.0437688 + 0.0758098i
$$523$$ 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i $$-0.138794\pi$$
−0.818980 + 0.573822i $$0.805460\pi$$
$$524$$ −12.0000 −0.524222
$$525$$ 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
$$530$$ 5.00000 + 8.66025i 0.217186 + 0.376177i
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ −20.0000 −0.866296
$$534$$ 3.00000 + 5.19615i 0.129823 + 0.224860i
$$535$$ −6.00000 + 10.3923i −0.259403 + 0.449299i
$$536$$ −18.0000 + 31.1769i −0.777482 + 1.34664i
$$537$$ −10.0000 17.3205i −0.431532 0.747435i
$$538$$ 14.0000 0.603583
$$539$$ 0 0
$$540$$ 1.00000 0.0430331
$$541$$ −15.0000 25.9808i −0.644900 1.11700i −0.984325 0.176367i $$-0.943566\pi$$
0.339424 0.940633i $$-0.389768\pi$$
$$542$$ −8.00000 + 13.8564i −0.343629 + 0.595184i
$$543$$ −5.00000 + 8.66025i −0.214571 + 0.371647i
$$544$$ −5.00000 8.66025i −0.214373 0.371305i
$$545$$ −14.0000 −0.599694
$$546$$ 0 0
$$547$$ −20.0000 −0.855138 −0.427569 0.903983i $$-0.640630\pi$$
−0.427569 + 0.903983i $$0.640630\pi$$
$$548$$ −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
$$554$$ −6.00000 −0.254916
$$555$$ −5.00000 8.66025i −0.212238 0.367607i
$$556$$ 2.00000 3.46410i 0.0848189 0.146911i
$$557$$ 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i $$-0.708795\pi$$
0.991254 + 0.131965i $$0.0421286\pi$$
$$558$$ 0 0
$$559$$ 8.00000 0.338364
$$560$$ 0 0
$$561$$ 8.00000 0.337760
$$562$$ −3.00000 5.19615i −0.126547 0.219186i
$$563$$ 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i $$-0.751959\pi$$
0.964315 + 0.264758i $$0.0852922\pi$$
$$564$$ −4.00000 + 6.92820i −0.168430 + 0.291730i
$$565$$ 1.00000 + 1.73205i 0.0420703 + 0.0728679i
$$566$$ −12.0000 −0.504398
$$567$$ 0 0
$$568$$ −24.0000 −1.00702
$$569$$ 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i $$-0.126528\pi$$
−0.796266 + 0.604947i $$0.793194\pi$$
$$570$$ 2.00000 3.46410i 0.0837708 0.145095i
$$571$$ 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
$$573$$ 16.0000 0.668410
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −3.50000 6.06218i −0.145833 0.252591i
$$577$$ 1.00000 1.73205i 0.0416305 0.0721062i −0.844459 0.535620i $$-0.820078\pi$$
0.886090 + 0.463513i $$0.153411\pi$$
$$578$$ −6.50000 + 11.2583i −0.270364 + 0.468285i
$$579$$ −1.00000 1.73205i −0.0415586 0.0719816i
$$580$$ −2.00000 −0.0830455
$$581$$ 0 0
$$582$$ 2.00000 0.0829027
$$583$$ −20.0000 34.6410i −0.828315 1.43468i
$$584$$ 15.0000 25.9808i 0.620704 1.07509i
$$585$$ 1.00000 1.73205i 0.0413449 0.0716115i
$$586$$ −3.00000 5.19615i −0.123929 0.214651i
$$587$$ 12.0000 0.495293 0.247647 0.968850i $$-0.420343\pi$$
0.247647 + 0.968850i $$0.420343\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ −2.00000 3.46410i −0.0823387 0.142615i
$$591$$ −3.00000 + 5.19615i −0.123404 + 0.213741i
$$592$$ −5.00000 + 8.66025i −0.205499 + 0.355934i
$$593$$ 17.0000 + 29.4449i 0.698106 + 1.20916i 0.969122 + 0.246581i $$0.0793071\pi$$
−0.271016 + 0.962575i $$0.587360\pi$$
$$594$$ 4.00000 0.164122
$$595$$ 0 0
$$596$$ −22.0000 −0.901155
$$597$$ −4.00000 6.92820i −0.163709 0.283552i
$$598$$ 0 0
$$599$$ 4.00000 6.92820i 0.163436 0.283079i −0.772663 0.634816i $$-0.781076\pi$$
0.936099 + 0.351738i $$0.114409\pi$$
$$600$$ −1.50000 2.59808i −0.0612372 0.106066i
$$601$$ −26.0000 −1.06056 −0.530281 0.847822i $$-0.677914\pi$$
−0.530281 + 0.847822i $$0.677914\pi$$
$$602$$ 0 0
$$603$$ 12.0000 0.488678
$$604$$ −4.00000 6.92820i −0.162758 0.281905i
$$605$$ 2.50000 4.33013i 0.101639 0.176045i
$$606$$ −3.00000 + 5.19615i −0.121867 + 0.211079i
$$607$$ −4.00000 6.92820i −0.162355 0.281207i 0.773358 0.633970i $$-0.218576\pi$$
−0.935713 + 0.352763i $$0.885242\pi$$
$$608$$ 20.0000 0.811107
$$609$$ 0 0
$$610$$ 2.00000 0.0809776
$$611$$ 8.00000 + 13.8564i 0.323645 + 0.560570i
$$612$$ −1.00000 + 1.73205i −0.0404226 + 0.0700140i
$$613$$ −11.0000 + 19.0526i −0.444286 + 0.769526i −0.998002 0.0631797i $$-0.979876\pi$$
0.553716 + 0.832705i $$0.313209\pi$$
$$614$$ −14.0000 24.2487i −0.564994 0.978598i
$$615$$ 10.0000 0.403239
$$616$$ 0 0
$$617$$ −6.00000 −0.241551 −0.120775 0.992680i $$-0.538538\pi$$
−0.120775 + 0.992680i $$0.538538\pi$$
$$618$$ 8.00000 + 13.8564i 0.321807 + 0.557386i
$$619$$ −2.00000 + 3.46410i −0.0803868 + 0.139234i −0.903416 0.428765i $$-0.858949\pi$$
0.823029 + 0.567999i $$0.192282\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −24.0000 −0.962312
$$623$$ 0 0
$$624$$ −2.00000 −0.0800641
$$625$$ −0.500000 0.866025i −0.0200000 0.0346410i
$$626$$ −13.0000 + 22.5167i −0.519584 + 0.899947i
$$627$$ −8.00000 + 13.8564i −0.319489 + 0.553372i
$$628$$ −7.00000 12.1244i −0.279330 0.483814i
$$629$$ 20.0000 0.797452
$$630$$ 0 0
$$631$$ −8.00000 −0.318475 −0.159237 0.987240i $$-0.550904\pi$$
−0.159237 + 0.987240i $$0.550904\pi$$
$$632$$ 0 0
$$633$$ −10.0000 + 17.3205i −0.397464 + 0.688428i
$$634$$ −1.00000 + 1.73205i −0.0397151 + 0.0687885i
$$635$$ −4.00000 6.92820i −0.158735 0.274937i
$$636$$ 10.0000 0.396526
$$637$$ 0 0
$$638$$ −8.00000 −0.316723
$$639$$ 4.00000 + 6.92820i 0.158238 + 0.274075i
$$640$$ 1.50000 2.59808i 0.0592927 0.102698i
$$641$$ 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i $$-0.631488\pi$$
0.993899 0.110291i $$-0.0351782\pi$$
$$642$$ −6.00000 10.3923i −0.236801 0.410152i
$$643$$ 36.0000 1.41970 0.709851 0.704352i $$-0.248762\pi$$
0.709851 + 0.704352i $$0.248762\pi$$
$$644$$ 0 0
$$645$$ −4.00000 −0.157500
$$646$$ 4.00000 + 6.92820i 0.157378 + 0.272587i
$$647$$ 16.0000 27.7128i 0.629025 1.08950i −0.358723 0.933444i $$-0.616788\pi$$
0.987748 0.156059i $$-0.0498790\pi$$
$$648$$ −1.50000 + 2.59808i −0.0589256 + 0.102062i
$$649$$ 8.00000 + 13.8564i 0.314027 + 0.543912i
$$650$$ −2.00000 −0.0784465
$$651$$ 0 0
$$652$$ 4.00000 0.156652
$$653$$ −23.0000 39.8372i −0.900060 1.55895i −0.827415 0.561591i $$-0.810189\pi$$
−0.0726446 0.997358i $$-0.523144\pi$$
$$654$$ 7.00000 12.1244i 0.273722 0.474100i
$$655$$ 6.00000 10.3923i 0.234439 0.406061i
$$656$$ −5.00000 8.66025i −0.195217 0.338126i
$$657$$ −10.0000 −0.390137
$$658$$ 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
$$661$$ 11.0000 19.0526i 0.427850 0.741059i −0.568831 0.822454i $$-0.692604\pi$$
0.996682 + 0.0813955i $$0.0259377\pi$$
$$662$$ 6.00000 10.3923i 0.233197 0.403908i
$$663$$ 2.00000 + 3.46410i 0.0776736 + 0.134535i
$$664$$ −36.0000 −1.39707
$$665$$ 0 0
$$666$$ 10.0000 0.387492
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 4.00000 6.92820i 0.154649 0.267860i
$$670$$ −6.00000 10.3923i −0.231800 0.401490i
$$671$$ −8.00000 −0.308837
$$672$$ 0 0
$$673$$ −30.0000 −1.15642 −0.578208 0.815890i $$-0.696248\pi$$
−0.578208 + 0.815890i $$0.696248\pi$$
$$674$$ −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
$$677$$ 3.00000 + 5.19615i 0.115299 + 0.199704i 0.917899 0.396813i $$-0.129884\pi$$
−0.802600 + 0.596518i $$0.796551\pi$$
$$678$$ −2.00000 −0.0768095
$$679$$ 0 0
$$680$$ 6.00000 0.230089
$$681$$ −10.0000 17.3205i −0.383201 0.663723i
$$682$$ 0 0
$$683$$ −18.0000 + 31.1769i −0.688751 + 1.19295i 0.283491 + 0.958975i $$0.408507\pi$$
−0.972242 + 0.233977i $$0.924826\pi$$
$$684$$ −2.00000 3.46410i −0.0764719 0.132453i
$$685$$ 6.00000 0.229248
$$686$$ 0 0
$$687$$ −6.00000 −0.228914
$$688$$ 2.00000 + 3.46410i 0.0762493 + 0.132068i
$$689$$ 10.0000 17.3205i 0.380970 0.659859i
$$690$$ 0 0
$$691$$ −22.0000 38.1051i −0.836919 1.44959i −0.892458 0.451130i $$-0.851021\pi$$
0.0555386 0.998457i $$-0.482312\pi$$
$$692$$ −18.0000 −0.684257
$$693$$ 0 0
$$694$$ 28.0000 1.06287
$$695$$ 2.00000 + 3.46410i 0.0758643 + 0.131401i
$$696$$ 3.00000 5.19615i 0.113715 0.196960i
$$697$$ −10.0000 + 17.3205i −0.378777 + 0.656061i
$$698$$ 1.00000 + 1.73205i 0.0378506 + 0.0655591i
$$699$$ −6.00000 −0.226941
$$700$$ 0 0
$$701$$ −2.00000 −0.0755390 −0.0377695 0.999286i $$-0.512025\pi$$
−0.0377695 + 0.999286i $$0.512025\pi$$
$$702$$ 1.00000 + 1.73205i 0.0377426 + 0.0653720i
$$703$$ −20.0000 + 34.6410i −0.754314 + 1.30651i
$$704$$ 14.0000 24.2487i 0.527645 0.913908i
$$705$$ −4.00000 6.92820i −0.150649 0.260931i
$$706$$ 18.0000 0.677439
$$707$$ 0 0
$$708$$ −4.00000 −0.150329
$$709$$ 13.0000 + 22.5167i 0.488225 + 0.845631i 0.999908 0.0135434i $$-0.00431112\pi$$
−0.511683 + 0.859174i $$0.670978\pi$$
$$710$$ 4.00000 6.92820i 0.150117 0.260011i
$$711$$ 0 0
$$712$$ −9.00000 15.5885i −0.337289 0.584202i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 8.00000 0.299183
$$716$$ 10.0000 + 17.3205i 0.373718 + 0.647298i
$$717$$ 8.00000 13.8564i 0.298765 0.517477i
$$718$$ −12.0000 + 20.7846i −0.447836 + 0.775675i
$$719$$ −24.0000 41.5692i −0.895049 1.55027i −0.833744 0.552151i $$-0.813807\pi$$
−0.0613050 0.998119i $$-0.519526\pi$$
$$720$$ 1.00000 0.0372678
$$721$$ 0 0
$$722$$ 3.00000 0.111648
$$723$$ −7.00000 12.1244i −0.260333 0.450910i
$$724$$ 5.00000 8.66025i 0.185824 0.321856i
$$725$$ 1.00000 1.73205i 0.0371391 0.0643268i
$$726$$ 2.50000 + 4.33013i 0.0927837 + 0.160706i
$$727$$ 16.0000 0.593407 0.296704 0.954970i $$-0.404113\pi$$
0.296704 + 0.954970i $$0.404113\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 5.00000 + 8.66025i 0.185058 + 0.320530i
$$731$$ 4.00000 6.92820i 0.147945 0.256249i
$$732$$ 1.00000 1.73205i 0.0369611 0.0640184i
$$733$$ 7.00000 + 12.1244i 0.258551 + 0.447823i 0.965854 0.259087i $$-0.0834217\pi$$
−0.707303 + 0.706910i $$0.750088\pi$$
$$734$$ −24.0000 −0.885856
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 24.0000 + 41.5692i 0.884051 + 1.53122i
$$738$$ −5.00000 + 8.66025i −0.184053 + 0.318788i
$$739$$ 22.0000 38.1051i 0.809283 1.40172i −0.104078 0.994569i $$-0.533189\pi$$
0.913361 0.407150i $$-0.133477\pi$$
$$740$$ 5.00000 + 8.66025i 0.183804 + 0.318357i
$$741$$ −8.00000 −0.293887
$$742$$ 0 0
$$743$$ −16.0000 −0.586983 −0.293492 0.955962i $$-0.594817\pi$$
−0.293492 + 0.955962i $$0.594817\pi$$
$$744$$ 0 0
$$745$$ 11.0000 19.0526i 0.403009 0.698032i
$$746$$ −13.0000 + 22.5167i −0.475964 + 0.824394i
$$747$$ 6.00000 + 10.3923i 0.219529 + 0.380235i
$$748$$ −8.00000 −0.292509
$$749$$ 0 0
$$750$$ 1.00000 0.0365148
$$751$$ −8.00000 13.8564i −0.291924 0.505627i 0.682341 0.731034i $$-0.260962\pi$$
−0.974265 + 0.225407i $$0.927629\pi$$
$$752$$ −4.00000 + 6.92820i −0.145865 + 0.252646i
$$753$$ 6.00000 10.3923i 0.218652 0.378717i
$$754$$ −2.00000 3.46410i −0.0728357 0.126155i
$$755$$ 8.00000 0.291150
$$756$$ 0 0
$$757$$ −26.0000 −0.944986 −0.472493 0.881334i $$-0.656646\pi$$
−0.472493 + 0.881334i $$0.656646\pi$$
$$758$$ −10.0000 17.3205i −0.363216 0.629109i
$$759$$ 0 0
$$760$$ −6.00000 + 10.3923i −0.217643 + 0.376969i
$$761$$ −3.00000 5.19615i −0.108750 0.188360i 0.806514 0.591215i $$-0.201351\pi$$
−0.915264 + 0.402854i $$0.868018\pi$$
$$762$$ 8.00000 0.289809
$$763$$ 0 0
$$764$$ −16.0000 −0.578860
$$765$$ −1.00000 1.73205i −0.0361551 0.0626224i
$$766$$ 12.0000 20.7846i 0.433578 0.750978i
$$767$$ −4.00000 + 6.92820i −0.144432 + 0.250163i
$$768$$ 8.50000 + 14.7224i 0.306717 + 0.531250i
$$769$$ −2.00000 −0.0721218 −0.0360609 0.999350i $$-0.511481\pi$$
−0.0360609 + 0.999350i $$0.511481\pi$$
$$770$$ 0 0
$$771$$ −18.0000 −0.648254
$$772$$ 1.00000 + 1.73205i 0.0359908 + 0.0623379i
$$773$$ 3.00000 5.19615i 0.107903 0.186893i −0.807018 0.590527i $$-0.798920\pi$$
0.914920 + 0.403634i $$0.132253\pi$$
$$774$$ 2.00000 3.46410i 0.0718885 0.124515i
$$775$$ 0 0
$$776$$ −6.00000 −0.215387
$$777$$ 0 0
$$778$$ −6.00000 −0.215110
$$779$$ −20.0000 34.6410i −0.716574 1.24114i
$$780$$ −1.00000 + 1.73205i −0.0358057 + 0.0620174i
$$781$$ −16.0000 + 27.7128i −0.572525 + 0.991642i
$$782$$ 0 0
$$783$$ −2.00000 −0.0714742
$$784$$