# Properties

 Label 1050.2.o.k.949.2 Level $1050$ Weight $2$ Character 1050.949 Analytic conductor $8.384$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1050.o (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.38429221223$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 949.2 Root $$-0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1050.949 Dual form 1050.2.o.k.499.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} +(0.866025 - 0.500000i) q^{12} -1.00000i q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.73205 - 1.00000i) q^{17} +(0.866025 + 0.500000i) q^{18} +(0.500000 + 0.866025i) q^{19} +(0.500000 - 2.59808i) q^{21} -4.00000i q^{22} +(1.73205 - 1.00000i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{26} +1.00000i q^{27} +(-2.59808 - 0.500000i) q^{28} -4.00000 q^{29} +(-0.866025 - 0.500000i) q^{32} +(3.46410 - 2.00000i) q^{33} -2.00000 q^{34} +1.00000 q^{36} +(2.59808 - 1.50000i) q^{37} +(0.866025 + 0.500000i) q^{38} +(0.500000 - 0.866025i) q^{39} +12.0000 q^{41} +(-0.866025 - 2.50000i) q^{42} -8.00000i q^{43} +(-2.00000 - 3.46410i) q^{44} +(1.00000 - 1.73205i) q^{46} +(-5.19615 + 3.00000i) q^{47} -1.00000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(-1.00000 - 1.73205i) q^{51} +(-0.866025 - 0.500000i) q^{52} +(1.73205 + 1.00000i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.50000 + 0.866025i) q^{56} +1.00000i q^{57} +(-3.46410 + 2.00000i) q^{58} +(3.00000 - 5.19615i) q^{59} +(6.50000 + 11.2583i) q^{61} +(1.73205 - 2.00000i) q^{63} -1.00000 q^{64} +(2.00000 - 3.46410i) q^{66} +(-2.59808 - 1.50000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +2.00000 q^{69} +16.0000 q^{71} +(0.866025 - 0.500000i) q^{72} +(-9.52628 - 5.50000i) q^{73} +(1.50000 - 2.59808i) q^{74} +1.00000 q^{76} +(-10.3923 - 2.00000i) q^{77} -1.00000i q^{78} +(6.50000 + 11.2583i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(10.3923 - 6.00000i) q^{82} +6.00000i q^{83} +(-2.00000 - 1.73205i) q^{84} +(-4.00000 - 6.92820i) q^{86} +(-3.46410 - 2.00000i) q^{87} +(-3.46410 - 2.00000i) q^{88} +(-1.00000 - 1.73205i) q^{89} +(-2.50000 + 0.866025i) q^{91} -2.00000i q^{92} +(-3.00000 + 5.19615i) q^{94} +(-0.500000 - 0.866025i) q^{96} +17.0000i q^{97} +(-2.59808 + 6.50000i) q^{98} +4.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{4} + 4q^{6} + 2q^{9} + O(q^{10})$$ $$4q + 2q^{4} + 4q^{6} + 2q^{9} + 8q^{11} - 8q^{14} - 2q^{16} + 2q^{19} + 2q^{21} + 2q^{24} - 2q^{26} - 16q^{29} - 8q^{34} + 4q^{36} + 2q^{39} + 48q^{41} - 8q^{44} + 4q^{46} - 22q^{49} - 4q^{51} + 2q^{54} - 10q^{56} + 12q^{59} + 26q^{61} - 4q^{64} + 8q^{66} + 8q^{69} + 64q^{71} + 6q^{74} + 4q^{76} + 26q^{79} - 2q^{81} - 8q^{84} - 16q^{86} - 4q^{89} - 10q^{91} - 12q^{94} - 2q^{96} + 16q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$701$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.866025 0.500000i 0.612372 0.353553i
$$3$$ 0.866025 + 0.500000i 0.500000 + 0.288675i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ 0 0
$$6$$ 1.00000 0.408248
$$7$$ −0.866025 2.50000i −0.327327 0.944911i
$$8$$ 1.00000i 0.353553i
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i $$-0.627296\pi$$
0.992361 0.123371i $$-0.0393705\pi$$
$$12$$ 0.866025 0.500000i 0.250000 0.144338i
$$13$$ 1.00000i 0.277350i −0.990338 0.138675i $$-0.955716\pi$$
0.990338 0.138675i $$-0.0442844\pi$$
$$14$$ −2.00000 1.73205i −0.534522 0.462910i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −1.73205 1.00000i −0.420084 0.242536i 0.275029 0.961436i $$-0.411312\pi$$
−0.695113 + 0.718900i $$0.744646\pi$$
$$18$$ 0.866025 + 0.500000i 0.204124 + 0.117851i
$$19$$ 0.500000 + 0.866025i 0.114708 + 0.198680i 0.917663 0.397360i $$-0.130073\pi$$
−0.802955 + 0.596040i $$0.796740\pi$$
$$20$$ 0 0
$$21$$ 0.500000 2.59808i 0.109109 0.566947i
$$22$$ 4.00000i 0.852803i
$$23$$ 1.73205 1.00000i 0.361158 0.208514i −0.308431 0.951247i $$-0.599804\pi$$
0.669588 + 0.742732i $$0.266471\pi$$
$$24$$ 0.500000 0.866025i 0.102062 0.176777i
$$25$$ 0 0
$$26$$ −0.500000 0.866025i −0.0980581 0.169842i
$$27$$ 1.00000i 0.192450i
$$28$$ −2.59808 0.500000i −0.490990 0.0944911i
$$29$$ −4.00000 −0.742781 −0.371391 0.928477i $$-0.621119\pi$$
−0.371391 + 0.928477i $$0.621119\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$32$$ −0.866025 0.500000i −0.153093 0.0883883i
$$33$$ 3.46410 2.00000i 0.603023 0.348155i
$$34$$ −2.00000 −0.342997
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ 2.59808 1.50000i 0.427121 0.246598i −0.270998 0.962580i $$-0.587354\pi$$
0.698119 + 0.715981i $$0.254020\pi$$
$$38$$ 0.866025 + 0.500000i 0.140488 + 0.0811107i
$$39$$ 0.500000 0.866025i 0.0800641 0.138675i
$$40$$ 0 0
$$41$$ 12.0000 1.87409 0.937043 0.349215i $$-0.113552\pi$$
0.937043 + 0.349215i $$0.113552\pi$$
$$42$$ −0.866025 2.50000i −0.133631 0.385758i
$$43$$ 8.00000i 1.21999i −0.792406 0.609994i $$-0.791172\pi$$
0.792406 0.609994i $$-0.208828\pi$$
$$44$$ −2.00000 3.46410i −0.301511 0.522233i
$$45$$ 0 0
$$46$$ 1.00000 1.73205i 0.147442 0.255377i
$$47$$ −5.19615 + 3.00000i −0.757937 + 0.437595i −0.828554 0.559908i $$-0.810836\pi$$
0.0706177 + 0.997503i $$0.477503\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ −5.50000 + 4.33013i −0.785714 + 0.618590i
$$50$$ 0 0
$$51$$ −1.00000 1.73205i −0.140028 0.242536i
$$52$$ −0.866025 0.500000i −0.120096 0.0693375i
$$53$$ 1.73205 + 1.00000i 0.237915 + 0.137361i 0.614218 0.789136i $$-0.289471\pi$$
−0.376303 + 0.926497i $$0.622805\pi$$
$$54$$ 0.500000 + 0.866025i 0.0680414 + 0.117851i
$$55$$ 0 0
$$56$$ −2.50000 + 0.866025i −0.334077 + 0.115728i
$$57$$ 1.00000i 0.132453i
$$58$$ −3.46410 + 2.00000i −0.454859 + 0.262613i
$$59$$ 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i $$-0.705612\pi$$
0.992524 + 0.122047i $$0.0389457\pi$$
$$60$$ 0 0
$$61$$ 6.50000 + 11.2583i 0.832240 + 1.44148i 0.896258 + 0.443533i $$0.146275\pi$$
−0.0640184 + 0.997949i $$0.520392\pi$$
$$62$$ 0 0
$$63$$ 1.73205 2.00000i 0.218218 0.251976i
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 2.00000 3.46410i 0.246183 0.426401i
$$67$$ −2.59808 1.50000i −0.317406 0.183254i 0.332830 0.942987i $$-0.391996\pi$$
−0.650236 + 0.759733i $$0.725330\pi$$
$$68$$ −1.73205 + 1.00000i −0.210042 + 0.121268i
$$69$$ 2.00000 0.240772
$$70$$ 0 0
$$71$$ 16.0000 1.89885 0.949425 0.313993i $$-0.101667\pi$$
0.949425 + 0.313993i $$0.101667\pi$$
$$72$$ 0.866025 0.500000i 0.102062 0.0589256i
$$73$$ −9.52628 5.50000i −1.11497 0.643726i −0.174855 0.984594i $$-0.555946\pi$$
−0.940111 + 0.340868i $$0.889279\pi$$
$$74$$ 1.50000 2.59808i 0.174371 0.302020i
$$75$$ 0 0
$$76$$ 1.00000 0.114708
$$77$$ −10.3923 2.00000i −1.18431 0.227921i
$$78$$ 1.00000i 0.113228i
$$79$$ 6.50000 + 11.2583i 0.731307 + 1.26666i 0.956325 + 0.292306i $$0.0944227\pi$$
−0.225018 + 0.974355i $$0.572244\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 10.3923 6.00000i 1.14764 0.662589i
$$83$$ 6.00000i 0.658586i 0.944228 + 0.329293i $$0.106810\pi$$
−0.944228 + 0.329293i $$0.893190\pi$$
$$84$$ −2.00000 1.73205i −0.218218 0.188982i
$$85$$ 0 0
$$86$$ −4.00000 6.92820i −0.431331 0.747087i
$$87$$ −3.46410 2.00000i −0.371391 0.214423i
$$88$$ −3.46410 2.00000i −0.369274 0.213201i
$$89$$ −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i $$-0.200471\pi$$
−0.914146 + 0.405385i $$0.867138\pi$$
$$90$$ 0 0
$$91$$ −2.50000 + 0.866025i −0.262071 + 0.0907841i
$$92$$ 2.00000i 0.208514i
$$93$$ 0 0
$$94$$ −3.00000 + 5.19615i −0.309426 + 0.535942i
$$95$$ 0 0
$$96$$ −0.500000 0.866025i −0.0510310 0.0883883i
$$97$$ 17.0000i 1.72609i 0.505128 + 0.863044i $$0.331445\pi$$
−0.505128 + 0.863044i $$0.668555\pi$$
$$98$$ −2.59808 + 6.50000i −0.262445 + 0.656599i
$$99$$ 4.00000 0.402015
$$100$$ 0 0
$$101$$ −6.00000 + 10.3923i −0.597022 + 1.03407i 0.396236 + 0.918149i $$0.370316\pi$$
−0.993258 + 0.115924i $$0.963017\pi$$
$$102$$ −1.73205 1.00000i −0.171499 0.0990148i
$$103$$ −6.06218 + 3.50000i −0.597324 + 0.344865i −0.767988 0.640464i $$-0.778742\pi$$
0.170664 + 0.985329i $$0.445409\pi$$
$$104$$ −1.00000 −0.0980581
$$105$$ 0 0
$$106$$ 2.00000 0.194257
$$107$$ 5.19615 3.00000i 0.502331 0.290021i −0.227345 0.973814i $$-0.573004\pi$$
0.729676 + 0.683793i $$0.239671\pi$$
$$108$$ 0.866025 + 0.500000i 0.0833333 + 0.0481125i
$$109$$ −9.50000 + 16.4545i −0.909935 + 1.57605i −0.0957826 + 0.995402i $$0.530535\pi$$
−0.814152 + 0.580651i $$0.802798\pi$$
$$110$$ 0 0
$$111$$ 3.00000 0.284747
$$112$$ −1.73205 + 2.00000i −0.163663 + 0.188982i
$$113$$ 18.0000i 1.69330i −0.532152 0.846649i $$-0.678617\pi$$
0.532152 0.846649i $$-0.321383\pi$$
$$114$$ 0.500000 + 0.866025i 0.0468293 + 0.0811107i
$$115$$ 0 0
$$116$$ −2.00000 + 3.46410i −0.185695 + 0.321634i
$$117$$ 0.866025 0.500000i 0.0800641 0.0462250i
$$118$$ 6.00000i 0.552345i
$$119$$ −1.00000 + 5.19615i −0.0916698 + 0.476331i
$$120$$ 0 0
$$121$$ −2.50000 4.33013i −0.227273 0.393648i
$$122$$ 11.2583 + 6.50000i 1.01928 + 0.588482i
$$123$$ 10.3923 + 6.00000i 0.937043 + 0.541002i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0.500000 2.59808i 0.0445435 0.231455i
$$127$$ 1.00000i 0.0887357i −0.999015 0.0443678i $$-0.985873\pi$$
0.999015 0.0443678i $$-0.0141274\pi$$
$$128$$ −0.866025 + 0.500000i −0.0765466 + 0.0441942i
$$129$$ 4.00000 6.92820i 0.352180 0.609994i
$$130$$ 0 0
$$131$$ −1.00000 1.73205i −0.0873704 0.151330i 0.819028 0.573753i $$-0.194513\pi$$
−0.906399 + 0.422423i $$0.861180\pi$$
$$132$$ 4.00000i 0.348155i
$$133$$ 1.73205 2.00000i 0.150188 0.173422i
$$134$$ −3.00000 −0.259161
$$135$$ 0 0
$$136$$ −1.00000 + 1.73205i −0.0857493 + 0.148522i
$$137$$ −8.66025 5.00000i −0.739895 0.427179i 0.0821359 0.996621i $$-0.473826\pi$$
−0.822031 + 0.569442i $$0.807159\pi$$
$$138$$ 1.73205 1.00000i 0.147442 0.0851257i
$$139$$ 13.0000 1.10265 0.551323 0.834292i $$-0.314123\pi$$
0.551323 + 0.834292i $$0.314123\pi$$
$$140$$ 0 0
$$141$$ −6.00000 −0.505291
$$142$$ 13.8564 8.00000i 1.16280 0.671345i
$$143$$ −3.46410 2.00000i −0.289683 0.167248i
$$144$$ 0.500000 0.866025i 0.0416667 0.0721688i
$$145$$ 0 0
$$146$$ −11.0000 −0.910366
$$147$$ −6.92820 + 1.00000i −0.571429 + 0.0824786i
$$148$$ 3.00000i 0.246598i
$$149$$ −8.00000 13.8564i −0.655386 1.13516i −0.981797 0.189933i $$-0.939173\pi$$
0.326411 0.945228i $$-0.394160\pi$$
$$150$$ 0 0
$$151$$ −9.50000 + 16.4545i −0.773099 + 1.33905i 0.162758 + 0.986666i $$0.447961\pi$$
−0.935857 + 0.352381i $$0.885372\pi$$
$$152$$ 0.866025 0.500000i 0.0702439 0.0405554i
$$153$$ 2.00000i 0.161690i
$$154$$ −10.0000 + 3.46410i −0.805823 + 0.279145i
$$155$$ 0 0
$$156$$ −0.500000 0.866025i −0.0400320 0.0693375i
$$157$$ 18.1865 + 10.5000i 1.45144 + 0.837991i 0.998564 0.0535803i $$-0.0170633\pi$$
0.452880 + 0.891572i $$0.350397\pi$$
$$158$$ 11.2583 + 6.50000i 0.895665 + 0.517112i
$$159$$ 1.00000 + 1.73205i 0.0793052 + 0.137361i
$$160$$ 0 0
$$161$$ −4.00000 3.46410i −0.315244 0.273009i
$$162$$ 1.00000i 0.0785674i
$$163$$ −19.9186 + 11.5000i −1.56014 + 0.900750i −0.562902 + 0.826523i $$0.690315\pi$$
−0.997241 + 0.0742262i $$0.976351\pi$$
$$164$$ 6.00000 10.3923i 0.468521 0.811503i
$$165$$ 0 0
$$166$$ 3.00000 + 5.19615i 0.232845 + 0.403300i
$$167$$ 10.0000i 0.773823i 0.922117 + 0.386912i $$0.126458\pi$$
−0.922117 + 0.386912i $$0.873542\pi$$
$$168$$ −2.59808 0.500000i −0.200446 0.0385758i
$$169$$ 12.0000 0.923077
$$170$$ 0 0
$$171$$ −0.500000 + 0.866025i −0.0382360 + 0.0662266i
$$172$$ −6.92820 4.00000i −0.528271 0.304997i
$$173$$ 5.19615 3.00000i 0.395056 0.228086i −0.289292 0.957241i $$-0.593420\pi$$
0.684349 + 0.729155i $$0.260087\pi$$
$$174$$ −4.00000 −0.303239
$$175$$ 0 0
$$176$$ −4.00000 −0.301511
$$177$$ 5.19615 3.00000i 0.390567 0.225494i
$$178$$ −1.73205 1.00000i −0.129823 0.0749532i
$$179$$ −4.00000 + 6.92820i −0.298974 + 0.517838i −0.975901 0.218212i $$-0.929978\pi$$
0.676927 + 0.736050i $$0.263311\pi$$
$$180$$ 0 0
$$181$$ −18.0000 −1.33793 −0.668965 0.743294i $$-0.733262\pi$$
−0.668965 + 0.743294i $$0.733262\pi$$
$$182$$ −1.73205 + 2.00000i −0.128388 + 0.148250i
$$183$$ 13.0000i 0.960988i
$$184$$ −1.00000 1.73205i −0.0737210 0.127688i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −6.92820 + 4.00000i −0.506640 + 0.292509i
$$188$$ 6.00000i 0.437595i
$$189$$ 2.50000 0.866025i 0.181848 0.0629941i
$$190$$ 0 0
$$191$$ −10.0000 17.3205i −0.723575 1.25327i −0.959558 0.281511i $$-0.909164\pi$$
0.235983 0.971757i $$-0.424169\pi$$
$$192$$ −0.866025 0.500000i −0.0625000 0.0360844i
$$193$$ −8.66025 5.00000i −0.623379 0.359908i 0.154805 0.987945i $$-0.450525\pi$$
−0.778183 + 0.628037i $$0.783859\pi$$
$$194$$ 8.50000 + 14.7224i 0.610264 + 1.05701i
$$195$$ 0 0
$$196$$ 1.00000 + 6.92820i 0.0714286 + 0.494872i
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 3.46410 2.00000i 0.246183 0.142134i
$$199$$ 7.50000 12.9904i 0.531661 0.920864i −0.467656 0.883911i $$-0.654901\pi$$
0.999317 0.0369532i $$-0.0117652\pi$$
$$200$$ 0 0
$$201$$ −1.50000 2.59808i −0.105802 0.183254i
$$202$$ 12.0000i 0.844317i
$$203$$ 3.46410 + 10.0000i 0.243132 + 0.701862i
$$204$$ −2.00000 −0.140028
$$205$$ 0 0
$$206$$ −3.50000 + 6.06218i −0.243857 + 0.422372i
$$207$$ 1.73205 + 1.00000i 0.120386 + 0.0695048i
$$208$$ −0.866025 + 0.500000i −0.0600481 + 0.0346688i
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ 3.00000 0.206529 0.103264 0.994654i $$-0.467071\pi$$
0.103264 + 0.994654i $$0.467071\pi$$
$$212$$ 1.73205 1.00000i 0.118958 0.0686803i
$$213$$ 13.8564 + 8.00000i 0.949425 + 0.548151i
$$214$$ 3.00000 5.19615i 0.205076 0.355202i
$$215$$ 0 0
$$216$$ 1.00000 0.0680414
$$217$$ 0 0
$$218$$ 19.0000i 1.28684i
$$219$$ −5.50000 9.52628i −0.371656 0.643726i
$$220$$ 0 0
$$221$$ −1.00000 + 1.73205i −0.0672673 + 0.116510i
$$222$$ 2.59808 1.50000i 0.174371 0.100673i
$$223$$ 19.0000i 1.27233i 0.771551 + 0.636167i $$0.219481\pi$$
−0.771551 + 0.636167i $$0.780519\pi$$
$$224$$ −0.500000 + 2.59808i −0.0334077 + 0.173591i
$$225$$ 0 0
$$226$$ −9.00000 15.5885i −0.598671 1.03693i
$$227$$ 6.92820 + 4.00000i 0.459841 + 0.265489i 0.711977 0.702202i $$-0.247800\pi$$
−0.252136 + 0.967692i $$0.581133\pi$$
$$228$$ 0.866025 + 0.500000i 0.0573539 + 0.0331133i
$$229$$ −3.50000 6.06218i −0.231287 0.400600i 0.726900 0.686743i $$-0.240960\pi$$
−0.958187 + 0.286143i $$0.907627\pi$$
$$230$$ 0 0
$$231$$ −8.00000 6.92820i −0.526361 0.455842i
$$232$$ 4.00000i 0.262613i
$$233$$ 3.46410 2.00000i 0.226941 0.131024i −0.382219 0.924072i $$-0.624840\pi$$
0.609160 + 0.793047i $$0.291507\pi$$
$$234$$ 0.500000 0.866025i 0.0326860 0.0566139i
$$235$$ 0 0
$$236$$ −3.00000 5.19615i −0.195283 0.338241i
$$237$$ 13.0000i 0.844441i
$$238$$ 1.73205 + 5.00000i 0.112272 + 0.324102i
$$239$$ 12.0000 0.776215 0.388108 0.921614i $$-0.373129\pi$$
0.388108 + 0.921614i $$0.373129\pi$$
$$240$$ 0 0
$$241$$ −6.50000 + 11.2583i −0.418702 + 0.725213i −0.995809 0.0914555i $$-0.970848\pi$$
0.577107 + 0.816668i $$0.304181\pi$$
$$242$$ −4.33013 2.50000i −0.278351 0.160706i
$$243$$ −0.866025 + 0.500000i −0.0555556 + 0.0320750i
$$244$$ 13.0000 0.832240
$$245$$ 0 0
$$246$$ 12.0000 0.765092
$$247$$ 0.866025 0.500000i 0.0551039 0.0318142i
$$248$$ 0 0
$$249$$ −3.00000 + 5.19615i −0.190117 + 0.329293i
$$250$$ 0 0
$$251$$ 24.0000 1.51487 0.757433 0.652913i $$-0.226453\pi$$
0.757433 + 0.652913i $$0.226453\pi$$
$$252$$ −0.866025 2.50000i −0.0545545 0.157485i
$$253$$ 8.00000i 0.502956i
$$254$$ −0.500000 0.866025i −0.0313728 0.0543393i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −6.92820 + 4.00000i −0.432169 + 0.249513i −0.700270 0.713878i $$-0.746937\pi$$
0.268101 + 0.963391i $$0.413604\pi$$
$$258$$ 8.00000i 0.498058i
$$259$$ −6.00000 5.19615i −0.372822 0.322873i
$$260$$ 0 0
$$261$$ −2.00000 3.46410i −0.123797 0.214423i
$$262$$ −1.73205 1.00000i −0.107006 0.0617802i
$$263$$ 27.7128 + 16.0000i 1.70885 + 0.986602i 0.935995 + 0.352014i $$0.114503\pi$$
0.772851 + 0.634588i $$0.218830\pi$$
$$264$$ −2.00000 3.46410i −0.123091 0.213201i
$$265$$ 0 0
$$266$$ 0.500000 2.59808i 0.0306570 0.159298i
$$267$$ 2.00000i 0.122398i
$$268$$ −2.59808 + 1.50000i −0.158703 + 0.0916271i
$$269$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$270$$ 0 0
$$271$$ 10.0000 + 17.3205i 0.607457 + 1.05215i 0.991658 + 0.128897i $$0.0411435\pi$$
−0.384201 + 0.923249i $$0.625523\pi$$
$$272$$ 2.00000i 0.121268i
$$273$$ −2.59808 0.500000i −0.157243 0.0302614i
$$274$$ −10.0000 −0.604122
$$275$$ 0 0
$$276$$ 1.00000 1.73205i 0.0601929 0.104257i
$$277$$ −0.866025 0.500000i −0.0520344 0.0300421i 0.473757 0.880656i $$-0.342897\pi$$
−0.525792 + 0.850613i $$0.676231\pi$$
$$278$$ 11.2583 6.50000i 0.675230 0.389844i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −18.0000 −1.07379 −0.536895 0.843649i $$-0.680403\pi$$
−0.536895 + 0.843649i $$0.680403\pi$$
$$282$$ −5.19615 + 3.00000i −0.309426 + 0.178647i
$$283$$ 11.2583 + 6.50000i 0.669238 + 0.386385i 0.795788 0.605575i $$-0.207057\pi$$
−0.126550 + 0.991960i $$0.540390\pi$$
$$284$$ 8.00000 13.8564i 0.474713 0.822226i
$$285$$ 0 0
$$286$$ −4.00000 −0.236525
$$287$$ −10.3923 30.0000i −0.613438 1.77084i
$$288$$ 1.00000i 0.0589256i
$$289$$ −6.50000 11.2583i −0.382353 0.662255i
$$290$$ 0 0
$$291$$ −8.50000 + 14.7224i −0.498279 + 0.863044i
$$292$$ −9.52628 + 5.50000i −0.557483 + 0.321863i
$$293$$ 12.0000i 0.701047i −0.936554 0.350524i $$-0.886004\pi$$
0.936554 0.350524i $$-0.113996\pi$$
$$294$$ −5.50000 + 4.33013i −0.320767 + 0.252538i
$$295$$ 0 0
$$296$$ −1.50000 2.59808i −0.0871857 0.151010i
$$297$$ 3.46410 + 2.00000i 0.201008 + 0.116052i
$$298$$ −13.8564 8.00000i −0.802680 0.463428i
$$299$$ −1.00000 1.73205i −0.0578315 0.100167i
$$300$$ 0 0
$$301$$ −20.0000 + 6.92820i −1.15278 + 0.399335i
$$302$$ 19.0000i 1.09333i
$$303$$ −10.3923 + 6.00000i −0.597022 + 0.344691i
$$304$$ 0.500000 0.866025i 0.0286770 0.0496700i
$$305$$ 0 0
$$306$$ −1.00000 1.73205i −0.0571662 0.0990148i
$$307$$ 20.0000i 1.14146i 0.821138 + 0.570730i $$0.193340\pi$$
−0.821138 + 0.570730i $$0.806660\pi$$
$$308$$ −6.92820 + 8.00000i −0.394771 + 0.455842i
$$309$$ −7.00000 −0.398216
$$310$$ 0 0
$$311$$ 7.00000 12.1244i 0.396934 0.687509i −0.596412 0.802678i $$-0.703408\pi$$
0.993346 + 0.115169i $$0.0367410\pi$$
$$312$$ −0.866025 0.500000i −0.0490290 0.0283069i
$$313$$ 15.5885 9.00000i 0.881112 0.508710i 0.0100869 0.999949i $$-0.496789\pi$$
0.871025 + 0.491239i $$0.163456\pi$$
$$314$$ 21.0000 1.18510
$$315$$ 0 0
$$316$$ 13.0000 0.731307
$$317$$ 19.0526 11.0000i 1.07010 0.617822i 0.141890 0.989882i $$-0.454682\pi$$
0.928208 + 0.372061i $$0.121349\pi$$
$$318$$ 1.73205 + 1.00000i 0.0971286 + 0.0560772i
$$319$$ −8.00000 + 13.8564i −0.447914 + 0.775810i
$$320$$ 0 0
$$321$$ 6.00000 0.334887
$$322$$ −5.19615 1.00000i −0.289570 0.0557278i
$$323$$ 2.00000i 0.111283i
$$324$$ 0.500000 + 0.866025i 0.0277778 + 0.0481125i
$$325$$ 0 0
$$326$$ −11.5000 + 19.9186i −0.636926 + 1.10319i
$$327$$ −16.4545 + 9.50000i −0.909935 + 0.525351i
$$328$$ 12.0000i 0.662589i
$$329$$ 12.0000 + 10.3923i 0.661581 + 0.572946i
$$330$$ 0 0
$$331$$ −10.5000 18.1865i −0.577132 0.999622i −0.995806 0.0914858i $$-0.970838\pi$$
0.418674 0.908137i $$-0.362495\pi$$
$$332$$ 5.19615 + 3.00000i 0.285176 + 0.164646i
$$333$$ 2.59808 + 1.50000i 0.142374 + 0.0821995i
$$334$$ 5.00000 + 8.66025i 0.273588 + 0.473868i
$$335$$ 0 0
$$336$$ −2.50000 + 0.866025i −0.136386 + 0.0472456i
$$337$$ 18.0000i 0.980522i −0.871576 0.490261i $$-0.836901\pi$$
0.871576 0.490261i $$-0.163099\pi$$
$$338$$ 10.3923 6.00000i 0.565267 0.326357i
$$339$$ 9.00000 15.5885i 0.488813 0.846649i
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 1.00000i 0.0540738i
$$343$$ 15.5885 + 10.0000i 0.841698 + 0.539949i
$$344$$ −8.00000 −0.431331
$$345$$ 0 0
$$346$$ 3.00000 5.19615i 0.161281 0.279347i
$$347$$ 19.0526 + 11.0000i 1.02279 + 0.590511i 0.914912 0.403653i $$-0.132260\pi$$
0.107883 + 0.994164i $$0.465593\pi$$
$$348$$ −3.46410 + 2.00000i −0.185695 + 0.107211i
$$349$$ −2.00000 −0.107058 −0.0535288 0.998566i $$-0.517047\pi$$
−0.0535288 + 0.998566i $$0.517047\pi$$
$$350$$ 0 0
$$351$$ 1.00000 0.0533761
$$352$$ −3.46410 + 2.00000i −0.184637 + 0.106600i
$$353$$ −17.3205 10.0000i −0.921878 0.532246i −0.0376440 0.999291i $$-0.511985\pi$$
−0.884234 + 0.467045i $$0.845319\pi$$
$$354$$ 3.00000 5.19615i 0.159448 0.276172i
$$355$$ 0 0
$$356$$ −2.00000 −0.106000
$$357$$ −3.46410 + 4.00000i −0.183340 + 0.211702i
$$358$$ 8.00000i 0.422813i
$$359$$ −3.00000 5.19615i −0.158334 0.274242i 0.775934 0.630814i $$-0.217279\pi$$
−0.934268 + 0.356572i $$0.883946\pi$$
$$360$$ 0 0
$$361$$ 9.00000 15.5885i 0.473684 0.820445i
$$362$$ −15.5885 + 9.00000i −0.819311 + 0.473029i
$$363$$ 5.00000i 0.262432i
$$364$$ −0.500000 + 2.59808i −0.0262071 + 0.136176i
$$365$$ 0 0
$$366$$ 6.50000 + 11.2583i 0.339760 + 0.588482i
$$367$$ 6.92820 + 4.00000i 0.361649 + 0.208798i 0.669804 0.742538i $$-0.266378\pi$$
−0.308155 + 0.951336i $$0.599711\pi$$
$$368$$ −1.73205 1.00000i −0.0902894 0.0521286i
$$369$$ 6.00000 + 10.3923i 0.312348 + 0.541002i
$$370$$ 0 0
$$371$$ 1.00000 5.19615i 0.0519174 0.269771i
$$372$$ 0 0
$$373$$ −19.9186 + 11.5000i −1.03135 + 0.595447i −0.917370 0.398036i $$-0.869692\pi$$
−0.113975 + 0.993484i $$0.536359\pi$$
$$374$$ −4.00000 + 6.92820i −0.206835 + 0.358249i
$$375$$ 0 0
$$376$$ 3.00000 + 5.19615i 0.154713 + 0.267971i
$$377$$ 4.00000i 0.206010i
$$378$$ 1.73205 2.00000i 0.0890871 0.102869i
$$379$$ 5.00000 0.256833 0.128416 0.991720i $$-0.459011\pi$$
0.128416 + 0.991720i $$0.459011\pi$$
$$380$$ 0 0
$$381$$ 0.500000 0.866025i 0.0256158 0.0443678i
$$382$$ −17.3205 10.0000i −0.886194 0.511645i
$$383$$ 12.1244 7.00000i 0.619526 0.357683i −0.157159 0.987573i $$-0.550233\pi$$
0.776684 + 0.629890i $$0.216900\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ −10.0000 −0.508987
$$387$$ 6.92820 4.00000i 0.352180 0.203331i
$$388$$ 14.7224 + 8.50000i 0.747418 + 0.431522i
$$389$$ −10.0000 + 17.3205i −0.507020 + 0.878185i 0.492947 + 0.870059i $$0.335920\pi$$
−0.999967 + 0.00812520i $$0.997414\pi$$
$$390$$ 0 0
$$391$$ −4.00000 −0.202289
$$392$$ 4.33013 + 5.50000i 0.218704 + 0.277792i
$$393$$ 2.00000i 0.100887i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 2.00000 3.46410i 0.100504 0.174078i
$$397$$ −15.5885 + 9.00000i −0.782362 + 0.451697i −0.837267 0.546795i $$-0.815848\pi$$
0.0549046 + 0.998492i $$0.482515\pi$$
$$398$$ 15.0000i 0.751882i
$$399$$ 2.50000 0.866025i 0.125157 0.0433555i
$$400$$ 0 0
$$401$$ −2.00000 3.46410i −0.0998752 0.172989i 0.811758 0.583994i $$-0.198511\pi$$
−0.911633 + 0.411005i $$0.865178\pi$$
$$402$$ −2.59808 1.50000i −0.129580 0.0748132i
$$403$$ 0 0
$$404$$ 6.00000 + 10.3923i 0.298511 + 0.517036i
$$405$$ 0 0
$$406$$ 8.00000 + 6.92820i 0.397033 + 0.343841i
$$407$$ 12.0000i 0.594818i
$$408$$ −1.73205 + 1.00000i −0.0857493 + 0.0495074i
$$409$$ −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i $$-0.921004\pi$$
0.697406 + 0.716677i $$0.254338\pi$$
$$410$$ 0 0
$$411$$ −5.00000 8.66025i −0.246632 0.427179i
$$412$$ 7.00000i 0.344865i
$$413$$ −15.5885 3.00000i −0.767058 0.147620i
$$414$$ 2.00000 0.0982946
$$415$$ 0 0
$$416$$ −0.500000 + 0.866025i −0.0245145 + 0.0424604i
$$417$$ 11.2583 + 6.50000i 0.551323 + 0.318306i
$$418$$ 3.46410 2.00000i 0.169435 0.0978232i
$$419$$ 16.0000 0.781651 0.390826 0.920465i $$-0.372190\pi$$
0.390826 + 0.920465i $$0.372190\pi$$
$$420$$ 0 0
$$421$$ 1.00000 0.0487370 0.0243685 0.999703i $$-0.492242\pi$$
0.0243685 + 0.999703i $$0.492242\pi$$
$$422$$ 2.59808 1.50000i 0.126472 0.0730189i
$$423$$ −5.19615 3.00000i −0.252646 0.145865i
$$424$$ 1.00000 1.73205i 0.0485643 0.0841158i
$$425$$ 0 0
$$426$$ 16.0000 0.775203
$$427$$ 22.5167 26.0000i 1.08966 1.25823i
$$428$$ 6.00000i 0.290021i
$$429$$ −2.00000 3.46410i −0.0965609 0.167248i
$$430$$ 0 0
$$431$$ −3.00000 + 5.19615i −0.144505 + 0.250290i −0.929188 0.369607i $$-0.879492\pi$$
0.784683 + 0.619897i $$0.212826\pi$$
$$432$$ 0.866025 0.500000i 0.0416667 0.0240563i
$$433$$ 2.00000i 0.0961139i 0.998845 + 0.0480569i $$0.0153029\pi$$
−0.998845 + 0.0480569i $$0.984697\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 9.50000 + 16.4545i 0.454967 + 0.788027i
$$437$$ 1.73205 + 1.00000i 0.0828552 + 0.0478365i
$$438$$ −9.52628 5.50000i −0.455183 0.262800i
$$439$$ −11.5000 19.9186i −0.548865 0.950662i −0.998353 0.0573756i $$-0.981727\pi$$
0.449488 0.893287i $$-0.351607\pi$$
$$440$$ 0 0
$$441$$ −6.50000 2.59808i −0.309524 0.123718i
$$442$$ 2.00000i 0.0951303i
$$443$$ −5.19615 + 3.00000i −0.246877 + 0.142534i −0.618333 0.785916i $$-0.712192\pi$$
0.371457 + 0.928450i $$0.378858\pi$$
$$444$$ 1.50000 2.59808i 0.0711868 0.123299i
$$445$$ 0 0
$$446$$ 9.50000 + 16.4545i 0.449838 + 0.779142i
$$447$$ 16.0000i 0.756774i
$$448$$ 0.866025 + 2.50000i 0.0409159 + 0.118114i
$$449$$ −2.00000 −0.0943858 −0.0471929 0.998886i $$-0.515028\pi$$
−0.0471929 + 0.998886i $$0.515028\pi$$
$$450$$ 0 0
$$451$$ 24.0000 41.5692i 1.13012 1.95742i
$$452$$ −15.5885 9.00000i −0.733219 0.423324i
$$453$$ −16.4545 + 9.50000i −0.773099 + 0.446349i
$$454$$ 8.00000 0.375459
$$455$$ 0 0
$$456$$ 1.00000 0.0468293
$$457$$ 32.0429 18.5000i 1.49891 0.865393i 0.498906 0.866656i $$-0.333735\pi$$
0.999999 + 0.00126243i $$0.000401844\pi$$
$$458$$ −6.06218 3.50000i −0.283267 0.163544i
$$459$$ 1.00000 1.73205i 0.0466760 0.0808452i
$$460$$ 0 0
$$461$$ 26.0000 1.21094 0.605470 0.795868i $$-0.292985\pi$$
0.605470 + 0.795868i $$0.292985\pi$$
$$462$$ −10.3923 2.00000i −0.483494 0.0930484i
$$463$$ 3.00000i 0.139422i 0.997567 + 0.0697109i $$0.0222077\pi$$
−0.997567 + 0.0697109i $$0.977792\pi$$
$$464$$ 2.00000 + 3.46410i 0.0928477 + 0.160817i
$$465$$ 0 0
$$466$$ 2.00000 3.46410i 0.0926482 0.160471i
$$467$$ 25.9808 15.0000i 1.20225 0.694117i 0.241192 0.970477i $$-0.422462\pi$$
0.961054 + 0.276360i $$0.0891283\pi$$
$$468$$ 1.00000i 0.0462250i
$$469$$ −1.50000 + 7.79423i −0.0692636 + 0.359904i
$$470$$ 0 0
$$471$$ 10.5000 + 18.1865i 0.483814 + 0.837991i
$$472$$ −5.19615 3.00000i −0.239172 0.138086i
$$473$$ −27.7128 16.0000i −1.27424 0.735681i
$$474$$ 6.50000 + 11.2583i 0.298555 + 0.517112i
$$475$$ 0 0
$$476$$ 4.00000 + 3.46410i 0.183340 + 0.158777i
$$477$$ 2.00000i 0.0915737i
$$478$$ 10.3923 6.00000i 0.475333 0.274434i
$$479$$ −17.0000 + 29.4449i −0.776750 + 1.34537i 0.157056 + 0.987590i $$0.449800\pi$$
−0.933806 + 0.357780i $$0.883534\pi$$
$$480$$ 0 0
$$481$$ −1.50000 2.59808i −0.0683941 0.118462i
$$482$$ 13.0000i 0.592134i
$$483$$ −1.73205 5.00000i −0.0788110 0.227508i
$$484$$ −5.00000 −0.227273
$$485$$ 0 0
$$486$$ −0.500000 + 0.866025i −0.0226805 + 0.0392837i
$$487$$ −34.6410 20.0000i −1.56973 0.906287i −0.996199 0.0871056i $$-0.972238\pi$$
−0.573535 0.819181i $$-0.694428\pi$$
$$488$$ 11.2583 6.50000i 0.509641 0.294241i
$$489$$ −23.0000 −1.04010
$$490$$ 0 0
$$491$$ 18.0000 0.812329 0.406164 0.913800i $$-0.366866\pi$$
0.406164 + 0.913800i $$0.366866\pi$$
$$492$$ 10.3923 6.00000i 0.468521 0.270501i
$$493$$ 6.92820 + 4.00000i 0.312031 + 0.180151i
$$494$$ 0.500000 0.866025i 0.0224961 0.0389643i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −13.8564 40.0000i −0.621545 1.79425i
$$498$$ 6.00000i 0.268866i
$$499$$ −13.5000 23.3827i −0.604343 1.04675i −0.992155 0.125014i $$-0.960102\pi$$
0.387812 0.921739i $$-0.373231\pi$$
$$500$$ 0 0
$$501$$ −5.00000 + 8.66025i −0.223384 + 0.386912i
$$502$$ 20.7846 12.0000i 0.927663 0.535586i
$$503$$ 4.00000i 0.178351i −0.996016 0.0891756i $$-0.971577\pi$$
0.996016 0.0891756i $$-0.0284232\pi$$
$$504$$ −2.00000 1.73205i −0.0890871 0.0771517i
$$505$$ 0 0
$$506$$ −4.00000 6.92820i −0.177822 0.307996i
$$507$$ 10.3923 + 6.00000i 0.461538 + 0.266469i
$$508$$ −0.866025 0.500000i −0.0384237 0.0221839i
$$509$$ −18.0000 31.1769i −0.797836 1.38189i −0.921023 0.389509i $$-0.872645\pi$$
0.123187 0.992384i $$-0.460689\pi$$
$$510$$ 0 0
$$511$$ −5.50000 + 28.5788i −0.243306 + 1.26425i
$$512$$ 1.00000i 0.0441942i
$$513$$ −0.866025 + 0.500000i −0.0382360 + 0.0220755i
$$514$$ −4.00000 + 6.92820i −0.176432 + 0.305590i
$$515$$ 0 0
$$516$$ −4.00000 6.92820i −0.176090 0.304997i
$$517$$ 24.0000i 1.05552i
$$518$$ −7.79423 1.50000i −0.342459 0.0659062i
$$519$$ 6.00000 0.263371
$$520$$ 0 0
$$521$$ −3.00000 + 5.19615i −0.131432 + 0.227648i −0.924229 0.381839i $$-0.875291\pi$$
0.792797 + 0.609486i $$0.208624\pi$$
$$522$$ −3.46410 2.00000i −0.151620 0.0875376i
$$523$$ −13.8564 + 8.00000i −0.605898 + 0.349816i −0.771358 0.636401i $$-0.780422\pi$$
0.165460 + 0.986216i $$0.447089\pi$$
$$524$$ −2.00000 −0.0873704
$$525$$ 0 0
$$526$$ 32.0000 1.39527
$$527$$ 0 0
$$528$$ −3.46410 2.00000i −0.150756 0.0870388i
$$529$$ −9.50000 + 16.4545i −0.413043 + 0.715412i
$$530$$ 0 0
$$531$$ 6.00000 0.260378
$$532$$ −0.866025 2.50000i −0.0375470 0.108389i
$$533$$ 12.0000i 0.519778i
$$534$$ −1.00000 1.73205i −0.0432742 0.0749532i
$$535$$ 0 0
$$536$$ −1.50000 + 2.59808i −0.0647901 + 0.112220i
$$537$$ −6.92820 + 4.00000i −0.298974 + 0.172613i
$$538$$ 0 0
$$539$$ 4.00000 + 27.7128i 0.172292 + 1.19368i
$$540$$ 0 0
$$541$$ −8.50000 14.7224i −0.365444 0.632967i 0.623404 0.781900i $$-0.285749\pi$$
−0.988847 + 0.148933i $$0.952416\pi$$
$$542$$ 17.3205 + 10.0000i 0.743980 + 0.429537i
$$543$$ −15.5885 9.00000i −0.668965 0.386227i
$$544$$ 1.00000 + 1.73205i 0.0428746 + 0.0742611i
$$545$$ 0 0
$$546$$ −2.50000 + 0.866025i −0.106990 + 0.0370625i
$$547$$ 12.0000i 0.513083i −0.966533 0.256541i $$-0.917417\pi$$
0.966533 0.256541i $$-0.0825830\pi$$
$$548$$ −8.66025 + 5.00000i −0.369948 + 0.213589i
$$549$$ −6.50000 + 11.2583i −0.277413 + 0.480494i
$$550$$ 0 0
$$551$$ −2.00000 3.46410i −0.0852029 0.147576i
$$552$$ 2.00000i 0.0851257i
$$553$$ 22.5167 26.0000i 0.957506 1.10563i
$$554$$ −1.00000 −0.0424859
$$555$$ 0 0
$$556$$ 6.50000 11.2583i 0.275661 0.477460i
$$557$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 0 0
$$561$$ −8.00000 −0.337760
$$562$$ −15.5885 + 9.00000i −0.657559 + 0.379642i
$$563$$ −24.2487 14.0000i −1.02196 0.590030i −0.107290 0.994228i $$-0.534217\pi$$
−0.914671 + 0.404198i $$0.867551\pi$$
$$564$$ −3.00000 + 5.19615i −0.126323 + 0.218797i
$$565$$ 0 0
$$566$$ 13.0000 0.546431
$$567$$ 2.59808 + 0.500000i 0.109109 + 0.0209980i
$$568$$ 16.0000i 0.671345i
$$569$$ −20.0000 34.6410i −0.838444 1.45223i −0.891196 0.453619i $$-0.850133\pi$$
0.0527519 0.998608i $$-0.483201\pi$$
$$570$$ 0 0
$$571$$ 17.5000 30.3109i 0.732352 1.26847i −0.223523 0.974699i $$-0.571756\pi$$
0.955875 0.293773i $$-0.0949108\pi$$
$$572$$ −3.46410 + 2.00000i −0.144841 + 0.0836242i
$$573$$ 20.0000i 0.835512i
$$574$$ −24.0000 20.7846i −1.00174 0.867533i
$$575$$ 0 0
$$576$$ −0.500000 0.866025i −0.0208333 0.0360844i
$$577$$ −19.0526 11.0000i −0.793168 0.457936i 0.0479084 0.998852i $$-0.484744\pi$$
−0.841077 + 0.540916i $$0.818078\pi$$
$$578$$ −11.2583 6.50000i −0.468285 0.270364i
$$579$$ −5.00000 8.66025i −0.207793 0.359908i
$$580$$ 0 0
$$581$$ 15.0000 5.19615i 0.622305 0.215573i
$$582$$ 17.0000i 0.704673i
$$583$$ 6.92820 4.00000i 0.286937 0.165663i
$$584$$ −5.50000 + 9.52628i −0.227592 + 0.394200i
$$585$$ 0 0
$$586$$ −6.00000 10.3923i −0.247858 0.429302i
$$587$$ 42.0000i 1.73353i −0.498721 0.866763i $$-0.666197\pi$$
0.498721 0.866763i $$-0.333803\pi$$
$$588$$ −2.59808 + 6.50000i −0.107143 + 0.268055i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −2.59808 1.50000i −0.106780 0.0616496i
$$593$$ −36.3731 + 21.0000i −1.49366 + 0.862367i −0.999974 0.00727173i $$-0.997685\pi$$
−0.493689 + 0.869638i $$0.664352\pi$$
$$594$$ 4.00000 0.164122
$$595$$ 0 0
$$596$$ −16.0000 −0.655386
$$597$$ 12.9904 7.50000i 0.531661 0.306955i
$$598$$ −1.73205 1.00000i −0.0708288 0.0408930i
$$599$$ −3.00000 + 5.19615i −0.122577 + 0.212309i −0.920783 0.390075i $$-0.872449\pi$$
0.798206 + 0.602384i $$0.205782\pi$$
$$600$$ 0 0
$$601$$ −29.0000 −1.18293 −0.591467 0.806329i $$-0.701451\pi$$
−0.591467 + 0.806329i $$0.701451\pi$$
$$602$$ −13.8564 + 16.0000i −0.564745 + 0.652111i
$$603$$ 3.00000i 0.122169i
$$604$$ 9.50000 + 16.4545i 0.386550 + 0.669523i
$$605$$ 0 0
$$606$$ −6.00000 + 10.3923i −0.243733 + 0.422159i
$$607$$ 0.866025 0.500000i 0.0351509 0.0202944i −0.482322 0.875994i $$-0.660206\pi$$
0.517472 + 0.855700i $$0.326873\pi$$
$$608$$ 1.00000i 0.0405554i
$$609$$ −2.00000 + 10.3923i −0.0810441 + 0.421117i
$$610$$ 0 0
$$611$$ 3.00000 + 5.19615i 0.121367 + 0.210214i
$$612$$ −1.73205 1.00000i −0.0700140 0.0404226i
$$613$$ 5.19615 + 3.00000i 0.209871 + 0.121169i 0.601251 0.799060i $$-0.294669\pi$$
−0.391381 + 0.920229i $$0.628002\pi$$
$$614$$ 10.0000 + 17.3205i 0.403567 + 0.698999i
$$615$$ 0 0
$$616$$ −2.00000 + 10.3923i −0.0805823 + 0.418718i
$$617$$ 44.0000i 1.77137i 0.464283 + 0.885687i $$0.346312\pi$$
−0.464283 + 0.885687i $$0.653688\pi$$
$$618$$ −6.06218 + 3.50000i −0.243857 + 0.140791i
$$619$$ 22.0000 38.1051i 0.884255 1.53157i 0.0376891 0.999290i $$-0.488000\pi$$
0.846566 0.532284i $$-0.178666\pi$$
$$620$$ 0 0
$$621$$ 1.00000 + 1.73205i 0.0401286 + 0.0695048i
$$622$$ 14.0000i 0.561349i
$$623$$ −3.46410 + 4.00000i −0.138786 + 0.160257i
$$624$$ −1.00000 −0.0400320
$$625$$ 0 0
$$626$$ 9.00000 15.5885i 0.359712 0.623040i
$$627$$ 3.46410 + 2.00000i 0.138343 + 0.0798723i
$$628$$ 18.1865 10.5000i 0.725722 0.418996i
$$629$$ −6.00000 −0.239236
$$630$$ 0 0
$$631$$ 17.0000 0.676759 0.338380 0.941010i $$-0.390121\pi$$
0.338380 + 0.941010i $$0.390121\pi$$
$$632$$ 11.2583 6.50000i 0.447832 0.258556i
$$633$$ 2.59808 + 1.50000i 0.103264 + 0.0596196i
$$634$$ 11.0000 19.0526i 0.436866 0.756674i
$$635$$ 0 0
$$636$$ 2.00000 0.0793052
$$637$$ 4.33013 + 5.50000i 0.171566 + 0.217918i
$$638$$ 16.0000i 0.633446i
$$639$$ 8.00000 + 13.8564i 0.316475 + 0.548151i
$$640$$ 0 0
$$641$$ −8.00000 + 13.8564i −0.315981 + 0.547295i −0.979646 0.200735i $$-0.935667\pi$$
0.663665 + 0.748030i $$0.269000\pi$$
$$642$$ 5.19615 3.00000i 0.205076 0.118401i
$$643$$ 11.0000i 0.433798i −0.976194 0.216899i $$-0.930406\pi$$
0.976194 0.216899i $$-0.0695942\pi$$
$$644$$ −5.00000 + 1.73205i −0.197028 + 0.0682524i
$$645$$ 0 0
$$646$$ −1.00000 1.73205i −0.0393445 0.0681466i
$$647$$ −10.3923 6.00000i −0.408564 0.235884i 0.281609 0.959529i $$-0.409132\pi$$
−0.690172 + 0.723645i $$0.742465\pi$$
$$648$$ 0.866025 + 0.500000i 0.0340207 + 0.0196419i
$$649$$ −12.0000 20.7846i −0.471041 0.815867i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 23.0000i 0.900750i
$$653$$ 13.8564 8.00000i 0.542243 0.313064i −0.203744 0.979024i $$-0.565311\pi$$
0.745988 + 0.665960i $$0.231978\pi$$
$$654$$ −9.50000 + 16.4545i −0.371479 + 0.643421i
$$655$$ 0 0
$$656$$ −6.00000 10.3923i −0.234261 0.405751i
$$657$$ 11.0000i 0.429151i
$$658$$ 15.5885 + 3.00000i 0.607701 + 0.116952i
$$659$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$660$$ 0 0
$$661$$ 12.5000 21.6506i 0.486194 0.842112i −0.513680 0.857982i $$-0.671718\pi$$
0.999874 + 0.0158695i $$0.00505163\pi$$
$$662$$ −18.1865 10.5000i −0.706840 0.408094i
$$663$$ −1.73205 + 1.00000i −0.0672673 + 0.0388368i
$$664$$ 6.00000 0.232845
$$665$$ 0 0
$$666$$ 3.00000 0.116248
$$667$$ −6.92820 + 4.00000i −0.268261 + 0.154881i
$$668$$ 8.66025 + 5.00000i 0.335075 + 0.193456i
$$669$$ −9.50000 + 16.4545i −0.367291 + 0.636167i
$$670$$ 0 0
$$671$$ 52.0000 2.00744
$$672$$ −1.73205 + 2.00000i −0.0668153 + 0.0771517i
$$673$$ 9.00000i 0.346925i 0.984841 + 0.173462i $$0.0554955\pi$$
−0.984841 + 0.173462i $$0.944505\pi$$
$$674$$ −9.00000 15.5885i −0.346667 0.600445i
$$675$$ 0 0
$$676$$ 6.00000 10.3923i 0.230769 0.399704i
$$677$$ −1.73205 + 1.00000i −0.0665681 + 0.0384331i −0.532915 0.846169i $$-0.678903\pi$$
0.466347 + 0.884602i $$0.345570\pi$$
$$678$$ 18.0000i 0.691286i
$$679$$ 42.5000 14.7224i 1.63100 0.564995i
$$680$$ 0 0
$$681$$ 4.00000 + 6.92820i 0.153280 + 0.265489i
$$682$$ 0 0
$$683$$ 41.5692 + 24.0000i 1.59060 + 0.918334i 0.993204 + 0.116390i $$0.0371322\pi$$
0.597398 + 0.801945i $$0.296201\pi$$
$$684$$ 0.500000 + 0.866025i 0.0191180 + 0.0331133i
$$685$$ 0 0
$$686$$ 18.5000 + 0.866025i 0.706333 + 0.0330650i
$$687$$ 7.00000i 0.267067i
$$688$$ −6.92820 + 4.00000i −0.264135 + 0.152499i
$$689$$ 1.00000 1.73205i 0.0380970 0.0659859i
$$690$$ 0 0
$$691$$ 19.5000 + 33.7750i 0.741815 + 1.28486i 0.951668 + 0.307128i $$0.0993681\pi$$
−0.209853 + 0.977733i $$0.567299\pi$$
$$692$$ 6.00000i 0.228086i
$$693$$ −3.46410 10.0000i −0.131590 0.379869i
$$694$$ 22.0000 0.835109
$$695$$ 0 0
$$696$$ −2.00000 + 3.46410i −0.0758098 + 0.131306i
$$697$$ −20.7846 12.0000i −0.787273 0.454532i
$$698$$ −1.73205 + 1.00000i −0.0655591 + 0.0378506i
$$699$$ 4.00000 0.151294
$$700$$ 0 0
$$701$$ −18.0000 −0.679851 −0.339925 0.940452i $$-0.610402\pi$$
−0.339925 + 0.940452i $$0.610402\pi$$
$$702$$ 0.866025 0.500000i 0.0326860 0.0188713i
$$703$$ 2.59808 + 1.50000i 0.0979883 + 0.0565736i
$$704$$ −2.00000 + 3.46410i −0.0753778 + 0.130558i
$$705$$ 0 0
$$706$$ −20.0000 −0.752710
$$707$$ 31.1769 + 6.00000i 1.17253 + 0.225653i
$$708$$ 6.00000i 0.225494i
$$709$$ −5.50000 9.52628i −0.206557 0.357767i 0.744071 0.668101i $$-0.232892\pi$$
−0.950628 + 0.310334i $$0.899559\pi$$
$$710$$ 0 0
$$711$$ −6.50000 + 11.2583i −0.243769 + 0.422220i
$$712$$ −1.73205 + 1.00000i −0.0649113 + 0.0374766i
$$713$$ 0 0
$$714$$ −1.00000 + 5.19615i −0.0374241 + 0.194461i
$$715$$ 0 0
$$716$$ 4.00000 + 6.92820i 0.149487 + 0.258919i
$$717$$ 10.3923 + 6.00000i 0.388108 + 0.224074i
$$718$$ −5.19615 3.00000i −0.193919 0.111959i
$$719$$ 4.00000 + 6.92820i 0.149175 + 0.258378i 0.930923 0.365216i $$-0.119005\pi$$
−0.781748 + 0.623595i $$0.785672\pi$$
$$720$$ 0 0
$$721$$ 14.0000 + 12.1244i 0.521387 + 0.451535i
$$722$$ 18.0000i 0.669891i
$$723$$ −11.2583 + 6.50000i −0.418702 + 0.241738i
$$724$$ −9.00000 + 15.5885i −0.334482 + 0.579340i
$$725$$ 0 0
$$726$$ −2.50000 4.33013i −0.0927837 0.160706i
$$727$$ 1.00000i 0.0370879i −0.999828 0.0185440i $$-0.994097\pi$$
0.999828 0.0185440i $$-0.00590307\pi$$
$$728$$ 0.866025 + 2.50000i 0.0320970 + 0.0926562i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ −8.00000 + 13.8564i −0.295891 + 0.512498i
$$732$$ 11.2583 + 6.50000i 0.416120 + 0.240247i
$$733$$ 30.3109 17.5000i 1.11956 0.646377i 0.178270 0.983982i $$-0.442950\pi$$
0.941288 + 0.337604i $$0.109617\pi$$
$$734$$ 8.00000 0.295285
$$735$$ 0 0
$$736$$ −2.00000 −0.0737210
$$737$$ −10.3923 + 6.00000i −0.382805 + 0.221013i
$$738$$ 10.3923 + 6.00000i 0.382546 + 0.220863i
$$739$$ −0.500000 + 0.866025i −0.0183928 + 0.0318573i −0.875075 0.483987i $$-0.839188\pi$$
0.856683 + 0.515844i $$0.172522\pi$$
$$740$$ 0 0
$$741$$ 1.00000 0.0367359
$$742$$ −1.73205 5.00000i −0.0635856 0.183556i
$$743$$ 6.00000i 0.220119i 0.993925 + 0.110059i $$0.0351041\pi$$
−0.993925 + 0.110059i $$0.964896\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −11.5000 + 19.9186i −0.421045 + 0.729271i
$$747$$ −5.19615 + 3.00000i −0.190117 + 0.109764i
$$748$$ 8.00000i 0.292509i
$$749$$ −12.0000 10.3923i −0.438470 0.379727i
$$750$$ 0 0
$$751$$ −9.50000 16.4545i −0.346660 0.600433i 0.638994 0.769212i $$-0.279351\pi$$
−0.985654 + 0.168779i $$0.946018\pi$$
$$752$$ 5.19615 + 3.00000i 0.189484 + 0.109399i
$$753$$ 20.7846 + 12.0000i 0.757433 + 0.437304i
$$754$$ 2.00000 + 3.46410i 0.0728357 + 0.126155i
$$755$$ 0 0
$$756$$ 0.500000 2.59808i 0.0181848 0.0944911i
$$757$$ 1.00000i 0.0363456i 0.999835 + 0.0181728i $$0.00578490\pi$$
−0.999835 + 0.0181728i $$0.994215\pi$$
$$758$$ 4.33013 2.50000i 0.157277 0.0908041i
$$759$$ 4.00000 6.92820i 0.145191 0.251478i
$$760$$ 0 0
$$761$$ −17.0000 29.4449i −0.616250 1.06738i −0.990164 0.139912i $$-0.955318\pi$$
0.373914 0.927463i $$-0.378015\pi$$
$$762$$ 1.00000i 0.0362262i
$$763$$ 49.3634 + 9.50000i 1.78708 + 0.343923i
$$764$$ −20.0000 −0.723575
$$765$$ 0 0
$$766$$ 7.00000 12.1244i 0.252920 0.438071i
$$767$$ −5.19615 3.00000i −0.187622 0.108324i
$$768$$ −0.866025 + 0.500000i −0.0312500 + 0.0180422i
$$769$$ 50.0000 1.80305 0.901523 0.432731i $$-0.142450\pi$$
0.901523 + 0.432731i $$0.142450\pi$$
$$770$$ 0 0
$$771$$ −8.00000 −0.288113
$$772$$ −8.66025 + 5.00000i −0.311689 + 0.179954i
$$773$$ −27.7128 16.0000i −0.996761 0.575480i −0.0894724 0.995989i $$-0.528518\pi$$
−0.907288 + 0.420509i $$0.861851\pi$$
$$774$$ 4.00000 6.92820i 0.143777 0.249029i
$$775$$ 0 0
$$776$$ 17.0000 0.610264
$$777$$ −2.59808 7.50000i −0.0932055 0.269061i
$$778$$ 20.0000i 0.717035i
$$779$$ 6.00000 + 10.3923i 0.214972 + 0.372343i
$$780$$ 0 0
$$781$$ 32.0000 55.4256i 1.14505 1.98328i
$$782$$ −3.46410 + 2.00000i −0.123876 + 0.0715199i
$$783$$ 4.00000i 0.142948i
$$784$$ 6.50000 + 2.59808i 0.232143 + 0.0927884i