# Properties

 Label 1950.2.z.j.1849.1 Level $1950$ Weight $2$ Character 1950.1849 Analytic conductor $15.571$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1950.z (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$15.5708283941$$ 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: no (minimal twist has level 390) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 1849.1 Root $$0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1950.1849 Dual form 1950.2.z.j.1699.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(4.33013 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(4.33013 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +1.00000i q^{12} +(-2.59808 + 2.50000i) q^{13} -5.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(6.92820 + 4.00000i) q^{17} +1.00000i q^{18} +(-2.50000 + 4.33013i) q^{19} -5.00000 q^{21} +(-2.59808 - 1.50000i) q^{22} +(3.46410 - 2.00000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.00000 - 3.46410i) q^{26} +1.00000i q^{27} +(4.33013 - 2.50000i) q^{28} +(-2.00000 - 3.46410i) q^{29} -2.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.59808 - 1.50000i) q^{33} -8.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-6.06218 + 3.50000i) q^{37} -5.00000i q^{38} +(1.00000 - 3.46410i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(4.33013 - 2.50000i) q^{42} +(5.19615 + 3.00000i) q^{43} +3.00000 q^{44} +(-2.00000 + 3.46410i) q^{46} -3.00000i q^{47} +(0.866025 + 0.500000i) q^{48} +(9.00000 + 15.5885i) q^{49} -8.00000 q^{51} +(0.866025 + 3.50000i) q^{52} -1.00000i q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.50000 + 4.33013i) q^{56} -5.00000i q^{57} +(3.46410 + 2.00000i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(1.73205 - 1.00000i) q^{62} +(4.33013 - 2.50000i) q^{63} -1.00000 q^{64} +3.00000 q^{66} +(6.92820 - 4.00000i) q^{67} +(6.92820 - 4.00000i) q^{68} +(-2.00000 + 3.46410i) q^{69} +(-1.00000 + 1.73205i) q^{71} +(0.866025 + 0.500000i) q^{72} +(3.50000 - 6.06218i) q^{74} +(2.50000 + 4.33013i) q^{76} +15.0000i q^{77} +(0.866025 + 3.50000i) q^{78} +2.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.19615 + 3.00000i) q^{82} -8.00000i q^{83} +(-2.50000 + 4.33013i) q^{84} -6.00000 q^{86} +(3.46410 + 2.00000i) q^{87} +(-2.59808 + 1.50000i) q^{88} +(-5.50000 - 9.52628i) q^{89} +(-17.5000 + 4.33013i) q^{91} -4.00000i q^{92} +(1.73205 - 1.00000i) q^{93} +(1.50000 + 2.59808i) q^{94} -1.00000 q^{96} +(-15.5885 - 9.00000i) q^{98} +3.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{4} + 2q^{6} + 2q^{9} + O(q^{10})$$ $$4q + 2q^{4} + 2q^{6} + 2q^{9} + 6q^{11} - 20q^{14} - 2q^{16} - 10q^{19} - 20q^{21} - 2q^{24} + 4q^{26} - 8q^{29} - 8q^{31} - 32q^{34} - 2q^{36} + 4q^{39} - 12q^{41} + 12q^{44} - 8q^{46} + 36q^{49} - 32q^{51} - 2q^{54} - 10q^{56} + 24q^{59} - 4q^{61} - 4q^{64} + 12q^{66} - 8q^{69} - 4q^{71} + 14q^{74} + 10q^{76} + 8q^{79} - 2q^{81} - 10q^{84} - 24q^{86} - 22q^{89} - 70q^{91} + 6q^{94} - 4q^{96} + 12q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$$.

 $$n$$ $$301$$ $$1301$$ $$1327$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 + 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
$$6$$ 0.500000 0.866025i 0.204124 0.353553i
$$7$$ 4.33013 + 2.50000i 1.63663 + 0.944911i 0.981981 + 0.188982i $$0.0605189\pi$$
0.654654 + 0.755929i $$0.272814\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 0.500000 0.866025i 0.166667 0.288675i
$$10$$ 0 0
$$11$$ 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i $$-0.0172821\pi$$
−0.546259 + 0.837616i $$0.683949\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ −2.59808 + 2.50000i −0.720577 + 0.693375i
$$14$$ −5.00000 −1.33631
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 6.92820 + 4.00000i 1.68034 + 0.970143i 0.961436 + 0.275029i $$0.0886875\pi$$
0.718900 + 0.695113i $$0.244646\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i $$0.361097\pi$$
−0.996199 + 0.0871106i $$0.972237\pi$$
$$20$$ 0 0
$$21$$ −5.00000 −1.09109
$$22$$ −2.59808 1.50000i −0.553912 0.319801i
$$23$$ 3.46410 2.00000i 0.722315 0.417029i −0.0932891 0.995639i $$-0.529738\pi$$
0.815604 + 0.578610i $$0.196405\pi$$
$$24$$ −0.500000 0.866025i −0.102062 0.176777i
$$25$$ 0 0
$$26$$ 1.00000 3.46410i 0.196116 0.679366i
$$27$$ 1.00000i 0.192450i
$$28$$ 4.33013 2.50000i 0.818317 0.472456i
$$29$$ −2.00000 3.46410i −0.371391 0.643268i 0.618389 0.785872i $$-0.287786\pi$$
−0.989780 + 0.142605i $$0.954452\pi$$
$$30$$ 0 0
$$31$$ −2.00000 −0.359211 −0.179605 0.983739i $$-0.557482\pi$$
−0.179605 + 0.983739i $$0.557482\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ −2.59808 1.50000i −0.452267 0.261116i
$$34$$ −8.00000 −1.37199
$$35$$ 0 0
$$36$$ −0.500000 0.866025i −0.0833333 0.144338i
$$37$$ −6.06218 + 3.50000i −0.996616 + 0.575396i −0.907245 0.420602i $$-0.861819\pi$$
−0.0893706 + 0.995998i $$0.528486\pi$$
$$38$$ 5.00000i 0.811107i
$$39$$ 1.00000 3.46410i 0.160128 0.554700i
$$40$$ 0 0
$$41$$ −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i $$-0.321880\pi$$
−0.999353 + 0.0359748i $$0.988546\pi$$
$$42$$ 4.33013 2.50000i 0.668153 0.385758i
$$43$$ 5.19615 + 3.00000i 0.792406 + 0.457496i 0.840809 0.541332i $$-0.182080\pi$$
−0.0484030 + 0.998828i $$0.515413\pi$$
$$44$$ 3.00000 0.452267
$$45$$ 0 0
$$46$$ −2.00000 + 3.46410i −0.294884 + 0.510754i
$$47$$ 3.00000i 0.437595i −0.975770 0.218797i $$-0.929787\pi$$
0.975770 0.218797i $$-0.0702134\pi$$
$$48$$ 0.866025 + 0.500000i 0.125000 + 0.0721688i
$$49$$ 9.00000 + 15.5885i 1.28571 + 2.22692i
$$50$$ 0 0
$$51$$ −8.00000 −1.12022
$$52$$ 0.866025 + 3.50000i 0.120096 + 0.485363i
$$53$$ 1.00000i 0.137361i −0.997639 0.0686803i $$-0.978121\pi$$
0.997639 0.0686803i $$-0.0218788\pi$$
$$54$$ −0.500000 0.866025i −0.0680414 0.117851i
$$55$$ 0 0
$$56$$ −2.50000 + 4.33013i −0.334077 + 0.578638i
$$57$$ 5.00000i 0.662266i
$$58$$ 3.46410 + 2.00000i 0.454859 + 0.262613i
$$59$$ 6.00000 10.3923i 0.781133 1.35296i −0.150148 0.988663i $$-0.547975\pi$$
0.931282 0.364299i $$-0.118692\pi$$
$$60$$ 0 0
$$61$$ −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i $$-0.874201\pi$$
0.794879 + 0.606768i $$0.207534\pi$$
$$62$$ 1.73205 1.00000i 0.219971 0.127000i
$$63$$ 4.33013 2.50000i 0.545545 0.314970i
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ 3.00000 0.369274
$$67$$ 6.92820 4.00000i 0.846415 0.488678i −0.0130248 0.999915i $$-0.504146\pi$$
0.859440 + 0.511237i $$0.170813\pi$$
$$68$$ 6.92820 4.00000i 0.840168 0.485071i
$$69$$ −2.00000 + 3.46410i −0.240772 + 0.417029i
$$70$$ 0 0
$$71$$ −1.00000 + 1.73205i −0.118678 + 0.205557i −0.919244 0.393688i $$-0.871199\pi$$
0.800566 + 0.599245i $$0.204532\pi$$
$$72$$ 0.866025 + 0.500000i 0.102062 + 0.0589256i
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 3.50000 6.06218i 0.406867 0.704714i
$$75$$ 0 0
$$76$$ 2.50000 + 4.33013i 0.286770 + 0.496700i
$$77$$ 15.0000i 1.70941i
$$78$$ 0.866025 + 3.50000i 0.0980581 + 0.396297i
$$79$$ 2.00000 0.225018 0.112509 0.993651i $$-0.464111\pi$$
0.112509 + 0.993651i $$0.464111\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 5.19615 + 3.00000i 0.573819 + 0.331295i
$$83$$ 8.00000i 0.878114i −0.898459 0.439057i $$-0.855313\pi$$
0.898459 0.439057i $$-0.144687\pi$$
$$84$$ −2.50000 + 4.33013i −0.272772 + 0.472456i
$$85$$ 0 0
$$86$$ −6.00000 −0.646997
$$87$$ 3.46410 + 2.00000i 0.371391 + 0.214423i
$$88$$ −2.59808 + 1.50000i −0.276956 + 0.159901i
$$89$$ −5.50000 9.52628i −0.582999 1.00978i −0.995122 0.0986553i $$-0.968546\pi$$
0.412123 0.911128i $$-0.364787\pi$$
$$90$$ 0 0
$$91$$ −17.5000 + 4.33013i −1.83450 + 0.453921i
$$92$$ 4.00000i 0.417029i
$$93$$ 1.73205 1.00000i 0.179605 0.103695i
$$94$$ 1.50000 + 2.59808i 0.154713 + 0.267971i
$$95$$ 0 0
$$96$$ −1.00000 −0.102062
$$97$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$98$$ −15.5885 9.00000i −1.57467 0.909137i
$$99$$ 3.00000 0.301511
$$100$$ 0 0
$$101$$ 4.00000 + 6.92820i 0.398015 + 0.689382i 0.993481 0.113998i $$-0.0363659\pi$$
−0.595466 + 0.803380i $$0.703033\pi$$
$$102$$ 6.92820 4.00000i 0.685994 0.396059i
$$103$$ 7.00000i 0.689730i 0.938652 + 0.344865i $$0.112075\pi$$
−0.938652 + 0.344865i $$0.887925\pi$$
$$104$$ −2.50000 2.59808i −0.245145 0.254762i
$$105$$ 0 0
$$106$$ 0.500000 + 0.866025i 0.0485643 + 0.0841158i
$$107$$ −5.19615 + 3.00000i −0.502331 + 0.290021i −0.729676 0.683793i $$-0.760329\pi$$
0.227345 + 0.973814i $$0.426996\pi$$
$$108$$ 0.866025 + 0.500000i 0.0833333 + 0.0481125i
$$109$$ −14.0000 −1.34096 −0.670478 0.741929i $$-0.733911\pi$$
−0.670478 + 0.741929i $$0.733911\pi$$
$$110$$ 0 0
$$111$$ 3.50000 6.06218i 0.332205 0.575396i
$$112$$ 5.00000i 0.472456i
$$113$$ 6.92820 + 4.00000i 0.651751 + 0.376288i 0.789127 0.614231i $$-0.210534\pi$$
−0.137376 + 0.990519i $$0.543867\pi$$
$$114$$ 2.50000 + 4.33013i 0.234146 + 0.405554i
$$115$$ 0 0
$$116$$ −4.00000 −0.371391
$$117$$ 0.866025 + 3.50000i 0.0800641 + 0.323575i
$$118$$ 12.0000i 1.10469i
$$119$$ 20.0000 + 34.6410i 1.83340 + 3.17554i
$$120$$ 0 0
$$121$$ 1.00000 1.73205i 0.0909091 0.157459i
$$122$$ 2.00000i 0.181071i
$$123$$ 5.19615 + 3.00000i 0.468521 + 0.270501i
$$124$$ −1.00000 + 1.73205i −0.0898027 + 0.155543i
$$125$$ 0 0
$$126$$ −2.50000 + 4.33013i −0.222718 + 0.385758i
$$127$$ −18.1865 + 10.5000i −1.61379 + 0.931724i −0.625314 + 0.780373i $$0.715029\pi$$
−0.988480 + 0.151351i $$0.951638\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ −6.00000 −0.528271
$$130$$ 0 0
$$131$$ −19.0000 −1.66004 −0.830019 0.557735i $$-0.811670\pi$$
−0.830019 + 0.557735i $$0.811670\pi$$
$$132$$ −2.59808 + 1.50000i −0.226134 + 0.130558i
$$133$$ −21.6506 + 12.5000i −1.87735 + 1.08389i
$$134$$ −4.00000 + 6.92820i −0.345547 + 0.598506i
$$135$$ 0 0
$$136$$ −4.00000 + 6.92820i −0.342997 + 0.594089i
$$137$$ 10.3923 + 6.00000i 0.887875 + 0.512615i 0.873247 0.487278i $$-0.162010\pi$$
0.0146279 + 0.999893i $$0.495344\pi$$
$$138$$ 4.00000i 0.340503i
$$139$$ 3.50000 6.06218i 0.296866 0.514187i −0.678551 0.734553i $$-0.737392\pi$$
0.975417 + 0.220366i $$0.0707252\pi$$
$$140$$ 0 0
$$141$$ 1.50000 + 2.59808i 0.126323 + 0.218797i
$$142$$ 2.00000i 0.167836i
$$143$$ −10.3923 3.00000i −0.869048 0.250873i
$$144$$ −1.00000 −0.0833333
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −15.5885 9.00000i −1.28571 0.742307i
$$148$$ 7.00000i 0.575396i
$$149$$ −1.00000 + 1.73205i −0.0819232 + 0.141895i −0.904076 0.427372i $$-0.859440\pi$$
0.822153 + 0.569267i $$0.192773\pi$$
$$150$$ 0 0
$$151$$ 22.0000 1.79033 0.895167 0.445730i $$-0.147056\pi$$
0.895167 + 0.445730i $$0.147056\pi$$
$$152$$ −4.33013 2.50000i −0.351220 0.202777i
$$153$$ 6.92820 4.00000i 0.560112 0.323381i
$$154$$ −7.50000 12.9904i −0.604367 1.04679i
$$155$$ 0 0
$$156$$ −2.50000 2.59808i −0.200160 0.208013i
$$157$$ 15.0000i 1.19713i 0.801074 + 0.598565i $$0.204262\pi$$
−0.801074 + 0.598565i $$0.795738\pi$$
$$158$$ −1.73205 + 1.00000i −0.137795 + 0.0795557i
$$159$$ 0.500000 + 0.866025i 0.0396526 + 0.0686803i
$$160$$ 0 0
$$161$$ 20.0000 1.57622
$$162$$ 0.866025 + 0.500000i 0.0680414 + 0.0392837i
$$163$$ −17.3205 10.0000i −1.35665 0.783260i −0.367477 0.930033i $$-0.619778\pi$$
−0.989170 + 0.146772i $$0.953112\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ 4.00000 + 6.92820i 0.310460 + 0.537733i
$$167$$ −19.9186 + 11.5000i −1.54135 + 0.889897i −0.542592 + 0.839996i $$0.682557\pi$$
−0.998754 + 0.0499004i $$0.984110\pi$$
$$168$$ 5.00000i 0.385758i
$$169$$ 0.500000 12.9904i 0.0384615 0.999260i
$$170$$ 0 0
$$171$$ 2.50000 + 4.33013i 0.191180 + 0.331133i
$$172$$ 5.19615 3.00000i 0.396203 0.228748i
$$173$$ 4.33013 + 2.50000i 0.329213 + 0.190071i 0.655492 0.755202i $$-0.272461\pi$$
−0.326278 + 0.945274i $$0.605795\pi$$
$$174$$ −4.00000 −0.303239
$$175$$ 0 0
$$176$$ 1.50000 2.59808i 0.113067 0.195837i
$$177$$ 12.0000i 0.901975i
$$178$$ 9.52628 + 5.50000i 0.714025 + 0.412242i
$$179$$ 2.00000 + 3.46410i 0.149487 + 0.258919i 0.931038 0.364922i $$-0.118904\pi$$
−0.781551 + 0.623841i $$0.785571\pi$$
$$180$$ 0 0
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 12.9904 12.5000i 0.962911 0.926562i
$$183$$ 2.00000i 0.147844i
$$184$$ 2.00000 + 3.46410i 0.147442 + 0.255377i
$$185$$ 0 0
$$186$$ −1.00000 + 1.73205i −0.0733236 + 0.127000i
$$187$$ 24.0000i 1.75505i
$$188$$ −2.59808 1.50000i −0.189484 0.109399i
$$189$$ −2.50000 + 4.33013i −0.181848 + 0.314970i
$$190$$ 0 0
$$191$$ −1.00000 + 1.73205i −0.0723575 + 0.125327i −0.899934 0.436026i $$-0.856386\pi$$
0.827577 + 0.561353i $$0.189719\pi$$
$$192$$ 0.866025 0.500000i 0.0625000 0.0360844i
$$193$$ −20.7846 + 12.0000i −1.49611 + 0.863779i −0.999990 0.00447566i $$-0.998575\pi$$
−0.496119 + 0.868255i $$0.665242\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 18.0000 1.28571
$$197$$ 2.59808 1.50000i 0.185105 0.106871i −0.404584 0.914501i $$-0.632584\pi$$
0.589689 + 0.807630i $$0.299250\pi$$
$$198$$ −2.59808 + 1.50000i −0.184637 + 0.106600i
$$199$$ 11.0000 19.0526i 0.779769 1.35060i −0.152305 0.988334i $$-0.548670\pi$$
0.932075 0.362267i $$-0.117997\pi$$
$$200$$ 0 0
$$201$$ −4.00000 + 6.92820i −0.282138 + 0.488678i
$$202$$ −6.92820 4.00000i −0.487467 0.281439i
$$203$$ 20.0000i 1.40372i
$$204$$ −4.00000 + 6.92820i −0.280056 + 0.485071i
$$205$$ 0 0
$$206$$ −3.50000 6.06218i −0.243857 0.422372i
$$207$$ 4.00000i 0.278019i
$$208$$ 3.46410 + 1.00000i 0.240192 + 0.0693375i
$$209$$ −15.0000 −1.03757
$$210$$ 0 0
$$211$$ 7.50000 + 12.9904i 0.516321 + 0.894295i 0.999820 + 0.0189499i $$0.00603229\pi$$
−0.483499 + 0.875345i $$0.660634\pi$$
$$212$$ −0.866025 0.500000i −0.0594789 0.0343401i
$$213$$ 2.00000i 0.137038i
$$214$$ 3.00000 5.19615i 0.205076 0.355202i
$$215$$ 0 0
$$216$$ −1.00000 −0.0680414
$$217$$ −8.66025 5.00000i −0.587896 0.339422i
$$218$$ 12.1244 7.00000i 0.821165 0.474100i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −28.0000 + 6.92820i −1.88348 + 0.466041i
$$222$$ 7.00000i 0.469809i
$$223$$ 2.59808 1.50000i 0.173980 0.100447i −0.410481 0.911869i $$-0.634639\pi$$
0.584461 + 0.811422i $$0.301306\pi$$
$$224$$ 2.50000 + 4.33013i 0.167038 + 0.289319i
$$225$$ 0 0
$$226$$ −8.00000 −0.532152
$$227$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$228$$ −4.33013 2.50000i −0.286770 0.165567i
$$229$$ −14.0000 −0.925146 −0.462573 0.886581i $$-0.653074\pi$$
−0.462573 + 0.886581i $$0.653074\pi$$
$$230$$ 0 0
$$231$$ −7.50000 12.9904i −0.493464 0.854704i
$$232$$ 3.46410 2.00000i 0.227429 0.131306i
$$233$$ 14.0000i 0.917170i 0.888650 + 0.458585i $$0.151644\pi$$
−0.888650 + 0.458585i $$0.848356\pi$$
$$234$$ −2.50000 2.59808i −0.163430 0.169842i
$$235$$ 0 0
$$236$$ −6.00000 10.3923i −0.390567 0.676481i
$$237$$ −1.73205 + 1.00000i −0.112509 + 0.0649570i
$$238$$ −34.6410 20.0000i −2.24544 1.29641i
$$239$$ 18.0000 1.16432 0.582162 0.813073i $$-0.302207\pi$$
0.582162 + 0.813073i $$0.302207\pi$$
$$240$$ 0 0
$$241$$ 12.5000 21.6506i 0.805196 1.39464i −0.110963 0.993825i $$-0.535394\pi$$
0.916159 0.400815i $$-0.131273\pi$$
$$242$$ 2.00000i 0.128565i
$$243$$ 0.866025 + 0.500000i 0.0555556 + 0.0320750i
$$244$$ 1.00000 + 1.73205i 0.0640184 + 0.110883i
$$245$$ 0 0
$$246$$ −6.00000 −0.382546
$$247$$ −4.33013 17.5000i −0.275519 1.11350i
$$248$$ 2.00000i 0.127000i
$$249$$ 4.00000 + 6.92820i 0.253490 + 0.439057i
$$250$$ 0 0
$$251$$ −7.50000 + 12.9904i −0.473396 + 0.819946i −0.999536 0.0304521i $$-0.990305\pi$$
0.526140 + 0.850398i $$0.323639\pi$$
$$252$$ 5.00000i 0.314970i
$$253$$ 10.3923 + 6.00000i 0.653359 + 0.377217i
$$254$$ 10.5000 18.1865i 0.658829 1.14112i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ 24.2487 14.0000i 1.51259 0.873296i 0.512702 0.858567i $$-0.328645\pi$$
0.999892 0.0147291i $$-0.00468859\pi$$
$$258$$ 5.19615 3.00000i 0.323498 0.186772i
$$259$$ −35.0000 −2.17479
$$260$$ 0 0
$$261$$ −4.00000 −0.247594
$$262$$ 16.4545 9.50000i 1.01656 0.586912i
$$263$$ 12.9904 7.50000i 0.801021 0.462470i −0.0428069 0.999083i $$-0.513630\pi$$
0.843828 + 0.536614i $$0.180297\pi$$
$$264$$ 1.50000 2.59808i 0.0923186 0.159901i
$$265$$ 0 0
$$266$$ 12.5000 21.6506i 0.766424 1.32749i
$$267$$ 9.52628 + 5.50000i 0.582999 + 0.336595i
$$268$$ 8.00000i 0.488678i
$$269$$ 2.00000 3.46410i 0.121942 0.211210i −0.798591 0.601874i $$-0.794421\pi$$
0.920534 + 0.390664i $$0.127754\pi$$
$$270$$ 0 0
$$271$$ −2.00000 3.46410i −0.121491 0.210429i 0.798865 0.601511i $$-0.205434\pi$$
−0.920356 + 0.391082i $$0.872101\pi$$
$$272$$ 8.00000i 0.485071i
$$273$$ 12.9904 12.5000i 0.786214 0.756534i
$$274$$ −12.0000 −0.724947
$$275$$ 0 0
$$276$$ 2.00000 + 3.46410i 0.120386 + 0.208514i
$$277$$ 12.9904 + 7.50000i 0.780516 + 0.450631i 0.836613 0.547794i $$-0.184532\pi$$
−0.0560969 + 0.998425i $$0.517866\pi$$
$$278$$ 7.00000i 0.419832i
$$279$$ −1.00000 + 1.73205i −0.0598684 + 0.103695i
$$280$$ 0 0
$$281$$ 18.0000 1.07379 0.536895 0.843649i $$-0.319597\pi$$
0.536895 + 0.843649i $$0.319597\pi$$
$$282$$ −2.59808 1.50000i −0.154713 0.0893237i
$$283$$ 8.66025 5.00000i 0.514799 0.297219i −0.220005 0.975499i $$-0.570607\pi$$
0.734804 + 0.678280i $$0.237274\pi$$
$$284$$ 1.00000 + 1.73205i 0.0593391 + 0.102778i
$$285$$ 0 0
$$286$$ 10.5000 2.59808i 0.620878 0.153627i
$$287$$ 30.0000i 1.77084i
$$288$$ 0.866025 0.500000i 0.0510310 0.0294628i
$$289$$ 23.5000 + 40.7032i 1.38235 + 2.39431i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −7.79423 4.50000i −0.455344 0.262893i 0.254741 0.967009i $$-0.418010\pi$$
−0.710084 + 0.704117i $$0.751343\pi$$
$$294$$ 18.0000 1.04978
$$295$$ 0 0
$$296$$ −3.50000 6.06218i −0.203433 0.352357i
$$297$$ −2.59808 + 1.50000i −0.150756 + 0.0870388i
$$298$$ 2.00000i 0.115857i
$$299$$ −4.00000 + 13.8564i −0.231326 + 0.801337i
$$300$$ 0 0
$$301$$ 15.0000 + 25.9808i 0.864586 + 1.49751i
$$302$$ −19.0526 + 11.0000i −1.09635 + 0.632979i
$$303$$ −6.92820 4.00000i −0.398015 0.229794i
$$304$$ 5.00000 0.286770
$$305$$ 0 0
$$306$$ −4.00000 + 6.92820i −0.228665 + 0.396059i
$$307$$ 6.00000i 0.342438i −0.985233 0.171219i $$-0.945229\pi$$
0.985233 0.171219i $$-0.0547706\pi$$
$$308$$ 12.9904 + 7.50000i 0.740196 + 0.427352i
$$309$$ −3.50000 6.06218i −0.199108 0.344865i
$$310$$ 0 0
$$311$$ −12.0000 −0.680458 −0.340229 0.940343i $$-0.610505\pi$$
−0.340229 + 0.940343i $$0.610505\pi$$
$$312$$ 3.46410 + 1.00000i 0.196116 + 0.0566139i
$$313$$ 6.00000i 0.339140i 0.985518 + 0.169570i $$0.0542379\pi$$
−0.985518 + 0.169570i $$0.945762\pi$$
$$314$$ −7.50000 12.9904i −0.423249 0.733090i
$$315$$ 0 0
$$316$$ 1.00000 1.73205i 0.0562544 0.0974355i
$$317$$ 23.0000i 1.29181i −0.763418 0.645904i $$-0.776480\pi$$
0.763418 0.645904i $$-0.223520\pi$$
$$318$$ −0.866025 0.500000i −0.0485643 0.0280386i
$$319$$ 6.00000 10.3923i 0.335936 0.581857i
$$320$$ 0 0
$$321$$ 3.00000 5.19615i 0.167444 0.290021i
$$322$$ −17.3205 + 10.0000i −0.965234 + 0.557278i
$$323$$ −34.6410 + 20.0000i −1.92748 + 1.11283i
$$324$$ −1.00000 −0.0555556
$$325$$ 0 0
$$326$$ 20.0000 1.10770
$$327$$ 12.1244 7.00000i 0.670478 0.387101i
$$328$$ 5.19615 3.00000i 0.286910 0.165647i
$$329$$ 7.50000 12.9904i 0.413488 0.716183i
$$330$$ 0 0
$$331$$ −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i $$-0.868396\pi$$
0.805812 + 0.592172i $$0.201729\pi$$
$$332$$ −6.92820 4.00000i −0.380235 0.219529i
$$333$$ 7.00000i 0.383598i
$$334$$ 11.5000 19.9186i 0.629252 1.08990i
$$335$$ 0 0
$$336$$ 2.50000 + 4.33013i 0.136386 + 0.236228i
$$337$$ 14.0000i 0.762629i 0.924445 + 0.381314i $$0.124528\pi$$
−0.924445 + 0.381314i $$0.875472\pi$$
$$338$$ 6.06218 + 11.5000i 0.329739 + 0.625518i
$$339$$ −8.00000 −0.434500
$$340$$ 0 0
$$341$$ −3.00000 5.19615i −0.162459 0.281387i
$$342$$ −4.33013 2.50000i −0.234146 0.135185i
$$343$$ 55.0000i 2.96972i
$$344$$ −3.00000 + 5.19615i −0.161749 + 0.280158i
$$345$$ 0 0
$$346$$ −5.00000 −0.268802
$$347$$ 13.8564 + 8.00000i 0.743851 + 0.429463i 0.823468 0.567363i $$-0.192036\pi$$
−0.0796169 + 0.996826i $$0.525370\pi$$
$$348$$ 3.46410 2.00000i 0.185695 0.107211i
$$349$$ 4.00000 + 6.92820i 0.214115 + 0.370858i 0.952998 0.302975i $$-0.0979799\pi$$
−0.738883 + 0.673833i $$0.764647\pi$$
$$350$$ 0 0
$$351$$ −2.50000 2.59808i −0.133440 0.138675i
$$352$$ 3.00000i 0.159901i
$$353$$ −13.8564 + 8.00000i −0.737502 + 0.425797i −0.821160 0.570697i $$-0.806673\pi$$
0.0836583 + 0.996495i $$0.473340\pi$$
$$354$$ −6.00000 10.3923i −0.318896 0.552345i
$$355$$ 0 0
$$356$$ −11.0000 −0.582999
$$357$$ −34.6410 20.0000i −1.83340 1.05851i
$$358$$ −3.46410 2.00000i −0.183083 0.105703i
$$359$$ 18.0000 0.950004 0.475002 0.879985i $$-0.342447\pi$$
0.475002 + 0.879985i $$0.342447\pi$$
$$360$$ 0 0
$$361$$ −3.00000 5.19615i −0.157895 0.273482i
$$362$$ 1.73205 1.00000i 0.0910346 0.0525588i
$$363$$ 2.00000i 0.104973i
$$364$$ −5.00000 + 17.3205i −0.262071 + 0.907841i
$$365$$ 0 0
$$366$$ 1.00000 + 1.73205i 0.0522708 + 0.0905357i
$$367$$ −6.92820 + 4.00000i −0.361649 + 0.208798i −0.669804 0.742538i $$-0.733622\pi$$
0.308155 + 0.951336i $$0.400289\pi$$
$$368$$ −3.46410 2.00000i −0.180579 0.104257i
$$369$$ −6.00000 −0.312348
$$370$$ 0 0
$$371$$ 2.50000 4.33013i 0.129794 0.224809i
$$372$$ 2.00000i 0.103695i
$$373$$ 32.9090 + 19.0000i 1.70396 + 0.983783i 0.941663 + 0.336557i $$0.109263\pi$$
0.762299 + 0.647225i $$0.224071\pi$$
$$374$$ −12.0000 20.7846i −0.620505 1.07475i
$$375$$ 0 0
$$376$$ 3.00000 0.154713
$$377$$ 13.8564 + 4.00000i 0.713641 + 0.206010i
$$378$$ 5.00000i 0.257172i
$$379$$ −12.5000 21.6506i −0.642082 1.11212i −0.984967 0.172741i $$-0.944738\pi$$
0.342885 0.939377i $$-0.388596\pi$$
$$380$$ 0 0
$$381$$ 10.5000 18.1865i 0.537931 0.931724i
$$382$$ 2.00000i 0.102329i
$$383$$ −24.2487 14.0000i −1.23905 0.715367i −0.270151 0.962818i $$-0.587074\pi$$
−0.968900 + 0.247451i $$0.920407\pi$$
$$384$$ −0.500000 + 0.866025i −0.0255155 + 0.0441942i
$$385$$ 0 0
$$386$$ 12.0000 20.7846i 0.610784 1.05791i
$$387$$ 5.19615 3.00000i 0.264135 0.152499i
$$388$$ 0 0
$$389$$ 32.0000 1.62246 0.811232 0.584724i $$-0.198797\pi$$
0.811232 + 0.584724i $$0.198797\pi$$
$$390$$ 0 0
$$391$$ 32.0000 1.61831
$$392$$ −15.5885 + 9.00000i −0.787336 + 0.454569i
$$393$$ 16.4545 9.50000i 0.830019 0.479212i
$$394$$ −1.50000 + 2.59808i −0.0755689 + 0.130889i
$$395$$ 0 0
$$396$$ 1.50000 2.59808i 0.0753778 0.130558i
$$397$$ −21.6506 12.5000i −1.08661 0.627357i −0.153941 0.988080i $$-0.549197\pi$$
−0.932673 + 0.360723i $$0.882530\pi$$
$$398$$ 22.0000i 1.10276i
$$399$$ 12.5000 21.6506i 0.625783 1.08389i
$$400$$ 0 0
$$401$$ 9.50000 + 16.4545i 0.474407 + 0.821698i 0.999571 0.0293039i $$-0.00932905\pi$$
−0.525163 + 0.851002i $$0.675996\pi$$
$$402$$ 8.00000i 0.399004i
$$403$$ 5.19615 5.00000i 0.258839 0.249068i
$$404$$ 8.00000 0.398015
$$405$$ 0 0
$$406$$ 10.0000 + 17.3205i 0.496292 + 0.859602i
$$407$$ −18.1865 10.5000i −0.901473 0.520466i
$$408$$ 8.00000i 0.396059i
$$409$$ 12.5000 21.6506i 0.618085 1.07056i −0.371750 0.928333i $$-0.621242\pi$$
0.989835 0.142222i $$-0.0454247\pi$$
$$410$$ 0 0
$$411$$ −12.0000 −0.591916
$$412$$ 6.06218 + 3.50000i 0.298662 + 0.172433i
$$413$$ 51.9615 30.0000i 2.55686 1.47620i
$$414$$ 2.00000 + 3.46410i 0.0982946 + 0.170251i
$$415$$ 0 0
$$416$$ −3.50000 + 0.866025i −0.171602 + 0.0424604i
$$417$$ 7.00000i 0.342791i
$$418$$ 12.9904 7.50000i 0.635380 0.366837i
$$419$$ −6.00000 10.3923i −0.293119 0.507697i 0.681426 0.731887i $$-0.261360\pi$$
−0.974546 + 0.224189i $$0.928027\pi$$
$$420$$ 0 0
$$421$$ 12.0000 0.584844 0.292422 0.956289i $$-0.405539\pi$$
0.292422 + 0.956289i $$0.405539\pi$$
$$422$$ −12.9904 7.50000i −0.632362 0.365094i
$$423$$ −2.59808 1.50000i −0.126323 0.0729325i
$$424$$ 1.00000 0.0485643
$$425$$ 0 0
$$426$$ 1.00000 + 1.73205i 0.0484502 + 0.0839181i
$$427$$ −8.66025 + 5.00000i −0.419099 + 0.241967i
$$428$$ 6.00000i 0.290021i
$$429$$ 10.5000 2.59808i 0.506945 0.125436i
$$430$$ 0 0
$$431$$ −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i $$-0.259993\pi$$
−0.973574 + 0.228373i $$0.926659\pi$$
$$432$$ 0.866025 0.500000i 0.0416667 0.0240563i
$$433$$ 13.8564 + 8.00000i 0.665896 + 0.384455i 0.794520 0.607238i $$-0.207723\pi$$
−0.128624 + 0.991693i $$0.541056\pi$$
$$434$$ 10.0000 0.480015
$$435$$ 0 0
$$436$$ −7.00000 + 12.1244i −0.335239 + 0.580651i
$$437$$ 20.0000i 0.956730i
$$438$$ 0 0
$$439$$ 5.00000 + 8.66025i 0.238637 + 0.413331i 0.960323 0.278889i $$-0.0899661\pi$$
−0.721686 + 0.692220i $$0.756633\pi$$
$$440$$ 0 0
$$441$$ 18.0000 0.857143
$$442$$ 20.7846 20.0000i 0.988623 0.951303i
$$443$$ 6.00000i 0.285069i −0.989790 0.142534i $$-0.954475\pi$$
0.989790 0.142534i $$-0.0455251\pi$$
$$444$$ −3.50000 6.06218i −0.166103 0.287698i
$$445$$ 0 0
$$446$$ −1.50000 + 2.59808i −0.0710271 + 0.123022i
$$447$$ 2.00000i 0.0945968i
$$448$$ −4.33013 2.50000i −0.204579 0.118114i
$$449$$ −13.5000 + 23.3827i −0.637104 + 1.10350i 0.348961 + 0.937137i $$0.386535\pi$$
−0.986065 + 0.166360i $$0.946799\pi$$
$$450$$ 0 0
$$451$$ 9.00000 15.5885i 0.423793 0.734032i
$$452$$ 6.92820 4.00000i 0.325875 0.188144i
$$453$$ −19.0526 + 11.0000i −0.895167 + 0.516825i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 5.00000 0.234146
$$457$$ 25.9808 15.0000i 1.21533 0.701670i 0.251414 0.967880i $$-0.419105\pi$$
0.963915 + 0.266209i $$0.0857713\pi$$
$$458$$ 12.1244 7.00000i 0.566534 0.327089i
$$459$$ −4.00000 + 6.92820i −0.186704 + 0.323381i
$$460$$ 0 0
$$461$$ −4.00000 + 6.92820i −0.186299 + 0.322679i −0.944013 0.329907i $$-0.892983\pi$$
0.757715 + 0.652586i $$0.226316\pi$$
$$462$$ 12.9904 + 7.50000i 0.604367 + 0.348932i
$$463$$ 8.00000i 0.371792i −0.982569 0.185896i $$-0.940481\pi$$
0.982569 0.185896i $$-0.0595187\pi$$
$$464$$ −2.00000 + 3.46410i −0.0928477 + 0.160817i
$$465$$ 0 0
$$466$$ −7.00000 12.1244i −0.324269 0.561650i
$$467$$ 24.0000i 1.11059i −0.831654 0.555294i $$-0.812606\pi$$
0.831654 0.555294i $$-0.187394\pi$$
$$468$$ 3.46410 + 1.00000i 0.160128 + 0.0462250i
$$469$$ 40.0000 1.84703
$$470$$ 0 0
$$471$$ −7.50000 12.9904i −0.345582 0.598565i
$$472$$ 10.3923 + 6.00000i 0.478345 + 0.276172i
$$473$$ 18.0000i 0.827641i
$$474$$ 1.00000 1.73205i 0.0459315 0.0795557i
$$475$$ 0 0
$$476$$ 40.0000 1.83340
$$477$$ −0.866025 0.500000i −0.0396526 0.0228934i
$$478$$ −15.5885 + 9.00000i −0.712999 + 0.411650i
$$479$$ −14.0000 24.2487i −0.639676 1.10795i −0.985504 0.169654i $$-0.945735\pi$$
0.345827 0.938298i $$-0.387598\pi$$
$$480$$ 0 0
$$481$$ 7.00000 24.2487i 0.319173 1.10565i
$$482$$ 25.0000i 1.13872i
$$483$$ −17.3205 + 10.0000i −0.788110 + 0.455016i
$$484$$ −1.00000 1.73205i −0.0454545 0.0787296i
$$485$$ 0 0
$$486$$ −1.00000 −0.0453609
$$487$$ −32.0429 18.5000i −1.45200 0.838315i −0.453409 0.891303i $$-0.649792\pi$$
−0.998595 + 0.0529875i $$0.983126\pi$$
$$488$$ −1.73205 1.00000i −0.0784063 0.0452679i
$$489$$ 20.0000 0.904431
$$490$$ 0 0
$$491$$ −10.5000 18.1865i −0.473858 0.820747i 0.525694 0.850674i $$-0.323806\pi$$
−0.999552 + 0.0299272i $$0.990472\pi$$
$$492$$ 5.19615 3.00000i 0.234261 0.135250i
$$493$$ 32.0000i 1.44121i
$$494$$ 12.5000 + 12.9904i 0.562402 + 0.584465i
$$495$$ 0 0
$$496$$ 1.00000 + 1.73205i 0.0449013 + 0.0777714i
$$497$$ −8.66025 + 5.00000i −0.388465 + 0.224281i
$$498$$ −6.92820 4.00000i −0.310460 0.179244i
$$499$$ −4.00000 −0.179065 −0.0895323 0.995984i $$-0.528537\pi$$
−0.0895323 + 0.995984i $$0.528537\pi$$
$$500$$ 0 0
$$501$$ 11.5000 19.9186i 0.513782 0.889897i
$$502$$ 15.0000i 0.669483i
$$503$$ −9.52628 5.50000i −0.424756 0.245233i 0.272354 0.962197i $$-0.412198\pi$$
−0.697110 + 0.716964i $$0.745531\pi$$
$$504$$ 2.50000 + 4.33013i 0.111359 + 0.192879i
$$505$$ 0 0
$$506$$ −12.0000 −0.533465
$$507$$ 6.06218 + 11.5000i 0.269231 + 0.510733i
$$508$$ 21.0000i 0.931724i
$$509$$ 5.00000 + 8.66025i 0.221621 + 0.383859i 0.955300 0.295637i $$-0.0955319\pi$$
−0.733679 + 0.679496i $$0.762199\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 1.00000i 0.0441942i
$$513$$ −4.33013 2.50000i −0.191180 0.110378i
$$514$$ −14.0000 + 24.2487i −0.617514 + 1.06956i
$$515$$ 0 0
$$516$$ −3.00000 + 5.19615i −0.132068 + 0.228748i
$$517$$ 7.79423 4.50000i 0.342790 0.197910i
$$518$$ 30.3109 17.5000i 1.33178 0.768906i
$$519$$ −5.00000 −0.219476
$$520$$ 0 0
$$521$$ 5.00000 0.219054 0.109527 0.993984i $$-0.465066\pi$$
0.109527 + 0.993984i $$0.465066\pi$$
$$522$$ 3.46410 2.00000i 0.151620 0.0875376i
$$523$$ 8.66025 5.00000i 0.378686 0.218635i −0.298560 0.954391i $$-0.596506\pi$$
0.677247 + 0.735756i $$0.263173\pi$$
$$524$$ −9.50000 + 16.4545i −0.415009 + 0.718817i
$$525$$ 0 0
$$526$$ −7.50000 + 12.9904i −0.327016 + 0.566408i
$$527$$ −13.8564 8.00000i −0.603595 0.348485i
$$528$$ 3.00000i 0.130558i
$$529$$ −3.50000 + 6.06218i −0.152174 + 0.263573i
$$530$$ 0 0
$$531$$ −6.00000 10.3923i −0.260378 0.450988i
$$532$$ 25.0000i 1.08389i
$$533$$ 20.7846 + 6.00000i 0.900281 + 0.259889i
$$534$$ −11.0000 −0.476017
$$535$$ 0 0
$$536$$ 4.00000 + 6.92820i 0.172774 + 0.299253i
$$537$$ −3.46410 2.00000i −0.149487 0.0863064i
$$538$$ 4.00000i 0.172452i
$$539$$ −27.0000 + 46.7654i −1.16297 + 2.01433i
$$540$$ 0 0
$$541$$ 34.0000 1.46177 0.730887 0.682498i $$-0.239107\pi$$
0.730887 + 0.682498i $$0.239107\pi$$
$$542$$ 3.46410 + 2.00000i 0.148796 + 0.0859074i
$$543$$ 1.73205 1.00000i 0.0743294 0.0429141i
$$544$$ 4.00000 + 6.92820i 0.171499 + 0.297044i
$$545$$ 0 0
$$546$$ −5.00000 + 17.3205i −0.213980 + 0.741249i
$$547$$ 6.00000i 0.256541i 0.991739 + 0.128271i $$0.0409426\pi$$
−0.991739 + 0.128271i $$0.959057\pi$$
$$548$$ 10.3923 6.00000i 0.443937 0.256307i
$$549$$ 1.00000 + 1.73205i 0.0426790 + 0.0739221i
$$550$$ 0 0
$$551$$ 20.0000 0.852029
$$552$$ −3.46410 2.00000i −0.147442 0.0851257i
$$553$$ 8.66025 + 5.00000i 0.368271 + 0.212622i
$$554$$ −15.0000 −0.637289
$$555$$ 0 0
$$556$$ −3.50000 6.06218i −0.148433 0.257094i
$$557$$ 12.9904 7.50000i 0.550420 0.317785i −0.198871 0.980026i $$-0.563728\pi$$
0.749291 + 0.662240i $$0.230394\pi$$
$$558$$ 2.00000i 0.0846668i
$$559$$ −21.0000 + 5.19615i −0.888205 + 0.219774i
$$560$$ 0 0
$$561$$ −12.0000 20.7846i −0.506640 0.877527i
$$562$$ −15.5885 + 9.00000i −0.657559 + 0.379642i
$$563$$ 31.1769 + 18.0000i 1.31395 + 0.758610i 0.982748 0.184950i $$-0.0592124\pi$$
0.331202 + 0.943560i $$0.392546\pi$$
$$564$$ 3.00000 0.126323
$$565$$ 0 0
$$566$$ −5.00000 + 8.66025i −0.210166 + 0.364018i
$$567$$ 5.00000i 0.209980i
$$568$$ −1.73205 1.00000i −0.0726752 0.0419591i
$$569$$ −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i $$-0.268475\pi$$
−0.979313 + 0.202350i $$0.935142\pi$$
$$570$$ 0 0
$$571$$ −33.0000 −1.38101 −0.690504 0.723329i $$-0.742611\pi$$
−0.690504 + 0.723329i $$0.742611\pi$$
$$572$$ −7.79423 + 7.50000i −0.325893 + 0.313591i
$$573$$ 2.00000i 0.0835512i
$$574$$ 15.0000 + 25.9808i 0.626088 + 1.08442i
$$575$$ 0 0
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 2.00000i 0.0832611i 0.999133 + 0.0416305i $$0.0132552\pi$$
−0.999133 + 0.0416305i $$0.986745\pi$$
$$578$$ −40.7032 23.5000i −1.69303 0.977471i
$$579$$ 12.0000 20.7846i 0.498703 0.863779i
$$580$$ 0 0
$$581$$ 20.0000 34.6410i 0.829740 1.43715i
$$582$$ 0 0
$$583$$ 2.59808 1.50000i 0.107601 0.0621237i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 9.00000 0.371787
$$587$$ 15.5885 9.00000i 0.643404 0.371470i −0.142520 0.989792i $$-0.545521\pi$$
0.785925 + 0.618322i $$0.212187\pi$$
$$588$$ −15.5885 + 9.00000i −0.642857 + 0.371154i
$$589$$ 5.00000 8.66025i 0.206021 0.356840i
$$590$$ 0 0
$$591$$ −1.50000 + 2.59808i −0.0617018 + 0.106871i
$$592$$ 6.06218 + 3.50000i 0.249154 + 0.143849i
$$593$$ 20.0000i 0.821302i −0.911793 0.410651i $$-0.865302\pi$$
0.911793 0.410651i $$-0.134698\pi$$
$$594$$ 1.50000 2.59808i 0.0615457 0.106600i
$$595$$ 0 0
$$596$$ 1.00000 + 1.73205i 0.0409616 + 0.0709476i
$$597$$ 22.0000i 0.900400i
$$598$$ −3.46410 14.0000i −0.141658 0.572503i
$$599$$ −34.0000 −1.38920 −0.694601 0.719395i $$-0.744419\pi$$
−0.694601 + 0.719395i $$0.744419\pi$$
$$600$$ 0 0
$$601$$ −18.5000 32.0429i −0.754631 1.30706i −0.945558 0.325455i $$-0.894483\pi$$
0.190927 0.981604i $$-0.438851\pi$$
$$602$$ −25.9808 15.0000i −1.05890 0.611354i
$$603$$ 8.00000i 0.325785i
$$604$$ 11.0000 19.0526i 0.447584 0.775238i
$$605$$ 0 0
$$606$$ 8.00000 0.324978
$$607$$ 25.1147 + 14.5000i 1.01938 + 0.588537i 0.913923 0.405887i $$-0.133038\pi$$
0.105453 + 0.994424i $$0.466371\pi$$
$$608$$ −4.33013 + 2.50000i −0.175610 + 0.101388i
$$609$$ 10.0000 + 17.3205i 0.405220 + 0.701862i
$$610$$ 0 0
$$611$$ 7.50000 + 7.79423i 0.303418 + 0.315321i
$$612$$ 8.00000i 0.323381i
$$613$$ −21.6506 + 12.5000i −0.874461 + 0.504870i −0.868828 0.495114i $$-0.835126\pi$$
−0.00563283 + 0.999984i $$0.501793\pi$$
$$614$$ 3.00000 + 5.19615i 0.121070 + 0.209700i
$$615$$ 0 0
$$616$$ −15.0000 −0.604367
$$617$$ 12.1244 + 7.00000i 0.488108 + 0.281809i 0.723789 0.690021i $$-0.242399\pi$$
−0.235681 + 0.971830i $$0.575732\pi$$
$$618$$ 6.06218 + 3.50000i 0.243857 + 0.140791i
$$619$$ −17.0000 −0.683288 −0.341644 0.939829i $$-0.610984\pi$$
−0.341644 + 0.939829i $$0.610984\pi$$
$$620$$ 0 0
$$621$$ 2.00000 + 3.46410i 0.0802572 + 0.139010i
$$622$$ 10.3923 6.00000i 0.416693 0.240578i
$$623$$ 55.0000i 2.20353i
$$624$$ −3.50000 + 0.866025i −0.140112 + 0.0346688i
$$625$$ 0 0
$$626$$ −3.00000 5.19615i −0.119904 0.207680i
$$627$$ 12.9904 7.50000i 0.518786 0.299521i
$$628$$ 12.9904 + 7.50000i 0.518373 + 0.299283i
$$629$$ −56.0000 −2.23287
$$630$$ 0 0
$$631$$ −6.00000 + 10.3923i −0.238856 + 0.413711i −0.960386 0.278672i $$-0.910106\pi$$
0.721530 + 0.692383i $$0.243439\pi$$
$$632$$ 2.00000i 0.0795557i
$$633$$ −12.9904 7.50000i −0.516321 0.298098i
$$634$$ 11.5000 + 19.9186i 0.456723 + 0.791068i
$$635$$ 0 0
$$636$$ 1.00000 0.0396526
$$637$$ −62.3538 18.0000i −2.47055 0.713186i
$$638$$ 12.0000i 0.475085i
$$639$$ 1.00000 + 1.73205i 0.0395594 + 0.0685189i
$$640$$ 0 0
$$641$$ −13.5000 + 23.3827i −0.533218 + 0.923561i 0.466029 + 0.884769i $$0.345684\pi$$
−0.999247 + 0.0387913i $$0.987649\pi$$
$$642$$ 6.00000i 0.236801i
$$643$$ −38.1051 22.0000i −1.50272 0.867595i −0.999995 0.00314839i $$-0.998998\pi$$
−0.502724 0.864447i $$-0.667669\pi$$
$$644$$ 10.0000 17.3205i 0.394055 0.682524i
$$645$$ 0 0
$$646$$ 20.0000 34.6410i 0.786889 1.36293i
$$647$$ 2.59808 1.50000i 0.102141 0.0589711i −0.448059 0.894004i $$-0.647885\pi$$
0.550200 + 0.835033i $$0.314551\pi$$
$$648$$ 0.866025 0.500000i 0.0340207 0.0196419i
$$649$$ 36.0000 1.41312
$$650$$ 0 0
$$651$$ 10.0000 0.391931
$$652$$ −17.3205 + 10.0000i −0.678323 + 0.391630i
$$653$$ −23.3827 + 13.5000i −0.915035 + 0.528296i −0.882048 0.471160i $$-0.843835\pi$$
−0.0329874 + 0.999456i $$0.510502\pi$$
$$654$$ −7.00000 + 12.1244i −0.273722 + 0.474100i
$$655$$ 0 0
$$656$$ −3.00000 + 5.19615i −0.117130 + 0.202876i
$$657$$ 0 0
$$658$$ 15.0000i 0.584761i
$$659$$ 18.0000 31.1769i 0.701180 1.21448i −0.266872 0.963732i $$-0.585990\pi$$
0.968052 0.250748i $$-0.0806766\pi$$
$$660$$ 0 0
$$661$$ 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i $$-0.104366\pi$$
−0.752252 + 0.658876i $$0.771032\pi$$
$$662$$ 4.00000i 0.155464i
$$663$$ 20.7846 20.0000i 0.807207 0.776736i
$$664$$ 8.00000 0.310460
$$665$$ 0 0
$$666$$ −3.50000 6.06218i −0.135622 0.234905i
$$667$$ −13.8564 8.00000i −0.536522 0.309761i
$$668$$ 23.0000i 0.889897i
$$669$$ −1.50000 + 2.59808i −0.0579934 + 0.100447i
$$670$$ 0 0
$$671$$ −6.00000 −0.231627
$$672$$ −4.33013 2.50000i −0.167038 0.0964396i
$$673$$ 27.7128 16.0000i 1.06825 0.616755i 0.140548 0.990074i $$-0.455114\pi$$
0.927703 + 0.373319i $$0.121780\pi$$
$$674$$ −7.00000 12.1244i −0.269630 0.467013i
$$675$$ 0 0
$$676$$ −11.0000 6.92820i −0.423077 0.266469i
$$677$$ 22.0000i 0.845529i −0.906240 0.422764i $$-0.861060\pi$$
0.906240 0.422764i $$-0.138940\pi$$
$$678$$ 6.92820 4.00000i 0.266076 0.153619i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 5.19615 + 3.00000i 0.198971 + 0.114876i
$$683$$ 25.9808 + 15.0000i 0.994126 + 0.573959i 0.906505 0.422195i $$-0.138740\pi$$
0.0876211 + 0.996154i $$0.472074\pi$$
$$684$$ 5.00000 0.191180
$$685$$ 0 0
$$686$$ −27.5000 47.6314i −1.04995 1.81858i
$$687$$ 12.1244 7.00000i 0.462573 0.267067i
$$688$$ 6.00000i 0.228748i
$$689$$ 2.50000 + 2.59808i 0.0952424 + 0.0989788i
$$690$$ 0 0
$$691$$ −8.50000 14.7224i −0.323355 0.560068i 0.657823 0.753173i $$-0.271478\pi$$
−0.981178 + 0.193105i $$0.938144\pi$$
$$692$$ 4.33013 2.50000i 0.164607 0.0950357i
$$693$$ 12.9904 + 7.50000i 0.493464 + 0.284901i
$$694$$ −16.0000 −0.607352
$$695$$ 0 0
$$696$$ −2.00000 + 3.46410i −0.0758098 + 0.131306i
$$697$$ 48.0000i 1.81813i
$$698$$ −6.92820 4.00000i −0.262236 0.151402i
$$699$$ −7.00000 12.1244i −0.264764 0.458585i
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 3.46410 + 1.00000i 0.130744 + 0.0377426i
$$703$$ 35.0000i 1.32005i
$$704$$ −1.50000 2.59808i −0.0565334 0.0979187i
$$705$$ 0 0
$$706$$ 8.00000 13.8564i 0.301084 0.521493i
$$707$$ 40.0000i 1.50435i
$$708$$ 10.3923 + 6.00000i 0.390567 + 0.225494i
$$709$$ 16.0000 27.7128i 0.600893 1.04078i −0.391794 0.920053i $$-0.628145\pi$$
0.992686 0.120723i $$-0.0385214\pi$$
$$710$$ 0 0
$$711$$ 1.00000 1.73205i 0.0375029 0.0649570i
$$712$$ 9.52628 5.50000i 0.357012 0.206121i
$$713$$ −6.92820 + 4.00000i −0.259463 + 0.149801i
$$714$$ 40.0000 1.49696
$$715$$ 0 0
$$716$$ 4.00000 0.149487
$$717$$ −15.5885 + 9.00000i −0.582162 + 0.336111i
$$718$$ −15.5885 + 9.00000i −0.581756 + 0.335877i
$$719$$ −10.0000 + 17.3205i −0.372937 + 0.645946i −0.990016 0.140955i $$-0.954983\pi$$
0.617079 + 0.786901i $$0.288316\pi$$
$$720$$ 0 0
$$721$$ −17.5000 + 30.3109i −0.651734 + 1.12884i
$$722$$ 5.19615 + 3.00000i 0.193381 + 0.111648i
$$723$$ 25.0000i 0.929760i
$$724$$ −1.00000 + 1.73205i −0.0371647 + 0.0643712i
$$725$$ 0 0
$$726$$ −1.00000 1.73205i −0.0371135 0.0642824i
$$727$$ 11.0000i 0.407967i −0.978974 0.203984i $$-0.934611\pi$$
0.978974 0.203984i $$-0.0653890\pi$$
$$728$$ −4.33013 17.5000i −0.160485 0.648593i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 24.0000 + 41.5692i 0.887672 + 1.53749i
$$732$$ −1.73205 1.00000i −0.0640184 0.0369611i
$$733$$ 43.0000i 1.58824i 0.607760 + 0.794121i $$0.292068\pi$$
−0.607760 + 0.794121i $$0.707932\pi$$
$$734$$ 4.00000 6.92820i 0.147643 0.255725i
$$735$$ 0 0
$$736$$ 4.00000 0.147442
$$737$$ 20.7846 + 12.0000i 0.765611 + 0.442026i
$$738$$ 5.19615 3.00000i 0.191273 0.110432i
$$739$$ 9.50000 + 16.4545i 0.349463 + 0.605288i 0.986154 0.165831i $$-0.0530307\pi$$
−0.636691 + 0.771119i $$0.719697\pi$$
$$740$$ 0 0
$$741$$ 12.5000 + 12.9904i 0.459199 + 0.477214i
$$742$$ 5.00000i 0.183556i
$$743$$ 13.8564 8.00000i 0.508342 0.293492i −0.223810 0.974633i $$-0.571849\pi$$
0.732152 + 0.681141i $$0.238516\pi$$
$$744$$ 1.00000 + 1.73205i 0.0366618 + 0.0635001i
$$745$$ 0 0
$$746$$ −38.0000 −1.39128
$$747$$ −6.92820 4.00000i −0.253490 0.146352i
$$748$$ 20.7846 + 12.0000i 0.759961 + 0.438763i
$$749$$ −30.0000 −1.09618
$$750$$ 0 0
$$751$$ 4.00000 + 6.92820i 0.145962 + 0.252814i 0.929731 0.368238i $$-0.120039\pi$$
−0.783769 + 0.621052i $$0.786706\pi$$
$$752$$ −2.59808 + 1.50000i −0.0947421 + 0.0546994i
$$753$$ 15.0000i 0.546630i
$$754$$ −14.0000 + 3.46410i −0.509850 + 0.126155i
$$755$$ 0 0
$$756$$ 2.50000 + 4.33013i 0.0909241 + 0.157485i
$$757$$ 14.7224 8.50000i 0.535096 0.308938i −0.207993 0.978130i $$-0.566693\pi$$
0.743089 + 0.669193i $$0.233360\pi$$
$$758$$ 21.6506 + 12.5000i 0.786386 + 0.454020i
$$759$$ −12.0000 −0.435572
$$760$$ 0 0
$$761$$ −4.50000 + 7.79423i −0.163125 + 0.282541i −0.935988 0.352032i $$-0.885491\pi$$
0.772863 + 0.634573i $$0.218824\pi$$
$$762$$ 21.0000i 0.760750i
$$763$$ −60.6218 35.0000i −2.19466 1.26709i
$$764$$ 1.00000 + 1.73205i 0.0361787 + 0.0626634i
$$765$$ 0 0
$$766$$ 28.0000 1.01168
$$767$$ 10.3923 + 42.0000i 0.375244 + 1.51653i
$$768$$ 1.00000i 0.0360844i
$$769$$ −17.0000 29.4449i −0.613036 1.06181i −0.990726 0.135877i $$-0.956615\pi$$
0.377690 0.925932i $$-0.376718\pi$$
$$770$$ 0 0
$$771$$ −14.0000 + 24.2487i −0.504198 + 0.873296i
$$772$$ 24.0000i 0.863779i
$$773$$ 0.866025 + 0.500000i 0.0311488 + 0.0179838i 0.515494 0.856893i $$-0.327609\pi$$
−0.484345 + 0.874877i $$0.660942\pi$$
$$774$$ −3.00000 + 5.19615i −0.107833 + 0.186772i
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 30.3109 17.5000i 1.08740 0.627809i
$$778$$ −27.7128 + 16.0000i −0.993552 + 0.573628i
$$779$$ 30.0000 1.07486
$$780$$ 0 0
$$781$$ −6.00000 −0.214697
$$782$$ −27.7128 + 16.0000i −0.991008 + 0.572159i
$$783$$ 3.46410 2.00000i 0.123797 0.0714742i
$$784$$ 9.00000 15.5885i 0.321429 0.556731i