# Properties

 Label 567.2.f.j.379.2 Level $567$ Weight $2$ Character 567.379 Analytic conductor $4.528$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$567 = 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 567.f (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.52751779461$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 63) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 379.2 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 567.379 Dual form 567.2.f.j.190.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 - 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.73205 - 3.00000i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.73205 q^{8} +O(q^{10})$$ $$q+(0.866025 - 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.73205 - 3.00000i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.73205 q^{8} -6.00000 q^{10} +(1.73205 - 3.00000i) q^{11} +(-1.00000 - 1.73205i) q^{13} +(0.866025 + 1.50000i) q^{14} +(2.50000 - 4.33013i) q^{16} -3.46410 q^{17} -4.00000 q^{19} +(-1.73205 + 3.00000i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(-1.73205 - 3.00000i) q^{23} +(-3.50000 + 6.06218i) q^{25} -3.46410 q^{26} +1.00000 q^{28} +(2.00000 + 3.46410i) q^{31} +(-2.59808 - 4.50000i) q^{32} +(-3.00000 + 5.19615i) q^{34} +3.46410 q^{35} +2.00000 q^{37} +(-3.46410 + 6.00000i) q^{38} +(-3.00000 - 5.19615i) q^{40} +(5.19615 + 9.00000i) q^{41} +(2.00000 - 3.46410i) q^{43} -3.46410 q^{44} -6.00000 q^{46} +(3.46410 - 6.00000i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(6.06218 + 10.5000i) q^{50} +(-1.00000 + 1.73205i) q^{52} +6.92820 q^{53} -12.0000 q^{55} +(-0.866025 + 1.50000i) q^{56} +(-3.46410 - 6.00000i) q^{59} +(5.00000 - 8.66025i) q^{61} +6.92820 q^{62} +1.00000 q^{64} +(-3.46410 + 6.00000i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.73205 + 3.00000i) q^{68} +(3.00000 - 5.19615i) q^{70} +10.3923 q^{71} +14.0000 q^{73} +(1.73205 - 3.00000i) q^{74} +(2.00000 + 3.46410i) q^{76} +(1.73205 + 3.00000i) q^{77} +(-4.00000 + 6.92820i) q^{79} -17.3205 q^{80} +18.0000 q^{82} +(6.00000 + 10.3923i) q^{85} +(-3.46410 - 6.00000i) q^{86} +(3.00000 - 5.19615i) q^{88} +3.46410 q^{89} +2.00000 q^{91} +(-1.73205 + 3.00000i) q^{92} +(-6.00000 - 10.3923i) q^{94} +(6.92820 + 12.0000i) q^{95} +(-7.00000 + 12.1244i) q^{97} -1.73205 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 2 q^{4} - 2 q^{7} + O(q^{10})$$ $$4 q - 2 q^{4} - 2 q^{7} - 24 q^{10} - 4 q^{13} + 10 q^{16} - 16 q^{19} - 12 q^{22} - 14 q^{25} + 4 q^{28} + 8 q^{31} - 12 q^{34} + 8 q^{37} - 12 q^{40} + 8 q^{43} - 24 q^{46} - 2 q^{49} - 4 q^{52} - 48 q^{55} + 20 q^{61} + 4 q^{64} + 8 q^{67} + 12 q^{70} + 56 q^{73} + 8 q^{76} - 16 q^{79} + 72 q^{82} + 24 q^{85} + 12 q^{88} + 8 q^{91} - 24 q^{94} - 28 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.866025 1.50000i 0.612372 1.06066i −0.378467 0.925615i $$-0.623549\pi$$
0.990839 0.135045i $$-0.0431180\pi$$
$$3$$ 0 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −1.73205 3.00000i −0.774597 1.34164i −0.935021 0.354593i $$-0.884620\pi$$
0.160424 0.987048i $$-0.448714\pi$$
$$6$$ 0 0
$$7$$ −0.500000 + 0.866025i −0.188982 + 0.327327i
$$8$$ 1.73205 0.612372
$$9$$ 0 0
$$10$$ −6.00000 −1.89737
$$11$$ 1.73205 3.00000i 0.522233 0.904534i −0.477432 0.878668i $$-0.658432\pi$$
0.999665 0.0258656i $$-0.00823419\pi$$
$$12$$ 0 0
$$13$$ −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i $$-0.256123\pi$$
−0.970725 + 0.240192i $$0.922790\pi$$
$$14$$ 0.866025 + 1.50000i 0.231455 + 0.400892i
$$15$$ 0 0
$$16$$ 2.50000 4.33013i 0.625000 1.08253i
$$17$$ −3.46410 −0.840168 −0.420084 0.907485i $$-0.637999\pi$$
−0.420084 + 0.907485i $$0.637999\pi$$
$$18$$ 0 0
$$19$$ −4.00000 −0.917663 −0.458831 0.888523i $$-0.651732\pi$$
−0.458831 + 0.888523i $$0.651732\pi$$
$$20$$ −1.73205 + 3.00000i −0.387298 + 0.670820i
$$21$$ 0 0
$$22$$ −3.00000 5.19615i −0.639602 1.10782i
$$23$$ −1.73205 3.00000i −0.361158 0.625543i 0.626994 0.779024i $$-0.284285\pi$$
−0.988152 + 0.153481i $$0.950952\pi$$
$$24$$ 0 0
$$25$$ −3.50000 + 6.06218i −0.700000 + 1.21244i
$$26$$ −3.46410 −0.679366
$$27$$ 0 0
$$28$$ 1.00000 0.188982
$$29$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$30$$ 0 0
$$31$$ 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i $$-0.0497126\pi$$
−0.628619 + 0.777714i $$0.716379\pi$$
$$32$$ −2.59808 4.50000i −0.459279 0.795495i
$$33$$ 0 0
$$34$$ −3.00000 + 5.19615i −0.514496 + 0.891133i
$$35$$ 3.46410 0.585540
$$36$$ 0 0
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ −3.46410 + 6.00000i −0.561951 + 0.973329i
$$39$$ 0 0
$$40$$ −3.00000 5.19615i −0.474342 0.821584i
$$41$$ 5.19615 + 9.00000i 0.811503 + 1.40556i 0.911812 + 0.410608i $$0.134683\pi$$
−0.100309 + 0.994956i $$0.531983\pi$$
$$42$$ 0 0
$$43$$ 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i $$-0.734678\pi$$
0.977261 + 0.212041i $$0.0680112\pi$$
$$44$$ −3.46410 −0.522233
$$45$$ 0 0
$$46$$ −6.00000 −0.884652
$$47$$ 3.46410 6.00000i 0.505291 0.875190i −0.494690 0.869069i $$-0.664718\pi$$
0.999981 0.00612051i $$-0.00194823\pi$$
$$48$$ 0 0
$$49$$ −0.500000 0.866025i −0.0714286 0.123718i
$$50$$ 6.06218 + 10.5000i 0.857321 + 1.48492i
$$51$$ 0 0
$$52$$ −1.00000 + 1.73205i −0.138675 + 0.240192i
$$53$$ 6.92820 0.951662 0.475831 0.879537i $$-0.342147\pi$$
0.475831 + 0.879537i $$0.342147\pi$$
$$54$$ 0 0
$$55$$ −12.0000 −1.61808
$$56$$ −0.866025 + 1.50000i −0.115728 + 0.200446i
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −3.46410 6.00000i −0.450988 0.781133i 0.547460 0.836832i $$-0.315595\pi$$
−0.998448 + 0.0556984i $$0.982261\pi$$
$$60$$ 0 0
$$61$$ 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i $$-0.612191\pi$$
0.985391 0.170305i $$-0.0544754\pi$$
$$62$$ 6.92820 0.879883
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −3.46410 + 6.00000i −0.429669 + 0.744208i
$$66$$ 0 0
$$67$$ 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i $$-0.0880957\pi$$
−0.717607 + 0.696449i $$0.754762\pi$$
$$68$$ 1.73205 + 3.00000i 0.210042 + 0.363803i
$$69$$ 0 0
$$70$$ 3.00000 5.19615i 0.358569 0.621059i
$$71$$ 10.3923 1.23334 0.616670 0.787222i $$-0.288481\pi$$
0.616670 + 0.787222i $$0.288481\pi$$
$$72$$ 0 0
$$73$$ 14.0000 1.63858 0.819288 0.573382i $$-0.194369\pi$$
0.819288 + 0.573382i $$0.194369\pi$$
$$74$$ 1.73205 3.00000i 0.201347 0.348743i
$$75$$ 0 0
$$76$$ 2.00000 + 3.46410i 0.229416 + 0.397360i
$$77$$ 1.73205 + 3.00000i 0.197386 + 0.341882i
$$78$$ 0 0
$$79$$ −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i $$-0.981922\pi$$
0.548352 + 0.836247i $$0.315255\pi$$
$$80$$ −17.3205 −1.93649
$$81$$ 0 0
$$82$$ 18.0000 1.98777
$$83$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$84$$ 0 0
$$85$$ 6.00000 + 10.3923i 0.650791 + 1.12720i
$$86$$ −3.46410 6.00000i −0.373544 0.646997i
$$87$$ 0 0
$$88$$ 3.00000 5.19615i 0.319801 0.553912i
$$89$$ 3.46410 0.367194 0.183597 0.983002i $$-0.441226\pi$$
0.183597 + 0.983002i $$0.441226\pi$$
$$90$$ 0 0
$$91$$ 2.00000 0.209657
$$92$$ −1.73205 + 3.00000i −0.180579 + 0.312772i
$$93$$ 0 0
$$94$$ −6.00000 10.3923i −0.618853 1.07188i
$$95$$ 6.92820 + 12.0000i 0.710819 + 1.23117i
$$96$$ 0 0
$$97$$ −7.00000 + 12.1244i −0.710742 + 1.23104i 0.253837 + 0.967247i $$0.418307\pi$$
−0.964579 + 0.263795i $$0.915026\pi$$
$$98$$ −1.73205 −0.174964
$$99$$ 0 0
$$100$$ 7.00000 0.700000
$$101$$ 1.73205 3.00000i 0.172345 0.298511i −0.766894 0.641774i $$-0.778199\pi$$
0.939239 + 0.343263i $$0.111532\pi$$
$$102$$ 0 0
$$103$$ 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i $$-0.103525\pi$$
−0.750510 + 0.660859i $$0.770192\pi$$
$$104$$ −1.73205 3.00000i −0.169842 0.294174i
$$105$$ 0 0
$$106$$ 6.00000 10.3923i 0.582772 1.00939i
$$107$$ −17.3205 −1.67444 −0.837218 0.546869i $$-0.815820\pi$$
−0.837218 + 0.546869i $$0.815820\pi$$
$$108$$ 0 0
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ −10.3923 + 18.0000i −0.990867 + 1.71623i
$$111$$ 0 0
$$112$$ 2.50000 + 4.33013i 0.236228 + 0.409159i
$$113$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$114$$ 0 0
$$115$$ −6.00000 + 10.3923i −0.559503 + 0.969087i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −12.0000 −1.10469
$$119$$ 1.73205 3.00000i 0.158777 0.275010i
$$120$$ 0 0
$$121$$ −0.500000 0.866025i −0.0454545 0.0787296i
$$122$$ −8.66025 15.0000i −0.784063 1.35804i
$$123$$ 0 0
$$124$$ 2.00000 3.46410i 0.179605 0.311086i
$$125$$ 6.92820 0.619677
$$126$$ 0 0
$$127$$ 8.00000 0.709885 0.354943 0.934888i $$-0.384500\pi$$
0.354943 + 0.934888i $$0.384500\pi$$
$$128$$ 6.06218 10.5000i 0.535826 0.928078i
$$129$$ 0 0
$$130$$ 6.00000 + 10.3923i 0.526235 + 0.911465i
$$131$$ −6.92820 12.0000i −0.605320 1.04844i −0.992001 0.126231i $$-0.959712\pi$$
0.386681 0.922214i $$-0.373621\pi$$
$$132$$ 0 0
$$133$$ 2.00000 3.46410i 0.173422 0.300376i
$$134$$ 6.92820 0.598506
$$135$$ 0 0
$$136$$ −6.00000 −0.514496
$$137$$ −3.46410 + 6.00000i −0.295958 + 0.512615i −0.975207 0.221293i $$-0.928972\pi$$
0.679249 + 0.733908i $$0.262306\pi$$
$$138$$ 0 0
$$139$$ 8.00000 + 13.8564i 0.678551 + 1.17529i 0.975417 + 0.220366i $$0.0707252\pi$$
−0.296866 + 0.954919i $$0.595942\pi$$
$$140$$ −1.73205 3.00000i −0.146385 0.253546i
$$141$$ 0 0
$$142$$ 9.00000 15.5885i 0.755263 1.30815i
$$143$$ −6.92820 −0.579365
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 12.1244 21.0000i 1.00342 1.73797i
$$147$$ 0 0
$$148$$ −1.00000 1.73205i −0.0821995 0.142374i
$$149$$ 3.46410 + 6.00000i 0.283790 + 0.491539i 0.972315 0.233674i $$-0.0750747\pi$$
−0.688525 + 0.725213i $$0.741741\pi$$
$$150$$ 0 0
$$151$$ −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i $$-0.938871\pi$$
0.656101 + 0.754673i $$0.272204\pi$$
$$152$$ −6.92820 −0.561951
$$153$$ 0 0
$$154$$ 6.00000 0.483494
$$155$$ 6.92820 12.0000i 0.556487 0.963863i
$$156$$ 0 0
$$157$$ 5.00000 + 8.66025i 0.399043 + 0.691164i 0.993608 0.112884i $$-0.0360089\pi$$
−0.594565 + 0.804048i $$0.702676\pi$$
$$158$$ 6.92820 + 12.0000i 0.551178 + 0.954669i
$$159$$ 0 0
$$160$$ −9.00000 + 15.5885i −0.711512 + 1.23238i
$$161$$ 3.46410 0.273009
$$162$$ 0 0
$$163$$ 20.0000 1.56652 0.783260 0.621694i $$-0.213555\pi$$
0.783260 + 0.621694i $$0.213555\pi$$
$$164$$ 5.19615 9.00000i 0.405751 0.702782i
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −10.3923 18.0000i −0.804181 1.39288i −0.916843 0.399248i $$-0.869271\pi$$
0.112662 0.993633i $$-0.464062\pi$$
$$168$$ 0 0
$$169$$ 4.50000 7.79423i 0.346154 0.599556i
$$170$$ 20.7846 1.59411
$$171$$ 0 0
$$172$$ −4.00000 −0.304997
$$173$$ 8.66025 15.0000i 0.658427 1.14043i −0.322596 0.946537i $$-0.604555\pi$$
0.981023 0.193892i $$-0.0621112\pi$$
$$174$$ 0 0
$$175$$ −3.50000 6.06218i −0.264575 0.458258i
$$176$$ −8.66025 15.0000i −0.652791 1.13067i
$$177$$ 0 0
$$178$$ 3.00000 5.19615i 0.224860 0.389468i
$$179$$ 17.3205 1.29460 0.647298 0.762237i $$-0.275899\pi$$
0.647298 + 0.762237i $$0.275899\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 1.73205 3.00000i 0.128388 0.222375i
$$183$$ 0 0
$$184$$ −3.00000 5.19615i −0.221163 0.383065i
$$185$$ −3.46410 6.00000i −0.254686 0.441129i
$$186$$ 0 0
$$187$$ −6.00000 + 10.3923i −0.438763 + 0.759961i
$$188$$ −6.92820 −0.505291
$$189$$ 0 0
$$190$$ 24.0000 1.74114
$$191$$ −12.1244 + 21.0000i −0.877288 + 1.51951i −0.0229818 + 0.999736i $$0.507316\pi$$
−0.854306 + 0.519771i $$0.826017\pi$$
$$192$$ 0 0
$$193$$ −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i $$-0.998575\pi$$
0.496119 0.868255i $$-0.334758\pi$$
$$194$$ 12.1244 + 21.0000i 0.870478 + 1.50771i
$$195$$ 0 0
$$196$$ −0.500000 + 0.866025i −0.0357143 + 0.0618590i
$$197$$ −20.7846 −1.48084 −0.740421 0.672143i $$-0.765374\pi$$
−0.740421 + 0.672143i $$0.765374\pi$$
$$198$$ 0 0
$$199$$ −16.0000 −1.13421 −0.567105 0.823646i $$-0.691937\pi$$
−0.567105 + 0.823646i $$0.691937\pi$$
$$200$$ −6.06218 + 10.5000i −0.428661 + 0.742462i
$$201$$ 0 0
$$202$$ −3.00000 5.19615i −0.211079 0.365600i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 18.0000 31.1769i 1.25717 2.17749i
$$206$$ 6.92820 0.482711
$$207$$ 0 0
$$208$$ −10.0000 −0.693375
$$209$$ −6.92820 + 12.0000i −0.479234 + 0.830057i
$$210$$ 0 0
$$211$$ −10.0000 17.3205i −0.688428 1.19239i −0.972346 0.233544i $$-0.924968\pi$$
0.283918 0.958849i $$-0.408366\pi$$
$$212$$ −3.46410 6.00000i −0.237915 0.412082i
$$213$$ 0 0
$$214$$ −15.0000 + 25.9808i −1.02538 + 1.77601i
$$215$$ −13.8564 −0.944999
$$216$$ 0 0
$$217$$ −4.00000 −0.271538
$$218$$ 1.73205 3.00000i 0.117309 0.203186i
$$219$$ 0 0
$$220$$ 6.00000 + 10.3923i 0.404520 + 0.700649i
$$221$$ 3.46410 + 6.00000i 0.233021 + 0.403604i
$$222$$ 0 0
$$223$$ −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i $$-0.919650\pi$$
0.700449 + 0.713702i $$0.252983\pi$$
$$224$$ 5.19615 0.347183
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −3.46410 + 6.00000i −0.229920 + 0.398234i −0.957784 0.287488i $$-0.907180\pi$$
0.727864 + 0.685722i $$0.240513\pi$$
$$228$$ 0 0
$$229$$ 11.0000 + 19.0526i 0.726900 + 1.25903i 0.958187 + 0.286143i $$0.0923732\pi$$
−0.231287 + 0.972886i $$0.574293\pi$$
$$230$$ 10.3923 + 18.0000i 0.685248 + 1.18688i
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −6.92820 −0.453882 −0.226941 0.973909i $$-0.572872\pi$$
−0.226941 + 0.973909i $$0.572872\pi$$
$$234$$ 0 0
$$235$$ −24.0000 −1.56559
$$236$$ −3.46410 + 6.00000i −0.225494 + 0.390567i
$$237$$ 0 0
$$238$$ −3.00000 5.19615i −0.194461 0.336817i
$$239$$ 5.19615 + 9.00000i 0.336111 + 0.582162i 0.983698 0.179830i $$-0.0575549\pi$$
−0.647586 + 0.761992i $$0.724222\pi$$
$$240$$ 0 0
$$241$$ 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i $$-0.728952\pi$$
0.980917 + 0.194429i $$0.0622852\pi$$
$$242$$ −1.73205 −0.111340
$$243$$ 0 0
$$244$$ −10.0000 −0.640184
$$245$$ −1.73205 + 3.00000i −0.110657 + 0.191663i
$$246$$ 0 0
$$247$$ 4.00000 + 6.92820i 0.254514 + 0.440831i
$$248$$ 3.46410 + 6.00000i 0.219971 + 0.381000i
$$249$$ 0 0
$$250$$ 6.00000 10.3923i 0.379473 0.657267i
$$251$$ −20.7846 −1.31191 −0.655956 0.754799i $$-0.727735\pi$$
−0.655956 + 0.754799i $$0.727735\pi$$
$$252$$ 0 0
$$253$$ −12.0000 −0.754434
$$254$$ 6.92820 12.0000i 0.434714 0.752947i
$$255$$ 0 0
$$256$$ −9.50000 16.4545i −0.593750 1.02841i
$$257$$ −1.73205 3.00000i −0.108042 0.187135i 0.806935 0.590641i $$-0.201125\pi$$
−0.914977 + 0.403506i $$0.867792\pi$$
$$258$$ 0 0
$$259$$ −1.00000 + 1.73205i −0.0621370 + 0.107624i
$$260$$ 6.92820 0.429669
$$261$$ 0 0
$$262$$ −24.0000 −1.48272
$$263$$ −8.66025 + 15.0000i −0.534014 + 0.924940i 0.465196 + 0.885208i $$0.345984\pi$$
−0.999210 + 0.0397320i $$0.987350\pi$$
$$264$$ 0 0
$$265$$ −12.0000 20.7846i −0.737154 1.27679i
$$266$$ −3.46410 6.00000i −0.212398 0.367884i
$$267$$ 0 0
$$268$$ 2.00000 3.46410i 0.122169 0.211604i
$$269$$ 17.3205 1.05605 0.528025 0.849229i $$-0.322933\pi$$
0.528025 + 0.849229i $$0.322933\pi$$
$$270$$ 0 0
$$271$$ 20.0000 1.21491 0.607457 0.794353i $$-0.292190\pi$$
0.607457 + 0.794353i $$0.292190\pi$$
$$272$$ −8.66025 + 15.0000i −0.525105 + 0.909509i
$$273$$ 0 0
$$274$$ 6.00000 + 10.3923i 0.362473 + 0.627822i
$$275$$ 12.1244 + 21.0000i 0.731126 + 1.26635i
$$276$$ 0 0
$$277$$ 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i $$-0.736206\pi$$
0.976231 + 0.216731i $$0.0695395\pi$$
$$278$$ 27.7128 1.66210
$$279$$ 0 0
$$280$$ 6.00000 0.358569
$$281$$ −10.3923 + 18.0000i −0.619953 + 1.07379i 0.369541 + 0.929214i $$0.379515\pi$$
−0.989494 + 0.144575i $$0.953818\pi$$
$$282$$ 0 0
$$283$$ 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i $$-0.128734\pi$$
−0.800439 + 0.599414i $$0.795400\pi$$
$$284$$ −5.19615 9.00000i −0.308335 0.534052i
$$285$$ 0 0
$$286$$ −6.00000 + 10.3923i −0.354787 + 0.614510i
$$287$$ −10.3923 −0.613438
$$288$$ 0 0
$$289$$ −5.00000 −0.294118
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −7.00000 12.1244i −0.409644 0.709524i
$$293$$ −5.19615 9.00000i −0.303562 0.525786i 0.673378 0.739299i $$-0.264843\pi$$
−0.976940 + 0.213513i $$0.931509\pi$$
$$294$$ 0 0
$$295$$ −12.0000 + 20.7846i −0.698667 + 1.21013i
$$296$$ 3.46410 0.201347
$$297$$ 0 0
$$298$$ 12.0000 0.695141
$$299$$ −3.46410 + 6.00000i −0.200334 + 0.346989i
$$300$$ 0 0
$$301$$ 2.00000 + 3.46410i 0.115278 + 0.199667i
$$302$$ 6.92820 + 12.0000i 0.398673 + 0.690522i
$$303$$ 0 0
$$304$$ −10.0000 + 17.3205i −0.573539 + 0.993399i
$$305$$ −34.6410 −1.98354
$$306$$ 0 0
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ 1.73205 3.00000i 0.0986928 0.170941i
$$309$$ 0 0
$$310$$ −12.0000 20.7846i −0.681554 1.18049i
$$311$$ 17.3205 + 30.0000i 0.982156 + 1.70114i 0.653950 + 0.756538i $$0.273111\pi$$
0.328206 + 0.944606i $$0.393556\pi$$
$$312$$ 0 0
$$313$$ −1.00000 + 1.73205i −0.0565233 + 0.0979013i −0.892903 0.450250i $$-0.851335\pi$$
0.836379 + 0.548151i $$0.184668\pi$$
$$314$$ 17.3205 0.977453
$$315$$ 0 0
$$316$$ 8.00000 0.450035
$$317$$ 3.46410 6.00000i 0.194563 0.336994i −0.752194 0.658942i $$-0.771004\pi$$
0.946757 + 0.321948i $$0.104338\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ −1.73205 3.00000i −0.0968246 0.167705i
$$321$$ 0 0
$$322$$ 3.00000 5.19615i 0.167183 0.289570i
$$323$$ 13.8564 0.770991
$$324$$ 0 0
$$325$$ 14.0000 0.776580
$$326$$ 17.3205 30.0000i 0.959294 1.66155i
$$327$$ 0 0
$$328$$ 9.00000 + 15.5885i 0.496942 + 0.860729i
$$329$$ 3.46410 + 6.00000i 0.190982 + 0.330791i
$$330$$ 0 0
$$331$$ −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i $$0.351905\pi$$
−0.998298 + 0.0583130i $$0.981428\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ −36.0000 −1.96983
$$335$$ 6.92820 12.0000i 0.378528 0.655630i
$$336$$ 0 0
$$337$$ −7.00000 12.1244i −0.381314 0.660456i 0.609936 0.792451i $$-0.291195\pi$$
−0.991250 + 0.131995i $$0.957862\pi$$
$$338$$ −7.79423 13.5000i −0.423950 0.734303i
$$339$$ 0 0
$$340$$ 6.00000 10.3923i 0.325396 0.563602i
$$341$$ 13.8564 0.750366
$$342$$ 0 0
$$343$$ 1.00000 0.0539949
$$344$$ 3.46410 6.00000i 0.186772 0.323498i
$$345$$ 0 0
$$346$$ −15.0000 25.9808i −0.806405 1.39673i
$$347$$ −8.66025 15.0000i −0.464907 0.805242i 0.534291 0.845301i $$-0.320579\pi$$
−0.999197 + 0.0400587i $$0.987246\pi$$
$$348$$ 0 0
$$349$$ −7.00000 + 12.1244i −0.374701 + 0.649002i −0.990282 0.139072i $$-0.955588\pi$$
0.615581 + 0.788074i $$0.288921\pi$$
$$350$$ −12.1244 −0.648074
$$351$$ 0 0
$$352$$ −18.0000 −0.959403
$$353$$ 1.73205 3.00000i 0.0921878 0.159674i −0.816244 0.577708i $$-0.803947\pi$$
0.908431 + 0.418034i $$0.137281\pi$$
$$354$$ 0 0
$$355$$ −18.0000 31.1769i −0.955341 1.65470i
$$356$$ −1.73205 3.00000i −0.0917985 0.159000i
$$357$$ 0 0
$$358$$ 15.0000 25.9808i 0.792775 1.37313i
$$359$$ 24.2487 1.27980 0.639899 0.768459i $$-0.278976\pi$$
0.639899 + 0.768459i $$0.278976\pi$$
$$360$$ 0 0
$$361$$ −3.00000 −0.157895
$$362$$ 1.73205 3.00000i 0.0910346 0.157676i
$$363$$ 0 0
$$364$$ −1.00000 1.73205i −0.0524142 0.0907841i
$$365$$ −24.2487 42.0000i −1.26924 2.19838i
$$366$$ 0 0
$$367$$ 8.00000 13.8564i 0.417597 0.723299i −0.578101 0.815966i $$-0.696206\pi$$
0.995697 + 0.0926670i $$0.0295392\pi$$
$$368$$ −17.3205 −0.902894
$$369$$ 0 0
$$370$$ −12.0000 −0.623850
$$371$$ −3.46410 + 6.00000i −0.179847 + 0.311504i
$$372$$ 0 0
$$373$$ 5.00000 + 8.66025i 0.258890 + 0.448411i 0.965945 0.258748i $$-0.0833099\pi$$
−0.707055 + 0.707159i $$0.749977\pi$$
$$374$$ 10.3923 + 18.0000i 0.537373 + 0.930758i
$$375$$ 0 0
$$376$$ 6.00000 10.3923i 0.309426 0.535942i
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −28.0000 −1.43826 −0.719132 0.694874i $$-0.755460\pi$$
−0.719132 + 0.694874i $$0.755460\pi$$
$$380$$ 6.92820 12.0000i 0.355409 0.615587i
$$381$$ 0 0
$$382$$ 21.0000 + 36.3731i 1.07445 + 1.86101i
$$383$$ −6.92820 12.0000i −0.354015 0.613171i 0.632934 0.774206i $$-0.281850\pi$$
−0.986949 + 0.161034i $$0.948517\pi$$
$$384$$ 0 0
$$385$$ 6.00000 10.3923i 0.305788 0.529641i
$$386$$ −24.2487 −1.23423
$$387$$ 0 0
$$388$$ 14.0000 0.710742
$$389$$ 6.92820 12.0000i 0.351274 0.608424i −0.635199 0.772348i $$-0.719082\pi$$
0.986473 + 0.163924i $$0.0524153\pi$$
$$390$$ 0 0
$$391$$ 6.00000 + 10.3923i 0.303433 + 0.525561i
$$392$$ −0.866025 1.50000i −0.0437409 0.0757614i
$$393$$ 0 0
$$394$$ −18.0000 + 31.1769i −0.906827 + 1.57067i
$$395$$ 27.7128 1.39438
$$396$$ 0 0
$$397$$ 38.0000 1.90717 0.953583 0.301131i $$-0.0973643\pi$$
0.953583 + 0.301131i $$0.0973643\pi$$
$$398$$ −13.8564 + 24.0000i −0.694559 + 1.20301i
$$399$$ 0 0
$$400$$ 17.5000 + 30.3109i 0.875000 + 1.51554i
$$401$$ 3.46410 + 6.00000i 0.172989 + 0.299626i 0.939463 0.342649i $$-0.111324\pi$$
−0.766475 + 0.642275i $$0.777991\pi$$
$$402$$ 0 0
$$403$$ 4.00000 6.92820i 0.199254 0.345118i
$$404$$ −3.46410 −0.172345
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 3.46410 6.00000i 0.171709 0.297409i
$$408$$ 0 0
$$409$$ −7.00000 12.1244i −0.346128 0.599511i 0.639430 0.768849i $$-0.279170\pi$$
−0.985558 + 0.169338i $$0.945837\pi$$
$$410$$ −31.1769 54.0000i −1.53972 2.66687i
$$411$$ 0 0
$$412$$ 2.00000 3.46410i 0.0985329 0.170664i
$$413$$ 6.92820 0.340915
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −5.19615 + 9.00000i −0.254762 + 0.441261i
$$417$$ 0 0
$$418$$ 12.0000 + 20.7846i 0.586939 + 1.01661i
$$419$$ 10.3923 + 18.0000i 0.507697 + 0.879358i 0.999960 + 0.00891102i $$0.00283650\pi$$
−0.492263 + 0.870447i $$0.663830\pi$$
$$420$$ 0 0
$$421$$ 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i $$-0.754977\pi$$
0.961761 + 0.273890i $$0.0883103\pi$$
$$422$$ −34.6410 −1.68630
$$423$$ 0 0
$$424$$ 12.0000 0.582772
$$425$$ 12.1244 21.0000i 0.588118 1.01865i
$$426$$ 0 0
$$427$$ 5.00000 + 8.66025i 0.241967 + 0.419099i
$$428$$ 8.66025 + 15.0000i 0.418609 + 0.725052i
$$429$$ 0 0
$$430$$ −12.0000 + 20.7846i −0.578691 + 1.00232i
$$431$$ −3.46410 −0.166860 −0.0834300 0.996514i $$-0.526587\pi$$
−0.0834300 + 0.996514i $$0.526587\pi$$
$$432$$ 0 0
$$433$$ 26.0000 1.24948 0.624740 0.780833i $$-0.285205\pi$$
0.624740 + 0.780833i $$0.285205\pi$$
$$434$$ −3.46410 + 6.00000i −0.166282 + 0.288009i
$$435$$ 0 0
$$436$$ −1.00000 1.73205i −0.0478913 0.0829502i
$$437$$ 6.92820 + 12.0000i 0.331421 + 0.574038i
$$438$$ 0 0
$$439$$ 8.00000 13.8564i 0.381819 0.661330i −0.609503 0.792784i $$-0.708631\pi$$
0.991322 + 0.131453i $$0.0419644\pi$$
$$440$$ −20.7846 −0.990867
$$441$$ 0 0
$$442$$ 12.0000 0.570782
$$443$$ −1.73205 + 3.00000i −0.0822922 + 0.142534i −0.904234 0.427037i $$-0.859557\pi$$
0.821942 + 0.569571i $$0.192891\pi$$
$$444$$ 0 0
$$445$$ −6.00000 10.3923i −0.284427 0.492642i
$$446$$ 6.92820 + 12.0000i 0.328060 + 0.568216i
$$447$$ 0 0
$$448$$ −0.500000 + 0.866025i −0.0236228 + 0.0409159i
$$449$$ −41.5692 −1.96177 −0.980886 0.194581i $$-0.937665\pi$$
−0.980886 + 0.194581i $$0.937665\pi$$
$$450$$ 0 0
$$451$$ 36.0000 1.69517
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 6.00000 + 10.3923i 0.281594 + 0.487735i
$$455$$ −3.46410 6.00000i −0.162400 0.281284i
$$456$$ 0 0
$$457$$ 5.00000 8.66025i 0.233890 0.405110i −0.725059 0.688686i $$-0.758188\pi$$
0.958950 + 0.283577i $$0.0915211\pi$$
$$458$$ 38.1051 1.78054
$$459$$ 0 0
$$460$$ 12.0000 0.559503
$$461$$ 15.5885 27.0000i 0.726027 1.25752i −0.232523 0.972591i $$-0.574698\pi$$
0.958550 0.284925i $$-0.0919685\pi$$
$$462$$ 0 0
$$463$$ −16.0000 27.7128i −0.743583 1.28792i −0.950854 0.309640i $$-0.899791\pi$$
0.207271 0.978284i $$-0.433542\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −6.00000 + 10.3923i −0.277945 + 0.481414i
$$467$$ −6.92820 −0.320599 −0.160300 0.987068i $$-0.551246\pi$$
−0.160300 + 0.987068i $$0.551246\pi$$
$$468$$ 0 0
$$469$$ −4.00000 −0.184703
$$470$$ −20.7846 + 36.0000i −0.958723 + 1.66056i
$$471$$ 0 0
$$472$$ −6.00000 10.3923i −0.276172 0.478345i
$$473$$ −6.92820 12.0000i −0.318559 0.551761i
$$474$$ 0 0
$$475$$ 14.0000 24.2487i 0.642364 1.11261i
$$476$$ −3.46410 −0.158777
$$477$$ 0 0
$$478$$ 18.0000 0.823301
$$479$$ −3.46410 + 6.00000i −0.158279 + 0.274147i −0.934248 0.356624i $$-0.883928\pi$$
0.775969 + 0.630771i $$0.217261\pi$$
$$480$$ 0 0
$$481$$ −2.00000 3.46410i −0.0911922 0.157949i
$$482$$ −8.66025 15.0000i −0.394464 0.683231i
$$483$$ 0 0
$$484$$ −0.500000 + 0.866025i −0.0227273 + 0.0393648i
$$485$$ 48.4974 2.20215
$$486$$ 0 0
$$487$$ −40.0000 −1.81257 −0.906287 0.422664i $$-0.861095\pi$$
−0.906287 + 0.422664i $$0.861095\pi$$
$$488$$ 8.66025 15.0000i 0.392031 0.679018i
$$489$$ 0 0
$$490$$ 3.00000 + 5.19615i 0.135526 + 0.234738i
$$491$$ 5.19615 + 9.00000i 0.234499 + 0.406164i 0.959127 0.282976i $$-0.0913217\pi$$
−0.724628 + 0.689140i $$0.757988\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 13.8564 0.623429
$$495$$ 0 0
$$496$$ 20.0000 0.898027
$$497$$ −5.19615 + 9.00000i −0.233079 + 0.403705i
$$498$$ 0 0
$$499$$ 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i $$-0.138129\pi$$
−0.817781 + 0.575529i $$0.804796\pi$$
$$500$$ −3.46410 6.00000i −0.154919 0.268328i
$$501$$ 0 0
$$502$$ −18.0000 + 31.1769i −0.803379 + 1.39149i
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ −12.0000 −0.533993
$$506$$ −10.3923 + 18.0000i −0.461994 + 0.800198i
$$507$$ 0 0
$$508$$ −4.00000 6.92820i −0.177471 0.307389i
$$509$$ −1.73205 3.00000i −0.0767718 0.132973i 0.825084 0.565011i $$-0.191128\pi$$
−0.901855 + 0.432038i $$0.857795\pi$$
$$510$$ 0 0
$$511$$ −7.00000 + 12.1244i −0.309662 + 0.536350i
$$512$$ −8.66025 −0.382733
$$513$$ 0 0
$$514$$ −6.00000 −0.264649
$$515$$ 6.92820 12.0000i 0.305293 0.528783i
$$516$$ 0 0
$$517$$ −12.0000 20.7846i −0.527759 0.914106i
$$518$$ 1.73205 + 3.00000i 0.0761019 + 0.131812i
$$519$$ 0 0
$$520$$ −6.00000 + 10.3923i −0.263117 + 0.455733i
$$521$$ −3.46410 −0.151765 −0.0758825 0.997117i $$-0.524177\pi$$
−0.0758825 + 0.997117i $$0.524177\pi$$
$$522$$ 0 0
$$523$$ −16.0000 −0.699631 −0.349816 0.936819i $$-0.613756\pi$$
−0.349816 + 0.936819i $$0.613756\pi$$
$$524$$ −6.92820 + 12.0000i −0.302660 + 0.524222i
$$525$$ 0 0
$$526$$ 15.0000 + 25.9808i 0.654031 + 1.13282i
$$527$$ −6.92820 12.0000i −0.301797 0.522728i
$$528$$ 0 0
$$529$$ 5.50000 9.52628i 0.239130 0.414186i
$$530$$ −41.5692 −1.80565
$$531$$ 0 0
$$532$$ −4.00000 −0.173422
$$533$$ 10.3923 18.0000i 0.450141 0.779667i
$$534$$ 0 0
$$535$$ 30.0000 + 51.9615i 1.29701 + 2.24649i
$$536$$ 3.46410 + 6.00000i 0.149626 + 0.259161i
$$537$$ 0 0
$$538$$ 15.0000 25.9808i 0.646696 1.12011i
$$539$$ −3.46410 −0.149209
$$540$$ 0 0
$$541$$ 14.0000 0.601907 0.300954 0.953639i $$-0.402695\pi$$
0.300954 + 0.953639i $$0.402695\pi$$
$$542$$ 17.3205 30.0000i 0.743980 1.28861i
$$543$$ 0 0
$$544$$ 9.00000 + 15.5885i 0.385872 + 0.668350i
$$545$$ −3.46410 6.00000i −0.148386 0.257012i
$$546$$ 0 0
$$547$$ 2.00000 3.46410i 0.0855138 0.148114i −0.820096 0.572226i $$-0.806080\pi$$
0.905610 + 0.424111i $$0.139413\pi$$
$$548$$ 6.92820 0.295958
$$549$$ 0 0
$$550$$ 42.0000 1.79089
$$551$$ 0 0
$$552$$ 0 0
$$553$$ −4.00000 6.92820i −0.170097 0.294617i
$$554$$ −8.66025 15.0000i −0.367939 0.637289i
$$555$$ 0 0
$$556$$ 8.00000 13.8564i 0.339276 0.587643i
$$557$$ 6.92820 0.293557 0.146779 0.989169i $$-0.453109\pi$$
0.146779 + 0.989169i $$0.453109\pi$$
$$558$$ 0 0
$$559$$ −8.00000 −0.338364
$$560$$ 8.66025 15.0000i 0.365963 0.633866i
$$561$$ 0 0
$$562$$ 18.0000 + 31.1769i 0.759284 + 1.31512i
$$563$$ 17.3205 + 30.0000i 0.729972 + 1.26435i 0.956894 + 0.290436i $$0.0938004\pi$$
−0.226922 + 0.973913i $$0.572866\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 6.92820 0.291214
$$567$$ 0 0
$$568$$ 18.0000 0.755263
$$569$$ 3.46410 6.00000i 0.145223 0.251533i −0.784233 0.620466i $$-0.786943\pi$$
0.929456 + 0.368933i $$0.120277\pi$$
$$570$$ 0 0
$$571$$ 14.0000 + 24.2487i 0.585882 + 1.01478i 0.994765 + 0.102190i $$0.0325850\pi$$
−0.408883 + 0.912587i $$0.634082\pi$$
$$572$$ 3.46410 + 6.00000i 0.144841 + 0.250873i
$$573$$ 0 0
$$574$$ −9.00000 + 15.5885i −0.375653 + 0.650650i
$$575$$ 24.2487 1.01124
$$576$$ 0 0
$$577$$ 2.00000 0.0832611 0.0416305 0.999133i $$-0.486745\pi$$
0.0416305 + 0.999133i $$0.486745\pi$$
$$578$$ −4.33013 + 7.50000i −0.180110 + 0.311959i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 12.0000 20.7846i 0.496989 0.860811i
$$584$$ 24.2487 1.00342
$$585$$ 0 0
$$586$$ −18.0000 −0.743573
$$587$$ −10.3923 + 18.0000i −0.428936 + 0.742940i −0.996779 0.0801976i $$-0.974445\pi$$
0.567843 + 0.823137i $$0.307778\pi$$
$$588$$ 0 0
$$589$$ −8.00000 13.8564i −0.329634 0.570943i
$$590$$ 20.7846 + 36.0000i 0.855689 + 1.48210i
$$591$$ 0 0
$$592$$ 5.00000 8.66025i 0.205499 0.355934i
$$593$$ 24.2487 0.995775 0.497888 0.867242i $$-0.334109\pi$$
0.497888 + 0.867242i $$0.334109\pi$$
$$594$$ 0 0
$$595$$ −12.0000 −0.491952
$$596$$ 3.46410 6.00000i 0.141895 0.245770i
$$597$$ 0 0
$$598$$ 6.00000 + 10.3923i 0.245358 + 0.424973i
$$599$$ 22.5167 + 39.0000i 0.920006 + 1.59350i 0.799402 + 0.600796i $$0.205150\pi$$
0.120603 + 0.992701i $$0.461517\pi$$
$$600$$ 0 0
$$601$$ 11.0000 19.0526i 0.448699 0.777170i −0.549602 0.835426i $$-0.685221\pi$$
0.998302 + 0.0582563i $$0.0185541\pi$$
$$602$$ 6.92820 0.282372
$$603$$ 0 0
$$604$$ 8.00000 0.325515
$$605$$ −1.73205 + 3.00000i −0.0704179 + 0.121967i
$$606$$ 0 0
$$607$$ −4.00000 6.92820i −0.162355 0.281207i 0.773358 0.633970i $$-0.218576\pi$$
−0.935713 + 0.352763i $$0.885242\pi$$
$$608$$ 10.3923 + 18.0000i 0.421464 + 0.729996i
$$609$$ 0 0
$$610$$ −30.0000 + 51.9615i −1.21466 + 2.10386i
$$611$$ −13.8564 −0.560570
$$612$$ 0 0
$$613$$ 38.0000 1.53481 0.767403 0.641165i $$-0.221549\pi$$
0.767403 + 0.641165i $$0.221549\pi$$
$$614$$ −24.2487 + 42.0000i −0.978598 + 1.69498i
$$615$$ 0 0
$$616$$ 3.00000 + 5.19615i 0.120873 + 0.209359i
$$617$$ −10.3923 18.0000i −0.418378 0.724653i 0.577398 0.816463i $$-0.304068\pi$$
−0.995777 + 0.0918100i $$0.970735\pi$$
$$618$$ 0 0
$$619$$ −4.00000 + 6.92820i −0.160774 + 0.278468i −0.935146 0.354262i $$-0.884732\pi$$
0.774373 + 0.632730i $$0.218066\pi$$
$$620$$ −13.8564 −0.556487
$$621$$ 0 0
$$622$$ 60.0000 2.40578
$$623$$ −1.73205 + 3.00000i −0.0693932 + 0.120192i
$$624$$ 0 0
$$625$$ 5.50000 + 9.52628i 0.220000 + 0.381051i
$$626$$ 1.73205 + 3.00000i 0.0692267 + 0.119904i
$$627$$ 0 0
$$628$$ 5.00000 8.66025i 0.199522 0.345582i
$$629$$ −6.92820 −0.276246
$$630$$ 0 0
$$631$$ 8.00000 0.318475 0.159237 0.987240i $$-0.449096\pi$$
0.159237 + 0.987240i $$0.449096\pi$$
$$632$$ −6.92820 + 12.0000i −0.275589 + 0.477334i
$$633$$ 0 0
$$634$$ −6.00000 10.3923i −0.238290 0.412731i
$$635$$ −13.8564 24.0000i −0.549875 0.952411i
$$636$$ 0 0
$$637$$ −1.00000 + 1.73205i −0.0396214 + 0.0686264i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ −42.0000 −1.66020
$$641$$ −24.2487 + 42.0000i −0.957767 + 1.65890i −0.229860 + 0.973224i $$0.573827\pi$$
−0.727906 + 0.685677i $$0.759506\pi$$
$$642$$ 0 0
$$643$$ −10.0000 17.3205i −0.394362 0.683054i 0.598658 0.801005i $$-0.295701\pi$$
−0.993019 + 0.117951i $$0.962368\pi$$
$$644$$ −1.73205 3.00000i −0.0682524 0.118217i
$$645$$ 0 0
$$646$$ 12.0000 20.7846i 0.472134 0.817760i
$$647$$ 6.92820 0.272376 0.136188 0.990683i $$-0.456515\pi$$
0.136188 + 0.990683i $$0.456515\pi$$
$$648$$ 0 0
$$649$$ −24.0000 −0.942082
$$650$$ 12.1244 21.0000i 0.475556 0.823688i
$$651$$ 0 0
$$652$$ −10.0000 17.3205i −0.391630 0.678323i
$$653$$ 13.8564 + 24.0000i 0.542243 + 0.939193i 0.998775 + 0.0494855i $$0.0157581\pi$$
−0.456532 + 0.889707i $$0.650909\pi$$
$$654$$ 0 0
$$655$$ −24.0000 + 41.5692i −0.937758 + 1.62424i
$$656$$ 51.9615 2.02876
$$657$$ 0 0
$$658$$ 12.0000 0.467809
$$659$$ −5.19615 + 9.00000i −0.202413 + 0.350590i −0.949306 0.314355i $$-0.898212\pi$$
0.746892 + 0.664945i $$0.231545\pi$$
$$660$$ 0 0
$$661$$ 5.00000 + 8.66025i 0.194477 + 0.336845i 0.946729 0.322031i $$-0.104366\pi$$
−0.752252 + 0.658876i $$0.771032\pi$$
$$662$$ 17.3205 + 30.0000i 0.673181 + 1.16598i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −13.8564 −0.537328
$$666$$ 0 0
$$667$$ 0 0
$$668$$ −10.3923 + 18.0000i −0.402090 + 0.696441i
$$669$$ 0 0
$$670$$ −12.0000 20.7846i −0.463600 0.802980i
$$671$$ −17.3205 30.0000i −0.668651 1.15814i
$$672$$ 0 0
$$673$$ 5.00000 8.66025i 0.192736 0.333828i −0.753420 0.657539i $$-0.771597\pi$$
0.946156 + 0.323711i $$0.104931\pi$$
$$674$$ −24.2487 −0.934025
$$675$$ 0 0
$$676$$ −9.00000 −0.346154
$$677$$ −12.1244 + 21.0000i −0.465977 + 0.807096i −0.999245 0.0388507i $$-0.987630\pi$$
0.533268 + 0.845946i $$0.320964\pi$$
$$678$$ 0 0
$$679$$ −7.00000 12.1244i −0.268635 0.465290i
$$680$$ 10.3923 + 18.0000i 0.398527 + 0.690268i
$$681$$ 0 0
$$682$$ 12.0000 20.7846i 0.459504 0.795884i
$$683$$ −24.2487 −0.927851 −0.463926 0.885874i $$-0.653559\pi$$
−0.463926 + 0.885874i $$0.653559\pi$$
$$684$$ 0 0
$$685$$ 24.0000 0.916993
$$686$$ 0.866025 1.50000i 0.0330650 0.0572703i
$$687$$ 0 0
$$688$$ −10.0000 17.3205i −0.381246 0.660338i
$$689$$ −6.92820 12.0000i −0.263944 0.457164i
$$690$$ 0 0
$$691$$ −4.00000 + 6.92820i −0.152167 + 0.263561i −0.932024 0.362397i $$-0.881959\pi$$
0.779857 + 0.625958i $$0.215292\pi$$
$$692$$ −17.3205 −0.658427
$$693$$ 0 0
$$694$$ −30.0000 −1.13878
$$695$$ 27.7128 48.0000i 1.05121 1.82074i
$$696$$ 0 0
$$697$$ −18.0000 31.1769i −0.681799 1.18091i
$$698$$ 12.1244 + 21.0000i 0.458914 + 0.794862i
$$699$$ 0 0
$$700$$ −3.50000 + 6.06218i −0.132288 + 0.229129i
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ −8.00000 −0.301726
$$704$$ 1.73205 3.00000i 0.0652791 0.113067i
$$705$$ 0 0
$$706$$ −3.00000 5.19615i −0.112906 0.195560i
$$707$$ 1.73205 + 3.00000i 0.0651405 + 0.112827i
$$708$$ 0 0
$$709$$ −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i $$-0.995689\pi$$
0.511683 + 0.859174i $$0.329022\pi$$
$$710$$ −62.3538 −2.34010
$$711$$ 0 0
$$712$$ 6.00000 0.224860
$$713$$ 6.92820 12.0000i 0.259463 0.449404i
$$714$$ 0 0
$$715$$ 12.0000 + 20.7846i 0.448775 + 0.777300i
$$716$$ −8.66025 15.0000i −0.323649 0.560576i
$$717$$ 0 0
$$718$$ 21.0000 36.3731i 0.783713 1.35743i
$$719$$ −27.7128 −1.03351 −0.516757 0.856132i $$-0.672861\pi$$
−0.516757 + 0.856132i $$0.672861\pi$$
$$720$$ 0 0
$$721$$ −4.00000 −0.148968
$$722$$ −2.59808 + 4.50000i −0.0966904 + 0.167473i
$$723$$ 0 0
$$724$$ −1.00000 1.73205i −0.0371647 0.0643712i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 2.00000 3.46410i 0.0741759 0.128476i −0.826552 0.562861i $$-0.809701\pi$$
0.900728 + 0.434384i $$0.143034\pi$$
$$728$$ 3.46410 0.128388
$$729$$ 0 0
$$730$$ −84.0000 −3.10898
$$731$$ −6.92820 + 12.0000i −0.256249 + 0.443836i
$$732$$ 0 0
$$733$$ 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i $$-0.0334875\pi$$
−0.588177 + 0.808732i $$0.700154\pi$$
$$734$$ −13.8564 24.0000i −0.511449 0.885856i
$$735$$ 0 0
$$736$$ −9.00000 + 15.5885i −0.331744 + 0.574598i
$$737$$ 13.8564 0.510407
$$738$$ 0 0
$$739$$ 20.0000 0.735712 0.367856 0.929883i $$-0.380092\pi$$
0.367856 + 0.929883i $$0.380092\pi$$
$$740$$ −3.46410 + 6.00000i −0.127343 + 0.220564i
$$741$$ 0 0
$$742$$ 6.00000 + 10.3923i 0.220267 + 0.381514i
$$743$$ −5.19615 9.00000i −0.190628 0.330178i 0.754830 0.655920i $$-0.227719\pi$$
−0.945459 + 0.325742i $$0.894386\pi$$
$$744$$ 0 0
$$745$$ 12.0000 20.7846i 0.439646 0.761489i
$$746$$ 17.3205 0.634149
$$747$$ 0 0
$$748$$ 12.0000 0.438763
$$749$$ 8.66025 15.0000i 0.316439 0.548088i
$$750$$ 0 0
$$751$$ −4.00000 6.92820i −0.145962 0.252814i 0.783769 0.621052i $$-0.213294\pi$$
−0.929731 + 0.368238i $$0.879961\pi$$
$$752$$ −17.3205 30.0000i −0.631614 1.09399i
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 27.7128 1.00857
$$756$$ 0 0
$$757$$ 26.0000 0.944986 0.472493 0.881334i $$-0.343354\pi$$
0.472493 + 0.881334i $$0.343354\pi$$
$$758$$ −24.2487 + 42.0000i −0.880753 + 1.52551i
$$759$$ 0 0
$$760$$ 12.0000 + 20.7846i 0.435286 + 0.753937i
$$761$$ 19.0526 + 33.0000i 0.690655 + 1.19625i 0.971624 + 0.236532i $$0.0760109\pi$$
−0.280969 + 0.959717i $$0.590656\pi$$
$$762$$ 0 0
$$763$$ −1.00000 + 1.73205i −0.0362024 + 0.0627044i
$$764$$ 24.2487 0.877288
$$765$$ 0 0
$$766$$ −24.0000 −0.867155
$$767$$ −6.92820 + 12.0000i −0.250163 + 0.433295i
$$768$$ 0 0
$$769$$ 11.0000 + 19.0526i 0.396670 + 0.687053i 0.993313 0.115454i $$-0.0368323\pi$$
−0.596643 + 0.802507i $$0.703499\pi$$
$$770$$ −10.3923 18.0000i −0.374513 0.648675i
$$771$$ 0 0
$$772$$ −7.00000 + 12.1244i −0.251936 + 0.436365i
$$773$$ −45.0333 −1.61974 −0.809868 0.586612i $$-0.800461\pi$$
−0.809868 + 0.586612i $$0.800461\pi$$
$$774$$ 0 0
$$775$$ −28.0000 −1.00579
$$776$$ −12.1244 + 21.0000i −0.435239 + 0.753856i
$$777$$ 0 0
$$778$$ −12.0000 20.7846i −0.430221 0.745164i
$$779$$ −20.7846 36.0000i −0.744686 1.28983i
$$780$$ 0 0
$$781$$ 18.0000 31.1769i 0.644091 1.11560i
$$782$$ 20.7846 0.743256
$$783$$ 0 0
$$784$$ −5.00000 −0.178571
$$785$$ 17.3205 30.0000i 0.618195 1.07075i
$$786$$ 0 0
$$787$$ −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i $$-0.973479\pi$$
0.426193 0.904632i $$-0.359855\pi$$
$$788$$ 10.3923 + 18.0000i 0.370211 + 0.641223i
$$789$$ 0 0
$$790$$ 24.0000 41.5692i 0.853882 1.47897i
$$791$$ 0 0