# Properties

 Label 144.2.x.c.61.1 Level $144$ Weight $2$ Character 144.61 Analytic conductor $1.150$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$144 = 2^{4} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 144.x (of order $$12$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.14984578911$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

## Embedding invariants

 Embedding label 61.1 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 144.61 Dual form 144.2.x.c.85.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.00000 + 0.267949i) q^{5} +(2.36603 + 0.633975i) q^{6} +(2.36603 + 1.36603i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(1.00000 + 0.267949i) q^{5} +(2.36603 + 0.633975i) q^{6} +(2.36603 + 1.36603i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +1.46410i q^{10} +(1.13397 + 4.23205i) q^{11} +3.46410i q^{12} +(0.901924 - 3.36603i) q^{13} +(-1.00000 + 3.73205i) q^{14} +(1.26795 - 1.26795i) q^{15} +(2.00000 - 3.46410i) q^{16} -5.73205 q^{17} +(3.00000 - 3.00000i) q^{18} +(-2.36603 - 2.36603i) q^{19} +(-2.00000 + 0.535898i) q^{20} +(4.09808 - 2.36603i) q^{21} +(-5.36603 + 3.09808i) q^{22} +(-4.09808 + 2.36603i) q^{23} +(-4.73205 + 1.26795i) q^{24} +(-3.40192 - 1.96410i) q^{25} +4.92820 q^{26} -5.19615 q^{27} -5.46410 q^{28} +(2.36603 - 0.633975i) q^{29} +(2.19615 + 1.26795i) q^{30} +(-0.267949 - 0.464102i) q^{31} +(5.46410 + 1.46410i) q^{32} +(7.33013 + 1.96410i) q^{33} +(-2.09808 - 7.83013i) q^{34} +(2.00000 + 2.00000i) q^{35} +(5.19615 + 3.00000i) q^{36} +(4.73205 - 4.73205i) q^{37} +(2.36603 - 4.09808i) q^{38} +(-4.26795 - 4.26795i) q^{39} +(-1.46410 - 2.53590i) q^{40} +(-2.59808 + 1.50000i) q^{41} +(4.73205 + 4.73205i) q^{42} +(2.23205 + 8.33013i) q^{43} +(-6.19615 - 6.19615i) q^{44} +(-0.803848 - 3.00000i) q^{45} +(-4.73205 - 4.73205i) q^{46} +(3.83013 - 6.63397i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(0.232051 + 0.401924i) q^{49} +(1.43782 - 5.36603i) q^{50} +(-4.96410 + 8.59808i) q^{51} +(1.80385 + 6.73205i) q^{52} +(-7.46410 + 7.46410i) q^{53} +(-1.90192 - 7.09808i) q^{54} +4.53590i q^{55} +(-2.00000 - 7.46410i) q^{56} +(-5.59808 + 1.50000i) q^{57} +(1.73205 + 3.00000i) q^{58} +(7.33013 + 1.96410i) q^{59} +(-0.928203 + 3.46410i) q^{60} +(11.1962 - 3.00000i) q^{61} +(0.535898 - 0.535898i) q^{62} -8.19615i q^{63} +8.00000i q^{64} +(1.80385 - 3.12436i) q^{65} +10.7321i q^{66} +(-1.76795 + 6.59808i) q^{67} +(9.92820 - 5.73205i) q^{68} +8.19615i q^{69} +(-2.00000 + 3.46410i) q^{70} +2.92820i q^{71} +(-2.19615 + 8.19615i) q^{72} -6.26795i q^{73} +(8.19615 + 4.73205i) q^{74} +(-5.89230 + 3.40192i) q^{75} +(6.46410 + 1.73205i) q^{76} +(-3.09808 + 11.5622i) q^{77} +(4.26795 - 7.39230i) q^{78} +(-6.00000 + 10.3923i) q^{79} +(2.92820 - 2.92820i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.00000 - 3.00000i) q^{82} +(-1.36603 + 0.366025i) q^{83} +(-4.73205 + 8.19615i) q^{84} +(-5.73205 - 1.53590i) q^{85} +(-10.5622 + 6.09808i) q^{86} +(1.09808 - 4.09808i) q^{87} +(6.19615 - 10.7321i) q^{88} -2.00000i q^{89} +(3.80385 - 2.19615i) q^{90} +(6.73205 - 6.73205i) q^{91} +(4.73205 - 8.19615i) q^{92} -0.928203 q^{93} +(10.4641 + 2.80385i) q^{94} +(-1.73205 - 3.00000i) q^{95} +(6.92820 - 6.92820i) q^{96} +(-5.86603 + 10.1603i) q^{97} +(-0.464102 + 0.464102i) q^{98} +(9.29423 - 9.29423i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{2} + 4q^{5} + 6q^{6} + 6q^{7} - 8q^{8} - 6q^{9} + O(q^{10})$$ $$4q - 2q^{2} + 4q^{5} + 6q^{6} + 6q^{7} - 8q^{8} - 6q^{9} + 8q^{11} + 14q^{13} - 4q^{14} + 12q^{15} + 8q^{16} - 16q^{17} + 12q^{18} - 6q^{19} - 8q^{20} + 6q^{21} - 18q^{22} - 6q^{23} - 12q^{24} - 24q^{25} - 8q^{26} - 8q^{28} + 6q^{29} - 12q^{30} - 8q^{31} + 8q^{32} + 12q^{33} + 2q^{34} + 8q^{35} + 12q^{37} + 6q^{38} - 24q^{39} + 8q^{40} + 12q^{42} + 2q^{43} - 4q^{44} - 24q^{45} - 12q^{46} - 2q^{47} - 6q^{49} + 30q^{50} - 6q^{51} + 28q^{52} - 16q^{53} - 18q^{54} - 8q^{56} - 12q^{57} + 12q^{59} + 24q^{60} + 24q^{61} + 16q^{62} + 28q^{65} - 14q^{67} + 12q^{68} - 8q^{70} + 12q^{72} + 12q^{74} + 18q^{75} + 12q^{76} - 2q^{77} + 24q^{78} - 24q^{79} - 16q^{80} - 18q^{81} - 12q^{82} - 2q^{83} - 12q^{84} - 16q^{85} - 18q^{86} - 6q^{87} + 4q^{88} + 36q^{90} + 20q^{91} + 12q^{92} + 24q^{93} + 28q^{94} - 20q^{97} + 12q^{98} + 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$$.

 $$n$$ $$37$$ $$65$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.366025 + 1.36603i 0.258819 + 0.965926i
$$3$$ 0.866025 1.50000i 0.500000 0.866025i
$$4$$ −1.73205 + 1.00000i −0.866025 + 0.500000i
$$5$$ 1.00000 + 0.267949i 0.447214 + 0.119831i 0.475395 0.879772i $$-0.342305\pi$$
−0.0281817 + 0.999603i $$0.508972\pi$$
$$6$$ 2.36603 + 0.633975i 0.965926 + 0.258819i
$$7$$ 2.36603 + 1.36603i 0.894274 + 0.516309i 0.875338 0.483512i $$-0.160639\pi$$
0.0189356 + 0.999821i $$0.493972\pi$$
$$8$$ −2.00000 2.00000i −0.707107 0.707107i
$$9$$ −1.50000 2.59808i −0.500000 0.866025i
$$10$$ 1.46410i 0.462990i
$$11$$ 1.13397 + 4.23205i 0.341906 + 1.27601i 0.896185 + 0.443680i $$0.146327\pi$$
−0.554279 + 0.832331i $$0.687006\pi$$
$$12$$ 3.46410i 1.00000i
$$13$$ 0.901924 3.36603i 0.250149 0.933567i −0.720577 0.693375i $$-0.756123\pi$$
0.970725 0.240192i $$-0.0772105\pi$$
$$14$$ −1.00000 + 3.73205i −0.267261 + 0.997433i
$$15$$ 1.26795 1.26795i 0.327383 0.327383i
$$16$$ 2.00000 3.46410i 0.500000 0.866025i
$$17$$ −5.73205 −1.39023 −0.695113 0.718900i $$-0.744646\pi$$
−0.695113 + 0.718900i $$0.744646\pi$$
$$18$$ 3.00000 3.00000i 0.707107 0.707107i
$$19$$ −2.36603 2.36603i −0.542803 0.542803i 0.381546 0.924350i $$-0.375392\pi$$
−0.924350 + 0.381546i $$0.875392\pi$$
$$20$$ −2.00000 + 0.535898i −0.447214 + 0.119831i
$$21$$ 4.09808 2.36603i 0.894274 0.516309i
$$22$$ −5.36603 + 3.09808i −1.14404 + 0.660512i
$$23$$ −4.09808 + 2.36603i −0.854508 + 0.493350i −0.862169 0.506620i $$-0.830895\pi$$
0.00766135 + 0.999971i $$0.497561\pi$$
$$24$$ −4.73205 + 1.26795i −0.965926 + 0.258819i
$$25$$ −3.40192 1.96410i −0.680385 0.392820i
$$26$$ 4.92820 0.966500
$$27$$ −5.19615 −1.00000
$$28$$ −5.46410 −1.03262
$$29$$ 2.36603 0.633975i 0.439360 0.117726i −0.0323566 0.999476i $$-0.510301\pi$$
0.471717 + 0.881750i $$0.343635\pi$$
$$30$$ 2.19615 + 1.26795i 0.400961 + 0.231495i
$$31$$ −0.267949 0.464102i −0.0481251 0.0833551i 0.840959 0.541098i $$-0.181991\pi$$
−0.889085 + 0.457743i $$0.848658\pi$$
$$32$$ 5.46410 + 1.46410i 0.965926 + 0.258819i
$$33$$ 7.33013 + 1.96410i 1.27601 + 0.341906i
$$34$$ −2.09808 7.83013i −0.359817 1.34286i
$$35$$ 2.00000 + 2.00000i 0.338062 + 0.338062i
$$36$$ 5.19615 + 3.00000i 0.866025 + 0.500000i
$$37$$ 4.73205 4.73205i 0.777944 0.777944i −0.201537 0.979481i $$-0.564594\pi$$
0.979481 + 0.201537i $$0.0645935\pi$$
$$38$$ 2.36603 4.09808i 0.383820 0.664796i
$$39$$ −4.26795 4.26795i −0.683419 0.683419i
$$40$$ −1.46410 2.53590i −0.231495 0.400961i
$$41$$ −2.59808 + 1.50000i −0.405751 + 0.234261i −0.688963 0.724797i $$-0.741934\pi$$
0.283211 + 0.959058i $$0.408600\pi$$
$$42$$ 4.73205 + 4.73205i 0.730171 + 0.730171i
$$43$$ 2.23205 + 8.33013i 0.340385 + 1.27033i 0.897912 + 0.440174i $$0.145083\pi$$
−0.557528 + 0.830158i $$0.688250\pi$$
$$44$$ −6.19615 6.19615i −0.934105 0.934105i
$$45$$ −0.803848 3.00000i −0.119831 0.447214i
$$46$$ −4.73205 4.73205i −0.697703 0.697703i
$$47$$ 3.83013 6.63397i 0.558681 0.967665i −0.438925 0.898523i $$-0.644641\pi$$
0.997607 0.0691412i $$-0.0220259\pi$$
$$48$$ −3.46410 6.00000i −0.500000 0.866025i
$$49$$ 0.232051 + 0.401924i 0.0331501 + 0.0574177i
$$50$$ 1.43782 5.36603i 0.203339 0.758871i
$$51$$ −4.96410 + 8.59808i −0.695113 + 1.20397i
$$52$$ 1.80385 + 6.73205i 0.250149 + 0.933567i
$$53$$ −7.46410 + 7.46410i −1.02527 + 1.02527i −0.0256010 + 0.999672i $$0.508150\pi$$
−0.999672 + 0.0256010i $$0.991850\pi$$
$$54$$ −1.90192 7.09808i −0.258819 0.965926i
$$55$$ 4.53590i 0.611620i
$$56$$ −2.00000 7.46410i −0.267261 0.997433i
$$57$$ −5.59808 + 1.50000i −0.741483 + 0.198680i
$$58$$ 1.73205 + 3.00000i 0.227429 + 0.393919i
$$59$$ 7.33013 + 1.96410i 0.954301 + 0.255704i 0.702186 0.711993i $$-0.252207\pi$$
0.252115 + 0.967697i $$0.418874\pi$$
$$60$$ −0.928203 + 3.46410i −0.119831 + 0.447214i
$$61$$ 11.1962 3.00000i 1.43352 0.384111i 0.543261 0.839564i $$-0.317189\pi$$
0.890260 + 0.455453i $$0.150523\pi$$
$$62$$ 0.535898 0.535898i 0.0680592 0.0680592i
$$63$$ 8.19615i 1.03262i
$$64$$ 8.00000i 1.00000i
$$65$$ 1.80385 3.12436i 0.223740 0.387529i
$$66$$ 10.7321i 1.32102i
$$67$$ −1.76795 + 6.59808i −0.215989 + 0.806083i 0.769827 + 0.638253i $$0.220343\pi$$
−0.985816 + 0.167830i $$0.946324\pi$$
$$68$$ 9.92820 5.73205i 1.20397 0.695113i
$$69$$ 8.19615i 0.986701i
$$70$$ −2.00000 + 3.46410i −0.239046 + 0.414039i
$$71$$ 2.92820i 0.347514i 0.984789 + 0.173757i $$0.0555907\pi$$
−0.984789 + 0.173757i $$0.944409\pi$$
$$72$$ −2.19615 + 8.19615i −0.258819 + 0.965926i
$$73$$ 6.26795i 0.733608i −0.930298 0.366804i $$-0.880452\pi$$
0.930298 0.366804i $$-0.119548\pi$$
$$74$$ 8.19615 + 4.73205i 0.952783 + 0.550090i
$$75$$ −5.89230 + 3.40192i −0.680385 + 0.392820i
$$76$$ 6.46410 + 1.73205i 0.741483 + 0.198680i
$$77$$ −3.09808 + 11.5622i −0.353059 + 1.31763i
$$78$$ 4.26795 7.39230i 0.483250 0.837014i
$$79$$ −6.00000 + 10.3923i −0.675053 + 1.16923i 0.301401 + 0.953498i $$0.402546\pi$$
−0.976453 + 0.215728i $$0.930788\pi$$
$$80$$ 2.92820 2.92820i 0.327383 0.327383i
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ −3.00000 3.00000i −0.331295 0.331295i
$$83$$ −1.36603 + 0.366025i −0.149941 + 0.0401765i −0.333009 0.942924i $$-0.608064\pi$$
0.183068 + 0.983100i $$0.441397\pi$$
$$84$$ −4.73205 + 8.19615i −0.516309 + 0.894274i
$$85$$ −5.73205 1.53590i −0.621728 0.166592i
$$86$$ −10.5622 + 6.09808i −1.13895 + 0.657572i
$$87$$ 1.09808 4.09808i 0.117726 0.439360i
$$88$$ 6.19615 10.7321i 0.660512 1.14404i
$$89$$ 2.00000i 0.212000i −0.994366 0.106000i $$-0.966196\pi$$
0.994366 0.106000i $$-0.0338043\pi$$
$$90$$ 3.80385 2.19615i 0.400961 0.231495i
$$91$$ 6.73205 6.73205i 0.705711 0.705711i
$$92$$ 4.73205 8.19615i 0.493350 0.854508i
$$93$$ −0.928203 −0.0962502
$$94$$ 10.4641 + 2.80385i 1.07929 + 0.289195i
$$95$$ −1.73205 3.00000i −0.177705 0.307794i
$$96$$ 6.92820 6.92820i 0.707107 0.707107i
$$97$$ −5.86603 + 10.1603i −0.595605 + 1.03162i 0.397857 + 0.917448i $$0.369754\pi$$
−0.993461 + 0.114170i $$0.963579\pi$$
$$98$$ −0.464102 + 0.464102i −0.0468813 + 0.0468813i
$$99$$ 9.29423 9.29423i 0.934105 0.934105i
$$100$$ 7.85641 0.785641
$$101$$ 0.535898 + 2.00000i 0.0533239 + 0.199007i 0.987449 0.157938i $$-0.0504847\pi$$
−0.934125 + 0.356946i $$0.883818\pi$$
$$102$$ −13.5622 3.63397i −1.34286 0.359817i
$$103$$ 13.0981 7.56218i 1.29059 0.745124i 0.311833 0.950137i $$-0.399057\pi$$
0.978759 + 0.205014i $$0.0657238\pi$$
$$104$$ −8.53590 + 4.92820i −0.837014 + 0.483250i
$$105$$ 4.73205 1.26795i 0.461801 0.123739i
$$106$$ −12.9282 7.46410i −1.25570 0.724978i
$$107$$ 12.4904 12.4904i 1.20749 1.20749i 0.235654 0.971837i $$-0.424277\pi$$
0.971837 0.235654i $$-0.0757231\pi$$
$$108$$ 9.00000 5.19615i 0.866025 0.500000i
$$109$$ 10.7321 + 10.7321i 1.02794 + 1.02794i 0.999598 + 0.0283459i $$0.00902398\pi$$
0.0283459 + 0.999598i $$0.490976\pi$$
$$110$$ −6.19615 + 1.66025i −0.590780 + 0.158299i
$$111$$ −3.00000 11.1962i −0.284747 1.06269i
$$112$$ 9.46410 5.46410i 0.894274 0.516309i
$$113$$ −6.92820 12.0000i −0.651751 1.12887i −0.982698 0.185216i $$-0.940702\pi$$
0.330947 0.943649i $$-0.392632\pi$$
$$114$$ −4.09808 7.09808i −0.383820 0.664796i
$$115$$ −4.73205 + 1.26795i −0.441266 + 0.118237i
$$116$$ −3.46410 + 3.46410i −0.321634 + 0.321634i
$$117$$ −10.0981 + 2.70577i −0.933567 + 0.250149i
$$118$$ 10.7321i 0.987965i
$$119$$ −13.5622 7.83013i −1.24324 0.717787i
$$120$$ −5.07180 −0.462990
$$121$$ −7.09808 + 4.09808i −0.645280 + 0.372552i
$$122$$ 8.19615 + 14.1962i 0.742045 + 1.28526i
$$123$$ 5.19615i 0.468521i
$$124$$ 0.928203 + 0.535898i 0.0833551 + 0.0481251i
$$125$$ −6.53590 6.53590i −0.584589 0.584589i
$$126$$ 11.1962 3.00000i 0.997433 0.267261i
$$127$$ 4.19615 0.372348 0.186174 0.982517i $$-0.440391\pi$$
0.186174 + 0.982517i $$0.440391\pi$$
$$128$$ −10.9282 + 2.92820i −0.965926 + 0.258819i
$$129$$ 14.4282 + 3.86603i 1.27033 + 0.340385i
$$130$$ 4.92820 + 1.32051i 0.432232 + 0.115816i
$$131$$ 2.09808 7.83013i 0.183310 0.684121i −0.811676 0.584108i $$-0.801445\pi$$
0.994986 0.100014i $$-0.0318887\pi$$
$$132$$ −14.6603 + 3.92820i −1.27601 + 0.341906i
$$133$$ −2.36603 8.83013i −0.205160 0.765669i
$$134$$ −9.66025 −0.834519
$$135$$ −5.19615 1.39230i −0.447214 0.119831i
$$136$$ 11.4641 + 11.4641i 0.983039 + 0.983039i
$$137$$ 8.25833 + 4.76795i 0.705557 + 0.407353i 0.809414 0.587239i $$-0.199785\pi$$
−0.103857 + 0.994592i $$0.533118\pi$$
$$138$$ −11.1962 + 3.00000i −0.953080 + 0.255377i
$$139$$ −11.4282 3.06218i −0.969328 0.259731i −0.260784 0.965397i $$-0.583981\pi$$
−0.708544 + 0.705667i $$0.750648\pi$$
$$140$$ −5.46410 1.46410i −0.461801 0.123739i
$$141$$ −6.63397 11.4904i −0.558681 0.967665i
$$142$$ −4.00000 + 1.07180i −0.335673 + 0.0899432i
$$143$$ 15.2679 1.27677
$$144$$ −12.0000 −1.00000
$$145$$ 2.53590 0.210595
$$146$$ 8.56218 2.29423i 0.708611 0.189872i
$$147$$ 0.803848 0.0663002
$$148$$ −3.46410 + 12.9282i −0.284747 + 1.06269i
$$149$$ 7.83013 + 2.09808i 0.641469 + 0.171881i 0.564869 0.825181i $$-0.308927\pi$$
0.0766003 + 0.997062i $$0.475593\pi$$
$$150$$ −6.80385 6.80385i −0.555532 0.555532i
$$151$$ 0.633975 + 0.366025i 0.0515921 + 0.0297867i 0.525574 0.850748i $$-0.323851\pi$$
−0.473982 + 0.880534i $$0.657184\pi$$
$$152$$ 9.46410i 0.767640i
$$153$$ 8.59808 + 14.8923i 0.695113 + 1.20397i
$$154$$ −16.9282 −1.36411
$$155$$ −0.143594 0.535898i −0.0115337 0.0430444i
$$156$$ 11.6603 + 3.12436i 0.933567 + 0.250149i
$$157$$ 1.26795 4.73205i 0.101193 0.377659i −0.896692 0.442655i $$-0.854037\pi$$
0.997886 + 0.0649959i $$0.0207034\pi$$
$$158$$ −16.3923 4.39230i −1.30410 0.349433i
$$159$$ 4.73205 + 17.6603i 0.375276 + 1.40055i
$$160$$ 5.07180 + 2.92820i 0.400961 + 0.231495i
$$161$$ −12.9282 −1.01889
$$162$$ −12.2942 3.29423i −0.965926 0.258819i
$$163$$ −7.00000 7.00000i −0.548282 0.548282i 0.377661 0.925944i $$-0.376728\pi$$
−0.925944 + 0.377661i $$0.876728\pi$$
$$164$$ 3.00000 5.19615i 0.234261 0.405751i
$$165$$ 6.80385 + 3.92820i 0.529679 + 0.305810i
$$166$$ −1.00000 1.73205i −0.0776151 0.134433i
$$167$$ 6.46410 3.73205i 0.500207 0.288795i −0.228592 0.973522i $$-0.573412\pi$$
0.728799 + 0.684728i $$0.240079\pi$$
$$168$$ −12.9282 3.46410i −0.997433 0.267261i
$$169$$ 0.741670 + 0.428203i 0.0570515 + 0.0329387i
$$170$$ 8.39230i 0.643660i
$$171$$ −2.59808 + 9.69615i −0.198680 + 0.741483i
$$172$$ −12.1962 12.1962i −0.929948 0.929948i
$$173$$ 1.63397 0.437822i 0.124229 0.0332870i −0.196169 0.980570i $$-0.562850\pi$$
0.320398 + 0.947283i $$0.396183\pi$$
$$174$$ 6.00000 0.454859
$$175$$ −5.36603 9.29423i −0.405633 0.702578i
$$176$$ 16.9282 + 4.53590i 1.27601 + 0.341906i
$$177$$ 9.29423 9.29423i 0.698597 0.698597i
$$178$$ 2.73205 0.732051i 0.204776 0.0548695i
$$179$$ −1.92820 1.92820i −0.144121 0.144121i 0.631365 0.775486i $$-0.282495\pi$$
−0.775486 + 0.631365i $$0.782495\pi$$
$$180$$ 4.39230 + 4.39230i 0.327383 + 0.327383i
$$181$$ −7.39230 + 7.39230i −0.549466 + 0.549466i −0.926286 0.376821i $$-0.877017\pi$$
0.376821 + 0.926286i $$0.377017\pi$$
$$182$$ 11.6603 + 6.73205i 0.864316 + 0.499013i
$$183$$ 5.19615 19.3923i 0.384111 1.43352i
$$184$$ 12.9282 + 3.46410i 0.953080 + 0.255377i
$$185$$ 6.00000 3.46410i 0.441129 0.254686i
$$186$$ −0.339746 1.26795i −0.0249114 0.0929705i
$$187$$ −6.50000 24.2583i −0.475327 1.77394i
$$188$$ 15.3205i 1.11736i
$$189$$ −12.2942 7.09808i −0.894274 0.516309i
$$190$$ 3.46410 3.46410i 0.251312 0.251312i
$$191$$ −12.0263 + 20.8301i −0.870191 + 1.50722i −0.00839227 + 0.999965i $$0.502671\pi$$
−0.861799 + 0.507250i $$0.830662\pi$$
$$192$$ 12.0000 + 6.92820i 0.866025 + 0.500000i
$$193$$ −10.8660 18.8205i −0.782154 1.35473i −0.930685 0.365822i $$-0.880788\pi$$
0.148531 0.988908i $$-0.452545\pi$$
$$194$$ −16.0263 4.29423i −1.15062 0.308308i
$$195$$ −3.12436 5.41154i −0.223740 0.387529i
$$196$$ −0.803848 0.464102i −0.0574177 0.0331501i
$$197$$ 13.6603 13.6603i 0.973253 0.973253i −0.0263987 0.999651i $$-0.508404\pi$$
0.999651 + 0.0263987i $$0.00840394\pi$$
$$198$$ 16.0981 + 9.29423i 1.14404 + 0.660512i
$$199$$ 25.1244i 1.78102i 0.454965 + 0.890509i $$0.349652\pi$$
−0.454965 + 0.890509i $$0.650348\pi$$
$$200$$ 2.87564 + 10.7321i 0.203339 + 0.758871i
$$201$$ 8.36603 + 8.36603i 0.590094 + 0.590094i
$$202$$ −2.53590 + 1.46410i −0.178425 + 0.103014i
$$203$$ 6.46410 + 1.73205i 0.453691 + 0.121566i
$$204$$ 19.8564i 1.39023i
$$205$$ −3.00000 + 0.803848i −0.209529 + 0.0561432i
$$206$$ 15.1244 + 15.1244i 1.05376 + 1.05376i
$$207$$ 12.2942 + 7.09808i 0.854508 + 0.493350i
$$208$$ −9.85641 9.85641i −0.683419 0.683419i
$$209$$ 7.33013 12.6962i 0.507035 0.878211i
$$210$$ 3.46410 + 6.00000i 0.239046 + 0.414039i
$$211$$ −1.09808 + 4.09808i −0.0755947 + 0.282123i −0.993367 0.114983i $$-0.963319\pi$$
0.917773 + 0.397106i $$0.129985\pi$$
$$212$$ 5.46410 20.3923i 0.375276 1.40055i
$$213$$ 4.39230 + 2.53590i 0.300956 + 0.173757i
$$214$$ 21.6340 + 12.4904i 1.47887 + 0.853825i
$$215$$ 8.92820i 0.608898i
$$216$$ 10.3923 + 10.3923i 0.707107 + 0.707107i
$$217$$ 1.46410i 0.0993897i
$$218$$ −10.7321 + 18.5885i −0.726866 + 1.25897i
$$219$$ −9.40192 5.42820i −0.635323 0.366804i
$$220$$ −4.53590 7.85641i −0.305810 0.529679i
$$221$$ −5.16987 + 19.2942i −0.347763 + 1.29787i
$$222$$ 14.1962 8.19615i 0.952783 0.550090i
$$223$$ −8.02628 + 13.9019i −0.537479 + 0.930942i 0.461559 + 0.887109i $$0.347290\pi$$
−0.999039 + 0.0438324i $$0.986043\pi$$
$$224$$ 10.9282 + 10.9282i 0.730171 + 0.730171i
$$225$$ 11.7846i 0.785641i
$$226$$ 13.8564 13.8564i 0.921714 0.921714i
$$227$$ 2.13397 0.571797i 0.141637 0.0379515i −0.187304 0.982302i $$-0.559975\pi$$
0.328941 + 0.944351i $$0.393308\pi$$
$$228$$ 8.19615 8.19615i 0.542803 0.542803i
$$229$$ 6.83013 + 1.83013i 0.451347 + 0.120938i 0.477330 0.878724i $$-0.341605\pi$$
−0.0259823 + 0.999662i $$0.508271\pi$$
$$230$$ −3.46410 6.00000i −0.228416 0.395628i
$$231$$ 14.6603 + 14.6603i 0.964574 + 0.964574i
$$232$$ −6.00000 3.46410i −0.393919 0.227429i
$$233$$ 3.19615i 0.209387i −0.994505 0.104693i $$-0.966614\pi$$
0.994505 0.104693i $$-0.0333861\pi$$
$$234$$ −7.39230 12.8038i −0.483250 0.837014i
$$235$$ 5.60770 5.60770i 0.365806 0.365806i
$$236$$ −14.6603 + 3.92820i −0.954301 + 0.255704i
$$237$$ 10.3923 + 18.0000i 0.675053 + 1.16923i
$$238$$ 5.73205 21.3923i 0.371554 1.38666i
$$239$$ −7.90192 13.6865i −0.511133 0.885308i −0.999917 0.0129033i $$-0.995893\pi$$
0.488784 0.872405i $$-0.337441\pi$$
$$240$$ −1.85641 6.92820i −0.119831 0.447214i
$$241$$ −11.5981 + 20.0885i −0.747098 + 1.29401i 0.202110 + 0.979363i $$0.435220\pi$$
−0.949208 + 0.314649i $$0.898113\pi$$
$$242$$ −8.19615 8.19615i −0.526869 0.526869i
$$243$$ 7.79423 + 13.5000i 0.500000 + 0.866025i
$$244$$ −16.3923 + 16.3923i −1.04941 + 1.04941i
$$245$$ 0.124356 + 0.464102i 0.00794479 + 0.0296504i
$$246$$ −7.09808 + 1.90192i −0.452557 + 0.121262i
$$247$$ −10.0981 + 5.83013i −0.642525 + 0.370962i
$$248$$ −0.392305 + 1.46410i −0.0249114 + 0.0929705i
$$249$$ −0.633975 + 2.36603i −0.0401765 + 0.149941i
$$250$$ 6.53590 11.3205i 0.413367 0.715972i
$$251$$ −5.83013 + 5.83013i −0.367994 + 0.367994i −0.866745 0.498751i $$-0.833792\pi$$
0.498751 + 0.866745i $$0.333792\pi$$
$$252$$ 8.19615 + 14.1962i 0.516309 + 0.894274i
$$253$$ −14.6603 14.6603i −0.921682 0.921682i
$$254$$ 1.53590 + 5.73205i 0.0963708 + 0.359661i
$$255$$ −7.26795 + 7.26795i −0.455137 + 0.455137i
$$256$$ −8.00000 13.8564i −0.500000 0.866025i
$$257$$ 9.42820 + 16.3301i 0.588115 + 1.01865i 0.994479 + 0.104934i $$0.0334632\pi$$
−0.406364 + 0.913711i $$0.633204\pi$$
$$258$$ 21.1244i 1.31514i
$$259$$ 17.6603 4.73205i 1.09735 0.294035i
$$260$$ 7.21539i 0.447480i
$$261$$ −5.19615 5.19615i −0.321634 0.321634i
$$262$$ 11.4641 0.708255
$$263$$ −2.49038 1.43782i −0.153563 0.0886599i 0.421249 0.906945i $$-0.361592\pi$$
−0.574813 + 0.818285i $$0.694925\pi$$
$$264$$ −10.7321 18.5885i −0.660512 1.14404i
$$265$$ −9.46410 + 5.46410i −0.581375 + 0.335657i
$$266$$ 11.1962 6.46410i 0.686480 0.396339i
$$267$$ −3.00000 1.73205i −0.183597 0.106000i
$$268$$ −3.53590 13.1962i −0.215989 0.806083i
$$269$$ 1.26795 + 1.26795i 0.0773082 + 0.0773082i 0.744704 0.667395i $$-0.232591\pi$$
−0.667395 + 0.744704i $$0.732591\pi$$
$$270$$ 7.60770i 0.462990i
$$271$$ −0.392305 −0.0238308 −0.0119154 0.999929i $$-0.503793\pi$$
−0.0119154 + 0.999929i $$0.503793\pi$$
$$272$$ −11.4641 + 19.8564i −0.695113 + 1.20397i
$$273$$ −4.26795 15.9282i −0.258308 0.964019i
$$274$$ −3.49038 + 13.0263i −0.210862 + 0.786946i
$$275$$ 4.45448 16.6244i 0.268615 1.00249i
$$276$$ −8.19615 14.1962i −0.493350 0.854508i
$$277$$ −6.75833 25.2224i −0.406069 1.51547i −0.802076 0.597222i $$-0.796271\pi$$
0.396007 0.918247i $$-0.370395\pi$$
$$278$$ 16.7321i 1.00352i
$$279$$ −0.803848 + 1.39230i −0.0481251 + 0.0833551i
$$280$$ 8.00000i 0.478091i
$$281$$ −8.66025 5.00000i −0.516627 0.298275i 0.218926 0.975741i $$-0.429745\pi$$
−0.735554 + 0.677466i $$0.763078\pi$$
$$282$$ 13.2679 13.2679i 0.790095 0.790095i
$$283$$ −19.5622 5.24167i −1.16285 0.311585i −0.374747 0.927127i $$-0.622270\pi$$
−0.788104 + 0.615542i $$0.788937\pi$$
$$284$$ −2.92820 5.07180i −0.173757 0.300956i
$$285$$ −6.00000 −0.355409
$$286$$ 5.58846 + 20.8564i 0.330452 + 1.23327i
$$287$$ −8.19615 −0.483804
$$288$$ −4.39230 16.3923i −0.258819 0.965926i
$$289$$ 15.8564 0.932730
$$290$$ 0.928203 + 3.46410i 0.0545060 + 0.203419i
$$291$$ 10.1603 + 17.5981i 0.595605 + 1.03162i
$$292$$ 6.26795 + 10.8564i 0.366804 + 0.635323i
$$293$$ −5.36603 1.43782i −0.313487 0.0839985i 0.0986454 0.995123i $$-0.468549\pi$$
−0.412132 + 0.911124i $$0.635216\pi$$
$$294$$ 0.294229 + 1.09808i 0.0171598 + 0.0640411i
$$295$$ 6.80385 + 3.92820i 0.396135 + 0.228709i
$$296$$ −18.9282 −1.10018
$$297$$ −5.89230 21.9904i −0.341906 1.27601i
$$298$$ 11.4641i 0.664098i
$$299$$ 4.26795 + 15.9282i 0.246822 + 0.921152i
$$300$$ 6.80385 11.7846i 0.392820 0.680385i
$$301$$ −6.09808 + 22.7583i −0.351487 + 1.31177i
$$302$$ −0.267949 + 1.00000i −0.0154187 + 0.0575435i
$$303$$ 3.46410 + 0.928203i 0.199007 + 0.0533239i
$$304$$ −12.9282 + 3.46410i −0.741483 + 0.198680i
$$305$$ 12.0000 0.687118
$$306$$ −17.1962 + 17.1962i −0.983039 + 0.983039i
$$307$$ 3.02628 + 3.02628i 0.172719 + 0.172719i 0.788173 0.615454i $$-0.211027\pi$$
−0.615454 + 0.788173i $$0.711027\pi$$
$$308$$ −6.19615 23.1244i −0.353059 1.31763i
$$309$$ 26.1962i 1.49025i
$$310$$ 0.679492 0.392305i 0.0385925 0.0222814i
$$311$$ −19.0981 + 11.0263i −1.08295 + 0.625243i −0.931691 0.363251i $$-0.881667\pi$$
−0.151261 + 0.988494i $$0.548333\pi$$
$$312$$ 17.0718i 0.966500i
$$313$$ 18.6506 + 10.7679i 1.05420 + 0.608640i 0.923821 0.382824i $$-0.125049\pi$$
0.130375 + 0.991465i $$0.458382\pi$$
$$314$$ 6.92820 0.390981
$$315$$ 2.19615 8.19615i 0.123739 0.461801i
$$316$$ 24.0000i 1.35011i
$$317$$ −20.5622 + 5.50962i −1.15489 + 0.309451i −0.784922 0.619595i $$-0.787297\pi$$
−0.369965 + 0.929046i $$0.620630\pi$$
$$318$$ −22.3923 + 12.9282i −1.25570 + 0.724978i
$$319$$ 5.36603 + 9.29423i 0.300440 + 0.520377i
$$320$$ −2.14359 + 8.00000i −0.119831 + 0.447214i
$$321$$ −7.91858 29.5526i −0.441972 1.64946i
$$322$$ −4.73205 17.6603i −0.263707 0.984167i
$$323$$ 13.5622 + 13.5622i 0.754620 + 0.754620i
$$324$$ 18.0000i 1.00000i
$$325$$ −9.67949 + 9.67949i −0.536922 + 0.536922i
$$326$$ 7.00000 12.1244i 0.387694 0.671506i
$$327$$ 25.3923 6.80385i 1.40420 0.376254i
$$328$$ 8.19615 + 2.19615i 0.452557 + 0.121262i
$$329$$ 18.1244 10.4641i 0.999228 0.576905i
$$330$$ −2.87564 + 10.7321i −0.158299 + 0.590780i
$$331$$ 0.0262794 + 0.0980762i 0.00144445 + 0.00539076i 0.966644 0.256123i $$-0.0824451\pi$$
−0.965200 + 0.261513i $$0.915778\pi$$
$$332$$ 2.00000 2.00000i 0.109764 0.109764i
$$333$$ −19.3923 5.19615i −1.06269 0.284747i
$$334$$ 7.46410 + 7.46410i 0.408417 + 0.408417i
$$335$$ −3.53590 + 6.12436i −0.193187 + 0.334609i
$$336$$ 18.9282i 1.03262i
$$337$$ 8.89230 + 15.4019i 0.484395 + 0.838996i 0.999839 0.0179267i $$-0.00570654\pi$$
−0.515445 + 0.856923i $$0.672373\pi$$
$$338$$ −0.313467 + 1.16987i −0.0170503 + 0.0636327i
$$339$$ −24.0000 −1.30350
$$340$$ 11.4641 3.07180i 0.621728 0.166592i
$$341$$ 1.66025 1.66025i 0.0899078 0.0899078i
$$342$$ −14.1962 −0.767640
$$343$$ 17.8564i 0.964155i
$$344$$ 12.1962 21.1244i 0.657572 1.13895i
$$345$$ −2.19615 + 8.19615i −0.118237 + 0.441266i
$$346$$ 1.19615 + 2.07180i 0.0643056 + 0.111380i
$$347$$ −17.6244 4.72243i −0.946125 0.253513i −0.247408 0.968911i $$-0.579579\pi$$
−0.698717 + 0.715398i $$0.746245\pi$$
$$348$$ 2.19615 + 8.19615i 0.117726 + 0.439360i
$$349$$ 15.9282 4.26795i 0.852617 0.228458i 0.194061 0.980989i $$-0.437834\pi$$
0.658556 + 0.752531i $$0.271167\pi$$
$$350$$ 10.7321 10.7321i 0.573652 0.573652i
$$351$$ −4.68653 + 17.4904i −0.250149 + 0.933567i
$$352$$ 24.7846i 1.32102i
$$353$$ 7.16025 12.4019i 0.381102 0.660088i −0.610118 0.792310i $$-0.708878\pi$$
0.991220 + 0.132223i $$0.0422114\pi$$
$$354$$ 16.0981 + 9.29423i 0.855603 + 0.493983i
$$355$$ −0.784610 + 2.92820i −0.0416428 + 0.155413i
$$356$$ 2.00000 + 3.46410i 0.106000 + 0.183597i
$$357$$ −23.4904 + 13.5622i −1.24324 + 0.717787i
$$358$$ 1.92820 3.33975i 0.101909 0.176511i
$$359$$ 11.2679i 0.594700i 0.954769 + 0.297350i $$0.0961028\pi$$
−0.954769 + 0.297350i $$0.903897\pi$$
$$360$$ −4.39230 + 7.60770i −0.231495 + 0.400961i
$$361$$ 7.80385i 0.410729i
$$362$$ −12.8038 7.39230i −0.672955 0.388531i
$$363$$ 14.1962i 0.745105i
$$364$$ −4.92820 + 18.3923i −0.258308 + 0.964019i
$$365$$ 1.67949 6.26795i 0.0879086 0.328079i
$$366$$ 28.3923 1.48409
$$367$$ 14.1244 24.4641i 0.737285 1.27702i −0.216428 0.976299i $$-0.569441\pi$$
0.953713 0.300717i $$-0.0972260\pi$$
$$368$$ 18.9282i 0.986701i
$$369$$ 7.79423 + 4.50000i 0.405751 + 0.234261i
$$370$$ 6.92820 + 6.92820i 0.360180 + 0.360180i
$$371$$ −27.8564 + 7.46410i −1.44623 + 0.387517i
$$372$$ 1.60770 0.928203i 0.0833551 0.0481251i
$$373$$ 27.4904 + 7.36603i 1.42340 + 0.381398i 0.886688 0.462368i $$-0.153000\pi$$
0.536710 + 0.843767i $$0.319667\pi$$
$$374$$ 30.7583 17.7583i 1.59048 0.918261i
$$375$$ −15.4641 + 4.14359i −0.798563 + 0.213974i
$$376$$ −20.9282 + 5.60770i −1.07929 + 0.289195i
$$377$$ 8.53590i 0.439621i
$$378$$ 5.19615 19.3923i 0.267261 0.997433i
$$379$$ 3.75833 3.75833i 0.193052 0.193052i −0.603961 0.797014i $$-0.706412\pi$$
0.797014 + 0.603961i $$0.206412\pi$$
$$380$$ 6.00000 + 3.46410i 0.307794 + 0.177705i
$$381$$ 3.63397 6.29423i 0.186174 0.322463i
$$382$$ −32.8564 8.80385i −1.68108 0.450444i
$$383$$ −6.73205 11.6603i −0.343992 0.595811i 0.641178 0.767392i $$-0.278446\pi$$
−0.985170 + 0.171581i $$0.945113\pi$$
$$384$$ −5.07180 + 18.9282i −0.258819 + 0.965926i
$$385$$ −6.19615 + 10.7321i −0.315785 + 0.546956i
$$386$$ 21.7321 21.7321i 1.10613 1.10613i
$$387$$ 18.2942 18.2942i 0.929948 0.929948i
$$388$$ 23.4641i 1.19121i
$$389$$ −5.29423 19.7583i −0.268428 1.00179i −0.960119 0.279593i $$-0.909800\pi$$
0.691691 0.722194i $$-0.256866\pi$$
$$390$$ 6.24871 6.24871i 0.316416 0.316416i
$$391$$ 23.4904 13.5622i 1.18796 0.685869i
$$392$$ 0.339746 1.26795i 0.0171598 0.0640411i
$$393$$ −9.92820 9.92820i −0.500812 0.500812i
$$394$$ 23.6603 + 13.6603i 1.19199 + 0.688194i
$$395$$ −8.78461 + 8.78461i −0.442002 + 0.442002i
$$396$$ −6.80385 + 25.3923i −0.341906 + 1.27601i
$$397$$ −9.26795 9.26795i −0.465145 0.465145i 0.435192 0.900337i $$-0.356680\pi$$
−0.900337 + 0.435192i $$0.856680\pi$$
$$398$$ −34.3205 + 9.19615i −1.72033 + 0.460961i
$$399$$ −15.2942 4.09808i −0.765669 0.205160i
$$400$$ −13.6077 + 7.85641i −0.680385 + 0.392820i
$$401$$ −1.79423 3.10770i −0.0895995 0.155191i 0.817742 0.575584i $$-0.195225\pi$$
−0.907342 + 0.420393i $$0.861892\pi$$
$$402$$ −8.36603 + 14.4904i −0.417259 + 0.722715i
$$403$$ −1.80385 + 0.483340i −0.0898560 + 0.0240769i
$$404$$ −2.92820 2.92820i −0.145684 0.145684i
$$405$$ −6.58846 + 6.58846i −0.327383 + 0.327383i
$$406$$ 9.46410i 0.469695i
$$407$$ 25.3923 + 14.6603i 1.25865 + 0.726682i
$$408$$ 27.1244 7.26795i 1.34286 0.359817i
$$409$$ 27.8660 16.0885i 1.37789 0.795523i 0.385981 0.922507i $$-0.373863\pi$$
0.991905 + 0.126984i $$0.0405295\pi$$
$$410$$ −2.19615 3.80385i −0.108460 0.187859i
$$411$$ 14.3038 8.25833i 0.705557 0.407353i
$$412$$ −15.1244 + 26.1962i −0.745124 + 1.29059i
$$413$$ 14.6603 + 14.6603i 0.721384 + 0.721384i
$$414$$ −5.19615 + 19.3923i −0.255377 + 0.953080i
$$415$$ −1.46410 −0.0718699
$$416$$ 9.85641 17.0718i 0.483250 0.837014i
$$417$$ −14.4904 + 14.4904i −0.709597 + 0.709597i
$$418$$ 20.0263 + 5.36603i 0.979517 + 0.262461i
$$419$$ 1.77757 6.63397i 0.0868399 0.324091i −0.908816 0.417196i $$-0.863013\pi$$
0.995656 + 0.0931055i $$0.0296794\pi$$
$$420$$ −6.92820 + 6.92820i −0.338062 + 0.338062i
$$421$$ 8.19615 + 30.5885i 0.399456 + 1.49079i 0.814056 + 0.580786i $$0.197255\pi$$
−0.414600 + 0.910004i $$0.636078\pi$$
$$422$$ −6.00000 −0.292075
$$423$$ −22.9808 −1.11736
$$424$$ 29.8564 1.44996
$$425$$ 19.5000 + 11.2583i 0.945889 + 0.546109i
$$426$$ −1.85641 + 6.92820i −0.0899432 + 0.335673i
$$427$$ 30.5885 + 8.19615i 1.48028 + 0.396640i
$$428$$ −9.14359 + 34.1244i −0.441972 + 1.64946i
$$429$$ 13.2224 22.9019i 0.638385 1.10572i
$$430$$ −12.1962 + 3.26795i −0.588151 + 0.157595i
$$431$$ −16.1962 −0.780141 −0.390071 0.920785i $$-0.627549\pi$$
−0.390071 + 0.920785i $$0.627549\pi$$
$$432$$ −10.3923 + 18.0000i −0.500000 + 0.866025i
$$433$$ −5.73205 −0.275465 −0.137732 0.990469i $$-0.543981\pi$$
−0.137732 + 0.990469i $$0.543981\pi$$
$$434$$ 2.00000 0.535898i 0.0960031 0.0257239i
$$435$$ 2.19615 3.80385i 0.105297 0.182381i
$$436$$ −29.3205 7.85641i −1.40420 0.376254i
$$437$$ 15.2942 + 4.09808i 0.731622 + 0.196038i
$$438$$ 3.97372 14.8301i 0.189872 0.708611i
$$439$$ −22.8564 13.1962i −1.09088 0.629818i −0.157067 0.987588i $$-0.550204\pi$$
−0.933810 + 0.357770i $$0.883537\pi$$
$$440$$ 9.07180 9.07180i 0.432481 0.432481i
$$441$$ 0.696152 1.20577i 0.0331501 0.0574177i
$$442$$ −28.2487 −1.34365
$$443$$ −4.62436 17.2583i −0.219710 0.819968i −0.984455 0.175636i $$-0.943802\pi$$
0.764745 0.644332i $$-0.222865\pi$$
$$444$$ 16.3923 + 16.3923i 0.777944 + 0.777944i
$$445$$ 0.535898 2.00000i 0.0254040 0.0948091i
$$446$$ −21.9282 5.87564i −1.03833 0.278220i
$$447$$ 9.92820 9.92820i 0.469588 0.469588i
$$448$$ −10.9282 + 18.9282i −0.516309 + 0.894274i
$$449$$ −3.33975 −0.157612 −0.0788062 0.996890i $$-0.525111\pi$$
−0.0788062 + 0.996890i $$0.525111\pi$$
$$450$$ −16.0981 + 4.31347i −0.758871 + 0.203339i
$$451$$ −9.29423 9.29423i −0.437648 0.437648i
$$452$$ 24.0000 + 13.8564i 1.12887 + 0.651751i
$$453$$ 1.09808 0.633975i 0.0515921 0.0297867i
$$454$$ 1.56218 + 2.70577i 0.0733166 + 0.126988i
$$455$$ 8.53590 4.92820i 0.400169 0.231038i
$$456$$ 14.1962 + 8.19615i 0.664796 + 0.383820i
$$457$$ 2.25833 + 1.30385i 0.105640 + 0.0609914i 0.551889 0.833917i $$-0.313907\pi$$
−0.446249 + 0.894909i $$0.647240\pi$$
$$458$$ 10.0000i 0.467269i
$$459$$ 29.7846 1.39023
$$460$$ 6.92820 6.92820i 0.323029 0.323029i
$$461$$ 35.6865 9.56218i 1.66209 0.445355i 0.699127 0.714997i $$-0.253572\pi$$
0.962961 + 0.269642i $$0.0869055\pi$$
$$462$$ −14.6603 + 25.3923i −0.682057 + 1.18136i
$$463$$ 1.19615 + 2.07180i 0.0555899 + 0.0962846i 0.892481 0.451085i $$-0.148963\pi$$
−0.836891 + 0.547369i $$0.815629\pi$$
$$464$$ 2.53590 9.46410i 0.117726 0.439360i
$$465$$ −0.928203 0.248711i −0.0430444 0.0115337i
$$466$$ 4.36603 1.16987i 0.202252 0.0541933i
$$467$$ 2.63397 + 2.63397i 0.121886 + 0.121886i 0.765419 0.643533i $$-0.222532\pi$$
−0.643533 + 0.765419i $$0.722532\pi$$
$$468$$ 14.7846 14.7846i 0.683419 0.683419i
$$469$$ −13.1962 + 13.1962i −0.609342 + 0.609342i
$$470$$ 9.71281 + 5.60770i 0.448019 + 0.258664i
$$471$$ −6.00000 6.00000i −0.276465 0.276465i
$$472$$ −10.7321 18.5885i −0.493983 0.855603i
$$473$$ −32.7224 + 18.8923i −1.50458 + 0.868669i
$$474$$ −20.7846 + 20.7846i −0.954669 + 0.954669i
$$475$$ 3.40192 + 12.6962i 0.156091 + 0.582539i
$$476$$ 31.3205 1.43557
$$477$$ 30.5885 + 8.19615i 1.40055 + 0.375276i
$$478$$ 15.8038 15.8038i 0.722851 0.722851i
$$479$$ 4.16987 7.22243i 0.190526 0.330001i −0.754898 0.655842i $$-0.772314\pi$$
0.945425 + 0.325840i $$0.105647\pi$$
$$480$$ 8.78461 5.07180i 0.400961 0.231495i
$$481$$ −11.6603 20.1962i −0.531662 0.920865i
$$482$$ −31.6865 8.49038i −1.44328 0.386726i
$$483$$ −11.1962 + 19.3923i −0.509443 + 0.882380i
$$484$$ 8.19615 14.1962i 0.372552 0.645280i
$$485$$ −8.58846 + 8.58846i −0.389982 + 0.389982i
$$486$$ −15.5885 + 15.5885i −0.707107 + 0.707107i
$$487$$ 5.80385i 0.262997i 0.991316 + 0.131499i $$0.0419789\pi$$
−0.991316 + 0.131499i $$0.958021\pi$$
$$488$$ −28.3923 16.3923i −1.28526 0.742045i
$$489$$ −16.5622 + 4.43782i −0.748968 + 0.200685i
$$490$$ −0.588457 + 0.339746i −0.0265838 + 0.0153482i
$$491$$ −13.8923 3.72243i −0.626951 0.167991i −0.0686652 0.997640i $$-0.521874\pi$$
−0.558286 + 0.829649i $$0.688541\pi$$
$$492$$ −5.19615 9.00000i −0.234261 0.405751i
$$493$$ −13.5622 + 3.63397i −0.610810 + 0.163666i
$$494$$ −11.6603 11.6603i −0.524620 0.524620i
$$495$$ 11.7846 6.80385i 0.529679 0.305810i
$$496$$ −2.14359 −0.0962502
$$497$$ −4.00000 + 6.92820i −0.179425 + 0.310772i
$$498$$ −3.46410 −0.155230
$$499$$ −2.33013 + 8.69615i −0.104311 + 0.389293i −0.998266 0.0588630i $$-0.981252\pi$$
0.893955 + 0.448156i $$0.147919\pi$$
$$500$$ 17.8564 + 4.78461i 0.798563 + 0.213974i
$$501$$ 12.9282i 0.577590i
$$502$$ −10.0981 5.83013i −0.450699 0.260211i
$$503$$ 27.7128i 1.23565i −0.786314 0.617827i $$-0.788013\pi$$
0.786314 0.617827i $$-0.211987\pi$$
$$504$$ −16.3923 + 16.3923i −0.730171 + 0.730171i
$$505$$ 2.14359i 0.0953887i
$$506$$ 14.6603 25.3923i 0.651728 1.12883i
$$507$$ 1.28461 0.741670i 0.0570515 0.0329387i
$$508$$ −7.26795 + 4.19615i −0.322463 + 0.186174i
$$509$$ 3.07180 11.4641i 0.136155 0.508137i −0.863835 0.503774i $$-0.831944\pi$$
0.999990 0.00436335i $$-0.00138890\pi$$
$$510$$ −12.5885 7.26795i −0.557426 0.321830i
$$511$$ 8.56218 14.8301i 0.378768 0.656046i
$$512$$ 16.0000 16.0000i 0.707107 0.707107i
$$513$$ 12.2942 + 12.2942i 0.542803 + 0.542803i
$$514$$ −18.8564 + 18.8564i −0.831720 + 0.831720i
$$515$$ 15.1244 4.05256i 0.666459 0.178577i
$$516$$ −28.8564 + 7.73205i −1.27033 + 0.340385i
$$517$$ 32.4186 + 8.68653i 1.42577 + 0.382033i
$$518$$ 12.9282 + 22.3923i 0.568033 + 0.983861i
$$519$$ 0.758330 2.83013i 0.0332870 0.124229i
$$520$$ −9.85641 + 2.64102i −0.432232 + 0.115816i
$$521$$ 13.0000i 0.569540i 0.958596 + 0.284770i $$0.0919173\pi$$
−0.958596 + 0.284770i $$0.908083\pi$$
$$522$$ 5.19615 9.00000i 0.227429 0.393919i
$$523$$ −7.53590 + 7.53590i −0.329522 + 0.329522i −0.852405 0.522883i $$-0.824857\pi$$
0.522883 + 0.852405i $$0.324857\pi$$
$$524$$ 4.19615 + 15.6603i 0.183310 + 0.684121i
$$525$$ −18.5885 −0.811267
$$526$$ 1.05256 3.92820i 0.0458937 0.171278i
$$527$$ 1.53590 + 2.66025i 0.0669048 + 0.115882i
$$528$$ 21.4641 21.4641i 0.934105 0.934105i
$$529$$ −0.303848 + 0.526279i −0.0132108 + 0.0228817i
$$530$$ −10.9282 10.9282i −0.474691 0.474691i
$$531$$ −5.89230 21.9904i −0.255704 0.954301i
$$532$$ 12.9282 + 12.9282i 0.560509 + 0.560509i
$$533$$ 2.70577 + 10.0981i 0.117200 + 0.437396i
$$534$$ 1.26795 4.73205i 0.0548695 0.204776i
$$535$$ 15.8372 9.14359i 0.684701 0.395312i
$$536$$ 16.7321 9.66025i 0.722715 0.417259i
$$537$$ −4.56218 + 1.22243i −0.196873 + 0.0527518i
$$538$$ −1.26795 + 2.19615i −0.0546652 + 0.0946829i
$$539$$ −1.43782 + 1.43782i −0.0619314 + 0.0619314i
$$540$$ 10.3923 2.78461i 0.447214 0.119831i
$$541$$ 2.19615 + 2.19615i 0.0944200 + 0.0944200i 0.752739 0.658319i $$-0.228732\pi$$
−0.658319 + 0.752739i $$0.728732\pi$$
$$542$$ −0.143594 0.535898i −0.00616787 0.0230188i
$$543$$ 4.68653 + 17.4904i 0.201118 + 0.750584i
$$544$$ −31.3205 8.39230i −1.34286 0.359817i
$$545$$ 7.85641 + 13.6077i 0.336531 + 0.582890i
$$546$$ 20.1962 11.6603i 0.864316 0.499013i
$$547$$ 32.6244 8.74167i 1.39492 0.373767i 0.518400 0.855138i $$-0.326528\pi$$
0.876517 + 0.481371i $$0.159861\pi$$
$$548$$ −19.0718 −0.814707
$$549$$ −24.5885 24.5885i −1.04941 1.04941i
$$550$$ 24.3397 1.03785
$$551$$ −7.09808 4.09808i −0.302388 0.174584i
$$552$$ 16.3923 16.3923i 0.697703 0.697703i
$$553$$ −28.3923 + 16.3923i −1.20736 + 0.697072i
$$554$$ 31.9808 18.4641i 1.35873 0.784465i
$$555$$ 12.0000i 0.509372i
$$556$$ 22.8564 6.12436i 0.969328 0.259731i
$$557$$ −14.8038 14.8038i −0.627259 0.627259i 0.320118 0.947378i $$-0.396277\pi$$
−0.947378 + 0.320118i $$0.896277\pi$$
$$558$$ −2.19615 0.588457i −0.0929705 0.0249114i
$$559$$ 30.0526 1.27109
$$560$$ 10.9282 2.92820i 0.461801 0.123739i
$$561$$ −42.0167 11.2583i −1.77394 0.475327i
$$562$$ 3.66025 13.6603i 0.154398 0.576223i
$$563$$ −7.23205 + 26.9904i −0.304795 + 1.13751i 0.628327 + 0.777949i $$0.283740\pi$$
−0.933122 + 0.359560i $$0.882927\pi$$
$$564$$ 22.9808 + 13.2679i 0.967665 + 0.558681i
$$565$$ −3.71281 13.8564i −0.156199 0.582943i
$$566$$ 28.6410i 1.20387i
$$567$$ −21.2942 + 12.2942i −0.894274 + 0.516309i
$$568$$ 5.85641 5.85641i 0.245729 0.245729i
$$569$$ −18.4019 10.6244i −0.771449 0.445396i 0.0619424 0.998080i $$-0.480270\pi$$
−0.833391 + 0.552684i $$0.813604\pi$$
$$570$$ −2.19615 8.19615i −0.0919867 0.343299i
$$571$$ −3.33013 0.892305i −0.139361 0.0373418i 0.188464 0.982080i $$-0.439649\pi$$
−0.327825 + 0.944738i $$0.606316\pi$$
$$572$$ −26.4449 + 15.2679i −1.10572 + 0.638385i
$$573$$ 20.8301 + 36.0788i 0.870191 + 1.50722i
$$574$$ −3.00000 11.1962i −0.125218 0.467318i
$$575$$ 18.5885 0.775192
$$576$$ 20.7846 12.0000i 0.866025 0.500000i
$$577$$ −5.78461 −0.240816 −0.120408 0.992724i $$-0.538420\pi$$
−0.120408 + 0.992724i $$0.538420\pi$$
$$578$$ 5.80385 + 21.6603i 0.241408 + 0.900948i
$$579$$ −37.6410 −1.56431
$$580$$ −4.39230 + 2.53590i −0.182381 + 0.105297i
$$581$$ −3.73205 1.00000i −0.154832 0.0414870i
$$582$$ −20.3205 + 20.3205i −0.842312 + 0.842312i
$$583$$ −40.0526 23.1244i −1.65881 0.957713i
$$584$$ −12.5359 + 12.5359i −0.518739 + 0.518739i
$$585$$ −10.8231 −0.447480
$$586$$ 7.85641i 0.324545i
$$587$$ 7.23205 + 26.9904i 0.298499 + 1.11401i 0.938399 + 0.345554i $$0.112309\pi$$
−0.639900 + 0.768458i $$0.721024\pi$$
$$588$$ −1.39230 + 0.803848i −0.0574177 + 0.0331501i
$$589$$ −0.464102 + 1.73205i −0.0191230 + 0.0713679i
$$590$$ −2.87564 + 10.7321i −0.118388 + 0.441832i
$$591$$ −8.66025 32.3205i −0.356235 1.32949i
$$592$$ −6.92820 25.8564i −0.284747 1.06269i
$$593$$ 17.4641 0.717165 0.358582 0.933498i $$-0.383260\pi$$
0.358582 + 0.933498i $$0.383260\pi$$
$$594$$ 27.8827 16.0981i 1.14404 0.660512i
$$595$$ −11.4641 11.4641i −0.469982 0.469982i
$$596$$ −15.6603 + 4.19615i −0.641469 + 0.171881i
$$597$$ 37.6865 + 21.7583i 1.54241 + 0.890509i
$$598$$ −20.1962 + 11.6603i −0.825882 + 0.476823i
$$599$$ 11.3205 6.53590i 0.462543 0.267050i −0.250570 0.968099i $$-0.580618\pi$$
0.713113 + 0.701049i $$0.247285\pi$$
$$600$$ 18.5885 + 4.98076i 0.758871 + 0.203339i
$$601$$ −20.5526 11.8660i −0.838356 0.484025i 0.0183488 0.999832i $$-0.494159\pi$$
−0.856705 + 0.515806i $$0.827492\pi$$
$$602$$ −33.3205 −1.35804
$$603$$ 19.7942 5.30385i 0.806083 0.215989i
$$604$$ −1.46410 −0.0595734
$$605$$ −8.19615 + 2.19615i −0.333221 + 0.0892863i
$$606$$ 5.07180i 0.206028i
$$607$$ −8.58846 14.8756i −0.348595 0.603784i 0.637405 0.770529i $$-0.280008\pi$$
−0.986000 + 0.166745i $$0.946674\pi$$
$$608$$ −9.46410 16.3923i −0.383820 0.664796i
$$609$$ 8.19615 8.19615i 0.332125 0.332125i
$$610$$ 4.39230 + 16.3923i 0.177839 + 0.663705i
$$611$$ −18.8756 18.8756i −0.763627 0.763627i
$$612$$ −29.7846 17.1962i −1.20397 0.695113i
$$613$$ −15.6603 + 15.6603i −0.632512 + 0.632512i −0.948697 0.316186i $$-0.897598\pi$$
0.316186 + 0.948697i $$0.397598\pi$$
$$614$$ −3.02628 + 5.24167i −0.122131 + 0.211537i
$$615$$ −1.39230 + 5.19615i −0.0561432 + 0.209529i
$$616$$ 29.3205 16.9282i 1.18136 0.682057i
$$617$$ −35.0885 + 20.2583i −1.41261 + 0.815570i −0.995633 0.0933485i $$-0.970243\pi$$
−0.416975 + 0.908918i $$0.636910\pi$$
$$618$$ 35.7846 9.58846i 1.43947 0.385704i
$$619$$ 4.17949 + 15.5981i 0.167988 + 0.626940i 0.997640 + 0.0686590i $$0.0218721\pi$$
−0.829652 + 0.558281i $$0.811461\pi$$
$$620$$ 0.784610 + 0.784610i 0.0315107 + 0.0315107i
$$621$$ 21.2942 12.2942i 0.854508 0.493350i
$$622$$ −22.0526 22.0526i −0.884227 0.884227i
$$623$$ 2.73205 4.73205i 0.109457 0.189586i
$$624$$ −23.3205 + 6.24871i −0.933567 + 0.250149i
$$625$$ 5.03590 + 8.72243i 0.201436 + 0.348897i
$$626$$ −7.88269 + 29.4186i −0.315055 + 1.17580i
$$627$$ −12.6962 21.9904i −0.507035 0.878211i
$$628$$ 2.53590 + 9.46410i 0.101193 + 0.377659i
$$629$$ −27.1244 + 27.1244i −1.08152 + 1.08152i
$$630$$ 12.0000 0.478091
$$631$$ 17.6077i 0.700951i 0.936572 + 0.350476i $$0.113980\pi$$
−0.936572 + 0.350476i $$0.886020\pi$$
$$632$$ 32.7846 8.78461i 1.30410 0.349433i
$$633$$ 5.19615 + 5.19615i 0.206529 + 0.206529i
$$634$$ −15.0526 26.0718i −0.597813 1.03544i
$$635$$ 4.19615 + 1.12436i 0.166519 + 0.0446187i
$$636$$ −25.8564 25.8564i −1.02527 1.02527i
$$637$$ 1.56218 0.418584i 0.0618957 0.0165849i
$$638$$ −10.7321 + 10.7321i −0.424886 + 0.424886i
$$639$$ 7.60770 4.39230i 0.300956 0.173757i
$$640$$ −11.7128 −0.462990
$$641$$ −19.7942 + 34.2846i −0.781825 + 1.35416i 0.149053 + 0.988829i $$0.452378\pi$$
−0.930878 + 0.365331i $$0.880956\pi$$
$$642$$ 37.4711 21.6340i 1.47887 0.853825i
$$643$$ −2.34936 + 8.76795i −0.0926499 + 0.345774i −0.996653 0.0817525i $$-0.973948\pi$$
0.904003 + 0.427527i $$0.140615\pi$$
$$644$$ 22.3923 12.9282i 0.882380 0.509443i
$$645$$ 13.3923 + 7.73205i 0.527321 + 0.304449i
$$646$$ −13.5622 + 23.4904i −0.533597 + 0.924217i
$$647$$ 16.7321i 0.657805i 0.944364 + 0.328902i $$0.106679\pi$$
−0.944364 + 0.328902i $$0.893321\pi$$
$$648$$ 24.5885 6.58846i 0.965926 0.258819i
$$649$$ 33.2487i 1.30513i
$$650$$ −16.7654 9.67949i −0.657592 0.379661i
$$651$$ −2.19615 1.26795i −0.0860740 0.0496948i
$$652$$ 19.1244 + 5.12436i 0.748968 + 0.200685i
$$653$$ 7.36603 27.4904i 0.288255 1.07578i −0.658173 0.752867i $$-0.728671\pi$$
0.946428 0.322915i $$-0.104663\pi$$
$$654$$ 18.5885 + 32.1962i 0.726866 + 1.25897i
$$655$$ 4.19615 7.26795i 0.163957 0.283982i
$$656$$ 12.0000i 0.468521i
$$657$$ −16.2846 + 9.40192i −0.635323 + 0.366804i
$$658$$ 20.9282 + 20.9282i 0.815866 + 0.815866i
$$659$$ −15.0263 + 4.02628i −0.585341 + 0.156842i −0.539323 0.842099i $$-0.681320\pi$$
−0.0460178 + 0.998941i $$0.514653\pi$$
$$660$$ −15.7128 −0.611620
$$661$$ −8.19615 2.19615i −0.318793 0.0854204i 0.0958740 0.995393i $$-0.469435\pi$$
−0.414667 + 0.909973i $$0.636102\pi$$
$$662$$ −0.124356 + 0.0717968i −0.00483322 + 0.00279046i
$$663$$ 24.4641 + 24.4641i 0.950107 + 0.950107i
$$664$$ 3.46410 + 2.00000i 0.134433 + 0.0776151i
$$665$$ 9.46410i 0.367002i
$$666$$ 28.3923i 1.10018i
$$667$$ −8.19615 + 8.19615i −0.317356 + 0.317356i
$$668$$ −7.46410 + 12.9282i −0.288795 + 0.500207i
$$669$$ 13.9019 + 24.0788i 0.537479 + 0.930942i
$$670$$ −9.66025 2.58846i −0.373208 0.100001i
$$671$$ 25.3923 + 43.9808i 0.980259 + 1.69786i
$$672$$ 25.8564 6.92820i 0.997433 0.267261i
$$673$$ 19.1962 33.2487i 0.739957 1.28164i −0.212557 0.977149i $$-0.568179\pi$$
0.952514 0.304495i $$-0.0984877\pi$$
$$674$$ −17.7846 + 17.7846i −0.685038 + 0.685038i
$$675$$ 17.6769 + 10.2058i 0.680385 + 0.392820i
$$676$$ −1.71281 −0.0658774
$$677$$ 1.26795 + 4.73205i 0.0487312 + 0.181867i 0.986002 0.166736i $$-0.0533227\pi$$
−0.937270 + 0.348603i $$0.886656\pi$$
$$678$$ −8.78461 32.7846i −0.337371 1.25909i
$$679$$ −27.7583 + 16.0263i −1.06527 + 0.615032i
$$680$$ 8.39230 + 14.5359i 0.321830 + 0.557426i
$$681$$ 0.990381 3.69615i 0.0379515 0.141637i
$$682$$ 2.87564 + 1.66025i 0.110114 + 0.0635744i
$$683$$ −20.2942 + 20.2942i −0.776537 + 0.776537i −0.979240 0.202703i $$-0.935027\pi$$
0.202703 + 0.979240i $$0.435027\pi$$
$$684$$ −5.19615 19.3923i −0.198680 0.741483i
$$685$$ 6.98076 + 6.98076i 0.266721 + 0.266721i
$$686$$ 24.3923 6.53590i 0.931303 0.249542i
$$687$$ 8.66025 8.66025i 0.330409 0.330409i
$$688$$ 33.3205 + 8.92820i 1.27033 + 0.340385i
$$689$$ 18.3923 + 31.8564i 0.700691 + 1.21363i
$$690$$ −12.0000 −0.456832
$$691$$ 9.29423 2.49038i 0.353569 0.0947386i −0.0776628 0.996980i $$-0.524746\pi$$
0.431232 + 0.902241i $$0.358079\pi$$
$$692$$ −2.39230 + 2.39230i −0.0909418 + 0.0909418i
$$693$$ 34.6865 9.29423i 1.31763 0.353059i
$$694$$ 25.8038i 0.979501i
$$695$$ −10.6077 6.12436i −0.402373 0.232310i
$$696$$ −10.3923 + 6.00000i −0.393919 + 0.227429i
$$697$$ 14.8923 8.59808i 0.564086 0.325675i
$$698$$ 11.6603 + 20.1962i 0.441347 + 0.764436i
$$699$$ −4.79423 2.76795i −0.181334 0.104693i
$$700$$ 18.5885 + 10.7321i 0.702578 + 0.405633i
$$701$$ −6.66025 6.66025i −0.251554 0.251554i 0.570053 0.821608i $$-0.306923\pi$$
−0.821608 + 0.570053i $$0.806923\pi$$
$$702$$ −25.6077 −0.966500
$$703$$ −22.3923 −0.844542
$$704$$ −33.8564 + 9.07180i −1.27601 + 0.341906i
$$705$$ −3.55514 13.2679i −0.133894 0.499700i
$$706$$ 19.5622 + 5.24167i 0.736232 + 0.197273i
$$707$$ −1.46410 + 5.46410i −0.0550632 + 0.205499i
$$708$$ −6.80385 + 25.3923i −0.255704 + 0.954301i
$$709$$ −9.80385 36.5885i −0.368191 1.37411i −0.863043 0.505131i $$-0.831444\pi$$
0.494852 0.868978i $$-0.335222\pi$$
$$710$$ −4.28719 −0.160895
$$711$$ 36.0000 1.35011
$$712$$ −4.00000 + 4.00000i −0.149906 + 0.149906i
$$713$$ 2.19615 + 1.26795i 0.0822466 + 0.0474851i
$$714$$ −27.1244 27.1244i −1.01510 1.01510i
$$715$$ 15.2679 + 4.09103i 0.570989 + 0.152996i
$$716$$ 5.26795 + 1.41154i 0.196873 + 0.0527518i
$$717$$ −27.3731 −1.02227
$$718$$ −15.3923 + 4.12436i −0.574436 + 0.153920i
$$719$$ 4.39230 0.163805 0.0819027 0.996640i $$-0.473900\pi$$
0.0819027 + 0.996640i $$0.473900\pi$$
$$720$$ −12.0000 3.21539i −0.447214 0.119831i
$$721$$ 41.3205 1.53886
$$722$$ 10.6603 2.85641i 0.396734 0.106304i
$$723$$ 20.0885 + 34.7942i 0.747098 + 1.29401i
$$724$$ 5.41154 20.1962i 0.201118 0.750584i
$$725$$ −9.29423 2.49038i −0.345179 0.0924904i
$$726$$ −19.3923 + 5.19615i −0.719716 + 0.192847i
$$727$$ −28.8109 16.6340i −1.06854 0.616920i −0.140755 0.990044i $$-0.544953\pi$$
−0.927781 + 0.373124i $$0.878286\pi$$
$$728$$ −26.9282 −0.998026
$$729$$ 27.0000 1.00000
$$730$$ 9.17691 0.339653
$$731$$ −12.7942 47.7487i −0.473212 1.76605i
$$732$$ 10.3923 + 38.7846i 0.384111 + 1.43352i
$$733$$ 2.95448 11.0263i 0.109126 0.407265i −0.889654 0.456635i $$-0.849055\pi$$
0.998781 + 0.0493698i $$0.0157213\pi$$
$$734$$ 38.5885 + 10.3397i 1.42433 + 0.381647i
$$735$$ 0.803848 + 0.215390i 0.0296504 + 0.00794479i
$$736$$ −25.8564 + 6.92820i −0.953080 + 0.255377i
$$737$$ −29.9282 −1.10242
$$738$$ −3.29423 + 12.2942i −0.121262 + 0.452557i
$$739$$ −8.22243 8.22243i −0.302467 0.302467i 0.539511 0.841978i $$-0.318609\pi$$
−0.841978 + 0.539511i $$0.818609\pi$$
$$740$$ −6.92820 + 12.0000i −0.254686 + 0.441129i
$$741$$ 20.1962i 0.741924i
$$742$$ −20.3923 35.3205i −0.748625 1.29666i
$$743$$ 24.7583 14.2942i 0.908295 0.524404i 0.0284129 0.999596i $$-0.490955\pi$$
0.879882 + 0.475192i $$0.157621\pi$$
$$744$$ 1.85641 + 1.85641i 0.0680592 + 0.0680592i
$$745$$ 7.26795 + 4.19615i 0.266277 + 0.153735i
$$746$$ 40.2487i 1.47361i
$$747$$ 3.00000 + 3.00000i 0.109764 + 0.109764i
$$748$$ 35.5167 + 35.5167i 1.29862 + 1.29862i
$$749$$ 46.6147 12.4904i 1.70327 0.456389i
$$750$$ −11.3205 19.6077i −0.413367 0.715972i
$$751$$ −8.85641 15.3397i −0.323175 0.559755i 0.657966 0.753047i $$-0.271417\pi$$
−0.981141 + 0.193292i $$0.938084\pi$$
$$752$$ −15.3205 26.5359i −0.558681 0.967665i
$$753$$ 3.69615 + 13.7942i 0.134695 + 0.502690i
$$754$$ 11.6603 3.12436i 0.424641 0.113782i
$$755$$ 0.535898 + 0.535898i 0.0195033 + 0.0195033i
$$756$$ 28.3923 1.03262
$$757$$ −19.9282 + 19.9282i −0.724303 + 0.724303i −0.969479 0.245176i $$-0.921154\pi$$
0.245176 + 0.969479i $$0.421154\pi$$
$$758$$ 6.50962 + 3.75833i 0.236440 + 0.136509i
$$759$$ −34.6865 + 9.29423i −1.25904 + 0.337359i
$$760$$ −2.53590 + 9.46410i −0.0919867 + 0.343299i
$$761$$ 45.3731 26.1962i 1.64477 0.949610i 0.665669 0.746247i $$-0.268146\pi$$
0.979104 0.203363i $$-0.0651870\pi$$
$$762$$ 9.92820 + 2.66025i 0.359661 + 0.0963708i
$$763$$ 10.7321 + 40.0526i 0.388526 + 1.45000i
$$764$$ 48.1051i 1.74038i
$$765$$ 4.60770 + 17.1962i 0.166592 + 0.621728i
$$766$$ 13.4641 13.4641i 0.486478 0.486478i
$$767$$ 13.2224 22.9019i 0.477434 0.826941i
$$768$$ −27.7128 −1.00000
$$769$$ −14.1244 24.4641i −0.509337 0.882198i −0.999942 0.0108155i $$-0.996557\pi$$
0.490604 0.871383i $$-0.336776\pi$$
$$770$$ −16.9282 4.53590i −0.610050 0.163462i
$$771$$ 32.6603 1.17623
$$772$$ 37.6410 + 21.7321i 1.35473 + 0.782154i