# Properties

 Label 845.2.e.n.146.2 Level $845$ Weight $2$ Character 845.146 Analytic conductor $6.747$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$845 = 5 \cdot 13^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 845.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.74735897080$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: 8.0.22581504.2 Defining polynomial: $$x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$3^{2}$$ Twist minimal: no (minimal twist has level 65) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 146.2 Root $$-1.27597 + 0.609843i$$ of defining polynomial Character $$\chi$$ $$=$$ 845.146 Dual form 845.2.e.n.191.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.109843 - 0.190254i) q^{2} +(0.800098 + 1.38581i) q^{3} +(0.975869 - 1.69025i) q^{4} +1.00000 q^{5} +(0.175771 - 0.304444i) q^{6} +(-0.166123 + 0.287734i) q^{7} -0.868145 q^{8} +(0.219687 - 0.380509i) q^{9} +O(q^{10})$$ $$q+(-0.109843 - 0.190254i) q^{2} +(0.800098 + 1.38581i) q^{3} +(0.975869 - 1.69025i) q^{4} +1.00000 q^{5} +(0.175771 - 0.304444i) q^{6} +(-0.166123 + 0.287734i) q^{7} -0.868145 q^{8} +(0.219687 - 0.380509i) q^{9} +(-0.109843 - 0.190254i) q^{10} +(-2.68591 - 4.65213i) q^{11} +3.12316 q^{12} +0.0729902 q^{14} +(0.800098 + 1.38581i) q^{15} +(-1.85638 - 3.21534i) q^{16} +(2.53215 - 4.38581i) q^{17} -0.0965246 q^{18} +(1.13397 - 1.96410i) q^{19} +(0.975869 - 1.69025i) q^{20} -0.531659 q^{21} +(-0.590059 + 1.02201i) q^{22} +(1.41959 + 2.45880i) q^{23} +(-0.694601 - 1.20308i) q^{24} +1.00000 q^{25} +5.50367 q^{27} +(0.324229 + 0.561581i) q^{28} +(1.45174 + 2.51448i) q^{29} +(0.175771 - 0.304444i) q^{30} -5.46410 q^{31} +(-1.27597 + 2.21004i) q^{32} +(4.29798 - 7.44432i) q^{33} -1.11256 q^{34} +(-0.166123 + 0.287734i) q^{35} +(-0.428771 - 0.742653i) q^{36} +(2.98601 + 5.17191i) q^{37} -0.498239 q^{38} -0.868145 q^{40} +(1.86603 + 3.23205i) q^{41} +(0.0583993 + 0.101151i) q^{42} +(2.53215 - 4.38581i) q^{43} -10.4844 q^{44} +(0.219687 - 0.380509i) q^{45} +(0.311865 - 0.540166i) q^{46} -8.34285 q^{47} +(2.97057 - 5.14517i) q^{48} +(3.44481 + 5.96658i) q^{49} +(-0.109843 - 0.190254i) q^{50} +8.10387 q^{51} -1.56063 q^{53} +(-0.604542 - 1.04710i) q^{54} +(-2.68591 - 4.65213i) q^{55} +(0.144219 - 0.249795i) q^{56} +3.62916 q^{57} +(0.318928 - 0.552399i) q^{58} +(1.35366 - 2.34461i) q^{59} +3.12316 q^{60} +(-7.05193 + 12.2143i) q^{61} +(0.600196 + 1.03957i) q^{62} +(0.0729902 + 0.126423i) q^{63} -6.86488 q^{64} -1.88842 q^{66} +(5.16612 + 8.94799i) q^{67} +(-4.94209 - 8.55995i) q^{68} +(-2.27162 + 3.93456i) q^{69} +0.0729902 q^{70} +(6.39866 - 11.0828i) q^{71} +(-0.190720 + 0.330337i) q^{72} +9.68922 q^{73} +(0.655986 - 1.13620i) q^{74} +(0.800098 + 1.38581i) q^{75} +(-2.21322 - 3.83341i) q^{76} +1.78477 q^{77} +4.51851 q^{79} +(-1.85638 - 3.21534i) q^{80} +(3.74441 + 6.48552i) q^{81} +(0.409941 - 0.710039i) q^{82} +4.26371 q^{83} +(-0.518830 + 0.898640i) q^{84} +(2.53215 - 4.38581i) q^{85} -1.11256 q^{86} +(-2.32306 + 4.02367i) q^{87} +(2.33176 + 4.03872i) q^{88} +(1.61292 + 2.79366i) q^{89} -0.0965246 q^{90} +5.54133 q^{92} +(-4.37182 - 7.57221i) q^{93} +(0.916407 + 1.58726i) q^{94} +(1.13397 - 1.96410i) q^{95} -4.08359 q^{96} +(-1.25396 + 2.17191i) q^{97} +(0.756779 - 1.31078i) q^{98} -2.36023 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 2q^{2} + 2q^{3} - 2q^{4} + 8q^{5} - 4q^{6} + 10q^{7} - 12q^{8} - 4q^{9} + O(q^{10})$$ $$8q + 2q^{2} + 2q^{3} - 2q^{4} + 8q^{5} - 4q^{6} + 10q^{7} - 12q^{8} - 4q^{9} + 2q^{10} - 20q^{12} + 4q^{14} + 2q^{15} - 2q^{16} + 2q^{17} - 40q^{18} + 16q^{19} - 2q^{20} - 8q^{21} - 12q^{22} + 10q^{23} - 24q^{24} + 8q^{25} - 4q^{27} + 8q^{28} - 8q^{29} - 4q^{30} - 16q^{31} + 4q^{32} + 18q^{33} + 8q^{34} + 10q^{35} - 20q^{36} - 2q^{37} + 16q^{38} - 12q^{40} + 8q^{41} + 4q^{42} + 2q^{43} - 24q^{44} - 4q^{45} + 16q^{46} - 16q^{47} + 28q^{48} - 12q^{49} + 2q^{50} + 8q^{51} - 24q^{53} - 16q^{54} - 12q^{56} + 28q^{57} + 22q^{58} + 12q^{59} - 20q^{60} - 28q^{61} - 4q^{62} + 4q^{63} + 8q^{64} + 12q^{66} + 30q^{67} - 14q^{68} + 16q^{69} + 4q^{70} + 4q^{71} + 12q^{72} + 16q^{73} + 10q^{74} + 2q^{75} + 20q^{76} + 36q^{77} - 16q^{79} - 2q^{80} + 8q^{81} - 4q^{82} + 24q^{83} - 28q^{84} + 2q^{85} + 8q^{86} + 22q^{87} + 18q^{88} - 12q^{89} - 40q^{90} + 44q^{92} + 8q^{93} + 32q^{94} + 16q^{95} - 8q^{96} + 2q^{97} - 24q^{98} - 48q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$$.

 $$n$$ $$171$$ $$677$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.109843 0.190254i −0.0776710 0.134530i 0.824574 0.565755i $$-0.191415\pi$$
−0.902245 + 0.431224i $$0.858082\pi$$
$$3$$ 0.800098 + 1.38581i 0.461937 + 0.800098i 0.999057 0.0434075i $$-0.0138214\pi$$
−0.537121 + 0.843505i $$0.680488\pi$$
$$4$$ 0.975869 1.69025i 0.487934 0.845127i
$$5$$ 1.00000 0.447214
$$6$$ 0.175771 0.304444i 0.0717582 0.124289i
$$7$$ −0.166123 + 0.287734i −0.0627887 + 0.108753i −0.895711 0.444637i $$-0.853333\pi$$
0.832922 + 0.553390i $$0.186666\pi$$
$$8$$ −0.868145 −0.306936
$$9$$ 0.219687 0.380509i 0.0732290 0.126836i
$$10$$ −0.109843 0.190254i −0.0347355 0.0601637i
$$11$$ −2.68591 4.65213i −0.809832 1.40267i −0.912980 0.408004i $$-0.866225\pi$$
0.103149 0.994666i $$-0.467108\pi$$
$$12$$ 3.12316 0.901579
$$13$$ 0 0
$$14$$ 0.0729902 0.0195074
$$15$$ 0.800098 + 1.38581i 0.206584 + 0.357815i
$$16$$ −1.85638 3.21534i −0.464094 0.803835i
$$17$$ 2.53215 4.38581i 0.614136 1.06372i −0.376399 0.926458i $$-0.622838\pi$$
0.990535 0.137258i $$-0.0438288\pi$$
$$18$$ −0.0965246 −0.0227511
$$19$$ 1.13397 1.96410i 0.260152 0.450596i −0.706130 0.708082i $$-0.749561\pi$$
0.966282 + 0.257486i $$0.0828941\pi$$
$$20$$ 0.975869 1.69025i 0.218211 0.377952i
$$21$$ −0.531659 −0.116018
$$22$$ −0.590059 + 1.02201i −0.125801 + 0.217894i
$$23$$ 1.41959 + 2.45880i 0.296005 + 0.512695i 0.975218 0.221246i $$-0.0710122\pi$$
−0.679213 + 0.733941i $$0.737679\pi$$
$$24$$ −0.694601 1.20308i −0.141785 0.245578i
$$25$$ 1.00000 0.200000
$$26$$ 0 0
$$27$$ 5.50367 1.05918
$$28$$ 0.324229 + 0.561581i 0.0612735 + 0.106129i
$$29$$ 1.45174 + 2.51448i 0.269581 + 0.466928i 0.968754 0.248025i $$-0.0797815\pi$$
−0.699173 + 0.714953i $$0.746448\pi$$
$$30$$ 0.175771 0.304444i 0.0320912 0.0555837i
$$31$$ −5.46410 −0.981382 −0.490691 0.871334i $$-0.663256\pi$$
−0.490691 + 0.871334i $$0.663256\pi$$
$$32$$ −1.27597 + 2.21004i −0.225561 + 0.390683i
$$33$$ 4.29798 7.44432i 0.748182 1.29589i
$$34$$ −1.11256 −0.190802
$$35$$ −0.166123 + 0.287734i −0.0280800 + 0.0486359i
$$36$$ −0.428771 0.742653i −0.0714619 0.123776i
$$37$$ 2.98601 + 5.17191i 0.490896 + 0.850257i 0.999945 0.0104803i $$-0.00333604\pi$$
−0.509049 + 0.860738i $$0.670003\pi$$
$$38$$ −0.498239 −0.0808250
$$39$$ 0 0
$$40$$ −0.868145 −0.137266
$$41$$ 1.86603 + 3.23205i 0.291424 + 0.504762i 0.974147 0.225916i $$-0.0725376\pi$$
−0.682723 + 0.730678i $$0.739204\pi$$
$$42$$ 0.0583993 + 0.101151i 0.00901121 + 0.0156079i
$$43$$ 2.53215 4.38581i 0.386149 0.668830i −0.605779 0.795633i $$-0.707138\pi$$
0.991928 + 0.126803i $$0.0404717\pi$$
$$44$$ −10.4844 −1.58058
$$45$$ 0.219687 0.380509i 0.0327490 0.0567229i
$$46$$ 0.311865 0.540166i 0.0459820 0.0796432i
$$47$$ −8.34285 −1.21693 −0.608465 0.793581i $$-0.708214\pi$$
−0.608465 + 0.793581i $$0.708214\pi$$
$$48$$ 2.97057 5.14517i 0.428764 0.742642i
$$49$$ 3.44481 + 5.96658i 0.492115 + 0.852368i
$$50$$ −0.109843 0.190254i −0.0155342 0.0269060i
$$51$$ 8.10387 1.13477
$$52$$ 0 0
$$53$$ −1.56063 −0.214369 −0.107184 0.994239i $$-0.534183\pi$$
−0.107184 + 0.994239i $$0.534183\pi$$
$$54$$ −0.604542 1.04710i −0.0822678 0.142492i
$$55$$ −2.68591 4.65213i −0.362168 0.627293i
$$56$$ 0.144219 0.249795i 0.0192721 0.0333802i
$$57$$ 3.62916 0.480694
$$58$$ 0.318928 0.552399i 0.0418773 0.0725335i
$$59$$ 1.35366 2.34461i 0.176232 0.305242i −0.764355 0.644795i $$-0.776943\pi$$
0.940587 + 0.339553i $$0.110276\pi$$
$$60$$ 3.12316 0.403199
$$61$$ −7.05193 + 12.2143i −0.902908 + 1.56388i −0.0792059 + 0.996858i $$0.525238\pi$$
−0.823702 + 0.567023i $$0.808095\pi$$
$$62$$ 0.600196 + 1.03957i 0.0762249 + 0.132025i
$$63$$ 0.0729902 + 0.126423i 0.00919590 + 0.0159278i
$$64$$ −6.86488 −0.858111
$$65$$ 0 0
$$66$$ −1.88842 −0.232448
$$67$$ 5.16612 + 8.94799i 0.631142 + 1.09317i 0.987319 + 0.158752i $$0.0507470\pi$$
−0.356176 + 0.934419i $$0.615920\pi$$
$$68$$ −4.94209 8.55995i −0.599316 1.03805i
$$69$$ −2.27162 + 3.93456i −0.273471 + 0.473666i
$$70$$ 0.0729902 0.00872400
$$71$$ 6.39866 11.0828i 0.759382 1.31529i −0.183785 0.982967i $$-0.558835\pi$$
0.943166 0.332321i $$-0.107832\pi$$
$$72$$ −0.190720 + 0.330337i −0.0224766 + 0.0389306i
$$73$$ 9.68922 1.13404 0.567019 0.823705i $$-0.308097\pi$$
0.567019 + 0.823705i $$0.308097\pi$$
$$74$$ 0.655986 1.13620i 0.0762569 0.132081i
$$75$$ 0.800098 + 1.38581i 0.0923873 + 0.160020i
$$76$$ −2.21322 3.83341i −0.253874 0.439722i
$$77$$ 1.78477 0.203393
$$78$$ 0 0
$$79$$ 4.51851 0.508372 0.254186 0.967155i $$-0.418192\pi$$
0.254186 + 0.967155i $$0.418192\pi$$
$$80$$ −1.85638 3.21534i −0.207549 0.359486i
$$81$$ 3.74441 + 6.48552i 0.416046 + 0.720613i
$$82$$ 0.409941 0.710039i 0.0452704 0.0784107i
$$83$$ 4.26371 0.468003 0.234001 0.972236i $$-0.424818\pi$$
0.234001 + 0.972236i $$0.424818\pi$$
$$84$$ −0.518830 + 0.898640i −0.0566090 + 0.0980496i
$$85$$ 2.53215 4.38581i 0.274650 0.475708i
$$86$$ −1.11256 −0.119970
$$87$$ −2.32306 + 4.02367i −0.249059 + 0.431382i
$$88$$ 2.33176 + 4.03872i 0.248566 + 0.430529i
$$89$$ 1.61292 + 2.79366i 0.170969 + 0.296127i 0.938759 0.344575i $$-0.111977\pi$$
−0.767790 + 0.640702i $$0.778644\pi$$
$$90$$ −0.0965246 −0.0101746
$$91$$ 0 0
$$92$$ 5.54133 0.577724
$$93$$ −4.37182 7.57221i −0.453336 0.785201i
$$94$$ 0.916407 + 1.58726i 0.0945202 + 0.163714i
$$95$$ 1.13397 1.96410i 0.116343 0.201513i
$$96$$ −4.08359 −0.416780
$$97$$ −1.25396 + 2.17191i −0.127320 + 0.220524i −0.922637 0.385669i $$-0.873971\pi$$
0.795318 + 0.606193i $$0.207304\pi$$
$$98$$ 0.756779 1.31078i 0.0764462 0.132409i
$$99$$ −2.36023 −0.237213
$$100$$ 0.975869 1.69025i 0.0975869 0.169025i
$$101$$ −6.22336 10.7792i −0.619247 1.07257i −0.989623 0.143686i $$-0.954105\pi$$
0.370376 0.928882i $$-0.379229\pi$$
$$102$$ −0.890157 1.54180i −0.0881386 0.152661i
$$103$$ −15.0247 −1.48043 −0.740215 0.672370i $$-0.765276\pi$$
−0.740215 + 0.672370i $$0.765276\pi$$
$$104$$ 0 0
$$105$$ −0.531659 −0.0518846
$$106$$ 0.171425 + 0.296916i 0.0166502 + 0.0288390i
$$107$$ 6.53215 + 11.3140i 0.631487 + 1.09377i 0.987248 + 0.159190i $$0.0508883\pi$$
−0.355761 + 0.934577i $$0.615778\pi$$
$$108$$ 5.37086 9.30260i 0.516811 0.895144i
$$109$$ 11.2325 1.07587 0.537937 0.842985i $$-0.319204\pi$$
0.537937 + 0.842985i $$0.319204\pi$$
$$110$$ −0.590059 + 1.02201i −0.0562599 + 0.0974450i
$$111$$ −4.77819 + 8.27607i −0.453526 + 0.785530i
$$112$$ 1.23355 0.116560
$$113$$ 9.17191 15.8862i 0.862821 1.49445i −0.00637349 0.999980i $$-0.502029\pi$$
0.869195 0.494470i $$-0.164638\pi$$
$$114$$ −0.398640 0.690464i −0.0373360 0.0646679i
$$115$$ 1.41959 + 2.45880i 0.132377 + 0.229284i
$$116$$ 5.66682 0.526151
$$117$$ 0 0
$$118$$ −0.594763 −0.0547524
$$119$$ 0.841298 + 1.45717i 0.0771216 + 0.133579i
$$120$$ −0.694601 1.20308i −0.0634081 0.109826i
$$121$$ −8.92820 + 15.4641i −0.811655 + 1.40583i
$$122$$ 3.09843 0.280519
$$123$$ −2.98601 + 5.17191i −0.269239 + 0.466336i
$$124$$ −5.33225 + 9.23572i −0.478850 + 0.829392i
$$125$$ 1.00000 0.0894427
$$126$$ 0.0160350 0.0277734i 0.00142851 0.00247425i
$$127$$ −1.61998 2.80589i −0.143750 0.248982i 0.785156 0.619298i $$-0.212583\pi$$
−0.928906 + 0.370316i $$0.879249\pi$$
$$128$$ 3.30600 + 5.72615i 0.292212 + 0.506125i
$$129$$ 8.10387 0.713506
$$130$$ 0 0
$$131$$ 0.175664 0.0153478 0.00767390 0.999971i $$-0.497557\pi$$
0.00767390 + 0.999971i $$0.497557\pi$$
$$132$$ −8.38853 14.5294i −0.730127 1.26462i
$$133$$ 0.376759 + 0.652566i 0.0326692 + 0.0565846i
$$134$$ 1.13493 1.96576i 0.0980430 0.169815i
$$135$$ 5.50367 0.473681
$$136$$ −2.19827 + 3.80752i −0.188500 + 0.326492i
$$137$$ −8.99144 + 15.5736i −0.768190 + 1.33054i 0.170353 + 0.985383i $$0.445509\pi$$
−0.938543 + 0.345162i $$0.887824\pi$$
$$138$$ 0.998090 0.0849631
$$139$$ −5.99307 + 10.3803i −0.508325 + 0.880445i 0.491628 + 0.870805i $$0.336402\pi$$
−0.999954 + 0.00964021i $$0.996931\pi$$
$$140$$ 0.324229 + 0.561581i 0.0274024 + 0.0474623i
$$141$$ −6.67510 11.5616i −0.562144 0.973663i
$$142$$ −2.81140 −0.235928
$$143$$ 0 0
$$144$$ −1.63129 −0.135941
$$145$$ 1.45174 + 2.51448i 0.120560 + 0.208816i
$$146$$ −1.06430 1.84342i −0.0880819 0.152562i
$$147$$ −5.51236 + 9.54769i −0.454652 + 0.787481i
$$148$$ 11.6558 0.958101
$$149$$ −1.70520 + 2.95350i −0.139696 + 0.241960i −0.927381 0.374117i $$-0.877946\pi$$
0.787686 + 0.616077i $$0.211279\pi$$
$$150$$ 0.175771 0.304444i 0.0143516 0.0248578i
$$151$$ −7.96141 −0.647890 −0.323945 0.946076i $$-0.605009\pi$$
−0.323945 + 0.946076i $$0.605009\pi$$
$$152$$ −0.984454 + 1.70512i −0.0798498 + 0.138304i
$$153$$ −1.11256 1.92701i −0.0899451 0.155790i
$$154$$ −0.196045 0.339560i −0.0157978 0.0273625i
$$155$$ −5.46410 −0.438887
$$156$$ 0 0
$$157$$ −16.4329 −1.31148 −0.655742 0.754985i $$-0.727644\pi$$
−0.655742 + 0.754985i $$0.727644\pi$$
$$158$$ −0.496329 0.859667i −0.0394858 0.0683914i
$$159$$ −1.24865 2.16273i −0.0990247 0.171516i
$$160$$ −1.27597 + 2.21004i −0.100874 + 0.174719i
$$161$$ −0.943307 −0.0743430
$$162$$ 0.822599 1.42478i 0.0646295 0.111942i
$$163$$ 8.90361 15.4215i 0.697384 1.20791i −0.271986 0.962301i $$-0.587680\pi$$
0.969370 0.245604i $$-0.0789862\pi$$
$$164$$ 7.28398 0.568784
$$165$$ 4.29798 7.44432i 0.334597 0.579539i
$$166$$ −0.468341 0.811190i −0.0363503 0.0629605i
$$167$$ −3.14683 5.45047i −0.243509 0.421770i 0.718202 0.695834i $$-0.244965\pi$$
−0.961711 + 0.274064i $$0.911632\pi$$
$$168$$ 0.461557 0.0356099
$$169$$ 0 0
$$170$$ −1.11256 −0.0853294
$$171$$ −0.498239 0.862975i −0.0381013 0.0659933i
$$172$$ −4.94209 8.55995i −0.376831 0.652690i
$$173$$ −7.98756 + 13.8349i −0.607283 + 1.05184i 0.384404 + 0.923165i $$0.374407\pi$$
−0.991686 + 0.128679i $$0.958926\pi$$
$$174$$ 1.02069 0.0773786
$$175$$ −0.166123 + 0.287734i −0.0125577 + 0.0217506i
$$176$$ −9.97212 + 17.2722i −0.751677 + 1.30194i
$$177$$ 4.33225 0.325632
$$178$$ 0.354337 0.613729i 0.0265587 0.0460010i
$$179$$ −11.8087 20.4533i −0.882625 1.52875i −0.848412 0.529336i $$-0.822441\pi$$
−0.0342123 0.999415i $$-0.510892\pi$$
$$180$$ −0.428771 0.742653i −0.0319587 0.0553541i
$$181$$ −2.62590 −0.195182 −0.0975909 0.995227i $$-0.531114\pi$$
−0.0975909 + 0.995227i $$0.531114\pi$$
$$182$$ 0 0
$$183$$ −22.5689 −1.66834
$$184$$ −1.23241 2.13459i −0.0908544 0.157364i
$$185$$ 2.98601 + 5.17191i 0.219536 + 0.380247i
$$186$$ −0.960431 + 1.66351i −0.0704222 + 0.121975i
$$187$$ −27.2045 −1.98939
$$188$$ −8.14153 + 14.1015i −0.593782 + 1.02846i
$$189$$ −0.914288 + 1.58359i −0.0665046 + 0.115189i
$$190$$ −0.498239 −0.0361460
$$191$$ 1.00791 1.74575i 0.0729298 0.126318i −0.827254 0.561828i $$-0.810098\pi$$
0.900184 + 0.435509i $$0.143432\pi$$
$$192$$ −5.49258 9.51343i −0.396393 0.686572i
$$193$$ 11.4105 + 19.7636i 0.821348 + 1.42262i 0.904678 + 0.426095i $$0.140111\pi$$
−0.0833298 + 0.996522i $$0.526555\pi$$
$$194$$ 0.550955 0.0395563
$$195$$ 0 0
$$196$$ 13.4467 0.960480
$$197$$ −0.321513 0.556877i −0.0229068 0.0396758i 0.854345 0.519707i $$-0.173959\pi$$
−0.877252 + 0.480031i $$0.840625\pi$$
$$198$$ 0.259256 + 0.449045i 0.0184245 + 0.0319122i
$$199$$ −1.53342 + 2.65596i −0.108701 + 0.188276i −0.915244 0.402899i $$-0.868003\pi$$
0.806543 + 0.591175i $$0.201336\pi$$
$$200$$ −0.868145 −0.0613871
$$201$$ −8.26681 + 14.3185i −0.583096 + 1.00995i
$$202$$ −1.36719 + 2.36804i −0.0961952 + 0.166615i
$$203$$ −0.964670 −0.0677065
$$204$$ 7.90831 13.6976i 0.553693 0.959024i
$$205$$ 1.86603 + 3.23205i 0.130329 + 0.225736i
$$206$$ 1.65037 + 2.85852i 0.114987 + 0.199163i
$$207$$ 1.24746 0.0867045
$$208$$ 0 0
$$209$$ −12.1830 −0.842716
$$210$$ 0.0583993 + 0.101151i 0.00402993 + 0.00698005i
$$211$$ 4.10020 + 7.10175i 0.282269 + 0.488904i 0.971943 0.235215i $$-0.0755796\pi$$
−0.689674 + 0.724120i $$0.742246\pi$$
$$212$$ −1.52297 + 2.63786i −0.104598 + 0.181169i
$$213$$ 20.4782 1.40314
$$214$$ 1.43503 2.48554i 0.0980964 0.169908i
$$215$$ 2.53215 4.38581i 0.172691 0.299110i
$$216$$ −4.77798 −0.325101
$$217$$ 0.907714 1.57221i 0.0616197 0.106728i
$$218$$ −1.23381 2.13703i −0.0835643 0.144738i
$$219$$ 7.75232 + 13.4274i 0.523854 + 0.907341i
$$220$$ −10.4844 −0.706856
$$221$$ 0 0
$$222$$ 2.09941 0.140903
$$223$$ 5.12210 + 8.87174i 0.343001 + 0.594095i 0.984989 0.172620i $$-0.0552232\pi$$
−0.641987 + 0.766715i $$0.721890\pi$$
$$224$$ −0.423935 0.734278i −0.0283254 0.0490610i
$$225$$ 0.219687 0.380509i 0.0146458 0.0253673i
$$226$$ −4.02990 −0.268065
$$227$$ 3.52190 6.10012i 0.233757 0.404879i −0.725154 0.688587i $$-0.758231\pi$$
0.958911 + 0.283708i $$0.0915646\pi$$
$$228$$ 3.54159 6.13421i 0.234547 0.406248i
$$229$$ −1.32899 −0.0878219 −0.0439109 0.999035i $$-0.513982\pi$$
−0.0439109 + 0.999035i $$0.513982\pi$$
$$230$$ 0.311865 0.540166i 0.0205638 0.0356175i
$$231$$ 1.42799 + 2.47335i 0.0939547 + 0.162734i
$$232$$ −1.26032 2.18294i −0.0827440 0.143317i
$$233$$ −1.24746 −0.0817238 −0.0408619 0.999165i $$-0.513010\pi$$
−0.0408619 + 0.999165i $$0.513010\pi$$
$$234$$ 0 0
$$235$$ −8.34285 −0.544227
$$236$$ −2.64199 4.57606i −0.171979 0.297876i
$$237$$ 3.61525 + 6.26180i 0.234836 + 0.406748i
$$238$$ 0.184822 0.320121i 0.0119802 0.0207504i
$$239$$ 9.94207 0.643099 0.321549 0.946893i $$-0.395796\pi$$
0.321549 + 0.946893i $$0.395796\pi$$
$$240$$ 2.97057 5.14517i 0.191749 0.332120i
$$241$$ −11.2934 + 19.5608i −0.727475 + 1.26002i 0.230472 + 0.973079i $$0.425973\pi$$
−0.957947 + 0.286944i $$0.907360\pi$$
$$242$$ 3.92282 0.252168
$$243$$ 2.26371 3.92086i 0.145217 0.251523i
$$244$$ 13.7635 + 23.8391i 0.881119 + 1.52614i
$$245$$ 3.44481 + 5.96658i 0.220081 + 0.381191i
$$246$$ 1.31197 0.0836483
$$247$$ 0 0
$$248$$ 4.74363 0.301221
$$249$$ 3.41139 + 5.90869i 0.216188 + 0.374448i
$$250$$ −0.109843 0.190254i −0.00694711 0.0120327i
$$251$$ 3.38418 5.86157i 0.213608 0.369979i −0.739233 0.673449i $$-0.764812\pi$$
0.952841 + 0.303470i $$0.0981453\pi$$
$$252$$ 0.284915 0.0179480
$$253$$ 7.62577 13.2082i 0.479428 0.830394i
$$254$$ −0.355888 + 0.616417i −0.0223304 + 0.0386774i
$$255$$ 8.10387 0.507484
$$256$$ −6.13860 + 10.6324i −0.383663 + 0.664523i
$$257$$ 5.12691 + 8.88007i 0.319808 + 0.553924i 0.980448 0.196779i $$-0.0630483\pi$$
−0.660640 + 0.750703i $$0.729715\pi$$
$$258$$ −0.890157 1.54180i −0.0554187 0.0959881i
$$259$$ −1.98418 −0.123291
$$260$$ 0 0
$$261$$ 1.27571 0.0789645
$$262$$ −0.0192955 0.0334208i −0.00119208 0.00206474i
$$263$$ −9.32850 16.1574i −0.575220 0.996310i −0.996018 0.0891555i $$-0.971583\pi$$
0.420798 0.907154i $$-0.361750\pi$$
$$264$$ −3.73127 + 6.46275i −0.229644 + 0.397754i
$$265$$ −1.56063 −0.0958685
$$266$$ 0.0827690 0.143360i 0.00507489 0.00878998i
$$267$$ −2.58098 + 4.47040i −0.157954 + 0.273584i
$$268$$ 20.1658 1.23182
$$269$$ −8.97894 + 15.5520i −0.547456 + 0.948221i 0.450992 + 0.892528i $$0.351070\pi$$
−0.998448 + 0.0556934i $$0.982263\pi$$
$$270$$ −0.604542 1.04710i −0.0367913 0.0637243i
$$271$$ 15.4488 + 26.7582i 0.938450 + 1.62544i 0.768363 + 0.640014i $$0.221071\pi$$
0.170086 + 0.985429i $$0.445595\pi$$
$$272$$ −18.8025 −1.14007
$$273$$ 0 0
$$274$$ 3.95060 0.238665
$$275$$ −2.68591 4.65213i −0.161966 0.280534i
$$276$$ 4.43361 + 7.67923i 0.266872 + 0.462235i
$$277$$ −13.2522 + 22.9536i −0.796250 + 1.37915i 0.125792 + 0.992057i $$0.459853\pi$$
−0.922042 + 0.387089i $$0.873481\pi$$
$$278$$ 2.63320 0.157929
$$279$$ −1.20039 + 2.07914i −0.0718656 + 0.124475i
$$280$$ 0.144219 0.249795i 0.00861874 0.0149281i
$$281$$ −4.97766 −0.296942 −0.148471 0.988917i $$-0.547435\pi$$
−0.148471 + 0.988917i $$0.547435\pi$$
$$282$$ −1.46643 + 2.53993i −0.0873247 + 0.151251i
$$283$$ 6.29317 + 10.9001i 0.374090 + 0.647943i 0.990190 0.139725i $$-0.0446218\pi$$
−0.616100 + 0.787668i $$0.711288\pi$$
$$284$$ −12.4885 21.6307i −0.741057 1.28355i
$$285$$ 3.62916 0.214973
$$286$$ 0 0
$$287$$ −1.23996 −0.0731926
$$288$$ 0.560626 + 0.971033i 0.0330352 + 0.0572187i
$$289$$ −4.32355 7.48861i −0.254327 0.440507i
$$290$$ 0.318928 0.552399i 0.0187281 0.0324380i
$$291$$ −4.01315 −0.235255
$$292$$ 9.45541 16.3772i 0.553336 0.958406i
$$293$$ 8.45880 14.6511i 0.494168 0.855925i −0.505809 0.862645i $$-0.668806\pi$$
0.999977 + 0.00672072i $$0.00213929\pi$$
$$294$$ 2.42199 0.141253
$$295$$ 1.35366 2.34461i 0.0788132 0.136508i
$$296$$ −2.59229 4.48997i −0.150674 0.260974i
$$297$$ −14.7824 25.6038i −0.857759 1.48568i
$$298$$ 0.749222 0.0434012
$$299$$ 0 0
$$300$$ 3.12316 0.180316
$$301$$ 0.841298 + 1.45717i 0.0484916 + 0.0839899i
$$302$$ 0.874509 + 1.51469i 0.0503223 + 0.0871608i
$$303$$ 9.95859 17.2488i 0.572106 0.990917i
$$304$$ −8.42034 −0.482940
$$305$$ −7.05193 + 12.2143i −0.403793 + 0.699389i
$$306$$ −0.244415 + 0.423339i −0.0139723 + 0.0242007i
$$307$$ 4.30426 0.245657 0.122828 0.992428i $$-0.460803\pi$$
0.122828 + 0.992428i $$0.460803\pi$$
$$308$$ 1.74170 3.01671i 0.0992425 0.171893i
$$309$$ −12.0213 20.8214i −0.683865 1.18449i
$$310$$ 0.600196 + 1.03957i 0.0340888 + 0.0590436i
$$311$$ −2.22512 −0.126175 −0.0630875 0.998008i $$-0.520095\pi$$
−0.0630875 + 0.998008i $$0.520095\pi$$
$$312$$ 0 0
$$313$$ 7.20887 0.407469 0.203735 0.979026i $$-0.434692\pi$$
0.203735 + 0.979026i $$0.434692\pi$$
$$314$$ 1.80504 + 3.12642i 0.101864 + 0.176434i
$$315$$ 0.0729902 + 0.126423i 0.00411253 + 0.00712311i
$$316$$ 4.40948 7.63744i 0.248052 0.429639i
$$317$$ 0.321644 0.0180653 0.00903266 0.999959i $$-0.497125\pi$$
0.00903266 + 0.999959i $$0.497125\pi$$
$$318$$ −0.274313 + 0.475124i −0.0153827 + 0.0266436i
$$319$$ 7.79847 13.5073i 0.436630 0.756266i
$$320$$ −6.86488 −0.383759
$$321$$ −10.4527 + 18.1046i −0.583414 + 1.01050i
$$322$$ 0.103616 + 0.179468i 0.00577430 + 0.0100014i
$$323$$ −5.74278 9.94679i −0.319537 0.553454i
$$324$$ 14.6162 0.812013
$$325$$ 0 0
$$326$$ −3.91201 −0.216666
$$327$$ 8.98707 + 15.5661i 0.496986 + 0.860805i
$$328$$ −1.61998 2.80589i −0.0894485 0.154929i
$$329$$ 1.38594 2.40052i 0.0764094 0.132345i
$$330$$ −1.88842 −0.103954
$$331$$ 8.31600 14.4037i 0.457089 0.791701i −0.541717 0.840561i $$-0.682225\pi$$
0.998806 + 0.0488600i $$0.0155588\pi$$
$$332$$ 4.16082 7.20676i 0.228355 0.395522i
$$333$$ 2.62395 0.143791
$$334$$ −0.691317 + 1.19740i −0.0378272 + 0.0655186i
$$335$$ 5.16612 + 8.94799i 0.282255 + 0.488881i
$$336$$ 0.986961 + 1.70947i 0.0538431 + 0.0932590i
$$337$$ 24.2186 1.31927 0.659636 0.751586i $$-0.270711\pi$$
0.659636 + 0.751586i $$0.270711\pi$$
$$338$$ 0 0
$$339$$ 29.3537 1.59427
$$340$$ −4.94209 8.55995i −0.268022 0.464229i
$$341$$ 14.6761 + 25.4197i 0.794754 + 1.37655i
$$342$$ −0.109456 + 0.189584i −0.00591873 + 0.0102515i
$$343$$ −4.61478 −0.249174
$$344$$ −2.19827 + 3.80752i −0.118523 + 0.205288i
$$345$$ −2.27162 + 3.93456i −0.122300 + 0.211830i
$$346$$ 3.50952 0.188673
$$347$$ 3.13680 5.43309i 0.168392 0.291664i −0.769463 0.638692i $$-0.779476\pi$$
0.937855 + 0.347028i $$0.112809\pi$$
$$348$$ 4.53401 + 7.85314i 0.243049 + 0.420972i
$$349$$ 3.53497 + 6.12275i 0.189223 + 0.327743i 0.944991 0.327095i $$-0.106070\pi$$
−0.755769 + 0.654839i $$0.772737\pi$$
$$350$$ 0.0729902 0.00390149
$$351$$ 0 0
$$352$$ 13.7085 0.730666
$$353$$ −10.8949 18.8705i −0.579878 1.00438i −0.995493 0.0948371i $$-0.969767\pi$$
0.415615 0.909541i $$-0.363566\pi$$
$$354$$ −0.475869 0.824229i −0.0252921 0.0438073i
$$355$$ 6.39866 11.0828i 0.339606 0.588214i
$$356$$ 6.29598 0.333687
$$357$$ −1.34624 + 2.33176i −0.0712506 + 0.123410i
$$358$$ −2.59422 + 4.49332i −0.137109 + 0.237479i
$$359$$ −23.9737 −1.26528 −0.632642 0.774444i $$-0.718029\pi$$
−0.632642 + 0.774444i $$0.718029\pi$$
$$360$$ −0.190720 + 0.330337i −0.0100518 + 0.0174103i
$$361$$ 6.92820 + 12.0000i 0.364642 + 0.631579i
$$362$$ 0.288438 + 0.499589i 0.0151600 + 0.0262578i
$$363$$ −28.5737 −1.49973
$$364$$ 0 0
$$365$$ 9.68922 0.507157
$$366$$ 2.47905 + 4.29384i 0.129582 + 0.224443i
$$367$$ −3.19566 5.53505i −0.166812 0.288927i 0.770485 0.637458i $$-0.220014\pi$$
−0.937297 + 0.348531i $$0.886681\pi$$
$$368$$ 5.27059 9.12892i 0.274748 0.475878i
$$369$$ 1.63977 0.0853628
$$370$$ 0.655986 1.13620i 0.0341031 0.0590683i
$$371$$ 0.259256 0.449045i 0.0134599 0.0233133i
$$372$$ −17.0653 −0.884793
$$373$$ 10.0401 17.3899i 0.519855 0.900414i −0.479879 0.877335i $$-0.659319\pi$$
0.999734 0.0230798i $$-0.00734719\pi$$
$$374$$ 2.98823 + 5.17577i 0.154518 + 0.267633i
$$375$$ 0.800098 + 1.38581i 0.0413169 + 0.0715629i
$$376$$ 7.24280 0.373519
$$377$$ 0 0
$$378$$ 0.401714 0.0206619
$$379$$ −2.73091 4.73007i −0.140277 0.242968i 0.787324 0.616540i $$-0.211466\pi$$
−0.927601 + 0.373572i $$0.878133\pi$$
$$380$$ −2.21322 3.83341i −0.113536 0.196650i
$$381$$ 2.59229 4.48997i 0.132807 0.230028i
$$382$$ −0.442849 −0.0226581
$$383$$ −2.83388 + 4.90842i −0.144804 + 0.250808i −0.929300 0.369326i $$-0.879589\pi$$
0.784496 + 0.620134i $$0.212922\pi$$
$$384$$ −5.29024 + 9.16297i −0.269966 + 0.467596i
$$385$$ 1.78477 0.0909602
$$386$$ 2.50675 4.34181i 0.127590 0.220992i
$$387$$ −1.11256 1.92701i −0.0565546 0.0979554i
$$388$$ 2.44739 + 4.23901i 0.124247 + 0.215203i
$$389$$ 10.6174 0.538325 0.269162 0.963095i $$-0.413253\pi$$
0.269162 + 0.963095i $$0.413253\pi$$
$$390$$ 0 0
$$391$$ 14.3784 0.727149
$$392$$ −2.99059 5.17986i −0.151048 0.261622i
$$393$$ 0.140548 + 0.243436i 0.00708971 + 0.0122797i
$$394$$ −0.0706321 + 0.122338i −0.00355840 + 0.00616332i
$$395$$ 4.51851 0.227351
$$396$$ −2.30328 + 3.98940i −0.115744 + 0.200475i
$$397$$ 14.0169 24.2780i 0.703487 1.21848i −0.263748 0.964592i $$-0.584959\pi$$
0.967235 0.253884i $$-0.0817081\pi$$
$$398$$ 0.673745 0.0337718
$$399$$ −0.602888 + 1.04423i −0.0301822 + 0.0522770i
$$400$$ −1.85638 3.21534i −0.0928189 0.160767i
$$401$$ −11.2571 19.4979i −0.562155 0.973680i −0.997308 0.0733241i $$-0.976639\pi$$
0.435154 0.900356i $$-0.356694\pi$$
$$402$$ 3.63222 0.181159
$$403$$ 0 0
$$404$$ −24.2927 −1.20861
$$405$$ 3.74441 + 6.48552i 0.186061 + 0.322268i
$$406$$ 0.105963 + 0.183533i 0.00525884 + 0.00910857i
$$407$$ 16.0403 27.7826i 0.795087 1.37713i
$$408$$ −7.03533 −0.348301
$$409$$ 2.14386 3.71328i 0.106007 0.183610i −0.808142 0.588988i $$-0.799527\pi$$
0.914149 + 0.405378i $$0.132860\pi$$
$$410$$ 0.409941 0.710039i 0.0202456 0.0350663i
$$411$$ −28.7761 −1.41942
$$412$$ −14.6622 + 25.3956i −0.722353 + 1.25115i
$$413$$ 0.449749 + 0.778989i 0.0221307 + 0.0383315i
$$414$$ −0.137025 0.237335i −0.00673443 0.0116644i
$$415$$ 4.26371 0.209297
$$416$$ 0 0
$$417$$ −19.1802 −0.939257
$$418$$ 1.33822 + 2.31787i 0.0654546 + 0.113371i
$$419$$ −8.85578 15.3387i −0.432633 0.749343i 0.564466 0.825456i $$-0.309082\pi$$
−0.997099 + 0.0761137i $$0.975749\pi$$
$$420$$ −0.518830 + 0.898640i −0.0253163 + 0.0438491i
$$421$$ −12.8787 −0.627672 −0.313836 0.949477i $$-0.601614\pi$$
−0.313836 + 0.949477i $$0.601614\pi$$
$$422$$ 0.900759 1.56016i 0.0438483 0.0759474i
$$423$$ −1.83281 + 3.17453i −0.0891145 + 0.154351i
$$424$$ 1.35485 0.0657973
$$425$$ 2.53215 4.38581i 0.122827 0.212743i
$$426$$ −2.24940 3.89607i −0.108984 0.188765i
$$427$$ −2.34298 4.05816i −0.113385 0.196388i
$$428$$ 25.4981 1.23250
$$429$$ 0 0
$$430$$ −1.11256 −0.0536524
$$431$$ 4.74923 + 8.22590i 0.228762 + 0.396228i 0.957442 0.288627i $$-0.0931988\pi$$
−0.728679 + 0.684855i $$0.759866\pi$$
$$432$$ −10.2169 17.6962i −0.491560 0.851408i
$$433$$ 0.698141 1.20922i 0.0335505 0.0581112i −0.848763 0.528774i $$-0.822652\pi$$
0.882313 + 0.470663i $$0.155985\pi$$
$$434$$ −0.398826 −0.0191443
$$435$$ −2.32306 + 4.02367i −0.111382 + 0.192920i
$$436$$ 10.9614 18.9857i 0.524956 0.909251i
$$437$$ 6.43911 0.308024
$$438$$ 1.70308 2.94983i 0.0813765 0.140948i
$$439$$ −2.08090 3.60422i −0.0993159 0.172020i 0.812086 0.583538i $$-0.198332\pi$$
−0.911402 + 0.411518i $$0.864999\pi$$
$$440$$ 2.33176 + 4.03872i 0.111162 + 0.192539i
$$441$$ 3.02711 0.144148
$$442$$ 0 0
$$443$$ 9.54563 0.453526 0.226763 0.973950i $$-0.427186\pi$$
0.226763 + 0.973950i $$0.427186\pi$$
$$444$$ 9.32578 + 16.1527i 0.442582 + 0.766574i
$$445$$ 1.61292 + 2.79366i 0.0764596 + 0.132432i
$$446$$ 1.12526 1.94900i 0.0532825 0.0922880i
$$447$$ −5.45732 −0.258122
$$448$$ 1.14042 1.97526i 0.0538796 0.0933223i
$$449$$ 10.8585 18.8075i 0.512446 0.887582i −0.487450 0.873151i $$-0.662073\pi$$
0.999896 0.0144310i $$-0.00459368\pi$$
$$450$$ −0.0965246 −0.00455022
$$451$$ 10.0239 17.3620i 0.472009 0.817544i
$$452$$ −17.9012 31.0057i −0.842000 1.45839i
$$453$$ −6.36991 11.0330i −0.299284 0.518376i
$$454$$ −1.54743 −0.0726246
$$455$$ 0 0
$$456$$ −3.15064 −0.147542
$$457$$ 2.36130 + 4.08989i 0.110457 + 0.191317i 0.915955 0.401282i $$-0.131435\pi$$
−0.805498 + 0.592599i $$0.798102\pi$$
$$458$$ 0.145980 + 0.252845i 0.00682122 + 0.0118147i
$$459$$ 13.9361 24.1381i 0.650482 1.12667i
$$460$$ 5.54133 0.258366
$$461$$ −0.890753 + 1.54283i −0.0414865 + 0.0718568i −0.886023 0.463641i $$-0.846543\pi$$
0.844537 + 0.535498i $$0.179876\pi$$
$$462$$ 0.313710 0.543362i 0.0145951 0.0252795i
$$463$$ −6.80200 −0.316116 −0.158058 0.987430i $$-0.550523\pi$$
−0.158058 + 0.987430i $$0.550523\pi$$
$$464$$ 5.38995 9.33566i 0.250222 0.433397i
$$465$$ −4.37182 7.57221i −0.202738 0.351153i
$$466$$ 0.137025 + 0.237335i 0.00634758 + 0.0109943i
$$467$$ 18.2374 0.843927 0.421963 0.906613i $$-0.361341\pi$$
0.421963 + 0.906613i $$0.361341\pi$$
$$468$$ 0 0
$$469$$ −3.43285 −0.158514
$$470$$ 0.916407 + 1.58726i 0.0422707 + 0.0732150i
$$471$$ −13.1479 22.7728i −0.605823 1.04932i
$$472$$ −1.17517 + 2.03546i −0.0540918 + 0.0936897i
$$473$$ −27.2045 −1.25086
$$474$$ 0.794223 1.37564i 0.0364799 0.0631850i
$$475$$ 1.13397 1.96410i 0.0520303 0.0901192i
$$476$$ 3.28398 0.150521
$$477$$ −0.342849 + 0.593832i −0.0156980 + 0.0271897i
$$478$$ −1.09207 1.89152i −0.0499502 0.0865162i
$$479$$ −17.5904 30.4674i −0.803724 1.39209i −0.917149 0.398544i $$-0.869515\pi$$
0.113425 0.993547i $$-0.463818\pi$$
$$480$$ −4.08359 −0.186390
$$481$$ 0 0
$$482$$ 4.96204 0.226015
$$483$$ −0.754738 1.30724i −0.0343418 0.0594817i
$$484$$ 17.4255 + 30.1819i 0.792069 + 1.37190i
$$485$$ −1.25396 + 2.17191i −0.0569392 + 0.0986215i
$$486$$ −0.994615 −0.0451166
$$487$$ −5.15200 + 8.92352i −0.233459 + 0.404363i −0.958824 0.284002i $$-0.908338\pi$$
0.725364 + 0.688365i $$0.241671\pi$$
$$488$$ 6.12210 10.6038i 0.277134 0.480011i
$$489$$ 28.4950 1.28859
$$490$$ 0.756779 1.31078i 0.0341878 0.0592150i
$$491$$ −4.66599 8.08174i −0.210573 0.364724i 0.741321 0.671151i $$-0.234200\pi$$
−0.951894 + 0.306427i $$0.900866\pi$$
$$492$$ 5.82790 + 10.0942i 0.262742 + 0.455083i
$$493$$ 14.7041 0.662238
$$494$$ 0 0
$$495$$ −2.36023 −0.106085
$$496$$ 10.1434 + 17.5689i 0.455454 + 0.788869i
$$497$$ 2.12593 + 3.68222i 0.0953611 + 0.165170i
$$498$$ 0.749437 1.29806i 0.0335831 0.0581676i
$$499$$ −23.9421 −1.07179 −0.535897 0.844283i $$-0.680026\pi$$
−0.535897 + 0.844283i $$0.680026\pi$$
$$500$$ 0.975869 1.69025i 0.0436422 0.0755905i
$$501$$ 5.03554 8.72181i 0.224971 0.389662i
$$502$$ −1.48692 −0.0663645
$$503$$ −21.0721 + 36.4980i −0.939560 + 1.62737i −0.173266 + 0.984875i $$0.555432\pi$$
−0.766294 + 0.642490i $$0.777901\pi$$
$$504$$ −0.0633661 0.109753i −0.00282255 0.00488880i
$$505$$ −6.22336 10.7792i −0.276936 0.479667i
$$506$$ −3.35056 −0.148951
$$507$$ 0 0
$$508$$ −6.32355 −0.280562
$$509$$ −16.7801 29.0640i −0.743765 1.28824i −0.950770 0.309899i $$-0.899705\pi$$
0.207005 0.978340i $$-0.433629\pi$$
$$510$$ −0.890157 1.54180i −0.0394168 0.0682719i
$$511$$ −1.60960 + 2.78792i −0.0712047 + 0.123330i
$$512$$ 15.9211 0.703621
$$513$$ 6.24102 10.8098i 0.275548 0.477263i
$$514$$ 1.12632 1.95084i 0.0496796 0.0860477i
$$515$$ −15.0247 −0.662069
$$516$$ 7.90831 13.6976i 0.348144 0.603003i
$$517$$ 22.4081 + 38.8120i 0.985508 + 1.70695i
$$518$$ 0.217949 + 0.377499i 0.00957614 + 0.0165864i
$$519$$ −25.5633 −1.12210
$$520$$ 0 0
$$521$$ 12.4649 0.546098 0.273049 0.962000i $$-0.411968\pi$$
0.273049 + 0.962000i $$0.411968\pi$$
$$522$$ −0.140128 0.242710i −0.00613326 0.0106231i
$$523$$ 2.82978 + 4.90132i 0.123738 + 0.214320i 0.921239 0.388998i $$-0.127179\pi$$
−0.797501 + 0.603317i $$0.793845\pi$$
$$524$$ 0.171425 0.296916i 0.00748872 0.0129708i
$$525$$ −0.531659 −0.0232035
$$526$$ −2.04935 + 3.54958i −0.0893558 + 0.154769i
$$527$$ −13.8359 + 23.9645i −0.602702 + 1.04391i
$$528$$ −31.9147 −1.38891
$$529$$ 7.46953 12.9376i 0.324762 0.562505i
$$530$$ 0.171425 + 0.296916i 0.00744621 + 0.0128972i
$$531$$ −0.594763 1.03016i −0.0258105 0.0447051i
$$532$$ 1.47067 0.0637616
$$533$$ 0 0
$$534$$ 1.13402 0.0490737
$$535$$ 6.53215 + 11.3140i 0.282409 + 0.489147i
$$536$$ −4.48494 7.76815i −0.193720 0.335533i
$$537$$ 18.8963 32.7293i 0.815433 1.41237i
$$538$$ 3.94511 0.170086
$$539$$ 18.5049 32.0514i 0.797061 1.38055i
$$540$$ 5.37086 9.30260i 0.231125 0.400320i
$$541$$ 15.4750 0.665321 0.332660 0.943047i $$-0.392054\pi$$
0.332660 + 0.943047i $$0.392054\pi$$
$$542$$ 3.39391 5.87842i 0.145781 0.252500i
$$543$$ −2.10098 3.63900i −0.0901616 0.156165i
$$544$$ 6.46187 + 11.1923i 0.277051 + 0.479866i
$$545$$ 11.2325 0.481146
$$546$$ 0 0
$$547$$ 25.1765 1.07647 0.538234 0.842795i $$-0.319092\pi$$
0.538234 + 0.842795i $$0.319092\pi$$
$$548$$ 17.5489 + 30.3956i 0.749653 + 1.29844i
$$549$$ 3.09843 + 5.36665i 0.132238 + 0.229043i
$$550$$ −0.590059 + 1.02201i −0.0251602 + 0.0435787i
$$551$$ 6.58493 0.280528
$$552$$ 1.97210 3.41577i 0.0839380 0.145385i
$$553$$ −0.750630 + 1.30013i −0.0319200 + 0.0552871i
$$554$$ 5.82269 0.247382
$$555$$ −4.77819 + 8.27607i −0.202823 + 0.351300i
$$556$$ 11.6969 + 20.2596i 0.496059 + 0.859199i
$$557$$ 21.1744 + 36.6752i 0.897190 + 1.55398i 0.831071 + 0.556167i $$0.187728\pi$$
0.0661194 + 0.997812i $$0.478938\pi$$
$$558$$ 0.527420 0.0223275
$$559$$ 0 0
$$560$$ 1.23355 0.0521270
$$561$$ −21.7662 37.7002i −0.918971 1.59171i
$$562$$ 0.546763 + 0.947022i 0.0230638 + 0.0399477i
$$563$$ −11.8953 + 20.6032i −0.501326 + 0.868322i 0.498673 + 0.866790i $$0.333821\pi$$
−0.999999 + 0.00153173i $$0.999512\pi$$
$$564$$ −26.0561 −1.09716
$$565$$ 9.17191 15.8862i 0.385865 0.668338i
$$566$$ 1.38253 2.39461i 0.0581119 0.100653i
$$567$$ −2.48814 −0.104492
$$568$$ −5.55497 + 9.62148i −0.233081 + 0.403709i
$$569$$ 13.3710 + 23.1593i 0.560543 + 0.970889i 0.997449 + 0.0713817i $$0.0227408\pi$$
−0.436906 + 0.899507i $$0.643926\pi$$
$$570$$ −0.398640 0.690464i −0.0166972 0.0289204i
$$571$$ −16.7159 −0.699539 −0.349769 0.936836i $$-0.613740\pi$$
−0.349769 + 0.936836i $$0.613740\pi$$
$$572$$ 0 0
$$573$$ 3.22571 0.134756
$$574$$ 0.136202 + 0.235908i 0.00568494 + 0.00984661i
$$575$$ 1.41959 + 2.45880i 0.0592010 + 0.102539i
$$576$$ −1.50812 + 2.61215i −0.0628385 + 0.108840i
$$577$$ 20.6768 0.860786 0.430393 0.902642i $$-0.358375\pi$$
0.430393 + 0.902642i $$0.358375\pi$$
$$578$$ −0.949828 + 1.64515i −0.0395076 + 0.0684292i
$$579$$ −18.2591 + 31.6257i −0.758822 + 1.31432i
$$580$$ 5.66682 0.235302
$$581$$ −0.708301 + 1.22681i −0.0293853 + 0.0508968i
$$582$$ 0.440818 + 0.763519i 0.0182725 + 0.0316489i
$$583$$ 4.19170 + 7.26023i 0.173602 + 0.300688i
$$584$$ −8.41165 −0.348076
$$585$$ 0 0
$$586$$ −3.71657 −0.153530
$$587$$ 10.3986 + 18.0109i 0.429196 + 0.743388i 0.996802 0.0799116i $$-0.0254638\pi$$
−0.567606 + 0.823300i $$0.692130\pi$$
$$588$$ 10.7587 + 18.6346i 0.443681 + 0.768478i
$$589$$ −6.19615 + 10.7321i −0.255308 + 0.442206i
$$590$$ −0.594763 −0.0244860
$$591$$ 0.514483 0.891111i 0.0211630 0.0366554i
$$592$$ 11.0863 19.2021i 0.455644 0.789199i
$$593$$ 21.8475 0.897169 0.448585 0.893740i $$-0.351928\pi$$
0.448585 + 0.893740i $$0.351928\pi$$
$$594$$ −3.24749 + 5.62482i −0.133246 + 0.230789i
$$595$$ 0.841298 + 1.45717i 0.0344898 + 0.0597381i
$$596$$ 3.32811 + 5.76446i 0.136325 + 0.236121i
$$597$$ −4.90755 −0.200853
$$598$$ 0 0
$$599$$ −3.58040 −0.146291 −0.0731456 0.997321i $$-0.523304\pi$$
−0.0731456 + 0.997321i $$0.523304\pi$$
$$600$$ −0.694601 1.20308i −0.0283570 0.0491157i
$$601$$ −10.6743 18.4885i −0.435414 0.754160i 0.561915 0.827195i $$-0.310065\pi$$
−0.997329 + 0.0730352i $$0.976731\pi$$
$$602$$ 0.184822 0.320121i 0.00753278 0.0130472i
$$603$$ 4.53972 0.184872
$$604$$ −7.76929 + 13.4568i −0.316128 + 0.547550i
$$605$$ −8.92820 + 15.4641i −0.362983 + 0.628705i
$$606$$ −4.37554 −0.177744
$$607$$ 1.64988 2.85767i 0.0669665 0.115989i −0.830598 0.556872i $$-0.812001\pi$$
0.897565 + 0.440883i $$0.145335\pi$$
$$608$$ 2.89383 + 5.01226i 0.117360 + 0.203274i
$$609$$ −0.771830 1.33685i −0.0312761 0.0541718i
$$610$$ 3.09843 0.125452
$$611$$ 0 0
$$612$$ −4.34285 −0.175549
$$613$$ 4.94318 + 8.56183i 0.199653 + 0.345809i 0.948416 0.317029i $$-0.102685\pi$$
−0.748763 + 0.662838i $$0.769352\pi$$
$$614$$ −0.472795 0.818904i −0.0190804 0.0330483i
$$615$$ −2.98601 + 5.17191i −0.120407 + 0.208552i
$$616$$ −1.54944 −0.0624286
$$617$$ −22.8584 + 39.5920i −0.920246 + 1.59391i −0.121213 + 0.992626i $$0.538679\pi$$
−0.799033 + 0.601287i $$0.794655\pi$$
$$618$$ −2.64091 + 4.57419i −0.106233 + 0.184001i
$$619$$ −19.9143 −0.800425 −0.400212 0.916422i $$-0.631064\pi$$
−0.400212 + 0.916422i $$0.631064\pi$$
$$620$$ −5.33225 + 9.23572i −0.214148 + 0.370916i
$$621$$ 7.81295 + 13.5324i 0.313523 + 0.543038i
$$622$$ 0.244415 + 0.423339i 0.00980014 + 0.0169743i
$$623$$ −1.07177 −0.0429397
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ −0.791847 1.37152i −0.0316486 0.0548169i
$$627$$ −9.74760 16.8833i −0.389282 0.674255i
$$628$$ −16.0363 + 27.7757i −0.639918 + 1.10837i
$$629$$ 30.2440 1.20591
$$630$$ 0.0160350 0.0277734i 0.000638849 0.00110652i
$$631$$ 7.29790 12.6403i 0.290525 0.503204i −0.683409 0.730036i $$-0.739503\pi$$
0.973934 + 0.226832i $$0.0728368\pi$$
$$632$$ −3.92272 −0.156038
$$633$$ −6.56112 + 11.3642i −0.260781 + 0.451686i
$$634$$ −0.0353305 0.0611942i −0.00140315 0.00243033i
$$635$$ −1.61998 2.80589i −0.0642870 0.111348i
$$636$$ −4.87409 −0.193270
$$637$$ 0 0
$$638$$ −3.42644 −0.135654
$$639$$ −2.81140 4.86950i −0.111217 0.192634i
$$640$$ 3.30600 + 5.72615i 0.130681 + 0.226346i
$$641$$ 7.08183 12.2661i 0.279716 0.484482i −0.691598 0.722282i $$-0.743093\pi$$
0.971314 + 0.237801i $$0.0764265\pi$$
$$642$$ 4.59265 0.181257
$$643$$ 8.38581 14.5246i 0.330704 0.572796i −0.651946 0.758265i $$-0.726047\pi$$
0.982650 + 0.185469i $$0.0593805\pi$$
$$644$$ −0.920544 + 1.59443i −0.0362745 + 0.0628293i
$$645$$ 8.10387 0.319089
$$646$$ −1.26161 + 2.18518i −0.0496376 + 0.0859748i
$$647$$ 1.49584 + 2.59087i 0.0588075 + 0.101858i 0.893930 0.448206i $$-0.147937\pi$$
−0.835123 + 0.550063i $$0.814604\pi$$
$$648$$ −3.25069 5.63037i −0.127699 0.221182i
$$649$$ −14.5432 −0.570872
$$650$$ 0 0
$$651$$ 2.90504 0.113858
$$652$$ −17.3775 30.0987i −0.680556 1.17876i
$$653$$ 5.83217 + 10.1016i 0.228230 + 0.395307i 0.957284 0.289150i $$-0.0933727\pi$$
−0.729053 + 0.684457i $$0.760039\pi$$
$$654$$ 1.97434 3.41966i 0.0772028 0.133719i
$$655$$ 0.175664 0.00686374
$$656$$ 6.92810 11.9998i 0.270497 0.468514i
$$657$$ 2.12859 3.68683i 0.0830444 0.143837i
$$658$$ −0.608946 −0.0237392
$$659$$ 0.905237 1.56792i 0.0352630 0.0610773i −0.847855 0.530228i $$-0.822106\pi$$
0.883118 + 0.469150i $$0.155440\pi$$
$$660$$ −8.38853 14.5294i −0.326523 0.565554i
$$661$$ −6.17028 10.6872i −0.239996 0.415686i 0.720717 0.693230i $$-0.243813\pi$$
−0.960713 + 0.277544i $$0.910480\pi$$
$$662$$ −3.65383 −0.142010
$$663$$ 0 0
$$664$$ −3.70152 −0.143647
$$665$$ 0.376759 + 0.652566i 0.0146101 + 0.0253054i
$$666$$ −0.288223 0.499217i −0.0111684 0.0193443i
$$667$$ −4.12174 + 7.13907i −0.159594 + 0.276426i
$$668$$ −12.2836 −0.475265
$$669$$ −8.19636 + 14.1965i −0.316890 + 0.548869i
$$670$$ 1.13493 1.96576i 0.0438461 0.0759438i
$$671$$ 75.7634 2.92481
$$672$$ 0.678380 1.17499i 0.0261691 0.0453262i
$$673$$ −4.63313 8.02481i −0.178594 0.309334i 0.762805 0.646628i $$-0.223822\pi$$
−0.941399 + 0.337295i $$0.890488\pi$$
$$674$$ −2.66025 4.60770i −0.102469 0.177482i
$$675$$ 5.50367 0.211836
$$676$$ 0 0
$$677$$ 13.8984 0.534158 0.267079 0.963675i $$-0.413941\pi$$
0.267079 + 0.963675i $$0.413941\pi$$
$$678$$ −3.22431 5.58467i −0.123829 0.214478i
$$679$$ −0.416622 0.721611i −0.0159885 0.0276929i
$$680$$ −2.19827 + 3.80752i −0.0842999 + 0.146012i
$$681$$ 11.2715 0.431924
$$682$$ 3.22414 5.58438i 0.123459 0.213837i
$$683$$ −18.8756 + 32.6935i −0.722255 + 1.25098i 0.237838 + 0.971305i $$0.423561\pi$$
−0.960094 + 0.279678i $$0.909772\pi$$
$$684$$ −1.94486 −0.0743637
$$685$$ −8.99144 + 15.5736i −0.343545 + 0.595038i
$$686$$ 0.506903 + 0.877981i 0.0193536 + 0.0335215i
$$687$$ −1.06332 1.84172i −0.0405681 0.0702661i
$$688$$ −18.8025 −0.716838
$$689$$ 0 0
$$690$$ 0.998090 0.0379966
$$691$$ −0.826456 1.43146i −0.0314399 0.0544554i 0.849877 0.526981i $$-0.176676\pi$$
−0.881317 + 0.472525i $$0.843343\pi$$
$$692$$ 15.5896 + 27.0020i 0.592628 + 1.02646i
$$693$$ 0.392090 0.679120i 0.0148943 0.0257976i
$$694$$ −1.37823 −0.0523168
$$695$$ −5.99307 + 10.3803i −0.227330 + 0.393747i
$$696$$ 2.01676 3.49312i 0.0764450 0.132407i
$$697$$ 18.9002 0.715897
$$698$$ 0.776587 1.34509i 0.0293943 0.0509123i
$$699$$ −0.998090 1.72874i −0.0377512 0.0653871i
$$700$$ 0.324229 + 0.561581i 0.0122547 + 0.0212258i
$$701$$ 20.4819 0.773590 0.386795 0.922166i $$-0.373582\pi$$
0.386795 + 0.922166i $$0.373582\pi$$
$$702$$ 0 0
$$703$$ 13.5442 0.510830
$$704$$ 18.4384 + 31.9363i 0.694925 + 1.20365i
$$705$$ −6.67510 11.5616i −0.251399 0.435435i
$$706$$ −2.39347 + 4.14561i −0.0900794 + 0.156022i
$$707$$ 4.13538 0.155527
$$708$$ 4.22770 7.32260i 0.158887 0.275200i
$$709$$ 10.9709 19.0021i 0.412020 0.713639i −0.583091 0.812407i $$-0.698157\pi$$
0.995110 + 0.0987679i $$0.0314902\pi$$
$$710$$ −2.81140 −0.105510
$$711$$ 0.992658 1.71933i 0.0372276 0.0644801i
$$712$$ −1.40025 2.42530i −0.0524764 0.0908919i
$$713$$ −7.75678 13.4351i −0.290494 0.503150i
$$714$$ 0.591503 0.0221364
$$715$$ 0 0
$$716$$ −46.0950 −1.72265
$$717$$ 7.95463 + 13.7778i 0.297071 + 0.514542i
$$718$$ 2.63335 + 4.56110i 0.0982759 + 0.170219i
$$719$$ −19.4237 + 33.6429i −0.724384 + 1.25467i 0.234844 + 0.972033i $$0.424542\pi$$
−0.959227 + 0.282636i $$0.908791\pi$$
$$720$$ −1.63129 −0.0607945
$$721$$ 2.49596 4.32312i 0.0929543 0.161002i
$$722$$ 1.52204 2.63624i 0.0566443 0.0981108i
$$723$$ −36.1434 −1.34419
$$724$$ −2.56254 + 4.43844i −0.0952359 + 0.164953i
$$725$$ 1.45174 + 2.51448i 0.0539162 + 0.0933856i
$$726$$ 3.13864 + 5.43628i 0.116486 + 0.201759i
$$727$$ −30.6598 −1.13711 −0.568555 0.822645i $$-0.692497\pi$$
−0.568555 + 0.822645i $$0.692497\pi$$
$$728$$ 0 0
$$729$$ 29.7112 1.10042
$$730$$ −1.06430 1.84342i −0.0393914 0.0682279i
$$731$$ −12.8236 22.2110i −0.474296 0.821505i
$$732$$ −22.0243 + 38.1473i −0.814043 + 1.40996i
$$733$$ −24.3858 −0.900709 −0.450355 0.892850i $$-0.648702\pi$$
−0.450355 + 0.892850i $$0.648702\pi$$
$$734$$ −0.702045 + 1.21598i −0.0259130 + 0.0448826i
$$735$$ −5.51236 + 9.54769i −0.203327 + 0.352172i
$$736$$ −7.24539 −0.267069
$$737$$ 27.7515 48.0669i 1.02224 1.77057i
$$738$$ −0.180117 0.311973i −0.00663021 0.0114839i
$$739$$ 19.1394 + 33.1504i 0.704054 + 1.21946i 0.967032 + 0.254656i $$0.0819623\pi$$
−0.262977 + 0.964802i $$0.584704\pi$$
$$740$$ 11.6558 0.428476
$$741$$ 0 0
$$742$$ −0.113910 −0.00418178
$$743$$ −20.0040 34.6479i −0.733874 1.27111i −0.955216 0.295910i $$-0.904377\pi$$
0.221342 0.975196i $$-0.428956\pi$$
$$744$$ 3.79537 + 6.57377i 0.139145 + 0.241006i
$$745$$ −1.70520 + 2.95350i −0.0624738 + 0.108208i
$$746$$ −4.41134 −0.161511
$$747$$ 0.936681 1.62238i 0.0342714 0.0593598i
$$748$$ −26.5480 + 45.9825i −0.970691 + 1.68129i
$$749$$ −4.34057 −0.158601
$$750$$ 0.175771 0.304444i 0.00641825 0.0111167i
$$751$$ −12.8010 22.1720i −0.467115 0.809067i 0.532179 0.846632i $$-0.321373\pi$$
−0.999294 + 0.0375648i $$0.988040\pi$$
$$752$$ 15.4875 + 26.8251i 0.564770 + 0.978211i
$$753$$ 10.8307 0.394693
$$754$$ 0 0
$$755$$ −7.96141 −0.289745
$$756$$ 1.78445 + 3.09076i 0.0648998 + 0.112410i
$$757$$ 0.924239 + 1.60083i 0.0335920 + 0.0581831i 0.882333 0.470626i $$-0.155972\pi$$
−0.848741 + 0.528809i $$0.822639\pi$$
$$758$$ −0.599945 + 1.03914i −0.0217910 + 0.0377431i
$$759$$ 24.4055 0.885862
$$760$$ −0.984454 + 1.70512i −0.0357099 + 0.0618514i
$$761$$ 13.1062 22.7006i 0.475099 0.822896i −0.524494 0.851414i $$-0.675745\pi$$
0.999593 + 0.0285179i $$0.00907876\pi$$
$$762$$ −1.13898 −0.0412610
$$763$$ −1.86597 + 3.23196i −0.0675528 + 0.117005i
$$764$$ −1.96718 3.40725i −0.0711699 0.123270i
$$765$$ −1.11256 1.92701i −0.0402247 0.0696712i
$$766$$ 1.24513 0.0449884
$$767$$ 0 0
$$768$$ −19.6459 −0.708911
$$769$$ −22.1747 38.4078i −0.799641 1.38502i −0.919850 0.392271i $$-0.871690\pi$$
0.120208 0.992749i $$-0.461644\pi$$
$$770$$ −0.196045 0.339560i −0.00706497 0.0122369i
$$771$$ −8.20406 + 14.2099i −0.295462 + 0.511755i
$$772$$ 44.5408 1.60306
$$773$$ −11.6319 + 20.1471i −0.418371 + 0.724640i −0.995776 0.0918181i $$-0.970732\pi$$
0.577405 + 0.816458i $$0.304065\pi$$
$$774$$ −0.244415 + 0.423339i −0.00878531 + 0.0152166i
$$775$$ −5.46410 −0.196276
$$776$$ 1.08861 1.88554i 0.0390790 0.0676868i
$$777$$ −1.58754 2.74970i −0.0569526 0.0986448i
$$778$$ −1.16625 2.02001i −0.0418122 0.0724209i
$$779$$ 8.46410 0.303258
$$780$$ 0 0