# Properties

 Label 637.2.g.d.263.2 Level $637$ Weight $2$ Character 637.263 Analytic conductor $5.086$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.g (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.08647060876$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{4}]$$ Coefficient ring index: $$3$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 263.2 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.263 Dual form 637.2.g.d.373.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.866025 - 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} +O(q^{10})$$ $$q+(0.866025 - 1.50000i) q^{2} +0.732051 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} -2.46410 q^{9} -3.00000 q^{10} +4.73205 q^{11} +(-0.366025 - 0.633975i) q^{12} +(1.59808 - 3.23205i) q^{13} +(-0.633975 - 1.09808i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-2.13397 - 3.69615i) q^{17} +(-2.13397 + 3.69615i) q^{18} -2.00000 q^{19} +(-0.866025 + 1.50000i) q^{20} +(4.09808 - 7.09808i) q^{22} +(-0.633975 + 1.09808i) q^{23} +1.26795 q^{24} +(1.00000 - 1.73205i) q^{25} +(-3.46410 - 5.19615i) q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} -2.19615 q^{30} +(-3.09808 + 5.36603i) q^{31} +(-2.59808 - 4.50000i) q^{32} +3.46410 q^{33} -7.39230 q^{34} +(1.23205 + 2.13397i) q^{36} +(3.50000 - 6.06218i) q^{37} +(-1.73205 + 3.00000i) q^{38} +(1.16987 - 2.36603i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(2.59808 + 4.50000i) q^{41} +(-5.09808 + 8.83013i) q^{43} +(-2.36603 - 4.09808i) q^{44} +(2.13397 + 3.69615i) q^{45} +(1.09808 + 1.90192i) q^{46} +(-0.464102 - 0.803848i) q^{47} +(1.83013 - 3.16987i) q^{48} +(-1.73205 - 3.00000i) q^{50} +(-1.56218 - 2.70577i) q^{51} +(-3.59808 + 0.232051i) q^{52} +(-1.96410 + 3.40192i) q^{53} +(-3.46410 + 6.00000i) q^{54} +(-4.09808 - 7.09808i) q^{55} -1.46410 q^{57} +5.19615 q^{58} +(5.36603 + 9.29423i) q^{59} +(-0.633975 + 1.09808i) q^{60} +15.1962 q^{61} +(5.36603 + 9.29423i) q^{62} +1.00000 q^{64} +(-6.23205 + 0.401924i) q^{65} +(3.00000 - 5.19615i) q^{66} +4.19615 q^{67} +(-2.13397 + 3.69615i) q^{68} +(-0.464102 + 0.803848i) q^{69} +(-3.00000 + 5.19615i) q^{71} -4.26795 q^{72} +(3.59808 - 6.23205i) q^{73} +(-6.06218 - 10.5000i) q^{74} +(0.732051 - 1.26795i) q^{75} +(1.00000 + 1.73205i) q^{76} +(-2.53590 - 3.80385i) q^{78} +(-2.90192 - 5.02628i) q^{79} -8.66025 q^{80} +4.46410 q^{81} +9.00000 q^{82} -8.19615 q^{83} +(-3.69615 + 6.40192i) q^{85} +(8.83013 + 15.2942i) q^{86} +(1.09808 + 1.90192i) q^{87} +8.19615 q^{88} +(-0.464102 + 0.803848i) q^{89} +7.39230 q^{90} +1.26795 q^{92} +(-2.26795 + 3.92820i) q^{93} -1.60770 q^{94} +(1.73205 + 3.00000i) q^{95} +(-1.90192 - 3.29423i) q^{96} +(-7.19615 + 12.4641i) q^{97} -11.6603 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10})$$ 4 * q - 4 * q^3 - 2 * q^4 + 6 * q^6 + 4 * q^9 $$4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9} - 12 q^{10} + 12 q^{11} + 2 q^{12} - 4 q^{13} - 6 q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 8 q^{19} + 6 q^{22} - 6 q^{23} + 12 q^{24} + 4 q^{25} - 16 q^{27} + 6 q^{29} + 12 q^{30} - 2 q^{31} + 12 q^{34} - 2 q^{36} + 14 q^{37} + 22 q^{39} - 6 q^{40} - 10 q^{43} - 6 q^{44} + 12 q^{45} - 6 q^{46} + 12 q^{47} - 10 q^{48} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 6 q^{55} + 8 q^{57} + 18 q^{59} - 6 q^{60} + 40 q^{61} + 18 q^{62} + 4 q^{64} - 18 q^{65} + 12 q^{66} - 4 q^{67} - 12 q^{68} + 12 q^{69} - 12 q^{71} - 24 q^{72} + 4 q^{73} - 4 q^{75} + 4 q^{76} - 24 q^{78} - 22 q^{79} + 4 q^{81} + 36 q^{82} - 12 q^{83} + 6 q^{85} + 18 q^{86} - 6 q^{87} + 12 q^{88} + 12 q^{89} - 12 q^{90} + 12 q^{92} - 16 q^{93} - 48 q^{94} - 18 q^{96} - 8 q^{97} - 12 q^{99}+O(q^{100})$$ 4 * q - 4 * q^3 - 2 * q^4 + 6 * q^6 + 4 * q^9 - 12 * q^10 + 12 * q^11 + 2 * q^12 - 4 * q^13 - 6 * q^15 + 10 * q^16 - 12 * q^17 - 12 * q^18 - 8 * q^19 + 6 * q^22 - 6 * q^23 + 12 * q^24 + 4 * q^25 - 16 * q^27 + 6 * q^29 + 12 * q^30 - 2 * q^31 + 12 * q^34 - 2 * q^36 + 14 * q^37 + 22 * q^39 - 6 * q^40 - 10 * q^43 - 6 * q^44 + 12 * q^45 - 6 * q^46 + 12 * q^47 - 10 * q^48 + 18 * q^51 - 4 * q^52 + 6 * q^53 - 6 * q^55 + 8 * q^57 + 18 * q^59 - 6 * q^60 + 40 * q^61 + 18 * q^62 + 4 * q^64 - 18 * q^65 + 12 * q^66 - 4 * q^67 - 12 * q^68 + 12 * q^69 - 12 * q^71 - 24 * q^72 + 4 * q^73 - 4 * q^75 + 4 * q^76 - 24 * q^78 - 22 * q^79 + 4 * q^81 + 36 * q^82 - 12 * q^83 + 6 * q^85 + 18 * q^86 - 6 * q^87 + 12 * q^88 + 12 * q^89 - 12 * q^90 + 12 * q^92 - 16 * q^93 - 48 * q^94 - 18 * q^96 - 8 * q^97 - 12 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.866025 1.50000i 0.612372 1.06066i −0.378467 0.925615i $$-0.623549\pi$$
0.990839 0.135045i $$-0.0431180\pi$$
$$3$$ 0.732051 0.422650 0.211325 0.977416i $$-0.432222\pi$$
0.211325 + 0.977416i $$0.432222\pi$$
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ −0.866025 1.50000i −0.387298 0.670820i 0.604787 0.796387i $$-0.293258\pi$$
−0.992085 + 0.125567i $$0.959925\pi$$
$$6$$ 0.633975 1.09808i 0.258819 0.448288i
$$7$$ 0 0
$$8$$ 1.73205 0.612372
$$9$$ −2.46410 −0.821367
$$10$$ −3.00000 −0.948683
$$11$$ 4.73205 1.42677 0.713384 0.700774i $$-0.247162\pi$$
0.713384 + 0.700774i $$0.247162\pi$$
$$12$$ −0.366025 0.633975i −0.105662 0.183013i
$$13$$ 1.59808 3.23205i 0.443227 0.896410i
$$14$$ 0 0
$$15$$ −0.633975 1.09808i −0.163692 0.283522i
$$16$$ 2.50000 4.33013i 0.625000 1.08253i
$$17$$ −2.13397 3.69615i −0.517565 0.896449i −0.999792 0.0204023i $$-0.993505\pi$$
0.482227 0.876046i $$-0.339828\pi$$
$$18$$ −2.13397 + 3.69615i −0.502983 + 0.871191i
$$19$$ −2.00000 −0.458831 −0.229416 0.973329i $$-0.573682\pi$$
−0.229416 + 0.973329i $$0.573682\pi$$
$$20$$ −0.866025 + 1.50000i −0.193649 + 0.335410i
$$21$$ 0 0
$$22$$ 4.09808 7.09808i 0.873713 1.51331i
$$23$$ −0.633975 + 1.09808i −0.132193 + 0.228965i −0.924522 0.381130i $$-0.875535\pi$$
0.792329 + 0.610094i $$0.208868\pi$$
$$24$$ 1.26795 0.258819
$$25$$ 1.00000 1.73205i 0.200000 0.346410i
$$26$$ −3.46410 5.19615i −0.679366 1.01905i
$$27$$ −4.00000 −0.769800
$$28$$ 0 0
$$29$$ 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i $$-0.0768152\pi$$
−0.692480 + 0.721437i $$0.743482\pi$$
$$30$$ −2.19615 −0.400961
$$31$$ −3.09808 + 5.36603i −0.556431 + 0.963767i 0.441360 + 0.897330i $$0.354496\pi$$
−0.997791 + 0.0664364i $$0.978837\pi$$
$$32$$ −2.59808 4.50000i −0.459279 0.795495i
$$33$$ 3.46410 0.603023
$$34$$ −7.39230 −1.26777
$$35$$ 0 0
$$36$$ 1.23205 + 2.13397i 0.205342 + 0.355662i
$$37$$ 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i $$-0.638181\pi$$
0.995998 0.0893706i $$-0.0284856\pi$$
$$38$$ −1.73205 + 3.00000i −0.280976 + 0.486664i
$$39$$ 1.16987 2.36603i 0.187330 0.378867i
$$40$$ −1.50000 2.59808i −0.237171 0.410792i
$$41$$ 2.59808 + 4.50000i 0.405751 + 0.702782i 0.994409 0.105601i $$-0.0336766\pi$$
−0.588657 + 0.808383i $$0.700343\pi$$
$$42$$ 0 0
$$43$$ −5.09808 + 8.83013i −0.777449 + 1.34658i 0.155958 + 0.987764i $$0.450153\pi$$
−0.933408 + 0.358818i $$0.883180\pi$$
$$44$$ −2.36603 4.09808i −0.356692 0.617808i
$$45$$ 2.13397 + 3.69615i 0.318114 + 0.550990i
$$46$$ 1.09808 + 1.90192i 0.161903 + 0.280423i
$$47$$ −0.464102 0.803848i −0.0676962 0.117253i 0.830191 0.557480i $$-0.188232\pi$$
−0.897887 + 0.440226i $$0.854898\pi$$
$$48$$ 1.83013 3.16987i 0.264156 0.457532i
$$49$$ 0 0
$$50$$ −1.73205 3.00000i −0.244949 0.424264i
$$51$$ −1.56218 2.70577i −0.218749 0.378884i
$$52$$ −3.59808 + 0.232051i −0.498963 + 0.0321797i
$$53$$ −1.96410 + 3.40192i −0.269790 + 0.467290i −0.968808 0.247814i $$-0.920288\pi$$
0.699017 + 0.715105i $$0.253621\pi$$
$$54$$ −3.46410 + 6.00000i −0.471405 + 0.816497i
$$55$$ −4.09808 7.09808i −0.552584 0.957104i
$$56$$ 0 0
$$57$$ −1.46410 −0.193925
$$58$$ 5.19615 0.682288
$$59$$ 5.36603 + 9.29423i 0.698597 + 1.21001i 0.968953 + 0.247245i $$0.0795253\pi$$
−0.270356 + 0.962760i $$0.587141\pi$$
$$60$$ −0.633975 + 1.09808i −0.0818458 + 0.141761i
$$61$$ 15.1962 1.94567 0.972834 0.231504i $$-0.0743646\pi$$
0.972834 + 0.231504i $$0.0743646\pi$$
$$62$$ 5.36603 + 9.29423i 0.681486 + 1.18037i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ −6.23205 + 0.401924i −0.772991 + 0.0498525i
$$66$$ 3.00000 5.19615i 0.369274 0.639602i
$$67$$ 4.19615 0.512642 0.256321 0.966592i $$-0.417490\pi$$
0.256321 + 0.966592i $$0.417490\pi$$
$$68$$ −2.13397 + 3.69615i −0.258782 + 0.448224i
$$69$$ −0.464102 + 0.803848i −0.0558713 + 0.0967719i
$$70$$ 0 0
$$71$$ −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i $$-0.949205\pi$$
0.631260 + 0.775571i $$0.282538\pi$$
$$72$$ −4.26795 −0.502983
$$73$$ 3.59808 6.23205i 0.421123 0.729406i −0.574927 0.818205i $$-0.694969\pi$$
0.996050 + 0.0887986i $$0.0283027\pi$$
$$74$$ −6.06218 10.5000i −0.704714 1.22060i
$$75$$ 0.732051 1.26795i 0.0845299 0.146410i
$$76$$ 1.00000 + 1.73205i 0.114708 + 0.198680i
$$77$$ 0 0
$$78$$ −2.53590 3.80385i −0.287134 0.430701i
$$79$$ −2.90192 5.02628i −0.326492 0.565501i 0.655321 0.755350i $$-0.272533\pi$$
−0.981813 + 0.189850i $$0.939200\pi$$
$$80$$ −8.66025 −0.968246
$$81$$ 4.46410 0.496011
$$82$$ 9.00000 0.993884
$$83$$ −8.19615 −0.899645 −0.449822 0.893118i $$-0.648513\pi$$
−0.449822 + 0.893118i $$0.648513\pi$$
$$84$$ 0 0
$$85$$ −3.69615 + 6.40192i −0.400904 + 0.694386i
$$86$$ 8.83013 + 15.2942i 0.952177 + 1.64922i
$$87$$ 1.09808 + 1.90192i 0.117726 + 0.203908i
$$88$$ 8.19615 0.873713
$$89$$ −0.464102 + 0.803848i −0.0491947 + 0.0852077i −0.889574 0.456791i $$-0.848999\pi$$
0.840379 + 0.541998i $$0.182332\pi$$
$$90$$ 7.39230 0.779217
$$91$$ 0 0
$$92$$ 1.26795 0.132193
$$93$$ −2.26795 + 3.92820i −0.235175 + 0.407336i
$$94$$ −1.60770 −0.165821
$$95$$ 1.73205 + 3.00000i 0.177705 + 0.307794i
$$96$$ −1.90192 3.29423i −0.194114 0.336216i
$$97$$ −7.19615 + 12.4641i −0.730659 + 1.26554i 0.225944 + 0.974140i $$0.427454\pi$$
−0.956602 + 0.291397i $$0.905880\pi$$
$$98$$ 0 0
$$99$$ −11.6603 −1.17190
$$100$$ −2.00000 −0.200000
$$101$$ 4.26795 0.424677 0.212338 0.977196i $$-0.431892\pi$$
0.212338 + 0.977196i $$0.431892\pi$$
$$102$$ −5.41154 −0.535823
$$103$$ 3.19615 + 5.53590i 0.314926 + 0.545468i 0.979422 0.201824i $$-0.0646869\pi$$
−0.664496 + 0.747292i $$0.731354\pi$$
$$104$$ 2.76795 5.59808i 0.271420 0.548937i
$$105$$ 0 0
$$106$$ 3.40192 + 5.89230i 0.330424 + 0.572311i
$$107$$ −9.92820 + 17.1962i −0.959796 + 1.66241i −0.236805 + 0.971557i $$0.576100\pi$$
−0.722991 + 0.690858i $$0.757233\pi$$
$$108$$ 2.00000 + 3.46410i 0.192450 + 0.333333i
$$109$$ −6.19615 + 10.7321i −0.593484 + 1.02794i 0.400275 + 0.916395i $$0.368915\pi$$
−0.993759 + 0.111549i $$0.964419\pi$$
$$110$$ −14.1962 −1.35355
$$111$$ 2.56218 4.43782i 0.243191 0.421219i
$$112$$ 0 0
$$113$$ 3.69615 6.40192i 0.347705 0.602242i −0.638137 0.769923i $$-0.720294\pi$$
0.985841 + 0.167681i $$0.0536278\pi$$
$$114$$ −1.26795 + 2.19615i −0.118754 + 0.205689i
$$115$$ 2.19615 0.204792
$$116$$ 1.50000 2.59808i 0.139272 0.241225i
$$117$$ −3.93782 + 7.96410i −0.364052 + 0.736281i
$$118$$ 18.5885 1.71121
$$119$$ 0 0
$$120$$ −1.09808 1.90192i −0.100240 0.173621i
$$121$$ 11.3923 1.03566
$$122$$ 13.1603 22.7942i 1.19147 2.06369i
$$123$$ 1.90192 + 3.29423i 0.171491 + 0.297031i
$$124$$ 6.19615 0.556431
$$125$$ −12.1244 −1.08444
$$126$$ 0 0
$$127$$ 1.19615 + 2.07180i 0.106141 + 0.183842i 0.914204 0.405254i $$-0.132817\pi$$
−0.808063 + 0.589097i $$0.799484\pi$$
$$128$$ 6.06218 10.5000i 0.535826 0.928078i
$$129$$ −3.73205 + 6.46410i −0.328589 + 0.569132i
$$130$$ −4.79423 + 9.69615i −0.420482 + 0.850409i
$$131$$ 1.73205 + 3.00000i 0.151330 + 0.262111i 0.931717 0.363186i $$-0.118311\pi$$
−0.780387 + 0.625297i $$0.784978\pi$$
$$132$$ −1.73205 3.00000i −0.150756 0.261116i
$$133$$ 0 0
$$134$$ 3.63397 6.29423i 0.313928 0.543739i
$$135$$ 3.46410 + 6.00000i 0.298142 + 0.516398i
$$136$$ −3.69615 6.40192i −0.316942 0.548960i
$$137$$ −10.9641 18.9904i −0.936726 1.62246i −0.771526 0.636198i $$-0.780506\pi$$
−0.165200 0.986260i $$-0.552827\pi$$
$$138$$ 0.803848 + 1.39230i 0.0684280 + 0.118521i
$$139$$ 10.2942 17.8301i 0.873145 1.51233i 0.0144194 0.999896i $$-0.495410\pi$$
0.858726 0.512436i $$-0.171257\pi$$
$$140$$ 0 0
$$141$$ −0.339746 0.588457i −0.0286118 0.0495570i
$$142$$ 5.19615 + 9.00000i 0.436051 + 0.755263i
$$143$$ 7.56218 15.2942i 0.632381 1.27897i
$$144$$ −6.16025 + 10.6699i −0.513355 + 0.889156i
$$145$$ 2.59808 4.50000i 0.215758 0.373705i
$$146$$ −6.23205 10.7942i −0.515768 0.893337i
$$147$$ 0 0
$$148$$ −7.00000 −0.575396
$$149$$ 0.464102 0.0380207 0.0190103 0.999819i $$-0.493948\pi$$
0.0190103 + 0.999819i $$0.493948\pi$$
$$150$$ −1.26795 2.19615i −0.103528 0.179315i
$$151$$ −1.00000 + 1.73205i −0.0813788 + 0.140952i −0.903842 0.427865i $$-0.859266\pi$$
0.822464 + 0.568818i $$0.192599\pi$$
$$152$$ −3.46410 −0.280976
$$153$$ 5.25833 + 9.10770i 0.425111 + 0.736314i
$$154$$ 0 0
$$155$$ 10.7321 0.862019
$$156$$ −2.63397 + 0.169873i −0.210887 + 0.0136007i
$$157$$ −4.59808 + 7.96410i −0.366966 + 0.635605i −0.989090 0.147315i $$-0.952937\pi$$
0.622123 + 0.782919i $$0.286270\pi$$
$$158$$ −10.0526 −0.799739
$$159$$ −1.43782 + 2.49038i −0.114027 + 0.197500i
$$160$$ −4.50000 + 7.79423i −0.355756 + 0.616188i
$$161$$ 0 0
$$162$$ 3.86603 6.69615i 0.303744 0.526099i
$$163$$ 5.80385 0.454592 0.227296 0.973826i $$-0.427011\pi$$
0.227296 + 0.973826i $$0.427011\pi$$
$$164$$ 2.59808 4.50000i 0.202876 0.351391i
$$165$$ −3.00000 5.19615i −0.233550 0.404520i
$$166$$ −7.09808 + 12.2942i −0.550918 + 0.954217i
$$167$$ 12.2942 + 21.2942i 0.951356 + 1.64780i 0.742495 + 0.669852i $$0.233642\pi$$
0.208861 + 0.977945i $$0.433024\pi$$
$$168$$ 0 0
$$169$$ −7.89230 10.3301i −0.607100 0.794625i
$$170$$ 6.40192 + 11.0885i 0.491005 + 0.850446i
$$171$$ 4.92820 0.376869
$$172$$ 10.1962 0.777449
$$173$$ −15.4641 −1.17571 −0.587857 0.808965i $$-0.700028\pi$$
−0.587857 + 0.808965i $$0.700028\pi$$
$$174$$ 3.80385 0.288369
$$175$$ 0 0
$$176$$ 11.8301 20.4904i 0.891729 1.54452i
$$177$$ 3.92820 + 6.80385i 0.295262 + 0.511409i
$$178$$ 0.803848 + 1.39230i 0.0602509 + 0.104358i
$$179$$ 6.92820 0.517838 0.258919 0.965899i $$-0.416634\pi$$
0.258919 + 0.965899i $$0.416634\pi$$
$$180$$ 2.13397 3.69615i 0.159057 0.275495i
$$181$$ 25.5885 1.90198 0.950988 0.309229i $$-0.100071\pi$$
0.950988 + 0.309229i $$0.100071\pi$$
$$182$$ 0 0
$$183$$ 11.1244 0.822336
$$184$$ −1.09808 + 1.90192i −0.0809513 + 0.140212i
$$185$$ −12.1244 −0.891400
$$186$$ 3.92820 + 6.80385i 0.288030 + 0.498882i
$$187$$ −10.0981 17.4904i −0.738444 1.27902i
$$188$$ −0.464102 + 0.803848i −0.0338481 + 0.0586266i
$$189$$ 0 0
$$190$$ 6.00000 0.435286
$$191$$ 1.26795 0.0917456 0.0458728 0.998947i $$-0.485393\pi$$
0.0458728 + 0.998947i $$0.485393\pi$$
$$192$$ 0.732051 0.0528312
$$193$$ 5.00000 0.359908 0.179954 0.983675i $$-0.442405\pi$$
0.179954 + 0.983675i $$0.442405\pi$$
$$194$$ 12.4641 + 21.5885i 0.894870 + 1.54996i
$$195$$ −4.56218 + 0.294229i −0.326704 + 0.0210702i
$$196$$ 0 0
$$197$$ −6.00000 10.3923i −0.427482 0.740421i 0.569166 0.822222i $$-0.307266\pi$$
−0.996649 + 0.0818013i $$0.973933\pi$$
$$198$$ −10.0981 + 17.4904i −0.717639 + 1.24299i
$$199$$ 1.00000 + 1.73205i 0.0708881 + 0.122782i 0.899291 0.437351i $$-0.144083\pi$$
−0.828403 + 0.560133i $$0.810750\pi$$
$$200$$ 1.73205 3.00000i 0.122474 0.212132i
$$201$$ 3.07180 0.216668
$$202$$ 3.69615 6.40192i 0.260060 0.450438i
$$203$$ 0 0
$$204$$ −1.56218 + 2.70577i −0.109374 + 0.189442i
$$205$$ 4.50000 7.79423i 0.314294 0.544373i
$$206$$ 11.0718 0.771409
$$207$$ 1.56218 2.70577i 0.108579 0.188064i
$$208$$ −10.0000 15.0000i −0.693375 1.04006i
$$209$$ −9.46410 −0.654646
$$210$$ 0 0
$$211$$ 6.09808 + 10.5622i 0.419809 + 0.727130i 0.995920 0.0902411i $$-0.0287638\pi$$
−0.576111 + 0.817371i $$0.695430\pi$$
$$212$$ 3.92820 0.269790
$$213$$ −2.19615 + 3.80385i −0.150478 + 0.260635i
$$214$$ 17.1962 + 29.7846i 1.17550 + 2.03603i
$$215$$ 17.6603 1.20442
$$216$$ −6.92820 −0.471405
$$217$$ 0 0
$$218$$ 10.7321 + 18.5885i 0.726866 + 1.25897i
$$219$$ 2.63397 4.56218i 0.177988 0.308283i
$$220$$ −4.09808 + 7.09808i −0.276292 + 0.478552i
$$221$$ −15.3564 + 0.990381i −1.03298 + 0.0666202i
$$222$$ −4.43782 7.68653i −0.297847 0.515886i
$$223$$ −5.00000 8.66025i −0.334825 0.579934i 0.648626 0.761107i $$-0.275344\pi$$
−0.983451 + 0.181173i $$0.942010\pi$$
$$224$$ 0 0
$$225$$ −2.46410 + 4.26795i −0.164273 + 0.284530i
$$226$$ −6.40192 11.0885i −0.425850 0.737593i
$$227$$ −5.83013 10.0981i −0.386959 0.670233i 0.605080 0.796165i $$-0.293141\pi$$
−0.992039 + 0.125932i $$0.959808\pi$$
$$228$$ 0.732051 + 1.26795i 0.0484812 + 0.0839720i
$$229$$ 3.19615 + 5.53590i 0.211208 + 0.365822i 0.952093 0.305809i $$-0.0989270\pi$$
−0.740885 + 0.671632i $$0.765594\pi$$
$$230$$ 1.90192 3.29423i 0.125409 0.217215i
$$231$$ 0 0
$$232$$ 2.59808 + 4.50000i 0.170572 + 0.295439i
$$233$$ −12.9282 22.3923i −0.846955 1.46697i −0.883913 0.467652i $$-0.845100\pi$$
0.0369580 0.999317i $$-0.488233\pi$$
$$234$$ 8.53590 + 12.8038i 0.558009 + 0.837014i
$$235$$ −0.803848 + 1.39230i −0.0524372 + 0.0908240i
$$236$$ 5.36603 9.29423i 0.349299 0.605003i
$$237$$ −2.12436 3.67949i −0.137992 0.239009i
$$238$$ 0 0
$$239$$ −26.1962 −1.69449 −0.847244 0.531204i $$-0.821740\pi$$
−0.847244 + 0.531204i $$0.821740\pi$$
$$240$$ −6.33975 −0.409229
$$241$$ −5.40192 9.35641i −0.347969 0.602699i 0.637920 0.770103i $$-0.279795\pi$$
−0.985888 + 0.167404i $$0.946462\pi$$
$$242$$ 9.86603 17.0885i 0.634212 1.09849i
$$243$$ 15.2679 0.979439
$$244$$ −7.59808 13.1603i −0.486417 0.842499i
$$245$$ 0 0
$$246$$ 6.58846 0.420065
$$247$$ −3.19615 + 6.46410i −0.203366 + 0.411301i
$$248$$ −5.36603 + 9.29423i −0.340743 + 0.590184i
$$249$$ −6.00000 −0.380235
$$250$$ −10.5000 + 18.1865i −0.664078 + 1.15022i
$$251$$ −11.1962 + 19.3923i −0.706695 + 1.22403i 0.259382 + 0.965775i $$0.416481\pi$$
−0.966076 + 0.258256i $$0.916852\pi$$
$$252$$ 0 0
$$253$$ −3.00000 + 5.19615i −0.188608 + 0.326679i
$$254$$ 4.14359 0.259992
$$255$$ −2.70577 + 4.68653i −0.169442 + 0.293482i
$$256$$ −9.50000 16.4545i −0.593750 1.02841i
$$257$$ −9.06218 + 15.6962i −0.565283 + 0.979099i 0.431740 + 0.901998i $$0.357900\pi$$
−0.997023 + 0.0771011i $$0.975434\pi$$
$$258$$ 6.46410 + 11.1962i 0.402437 + 0.697042i
$$259$$ 0 0
$$260$$ 3.46410 + 5.19615i 0.214834 + 0.322252i
$$261$$ −3.69615 6.40192i −0.228786 0.396269i
$$262$$ 6.00000 0.370681
$$263$$ 4.73205 0.291791 0.145895 0.989300i $$-0.453394\pi$$
0.145895 + 0.989300i $$0.453394\pi$$
$$264$$ 6.00000 0.369274
$$265$$ 6.80385 0.417957
$$266$$ 0 0
$$267$$ −0.339746 + 0.588457i −0.0207921 + 0.0360130i
$$268$$ −2.09808 3.63397i −0.128160 0.221980i
$$269$$ 9.46410 + 16.3923i 0.577036 + 0.999456i 0.995817 + 0.0913690i $$0.0291243\pi$$
−0.418781 + 0.908087i $$0.637542\pi$$
$$270$$ 12.0000 0.730297
$$271$$ 8.09808 14.0263i 0.491923 0.852036i −0.508034 0.861337i $$-0.669627\pi$$
0.999957 + 0.00930143i $$0.00296078\pi$$
$$272$$ −21.3397 −1.29391
$$273$$ 0 0
$$274$$ −37.9808 −2.29450
$$275$$ 4.73205 8.19615i 0.285353 0.494247i
$$276$$ 0.928203 0.0558713
$$277$$ −8.50000 14.7224i −0.510716 0.884585i −0.999923 0.0124177i $$-0.996047\pi$$
0.489207 0.872167i $$-0.337286\pi$$
$$278$$ −17.8301 30.8827i −1.06938 1.85222i
$$279$$ 7.63397 13.2224i 0.457034 0.791606i
$$280$$ 0 0
$$281$$ −7.39230 −0.440988 −0.220494 0.975388i $$-0.570767\pi$$
−0.220494 + 0.975388i $$0.570767\pi$$
$$282$$ −1.17691 −0.0700842
$$283$$ 0.196152 0.0116601 0.00583003 0.999983i $$-0.498144\pi$$
0.00583003 + 0.999983i $$0.498144\pi$$
$$284$$ 6.00000 0.356034
$$285$$ 1.26795 + 2.19615i 0.0751068 + 0.130089i
$$286$$ −16.3923 24.5885i −0.969297 1.45395i
$$287$$ 0 0
$$288$$ 6.40192 + 11.0885i 0.377237 + 0.653394i
$$289$$ −0.607695 + 1.05256i −0.0357468 + 0.0619152i
$$290$$ −4.50000 7.79423i −0.264249 0.457693i
$$291$$ −5.26795 + 9.12436i −0.308813 + 0.534879i
$$292$$ −7.19615 −0.421123
$$293$$ −5.59808 + 9.69615i −0.327043 + 0.566455i −0.981924 0.189277i $$-0.939386\pi$$
0.654881 + 0.755732i $$0.272719\pi$$
$$294$$ 0 0
$$295$$ 9.29423 16.0981i 0.541131 0.937266i
$$296$$ 6.06218 10.5000i 0.352357 0.610300i
$$297$$ −18.9282 −1.09833
$$298$$ 0.401924 0.696152i 0.0232828 0.0403270i
$$299$$ 2.53590 + 3.80385i 0.146655 + 0.219982i
$$300$$ −1.46410 −0.0845299
$$301$$ 0 0
$$302$$ 1.73205 + 3.00000i 0.0996683 + 0.172631i
$$303$$ 3.12436 0.179490
$$304$$ −5.00000 + 8.66025i −0.286770 + 0.496700i
$$305$$ −13.1603 22.7942i −0.753554 1.30519i
$$306$$ 18.2154 1.04130
$$307$$ −26.5885 −1.51748 −0.758742 0.651392i $$-0.774186\pi$$
−0.758742 + 0.651392i $$0.774186\pi$$
$$308$$ 0 0
$$309$$ 2.33975 + 4.05256i 0.133103 + 0.230542i
$$310$$ 9.29423 16.0981i 0.527877 0.914309i
$$311$$ 2.36603 4.09808i 0.134165 0.232381i −0.791113 0.611670i $$-0.790498\pi$$
0.925278 + 0.379289i $$0.123831\pi$$
$$312$$ 2.02628 4.09808i 0.114715 0.232008i
$$313$$ −6.39230 11.0718i −0.361314 0.625815i 0.626863 0.779129i $$-0.284339\pi$$
−0.988177 + 0.153315i $$0.951005\pi$$
$$314$$ 7.96410 + 13.7942i 0.449440 + 0.778453i
$$315$$ 0 0
$$316$$ −2.90192 + 5.02628i −0.163246 + 0.282750i
$$317$$ −0.232051 0.401924i −0.0130333 0.0225743i 0.859435 0.511245i $$-0.170815\pi$$
−0.872468 + 0.488670i $$0.837482\pi$$
$$318$$ 2.49038 + 4.31347i 0.139654 + 0.241887i
$$319$$ 7.09808 + 12.2942i 0.397416 + 0.688345i
$$320$$ −0.866025 1.50000i −0.0484123 0.0838525i
$$321$$ −7.26795 + 12.5885i −0.405657 + 0.702619i
$$322$$ 0 0
$$323$$ 4.26795 + 7.39230i 0.237475 + 0.411319i
$$324$$ −2.23205 3.86603i −0.124003 0.214779i
$$325$$ −4.00000 6.00000i −0.221880 0.332820i
$$326$$ 5.02628 8.70577i 0.278380 0.482168i
$$327$$ −4.53590 + 7.85641i −0.250836 + 0.434460i
$$328$$ 4.50000 + 7.79423i 0.248471 + 0.430364i
$$329$$ 0 0
$$330$$ −10.3923 −0.572078
$$331$$ −26.9808 −1.48300 −0.741498 0.670955i $$-0.765885\pi$$
−0.741498 + 0.670955i $$0.765885\pi$$
$$332$$ 4.09808 + 7.09808i 0.224911 + 0.389558i
$$333$$ −8.62436 + 14.9378i −0.472612 + 0.818588i
$$334$$ 42.5885 2.33034
$$335$$ −3.63397 6.29423i −0.198545 0.343890i
$$336$$ 0 0
$$337$$ 11.0000 0.599208 0.299604 0.954064i $$-0.403145\pi$$
0.299604 + 0.954064i $$0.403145\pi$$
$$338$$ −22.3301 + 2.89230i −1.21460 + 0.157321i
$$339$$ 2.70577 4.68653i 0.146957 0.254538i
$$340$$ 7.39230 0.400904
$$341$$ −14.6603 + 25.3923i −0.793897 + 1.37507i
$$342$$ 4.26795 7.39230i 0.230784 0.399730i
$$343$$ 0 0
$$344$$ −8.83013 + 15.2942i −0.476089 + 0.824610i
$$345$$ 1.60770 0.0865554
$$346$$ −13.3923 + 23.1962i −0.719975 + 1.24703i
$$347$$ −5.36603 9.29423i −0.288063 0.498940i 0.685284 0.728276i $$-0.259678\pi$$
−0.973347 + 0.229336i $$0.926345\pi$$
$$348$$ 1.09808 1.90192i 0.0588631 0.101954i
$$349$$ 8.39230 + 14.5359i 0.449230 + 0.778089i 0.998336 0.0576637i $$-0.0183651\pi$$
−0.549106 + 0.835753i $$0.685032\pi$$
$$350$$ 0 0
$$351$$ −6.39230 + 12.9282i −0.341196 + 0.690056i
$$352$$ −12.2942 21.2942i −0.655285 1.13499i
$$353$$ −3.33975 −0.177757 −0.0888784 0.996042i $$-0.528328\pi$$
−0.0888784 + 0.996042i $$0.528328\pi$$
$$354$$ 13.6077 0.723241
$$355$$ 10.3923 0.551566
$$356$$ 0.928203 0.0491947
$$357$$ 0 0
$$358$$ 6.00000 10.3923i 0.317110 0.549250i
$$359$$ −2.53590 4.39230i −0.133840 0.231817i 0.791314 0.611410i $$-0.209397\pi$$
−0.925154 + 0.379593i $$0.876064\pi$$
$$360$$ 3.69615 + 6.40192i 0.194804 + 0.337411i
$$361$$ −15.0000 −0.789474
$$362$$ 22.1603 38.3827i 1.16472 2.01735i
$$363$$ 8.33975 0.437723
$$364$$ 0 0
$$365$$ −12.4641 −0.652401
$$366$$ 9.63397 16.6865i 0.503576 0.872219i
$$367$$ 6.19615 0.323437 0.161718 0.986837i $$-0.448296\pi$$
0.161718 + 0.986837i $$0.448296\pi$$
$$368$$ 3.16987 + 5.49038i 0.165241 + 0.286206i
$$369$$ −6.40192 11.0885i −0.333271 0.577242i
$$370$$ −10.5000 + 18.1865i −0.545869 + 0.945473i
$$371$$ 0 0
$$372$$ 4.53590 0.235175
$$373$$ 9.39230 0.486315 0.243158 0.969987i $$-0.421817\pi$$
0.243158 + 0.969987i $$0.421817\pi$$
$$374$$ −34.9808 −1.80881
$$375$$ −8.87564 −0.458336
$$376$$ −0.803848 1.39230i −0.0414553 0.0718026i
$$377$$ 10.7942 0.696152i 0.555931 0.0358537i
$$378$$ 0 0
$$379$$ 2.29423 + 3.97372i 0.117847 + 0.204116i 0.918914 0.394458i $$-0.129068\pi$$
−0.801067 + 0.598574i $$0.795734\pi$$
$$380$$ 1.73205 3.00000i 0.0888523 0.153897i
$$381$$ 0.875644 + 1.51666i 0.0448606 + 0.0777009i
$$382$$ 1.09808 1.90192i 0.0561825 0.0973109i
$$383$$ −5.66025 −0.289225 −0.144613 0.989488i $$-0.546194\pi$$
−0.144613 + 0.989488i $$0.546194\pi$$
$$384$$ 4.43782 7.68653i 0.226467 0.392252i
$$385$$ 0 0
$$386$$ 4.33013 7.50000i 0.220398 0.381740i
$$387$$ 12.5622 21.7583i 0.638571 1.10604i
$$388$$ 14.3923 0.730659
$$389$$ 15.2321 26.3827i 0.772296 1.33766i −0.164006 0.986459i $$-0.552442\pi$$
0.936302 0.351196i $$-0.114225\pi$$
$$390$$ −3.50962 + 7.09808i −0.177716 + 0.359425i
$$391$$ 5.41154 0.273673
$$392$$ 0 0
$$393$$ 1.26795 + 2.19615i 0.0639596 + 0.110781i
$$394$$ −20.7846 −1.04711
$$395$$ −5.02628 + 8.70577i −0.252900 + 0.438035i
$$396$$ 5.83013 + 10.0981i 0.292975 + 0.507447i
$$397$$ −22.7846 −1.14353 −0.571763 0.820419i $$-0.693740\pi$$
−0.571763 + 0.820419i $$0.693740\pi$$
$$398$$ 3.46410 0.173640
$$399$$ 0 0
$$400$$ −5.00000 8.66025i −0.250000 0.433013i
$$401$$ −8.42820 + 14.5981i −0.420884 + 0.728993i −0.996026 0.0890606i $$-0.971614\pi$$
0.575142 + 0.818054i $$0.304947\pi$$
$$402$$ 2.66025 4.60770i 0.132681 0.229811i
$$403$$ 12.3923 + 18.5885i 0.617305 + 0.925957i
$$404$$ −2.13397 3.69615i −0.106169 0.183890i
$$405$$ −3.86603 6.69615i −0.192104 0.332734i
$$406$$ 0 0
$$407$$ 16.5622 28.6865i 0.820957 1.42194i
$$408$$ −2.70577 4.68653i −0.133956 0.232018i
$$409$$ −13.5981 23.5526i −0.672382 1.16460i −0.977227 0.212197i $$-0.931938\pi$$
0.304845 0.952402i $$-0.401395\pi$$
$$410$$ −7.79423 13.5000i −0.384930 0.666717i
$$411$$ −8.02628 13.9019i −0.395907 0.685731i
$$412$$ 3.19615 5.53590i 0.157463 0.272734i
$$413$$ 0 0
$$414$$ −2.70577 4.68653i −0.132981 0.230331i
$$415$$ 7.09808 + 12.2942i 0.348431 + 0.603500i
$$416$$ −18.6962 + 1.20577i −0.916654 + 0.0591178i
$$417$$ 7.53590 13.0526i 0.369035 0.639187i
$$418$$ −8.19615 + 14.1962i −0.400887 + 0.694357i
$$419$$ −10.9019 18.8827i −0.532594 0.922480i −0.999276 0.0380543i $$-0.987884\pi$$
0.466682 0.884425i $$-0.345449\pi$$
$$420$$ 0 0
$$421$$ 30.1769 1.47073 0.735366 0.677670i $$-0.237010\pi$$
0.735366 + 0.677670i $$0.237010\pi$$
$$422$$ 21.1244 1.02832
$$423$$ 1.14359 + 1.98076i 0.0556034 + 0.0963079i
$$424$$ −3.40192 + 5.89230i −0.165212 + 0.286156i
$$425$$ −8.53590 −0.414052
$$426$$ 3.80385 + 6.58846i 0.184297 + 0.319212i
$$427$$ 0 0
$$428$$ 19.8564 0.959796
$$429$$ 5.53590 11.1962i 0.267276 0.540555i
$$430$$ 15.2942 26.4904i 0.737553 1.27748i
$$431$$ 35.3205 1.70133 0.850665 0.525709i $$-0.176200\pi$$
0.850665 + 0.525709i $$0.176200\pi$$
$$432$$ −10.0000 + 17.3205i −0.481125 + 0.833333i
$$433$$ 8.79423 15.2321i 0.422624 0.732006i −0.573572 0.819155i $$-0.694443\pi$$
0.996195 + 0.0871498i $$0.0277759\pi$$
$$434$$ 0 0
$$435$$ 1.90192 3.29423i 0.0911903 0.157946i
$$436$$ 12.3923 0.593484
$$437$$ 1.26795 2.19615i 0.0606542 0.105056i
$$438$$ −4.56218 7.90192i −0.217989 0.377569i
$$439$$ −8.29423 + 14.3660i −0.395862 + 0.685653i −0.993211 0.116329i $$-0.962887\pi$$
0.597349 + 0.801982i $$0.296221\pi$$
$$440$$ −7.09808 12.2942i −0.338388 0.586104i
$$441$$ 0 0
$$442$$ −11.8135 + 23.8923i −0.561909 + 1.13644i
$$443$$ 5.66025 + 9.80385i 0.268927 + 0.465795i 0.968585 0.248683i $$-0.0799977\pi$$
−0.699658 + 0.714478i $$0.746664\pi$$
$$444$$ −5.12436 −0.243191
$$445$$ 1.60770 0.0762121
$$446$$ −17.3205 −0.820150
$$447$$ 0.339746 0.0160694
$$448$$ 0 0
$$449$$ 6.00000 10.3923i 0.283158 0.490443i −0.689003 0.724758i $$-0.741951\pi$$
0.972161 + 0.234315i $$0.0752847\pi$$
$$450$$ 4.26795 + 7.39230i 0.201193 + 0.348477i
$$451$$ 12.2942 + 21.2942i 0.578913 + 1.00271i
$$452$$ −7.39230 −0.347705
$$453$$ −0.732051 + 1.26795i −0.0343947 + 0.0595734i
$$454$$ −20.1962 −0.947852
$$455$$ 0 0
$$456$$ −2.53590 −0.118754
$$457$$ −5.50000 + 9.52628i −0.257279 + 0.445621i −0.965512 0.260358i $$-0.916159\pi$$
0.708233 + 0.705979i $$0.249493\pi$$
$$458$$ 11.0718 0.517351
$$459$$ 8.53590 + 14.7846i 0.398422 + 0.690086i
$$460$$ −1.09808 1.90192i −0.0511981 0.0886777i
$$461$$ 7.79423 13.5000i 0.363013 0.628758i −0.625442 0.780271i $$-0.715081\pi$$
0.988455 + 0.151513i $$0.0484146\pi$$
$$462$$ 0 0
$$463$$ 26.5885 1.23567 0.617835 0.786308i $$-0.288010\pi$$
0.617835 + 0.786308i $$0.288010\pi$$
$$464$$ 15.0000 0.696358
$$465$$ 7.85641 0.364332
$$466$$ −44.7846 −2.07461
$$467$$ −9.75833 16.9019i −0.451562 0.782128i 0.546922 0.837184i $$-0.315800\pi$$
−0.998483 + 0.0550561i $$0.982466\pi$$
$$468$$ 8.86603 0.571797i 0.409832 0.0264313i
$$469$$ 0 0
$$470$$ 1.39230 + 2.41154i 0.0642222 + 0.111236i
$$471$$ −3.36603 + 5.83013i −0.155098 + 0.268638i
$$472$$ 9.29423 + 16.0981i 0.427802 + 0.740974i
$$473$$ −24.1244 + 41.7846i −1.10924 + 1.92126i
$$474$$ −7.35898 −0.338009
$$475$$ −2.00000 + 3.46410i −0.0917663 + 0.158944i
$$476$$ 0 0
$$477$$ 4.83975 8.38269i 0.221597 0.383817i
$$478$$ −22.6865 + 39.2942i −1.03766 + 1.79728i
$$479$$ −4.73205 −0.216213 −0.108106 0.994139i $$-0.534479\pi$$
−0.108106 + 0.994139i $$0.534479\pi$$
$$480$$ −3.29423 + 5.70577i −0.150360 + 0.260432i
$$481$$ −14.0000 21.0000i −0.638345 0.957518i
$$482$$ −18.7128 −0.852345
$$483$$ 0 0
$$484$$ −5.69615 9.86603i −0.258916 0.448456i
$$485$$ 24.9282 1.13193
$$486$$ 13.2224 22.9019i 0.599782 1.03885i
$$487$$ 0.392305 + 0.679492i 0.0177770 + 0.0307907i 0.874777 0.484526i $$-0.161008\pi$$
−0.857000 + 0.515316i $$0.827674\pi$$
$$488$$ 26.3205 1.19147
$$489$$ 4.24871 0.192133
$$490$$ 0 0
$$491$$ −14.1962 24.5885i −0.640663 1.10966i −0.985285 0.170920i $$-0.945326\pi$$
0.344622 0.938742i $$-0.388007\pi$$
$$492$$ 1.90192 3.29423i 0.0857453 0.148515i
$$493$$ 6.40192 11.0885i 0.288328 0.499399i
$$494$$ 6.92820 + 10.3923i 0.311715 + 0.467572i
$$495$$ 10.0981 + 17.4904i 0.453875 + 0.786134i
$$496$$ 15.4904 + 26.8301i 0.695539 + 1.20471i
$$497$$ 0 0
$$498$$ −5.19615 + 9.00000i −0.232845 + 0.403300i
$$499$$ −6.49038 11.2417i −0.290549 0.503246i 0.683390 0.730053i $$-0.260505\pi$$
−0.973940 + 0.226807i $$0.927171\pi$$
$$500$$ 6.06218 + 10.5000i 0.271109 + 0.469574i
$$501$$ 9.00000 + 15.5885i 0.402090 + 0.696441i
$$502$$ 19.3923 + 33.5885i 0.865521 + 1.49913i
$$503$$ 6.29423 10.9019i 0.280646 0.486093i −0.690898 0.722952i $$-0.742785\pi$$
0.971544 + 0.236859i $$0.0761181\pi$$
$$504$$ 0 0
$$505$$ −3.69615 6.40192i −0.164477 0.284882i
$$506$$ 5.19615 + 9.00000i 0.230997 + 0.400099i
$$507$$ −5.77757 7.56218i −0.256591 0.335848i
$$508$$ 1.19615 2.07180i 0.0530707 0.0919211i
$$509$$ 5.13397 8.89230i 0.227559 0.394144i −0.729525 0.683954i $$-0.760259\pi$$
0.957084 + 0.289810i $$0.0935921\pi$$
$$510$$ 4.68653 + 8.11731i 0.207523 + 0.359441i
$$511$$ 0 0
$$512$$ −8.66025 −0.382733
$$513$$ 8.00000 0.353209
$$514$$ 15.6962 + 27.1865i 0.692328 + 1.19915i
$$515$$ 5.53590 9.58846i 0.243941 0.422518i
$$516$$ 7.46410 0.328589
$$517$$ −2.19615 3.80385i −0.0965867 0.167293i
$$518$$ 0 0
$$519$$ −11.3205 −0.496915
$$520$$ −10.7942 + 0.696152i −0.473358 + 0.0305283i
$$521$$ 0.0621778 0.107695i 0.00272406 0.00471821i −0.864660 0.502357i $$-0.832466\pi$$
0.867384 + 0.497639i $$0.165800\pi$$
$$522$$ −12.8038 −0.560409
$$523$$ 16.5885 28.7321i 0.725363 1.25636i −0.233462 0.972366i $$-0.575005\pi$$
0.958825 0.283999i $$-0.0916612\pi$$
$$524$$ 1.73205 3.00000i 0.0756650 0.131056i
$$525$$ 0 0
$$526$$ 4.09808 7.09808i 0.178685 0.309491i
$$527$$ 26.4449 1.15196
$$528$$ 8.66025 15.0000i 0.376889 0.652791i
$$529$$ 10.6962 + 18.5263i 0.465050 + 0.805490i
$$530$$ 5.89230 10.2058i 0.255945 0.443310i
$$531$$ −13.2224 22.9019i −0.573805 0.993859i
$$532$$ 0 0
$$533$$ 18.6962 1.20577i 0.809820 0.0522278i
$$534$$ 0.588457 + 1.01924i 0.0254650 + 0.0441067i
$$535$$ 34.3923 1.48691
$$536$$ 7.26795 0.313928
$$537$$ 5.07180 0.218864
$$538$$ 32.7846 1.41344
$$539$$ 0 0
$$540$$ 3.46410 6.00000i 0.149071 0.258199i
$$541$$ 17.6962 + 30.6506i 0.760817 + 1.31777i 0.942430 + 0.334404i $$0.108535\pi$$
−0.181613 + 0.983370i $$0.558132\pi$$
$$542$$ −14.0263 24.2942i −0.602480 1.04353i
$$543$$ 18.7321 0.803869
$$544$$ −11.0885 + 19.2058i −0.475414 + 0.823441i
$$545$$ 21.4641 0.919421
$$546$$ 0 0
$$547$$ 28.1962 1.20558 0.602790 0.797900i $$-0.294056\pi$$
0.602790 + 0.797900i $$0.294056\pi$$
$$548$$ −10.9641 + 18.9904i −0.468363 + 0.811229i
$$549$$ −37.4449 −1.59811
$$550$$ −8.19615 14.1962i −0.349485 0.605326i
$$551$$ −3.00000 5.19615i −0.127804 0.221364i
$$552$$ −0.803848 + 1.39230i −0.0342140 + 0.0592604i
$$553$$ 0 0
$$554$$ −29.4449 −1.25099
$$555$$ −8.87564 −0.376750
$$556$$ −20.5885 −0.873145
$$557$$ −25.6410 −1.08644 −0.543222 0.839589i $$-0.682796\pi$$
−0.543222 + 0.839589i $$0.682796\pi$$
$$558$$ −13.2224 22.9019i −0.559750 0.969516i
$$559$$ 20.3923 + 30.5885i 0.862503 + 1.29375i
$$560$$ 0 0
$$561$$ −7.39230 12.8038i −0.312103 0.540579i
$$562$$ −6.40192 + 11.0885i −0.270049 + 0.467738i
$$563$$ −5.02628 8.70577i −0.211832 0.366905i 0.740456 0.672105i $$-0.234610\pi$$
−0.952288 + 0.305201i $$0.901276\pi$$
$$564$$ −0.339746 + 0.588457i −0.0143059 + 0.0247785i
$$565$$ −12.8038 −0.538662
$$566$$ 0.169873 0.294229i 0.00714029 0.0123674i
$$567$$ 0 0
$$568$$ −5.19615 + 9.00000i −0.218026 + 0.377632i
$$569$$ −14.5359 + 25.1769i −0.609377 + 1.05547i 0.381967 + 0.924176i $$0.375247\pi$$
−0.991343 + 0.131295i $$0.958086\pi$$
$$570$$ 4.39230 0.183973
$$571$$ 12.3923 21.4641i 0.518602 0.898245i −0.481165 0.876630i $$-0.659786\pi$$
0.999766 0.0216144i $$-0.00688062\pi$$
$$572$$ −17.0263 + 1.09808i −0.711905 + 0.0459129i
$$573$$ 0.928203 0.0387762
$$574$$ 0 0
$$575$$ 1.26795 + 2.19615i 0.0528771 + 0.0915859i
$$576$$ −2.46410 −0.102671
$$577$$ 16.4019 28.4090i 0.682821 1.18268i −0.291295 0.956633i $$-0.594086\pi$$
0.974116 0.226048i $$-0.0725805\pi$$
$$578$$ 1.05256 + 1.82309i 0.0437807 + 0.0758304i
$$579$$ 3.66025 0.152115
$$580$$ −5.19615 −0.215758
$$581$$ 0 0
$$582$$ 9.12436 + 15.8038i 0.378217 + 0.655091i
$$583$$ −9.29423 + 16.0981i −0.384928 + 0.666714i
$$584$$ 6.23205 10.7942i 0.257884 0.446668i
$$585$$ 15.3564 0.990381i 0.634909 0.0409472i
$$586$$ 9.69615 + 16.7942i 0.400544 + 0.693763i
$$587$$ −2.19615 3.80385i −0.0906449 0.157002i 0.817138 0.576442i $$-0.195559\pi$$
−0.907783 + 0.419441i $$0.862226\pi$$
$$588$$ 0 0
$$589$$ 6.19615 10.7321i 0.255308 0.442206i
$$590$$ −16.0981 27.8827i −0.662747 1.14791i
$$591$$ −4.39230 7.60770i −0.180675 0.312939i
$$592$$ −17.5000 30.3109i −0.719246 1.24577i
$$593$$ 20.7224 + 35.8923i 0.850968 + 1.47392i 0.880335 + 0.474352i $$0.157317\pi$$
−0.0293672 + 0.999569i $$0.509349\pi$$
$$594$$ −16.3923 + 28.3923i −0.672584 + 1.16495i
$$595$$ 0 0
$$596$$ −0.232051 0.401924i −0.00950517 0.0164634i
$$597$$ 0.732051 + 1.26795i 0.0299608 + 0.0518937i
$$598$$ 7.90192 0.509619i 0.323134 0.0208399i
$$599$$ −8.07180 + 13.9808i −0.329805 + 0.571238i −0.982473 0.186405i $$-0.940316\pi$$
0.652668 + 0.757644i $$0.273650\pi$$
$$600$$ 1.26795 2.19615i 0.0517638 0.0896575i
$$601$$ 10.9904 + 19.0359i 0.448307 + 0.776490i 0.998276 0.0586946i $$-0.0186938\pi$$
−0.549969 + 0.835185i $$0.685360\pi$$
$$602$$ 0 0
$$603$$ −10.3397 −0.421067
$$604$$ 2.00000 0.0813788
$$605$$ −9.86603 17.0885i −0.401111 0.694745i
$$606$$ 2.70577 4.68653i 0.109914 0.190377i
$$607$$ −6.39230 −0.259456 −0.129728 0.991550i $$-0.541410\pi$$
−0.129728 + 0.991550i $$0.541410\pi$$
$$608$$ 5.19615 + 9.00000i 0.210732 + 0.364998i
$$609$$ 0 0
$$610$$ −45.5885 −1.84582
$$611$$ −3.33975 + 0.215390i −0.135112 + 0.00871376i
$$612$$ 5.25833 9.10770i 0.212555 0.368157i
$$613$$ −17.3923 −0.702469 −0.351234 0.936288i $$-0.614238\pi$$
−0.351234 + 0.936288i $$0.614238\pi$$
$$614$$ −23.0263 + 39.8827i −0.929265 + 1.60953i
$$615$$ 3.29423 5.70577i 0.132836 0.230079i
$$616$$ 0 0
$$617$$ −14.3038 + 24.7750i −0.575851 + 0.997404i 0.420097 + 0.907479i $$0.361996\pi$$
−0.995949 + 0.0899245i $$0.971337\pi$$
$$618$$ 8.10512 0.326036
$$619$$ −18.6865 + 32.3660i −0.751075 + 1.30090i 0.196227 + 0.980559i $$0.437131\pi$$
−0.947302 + 0.320342i $$0.896202\pi$$
$$620$$ −5.36603 9.29423i −0.215505 0.373265i
$$621$$ 2.53590 4.39230i 0.101762 0.176257i
$$622$$ −4.09808 7.09808i −0.164318 0.284607i
$$623$$ 0 0
$$624$$ −7.32051 10.9808i −0.293055 0.439582i
$$625$$ 5.50000 + 9.52628i 0.220000 + 0.381051i
$$626$$ −22.1436 −0.885036
$$627$$ −6.92820 −0.276686
$$628$$ 9.19615 0.366966
$$629$$ −29.8756 −1.19122
$$630$$ 0 0
$$631$$ −14.3923 + 24.9282i −0.572949 + 0.992376i 0.423313 + 0.905984i $$0.360867\pi$$
−0.996261 + 0.0863924i $$0.972466\pi$$
$$632$$ −5.02628 8.70577i −0.199935 0.346297i
$$633$$ 4.46410 + 7.73205i 0.177432 + 0.307321i
$$634$$ −0.803848 −0.0319249
$$635$$ 2.07180 3.58846i 0.0822167 0.142404i
$$636$$ 2.87564 0.114027
$$637$$ 0 0
$$638$$ 24.5885 0.973466
$$639$$ 7.39230 12.8038i 0.292435 0.506512i
$$640$$ −21.0000 −0.830098
$$641$$ −0.571797 0.990381i −0.0225846 0.0391177i 0.854512 0.519431i $$-0.173856\pi$$
−0.877097 + 0.480314i $$0.840523\pi$$
$$642$$ 12.5885 + 21.8038i 0.496827 + 0.860529i
$$643$$ 20.3923 35.3205i 0.804194 1.39290i −0.112640 0.993636i $$-0.535931\pi$$
0.916834 0.399269i $$-0.130736\pi$$
$$644$$ 0 0
$$645$$ 12.9282 0.509048
$$646$$ 14.7846 0.581693
$$647$$ 45.0333 1.77044 0.885221 0.465170i $$-0.154007\pi$$
0.885221 + 0.465170i $$0.154007\pi$$
$$648$$ 7.73205 0.303744
$$649$$ 25.3923 + 43.9808i 0.996735 + 1.72640i
$$650$$ −12.4641 + 0.803848i −0.488882 + 0.0315295i
$$651$$ 0 0
$$652$$ −2.90192 5.02628i −0.113648 0.196844i
$$653$$ 5.07180 8.78461i 0.198475 0.343768i −0.749559 0.661937i $$-0.769735\pi$$
0.948034 + 0.318169i $$0.103068\pi$$
$$654$$ 7.85641 + 13.6077i 0.307210 + 0.532103i
$$655$$ 3.00000 5.19615i 0.117220 0.203030i
$$656$$ 25.9808 1.01438
$$657$$ −8.86603 + 15.3564i −0.345897 + 0.599110i
$$658$$ 0 0
$$659$$ −3.80385 + 6.58846i −0.148177 + 0.256650i −0.930554 0.366156i $$-0.880674\pi$$
0.782377 + 0.622805i $$0.214007\pi$$
$$660$$ −3.00000 + 5.19615i −0.116775 + 0.202260i
$$661$$ 22.8038 0.886967 0.443483 0.896283i $$-0.353742\pi$$
0.443483 + 0.896283i $$0.353742\pi$$
$$662$$ −23.3660 + 40.4711i −0.908146 + 1.57296i
$$663$$ −11.2417 + 0.725009i −0.436590 + 0.0281570i
$$664$$ −14.1962 −0.550918
$$665$$ 0 0
$$666$$ 14.9378 + 25.8731i 0.578829 + 1.00256i
$$667$$ −3.80385 −0.147286
$$668$$ 12.2942 21.2942i 0.475678 0.823898i
$$669$$ −3.66025 6.33975i −0.141514 0.245109i
$$670$$ −12.5885 −0.486335
$$671$$ 71.9090 2.77601
$$672$$ 0 0
$$673$$ −9.08846 15.7417i −0.350334 0.606797i 0.635974 0.771711i $$-0.280599\pi$$
−0.986308 + 0.164914i $$0.947265\pi$$
$$674$$ 9.52628 16.5000i 0.366939 0.635556i
$$675$$ −4.00000 + 6.92820i −0.153960 + 0.266667i
$$676$$ −5.00000 + 12.0000i −0.192308 + 0.461538i
$$677$$ −18.4641 31.9808i −0.709633 1.22912i −0.964993 0.262275i $$-0.915527\pi$$
0.255360 0.966846i $$-0.417806\pi$$
$$678$$ −4.68653 8.11731i −0.179985 0.311744i
$$679$$ 0 0
$$680$$ −6.40192 + 11.0885i −0.245503 + 0.425223i
$$681$$ −4.26795 7.39230i −0.163548 0.283274i
$$682$$ 25.3923 + 43.9808i 0.972322 + 1.68411i
$$683$$ −4.26795 7.39230i −0.163309 0.282859i 0.772745 0.634717i $$-0.218883\pi$$
−0.936053 + 0.351858i $$0.885550\pi$$
$$684$$ −2.46410 4.26795i −0.0942173 0.163189i
$$685$$ −18.9904 + 32.8923i −0.725585 + 1.25675i
$$686$$ 0 0
$$687$$ 2.33975 + 4.05256i 0.0892669 + 0.154615i
$$688$$ 25.4904 + 44.1506i 0.971812 + 1.68323i
$$689$$ 7.85641 + 11.7846i 0.299305 + 0.448958i
$$690$$ 1.39230 2.41154i 0.0530041 0.0918059i
$$691$$ −10.1962 + 17.6603i −0.387880 + 0.671828i −0.992164 0.124941i $$-0.960126\pi$$
0.604284 + 0.796769i $$0.293459\pi$$
$$692$$ 7.73205 + 13.3923i 0.293928 + 0.509099i
$$693$$ 0 0
$$694$$ −18.5885 −0.705608
$$695$$ −35.6603 −1.35267
$$696$$ 1.90192 + 3.29423i 0.0720922 + 0.124867i
$$697$$ 11.0885 19.2058i 0.420005 0.727470i
$$698$$ 29.0718 1.10038
$$699$$ −9.46410 16.3923i −0.357965 0.620014i
$$700$$ 0 0
$$701$$ −20.7846 −0.785024 −0.392512 0.919747i $$-0.628394\pi$$
−0.392512 + 0.919747i $$0.628394\pi$$
$$702$$ 13.8564 + 20.7846i 0.522976 + 0.784465i
$$703$$ −7.00000 + 12.1244i −0.264010 + 0.457279i
$$704$$ 4.73205 0.178346
$$705$$ −0.588457 + 1.01924i −0.0221626 + 0.0383867i
$$706$$ −2.89230 + 5.00962i −0.108853 + 0.188539i
$$707$$ 0 0
$$708$$ 3.92820 6.80385i 0.147631 0.255704i
$$709$$ −32.1769 −1.20843 −0.604215 0.796822i $$-0.706513\pi$$
−0.604215 + 0.796822i $$0.706513\pi$$
$$710$$ 9.00000 15.5885i 0.337764 0.585024i
$$711$$ 7.15064 + 12.3853i 0.268170 + 0.464484i
$$712$$ −0.803848 + 1.39230i −0.0301255 + 0.0521788i
$$713$$ −3.92820 6.80385i −0.147112 0.254806i
$$714$$ 0 0
$$715$$ −29.4904 + 1.90192i −1.10288 + 0.0711279i
$$716$$ −3.46410 6.00000i −0.129460 0.224231i
$$717$$ −19.1769 −0.716175
$$718$$ −8.78461 −0.327839
$$719$$ 10.7321 0.400238 0.200119 0.979772i $$-0.435867\pi$$
0.200119 + 0.979772i $$0.435867\pi$$
$$720$$ 21.3397 0.795285
$$721$$ 0 0
$$722$$ −12.9904 + 22.5000i −0.483452 + 0.837363i
$$723$$ −3.95448 6.84936i −0.147069 0.254731i
$$724$$ −12.7942 22.1603i −0.475494 0.823579i
$$725$$ 6.00000 0.222834
$$726$$ 7.22243 12.5096i 0.268050 0.464276i
$$727$$ −21.1769 −0.785408 −0.392704 0.919665i $$-0.628460\pi$$
−0.392704 + 0.919665i $$0.628460\pi$$
$$728$$ 0 0
$$729$$ −2.21539 −0.0820515
$$730$$ −10.7942 + 18.6962i −0.399512 + 0.691976i
$$731$$ 43.5167 1.60952
$$732$$ −5.56218 9.63397i −0.205584 0.356082i
$$733$$ −3.79423 6.57180i −0.140143 0.242735i 0.787407 0.616433i $$-0.211423\pi$$
−0.927550 + 0.373698i $$0.878090\pi$$
$$734$$ 5.36603 9.29423i 0.198064 0.343056i
$$735$$ 0 0
$$736$$ 6.58846 0.242854
$$737$$ 19.8564 0.731420
$$738$$ −22.1769 −0.816344
$$739$$ −0.784610 −0.0288623 −0.0144312 0.999896i $$-0.504594\pi$$
−0.0144312 + 0.999896i $$0.504594\pi$$
$$740$$ 6.06218 + 10.5000i 0.222850 + 0.385988i
$$741$$ −2.33975 + 4.73205i −0.0859527 + 0.173836i
$$742$$ 0 0
$$743$$ 14.1962 + 24.5885i 0.520806 + 0.902063i 0.999707 + 0.0241941i $$0.00770196\pi$$
−0.478901 + 0.877869i $$0.658965\pi$$
$$744$$ −3.92820 + 6.80385i −0.144015 + 0.249441i
$$745$$ −0.401924 0.696152i −0.0147253 0.0255051i
$$746$$ 8.13397 14.0885i 0.297806 0.515815i
$$747$$ 20.1962 0.738939
$$748$$ −10.0981 + 17.4904i −0.369222 + 0.639512i
$$749$$ 0 0
$$750$$ −7.68653 + 13.3135i −0.280673 + 0.486139i
$$751$$ −23.0981 + 40.0070i −0.842861 + 1.45988i 0.0446053 + 0.999005i $$0.485797\pi$$
−0.887466 + 0.460873i $$0.847536\pi$$
$$752$$ −4.64102 −0.169240
$$753$$ −8.19615 + 14.1962i −0.298684 + 0.517337i
$$754$$ 8.30385 16.7942i 0.302408 0.611610i
$$755$$ 3.46410 0.126072
$$756$$ 0 0
$$757$$ 8.00000 + 13.8564i 0.290765 + 0.503620i 0.973991 0.226587i $$-0.0727569\pi$$
−0.683226 + 0.730207i $$0.739424\pi$$
$$758$$ 7.94744 0.288664
$$759$$ −2.19615 + 3.80385i −0.0797153 + 0.138071i
$$760$$ 3.00000 + 5.19615i 0.108821 + 0.188484i
$$761$$ −6.67949 −0.242131 −0.121066 0.992644i $$-0.538631\pi$$
−0.121066 + 0.992644i $$0.538631\pi$$
$$762$$ 3.03332 0.109886
$$763$$ 0 0
$$764$$ −0.633975 1.09808i −0.0229364 0.0397270i
$$765$$ 9.10770 15.7750i 0.329289 0.570346i
$$766$$ −4.90192 + 8.49038i −0.177114 + 0.306770i
$$767$$ 38.6147 2.49038i 1.39430 0.0899224i
$$768$$ −6.95448 12.0455i −0.250948 0.434655i
$$769$$ −23.5885 40.8564i −0.850622 1.47332i −0.880648 0.473771i $$-0.842893\pi$$
0.0300268 0.999549i $$-0.490441\pi$$
$$770$$ 0 0
$$771$$ −6.63397 + 11.4904i −0.238917 + 0.413816i
$$772$$ −2.50000 4.33013i −0.0899770 0.155845i
$$773$$ 0.464102 + 0.803848i 0.0166926 + 0.0289124i 0.874251 0.485474i $$-0.161353\pi$$
−0.857558 + 0.514387i $$0.828020\pi$$
$$774$$ −21.7583 37.6865i −0.782087 1.35461i
$$775$$ 6.19615 + 10.7321i 0.222572 + 0.385507i
$$776$$ −12.4641 + 21.5885i −0.447435 + 0.774980i
$$777$$ 0 0
$$778$$ −26.3827 45.6962i −0.945865 1.63829i
$$779$$ −5.19615 9.00000i −0.186171 0.322458i
$$780$$ 2.53590