# Properties

 Label 144.2.k.b.37.2 Level $144$ Weight $2$ Character 144.37 Analytic conductor $1.150$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

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

## Newform invariants

 Self dual: no Analytic conductor: $$1.14984578911$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: 8.0.18939904.2 Defining polynomial: $$x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 43 x^{4} - 44 x^{3} + 30 x^{2} - 12 x + 2$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 48) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 37.2 Root $$0.500000 + 0.691860i$$ of defining polynomial Character $$\chi$$ $$=$$ 144.37 Dual form 144.2.k.b.109.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.635665 - 1.26330i) q^{2} +(-1.19186 + 1.60607i) q^{4} +(2.68554 + 2.68554i) q^{5} +2.15894i q^{7} +(2.78658 + 0.484753i) q^{8} +O(q^{10})$$ $$q+(-0.635665 - 1.26330i) q^{2} +(-1.19186 + 1.60607i) q^{4} +(2.68554 + 2.68554i) q^{5} +2.15894i q^{7} +(2.78658 + 0.484753i) q^{8} +(1.68554 - 5.09976i) q^{10} +(-1.79793 - 1.79793i) q^{11} +(1.38372 - 1.38372i) q^{13} +(2.72739 - 1.37236i) q^{14} +(-1.15894 - 3.82843i) q^{16} +0.224777 q^{17} +(0.158942 - 0.158942i) q^{19} +(-7.51397 + 1.11239i) q^{20} +(-1.12845 + 3.41421i) q^{22} -2.82843i q^{23} +9.42429i q^{25} +(-2.62764 - 0.868472i) q^{26} +(-3.46742 - 2.57316i) q^{28} +(1.85712 - 1.85712i) q^{29} +1.84106 q^{31} +(-4.09976 + 3.89769i) q^{32} +(-0.142883 - 0.283962i) q^{34} +(-5.79793 + 5.79793i) q^{35} +(-3.66949 - 3.66949i) q^{37} +(-0.301825 - 0.0997575i) q^{38} +(6.18165 + 8.78530i) q^{40} +5.88163i q^{41} +(-7.75481 - 7.75481i) q^{43} +(5.03049 - 0.744728i) q^{44} +(-3.57316 + 1.79793i) q^{46} +2.82843 q^{47} +2.33897 q^{49} +(11.9057 - 5.99069i) q^{50} +(0.573155 + 3.87155i) q^{52} +(-7.51397 - 7.51397i) q^{53} -9.65685i q^{55} +(-1.04655 + 6.01606i) q^{56} +(-3.52660 - 1.16559i) q^{58} +(-4.00000 - 4.00000i) q^{59} +(5.98737 - 5.98737i) q^{61} +(-1.17030 - 2.32581i) q^{62} +(7.53003 + 2.70160i) q^{64} +7.43208 q^{65} +(-10.4243 + 10.4243i) q^{67} +(-0.267903 + 0.361009i) q^{68} +(11.0101 + 3.63899i) q^{70} +4.31788i q^{71} -5.97474i q^{73} +(-2.30310 + 6.96823i) q^{74} +(0.0658358 + 0.444708i) q^{76} +(3.88163 - 3.88163i) q^{77} +15.0075 q^{79} +(7.16902 - 13.3938i) q^{80} +(7.43027 - 3.73875i) q^{82} +(10.1158 - 10.1158i) q^{83} +(0.603650 + 0.603650i) q^{85} +(-4.86720 + 14.7261i) q^{86} +(-4.13853 - 5.88163i) q^{88} +1.42847i q^{89} +(2.98737 + 2.98737i) q^{91} +(4.54266 + 3.37109i) q^{92} +(-1.79793 - 3.57316i) q^{94} +0.853690 q^{95} -16.3990 q^{97} +(-1.48680 - 2.95482i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 4q^{4} + 12q^{8} + O(q^{10})$$ $$8q - 4q^{4} + 12q^{8} - 8q^{10} + 8q^{11} - 12q^{14} - 8q^{19} - 16q^{20} - 20q^{26} + 8q^{28} + 16q^{29} + 24q^{31} - 24q^{35} - 16q^{37} + 8q^{38} + 16q^{40} - 8q^{43} + 40q^{44} - 8q^{46} - 8q^{49} + 36q^{50} - 16q^{52} - 16q^{53} - 16q^{58} - 32q^{59} + 16q^{61} + 12q^{62} + 8q^{64} + 16q^{65} - 16q^{67} - 32q^{68} + 32q^{70} - 52q^{74} + 8q^{76} - 16q^{77} - 24q^{79} - 8q^{80} + 40q^{82} + 40q^{83} - 16q^{85} + 16q^{86} + 32q^{88} - 8q^{91} + 16q^{92} + 8q^{94} + 48q^{95} + 40q^{98} + O(q^{100})$$

## Character values

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

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

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.635665 1.26330i −0.449483 0.893289i
$$3$$ 0 0
$$4$$ −1.19186 + 1.60607i −0.595930 + 0.803037i
$$5$$ 2.68554 + 2.68554i 1.20101 + 1.20101i 0.973859 + 0.227153i $$0.0729416\pi$$
0.227153 + 0.973859i $$0.427058\pi$$
$$6$$ 0 0
$$7$$ 2.15894i 0.816003i 0.912981 + 0.408002i $$0.133774\pi$$
−0.912981 + 0.408002i $$0.866226\pi$$
$$8$$ 2.78658 + 0.484753i 0.985204 + 0.171386i
$$9$$ 0 0
$$10$$ 1.68554 5.09976i 0.533016 1.61268i
$$11$$ −1.79793 1.79793i −0.542097 0.542097i 0.382046 0.924143i $$-0.375220\pi$$
−0.924143 + 0.382046i $$0.875220\pi$$
$$12$$ 0 0
$$13$$ 1.38372 1.38372i 0.383775 0.383775i −0.488685 0.872460i $$-0.662523\pi$$
0.872460 + 0.488685i $$0.162523\pi$$
$$14$$ 2.72739 1.37236i 0.728927 0.366780i
$$15$$ 0 0
$$16$$ −1.15894 3.82843i −0.289735 0.957107i
$$17$$ 0.224777 0.0545165 0.0272583 0.999628i $$-0.491322\pi$$
0.0272583 + 0.999628i $$0.491322\pi$$
$$18$$ 0 0
$$19$$ 0.158942 0.158942i 0.0364637 0.0364637i −0.688640 0.725104i $$-0.741792\pi$$
0.725104 + 0.688640i $$0.241792\pi$$
$$20$$ −7.51397 + 1.11239i −1.68018 + 0.248738i
$$21$$ 0 0
$$22$$ −1.12845 + 3.41421i −0.240586 + 0.727913i
$$23$$ 2.82843i 0.589768i −0.955533 0.294884i $$-0.904719\pi$$
0.955533 0.294884i $$-0.0952810\pi$$
$$24$$ 0 0
$$25$$ 9.42429i 1.88486i
$$26$$ −2.62764 0.868472i −0.515322 0.170321i
$$27$$ 0 0
$$28$$ −3.46742 2.57316i −0.655280 0.486281i
$$29$$ 1.85712 1.85712i 0.344858 0.344858i −0.513332 0.858190i $$-0.671589\pi$$
0.858190 + 0.513332i $$0.171589\pi$$
$$30$$ 0 0
$$31$$ 1.84106 0.330664 0.165332 0.986238i $$-0.447130\pi$$
0.165332 + 0.986238i $$0.447130\pi$$
$$32$$ −4.09976 + 3.89769i −0.724742 + 0.689021i
$$33$$ 0 0
$$34$$ −0.142883 0.283962i −0.0245043 0.0486990i
$$35$$ −5.79793 + 5.79793i −0.980029 + 0.980029i
$$36$$ 0 0
$$37$$ −3.66949 3.66949i −0.603260 0.603260i 0.337916 0.941176i $$-0.390278\pi$$
−0.941176 + 0.337916i $$0.890278\pi$$
$$38$$ −0.301825 0.0997575i −0.0489625 0.0161828i
$$39$$ 0 0
$$40$$ 6.18165 + 8.78530i 0.977405 + 1.38908i
$$41$$ 5.88163i 0.918557i 0.888292 + 0.459278i $$0.151892\pi$$
−0.888292 + 0.459278i $$0.848108\pi$$
$$42$$ 0 0
$$43$$ −7.75481 7.75481i −1.18260 1.18260i −0.979069 0.203528i $$-0.934759\pi$$
−0.203528 0.979069i $$-0.565241\pi$$
$$44$$ 5.03049 0.744728i 0.758376 0.112272i
$$45$$ 0 0
$$46$$ −3.57316 + 1.79793i −0.526833 + 0.265091i
$$47$$ 2.82843 0.412568 0.206284 0.978492i $$-0.433863\pi$$
0.206284 + 0.978492i $$0.433863\pi$$
$$48$$ 0 0
$$49$$ 2.33897 0.334139
$$50$$ 11.9057 5.99069i 1.68372 0.847212i
$$51$$ 0 0
$$52$$ 0.573155 + 3.87155i 0.0794823 + 0.536888i
$$53$$ −7.51397 7.51397i −1.03212 1.03212i −0.999467 0.0326567i $$-0.989603\pi$$
−0.0326567 0.999467i $$-0.510397\pi$$
$$54$$ 0 0
$$55$$ 9.65685i 1.30213i
$$56$$ −1.04655 + 6.01606i −0.139852 + 0.803930i
$$57$$ 0 0
$$58$$ −3.52660 1.16559i −0.463066 0.153050i
$$59$$ −4.00000 4.00000i −0.520756 0.520756i 0.397044 0.917800i $$-0.370036\pi$$
−0.917800 + 0.397044i $$0.870036\pi$$
$$60$$ 0 0
$$61$$ 5.98737 5.98737i 0.766604 0.766604i −0.210903 0.977507i $$-0.567640\pi$$
0.977507 + 0.210903i $$0.0676404\pi$$
$$62$$ −1.17030 2.32581i −0.148628 0.295378i
$$63$$ 0 0
$$64$$ 7.53003 + 2.70160i 0.941254 + 0.337700i
$$65$$ 7.43208 0.921836
$$66$$ 0 0
$$67$$ −10.4243 + 10.4243i −1.27353 + 1.27353i −0.329307 + 0.944223i $$0.606815\pi$$
−0.944223 + 0.329307i $$0.893185\pi$$
$$68$$ −0.267903 + 0.361009i −0.0324880 + 0.0437788i
$$69$$ 0 0
$$70$$ 11.0101 + 3.63899i 1.31596 + 0.434943i
$$71$$ 4.31788i 0.512438i 0.966619 + 0.256219i $$0.0824769\pi$$
−0.966619 + 0.256219i $$0.917523\pi$$
$$72$$ 0 0
$$73$$ 5.97474i 0.699290i −0.936882 0.349645i $$-0.886302\pi$$
0.936882 0.349645i $$-0.113698\pi$$
$$74$$ −2.30310 + 6.96823i −0.267730 + 0.810040i
$$75$$ 0 0
$$76$$ 0.0658358 + 0.444708i 0.00755188 + 0.0510115i
$$77$$ 3.88163 3.88163i 0.442353 0.442353i
$$78$$ 0 0
$$79$$ 15.0075 1.68848 0.844239 0.535966i $$-0.180053\pi$$
0.844239 + 0.535966i $$0.180053\pi$$
$$80$$ 7.16902 13.3938i 0.801521 1.49747i
$$81$$ 0 0
$$82$$ 7.43027 3.73875i 0.820536 0.412876i
$$83$$ 10.1158 10.1158i 1.11036 1.11036i 0.117253 0.993102i $$-0.462591\pi$$
0.993102 0.117253i $$-0.0374088\pi$$
$$84$$ 0 0
$$85$$ 0.603650 + 0.603650i 0.0654750 + 0.0654750i
$$86$$ −4.86720 + 14.7261i −0.524843 + 1.58796i
$$87$$ 0 0
$$88$$ −4.13853 5.88163i −0.441168 0.626984i
$$89$$ 1.42847i 0.151417i 0.997130 + 0.0757086i $$0.0241219\pi$$
−0.997130 + 0.0757086i $$0.975878\pi$$
$$90$$ 0 0
$$91$$ 2.98737 + 2.98737i 0.313161 + 0.313161i
$$92$$ 4.54266 + 3.37109i 0.473605 + 0.351460i
$$93$$ 0 0
$$94$$ −1.79793 3.57316i −0.185443 0.368543i
$$95$$ 0.853690 0.0875867
$$96$$ 0 0
$$97$$ −16.3990 −1.66507 −0.832535 0.553973i $$-0.813111\pi$$
−0.832535 + 0.553973i $$0.813111\pi$$
$$98$$ −1.48680 2.95482i −0.150190 0.298482i
$$99$$ 0 0
$$100$$ −15.1361 11.2324i −1.51361 1.12324i
$$101$$ −0.0818942 0.0818942i −0.00814878 0.00814878i 0.703021 0.711169i $$-0.251834\pi$$
−0.711169 + 0.703021i $$0.751834\pi$$
$$102$$ 0 0
$$103$$ 13.3507i 1.31548i 0.753245 + 0.657740i $$0.228488\pi$$
−0.753245 + 0.657740i $$0.771512\pi$$
$$104$$ 4.52660 3.18508i 0.443870 0.312323i
$$105$$ 0 0
$$106$$ −4.71604 + 14.2688i −0.458062 + 1.38591i
$$107$$ 7.27798 + 7.27798i 0.703589 + 0.703589i 0.965179 0.261590i $$-0.0842468\pi$$
−0.261590 + 0.965179i $$0.584247\pi$$
$$108$$ 0 0
$$109$$ −7.04057 + 7.04057i −0.674365 + 0.674365i −0.958719 0.284355i $$-0.908221\pi$$
0.284355 + 0.958719i $$0.408221\pi$$
$$110$$ −12.1995 + 6.13853i −1.16318 + 0.585285i
$$111$$ 0 0
$$112$$ 8.26535 2.50209i 0.781002 0.236425i
$$113$$ −18.8486 −1.77313 −0.886563 0.462608i $$-0.846914\pi$$
−0.886563 + 0.462608i $$0.846914\pi$$
$$114$$ 0 0
$$115$$ 7.59587 7.59587i 0.708318 0.708318i
$$116$$ 0.769243 + 5.19609i 0.0714224 + 0.482445i
$$117$$ 0 0
$$118$$ −2.51054 + 7.59587i −0.231114 + 0.699256i
$$119$$ 0.485281i 0.0444857i
$$120$$ 0 0
$$121$$ 4.53488i 0.412261i
$$122$$ −11.3698 3.75789i −1.02937 0.340223i
$$123$$ 0 0
$$124$$ −2.19428 + 2.95687i −0.197052 + 0.265535i
$$125$$ −11.8816 + 11.8816i −1.06273 + 1.06273i
$$126$$ 0 0
$$127$$ −3.81580 −0.338597 −0.169299 0.985565i $$-0.554150\pi$$
−0.169299 + 0.985565i $$0.554150\pi$$
$$128$$ −1.37364 11.2300i −0.121414 0.992602i
$$129$$ 0 0
$$130$$ −4.72431 9.38895i −0.414350 0.823465i
$$131$$ 0.767438 0.767438i 0.0670514 0.0670514i −0.672786 0.739837i $$-0.734902\pi$$
0.739837 + 0.672786i $$0.234902\pi$$
$$132$$ 0 0
$$133$$ 0.343146 + 0.343146i 0.0297545 + 0.0297545i
$$134$$ 19.7954 + 6.54266i 1.71006 + 0.565200i
$$135$$ 0 0
$$136$$ 0.626360 + 0.108961i 0.0537099 + 0.00934337i
$$137$$ 5.31010i 0.453672i −0.973933 0.226836i $$-0.927162\pi$$
0.973933 0.226836i $$-0.0728382\pi$$
$$138$$ 0 0
$$139$$ 8.76744 + 8.76744i 0.743644 + 0.743644i 0.973277 0.229633i $$-0.0737526\pi$$
−0.229633 + 0.973277i $$0.573753\pi$$
$$140$$ −2.40158 16.2222i −0.202971 1.37103i
$$141$$ 0 0
$$142$$ 5.45479 2.74473i 0.457756 0.230332i
$$143$$ −4.97567 −0.416086
$$144$$ 0 0
$$145$$ 9.97474 0.828357
$$146$$ −7.54789 + 3.79793i −0.624668 + 0.314319i
$$147$$ 0 0
$$148$$ 10.2670 1.51995i 0.843940 0.124939i
$$149$$ 1.02869 + 1.02869i 0.0842735 + 0.0842735i 0.747987 0.663713i $$-0.231021\pi$$
−0.663713 + 0.747987i $$0.731021\pi$$
$$150$$ 0 0
$$151$$ 2.03696i 0.165766i −0.996559 0.0828829i $$-0.973587\pi$$
0.996559 0.0828829i $$-0.0264127\pi$$
$$152$$ 0.519951 0.365856i 0.0421736 0.0296748i
$$153$$ 0 0
$$154$$ −7.37109 2.43625i −0.593979 0.196319i
$$155$$ 4.94424 + 4.94424i 0.397131 + 0.397131i
$$156$$ 0 0
$$157$$ 6.09378 6.09378i 0.486336 0.486336i −0.420812 0.907148i $$-0.638255\pi$$
0.907148 + 0.420812i $$0.138255\pi$$
$$158$$ −9.53976 18.9590i −0.758943 1.50830i
$$159$$ 0 0
$$160$$ −21.4775 0.542661i −1.69795 0.0429011i
$$161$$ 6.10641 0.481252
$$162$$ 0 0
$$163$$ 3.43692 3.43692i 0.269201 0.269201i −0.559577 0.828778i $$-0.689037\pi$$
0.828778 + 0.559577i $$0.189037\pi$$
$$164$$ −9.44633 7.01008i −0.737634 0.547395i
$$165$$ 0 0
$$166$$ −19.2096 6.34905i −1.49095 0.492782i
$$167$$ 21.7023i 1.67937i 0.543072 + 0.839686i $$0.317261\pi$$
−0.543072 + 0.839686i $$0.682739\pi$$
$$168$$ 0 0
$$169$$ 9.17064i 0.705434i
$$170$$ 0.378872 1.14631i 0.0290582 0.0879180i
$$171$$ 0 0
$$172$$ 21.6974 3.21215i 1.65441 0.244924i
$$173$$ 8.74653 8.74653i 0.664987 0.664987i −0.291565 0.956551i $$-0.594176\pi$$
0.956551 + 0.291565i $$0.0941758\pi$$
$$174$$ 0 0
$$175$$ −20.3465 −1.53805
$$176$$ −4.79956 + 8.96695i −0.361780 + 0.675910i
$$177$$ 0 0
$$178$$ 1.80458 0.908027i 0.135259 0.0680595i
$$179$$ −8.23163 + 8.23163i −0.615261 + 0.615261i −0.944312 0.329051i $$-0.893271\pi$$
0.329051 + 0.944312i $$0.393271\pi$$
$$180$$ 0 0
$$181$$ 6.72269 + 6.72269i 0.499694 + 0.499694i 0.911343 0.411649i $$-0.135047\pi$$
−0.411649 + 0.911343i $$0.635047\pi$$
$$182$$ 1.87498 5.67291i 0.138983 0.420504i
$$183$$ 0 0
$$184$$ 1.37109 7.88163i 0.101078 0.581042i
$$185$$ 19.7091i 1.44904i
$$186$$ 0 0
$$187$$ −0.404135 0.404135i −0.0295533 0.0295533i
$$188$$ −3.37109 + 4.54266i −0.245862 + 0.331308i
$$189$$ 0 0
$$190$$ −0.542661 1.07847i −0.0393687 0.0782402i
$$191$$ 20.8032 1.50526 0.752632 0.658441i $$-0.228784\pi$$
0.752632 + 0.658441i $$0.228784\pi$$
$$192$$ 0 0
$$193$$ 14.1454 1.01821 0.509103 0.860705i $$-0.329977\pi$$
0.509103 + 0.860705i $$0.329977\pi$$
$$194$$ 10.4243 + 20.7169i 0.748421 + 1.48739i
$$195$$ 0 0
$$196$$ −2.78772 + 3.75656i −0.199123 + 0.268326i
$$197$$ 2.42865 + 2.42865i 0.173034 + 0.173034i 0.788311 0.615277i $$-0.210956\pi$$
−0.615277 + 0.788311i $$0.710956\pi$$
$$198$$ 0 0
$$199$$ 0.306182i 0.0217047i 0.999941 + 0.0108523i $$0.00345447\pi$$
−0.999941 + 0.0108523i $$0.996546\pi$$
$$200$$ −4.56845 + 26.2615i −0.323038 + 1.85697i
$$201$$ 0 0
$$202$$ −0.0513998 + 0.155514i −0.00361648 + 0.0109420i
$$203$$ 4.00941 + 4.00941i 0.281405 + 0.281405i
$$204$$ 0 0
$$205$$ −15.7954 + 15.7954i −1.10320 + 1.10320i
$$206$$ 16.8659 8.48656i 1.17510 0.591286i
$$207$$ 0 0
$$208$$ −6.90112 3.69382i −0.478506 0.256120i
$$209$$ −0.571533 −0.0395337
$$210$$ 0 0
$$211$$ 7.23256 7.23256i 0.497910 0.497910i −0.412877 0.910787i $$-0.635476\pi$$
0.910787 + 0.412877i $$0.135476\pi$$
$$212$$ 21.0236 3.11239i 1.44391 0.213760i
$$213$$ 0 0
$$214$$ 4.56792 13.8206i 0.312257 0.944760i
$$215$$ 41.6517i 2.84063i
$$216$$ 0 0
$$217$$ 3.97474i 0.269823i
$$218$$ 13.3698 + 4.41892i 0.905518 + 0.299287i
$$219$$ 0 0
$$220$$ 15.5096 + 11.5096i 1.04566 + 0.775978i
$$221$$ 0.311029 0.311029i 0.0209221 0.0209221i
$$222$$ 0 0
$$223$$ −1.71908 −0.115118 −0.0575591 0.998342i $$-0.518332\pi$$
−0.0575591 + 0.998342i $$0.518332\pi$$
$$224$$ −8.41489 8.85114i −0.562243 0.591391i
$$225$$ 0 0
$$226$$ 11.9814 + 23.8114i 0.796990 + 1.58391i
$$227$$ −10.1158 + 10.1158i −0.671410 + 0.671410i −0.958041 0.286631i $$-0.907465\pi$$
0.286631 + 0.958041i $$0.407465\pi$$
$$228$$ 0 0
$$229$$ −12.0195 12.0195i −0.794270 0.794270i 0.187915 0.982185i $$-0.439827\pi$$
−0.982185 + 0.187915i $$0.939827\pi$$
$$230$$ −14.4243 4.76744i −0.951110 0.314356i
$$231$$ 0 0
$$232$$ 6.07524 4.27476i 0.398859 0.280652i
$$233$$ 13.3779i 0.876418i 0.898873 + 0.438209i $$0.144387\pi$$
−0.898873 + 0.438209i $$0.855613\pi$$
$$234$$ 0 0
$$235$$ 7.59587 + 7.59587i 0.495500 + 0.495500i
$$236$$ 11.1917 1.65685i 0.728520 0.107852i
$$237$$ 0 0
$$238$$ 0.613057 0.308476i 0.0397386 0.0199956i
$$239$$ −13.3675 −0.864670 −0.432335 0.901713i $$-0.642310\pi$$
−0.432335 + 0.901713i $$0.642310\pi$$
$$240$$ 0 0
$$241$$ 0.211474 0.0136222 0.00681112 0.999977i $$-0.497832\pi$$
0.00681112 + 0.999977i $$0.497832\pi$$
$$242$$ −5.72891 + 2.88266i −0.368269 + 0.185305i
$$243$$ 0 0
$$244$$ 2.48005 + 16.7523i 0.158769 + 1.07245i
$$245$$ 6.28141 + 6.28141i 0.401305 + 0.401305i
$$246$$ 0 0
$$247$$ 0.439861i 0.0279877i
$$248$$ 5.13025 + 0.892458i 0.325771 + 0.0566711i
$$249$$ 0 0
$$250$$ 22.5628 + 7.45734i 1.42700 + 0.471644i
$$251$$ −10.4337 10.4337i −0.658569 0.658569i 0.296472 0.955041i $$-0.404190\pi$$
−0.955041 + 0.296472i $$0.904190\pi$$
$$252$$ 0 0
$$253$$ −5.08532 + 5.08532i −0.319711 + 0.319711i
$$254$$ 2.42557 + 4.82050i 0.152194 + 0.302465i
$$255$$ 0 0
$$256$$ −13.3137 + 8.87385i −0.832107 + 0.554615i
$$257$$ 0.742176 0.0462957 0.0231478 0.999732i $$-0.492631\pi$$
0.0231478 + 0.999732i $$0.492631\pi$$
$$258$$ 0 0
$$259$$ 7.92221 7.92221i 0.492262 0.492262i
$$260$$ −8.85799 + 11.9365i −0.549349 + 0.740268i
$$261$$ 0 0
$$262$$ −1.45734 0.481672i −0.0900347 0.0297578i
$$263$$ 5.48435i 0.338180i −0.985601 0.169090i $$-0.945917\pi$$
0.985601 0.169090i $$-0.0540828\pi$$
$$264$$ 0 0
$$265$$ 40.3582i 2.47918i
$$266$$ 0.215371 0.651622i 0.0132052 0.0399535i
$$267$$ 0 0
$$268$$ −4.31788 29.1665i −0.263757 1.78163i
$$269$$ −14.4741 + 14.4741i −0.882500 + 0.882500i −0.993788 0.111289i $$-0.964502\pi$$
0.111289 + 0.993788i $$0.464502\pi$$
$$270$$ 0 0
$$271$$ −14.0370 −0.852685 −0.426342 0.904562i $$-0.640198\pi$$
−0.426342 + 0.904562i $$0.640198\pi$$
$$272$$ −0.260504 0.860544i −0.0157954 0.0521781i
$$273$$ 0 0
$$274$$ −6.70825 + 3.37545i −0.405260 + 0.203918i
$$275$$ 16.9442 16.9442i 1.02178 1.02178i
$$276$$ 0 0
$$277$$ 9.49013 + 9.49013i 0.570207 + 0.570207i 0.932186 0.361980i $$-0.117899\pi$$
−0.361980 + 0.932186i $$0.617899\pi$$
$$278$$ 5.50276 16.6491i 0.330034 0.998545i
$$279$$ 0 0
$$280$$ −18.9670 + 13.3458i −1.13349 + 0.797566i
$$281$$ 3.89359i 0.232272i −0.993233 0.116136i $$-0.962949\pi$$
0.993233 0.116136i $$-0.0370509\pi$$
$$282$$ 0 0
$$283$$ −12.4853 12.4853i −0.742173 0.742173i 0.230823 0.972996i $$-0.425858\pi$$
−0.972996 + 0.230823i $$0.925858\pi$$
$$284$$ −6.93484 5.14631i −0.411507 0.305377i
$$285$$ 0 0
$$286$$ 3.16286 + 6.28577i 0.187024 + 0.371685i
$$287$$ −12.6981 −0.749545
$$288$$ 0 0
$$289$$ −16.9495 −0.997028
$$290$$ −6.34059 12.6011i −0.372332 0.739962i
$$291$$ 0 0
$$292$$ 9.59587 + 7.12105i 0.561556 + 0.416728i
$$293$$ 11.1553 + 11.1553i 0.651697 + 0.651697i 0.953402 0.301704i $$-0.0975556\pi$$
−0.301704 + 0.953402i $$0.597556\pi$$
$$294$$ 0 0
$$295$$ 21.4844i 1.25087i
$$296$$ −8.44651 12.0041i −0.490944 0.697724i
$$297$$ 0 0
$$298$$ 0.645643 1.95345i 0.0374011 0.113160i
$$299$$ −3.91375 3.91375i −0.226338 0.226338i
$$300$$ 0 0
$$301$$ 16.7422 16.7422i 0.965003 0.965003i
$$302$$ −2.57330 + 1.29483i −0.148077 + 0.0745089i
$$303$$ 0 0
$$304$$ −0.792701 0.424292i −0.0454645 0.0243348i
$$305$$ 32.1587 1.84140
$$306$$ 0 0
$$307$$ −5.40320 + 5.40320i −0.308377 + 0.308377i −0.844280 0.535903i $$-0.819971\pi$$
0.535903 + 0.844280i $$0.319971\pi$$
$$308$$ 1.60782 + 10.8605i 0.0916143 + 0.618837i
$$309$$ 0 0
$$310$$ 3.10318 9.38895i 0.176249 0.533257i
$$311$$ 24.1623i 1.37012i 0.728488 + 0.685059i $$0.240224\pi$$
−0.728488 + 0.685059i $$0.759776\pi$$
$$312$$ 0 0
$$313$$ 16.6105i 0.938881i −0.882964 0.469441i $$-0.844456\pi$$
0.882964 0.469441i $$-0.155544\pi$$
$$314$$ −11.5719 3.82467i −0.653039 0.215839i
$$315$$ 0 0
$$316$$ −17.8869 + 24.1032i −1.00621 + 1.35591i
$$317$$ −1.81170 + 1.81170i −0.101755 + 0.101755i −0.756152 0.654397i $$-0.772923\pi$$
0.654397 + 0.756152i $$0.272923\pi$$
$$318$$ 0 0
$$319$$ −6.67794 −0.373893
$$320$$ 12.9670 + 27.4775i 0.724875 + 1.53604i
$$321$$ 0 0
$$322$$ −3.88163 7.71423i −0.216315 0.429897i
$$323$$ 0.0357265 0.0357265i 0.00198788 0.00198788i
$$324$$ 0 0
$$325$$ 13.0406 + 13.0406i 0.723361 + 0.723361i
$$326$$ −6.52660 2.15714i −0.361475 0.119473i
$$327$$ 0 0
$$328$$ −2.85114 + 16.3896i −0.157428 + 0.904966i
$$329$$ 6.10641i 0.336657i
$$330$$ 0 0
$$331$$ 13.5252 + 13.5252i 0.743411 + 0.743411i 0.973233 0.229822i $$-0.0738142\pi$$
−0.229822 + 0.973233i $$0.573814\pi$$
$$332$$ 4.19011 + 28.3034i 0.229962 + 1.55335i
$$333$$ 0 0
$$334$$ 27.4165 13.7954i 1.50016 0.754850i
$$335$$ −55.9898 −3.05905
$$336$$ 0 0
$$337$$ −1.12615 −0.0613454 −0.0306727 0.999529i $$-0.509765\pi$$
−0.0306727 + 0.999529i $$0.509765\pi$$
$$338$$ 11.5853 5.82946i 0.630156 0.317081i
$$339$$ 0 0
$$340$$ −1.68897 + 0.250040i −0.0915973 + 0.0135603i
$$341$$ −3.31010 3.31010i −0.179252 0.179252i
$$342$$ 0 0
$$343$$ 20.1623i 1.08866i
$$344$$ −17.8502 25.3685i −0.962419 1.36778i
$$345$$ 0 0
$$346$$ −16.6094 5.48964i −0.892925 0.295125i
$$347$$ −20.7938 20.7938i −1.11627 1.11627i −0.992284 0.123983i $$-0.960433\pi$$
−0.123983 0.992284i $$-0.539567\pi$$
$$348$$ 0 0
$$349$$ −19.2855 + 19.2855i −1.03233 + 1.03233i −0.0328700 + 0.999460i $$0.510465\pi$$
−0.999460 + 0.0328700i $$0.989535\pi$$
$$350$$ 12.9336 + 25.7038i 0.691328 + 1.37392i
$$351$$ 0 0
$$352$$ 14.3789 + 0.363303i 0.766396 + 0.0193641i
$$353$$ −25.5908 −1.36206 −0.681029 0.732256i $$-0.738467\pi$$
−0.681029 + 0.732256i $$0.738467\pi$$
$$354$$ 0 0
$$355$$ −11.5959 + 11.5959i −0.615445 + 0.615445i
$$356$$ −2.29422 1.70253i −0.121594 0.0902340i
$$357$$ 0 0
$$358$$ 15.6316 + 5.16647i 0.826155 + 0.273056i
$$359$$ 3.77296i 0.199129i −0.995031 0.0995645i $$-0.968255\pi$$
0.995031 0.0995645i $$-0.0317450\pi$$
$$360$$ 0 0
$$361$$ 18.9495i 0.997341i
$$362$$ 4.21940 12.7662i 0.221767 0.670975i
$$363$$ 0 0
$$364$$ −8.35846 + 1.23741i −0.438102 + 0.0648578i
$$365$$ 16.0454 16.0454i 0.839856 0.839856i
$$366$$ 0 0
$$367$$ −27.4474 −1.43274 −0.716371 0.697720i $$-0.754198\pi$$
−0.716371 + 0.697720i $$0.754198\pi$$
$$368$$ −10.8284 + 3.27798i −0.564471 + 0.170877i
$$369$$ 0 0
$$370$$ −24.8986 + 12.5284i −1.29441 + 0.651321i
$$371$$ 16.2222 16.2222i 0.842216 0.842216i
$$372$$ 0 0
$$373$$ 12.6231 + 12.6231i 0.653601 + 0.653601i 0.953858 0.300257i $$-0.0970725\pi$$
−0.300257 + 0.953858i $$0.597072\pi$$
$$374$$ −0.253649 + 0.767438i −0.0131159 + 0.0396833i
$$375$$ 0 0
$$376$$ 7.88163 + 1.37109i 0.406464 + 0.0707085i
$$377$$ 5.13946i 0.264695i
$$378$$ 0 0
$$379$$ −11.6686 11.6686i −0.599373 0.599373i 0.340772 0.940146i $$-0.389311\pi$$
−0.940146 + 0.340772i $$0.889311\pi$$
$$380$$ −1.01748 + 1.37109i −0.0521955 + 0.0703353i
$$381$$ 0 0
$$382$$ −13.2238 26.2807i −0.676591 1.34464i
$$383$$ 17.1885 0.878291 0.439145 0.898416i $$-0.355281\pi$$
0.439145 + 0.898416i $$0.355281\pi$$
$$384$$ 0 0
$$385$$ 20.8486 1.06254
$$386$$ −8.99173 17.8699i −0.457667 0.909553i
$$387$$ 0 0
$$388$$ 19.5453 26.3380i 0.992264 1.33711i
$$389$$ 1.88238 + 1.88238i 0.0954404 + 0.0954404i 0.753215 0.657774i $$-0.228502\pi$$
−0.657774 + 0.753215i $$0.728502\pi$$
$$390$$ 0 0
$$391$$ 0.635767i 0.0321521i
$$392$$ 6.51772 + 1.13382i 0.329195 + 0.0572667i
$$393$$ 0 0
$$394$$ 1.52431 4.61192i 0.0767935 0.232345i
$$395$$ 40.3034 + 40.3034i 2.02788 + 2.02788i
$$396$$ 0 0
$$397$$ 8.41166 8.41166i 0.422169 0.422169i −0.463781 0.885950i $$-0.653507\pi$$
0.885950 + 0.463781i $$0.153507\pi$$
$$398$$ 0.386800 0.194629i 0.0193885 0.00975588i
$$399$$ 0 0
$$400$$ 36.0802 10.9222i 1.80401 0.546110i
$$401$$ −1.12389 −0.0561242 −0.0280621 0.999606i $$-0.508934\pi$$
−0.0280621 + 0.999606i $$0.508934\pi$$
$$402$$ 0 0
$$403$$ 2.54751 2.54751i 0.126900 0.126900i
$$404$$ 0.229135 0.0339217i 0.0113999 0.00168767i
$$405$$ 0 0
$$406$$ 2.51645 7.61373i 0.124889 0.377863i
$$407$$ 13.1950i 0.654051i
$$408$$ 0 0
$$409$$ 13.7211i 0.678464i 0.940703 + 0.339232i $$0.110167\pi$$
−0.940703 + 0.339232i $$0.889833\pi$$
$$410$$ 29.9949 + 9.91375i 1.48134 + 0.489605i
$$411$$ 0 0
$$412$$ −21.4422 15.9121i −1.05638 0.783934i
$$413$$ 8.63577 8.63577i 0.424938 0.424938i
$$414$$ 0 0
$$415$$ 54.3329 2.66710
$$416$$ −0.279604 + 11.0662i −0.0137087 + 0.542566i
$$417$$ 0 0
$$418$$ 0.363303 + 0.722018i 0.0177698 + 0.0353151i
$$419$$ 9.30755 9.30755i 0.454703 0.454703i −0.442209 0.896912i $$-0.645805\pi$$
0.896912 + 0.442209i $$0.145805\pi$$
$$420$$ 0 0
$$421$$ 8.44378 + 8.44378i 0.411525 + 0.411525i 0.882269 0.470745i $$-0.156015\pi$$
−0.470745 + 0.882269i $$0.656015\pi$$
$$422$$ −13.7344 4.53942i −0.668580 0.220975i
$$423$$ 0 0
$$424$$ −17.2958 24.5807i −0.839960 1.19374i
$$425$$ 2.11837i 0.102756i
$$426$$ 0 0
$$427$$ 12.9264 + 12.9264i 0.625551 + 0.625551i
$$428$$ −20.3633 + 3.01464i −0.984297 + 0.145718i
$$429$$ 0 0
$$430$$ −52.6187 + 26.4766i −2.53750 + 1.27681i
$$431$$ 30.6054 1.47421 0.737105 0.675778i $$-0.236192\pi$$
0.737105 + 0.675778i $$0.236192\pi$$
$$432$$ 0 0
$$433$$ −15.3137 −0.735930 −0.367965 0.929840i $$-0.619945\pi$$
−0.367965 + 0.929840i $$0.619945\pi$$
$$434$$ 5.02129 2.52660i 0.241030 0.121281i
$$435$$ 0 0
$$436$$ −2.91630 19.6991i −0.139665 0.943413i
$$437$$ −0.449555 0.449555i −0.0215051 0.0215051i
$$438$$ 0 0
$$439$$ 33.3676i 1.59255i −0.604936 0.796274i $$-0.706801\pi$$
0.604936 0.796274i $$-0.293199\pi$$
$$440$$ 4.68119 26.9096i 0.223167 1.28286i
$$441$$ 0 0
$$442$$ −0.590633 0.195213i −0.0280936 0.00928533i
$$443$$ −2.28832 2.28832i −0.108721 0.108721i 0.650653 0.759375i $$-0.274495\pi$$
−0.759375 + 0.650653i $$0.774495\pi$$
$$444$$ 0 0
$$445$$ −3.83621 + 3.83621i −0.181854 + 0.181854i
$$446$$ 1.09276 + 2.17172i 0.0517437 + 0.102834i
$$447$$ 0 0
$$448$$ −5.83260 + 16.2569i −0.275565 + 0.768066i
$$449$$ 27.4165 1.29387 0.646933 0.762547i $$-0.276052\pi$$
0.646933 + 0.762547i $$0.276052\pi$$
$$450$$ 0 0
$$451$$ 10.5748 10.5748i 0.497947 0.497947i
$$452$$ 22.4649 30.2722i 1.05666 1.42388i
$$453$$ 0 0
$$454$$ 19.2096 + 6.34905i 0.901551 + 0.297976i
$$455$$ 16.0454i 0.752221i
$$456$$ 0 0
$$457$$ 10.9147i 0.510567i 0.966866 + 0.255284i $$0.0821688\pi$$
−0.966866 + 0.255284i $$0.917831\pi$$
$$458$$ −7.54386 + 22.8246i −0.352501 + 1.06652i
$$459$$ 0 0
$$460$$ 3.14631 + 21.2527i 0.146697 + 0.990913i
$$461$$ −17.8319 + 17.8319i −0.830512 + 0.830512i −0.987587 0.157075i $$-0.949794\pi$$
0.157075 + 0.987587i $$0.449794\pi$$
$$462$$ 0 0
$$463$$ 22.4937 1.04537 0.522686 0.852525i $$-0.324930\pi$$
0.522686 + 0.852525i $$0.324930\pi$$
$$464$$ −9.26213 4.95755i −0.429983 0.230148i
$$465$$ 0 0
$$466$$ 16.9004 8.50389i 0.782895 0.393935i
$$467$$ −24.2171 + 24.2171i −1.12063 + 1.12063i −0.128989 + 0.991646i $$0.541173\pi$$
−0.991646 + 0.128989i $$0.958827\pi$$
$$468$$ 0 0
$$469$$ −22.5054 22.5054i −1.03920 1.03920i
$$470$$ 4.76744 14.4243i 0.219906 0.665343i
$$471$$ 0 0
$$472$$ −9.20730 13.0853i −0.423800 0.602301i
$$473$$ 27.8852i 1.28216i
$$474$$ 0 0
$$475$$ 1.49791 + 1.49791i 0.0687289 + 0.0687289i
$$476$$ −0.779397 0.578387i −0.0357236 0.0265103i
$$477$$ 0 0
$$478$$ 8.49724 + 16.8872i 0.388655 + 0.772400i
$$479$$ 36.2362 1.65568 0.827838 0.560968i $$-0.189571\pi$$
0.827838 + 0.560968i $$0.189571\pi$$
$$480$$ 0 0
$$481$$ −10.1551 −0.463032
$$482$$ −0.134427 0.267156i −0.00612297 0.0121686i
$$483$$ 0 0
$$484$$ 7.28334 + 5.40494i 0.331061 + 0.245679i
$$485$$ −44.0403 44.0403i −1.99977 1.99977i
$$486$$ 0 0
$$487$$ 16.8200i 0.762186i 0.924537 + 0.381093i $$0.124452\pi$$
−0.924537 + 0.381093i $$0.875548\pi$$
$$488$$ 19.5867 13.7819i 0.886646 0.623876i
$$489$$ 0 0
$$490$$ 3.94244 11.9282i 0.178101 0.538860i
$$491$$ −6.10641 6.10641i −0.275578 0.275578i 0.555763 0.831341i $$-0.312426\pi$$
−0.831341 + 0.555763i $$0.812426\pi$$
$$492$$ 0 0
$$493$$ 0.417438 0.417438i 0.0188005 0.0188005i
$$494$$ −0.555677 + 0.279604i −0.0250011 + 0.0125800i
$$495$$ 0 0
$$496$$ −2.13368 7.04836i −0.0958050 0.316481i
$$497$$ −9.32206 −0.418151
$$498$$ 0 0
$$499$$ −19.6770 + 19.6770i −0.880864 + 0.880864i −0.993622 0.112758i $$-0.964031\pi$$
0.112758 + 0.993622i $$0.464031\pi$$
$$500$$ −4.92153 33.2440i −0.220098 1.48672i
$$501$$ 0 0
$$502$$ −6.54856 + 19.8132i −0.292277 + 0.884308i
$$503$$ 25.7308i 1.14728i −0.819108 0.573639i $$-0.805531\pi$$
0.819108 0.573639i $$-0.194469\pi$$
$$504$$ 0 0
$$505$$ 0.439861i 0.0195736i
$$506$$ 9.65685 + 3.19173i 0.429300 + 0.141890i
$$507$$ 0 0
$$508$$ 4.54789 6.12845i 0.201780 0.271906i
$$509$$ −1.73514 + 1.73514i −0.0769087 + 0.0769087i −0.744515 0.667606i $$-0.767319\pi$$
0.667606 + 0.744515i $$0.267319\pi$$
$$510$$ 0 0
$$511$$ 12.8991 0.570623
$$512$$ 19.6734 + 11.1784i 0.869450 + 0.494021i
$$513$$ 0 0
$$514$$ −0.471775 0.937591i −0.0208091 0.0413554i
$$515$$ −35.8538 + 35.8538i −1.57991 + 1.57991i
$$516$$ 0 0
$$517$$ −5.08532 5.08532i −0.223652 0.223652i
$$518$$ −15.0440 4.97226i −0.660995 0.218469i
$$519$$ 0 0
$$520$$ 20.7101 + 3.60272i 0.908196 + 0.157990i
$$521$$ 33.5944i 1.47180i −0.677092 0.735898i $$-0.736760\pi$$
0.677092 0.735898i $$-0.263240\pi$$
$$522$$ 0 0
$$523$$ −21.8158 21.8158i −0.953938 0.953938i 0.0450467 0.998985i $$-0.485656\pi$$
−0.998985 + 0.0450467i $$0.985656\pi$$
$$524$$ 0.317883 + 2.14724i 0.0138868 + 0.0938026i
$$525$$ 0 0
$$526$$ −6.92839 + 3.48621i −0.302092 + 0.152006i
$$527$$ 0.413828 0.0180266
$$528$$ 0 0
$$529$$ 15.0000 0.652174
$$530$$ −50.9846 + 25.6543i −2.21463 + 1.11435i
$$531$$ 0 0
$$532$$ −0.960099 + 0.142136i −0.0416256 + 0.00616236i
$$533$$ 8.13853 + 8.13853i 0.352519 + 0.352519i
$$534$$ 0 0
$$535$$ 39.0907i 1.69004i
$$536$$ −34.1013 + 23.9949i −1.47295 + 1.03642i
$$537$$ 0 0
$$538$$ 27.4858 + 9.08445i 1.18500 + 0.391658i
$$539$$ −4.20531 4.20531i −0.181136 0.181136i
$$540$$ 0 0
$$541$$ 27.2112 27.2112i 1.16990 1.16990i 0.187669 0.982232i $$-0.439907\pi$$
0.982232 0.187669i $$-0.0600933\pi$$
$$542$$ 8.92281 + 17.7329i 0.383267 + 0.761694i
$$543$$ 0 0
$$544$$ −0.921533 + 0.876113i −0.0395104 + 0.0375630i
$$545$$ −37.8155 −1.61984
$$546$$ 0 0
$$547$$ −6.80116 + 6.80116i −0.290796 + 0.290796i −0.837395 0.546598i $$-0.815922\pi$$
0.546598 + 0.837395i $$0.315922\pi$$
$$548$$ 8.52841 + 6.32889i 0.364315 + 0.270357i
$$549$$ 0 0
$$550$$ −32.1765 10.6348i −1.37201 0.453470i
$$551$$ 0.590346i 0.0251496i
$$552$$ 0 0
$$553$$ 32.4004i 1.37780i
$$554$$ 5.95635 18.0214i 0.253061 0.765657i
$$555$$ 0 0
$$556$$ −24.5307 + 3.63159i −1.04033 + 0.154014i
$$557$$ 4.29337 4.29337i 0.181916 0.181916i −0.610274 0.792190i $$-0.708941\pi$$
0.792190 + 0.610274i $$0.208941\pi$$
$$558$$ 0 0
$$559$$ −21.4609 −0.907701
$$560$$ 28.9164 + 15.4775i 1.22194 + 0.654044i
$$561$$ 0 0
$$562$$ −4.91878 + 2.47502i −0.207486 + 0.104402i
$$563$$ 10.0801 10.0801i 0.424825 0.424825i −0.462036 0.886861i $$-0.652881\pi$$
0.886861 + 0.462036i $$0.152881\pi$$
$$564$$ 0 0
$$565$$ −50.6187 50.6187i −2.12954 2.12954i
$$566$$ −7.83621 + 23.7091i −0.329381 + 0.996569i
$$567$$ 0 0
$$568$$ −2.09311 + 12.0321i −0.0878248 + 0.504856i
$$569$$ 32.5018i 1.36255i 0.732029 + 0.681274i $$0.238574\pi$$
−0.732029 + 0.681274i $$0.761426\pi$$
$$570$$ 0 0
$$571$$ −9.17157 9.17157i −0.383818 0.383818i 0.488657 0.872476i $$-0.337487\pi$$
−0.872476 + 0.488657i $$0.837487\pi$$
$$572$$ 5.93030 7.99129i 0.247958 0.334132i
$$573$$ 0 0
$$574$$ 8.07174 + 16.0415i 0.336908 + 0.669560i
$$575$$ 26.6559 1.11163
$$576$$ 0 0
$$577$$ 11.7536 0.489308 0.244654 0.969611i $$-0.421326\pi$$
0.244654 + 0.969611i $$0.421326\pi$$
$$578$$ 10.7742 + 21.4123i 0.448147 + 0.890634i
$$579$$ 0 0
$$580$$ −11.8885 + 16.0202i −0.493643 + 0.665201i
$$581$$ 21.8395 + 21.8395i 0.906053 + 0.906053i
$$582$$ 0 0
$$583$$ 27.0192i 1.11902i
$$584$$ 2.89627 16.6491i 0.119849 0.688943i
$$585$$ 0 0
$$586$$ 7.00144 21.1835i 0.289227 0.875081i
$$587$$ −6.46002 6.46002i −0.266634 0.266634i 0.561109 0.827742i $$-0.310375\pi$$
−0.827742 + 0.561109i $$0.810375\pi$$
$$588$$ 0 0
$$589$$ 0.292621 0.292621i 0.0120572 0.0120572i
$$590$$ −27.1412 + 13.6569i −1.11739 + 0.562244i
$$591$$ 0 0
$$592$$ −9.79564 + 18.3011i −0.402598 + 0.752170i
$$593$$ −5.49270 −0.225558 −0.112779 0.993620i $$-0.535975\pi$$
−0.112779 + 0.993620i $$0.535975\pi$$
$$594$$ 0 0
$$595$$ −1.30324 + 1.30324i −0.0534278 + 0.0534278i
$$596$$ −2.87820 + 0.426097i −0.117896 + 0.0174536i
$$597$$ 0 0
$$598$$ −2.45641 + 7.43208i −0.100450 + 0.303920i
$$599$$ 36.4348i 1.48868i −0.667799 0.744342i $$-0.732763\pi$$
0.667799 0.744342i $$-0.267237\pi$$
$$600$$ 0 0
$$601$$ 9.97474i 0.406878i −0.979088 0.203439i $$-0.934788\pi$$
0.979088 0.203439i $$-0.0652119\pi$$
$$602$$ −31.7928 10.5080i −1.29578 0.428274i
$$603$$ 0 0
$$604$$ 3.27151 + 2.42777i 0.133116 + 0.0987848i
$$605$$ 12.1786 12.1786i 0.495131 0.495131i
$$606$$ 0 0
$$607$$ 4.51900 0.183421 0.0917103 0.995786i $$-0.470767\pi$$
0.0917103 + 0.995786i $$0.470767\pi$$
$$608$$ −0.0321169 + 1.27113i −0.00130251 + 0.0515510i
$$609$$ 0 0
$$610$$ −20.4422 40.6261i −0.827679 1.64490i
$$611$$ 3.91375 3.91375i 0.158333 0.158333i
$$612$$ 0 0
$$613$$ −8.43692 8.43692i −0.340764 0.340764i 0.515890 0.856655i $$-0.327461\pi$$
−0.856655 + 0.515890i $$0.827461\pi$$
$$614$$ 10.2605 + 3.39125i 0.414080 + 0.136860i
$$615$$ 0 0
$$616$$ 12.6981 8.93484i 0.511621 0.359995i
$$617$$ 32.1201i 1.29311i −0.762869 0.646554i $$-0.776210\pi$$
0.762869 0.646554i $$-0.223790\pi$$
$$618$$ 0 0
$$619$$ 15.0412 + 15.0412i 0.604559 + 0.604559i 0.941519 0.336960i $$-0.109399\pi$$
−0.336960 + 0.941519i $$0.609399\pi$$
$$620$$ −13.8337 + 2.04797i −0.555573 + 0.0822486i
$$621$$ 0 0
$$622$$ 30.5243 15.3591i 1.22391 0.615845i
$$623$$ −3.08398 −0.123557
$$624$$ 0 0
$$625$$ −16.6958 −0.667833
$$626$$ −20.9841 + 10.5587i −0.838692 + 0.422011i
$$627$$ 0 0
$$628$$ 2.52413 + 17.0500i 0.100724 + 0.680368i
$$629$$ −0.824818 0.824818i −0.0328876 0.0328876i
$$630$$ 0 0
$$631$$ 36.4685i 1.45179i −0.687807 0.725894i $$-0.741426\pi$$
0.687807 0.725894i $$-0.258574\pi$$
$$632$$ 41.8196 + 7.27494i 1.66350 + 0.289382i
$$633$$ 0 0
$$634$$ 3.44035 + 1.13709i 0.136634 + 0.0451595i
$$635$$ −10.2475 10.2475i −0.406659 0.406659i
$$636$$ 0 0
$$637$$ 3.23648 3.23648i 0.128234 0.128234i
$$638$$ 4.24494 + 8.43625i 0.168059 + 0.333994i
$$639$$ 0 0
$$640$$ 26.4697 33.8477i 1.04631 1.33795i
$$641$$ −14.0036 −0.553109 −0.276555 0.960998i $$-0.589193\pi$$
−0.276555 + 0.960998i $$0.589193\pi$$
$$642$$ 0 0
$$643$$ 16.6034 16.6034i 0.654774 0.654774i −0.299365 0.954139i $$-0.596775\pi$$
0.954139 + 0.299365i $$0.0967748\pi$$
$$644$$ −7.27798 + 9.80734i −0.286793 + 0.386463i
$$645$$ 0 0
$$646$$ −0.0678434 0.0224232i −0.00266926 0.000882230i
$$647$$ 12.1908i 0.479270i 0.970863 + 0.239635i $$0.0770277\pi$$
−0.970863 + 0.239635i $$0.922972\pi$$
$$648$$ 0 0
$$649$$ 14.3835i 0.564600i
$$650$$ 8.18473 24.7636i 0.321032 0.971309i
$$651$$ 0 0
$$652$$ 1.42362 + 9.61628i 0.0557533 + 0.376603i
$$653$$ −0.983270 + 0.983270i −0.0384783 + 0.0384783i −0.726084 0.687606i $$-0.758662\pi$$
0.687606 + 0.726084i $$0.258662\pi$$
$$654$$ 0 0
$$655$$ 4.12198 0.161059
$$656$$ 22.5174 6.81647i 0.879157 0.266138i
$$657$$ 0 0
$$658$$ 7.71423 3.88163i 0.300732 0.151322i
$$659$$ 18.0559 18.0559i 0.703357 0.703357i −0.261772 0.965130i $$-0.584307\pi$$
0.965130 + 0.261772i $$0.0843069\pi$$
$$660$$ 0 0
$$661$$ −4.55890 4.55890i −0.177321 0.177321i 0.612866 0.790187i $$-0.290017\pi$$
−0.790187 + 0.612866i $$0.790017\pi$$
$$662$$ 8.48889 25.6839i 0.329930 0.998232i
$$663$$ 0 0
$$664$$ 33.0922 23.2848i 1.28423 0.903627i
$$665$$ 1.84307i 0.0714710i
$$666$$ 0 0
$$667$$ −5.25272 5.25272i −0.203386 0.203386i
$$668$$ −34.8554 25.8661i −1.34860 1.00079i
$$669$$ 0 0
$$670$$ 35.5908 + 70.7320i 1.37499 + 2.73261i
$$671$$ −21.5298 −0.831148
$$672$$ 0 0
$$673$$ −10.8569 −0.418504 −0.209252 0.977862i $$-0.567103\pi$$
−0.209252 + 0.977862i $$0.567103\pi$$
$$674$$ 0.715856 + 1.42267i 0.0275737 + 0.0547992i
$$675$$ 0 0
$$676$$ −14.7287 10.9301i −0.566489 0.420389i
$$677$$ −23.7066 23.7066i −0.911120 0.911120i 0.0852405 0.996360i $$-0.472834\pi$$
−0.996360 + 0.0852405i $$0.972834\pi$$
$$678$$ 0 0
$$679$$ 35.4045i 1.35870i
$$680$$ 1.38950 + 1.97474i 0.0532847 + 0.0757277i
$$681$$ 0 0
$$682$$ −2.07754 + 6.28577i −0.0795530 + 0.240694i
$$683$$ 17.8337 + 17.8337i 0.682386 + 0.682386i 0.960537 0.278151i $$-0.0897217\pi$$
−0.278151 + 0.960537i $$0.589722\pi$$
$$684$$ 0 0
$$685$$ 14.2605 14.2605i 0.544866 0.544866i
$$686$$ 25.4710 12.8165i 0.972489 0.489335i
$$687$$ 0 0
$$688$$ −20.7013 + 38.6761i −0.789231 + 1.47451i
$$689$$ −20.7945 −0.792205
$$690$$ 0 0
$$691$$ 10.8557 10.8557i 0.412970 0.412970i −0.469802 0.882772i $$-0.655675\pi$$
0.882772 + 0.469802i $$0.155675\pi$$
$$692$$ 3.62293 + 24.4722i 0.137723 + 0.930294i
$$693$$ 0 0
$$694$$ −13.0509 + 39.4866i −0.495406 + 1.49889i
$$695$$ 47.0907i 1.78625i
$$696$$ 0 0
$$697$$ 1.32206i 0.0500765i
$$698$$ 36.6225 + 12.1043i 1.38618 + 0.458154i
$$699$$ 0 0
$$700$$ 24.2502 32.6780i 0.916570 1.23511i
$$701$$ 6.08875 6.08875i 0.229969 0.229969i −0.582711 0.812680i $$-0.698008\pi$$
0.812680 + 0.582711i $$0.198008\pi$$
$$702$$ 0 0
$$703$$ −1.16647 −0.0439942
$$704$$ −8.68119 18.3958i −0.327185 0.693317i
$$705$$ 0 0
$$706$$ 16.2672 + 32.3288i 0.612222 + 1.21671i
$$707$$ 0.176805 0.176805i 0.00664943 0.00664943i
$$708$$ 0 0
$$709$$ 22.8836 + 22.8836i 0.859413 + 0.859413i 0.991269 0.131856i $$-0.0420936\pi$$
−0.131856 + 0.991269i $$0.542094\pi$$
$$710$$ 22.0202 + 7.27798i 0.826402 + 0.273138i
$$711$$ 0 0
$$712$$ −0.692453 + 3.98053i −0.0259508 + 0.149177i
$$713$$ 5.20730i 0.195015i
$$714$$ 0 0
$$715$$ −13.3624 13.3624i −0.499724 0.499724i
$$716$$ −3.40965 23.0316i −0.127425 0.860729i
$$717$$ 0 0
$$718$$ −4.76638 + 2.39834i −0.177880 + 0.0895052i
$$719$$ 1.46744 0.0547262 0.0273631 0.999626i $$-0.491289\pi$$
0.0273631 + 0.999626i $$0.491289\pi$$
$$720$$ 0 0
$$721$$ −28.8233 −1.07344
$$722$$ 23.9389 12.0455i 0.890913 0.448288i
$$723$$ 0 0
$$724$$ −18.8096 + 2.78463i −0.699055 + 0.103490i
$$725$$ 17.5020 + 17.5020i 0.650008 + 0.650008i
$$726$$ 0 0
$$727$$ 15.3928i 0.570889i 0.958395 + 0.285445i $$0.0921412\pi$$
−0.958395 + 0.285445i $$0.907859\pi$$
$$728$$ 6.87640 + 9.77267i 0.254856 + 0.362199i
$$729$$ 0 0
$$730$$ −30.4697 10.0707i −1.12773 0.372733i
$$731$$ −1.74311 1.74311i −0.0644711 0.0644711i
$$732$$ 0 0
$$733$$ −12.4185 + 12.4185i −0.458688 + 0.458688i −0.898225 0.439536i $$-0.855143\pi$$
0.439536 + 0.898225i $$0.355143\pi$$
$$734$$ 17.4473 + 34.6743i 0.643993 + 1.27985i
$$735$$ 0 0
$$736$$ 11.0243 + 11.5959i 0.406362 + 0.427429i
$$737$$ 37.4844 1.38075
$$738$$ 0 0
$$739$$ −14.6559 + 14.6559i −0.539127 + 0.539127i −0.923273 0.384146i $$-0.874496\pi$$
0.384146 + 0.923273i $$0.374496\pi$$
$$740$$ 31.6543 + 23.4905i 1.16364 + 0.863528i
$$741$$ 0 0
$$742$$ −30.8055 10.1817i −1.13090 0.373780i
$$743$$ 31.7821i 1.16597i 0.812482 + 0.582986i $$0.198116\pi$$
−0.812482 + 0.582986i $$0.801884\pi$$
$$744$$ 0 0
$$745$$ 5.52518i 0.202427i
$$746$$ 7.92273 23.9709i 0.290072 0.877637i
$$747$$ 0 0
$$748$$ 1.13074 0.167398i 0.0413440 0.00612068i
$$749$$ −15.7127 + 15.7127i −0.574131 + 0.574131i
$$750$$ 0 0
$$751$$ 29.7594 1.08594 0.542968 0.839753i $$-0.317301\pi$$
0.542968 + 0.839753i $$0.317301\pi$$
$$752$$ −3.27798 10.8284i −0.119536 0.394872i
$$753$$ 0 0
$$754$$ −6.49268 + 3.26697i −0.236449 + 0.118976i
$$755$$ 5.47036 5.47036i 0.199087 0.199087i
$$756$$ 0 0
$$757$$ 15.6355 + 15.6355i 0.568282 + 0.568282i 0.931647 0.363365i $$-0.118372\pi$$
−0.363365 + 0.931647i $$0.618372\pi$$
$$758$$ −7.32361 + 22.1582i −0.266005 + 0.804822i
$$759$$ 0 0
$$760$$ 2.37887 + 0.413828i 0.0862908 + 0.0150111i
$$761$$ 4.55957i 0.165284i 0.996579 + 0.0826422i $$0.0263359\pi$$
−0.996579 + 0.0826422i $$0.973664\pi$$
$$762$$ 0 0
$$763$$ −15.2002 15.2002i −0.550284 0.550284i
$$764$$ −24.7945 + 33.4114i −0.897032 + 1.20878i
$$765$$ 0 0
$$766$$ −10.9261 21.7142i −0.394777 0.784567i
$$767$$ −11.0698 −0.399706
$$768$$ 0 0
$$769$$ 36.5794 1.31909 0.659543 0.751667i $$-0.270750\pi$$
0.659543 + 0.751667i $$0.270750\pi$$
$$770$$ −13.2527 26.3380i −0.477595 0.949157i
$$771$$ 0 0
$$772$$ −16.8593 + 22.7185i −0.606780 + 0.817657i
$$773$$ 18.7108 + 18.7108i 0.672981 + 0.672981i 0.958402 0.285421i $$-0.0921335\pi$$
−0.285421 + 0.958402i $$0.592133\pi$$
$$774$$ 0 0
$$775$$ 17.3507i 0.623255i
$$776$$ −45.6972 7.94948i −1.64043 0.285370i
$$777$$ 0 0
$$778$$ 1.18145 3.57457i 0.0423570 0.128155i
$$779$$ 0.934836 + 0.934836i 0.0334940 + 0.0334940i
$$780$$ 0 0
$$781$$ 7.76326 7.76326i 0.277791 0.277791i
$$782$$ −0.803165 + 0.404135i −0.0287211 + 0.0144518i
$$783$$ 0 0
$$784$$ −2.71073 8.95458i −0.0968118 0.319806i
$$785$$ 32.7302 1.16819
$$786$$ 0 0
$$787$$ 13.3759 13.3759i 0.476801 0.476801i −0.427306 0.904107i $$-0.640537\pi$$
0.904107 + 0.427306i $$0.140537\pi$$
$$788$$ −6.79520