# Properties

 Label 600.2.k.f.301.4 Level 600 Weight 2 Character 600.301 Analytic conductor 4.791 Analytic rank 0 Dimension 12 CM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$600 = 2^{3} \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 600.k (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.79102412128$$ Analytic rank: $$0$$ Dimension: $$12$$ Coefficient field: 12.0.180227832610816.1 Defining polynomial: $$x^{12} + x^{10} - 8 x^{6} + 16 x^{2} + 64$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: no (minimal twist has level 120) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 301.4 Root $$-0.806504 + 1.16170i$$ of defining polynomial Character $$\chi$$ $$=$$ 600.301 Dual form 600.2.k.f.301.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.806504 + 1.16170i) q^{2} -1.00000i q^{3} +(-0.699104 - 1.87383i) q^{4} +(1.16170 + 0.806504i) q^{6} -0.746175 q^{7} +(2.74067 + 0.699104i) q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q+(-0.806504 + 1.16170i) q^{2} -1.00000i q^{3} +(-0.699104 - 1.87383i) q^{4} +(1.16170 + 0.806504i) q^{6} -0.746175 q^{7} +(2.74067 + 0.699104i) q^{8} -1.00000 q^{9} -5.36068i q^{11} +(-1.87383 + 0.699104i) q^{12} +2.92520i q^{13} +(0.601793 - 0.866833i) q^{14} +(-3.02251 + 2.62001i) q^{16} -2.13466 q^{17} +(0.806504 - 1.16170i) q^{18} -1.73367i q^{19} +0.746175i q^{21} +(6.22751 + 4.32340i) q^{22} -7.49534 q^{23} +(0.699104 - 2.74067i) q^{24} +(-3.39821 - 2.35918i) q^{26} +1.00000i q^{27} +(0.521653 + 1.39821i) q^{28} -6.74916i q^{29} +2.64681 q^{31} +(-0.606006 - 5.62430i) q^{32} -5.36068 q^{33} +(1.72161 - 2.47984i) q^{34} +(0.699104 + 1.87383i) q^{36} -1.07480i q^{37} +(2.01400 + 1.39821i) q^{38} +2.92520 q^{39} -11.2936 q^{41} +(-0.866833 - 0.601793i) q^{42} -7.44322i q^{43} +(-10.0450 + 3.74767i) q^{44} +(6.04502 - 8.70735i) q^{46} -1.73367 q^{47} +(2.62001 + 3.02251i) q^{48} -6.44322 q^{49} +2.13466i q^{51} +(5.48133 - 2.04502i) q^{52} -7.72161i q^{53} +(-1.16170 - 0.806504i) q^{54} +(-2.04502 - 0.521653i) q^{56} -1.73367 q^{57} +(7.84052 + 5.44322i) q^{58} -6.85302i q^{59} +6.45203i q^{61} +(-2.13466 + 3.07480i) q^{62} +0.746175 q^{63} +(7.02251 + 3.83202i) q^{64} +(4.32340 - 6.22751i) q^{66} -7.44322i q^{67} +(1.49235 + 4.00000i) q^{68} +7.49534i q^{69} +13.2936 q^{71} +(-2.74067 - 0.699104i) q^{72} +0.690358 q^{73} +(1.24860 + 0.866833i) q^{74} +(-3.24860 + 1.21201i) q^{76} +4.00000i q^{77} +(-2.35918 + 3.39821i) q^{78} +2.64681 q^{79} +1.00000 q^{81} +(9.10834 - 13.1198i) q^{82} +5.85039i q^{83} +(1.39821 - 0.521653i) q^{84} +(8.64681 + 6.00299i) q^{86} -6.74916 q^{87} +(3.74767 - 14.6918i) q^{88} +7.59283 q^{89} -2.18271i q^{91} +(5.24002 + 14.0450i) q^{92} -2.64681i q^{93} +(1.39821 - 2.01400i) q^{94} +(-5.62430 + 0.606006i) q^{96} +14.1887 q^{97} +(5.19648 - 7.48511i) q^{98} +5.36068i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q - 2q^{4} - 2q^{6} - 12q^{9} + O(q^{10})$$ $$12q - 2q^{4} - 2q^{6} - 12q^{9} + 20q^{14} + 2q^{16} + 2q^{24} - 28q^{26} - 32q^{31} - 24q^{34} + 2q^{36} + 16q^{39} - 8q^{41} - 44q^{44} - 4q^{46} + 12q^{49} + 2q^{54} + 52q^{56} + 46q^{64} + 20q^{66} + 32q^{71} - 36q^{74} + 12q^{76} - 32q^{79} + 12q^{81} + 4q^{84} + 40q^{86} + 40q^{89} + 4q^{94} - 42q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$$.

 $$n$$ $$151$$ $$301$$ $$401$$ $$577$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.806504 + 1.16170i −0.570284 + 0.821447i
$$3$$ 1.00000i 0.577350i
$$4$$ −0.699104 1.87383i −0.349552 0.936917i
$$5$$ 0 0
$$6$$ 1.16170 + 0.806504i 0.474263 + 0.329254i
$$7$$ −0.746175 −0.282028 −0.141014 0.990008i $$-0.545036\pi$$
−0.141014 + 0.990008i $$0.545036\pi$$
$$8$$ 2.74067 + 0.699104i 0.968972 + 0.247170i
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ 5.36068i 1.61630i −0.588974 0.808152i $$-0.700468\pi$$
0.588974 0.808152i $$-0.299532\pi$$
$$12$$ −1.87383 + 0.699104i −0.540929 + 0.201814i
$$13$$ 2.92520i 0.811304i 0.914028 + 0.405652i $$0.132955\pi$$
−0.914028 + 0.405652i $$0.867045\pi$$
$$14$$ 0.601793 0.866833i 0.160836 0.231671i
$$15$$ 0 0
$$16$$ −3.02251 + 2.62001i −0.755627 + 0.655002i
$$17$$ −2.13466 −0.517731 −0.258866 0.965913i $$-0.583349\pi$$
−0.258866 + 0.965913i $$0.583349\pi$$
$$18$$ 0.806504 1.16170i 0.190095 0.273816i
$$19$$ 1.73367i 0.397730i −0.980027 0.198865i $$-0.936274\pi$$
0.980027 0.198865i $$-0.0637255\pi$$
$$20$$ 0 0
$$21$$ 0.746175i 0.162829i
$$22$$ 6.22751 + 4.32340i 1.32771 + 0.921753i
$$23$$ −7.49534 −1.56289 −0.781443 0.623977i $$-0.785516\pi$$
−0.781443 + 0.623977i $$0.785516\pi$$
$$24$$ 0.699104 2.74067i 0.142704 0.559436i
$$25$$ 0 0
$$26$$ −3.39821 2.35918i −0.666443 0.462674i
$$27$$ 1.00000i 0.192450i
$$28$$ 0.521653 + 1.39821i 0.0985832 + 0.264236i
$$29$$ 6.74916i 1.25329i −0.779306 0.626644i $$-0.784428\pi$$
0.779306 0.626644i $$-0.215572\pi$$
$$30$$ 0 0
$$31$$ 2.64681 0.475381 0.237690 0.971341i $$-0.423610\pi$$
0.237690 + 0.971341i $$0.423610\pi$$
$$32$$ −0.606006 5.62430i −0.107128 0.994245i
$$33$$ −5.36068 −0.933174
$$34$$ 1.72161 2.47984i 0.295254 0.425289i
$$35$$ 0 0
$$36$$ 0.699104 + 1.87383i 0.116517 + 0.312306i
$$37$$ 1.07480i 0.176697i −0.996090 0.0883483i $$-0.971841\pi$$
0.996090 0.0883483i $$-0.0281588\pi$$
$$38$$ 2.01400 + 1.39821i 0.326714 + 0.226819i
$$39$$ 2.92520 0.468406
$$40$$ 0 0
$$41$$ −11.2936 −1.76377 −0.881883 0.471468i $$-0.843724\pi$$
−0.881883 + 0.471468i $$0.843724\pi$$
$$42$$ −0.866833 0.601793i −0.133755 0.0928586i
$$43$$ 7.44322i 1.13508i −0.823346 0.567540i $$-0.807895\pi$$
0.823346 0.567540i $$-0.192105\pi$$
$$44$$ −10.0450 + 3.74767i −1.51434 + 0.564982i
$$45$$ 0 0
$$46$$ 6.04502 8.70735i 0.891289 1.28383i
$$47$$ −1.73367 −0.252881 −0.126441 0.991974i $$-0.540355\pi$$
−0.126441 + 0.991974i $$0.540355\pi$$
$$48$$ 2.62001 + 3.02251i 0.378166 + 0.436261i
$$49$$ −6.44322 −0.920460
$$50$$ 0 0
$$51$$ 2.13466i 0.298912i
$$52$$ 5.48133 2.04502i 0.760124 0.283593i
$$53$$ 7.72161i 1.06064i −0.847796 0.530322i $$-0.822071\pi$$
0.847796 0.530322i $$-0.177929\pi$$
$$54$$ −1.16170 0.806504i −0.158088 0.109751i
$$55$$ 0 0
$$56$$ −2.04502 0.521653i −0.273277 0.0697089i
$$57$$ −1.73367 −0.229630
$$58$$ 7.84052 + 5.44322i 1.02951 + 0.714730i
$$59$$ 6.85302i 0.892188i −0.894986 0.446094i $$-0.852815\pi$$
0.894986 0.446094i $$-0.147185\pi$$
$$60$$ 0 0
$$61$$ 6.45203i 0.826098i 0.910709 + 0.413049i $$0.135536\pi$$
−0.910709 + 0.413049i $$0.864464\pi$$
$$62$$ −2.13466 + 3.07480i −0.271102 + 0.390500i
$$63$$ 0.746175 0.0940092
$$64$$ 7.02251 + 3.83202i 0.877813 + 0.479003i
$$65$$ 0 0
$$66$$ 4.32340 6.22751i 0.532174 0.766553i
$$67$$ 7.44322i 0.909334i −0.890661 0.454667i $$-0.849758\pi$$
0.890661 0.454667i $$-0.150242\pi$$
$$68$$ 1.49235 + 4.00000i 0.180974 + 0.485071i
$$69$$ 7.49534i 0.902332i
$$70$$ 0 0
$$71$$ 13.2936 1.57766 0.788831 0.614610i $$-0.210687\pi$$
0.788831 + 0.614610i $$0.210687\pi$$
$$72$$ −2.74067 0.699104i −0.322991 0.0823902i
$$73$$ 0.690358 0.0808003 0.0404002 0.999184i $$-0.487137\pi$$
0.0404002 + 0.999184i $$0.487137\pi$$
$$74$$ 1.24860 + 0.866833i 0.145147 + 0.100767i
$$75$$ 0 0
$$76$$ −3.24860 + 1.21201i −0.372640 + 0.139027i
$$77$$ 4.00000i 0.455842i
$$78$$ −2.35918 + 3.39821i −0.267125 + 0.384771i
$$79$$ 2.64681 0.297789 0.148895 0.988853i $$-0.452428\pi$$
0.148895 + 0.988853i $$0.452428\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 9.10834 13.1198i 1.00585 1.44884i
$$83$$ 5.85039i 0.642164i 0.947051 + 0.321082i $$0.104047\pi$$
−0.947051 + 0.321082i $$0.895953\pi$$
$$84$$ 1.39821 0.521653i 0.152557 0.0569171i
$$85$$ 0 0
$$86$$ 8.64681 + 6.00299i 0.932409 + 0.647319i
$$87$$ −6.74916 −0.723586
$$88$$ 3.74767 14.6918i 0.399503 1.56615i
$$89$$ 7.59283 0.804838 0.402419 0.915456i $$-0.368169\pi$$
0.402419 + 0.915456i $$0.368169\pi$$
$$90$$ 0 0
$$91$$ 2.18271i 0.228810i
$$92$$ 5.24002 + 14.0450i 0.546310 + 1.46429i
$$93$$ 2.64681i 0.274461i
$$94$$ 1.39821 2.01400i 0.144214 0.207729i
$$95$$ 0 0
$$96$$ −5.62430 + 0.606006i −0.574028 + 0.0618502i
$$97$$ 14.1887 1.44064 0.720321 0.693641i $$-0.243994\pi$$
0.720321 + 0.693641i $$0.243994\pi$$
$$98$$ 5.19648 7.48511i 0.524924 0.756110i
$$99$$ 5.36068i 0.538768i
$$100$$ 0 0
$$101$$ 7.43952i 0.740260i 0.928980 + 0.370130i $$0.120687\pi$$
−0.928980 + 0.370130i $$0.879313\pi$$
$$102$$ −2.47984 1.72161i −0.245541 0.170465i
$$103$$ −7.19820 −0.709260 −0.354630 0.935007i $$-0.615393\pi$$
−0.354630 + 0.935007i $$0.615393\pi$$
$$104$$ −2.04502 + 8.01699i −0.200530 + 0.786131i
$$105$$ 0 0
$$106$$ 8.97021 + 6.22751i 0.871264 + 0.604869i
$$107$$ 4.00000i 0.386695i −0.981130 0.193347i $$-0.938066\pi$$
0.981130 0.193347i $$-0.0619344\pi$$
$$108$$ 1.87383 0.699104i 0.180310 0.0672713i
$$109$$ 19.9504i 1.91090i 0.295158 + 0.955449i $$0.404628\pi$$
−0.295158 + 0.955449i $$0.595372\pi$$
$$110$$ 0 0
$$111$$ −1.07480 −0.102016
$$112$$ 2.25532 1.95498i 0.213108 0.184729i
$$113$$ −12.0540 −1.13395 −0.566973 0.823736i $$-0.691886\pi$$
−0.566973 + 0.823736i $$0.691886\pi$$
$$114$$ 1.39821 2.01400i 0.130954 0.188629i
$$115$$ 0 0
$$116$$ −12.6468 + 4.71836i −1.17423 + 0.438089i
$$117$$ 2.92520i 0.270435i
$$118$$ 7.96117 + 5.52699i 0.732885 + 0.508801i
$$119$$ 1.59283 0.146014
$$120$$ 0 0
$$121$$ −17.7368 −1.61244
$$122$$ −7.49534 5.20359i −0.678596 0.471110i
$$123$$ 11.2936i 1.01831i
$$124$$ −1.85039 4.95968i −0.166170 0.445392i
$$125$$ 0 0
$$126$$ −0.601793 + 0.866833i −0.0536119 + 0.0772236i
$$127$$ 4.21351 0.373888 0.186944 0.982371i $$-0.440142\pi$$
0.186944 + 0.982371i $$0.440142\pi$$
$$128$$ −10.1153 + 5.06752i −0.894079 + 0.447910i
$$129$$ −7.44322 −0.655339
$$130$$ 0 0
$$131$$ 10.3204i 0.901694i −0.892601 0.450847i $$-0.851122\pi$$
0.892601 0.450847i $$-0.148878\pi$$
$$132$$ 3.74767 + 10.0450i 0.326193 + 0.874306i
$$133$$ 1.29362i 0.112171i
$$134$$ 8.64681 + 6.00299i 0.746970 + 0.518579i
$$135$$ 0 0
$$136$$ −5.85039 1.49235i −0.501667 0.127968i
$$137$$ −15.0387 −1.28484 −0.642422 0.766351i $$-0.722070\pi$$
−0.642422 + 0.766351i $$0.722070\pi$$
$$138$$ −8.70735 6.04502i −0.741219 0.514586i
$$139$$ 9.47032i 0.803262i 0.915802 + 0.401631i $$0.131557\pi$$
−0.915802 + 0.401631i $$0.868443\pi$$
$$140$$ 0 0
$$141$$ 1.73367i 0.146001i
$$142$$ −10.7214 + 15.4432i −0.899716 + 1.29597i
$$143$$ 15.6810 1.31131
$$144$$ 3.02251 2.62001i 0.251876 0.218334i
$$145$$ 0 0
$$146$$ −0.556777 + 0.801991i −0.0460792 + 0.0663732i
$$147$$ 6.44322i 0.531428i
$$148$$ −2.01400 + 0.751399i −0.165550 + 0.0617646i
$$149$$ 1.78948i 0.146600i −0.997310 0.0733000i $$-0.976647\pi$$
0.997310 0.0733000i $$-0.0233531\pi$$
$$150$$ 0 0
$$151$$ 10.6468 0.866425 0.433212 0.901292i $$-0.357380\pi$$
0.433212 + 0.901292i $$0.357380\pi$$
$$152$$ 1.21201 4.75140i 0.0983071 0.385389i
$$153$$ 2.13466 0.172577
$$154$$ −4.64681 3.22601i −0.374451 0.259960i
$$155$$ 0 0
$$156$$ −2.04502 5.48133i −0.163732 0.438858i
$$157$$ 6.92520i 0.552691i 0.961058 + 0.276345i $$0.0891234\pi$$
−0.961058 + 0.276345i $$0.910877\pi$$
$$158$$ −2.13466 + 3.07480i −0.169824 + 0.244618i
$$159$$ −7.72161 −0.612364
$$160$$ 0 0
$$161$$ 5.59283 0.440777
$$162$$ −0.806504 + 1.16170i −0.0633649 + 0.0912719i
$$163$$ 7.70079i 0.603172i −0.953439 0.301586i $$-0.902484\pi$$
0.953439 0.301586i $$-0.0975161\pi$$
$$164$$ 7.89541 + 21.1624i 0.616528 + 1.65250i
$$165$$ 0 0
$$166$$ −6.79641 4.71836i −0.527504 0.366216i
$$167$$ 3.22601 0.249637 0.124818 0.992180i $$-0.460165\pi$$
0.124818 + 0.992180i $$0.460165\pi$$
$$168$$ −0.521653 + 2.04502i −0.0402464 + 0.157776i
$$169$$ 4.44322 0.341786
$$170$$ 0 0
$$171$$ 1.73367i 0.132577i
$$172$$ −13.9474 + 5.20359i −1.06348 + 0.396770i
$$173$$ 6.42799i 0.488711i 0.969686 + 0.244356i $$0.0785764\pi$$
−0.969686 + 0.244356i $$0.921424\pi$$
$$174$$ 5.44322 7.84052i 0.412650 0.594388i
$$175$$ 0 0
$$176$$ 14.0450 + 16.2027i 1.05868 + 1.22132i
$$177$$ −6.85302 −0.515105
$$178$$ −6.12364 + 8.82061i −0.458987 + 0.661132i
$$179$$ 8.13765i 0.608236i −0.952634 0.304118i $$-0.901638\pi$$
0.952634 0.304118i $$-0.0983618\pi$$
$$180$$ 0 0
$$181$$ 1.49235i 0.110925i 0.998461 + 0.0554627i $$0.0176634\pi$$
−0.998461 + 0.0554627i $$0.982337\pi$$
$$182$$ 2.53566 + 1.76036i 0.187955 + 0.130487i
$$183$$ 6.45203 0.476948
$$184$$ −20.5422 5.24002i −1.51439 0.386299i
$$185$$ 0 0
$$186$$ 3.07480 + 2.13466i 0.225456 + 0.156521i
$$187$$ 11.4432i 0.836811i
$$188$$ 1.21201 + 3.24860i 0.0883951 + 0.236929i
$$189$$ 0.746175i 0.0542762i
$$190$$ 0 0
$$191$$ 6.88645 0.498286 0.249143 0.968467i $$-0.419851\pi$$
0.249143 + 0.968467i $$0.419851\pi$$
$$192$$ 3.83202 7.02251i 0.276552 0.506806i
$$193$$ 16.4830 1.18647 0.593237 0.805028i $$-0.297850\pi$$
0.593237 + 0.805028i $$0.297850\pi$$
$$194$$ −11.4432 + 16.4830i −0.821576 + 1.18341i
$$195$$ 0 0
$$196$$ 4.50448 + 12.0735i 0.321749 + 0.862395i
$$197$$ 13.5720i 0.966965i −0.875354 0.483483i $$-0.839372\pi$$
0.875354 0.483483i $$-0.160628\pi$$
$$198$$ −6.22751 4.32340i −0.442570 0.307251i
$$199$$ 9.05398 0.641820 0.320910 0.947110i $$-0.396011\pi$$
0.320910 + 0.947110i $$0.396011\pi$$
$$200$$ 0 0
$$201$$ −7.44322 −0.525005
$$202$$ −8.64251 6.00000i −0.608085 0.422159i
$$203$$ 5.03605i 0.353462i
$$204$$ 4.00000 1.49235i 0.280056 0.104485i
$$205$$ 0 0
$$206$$ 5.80538 8.36217i 0.404480 0.582620i
$$207$$ 7.49534 0.520962
$$208$$ −7.66404 8.84143i −0.531406 0.613043i
$$209$$ −9.29362 −0.642853
$$210$$ 0 0
$$211$$ 2.53566i 0.174562i −0.996184 0.0872809i $$-0.972182\pi$$
0.996184 0.0872809i $$-0.0278178\pi$$
$$212$$ −14.4690 + 5.39821i −0.993736 + 0.370750i
$$213$$ 13.2936i 0.910864i
$$214$$ 4.64681 + 3.22601i 0.317649 + 0.220526i
$$215$$ 0 0
$$216$$ −0.699104 + 2.74067i −0.0475680 + 0.186479i
$$217$$ −1.97498 −0.134070
$$218$$ −23.1764 16.0900i −1.56970 1.08975i
$$219$$ 0.690358i 0.0466501i
$$220$$ 0 0
$$221$$ 6.24430i 0.420037i
$$222$$ 0.866833 1.24860i 0.0581780 0.0838006i
$$223$$ −12.1579 −0.814152 −0.407076 0.913394i $$-0.633452\pi$$
−0.407076 + 0.913394i $$0.633452\pi$$
$$224$$ 0.452186 + 4.19671i 0.0302130 + 0.280405i
$$225$$ 0 0
$$226$$ 9.72161 14.0032i 0.646672 0.931478i
$$227$$ 20.7368i 1.37635i 0.725544 + 0.688176i $$0.241588\pi$$
−0.725544 + 0.688176i $$0.758412\pi$$
$$228$$ 1.21201 + 3.24860i 0.0802674 + 0.215144i
$$229$$ 19.9504i 1.31836i −0.751987 0.659178i $$-0.770904\pi$$
0.751987 0.659178i $$-0.229096\pi$$
$$230$$ 0 0
$$231$$ 4.00000 0.263181
$$232$$ 4.71836 18.4972i 0.309776 1.21440i
$$233$$ 13.3386 0.873844 0.436922 0.899499i $$-0.356069\pi$$
0.436922 + 0.899499i $$0.356069\pi$$
$$234$$ 3.39821 + 2.35918i 0.222148 + 0.154225i
$$235$$ 0 0
$$236$$ −12.8414 + 4.79097i −0.835906 + 0.311866i
$$237$$ 2.64681i 0.171929i
$$238$$ −1.28462 + 1.85039i −0.0832697 + 0.119943i
$$239$$ 22.8864 1.48040 0.740201 0.672386i $$-0.234731\pi$$
0.740201 + 0.672386i $$0.234731\pi$$
$$240$$ 0 0
$$241$$ 3.59283 0.231435 0.115717 0.993282i $$-0.463083\pi$$
0.115717 + 0.993282i $$0.463083\pi$$
$$242$$ 14.3048 20.6049i 0.919549 1.32453i
$$243$$ 1.00000i 0.0641500i
$$244$$ 12.0900 4.51064i 0.773985 0.288764i
$$245$$ 0 0
$$246$$ −13.1198 9.10834i −0.836489 0.580727i
$$247$$ 5.07131 0.322680
$$248$$ 7.25402 + 1.85039i 0.460631 + 0.117500i
$$249$$ 5.85039 0.370754
$$250$$ 0 0
$$251$$ 8.82801i 0.557219i 0.960404 + 0.278609i $$0.0898735\pi$$
−0.960404 + 0.278609i $$0.910127\pi$$
$$252$$ −0.521653 1.39821i −0.0328611 0.0880788i
$$253$$ 40.1801i 2.52610i
$$254$$ −3.39821 + 4.89484i −0.213222 + 0.307129i
$$255$$ 0 0
$$256$$ 2.27111 15.8380i 0.141944 0.989875i
$$257$$ 22.2927 1.39058 0.695291 0.718728i $$-0.255275\pi$$
0.695291 + 0.718728i $$0.255275\pi$$
$$258$$ 6.00299 8.64681i 0.373730 0.538327i
$$259$$ 0.801991i 0.0498333i
$$260$$ 0 0
$$261$$ 6.74916i 0.417763i
$$262$$ 11.9892 + 8.32340i 0.740694 + 0.514222i
$$263$$ 21.2014 1.30733 0.653667 0.756783i $$-0.273230\pi$$
0.653667 + 0.756783i $$0.273230\pi$$
$$264$$ −14.6918 3.74767i −0.904219 0.230653i
$$265$$ 0 0
$$266$$ −1.50280 1.04331i −0.0921424 0.0639693i
$$267$$ 7.59283i 0.464674i
$$268$$ −13.9474 + 5.20359i −0.851971 + 0.317860i
$$269$$ 14.6935i 0.895881i −0.894063 0.447940i $$-0.852158\pi$$
0.894063 0.447940i $$-0.147842\pi$$
$$270$$ 0 0
$$271$$ −20.2396 −1.22947 −0.614735 0.788734i $$-0.710737\pi$$
−0.614735 + 0.788734i $$0.710737\pi$$
$$272$$ 6.45203 5.59283i 0.391212 0.339115i
$$273$$ −2.18271 −0.132103
$$274$$ 12.1288 17.4705i 0.732727 1.05543i
$$275$$ 0 0
$$276$$ 14.0450 5.24002i 0.845411 0.315412i
$$277$$ 0.518027i 0.0311252i 0.999879 + 0.0155626i $$0.00495393\pi$$
−0.999879 + 0.0155626i $$0.995046\pi$$
$$278$$ −11.0017 7.63785i −0.659837 0.458088i
$$279$$ −2.64681 −0.158460
$$280$$ 0 0
$$281$$ 13.7008 0.817320 0.408660 0.912687i $$-0.365996\pi$$
0.408660 + 0.912687i $$0.365996\pi$$
$$282$$ −2.01400 1.39821i −0.119932 0.0832620i
$$283$$ 18.0305i 1.07180i −0.844282 0.535900i $$-0.819973\pi$$
0.844282 0.535900i $$-0.180027\pi$$
$$284$$ −9.29362 24.9100i −0.551475 1.47814i
$$285$$ 0 0
$$286$$ −12.6468 + 18.2167i −0.747821 + 1.07718i
$$287$$ 8.42701 0.497431
$$288$$ 0.606006 + 5.62430i 0.0357092 + 0.331415i
$$289$$ −12.4432 −0.731954
$$290$$ 0 0
$$291$$ 14.1887i 0.831755i
$$292$$ −0.482632 1.29362i −0.0282439 0.0757032i
$$293$$ 15.9792i 0.933513i −0.884386 0.466757i $$-0.845422\pi$$
0.884386 0.466757i $$-0.154578\pi$$
$$294$$ −7.48511 5.19648i −0.436540 0.303065i
$$295$$ 0 0
$$296$$ 0.751399 2.94568i 0.0436742 0.171214i
$$297$$ 5.36068 0.311058
$$298$$ 2.07884 + 1.44322i 0.120424 + 0.0836037i
$$299$$ 21.9253i 1.26797i
$$300$$ 0 0
$$301$$ 5.55394i 0.320124i
$$302$$ −8.58669 + 12.3684i −0.494108 + 0.711723i
$$303$$ 7.43952 0.427389
$$304$$ 4.54222 + 5.24002i 0.260514 + 0.300536i
$$305$$ 0 0
$$306$$ −1.72161 + 2.47984i −0.0984180 + 0.141763i
$$307$$ 22.5872i 1.28912i −0.764553 0.644561i $$-0.777040\pi$$
0.764553 0.644561i $$-0.222960\pi$$
$$308$$ 7.49534 2.79641i 0.427086 0.159341i
$$309$$ 7.19820i 0.409492i
$$310$$ 0 0
$$311$$ −18.5872 −1.05399 −0.526993 0.849870i $$-0.676680\pi$$
−0.526993 + 0.849870i $$0.676680\pi$$
$$312$$ 8.01699 + 2.04502i 0.453873 + 0.115776i
$$313$$ 29.3871 1.66106 0.830528 0.556977i $$-0.188039\pi$$
0.830528 + 0.556977i $$0.188039\pi$$
$$314$$ −8.04502 5.58520i −0.454007 0.315191i
$$315$$ 0 0
$$316$$ −1.85039 4.95968i −0.104093 0.279004i
$$317$$ 5.57201i 0.312955i −0.987682 0.156478i $$-0.949986\pi$$
0.987682 0.156478i $$-0.0500139\pi$$
$$318$$ 6.22751 8.97021i 0.349221 0.503025i
$$319$$ −36.1801 −2.02569
$$320$$ 0 0
$$321$$ −4.00000 −0.223258
$$322$$ −4.51064 + 6.49720i −0.251368 + 0.362075i
$$323$$ 3.70079i 0.205917i
$$324$$ −0.699104 1.87383i −0.0388391 0.104102i
$$325$$ 0 0
$$326$$ 8.94602 + 6.21071i 0.495474 + 0.343980i
$$327$$ 19.9504 1.10326
$$328$$ −30.9520 7.89541i −1.70904 0.435951i
$$329$$ 1.29362 0.0713194
$$330$$ 0 0
$$331$$ 13.7396i 0.755199i −0.925969 0.377599i $$-0.876750\pi$$
0.925969 0.377599i $$-0.123250\pi$$
$$332$$ 10.9627 4.09003i 0.601655 0.224470i
$$333$$ 1.07480i 0.0588989i
$$334$$ −2.60179 + 3.74767i −0.142364 + 0.205063i
$$335$$ 0 0
$$336$$ −1.95498 2.25532i −0.106653 0.123038i
$$337$$ −20.7523 −1.13045 −0.565226 0.824936i $$-0.691211\pi$$
−0.565226 + 0.824936i $$0.691211\pi$$
$$338$$ −3.58348 + 5.16170i −0.194915 + 0.280760i
$$339$$ 12.0540i 0.654685i
$$340$$ 0 0
$$341$$ 14.1887i 0.768360i
$$342$$ −2.01400 1.39821i −0.108905 0.0756064i
$$343$$ 10.0310 0.541623
$$344$$ 5.20359 20.3994i 0.280559 1.09986i
$$345$$ 0 0
$$346$$ −7.46742 5.18420i −0.401451 0.278704i
$$347$$ 4.73684i 0.254287i −0.991884 0.127143i $$-0.959419\pi$$
0.991884 0.127143i $$-0.0405809\pi$$
$$348$$ 4.71836 + 12.6468i 0.252931 + 0.677940i
$$349$$ 0.482632i 0.0258347i −0.999917 0.0129174i $$-0.995888\pi$$
0.999917 0.0129174i $$-0.00411184\pi$$
$$350$$ 0 0
$$351$$ −2.92520 −0.156135
$$352$$ −30.1500 + 3.24860i −1.60700 + 0.173151i
$$353$$ 2.13466 0.113617 0.0568083 0.998385i $$-0.481908\pi$$
0.0568083 + 0.998385i $$0.481908\pi$$
$$354$$ 5.52699 7.96117i 0.293756 0.423132i
$$355$$ 0 0
$$356$$ −5.30818 14.2277i −0.281333 0.754067i
$$357$$ 1.59283i 0.0843015i
$$358$$ 9.45352 + 6.56304i 0.499634 + 0.346868i
$$359$$ −9.59283 −0.506290 −0.253145 0.967428i $$-0.581465\pi$$
−0.253145 + 0.967428i $$0.581465\pi$$
$$360$$ 0 0
$$361$$ 15.9944 0.841811
$$362$$ −1.73367 1.20359i −0.0911194 0.0632590i
$$363$$ 17.7368i 0.930943i
$$364$$ −4.09003 + 1.52594i −0.214376 + 0.0799809i
$$365$$ 0 0
$$366$$ −5.20359 + 7.49534i −0.271996 + 0.391787i
$$367$$ −34.0832 −1.77913 −0.889565 0.456809i $$-0.848992\pi$$
−0.889565 + 0.456809i $$0.848992\pi$$
$$368$$ 22.6547 19.6378i 1.18096 1.02369i
$$369$$ 11.2936 0.587922
$$370$$ 0 0
$$371$$ 5.76167i 0.299131i
$$372$$ −4.95968 + 1.85039i −0.257147 + 0.0959384i
$$373$$ 4.33796i 0.224611i −0.993674 0.112306i $$-0.964176\pi$$
0.993674 0.112306i $$-0.0358236\pi$$
$$374$$ −13.2936 9.22900i −0.687397 0.477220i
$$375$$ 0 0
$$376$$ −4.75140 1.21201i −0.245035 0.0625047i
$$377$$ 19.7426 1.01680
$$378$$ 0.866833 + 0.601793i 0.0445851 + 0.0309529i
$$379$$ 6.90107i 0.354484i 0.984167 + 0.177242i $$0.0567176\pi$$
−0.984167 + 0.177242i $$0.943282\pi$$
$$380$$ 0 0
$$381$$ 4.21351i 0.215864i
$$382$$ −5.55394 + 8.00000i −0.284165 + 0.409316i
$$383$$ −22.3744 −1.14328 −0.571639 0.820506i $$-0.693692\pi$$
−0.571639 + 0.820506i $$0.693692\pi$$
$$384$$ 5.06752 + 10.1153i 0.258601 + 0.516197i
$$385$$ 0 0
$$386$$ −13.2936 + 19.1484i −0.676627 + 0.974626i
$$387$$ 7.44322i 0.378360i
$$388$$ −9.91936 26.5872i −0.503579 1.34976i
$$389$$ 11.0185i 0.558659i 0.960195 + 0.279330i $$0.0901122\pi$$
−0.960195 + 0.279330i $$0.909888\pi$$
$$390$$ 0 0
$$391$$ 16.0000 0.809155
$$392$$ −17.6587 4.50448i −0.891900 0.227511i
$$393$$ −10.3204 −0.520593
$$394$$ 15.7666 + 10.9459i 0.794311 + 0.551445i
$$395$$ 0 0
$$396$$ 10.0450 3.74767i 0.504781 0.188327i
$$397$$ 25.2549i 1.26751i 0.773536 + 0.633753i $$0.218486\pi$$
−0.773536 + 0.633753i $$0.781514\pi$$
$$398$$ −7.30207 + 10.5180i −0.366020 + 0.527221i
$$399$$ 1.29362 0.0647619
$$400$$ 0 0
$$401$$ 7.29362 0.364226 0.182113 0.983278i $$-0.441706\pi$$
0.182113 + 0.983278i $$0.441706\pi$$
$$402$$ 6.00299 8.64681i 0.299402 0.431264i
$$403$$ 7.74244i 0.385678i
$$404$$ 13.9404 5.20100i 0.693562 0.258759i
$$405$$ 0 0
$$406$$ −5.85039 4.06160i −0.290350 0.201574i
$$407$$ −5.76167 −0.285595
$$408$$ −1.49235 + 5.85039i −0.0738823 + 0.289638i
$$409$$ 15.8504 0.783752 0.391876 0.920018i $$-0.371826\pi$$
0.391876 + 0.920018i $$0.371826\pi$$
$$410$$ 0 0
$$411$$ 15.0387i 0.741805i
$$412$$ 5.03229 + 13.4882i 0.247923 + 0.664518i
$$413$$ 5.11355i 0.251622i
$$414$$ −6.04502 + 8.70735i −0.297096 + 0.427943i
$$415$$ 0 0
$$416$$ 16.4522 1.77269i 0.806635 0.0869131i
$$417$$ 9.47032 0.463763
$$418$$ 7.49534 10.7964i 0.366609 0.528070i
$$419$$ 8.02602i 0.392097i 0.980594 + 0.196048i $$0.0628109\pi$$
−0.980594 + 0.196048i $$0.937189\pi$$
$$420$$ 0 0
$$421$$ 22.9351i 1.11779i −0.829240 0.558893i $$-0.811226\pi$$
0.829240 0.558893i $$-0.188774\pi$$
$$422$$ 2.94568 + 2.04502i 0.143393 + 0.0995498i
$$423$$ 1.73367 0.0842937
$$424$$ 5.39821 21.1624i 0.262160 1.02774i
$$425$$ 0 0
$$426$$ 15.4432 + 10.7214i 0.748227 + 0.519451i
$$427$$ 4.81434i 0.232982i
$$428$$ −7.49534 + 2.79641i −0.362301 + 0.135170i
$$429$$ 15.6810i 0.757087i
$$430$$ 0 0
$$431$$ −35.0665 −1.68909 −0.844547 0.535481i $$-0.820130\pi$$
−0.844547 + 0.535481i $$0.820130\pi$$
$$432$$ −2.62001 3.02251i −0.126055 0.145420i
$$433$$ −17.0773 −0.820682 −0.410341 0.911932i $$-0.634590\pi$$
−0.410341 + 0.911932i $$0.634590\pi$$
$$434$$ 1.59283 2.29434i 0.0764583 0.110132i
$$435$$ 0 0
$$436$$ 37.3836 13.9474i 1.79035 0.667958i
$$437$$ 12.9944i 0.621607i
$$438$$ 0.801991 + 0.556777i 0.0383206 + 0.0266038i
$$439$$ 8.53885 0.407537 0.203769 0.979019i $$-0.434681\pi$$
0.203769 + 0.979019i $$0.434681\pi$$
$$440$$ 0 0
$$441$$ 6.44322 0.306820
$$442$$ 7.25402 + 5.03605i 0.345039 + 0.239541i
$$443$$ 20.7368i 0.985237i 0.870245 + 0.492619i $$0.163960\pi$$
−0.870245 + 0.492619i $$0.836040\pi$$
$$444$$ 0.751399 + 2.01400i 0.0356598 + 0.0955803i
$$445$$ 0 0
$$446$$ 9.80538 14.1238i 0.464298 0.668783i
$$447$$ −1.78948 −0.0846396
$$448$$ −5.24002 2.85936i −0.247568 0.135092i
$$449$$ −2.00000 −0.0943858 −0.0471929 0.998886i $$-0.515028\pi$$
−0.0471929 + 0.998886i $$0.515028\pi$$
$$450$$ 0 0
$$451$$ 60.5414i 2.85078i
$$452$$ 8.42701 + 22.5872i 0.396373 + 1.06241i
$$453$$ 10.6468i 0.500231i
$$454$$ −24.0900 16.7243i −1.13060 0.784912i
$$455$$ 0 0
$$456$$ −4.75140 1.21201i −0.222505 0.0567577i
$$457$$ −1.28462 −0.0600921 −0.0300461 0.999549i $$-0.509565\pi$$
−0.0300461 + 0.999549i $$0.509565\pi$$
$$458$$ 23.1764 + 16.0900i 1.08296 + 0.751838i
$$459$$ 2.13466i 0.0996374i
$$460$$ 0 0
$$461$$ 15.7033i 0.731374i −0.930738 0.365687i $$-0.880834\pi$$
0.930738 0.365687i $$-0.119166\pi$$
$$462$$ −3.22601 + 4.64681i −0.150088 + 0.216189i
$$463$$ −18.7215 −0.870064 −0.435032 0.900415i $$-0.643263\pi$$
−0.435032 + 0.900415i $$0.643263\pi$$
$$464$$ 17.6829 + 20.3994i 0.820906 + 0.947018i
$$465$$ 0 0
$$466$$ −10.7577 + 15.4955i −0.498339 + 0.717817i
$$467$$ 2.14961i 0.0994719i −0.998762 0.0497360i $$-0.984162\pi$$
0.998762 0.0497360i $$-0.0158380\pi$$
$$468$$ −5.48133 + 2.04502i −0.253375 + 0.0945309i
$$469$$ 5.55394i 0.256457i
$$470$$ 0 0
$$471$$ 6.92520 0.319096
$$472$$ 4.79097 18.7819i 0.220522 0.864505i
$$473$$ −39.9007 −1.83464
$$474$$ 3.07480 + 2.13466i 0.141230 + 0.0980482i
$$475$$ 0 0
$$476$$ −1.11355 2.98470i −0.0510396 0.136803i
$$477$$ 7.72161i 0.353548i
$$478$$ −18.4580 + 26.5872i −0.844249 + 1.21607i
$$479$$ −12.1801 −0.556521 −0.278261 0.960506i $$-0.589758\pi$$
−0.278261 + 0.960506i $$0.589758\pi$$
$$480$$ 0 0
$$481$$ 3.14401 0.143355
$$482$$ −2.89763 + 4.17380i −0.131983 + 0.190111i
$$483$$ 5.59283i 0.254483i
$$484$$ 12.3999 + 33.2359i 0.563631 + 1.51072i
$$485$$ 0 0
$$486$$ 1.16170 + 0.806504i 0.0526959 + 0.0365837i
$$487$$ −25.7678 −1.16765 −0.583826 0.811879i $$-0.698445\pi$$
−0.583826 + 0.811879i $$0.698445\pi$$
$$488$$ −4.51064 + 17.6829i −0.204187 + 0.800466i
$$489$$ −7.70079 −0.348242
$$490$$ 0 0
$$491$$ 16.7724i 0.756927i 0.925616 + 0.378464i $$0.123547\pi$$
−0.925616 + 0.378464i $$0.876453\pi$$
$$492$$ 21.1624 7.89541i 0.954073 0.355953i
$$493$$ 14.4072i 0.648866i
$$494$$ −4.09003 + 5.89135i −0.184019 + 0.265065i
$$495$$ 0 0
$$496$$ −8.00000 + 6.93466i −0.359211 + 0.311375i
$$497$$ −9.91936 −0.444944
$$498$$ −4.71836 + 6.79641i −0.211435 + 0.304555i
$$499$$ 17.6224i 0.788888i −0.918920 0.394444i $$-0.870937\pi$$
0.918920 0.394444i $$-0.129063\pi$$
$$500$$ 0 0
$$501$$ 3.22601i 0.144128i
$$502$$ −10.2555 7.11982i −0.457726 0.317773i
$$503$$ 27.1263 1.20950 0.604752 0.796414i $$-0.293272\pi$$
0.604752 + 0.796414i $$0.293272\pi$$
$$504$$ 2.04502 + 0.521653i 0.0910923 + 0.0232363i
$$505$$ 0 0
$$506$$ −46.6773 32.4054i −2.07506 1.44059i
$$507$$ 4.44322i 0.197330i
$$508$$ −2.94568 7.89541i −0.130693 0.350302i
$$509$$ 15.9782i 0.708220i 0.935204 + 0.354110i $$0.115216\pi$$
−0.935204 + 0.354110i $$0.884784\pi$$
$$510$$ 0 0
$$511$$ −0.515128 −0.0227879
$$512$$ 16.5674 + 15.4118i 0.732181 + 0.681110i
$$513$$ 1.73367 0.0765432
$$514$$ −17.9792 + 25.8975i −0.793027 + 1.14229i
$$515$$ 0 0
$$516$$ 5.20359 + 13.9474i 0.229075 + 0.613999i
$$517$$ 9.29362i 0.408733i
$$518$$ −0.931674 0.646809i −0.0409354 0.0284191i
$$519$$ 6.42799 0.282158
$$520$$ 0 0
$$521$$ 0.886447 0.0388359 0.0194180 0.999811i $$-0.493819\pi$$
0.0194180 + 0.999811i $$0.493819\pi$$
$$522$$ −7.84052 5.44322i −0.343170 0.238243i
$$523$$ 41.7729i 1.82660i −0.407286 0.913301i $$-0.633525\pi$$
0.407286 0.913301i $$-0.366475\pi$$
$$524$$ −19.3386 + 7.21500i −0.844812 + 0.315189i
$$525$$ 0 0
$$526$$ −17.0990 + 24.6297i −0.745552 + 1.07391i
$$527$$ −5.65004 −0.246120
$$528$$ 16.2027 14.0450i 0.705131 0.611231i
$$529$$ 33.1801 1.44261
$$530$$ 0 0
$$531$$ 6.85302i 0.297396i
$$532$$ 2.42402 0.904373i 0.105095 0.0392095i
$$533$$ 33.0361i 1.43095i
$$534$$ 8.82061 + 6.12364i 0.381705 + 0.264996i
$$535$$ 0 0
$$536$$ 5.20359 20.3994i 0.224761 0.881120i
$$537$$ −8.13765 −0.351165
$$538$$ 17.0695 + 11.8504i 0.735919 + 0.510907i
$$539$$ 34.5400i 1.48774i
$$540$$ 0 0
$$541$$ 4.47705i 0.192483i 0.995358 + 0.0962417i $$0.0306822\pi$$
−0.995358 + 0.0962417i $$0.969318\pi$$
$$542$$ 16.3233 23.5124i 0.701148 1.00995i
$$543$$ 1.49235 0.0640428
$$544$$ 1.29362 + 12.0060i 0.0554634 + 0.514752i
$$545$$ 0 0
$$546$$ 1.76036 2.53566i 0.0753365 0.108516i
$$547$$ 14.3297i 0.612692i −0.951920 0.306346i $$-0.900893\pi$$
0.951920 0.306346i $$-0.0991065\pi$$
$$548$$ 10.5136 + 28.1801i 0.449120 + 1.20379i
$$549$$ 6.45203i 0.275366i
$$550$$ 0 0
$$551$$ −11.7008 −0.498470
$$552$$ −5.24002 + 20.5422i −0.223030 + 0.874335i
$$553$$ −1.97498 −0.0839848
$$554$$ −0.601793 0.417790i −0.0255677 0.0177502i
$$555$$ 0 0
$$556$$ 17.7458 6.62073i 0.752590 0.280782i
$$557$$ 2.68556i 0.113791i 0.998380 + 0.0568954i $$0.0181201\pi$$
−0.998380 + 0.0568954i $$0.981880\pi$$
$$558$$ 2.13466 3.07480i 0.0903674 0.130167i
$$559$$ 21.7729 0.920895
$$560$$ 0 0
$$561$$ 11.4432 0.483133
$$562$$ −11.0497 + 15.9162i −0.466105 + 0.671386i
$$563$$ 20.7368i 0.873954i −0.899473 0.436977i $$-0.856049\pi$$
0.899473 0.436977i $$-0.143951\pi$$
$$564$$ 3.24860 1.21201i 0.136791 0.0510349i
$$565$$ 0 0
$$566$$ 20.9460 + 14.5416i 0.880427 + 0.611230i
$$567$$ −0.746175 −0.0313364
$$568$$ 36.4334 + 9.29362i 1.52871 + 0.389952i
$$569$$ 4.40717 0.184758 0.0923791 0.995724i $$-0.470553\pi$$
0.0923791 + 0.995724i $$0.470553\pi$$
$$570$$ 0 0
$$571$$ 23.6590i 0.990098i −0.868865 0.495049i $$-0.835150\pi$$
0.868865 0.495049i $$-0.164850\pi$$
$$572$$ −10.9627 29.3836i −0.458372 1.22859i
$$573$$ 6.88645i 0.287685i
$$574$$ −6.79641 + 9.78968i −0.283677 + 0.408613i
$$575$$ 0 0
$$576$$ −7.02251 3.83202i −0.292604 0.159668i
$$577$$ 6.56366 0.273249 0.136624 0.990623i $$-0.456375\pi$$
0.136624 + 0.990623i $$0.456375\pi$$
$$578$$ 10.0355 14.4553i 0.417422 0.601262i
$$579$$ 16.4830i 0.685011i
$$580$$ 0 0
$$581$$ 4.36542i 0.181108i
$$582$$ 16.4830 + 11.4432i 0.683243 + 0.474337i
$$583$$ −41.3931 −1.71433
$$584$$ 1.89204 + 0.482632i 0.0782933 + 0.0199715i
$$585$$ 0 0
$$586$$ 18.5630 + 12.8873i 0.766832 + 0.532368i
$$587$$ 16.2992i 0.672741i −0.941730 0.336370i $$-0.890801\pi$$
0.941730 0.336370i $$-0.109199\pi$$
$$588$$ 12.0735 4.50448i 0.497904 0.185762i
$$589$$ 4.58868i 0.189073i
$$590$$ 0 0
$$591$$ −13.5720 −0.558278
$$592$$ 2.81599 + 3.24860i 0.115737 + 0.133517i
$$593$$ 16.3233 0.670319 0.335160 0.942161i $$-0.391210\pi$$
0.335160 + 0.942161i $$0.391210\pi$$
$$594$$ −4.32340 + 6.22751i −0.177391 + 0.255518i
$$595$$ 0 0
$$596$$ −3.35319 + 1.25103i −0.137352 + 0.0512443i
$$597$$ 9.05398i 0.370555i
$$598$$ 25.4707 + 17.6829i 1.04157 + 0.723106i
$$599$$ −25.5928 −1.04569 −0.522847 0.852426i $$-0.675130\pi$$
−0.522847 + 0.852426i $$0.675130\pi$$
$$600$$ 0 0
$$601$$ 29.9225 1.22056 0.610282 0.792184i $$-0.291056\pi$$
0.610282 + 0.792184i $$0.291056\pi$$
$$602$$ −6.45203 4.47928i −0.262965 0.182562i
$$603$$ 7.44322i 0.303111i
$$604$$ −7.44322 19.9504i −0.302860 0.811768i
$$605$$ 0 0
$$606$$ −6.00000 + 8.64251i −0.243733 + 0.351078i
$$607$$ 20.6965 0.840046 0.420023 0.907513i $$-0.362022\pi$$
0.420023 + 0.907513i $$0.362022\pi$$
$$608$$ −9.75065 + 1.05061i −0.395441 + 0.0426079i
$$609$$ 5.03605 0.204071
$$610$$ 0 0
$$611$$ 5.07131i 0.205163i
$$612$$ −1.49235 4.00000i −0.0603246 0.161690i
$$613$$ 22.6676i 0.915537i −0.889071 0.457769i $$-0.848649\pi$$
0.889071 0.457769i $$-0.151351\pi$$
$$614$$ 26.2396 + 18.2167i 1.05895 + 0.735166i
$$615$$ 0 0
$$616$$ −2.79641 + 10.9627i −0.112671 + 0.441698i
$$617$$ −22.1966 −0.893603 −0.446802 0.894633i $$-0.647437\pi$$
−0.446802 + 0.894633i $$0.647437\pi$$
$$618$$ −8.36217 5.80538i −0.336376 0.233527i
$$619$$ 16.8204i 0.676070i 0.941133 + 0.338035i $$0.109762\pi$$
−0.941133 + 0.338035i $$0.890238\pi$$
$$620$$ 0 0
$$621$$ 7.49534i 0.300777i
$$622$$ 14.9907 21.5928i 0.601071 0.865794i
$$623$$ −5.66558 −0.226987
$$624$$ −8.84143 + 7.66404i −0.353940 + 0.306807i
$$625$$ 0 0
$$626$$ −23.7008 + 34.1390i −0.947274 + 1.36447i
$$627$$ 9.29362i 0.371151i
$$628$$ 12.9767 4.84143i 0.517825 0.193194i
$$629$$ 2.29434i 0.0914813i
$$630$$ 0 0
$$631$$ −44.1205 −1.75641 −0.878204 0.478285i $$-0.841258\pi$$
−0.878204 + 0.478285i $$0.841258\pi$$
$$632$$ 7.25402 + 1.85039i 0.288549 + 0.0736047i
$$633$$ −2.53566 −0.100783
$$634$$ 6.47301 + 4.49384i 0.257076 + 0.178473i
$$635$$ 0 0
$$636$$ 5.39821 + 14.4690i 0.214053 + 0.573734i
$$637$$ 18.8477i 0.746773i
$$638$$ 29.1794 42.0305i 1.15522 1.66400i
$$639$$ −13.2936 −0.525887
$$640$$ 0 0
$$641$$ −1.18566 −0.0468307 −0.0234154 0.999726i $$-0.507454\pi$$
−0.0234154 + 0.999726i $$0.507454\pi$$
$$642$$ 3.22601 4.64681i 0.127321 0.183395i
$$643$$ 22.5872i 0.890754i 0.895343 + 0.445377i $$0.146930\pi$$
−0.895343 + 0.445377i $$0.853070\pi$$
$$644$$ −3.90997 10.4800i −0.154074 0.412971i
$$645$$ 0 0
$$646$$ −4.29921 2.98470i −0.169150 0.117431i
$$647$$ 19.7090 0.774842 0.387421 0.921903i $$-0.373366\pi$$
0.387421 + 0.921903i $$0.373366\pi$$
$$648$$ 2.74067 + 0.699104i 0.107664 + 0.0274634i
$$649$$ −36.7368 −1.44205
$$650$$ 0 0
$$651$$ 1.97498i 0.0774056i
$$652$$ −14.4300 + 5.38365i −0.565122 + 0.210840i
$$653$$ 44.4585i 1.73979i 0.493234 + 0.869897i $$0.335815\pi$$
−0.493234 + 0.869897i $$0.664185\pi$$
$$654$$ −16.0900 + 23.1764i −0.629170 + 0.906268i
$$655$$ 0 0
$$656$$ 34.1350 29.5894i 1.33275 1.15527i
$$657$$ −0.690358 −0.0269334
$$658$$ −1.04331 + 1.50280i −0.0406723 + 0.0585852i
$$659$$ 41.5863i 1.61997i 0.586448 + 0.809987i $$0.300526\pi$$
−0.586448 + 0.809987i $$0.699474\pi$$
$$660$$ 0 0
$$661$$ 12.0060i 0.466978i 0.972359 + 0.233489i $$0.0750143\pi$$
−0.972359 + 0.233489i $$0.924986\pi$$
$$662$$ 15.9614 + 11.0811i 0.620356 + 0.430678i
$$663$$ −6.24430 −0.242509
$$664$$ −4.09003 + 16.0340i −0.158724 + 0.622239i
$$665$$ 0 0
$$666$$ −1.24860 0.866833i −0.0483823 0.0335891i
$$667$$ 50.5872i 1.95875i
$$668$$ −2.25532 6.04502i −0.0872609 0.233889i
$$669$$ 12.1579i 0.470051i
$$670$$ 0 0
$$671$$ 34.5872 1.33523
$$672$$ 4.19671 0.452186i 0.161892 0.0174435i
$$673$$ −14.5080 −0.559244 −0.279622 0.960110i $$-0.590209\pi$$
−0.279622 + 0.960110i $$0.590209\pi$$
$$674$$ 16.7368 24.1080i 0.644679 0.928607i
$$675$$ 0 0
$$676$$ −3.10627 8.32586i −0.119472 0.320226i
$$677$$ 43.8600i 1.68568i −0.538166 0.842839i $$-0.680883\pi$$
0.538166 0.842839i $$-0.319117\pi$$
$$678$$ −14.0032 9.72161i −0.537789 0.373356i
$$679$$ −10.5872 −0.406301
$$680$$ 0 0
$$681$$ 20.7368 0.794637
$$682$$ 16.4830 + 11.4432i 0.631168 + 0.438184i
$$683$$ 5.33527i 0.204148i −0.994777 0.102074i $$-0.967452\pi$$
0.994777 0.102074i $$-0.0325479\pi$$
$$684$$ 3.24860 1.21201i 0.124213 0.0463424i
$$685$$ 0 0
$$686$$ −8.09003 + 11.6530i −0.308879 + 0.444915i
$$687$$ −19.9504 −0.761153
$$688$$ 19.5013 + 22.4972i 0.743480 + 0.857698i
$$689$$ 22.5872 0.860505
$$690$$ 0 0
$$691$$ 39.7710i 1.51296i −0.654016 0.756480i $$-0.726917\pi$$
0.654016 0.756480i $$-0.273083\pi$$
$$692$$ 12.0450 4.49383i 0.457882 0.170830i
$$693$$ 4.00000i 0.151947i
$$694$$ 5.50280 + 3.82028i 0.208883 + 0.145016i
$$695$$ 0 0
$$696$$ −18.4972 4.71836i −0.701135 0.178849i
$$697$$ 24.1080 0.913157
$$698$$ 0.560675 + 0.389245i 0.0212219 + 0.0147331i
$$699$$ 13.3386i 0.504514i
$$700$$ 0 0
$$701$$ 27.5015i 1.03872i 0.854556 + 0.519359i $$0.173829\pi$$
−0.854556 + 0.519359i $$0.826171\pi$$
$$702$$ 2.35918 3.39821i 0.0890416 0.128257i
$$703$$ −1.86335 −0.0702775
$$704$$ 20.5422 37.6454i 0.774214 1.41881i
$$705$$ 0 0
$$706$$ −1.72161 + 2.47984i −0.0647937 + 0.0933300i
$$707$$ 5.55118i 0.208774i
$$708$$ 4.79097 + 12.8414i 0.180056 + 0.482611i
$$709$$ 0.111632i 0.00419244i −0.999998 0.00209622i $$-0.999333\pi$$
0.999998 0.00209622i $$-0.000667249\pi$$
$$710$$ 0 0
$$711$$ −2.64681 −0.0992631
$$712$$ 20.8094 + 5.30818i 0.779866 + 0.198932i
$$713$$ −19.8387 −0.742966
$$714$$ 1.85039 + 1.28462i 0.0692492 + 0.0480758i
$$715$$ 0 0
$$716$$ −15.2486 + 5.68906i −0.569867 + 0.212610i
$$717$$ 22.8864i 0.854710i
$$718$$ 7.73665 11.1440i 0.288729 0.415891i
$$719$$ 10.7064 0.399281 0.199640 0.979869i $$-0.436023\pi$$
0.199640 + 0.979869i $$0.436023\pi$$
$$720$$ 0 0
$$721$$ 5.37112 0.200031
$$722$$ −12.8995 + 18.5807i −0.480071 + 0.691503i
$$723$$ 3.59283i 0.133619i
$$724$$ 2.79641 1.04331i 0.103928 0.0387742i
$$725$$ 0 0
$$726$$ −20.6049 14.3048i −0.764721 0.530902i
$$727$$ 25.6562 0.951536 0.475768 0.879571i $$-0.342170\pi$$
0.475768 + 0.879571i $$0.342170\pi$$
$$728$$ 1.52594 5.98207i 0.0565551 0.221710i
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 15.8888i 0.587667i
$$732$$ −4.51064 12.0900i −0.166718 0.446860i
$$733$$ 30.3684i 1.12168i 0.827923 + 0.560842i $$0.189522\pi$$
−0.827923 + 0.560842i $$0.810478\pi$$
$$734$$ 27.4882 39.5945i 1.01461 1.46146i
$$735$$ 0 0
$$736$$ 4.54222 + 42.1560i 0.167428 + 1.55389i
$$737$$ −39.9007 −1.46976
$$738$$ −9.10834 + 13.1198i −0.335283 + 0.482947i
$$739$$ 20.1917i 0.742763i −0.928480 0.371381i $$-0.878884\pi$$
0.928480 0.371381i $$-0.121116\pi$$
$$740$$ 0 0
$$741$$ 5.07131i 0.186299i
$$742$$ −6.69335 4.64681i −0.245720 0.170590i
$$743$$ −46.3863 −1.70175 −0.850875 0.525369i $$-0.823927\pi$$
−0.850875 + 0.525369i $$0.823927\pi$$
$$744$$ 1.85039 7.25402i 0.0678387 0.265945i
$$745$$ 0 0
$$746$$ 5.03942 + 3.49858i 0.184506 + 0.128092i
$$747$$ 5.85039i 0.214055i
$$748$$ 21.4427 8.00000i 0.784023 0.292509i
$$749$$ 2.98470i 0.109059i
$$750$$ 0 0
$$751$$ −27.1261 −0.989845 −0.494922 0.868937i $$-0.664804\pi$$
−0.494922 + 0.868937i $$0.664804\pi$$
$$752$$ 5.24002 4.54222i 0.191084 0.165638i
$$753$$ 8.82801 0.321710
$$754$$ −15.9225 + 22.9351i −0.579863 + 0.835245i
$$755$$ 0 0
$$756$$ −1.39821 + 0.521653i −0.0508523 + 0.0189724i
$$757$$ 45.2549i 1.64482i −0.568898 0.822408i $$-0.692630\pi$$
0.568898 0.822408i $$-0.307370\pi$$
$$758$$ −8.01699 5.56574i −0.291190 0.202157i
$$759$$ 40.1801 1.45844
$$760$$ 0 0
$$761$$ 16.8864 0.612133 0.306067 0.952010i $$-0.400987\pi$$
0.306067 + 0.952010i $$0.400987\pi$$
$$762$$ 4.89484 + 3.39821i 0.177321 + 0.123104i
$$763$$ 14.8864i 0.538926i
$$764$$ −4.81434 12.9041i −0.174177 0.466852i
$$765$$ 0 0
$$766$$ 18.0450 25.9924i 0.651993 0.939142i
$$767$$ 20.0464 0.723835
$$768$$ −15.8380 2.27111i −0.571504 0.0819516i
$$769$$ 16.3297 0.588863 0.294431 0.955673i $$-0.404870\pi$$
0.294431 + 0.955673i $$0.404870\pi$$
$$770$$ 0 0
$$771$$ 22.2927i 0.802853i
$$772$$ −11.5233 30.8864i −0.414734 1.11163i
$$773$$ 41.3144i 1.48598i −0.669304 0.742989i $$-0.733408\pi$$
0.669304 0.742989i $$-0.266592\pi$$
$$774$$ −8.64681 6.00299i −0.310803 0.215773i
$$775$$ 0 0
$$776$$ 38.8864 + 9.91936i 1.39594 + 0.356084i
$$777$$ 0.801991 0.0287713
$$778$$ −12.8002 8.88645i −0.458909 0.318595i
$$779$$ 19.5794i 0.701503i
$$780$$ 0 0
$$781$$ 71.2628i 2.54998i
$$782$$ −12.9041 + 18.5872i −0.461448 + 0.664678i
$$783$$ 6.74916 0.241195
$$784$$ 19.4747 16.8813i 0.695525 0.602904i
$$785$$ 0 0
$$786$$ 8.32340 11.9892i 0.296886 0.427640i
$$787$$ 11.4849i 0.409391i