# Properties

 Label 450.2.h.b.91.1 Level $450$ Weight $2$ Character 450.91 Analytic conductor $3.593$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$450 = 2 \cdot 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 450.h (of order $$5$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.59326809096$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{10})$$ Defining polynomial: $$x^{4} - x^{3} + x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 150) Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

## Embedding invariants

 Embedding label 91.1 Root $$0.809017 - 0.587785i$$ of defining polynomial Character $$\chi$$ $$=$$ 450.91 Dual form 450.2.h.b.361.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.690983 + 2.12663i) q^{5} +2.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +O(q^{10})$$ $$q+(-0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.690983 + 2.12663i) q^{5} +2.00000 q^{7} +(0.309017 - 0.951057i) q^{8} +(1.80902 - 1.31433i) q^{10} +(-0.618034 - 0.449028i) q^{11} +(-1.50000 + 1.08981i) q^{13} +(-1.61803 - 1.17557i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-0.354102 + 1.08981i) q^{17} +(-2.23607 + 6.88191i) q^{19} -2.23607 q^{20} +(0.236068 + 0.726543i) q^{22} +(4.85410 + 3.52671i) q^{23} +(-4.04508 - 2.93893i) q^{25} +1.85410 q^{26} +(0.618034 + 1.90211i) q^{28} +(1.11803 + 3.44095i) q^{29} +(-3.00000 + 9.23305i) q^{31} +1.00000 q^{32} +(0.927051 - 0.673542i) q^{34} +(-1.38197 + 4.25325i) q^{35} +(7.16312 - 5.20431i) q^{37} +(5.85410 - 4.25325i) q^{38} +(1.80902 + 1.31433i) q^{40} +(4.11803 - 2.99193i) q^{41} +3.23607 q^{43} +(0.236068 - 0.726543i) q^{44} +(-1.85410 - 5.70634i) q^{46} +(-2.85410 - 8.78402i) q^{47} -3.00000 q^{49} +(1.54508 + 4.75528i) q^{50} +(-1.50000 - 1.08981i) q^{52} +(3.57295 + 10.9964i) q^{53} +(1.38197 - 1.00406i) q^{55} +(0.618034 - 1.90211i) q^{56} +(1.11803 - 3.44095i) q^{58} +(-7.23607 + 5.25731i) q^{59} +(1.73607 + 1.26133i) q^{61} +(7.85410 - 5.70634i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(-1.28115 - 3.94298i) q^{65} +(1.14590 - 3.52671i) q^{67} -1.14590 q^{68} +(3.61803 - 2.62866i) q^{70} +(-2.52786 - 7.77997i) q^{71} +(7.97214 + 5.79210i) q^{73} -8.85410 q^{74} -7.23607 q^{76} +(-1.23607 - 0.898056i) q^{77} +(-0.690983 - 2.12663i) q^{80} -5.09017 q^{82} +(-1.85410 + 5.70634i) q^{83} +(-2.07295 - 1.50609i) q^{85} +(-2.61803 - 1.90211i) q^{86} +(-0.618034 + 0.449028i) q^{88} +(2.92705 + 2.12663i) q^{89} +(-3.00000 + 2.17963i) q^{91} +(-1.85410 + 5.70634i) q^{92} +(-2.85410 + 8.78402i) q^{94} +(-13.0902 - 9.51057i) q^{95} +(-2.20820 - 6.79615i) q^{97} +(2.42705 + 1.76336i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - q^{2} - q^{4} - 5q^{5} + 8q^{7} - q^{8} + O(q^{10})$$ $$4q - q^{2} - q^{4} - 5q^{5} + 8q^{7} - q^{8} + 5q^{10} + 2q^{11} - 6q^{13} - 2q^{14} - q^{16} + 12q^{17} - 8q^{22} + 6q^{23} - 5q^{25} - 6q^{26} - 2q^{28} - 12q^{31} + 4q^{32} - 3q^{34} - 10q^{35} + 13q^{37} + 10q^{38} + 5q^{40} + 12q^{41} + 4q^{43} - 8q^{44} + 6q^{46} + 2q^{47} - 12q^{49} - 5q^{50} - 6q^{52} + 21q^{53} + 10q^{55} - 2q^{56} - 20q^{59} - 2q^{61} + 18q^{62} - q^{64} + 15q^{65} + 18q^{67} - 18q^{68} + 10q^{70} - 28q^{71} + 14q^{73} - 22q^{74} - 20q^{76} + 4q^{77} - 5q^{80} + 2q^{82} + 6q^{83} - 15q^{85} - 6q^{86} + 2q^{88} + 5q^{89} - 12q^{91} + 6q^{92} + 2q^{94} - 30q^{95} + 18q^{97} + 3q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.809017 0.587785i −0.572061 0.415627i
$$3$$ 0 0
$$4$$ 0.309017 + 0.951057i 0.154508 + 0.475528i
$$5$$ −0.690983 + 2.12663i −0.309017 + 0.951057i
$$6$$ 0 0
$$7$$ 2.00000 0.755929 0.377964 0.925820i $$-0.376624\pi$$
0.377964 + 0.925820i $$0.376624\pi$$
$$8$$ 0.309017 0.951057i 0.109254 0.336249i
$$9$$ 0 0
$$10$$ 1.80902 1.31433i 0.572061 0.415627i
$$11$$ −0.618034 0.449028i −0.186344 0.135387i 0.490702 0.871327i $$-0.336740\pi$$
−0.677046 + 0.735940i $$0.736740\pi$$
$$12$$ 0 0
$$13$$ −1.50000 + 1.08981i −0.416025 + 0.302260i −0.776037 0.630688i $$-0.782773\pi$$
0.360011 + 0.932948i $$0.382773\pi$$
$$14$$ −1.61803 1.17557i −0.432438 0.314184i
$$15$$ 0 0
$$16$$ −0.809017 + 0.587785i −0.202254 + 0.146946i
$$17$$ −0.354102 + 1.08981i −0.0858823 + 0.264319i −0.984770 0.173860i $$-0.944376\pi$$
0.898888 + 0.438178i $$0.144376\pi$$
$$18$$ 0 0
$$19$$ −2.23607 + 6.88191i −0.512989 + 1.57882i 0.273922 + 0.961752i $$0.411679\pi$$
−0.786911 + 0.617066i $$0.788321\pi$$
$$20$$ −2.23607 −0.500000
$$21$$ 0 0
$$22$$ 0.236068 + 0.726543i 0.0503299 + 0.154899i
$$23$$ 4.85410 + 3.52671i 1.01215 + 0.735370i 0.964659 0.263501i $$-0.0848774\pi$$
0.0474912 + 0.998872i $$0.484877\pi$$
$$24$$ 0 0
$$25$$ −4.04508 2.93893i −0.809017 0.587785i
$$26$$ 1.85410 0.363619
$$27$$ 0 0
$$28$$ 0.618034 + 1.90211i 0.116797 + 0.359466i
$$29$$ 1.11803 + 3.44095i 0.207614 + 0.638969i 0.999596 + 0.0284251i $$0.00904922\pi$$
−0.791982 + 0.610544i $$0.790951\pi$$
$$30$$ 0 0
$$31$$ −3.00000 + 9.23305i −0.538816 + 1.65830i 0.196440 + 0.980516i $$0.437062\pi$$
−0.735256 + 0.677789i $$0.762938\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 0.927051 0.673542i 0.158988 0.115511i
$$35$$ −1.38197 + 4.25325i −0.233595 + 0.718931i
$$36$$ 0 0
$$37$$ 7.16312 5.20431i 1.17761 0.855583i 0.185710 0.982605i $$-0.440542\pi$$
0.991900 + 0.127021i $$0.0405417\pi$$
$$38$$ 5.85410 4.25325i 0.949661 0.689969i
$$39$$ 0 0
$$40$$ 1.80902 + 1.31433i 0.286031 + 0.207813i
$$41$$ 4.11803 2.99193i 0.643129 0.467260i −0.217795 0.975995i $$-0.569886\pi$$
0.860924 + 0.508734i $$0.169886\pi$$
$$42$$ 0 0
$$43$$ 3.23607 0.493496 0.246748 0.969080i $$-0.420638\pi$$
0.246748 + 0.969080i $$0.420638\pi$$
$$44$$ 0.236068 0.726543i 0.0355886 0.109530i
$$45$$ 0 0
$$46$$ −1.85410 5.70634i −0.273372 0.841354i
$$47$$ −2.85410 8.78402i −0.416314 1.28128i −0.911071 0.412250i $$-0.864743\pi$$
0.494757 0.869031i $$-0.335257\pi$$
$$48$$ 0 0
$$49$$ −3.00000 −0.428571
$$50$$ 1.54508 + 4.75528i 0.218508 + 0.672499i
$$51$$ 0 0
$$52$$ −1.50000 1.08981i −0.208013 0.151130i
$$53$$ 3.57295 + 10.9964i 0.490782 + 1.51047i 0.823428 + 0.567421i $$0.192059\pi$$
−0.332646 + 0.943052i $$0.607941\pi$$
$$54$$ 0 0
$$55$$ 1.38197 1.00406i 0.186344 0.135387i
$$56$$ 0.618034 1.90211i 0.0825883 0.254181i
$$57$$ 0 0
$$58$$ 1.11803 3.44095i 0.146805 0.451820i
$$59$$ −7.23607 + 5.25731i −0.942056 + 0.684444i −0.948915 0.315533i $$-0.897817\pi$$
0.00685884 + 0.999976i $$0.497817\pi$$
$$60$$ 0 0
$$61$$ 1.73607 + 1.26133i 0.222281 + 0.161496i 0.693353 0.720598i $$-0.256133\pi$$
−0.471072 + 0.882095i $$0.656133\pi$$
$$62$$ 7.85410 5.70634i 0.997472 0.724706i
$$63$$ 0 0
$$64$$ −0.809017 0.587785i −0.101127 0.0734732i
$$65$$ −1.28115 3.94298i −0.158907 0.489067i
$$66$$ 0 0
$$67$$ 1.14590 3.52671i 0.139994 0.430856i −0.856340 0.516413i $$-0.827267\pi$$
0.996333 + 0.0855568i $$0.0272669\pi$$
$$68$$ −1.14590 −0.138961
$$69$$ 0 0
$$70$$ 3.61803 2.62866i 0.432438 0.314184i
$$71$$ −2.52786 7.77997i −0.300002 0.923312i −0.981495 0.191487i $$-0.938669\pi$$
0.681493 0.731825i $$-0.261331\pi$$
$$72$$ 0 0
$$73$$ 7.97214 + 5.79210i 0.933068 + 0.677914i 0.946742 0.321993i $$-0.104353\pi$$
−0.0136741 + 0.999907i $$0.504353\pi$$
$$74$$ −8.85410 −1.02927
$$75$$ 0 0
$$76$$ −7.23607 −0.830034
$$77$$ −1.23607 0.898056i −0.140863 0.102343i
$$78$$ 0 0
$$79$$ 0 0 0.951057 0.309017i $$-0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$80$$ −0.690983 2.12663i −0.0772542 0.237764i
$$81$$ 0 0
$$82$$ −5.09017 −0.562115
$$83$$ −1.85410 + 5.70634i −0.203514 + 0.626352i 0.796257 + 0.604959i $$0.206810\pi$$
−0.999771 + 0.0213936i $$0.993190\pi$$
$$84$$ 0 0
$$85$$ −2.07295 1.50609i −0.224843 0.163358i
$$86$$ −2.61803 1.90211i −0.282310 0.205110i
$$87$$ 0 0
$$88$$ −0.618034 + 0.449028i −0.0658826 + 0.0478665i
$$89$$ 2.92705 + 2.12663i 0.310267 + 0.225422i 0.732011 0.681293i $$-0.238582\pi$$
−0.421744 + 0.906715i $$0.638582\pi$$
$$90$$ 0 0
$$91$$ −3.00000 + 2.17963i −0.314485 + 0.228487i
$$92$$ −1.85410 + 5.70634i −0.193303 + 0.594927i
$$93$$ 0 0
$$94$$ −2.85410 + 8.78402i −0.294378 + 0.906003i
$$95$$ −13.0902 9.51057i −1.34302 0.975763i
$$96$$ 0 0
$$97$$ −2.20820 6.79615i −0.224209 0.690045i −0.998371 0.0570570i $$-0.981828\pi$$
0.774162 0.632988i $$-0.218172\pi$$
$$98$$ 2.42705 + 1.76336i 0.245169 + 0.178126i
$$99$$ 0 0
$$100$$ 1.54508 4.75528i 0.154508 0.475528i
$$101$$ −17.3262 −1.72403 −0.862013 0.506887i $$-0.830796\pi$$
−0.862013 + 0.506887i $$0.830796\pi$$
$$102$$ 0 0
$$103$$ −4.85410 14.9394i −0.478289 1.47202i −0.841470 0.540303i $$-0.818309\pi$$
0.363181 0.931718i $$-0.381691\pi$$
$$104$$ 0.572949 + 1.76336i 0.0561823 + 0.172911i
$$105$$ 0 0
$$106$$ 3.57295 10.9964i 0.347035 1.06807i
$$107$$ 6.94427 0.671328 0.335664 0.941982i $$-0.391039\pi$$
0.335664 + 0.941982i $$0.391039\pi$$
$$108$$ 0 0
$$109$$ 14.2082 10.3229i 1.36090 0.988751i 0.362512 0.931979i $$-0.381919\pi$$
0.998387 0.0567720i $$-0.0180808\pi$$
$$110$$ −1.70820 −0.162871
$$111$$ 0 0
$$112$$ −1.61803 + 1.17557i −0.152890 + 0.111081i
$$113$$ 6.92705 5.03280i 0.651642 0.473446i −0.212188 0.977229i $$-0.568059\pi$$
0.863830 + 0.503783i $$0.168059\pi$$
$$114$$ 0 0
$$115$$ −10.8541 + 7.88597i −1.01215 + 0.735370i
$$116$$ −2.92705 + 2.12663i −0.271770 + 0.197452i
$$117$$ 0 0
$$118$$ 8.94427 0.823387
$$119$$ −0.708204 + 2.17963i −0.0649209 + 0.199806i
$$120$$ 0 0
$$121$$ −3.21885 9.90659i −0.292622 0.900599i
$$122$$ −0.663119 2.04087i −0.0600360 0.184772i
$$123$$ 0 0
$$124$$ −9.70820 −0.871822
$$125$$ 9.04508 6.57164i 0.809017 0.587785i
$$126$$ 0 0
$$127$$ −11.0902 8.05748i −0.984093 0.714986i −0.0254737 0.999675i $$-0.508109\pi$$
−0.958620 + 0.284690i $$0.908109\pi$$
$$128$$ 0.309017 + 0.951057i 0.0273135 + 0.0840623i
$$129$$ 0 0
$$130$$ −1.28115 + 3.94298i −0.112365 + 0.345823i
$$131$$ 1.61803 4.97980i 0.141368 0.435087i −0.855158 0.518368i $$-0.826540\pi$$
0.996526 + 0.0832809i $$0.0265399\pi$$
$$132$$ 0 0
$$133$$ −4.47214 + 13.7638i −0.387783 + 1.19347i
$$134$$ −3.00000 + 2.17963i −0.259161 + 0.188291i
$$135$$ 0 0
$$136$$ 0.927051 + 0.673542i 0.0794940 + 0.0577557i
$$137$$ 11.3541 8.24924i 0.970046 0.704780i 0.0145842 0.999894i $$-0.495358\pi$$
0.955462 + 0.295114i $$0.0953575\pi$$
$$138$$ 0 0
$$139$$ −10.8541 7.88597i −0.920633 0.668879i 0.0230486 0.999734i $$-0.492663\pi$$
−0.943681 + 0.330855i $$0.892663\pi$$
$$140$$ −4.47214 −0.377964
$$141$$ 0 0
$$142$$ −2.52786 + 7.77997i −0.212134 + 0.652880i
$$143$$ 1.41641 0.118446
$$144$$ 0 0
$$145$$ −8.09017 −0.671852
$$146$$ −3.04508 9.37181i −0.252013 0.775616i
$$147$$ 0 0
$$148$$ 7.16312 + 5.20431i 0.588805 + 0.427792i
$$149$$ 22.0344 1.80513 0.902566 0.430552i $$-0.141681\pi$$
0.902566 + 0.430552i $$0.141681\pi$$
$$150$$ 0 0
$$151$$ 10.9443 0.890632 0.445316 0.895373i $$-0.353091\pi$$
0.445316 + 0.895373i $$0.353091\pi$$
$$152$$ 5.85410 + 4.25325i 0.474830 + 0.344984i
$$153$$ 0 0
$$154$$ 0.472136 + 1.45309i 0.0380458 + 0.117093i
$$155$$ −17.5623 12.7598i −1.41064 1.02489i
$$156$$ 0 0
$$157$$ 11.1459 0.889540 0.444770 0.895645i $$-0.353286\pi$$
0.444770 + 0.895645i $$0.353286\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ −0.690983 + 2.12663i −0.0546270 + 0.168125i
$$161$$ 9.70820 + 7.05342i 0.765114 + 0.555888i
$$162$$ 0 0
$$163$$ −9.32624 + 6.77591i −0.730487 + 0.530730i −0.889718 0.456511i $$-0.849099\pi$$
0.159230 + 0.987241i $$0.449099\pi$$
$$164$$ 4.11803 + 2.99193i 0.321564 + 0.233630i
$$165$$ 0 0
$$166$$ 4.85410 3.52671i 0.376751 0.273726i
$$167$$ 0.763932 2.35114i 0.0591148 0.181937i −0.917139 0.398569i $$-0.869507\pi$$
0.976253 + 0.216632i $$0.0695071\pi$$
$$168$$ 0 0
$$169$$ −2.95492 + 9.09429i −0.227301 + 0.699561i
$$170$$ 0.791796 + 2.43690i 0.0607280 + 0.186902i
$$171$$ 0 0
$$172$$ 1.00000 + 3.07768i 0.0762493 + 0.234671i
$$173$$ −17.8713 12.9843i −1.35873 0.987176i −0.998524 0.0543039i $$-0.982706\pi$$
−0.360207 0.932872i $$-0.617294\pi$$
$$174$$ 0 0
$$175$$ −8.09017 5.87785i −0.611559 0.444324i
$$176$$ 0.763932 0.0575835
$$177$$ 0 0
$$178$$ −1.11803 3.44095i −0.0838002 0.257910i
$$179$$ 8.09017 + 24.8990i 0.604688 + 1.86104i 0.498923 + 0.866646i $$0.333729\pi$$
0.105764 + 0.994391i $$0.466271\pi$$
$$180$$ 0 0
$$181$$ 2.79180 8.59226i 0.207513 0.638658i −0.792088 0.610407i $$-0.791006\pi$$
0.999601 0.0282515i $$-0.00899392\pi$$
$$182$$ 3.70820 0.274870
$$183$$ 0 0
$$184$$ 4.85410 3.52671i 0.357849 0.259993i
$$185$$ 6.11803 + 18.8294i 0.449807 + 1.38436i
$$186$$ 0 0
$$187$$ 0.708204 0.514540i 0.0517890 0.0376269i
$$188$$ 7.47214 5.42882i 0.544962 0.395938i
$$189$$ 0 0
$$190$$ 5.00000 + 15.3884i 0.362738 + 1.11639i
$$191$$ −4.23607 + 3.07768i −0.306511 + 0.222693i −0.730398 0.683022i $$-0.760665\pi$$
0.423887 + 0.905715i $$0.360665\pi$$
$$192$$ 0 0
$$193$$ 4.61803 0.332413 0.166207 0.986091i $$-0.446848\pi$$
0.166207 + 0.986091i $$0.446848\pi$$
$$194$$ −2.20820 + 6.79615i −0.158540 + 0.487935i
$$195$$ 0 0
$$196$$ −0.927051 2.85317i −0.0662179 0.203798i
$$197$$ −0.718847 2.21238i −0.0512157 0.157626i 0.922177 0.386767i $$-0.126408\pi$$
−0.973393 + 0.229141i $$0.926408\pi$$
$$198$$ 0 0
$$199$$ 16.1803 1.14699 0.573497 0.819208i $$-0.305586\pi$$
0.573497 + 0.819208i $$0.305586\pi$$
$$200$$ −4.04508 + 2.93893i −0.286031 + 0.207813i
$$201$$ 0 0
$$202$$ 14.0172 + 10.1841i 0.986248 + 0.716551i
$$203$$ 2.23607 + 6.88191i 0.156941 + 0.483015i
$$204$$ 0 0
$$205$$ 3.51722 + 10.8249i 0.245653 + 0.756043i
$$206$$ −4.85410 + 14.9394i −0.338201 + 1.04088i
$$207$$ 0 0
$$208$$ 0.572949 1.76336i 0.0397269 0.122267i
$$209$$ 4.47214 3.24920i 0.309344 0.224752i
$$210$$ 0 0
$$211$$ 6.47214 + 4.70228i 0.445560 + 0.323718i 0.787840 0.615880i $$-0.211199\pi$$
−0.342280 + 0.939598i $$0.611199\pi$$
$$212$$ −9.35410 + 6.79615i −0.642442 + 0.466762i
$$213$$ 0 0
$$214$$ −5.61803 4.08174i −0.384041 0.279022i
$$215$$ −2.23607 + 6.88191i −0.152499 + 0.469342i
$$216$$ 0 0
$$217$$ −6.00000 + 18.4661i −0.407307 + 1.25356i
$$218$$ −17.5623 −1.18947
$$219$$ 0 0
$$220$$ 1.38197 + 1.00406i 0.0931721 + 0.0676935i
$$221$$ −0.656541 2.02063i −0.0441637 0.135922i
$$222$$ 0 0
$$223$$ 12.7082 + 9.23305i 0.851004 + 0.618291i 0.925423 0.378936i $$-0.123710\pi$$
−0.0744185 + 0.997227i $$0.523710\pi$$
$$224$$ 2.00000 0.133631
$$225$$ 0 0
$$226$$ −8.56231 −0.569556
$$227$$ 0.763932 + 0.555029i 0.0507039 + 0.0368386i 0.612849 0.790200i $$-0.290024\pi$$
−0.562145 + 0.827039i $$0.690024\pi$$
$$228$$ 0 0
$$229$$ 2.86475 + 8.81678i 0.189308 + 0.582629i 0.999996 0.00284891i $$-0.000906837\pi$$
−0.810688 + 0.585478i $$0.800907\pi$$
$$230$$ 13.4164 0.884652
$$231$$ 0 0
$$232$$ 3.61803 0.237536
$$233$$ 3.37132 10.3759i 0.220863 0.679746i −0.777823 0.628484i $$-0.783676\pi$$
0.998685 0.0512616i $$-0.0163242\pi$$
$$234$$ 0 0
$$235$$ 20.6525 1.34722
$$236$$ −7.23607 5.25731i −0.471028 0.342222i
$$237$$ 0 0
$$238$$ 1.85410 1.34708i 0.120184 0.0873185i
$$239$$ −21.7082 15.7719i −1.40419 1.02020i −0.994136 0.108139i $$-0.965511\pi$$
−0.410051 0.912063i $$-0.634489\pi$$
$$240$$ 0 0
$$241$$ 5.78115 4.20025i 0.372397 0.270562i −0.385807 0.922579i $$-0.626077\pi$$
0.758204 + 0.652017i $$0.226077\pi$$
$$242$$ −3.21885 + 9.90659i −0.206915 + 0.636820i
$$243$$ 0 0
$$244$$ −0.663119 + 2.04087i −0.0424518 + 0.130653i
$$245$$ 2.07295 6.37988i 0.132436 0.407596i
$$246$$ 0 0
$$247$$ −4.14590 12.7598i −0.263797 0.811884i
$$248$$ 7.85410 + 5.70634i 0.498736 + 0.362353i
$$249$$ 0 0
$$250$$ −11.1803 −0.707107
$$251$$ 3.52786 0.222677 0.111338 0.993783i $$-0.464486\pi$$
0.111338 + 0.993783i $$0.464486\pi$$
$$252$$ 0 0
$$253$$ −1.41641 4.35926i −0.0890488 0.274064i
$$254$$ 4.23607 + 13.0373i 0.265795 + 0.818031i
$$255$$ 0 0
$$256$$ 0.309017 0.951057i 0.0193136 0.0594410i
$$257$$ 9.38197 0.585231 0.292615 0.956230i $$-0.405474\pi$$
0.292615 + 0.956230i $$0.405474\pi$$
$$258$$ 0 0
$$259$$ 14.3262 10.4086i 0.890189 0.646760i
$$260$$ 3.35410 2.43690i 0.208013 0.151130i
$$261$$ 0 0
$$262$$ −4.23607 + 3.07768i −0.261705 + 0.190140i
$$263$$ −6.85410 + 4.97980i −0.422642 + 0.307067i −0.778700 0.627396i $$-0.784121\pi$$
0.356058 + 0.934464i $$0.384121\pi$$
$$264$$ 0 0
$$265$$ −25.8541 −1.58820
$$266$$ 11.7082 8.50651i 0.717876 0.521567i
$$267$$ 0 0
$$268$$ 3.70820 0.226515
$$269$$ 4.04508 12.4495i 0.246633 0.759059i −0.748730 0.662875i $$-0.769336\pi$$
0.995364 0.0961842i $$-0.0306638\pi$$
$$270$$ 0 0
$$271$$ 1.79837 + 5.53483i 0.109243 + 0.336217i 0.990703 0.136043i $$-0.0434385\pi$$
−0.881460 + 0.472260i $$0.843438\pi$$
$$272$$ −0.354102 1.08981i −0.0214706 0.0660797i
$$273$$ 0 0
$$274$$ −14.0344 −0.847852
$$275$$ 1.18034 + 3.63271i 0.0711772 + 0.219061i
$$276$$ 0 0
$$277$$ 23.3435 + 16.9600i 1.40257 + 1.01903i 0.994351 + 0.106146i $$0.0338510\pi$$
0.408222 + 0.912883i $$0.366149\pi$$
$$278$$ 4.14590 + 12.7598i 0.248654 + 0.765280i
$$279$$ 0 0
$$280$$ 3.61803 + 2.62866i 0.216219 + 0.157092i
$$281$$ −1.57295 + 4.84104i −0.0938343 + 0.288792i −0.986948 0.161038i $$-0.948516\pi$$
0.893114 + 0.449831i $$0.148516\pi$$
$$282$$ 0 0
$$283$$ −0.381966 + 1.17557i −0.0227055 + 0.0698804i −0.961767 0.273868i $$-0.911697\pi$$
0.939062 + 0.343749i $$0.111697\pi$$
$$284$$ 6.61803 4.80828i 0.392708 0.285319i
$$285$$ 0 0
$$286$$ −1.14590 0.832544i −0.0677584 0.0492293i
$$287$$ 8.23607 5.98385i 0.486160 0.353216i
$$288$$ 0 0
$$289$$ 12.6910 + 9.22054i 0.746528 + 0.542385i
$$290$$ 6.54508 + 4.75528i 0.384341 + 0.279240i
$$291$$ 0 0
$$292$$ −3.04508 + 9.37181i −0.178200 + 0.548444i
$$293$$ 4.20163 0.245462 0.122731 0.992440i $$-0.460835\pi$$
0.122731 + 0.992440i $$0.460835\pi$$
$$294$$ 0 0
$$295$$ −6.18034 19.0211i −0.359833 1.10745i
$$296$$ −2.73607 8.42075i −0.159031 0.489446i
$$297$$ 0 0
$$298$$ −17.8262 12.9515i −1.03265 0.750261i
$$299$$ −11.1246 −0.643353
$$300$$ 0 0
$$301$$ 6.47214 0.373048
$$302$$ −8.85410 6.43288i −0.509496 0.370171i
$$303$$ 0 0
$$304$$ −2.23607 6.88191i −0.128247 0.394705i
$$305$$ −3.88197 + 2.82041i −0.222281 + 0.161496i
$$306$$ 0 0
$$307$$ −29.7082 −1.69554 −0.847768 0.530367i $$-0.822054\pi$$
−0.847768 + 0.530367i $$0.822054\pi$$
$$308$$ 0.472136 1.45309i 0.0269024 0.0827972i
$$309$$ 0 0
$$310$$ 6.70820 + 20.6457i 0.381000 + 1.17260i
$$311$$ 10.2361 + 7.43694i 0.580434 + 0.421710i 0.838881 0.544315i $$-0.183211\pi$$
−0.258446 + 0.966026i $$0.583211\pi$$
$$312$$ 0 0
$$313$$ −14.8541 + 10.7921i −0.839603 + 0.610008i −0.922260 0.386570i $$-0.873660\pi$$
0.0826564 + 0.996578i $$0.473660\pi$$
$$314$$ −9.01722 6.55139i −0.508871 0.369717i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −3.38197 + 10.4086i −0.189950 + 0.584606i −0.999998 0.00175672i $$-0.999441\pi$$
0.810048 + 0.586363i $$0.199441\pi$$
$$318$$ 0 0
$$319$$ 0.854102 2.62866i 0.0478205 0.147176i
$$320$$ 1.80902 1.31433i 0.101127 0.0734732i
$$321$$ 0 0
$$322$$ −3.70820 11.4127i −0.206650 0.636004i
$$323$$ −6.70820 4.87380i −0.373254 0.271185i
$$324$$ 0 0
$$325$$ 9.27051 0.514235
$$326$$ 11.5279 0.638469
$$327$$ 0 0
$$328$$ −1.57295 4.84104i −0.0868516 0.267302i
$$329$$ −5.70820 17.5680i −0.314703 0.968558i
$$330$$ 0 0
$$331$$ −7.27051 + 22.3763i −0.399623 + 1.22991i 0.525679 + 0.850683i $$0.323811\pi$$
−0.925302 + 0.379231i $$0.876189\pi$$
$$332$$ −6.00000 −0.329293
$$333$$ 0 0
$$334$$ −2.00000 + 1.45309i −0.109435 + 0.0795093i
$$335$$ 6.70820 + 4.87380i 0.366508 + 0.266284i
$$336$$ 0 0
$$337$$ 20.0902 14.5964i 1.09438 0.795115i 0.114248 0.993452i $$-0.463554\pi$$
0.980134 + 0.198338i $$0.0635543\pi$$
$$338$$ 7.73607 5.62058i 0.420787 0.305719i
$$339$$ 0 0
$$340$$ 0.791796 2.43690i 0.0429412 0.132159i
$$341$$ 6.00000 4.35926i 0.324918 0.236067i
$$342$$ 0 0
$$343$$ −20.0000 −1.07990
$$344$$ 1.00000 3.07768i 0.0539164 0.165938i
$$345$$ 0 0
$$346$$ 6.82624 + 21.0090i 0.366981 + 1.12945i
$$347$$ 0.236068 + 0.726543i 0.0126728 + 0.0390028i 0.957193 0.289451i $$-0.0934726\pi$$
−0.944520 + 0.328453i $$0.893473\pi$$
$$348$$ 0 0
$$349$$ −9.79837 −0.524495 −0.262247 0.965001i $$-0.584464\pi$$
−0.262247 + 0.965001i $$0.584464\pi$$
$$350$$ 3.09017 + 9.51057i 0.165177 + 0.508361i
$$351$$ 0 0
$$352$$ −0.618034 0.449028i −0.0329413 0.0239333i
$$353$$ −3.56231 10.9637i −0.189602 0.583536i 0.810395 0.585884i $$-0.199253\pi$$
−0.999997 + 0.00234791i $$0.999253\pi$$
$$354$$ 0 0
$$355$$ 18.2918 0.970828
$$356$$ −1.11803 + 3.44095i −0.0592557 + 0.182370i
$$357$$ 0 0
$$358$$ 8.09017 24.8990i 0.427579 1.31595i
$$359$$ 6.38197 4.63677i 0.336827 0.244719i −0.406495 0.913653i $$-0.633249\pi$$
0.743322 + 0.668934i $$0.233249\pi$$
$$360$$ 0 0
$$361$$ −26.9894 19.6089i −1.42049 1.03205i
$$362$$ −7.30902 + 5.31031i −0.384153 + 0.279104i
$$363$$ 0 0
$$364$$ −3.00000 2.17963i −0.157243 0.114244i
$$365$$ −17.8262 + 12.9515i −0.933068 + 0.677914i
$$366$$ 0 0
$$367$$ −1.09017 + 3.35520i −0.0569064 + 0.175140i −0.975470 0.220134i $$-0.929350\pi$$
0.918563 + 0.395274i $$0.129350\pi$$
$$368$$ −6.00000 −0.312772
$$369$$ 0 0
$$370$$ 6.11803 18.8294i 0.318061 0.978892i
$$371$$ 7.14590 + 21.9928i 0.370997 + 1.14181i
$$372$$ 0 0
$$373$$ −23.7984 17.2905i −1.23223 0.895270i −0.235178 0.971952i $$-0.575567\pi$$
−0.997056 + 0.0766827i $$0.975567\pi$$
$$374$$ −0.875388 −0.0452652
$$375$$ 0 0
$$376$$ −9.23607 −0.476314
$$377$$ −5.42705 3.94298i −0.279507 0.203074i
$$378$$ 0 0
$$379$$ 7.23607 + 22.2703i 0.371692 + 1.14395i 0.945684 + 0.325089i $$0.105394\pi$$
−0.573992 + 0.818861i $$0.694606\pi$$
$$380$$ 5.00000 15.3884i 0.256495 0.789409i
$$381$$ 0 0
$$382$$ 5.23607 0.267901
$$383$$ −3.56231 + 10.9637i −0.182025 + 0.560216i −0.999884 0.0152022i $$-0.995161\pi$$
0.817859 + 0.575419i $$0.195161\pi$$
$$384$$ 0 0
$$385$$ 2.76393 2.00811i 0.140863 0.102343i
$$386$$ −3.73607 2.71441i −0.190161 0.138160i
$$387$$ 0 0
$$388$$ 5.78115 4.20025i 0.293494 0.213236i
$$389$$ −25.0623 18.2088i −1.27071 0.923224i −0.271479 0.962444i $$-0.587513\pi$$
−0.999231 + 0.0392200i $$0.987513\pi$$
$$390$$ 0 0
$$391$$ −5.56231 + 4.04125i −0.281298 + 0.204375i
$$392$$ −0.927051 + 2.85317i −0.0468231 + 0.144107i
$$393$$ 0 0
$$394$$ −0.718847 + 2.21238i −0.0362150 + 0.111458i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −7.67376 23.6174i −0.385135 1.18532i −0.936382 0.350982i $$-0.885848\pi$$
0.551247 0.834342i $$-0.314152\pi$$
$$398$$ −13.0902 9.51057i −0.656151 0.476722i
$$399$$ 0 0
$$400$$ 5.00000 0.250000
$$401$$ 14.9098 0.744561 0.372281 0.928120i $$-0.378576\pi$$
0.372281 + 0.928120i $$0.378576\pi$$
$$402$$ 0 0
$$403$$ −5.56231 17.1190i −0.277078 0.852759i
$$404$$ −5.35410 16.4782i −0.266377 0.819823i
$$405$$ 0 0
$$406$$ 2.23607 6.88191i 0.110974 0.341543i
$$407$$ −6.76393 −0.335276
$$408$$ 0 0
$$409$$ 21.0172 15.2699i 1.03923 0.755048i 0.0690987 0.997610i $$-0.477988\pi$$
0.970136 + 0.242562i $$0.0779877\pi$$
$$410$$ 3.51722 10.8249i 0.173703 0.534603i
$$411$$ 0 0
$$412$$ 12.7082 9.23305i 0.626088 0.454880i
$$413$$ −14.4721 + 10.5146i −0.712127 + 0.517391i
$$414$$ 0 0
$$415$$ −10.8541 7.88597i −0.532807 0.387107i
$$416$$ −1.50000 + 1.08981i −0.0735436 + 0.0534325i
$$417$$ 0 0
$$418$$ −5.52786 −0.270377
$$419$$ 0.652476 2.00811i 0.0318755 0.0981028i −0.933853 0.357657i $$-0.883576\pi$$
0.965729 + 0.259554i $$0.0835757\pi$$
$$420$$ 0 0
$$421$$ 0.0278640 + 0.0857567i 0.00135801 + 0.00417953i 0.951733 0.306926i $$-0.0993006\pi$$
−0.950375 + 0.311106i $$0.899301\pi$$
$$422$$ −2.47214 7.60845i −0.120342 0.370374i
$$423$$ 0 0
$$424$$ 11.5623 0.561515
$$425$$ 4.63525 3.36771i 0.224843 0.163358i
$$426$$ 0 0
$$427$$ 3.47214 + 2.52265i 0.168028 + 0.122080i
$$428$$ 2.14590 + 6.60440i 0.103726 + 0.319235i
$$429$$ 0 0
$$430$$ 5.85410 4.25325i 0.282310 0.205110i
$$431$$ 3.00000 9.23305i 0.144505 0.444740i −0.852442 0.522822i $$-0.824879\pi$$
0.996947 + 0.0780813i $$0.0248794\pi$$
$$432$$ 0 0
$$433$$ −9.22542 + 28.3929i −0.443346 + 1.36448i 0.440942 + 0.897535i $$0.354644\pi$$
−0.884288 + 0.466942i $$0.845356\pi$$
$$434$$ 15.7082 11.4127i 0.754018 0.547826i
$$435$$ 0 0
$$436$$ 14.2082 + 10.3229i 0.680450 + 0.494376i
$$437$$ −35.1246 + 25.5195i −1.68024 + 1.22076i
$$438$$ 0 0
$$439$$ −12.2361 8.89002i −0.583996 0.424298i 0.256167 0.966633i $$-0.417540\pi$$
−0.840162 + 0.542335i $$0.817540\pi$$
$$440$$ −0.527864 1.62460i −0.0251649 0.0774497i
$$441$$ 0 0
$$442$$ −0.656541 + 2.02063i −0.0312285 + 0.0961114i
$$443$$ 28.0689 1.33359 0.666796 0.745240i $$-0.267665\pi$$
0.666796 + 0.745240i $$0.267665\pi$$
$$444$$ 0 0
$$445$$ −6.54508 + 4.75528i −0.310267 + 0.225422i
$$446$$ −4.85410 14.9394i −0.229848 0.707401i
$$447$$ 0 0
$$448$$ −1.61803 1.17557i −0.0764449 0.0555405i
$$449$$ 19.7984 0.934343 0.467172 0.884167i $$-0.345273\pi$$
0.467172 + 0.884167i $$0.345273\pi$$
$$450$$ 0 0
$$451$$ −3.88854 −0.183104
$$452$$ 6.92705 + 5.03280i 0.325821 + 0.236723i
$$453$$ 0 0
$$454$$ −0.291796 0.898056i −0.0136947 0.0421479i
$$455$$ −2.56231 7.88597i −0.120123 0.369700i
$$456$$ 0 0
$$457$$ −3.52786 −0.165027 −0.0825133 0.996590i $$-0.526295\pi$$
−0.0825133 + 0.996590i $$0.526295\pi$$
$$458$$ 2.86475 8.81678i 0.133861 0.411981i
$$459$$ 0 0
$$460$$ −10.8541 7.88597i −0.506075 0.367685i
$$461$$ 11.2533 + 8.17599i 0.524118 + 0.380794i 0.818153 0.575001i $$-0.194998\pi$$
−0.294035 + 0.955795i $$0.594998\pi$$
$$462$$ 0 0
$$463$$ 20.7984 15.1109i 0.966582 0.702263i 0.0119123 0.999929i $$-0.496208\pi$$
0.954670 + 0.297666i $$0.0962081\pi$$
$$464$$ −2.92705 2.12663i −0.135885 0.0987262i
$$465$$ 0 0
$$466$$ −8.82624 + 6.41264i −0.408868 + 0.297060i
$$467$$ −11.7984 + 36.3117i −0.545964 + 1.68030i 0.172724 + 0.984970i $$0.444743\pi$$
−0.718688 + 0.695333i $$0.755257\pi$$
$$468$$ 0 0
$$469$$ 2.29180 7.05342i 0.105825 0.325697i
$$470$$ −16.7082 12.1392i −0.770692 0.559940i
$$471$$ 0 0
$$472$$ 2.76393 + 8.50651i 0.127220 + 0.391544i
$$473$$ −2.00000 1.45309i −0.0919601 0.0668129i
$$474$$ 0 0
$$475$$ 29.2705 21.2663i 1.34302 0.975763i
$$476$$ −2.29180 −0.105044
$$477$$ 0 0
$$478$$ 8.29180 + 25.5195i 0.379258 + 1.16724i
$$479$$ 1.38197 + 4.25325i 0.0631436 + 0.194336i 0.977652 0.210232i $$-0.0674219\pi$$
−0.914508 + 0.404568i $$0.867422\pi$$
$$480$$ 0 0
$$481$$ −5.07295 + 15.6129i −0.231307 + 0.711888i
$$482$$ −7.14590 −0.325487
$$483$$ 0 0
$$484$$ 8.42705 6.12261i 0.383048 0.278300i
$$485$$ 15.9787 0.725556
$$486$$ 0 0
$$487$$ −19.1803 + 13.9353i −0.869144 + 0.631470i −0.930357 0.366655i $$-0.880503\pi$$
0.0612130 + 0.998125i $$0.480503\pi$$
$$488$$ 1.73607 1.26133i 0.0785881 0.0570976i
$$489$$ 0 0
$$490$$ −5.42705 + 3.94298i −0.245169 + 0.178126i
$$491$$ −4.76393 + 3.46120i −0.214993 + 0.156202i −0.690070 0.723743i $$-0.742420\pi$$
0.475077 + 0.879944i $$0.342420\pi$$
$$492$$ 0 0
$$493$$ −4.14590 −0.186722
$$494$$ −4.14590 + 12.7598i −0.186533 + 0.574089i
$$495$$ 0 0
$$496$$ −3.00000 9.23305i −0.134704 0.414576i
$$497$$ −5.05573 15.5599i −0.226780 0.697958i
$$498$$ 0 0
$$499$$ −6.58359 −0.294722 −0.147361 0.989083i $$-0.547078\pi$$
−0.147361 + 0.989083i $$0.547078\pi$$
$$500$$ 9.04508 + 6.57164i 0.404508 + 0.293893i
$$501$$ 0 0
$$502$$ −2.85410 2.07363i −0.127385 0.0925505i
$$503$$ −9.41641 28.9807i −0.419857 1.29219i −0.907834 0.419330i $$-0.862265\pi$$
0.487977 0.872857i $$-0.337735\pi$$
$$504$$ 0 0
$$505$$ 11.9721 36.8464i 0.532753 1.63965i
$$506$$ −1.41641 + 4.35926i −0.0629670 + 0.193793i
$$507$$ 0 0
$$508$$ 4.23607 13.0373i 0.187945 0.578436i
$$509$$ 23.2533 16.8945i 1.03068 0.748836i 0.0622385 0.998061i $$-0.480176\pi$$
0.968445 + 0.249226i $$0.0801761\pi$$
$$510$$ 0 0
$$511$$ 15.9443 + 11.5842i 0.705333 + 0.512454i
$$512$$ −0.809017 + 0.587785i −0.0357538 + 0.0259767i
$$513$$ 0 0
$$514$$ −7.59017 5.51458i −0.334788 0.243238i
$$515$$ 35.1246 1.54778
$$516$$ 0 0
$$517$$ −2.18034 + 6.71040i −0.0958912 + 0.295123i
$$518$$ −17.7082 −0.778054
$$519$$ 0 0
$$520$$ −4.14590 −0.181810
$$521$$ 8.42705 + 25.9358i 0.369196 + 1.13627i 0.947312 + 0.320313i $$0.103788\pi$$
−0.578116 + 0.815955i $$0.696212\pi$$
$$522$$ 0 0
$$523$$ 12.7082 + 9.23305i 0.555691 + 0.403733i 0.829879 0.557943i $$-0.188409\pi$$
−0.274188 + 0.961676i $$0.588409\pi$$
$$524$$ 5.23607 0.228739
$$525$$ 0 0
$$526$$ 8.47214 0.369403
$$527$$ −9.00000 6.53888i −0.392046 0.284838i
$$528$$ 0 0
$$529$$ 4.01722 + 12.3637i 0.174662 + 0.537554i
$$530$$ 20.9164 + 15.1967i 0.908551 + 0.660101i
$$531$$ 0 0
$$532$$ −14.4721 −0.627447
$$533$$ −2.91641 + 8.97578i −0.126324 + 0.388784i
$$534$$ 0 0
$$535$$ −4.79837 + 14.7679i −0.207452 + 0.638471i
$$536$$ −3.00000 2.17963i −0.129580 0.0941456i
$$537$$ 0 0
$$538$$ −10.5902 + 7.69421i −0.456575 + 0.331721i
$$539$$ 1.85410 + 1.34708i 0.0798618 + 0.0580230i
$$540$$ 0 0
$$541$$ 9.92705 7.21242i 0.426797 0.310086i −0.353570 0.935408i $$-0.615032\pi$$
0.780367 + 0.625322i $$0.215032\pi$$
$$542$$ 1.79837 5.53483i 0.0772468 0.237741i
$$543$$ 0 0
$$544$$ −0.354102 + 1.08981i −0.0151820 + 0.0467254i
$$545$$ 12.1353 + 37.3485i 0.519817 + 1.59983i
$$546$$ 0 0
$$547$$ 0.618034 + 1.90211i 0.0264252 + 0.0813285i 0.963399 0.268070i $$-0.0863859\pi$$
−0.936974 + 0.349399i $$0.886386\pi$$
$$548$$ 11.3541 + 8.24924i 0.485023 + 0.352390i
$$549$$ 0 0
$$550$$ 1.18034 3.63271i 0.0503299 0.154899i
$$551$$ −26.1803 −1.11532
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −8.91641 27.4419i −0.378822 1.16589i
$$555$$ 0 0
$$556$$ 4.14590 12.7598i 0.175825 0.541134i
$$557$$ −6.27051 −0.265690 −0.132845 0.991137i $$-0.542411\pi$$
−0.132845 + 0.991137i $$0.542411\pi$$
$$558$$ 0 0
$$559$$ −4.85410 + 3.52671i −0.205307 + 0.149164i
$$560$$ −1.38197 4.25325i −0.0583987 0.179733i
$$561$$ 0 0
$$562$$ 4.11803 2.99193i 0.173709 0.126207i
$$563$$ 1.23607 0.898056i 0.0520941 0.0378485i −0.561434 0.827522i $$-0.689750\pi$$
0.613528 + 0.789673i $$0.289750\pi$$
$$564$$ 0 0
$$565$$ 5.91641 + 18.2088i 0.248905 + 0.766051i
$$566$$ 1.00000 0.726543i 0.0420331 0.0305389i
$$567$$ 0 0
$$568$$ −8.18034 −0.343239
$$569$$ −7.29837 + 22.4621i −0.305964 + 0.941660i 0.673352 + 0.739322i $$0.264854\pi$$
−0.979316 + 0.202338i $$0.935146\pi$$
$$570$$ 0 0
$$571$$ 6.27051 + 19.2986i 0.262413 + 0.807623i 0.992278 + 0.124032i $$0.0395827\pi$$
−0.729866 + 0.683591i $$0.760417\pi$$
$$572$$ 0.437694 + 1.34708i 0.0183009 + 0.0563244i
$$573$$ 0 0
$$574$$ −10.1803 −0.424919
$$575$$ −9.27051 28.5317i −0.386607 1.18985i
$$576$$ 0 0
$$577$$ 20.0902 + 14.5964i 0.836365 + 0.607655i 0.921353 0.388727i $$-0.127085\pi$$
−0.0849881 + 0.996382i $$0.527085\pi$$
$$578$$ −4.84752 14.9191i −0.201630 0.620555i
$$579$$ 0 0
$$580$$ −2.50000 7.69421i −0.103807 0.319485i
$$581$$ −3.70820 + 11.4127i −0.153842 + 0.473478i
$$582$$ 0 0
$$583$$ 2.72949 8.40051i 0.113044 0.347913i
$$584$$ 7.97214 5.79210i 0.329889 0.239679i
$$585$$ 0 0
$$586$$ −3.39919 2.46965i −0.140419 0.102020i
$$587$$ 16.0902 11.6902i 0.664112 0.482506i −0.203937 0.978984i $$-0.565374\pi$$
0.868049 + 0.496478i $$0.165374\pi$$
$$588$$ 0 0
$$589$$ −56.8328 41.2915i −2.34176 1.70138i
$$590$$ −6.18034 + 19.0211i −0.254441 + 0.783088i
$$591$$ 0 0
$$592$$ −2.73607 + 8.42075i −0.112452 + 0.346091i
$$593$$ −23.0344 −0.945911 −0.472956 0.881086i $$-0.656813\pi$$
−0.472956 + 0.881086i $$0.656813\pi$$
$$594$$ 0 0
$$595$$ −4.14590 3.01217i −0.169965 0.123487i
$$596$$ 6.80902 + 20.9560i 0.278908 + 0.858391i
$$597$$ 0 0
$$598$$ 9.00000 + 6.53888i 0.368037 + 0.267395i
$$599$$ −18.9443 −0.774042 −0.387021 0.922071i $$-0.626496\pi$$
−0.387021 + 0.922071i $$0.626496\pi$$
$$600$$ 0 0
$$601$$ −8.32624 −0.339634 −0.169817 0.985476i $$-0.554318\pi$$
−0.169817 + 0.985476i $$0.554318\pi$$
$$602$$ −5.23607 3.80423i −0.213406 0.155049i
$$603$$ 0 0
$$604$$ 3.38197 + 10.4086i 0.137610 + 0.423521i
$$605$$ 23.2918 0.946946
$$606$$ 0 0
$$607$$ −24.1803 −0.981450 −0.490725 0.871315i $$-0.663268\pi$$
−0.490725 + 0.871315i $$0.663268\pi$$
$$608$$ −2.23607 + 6.88191i −0.0906845 + 0.279098i
$$609$$ 0 0
$$610$$ 4.79837 0.194280
$$611$$ 13.8541 + 10.0656i 0.560477 + 0.407210i
$$612$$ 0 0
$$613$$ 1.16312 0.845055i 0.0469779 0.0341315i −0.564048 0.825742i $$-0.690757\pi$$
0.611026 + 0.791610i $$0.290757\pi$$
$$614$$ 24.0344 + 17.4620i 0.969951 + 0.704711i
$$615$$ 0 0
$$616$$ −1.23607 + 0.898056i −0.0498026 + 0.0361837i
$$617$$ −3.28115 + 10.0984i −0.132094 + 0.406544i −0.995127 0.0986041i $$-0.968562\pi$$
0.863032 + 0.505148i $$0.168562\pi$$
$$618$$ 0 0
$$619$$ −7.23607 + 22.2703i −0.290842 + 0.895120i 0.693744 + 0.720221i $$0.255960\pi$$
−0.984586 + 0.174899i $$0.944040\pi$$
$$620$$ 6.70820 20.6457i 0.269408 0.829152i
$$621$$ 0 0
$$622$$ −3.90983 12.0332i −0.156770 0.482488i
$$623$$ 5.85410 + 4.25325i 0.234540 + 0.170403i
$$624$$ 0 0
$$625$$ 7.72542 + 23.7764i 0.309017 + 0.951057i
$$626$$ 18.3607 0.733840
$$627$$ 0 0
$$628$$ 3.44427 + 10.6004i 0.137441 + 0.423001i
$$629$$ 3.13525 + 9.64932i 0.125011 + 0.384744i
$$630$$ 0 0
$$631$$ −0.888544 + 2.73466i −0.0353724 + 0.108865i −0.967184 0.254078i $$-0.918228\pi$$
0.931811 + 0.362943i $$0.118228\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 8.85410 6.43288i 0.351641 0.255482i
$$635$$ 24.7984 18.0171i 0.984093 0.714986i
$$636$$ 0 0
$$637$$ 4.50000 3.26944i 0.178296 0.129540i
$$638$$ −2.23607 + 1.62460i −0.0885268 + 0.0643185i
$$639$$ 0 0
$$640$$ −2.23607 −0.0883883
$$641$$ −7.32624 + 5.32282i −0.289369 + 0.210239i −0.722994 0.690855i $$-0.757234\pi$$
0.433625 + 0.901094i $$0.357234\pi$$
$$642$$ 0 0
$$643$$ 31.7771 1.25317 0.626583 0.779355i $$-0.284453\pi$$
0.626583 + 0.779355i $$0.284453\pi$$
$$644$$ −3.70820 + 11.4127i −0.146124 + 0.449723i
$$645$$ 0 0
$$646$$ 2.56231 + 7.88597i 0.100813 + 0.310269i
$$647$$ 0.0344419 + 0.106001i 0.00135405 + 0.00416733i 0.951731 0.306933i $$-0.0993026\pi$$
−0.950377 + 0.311100i $$0.899303\pi$$
$$648$$ 0 0
$$649$$ 6.83282 0.268211
$$650$$ −7.50000 5.44907i −0.294174 0.213730i
$$651$$ 0 0
$$652$$ −9.32624 6.77591i −0.365244 0.265365i
$$653$$ −5.93769 18.2743i −0.232360 0.715130i −0.997461 0.0712197i $$-0.977311\pi$$
0.765101 0.643911i $$-0.222689\pi$$
$$654$$ 0 0
$$655$$ 9.47214 + 6.88191i 0.370107 + 0.268898i
$$656$$ −1.57295 + 4.84104i −0.0614133 + 0.189011i
$$657$$ 0 0
$$658$$ −5.70820 + 17.5680i −0.222529 + 0.684874i
$$659$$ 17.0344 12.3762i 0.663568 0.482110i −0.204298 0.978909i $$-0.565491\pi$$
0.867866 + 0.496799i $$0.165491\pi$$
$$660$$ 0 0
$$661$$ 26.2705 + 19.0866i 1.02180 + 0.742384i 0.966652 0.256094i $$-0.0824355\pi$$
0.0551524 + 0.998478i $$0.482436\pi$$
$$662$$ 19.0344 13.8293i 0.739795 0.537492i
$$663$$ 0 0
$$664$$ 4.85410 + 3.52671i 0.188376 + 0.136863i
$$665$$ −26.1803 19.0211i −1.01523 0.737608i
$$666$$ 0 0
$$667$$ −6.70820 + 20.6457i −0.259743 + 0.799406i
$$668$$ 2.47214 0.0956498
$$669$$ 0 0
$$670$$ −2.56231 7.88597i −0.0989905 0.304661i
$$671$$ −0.506578 1.55909i −0.0195562 0.0601879i
$$672$$ 0 0
$$673$$ −4.69098 3.40820i −0.180824 0.131376i 0.493691 0.869637i $$-0.335647\pi$$
−0.674515 + 0.738261i $$0.735647\pi$$
$$674$$ −24.8328 −0.956524
$$675$$ 0 0
$$676$$ −9.56231 −0.367781
$$677$$ 22.2705 + 16.1805i 0.855925 + 0.621866i 0.926773 0.375621i $$-0.122571\pi$$
−0.0708481 + 0.997487i $$0.522571\pi$$
$$678$$ 0 0
$$679$$ −4.41641 13.5923i −0.169486 0.521625i
$$680$$ −2.07295 + 1.50609i −0.0794940 + 0.0577557i
$$681$$ 0 0
$$682$$ −7.41641 −0.283989
$$683$$ 2.29180 7.05342i 0.0876931 0.269892i −0.897588 0.440836i $$-0.854682\pi$$
0.985281 + 0.170945i $$0.0546819\pi$$
$$684$$ 0 0
$$685$$ 9.69756 + 29.8460i 0.370525 + 1.14036i
$$686$$ 16.1803 + 11.7557i 0.617768 + 0.448835i
$$687$$ 0 0
$$688$$ −2.61803 + 1.90211i −0.0998116 + 0.0725174i
$$689$$ −17.3435 12.6008i −0.660733 0.480051i
$$690$$ 0 0
$$691$$ 1.47214 1.06957i 0.0560027 0.0406883i −0.559432 0.828876i $$-0.688981\pi$$
0.615434 + 0.788188i $$0.288981\pi$$
$$692$$ 6.82624 21.0090i 0.259495 0.798642i
$$693$$ 0 0
$$694$$ 0.236068 0.726543i 0.00896102 0.0275792i
$$695$$ 24.2705 17.6336i 0.920633 0.668879i
$$696$$ 0 0
$$697$$ 1.80244 + 5.54734i 0.0682723 + 0.210120i
$$698$$ 7.92705 + 5.75934i 0.300043 + 0.217994i
$$699$$ 0 0
$$700$$ 3.09017 9.51057i 0.116797 0.359466i
$$701$$ −49.1591 −1.85671 −0.928356 0.371692i $$-0.878778\pi$$
−0.928356 + 0.371692i $$0.878778\pi$$
$$702$$ 0 0
$$703$$ 19.7984 + 60.9331i 0.746710 + 2.29814i
$$704$$ 0.236068 + 0.726543i 0.00889715 + 0.0273826i
$$705$$ 0 0
$$706$$ −3.56231 + 10.9637i −0.134069 + 0.412622i
$$707$$ −34.6525 −1.30324
$$708$$ 0 0
$$709$$ 4.20820 3.05744i 0.158042 0.114825i −0.505953 0.862561i $$-0.668859\pi$$
0.663996 + 0.747736i $$0.268859\pi$$
$$710$$ −14.7984 10.7516i −0.555373 0.403502i
$$711$$ 0 0
$$712$$ 2.92705 2.12663i 0.109696 0.0796987i
$$713$$ −47.1246 + 34.2380i −1.76483 + 1.28222i
$$714$$ 0 0
$$715$$ −0.978714 + 3.01217i −0.0366018 + 0.112649i
$$716$$ −21.1803 + 15.3884i −0.791546 + 0.575092i
$$717$$ 0 0
$$718$$ −7.88854 −0.294398
$$719$$ 6.90983 21.2663i 0.257693 0.793098i −0.735594 0.677423i $$-0.763097\pi$$
0.993287 0.115675i $$-0.0369032\pi$$
$$720$$ 0 0
$$721$$ −9.70820 29.8788i −0.361552 1.11274i
$$722$$ 10.3090 + 31.7279i 0.383662 + 1.18079i
$$723$$ 0 0
$$724$$ 9.03444 0.335762
$$725$$ 5.59017 17.2048i 0.207614 0.638969i
$$726$$ 0 0
$$727$$ −19.1803 13.9353i −0.711359 0.516833i 0.172253 0.985053i $$-0.444895\pi$$
−0.883612 + 0.468220i $$0.844895\pi$$
$$728$$ 1.14590 + 3.52671i 0.0424698 + 0.130709i
$$729$$ 0 0
$$730$$ 22.0344 0.815531
$$731$$ −1.14590 + 3.52671i −0.0423826 + 0.130440i
$$732$$ 0 0
$$733$$ 11.8541 36.4832i 0.437841 1.34754i −0.452306 0.891863i $$-0.649398\pi$$
0.890147 0.455674i $$-0.150602\pi$$
$$734$$ 2.85410 2.07363i 0.105347 0.0765389i
$$735$$ 0 0
$$736$$ 4.85410 + 3.52671i 0.178925 + 0.129996i
$$737$$ −2.29180 + 1.66509i −0.0844194 + 0.0613343i
$$738$$ 0 0
$$739$$ −17.5623 12.7598i −0.646040 0.469375i 0.215880 0.976420i $$-0.430738\pi$$
−0.861920 + 0.507044i $$0.830738\pi$$
$$740$$ −16.0172 + 11.6372i −0.588805 + 0.427792i
$$741$$ 0 0
$$742$$ 7.14590 21.9928i 0.262334 0.807382i
$$743$$ 24.6525 0.904412 0.452206 0.891914i $$-0.350637\pi$$
0.452206 + 0.891914i $$0.350637\pi$$
$$744$$ 0 0
$$745$$ −15.2254 + 46.8590i −0.557816 + 1.71678i
$$746$$ 9.09017 + 27.9767i 0.332815 + 1.02430i
$$747$$ 0 0
$$748$$ 0.708204 + 0.514540i 0.0258945 + 0.0188135i
$$749$$ 13.8885 0.507476
$$750$$ 0 0
$$751$$ 19.2361 0.701934 0.350967 0.936388i $$-0.385853\pi$$
0.350967 + 0.936388i $$0.385853\pi$$
$$752$$ 7.47214 + 5.42882i 0.272481 + 0.197969i
$$753$$ 0 0
$$754$$ 2.07295 + 6.37988i 0.0754924 + 0.232342i
$$755$$ −7.56231 + 23.2744i −0.275220 + 0.847042i
$$756$$ 0 0
$$757$$ −22.1459 −0.804906 −0.402453 0.915441i $$-0.631842\pi$$
−0.402453 + 0.915441i $$0.631842\pi$$
$$758$$ 7.23607 22.2703i 0.262826 0.808895i
$$759$$ 0 0
$$760$$ −13.0902 + 9.51057i −0.474830 + 0.344984i
$$761$$ −36.5344 26.5438i −1.32437 0.962213i −0.999867 0.0163292i $$-0.994802\pi$$
−0.324506 0.945884i $$-0.605198\pi$$
$$762$$ 0 0
$$763$$ 28.4164 20.6457i 1.02874 0.747426i
$$764$$ −4.23607 3.07768i −0.153256 0.111347i
$$765$$ 0 0
$$766$$ 9.32624 6.77591i 0.336971 0.244824i
$$767$$ 5.12461 15.7719i 0.185039 0.569492i
$$768$$ 0 0
$$769$$ 13.0902 40.2874i 0.472044 1.45280i −0.377860 0.925863i $$-0.623340\pi$$
0.849904 0.526938i $$-0.176660\pi$$
$$770$$ −3.41641 −0.123119
$$771$$ 0 0
$$772$$ 1.42705 + 4.39201i 0.0513607 + 0.158072i
$$773$$ 2.35410 + 1.71036i 0.0846712 + 0.0615172i 0.629315 0.777150i $$-0.283335\pi$$
−0.544644 + 0.838667i $$0.683335\pi$$
$$774$$ 0 0
$$775$$ 39.2705 28.5317i 1.41064 1.02489i
$$776$$ −7.14590 −0.256523
$$777$$ 0 0
$$778$$ 9.57295 + 29.4625i 0.343207 + 1.05628i
$$779$$ 11.3820 + 35.0301i 0.407801 + 1.25508i
$$780$$ 0 0
$$781$$ −1.93112 + 5.94336i −0.0691008 + 0.212670i
$$782$$ 6.87539 0.245863
$$783$$ 0 0
$$784$$ 2.42705 1.76336i 0.0866804 0.0629770i
$$785$$ −7.70163 + 23.7032i −0.274883 + 0.846002i
$$786$$ 0 0
$$787$$ 29.5623 21.4783i 1.05378 0.765618i 0.0808543 0.996726i $$-0.474235\pi$$
0.972928 + 0.231108i $$0.0742351\pi$$
$$788$$ 1.88197 1.36733i