# Properties

 Label 570.2.m.a.493.8 Level $570$ Weight $2$ Character 570.493 Analytic conductor $4.551$ Analytic rank $0$ Dimension $20$ CM no Inner twists $4$

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## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.m (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$20$$ Relative dimension: $$10$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ Defining polynomial: $$x^{20} + 153 x^{16} + 6416 x^{12} + 78648 x^{8} + 19120 x^{4} + 16$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{10}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 493.8 Root $$1.75036 + 1.75036i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.493 Dual form 570.2.m.a.37.8

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.253765 + 2.22162i) q^{5} +1.00000 q^{6} +(-2.47539 + 2.47539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$$ $$q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.253765 + 2.22162i) q^{5} +1.00000 q^{6} +(-2.47539 + 2.47539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(-1.75036 + 1.39149i) q^{10} +2.74367 q^{11} +(0.707107 + 0.707107i) q^{12} +(-1.20178 + 1.20178i) q^{13} -3.50073 q^{14} +(1.39149 + 1.75036i) q^{15} -1.00000 q^{16} +(-4.87121 + 4.87121i) q^{17} +(0.707107 - 0.707107i) q^{18} +(1.94007 - 3.90335i) q^{19} +(-2.22162 - 0.253765i) q^{20} +3.50073i q^{21} +(1.94007 + 1.94007i) q^{22} +(0.0321428 + 0.0321428i) q^{23} +1.00000i q^{24} +(-4.87121 - 1.12754i) q^{25} -1.69957 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.47539 - 2.47539i) q^{28} +6.50952 q^{29} +(-0.253765 + 2.22162i) q^{30} +6.50952i q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.94007 - 1.94007i) q^{33} -6.88893 q^{34} +(-4.87121 - 6.12754i) q^{35} +1.00000 q^{36} +(4.58998 + 4.58998i) q^{37} +(4.13192 - 1.38825i) q^{38} +1.69957i q^{39} +(-1.39149 - 1.75036i) q^{40} -5.96665i q^{41} +(-2.47539 + 2.47539i) q^{42} +(5.39582 + 5.39582i) q^{43} +2.74367i q^{44} +(2.22162 + 0.253765i) q^{45} +0.0454567i q^{46} +(3.66743 - 3.66743i) q^{47} +(-0.707107 + 0.707107i) q^{48} -5.25508i q^{49} +(-2.64717 - 4.24175i) q^{50} +6.88893i q^{51} +(-1.20178 - 1.20178i) q^{52} +(8.97544 - 8.97544i) q^{53} -1.00000i q^{54} +(-0.696246 + 6.09540i) q^{55} -3.50073i q^{56} +(-1.38825 - 4.13192i) q^{57} +(4.60292 + 4.60292i) q^{58} +4.42301 q^{59} +(-1.75036 + 1.39149i) q^{60} -2.95077 q^{61} +(-4.60292 + 4.60292i) q^{62} +(2.47539 + 2.47539i) q^{63} -1.00000i q^{64} +(-2.36493 - 2.97487i) q^{65} +2.74367 q^{66} +(7.00145 + 7.00145i) q^{67} +(-4.87121 - 4.87121i) q^{68} +0.0454567 q^{69} +(0.888360 - 7.77729i) q^{70} -5.56594i q^{71} +(0.707107 + 0.707107i) q^{72} +(-2.19205 - 2.19205i) q^{73} +6.49122i q^{74} +(-4.24175 + 2.64717i) q^{75} +(3.90335 + 1.94007i) q^{76} +(-6.79164 + 6.79164i) q^{77} +(-1.20178 + 1.20178i) q^{78} -0.225823 q^{79} +(0.253765 - 2.22162i) q^{80} -1.00000 q^{81} +(4.21906 - 4.21906i) q^{82} +(-3.87246 - 3.87246i) q^{83} -3.50073 q^{84} +(-9.58584 - 12.0581i) q^{85} +7.63084i q^{86} +(4.60292 - 4.60292i) q^{87} +(-1.94007 + 1.94007i) q^{88} -9.13628 q^{89} +(1.39149 + 1.75036i) q^{90} -5.94974i q^{91} +(-0.0321428 + 0.0321428i) q^{92} +(4.60292 + 4.60292i) q^{93} +5.18653 q^{94} +(8.17945 + 5.30063i) q^{95} -1.00000 q^{96} +(-8.76663 - 8.76663i) q^{97} +(3.71590 - 3.71590i) q^{98} -2.74367i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$20q - 4q^{5} + 20q^{6} - 4q^{7} + O(q^{10})$$ $$20q - 4q^{5} + 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} + 4q^{17} + 44q^{23} + 4q^{25} - 8q^{26} - 4q^{28} - 4q^{30} + 4q^{35} + 20q^{36} - 4q^{38} - 4q^{42} + 52q^{43} + 4q^{47} + 16q^{55} - 4q^{57} + 8q^{58} + 32q^{61} - 8q^{62} + 4q^{63} - 8q^{66} + 4q^{68} - 20q^{73} + 20q^{76} - 24q^{77} + 4q^{80} - 20q^{81} - 24q^{82} - 116q^{83} - 60q^{85} + 8q^{87} - 44q^{92} + 8q^{93} - 32q^{95} - 20q^{96} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$1$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.707107 + 0.707107i 0.500000 + 0.500000i
$$3$$ 0.707107 0.707107i 0.408248 0.408248i
$$4$$ 1.00000i 0.500000i
$$5$$ −0.253765 + 2.22162i −0.113487 + 0.993539i
$$6$$ 1.00000 0.408248
$$7$$ −2.47539 + 2.47539i −0.935608 + 0.935608i −0.998049 0.0624406i $$-0.980112\pi$$
0.0624406 + 0.998049i $$0.480112\pi$$
$$8$$ −0.707107 + 0.707107i −0.250000 + 0.250000i
$$9$$ 1.00000i 0.333333i
$$10$$ −1.75036 + 1.39149i −0.553513 + 0.440026i
$$11$$ 2.74367 0.827247 0.413624 0.910448i $$-0.364263\pi$$
0.413624 + 0.910448i $$0.364263\pi$$
$$12$$ 0.707107 + 0.707107i 0.204124 + 0.204124i
$$13$$ −1.20178 + 1.20178i −0.333314 + 0.333314i −0.853844 0.520530i $$-0.825735\pi$$
0.520530 + 0.853844i $$0.325735\pi$$
$$14$$ −3.50073 −0.935608
$$15$$ 1.39149 + 1.75036i 0.359280 + 0.451942i
$$16$$ −1.00000 −0.250000
$$17$$ −4.87121 + 4.87121i −1.18144 + 1.18144i −0.202070 + 0.979371i $$0.564767\pi$$
−0.979371 + 0.202070i $$0.935233\pi$$
$$18$$ 0.707107 0.707107i 0.166667 0.166667i
$$19$$ 1.94007 3.90335i 0.445082 0.895490i
$$20$$ −2.22162 0.253765i −0.496770 0.0567435i
$$21$$ 3.50073i 0.763921i
$$22$$ 1.94007 + 1.94007i 0.413624 + 0.413624i
$$23$$ 0.0321428 + 0.0321428i 0.00670223 + 0.00670223i 0.710450 0.703748i $$-0.248491\pi$$
−0.703748 + 0.710450i $$0.748491\pi$$
$$24$$ 1.00000i 0.204124i
$$25$$ −4.87121 1.12754i −0.974241 0.225508i
$$26$$ −1.69957 −0.333314
$$27$$ −0.707107 0.707107i −0.136083 0.136083i
$$28$$ −2.47539 2.47539i −0.467804 0.467804i
$$29$$ 6.50952 1.20879 0.604394 0.796686i $$-0.293415\pi$$
0.604394 + 0.796686i $$0.293415\pi$$
$$30$$ −0.253765 + 2.22162i −0.0463309 + 0.405611i
$$31$$ 6.50952i 1.16914i 0.811342 + 0.584572i $$0.198738\pi$$
−0.811342 + 0.584572i $$0.801262\pi$$
$$32$$ −0.707107 0.707107i −0.125000 0.125000i
$$33$$ 1.94007 1.94007i 0.337722 0.337722i
$$34$$ −6.88893 −1.18144
$$35$$ −4.87121 6.12754i −0.823384 1.03574i
$$36$$ 1.00000 0.166667
$$37$$ 4.58998 + 4.58998i 0.754589 + 0.754589i 0.975332 0.220743i $$-0.0708483\pi$$
−0.220743 + 0.975332i $$0.570848\pi$$
$$38$$ 4.13192 1.38825i 0.670286 0.225204i
$$39$$ 1.69957i 0.272150i
$$40$$ −1.39149 1.75036i −0.220013 0.276757i
$$41$$ 5.96665i 0.931833i −0.884829 0.465917i $$-0.845725\pi$$
0.884829 0.465917i $$-0.154275\pi$$
$$42$$ −2.47539 + 2.47539i −0.381960 + 0.381960i
$$43$$ 5.39582 + 5.39582i 0.822855 + 0.822855i 0.986517 0.163662i $$-0.0523305\pi$$
−0.163662 + 0.986517i $$0.552331\pi$$
$$44$$ 2.74367i 0.413624i
$$45$$ 2.22162 + 0.253765i 0.331180 + 0.0378290i
$$46$$ 0.0454567i 0.00670223i
$$47$$ 3.66743 3.66743i 0.534950 0.534950i −0.387091 0.922041i $$-0.626520\pi$$
0.922041 + 0.387091i $$0.126520\pi$$
$$48$$ −0.707107 + 0.707107i −0.102062 + 0.102062i
$$49$$ 5.25508i 0.750725i
$$50$$ −2.64717 4.24175i −0.374367 0.599875i
$$51$$ 6.88893i 0.964643i
$$52$$ −1.20178 1.20178i −0.166657 0.166657i
$$53$$ 8.97544 8.97544i 1.23287 1.23287i 0.270015 0.962856i $$-0.412971\pi$$
0.962856 0.270015i $$-0.0870288\pi$$
$$54$$ 1.00000i 0.136083i
$$55$$ −0.696246 + 6.09540i −0.0938818 + 0.821903i
$$56$$ 3.50073i 0.467804i
$$57$$ −1.38825 4.13192i −0.183878 0.547286i
$$58$$ 4.60292 + 4.60292i 0.604394 + 0.604394i
$$59$$ 4.42301 0.575826 0.287913 0.957657i $$-0.407039\pi$$
0.287913 + 0.957657i $$0.407039\pi$$
$$60$$ −1.75036 + 1.39149i −0.225971 + 0.179640i
$$61$$ −2.95077 −0.377808 −0.188904 0.981996i $$-0.560493\pi$$
−0.188904 + 0.981996i $$0.560493\pi$$
$$62$$ −4.60292 + 4.60292i −0.584572 + 0.584572i
$$63$$ 2.47539 + 2.47539i 0.311869 + 0.311869i
$$64$$ 1.00000i 0.125000i
$$65$$ −2.36493 2.97487i −0.293334 0.368987i
$$66$$ 2.74367 0.337722
$$67$$ 7.00145 + 7.00145i 0.855363 + 0.855363i 0.990788 0.135424i $$-0.0432398\pi$$
−0.135424 + 0.990788i $$0.543240\pi$$
$$68$$ −4.87121 4.87121i −0.590721 0.590721i
$$69$$ 0.0454567 0.00547235
$$70$$ 0.888360 7.77729i 0.106179 0.929564i
$$71$$ 5.56594i 0.660556i −0.943884 0.330278i $$-0.892858\pi$$
0.943884 0.330278i $$-0.107142\pi$$
$$72$$ 0.707107 + 0.707107i 0.0833333 + 0.0833333i
$$73$$ −2.19205 2.19205i −0.256560 0.256560i 0.567094 0.823653i $$-0.308068\pi$$
−0.823653 + 0.567094i $$0.808068\pi$$
$$74$$ 6.49122i 0.754589i
$$75$$ −4.24175 + 2.64717i −0.489795 + 0.305669i
$$76$$ 3.90335 + 1.94007i 0.447745 + 0.222541i
$$77$$ −6.79164 + 6.79164i −0.773979 + 0.773979i
$$78$$ −1.20178 + 1.20178i −0.136075 + 0.136075i
$$79$$ −0.225823 −0.0254070 −0.0127035 0.999919i $$-0.504044\pi$$
−0.0127035 + 0.999919i $$0.504044\pi$$
$$80$$ 0.253765 2.22162i 0.0283717 0.248385i
$$81$$ −1.00000 −0.111111
$$82$$ 4.21906 4.21906i 0.465917 0.465917i
$$83$$ −3.87246 3.87246i −0.425058 0.425058i 0.461883 0.886941i $$-0.347174\pi$$
−0.886941 + 0.461883i $$0.847174\pi$$
$$84$$ −3.50073 −0.381960
$$85$$ −9.58584 12.0581i −1.03973 1.30789i
$$86$$ 7.63084i 0.822855i
$$87$$ 4.60292 4.60292i 0.493485 0.493485i
$$88$$ −1.94007 + 1.94007i −0.206812 + 0.206812i
$$89$$ −9.13628 −0.968444 −0.484222 0.874945i $$-0.660897\pi$$
−0.484222 + 0.874945i $$0.660897\pi$$
$$90$$ 1.39149 + 1.75036i 0.146675 + 0.184504i
$$91$$ 5.94974i 0.623703i
$$92$$ −0.0321428 + 0.0321428i −0.00335112 + 0.00335112i
$$93$$ 4.60292 + 4.60292i 0.477301 + 0.477301i
$$94$$ 5.18653 0.534950
$$95$$ 8.17945 + 5.30063i 0.839194 + 0.543833i
$$96$$ −1.00000 −0.102062
$$97$$ −8.76663 8.76663i −0.890117 0.890117i 0.104417 0.994534i $$-0.466702\pi$$
−0.994534 + 0.104417i $$0.966702\pi$$
$$98$$ 3.71590 3.71590i 0.375363 0.375363i
$$99$$ 2.74367i 0.275749i
$$100$$ 1.12754 4.87121i 0.112754 0.487121i
$$101$$ 11.2650 1.12091 0.560455 0.828185i $$-0.310626\pi$$
0.560455 + 0.828185i $$0.310626\pi$$
$$102$$ −4.87121 + 4.87121i −0.482321 + 0.482321i
$$103$$ 0.762447 0.762447i 0.0751262 0.0751262i −0.668545 0.743671i $$-0.733083\pi$$
0.743671 + 0.668545i $$0.233083\pi$$
$$104$$ 1.69957i 0.166657i
$$105$$ −7.77729 0.888360i −0.758986 0.0866951i
$$106$$ 12.6932 1.23287
$$107$$ −13.5351 13.5351i −1.30849 1.30849i −0.922505 0.385985i $$-0.873861\pi$$
−0.385985 0.922505i $$-0.626139\pi$$
$$108$$ 0.707107 0.707107i 0.0680414 0.0680414i
$$109$$ −4.37207 −0.418768 −0.209384 0.977833i $$-0.567146\pi$$
−0.209384 + 0.977833i $$0.567146\pi$$
$$110$$ −4.80242 + 3.81777i −0.457892 + 0.364011i
$$111$$ 6.49122 0.616119
$$112$$ 2.47539 2.47539i 0.233902 0.233902i
$$113$$ 6.95599 6.95599i 0.654365 0.654365i −0.299676 0.954041i $$-0.596879\pi$$
0.954041 + 0.299676i $$0.0968786\pi$$
$$114$$ 1.94007 3.90335i 0.181704 0.365582i
$$115$$ −0.0795658 + 0.0632524i −0.00741955 + 0.00589832i
$$116$$ 6.50952i 0.604394i
$$117$$ 1.20178 + 1.20178i 0.111105 + 0.111105i
$$118$$ 3.12754 + 3.12754i 0.287913 + 0.287913i
$$119$$ 24.1162i 2.21073i
$$120$$ −2.22162 0.253765i −0.202805 0.0231654i
$$121$$ −3.47228 −0.315662
$$122$$ −2.08651 2.08651i −0.188904 0.188904i
$$123$$ −4.21906 4.21906i −0.380419 0.380419i
$$124$$ −6.50952 −0.584572
$$125$$ 3.74110 10.5359i 0.334614 0.942355i
$$126$$ 3.50073i 0.311869i
$$127$$ 13.7136 + 13.7136i 1.21689 + 1.21689i 0.968716 + 0.248173i $$0.0798302\pi$$
0.248173 + 0.968716i $$0.420170\pi$$
$$128$$ 0.707107 0.707107i 0.0625000 0.0625000i
$$129$$ 7.63084 0.671858
$$130$$ 0.431292 3.77581i 0.0378268 0.331161i
$$131$$ 8.01380 0.700169 0.350085 0.936718i $$-0.386153\pi$$
0.350085 + 0.936718i $$0.386153\pi$$
$$132$$ 1.94007 + 1.94007i 0.168861 + 0.168861i
$$133$$ 4.85988 + 14.4647i 0.421405 + 1.25425i
$$134$$ 9.90155i 0.855363i
$$135$$ 1.75036 1.39149i 0.150647 0.119760i
$$136$$ 6.88893i 0.590721i
$$137$$ −12.6299 + 12.6299i −1.07905 + 1.07905i −0.0824532 + 0.996595i $$0.526275\pi$$
−0.996595 + 0.0824532i $$0.973725\pi$$
$$138$$ 0.0321428 + 0.0321428i 0.00273617 + 0.00273617i
$$139$$ 10.3499i 0.877869i 0.898519 + 0.438934i $$0.144644\pi$$
−0.898519 + 0.438934i $$0.855356\pi$$
$$140$$ 6.12754 4.87121i 0.517871 0.411692i
$$141$$ 5.18653i 0.436785i
$$142$$ 3.93571 3.93571i 0.330278 0.330278i
$$143$$ −3.29729 + 3.29729i −0.275733 + 0.275733i
$$144$$ 1.00000i 0.0833333i
$$145$$ −1.65189 + 14.4617i −0.137182 + 1.20098i
$$146$$ 3.10002i 0.256560i
$$147$$ −3.71590 3.71590i −0.306482 0.306482i
$$148$$ −4.58998 + 4.58998i −0.377294 + 0.377294i
$$149$$ 9.07466i 0.743425i −0.928348 0.371712i $$-0.878771\pi$$
0.928348 0.371712i $$-0.121229\pi$$
$$150$$ −4.87121 1.12754i −0.397732 0.0920631i
$$151$$ 1.75287i 0.142647i 0.997453 + 0.0713234i $$0.0227222\pi$$
−0.997453 + 0.0713234i $$0.977278\pi$$
$$152$$ 1.38825 + 4.13192i 0.112602 + 0.335143i
$$153$$ 4.87121 + 4.87121i 0.393814 + 0.393814i
$$154$$ −9.60483 −0.773979
$$155$$ −14.4617 1.65189i −1.16159 0.132683i
$$156$$ −1.69957 −0.136075
$$157$$ 7.20733 7.20733i 0.575207 0.575207i −0.358372 0.933579i $$-0.616668\pi$$
0.933579 + 0.358372i $$0.116668\pi$$
$$158$$ −0.159681 0.159681i −0.0127035 0.0127035i
$$159$$ 12.6932i 1.00664i
$$160$$ 1.75036 1.39149i 0.138378 0.110007i
$$161$$ −0.159132 −0.0125413
$$162$$ −0.707107 0.707107i −0.0555556 0.0555556i
$$163$$ 9.60292 + 9.60292i 0.752159 + 0.752159i 0.974882 0.222723i $$-0.0714945\pi$$
−0.222723 + 0.974882i $$0.571494\pi$$
$$164$$ 5.96665 0.465917
$$165$$ 3.81777 + 4.80242i 0.297213 + 0.373868i
$$166$$ 5.47649i 0.425058i
$$167$$ 12.9013 + 12.9013i 0.998336 + 0.998336i 0.999999 0.00166271i $$-0.000529259\pi$$
−0.00166271 + 0.999999i $$0.500529\pi$$
$$168$$ −2.47539 2.47539i −0.190980 0.190980i
$$169$$ 10.1114i 0.777804i
$$170$$ 1.74817 15.3046i 0.134078 1.17381i
$$171$$ −3.90335 1.94007i −0.298497 0.148361i
$$172$$ −5.39582 + 5.39582i −0.411427 + 0.411427i
$$173$$ 0.271593 0.271593i 0.0206488 0.0206488i −0.696707 0.717356i $$-0.745352\pi$$
0.717356 + 0.696707i $$0.245352\pi$$
$$174$$ 6.50952 0.493485
$$175$$ 14.8492 9.26703i 1.12249 0.700521i
$$176$$ −2.74367 −0.206812
$$177$$ 3.12754 3.12754i 0.235080 0.235080i
$$178$$ −6.46033 6.46033i −0.484222 0.484222i
$$179$$ 16.1543 1.20743 0.603715 0.797200i $$-0.293686\pi$$
0.603715 + 0.797200i $$0.293686\pi$$
$$180$$ −0.253765 + 2.22162i −0.0189145 + 0.165590i
$$181$$ 16.1980i 1.20399i −0.798501 0.601994i $$-0.794373\pi$$
0.798501 0.601994i $$-0.205627\pi$$
$$182$$ 4.20710 4.20710i 0.311851 0.311851i
$$183$$ −2.08651 + 2.08651i −0.154239 + 0.154239i
$$184$$ −0.0454567 −0.00335112
$$185$$ −11.3620 + 9.03243i −0.835349 + 0.664078i
$$186$$ 6.50952i 0.477301i
$$187$$ −13.3650 + 13.3650i −0.977344 + 0.977344i
$$188$$ 3.66743 + 3.66743i 0.267475 + 0.267475i
$$189$$ 3.50073 0.254640
$$190$$ 2.03563 + 9.53185i 0.147680 + 0.691513i
$$191$$ 14.6162 1.05759 0.528795 0.848750i $$-0.322644\pi$$
0.528795 + 0.848750i $$0.322644\pi$$
$$192$$ −0.707107 0.707107i −0.0510310 0.0510310i
$$193$$ 6.20432 6.20432i 0.446597 0.446597i −0.447625 0.894221i $$-0.647730\pi$$
0.894221 + 0.447625i $$0.147730\pi$$
$$194$$ 12.3979i 0.890117i
$$195$$ −3.77581 0.431292i −0.270392 0.0308855i
$$196$$ 5.25508 0.375363
$$197$$ −9.77456 + 9.77456i −0.696408 + 0.696408i −0.963634 0.267226i $$-0.913893\pi$$
0.267226 + 0.963634i $$0.413893\pi$$
$$198$$ 1.94007 1.94007i 0.137875 0.137875i
$$199$$ 7.77253i 0.550980i 0.961304 + 0.275490i $$0.0888401\pi$$
−0.961304 + 0.275490i $$0.911160\pi$$
$$200$$ 4.24175 2.64717i 0.299937 0.187183i
$$201$$ 9.90155 0.698401
$$202$$ 7.96556 + 7.96556i 0.560455 + 0.560455i
$$203$$ −16.1136 + 16.1136i −1.13095 + 1.13095i
$$204$$ −6.88893 −0.482321
$$205$$ 13.2556 + 1.51412i 0.925813 + 0.105751i
$$206$$ 1.07826 0.0751262
$$207$$ 0.0321428 0.0321428i 0.00223408 0.00223408i
$$208$$ 1.20178 1.20178i 0.0833285 0.0833285i
$$209$$ 5.32290 10.7095i 0.368193 0.740792i
$$210$$ −4.87121 6.12754i −0.336145 0.422840i
$$211$$ 7.91902i 0.545168i −0.962132 0.272584i $$-0.912122\pi$$
0.962132 0.272584i $$-0.0878783\pi$$
$$212$$ 8.97544 + 8.97544i 0.616436 + 0.616436i
$$213$$ −3.93571 3.93571i −0.269671 0.269671i
$$214$$ 19.1416i 1.30849i
$$215$$ −13.3567 + 10.6182i −0.910922 + 0.724156i
$$216$$ 1.00000 0.0680414
$$217$$ −16.1136 16.1136i −1.09386 1.09386i
$$218$$ −3.09152 3.09152i −0.209384 0.209384i
$$219$$ −3.10002 −0.209480
$$220$$ −6.09540 0.696246i −0.410951 0.0469409i
$$221$$ 11.7082i 0.787582i
$$222$$ 4.58998 + 4.58998i 0.308059 + 0.308059i
$$223$$ −14.3643 + 14.3643i −0.961907 + 0.961907i −0.999301 0.0373940i $$-0.988094\pi$$
0.0373940 + 0.999301i $$0.488094\pi$$
$$224$$ 3.50073 0.233902
$$225$$ −1.12754 + 4.87121i −0.0751692 + 0.324747i
$$226$$ 9.83726 0.654365
$$227$$ −15.0385 15.0385i −0.998139 0.998139i 0.00185921 0.999998i $$-0.499408\pi$$
−0.999998 + 0.00185921i $$0.999408\pi$$
$$228$$ 4.13192 1.38825i 0.273643 0.0919391i
$$229$$ 2.69570i 0.178137i 0.996026 + 0.0890683i $$0.0283890\pi$$
−0.996026 + 0.0890683i $$0.971611\pi$$
$$230$$ −0.100988 0.0115353i −0.00665893 0.000760616i
$$231$$ 9.60483i 0.631951i
$$232$$ −4.60292 + 4.60292i −0.302197 + 0.302197i
$$233$$ −12.4775 12.4775i −0.817426 0.817426i 0.168309 0.985734i $$-0.446169\pi$$
−0.985734 + 0.168309i $$0.946169\pi$$
$$234$$ 1.69957i 0.111105i
$$235$$ 7.21698 + 9.07831i 0.470784 + 0.592204i
$$236$$ 4.42301i 0.287913i
$$237$$ −0.159681 + 0.159681i −0.0103724 + 0.0103724i
$$238$$ 17.0528 17.0528i 1.10537 1.10537i
$$239$$ 27.2150i 1.76039i 0.474613 + 0.880195i $$0.342588\pi$$
−0.474613 + 0.880195i $$0.657412\pi$$
$$240$$ −1.39149 1.75036i −0.0898200 0.112985i
$$241$$ 25.1111i 1.61755i −0.588120 0.808774i $$-0.700132\pi$$
0.588120 0.808774i $$-0.299868\pi$$
$$242$$ −2.45527 2.45527i −0.157831 0.157831i
$$243$$ −0.707107 + 0.707107i −0.0453609 + 0.0453609i
$$244$$ 2.95077i 0.188904i
$$245$$ 11.6748 + 1.33355i 0.745875 + 0.0851975i
$$246$$ 5.96665i 0.380419i
$$247$$ 2.35944 + 7.02251i 0.150127 + 0.446831i
$$248$$ −4.60292 4.60292i −0.292286 0.292286i
$$249$$ −5.47649 −0.347058
$$250$$ 10.0953 4.80461i 0.638485 0.303870i
$$251$$ −2.30195 −0.145298 −0.0726489 0.997358i $$-0.523145\pi$$
−0.0726489 + 0.997358i $$0.523145\pi$$
$$252$$ −2.47539 + 2.47539i −0.155935 + 0.155935i
$$253$$ 0.0881891 + 0.0881891i 0.00554440 + 0.00554440i
$$254$$ 19.3940i 1.21689i
$$255$$ −15.3046 1.74817i −0.958411 0.109474i
$$256$$ 1.00000 0.0625000
$$257$$ 15.7752 + 15.7752i 0.984032 + 0.984032i 0.999874 0.0158429i $$-0.00504315\pi$$
−0.0158429 + 0.999874i $$0.505043\pi$$
$$258$$ 5.39582 + 5.39582i 0.335929 + 0.335929i
$$259$$ −22.7240 −1.41200
$$260$$ 2.97487 2.36493i 0.184494 0.146667i
$$261$$ 6.50952i 0.402929i
$$262$$ 5.66661 + 5.66661i 0.350085 + 0.350085i
$$263$$ −1.21906 1.21906i −0.0751702 0.0751702i 0.668522 0.743692i $$-0.266927\pi$$
−0.743692 + 0.668522i $$0.766927\pi$$
$$264$$ 2.74367i 0.168861i
$$265$$ 17.6624 + 22.2177i 1.08499 + 1.36482i
$$266$$ −6.79164 + 13.6646i −0.416422 + 0.837828i
$$267$$ −6.46033 + 6.46033i −0.395366 + 0.395366i
$$268$$ −7.00145 + 7.00145i −0.427682 + 0.427682i
$$269$$ −7.58430 −0.462423 −0.231211 0.972904i $$-0.574269\pi$$
−0.231211 + 0.972904i $$0.574269\pi$$
$$270$$ 2.22162 + 0.253765i 0.135204 + 0.0154436i
$$271$$ −25.6741 −1.55959 −0.779795 0.626036i $$-0.784676\pi$$
−0.779795 + 0.626036i $$0.784676\pi$$
$$272$$ 4.87121 4.87121i 0.295360 0.295360i
$$273$$ −4.20710 4.20710i −0.254626 0.254626i
$$274$$ −17.8614 −1.07905
$$275$$ −13.3650 3.09359i −0.805939 0.186551i
$$276$$ 0.0454567i 0.00273617i
$$277$$ −21.7414 + 21.7414i −1.30631 + 1.30631i −0.382257 + 0.924056i $$0.624853\pi$$
−0.924056 + 0.382257i $$0.875147\pi$$
$$278$$ −7.31850 + 7.31850i −0.438934 + 0.438934i
$$279$$ 6.50952 0.389715
$$280$$ 7.77729 + 0.888360i 0.464782 + 0.0530897i
$$281$$ 21.9050i 1.30674i −0.757037 0.653372i $$-0.773354\pi$$
0.757037 0.653372i $$-0.226646\pi$$
$$282$$ 3.66743 3.66743i 0.218392 0.218392i
$$283$$ 15.7217 + 15.7217i 0.934557 + 0.934557i 0.997986 0.0634298i $$-0.0202039\pi$$
−0.0634298 + 0.997986i $$0.520204\pi$$
$$284$$ 5.56594 0.330278
$$285$$ 9.53185 2.03563i 0.564618 0.120580i
$$286$$ −4.66307 −0.275733
$$287$$ 14.7698 + 14.7698i 0.871831 + 0.871831i
$$288$$ −0.707107 + 0.707107i −0.0416667 + 0.0416667i
$$289$$ 30.4573i 1.79161i
$$290$$ −11.3940 + 9.05790i −0.669080 + 0.531898i
$$291$$ −12.3979 −0.726777
$$292$$ 2.19205 2.19205i 0.128280 0.128280i
$$293$$ −8.25768 + 8.25768i −0.482419 + 0.482419i −0.905903 0.423484i $$-0.860807\pi$$
0.423484 + 0.905903i $$0.360807\pi$$
$$294$$ 5.25508i 0.306482i
$$295$$ −1.12240 + 9.82625i −0.0653488 + 0.572106i
$$296$$ −6.49122 −0.377294
$$297$$ −1.94007 1.94007i −0.112574 0.112574i
$$298$$ 6.41675 6.41675i 0.371712 0.371712i
$$299$$ −0.0772571 −0.00446790
$$300$$ −2.64717 4.24175i −0.152835 0.244898i
$$301$$ −26.7135 −1.53974
$$302$$ −1.23947 + 1.23947i −0.0713234 + 0.0713234i
$$303$$ 7.96556 7.96556i 0.457609 0.457609i
$$304$$ −1.94007 + 3.90335i −0.111270 + 0.223872i
$$305$$ 0.748802 6.55550i 0.0428763 0.375367i
$$306$$ 6.88893i 0.393814i
$$307$$ −22.1239 22.1239i −1.26268 1.26268i −0.949790 0.312887i $$-0.898704\pi$$
−0.312887 0.949790i $$-0.601296\pi$$
$$308$$ −6.79164 6.79164i −0.386990 0.386990i
$$309$$ 1.07826i 0.0613403i
$$310$$ −9.05790 11.3940i −0.514454 0.647137i
$$311$$ 3.22108 0.182651 0.0913254 0.995821i $$-0.470890\pi$$
0.0913254 + 0.995821i $$0.470890\pi$$
$$312$$ −1.20178 1.20178i −0.0680374 0.0680374i
$$313$$ −14.9801 14.9801i −0.846724 0.846724i 0.142999 0.989723i $$-0.454326\pi$$
−0.989723 + 0.142999i $$0.954326\pi$$
$$314$$ 10.1927 0.575207
$$315$$ −6.12754 + 4.87121i −0.345248 + 0.274461i
$$316$$ 0.225823i 0.0127035i
$$317$$ −13.3317 13.3317i −0.748782 0.748782i 0.225468 0.974251i $$-0.427609\pi$$
−0.974251 + 0.225468i $$0.927609\pi$$
$$318$$ 8.97544 8.97544i 0.503318 0.503318i
$$319$$ 17.8600 0.999966
$$320$$ 2.22162 + 0.253765i 0.124192 + 0.0141859i
$$321$$ −19.1416 −1.06838
$$322$$ −0.112523 0.112523i −0.00627066 0.00627066i
$$323$$ 9.56356 + 28.4645i 0.532131 + 1.58381i
$$324$$ 1.00000i 0.0555556i
$$325$$ 7.20918 4.49907i 0.399893 0.249563i
$$326$$ 13.5806i 0.752159i
$$327$$ −3.09152 + 3.09152i −0.170961 + 0.170961i
$$328$$ 4.21906 + 4.21906i 0.232958 + 0.232958i
$$329$$ 18.1566i 1.00101i
$$330$$ −0.696246 + 6.09540i −0.0383271 + 0.335540i
$$331$$ 6.73163i 0.370004i 0.982738 + 0.185002i $$0.0592292\pi$$
−0.982738 + 0.185002i $$0.940771\pi$$
$$332$$ 3.87246 3.87246i 0.212529 0.212529i
$$333$$ 4.58998 4.58998i 0.251530 0.251530i
$$334$$ 18.2453i 0.998336i
$$335$$ −17.3313 + 13.7779i −0.946910 + 0.752765i
$$336$$ 3.50073i 0.190980i
$$337$$ 14.1501 + 14.1501i 0.770806 + 0.770806i 0.978247 0.207441i $$-0.0665136\pi$$
−0.207441 + 0.978247i $$0.566514\pi$$
$$338$$ −7.14987 + 7.14987i −0.388902 + 0.388902i
$$339$$ 9.83726i 0.534287i
$$340$$ 12.0581 9.58584i 0.653943 0.519865i
$$341$$ 17.8600i 0.967171i
$$342$$ −1.38825 4.13192i −0.0750680 0.223429i
$$343$$ −4.31936 4.31936i −0.233224 0.233224i
$$344$$ −7.63084 −0.411427
$$345$$ −0.0115353 + 0.100988i −0.000621040 + 0.00543700i
$$346$$ 0.384091 0.0206488
$$347$$ 6.84109 6.84109i 0.367249 0.367249i −0.499224 0.866473i $$-0.666382\pi$$
0.866473 + 0.499224i $$0.166382\pi$$
$$348$$ 4.60292 + 4.60292i 0.246743 + 0.246743i
$$349$$ 33.2298i 1.77875i 0.457181 + 0.889374i $$0.348859\pi$$
−0.457181 + 0.889374i $$0.651141\pi$$
$$350$$ 17.0528 + 3.94720i 0.911508 + 0.210987i
$$351$$ 1.69957 0.0907166
$$352$$ −1.94007 1.94007i −0.103406 0.103406i
$$353$$ 25.3639 + 25.3639i 1.34999 + 1.34999i 0.885668 + 0.464318i $$0.153701\pi$$
0.464318 + 0.885668i $$0.346299\pi$$
$$354$$ 4.42301 0.235080
$$355$$ 12.3654 + 1.41244i 0.656288 + 0.0749645i
$$356$$ 9.13628i 0.484222i
$$357$$ −17.0528 17.0528i −0.902528 0.902528i
$$358$$ 11.4228 + 11.4228i 0.603715 + 0.603715i
$$359$$ 9.12994i 0.481860i −0.970543 0.240930i $$-0.922548\pi$$
0.970543 0.240930i $$-0.0774524\pi$$
$$360$$ −1.75036 + 1.39149i −0.0922522 + 0.0733377i
$$361$$ −11.4723 15.1455i −0.603804 0.797133i
$$362$$ 11.4537 11.4537i 0.601994 0.601994i
$$363$$ −2.45527 + 2.45527i −0.128868 + 0.128868i
$$364$$ 5.94974 0.311851
$$365$$ 5.42616 4.31363i 0.284018 0.225786i
$$366$$ −2.95077 −0.154239
$$367$$ 12.9778 12.9778i 0.677435 0.677435i −0.281984 0.959419i $$-0.590993\pi$$
0.959419 + 0.281984i $$0.0909926\pi$$
$$368$$ −0.0321428 0.0321428i −0.00167556 0.00167556i
$$369$$ −5.96665 −0.310611
$$370$$ −14.4210 1.64724i −0.749713 0.0856360i
$$371$$ 44.4354i 2.30697i
$$372$$ −4.60292 + 4.60292i −0.238651 + 0.238651i
$$373$$ 6.92570 6.92570i 0.358599 0.358599i −0.504697 0.863296i $$-0.668396\pi$$
0.863296 + 0.504697i $$0.168396\pi$$
$$374$$ −18.9009 −0.977344
$$375$$ −4.80461 10.0953i −0.248109 0.521321i
$$376$$ 5.18653i 0.267475i
$$377$$ −7.82301 + 7.82301i −0.402906 + 0.402906i
$$378$$ 2.47539 + 2.47539i 0.127320 + 0.127320i
$$379$$ 22.4882 1.15514 0.577570 0.816341i $$-0.304001\pi$$
0.577570 + 0.816341i $$0.304001\pi$$
$$380$$ −5.30063 + 8.17945i −0.271916 + 0.419597i
$$381$$ 19.3940 0.993586
$$382$$ 10.3352 + 10.3352i 0.528795 + 0.528795i
$$383$$ 14.9680 14.9680i 0.764830 0.764830i −0.212361 0.977191i $$-0.568115\pi$$
0.977191 + 0.212361i $$0.0681153\pi$$
$$384$$ 1.00000i 0.0510310i
$$385$$ −13.3650 16.8119i −0.681142 0.856816i
$$386$$ 8.77423 0.446597
$$387$$ 5.39582 5.39582i 0.274285 0.274285i
$$388$$ 8.76663 8.76663i 0.445058 0.445058i
$$389$$ 10.1897i 0.516639i −0.966060 0.258319i $$-0.916831\pi$$
0.966060 0.258319i $$-0.0831687\pi$$
$$390$$ −2.36493 2.97487i −0.119753 0.150638i
$$391$$ −0.313148 −0.0158366
$$392$$ 3.71590 + 3.71590i 0.187681 + 0.187681i
$$393$$ 5.66661 5.66661i 0.285843 0.285843i
$$394$$ −13.8233 −0.696408
$$395$$ 0.0573058 0.501693i 0.00288337 0.0252429i
$$396$$ 2.74367 0.137875
$$397$$ 14.9493 14.9493i 0.750284 0.750284i −0.224248 0.974532i $$-0.571993\pi$$
0.974532 + 0.224248i $$0.0719927\pi$$
$$398$$ −5.49601 + 5.49601i −0.275490 + 0.275490i
$$399$$ 13.6646 + 6.79164i 0.684083 + 0.340007i
$$400$$ 4.87121 + 1.12754i 0.243560 + 0.0563769i
$$401$$ 17.1894i 0.858400i −0.903210 0.429200i $$-0.858796\pi$$
0.903210 0.429200i $$-0.141204\pi$$
$$402$$ 7.00145 + 7.00145i 0.349201 + 0.349201i
$$403$$ −7.82301 7.82301i −0.389692 0.389692i
$$404$$ 11.2650i 0.560455i
$$405$$ 0.253765 2.22162i 0.0126097 0.110393i
$$406$$ −22.7880 −1.13095
$$407$$ 12.5934 + 12.5934i 0.624231 + 0.624231i
$$408$$ −4.87121 4.87121i −0.241161 0.241161i
$$409$$ −23.9489 −1.18420 −0.592099 0.805865i $$-0.701701\pi$$
−0.592099 + 0.805865i $$0.701701\pi$$
$$410$$ 8.30250 + 10.4438i 0.410031 + 0.515782i
$$411$$ 17.8614i 0.881039i
$$412$$ 0.762447 + 0.762447i 0.0375631 + 0.0375631i
$$413$$ −10.9487 + 10.9487i −0.538748 + 0.538748i
$$414$$ 0.0454567 0.00223408
$$415$$ 9.58584 7.62045i 0.470550 0.374073i
$$416$$ 1.69957 0.0833285
$$417$$ 7.31850 + 7.31850i 0.358388 + 0.358388i
$$418$$ 11.3366 3.80890i 0.554492 0.186299i
$$419$$ 21.4134i 1.04611i 0.852298 + 0.523056i $$0.175208\pi$$
−0.852298 + 0.523056i $$0.824792\pi$$
$$420$$ 0.888360 7.77729i 0.0433475 0.379493i
$$421$$ 1.72609i 0.0841246i 0.999115 + 0.0420623i $$0.0133928\pi$$
−0.999115 + 0.0420623i $$0.986607\pi$$
$$422$$ 5.59960 5.59960i 0.272584 0.272584i
$$423$$ −3.66743 3.66743i −0.178317 0.178317i
$$424$$ 12.6932i 0.616436i
$$425$$ 29.2211 18.2362i 1.41743 0.884585i
$$426$$ 5.56594i 0.269671i
$$427$$ 7.30430 7.30430i 0.353480 0.353480i
$$428$$ 13.5351 13.5351i 0.654245 0.654245i
$$429$$ 4.66307i 0.225135i
$$430$$ −16.9528 1.93644i −0.817539 0.0933833i
$$431$$ 29.5770i 1.42467i 0.701838 + 0.712337i $$0.252363\pi$$
−0.701838 + 0.712337i $$0.747637\pi$$
$$432$$ 0.707107 + 0.707107i 0.0340207 + 0.0340207i
$$433$$ −18.7711 + 18.7711i −0.902081 + 0.902081i −0.995616 0.0935354i $$-0.970183\pi$$
0.0935354 + 0.995616i $$0.470183\pi$$
$$434$$ 22.7880i 1.09386i
$$435$$ 9.05790 + 11.3940i 0.434293 + 0.546301i
$$436$$ 4.37207i 0.209384i
$$437$$ 0.187824 0.0631054i 0.00898482 0.00301874i
$$438$$ −2.19205 2.19205i −0.104740 0.104740i
$$439$$ 8.66125 0.413379 0.206690 0.978407i $$-0.433731\pi$$
0.206690 + 0.978407i $$0.433731\pi$$
$$440$$ −3.81777 4.80242i −0.182005 0.228946i
$$441$$ −5.25508 −0.250242
$$442$$ 8.27898 8.27898i 0.393791 0.393791i
$$443$$ −19.5669 19.5669i −0.929652 0.929652i 0.0680315 0.997683i $$-0.478328\pi$$
−0.997683 + 0.0680315i $$0.978328\pi$$
$$444$$ 6.49122i 0.308059i
$$445$$ 2.31847 20.2974i 0.109906 0.962187i
$$446$$ −20.3142 −0.961907
$$447$$ −6.41675 6.41675i −0.303502 0.303502i
$$448$$ 2.47539 + 2.47539i 0.116951 + 0.116951i
$$449$$ 21.3429 1.00724 0.503618 0.863927i $$-0.332002\pi$$
0.503618 + 0.863927i $$0.332002\pi$$
$$450$$ −4.24175 + 2.64717i −0.199958 + 0.124789i
$$451$$ 16.3705i 0.770857i
$$452$$ 6.95599 + 6.95599i 0.327182 + 0.327182i
$$453$$ 1.23947 + 1.23947i 0.0582353 + 0.0582353i
$$454$$ 21.2676i 0.998139i
$$455$$ 13.2181 + 1.50983i 0.619673 + 0.0707821i
$$456$$ 3.90335 + 1.94007i 0.182791 + 0.0908520i
$$457$$ 21.3371 21.3371i 0.998110 0.998110i −0.00188859 0.999998i $$-0.500601\pi$$
0.999998 + 0.00188859i $$0.000601157\pi$$
$$458$$ −1.90615 + 1.90615i −0.0890683 + 0.0890683i
$$459$$ 6.88893 0.321548
$$460$$ −0.0632524 0.0795658i −0.00294916 0.00370977i
$$461$$ 0.603474 0.0281066 0.0140533 0.999901i $$-0.495527\pi$$
0.0140533 + 0.999901i $$0.495527\pi$$
$$462$$ −6.79164 + 6.79164i −0.315976 + 0.315976i
$$463$$ −13.8679 13.8679i −0.644495 0.644495i 0.307162 0.951657i $$-0.400621\pi$$
−0.951657 + 0.307162i $$0.900621\pi$$
$$464$$ −6.50952 −0.302197
$$465$$ −11.3940 + 9.05790i −0.528385 + 0.420050i
$$466$$ 17.6458i 0.817426i
$$467$$ 5.10843 5.10843i 0.236390 0.236390i −0.578964 0.815353i $$-0.696543\pi$$
0.815353 + 0.578964i $$0.196543\pi$$
$$468$$ −1.20178 + 1.20178i −0.0555523 + 0.0555523i
$$469$$ −34.6626 −1.60057
$$470$$ −1.31616 + 11.5225i −0.0607098 + 0.531494i
$$471$$ 10.1927i 0.469655i
$$472$$ −3.12754 + 3.12754i −0.143957 + 0.143957i
$$473$$ 14.8043 + 14.8043i 0.680705 + 0.680705i
$$474$$ −0.225823 −0.0103724
$$475$$ −13.8516 + 16.8265i −0.635557 + 0.772054i
$$476$$ 24.1162 1.10537
$$477$$ −8.97544 8.97544i −0.410957 0.410957i
$$478$$ −19.2439 + 19.2439i −0.880195 + 0.880195i
$$479$$ 0.676761i 0.0309220i −0.999880 0.0154610i $$-0.995078\pi$$
0.999880 0.0154610i $$-0.00492158\pi$$
$$480$$ 0.253765 2.22162i 0.0115827 0.101403i
$$481$$ −11.0323 −0.503030
$$482$$ 17.7562 17.7562i 0.808774 0.808774i
$$483$$ −0.112523 + 0.112523i −0.00511997 + 0.00511997i
$$484$$ 3.47228i 0.157831i
$$485$$ 21.7008 17.2515i 0.985383 0.783350i
$$486$$ −1.00000 −0.0453609
$$487$$ −2.31334 2.31334i −0.104828 0.104828i 0.652748 0.757575i $$-0.273616\pi$$
−0.757575 + 0.652748i $$0.773616\pi$$
$$488$$ 2.08651 2.08651i 0.0944519 0.0944519i
$$489$$ 13.5806 0.614135
$$490$$ 7.31236 + 9.19829i 0.330339 + 0.415536i
$$491$$ −0.0138034 −0.000622939 −0.000311469 1.00000i $$-0.500099\pi$$
−0.000311469 1.00000i $$0.500099\pi$$
$$492$$ 4.21906 4.21906i 0.190210 0.190210i
$$493$$ −31.7092 + 31.7092i −1.42811 + 1.42811i
$$494$$ −3.29729 + 6.63403i −0.148352 + 0.298479i
$$495$$ 6.09540 + 0.696246i 0.273968 + 0.0312939i
$$496$$ 6.50952i 0.292286i
$$497$$ 13.7779 + 13.7779i 0.618021 + 0.618021i
$$498$$ −3.87246 3.87246i −0.173529 0.173529i
$$499$$ 19.0461i 0.852619i −0.904577 0.426309i $$-0.859813\pi$$
0.904577 0.426309i $$-0.140187\pi$$
$$500$$ 10.5359 + 3.74110i 0.471178 + 0.167307i
$$501$$ 18.2453 0.815138
$$502$$ −1.62772 1.62772i −0.0726489 0.0726489i
$$503$$ −15.5475 15.5475i −0.693230 0.693230i 0.269711 0.962941i $$-0.413072\pi$$
−0.962941 + 0.269711i $$0.913072\pi$$
$$504$$ −3.50073 −0.155935
$$505$$ −2.85866 + 25.0266i −0.127209 + 1.11367i
$$506$$ 0.124718i 0.00554440i
$$507$$ 7.14987 + 7.14987i 0.317537 + 0.317537i
$$508$$ −13.7136 + 13.7136i −0.608444 + 0.608444i
$$509$$ 4.08859 0.181224 0.0906118 0.995886i $$-0.471118\pi$$
0.0906118 + 0.995886i $$0.471118\pi$$
$$510$$ −9.58584 12.0581i −0.424468 0.533943i
$$511$$ 10.8523 0.480078
$$512$$ 0.707107 + 0.707107i 0.0312500 + 0.0312500i
$$513$$ −4.13192 + 1.38825i −0.182429 + 0.0612928i
$$514$$ 22.3095i 0.984032i
$$515$$ 1.50039 + 1.88735i 0.0661150 + 0.0831667i
$$516$$ 7.63084i 0.335929i
$$517$$ 10.0622 10.0622i 0.442536 0.442536i
$$518$$ −16.0683 16.0683i −0.705999 0.705999i
$$519$$ 0.384091i 0.0168597i
$$520$$ 3.77581 + 0.431292i 0.165580 + 0.0189134i
$$521$$ 29.8730i 1.30876i 0.756166 + 0.654380i $$0.227070\pi$$
−0.756166 + 0.654380i $$0.772930\pi$$
$$522$$ 4.60292 4.60292i 0.201465 0.201465i
$$523$$ −20.1935 + 20.1935i −0.883001 + 0.883001i −0.993839 0.110837i $$-0.964647\pi$$
0.110837 + 0.993839i $$0.464647\pi$$
$$524$$ 8.01380i 0.350085i
$$525$$ 3.94720 17.0528i 0.172270 0.744243i
$$526$$ 1.72400i 0.0751702i
$$527$$ −31.7092 31.7092i −1.38127 1.38127i
$$528$$ −1.94007 + 1.94007i −0.0844306 + 0.0844306i
$$529$$ 22.9979i 0.999910i
$$530$$ −3.22108 + 28.1995i −0.139915 + 1.22491i
$$531$$ 4.42301i 0.191942i
$$532$$ −14.4647 + 4.85988i −0.627125 + 0.210703i
$$533$$ 7.17060 + 7.17060i 0.310593 + 0.310593i
$$534$$ −9.13628 −0.395366
$$535$$ 33.5047 26.6352i 1.44853 1.15154i
$$536$$ −9.90155 −0.427682
$$537$$ 11.4228 11.4228i 0.492932 0.492932i
$$538$$ −5.36291 5.36291i −0.231211 0.231211i
$$539$$ 14.4182i 0.621035i
$$540$$ 1.39149 + 1.75036i 0.0598800 + 0.0753236i
$$541$$ −25.3583 −1.09024 −0.545120 0.838358i $$-0.683516\pi$$
−0.545120 + 0.838358i $$0.683516\pi$$
$$542$$ −18.1543 18.1543i −0.779795 0.779795i
$$543$$ −11.4537 11.4537i −0.491526 0.491526i
$$544$$ 6.88893 0.295360
$$545$$ 1.10948 9.71308i 0.0475247 0.416063i
$$546$$ 5.94974i 0.254626i
$$547$$ −13.3457 13.3457i −0.570622 0.570622i 0.361680 0.932302i $$-0.382203\pi$$
−0.932302 + 0.361680i $$0.882203\pi$$
$$548$$ −12.6299 12.6299i −0.539524 0.539524i
$$549$$ 2.95077i 0.125936i
$$550$$ −7.26297 11.6380i −0.309694 0.496245i
$$551$$ 12.6289 25.4089i 0.538009 1.08246i
$$552$$ −0.0321428 + 0.0321428i −0.00136809 + 0.00136809i
$$553$$ 0.558998 0.558998i 0.0237710 0.0237710i
$$554$$ −30.7470 −1.30631
$$555$$ −1.64724 + 14.4210i −0.0699215 + 0.612138i
$$556$$ −10.3499 −0.438934
$$557$$ −8.05867 + 8.05867i −0.341457 + 0.341457i −0.856915 0.515458i $$-0.827622\pi$$
0.515458 + 0.856915i $$0.327622\pi$$
$$558$$ 4.60292 + 4.60292i 0.194857 + 0.194857i
$$559$$ −12.9692 −0.548538
$$560$$ 4.87121 + 6.12754i 0.205846 + 0.258936i
$$561$$ 18.9009i 0.797998i
$$562$$ 15.4892 15.4892i 0.653372 0.653372i
$$563$$ 28.6648 28.6648i 1.20808 1.20808i 0.236430 0.971648i $$-0.424022\pi$$
0.971648 0.236430i $$-0.0759775\pi$$
$$564$$ 5.18653 0.218392
$$565$$ 13.6884 + 17.2188i 0.575875 + 0.724399i
$$566$$ 22.2338i 0.934557i
$$567$$ 2.47539 2.47539i 0.103956 0.103956i
$$568$$ 3.93571 + 3.93571i 0.165139 + 0.165139i
$$569$$ −8.54540 −0.358242 −0.179121 0.983827i $$-0.557325\pi$$
−0.179121 + 0.983827i $$0.557325\pi$$
$$570$$ 8.17945 + 5.30063i 0.342599 + 0.222019i
$$571$$ 45.4169 1.90064 0.950320 0.311275i $$-0.100756\pi$$
0.950320 + 0.311275i $$0.100756\pi$$
$$572$$ −3.29729 3.29729i −0.137867 0.137867i
$$573$$ 10.3352 10.3352i 0.431759 0.431759i
$$574$$ 20.8876i 0.871831i
$$575$$ −0.120332 0.192816i −0.00501819 0.00804100i
$$576$$ −1.00000 −0.0416667
$$577$$ 12.1650 12.1650i 0.506437 0.506437i −0.406994 0.913431i $$-0.633423\pi$$
0.913431 + 0.406994i $$0.133423\pi$$
$$578$$ 21.5366 21.5366i 0.895803 0.895803i
$$579$$ 8.77423i 0.364645i
$$580$$ −14.4617 1.65189i −0.600489 0.0685908i
$$581$$ 19.1717 0.795375
$$582$$ −8.76663 8.76663i −0.363389 0.363389i
$$583$$ 24.6256 24.6256i 1.01989 1.01989i
$$584$$ 3.10002 0.128280
$$585$$ −2.97487 + 2.36493i −0.122996 + 0.0977779i
$$586$$ −11.6781 −0.482419
$$587$$ −5.32968 + 5.32968i −0.219980 + 0.219980i −0.808490 0.588510i $$-0.799715\pi$$
0.588510 + 0.808490i $$0.299715\pi$$
$$588$$ 3.71590 3.71590i 0.153241 0.153241i
$$589$$ 25.4089 + 12.6289i 1.04696 + 0.520365i
$$590$$ −7.74186 + 6.15455i −0.318728 + 0.253379i
$$591$$ 13.8233i 0.568615i
$$592$$ −4.58998 4.58998i −0.188647 0.188647i
$$593$$ −1.80818 1.80818i −0.0742529 0.0742529i 0.669005 0.743258i $$-0.266720\pi$$
−0.743258 + 0.669005i $$0.766720\pi$$
$$594$$ 2.74367i 0.112574i
$$595$$ 53.5772 + 6.11985i 2.19645 + 0.250889i
$$596$$ 9.07466 0.371712
$$597$$ 5.49601 + 5.49601i 0.224937 + 0.224937i
$$598$$ −0.0546290 0.0546290i −0.00223395 0.00223395i
$$599$$ 25.3131 1.03426 0.517132 0.855906i $$-0.327000\pi$$
0.517132 + 0.855906i $$0.327000\pi$$
$$600$$ 1.12754 4.87121i 0.0460315 0.198866i
$$601$$ 18.5367i 0.756126i −0.925780 0.378063i $$-0.876590\pi$$
0.925780 0.378063i $$-0.123410\pi$$
$$602$$ −18.8893 18.8893i −0.769870 0.769870i
$$603$$ 7.00145 7.00145i 0.285121 0.285121i
$$604$$ −1.75287 −0.0713234
$$605$$ 0.881142 7.71409i 0.0358235 0.313622i
$$606$$ 11.2650 0.457609
$$607$$ −11.5164 11.5164i −0.467435 0.467435i 0.433647 0.901083i $$-0.357226\pi$$
−0.901083 + 0.433647i $$0.857226\pi$$
$$608$$ −4.13192 + 1.38825i −0.167571 + 0.0563010i
$$609$$ 22.7880i 0.923418i
$$610$$ 5.16492 4.10596i 0.209122 0.166245i
$$611$$ 8.81490i 0.356613i
$$612$$ −4.87121 + 4.87121i −0.196907 + 0.196907i
$$613$$ −7.66890 7.66890i −0.309744 0.309744i 0.535066 0.844810i $$-0.320287\pi$$
−0.844810 + 0.535066i $$0.820287\pi$$
$$614$$ 31.2879i 1.26268i
$$615$$ 10.4438 8.30250i 0.421134 0.334789i
$$616$$ 9.60483i 0.386990i
$$617$$ 33.2792 33.2792i 1.33977 1.33977i 0.443492 0.896278i $$-0.353740\pi$$
0.896278 0.443492i $$-0.146260\pi$$
$$618$$ 0.762447 0.762447i 0.0306701 0.0306701i
$$619$$ 3.87513i 0.155755i 0.996963 + 0.0778774i $$0.0248143\pi$$
−0.996963 + 0.0778774i $$0.975186\pi$$
$$620$$ 1.65189 14.4617i 0.0663413 0.580795i
$$621$$ 0.0454567i 0.00182412i
$$622$$ 2.27765 + 2.27765i 0.0913254 + 0.0913254i
$$623$$ 22.6158 22.6158i 0.906084 0.906084i
$$624$$ 1.69957i 0.0680374i
$$625$$ 22.4573 + 10.9849i 0.898293 + 0.439398i
$$626$$ 21.1850i 0.846724i
$$627$$ −3.80890 11.3366i −0.152113 0.452741i
$$628$$ 7.20733 + 7.20733i 0.287604 + 0.287604i
$$629$$ −44.7175 −1.78300
$$630$$ −7.77729 0.888360i −0.309855 0.0353931i
$$631$$ 1.80965 0.0720412 0.0360206 0.999351i $$-0.488532\pi$$
0.0360206 + 0.999351i $$0.488532\pi$$
$$632$$ 0.159681 0.159681i 0.00635176 0.00635176i
$$633$$ −5.59960 5.59960i −0.222564 0.222564i
$$634$$ 18.8539i 0.748782i
$$635$$ −33.9466 + 26.9865i −1.34713 + 1.07093i
$$636$$ 12.6932 0.503318
$$637$$ 6.31545 + 6.31545i 0.250227 + 0.250227i
$$638$$ 12.6289 + 12.6289i 0.499983 + 0.499983i
$$639$$ −5.56594 −0.220185
$$640$$ 1.39149 + 1.75036i 0.0550033 + 0.0691892i
$$641$$ 6.61503i 0.261278i −0.991430 0.130639i $$-0.958297\pi$$
0.991430 0.130639i $$-0.0417029\pi$$
$$642$$ −13.5351 13.5351i −0.534189 0.534189i
$$643$$ −30.3608 30.3608i −1.19731 1.19731i −0.974968 0.222347i $$-0.928628\pi$$
−0.222347 0.974968i $$-0.571372\pi$$
$$644$$ 0.159132i 0.00627066i
$$645$$ −1.93644 + 16.9528i −0.0762472 + 0.667518i
$$646$$ −13.3650 + 26.8899i −0.525838 + 1.05797i
$$647$$ 5.83884 5.83884i 0.229549 0.229549i −0.582956 0.812504i $$-0.698104\pi$$
0.812504 + 0.582956i $$0.198104\pi$$
$$648$$ 0.707107 0.707107i 0.0277778 0.0277778i
$$649$$ 12.1353 0.476351
$$650$$ 8.27898 + 1.91633i 0.324728 + 0.0751648i
$$651$$ −22.7880 −0.893133
$$652$$ −9.60292 + 9.60292i −0.376080 + 0.376080i
$$653$$ −19.7797 19.7797i −0.774039 0.774039i 0.204771 0.978810i $$-0.434355\pi$$
−0.978810 + 0.204771i $$0.934355\pi$$
$$654$$ −4.37207 −0.170961
$$655$$ −2.03362 + 17.8036i −0.0794601 + 0.695646i
$$656$$ 5.96665i 0.232958i
$$657$$ −2.19205 + 2.19205i −0.0855198 + 0.0855198i
$$658$$ −12.8387 + 12.8387i −0.500503 + 0.500503i
$$659$$ 8.44761 0.329072 0.164536 0.986371i $$-0.447387\pi$$
0.164536 + 0.986371i $$0.447387\pi$$
$$660$$ −4.80242 + 3.81777i −0.186934 + 0.148607i
$$661$$ 23.8283i 0.926814i −0.886146 0.463407i $$-0.846627\pi$$
0.886146 0.463407i $$-0.153373\pi$$
$$662$$ −4.75998 + 4.75998i −0.185002 + 0.185002i
$$663$$ −8.27898 8.27898i −0.321529 0.321529i
$$664$$ 5.47649 0.212529
$$665$$ −33.3684 + 7.12619i −1.29397 + 0.276342i
$$666$$ 6.49122 0.251530
$$667$$ 0.209234 + 0.209234i 0.00810157 + 0.00810157i
$$668$$ −12.9013 + 12.9013i −0.499168 + 0.499168i
$$669$$ 20.3142i 0.785393i
$$670$$ −21.9975 2.51266i −0.849837 0.0970726i
$$671$$ −8.09594 −0.312540
$$672$$ 2.47539 2.47539i 0.0954901 0.0954901i
$$673$$ −31.9422 + 31.9422i −1.23128 + 1.23128i −0.267812 + 0.963471i $$0.586300\pi$$
−0.963471 + 0.267812i $$0.913700\pi$$
$$674$$ 20.0113i 0.770806i
$$675$$ 2.64717 + 4.24175i 0.101890 + 0.163265i
$$676$$ −10.1114 −0.388902
$$677$$ −11.7115 11.7115i −0.450111 0.450111i 0.445280 0.895391i $$-0.353104\pi$$
−0.895391 + 0.445280i $$0.853104\pi$$
$$678$$ 6.95599 6.95599i 0.267143 0.267143i
$$679$$ 43.4016 1.66560
$$680$$ 15.3046 + 1.74817i 0.586904 + 0.0670391i
$$681$$ −21.2676 −0.814977
$$682$$ −12.6289 + 12.6289i −0.483586 + 0.483586i
$$683$$ −3.55375 + 3.55375i −0.135981 + 0.135981i −0.771821 0.635840i $$-0.780654\pi$$
0.635840 + 0.771821i $$0.280654\pi$$
$$684$$ 1.94007 3.90335i 0.0741803 0.149248i
$$685$$ −24.8539 31.2640i −0.949619 1.19453i
$$686$$ 6.10850i 0.233224i
$$687$$ 1.90615 + 1.90615i 0.0727240 + 0.0727240i
$$688$$ −5.39582 5.39582i −0.205714 0.205714i
$$689$$ 21.5730i 0.821867i
$$690$$ −0.0795658 + 0.0632524i −0.00302902 + 0.00240798i
$$691$$ 9.74241 0.370619 0.185309 0.982680i $$-0.440671\pi$$
0.185309 + 0.982680i $$0.440671\pi$$
$$692$$ 0.271593 + 0.271593i 0.0103244 + 0.0103244i
$$693$$ 6.79164 + 6.79164i 0.257993 + 0.257993i
$$694$$ 9.67476 0.367249
$$695$$ −22.9936 2.62644i −0.872197 0.0996267i
$$696$$ 6.50952i 0.246743i
$$697$$ 29.0648 + 29.0648i 1.10091 + 1.10091i
$$698$$ −23.4970 + 23.4970i −0.889374 + 0.889374i
$$699$$ −17.6458 −0.667425
$$700$$ 9.26703 + 14.8492i 0.350261 + 0.561247i
$$701$$ −10.3224 −0.389873 −0.194936 0.980816i $$-0.562450\pi$$
−0.194936 + 0.980816i $$0.562450\pi$$
$$702$$ 1.20178 + 1.20178i 0.0453583 + 0.0453583i
$$703$$ 26.8212 9.01143i 1.01158 0.339873i
$$704$$ 2.74367i 0.103406i
$$705$$ 11.5225 + 1.31616i 0.433963 + 0.0495694i
$$706$$ 35.8700i 1.34999i
$$707$$ −27.8852 + 27.8852i −1.04873 + 1.04873i
$$708$$ 3.12754 + 3.12754i 0.117540 + 0.117540i
$$709$$ 10.3223i 0.387663i 0.981035 + 0.193831i $$0.0620915\pi$$
−0.981035 + 0.193831i $$0.937909\pi$$
$$710$$ 7.74492 + 9.74241i 0.290662 + 0.365626i
$$711$$ 0.225823i 0.00846901i
$$712$$ 6.46033 6.46033i 0.242111 0.242111i
$$713$$ −0.209234 + 0.209234i −0.00783587 + 0.00783587i
$$714$$ 24.1162i 0.902528i
$$715$$ −6.48859 8.16206i −0.242660 0.305244i
$$716$$ 16.1543i 0.603715i
$$717$$ 19.2439 + 19.2439i 0.718676 + 0.718676i
$$718$$ 6.45584 6.45584i 0.240930 0.240930i
$$719$$ 34.9029i 1.30166i −0.759224 0.650830i $$-0.774421\pi$$
0.759224 0.650830i $$-0.225579\pi$$
$$720$$ −2.22162 0.253765i −0.0827950 0.00945725i
$$721$$ 3.77470i 0.140577i
$$722$$ 2.59737 18.8216i 0.0966642 0.700468i
$$723$$ −17.7562 17.7562i −0.660361 0.660361i
$$724$$ 16.1980 0.601994
$$725$$ −31.7092 7.33973i −1.17765 0.272591i
$$726$$ −3.47228 −0.128868
$$727$$ 12.8595 12.8595i 0.476932 0.476932i −0.427217 0.904149i $$-0.640506\pi$$
0.904149 + 0.427217i $$0.140506\pi$$
$$728$$ 4.20710 + 4.20710i 0.155926 + 0.155926i
$$729$$ 1.00000i 0.0370370i
$$730$$ 6.88707 + 0.786675i 0.254902 + 0.0291162i
$$731$$ −52.5683 −1.94431
$$732$$ −2.08651 2.08651i −0.0771197 0.0771197i
$$733$$ 11.1047 + 11.1047i 0.410162 + 0.410162i 0.881795 0.471633i $$-0.156335\pi$$
−0.471633 + 0.881795i $$0.656335\pi$$
$$734$$ 18.3534 0.677435
$$735$$ 9.19829 7.31236i 0.339284 0.269720i
$$736$$ 0.0454567i 0.00167556i
$$737$$ 19.2097 + 19.2097i 0.707597 + 0.707597i
$$738$$ −4.21906 4.21906i −0.155306 0.155306i
$$739$$ 18.1001i 0.665823i 0.942958 + 0.332911i $$0.108031\pi$$
−0.942958 + 0.332911i $$0.891969\pi$$
$$740$$ −9.03243 11.3620i −0.332039 0.417675i
$$741$$ 6.63403 + 3.29729i 0.243707 + 0.121129i
$$742$$ −31.4205 + 31.4205i −1.15348 + 1.15348i
$$743$$ 26.9208 26.9208i 0.987630 0.987630i −0.0122949 0.999924i $$-0.503914\pi$$
0.999924 + 0.0122949i $$0.00391368\pi$$
$$744$$ −6.50952 −0.238651
$$745$$ 20.1605 + 2.30283i 0.738622 + 0.0843690i
$$746$$ 9.79442 0.358599
$$747$$ −3.87246 + 3.87246i −0.141686 + 0.141686i
$$748$$ −13.3650 13.3650i −0.488672 0.488672i
$$749$$ 67.0093 2.44847
$$750$$ 3.74110 10.5359i 0.136606 0.384715i
$$751$$ 9.91849i 0.361931i −0.983489 0.180965i $$-0.942078\pi$$
0.983489 0.180965i $$-0.0579222\pi$$
$$752$$ −3.66743 + 3.66743i −0.133737 + 0.133737i
$$753$$ −1.62772 + 1.62772i −0.0593176 + 0.0593176i
$$754$$ −11.0634 −0.402906
$$755$$ −3.89422 0.444817i −0.141725 0.0161886i
$$756$$ 3.50073i 0.127320i
$$757$$ 3.01763 3.01763i 0.109678 0.109678i −0.650138 0.759816i $$-0.725289\pi$$
0.759816 + 0.650138i $$0.225289\pi$$
$$758$$ 15.9015 + 15.9015i 0.577570 + 0.577570i
$$759$$ 0.124718 0.00452699
$$760$$ −9.53185 + 2.03563i −0.345757 + 0.0738402i
$$761$$ −11.1416 −0.403881 −0.201941 0.979398i $$-0.564725\pi$$
−0.201941 + 0.979398i $$0.564725\pi$$
$$762$$ 13.7136 + 13.7136i 0.496793 + 0.496793i
$$763$$ 10.8226 10.8226i 0.391803 0.391803i
$$764$$ 14.6162i 0.528795i
$$765$$ −12.0581 + 9.58584i −0.435962 + 0.346577i
$$766$$ 21.1680 0.764830
$$767$$ −5.31548 + 5.31548i −0.191931 + 0.191931i
$$768$$ 0.707107 0.707107i 0.0255155 0.0255155i
$$769$$ 32.8840i 1.18583i −0.805266 0.592913i $$-0.797978\pi$$
0.805266 0.592913i $$-0.202022\pi$$
$$770$$ 2.43737 21.3383i 0.0878366 0.768979i
$$771$$ 22.3095 0.803458
$$772$$ 6.20432 + 6.20432i 0.223298 + 0.223298i
$$773$$ −31.2573 + 31.2573i −1.12425 + 1.12425i −0.133152 + 0.991096i $$0.542510\pi$$
−0.991096 + 0.133152i $$0.957490\pi$$
$$774$$ 7.63084 0.274285
$$775$$ 7.33973 31.7092i 0.263651 1.13903i
$$776$$ 12.3979 0.445058
$$777$$ −16.0683 + 16.0683i −0.576446 + 0.576446i
$$778$$ 7.20521 7.20521i 0.258319 0.258319i