LMFDB - Embedded newform 770.2.bv.a.3.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.15
Character	$\chi$	$=$	770.3
Dual form			770.2.bv.a.257.15

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.933580 + 0.358368i) q^{2} +(0.874801 - 0.568102i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.233574 - 2.22384i) q^{5} +(-0.613107 + 0.843870i) q^{6} +(-2.62366 - 0.341186i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.777674 + 1.74668i) q^{9} +O(q^{10})$	\(q+(-0.933580 + 0.358368i) q^{2} +(0.874801 - 0.568102i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.233574 - 2.22384i) q^{5} +(-0.613107 + 0.843870i) q^{6} +(-2.62366 - 0.341186i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.777674 + 1.74668i) q^{9} +(1.01501 + 1.99242i) q^{10} +(-1.70843 + 2.84276i) q^{11} +(0.269969 - 1.00754i) q^{12} +(0.0349206 - 0.220480i) q^{13} +(2.57167 - 0.621711i) q^{14} +(-1.46770 - 1.81272i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-3.37203 - 1.29440i) q^{17} +(0.100065 - 1.90936i) q^{18} +(-2.63932 + 2.93126i) q^{19} +(-1.66162 - 1.49634i) q^{20} +(-2.48901 + 1.19204i) q^{21} +(0.576206 - 3.26619i) q^{22} +(0.473144 - 1.76580i) q^{23} +(0.109032 + 1.03737i) q^{24} +(-4.89089 + 1.03886i) q^{25} +(0.0464117 + 0.218350i) q^{26} +(0.801507 + 5.06051i) q^{27} +(-2.17806 + 1.50202i) q^{28} +(5.85718 + 1.90311i) q^{29} +(2.01983 + 1.16634i) q^{30} +(-4.88913 + 0.513868i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.120439 + 3.45741i) q^{33} +3.61194 q^{34} +(-0.145924 + 5.91428i) q^{35} +(0.590835 + 1.81840i) q^{36} +(0.472864 - 0.728146i) q^{37} +(1.41355 - 3.68242i) q^{38} +(-0.0947066 - 0.212714i) q^{39} +(2.08749 + 0.801484i) q^{40} +(-11.9022 + 3.86725i) q^{41} +(1.89650 - 2.00484i) q^{42} +(8.91946 + 8.91946i) q^{43} +(0.632563 + 3.25574i) q^{44} +(4.06598 + 1.32144i) q^{45} +(0.191087 + 1.81807i) q^{46} +(-5.41486 + 0.283781i) q^{47} +(-0.473549 - 0.929392i) q^{48} +(6.76718 + 1.79031i) q^{49} +(4.19374 - 2.72260i) q^{50} +(-3.68521 + 0.783316i) q^{51} +(-0.121579 - 0.187215i) q^{52} +(7.52398 - 9.29134i) q^{53} +(-2.56180 - 4.43716i) q^{54} +(6.72087 + 3.13528i) q^{55} +(1.49512 - 2.18280i) q^{56} +(-0.643623 + 4.06368i) q^{57} +(-6.15016 + 0.322316i) q^{58} +(-3.67061 - 4.07663i) q^{59} +(-2.30366 - 0.365032i) q^{60} +(-1.83333 - 0.192691i) q^{61} +(4.38024 - 2.23184i) q^{62} +(2.63630 - 4.31737i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-0.498467 - 0.0261593i) q^{65} +(-1.35146 - 3.18461i) q^{66} +(-0.133324 - 0.497574i) q^{67} +(-3.37203 + 1.29440i) q^{68} +(-0.589247 - 1.81352i) q^{69} +(-1.98326 - 5.57375i) q^{70} +(-1.54572 - 1.12303i) q^{71} +(-1.20325 - 1.48589i) q^{72} +(-13.1903 - 0.691276i) q^{73} +(-0.180512 + 0.849243i) q^{74} +(-3.68837 + 3.68732i) q^{75} +3.94440i q^{76} +(5.45225 - 6.87553i) q^{77} +(0.164646 + 0.164646i) q^{78} +(-5.96218 + 13.3913i) q^{79} +(-2.23607 - 0.000159995i) q^{80} +(-0.262050 - 0.291036i) q^{81} +(9.72574 - 7.87575i) q^{82} +(-6.12892 + 0.970725i) q^{83} +(-1.05207 + 2.55133i) q^{84} +(-2.09092 + 7.80118i) q^{85} +(-11.5235 - 5.13059i) q^{86} +(6.20502 - 1.66263i) q^{87} +(-1.75730 - 2.81281i) q^{88} +(-3.16453 - 5.48113i) q^{89} +(-4.26948 + 0.223448i) q^{90} +(-0.166844 + 0.566550i) q^{91} +(-0.829935 - 1.62884i) q^{92} +(-3.98508 + 3.22706i) q^{93} +(4.95351 - 2.20545i) q^{94} +(7.13512 + 5.18475i) q^{95} +(0.775160 + 0.697957i) q^{96} +(-0.105332 - 0.0166830i) q^{97} +(-6.95930 + 0.753741i) q^{98} +(-3.63679 - 5.19483i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$2$	−0.933580	+	0.358368i	−0.660141	+	0.253404i
$3$	0.874801	−	0.568102i	0.505067	−	0.327994i	−0.266828	−	0.963744i	$-0.585976\pi$
$3$	0.874801	−	0.568102i	0.505067	−	0.327994i	0.771895	+	0.635750i	$0.219309\pi$
$4$	0.743145	−	0.669131i	0.371572	−	0.334565i
$5$	−0.233574	−	2.22384i	−0.104457	−	0.994529i
$5$	−0.233574	−	2.22384i	−0.104457	−	0.994529i
$6$	−0.613107	+	0.843870i	−0.250300	+	0.344508i
$7$	−2.62366	−	0.341186i	−0.991650	−	0.128956i
$7$	−2.62366	−	0.341186i	−0.991650	−	0.128956i
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	−0.777674	+	1.74668i	−0.259225	+	0.582228i
$10$	1.01501	+	1.99242i	0.320975	+	0.630060i
$11$	−1.70843	+	2.84276i	−0.515112	+	0.857123i
$11$	−1.70843	+	2.84276i	−0.515112	+	0.857123i
$12$	0.269969	−	1.00754i	0.0779334	−	0.290851i
$13$	0.0349206	−	0.220480i	0.00968523	−	0.0611501i	−0.982372	−	0.186935i	$-0.940145\pi$
$13$	0.0349206	−	0.220480i	0.00968523	−	0.0611501i	0.992058	+	0.125784i	$0.0401448\pi$
$14$	2.57167	−	0.621711i	0.687307	−	0.166159i
$15$	−1.46770	−	1.81272i	−0.378958	−	0.468042i
$16$	0.104528	−	0.994522i	0.0261321	−	0.248630i
$17$	−3.37203	−	1.29440i	−0.817838	−	0.313939i	−0.0867572	−	0.996229i	$-0.527650\pi$
$17$	−3.37203	−	1.29440i	−0.817838	−	0.313939i	−0.731081	+	0.682291i	$0.760984\pi$
$18$	0.100065	−	1.90936i	0.0235857	−	0.450041i
$19$	−2.63932	+	2.93126i	−0.605502	+	0.672478i	−0.965478	−	0.260484i	$-0.916118\pi$
$19$	−2.63932	+	2.93126i	−0.605502	+	0.672478i	0.359977	+	0.932961i	$0.382785\pi$
$20$	−1.66162	−	1.49634i	−0.371548	−	0.334592i
$21$	−2.48901	+	1.19204i	−0.543146	+	0.260124i
$22$	0.576206	−	3.26619i	0.122848	−	0.696354i
$23$	0.473144	−	1.76580i	0.0986574	−	0.368194i	−0.898891	−	0.438172i	$-0.855626\pi$
$23$	0.473144	−	1.76580i	0.0986574	−	0.368194i	0.997549	+	0.0699776i	$0.0222928\pi$
$24$	0.109032	+	1.03737i	0.0222560	+	0.211752i
$25$	−4.89089	+	1.03886i	−0.978177	+	0.207772i
$26$	0.0464117	+	0.218350i	0.00910209	+	0.0428220i
$27$	0.801507	+	5.06051i	0.154250	+	0.973896i
$28$	−2.17806	+	1.50202i	−0.411614	+	0.283855i
$29$	5.85718	+	1.90311i	1.08765	+	0.353399i	0.797338	−	0.603533i	$-0.206241\pi$
$29$	5.85718	+	1.90311i	1.08765	+	0.353399i	0.290312	+	0.956932i	$0.406241\pi$
$30$	2.01983	+	1.16634i	0.368769	+	0.212944i
$31$	−4.88913	+	0.513868i	−0.878113	+	0.0922934i	−0.532847	−	0.846212i	$-0.678878\pi$
$31$	−4.88913	+	0.513868i	−0.878113	+	0.0922934i	−0.345266	+	0.938505i	$0.612211\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	0.120439	+	3.45741i	0.0209657	+	0.601858i
$34$	3.61194			0.619442
$35$	−0.145924	+	5.91428i	−0.0246657	+	0.999696i
$36$	0.590835	+	1.81840i	0.0984725	+	0.303067i
$37$	0.472864	−	0.728146i	0.0777383	−	0.119707i	−0.797663	−	0.603104i	$-0.793931\pi$
$37$	0.472864	−	0.728146i	0.0777383	−	0.119707i	0.875401	+	0.483397i	$0.160597\pi$
$38$	1.41355	−	3.68242i	0.229308	−	0.597367i
$39$	−0.0947066	−	0.212714i	−0.0151652	−	0.0340616i
$40$	2.08749	+	0.801484i	0.330061	+	0.126726i
$41$	−11.9022	+	3.86725i	−1.85881	+	0.603963i	−0.863840	+	0.503766i	$0.831947\pi$
$41$	−11.9022	+	3.86725i	−1.85881	+	0.603963i	−0.994968	+	0.100198i	$0.968053\pi$
$42$	1.89650	−	2.00484i	0.292637	−	0.309354i
$43$	8.91946	+	8.91946i	1.36021	+	1.36021i	0.873650	+	0.486555i	$0.161747\pi$
$43$	8.91946	+	8.91946i	1.36021	+	1.36021i	0.486555	+	0.873650i	$0.338253\pi$
$44$	0.632563	+	3.25574i	0.0953624	+	0.490822i
$45$	4.06598	+	1.32144i	0.606121	+	0.196988i
$46$	0.191087	+	1.81807i	0.0281743	+	0.268060i
$47$	−5.41486	+	0.283781i	−0.789839	+	0.0413937i	−0.442989	−	0.896527i	$-0.646082\pi$
$47$	−5.41486	+	0.283781i	−0.789839	+	0.0413937i	−0.346850	+	0.937921i	$0.612749\pi$
$48$	−0.473549	−	0.929392i	−0.0683509	−	0.134146i
$49$	6.76718	+	1.79031i	0.966741	+	0.255759i
$50$	4.19374	−	2.72260i	0.593085	−	0.385033i
$51$	−3.68521	+	0.783316i	−0.516033	+	0.109686i
$52$	−0.121579	−	0.187215i	−0.0168599	−	0.0259620i
$53$	7.52398	−	9.29134i	1.03350	−	1.27626i	0.0731907	−	0.997318i	$-0.476682\pi$
$53$	7.52398	−	9.29134i	1.03350	−	1.27626i	0.960307	−	0.278945i	$-0.0899848\pi$
$54$	−2.56180	−	4.43716i	−0.348616	−	0.603821i
$55$	6.72087	+	3.13528i	0.906241	+	0.422761i
$56$	1.49512	−	2.18280i	0.199793	−	0.291689i
$57$	−0.643623	+	4.06368i	−0.0852499	+	0.538247i
$58$	−6.15016	+	0.322316i	−0.807555	+	0.0423222i
$59$	−3.67061	−	4.07663i	−0.477873	−	0.530732i	0.455214	−	0.890382i	$-0.349563\pi$
$59$	−3.67061	−	4.07663i	−0.477873	−	0.530732i	−0.933087	+	0.359650i	$0.882896\pi$
$60$	−2.30366	−	0.365032i	−0.297401	−	0.0471255i
$61$	−1.83333	−	0.192691i	−0.234734	−	0.0246715i	−0.0135688	−	0.999908i	$-0.504319\pi$
$61$	−1.83333	−	0.192691i	−0.234734	−	0.0246715i	−0.221165	+	0.975236i	$0.570986\pi$
$62$	4.38024	−	2.23184i	0.556291	−	0.283444i
$63$	2.63630	−	4.31737i	0.332142	−	0.543938i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−0.498467	−	0.0261593i	−0.0618273	−	0.00324467i
$66$	−1.35146	−	3.18461i	−0.166354	−	0.391998i
$67$	−0.133324	−	0.497574i	−0.0162882	−	0.0607883i	0.957303	−	0.289085i	$-0.0933510\pi$
$67$	−0.133324	−	0.497574i	−0.0162882	−	0.0607883i	−0.973592	+	0.228297i	$0.926684\pi$
$68$	−3.37203	+	1.29440i	−0.408919	+	0.156969i
$69$	−0.589247	−	1.81352i	−0.0709370	−	0.218322i
$70$	−1.98326	−	5.57375i	−0.237044	−	0.666191i
$71$	−1.54572	−	1.12303i	−0.183443	−	0.133279i	0.492274	−	0.870440i	$-0.336166\pi$
$71$	−1.54572	−	1.12303i	−0.183443	−	0.133279i	−0.675717	+	0.737161i	$0.736166\pi$
$72$	−1.20325	−	1.48589i	−0.141804	−	0.175114i
$73$	−13.1903	−	0.691276i	−1.54381	−	0.0809077i	−0.738701	−	0.674034i	$-0.764560\pi$
$73$	−13.1903	−	0.691276i	−1.54381	−	0.0809077i	−0.805110	+	0.593126i	$0.797894\pi$
$74$	−0.180512	+	0.849243i	−0.0209841	+	0.0987224i
$75$	−3.68837	+	3.68732i	−0.425897	+	0.425775i
$76$			3.94440i			0.452454i
$77$	5.45225	−	6.87553i	0.621342	−	0.783540i
$78$	0.164646	+	0.164646i	0.0186425	+	0.0186425i
$79$	−5.96218	+	13.3913i	−0.670797	+	1.50664i	0.181397	+	0.983410i	$0.441938\pi$
$79$	−5.96218	+	13.3913i	−0.670797	+	1.50664i	−0.852194	+	0.523226i	$0.824729\pi$
$80$	−2.23607		0.000159995i	−0.250000		1.78880e-5i
$81$	−0.262050	−	0.291036i	−0.0291167	−	0.0323374i
$82$	9.72574	−	7.87575i	1.07403	−	0.869731i
$83$	−6.12892	+	0.970725i	−0.672736	+	0.106551i	−0.483451	−	0.875371i	$-0.660617\pi$
$83$	−6.12892	+	0.970725i	−0.672736	+	0.106551i	−0.189285	+	0.981922i	$0.560617\pi$
$84$	−1.05207	+	2.55133i	−0.114790	+	0.278373i
$85$	−2.09092	+	7.80118i	−0.226792	+	0.846157i
$86$	−11.5235	−	5.13059i	−1.24261	−	0.553245i
$87$	6.20502	−	1.66263i	0.665249	−	0.178253i
$88$	−1.75730	−	2.81281i	−0.187329	−	0.299846i
$89$	−3.16453	−	5.48113i	−0.335440	−	0.580999i	0.648129	−	0.761530i	$-0.275552\pi$
$89$	−3.16453	−	5.48113i	−0.335440	−	0.580999i	−0.983569	+	0.180531i	$0.942218\pi$
$90$	−4.26948	+	0.223448i	−0.450043	+	0.0235535i
$91$	−0.166844	+	0.566550i	−0.0174900	+	0.0593906i
$92$	−0.829935	−	1.62884i	−0.0865267	−	0.169818i
$93$	−3.98508	+	3.22706i	−0.413234	+	0.334630i
$94$	4.95351	−	2.20545i	0.510916	−	0.227474i
$95$	7.13512	+	5.18475i	0.732048	+	0.531944i
$96$	0.775160	+	0.697957i	0.0791144	+	0.0712350i
$97$	−0.105332	−	0.0166830i	−0.0106949	−	0.00169390i	0.151085	−	0.988521i	$-0.451723\pi$
$97$	−0.105332	−	0.0166830i	−0.0106949	−	0.00169390i	−0.161780	+	0.986827i	$0.551723\pi$
$98$	−6.95930	+	0.753741i	−0.702996	+	0.0761393i
$99$	−3.63679	−	5.19483i	−0.365511	−	0.522100i
$100$	−2.93951	+	4.04466i	−0.293951	+	0.404466i
$101$	−8.74720	+	0.919367i	−0.870379	+	0.0914805i	−0.529179	−	0.848510i	$-0.677500\pi$
$101$	−8.74720	+	0.919367i	−0.870379	+	0.0914805i	−0.341200	+	0.939991i	$0.610833\pi$
$102$	3.15972	−	2.05195i	0.312859	−	0.203173i
$103$	0.382980	−	0.589737i	0.0377361	−	0.0581085i	−0.819299	−	0.573366i	$-0.805637\pi$
$103$	0.382980	−	0.589737i	0.0377361	−	0.0581085i	0.857035	+	0.515258i	$0.172304\pi$
$104$	0.180595	+	0.131210i	0.0177088	+	0.0128662i
$105$	3.23226	+	5.25672i	0.315436	+	0.513003i
$106$	−3.69452	+	11.3706i	−0.358843	+	1.10441i
$107$	−0.891342	−	17.0078i	−0.0861693	−	1.64421i	−0.610011	−	0.792393i	$-0.708835\pi$
$107$	−0.891342	−	17.0078i	−0.0861693	−	1.64421i	0.523842	−	0.851816i	$-0.324498\pi$
$108$	3.98178	+	3.22438i	0.383147	+	0.310266i
$109$	8.57110	+	4.94853i	0.820962	+	0.473983i	0.850748	−	0.525573i	$-0.176149\pi$
$109$	8.57110	+	4.94853i	0.820962	+	0.473983i	−0.0297858	+	0.999556i	$0.509483\pi$
$110$	−7.39805	−	0.518492i	−0.705377	−	0.0494362i
$111$		−	0.905618i		−	0.0859575i
$112$	−0.613564	+	2.57362i	−0.0579764	+	0.243185i
$113$	2.90898	−	5.70919i	0.273654	−	0.537076i	−0.712749	−	0.701419i	$-0.752550\pi$
$113$	2.90898	−	5.70919i	0.273654	−	0.537076i	0.986403	+	0.164343i	$0.0525504\pi$
$114$	−0.855417	−	4.02442i	−0.0801172	−	0.376922i
$115$	−4.03736	−	0.639751i	−0.376486	−	0.0596571i
$116$	5.62616	−	2.50493i	0.522376	−	0.232577i
$117$	0.357952	+	0.232457i	0.0330926	+	0.0214906i
$118$	4.88775	+	2.49043i	0.449953	+	0.229263i
$119$	8.40544	+	4.54656i	0.770525	+	0.416783i
$120$	2.28147	−	0.484770i	0.208268	−	0.0442532i
$121$	−5.16252	−	9.71331i	−0.469320	−	0.883028i
$122$	1.78061	−	0.477114i	0.161209	−	0.0431959i
$123$	−8.21504	+	10.1447i	−0.740725	+	0.914720i
$124$	−3.28948	+	3.65334i	−0.295404	+	0.328080i
$125$	3.45263	+	10.6339i	0.308813	+	0.951123i
$126$	−0.913986	+	4.97538i	−0.0814243	+	0.443242i
$127$	−13.0945	+	2.07396i	−1.16195	+	0.184035i	−0.707483	−	0.706730i	$-0.750170\pi$
$127$	−13.0945	+	2.07396i	−1.16195	+	0.184035i	−0.454465	+	0.890765i	$0.650170\pi$
$128$	0.838671	+	0.544639i	0.0741287	+	0.0481397i
$129$	12.8699	+	2.73559i	1.13313	+	0.240855i
$130$	0.474734	−	0.154213i	0.0416369	−	0.0135254i
$131$	13.1134	−	7.57101i	1.14572	−	0.661482i	0.197880	−	0.980226i	$-0.436594\pi$
$131$	13.1134	−	7.57101i	1.14572	−	0.661482i	0.947841	+	0.318744i	$0.103261\pi$
$132$	2.40296	+	2.48877i	0.209151	+	0.216619i
$133$	7.92479	−	6.79014i	0.687166	−	0.588779i
$134$	0.302784	+	0.416746i	0.0261565	+	0.0360014i
$135$	11.0665	−	2.96442i	0.952456	−	0.255137i
$136$	2.68419	−	2.41686i	0.230168	−	0.207244i
$137$	−0.0880636	+	0.229414i	−0.00752378	+	0.0196001i	−0.937291	−	0.348548i	$-0.886675\pi$
$137$	−0.0880636	+	0.229414i	−0.00752378	+	0.0196001i	0.929767	+	0.368148i	$0.120008\pi$
$138$	1.20002	+	1.48190i	0.102152	+	0.126147i
$139$	−0.261807	+	0.805759i	−0.0222062	+	0.0683436i	−0.961546	−	0.274646i	$-0.911439\pi$
$139$	−0.261807	+	0.805759i	−0.0222062	+	0.0683436i	0.939339	+	0.342989i	$0.111439\pi$
$140$	3.84898	+	4.49281i	0.325298	+	0.379712i
$141$	−4.57571	+	3.32445i	−0.385344	+	0.279969i
$142$	1.84551	+	0.494503i	0.154872	+	0.0414978i
$143$	0.567111	+	0.475945i	0.0474242	+	0.0398006i
$144$	1.65583	+	0.955991i	0.137985	+	0.0796660i
$145$	2.86413	−	13.4699i	0.237853	−	1.11862i
$146$	12.5620	−	4.08163i	1.03964	−	0.337798i
$147$	6.93702	−	2.27829i	0.572156	−	0.187910i
$148$	−0.135819	−	0.857526i	−0.0111642	−	0.0704882i
$149$	−21.5183	−	2.26167i	−1.76285	−	0.185283i	−0.833013	−	0.553254i	$-0.813386\pi$
$149$	−21.5183	−	2.26167i	−1.76285	−	0.185283i	−0.929837	+	0.367971i	$0.880053\pi$
$150$	2.12198	−	4.76420i	0.173259	−	0.388996i
$151$	−5.54197	−	1.17798i	−0.450999	−	0.0958629i	−0.0231884	−	0.999731i	$-0.507382\pi$
$151$	−5.54197	−	1.17798i	−0.450999	−	0.0958629i	−0.427811	+	0.903868i	$0.640715\pi$
$152$	−1.41355	−	3.68242i	−0.114654	−	0.298683i
$153$	4.88325	−	4.88325i	0.394787	−	0.394787i
$154$	−2.62615	+	8.37277i	−0.211621	+	0.674697i
$155$	2.28473	+	10.7526i	0.183514	+	0.863668i
$156$	−0.212714	−	0.0947066i	−0.0170308	−	0.00758259i
$157$	−11.7025	−	18.0203i	−0.933963	−	1.43818i	−0.898583	−	0.438803i	$-0.855403\pi$
$157$	−11.7025	−	18.0203i	−0.933963	−	1.43818i	−0.0353795	−	0.999374i	$-0.511264\pi$
$158$	0.767170	−	14.6385i	0.0610328	−	1.16458i
$159$	1.30355	−	12.4025i	0.103378	−	0.983579i
$160$	2.08761	−	0.801186i	0.165040	−	0.0633393i
$161$	−1.84384	+	4.47142i	−0.145315	+	0.352398i
$162$	0.348943	+	0.177795i	0.0274155	+	0.0139689i
$163$	0.0201416	+	0.0524708i	0.00157762	+	0.00410983i	0.934367	−	0.356312i	$-0.115966\pi$
$163$	0.0201416	+	0.0524708i	0.00157762	+	0.00410983i	−0.932789	+	0.360422i	$0.882633\pi$
$164$	−6.25735	+	10.8380i	−0.488617	+	0.846309i
$165$	7.66058	−	1.07540i	0.596375	−	0.0837194i
$166$	5.37396	−	3.10266i	0.417100	−	0.240813i
$167$	7.85371	+	1.24391i	0.607738	+	0.0962563i	0.452716	−	0.891655i	$-0.350455\pi$
$167$	7.85371	+	1.24391i	0.607738	+	0.0962563i	0.155022	+	0.987911i	$0.450455\pi$
$168$	0.0678732	−	2.75890i	0.00523653	−	0.212854i
$169$	12.3163	+	4.00182i	0.947411	+	0.307832i
$170$	−0.843653	−	8.03235i	−0.0647052	−	0.616053i
$171$	−3.06746	−	6.88962i	−0.234574	−	0.526863i
$172$	12.5967	+	0.660167i	0.960492	+	0.0503373i
$173$	0.365330	+	6.97091i	0.0277755	+	0.529989i	0.976716	+	0.214535i	$0.0688235\pi$
$173$	0.365330	+	6.97091i	0.0277755	+	0.529989i	−0.948941	+	0.315454i	$0.897843\pi$
$174$	−5.19706	+	3.77588i	−0.393988	+	0.286249i
$175$	13.1865	−	1.05691i	0.996803	−	0.0798948i
$176$	2.64860	+	1.99622i	0.199646	+	0.150471i
$177$	−5.52700	−	1.48095i	−0.415435	−	0.111315i
$178$	4.91861	+	3.98301i	0.368665	+	0.298539i
$179$	−0.137145	+	0.645218i	−0.0102507	+	0.0482259i	−0.982976	−	0.183736i	$-0.941181\pi$
$179$	−0.137145	+	0.645218i	−0.0102507	+	0.0482259i	0.972725	+	0.231961i	$0.0745143\pi$
$180$	3.90583	−	1.73865i	0.291123	−	0.129591i
$181$	−6.09634	+	8.39089i	−0.453137	+	0.623690i	−0.973068	−	0.230519i	$-0.925958\pi$
$181$	−6.09634	+	8.39089i	−0.453137	+	0.623690i	0.519931	+	0.854208i	$0.325958\pi$
$182$	−0.0472706	−	0.588711i	−0.00350393	−	0.0436382i
$183$	−1.71327	+	0.872952i	−0.126648	+	0.0645305i
$184$	1.35853	+	1.22323i	0.100152	+	0.0901777i
$185$	−1.72973	−	0.881496i	−0.127172	−	0.0648088i
$186$	2.56392	−	4.44084i	0.187996	−	0.325618i
$187$	9.44056	−	7.37447i	0.690362	−	0.539275i
$188$	−3.83414	+	3.83414i	−0.279633	+	0.279633i
$189$	−0.376304	−	13.5505i	−0.0273721	−	0.985656i
$190$	−8.51926	−	2.28338i	−0.618052	−	0.165654i
$191$	18.4625	−	3.92432i	1.33590	−	0.283954i	0.516061	−	0.856552i	$-0.327398\pi$
$191$	18.4625	−	3.92432i	1.33590	−	0.283954i	0.819836	+	0.572598i	$0.194065\pi$
$192$	−0.973800	−	0.373807i	−0.0702779	−	0.0269772i
$193$	13.0239	+	4.99940i	0.937479	+	0.359864i	0.778662	−	0.627444i	$-0.215899\pi$
$193$	13.0239	+	4.99940i	0.937479	+	0.359864i	0.158817	+	0.987308i	$0.449232\pi$
$194$	0.104315	−	0.0221728i	0.00748937	−	0.00159191i
$195$	−0.450921	+	0.260296i	−0.0322911	+	0.0186402i
$196$	6.22695	−	3.19767i	0.444782	−	0.228405i
$197$	17.8445	−	17.8445i	1.27137	−	1.27137i	0.325999	−	0.945370i	$-0.394299\pi$
$197$	17.8445	−	17.8445i	1.27137	−	1.27137i	0.945370	−	0.325999i	$-0.105701\pi$
$198$	5.25690	+	3.54648i	0.373591	+	0.252037i
$199$	−3.32097	+	5.75208i	−0.235417	+	0.407754i	−0.959394	−	0.282070i	$-0.908979\pi$
$199$	−3.32097	+	5.75208i	−0.235417	+	0.407754i	0.723977	+	0.689824i	$0.242312\pi$
$200$	1.29479	−	4.82944i	0.0915552	−	0.341493i
$201$	−0.399305	−	0.359536i	−0.0281648	−	0.0253597i
$202$	7.83674	−	3.99302i	0.551391	−	0.280948i
$203$	−14.7179	−	6.99151i	−1.03300	−	0.490707i
$204$	−2.21450	+	3.04800i	−0.155046	+	0.213403i
$205$	11.3802	+	25.5652i	0.794825	+	1.78555i
$206$	−0.146200	+	0.687815i	−0.0101862	+	0.0479223i
$207$	2.71634	+	2.19965i	0.188799	+	0.152886i
$208$	−0.215622	−	0.0577757i	−0.0149507	−	0.00400602i
$209$	−3.82376	−	12.5108i	−0.264495	−	0.865390i
$210$	−4.90142	−	3.74923i	−0.338230	−	0.258721i
$211$	−11.0172	+	8.00444i	−0.758453	+	0.551048i	−0.898435	−	0.439106i	$-0.855295\pi$
$211$	−11.0172	+	8.00444i	−0.758453	+	0.551048i	0.139982	+	0.990154i	$0.455295\pi$
$212$	−0.625714	−	11.9393i	−0.0429742	−	0.819997i
$213$	−1.99019	−	0.104302i	−0.136366	−	0.00714663i
$214$	6.92720	+	15.5587i	0.473534	+	1.06357i
$215$	17.7521	−	21.9188i	1.21068	−	1.49485i
$216$	−4.87283	−	1.58328i	−0.331554	−	0.107728i
$217$	13.0027	+	0.319888i	0.882683	+	0.0217154i
$218$	−9.77520	−	1.54824i	−0.662060	−	0.104860i
$219$	−11.9316	+	6.88873i	−0.806264	+	0.465497i
$220$	7.09249	−	2.16717i	0.478175	−	0.146111i
$221$	−0.403143	+	0.698264i	−0.0271183	+	0.0469703i
$222$	0.324545	+	0.845468i	0.0217820	+	0.0567441i
$223$	16.3063	+	8.30848i	1.09195	+	0.556377i	0.904749	−	0.425944i	$-0.140058\pi$
$223$	16.3063	+	8.30848i	1.09195	+	0.556377i	0.187202	+	0.982321i	$0.440058\pi$
$224$	−0.349493	−	2.62257i	−0.0233515	−	0.175228i
$225$	1.98896	−	9.35072i	0.132597	−	0.623382i
$226$	−0.669774	+	6.37248i	−0.0445527	+	0.423891i
$227$	−0.564438	+	10.7701i	−0.0374631	+	0.714838i	0.913745	+	0.406288i	$0.133177\pi$
$227$	−0.564438	+	10.7701i	−0.0374631	+	0.714838i	−0.951208	+	0.308550i	$0.900156\pi$
$228$	2.24082	+	3.45057i	0.148402	+	0.228519i
$229$	10.2418	+	4.55992i	0.676794	+	0.301328i	0.716200	−	0.697895i	$-0.245880\pi$
$229$	10.2418	+	4.55992i	0.676794	+	0.301328i	−0.0394057	+	0.999223i	$0.512546\pi$
$230$	3.99846	−	0.849601i	0.263651	−	0.0560210i
$231$	0.863630	−	9.11216i	0.0568227	−	0.599536i
$232$	−4.35479	+	4.35479i	−0.285906	+	0.285906i
$233$	−10.0467	−	26.1725i	−0.658180	−	1.71462i	−0.698677	−	0.715437i	$-0.746228\pi$
$233$	−10.0467	−	26.1725i	−0.658180	−	1.71462i	0.0404977	−	0.999180i	$-0.487106\pi$
$234$	−0.417482	−	0.0887385i	−0.0272916	−	0.00580102i
$235$	1.89585	+	11.9755i	0.123672	+	0.781194i
$236$	−5.45559	−	0.573406i	−0.355129	−	0.0373256i
$237$	2.39189	+	15.1018i	0.155370	+	0.980969i
$238$	−9.47649	−	1.23234i	−0.614270	−	0.0798809i
$239$	10.0720	−	3.27259i	0.651504	−	0.211687i	0.0354269	−	0.999372i	$-0.488721\pi$
$239$	10.0720	−	3.27259i	0.651504	−	0.211687i	0.616077	+	0.787686i	$0.288721\pi$
$240$	−1.95621	+	1.27018i	−0.126273	+	0.0819895i
$241$	11.9218	+	6.88304i	0.767949	+	0.443376i	0.832142	−	0.554562i	$-0.187114\pi$
$241$	11.9218	+	6.88304i	0.767949	+	0.443376i	−0.0641934	+	0.997937i	$0.520447\pi$
$242$	8.30057	+	7.21807i	0.533581	+	0.463995i
$243$	−15.2416	−	4.08398i	−0.977750	−	0.261987i
$244$	−1.49136	+	1.08354i	−0.0954748	+	0.0693665i
$245$	2.40073	−	15.4673i	0.153377	−	0.988168i
$246$	4.03386	−	12.4149i	0.257189	−	0.791547i
$247$	0.554118	+	0.684278i	0.0352577	+	0.0435396i
$248$	1.76176	−	4.58953i	0.111872	−	0.291436i
$249$	−4.81011	+	4.33104i	−0.304828	+	0.274469i
$250$	−7.03415	−	8.69027i	−0.444879	−	0.549621i
$251$	10.8796	+	14.9745i	0.686714	+	0.945181i	0.999990	−	0.00448126i	$-0.00142643\pi$
$251$	10.8796	+	14.9745i	0.686714	+	0.945181i	−0.313276	+	0.949662i	$0.601426\pi$
$252$	−0.929737	−	4.97246i	−0.0585679	−	0.313235i
$253$	4.21140	+	4.36178i	0.264768	+	0.274223i
$254$	11.4815	−	6.62886i	0.720415	−	0.415932i
$255$	2.60273	+	8.01234i	0.162989	+	0.501752i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−24.9192	−	16.1827i	−1.55442	−	1.00945i	−0.981864	−	0.189586i	$-0.939285\pi$
$257$	−24.9192	−	16.1827i	−1.55442	−	1.00945i	−0.572555	−	0.819866i	$-0.694048\pi$
$258$	−12.9955	+	2.05828i	−0.809062	+	0.128143i
$259$	−1.48907	+	1.74907i	−0.0925262	+	0.108682i
$260$	−0.387938	+	0.314100i	−0.0240589	+	0.0194796i
$261$	−7.87910	+	8.75063i	−0.487704	+	0.541650i
$262$	−9.52918	+	11.7676i	−0.588715	+	0.727002i
$263$	−12.4718	+	3.34180i	−0.769041	+	0.206064i	−0.621948	−	0.783059i	$-0.713658\pi$
$263$	−12.4718	+	3.34180i	−0.769041	+	0.206064i	−0.147093	+	0.989123i	$0.546992\pi$
$264$	−3.13525	−	1.46232i	−0.192961	−	0.0899995i
$265$	−22.4198	−	14.5619i	−1.37724	−	0.894529i
$266$	−4.96506	+	9.17913i	−0.304427	+	0.562808i
$267$	−5.88218	−	2.99712i	−0.359984	−	0.183421i
$268$	−0.432021	−	0.280558i	−0.0263899	−	0.0171378i
$269$	8.29695	−	3.69404i	0.505874	−	0.225229i	−0.137899	−	0.990446i	$-0.544035\pi$
$269$	8.29695	−	3.69404i	0.505874	−	0.225229i	0.643773	+	0.765217i	$0.277368\pi$
$270$	−9.26915	+	6.73342i	−0.564103	+	0.409783i
$271$	1.46144	+	6.87553i	0.0887761	+	0.417659i	0.999984	+	0.00571133i	$0.00181798\pi$
$271$	1.46144	+	6.87553i	0.0887761	+	0.417659i	−0.911208	+	0.411948i	$0.864849\pi$
$272$	−1.63978	+	3.21826i	−0.0994265	+	0.195136i
$273$	0.175903	+	0.590403i	0.0106461	+	0.0357328i
$274$		−	0.245735i		−	0.0148454i
$275$	5.40253	−	15.6784i	0.325785	−	0.945444i
$276$	−1.65138	−	0.953422i	−0.0994011	−	0.0573892i
$277$	6.61215	+	5.35442i	0.397286	+	0.321716i	0.807058	−	0.590472i	$-0.201058\pi$
$277$	6.61215	+	5.35442i	0.397286	+	0.321716i	−0.409772	+	0.912188i	$0.634392\pi$
$278$	−0.0443403	−	0.846064i	−0.00265936	−	0.0507436i
$279$	2.90458	−	8.93938i	0.173893	−	0.535186i
$280$	−5.20341	−	2.81505i	−0.310963	−	0.168231i
$281$	1.99550	+	1.44982i	0.119042	+	0.0864889i	0.645713	−	0.763580i	$-0.276560\pi$
$281$	1.99550	+	1.44982i	0.119042	+	0.0864889i	−0.526671	+	0.850069i	$0.676560\pi$
$282$	3.08042	−	4.74343i	0.183436	−	0.282467i
$283$	−11.0703	+	7.18912i	−0.658059	+	0.427349i	−0.830004	−	0.557758i	$-0.811662\pi$
$283$	−11.0703	+	7.18912i	−0.658059	+	0.427349i	0.171944	+	0.985107i	$0.444995\pi$
$284$	−1.90015	+	0.199714i	−0.112753	+	0.0118508i
$285$	9.18728	+	0.482144i	0.544207	+	0.0285597i
$286$	−0.700007	−	0.241099i	−0.0413923	−	0.0142565i
$287$	32.5467	−	6.08550i	1.92117	−	0.359215i
$288$	−1.88844	−	0.299100i	−0.111278	−	0.0176246i
$289$	−2.93833	−	2.64569i	−0.172843	−	0.155629i
$290$	2.15329	+	13.6017i	0.126446	+	0.798717i
$291$	−0.101622	+	0.0452452i	−0.00595721	+	0.00265232i
$292$	−10.2649	+	8.31233i	−0.600706	+	0.486442i
$293$	−0.207278	−	0.406807i	−0.0121093	−	0.0237659i	0.884873	−	0.465833i	$-0.154245\pi$
$293$	−0.207278	−	0.406807i	−0.0121093	−	0.0237659i	−0.896982	+	0.442067i	$0.854245\pi$
$294$	−5.65980	+	4.61297i	−0.330086	+	0.269034i
$295$	−8.20839	+	9.11503i	−0.477911	+	0.530698i
$296$	0.434108	+	0.751896i	0.0252320	+	0.0437031i
$297$	−15.7551	−	6.36706i	−0.914205	−	0.369454i
$298$	20.8996	−	5.60003i	1.21068	−	0.324401i
$299$	−0.372800	−	0.165981i	−0.0215596	−	0.00959895i
$300$	−0.273698	+	5.20822i	−0.0158020	+	0.300696i
$301$	−20.3584	−	26.4448i	−1.17344	−	1.52425i
$302$	5.59603	−	0.886324i	0.322015	−	0.0510022i
$303$	−7.12976	+	5.77357i	−0.409594	+	0.331683i
$304$	2.63932	+	2.93126i	0.151375	+	0.168119i
$305$	−0.000294940		4.12203i	−1.68882e−5		0.236027i
$306$	−2.80891	+	6.30891i	−0.160575	+	0.360656i
$307$	22.4571	+	22.4571i	1.28170	+	1.28170i	0.939703	+	0.341992i	$0.111102\pi$
$307$	22.4571	+	22.4571i	1.28170	+	1.28170i	0.341992	+	0.939703i	$0.388898\pi$
$308$	−0.548815	−	8.75779i	−0.0312716	−	0.499021i
$309$		−	0.733474i		−	0.0417259i
$310$	−5.98636	−	9.21963i	−0.340002	−	0.523640i
$311$	−2.34282	+	11.0221i	−0.132849	+	0.625005i	0.860460	+	0.509518i	$0.170176\pi$
$311$	−2.34282	+	11.0221i	−0.132849	+	0.625005i	−0.993309	+	0.115487i	$0.963157\pi$
$312$	0.232526	+	0.0121862i	0.0131642	+	0.000689906i
$313$	4.43332	+	5.47469i	0.250586	+	0.309448i	0.886881	−	0.461998i	$-0.152867\pi$
$313$	4.43332	+	5.47469i	0.250586	+	0.309448i	−0.636295	+	0.771446i	$0.719534\pi$
$314$	17.3831	+	12.6296i	0.980988	+	0.712729i
$315$	−10.2169	−	4.85426i	−0.575657	−	0.273507i
$316$	4.52975	+	13.9411i	0.254818	+	0.784250i
$317$	−23.3180	+	8.95095i	−1.30967	+	0.502735i	−0.910260	−	0.414037i	$-0.864118\pi$
$317$	−23.3180	+	8.95095i	−1.30967	+	0.502735i	−0.399410	+	0.916772i	$0.630785\pi$
$318$	3.22767	+	12.0458i	0.180999	+	0.675497i
$319$	−15.4167	+	13.3992i	−0.863168	+	0.750210i
$320$	−1.66183	+	1.49610i	−0.0928991	+	0.0836347i
$321$	−10.4419	−	14.3721i	−0.582812	−	0.802172i
$322$	0.118954	−	4.83520i	0.00662903	−	0.269455i
$323$	12.6941	−	6.46797i	0.706319	−	0.359887i
$324$	−0.389482	−	0.0409363i	−0.0216379	−	0.00227424i
$325$	0.0582548	+	1.11462i	0.00323139	+	0.0618280i
$326$	−0.0376077	−	0.0417676i	−0.00208290	−	0.00231329i
$327$	10.3093	−	0.540286i	0.570104	−	0.0298779i
$328$	1.95773	−	12.3606i	0.108097	−	0.682501i
$329$	14.3036	+	1.10293i	0.788582	+	0.0608066i
$330$	−6.76638	+	3.74927i	−0.372477	+	0.206391i
$331$	3.89499	+	6.74631i	0.214088	+	0.370811i	0.952990	−	0.303002i	$-0.0979888\pi$
$331$	3.89499	+	6.74631i	0.214088	+	0.370811i	−0.738902	+	0.673813i	$0.764655\pi$
$332$	−3.90513	+	4.82243i	−0.214322	+	0.264665i
$333$	0.904108	+	1.39220i	0.0495448	+	0.0762923i
$334$	−7.77785	+	1.65323i	−0.425585	+	0.0904608i
$335$	−1.07538	+	0.412712i	−0.0587543	+	0.0225489i
$336$	0.925335	+	2.59998i	0.0504812	+	0.141840i
$337$	−6.66701	−	13.0847i	−0.363175	−	0.712772i	0.635041	−	0.772479i	$-0.280983\pi$
$337$	−6.66701	−	13.0847i	−0.363175	−	0.712772i	−0.998216	+	0.0597071i	$0.980983\pi$
$338$	−12.9324	+	0.677759i	−0.703431	+	0.0368653i
$339$	−0.698629	−	6.64701i	−0.0379443	−	0.361016i
$340$	3.66615	+	7.19651i	0.198825	+	0.390285i
$341$	6.89194	−	14.7765i	0.373219	−	0.800192i
$342$	5.33274	+	5.33274i	0.288361	+	0.288361i
$343$	−17.1440	−	7.00604i	−0.925687	−	0.378291i
$344$	−11.9966	+	3.89795i	−0.646816	+	0.210163i
$345$	−3.89533	+	1.73398i	−0.209717	+	0.0933542i
$346$	−2.83922	−	6.37698i	−0.152637	−	0.342829i
$347$	5.13461	−	13.3761i	0.275640	−	0.718068i	−0.723961	−	0.689841i	$-0.757681\pi$
$347$	5.13461	−	13.3761i	0.275640	−	0.718068i	0.999602	−	0.0282269i	$-0.00898609\pi$
$348$	3.49871	−	5.38755i	0.187551	−	0.288803i
$349$	−6.18158	−	19.0249i	−0.330892	−	1.01838i	−0.968710	−	0.248194i	$-0.920163\pi$
$349$	−6.18158	−	19.0249i	−0.330892	−	1.01838i	0.637818	−	0.770187i	$-0.279837\pi$
$350$	−11.9319	+	5.71232i	−0.637785	+	0.305336i
$351$	1.14373			0.0610478
$352$	−3.18807	−	0.914459i	−0.169924	−	0.0487408i
$353$	−1.73519	−	6.47581i	−0.0923547	−	0.344673i	0.904250	−	0.427003i	$-0.140430\pi$
$353$	−1.73519	−	6.47581i	−0.0923547	−	0.344673i	−0.996605	+	0.0823301i	$0.973764\pi$
$354$	5.69062	−	0.598109i	0.302453	−	0.0317891i
$355$	−2.13640	+	3.69974i	−0.113388	+	0.196362i
$356$	−6.01930	−	1.95579i	−0.319022	−	0.103657i
$357$	9.93600	−	0.797811i	0.525869	−	0.0422246i
$358$	−0.103189	−	0.651511i	−0.00545372	−	0.0344335i
$359$	4.89279	+	23.0188i	0.258232	+	1.21488i	0.895788	+	0.444481i	$0.146612\pi$
$359$	4.89279	+	23.0188i	0.258232	+	1.21488i	−0.637557	+	0.770403i	$0.720055\pi$
$360$	−3.02333	+	3.02289i	−0.159343	+	0.159321i
$361$	0.359754	+	3.42284i	0.0189344	+	0.180149i
$362$	2.68440	−	10.0183i	0.141089	−	0.526550i
$363$	−10.0343	−	5.56437i	−0.526666	−	0.292054i
$364$	0.255106	+	0.532669i	0.0133712	+	0.0279195i
$365$	1.54363	+	29.4946i	0.0807972	+	1.54382i
$366$	1.28663	−	1.42895i	0.0672534	−	0.0746924i
$367$	−0.870252	+	16.6054i	−0.0454268	+	0.866795i	0.876969	+	0.480548i	$0.159562\pi$
$367$	−0.870252	+	16.6054i	−0.0454268	+	0.866795i	−0.922395	+	0.386247i	$0.873771\pi$
$368$	−1.70667	−	0.655128i	−0.0889662	−	0.0341509i
$369$	2.50114	−	23.7968i	0.130204	−	1.23881i
$370$	1.93074	+	0.203068i	0.100374	+	0.0105570i
$371$	−22.9104	+	21.8102i	−1.18945	+	1.13233i
$372$	−0.802171	+	5.06471i	−0.0415906	+	0.262593i
$373$	0.864746	−	3.22727i	0.0447748	−	0.167102i	−0.939918	−	0.341400i	$-0.889099\pi$
$373$	0.864746	−	3.22727i	0.0447748	−	0.167102i	0.984693	+	0.174298i	$0.0557656\pi$
$374$	−6.17075	+	10.2679i	−0.319082	+	0.530938i
$375$	9.06150	+	7.34108i	0.467934	+	0.379092i
$376$	2.20545	−	4.95351i	0.113737	−	0.255458i
$377$	0.624134	−	1.22493i	0.0321445	−	0.0630872i
$378$	5.20739	+	12.5157i	0.267839	+	0.643736i
$379$	−14.9490	+	20.5755i	−0.767878	+	1.05689i	0.228640	+	0.973511i	$0.426572\pi$
$379$	−14.9490	+	20.5755i	−0.767878	+	1.05689i	−0.996518	+	0.0833820i	$0.973428\pi$
$380$	8.77170	−	0.921308i	0.449979	−	0.0472621i
$381$	−10.2769	+	9.25332i	−0.526499	+	0.474062i
$382$	−15.8298	+	10.2800i	−0.809925	+	0.525972i
$383$	0.588512	−	0.225909i	0.0300716	−	0.0115434i	−0.343286	−	0.939231i	$-0.611540\pi$
$383$	0.588512	−	0.225909i	0.0300716	−	0.0115434i	0.373357	+	0.927688i	$0.378207\pi$
$384$	1.04308			0.0532295
$385$	−16.5636	−	10.5190i	−0.844157	−	0.536096i
$386$	−13.9505			−0.710060
$387$	−22.5159	+	8.64305i	−1.14455	+	0.439351i
$388$	−0.0894402	+	0.0580832i	−0.00454064	+	0.00294873i
$389$	−9.04699	+	8.14594i	−0.458700	+	0.413016i	−0.865817	−	0.500360i	$-0.833201\pi$
$389$	−9.04699	+	8.14594i	−0.458700	+	0.413016i	0.407117	+	0.913376i	$0.366534\pi$
$390$	0.327689	−	0.404603i	0.0165932	−	0.0204879i
$391$	−3.88111	+	5.34189i	−0.196276	+	0.270151i
$392$	−4.66742	+	5.21682i	−0.235740	+	0.263489i
$393$	7.17048	−	14.0729i	0.361703	−	0.709882i
$394$	−10.2644	+	23.0542i	−0.517112	+	1.16145i
$395$	31.1726	+	10.1311i	1.56846	+	0.509749i
$396$	−6.17868	−	1.42702i	−0.310490	−	0.0717104i
$397$	−1.16913	+	4.36324i	−0.0586768	+	0.218985i	−0.989038	−	0.147659i	$-0.952826\pi$
$397$	−1.16913	+	4.36324i	−0.0586768	+	0.218985i	0.930362	+	0.366643i	$0.119493\pi$
$398$	1.03903	−	6.56016i	0.0520817	−	0.328831i
$399$	3.07512	−	10.4421i	0.153948	−	0.522759i
$400$	0.521931	+	4.97268i	0.0260965	+	0.248634i
$401$	−4.09982	+	39.0072i	−0.204735	+	1.94792i	0.0988062	+	0.995107i	$0.468498\pi$
$401$	−4.09982	+	39.0072i	−0.204735	+	1.94792i	−0.303541	+	0.952818i	$0.598169\pi$
$402$	0.501630	+	0.192558i	0.0250190	+	0.00960390i
$403$	−0.0574336	+	1.09590i	−0.00286097	+	0.0545906i
$404$	−5.88526	+	6.53624i	−0.292802	+	0.325190i
$405$	−0.586009	+	0.650735i	−0.0291190	+	0.0323353i
$406$	16.2459	+	1.25270i	0.806270	+	0.0621705i
$407$	1.26209	+	2.58823i	0.0625593	+	0.128294i
$408$	0.975111	−	3.63916i	0.0482752	−	0.180165i
$409$	−3.57124	−	33.9781i	−0.176587	−	1.68011i	−0.620630	−	0.784104i	$-0.713123\pi$
$409$	−3.57124	−	33.9781i	−0.176587	−	1.68011i	0.444043	−	0.896005i	$-0.353544\pi$
$410$	−19.7860	−	19.7889i	−0.977163	−	0.977303i
$411$	0.0532923	+	0.250720i	0.00262871	+	0.0123671i
$412$	−0.110002	−	0.694524i	−0.00541940	−	0.0342167i
$413$	8.23955	+	11.9481i	0.405442	+	0.587925i
$414$	−3.32420	−	1.08010i	−0.163376	−	0.0530840i
$415$	3.59029	+	13.4030i	0.176240	+	0.657926i
$416$	0.222005	−	0.0233337i	0.0108847	−	0.00114403i
$417$	0.228725	+	0.853612i	0.0112007	+	0.0418016i
$418$	8.05326	+	10.3095i	0.393898	+	0.504256i
$419$	−18.9733			−0.926904			−0.463452	−	0.886122i	$-0.653389\pi$
$419$	−18.9733			−0.926904			−0.463452	+	0.886122i	$0.653389\pi$
$420$	5.91947	+	1.74370i	0.288841	+	0.0850837i
$421$	−3.27414	−	10.0768i	−0.159572	−	0.491111i	0.839024	−	0.544095i	$-0.183127\pi$
$421$	−3.27414	−	10.0768i	−0.159572	−	0.491111i	−0.998595	+	0.0529839i	$0.983127\pi$
$422$	7.41688	−	11.4210i	0.361048	−	0.555965i
$423$	3.71532	−	9.67874i	0.180645	−	0.470596i
$424$	4.86283	+	10.9221i	0.236160	+	0.530424i
$425$	17.8369	+	2.82771i	0.865218	+	0.137164i
$426$	1.89538	−	0.615848i	0.0918317	−	0.0298379i
$427$	4.74429	+	1.13106i	0.229592	+	0.0547359i
$428$	−12.0429	−	12.0429i	−0.582113	−	0.582113i
$429$	0.766495	+	0.0941805i	0.0370067	+	0.00454708i
$430$	−8.71800	+	26.8247i	−0.420419	+	1.29360i
$431$	−1.32430	−	12.5999i	−0.0637893	−	0.606914i	−0.978989	−	0.203914i	$-0.934634\pi$
$431$	−1.32430	−	12.5999i	−0.0637893	−	0.606914i	0.915200	−	0.403001i	$-0.132033\pi$
$432$	5.11657	−	0.268148i	0.246171	−	0.0129013i
$433$	4.47130	+	8.77543i	0.214877	+	0.421720i	0.973135	−	0.230234i	$-0.0739493\pi$
$433$	4.47130	+	8.77543i	0.214877	+	0.421720i	−0.758258	+	0.651954i	$0.773949\pi$
$434$	−12.2537	+	4.36112i	−0.588198	+	0.209340i
$435$	−5.14675	−	13.4106i	−0.246768	−	0.642989i
$436$	9.68078	−	2.05771i	0.463625	−	0.0985466i
$437$	3.92724	+	6.04742i	0.187865	+	0.289287i
$438$	8.67043	−	10.7071i	0.414289	−	0.511605i
$439$	−12.3450	−	21.3822i	−0.589195	−	1.02051i	−0.994338	−	0.106262i	$-0.966112\pi$
$439$	−12.3450	−	21.3822i	−0.589195	−	1.02051i	0.405144	−	0.914253i	$-0.367221\pi$
$440$	−5.84476	+	4.56495i	−0.278638	+	0.217625i
$441$	−8.38977	+	10.4278i	−0.399513	+	0.496564i
$442$	0.126131	−	0.796359i	0.00599943	−	0.0378789i
$443$	−3.94182	+	0.206582i	−0.187282	+	0.00981501i	−0.145746	−	0.989322i	$-0.546558\pi$
$443$	−3.94182	+	0.206582i	−0.187282	+	0.00981501i	−0.0415354	+	0.999137i	$0.513225\pi$
$444$	−0.605977	−	0.673006i	−0.0287584	−	0.0319394i
$445$	−11.4500	+	8.31765i	−0.542781	+	0.394294i
$446$	−18.2008	−	1.91298i	−0.861831	−	0.0905820i
$447$	−20.1091	+	10.2461i	−0.951129	+	0.484624i
$448$	1.26612	+	2.32313i	0.0598187	+	0.109758i
$449$	−1.88947	−	2.60063i	−0.0891696	−	0.122731i	0.762101	−	0.647458i	$-0.224168\pi$
$449$	−1.88947	−	2.60063i	−0.0891696	−	0.122731i	−0.851271	+	0.524726i	$0.824168\pi$
$450$	1.49415	+	9.44243i	0.0704349	+	0.445120i
$451$	9.34041	−	40.4419i	0.439823	−	1.90434i
$452$	−1.65840	−	6.18924i	−0.0780047	−	0.291118i
$453$	−5.51734	+	2.11791i	−0.259227	+	0.0995080i
$454$	−3.33272	−	10.2571i	−0.156412	−	0.481387i
$455$	1.29888	+	0.238703i	0.0608926	+	0.0111906i
$456$	−3.32856	−	2.41834i	−0.155874	−	0.113249i
$457$	−11.0884	−	13.6930i	−0.518691	−	0.640530i	0.448741	−	0.893662i	$-0.351873\pi$
$457$	−11.0884	−	13.6930i	−0.518691	−	0.640530i	−0.967432	+	0.253132i	$0.918539\pi$
$458$	−11.1956	−	0.586738i	−0.523138	−	0.0274165i
$459$	3.84763	−	18.1017i	0.179592	−	0.844915i
$460$	−3.42842	+	2.22609i	−0.159851	+	0.103792i
$461$		−	17.8512i		−	0.831415i	−0.909498	−	0.415708i	$-0.863534\pi$
$461$		−	17.8512i		−	0.831415i	0.909498	−	0.415708i	$-0.136466\pi$
$462$	2.45924	+	8.81643i	0.114414	+	0.410178i
$463$	20.1385	+	20.1385i	0.935917	+	0.935917i	0.998067	−	0.0621496i	$-0.0197956\pi$
$463$	20.1385	+	20.1385i	0.935917	+	0.935917i	−0.0621496	+	0.998067i	$0.519796\pi$
$464$	2.50493	−	5.62616i	0.116288	−	0.261188i
$465$	8.10725	+	8.10841i	0.375965	+	0.376019i
$466$	18.7588	+	20.8337i	0.868983	+	0.965103i
$467$	−23.5338	+	19.0573i	−1.08901	+	0.881866i	−0.993531	−	0.113566i	$-0.963773\pi$
$467$	−23.5338	+	19.0573i	−1.08901	+	0.881866i	−0.0954827	+	0.995431i	$0.530439\pi$
$468$	0.421554	−	0.0667676i	0.0194863	−	0.00308633i
$469$	0.180033	+	1.35095i	0.00831314	+	0.0623812i
$470$	−6.06156	−	10.5007i	−0.279599	−	0.484359i
$471$	−20.4748	−	9.11595i	−0.943427	−	0.420041i
$472$	5.29873	−	1.41979i	0.243894	−	0.0653511i
$473$	−40.5941	+	10.1176i	−1.86652	+	0.465206i
$474$	−7.64503	−	13.2416i	−0.351148	−	0.608206i
$475$	9.86345	−	17.0784i	0.452566	−	0.783609i
$476$	9.28870	−	2.24558i	0.425747	−	0.102926i
$477$	10.3778	+	20.3676i	0.475168	+	0.932570i
$478$	−8.23024	+	6.66471i	−0.376442	+	0.304837i
$479$	31.2361	−	13.9072i	1.42721	−	0.635437i	0.459659	−	0.888096i	$-0.347972\pi$
$479$	31.2361	−	13.9072i	1.42721	−	0.635437i	0.967555	+	0.252659i	$0.0813050\pi$
$480$	1.37108	−	1.88685i	0.0625812	−	0.0861226i
$481$	−0.144029	−	0.129684i	−0.00656716	−	0.00591309i
$482$	−13.5966	−	2.15349i	−0.619308	−	0.0980888i
$483$	0.927237	+	4.95909i	0.0421908	+	0.225647i
$484$	−10.3360	−	3.76399i	−0.469817	−	0.171091i
$485$	−0.0124974	+	0.238138i	−0.000567477	+	0.0108133i
$486$	15.6928	−	1.64938i	0.711842	−	0.0748176i
$487$	−17.2041	+	11.1725i	−0.779593	+	0.506273i	−0.872034	−	0.489445i	$-0.837200\pi$
$487$	−17.2041	+	11.1725i	−0.779593	+	0.506273i	0.0924416	+	0.995718i	$0.470533\pi$
$488$	1.00400	−	1.54603i	0.0454490	−	0.0699854i
$489$	0.0474287	+	0.0344590i	0.00214480	+	0.00155829i
$490$	3.30170	+	15.3003i	0.149156	+	0.691196i
$491$	3.23142	−	9.94528i	0.145832	−	0.448824i	−0.851285	−	0.524703i	$-0.824176\pi$
$491$	3.23142	−	9.94528i	0.145832	−	0.448824i	0.997117	+	0.0758790i	$0.0241763\pi$
$492$	0.683185	+	13.0359i	0.0308003	+	0.587706i
$493$	−17.2872	−	13.9989i	−0.778576	−	0.630479i
$494$	−0.762537	−	0.440251i	−0.0343082	−	0.0198078i
$495$	−10.7030	+	9.30100i	−0.481063	+	0.418049i
$496$			4.91606i			0.220737i
$497$	3.67228	+	3.47383i	0.164724	+	0.155823i
$498$	2.93852	−	5.76717i	0.131678	−	0.258433i
$499$	−4.37152	−	20.5664i	−0.195696	−	0.920677i	−0.960901	−	0.276891i	$-0.910696\pi$
$499$	−4.37152	−	20.5664i	−0.195696	−	0.920677i	0.765205	−	0.643786i	$-0.222637\pi$
$500$	9.68126	+	5.59225i	0.432959	+	0.250093i
$501$	7.57710	−	3.37354i	0.338520	−	0.150719i
$502$	−15.5234	−	10.0810i	−0.692841	−	0.449936i
$503$	2.71482	+	1.38327i	0.121048	+	0.0616769i	0.513466	−	0.858110i	$-0.328361\pi$
$503$	2.71482	+	1.38327i	0.121048	+	0.0616769i	−0.392418	+	0.919787i	$0.628361\pi$
$504$	2.64995	+	4.30900i	0.118038	+	0.191938i
$505$	4.08764	+	19.2376i	0.181897	+	0.856061i
$506$	−5.49480	−	2.56284i	−0.244274	−	0.113932i
$507$	13.0478	−	3.49615i	0.579473	−	0.155269i
$508$	−8.34335	+	10.3032i	−0.370176	+	0.457130i
$509$	11.7609	−	13.0618i	0.521294	−	0.578955i	−0.423800	−	0.905756i	$-0.639304\pi$
$509$	11.7609	−	13.0618i	0.521294	−	0.578955i	0.945093	+	0.326801i	$0.105971\pi$
$510$	−5.30123	−	6.54743i	−0.234742	−	0.289925i
$511$	34.3711	+	6.31403i	1.52049	+	0.279316i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	−16.9491	−	11.0069i	−0.748322	−	0.485966i
$514$	29.0635	+	6.17764i	1.28194	+	0.272484i
$515$	−1.40093	−	0.713937i	−0.0617324	−	0.0314598i
$516$	11.3947	−	6.57872i	0.501623	−	0.289612i
$517$	8.44420	−	15.8780i	0.371376	−	0.698312i
$518$	0.763352	−	2.16654i	0.0335398	−	0.0951921i
$519$	4.27978	+	5.89062i	0.187862	+	0.258569i
$520$	0.249608	−	0.432262i	0.0109460	−	0.0189559i
$521$	23.9305	−	21.5471i	1.04841	−	0.943997i	0.0499152	−	0.998753i	$-0.484105\pi$
$521$	23.9305	−	21.5471i	1.04841	−	0.943997i	0.998500	+	0.0547564i	$0.0174382\pi$
$522$	4.21983	−	10.9930i	0.184697	−	0.481152i
$523$	12.7096	+	15.6951i	0.555754	+	0.686299i	0.975160	−	0.221500i	$-0.0710952\pi$
$523$	12.7096	+	15.6951i	0.555754	+	0.686299i	−0.419407	+	0.907799i	$0.637762\pi$
$524$	4.67914	−	14.4009i	0.204409	−	0.629107i
$525$	10.9351	−	8.41585i	0.477247	−	0.367298i
$526$	10.4458	−	7.58931i	0.455458	−	0.330910i
$527$	17.1514	+	4.59572i	0.747129	+	0.200193i
$528$	3.45106	+	0.241619i	0.150188	+	0.0105151i
$529$	17.0244	+	9.82905i	0.740192	+	0.427350i
$530$	26.1492	+	5.56014i	1.13585	+	0.241517i
$531$	9.97512	−	3.24111i	0.432883	−	0.140652i
$532$	1.34578	−	10.3488i	0.0583468	−	0.448676i
$533$	0.437020	+	2.75924i	0.0189294	+	0.119516i
$534$	6.56556	+	0.690068i	0.284120	+	0.0298622i
$535$	−37.6144	+	5.95478i	−1.62621	+	0.257447i
$536$	0.503869	+	0.107101i	0.0217638	+	0.00462605i
$537$	0.246575	+	0.642350i	0.0106405	+	0.0277194i
$538$	−6.42204	+	6.42204i	−0.276874	+	0.276874i
$539$	−16.6507	+	16.1788i	−0.717196	+	0.696871i
$540$	6.24046	−	9.60795i	0.268546	−	0.413461i
$541$	5.91803	+	2.63488i	0.254436	+	0.113282i	0.529992	−	0.848003i	$-0.322195\pi$
$541$	5.91803	+	2.63488i	0.254436	+	0.113282i	−0.275555	+	0.961285i	$0.588862\pi$
$542$	−3.82834	−	5.89513i	−0.164441	−	0.253218i
$543$	−0.566198	+	10.8037i	−0.0242979	+	0.463631i
$544$	0.377550	−	3.59215i	0.0161873	−	0.154012i
$545$	9.00273	−	20.2166i	0.385634	−	0.865982i
$546$	−0.375801	−	0.488151i	−0.0160828	−	0.0208909i
$547$	−11.3195	−	5.76759i	−0.483988	−	0.246604i	0.194931	−	0.980817i	$-0.437552\pi$
$547$	−11.3195	−	5.76759i	−0.483988	−	0.246604i	−0.678920	+	0.734213i	$0.737552\pi$
$548$	0.0880636	+	0.229414i	0.00376189	+	0.00980006i
$549$	1.76230	−	3.05239i	0.0752132	−	0.130273i
$550$	0.574950	+	16.5732i	0.0245159	+	0.706682i
$551$	−21.0375	+	12.1460i	−0.896227	+	0.517437i
$552$	1.88337	+	0.298296i	0.0801614	+	0.0126963i
$553$	20.2116	−	33.0999i	0.859486	−	1.40755i
$554$	−8.09183	−	2.62919i	−0.343789	−	0.111704i
$555$	−2.01395	+	0.211529i	−0.0854872	+	0.00897889i
$556$	0.344598	+	0.773979i	0.0146142	+	0.0328240i
$557$	−25.3227	−	1.32711i	−1.07296	−	0.0562314i	−0.492337	−	0.870405i	$-0.663857\pi$
$557$	−25.3227	−	1.32711i	−1.07296	−	0.0562314i	−0.580622	+	0.814173i	$0.697191\pi$
$558$	0.491927	+	9.38654i	0.0208250	+	0.397364i
$559$	2.27803	−	1.65509i	0.0963506	−	0.0700028i
$560$	5.86663	+	0.763335i	0.247910	+	0.0322568i
$561$	4.06916	−	11.8144i	0.171800	−	0.498804i
$562$	−2.38253	−	0.638398i	−0.100501	−	0.0269292i
$563$	19.8236	+	16.0529i	0.835466	+	0.676547i	0.948407	−	0.317054i	$-0.102694\pi$
$563$	19.8236	+	16.0529i	0.835466	+	0.676547i	−0.112941	+	0.993602i	$0.536027\pi$
$564$	−1.17593	+	5.53229i	−0.0495154	+	0.232952i
$565$	−13.3758	−	5.13557i	−0.562723	−	0.216055i
$566$	7.75864	−	10.6788i	0.326120	−	0.448866i
$567$	0.588233	+	0.852988i	0.0247035	+	0.0358221i
$568$	1.70237	−	0.867401i	0.0714299	−	0.0363953i
$569$	11.3190	+	10.1916i	0.474516	+	0.427256i	0.871371	−	0.490625i	$-0.163232\pi$
$569$	11.3190	+	10.1916i	0.474516	+	0.427256i	−0.396855	+	0.917881i	$0.629898\pi$
$570$	−8.74985	+	2.84231i	−0.366491	+	0.119051i
$571$	−8.05094	+	13.9446i	−0.336921	+	0.583565i	−0.983852	−	0.178984i	$-0.942719\pi$
$571$	−8.05094	+	13.9446i	−0.336921	+	0.583565i	0.646931	+	0.762549i	$0.276052\pi$
$572$	0.739915	−	0.0257749i	0.0309374	−	0.00107770i
$573$	13.9216	−	13.9216i	0.581582	−	0.581582i
$574$	−28.2041	+	17.3450i	−1.17722	+	0.723966i
$575$	−0.479680	+	9.12785i	−0.0200040	+	0.380658i
$576$	1.87020	−	0.397524i	0.0779251	−	0.0165635i
$577$	21.0644	+	8.08588i	0.876924	+	0.336620i	0.754847	−	0.655901i	$-0.227711\pi$
$577$	21.0644	+	8.08588i	0.876924	+	0.336620i	0.122077	+	0.992521i	$0.461045\pi$
$578$	3.69130	+	1.41696i	0.153538	+	0.0589377i
$579$	14.2335	−	3.02542i	0.591523	−	0.125732i
$580$	−6.88467	−	11.9266i	−0.285870	−	0.495224i
$581$	16.4114	−	0.455751i	0.680859	−	0.0189077i
$582$	0.0786583	−	0.0786583i	0.00326049	−	0.00326049i
$583$	13.5588	+	37.2624i	0.561548	+	1.54325i
$584$	6.60421	−	11.4388i	0.273284	−	0.473342i
$585$	0.433337	−	0.850321i	0.0179163	−	0.0351565i
$586$	0.339298	+	0.305505i	0.0140163	+	0.0126203i
$587$	−33.3449	+	16.9901i	−1.37629	+	0.701256i	−0.976534	−	0.215365i	$-0.930906\pi$
$587$	−33.3449	+	16.9901i	−1.37629	+	0.701256i	−0.399758	+	0.916621i	$0.630906\pi$
$588$	3.63074	−	6.33487i	0.149729	−	0.261246i
$589$	11.3977	−	15.6876i	0.469634	−	0.646395i
$590$	4.39666	−	11.4512i	0.181008	−	0.471440i
$591$	5.47289	−	25.7479i	0.225124	−	1.05913i
$592$	−0.674730	−	0.546385i	−0.0277312	−	0.0224563i
$593$	−9.16884	−	2.45678i	−0.376519	−	0.100888i	0.0655960	−	0.997846i	$-0.479105\pi$
$593$	−9.16884	−	2.45678i	−0.376519	−	0.100888i	−0.442115	+	0.896958i	$0.645772\pi$
$594$	16.9904	+	0.298026i	0.697126	+	0.0122282i
$595$	8.14752	−	19.7543i	0.334016	−	0.809846i
$596$	−17.5046	+	12.7178i	−0.717016	+	0.520943i
$597$	0.362587	+	6.91857i	0.0148397	+	0.283158i
$598$	0.407522	+	0.0213573i	0.0166648	+	0.000873365i
$599$	14.2263	+	31.9527i	0.581269	+	1.30555i	0.929735	+	0.368230i	$0.120036\pi$
$599$	14.2263	+	31.9527i	0.581269	+	1.30555i	−0.348466	+	0.937321i	$0.613297\pi$
$600$	−1.61094	−	4.96037i	−0.0657663	−	0.202506i
$601$	24.6598	+	8.01245i	1.00589	+	0.326835i	0.765218	−	0.643771i	$-0.222631\pi$
$601$	24.6598	+	8.01245i	1.00589	+	0.326835i	0.240676	+	0.970606i	$0.422631\pi$
$602$	28.4832	+	17.3926i	1.16089	+	0.708868i
$603$	0.972787	+	0.154074i	0.0396149	+	0.00627439i
$604$	−4.90671	+	2.83289i	−0.199651	+	0.115269i
$605$	−20.3950	+	13.7494i	−0.829173	+	0.558991i
$606$	4.58714	−	7.94517i	0.186340	−	0.322750i
$607$	8.50338	+	22.1521i	0.345141	+	0.899124i	0.990780	+	0.135481i	$0.0432580\pi$
$607$	8.50338	+	22.1521i	0.345141	+	0.899124i	−0.645638	+	0.763643i	$0.723409\pi$
$608$	−3.51449	−	1.79072i	−0.142531	−	0.0726233i
$609$	−16.8471	+	2.24511i	−0.682681	+	0.0909765i
$610$	−1.47693	−	3.84835i	−0.0597990	−	0.155815i
$611$	−0.126522	+	1.20378i	−0.00511854	+	0.0486996i
$612$	0.361430	−	6.89650i	0.0146099	−	0.278774i
$613$	−2.29988	−	3.54150i	−0.0928911	−	0.143040i	0.789170	−	0.614175i	$-0.210511\pi$
$613$	−2.29988	−	3.54150i	−0.0928911	−	0.143040i	−0.882061	+	0.471135i	$0.843844\pi$
$614$	−29.0134	−	12.9176i	−1.17089	−	0.521312i
$615$	24.4790	+	15.8994i	0.987090	+	0.641124i
$616$	3.65087	+	7.97942i	0.147098	+	0.321500i
$617$	−13.8085	+	13.8085i	−0.555911	+	0.555911i	−0.928141	−	0.372230i	$-0.878593\pi$
$617$	−13.8085	+	13.8085i	−0.555911	+	0.555911i	0.372230	+	0.928141i	$0.378593\pi$
$618$	0.262854	+	0.684757i	0.0105735	+	0.0275450i
$619$	−25.3192	−	5.38175i	−1.01766	−	0.216311i	−0.331266	−	0.943538i	$-0.607476\pi$
$619$	−25.3192	−	5.38175i	−1.01766	−	0.216311i	−0.686397	+	0.727227i	$0.740809\pi$
$620$	8.89277	+	6.46195i	0.357142	+	0.259518i
$621$	9.31507	+	0.979054i	0.373801	+	0.0392881i
$622$	−1.76275	−	11.1296i	−0.0706800	−	0.446256i
$623$	6.43257	+	15.4603i	0.257716	+	0.619405i
$624$	−0.221449	+	0.0719531i	−0.00886504	+	0.00288043i
$625$	22.8415	−	10.1619i	0.913662	−	0.406475i
$626$	−6.10082	−	3.52231i	−0.243838	−	0.140780i
$627$	−10.4525	−	8.77217i	−0.417431	−	0.350327i
$628$	−20.7546	−	5.56118i	−0.828199	−	0.221915i
$629$	−2.53703	+	1.84326i	−0.101158	+	0.0734955i
$630$	11.2779	+	0.870437i	0.449322	+	0.0346790i
$631$	10.9374	−	33.6620i	0.435412	−	1.34006i	−0.457251	−	0.889338i	$-0.651166\pi$
$631$	10.9374	−	33.6620i	0.435412	−	1.34006i	0.892663	−	0.450724i	$-0.148834\pi$
$632$	−9.22494	−	11.3918i	−0.366948	−	0.453143i
$633$	−5.09049	+	13.2612i	−0.202329	+	0.527084i
$634$	18.5615	−	16.7129i	0.737172	−	0.663753i
$635$	7.67068	+	28.6356i	0.304402	+	1.13637i
$636$	−7.33014	−	10.0891i	−0.290659	−	0.400058i
$637$	0.631042	−	1.42951i	0.0250028	−	0.0566392i
$638$	9.59086	−	18.0341i	0.379706	−	0.713975i
$639$	3.16365	−	1.82653i	0.125152	−	0.0722565i
$640$	1.01530	−	1.99228i	0.0401331	−	0.0787517i
$641$	32.1299	+	6.82943i	1.26906	+	0.269746i	0.792758	−	0.609537i	$-0.208645\pi$
$641$	32.1299	+	6.82943i	1.26906	+	0.269746i	0.476299	+	0.879283i	$0.341978\pi$
$642$	14.8989	+	9.67545i	0.588012	+	0.381859i
$643$	39.7994	−	6.30361i	1.56954	−	0.248590i	0.689781	−	0.724018i	$-0.257707\pi$
$643$	39.7994	−	6.30361i	1.56954	−	0.248590i	0.879755	+	0.475428i	$0.157707\pi$
$644$	1.62173	+	4.55668i	0.0639051	+	0.179558i
$645$	3.07742	−	29.2595i	0.121173	−	1.15209i
$646$	−9.53306	+	10.5875i	−0.375073	+	0.416561i
$647$	−20.9529	+	25.8747i	−0.823745	+	1.01724i	0.175717	+	0.984441i	$0.443776\pi$
$647$	−20.9529	+	25.8747i	−0.823745	+	1.01724i	−0.999462	+	0.0327999i	$0.989558\pi$
$648$	0.378283	−	0.101361i	0.0148604	−	0.00398183i
$649$	17.8599	−	3.47001i	0.701061	−	0.136210i
$650$	−0.453829	−	1.01971i	−0.0178007	−	0.0399963i
$651$	11.5565	−	7.10704i	0.452936	−	0.278547i
$652$	0.0500780	+	0.0255160i	0.00196120	+	0.000999283i
$653$	−3.71717	−	2.41396i	−0.145464	−	0.0944656i	0.469855	−	0.882744i	$-0.344306\pi$
$653$	−3.71717	−	2.41396i	−0.145464	−	0.0944656i	−0.615319	+	0.788278i	$0.710973\pi$
$654$	−9.43092	+	4.19891i	−0.368778	+	0.164191i
$655$	−19.8996	−	27.3936i	−0.777542	−	1.07036i
$656$	2.60195	+	12.2412i	0.101589	+	0.477939i
$657$	11.4652	−	22.5017i	0.447300	−	0.877876i
$658$	−13.7488	+	4.09627i	−0.535984	+	0.159689i
$659$		−	16.8122i		−	0.654911i	−0.944867	−	0.327455i	$-0.893809\pi$
$659$		−	16.8122i		−	0.654911i	0.944867	−	0.327455i	$-0.106191\pi$
$660$	4.97334	−	5.92510i	0.193587	−	0.230634i
$661$	−28.0872	−	16.2162i	−1.09247	−	0.630736i	−0.158234	−	0.987402i	$-0.550580\pi$
$661$	−28.0872	−	16.2162i	−1.09247	−	0.630736i	−0.934232	+	0.356666i	$0.883913\pi$
$662$	−6.05395	−	4.90239i	−0.235293	−	0.190537i
$663$	0.0440156	+	0.839868i	0.00170943	+	0.0326178i
$664$	1.91755	−	5.90160i	0.0744153	−	0.229027i
$665$	−16.9512	−	16.0374i	−0.657338	−	0.621905i
$666$	−1.34298	−	0.975731i	−0.0520394	−	0.0378088i
$667$	6.13180	−	9.44214i	0.237424	−	0.365601i
$668$	6.66878	−	4.33076i	0.258023	−	0.167562i
$669$	18.9849	−	1.99539i	0.733997	−	0.0771462i
$670$	0.856052	−	0.770682i	0.0330722	−	0.0297740i
$671$	3.67989	−	4.88251i	0.142061	−	0.188487i
$672$	−1.79562	−	2.09568i	−0.0692677	−	0.0808425i
$673$	14.4402	+	2.28711i	0.556631	+	0.0881616i	0.428411	−	0.903584i	$-0.359074\pi$
$673$	14.4402	+	2.28711i	0.556631	+	0.0881616i	0.128220	+	0.991746i	$0.459074\pi$
$674$	10.9133	+	9.82642i	0.420366	+	0.378500i
$675$	−9.17724	−	23.9177i	−0.353232	−	0.920595i
$676$	11.8306	−	5.26731i	0.455022	−	0.202589i
$677$	−29.7287	+	24.0738i	−1.14257	+	0.925233i	−0.997934	−	0.0642528i	$-0.979534\pi$
$677$	−29.7287	+	24.0738i	−1.14257	+	0.925233i	−0.144633	+	0.989485i	$0.546200\pi$
$678$	3.03430	+	5.95515i	0.116532	+	0.228706i
$679$	0.270664	+	0.0797084i	0.0103871	+	0.00305893i
$680$	−6.00165	−	5.40469i	−0.230153	−	0.207260i
$681$	5.62476	+	9.74238i	0.215541	+	0.373329i
$682$	−1.13875	+	16.2649i	−0.0436051	+	0.622815i
$683$	−16.0334	+	4.29613i	−0.613500	+	0.164387i	−0.552171	−	0.833731i	$-0.686201\pi$
$683$	−16.0334	+	4.29613i	−0.613500	+	0.164387i	−0.0613289	+	0.998118i	$0.519534\pi$
$684$	−6.88962	−	3.06746i	−0.263431	−	0.117287i
$685$	0.530747	+	0.142254i	0.0202788	+	0.00543525i
$686$	18.5160	+	0.396858i	0.706944	+	0.0151521i
$687$	11.5500	−	1.82934i	0.440660	−	0.0697937i
$688$	9.80294	−	7.93826i	0.373733	−	0.302643i
$689$	−1.78581	−	1.98334i	−0.0680340	−	0.0755594i
$690$	3.01520	−	3.01477i	0.114787	−	0.114770i
$691$	−3.48732	+	7.83264i	−0.132664	+	0.297968i	−0.967647	−	0.252308i	$-0.918811\pi$
$691$	−3.48732	+	7.83264i	−0.132664	+	0.297968i	0.834983	+	0.550275i	$0.185477\pi$
$692$	4.93594	+	4.93594i	0.187636	+	0.187636i
$693$	7.76930	+	14.8703i	0.295131	+	0.564875i
$694$			14.3278i			0.543874i
$695$	1.85303	+	0.394012i	0.0702893	+	0.0149457i
$696$	−1.33561	+	6.28354i	−0.0506261	+	0.238177i
$697$	45.1403	+	2.36570i	1.70981	+	0.0896074i
$698$	12.5889	+	15.5460i	0.476498	+	0.588426i
$699$	−23.6575	−	17.1882i	−0.894809	−	0.650116i
$700$	9.09225	−	9.60891i	0.343655	−	0.363183i
$701$	6.73872	+	20.7397i	0.254518	+	0.783326i	0.993924	+	0.110067i	$0.0351064\pi$
$701$	6.73872	+	20.7397i	0.254518	+	0.783326i	−0.739406	+	0.673260i	$0.764894\pi$
$702$	−1.06776	+	0.409876i	−0.0403002	+	0.0154698i
$703$	0.886349	+	3.30790i	0.0334293	+	0.124760i
$704$	3.30403	−	0.288780i	0.124525	−	0.0108838i
$705$	8.46179	+	9.39912i	0.318689	+	0.353991i
$706$	3.94066	+	5.42385i	0.148309	+	0.204129i
$707$	23.2633	+	0.572315i	0.874908	+	0.0215241i
$708$	−5.09831	+	2.59772i	−0.191606	+	0.0976283i
$709$	6.97141	+	0.732725i	0.261817	+	0.0275181i	0.234527	−	0.972110i	$-0.424646\pi$
$709$	6.97141	+	0.732725i	0.261817	+	0.0275181i	0.0272894	+	0.999628i	$0.491312\pi$
$710$	0.668631	−	4.21962i	0.0250933	−	0.158359i
$711$	−18.7537	−	20.8281i	−0.703318	−	0.781114i
$712$	6.32039	−	0.331238i	0.236867	−	0.0124137i
$713$	−1.40587	+	8.87634i	−0.0526504	+	0.332422i
$714$	−8.99014	+	4.30556i	−0.336448	+	0.161132i
$715$	0.925962	−	1.37233i	0.0346290	−	0.0513222i
$716$	0.329816	+	0.571259i	0.0123258	+	0.0213489i
$717$	6.95183	−	8.58480i	0.259621	−	0.320605i
$718$	−12.8170	−	19.7364i	−0.478326	−	0.736558i
$719$	25.4261	−	5.40448i	0.948233	−	0.201553i	0.292261	−	0.956339i	$-0.405592\pi$
$719$	25.4261	−	5.40448i	0.948233	−	0.201553i	0.655972	+	0.754785i	$0.272259\pi$
$720$	1.73921	−	3.90558i	0.0648165	−	0.145552i
$721$	−1.20602	+	1.41660i	−0.0449145	+	0.0527570i
$722$	−1.56249	−	3.06657i	−0.0581500	−	0.114126i
$723$	14.3395	−	0.751499i	0.533290	−	0.0279485i
$724$	1.08414	+	10.3149i	0.0402917	+	0.383350i
$725$	−30.6238	−	3.22313i	−1.13734	−	0.119704i
$726$	11.3619	+	1.59880i	0.421681	+	0.0593372i
$727$	−21.5364	−	21.5364i	−0.798742	−	0.798742i	0.184155	−	0.982897i	$-0.441045\pi$
$727$	−21.5364	−	21.5364i	−0.798742	−	0.798742i	−0.982897	+	0.184155i	$0.941045\pi$
$728$	−0.429054	−	0.405868i	−0.0159018	−	0.0150425i
$729$	−14.5361	+	4.72307i	−0.538375	+	0.174929i
$730$	−12.0110	−	26.9824i	−0.444547	−	0.998662i
$731$	−18.5313	−	41.6221i	−0.685407	−	1.53945i
$732$	−0.689085	+	1.79513i	−0.0254693	+	0.0663499i
$733$	−8.18356	+	12.6016i	−0.302267	+	0.465450i	−0.956867	−	0.290525i	$-0.906170\pi$
$733$	−8.18356	+	12.6016i	−0.302267	+	0.465450i	0.654601	+	0.755975i	$0.272837\pi$
$734$	−5.13839	−	15.8143i	−0.189662	−	0.583718i
$735$	−6.68684	−	14.8946i	−0.246648	−	0.549397i
$736$	1.82809			0.0673842
$737$	1.64226	+	0.471062i	0.0604933	+	0.0173518i
$738$	6.19299	+	23.1126i	0.227967	+	0.850785i
$739$	−38.6613	+	4.06347i	−1.42218	+	0.149477i	−0.784167	−	0.620550i	$-0.786910\pi$
$739$	−38.6613	+	4.06347i	−1.42218	+	0.149477i	−0.638012	+	0.770027i	$0.720243\pi$
$740$	−1.87527	+	0.502334i	−0.0689364	+	0.0184662i
$741$	0.873483	+	0.283812i	0.0320882	+	0.0104261i
$742$	13.5726	−	28.5720i	0.498267	−	1.04891i
$743$	3.73015	+	23.5513i	0.136846	+	0.864012i	0.956623	+	0.291329i	$0.0940974\pi$
$743$	3.73015	+	23.5513i	0.136846	+	0.864012i	−0.819777	+	0.572683i	$0.805903\pi$
$744$	−1.06614	−	5.01579i	−0.0390865	−	0.183888i
$745$	−0.00346180	+	48.3815i	−0.000126831	+	1.77256i
$746$	0.349242	+	3.32282i	0.0127867	+	0.121657i
$747$	3.07075	−	11.4602i	0.112353	−	0.419306i
$748$	2.08122	−	11.7973i	0.0760969	−	0.431351i
$749$	−3.46426	+	44.9269i	−0.126581	+	1.64159i
$750$	−11.0904	−	3.60614i	−0.404966	−	0.131677i
$751$	−7.96915	+	8.85064i	−0.290799	+	0.322964i	−0.870787	−	0.491660i	$-0.836390\pi$
$751$	−7.96915	+	8.85064i	−0.290799	+	0.322964i	0.579989	+	0.814625i	$0.303057\pi$
$752$	−0.283781	+	5.41486i	−0.0103484	+	0.197460i
$753$	18.0245	+	6.91897i	0.656850	+	0.252141i
$754$	−0.143703	+	1.36724i	−0.00523335	+	0.0497920i
$755$	−1.32518	+	12.5996i	−0.0482283	+	0.458546i
$756$	−9.34672	−	9.81821i	−0.339937	−	0.357085i
$757$	−0.503469	+	3.17878i	−0.0182989	+	0.115535i	−0.995147	−	0.0983994i	$-0.968628\pi$
$757$	−0.503469	+	3.17878i	−0.0182989	+	0.115535i	0.976848	+	0.213934i	$0.0686277\pi$
$758$	6.58248	−	24.5661i	0.239086	−	0.892282i
$759$	6.16207	+	1.42318i	0.223669	+	0.0516583i
$760$	−7.85892	+	4.00361i	−0.285073	+	0.145226i
$761$	−2.98269	+	6.69922i	−0.108122	+	0.242847i	−0.959501	−	0.281705i	$-0.909100\pi$
$761$	−2.98269	+	6.69922i	−0.108122	+	0.242847i	0.851379	+	0.524551i	$0.175767\pi$
$762$	6.27817	−	12.3216i	0.227434	−	0.446365i
$763$	−20.7993	−	15.9076i	−0.752985	−	0.575894i
$764$	11.0944	−	15.2701i	0.401381	−	0.552454i
$765$	−12.0001	−	9.71895i	−0.433866	−	0.351389i
$766$	−0.468465	+	0.421808i	−0.0169263	+	0.0152405i
$767$	−1.02699	+	0.666938i	−0.0370826	+	0.0240817i
$768$	−0.973800	+	0.373807i	−0.0351390	+	0.0134886i
$769$	−14.0009			−0.504886			−0.252443	−	0.967612i	$-0.581234\pi$
$769$	−14.0009			−0.504886			−0.252443	+	0.967612i	$0.581234\pi$
$770$	19.2331	+	3.88446i	0.693112	+	0.139986i
$771$	−30.9928			−1.11618
$772$	13.0239	−	4.99940i	0.468739	−	0.179932i
$773$	14.0482	−	9.12299i	0.505277	−	0.328131i	−0.266701	−	0.963779i	$-0.585934\pi$
$773$	14.0482	−	9.12299i	0.505277	−	0.328131i	0.771979	+	0.635648i	$0.219267\pi$
$774$	17.9230	−	16.1380i	0.644230	−	0.580067i
$775$	23.3783	−	7.59238i	0.839774	−	0.272726i
$776$	0.0626845	−	0.0862778i	0.00225024	−	0.00309719i
$777$	−0.308984	+	2.37603i	−0.0110848	+	0.0852398i
$778$	5.52684	−	10.8470i	0.198147	−	0.388885i
$779$	20.0777	−	45.0953i	0.719359	−	1.61571i
$780$	−0.160927	+	0.495163i	−0.00576212	+	0.0177297i
$781$	5.83326	−	2.47548i	0.208730	−	0.0885797i
$782$	1.70897	−	6.37795i	0.0611125	−	0.228075i
$783$	−4.93616	+	31.1657i	−0.176404	+	1.11377i
$784$	2.48787	−	6.54297i	0.0888525	−	0.233678i
$785$	−37.3408	+	30.2335i	−1.33275	+	1.07908i
$786$	−1.65096	+	15.7078i	−0.0588877	+	0.560279i
$787$	−43.3801	−	16.6521i	−1.54633	−	0.593582i	−0.572312	−	0.820036i	$-0.693953\pi$
$787$	−43.3801	−	16.6521i	−1.54633	−	0.593582i	−0.974022	+	0.226454i	$0.927287\pi$
$788$	1.32075	−	25.2014i	0.0470497	−	0.897762i
$789$	−9.01182	+	10.0086i	−0.320829	+	0.356317i
$790$	−32.7328	+	1.71310i	−1.16458	+	0.0609495i
$791$	−9.58007	+	13.9865i	−0.340628	+	0.497302i
$792$	6.27969	−	0.882004i	0.223139	−	0.0313407i
$793$	−0.106505	+	0.397483i	−0.00378211	+	0.0141150i
$794$	−0.472171	−	4.49241i	−0.0167567	−	0.159430i
$795$	−27.8855	−	0.00199527i	−0.988997	−	7.07649e-5i
$796$	1.38094	+	6.49679i	0.0489459	+	0.230273i
$797$	2.15651	+	13.6156i	0.0763874	+	0.482291i	0.995992	+	0.0894452i	$0.0285094\pi$
$797$	2.15651	+	13.6156i	0.0763874	+	0.482291i	−0.919604	+	0.392846i	$0.871491\pi$
$798$	0.871247	+	10.8506i	0.0308418	+	0.384106i
$799$	18.6264	+	6.05209i	0.658955	+	0.214108i
$800$	−2.26931	−	4.45536i	−0.0802324	−	0.157521i
$801$	12.0348	−	1.26491i	0.425228	−	0.0446933i
$802$	−10.1514	−	37.8856i	−0.358459	−	1.33779i
$803$	24.4999	−	36.3159i	0.864582	−	1.28156i
$804$	−0.537318			−0.0189497
$805$	10.3744	+	3.05598i	0.365649	+	0.107709i
$806$	−0.339116	−	1.04369i	−0.0119449	−	0.0367625i
$807$	5.15958	−	7.94506i	0.181626	−	0.279679i
$808$	3.15198	−	8.21119i	0.110886	−	0.288869i
$809$	1.77121	+	3.97820i	0.0622724	+	0.139866i	0.942001	−	0.335610i	$-0.108942\pi$
$809$	1.77121	+	3.97820i	0.0622724	+	0.139866i	−0.879729	+	0.475476i	$0.842276\pi$
$810$	0.313884	−	0.817520i	0.0110287	−	0.0287247i
$811$	24.4549	−	7.94588i	0.858728	−	0.279018i	0.153631	−	0.988128i	$-0.450903\pi$
$811$	24.4549	−	7.94588i	0.858728	−	0.279018i	0.705097	+	0.709111i	$0.250903\pi$
$812$	−15.6158	+	4.65251i	−0.548006	+	0.163271i
$813$	5.18448	+	5.18448i	0.181827	+	0.181827i
$814$	−2.10580	−	1.96402i	−0.0738081	−	0.0688390i
$815$	0.111982	−	0.0570475i	0.00392255	−	0.00199829i
$816$	0.393815	+	3.74690i	0.0137863	+	0.131168i
$817$	−49.6866	+	2.60396i	−1.73831	+	0.0911012i
$818$	15.5107	+	30.4415i	0.542319	+	1.06436i
$819$	−0.859833	−	0.732015i	−0.0300450	−	0.0255787i
$820$	25.5636	+	11.3838i	0.892718	+	0.397540i
$821$	22.3855	−	4.75819i	0.781260	−	0.166062i	0.200017	−	0.979792i	$-0.435900\pi$
$821$	22.3855	−	4.75819i	0.781260	−	0.166062i	0.581242	+	0.813730i	$0.302567\pi$
$822$	−0.139603	−	0.214969i	−0.00486920	−	0.00749792i
$823$	−7.21533	+	8.91019i	−0.251511	+	0.310590i	−0.887227	−	0.461333i	$-0.847371\pi$
$823$	−7.21533	+	8.91019i	−0.251511	+	0.310590i	0.635716	+	0.771923i	$0.280705\pi$
$824$	0.351590	+	0.608972i	0.0122482	+	0.0212146i
$825$	−4.18081	−	16.7847i	−0.145557	−	0.584368i
$826$	−11.9741	−	8.20167i	−0.416632	−	0.285373i
$827$	−4.43293	+	27.9884i	−0.154148	+	0.973253i	0.782416	+	0.622756i	$0.213987\pi$
$827$	−4.43293	+	27.9884i	−0.154148	+	0.973253i	−0.936564	+	0.350496i	$0.886013\pi$
$828$	3.49048	−	0.182929i	0.121303	−	0.00635721i
$829$	6.91273	+	7.67737i	0.240089	+	0.266646i	0.851132	−	0.524951i	$-0.175916\pi$
$829$	6.91273	+	7.67737i	0.240089	+	0.266646i	−0.611043	+	0.791597i	$0.709250\pi$
$830$	−8.15501	−	11.2261i	−0.283065	−	0.389664i
$831$	8.82617	+	0.927668i	0.306177	+	0.0321805i
$832$	−0.198898	+	0.101343i	−0.00689554	+	0.00351345i
$833$	−20.5018	−	14.7965i	−0.710345	−	0.512667i
$834$	−0.519440	−	0.714948i	−0.0179867	−	0.0247566i
$835$	0.931821	−	17.7559i	0.0322470	−	0.614468i
$836$	−11.2130	−	6.73874i	−0.387809	−	0.233064i
$837$	−6.51910	−	24.3296i	−0.225333	−	0.840955i
$838$	17.7131	−	6.79941i	0.611887	−	0.234882i
$839$	−2.05741	−	6.33206i	−0.0710297	−	0.218607i	0.909240	−	0.416273i	$-0.136664\pi$
$839$	−2.05741	−	6.33206i	−0.0710297	−	0.218607i	−0.980269	+	0.197666i	$0.936664\pi$
$840$	−6.15119	+	0.493467i	−0.212236	+	0.0170262i
$841$	7.22318	+	5.24795i	0.249075	+	0.180964i
$842$	6.66785	+	8.23411i	0.229789	+	0.283766i
$843$	2.56931	+	0.134652i	0.0884919	+	0.00463766i
$844$	−2.83133	+	13.3204i	−0.0974586	+	0.458506i
$845$	6.02262	−	28.3242i	0.207184	−	0.974383i
$846$			10.3673i			0.356436i
$847$	10.2307	+	27.2458i	0.351529	+	0.936177i
$848$	−8.45397	−	8.45397i	−0.290310	−	0.290310i
$849$	−5.60013	+	12.5781i	−0.192196	+	0.431679i
$850$	−17.6656	+	3.75229i	−0.605924	+	0.128703i
$851$	−1.06203	−	1.17950i	−0.0364058	−	0.0404327i
$852$	−1.54879	+	1.25419i	−0.0530608	+	0.0429678i
$853$	13.2422	−	2.09735i	0.453403	−	0.0718121i	0.0744437	−	0.997225i	$-0.476282\pi$
$853$	13.2422	−	2.09735i	0.453403	−	0.0718121i	0.378960	+	0.925413i	$0.376282\pi$
$854$	−4.83451	+	0.644264i	−0.165434	+	0.0220463i
$855$	−14.6049	+	8.43075i	−0.499477	+	0.288326i
$856$	15.5587	+	6.92720i	0.531787	+	0.236767i
$857$	−8.63927	+	2.31489i	−0.295112	+	0.0790750i	−0.403337	−	0.915051i	$-0.632150\pi$
$857$	−8.63927	+	2.31489i	−0.295112	+	0.0790750i	0.108225	+	0.994126i	$0.465483\pi$
$858$	−0.749336	+	0.186762i	−0.0255819	+	0.00637596i
$859$	6.51683	+	11.2875i	0.222351	+	0.385124i	0.955522	−	0.294921i	$-0.0952934\pi$
$859$	6.51683	+	11.2875i	0.222351	+	0.385124i	−0.733170	+	0.680045i	$0.761960\pi$
$860$	−1.47416	−	28.1673i	−0.0502685	−	0.960496i
$861$	25.0147	−	23.8135i	0.852499	−	0.811561i
$862$	5.75173	+	11.2884i	0.195905	+	0.384485i
$863$	4.69038	−	3.79820i	0.159663	−	0.129292i	−0.546160	−	0.837681i	$-0.683911\pi$
$863$	4.69038	−	3.79820i	0.159663	−	0.129292i	0.705823	+	0.708389i	$0.250578\pi$
$864$	−4.68064	+	2.08395i	−0.159238	+	0.0708975i
$865$	15.4168	−	2.44066i	0.524188	−	0.0829848i
$866$	−7.31915	−	6.59019i	−0.248715	−	0.223944i
$867$	−4.07348	−	0.645176i	−0.138343	−	0.0219113i
$868$	9.87696	−	8.46280i	0.335246	−	0.287246i
$869$	−27.8821	−	39.8271i	−0.945837	−	1.35104i
$870$	9.61084	+	10.6755i	0.325838	+	0.361932i
$871$	−0.114361	+	0.0120198i	−0.00387497	+	0.000407275i
$872$	−8.30037	+	5.39032i	−0.281086	+	0.182539i
$873$	0.111054	−	0.171008i	0.00375861	−	0.00578775i
$874$	−5.83359	−	4.23835i	−0.197324	−	0.143364i
$875$	−5.43040	−	29.0777i	−0.183581	−	0.983005i
$876$	−4.25747	+	13.1031i	−0.143846	+	0.442714i
$877$	2.30744	+	44.0286i	0.0779168	+	1.48674i	0.705787	+	0.708424i	$0.250593\pi$
$877$	2.30744	+	44.0286i	0.0779168	+	1.48674i	−0.627871	+	0.778318i	$0.716073\pi$
$878$	19.1877	+	15.5379i	0.647554	+	0.524379i
$879$	−0.412435	−	0.238120i	−0.0139111	−	0.00803158i
$880$	3.82062	−	6.35632i	0.128793	−	0.214272i
$881$			30.0748i			1.01325i	0.862168	+	0.506623i	$0.169106\pi$
$881$			30.0748i			1.01325i	−0.862168	+	0.506623i	$0.830894\pi$
$882$	4.09552	−	12.7419i	0.137903	−	0.429041i
$883$	−13.6969	+	26.8816i	−0.460936	+	0.904638i	0.537191	+	0.843461i	$0.319486\pi$
$883$	−13.6969	+	26.8816i	−0.460936	+	0.904638i	−0.998127	+	0.0611776i	$0.980514\pi$
$884$	0.167636	+	0.788667i	0.00563822	+	0.0265257i
$885$	−2.00244	+	12.6370i	−0.0673112	+	0.424790i
$886$	3.60597	−	1.60548i	0.121145	−	0.0539373i
$887$	−20.5150	−	13.3226i	−0.688827	−	0.447329i	0.152181	−	0.988353i	$-0.451370\pi$
$887$	−20.5150	−	13.3226i	−0.688827	−	0.447329i	−0.841008	+	0.541023i	$0.818037\pi$
$888$	0.806912	+	0.411142i	0.0270782	+	0.0137970i
$889$	35.0631	−	0.973717i	1.17598	−	0.0326574i
$890$	7.70870	−	11.8685i	0.258396	−	0.397833i
$891$	1.27504	−	0.247729i	0.0427154	−	0.00829924i
$892$	17.6774	−	4.73665i	0.591884	−	0.158595i
$893$	13.4597	−	16.6214i	0.450412	−	0.556213i
$894$	15.1016	−	16.7720i	0.505073	−	0.560940i
$895$	1.46689	+	0.154283i	0.0490328	+	0.00515710i
$896$	−2.01456	−	1.71509i	−0.0673018	−	0.0572972i
$897$	−0.420421	+	0.0665881i	−0.0140374	+	0.00222331i
$898$	2.69596	+	1.75077i	0.0899652	+	0.0584241i
$899$	−29.6144	−	6.29474i	−0.987696	−	0.209941i
$900$	−4.77877	−	8.27981i	−0.159292	−	0.275994i
$901$	−37.3978	+	21.5916i	−1.24590	+	0.719322i
$902$	5.77307	+	41.1031i	0.192222	+	1.36858i
$903$	−32.8330	−	11.5683i	−1.09261	−	0.384968i
$904$	3.76628	+	5.18384i	0.125265	+	0.172412i
$905$	20.0839	+	11.5974i	0.667611	+	0.385509i
$906$	4.39189	−	3.95447i	0.145911	−	0.131379i
$907$	−0.0346340	+	0.0902247i	−0.00115000	+	0.00299586i	−0.934154	−	0.356870i	$-0.883844\pi$
$907$	−0.0346340	+	0.0902247i	−0.00115000	+	0.00299586i	0.933004	+	0.359865i	$0.117177\pi$
$908$	6.78716	+	8.38145i	0.225240	+	0.278148i
$909$	5.19662	−	15.9936i	0.172361	−	0.530473i
$910$	−1.29816	+	0.242630i	−0.0430335	+	0.00804309i
$911$	−25.3031	+	18.3838i	−0.838328	+	0.609081i	−0.921903	−	0.387421i	$-0.873366\pi$
$911$	−25.3031	+	18.3838i	−0.838328	+	0.609081i	0.0835752	+	0.996501i	$0.473366\pi$
$912$	3.97414	+	1.06487i	0.131597	+	0.0352613i
$913$	7.71130	−	19.0814i	0.255207	−	0.631503i
$914$	15.2590	+	8.80978i	0.504723	+	0.291402i
$915$	2.34148	+	3.60612i	0.0774068	+	0.119215i
$916$	10.6623	−	3.46439i	0.352292	−	0.114467i
$917$	−36.9881	+	15.3896i	−1.22146	+	0.508211i
$918$	2.89499	+	18.2783i	0.0955489	+	0.603272i
$919$	−17.0454	−	1.79154i	−0.562275	−	0.0590975i	−0.180873	−	0.983507i	$-0.557892\pi$
$919$	−17.0454	−	1.79154i	−0.562275	−	0.0590975i	−0.381403	+	0.924409i	$0.624559\pi$
$920$	2.40294	−	3.30687i	0.0792227	−	0.109024i
$921$	32.4034	+	6.88756i	1.06773	+	0.226953i
$922$	6.39731	+	16.6656i	0.210684	+	0.548851i
$923$	−0.301583	+	0.301583i	−0.00992673	+	0.00992673i
$924$	−5.45542	−	7.34954i	−0.179470	−	0.241782i
$925$	−1.55628	+	4.05252i	−0.0511702	+	0.133246i
$926$	−26.0180	−	11.5839i	−0.855003	−	0.380672i
$927$	0.732251	+	1.12757i	0.0240503	+	0.0370342i
$928$	−0.322316	+	6.15016i	−0.0105805	+	0.201889i
$929$	−5.93232	+	56.4423i	−0.194633	+	1.85181i	0.265689	+	0.964059i	$0.414401\pi$
$929$	−5.93232	+	56.4423i	−0.194633	+	1.85181i	−0.460322	+	0.887752i	$0.652266\pi$
$930$	−10.4746	−	4.66448i	−0.343475	−	0.152954i
$931$	−23.1086	+	15.1112i	−0.757355	+	0.495249i
$932$	−24.9789	−	12.7274i	−0.818213	−	0.416900i
$933$	4.21217	+	10.9731i	0.137900	+	0.359243i
$934$	15.1412	−	26.2252i	0.495434	−	0.858116i
$935$	−18.6047	−	19.2718i	−0.608438	−	0.630254i
$936$	−0.369627	+	0.213404i	−0.0120816	+	0.00697534i
$937$	−45.0370	−	7.13316i	−1.47130	−	0.233030i	−0.631264	−	0.775568i	$-0.717464\pi$
$937$	−45.0370	−	7.13316i	−1.47130	−	0.233030i	−0.840031	+	0.542538i	$0.817464\pi$
$938$	−0.652213	−	1.19670i	−0.0212955	−	0.0390738i
$939$	6.98846	+	2.27069i	0.228060	+	0.0741011i
$940$	9.42205	+	7.63094i	0.307313	+	0.248894i
$941$	21.9789	+	49.3654i	0.716491	+	1.60927i	0.790833	+	0.612032i	$0.209648\pi$
$941$	21.9789	+	49.3654i	0.716491	+	1.60927i	−0.0743419	+	0.997233i	$0.523686\pi$
$942$	22.3817	+	1.17297i	0.729235	+	0.0382176i
$943$	1.19734	+	22.8466i	0.0389908	+	0.743988i
$944$	−4.43798	+	3.22438i	−0.144444	+	0.104945i
$945$	−30.0463	+	4.00188i	−0.977405	+	0.130181i
$946$	34.2721	−	23.9932i	1.11428	−	0.780086i
$947$	38.7809	+	10.3913i	1.26021	+	0.337672i	0.826273	−	0.563270i	$-0.190457\pi$
$947$	38.7809	+	10.3913i	1.26021	+	0.337672i	0.433938	+	0.900943i	$0.357124\pi$
$948$	11.8826	+	9.62235i	0.385929	+	0.312519i
$949$	−0.613026	+	2.88406i	−0.0198997	+	0.0936206i
$950$	−3.08799	+	19.4788i	−0.100188	+	0.631974i
$951$	−15.3136	+	21.0773i	−0.496577	+	0.683479i
$952$	−7.86700	+	5.42520i	−0.254971	+	0.175832i
$953$	−14.4390	+	7.35705i	−0.467726	+	0.238318i	−0.671936	−	0.740609i	$-0.734537\pi$
$953$	−14.4390	+	7.35705i	−0.467726	+	0.238318i	0.204211	+	0.978927i	$0.434537\pi$
$954$	−16.9876	−	15.2957i	−0.549995	−	0.495218i
$955$	−13.0394	−	40.1409i	−0.421944	−	1.29893i
$956$	5.29517	−	9.17150i	0.171258	−	0.296628i
$957$	−5.87441	+	20.4799i	−0.189893	+	0.662020i
$958$	−24.1775	+	24.1775i	−0.781140	+	0.781140i
$959$	0.309322	−	0.571857i	0.00998852	−	0.0184662i
$960$	−0.603830	+	2.25288i	−0.0194885	+	0.0727114i
$961$	−6.68308	+	1.42053i	−0.215583	+	0.0458236i
$962$	0.180937	+	0.0694553i	0.00583365	+	0.00223933i
$963$	30.4005	+	11.6696i	0.979641	+	0.376049i
$964$	13.4653	−	2.86213i	0.433687	−	0.0921830i
$965$	8.07580	−	30.1307i	0.259969	−	0.969941i
$966$	−2.64283	−	4.29742i	−0.0850317	−	0.138267i
$967$	27.9511	−	27.9511i	0.898846	−	0.898846i	−0.0964879	−	0.995334i	$-0.530761\pi$
$967$	27.9511	−	27.9511i	0.898846	−	0.898846i	0.995334	+	0.0964879i	$0.0307609\pi$
$968$	10.9984	−	0.190090i	0.353501	−	0.00610974i
$969$	7.43035	−	12.8697i	0.238697	−	0.413436i
$970$	−0.0736738	−	0.226800i	−0.00236552	−	0.00728211i
$971$	38.4487	+	34.6194i	1.23388	+	1.11099i	0.989983	+	0.141187i	$0.0450920\pi$
$971$	38.4487	+	34.6194i	1.23388	+	1.11099i	0.243895	+	0.969802i	$0.421575\pi$
$972$	−14.0594	+	7.16364i	−0.450957	+	0.229774i
$973$	0.961806	−	2.02471i	0.0308341	−	0.0649093i
$974$	12.0576	−	16.5958i	0.386349	−	0.531764i
$975$	0.684179	+	0.941976i	0.0219113	+	0.0301674i
$976$	−0.383270	+	1.80314i	−0.0122682	+	0.0577172i
$977$	−13.4064	−	10.8563i	−0.428909	−	0.347324i	0.390430	−	0.920633i	$-0.372326\pi$
$977$	−13.4064	−	10.8563i	−0.428909	−	0.347324i	−0.819339	+	0.573309i	$0.805660\pi$
$978$	−0.0566275	−	0.0151733i	−0.00181075	−	0.000485188i
$979$	20.9879	+	0.368146i	0.670777	+	0.0117660i
$980$	−8.56554	−	13.1008i	−0.273616	−	0.418490i
$981$	−15.3090	+	11.1227i	−0.488780	+	0.355119i
$982$	0.547282	+	10.4428i	0.0174645	+	0.333242i
$983$	2.19462	+	0.115015i	0.0699975	+	0.00366841i	0.0873026	−	0.996182i	$-0.472175\pi$
$983$	2.19462	+	0.115015i	0.0699975	+	0.00366841i	−0.0173051	+	0.999850i	$0.505509\pi$
$984$	−5.30947	−	11.9253i	−0.169260	−	0.380164i
$985$	−43.8513	−	35.5153i	−1.39722	−	1.13161i
$986$	21.1557	+	6.87392i	0.673736	+	0.218910i
$987$	13.1394	−	7.16105i	0.418231	−	0.227939i
$988$	0.869661	+	0.137741i	0.0276676	+	0.00438212i
$989$	19.9702	−	11.5298i	0.635014	−	0.366626i
$990$	6.65891	−	12.5188i	0.211634	−	0.397875i
$991$	14.7125	−	25.4828i	0.467357	−	0.809486i	−0.531947	−	0.846778i	$-0.678540\pi$
$991$	14.7125	−	25.4828i	0.467357	−	0.809486i	0.999304	+	0.0372910i	$0.0118729\pi$
$992$	−1.76176	−	4.58953i	−0.0559358	−	0.145718i
$993$	7.23993	+	3.68893i	0.229752	+	0.117065i
$994$	−4.67328	−	1.92707i	−0.148227	−	0.0611230i
$995$	13.5674	+	6.04175i	0.430115	+	0.191536i
$996$	−0.676575	+	6.43718i	−0.0214381	+	0.203970i
$997$	0.137672	−	2.62693i	0.00436011	−	0.0831958i	−0.995583	−	0.0938884i	$-0.970070\pi$
$997$	0.137672	−	2.62693i	0.00436011	−	0.0831958i	0.999943	+	0.0106926i	$0.00340363\pi$
$998$	11.4515	+	17.6338i	0.362491	+	0.558187i
$999$	4.06380	+	1.80932i	0.128573	+	0.0572443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.3.15	✓	768
5.2	odd	4	inner	770.2.bv.a.157.10	yes	768
7.5	odd	6	inner	770.2.bv.a.663.34	yes	768
11.4	even	5	inner	770.2.bv.a.213.10	yes	768
35.12	even	12	inner	770.2.bv.a.47.10	yes	768
55.37	odd	20	inner	770.2.bv.a.367.34	yes	768
77.26	odd	30	inner	770.2.bv.a.103.10	yes	768
385.257	even	60	inner	770.2.bv.a.257.15	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.15	✓	768	1.1	even	1	trivial
770.2.bv.a.47.10	yes	768	35.12	even	12	inner
770.2.bv.a.103.10	yes	768	77.26	odd	30	inner
770.2.bv.a.157.10	yes	768	5.2	odd	4	inner
770.2.bv.a.213.10	yes	768	11.4	even	5	inner
770.2.bv.a.257.15	yes	768	385.257	even	60	inner
770.2.bv.a.367.34	yes	768	55.37	odd	20	inner
770.2.bv.a.663.34	yes	768	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933580 + 0.358368i) q^{2} +(0.874801 - 0.568102i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.233574 - 2.22384i) q^{5} +(-0.613107 + 0.843870i) q^{6} +(-2.62366 - 0.341186i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.777674 + 1.74668i) q^{9} +O(q^{10})\)	\(q+(-0.933580 + 0.358368i) q^{2} +(0.874801 - 0.568102i) q^{3} +(0.743145 - 0.669131i) q^{4} +(-0.233574 - 2.22384i) q^{5} +(-0.613107 + 0.843870i) q^{6} +(-2.62366 - 0.341186i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-0.777674 + 1.74668i) q^{9} +(1.01501 + 1.99242i) q^{10} +(-1.70843 + 2.84276i) q^{11} +(0.269969 - 1.00754i) q^{12} +(0.0349206 - 0.220480i) q^{13} +(2.57167 - 0.621711i) q^{14} +(-1.46770 - 1.81272i) q^{15} +(0.104528 - 0.994522i) q^{16} +(-3.37203 - 1.29440i) q^{17} +(0.100065 - 1.90936i) q^{18} +(-2.63932 + 2.93126i) q^{19} +(-1.66162 - 1.49634i) q^{20} +(-2.48901 + 1.19204i) q^{21} +(0.576206 - 3.26619i) q^{22} +(0.473144 - 1.76580i) q^{23} +(0.109032 + 1.03737i) q^{24} +(-4.89089 + 1.03886i) q^{25} +(0.0464117 + 0.218350i) q^{26} +(0.801507 + 5.06051i) q^{27} +(-2.17806 + 1.50202i) q^{28} +(5.85718 + 1.90311i) q^{29} +(2.01983 + 1.16634i) q^{30} +(-4.88913 + 0.513868i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.120439 + 3.45741i) q^{33} +3.61194 q^{34} +(-0.145924 + 5.91428i) q^{35} +(0.590835 + 1.81840i) q^{36} +(0.472864 - 0.728146i) q^{37} +(1.41355 - 3.68242i) q^{38} +(-0.0947066 - 0.212714i) q^{39} +(2.08749 + 0.801484i) q^{40} +(-11.9022 + 3.86725i) q^{41} +(1.89650 - 2.00484i) q^{42} +(8.91946 + 8.91946i) q^{43} +(0.632563 + 3.25574i) q^{44} +(4.06598 + 1.32144i) q^{45} +(0.191087 + 1.81807i) q^{46} +(-5.41486 + 0.283781i) q^{47} +(-0.473549 - 0.929392i) q^{48} +(6.76718 + 1.79031i) q^{49} +(4.19374 - 2.72260i) q^{50} +(-3.68521 + 0.783316i) q^{51} +(-0.121579 - 0.187215i) q^{52} +(7.52398 - 9.29134i) q^{53} +(-2.56180 - 4.43716i) q^{54} +(6.72087 + 3.13528i) q^{55} +(1.49512 - 2.18280i) q^{56} +(-0.643623 + 4.06368i) q^{57} +(-6.15016 + 0.322316i) q^{58} +(-3.67061 - 4.07663i) q^{59} +(-2.30366 - 0.365032i) q^{60} +(-1.83333 - 0.192691i) q^{61} +(4.38024 - 2.23184i) q^{62} +(2.63630 - 4.31737i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-0.498467 - 0.0261593i) q^{65} +(-1.35146 - 3.18461i) q^{66} +(-0.133324 - 0.497574i) q^{67} +(-3.37203 + 1.29440i) q^{68} +(-0.589247 - 1.81352i) q^{69} +(-1.98326 - 5.57375i) q^{70} +(-1.54572 - 1.12303i) q^{71} +(-1.20325 - 1.48589i) q^{72} +(-13.1903 - 0.691276i) q^{73} +(-0.180512 + 0.849243i) q^{74} +(-3.68837 + 3.68732i) q^{75} +3.94440i q^{76} +(5.45225 - 6.87553i) q^{77} +(0.164646 + 0.164646i) q^{78} +(-5.96218 + 13.3913i) q^{79} +(-2.23607 - 0.000159995i) q^{80} +(-0.262050 - 0.291036i) q^{81} +(9.72574 - 7.87575i) q^{82} +(-6.12892 + 0.970725i) q^{83} +(-1.05207 + 2.55133i) q^{84} +(-2.09092 + 7.80118i) q^{85} +(-11.5235 - 5.13059i) q^{86} +(6.20502 - 1.66263i) q^{87} +(-1.75730 - 2.81281i) q^{88} +(-3.16453 - 5.48113i) q^{89} +(-4.26948 + 0.223448i) q^{90} +(-0.166844 + 0.566550i) q^{91} +(-0.829935 - 1.62884i) q^{92} +(-3.98508 + 3.22706i) q^{93} +(4.95351 - 2.20545i) q^{94} +(7.13512 + 5.18475i) q^{95} +(0.775160 + 0.697957i) q^{96} +(-0.105332 - 0.0166830i) q^{97} +(-6.95930 + 0.753741i) q^{98} +(-3.63679 - 5.19483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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