LMFDB - Embedded newform 546.2.z.a.131.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (of order $6$, degree $2$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.10
Character	$\chi$	$=$	546.131
Dual form			546.2.z.a.521.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.61832 + 0.617297i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.166488 + 0.288366i) q^{5} +(-1.71015 - 0.274563i) q^{6} +(-2.56503 + 0.648546i) q^{7} +1.00000i q^{8} +(2.23789 - 1.99796i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.61832 + 0.617297i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.166488 + 0.288366i) q^{5} +(-1.71015 - 0.274563i) q^{6} +(-2.56503 + 0.648546i) q^{7} +1.00000i q^{8} +(2.23789 - 1.99796i) q^{9} +(-0.288366 + 0.166488i) q^{10} +(-3.91988 + 2.26314i) q^{11} +(-1.34375 - 1.09285i) q^{12} -1.00000i q^{13} +(-2.54566 - 0.720858i) q^{14} +(0.0914229 - 0.569440i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.90492 - 5.03147i) q^{17} +(2.93705 - 0.611342i) q^{18} +(-1.59628 - 0.921615i) q^{19} -0.332977 q^{20} +(3.75068 - 2.63294i) q^{21} -4.52628 q^{22} +(-1.81782 - 1.04952i) q^{23} +(-0.617297 - 1.61832i) q^{24} +(2.44456 + 4.23411i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-2.38827 + 4.61478i) q^{27} +(-1.84417 - 1.89711i) q^{28} -2.22072i q^{29} +(0.363895 - 0.447438i) q^{30} +(-8.08293 + 4.66668i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.94657 - 6.08221i) q^{33} -5.80984i q^{34} +(0.240029 - 0.847644i) q^{35} +(2.84923 + 0.939087i) q^{36} +(-1.22173 + 2.11609i) q^{37} +(-0.921615 - 1.59628i) q^{38} +(0.617297 + 1.61832i) q^{39} +(-0.288366 - 0.166488i) q^{40} -11.9737 q^{41} +(4.56466 - 0.404850i) q^{42} +5.15504 q^{43} +(-3.91988 - 2.26314i) q^{44} +(0.203563 + 0.977969i) q^{45} +(-1.04952 - 1.81782i) q^{46} +(5.51184 - 9.54679i) q^{47} +(0.274563 - 1.71015i) q^{48} +(6.15878 - 3.32708i) q^{49} +4.88913i q^{50} +(7.80699 + 6.34931i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-5.31065 + 3.06610i) q^{53} +(-4.37569 + 2.80238i) q^{54} -1.50715i q^{55} +(-0.648546 - 2.56503i) q^{56} +(3.15220 + 0.506082i) q^{57} +(1.11036 - 1.92320i) q^{58} +(-0.345500 - 0.598424i) q^{59} +(0.538861 - 0.205545i) q^{60} +(9.64503 + 5.56856i) q^{61} -9.33337 q^{62} +(-4.44448 + 6.57621i) q^{63} -1.00000 q^{64} +(0.288366 + 0.166488i) q^{65} +(7.32495 - 2.79406i) q^{66} +(5.98398 + 10.3646i) q^{67} +(2.90492 - 5.03147i) q^{68} +(3.58968 + 0.576319i) q^{69} +(0.631693 - 0.614066i) q^{70} +10.4226i q^{71} +(1.99796 + 2.23789i) q^{72} +(-2.93856 + 1.69658i) q^{73} +(-2.11609 + 1.22173i) q^{74} +(-6.56978 - 5.34310i) q^{75} -1.84323i q^{76} +(8.58686 - 8.34725i) q^{77} +(-0.274563 + 1.71015i) q^{78} +(-2.99792 + 5.19255i) q^{79} +(-0.166488 - 0.288366i) q^{80} +(1.01629 - 8.94244i) q^{81} +(-10.3695 - 5.98683i) q^{82} -0.511689 q^{83} +(4.15553 + 1.93172i) q^{84} +1.93454 q^{85} +(4.46439 + 2.57752i) q^{86} +(1.37084 + 3.59383i) q^{87} +(-2.26314 - 3.91988i) q^{88} +(-8.07492 + 13.9862i) q^{89} +(-0.312694 + 0.948727i) q^{90} +(0.648546 + 2.56503i) q^{91} -2.09904i q^{92} +(10.2000 - 12.5417i) q^{93} +(9.54679 - 5.51184i) q^{94} +(0.531525 - 0.306876i) q^{95} +(1.09285 - 1.34375i) q^{96} -1.07047i q^{97} +(6.99720 + 0.198048i) q^{98} +(-4.25057 + 12.8964i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.61832	+	0.617297i	−0.934335	+	0.356397i
$3$	−1.61832	+	0.617297i	−0.934335	+	0.356397i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.166488	+	0.288366i	−0.0744558	+	0.128961i	−0.900849	−	0.434132i	$-0.857055\pi$
$5$	−0.166488	+	0.288366i	−0.0744558	+	0.128961i	0.826394	+	0.563093i	$0.190389\pi$
$6$	−1.71015	−	0.274563i	−0.698166	−	0.112090i
$7$	−2.56503	+	0.648546i	−0.969491	+	0.245127i
$7$	−2.56503	+	0.648546i	−0.969491	+	0.245127i
$8$			1.00000i			0.353553i
$9$	2.23789	−	1.99796i	0.745963	−	0.665988i
$10$	−0.288366	+	0.166488i	−0.0911894	+	0.0526482i
$11$	−3.91988	+	2.26314i	−1.18189	+	0.682363i	−0.956450	−	0.291895i	$-0.905714\pi$
$11$	−3.91988	+	2.26314i	−1.18189	+	0.682363i	−0.225437	+	0.974258i	$0.572381\pi$
$12$	−1.34375	−	1.09285i	−0.387908	−	0.315480i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−2.54566	−	0.720858i	−0.680355	−	0.192657i
$15$	0.0914229	−	0.569440i	0.0236053	−	0.147029i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.90492	−	5.03147i	−0.704547	−	1.22031i	−0.966855	−	0.255327i	$-0.917817\pi$
$17$	−2.90492	−	5.03147i	−0.704547	−	1.22031i	0.262308	−	0.964984i	$-0.415516\pi$
$18$	2.93705	−	0.611342i	0.692269	−	0.144095i
$19$	−1.59628	−	0.921615i	−0.366213	−	0.211433i	0.305590	−	0.952163i	$-0.401146\pi$
$19$	−1.59628	−	0.921615i	−0.366213	−	0.211433i	−0.671803	+	0.740730i	$0.734480\pi$
$20$	−0.332977			−0.0744558
$21$	3.75068	−	2.63294i	0.818466	−	0.574554i
$22$	−4.52628			−0.965007
$23$	−1.81782	−	1.04952i	−0.379042	−	0.218840i	0.298359	−	0.954454i	$-0.403561\pi$
$23$	−1.81782	−	1.04952i	−0.379042	−	0.218840i	−0.677402	+	0.735613i	$0.736894\pi$
$24$	−0.617297	−	1.61832i	−0.126005	−	0.330337i
$25$	2.44456	+	4.23411i	0.488913	+	0.846822i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	−2.38827	+	4.61478i	−0.459623	+	0.888114i
$28$	−1.84417	−	1.89711i	−0.348516	−	0.358520i
$29$		−	2.22072i		−	0.412377i	−0.978512	−	0.206189i	$-0.933894\pi$
$29$		−	2.22072i		−	0.412377i	0.978512	−	0.206189i	$-0.0661061\pi$
$30$	0.363895	−	0.447438i	0.0664378	−	0.0816906i
$31$	−8.08293	+	4.66668i	−1.45174	+	0.838161i	−0.998580	−	0.0532691i	$-0.983036\pi$
$31$	−8.08293	+	4.66668i	−1.45174	+	0.838161i	−0.453158	+	0.891430i	$0.649703\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	4.94657	−	6.08221i	0.861087	−	1.05878i
$34$		−	5.80984i		−	0.996380i
$35$	0.240029	−	0.847644i	0.0405723	−	0.143278i
$36$	2.84923	+	0.939087i	0.474872	+	0.156515i
$37$	−1.22173	+	2.11609i	−0.200851	+	0.347884i	−0.948803	−	0.315869i	$-0.897704\pi$
$37$	−1.22173	+	2.11609i	−0.200851	+	0.347884i	0.747952	+	0.663753i	$0.231037\pi$
$38$	−0.921615	−	1.59628i	−0.149506	−	0.258951i
$39$	0.617297	+	1.61832i	0.0988466	+	0.259138i
$40$	−0.288366	−	0.166488i	−0.0455947	−	0.0263241i
$41$	−11.9737			−1.86997			−0.934985	−	0.354686i	$-0.884588\pi$
$41$	−11.9737			−1.86997			−0.934985	+	0.354686i	$0.884588\pi$
$42$	4.56466	−	0.404850i	0.704342	−	0.0624697i
$43$	5.15504			0.786136			0.393068	−	0.919510i	$-0.371414\pi$
$43$	5.15504			0.786136			0.393068	+	0.919510i	$0.371414\pi$
$44$	−3.91988	−	2.26314i	−0.590944	−	0.341181i
$45$	0.203563	+	0.977969i	0.0303453	+	0.145787i
$46$	−1.04952	−	1.81782i	−0.154743	−	0.268024i
$47$	5.51184	−	9.54679i	0.803985	−	1.39254i	−0.112990	−	0.993596i	$-0.536043\pi$
$47$	5.51184	−	9.54679i	0.803985	−	1.39254i	0.916974	−	0.398946i	$-0.130624\pi$
$48$	0.274563	−	1.71015i	0.0396297	−	0.246839i
$49$	6.15878	−	3.32708i	0.879825	−	0.475298i
$50$			4.88913i			0.691427i
$51$	7.80699	+	6.34931i	1.09320	+	0.889081i
$52$	0.866025	−	0.500000i	0.120096	−	0.0693375i
$53$	−5.31065	+	3.06610i	−0.729474	+	0.421162i	−0.818230	−	0.574892i	$-0.805044\pi$
$53$	−5.31065	+	3.06610i	−0.729474	+	0.421162i	0.0887560	+	0.996053i	$0.471711\pi$
$54$	−4.37569	+	2.80238i	−0.595456	+	0.381355i
$55$		−	1.50715i		−	0.203224i
$56$	−0.648546	−	2.56503i	−0.0866657	−	0.342767i
$57$	3.15220	+	0.506082i	0.417519	+	0.0670322i
$58$	1.11036	−	1.92320i	0.145797	−	0.252529i
$59$	−0.345500	−	0.598424i	−0.0449803	−	0.0779082i	0.842659	−	0.538448i	$-0.180989\pi$
$59$	−0.345500	−	0.598424i	−0.0449803	−	0.0779082i	−0.887639	+	0.460540i	$0.847656\pi$
$60$	0.538861	−	0.205545i	0.0695667	−	0.0265358i
$61$	9.64503	+	5.56856i	1.23492	+	0.712981i	0.968051	−	0.250752i	$-0.0806778\pi$
$61$	9.64503	+	5.56856i	1.23492	+	0.712981i	0.266868	+	0.963733i	$0.414011\pi$
$62$	−9.33337			−1.18534
$63$	−4.44448	+	6.57621i	−0.559952	+	0.828525i
$64$	−1.00000			−0.125000
$65$	0.288366	+	0.166488i	0.0357674	+	0.0206503i
$66$	7.32495	−	2.79406i	0.901640	−	0.343925i
$67$	5.98398	+	10.3646i	0.731059	+	1.26623i	0.956431	+	0.291959i	$0.0943070\pi$
$67$	5.98398	+	10.3646i	0.731059	+	1.26623i	−0.225372	+	0.974273i	$0.572360\pi$
$68$	2.90492	−	5.03147i	0.352273	−	0.610156i
$69$	3.58968	+	0.576319i	0.432147	+	0.0693806i
$70$	0.631693	−	0.614066i	0.0755017	−	0.0733950i
$71$			10.4226i			1.23693i	0.785811	+	0.618467i	$0.212246\pi$
$71$			10.4226i			1.23693i	−0.785811	+	0.618467i	$0.787754\pi$
$72$	1.99796	+	2.23789i	0.235462	+	0.263738i
$73$	−2.93856	+	1.69658i	−0.343932	+	0.198569i	−0.662009	−	0.749496i	$-0.730296\pi$
$73$	−2.93856	+	1.69658i	−0.343932	+	0.198569i	0.318077	+	0.948065i	$0.396963\pi$
$74$	−2.11609	+	1.22173i	−0.245991	+	0.142023i
$75$	−6.56978	−	5.34310i	−0.758612	−	0.616968i
$76$		−	1.84323i		−	0.211433i
$77$	8.58686	−	8.34725i	0.978563	−	0.951258i
$78$	−0.274563	+	1.71015i	−0.0310881	+	0.193636i
$79$	−2.99792	+	5.19255i	−0.337293	+	0.584208i	−0.983923	−	0.178596i	$-0.942845\pi$
$79$	−2.99792	+	5.19255i	−0.337293	+	0.584208i	0.646630	+	0.762804i	$0.276178\pi$
$80$	−0.166488	−	0.288366i	−0.0186140	−	0.0322403i
$81$	1.01629	−	8.94244i	0.112921	−	0.993604i
$82$	−10.3695	−	5.98683i	−1.14512	−	0.661134i
$83$	−0.511689			−0.0561651			−0.0280826	−	0.999606i	$-0.508940\pi$
$83$	−0.511689			−0.0561651			−0.0280826	+	0.999606i	$0.508940\pi$
$84$	4.15553	+	1.93172i	0.453406	+	0.210768i
$85$	1.93454			0.209830
$86$	4.46439	+	2.57752i	0.481408	+	0.277941i
$87$	1.37084	+	3.59383i	0.146970	+	0.385299i
$88$	−2.26314	−	3.91988i	−0.241252	−	0.417860i
$89$	−8.07492	+	13.9862i	−0.855940	+	1.48253i	0.0198299	+	0.999803i	$0.493688\pi$
$89$	−8.07492	+	13.9862i	−0.855940	+	1.48253i	−0.875770	+	0.482728i	$0.839646\pi$
$90$	−0.312694	+	0.948727i	−0.0329608	+	0.100005i
$91$	0.648546	+	2.56503i	0.0679861	+	0.268888i
$92$		−	2.09904i		−	0.218840i
$93$	10.2000	−	12.5417i	1.05769	−	1.30052i
$94$	9.54679	−	5.51184i	0.984676	−	0.568503i
$95$	0.531525	−	0.306876i	0.0545333	−	0.0314848i
$96$	1.09285	−	1.34375i	0.111539	−	0.137146i
$97$		−	1.07047i		−	0.108689i	−0.998522	−	0.0543447i	$-0.982693\pi$
$97$		−	1.07047i		−	0.108689i	0.998522	−	0.0543447i	$-0.0173070\pi$
$98$	6.99720	+	0.198048i	0.706824	+	0.0200059i
$99$	−4.25057	+	12.8964i	−0.427199	+	1.29614i
$100$	−2.44456	+	4.23411i	−0.244456	+	0.423411i
$101$	4.58241	+	7.93697i	0.455967	+	0.789758i	0.998743	−	0.0501196i	$-0.0159603\pi$
$101$	4.58241	+	7.93697i	0.455967	+	0.789758i	−0.542776	+	0.839877i	$0.682627\pi$
$102$	3.58640	+	9.40216i	0.355106	+	0.930952i
$103$	−0.818994	−	0.472846i	−0.0806978	−	0.0465909i	0.459108	−	0.888380i	$-0.348169\pi$
$103$	−0.818994	−	0.472846i	−0.0806978	−	0.0465909i	−0.539806	+	0.841789i	$0.681502\pi$
$104$	1.00000			0.0980581
$105$	0.134806	+	1.51992i	0.0131557	+	0.148329i
$106$	−6.13221			−0.595613
$107$	−0.176096	−	0.101669i	−0.0170238	−	0.00982870i	0.491464	−	0.870898i	$-0.336462\pi$
$107$	−0.176096	−	0.101669i	−0.0170238	−	0.00982870i	−0.508488	+	0.861069i	$0.669795\pi$
$108$	−5.19065	+	0.239083i	−0.499470	+	0.0230057i
$109$	−0.166166	−	0.287808i	−0.0159158	−	0.0275670i	0.857958	−	0.513720i	$-0.171733\pi$
$109$	−0.166166	−	0.287808i	−0.0159158	−	0.0275670i	−0.873874	+	0.486153i	$0.838400\pi$
$110$	0.753573	−	1.30523i	0.0718504	−	0.124448i
$111$	0.670882	−	4.17868i	0.0636773	−	0.396622i
$112$	0.720858	−	2.54566i	0.0681147	−	0.240542i
$113$			5.94348i			0.559115i	0.960129	+	0.279558i	$0.0901878\pi$
$113$			5.94348i			0.559115i	−0.960129	+	0.279558i	$0.909812\pi$
$114$	2.47684	+	2.01438i	0.231978	+	0.188664i
$115$	0.605293	−	0.349466i	0.0564438	−	0.0325879i
$116$	1.92320	−	1.11036i	0.178565	−	0.103094i
$117$	−1.99796	−	2.23789i	−0.184712	−	0.206893i
$118$		−	0.691001i		−	0.0636118i
$119$	10.7144	+	11.0219i	0.982184	+	1.01038i
$120$	0.569440	+	0.0914229i	0.0519825	+	0.00834573i
$121$	4.74362	−	8.21619i	0.431238	−	0.746927i
$122$	5.56856	+	9.64503i	0.504154	+	0.873220i
$123$	19.3771	−	7.39130i	1.74718	−	0.666451i
$124$	−8.08293	−	4.66668i	−0.725869	−	0.419081i
$125$	−3.29285			−0.294521
$126$	−7.13714	+	3.47292i	−0.635827	+	0.309393i
$127$	5.83996			0.518213			0.259106	−	0.965849i	$-0.416572\pi$
$127$	5.83996			0.518213			0.259106	+	0.965849i	$0.416572\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−8.34247	+	3.18219i	−0.734514	+	0.280176i
$130$	0.166488	+	0.288366i	0.0146020	+	0.0252914i
$131$	8.26642	−	14.3179i	0.722241	−	1.25096i	−0.237859	−	0.971300i	$-0.576446\pi$
$131$	8.26642	−	14.3179i	0.722241	−	1.25096i	0.960100	−	0.279658i	$-0.0902210\pi$
$132$	7.74063	+	1.24275i	0.673735	+	0.108167i
$133$	4.69223	+	1.32871i	0.406868	+	0.115213i
$134$			11.9680i			1.03387i
$135$	−0.933125	−	1.45700i	−0.0803107	−	0.125399i
$136$	5.03147	−	2.90492i	0.431445	−	0.249095i
$137$	15.8292	−	9.13900i	1.35238	−	0.780797i	0.363798	−	0.931478i	$-0.381480\pi$
$137$	15.8292	−	9.13900i	1.35238	−	0.780797i	0.988582	+	0.150681i	$0.0481466\pi$
$138$	2.82059	+	2.29395i	0.240105	+	0.195274i
$139$			14.3010i			1.21300i	0.795085	+	0.606498i	$0.207426\pi$
$139$			14.3010i			1.21300i	−0.795085	+	0.606498i	$0.792574\pi$
$140$	0.854095	−	0.215951i	0.0721842	−	0.0182512i
$141$	−3.02669	+	18.8522i	−0.254893	+	1.58764i
$142$	−5.21129	+	9.02622i	−0.437322	+	0.757464i
$143$	2.26314	+	3.91988i	0.189253	+	0.327797i
$144$	0.611342	+	2.93705i	0.0509452	+	0.244754i
$145$	0.640380	+	0.369724i	0.0531807	+	0.0307039i
$146$	−3.39315			−0.280819
$147$	−7.91304	+	9.18606i	−0.652657	+	0.757654i
$148$	−2.44346			−0.200851
$149$	−4.91971	−	2.84040i	−0.403038	−	0.232694i	0.284756	−	0.958600i	$-0.408088\pi$
$149$	−4.91971	−	2.84040i	−0.403038	−	0.232694i	−0.687794	+	0.725906i	$0.741421\pi$
$150$	−3.01804	−	7.91215i	−0.246422	−	0.646024i
$151$	−10.0055	−	17.3301i	−0.814238	−	1.41030i	−0.909874	−	0.414885i	$-0.863822\pi$
$151$	−10.0055	−	17.3301i	−0.814238	−	1.41030i	0.0956355	−	0.995416i	$-0.469512\pi$
$152$	0.921615	−	1.59628i	0.0747528	−	0.129476i
$153$	−16.5536	−	5.45595i	−1.33828	−	0.441087i
$154$	11.6101	−	2.93550i	0.935565	−	0.236550i
$155$		−	3.10779i		−	0.249624i
$156$	−1.09285	+	1.34375i	−0.0874983	+	0.107586i
$157$	−12.6959	+	7.32998i	−1.01324	+	0.584996i	−0.912140	−	0.409880i	$-0.865571\pi$
$157$	−12.6959	+	7.32998i	−1.01324	+	0.584996i	−0.101104	+	0.994876i	$0.532237\pi$
$158$	−5.19255	+	2.99792i	−0.413097	+	0.238502i
$159$	6.70160	−	8.24017i	0.531472	−	0.653488i
$160$		−	0.332977i		−	0.0263241i
$161$	5.34344	+	1.51311i	0.421122	+	0.119250i
$162$	5.35135	−	7.23623i	0.420442	−	0.568532i
$163$	10.8138	−	18.7301i	0.847003	−	1.46705i	−0.0368682	−	0.999320i	$-0.511738\pi$
$163$	10.8138	−	18.7301i	0.847003	−	1.46705i	0.883871	−	0.467731i	$-0.154928\pi$
$164$	−5.98683	−	10.3695i	−0.467493	−	0.809721i
$165$	0.930357	+	2.43904i	0.0724282	+	0.189879i
$166$	−0.443135	−	0.255844i	−0.0343940	−	0.0198574i
$167$	−18.0059			−1.39334			−0.696670	−	0.717392i	$-0.745336\pi$
$167$	−18.0059			−1.39334			−0.696670	+	0.717392i	$0.745336\pi$
$168$	2.63294	+	3.75068i	0.203136	+	0.289372i
$169$	−1.00000			−0.0769231
$170$	1.67536	+	0.967271i	0.128494	+	0.0741863i
$171$	−5.41366	+	1.12684i	−0.413993	+	0.0861719i
$172$	2.57752	+	4.46439i	0.196534	+	0.340407i
$173$	7.62135	−	13.2006i	0.579440	−	1.00362i	−0.416103	−	0.909317i	$-0.636605\pi$
$173$	7.62135	−	13.2006i	0.579440	−	1.00362i	0.995544	−	0.0943025i	$-0.0300621\pi$
$174$	−0.609727	+	3.79777i	−0.0462233	+	0.287908i
$175$	−9.01640	−	9.27521i	−0.681576	−	0.701140i
$176$		−	4.52628i		−	0.341181i
$177$	0.928534	+	0.755162i	0.0697929	+	0.0567615i
$178$	−13.9862	+	8.07492i	−1.04831	+	0.605241i
$179$	−19.9262	+	11.5044i	−1.48936	+	0.859881i	−0.999926	−	0.0121613i	$-0.996129\pi$
$179$	−19.9262	+	11.5044i	−1.48936	+	0.859881i	−0.489431	+	0.872042i	$0.662796\pi$
$180$	−0.745164	+	0.665275i	−0.0555413	+	0.0495866i
$181$		−	2.21511i		−	0.164648i	−0.996606	−	0.0823239i	$-0.973766\pi$
$181$		−	2.21511i		−	0.164648i	0.996606	−	0.0823239i	$-0.0262342\pi$
$182$	−0.720858	+	2.54566i	−0.0534336	+	0.188697i
$183$	−19.0462	−	3.05784i	−1.40793	−	0.226042i
$184$	1.04952	−	1.81782i	0.0773717	−	0.134012i
$185$	−0.406807	−	0.704610i	−0.0299090	−	0.0518039i
$186$	15.1043	−	5.76146i	1.10750	−	0.422451i
$187$	22.7739	+	13.1485i	1.66539	+	0.961513i
$188$	11.0237			0.803985
$189$	3.13310	−	13.3860i	0.227899	−	0.973685i
$190$	0.613752			0.0445263
$191$	−22.1096	−	12.7650i	−1.59980	−	0.923644i	−0.991525	−	0.129916i	$-0.958529\pi$
$191$	−22.1096	−	12.7650i	−1.59980	−	0.923644i	−0.608273	−	0.793728i	$-0.708137\pi$
$192$	1.61832	−	0.617297i	0.116792	−	0.0445496i
$193$	−3.85366	−	6.67474i	−0.277393	−	0.480458i	0.693343	−	0.720607i	$-0.256137\pi$
$193$	−3.85366	−	6.67474i	−0.277393	−	0.480458i	−0.970736	+	0.240149i	$0.922804\pi$
$194$	0.535233	−	0.927051i	0.0384275	−	0.0665584i
$195$	−0.569440	−	0.0914229i	−0.0407784	−	0.00654693i
$196$	5.96073	+	3.67011i	0.425766	+	0.262151i
$197$		−	0.247179i		−	0.0176108i	−0.999961	−	0.00880540i	$-0.997197\pi$
$197$		−	0.247179i		−	0.0176108i	0.999961	−	0.00880540i	$-0.00280288\pi$
$198$	−10.1293	+	9.04335i	−0.719859	+	0.642683i
$199$	−5.12047	+	2.95631i	−0.362981	+	0.209567i	−0.670387	−	0.742011i	$-0.733872\pi$
$199$	−5.12047	+	2.95631i	−0.362981	+	0.209567i	0.307407	+	0.951578i	$0.400539\pi$
$200$	−4.23411	+	2.44456i	−0.299397	+	0.172857i
$201$	−16.0820	−	13.0792i	−1.13433	−	0.922537i
$202$			9.16482i			0.644834i
$203$	1.44024	+	5.69622i	0.101085	+	0.399796i
$204$	−1.59517	+	9.93571i	−0.111684	+	0.695639i
$205$	1.99347	−	3.45280i	0.139230	−	0.241154i
$206$	−0.472846	−	0.818994i	−0.0329448	−	0.0570620i
$207$	−6.16499	+	1.28323i	−0.428497	+	0.0891908i
$208$	0.866025	+	0.500000i	0.0600481	+	0.0346688i
$209$	8.34298			0.577096
$210$	−0.643217	+	1.38370i	−0.0443862	+	0.0954840i
$211$	−15.3534			−1.05697			−0.528487	−	0.848941i	$-0.677240\pi$
$211$	−15.3534			−1.05697			−0.528487	+	0.848941i	$0.677240\pi$
$212$	−5.31065	−	3.06610i	−0.364737	−	0.210581i
$213$	−6.43383	−	16.8670i	−0.440839	−	1.15571i
$214$	−0.101669	−	0.176096i	−0.00694994	−	0.0120376i
$215$	−0.858253	+	1.48654i	−0.0585324	+	0.101381i
$216$	−4.61478	−	2.38827i	−0.313996	−	0.162501i
$217$	17.7064	−	17.2124i	1.20199	−	1.16845i
$218$		−	0.332332i		−	0.0225084i
$219$	3.70822	−	4.55956i	0.250578	−	0.308106i
$220$	1.30523	−	0.753573i	0.0879984	−	0.0508059i
$221$	−5.03147	+	2.90492i	−0.338453	+	0.195406i
$222$	2.67034	−	3.28340i	0.179221	−	0.220367i
$223$		−	4.78734i		−	0.320584i	−0.987070	−	0.160292i	$-0.948756\pi$
$223$		−	4.78734i		−	0.320584i	0.987070	−	0.160292i	$-0.0512436\pi$
$224$	1.89711	−	1.84417i	0.126756	−	0.123219i
$225$	13.9302	+	4.59132i	0.928683	+	0.306088i
$226$	−2.97174	+	5.14720i	−0.197677	+	0.342387i
$227$	2.51933	+	4.36360i	0.167213	+	0.289622i	0.937439	−	0.348149i	$-0.113190\pi$
$227$	2.51933	+	4.36360i	0.167213	+	0.289622i	−0.770226	+	0.637771i	$0.779856\pi$
$228$	1.13782	+	2.98293i	0.0753540	+	0.197549i
$229$	18.2787	+	10.5532i	1.20789	+	0.697376i	0.962298	−	0.271997i	$-0.0876842\pi$
$229$	18.2787	+	10.5532i	1.20789	+	0.697376i	0.245592	+	0.969373i	$0.421018\pi$
$230$	0.698932			0.0460862
$231$	−8.74350	+	18.8091i	−0.575280	+	1.23755i
$232$	2.22072			0.145797
$233$	−5.86421	−	3.38570i	−0.384177	−	0.221805i	0.295457	−	0.955356i	$-0.404528\pi$
$233$	−5.86421	−	3.38570i	−0.384177	−	0.221805i	−0.679634	+	0.733551i	$0.737861\pi$
$234$	−0.611342	−	2.93705i	−0.0399647	−	0.192001i
$235$	1.83531	+	3.17886i	0.119723	+	0.207366i
$236$	0.345500	−	0.598424i	0.0224902	−	0.0389541i
$237$	1.64624	−	10.2538i	0.106934	−	0.666056i
$238$	3.76795	+	14.9024i	0.244240	+	0.965981i
$239$			22.9725i			1.48597i	0.669308	+	0.742985i	$0.266591\pi$
$239$			22.9725i			1.48597i	−0.669308	+	0.742985i	$0.733409\pi$
$240$	0.447438	+	0.363895i	0.0288820	+	0.0234893i
$241$	2.68769	−	1.55174i	0.173129	−	0.0999563i	−0.410931	−	0.911666i	$-0.634796\pi$
$241$	2.68769	−	1.55174i	0.173129	−	0.0999563i	0.584061	+	0.811710i	$0.301463\pi$
$242$	8.21619	−	4.74362i	0.528157	−	0.304932i
$243$	3.87546	+	15.0990i	0.248611	+	0.968603i
$244$			11.1371i			0.712981i
$245$	−0.0659454	+	2.32990i	−0.00421310	+	0.148852i
$246$	20.4768	+	3.28752i	1.30555	+	0.209605i
$247$	−0.921615	+	1.59628i	−0.0586409	+	0.101569i
$248$	−4.66668	−	8.08293i	−0.296335	−	0.513267i
$249$	0.828073	−	0.315864i	0.0524770	−	0.0200171i
$250$	−2.85169	−	1.64642i	−0.180357	−	0.104129i
$251$	10.9253			0.689598			0.344799	−	0.938677i	$-0.387947\pi$
$251$	10.9253			0.689598			0.344799	+	0.938677i	$0.387947\pi$
$252$	−7.91741	−	0.560930i	−0.498750	−	0.0353353i
$253$	9.50086			0.597314
$254$	5.05755	+	2.91998i	0.317339	+	0.183216i
$255$	−3.13070	+	1.19419i	−0.196052	+	0.0747829i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.28730	+	7.42583i	−0.267435	+	0.463210i	−0.968199	−	0.250183i	$-0.919509\pi$
$257$	−4.28730	+	7.42583i	−0.267435	+	0.463210i	0.700764	+	0.713393i	$0.252843\pi$
$258$	−8.81589	−	1.41538i	−0.548853	−	0.0881177i
$259$	1.76138	−	6.22020i	0.109447	−	0.386504i
$260$			0.332977i			0.0206503i
$261$	−4.43692	−	4.96972i	−0.274638	−	0.307618i
$262$	14.3179	−	8.26642i	0.884561	−	0.510701i
$263$	15.3736	−	8.87594i	0.947976	−	0.547314i	0.0555242	−	0.998457i	$-0.482317\pi$
$263$	15.3736	−	8.87594i	0.947976	−	0.547314i	0.892452	+	0.451143i	$0.148984\pi$
$264$	6.08221	+	4.94657i	0.374334	+	0.304440i
$265$		−	2.04188i		−	0.125432i
$266$	3.39923	+	3.49681i	0.208420	+	0.214403i
$267$	4.43415	−	27.6187i	0.271365	−	1.69024i
$268$	−5.98398	+	10.3646i	−0.365530	+	0.633116i
$269$	−2.13368	−	3.69565i	−0.130093	−	0.225328i	0.793619	−	0.608415i	$-0.208194\pi$
$269$	−2.13368	−	3.69565i	−0.130093	−	0.225328i	−0.923712	+	0.383087i	$0.874861\pi$
$270$	−0.0796089	−	1.72836i	−0.00484484	−	0.105185i
$271$	−8.62343	−	4.97874i	−0.523836	−	0.302437i	0.214667	−	0.976687i	$-0.431134\pi$
$271$	−8.62343	−	4.97874i	−0.523836	−	0.302437i	−0.738503	+	0.674250i	$0.764467\pi$
$272$	5.80984			0.352273
$273$	−2.63294	−	3.75068i	−0.159353	−	0.227002i
$274$	18.2780			1.10421
$275$	−19.1648	−	11.0648i	−1.15568	−	0.667232i
$276$	1.29573	+	3.39691i	0.0779939	+	0.204470i
$277$	−6.09028	−	10.5487i	−0.365929	−	0.633808i	0.622996	−	0.782225i	$-0.285915\pi$
$277$	−6.09028	−	10.5487i	−0.365929	−	0.633808i	−0.988925	+	0.148417i	$0.952582\pi$
$278$	−7.15050	+	12.3850i	−0.428859	+	0.742805i
$279$	−8.76485	+	26.5929i	−0.524738	+	1.59208i
$280$	0.847644	+	0.240029i	0.0506564	+	0.0143445i
$281$		−	21.6407i		−	1.29098i	−0.763771	−	0.645488i	$-0.776654\pi$
$281$		−	21.6407i		−	1.29098i	0.763771	−	0.645488i	$-0.223346\pi$
$282$	−12.0473	+	14.8131i	−0.717405	+	0.882107i
$283$	7.20489	−	4.15974i	0.428286	−	0.247271i	−0.270330	−	0.962768i	$-0.587133\pi$
$283$	7.20489	−	4.15974i	0.428286	−	0.247271i	0.698616	+	0.715497i	$0.253799\pi$
$284$	−9.02622	+	5.21129i	−0.535608	+	0.309233i
$285$	−0.670741	+	0.824731i	−0.0397313	+	0.0488528i
$286$			4.52628i			0.267645i
$287$	30.7128	−	7.76547i	1.81292	−	0.458381i
$288$	−0.939087	+	2.84923i	−0.0553362	+	0.167893i
$289$	−8.37714	+	14.5096i	−0.492773	+	0.853508i
$290$	0.369724	+	0.640380i	0.0217109	+	0.0376044i
$291$	0.660796	+	1.73235i	0.0387365	+	0.101552i
$292$	−2.93856	−	1.69658i	−0.171966	−	0.0992846i
$293$	−11.4700			−0.670085			−0.335043	−	0.942203i	$-0.608751\pi$
$293$	−11.4700			−0.670085			−0.335043	+	0.942203i	$0.608751\pi$
$294$	−11.4459	+	3.99885i	−0.667540	+	0.233217i
$295$	0.230087			0.0133962
$296$	−2.11609	−	1.22173i	−0.122995	−	0.0710115i
$297$	−1.08216	−	23.4944i	−0.0627930	−	1.36328i
$298$	−2.84040	−	4.91971i	−0.164540	−	0.284991i
$299$	−1.04952	+	1.81782i	−0.0606954	+	0.105127i
$300$	1.34237	−	8.36114i	0.0775019	−	0.482731i
$301$	−13.2228	+	3.34328i	−0.762151	+	0.192703i
$302$		−	20.0111i		−	1.15151i
$303$	−12.3152	−	10.0158i	−0.707492	−	0.575393i
$304$	1.59628	−	0.921615i	0.0915531	−	0.0528582i
$305$	−3.21157	+	1.85420i	−0.183894	+	0.106171i
$306$	−11.6078	−	13.0018i	−0.663577	−	0.743262i
$307$		−	27.9400i		−	1.59462i	−0.603569	−	0.797311i	$-0.706255\pi$
$307$		−	27.9400i		−	1.59462i	0.603569	−	0.797311i	$-0.293745\pi$
$308$	11.5224	+	3.26281i	0.656547	+	0.185916i
$309$	1.61728	+	0.259652i	0.0920036	+	0.0147711i
$310$	1.55390	−	2.69143i	0.0882554	−	0.152863i
$311$	−1.85576	−	3.21428i	−0.105231	−	0.182265i	0.808602	−	0.588356i	$-0.200225\pi$
$311$	−1.85576	−	3.21428i	−0.105231	−	0.182265i	−0.913832	+	0.406091i	$0.866891\pi$
$312$	−1.61832	+	0.617297i	−0.0916191	+	0.0349476i
$313$	−1.09308	−	0.631090i	−0.0617845	−	0.0356713i	0.468790	−	0.883310i	$-0.344690\pi$
$313$	−1.09308	−	0.631090i	−0.0617845	−	0.0356713i	−0.530574	+	0.847639i	$0.678024\pi$
$314$	−14.6600			−0.827310
$315$	−1.15640	−	2.37650i	−0.0651559	−	0.133901i
$316$	−5.99585			−0.337293
$317$	1.13709	+	0.656499i	0.0638653	+	0.0368727i	0.531593	−	0.847000i	$-0.321594\pi$
$317$	1.13709	+	0.656499i	0.0638653	+	0.0368727i	−0.467727	+	0.883873i	$0.654927\pi$
$318$	9.92384	−	3.78539i	0.556502	−	0.212274i
$319$	5.02580	+	8.70495i	0.281391	+	0.487384i
$320$	0.166488	−	0.288366i	0.00930698	−	0.0161202i
$321$	0.347738	+	0.0558289i	0.0194088	+	0.00311607i
$322$	3.87100	+	3.98211i	0.215722	+	0.221914i
$323$			10.7089i			0.595858i
$324$	8.25252	−	3.59108i	0.458473	−	0.199505i
$325$	4.23411	−	2.44456i	0.234866	−	0.135600i
$326$	18.7301	−	10.8138i	1.03736	−	0.598921i
$327$	0.446572	+	0.363190i	0.0246955	+	0.0200845i
$328$		−	11.9737i		−	0.661134i
$329$	−7.94651	+	28.0625i	−0.438105	+	1.54714i
$330$	−0.413806	+	2.57745i	−0.0227793	+	0.141884i
$331$	−11.5713	+	20.0420i	−0.636014	+	1.10161i	0.350285	+	0.936643i	$0.386085\pi$
$331$	−11.5713	+	20.0420i	−0.636014	+	1.10161i	−0.986299	+	0.164966i	$0.947249\pi$
$332$	−0.255844	−	0.443135i	−0.0140413	−	0.0243202i
$333$	1.49379	+	7.17655i	0.0818590	+	0.393272i
$334$	−15.5936	−	9.00296i	−0.853243	−	0.492620i
$335$	−3.98505			−0.217726
$336$	0.404850	+	4.56466i	0.0220864	+	0.249022i
$337$	−7.47071			−0.406955			−0.203478	−	0.979080i	$-0.565224\pi$
$337$	−7.47071			−0.406955			−0.203478	+	0.979080i	$0.565224\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	−3.66889	−	9.61842i	−0.199267	−	0.522401i
$340$	0.967271	+	1.67536i	0.0524576	+	0.0908593i
$341$	21.1227	−	36.5857i	1.14386	−	1.98122i
$342$	−5.25179	−	1.73095i	−0.283984	−	0.0935992i
$343$	−13.6397	+	12.5283i	−0.736474	+	0.676466i
$344$			5.15504i			0.277941i
$345$	−0.763830	+	0.939191i	−0.0411232	+	0.0505644i
$346$	13.2006	−	7.62135i	0.709666	−	0.409726i
$347$	13.2900	−	7.67298i	0.713444	−	0.411907i	−0.0988910	−	0.995098i	$-0.531530\pi$
$347$	13.2900	−	7.67298i	0.713444	−	0.411907i	0.812335	+	0.583191i	$0.198196\pi$
$348$	−2.42692	+	2.98410i	−0.130097	+	0.159964i
$349$			22.1082i			1.18343i	0.806149	+	0.591713i	$0.201548\pi$
$349$			22.1082i			1.18343i	−0.806149	+	0.591713i	$0.798452\pi$
$350$	−3.17083	−	12.5408i	−0.169488	−	0.670332i
$351$	4.61478	+	2.38827i	0.246318	+	0.127477i
$352$	2.26314	−	3.91988i	0.120626	−	0.208930i
$353$	12.9011	+	22.3454i	0.686657	+	1.18932i	0.972913	+	0.231172i	$0.0742559\pi$
$353$	12.9011	+	22.3454i	0.686657	+	1.18932i	−0.286256	+	0.958153i	$0.592411\pi$
$354$	0.426553	+	1.11826i	0.0226710	+	0.0594347i
$355$	−3.00552	−	1.73524i	−0.159516	−	0.0920969i
$356$	−16.1498			−0.855940
$357$	−24.1430	−	11.2230i	−1.27778	−	0.593983i
$358$	−23.0088			−1.21605
$359$	4.45682	+	2.57315i	0.235222	+	0.135805i	0.612979	−	0.790099i	$-0.289971\pi$
$359$	4.45682	+	2.57315i	0.235222	+	0.135805i	−0.377757	+	0.925905i	$0.623304\pi$
$360$	−0.977969	+	0.203563i	−0.0515435	+	0.0107287i
$361$	−7.80125	−	13.5122i	−0.410592	−	0.711167i
$362$	1.10755	−	1.91834i	0.0582118	−	0.100826i
$363$	−2.60484	+	16.2246i	−0.136719	+	0.851572i
$364$	−1.89711	+	1.84417i	−0.0994356	+	0.0966610i
$365$		−	1.12984i		−	0.0591385i
$366$	−14.9655	−	12.1712i	−0.782261	−	0.636201i
$367$	−16.7000	+	9.64174i	−0.871732	+	0.503295i	−0.867924	−	0.496698i	$-0.834546\pi$
$367$	−16.7000	+	9.64174i	−0.871732	+	0.503295i	−0.00380887	+	0.999993i	$0.501212\pi$
$368$	1.81782	−	1.04952i	0.0947606	−	0.0547101i
$369$	−26.7957	+	23.9229i	−1.39493	+	1.24538i
$370$		−	0.813613i		−	0.0422977i
$371$	11.6335	−	11.3089i	0.603980	−	0.587126i
$372$	15.9615	+	2.56259i	0.827564	+	0.132864i
$373$	−3.20259	+	5.54705i	−0.165824	+	0.287216i	−0.936948	−	0.349470i	$-0.886362\pi$
$373$	−3.20259	+	5.54705i	−0.165824	+	0.287216i	0.771124	+	0.636685i	$0.219695\pi$
$374$	13.1485	+	22.7739i	0.679893	+	1.17761i
$375$	5.32886	−	2.03266i	0.275181	−	0.104966i
$376$	9.54679	+	5.51184i	0.492338	+	0.284252i
$377$	−2.22072			−0.114373
$378$	9.40632	−	10.0260i	0.483809	−	0.515683i
$379$	5.46425			0.280680			0.140340	−	0.990103i	$-0.455180\pi$
$379$	5.46425			0.280680			0.140340	+	0.990103i	$0.455180\pi$
$380$	0.531525	+	0.306876i	0.0272666	+	0.0157424i
$381$	−9.45089	+	3.60499i	−0.484184	+	0.184689i
$382$	−12.7650	−	22.1096i	−0.653115	−	1.13123i
$383$	0.116295	−	0.201428i	0.00594239	−	0.0102925i	−0.863039	−	0.505137i	$-0.831442\pi$
$383$	0.116295	−	0.201428i	0.00594239	−	0.0102925i	0.868981	+	0.494845i	$0.164775\pi$
$384$	1.71015	+	0.274563i	0.0872708	+	0.0140112i
$385$	0.977454	+	3.86588i	0.0498157	+	0.197023i
$386$		−	7.70733i		−	0.392293i
$387$	11.5364	−	10.2996i	0.586428	−	0.523556i
$388$	0.927051	−	0.535233i	0.0470639	−	0.0271724i
$389$	−12.3742	+	7.14424i	−0.627396	+	0.362227i	−0.779743	−	0.626100i	$-0.784650\pi$
$389$	−12.3742	+	7.14424i	−0.627396	+	0.362227i	0.152347	+	0.988327i	$0.451317\pi$
$390$	−0.447438	−	0.363895i	−0.0226569	−	0.0184265i
$391$			12.1951i			0.616733i
$392$	3.32708	+	6.15878i	0.168043	+	0.311065i
$393$	−4.53930	+	28.2737i	−0.228978	+	1.42622i
$394$	0.123590	−	0.214063i	0.00622635	−	0.0107844i
$395$	−0.998238	−	1.72900i	−0.0502268	−	0.0869954i
$396$	−13.2939	+	2.76711i	−0.668045	+	0.139052i
$397$	14.4770	+	8.35830i	0.726580	+	0.419491i	0.817170	−	0.576397i	$-0.195542\pi$
$397$	14.4770	+	8.35830i	0.726580	+	0.419491i	−0.0905897	+	0.995888i	$0.528875\pi$
$398$	−5.91261			−0.296372
$399$	−8.41371	+	0.746231i	−0.421212	+	0.0373583i
$400$	−4.88913			−0.244456
$401$	29.7114	+	17.1539i	1.48372	+	0.856624i	0.999829	−	0.0185071i	$-0.00589135\pi$
$401$	29.7114	+	17.1539i	1.48372	+	0.856624i	0.483887	+	0.875131i	$0.339225\pi$
$402$	−7.38778	−	19.3679i	−0.368469	−	0.965984i
$403$	4.66668	+	8.08293i	0.232464	+	0.402640i
$404$	−4.58241	+	7.93697i	−0.227983	+	0.394879i
$405$	2.40949	+	1.78187i	0.119729	+	0.0885421i
$406$	−1.60082	+	5.65319i	−0.0794476	+	0.280563i
$407$		−	11.0598i		−	0.548213i
$408$	−6.34931	+	7.80699i	−0.314338	+	0.386504i
$409$	−15.3149	+	8.84208i	−0.757274	+	0.437212i	−0.828316	−	0.560261i	$-0.810701\pi$
$409$	−15.3149	+	8.84208i	−0.757274	+	0.437212i	0.0710420	+	0.997473i	$0.477368\pi$
$410$	3.45280	−	1.99347i	0.170521	−	0.0984506i
$411$	−19.9752	+	24.5611i	−0.985302	+	1.21151i
$412$		−	0.945692i		−	0.0465909i
$413$	1.27432	+	1.31090i	0.0627054	+	0.0645053i
$414$	−5.98066	−	1.97118i	−0.293933	−	0.0968784i
$415$	0.0851901	−	0.147554i	0.00418182	−	0.00724312i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	−8.82797	−	23.1435i	−0.432308	−	1.13334i
$418$	7.22523	+	4.17149i	0.353398	+	0.204034i
$419$	13.1936			0.644550			0.322275	−	0.946646i	$-0.395552\pi$
$419$	13.1936			0.644550			0.322275	+	0.946646i	$0.395552\pi$
$420$	−1.24889	+	0.876707i	−0.0609396	+	0.0427789i
$421$	18.6418			0.908546			0.454273	−	0.890863i	$-0.349899\pi$
$421$	18.6418			0.908546			0.454273	+	0.890863i	$0.349899\pi$
$422$	−13.2965	−	7.67672i	−0.647262	−	0.373697i
$423$	−6.73924	−	32.3771i	−0.327673	−	1.57423i
$424$	−3.06610	−	5.31065i	−0.148903	−	0.257908i
$425$	14.2025	−	24.5995i	0.688924	−	1.19325i
$426$	2.86165	−	17.8242i	0.138648	−	0.863585i
$427$	−28.3513	−	8.02829i	−1.37201	−	0.388516i
$428$		−	0.203338i		−	0.00982870i
$429$	−6.08221	−	4.94657i	−0.293652	−	0.238822i
$430$	−1.48654	+	0.858253i	−0.0716872	+	0.0413886i
$431$	−7.23932	+	4.17962i	−0.348706	+	0.201325i	−0.664115	−	0.747630i	$-0.731191\pi$
$431$	−7.23932	+	4.17962i	−0.348706	+	0.201325i	0.315409	+	0.948956i	$0.397858\pi$
$432$	−2.80238	−	4.37569i	−0.134829	−	0.210526i
$433$		−	21.2262i		−	1.02007i	−0.860154	−	0.510034i	$-0.829633\pi$
$433$		−	21.2262i		−	1.02007i	0.860154	−	0.510034i	$-0.170367\pi$
$434$	23.9404	−	6.05312i	1.14918	−	0.290559i
$435$	−1.26457	−	0.203025i	−0.0606313	−	0.00973429i
$436$	0.166166	−	0.287808i	0.00795791	−	0.0137835i
$437$	1.93451	+	3.35067i	0.0925401	+	0.160284i
$438$	5.49119	−	2.09458i	0.262379	−	0.100083i
$439$	9.63394	+	5.56216i	0.459803	+	0.265467i	0.711961	−	0.702219i	$-0.247807\pi$
$439$	9.63394	+	5.56216i	0.459803	+	0.265467i	−0.252158	+	0.967686i	$0.581140\pi$
$440$	1.50715			0.0718504
$441$	7.13526	−	19.7506i	0.339774	−	0.940507i
$442$	−5.80984			−0.276346
$443$	−4.41605	−	2.54961i	−0.209813	−	0.121136i	0.391411	−	0.920216i	$-0.371987\pi$
$443$	−4.41605	−	2.54961i	−0.209813	−	0.121136i	−0.601224	+	0.799080i	$0.705320\pi$
$444$	3.95428	−	1.50834i	0.187662	−	0.0715825i
$445$	−2.68876	−	4.65707i	−0.127459	−	0.220766i
$446$	2.39367	−	4.14596i	0.113344	−	0.196317i
$447$	9.71501	+	1.55973i	0.459504	+	0.0737729i
$448$	2.56503	−	0.648546i	0.121186	−	0.0306409i
$449$		−	26.3966i		−	1.24573i	−0.782328	−	0.622867i	$-0.785968\pi$
$449$		−	26.3966i		−	1.24573i	0.782328	−	0.622867i	$-0.214032\pi$
$450$	9.76829	+	10.9413i	0.460482	+	0.515779i
$451$	46.9352	−	27.0981i	2.21009	−	1.27600i
$452$	−5.14720	+	2.97174i	−0.242104	+	0.139779i
$453$	26.8899	+	21.8691i	1.26340	+	1.02750i
$454$			5.03865i			0.236476i
$455$	−0.847644	−	0.240029i	−0.0397381	−	0.0112527i
$456$	−0.506082	+	3.15220i	−0.0236995	+	0.147615i
$457$	−15.9720	+	27.6643i	−0.747138	+	1.29408i	0.202051	+	0.979375i	$0.435239\pi$
$457$	−15.9720	+	27.6643i	−0.747138	+	1.29408i	−0.949189	+	0.314706i	$0.898094\pi$
$458$	10.5532	+	18.2787i	0.493119	+	0.854108i
$459$	30.1569	−	1.38903i	1.40760	−	0.0648345i
$460$	0.605293	+	0.349466i	0.0282219	+	0.0162939i
$461$	4.47836			0.208578			0.104289	−	0.994547i	$-0.466743\pi$
$461$	4.47836			0.208578			0.104289	+	0.994547i	$0.466743\pi$
$462$	−16.9767	+	11.9174i	−0.789826	+	0.554449i
$463$	−33.1268			−1.53953			−0.769766	−	0.638327i	$-0.779627\pi$
$463$	−33.1268			−1.53953			−0.769766	+	0.638327i	$0.779627\pi$
$464$	1.92320	+	1.11036i	0.0892823	+	0.0515472i
$465$	1.91843	+	5.02939i	0.0889651	+	0.233232i
$466$	−3.38570	−	5.86421i	−0.156840	−	0.271654i
$467$	−9.54791	+	16.5375i	−0.441825	+	0.765263i	−0.997825	−	0.0659195i	$-0.979002\pi$
$467$	−9.54791	+	16.5375i	−0.441825	+	0.765263i	0.556000	+	0.831182i	$0.312335\pi$
$468$	0.939087	−	2.84923i	0.0434093	−	0.131706i
$469$	−22.0710	−	22.7045i	−1.01914	−	1.04840i
$470$			3.67063i			0.169313i
$471$	16.0212	−	19.6994i	0.738218	−	0.907699i
$472$	0.598424	−	0.345500i	0.0275447	−	0.0159029i
$473$	−20.2071	+	11.6666i	−0.929124	+	0.536430i
$474$	6.55258	−	8.05693i	0.300970	−	0.370067i
$475$		−	9.01178i		−	0.413489i
$476$	−4.18807	+	14.7899i	−0.191960	+	0.677892i
$477$	−5.75868	+	17.4721i	−0.263672	+	0.799991i
$478$	−11.4863	+	19.8948i	−0.525370	+	0.909967i
$479$	−0.0824984	−	0.142891i	−0.00376945	−	0.00652888i	0.864135	−	0.503261i	$-0.167867\pi$
$479$	−0.0824984	−	0.142891i	−0.00376945	−	0.00652888i	−0.867904	+	0.496732i	$0.834533\pi$
$480$	0.205545	+	0.538861i	0.00938182	+	0.0245955i
$481$	2.11609	+	1.22173i	0.0964856	+	0.0557060i
$482$	3.10348			0.141360
$483$	−9.58141	+	0.849797i	−0.435969	+	0.0386671i
$484$	9.48724			0.431238
$485$	0.308686	+	0.178220i	0.0140167	+	0.00809256i
$486$	−4.19327	+	15.0139i	−0.190211	+	0.681043i
$487$	7.73446	+	13.3965i	0.350482	+	0.607053i	0.986334	−	0.164758i	$-0.0526845\pi$
$487$	7.73446	+	13.3965i	0.350482	+	0.607053i	−0.635852	+	0.771811i	$0.719351\pi$
$488$	−5.56856	+	9.64503i	−0.252077	+	0.436610i
$489$	−5.93813	+	36.9865i	−0.268532	+	1.67259i
$490$	−1.22206	+	1.98478i	−0.0552071	+	0.0896633i
$491$		−	19.5193i		−	0.880892i	−0.897779	−	0.440446i	$-0.854820\pi$
$491$		−	19.5193i		−	0.880892i	0.897779	−	0.440446i	$-0.145180\pi$
$492$	16.0896	+	13.0855i	0.725376	+	0.589938i
$493$	−11.1735	+	6.45102i	−0.503229	+	0.290539i
$494$	−1.59628	+	0.921615i	−0.0718202	+	0.0414654i
$495$	−3.01122	−	3.37283i	−0.135344	−	0.151597i
$496$		−	9.33337i		−	0.419081i
$497$	−6.75953	−	26.7343i	−0.303206	−	1.19920i
$498$	0.875065	+	0.140491i	0.0392126	+	0.00629553i
$499$	16.0973	−	27.8814i	0.720614	−	1.24814i	−0.240139	−	0.970738i	$-0.577193\pi$
$499$	16.0973	−	27.8814i	0.720614	−	1.24814i	0.960754	−	0.277402i	$-0.0894735\pi$
$500$	−1.64642	−	2.85169i	−0.0736303	−	0.127531i
$501$	29.1393	−	11.1150i	1.30185	−	0.496582i
$502$	9.46157	+	5.46264i	0.422291	+	0.243810i
$503$	39.0633			1.74174			0.870872	−	0.491509i	$-0.163555\pi$
$503$	39.0633			1.74174			0.870872	+	0.491509i	$0.163555\pi$
$504$	−6.57621	−	4.44448i	−0.292928	−	0.197973i
$505$	−3.05167			−0.135797
$506$	8.22799	+	4.75043i	0.365779	+	0.211182i
$507$	1.61832	−	0.617297i	0.0718719	−	0.0274151i
$508$	2.91998	+	5.05755i	0.129553	+	0.224393i
$509$	−17.4524	+	30.2285i	−0.773566	+	1.33986i	0.162031	+	0.986786i	$0.448196\pi$
$509$	−17.4524	+	30.2285i	−0.773566	+	1.33986i	−0.935597	+	0.353070i	$0.885138\pi$
$510$	−3.30836	−	0.531153i	−0.146497	−	0.0235198i
$511$	6.43718	−	6.25756i	0.284764	−	0.276818i
$512$		−	1.00000i		−	0.0441942i
$513$	8.06540	−	5.16542i	0.356096	−	0.228059i
$514$	−7.42583	+	4.28730i	−0.327539	+	0.189105i
$515$	0.272706	−	0.157447i	0.0120168	−	0.00693793i
$516$	−6.92709	−	5.63370i	−0.304948	−	0.248010i
$517$			49.8963i			2.19444i
$518$	4.63550	−	4.50616i	0.203672	−	0.197989i
$519$	−4.18507	+	26.0673i	−0.183704	+	1.14423i
$520$	−0.166488	+	0.288366i	−0.00730099	+	0.0126457i
$521$	10.7931	+	18.6942i	0.472855	+	0.819009i	0.999517	−	0.0310658i	$-0.00989016\pi$
$521$	10.7931	+	18.6942i	0.472855	+	0.819009i	−0.526662	+	0.850074i	$0.676557\pi$
$522$	−1.35762	−	6.52237i	−0.0594214	−	0.285476i
$523$	24.1312	+	13.9322i	1.05518	+	0.609211i	0.924096	−	0.382159i	$-0.124819\pi$
$523$	24.1312	+	13.9322i	1.05518	+	0.609211i	0.131089	+	0.991371i	$0.458153\pi$
$524$	16.5328			0.722241
$525$	20.3169	+	9.44442i	0.886704	+	0.412188i
$526$	17.7519			0.774019
$527$	46.9606	+	27.1127i	2.04563	+	1.18105i
$528$	2.79406	+	7.32495i	0.121596	+	0.318778i
$529$	−9.29701	−	16.1029i	−0.404218	−	0.700126i
$530$	1.02094	−	1.76832i	0.0443468	−	0.0768109i
$531$	−1.96882	−	0.648910i	−0.0854395	−	0.0281603i
$532$	1.19542	+	4.72794i	0.0518280	+	0.204982i
$533$			11.9737i			0.518637i
$534$	17.6494	−	21.7014i	0.763765	−	0.939111i
$535$	0.0586357	−	0.0338533i	0.00253504	−	0.00146361i
$536$	−10.3646	+	5.98398i	−0.447680	+	0.258468i
$537$	25.1453	−	30.9182i	1.08510	−	1.33422i
$538$		−	4.26737i		−	0.183979i
$539$	−16.6120	+	26.9799i	−0.715528	+	1.16211i
$540$	0.795239	−	1.53661i	0.0342216	−	0.0661252i
$541$	5.20234	−	9.01072i	0.223666	−	0.387401i	−0.732252	−	0.681033i	$-0.761531\pi$
$541$	5.20234	−	9.01072i	0.223666	−	0.387401i	0.955918	+	0.293632i	$0.0948641\pi$
$542$	−4.97874	−	8.62343i	−0.213855	−	0.370408i
$543$	1.36738	+	3.58474i	0.0586799	+	0.153836i
$544$	5.03147	+	2.90492i	0.215723	+	0.124547i
$545$	0.110659			0.00474010
$546$	−0.404850	−	4.56466i	−0.0173260	−	0.195349i
$547$	16.7414			0.715811			0.357905	−	0.933758i	$-0.383491\pi$
$547$	16.7414			0.715811			0.357905	+	0.933758i	$0.383491\pi$
$548$	15.8292	+	9.13900i	0.676190	+	0.390399i
$549$	32.7103	−	6.80859i	1.39604	−	0.290584i
$550$	−11.0648	−	19.1648i	−0.471804	−	0.817189i
$551$	−2.04665	+	3.54490i	−0.0871901	+	0.151018i
$552$	−0.576319	+	3.58968i	−0.0245298	+	0.152787i
$553$	4.32215	−	15.2634i	0.183797	−	0.649064i
$554$		−	12.1806i		−	0.517502i
$555$	1.09329	+	0.889160i	0.0464078	+	0.0377427i
$556$	−12.3850	+	7.15050i	−0.525243	+	0.303249i
$557$	−8.21658	+	4.74385i	−0.348148	+	0.201003i	−0.663869	−	0.747849i	$-0.731087\pi$
$557$	−8.21658	+	4.74385i	−0.348148	+	0.201003i	0.315721	+	0.948852i	$0.397753\pi$
$558$	−20.8870	+	18.6477i	−0.884219	+	0.789421i
$559$		−	5.15504i		−	0.218035i
$560$	0.614066	+	0.631693i	0.0259490	+	0.0266939i
$561$	−44.9718	−	7.22017i	−1.89871	−	0.304836i
$562$	10.8203	−	18.7414i	0.456429	−	0.790558i
$563$	18.4173	+	31.8997i	0.776197	+	1.34441i	0.934119	+	0.356961i	$0.116187\pi$
$563$	18.4173	+	31.8997i	0.776197	+	1.34441i	−0.157922	+	0.987452i	$0.550479\pi$
$564$	−17.8398	+	6.80489i	−0.751191	+	0.286537i
$565$	−1.71390	−	0.989519i	−0.0721042	−	0.0416294i
$566$	8.31949			0.349694
$567$	3.19276	+	23.5967i	0.134084	+	0.990970i
$568$	−10.4226			−0.437322
$569$	26.2236	+	15.1402i	1.09935	+	0.634711i	0.936050	−	0.351866i	$-0.114453\pi$
$569$	26.2236	+	15.1402i	1.09935	+	0.634711i	0.163301	+	0.986576i	$0.447786\pi$
$570$	−0.993244	+	0.378867i	−0.0416024	+	0.0158690i
$571$	12.5799	+	21.7890i	0.526451	+	0.911840i	0.999525	+	0.0308175i	$0.00981106\pi$
$571$	12.5799	+	21.7890i	0.526451	+	0.911840i	−0.473074	+	0.881023i	$0.656856\pi$
$572$	−2.26314	+	3.91988i	−0.0946267	+	0.163898i
$573$	43.6602	+	7.00959i	1.82393	+	0.292830i
$574$	30.4808	+	8.63131i	1.27224	+	0.360264i
$575$		−	10.2625i		−	0.427975i
$576$	−2.23789	+	1.99796i	−0.0932454	+	0.0832484i
$577$	−19.3209	+	11.1549i	−0.804341	+	0.464386i	−0.844987	−	0.534787i	$-0.820392\pi$
$577$	−19.3209	+	11.1549i	−0.804341	+	0.464386i	0.0406461	+	0.999174i	$0.487058\pi$
$578$	−14.5096	+	8.37714i	−0.603521	+	0.348443i
$579$	10.3567	+	8.42298i	0.430411	+	0.350047i
$580$			0.739448i			0.0307039i
$581$	1.31250	−	0.331854i	0.0544516	−	0.0137676i
$582$	−0.293910	+	1.83066i	−0.0121830	+	0.0758833i
$583$	13.8781	−	24.0375i	0.574770	−	0.995531i
$584$	−1.69658	−	2.93856i	−0.0702048	−	0.121598i
$585$	0.977969	−	0.203563i	0.0404340	−	0.00841627i
$586$	−9.93332	−	5.73501i	−0.410342	−	0.236911i
$587$	−11.7401			−0.484565			−0.242283	−	0.970206i	$-0.577896\pi$
$587$	−11.7401			−0.484565			−0.242283	+	0.970206i	$0.577896\pi$
$588$	−11.9119	−	2.25986i	−0.491238	−	0.0931951i
$589$	17.2035			0.708859
$590$	0.199261	+	0.115043i	0.00820345	+	0.00473626i
$591$	0.152583	+	0.400014i	0.00627643	+	0.0164544i
$592$	−1.22173	−	2.11609i	−0.0502127	−	0.0869709i
$593$	1.64629	−	2.85145i	0.0676050	−	0.117095i	−0.830242	−	0.557404i	$-0.811798\pi$
$593$	1.64629	−	2.85145i	0.0676050	−	0.117095i	0.897847	+	0.440308i	$0.145131\pi$
$594$	10.8100	−	20.8878i	0.443540	−	0.857036i
$595$	−4.96216	+	1.25464i	−0.203429	+	0.0514352i
$596$		−	5.68079i		−	0.232694i
$597$	6.46162	−	7.94509i	0.264456	−	0.325171i
$598$	−1.81782	+	1.04952i	−0.0743363	+	0.0429181i
$599$	−15.6640	+	9.04361i	−0.640013	+	0.369512i	−0.784620	−	0.619977i	$-0.787142\pi$
$599$	−15.6640	+	9.04361i	−0.640013	+	0.369512i	0.144606	+	0.989489i	$0.453808\pi$
$600$	5.34310	−	6.56978i	0.218131	−	0.268210i
$601$			9.76688i			0.398399i	0.979959	+	0.199200i	$0.0638342\pi$
$601$			9.76688i			0.398399i	−0.979959	+	0.199200i	$0.936166\pi$
$602$	−13.1229	−	3.71605i	−0.534851	−	0.151455i
$603$	34.0995	+	11.2390i	1.38864	+	0.457686i
$604$	10.0055	−	17.3301i	0.407119	−	0.705151i
$605$	1.57951	+	2.73580i	0.0642164	+	0.111226i
$606$	−5.65742	−	14.8316i	−0.229817	−	0.602491i
$607$	−30.5287	−	17.6258i	−1.23912	−	0.715407i	−0.270207	−	0.962802i	$-0.587092\pi$
$607$	−30.5287	−	17.6258i	−1.23912	−	0.715407i	−0.968915	+	0.247395i	$0.920425\pi$
$608$	1.84323			0.0747528
$609$	−5.84702	−	8.32922i	−0.236933	−	0.337517i
$610$	−3.70840			−0.150149
$611$	−9.54679	−	5.51184i	−0.386222	−	0.222985i
$612$	−3.55180	−	17.0638i	−0.143573	−	0.689763i
$613$	2.79282	+	4.83731i	0.112801	+	0.195377i	0.916899	−	0.399120i	$-0.130684\pi$
$613$	2.79282	+	4.83731i	0.112801	+	0.195377i	−0.804098	+	0.594497i	$0.797351\pi$
$614$	13.9700	−	24.1968i	0.563784	−	0.976503i
$615$	−1.09467	+	6.81828i	−0.0441412	+	0.274939i
$616$	8.34725	+	8.58686i	0.336320	+	0.345974i
$617$		−	8.51510i		−	0.342805i	−0.985201	−	0.171402i	$-0.945170\pi$
$617$		−	8.51510i		−	0.342805i	0.985201	−	0.171402i	$-0.0548298\pi$
$618$	1.27078	+	1.03350i	0.0511181	+	0.0415736i
$619$	−1.25386	+	0.723914i	−0.0503967	+	0.0290966i	−0.524987	−	0.851110i	$-0.675930\pi$
$619$	−1.25386	+	0.723914i	−0.0503967	+	0.0290966i	0.474590	+	0.880207i	$0.342596\pi$
$620$	2.69143	−	1.55390i	0.108090	−	0.0624060i
$621$	9.18476	−	5.88231i	0.368572	−	0.236049i
$622$		−	3.71153i		−	0.148819i
$623$	11.6417	−	41.1120i	0.466417	−	1.64712i
$624$	−1.71015	−	0.274563i	−0.0684608	−	0.0109913i
$625$	−11.6746	+	20.2210i	−0.466984	+	0.808840i
$626$	−0.631090	−	1.09308i	−0.0252234	−	0.0436883i
$627$	−13.5016	+	5.15010i	−0.539201	+	0.205675i
$628$	−12.6959	−	7.32998i	−0.506622	−	0.292498i
$629$	14.1961			0.566035
$630$	0.186777	−	2.63631i	0.00744136	−	0.105033i
$631$	−23.3427			−0.929257			−0.464628	−	0.885506i	$-0.653812\pi$
$631$	−23.3427			−0.929257			−0.464628	+	0.885506i	$0.653812\pi$
$632$	−5.19255	−	2.99792i	−0.206549	−	0.119251i
$633$	24.8467	−	9.47763i	0.987567	−	0.376702i
$634$	0.656499	+	1.13709i	0.0260729	+	0.0451596i
$635$	−0.972285	+	1.68405i	−0.0385839	+	0.0668293i
$636$	10.4870	+	1.68368i	0.415837	+	0.0667621i
$637$	−3.32708	−	6.15878i	−0.131824	−	0.244020i
$638$			10.0516i			0.397947i
$639$	20.8239	+	23.3246i	0.823782	+	0.922706i
$640$	0.288366	−	0.166488i	0.0113987	−	0.00658103i
$641$	−28.1042	+	16.2260i	−1.11005	+	0.640888i	−0.938842	−	0.344347i	$-0.888100\pi$
$641$	−28.1042	+	16.2260i	−1.11005	+	0.640888i	−0.171208	+	0.985235i	$0.554767\pi$
$642$	0.273236	+	0.222218i	0.0107837	+	0.00877026i
$643$		−	37.0238i		−	1.46007i	−0.683407	−	0.730037i	$-0.739503\pi$
$643$		−	37.0238i		−	1.46007i	0.683407	−	0.730037i	$-0.260497\pi$
$644$	1.36133	+	5.38411i	0.0536438	+	0.212164i
$645$	0.471288	−	2.93548i	0.0185570	−	0.115585i
$646$	−5.35444	+	9.27416i	−0.210667	+	0.364887i
$647$	2.97778	+	5.15766i	0.117069	+	0.202769i	0.918605	−	0.395178i	$-0.129317\pi$
$647$	2.97778	+	5.15766i	0.117069	+	0.202769i	−0.801536	+	0.597946i	$0.795984\pi$
$648$	8.94244	+	1.01629i	0.351292	+	0.0399237i
$649$	2.70864	+	1.56383i	0.106323	+	0.0613858i
$650$	4.88913			0.191767
$651$	−18.0294	+	38.7851i	−0.706629	+	1.52011i
$652$	21.6276			0.847003
$653$	−16.8532	−	9.73022i	−0.659518	−	0.380773i	0.132575	−	0.991173i	$-0.457675\pi$
$653$	−16.8532	−	9.73022i	−0.659518	−	0.380773i	−0.792093	+	0.610400i	$0.791009\pi$
$654$	0.205148	+	0.537818i	0.00802191	+	0.0210303i
$655$	2.75252	+	4.76751i	0.107550	+	0.186282i
$656$	5.98683	−	10.3695i	0.233746	−	0.404861i
$657$	−3.18647	+	9.66787i	−0.124316	+	0.377180i
$658$	−20.9131	+	20.3296i	−0.815279	+	0.792530i
$659$		−	29.7099i		−	1.15733i	−0.815564	−	0.578667i	$-0.803573\pi$
$659$		−	29.7099i		−	1.15733i	0.815564	−	0.578667i	$-0.196427\pi$
$660$	−1.64709	+	2.02523i	−0.0641129	+	0.0788320i
$661$	3.03239	−	1.75075i	0.117946	−	0.0680963i	−0.439866	−	0.898063i	$-0.644974\pi$
$661$	3.03239	−	1.75075i	0.117946	−	0.0680963i	0.557813	+	0.829967i	$0.311641\pi$
$662$	−20.0420	+	11.5713i	−0.778955	+	0.449730i
$663$	6.34931	−	7.80699i	0.246587	−	0.303198i
$664$		−	0.511689i		−	0.0198574i
$665$	−1.16435	+	1.13187i	−0.0451517	+	0.0438919i
$666$	−2.29462	+	6.96197i	−0.0889146	+	0.269771i
$667$	−2.33069	+	4.03688i	−0.0902448	+	0.156309i
$668$	−9.00296	−	15.5936i	−0.348335	−	0.603334i
$669$	2.95521	+	7.74743i	0.114255	+	0.299533i
$670$	−3.45115	−	1.99252i	−0.133330	−	0.0769779i
$671$	−50.4098			−1.94605
$672$	−1.93172	+	4.15553i	−0.0745176	+	0.160303i
$673$	42.6768			1.64507			0.822535	−	0.568714i	$-0.192559\pi$
$673$	42.6768			1.64507			0.822535	+	0.568714i	$0.192559\pi$
$674$	−6.46982	−	3.73535i	−0.249208	−	0.143880i
$675$	−25.3777	+	1.16890i	−0.976790	+	0.0449912i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	8.56746	−	14.8393i	0.329274	−	0.570320i	−0.653094	−	0.757277i	$-0.726529\pi$
$677$	8.56746	−	14.8393i	0.329274	−	0.570320i	0.982368	+	0.186957i	$0.0598626\pi$
$678$	1.63186	−	10.1642i	0.0626711	−	0.390355i
$679$	0.694247	+	2.74578i	0.0266428	+	0.105373i
$680$			1.93454i			0.0741863i
$681$	−6.77070	−	5.50651i	−0.259454	−	0.211010i
$682$	36.5857	−	21.1227i	1.40094	−	0.808831i
$683$	−14.2604	+	8.23324i	−0.545659	+	0.315036i	−0.747369	−	0.664409i	$-0.768683\pi$
$683$	−14.2604	+	8.23324i	−0.545659	+	0.315036i	0.201710	+	0.979445i	$0.435350\pi$
$684$	−3.68270	−	4.12494i	−0.140812	−	0.157721i
$685$			6.08614i			0.232540i
$686$	−18.0765	+	4.03001i	−0.690163	+	0.153866i
$687$	−36.0952	−	5.79504i	−1.37712	−	0.221094i
$688$	−2.57752	+	4.46439i	−0.0982669	+	0.170203i
$689$	3.06610	+	5.31065i	0.116809	+	0.202320i
$690$	−1.13109	+	0.431449i	−0.0430599	+	0.0164250i
$691$	4.59956	+	2.65556i	0.174975	+	0.101022i	0.584930	−	0.811084i	$-0.301122\pi$
$691$	4.59956	+	2.65556i	0.174975	+	0.101022i	−0.409954	+	0.912106i	$0.634455\pi$
$692$	15.2427			0.579440
$693$	2.53893	−	35.8364i	0.0964459	−	1.36131i
$694$	15.3460			0.582525
$695$	−4.12393	−	2.38095i	−0.156429	−	0.0903146i
$696$	−3.59383	+	1.37084i	−0.136224	+	0.0519617i
$697$	34.7825	+	60.2451i	1.31748	+	2.28195i
$698$	−11.0541	+	19.1463i	−0.418404	+	0.724697i
$699$	11.5801	+	1.85918i	0.438001	+	0.0703205i
$700$	3.52437	−	12.4460i	0.133209	−	0.470416i
$701$			0.375235i			0.0141724i	0.999975	+	0.00708622i	$0.00225563\pi$
$701$			0.375235i			0.0141724i	−0.999975	+	0.00708622i	$0.997744\pi$
$702$	2.80238	+	4.37569i	0.105769	+	0.165150i
$703$	3.90045	−	2.25192i	0.147108	−	0.0849329i
$704$	3.91988	−	2.26314i	0.147736	−	0.0852954i
$705$	−4.93242	−	4.01146i	−0.185766	−	0.151080i
$706$			25.8022i			0.971080i
$707$	−16.9015	−	17.3867i	−0.635647	−	0.653893i
$708$	−0.189723	+	1.18171i	−0.00713023	+	0.0444116i
$709$	−17.7437	+	30.7330i	−0.666379	+	1.15420i	0.312531	+	0.949908i	$0.398823\pi$
$709$	−17.7437	+	30.7330i	−0.666379	+	1.15420i	−0.978910	+	0.204294i	$0.934510\pi$
$710$	−1.73524	−	3.00552i	−0.0651223	−	0.112795i
$711$	3.66551	+	17.6101i	0.137467	+	0.660430i
$712$	−13.9862	−	8.07492i	−0.524154	−	0.302621i
$713$	19.5911			0.733694
$714$	−15.2970	−	21.7909i	−0.572474	−	0.815503i
$715$	−1.50715			−0.0563641
$716$	−19.9262	−	11.5044i	−0.744679	−	0.429940i
$717$	−14.1809	−	37.1768i	−0.529595	−	1.38839i
$718$	2.57315	+	4.45682i	0.0960290	+	0.166327i
$719$	−8.47173	+	14.6735i	−0.315942	+	0.547228i	−0.979637	−	0.200775i	$-0.935654\pi$
$719$	−8.47173	+	14.6735i	−0.315942	+	0.547228i	0.663695	+	0.748003i	$0.268987\pi$
$720$	−0.948727	−	0.312694i	−0.0353570	−	0.0116534i
$721$	2.40741	+	0.681710i	0.0896565	+	0.0253882i
$722$		−	15.6025i		−	0.580665i
$723$	−3.39165	+	4.17031i	−0.126137	+	0.155095i
$724$	1.91834	−	1.10755i	0.0712946	−	0.0411619i
$725$	9.40277	−	5.42869i	0.349210	−	0.201617i
$726$	−10.3682	+	12.7485i	−0.384799	+	0.473142i
$727$		−	35.1696i		−	1.30437i	−0.758061	−	0.652183i	$-0.773853\pi$
$727$		−	35.1696i		−	1.30437i	0.758061	−	0.652183i	$-0.226147\pi$
$728$	−2.56503	+	0.648546i	−0.0950664	+	0.0240367i
$729$	−15.5923	−	22.0427i	−0.577493	−	0.816396i
$730$	0.564920	−	0.978470i	0.0209086	−	0.0362148i
$731$	−14.9750	−	25.9374i	−0.553869	−	0.959330i
$732$	−6.87491	−	18.0234i	−0.254104	−	0.666163i
$733$	−27.3968	−	15.8176i	−1.01193	−	0.584236i	−0.100171	−	0.994970i	$-0.531939\pi$
$733$	−27.3968	−	15.8176i	−1.01193	−	0.584236i	−0.911755	+	0.410735i	$0.865272\pi$
$734$	−19.2835			−0.711767
$735$	−1.33152	−	3.81122i	−0.0491139	−	0.140579i
$736$	2.09904			0.0773717
$737$	−46.9129	−	27.0852i	−1.72806	−	0.997695i
$738$	−35.1672	+	7.32000i	−1.29452	+	0.269453i
$739$	9.97344	+	17.2745i	0.366879	+	0.635453i	0.989076	−	0.147408i	$-0.0470930\pi$
$739$	9.97344	+	17.2745i	0.366879	+	0.635453i	−0.622197	+	0.782861i	$0.713760\pi$
$740$	0.406807	−	0.704610i	0.0149545	−	0.0259020i
$741$	0.506082	−	3.15220i	0.0185914	−	0.115799i
$742$	15.7293	−	3.97702i	0.577441	−	0.146001i
$743$			0.533933i			0.0195881i	0.999952	+	0.00979405i	$0.00311759\pi$
$743$			0.533933i			0.0195881i	−0.999952	+	0.00979405i	$0.996882\pi$
$744$	12.5417	+	10.2000i	0.459802	+	0.373950i
$745$	1.63815	−	0.945785i	0.0600171	−	0.0346509i
$746$	−5.54705	+	3.20259i	−0.203092	+	0.117255i
$747$	−1.14510	+	1.02233i	−0.0418971	+	0.0374053i
$748$			26.2970i			0.961513i
$749$	0.517628	+	0.146578i	0.0189137	+	0.00535583i
$750$	5.63126	+	0.904093i	0.205625	+	0.0330128i
$751$	16.7867	−	29.0754i	0.612554	−	1.06097i	−0.378254	−	0.925702i	$-0.623475\pi$
$751$	16.7867	−	29.0754i	0.612554	−	1.06097i	0.990808	−	0.135273i	$-0.0431912\pi$
$752$	5.51184	+	9.54679i	0.200996	+	0.348136i
$753$	−17.6806	+	6.74415i	−0.644315	+	0.245770i
$754$	−1.92320	−	1.11036i	−0.0700388	−	0.0404369i
$755$	6.66321			0.242499
$756$	13.1591	−	3.97963i	0.478593	−	0.144738i
$757$	−4.70230			−0.170908			−0.0854540	−	0.996342i	$-0.527234\pi$
$757$	−4.70230			−0.170908			−0.0854540	+	0.996342i	$0.527234\pi$
$758$	4.73218	+	2.73213i	0.171881	+	0.0992353i
$759$	−15.3754	+	5.86485i	−0.558091	+	0.212881i
$760$	0.306876	+	0.531525i	0.0111316	+	0.0192804i
$761$	−12.0297	+	20.8361i	−0.436077	+	0.755307i	−0.997383	−	0.0723010i	$-0.976966\pi$
$761$	−12.0297	+	20.8361i	−0.436077	+	0.755307i	0.561306	+	0.827608i	$0.310299\pi$
$762$	−9.98721	−	1.60343i	−0.361798	−	0.0580863i
$763$	0.612878	+	0.630470i	0.0221877	+	0.0228246i
$764$		−	25.5300i		−	0.923644i
$765$	4.32929	−	3.86514i	0.156526	−	0.139744i
$766$	0.201428	−	0.116295i	0.00727791	−	0.00420190i
$767$	−0.598424	+	0.345500i	−0.0216078	+	0.0124753i
$768$	1.34375	+	1.09285i	0.0484885	+	0.0394350i
$769$		−	5.11010i		−	0.184275i	−0.995746	−	0.0921375i	$-0.970630\pi$
$769$		−	5.11010i		−	0.184275i	0.995746	−	0.0921375i	$-0.0293699\pi$
$770$	−1.08644	+	3.83668i	−0.0391525	+	0.138264i
$771$	2.35427	−	14.6639i	0.0847869	−	0.528106i
$772$	3.85366	−	6.67474i	0.138696	−	0.240229i
$773$	18.9887	+	32.8893i	0.682974	+	1.18295i	0.974069	+	0.226252i	$0.0726473\pi$
$773$	18.9887	+	32.8893i	0.682974	+	1.18295i	−0.291094	+	0.956694i	$0.594019\pi$
$774$	15.1406	−	3.15149i	0.544217	−	0.113278i
$775$	−39.5185	−	22.8160i	−1.41955	−	0.819575i
$776$	1.07047			0.0384275
$777$	0.989233	+	11.1535i	0.0354885	+	0.400131i
$778$	−14.2885			−0.512267
$779$	19.1133	+	11.0351i	0.684807	+	0.395373i
$780$	−0.205545	−	0.538861i	−0.00735971	−	0.0192943i
$781$	−23.5878	−	40.8552i	−0.844037	−	1.46192i
$782$	−6.09755	+	10.5613i	−0.218048	+	0.377670i
$783$	10.2481	+	5.30369i	0.366238	+	0.189538i
$784$	−0.198048	+	6.99720i	−0.00707315	+	0.249900i
$785$		−	4.88142i		−	0.174225i
$786$	−18.0680	+	22.2161i	−0.644463	+	0.792420i
$787$	14.5253	−	8.38619i	0.517771	−	0.298936i	−0.218251	−	0.975893i	$-0.570035\pi$
$787$	14.5253	−	8.38619i	0.517771	−	0.298936i	0.736022	+	0.676957i	$0.236702\pi$
$788$	0.214063	−	0.123590i	0.00762570	−	0.00440270i
$789$	−19.4002	+	23.8541i	−0.690666	+	0.849230i
$790$		−	1.99648i		−	0.0710314i
$791$	−3.85462	−	15.2452i	−0.137055	−	0.542057i
$792$	−12.8964	−	4.25057i	−0.458255	−	0.151038i
$793$	5.56856	−	9.64503i	0.197745	−	0.342505i
$794$	8.35830	+	14.4770i	0.296625	+	0.513770i
$795$	1.26045	+	3.30441i	0.0447035	+	0.117195i
$796$	−5.12047	−	2.95631i	−0.181490	−	0.104783i
$797$	5.64845			0.200078			0.100039	−	0.994984i	$-0.468103\pi$
$797$	5.64845			0.200078			0.100039	+	0.994984i	$0.468103\pi$
$798$	−7.65960	−	3.56060i	−0.271147	−	0.126044i
$799$	−64.0459			−2.26578
$800$	−4.23411	−	2.44456i	−0.149698	−	0.0864284i
$801$	9.87308	+	47.4329i	0.348848	+	1.67596i
$802$	17.1539	+	29.7114i	0.605724	+	1.04915i
$803$	7.67918	−	13.3007i	0.270992	−	0.469373i
$804$	3.28595	−	20.4670i	0.115887	−	0.721816i
$805$	−1.32595	+	1.28895i	−0.0467336	+	0.0454296i
$806$			9.33337i			0.328754i
$807$	5.73428	+	4.66361i	0.201856	+	0.164167i
$808$	−7.93697	+	4.58241i	−0.279221	+	0.161209i
$809$	−4.06321	+	2.34590i	−0.142855	+	0.0824774i	−0.569724	−	0.821836i	$-0.692950\pi$
$809$	−4.06321	+	2.34590i	−0.142855	+	0.0824774i	0.426869	+	0.904313i	$0.359617\pi$
$810$	1.19575	+	2.74790i	0.0420142	+	0.0965512i
$811$		−	15.7561i		−	0.553272i	−0.960975	−	0.276636i	$-0.910780\pi$
$811$		−	15.7561i		−	0.553272i	0.960975	−	0.276636i	$-0.0892197\pi$
$812$	−4.21295	+	4.09539i	−0.147846	+	0.143720i
$813$	17.0288	+	2.73395i	0.597226	+	0.0958839i
$814$	5.52989	−	9.57804i	0.193822	−	0.335710i
$815$	3.60074	+	6.23667i	0.126129	+	0.218461i
$816$	−9.40216	+	3.58640i	−0.329141	+	0.125549i
$817$	−8.22890	−	4.75096i	−0.287893	−	0.166215i
$818$	−17.6842			−0.618312
$819$	6.57621	+	4.44448i	0.229791	+	0.155303i
$820$	3.98695			0.139230
$821$	11.3567	+	6.55682i	0.396353	+	0.228834i	0.684909	−	0.728628i	$-0.259842\pi$
$821$	11.3567	+	6.55682i	0.396353	+	0.228834i	−0.288556	+	0.957463i	$0.593175\pi$
$822$	−29.5796	+	11.2830i	−1.03171	+	0.393538i
$823$	−26.3375	−	45.6180i	−0.918069	−	1.59014i	−0.802345	−	0.596861i	$-0.796415\pi$
$823$	−26.3375	−	45.6180i	−0.918069	−	1.59014i	−0.115724	−	0.993281i	$-0.536919\pi$
$824$	0.472846	−	0.818994i	0.0164724	−	0.0285310i
$825$	37.8449	+	6.07596i	1.31759	+	0.211538i
$826$	0.448146	+	1.77244i	0.0155930	+	0.0616710i
$827$		−	48.4120i		−	1.68345i	−0.539905	−	0.841726i	$-0.681540\pi$
$827$		−	48.4120i		−	1.68345i	0.539905	−	0.841726i	$-0.318460\pi$
$828$	−4.19381	−	4.69742i	−0.145745	−	0.163247i
$829$	−33.0526	+	19.0829i	−1.14796	+	0.662777i	−0.948390	−	0.317106i	$-0.897289\pi$
$829$	−33.0526	+	19.0829i	−1.14796	+	0.662777i	−0.199573	+	0.979883i	$0.563956\pi$
$830$	0.147554	−	0.0851901i	0.00512166	−	0.00295699i
$831$	16.3677	+	13.3116i	0.567788	+	0.461773i
$832$			1.00000i			0.0346688i
$833$	−34.6309	−	21.3228i	−1.19989	−	0.738791i
$834$	3.92652	−	24.4569i	0.135964	−	0.846872i
$835$	2.99777	−	5.19230i	0.103742	−	0.179687i
$836$	4.17149	+	7.22523i	0.144274	+	0.249890i
$837$	−2.23145	−	48.4462i	−0.0771300	−	1.67455i
$838$	11.4260	+	6.59681i	0.394705	+	0.227883i
$839$	−35.4568			−1.22410			−0.612052	−	0.790817i	$-0.709656\pi$
$839$	−35.4568			−1.22410			−0.612052	+	0.790817i	$0.709656\pi$
$840$	−1.51992	+	0.134806i	−0.0524423	+	0.00465123i
$841$	24.0684			0.829945
$842$	16.1443	+	9.32090i	0.556368	+	0.321219i
$843$	13.3587	+	35.0215i	0.460099	+	1.20620i
$844$	−7.67672	−	13.2965i	−0.264243	−	0.457683i
$845$	0.166488	−	0.288366i	0.00572737	−	0.00992010i
$846$	10.3522	−	31.4090i	0.355916	−	1.07986i
$847$	−6.83896	+	24.1513i	−0.234989	+	0.829847i
$848$		−	6.13221i		−	0.210581i
$849$	−9.09198	+	11.1793i	−0.312036	+	0.383674i
$850$	24.5995	−	14.2025i	0.843756	−	0.487143i
$851$	4.44177	−	2.56446i	0.152262	−	0.0879085i
$852$	11.3904	−	14.0054i	0.390227	−	0.479816i
$853$			22.2598i			0.762160i	0.924542	+	0.381080i	$0.124448\pi$
$853$			22.2598i			0.762160i	−0.924542	+	0.381080i	$0.875552\pi$
$854$	−20.5388	−	21.1283i	−0.702823	−	0.722997i
$855$	0.576367	−	1.74872i	0.0197113	−	0.0598050i
$856$	0.101669	−	0.176096i	0.00347497	−	0.00601882i
$857$	−17.5703	−	30.4327i	−0.600191	−	1.03956i	−0.992792	−	0.119852i	$-0.961758\pi$
$857$	−17.5703	−	30.4327i	−0.600191	−	1.03956i	0.392601	−	0.919709i	$-0.371575\pi$
$858$	−2.79406	−	7.32495i	−0.0953877	−	0.250070i
$859$	22.9500	+	13.2502i	0.783043	+	0.452090i	0.837508	−	0.546426i	$-0.184012\pi$
$859$	22.9500	+	13.2502i	0.783043	+	0.452090i	−0.0544648	+	0.998516i	$0.517345\pi$
$860$	−1.71651			−0.0585324
$861$	−44.9094	+	31.5259i	−1.53051	+	1.07440i
$862$	−8.35924			−0.284717
$863$	−42.4767	−	24.5239i	−1.44592	−	0.834804i	−0.447688	−	0.894190i	$-0.647752\pi$
$863$	−42.4767	−	24.5239i	−1.44592	−	0.834804i	−0.998235	+	0.0593862i	$0.981086\pi$
$864$	−0.239083	−	5.19065i	−0.00813375	−	0.176589i
$865$	2.53773	+	4.39548i	0.0862854	+	0.149451i
$866$	10.6131	−	18.3824i	0.360648	−	0.624661i
$867$	4.60010	−	28.6523i	0.156228	−	0.973084i
$868$	23.7595	+	6.72804i	0.806451	+	0.228364i
$869$		−	27.1389i		−	0.920624i
$870$	−0.993635	−	0.808108i	−0.0336874	−	0.0273974i
$871$	10.3646	−	5.98398i	0.351189	−	0.202759i
$872$	0.287808	−	0.166166i	0.00974641	−	0.00562709i
$873$	−2.13875	−	2.39559i	−0.0723858	−	0.0810783i
$874$			3.86902i			0.130871i
$875$	8.44626	−	2.13556i	0.285536	−	0.0721952i
$876$	5.80280	+	0.931633i	0.196058	+	0.0314770i
$877$	−24.5895	+	42.5902i	−0.830328	+	1.43817i	0.0674507	+	0.997723i	$0.478513\pi$
$877$	−24.5895	+	42.5902i	−0.830328	+	1.43817i	−0.897778	+	0.440447i	$0.854820\pi$
$878$	5.56216	+	9.63394i	0.187714	+	0.325130i
$879$	18.5621	−	7.08040i	0.626084	−	0.238816i
$880$	1.30523	+	0.753573i	0.0439992	+	0.0254029i
$881$	−57.1860			−1.92665			−0.963323	−	0.268345i	$-0.913523\pi$
$881$	−57.1860			−1.92665			−0.963323	+	0.268345i	$0.913523\pi$
$882$	16.0546	−	13.5369i	0.540588	−	0.455812i
$883$	30.3137			1.02014			0.510068	−	0.860134i	$-0.329620\pi$
$883$	30.3137			1.02014			0.510068	+	0.860134i	$0.329620\pi$
$884$	−5.03147	−	2.90492i	−0.169227	−	0.0977031i
$885$	−0.372353	+	0.142032i	−0.0125165	+	0.00477435i
$886$	−2.54961	−	4.41605i	−0.0856558	−	0.148360i
$887$	−9.26591	+	16.0490i	−0.311119	+	0.538874i	−0.978605	−	0.205749i	$-0.934037\pi$
$887$	−9.26591	+	16.0490i	−0.311119	+	0.538874i	0.667486	+	0.744622i	$0.267370\pi$
$888$	4.17868	+	0.670882i	0.140227	+	0.0225133i
$889$	−14.9797	+	3.78748i	−0.502402	+	0.127028i
$890$		−	5.37752i		−	0.180255i
$891$	16.2543	+	37.3533i	0.544538	+	1.25138i
$892$	4.14596	−	2.39367i	0.138817	−	0.0801461i
$893$	−17.5969	+	10.1596i	−0.588859	+	0.339978i
$894$	7.63358	+	6.20828i	0.255305	+	0.207636i
$895$		−	7.66140i		−	0.256092i
$896$	2.54566	+	0.720858i	0.0850444	+	0.0240822i
$897$	0.576319	−	3.58968i	0.0192427	−	0.119856i
$898$	13.1983	−	22.8601i	0.440433	−	0.762853i
$899$	10.3634	+	17.9499i	0.345639	+	0.598664i
$900$	2.98893	+	14.3596i	0.0996309	+	0.478654i
$901$	30.8540	+	17.8136i	1.02790	+	0.593456i
$902$	54.1962			1.80453
$903$	19.3349	−	13.5729i	0.643426	−	0.451678i
$904$	−5.94348			−0.197677
$905$	0.638762	+	0.368790i	0.0212332	+	0.0122590i
$906$	12.3528	+	32.3842i	0.410393	+	1.07589i
$907$	8.61820	+	14.9272i	0.286163	+	0.495648i	0.972890	−	0.231266i	$-0.0742869\pi$
$907$	8.61820	+	14.9272i	0.286163	+	0.495648i	−0.686728	+	0.726915i	$0.740954\pi$
$908$	−2.51933	+	4.36360i	−0.0836067	+	0.144811i
$909$	26.1127	+	8.60656i	0.866103	+	0.285462i
$910$	−0.614066	−	0.631693i	−0.0203561	−	0.0209404i
$911$			18.6840i			0.619028i	0.950895	+	0.309514i	$0.100166\pi$
$911$			18.6840i			0.619028i	−0.950895	+	0.309514i	$0.899834\pi$
$912$	−2.01438	+	2.47684i	−0.0667028	+	0.0820165i
$913$	2.00576	−	1.15802i	0.0663808	−	0.0383250i
$914$	−27.6643	+	15.9720i	−0.915054	+	0.528306i
$915$	4.05274	−	4.98317i	0.133979	−	0.164739i
$916$			21.1064i			0.697376i
$917$	−11.9178	+	42.0869i	−0.393562	+	1.38983i
$918$	26.8111	+	13.8755i	0.884899	+	0.457959i
$919$	−1.74587	+	3.02394i	−0.0575909	+	0.0997504i	−0.893384	−	0.449295i	$-0.851675\pi$
$919$	−1.74587	+	3.02394i	−0.0575909	+	0.0997504i	0.835793	+	0.549045i	$0.185009\pi$
$920$	0.349466	+	0.605293i	0.0115215	+	0.0199559i
$921$	17.2473	+	45.2158i	0.568318	+	1.48991i
$922$	3.87837	+	2.23918i	0.127727	+	0.0737435i
$923$	10.4226			0.343064
$924$	−20.6609	+	1.83247i	−0.679695	+	0.0602837i
$925$	−11.9464			−0.392794
$926$	−28.6886	−	16.5634i	−0.942767	−	0.544307i
$927$	−2.77755	+	0.578141i	−0.0912266	+	0.0189887i
$928$	1.11036	+	1.92320i	0.0364494	+	0.0631321i
$929$	13.0403	−	22.5864i	0.427837	−	0.741036i	−0.568843	−	0.822446i	$-0.692609\pi$
$929$	13.0403	−	22.5864i	0.427837	−	0.741036i	0.996681	+	0.0814097i	$0.0259422\pi$
$930$	−0.853284	+	5.31479i	−0.0279803	+	0.174279i
$931$	−12.8974	−	0.365048i	−0.422697	−	0.0119640i
$932$		−	6.77141i		−	0.221805i
$933$	4.98738	+	4.05616i	0.163279	+	0.132793i
$934$	−16.5375	+	9.54791i	−0.541122	+	0.312417i
$935$	−7.58316	+	4.37814i	−0.247996	+	0.143181i
$936$	2.23789	−	1.99796i	0.0731477	−	0.0653054i
$937$		−	10.6405i		−	0.347609i	−0.984780	−	0.173805i	$-0.944394\pi$
$937$		−	10.6405i		−	0.347609i	0.984780	−	0.173805i	$-0.0556061\pi$
$938$	−7.76177	−	30.6982i	−0.253431	−	1.00233i
$939$	2.15852	+	0.346548i	0.0704406	+	0.0113092i
$940$	−1.83531	+	3.17886i	−0.0598613	+	0.103683i
$941$	−2.76752	−	4.79349i	−0.0902186	−	0.156263i	0.817384	−	0.576093i	$-0.195423\pi$
$941$	−2.76752	−	4.79349i	−0.0902186	−	0.156263i	−0.907603	+	0.419829i	$0.862090\pi$
$942$	23.7244	−	9.04955i	0.772984	−	0.294850i
$943$	21.7660	+	12.5666i	0.708798	+	0.409225i
$944$	0.691001			0.0224902
$945$	3.33843	+	3.13208i	0.108599	+	0.101887i
$946$	−23.3332			−0.758626
$947$	18.0236	+	10.4059i	0.585689	+	0.338148i	0.763391	−	0.645936i	$-0.223533\pi$
$947$	18.0236	+	10.4059i	0.585689	+	0.338148i	−0.177702	+	0.984084i	$0.556866\pi$
$948$	9.70317	−	3.70122i	0.315144	−	0.120210i
$949$	1.69658	+	2.93856i	0.0550732	+	0.0953895i
$950$	4.50589	−	7.80443i	0.146190	−	0.253209i
$951$	−2.24542	−	0.360500i	−0.0728129	−	0.0116900i
$952$	−11.0219	+	10.7144i	−0.357222	+	0.347254i
$953$			11.3489i			0.367627i	0.982961	+	0.183814i	$0.0588443\pi$
$953$			11.3489i			0.367627i	−0.982961	+	0.183814i	$0.941156\pi$
$954$	−13.7232	+	12.2519i	−0.444305	+	0.396671i
$955$	7.36199	−	4.25045i	0.238229	−	0.137541i
$956$	−19.8948	+	11.4863i	−0.643444	+	0.371493i
$957$	−13.5069	−	10.9849i	−0.436615	−	0.355093i
$958$		−	0.164997i		−	0.00533081i
$959$	−34.6753	+	33.7078i	−1.11973	+	1.08848i
$960$	−0.0914229	+	0.569440i	−0.00295066	+	0.0183786i
$961$	28.0559	−	48.5942i	0.905029	−	1.56756i
$962$	1.22173	+	2.11609i	0.0393901	+	0.0682256i
$963$	−0.597213	+	0.124309i	−0.0192449	+	0.00400580i
$964$	2.68769	+	1.55174i	0.0865647	+	0.0499781i
$965$	2.56636			0.0826140
$966$	−8.72264	−	4.05476i	−0.280646	−	0.130460i
$967$	−55.6894			−1.79085			−0.895426	−	0.445210i	$-0.853129\pi$
$967$	−55.6894			−1.79085			−0.895426	+	0.445210i	$0.853129\pi$
$968$	8.21619	+	4.74362i	0.264078	+	0.152466i
$969$	−6.61056	−	17.3303i	−0.212362	−	0.556730i
$970$	0.178220	+	0.308686i	0.00572230	+	0.00991132i
$971$	−5.96226	+	10.3269i	−0.191338	+	0.331407i	−0.945694	−	0.325058i	$-0.894616\pi$
$971$	−5.96226	+	10.3269i	−0.191338	+	0.331407i	0.754356	+	0.656466i	$0.227949\pi$
$972$	−11.1384	+	10.9058i	−0.357265	+	0.349803i
$973$	−9.27487	−	36.6825i	−0.297339	−	1.17599i
$974$			15.4689i			0.495656i
$975$	−5.34310	+	6.56978i	−0.171116	+	0.210401i
$976$	−9.64503	+	5.56856i	−0.308730	+	0.178245i
$977$	47.2707	−	27.2918i	1.51232	−	0.873141i	0.512428	−	0.858730i	$-0.328746\pi$
$977$	47.2707	−	27.2918i	1.51232	−	0.873141i	0.999896	−	0.0144109i	$-0.00458728\pi$
$978$	−23.6358	+	29.0622i	−0.755790	+	0.929305i
$979$		−	73.0988i		−	2.33625i
$980$	−2.05073	+	1.10784i	−0.0655081	+	0.0353887i
$981$	−0.946891	−	0.312089i	−0.0302319	−	0.00996423i
$982$	9.75963	−	16.9042i	0.311442	−	0.539434i
$983$	5.42233	+	9.39175i	0.172945	+	0.299550i	0.939448	−	0.342691i	$-0.111338\pi$
$983$	5.42233	+	9.39175i	0.172945	+	0.299550i	−0.766503	+	0.642241i	$0.778005\pi$
$984$	7.39130	+	19.3771i	0.235626	+	0.617721i
$985$	0.0712781	+	0.0411524i	0.00227111	+	0.00131123i
$986$	−12.9020			−0.410885
$987$	−4.46294	−	50.3193i	−0.142057	−	1.60168i
$988$	−1.84323			−0.0586409
$989$	−9.37095	−	5.41032i	−0.297979	−	0.172038i
$990$	−0.921382	−	4.42656i	−0.0292834	−	0.140685i
$991$	11.5102	+	19.9362i	0.365633	+	0.633295i	0.988878	−	0.148732i	$-0.0475192\pi$
$991$	11.5102	+	19.9362i	0.365633	+	0.633295i	−0.623245	+	0.782027i	$0.714186\pi$
$992$	4.66668	−	8.08293i	0.148167	−	0.256633i
$993$	6.35408	−	39.5772i	0.201641	−	1.25595i
$994$	7.51321	−	26.5323i	0.238304	−	0.841554i
$995$		−	1.96876i		−	0.0624139i
$996$	0.687583	+	0.559201i	0.0217869	+	0.0177190i
$997$	−15.7798	+	9.11048i	−0.499752	+	0.288532i	−0.728611	−	0.684928i	$-0.759834\pi$
$997$	−15.7798	+	9.11048i	−0.499752	+	0.288532i	0.228859	+	0.973460i	$0.426500\pi$
$998$	27.8814	−	16.0973i	0.882569	−	0.509551i
$999$	−6.84748	−	10.6918i	−0.216645	−	0.338274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.a.131.10	✓	32
3.2	odd	2		546.2.z.b.131.3	yes	32
7.3	odd	6		546.2.z.b.521.3	yes	32
21.17	even	6	inner	546.2.z.a.521.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.10	✓	32	1.1	even	1	trivial
546.2.z.a.521.10	yes	32	21.17	even	6	inner
546.2.z.b.131.3	yes	32	3.2	odd	2
546.2.z.b.521.3	yes	32	7.3	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.61832 + 0.617297i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.166488 + 0.288366i) q^{5} +(-1.71015 - 0.274563i) q^{6} +(-2.56503 + 0.648546i) q^{7} +1.00000i q^{8} +(2.23789 - 1.99796i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.61832 + 0.617297i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.166488 + 0.288366i) q^{5} +(-1.71015 - 0.274563i) q^{6} +(-2.56503 + 0.648546i) q^{7} +1.00000i q^{8} +(2.23789 - 1.99796i) q^{9} +(-0.288366 + 0.166488i) q^{10} +(-3.91988 + 2.26314i) q^{11} +(-1.34375 - 1.09285i) q^{12} -1.00000i q^{13} +(-2.54566 - 0.720858i) q^{14} +(0.0914229 - 0.569440i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.90492 - 5.03147i) q^{17} +(2.93705 - 0.611342i) q^{18} +(-1.59628 - 0.921615i) q^{19} -0.332977 q^{20} +(3.75068 - 2.63294i) q^{21} -4.52628 q^{22} +(-1.81782 - 1.04952i) q^{23} +(-0.617297 - 1.61832i) q^{24} +(2.44456 + 4.23411i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-2.38827 + 4.61478i) q^{27} +(-1.84417 - 1.89711i) q^{28} -2.22072i q^{29} +(0.363895 - 0.447438i) q^{30} +(-8.08293 + 4.66668i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(4.94657 - 6.08221i) q^{33} -5.80984i q^{34} +(0.240029 - 0.847644i) q^{35} +(2.84923 + 0.939087i) q^{36} +(-1.22173 + 2.11609i) q^{37} +(-0.921615 - 1.59628i) q^{38} +(0.617297 + 1.61832i) q^{39} +(-0.288366 - 0.166488i) q^{40} -11.9737 q^{41} +(4.56466 - 0.404850i) q^{42} +5.15504 q^{43} +(-3.91988 - 2.26314i) q^{44} +(0.203563 + 0.977969i) q^{45} +(-1.04952 - 1.81782i) q^{46} +(5.51184 - 9.54679i) q^{47} +(0.274563 - 1.71015i) q^{48} +(6.15878 - 3.32708i) q^{49} +4.88913i q^{50} +(7.80699 + 6.34931i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-5.31065 + 3.06610i) q^{53} +(-4.37569 + 2.80238i) q^{54} -1.50715i q^{55} +(-0.648546 - 2.56503i) q^{56} +(3.15220 + 0.506082i) q^{57} +(1.11036 - 1.92320i) q^{58} +(-0.345500 - 0.598424i) q^{59} +(0.538861 - 0.205545i) q^{60} +(9.64503 + 5.56856i) q^{61} -9.33337 q^{62} +(-4.44448 + 6.57621i) q^{63} -1.00000 q^{64} +(0.288366 + 0.166488i) q^{65} +(7.32495 - 2.79406i) q^{66} +(5.98398 + 10.3646i) q^{67} +(2.90492 - 5.03147i) q^{68} +(3.58968 + 0.576319i) q^{69} +(0.631693 - 0.614066i) q^{70} +10.4226i q^{71} +(1.99796 + 2.23789i) q^{72} +(-2.93856 + 1.69658i) q^{73} +(-2.11609 + 1.22173i) q^{74} +(-6.56978 - 5.34310i) q^{75} -1.84323i q^{76} +(8.58686 - 8.34725i) q^{77} +(-0.274563 + 1.71015i) q^{78} +(-2.99792 + 5.19255i) q^{79} +(-0.166488 - 0.288366i) q^{80} +(1.01629 - 8.94244i) q^{81} +(-10.3695 - 5.98683i) q^{82} -0.511689 q^{83} +(4.15553 + 1.93172i) q^{84} +1.93454 q^{85} +(4.46439 + 2.57752i) q^{86} +(1.37084 + 3.59383i) q^{87} +(-2.26314 - 3.91988i) q^{88} +(-8.07492 + 13.9862i) q^{89} +(-0.312694 + 0.948727i) q^{90} +(0.648546 + 2.56503i) q^{91} -2.09904i q^{92} +(10.2000 - 12.5417i) q^{93} +(9.54679 - 5.51184i) q^{94} +(0.531525 - 0.306876i) q^{95} +(1.09285 - 1.34375i) q^{96} -1.07047i q^{97} +(6.99720 + 0.198048i) q^{98} +(-4.25057 + 12.8964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

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