LMFDB - Embedded newform 384.2.w.a.107.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(11,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([16, 21, 16]))

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

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

chi := DirichletCharacter("384.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.w (of order $32$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$62$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			107.29
Character	$\chi$	$=$	384.107
Dual form			384.2.w.a.323.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.201228 + 1.39982i) q^{2} +(1.68739 + 0.390795i) q^{3} +(-1.91901 - 0.563368i) q^{4} +(0.582673 - 0.176752i) q^{5} +(-0.886595 + 2.28341i) q^{6} +(-0.838076 + 4.21329i) q^{7} +(1.17478 - 2.57292i) q^{8} +(2.69456 + 1.31885i) q^{9} +O(q^{10})$	\(q+(-0.201228 + 1.39982i) q^{2} +(1.68739 + 0.390795i) q^{3} +(-1.91901 - 0.563368i) q^{4} +(0.582673 - 0.176752i) q^{5} +(-0.886595 + 2.28341i) q^{6} +(-0.838076 + 4.21329i) q^{7} +(1.17478 - 2.57292i) q^{8} +(2.69456 + 1.31885i) q^{9} +(0.130171 + 0.851207i) q^{10} +(-0.134962 + 1.37029i) q^{11} +(-3.01796 - 1.70056i) q^{12} +(-3.09867 - 0.939972i) q^{13} +(-5.72922 - 2.02099i) q^{14} +(1.05227 - 0.0705433i) q^{15} +(3.36523 + 2.16222i) q^{16} +(6.20100 - 2.56854i) q^{17} +(-2.38837 + 3.50652i) q^{18} +(-1.30230 + 0.696094i) q^{19} +(-1.21773 + 0.0109301i) q^{20} +(-3.06069 + 6.78194i) q^{21} +(-1.89101 - 0.464664i) q^{22} +(-2.82362 + 4.22585i) q^{23} +(2.98779 - 3.88241i) q^{24} +(-3.84908 + 2.57187i) q^{25} +(1.93934 - 4.14845i) q^{26} +(4.03137 + 3.27843i) q^{27} +(3.98191 - 7.61322i) q^{28} +(0.282319 + 2.86643i) q^{29} +(-0.112998 + 1.48719i) q^{30} +(4.60627 - 4.60627i) q^{31} +(-3.70391 + 4.27563i) q^{32} +(-0.763237 + 2.25947i) q^{33} +(2.34769 + 9.19717i) q^{34} +(0.256383 + 2.60310i) q^{35} +(-4.42790 - 4.04891i) q^{36} +(0.0723953 + 0.0386961i) q^{37} +(-0.712349 - 1.96306i) q^{38} +(-4.86133 - 2.79704i) q^{39} +(0.229742 - 1.70681i) q^{40} +(5.98777 - 8.96133i) q^{41} +(-8.87763 - 5.64915i) q^{42} +(-5.22289 - 6.36410i) q^{43} +(1.03097 - 2.55358i) q^{44} +(1.80316 + 0.292188i) q^{45} +(-5.34726 - 4.80294i) q^{46} +(5.23083 - 2.16668i) q^{47} +(4.83347 + 4.96363i) q^{48} +(-10.5823 - 4.38333i) q^{49} +(-2.82563 - 5.90557i) q^{50} +(11.4673 - 1.91080i) q^{51} +(5.41685 + 3.54951i) q^{52} +(0.882057 - 8.95568i) q^{53} +(-5.40045 + 4.98349i) q^{54} +(0.163563 + 0.822287i) q^{55} +(9.85590 + 7.10597i) q^{56} +(-2.46952 + 0.665648i) q^{57} +(-4.06931 - 0.181610i) q^{58} +(3.26934 - 0.991745i) q^{59} +(-2.05906 - 0.457442i) q^{60} +(-1.31079 + 1.59720i) q^{61} +(5.52106 + 7.37488i) q^{62} +(-7.81493 + 10.2477i) q^{63} +(-5.23980 - 6.04520i) q^{64} -1.97165 q^{65} +(-3.00928 - 1.52307i) q^{66} +(5.94389 + 4.87803i) q^{67} +(-13.3468 + 1.43562i) q^{68} +(-6.41599 + 6.02719i) q^{69} +(-3.69548 - 0.164926i) q^{70} +(-0.636693 + 3.20087i) q^{71} +(6.55878 - 5.38352i) q^{72} +(6.53271 - 1.29944i) q^{73} +(-0.0687357 + 0.0935539i) q^{74} +(-7.49997 + 2.83555i) q^{75} +(2.89129 - 0.602140i) q^{76} +(-5.66033 - 1.71704i) q^{77} +(4.89360 - 6.24216i) q^{78} +(1.53897 - 3.71541i) q^{79} +(2.34301 + 0.665058i) q^{80} +(5.52129 + 7.10742i) q^{81} +(11.3394 + 10.1851i) q^{82} +(9.82436 - 5.25123i) q^{83} +(9.69425 - 11.2903i) q^{84} +(3.15916 - 2.59266i) q^{85} +(9.95962 - 6.03048i) q^{86} +(-0.643806 + 4.94711i) q^{87} +(3.36710 + 1.95703i) q^{88} +(1.61068 - 1.07622i) q^{89} +(-0.771858 + 2.46530i) q^{90} +(6.55730 - 12.2678i) q^{91} +(7.79929 - 6.51873i) q^{92} +(9.57268 - 5.97246i) q^{93} +(1.98038 + 7.75824i) q^{94} +(-0.635779 + 0.635779i) q^{95} +(-7.92083 + 5.76718i) q^{96} +(-11.7437 - 11.7437i) q^{97} +(8.26535 - 13.9313i) q^{98} +(-2.17087 + 3.51434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9}+O(q^{10}) $ 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9	$ 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9} - 32 q^{10} - 16 q^{12} - 32 q^{13} - 16 q^{15} - 32 q^{16} - 16 q^{18} - 32 q^{19} - 16 q^{21} - 32 q^{22} - 16 q^{24} - 32 q^{25} - 16 q^{27} - 32 q^{28} - 16 q^{30} - 32 q^{31} - 16 q^{33} - 32 q^{34} - 16 q^{36} - 32 q^{37} - 16 q^{39} - 32 q^{40} - 16 q^{42} - 32 q^{43} - 16 q^{45} - 32 q^{46} - 16 q^{48} - 32 q^{49} - 16 q^{51} - 128 q^{52} - 16 q^{54} - 32 q^{55} - 16 q^{57} - 320 q^{58} - 16 q^{60} - 32 q^{61} - 32 q^{63} - 224 q^{64} - 16 q^{66} - 32 q^{67} - 16 q^{69} - 224 q^{70} - 16 q^{72} - 32 q^{73} - 16 q^{75} - 256 q^{76} - 16 q^{78} - 32 q^{79} - 16 q^{81} - 32 q^{82} - 16 q^{84} - 32 q^{85} - 16 q^{87} - 32 q^{88} - 16 q^{90} - 32 q^{91} - 16 q^{93} - 32 q^{94} - 16 q^{96} - 32 q^{97} - 16 q^{99}+O(q^{100}) $ 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9 - 32 * q^10 - 16 * q^12 - 32 * q^13 - 16 * q^15 - 32 * q^16 - 16 * q^18 - 32 * q^19 - 16 * q^21 - 32 * q^22 - 16 * q^24 - 32 * q^25 - 16 * q^27 - 32 * q^28 - 16 * q^30 - 32 * q^31 - 16 * q^33 - 32 * q^34 - 16 * q^36 - 32 * q^37 - 16 * q^39 - 32 * q^40 - 16 * q^42 - 32 * q^43 - 16 * q^45 - 32 * q^46 - 16 * q^48 - 32 * q^49 - 16 * q^51 - 128 * q^52 - 16 * q^54 - 32 * q^55 - 16 * q^57 - 320 * q^58 - 16 * q^60 - 32 * q^61 - 32 * q^63 - 224 * q^64 - 16 * q^66 - 32 * q^67 - 16 * q^69 - 224 * q^70 - 16 * q^72 - 32 * q^73 - 16 * q^75 - 256 * q^76 - 16 * q^78 - 32 * q^79 - 16 * q^81 - 32 * q^82 - 16 * q^84 - 32 * q^85 - 16 * q^87 - 32 * q^88 - 16 * q^90 - 32 * q^91 - 16 * q^93 - 32 * q^94 - 16 * q^96 - 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{13}{32}\right)$	$-1$

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 $

$2$	−0.201228	+	1.39982i	−0.142290	+	0.989825i
$2$	−0.201228	+	1.39982i	−0.142290	+	0.989825i
$3$	1.68739	+	0.390795i	0.974214	+	0.225626i
$3$	1.68739	+	0.390795i	0.974214	+	0.225626i
$4$	−1.91901	−	0.563368i	−0.959507	−	0.281684i
$5$	0.582673	−	0.176752i	0.260579	−	0.0790459i	−0.157292	−	0.987552i	$-0.550276\pi$
$5$	0.582673	−	0.176752i	0.260579	−	0.0790459i	0.417871	+	0.908506i	$0.362776\pi$
$6$	−0.886595	+	2.28341i	−0.361951	+	0.932197i
$7$	−0.838076	+	4.21329i	−0.316763	+	1.59247i	0.414284	+	0.910148i	$0.364032\pi$
$7$	−0.838076	+	4.21329i	−0.316763	+	1.59247i	−0.731047	+	0.682327i	$0.760968\pi$
$8$	1.17478	−	2.57292i	0.415346	−	0.909663i
$9$	2.69456	+	1.31885i	0.898186	+	0.439616i
$10$	0.130171	+	0.851207i	0.0411638	+	0.269175i
$11$	−0.134962	+	1.37029i	−0.0406926	+	0.413159i	0.953162	+	0.302461i	$0.0978084\pi$
$11$	−0.134962	+	1.37029i	−0.0406926	+	0.413159i	−0.993854	+	0.110697i	$0.964692\pi$
$12$	−3.01796	−	1.70056i	−0.871210	−	0.490910i
$13$	−3.09867	−	0.939972i	−0.859417	−	0.260701i	−0.170336	−	0.985386i	$-0.554485\pi$
$13$	−3.09867	−	0.939972i	−0.859417	−	0.260701i	−0.689081	+	0.724685i	$0.741985\pi$
$14$	−5.72922	−	2.02099i	−1.53120	−	0.540133i
$15$	1.05227	−	0.0705433i	0.271695	−	0.0182142i
$16$	3.36523	+	2.16222i	0.841308	+	0.540556i
$17$	6.20100	−	2.56854i	1.50396	−	0.622962i	0.529662	−	0.848209i	$-0.322319\pi$
$17$	6.20100	−	2.56854i	1.50396	−	0.622962i	0.974302	+	0.225247i	$0.0723189\pi$
$18$	−2.38837	+	3.50652i	−0.562945	+	0.826494i
$19$	−1.30230	+	0.696094i	−0.298768	+	0.159695i	−0.613969	−	0.789330i	$-0.710428\pi$
$19$	−1.30230	+	0.696094i	−0.298768	+	0.159695i	0.315201	+	0.949025i	$0.397928\pi$
$20$	−1.21773	+	0.0109301i	−0.272294	+	0.00244404i
$21$	−3.06069	+	6.78194i	−0.667898	+	1.47994i
$22$	−1.89101	−	0.464664i	−0.403165	−	0.0990668i
$23$	−2.82362	+	4.22585i	−0.588766	+	0.881151i	−0.999532	−	0.0305898i	$-0.990261\pi$
$23$	−2.82362	+	4.22585i	−0.588766	+	0.881151i	0.410766	+	0.911741i	$0.365261\pi$
$24$	2.98779	−	3.88241i	0.609879	−	0.792494i
$25$	−3.84908	+	2.57187i	−0.769816	+	0.514375i
$26$	1.93934	−	4.14845i	0.380335	−	0.813577i
$27$	4.03137	+	3.27843i	0.775837	+	0.630934i
$28$	3.98191	−	7.61322i	0.752511	−	1.43876i
$29$	0.282319	+	2.86643i	0.0524253	+	0.532283i	0.985150	+	0.171694i	$0.0549241\pi$
$29$	0.282319	+	2.86643i	0.0524253	+	0.532283i	−0.932725	+	0.360588i	$0.882576\pi$
$30$	−0.112998	+	1.48719i	−0.0206305	+	0.271522i
$31$	4.60627	−	4.60627i	0.827311	−	0.827311i	−0.159833	−	0.987144i	$-0.551096\pi$
$31$	4.60627	−	4.60627i	0.827311	−	0.827311i	0.987144	+	0.159833i	$0.0510957\pi$
$32$	−3.70391	+	4.27563i	−0.654765	+	0.755832i
$33$	−0.763237	+	2.25947i	−0.132862	+	0.393324i
$34$	2.34769	+	9.19717i	0.402625	+	1.57730i
$35$	0.256383	+	2.60310i	0.0433367	+	0.440005i
$36$	−4.42790	−	4.04891i	−0.737983	−	0.674819i
$37$	0.0723953	+	0.0386961i	0.0119017	+	0.00636160i	0.477337	−	0.878720i	$-0.341602\pi$
$37$	0.0723953	+	0.0386961i	0.0119017	+	0.00636160i	−0.465435	+	0.885082i	$0.654102\pi$
$38$	−0.712349	−	1.96306i	−0.115558	−	0.318451i
$39$	−4.86133	−	2.79704i	−0.778435	−	0.447885i
$40$	0.229742	−	1.70681i	0.0363255	−	0.269871i
$41$	5.98777	−	8.96133i	0.935132	−	1.39952i	0.0184842	−	0.999829i	$-0.494116\pi$
$41$	5.98777	−	8.96133i	0.935132	−	1.39952i	0.916648	−	0.399695i	$-0.130884\pi$
$42$	−8.87763	−	5.64915i	−1.36985	−	0.871683i
$43$	−5.22289	−	6.36410i	−0.796483	−	0.970517i	0.203481	−	0.979079i	$-0.434775\pi$
$43$	−5.22289	−	6.36410i	−0.796483	−	0.970517i	−0.999963	+	0.00856212i	$0.997275\pi$
$44$	1.03097	−	2.55358i	0.155425	−	0.384966i
$45$	1.80316	+	0.292188i	0.268799	+	0.0435568i
$46$	−5.34726	−	4.80294i	−0.788410	−	0.708155i
$47$	5.23083	−	2.16668i	0.762995	−	0.316043i	0.0329639	−	0.999457i	$-0.489505\pi$
$47$	5.23083	−	2.16668i	0.762995	−	0.316043i	0.730032	+	0.683413i	$0.239505\pi$
$48$	4.83347	+	4.96363i	0.697651	+	0.716438i
$49$	−10.5823	−	4.38333i	−1.51176	−	0.626190i
$50$	−2.82563	−	5.90557i	−0.399604	−	0.835174i
$51$	11.4673	−	1.91080i	1.60574	−	0.267566i
$52$	5.41685	+	3.54951i	0.751181	+	0.492229i
$53$	0.882057	−	8.95568i	0.121160	−	1.23016i	−0.721770	−	0.692133i	$-0.756671\pi$
$53$	0.882057	−	8.95568i	0.121160	−	1.23016i	0.842930	−	0.538024i	$-0.180829\pi$
$54$	−5.40045	+	4.98349i	−0.734907	+	0.678167i
$55$	0.163563	+	0.822287i	0.0220548	+	0.110877i
$56$	9.85590	+	7.10597i	1.31705	+	0.949576i
$57$	−2.46952	+	0.665648i	−0.327095	+	0.0881672i
$58$	−4.06931	−	0.181610i	−0.534326	−	0.0238466i
$59$	3.26934	−	0.991745i	0.425632	−	0.129114i	−0.0701990	−	0.997533i	$-0.522363\pi$
$59$	3.26934	−	0.991745i	0.425632	−	0.129114i	0.495831	+	0.868419i	$0.334863\pi$
$60$	−2.05906	−	0.457442i	−0.265824	−	0.0590555i
$61$	−1.31079	+	1.59720i	−0.167830	+	0.204501i	−0.850133	−	0.526568i	$-0.823478\pi$
$61$	−1.31079	+	1.59720i	−0.167830	+	0.204501i	0.682303	+	0.731069i	$0.260978\pi$
$62$	5.52106	+	7.37488i	0.701175	+	0.936611i
$63$	−7.81493	+	10.2477i	−0.984589	+	1.29108i
$64$	−5.23980	−	6.04520i	−0.654975	−	0.755650i
$65$	−1.97165			−0.244554
$66$	−3.00928	−	1.52307i	−0.370417	−	0.187477i
$67$	5.94389	+	4.87803i	0.726162	+	0.595946i	0.923141	−	0.384462i	$-0.125613\pi$
$67$	5.94389	+	4.87803i	0.726162	+	0.595946i	−0.196979	+	0.980408i	$0.563113\pi$
$68$	−13.3468	+	1.43562i	−1.61854	+	0.174094i
$69$	−6.41599	+	6.02719i	−0.772395	+	0.725589i
$70$	−3.69548	−	0.164926i	−0.441694	−	0.0197125i
$71$	−0.636693	+	3.20087i	−0.0755615	+	0.379873i	−0.999999	−	0.00146038i	$-0.999535\pi$
$71$	−0.636693	+	3.20087i	−0.0755615	+	0.379873i	0.924437	+	0.381334i	$0.124535\pi$
$72$	6.55878	−	5.38352i	0.772960	−	0.634454i
$73$	6.53271	−	1.29944i	0.764596	−	0.152088i	0.202638	−	0.979254i	$-0.435048\pi$
$73$	6.53271	−	1.29944i	0.764596	−	0.152088i	0.561958	+	0.827166i	$0.310048\pi$
$74$	−0.0687357	+	0.0935539i	−0.00799036	+	0.0108754i
$75$	−7.49997	+	2.83555i	−0.866022	+	0.327421i
$76$	2.89129	−	0.602140i	0.331654	−	0.0690702i
$77$	−5.66033	−	1.71704i	−0.645055	−	0.195675i
$78$	4.89360	−	6.24216i	0.554092	−	0.706785i
$79$	1.53897	−	3.71541i	0.173148	−	0.418017i	−0.813353	−	0.581770i	$-0.802360\pi$
$79$	1.53897	−	3.71541i	0.173148	−	0.418017i	0.986501	+	0.163754i	$0.0523603\pi$
$80$	2.34301	+	0.665058i	0.261956	+	0.0743557i
$81$	5.52129	+	7.10742i	0.613476	+	0.789713i
$82$	11.3394	+	10.1851i	1.25222	+	1.12476i
$83$	9.82436	−	5.25123i	1.07836	−	0.576398i	0.166145	−	0.986101i	$-0.446868\pi$
$83$	9.82436	−	5.25123i	1.07836	−	0.576398i	0.912219	+	0.409704i	$0.134368\pi$
$84$	9.69425	−	11.2903i	1.05773	−	1.23188i
$85$	3.15916	−	2.59266i	0.342659	−	0.281213i
$86$	9.95962	−	6.03048i	1.07397	−	0.650284i
$87$	−0.643806	+	4.94711i	−0.0690232	+	0.530386i
$88$	3.36710	+	1.95703i	0.358934	+	0.208620i
$89$	1.61068	−	1.07622i	0.170732	−	0.114079i	−0.467269	−	0.884115i	$-0.654762\pi$
$89$	1.61068	−	1.07622i	0.170732	−	0.114079i	0.638000	+	0.770036i	$0.279762\pi$
$90$	−0.771858	+	2.46530i	−0.0813609	+	0.259866i
$91$	6.55730	−	12.2678i	0.687392	−	1.28602i
$92$	7.79929	−	6.51873i	0.813132	−	0.679625i
$93$	9.57268	−	5.97246i	0.992640	−	0.619315i
$94$	1.98038	+	7.75824i	0.204261	+	0.800202i
$95$	−0.635779	+	0.635779i	−0.0652296	+	0.0652296i
$96$	−7.92083	+	5.76718i	−0.808417	+	0.588611i
$97$	−11.7437	−	11.7437i	−1.19239	−	1.19239i	−0.976393	−	0.216002i	$-0.930698\pi$
$97$	−11.7437	−	11.7437i	−1.19239	−	1.19239i	−0.216002	−	0.976393i	$-0.569302\pi$
$98$	8.26535	−	13.9313i	0.834927	−	1.40727i
$99$	−2.17087	+	3.51434i	−0.218180	+	0.353204i
$100$	8.83535	−	2.76701i	0.883535	−	0.276701i
$101$	−7.66759	−	4.09841i	−0.762954	−	0.407808i	0.0435384	−	0.999052i	$-0.486137\pi$
$101$	−7.66759	−	4.09841i	−0.762954	−	0.407808i	−0.806493	+	0.591244i	$0.798637\pi$
$102$	0.367246	+	16.4367i	0.0363628	+	1.62747i
$103$	8.18400	+	12.2482i	0.806394	+	1.20685i	0.975226	+	0.221209i	$0.0710003\pi$
$103$	8.18400	+	12.2482i	0.806394	+	1.20685i	−0.168833	+	0.985645i	$0.554000\pi$
$104$	−6.05871	+	6.86837i	−0.594106	+	0.673499i
$105$	−0.584662	+	4.49264i	−0.0570572	+	0.438437i
$106$	12.3589	+	3.03686i	1.20040	+	0.294966i
$107$	3.35795	+	4.09168i	0.324626	+	0.395557i	0.909594	−	0.415499i	$-0.136393\pi$
$107$	3.35795	+	4.09168i	0.324626	+	0.395557i	−0.584968	+	0.811056i	$0.698893\pi$
$108$	−5.88929	−	8.56249i	−0.566697	−	0.823926i
$109$	−9.03421	−	16.9018i	−0.865320	−	1.61890i	−0.782768	−	0.622314i	$-0.786193\pi$
$109$	−9.03421	−	16.9018i	−0.865320	−	1.61890i	−0.0825525	−	0.996587i	$-0.526307\pi$
$110$	−1.18397	+	0.0634922i	−0.112887	+	0.00605374i
$111$	0.107037	+	0.0935871i	0.0101595	+	0.00888289i
$112$	−11.9304	+	12.3666i	−1.12732	+	1.16853i
$113$	8.12952	+	3.36736i	0.764761	+	0.316774i	0.730748	−	0.682647i	$-0.239171\pi$
$113$	8.12952	+	3.36736i	0.764761	+	0.316774i	0.0340125	+	0.999421i	$0.489171\pi$
$114$	−0.434854	−	3.59083i	−0.0407278	−	0.336312i
$115$	−0.898322	+	2.96137i	−0.0837690	+	0.276149i
$116$	1.07308	−	5.65977i	0.0996331	−	0.525496i
$117$	−7.10987	−	6.61948i	−0.657308	−	0.611971i
$118$	0.730384	+	4.77607i	0.0672373	+	0.439673i
$119$	5.62509	+	28.2793i	0.515651	+	2.59236i
$120$	1.05468	−	2.79028i	0.0962786	−	0.254716i
$121$	8.92915	+	1.77612i	0.811741	+	0.161465i
$122$	−1.97204	−	2.15628i	−0.178540	−	0.195220i
$123$	13.6057	−	12.7812i	1.22679	−	1.15245i
$124$	−11.4345	+	6.24447i	−1.02685	+	0.560770i
$125$	−3.71956	+	4.53229i	−0.332687	+	0.405381i
$126$	−12.7723	−	13.0016i	−1.13785	−	1.15828i
$127$			15.1935i			1.34821i	0.738637	+	0.674104i	$0.235470\pi$
$127$			15.1935i			1.34821i	−0.738637	+	0.674104i	$0.764530\pi$
$128$	9.51662	−	6.11834i	0.841158	−	0.540790i
$129$	−6.32597	−	12.7798i	−0.556971	−	1.12520i
$130$	0.396753	−	2.75997i	0.0347975	−	0.242065i
$131$	−13.2348	−	10.8615i	−1.15633	−	0.948974i	−0.157074	−	0.987587i	$-0.550206\pi$
$131$	−13.2348	−	10.8615i	−1.15633	−	0.948974i	−0.999254	+	0.0386123i	$0.987706\pi$
$132$	2.73758	−	3.90598i	0.238276	−	0.339972i
$133$	−1.84142	−	6.07035i	−0.159671	−	0.526366i
$134$	−8.02446	+	7.33881i	−0.693208	+	0.633977i
$135$	2.92844	+	1.19770i	0.252040	+	0.103082i
$136$	0.676151	−	18.9721i	0.0579794	−	1.62685i
$137$	−5.15052	+	1.02450i	−0.440039	+	0.0875292i	−0.410138	−	0.912024i	$-0.634519\pi$
$137$	−5.15052	+	1.02450i	−0.440039	+	0.0875292i	−0.0299014	+	0.999553i	$0.509519\pi$
$138$	−7.14593	−	10.1941i	−0.608302	−	0.867780i
$139$	8.23806	+	0.811378i	0.698743	+	0.0688202i	0.441150	−	0.897433i	$-0.354571\pi$
$139$	8.23806	+	0.811378i	0.698743	+	0.0688202i	0.257593	+	0.966254i	$0.417071\pi$
$140$	0.974502	−	5.13983i	0.0823605	−	0.434395i
$141$	9.67318	−	1.61185i	0.814628	−	0.135742i
$142$	−4.35253	−	1.53536i	−0.365257	−	0.128845i
$143$	1.70624	−	4.11922i	0.142683	−	0.344467i
$144$	6.21617	+	10.2645i	0.518015	+	0.855372i
$145$	0.671147	+	1.62029i	0.0557357	+	0.134558i
$146$	0.504417	+	9.40613i	0.0417459	+	0.778457i
$147$	−16.1435	−	11.5319i	−1.33149	−	0.951135i
$148$	−0.117127	−	0.115044i	−0.00962782	−	0.00945652i
$149$	−14.0580	+	11.5371i	−1.15168	+	0.945157i	−0.999069	−	0.0431297i	$-0.986267\pi$
$149$	−14.0580	+	11.5371i	−1.15168	+	0.945157i	−0.152608	+	0.988287i	$0.548767\pi$
$150$	−2.46006	−	11.0692i	−0.200863	−	0.903799i
$151$	−9.13712	−	6.10523i	−0.743568	−	0.496836i	0.125153	−	0.992137i	$-0.460058\pi$
$151$	−9.13712	−	6.10523i	−0.743568	−	0.496836i	−0.868721	+	0.495301i	$0.835058\pi$
$152$	0.261081	+	4.16846i	0.0211764	+	0.338107i
$153$	20.0965	+	1.25709i	1.62470	+	0.101630i
$154$	3.54258	−	7.57795i	0.285469	−	0.610649i
$155$	1.86978	−	3.49812i	0.150185	−	0.280976i
$156$	7.75319	+	8.10628i	0.620752	+	0.649022i
$157$	14.3625	−	1.41459i	1.14625	−	0.112896i	0.492996	−	0.870031i	$-0.335902\pi$
$157$	14.3625	−	1.41459i	1.14625	−	0.112896i	0.653258	+	0.757135i	$0.273402\pi$
$158$	4.89124	+	2.90194i	0.389126	+	0.230866i
$159$	4.98821	−	14.7670i	0.395591	−	1.17110i
$160$	−1.40244	+	3.14597i	−0.110873	+	0.248711i
$161$	−15.4383	−	15.4383i	−1.21671	−	1.21671i
$162$	−11.0602	+	6.29862i	−0.868969	+	0.494866i
$163$	−16.1903	+	1.59461i	−1.26812	+	0.124899i	−0.709609	−	0.704596i	$-0.751128\pi$
$163$	−16.1903	+	1.59461i	−1.26812	+	0.124899i	−0.558514	+	0.829495i	$0.688628\pi$
$164$	−16.5391	+	13.8236i	−1.29149	+	1.07944i
$165$	−0.0453515	+	1.45144i	−0.00353061	+	0.112994i
$166$	5.37386	+	14.8091i	0.417093	+	1.14941i
$167$	0.773733	+	1.15797i	0.0598732	+	0.0896066i	0.860198	−	0.509960i	$-0.170340\pi$
$167$	0.773733	+	1.15797i	0.0598732	+	0.0896066i	−0.800325	+	0.599566i	$0.795340\pi$
$168$	13.8537	+	15.8422i	1.06884	+	1.22225i
$169$	−2.09089	−	1.39709i	−0.160837	−	0.107468i
$170$	2.99355	+	4.94399i	0.229595	+	0.379187i
$171$	−4.42716	+	0.158131i	−0.338554	+	0.0120926i
$172$	6.43746	+	15.1552i	0.490852	+	1.15557i
$173$	2.60055	+	4.86528i	0.197716	+	0.369900i	0.961168	−	0.275964i	$-0.0889971\pi$
$173$	2.60055	+	4.86528i	0.197716	+	0.369900i	−0.763452	+	0.645864i	$0.776497\pi$
$174$	−6.79553	−	1.89671i	−0.515168	−	0.143789i
$175$	−7.61023	−	18.3727i	−0.575280	−	1.38885i
$176$	−3.41706	+	4.31953i	−0.257570	+	0.325597i
$177$	5.90422	−	0.395814i	0.443788	−	0.0297512i
$178$	1.18241	+	2.47123i	0.0886251	+	0.185227i
$179$	−1.89839	+	6.25816i	−0.141893	+	0.467757i	−0.998866	−	0.0476029i	$-0.984842\pi$
$179$	−1.89839	+	6.25816i	−0.141893	+	0.467757i	0.856974	+	0.515360i	$0.172342\pi$
$180$	−3.29567	−	1.57655i	−0.245645	−	0.117509i
$181$	−16.7184	−	1.64662i	−1.24267	−	0.122392i	−0.544769	−	0.838586i	$-0.683383\pi$
$181$	−16.7184	−	1.64662i	−1.24267	−	0.122392i	−0.697901	+	0.716194i	$0.745883\pi$
$182$	15.8533	+	11.6477i	1.17513	+	0.863385i
$183$	−2.83599	+	2.18285i	−0.209643	+	0.161361i
$184$	7.55564	+	12.2294i	0.557009	+	0.901562i
$185$	0.0490224	+	0.00975116i	0.00360420	+	0.000716920i
$186$	6.43410	+	14.6019i	0.471771	+	1.07066i
$187$	2.68275	+	8.84384i	0.196182	+	0.646725i
$188$	−11.2587	+	1.21101i	−0.821124	+	0.0883219i
$189$	−17.1916	+	14.2378i	−1.25050	+	1.03564i
$190$	−0.762042	−	1.01792i	−0.0552844	−	0.0738474i
$191$		−	0.529619i		−	0.0383219i	−0.999816	−	0.0191609i	$-0.993901\pi$
$191$		−	0.529619i		−	0.0383219i	0.999816	−	0.0191609i	$-0.00609949\pi$
$192$	−6.47914	−	12.2483i	−0.467592	−	0.883944i
$193$			22.9630i			1.65291i	0.562999	+	0.826457i	$0.309647\pi$
$193$			22.9630i			1.65291i	−0.562999	+	0.826457i	$0.690353\pi$
$194$	18.8023	−	14.0760i	1.34993	−	1.01060i
$195$	−3.32695	−	0.770513i	−0.238248	−	0.0551776i
$196$	17.8382	+	14.3734i	1.27415	+	1.02667i
$197$	−4.66417	−	15.3757i	−0.332309	−	1.09547i	−0.950832	−	0.309708i	$-0.899769\pi$
$197$	−4.66417	−	15.3757i	−0.332309	−	1.09547i	0.618523	−	0.785767i	$-0.287731\pi$
$198$	−4.48261	−	3.74602i	−0.318566	−	0.266218i
$199$	7.73241	+	1.53807i	0.548136	+	0.109031i	0.461387	−	0.887199i	$-0.347352\pi$
$199$	7.73241	+	1.53807i	0.548136	+	0.109031i	0.0867494	+	0.996230i	$0.472352\pi$
$200$	2.09541	+	12.9247i	0.148168	+	0.913917i
$201$	8.12335	+	10.5540i	0.572977	+	0.744420i
$202$	7.28000	−	9.90857i	0.512219	−	0.697164i
$203$	−12.3137	−	1.21279i	−0.864253	−	0.0851215i
$204$	−23.0823	−	2.79344i	−1.61609	−	0.195580i
$205$	1.90498	−	6.27988i	0.133050	−	0.438606i
$206$	−18.7922	+	8.99148i	−1.30932	+	0.626466i
$207$	−13.1817	+	7.66288i	−0.916189	+	0.532607i
$208$	−8.39532	−	9.86324i	−0.582111	−	0.683893i
$209$	−0.778091	−	1.87848i	−0.0538217	−	0.129937i
$210$	−6.17126	−	1.72247i	−0.425857	−	0.118862i
$211$	−8.89469	−	16.6408i	−0.612335	−	1.14560i	−0.976754	−	0.214364i	$-0.931232\pi$
$211$	−8.89469	−	16.6408i	−0.612335	−	1.14560i	0.364418	−	0.931235i	$-0.381268\pi$
$212$	−6.73803	+	16.6892i	−0.462769	+	1.14622i
$213$	−2.32523	+	5.15229i	−0.159322	+	0.353029i
$214$	−6.40334	+	3.87718i	−0.437724	+	0.265039i
$215$	−4.16810	−	2.78504i	−0.284262	−	0.189938i
$216$	13.1711	−	6.52095i	0.896178	−	0.443695i
$217$	15.5472	+	23.2680i	1.05541	+	1.57953i
$218$	25.4775	−	9.24518i	1.72555	−	0.626163i
$219$	11.5310	+	0.360298i	0.779195	+	0.0243467i
$220$	0.149370	−	1.67013i	0.0100706	−	0.112600i
$221$	−21.6292	+	2.13029i	−1.45494	+	0.143299i
$222$	−0.152544	+	0.131000i	−0.0102381	+	0.00879216i
$223$	−5.97035	−	5.97035i	−0.399804	−	0.399804i	0.478360	−	0.878164i	$-0.341232\pi$
$223$	−5.97035	−	5.97035i	−0.399804	−	0.399804i	−0.878164	+	0.478360i	$0.841232\pi$
$224$	−14.9103	−	19.1890i	−0.996238	−	1.28212i
$225$	−13.7635	+	1.85372i	−0.917565	+	0.123581i
$226$	−6.34959	+	10.7023i	−0.422369	+	0.711905i
$227$	−9.89842	+	0.974910i	−0.656981	+	0.0647070i	−0.421014	−	0.907054i	$-0.638326\pi$
$227$	−9.89842	+	0.974910i	−0.656981	+	0.0647070i	−0.235967	+	0.971761i	$0.575826\pi$
$228$	5.11404	+	0.113859i	0.338686	+	0.00754047i
$229$	−2.09875	+	3.92649i	−0.138689	+	0.259470i	−0.941671	−	0.336534i	$-0.890745\pi$
$229$	−2.09875	+	3.92649i	−0.138689	+	0.259470i	0.802982	+	0.596003i	$0.203245\pi$
$230$	−3.96463	−	1.85340i	−0.261420	−	0.122210i
$231$	−8.88017	−	5.10935i	−0.584272	−	0.336170i
$232$	7.70675	+	2.64103i	0.505973	+	0.173392i
$233$	7.98092	+	5.33268i	0.522847	+	0.349355i	0.788819	−	0.614625i	$-0.210693\pi$
$233$	7.98092	+	5.33268i	0.522847	+	0.349355i	−0.265972	+	0.963981i	$0.585693\pi$
$234$	10.6968	−	8.62054i	0.699273	−	0.563543i
$235$	2.66490	−	2.18703i	0.173839	−	0.142666i
$236$	−6.83264	+	0.0613281i	−0.444767	+	0.00399212i
$237$	4.04881	−	5.66792i	0.262999	−	0.368171i
$238$	−40.7179	+	2.18356i	−2.63935	+	0.141539i
$239$	−4.33654	−	10.4693i	−0.280508	−	0.677206i	0.719340	−	0.694658i	$-0.244444\pi$
$239$	−4.33654	−	10.4693i	−0.280508	−	0.677206i	−0.999848	+	0.0174526i	$0.994444\pi$
$240$	3.69366	+	2.03785i	0.238425	+	0.131542i
$241$	−11.8243	+	28.5464i	−0.761670	+	1.83883i	−0.290141	+	0.956984i	$0.593702\pi$
$241$	−11.8243	+	28.5464i	−0.761670	+	1.83883i	−0.471529	+	0.881851i	$0.656298\pi$
$242$	−4.28305	+	12.1418i	−0.275325	+	0.780507i
$243$	6.53901	+	14.1507i	0.419478	+	0.907766i
$244$	3.41524	−	2.32660i	0.218638	−	0.148945i
$245$	−6.94079	−	0.683608i	−0.443431	−	0.0436741i
$246$	15.1536	+	21.6176i	0.966161	+	1.37829i
$247$	4.68971	−	0.932841i	0.298399	−	0.0593552i
$248$	−6.44022	−	17.2629i	−0.408954	−	1.09619i
$249$	18.6297	−	5.02155i	1.18061	−	0.318228i
$250$	−5.59593	−	6.11875i	−0.353918	−	0.386984i
$251$	2.44837	+	8.07121i	0.154540	+	0.509450i	0.999685	−	0.0250865i	$-0.00798611\pi$
$251$	2.44837	+	8.07121i	0.154540	+	0.509450i	−0.845145	+	0.534537i	$0.820486\pi$
$252$	20.7702	−	15.2627i	1.30840	−	0.961462i
$253$	−5.40957	−	4.43952i	−0.340097	−	0.279110i
$254$	−21.2683	−	3.05737i	−1.33449	−	0.191836i
$255$	6.34393	−	3.14023i	0.397272	−	0.196649i
$256$	6.64958	+	14.5528i	0.415599	+	0.909548i
$257$			7.35748i			0.458947i	0.973315	+	0.229474i	$0.0737005\pi$
$257$			7.35748i			0.458947i	−0.973315	+	0.229474i	$0.926300\pi$
$258$	19.1624	−	6.28360i	1.19300	−	0.391200i
$259$	−0.223711	+	0.272592i	−0.0139007	+	0.0169381i
$260$	3.78363	+	1.11077i	0.234651	+	0.0688869i
$261$	−3.01966	+	8.09610i	−0.186912	+	0.501136i
$262$	17.8674	−	16.3407i	1.10385	−	1.00953i
$263$	−0.432230	−	0.0859758i	−0.0266524	−	0.00530149i	0.181746	−	0.983345i	$-0.441825\pi$
$263$	−0.432230	−	0.0859758i	−0.0266524	−	0.00530149i	−0.208399	+	0.978044i	$0.566825\pi$
$264$	4.91680	+	4.61812i	0.302608	+	0.284226i
$265$	−1.06898	−	5.37414i	−0.0656671	−	0.330131i
$266$	8.86797	−	1.35614i	0.543730	−	0.0831502i
$267$	3.13842	−	1.18656i	0.192068	−	0.0726161i
$268$	−8.65829	−	12.7096i	−0.528889	−	0.776363i
$269$	3.23570	−	10.6667i	0.197284	−	0.650359i	−0.801354	−	0.598190i	$-0.795887\pi$
$269$	3.23570	−	10.6667i	0.197284	−	0.650359i	0.998638	−	0.0521684i	$-0.0166133\pi$
$270$	−2.26585	+	3.85829i	−0.137895	+	0.234808i
$271$	−9.19695	−	3.80950i	−0.558675	−	0.231411i	0.0854348	−	0.996344i	$-0.472772\pi$
$271$	−9.19695	−	3.80950i	−0.558675	−	0.231411i	−0.644110	+	0.764933i	$0.722772\pi$
$272$	26.4216	+	4.76422i	1.60204	+	0.288873i
$273$	15.8589	−	18.1380i	0.959825	−	1.09776i
$274$	−0.397693	−	7.41599i	−0.0240255	−	0.448016i
$275$	−3.00474	−	5.62147i	−0.181193	−	0.338987i
$276$	15.7079	−	7.95171i	0.945505	−	0.478637i
$277$	8.38631	+	10.2187i	0.503885	+	0.613985i	0.961379	−	0.275227i	$-0.0887531\pi$
$277$	8.38631	+	10.2187i	0.503885	+	0.613985i	−0.457495	+	0.889212i	$0.651253\pi$
$278$	−2.79352	+	11.3686i	−0.167544	+	0.681841i
$279$	18.4868	−	6.33690i	1.10678	−	0.379380i
$280$	6.99876	+	2.39841i	0.418256	+	0.143332i
$281$	−5.28561	−	7.91047i	−0.315313	−	0.471899i	0.639632	−	0.768681i	$-0.279087\pi$
$281$	−5.28561	−	7.91047i	−0.315313	−	0.471899i	−0.954945	+	0.296782i	$0.904087\pi$
$282$	0.309789	+	13.8651i	0.0184477	+	0.825654i
$283$	−9.74997	−	5.21147i	−0.579575	−	0.309789i	0.155434	−	0.987846i	$-0.450322\pi$
$283$	−9.74997	−	5.21147i	−0.579575	−	0.309789i	−0.735010	+	0.678057i	$0.762822\pi$
$284$	3.02509	−	5.78382i	0.179506	−	0.343207i
$285$	−1.32127	+	0.824347i	−0.0782650	+	0.0488301i
$286$	5.42285	+	3.21734i	0.320660	+	0.190245i
$287$	32.7385	+	32.7385i	1.93249	+	1.93249i
$288$	−15.6193	+	6.63605i	−0.920377	+	0.391033i
$289$	19.8342	−	19.8342i	1.16672	−	1.16672i
$290$	−2.40318	+	0.613439i	−0.141119	+	0.0360224i
$291$	−15.2268	−	24.4056i	−0.892613	−	1.43068i
$292$	−13.2684	−	1.18668i	−0.776476	−	0.0694453i
$293$	14.4248	−	26.9870i	0.842708	−	1.57660i	0.0259165	−	0.999664i	$-0.491750\pi$
$293$	14.4248	−	26.9870i	0.842708	−	1.57660i	0.816792	−	0.576932i	$-0.195750\pi$
$294$	19.3911	−	20.2775i	1.13091	−	1.18261i
$295$	1.72967	−	1.15573i	0.100705	−	0.0672890i
$296$	0.184610	−	0.140808i	0.0107302	−	0.00818429i
$297$	−5.03648	+	5.08169i	−0.292246	+	0.294869i
$298$	−13.3211	−	22.0003i	−0.771668	−	1.27445i
$299$	12.7217	−	10.4404i	0.735713	−	0.603784i
$300$	15.9900	−	1.21621i	0.923184	−	0.0702180i
$301$	31.1910	−	16.6719i	1.79782	−	0.960955i
$302$	10.3849	−	11.5618i	0.597583	−	0.665308i
$303$	−11.3366	−	9.91208i	−0.651269	−	0.569434i
$304$	−5.88765	−	0.473345i	−0.337680	−	0.0271482i
$305$	−0.481454	+	1.16233i	−0.0275680	+	0.0665550i
$306$	−5.80368	+	27.8786i	−0.331774	+	1.59371i
$307$	−18.2616	−	5.53961i	−1.04225	−	0.316162i	−0.277658	−	0.960680i	$-0.589558\pi$
$307$	−18.2616	−	5.53961i	−1.04225	−	0.316162i	−0.764589	+	0.644518i	$0.777058\pi$
$308$	9.89493	+	6.48388i	0.563816	+	0.369453i
$309$	9.02304	+	23.8658i	0.513303	+	1.35768i
$310$	4.52050	+	3.32129i	0.256747	+	0.188636i
$311$	−17.6749	+	3.51576i	−1.00225	+	0.199360i	−0.668829	−	0.743417i	$-0.733204\pi$
$311$	−17.6749	+	3.51576i	−1.00225	+	0.199360i	−0.333424	+	0.942777i	$0.608204\pi$
$312$	−12.9075	+	9.22189i	−0.730745	+	0.522087i
$313$	−1.77203	+	8.90862i	−0.100161	+	0.503545i	0.897838	+	0.440325i	$0.145137\pi$
$313$	−1.77203	+	8.90862i	−0.100161	+	0.503545i	−0.998000	+	0.0632196i	$0.979863\pi$
$314$	−0.909975	+	20.3897i	−0.0513529	+	1.15066i
$315$	−2.74225	+	7.35235i	−0.154509	+	0.414258i
$316$	−5.04646	+	6.26292i	−0.283885	+	0.352317i
$317$	24.8376	+	20.3837i	1.39502	+	1.14486i	0.970963	+	0.239228i	$0.0768943\pi$
$317$	24.8376	+	20.3837i	1.39502	+	1.14486i	0.424057	+	0.905636i	$0.360606\pi$
$318$	19.6674	+	9.95415i	1.10290	+	0.558201i
$319$	−3.96595			−0.222050
$320$	−4.12159	−	2.59623i	−0.230404	−	0.145134i
$321$	4.06716	+	8.21652i	0.227007	+	0.458601i
$322$	24.7176	−	18.5043i	1.37746	−	1.03121i
$323$	−6.28762	+	7.66149i	−0.349852	+	0.426296i
$324$	−6.59134	−	16.7498i	−0.366185	−	0.930542i
$325$	14.3445	−	4.35136i	0.795691	−	0.241370i
$326$	1.02578	−	22.9845i	0.0568126	−	1.27299i
$327$	−8.63907	−	32.0505i	−0.477742	−	1.77239i
$328$	−16.0225	−	25.9336i	−0.884693	−	1.43194i
$329$	4.74503	+	23.8549i	0.261602	+	1.31516i
$330$	−2.02263	−	0.355554i	−0.111342	−	0.0195726i
$331$	−0.829850	+	8.42561i	−0.0456127	+	0.463113i	0.945065	+	0.326884i	$0.105999\pi$
$331$	−0.829850	+	8.42561i	−0.0456127	+	0.463113i	−0.990677	+	0.136230i	$0.956501\pi$
$332$	−21.8115	+	4.54246i	−1.19706	+	0.249300i
$333$	0.144039	+	0.199747i	0.00789329	+	0.0109461i
$334$	−1.77666	+	0.850073i	−0.0972142	+	0.0465139i
$335$	4.32555	+	1.79170i	0.236330	+	0.0978911i
$336$	−24.9640	+	16.2049i	−1.36190	+	0.884051i
$337$	−8.26083	+	3.42175i	−0.449996	+	0.186394i	−0.596160	−	0.802866i	$-0.703307\pi$
$337$	−8.26083	+	3.42175i	−0.449996	+	0.186394i	0.146164	+	0.989260i	$0.453307\pi$
$338$	2.37642	−	2.64574i	0.129260	−	0.143909i
$339$	12.4017	+	8.85901i	0.673568	+	0.481156i
$340$	−7.52310	+	3.19558i	−0.407997	+	0.173304i
$341$	5.69027	+	6.93361i	0.308145	+	0.375476i
$342$	0.669514	−	6.22907i	0.0362032	−	0.336830i
$343$	10.6306	−	15.9098i	0.573997	−	0.859047i
$344$	−22.5100	+	5.96165i	−1.21366	+	0.321431i
$345$	−2.67311	+	4.64592i	−0.143915	+	0.250128i
$346$	−7.33384	+	2.66128i	−0.394270	+	0.143071i
$347$	−27.3555	−	14.6218i	−1.46852	−	0.784941i	−0.473143	−	0.880985i	$-0.656881\pi$
$347$	−27.3555	−	14.6218i	−1.46852	−	0.784941i	−0.995377	+	0.0960449i	$0.969381\pi$
$348$	4.02252	−	9.13087i	0.215629	−	0.489466i
$349$	−2.71172	−	27.5326i	−0.145155	−	1.47378i	−0.741444	−	0.671014i	$-0.765859\pi$
$349$	−2.71172	−	27.5326i	−0.145155	−	1.47378i	0.596289	−	0.802770i	$-0.296641\pi$
$350$	27.2500	−	6.95588i	1.45657	−	0.371807i
$351$	−9.41025	−	13.9481i	−0.502282	−	0.744497i
$352$	−5.35898	−	5.65249i	−0.285635	−	0.301279i
$353$	11.9926	−	11.9926i	0.638300	−	0.638300i	−0.311836	−	0.950136i	$-0.600944\pi$
$353$	11.9926	−	11.9926i	0.638300	−	0.638300i	0.950136	+	0.311836i	$0.100944\pi$
$354$	−0.634026	+	8.34452i	−0.0336981	+	0.443506i
$355$	0.194776	+	1.97760i	0.0103377	+	0.104960i
$356$	−3.69722	+	1.15788i	−0.195952	+	0.0613674i
$357$	−1.55968	+	49.9163i	−0.0825471	+	2.64185i
$358$	−8.37832	−	3.91674i	−0.442808	−	0.207006i
$359$	−8.76693	+	5.85788i	−0.462701	+	0.309167i	−0.764982	−	0.644052i	$-0.777252\pi$
$359$	−8.76693	+	5.85788i	−0.462701	+	0.309167i	0.302281	+	0.953219i	$0.402252\pi$
$360$	2.87008	−	4.29611i	0.151266	−	0.226425i
$361$	−9.34440	+	13.9849i	−0.491810	+	0.736046i
$362$	5.66920	−	23.0715i	0.297966	−	1.21261i
$363$	14.3728	+	6.48647i	0.754379	+	0.340452i
$364$	−19.4949	+	19.8480i	−1.02181	+	1.04032i
$365$	3.57676	−	1.91182i	0.187216	−	0.100069i
$366$	−2.48493	−	4.40914i	−0.129889	−	0.230470i
$367$	−0.172078	+	0.0712772i	−0.00898242	+	0.00372064i	−0.387170	−	0.922008i	$-0.626547\pi$
$367$	−0.172078	+	0.0712772i	−0.00898242	+	0.00372064i	0.378188	+	0.925729i	$0.376547\pi$
$368$	−18.6394	+	8.11567i	−0.971645	+	0.423059i
$369$	27.9530	−	16.2499i	1.45518	−	0.845935i
$370$	−0.0235146	+	0.0666605i	−0.00122247	+	0.00346552i
$371$	36.9937	+	11.2219i	1.92062	+	0.582612i
$372$	−21.7348	+	6.06829i	−1.12690	+	0.314626i
$373$	0.712710	−	7.23626i	0.0369027	−	0.374680i	−0.958941	−	0.283605i	$-0.908470\pi$
$373$	0.712710	−	7.23626i	0.0369027	−	0.374680i	0.995844	−	0.0910750i	$-0.0290303\pi$
$374$	−12.9197	+	1.97575i	−0.668060	+	0.102163i
$375$	−8.04754	+	6.19415i	−0.415573	+	0.319865i
$376$	0.570365	−	16.0039i	0.0294143	−	0.825336i
$377$	1.81955	−	9.14749i	0.0937116	−	0.471120i
$378$	−16.4709	−	26.9302i	−0.847173	−	1.38514i
$379$	11.6373	−	3.53013i	0.597767	−	0.181331i	0.0231208	−	0.999733i	$-0.492640\pi$
$379$	11.6373	−	3.53013i	0.597767	−	0.181331i	0.574646	+	0.818402i	$0.305140\pi$
$380$	1.57825	−	0.861892i	0.0809624	−	0.0442141i
$381$	−5.93756	+	25.6374i	−0.304190	+	1.31344i
$382$	0.741373	+	0.106574i	0.0379319	+	0.00545281i
$383$	25.6239			1.30932			0.654659	−	0.755925i	$-0.272812\pi$
$383$	25.6239			1.30932			0.654659	+	0.755925i	$0.272812\pi$
$384$	18.4492	−	6.60496i	0.941484	−	0.337058i
$385$	−3.60161			−0.183555
$386$	−32.1442	−	4.62081i	−1.63610	−	0.235193i
$387$	−5.68009	−	24.0366i	−0.288735	−	1.22185i
$388$	15.9203	+	29.1524i	0.808233	+	1.47999i
$389$	10.7486	−	3.26055i	0.544975	−	0.165316i	−0.00578008	−	0.999983i	$-0.501840\pi$
$389$	10.7486	−	3.26055i	0.544975	−	0.165316i	0.550755	+	0.834667i	$0.314340\pi$
$390$	1.74806	−	4.50209i	0.0885164	−	0.227972i
$391$	−6.65503	+	33.4571i	−0.336559	+	1.69200i
$392$	−23.7098	+	22.0779i	−1.19752	+	1.11510i
$393$	−18.0876	−	23.4997i	−0.912399	−	1.18540i
$394$	22.4619	−	3.43499i	1.13161	−	0.173052i
$395$	0.240013	−	2.43689i	0.0120763	−	0.122613i
$396$	6.14579	−	5.52107i	0.308838	−	0.277444i
$397$	6.74237	+	2.04528i	0.338390	+	0.102649i	0.454906	−	0.890539i	$-0.349673\pi$
$397$	6.74237	+	2.04528i	0.338390	+	0.102649i	−0.116516	+	0.993189i	$0.537173\pi$
$398$	−3.70901	+	10.5145i	−0.185916	+	0.527045i
$399$	−0.734927	−	10.9627i	−0.0367924	−	0.548819i
$400$	−18.5140	+	0.332382i	−0.925701	+	0.0166191i
$401$	−3.50424	+	1.45150i	−0.174993	+	0.0724846i	−0.468460	−	0.883485i	$-0.655191\pi$
$401$	−3.50424	+	1.45150i	−0.174993	+	0.0724846i	0.293467	+	0.955969i	$0.405191\pi$
$402$	−16.4084	+	9.24750i	−0.818374	+	0.461223i
$403$	−18.6031	+	9.94356i	−0.926686	+	0.495324i
$404$	12.4053	+	12.1846i	0.617187	+	0.606206i
$405$	4.47336	+	3.16540i	0.222283	+	0.157290i
$406$	4.17556	−	16.9930i	0.207230	−	0.843347i
$407$	−0.0627956	+	0.0939802i	−0.00311266	+	0.00465842i
$408$	8.55514	−	31.7491i	0.423543	−	1.57181i
$409$	−7.53602	+	5.03541i	−0.372632	+	0.248985i	−0.727759	−	0.685833i	$-0.759438\pi$
$409$	−7.53602	+	5.03541i	−0.372632	+	0.248985i	0.355126	+	0.934818i	$0.384438\pi$
$410$	8.40739	+	3.93032i	0.415211	+	0.194105i
$411$	−9.09130	−	0.284066i	−0.448441	−	0.0140119i
$412$	−8.80496	−	28.1151i	−0.433789	−	1.38513i
$413$	1.43855	+	14.6059i	0.0707865	+	0.718707i
$414$	−8.07416	−	19.9940i	−0.396823	−	0.982652i
$415$	4.79623	−	4.79623i	0.235438	−	0.235438i
$416$	15.4962	−	9.76721i	0.759763	−	0.478877i
$417$	13.5837	+	4.58850i	0.665198	+	0.224700i
$418$	2.78611	−	0.711188i	0.136273	−	0.0347853i
$419$	2.86844	+	29.1238i	0.140133	+	1.42279i	0.765990	+	0.642853i	$0.222249\pi$
$419$	2.86844	+	29.1238i	0.140133	+	1.42279i	−0.625857	+	0.779938i	$0.715251\pi$
$420$	3.65299	−	8.29206i	0.178247	−	0.404611i
$421$	30.1769	+	16.1299i	1.47073	+	0.786122i	0.995592	−	0.0937898i	$-0.0298982\pi$
$421$	30.1769	+	16.1299i	1.47073	+	0.786122i	0.475138	+	0.879911i	$0.342398\pi$
$422$	25.0840	−	9.10240i	1.22107	−	0.443098i
$423$	16.9523	+	1.06042i	0.824249	+	0.0515592i
$424$	−22.0060	−	12.7904i	−1.06871	−	0.621156i
$425$	−17.2622	+	25.8347i	−0.837340	+	1.25317i
$426$	−6.74440	−	4.29170i	−0.326767	−	0.207934i
$427$	−5.63094	−	6.86132i	−0.272500	−	0.332043i
$428$	−4.13884	−	9.74375i	−0.200058	−	0.470982i
$429$	4.48886	−	6.28394i	0.216724	−	0.303392i
$430$	4.73730	−	5.27418i	0.228453	−	0.254344i
$431$	−24.9254	+	10.3244i	−1.20061	+	0.497310i	−0.891197	−	0.453617i	$-0.850133\pi$
$431$	−24.9254	+	10.3244i	−1.20061	+	0.497310i	−0.309416	+	0.950927i	$0.600133\pi$
$432$	6.47780	+	19.7494i	0.311663	+	0.950193i
$433$	10.2109	+	4.22951i	0.490706	+	0.203257i	0.614295	−	0.789076i	$-0.289440\pi$
$433$	10.2109	+	4.22951i	0.490706	+	0.203257i	−0.123589	+	0.992334i	$0.539440\pi$
$434$	−35.6996	+	17.0811i	−1.71364	+	0.819920i
$435$	0.499283	+	2.99634i	0.0239388	+	0.143664i
$436$	7.81483	+	37.5244i	0.374263	+	1.79709i
$437$	0.735616	−	7.46883i	0.0351893	−	0.357283i
$438$	−2.82472	+	16.0689i	−0.134970	+	0.767802i
$439$	5.81467	+	29.2323i	0.277519	+	1.39518i	0.828184	+	0.560456i	$0.189374\pi$
$439$	5.81467	+	29.2323i	0.277519	+	1.39518i	−0.550665	+	0.834726i	$0.685626\pi$
$440$	2.30783	+	0.545169i	0.110021	+	0.0259899i
$441$	−22.7337	−	25.7676i	−1.08256	−	1.22703i
$442$	1.37037	−	30.7058i	0.0651821	−	1.46052i
$443$	17.8153	−	5.40420i	0.846428	−	0.256761i	0.162861	−	0.986649i	$-0.447928\pi$
$443$	17.8153	−	5.40420i	0.846428	−	0.256761i	0.683567	+	0.729888i	$0.260428\pi$
$444$	−0.152681	−	0.239896i	−0.00724592	−	0.0113850i
$445$	0.748275	−	0.911775i	0.0354716	−	0.0432223i
$446$	9.55884	−	7.15604i	0.452624	−	0.338848i
$447$	−28.2300	+	13.9738i	−1.33523	+	0.660937i
$448$	29.8616	−	17.0105i	1.41083	−	0.803670i
$449$	−22.2311			−1.04915			−0.524576	−	0.851363i	$-0.675776\pi$
$449$	−22.2311			−1.04915			−0.524576	+	0.851363i	$0.675776\pi$
$450$	0.174724	−	19.6395i	0.00823658	−	0.925814i
$451$	11.4715	+	9.41443i	0.540173	+	0.443308i
$452$	−13.7036	−	11.0419i	−0.644563	−	0.519368i
$453$	−13.0320	−	13.8726i	−0.612295	−	0.651793i
$454$	0.627140	−	14.0522i	0.0294331	−	0.659504i
$455$	1.65240	−	8.30716i	0.0774655	−	0.389446i
$456$	−1.18847	+	7.13585i	−0.0556553	+	0.334167i
$457$	−5.17851	+	1.03007i	−0.242240	+	0.0481846i	−0.314717	−	0.949185i	$-0.601910\pi$
$457$	−5.17851	+	1.03007i	−0.242240	+	0.0481846i	0.0724768	+	0.997370i	$0.476910\pi$
$458$	−5.07407	−	3.72800i	−0.237095	−	0.174198i
$459$	33.4193	+	9.97480i	1.55988	+	0.465584i
$460$	3.39224	−	5.17683i	0.158164	−	0.241371i
$461$	0.456002	+	0.138327i	0.0212381	+	0.00644252i	0.300886	−	0.953660i	$-0.402718\pi$
$461$	0.456002	+	0.138327i	0.0212381	+	0.00644252i	−0.279648	+	0.960103i	$0.590218\pi$
$462$	8.93913	−	11.4025i	0.415886	−	0.530493i
$463$	10.2065	−	24.6406i	0.474336	−	1.14515i	−0.487892	−	0.872904i	$-0.662234\pi$
$463$	10.2065	−	24.6406i	0.474336	−	1.14515i	0.962228	−	0.272244i	$-0.0877658\pi$
$464$	−5.24779	+	10.2566i	−0.243623	+	0.476152i
$465$	4.52210	−	5.17198i	0.209707	−	0.239845i
$466$	−9.07080	+	10.0988i	−0.420197	+	0.467818i
$467$	2.14486	−	1.14645i	0.0992523	−	0.0530515i	−0.421024	−	0.907050i	$-0.638329\pi$
$467$	2.14486	−	1.14645i	0.0992523	−	0.0530515i	0.520276	+	0.853998i	$0.325829\pi$
$468$	9.91474	+	16.7084i	0.458309	+	0.772344i
$469$	−25.5340	+	20.9552i	−1.17905	+	0.967621i
$470$	2.52520	+	4.17048i	0.116479	+	0.192370i
$471$	24.7880	+	3.22585i	1.14217	+	0.148639i
$472$	1.28907	−	9.57683i	0.0593343	−	0.440809i
$473$	9.42557	−	6.29797i	0.433388	−	0.289581i
$474$	7.11935	+	6.80817i	0.327003	+	0.312710i
$475$	3.22239	−	6.02867i	0.147854	−	0.276614i
$476$	5.13700	−	57.4373i	0.235454	−	2.63263i
$477$	14.1879	−	22.9683i	0.649620	−	1.05165i
$478$	15.5279	−	3.96367i	0.710229	−	0.181294i
$479$	6.76388	−	6.76388i	0.309049	−	0.309049i	−0.535491	−	0.844541i	$-0.679874\pi$
$479$	6.76388	−	6.76388i	0.309049	−	0.309049i	0.844541	+	0.535491i	$0.179874\pi$
$480$	−3.59590	+	4.76041i	−0.164129	+	0.217282i
$481$	−0.187956	−	0.187956i	−0.00857006	−	0.00857006i
$482$	−37.5805	−	22.2963i	−1.71175	−	1.01557i
$483$	−20.0172	−	32.0837i	−0.910816	−	1.45986i
$484$	−16.1346	−	8.43880i	−0.733389	−	0.383582i
$485$	−8.91848	−	4.76703i	−0.404967	−	0.216460i
$486$	−21.1243	+	6.30595i	−0.958217	+	0.286044i
$487$	10.5550	+	15.7966i	0.478292	+	0.715814i	0.989642	−	0.143558i	$-0.0458544\pi$
$487$	10.5550	+	15.7966i	0.478292	+	0.715814i	−0.511350	+	0.859373i	$0.670854\pi$
$488$	2.56959	+	5.24891i	0.116320	+	0.237607i
$489$	−27.9425	−	3.63637i	−1.26360	−	0.164443i
$490$	2.35361	−	9.57832i	0.106325	−	0.432704i
$491$	20.5371	+	25.0246i	0.926827	+	1.12934i	0.991326	+	0.131424i	$0.0419551\pi$
$491$	20.5371	+	25.0246i	0.926827	+	1.12934i	−0.0644990	+	0.997918i	$0.520545\pi$
$492$	−33.3101	+	16.8624i	−1.50174	+	0.760214i
$493$	9.11319	+	17.0496i	0.410438	+	0.767875i
$494$	0.362112	+	6.75248i	0.0162922	+	0.303808i
$495$	−0.643740	+	2.43142i	−0.0289340	+	0.109284i
$496$	25.4610	−	5.54139i	1.14323	−	0.248816i
$497$	−12.9526	−	5.36514i	−0.581004	−	0.240660i
$498$	3.28047	+	27.0887i	0.147002	+	1.21388i
$499$	4.49388	−	14.8144i	0.201174	−	0.663181i	−0.797067	−	0.603891i	$-0.793616\pi$
$499$	4.49388	−	14.8144i	0.201174	−	0.663181i	0.998241	−	0.0592904i	$-0.0188838\pi$
$500$	9.69123	−	6.60206i	0.433405	−	0.295253i
$501$	0.853057	+	2.25632i	0.0381118	+	0.100805i
$502$	−11.7910	+	1.80314i	−0.526256	+	0.0804780i
$503$	−6.59114	−	33.1359i	−0.293884	−	1.47746i	−0.792094	−	0.610400i	$-0.791009\pi$
$503$	−6.59114	−	33.1359i	−0.293884	−	1.47746i	0.498209	−	0.867057i	$-0.333991\pi$
$504$	17.1856	+	32.1459i	0.765508	+	1.43189i
$505$	−5.19210	−	1.03277i	−0.231046	−	0.0459578i
$506$	7.30310	−	6.67909i	0.324663	−	0.296922i
$507$	−2.98216	−	3.17453i	−0.132443	−	0.140986i
$508$	8.55955	−	29.1566i	0.379768	−	1.29361i
$509$	13.7349	−	16.7361i	0.608790	−	0.741813i	−0.373819	−	0.927502i	$-0.621952\pi$
$509$	13.7349	−	16.7361i	0.608790	−	0.741813i	0.982609	+	0.185689i	$0.0594517\pi$
$510$	3.11920	+	9.51229i	0.138120	+	0.421211i
$511$			28.6132i			1.26578i
$512$	−21.7094	+	6.37982i	−0.959429	+	0.281951i
$513$	−7.53214	−	1.46329i	−0.332552	−	0.0646056i
$514$	−10.2992	−	1.48053i	−0.454277	−	0.0653035i
$515$	6.93350	+	5.69017i	0.305526	+	0.250739i
$516$	4.93991	+	28.0885i	0.217467	+	1.23653i
$517$	2.26302	+	7.46019i	0.0995277	+	0.328099i
$518$	−0.336564	−	0.368009i	−0.0147878	−	0.0161694i
$519$	2.48680	+	9.22590i	0.109159	+	0.404972i
$520$	−2.31625	+	5.07290i	−0.101574	+	0.222462i
$521$	0.551890	−	0.109778i	0.0241787	−	0.00480945i	−0.182986	−	0.983115i	$-0.558576\pi$
$521$	0.551890	−	0.109778i	0.0241787	−	0.00480945i	0.207165	+	0.978306i	$0.433576\pi$
$522$	−10.7255	−	5.85615i	−0.469441	−	0.256317i
$523$	−8.89055	−	0.875643i	−0.388757	−	0.0382892i	−0.0982491	−	0.995162i	$-0.531324\pi$
$523$	−8.89055	−	0.875643i	−0.388757	−	0.0382892i	−0.290508	+	0.956873i	$0.593824\pi$
$524$	19.2787	+	28.2995i	0.842195	+	1.23627i
$525$	−5.66144	−	33.9760i	−0.247086	−	1.48283i
$526$	0.207328	−	0.587744i	0.00903992	−	0.0256269i
$527$	16.7321	−	40.3949i	0.728862	−	1.75963i
$528$	−7.45395	+	5.95336i	−0.324392	+	0.259087i
$529$	−1.08326	−	2.61521i	−0.0470980	−	0.113705i
$530$	7.73796	−	0.414959i	0.336115	−	0.0180247i
$531$	10.1174	+	1.63945i	0.439058	+	0.0711460i
$532$	0.113871	+	12.6865i	0.00493693	+	0.550029i
$533$	−26.9775	+	22.1399i	−1.16853	+	0.958985i
$534$	1.02943	+	4.63201i	0.0445479	+	0.200447i
$535$	2.67980	+	1.79059i	0.115858	+	0.0774138i
$536$	19.5335	−	9.56256i	0.843719	−	0.413040i
$537$	−5.64899	+	9.81807i	−0.243772	+	0.423681i
$538$	14.2804	+	6.67585i	0.615670	+	0.287816i
$539$	7.43465	−	13.9093i	0.320233	−	0.599114i
$540$	−4.94497	−	3.94819i	−0.212798	−	0.169903i
$541$	−24.6763	+	2.43040i	−1.06092	+	0.104491i	−0.613391	−	0.789780i	$-0.710195\pi$
$541$	−24.6763	+	2.43040i	−1.06092	+	0.104491i	−0.447526	+	0.894271i	$0.647695\pi$
$542$	7.18332	−	12.1075i	0.308550	−	0.520063i
$543$	−27.5670	−	9.31197i	−1.18301	−	0.399615i
$544$	−11.9858	+	36.0268i	−0.513888	+	1.54464i
$545$	−8.25142	−	8.25142i	−0.353452	−	0.353452i
$546$	22.1988	+	25.8496i	0.950022	+	1.10626i
$547$	−8.84311	+	0.870970i	−0.378104	+	0.0372400i	−0.285284	−	0.958443i	$-0.592088\pi$
$547$	−8.84311	+	0.870970i	−0.378104	+	0.0372400i	−0.0928198	+	0.995683i	$0.529588\pi$
$548$	10.4611	+	0.935605i	0.446876	+	0.0399671i
$549$	−5.63847	+	2.57503i	−0.240644	+	0.109899i
$550$	8.47371	−	3.07491i	0.361320	−	0.131114i
$551$	−2.36297	−	3.53643i	−0.100666	−	0.150657i
$552$	7.97012	+	23.5884i	0.339231	+	1.00399i
$553$	14.3643	+	9.59795i	0.610834	+	0.408146i
$554$	−15.9920	+	9.68306i	−0.679436	+	0.411394i
$555$	0.0789091	+	0.0356117i	0.00334951	+	0.00151163i
$556$	−15.3519	−	6.19811i	−0.651063	−	0.262858i
$557$	−5.73588	−	10.7311i	−0.243037	−	0.454690i	0.730596	−	0.682810i	$-0.239242\pi$
$557$	−5.73588	−	10.7311i	−0.243037	−	0.454690i	−0.973633	+	0.228120i	$0.926742\pi$
$558$	5.15047	+	27.1535i	0.218037	+	1.14950i
$559$	10.2019	+	24.6296i	0.431496	+	1.04172i
$560$	−4.76570	+	9.31441i	−0.201388	+	0.393606i
$561$	1.07071	+	15.9714i	0.0452054	+	0.674313i
$562$	12.1369	−	5.80711i	0.511963	−	0.244958i
$563$	5.39635	−	17.7894i	0.227429	−	0.749733i	−0.766745	−	0.641951i	$-0.778125\pi$
$563$	5.39635	−	17.7894i	0.227429	−	0.749733i	0.994175	−	0.107782i	$-0.0343749\pi$
$564$	−19.4710	−	2.35640i	−0.819878	−	0.0992222i
$565$	5.33204	+	0.525160i	0.224321	+	0.0220936i
$566$	9.25710	−	12.5995i	0.389105	−	0.529598i
$567$	−34.5729	+	17.3062i	−1.45192	+	0.726794i
$568$	7.48760	+	5.39846i	0.314173	+	0.226514i
$569$	34.4086	+	6.84430i	1.44248	+	0.286928i	0.853448	−	0.521178i	$-0.174507\pi$
$569$	34.4086	+	6.84430i	1.44248	+	0.286928i	0.589037	+	0.808106i	$0.299507\pi$
$570$	−0.888065	−	2.01542i	−0.0371969	−	0.0844167i
$571$	1.23344	+	4.06609i	0.0516177	+	0.170161i	0.978959	−	0.204055i	$-0.0654121\pi$
$571$	1.23344	+	4.06609i	0.0516177	+	0.170161i	−0.927342	+	0.374215i	$0.877912\pi$
$572$	−5.59494	+	6.94361i	−0.233936	+	0.290327i
$573$	0.206972	−	0.893672i	0.00864640	−	0.0373337i
$574$	−52.4160	+	39.2402i	−2.18780	+	1.63785i
$575$		−	23.5277i		−	0.981171i
$576$	−6.14626	−	23.1996i	−0.256094	−	0.966652i
$577$		−	9.62571i		−	0.400724i	−0.979722	−	0.200362i	$-0.935788\pi$
$577$		−	9.62571i		−	0.400724i	0.979722	−	0.200362i	$-0.0642117\pi$
$578$	23.7732	+	31.7556i	0.988834	+	1.32086i
$579$	−8.97384	+	38.7475i	−0.372940	+	1.61029i
$580$	−0.375120	−	3.48746i	−0.0155760	−	0.144809i
$581$	13.8914	+	45.7938i	0.576313	+	1.89985i
$582$	37.2276	−	16.4038i	1.54314	−	0.679959i
$583$	12.1529	+	2.41735i	0.503320	+	0.100117i
$584$	4.33113	−	18.3347i	0.179223	−	0.758694i
$585$	−5.31274	−	2.60031i	−0.219655	−	0.107510i
$586$	34.8743	+	25.6228i	1.44065	+	1.05847i
$587$	−5.03642	−	0.496044i	−0.207875	−	0.0204739i	−0.00645651	−	0.999979i	$-0.502055\pi$
$587$	−5.03642	−	0.496044i	−0.207875	−	0.0204739i	−0.201419	+	0.979505i	$0.564555\pi$
$588$	24.4828	+	31.2246i	1.00966	+	1.28768i
$589$	−2.79235	+	9.20514i	−0.115057	+	0.379291i
$590$	1.26976	+	2.65379i	0.0522750	+	0.109255i
$591$	−1.86151	−	27.7675i	−0.0765724	−	1.14220i
$592$	0.159957	+	0.286756i	0.00657421	+	0.0117856i
$593$	−13.6108	−	32.8595i	−0.558930	−	1.34938i	−0.910614	−	0.413257i	$-0.864391\pi$
$593$	−13.6108	−	32.8595i	−0.558930	−	1.34938i	0.351684	−	0.936119i	$-0.385609\pi$
$594$	−6.09998	−	8.07277i	−0.250285	−	0.331230i
$595$	8.27601	+	15.4833i	0.339283	+	0.634754i
$596$	33.4772	−	14.2201i	1.37128	−	0.582476i
$597$	12.4465	+	5.61711i	0.509402	+	0.229893i
$598$	12.0548	+	19.9090i	0.492956	+	0.814139i
$599$	−31.0103	−	20.7204i	−1.26705	−	0.846614i	−0.273704	−	0.961814i	$-0.588249\pi$
$599$	−31.0103	−	20.7204i	−1.26705	−	0.846614i	−0.993342	+	0.115200i	$0.963249\pi$
$600$	−1.51516	+	22.6279i	−0.0618561	+	0.923782i
$601$	1.14679	+	1.71629i	0.0467785	+	0.0700090i	0.854122	−	0.520073i	$-0.174095\pi$
$601$	1.14679	+	1.71629i	0.0467785	+	0.0700090i	−0.807343	+	0.590082i	$0.799095\pi$
$602$	17.0613	+	47.0168i	0.695365	+	1.91626i
$603$	9.58280	+	20.9832i	0.390242	+	0.854503i
$604$	14.0948	+	16.8636i	0.573508	+	0.686169i
$605$	5.51671	−	0.543349i	0.224286	−	0.0220903i
$606$	16.1564	−	13.8746i	0.656309	−	0.563618i
$607$	17.4491	+	17.4491i	0.708235	+	0.708235i	0.966164	−	0.257929i	$-0.0830399\pi$
$607$	17.4491	+	17.4491i	0.708235	+	0.708235i	−0.257929	+	0.966164i	$0.583040\pi$
$608$	1.84736	−	8.14643i	0.0749204	−	0.330381i
$609$	−20.3041	−	6.85859i	−0.822762	−	0.277924i
$610$	−1.53018	−	0.907845i	−0.0619551	−	0.0367576i
$611$	−18.2453	+	1.79700i	−0.738124	+	0.0726989i
$612$	−37.8572	−	13.7341i	−1.53029	−	0.555167i
$613$	−8.91954	+	16.6873i	−0.360257	+	0.673993i	−0.995124	−	0.0986277i	$-0.968555\pi$
$613$	−8.91954	+	16.6873i	−0.360257	+	0.673993i	0.634867	+	0.772621i	$0.281055\pi$
$614$	11.4292	−	24.4484i	0.461247	−	0.986656i
$615$	5.66859	−	9.85213i	0.228579	−	0.397276i
$616$	−11.0674	+	12.5464i	−0.445920	+	0.505510i
$617$	6.41034	+	4.28325i	0.258070	+	0.172437i	0.677875	−	0.735178i	$-0.262901\pi$
$617$	6.41034	+	4.28325i	0.258070	+	0.172437i	−0.419804	+	0.907615i	$0.637901\pi$
$618$	−35.2236	+	7.82820i	−1.41690	+	0.314897i
$619$	−32.9830	+	27.0684i	−1.32570	+	1.08797i	−0.336454	+	0.941700i	$0.609228\pi$
$619$	−32.9830	+	27.0684i	−1.32570	+	1.08797i	−0.989244	+	0.146273i	$0.953272\pi$
$620$	−5.55887	+	5.65956i	−0.223250	+	0.227294i
$621$	−25.2372	+	7.77892i	−1.01273	+	0.312157i
$622$	−1.36475	−	25.4492i	−0.0547216	−	1.02042i
$623$	3.18456	+	7.68821i	0.127587	+	0.308022i
$624$	−10.3117	−	19.9240i	−0.412797	−	0.797597i
$625$	7.49149	−	18.0861i	0.299660	−	0.723443i
$626$	−12.1139	−	4.27320i	−0.484169	−	0.170791i
$627$	−0.578841	−	3.47380i	−0.0231167	−	0.138730i
$628$	−28.3588	−	5.37678i	−1.13164	−	0.214557i
$629$	0.548316	+	0.0540044i	0.0218628	+	0.00215330i
$630$	−9.74017	−	5.31817i	−0.388058	−	0.211881i
$631$	−15.8609	+	3.15494i	−0.631414	+	0.125596i	−0.500414	−	0.865786i	$-0.666819\pi$
$631$	−15.8609	+	3.15494i	−0.631414	+	0.125596i	−0.131000	+	0.991382i	$0.541819\pi$
$632$	−7.75150	−	8.32443i	−0.308338	−	0.331128i
$633$	−8.50565	−	31.5555i	−0.338069	−	1.25422i
$634$	−33.5316	+	30.6665i	−1.33171	+	1.21792i
$635$	2.68549	+	8.85286i	0.106570	+	0.351315i
$636$	−17.8917	+	25.5279i	−0.709452	+	1.01225i
$637$	28.6709	+	23.5296i	1.13598	+	0.932276i
$638$	0.798061	−	5.55163i	0.0315955	−	0.219791i
$639$	−5.93706	+	7.78523i	−0.234867	+	0.307979i
$640$	4.46365	−	5.24707i	0.176441	−	0.207409i
$641$		−	17.2085i		−	0.679696i	−0.940480	−	0.339848i	$-0.889624\pi$
$641$		−	17.2085i		−	0.679696i	0.940480	−	0.339848i	$-0.110376\pi$
$642$	−12.3201	+	4.03992i	−0.486236	+	0.159443i
$643$	−10.9486	+	13.3410i	−0.431772	+	0.526116i	−0.942760	−	0.333472i	$-0.891780\pi$
$643$	−10.9486	+	13.3410i	−0.431772	+	0.526116i	0.510988	+	0.859588i	$0.329280\pi$
$644$	20.9289	+	38.3239i	0.824715	+	1.51017i
$645$	−5.94483	−	6.32831i	−0.234077	−	0.249177i
$646$	−9.45949	−	10.3433i	−0.372178	−	0.406950i
$647$	−11.3793	−	2.26348i	−0.447366	−	0.0889867i	−0.0337342	−	0.999431i	$-0.510740\pi$
$647$	−11.3793	−	2.26348i	−0.447366	−	0.0889867i	−0.413632	+	0.910444i	$0.635740\pi$
$648$	24.7731	−	5.85619i	0.973178	−	0.230053i
$649$	0.917743	+	4.61380i	0.0360245	+	0.181108i
$650$	3.20462	+	20.9554i	0.125696	+	0.821940i
$651$	17.1411	+	45.3379i	0.671812	+	1.77693i
$652$	31.9678	+	6.06103i	1.25195	+	0.237368i
$653$	2.09983	−	6.92220i	0.0821725	−	0.270887i	−0.906220	−	0.422806i	$-0.861045\pi$
$653$	2.09983	−	6.92220i	0.0821725	−	0.270887i	0.988393	+	0.151919i	$0.0485453\pi$
$654$	46.6034	−	5.64372i	1.82234	−	0.220687i
$655$	−9.63135	−	3.98944i	−0.376328	−	0.155880i
$656$	39.5266	−	17.2101i	1.54326	−	0.671940i
$657$	19.3165	+	5.11423i	0.753609	+	0.199525i
$658$	−34.3475	+	1.84193i	−1.33900	+	0.0718060i
$659$	20.0680	+	37.5446i	0.781739	+	1.46253i	0.883857	+	0.467758i	$0.154938\pi$
$659$	20.0680	+	37.5446i	0.781739	+	1.46253i	−0.102118	+	0.994772i	$0.532562\pi$
$660$	0.904724	−	2.75978i	0.0352163	−	0.107424i
$661$	−15.3659	−	18.7234i	−0.597663	−	0.728255i	0.383046	−	0.923729i	$-0.374875\pi$
$661$	−15.3659	−	18.7234i	−0.597663	−	0.728255i	−0.980709	+	0.195475i	$0.937375\pi$
$662$	−11.6274	−	2.85711i	−0.451911	−	0.111045i
$663$	−37.3294	−	4.85797i	−1.44975	−	0.188668i
$664$	−1.96956	−	31.4463i	−0.0764336	−	1.22035i
$665$	−2.14589	−	3.21156i	−0.0832141	−	0.124539i
$666$	−0.308596	+	0.161435i	−0.0119578	+	0.00625547i
$667$	−12.9103	−	6.90068i	−0.499888	−	0.267195i
$668$	−0.832439	−	2.65806i	−0.0322080	−	0.102844i
$669$	−7.74112	−	12.4075i	−0.299289	−	0.479701i
$670$	−3.37849	+	5.69447i	−0.130522	+	0.219996i
$671$	−2.01173	−	2.01173i	−0.0776619	−	0.0776619i
$672$	−17.6606	−	38.2061i	−0.681271	−	1.47383i
$673$	6.79275	−	6.79275i	0.261841	−	0.261841i	−0.563960	−	0.825802i	$-0.690723\pi$
$673$	6.79275	−	6.79275i	0.261841	−	0.261841i	0.825802	+	0.563960i	$0.190723\pi$
$674$	−3.12753	−	12.2523i	−0.120468	−	0.471939i
$675$	−23.9488	−	2.25076i	−0.921788	−	0.0866319i
$676$	3.22537	+	3.85897i	0.124053	+	0.148422i
$677$	14.7513	−	27.5978i	0.566939	−	1.06067i	−0.421180	−	0.906977i	$-0.638384\pi$
$677$	14.7513	−	27.5978i	0.566939	−	1.06067i	0.988119	−	0.153691i	$-0.0491161\pi$
$678$	−14.8966	+	15.5775i	−0.572102	+	0.598251i
$679$	59.3219	−	39.6376i	2.27656	−	1.52115i
$680$	−2.95938	−	11.1741i	−0.113487	−	0.428505i
$681$	−17.0835	−	2.22321i	−0.654640	−	0.0851934i
$682$	−10.8509	+	6.57013i	−0.415501	+	0.251583i
$683$	−34.2348	+	28.0957i	−1.30996	+	1.07505i	−0.318051	+	0.948073i	$0.603028\pi$
$683$	−34.2348	+	28.0957i	−1.30996	+	1.07505i	−0.991905	+	0.126980i	$0.959472\pi$
$684$	8.58488	+	2.19067i	0.328251	+	0.0837622i
$685$	−2.81999	+	1.50732i	−0.107746	+	0.0575916i
$686$	20.1317	+	18.0824i	0.768632	+	0.690390i
$687$	−5.07586	+	5.80533i	−0.193656	+	0.221487i
$688$	−3.81561	−	32.7097i	−0.145469	−	1.24705i
$689$	−11.1513	+	26.9216i	−0.424830	+	1.02563i
$690$	−5.96557	−	4.67677i	−0.227105	−	0.178042i
$691$	0.147932	+	0.0448746i	0.00562759	+	0.00170711i	0.293097	−	0.956083i	$-0.405314\pi$
$691$	0.147932	+	0.0448746i	0.00562759	+	0.00170711i	−0.287470	+	0.957790i	$0.592814\pi$
$692$	−2.24954	−	10.8016i	−0.0855148	−	0.410616i
$693$	−12.9876	−	12.0918i	−0.493357	−	0.459329i
$694$	25.9727	−	35.3506i	0.985909	−	1.34189i
$695$	4.94351	−	0.983325i	0.187518	−	0.0372996i
$696$	11.9722	+	7.46820i	0.453804	+	0.283081i
$697$	14.1126	−	70.9490i	0.534554	−	2.68739i
$698$	39.0864	+	1.74440i	1.47944	+	0.0660264i
$699$	11.3829	+	12.1172i	0.430542	+	0.458315i
$700$	4.25354	+	39.5449i	0.160769	+	1.49466i
$701$	10.6078	+	8.70563i	0.400653	+	0.328807i	0.813047	−	0.582198i	$-0.197807\pi$
$701$	10.6078	+	8.70563i	0.400653	+	0.328807i	−0.412394	+	0.911006i	$0.635307\pi$
$702$	21.4185	−	10.3659i	0.808391	−	0.391237i
$703$	−0.121216			−0.00457177
$704$	8.99087	−	6.36419i	0.338856	−	0.239859i
$705$	5.35140	−	2.64893i	0.201545	−	0.0997646i
$706$	14.3742	+	19.2007i	0.540981	+	0.722628i
$707$	23.6938	−	28.8710i	0.891099	−	1.08581i
$708$	−11.5533	−	2.56668i	−0.434199	−	0.0964616i
$709$	31.2916	−	9.49220i	1.17518	−	0.356487i	0.358474	−	0.933540i	$-0.383297\pi$
$709$	31.2916	−	9.49220i	1.17518	−	0.356487i	0.816707	+	0.577053i	$0.195797\pi$
$710$	−2.80748	−	0.125296i	−0.105363	−	0.00470227i
$711$	9.04691	−	7.98172i	0.339286	−	0.299338i
$712$	−0.876840	−	5.40846i	−0.0328610	−	0.202691i
$713$	6.45904	+	32.4718i	0.241893	+	1.21608i
$714$	−69.5602	−	12.2279i	−2.60323	−	0.457616i
$715$	0.266098	−	2.70174i	0.00995152	−	0.101039i
$716$	7.16869	−	10.9400i	0.267907	−	0.408848i
$717$	−3.22606	−	19.3606i	−0.120480	−	0.723033i
$718$	−6.43584	−	13.4509i	−0.240184	−	0.501984i
$719$	−20.7103	−	8.57848i	−0.772363	−	0.319923i	−0.0385338	−	0.999257i	$-0.512269\pi$
$719$	−20.7103	−	8.57848i	−0.772363	−	0.319923i	−0.733829	+	0.679334i	$0.762269\pi$
$720$	5.43626	+	4.88211i	0.202598	+	0.181945i
$721$	−58.4642	+	24.2167i	−2.17732	+	0.901875i
$722$	−17.6960	−	15.8947i	−0.658577	−	0.591538i
$723$	−31.1080	+	43.5480i	−1.15692	+	1.61957i
$724$	31.1552	+	12.5785i	1.15788	+	0.467477i
$725$	−8.45876	−	10.3070i	−0.314151	−	0.382794i
$726$	−11.9721	+	18.8142i	−0.444328	+	0.698260i
$727$	10.1372	−	15.1714i	0.375968	−	0.562676i	−0.594442	−	0.804138i	$-0.702627\pi$
$727$	10.1372	−	15.1714i	0.375968	−	0.562676i	0.970410	+	0.241463i	$0.0776271\pi$
$728$	−23.8608	−	31.2833i	−0.884339	−	1.15944i
$729$	5.50384	+	26.4331i	0.203846	+	0.979003i
$730$	1.95646	+	5.39154i	0.0724119	+	0.199550i
$731$	−48.7336	−	26.0486i	−1.80248	−	0.963443i
$732$	6.67206	−	2.59122i	0.246606	−	0.0957741i
$733$	−3.84652	−	39.0544i	−0.142075	−	1.44251i	−0.756738	−	0.653718i	$-0.773208\pi$
$733$	−3.84652	−	39.0544i	−0.142075	−	1.44251i	0.614664	−	0.788789i	$-0.289292\pi$
$734$	−0.0651485	−	0.255223i	−0.00240468	−	0.00942043i
$735$	−11.4447	−	3.86594i	−0.422142	−	0.142597i
$736$	−7.60974	−	27.7250i	−0.280499	−	1.02196i
$737$	−7.48652	+	7.48652i	−0.275770	+	0.275770i
$738$	17.1220	+	42.3992i	0.630271	+	1.56074i
$739$	−5.29102	−	53.7206i	−0.194633	−	1.97614i	−0.216083	−	0.976375i	$-0.569328\pi$
$739$	−5.29102	−	53.7206i	−0.194633	−	1.97614i	0.0214501	−	0.999770i	$-0.493172\pi$
$740$	−0.0885812	−	0.0463303i	−0.00325631	−	0.00170313i
$741$	8.27791	+	0.258651i	0.304097	+	0.00950177i
$742$	−23.1529	+	49.5264i	−0.849968	+	1.81817i
$743$	22.8996	−	15.3011i	0.840107	−	0.561341i	−0.0594071	−	0.998234i	$-0.518921\pi$
$743$	22.8996	−	15.3011i	0.840107	−	0.561341i	0.899514	+	0.436893i	$0.143921\pi$
$744$	−4.12089	−	31.6460i	−0.151079	−	1.16020i
$745$	−6.15202	+	9.20715i	−0.225393	+	0.337324i
$746$	9.98608	+	2.45381i	0.365616	+	0.0898403i
$747$	33.3979	−	1.19292i	1.22196	−	0.0436467i
$748$	−0.165897	−	18.4828i	−0.00606581	−	0.675799i
$749$	−20.0537	+	10.7189i	−0.732744	+	0.391660i
$750$	−7.05133	−	12.5116i	−0.257478	−	0.456858i
$751$	41.9847	−	17.3906i	1.53204	−	0.634594i	0.552084	−	0.833788i	$-0.313833\pi$
$751$	41.9847	−	17.3906i	1.53204	−	0.634594i	0.979960	+	0.199195i	$0.0638326\pi$
$752$	22.2878	+	4.01884i	0.812753	+	0.146552i
$753$	0.977168	+	14.5761i	0.0356100	+	0.531182i
$754$	12.4387	+	4.38778i	0.452992	+	0.159794i
$755$	−6.40306	−	1.94235i	−0.233031	−	0.0706893i
$756$	41.0119	−	17.6373i	1.49159	−	0.641462i
$757$	−0.0222091	+	0.225492i	−0.000807202	+	0.00819566i	−0.995580	−	0.0939185i	$-0.970061\pi$
$757$	−0.0222091	+	0.225492i	−0.000807202	+	0.00819566i	0.994773	+	0.102114i	$0.0325607\pi$
$758$	2.59981	+	17.0005i	0.0944294	+	0.617486i
$759$	−7.39310	−	9.60523i	−0.268353	−	0.348648i
$760$	0.888909	+	2.38271i	0.0322441	+	0.0864298i
$761$	6.22899	−	31.3152i	0.225801	−	1.13518i	−0.686964	−	0.726691i	$-0.741057\pi$
$761$	6.22899	−	31.3152i	0.225801	−	1.13518i	0.912765	−	0.408485i	$-0.133943\pi$
$762$	−34.6930	−	13.4705i	−1.25679	−	0.487985i
$763$	78.7836	−	23.8988i	2.85216	−	0.865193i
$764$	−0.298370	+	1.01635i	−0.0107947	+	0.0367701i
$765$	11.9319	−	2.81962i	0.431397	−	0.101943i
$766$	−5.15624	+	35.8689i	−0.186303	+	1.29600i
$767$	−11.0628			−0.399456
$768$	5.53327	+	27.1548i	0.199665	+	0.979864i
$769$	−18.5929			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$769$	−18.5929			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$770$	0.724746	−	5.04163i	0.0261180	−	0.181688i
$771$	−2.87527	+	12.4149i	−0.103550	+	0.447113i
$772$	12.9366	−	44.0664i	0.465600	−	1.58598i
$773$	36.3165	−	11.0165i	1.30621	−	0.396235i	0.440940	−	0.897537i	$-0.354645\pi$
$773$	36.3165	−	11.0165i	1.30621	−	0.396235i	0.865273	+	0.501302i	$0.167145\pi$
$774$	34.7901	−	3.11428i	1.25050	−	0.111940i
$775$	−5.88316	+	29.5767i	−0.211329	+	1.06242i
$776$	−44.0119	+	16.4194i	−1.57993	+	0.589422i
$777$	−0.484014	+	0.372544i	−0.0173639	+	0.0133649i
$778$	2.40127	+	15.7022i	0.0860899	+	0.562953i
$779$	−1.55994	+	15.8384i	−0.0558908	+	0.567469i
$780$	5.95038	+	3.35292i	0.213058	+	0.120054i
$781$	−4.30020	−	1.30445i	−0.153873	−	0.0466769i
$782$	−45.4949	−	16.0484i	−1.62689	−	0.573889i
$783$	−8.25925	+	12.4812i	−0.295161	+	0.446041i
$784$	−26.1342	−	37.6322i	−0.933363	−	1.34401i
$785$	8.11863	−	3.36285i	0.289766	−	0.120025i
$786$	36.5351	−	20.5907i	1.30317	−	0.734444i
$787$	−14.9755	+	8.00455i	−0.533818	+	0.285331i	−0.716199	−	0.697896i	$-0.754120\pi$
$787$	−14.9755	+	8.00455i	−0.533818	+	0.285331i	0.182381	+	0.983228i	$0.441620\pi$
$788$	0.288426	+	32.1339i	0.0102747	+	1.14472i
$789$	−0.695740	−	0.313988i	−0.0247690	−	0.0111783i
$790$	3.36292	+	0.826346i	0.119647	+	0.0294001i
$791$	−21.0008	+	31.4299i	−0.746703	+	1.11752i
$792$	6.49181	+	9.71402i	0.230677	+	0.345173i
$793$	5.56304	−	3.71710i	0.197549	−	0.131998i
$794$	−4.21978	+	9.02657i	−0.149754	+	0.320341i
$795$	0.296399	−	9.48601i	0.0105122	−	0.336434i
$796$	−13.9721	−	7.30778i	−0.495228	−	0.259017i
$797$	2.17146	+	22.0472i	0.0769171	+	0.780952i	0.953839	+	0.300319i	$0.0970931\pi$
$797$	2.17146	+	22.0472i	0.0769171	+	0.780952i	−0.876922	+	0.480633i	$0.840407\pi$
$798$	15.4937	+	1.17723i	0.548470	+	0.0416734i
$799$	26.8712	−	26.8712i	0.950634	−	0.950634i
$800$	3.26027	−	25.9833i	0.115268	−	0.918647i
$801$	5.75944	−	0.775702i	0.203500	−	0.0274081i
$802$	−1.32670	−	5.19740i	−0.0468473	−	0.183526i
$803$	0.898940	+	9.12709i	0.0317229	+	0.322088i
$804$	−9.64305	−	24.8297i	−0.340084	−	0.875675i
$805$	−11.7243	−	6.26675i	−0.413226	−	0.220874i
$806$	−10.1758	−	28.0420i	−0.358426	−	0.987736i
$807$	9.62837	−	16.7343i	0.338935	−	0.589076i
$808$	−19.5526	+	14.9134i	−0.687858	+	0.524650i
$809$	6.78232	−	10.1505i	0.238454	−	0.356871i	−0.692871	−	0.721062i	$-0.743654\pi$
$809$	6.78232	−	10.1505i	0.238454	−	0.356871i	0.931324	+	0.364191i	$0.118654\pi$
$810$	−5.33117	+	5.62494i	−0.187318	+	0.197640i
$811$	−12.4317	−	15.1481i	−0.436536	−	0.531921i	0.507549	−	0.861623i	$-0.330552\pi$
$811$	−12.4317	−	15.1481i	−0.436536	−	0.531921i	−0.944085	+	0.329702i	$0.893052\pi$
$812$	22.9469	+	9.26452i	0.805280	+	0.325121i
$813$	−14.0301	−	10.0222i	−0.492057	−	0.351495i
$814$	−0.118919	−	0.106814i	−0.00416813	−	0.00374384i
$815$	−9.15180	+	3.79080i	−0.320574	+	0.132786i
$816$	42.7216	+	18.3645i	1.49556	+	0.642886i
$817$	11.2318	+	4.65235i	0.392950	+	0.162765i
$818$	−5.53223	−	11.5624i	−0.193430	−	0.404269i
$819$	33.8484	−	24.4083i	1.18276	−	0.852896i
$820$	−7.19356	+	10.9780i	−0.251210	+	0.383367i
$821$	3.34853	−	33.9982i	0.116865	−	1.18655i	−0.740580	−	0.671968i	$-0.765449\pi$
$821$	3.34853	−	33.9982i	0.116865	−	1.18655i	0.857444	−	0.514577i	$-0.172051\pi$
$822$	2.22707	−	12.6691i	0.0776780	−	0.441884i
$823$	−10.2569	−	51.5647i	−0.357532	−	1.79743i	−0.571511	−	0.820595i	$-0.693642\pi$
$823$	−10.2569	−	51.5647i	−0.357532	−	1.79743i	0.213979	−	0.976838i	$-0.431358\pi$
$824$	41.1280	−	6.66784i	1.43276	−	0.232285i
$825$	−2.87332	−	10.6598i	−0.100036	−	0.371128i
$826$	−20.7351	−	0.925392i	−0.721467	−	0.0321985i
$827$	7.19771	−	2.18340i	0.250289	−	0.0759244i	−0.162647	−	0.986684i	$-0.552003\pi$
$827$	7.19771	−	2.18340i	0.250289	−	0.0759244i	0.412936	+	0.910760i	$0.364503\pi$
$828$	29.6128	−	7.27904i	1.02912	−	0.252964i
$829$	−16.7769	+	20.4427i	−0.582685	+	0.710003i	−0.978015	−	0.208536i	$-0.933130\pi$
$829$	−16.7769	+	20.4427i	−0.582685	+	0.710003i	0.395330	+	0.918539i	$0.370630\pi$
$830$	5.74874	+	7.67901i	0.199542	+	0.266542i
$831$	10.1575	+	20.5203i	0.352361	+	0.711842i
$832$	10.5541	+	23.6574i	0.365898	+	0.820171i
$833$	−76.8796			−2.66372
$834$	−9.15653	+	18.0915i	−0.317065	+	0.626457i
$835$	0.655507	+	0.537961i	0.0226848	+	0.0186169i
$836$	0.434893	+	4.04318i	0.0150411	+	0.139836i
$837$	33.6709	−	3.46825i	1.16384	−	0.119880i
$838$	−41.3454	−	1.84521i	−1.42825	−	0.0637418i
$839$	5.75838	−	28.9493i	0.198801	−	0.999441i	−0.744530	−	0.667589i	$-0.767326\pi$
$839$	5.75838	−	28.9493i	0.198801	−	0.999441i	0.943331	−	0.331852i	$-0.107674\pi$
$840$	10.8723	+	6.78213i	0.375131	+	0.234006i
$841$	20.3061	−	4.03913i	0.700209	−	0.139280i
$842$	−28.6514	+	38.9965i	−0.987393	+	1.34391i
$843$	−5.82750	−	15.4136i	−0.200710	−	0.530873i
$844$	7.69414	+	36.9449i	0.264843	+	1.27170i
$845$	−1.46524	−	0.444476i	−0.0504058	−	0.0152904i
$846$	−4.89568	+	23.5169i	−0.168317	+	0.808526i
$847$	−14.9666	+	36.1326i	−0.514259	+	1.24153i
$848$	22.3325	−	28.2307i	0.766901	−	0.969448i
$849$	−14.4154	−	12.6040i	−0.494734	−	0.432568i
$850$	−32.6904	−	29.3627i	−1.12127	−	1.00713i
$851$	−0.367941	+	0.196669i	−0.0126129	+	0.00674171i
$852$	7.36479	−	8.57737i	0.252314	−	0.293856i
$853$	−0.660716	+	0.542235i	−0.0226225	+	0.0185658i	−0.645637	−	0.763645i	$-0.723408\pi$
$853$	−0.660716	+	0.542235i	−0.0226225	+	0.0185658i	0.623014	+	0.782211i	$0.285908\pi$
$854$	10.7377	−	6.50164i	0.367438	−	0.222481i
$855$	−2.55164	+	0.874649i	−0.0872642	+	0.0299124i
$856$	14.4724	−	3.83293i	0.494656	−	0.131007i
$857$	−42.5087	+	28.4034i	−1.45207	+	0.970241i	−0.455264	+	0.890356i	$0.650455\pi$
$857$	−42.5087	+	28.4034i	−1.45207	+	0.970241i	−0.996804	+	0.0798848i	$0.974545\pi$
$858$	7.89313	+	7.54812i	0.269467	+	0.257689i
$859$	−16.0564	+	30.0394i	−0.547838	+	1.02493i	0.443830	+	0.896111i	$0.353619\pi$
$859$	−16.0564	+	30.0394i	−0.547838	+	1.02493i	−0.991668	+	0.128822i	$0.958881\pi$
$860$	6.42965	+	7.69270i	0.219249	+	0.262319i
$861$	42.4485	+	68.0366i	1.44664	+	2.31868i
$862$	−9.43669	−	36.9687i	−0.321415	−	1.25916i
$863$	5.56313	−	5.56313i	0.189371	−	0.189371i	−0.606053	−	0.795424i	$-0.707248\pi$
$863$	5.56313	−	5.56313i	0.189371	−	0.189371i	0.795424	+	0.606053i	$0.207248\pi$
$864$	−28.9492	+	5.09364i	−0.984871	+	0.173289i
$865$	2.37522	+	2.37522i	0.0807598	+	0.0807598i
$866$	−7.97530	+	13.4424i	−0.271012	+	0.456792i
$867$	41.2191	−	25.7169i	1.39987	−	0.873391i
$868$	−16.7268	−	53.4103i	−0.567744	−	1.81287i
$869$	4.88350	+	2.61028i	0.165661	+	0.0885478i
$870$	−4.29482	+	0.0959597i	−0.145608	+	0.00325334i
$871$	−13.8330	−	20.7025i	−0.468712	−	0.701477i
$872$	−54.1001	+	3.38842i	−1.83206	+	0.114746i
$873$	−16.1560	−	47.1323i	−0.546797	−	1.59519i
$874$	10.3070	+	2.53267i	0.348640	+	0.0856689i
$875$	−15.9786	−	19.4700i	−0.540175	−	0.658206i
$876$	−21.9252	−	7.18763i	−0.740785	−	0.242848i
$877$	14.5236	+	27.1718i	0.490427	+	0.917525i	0.998422	+	0.0561644i	$0.0178871\pi$
$877$	14.5236	+	27.1718i	0.490427	+	0.917525i	−0.507994	+	0.861360i	$0.669613\pi$
$878$	−42.0902	+	2.25715i	−1.42048	+	0.0761750i
$879$	34.8867	−	39.9004i	1.17670	−	1.34581i
$880$	−1.22754	+	3.12085i	−0.0413804	+	0.105204i
$881$	29.3387	+	12.1525i	0.988448	+	0.409428i	0.817548	−	0.575860i	$-0.195333\pi$
$881$	29.3387	+	12.1525i	0.988448	+	0.409428i	0.170899	+	0.985288i	$0.445333\pi$
$882$	40.6447	−	26.6380i	1.36858	−	0.896948i
$883$	−2.46093	+	8.11260i	−0.0828169	+	0.273011i	−0.988563	−	0.150811i	$-0.951812\pi$
$883$	−2.46093	+	8.11260i	−0.0828169	+	0.273011i	0.905746	+	0.423821i	$0.139312\pi$
$884$	42.7069	+	8.09715i	1.43639	+	0.272337i
$885$	3.37027	−	1.27421i	0.113290	−	0.0428322i
$886$	3.97999	+	26.0257i	0.133711	+	0.874350i
$887$	10.5204	+	52.8899i	0.353242	+	1.77587i	0.593170	+	0.805077i	$0.297876\pi$
$887$	10.5204	+	52.8899i	0.353242	+	1.77587i	−0.239928	+	0.970791i	$0.577124\pi$
$888$	0.366536	−	0.165453i	0.0123001	−	0.00555223i
$889$	−64.0147	−	12.7333i	−2.14699	−	0.427062i
$890$	1.12575	+	1.23093i	0.0377353	+	0.0412608i
$891$	−10.4844	+	6.60655i	−0.351241	+	0.221328i
$892$	8.09368	+	14.8207i	0.270997	+	0.496234i
$893$	−5.30390	+	6.46282i	−0.177488	+	0.216270i
$894$	−13.8802	−	42.3289i	−0.464222	−	1.41569i
$895$			3.98201i			0.133104i
$896$	17.8027	+	45.2239i	0.594746	+	1.51082i
$897$	25.5464	−	12.6454i	0.852971	−	0.422219i
$898$	4.47353	−	31.1197i	0.149284	−	1.03848i
$899$	14.5040	+	11.9031i	0.483735	+	0.396991i
$900$	27.4566	+	4.19660i	0.915221	+	0.139887i
$901$	−17.5334	−	57.7998i	−0.584121	−	1.92559i
$902$	−15.4869	+	14.1637i	−0.515659	+	0.471598i
$903$	59.1466	−	15.9427i	1.96828	−	0.530541i
$904$	18.2143	−	16.9607i	0.605798	−	0.564104i
$905$	−10.0324	+	1.99557i	−0.333489	+	0.0663351i
$906$	22.0416	−	15.4509i	0.732284	−	0.513322i
$907$	−40.9801	−	4.03618i	−1.36072	−	0.134019i	−0.608826	−	0.793303i	$-0.708359\pi$
$907$	−40.9801	−	4.03618i	−1.36072	−	0.134019i	−0.751894	+	0.659284i	$0.770859\pi$
$908$	19.5445	+	3.70559i	0.648605	+	0.122974i
$909$	−15.2556	−	21.1558i	−0.505996	−	0.701694i
$910$	11.2960	+	3.98470i	0.374460	+	0.132091i
$911$	−0.734792	+	1.77394i	−0.0243447	+	0.0587734i	−0.935584	−	0.353103i	$-0.885126\pi$
$911$	−0.734792	+	1.77394i	−0.0243447	+	0.0587734i	0.911240	+	0.411876i	$0.135126\pi$
$912$	−9.74977	−	3.09958i	−0.322847	−	0.102637i
$913$	5.86981	+	14.1710i	0.194262	+	0.468991i
$914$	−0.399854	−	7.45628i	−0.0132260	−	0.246632i
$915$	−1.26663	+	1.77316i	−0.0418736	+	0.0586187i
$916$	6.23959	−	6.35262i	0.206162	−	0.209896i
$917$	56.8545	−	46.6593i	1.87750	−	1.54082i
$918$	−20.6879	+	44.7739i	−0.682801	+	1.47776i
$919$	9.13920	+	6.10662i	0.301474	+	0.201439i	0.697101	−	0.716972i	$-0.254473\pi$
$919$	9.13920	+	6.10662i	0.301474	+	0.201439i	−0.395627	+	0.918411i	$0.629473\pi$
$920$	6.56404	+	5.79026i	0.216410	+	0.190899i
$921$	−28.6496	−	16.4840i	−0.944038	−	0.543168i
$922$	−0.285394	+	0.610488i	−0.00939894	+	0.0201053i
$923$	4.98163	−	9.31997i	0.163972	−	0.306771i
$924$	14.1627	+	14.8077i	0.465919	+	0.487138i
$925$	−0.378177	+	0.0372472i	−0.0124344	+	0.00122468i
$926$	32.4387	+	19.2457i	1.06600	+	0.632452i
$927$	5.89874	+	43.7970i	0.193740	+	1.43848i
$928$	−13.3015	−	9.40991i	−0.436643	−	0.308895i
$929$	1.76745	+	1.76745i	0.0579881	+	0.0579881i	0.735506	−	0.677518i	$-0.236944\pi$
$929$	1.76745	+	1.76745i	0.0579881	+	0.0579881i	−0.677518	+	0.735506i	$0.736944\pi$
$930$	6.32989	+	7.37089i	0.207565	+	0.241701i
$931$	16.8325	−	1.65786i	0.551664	−	0.0543342i
$932$	−12.3112	−	14.7297i	−0.403268	−	0.482487i
$933$	−31.1984	−	0.974822i	−1.02139	−	0.0319142i
$934$	1.17322	+	3.23313i	0.0383891	+	0.105791i
$935$	3.12633	+	4.67889i	0.102242	+	0.153016i
$936$	−25.3839	+	10.5167i	−0.829698	+	0.343749i
$937$	11.3205	+	7.56409i	0.369823	+	0.247108i	0.726569	−	0.687094i	$-0.241114\pi$
$937$	11.3205	+	7.56409i	0.369823	+	0.247108i	−0.356746	+	0.934201i	$0.616114\pi$
$938$	−24.1954	−	39.9599i	−0.790009	−	1.30474i
$939$	−6.47155	+	14.3398i	−0.211191	+	0.467961i
$940$	−6.34608	+	2.69562i	−0.206986	+	0.0879213i
$941$	7.35184	+	13.7543i	0.239663	+	0.448378i	0.972782	−	0.231722i	$-0.0744361\pi$
$941$	7.35184	+	13.7543i	0.239663	+	0.448378i	−0.733119	+	0.680101i	$0.761936\pi$
$942$	−9.50367	+	34.0497i	−0.309646	+	1.10940i
$943$	20.9620	+	50.6068i	0.682618	+	1.64799i
$944$	13.1465	+	3.73160i	0.427881	+	0.121453i
$945$	−7.50051	+	11.3346i	−0.243992	+	0.368715i
$946$	6.91935	+	14.4615i	0.224968	+	0.470183i
$947$	−14.9699	+	49.3492i	−0.486457	+	1.60363i	0.279098	+	0.960263i	$0.409965\pi$
$947$	−14.9699	+	49.3492i	−0.486457	+	1.60363i	−0.765555	+	0.643371i	$0.777535\pi$
$948$	−10.9629	+	8.59585i	−0.356057	+	0.279180i
$949$	−21.4642	−	2.11403i	−0.696756	−	0.0686245i
$950$	7.79064	+	5.72392i	0.252762	+	0.185709i
$951$	33.9449	+	44.1017i	1.10074	+	1.43009i
$952$	79.3684	+	18.7489i	2.57234	+	0.607655i
$953$	56.7368	+	11.2857i	1.83789	+	0.365578i	0.987122	−	0.159969i	$-0.0511393\pi$
$953$	56.7368	+	11.2857i	1.83789	+	0.365578i	0.850765	+	0.525547i	$0.176139\pi$
$954$	29.2966	+	24.4825i	0.948511	+	0.792649i
$955$	−0.0936111	−	0.308595i	−0.00302919	−	0.00998589i
$956$	2.42380	+	22.5339i	0.0783912	+	0.728798i
$957$	−6.69209	−	1.54987i	−0.216325	−	0.0501003i
$958$	8.10716	+	10.8293i	0.261930	+	0.349880i
$959$		−	22.5593i		−	0.728477i
$960$	−5.94013	−	5.99155i	−0.191717	−	0.193376i
$961$		−	11.4355i		−	0.368886i
$962$	0.300927	−	0.225283i	0.00970229	−	0.00726342i
$963$	3.65190	+	15.4539i	0.117681	+	0.497995i
$964$	38.7731	−	48.1195i	1.24880	−	1.54982i
$965$	4.05876	+	13.3799i	0.130656	+	0.430716i
$966$	48.9396	−	21.5645i	1.57460	−	0.693825i
$967$	−31.0475	−	6.17573i	−0.998421	−	0.198598i	−0.331282	−	0.943532i	$-0.607481\pi$
$967$	−31.0475	−	6.17573i	−0.998421	−	0.198598i	−0.667139	+	0.744934i	$0.732481\pi$
$968$	15.0596	−	20.8874i	0.484033	−	0.671347i
$969$	−13.6037	+	10.4707i	−0.437015	+	0.336368i
$970$	8.46765	−	11.5250i	0.271880	−	0.370047i
$971$	−24.9855	−	2.46086i	−0.801824	−	0.0789728i	−0.311200	−	0.950344i	$-0.600731\pi$
$971$	−24.9855	−	2.46086i	−0.801824	−	0.0789728i	−0.490624	+	0.871372i	$0.663231\pi$
$972$	−4.57642	−	30.8392i	−0.146789	−	0.989168i
$973$	−10.3227	+	34.0294i	−0.330930	+	1.09093i
$974$	−24.2365	+	11.5964i	−0.776587	+	0.371572i
$975$	25.9053	−	1.73667i	0.829633	−	0.0556179i
$976$	−7.86463	+	2.54074i	−0.251741	+	0.0813271i
$977$	5.66266	+	13.6709i	0.181165	+	0.437370i	0.988207	−	0.153123i	$-0.0489332\pi$
$977$	5.66266	+	13.6709i	0.181165	+	0.437370i	−0.807042	+	0.590493i	$0.798933\pi$
$978$	10.7131	−	38.3828i	0.342567	−	1.22735i
$979$	1.25736	+	2.35235i	0.0401853	+	0.0751814i
$980$	12.9343	+	5.22207i	0.413173	+	0.166813i
$981$	−2.05230	−	57.4577i	−0.0655249	−	1.83448i
$982$	−39.1626	+	23.7127i	−1.24973	+	0.756703i
$983$	31.0237	+	20.7294i	0.989503	+	0.661164i	0.941264	−	0.337671i	$-0.109639\pi$
$983$	31.0237	+	20.7294i	0.989503	+	0.661164i	0.0482385	+	0.998836i	$0.484639\pi$
$984$	−16.9014	−	50.0215i	−0.538797	−	1.59463i
$985$	−5.43538	−	8.13462i	−0.173186	−	0.259190i
$986$	−25.7002	+	9.32601i	−0.818463	+	0.297001i
$987$	−1.31566	+	42.1068i	−0.0418780	+	1.34027i
$988$	−9.52515	−	0.851897i	−0.303035	−	0.0271025i
$989$	41.6412	−	4.10130i	1.32411	−	0.130414i
$990$	−3.27402	−	1.39039i	−0.104055	−	0.0441896i
$991$	−10.5245	−	10.5245i	−0.334323	−	0.334323i	0.519902	−	0.854226i	$-0.325968\pi$
$991$	−10.5245	−	10.5245i	−0.334323	−	0.334323i	−0.854226	+	0.519902i	$0.825968\pi$
$992$	2.63350	+	36.7559i	0.0836139	+	1.16700i
$993$	−4.69297	+	13.8930i	−0.148927	+	0.440880i
$994$	10.1167	−	17.0517i	0.320882	−	0.540849i
$995$	4.77733	−	0.470526i	0.151451	−	0.0149167i
$996$	−38.5796	−	0.858932i	−1.22244	−	0.0272163i
$997$	−14.7138	+	27.5276i	−0.465991	+	0.871808i	0.533668	+	0.845694i	$0.320813\pi$
$997$	−14.7138	+	27.5276i	−0.465991	+	0.871808i	−0.999659	+	0.0261137i	$0.991687\pi$
$998$	19.8332	+	9.27171i	0.627809	+	0.293491i
$999$	0.164990	+	0.393341i	0.00522004	+	0.0124448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.w.a.107.29	✓	992
3.2	odd	2	inner	384.2.w.a.107.34	yes	992
128.67	odd	32	inner	384.2.w.a.323.34	yes	992
384.323	even	32	inner	384.2.w.a.323.29	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.w.a.107.29	✓	992	1.1	even	1	trivial
384.2.w.a.107.34	yes	992	3.2	odd	2	inner
384.2.w.a.323.29	yes	992	384.323	even	32	inner
384.2.w.a.323.34	yes	992	128.67	odd	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.w (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.201228 + 1.39982i) q^{2} +(1.68739 + 0.390795i) q^{3} +(-1.91901 - 0.563368i) q^{4} +(0.582673 - 0.176752i) q^{5} +(-0.886595 + 2.28341i) q^{6} +(-0.838076 + 4.21329i) q^{7} +(1.17478 - 2.57292i) q^{8} +(2.69456 + 1.31885i) q^{9} +O(q^{10})\)	\(q+(-0.201228 + 1.39982i) q^{2} +(1.68739 + 0.390795i) q^{3} +(-1.91901 - 0.563368i) q^{4} +(0.582673 - 0.176752i) q^{5} +(-0.886595 + 2.28341i) q^{6} +(-0.838076 + 4.21329i) q^{7} +(1.17478 - 2.57292i) q^{8} +(2.69456 + 1.31885i) q^{9} +(0.130171 + 0.851207i) q^{10} +(-0.134962 + 1.37029i) q^{11} +(-3.01796 - 1.70056i) q^{12} +(-3.09867 - 0.939972i) q^{13} +(-5.72922 - 2.02099i) q^{14} +(1.05227 - 0.0705433i) q^{15} +(3.36523 + 2.16222i) q^{16} +(6.20100 - 2.56854i) q^{17} +(-2.38837 + 3.50652i) q^{18} +(-1.30230 + 0.696094i) q^{19} +(-1.21773 + 0.0109301i) q^{20} +(-3.06069 + 6.78194i) q^{21} +(-1.89101 - 0.464664i) q^{22} +(-2.82362 + 4.22585i) q^{23} +(2.98779 - 3.88241i) q^{24} +(-3.84908 + 2.57187i) q^{25} +(1.93934 - 4.14845i) q^{26} +(4.03137 + 3.27843i) q^{27} +(3.98191 - 7.61322i) q^{28} +(0.282319 + 2.86643i) q^{29} +(-0.112998 + 1.48719i) q^{30} +(4.60627 - 4.60627i) q^{31} +(-3.70391 + 4.27563i) q^{32} +(-0.763237 + 2.25947i) q^{33} +(2.34769 + 9.19717i) q^{34} +(0.256383 + 2.60310i) q^{35} +(-4.42790 - 4.04891i) q^{36} +(0.0723953 + 0.0386961i) q^{37} +(-0.712349 - 1.96306i) q^{38} +(-4.86133 - 2.79704i) q^{39} +(0.229742 - 1.70681i) q^{40} +(5.98777 - 8.96133i) q^{41} +(-8.87763 - 5.64915i) q^{42} +(-5.22289 - 6.36410i) q^{43} +(1.03097 - 2.55358i) q^{44} +(1.80316 + 0.292188i) q^{45} +(-5.34726 - 4.80294i) q^{46} +(5.23083 - 2.16668i) q^{47} +(4.83347 + 4.96363i) q^{48} +(-10.5823 - 4.38333i) q^{49} +(-2.82563 - 5.90557i) q^{50} +(11.4673 - 1.91080i) q^{51} +(5.41685 + 3.54951i) q^{52} +(0.882057 - 8.95568i) q^{53} +(-5.40045 + 4.98349i) q^{54} +(0.163563 + 0.822287i) q^{55} +(9.85590 + 7.10597i) q^{56} +(-2.46952 + 0.665648i) q^{57} +(-4.06931 - 0.181610i) q^{58} +(3.26934 - 0.991745i) q^{59} +(-2.05906 - 0.457442i) q^{60} +(-1.31079 + 1.59720i) q^{61} +(5.52106 + 7.37488i) q^{62} +(-7.81493 + 10.2477i) q^{63} +(-5.23980 - 6.04520i) q^{64} -1.97165 q^{65} +(-3.00928 - 1.52307i) q^{66} +(5.94389 + 4.87803i) q^{67} +(-13.3468 + 1.43562i) q^{68} +(-6.41599 + 6.02719i) q^{69} +(-3.69548 - 0.164926i) q^{70} +(-0.636693 + 3.20087i) q^{71} +(6.55878 - 5.38352i) q^{72} +(6.53271 - 1.29944i) q^{73} +(-0.0687357 + 0.0935539i) q^{74} +(-7.49997 + 2.83555i) q^{75} +(2.89129 - 0.602140i) q^{76} +(-5.66033 - 1.71704i) q^{77} +(4.89360 - 6.24216i) q^{78} +(1.53897 - 3.71541i) q^{79} +(2.34301 + 0.665058i) q^{80} +(5.52129 + 7.10742i) q^{81} +(11.3394 + 10.1851i) q^{82} +(9.82436 - 5.25123i) q^{83} +(9.69425 - 11.2903i) q^{84} +(3.15916 - 2.59266i) q^{85} +(9.95962 - 6.03048i) q^{86} +(-0.643806 + 4.94711i) q^{87} +(3.36710 + 1.95703i) q^{88} +(1.61068 - 1.07622i) q^{89} +(-0.771858 + 2.46530i) q^{90} +(6.55730 - 12.2678i) q^{91} +(7.79929 - 6.51873i) q^{92} +(9.57268 - 5.97246i) q^{93} +(1.98038 + 7.75824i) q^{94} +(-0.635779 + 0.635779i) q^{95} +(-7.92083 + 5.76718i) q^{96} +(-11.7437 - 11.7437i) q^{97} +(8.26535 - 13.9313i) q^{98} +(-2.17087 + 3.51434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9}+O(q^{10}) \) 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9	\( 992 q - 16 q^{3} - 32 q^{4} - 16 q^{6} - 32 q^{7} - 16 q^{9} - 32 q^{10} - 16 q^{12} - 32 q^{13} - 16 q^{15} - 32 q^{16} - 16 q^{18} - 32 q^{19} - 16 q^{21} - 32 q^{22} - 16 q^{24} - 32 q^{25} - 16 q^{27} - 32 q^{28} - 16 q^{30} - 32 q^{31} - 16 q^{33} - 32 q^{34} - 16 q^{36} - 32 q^{37} - 16 q^{39} - 32 q^{40} - 16 q^{42} - 32 q^{43} - 16 q^{45} - 32 q^{46} - 16 q^{48} - 32 q^{49} - 16 q^{51} - 128 q^{52} - 16 q^{54} - 32 q^{55} - 16 q^{57} - 320 q^{58} - 16 q^{60} - 32 q^{61} - 32 q^{63} - 224 q^{64} - 16 q^{66} - 32 q^{67} - 16 q^{69} - 224 q^{70} - 16 q^{72} - 32 q^{73} - 16 q^{75} - 256 q^{76} - 16 q^{78} - 32 q^{79} - 16 q^{81} - 32 q^{82} - 16 q^{84} - 32 q^{85} - 16 q^{87} - 32 q^{88} - 16 q^{90} - 32 q^{91} - 16 q^{93} - 32 q^{94} - 16 q^{96} - 32 q^{97} - 16 q^{99}+O(q^{100}) \) 992 * q - 16 * q^3 - 32 * q^4 - 16 * q^6 - 32 * q^7 - 16 * q^9 - 32 * q^10 - 16 * q^12 - 32 * q^13 - 16 * q^15 - 32 * q^16 - 16 * q^18 - 32 * q^19 - 16 * q^21 - 32 * q^22 - 16 * q^24 - 32 * q^25 - 16 * q^27 - 32 * q^28 - 16 * q^30 - 32 * q^31 - 16 * q^33 - 32 * q^34 - 16 * q^36 - 32 * q^37 - 16 * q^39 - 32 * q^40 - 16 * q^42 - 32 * q^43 - 16 * q^45 - 32 * q^46 - 16 * q^48 - 32 * q^49 - 16 * q^51 - 128 * q^52 - 16 * q^54 - 32 * q^55 - 16 * q^57 - 320 * q^58 - 16 * q^60 - 32 * q^61 - 32 * q^63 - 224 * q^64 - 16 * q^66 - 32 * q^67 - 16 * q^69 - 224 * q^70 - 16 * q^72 - 32 * q^73 - 16 * q^75 - 256 * q^76 - 16 * q^78 - 32 * q^79 - 16 * q^81 - 32 * q^82 - 16 * q^84 - 32 * q^85 - 16 * q^87 - 32 * q^88 - 16 * q^90 - 32 * q^91 - 16 * q^93 - 32 * q^94 - 16 * q^96 - 32 * q^97 - 16 * q^99

Introduction

L-functions

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