LMFDB - Embedded newform 192.2.r.a.37.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.15
Character	$\chi$	$=$	192.37
Dual form			192.2.r.a.109.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40172 - 0.187577i) q^{2} +(-0.555570 + 0.831470i) q^{3} +(1.92963 - 0.525860i) q^{4} +(-0.451487 + 2.26978i) q^{5} +(-0.622789 + 1.26970i) q^{6} +(-1.32215 + 3.19196i) q^{7} +(2.60616 - 1.09906i) q^{8} +(-0.382683 - 0.923880i) q^{9} +O(q^{10})$	\(q+(1.40172 - 0.187577i) q^{2} +(-0.555570 + 0.831470i) q^{3} +(1.92963 - 0.525860i) q^{4} +(-0.451487 + 2.26978i) q^{5} +(-0.622789 + 1.26970i) q^{6} +(-1.32215 + 3.19196i) q^{7} +(2.60616 - 1.09906i) q^{8} +(-0.382683 - 0.923880i) q^{9} +(-0.207100 + 3.26628i) q^{10} +(3.07181 - 2.05252i) q^{11} +(-0.634809 + 1.89658i) q^{12} +(-1.14806 - 5.77170i) q^{13} +(-1.25455 + 4.72223i) q^{14} +(-1.63642 - 1.63642i) q^{15} +(3.44694 - 2.02943i) q^{16} +(3.36530 - 3.36530i) q^{17} +(-0.709713 - 1.22324i) q^{18} +(-6.10247 + 1.21386i) q^{19} +(0.322382 + 4.61725i) q^{20} +(-1.91947 - 2.87269i) q^{21} +(3.92080 - 3.45325i) q^{22} +(-1.30179 + 0.539218i) q^{23} +(-0.534069 + 2.77755i) q^{24} +(-0.328659 - 0.136135i) q^{25} +(-2.69190 - 7.87495i) q^{26} +(0.980785 + 0.195090i) q^{27} +(-0.872742 + 6.85456i) q^{28} +(-0.714865 - 0.477658i) q^{29} +(-2.60075 - 1.98685i) q^{30} +7.07077i q^{31} +(4.45097 - 3.49125i) q^{32} +3.69443i q^{33} +(4.08595 - 5.34846i) q^{34} +(-6.64810 - 4.44212i) q^{35} +(-1.22427 - 1.58151i) q^{36} +(-2.72547 - 0.542129i) q^{37} +(-8.32625 + 2.84617i) q^{38} +(5.43682 + 2.25200i) q^{39} +(1.31798 + 6.41162i) q^{40} +(1.11548 - 0.462047i) q^{41} +(-3.22940 - 3.66665i) q^{42} +(-6.65231 - 9.95589i) q^{43} +(4.84811 - 5.57593i) q^{44} +(2.26978 - 0.451487i) q^{45} +(-1.72360 + 1.00002i) q^{46} +(2.55213 - 2.55213i) q^{47} +(-0.227611 + 3.99352i) q^{48} +(-3.49076 - 3.49076i) q^{49} +(-0.486223 - 0.129174i) q^{50} +(0.928485 + 4.66781i) q^{51} +(-5.25044 - 10.5335i) q^{52} +(6.68612 - 4.46752i) q^{53} +(1.41138 + 0.0894892i) q^{54} +(3.27188 + 7.89901i) q^{55} +(0.0624172 + 9.77187i) q^{56} +(2.38106 - 5.74840i) q^{57} +(-1.09164 - 0.535450i) q^{58} +(-1.36523 + 6.86345i) q^{59} +(-4.01821 - 2.29716i) q^{60} +(-7.61906 + 11.4027i) q^{61} +(1.32631 + 9.91123i) q^{62} +3.45495 q^{63} +(5.58413 - 5.72866i) q^{64} +13.6188 q^{65} +(0.692989 + 5.17855i) q^{66} +(-1.53277 + 2.29395i) q^{67} +(4.72411 - 8.26346i) q^{68} +(0.274891 - 1.38197i) q^{69} +(-10.1520 - 4.97957i) q^{70} +(-1.95859 + 4.72846i) q^{71} +(-2.01273 - 1.98718i) q^{72} +(-3.79524 - 9.16252i) q^{73} +(-3.92203 - 0.248678i) q^{74} +(0.295785 - 0.197637i) q^{75} +(-11.1372 + 5.55133i) q^{76} +(2.49015 + 12.5188i) q^{77} +(8.04332 + 2.13686i) q^{78} +(3.88839 + 3.88839i) q^{79} +(3.05010 + 8.74006i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(1.47692 - 0.856898i) q^{82} +(9.26891 - 1.84370i) q^{83} +(-5.21449 - 4.53385i) q^{84} +(6.11910 + 9.15788i) q^{85} +(-11.1922 - 12.7075i) q^{86} +(0.794316 - 0.329016i) q^{87} +(5.74978 - 8.72528i) q^{88} +(-5.39002 - 2.23262i) q^{89} +(3.09690 - 1.05862i) q^{90} +(19.9409 + 3.96650i) q^{91} +(-2.22842 + 1.72505i) q^{92} +(-5.87913 - 3.92831i) q^{93} +(3.09865 - 4.05609i) q^{94} -14.3993i q^{95} +(0.430045 + 5.64048i) q^{96} +7.50832i q^{97} +(-5.54784 - 4.23827i) q^{98} +(-3.07181 - 2.05252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{16}\right)$

Coefficient data

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

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

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

$2$	1.40172	−	0.187577i	0.991165	−	0.132637i
$2$	1.40172	−	0.187577i	0.991165	−	0.132637i
$3$	−0.555570	+	0.831470i	−0.320759	+	0.480049i
$3$	−0.555570	+	0.831470i	−0.320759	+	0.480049i
$4$	1.92963	−	0.525860i	0.964815	−	0.262930i
$5$	−0.451487	+	2.26978i	−0.201911	+	1.01508i	0.738297	+	0.674476i	$0.235630\pi$
$5$	−0.451487	+	2.26978i	−0.201911	+	1.01508i	−0.940208	+	0.340600i	$0.889370\pi$
$6$	−0.622789	+	1.26970i	−0.254252	+	0.518352i
$7$	−1.32215	+	3.19196i	−0.499726	+	1.20645i	0.449905	+	0.893077i	$0.351458\pi$
$7$	−1.32215	+	3.19196i	−0.499726	+	1.20645i	−0.949631	+	0.313370i	$0.898542\pi$
$8$	2.60616	−	1.09906i	0.921416	−	0.388577i
$9$	−0.382683	−	0.923880i	−0.127561	−	0.307960i
$10$	−0.207100	+	3.26628i	−0.0654908	+	1.03289i
$11$	3.07181	−	2.05252i	0.926184	−	0.618857i	0.00166784	−	0.999999i	$-0.499469\pi$
$11$	3.07181	−	2.05252i	0.926184	−	0.618857i	0.924517	+	0.381142i	$0.124469\pi$
$12$	−0.634809	+	1.89658i	−0.183253	+	0.547496i
$13$	−1.14806	−	5.77170i	−0.318415	−	1.60078i	−0.726054	−	0.687638i	$-0.758648\pi$
$13$	−1.14806	−	5.77170i	−0.318415	−	1.60078i	0.407639	−	0.913143i	$-0.366352\pi$
$14$	−1.25455	+	4.72223i	−0.335292	+	1.26207i
$15$	−1.63642	−	1.63642i	−0.422522	−	0.422522i
$16$	3.44694	−	2.02943i	0.861736	−	0.507357i
$17$	3.36530	−	3.36530i	0.816205	−	0.816205i	−0.169350	−	0.985556i	$-0.554167\pi$
$17$	3.36530	−	3.36530i	0.816205	−	0.816205i	0.985556	+	0.169350i	$0.0541670\pi$
$18$	−0.709713	−	1.22324i	−0.167281	−	0.288320i
$19$	−6.10247	+	1.21386i	−1.40000	+	0.278478i	−0.836649	−	0.547739i	$-0.815489\pi$
$19$	−6.10247	+	1.21386i	−1.40000	+	0.278478i	−0.563353	+	0.826217i	$0.690489\pi$
$20$	0.322382	+	4.61725i	0.0720868	+	1.03245i
$21$	−1.91947	−	2.87269i	−0.418862	−	0.626871i
$22$	3.92080	−	3.45325i	0.835918	−	0.736235i
$23$	−1.30179	+	0.539218i	−0.271442	+	0.112435i	−0.514252	−	0.857639i	$-0.671931\pi$
$23$	−1.30179	+	0.539218i	−0.271442	+	0.112435i	0.242811	+	0.970074i	$0.421931\pi$
$24$	−0.534069	+	2.77755i	−0.109016	+	0.566965i
$25$	−0.328659	−	0.136135i	−0.0657318	−	0.0272270i
$26$	−2.69190	−	7.87495i	−0.527924	−	1.54440i
$27$	0.980785	+	0.195090i	0.188752	+	0.0375451i
$28$	−0.872742	+	6.85456i	−0.164933	+	1.29539i
$29$	−0.714865	−	0.477658i	−0.132747	−	0.0886988i	0.487424	−	0.873166i	$-0.337937\pi$
$29$	−0.714865	−	0.477658i	−0.132747	−	0.0886988i	−0.620171	+	0.784467i	$0.712937\pi$
$30$	−2.60075	−	1.98685i	−0.474831	−	0.362747i
$31$			7.07077i			1.26995i	0.772533	+	0.634974i	$0.218989\pi$
$31$			7.07077i			1.26995i	−0.772533	+	0.634974i	$0.781011\pi$
$32$	4.45097	−	3.49125i	0.786828	−	0.617172i
$33$			3.69443i			0.643118i
$34$	4.08595	−	5.34846i	0.700735	−	0.917253i
$35$	−6.64810	−	4.44212i	−1.12373	−	0.750855i
$36$	−1.22427	−	1.58151i	−0.204045	−	0.263585i
$37$	−2.72547	−	0.542129i	−0.448064	−	0.0891255i	−0.0340994	−	0.999418i	$-0.510856\pi$
$37$	−2.72547	−	0.542129i	−0.448064	−	0.0891255i	−0.413965	+	0.910293i	$0.635856\pi$
$38$	−8.32625	+	2.84617i	−1.35070	+	0.461709i
$39$	5.43682	+	2.25200i	0.870588	+	0.360609i
$40$	1.31798	+	6.41162i	0.208391	+	1.01377i
$41$	1.11548	−	0.462047i	0.174209	−	0.0721596i	−0.293874	−	0.955844i	$-0.594945\pi$
$41$	1.11548	−	0.462047i	0.174209	−	0.0721596i	0.468083	+	0.883684i	$0.344945\pi$
$42$	−3.22940	−	3.66665i	−0.498307	−	0.565776i
$43$	−6.65231	−	9.95589i	−1.01447	−	1.51826i	−0.846446	−	0.532475i	$-0.821262\pi$
$43$	−6.65231	−	9.95589i	−1.01447	−	1.51826i	−0.168022	−	0.985783i	$-0.553738\pi$
$44$	4.84811	−	5.57593i	0.730881	−	0.840604i
$45$	2.26978	−	0.451487i	0.338359	−	0.0673037i
$46$	−1.72360	+	1.00002i	−0.254130	+	0.147445i
$47$	2.55213	−	2.55213i	0.372266	−	0.372266i	−0.496036	−	0.868302i	$-0.665212\pi$
$47$	2.55213	−	2.55213i	0.372266	−	0.372266i	0.868302	+	0.496036i	$0.165212\pi$
$48$	−0.227611	+	3.99352i	−0.0328528	+	0.576415i
$49$	−3.49076	−	3.49076i	−0.498680	−	0.498680i
$50$	−0.486223	−	0.129174i	−0.0687623	−	0.0182680i
$51$	0.928485	+	4.66781i	0.130014	+	0.653624i
$52$	−5.25044	−	10.5335i	−0.728105	−	1.46074i
$53$	6.68612	−	4.46752i	0.918409	−	0.613661i	−0.00395107	−	0.999992i	$-0.501258\pi$
$53$	6.68612	−	4.46752i	0.918409	−	0.613661i	0.922360	+	0.386331i	$0.126258\pi$
$54$	1.41138	+	0.0894892i	0.192064	+	0.0121779i
$55$	3.27188	+	7.89901i	0.441180	+	1.06510i
$56$	0.0624172	+	9.77187i	0.00834084	+	1.30582i
$57$	2.38106	−	5.74840i	0.315380	−	0.761394i
$58$	−1.09164	−	0.535450i	−0.143339	−	0.0703080i
$59$	−1.36523	+	6.86345i	−0.177737	+	0.893546i	0.784249	+	0.620447i	$0.213049\pi$
$59$	−1.36523	+	6.86345i	−0.177737	+	0.893546i	−0.961986	+	0.273099i	$0.911951\pi$
$60$	−4.01821	−	2.29716i	−0.518749	−	0.296562i
$61$	−7.61906	+	11.4027i	−0.975521	+	1.45997i	−0.0896853	+	0.995970i	$0.528586\pi$
$61$	−7.61906	+	11.4027i	−0.975521	+	1.45997i	−0.885835	+	0.464000i	$0.846414\pi$
$62$	1.32631	+	9.91123i	0.168442	+	1.25873i
$63$	3.45495			0.435283
$64$	5.58413	−	5.72866i	0.698016	−	0.716082i
$65$	13.6188			1.68921
$66$	0.692989	+	5.17855i	0.0853011	+	0.637436i
$67$	−1.53277	+	2.29395i	−0.187258	+	0.280251i	−0.913206	−	0.407498i	$-0.866401\pi$
$67$	−1.53277	+	2.29395i	−0.187258	+	0.280251i	0.725948	+	0.687749i	$0.241401\pi$
$68$	4.72411	−	8.26346i	0.572882	−	1.00209i
$69$	0.274891	−	1.38197i	0.0330930	−	0.166370i
$70$	−10.1520	−	4.97957i	−1.21340	−	0.595173i
$71$	−1.95859	+	4.72846i	−0.232442	+	0.561165i	−0.996464	−	0.0840259i	$-0.973222\pi$
$71$	−1.95859	+	4.72846i	−0.232442	+	0.561165i	0.764021	+	0.645191i	$0.223222\pi$
$72$	−2.01273	−	1.98718i	−0.237203	−	0.234192i
$73$	−3.79524	−	9.16252i	−0.444199	−	1.07239i	−0.974461	−	0.224558i	$-0.927906\pi$
$73$	−3.79524	−	9.16252i	−0.444199	−	1.07239i	0.530262	−	0.847834i	$-0.322094\pi$
$74$	−3.92203	−	0.248678i	−0.455927	−	0.0289082i
$75$	0.295785	−	0.197637i	0.0341543	−	0.0228212i
$76$	−11.1372	+	5.55133i	−1.27752	+	0.636782i
$77$	2.49015	+	12.5188i	0.283778	+	1.42665i
$78$	8.04332	+	2.13686i	0.910726	+	0.241951i
$79$	3.88839	+	3.88839i	0.437478	+	0.437478i	0.891162	−	0.453684i	$-0.149891\pi$
$79$	3.88839	+	3.88839i	0.437478	+	0.437478i	−0.453684	+	0.891162i	$0.649891\pi$
$80$	3.05010	+	8.74006i	0.341012	+	0.977169i
$81$	−0.707107	+	0.707107i	−0.0785674	+	0.0785674i
$82$	1.47692	−	0.856898i	0.163099	−	0.0946286i
$83$	9.26891	−	1.84370i	1.01740	−	0.202373i	0.341900	−	0.939736i	$-0.388930\pi$
$83$	9.26891	−	1.84370i	1.01740	−	0.202373i	0.675496	+	0.737364i	$0.263930\pi$
$84$	−5.21449	−	4.53385i	−0.568948	−	0.494684i
$85$	6.11910	+	9.15788i	0.663710	+	0.993312i
$86$	−11.1922	−	12.7075i	−1.20688	−	1.37029i
$87$	0.794316	−	0.329016i	0.0851596	−	0.0352743i
$88$	5.74978	−	8.72528i	0.612928	−	0.930118i
$89$	−5.39002	−	2.23262i	−0.571341	−	0.236657i	0.0782592	−	0.996933i	$-0.475064\pi$
$89$	−5.39002	−	2.23262i	−0.571341	−	0.236657i	−0.649601	+	0.760276i	$0.725064\pi$
$90$	3.09690	−	1.05862i	0.326442	−	0.111588i
$91$	19.9409	+	3.96650i	2.09038	+	0.415802i
$92$	−2.22842	+	1.72505i	−0.232329	+	0.179849i
$93$	−5.87913	−	3.92831i	−0.609638	−	0.407347i
$94$	3.09865	−	4.05609i	0.319601	−	0.418353i
$95$		−	14.3993i		−	1.47734i
$96$	0.430045	+	5.64048i	0.0438913	+	0.575679i
$97$			7.50832i			0.762355i	0.924502	+	0.381177i	$0.124481\pi$
$97$			7.50832i			0.762355i	−0.924502	+	0.381177i	$0.875519\pi$
$98$	−5.54784	−	4.23827i	−0.560417	−	0.428130i
$99$	−3.07181	−	2.05252i	−0.308728	−	0.206286i
$100$	−0.705778	−	0.0898616i	−0.0705778	−	0.00898616i
$101$	−14.0376	−	2.79224i	−1.39679	−	0.277839i	−0.561421	−	0.827530i	$-0.689745\pi$
$101$	−14.0376	−	2.79224i	−1.39679	−	0.277839i	−0.835368	+	0.549692i	$0.814745\pi$
$102$	2.17705	+	6.36879i	0.215560	+	0.630604i
$103$	−4.25415	−	1.76213i	−0.419174	−	0.173628i	0.163119	−	0.986606i	$-0.447844\pi$
$103$	−4.25415	−	1.76213i	−0.419174	−	0.173628i	−0.582293	+	0.812979i	$0.697844\pi$
$104$	−9.33548	−	13.7802i	−0.915419	−	1.35126i
$105$	7.38698	−	3.05979i	0.720895	−	0.298605i
$106$	8.53406	−	7.51637i	0.828901	−	0.730054i
$107$	−4.71545	−	7.05717i	−0.455860	−	0.682242i	0.530343	−	0.847783i	$-0.322063\pi$
$107$	−4.71545	−	7.05717i	−0.455860	−	0.682242i	−0.986203	+	0.165541i	$0.947063\pi$
$108$	1.99514	−	0.139303i	0.191983	−	0.0134045i
$109$	0.121859	−	0.0242392i	0.0116719	−	0.00232169i	−0.189251	−	0.981929i	$-0.560606\pi$
$109$	0.121859	−	0.0242392i	0.0116719	−	0.00232169i	0.200923	+	0.979607i	$0.435606\pi$
$110$	6.06792	+	10.4585i	0.578553	+	0.997175i
$111$	1.96495	−	1.96495i	0.186505	−	0.186505i
$112$	1.92047	+	13.6857i	0.181467	+	1.29318i
$113$	8.80505	+	8.80505i	0.828309	+	0.828309i	0.987283	−	0.158974i	$-0.0508185\pi$
$113$	8.80505	+	8.80505i	0.828309	+	0.828309i	−0.158974	+	0.987283i	$0.550819\pi$
$114$	2.25932	−	8.50427i	0.211604	−	0.796498i
$115$	−0.636166	−	3.19822i	−0.0593228	−	0.298236i
$116$	−1.63061	−	0.545784i	−0.151398	−	0.0506747i
$117$	−4.89301	+	3.26940i	−0.452359	+	0.302257i
$118$	−0.626238	+	9.87672i	−0.0576499	+	0.909226i
$119$	6.29246	+	15.1913i	0.576829	+	1.39259i
$120$	−6.06329	−	2.46624i	−0.553501	−	0.225136i
$121$	1.01366	−	2.44718i	0.0921505	−	0.222471i
$122$	−8.54089	+	17.4126i	−0.773256	+	1.57646i
$123$	−0.235550	+	1.18419i	−0.0212388	+	0.106775i
$124$	3.71823	+	13.6440i	0.333907	+	1.22526i
$125$	−5.97125	+	8.93661i	−0.534085	+	0.799315i
$126$	4.84287	−	0.648068i	0.431437	−	0.0577345i
$127$	0.515837			0.0457731			0.0228866	−	0.999738i	$-0.492714\pi$
$127$	0.515837			0.0457731			0.0228866	+	0.999738i	$0.492714\pi$
$128$	6.75282	−	9.07742i	0.596870	−	0.802338i
$129$	11.9738			1.05424
$130$	19.0897	−	2.55457i	1.67428	−	0.224051i
$131$	−2.76483	+	4.13786i	−0.241565	+	0.361527i	−0.932365	−	0.361519i	$-0.882258\pi$
$131$	−2.76483	+	4.13786i	−0.241565	+	0.361527i	0.690800	+	0.723046i	$0.257258\pi$
$132$	1.94275	+	7.12888i	0.169095	+	0.620490i
$133$	4.19381	−	21.0837i	0.363650	−	1.82819i
$134$	−1.71822	+	3.50299i	−0.148432	+	0.302612i
$135$	−0.885624	+	2.13809i	−0.0762224	+	0.184017i
$136$	5.07184	−	12.4692i	0.434907	−	1.06922i
$137$	5.74289	+	13.8646i	0.490648	+	1.18453i	0.954391	+	0.298559i	$0.0965061\pi$
$137$	5.74289	+	13.8646i	0.490648	+	1.18453i	−0.463743	+	0.885970i	$0.653494\pi$
$138$	0.126094	−	1.98870i	0.0107339	−	0.169289i
$139$	9.08522	−	6.07055i	0.770598	−	0.514897i	−0.107020	−	0.994257i	$-0.534131\pi$
$139$	9.08522	−	6.07055i	0.770598	−	0.514897i	0.877619	+	0.479359i	$0.159131\pi$
$140$	−15.1643	−	5.07568i	−1.28162	−	0.428973i
$141$	0.704131	+	3.53991i	0.0592985	+	0.298114i
$142$	−1.85845	+	6.99536i	−0.155957	+	0.587037i
$143$	−15.3731	−	15.3731i	−1.28556	−	1.28556i
$144$	−3.19404	−	2.40793i	−0.266170	−	0.200661i
$145$	1.40693	−	1.40693i	0.116839	−	0.116839i
$146$	−7.03853	−	12.1314i	−0.582513	−	1.00400i
$147$	4.84182	−	0.963098i	0.399346	−	0.0794350i
$148$	−5.54423	+	0.387105i	−0.455733	+	0.0318198i
$149$	7.13433	+	10.6773i	0.584467	+	0.874717i	0.999382	−	0.0351430i	$-0.0111887\pi$
$149$	7.13433	+	10.6773i	0.584467	+	0.874717i	−0.414915	+	0.909860i	$0.636189\pi$
$150$	0.377535	−	0.332514i	0.0308256	−	0.0271497i
$151$	−2.48617	+	1.02981i	−0.202322	+	0.0838045i	−0.481543	−	0.876422i	$-0.659924\pi$
$151$	−2.48617	+	1.02981i	−0.202322	+	0.0838045i	0.279221	+	0.960227i	$0.409924\pi$
$152$	−14.5699	+	9.87048i	−1.18177	+	0.800602i
$153$	−4.39698	−	1.82129i	−0.355475	−	0.147242i
$154$	5.83872	+	17.0808i	0.470498	+	1.37641i
$155$	−16.0491	−	3.19236i	−1.28909	−	0.256417i
$156$	11.6753	+	1.48653i	0.934771	+	0.119018i
$157$	11.8211	+	7.89858i	0.943423	+	0.630375i	0.929221	−	0.369524i	$-0.120479\pi$
$157$	11.8211	+	7.89858i	0.943423	+	0.630375i	0.0142020	+	0.999899i	$0.495479\pi$
$158$	6.17980	+	4.72106i	0.491639	+	0.375587i
$159$			8.04133i			0.637719i
$160$	5.91482	+	11.6790i	0.467608	+	0.923304i
$161$		−	4.86818i		−	0.383666i
$162$	−0.858528	+	1.12380i	−0.0674523	+	0.0882942i
$163$	−8.81534	−	5.89022i	−0.690471	−	0.461358i	0.160181	−	0.987088i	$-0.448792\pi$
$163$	−8.81534	−	5.89022i	−0.690471	−	0.461358i	−0.850652	+	0.525730i	$0.823792\pi$
$164$	1.90949	−	1.47817i	0.149106	−	0.115425i
$165$	−8.38554	−	1.66799i	−0.652813	−	0.129853i
$166$	12.6466	−	4.32298i	0.981564	−	0.335529i
$167$	−8.49593	−	3.51913i	−0.657435	−	0.272319i	0.0289237	−	0.999582i	$-0.490792\pi$
$167$	−8.49593	−	3.51913i	−0.657435	−	0.272319i	−0.686359	+	0.727263i	$0.740792\pi$
$168$	−8.15969	−	5.37706i	−0.629534	−	0.414849i
$169$	−19.9840	+	8.27765i	−1.53723	+	0.636742i
$170$	10.2951	+	11.6890i	0.789595	+	0.896503i
$171$	3.45677	+	5.17342i	0.264346	+	0.395621i
$172$	−18.0719	−	15.7130i	−1.37797	−	1.19810i
$173$	−14.9143	+	2.96665i	−1.13392	+	0.225550i	−0.726150	−	0.687536i	$-0.758692\pi$
$173$	−14.9143	+	2.96665i	−1.13392	+	0.225550i	−0.407766	+	0.913086i	$0.633692\pi$
$174$	1.05169	−	0.610183i	0.0797285	−	0.0462579i
$175$	0.869074	−	0.869074i	0.0656958	−	0.0656958i
$176$	6.42291	−	13.3089i	0.484145	−	1.00320i
$177$	−4.94828	−	4.94828i	−0.371935	−	0.371935i
$178$	−7.97408	−	2.11846i	−0.597683	−	0.158786i
$179$	−3.89142	−	19.5635i	−0.290858	−	1.46224i	−0.799188	−	0.601082i	$-0.794737\pi$
$179$	−3.89142	−	19.5635i	−0.290858	−	1.46224i	0.508329	−	0.861163i	$-0.330263\pi$
$180$	4.14241	−	2.06479i	0.308757	−	0.153900i
$181$	10.6665	−	7.12710i	0.792831	−	0.529753i	−0.0919476	−	0.995764i	$-0.529309\pi$
$181$	10.6665	−	7.12710i	0.792831	−	0.529753i	0.884779	+	0.466011i	$0.154309\pi$
$182$	28.6956	+	1.81946i	2.12706	+	0.134867i
$183$	−5.24810	−	12.6700i	−0.387951	−	0.936596i
$184$	−2.80003	+	2.83603i	−0.206421	+	0.209075i
$185$	2.46103	−	5.94144i	0.180938	−	0.436824i
$186$	−8.97775	−	4.40360i	−0.658280	−	0.322887i
$187$	3.43022	−	17.2449i	0.250843	−	1.26107i
$188$	3.58260	−	6.26673i	0.261288	−	0.457048i
$189$	−1.91947	+	2.87269i	−0.139621	+	0.208957i
$190$	−2.70097	−	20.1838i	−0.195949	−	1.46428i
$191$	−4.45588			−0.322416			−0.161208	−	0.986920i	$-0.551539\pi$
$191$	−4.45588			−0.322416			−0.161208	+	0.986920i	$0.551539\pi$
$192$	1.66083	+	7.82570i	0.119860	+	0.564772i
$193$	−0.472106			−0.0339830			−0.0169915	−	0.999856i	$-0.505409\pi$
$193$	−0.472106			−0.0339830			−0.0169915	+	0.999856i	$0.505409\pi$
$194$	1.40839	+	10.5246i	0.101116	+	0.755619i
$195$	−7.56621	+	11.3236i	−0.541827	+	0.810902i
$196$	−8.57152	−	4.90022i	−0.612251	−	0.350016i
$197$	1.05093	−	5.28337i	0.0748755	−	0.376424i	−0.925119	−	0.379677i	$-0.876035\pi$
$197$	1.05093	−	5.28337i	0.0748755	−	0.376424i	0.999995	+	0.00325226i	$0.00103523\pi$
$198$	−4.69081	−	2.30085i	−0.333361	−	0.163514i
$199$	6.34182	−	15.3105i	0.449560	−	1.08533i	−0.522928	−	0.852377i	$-0.675160\pi$
$199$	6.34182	−	15.3105i	0.449560	−	1.08533i	0.972487	−	0.232956i	$-0.0748398\pi$
$200$	−1.00616	+	0.00642676i	−0.0711461	+	0.000454441i
$201$	−1.05579	−	2.54891i	−0.0744698	−	0.179786i
$202$	−20.2005	−	1.28082i	−1.42130	−	0.0901182i
$203$	2.46982	−	1.65028i	0.173348	−	0.115827i
$204$	4.24624	+	8.51889i	0.297296	+	0.596441i
$205$	0.545120	+	2.74050i	0.0380728	+	0.191405i
$206$	−6.29366	−	1.67203i	−0.438500	−	0.116496i
$207$	0.996346	+	0.996346i	0.0692508	+	0.0692508i
$208$	−15.6706	−	17.5648i	−1.08656	−	1.21790i
$209$	−16.2541	+	16.2541i	−1.12432	+	1.12432i
$210$	9.78052	−	5.67458i	0.674920	−	0.391583i
$211$	−6.77835	+	1.34830i	−0.466641	+	0.0928206i	−0.422810	−	0.906218i	$-0.638956\pi$
$211$	−6.77835	+	1.34830i	−0.466641	+	0.0928206i	−0.0438308	+	0.999039i	$0.513956\pi$
$212$	10.5524	−	12.1366i	0.724745	−	0.833547i
$213$	−2.84344	−	4.25550i	−0.194829	−	0.291582i
$214$	−7.93349	−	9.00765i	−0.542322	−	0.615751i
$215$	25.6011	−	10.6043i	1.74598	−	0.723209i
$216$	2.77050	−	0.569506i	0.188509	−	0.0387500i
$217$	−22.5696	−	9.34863i	−1.53212	−	0.634627i
$218$	0.166265	−	0.0568344i	0.0112609	−	0.00384931i
$219$	9.72688	+	1.93480i	0.657281	+	0.130741i
$220$	10.4673	+	13.5216i	0.705704	+	0.911627i
$221$	−23.2871	−	15.5599i	−1.56646	−	1.04667i
$222$	2.38573	−	3.12289i	0.160120	−	0.209595i
$223$			10.7249i			0.718194i	0.933300	+	0.359097i	$0.116915\pi$
$223$			10.7249i			0.718194i	−0.933300	+	0.359097i	$0.883085\pi$
$224$	5.25908	+	18.8233i	0.351387	+	1.25768i
$225$			0.355738i			0.0237158i
$226$	13.9938	+	10.6906i	0.930855	+	0.711126i
$227$	9.54081	+	6.37497i	0.633246	+	0.423121i	0.830335	−	0.557264i	$-0.188149\pi$
$227$	9.54081	+	6.37497i	0.633246	+	0.423121i	−0.197089	+	0.980386i	$0.563149\pi$
$228$	1.57172	−	12.3444i	0.104090	−	0.817527i
$229$	9.95190	+	1.97956i	0.657640	+	0.130813i	0.512619	−	0.858616i	$-0.328675\pi$
$229$	9.95190	+	1.97956i	0.657640	+	0.130813i	0.145021	+	0.989429i	$0.453675\pi$
$230$	−1.49164	−	4.36368i	−0.0983557	−	0.287732i
$231$	−11.7925	−	4.88460i	−0.775887	−	0.321383i
$232$	−2.38803	−	0.459171i	−0.156782	−	0.0301461i
$233$	−22.8056	+	9.44637i	−1.49404	+	0.618852i	−0.972192	−	0.234185i	$-0.924758\pi$
$233$	−22.8056	+	9.44637i	−1.49404	+	0.618852i	−0.521849	+	0.853038i	$0.674758\pi$
$234$	−6.24536	+	5.50060i	−0.408272	+	0.359585i
$235$	4.64052	+	6.94502i	0.302714	+	0.453043i
$236$	0.974833	+	13.9618i	0.0634562	+	0.908839i
$237$	−5.39335	+	1.07280i	−0.350336	+	0.0696862i
$238$	11.6698	+	20.1137i	0.756441	+	1.30377i
$239$	12.4177	−	12.4177i	0.803236	−	0.803236i	−0.180364	−	0.983600i	$-0.557727\pi$
$239$	12.4177	−	12.4177i	0.803236	−	0.803236i	0.983600	+	0.180364i	$0.0577275\pi$
$240$	−8.96164	−	2.31965i	−0.578472	−	0.149733i
$241$	1.20354	+	1.20354i	0.0775270	+	0.0775270i	0.744807	−	0.667280i	$-0.232542\pi$
$241$	1.20354	+	1.20354i	0.0775270	+	0.0775270i	−0.667280	+	0.744807i	$0.732542\pi$
$242$	0.961826	−	3.62040i	0.0618285	−	0.232728i
$243$	−0.195090	−	0.980785i	−0.0125150	−	0.0629174i
$244$	−8.70573	+	26.0096i	−0.557327	+	1.66509i
$245$	9.49928	−	6.34722i	0.606887	−	0.405509i
$246$	−0.108048	+	1.70408i	−0.00688890	+	0.108648i
$247$	14.0120	+	33.8280i	0.891563	+	2.15242i
$248$	7.77121	+	18.4276i	0.493472	+	1.17015i
$249$	−3.61655	+	8.73113i	−0.229190	+	0.553313i
$250$	−6.69371	+	13.6467i	−0.423348	+	0.863092i
$251$	−4.39926	+	22.1166i	−0.277679	+	1.39599i	0.550178	+	0.835047i	$0.314560\pi$
$251$	−4.39926	+	22.1166i	−0.277679	+	1.39599i	−0.827857	+	0.560939i	$0.810440\pi$
$252$	6.66677	−	1.81682i	0.419967	−	0.114449i
$253$	−2.89209	+	4.32832i	−0.181824	+	0.272119i
$254$	0.723058	−	0.0967590i	0.0453687	−	0.00607120i
$255$	−11.0141			−0.689729
$256$	7.76284	−	13.9907i	0.485177	−	0.874416i
$257$	16.2757			1.01525			0.507625	−	0.861578i	$-0.330524\pi$
$257$	16.2757			1.01525			0.507625	+	0.861578i	$0.330524\pi$
$258$	16.7840	−	2.24601i	1.04492	−	0.139831i
$259$	5.33393	−	7.98280i	0.331435	−	0.496027i
$260$	26.2793	−	7.16158i	1.62977	−	0.444143i
$261$	−0.167731	+	0.843241i	−0.0103823	+	0.0521953i
$262$	−3.09935	+	6.31874i	−0.191478	+	0.390373i
$263$	1.82556	−	4.40729i	0.112569	−	0.271765i	−0.857548	−	0.514404i	$-0.828013\pi$
$263$	1.82556	−	4.40729i	0.112569	−	0.271765i	0.970117	+	0.242639i	$0.0780131\pi$
$264$	4.06040	+	9.62827i	0.249901	+	0.592579i
$265$	7.12159	+	17.1930i	0.437476	+	1.05616i
$266$	1.92373	−	30.3401i	0.117951	−	1.86027i
$267$	4.85089	−	3.24126i	0.296870	−	0.198362i
$268$	−1.75138	+	5.23250i	−0.106983	+	0.319626i
$269$	−2.89668	−	14.5626i	−0.176614	−	0.887898i	−0.962863	−	0.269989i	$-0.912980\pi$
$269$	−2.89668	−	14.5626i	−0.176614	−	0.887898i	0.786250	−	0.617909i	$-0.212020\pi$
$270$	−0.840340	+	3.16312i	−0.0511415	+	0.192501i
$271$	−14.2501	−	14.2501i	−0.865629	−	0.865629i	0.126356	−	0.991985i	$-0.459672\pi$
$271$	−14.2501	−	14.2501i	−0.865629	−	0.865629i	−0.991985	+	0.126356i	$0.959672\pi$
$272$	4.77036	−	18.4296i	0.289246	−	1.11746i
$273$	−14.3766	+	14.3766i	−0.870112	+	0.870112i
$274$	10.6506	+	18.3570i	0.643425	+	1.10899i
$275$	−1.28900	+	0.256397i	−0.0777293	+	0.0154613i
$276$	−0.196285	−	2.81125i	−0.0118149	−	0.169217i
$277$	−3.88185	−	5.80960i	−0.233238	−	0.349065i	0.696326	−	0.717725i	$-0.254817\pi$
$277$	−3.88185	−	5.80960i	−0.233238	−	0.349065i	−0.929564	+	0.368660i	$0.879817\pi$
$278$	11.5962	−	10.2134i	0.695496	−	0.612558i
$279$	6.53254	−	2.70587i	0.391093	−	0.161996i
$280$	−22.2082	−	4.27020i	−1.32719	−	0.255193i
$281$	20.0502	+	8.30507i	1.19610	+	0.495439i	0.889736	−	0.456476i	$-0.150889\pi$
$281$	20.0502	+	8.30507i	1.19610	+	0.495439i	0.306361	+	0.951916i	$0.400889\pi$
$282$	1.65100	+	4.82987i	0.0983155	+	0.287615i
$283$	10.6273	+	2.11390i	0.631727	+	0.125658i	0.500560	−	0.865702i	$-0.333128\pi$
$283$	10.6273	+	2.11390i	0.631727	+	0.125658i	0.131167	+	0.991360i	$0.458128\pi$
$284$	−1.29285	+	10.1541i	−0.0767167	+	0.602536i
$285$	11.9726	+	7.99982i	0.709194	+	0.473868i
$286$	−24.4324	−	18.6651i	−1.44472	−	1.10369i
$287$			4.17146i			0.246234i
$288$	−4.92881	−	2.77612i	−0.290433	−	0.163584i
$289$		−	5.65051i		−	0.332383i
$290$	1.70821	−	2.23603i	0.100310	−	0.131304i
$291$	−6.24294	−	4.17140i	−0.365968	−	0.244532i
$292$	−12.1416	−	15.6845i	−0.710534	−	0.917866i
$293$	26.9907	+	5.36879i	1.57682	+	0.313648i	0.904453	−	0.426574i	$-0.140280\pi$
$293$	26.9907	+	5.36879i	1.57682	+	0.313648i	0.672362	+	0.740222i	$0.265280\pi$
$294$	6.60621	−	2.25820i	0.385282	−	0.131701i
$295$	−14.9621	−	6.19752i	−0.871130	−	0.360834i
$296$	−7.69883	+	1.58258i	−0.447486	+	0.0919856i
$297$	3.41321	−	1.41380i	0.198054	−	0.0820368i
$298$	12.0031	+	13.6283i	0.695323	+	0.789467i
$299$	4.60674	+	6.89447i	0.266415	+	0.398718i
$300$	0.466826	−	0.536908i	0.0269522	−	0.0309984i
$301$	40.5741	−	8.07070i	2.33865	−	0.465187i
$302$	−3.29175	+	1.90985i	−0.189419	+	0.109899i
$303$	10.1205	−	10.1205i	0.581408	−	0.581408i
$304$	−18.5714	+	16.5686i	−1.06514	+	0.950275i
$305$	−22.4418	−	22.4418i	−1.28501	−	1.28501i
$306$	−6.50496	−	1.72816i	−0.371864	−	0.0987925i
$307$	1.08426	+	5.45093i	0.0618818	+	0.311101i	0.999313	−	0.0370706i	$-0.0118026\pi$
$307$	1.08426	+	5.45093i	0.0618818	+	0.311101i	−0.937431	+	0.348172i	$0.886803\pi$
$308$	11.3882	+	22.8472i	0.648903	+	1.30184i
$309$	3.82864	−	2.55821i	0.217804	−	0.145532i
$310$	−23.0951	−	1.46436i	−1.31171	−	0.0831699i
$311$	3.50581	+	8.46376i	0.198796	+	0.479936i	0.991569	−	0.129581i	$-0.0413633\pi$
$311$	3.50581	+	8.46376i	0.198796	+	0.479936i	−0.792773	+	0.609517i	$0.791363\pi$
$312$	16.6443	−	0.106314i	0.942298	−	0.00601887i
$313$	13.1380	−	31.7179i	0.742603	−	1.79280i	0.147656	−	0.989039i	$-0.452827\pi$
$313$	13.1380	−	31.7179i	0.742603	−	1.79280i	0.594947	−	0.803765i	$-0.297173\pi$
$314$	18.0514	+	8.85423i	1.01870	+	0.499673i
$315$	−1.55987	+	7.84197i	−0.0878884	+	0.441845i
$316$	9.54790	+	5.45841i	0.537112	+	0.307059i
$317$	4.18358	−	6.26117i	0.234973	−	0.351663i	−0.695179	−	0.718837i	$-0.744675\pi$
$317$	4.18358	−	6.26117i	0.234973	−	0.351663i	0.930152	+	0.367174i	$0.119675\pi$
$318$	1.50837	+	11.2717i	0.0845850	+	0.632084i
$319$	−3.17633			−0.177840
$320$	10.4816	+	15.2612i	0.585940	+	0.853125i
$321$	8.48758			0.473731
$322$	−0.913158	−	6.82382i	−0.0508883	−	0.380277i
$323$	−16.4516	+	24.6216i	−0.915394	+	1.36998i
$324$	−0.992615	+	1.73629i	−0.0551453	+	0.0964607i
$325$	−0.408409	+	2.05321i	−0.0226545	+	0.113892i
$326$	−13.4615	−	6.60288i	−0.745563	−	0.365700i
$327$	−0.0475469	+	0.114788i	−0.00262935	+	0.00634781i
$328$	2.39930	−	2.43015i	0.132479	−	0.134183i
$329$	4.77198	+	11.5206i	0.263088	+	0.635151i
$330$	−12.0670	−	0.765117i	−0.664269	−	0.0421183i
$331$	−4.69418	+	3.13655i	−0.258016	+	0.172401i	−0.677850	−	0.735200i	$-0.737088\pi$
$331$	−4.69418	+	3.13655i	−0.258016	+	0.172401i	0.419834	+	0.907601i	$0.362088\pi$
$332$	16.9160	−	8.43181i	0.928389	−	0.462756i
$333$	0.542129	+	2.72547i	0.0297085	+	0.149355i
$334$	−12.5690	−	3.33919i	−0.687746	−	0.182712i
$335$	−4.51474	−	4.51474i	−0.246667	−	0.246667i
$336$	−12.4462	−	6.00656i	−0.678996	−	0.327685i
$337$	−12.5263	+	12.5263i	−0.682350	+	0.682350i	−0.960529	−	0.278179i	$-0.910269\pi$
$337$	−12.5263	+	12.5263i	−0.682350	+	0.682350i	0.278179	+	0.960529i	$0.410269\pi$
$338$	−26.4593	+	15.3515i	−1.43919	+	0.835010i
$339$	−12.2129	+	2.42931i	−0.663316	+	0.131942i
$340$	16.6234	+	14.4535i	0.901528	+	0.783853i
$341$	14.5129	+	21.7200i	0.785916	+	1.17621i
$342$	5.81583	+	6.60327i	0.314484	+	0.357064i
$343$	−6.58604	+	2.72803i	−0.355613	+	0.147300i
$344$	−28.2791	−	18.6353i	−1.52471	−	1.00475i
$345$	3.01266	+	1.24788i	0.162196	+	0.0671838i
$346$	−20.3492	+	6.95599i	−1.09398	+	0.373956i
$347$	20.2675	+	4.03147i	1.08802	+	0.216420i	0.706339	−	0.707874i	$-0.250346\pi$
$347$	20.2675	+	4.03147i	1.08802	+	0.216420i	0.381680	+	0.924294i	$0.375346\pi$
$348$	1.35972	−	1.05258i	0.0728886	−	0.0564241i
$349$	11.9683	+	7.99698i	0.640650	+	0.428068i	0.833011	−	0.553256i	$-0.186615\pi$
$349$	11.9683	+	7.99698i	0.640650	+	0.428068i	−0.192362	+	0.981324i	$0.561615\pi$
$350$	1.05518	−	1.38121i	0.0564017	−	0.0738290i
$351$		−	5.88477i		−	0.314106i
$352$	6.50667	−	19.8601i	0.346806	−	1.05855i
$353$		−	17.3846i		−	0.925289i	−0.886544	−	0.462644i	$-0.846901\pi$
$353$		−	17.3846i		−	0.925289i	0.886544	−	0.462644i	$-0.153099\pi$
$354$	−7.86427	−	6.00791i	−0.417981	−	0.319317i
$355$	−9.84828	−	6.58041i	−0.522693	−	0.349252i
$356$	−11.5748	−	1.47374i	−0.613463	−	0.0781079i
$357$	−16.1270	−	3.20787i	−0.853533	−	0.169778i
$358$	−9.12433	−	26.6926i	−0.482236	−	1.41075i
$359$	6.87485	+	2.84766i	0.362841	+	0.150294i	0.556653	−	0.830745i	$-0.312085\pi$
$359$	6.87485	+	2.84766i	0.362841	+	0.150294i	−0.193812	+	0.981039i	$0.562085\pi$
$360$	5.41919	−	3.67127i	0.285617	−	0.193493i
$361$	18.2129	−	7.54405i	0.958576	−	0.397055i
$362$	13.6145	−	11.9910i	0.715562	−	0.630231i
$363$	1.47160	+	2.20241i	0.0772390	+	0.115596i
$364$	40.5644	−	2.83226i	2.12615	−	0.148451i
$365$	22.5104	−	4.47760i	1.17825	−	0.234368i
$366$	−9.73296	−	16.7754i	−0.508750	−	0.876864i
$367$	14.7935	−	14.7935i	0.772213	−	0.772213i	−0.206280	−	0.978493i	$-0.566136\pi$
$367$	14.7935	−	14.7935i	0.772213	−	0.772213i	0.978493	+	0.206280i	$0.0661359\pi$
$368$	−3.39289	+	4.50054i	−0.176866	+	0.234607i
$369$	−0.853752	−	0.853752i	−0.0444445	−	0.0444445i
$370$	2.33519	−	8.78986i	0.121401	−	0.456963i
$371$	5.42007	+	27.2486i	0.281396	+	1.41467i
$372$	−13.4103	−	4.48859i	−0.695291	−	0.232722i
$373$	−26.2815	+	17.5607i	−1.36080	+	0.909261i	−0.999729	−	0.0232756i	$-0.992590\pi$
$373$	−26.2815	+	17.5607i	−1.36080	+	0.909261i	−0.361076	+	0.932536i	$0.617590\pi$
$374$	1.57346	−	24.8159i	0.0813619	−	1.28320i
$375$	−4.11307	−	9.92983i	−0.212398	−	0.512774i
$376$	3.84631	−	9.45620i	0.198358	−	0.487666i
$377$	−1.93619	+	4.67437i	−0.0997187	+	0.240742i
$378$	−2.15170	+	4.38674i	−0.110672	+	0.225630i
$379$	−5.75679	+	28.9413i	−0.295706	+	1.48662i	0.492016	+	0.870586i	$0.336260\pi$
$379$	−5.75679	+	28.9413i	−0.295706	+	1.48662i	−0.787723	+	0.616030i	$0.788740\pi$
$380$	−7.57201	−	27.7853i	−0.388436	−	1.42536i
$381$	−0.286584	+	0.428903i	−0.0146821	+	0.0219733i
$382$	−6.24589	+	0.835820i	−0.319568	+	0.0427643i
$383$	−35.6425			−1.82124			−0.910622	−	0.413240i	$-0.864397\pi$
$383$	−35.6425			−1.82124			−0.910622	+	0.413240i	$0.864397\pi$
$384$	3.79593	+	10.6579i	0.193710	+	0.543884i
$385$	−29.5392			−1.50546
$386$	−0.661760	+	0.0885562i	−0.0336827	+	0.00450739i
$387$	−6.65231	+	9.95589i	−0.338156	+	0.506086i
$388$	3.94832	+	14.4883i	0.200446	+	0.735531i
$389$	3.66794	−	18.4400i	0.185972	−	0.934944i	−0.769226	−	0.638977i	$-0.779358\pi$
$389$	3.66794	−	18.4400i	0.185972	−	0.934944i	0.955198	−	0.295968i	$-0.0956420\pi$
$390$	−8.48164	+	17.2918i	−0.429485	+	0.875604i
$391$	−2.56628	+	6.19554i	−0.129782	+	0.313322i
$392$	−12.9340	−	5.26091i	−0.653267	−	0.265716i
$393$	−1.90445	−	4.59775i	−0.0960668	−	0.231926i
$394$	0.482067	−	7.60293i	0.0242862	−	0.383030i
$395$	−10.5813	+	7.07023i	−0.532405	+	0.355742i
$396$	−7.00678	−	2.34526i	−0.352104	−	0.117854i
$397$	−2.42523	−	12.1924i	−0.121719	−	0.611921i	−0.992700	−	0.120606i	$-0.961516\pi$
$397$	−2.42523	−	12.1924i	−0.121719	−	0.611921i	0.870982	−	0.491315i	$-0.163484\pi$
$398$	6.01755	−	22.6506i	0.301633	−	1.13537i
$399$	15.2005	+	15.2005i	0.760977	+	0.760977i
$400$	−1.40914	+	0.197740i	−0.0704572	+	0.00988702i
$401$	16.0561	−	16.0561i	0.801805	−	0.801805i	−0.181572	−	0.983378i	$-0.558119\pi$
$401$	16.0561	−	16.0561i	0.801805	−	0.801805i	0.983378	+	0.181572i	$0.0581187\pi$
$402$	−1.95804	−	3.37481i	−0.0976580	−	0.168320i
$403$	40.8104	−	8.11768i	2.03291	−	0.404371i
$404$	−28.5556	+	1.99379i	−1.42069	+	0.0991946i
$405$	−1.28573	−	1.92423i	−0.0638883	−	0.0956155i
$406$	3.15244	−	2.77651i	0.156453	−	0.137796i
$407$	−9.48483	+	3.92875i	−0.470146	+	0.194741i
$408$	7.54998	+	11.1446i	0.373780	+	0.551739i
$409$	−1.31386	−	0.544220i	−0.0649664	−	0.0269100i	0.349964	−	0.936763i	$-0.386194\pi$
$409$	−1.31386	−	0.544220i	−0.0649664	−	0.0269100i	−0.414930	+	0.909853i	$0.636194\pi$
$410$	1.27816	+	3.73916i	0.0631238	+	0.184664i
$411$	−14.7185	−	2.92770i	−0.726012	−	0.144413i
$412$	−9.13557	−	1.16317i	−0.450077	−	0.0573051i
$413$	−20.1028	−	13.4323i	−0.989195	−	0.660959i
$414$	1.58349	+	1.20971i	0.0778242	+	0.0594538i
$415$			21.8708i			1.07359i
$416$	−25.2605	−	21.6815i	−1.23850	−	1.06302i
$417$			10.9267i			0.535083i
$418$	−19.7348	+	25.8326i	−0.965262	+	1.26351i
$419$	24.7591	+	16.5435i	1.20956	+	0.808203i	0.986042	−	0.166496i	$-0.0532453\pi$
$419$	24.7591	+	16.5435i	1.20956	+	0.808203i	0.223520	+	0.974699i	$0.428245\pi$
$420$	12.6451	−	9.78877i	0.617018	−	0.477643i
$421$	−1.82344	−	0.362705i	−0.0888691	−	0.0176772i	0.150455	−	0.988617i	$-0.451926\pi$
$421$	−1.82344	−	0.362705i	−0.0888691	−	0.0176772i	−0.239325	+	0.970940i	$0.576926\pi$
$422$	−9.24843	+	3.16139i	−0.450206	+	0.153894i
$423$	−3.33452	−	1.38120i	−0.162130	−	0.0671564i
$424$	12.5150	−	18.9915i	0.607783	−	0.922310i
$425$	−1.56417	+	0.647901i	−0.0758734	+	0.0314278i
$426$	−4.78393	−	5.43165i	−0.231782	−	0.263164i
$427$	−26.3235	−	39.3959i	−1.27388	−	1.90650i
$428$	−12.8101	−	11.1381i	−0.619202	−	0.538378i
$429$	21.3231	−	4.24143i	1.02949	−	0.204778i
$430$	33.8964	−	19.6664i	1.63463	−	0.948400i
$431$	2.94384	−	2.94384i	0.141800	−	0.141800i	−0.632643	−	0.774443i	$-0.718030\pi$
$431$	2.94384	−	2.94384i	0.141800	−	0.141800i	0.774443	+	0.632643i	$0.218030\pi$
$432$	3.77663	−	1.31797i	0.181703	−	0.0634108i
$433$	19.1379	+	19.1379i	0.919710	+	0.919710i	0.997008	−	0.0772980i	$-0.0246293\pi$
$433$	19.1379	+	19.1379i	0.919710	+	0.919710i	−0.0772980	+	0.997008i	$0.524629\pi$
$434$	−33.3898	−	8.87062i	−1.60276	−	0.425803i
$435$	0.388171	+	1.95147i	0.0186114	+	0.0935657i
$436$	0.222396	−	0.110853i	0.0106508	−	0.00530890i
$437$	7.28959	−	4.87075i	0.348708	−	0.232999i
$438$	13.9973	+	0.887504i	0.668815	+	0.0424066i
$439$	−8.09005	−	19.5311i	−0.386117	−	0.932169i	−0.990754	−	0.135668i	$-0.956682\pi$
$439$	−8.09005	−	19.5311i	−0.386117	−	0.932169i	0.604637	−	0.796501i	$-0.293318\pi$
$440$	17.2085	+	16.9901i	0.820384	+	0.809970i
$441$	−1.88918	+	4.56089i	−0.0899611	+	0.217185i
$442$	−35.5606	−	17.4425i	−1.69145	−	0.829656i
$443$	2.56604	−	12.9004i	0.121916	−	0.612915i	−0.870720	−	0.491780i	$-0.836347\pi$
$443$	2.56604	−	12.9004i	0.121916	−	0.612915i	0.992636	−	0.121135i	$-0.0386534\pi$
$444$	2.75834	−	4.82492i	0.130905	−	0.228981i
$445$	7.50108	−	11.2262i	0.355585	−	0.532171i
$446$	2.01175	+	15.0333i	0.0952589	+	0.711848i
$447$	−12.8415			−0.607380
$448$	10.9026	+	25.3985i	0.515097	+	1.19996i
$449$	−2.46594			−0.116375			−0.0581874	−	0.998306i	$-0.518532\pi$
$449$	−2.46594			−0.116375			−0.0581874	+	0.998306i	$0.518532\pi$
$450$	0.0667281	+	0.498644i	0.00314559	+	0.0235063i
$451$	2.47818	−	3.70886i	0.116693	−	0.174643i
$452$	21.6207	+	12.3603i	1.01695	+	0.581378i
$453$	0.524991	−	2.63931i	0.0246662	−	0.124006i
$454$	14.5693	+	7.14627i	0.683772	+	0.335391i
$455$	−18.0061	+	43.4707i	−0.844141	+	2.03794i
$456$	−0.112407	−	17.5982i	−0.00526394	−	0.824110i
$457$	11.7772	+	28.4327i	0.550915	+	1.33003i	0.916793	+	0.399363i	$0.130769\pi$
$457$	11.7772	+	28.4327i	0.550915	+	1.33003i	−0.365878	+	0.930663i	$0.619231\pi$
$458$	14.3211	+	0.908035i	0.669180	+	0.0424297i
$459$	3.95718	−	2.64410i	0.184705	−	0.123416i
$460$	−2.90938	−	5.83685i	−0.135651	−	0.272145i
$461$	−5.07009	−	25.4891i	−0.236138	−	1.18714i	−0.898845	−	0.438266i	$-0.855593\pi$
$461$	−5.07009	−	25.4891i	−0.236138	−	1.18714i	0.662707	−	0.748878i	$-0.269407\pi$
$462$	−17.4459	−	4.63484i	−0.811659	−	0.215632i
$463$	4.28173	+	4.28173i	0.198989	+	0.198989i	0.799566	−	0.600578i	$-0.205063\pi$
$463$	4.28173	+	4.28173i	0.198989	+	0.198989i	−0.600578	+	0.799566i	$0.705063\pi$
$464$	−3.43347	−	0.195691i	−0.159395	−	0.00908471i
$465$	11.5707	−	11.5707i	0.536581	−	0.536581i
$466$	−30.1950	+	17.5189i	−1.39876	+	0.811549i
$467$	40.5660	−	8.06907i	1.87717	−	0.373392i	0.881973	−	0.471300i	$-0.156215\pi$
$467$	40.5660	−	8.06907i	1.87717	−	0.373392i	0.995195	+	0.0979080i	$0.0312151\pi$
$468$	−7.72245	+	8.88178i	−0.356970	+	0.410560i
$469$	−5.29565	−	7.92550i	−0.244530	−	0.365965i
$470$	7.80742	+	8.86452i	0.360130	+	0.408890i
$471$	−13.1349	+	5.44064i	−0.605222	+	0.250691i
$472$	3.98536	+	19.3877i	0.183441	+	0.892392i
$473$	−40.8692	−	16.9286i	−1.87917	−	0.778377i
$474$	−7.35873	+	2.51544i	−0.337998	+	0.115538i
$475$	2.17088	+	0.431814i	0.0996067	+	0.0198130i
$476$	20.1306	+	26.0047i	0.922686	+	1.19192i
$477$	−6.68612	−	4.46752i	−0.306136	−	0.204554i
$478$	15.0769	−	19.7354i	0.689601	−	0.902678i
$479$		−	8.21353i		−	0.375286i	−0.982237	−	0.187643i	$-0.939915\pi$
$479$		−	8.21353i		−	0.375286i	0.982237	−	0.187643i	$-0.0600847\pi$
$480$	−12.9968	−	1.57050i	−0.593221	−	0.0716831i
$481$			16.3530i			0.745631i
$482$	1.91278	+	1.46127i	0.0871249	+	0.0665591i
$483$	4.04775	+	2.70462i	0.184179	+	0.123064i
$484$	0.669107	−	5.25520i	0.0304139	−	0.238873i
$485$	−17.0422	−	3.38991i	−0.773848	−	0.153928i
$486$	−0.457434	−	1.33819i	−0.0207496	−	0.0607016i
$487$	−13.2943	−	5.50667i	−0.602421	−	0.249531i	0.0605630	−	0.998164i	$-0.480710\pi$
$487$	−13.2943	−	5.50667i	−0.602421	−	0.249531i	−0.662984	+	0.748633i	$0.730710\pi$
$488$	−7.32419	+	38.0911i	−0.331550	+	1.72430i
$489$	9.79508	−	4.05726i	0.442949	−	0.183475i
$490$	12.1247	−	10.6789i	0.547739	−	0.482421i
$491$	2.45884	+	3.67992i	0.110966	+	0.166072i	0.882796	−	0.469757i	$-0.155658\pi$
$491$	2.45884	+	3.67992i	0.110966	+	0.166072i	−0.771830	+	0.635829i	$0.780658\pi$
$492$	0.168193	+	2.40891i	0.00758272	+	0.108602i
$493$	−4.01320	+	0.798275i	−0.180745	+	0.0359525i
$494$	25.9863	+	44.7890i	1.16918	+	2.01515i
$495$	6.04564	−	6.04564i	0.271731	−	0.271731i
$496$	14.3496	+	24.3725i	0.644317	+	1.09436i
$497$	−12.5035	−	12.5035i	−0.560858	−	0.560858i
$498$	−3.43163	+	12.9170i	−0.153775	+	0.578823i
$499$	3.12880	+	15.7296i	0.140064	+	0.704151i	0.985446	+	0.169989i	$0.0543731\pi$
$499$	3.12880	+	15.7296i	0.140064	+	0.704151i	−0.845382	+	0.534163i	$0.820627\pi$
$500$	−6.82290	+	20.3844i	−0.305130	+	0.911618i
$501$	7.64614	−	5.10899i	0.341604	−	0.228253i
$502$	−2.01797	+	31.8264i	−0.0900664	+	1.42048i
$503$	−13.7964	−	33.3074i	−0.615150	−	1.48510i	−0.857275	−	0.514858i	$-0.827844\pi$
$503$	−13.7964	−	33.3074i	−0.615150	−	1.48510i	0.242125	−	0.970245i	$-0.422156\pi$
$504$	9.00415	−	3.79720i	0.401077	−	0.169141i
$505$	12.6756	−	30.6015i	0.564055	−	1.36175i
$506$	−3.24200	+	6.60957i	−0.144125	+	0.293831i
$507$	4.21991	−	21.2149i	0.187413	−	0.942188i
$508$	0.995374	−	0.271258i	0.0441626	−	0.0120351i
$509$	−17.2592	+	25.8302i	−0.765001	+	1.14491i	0.220525	+	0.975381i	$0.429223\pi$
$509$	−17.2592	+	25.8302i	−0.765001	+	1.14491i	−0.985526	+	0.169524i	$0.945777\pi$
$510$	−15.4387	+	2.06599i	−0.683635	+	0.0914835i
$511$	34.2642			1.51576
$512$	8.25699	−	21.0671i	0.364911	−	0.931042i
$513$	−6.22202			−0.274709
$514$	22.8139	−	3.05294i	1.00628	−	0.134659i
$515$	5.92034	−	8.86041i	0.260881	−	0.390436i
$516$	23.1051	−	6.29656i	1.01714	−	0.277191i
$517$	2.60136	−	13.0779i	0.114408	−	0.575167i
$518$	5.97929	−	12.1902i	0.262715	−	0.535605i
$519$	5.81929	−	14.0490i	0.255438	−	0.616683i
$520$	35.4928	−	14.9679i	1.55646	−	0.656386i
$521$	−7.54819	−	18.2229i	−0.330692	−	0.798362i	−0.998538	−	0.0540616i	$-0.982783\pi$
$521$	−7.54819	−	18.2229i	−0.330692	−	0.798362i	0.667845	−	0.744300i	$-0.267217\pi$
$522$	−0.0769393	+	1.21345i	−0.00336754	+	0.0531112i
$523$	−17.0859	+	11.4164i	−0.747114	+	0.499206i	−0.869900	−	0.493228i	$-0.835817\pi$
$523$	−17.0859	+	11.4164i	−0.747114	+	0.499206i	0.122786	+	0.992433i	$0.460817\pi$
$524$	−3.15917	+	9.43846i	−0.138009	+	0.412321i
$525$	0.239777	+	1.20544i	0.0104647	+	0.0526097i
$526$	1.73222	−	6.52021i	0.0755282	−	0.284295i
$527$	23.7953	+	23.7953i	1.03654	+	1.03654i
$528$	7.49758	+	12.7345i	0.326290	+	0.554198i
$529$	−14.8596	+	14.8596i	−0.646068	+	0.646068i
$530$	13.2075	+	22.7640i	0.573696	+	0.988803i
$531$	6.86345	−	1.36523i	0.297849	−	0.0592458i
$532$	−2.99457	−	42.8891i	−0.129831	−	1.85948i
$533$	−3.94744	−	5.90776i	−0.170982	−	0.255893i
$534$	6.19160	−	5.45325i	0.267937	−	0.235985i
$535$	18.1472	−	7.51681i	0.784571	−	0.324980i
$536$	−1.47345	+	7.66302i	−0.0636433	+	0.330992i
$537$	18.4284	+	7.63330i	0.795245	+	0.329401i
$538$	−6.79194	−	19.8693i	−0.292821	−	0.856628i
$539$	−17.8878	−	3.55810i	−0.770480	−	0.153258i
$540$	−0.584594	+	4.59143i	−0.0251569	+	0.197584i
$541$	36.8870	+	24.6471i	1.58590	+	1.05966i	0.960092	+	0.279683i	$0.0902295\pi$
$541$	36.8870	+	24.6471i	1.58590	+	1.05966i	0.625805	+	0.779979i	$0.284771\pi$
$542$	−22.6475	−	17.3016i	−0.972795	−	0.743167i
$543$			12.8284i			0.550521i
$544$	3.22973	−	26.7280i	0.138474	−	1.14595i
$545$			0.287536i			0.0123167i
$546$	−17.4552	+	22.8487i	−0.747015	+	0.977833i
$547$	−13.0787	−	8.73891i	−0.559205	−	0.373649i	0.243614	−	0.969872i	$-0.421667\pi$
$547$	−13.0787	−	8.73891i	−0.559205	−	0.373649i	−0.802818	+	0.596224i	$0.796667\pi$
$548$	18.3725	+	23.7335i	0.784833	+	1.01385i
$549$	13.4504	+	2.67546i	0.574051	+	0.114186i
$550$	−1.75871	+	0.601182i	−0.0749918	+	0.0256345i
$551$	4.94225	+	2.04715i	0.210547	+	0.0872114i
$552$	−0.802461	−	3.90376i	−0.0341550	−	0.166155i
$553$	−17.5526	+	7.27053i	−0.746413	+	0.309175i
$554$	−6.53101	−	7.41528i	−0.277476	−	0.315045i
$555$	3.57286	+	5.34716i	0.151659	+	0.226974i
$556$	14.3389	−	16.4915i	0.608103	−	0.699394i
$557$	−16.7219	+	3.32619i	−0.708530	+	0.140935i	−0.536184	−	0.844101i	$-0.680135\pi$
$557$	−16.7219	+	3.32619i	−0.708530	+	0.140935i	−0.172346	+	0.985036i	$0.555135\pi$
$558$	8.64923	−	5.01822i	0.366151	−	0.212438i
$559$	−49.8251	+	49.8251i	−2.10738	+	2.10738i
$560$	−31.9306	−	1.81988i	−1.34931	−	0.0769041i
$561$	12.4329	+	12.4329i	0.524916	+	0.524916i
$562$	29.6626	+	7.88042i	1.25124	+	0.332416i
$563$	−5.10059	−	25.6424i	−0.214964	−	1.08070i	−0.925994	−	0.377537i	$-0.876771\pi$
$563$	−5.10059	−	25.6424i	−0.214964	−	1.08070i	0.711030	−	0.703161i	$-0.248229\pi$
$564$	3.22021	+	6.46043i	0.135595	+	0.272033i
$565$	−23.9609	+	16.0101i	−1.00804	+	0.673552i
$566$	15.2930	+	0.969660i	0.642812	+	0.0407578i
$567$	−1.32215	−	3.19196i	−0.0555252	−	0.134050i
$568$	0.0924627	+	14.4757i	0.00387965	+	0.607388i
$569$	−15.8821	+	38.3428i	−0.665813	+	1.60741i	0.122735	+	0.992440i	$0.460834\pi$
$569$	−15.8821	+	38.3428i	−0.665813	+	1.60741i	−0.788547	+	0.614974i	$0.789166\pi$
$570$	18.2828	+	8.96772i	0.765780	+	0.375616i
$571$	−6.01686	+	30.2488i	−0.251798	+	1.26587i	0.623321	+	0.781966i	$0.285783\pi$
$571$	−6.01686	+	30.2488i	−0.251798	+	1.26587i	−0.875119	+	0.483907i	$0.839217\pi$
$572$	−37.7485	−	21.5803i	−1.57835	−	0.902319i
$573$	2.47556	−	3.70493i	0.103418	−	0.154776i
$574$	0.782469	+	5.84722i	0.0326596	+	0.244058i
$575$	0.501251			0.0209036
$576$	−7.42954	−	2.96680i	−0.309564	−	0.123617i
$577$	0.352285			0.0146658			0.00733290	−	0.999973i	$-0.497666\pi$
$577$	0.352285			0.0146658			0.00733290	+	0.999973i	$0.497666\pi$
$578$	−1.05990	−	7.92042i	−0.0440862	−	0.329446i
$579$	0.262288	−	0.392542i	0.0109003	−	0.0163135i
$580$	1.97501	−	3.45470i	0.0820077	−	0.143449i
$581$	−6.36990	+	32.0236i	−0.264268	+	1.32856i
$582$	−9.53330	−	4.67610i	−0.395168	−	0.193831i
$583$	11.3688	−	27.4467i	0.470848	−	1.13673i
$584$	−19.9612	−	19.7078i	−0.825999	−	0.815514i
$585$	−5.21169	−	12.5821i	−0.215477	−	0.520208i
$586$	38.8405	+	2.46270i	1.60448	+	0.101733i
$587$	−30.7050	+	20.5164i	−1.26733	+	0.846803i	−0.993373	−	0.114938i	$-0.963333\pi$
$587$	−30.7050	+	20.5164i	−1.26733	+	0.846803i	−0.273958	+	0.961742i	$0.588333\pi$
$588$	8.83646	−	4.40454i	0.364410	−	0.181640i
$589$	−8.58290	−	43.1491i	−0.353652	−	1.77793i
$590$	−22.1352	−	5.88063i	−0.911293	−	0.242102i
$591$	3.80910	+	3.80910i	0.156685	+	0.156685i
$592$	−10.4947	+	3.66245i	−0.431331	+	0.150526i
$593$	30.0419	−	30.0419i	1.23367	−	1.23367i	0.271129	−	0.962543i	$-0.412603\pi$
$593$	30.0419	−	30.0419i	1.23367	−	1.23367i	0.962543	−	0.271129i	$-0.0873968\pi$
$594$	4.51916	−	2.62198i	0.185423	−	0.107581i
$595$	−37.3219	+	7.42380i	−1.53005	+	0.304346i
$596$	19.3814	+	16.8515i	0.793892	+	0.690266i
$597$	9.20690	+	13.7791i	0.376813	+	0.563941i
$598$	7.75060	+	8.79999i	0.316945	+	0.359859i
$599$	11.5871	−	4.79955i	0.473438	−	0.196104i	−0.133190	−	0.991091i	$-0.542522\pi$
$599$	11.5871	−	4.79955i	0.473438	−	0.196104i	0.606627	+	0.794986i	$0.292522\pi$
$600$	0.553648	−	0.840160i	0.0226026	−	0.0342994i
$601$	−10.0324	−	4.15555i	−0.409229	−	0.169508i	0.168565	−	0.985690i	$-0.446087\pi$
$601$	−10.0324	−	4.15555i	−0.409229	−	0.169508i	−0.577795	+	0.816182i	$0.696087\pi$
$602$	55.3596	−	18.9236i	2.25629	−	0.771269i
$603$	2.70590	+	0.538238i	0.110193	+	0.0219187i
$604$	−4.25586	+	3.29453i	−0.173169	+	0.134052i
$605$	5.09691	+	3.40565i	0.207219	+	0.138459i
$606$	12.2877	−	16.0845i	0.499155	−	0.653388i
$607$		−	24.6081i		−	0.998812i	−0.866368	−	0.499406i	$-0.833552\pi$
$607$		−	24.6081i		−	0.998812i	0.866368	−	0.499406i	$-0.166448\pi$
$608$	−22.9240	+	26.7081i	−0.929692	+	1.08316i
$609$			2.97043i			0.120368i
$610$	−35.6666	−	27.2475i	−1.44410	−	1.10322i
$611$	−17.6601	−	11.8001i	−0.714452	−	0.477382i
$612$	−9.44228	−	1.20222i	−0.381682	−	0.0485968i
$613$	−0.834280	−	0.165949i	−0.0336962	−	0.00670260i	0.178213	−	0.983992i	$-0.442968\pi$
$613$	−0.834280	−	0.165949i	−0.0336962	−	0.00670260i	−0.211910	+	0.977289i	$0.567968\pi$
$614$	2.54229	+	7.43729i	0.102599	+	0.300145i
$615$	−2.58150	−	1.06929i	−0.104096	−	0.0431180i
$616$	20.2487	+	29.8892i	0.815841	+	1.20427i
$617$	23.9216	−	9.90863i	0.963045	−	0.398907i	0.154927	−	0.987926i	$-0.450486\pi$
$617$	23.9216	−	9.90863i	0.963045	−	0.398907i	0.808119	+	0.589019i	$0.200486\pi$
$618$	4.88681	−	4.30406i	0.196576	−	0.173135i
$619$	−8.84037	−	13.2305i	−0.355324	−	0.531781i	0.610147	−	0.792288i	$-0.291110\pi$
$619$	−8.84037	−	13.2305i	−0.355324	−	0.531781i	−0.965472	+	0.260507i	$0.916110\pi$
$620$	−32.6475	+	2.27949i	−1.31116	+	0.0915465i
$621$	−1.38197	+	0.274891i	−0.0554566	+	0.0110310i
$622$	6.50176	+	11.2062i	0.260697	+	0.449328i
$623$	14.2529	−	14.2529i	0.571029	−	0.571029i
$624$	23.3107	−	3.27111i	0.933175	−	0.130949i
$625$	−18.8459	−	18.8459i	−0.753836	−	0.753836i
$626$	12.4662	−	46.9240i	0.498251	−	1.87546i
$627$	−4.48451	−	22.5451i	−0.179094	−	0.900366i
$628$	26.9638	+	9.02512i	1.07597	+	0.360141i
$629$	−10.9964	+	7.34759i	−0.438457	+	0.292968i
$630$	−0.715520	+	11.2848i	−0.0285070	+	0.449598i
$631$	−15.9425	−	38.4885i	−0.634660	−	1.53220i	−0.833703	−	0.552213i	$-0.813783\pi$
$631$	−15.9425	−	38.4885i	−0.634660	−	1.53220i	0.199043	−	0.979991i	$-0.436217\pi$
$632$	14.4073	+	5.86019i	0.573093	+	0.233106i
$633$	2.64478	−	6.38506i	0.105121	−	0.253784i
$634$	4.68975	−	9.56115i	0.186254	−	0.379722i
$635$	−0.232894	+	1.17084i	−0.00924210	+	0.0464632i
$636$	4.22861	+	15.5168i	0.167675	+	0.615281i
$637$	−16.1400	+	24.1552i	−0.639490	+	0.957064i
$638$	−4.45232	+	0.595805i	−0.176269	+	0.0235881i
$639$	5.11805			0.202467
$640$	17.5549	+	19.4257i	0.693919	+	0.767870i
$641$	14.3263			0.565854			0.282927	−	0.959141i	$-0.408695\pi$
$641$	14.3263			0.565854			0.282927	+	0.959141i	$0.408695\pi$
$642$	11.8972	−	1.59207i	0.469545	−	0.0628341i
$643$	0.592690	−	0.887023i	0.0233734	−	0.0349808i	−0.819599	−	0.572938i	$-0.805804\pi$
$643$	0.592690	−	0.887023i	0.0233734	−	0.0349808i	0.842972	+	0.537957i	$0.180804\pi$
$644$	−2.55998	−	9.39379i	−0.100877	−	0.370167i
$645$	−5.40604	+	27.1780i	−0.212862	+	1.07013i
$646$	−18.4421	+	37.5985i	−0.725596	+	1.47929i
$647$	3.57694	−	8.63549i	0.140624	−	0.339496i	−0.837839	−	0.545917i	$-0.816181\pi$
$647$	3.57694	−	8.63549i	0.140624	−	0.339496i	0.978463	+	0.206421i	$0.0661815\pi$
$648$	−1.06568	+	2.61999i	−0.0418638	+	0.102923i
$649$	9.89364	+	23.8853i	0.388359	+	0.937582i
$650$	−0.187340	+	2.95463i	−0.00734807	+	0.115890i
$651$	20.3121	−	13.5721i	0.796094	−	0.531933i
$652$	−20.1078	−	6.73032i	−0.787481	−	0.263580i
$653$	4.19559	+	21.0926i	0.164186	+	0.825418i	0.971818	+	0.235732i	$0.0757487\pi$
$653$	4.19559	+	21.0926i	0.164186	+	0.825418i	−0.807632	+	0.589687i	$0.799251\pi$
$654$	−0.0451157	+	0.169820i	−0.00176416	+	0.00664047i
$655$	−8.14375	−	8.14375i	−0.318203	−	0.318203i
$656$	2.90731	−	3.85644i	0.113511	−	0.150569i
$657$	−7.01269	+	7.01269i	−0.273591	+	0.273591i
$658$	8.84997	+	15.2535i	0.345008	+	0.594644i
$659$	40.9056	−	8.13663i	1.59346	−	0.316958i	0.682954	−	0.730461i	$-0.260695\pi$
$659$	40.9056	−	8.13663i	1.59346	−	0.316958i	0.910503	+	0.413503i	$0.135695\pi$
$660$	−17.0581	+	1.19102i	−0.663986	+	0.0463603i
$661$	9.37446	+	14.0299i	0.364624	+	0.545699i	0.967739	−	0.251956i	$-0.0810738\pi$
$661$	9.37446	+	14.0299i	0.364624	+	0.545699i	−0.603115	+	0.797655i	$0.706074\pi$
$662$	−5.99158	+	5.27709i	−0.232869	+	0.205100i
$663$	25.8752	−	10.7179i	1.00491	−	0.416247i
$664$	22.1299	−	14.9921i	0.858808	−	0.581806i
$665$	45.9619	+	19.0380i	1.78233	+	0.738264i
$666$	1.27115	+	3.71865i	0.0492559	+	0.144095i
$667$	1.18817	+	0.236341i	0.0460059	+	0.00915115i
$668$	−18.2446	−	2.32295i	−0.705904	−	0.0898777i
$669$	−8.91744	−	5.95844i	−0.344768	−	0.230367i
$670$	−7.17526	−	5.48154i	−0.277204	−	0.211770i
$671$			50.6652i			1.95591i
$672$	−18.5728	−	6.08489i	−0.716460	−	0.234730i
$673$		−	18.1142i		−	0.698252i	−0.937076	−	0.349126i	$-0.886479\pi$
$673$		−	18.1142i		−	0.698252i	0.937076	−	0.349126i	$-0.113521\pi$
$674$	−15.2087	+	19.9080i	−0.585817	+	0.766826i
$675$	−0.295785	−	0.197637i	−0.0113848	−	0.00760706i
$676$	−34.2089	+	26.4816i	−1.31573	+	1.01852i
$677$	−27.9204	−	5.55371i	−1.07307	−	0.213446i	−0.373223	−	0.927742i	$-0.621747\pi$
$677$	−27.9204	−	5.55371i	−1.07307	−	0.213446i	−0.699844	+	0.714295i	$0.746747\pi$
$678$	−16.6634	+	5.69607i	−0.639955	+	0.218756i
$679$	−23.9662	−	9.92714i	−0.919740	−	0.380969i
$680$	26.0124	+	17.1416i	0.997531	+	0.657352i
$681$	−10.6012	+	4.39115i	−0.406238	+	0.168269i
$682$	24.4171	+	27.7231i	0.934980	+	1.06157i
$683$	12.4235	+	18.5931i	0.475373	+	0.711446i	0.989220	−	0.146436i	$-0.0467802\pi$
$683$	12.4235	+	18.5931i	0.475373	+	0.711446i	−0.513847	+	0.857882i	$0.671780\pi$
$684$	9.39078	+	8.16501i	0.359065	+	0.312197i
$685$	−34.0623	+	6.77542i	−1.30145	+	0.258875i
$686$	−8.72006	+	5.05932i	−0.332934	+	0.193166i
$687$	−7.17492	+	7.17492i	−0.273740	+	0.273740i
$688$	−43.1349	−	20.8170i	−1.64450	−	0.793640i
$689$	−33.4613	−	33.4613i	−1.27477	−	1.27477i
$690$	4.45698	+	1.18408i	0.169674	+	0.0450771i
$691$	3.90469	+	19.6302i	0.148541	+	0.746768i	0.981202	+	0.192984i	$0.0618166\pi$
$691$	3.90469	+	19.6302i	0.148541	+	0.746768i	−0.832660	+	0.553784i	$0.813183\pi$
$692$	−27.2191	+	13.5674i	−1.03472	+	0.515755i
$693$	10.6129	−	7.09134i	0.403152	−	0.269378i
$694$	29.1656	+	1.84926i	1.10711	+	0.0701970i
$695$	9.67695	+	23.3622i	0.367068	+	0.886180i
$696$	1.70850	−	1.73047i	0.0647607	−	0.0655933i
$697$	2.19900	−	5.30885i	0.0832931	−	0.201087i
$698$	18.2763	+	8.96453i	0.691767	+	0.339313i
$699$	4.81572	−	24.2102i	0.182147	−	0.915716i
$700$	1.21998	−	2.13400i	0.0461109	−	0.0806577i
$701$	21.8170	−	32.6514i	0.824016	−	1.23323i	−0.145781	−	0.989317i	$-0.546570\pi$
$701$	21.8170	−	32.6514i	0.824016	−	1.23323i	0.969798	−	0.243911i	$-0.0784305\pi$
$702$	−1.10385	−	8.24879i	−0.0416620	−	0.311331i
$703$	17.2901			0.652110
$704$	5.39521	−	29.0588i	0.203340	−	1.09520i
$705$	−8.35271			−0.314581
$706$	−3.26095	−	24.3683i	−0.122727	−	0.917114i
$707$	27.4725	−	41.1155i	1.03321	−	1.54631i
$708$	−12.1504	−	6.94624i	−0.456641	−	0.261056i
$709$	−5.68241	+	28.5674i	−0.213407	+	1.07287i	0.714379	+	0.699759i	$0.246709\pi$
$709$	−5.68241	+	28.5674i	−0.213407	+	1.07287i	−0.927786	+	0.373112i	$0.878291\pi$
$710$	−15.0389	−	7.37658i	−0.564398	−	0.276838i
$711$	2.10438	−	5.08043i	0.0789205	−	0.190531i
$712$	−16.5010	+	0.105399i	−0.618403	+	0.00395000i
$713$	−3.81269	−	9.20465i	−0.142786	−	0.344717i
$714$	−23.2073	−	1.47147i	−0.868511	−	0.0550684i
$715$	41.8344	−	27.9528i	1.56452	−	1.04538i
$716$	−17.7967	−	35.7040i	−0.665092	−	1.33432i
$717$	3.42604	+	17.2239i	0.127948	+	0.643238i
$718$	10.1708	+	2.70205i	0.379570	+	0.100840i
$719$	7.40527	+	7.40527i	0.276170	+	0.276170i	0.831578	−	0.555408i	$-0.187438\pi$
$719$	7.40527	+	7.40527i	0.276170	+	0.276170i	−0.555408	+	0.831578i	$0.687438\pi$
$720$	6.90754	−	6.16261i	0.257429	−	0.229667i
$721$	11.2493	−	11.2493i	0.418945	−	0.418945i
$722$	24.1143	−	13.9910i	0.897442	−	0.520689i
$723$	−1.66936	+	0.332057i	−0.0620842	+	0.0123493i
$724$	16.8345	−	19.3617i	0.625648	−	0.719573i
$725$	0.169921	+	0.254305i	0.00631070	+	0.00944463i
$726$	2.47589	+	2.81111i	0.0918889	+	0.104330i
$727$	2.43229	−	1.00749i	0.0902085	−	0.0373656i	−0.337123	−	0.941461i	$-0.609454\pi$
$727$	2.43229	−	1.00749i	0.0902085	−	0.0373656i	0.427331	+	0.904095i	$0.359454\pi$
$728$	56.3286	−	11.5790i	2.08768	−	0.429145i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	30.7133	−	10.4988i	1.13675	−	0.388576i
$731$	−55.8916	−	11.1175i	−2.06723	−	0.411197i
$732$	−16.7895	−	21.6887i	−0.620560	−	0.801638i
$733$	−27.3080	−	18.2466i	−1.00864	−	0.673953i	−0.0626144	−	0.998038i	$-0.519944\pi$
$733$	−27.3080	−	18.2466i	−1.00864	−	0.673953i	−0.946028	+	0.324084i	$0.894944\pi$
$734$	17.9614	−	23.5112i	0.662966	−	0.867814i
$735$			11.4247i			0.421406i
$736$	−3.91167	+	6.94492i	−0.144186	+	0.255993i
$737$			10.1926i			0.375450i
$738$	−1.35686	−	1.03658i	−0.0499468	−	0.0381569i
$739$	23.4909	+	15.6961i	0.864125	+	0.577390i	0.906735	−	0.421702i	$-0.138567\pi$
$739$	23.4909	+	15.6961i	0.864125	+	0.577390i	−0.0426092	+	0.999092i	$0.513567\pi$
$740$	1.62451	−	12.7589i	0.0597180	−	0.469028i
$741$	−35.9116	−	7.14327i	−1.31925	−	0.262414i
$742$	12.7086	+	37.1781i	0.466548	+	1.36485i
$743$	19.6614	+	8.14402i	0.721307	+	0.298775i	0.712974	−	0.701190i	$-0.247348\pi$
$743$	19.6614	+	8.14402i	0.721307	+	0.298775i	0.00833248	+	0.999965i	$0.497348\pi$
$744$	−19.6394	−	3.77628i	−0.720016	−	0.138445i
$745$	−27.4561	+	11.3727i	−1.00592	+	0.416664i
$746$	−33.5453	+	29.5450i	−1.22818	+	1.08172i
$747$	−5.25042	−	7.85781i	−0.192103	−	0.287502i
$748$	−2.44933	−	35.0801i	−0.0895565	−	1.28265i
$749$	28.7607	−	5.72086i	1.05089	−	0.209036i
$750$	−7.62797	−	13.1473i	−0.278534	−	0.480072i
$751$	−12.0919	+	12.0919i	−0.441238	+	0.441238i	−0.892428	−	0.451190i	$-0.851000\pi$
$751$	−12.0919	+	12.0919i	−0.441238	+	0.441238i	0.451190	+	0.892428i	$0.351000\pi$
$752$	3.61768	−	13.9764i	0.131923	−	0.509667i
$753$	−15.9452	−	15.9452i	−0.581074	−	0.581074i
$754$	−1.83719	+	6.91533i	−0.0669063	+	0.251841i
$755$	−1.21496	−	6.10801i	−0.0442169	−	0.222293i
$756$	−2.19323	+	6.55259i	−0.0797671	+	0.238315i
$757$	−24.2442	+	16.1995i	−0.881171	+	0.588779i	−0.911747	−	0.410753i	$-0.865266\pi$
$757$	−24.2442	+	16.1995i	−0.881171	+	0.588779i	0.0305760	+	0.999532i	$0.490266\pi$
$758$	−2.64068	+	41.6474i	−0.0959137	+	1.51270i
$759$	−1.99210	−	4.80937i	−0.0723088	−	0.174569i
$760$	−15.8257	−	37.5268i	−0.574058	−	1.36124i
$761$	0.510974	−	1.23360i	0.0185228	−	0.0447180i	−0.914348	−	0.404930i	$-0.867296\pi$
$761$	0.510974	−	1.23360i	0.0185228	−	0.0447180i	0.932870	+	0.360212i	$0.117296\pi$
$762$	−0.321257	+	0.654957i	−0.0116379	+	0.0237266i
$763$	−0.0837452	+	0.421015i	−0.00303178	+	0.0152418i
$764$	−8.59821	+	2.34317i	−0.311072	+	0.0847729i
$765$	6.11910	−	9.15788i	0.221237	−	0.331104i
$766$	−49.9607	+	6.68570i	−1.80515	+	0.241564i
$767$	41.1812			1.48697
$768$	7.32000	+	14.2274i	0.264138	+	0.513385i
$769$	5.98874			0.215959			0.107980	−	0.994153i	$-0.465562\pi$
$769$	5.98874			0.215959			0.107980	+	0.994153i	$0.465562\pi$
$770$	−41.4056	+	5.54087i	−1.49216	+	0.199679i
$771$	−9.04229	+	13.5327i	−0.325650	+	0.487370i
$772$	−0.910991	+	0.248262i	−0.0327873	+	0.00893514i
$773$	−5.43505	+	27.3239i	−0.195485	+	0.982771i	0.751068	+	0.660224i	$0.229539\pi$
$773$	−5.43505	+	27.3239i	−0.195485	+	0.982771i	−0.946554	+	0.322546i	$0.895461\pi$
$774$	−7.45717	+	15.2032i	−0.268043	+	0.546467i
$775$	0.962579	−	2.32387i	0.0345769	−	0.0834759i
$776$	8.25210	+	19.5679i	0.296233	+	0.702446i
$777$	3.67408	+	8.87001i	0.131807	+	0.318210i
$778$	1.68251	−	26.5357i	0.0603209	−	0.951351i
$779$	−6.24632	+	4.17366i	−0.223798	+	0.149537i
$780$	−8.64534	+	25.8292i	−0.309553	+	0.924833i
$781$	3.68882	+	18.5450i	0.131996	+	0.663591i
$782$	−2.43506	+	9.16578i	−0.0870776	+	0.327768i
$783$	−0.607943	−	0.607943i	−0.0217261	−	0.0217261i
$784$	−19.1167	−	4.94820i	−0.682739	−	0.176721i
$785$	−23.2651	+	23.2651i	−0.830367	+	0.830367i
$786$	−3.53193	−	6.08752i	−0.125980	−	0.217135i
$787$	−31.2656	+	6.21911i	−1.11450	+	0.221687i	−0.717792	−	0.696258i	$-0.754847\pi$
$787$	−31.2656	+	6.21911i	−1.11450	+	0.221687i	−0.396706	+	0.917946i	$0.629847\pi$
$788$	−0.750410	−	10.7476i	−0.0267322	−	0.382867i
$789$	2.65030	+	3.96646i	0.0943532	+	0.141210i
$790$	−13.5059	+	11.8953i	−0.480517	+	0.423215i
$791$	−39.7469	+	16.4637i	−1.41324	+	0.585382i
$792$	−10.2615	−	1.97308i	−0.364625	−	0.0701103i
$793$	74.5603	+	30.8839i	2.64771	+	1.09672i
$794$	−5.68651	−	16.6355i	−0.201807	−	0.590370i
$795$	−18.2520	−	3.63056i	−0.647333	−	0.128763i
$796$	4.18619	−	32.8785i	0.148375	−	1.16535i
$797$	12.0808	+	8.07213i	0.427924	+	0.285929i	0.750822	−	0.660504i	$-0.229657\pi$
$797$	12.0808	+	8.07213i	0.427924	+	0.285929i	−0.322899	+	0.946433i	$0.604657\pi$
$798$	24.1581	+	18.4556i	0.855187	+	0.653320i
$799$		−	17.1774i		−	0.607692i
$800$	−1.93813	+	0.541499i	−0.0685233	+	0.0191449i
$801$			5.83412i			0.206138i
$802$	19.4944	−	25.5179i	0.688372	−	0.901070i
$803$	−30.4644	−	20.3557i	−1.07507	−	0.718337i
$804$	−3.37765	−	4.36325i	−0.119121	−	0.153880i
$805$	11.0497	+	2.19792i	0.389451	+	0.0774666i
$806$	55.6819	−	19.0338i	1.96131	−	0.670436i
$807$	13.7177	+	5.68205i	0.482885	+	0.200018i
$808$	−39.6529	+	8.15110i	−1.39499	+	0.286755i
$809$	−14.8890	+	6.16722i	−0.523469	+	0.216828i	−0.628740	−	0.777616i	$-0.716429\pi$
$809$	−14.8890	+	6.16722i	−0.523469	+	0.216828i	0.105271	+	0.994444i	$0.466429\pi$
$810$	−2.16317	−	2.45605i	−0.0760059	−	0.0862968i
$811$	−9.74149	−	14.5792i	−0.342070	−	0.511944i	0.620053	−	0.784560i	$-0.287111\pi$
$811$	−9.74149	−	14.5792i	−0.342070	−	0.511944i	−0.962123	+	0.272616i	$0.912111\pi$
$812$	3.89803	−	4.48322i	0.136794	−	0.157330i
$813$	19.7654	−	3.93158i	0.693203	−	0.137887i
$814$	−12.5581	+	7.28613i	−0.440162	+	0.255379i
$815$	17.3495	−	17.3495i	0.607727	−	0.607727i
$816$	12.6734	+	14.2054i	0.443658	+	0.497288i
$817$	52.6805	+	52.6805i	1.84306	+	1.84306i
$818$	−1.94375	−	0.516393i	−0.0679616	−	0.0180553i
$819$	−3.96650	−	19.9409i	−0.138601	−	0.696792i
$820$	2.49300	+	5.00150i	0.0870593	+	0.174660i
$821$	21.2733	−	14.2144i	0.742445	−	0.496086i	−0.125903	−	0.992043i	$-0.540183\pi$
$821$	21.2733	−	14.2144i	0.742445	−	0.496086i	0.868347	+	0.495957i	$0.165183\pi$
$822$	−21.1804	−	1.34295i	−0.738752	−	0.0468409i
$823$	16.5222	+	39.8881i	0.575927	+	1.39041i	0.896440	+	0.443166i	$0.146145\pi$
$823$	16.5222	+	39.8881i	0.575927	+	1.39041i	−0.320513	+	0.947244i	$0.603855\pi$
$824$	−13.0237	+	0.0831879i	−0.453702	+	0.00289799i
$825$	0.502941	−	1.21421i	0.0175102	−	0.0422733i
$826$	−30.6981	−	15.0574i	−1.06812	−	0.523916i
$827$	1.45604	−	7.31999i	0.0506313	−	0.254541i	−0.947177	−	0.320711i	$-0.896078\pi$
$827$	1.45604	−	7.31999i	0.0506313	−	0.254541i	0.997808	+	0.0661703i	$0.0210781\pi$
$828$	2.44652	+	1.39864i	0.0850223	+	0.0486061i
$829$	21.2991	−	31.8763i	0.739747	−	1.10711i	−0.250544	−	0.968105i	$-0.580610\pi$
$829$	21.2991	−	31.8763i	0.739747	−	1.10711i	0.990292	−	0.139005i	$-0.0443905\pi$
$830$	4.10245	+	30.6567i	0.142398	+	1.06411i
$831$	6.98715			0.242381
$832$	−39.4750	−	25.6531i	−1.36855	−	0.889360i
$833$	−23.4949			−0.814050
$834$	2.04960	+	15.3162i	0.0709717	+	0.530355i
$835$	11.8235	−	17.6950i	0.409168	−	0.612362i
$836$	−22.8171	+	39.9119i	−0.789145	+	1.38038i
$837$	−1.37944	+	6.93491i	−0.0476804	+	0.239706i
$838$	37.8085	+	18.5451i	1.30607	+	0.640630i
$839$	10.4256	−	25.1696i	0.359931	−	0.868951i	−0.635378	−	0.772202i	$-0.719156\pi$
$839$	10.4256	−	25.1696i	0.359931	−	0.868951i	0.995309	−	0.0967492i	$-0.0308445\pi$
$840$	15.8887	−	16.0930i	0.548214	−	0.555262i
$841$	−10.8149	−	26.1096i	−0.372929	−	0.900331i
$842$	−2.62399	−	0.166375i	−0.0904285	−	0.00573366i
$843$	−18.0447	+	12.0571i	−0.621493	+	0.415269i
$844$	−12.3707	+	6.16617i	−0.425817	+	0.212248i
$845$	−9.76591	−	49.0966i	−0.335958	−	1.68897i
$846$	−4.93314	−	1.31058i	−0.169605	−	0.0450586i
$847$	6.47109	+	6.47109i	0.222349	+	0.222349i
$848$	13.9802	−	28.9683i	0.480081	−	0.994776i
$849$	−7.66185	+	7.66185i	−0.262954	+	0.262954i
$850$	−2.07100	+	1.20158i	−0.0710346	+	0.0412137i
$851$	3.84031	−	0.763885i	0.131644	−	0.0261856i
$852$	−7.72458	−	6.71630i	−0.264640	−	0.230097i
$853$	6.59933	+	9.87659i	0.225957	+	0.338168i	0.927074	−	0.374878i	$-0.122315\pi$
$853$	6.59933	+	9.87659i	0.225957	+	0.338168i	−0.701118	+	0.713046i	$0.747315\pi$
$854$	−44.2878	−	50.2842i	−1.51550	−	1.72069i
$855$	−13.3032	+	5.51037i	−0.454960	+	0.188451i
$856$	−20.0455	−	13.2095i	−0.685140	−	0.451493i
$857$	16.7959	+	6.95709i	0.573737	+	0.237650i	0.650637	−	0.759389i	$-0.274502\pi$
$857$	16.7959	+	6.95709i	0.573737	+	0.237650i	−0.0768995	+	0.997039i	$0.524502\pi$
$858$	29.0934	−	9.94502i	0.993233	−	0.339517i
$859$	−15.8632	−	3.15540i	−0.541247	−	0.107661i	−0.0831068	−	0.996541i	$-0.526484\pi$
$859$	−15.8632	−	3.15540i	−0.541247	−	0.107661i	−0.458140	+	0.888880i	$0.651484\pi$
$860$	43.8243	−	33.9250i	1.49439	−	1.15683i
$861$	−3.46844	−	2.31754i	−0.118204	−	0.0789815i
$862$	3.57424	−	4.67863i	0.121739	−	0.159355i
$863$		−	9.47503i		−	0.322534i	−0.986911	−	0.161267i	$-0.948442\pi$
$863$		−	9.47503i		−	0.322534i	0.986911	−	0.161267i	$-0.0515580\pi$
$864$	5.04656	−	2.55583i	0.171687	−	0.0869511i
$865$		−	35.1917i		−	1.19655i
$866$	30.4158	+	23.2362i	1.03357	+	0.789597i
$867$	4.69822	+	3.13925i	0.159560	+	0.106615i
$868$	−48.4670	−	6.17096i	−1.64508	−	0.209456i
$869$	19.9254	+	3.96340i	0.675922	+	0.134449i
$870$	0.910157	+	2.66260i	0.0308572	+	0.0902705i
$871$	14.9997	+	6.21309i	0.508246	+	0.210523i
$872$	0.290943	−	0.197101i	0.00985256	−	0.00667469i
$873$	6.93678	−	2.87331i	0.234775	−	0.0972468i
$874$	9.30431	−	8.19477i	0.314723	−	0.277192i
$875$	−20.6304	−	30.8755i	−0.697434	−	1.04378i
$876$	19.7867	−	1.38153i	0.668531	−	0.0466776i
$877$	−48.1889	+	9.58538i	−1.62722	+	0.323675i	−0.922557	−	0.385862i	$-0.873904\pi$
$877$	−48.1889	+	9.58538i	−1.62722	+	0.323675i	−0.704668	+	0.709537i	$0.748904\pi$
$878$	−15.0036	−	25.8596i	−0.506346	−	0.872720i
$879$	−19.4592	+	19.4592i	−0.656343	+	0.656343i
$880$	27.3084	+	20.5874i	0.920567	+	0.694001i
$881$	29.7953	+	29.7953i	1.00383	+	1.00383i	0.999993	+	0.00383516i	$0.00122077\pi$
$881$	29.7953	+	29.7953i	1.00383	+	1.00383i	0.00383516	+	0.999993i	$0.498779\pi$
$882$	−1.79259	+	6.74746i	−0.0603595	+	0.227199i
$883$	−0.516501	−	2.59663i	−0.0173817	−	0.0873835i	0.971121	−	0.238588i	$-0.0766847\pi$
$883$	−0.516501	−	2.59663i	−0.0173817	−	0.0873835i	−0.988502	+	0.151205i	$0.951685\pi$
$884$	−53.1178	−	17.7792i	−1.78654	−	0.597978i
$885$	13.4656	−	8.99741i	0.452640	−	0.302445i
$886$	1.17706	−	18.5640i	0.0395441	−	0.623670i
$887$	5.25375	+	12.6837i	0.176403	+	0.425876i	0.987207	−	0.159442i	$-0.0509696\pi$
$887$	5.25375	+	12.6837i	0.176403	+	0.425876i	−0.810804	+	0.585318i	$0.800970\pi$
$888$	2.96138	−	7.28058i	0.0993773	−	0.244320i
$889$	−0.682015	+	1.64653i	−0.0228740	+	0.0552228i
$890$	8.40864	−	17.1429i	0.281858	−	0.574633i
$891$	−0.720747	+	3.62344i	−0.0241459	+	0.121390i
$892$	5.63980	+	20.6951i	0.188835	+	0.692924i
$893$	−12.4764	+	18.6722i	−0.417506	+	0.624841i
$894$	−18.0001	+	2.40876i	−0.602014	+	0.0805610i
$895$	46.1617			1.54302
$896$	20.0465	+	33.5564i	0.669706	+	1.12104i
$897$	−8.29191			−0.276859
$898$	−3.45655	+	0.462552i	−0.115347	+	0.0154356i
$899$	3.37741	−	5.05465i	0.112643	−	0.168582i
$900$	0.187068	+	0.686442i	0.00623560	+	0.0228814i
$901$	7.46625	−	37.5354i	0.248737	−	1.25048i
$902$	2.77802	−	5.66363i	0.0924978	−	0.188578i
$903$	−15.8312	+	38.2200i	−0.526831	+	1.27188i
$904$	32.6246	+	13.2701i	1.08508	+	0.441356i
$905$	11.3612	+	27.4283i	0.377658	+	0.911747i
$906$	0.240817	−	3.79804i	0.00800060	−	0.126182i
$907$	−11.3931	+	7.61262i	−0.378301	+	0.252773i	−0.730154	−	0.683282i	$-0.760552\pi$
$907$	−11.3931	+	7.61262i	−0.378301	+	0.252773i	0.351853	+	0.936055i	$0.385552\pi$
$908$	21.7626	+	7.28420i	0.722216	+	0.241735i
$909$	2.79224	+	14.0376i	0.0926129	+	0.465596i
$910$	−17.0855	+	64.3112i	−0.566377	+	2.13189i
$911$	−0.446767	−	0.446767i	−0.0148021	−	0.0148021i	0.699667	−	0.714469i	$-0.253332\pi$
$911$	−0.446767	−	0.446767i	−0.0148021	−	0.0148021i	−0.714469	+	0.699667i	$0.753332\pi$
$912$	−3.45857	−	24.6466i	−0.114525	−	0.816131i
$913$	24.6881	−	24.6881i	0.817056	−	0.817056i
$914$	21.8416	+	37.6455i	0.722457	+	1.24520i
$915$	31.1276	−	6.19167i	1.02905	−	0.204690i
$916$	20.2444	−	1.41349i	0.668895	−	0.0467031i
$917$	−9.55236	−	14.2961i	−0.315447	−	0.472099i
$918$	5.05088	−	4.44856i	0.166704	−	0.146824i
$919$	13.9255	−	5.76812i	0.459359	−	0.190273i	−0.140990	−	0.990011i	$-0.545028\pi$
$919$	13.9255	−	5.76812i	0.459359	−	0.190273i	0.600349	+	0.799738i	$0.295028\pi$
$920$	−5.17299	−	7.63589i	−0.170548	−	0.251748i
$921$	−5.13466	−	2.12685i	−0.169193	−	0.0700820i
$922$	−11.8880	−	34.7775i	−0.391510	−	1.14534i
$923$	29.5398	+	5.87584i	0.972315	+	0.193406i
$924$	−25.3237	−	3.22429i	−0.833088	−	0.106071i
$925$	0.821946	+	0.549207i	0.0270254	+	0.0180578i
$926$	6.80493	+	5.19862i	0.223624	+	0.170837i
$927$			4.60466i			0.151237i
$928$	−4.84947	+	0.369736i	−0.159192	+	0.0121372i
$929$		−	6.30777i		−	0.206951i	−0.994632	−	0.103476i	$-0.967004\pi$
$929$		−	6.30777i		−	0.206951i	0.994632	−	0.103476i	$-0.0329964\pi$
$930$	14.0485	−	18.3893i	0.460669	−	0.603010i
$931$	25.5395	+	17.0649i	0.837023	+	0.559281i
$932$	−39.0388	+	30.2205i	−1.27876	+	0.989906i
$933$	−8.98508	−	1.78724i	−0.294158	−	0.0585118i
$934$	55.3485	−	18.9198i	1.81106	−	0.619075i
$935$	37.5934	+	15.5717i	1.22943	+	0.509249i
$936$	−9.15869	+	13.8983i	−0.299361	+	0.454280i
$937$	47.9210	−	19.8495i	1.56551	−	0.648455i	0.579474	−	0.814991i	$-0.303258\pi$
$937$	47.9210	−	19.8495i	1.56551	−	0.648455i	0.986035	+	0.166535i	$0.0532580\pi$
$938$	−8.90965	−	10.1160i	−0.290910	−	0.330298i
$939$	19.0734	+	28.5454i	0.622437	+	0.931543i
$940$	12.6066	+	10.9611i	0.411182	+	0.357511i
$941$	−14.7351	+	2.93100i	−0.480352	+	0.0955479i	−0.429326	−	0.903149i	$-0.641249\pi$
$941$	−14.7351	+	2.93100i	−0.480352	+	0.0955479i	−0.0510254	+	0.998697i	$0.516249\pi$
$942$	−17.3908	+	10.0900i	−0.566624	+	0.328751i
$943$	−1.20298	+	1.20298i	−0.0391743	+	0.0391743i
$944$	9.22304	+	26.4286i	0.300184	+	0.860177i
$945$	−5.65375	−	5.65375i	−0.183916	−	0.183916i
$946$	−60.4625	−	16.0630i	−1.96581	−	0.522253i
$947$	−2.61112	−	13.1270i	−0.0848500	−	0.426570i	−0.999739	−	0.0228635i	$-0.992722\pi$
$947$	−2.61112	−	13.1270i	−0.0848500	−	0.426570i	0.914889	−	0.403707i	$-0.132278\pi$
$948$	−9.84303	+	4.90626i	−0.319687	+	0.159348i
$949$	−48.5261	+	32.4241i	−1.57522	+	1.05253i
$950$	3.12396	+	0.198076i	0.101355	+	0.00642644i
$951$	2.88170	+	6.95704i	0.0934456	+	0.225598i
$952$	33.0954	+	32.6752i	1.07263	+	1.05901i
$953$	−17.6374	+	42.5805i	−0.571332	+	1.37932i	0.329090	+	0.944299i	$0.393258\pi$
$953$	−17.6374	+	42.5805i	−0.571332	+	1.37932i	−0.900422	+	0.435018i	$0.856742\pi$
$954$	−10.2101	−	5.00805i	−0.330563	−	0.162142i
$955$	2.01177	−	10.1139i	0.0650995	−	0.327277i
$956$	17.4316	−	30.4916i	0.563780	−	0.986169i
$957$	1.76467	−	2.64102i	0.0570438	−	0.0853720i
$958$	−1.54067	−	11.5131i	−0.0497767	−	0.371970i
$959$	−51.8480			−1.67426
$960$	−18.5125	+	0.236504i	−0.597487	+	0.00763313i
$961$	−18.9958			−0.612768
$962$	3.06744	+	22.9223i	0.0988981	+	0.739043i
$963$	−4.71545	+	7.05717i	−0.151953	+	0.227414i
$964$	2.95529	+	1.68950i	0.0951833	+	0.0544150i
$965$	0.213150	−	1.07158i	0.00686154	−	0.0344953i
$966$	6.18112	+	3.03185i	0.198874	+	0.0975481i
$967$	5.37471	−	12.9757i	0.172839	−	0.417270i	−0.813594	−	0.581433i	$-0.802492\pi$
$967$	5.37471	−	12.9757i	0.172839	−	0.417270i	0.986433	+	0.164163i	$0.0524922\pi$
$968$	−0.0478534	−	7.49181i	−0.00153807	−	0.240796i
$969$	−11.3321	−	27.3581i	−0.364039	−	0.878868i
$970$	−24.5243	−	1.55497i	−0.787427	−	0.0499272i
$971$	31.3078	−	20.9192i	1.00472	−	0.671329i	0.0596527	−	0.998219i	$-0.481001\pi$
$971$	31.3078	−	20.9192i	1.00472	−	0.671329i	0.945062	+	0.326890i	$0.106001\pi$
$972$	−0.892208	−	1.78996i	−0.0286176	−	0.0574131i
$973$	7.36489	+	37.0258i	0.236108	+	1.18699i
$974$	−19.6678	−	5.22511i	−0.630196	−	0.167423i
$975$	−1.48028	−	1.48028i	−0.0474070	−	0.0474070i
$976$	−3.12144	+	54.7669i	−0.0999148	+	1.75305i
$977$	−25.1444	+	25.1444i	−0.804442	+	0.804442i	−0.983786	−	0.179345i	$-0.942602\pi$
$977$	−25.1444	+	25.1444i	−0.804442	+	0.804442i	0.179345	+	0.983786i	$0.442602\pi$
$978$	12.9689	−	7.52446i	0.414700	−	0.240606i
$979$	−21.1396	+	4.20493i	−0.675624	+	0.134390i
$980$	14.9923	−	17.2431i	0.478913	−	0.550809i
$981$	−0.0690274	−	0.103307i	−0.00220387	−	0.00329833i
$982$	4.13687	+	4.69698i	0.132013	+	0.149887i
$983$	−3.09803	+	1.28325i	−0.0988119	+	0.0409292i	−0.431542	−	0.902093i	$-0.642030\pi$
$983$	−3.09803	+	1.28325i	−0.0988119	+	0.0409292i	0.332730	+	0.943022i	$0.392030\pi$
$984$	0.687615	+	3.34506i	0.0219204	+	0.106637i
$985$	11.5176	+	4.77075i	0.366981	+	0.152009i
$986$	−5.47564	+	1.87174i	−0.174380	+	0.0596083i
$987$	−12.2302	−	2.43274i	−0.389291	−	0.0774349i
$988$	44.8268	+	57.9072i	1.42613	+	1.84227i
$989$	14.0283	+	9.37341i	0.446074	+	0.298057i
$990$	7.34026	−	9.60830i	0.233289	−	0.305372i
$991$			13.8824i			0.440989i	0.975388	+	0.220494i	$0.0707671\pi$
$991$			13.8824i			0.440989i	−0.975388	+	0.220494i	$0.929233\pi$
$992$	24.6859	+	31.4718i	0.783777	+	0.999231i
$993$		−	5.64565i		−	0.179159i
$994$	−19.8717	−	15.1810i	−0.630293	−	0.481512i
$995$	31.8882	+	21.3070i	1.01092	+	0.675478i
$996$	−2.38726	+	18.7496i	−0.0756432	+	0.594105i
$997$	1.25327	+	0.249290i	0.0396913	+	0.00789509i	0.214896	−	0.976637i	$-0.431059\pi$
$997$	1.25327	+	0.249290i	0.0396913	+	0.00789509i	−0.175205	+	0.984532i	$0.556059\pi$
$998$	7.33620	+	21.4615i	0.232223	+	0.679352i
$999$	−2.56733	−	1.06342i	−0.0812268	−	0.0336453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.37.15	✓	128
3.2	odd	2		576.2.bd.b.37.2		128
4.3	odd	2		768.2.r.a.241.9		128
64.19	odd	16		768.2.r.a.529.9		128
64.45	even	16	inner	192.2.r.a.109.15	yes	128
192.173	odd	16		576.2.bd.b.109.2		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.37.15	✓	128	1.1	even	1	trivial
192.2.r.a.109.15	yes	128	64.45	even	16	inner
576.2.bd.b.37.2		128	3.2	odd	2
576.2.bd.b.109.2		128	192.173	odd	16
768.2.r.a.241.9		128	4.3	odd	2
768.2.r.a.529.9		128	64.19	odd	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40172 - 0.187577i) q^{2} +(-0.555570 + 0.831470i) q^{3} +(1.92963 - 0.525860i) q^{4} +(-0.451487 + 2.26978i) q^{5} +(-0.622789 + 1.26970i) q^{6} +(-1.32215 + 3.19196i) q^{7} +(2.60616 - 1.09906i) q^{8} +(-0.382683 - 0.923880i) q^{9} +O(q^{10})\)	\(q+(1.40172 - 0.187577i) q^{2} +(-0.555570 + 0.831470i) q^{3} +(1.92963 - 0.525860i) q^{4} +(-0.451487 + 2.26978i) q^{5} +(-0.622789 + 1.26970i) q^{6} +(-1.32215 + 3.19196i) q^{7} +(2.60616 - 1.09906i) q^{8} +(-0.382683 - 0.923880i) q^{9} +(-0.207100 + 3.26628i) q^{10} +(3.07181 - 2.05252i) q^{11} +(-0.634809 + 1.89658i) q^{12} +(-1.14806 - 5.77170i) q^{13} +(-1.25455 + 4.72223i) q^{14} +(-1.63642 - 1.63642i) q^{15} +(3.44694 - 2.02943i) q^{16} +(3.36530 - 3.36530i) q^{17} +(-0.709713 - 1.22324i) q^{18} +(-6.10247 + 1.21386i) q^{19} +(0.322382 + 4.61725i) q^{20} +(-1.91947 - 2.87269i) q^{21} +(3.92080 - 3.45325i) q^{22} +(-1.30179 + 0.539218i) q^{23} +(-0.534069 + 2.77755i) q^{24} +(-0.328659 - 0.136135i) q^{25} +(-2.69190 - 7.87495i) q^{26} +(0.980785 + 0.195090i) q^{27} +(-0.872742 + 6.85456i) q^{28} +(-0.714865 - 0.477658i) q^{29} +(-2.60075 - 1.98685i) q^{30} +7.07077i q^{31} +(4.45097 - 3.49125i) q^{32} +3.69443i q^{33} +(4.08595 - 5.34846i) q^{34} +(-6.64810 - 4.44212i) q^{35} +(-1.22427 - 1.58151i) q^{36} +(-2.72547 - 0.542129i) q^{37} +(-8.32625 + 2.84617i) q^{38} +(5.43682 + 2.25200i) q^{39} +(1.31798 + 6.41162i) q^{40} +(1.11548 - 0.462047i) q^{41} +(-3.22940 - 3.66665i) q^{42} +(-6.65231 - 9.95589i) q^{43} +(4.84811 - 5.57593i) q^{44} +(2.26978 - 0.451487i) q^{45} +(-1.72360 + 1.00002i) q^{46} +(2.55213 - 2.55213i) q^{47} +(-0.227611 + 3.99352i) q^{48} +(-3.49076 - 3.49076i) q^{49} +(-0.486223 - 0.129174i) q^{50} +(0.928485 + 4.66781i) q^{51} +(-5.25044 - 10.5335i) q^{52} +(6.68612 - 4.46752i) q^{53} +(1.41138 + 0.0894892i) q^{54} +(3.27188 + 7.89901i) q^{55} +(0.0624172 + 9.77187i) q^{56} +(2.38106 - 5.74840i) q^{57} +(-1.09164 - 0.535450i) q^{58} +(-1.36523 + 6.86345i) q^{59} +(-4.01821 - 2.29716i) q^{60} +(-7.61906 + 11.4027i) q^{61} +(1.32631 + 9.91123i) q^{62} +3.45495 q^{63} +(5.58413 - 5.72866i) q^{64} +13.6188 q^{65} +(0.692989 + 5.17855i) q^{66} +(-1.53277 + 2.29395i) q^{67} +(4.72411 - 8.26346i) q^{68} +(0.274891 - 1.38197i) q^{69} +(-10.1520 - 4.97957i) q^{70} +(-1.95859 + 4.72846i) q^{71} +(-2.01273 - 1.98718i) q^{72} +(-3.79524 - 9.16252i) q^{73} +(-3.92203 - 0.248678i) q^{74} +(0.295785 - 0.197637i) q^{75} +(-11.1372 + 5.55133i) q^{76} +(2.49015 + 12.5188i) q^{77} +(8.04332 + 2.13686i) q^{78} +(3.88839 + 3.88839i) q^{79} +(3.05010 + 8.74006i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(1.47692 - 0.856898i) q^{82} +(9.26891 - 1.84370i) q^{83} +(-5.21449 - 4.53385i) q^{84} +(6.11910 + 9.15788i) q^{85} +(-11.1922 - 12.7075i) q^{86} +(0.794316 - 0.329016i) q^{87} +(5.74978 - 8.72528i) q^{88} +(-5.39002 - 2.23262i) q^{89} +(3.09690 - 1.05862i) q^{90} +(19.9409 + 3.96650i) q^{91} +(-2.22842 + 1.72505i) q^{92} +(-5.87913 - 3.92831i) q^{93} +(3.09865 - 4.05609i) q^{94} -14.3993i q^{95} +(0.430045 + 5.64048i) q^{96} +7.50832i q^{97} +(-5.54784 - 4.23827i) q^{98} +(-3.07181 - 2.05252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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