LMFDB - Embedded newform 961.2.c.j.521.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(439,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.439"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,3,16,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			521.6
Root			$2.52368i$ of defining polynomial
Character	$\chi$	$=$	961.521
Dual form			961.2.c.j.439.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.26660 q^{2} +(-0.742157 - 1.28545i) q^{3} -0.395721 q^{4} +(1.90016 - 3.29117i) q^{5} +(-0.940018 - 1.62816i) q^{6} +(-1.09449 - 1.89572i) q^{7} -3.03442 q^{8} +(0.398405 - 0.690057i) q^{9} +(2.40675 - 4.16861i) q^{10} +(0.475298 - 0.823240i) q^{11} +(0.293687 + 0.508681i) q^{12} +(-0.0840712 + 0.145616i) q^{13} +(-1.38629 - 2.40112i) q^{14} -5.64087 q^{15} -3.05196 q^{16} +(3.28833 + 5.69555i) q^{17} +(0.504620 - 0.874027i) q^{18} +(0.576421 + 0.998390i) q^{19} +(-0.751933 + 1.30239i) q^{20} +(-1.62457 + 2.81385i) q^{21} +(0.602013 - 1.04272i) q^{22} -4.62850 q^{23} +(2.25202 + 3.90061i) q^{24} +(-4.72122 - 8.17739i) q^{25} +(-0.106485 + 0.184437i) q^{26} -5.63566 q^{27} +(0.433114 + 0.750176i) q^{28} +1.33672 q^{29} -7.14474 q^{30} +2.20322 q^{32} -1.41098 q^{33} +(4.16500 + 7.21399i) q^{34} -8.31886 q^{35} +(-0.157657 + 0.273070i) q^{36} +(1.93582 + 3.35295i) q^{37} +(0.730096 + 1.26456i) q^{38} +0.249576 q^{39} +(-5.76589 + 9.98682i) q^{40} +(-0.164101 + 0.284232i) q^{41} +(-2.05769 + 3.56402i) q^{42} +(-4.81529 - 8.34032i) q^{43} +(-0.188085 + 0.325773i) q^{44} +(-1.51407 - 2.62244i) q^{45} -5.86247 q^{46} +5.63858 q^{47} +(2.26504 + 3.92316i) q^{48} +(1.10416 - 1.91247i) q^{49} +(-5.97990 - 10.3575i) q^{50} +(4.88091 - 8.45399i) q^{51} +(0.0332687 - 0.0576231i) q^{52} +(3.66647 - 6.35052i) q^{53} -7.13814 q^{54} +(-1.80628 - 3.12858i) q^{55} +(3.32116 + 5.75242i) q^{56} +(0.855590 - 1.48193i) q^{57} +1.69309 q^{58} +(1.32656 + 2.29767i) q^{59} +2.23221 q^{60} -1.74967 q^{61} -1.74421 q^{63} +8.89454 q^{64} +(0.319498 + 0.553386i) q^{65} -1.78715 q^{66} +(-0.276003 + 0.478052i) q^{67} +(-1.30126 - 2.25385i) q^{68} +(3.43508 + 5.94973i) q^{69} -10.5367 q^{70} +(-0.568494 + 0.984661i) q^{71} +(-1.20893 + 2.09393i) q^{72} +(3.96130 - 6.86117i) q^{73} +(2.45192 + 4.24685i) q^{74} +(-7.00778 + 12.1378i) q^{75} +(-0.228102 - 0.395084i) q^{76} -2.08084 q^{77} +0.316114 q^{78} +(-2.27114 - 3.93373i) q^{79} +(-5.79922 + 10.0445i) q^{80} +(2.98733 + 5.17421i) q^{81} +(-0.207851 + 0.360008i) q^{82} +(-0.163198 + 0.282667i) q^{83} +(0.642878 - 1.11350i) q^{84} +24.9934 q^{85} +(-6.09905 - 10.5639i) q^{86} +(-0.992053 - 1.71829i) q^{87} +(-1.44225 + 2.49806i) q^{88} -14.7102 q^{89} +(-1.91772 - 3.32158i) q^{90} +0.368062 q^{91} +1.83159 q^{92} +7.14183 q^{94} +4.38117 q^{95} +(-1.63514 - 2.83214i) q^{96} +15.5192 q^{97} +(1.39853 - 2.42233i) q^{98} +(-0.378722 - 0.655965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 3 q^{3} + 16 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} + 18 q^{11} + 8 q^{13} + 9 q^{14} - 36 q^{15} + 8 q^{16} + 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 + 3 * q^3 + 16 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 + 18 * q^11 + 8 * q^13 + 9 * q^14 - 36 * q^15 + 8 * q^16 + 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 - q^21 + 4 * q^22 - 44 * q^23 + 30 * q^24 - 13 * q^25 + 9 * q^26 - 36 * q^27 + 5 * q^28 - 24 * q^29 - 22 * q^30 - 42 * q^32 + 12 * q^33 - 7 * q^34 - 24 * q^35 + q^36 - 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 - 6 * q^42 - 2 * q^43 + 4 * q^44 - 36 * q^46 - 36 * q^47 - q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 - q^52 + 6 * q^53 + 14 * q^54 + 28 * q^55 - 30 * q^56 - 17 * q^57 + 10 * q^58 + 4 * q^59 + 80 * q^60 - 60 * q^61 - 46 * q^63 + 18 * q^64 + 3 * q^65 + 20 * q^66 + 13 * q^67 + 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 + 2 * q^73 + 8 * q^74 + 23 * q^75 + 33 * q^76 + 48 * q^77 + 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 + 39 * q^83 + 8 * q^84 + 52 * q^85 - 16 * q^86 + 15 * q^87 - 17 * q^88 - 54 * q^89 - 8 * q^90 - 32 * q^91 - 64 * q^92 + 44 * q^94 - 12 * q^95 - 12 * q^96 + 68 * q^97 - 10 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.26660			0.895623			0.447811	−	0.894128i	$-0.352204\pi$
$2$	1.26660			0.895623			0.447811	+	0.894128i	$0.352204\pi$
$3$	−0.742157	−	1.28545i	−0.428485	−	0.742157i	0.568254	−	0.822853i	$-0.307619\pi$
$3$	−0.742157	−	1.28545i	−0.428485	−	0.742157i	−0.996739	+	0.0806958i	$0.974286\pi$
$4$	−0.395721			−0.197860
$5$	1.90016	−	3.29117i	0.849778	−	1.47186i	−0.0316291	−	0.999500i	$-0.510070\pi$
$5$	1.90016	−	3.29117i	0.849778	−	1.47186i	0.881407	−	0.472358i	$-0.156597\pi$
$6$	−0.940018	−	1.62816i	−0.383761	−	0.664693i
$7$	−1.09449	−	1.89572i	−0.413680	−	0.716515i	0.581609	−	0.813469i	$-0.302423\pi$
$7$	−1.09449	−	1.89572i	−0.413680	−	0.716515i	−0.995289	+	0.0969536i	$0.969090\pi$
$8$	−3.03442			−1.07283
$9$	0.398405	−	0.690057i	0.132802	−	0.230019i
$10$	2.40675	−	4.16861i	0.761080	−	1.31823i
$11$	0.475298	−	0.823240i	0.143308	−	0.248216i	−0.785433	−	0.618947i	$-0.787559\pi$
$11$	0.475298	−	0.823240i	0.143308	−	0.248216i	0.928740	+	0.370731i	$0.120893\pi$
$12$	0.293687	+	0.508681i	0.0847801	+	0.146843i
$13$	−0.0840712	+	0.145616i	−0.0233172	+	0.0403865i	−0.877449	−	0.479671i	$-0.840756\pi$
$13$	−0.0840712	+	0.145616i	−0.0233172	+	0.0403865i	0.854131	+	0.520057i	$0.174089\pi$
$14$	−1.38629	−	2.40112i	−0.370501	−	0.641727i
$15$	−5.64087			−1.45647
$16$	−3.05196			−0.762991
$17$	3.28833	+	5.69555i	0.797537	+	1.38137i	0.921216	+	0.389052i	$0.127197\pi$
$17$	3.28833	+	5.69555i	0.797537	+	1.38137i	−0.123679	+	0.992322i	$0.539469\pi$
$18$	0.504620	−	0.874027i	0.118940	−	0.206010i
$19$	0.576421	+	0.998390i	0.132240	+	0.229046i	0.924540	−	0.381086i	$-0.124450\pi$
$19$	0.576421	+	0.998390i	0.132240	+	0.229046i	−0.792300	+	0.610132i	$0.791116\pi$
$20$	−0.751933	+	1.30239i	−0.168137	+	0.291222i
$21$	−1.62457	+	2.81385i	−0.354511	+	0.614032i
$22$	0.602013	−	1.04272i	0.128350	−	0.222308i
$23$	−4.62850			−0.965109			−0.482554	−	0.875866i	$-0.660291\pi$
$23$	−4.62850			−0.965109			−0.482554	+	0.875866i	$0.660291\pi$
$24$	2.25202	+	3.90061i	0.459692	+	0.796209i
$25$	−4.72122	−	8.17739i	−0.944244	−	1.63548i
$26$	−0.106485	+	0.184437i	−0.0208834	+	0.0361711i
$27$	−5.63566			−1.08458
$28$	0.433114	+	0.750176i	0.0818509	+	0.141770i
$29$	1.33672			0.248222			0.124111	−	0.992268i	$-0.460392\pi$
$29$	1.33672			0.248222			0.124111	+	0.992268i	$0.460392\pi$
$30$	−7.14474			−1.30444
$31$		0			0
$31$		0			0
$32$	2.20322			0.389479
$33$	−1.41098			−0.245621
$34$	4.16500	+	7.21399i	0.714292	+	1.23719i
$35$	−8.31886			−1.40614
$36$	−0.157657	+	0.273070i	−0.0262762	+	0.0455116i
$37$	1.93582	+	3.35295i	0.318248	+	0.551221i	0.980122	−	0.198393i	$-0.0635723\pi$
$37$	1.93582	+	3.35295i	0.318248	+	0.551221i	−0.661875	+	0.749614i	$0.730239\pi$
$38$	0.730096	+	1.26456i	0.118437	+	0.205139i
$39$	0.249576			0.0399642
$40$	−5.76589	+	9.98682i	−0.911667	+	1.57905i
$41$	−0.164101	+	0.284232i	−0.0256283	+	0.0443895i	−0.878555	−	0.477641i	$-0.841492\pi$
$41$	−0.164101	+	0.284232i	−0.0256283	+	0.0443895i	0.852927	+	0.522031i	$0.174825\pi$
$42$	−2.05769	+	3.56402i	−0.317508	+	0.549941i
$43$	−4.81529	−	8.34032i	−0.734324	−	1.27189i	−0.955019	−	0.296544i	$-0.904166\pi$
$43$	−4.81529	−	8.34032i	−0.734324	−	1.27189i	0.220695	−	0.975343i	$-0.429167\pi$
$44$	−0.188085	+	0.325773i	−0.0283549	+	0.0491121i
$45$	−1.51407	−	2.62244i	−0.225704	−	0.390930i
$46$	−5.86247			−0.864373
$47$	5.63858			0.822471			0.411235	−	0.911529i	$-0.365097\pi$
$47$	5.63858			0.822471			0.411235	+	0.911529i	$0.365097\pi$
$48$	2.26504	+	3.92316i	0.326930	+	0.566259i
$49$	1.10416	−	1.91247i	0.157737	−	0.273209i
$50$	−5.97990	−	10.3575i	−0.845686	−	1.46477i
$51$	4.88091	−	8.45399i	0.683465	−	1.18380i
$52$	0.0332687	−	0.0576231i	0.00461354	−	0.00799089i
$53$	3.66647	−	6.35052i	0.503629	−	0.872311i	−0.496362	−	0.868115i	$-0.665331\pi$
$53$	3.66647	−	6.35052i	0.503629	−	0.872311i	0.999991	−	0.00419517i	$-0.00133537\pi$
$54$	−7.13814			−0.971377
$55$	−1.80628	−	3.12858i	−0.243559	−	0.421857i
$56$	3.32116	+	5.75242i	0.443809	+	0.768699i
$57$	0.855590	−	1.48193i	0.113326	−	0.196286i
$58$	1.69309			0.222313
$59$	1.32656	+	2.29767i	0.172703	+	0.299131i	0.939364	−	0.342921i	$-0.111416\pi$
$59$	1.32656	+	2.29767i	0.172703	+	0.299131i	−0.766661	+	0.642052i	$0.778083\pi$
$60$	2.23221			0.288177
$61$	−1.74967			−0.224023			−0.112011	−	0.993707i	$-0.535729\pi$
$61$	−1.74967			−0.224023			−0.112011	+	0.993707i	$0.535729\pi$
$62$		0			0
$63$	−1.74421			−0.219749
$64$	8.89454			1.11182
$65$	0.319498	+	0.553386i	0.0396288	+	0.0686391i
$66$	−1.78715			−0.219983
$67$	−0.276003	+	0.478052i	−0.0337192	+	0.0584033i	−0.882393	−	0.470514i	$-0.844069\pi$
$67$	−0.276003	+	0.478052i	−0.0337192	+	0.0584033i	0.848673	+	0.528917i	$0.177402\pi$
$68$	−1.30126	−	2.25385i	−0.157801	−	0.273319i
$69$	3.43508	+	5.94973i	0.413535	+	0.716263i
$70$	−10.5367			−1.25937
$71$	−0.568494	+	0.984661i	−0.0674679	+	0.116858i	−0.897786	−	0.440432i	$-0.854825\pi$
$71$	−0.568494	+	0.984661i	−0.0674679	+	0.116858i	0.830318	+	0.557290i	$0.188159\pi$
$72$	−1.20893	+	2.09393i	−0.142474	+	0.246771i
$73$	3.96130	−	6.86117i	0.463635	−	0.803039i	−0.535504	−	0.844533i	$-0.679878\pi$
$73$	3.96130	−	6.86117i	0.463635	−	0.803039i	0.999139	+	0.0414935i	$0.0132116\pi$
$74$	2.45192	+	4.24685i	0.285030	+	0.493686i
$75$	−7.00778	+	12.1378i	−0.809188	+	1.40156i
$76$	−0.228102	−	0.395084i	−0.0261650	−	0.0453192i
$77$	−2.08084			−0.237134
$78$	0.316114			0.0357928
$79$	−2.27114	−	3.93373i	−0.255523	−	0.442579i	0.709514	−	0.704691i	$-0.248914\pi$
$79$	−2.27114	−	3.93373i	−0.255523	−	0.442579i	−0.965037	+	0.262112i	$0.915581\pi$
$80$	−5.79922	+	10.0445i	−0.648373	+	1.12301i
$81$	2.98733	+	5.17421i	0.331926	+	0.574913i
$82$	−0.207851	+	0.360008i	−0.0229533	+	0.0397563i
$83$	−0.163198	+	0.282667i	−0.0179133	+	0.0310268i	−0.874843	−	0.484406i	$-0.839036\pi$
$83$	−0.163198	+	0.282667i	−0.0179133	+	0.0310268i	0.856930	+	0.515433i	$0.172369\pi$
$84$	0.642878	−	1.11350i	0.0701437	−	0.121492i
$85$	24.9934			2.71091
$86$	−6.09905	−	10.5639i	−0.657677	−	1.13913i
$87$	−0.992053	−	1.71829i	−0.106359	−	0.184220i
$88$	−1.44225	+	2.49806i	−0.153745	+	0.266294i
$89$	−14.7102			−1.55927			−0.779637	−	0.626232i	$-0.784596\pi$
$89$	−14.7102			−1.55927			−0.779637	+	0.626232i	$0.784596\pi$
$90$	−1.91772	−	3.32158i	−0.202145	−	0.350126i
$91$	0.368062			0.0385834
$92$	1.83159			0.190957
$93$		0			0
$94$	7.14183			0.736623
$95$	4.38117			0.449498
$96$	−1.63514	−	2.83214i	−0.166886	−	0.289055i
$97$	15.5192			1.57573			0.787867	−	0.615845i	$-0.211185\pi$
$97$	15.5192			1.57573			0.787867	+	0.615845i	$0.211185\pi$
$98$	1.39853	−	2.42233i	0.141273	−	0.244692i
$99$	−0.378722	−	0.655965i	−0.0380630	−	0.0659270i
$100$	1.86828	+	3.23596i	0.186828	+	0.323596i
$101$	4.87360			0.484941			0.242471	−	0.970159i	$-0.422042\pi$
$101$	4.87360			0.484941			0.242471	+	0.970159i	$0.422042\pi$
$102$	6.18217	−	10.7078i	0.612126	−	1.06023i
$103$	−0.965310	+	1.67197i	−0.0951148	+	0.164744i	−0.909657	−	0.415361i	$-0.863655\pi$
$103$	−0.965310	+	1.67197i	−0.0951148	+	0.164744i	0.814542	+	0.580105i	$0.196988\pi$
$104$	0.255108	−	0.441859i	0.0250154	−	0.0433279i
$105$	6.17391	+	10.6935i	0.602512	+	1.04358i
$106$	4.64396	−	8.04357i	0.451061	−	0.781261i
$107$	−6.26376	−	10.8491i	−0.605540	−	1.04883i	−0.991966	−	0.126506i	$-0.959624\pi$
$107$	−6.26376	−	10.8491i	−0.605540	−	1.04883i	0.386426	−	0.922321i	$-0.373710\pi$
$108$	2.23015			0.214596
$109$	−10.2625			−0.982968			−0.491484	−	0.870887i	$-0.663545\pi$
$109$	−10.2625			−0.982968			−0.491484	+	0.870887i	$0.663545\pi$
$110$	−2.28784	−	3.96266i	−0.218137	−	0.377825i
$111$	2.87337	−	4.97683i	0.272728	−	0.472380i
$112$	3.34036	+	5.78567i	0.315634	+	0.546695i
$113$	1.92147	−	3.32809i	0.180757	−	0.313080i	−0.761382	−	0.648304i	$-0.775479\pi$
$113$	1.92147	−	3.32809i	0.180757	−	0.313080i	0.942138	+	0.335224i	$0.108812\pi$
$114$	1.08369	−	1.87701i	0.101497	−	0.175798i
$115$	−8.79489	+	15.2332i	−0.820128	+	1.42050i
$116$	−0.528966			−0.0491132
$117$	0.0669887	+	0.116028i	0.00619311	+	0.0107268i
$118$	1.68022	+	2.91023i	0.154677	+	0.267908i
$119$	7.19811	−	12.4675i	0.659850	−	1.14289i
$120$	17.1168			1.56254
$121$	5.04818	+	8.74371i	0.458926	+	0.794883i
$122$	−2.21614			−0.200640
$123$	0.487156			0.0439254
$124$		0			0
$125$	−16.8827			−1.51003
$126$	−2.20922			−0.196813
$127$	−3.67194	−	6.35999i	−0.325832	−	0.564358i	0.655848	−	0.754893i	$-0.272311\pi$
$127$	−3.67194	−	6.35999i	−0.325832	−	0.564358i	−0.981680	+	0.190535i	$0.938978\pi$
$128$	6.85938			0.606290
$129$	−7.14740	+	12.3797i	−0.629294	+	1.08997i
$130$	0.404676	+	0.700920i	0.0354924	+	0.0614747i
$131$	−6.51684	−	11.2875i	−0.569379	−	0.986193i	−0.996628	−	0.0820586i	$-0.973851\pi$
$131$	−6.51684	−	11.2875i	−0.569379	−	0.986193i	0.427249	−	0.904134i	$-0.359483\pi$
$132$	0.558355			0.0485986
$133$	1.26178	−	2.18547i	0.109410	−	0.189504i
$134$	−0.349586	+	0.605501i	−0.0301997	+	0.0523073i
$135$	−10.7087	+	18.5479i	−0.921655	+	1.59635i
$136$	−9.97818	−	17.2827i	−0.855622	−	1.48198i
$137$	0.0671497	−	0.116307i	0.00573698	−	0.00993674i	−0.863143	−	0.504960i	$-0.831507\pi$
$137$	0.0671497	−	0.116307i	0.00573698	−	0.00993674i	0.868880	+	0.495023i	$0.164841\pi$
$138$	4.35087	+	7.53593i	0.370371	+	0.641501i
$139$	11.5275			0.977749			0.488874	−	0.872354i	$-0.337408\pi$
$139$	11.5275			0.977749			0.488874	+	0.872354i	$0.337408\pi$
$140$	3.29195			0.278220
$141$	−4.18471	−	7.24813i	−0.352416	−	0.610403i
$142$	−0.720056	+	1.24717i	−0.0604257	+	0.104660i
$143$	0.0799177	+	0.138422i	0.00668306	+	0.0115754i
$144$	−1.21592	+	2.10603i	−0.101326	+	0.175502i
$145$	2.53997	−	4.39936i	0.210933	−	0.365347i
$146$	5.01739	−	8.69037i	0.415242	−	0.719220i
$147$	−3.27785			−0.270352
$148$	−0.766046	−	1.32683i	−0.0629686	−	0.109065i
$149$	2.72054	+	4.71211i	0.222875	+	0.386031i	0.955680	−	0.294408i	$-0.0951224\pi$
$149$	2.72054	+	4.71211i	0.222875	+	0.386031i	−0.732805	+	0.680439i	$0.761789\pi$
$150$	−8.87606	+	15.3738i	−0.724727	+	1.25526i
$151$	13.6892			1.11401			0.557005	−	0.830509i	$-0.311950\pi$
$151$	13.6892			1.11401			0.557005	+	0.830509i	$0.311950\pi$
$152$	−1.74910	−	3.02954i	−0.141871	−	0.245728i
$153$	5.24034			0.423656
$154$	−2.63560			−0.212383
$155$		0			0
$156$	−0.0987625			−0.00790733
$157$	−15.0553			−1.20155			−0.600774	−	0.799419i	$-0.705141\pi$
$157$	−15.0553			−1.20155			−0.600774	+	0.799419i	$0.705141\pi$
$158$	−2.87663	−	4.98247i	−0.228852	−	0.396384i
$159$	−10.8844			−0.863189
$160$	4.18648	−	7.25120i	0.330970	−	0.573257i
$161$	5.06587	+	8.77434i	0.399246	+	0.691515i
$162$	3.78376	+	6.55367i	0.297280	+	0.514905i
$163$	17.0381			1.33453			0.667263	−	0.744822i	$-0.267466\pi$
$163$	17.0381			1.33453			0.667263	+	0.744822i	$0.267466\pi$
$164$	0.0649383	−	0.112476i	0.00507083	−	0.00878293i
$165$	−2.68109	+	4.64379i	−0.208723	+	0.361519i
$166$	−0.206707	+	0.358027i	−0.0160436	+	0.0277883i
$167$	8.09912	+	14.0281i	0.626729	+	1.08553i	0.988204	+	0.153144i	$0.0489399\pi$
$167$	8.09912	+	14.0281i	0.626729	+	1.08553i	−0.361475	+	0.932382i	$0.617727\pi$
$168$	4.92965	−	8.53840i	0.380331	−	0.658752i
$169$	6.48586	+	11.2338i	0.498913	+	0.864142i
$170$	31.6567			2.42796
$171$	0.918595			0.0702467
$172$	1.90551	+	3.30044i	0.145294	+	0.251656i
$173$	1.16561	−	2.01889i	0.0886196	−	0.153494i	−0.818308	−	0.574780i	$-0.805088\pi$
$173$	1.16561	−	2.01889i	0.0886196	−	0.153494i	0.906928	+	0.421286i	$0.138421\pi$
$174$	−1.25654	−	2.17638i	−0.0952577	−	0.164991i
$175$	−10.3347	+	17.9002i	−0.781230	+	1.35313i
$176$	−1.45059	+	2.51250i	−0.109342	+	0.189387i
$177$	1.96903	−	3.41046i	0.148002	−	0.256346i
$178$	−18.6319			−1.39652
$179$	8.48531	+	14.6970i	0.634222	+	1.09850i	0.986679	+	0.162677i	$0.0520128\pi$
$179$	8.48531	+	14.6970i	0.634222	+	1.09850i	−0.352457	+	0.935828i	$0.614654\pi$
$180$	0.599147	+	1.03775i	0.0446578	+	0.0773495i
$181$	3.66788	−	6.35296i	0.272631	−	0.472211i	−0.696903	−	0.717165i	$-0.745439\pi$
$181$	3.66788	−	6.35296i	0.272631	−	0.472211i	0.969535	+	0.244954i	$0.0787727\pi$
$182$	0.466188			0.0345561
$183$	1.29853	+	2.24913i	0.0959903	+	0.166260i
$184$	14.0448			1.03540
$185$	14.7135			1.08176
$186$		0			0
$187$	6.25174			0.457173
$188$	−2.23130			−0.162734
$189$	6.16820	+	10.6836i	0.448671	+	0.777120i
$190$	5.54919			0.402581
$191$	−3.91138	+	6.77471i	−0.283018	+	0.490201i	−0.972127	−	0.234457i	$-0.924669\pi$
$191$	−3.91138	+	6.77471i	−0.283018	+	0.490201i	0.689109	+	0.724658i	$0.258002\pi$
$192$	−6.60115	−	11.4335i	−0.476397	−	0.825143i
$193$	2.31575	+	4.01100i	0.166692	+	0.288718i	0.937255	−	0.348645i	$-0.113358\pi$
$193$	2.31575	+	4.01100i	0.166692	+	0.288718i	−0.770563	+	0.637364i	$0.780025\pi$
$194$	19.6566			1.41126
$195$	0.474235	−	0.821399i	0.0339607	−	0.0588216i
$196$	−0.436940	+	0.756802i	−0.0312100	+	0.0540573i
$197$	11.1922	−	19.3854i	0.797411	−	1.38116i	−0.123887	−	0.992296i	$-0.539536\pi$
$197$	11.1922	−	19.3854i	0.797411	−	1.38116i	0.921297	−	0.388859i	$-0.127131\pi$
$198$	−0.479690	−	0.830847i	−0.0340900	−	0.0590457i
$199$	13.3019	−	23.0395i	0.942945	−	1.63323i	0.183131	−	0.983089i	$-0.441377\pi$
$199$	13.3019	−	23.0395i	0.942945	−	1.63323i	0.759814	−	0.650140i	$-0.225290\pi$
$200$	14.3262	+	24.8137i	1.01301	+	1.75459i
$201$	0.819352			0.0577926
$202$	6.17291			0.434324
$203$	−1.46303	−	2.53404i	−0.102684	−	0.177855i
$204$	−1.93148	+	3.34542i	−0.135231	+	0.234226i
$205$	0.623638	+	1.08017i	0.0435567	+	0.0754425i
$206$	−1.22266	+	2.11771i	−0.0851869	+	0.147548i
$207$	−1.84402	+	3.19393i	−0.128168	+	0.221993i
$208$	0.256582	−	0.444414i	0.0177908	−	0.0308145i
$209$	1.09589			0.0758040
$210$	7.81988	+	13.5444i	0.539623	+	0.934654i
$211$	−0.663069	−	1.14847i	−0.0456476	−	0.0790639i	0.842299	−	0.539011i	$-0.181202\pi$
$211$	−0.663069	−	1.14847i	−0.0456476	−	0.0790639i	−0.887946	+	0.459947i	$0.847868\pi$
$212$	−1.45090	+	2.51303i	−0.0996481	+	0.172596i
$213$	1.68765			0.115636
$214$	−7.93368	−	13.7415i	−0.542335	−	0.939353i
$215$	−36.5993			−2.49605
$216$	17.1010			1.16357
$217$		0			0
$218$	−12.9985			−0.880368
$219$	−11.7596			−0.794642
$220$	0.714784	+	1.23804i	0.0481907	+	0.0834688i
$221$	−1.10581			−0.0743851
$222$	3.63942	−	6.30366i	0.244262	−	0.423074i
$223$	6.05997	+	10.4962i	0.405806	+	0.702876i	0.994415	−	0.105542i	$-0.0336576\pi$
$223$	6.05997	+	10.4962i	0.405806	+	0.702876i	−0.588609	+	0.808418i	$0.700324\pi$
$224$	−2.41142	−	4.17670i	−0.161120	−	0.279067i
$225$	−7.52382			−0.501588
$226$	2.43374	−	4.21536i	0.161890	−	0.280401i
$227$	7.95108	−	13.7717i	0.527732	−	0.914058i	−0.471746	−	0.881735i	$-0.656376\pi$
$227$	7.95108	−	13.7717i	0.527732	−	0.914058i	0.999477	−	0.0323233i	$-0.0102906\pi$
$228$	−0.338575	+	0.586428i	−0.0224227	+	0.0388372i
$229$	8.14930	+	14.1150i	0.538521	+	0.932746i	0.998984	+	0.0450670i	$0.0143501\pi$
$229$	8.14930	+	14.1150i	0.538521	+	0.932746i	−0.460463	+	0.887679i	$0.652317\pi$
$230$	−11.1396	+	19.2944i	−0.734525	+	1.27223i
$231$	1.54431	+	2.67483i	0.101608	+	0.175991i
$232$	−4.05616			−0.266300
$233$	−5.12296			−0.335616			−0.167808	−	0.985820i	$-0.553669\pi$
$233$	−5.12296			−0.335616			−0.167808	+	0.985820i	$0.553669\pi$
$234$	0.0848480	+	0.146961i	0.00554669	+	0.00960715i
$235$	10.7142	−	18.5575i	0.698917	−	1.21056i
$236$	−0.524947	−	0.909235i	−0.0341711	−	0.0591861i
$237$	−3.37109	+	5.83889i	−0.218976	+	0.379277i
$238$	9.11714	−	15.7914i	0.590977	−	1.02360i
$239$	−4.28400	+	7.42010i	−0.277109	+	0.479967i	−0.970665	−	0.240436i	$-0.922710\pi$
$239$	−4.28400	+	7.42010i	−0.277109	+	0.479967i	0.693556	+	0.720403i	$0.256043\pi$
$240$	17.2157			1.11127
$241$	3.42338	+	5.92947i	0.220519	+	0.381951i	0.954966	−	0.296716i	$-0.0958914\pi$
$241$	3.42338	+	5.92947i	0.220519	+	0.381951i	−0.734446	+	0.678667i	$0.762558\pi$
$242$	6.39404	+	11.0748i	0.411024	+	0.711915i
$243$	−4.01935	+	6.96171i	−0.257841	+	0.446594i
$244$	0.692382			0.0443252
$245$	−4.19617	−	7.26798i	−0.268084	−	0.464334i
$246$	0.617033			0.0393406
$247$	−0.193842			−0.0123338
$248$		0			0
$249$	0.484474			0.0307023
$250$	−21.3836			−1.35242
$251$	−11.3330	−	19.6294i	−0.715336	−	1.23900i	−0.962830	−	0.270108i	$-0.912940\pi$
$251$	−11.3330	−	19.6294i	−0.715336	−	1.23900i	0.247494	−	0.968889i	$-0.420393\pi$
$252$	0.690219			0.0434797
$253$	−2.19992	+	3.81037i	−0.138308	+	0.239556i
$254$	−4.65089	−	8.05558i	−0.291823	−	0.505452i
$255$	−18.5490	−	32.1279i	−1.16159	−	2.01193i
$256$	−9.10097			−0.568810
$257$	8.32918	−	14.4266i	0.519560	−	0.899904i	−0.480181	−	0.877169i	$-0.659429\pi$
$257$	8.32918	−	14.4266i	0.519560	−	0.899904i	0.999742	−	0.0227352i	$-0.00723746\pi$
$258$	−9.05291	+	15.6801i	−0.563610	+	0.976200i
$259$	4.23750	−	7.33956i	0.263305	−	0.456058i
$260$	−0.126432	−	0.218986i	−0.00784097	−	0.0135810i
$261$	0.532553	−	0.922410i	0.0329642	−	0.0570957i
$262$	−8.25423	−	14.2968i	−0.509948	−	0.883256i
$263$	−24.5864			−1.51606			−0.758030	−	0.652220i	$-0.773838\pi$
$263$	−24.5864			−1.51606			−0.758030	+	0.652220i	$0.773838\pi$
$264$	4.28152			0.263509
$265$	−13.9338	−	24.1340i	−0.855945	−	1.48254i
$266$	1.59817	−	2.76811i	0.0979902	−	0.169724i
$267$	10.9173	+	18.9092i	0.668125	+	1.15723i
$268$	0.109220	−	0.189175i	0.00667169	−	0.0115557i
$269$	−6.25707	+	10.8376i	−0.381501	+	0.660778i	−0.991277	−	0.131795i	$-0.957926\pi$
$269$	−6.25707	+	10.8376i	−0.381501	+	0.660778i	0.609776	+	0.792573i	$0.291259\pi$
$270$	−13.5636	+	23.4929i	−0.825455	+	1.42973i
$271$	−27.1673			−1.65030			−0.825148	−	0.564917i	$-0.808908\pi$
$271$	−27.1673			−1.65030			−0.825148	+	0.564917i	$0.808908\pi$
$272$	−10.0359	−	17.3826i	−0.608513	−	1.05398i
$273$	−0.273160	−	0.473127i	−0.0165324	−	0.0286349i
$274$	0.0850519	−	0.147314i	0.00513817	−	0.00889957i
$275$	−8.97594			−0.541270
$276$	−1.35933	−	2.35443i	−0.0818221	−	0.141720i
$277$	−15.1573			−0.910716			−0.455358	−	0.890308i	$-0.650489\pi$
$277$	−15.1573			−0.910716			−0.455358	+	0.890308i	$0.650489\pi$
$278$	14.6007			0.875694
$279$		0			0
$280$	25.2430			1.50855
$281$	30.2477			1.80443			0.902214	−	0.431289i	$-0.141941\pi$
$281$	30.2477			1.80443			0.902214	+	0.431289i	$0.141941\pi$
$282$	−5.30036	−	9.18049i	−0.315632	−	0.546690i
$283$	3.14532			0.186970			0.0934850	−	0.995621i	$-0.470199\pi$
$283$	3.14532			0.186970			0.0934850	+	0.995621i	$0.470199\pi$
$284$	0.224965	−	0.389651i	0.0133492	−	0.0231215i
$285$	−3.25152	−	5.63179i	−0.192603	−	0.333599i
$286$	0.101224	+	0.175325i	0.00598550	+	0.0103672i
$287$	0.718432			0.0424077
$288$	0.877775	−	1.52035i	0.0517234	−	0.0895875i
$289$	−13.1262	+	22.7352i	−0.772129	+	1.33737i
$290$	3.21713	−	5.57224i	0.188917	−	0.327213i
$291$	−11.5177	−	19.9492i	−0.675178	−	1.16944i
$292$	−1.56757	+	2.71511i	−0.0917350	+	0.158890i
$293$	−0.950041	−	1.64552i	−0.0555020	−	0.0961322i	0.836940	−	0.547295i	$-0.184343\pi$
$293$	−0.950041	−	1.64552i	−0.0555020	−	0.0961322i	−0.892441	+	0.451163i	$0.851009\pi$
$294$	−4.15173			−0.242134
$295$	10.0827			0.587038
$296$	−5.87411	−	10.1743i	−0.341426	−	0.591367i
$297$	−2.67862	+	4.63950i	−0.155429	+	0.269211i
$298$	3.44584	+	5.96837i	0.199612	+	0.345738i
$299$	0.389124	−	0.673982i	0.0225036	−	0.0389774i
$300$	2.77312	−	4.80319i	0.160106	−	0.277312i
$301$	−10.5406	+	18.2569i	−0.607551	+	1.05231i
$302$	17.3387			0.997733
$303$	−3.61698	−	6.26479i	−0.207790	−	0.359903i
$304$	−1.75922	−	3.04705i	−0.100898	−	0.174760i
$305$	−3.32466	+	5.75848i	−0.190370	+	0.329730i
$306$	6.63742			0.379436
$307$	−11.3640	−	19.6831i	−0.648580	−	1.12337i	−0.983462	−	0.181114i	$-0.942030\pi$
$307$	−11.3640	−	19.6831i	−0.648580	−	1.12337i	0.334882	−	0.942260i	$-0.391304\pi$
$308$	0.823433			0.0469194
$309$	2.86565			0.163021
$310$		0			0
$311$	15.8754			0.900213			0.450106	−	0.892975i	$-0.351386\pi$
$311$	15.8754			0.900213			0.450106	+	0.892975i	$0.351386\pi$
$312$	−0.757320			−0.0428748
$313$	−3.17467	−	5.49870i	−0.179443	−	0.310805i	0.762247	−	0.647287i	$-0.224096\pi$
$313$	−3.17467	−	5.49870i	−0.179443	−	0.310805i	−0.941690	+	0.336482i	$0.890763\pi$
$314$	−19.0691			−1.07613
$315$	−3.31427	+	5.74049i	−0.186738	+	0.323440i
$316$	0.898737	+	1.55666i	0.0505579	+	0.0875689i
$317$	7.65050	+	13.2511i	0.429695	+	0.744254i	0.996846	−	0.0793603i	$-0.0252878\pi$
$317$	7.65050	+	13.2511i	0.429695	+	0.744254i	−0.567151	+	0.823614i	$0.691954\pi$
$318$	−13.7862			−0.773092
$319$	0.635338	−	1.10044i	0.0355721	−	0.0616127i
$320$	16.9010	−	29.2735i	0.944797	−	1.63644i
$321$	−9.29739	+	16.1035i	−0.518930	+	0.898812i
$322$	6.41644	+	11.1136i	0.357574	+	0.619336i
$323$	−3.79092	+	6.56607i	−0.210932	+	0.365346i
$324$	−1.18215	−	2.04754i	−0.0656750	−	0.113752i
$325$	1.58767			0.0880683
$326$	21.5805			1.19523
$327$	7.61638	+	13.1920i	0.421187	+	0.729517i
$328$	0.497953	−	0.862480i	0.0274948	−	0.0476225i
$329$	−6.17139	−	10.6892i	−0.340240	−	0.589313i
$330$	−3.39588	+	5.88183i	−0.186937	+	0.323784i
$331$	4.48398	−	7.76648i	0.246462	−	0.426884i	−0.716080	−	0.698018i	$-0.754065\pi$
$331$	4.48398	−	7.76648i	0.246462	−	0.426884i	0.962542	+	0.271134i	$0.0873987\pi$
$332$	0.0645808	−	0.111857i	0.00354433	−	0.00613896i
$333$	3.08497			0.169055
$334$	10.2584	+	17.7680i	0.561312	+	0.972221i
$335$	1.04890	+	1.81675i	0.0573076	+	0.0992597i
$336$	4.95814	−	8.58776i	0.270489	−	0.468501i
$337$	−4.36877			−0.237982			−0.118991	−	0.992895i	$-0.537966\pi$
$337$	−4.36877			−0.237982			−0.118991	+	0.992895i	$0.537966\pi$
$338$	8.21501	+	14.2288i	0.446837	+	0.773945i
$339$	−5.70414			−0.309806
$340$	−9.89040			−0.536382
$341$		0			0
$342$	1.16349			0.0629145
$343$	−20.1569			−1.08837
$344$	14.6116	+	25.3081i	0.787806	+	1.36452i
$345$	26.1088			1.40565
$346$	1.47636	−	2.55713i	0.0793697	−	0.137472i
$347$	−12.2026	−	21.1356i	−0.655073	−	1.13462i	−0.981876	−	0.189526i	$-0.939305\pi$
$347$	−12.2026	−	21.1356i	−0.655073	−	1.13462i	0.326803	−	0.945092i	$-0.394029\pi$
$348$	0.392576	+	0.679961i	0.0210443	+	0.0364498i
$349$	13.0439			0.698224			0.349112	−	0.937081i	$-0.386483\pi$
$349$	13.0439			0.698224			0.349112	+	0.937081i	$0.386483\pi$
$350$	−13.0899	+	22.6724i	−0.699687	+	1.21189i
$351$	0.473797	−	0.820640i	0.0252894	−	0.0438025i
$352$	1.04719	−	1.81378i	0.0558153	−	0.0966749i
$353$	−5.41240	−	9.37456i	−0.288073	−	0.498957i	0.685277	−	0.728283i	$-0.259681\pi$
$353$	−5.41240	−	9.37456i	−0.288073	−	0.498957i	−0.973350	+	0.229325i	$0.926348\pi$
$354$	2.49398	−	4.31970i	0.132554	−	0.229589i
$355$	2.16046	+	3.74203i	0.114665	+	0.198606i
$356$	5.82111			0.308518
$357$	−21.3685			−1.13094
$358$	10.7475	+	18.6152i	0.568024	+	0.983846i
$359$	−16.8917	+	29.2573i	−0.891510	+	1.54414i	−0.0534446	+	0.998571i	$0.517020\pi$
$359$	−16.8917	+	29.2573i	−0.891510	+	1.54414i	−0.838065	+	0.545570i	$0.816313\pi$
$360$	4.59432	+	7.95759i	0.242142	+	0.419402i
$361$	8.83548	−	15.3035i	0.465025	−	0.805447i
$362$	4.64574	−	8.04666i	0.244175	−	0.422923i
$363$	7.49309	−	12.9784i	0.393285	−	0.681190i
$364$	−0.145650			−0.00763412
$365$	−15.0542	−	26.0746i	−0.787973	−	1.36481i
$366$	1.64472	+	2.84875i	0.0859711	+	0.148906i
$367$	−11.3157	+	19.5993i	−0.590673	+	1.02308i	0.403469	+	0.914993i	$0.367804\pi$
$367$	−11.3157	+	19.5993i	−0.590673	+	1.02308i	−0.994142	+	0.108082i	$0.965529\pi$
$368$	14.1260			0.736369
$369$	0.130757	+	0.226479i	0.00680696	+	0.0117900i
$370$	18.6362			0.968847
$371$	−16.0517			−0.833365
$372$		0			0
$373$	−32.9720			−1.70723			−0.853613	−	0.520908i	$-0.825593\pi$
$373$	−32.9720			−1.70723			−0.853613	+	0.520908i	$0.825593\pi$
$374$	7.91846			0.409454
$375$	12.5296	+	21.7019i	0.647026	+	1.12068i
$376$	−17.1098			−0.882372
$377$	−0.112379	+	0.194647i	−0.00578783	+	0.0100248i
$378$	7.81265	+	13.5319i	0.401840	+	0.696006i
$379$	16.2459	+	28.1388i	0.834498	+	1.44539i	0.894439	+	0.447190i	$0.147575\pi$
$379$	16.2459	+	28.1388i	0.834498	+	1.44539i	−0.0599413	+	0.998202i	$0.519091\pi$
$380$	−1.73372			−0.0889379
$381$	−5.45032	+	9.44023i	−0.279228	+	0.483638i
$382$	−4.95416	+	8.58086i	−0.253477	+	0.439035i
$383$	13.3902	−	23.1925i	0.684208	−	1.18508i	−0.289477	−	0.957185i	$-0.593481\pi$
$383$	13.3902	−	23.1925i	0.684208	−	1.18508i	0.973685	−	0.227898i	$-0.0731853\pi$
$384$	−5.09074	−	8.81742i	−0.259786	−	0.449962i
$385$	−3.95394	+	6.84842i	−0.201511	+	0.349028i
$386$	2.93314	+	5.08034i	0.149293	+	0.258583i
$387$	−7.67373			−0.390078
$388$	−6.14126			−0.311775
$389$	8.86875	+	15.3611i	0.449663	+	0.778840i	0.998364	−	0.0571790i	$-0.0182106\pi$
$389$	8.86875	+	15.3611i	0.449663	+	0.778840i	−0.548700	+	0.836019i	$0.684877\pi$
$390$	0.600667	−	1.04039i	0.0304159	−	0.0526820i
$391$	−15.2200	−	26.3619i	−0.769710	−	1.33318i
$392$	−3.35050	+	5.80323i	−0.169226	+	0.293107i
$393$	−9.67304	+	16.7542i	−0.487940	+	0.845137i
$394$	14.1760	−	24.5536i	0.714179	−	1.23699i
$395$	−17.2621			−0.868552
$396$	0.149868	+	0.259579i	0.00753115	+	0.0130443i
$397$	−4.97476	−	8.61654i	−0.249676	−	0.432452i	0.713760	−	0.700391i	$-0.246991\pi$
$397$	−4.97476	−	8.61654i	−0.249676	−	0.432452i	−0.963436	+	0.267939i	$0.913658\pi$
$398$	16.8482	−	29.1819i	0.844523	−	1.46276i
$399$	−3.74576			−0.187522
$400$	14.4090	+	24.9571i	0.720449	+	1.24786i
$401$	19.8956			0.993538			0.496769	−	0.867883i	$-0.334520\pi$
$401$	19.8956			0.993538			0.496769	+	0.867883i	$0.334520\pi$
$402$	1.03779			0.0517604
$403$		0			0
$404$	−1.92858			−0.0959506
$405$	22.7057			1.12825
$406$	−1.85307	−	3.20962i	−0.0919665	−	0.159291i
$407$	3.68037			0.182429
$408$	−14.8108	+	25.6530i	−0.733242	+	1.27001i
$409$	12.1628	+	21.0665i	0.601410	+	1.04167i	0.992608	+	0.121365i	$0.0387273\pi$
$409$	12.1628	+	21.0665i	0.601410	+	1.04167i	−0.391198	+	0.920306i	$0.627939\pi$
$410$	0.789900	+	1.36815i	0.0390104	+	0.0675680i
$411$	−0.199342			−0.00983284
$412$	0.381993	−	0.661631i	0.0188194	−	0.0325962i
$413$	2.90383	−	5.02957i	0.142888	−	0.247489i
$414$	−2.33563	+	4.04544i	−0.114790	+	0.198822i
$415$	0.620205	+	1.07423i	0.0304446	+	0.0527317i
$416$	−0.185228	+	0.320824i	−0.00908154	+	0.0157297i
$417$	−8.55521	−	14.8181i	−0.418951	−	0.725644i
$418$	1.38805			0.0678918
$419$	−4.40675			−0.215284			−0.107642	−	0.994190i	$-0.534330\pi$
$419$	−4.40675			−0.215284			−0.107642	+	0.994190i	$0.534330\pi$
$420$	−2.44314	−	4.23165i	−0.119213	−	0.206483i
$421$	6.21184	−	10.7592i	0.302746	−	0.524372i	−0.674011	−	0.738722i	$-0.735430\pi$
$421$	6.21184	−	10.7592i	0.302746	−	0.524372i	0.976757	+	0.214349i	$0.0687631\pi$
$422$	−0.839844	−	1.45465i	−0.0408830	−	0.0708114i
$423$	2.24643	−	3.89094i	0.109225	−	0.189184i
$424$	−11.1256	+	19.2702i	−0.540308	+	0.935841i
$425$	31.0498	−	53.7799i	1.50614	−	2.60871i
$426$	2.13758			0.103566
$427$	1.91501	+	3.31689i	0.0926738	+	0.160516i
$428$	2.47870	+	4.29323i	0.119812	+	0.207521i
$429$	0.118623	−	0.205461i	0.00572718	−	0.00991976i
$430$	−46.3567			−2.23552
$431$	9.28265	+	16.0780i	0.447130	+	0.774451i	0.998198	−	0.0600091i	$-0.0191130\pi$
$431$	9.28265	+	16.0780i	0.447130	+	0.774451i	−0.551068	+	0.834460i	$0.685780\pi$
$432$	17.1998			0.827527
$433$	−36.1204			−1.73584			−0.867918	−	0.496708i	$-0.834542\pi$
$433$	−36.1204			−1.73584			−0.867918	+	0.496708i	$0.834542\pi$
$434$		0			0
$435$	−7.54024			−0.361527
$436$	4.06108			0.194490
$437$	−2.66796	−	4.62105i	−0.127626	−	0.221055i
$438$	−14.8948			−0.711699
$439$	9.50469	−	16.4626i	0.453634	−	0.785718i	−0.544974	−	0.838453i	$-0.683461\pi$
$439$	9.50469	−	16.4626i	0.453634	−	0.785718i	0.998609	+	0.0527352i	$0.0167939\pi$
$440$	5.48103	+	9.49342i	0.261298	+	0.452581i
$441$	−0.879807	−	1.52387i	−0.0418956	−	0.0725652i
$442$	−1.40063			−0.0666210
$443$	−6.22702	+	10.7855i	−0.295854	+	0.512435i	−0.975183	−	0.221399i	$-0.928938\pi$
$443$	−6.22702	+	10.7855i	−0.295854	+	0.512435i	0.679329	+	0.733834i	$0.262271\pi$
$444$	−1.13705	+	1.96943i	−0.0539621	+	0.0934652i
$445$	−27.9517	+	48.4137i	−1.32504	+	2.29503i
$446$	7.67557	+	13.2945i	0.363449	+	0.629512i
$447$	4.03814	−	6.99426i	0.190997	−	0.330817i
$448$	−9.73502	−	16.8616i	−0.459937	−	0.796634i
$449$	25.4366			1.20043			0.600214	−	0.799840i	$-0.295082\pi$
$449$	25.4366			1.20043			0.600214	+	0.799840i	$0.295082\pi$
$450$	−9.52968			−0.449234
$451$	0.155994	+	0.270190i	0.00734547	+	0.0127227i
$452$	−0.760366	+	1.31699i	−0.0357646	+	0.0619461i
$453$	−10.1595	−	17.5968i	−0.477336	−	0.826771i
$454$	10.0708	−	17.4432i	0.472648	−	0.818651i
$455$	0.699377	−	1.21136i	0.0327873	−	0.0567893i
$456$	−2.59622	+	4.49679i	−0.121579	+	0.210581i
$457$	31.9740			1.49568			0.747839	−	0.663880i	$-0.231091\pi$
$457$	31.9740			1.49568			0.747839	+	0.663880i	$0.231091\pi$
$458$	10.3219	+	17.8781i	0.482312	+	0.835388i
$459$	−18.5319	−	32.0982i	−0.864995	−	1.49822i
$460$	3.48032	−	6.02809i	0.162271	−	0.281061i
$461$	19.3501			0.901223			0.450612	−	0.892720i	$-0.351206\pi$
$461$	19.3501			0.901223			0.450612	+	0.892720i	$0.351206\pi$
$462$	1.95603	+	3.38794i	0.0910028	+	0.157621i
$463$	0.0414625			0.00192693			0.000963463	−	1.00000i	$-0.499693\pi$
$463$	0.0414625			0.00192693			0.000963463		1.00000i	$0.499693\pi$
$464$	−4.07961			−0.189391
$465$		0			0
$466$	−6.48875			−0.300586
$467$	25.3083			1.17113			0.585564	−	0.810626i	$-0.300873\pi$
$467$	25.3083			1.17113			0.585564	+	0.810626i	$0.300873\pi$
$468$	−0.0265088	−	0.0459146i	−0.00122537	−	0.00212240i
$469$	1.20834			0.0557958
$470$	13.5706	−	23.5050i	0.625966	−	1.08420i
$471$	11.1734	+	19.3530i	0.514845	+	0.891737i
$472$	−4.02534	−	6.97210i	−0.185281	−	0.320917i
$473$	−9.15478			−0.420937
$474$	−4.26982	+	7.39555i	−0.196120	+	0.339689i
$475$	5.44282	−	9.42724i	0.249734	−	0.432551i
$476$	−2.84844	+	4.93365i	−0.130558	+	0.226133i
$477$	−2.92148	−	5.06015i	−0.133765	−	0.231688i
$478$	−5.42612	+	9.39831i	−0.248185	+	0.429869i
$479$	10.6206	+	18.3954i	0.485266	+	0.840506i	0.999857	−	0.0169301i	$-0.00538928\pi$
$479$	10.6206	+	18.3954i	0.485266	+	0.840506i	−0.514590	+	0.857436i	$0.672056\pi$
$480$	−12.4281			−0.567263
$481$	−0.650988			−0.0296825
$482$	4.33606	+	7.51028i	0.197502	+	0.342084i
$483$	7.51935	−	13.0239i	0.342142	−	0.592607i
$484$	−1.99767	−	3.46007i	−0.0908032	−	0.157276i
$485$	29.4889	−	51.0763i	1.33902	−	2.31926i
$486$	−5.09091	+	8.81772i	−0.230928	+	0.399980i
$487$	−13.3810	+	23.1765i	−0.606350	+	1.05023i	0.385486	+	0.922714i	$0.374034\pi$
$487$	−13.3810	+	23.1765i	−0.606350	+	1.05023i	−0.991837	+	0.127516i	$0.959300\pi$
$488$	5.30925			0.240338
$489$	−12.6450	−	21.9017i	−0.571824	−	0.990429i
$490$	−5.31488	−	9.20564i	−0.240102	−	0.415868i
$491$	6.28320	−	10.8828i	0.283557	−	0.491135i	−0.688701	−	0.725045i	$-0.741819\pi$
$491$	6.28320	−	10.8828i	0.283557	−	0.491135i	0.972258	+	0.233910i	$0.0751522\pi$
$492$	−0.192778			−0.00869109
$493$	4.39556	+	7.61333i	0.197966	+	0.342887i
$494$	−0.245520			−0.0110465
$495$	−2.87853			−0.129380
$496$		0			0
$497$	2.48886			0.111640
$498$	0.613636			0.0274977
$499$	11.5152	+	19.9449i	0.515490	+	0.892856i	0.999838	+	0.0179802i	$0.00572357\pi$
$499$	11.5152	+	19.9449i	0.515490	+	0.892856i	−0.484348	+	0.874875i	$0.660943\pi$
$500$	6.68083			0.298776
$501$	12.0216	−	20.8221i	0.537087	−	0.930263i
$502$	−14.3545	−	24.8626i	−0.640671	−	1.10967i
$503$	−0.330789	−	0.572944i	−0.0147492	−	0.0255463i	0.858557	−	0.512719i	$-0.171362\pi$
$503$	−0.330789	−	0.572944i	−0.0147492	−	0.0255463i	−0.873306	+	0.487172i	$0.838028\pi$
$504$	5.29266			0.235754
$505$	9.26062	−	16.0399i	0.412092	−	0.713764i
$506$	−2.78642	+	4.82622i	−0.123871	+	0.214551i
$507$	9.62706	−	16.6746i	0.427553	−	0.740543i
$508$	1.45306	+	2.51678i	0.0644693	+	0.111664i
$509$	5.83370	−	10.1043i	0.258574	−	0.447864i	−0.707286	−	0.706928i	$-0.750081\pi$
$509$	5.83370	−	10.1043i	0.258574	−	0.447864i	0.965860	+	0.259064i	$0.0834140\pi$
$510$	−23.4942	−	40.6932i	−1.04034	−	1.80193i
$511$	−17.3425			−0.767186
$512$	−25.2461			−1.11573
$513$	−3.24851	−	5.62659i	−0.143425	−	0.248420i
$514$	10.5498	−	18.2727i	0.465330	−	0.805975i
$515$	3.66849	+	6.35400i	0.161653	+	0.279991i
$516$	2.82837	−	4.89889i	0.124512	−	0.215661i
$517$	2.68000	−	4.64190i	0.117866	−	0.204151i
$518$	5.36722	−	9.29630i	0.235822	−	0.408456i
$519$	−3.46026			−0.151889
$520$	−0.969491	−	1.67921i	−0.0425150	−	0.0736381i
$521$	15.9592	+	27.6422i	0.699186	+	1.21103i	0.968749	+	0.248043i	$0.0797874\pi$
$521$	15.9592	+	27.6422i	0.699186	+	1.21103i	−0.269563	+	0.962983i	$0.586879\pi$
$522$	0.674533	−	1.16833i	0.0295235	−	0.0511362i
$523$	−0.00415040			−0.000181484			−9.07421e−5	−	1.00000i	$-0.500029\pi$
$523$	−0.00415040			−0.000181484			−9.07421e−5		1.00000i	$0.500029\pi$
$524$	2.57885	+	4.46669i	0.112657	+	0.195128i
$525$	30.6799			1.33898
$526$	−31.1411			−1.35782
$527$		0			0
$528$	4.30627			0.187406
$529$	−1.57699			−0.0685646
$530$	−17.6485	−	30.5682i	−0.766603	−	1.32780i
$531$	2.11403			0.0917411
$532$	−0.499312	+	0.864834i	−0.0216479	+	0.0374953i
$533$	−0.0275924	−	0.0477914i	−0.00119516	−	0.00207008i
$534$	13.8278	+	23.9505i	0.598388	+	1.03644i
$535$	−47.6086			−2.05830
$536$	0.837511	−	1.45061i	0.0361750	−	0.0626569i
$537$	12.5949	−	21.8150i	0.543509	−	0.941385i
$538$	−7.92522	+	13.7269i	−0.341680	+	0.591808i
$539$	−1.04961	−	1.81798i	−0.0452100	−	0.0783060i
$540$	4.23764	−	7.33980i	0.182359	−	0.315855i
$541$	−14.6375	−	25.3529i	−0.629316	−	1.09001i	−0.987689	−	0.156429i	$-0.950002\pi$
$541$	−14.6375	−	25.3529i	−0.629316	−	1.09001i	0.358373	−	0.933578i	$-0.383332\pi$
$542$	−34.4101			−1.47804
$543$	−10.8886			−0.467274
$544$	7.24492	+	12.5486i	0.310624	+	0.538016i
$545$	−19.5004	+	33.7756i	−0.835304	+	1.44679i
$546$	−0.345985	−	0.599263i	−0.0148068	−	0.0256461i
$547$	−20.5826	+	35.6502i	−0.880050	+	1.52429i	−0.0287668	+	0.999586i	$0.509158\pi$
$547$	−20.5826	+	35.6502i	−0.880050	+	1.52429i	−0.851284	+	0.524706i	$0.824175\pi$
$548$	−0.0265725	+	0.0460249i	−0.00113512	+	0.00196609i
$549$	−0.697078	+	1.20737i	−0.0297506	+	0.0515295i
$550$	−11.3689			−0.484773
$551$	0.770510	+	1.33456i	0.0328248	+	0.0568543i
$552$	−10.4235	−	18.0540i	−0.443653	−	0.768429i
$553$	−4.97150	+	8.61089i	−0.211410	+	0.366172i
$554$	−19.1983			−0.815658
$555$	−10.9197	−	18.9135i	−0.463517	−	0.802835i
$556$	−4.56167			−0.193458
$557$	−5.73810			−0.243131			−0.121566	−	0.992583i	$-0.538791\pi$
$557$	−5.73810			−0.243131			−0.121566	+	0.992583i	$0.538791\pi$
$558$		0			0
$559$	1.61931			0.0684894
$560$	25.3889			1.07288
$561$	−4.63978	−	8.03633i	−0.195891	−	0.339294i
$562$	38.3118			1.61609
$563$	7.14710	−	12.3791i	0.301214	−	0.521718i	−0.675197	−	0.737637i	$-0.735941\pi$
$563$	7.14710	−	12.3791i	0.301214	−	0.521718i	0.976411	+	0.215919i	$0.0692748\pi$
$564$	1.65598	+	2.86823i	0.0697292	+	0.120774i
$565$	−7.30221	−	12.6478i	−0.307206	−	0.532097i
$566$	3.98387			0.167455
$567$	6.53924	−	11.3263i	0.274622	−	0.475660i
$568$	1.72505	−	2.98788i	0.0723816	−	0.125369i
$569$	−7.18090	+	12.4377i	−0.301039	+	0.521414i	−0.976372	−	0.216099i	$-0.930667\pi$
$569$	−7.18090	+	12.4377i	−0.301039	+	0.521414i	0.675333	+	0.737513i	$0.264000\pi$
$570$	−4.11838	−	7.13324i	−0.172500	−	0.298778i
$571$	−16.6895	+	28.9071i	−0.698434	+	1.20972i	0.270575	+	0.962699i	$0.412786\pi$
$571$	−16.6895	+	28.9071i	−0.698434	+	1.20972i	−0.969009	+	0.247024i	$0.920547\pi$
$572$	−0.0316251	−	0.0547763i	−0.00132231	−	0.00229031i
$573$	11.6114			0.485075
$574$	0.909967			0.0379813
$575$	21.8522	+	37.8491i	0.911298	+	1.57841i
$576$	3.54362	−	6.13774i	0.147651	−	0.255739i
$577$	11.2398	+	19.4679i	0.467919	+	0.810460i	0.999328	−	0.0366557i	$-0.0116705\pi$
$577$	11.2398	+	19.4679i	0.467919	+	0.810460i	−0.531409	+	0.847116i	$0.678337\pi$
$578$	−16.6257	+	28.7965i	−0.691536	+	1.19778i
$579$	3.43731	−	5.95359i	0.142850	−	0.247423i
$580$	−1.00512	+	1.74092i	−0.0417353	+	0.0722877i
$581$	0.714477			0.0296415
$582$	−14.5883	−	25.2677i	−0.604705	−	1.04738i
$583$	−3.48533	−	6.03677i	−0.144348	−	0.250018i
$584$	−12.0203	+	20.8197i	−0.497402	+	0.861525i
$585$	0.509157			0.0210511
$586$	−1.20332	−	2.08422i	−0.0497088	−	0.0860982i
$587$	−6.41617			−0.264824			−0.132412	−	0.991195i	$-0.542272\pi$
$587$	−6.41617			−0.264824			−0.132412	+	0.991195i	$0.542272\pi$
$588$	1.29711			0.0534920
$589$		0			0
$590$	12.7708			0.525764
$591$	−33.2255			−1.36671
$592$	−5.90807	−	10.2331i	−0.242820	−	0.420577i
$593$	−20.8601			−0.856623			−0.428312	−	0.903631i	$-0.640891\pi$
$593$	−20.8601			−0.856623			−0.428312	+	0.903631i	$0.640891\pi$
$594$	−3.39274	+	5.87640i	−0.139206	+	0.241112i
$595$	−27.3551	−	47.3805i	−1.12145	−	1.94241i
$596$	−1.07657	−	1.86468i	−0.0440982	−	0.0763803i
$597$	−39.4884			−1.61615
$598$	0.492865	−	0.853666i	0.0201547	−	0.0349090i
$599$	5.77919	−	10.0099i	0.236131	−	0.408992i	−0.723469	−	0.690356i	$-0.757454\pi$
$599$	5.77919	−	10.0099i	0.236131	−	0.408992i	0.959601	+	0.281365i	$0.0907871\pi$
$600$	21.2646	−	36.8313i	0.868122	−	1.50363i
$601$	−2.15871	−	3.73899i	−0.0880555	−	0.152517i	0.818634	−	0.574316i	$-0.194732\pi$
$601$	−2.15871	−	3.73899i	−0.0880555	−	0.152517i	−0.906689	+	0.421799i	$0.861399\pi$
$602$	−13.3508	+	23.1242i	−0.544136	+	0.942471i
$603$	0.219922	+	0.380916i	0.00895592	+	0.0155121i
$604$	−5.41709			−0.220418
$605$	38.3694			1.55994
$606$	−4.58127	−	7.93499i	−0.186101	−	0.322337i
$607$	−22.4546	+	38.8925i	−0.911405	+	1.57860i	−0.0993241	+	0.995055i	$0.531668\pi$
$607$	−22.4546	+	38.8925i	−0.911405	+	1.57860i	−0.812081	+	0.583545i	$0.801665\pi$
$608$	1.26998	+	2.19968i	0.0515047	+	0.0892087i
$609$	−2.17159	+	3.76131i	−0.0879974	+	0.152416i
$610$	−4.21102	+	7.29370i	−0.170499	+	0.295313i
$611$	−0.474042	+	0.821065i	−0.0191777	+	0.0332167i
$612$	−2.07371			−0.0838248
$613$	1.30258	+	2.25614i	0.0526108	+	0.0911245i	0.891131	−	0.453745i	$-0.149912\pi$
$613$	1.30258	+	2.25614i	0.0526108	+	0.0911245i	−0.838521	+	0.544870i	$0.816579\pi$
$614$	−14.3937	−	24.9306i	−0.580883	−	1.00612i
$615$	0.925674	−	1.60332i	0.0373268	−	0.0646519i
$616$	6.31416			0.254405
$617$	12.4934	+	21.6392i	0.502965	+	0.871161i	0.999994	+	0.00342740i	$0.00109098\pi$
$617$	12.4934	+	21.6392i	0.502965	+	0.871161i	−0.497029	+	0.867734i	$0.665576\pi$
$618$	3.62963			0.146005
$619$	31.9083			1.28250			0.641252	−	0.767330i	$-0.278415\pi$
$619$	31.9083			1.28250			0.641252	+	0.767330i	$0.278415\pi$
$620$		0			0
$621$	26.0847			1.04674
$622$	20.1078			0.806251
$623$	16.1002	+	27.8863i	0.645040	+	1.11724i
$624$	−0.761698			−0.0304923
$625$	−8.47372	+	14.6769i	−0.338949	+	0.587077i
$626$	−4.02105	−	6.96466i	−0.160713	−	0.278364i
$627$	−0.813320	−	1.40871i	−0.0324809	−	0.0562585i
$628$	5.95771			0.237739
$629$	−12.7312	+	22.0512i	−0.507628	+	0.879238i
$630$	−4.19786	+	7.27091i	−0.167247	+	0.289680i
$631$	0.179876	−	0.311554i	0.00716073	−	0.0124028i	−0.862423	−	0.506189i	$-0.831054\pi$
$631$	0.179876	−	0.311554i	0.00716073	−	0.0124028i	0.869584	+	0.493786i	$0.164387\pi$
$632$	6.89160	+	11.9366i	0.274133	+	0.474813i
$633$	−0.984204	+	1.70469i	−0.0391186	+	0.0677554i
$634$	9.69014	+	16.7838i	0.384844	+	0.666570i
$635$	−27.9091			−1.10754
$636$	4.30718			0.170791
$637$	0.185657	+	0.321567i	0.00735598	+	0.0127409i
$638$	0.804720	−	1.39382i	0.0318592	−	0.0551817i
$639$	0.452982	+	0.784587i	0.0179197	+	0.0310378i
$640$	13.0339	−	22.5754i	0.515211	−	0.892372i
$641$	15.4035	−	26.6796i	0.608400	−	1.05378i	−0.383104	−	0.923705i	$-0.625145\pi$
$641$	15.4035	−	26.6796i	0.608400	−	1.05378i	0.991504	−	0.130075i	$-0.0415217\pi$
$642$	−11.7761	+	20.3968i	−0.464765	+	0.804997i
$643$	−1.75184			−0.0690856			−0.0345428	−	0.999403i	$-0.510998\pi$
$643$	−1.75184			−0.0690856			−0.0345428	+	0.999403i	$0.510998\pi$
$644$	−2.00467	−	3.47219i	−0.0789950	−	0.136823i
$645$	27.1624	+	47.0467i	1.06952	+	1.85246i
$646$	−4.80159	+	8.31659i	−0.188916	+	0.327212i
$647$	−24.6504			−0.969106			−0.484553	−	0.874762i	$-0.661018\pi$
$647$	−24.6504			−0.969106			−0.484553	+	0.874762i	$0.661018\pi$
$648$	−9.06483	−	15.7008i	−0.356100	−	0.616784i
$649$	2.52204			0.0989989
$650$	2.01095			0.0788760
$651$		0			0
$652$	−6.74233			−0.264050
$653$	−0.285664			−0.0111789			−0.00558946	−	0.999984i	$-0.501779\pi$
$653$	−0.285664			−0.0111789			−0.00558946	+	0.999984i	$0.501779\pi$
$654$	9.64692	+	16.7090i	0.377224	+	0.653372i
$655$	−49.5321			−1.93538
$656$	0.500831	−	0.867465i	0.0195542	−	0.0338688i
$657$	−3.15640	−	5.46704i	−0.123143	−	0.213290i
$658$	−7.81669	−	13.5389i	−0.304726	−	0.527802i
$659$	37.4247			1.45786			0.728929	−	0.684589i	$-0.240018\pi$
$659$	37.4247			1.45786			0.728929	+	0.684589i	$0.240018\pi$
$660$	1.06096	−	1.83764i	0.0412980	−	0.0715302i
$661$	−2.09579	+	3.63001i	−0.0815167	+	0.141191i	−0.903902	−	0.427740i	$-0.859310\pi$
$661$	−2.09579	+	3.63001i	−0.0815167	+	0.141191i	0.822385	+	0.568931i	$0.192643\pi$
$662$	5.67941	−	9.83703i	0.220737	−	0.382327i
$663$	0.820689	+	1.42147i	0.0318729	+	0.0552055i
$664$	0.495212	−	0.857732i	0.0192179	−	0.0332864i
$665$	−4.79517	−	8.30547i	−0.185949	−	0.322072i
$666$	3.90742			0.151410
$667$	−6.18699			−0.239561
$668$	−3.20499	−	5.55120i	−0.124005	−	0.214782i
$669$	8.99491	−	15.5796i	0.347763	−	0.602344i
$670$	1.32854	+	2.30110i	0.0513260	+	0.0888992i
$671$	−0.831616	+	1.44040i	−0.0321042	+	0.0556061i
$672$	−3.57930	+	6.19954i	−0.138075	+	0.239152i
$673$	−4.98633	+	8.63658i	−0.192209	+	0.332916i	−0.945982	−	0.324219i	$-0.894899\pi$
$673$	−4.98633	+	8.63658i	−0.192209	+	0.332916i	0.753773	+	0.657135i	$0.228232\pi$
$674$	−5.53349			−0.213142
$675$	26.6072	+	46.0850i	1.02411	+	1.77381i
$676$	−2.56659	−	4.44546i	−0.0987150	−	0.170979i
$677$	23.8788	−	41.3594i	0.917738	−	1.58957i	0.114896	−	0.993377i	$-0.463346\pi$
$677$	23.8788	−	41.3594i	0.917738	−	1.58957i	0.802842	−	0.596192i	$-0.203320\pi$
$678$	−7.22487			−0.277469
$679$	−16.9857	−	29.4200i	−0.651850	−	1.12904i
$680$	−75.8406			−2.90835
$681$	−23.6038			−0.904500
$682$		0			0
$683$	27.7600			1.06221			0.531104	−	0.847307i	$-0.321777\pi$
$683$	27.7600			1.06221			0.531104	+	0.847307i	$0.321777\pi$
$684$	−0.363507			−0.0138990
$685$	−0.255190	−	0.442002i	−0.00975032	−	0.0168880i
$686$	−25.5308			−0.974770
$687$	12.0961	−	20.9511i	0.461496	−	0.799335i
$688$	14.6961	+	25.4544i	0.560283	+	0.970438i
$689$	0.616490	+	1.06779i	0.0234864	+	0.0406796i
$690$	33.0694			1.25893
$691$	−19.0155	+	32.9358i	−0.723383	+	1.25294i	0.236253	+	0.971692i	$0.424081\pi$
$691$	−19.0155	+	32.9358i	−0.723383	+	1.25294i	−0.959636	+	0.281244i	$0.909253\pi$
$692$	−0.461255	+	0.798918i	−0.0175343	+	0.0303703i
$693$	−0.829018	+	1.43590i	−0.0314918	+	0.0545454i
$694$	−15.4559	−	26.7704i	−0.586698	−	1.01619i
$695$	21.9041	−	37.9390i	0.830869	−	1.43911i
$696$	3.01031	+	5.21401i	0.114105	+	0.197636i
$697$	−2.15848			−0.0817581
$698$	16.5214			0.625346
$699$	3.80205	+	6.58534i	0.143807	+	0.249080i
$700$	4.08965	−	7.08349i	0.154574	−	0.267731i
$701$	−20.5281	−	35.5558i	−0.775336	−	1.34292i	−0.934605	−	0.355687i	$-0.884247\pi$
$701$	−20.5281	−	35.5558i	−0.775336	−	1.34292i	0.159269	−	0.987235i	$-0.449086\pi$
$702$	0.600112	−	1.03942i	0.0226498	−	0.0392305i
$703$	−2.23170	+	3.86542i	−0.0841701	+	0.145787i
$704$	4.22755	−	7.32234i	0.159332	−	0.275971i
$705$	−31.8065			−1.19790
$706$	−6.85536	−	11.8738i	−0.258005	−	0.446878i
$707$	−5.33413	−	9.23898i	−0.200611	−	0.347468i
$708$	−0.779187	+	1.34959i	−0.0292836	+	0.0507207i
$709$	42.0657			1.57981			0.789906	−	0.613229i	$-0.210130\pi$
$709$	42.0657			1.57981			0.789906	+	0.613229i	$0.210130\pi$
$710$	2.73644	+	4.73966i	0.102697	+	0.177876i
$711$	−3.61933			−0.135736
$712$	44.6368			1.67284
$713$		0			0
$714$	−27.0654			−1.01290
$715$	0.607426			0.0227164
$716$	−3.35781	−	5.81590i	−0.125487	−	0.217350i
$717$	12.7176			0.474948
$718$	−21.3951	+	37.0573i	−0.798456	+	1.38297i
$719$	16.6345	+	28.8118i	0.620362	+	1.07450i	0.989418	+	0.145092i	$0.0463477\pi$
$719$	16.6345	+	28.8118i	0.620362	+	1.07450i	−0.369056	+	0.929407i	$0.620319\pi$
$720$	4.62087	+	8.00359i	0.172210	+	0.298276i
$721$	4.22611			0.157388
$722$	11.1910	−	19.3834i	0.416487	−	0.721377i
$723$	5.08138	−	8.80120i	0.188978	−	0.327320i
$724$	−1.45146	+	2.51400i	−0.0539429	+	0.0934319i
$725$	−6.31092	−	10.9308i	−0.234382	−	0.405961i
$726$	9.49077	−	16.4385i	0.352235	−	0.610089i
$727$	16.3614	+	28.3389i	0.606813	+	1.05103i	0.991762	+	0.128093i	$0.0408855\pi$
$727$	16.3614	+	28.3389i	0.606813	+	1.05103i	−0.384950	+	0.922938i	$0.625781\pi$
$728$	−1.11686			−0.0413934
$729$	29.8560			1.10578
$730$	−19.0677	−	33.0262i	−0.705726	−	1.22235i
$731$	31.6685	−	54.8514i	1.17130	−	2.02875i
$732$	−0.513856	−	0.890025i	−0.0189927	−	0.0328963i
$733$	4.98195	−	8.62900i	0.184013	−	0.318719i	−0.759231	−	0.650822i	$-0.774425\pi$
$733$	4.98195	−	8.62900i	0.184013	−	0.318719i	0.943243	+	0.332102i	$0.107758\pi$
$734$	−14.3324	+	24.8245i	−0.529020	+	0.916289i
$735$	−6.22844	+	10.7880i	−0.229739	+	0.397920i
$736$	−10.1976			−0.375889
$737$	0.262368	+	0.454434i	0.00966443	+	0.0167393i
$738$	0.165618	+	0.286858i	0.00609647	+	0.0105594i
$739$	−15.4792	+	26.8108i	−0.569412	+	0.986251i	0.427212	+	0.904152i	$0.359496\pi$
$739$	−15.4792	+	26.8108i	−0.569412	+	0.986251i	−0.996624	+	0.0820995i	$0.973837\pi$
$740$	−5.82244			−0.214037
$741$	0.143861	+	0.249175i	0.00528487	+	0.00915366i
$742$	−20.3312			−0.746380
$743$	1.11003			0.0407231			0.0203615	−	0.999793i	$-0.493518\pi$
$743$	1.11003			0.0407231			0.0203615	+	0.999793i	$0.493518\pi$
$744$		0			0
$745$	20.6778			0.757578
$746$	−41.7624			−1.52903
$747$	0.130038	+	0.225232i	0.00475783	+	0.00824080i
$748$	−2.47394			−0.0904563
$749$	−13.7113	+	23.7487i	−0.501000	+	0.867757i
$750$	15.8700	+	27.4877i	0.579491	+	1.00371i
$751$	−14.0777	−	24.3832i	−0.513701	−	0.889756i	−0.999874	−	0.0158933i	$-0.994941\pi$
$751$	−14.0777	−	24.3832i	−0.513701	−	0.889756i	0.486173	−	0.873863i	$-0.338393\pi$
$752$	−17.2087			−0.627538
$753$	−16.8218	+	29.1362i	−0.613021	+	1.06178i
$754$	−0.142340	+	0.246540i	−0.00518371	+	0.00897844i
$755$	26.0116	−	45.0535i	0.946661	−	1.63966i
$756$	−2.44088	−	4.22774i	−0.0887741	−	0.153761i
$757$	−19.3612	+	33.5345i	−0.703693	+	1.21883i	0.263468	+	0.964668i	$0.415134\pi$
$757$	−19.3612	+	33.5345i	−0.703693	+	1.21883i	−0.967161	+	0.254164i	$0.918200\pi$
$758$	20.5771	+	35.6406i	0.747395	+	1.29453i
$759$	6.53074			0.237051
$760$	−13.2943			−0.482236
$761$	−21.7184	−	37.6174i	−0.787293	−	1.36363i	−0.927620	−	0.373526i	$-0.878149\pi$
$761$	−21.7184	−	37.6174i	−0.787293	−	1.36363i	0.140327	−	0.990105i	$-0.455185\pi$
$762$	−6.90338	+	11.9570i	−0.250083	+	0.433157i
$763$	11.2322	+	19.4548i	0.406634	+	0.704311i
$764$	1.54781	−	2.68089i	0.0559979	−	0.0969913i
$765$	9.95749	−	17.2469i	0.360014	−	0.623562i
$766$	16.9601	−	29.3757i	0.612792	−	1.06139i
$767$	−0.446102			−0.0161078
$768$	6.75435	+	11.6989i	0.243727	+	0.422147i
$769$	1.55509	+	2.69350i	0.0560781	+	0.0971302i	0.892702	−	0.450648i	$-0.148807\pi$
$769$	1.55509	+	2.69350i	0.0560781	+	0.0971302i	−0.836624	+	0.547778i	$0.815474\pi$
$770$	−5.00806	+	8.67422i	−0.180478	+	0.312597i
$771$	−24.7263			−0.890494
$772$	−0.916391	−	1.58724i	−0.0329816	−	0.0571259i
$773$	21.6402			0.778343			0.389172	−	0.921165i	$-0.372761\pi$
$773$	21.6402			0.778343			0.389172	+	0.921165i	$0.372761\pi$
$774$	−9.71956			−0.349362
$775$		0			0
$776$	−47.0918			−1.69050
$777$	−12.5796			−0.451289
$778$	11.2332	+	19.4564i	0.402729	+	0.697547i
$779$	−0.378366			−0.0135564
$780$	−0.187665	+	0.325045i	−0.00671947	+	0.0116385i
$781$	0.540408	+	0.936015i	0.0193373	+	0.0334932i
$782$	−19.2777	−	33.3900i	−0.689369	−	1.19402i
$783$	−7.53327			−0.269217
$784$	−3.36986	+	5.83678i	−0.120352	+	0.208456i
$785$	−28.6076	+	49.5498i	−1.02105	+	1.76851i
$786$	−12.2519	+	21.2209i	−0.437010	+	0.756924i
$787$	3.93827	+	6.82128i	0.140384	+	0.243152i	0.927641	−	0.373472i	$-0.121833\pi$
$787$	3.93827	+	6.82128i	0.140384	+	0.243152i	−0.787257	+	0.616625i	$0.788500\pi$
$788$	−4.42898	+	7.67122i	−0.157776	+	0.273276i
$789$	18.2470	+	31.6046i	0.649609	+	1.12516i
$790$	−21.8642			−0.777894
$791$	−8.41216			−0.299102
$792$	1.14920	+	1.99048i	0.0408351	+	0.0707285i
$793$	0.147097	−	0.254780i	0.00522357	−	0.00904750i
$794$	−6.30104	−	10.9137i	−0.223616	−	0.387314i
$795$	−20.6821	+	35.8225i	−0.733519	+	1.27049i
$796$	−5.26383	+	9.11722i	−0.186571	+	0.323151i
$797$	−14.7591	+	25.5635i	−0.522793	+	0.905505i	0.476855	+	0.878982i	$0.341777\pi$
$797$	−14.7591	+	25.5635i	−0.522793	+	0.905505i	−0.999648	+	0.0265226i	$0.991557\pi$
$798$	−4.74438			−0.167949
$799$	18.5415	+	32.1148i	0.655950	+	1.13614i
$800$	−10.4019	−	18.0166i	−0.367763	−	0.636984i
$801$	−5.86059	+	10.1508i	−0.207074	+	0.358663i
$802$	25.1998			0.889835
$803$	−3.76559	−	6.52220i	−0.132885	−	0.230163i
$804$	−0.324234			−0.0114349
$805$	38.5039			1.35708
$806$		0			0
$807$	18.5749			0.653869
$808$	−14.7886			−0.520260
$809$	1.06376	+	1.84249i	0.0373999	+	0.0647786i	0.884119	−	0.467261i	$-0.154759\pi$
$809$	1.06376	+	1.84249i	0.0373999	+	0.0647786i	−0.846720	+	0.532039i	$0.821426\pi$
$810$	28.7590			1.01049
$811$	−3.60252	+	6.23975i	−0.126502	+	0.219107i	−0.922319	−	0.386430i	$-0.873708\pi$
$811$	−3.60252	+	6.23975i	−0.126502	+	0.219107i	0.795817	+	0.605537i	$0.207042\pi$
$812$	0.578950	+	1.00277i	0.0203172	+	0.0351904i
$813$	20.1624	+	34.9223i	0.707127	+	1.22478i
$814$	4.66157			0.163388
$815$	32.3751	−	56.0753i	1.13405	−	1.96423i
$816$	−14.8964	+	25.8013i	−0.521477	+	0.903225i
$817$	5.55126	−	9.61507i	0.194214	−	0.336389i
$818$	15.4054	+	26.6829i	0.538636	+	0.932945i
$819$	0.146638	−	0.253984i	0.00512393	−	0.00887491i
$820$	−0.246786	−	0.427446i	−0.00861815	−	0.0149271i
$821$	42.0597			1.46789			0.733947	−	0.679206i	$-0.237676\pi$
$821$	42.0597			1.46789			0.733947	+	0.679206i	$0.237676\pi$
$822$	−0.252487			−0.00880651
$823$	15.0865	+	26.1306i	0.525882	+	0.910854i	0.999545	+	0.0301481i	$0.00959789\pi$
$823$	15.0865	+	26.1306i	0.525882	+	0.910854i	−0.473664	+	0.880706i	$0.657069\pi$
$824$	2.92916	−	5.07345i	0.102042	−	0.176742i
$825$	6.66156	+	11.5382i	0.231926	+	0.401707i
$826$	3.67799	−	6.37046i	0.127974	−	0.221657i
$827$	1.93523	−	3.35191i	0.0672945	−	0.116557i	−0.830415	−	0.557145i	$-0.811897\pi$
$827$	1.93523	−	3.35191i	0.0672945	−	0.116557i	0.897710	+	0.440588i	$0.145230\pi$
$828$	0.729715	−	1.26390i	0.0253594	−	0.0439237i
$829$	13.1716			0.457469			0.228735	−	0.973489i	$-0.426541\pi$
$829$	13.1716			0.457469			0.228735	+	0.973489i	$0.426541\pi$
$830$	0.785552	+	1.36062i	0.0272669	+	0.0472277i
$831$	11.2491	+	19.4841i	0.390228	+	0.675895i
$832$	−0.747774	+	1.29518i	−0.0259244	+	0.0449024i
$833$	14.5234			0.503206
$834$	−10.8360	−	18.7686i	−0.375222	−	0.649903i
$835$	61.5585			2.13032
$836$	−0.433665			−0.0149986
$837$		0			0
$838$	−5.58159			−0.192813
$839$	−34.2490			−1.18241			−0.591204	−	0.806522i	$-0.701347\pi$
$839$	−34.2490			−1.18241			−0.591204	+	0.806522i	$0.701347\pi$
$840$	−18.7342	−	32.4487i	−0.646393	−	1.11959i
$841$	−27.2132			−0.938386
$842$	7.86792	−	13.6276i	0.271147	−	0.469640i
$843$	−22.4486	−	38.8821i	−0.773170	−	1.33917i
$844$	0.262390	+	0.454473i	0.00903184	+	0.0156436i
$845$	49.2967			1.69586
$846$	2.84534	−	4.92827i	0.0978247	−	0.169437i
$847$	11.0504	−	19.1399i	0.379697	−	0.657654i
$848$	−11.1899	+	19.3815i	−0.384264	+	0.665565i
$849$	−2.33432	−	4.04317i	−0.0801138	−	0.138761i
$850$	39.3278	−	68.1177i	1.34893	−	2.33642i
$851$	−8.95996	−	15.5191i	−0.307144	−	0.531988i
$852$	−0.667838			−0.0228797
$853$	−14.4479			−0.494686			−0.247343	−	0.968928i	$-0.579557\pi$
$853$	−14.4479			−0.494686			−0.247343	+	0.968928i	$0.579557\pi$
$854$	2.42555	+	4.20118i	0.0830007	+	0.143761i
$855$	1.74548	−	3.02326i	0.0596941	−	0.103393i
$856$	19.0069	+	32.9209i	0.649642	+	1.12521i
$857$	−13.9165	+	24.1041i	−0.475379	+	0.823381i	−0.999602	−	0.0281998i	$-0.991023\pi$
$857$	−13.9165	+	24.1041i	−0.475379	+	0.823381i	0.524223	+	0.851581i	$0.324356\pi$
$858$	0.150248	−	0.260237i	0.00512939	−	0.00888436i
$859$	23.6601	−	40.9805i	0.807272	−	1.39824i	−0.107475	−	0.994208i	$-0.534277\pi$
$859$	23.6601	−	40.9805i	0.807272	−	1.39824i	0.914747	−	0.404028i	$-0.132390\pi$
$860$	14.4831			0.493869
$861$	−0.533190	−	0.923512i	−0.0181711	−	0.0314732i
$862$	11.7574	+	20.3644i	0.400459	+	0.693616i
$863$	−13.0267	+	22.5629i	−0.443434	+	0.768049i	−0.997942	−	0.0641289i	$-0.979573\pi$
$863$	−13.0267	+	22.5629i	−0.443434	+	0.768049i	0.554508	+	0.832178i	$0.312906\pi$
$864$	−12.4166			−0.422422
$865$	−4.42969	−	7.67244i	−0.150614	−	0.260871i
$866$	−45.7502			−1.55465
$867$	38.9668			1.32338
$868$		0			0
$869$	−4.31787			−0.146474
$870$	−9.55048			−0.323792
$871$	−0.0464079	−	0.0803808i	−0.00157247	−	0.00272360i
$872$	31.1407			1.05456
$873$	6.18291	−	10.7091i	0.209260	−	0.362449i
$874$	−3.37925	−	5.85303i	−0.114305	−	0.197982i
$875$	18.4780	+	32.0049i	0.624671	+	1.08196i
$876$	4.65353			0.157228
$877$	17.1607	−	29.7233i	0.579477	−	1.00368i	−0.416062	−	0.909336i	$-0.636590\pi$
$877$	17.1607	−	29.7233i	0.579477	−	1.00368i	0.995539	−	0.0943474i	$-0.0300764\pi$
$878$	12.0387	−	20.8516i	0.406285	−	0.703706i
$879$	−1.41016	+	2.44247i	−0.0475635	+	0.0823824i
$880$	5.51271	+	9.54830i	0.185834	+	0.321873i
$881$	1.81734	−	3.14772i	0.0612276	−	0.106049i	−0.833787	−	0.552087i	$-0.813832\pi$
$881$	1.81734	−	3.14772i	0.0612276	−	0.106049i	0.895014	+	0.446037i	$0.147165\pi$
$882$	−1.11436	−	1.93014i	−0.0375226	−	0.0649911i
$883$	39.4574			1.32785			0.663923	−	0.747801i	$-0.268890\pi$
$883$	39.4574			1.32785			0.663923	+	0.747801i	$0.268890\pi$
$884$	0.437594			0.0147179
$885$	−7.48295	−	12.9609i	−0.251537	−	0.435674i
$886$	−7.88715	+	13.6609i	−0.264974	+	0.458948i
$887$	21.1514	+	36.6352i	0.710194	+	1.23009i	0.964784	+	0.263042i	$0.0847259\pi$
$887$	21.1514	+	36.6352i	0.710194	+	1.23009i	−0.254591	+	0.967049i	$0.581941\pi$
$888$	−8.71903	+	15.1018i	−0.292591	+	0.506783i
$889$	−8.03785	+	13.9220i	−0.269581	+	0.466927i
$890$	−35.4036	+	61.3209i	−1.18673	+	2.05548i
$891$	5.67949			0.190270
$892$	−2.39806	−	4.15355i	−0.0802929	−	0.139071i
$893$	3.25019	+	5.62950i	0.108764	+	0.188384i
$894$	5.11471	−	8.85894i	0.171062	−	0.296287i
$895$	64.4938			2.15579
$896$	−7.50756	−	13.0035i	−0.250810	−	0.434416i
$897$	−1.15516			−0.0385698
$898$	32.2180			1.07513
$899$		0			0
$900$	2.97733			0.0992444
$901$	48.2262			1.60665
$902$	0.197582	+	0.342222i	0.00657877	+	0.0113948i
$903$	31.2912			1.04131
$904$	−5.83056	+	10.0988i	−0.193921	+	0.335882i
$905$	−13.9391	−	24.1433i	−0.463352	−	0.802549i
$906$	−12.8681	−	22.2882i	−0.427513	−	0.740475i
$907$	−32.3680			−1.07476			−0.537381	−	0.843339i	$-0.680586\pi$
$907$	−32.3680			−1.07476			−0.537381	+	0.843339i	$0.680586\pi$
$908$	−3.14641	+	5.44973i	−0.104417	+	0.180856i
$909$	1.94166	−	3.36306i	0.0644009	−	0.111546i
$910$	0.885832	−	1.53431i	0.0293650	−	0.0508617i
$911$	13.5304	+	23.4353i	0.448281	+	0.776446i	0.998274	−	0.0587233i	$-0.0187030\pi$
$911$	13.5304	+	23.4353i	0.448281	+	0.776446i	−0.549993	+	0.835169i	$0.685370\pi$
$912$	−2.61123	+	4.52278i	−0.0864665	+	0.149764i
$913$	0.155135	+	0.268702i	0.00513423	+	0.00889274i
$914$	40.4983			1.33956
$915$	9.86969			0.326282
$916$	−3.22485	−	5.58560i	−0.106552	−	0.184553i
$917$	−14.2653	+	24.7082i	−0.471081	+	0.815937i
$918$	−23.4725	−	40.6556i	−0.774709	−	1.34184i
$919$	−10.3825	+	17.9830i	−0.342486	+	0.593203i	−0.984894	−	0.173160i	$-0.944602\pi$
$919$	−10.3825	+	17.9830i	−0.342486	+	0.593203i	0.642408	+	0.766363i	$0.277936\pi$
$920$	26.6874	−	46.2240i	0.879858	−	1.52396i
$921$	−16.8678	+	29.2159i	−0.555814	+	0.962697i
$922$	24.5088			0.807156
$923$	−0.0955880	−	0.165563i	−0.00314632	−	0.00544958i
$924$	−0.611117	−	1.05849i	−0.0201043	−	0.0348216i
$925$	18.2789	−	31.6600i	0.601007	−	1.04097i
$926$	0.0525165			0.00172580
$927$	0.769168	+	1.33224i	0.0252628	+	0.0437564i
$928$	2.94508			0.0966771
$929$	−20.6589			−0.677798			−0.338899	−	0.940823i	$-0.610055\pi$
$929$	−20.6589			−0.677798			−0.338899	+	0.940823i	$0.610055\pi$
$930$		0			0
$931$	2.54585			0.0834368
$932$	2.02726			0.0664052
$933$	−11.7821	−	20.4071i	−0.385728	−	0.668100i
$934$	32.0555			1.04889
$935$	11.8793	−	20.5756i	0.388495	−	0.672893i
$936$	−0.203272	−	0.352078i	−0.00664416	−	0.0115080i
$937$	−1.46030	−	2.52931i	−0.0477059	−	0.0826291i	0.841186	−	0.540745i	$-0.181858\pi$
$937$	−1.46030	−	2.52931i	−0.0477059	−	0.0826291i	−0.888892	+	0.458116i	$0.848524\pi$
$938$	1.53048			0.0499720
$939$	−4.71222	+	8.16180i	−0.153777	+	0.266350i
$940$	−4.23983	+	7.34360i	−0.138288	+	0.239522i
$941$	−16.4250	+	28.4490i	−0.535441	+	0.927411i	0.463701	+	0.885992i	$0.346521\pi$
$941$	−16.4250	+	28.4490i	−0.535441	+	0.927411i	−0.999142	+	0.0414194i	$0.986812\pi$
$942$	14.1523	+	24.5125i	0.461107	+	0.798660i
$943$	0.759543	−	1.31557i	0.0247341	−	0.0428407i
$944$	−4.04861	−	7.01240i	−0.131771	−	0.228234i
$945$	46.8823			1.52508
$946$	−11.5955			−0.377001
$947$	−19.5624	−	33.8830i	−0.635692	−	1.10105i	−0.986368	−	0.164553i	$-0.947382\pi$
$947$	−19.5624	−	33.8830i	−0.635692	−	1.10105i	0.350677	−	0.936497i	$-0.385952\pi$
$948$	1.33401	−	2.31057i	0.0433266	−	0.0750438i
$949$	0.666062	+	1.15365i	0.0216213	+	0.0374492i
$950$	6.89388	−	11.9406i	0.223667	−	0.387403i
$951$	11.3558	−	19.6687i	0.368236	−	0.637803i
$952$	−21.8421	+	37.8317i	−0.707907	+	1.22613i
$953$	6.01975			0.194999			0.0974994	−	0.995236i	$-0.468916\pi$
$953$	6.01975			0.194999			0.0974994	+	0.995236i	$0.468916\pi$
$954$	−3.70035	−	6.40919i	−0.119803	−	0.207505i
$955$	14.8645	+	25.7461i	0.481004	+	0.833123i
$956$	1.69527	−	2.93629i	0.0548288	−	0.0949663i
$957$	−1.88608			−0.0609684
$958$	13.4520	+	23.2996i	0.434616	+	0.752776i
$959$	−0.293980			−0.00949310
$960$	−50.1729			−1.61932
$961$		0			0
$962$	−0.824543			−0.0265843
$963$	−9.98204			−0.321667
$964$	−1.35470	−	2.34641i	−0.0436320	−	0.0755729i
$965$	17.6012			0.566603
$966$	9.52401	−	16.4961i	0.306430	−	0.530753i
$967$	−13.1552	−	22.7854i	−0.423042	−	0.732730i	0.573194	−	0.819420i	$-0.305704\pi$
$967$	−13.1552	−	22.7854i	−0.423042	−	0.732730i	−0.996235	+	0.0866903i	$0.972371\pi$
$968$	−15.3183	−	26.5321i	−0.492350	−	0.852775i
$969$	11.2538			0.361525
$970$	37.3507	−	64.6934i	1.19926	−	2.07718i
$971$	2.36793	−	4.10138i	0.0759906	−	0.131620i	−0.825526	−	0.564364i	$-0.809121\pi$
$971$	2.36793	−	4.10138i	0.0759906	−	0.131620i	0.901517	+	0.432744i	$0.142455\pi$
$972$	1.59054	−	2.75489i	0.0510165	−	0.0883632i
$973$	−12.6168	−	21.8529i	−0.404475	−	0.700572i
$974$	−16.9484	+	29.3554i	−0.543061	+	0.940609i
$975$	−1.17830	−	2.04088i	−0.0377359	−	0.0653606i
$976$	5.33994			0.170927
$977$	−17.2800			−0.552837			−0.276419	−	0.961037i	$-0.589148\pi$
$977$	−17.2800			−0.552837			−0.276419	+	0.961037i	$0.589148\pi$
$978$	−16.0161	−	27.7407i	−0.512139	−	0.887050i
$979$	−6.99171	+	12.1100i	−0.223456	+	0.387037i
$980$	1.66051	+	2.87609i	0.0530431	+	0.0918733i
$981$	−4.08862	+	7.08170i	−0.130540	+	0.226101i
$982$	7.95831	−	13.7842i	0.253960	−	0.439871i
$983$	20.4833	−	35.4781i	0.653315	−	1.13157i	−0.328999	−	0.944330i	$-0.606711\pi$
$983$	20.4833	−	35.4781i	0.653315	−	1.13157i	0.982313	−	0.187244i	$-0.0599554\pi$
$984$	−1.47824			−0.0471245
$985$	−42.5339	−	73.6709i	−1.35524	−	2.34735i
$986$	5.56742	+	9.64305i	0.177303	+	0.307097i
$987$	−9.16029	+	15.8661i	−0.291575	+	0.505023i
$988$	0.0767071			0.00244038
$989$	22.2876	+	38.6032i	0.708703	+	1.22751i
$990$	−3.64595			−0.115876
$991$	14.1338			0.448975			0.224487	−	0.974477i	$-0.427929\pi$
$991$	14.1338			0.448975			0.224487	+	0.974477i	$0.427929\pi$
$992$		0			0
$993$	−13.3113			−0.422420
$994$	3.15239			0.0999877
$995$	−50.5514	−	87.5576i	−1.60259	−	2.77576i
$996$	−0.191716			−0.00607477
$997$	−7.72692	+	13.3834i	−0.244714	+	0.423857i	−0.962051	−	0.272869i	$-0.912027\pi$
$997$	−7.72692	+	13.3834i	−0.244714	+	0.423857i	0.717337	+	0.696726i	$0.245361\pi$
$998$	14.5852	+	25.2622i	0.461685	+	0.799662i
$999$	−10.9096	−	18.8961i	−0.345166	−	0.597845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.j.521.6		16
31.2	even	5		961.2.g.t.844.2		16
31.3	odd	30		961.2.d.q.628.3		16
31.4	even	5		31.2.g.a.28.1	yes	16
31.5	even	3	inner	961.2.c.j.439.6		16
31.6	odd	6		961.2.a.j.1.6		8
31.7	even	15		961.2.d.o.388.2		16
31.8	even	5		961.2.g.k.732.1		16
31.9	even	15		31.2.g.a.10.1	✓	16
31.10	even	15		961.2.g.s.547.2		16
31.11	odd	30		961.2.g.j.235.1		16
31.12	odd	30		961.2.d.q.531.3		16
31.13	odd	30		961.2.g.n.846.2		16
31.14	even	15		961.2.d.o.374.2		16
31.15	odd	10		961.2.g.m.448.2		16
31.16	even	5		961.2.g.s.448.2		16
31.17	odd	30		961.2.d.n.374.2		16
31.18	even	15		961.2.g.t.846.2		16
31.19	even	15		961.2.d.p.531.3		16
31.20	even	15		961.2.g.k.235.1		16
31.21	odd	30		961.2.g.m.547.2		16
31.22	odd	30		961.2.g.l.816.1		16
31.23	odd	10		961.2.g.j.732.1		16
31.24	odd	30		961.2.d.n.388.2		16
31.25	even	3		961.2.a.i.1.6		8
31.26	odd	6		961.2.c.i.439.6		16
31.27	odd	10		961.2.g.l.338.1		16
31.28	even	15		961.2.d.p.628.3		16
31.29	odd	10		961.2.g.n.844.2		16
31.30	odd	2		961.2.c.i.521.6		16
93.35	odd	10		279.2.y.c.28.2		16
93.56	odd	6		8649.2.a.bf.1.3		8
93.68	even	6		8649.2.a.be.1.3		8
93.71	odd	30		279.2.y.c.10.2		16
124.35	odd	10		496.2.bg.c.369.2		16
124.71	odd	30		496.2.bg.c.289.2		16
155.4	even	10		775.2.bl.a.276.2		16
155.9	even	30		775.2.bl.a.351.2		16
155.97	odd	20		775.2.ck.a.524.1		32
155.102	odd	60		775.2.ck.a.599.4		32
155.128	odd	20		775.2.ck.a.524.4		32
155.133	odd	60		775.2.ck.a.599.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.1	✓	16	31.9	even	15
31.2.g.a.28.1	yes	16	31.4	even	5
279.2.y.c.10.2		16	93.71	odd	30
279.2.y.c.28.2		16	93.35	odd	10
496.2.bg.c.289.2		16	124.71	odd	30
496.2.bg.c.369.2		16	124.35	odd	10
775.2.bl.a.276.2		16	155.4	even	10
775.2.bl.a.351.2		16	155.9	even	30
775.2.ck.a.524.1		32	155.97	odd	20
775.2.ck.a.524.4		32	155.128	odd	20
775.2.ck.a.599.1		32	155.133	odd	60
775.2.ck.a.599.4		32	155.102	odd	60
961.2.a.i.1.6		8	31.25	even	3
961.2.a.j.1.6		8	31.6	odd	6
961.2.c.i.439.6		16	31.26	odd	6
961.2.c.i.521.6		16	31.30	odd	2
961.2.c.j.439.6		16	31.5	even	3	inner
961.2.c.j.521.6		16	1.1	even	1	trivial
961.2.d.n.374.2		16	31.17	odd	30
961.2.d.n.388.2		16	31.24	odd	30
961.2.d.o.374.2		16	31.14	even	15
961.2.d.o.388.2		16	31.7	even	15
961.2.d.p.531.3		16	31.19	even	15
961.2.d.p.628.3		16	31.28	even	15
961.2.d.q.531.3		16	31.12	odd	30
961.2.d.q.628.3		16	31.3	odd	30
961.2.g.j.235.1		16	31.11	odd	30
961.2.g.j.732.1		16	31.23	odd	10
961.2.g.k.235.1		16	31.20	even	15
961.2.g.k.732.1		16	31.8	even	5
961.2.g.l.338.1		16	31.27	odd	10
961.2.g.l.816.1		16	31.22	odd	30
961.2.g.m.448.2		16	31.15	odd	10
961.2.g.m.547.2		16	31.21	odd	30
961.2.g.n.844.2		16	31.29	odd	10
961.2.g.n.846.2		16	31.13	odd	30
961.2.g.s.448.2		16	31.16	even	5
961.2.g.s.547.2		16	31.10	even	15
961.2.g.t.844.2		16	31.2	even	5
961.2.g.t.846.2		16	31.18	even	15
8649.2.a.be.1.3		8	93.68	even	6
8649.2.a.bf.1.3		8	93.56	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.26660 q^{2} +(-0.742157 - 1.28545i) q^{3} -0.395721 q^{4} +(1.90016 - 3.29117i) q^{5} +(-0.940018 - 1.62816i) q^{6} +(-1.09449 - 1.89572i) q^{7} -3.03442 q^{8} +(0.398405 - 0.690057i) q^{9} +(2.40675 - 4.16861i) q^{10} +(0.475298 - 0.823240i) q^{11} +(0.293687 + 0.508681i) q^{12} +(-0.0840712 + 0.145616i) q^{13} +(-1.38629 - 2.40112i) q^{14} -5.64087 q^{15} -3.05196 q^{16} +(3.28833 + 5.69555i) q^{17} +(0.504620 - 0.874027i) q^{18} +(0.576421 + 0.998390i) q^{19} +(-0.751933 + 1.30239i) q^{20} +(-1.62457 + 2.81385i) q^{21} +(0.602013 - 1.04272i) q^{22} -4.62850 q^{23} +(2.25202 + 3.90061i) q^{24} +(-4.72122 - 8.17739i) q^{25} +(-0.106485 + 0.184437i) q^{26} -5.63566 q^{27} +(0.433114 + 0.750176i) q^{28} +1.33672 q^{29} -7.14474 q^{30} +2.20322 q^{32} -1.41098 q^{33} +(4.16500 + 7.21399i) q^{34} -8.31886 q^{35} +(-0.157657 + 0.273070i) q^{36} +(1.93582 + 3.35295i) q^{37} +(0.730096 + 1.26456i) q^{38} +0.249576 q^{39} +(-5.76589 + 9.98682i) q^{40} +(-0.164101 + 0.284232i) q^{41} +(-2.05769 + 3.56402i) q^{42} +(-4.81529 - 8.34032i) q^{43} +(-0.188085 + 0.325773i) q^{44} +(-1.51407 - 2.62244i) q^{45} -5.86247 q^{46} +5.63858 q^{47} +(2.26504 + 3.92316i) q^{48} +(1.10416 - 1.91247i) q^{49} +(-5.97990 - 10.3575i) q^{50} +(4.88091 - 8.45399i) q^{51} +(0.0332687 - 0.0576231i) q^{52} +(3.66647 - 6.35052i) q^{53} -7.13814 q^{54} +(-1.80628 - 3.12858i) q^{55} +(3.32116 + 5.75242i) q^{56} +(0.855590 - 1.48193i) q^{57} +1.69309 q^{58} +(1.32656 + 2.29767i) q^{59} +2.23221 q^{60} -1.74967 q^{61} -1.74421 q^{63} +8.89454 q^{64} +(0.319498 + 0.553386i) q^{65} -1.78715 q^{66} +(-0.276003 + 0.478052i) q^{67} +(-1.30126 - 2.25385i) q^{68} +(3.43508 + 5.94973i) q^{69} -10.5367 q^{70} +(-0.568494 + 0.984661i) q^{71} +(-1.20893 + 2.09393i) q^{72} +(3.96130 - 6.86117i) q^{73} +(2.45192 + 4.24685i) q^{74} +(-7.00778 + 12.1378i) q^{75} +(-0.228102 - 0.395084i) q^{76} -2.08084 q^{77} +0.316114 q^{78} +(-2.27114 - 3.93373i) q^{79} +(-5.79922 + 10.0445i) q^{80} +(2.98733 + 5.17421i) q^{81} +(-0.207851 + 0.360008i) q^{82} +(-0.163198 + 0.282667i) q^{83} +(0.642878 - 1.11350i) q^{84} +24.9934 q^{85} +(-6.09905 - 10.5639i) q^{86} +(-0.992053 - 1.71829i) q^{87} +(-1.44225 + 2.49806i) q^{88} -14.7102 q^{89} +(-1.91772 - 3.32158i) q^{90} +0.368062 q^{91} +1.83159 q^{92} +7.14183 q^{94} +4.38117 q^{95} +(-1.63514 - 2.83214i) q^{96} +15.5192 q^{97} +(1.39853 - 2.42233i) q^{98} +(-0.378722 - 0.655965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 3 q^{3} + 16 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} - 18 q^{8} - 5 q^{9} + 13 q^{10} + 18 q^{11} + 8 q^{13} + 9 q^{14} - 36 q^{15} + 8 q^{16} + 14 q^{17} - 23 q^{18} + 6 q^{19} + 7 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 3 * q^3 + 16 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 - 18 * q^8 - 5 * q^9 + 13 * q^10 + 18 * q^11 + 8 * q^13 + 9 * q^14 - 36 * q^15 + 8 * q^16 + 14 * q^17 - 23 * q^18 + 6 * q^19 + 7 * q^20 - q^21 + 4 * q^22 - 44 * q^23 + 30 * q^24 - 13 * q^25 + 9 * q^26 - 36 * q^27 + 5 * q^28 - 24 * q^29 - 22 * q^30 - 42 * q^32 + 12 * q^33 - 7 * q^34 - 24 * q^35 + q^36 - 8 * q^37 - 7 * q^38 + 2 * q^39 - 11 * q^40 + 22 * q^41 - 6 * q^42 - 2 * q^43 + 4 * q^44 - 36 * q^46 - 36 * q^47 - q^48 + 2 * q^49 - 27 * q^50 - 2 * q^51 - q^52 + 6 * q^53 + 14 * q^54 + 28 * q^55 - 30 * q^56 - 17 * q^57 + 10 * q^58 + 4 * q^59 + 80 * q^60 - 60 * q^61 - 46 * q^63 + 18 * q^64 + 3 * q^65 + 20 * q^66 + 13 * q^67 + 30 * q^68 - 22 * q^69 - 78 * q^70 + q^71 - 3 * q^72 + 2 * q^73 + 8 * q^74 + 23 * q^75 + 33 * q^76 + 48 * q^77 + 8 * q^79 - 24 * q^80 + 28 * q^81 + 19 * q^82 + 39 * q^83 + 8 * q^84 + 52 * q^85 - 16 * q^86 + 15 * q^87 - 17 * q^88 - 54 * q^89 - 8 * q^90 - 32 * q^91 - 64 * q^92 + 44 * q^94 - 12 * q^95 - 12 * q^96 + 68 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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