LMFDB - Embedded newform 572.2.i.a.133.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(133,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("572.133");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			133.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	572.133
Dual form			572.2.i.a.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 0.633975i) q^{3} -1.00000 q^{5} +(0.366025 - 0.633975i) q^{7} +(1.23205 - 2.13397i) q^{9} +O(q^{10})$	\(q+(-0.366025 - 0.633975i) q^{3} -1.00000 q^{5} +(0.366025 - 0.633975i) q^{7} +(1.23205 - 2.13397i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-3.59808 - 0.232051i) q^{13} +(0.366025 + 0.633975i) q^{15} +(1.59808 - 2.76795i) q^{17} +(1.36603 - 2.36603i) q^{19} -0.535898 q^{21} +(-3.73205 - 6.46410i) q^{23} -4.00000 q^{25} -4.00000 q^{27} +(0.133975 + 0.232051i) q^{29} +6.00000 q^{31} +(0.366025 - 0.633975i) q^{33} +(-0.366025 + 0.633975i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(1.16987 + 2.36603i) q^{39} +(-2.86603 - 4.96410i) q^{41} +(5.46410 - 9.46410i) q^{43} +(-1.23205 + 2.13397i) q^{45} +3.26795 q^{47} +(3.23205 + 5.59808i) q^{49} -2.33975 q^{51} -11.3923 q^{53} +(-0.500000 - 0.866025i) q^{55} -2.00000 q^{57} +(2.63397 - 4.56218i) q^{59} +(-5.86603 + 10.1603i) q^{61} +(-0.901924 - 1.56218i) q^{63} +(3.59808 + 0.232051i) q^{65} +(7.83013 + 13.5622i) q^{67} +(-2.73205 + 4.73205i) q^{69} +(-3.00000 + 5.19615i) q^{71} +10.6603 q^{73} +(1.46410 + 2.53590i) q^{75} +0.732051 q^{77} +5.80385 q^{79} +(-2.23205 - 3.86603i) q^{81} -2.19615 q^{83} +(-1.59808 + 2.76795i) q^{85} +(0.0980762 - 0.169873i) q^{87} +(-4.92820 - 8.53590i) q^{89} +(-1.46410 + 2.19615i) q^{91} +(-2.19615 - 3.80385i) q^{93} +(-1.36603 + 2.36603i) q^{95} +(8.00000 - 13.8564i) q^{97} +2.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 2 * q^9	$ 4 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 2 q^{9} + 2 q^{11} - 4 q^{13} - 2 q^{15} - 4 q^{17} + 2 q^{19} - 16 q^{21} - 8 q^{23} - 16 q^{25} - 16 q^{27} + 4 q^{29} + 24 q^{31} - 2 q^{33} + 2 q^{35} - 14 q^{37} + 22 q^{39} - 8 q^{41} + 8 q^{43} + 2 q^{45} + 20 q^{47} + 6 q^{49} - 44 q^{51} - 4 q^{53} - 2 q^{55} - 8 q^{57} + 14 q^{59} - 20 q^{61} - 14 q^{63} + 4 q^{65} + 14 q^{67} - 4 q^{69} - 12 q^{71} + 8 q^{73} - 8 q^{75} - 4 q^{77} + 44 q^{79} - 2 q^{81} + 12 q^{83} + 4 q^{85} - 10 q^{87} + 8 q^{89} + 8 q^{91} + 12 q^{93} - 2 q^{95} + 32 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 2 * q^9 + 2 * q^11 - 4 * q^13 - 2 * q^15 - 4 * q^17 + 2 * q^19 - 16 * q^21 - 8 * q^23 - 16 * q^25 - 16 * q^27 + 4 * q^29 + 24 * q^31 - 2 * q^33 + 2 * q^35 - 14 * q^37 + 22 * q^39 - 8 * q^41 + 8 * q^43 + 2 * q^45 + 20 * q^47 + 6 * q^49 - 44 * q^51 - 4 * q^53 - 2 * q^55 - 8 * q^57 + 14 * q^59 - 20 * q^61 - 14 * q^63 + 4 * q^65 + 14 * q^67 - 4 * q^69 - 12 * q^71 + 8 * q^73 - 8 * q^75 - 4 * q^77 + 44 * q^79 - 2 * q^81 + 12 * q^83 + 4 * q^85 - 10 * q^87 + 8 * q^89 + 8 * q^91 + 12 * q^93 - 2 * q^95 + 32 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.366025	−	0.633975i	−0.211325	−	0.366025i	0.740805	−	0.671721i	$-0.234444\pi$
$3$	−0.366025	−	0.633975i	−0.211325	−	0.366025i	−0.952129	+	0.305695i	$0.901111\pi$
$4$		0			0
$5$	−1.00000			−0.447214			−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$		0			0
$7$	0.366025	−	0.633975i	0.138345	−	0.239620i	−0.788526	−	0.615002i	$-0.789155\pi$
$7$	0.366025	−	0.633975i	0.138345	−	0.239620i	0.926870	+	0.375382i	$0.122489\pi$
$8$		0			0
$9$	1.23205	−	2.13397i	0.410684	−	0.711325i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$14$		0			0
$15$	0.366025	+	0.633975i	0.0945074	+	0.163692i
$16$		0			0
$17$	1.59808	−	2.76795i	0.387590	−	0.671326i	−0.604534	−	0.796579i	$-0.706641\pi$
$17$	1.59808	−	2.76795i	0.387590	−	0.671326i	0.992125	+	0.125253i	$0.0399742\pi$
$18$		0			0
$19$	1.36603	−	2.36603i	0.313388	−	0.542803i	−0.665706	−	0.746214i	$-0.731869\pi$
$19$	1.36603	−	2.36603i	0.313388	−	0.542803i	0.979093	+	0.203411i	$0.0652027\pi$
$20$		0			0
$21$	−0.535898			−0.116943
$22$		0			0
$23$	−3.73205	−	6.46410i	−0.778186	−	1.34786i	−0.932986	−	0.359912i	$-0.882807\pi$
$23$	−3.73205	−	6.46410i	−0.778186	−	1.34786i	0.154800	−	0.987946i	$-0.450527\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	0.133975	+	0.232051i	0.0248785	+	0.0430908i	0.878197	−	0.478300i	$-0.158747\pi$
$29$	0.133975	+	0.232051i	0.0248785	+	0.0430908i	−0.853318	+	0.521391i	$0.825413\pi$
$30$		0			0
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$		0			0
$33$	0.366025	−	0.633975i	0.0637168	−	0.110361i
$34$		0			0
$35$	−0.366025	+	0.633975i	−0.0618696	+	0.107161i
$36$		0			0
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$		0			0
$39$	1.16987	+	2.36603i	0.187330	+	0.378867i
$40$		0			0
$41$	−2.86603	−	4.96410i	−0.447598	−	0.775262i	0.550631	−	0.834749i	$-0.314387\pi$
$41$	−2.86603	−	4.96410i	−0.447598	−	0.775262i	−0.998229	+	0.0594862i	$0.981054\pi$
$42$		0			0
$43$	5.46410	−	9.46410i	0.833268	−	1.44326i	−0.0621654	−	0.998066i	$-0.519801\pi$
$43$	5.46410	−	9.46410i	0.833268	−	1.44326i	0.895433	−	0.445196i	$-0.146866\pi$
$44$		0			0
$45$	−1.23205	+	2.13397i	−0.183663	+	0.318114i
$46$		0			0
$47$	3.26795			0.476679			0.238340	−	0.971182i	$-0.423397\pi$
$47$	3.26795			0.476679			0.238340	+	0.971182i	$0.423397\pi$
$48$		0			0
$49$	3.23205	+	5.59808i	0.461722	+	0.799725i
$50$		0			0
$51$	−2.33975			−0.327630
$52$		0			0
$53$	−11.3923			−1.56485			−0.782427	−	0.622743i	$-0.786018\pi$
$53$	−11.3923			−1.56485			−0.782427	+	0.622743i	$0.786018\pi$
$54$		0			0
$55$	−0.500000	−	0.866025i	−0.0674200	−	0.116775i
$56$		0			0
$57$	−2.00000			−0.264906
$58$		0			0
$59$	2.63397	−	4.56218i	0.342914	−	0.593945i	−0.642058	−	0.766656i	$-0.721919\pi$
$59$	2.63397	−	4.56218i	0.342914	−	0.593945i	0.984973	+	0.172711i	$0.0552526\pi$
$60$		0			0
$61$	−5.86603	+	10.1603i	−0.751068	+	1.30089i	0.196238	+	0.980556i	$0.437127\pi$
$61$	−5.86603	+	10.1603i	−0.751068	+	1.30089i	−0.947306	+	0.320331i	$0.896206\pi$
$62$		0			0
$63$	−0.901924	−	1.56218i	−0.113632	−	0.196816i
$64$		0			0
$65$	3.59808	+	0.232051i	0.446286	+	0.0287824i
$66$		0			0
$67$	7.83013	+	13.5622i	0.956602	+	1.65688i	0.730658	+	0.682743i	$0.239213\pi$
$67$	7.83013	+	13.5622i	0.956602	+	1.65688i	0.225944	+	0.974140i	$0.427453\pi$
$68$		0			0
$69$	−2.73205	+	4.73205i	−0.328900	+	0.569672i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$		0			0
$73$	10.6603			1.24769			0.623844	−	0.781549i	$-0.285570\pi$
$73$	10.6603			1.24769			0.623844	+	0.781549i	$0.285570\pi$
$74$		0			0
$75$	1.46410	+	2.53590i	0.169060	+	0.292820i
$76$		0			0
$77$	0.732051			0.0834249
$78$		0			0
$79$	5.80385			0.652984			0.326492	−	0.945200i	$-0.394133\pi$
$79$	5.80385			0.652984			0.326492	+	0.945200i	$0.394133\pi$
$80$		0			0
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$		0			0
$83$	−2.19615			−0.241059			−0.120530	−	0.992710i	$-0.538459\pi$
$83$	−2.19615			−0.241059			−0.120530	+	0.992710i	$0.538459\pi$
$84$		0			0
$85$	−1.59808	+	2.76795i	−0.173336	+	0.300226i
$86$		0			0
$87$	0.0980762	−	0.169873i	0.0105149	−	0.0182123i
$88$		0			0
$89$	−4.92820	−	8.53590i	−0.522388	−	0.904803i	−0.999661	−	0.0260479i	$-0.991708\pi$
$89$	−4.92820	−	8.53590i	−0.522388	−	0.904803i	0.477272	−	0.878756i	$-0.341626\pi$
$90$		0			0
$91$	−1.46410	+	2.19615i	−0.153480	+	0.230219i
$92$		0			0
$93$	−2.19615	−	3.80385i	−0.227730	−	0.394441i
$94$		0			0
$95$	−1.36603	+	2.36603i	−0.140151	+	0.242749i
$96$		0			0
$97$	8.00000	−	13.8564i	0.812277	−	1.40690i	−0.0989899	−	0.995088i	$-0.531561\pi$
$97$	8.00000	−	13.8564i	0.812277	−	1.40690i	0.911267	−	0.411816i	$-0.135106\pi$
$98$		0			0
$99$	2.46410			0.247652
$100$		0			0
$101$	0.401924	+	0.696152i	0.0399929	+	0.0692698i	0.885329	−	0.464965i	$-0.153933\pi$
$101$	0.401924	+	0.696152i	0.0399929	+	0.0692698i	−0.845336	+	0.534235i	$0.820600\pi$
$102$		0			0
$103$	8.92820			0.879722			0.439861	−	0.898066i	$-0.355028\pi$
$103$	8.92820			0.879722			0.439861	+	0.898066i	$0.355028\pi$
$104$		0			0
$105$	0.535898			0.0522983
$106$		0			0
$107$	7.36603	+	12.7583i	0.712101	+	1.23339i	0.964067	+	0.265658i	$0.0855893\pi$
$107$	7.36603	+	12.7583i	0.712101	+	1.23339i	−0.251967	+	0.967736i	$0.581077\pi$
$108$		0			0
$109$	10.9282			1.04673			0.523366	−	0.852108i	$-0.324676\pi$
$109$	10.9282			1.04673			0.523366	+	0.852108i	$0.324676\pi$
$110$		0			0
$111$	−2.56218	+	4.43782i	−0.243191	+	0.421219i
$112$		0			0
$113$	−8.69615	+	15.0622i	−0.818065	+	1.41693i	0.0890407	+	0.996028i	$0.471620\pi$
$113$	−8.69615	+	15.0622i	−0.818065	+	1.41693i	−0.907106	+	0.420903i	$0.861713\pi$
$114$		0			0
$115$	3.73205	+	6.46410i	0.348016	+	0.602781i
$116$		0			0
$117$	−4.92820	+	7.39230i	−0.455613	+	0.683419i
$118$		0			0
$119$	−1.16987	−	2.02628i	−0.107242	−	0.185749i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−2.09808	+	3.63397i	−0.189177	+	0.327664i
$124$		0			0
$125$	9.00000			0.804984
$126$		0			0
$127$	−1.53590	−	2.66025i	−0.136289	−	0.236059i	0.789800	−	0.613364i	$-0.210184\pi$
$127$	−1.53590	−	2.66025i	−0.136289	−	0.236059i	−0.926089	+	0.377305i	$0.876851\pi$
$128$		0			0
$129$	−8.00000			−0.704361
$130$		0			0
$131$	12.5885			1.09986			0.549929	−	0.835211i	$-0.314655\pi$
$131$	12.5885			1.09986			0.549929	+	0.835211i	$0.314655\pi$
$132$		0			0
$133$	−1.00000	−	1.73205i	−0.0867110	−	0.150188i
$134$		0			0
$135$	4.00000			0.344265
$136$		0			0
$137$	−5.23205	+	9.06218i	−0.447004	+	0.774234i	−0.998189	−	0.0601489i	$-0.980842\pi$
$137$	−5.23205	+	9.06218i	−0.447004	+	0.774234i	0.551185	+	0.834383i	$0.314176\pi$
$138$		0			0
$139$	−3.46410	+	6.00000i	−0.293821	+	0.508913i	−0.974710	−	0.223474i	$-0.928260\pi$
$139$	−3.46410	+	6.00000i	−0.293821	+	0.508913i	0.680889	+	0.732387i	$0.261594\pi$
$140$		0			0
$141$	−1.19615	−	2.07180i	−0.100734	−	0.174477i
$142$		0			0
$143$	−1.59808	−	3.23205i	−0.133638	−	0.270278i
$144$		0			0
$145$	−0.133975	−	0.232051i	−0.0111260	−	0.0192708i
$146$		0			0
$147$	2.36603	−	4.09808i	0.195146	−	0.338004i
$148$		0			0
$149$	−11.7942	+	20.4282i	−0.966221	+	1.67354i	−0.259922	+	0.965630i	$0.583697\pi$
$149$	−11.7942	+	20.4282i	−0.966221	+	1.67354i	−0.706299	+	0.707914i	$0.749636\pi$
$150$		0			0
$151$	16.9282			1.37760			0.688799	−	0.724953i	$-0.258138\pi$
$151$	16.9282			1.37760			0.688799	+	0.724953i	$0.258138\pi$
$152$		0			0
$153$	−3.93782	−	6.82051i	−0.318354	−	0.551405i
$154$		0			0
$155$	−6.00000			−0.481932
$156$		0			0
$157$	−1.92820			−0.153887			−0.0769437	−	0.997035i	$-0.524516\pi$
$157$	−1.92820			−0.153887			−0.0769437	+	0.997035i	$0.524516\pi$
$158$		0			0
$159$	4.16987	+	7.22243i	0.330692	+	0.572776i
$160$		0			0
$161$	−5.46410			−0.430632
$162$		0			0
$163$	−9.02628	+	15.6340i	−0.706993	+	1.22455i	0.258975	+	0.965884i	$0.416615\pi$
$163$	−9.02628	+	15.6340i	−0.706993	+	1.22455i	−0.965968	+	0.258663i	$0.916718\pi$
$164$		0			0
$165$	−0.366025	+	0.633975i	−0.0284950	+	0.0493549i
$166$		0			0
$167$	−3.26795	−	5.66025i	−0.252882	−	0.438004i	0.711436	−	0.702750i	$-0.248045\pi$
$167$	−3.26795	−	5.66025i	−0.252882	−	0.438004i	−0.964318	+	0.264747i	$0.914712\pi$
$168$		0			0
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$		0			0
$171$	−3.36603	−	5.83013i	−0.257406	−	0.445841i
$172$		0			0
$173$	10.9282	−	18.9282i	0.830856	−	1.43908i	−0.0665045	−	0.997786i	$-0.521185\pi$
$173$	10.9282	−	18.9282i	0.830856	−	1.43908i	0.897360	−	0.441299i	$-0.145482\pi$
$174$		0			0
$175$	−1.46410	+	2.53590i	−0.110676	+	0.191696i
$176$		0			0
$177$	−3.85641			−0.289865
$178$		0			0
$179$	0.633975	+	1.09808i	0.0473855	+	0.0820741i	0.888745	−	0.458401i	$-0.151578\pi$
$179$	0.633975	+	1.09808i	0.0473855	+	0.0820741i	−0.841360	+	0.540475i	$0.818244\pi$
$180$		0			0
$181$	−9.39230			−0.698125			−0.349062	−	0.937100i	$-0.613500\pi$
$181$	−9.39230			−0.698125			−0.349062	+	0.937100i	$0.613500\pi$
$182$		0			0
$183$	8.58846			0.634877
$184$		0			0
$185$	3.50000	+	6.06218i	0.257325	+	0.445700i
$186$		0			0
$187$	3.19615			0.233726
$188$		0			0
$189$	−1.46410	+	2.53590i	−0.106498	+	0.184459i
$190$		0			0
$191$	4.56218	−	7.90192i	0.330108	−	0.571763i	−0.652425	−	0.757853i	$-0.726248\pi$
$191$	4.56218	−	7.90192i	0.330108	−	0.571763i	0.982533	+	0.186090i	$0.0595816\pi$
$192$		0			0
$193$	−3.40192	−	5.89230i	−0.244876	−	0.424137i	0.717221	−	0.696846i	$-0.245414\pi$
$193$	−3.40192	−	5.89230i	−0.244876	−	0.424137i	−0.962097	+	0.272709i	$0.912081\pi$
$194$		0			0
$195$	−1.16987	−	2.36603i	−0.0837763	−	0.169435i
$196$		0			0
$197$	−1.00000	−	1.73205i	−0.0712470	−	0.123404i	0.828201	−	0.560431i	$-0.189365\pi$
$197$	−1.00000	−	1.73205i	−0.0712470	−	0.123404i	−0.899448	+	0.437028i	$0.856031\pi$
$198$		0			0
$199$	−6.02628	+	10.4378i	−0.427192	+	0.739918i	−0.996622	−	0.0821218i	$-0.973830\pi$
$199$	−6.02628	+	10.4378i	−0.427192	+	0.739918i	0.569431	+	0.822039i	$0.307164\pi$
$200$		0			0
$201$	5.73205	−	9.92820i	0.404308	−	0.700281i
$202$		0			0
$203$	0.196152			0.0137672
$204$		0			0
$205$	2.86603	+	4.96410i	0.200172	+	0.346708i
$206$		0			0
$207$	−18.3923			−1.27835
$208$		0			0
$209$	2.73205			0.188980
$210$		0			0
$211$	−2.83013	−	4.90192i	−0.194834	−	0.337462i	0.752012	−	0.659149i	$-0.229083\pi$
$211$	−2.83013	−	4.90192i	−0.194834	−	0.337462i	−0.946846	+	0.321687i	$0.895750\pi$
$212$		0			0
$213$	4.39230			0.300956
$214$		0			0
$215$	−5.46410	+	9.46410i	−0.372649	+	0.645446i
$216$		0			0
$217$	2.19615	−	3.80385i	0.149085	−	0.258222i
$218$		0			0
$219$	−3.90192	−	6.75833i	−0.263668	−	0.456686i
$220$		0			0
$221$	−6.39230	+	9.58846i	−0.429993	+	0.644989i
$222$		0			0
$223$	1.83013	+	3.16987i	0.122554	+	0.212270i	0.920774	−	0.390096i	$-0.127558\pi$
$223$	1.83013	+	3.16987i	0.122554	+	0.212270i	−0.798220	+	0.602366i	$0.794225\pi$
$224$		0			0
$225$	−4.92820	+	8.53590i	−0.328547	+	0.569060i
$226$		0			0
$227$	13.3923	−	23.1962i	0.888878	−	1.53958i	0.0476758	−	0.998863i	$-0.484819\pi$
$227$	13.3923	−	23.1962i	0.888878	−	1.53958i	0.841203	−	0.540720i	$-0.181848\pi$
$228$		0			0
$229$	6.92820			0.457829			0.228914	−	0.973447i	$-0.426482\pi$
$229$	6.92820			0.457829			0.228914	+	0.973447i	$0.426482\pi$
$230$		0			0
$231$	−0.267949	−	0.464102i	−0.0176298	−	0.0305356i
$232$		0			0
$233$	−5.60770			−0.367372			−0.183686	−	0.982985i	$-0.558803\pi$
$233$	−5.60770			−0.367372			−0.183686	+	0.982985i	$0.558803\pi$
$234$		0			0
$235$	−3.26795			−0.213177
$236$		0			0
$237$	−2.12436	−	3.67949i	−0.137992	−	0.239009i
$238$		0			0
$239$	5.07180			0.328067			0.164034	−	0.986455i	$-0.447549\pi$
$239$	5.07180			0.328067			0.164034	+	0.986455i	$0.447549\pi$
$240$		0			0
$241$	13.2583	−	22.9641i	0.854044	−	1.47925i	−0.0234848	−	0.999724i	$-0.507476\pi$
$241$	13.2583	−	22.9641i	0.854044	−	1.47925i	0.877529	−	0.479524i	$-0.159191\pi$
$242$		0			0
$243$	−7.63397	+	13.2224i	−0.489720	+	0.848219i
$244$		0			0
$245$	−3.23205	−	5.59808i	−0.206488	−	0.357648i
$246$		0			0
$247$	−5.46410	+	8.19615i	−0.347672	+	0.521509i
$248$		0			0
$249$	0.803848	+	1.39230i	0.0509418	+	0.0882337i
$250$		0			0
$251$	10.5622	−	18.2942i	0.666679	−	1.15472i	−0.312148	−	0.950033i	$-0.601049\pi$
$251$	10.5622	−	18.2942i	0.666679	−	1.15472i	0.978827	−	0.204688i	$-0.0656180\pi$
$252$		0			0
$253$	3.73205	−	6.46410i	0.234632	−	0.406395i
$254$		0			0
$255$	2.33975			0.146521
$256$		0			0
$257$	−9.23205	−	15.9904i	−0.575880	−	0.997453i	−0.995945	−	0.0899590i	$-0.971326\pi$
$257$	−9.23205	−	15.9904i	−0.575880	−	0.997453i	0.420066	−	0.907494i	$-0.362007\pi$
$258$		0			0
$259$	−5.12436			−0.318412
$260$		0			0
$261$	0.660254			0.0408687
$262$		0			0
$263$	−14.1962	−	24.5885i	−0.875372	−	1.51619i	−0.856366	−	0.516370i	$-0.827283\pi$
$263$	−14.1962	−	24.5885i	−0.875372	−	1.51619i	−0.0190066	−	0.999819i	$-0.506050\pi$
$264$		0			0
$265$	11.3923			0.699824
$266$		0			0
$267$	−3.60770	+	6.24871i	−0.220787	+	0.382415i
$268$		0			0
$269$	−15.9282	+	27.5885i	−0.971160	+	1.68210i	−0.279093	+	0.960264i	$0.590034\pi$
$269$	−15.9282	+	27.5885i	−0.971160	+	1.68210i	−0.692066	+	0.721834i	$0.743299\pi$
$270$		0			0
$271$	−11.4641	−	19.8564i	−0.696395	−	1.20619i	−0.969708	−	0.244266i	$-0.921453\pi$
$271$	−11.4641	−	19.8564i	−0.696395	−	1.20619i	0.273314	−	0.961925i	$-0.411880\pi$
$272$		0			0
$273$	1.92820	+	0.124356i	0.116700	+	0.00752635i
$274$		0			0
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$		0			0
$277$	1.59808	−	2.76795i	0.0960191	−	0.166310i	−0.814014	−	0.580845i	$-0.802722\pi$
$277$	1.59808	−	2.76795i	0.0960191	−	0.166310i	0.910033	+	0.414535i	$0.136056\pi$
$278$		0			0
$279$	7.39230	−	12.8038i	0.442566	−	0.766546i
$280$		0			0
$281$	20.6603			1.23249			0.616244	−	0.787556i	$-0.288654\pi$
$281$	20.6603			1.23249			0.616244	+	0.787556i	$0.288654\pi$
$282$		0			0
$283$	−9.29423	−	16.0981i	−0.552485	−	0.956931i	−0.998094	−	0.0617041i	$-0.980346\pi$
$283$	−9.29423	−	16.0981i	−0.552485	−	0.956931i	0.445610	−	0.895227i	$-0.352987\pi$
$284$		0			0
$285$	2.00000			0.118470
$286$		0			0
$287$	−4.19615			−0.247691
$288$		0			0
$289$	3.39230	+	5.87564i	0.199547	+	0.345626i
$290$		0			0
$291$	−11.7128			−0.686617
$292$		0			0
$293$	−1.06218	+	1.83975i	−0.0620531	+	0.107479i	−0.895383	−	0.445297i	$-0.853098\pi$
$293$	−1.06218	+	1.83975i	−0.0620531	+	0.107479i	0.833330	+	0.552776i	$0.186431\pi$
$294$		0			0
$295$	−2.63397	+	4.56218i	−0.153356	+	0.265620i
$296$		0			0
$297$	−2.00000	−	3.46410i	−0.116052	−	0.201008i
$298$		0			0
$299$	11.9282	+	24.1244i	0.689826	+	1.39515i
$300$		0			0
$301$	−4.00000	−	6.92820i	−0.230556	−	0.399335i
$302$		0			0
$303$	0.294229	−	0.509619i	0.0169030	−	0.0292768i
$304$		0			0
$305$	5.86603	−	10.1603i	0.335888	−	0.581774i
$306$		0			0
$307$	34.0526			1.94348			0.971741	−	0.236049i	$-0.0758527\pi$
$307$	34.0526			1.94348			0.971741	+	0.236049i	$0.0758527\pi$
$308$		0			0
$309$	−3.26795	−	5.66025i	−0.185907	−	0.322001i
$310$		0			0
$311$	−20.0526			−1.13708			−0.568538	−	0.822657i	$-0.692491\pi$
$311$	−20.0526			−1.13708			−0.568538	+	0.822657i	$0.692491\pi$
$312$		0			0
$313$	−6.92820			−0.391605			−0.195803	−	0.980643i	$-0.562731\pi$
$313$	−6.92820			−0.391605			−0.195803	+	0.980643i	$0.562731\pi$
$314$		0			0
$315$	0.901924	+	1.56218i	0.0508176	+	0.0880187i
$316$		0			0
$317$	−8.60770			−0.483456			−0.241728	−	0.970344i	$-0.577714\pi$
$317$	−8.60770			−0.483456			−0.241728	+	0.970344i	$0.577714\pi$
$318$		0			0
$319$	−0.133975	+	0.232051i	−0.00750114	+	0.0129924i
$320$		0			0
$321$	5.39230	−	9.33975i	0.300969	−	0.521294i
$322$		0			0
$323$	−4.36603	−	7.56218i	−0.242932	−	0.420771i
$324$		0			0
$325$	14.3923	+	0.928203i	0.798341	+	0.0514875i
$326$		0			0
$327$	−4.00000	−	6.92820i	−0.221201	−	0.383131i
$328$		0			0
$329$	1.19615	−	2.07180i	0.0659460	−	0.114222i
$330$		0			0
$331$	−5.80385	+	10.0526i	−0.319008	+	0.552539i	−0.980281	−	0.197607i	$-0.936683\pi$
$331$	−5.80385	+	10.0526i	−0.319008	+	0.552539i	0.661273	+	0.750145i	$0.270016\pi$
$332$		0			0
$333$	−17.2487			−0.945224
$334$		0			0
$335$	−7.83013	−	13.5622i	−0.427806	−	0.740981i
$336$		0			0
$337$	20.5167			1.11761			0.558807	−	0.829298i	$-0.311259\pi$
$337$	20.5167			1.11761			0.558807	+	0.829298i	$0.311259\pi$
$338$		0			0
$339$	12.7321			0.691510
$340$		0			0
$341$	3.00000	+	5.19615i	0.162459	+	0.281387i
$342$		0			0
$343$	9.85641			0.532196
$344$		0			0
$345$	2.73205	−	4.73205i	0.147089	−	0.254765i
$346$		0			0
$347$	−2.83013	+	4.90192i	−0.151929	+	0.263149i	−0.931937	−	0.362621i	$-0.881882\pi$
$347$	−2.83013	+	4.90192i	−0.151929	+	0.263149i	0.780007	+	0.625770i	$0.215215\pi$
$348$		0			0
$349$	5.39230	+	9.33975i	0.288643	+	0.499945i	0.973486	−	0.228746i	$-0.0734624\pi$
$349$	5.39230	+	9.33975i	0.288643	+	0.499945i	−0.684843	+	0.728691i	$0.740129\pi$
$350$		0			0
$351$	14.3923	+	0.928203i	0.768204	+	0.0495438i
$352$		0			0
$353$	−10.9641	−	18.9904i	−0.583560	−	1.01076i	−0.995053	−	0.0993431i	$-0.968326\pi$
$353$	−10.9641	−	18.9904i	−0.583560	−	1.01076i	0.411493	−	0.911413i	$-0.365007\pi$
$354$		0			0
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$		0			0
$357$	−0.856406	+	1.48334i	−0.0453258	+	0.0785067i
$358$		0			0
$359$	−9.85641			−0.520201			−0.260101	−	0.965582i	$-0.583756\pi$
$359$	−9.85641			−0.520201			−0.260101	+	0.965582i	$0.583756\pi$
$360$		0			0
$361$	5.76795	+	9.99038i	0.303576	+	0.525810i
$362$		0			0
$363$	0.732051			0.0384227
$364$		0			0
$365$	−10.6603			−0.557983
$366$		0			0
$367$	12.1244	+	21.0000i	0.632886	+	1.09619i	0.986959	+	0.160973i	$0.0514632\pi$
$367$	12.1244	+	21.0000i	0.632886	+	1.09619i	−0.354073	+	0.935218i	$0.615203\pi$
$368$		0			0
$369$	−14.1244			−0.735285
$370$		0			0
$371$	−4.16987	+	7.22243i	−0.216489	+	0.374970i
$372$		0			0
$373$	−2.33013	+	4.03590i	−0.120649	+	0.208971i	−0.920024	−	0.391862i	$-0.871831\pi$
$373$	−2.33013	+	4.03590i	−0.120649	+	0.208971i	0.799375	+	0.600833i	$0.205164\pi$
$374$		0			0
$375$	−3.29423	−	5.70577i	−0.170113	−	0.294645i
$376$		0			0
$377$	−0.428203	−	0.866025i	−0.0220536	−	0.0446026i
$378$		0			0
$379$	−9.39230	−	16.2679i	−0.482450	−	0.835628i	0.517347	−	0.855776i	$-0.326920\pi$
$379$	−9.39230	−	16.2679i	−0.482450	−	0.835628i	−0.999797	+	0.0201475i	$0.993586\pi$
$380$		0			0
$381$	−1.12436	+	1.94744i	−0.0576025	+	0.0997704i
$382$		0			0
$383$	−2.73205	+	4.73205i	−0.139601	+	0.241797i	−0.927346	−	0.374206i	$-0.877915\pi$
$383$	−2.73205	+	4.73205i	−0.139601	+	0.241797i	0.787744	+	0.616002i	$0.211249\pi$
$384$		0			0
$385$	−0.732051			−0.0373088
$386$		0			0
$387$	−13.4641	−	23.3205i	−0.684419	−	1.18545i
$388$		0			0
$389$	2.32051			0.117654			0.0588272	−	0.998268i	$-0.481264\pi$
$389$	2.32051			0.117654			0.0588272	+	0.998268i	$0.481264\pi$
$390$		0			0
$391$	−23.8564			−1.20647
$392$		0			0
$393$	−4.60770	−	7.98076i	−0.232427	−	0.402576i
$394$		0			0
$395$	−5.80385			−0.292023
$396$		0			0
$397$	−7.26795	+	12.5885i	−0.364768	+	0.631797i	−0.988739	−	0.149651i	$-0.952185\pi$
$397$	−7.26795	+	12.5885i	−0.364768	+	0.631797i	0.623971	+	0.781448i	$0.285518\pi$
$398$		0			0
$399$	−0.732051	+	1.26795i	−0.0366484	+	0.0634769i
$400$		0			0
$401$	−0.571797	−	0.990381i	−0.0285542	−	0.0494573i	0.851395	−	0.524525i	$-0.175757\pi$
$401$	−0.571797	−	0.990381i	−0.0285542	−	0.0494573i	−0.879949	+	0.475067i	$0.842424\pi$
$402$		0			0
$403$	−21.5885	−	1.39230i	−1.07540	−	0.0693556i
$404$		0			0
$405$	2.23205	+	3.86603i	0.110911	+	0.192104i
$406$		0			0
$407$	3.50000	−	6.06218i	0.173489	−	0.300491i
$408$		0			0
$409$	3.06218	−	5.30385i	0.151415	−	0.262258i	−0.780333	−	0.625364i	$-0.784950\pi$
$409$	3.06218	−	5.30385i	0.151415	−	0.262258i	0.931748	+	0.363106i	$0.118284\pi$
$410$		0			0
$411$	7.66025			0.377852
$412$		0			0
$413$	−1.92820	−	3.33975i	−0.0948807	−	0.164338i
$414$		0			0
$415$	2.19615			0.107805
$416$		0			0
$417$	5.07180			0.248367
$418$		0			0
$419$	13.1962	+	22.8564i	0.644674	+	1.11661i	0.984377	+	0.176076i	$0.0563403\pi$
$419$	13.1962	+	22.8564i	0.644674	+	1.11661i	−0.339702	+	0.940533i	$0.610326\pi$
$420$		0			0
$421$	3.39230			0.165331			0.0826654	−	0.996577i	$-0.473657\pi$
$421$	3.39230			0.165331			0.0826654	+	0.996577i	$0.473657\pi$
$422$		0			0
$423$	4.02628	−	6.97372i	0.195764	−	0.339074i
$424$		0			0
$425$	−6.39230	+	11.0718i	−0.310072	+	0.537061i
$426$		0			0
$427$	4.29423	+	7.43782i	0.207812	+	0.359941i
$428$		0			0
$429$	−1.46410	+	2.19615i	−0.0706875	+	0.106031i
$430$		0			0
$431$	15.0981	+	26.1506i	0.727249	+	1.25963i	0.958042	+	0.286629i	$0.0925347\pi$
$431$	15.0981	+	26.1506i	0.727249	+	1.25963i	−0.230793	+	0.973003i	$0.574132\pi$
$432$		0			0
$433$	13.5000	−	23.3827i	0.648769	−	1.12370i	−0.334649	−	0.942343i	$-0.608618\pi$
$433$	13.5000	−	23.3827i	0.648769	−	1.12370i	0.983417	−	0.181357i	$-0.0580490\pi$
$434$		0			0
$435$	−0.0980762	+	0.169873i	−0.00470239	+	0.00814479i
$436$		0			0
$437$	−20.3923			−0.975496
$438$		0			0
$439$	−6.16987	−	10.6865i	−0.294472	−	0.510040i	0.680390	−	0.732850i	$-0.261810\pi$
$439$	−6.16987	−	10.6865i	−0.294472	−	0.510040i	−0.974862	+	0.222810i	$0.928477\pi$
$440$		0			0
$441$	15.9282			0.758486
$442$		0			0
$443$	−1.66025			−0.0788810			−0.0394405	−	0.999222i	$-0.512558\pi$
$443$	−1.66025			−0.0788810			−0.0394405	+	0.999222i	$0.512558\pi$
$444$		0			0
$445$	4.92820	+	8.53590i	0.233619	+	0.404640i
$446$		0			0
$447$	17.2679			0.816746
$448$		0			0
$449$	7.85641	−	13.6077i	0.370767	−	0.642187i	−0.618917	−	0.785456i	$-0.712428\pi$
$449$	7.85641	−	13.6077i	0.370767	−	0.642187i	0.989684	+	0.143270i	$0.0457616\pi$
$450$		0			0
$451$	2.86603	−	4.96410i	0.134956	−	0.233750i
$452$		0			0
$453$	−6.19615	−	10.7321i	−0.291121	−	0.504236i
$454$		0			0
$455$	1.46410	−	2.19615i	0.0686381	−	0.102957i
$456$		0			0
$457$	10.5981	+	18.3564i	0.495757	+	0.858676i	0.999988	−	0.00489238i	$-0.00155730\pi$
$457$	10.5981	+	18.3564i	0.495757	+	0.858676i	−0.504231	+	0.863569i	$0.668224\pi$
$458$		0			0
$459$	−6.39230	+	11.0718i	−0.298367	+	0.516787i
$460$		0			0
$461$	7.40192	−	12.8205i	0.344742	−	0.597111i	−0.640565	−	0.767904i	$-0.721300\pi$
$461$	7.40192	−	12.8205i	0.344742	−	0.597111i	0.985307	+	0.170793i	$0.0546331\pi$
$462$		0			0
$463$	8.87564			0.412486			0.206243	−	0.978501i	$-0.433876\pi$
$463$	8.87564			0.412486			0.206243	+	0.978501i	$0.433876\pi$
$464$		0			0
$465$	2.19615	+	3.80385i	0.101844	+	0.176399i
$466$		0			0
$467$	−27.5167			−1.27332			−0.636660	−	0.771145i	$-0.719684\pi$
$467$	−27.5167			−1.27332			−0.636660	+	0.771145i	$0.719684\pi$
$468$		0			0
$469$	11.4641			0.529363
$470$		0			0
$471$	0.705771	+	1.22243i	0.0325202	+	0.0563267i
$472$		0			0
$473$	10.9282			0.502479
$474$		0			0
$475$	−5.46410	+	9.46410i	−0.250710	+	0.434243i
$476$		0			0
$477$	−14.0359	+	24.3109i	−0.642660	+	1.11312i
$478$		0			0
$479$	9.75833	+	16.9019i	0.445869	+	0.772269i	0.998112	−	0.0614147i	$-0.0195612\pi$
$479$	9.75833	+	16.9019i	0.445869	+	0.772269i	−0.552243	+	0.833683i	$0.686228\pi$
$480$		0			0
$481$	11.1865	+	22.6244i	0.510062	+	1.03158i
$482$		0			0
$483$	2.00000	+	3.46410i	0.0910032	+	0.157622i
$484$		0			0
$485$	−8.00000	+	13.8564i	−0.363261	+	0.629187i
$486$		0			0
$487$	−10.8301	+	18.7583i	−0.490760	+	0.850021i	−0.999943	−	0.0106369i	$-0.996614\pi$
$487$	−10.8301	+	18.7583i	−0.490760	+	0.850021i	0.509184	+	0.860658i	$0.329947\pi$
$488$		0			0
$489$	13.2154			0.597621
$490$		0			0
$491$	−18.7583	−	32.4904i	−0.846552	−	1.46627i	−0.884267	−	0.466982i	$-0.845341\pi$
$491$	−18.7583	−	32.4904i	−0.846552	−	1.46627i	0.0377153	−	0.999289i	$-0.487992\pi$
$492$		0			0
$493$	0.856406			0.0385706
$494$		0			0
$495$	−2.46410			−0.110753
$496$		0			0
$497$	2.19615	+	3.80385i	0.0985109	+	0.170626i
$498$		0			0
$499$	9.41154			0.421319			0.210659	−	0.977560i	$-0.432439\pi$
$499$	9.41154			0.421319			0.210659	+	0.977560i	$0.432439\pi$
$500$		0			0
$501$	−2.39230	+	4.14359i	−0.106880	+	0.185122i
$502$		0			0
$503$	9.29423	−	16.0981i	0.414409	−	0.717778i	−0.580957	−	0.813934i	$-0.697322\pi$
$503$	9.29423	−	16.0981i	0.414409	−	0.717778i	0.995366	+	0.0961565i	$0.0306549\pi$
$504$		0			0
$505$	−0.401924	−	0.696152i	−0.0178854	−	0.0309784i
$506$		0			0
$507$	−3.66025	−	8.78461i	−0.162558	−	0.390138i
$508$		0			0
$509$	8.42820	+	14.5981i	0.373574	+	0.647048i	0.990112	−	0.140276i	$-0.0447990\pi$
$509$	8.42820	+	14.5981i	0.373574	+	0.647048i	−0.616539	+	0.787324i	$0.711466\pi$
$510$		0			0
$511$	3.90192	−	6.75833i	0.172611	−	0.298971i
$512$		0			0
$513$	−5.46410	+	9.46410i	−0.241246	+	0.417850i
$514$		0			0
$515$	−8.92820			−0.393424
$516$		0			0
$517$	1.63397	+	2.83013i	0.0718621	+	0.124469i
$518$		0			0
$519$	−16.0000			−0.702322
$520$		0			0
$521$	7.78461			0.341050			0.170525	−	0.985353i	$-0.445454\pi$
$521$	7.78461			0.341050			0.170525	+	0.985353i	$0.445454\pi$
$522$		0			0
$523$	3.83013	+	6.63397i	0.167480	+	0.290083i	0.937533	−	0.347896i	$-0.113104\pi$
$523$	3.83013	+	6.63397i	0.167480	+	0.290083i	−0.770053	+	0.637979i	$0.779770\pi$
$524$		0			0
$525$	2.14359			0.0935541
$526$		0			0
$527$	9.58846	−	16.6077i	0.417680	−	0.723443i
$528$		0			0
$529$	−16.3564	+	28.3301i	−0.711148	+	1.23174i
$530$		0			0
$531$	−6.49038	−	11.2417i	−0.281659	−	0.487847i
$532$		0			0
$533$	9.16025	+	18.5263i	0.396775	+	0.802462i
$534$		0			0
$535$	−7.36603	−	12.7583i	−0.318461	−	0.551591i
$536$		0			0
$537$	0.464102	−	0.803848i	0.0200275	−	0.0346886i
$538$		0			0
$539$	−3.23205	+	5.59808i	−0.139214	+	0.241126i
$540$		0			0
$541$	32.6603			1.40417			0.702087	−	0.712091i	$-0.252252\pi$
$541$	32.6603			1.40417			0.702087	+	0.712091i	$0.252252\pi$
$542$		0			0
$543$	3.43782	+	5.95448i	0.147531	+	0.255531i
$544$		0			0
$545$	−10.9282			−0.468113
$546$		0			0
$547$	18.3923			0.786398			0.393199	−	0.919453i	$-0.371368\pi$
$547$	18.3923			0.786398			0.393199	+	0.919453i	$0.371368\pi$
$548$		0			0
$549$	14.4545	+	25.0359i	0.616902	+	1.06851i
$550$		0			0
$551$	0.732051			0.0311864
$552$		0			0
$553$	2.12436	−	3.67949i	0.0903368	−	0.156468i
$554$		0			0
$555$	2.56218	−	4.43782i	0.108758	−	0.188375i
$556$		0			0
$557$	11.5981	+	20.0885i	0.491426	+	0.851175i	0.999951	−	0.00987197i	$-0.00314240\pi$
$557$	11.5981	+	20.0885i	0.491426	+	0.851175i	−0.508525	+	0.861047i	$0.669809\pi$
$558$		0			0
$559$	−21.8564	+	32.7846i	−0.924427	+	1.38664i
$560$		0			0
$561$	−1.16987	−	2.02628i	−0.0493921	−	0.0855496i
$562$		0			0
$563$	−12.7583	+	22.0981i	−0.537700	+	0.931323i	0.461328	+	0.887230i	$0.347373\pi$
$563$	−12.7583	+	22.0981i	−0.537700	+	0.931323i	−0.999027	+	0.0440932i	$0.985960\pi$
$564$		0			0
$565$	8.69615	−	15.0622i	0.365850	−	0.633671i
$566$		0			0
$567$	−3.26795			−0.137241
$568$		0			0
$569$	19.0000	+	32.9090i	0.796521	+	1.37962i	0.921869	+	0.387503i	$0.126662\pi$
$569$	19.0000	+	32.9090i	0.796521	+	1.37962i	−0.125347	+	0.992113i	$0.540004\pi$
$570$		0			0
$571$	−35.3731			−1.48032			−0.740158	−	0.672433i	$-0.765249\pi$
$571$	−35.3731			−1.48032			−0.740158	+	0.672433i	$0.765249\pi$
$572$		0			0
$573$	−6.67949			−0.279040
$574$		0			0
$575$	14.9282	+	25.8564i	0.622549	+	1.07829i
$576$		0			0
$577$	3.53590			0.147201			0.0736007	−	0.997288i	$-0.476551\pi$
$577$	3.53590			0.147201			0.0736007	+	0.997288i	$0.476551\pi$
$578$		0			0
$579$	−2.49038	+	4.31347i	−0.103497	+	0.179262i
$580$		0			0
$581$	−0.803848	+	1.39230i	−0.0333492	+	0.0577625i
$582$		0			0
$583$	−5.69615	−	9.86603i	−0.235911	−	0.408609i
$584$		0			0
$585$	4.92820	−	7.39230i	0.203756	−	0.305634i
$586$		0			0
$587$	−6.63397	−	11.4904i	−0.273813	−	0.474259i	0.696022	−	0.718021i	$-0.254952\pi$
$587$	−6.63397	−	11.4904i	−0.273813	−	0.474259i	−0.969835	+	0.243762i	$0.921618\pi$
$588$		0			0
$589$	8.19615	−	14.1962i	0.337717	−	0.584942i
$590$		0			0
$591$	−0.732051	+	1.26795i	−0.0301125	+	0.0521565i
$592$		0			0
$593$	30.8038			1.26496			0.632481	−	0.774576i	$-0.282037\pi$
$593$	30.8038			1.26496			0.632481	+	0.774576i	$0.282037\pi$
$594$		0			0
$595$	1.16987	+	2.02628i	0.0479601	+	0.0830694i
$596$		0			0
$597$	8.82309			0.361105
$598$		0			0
$599$	20.5359			0.839074			0.419537	−	0.907738i	$-0.362192\pi$
$599$	20.5359			0.839074			0.419537	+	0.907738i	$0.362192\pi$
$600$		0			0
$601$	−3.93782	−	6.82051i	−0.160627	−	0.278214i	0.774467	−	0.632615i	$-0.218018\pi$
$601$	−3.93782	−	6.82051i	−0.160627	−	0.278214i	−0.935094	+	0.354400i	$0.884685\pi$
$602$		0			0
$603$	38.5885			1.57144
$604$		0			0
$605$	0.500000	−	0.866025i	0.0203279	−	0.0352089i
$606$		0			0
$607$	−16.2942	+	28.2224i	−0.661362	+	1.14551i	0.318896	+	0.947790i	$0.396688\pi$
$607$	−16.2942	+	28.2224i	−0.661362	+	1.14551i	−0.980258	+	0.197723i	$0.936645\pi$
$608$		0			0
$609$	−0.0717968	−	0.124356i	−0.00290935	−	0.00503915i
$610$		0			0
$611$	−11.7583	−	0.758330i	−0.475691	−	0.0306788i
$612$		0			0
$613$	−11.9904	−	20.7679i	−0.484287	−	0.838810i	0.515550	−	0.856859i	$-0.327588\pi$
$613$	−11.9904	−	20.7679i	−0.484287	−	0.838810i	−0.999837	+	0.0180498i	$0.994254\pi$
$614$		0			0
$615$	2.09808	−	3.63397i	0.0846026	−	0.146536i
$616$		0			0
$617$	8.89230	−	15.4019i	0.357991	−	0.620058i	−0.629634	−	0.776892i	$-0.716795\pi$
$617$	8.89230	−	15.4019i	0.357991	−	0.620058i	0.987625	+	0.156834i	$0.0501286\pi$
$618$		0			0
$619$	2.33975			0.0940423			0.0470212	−	0.998894i	$-0.485027\pi$
$619$	2.33975			0.0940423			0.0470212	+	0.998894i	$0.485027\pi$
$620$		0			0
$621$	14.9282	+	25.8564i	0.599048	+	1.03758i
$622$		0			0
$623$	−7.21539			−0.289079
$624$		0			0
$625$	11.0000			0.440000
$626$		0			0
$627$	−1.00000	−	1.73205i	−0.0399362	−	0.0691714i
$628$		0			0
$629$	−22.3731			−0.892073
$630$		0			0
$631$	−13.9019	+	24.0788i	−0.553427	+	0.958563i	0.444597	+	0.895731i	$0.353347\pi$
$631$	−13.9019	+	24.0788i	−0.553427	+	0.958563i	−0.998024	+	0.0628328i	$0.979987\pi$
$632$		0			0
$633$	−2.07180	+	3.58846i	−0.0823465	+	0.142628i
$634$		0			0
$635$	1.53590	+	2.66025i	0.0609503	+	0.105569i
$636$		0			0
$637$	−10.3301	−	20.8923i	−0.409295	−	0.827783i
$638$		0			0
$639$	7.39230	+	12.8038i	0.292435	+	0.506512i
$640$		0			0
$641$	−10.6244	+	18.4019i	−0.419637	+	0.726832i	−0.995903	−	0.0904299i	$-0.971176\pi$
$641$	−10.6244	+	18.4019i	−0.419637	+	0.726832i	0.576266	+	0.817262i	$0.304509\pi$
$642$		0			0
$643$	−2.43782	+	4.22243i	−0.0961383	+	0.166516i	−0.910083	−	0.414426i	$-0.863982\pi$
$643$	−2.43782	+	4.22243i	−0.0961383	+	0.166516i	0.813945	+	0.580942i	$0.197316\pi$
$644$		0			0
$645$	8.00000			0.315000
$646$		0			0
$647$	6.12436	+	10.6077i	0.240773	+	0.417032i	0.960935	−	0.276775i	$-0.0892656\pi$
$647$	6.12436	+	10.6077i	0.240773	+	0.417032i	−0.720162	+	0.693806i	$0.755932\pi$
$648$		0			0
$649$	5.26795			0.206785
$650$		0			0
$651$	−3.21539			−0.126021
$652$		0			0
$653$	−0.196152	−	0.339746i	−0.00767604	−	0.0132953i	0.862162	−	0.506633i	$-0.169110\pi$
$653$	−0.196152	−	0.339746i	−0.00767604	−	0.0132953i	−0.869838	+	0.493338i	$0.835777\pi$
$654$		0			0
$655$	−12.5885			−0.491872
$656$		0			0
$657$	13.1340	−	22.7487i	0.512405	−	0.887512i
$658$		0			0
$659$	11.0981	−	19.2224i	0.432320	−	0.748800i	−0.564753	−	0.825260i	$-0.691029\pi$
$659$	11.0981	−	19.2224i	0.432320	−	0.748800i	0.997073	+	0.0764604i	$0.0243619\pi$
$660$		0			0
$661$	−10.7679	−	18.6506i	−0.418825	−	0.725426i	0.576997	−	0.816746i	$-0.304224\pi$
$661$	−10.7679	−	18.6506i	−0.418825	−	0.725426i	−0.995822	+	0.0913207i	$0.970891\pi$
$662$		0			0
$663$	8.41858	+	0.542940i	0.326951	+	0.0210860i
$664$		0			0
$665$	1.00000	+	1.73205i	0.0387783	+	0.0671660i
$666$		0			0
$667$	1.00000	−	1.73205i	0.0387202	−	0.0670653i
$668$		0			0
$669$	1.33975	−	2.32051i	0.0517976	−	0.0897160i
$670$		0			0
$671$	−11.7321			−0.452911
$672$		0			0
$673$	−7.59808	−	13.1603i	−0.292884	−	0.507291i	0.681606	−	0.731719i	$-0.261282\pi$
$673$	−7.59808	−	13.1603i	−0.292884	−	0.507291i	−0.974491	+	0.224429i	$0.927948\pi$
$674$		0			0
$675$	16.0000			0.615840
$676$		0			0
$677$	−7.85641			−0.301946			−0.150973	−	0.988538i	$-0.548241\pi$
$677$	−7.85641			−0.301946			−0.150973	+	0.988538i	$0.548241\pi$
$678$		0			0
$679$	−5.85641	−	10.1436i	−0.224748	−	0.389275i
$680$		0			0
$681$	−19.6077			−0.751369
$682$		0			0
$683$	17.5885	−	30.4641i	0.673004	−	1.16568i	−0.304045	−	0.952658i	$-0.598337\pi$
$683$	17.5885	−	30.4641i	0.673004	−	1.16568i	0.977048	−	0.213019i	$-0.0683295\pi$
$684$		0			0
$685$	5.23205	−	9.06218i	0.199906	−	0.346248i
$686$		0			0
$687$	−2.53590	−	4.39230i	−0.0967506	−	0.167577i
$688$		0			0
$689$	40.9904	+	2.64359i	1.56161	+	0.100713i
$690$		0			0
$691$	−2.53590	−	4.39230i	−0.0964701	−	0.167091i	0.813751	−	0.581214i	$-0.197422\pi$
$691$	−2.53590	−	4.39230i	−0.0964701	−	0.167091i	−0.910221	+	0.414122i	$0.864089\pi$
$692$		0			0
$693$	0.901924	−	1.56218i	0.0342613	−	0.0593422i
$694$		0			0
$695$	3.46410	−	6.00000i	0.131401	−	0.227593i
$696$		0			0
$697$	−18.3205			−0.693939
$698$		0			0
$699$	2.05256	+	3.55514i	0.0776349	+	0.134468i
$700$		0			0
$701$	−10.9282			−0.412753			−0.206376	−	0.978473i	$-0.566167\pi$
$701$	−10.9282			−0.412753			−0.206376	+	0.978473i	$0.566167\pi$
$702$		0			0
$703$	−19.1244			−0.721289
$704$		0			0
$705$	1.19615	+	2.07180i	0.0450497	+	0.0780284i
$706$		0			0
$707$	0.588457			0.0221312
$708$		0			0
$709$	−10.8923	+	18.8660i	−0.409069	+	0.708528i	−0.994786	−	0.101987i	$-0.967480\pi$
$709$	−10.8923	+	18.8660i	−0.409069	+	0.708528i	0.585717	+	0.810516i	$0.300813\pi$
$710$		0			0
$711$	7.15064	−	12.3853i	0.268170	−	0.464484i
$712$		0			0
$713$	−22.3923	−	38.7846i	−0.838598	−	1.45250i
$714$		0			0
$715$	1.59808	+	3.23205i	0.0597647	+	0.120872i
$716$		0			0
$717$	−1.85641	−	3.21539i	−0.0693288	−	0.120081i
$718$		0			0
$719$	−14.5885	+	25.2679i	−0.544058	+	0.942335i	0.454608	+	0.890692i	$0.349779\pi$
$719$	−14.5885	+	25.2679i	−0.544058	+	0.942335i	−0.998666	+	0.0516438i	$0.983554\pi$
$720$		0			0
$721$	3.26795	−	5.66025i	0.121705	−	0.210799i
$722$		0			0
$723$	−19.4115			−0.721923
$724$		0			0
$725$	−0.535898	−	0.928203i	−0.0199028	−	0.0344726i
$726$		0			0
$727$	16.0000			0.593407			0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000			0.593407			0.296704	+	0.954970i	$0.404113\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$		0			0
$731$	−17.4641	−	30.2487i	−0.645933	−	1.11879i
$732$		0			0
$733$	−30.9090			−1.14165			−0.570824	−	0.821072i	$-0.693376\pi$
$733$	−30.9090			−1.14165			−0.570824	+	0.821072i	$0.693376\pi$
$734$		0			0
$735$	−2.36603	+	4.09808i	−0.0872722	+	0.151160i
$736$		0			0
$737$	−7.83013	+	13.5622i	−0.288426	+	0.499569i
$738$		0			0
$739$	15.6603	+	27.1244i	0.576072	+	0.997786i	0.995924	+	0.0901932i	$0.0287485\pi$
$739$	15.6603	+	27.1244i	0.576072	+	0.997786i	−0.419853	+	0.907592i	$0.637918\pi$
$740$		0			0
$741$	7.19615	+	0.464102i	0.264357	+	0.0170492i
$742$		0			0
$743$	−16.2224	−	28.0981i	−0.595143	−	1.03082i	−0.993527	−	0.113599i	$-0.963762\pi$
$743$	−16.2224	−	28.0981i	−0.595143	−	1.03082i	0.398383	−	0.917219i	$-0.369571\pi$
$744$		0			0
$745$	11.7942	−	20.4282i	0.432107	−	0.748431i
$746$		0			0
$747$	−2.70577	+	4.68653i	−0.0989990	+	0.171471i
$748$		0			0
$749$	10.7846			0.394061
$750$		0			0
$751$	−3.80385	−	6.58846i	−0.138804	−	0.240416i	0.788240	−	0.615368i	$-0.210993\pi$
$751$	−3.80385	−	6.58846i	−0.138804	−	0.240416i	−0.927044	+	0.374952i	$0.877659\pi$
$752$		0			0
$753$	−15.4641			−0.563543
$754$		0			0
$755$	−16.9282			−0.616080
$756$		0			0
$757$	−13.2679	−	22.9808i	−0.482232	−	0.835250i	0.517560	−	0.855647i	$-0.326840\pi$
$757$	−13.2679	−	22.9808i	−0.482232	−	0.835250i	−0.999792	+	0.0203968i	$0.993507\pi$
$758$		0			0
$759$	−5.46410			−0.198334
$760$		0			0
$761$	2.80385	−	4.85641i	0.101639	−	0.176045i	−0.810721	−	0.585433i	$-0.800925\pi$
$761$	2.80385	−	4.85641i	0.101639	−	0.176045i	0.912360	+	0.409388i	$0.134258\pi$
$762$		0			0
$763$	4.00000	−	6.92820i	0.144810	−	0.250818i
$764$		0			0
$765$	3.93782	+	6.82051i	0.142372	+	0.246596i
$766$		0			0
$767$	−10.5359	+	15.8038i	−0.380429	+	0.570644i
$768$		0			0
$769$	24.1244	+	41.7846i	0.869947	+	1.50679i	0.862050	+	0.506823i	$0.169180\pi$
$769$	24.1244	+	41.7846i	0.869947	+	1.50679i	0.00789622	+	0.999969i	$0.497487\pi$
$770$		0			0
$771$	−6.75833	+	11.7058i	−0.243395	+	0.421573i
$772$		0			0
$773$	3.80385	−	6.58846i	0.136815	−	0.236970i	−0.789474	−	0.613783i	$-0.789647\pi$
$773$	3.80385	−	6.58846i	0.136815	−	0.236970i	0.926289	+	0.376813i	$0.122980\pi$
$774$		0			0
$775$	−24.0000			−0.862105
$776$		0			0
$777$	1.87564	+	3.24871i	0.0672884	+	0.116547i
$778$		0			0
$779$	−15.6603			−0.561087
$780$		0			0
$781$	−6.00000			−0.214697
$782$		0			0
$783$	−0.535898	−	0.928203i	−0.0191514	−	0.0331713i
$784$		0			0
$785$	1.92820			0.0688205
$786$		0			0
$787$	2.83013	−	4.90192i	0.100883	−	0.174735i	−0.811166	−	0.584816i	$-0.801167\pi$
$787$	2.83013	−	4.90192i	0.100883	−	0.174735i	0.912049	+	0.410082i	$0.134500\pi$
$788$		0			0
$789$	−10.3923	+	18.0000i	−0.369976	+	0.640817i
$790$		0			0
$791$	6.36603	+	11.0263i	0.226350	+	0.392049i
$792$		0			0
$793$	23.4641	−	35.1962i	0.833235	−	1.24985i
$794$		0			0
$795$	−4.16987	−	7.22243i	−0.147890	−	0.256153i
$796$		0			0
$797$	21.8564	−	37.8564i	0.774194	−	1.34094i	−0.161053	−	0.986946i	$-0.551489\pi$
$797$	21.8564	−	37.8564i	0.774194	−	1.34094i	0.935247	−	0.353997i	$-0.115178\pi$
$798$		0			0
$799$	5.22243	−	9.04552i	0.184756	−	0.320007i
$800$		0			0
$801$	−24.2872			−0.858146
$802$		0			0
$803$	5.33013	+	9.23205i	0.188096	+	0.325792i
$804$		0			0
$805$	5.46410			0.192584
$806$		0			0
$807$	23.3205			0.820921
$808$		0			0
$809$	−2.59808	−	4.50000i	−0.0913435	−	0.158212i	0.816733	−	0.577016i	$-0.195783\pi$
$809$	−2.59808	−	4.50000i	−0.0913435	−	0.158212i	−0.908077	+	0.418804i	$0.862449\pi$
$810$		0			0
$811$	15.4641			0.543018			0.271509	−	0.962436i	$-0.412477\pi$
$811$	15.4641			0.543018			0.271509	+	0.962436i	$0.412477\pi$
$812$		0			0
$813$	−8.39230	+	14.5359i	−0.294331	+	0.509796i
$814$		0			0
$815$	9.02628	−	15.6340i	0.316177	−	0.547634i
$816$		0			0
$817$	−14.9282	−	25.8564i	−0.522272	−	0.904601i
$818$		0			0
$819$	2.88269	+	5.83013i	0.100729	+	0.203721i
$820$		0			0
$821$	11.1962	+	19.3923i	0.390748	+	0.676796i	0.992548	−	0.121851i	$-0.0388829\pi$
$821$	11.1962	+	19.3923i	0.390748	+	0.676796i	−0.601800	+	0.798647i	$0.705550\pi$
$822$		0			0
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$		0			0
$825$	−1.46410	+	2.53590i	−0.0509735	+	0.0882886i
$826$		0			0
$827$	24.7321			0.860018			0.430009	−	0.902825i	$-0.358510\pi$
$827$	24.7321			0.860018			0.430009	+	0.902825i	$0.358510\pi$
$828$		0			0
$829$	−9.89230	−	17.1340i	−0.343574	−	0.595088i	0.641520	−	0.767107i	$-0.278304\pi$
$829$	−9.89230	−	17.1340i	−0.343574	−	0.595088i	−0.985094	+	0.172019i	$0.944971\pi$
$830$		0			0
$831$	−2.33975			−0.0811649
$832$		0			0
$833$	20.6603			0.715835
$834$		0			0
$835$	3.26795	+	5.66025i	0.113092	+	0.195881i
$836$		0			0
$837$	−24.0000			−0.829561
$838$		0			0
$839$	26.7583	−	46.3468i	0.923800	−	1.60007i	0.130321	−	0.991472i	$-0.458399\pi$
$839$	26.7583	−	46.3468i	0.923800	−	1.60007i	0.793480	−	0.608597i	$-0.208267\pi$
$840$		0			0
$841$	14.4641	−	25.0526i	0.498762	−	0.863881i
$842$		0			0
$843$	−7.56218	−	13.0981i	−0.260455	−	0.451122i
$844$		0			0
$845$	−12.8923	−	1.66987i	−0.443509	−	0.0574454i
$846$		0			0
$847$	0.366025	+	0.633975i	0.0125768	+	0.0217836i
$848$		0			0
$849$	−6.80385	+	11.7846i	−0.233507	+	0.404447i
$850$		0			0
$851$	−26.1244	+	45.2487i	−0.895531	+	1.55111i
$852$		0			0
$853$	1.58846			0.0543877			0.0271939	−	0.999630i	$-0.491343\pi$
$853$	1.58846			0.0543877			0.0271939	+	0.999630i	$0.491343\pi$
$854$		0			0
$855$	3.36603	+	5.83013i	0.115116	+	0.199386i
$856$		0			0
$857$	−5.58846			−0.190898			−0.0954490	−	0.995434i	$-0.530429\pi$
$857$	−5.58846			−0.190898			−0.0954490	+	0.995434i	$0.530429\pi$
$858$		0			0
$859$	−23.3731			−0.797479			−0.398739	−	0.917064i	$-0.630552\pi$
$859$	−23.3731			−0.797479			−0.398739	+	0.917064i	$0.630552\pi$
$860$		0			0
$861$	1.53590	+	2.66025i	0.0523433	+	0.0906612i
$862$		0			0
$863$	22.6410			0.770709			0.385355	−	0.922769i	$-0.374079\pi$
$863$	22.6410			0.770709			0.385355	+	0.922769i	$0.374079\pi$
$864$		0			0
$865$	−10.9282	+	18.9282i	−0.371570	+	0.643578i
$866$		0			0
$867$	2.48334	−	4.30127i	0.0843386	−	0.146079i
$868$		0			0
$869$	2.90192	+	5.02628i	0.0984410	+	0.170505i
$870$		0			0
$871$	−25.0263	−	50.6147i	−0.847983	−	1.71501i
$872$		0			0
$873$	−19.7128	−	34.1436i	−0.667178	−	1.15559i
$874$		0			0
$875$	3.29423	−	5.70577i	0.111365	−	0.192890i
$876$		0			0
$877$	4.25833	−	7.37564i	0.143794	−	0.249058i	−0.785129	−	0.619333i	$-0.787403\pi$
$877$	4.25833	−	7.37564i	0.143794	−	0.249058i	0.928922	+	0.370275i	$0.120737\pi$
$878$		0			0
$879$	1.55514			0.0524534
$880$		0			0
$881$	−13.1603	−	22.7942i	−0.443380	−	0.767957i	0.554558	−	0.832145i	$-0.312888\pi$
$881$	−13.1603	−	22.7942i	−0.443380	−	0.767957i	−0.997938	+	0.0641883i	$0.979554\pi$
$882$		0			0
$883$	−20.2487			−0.681423			−0.340712	−	0.940168i	$-0.610668\pi$
$883$	−20.2487			−0.681423			−0.340712	+	0.940168i	$0.610668\pi$
$884$		0			0
$885$	3.85641			0.129632
$886$		0			0
$887$	−5.66025	−	9.80385i	−0.190053	−	0.329181i	0.755215	−	0.655477i	$-0.227533\pi$
$887$	−5.66025	−	9.80385i	−0.190053	−	0.329181i	−0.945267	+	0.326296i	$0.894199\pi$
$888$		0			0
$889$	−2.24871			−0.0754194
$890$		0			0
$891$	2.23205	−	3.86603i	0.0747765	−	0.129517i
$892$		0			0
$893$	4.46410	−	7.73205i	0.149385	−	0.258743i
$894$		0			0
$895$	−0.633975	−	1.09808i	−0.0211914	−	0.0367046i
$896$		0			0
$897$	10.9282	−	16.3923i	0.364882	−	0.547323i
$898$		0			0
$899$	0.803848	+	1.39230i	0.0268098	+	0.0464360i
$900$		0			0
$901$	−18.2058	+	31.5333i	−0.606522	+	1.05053i
$902$		0			0
$903$	−2.92820	+	5.07180i	−0.0974445	+	0.168779i
$904$		0			0
$905$	9.39230			0.312211
$906$		0			0
$907$	−6.68653	−	11.5814i	−0.222023	−	0.384555i	0.733399	−	0.679798i	$-0.237933\pi$
$907$	−6.68653	−	11.5814i	−0.222023	−	0.384555i	−0.955422	+	0.295243i	$0.904599\pi$
$908$		0			0
$909$	1.98076			0.0656977
$910$		0			0
$911$	36.1962			1.19923			0.599616	−	0.800288i	$-0.295320\pi$
$911$	36.1962			1.19923			0.599616	+	0.800288i	$0.295320\pi$
$912$		0			0
$913$	−1.09808	−	1.90192i	−0.0363410	−	0.0629445i
$914$		0			0
$915$	−8.58846			−0.283926
$916$		0			0
$917$	4.60770	−	7.98076i	0.152159	−	0.263548i
$918$		0			0
$919$	13.5885	−	23.5359i	0.448242	−	0.776378i	−0.550030	−	0.835145i	$-0.685384\pi$
$919$	13.5885	−	23.5359i	0.448242	−	0.776378i	0.998272	+	0.0587673i	$0.0187170\pi$
$920$		0			0
$921$	−12.4641	−	21.5885i	−0.410706	−	0.711364i
$922$		0			0
$923$	12.0000	−	18.0000i	0.394985	−	0.592477i
$924$		0			0
$925$	14.0000	+	24.2487i	0.460317	+	0.797293i
$926$		0			0
$927$	11.0000	−	19.0526i	0.361287	−	0.625768i
$928$		0			0
$929$	11.0885	−	19.2058i	0.363800	−	0.630121i	−0.624782	−	0.780799i	$-0.714812\pi$
$929$	11.0885	−	19.2058i	0.363800	−	0.630121i	0.988583	+	0.150678i	$0.0481457\pi$
$930$		0			0
$931$	17.6603			0.578791
$932$		0			0
$933$	7.33975	+	12.7128i	0.240292	+	0.416199i
$934$		0			0
$935$	−3.19615			−0.104525
$936$		0			0
$937$	5.44486			0.177876			0.0889380	−	0.996037i	$-0.471653\pi$
$937$	5.44486			0.177876			0.0889380	+	0.996037i	$0.471653\pi$
$938$		0			0
$939$	2.53590	+	4.39230i	0.0827559	+	0.143337i
$940$		0			0
$941$	45.7128			1.49020			0.745098	−	0.666955i	$-0.232403\pi$
$941$	45.7128			1.49020			0.745098	+	0.666955i	$0.232403\pi$
$942$		0			0
$943$	−21.3923	+	37.0526i	−0.696629	+	1.20660i
$944$		0			0
$945$	1.46410	−	2.53590i	0.0476272	−	0.0824928i
$946$		0			0
$947$	0.464102	+	0.803848i	0.0150813	+	0.0261215i	0.873468	−	0.486882i	$-0.161866\pi$
$947$	0.464102	+	0.803848i	0.0150813	+	0.0261215i	−0.858386	+	0.513004i	$0.828533\pi$
$948$		0			0
$949$	−38.3564	−	2.47372i	−1.24510	−	0.0803004i
$950$		0			0
$951$	3.15064	+	5.45706i	0.102166	+	0.176957i
$952$		0			0
$953$	−18.4641	+	31.9808i	−0.598111	+	1.03596i	0.394989	+	0.918686i	$0.370748\pi$
$953$	−18.4641	+	31.9808i	−0.598111	+	1.03596i	−0.993100	+	0.117273i	$0.962585\pi$
$954$		0			0
$955$	−4.56218	+	7.90192i	−0.147629	+	0.255700i
$956$		0			0
$957$	0.196152			0.00634071
$958$		0			0
$959$	3.83013	+	6.63397i	0.123681	+	0.214222i
$960$		0			0
$961$	5.00000			0.161290
$962$		0			0
$963$	36.3013			1.16979
$964$		0			0
$965$	3.40192	+	5.89230i	0.109512	+	0.189680i
$966$		0			0
$967$	−9.94744			−0.319888			−0.159944	−	0.987126i	$-0.551131\pi$
$967$	−9.94744			−0.319888			−0.159944	+	0.987126i	$0.551131\pi$
$968$		0			0
$969$	−3.19615	+	5.53590i	−0.102675	+	0.177839i
$970$		0			0
$971$	−6.95448	+	12.0455i	−0.223180	+	0.386559i	−0.955772	−	0.294109i	$-0.904977\pi$
$971$	−6.95448	+	12.0455i	−0.223180	+	0.386559i	0.732592	+	0.680668i	$0.238310\pi$
$972$		0			0
$973$	2.53590	+	4.39230i	0.0812972	+	0.140811i
$974$		0			0
$975$	−4.67949	−	9.46410i	−0.149864	−	0.303094i
$976$		0			0
$977$	−10.1603	−	17.5981i	−0.325055	−	0.563012i	0.656468	−	0.754354i	$-0.272050\pi$
$977$	−10.1603	−	17.5981i	−0.325055	−	0.563012i	−0.981524	+	0.191341i	$0.938716\pi$
$978$		0			0
$979$	4.92820	−	8.53590i	0.157506	−	0.272808i
$980$		0			0
$981$	13.4641	−	23.3205i	0.429876	−	0.744567i
$982$		0			0
$983$	−4.92820			−0.157185			−0.0785926	−	0.996907i	$-0.525043\pi$
$983$	−4.92820			−0.157185			−0.0785926	+	0.996907i	$0.525043\pi$
$984$		0			0
$985$	1.00000	+	1.73205i	0.0318626	+	0.0551877i
$986$		0			0
$987$	−1.75129			−0.0557441
$988$		0			0
$989$	−81.5692			−2.59375
$990$		0			0
$991$	−7.29423	−	12.6340i	−0.231709	−	0.401331i	0.726602	−	0.687058i	$-0.241098\pi$
$991$	−7.29423	−	12.6340i	−0.231709	−	0.401331i	−0.958311	+	0.285727i	$0.907765\pi$
$992$		0			0
$993$	8.49742			0.269658
$994$		0			0
$995$	6.02628	−	10.4378i	0.191046	−	0.330901i
$996$		0			0
$997$	5.72243	−	9.91154i	0.181231	−	0.313902i	−0.761069	−	0.648671i	$-0.775325\pi$
$997$	5.72243	−	9.91154i	0.181231	−	0.313902i	0.942300	+	0.334769i	$0.108658\pi$
$998$		0			0
$999$	14.0000	+	24.2487i	0.442940	+	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.i.a.133.1	✓	4
13.3	even	3		7436.2.a.f.1.2		2
13.9	even	3	inner	572.2.i.a.529.1	yes	4
13.10	even	6		7436.2.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.i.a.133.1	✓	4	1.1	even	1	trivial
572.2.i.a.529.1	yes	4	13.9	even	3	inner
7436.2.a.f.1.2		2	13.3	even	3
7436.2.a.g.1.2		2	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 0.633975i) q^{3} -1.00000 q^{5} +(0.366025 - 0.633975i) q^{7} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\)	\(q+(-0.366025 - 0.633975i) q^{3} -1.00000 q^{5} +(0.366025 - 0.633975i) q^{7} +(1.23205 - 2.13397i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-3.59808 - 0.232051i) q^{13} +(0.366025 + 0.633975i) q^{15} +(1.59808 - 2.76795i) q^{17} +(1.36603 - 2.36603i) q^{19} -0.535898 q^{21} +(-3.73205 - 6.46410i) q^{23} -4.00000 q^{25} -4.00000 q^{27} +(0.133975 + 0.232051i) q^{29} +6.00000 q^{31} +(0.366025 - 0.633975i) q^{33} +(-0.366025 + 0.633975i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(1.16987 + 2.36603i) q^{39} +(-2.86603 - 4.96410i) q^{41} +(5.46410 - 9.46410i) q^{43} +(-1.23205 + 2.13397i) q^{45} +3.26795 q^{47} +(3.23205 + 5.59808i) q^{49} -2.33975 q^{51} -11.3923 q^{53} +(-0.500000 - 0.866025i) q^{55} -2.00000 q^{57} +(2.63397 - 4.56218i) q^{59} +(-5.86603 + 10.1603i) q^{61} +(-0.901924 - 1.56218i) q^{63} +(3.59808 + 0.232051i) q^{65} +(7.83013 + 13.5622i) q^{67} +(-2.73205 + 4.73205i) q^{69} +(-3.00000 + 5.19615i) q^{71} +10.6603 q^{73} +(1.46410 + 2.53590i) q^{75} +0.732051 q^{77} +5.80385 q^{79} +(-2.23205 - 3.86603i) q^{81} -2.19615 q^{83} +(-1.59808 + 2.76795i) q^{85} +(0.0980762 - 0.169873i) q^{87} +(-4.92820 - 8.53590i) q^{89} +(-1.46410 + 2.19615i) q^{91} +(-2.19615 - 3.80385i) q^{93} +(-1.36603 + 2.36603i) q^{95} +(8.00000 - 13.8564i) q^{97} +2.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 2 * q^9	\( 4 q + 2 q^{3} - 4 q^{5} - 2 q^{7} - 2 q^{9} + 2 q^{11} - 4 q^{13} - 2 q^{15} - 4 q^{17} + 2 q^{19} - 16 q^{21} - 8 q^{23} - 16 q^{25} - 16 q^{27} + 4 q^{29} + 24 q^{31} - 2 q^{33} + 2 q^{35} - 14 q^{37} + 22 q^{39} - 8 q^{41} + 8 q^{43} + 2 q^{45} + 20 q^{47} + 6 q^{49} - 44 q^{51} - 4 q^{53} - 2 q^{55} - 8 q^{57} + 14 q^{59} - 20 q^{61} - 14 q^{63} + 4 q^{65} + 14 q^{67} - 4 q^{69} - 12 q^{71} + 8 q^{73} - 8 q^{75} - 4 q^{77} + 44 q^{79} - 2 q^{81} + 12 q^{83} + 4 q^{85} - 10 q^{87} + 8 q^{89} + 8 q^{91} + 12 q^{93} - 2 q^{95} + 32 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 4 * q^5 - 2 * q^7 - 2 * q^9 + 2 * q^11 - 4 * q^13 - 2 * q^15 - 4 * q^17 + 2 * q^19 - 16 * q^21 - 8 * q^23 - 16 * q^25 - 16 * q^27 + 4 * q^29 + 24 * q^31 - 2 * q^33 + 2 * q^35 - 14 * q^37 + 22 * q^39 - 8 * q^41 + 8 * q^43 + 2 * q^45 + 20 * q^47 + 6 * q^49 - 44 * q^51 - 4 * q^53 - 2 * q^55 - 8 * q^57 + 14 * q^59 - 20 * q^61 - 14 * q^63 + 4 * q^65 + 14 * q^67 - 4 * q^69 - 12 * q^71 + 8 * q^73 - 8 * q^75 - 4 * q^77 + 44 * q^79 - 2 * q^81 + 12 * q^83 + 4 * q^85 - 10 * q^87 + 8 * q^89 + 8 * q^91 + 12 * q^93 - 2 * q^95 + 32 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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