LMFDB - Embedded newform 225.2.p.b.68.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(32,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.p (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 36x^13 + 34x^12 + 18x^11 - 72x^10 + 132x^9 - 93x^8 - 102x^7 + 144x^6 - 432x^5 + 502x^4 + 288x^3 + 72x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			68.2
Root			$-0.0499037 - 0.186243i$ of defining polynomial
Character	$\chi$	$=$	225.68
Dual form			225.2.p.b.182.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0499037 + 0.186243i) q^{2} +(0.806271 - 1.53295i) q^{3} +(1.69985 + 0.981412i) q^{4} +(0.245265 + 0.226662i) q^{6} +(2.35868 + 0.632007i) q^{7} +(-0.540289 + 0.540289i) q^{8} +(-1.69985 - 2.47194i) q^{9} +O(q^{10})$	\(q+(-0.0499037 + 0.186243i) q^{2} +(0.806271 - 1.53295i) q^{3} +(1.69985 + 0.981412i) q^{4} +(0.245265 + 0.226662i) q^{6} +(2.35868 + 0.632007i) q^{7} +(-0.540289 + 0.540289i) q^{8} +(-1.69985 - 2.47194i) q^{9} +(-2.14390 + 1.23778i) q^{11} +(2.87500 - 1.81450i) q^{12} +(-1.57505 + 0.422032i) q^{13} +(-0.235414 + 0.407749i) q^{14} +(1.88916 + 3.27212i) q^{16} +(0.403949 + 0.403949i) q^{17} +(0.545211 - 0.193227i) q^{18} -4.28779i q^{19} +(2.87057 - 3.10617i) q^{21} +(-0.123539 - 0.461055i) q^{22} +(-1.82845 - 6.82387i) q^{23} +(0.392615 + 1.26385i) q^{24} -0.314402i q^{26} +(-5.15990 + 0.612733i) q^{27} +(3.38916 + 3.38916i) q^{28} +(3.20524 + 5.55164i) q^{29} +(-1.97194 + 3.41550i) q^{31} +(-2.17978 + 0.584071i) q^{32} +(0.168889 + 4.28446i) q^{33} +(-0.0953913 + 0.0550742i) q^{34} +(-0.463514 - 5.87020i) q^{36} +(0.171954 - 0.171954i) q^{37} +(0.798571 + 0.213977i) q^{38} +(-0.622960 + 2.75474i) q^{39} +(-6.52359 - 3.76639i) q^{41} +(0.435250 + 0.689633i) q^{42} +(-1.32695 + 4.95226i) q^{43} -4.85908 q^{44} +1.36214 q^{46} +(-0.780885 + 2.91430i) q^{47} +(6.53917 - 0.257767i) q^{48} +(-0.898221 - 0.518588i) q^{49} +(0.944926 - 0.293541i) q^{51} +(-3.09154 - 0.828375i) q^{52} +(-6.12030 + 6.12030i) q^{53} +(0.143381 - 0.991573i) q^{54} +(-1.61584 + 0.932904i) q^{56} +(-6.57296 - 3.45712i) q^{57} +(-1.19391 + 0.319907i) q^{58} +(2.27234 - 3.93581i) q^{59} +(-0.235795 - 0.408408i) q^{61} +(-0.537706 - 0.537706i) q^{62} +(-2.44713 - 6.90485i) q^{63} +7.12153i q^{64} +(-0.806380 - 0.182356i) q^{66} +(0.443446 + 1.65496i) q^{67} +(0.290215 + 1.08310i) q^{68} +(-11.9349 - 2.69897i) q^{69} +3.50583i q^{71} +(2.25397 + 0.417150i) q^{72} +(-6.88847 - 6.88847i) q^{73} +(0.0234441 + 0.0406064i) q^{74} +(4.20809 - 7.28862i) q^{76} +(-5.83906 + 1.56457i) q^{77} +(-0.481962 - 0.253493i) q^{78} +(6.50159 - 3.75369i) q^{79} +(-3.22099 + 8.40388i) q^{81} +(1.02702 - 1.02702i) q^{82} +(10.6660 + 2.85794i) q^{83} +(7.92799 - 2.46282i) q^{84} +(-0.856104 - 0.494272i) q^{86} +(11.0947 - 0.437340i) q^{87} +(0.489565 - 1.82708i) q^{88} -2.90124 q^{89} -3.98176 q^{91} +(3.58893 - 13.3941i) q^{92} +(3.64587 + 5.77670i) q^{93} +(-0.503800 - 0.290869i) q^{94} +(-0.862145 + 3.81241i) q^{96} +(-1.41681 - 0.379633i) q^{97} +(0.141408 - 0.141408i) q^{98} +(6.70403 + 3.19554i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7}+O(q^{10}) $ 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7	$ 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7} + 6 q^{12} + 2 q^{13} - 8 q^{16} - 36 q^{18} - 12 q^{21} + 10 q^{22} - 18 q^{23} - 18 q^{27} + 16 q^{28} - 4 q^{31} - 30 q^{32} + 12 q^{33} - 48 q^{36} - 4 q^{37} + 30 q^{38} - 24 q^{41} - 6 q^{42} + 2 q^{43} + 32 q^{46} + 12 q^{47} + 30 q^{48} + 36 q^{51} + 14 q^{52} + 36 q^{56} + 6 q^{57} + 6 q^{58} + 8 q^{61} - 36 q^{63} + 36 q^{66} - 4 q^{67} - 42 q^{68} - 18 q^{72} + 8 q^{73} + 24 q^{76} + 6 q^{77} + 42 q^{78} - 48 q^{81} - 32 q^{82} + 66 q^{83} - 48 q^{86} + 18 q^{87} - 18 q^{88} - 40 q^{91} + 60 q^{92} + 18 q^{93} - 24 q^{96} - 28 q^{97}+O(q^{100}) $ 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7 + 6 * q^12 + 2 * q^13 - 8 * q^16 - 36 * q^18 - 12 * q^21 + 10 * q^22 - 18 * q^23 - 18 * q^27 + 16 * q^28 - 4 * q^31 - 30 * q^32 + 12 * q^33 - 48 * q^36 - 4 * q^37 + 30 * q^38 - 24 * q^41 - 6 * q^42 + 2 * q^43 + 32 * q^46 + 12 * q^47 + 30 * q^48 + 36 * q^51 + 14 * q^52 + 36 * q^56 + 6 * q^57 + 6 * q^58 + 8 * q^61 - 36 * q^63 + 36 * q^66 - 4 * q^67 - 42 * q^68 - 18 * q^72 + 8 * q^73 + 24 * q^76 + 6 * q^77 + 42 * q^78 - 48 * q^81 - 32 * q^82 + 66 * q^83 - 48 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^91 + 60 * q^92 + 18 * q^93 - 24 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.0499037	+	0.186243i	−0.0352872	+	0.131694i	−0.981322	−	0.192370i	$-0.938383\pi$
$2$	−0.0499037	+	0.186243i	−0.0352872	+	0.131694i	0.946035	+	0.324064i	$0.105049\pi$
$3$	0.806271	−	1.53295i	0.465501	−	0.885048i
$3$	0.806271	−	1.53295i	0.465501	−	0.885048i
$4$	1.69985	+	0.981412i	0.849927	+	0.490706i
$5$		0			0
$5$		0			0
$6$	0.245265	+	0.226662i	0.100129	+	0.0925344i
$7$	2.35868	+	0.632007i	0.891499	+	0.238876i	0.675362	−	0.737487i	$-0.263988\pi$
$7$	2.35868	+	0.632007i	0.891499	+	0.238876i	0.216137	+	0.976363i	$0.430654\pi$
$8$	−0.540289	+	0.540289i	−0.191021	+	0.191021i
$9$	−1.69985	−	2.47194i	−0.566618	−	0.823980i
$10$		0			0
$11$	−2.14390	+	1.23778i	−0.646409	+	0.373204i	−0.787079	−	0.616852i	$-0.788408\pi$
$11$	−2.14390	+	1.23778i	−0.646409	+	0.373204i	0.140670	+	0.990057i	$0.455074\pi$
$12$	2.87500	−	1.81450i	0.829940	−	0.523802i
$13$	−1.57505	+	0.422032i	−0.436839	+	0.117051i	−0.470535	−	0.882381i	$-0.655939\pi$
$13$	−1.57505	+	0.422032i	−0.436839	+	0.117051i	0.0336956	+	0.999432i	$0.489272\pi$
$14$	−0.235414	+	0.407749i	−0.0629170	+	0.108975i
$15$		0			0
$16$	1.88916	+	3.27212i	0.472290	+	0.818031i
$17$	0.403949	+	0.403949i	0.0979721	+	0.0979721i	0.754394	−	0.656422i	$-0.227931\pi$
$17$	0.403949	+	0.403949i	0.0979721	+	0.0979721i	−0.656422	+	0.754394i	$0.727931\pi$
$18$	0.545211	−	0.193227i	0.128507	−	0.0455441i
$19$		−	4.28779i		−	0.983687i	−0.870684	−	0.491843i	$-0.836323\pi$
$19$		−	4.28779i		−	0.983687i	0.870684	−	0.491843i	$-0.163677\pi$
$20$		0			0
$21$	2.87057	−	3.10617i	0.626410	−	0.677822i
$22$	−0.123539	−	0.461055i	−0.0263387	−	0.0982973i
$23$	−1.82845	−	6.82387i	−0.381258	−	1.42288i	−0.843981	−	0.536373i	$-0.819794\pi$
$23$	−1.82845	−	6.82387i	−0.381258	−	1.42288i	0.462723	−	0.886503i	$-0.346872\pi$
$24$	0.392615	+	1.26385i	0.0801422	+	0.257983i
$25$		0			0
$26$		−	0.314402i		−	0.0616594i
$27$	−5.15990	+	0.612733i	−0.993023	+	0.117921i
$28$	3.38916	+	3.38916i	0.640491	+	0.640491i
$29$	3.20524	+	5.55164i	0.595199	+	1.03091i	0.993519	+	0.113668i	$0.0362600\pi$
$29$	3.20524	+	5.55164i	0.595199	+	1.03091i	−0.398320	+	0.917247i	$0.630407\pi$
$30$		0			0
$31$	−1.97194	+	3.41550i	−0.354171	+	0.613442i	−0.986976	−	0.160869i	$-0.948570\pi$
$31$	−1.97194	+	3.41550i	−0.354171	+	0.613442i	0.632805	+	0.774312i	$0.281904\pi$
$32$	−2.17978	+	0.584071i	−0.385335	+	0.103250i
$33$	0.168889	+	4.28446i	0.0293998	+	0.745829i
$34$	−0.0953913	+	0.0550742i	−0.0163595	+	0.00944515i
$35$		0			0
$36$	−0.463514	−	5.87020i	−0.0772524	−	0.978366i
$37$	0.171954	−	0.171954i	0.0282691	−	0.0282691i	−0.692831	−	0.721100i	$-0.743637\pi$
$37$	0.171954	−	0.171954i	0.0282691	−	0.0282691i	0.721100	+	0.692831i	$0.243637\pi$
$38$	0.798571	+	0.213977i	0.129545	+	0.0347116i
$39$	−0.622960	+	2.75474i	−0.0997535	+	0.441111i
$40$		0			0
$41$	−6.52359	−	3.76639i	−1.01881	−	0.588212i	−0.105053	−	0.994467i	$-0.533501\pi$
$41$	−6.52359	−	3.76639i	−1.01881	−	0.588212i	−0.913760	+	0.406255i	$0.866835\pi$
$42$	0.435250	+	0.689633i	0.0671606	+	0.106413i
$43$	−1.32695	+	4.95226i	−0.202359	+	0.755213i	0.787880	+	0.615829i	$0.211179\pi$
$43$	−1.32695	+	4.95226i	−0.202359	+	0.755213i	−0.990238	+	0.139384i	$0.955488\pi$
$44$	−4.85908			−0.732534
$45$		0			0
$46$	1.36214			0.200837
$47$	−0.780885	+	2.91430i	−0.113904	+	0.425095i	−0.999203	−	0.0399279i	$-0.987287\pi$
$47$	−0.780885	+	2.91430i	−0.113904	+	0.425095i	0.885299	+	0.465023i	$0.153954\pi$
$48$	6.53917	−	0.257767i	0.943847	−	0.0372055i
$49$	−0.898221	−	0.518588i	−0.128317	−	0.0740841i
$50$		0			0
$51$	0.944926	−	0.293541i	0.132316	−	0.0411039i
$52$	−3.09154	−	0.828375i	−0.428719	−	0.114875i
$53$	−6.12030	+	6.12030i	−0.840688	+	0.840688i	−0.988948	−	0.148260i	$-0.952633\pi$
$53$	−6.12030	+	6.12030i	−0.840688	+	0.840688i	0.148260	+	0.988948i	$0.452633\pi$
$54$	0.143381	−	0.991573i	0.0195116	−	0.134936i
$55$		0			0
$56$	−1.61584	+	0.932904i	−0.215925	+	0.124665i
$57$	−6.57296	−	3.45712i	−0.870610	−	0.457907i
$58$	−1.19391	+	0.319907i	−0.156768	+	0.0420058i
$59$	2.27234	−	3.93581i	0.295833	−	0.512399i	−0.679345	−	0.733819i	$-0.737736\pi$
$59$	2.27234	−	3.93581i	0.295833	−	0.512399i	0.975178	+	0.221421i	$0.0710693\pi$
$60$		0			0
$61$	−0.235795	−	0.408408i	−0.0301904	−	0.0522913i	0.850535	−	0.525918i	$-0.176278\pi$
$61$	−0.235795	−	0.408408i	−0.0301904	−	0.0522913i	−0.880726	+	0.473626i	$0.842945\pi$
$62$	−0.537706	−	0.537706i	−0.0682888	−	0.0682888i
$63$	−2.44713	−	6.90485i	−0.308310	−	0.869929i
$64$			7.12153i			0.890191i
$65$		0			0
$66$	−0.806380	−	0.182356i	−0.0992585	−	0.0224465i
$67$	0.443446	+	1.65496i	0.0541756	+	0.202186i	0.987709	−	0.156305i	$-0.0499582\pi$
$67$	0.443446	+	1.65496i	0.0541756	+	0.202186i	−0.933533	+	0.358491i	$0.883291\pi$
$68$	0.290215	+	1.08310i	0.0351937	+	0.131345i
$69$	−11.9349	−	2.69897i	−1.43679	−	0.324918i
$70$		0			0
$71$			3.50583i			0.416065i	0.978122	+	0.208032i	$0.0667060\pi$
$71$			3.50583i			0.416065i	−0.978122	+	0.208032i	$0.933294\pi$
$72$	2.25397	+	0.417150i	0.265633	+	0.0491616i
$73$	−6.88847	−	6.88847i	−0.806234	−	0.806234i	0.177827	−	0.984062i	$-0.443093\pi$
$73$	−6.88847	−	6.88847i	−0.806234	−	0.806234i	−0.984062	+	0.177827i	$0.943093\pi$
$74$	0.0234441	+	0.0406064i	0.00272533	+	0.00472040i
$75$		0			0
$76$	4.20809	−	7.28862i	0.482701	−	0.836062i
$77$	−5.83906	+	1.56457i	−0.665422	+	0.178299i
$78$	−0.481962	−	0.253493i	−0.0545715	−	0.0287025i
$79$	6.50159	−	3.75369i	0.731485	−	0.422323i	−0.0874799	−	0.996166i	$-0.527881\pi$
$79$	6.50159	−	3.75369i	0.731485	−	0.422323i	0.818965	+	0.573843i	$0.194548\pi$
$80$		0			0
$81$	−3.22099	+	8.40388i	−0.357888	+	0.933765i
$82$	1.02702	−	1.02702i	0.113415	−	0.113415i
$83$	10.6660	+	2.85794i	1.17074	+	0.313700i	0.791249	−	0.611493i	$-0.209431\pi$
$83$	10.6660	+	2.85794i	1.17074	+	0.313700i	0.379495	+	0.925194i	$0.376098\pi$
$84$	7.92799	−	2.46282i	0.865014	−	0.268716i
$85$		0			0
$86$	−0.856104	−	0.494272i	−0.0923161	−	0.0532987i
$87$	11.0947	−	0.437340i	1.18947	−	0.0468878i
$88$	0.489565	−	1.82708i	0.0521878	−	0.194767i
$89$	−2.90124			−0.307531			−0.153765	−	0.988107i	$-0.549140\pi$
$89$	−2.90124			−0.307531			−0.153765	+	0.988107i	$0.549140\pi$
$90$		0			0
$91$	−3.98176			−0.417402
$92$	3.58893	−	13.3941i	0.374171	−	1.39643i
$93$	3.64587	+	5.77670i	0.378059	+	0.599016i
$94$	−0.503800	−	0.290869i	−0.0519630	−	0.0300008i
$95$		0			0
$96$	−0.862145	+	3.81241i	−0.0879923	+	0.389103i
$97$	−1.41681	−	0.379633i	−0.143855	−	0.0385459i	0.186173	−	0.982517i	$-0.440392\pi$
$97$	−1.41681	−	0.379633i	−0.143855	−	0.0385459i	−0.330028	+	0.943971i	$0.607058\pi$
$98$	0.141408	−	0.141408i	0.0142844	−	0.0142844i
$99$	6.70403	+	3.19554i	0.673780	+	0.321164i
$100$		0			0
$101$	15.3563	−	8.86596i	1.52801	−	0.882196i	0.528563	−	0.848894i	$-0.322731\pi$
$101$	15.3563	−	8.86596i	1.52801	−	0.882196i	0.999445	−	0.0333015i	$-0.0106022\pi$
$102$	0.00751461	+	0.190635i	0.000744058	+	0.0188756i
$103$	10.2381	−	2.74330i	1.00879	−	0.270305i	0.283668	−	0.958922i	$-0.408449\pi$
$103$	10.2381	−	2.74330i	1.00879	−	0.270305i	0.725125	+	0.688617i	$0.241782\pi$
$104$	0.622960	−	1.07900i	0.0610863	−	0.105805i
$105$		0			0
$106$	−0.834438	−	1.44529i	−0.0810478	−	0.140379i
$107$	10.4591	+	10.4591i	1.01112	+	1.01112i	0.999937	+	0.0111806i	$0.00355898\pi$
$107$	10.4591	+	10.4591i	1.01112	+	1.01112i	0.0111806	+	0.999937i	$0.496441\pi$
$108$	−9.37242	−	4.02243i	−0.901862	−	0.387058i
$109$		−	0.343204i		−	0.0328730i	−0.999865	−	0.0164365i	$-0.994768\pi$
$109$		−	0.343204i		−	0.0328730i	0.999865	−	0.0164365i	$-0.00523214\pi$
$110$		0			0
$111$	−0.124955	−	0.402239i	−0.0118602	−	0.0381788i
$112$	2.38793	+	8.91187i	0.225638	+	0.842092i
$113$	−1.39133	−	5.19250i	−0.130885	−	0.488469i	0.869096	−	0.494643i	$-0.164701\pi$
$113$	−1.39133	−	5.19250i	−0.130885	−	0.488469i	−0.999981	+	0.00617426i	$0.998035\pi$
$114$	0.971879	−	1.05164i	0.0910248	−	0.0984955i
$115$		0			0
$116$			12.5827i			1.16827i
$117$	3.72059	+	3.17603i	0.343969	+	0.293624i
$118$	0.619619	+	0.619619i	0.0570405	+	0.0570405i
$119$	0.697490	+	1.20809i	0.0639388	+	0.110745i
$120$		0			0
$121$	−2.43581	+	4.21894i	−0.221437	+	0.383540i
$122$	0.0878302	−	0.0235340i	0.00795177	−	0.00213067i
$123$	−11.0335	+	6.96358i	−0.994854	+	0.627885i
$124$	−6.70403	+	3.87057i	−0.602039	+	0.347588i
$125$		0			0
$126$	1.40810	−	0.111184i	0.125444	−	0.00990510i
$127$	3.59190	−	3.59190i	0.318729	−	0.318729i	−0.529550	−	0.848279i	$-0.677639\pi$
$127$	3.59190	−	3.59190i	0.318729	−	0.318729i	0.848279	+	0.529550i	$0.177639\pi$
$128$	−5.68590	−	1.52353i	−0.502567	−	0.134662i
$129$	6.52167	+	6.02702i	0.574201	+	0.530649i
$130$		0			0
$131$	14.5188	+	8.38241i	1.26851	+	0.732375i	0.974706	−	0.223491i	$-0.0717453\pi$
$131$	14.5188	+	8.38241i	1.26851	+	0.732375i	0.293804	+	0.955866i	$0.405079\pi$
$132$	−3.91774	+	7.44872i	−0.340995	+	0.648327i
$133$	2.70992	−	10.1135i	0.234980	−	0.876956i
$134$	−0.330355			−0.0285383
$135$		0			0
$136$	−0.436499			−0.0374295
$137$	1.65517	−	6.17718i	0.141411	−	0.527752i	−0.858478	−	0.512850i	$-0.828590\pi$
$137$	1.65517	−	6.17718i	0.141411	−	0.527752i	0.999889	−	0.0149021i	$-0.00474367\pi$
$138$	1.09826	−	2.08810i	0.0934899	−	0.177751i
$139$	−9.09433	−	5.25061i	−0.771371	−	0.445351i	0.0619924	−	0.998077i	$-0.480255\pi$
$139$	−9.09433	−	5.25061i	−0.771371	−	0.445351i	−0.833364	+	0.552725i	$0.813588\pi$
$140$		0			0
$141$	3.83787	+	3.54677i	0.323207	+	0.298692i
$142$	−0.652936	−	0.174954i	−0.0547931	−	0.0146818i
$143$	2.85435	−	2.85435i	0.238693	−	0.238693i
$144$	4.87720	−	10.2320i	0.406433	−	0.852669i
$145$		0			0
$146$	1.62669	−	0.939170i	0.134626	−	0.0777262i
$147$	−1.51918	+	0.958803i	−0.125300	+	0.0790808i
$148$	0.461055	−	0.123539i	0.0378985	−	0.0101549i
$149$	4.96581	−	8.60103i	0.406815	−	0.704624i	−0.587716	−	0.809067i	$-0.699973\pi$
$149$	4.96581	−	8.60103i	0.406815	−	0.704624i	0.994531	+	0.104443i	$0.0333061\pi$
$150$		0			0
$151$	−6.95939	−	12.0540i	−0.566347	−	0.980942i	−0.996923	−	0.0783879i	$-0.975023\pi$
$151$	−6.95939	−	12.0540i	−0.566347	−	0.980942i	0.430576	−	0.902555i	$-0.358311\pi$
$152$	2.31665	+	2.31665i	0.187905	+	0.187905i
$153$	0.311884	−	1.68519i	0.0252143	−	0.136240i
$154$		−	1.16556i		−	0.0939236i
$155$		0			0
$156$	−3.76247	+	4.07127i	−0.301239	+	0.325962i
$157$	−5.42234	−	20.2365i	−0.432750	−	1.61505i	−0.746394	−	0.665504i	$-0.768216\pi$
$157$	−5.42234	−	20.2365i	−0.432750	−	1.61505i	0.313644	−	0.949541i	$-0.398450\pi$
$158$	0.374646	+	1.39820i	0.0298052	+	0.111235i
$159$	4.44748	+	14.3167i	0.352708	+	1.13539i
$160$		0			0
$161$		−	17.2510i		−	1.35957i
$162$	−1.40443	−	1.01927i	−0.110342	−	0.0800815i
$163$	2.42872	+	2.42872i	0.190232	+	0.190232i	0.795796	−	0.605564i	$-0.207052\pi$
$163$	2.42872	+	2.42872i	0.190232	+	0.190232i	−0.605564	+	0.795796i	$0.707052\pi$
$164$	−7.39277	−	12.8046i	−0.577278	−	0.999875i
$165$		0			0
$166$	−1.06454	+	1.84385i	−0.0826247	+	0.143110i
$167$	8.23252	−	2.20590i	0.637052	−	0.170697i	0.0741841	−	0.997245i	$-0.476365\pi$
$167$	8.23252	−	2.20590i	0.637052	−	0.170697i	0.562868	+	0.826547i	$0.309698\pi$
$168$	0.127290	+	3.22917i	0.00982066	+	0.249136i
$169$	−8.95567	+	5.17056i	−0.688898	+	0.397735i
$170$		0			0
$171$	−10.5992	+	7.28862i	−0.810539	+	0.557375i
$172$	−7.11584	+	7.11584i	−0.542577	+	0.542577i
$173$	17.0726	+	4.57458i	1.29800	+	0.347799i	0.840695	−	0.541509i	$-0.182147\pi$
$173$	17.0726	+	4.57458i	1.29800	+	0.347799i	0.457308	+	0.889308i	$0.348814\pi$
$174$	−0.472213	+	2.08813i	−0.0357984	+	0.158301i
$175$		0			0
$176$	−8.10033	−	4.67673i	−0.610585	−	0.352521i
$177$	−4.20126	−	6.65670i	−0.315786	−	0.500348i
$178$	0.144783	−	0.540336i	0.0108519	−	0.0404999i
$179$	8.30788			0.620960			0.310480	−	0.950580i	$-0.399510\pi$
$179$	8.30788			0.620960			0.310480	+	0.950580i	$0.399510\pi$
$180$		0			0
$181$	−4.73429			−0.351897			−0.175948	−	0.984399i	$-0.556299\pi$
$181$	−4.73429			−0.351897			−0.175948	+	0.984399i	$0.556299\pi$
$182$	0.198705	−	0.741576i	0.0147290	−	0.0549693i
$183$	−0.816183	+	0.0321731i	−0.0603340	+	0.00237830i
$184$	4.67475	+	2.69897i	0.344627	+	0.198971i
$185$		0			0
$186$	−1.25781	+	0.390739i	−0.0922273	+	0.0286503i
$187$	−1.36603	−	0.366025i	−0.0998937	−	0.0267664i
$188$	−4.18752	+	4.18752i	−0.305406	+	0.305406i
$189$	−12.5578	−	1.81585i	−0.913447	−	0.132084i
$190$		0			0
$191$	−3.34902	+	1.93356i	−0.242327	+	0.139907i	−0.616246	−	0.787554i	$-0.711347\pi$
$191$	−3.34902	+	1.93356i	−0.242327	+	0.139907i	0.373919	+	0.927461i	$0.378014\pi$
$192$	10.9169	+	5.74188i	0.787861	+	0.414384i
$193$	−16.5901	+	4.44530i	−1.19418	+	0.319979i	−0.800536	−	0.599284i	$-0.795452\pi$
$193$	−16.5901	+	4.44530i	−1.19418	+	0.319979i	−0.393643	+	0.919263i	$0.628785\pi$
$194$	0.141408	−	0.244926i	0.0101525	−	0.0175847i
$195$		0			0
$196$	−1.01790	−	1.76305i	−0.0727070	−	0.125932i
$197$	−11.0386	−	11.0386i	−0.786469	−	0.786469i	0.194445	−	0.980913i	$-0.437709\pi$
$197$	−11.0386	−	11.0386i	−0.786469	−	0.786469i	−0.980913	+	0.194445i	$0.937709\pi$
$198$	−0.929703	+	1.08911i	−0.0660711	+	0.0773996i
$199$			3.60138i			0.255295i	0.991820	+	0.127648i	$0.0407427\pi$
$199$			3.60138i			0.255295i	−0.991820	+	0.127648i	$0.959257\pi$
$200$		0			0
$201$	2.89451	+	0.654569i	0.204163	+	0.0461698i
$202$	0.884888	+	3.30245i	0.0622605	+	0.232359i
$203$	4.05148	+	15.1203i	0.284358	+	1.06124i
$204$	1.89432	+	0.428385i	0.132629	+	0.0299929i
$205$		0			0
$206$			2.04368i			0.142390i
$207$	−13.7601	+	16.1194i	−0.956394	+	1.12038i
$208$	−4.35646	−	4.35646i	−0.302066	−	0.302066i
$209$	5.30734	+	9.19258i	0.367116	+	0.635864i
$210$		0			0
$211$	9.56007	−	16.5585i	0.658142	−	1.13994i	−0.322954	−	0.946415i	$-0.604676\pi$
$211$	9.56007	−	16.5585i	0.658142	−	1.13994i	0.981096	−	0.193521i	$-0.0619909\pi$
$212$	−16.4102	+	4.39709i	−1.12705	+	0.301993i
$213$	5.37425	+	2.82664i	0.368237	+	0.193678i
$214$	−2.46988	+	1.42599i	−0.168837	+	0.0974783i
$215$		0			0
$216$	2.45678	−	3.11889i	0.167163	−	0.212213i
$217$	−6.80981	+	6.80981i	−0.462280	+	0.462280i
$218$	0.0639194	+	0.0171272i	0.00432917	+	0.00116000i
$219$	−16.1136	+	5.00569i	−1.08886	+	0.338253i
$220$		0			0
$221$	−0.806719	−	0.465759i	−0.0542658	−	0.0313304i
$222$	0.0811499	−	0.00319884i	0.00544642	−	0.000214692i
$223$	1.08126	−	4.03530i	0.0724062	−	0.270224i	−0.920226	−	0.391386i	$-0.871996\pi$
$223$	1.08126	−	4.03530i	0.0724062	−	0.270224i	0.992633	+	0.121163i	$0.0386623\pi$
$224$	−5.51055			−0.368189
$225$		0			0
$226$	1.03650			0.0689469
$227$	−3.55990	+	13.2857i	−0.236279	+	0.881803i	0.741290	+	0.671185i	$0.234214\pi$
$227$	−3.55990	+	13.2857i	−0.236279	+	0.881803i	−0.977568	+	0.210618i	$0.932452\pi$
$228$	−7.78022	−	12.3274i	−0.515257	−	0.816401i
$229$	13.2694	+	7.66109i	0.876866	+	0.506259i	0.869624	−	0.493715i	$-0.164361\pi$
$229$	13.2694	+	7.66109i	0.876866	+	0.506259i	0.00724242	+	0.999974i	$0.497695\pi$
$230$		0			0
$231$	−2.30946	+	10.2124i	−0.151951	+	0.671929i
$232$	−4.73125	−	1.26773i	−0.310622	−	0.0832308i
$233$	−2.98562	+	2.98562i	−0.195595	+	0.195595i	−0.798108	−	0.602514i	$-0.794166\pi$
$233$	−2.98562	+	2.98562i	−0.195595	+	0.195595i	0.602514	+	0.798108i	$0.294166\pi$
$234$	−0.777184	+	0.534438i	−0.0508061	+	0.0349373i
$235$		0			0
$236$	7.72529	−	4.46020i	0.502874	−	0.290334i
$237$	−0.512173	−	12.9931i	−0.0332692	−	0.843991i
$238$	−0.259805	+	0.0696146i	−0.0168407	+	0.00451245i
$239$	−2.59439	+	4.49362i	−0.167817	+	0.290668i	−0.937652	−	0.347575i	$-0.887005\pi$
$239$	−2.59439	+	4.49362i	−0.167817	+	0.290668i	0.769835	+	0.638243i	$0.220339\pi$
$240$		0			0
$241$	1.85872	+	3.21939i	0.119730	+	0.207379i	0.919661	−	0.392714i	$-0.128464\pi$
$241$	1.85872	+	3.21939i	0.119730	+	0.207379i	−0.799930	+	0.600093i	$0.795130\pi$
$242$	−0.664193	−	0.664193i	−0.0426959	−	0.0426959i
$243$	10.2857	+	11.7134i	0.659829	+	0.751416i
$244$		−	0.925646i		−	0.0592584i
$245$		0			0
$246$	−0.746308	−	2.40241i	−0.0475829	−	0.153172i
$247$	1.80959	+	6.75347i	0.115141	+	0.429713i
$248$	−0.779940	−	2.91078i	−0.0495262	−	0.184834i
$249$	12.9808	−	14.0461i	0.822622	−	0.890137i
$250$		0			0
$251$			3.97271i			0.250755i	0.992109	+	0.125378i	$0.0400142\pi$
$251$			3.97271i			0.250755i	−0.992109	+	0.125378i	$0.959986\pi$
$252$	2.61673	−	14.1389i	0.164838	−	0.890666i
$253$	12.3665	+	12.3665i	0.777472	+	0.777472i
$254$	0.489717	+	0.848215i	0.0307276	+	0.0532217i
$255$		0			0
$256$	−6.55403	+	11.3519i	−0.409627	+	0.709495i
$257$	16.5120	−	4.42437i	1.02999	−	0.275985i	0.296030	−	0.955179i	$-0.404337\pi$
$257$	16.5120	−	4.42437i	1.02999	−	0.275985i	0.733959	+	0.679194i	$0.237671\pi$
$258$	−1.44794	+	0.913846i	−0.0901451	+	0.0568935i
$259$	0.514262	−	0.296909i	0.0319547	−	0.0184491i
$260$		0			0
$261$	8.27489	−	17.3602i	0.512203	−	1.07457i
$262$	−2.28571	+	2.28571i	−0.141211	+	0.141211i
$263$	−10.3436	−	2.77155i	−0.637812	−	0.170901i	−0.0746001	−	0.997214i	$-0.523768\pi$
$263$	−10.3436	−	2.77155i	−0.637812	−	0.170901i	−0.563212	+	0.826312i	$0.690435\pi$
$264$	−2.40610	−	2.22360i	−0.148085	−	0.136853i
$265$		0			0
$266$	1.74834	+	1.00941i	0.107198	+	0.0618907i
$267$	−2.33919	+	4.44745i	−0.143156	+	0.272179i
$268$	−0.870407	+	3.24840i	−0.0531685	+	0.198428i
$269$	−15.8925			−0.968985			−0.484492	−	0.874796i	$-0.660996\pi$
$269$	−15.8925			−0.968985			−0.484492	+	0.874796i	$0.660996\pi$
$270$		0			0
$271$	0.974200			0.0591785			0.0295892	−	0.999562i	$-0.490580\pi$
$271$	0.974200			0.0591785			0.0295892	+	0.999562i	$0.490580\pi$
$272$	−0.558646	+	2.08490i	−0.0338729	+	0.126415i
$273$	−3.21038	+	6.10383i	−0.194301	+	0.369421i
$274$	1.06786	+	0.616528i	0.0645117	+	0.0372458i
$275$		0			0
$276$	−17.6387	−	16.3009i	−1.06173	−	0.981197i
$277$	23.0788	+	6.18395i	1.38667	+	0.371557i	0.873540	−	0.486753i	$-0.161819\pi$
$277$	23.0788	+	6.18395i	1.38667	+	0.371557i	0.513131	+	0.858310i	$0.328485\pi$
$278$	1.43173	−	1.43173i	0.0858695	−	0.0858695i
$279$	11.7949	−	0.931335i	0.706144	−	0.0557576i
$280$		0			0
$281$	−23.9241	+	13.8126i	−1.42720	+	0.823991i	−0.996899	−	0.0786961i	$-0.974924\pi$
$281$	−23.9241	+	13.8126i	−1.42720	+	0.823991i	−0.430296	+	0.902688i	$0.641591\pi$
$282$	−0.852086	+	0.537779i	−0.0507410	+	0.0320243i
$283$	16.4535	−	4.40870i	0.978058	−	0.262070i	0.265831	−	0.964020i	$-0.414354\pi$
$283$	16.4535	−	4.40870i	0.978058	−	0.262070i	0.712227	+	0.701950i	$0.247687\pi$
$284$	−3.44066	+	5.95939i	−0.204165	+	0.353625i
$285$		0			0
$286$	0.389161	+	0.674046i	0.0230115	+	0.0398572i
$287$	−13.0067	−	13.0067i	−0.767761	−	0.767761i
$288$	5.14910	+	4.39546i	0.303414	+	0.259005i
$289$		−	16.6736i		−	0.980803i
$290$		0			0
$291$	−1.72429	+	1.86581i	−0.101080	+	0.109376i
$292$	−4.94897	−	18.4698i	−0.289617	−	1.08086i
$293$	−6.90146	−	25.7566i	−0.403188	−	1.50472i	−0.807374	−	0.590041i	$-0.799112\pi$
$293$	−6.90146	−	25.7566i	−0.403188	−	1.50472i	0.404186	−	0.914677i	$-0.367555\pi$
$294$	−0.102758	−	0.330784i	−0.00599296	−	0.0192917i
$295$		0			0
$296$			0.185810i			0.0108000i
$297$	10.3039	−	7.70045i	0.597890	−	0.446825i
$298$	1.35407	+	1.35407i	0.0784392	+	0.0784392i
$299$	5.75979	+	9.97625i	0.333097	+	0.576941i
$300$		0			0
$301$	−6.25973	+	10.8422i	−0.360805	+	0.624933i
$302$	2.59228	−	0.694599i	0.149169	−	0.0399697i
$303$	−1.20972	−	30.6887i	−0.0694965	−	1.76302i
$304$	14.0302	−	8.10033i	0.804686	−	0.464586i
$305$		0			0
$306$	0.298292	+	0.142184i	0.0170522	+	0.00812810i
$307$	12.3556	−	12.3556i	0.705171	−	0.705171i	−0.260345	−	0.965516i	$-0.583836\pi$
$307$	12.3556	−	12.3556i	0.705171	−	0.705171i	0.965516	+	0.260345i	$0.0838363\pi$
$308$	−11.4610	−	3.07098i	−0.653053	−	0.174985i
$309$	4.04938	−	17.9064i	0.230361	−	1.01866i
$310$		0			0
$311$	7.49228	+	4.32567i	0.424848	+	0.245286i	0.697149	−	0.716926i	$-0.254451\pi$
$311$	7.49228	+	4.32567i	0.424848	+	0.245286i	−0.272301	+	0.962212i	$0.587785\pi$
$312$	−1.15177	−	1.82493i	−0.0652064	−	0.103316i
$313$	−4.85240	+	18.1094i	−0.274274	+	1.02360i	0.682052	+	0.731303i	$0.261088\pi$
$313$	−4.85240	+	18.1094i	−0.274274	+	1.02360i	−0.956326	+	0.292301i	$0.905579\pi$
$314$	4.03949			0.227962
$315$		0			0
$316$	14.7357			0.828946
$317$	−5.02186	+	18.7418i	−0.282056	+	1.05265i	0.668908	+	0.743345i	$0.266762\pi$
$317$	−5.02186	+	18.7418i	−0.282056	+	1.05265i	−0.950964	+	0.309301i	$0.899905\pi$
$318$	−2.88834	+	0.113855i	−0.161970	+	0.00638468i
$319$	−13.7434	−	7.93476i	−0.769484	−	0.444262i
$320$		0			0
$321$	24.4661	−	7.60037i	1.36556	−	0.424211i
$322$	3.21287	+	0.860886i	0.179046	+	0.0479753i
$323$	1.73205	−	1.73205i	0.0963739	−	0.0963739i
$324$	−13.7229	+	11.1243i	−0.762382	+	0.618015i
$325$		0			0
$326$	−0.573535	+	0.331131i	−0.0317652	+	0.0183396i
$327$	−0.526114	−	0.276716i	−0.0290942	−	0.0153024i
$328$	5.55956	−	1.48968i	0.306975	−	0.0822538i
$329$	−3.68372	+	6.38039i	−0.203090	+	0.351763i
$330$		0			0
$331$	17.1969	+	29.7859i	0.945226	+	1.63718i	0.755298	+	0.655382i	$0.227492\pi$
$331$	17.1969	+	29.7859i	0.945226	+	1.63718i	0.189929	+	0.981798i	$0.439174\pi$
$332$	15.3258	+	15.3258i	0.841114	+	0.841114i
$333$	−0.717358	−	0.132764i	−0.0393110	−	0.00727540i
$334$			1.64333i			0.0899191i
$335$		0			0
$336$	15.5867	+	3.52481i	0.850326	+	0.192294i
$337$	8.28744	+	30.9291i	0.451445	+	1.68482i	0.698333	+	0.715773i	$0.253925\pi$
$337$	8.28744	+	30.9291i	0.451445	+	1.68482i	−0.246888	+	0.969044i	$0.579408\pi$
$338$	−0.516060	−	1.92596i	−0.0280700	−	0.104758i
$339$	−9.08161	−	2.05373i	−0.493245	−	0.111543i
$340$		0			0
$341$		−	9.76331i		−	0.528713i
$342$	−0.828518	−	2.33775i	−0.0448011	−	0.126411i
$343$	−13.8776	−	13.8776i	−0.749320	−	0.749320i
$344$	−1.95871	−	3.39259i	−0.105607	−	0.182916i
$345$		0			0
$346$	−1.70397	+	2.95136i	−0.0916059	+	0.158666i
$347$	15.5122	−	4.15647i	0.832737	−	0.223131i	0.182829	−	0.983145i	$-0.441474\pi$
$347$	15.5122	−	4.15647i	0.832737	−	0.223131i	0.649907	+	0.760014i	$0.274808\pi$
$348$	19.2885	+	10.1450i	1.03397	+	0.543830i
$349$	15.1664	−	8.75630i	0.811837	−	0.468714i	−0.0357566	−	0.999361i	$-0.511384\pi$
$349$	15.1664	−	8.75630i	0.811837	−	0.468714i	0.847593	+	0.530646i	$0.178051\pi$
$350$		0			0
$351$	7.86849	−	3.14273i	0.419989	−	0.167746i
$352$	3.95028	−	3.95028i	0.210550	−	0.210550i
$353$	−18.4846	−	4.95294i	−0.983837	−	0.263618i	−0.269177	−	0.963091i	$-0.586752\pi$
$353$	−18.4846	−	4.95294i	−0.983837	−	0.263618i	−0.714660	+	0.699472i	$0.753418\pi$
$354$	1.44942	−	0.450262i	0.0770360	−	0.0239312i
$355$		0			0
$356$	−4.93169	−	2.84731i	−0.261379	−	0.150907i
$357$	2.41430	−	0.0951692i	0.127778	−	0.00503689i
$358$	−0.414594	+	1.54728i	−0.0219120	+	0.0817766i
$359$	23.0127			1.21457			0.607283	−	0.794486i	$-0.292259\pi$
$359$	23.0127			1.21457			0.607283	+	0.794486i	$0.292259\pi$
$360$		0			0
$361$	0.614846			0.0323603
$362$	0.236258	−	0.881728i	0.0124175	−	0.0463426i
$363$	4.50350	+	7.13557i	0.236372	+	0.374521i
$364$	−6.76842	−	3.90775i	−0.354762	−	0.204822i
$365$		0			0
$366$	0.0347385	−	0.153614i	0.00181581	−	0.00802953i
$367$	−26.1875	−	7.01692i	−1.36698	−	0.366280i	−0.500603	−	0.865677i	$-0.666888\pi$
$367$	−26.1875	−	7.01692i	−1.36698	−	0.366280i	−0.866373	+	0.499397i	$0.833555\pi$
$368$	18.8743	−	18.8743i	0.983891	−	0.983891i
$369$	1.77884	+	22.5282i	0.0926029	+	1.17277i
$370$		0			0
$371$	−18.3039	+	10.5678i	−0.950293	+	0.548652i
$372$	0.528121	+	13.3977i	0.0273818	+	0.694636i
$373$	−28.9771	+	7.76440i	−1.50038	+	0.402025i	−0.913227	−	0.407451i	$-0.866418\pi$
$373$	−28.9771	+	7.76440i	−1.50038	+	0.402025i	−0.587152	+	0.809477i	$0.699751\pi$
$374$	0.136339	−	0.236147i	0.00704994	−	0.0122109i
$375$		0			0
$376$	−1.15266	−	1.99647i	−0.0594440	−	0.102960i
$377$	−7.39138	−	7.39138i	−0.380675	−	0.380675i
$378$	0.964871	−	2.24819i	0.0496276	−	0.115634i
$379$			20.0943i			1.03218i	0.856535	+	0.516089i	$0.172612\pi$
$379$			20.0943i			1.03218i	−0.856535	+	0.516089i	$0.827388\pi$
$380$		0			0
$381$	−2.61015	−	8.40224i	−0.133722	−	0.430460i
$382$	−0.192983	−	0.720223i	−0.00987388	−	0.0368498i
$383$	7.14181	+	26.6536i	0.364929	+	1.36194i	0.867516	+	0.497409i	$0.165715\pi$
$383$	7.14181	+	26.6536i	0.364929	+	1.36194i	−0.502587	+	0.864527i	$0.667618\pi$
$384$	−6.91987	+	7.48780i	−0.353128	+	0.382110i
$385$		0			0
$386$		−	3.31162i		−	0.168557i
$387$	14.4973	−	5.13797i	0.736941	−	0.261178i
$388$	−2.03579	−	2.03579i	−0.103352	−	0.103352i
$389$	−6.71184	−	11.6253i	−0.340304	−	0.589424i	0.644185	−	0.764870i	$-0.277197\pi$
$389$	−6.71184	−	11.6253i	−0.340304	−	0.589424i	−0.984489	+	0.175446i	$0.943863\pi$
$390$		0			0
$391$	2.01790	−	3.49510i	0.102049	−	0.176755i
$392$	0.765487	−	0.205111i	0.0386629	−	0.0103597i
$393$	24.5558	−	15.4980i	1.23868	−	0.781771i
$394$	2.60673	−	1.50500i	0.131325	−	0.0758207i
$395$		0			0
$396$	8.25973	+	12.0114i	0.415067	+	0.603594i
$397$	12.8716	−	12.8716i	0.646008	−	0.646008i	−0.306018	−	0.952026i	$-0.598997\pi$
$397$	12.8716	−	12.8716i	0.646008	−	0.646008i	0.952026	+	0.306018i	$0.0989967\pi$
$398$	−0.670732	−	0.179722i	−0.0336208	−	0.00900866i
$399$	−13.3186	−	12.3084i	−0.666764	−	0.616191i
$400$		0			0
$401$	−21.7606	−	12.5635i	−1.08667	−	0.627391i	−0.153985	−	0.988073i	$-0.549211\pi$
$401$	−21.7606	−	12.5635i	−1.08667	−	0.627391i	−0.932689	+	0.360682i	$0.882544\pi$
$402$	−0.266356	+	0.506417i	−0.0132846	+	0.0252578i
$403$	1.66445	−	6.21180i	0.0829120	−	0.309432i
$404$	34.8046			1.73159
$405$		0			0
$406$	−3.01824			−0.149793
$407$	−0.155811	+	0.581494i	−0.00772325	+	0.0288236i
$408$	−0.351936	+	0.669129i	−0.0174234	+	0.0331268i
$409$	9.81878	+	5.66888i	0.485508	+	0.280308i	0.722709	−	0.691153i	$-0.242897\pi$
$409$	9.81878	+	5.66888i	0.485508	+	0.280308i	−0.237201	+	0.971461i	$0.576230\pi$
$410$		0			0
$411$	−8.13478	−	7.51777i	−0.401259	−	0.370824i
$412$	20.0957	+	5.38461i	0.990042	+	0.265281i
$413$	7.84719	−	7.84719i	0.386135	−	0.386135i
$414$	−2.31545	−	3.36714i	−0.113798	−	0.165486i
$415$		0			0
$416$	3.18676	−	1.83988i	0.156244	−	0.0902074i
$417$	−15.3814	+	9.70771i	−0.753231	+	0.475389i
$418$	−1.97691	+	0.529711i	−0.0966938	+	0.0259090i
$419$	−4.26264	+	7.38311i	−0.208244	+	0.360688i	−0.951161	−	0.308694i	$-0.900108\pi$
$419$	−4.26264	+	7.38311i	−0.208244	+	0.360688i	0.742918	+	0.669383i	$0.233441\pi$
$420$		0			0
$421$	1.10329	+	1.91095i	0.0537710	+	0.0931341i	0.891658	−	0.452710i	$-0.149543\pi$
$421$	1.10329	+	1.91095i	0.0537710	+	0.0931341i	−0.837887	+	0.545844i	$0.816209\pi$
$422$	2.60683	+	2.60683i	0.126898	+	0.126898i
$423$	8.53138	−	3.02359i	0.414810	−	0.147012i
$424$		−	6.61346i		−	0.321178i
$425$		0			0
$426$	−0.794637	+	0.859856i	−0.0385003	+	0.0416601i
$427$	−0.298048	−	1.11233i	−0.0144235	−	0.0538294i
$428$	7.51426	+	28.0436i	0.363215	+	1.35554i
$429$	−2.07419	−	6.67695i	−0.100143	−	0.322366i
$430$		0			0
$431$		−	1.95738i		−	0.0942838i	−0.998888	−	0.0471419i	$-0.984989\pi$
$431$		−	1.95738i		−	0.0942838i	0.998888	−	0.0471419i	$-0.0150113\pi$
$432$	−11.7528	−	15.7263i	−0.565458	−	0.756630i
$433$	9.71652	+	9.71652i	0.466946	+	0.466946i	0.900924	−	0.433978i	$-0.142890\pi$
$433$	9.71652	+	9.71652i	0.466946	+	0.466946i	−0.433978	+	0.900924i	$0.642890\pi$
$434$	−0.928445	−	1.60811i	−0.0445668	−	0.0771919i
$435$		0			0
$436$	0.336825	−	0.583398i	0.0161310	−	0.0279397i
$437$	−29.2593	+	7.84002i	−1.39966	+	0.375039i
$438$	−0.128145	−	3.25085i	−0.00612302	−	0.155332i
$439$	4.68008	−	2.70205i	0.223368	−	0.128962i	−0.384141	−	0.923275i	$-0.625502\pi$
$439$	4.68008	−	2.70205i	0.223368	−	0.128962i	0.607509	+	0.794313i	$0.292169\pi$
$440$		0			0
$441$	0.244926	+	3.10188i	0.0116631	+	0.147708i
$442$	0.127003	−	0.127003i	0.00604090	−	0.00604090i
$443$	−26.0848	−	6.98940i	−1.23933	−	0.332077i	−0.421122	−	0.907004i	$-0.638364\pi$
$443$	−26.0848	−	6.98940i	−1.23933	−	0.332077i	−0.818204	+	0.574927i	$0.805030\pi$
$444$	0.182356	−	0.806380i	0.00865424	−	0.0382691i
$445$		0			0
$446$	0.697588	+	0.402752i	0.0330317	+	0.0190709i
$447$	−9.18114	−	14.5471i	−0.434253	−	0.688053i
$448$	−4.50086	+	16.7974i	−0.212646	+	0.793604i
$449$	−23.8541			−1.12574			−0.562872	−	0.826544i	$-0.690304\pi$
$449$	−23.8541			−1.12574			−0.562872	+	0.826544i	$0.690304\pi$
$450$		0			0
$451$	18.6479			0.878093
$452$	2.73093	−	10.1920i	0.128452	−	0.479389i
$453$	−24.0893	+	0.949576i	−1.13182	+	0.0446150i
$454$	−2.29672	−	1.32601i	−0.107790	−	0.0622328i
$455$		0			0
$456$	5.41914	−	1.68345i	0.253774	−	0.0788349i
$457$	−19.1467	−	5.13035i	−0.895647	−	0.239988i	−0.218501	−	0.975837i	$-0.570117\pi$
$457$	−19.1467	−	5.13035i	−0.895647	−	0.239988i	−0.677146	+	0.735849i	$0.736783\pi$
$458$	−2.08902	+	2.08902i	−0.0976133	+	0.0976133i
$459$	−2.33185	−	1.83682i	−0.108842	−	0.0857356i
$460$		0			0
$461$	−1.14371	+	0.660321i	−0.0532679	+	0.0307542i	−0.526397	−	0.850239i	$-0.676458\pi$
$461$	−1.14371	+	0.660321i	−0.0532679	+	0.0307542i	0.473130	+	0.880993i	$0.343124\pi$
$462$	−1.78674	−	0.939758i	−0.0831269	−	0.0437215i
$463$	14.8827	−	3.98780i	0.691656	−	0.185329i	0.104166	−	0.994560i	$-0.466783\pi$
$463$	14.8827	−	3.98780i	0.691656	−	0.185329i	0.587490	+	0.809231i	$0.300116\pi$
$464$	−12.1104	+	20.9759i	−0.562213	+	0.973782i
$465$		0			0
$466$	−0.407058	−	0.705045i	−0.0188566	−	0.0326606i
$467$	−1.77645	−	1.77645i	−0.0822044	−	0.0822044i	0.664809	−	0.747013i	$-0.268513\pi$
$467$	−1.77645	−	1.77645i	−0.0822044	−	0.0822044i	−0.747013	+	0.664809i	$0.768513\pi$
$468$	3.20747	+	9.05022i	0.148265	+	0.418346i
$469$			4.18380i			0.193190i
$470$		0			0
$471$	−35.3933	−	8.00390i	−1.63084	−	0.368800i
$472$	0.898753	+	3.35419i	0.0413685	+	0.154389i
$473$	−3.28495	−	12.2596i	−0.151042	−	0.563697i
$474$	2.44543	+	0.553014i	0.112322	+	0.0254008i
$475$		0			0
$476$			2.73810i			0.125501i
$477$	25.5327	+	4.72541i	1.16906	+	0.216361i
$478$	−0.707436	−	0.707436i	−0.0323574	−	0.0323574i
$479$	−18.9907	−	32.8928i	−0.867705	−	1.50291i	−0.864336	−	0.502915i	$-0.832261\pi$
$479$	−18.9907	−	32.8928i	−0.867705	−	1.50291i	−0.00336919	−	0.999994i	$-0.501072\pi$
$480$		0			0
$481$	−0.198266	+	0.343406i	−0.00904014	+	0.0156580i
$482$	−0.692346	+	0.185513i	−0.0315355	+	0.00844991i
$483$	−26.4448	−	13.9089i	−1.20328	−	0.632879i
$484$	−8.28104	+	4.78106i	−0.376411	+	0.217321i
$485$		0			0
$486$	−2.69484	+	1.33110i	−0.122240	+	0.0603800i
$487$	−23.6900	+	23.6900i	−1.07350	+	1.07350i	−0.0764213	+	0.997076i	$0.524349\pi$
$487$	−23.6900	+	23.6900i	−1.07350	+	1.07350i	−0.997076	+	0.0764213i	$0.975651\pi$
$488$	0.348056	+	0.0932612i	0.0157557	+	0.00422174i
$489$	5.68131	−	1.76490i	0.256918	−	0.0798114i
$490$		0			0
$491$	18.9114	+	10.9185i	0.853460	+	0.492746i	0.861817	−	0.507220i	$-0.169327\pi$
$491$	18.9114	+	10.9185i	0.853460	+	0.492746i	−0.00835660	+	0.999965i	$0.502660\pi$
$492$	−25.5894	+	1.00871i	−1.15366	+	0.0454761i
$493$	−0.947827	+	3.53734i	−0.0426880	+	0.159314i
$494$	−1.34809			−0.0606535
$495$		0			0
$496$	−14.9013			−0.669086
$497$	−2.21571	+	8.26913i	−0.0993881	+	0.370921i
$498$	1.96821	+	3.11853i	0.0881974	+	0.139745i
$499$	2.74862	+	1.58691i	0.123045	+	0.0710401i	0.560259	−	0.828317i	$-0.310702\pi$
$499$	2.74862	+	1.58691i	0.123045	+	0.0710401i	−0.437214	+	0.899357i	$0.644035\pi$
$500$		0			0
$501$	3.25612	−	14.3986i	0.145473	−	0.643281i
$502$	−0.739889	−	0.198253i	−0.0330229	−	0.00884845i
$503$	−7.00484	+	7.00484i	−0.312330	+	0.312330i	−0.845812	−	0.533481i	$-0.820883\pi$
$503$	−7.00484	+	7.00484i	−0.312330	+	0.312330i	0.533481	+	0.845812i	$0.320883\pi$
$504$	5.05277	+	2.40845i	0.225068	+	0.107281i
$505$		0			0
$506$	−2.92030	+	1.68603i	−0.129823	+	0.0749534i
$507$	0.705498	+	17.8974i	0.0313323	+	0.794853i
$508$	9.63084	−	2.58058i	0.427299	−	0.114495i
$509$	−8.36206	+	14.4835i	−0.370642	+	0.641971i	−0.989664	−	0.143403i	$-0.954196\pi$
$509$	−8.36206	+	14.4835i	−0.370642	+	0.641971i	0.619023	+	0.785373i	$0.287529\pi$
$510$		0			0
$511$	−11.8942	−	20.6013i	−0.526167	−	0.911347i
$512$	−10.1119	−	10.1119i	−0.446886	−	0.446886i
$513$	2.62727	+	22.1246i	0.115997	+	0.976824i
$514$			3.29603i			0.145382i
$515$		0			0
$516$	5.17091	+	16.6455i	0.227637	+	0.732777i
$517$	−1.93313	−	7.21452i	−0.0850188	−	0.317294i
$518$	0.0296337	+	0.110595i	0.00130203	+	0.00485925i
$519$	20.7777	−	22.4830i	0.912040	−	0.986894i
$520$		0			0
$521$			1.34092i			0.0587466i	0.999569	+	0.0293733i	$0.00935116\pi$
$521$			1.34092i			0.0587466i	−0.999569	+	0.0293733i	$0.990649\pi$
$522$	2.82026	+	2.40748i	0.123440	+	0.105372i
$523$	9.19187	+	9.19187i	0.401933	+	0.401933i	0.878914	−	0.476981i	$-0.158269\pi$
$523$	9.19187	+	9.19187i	0.401933	+	0.401933i	−0.476981	+	0.878914i	$0.658269\pi$
$524$	16.4532	+	28.4978i	0.718761	+	1.24493i
$525$		0			0
$526$	1.03237	−	1.78811i	0.0450133	−	0.0779653i
$527$	−2.17625	+	0.583126i	−0.0947991	+	0.0254014i
$528$	−13.7002	+	8.64667i	−0.596226	+	0.376298i
$529$	−23.3034	+	13.4542i	−1.01319	+	0.584967i
$530$		0			0
$531$	−13.5917	+	1.07321i	−0.589831	+	0.0465734i
$532$	14.5320	−	14.5320i	0.630043	−	0.630043i
$533$	11.8645	+	3.17908i	0.513908	+	0.137701i
$534$	−0.711572	−	0.657601i	−0.0307927	−	0.0284572i
$535$		0			0
$536$	−1.13375	−	0.654569i	−0.0489704	−	0.0282731i
$537$	6.69840	−	12.7355i	0.289057	−	0.549579i
$538$	0.793096	−	2.95987i	0.0341928	−	0.127609i
$539$	2.56759			0.110594
$540$		0			0
$541$	−34.0389			−1.46345			−0.731724	−	0.681601i	$-0.761284\pi$
$541$	−34.0389			−1.46345			−0.731724	+	0.681601i	$0.761284\pi$
$542$	−0.0486162	+	0.181438i	−0.00208824	+	0.00779343i
$543$	−3.81712	+	7.25741i	−0.163808	+	0.311445i
$544$	−1.11646	−	0.644587i	−0.0478677	−	0.0276364i
$545$		0			0
$546$	−0.976587	−	0.902515i	−0.0417941	−	0.0386241i
$547$	9.12437	+	2.44487i	0.390130	+	0.104535i	0.448552	−	0.893757i	$-0.351940\pi$
$547$	9.12437	+	2.44487i	0.390130	+	0.104535i	−0.0584215	+	0.998292i	$0.518607\pi$
$548$	8.87591	−	8.87591i	0.379160	−	0.379160i
$549$	−0.608745	+	1.27711i	−0.0259806	+	0.0545055i
$550$		0			0
$551$	23.8043	−	13.7434i	1.01410	−	0.585489i
$552$	7.90650	−	4.99005i	0.336523	−	0.212391i
$553$	17.7075	−	4.74472i	0.753001	−	0.201766i
$554$	−2.30343	+	3.98967i	−0.0978636	+	0.169505i
$555$		0			0
$556$	−10.3060	−	17.8506i	−0.437073	−	0.757033i
$557$	1.48579	+	1.48579i	0.0629551	+	0.0629551i	0.737883	−	0.674928i	$-0.235825\pi$
$557$	1.48579	+	1.48579i	0.0629551	+	0.0629551i	−0.674928	+	0.737883i	$0.735825\pi$
$558$	−0.415156	+	2.24320i	−0.0175750	+	0.0949623i
$559$		−	8.36006i		−	0.353593i
$560$		0			0
$561$	−1.66248	+	1.79893i	−0.0701901	+	0.0759509i
$562$	−1.37860	−	5.14501i	−0.0581527	−	0.217029i
$563$	5.52969	+	20.6371i	0.233049	+	0.869750i	0.979019	+	0.203770i	$0.0653195\pi$
$563$	5.52969	+	20.6371i	0.233049	+	0.869750i	−0.745970	+	0.665979i	$0.768014\pi$
$564$	3.04297	+	9.79553i	0.128132	+	0.412466i
$565$		0			0
$566$			3.28436i			0.138052i
$567$	−12.9086	+	17.7864i	−0.542111	+	0.746959i
$568$	−1.89416	−	1.89416i	−0.0794771	−	0.0794771i
$569$	−5.82589	−	10.0907i	−0.244234	−	0.423026i	0.717682	−	0.696371i	$-0.245203\pi$
$569$	−5.82589	−	10.0907i	−0.244234	−	0.423026i	−0.961916	+	0.273345i	$0.911870\pi$
$570$		0			0
$571$	10.5623	−	18.2945i	0.442020	−	0.765601i	−0.555819	−	0.831303i	$-0.687595\pi$
$571$	10.5623	−	18.2945i	0.442020	−	0.765601i	0.997839	+	0.0657023i	$0.0209288\pi$
$572$	7.65328	−	2.05069i	0.320000	−	0.0857436i
$573$	0.263825	+	6.69284i	0.0110214	+	0.279598i
$574$	3.07149	−	1.77332i	0.128201	−	0.0740171i
$575$		0			0
$576$	17.6040	−	12.1056i	0.733500	−	0.504398i
$577$	−30.1119	+	30.1119i	−1.25357	+	1.25357i	−0.299469	+	0.954106i	$0.596809\pi$
$577$	−30.1119	+	30.1119i	−1.25357	+	1.25357i	−0.954106	+	0.299469i	$0.903191\pi$
$578$	3.10535	+	0.832076i	0.129166	+	0.0346098i
$579$	−6.56168	+	29.0158i	−0.272694	+	1.20586i
$580$		0			0
$581$	23.3515	+	13.4820i	0.968782	+	0.559327i
$582$	−0.261445	−	0.414248i	−0.0108373	−	0.0171711i
$583$	5.54571	−	20.6969i	0.229680	−	0.857177i
$584$	7.44353			0.308015
$585$		0			0
$586$	5.14140			0.212389
$587$	2.28631	−	8.53262i	0.0943661	−	0.352179i	−0.902556	−	0.430571i	$-0.858312\pi$
$587$	2.28631	−	8.53262i	0.0943661	−	0.352179i	0.996923	+	0.0783924i	$0.0249787\pi$
$588$	−3.52336	+	0.138887i	−0.145301	+	0.00572761i
$589$	14.6450	+	8.45527i	0.603435	+	0.348393i
$590$		0			0
$591$	−25.8217	+	8.02150i	−1.06216	+	0.329960i
$592$	0.887505	+	0.237806i	0.0364762	+	0.00977377i
$593$	24.5829	−	24.5829i	1.00950	−	1.00950i	0.00954475	−	0.999954i	$-0.496962\pi$
$593$	24.5829	−	24.5829i	1.00950	−	1.00950i	0.999954	−	0.00954475i	$-0.00303823\pi$
$594$	0.919955	+	2.30330i	0.0377462	+	0.0945056i
$595$		0			0
$596$	16.8823	−	9.74700i	0.691526	−	0.399253i
$597$	5.52073	+	2.90369i	0.225948	+	0.118840i
$598$	−2.14544	+	0.574869i	−0.0877336	+	0.0235082i
$599$	18.8291	−	32.6129i	0.769335	−	1.33253i	−0.168590	−	0.985686i	$-0.553921\pi$
$599$	18.8291	−	32.6129i	0.769335	−	1.33253i	0.937924	−	0.346840i	$-0.112745\pi$
$600$		0			0
$601$	11.1158	+	19.2532i	0.453424	+	0.785354i	0.998596	−	0.0529703i	$-0.0168689\pi$
$601$	11.1158	+	19.2532i	0.453424	+	0.785354i	−0.545172	+	0.838324i	$0.683536\pi$
$602$	−1.70690	−	1.70690i	−0.0695679	−	0.0695679i
$603$	3.33718	−	3.90937i	0.135900	−	0.159202i
$604$		−	27.3201i		−	1.11164i
$605$		0			0
$606$	5.77593	+	1.30618i	0.234631	+	0.0530599i
$607$	−5.59982	−	20.8988i	−0.227290	−	0.848257i	−0.981474	−	0.191594i	$-0.938634\pi$
$607$	−5.59982	−	20.8988i	−0.227290	−	0.848257i	0.754184	−	0.656663i	$-0.228032\pi$
$608$	2.50437	+	9.34645i	0.101566	+	0.379049i
$609$	26.4452	+	5.98037i	1.07161	+	0.242337i
$610$		0			0
$611$		−	4.91972i		−	0.199031i
$612$	2.18403	−	2.55850i	0.0882841	−	0.103421i
$613$	−15.7726	−	15.7726i	−0.637051	−	0.637051i	0.312776	−	0.949827i	$-0.398741\pi$
$613$	−15.7726	−	15.7726i	−0.637051	−	0.637051i	−0.949827	+	0.312776i	$0.898741\pi$
$614$	1.68455	+	2.91773i	0.0679830	+	0.117750i
$615$		0			0
$616$	2.30946	−	4.00010i	0.0930507	−	0.161169i
$617$	40.8914	−	10.9568i	1.64622	−	0.441104i	0.687672	−	0.726021i	$-0.258633\pi$
$617$	40.8914	−	10.9568i	1.64622	−	0.441104i	0.958552	+	0.284917i	$0.0919660\pi$
$618$	3.13286	+	1.64776i	0.126022	+	0.0662827i
$619$	−27.5855	+	15.9265i	−1.10876	+	0.640141i	−0.938507	−	0.345260i	$-0.887791\pi$
$619$	−27.5855	+	15.9265i	−1.10876	+	0.640141i	−0.170250	+	0.985401i	$0.554457\pi$
$620$		0			0
$621$	13.6158	+	34.0901i	0.546385	+	1.36799i
$622$	−1.17952	+	1.17952i	−0.0472944	+	0.0472944i
$623$	−6.84311	−	1.83361i	−0.274163	−	0.0734619i
$624$	−10.1907	+	3.16573i	−0.407955	+	0.126731i
$625$		0			0
$626$	−3.13060	−	1.80745i	−0.125124	−	0.0722403i
$627$	18.3709	−	0.724161i	0.733663	−	0.0289202i
$628$	10.6431	−	39.7206i	0.424706	−	1.58502i
$629$	0.138922			0.00553917
$630$		0			0
$631$	15.7931			0.628713			0.314356	−	0.949305i	$-0.398211\pi$
$631$	15.7931			0.628713			0.314356	+	0.949305i	$0.398211\pi$
$632$	−1.48466	+	5.54081i	−0.0590564	+	0.220402i
$633$	−17.6753	−	28.0057i	−0.702532	−	1.11313i
$634$	−3.23993	−	1.87057i	−0.128674	−	0.0742899i
$635$		0			0
$636$	−6.49053	+	28.7012i	−0.257366	+	1.13808i
$637$	1.63360	+	0.437722i	0.0647256	+	0.0173432i
$638$	2.16364	−	2.16364i	0.0856594	−	0.0856594i
$639$	8.66619	−	5.95939i	0.342829	−	0.235750i
$640$		0			0
$641$	−8.57453	+	4.95051i	−0.338673	+	0.195533i	−0.659685	−	0.751542i	$-0.729310\pi$
$641$	−8.57453	+	4.95051i	−0.338673	+	0.195533i	0.321012	+	0.947075i	$0.395977\pi$
$642$	0.194569	+	4.93592i	0.00767902	+	0.194805i
$643$	−45.6232	+	12.2247i	−1.79920	+	0.482095i	−0.993853	−	0.110706i	$-0.964689\pi$
$643$	−45.6232	+	12.2247i	−1.79920	+	0.482095i	−0.805349	+	0.592801i	$0.798022\pi$
$644$	16.9303	−	29.3241i	0.667147	−	1.15553i
$645$		0			0
$646$	0.236147	+	0.409018i	0.00929107	+	0.0160926i
$647$	−9.75824	−	9.75824i	−0.383636	−	0.383636i	0.488774	−	0.872410i	$-0.337444\pi$
$647$	−9.75824	−	9.75824i	−0.383636	−	0.383636i	−0.872410	+	0.488774i	$0.837444\pi$
$648$	−2.80026	−	6.28079i	−0.110005	−	0.246733i
$649$			11.2506i			0.441625i
$650$		0			0
$651$	4.94853	+	15.9296i	0.193948	+	0.624331i
$652$	1.74490	+	6.51206i	0.0683356	+	0.255032i
$653$	0.802065	+	2.99335i	0.0313872	+	0.117139i	0.979842	−	0.199773i	$-0.0640206\pi$
$653$	0.802065	+	2.99335i	0.0313872	+	0.117139i	−0.948455	+	0.316912i	$0.897354\pi$
$654$	0.0777914	−	0.0841760i	0.00304189	−	0.00329154i
$655$		0			0
$656$		−	28.4613i		−	1.11123i
$657$	−5.31850	+	28.7373i	−0.207494	+	1.12115i
$658$	−1.00447	−	1.00447i	−0.0391584	−	0.0391584i
$659$	−13.5644	−	23.4942i	−0.528393	−	0.915204i	−0.999452	−	0.0331023i	$-0.989461\pi$
$659$	−13.5644	−	23.4942i	−0.528393	−	0.915204i	0.471059	−	0.882102i	$-0.343872\pi$
$660$		0			0
$661$	−9.54526	+	16.5329i	−0.371268	+	0.643055i	−0.989761	−	0.142736i	$-0.954410\pi$
$661$	−9.54526	+	16.5329i	−0.371268	+	0.643055i	0.618493	+	0.785790i	$0.287743\pi$
$662$	−6.40560	+	1.71638i	−0.248961	+	0.0667088i
$663$	−1.36442	+	0.861129i	−0.0529896	+	0.0334435i
$664$	−7.30683	+	4.21860i	−0.283560	+	0.163713i
$665$		0			0
$666$	0.0605251	−	0.126978i	0.00234530	−	0.00492028i
$667$	32.0231	−	32.0231i	1.23994	−	1.23994i
$668$	16.1590	+	4.32979i	0.625210	+	0.167524i
$669$	−5.31412	−	4.91105i	−0.205456	−	0.189872i
$670$		0			0
$671$	1.01104	+	0.583723i	0.0390307	+	0.0225344i
$672$	−4.44300	+	8.44739i	−0.171392	+	0.325865i
$673$	−0.0359820	+	0.134287i	−0.00138701	+	0.00517638i	−0.966616	−	0.256230i	$-0.917520\pi$
$673$	−0.0359820	+	0.134287i	−0.00138701	+	0.00517638i	0.965229	+	0.261406i	$0.0841862\pi$
$674$	−6.17391			−0.237810
$675$		0			0
$676$	−20.2978			−0.780684
$677$	2.09108	−	7.80401i	0.0803667	−	0.299933i	−0.914030	−	0.405647i	$-0.867046\pi$
$677$	2.09108	−	7.80401i	0.0803667	−	0.299933i	0.994397	+	0.105714i	$0.0337129\pi$
$678$	0.835699	−	1.58890i	0.0320948	−	0.0610213i
$679$	−3.10188	−	1.79087i	−0.119039	−	0.0687272i
$680$		0			0
$681$	17.4961	+	16.1690i	0.670450	+	0.619598i
$682$	1.81835	+	0.487225i	0.0696281	+	0.0186568i
$683$	−35.0271	+	35.0271i	−1.34027	+	1.34027i	−0.444490	+	0.895784i	$0.646615\pi$
$683$	−35.0271	+	35.0271i	−1.34027	+	1.34027i	−0.895784	+	0.444490i	$0.853385\pi$
$684$	−25.1702	+	1.98745i	−0.962406	+	0.0759921i
$685$		0			0
$686$	3.27715	−	1.89206i	0.125122	−	0.0722393i
$687$	22.4428	−	14.1644i	0.856245	−	0.540404i
$688$	−18.7112	+	5.01366i	−0.713359	+	0.191144i
$689$	7.05680	−	12.2227i	0.268843	−	0.465649i
$690$		0			0
$691$	−20.5195	−	35.5408i	−0.780597	−	1.35203i	−0.931594	−	0.363500i	$-0.881582\pi$
$691$	−20.5195	−	35.5408i	−0.780597	−	1.35203i	0.150997	−	0.988534i	$-0.451752\pi$
$692$	24.5313	+	24.5313i	0.932541	+	0.932541i
$693$	13.7931	+	11.7743i	0.523956	+	0.447267i
$694$			3.09646i			0.117540i
$695$		0			0
$696$	−5.75804	+	6.23062i	−0.218258	+	0.236171i
$697$	−1.11377	−	4.15663i	−0.0421869	−	0.157444i
$698$	0.873943	+	3.26160i	0.0330792	+	0.123453i
$699$	2.16958	+	6.98402i	0.0820611	+	0.264160i
$700$		0			0
$701$			37.2173i			1.40568i	0.711348	+	0.702840i	$0.248085\pi$
$701$			37.2173i			1.40568i	−0.711348	+	0.702840i	$0.751915\pi$
$702$	0.192645	+	1.62228i	0.00727091	+	0.0612292i
$703$	−0.737304	−	0.737304i	−0.0278080	−	0.0278080i
$704$	−8.81487	−	15.2678i	−0.332223	−	0.575427i
$705$		0			0
$706$	1.84490	−	3.19546i	0.0694337	−	0.120263i
$707$	41.8240	−	11.2067i	1.57295	−	0.421471i
$708$	−0.608573	−	15.4386i	−0.0228716	−	0.580218i
$709$	13.3449	−	7.70466i	0.501177	−	0.289355i	−0.228023	−	0.973656i	$-0.573226\pi$
$709$	13.3449	−	7.70466i	0.501177	−	0.289355i	0.729199	+	0.684301i	$0.239893\pi$
$710$		0			0
$711$	−20.3307	−	9.69081i	−0.762459	−	0.363434i
$712$	1.56751	−	1.56751i	0.0587448	−	0.0587448i
$713$	26.9125	+	7.21120i	1.00788	+	0.270061i
$714$	−0.102758	+	0.454396i	−0.00384562	+	0.0170053i
$715$		0			0
$716$	14.1222	+	8.15345i	0.527771	+	0.304709i
$717$	4.79670	+	7.60014i	0.179136	+	0.283833i
$718$	−1.14842	+	4.28596i	−0.0428587	+	0.159951i
$719$	11.9324			0.445002			0.222501	−	0.974932i	$-0.428578\pi$
$719$	11.9324			0.445002			0.222501	+	0.974932i	$0.428578\pi$
$720$		0			0
$721$	25.8823			0.963908
$722$	−0.0306831	+	0.114511i	−0.00114191	+	0.00426165i
$723$	6.43378	−	0.253613i	0.239275	−	0.00943196i
$724$	−8.04760	−	4.64628i	−0.299087	−	0.172678i
$725$		0			0
$726$	−1.55369	+	0.482653i	−0.0576629	+	0.0179129i
$727$	4.20134	+	1.12575i	0.155819	+	0.0417516i	0.335885	−	0.941903i	$-0.390965\pi$
$727$	4.20134	+	1.12575i	0.155819	+	0.0417516i	−0.180066	+	0.983654i	$0.557631\pi$
$728$	2.15130	−	2.15130i	0.0797326	−	0.0797326i
$729$	26.2491	−	6.32329i	0.972189	−	0.234196i
$730$		0			0
$731$	−2.53649	+	1.46444i	−0.0938153	+	0.0541643i
$732$	−1.41897	−	0.746322i	−0.0524465	−	0.0275848i
$733$	47.6943	−	12.7796i	1.76163	−	0.472027i	0.774583	−	0.632473i	$-0.217960\pi$
$733$	47.6943	−	12.7796i	1.76163	−	0.472027i	0.987045	+	0.160446i	$0.0512932\pi$
$734$	2.61370	−	4.52707i	0.0964736	−	0.167097i
$735$		0			0
$736$	7.97125	+	13.8066i	0.293824	+	0.508918i
$737$	−2.99918	−	2.99918i	−0.110476	−	0.110476i
$738$	−4.28450	−	0.792945i	−0.157715	−	0.0291887i
$739$			16.1890i			0.595523i	0.954640	+	0.297761i	$0.0962400\pi$
$739$			16.1890i			0.595523i	−0.954640	+	0.297761i	$0.903760\pi$
$740$		0			0
$741$	11.8117	+	2.67112i	0.433915	+	0.0981262i
$742$	−1.05474	−	3.93635i	−0.0387208	−	0.144508i
$743$	−5.14520	−	19.2021i	−0.188759	−	0.704458i	−0.993795	−	0.111232i	$-0.964520\pi$
$743$	−5.14520	−	19.2021i	−0.188759	−	0.704458i	0.805035	−	0.593227i	$-0.202146\pi$
$744$	−5.09091	−	1.15127i	−0.186642	−	0.0422075i
$745$		0			0
$746$		−	5.78426i		−	0.211777i
$747$	−11.0660	−	31.2238i	−0.404883	−	1.14242i
$748$	−1.96282	−	1.96282i	−0.0717679	−	0.0717679i
$749$	18.0595	+	31.2799i	0.659878	+	1.14294i
$750$		0			0
$751$	7.95061	−	13.7709i	0.290122	−	0.502506i	−0.683716	−	0.729748i	$-0.739637\pi$
$751$	7.95061	−	13.7709i	0.290122	−	0.502506i	0.973838	+	0.227242i	$0.0729708\pi$
$752$	−11.0112	+	2.95043i	−0.401536	+	0.107591i
$753$	6.08995	+	3.20308i	0.221930	+	0.116727i
$754$	1.74545	−	1.00774i	0.0635655	−	0.0366996i
$755$		0			0
$756$	−19.5644	−	15.4111i	−0.711550	−	0.560495i
$757$	−21.3482	+	21.3482i	−0.775914	+	0.775914i	−0.979133	−	0.203219i	$-0.934860\pi$
$757$	−21.3482	+	21.3482i	−0.775914	+	0.775914i	0.203219	+	0.979133i	$0.434860\pi$
$758$	−3.74243	−	1.00278i	−0.135931	−	0.0364227i
$759$	28.9278	−	8.98641i	1.05001	−	0.326186i
$760$		0			0
$761$	4.74778	+	2.74113i	0.172107	+	0.0993659i	0.583579	−	0.812056i	$-0.301652\pi$
$761$	4.74778	+	2.74113i	0.172107	+	0.0993659i	−0.411472	+	0.911422i	$0.634985\pi$
$762$	1.69511	−	0.0668196i	0.0614075	−	0.00242062i
$763$	0.216908	−	0.809511i	0.00785259	−	0.0293063i
$764$	−7.59046			−0.274613
$765$		0			0
$766$	−5.32045			−0.192236
$767$	−1.91800	+	7.15808i	−0.0692550	+	0.258463i
$768$	12.1176	+	19.1997i	0.437255	+	0.692810i
$769$	7.13004	+	4.11653i	0.257116	+	0.148446i	0.623018	−	0.782207i	$-0.285906\pi$
$769$	7.13004	+	4.11653i	0.257116	+	0.148446i	−0.365902	+	0.930653i	$0.619240\pi$
$770$		0			0
$771$	6.53080	−	28.8792i	0.235201	−	1.04006i
$772$	−32.5634	−	8.72533i	−1.17198	−	0.314031i
$773$	−14.0889	+	14.0889i	−0.506743	+	0.506743i	−0.913525	−	0.406782i	$-0.866651\pi$
$773$	−14.0889	+	14.0889i	−0.506743	+	0.506743i	0.406782	+	0.913525i	$0.366651\pi$
$774$	0.233441	+	2.95643i	0.00839088	+	0.106267i
$775$		0			0
$776$	0.970598	−	0.560375i	0.0348424	−	0.0201163i
$777$	−0.0405119	−	1.02773i	−0.00145336	−	0.0368695i
$778$	2.50007	−	0.669891i	0.0896318	−	0.0240168i
$779$	−16.1495	+	27.9718i	−0.578616	+	1.00219i
$780$		0			0
$781$	−4.33944	−	7.51612i	−0.155277	−	0.268948i
$782$	0.550238	+	0.550238i	0.0196765	+	0.0196765i
$783$	−19.9404	−	26.6820i	−0.712612	−	0.953536i
$784$		−	3.91879i		−	0.139957i
$785$		0			0
$786$	1.66097	+	5.34676i	0.0592448	+	0.190713i
$787$	5.21175	+	19.4505i	0.185779	+	0.693336i	0.994462	+	0.105092i	$0.0335138\pi$
$787$	5.21175	+	19.4505i	0.185779	+	0.693336i	−0.808684	+	0.588244i	$0.799820\pi$
$788$	−7.93062	−	29.5975i	−0.282516	−	1.05437i
$789$	−12.5884	+	13.6215i	−0.448158	+	0.484940i
$790$		0			0
$791$		−	13.1268i		−	0.466735i
$792$	−5.34863	+	1.89560i	−0.190055	+	0.0673571i
$793$	0.543749	+	0.543749i	0.0193091	+	0.0193091i
$794$	1.75491	+	3.03959i	0.0622793	+	0.107871i
$795$		0			0
$796$	−3.53444	+	6.12183i	−0.125275	+	0.216982i
$797$	−42.7605	+	11.4576i	−1.51465	+	0.405850i	−0.917978	−	0.396632i	$-0.870179\pi$
$797$	−42.7605	+	11.4576i	−1.51465	+	0.405850i	−0.596676	+	0.802483i	$0.703512\pi$
$798$	2.95700	−	1.86626i	0.104677	−	0.0660650i
$799$	−1.49267	+	0.861793i	−0.0528068	+	0.0304880i
$800$		0			0
$801$	4.93169	+	7.17170i	0.174253	+	0.253399i
$802$	3.42580	−	3.42580i	0.120969	−	0.120969i
$803$	23.2946	+	6.24176i	0.822047	+	0.220267i
$804$	4.27784	+	3.95338i	0.150868	+	0.139425i
$805$		0			0
$806$	1.07384	+	0.619983i	0.0378245	+	0.0218380i
$807$	−12.8137	+	24.3624i	−0.451063	+	0.857597i
$808$	−3.50665	+	13.0870i	−0.123364	+	0.460399i
$809$	−35.4591			−1.24667			−0.623337	−	0.781953i	$-0.714223\pi$
$809$	−35.4591			−1.24667			−0.623337	+	0.781953i	$0.714223\pi$
$810$		0			0
$811$	−9.68119			−0.339952			−0.169976	−	0.985448i	$-0.554369\pi$
$811$	−9.68119			−0.339952			−0.169976	+	0.985448i	$0.554369\pi$
$812$	−7.95233	+	29.6785i	−0.279072	+	1.04151i
$813$	0.785469	−	1.49340i	0.0275476	−	0.0523757i
$814$	−0.100524	−	0.0580373i	−0.00352335	−	0.00203421i
$815$		0			0
$816$	2.74562	+	2.53737i	0.0961158	+	0.0888256i
$817$	21.2343	+	5.68970i	0.742893	+	0.199058i
$818$	−1.54578	+	1.54578i	−0.0540470	+	0.0540470i
$819$	6.76842	+	9.84269i	0.236508	+	0.343931i
$820$		0			0
$821$	14.6602	−	8.46408i	0.511645	−	0.295398i	−0.221865	−	0.975077i	$-0.571214\pi$
$821$	14.6602	−	8.46408i	0.511645	−	0.295398i	0.733510	+	0.679679i	$0.237881\pi$
$822$	1.80609	−	1.13988i	0.0629945	−	0.0397579i
$823$	34.3102	−	9.19340i	1.19598	−	0.320462i	0.394733	−	0.918796i	$-0.370837\pi$
$823$	34.3102	−	9.19340i	1.19598	−	0.320462i	0.801247	+	0.598334i	$0.204170\pi$
$824$	−4.04938	+	7.01372i	−0.141067	+	0.244335i
$825$		0			0
$826$	1.06988	+	1.85309i	0.0372259	+	0.0644772i
$827$	−31.4545	−	31.4545i	−1.09378	−	1.09378i	−0.995121	−	0.0986577i	$-0.968545\pi$
$827$	−31.4545	−	31.4545i	−1.09378	−	1.09378i	−0.0986577	−	0.995121i	$-0.531455\pi$
$828$	−39.2100	+	13.8963i	−1.36264	+	0.482931i
$829$			17.3376i			0.602161i	0.953599	+	0.301081i	$0.0973474\pi$
$829$			17.3376i			0.602161i	−0.953599	+	0.301081i	$0.902653\pi$
$830$		0			0
$831$	28.0874	−	30.3927i	0.974342	−	1.05431i
$832$	−3.00551	−	11.2167i	−0.104197	−	0.388870i
$833$	−0.153353	−	0.572320i	−0.00531335	−	0.0198297i
$834$	−1.04041	−	3.34913i	−0.0360263	−	0.115971i
$835$		0			0
$836$			20.8347i			0.720584i
$837$	8.08223	−	18.8319i	0.279363	−	0.650926i
$838$	−1.16233	−	1.16233i	−0.0401521	−	0.0401521i
$839$	12.8988	+	22.3413i	0.445315	+	0.771308i	0.998074	−	0.0620331i	$-0.0197584\pi$
$839$	12.8988	+	22.3413i	0.445315	+	0.771308i	−0.552759	+	0.833341i	$0.686425\pi$
$840$		0			0
$841$	−6.04717	+	10.4740i	−0.208523	+	0.361173i
$842$	−0.410960	+	0.110116i	−0.0141626	+	0.00379486i
$843$	1.88467	+	47.8112i	0.0649113	+	1.64670i
$844$	32.5015	−	18.7647i	1.11875	−	0.645909i
$845$		0			0
$846$	0.137375	+	1.73980i	0.00472306	+	0.0598155i
$847$	−8.41170	+	8.41170i	−0.289030	+	0.289030i
$848$	−31.5886	−	8.46415i	−1.08476	−	0.290660i
$849$	6.50766	−	28.7769i	0.223342	−	0.987622i
$850$		0			0
$851$	−1.48780	−	0.858984i	−0.0510013	−	0.0294456i
$852$	6.36133	+	10.0792i	0.217936	+	0.345309i
$853$	−3.67518	+	13.7160i	−0.125836	+	0.469626i	−0.999868	−	0.0162423i	$-0.994830\pi$
$853$	−3.67518	+	13.7160i	−0.125836	+	0.469626i	0.874032	+	0.485868i	$0.161496\pi$
$854$	0.222037			0.00759796
$855$		0			0
$856$	−11.3019			−0.386289
$857$	12.9182	−	48.2115i	0.441278	−	1.64687i	−0.284303	−	0.958735i	$-0.591762\pi$
$857$	12.9182	−	48.2115i	0.441278	−	1.64687i	0.725581	−	0.688137i	$-0.241571\pi$
$858$	1.34705	−	0.0530991i	0.0459874	−	0.00181277i
$859$	−35.6374	−	20.5752i	−1.21593	−	0.702018i	−0.251886	−	0.967757i	$-0.581051\pi$
$859$	−35.6374	−	20.5752i	−1.21593	−	0.702018i	−0.964045	+	0.265739i	$0.914384\pi$
$860$		0			0
$861$	−30.4255	+	9.45165i	−1.03690	+	0.322112i
$862$	0.364549	+	0.0976806i	0.0124166	+	0.00332701i
$863$	20.5637	−	20.5637i	0.699996	−	0.699996i	−0.264413	−	0.964410i	$-0.585178\pi$
$863$	20.5637	−	20.5637i	0.699996	−	0.699996i	0.964410	+	0.264413i	$0.0851783\pi$
$864$	10.8896	−	4.34937i	0.370471	−	0.147969i
$865$		0			0
$866$	−2.29452	+	1.32474i	−0.0779711	+	0.0450166i
$867$	−25.5598	−	13.4435i	−0.868057	−	0.456564i
$868$	−18.2589	+	4.89246i	−0.619748	+	0.166061i
$869$	−9.29248	+	16.0950i	−0.315226	+	0.545987i
$870$		0			0
$871$	−1.39690	−	2.41950i	−0.0473320	−	0.0819815i
$872$	0.185430	+	0.185430i	0.00627944	+	0.00627944i
$873$	1.46994	+	4.14759i	0.0497499	+	0.140375i
$874$		−	5.84059i		−	0.197561i
$875$		0			0
$876$	−32.3035	−	7.30516i	−1.09143	−	0.246819i
$877$	12.9568	+	48.3556i	0.437521	+	1.63285i	0.734959	+	0.678111i	$0.237201\pi$
$877$	12.9568	+	48.3556i	0.437521	+	1.63285i	−0.297438	+	0.954741i	$0.596132\pi$
$878$	0.269684	+	1.00647i	0.00910140	+	0.0339669i
$879$	−45.0480	−	10.1872i	−1.51943	−	0.343607i
$880$		0			0
$881$		−	25.4215i		−	0.856471i	−0.903667	−	0.428235i	$-0.859135\pi$
$881$		−	25.4215i		−	0.856471i	0.903667	−	0.428235i	$-0.140865\pi$
$882$	−0.589925	−	0.109179i	−0.0198638	−	0.00367626i
$883$	27.7207	+	27.7207i	0.932874	+	0.932874i	0.997885	−	0.0650103i	$-0.0207080\pi$
$883$	27.7207	+	27.7207i	0.932874	+	0.932874i	−0.0650103	+	0.997885i	$0.520708\pi$
$884$	−0.914203	−	1.58345i	−0.0307480	−	0.0532571i
$885$		0			0
$886$	2.60346	−	4.50932i	0.0874648	−	0.151493i
$887$	−19.9334	+	5.34114i	−0.669298	+	0.179338i	−0.577439	−	0.816434i	$-0.695948\pi$
$887$	−19.9334	+	5.34114i	−0.669298	+	0.179338i	−0.0918595	+	0.995772i	$0.529281\pi$
$888$	0.284837	+	0.149813i	0.00955850	+	0.00502740i
$889$	10.7423	−	6.20205i	0.360284	−	0.208010i
$890$		0			0
$891$	−3.49668	−	22.0039i	−0.117143	−	0.737159i
$892$	5.79827	−	5.79827i	0.194140	−	0.194140i
$893$	12.4959	+	3.34827i	0.418160	+	0.112046i
$894$	3.16746	−	0.983971i	0.105936	−	0.0329089i
$895$		0			0
$896$	−12.4484	−	7.18706i	−0.415870	−	0.240103i
$897$	19.9370	−	0.785896i	0.665677	−	0.0262403i
$898$	1.19041	−	4.44266i	0.0397244	−	0.148253i
$899$	−25.2822			−0.843209
$900$		0			0
$901$	−4.94459			−0.164728
$902$	−0.930596	+	3.47303i	−0.0309855	+	0.115639i
$903$	11.5734	+	18.3376i	0.385140	+	0.610236i
$904$	3.55717	+	2.05373i	0.118310	+	0.0683061i
$905$		0			0
$906$	1.02529	−	4.53386i	0.0340631	−	0.150627i
$907$	−38.0242	−	10.1886i	−1.26257	−	0.338305i	−0.435392	−	0.900241i	$-0.643390\pi$
$907$	−38.0242	−	10.1886i	−1.26257	−	0.338305i	−0.827181	+	0.561935i	$0.810057\pi$
$908$	−19.0901	+	19.0901i	−0.633526	+	0.633526i
$909$	−48.0196	−	22.8890i	−1.59271	−	0.759180i
$910$		0			0
$911$	−42.5747	+	24.5805i	−1.41056	+	0.814389i	−0.995441	−	0.0953768i	$-0.969594\pi$
$911$	−42.5747	+	24.5805i	−1.41056	+	0.814389i	−0.415122	+	0.909766i	$0.636261\pi$
$912$	−1.10525	−	28.0386i	−0.0365985	−	0.928450i
$913$	−26.4043	+	7.07501i	−0.873854	+	0.234149i
$914$	1.91099	−	3.30992i	0.0632098	−	0.109483i
$915$		0			0
$916$	15.0374	+	26.0455i	0.496848	+	0.860567i
$917$	28.9474	+	28.9474i	0.955928	+	0.955928i
$918$	0.458464	−	0.342627i	0.0151316	−	0.0113084i
$919$		−	7.00522i		−	0.231081i	−0.993303	−	0.115540i	$-0.963140\pi$
$919$		−	7.00522i		−	0.231081i	0.993303	−	0.115540i	$-0.0368600\pi$
$920$		0			0
$921$	−8.97851	−	28.9024i	−0.295852	−	0.952367i
$922$	−0.0659049	−	0.245960i	−0.00217046	−	0.00810028i
$923$	−1.47957	−	5.52184i	−0.0487007	−	0.181753i
$924$	−13.9483	+	15.0931i	−0.458867	+	0.496527i
$925$		0			0
$926$			2.97080i			0.0976265i
$927$	−24.1846	−	20.6449i	−0.794327	−	0.678066i
$928$	−10.2293	−	10.2293i	−0.335793	−	0.335793i
$929$	1.96179	+	3.39791i	0.0643641	+	0.111482i	0.896412	−	0.443222i	$-0.146165\pi$
$929$	1.96179	+	3.39791i	0.0643641	+	0.111482i	−0.832048	+	0.554704i	$0.812831\pi$
$930$		0			0
$931$	−2.22360	+	3.85139i	−0.0728755	+	0.126224i
$932$	−8.00525	+	2.14500i	−0.262221	+	0.0702618i
$933$	12.6718	−	7.99761i	0.414857	−	0.261830i
$934$	0.419503	−	0.242200i	0.0137266	−	0.00792504i
$935$		0			0
$936$	−3.72616	+	0.294220i	−0.121794	+	0.00961688i
$937$	28.6351	−	28.6351i	0.935468	−	0.935468i	−0.0625728	−	0.998040i	$-0.519931\pi$
$937$	28.6351	−	28.6351i	0.935468	−	0.935468i	0.998040	+	0.0625728i	$0.0199305\pi$
$938$	−0.779203	−	0.208787i	−0.0254419	−	0.00681713i
$939$	23.8484	+	22.0396i	0.778264	+	0.719234i
$940$		0			0
$941$	−50.0184	−	28.8781i	−1.63055	−	0.941400i	−0.983922	−	0.178596i	$-0.942844\pi$
$941$	−50.0184	−	28.8781i	−1.63055	−	0.941400i	−0.646630	−	0.762804i	$-0.723822\pi$
$942$	3.25693	−	6.19233i	0.106116	−	0.201757i
$943$	−13.7733	+	51.4028i	−0.448521	+	1.67390i
$944$	17.1713			0.558877
$945$		0			0
$946$	2.44720			0.0795653
$947$	−2.14989	+	8.02351i	−0.0698622	+	0.260729i	−0.992019	−	0.126086i	$-0.959758\pi$
$947$	−2.14989	+	8.02351i	−0.0698622	+	0.260729i	0.922157	+	0.386816i	$0.126425\pi$
$948$	11.8809	−	22.5890i	0.385875	−	0.733657i
$949$	13.7568	+	7.94250i	0.446565	+	0.257824i
$950$		0			0
$951$	24.6813	+	22.8092i	0.800345	+	0.739640i
$952$	−1.02956	−	0.275870i	−0.0333683	−	0.00894101i
$953$	−27.2237	+	27.2237i	−0.881861	+	0.881861i	−0.993724	−	0.111862i	$-0.964318\pi$
$953$	−27.2237	+	27.2237i	−0.881861	+	0.881861i	0.111862	+	0.993724i	$0.464318\pi$
$954$	−2.15425	+	4.51947i	−0.0697463	+	0.146323i
$955$		0			0
$956$	−8.82018	+	5.09233i	−0.285265	+	0.164698i
$957$	−23.2445	+	14.6704i	−0.751388	+	0.474225i
$958$	7.07375	−	1.89541i	0.228543	−	0.0612378i
$959$	7.80805	−	13.5239i	0.252135	−	0.436711i
$960$		0			0
$961$	7.72289	+	13.3764i	0.249126	+	0.431498i
$962$	−0.0540628	−	0.0540628i	−0.00174306	−	0.00174306i
$963$	8.07532	−	43.6332i	0.260224	−	1.40606i
$964$			7.29666i			0.235010i
$965$		0			0
$966$	3.91014	−	4.23105i	0.125807	−	0.136132i
$967$	−12.2085	−	45.5627i	−0.392598	−	1.46520i	−0.825832	−	0.563916i	$-0.809294\pi$
$967$	−12.2085	−	45.5627i	−0.392598	−	1.46520i	0.433234	−	0.901282i	$-0.357372\pi$
$968$	−0.963408	−	3.59549i	−0.0309651	−	0.115563i
$969$	−1.25864	−	4.05164i	−0.0404334	−	0.130158i
$970$		0			0
$971$			20.4752i			0.657080i	0.944490	+	0.328540i	$0.106557\pi$
$971$			20.4752i			0.657080i	−0.944490	+	0.328540i	$0.893443\pi$
$972$	5.98855	+	30.0056i	0.192083	+	0.962431i
$973$	−18.1322	−	18.1322i	−0.581292	−	0.581292i
$974$	−3.22988	−	5.59432i	−0.103492	−	0.179254i
$975$		0			0
$976$	0.890908	−	1.54310i	0.0285173	−	0.0493934i
$977$	−34.9400	+	9.36214i	−1.11783	+	0.299521i	−0.770005	−	0.638038i	$-0.779746\pi$
$977$	−34.9400	+	9.36214i	−1.11783	+	0.299521i	−0.347824	+	0.937560i	$0.613079\pi$
$978$	0.0451812	+	1.14618i	0.00144474	+	0.0366508i
$979$	6.21996	−	3.59109i	0.198791	−	0.114772i
$980$		0			0
$981$	−0.848381	+	0.583398i	−0.0270867	+	0.0186265i
$982$	−2.97725	+	2.97725i	−0.0950077	+	0.0950077i
$983$	−19.0596	−	5.10700i	−0.607906	−	0.162888i	−0.0582820	−	0.998300i	$-0.518562\pi$
$983$	−19.0596	−	5.10700i	−0.607906	−	0.162888i	−0.549624	+	0.835412i	$0.685229\pi$
$984$	2.19891	−	9.72360i	0.0700987	−	0.309977i
$985$		0			0
$986$	−0.611505	−	0.353052i	−0.0194743	−	0.0112435i
$987$	6.81073	+	10.7913i	0.216788	+	0.343490i
$988$	−3.55190	+	13.2559i	−0.113001	+	0.421725i
$989$	36.2199			1.15172
$990$		0			0
$991$	53.0916			1.68651			0.843255	−	0.537513i	$-0.180636\pi$
$991$	53.0916			1.68651			0.843255	+	0.537513i	$0.180636\pi$
$992$	2.30351	−	8.59681i	0.0731364	−	0.272949i
$993$	59.5255	−	2.34643i	1.88899	−	0.0744618i
$994$	−1.42950	−	0.825320i	−0.0453409	−	0.0261776i
$995$		0			0
$996$	35.8504	−	11.1369i	1.13596	−	0.352887i
$997$	36.6745	+	9.82689i	1.16149	+	0.311221i	0.787562	−	0.616236i	$-0.211343\pi$
$997$	36.6745	+	9.82689i	1.16149	+	0.311221i	0.373930	+	0.927457i	$0.378010\pi$
$998$	−0.432718	+	0.432718i	−0.0136974	+	0.0136974i
$999$	−0.781905	+	0.992629i	−0.0247384	+	0.0314054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.p.b.68.2		16
3.2	odd	2		675.2.q.a.368.3		16
5.2	odd	4	inner	225.2.p.b.32.2		16
5.3	odd	4		45.2.l.a.32.3	yes	16
5.4	even	2		45.2.l.a.23.3	yes	16
9.2	odd	6	inner	225.2.p.b.218.2		16
9.7	even	3		675.2.q.a.143.3		16
15.2	even	4		675.2.q.a.557.3		16
15.8	even	4		135.2.m.a.17.2		16
15.14	odd	2		135.2.m.a.98.2		16
20.3	even	4		720.2.cu.c.257.1		16
20.19	odd	2		720.2.cu.c.113.2		16
45.2	even	12	inner	225.2.p.b.182.2		16
45.4	even	6		405.2.f.a.323.5		16
45.7	odd	12		675.2.q.a.332.3		16
45.13	odd	12		405.2.f.a.242.4		16
45.14	odd	6		405.2.f.a.323.4		16
45.23	even	12		405.2.f.a.242.5		16
45.29	odd	6		45.2.l.a.38.3	yes	16
45.34	even	6		135.2.m.a.8.2		16
45.38	even	12		45.2.l.a.2.3	✓	16
45.43	odd	12		135.2.m.a.62.2		16
180.83	odd	12		720.2.cu.c.497.2		16
180.119	even	6		720.2.cu.c.353.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.3	✓	16	45.38	even	12
45.2.l.a.23.3	yes	16	5.4	even	2
45.2.l.a.32.3	yes	16	5.3	odd	4
45.2.l.a.38.3	yes	16	45.29	odd	6
135.2.m.a.8.2		16	45.34	even	6
135.2.m.a.17.2		16	15.8	even	4
135.2.m.a.62.2		16	45.43	odd	12
135.2.m.a.98.2		16	15.14	odd	2
225.2.p.b.32.2		16	5.2	odd	4	inner
225.2.p.b.68.2		16	1.1	even	1	trivial
225.2.p.b.182.2		16	45.2	even	12	inner
225.2.p.b.218.2		16	9.2	odd	6	inner
405.2.f.a.242.4		16	45.13	odd	12
405.2.f.a.242.5		16	45.23	even	12
405.2.f.a.323.4		16	45.14	odd	6
405.2.f.a.323.5		16	45.4	even	6
675.2.q.a.143.3		16	9.7	even	3
675.2.q.a.332.3		16	45.7	odd	12
675.2.q.a.368.3		16	3.2	odd	2
675.2.q.a.557.3		16	15.2	even	4
720.2.cu.c.113.2		16	20.19	odd	2
720.2.cu.c.257.1		16	20.3	even	4
720.2.cu.c.353.1		16	180.119	even	6
720.2.cu.c.497.2		16	180.83	odd	12

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0499037 + 0.186243i) q^{2} +(0.806271 - 1.53295i) q^{3} +(1.69985 + 0.981412i) q^{4} +(0.245265 + 0.226662i) q^{6} +(2.35868 + 0.632007i) q^{7} +(-0.540289 + 0.540289i) q^{8} +(-1.69985 - 2.47194i) q^{9} +O(q^{10})\)	\(q+(-0.0499037 + 0.186243i) q^{2} +(0.806271 - 1.53295i) q^{3} +(1.69985 + 0.981412i) q^{4} +(0.245265 + 0.226662i) q^{6} +(2.35868 + 0.632007i) q^{7} +(-0.540289 + 0.540289i) q^{8} +(-1.69985 - 2.47194i) q^{9} +(-2.14390 + 1.23778i) q^{11} +(2.87500 - 1.81450i) q^{12} +(-1.57505 + 0.422032i) q^{13} +(-0.235414 + 0.407749i) q^{14} +(1.88916 + 3.27212i) q^{16} +(0.403949 + 0.403949i) q^{17} +(0.545211 - 0.193227i) q^{18} -4.28779i q^{19} +(2.87057 - 3.10617i) q^{21} +(-0.123539 - 0.461055i) q^{22} +(-1.82845 - 6.82387i) q^{23} +(0.392615 + 1.26385i) q^{24} -0.314402i q^{26} +(-5.15990 + 0.612733i) q^{27} +(3.38916 + 3.38916i) q^{28} +(3.20524 + 5.55164i) q^{29} +(-1.97194 + 3.41550i) q^{31} +(-2.17978 + 0.584071i) q^{32} +(0.168889 + 4.28446i) q^{33} +(-0.0953913 + 0.0550742i) q^{34} +(-0.463514 - 5.87020i) q^{36} +(0.171954 - 0.171954i) q^{37} +(0.798571 + 0.213977i) q^{38} +(-0.622960 + 2.75474i) q^{39} +(-6.52359 - 3.76639i) q^{41} +(0.435250 + 0.689633i) q^{42} +(-1.32695 + 4.95226i) q^{43} -4.85908 q^{44} +1.36214 q^{46} +(-0.780885 + 2.91430i) q^{47} +(6.53917 - 0.257767i) q^{48} +(-0.898221 - 0.518588i) q^{49} +(0.944926 - 0.293541i) q^{51} +(-3.09154 - 0.828375i) q^{52} +(-6.12030 + 6.12030i) q^{53} +(0.143381 - 0.991573i) q^{54} +(-1.61584 + 0.932904i) q^{56} +(-6.57296 - 3.45712i) q^{57} +(-1.19391 + 0.319907i) q^{58} +(2.27234 - 3.93581i) q^{59} +(-0.235795 - 0.408408i) q^{61} +(-0.537706 - 0.537706i) q^{62} +(-2.44713 - 6.90485i) q^{63} +7.12153i q^{64} +(-0.806380 - 0.182356i) q^{66} +(0.443446 + 1.65496i) q^{67} +(0.290215 + 1.08310i) q^{68} +(-11.9349 - 2.69897i) q^{69} +3.50583i q^{71} +(2.25397 + 0.417150i) q^{72} +(-6.88847 - 6.88847i) q^{73} +(0.0234441 + 0.0406064i) q^{74} +(4.20809 - 7.28862i) q^{76} +(-5.83906 + 1.56457i) q^{77} +(-0.481962 - 0.253493i) q^{78} +(6.50159 - 3.75369i) q^{79} +(-3.22099 + 8.40388i) q^{81} +(1.02702 - 1.02702i) q^{82} +(10.6660 + 2.85794i) q^{83} +(7.92799 - 2.46282i) q^{84} +(-0.856104 - 0.494272i) q^{86} +(11.0947 - 0.437340i) q^{87} +(0.489565 - 1.82708i) q^{88} -2.90124 q^{89} -3.98176 q^{91} +(3.58893 - 13.3941i) q^{92} +(3.64587 + 5.77670i) q^{93} +(-0.503800 - 0.290869i) q^{94} +(-0.862145 + 3.81241i) q^{96} +(-1.41681 - 0.379633i) q^{97} +(0.141408 - 0.141408i) q^{98} +(6.70403 + 3.19554i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7}+O(q^{10}) \) 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7	\( 16 q + 6 q^{2} + 6 q^{3} + 2 q^{7} + 6 q^{12} + 2 q^{13} - 8 q^{16} - 36 q^{18} - 12 q^{21} + 10 q^{22} - 18 q^{23} - 18 q^{27} + 16 q^{28} - 4 q^{31} - 30 q^{32} + 12 q^{33} - 48 q^{36} - 4 q^{37} + 30 q^{38} - 24 q^{41} - 6 q^{42} + 2 q^{43} + 32 q^{46} + 12 q^{47} + 30 q^{48} + 36 q^{51} + 14 q^{52} + 36 q^{56} + 6 q^{57} + 6 q^{58} + 8 q^{61} - 36 q^{63} + 36 q^{66} - 4 q^{67} - 42 q^{68} - 18 q^{72} + 8 q^{73} + 24 q^{76} + 6 q^{77} + 42 q^{78} - 48 q^{81} - 32 q^{82} + 66 q^{83} - 48 q^{86} + 18 q^{87} - 18 q^{88} - 40 q^{91} + 60 q^{92} + 18 q^{93} - 24 q^{96} - 28 q^{97}+O(q^{100}) \) 16 * q + 6 * q^2 + 6 * q^3 + 2 * q^7 + 6 * q^12 + 2 * q^13 - 8 * q^16 - 36 * q^18 - 12 * q^21 + 10 * q^22 - 18 * q^23 - 18 * q^27 + 16 * q^28 - 4 * q^31 - 30 * q^32 + 12 * q^33 - 48 * q^36 - 4 * q^37 + 30 * q^38 - 24 * q^41 - 6 * q^42 + 2 * q^43 + 32 * q^46 + 12 * q^47 + 30 * q^48 + 36 * q^51 + 14 * q^52 + 36 * q^56 + 6 * q^57 + 6 * q^58 + 8 * q^61 - 36 * q^63 + 36 * q^66 - 4 * q^67 - 42 * q^68 - 18 * q^72 + 8 * q^73 + 24 * q^76 + 6 * q^77 + 42 * q^78 - 48 * q^81 - 32 * q^82 + 66 * q^83 - 48 * q^86 + 18 * q^87 - 18 * q^88 - 40 * q^91 + 60 * q^92 + 18 * q^93 - 24 * q^96 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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