LMFDB - Embedded newform 225.2.p.b.218.2

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			218.2
Root			$-0.186243 - 0.0499037i$ of defining polynomial
Character	$\chi$	$=$	225.218
Dual form			225.2.p.b.32.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.186243 + 0.0499037i) q^{2} +(-1.53295 + 0.806271i) q^{3} +(-1.69985 + 0.981412i) q^{4} +(0.245265 - 0.226662i) q^{6} +(-0.632007 - 2.35868i) q^{7} +(0.540289 - 0.540289i) q^{8} +(1.69985 - 2.47194i) q^{9} +O(q^{10})$	\(q+(-0.186243 + 0.0499037i) q^{2} +(-1.53295 + 0.806271i) q^{3} +(-1.69985 + 0.981412i) q^{4} +(0.245265 - 0.226662i) q^{6} +(-0.632007 - 2.35868i) q^{7} +(0.540289 - 0.540289i) q^{8} +(1.69985 - 2.47194i) q^{9} +(-2.14390 - 1.23778i) q^{11} +(1.81450 - 2.87500i) q^{12} +(0.422032 - 1.57505i) q^{13} +(0.235414 + 0.407749i) q^{14} +(1.88916 - 3.27212i) q^{16} +(-0.403949 - 0.403949i) q^{17} +(-0.193227 + 0.545211i) q^{18} -4.28779i q^{19} +(2.87057 + 3.10617i) q^{21} +(0.461055 + 0.123539i) q^{22} +(-6.82387 - 1.82845i) q^{23} +(-0.392615 + 1.26385i) q^{24} +0.314402i q^{26} +(-0.612733 + 5.15990i) q^{27} +(3.38916 + 3.38916i) q^{28} +(-3.20524 + 5.55164i) q^{29} +(-1.97194 - 3.41550i) q^{31} +(-0.584071 + 2.17978i) q^{32} +(4.28446 + 0.168889i) q^{33} +(0.0953913 + 0.0550742i) q^{34} +(-0.463514 + 5.87020i) q^{36} +(0.171954 - 0.171954i) q^{37} +(0.213977 + 0.798571i) q^{38} +(0.622960 + 2.75474i) q^{39} +(-6.52359 + 3.76639i) q^{41} +(-0.689633 - 0.435250i) q^{42} +(4.95226 - 1.32695i) q^{43} +4.85908 q^{44} +1.36214 q^{46} +(-2.91430 + 0.780885i) q^{47} +(-0.257767 + 6.53917i) q^{48} +(0.898221 - 0.518588i) q^{49} +(0.944926 + 0.293541i) q^{51} +(0.828375 + 3.09154i) q^{52} +(6.12030 - 6.12030i) q^{53} +(-0.143381 - 0.991573i) q^{54} +(-1.61584 - 0.932904i) q^{56} +(3.45712 + 6.57296i) q^{57} +(0.319907 - 1.19391i) q^{58} +(-2.27234 - 3.93581i) q^{59} +(-0.235795 + 0.408408i) q^{61} +(0.537706 + 0.537706i) q^{62} +(-6.90485 - 2.44713i) q^{63} +7.12153i q^{64} +(-0.806380 + 0.182356i) q^{66} +(-1.65496 - 0.443446i) q^{67} +(1.08310 + 0.290215i) q^{68} +(11.9349 - 2.69897i) q^{69} -3.50583i q^{71} +(-0.417150 - 2.25397i) q^{72} +(-6.88847 - 6.88847i) q^{73} +(-0.0234441 + 0.0406064i) q^{74} +(4.20809 + 7.28862i) q^{76} +(-1.56457 + 5.83906i) q^{77} +(-0.253493 - 0.481962i) q^{78} +(-6.50159 - 3.75369i) q^{79} +(-3.22099 - 8.40388i) q^{81} +(1.02702 - 1.02702i) q^{82} +(2.85794 + 10.6660i) q^{83} +(-7.92799 - 2.46282i) q^{84} +(-0.856104 + 0.494272i) q^{86} +(0.437340 - 11.0947i) q^{87} +(-1.82708 + 0.489565i) q^{88} +2.90124 q^{89} -3.98176 q^{91} +(13.3941 - 3.58893i) q^{92} +(5.77670 + 3.64587i) q^{93} +(0.503800 - 0.290869i) q^{94} +(-0.862145 - 3.81241i) q^{96} +(0.379633 + 1.41681i) 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.186243	+	0.0499037i	−0.131694	+	0.0352872i	−0.324064	−	0.946035i	$-0.605049\pi$
$2$	−0.186243	+	0.0499037i	−0.131694	+	0.0352872i	0.192370	+	0.981322i	$0.438383\pi$
$3$	−1.53295	+	0.806271i	−0.885048	+	0.465501i
$3$	−1.53295	+	0.806271i	−0.885048	+	0.465501i
$4$	−1.69985	+	0.981412i	−0.849927	+	0.490706i
$5$		0			0
$5$		0			0
$6$	0.245265	−	0.226662i	0.100129	−	0.0925344i
$7$	−0.632007	−	2.35868i	−0.238876	−	0.891499i	−0.976363	−	0.216137i	$-0.930654\pi$
$7$	−0.632007	−	2.35868i	−0.238876	−	0.891499i	0.737487	−	0.675362i	$-0.236012\pi$
$8$	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	0.140670	−	0.990057i	$-0.455074\pi$
$11$	−2.14390	−	1.23778i	−0.646409	−	0.373204i	−0.787079	+	0.616852i	$0.788408\pi$
$12$	1.81450	−	2.87500i	0.523802	−	0.829940i
$13$	0.422032	−	1.57505i	0.117051	−	0.436839i	−0.882381	−	0.470535i	$-0.844061\pi$
$13$	0.422032	−	1.57505i	0.117051	−	0.436839i	0.999432	+	0.0336956i	$0.0107277\pi$
$14$	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	0.656422	−	0.754394i	$-0.272069\pi$
$17$	−0.403949	−	0.403949i	−0.0979721	−	0.0979721i	−0.754394	+	0.656422i	$0.772069\pi$
$18$	−0.193227	+	0.545211i	−0.0455441	+	0.128507i
$19$		−	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
$22$	0.461055	+	0.123539i	0.0982973	+	0.0263387i
$23$	−6.82387	−	1.82845i	−1.42288	−	0.381258i	−0.536373	−	0.843981i	$-0.680206\pi$
$23$	−6.82387	−	1.82845i	−1.42288	−	0.381258i	−0.886503	+	0.462723i	$0.846872\pi$
$24$	−0.392615	+	1.26385i	−0.0801422	+	0.257983i
$25$		0			0
$26$			0.314402i			0.0616594i
$27$	−0.612733	+	5.15990i	−0.117921	+	0.993023i
$28$	3.38916	+	3.38916i	0.640491	+	0.640491i
$29$	−3.20524	+	5.55164i	−0.595199	+	1.03091i	0.398320	+	0.917247i	$0.369593\pi$
$29$	−3.20524	+	5.55164i	−0.595199	+	1.03091i	−0.993519	+	0.113668i	$0.963740\pi$
$30$		0			0
$31$	−1.97194	−	3.41550i	−0.354171	−	0.613442i	0.632805	−	0.774312i	$-0.281904\pi$
$31$	−1.97194	−	3.41550i	−0.354171	−	0.613442i	−0.986976	+	0.160869i	$0.948570\pi$
$32$	−0.584071	+	2.17978i	−0.103250	+	0.385335i
$33$	4.28446	+	0.168889i	0.745829	+	0.0293998i
$34$	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	$0.243637\pi$
$38$	0.213977	+	0.798571i	0.0347116	+	0.129545i
$39$	0.622960	+	2.75474i	0.0997535	+	0.441111i
$40$		0			0
$41$	−6.52359	+	3.76639i	−1.01881	+	0.588212i	−0.913760	−	0.406255i	$-0.866835\pi$
$41$	−6.52359	+	3.76639i	−1.01881	+	0.588212i	−0.105053	+	0.994467i	$0.533501\pi$
$42$	−0.689633	−	0.435250i	−0.106413	−	0.0671606i
$43$	4.95226	−	1.32695i	0.755213	−	0.202359i	0.139384	−	0.990238i	$-0.455488\pi$
$43$	4.95226	−	1.32695i	0.755213	−	0.202359i	0.615829	+	0.787880i	$0.288821\pi$
$44$	4.85908			0.732534
$45$		0			0
$46$	1.36214			0.200837
$47$	−2.91430	+	0.780885i	−0.425095	+	0.113904i	−0.465023	−	0.885299i	$-0.653954\pi$
$47$	−2.91430	+	0.780885i	−0.425095	+	0.113904i	0.0399279	+	0.999203i	$0.487287\pi$
$48$	−0.257767	+	6.53917i	−0.0372055	+	0.943847i
$49$	0.898221	−	0.518588i	0.128317	−	0.0740841i
$50$		0			0
$51$	0.944926	+	0.293541i	0.132316	+	0.0411039i
$52$	0.828375	+	3.09154i	0.114875	+	0.428719i
$53$	6.12030	−	6.12030i	0.840688	−	0.840688i	−0.148260	−	0.988948i	$-0.547367\pi$
$53$	6.12030	−	6.12030i	0.840688	−	0.840688i	0.988948	+	0.148260i	$0.0473672\pi$
$54$	−0.143381	−	0.991573i	−0.0195116	−	0.134936i
$55$		0			0
$56$	−1.61584	−	0.932904i	−0.215925	−	0.124665i
$57$	3.45712	+	6.57296i	0.457907	+	0.870610i
$58$	0.319907	−	1.19391i	0.0420058	−	0.156768i
$59$	−2.27234	−	3.93581i	−0.295833	−	0.512399i	0.679345	−	0.733819i	$-0.262264\pi$
$59$	−2.27234	−	3.93581i	−0.295833	−	0.512399i	−0.975178	+	0.221421i	$0.928931\pi$
$60$		0			0
$61$	−0.235795	+	0.408408i	−0.0301904	+	0.0522913i	−0.880726	−	0.473626i	$-0.842945\pi$
$61$	−0.235795	+	0.408408i	−0.0301904	+	0.0522913i	0.850535	+	0.525918i	$0.176278\pi$
$62$	0.537706	+	0.537706i	0.0682888	+	0.0682888i
$63$	−6.90485	−	2.44713i	−0.869929	−	0.308310i
$64$			7.12153i			0.890191i
$65$		0			0
$66$	−0.806380	+	0.182356i	−0.0992585	+	0.0224465i
$67$	−1.65496	−	0.443446i	−0.202186	−	0.0541756i	0.156305	−	0.987709i	$-0.450042\pi$
$67$	−1.65496	−	0.443446i	−0.202186	−	0.0541756i	−0.358491	+	0.933533i	$0.616709\pi$
$68$	1.08310	+	0.290215i	0.131345	+	0.0351937i
$69$	11.9349	−	2.69897i	1.43679	−	0.324918i
$70$		0			0
$71$		−	3.50583i		−	0.416065i	−0.978122	−	0.208032i	$-0.933294\pi$
$71$		−	3.50583i		−	0.416065i	0.978122	−	0.208032i	$-0.0667060\pi$
$72$	−0.417150	−	2.25397i	−0.0491616	−	0.265633i
$73$	−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
$77$	−1.56457	+	5.83906i	−0.178299	+	0.665422i
$78$	−0.253493	−	0.481962i	−0.0287025	−	0.0545715i
$79$	−6.50159	−	3.75369i	−0.731485	−	0.422323i	0.0874799	−	0.996166i	$-0.472119\pi$
$79$	−6.50159	−	3.75369i	−0.731485	−	0.422323i	−0.818965	+	0.573843i	$0.805452\pi$
$80$		0			0
$81$	−3.22099	−	8.40388i	−0.357888	−	0.933765i
$82$	1.02702	−	1.02702i	0.113415	−	0.113415i
$83$	2.85794	+	10.6660i	0.313700	+	1.17074i	0.925194	+	0.379495i	$0.123902\pi$
$83$	2.85794	+	10.6660i	0.313700	+	1.17074i	−0.611493	+	0.791249i	$0.709431\pi$
$84$	−7.92799	−	2.46282i	−0.865014	−	0.268716i
$85$		0			0
$86$	−0.856104	+	0.494272i	−0.0923161	+	0.0532987i
$87$	0.437340	−	11.0947i	0.0468878	−	1.18947i
$88$	−1.82708	+	0.489565i	−0.194767	+	0.0521878i
$89$	2.90124			0.307531			0.153765	−	0.988107i	$-0.450860\pi$
$89$	2.90124			0.307531			0.153765	+	0.988107i	$0.450860\pi$
$90$		0			0
$91$	−3.98176			−0.417402
$92$	13.3941	−	3.58893i	1.39643	−	0.374171i
$93$	5.77670	+	3.64587i	0.599016	+	0.378059i
$94$	0.503800	−	0.290869i	0.0519630	−	0.0300008i
$95$		0			0
$96$	−0.862145	−	3.81241i	−0.0879923	−	0.389103i
$97$	0.379633	+	1.41681i	0.0385459	+	0.143855i	0.982517	−	0.186173i	$-0.0596084\pi$
$97$	0.379633	+	1.41681i	0.0385459	+	0.143855i	−0.943971	+	0.330028i	$0.892942\pi$
$98$	−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	0.999445	+	0.0333015i	$0.0106022\pi$
$101$	15.3563	+	8.86596i	1.52801	+	0.882196i	0.528563	+	0.848894i	$0.322731\pi$
$102$	−0.190635	−	0.00751461i	−0.0188756	−	0.000744058i
$103$	−2.74330	+	10.2381i	−0.270305	+	1.00879i	0.688617	+	0.725125i	$0.258218\pi$
$103$	−2.74330	+	10.2381i	−0.270305	+	1.00879i	−0.958922	+	0.283668i	$0.908449\pi$
$104$	−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	$-0.996441\pi$
$107$	−10.4591	−	10.4591i	−1.01112	−	1.01112i	−0.0111806	−	0.999937i	$-0.503559\pi$
$108$	−4.02243	−	9.37242i	−0.387058	−	0.901862i
$109$		−	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
$112$	−8.91187	−	2.38793i	−0.842092	−	0.225638i
$113$	−5.19250	−	1.39133i	−0.488469	−	0.130885i	0.00617426	−	0.999981i	$-0.498035\pi$
$113$	−5.19250	−	1.39133i	−0.488469	−	0.130885i	−0.494643	+	0.869096i	$0.664701\pi$
$114$	−0.971879	−	1.05164i	−0.0910248	−	0.0984955i
$115$		0			0
$116$		−	12.5827i		−	1.16827i
$117$	−3.17603	−	3.72059i	−0.293624	−	0.343969i
$118$	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
$122$	0.0235340	−	0.0878302i	0.00213067	−	0.00795177i
$123$	6.96358	−	11.0335i	0.627885	−	0.994854i
$124$	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	$0.177639\pi$
$128$	−1.52353	−	5.68590i	−0.134662	−	0.502567i
$129$	−6.52167	+	6.02702i	−0.574201	+	0.530649i
$130$		0			0
$131$	14.5188	−	8.38241i	1.26851	−	0.732375i	0.293804	−	0.955866i	$-0.405079\pi$
$131$	14.5188	−	8.38241i	1.26851	−	0.732375i	0.974706	+	0.223491i	$0.0717453\pi$
$132$	−7.44872	+	3.91774i	−0.648327	+	0.340995i
$133$	−10.1135	+	2.70992i	−0.876956	+	0.234980i
$134$	0.330355			0.0285383
$135$		0			0
$136$	−0.436499			−0.0374295
$137$	6.17718	−	1.65517i	0.527752	−	0.141411i	0.0149021	−	0.999889i	$-0.495256\pi$
$137$	6.17718	−	1.65517i	0.527752	−	0.141411i	0.512850	+	0.858478i	$0.328590\pi$
$138$	−2.08810	+	1.09826i	−0.177751	+	0.0934899i
$139$	9.09433	−	5.25061i	0.771371	−	0.445351i	−0.0619924	−	0.998077i	$-0.519745\pi$
$139$	9.09433	−	5.25061i	0.771371	−	0.445351i	0.833364	+	0.552725i	$0.186412\pi$
$140$		0			0
$141$	3.83787	−	3.54677i	0.323207	−	0.298692i
$142$	0.174954	+	0.652936i	0.0146818	+	0.0547931i
$143$	−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
$147$	−0.958803	+	1.51918i	−0.0790808	+	0.125300i
$148$	−0.123539	+	0.461055i	−0.0101549	+	0.0378985i
$149$	−4.96581	−	8.60103i	−0.406815	−	0.704624i	0.587716	−	0.809067i	$-0.300027\pi$
$149$	−4.96581	−	8.60103i	−0.406815	−	0.704624i	−0.994531	+	0.104443i	$0.966694\pi$
$150$		0			0
$151$	−6.95939	+	12.0540i	−0.566347	+	0.980942i	0.430576	+	0.902555i	$0.358311\pi$
$151$	−6.95939	+	12.0540i	−0.566347	+	0.980942i	−0.996923	+	0.0783879i	$0.975023\pi$
$152$	−2.31665	−	2.31665i	−0.187905	−	0.187905i
$153$	−1.68519	+	0.311884i	−0.136240	+	0.0252143i
$154$		−	1.16556i		−	0.0939236i
$155$		0			0
$156$	−3.76247	−	4.07127i	−0.301239	−	0.325962i
$157$	20.2365	+	5.42234i	1.61505	+	0.432750i	0.949541	−	0.313644i	$-0.101550\pi$
$157$	20.2365	+	5.42234i	1.61505	+	0.432750i	0.665504	+	0.746394i	$0.268216\pi$
$158$	1.39820	+	0.374646i	0.111235	+	0.0298052i
$159$	−4.44748	+	14.3167i	−0.352708	+	1.13539i
$160$		0			0
$161$			17.2510i			1.35957i
$162$	1.01927	+	1.40443i	0.0800815	+	0.110342i
$163$	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
$167$	2.20590	−	8.23252i	0.170697	−	0.637052i	−0.826547	−	0.562868i	$-0.809698\pi$
$167$	2.20590	−	8.23252i	0.170697	−	0.637052i	0.997245	−	0.0741841i	$-0.0236352\pi$
$168$	3.22917	+	0.127290i	0.249136	+	0.00982066i
$169$	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
$173$	4.57458	+	17.0726i	0.347799	+	1.29800i	0.889308	+	0.457308i	$0.151186\pi$
$173$	4.57458	+	17.0726i	0.347799	+	1.29800i	−0.541509	+	0.840695i	$0.682147\pi$
$174$	0.472213	+	2.08813i	0.0357984	+	0.158301i
$175$		0			0
$176$	−8.10033	+	4.67673i	−0.610585	+	0.352521i
$177$	6.65670	+	4.20126i	0.500348	+	0.315786i
$178$	−0.540336	+	0.144783i	−0.0404999	+	0.0108519i
$179$	−8.30788			−0.620960			−0.310480	−	0.950580i	$-0.600490\pi$
$179$	−8.30788			−0.620960			−0.310480	+	0.950580i	$0.600490\pi$
$180$		0			0
$181$	−4.73429			−0.351897			−0.175948	−	0.984399i	$-0.556299\pi$
$181$	−4.73429			−0.351897			−0.175948	+	0.984399i	$0.556299\pi$
$182$	0.741576	−	0.198705i	0.0549693	−	0.0147290i
$183$	0.0321731	−	0.816183i	0.00237830	−	0.0603340i
$184$	−4.67475	+	2.69897i	−0.344627	+	0.198971i
$185$		0			0
$186$	−1.25781	−	0.390739i	−0.0922273	−	0.0286503i
$187$	0.366025	+	1.36603i	0.0267664	+	0.0998937i
$188$	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	0.373919	−	0.927461i	$-0.378014\pi$
$191$	−3.34902	−	1.93356i	−0.242327	−	0.139907i	−0.616246	+	0.787554i	$0.711347\pi$
$192$	−5.74188	−	10.9169i	−0.414384	−	0.787861i
$193$	4.44530	−	16.5901i	0.319979	−	1.19418i	−0.599284	−	0.800536i	$-0.704548\pi$
$193$	4.44530	−	16.5901i	0.319979	−	1.19418i	0.919263	−	0.393643i	$-0.128785\pi$
$194$	−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	0.980913	−	0.194445i	$-0.0622905\pi$
$197$	11.0386	+	11.0386i	0.786469	+	0.786469i	−0.194445	+	0.980913i	$0.562291\pi$
$198$	1.08911	−	0.929703i	0.0773996	−	0.0660711i
$199$			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
$202$	−3.30245	−	0.884888i	−0.232359	−	0.0622605i
$203$	15.1203	+	4.05148i	1.06124	+	0.284358i
$204$	−1.89432	+	0.428385i	−0.132629	+	0.0299929i
$205$		0			0
$206$		−	2.04368i		−	0.142390i
$207$	−16.1194	+	13.7601i	−1.12038	+	0.956394i
$208$	−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	0.981096	+	0.193521i	$0.0619909\pi$
$211$	9.56007	+	16.5585i	0.658142	+	1.13994i	−0.322954	+	0.946415i	$0.604676\pi$
$212$	−4.39709	+	16.4102i	−0.301993	+	1.12705i
$213$	2.82664	+	5.37425i	0.193678	+	0.368237i
$214$	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
$218$	0.0171272	+	0.0639194i	0.00116000	+	0.00432917i
$219$	16.1136	+	5.00569i	1.08886	+	0.338253i
$220$		0			0
$221$	−0.806719	+	0.465759i	−0.0542658	+	0.0313304i
$222$	0.00319884	−	0.0811499i	0.000214692	−	0.00544642i
$223$	−4.03530	+	1.08126i	−0.270224	+	0.0724062i	−0.391386	−	0.920226i	$-0.628004\pi$
$223$	−4.03530	+	1.08126i	−0.270224	+	0.0724062i	0.121163	+	0.992633i	$0.461338\pi$
$224$	5.51055			0.368189
$225$		0			0
$226$	1.03650			0.0689469
$227$	−13.2857	+	3.55990i	−0.881803	+	0.236279i	−0.671185	−	0.741290i	$-0.734214\pi$
$227$	−13.2857	+	3.55990i	−0.881803	+	0.236279i	−0.210618	+	0.977568i	$0.567548\pi$
$228$	−12.3274	−	7.78022i	−0.816401	−	0.515257i
$229$	−13.2694	+	7.66109i	−0.876866	+	0.506259i	−0.869624	−	0.493715i	$-0.835639\pi$
$229$	−13.2694	+	7.66109i	−0.876866	+	0.506259i	−0.00724242	+	0.999974i	$0.502305\pi$
$230$		0			0
$231$	−2.30946	−	10.2124i	−0.151951	−	0.671929i
$232$	1.26773	+	4.73125i	0.0832308	+	0.310622i
$233$	2.98562	−	2.98562i	0.195595	−	0.195595i	−0.602514	−	0.798108i	$-0.705834\pi$
$233$	2.98562	−	2.98562i	0.195595	−	0.195595i	0.798108	+	0.602514i	$0.205834\pi$
$234$	0.777184	+	0.534438i	0.0508061	+	0.0349373i
$235$		0			0
$236$	7.72529	+	4.46020i	0.502874	+	0.290334i
$237$	12.9931	+	0.512173i	0.843991	+	0.0332692i
$238$	0.0696146	−	0.259805i	0.00451245	−	0.0168407i
$239$	2.59439	+	4.49362i	0.167817	+	0.290668i	0.937652	−	0.347575i	$-0.112995\pi$
$239$	2.59439	+	4.49362i	0.167817	+	0.290668i	−0.769835	+	0.638243i	$0.779661\pi$
$240$		0			0
$241$	1.85872	−	3.21939i	0.119730	−	0.207379i	−0.799930	−	0.600093i	$-0.795130\pi$
$241$	1.85872	−	3.21939i	0.119730	−	0.207379i	0.919661	+	0.392714i	$0.128464\pi$
$242$	0.664193	+	0.664193i	0.0426959	+	0.0426959i
$243$	11.7134	+	10.2857i	0.751416	+	0.659829i
$244$		−	0.925646i		−	0.0592584i
$245$		0			0
$246$	−0.746308	+	2.40241i	−0.0475829	+	0.153172i
$247$	−6.75347	−	1.80959i	−0.429713	−	0.115141i
$248$	−2.91078	−	0.779940i	−0.184834	−	0.0495262i
$249$	−12.9808	−	14.0461i	−0.822622	−	0.890137i
$250$		0			0
$251$		−	3.97271i		−	0.250755i	−0.992109	−	0.125378i	$-0.959986\pi$
$251$		−	3.97271i		−	0.250755i	0.992109	−	0.125378i	$-0.0400142\pi$
$252$	14.1389	−	2.61673i	0.890666	−	0.164838i
$253$	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
$257$	4.42437	−	16.5120i	0.275985	−	1.02999i	−0.679194	−	0.733959i	$-0.737671\pi$
$257$	4.42437	−	16.5120i	0.275985	−	1.02999i	0.955179	−	0.296030i	$-0.0956628\pi$
$258$	0.913846	−	1.44794i	0.0568935	−	0.0901451i
$259$	−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
$263$	−2.77155	−	10.3436i	−0.170901	−	0.637812i	−0.997214	−	0.0746001i	$-0.976232\pi$
$263$	−2.77155	−	10.3436i	−0.170901	−	0.637812i	0.826312	−	0.563212i	$-0.190435\pi$
$264$	2.40610	−	2.22360i	0.148085	−	0.136853i
$265$		0			0
$266$	1.74834	−	1.00941i	0.107198	−	0.0618907i
$267$	−4.44745	+	2.33919i	−0.272179	+	0.143156i
$268$	3.24840	−	0.870407i	0.198428	−	0.0531685i
$269$	15.8925			0.968985			0.484492	−	0.874796i	$-0.339004\pi$
$269$	15.8925			0.968985			0.484492	+	0.874796i	$0.339004\pi$
$270$		0			0
$271$	0.974200			0.0591785			0.0295892	−	0.999562i	$-0.490580\pi$
$271$	0.974200			0.0591785			0.0295892	+	0.999562i	$0.490580\pi$
$272$	−2.08490	+	0.558646i	−0.126415	+	0.0338729i
$273$	6.10383	−	3.21038i	0.369421	−	0.194301i
$274$	−1.06786	+	0.616528i	−0.0645117	+	0.0372458i
$275$		0			0
$276$	−17.6387	+	16.3009i	−1.06173	+	0.981197i
$277$	−6.18395	−	23.0788i	−0.371557	−	1.38667i	−0.858310	−	0.513131i	$-0.828485\pi$
$277$	−6.18395	−	23.0788i	−0.371557	−	1.38667i	0.486753	−	0.873540i	$-0.338181\pi$
$278$	−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	−0.430296	−	0.902688i	$-0.641591\pi$
$281$	−23.9241	−	13.8126i	−1.42720	−	0.823991i	−0.996899	+	0.0786961i	$0.974924\pi$
$282$	−0.537779	+	0.852086i	−0.0320243	+	0.0507410i
$283$	−4.40870	+	16.4535i	−0.262070	+	0.978058i	0.701950	+	0.712227i	$0.252313\pi$
$283$	−4.40870	+	16.4535i	−0.262070	+	0.978058i	−0.964020	+	0.265831i	$0.914354\pi$
$284$	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
$288$	4.39546	+	5.14910i	0.259005	+	0.303414i
$289$		−	16.6736i		−	0.980803i
$290$		0			0
$291$	−1.72429	−	1.86581i	−0.101080	−	0.109376i
$292$	18.4698	+	4.94897i	1.08086	+	0.289617i
$293$	−25.7566	−	6.90146i	−1.50472	−	0.403188i	−0.590041	−	0.807374i	$-0.700888\pi$
$293$	−25.7566	−	6.90146i	−1.50472	−	0.403188i	−0.914677	+	0.404186i	$0.867555\pi$
$294$	0.102758	−	0.330784i	0.00599296	−	0.0192917i
$295$		0			0
$296$		−	0.185810i		−	0.0108000i
$297$	7.70045	−	10.3039i	0.446825	−	0.597890i
$298$	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
$302$	0.694599	−	2.59228i	0.0399697	−	0.149169i
$303$	−30.6887	−	1.20972i	−1.76302	−	0.0694965i
$304$	−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	$0.0838363\pi$
$308$	−3.07098	−	11.4610i	−0.174985	−	0.653053i
$309$	−4.04938	−	17.9064i	−0.230361	−	1.01866i
$310$		0			0
$311$	7.49228	−	4.32567i	0.424848	−	0.245286i	−0.272301	−	0.962212i	$-0.587785\pi$
$311$	7.49228	−	4.32567i	0.424848	−	0.245286i	0.697149	+	0.716926i	$0.254451\pi$
$312$	1.82493	+	1.15177i	0.103316	+	0.0652064i
$313$	18.1094	−	4.85240i	1.02360	−	0.274274i	0.292301	−	0.956326i	$-0.405579\pi$
$313$	18.1094	−	4.85240i	1.02360	−	0.274274i	0.731303	+	0.682052i	$0.238912\pi$
$314$	−4.03949			−0.227962
$315$		0			0
$316$	14.7357			0.828946
$317$	−18.7418	+	5.02186i	−1.05265	+	0.282056i	−0.743345	−	0.668908i	$-0.766762\pi$
$317$	−18.7418	+	5.02186i	−1.05265	+	0.282056i	−0.309301	+	0.950964i	$0.600095\pi$
$318$	0.113855	−	2.88834i	0.00638468	−	0.161970i
$319$	13.7434	−	7.93476i	0.769484	−	0.444262i
$320$		0			0
$321$	24.4661	+	7.60037i	1.36556	+	0.424211i
$322$	−0.860886	−	3.21287i	−0.0479753	−	0.179046i
$323$	−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
$327$	0.276716	+	0.526114i	0.0153024	+	0.0290942i
$328$	−1.48968	+	5.55956i	−0.0822538	+	0.306975i
$329$	3.68372	+	6.38039i	0.203090	+	0.351763i
$330$		0			0
$331$	17.1969	−	29.7859i	0.945226	−	1.63718i	0.189929	−	0.981798i	$-0.439174\pi$
$331$	17.1969	−	29.7859i	0.945226	−	1.63718i	0.755298	−	0.655382i	$-0.227492\pi$
$332$	−15.3258	−	15.3258i	−0.841114	−	0.841114i
$333$	−0.132764	−	0.717358i	−0.00727540	−	0.0393110i
$334$			1.64333i			0.0899191i
$335$		0			0
$336$	15.5867	−	3.52481i	0.850326	−	0.192294i
$337$	−30.9291	−	8.28744i	−1.68482	−	0.451445i	−0.715773	−	0.698333i	$-0.753925\pi$
$337$	−30.9291	−	8.28744i	−1.68482	−	0.451445i	−0.969044	+	0.246888i	$0.920592\pi$
$338$	−1.92596	−	0.516060i	−0.104758	−	0.0280700i
$339$	9.08161	−	2.05373i	0.493245	−	0.111543i
$340$		0			0
$341$			9.76331i			0.528713i
$342$	2.33775	+	0.828518i	0.126411	+	0.0448011i
$343$	−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
$347$	4.15647	−	15.5122i	0.223131	−	0.832737i	−0.760014	−	0.649907i	$-0.774808\pi$
$347$	4.15647	−	15.5122i	0.223131	−	0.832737i	0.983145	−	0.182829i	$-0.0585256\pi$
$348$	10.1450	+	19.2885i	0.543830	+	1.03397i
$349$	−15.1664	−	8.75630i	−0.811837	−	0.468714i	0.0357566	−	0.999361i	$-0.488616\pi$
$349$	−15.1664	−	8.75630i	−0.811837	−	0.468714i	−0.847593	+	0.530646i	$0.821949\pi$
$350$		0			0
$351$	7.86849	+	3.14273i	0.419989	+	0.167746i
$352$	3.95028	−	3.95028i	0.210550	−	0.210550i
$353$	−4.95294	−	18.4846i	−0.263618	−	0.983837i	−0.963091	−	0.269177i	$-0.913248\pi$
$353$	−4.95294	−	18.4846i	−0.263618	−	0.983837i	0.699472	−	0.714660i	$-0.253418\pi$
$354$	−1.44942	−	0.450262i	−0.0770360	−	0.0239312i
$355$		0			0
$356$	−4.93169	+	2.84731i	−0.261379	+	0.150907i
$357$	0.0951692	−	2.41430i	0.00503689	−	0.127778i
$358$	1.54728	−	0.414594i	0.0817766	−	0.0219120i
$359$	−23.0127			−1.21457			−0.607283	−	0.794486i	$-0.707741\pi$
$359$	−23.0127			−1.21457			−0.607283	+	0.794486i	$0.707741\pi$
$360$		0			0
$361$	0.614846			0.0323603
$362$	0.881728	−	0.236258i	0.0463426	−	0.0124175i
$363$	7.13557	+	4.50350i	0.374521	+	0.236372i
$364$	6.76842	−	3.90775i	0.354762	−	0.204822i
$365$		0			0
$366$	0.0347385	+	0.153614i	0.00181581	+	0.00802953i
$367$	7.01692	+	26.1875i	0.366280	+	1.36698i	0.865677	+	0.500603i	$0.166888\pi$
$367$	7.01692	+	26.1875i	0.366280	+	1.36698i	−0.499397	+	0.866373i	$0.666445\pi$
$368$	−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
$372$	−13.3977	−	0.528121i	−0.694636	−	0.0273818i
$373$	7.76440	−	28.9771i	0.402025	−	1.50038i	−0.407451	−	0.913227i	$-0.633582\pi$
$373$	7.76440	−	28.9771i	0.402025	−	1.50038i	0.809477	−	0.587152i	$-0.199751\pi$
$374$	−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
$378$	−2.24819	+	0.964871i	−0.115634	+	0.0496276i
$379$			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
$382$	0.720223	+	0.192983i	0.0368498	+	0.00987388i
$383$	26.6536	+	7.14181i	1.36194	+	0.364929i	0.864527	−	0.502587i	$-0.167618\pi$
$383$	26.6536	+	7.14181i	1.36194	+	0.364929i	0.497409	+	0.867516i	$0.334285\pi$
$384$	6.91987	+	7.48780i	0.353128	+	0.382110i
$385$		0			0
$386$			3.31162i			0.168557i
$387$	5.13797	−	14.4973i	0.261178	−	0.736941i
$388$	−2.03579	−	2.03579i	−0.103352	−	0.103352i
$389$	6.71184	−	11.6253i	0.340304	−	0.589424i	−0.644185	−	0.764870i	$-0.722803\pi$
$389$	6.71184	−	11.6253i	0.340304	−	0.589424i	0.984489	+	0.175446i	$0.0561367\pi$
$390$		0			0
$391$	2.01790	+	3.49510i	0.102049	+	0.176755i
$392$	0.205111	−	0.765487i	0.0103597	−	0.0386629i
$393$	−15.4980	+	24.5558i	−0.781771	+	1.23868i
$394$	−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	$0.0989967\pi$
$398$	−0.179722	−	0.670732i	−0.00900866	−	0.0336208i
$399$	13.3186	−	12.3084i	0.666764	−	0.616191i
$400$		0			0
$401$	−21.7606	+	12.5635i	−1.08667	+	0.627391i	−0.932689	−	0.360682i	$-0.882544\pi$
$401$	−21.7606	+	12.5635i	−1.08667	+	0.627391i	−0.153985	+	0.988073i	$0.549211\pi$
$402$	−0.506417	+	0.266356i	−0.0252578	+	0.0132846i
$403$	−6.21180	+	1.66445i	−0.309432	+	0.0829120i
$404$	−34.8046			−1.73159
$405$		0			0
$406$	−3.01824			−0.149793
$407$	−0.581494	+	0.155811i	−0.0288236	+	0.00772325i
$408$	0.669129	−	0.351936i	0.0331268	−	0.0174234i
$409$	−9.81878	+	5.66888i	−0.485508	+	0.280308i	−0.722709	−	0.691153i	$-0.757103\pi$
$409$	−9.81878	+	5.66888i	−0.485508	+	0.280308i	0.237201	+	0.971461i	$0.423770\pi$
$410$		0			0
$411$	−8.13478	+	7.51777i	−0.401259	+	0.370824i
$412$	−5.38461	−	20.0957i	−0.265281	−	0.990042i
$413$	−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
$417$	−9.70771	+	15.3814i	−0.475389	+	0.753231i
$418$	0.529711	−	1.97691i	0.0259090	−	0.0966938i
$419$	4.26264	+	7.38311i	0.208244	+	0.360688i	0.951161	−	0.308694i	$-0.0998920\pi$
$419$	4.26264	+	7.38311i	0.208244	+	0.360688i	−0.742918	+	0.669383i	$0.766559\pi$
$420$		0			0
$421$	1.10329	−	1.91095i	0.0537710	−	0.0931341i	−0.837887	−	0.545844i	$-0.816209\pi$
$421$	1.10329	−	1.91095i	0.0537710	−	0.0931341i	0.891658	+	0.452710i	$0.149543\pi$
$422$	−2.60683	−	2.60683i	−0.126898	−	0.126898i
$423$	−3.02359	+	8.53138i	−0.147012	+	0.414810i
$424$		−	6.61346i		−	0.321178i
$425$		0			0
$426$	−0.794637	−	0.859856i	−0.0385003	−	0.0416601i
$427$	1.11233	+	0.298048i	0.0538294	+	0.0144235i
$428$	28.0436	+	7.51426i	1.35554	+	0.363215i
$429$	2.07419	−	6.67695i	0.100143	−	0.322366i
$430$		0			0
$431$			1.95738i			0.0942838i	0.998888	+	0.0471419i	$0.0150113\pi$
$431$			1.95738i			0.0942838i	−0.998888	+	0.0471419i	$0.984989\pi$
$432$	15.7263	+	11.7528i	0.756630	+	0.565458i
$433$	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
$437$	−7.84002	+	29.2593i	−0.375039	+	1.39966i
$438$	−3.25085	−	0.128145i	−0.155332	−	0.00612302i
$439$	−4.68008	−	2.70205i	−0.223368	−	0.128962i	0.384141	−	0.923275i	$-0.374498\pi$
$439$	−4.68008	−	2.70205i	−0.223368	−	0.128962i	−0.607509	+	0.794313i	$0.707831\pi$
$440$		0			0
$441$	0.244926	−	3.10188i	0.0116631	−	0.147708i
$442$	0.127003	−	0.127003i	0.00604090	−	0.00604090i
$443$	−6.98940	−	26.0848i	−0.332077	−	1.23933i	−0.907004	−	0.421122i	$-0.861636\pi$
$443$	−6.98940	−	26.0848i	−0.332077	−	1.23933i	0.574927	−	0.818204i	$-0.305030\pi$
$444$	−0.182356	−	0.806380i	−0.00865424	−	0.0382691i
$445$		0			0
$446$	0.697588	−	0.402752i	0.0330317	−	0.0190709i
$447$	14.5471	+	9.18114i	0.688053	+	0.434253i
$448$	16.7974	−	4.50086i	0.793604	−	0.212646i
$449$	23.8541			1.12574			0.562872	−	0.826544i	$-0.309696\pi$
$449$	23.8541			1.12574			0.562872	+	0.826544i	$0.309696\pi$
$450$		0			0
$451$	18.6479			0.878093
$452$	10.1920	−	2.73093i	0.479389	−	0.128452i
$453$	0.949576	−	24.0893i	0.0446150	−	1.13182i
$454$	2.29672	−	1.32601i	0.107790	−	0.0622328i
$455$		0			0
$456$	5.41914	+	1.68345i	0.253774	+	0.0788349i
$457$	5.13035	+	19.1467i	0.239988	+	0.895647i	0.975837	+	0.218501i	$0.0701167\pi$
$457$	5.13035	+	19.1467i	0.239988	+	0.895647i	−0.735849	+	0.677146i	$0.763217\pi$
$458$	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	0.473130	−	0.880993i	$-0.343124\pi$
$461$	−1.14371	−	0.660321i	−0.0532679	−	0.0307542i	−0.526397	+	0.850239i	$0.676458\pi$
$462$	0.939758	+	1.78674i	0.0437215	+	0.0831269i
$463$	−3.98780	+	14.8827i	−0.185329	+	0.691656i	0.809231	+	0.587490i	$0.199884\pi$
$463$	−3.98780	+	14.8827i	−0.185329	+	0.691656i	−0.994560	+	0.104166i	$0.966783\pi$
$464$	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	0.747013	−	0.664809i	$-0.231487\pi$
$467$	1.77645	+	1.77645i	0.0822044	+	0.0822044i	−0.664809	+	0.747013i	$0.731487\pi$
$468$	9.05022	+	3.20747i	0.418346	+	0.148265i
$469$			4.18380i			0.193190i
$470$		0			0
$471$	−35.3933	+	8.00390i	−1.63084	+	0.368800i
$472$	−3.35419	−	0.898753i	−0.154389	−	0.0413685i
$473$	−12.2596	−	3.28495i	−0.563697	−	0.151042i
$474$	−2.44543	+	0.553014i	−0.112322	+	0.0254008i
$475$		0			0
$476$		−	2.73810i		−	0.125501i
$477$	−4.72541	−	25.5327i	−0.216361	−	1.16906i
$478$	−0.707436	−	0.707436i	−0.0323574	−	0.0323574i
$479$	18.9907	−	32.8928i	0.867705	−	1.50291i	0.00336919	−	0.999994i	$-0.498928\pi$
$479$	18.9907	−	32.8928i	0.867705	−	1.50291i	0.864336	−	0.502915i	$-0.167739\pi$
$480$		0			0
$481$	−0.198266	−	0.343406i	−0.00904014	−	0.0156580i
$482$	−0.185513	+	0.692346i	−0.00844991	+	0.0315355i
$483$	−13.9089	−	26.4448i	−0.632879	−	1.20328i
$484$	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	$0.975651\pi$
$488$	0.0932612	+	0.348056i	0.00422174	+	0.0157557i
$489$	−5.68131	−	1.76490i	−0.256918	−	0.0798114i
$490$		0			0
$491$	18.9114	−	10.9185i	0.853460	−	0.492746i	−0.00835660	−	0.999965i	$-0.502660\pi$
$491$	18.9114	−	10.9185i	0.853460	−	0.492746i	0.861817	+	0.507220i	$0.169327\pi$
$492$	−1.00871	+	25.5894i	−0.0454761	+	1.15366i
$493$	3.53734	−	0.947827i	0.159314	−	0.0426880i
$494$	1.34809			0.0606535
$495$		0			0
$496$	−14.9013			−0.669086
$497$	−8.26913	+	2.21571i	−0.370921	+	0.0993881i
$498$	3.11853	+	1.96821i	0.139745	+	0.0881974i
$499$	−2.74862	+	1.58691i	−0.123045	+	0.0710401i	−0.560259	−	0.828317i	$-0.689298\pi$
$499$	−2.74862	+	1.58691i	−0.123045	+	0.0710401i	0.437214	+	0.899357i	$0.355965\pi$
$500$		0			0
$501$	3.25612	+	14.3986i	0.145473	+	0.643281i
$502$	0.198253	+	0.739889i	0.00884845	+	0.0330229i
$503$	7.00484	−	7.00484i	0.312330	−	0.312330i	−0.533481	−	0.845812i	$-0.679117\pi$
$503$	7.00484	−	7.00484i	0.312330	−	0.312330i	0.845812	+	0.533481i	$0.179117\pi$
$504$	−5.05277	+	2.40845i	−0.225068	+	0.107281i
$505$		0			0
$506$	−2.92030	−	1.68603i	−0.129823	−	0.0749534i
$507$	−17.8974	−	0.705498i	−0.794853	−	0.0313323i
$508$	−2.58058	+	9.63084i	−0.114495	+	0.427299i
$509$	8.36206	+	14.4835i	0.370642	+	0.641971i	0.989664	−	0.143403i	$-0.0458044\pi$
$509$	8.36206	+	14.4835i	0.370642	+	0.641971i	−0.619023	+	0.785373i	$0.712471\pi$
$510$		0			0
$511$	−11.8942	+	20.6013i	−0.526167	+	0.911347i
$512$	10.1119	+	10.1119i	0.446886	+	0.446886i
$513$	22.1246	+	2.62727i	0.976824	+	0.115997i
$514$			3.29603i			0.145382i
$515$		0			0
$516$	5.17091	−	16.6455i	0.227637	−	0.732777i
$517$	7.21452	+	1.93313i	0.317294	+	0.0850188i
$518$	0.110595	+	0.0296337i	0.00485925	+	0.00130203i
$519$	−20.7777	−	22.4830i	−0.912040	−	0.986894i
$520$		0			0
$521$		−	1.34092i		−	0.0587466i	−0.999569	−	0.0293733i	$-0.990649\pi$
$521$		−	1.34092i		−	0.0587466i	0.999569	−	0.0293733i	$-0.00935116\pi$
$522$	−2.40748	−	2.82026i	−0.105372	−	0.123440i
$523$	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
$527$	−0.583126	+	2.17625i	−0.0254014	+	0.0947991i
$528$	8.64667	−	13.7002i	0.376298	−	0.596226i
$529$	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
$533$	3.17908	+	11.8645i	0.137701	+	0.513908i
$534$	0.711572	−	0.657601i	0.0307927	−	0.0284572i
$535$		0			0
$536$	−1.13375	+	0.654569i	−0.0489704	+	0.0282731i
$537$	12.7355	−	6.69840i	0.549579	−	0.289057i
$538$	−2.95987	+	0.793096i	−0.127609	+	0.0341928i
$539$	−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	$0.761284\pi$
$542$	−0.181438	+	0.0486162i	−0.00779343	+	0.00208824i
$543$	7.25741	−	3.81712i	0.311445	−	0.163808i
$544$	1.11646	−	0.644587i	0.0478677	−	0.0276364i
$545$		0			0
$546$	−0.976587	+	0.902515i	−0.0417941	+	0.0386241i
$547$	−2.44487	−	9.12437i	−0.104535	−	0.390130i	0.893757	−	0.448552i	$-0.148060\pi$
$547$	−2.44487	−	9.12437i	−0.104535	−	0.390130i	−0.998292	+	0.0584215i	$0.981393\pi$
$548$	−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
$552$	4.99005	−	7.90650i	0.212391	−	0.336523i
$553$	−4.74472	+	17.7075i	−0.201766	+	0.753001i
$554$	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	0.674928	−	0.737883i	$-0.264175\pi$
$557$	−1.48579	−	1.48579i	−0.0629551	−	0.0629551i	−0.737883	+	0.674928i	$0.764175\pi$
$558$	2.24320	−	0.415156i	0.0949623	−	0.0175750i
$559$		−	8.36006i		−	0.353593i
$560$		0			0
$561$	−1.66248	−	1.79893i	−0.0701901	−	0.0759509i
$562$	5.14501	+	1.37860i	0.217029	+	0.0581527i
$563$	20.6371	+	5.52969i	0.869750	+	0.233049i	0.665979	−	0.745970i	$-0.268014\pi$
$563$	20.6371	+	5.52969i	0.869750	+	0.233049i	0.203770	+	0.979019i	$0.434681\pi$
$564$	−3.04297	+	9.79553i	−0.128132	+	0.412466i
$565$		0			0
$566$		−	3.28436i		−	0.138052i
$567$	−17.7864	+	12.9086i	−0.746959	+	0.542111i
$568$	−1.89416	−	1.89416i	−0.0794771	−	0.0794771i
$569$	5.82589	−	10.0907i	0.244234	−	0.423026i	−0.717682	−	0.696371i	$-0.754797\pi$
$569$	5.82589	−	10.0907i	0.244234	−	0.423026i	0.961916	+	0.273345i	$0.0881301\pi$
$570$		0			0
$571$	10.5623	+	18.2945i	0.442020	+	0.765601i	0.997839	−	0.0657023i	$-0.0209288\pi$
$571$	10.5623	+	18.2945i	0.442020	+	0.765601i	−0.555819	+	0.831303i	$0.687595\pi$
$572$	2.05069	−	7.65328i	0.0857436	−	0.320000i
$573$	6.69284	+	0.263825i	0.279598	+	0.0110214i
$574$	−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	$0.903191\pi$
$578$	0.832076	+	3.10535i	0.0346098	+	0.129166i
$579$	6.56168	+	29.0158i	0.272694	+	1.20586i
$580$		0			0
$581$	23.3515	−	13.4820i	0.968782	−	0.559327i
$582$	0.414248	+	0.261445i	0.0171711	+	0.0108373i
$583$	−20.6969	+	5.54571i	−0.857177	+	0.229680i
$584$	−7.44353			−0.308015
$585$		0			0
$586$	5.14140			0.212389
$587$	8.53262	−	2.28631i	0.352179	−	0.0943661i	−0.0783924	−	0.996923i	$-0.524979\pi$
$587$	8.53262	−	2.28631i	0.352179	−	0.0943661i	0.430571	+	0.902556i	$0.358312\pi$
$588$	0.138887	−	3.52336i	0.00572761	−	0.145301i
$589$	−14.6450	+	8.45527i	−0.603435	+	0.348393i
$590$		0			0
$591$	−25.8217	−	8.02150i	−1.06216	−	0.329960i
$592$	−0.237806	−	0.887505i	−0.00977377	−	0.0364762i
$593$	−24.5829	+	24.5829i	−1.00950	+	1.00950i	−0.00954475	+	0.999954i	$0.503038\pi$
$593$	−24.5829	+	24.5829i	−1.00950	+	1.00950i	−0.999954	+	0.00954475i	$0.996962\pi$
$594$	−0.919955	+	2.30330i	−0.0377462	+	0.0945056i
$595$		0			0
$596$	16.8823	+	9.74700i	0.691526	+	0.399253i
$597$	−2.90369	−	5.52073i	−0.118840	−	0.225948i
$598$	0.574869	−	2.14544i	0.0235082	−	0.0877336i
$599$	−18.8291	−	32.6129i	−0.769335	−	1.33253i	−0.937924	−	0.346840i	$-0.887255\pi$
$599$	−18.8291	−	32.6129i	−0.769335	−	1.33253i	0.168590	−	0.985686i	$-0.446079\pi$
$600$		0			0
$601$	11.1158	−	19.2532i	0.453424	−	0.785354i	−0.545172	−	0.838324i	$-0.683536\pi$
$601$	11.1158	−	19.2532i	0.453424	−	0.785354i	0.998596	+	0.0529703i	$0.0168689\pi$
$602$	1.70690	+	1.70690i	0.0695679	+	0.0695679i
$603$	−3.90937	+	3.33718i	−0.159202	+	0.135900i
$604$		−	27.3201i		−	1.11164i
$605$		0			0
$606$	5.77593	−	1.30618i	0.234631	−	0.0530599i
$607$	20.8988	+	5.59982i	0.848257	+	0.227290i	0.656663	−	0.754184i	$-0.271968\pi$
$607$	20.8988	+	5.59982i	0.848257	+	0.227290i	0.191594	+	0.981474i	$0.438634\pi$
$608$	9.34645	+	2.50437i	0.379049	+	0.101566i
$609$	−26.4452	+	5.98037i	−1.07161	+	0.242337i
$610$		0			0
$611$			4.91972i			0.199031i
$612$	2.55850	−	2.18403i	0.103421	−	0.0882841i
$613$	−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
$617$	10.9568	−	40.8914i	0.441104	−	1.64622i	−0.284917	−	0.958552i	$-0.591966\pi$
$617$	10.9568	−	40.8914i	0.441104	−	1.64622i	0.726021	−	0.687672i	$-0.241367\pi$
$618$	1.64776	+	3.13286i	0.0662827	+	0.126022i
$619$	27.5855	+	15.9265i	1.10876	+	0.640141i	0.938507	−	0.345260i	$-0.112209\pi$
$619$	27.5855	+	15.9265i	1.10876	+	0.640141i	0.170250	+	0.985401i	$0.445543\pi$
$620$		0			0
$621$	13.6158	−	34.0901i	0.546385	−	1.36799i
$622$	−1.17952	+	1.17952i	−0.0472944	+	0.0472944i
$623$	−1.83361	−	6.84311i	−0.0734619	−	0.274163i
$624$	10.1907	+	3.16573i	0.407955	+	0.126731i
$625$		0			0
$626$	−3.13060	+	1.80745i	−0.125124	+	0.0722403i
$627$	0.724161	−	18.3709i	0.0289202	−	0.733663i
$628$	−39.7206	+	10.6431i	−1.58502	+	0.424706i
$629$	−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	$0.398211\pi$
$632$	−5.54081	+	1.48466i	−0.220402	+	0.0590564i
$633$	−28.0057	−	17.6753i	−1.11313	−	0.702532i
$634$	3.23993	−	1.87057i	0.128674	−	0.0742899i
$635$		0			0
$636$	−6.49053	−	28.7012i	−0.257366	−	1.13808i
$637$	−0.437722	−	1.63360i	−0.0173432	−	0.0647256i
$638$	−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	0.321012	−	0.947075i	$-0.395977\pi$
$641$	−8.57453	−	4.95051i	−0.338673	−	0.195533i	−0.659685	+	0.751542i	$0.729310\pi$
$642$	−4.93592	−	0.194569i	−0.194805	−	0.00767902i
$643$	12.2247	−	45.6232i	0.482095	−	1.79920i	−0.110706	−	0.993853i	$-0.535311\pi$
$643$	12.2247	−	45.6232i	0.482095	−	1.79920i	0.592801	−	0.805349i	$-0.298022\pi$
$644$	−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	0.872410	−	0.488774i	$-0.162556\pi$
$647$	9.75824	+	9.75824i	0.383636	+	0.383636i	−0.488774	+	0.872410i	$0.662556\pi$
$648$	−6.28079	−	2.80026i	−0.246733	−	0.110005i
$649$			11.2506i			0.441625i
$650$		0			0
$651$	4.94853	−	15.9296i	0.193948	−	0.624331i
$652$	−6.51206	−	1.74490i	−0.255032	−	0.0683356i
$653$	2.99335	+	0.802065i	0.117139	+	0.0313872i	0.316912	−	0.948455i	$-0.397354\pi$
$653$	2.99335	+	0.802065i	0.117139	+	0.0313872i	−0.199773	+	0.979842i	$0.564021\pi$
$654$	−0.0777914	−	0.0841760i	−0.00304189	−	0.00329154i
$655$		0			0
$656$			28.4613i			1.11123i
$657$	−28.7373	+	5.31850i	−1.12115	+	0.207494i
$658$	−1.00447	−	1.00447i	−0.0391584	−	0.0391584i
$659$	13.5644	−	23.4942i	0.528393	−	0.915204i	−0.471059	−	0.882102i	$-0.656128\pi$
$659$	13.5644	−	23.4942i	0.528393	−	0.915204i	0.999452	−	0.0331023i	$-0.0105387\pi$
$660$		0			0
$661$	−9.54526	−	16.5329i	−0.371268	−	0.643055i	0.618493	−	0.785790i	$-0.287743\pi$
$661$	−9.54526	−	16.5329i	−0.371268	−	0.643055i	−0.989761	+	0.142736i	$0.954410\pi$
$662$	−1.71638	+	6.40560i	−0.0667088	+	0.248961i
$663$	0.861129	−	1.36442i	0.0334435	−	0.0529896i
$664$	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
$668$	4.32979	+	16.1590i	0.167524	+	0.625210i
$669$	5.31412	−	4.91105i	0.205456	−	0.189872i
$670$		0			0
$671$	1.01104	−	0.583723i	0.0390307	−	0.0225344i
$672$	−8.44739	+	4.44300i	−0.325865	+	0.171392i
$673$	0.134287	−	0.0359820i	0.00517638	−	0.00138701i	−0.256230	−	0.966616i	$-0.582480\pi$
$673$	0.134287	−	0.0359820i	0.00517638	−	0.00138701i	0.261406	+	0.965229i	$0.415814\pi$
$674$	6.17391			0.237810
$675$		0			0
$676$	−20.2978			−0.780684
$677$	7.80401	−	2.09108i	0.299933	−	0.0803667i	−0.105714	−	0.994397i	$-0.533713\pi$
$677$	7.80401	−	2.09108i	0.299933	−	0.0803667i	0.405647	+	0.914030i	$0.367046\pi$
$678$	−1.58890	+	0.835699i	−0.0610213	+	0.0320948i
$679$	3.10188	−	1.79087i	0.119039	−	0.0687272i
$680$		0			0
$681$	17.4961	−	16.1690i	0.670450	−	0.619598i
$682$	−0.487225	−	1.81835i	−0.0186568	−	0.0696281i
$683$	35.0271	−	35.0271i	1.34027	−	1.34027i	0.444490	−	0.895784i	$-0.353385\pi$
$683$	35.0271	−	35.0271i	1.34027	−	1.34027i	0.895784	−	0.444490i	$-0.146615\pi$
$684$	25.1702	+	1.98745i	0.962406	+	0.0759921i
$685$		0			0
$686$	3.27715	+	1.89206i	0.125122	+	0.0722393i
$687$	14.1644	−	22.4428i	0.540404	−	0.856245i
$688$	5.01366	−	18.7112i	0.191144	−	0.713359i
$689$	−7.05680	−	12.2227i	−0.268843	−	0.465649i
$690$		0			0
$691$	−20.5195	+	35.5408i	−0.780597	+	1.35203i	0.150997	+	0.988534i	$0.451752\pi$
$691$	−20.5195	+	35.5408i	−0.780597	+	1.35203i	−0.931594	+	0.363500i	$0.881582\pi$
$692$	−24.5313	−	24.5313i	−0.932541	−	0.932541i
$693$	11.7743	+	13.7931i	0.447267	+	0.523956i
$694$			3.09646i			0.117540i
$695$		0			0
$696$	−5.75804	−	6.23062i	−0.218258	−	0.236171i
$697$	4.15663	+	1.11377i	0.157444	+	0.0421869i
$698$	3.26160	+	0.873943i	0.123453	+	0.0330792i
$699$	−2.16958	+	6.98402i	−0.0820611	+	0.264160i
$700$		0			0
$701$		−	37.2173i		−	1.40568i	−0.711348	−	0.702840i	$-0.751915\pi$
$701$		−	37.2173i		−	1.40568i	0.711348	−	0.702840i	$-0.248085\pi$
$702$	−1.62228	−	0.192645i	−0.0612292	−	0.00727091i
$703$	−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
$707$	11.2067	−	41.8240i	0.421471	−	1.57295i
$708$	−15.4386	−	0.608573i	−0.580218	−	0.0228716i
$709$	−13.3449	−	7.70466i	−0.501177	−	0.289355i	0.228023	−	0.973656i	$-0.426774\pi$
$709$	−13.3449	−	7.70466i	−0.501177	−	0.289355i	−0.729199	+	0.684301i	$0.760107\pi$
$710$		0			0
$711$	−20.3307	+	9.69081i	−0.762459	+	0.363434i
$712$	1.56751	−	1.56751i	0.0587448	−	0.0587448i
$713$	7.21120	+	26.9125i	0.270061	+	1.00788i
$714$	0.102758	+	0.454396i	0.00384562	+	0.0170053i
$715$		0			0
$716$	14.1222	−	8.15345i	0.527771	−	0.304709i
$717$	−7.60014	−	4.79670i	−0.283833	−	0.179136i
$718$	4.28596	−	1.14842i	0.159951	−	0.0428587i
$719$	−11.9324			−0.445002			−0.222501	−	0.974932i	$-0.571422\pi$
$719$	−11.9324			−0.445002			−0.222501	+	0.974932i	$0.571422\pi$
$720$		0			0
$721$	25.8823			0.963908
$722$	−0.114511	+	0.0306831i	−0.00426165	+	0.00114191i
$723$	−0.253613	+	6.43378i	−0.00943196	+	0.239275i
$724$	8.04760	−	4.64628i	0.299087	−	0.172678i
$725$		0			0
$726$	−1.55369	−	0.482653i	−0.0576629	−	0.0179129i
$727$	−1.12575	−	4.20134i	−0.0417516	−	0.155819i	0.941903	−	0.335885i	$-0.109035\pi$
$727$	−1.12575	−	4.20134i	−0.0417516	−	0.155819i	−0.983654	+	0.180066i	$0.942369\pi$
$728$	−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
$732$	0.746322	+	1.41897i	0.0275848	+	0.0524465i
$733$	−12.7796	+	47.6943i	−0.472027	+	1.76163i	0.160446	+	0.987045i	$0.448707\pi$
$733$	−12.7796	+	47.6943i	−0.472027	+	1.76163i	−0.632473	+	0.774583i	$0.717960\pi$
$734$	−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
$738$	−0.792945	−	4.28450i	−0.0291887	−	0.157715i
$739$			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
$742$	3.93635	+	1.05474i	0.144508	+	0.0387208i
$743$	−19.2021	−	5.14520i	−0.704458	−	0.188759i	−0.111232	−	0.993795i	$-0.535480\pi$
$743$	−19.2021	−	5.14520i	−0.704458	−	0.188759i	−0.593227	+	0.805035i	$0.702146\pi$
$744$	5.09091	−	1.15127i	0.186642	−	0.0422075i
$745$		0			0
$746$			5.78426i			0.211777i
$747$	31.2238	+	11.0660i	1.14242	+	0.404883i
$748$	−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	0.973838	−	0.227242i	$-0.0729708\pi$
$751$	7.95061	+	13.7709i	0.290122	+	0.502506i	−0.683716	+	0.729748i	$0.739637\pi$
$752$	−2.95043	+	11.0112i	−0.107591	+	0.401536i
$753$	3.20308	+	6.08995i	0.116727	+	0.221930i
$754$	−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	$0.434860\pi$
$758$	−1.00278	−	3.74243i	−0.0364227	−	0.135931i
$759$	−28.9278	−	8.98641i	−1.05001	−	0.326186i
$760$		0			0
$761$	4.74778	−	2.74113i	0.172107	−	0.0993659i	−0.411472	−	0.911422i	$-0.634985\pi$
$761$	4.74778	−	2.74113i	0.172107	−	0.0993659i	0.583579	+	0.812056i	$0.301652\pi$
$762$	0.0668196	−	1.69511i	0.00242062	−	0.0614075i
$763$	−0.809511	+	0.216908i	−0.0293063	+	0.00785259i
$764$	7.59046			0.274613
$765$		0			0
$766$	−5.32045			−0.192236
$767$	−7.15808	+	1.91800i	−0.258463	+	0.0692550i
$768$	19.1997	+	12.1176i	0.692810	+	0.437255i
$769$	−7.13004	+	4.11653i	−0.257116	+	0.148446i	−0.623018	−	0.782207i	$-0.714094\pi$
$769$	−7.13004	+	4.11653i	−0.257116	+	0.148446i	0.365902	+	0.930653i	$0.380760\pi$
$770$		0			0
$771$	6.53080	+	28.8792i	0.235201	+	1.04006i
$772$	8.72533	+	32.5634i	0.314031	+	1.17198i
$773$	14.0889	−	14.0889i	0.506743	−	0.506743i	−0.406782	−	0.913525i	$-0.633349\pi$
$773$	14.0889	−	14.0889i	0.506743	−	0.506743i	0.913525	+	0.406782i	$0.133349\pi$
$774$	−0.233441	+	2.95643i	−0.00839088	+	0.106267i
$775$		0			0
$776$	0.970598	+	0.560375i	0.0348424	+	0.0201163i
$777$	1.02773	+	0.0405119i	0.0368695	+	0.00145336i
$778$	−0.669891	+	2.50007i	−0.0240168	+	0.0896318i
$779$	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
$783$	−26.6820	−	19.9404i	−0.953536	−	0.712612i
$784$		−	3.91879i		−	0.139957i
$785$		0			0
$786$	1.66097	−	5.34676i	0.0592448	−	0.190713i
$787$	−19.4505	−	5.21175i	−0.693336	−	0.185779i	−0.105092	−	0.994462i	$-0.533514\pi$
$787$	−19.4505	−	5.21175i	−0.693336	−	0.185779i	−0.588244	+	0.808684i	$0.700180\pi$
$788$	−29.5975	−	7.93062i	−1.05437	−	0.282516i
$789$	12.5884	+	13.6215i	0.448158	+	0.484940i
$790$		0			0
$791$			13.1268i			0.466735i
$792$	−1.89560	+	5.34863i	−0.0673571	+	0.190055i
$793$	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
$797$	−11.4576	+	42.7605i	−0.405850	+	1.51465i	0.396632	+	0.917978i	$0.370179\pi$
$797$	−11.4576	+	42.7605i	−0.405850	+	1.51465i	−0.802483	+	0.596676i	$0.796488\pi$
$798$	−1.86626	+	2.95700i	−0.0660650	+	0.104677i
$799$	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
$803$	6.24176	+	23.2946i	0.220267	+	0.822047i
$804$	−4.27784	+	3.95338i	−0.150868	+	0.139425i
$805$		0			0
$806$	1.07384	−	0.619983i	0.0378245	−	0.0218380i
$807$	−24.3624	+	12.8137i	−0.857597	+	0.451063i
$808$	13.0870	−	3.50665i	0.460399	−	0.123364i
$809$	35.4591			1.24667			0.623337	−	0.781953i	$-0.285777\pi$
$809$	35.4591			1.24667			0.623337	+	0.781953i	$0.285777\pi$
$810$		0			0
$811$	−9.68119			−0.339952			−0.169976	−	0.985448i	$-0.554369\pi$
$811$	−9.68119			−0.339952			−0.169976	+	0.985448i	$0.554369\pi$
$812$	−29.6785	+	7.95233i	−1.04151	+	0.279072i
$813$	−1.49340	+	0.785469i	−0.0523757	+	0.0275476i
$814$	0.100524	−	0.0580373i	0.00352335	−	0.00203421i
$815$		0			0
$816$	2.74562	−	2.53737i	0.0961158	−	0.0888256i
$817$	−5.68970	−	21.2343i	−0.199058	−	0.742893i
$818$	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	0.733510	−	0.679679i	$-0.237881\pi$
$821$	14.6602	+	8.46408i	0.511645	+	0.295398i	−0.221865	+	0.975077i	$0.571214\pi$
$822$	1.13988	−	1.80609i	0.0397579	−	0.0629945i
$823$	−9.19340	+	34.3102i	−0.320462	+	1.19598i	0.598334	+	0.801247i	$0.295830\pi$
$823$	−9.19340	+	34.3102i	−0.320462	+	1.19598i	−0.918796	+	0.394733i	$0.870837\pi$
$824$	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	$0.0314549\pi$
$827$	31.4545	+	31.4545i	1.09378	+	1.09378i	0.0986577	+	0.995121i	$0.468545\pi$
$828$	13.8963	−	39.2100i	0.482931	−	1.36264i
$829$			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
$832$	11.2167	+	3.00551i	0.388870	+	0.104197i
$833$	−0.572320	−	0.153353i	−0.0198297	−	0.00531335i
$834$	1.04041	−	3.34913i	0.0360263	−	0.115971i
$835$		0			0
$836$		−	20.8347i		−	0.720584i
$837$	18.8319	−	8.08223i	0.650926	−	0.279363i
$838$	−1.16233	−	1.16233i	−0.0401521	−	0.0401521i
$839$	−12.8988	+	22.3413i	−0.445315	+	0.771308i	−0.998074	−	0.0620331i	$-0.980242\pi$
$839$	−12.8988	+	22.3413i	−0.445315	+	0.771308i	0.552759	+	0.833341i	$0.313575\pi$
$840$		0			0
$841$	−6.04717	−	10.4740i	−0.208523	−	0.361173i
$842$	−0.110116	+	0.410960i	−0.00379486	+	0.0141626i
$843$	47.8112	+	1.88467i	1.64670	+	0.0649113i
$844$	−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
$848$	−8.46415	−	31.5886i	−0.290660	−	1.08476i
$849$	−6.50766	−	28.7769i	−0.223342	−	0.987622i
$850$		0			0
$851$	−1.48780	+	0.858984i	−0.0510013	+	0.0294456i
$852$	−10.0792	−	6.36133i	−0.345309	−	0.217936i
$853$	13.7160	−	3.67518i	0.469626	−	0.125836i	−0.0162423	−	0.999868i	$-0.505170\pi$
$853$	13.7160	−	3.67518i	0.469626	−	0.125836i	0.485868	+	0.874032i	$0.338504\pi$
$854$	−0.222037			−0.00759796
$855$		0			0
$856$	−11.3019			−0.386289
$857$	48.2115	−	12.9182i	1.64687	−	0.441278i	0.688137	−	0.725581i	$-0.258429\pi$
$857$	48.2115	−	12.9182i	1.64687	−	0.441278i	0.958735	+	0.284303i	$0.0917620\pi$
$858$	−0.0530991	+	1.34705i	−0.00181277	+	0.0459874i
$859$	35.6374	−	20.5752i	1.21593	−	0.702018i	0.251886	−	0.967757i	$-0.418949\pi$
$859$	35.6374	−	20.5752i	1.21593	−	0.702018i	0.964045	+	0.265739i	$0.0856158\pi$
$860$		0			0
$861$	−30.4255	−	9.45165i	−1.03690	−	0.322112i
$862$	−0.0976806	−	0.364549i	−0.00332701	−	0.0124166i
$863$	−20.5637	+	20.5637i	−0.699996	+	0.699996i	−0.964410	−	0.264413i	$-0.914822\pi$
$863$	−20.5637	+	20.5637i	−0.699996	+	0.699996i	0.264413	+	0.964410i	$0.414822\pi$
$864$	−10.8896	−	4.34937i	−0.370471	−	0.147969i
$865$		0			0
$866$	−2.29452	−	1.32474i	−0.0779711	−	0.0450166i
$867$	13.4435	+	25.5598i	0.456564	+	0.868057i
$868$	4.89246	−	18.2589i	0.166061	−	0.619748i
$869$	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
$873$	4.14759	+	1.46994i	0.140375	+	0.0497499i
$874$		−	5.84059i		−	0.197561i
$875$		0			0
$876$	−32.3035	+	7.30516i	−1.09143	+	0.246819i
$877$	−48.3556	−	12.9568i	−1.63285	−	0.437521i	−0.678111	−	0.734959i	$-0.737201\pi$
$877$	−48.3556	−	12.9568i	−1.63285	−	0.437521i	−0.954741	+	0.297438i	$0.903868\pi$
$878$	1.00647	+	0.269684i	0.0339669	+	0.00910140i
$879$	45.0480	−	10.1872i	1.51943	−	0.343607i
$880$		0			0
$881$			25.4215i			0.856471i	0.903667	+	0.428235i	$0.140865\pi$
$881$			25.4215i			0.856471i	−0.903667	+	0.428235i	$0.859135\pi$
$882$	0.109179	+	0.589925i	0.00367626	+	0.0198638i
$883$	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
$887$	−5.34114	+	19.9334i	−0.179338	+	0.669298i	0.816434	+	0.577439i	$0.195948\pi$
$887$	−5.34114	+	19.9334i	−0.179338	+	0.669298i	−0.995772	+	0.0918595i	$0.970719\pi$
$888$	0.149813	+	0.284837i	0.00502740	+	0.00955850i
$889$	−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
$893$	3.34827	+	12.4959i	0.112046	+	0.418160i
$894$	−3.16746	−	0.983971i	−0.105936	−	0.0329089i
$895$		0			0
$896$	−12.4484	+	7.18706i	−0.415870	+	0.240103i
$897$	0.785896	−	19.9370i	0.0262403	−	0.665677i
$898$	−4.44266	+	1.19041i	−0.148253	+	0.0397244i
$899$	25.2822			0.843209
$900$		0			0
$901$	−4.94459			−0.164728
$902$	−3.47303	+	0.930596i	−0.115639	+	0.0309855i
$903$	18.3376	+	11.5734i	0.610236	+	0.385140i
$904$	−3.55717	+	2.05373i	−0.118310	+	0.0683061i
$905$		0			0
$906$	1.02529	+	4.53386i	0.0340631	+	0.150627i
$907$	10.1886	+	38.0242i	0.338305	+	1.26257i	0.900241	+	0.435392i	$0.143390\pi$
$907$	10.1886	+	38.0242i	0.338305	+	1.26257i	−0.561935	+	0.827181i	$0.689943\pi$
$908$	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	−0.415122	−	0.909766i	$-0.636261\pi$
$911$	−42.5747	−	24.5805i	−1.41056	−	0.814389i	−0.995441	+	0.0953768i	$0.969594\pi$
$912$	28.0386	+	1.10525i	0.928450	+	0.0365985i
$913$	7.07501	−	26.4043i	0.234149	−	0.873854i
$914$	−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
$918$	−0.342627	+	0.458464i	−0.0113084	+	0.0151316i
$919$		−	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
$922$	0.245960	+	0.0659049i	0.00810028	+	0.00217046i
$923$	−5.52184	−	1.47957i	−0.181753	−	0.0487007i
$924$	13.9483	+	15.0931i	0.458867	+	0.496527i
$925$		0			0
$926$		−	2.97080i		−	0.0976265i
$927$	20.6449	+	24.1846i	0.678066	+	0.794327i
$928$	−10.2293	−	10.2293i	−0.335793	−	0.335793i
$929$	−1.96179	+	3.39791i	−0.0643641	+	0.111482i	−0.896412	−	0.443222i	$-0.853835\pi$
$929$	−1.96179	+	3.39791i	−0.0643641	+	0.111482i	0.832048	+	0.554704i	$0.187169\pi$
$930$		0			0
$931$	−2.22360	−	3.85139i	−0.0728755	−	0.126224i
$932$	−2.14500	+	8.00525i	−0.0702618	+	0.262221i
$933$	−7.99761	+	12.6718i	−0.261830	+	0.414857i
$934$	−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	$0.0199305\pi$
$938$	−0.208787	−	0.779203i	−0.00681713	−	0.0254419i
$939$	−23.8484	+	22.0396i	−0.778264	+	0.719234i
$940$		0			0
$941$	−50.0184	+	28.8781i	−1.63055	+	0.941400i	−0.646630	+	0.762804i	$0.723822\pi$
$941$	−50.0184	+	28.8781i	−1.63055	+	0.941400i	−0.983922	+	0.178596i	$0.942844\pi$
$942$	6.19233	−	3.25693i	0.201757	−	0.106116i
$943$	51.4028	−	13.7733i	1.67390	−	0.448521i
$944$	−17.1713			−0.558877
$945$		0			0
$946$	2.44720			0.0795653
$947$	−8.02351	+	2.14989i	−0.260729	+	0.0698622i	−0.386816	−	0.922157i	$-0.626425\pi$
$947$	−8.02351	+	2.14989i	−0.260729	+	0.0698622i	0.126086	+	0.992019i	$0.459758\pi$
$948$	−22.5890	+	11.8809i	−0.733657	+	0.385875i
$949$	−13.7568	+	7.94250i	−0.446565	+	0.257824i
$950$		0			0
$951$	24.6813	−	22.8092i	0.800345	−	0.739640i
$952$	0.275870	+	1.02956i	0.00894101	+	0.0333683i
$953$	27.2237	−	27.2237i	0.881861	−	0.881861i	−0.111862	−	0.993724i	$-0.535682\pi$
$953$	27.2237	−	27.2237i	0.881861	−	0.881861i	0.993724	+	0.111862i	$0.0356816\pi$
$954$	2.15425	+	4.51947i	0.0697463	+	0.146323i
$955$		0			0
$956$	−8.82018	−	5.09233i	−0.285265	−	0.164698i
$957$	−14.6704	+	23.2445i	−0.474225	+	0.751388i
$958$	−1.89541	+	7.07375i	−0.0612378	+	0.228543i
$959$	−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
$963$	−43.6332	+	8.07532i	−1.40606	+	0.260224i
$964$			7.29666i			0.235010i
$965$		0			0
$966$	3.91014	+	4.23105i	0.125807	+	0.136132i
$967$	45.5627	+	12.2085i	1.46520	+	0.392598i	0.901282	−	0.433234i	$-0.142628\pi$
$967$	45.5627	+	12.2085i	1.46520	+	0.392598i	0.563916	+	0.825832i	$0.309294\pi$
$968$	−3.59549	−	0.963408i	−0.115563	−	0.0309651i
$969$	1.25864	−	4.05164i	0.0404334	−	0.130158i
$970$		0			0
$971$		−	20.4752i		−	0.657080i	−0.944490	−	0.328540i	$-0.893443\pi$
$971$		−	20.4752i		−	0.657080i	0.944490	−	0.328540i	$-0.106557\pi$
$972$	−30.0056	−	5.98855i	−0.962431	−	0.192083i
$973$	−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
$977$	−9.36214	+	34.9400i	−0.299521	+	1.11783i	0.638038	+	0.770005i	$0.279746\pi$
$977$	−9.36214	+	34.9400i	−0.299521	+	1.11783i	−0.937560	+	0.347824i	$0.886921\pi$
$978$	1.14618	+	0.0451812i	0.0366508	+	0.00144474i
$979$	−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
$983$	−5.10700	−	19.0596i	−0.162888	−	0.607906i	−0.998300	−	0.0582820i	$-0.981438\pi$
$983$	−5.10700	−	19.0596i	−0.162888	−	0.607906i	0.835412	−	0.549624i	$-0.185229\pi$
$984$	−2.19891	−	9.72360i	−0.0700987	−	0.309977i
$985$		0			0
$986$	−0.611505	+	0.353052i	−0.0194743	+	0.0112435i
$987$	−10.7913	−	6.81073i	−0.343490	−	0.216788i
$988$	13.2559	−	3.55190i	0.421725	−	0.113001i
$989$	−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	$0.180636\pi$
$992$	8.59681	−	2.30351i	0.272949	−	0.0731364i
$993$	−2.34643	+	59.5255i	−0.0744618	+	1.88899i
$994$	1.42950	−	0.825320i	0.0453409	−	0.0261776i
$995$		0			0
$996$	35.8504	+	11.1369i	1.13596	+	0.352887i
$997$	−9.82689	−	36.6745i	−0.311221	−	1.16149i	−0.927457	−	0.373930i	$-0.878010\pi$
$997$	−9.82689	−	36.6745i	−0.311221	−	1.16149i	0.616236	−	0.787562i	$-0.288657\pi$
$998$	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.218.2		16
3.2	odd	2		675.2.q.a.143.3		16
5.2	odd	4	inner	225.2.p.b.182.2		16
5.3	odd	4		45.2.l.a.2.3	✓	16
5.4	even	2		45.2.l.a.38.3	yes	16
9.4	even	3		675.2.q.a.368.3		16
9.5	odd	6	inner	225.2.p.b.68.2		16
15.2	even	4		675.2.q.a.332.3		16
15.8	even	4		135.2.m.a.62.2		16
15.14	odd	2		135.2.m.a.8.2		16
20.3	even	4		720.2.cu.c.497.2		16
20.19	odd	2		720.2.cu.c.353.1		16
45.4	even	6		135.2.m.a.98.2		16
45.13	odd	12		135.2.m.a.17.2		16
45.14	odd	6		45.2.l.a.23.3	yes	16
45.22	odd	12		675.2.q.a.557.3		16
45.23	even	12		45.2.l.a.32.3	yes	16
45.29	odd	6		405.2.f.a.323.5		16
45.32	even	12	inner	225.2.p.b.32.2		16
45.34	even	6		405.2.f.a.323.4		16
45.38	even	12		405.2.f.a.242.4		16
45.43	odd	12		405.2.f.a.242.5		16
180.23	odd	12		720.2.cu.c.257.1		16
180.59	even	6		720.2.cu.c.113.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.l.a.2.3	✓	16	5.3	odd	4
45.2.l.a.23.3	yes	16	45.14	odd	6
45.2.l.a.32.3	yes	16	45.23	even	12
45.2.l.a.38.3	yes	16	5.4	even	2
135.2.m.a.8.2		16	15.14	odd	2
135.2.m.a.17.2		16	45.13	odd	12
135.2.m.a.62.2		16	15.8	even	4
135.2.m.a.98.2		16	45.4	even	6
225.2.p.b.32.2		16	45.32	even	12	inner
225.2.p.b.68.2		16	9.5	odd	6	inner
225.2.p.b.182.2		16	5.2	odd	4	inner
225.2.p.b.218.2		16	1.1	even	1	trivial
405.2.f.a.242.4		16	45.38	even	12
405.2.f.a.242.5		16	45.43	odd	12
405.2.f.a.323.4		16	45.34	even	6
405.2.f.a.323.5		16	45.29	odd	6
675.2.q.a.143.3		16	3.2	odd	2
675.2.q.a.332.3		16	15.2	even	4
675.2.q.a.368.3		16	9.4	even	3
675.2.q.a.557.3		16	45.22	odd	12
720.2.cu.c.113.2		16	180.59	even	6
720.2.cu.c.257.1		16	180.23	odd	12
720.2.cu.c.353.1		16	20.19	odd	2
720.2.cu.c.497.2		16	20.3	even	4

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)

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