LMFDB - Embedded newform 450.2.l.d.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(19,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("450.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.l (of order $10$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
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} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 $ x^16 + x^14 - 4x^12 - 49x^10 + 11x^8 + 395x^6 + 900x^4 + 1125x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.1
Root			$1.86824 - 0.357358i$ of defining polynomial
Character	$\chi$	$=$	450.19
Dual form			450.2.l.d.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-1.95894 - 1.07822i) q^{5} +3.03582i q^{7} +(-0.587785 + 0.809017i) q^{8} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-1.95894 - 1.07822i) q^{5} +3.03582i q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.19625 + 0.420099i) q^{10} +(-0.791366 - 2.43557i) q^{11} +(-0.945515 - 0.307217i) q^{13} +(-0.938119 - 2.88723i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.558856 - 0.769200i) q^{17} +(-5.39250 - 3.91788i) q^{19} +(-2.21858 + 0.279141i) q^{20} +(1.50527 + 2.07182i) q^{22} +(-5.81999 + 1.89103i) q^{23} +(2.67490 + 4.22433i) q^{25} +0.994174 q^{26} +(1.78441 + 2.45603i) q^{28} +(-7.82205 + 5.68305i) q^{29} +(-5.65556 - 4.10900i) q^{31} +1.00000i q^{32} +(-0.293808 + 0.904248i) q^{34} +(3.27327 - 5.94699i) q^{35} +(-2.94226 - 0.955998i) q^{37} +(6.33927 + 2.05975i) q^{38} +(2.02373 - 0.951057i) q^{40} +(-0.167686 + 0.516085i) q^{41} -3.08173i q^{43} +(-2.07182 - 1.50527i) q^{44} +(4.95078 - 3.59695i) q^{46} +(1.62460 + 2.23607i) q^{47} -2.21619 q^{49} +(-3.84937 - 3.19098i) q^{50} +(-0.945515 + 0.307217i) q^{52} +(-1.08362 - 1.49148i) q^{53} +(-1.07584 + 5.62441i) q^{55} +(-2.45603 - 1.78441i) q^{56} +(5.68305 - 7.82205i) q^{58} +(0.998638 - 3.07349i) q^{59} +(-3.68305 - 11.3353i) q^{61} +(6.64851 + 2.16023i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(1.52096 + 1.62129i) q^{65} +(-7.32046 + 10.0758i) q^{67} -0.950783i q^{68} +(-1.27534 + 6.66742i) q^{70} +(8.64854 - 6.28353i) q^{71} +(13.7780 - 4.47674i) q^{73} +3.09368 q^{74} -6.66550 q^{76} +(7.39396 - 2.40244i) q^{77} +(-12.3272 + 8.95623i) q^{79} +(-1.63079 + 1.52988i) q^{80} -0.542644i q^{82} +(-5.22672 + 7.19396i) q^{83} +(-1.92413 + 0.904248i) q^{85} +(0.952307 + 2.93090i) q^{86} +(2.43557 + 0.791366i) q^{88} +(2.76450 + 8.50824i) q^{89} +(0.932653 - 2.87041i) q^{91} +(-3.59695 + 4.95078i) q^{92} +(-2.23607 - 1.62460i) q^{94} +(6.33927 + 13.4892i) q^{95} +(-0.835952 - 1.15059i) q^{97} +(2.10772 - 0.684839i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4}+O(q^{10}) $ 16 * q + 4 * q^4	$ 16 q + 4 q^{4} - 4 q^{16} - 16 q^{19} - 20 q^{22} + 20 q^{25} - 10 q^{28} + 6 q^{31} - 26 q^{34} + 10 q^{37} + 20 q^{46} + 28 q^{49} - 20 q^{55} + 32 q^{61} + 4 q^{64} - 40 q^{67} - 30 q^{70} - 24 q^{76} - 36 q^{79} - 70 q^{85} + 10 q^{88} + 52 q^{91} - 70 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 - 4 * q^16 - 16 * q^19 - 20 * q^22 + 20 * q^25 - 10 * q^28 + 6 * q^31 - 26 * q^34 + 10 * q^37 + 20 * q^46 + 28 * q^49 - 20 * q^55 + 32 * q^61 + 4 * q^64 - 40 * q^67 - 30 * q^70 - 24 * q^76 - 36 * q^79 - 70 * q^85 + 10 * q^88 + 52 * q^91 - 70 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−1.95894	−	1.07822i	−0.876065	−	0.482193i
$5$	−1.95894	−	1.07822i	−0.876065	−	0.482193i
$6$		0			0
$7$			3.03582i			1.14743i	0.819055	+	0.573716i	$0.194498\pi$
$7$			3.03582i			1.14743i	−0.819055	+	0.573716i	$0.805502\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$		0			0
$10$	2.19625	+	0.420099i	0.694515	+	0.132847i
$11$	−0.791366	−	2.43557i	−0.238606	−	0.734353i	−0.996623	−	0.0821182i	$-0.973832\pi$
$11$	−0.791366	−	2.43557i	−0.238606	−	0.734353i	0.758017	−	0.652235i	$-0.226168\pi$
$12$		0			0
$13$	−0.945515	−	0.307217i	−0.262239	−	0.0852066i	0.174947	−	0.984578i	$-0.444025\pi$
$13$	−0.945515	−	0.307217i	−0.262239	−	0.0852066i	−0.437186	+	0.899371i	$0.644025\pi$
$14$	−0.938119	−	2.88723i	−0.250723	−	0.771646i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.558856	−	0.769200i	0.135543	−	0.186558i	−0.735850	−	0.677144i	$-0.763217\pi$
$17$	0.558856	−	0.769200i	0.135543	−	0.186558i	0.871393	+	0.490586i	$0.163217\pi$
$18$		0			0
$19$	−5.39250	−	3.91788i	−1.23712	−	0.898824i	−0.239721	−	0.970842i	$-0.577056\pi$
$19$	−5.39250	−	3.91788i	−1.23712	−	0.898824i	−0.997403	+	0.0720181i	$0.977056\pi$
$20$	−2.21858	+	0.279141i	−0.496089	+	0.0624178i
$21$		0			0
$22$	1.50527	+	2.07182i	0.320924	+	0.441714i
$23$	−5.81999	+	1.89103i	−1.21355	+	0.394307i	−0.844730	−	0.535193i	$-0.820239\pi$
$23$	−5.81999	+	1.89103i	−1.21355	+	0.394307i	−0.368823	+	0.929500i	$0.620239\pi$
$24$		0			0
$25$	2.67490	+	4.22433i	0.534980	+	0.844865i
$26$	0.994174			0.194974
$27$		0			0
$28$	1.78441	+	2.45603i	0.337222	+	0.464146i
$29$	−7.82205	+	5.68305i	−1.45252	+	1.05532i	−0.467284	+	0.884107i	$0.654767\pi$
$29$	−7.82205	+	5.68305i	−1.45252	+	1.05532i	−0.985235	+	0.171209i	$0.945233\pi$
$30$		0			0
$31$	−5.65556	−	4.10900i	−1.01577	−	0.737999i	−0.0503570	−	0.998731i	$-0.516036\pi$
$31$	−5.65556	−	4.10900i	−1.01577	−	0.737999i	−0.965411	+	0.260733i	$0.916036\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−0.293808	+	0.904248i	−0.0503877	+	0.155077i
$35$	3.27327	−	5.94699i	0.553283	−	1.00522i
$36$		0			0
$37$	−2.94226	−	0.955998i	−0.483705	−	0.157165i	0.0570060	−	0.998374i	$-0.481845\pi$
$37$	−2.94226	−	0.955998i	−0.483705	−	0.157165i	−0.540711	+	0.841209i	$0.681845\pi$
$38$	6.33927	+	2.05975i	1.02836	+	0.334136i
$39$		0			0
$40$	2.02373	−	0.951057i	0.319980	−	0.150375i
$41$	−0.167686	+	0.516085i	−0.0261882	+	0.0805990i	−0.963296	−	0.268440i	$-0.913492\pi$
$41$	−0.167686	+	0.516085i	−0.0261882	+	0.0805990i	0.937108	+	0.349039i	$0.113492\pi$
$42$		0			0
$43$		−	3.08173i		−	0.469960i	−0.972000	−	0.234980i	$-0.924498\pi$
$43$		−	3.08173i		−	0.469960i	0.972000	−	0.234980i	$-0.0755024\pi$
$44$	−2.07182	−	1.50527i	−0.312339	−	0.226928i
$45$		0			0
$46$	4.95078	−	3.59695i	0.729953	−	0.530342i
$47$	1.62460	+	2.23607i	0.236972	+	0.326164i	0.910895	−	0.412637i	$-0.135392\pi$
$47$	1.62460	+	2.23607i	0.236972	+	0.326164i	−0.673923	+	0.738801i	$0.735392\pi$
$48$		0			0
$49$	−2.21619			−0.316598
$50$	−3.84937	−	3.19098i	−0.544383	−	0.451273i
$51$		0			0
$52$	−0.945515	+	0.307217i	−0.131119	+	0.0426033i
$53$	−1.08362	−	1.49148i	−0.148847	−	0.204870i	0.728082	−	0.685490i	$-0.240412\pi$
$53$	−1.08362	−	1.49148i	−0.148847	−	0.204870i	−0.876929	+	0.480620i	$0.840412\pi$
$54$		0			0
$55$	−1.07584	+	5.62441i	−0.145066	+	0.758395i
$56$	−2.45603	−	1.78441i	−0.328200	−	0.238452i
$57$		0			0
$58$	5.68305	−	7.82205i	0.746222	−	1.02709i
$59$	0.998638	−	3.07349i	0.130012	−	0.400134i	−0.864769	−	0.502169i	$-0.832535\pi$
$59$	0.998638	−	3.07349i	0.130012	−	0.400134i	0.994781	+	0.102035i	$0.0325354\pi$
$60$		0			0
$61$	−3.68305	−	11.3353i	−0.471567	−	1.45133i	−0.850533	−	0.525922i	$-0.823720\pi$
$61$	−3.68305	−	11.3353i	−0.471567	−	1.45133i	0.378966	−	0.925411i	$-0.376280\pi$
$62$	6.64851	+	2.16023i	0.844361	+	0.274350i
$63$		0			0
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	1.52096	+	1.62129i	0.188652	+	0.201096i
$66$		0			0
$67$	−7.32046	+	10.0758i	−0.894337	+	1.23095i	0.0779029	+	0.996961i	$0.475178\pi$
$67$	−7.32046	+	10.0758i	−0.894337	+	1.23095i	−0.972240	+	0.233988i	$0.924822\pi$
$68$		−	0.950783i		−	0.115299i
$69$		0			0
$70$	−1.27534	+	6.66742i	−0.152433	+	0.796909i
$71$	8.64854	−	6.28353i	1.02639	−	0.745718i	0.0588093	−	0.998269i	$-0.481270\pi$
$71$	8.64854	−	6.28353i	1.02639	−	0.745718i	0.967584	+	0.252551i	$0.0812696\pi$
$72$		0			0
$73$	13.7780	−	4.47674i	1.61259	−	0.523963i	0.642413	−	0.766358i	$-0.277933\pi$
$73$	13.7780	−	4.47674i	1.61259	−	0.523963i	0.970177	+	0.242396i	$0.0779332\pi$
$74$	3.09368			0.359632
$75$		0			0
$76$	−6.66550			−0.764585
$77$	7.39396	−	2.40244i	0.842620	−	0.273784i
$78$		0			0
$79$	−12.3272	+	8.95623i	−1.38692	+	1.00766i	−0.390723	+	0.920508i	$0.627775\pi$
$79$	−12.3272	+	8.95623i	−1.38692	+	1.00766i	−0.996195	+	0.0871467i	$0.972225\pi$
$80$	−1.63079	+	1.52988i	−0.182328	+	0.171045i
$81$		0			0
$82$		−	0.542644i		−	0.0599250i
$83$	−5.22672	+	7.19396i	−0.573707	+	0.789639i	−0.992988	−	0.118217i	$-0.962282\pi$
$83$	−5.22672	+	7.19396i	−0.573707	+	0.789639i	0.419281	+	0.907856i	$0.362282\pi$
$84$		0			0
$85$	−1.92413	+	0.904248i	−0.208701	+	0.0980795i
$86$	0.952307	+	2.93090i	0.102690	+	0.316047i
$87$		0			0
$88$	2.43557	+	0.791366i	0.259633	+	0.0843599i
$89$	2.76450	+	8.50824i	0.293036	+	0.901872i	0.983874	+	0.178862i	$0.0572417\pi$
$89$	2.76450	+	8.50824i	0.293036	+	0.901872i	−0.690838	+	0.723009i	$0.742758\pi$
$90$		0			0
$91$	0.932653	−	2.87041i	0.0977686	−	0.300901i
$92$	−3.59695	+	4.95078i	−0.375008	+	0.516155i
$93$		0			0
$94$	−2.23607	−	1.62460i	−0.230633	−	0.167565i
$95$	6.33927	+	13.4892i	0.650395	+	1.38396i
$96$		0			0
$97$	−0.835952	−	1.15059i	−0.0848781	−	0.116825i	0.764466	−	0.644664i	$-0.223003\pi$
$97$	−0.835952	−	1.15059i	−0.0848781	−	0.116825i	−0.849345	+	0.527839i	$0.823003\pi$
$98$	2.10772	−	0.684839i	0.212912	−	0.0691792i
$99$		0			0
$100$	4.64703	+	1.84529i	0.464703	+	0.184529i
$101$	18.3281			1.82372			0.911858	−	0.410506i	$-0.134648\pi$
$101$	18.3281			1.82372			0.911858	+	0.410506i	$0.134648\pi$
$102$		0			0
$103$	6.65080	+	9.15404i	0.655323	+	0.901974i	0.999315	−	0.0369981i	$-0.0117795\pi$
$103$	6.65080	+	9.15404i	0.655323	+	0.901974i	−0.343993	+	0.938972i	$0.611780\pi$
$104$	0.804303	−	0.584361i	0.0788684	−	0.0573013i
$105$		0			0
$106$	1.49148	+	1.08362i	0.144865	+	0.105251i
$107$		−	6.68538i		−	0.646300i	−0.946348	−	0.323150i	$-0.895258\pi$
$107$		−	6.68538i		−	0.646300i	0.946348	−	0.323150i	$-0.104742\pi$
$108$		0			0
$109$	1.44405	−	4.44431i	0.138314	−	0.425688i	−0.857776	−	0.514023i	$-0.828155\pi$
$109$	1.44405	−	4.44431i	0.138314	−	0.425688i	0.996091	+	0.0883350i	$0.0281546\pi$
$110$	−0.714856	−	5.68158i	−0.0681588	−	0.541718i
$111$		0			0
$112$	2.88723	+	0.938119i	0.272818	+	0.0886439i
$113$	13.6062	+	4.42091i	1.27996	+	0.415884i	0.868566	−	0.495574i	$-0.165042\pi$
$113$	13.6062	+	4.42091i	1.27996	+	0.415884i	0.411393	+	0.911458i	$0.365042\pi$
$114$		0			0
$115$	13.4400	+	2.57080i	1.25328	+	0.239728i
$116$	−2.98776	+	9.19537i	−0.277406	+	0.853769i
$117$		0			0
$118$			3.23166i			0.297498i
$119$	2.33515	+	1.69659i	0.214063	+	0.155526i
$120$		0			0
$121$	3.59343	−	2.61078i	0.326675	−	0.237343i
$122$	7.00558	+	9.64236i	0.634256	+	0.872978i
$123$		0			0
$124$	−6.99065			−0.627779
$125$	−0.685229	−	11.1593i	−0.0612887	−	0.998120i
$126$		0			0
$127$	−5.10107	+	1.65744i	−0.452647	+	0.147074i	−0.526463	−	0.850198i	$-0.676482\pi$
$127$	−5.10107	+	1.65744i	−0.452647	+	0.147074i	0.0738162	+	0.997272i	$0.476482\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$		0			0
$130$	−1.94753	−	1.07193i	−0.170809	−	0.0940149i
$131$	−4.32100	−	3.13939i	−0.377527	−	0.274290i	0.382798	−	0.923832i	$-0.374960\pi$
$131$	−4.32100	−	3.13939i	−0.377527	−	0.274290i	−0.760325	+	0.649542i	$0.774960\pi$
$132$		0			0
$133$	11.8940	−	16.3706i	1.03134	−	1.41952i
$134$	3.84859	−	11.8448i	0.332468	−	1.02323i
$135$		0			0
$136$	0.293808	+	0.904248i	0.0251938	+	0.0775387i
$137$	−16.8199	−	5.46512i	−1.43702	−	0.466916i	−0.516053	−	0.856556i	$-0.672599\pi$
$137$	−16.8199	−	5.46512i	−1.43702	−	0.466916i	−0.920967	+	0.389640i	$0.872599\pi$
$138$		0			0
$139$	−0.314619	−	0.968299i	−0.0266857	−	0.0821300i	0.936827	−	0.349794i	$-0.113748\pi$
$139$	−0.314619	−	0.968299i	−0.0266857	−	0.0821300i	−0.963512	+	0.267664i	$0.913748\pi$
$140$	−0.847421	−	6.73519i	−0.0716201	−	0.569228i
$141$		0			0
$142$	−6.28353	+	8.64854i	−0.527302	+	0.725769i
$143$			2.54599i			0.212907i
$144$		0			0
$145$	21.4505	−	2.69890i	1.78137	−	0.224131i
$146$	−11.7203	+	8.51526i	−0.969975	+	0.704728i
$147$		0			0
$148$	−2.94226	+	0.955998i	−0.241852	+	0.0785826i
$149$	0.424699			0.0347927			0.0173964	−	0.999849i	$-0.494462\pi$
$149$	0.424699			0.0347927			0.0173964	+	0.999849i	$0.494462\pi$
$150$		0			0
$151$	10.7386			0.873897			0.436948	−	0.899487i	$-0.356059\pi$
$151$	10.7386			0.873897			0.436948	+	0.899487i	$0.356059\pi$
$152$	6.33927	−	2.05975i	0.514182	−	0.167068i
$153$		0			0
$154$	−6.28968	+	4.56972i	−0.506837	+	0.368238i
$155$	6.64851	+	14.1472i	0.534021	+	1.13633i
$156$		0			0
$157$			23.5242i			1.87744i	0.344683	+	0.938719i	$0.387986\pi$
$157$			23.5242i			1.87744i	−0.344683	+	0.938719i	$0.612014\pi$
$158$	8.95623	−	12.3272i	0.712520	−	0.980699i
$159$		0			0
$160$	1.07822	−	1.95894i	0.0852405	−	0.154868i
$161$	−5.74082	−	17.6684i	−0.452440	−	1.39247i
$162$		0			0
$163$	−7.01988	−	2.28090i	−0.549840	−	0.178654i	0.0209048	−	0.999781i	$-0.493345\pi$
$163$	−7.01988	−	2.28090i	−0.549840	−	0.178654i	−0.570744	+	0.821128i	$0.693345\pi$
$164$	0.167686	+	0.516085i	0.0130941	+	0.0402995i
$165$		0			0
$166$	2.74785	−	8.45700i	0.213274	−	0.656391i
$167$	−0.492440	+	0.677786i	−0.0381062	+	0.0524487i	−0.827645	−	0.561252i	$-0.810320\pi$
$167$	−0.492440	+	0.677786i	−0.0381062	+	0.0524487i	0.789539	+	0.613701i	$0.210320\pi$
$168$		0			0
$169$	−9.71760	−	7.06025i	−0.747508	−	0.543096i
$170$	1.55053	−	1.45458i	0.118920	−	0.111561i
$171$		0			0
$172$	−1.81140	−	2.49317i	−0.138118	−	0.190103i
$173$	−17.9180	+	5.82190i	−1.36228	+	0.442631i	−0.896803	−	0.442430i	$-0.854116\pi$
$173$	−17.9180	+	5.82190i	−1.36228	+	0.442631i	−0.465475	+	0.885061i	$0.654116\pi$
$174$		0			0
$175$	−12.8243	+	8.12050i	−0.969424	+	0.613852i
$176$	−2.56091			−0.193036
$177$		0			0
$178$	−5.25838	−	7.23754i	−0.394132	−	0.542477i
$179$	0.721821	−	0.524434i	0.0539515	−	0.0391980i	−0.560483	−	0.828166i	$-0.689384\pi$
$179$	0.721821	−	0.524434i	0.0539515	−	0.0391980i	0.614434	+	0.788968i	$0.289384\pi$
$180$		0			0
$181$	1.77973	+	1.29305i	0.132287	+	0.0961119i	0.651961	−	0.758253i	$-0.273947\pi$
$181$	1.77973	+	1.29305i	0.132287	+	0.0961119i	−0.519674	+	0.854365i	$0.673947\pi$
$182$			3.01813i			0.223719i
$183$		0			0
$184$	1.89103	−	5.81999i	0.139409	−	0.429056i
$185$	4.73294	+	5.04514i	0.347973	+	0.370926i
$186$		0			0
$187$	−2.31570	−	0.752417i	−0.169341	−	0.0550222i
$188$	2.62866	+	0.854102i	0.191714	+	0.0622918i
$189$		0			0
$190$	−10.1974	−	10.8700i	−0.739796	−	0.788595i
$191$	−6.72639	+	20.7017i	−0.486704	+	1.49792i	0.342793	+	0.939411i	$0.388627\pi$
$191$	−6.72639	+	20.7017i	−0.486704	+	1.49792i	−0.829497	+	0.558511i	$0.811373\pi$
$192$		0			0
$193$			3.52671i			0.253858i	0.991912	+	0.126929i	$0.0405121\pi$
$193$			3.52671i			0.253858i	−0.991912	+	0.126929i	$0.959488\pi$
$194$	1.15059	+	0.835952i	0.0826075	+	0.0600179i
$195$		0			0
$196$	−1.79293	+	1.30264i	−0.128067	+	0.0930458i
$197$	−10.4672	−	14.4069i	−0.745758	−	1.02645i	−0.998267	−	0.0588534i	$-0.981256\pi$
$197$	−10.4672	−	14.4069i	−0.745758	−	1.02645i	0.252508	−	0.967595i	$-0.418744\pi$
$198$		0			0
$199$	−2.93741			−0.208228			−0.104114	−	0.994565i	$-0.533201\pi$
$199$	−2.93741			−0.208228			−0.104114	+	0.994565i	$0.533201\pi$
$200$	−4.98982	−	0.318958i	−0.352833	−	0.0225538i
$201$		0			0
$202$	−17.4311	+	5.66370i	−1.22645	+	0.398497i
$203$	−17.2527	−	23.7463i	−1.21090	−	1.66666i
$204$		0			0
$205$	0.884939	−	0.830178i	0.0618068	−	0.0579822i
$206$	−9.15404	−	6.65080i	−0.637792	−	0.463383i
$207$		0			0
$208$	−0.584361	+	0.804303i	−0.0405181	+	0.0557684i
$209$	−5.27485	+	16.2343i	−0.364869	+	1.12295i
$210$		0			0
$211$	−0.332749	−	1.02410i	−0.0229074	−	0.0705017i	0.938949	−	0.344056i	$-0.111801\pi$
$211$	−0.332749	−	1.02410i	−0.0229074	−	0.0705017i	−0.961857	+	0.273554i	$0.911801\pi$
$212$	−1.75334	−	0.569693i	−0.120420	−	0.0391267i
$213$		0			0
$214$	2.06590	+	6.35817i	0.141222	+	0.434636i
$215$	−3.32277	+	6.03693i	−0.226611	+	0.411715i
$216$		0			0
$217$	12.4742	−	17.1692i	0.846803	−	1.16552i
$218$			4.67303i			0.316497i
$219$		0			0
$220$	2.43557	+	5.18260i	0.164206	+	0.349411i
$221$	−0.764718	+	0.555600i	−0.0514405	+	0.0373737i
$222$		0			0
$223$	−6.53226	+	2.12246i	−0.437432	+	0.142130i	−0.519451	−	0.854500i	$-0.673863\pi$
$223$	−6.53226	+	2.12246i	−0.437432	+	0.142130i	0.0820184	+	0.996631i	$0.473863\pi$
$224$	−3.03582			−0.202839
$225$		0			0
$226$	−14.3064			−0.951645
$227$	−15.7573	+	5.11987i	−1.04585	+	0.339818i	−0.781039	−	0.624482i	$-0.785310\pi$
$227$	−15.7573	+	5.11987i	−1.04585	+	0.339818i	−0.264813	+	0.964300i	$0.585310\pi$
$228$		0			0
$229$	6.06125	−	4.40376i	0.400539	−	0.291009i	−0.369221	−	0.929341i	$-0.620376\pi$
$229$	6.06125	−	4.40376i	0.400539	−	0.291009i	0.769761	+	0.638333i	$0.220376\pi$
$230$	−13.5766	+	1.70820i	−0.895214	+	0.112636i
$231$		0			0
$232$		−	9.66859i		−	0.634774i
$233$	14.1650	−	19.4965i	0.927981	−	1.27726i	−0.0326615	−	0.999466i	$-0.510398\pi$
$233$	14.1650	−	19.4965i	0.927981	−	1.27726i	0.960642	−	0.277789i	$-0.0896017\pi$
$234$		0			0
$235$	−0.771526	−	6.13199i	−0.0503288	−	0.400007i
$236$	−0.998638	−	3.07349i	−0.0650058	−	0.200067i
$237$		0			0
$238$	−2.74513	−	0.891948i	−0.177941	−	0.0578164i
$239$	−5.22310	−	16.0750i	−0.337854	−	1.03981i	−0.965299	−	0.261147i	$-0.915899\pi$
$239$	−5.22310	−	16.0750i	−0.337854	−	1.03981i	0.627445	−	0.778661i	$-0.284101\pi$
$240$		0			0
$241$	4.12129	−	12.6840i	0.265476	−	0.817050i	−0.726108	−	0.687581i	$-0.758673\pi$
$241$	4.12129	−	12.6840i	0.265476	−	0.817050i	0.991583	−	0.129469i	$-0.0413273\pi$
$242$	−2.61078	+	3.59343i	−0.167827	+	0.230994i
$243$		0			0
$244$	−9.64236	−	7.00558i	−0.617289	−	0.448487i
$245$	4.34138	+	2.38953i	0.277360	+	0.152661i
$246$		0			0
$247$	3.89505	+	5.36108i	0.247836	+	0.341118i
$248$	6.64851	−	2.16023i	0.422181	−	0.137175i
$249$		0			0
$250$	4.10011	+	10.4014i	0.259314	+	0.657842i
$251$	18.2527			1.15210			0.576051	−	0.817414i	$-0.304593\pi$
$251$	18.2527			1.15210			0.576051	+	0.817414i	$0.304593\pi$
$252$		0			0
$253$	9.21149	+	12.6785i	0.579122	+	0.797092i
$254$	4.33923	−	3.15264i	0.272268	−	0.197814i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$		−	9.85778i		−	0.614911i	−0.951562	−	0.307456i	$-0.900522\pi$
$257$		−	9.85778i		−	0.614911i	0.951562	−	0.307456i	$-0.0994776\pi$
$258$		0			0
$259$	2.90224	−	8.93216i	0.180336	−	0.555018i
$260$	2.18345	+	0.417651i	0.135412	+	0.0259016i
$261$		0			0
$262$	5.07963	+	1.65047i	0.313821	+	0.101967i
$263$	−22.4833	−	7.30527i	−1.38638	−	0.450462i	−0.481619	−	0.876381i	$-0.659951\pi$
$263$	−22.4833	−	7.30527i	−1.38638	−	0.450462i	−0.904762	+	0.425918i	$0.859951\pi$
$264$		0			0
$265$	0.514615	+	4.09009i	0.0316125	+	0.251252i
$266$	−6.25303	+	19.2449i	−0.383398	+	1.17998i
$267$		0			0
$268$			12.4543i			0.760768i
$269$	15.8133	+	11.4890i	0.964152	+	0.700497i	0.954111	−	0.299452i	$-0.0968040\pi$
$269$	15.8133	+	11.4890i	0.964152	+	0.700497i	0.0100404	+	0.999950i	$0.496804\pi$
$270$		0			0
$271$	−21.9619	+	15.9563i	−1.33409	+	0.969274i	−0.334452	+	0.942413i	$0.608551\pi$
$271$	−21.9619	+	15.9563i	−1.33409	+	0.969274i	−0.999639	+	0.0268612i	$0.991449\pi$
$272$	−0.558856	−	0.769200i	−0.0338856	−	0.0466396i
$273$		0			0
$274$	17.6855			1.06842
$275$	8.17183	−	9.85790i	0.492780	−	0.594454i
$276$		0			0
$277$	16.9101	−	5.49442i	1.01603	−	0.330128i	0.246776	−	0.969073i	$-0.420629\pi$
$277$	16.9101	−	5.49442i	1.01603	−	0.330128i	0.769253	+	0.638945i	$0.220629\pi$
$278$	0.598442	+	0.823684i	0.0358921	+	0.0494013i
$279$		0			0
$280$	2.88723	+	6.14368i	0.172545	+	0.367155i
$281$	−25.6840	−	18.6605i	−1.53218	−	1.11319i	−0.955013	−	0.296563i	$-0.904160\pi$
$281$	−25.6840	−	18.6605i	−1.53218	−	1.11319i	−0.577163	−	0.816629i	$-0.695840\pi$
$282$		0			0
$283$	10.5887	−	14.5741i	0.629433	−	0.866340i	−0.368564	−	0.929602i	$-0.620150\pi$
$283$	10.5887	−	14.5741i	0.629433	−	0.866340i	0.997997	+	0.0632623i	$0.0201505\pi$
$284$	3.30345	−	10.1670i	0.196024	−	0.603299i
$285$		0			0
$286$	−0.786755	−	2.42138i	−0.0465218	−	0.143179i
$287$	−1.56674	−	0.509065i	−0.0924818	−	0.0300491i
$288$		0			0
$289$	4.97394	+	15.3082i	0.292585	+	0.900483i
$290$	−19.5666	+	9.19537i	−1.14899	+	0.539971i
$291$		0			0
$292$	8.51526	−	11.7203i	0.498318	−	0.685876i
$293$			24.0344i			1.40411i	0.712124	+	0.702054i	$0.247733\pi$
$293$			24.0344i			1.40411i	−0.712124	+	0.702054i	$0.752267\pi$
$294$		0			0
$295$	−5.27016	+	4.94404i	−0.306841	+	0.287853i
$296$	2.50284	−	1.81842i	0.145474	−	0.105693i
$297$		0			0
$298$	−0.403913	+	0.131239i	−0.0233980	+	0.00760249i
$299$	6.08385			0.351838
$300$		0			0
$301$	9.35557			0.539246
$302$	−10.2130	+	3.31842i	−0.587694	+	0.190953i
$303$		0			0
$304$	−5.39250	+	3.91788i	−0.309281	+	0.224706i
$305$	−5.00700	+	26.1763i	−0.286700	+	1.49885i
$306$		0			0
$307$		−	18.2870i		−	1.04369i	−0.853040	−	0.521846i	$-0.825244\pi$
$307$		−	18.2870i		−	1.04369i	0.853040	−	0.521846i	$-0.174756\pi$
$308$	4.56972	−	6.28968i	0.260384	−	0.358388i
$309$		0			0
$310$	−10.6948	−	11.4003i	−0.607426	−	0.647493i
$311$	1.93814	+	5.96499i	0.109902	+	0.338244i	0.990850	−	0.134970i	$-0.0430938\pi$
$311$	1.93814	+	5.96499i	0.109902	+	0.338244i	−0.880948	+	0.473214i	$0.843094\pi$
$312$		0			0
$313$	−18.0764	−	5.87339i	−1.02174	−	0.331984i	−0.250221	−	0.968189i	$-0.580503\pi$
$313$	−18.0764	−	5.87339i	−1.02174	−	0.331984i	−0.771520	+	0.636205i	$0.780503\pi$
$314$	−7.26939	−	22.3729i	−0.410235	−	1.26257i
$315$		0			0
$316$	−4.70857	+	14.4915i	−0.264878	+	0.815210i
$317$	10.1463	−	13.9651i	0.569870	−	0.784359i	−0.422669	−	0.906284i	$-0.638907\pi$
$317$	10.1463	−	13.9651i	0.569870	−	0.784359i	0.992539	+	0.121925i	$0.0389068\pi$
$318$		0			0
$319$	20.0316	+	14.5538i	1.12155	+	0.814857i
$320$	−0.420099	+	2.19625i	−0.0234842	+	0.122774i
$321$		0			0
$322$	10.9197	+	15.0297i	0.608531	+	0.837571i
$323$	−6.02727	+	1.95838i	−0.335366	+	0.108967i
$324$		0			0
$325$	−1.23137	−	4.81594i	−0.0683044	−	0.267140i
$326$	7.38114			0.408804
$327$		0			0
$328$	−0.318958	−	0.439008i	−0.0176115	−	0.0242402i
$329$	−6.78829	+	4.93198i	−0.374251	+	0.271909i
$330$		0			0
$331$	−8.89681	−	6.46391i	−0.489013	−	0.355289i	0.315792	−	0.948829i	$-0.397730\pi$
$331$	−8.89681	−	6.46391i	−0.489013	−	0.355289i	−0.804805	+	0.593540i	$0.797730\pi$
$332$			8.89222i			0.488024i
$333$		0			0
$334$	0.258891	−	0.796785i	0.0141659	−	0.0435982i
$335$	25.2042	−	11.8448i	1.37705	−	0.647148i
$336$		0			0
$337$	−7.38979	−	2.40109i	−0.402547	−	0.130796i	0.100744	−	0.994912i	$-0.467878\pi$
$337$	−7.38979	−	2.40109i	−0.402547	−	0.130796i	−0.503291	+	0.864117i	$0.667878\pi$
$338$	11.4237	+	3.71179i	0.621369	+	0.201895i
$339$		0			0
$340$	−1.02515	+	1.86253i	−0.0555966	+	0.101010i
$341$	−5.53217	+	17.0263i	−0.299584	+	0.922023i
$342$		0			0
$343$			14.5228i			0.784157i
$344$	2.49317	+	1.81140i	0.134423	+	0.0976639i
$345$		0			0
$346$	15.2419	−	11.0739i	0.819411	−	0.595337i
$347$	−6.50588	−	8.95458i	−0.349254	−	0.480707i	0.597862	−	0.801599i	$-0.296017\pi$
$347$	−6.50588	−	8.95458i	−0.349254	−	0.480707i	−0.947116	+	0.320892i	$0.896017\pi$
$348$		0			0
$349$	27.8764			1.49219			0.746094	−	0.665841i	$-0.231927\pi$
$349$	27.8764			1.49219			0.746094	+	0.665841i	$0.231927\pi$
$350$	9.68724	−	11.6860i	0.517805	−	0.624642i
$351$		0			0
$352$	2.43557	−	0.791366i	0.129817	−	0.0421800i
$353$	1.63019	+	2.24377i	0.0867664	+	0.119424i	0.850194	−	0.526470i	$-0.176485\pi$
$353$	1.63019	+	2.24377i	0.0867664	+	0.119424i	−0.763427	+	0.645894i	$0.776485\pi$
$354$		0			0
$355$	−23.7170	+	2.98407i	−1.25877	+	0.158378i
$356$	7.23754	+	5.25838i	0.383589	+	0.278694i
$357$		0			0
$358$	−0.524434	+	0.721821i	−0.0277172	+	0.0381494i
$359$	−3.13804	+	9.65790i	−0.165620	+	0.509725i	−0.999081	−	0.0428524i	$-0.986355\pi$
$359$	−3.13804	+	9.65790i	−0.165620	+	0.509725i	0.833462	+	0.552577i	$0.186355\pi$
$360$		0			0
$361$	7.85795	+	24.1843i	0.413576	+	1.27286i
$362$	−2.09220	−	0.679798i	−0.109964	−	0.0357294i
$363$		0			0
$364$	−0.932653	−	2.87041i	−0.0488843	−	0.150450i
$365$	−31.8171	−	6.08599i	−1.66539	−	0.318555i
$366$		0			0
$367$	−6.04330	+	8.31789i	−0.315458	+	0.434190i	−0.937074	−	0.349132i	$-0.886476\pi$
$367$	−6.04330	+	8.31789i	−0.315458	+	0.434190i	0.621616	+	0.783322i	$0.286476\pi$
$368$			6.11950i			0.319001i
$369$		0			0
$370$	−6.06033	−	3.33565i	−0.315061	−	0.173412i
$371$	4.52785	−	3.28968i	0.235074	−	0.170791i
$372$		0			0
$373$	−27.1805	+	8.83148i	−1.40735	+	0.457277i	−0.911561	−	0.411164i	$-0.865122\pi$
$373$	−27.1805	+	8.83148i	−1.40735	+	0.457277i	−0.495792	+	0.868441i	$0.665122\pi$
$374$	2.43487			0.125904
$375$		0			0
$376$	−2.76393			−0.142539
$377$	9.14180	−	2.97035i	0.470827	−	0.152981i
$378$		0			0
$379$	−2.01988	+	1.46753i	−0.103754	+	0.0753820i	−0.638453	−	0.769661i	$-0.720425\pi$
$379$	−2.01988	+	1.46753i	−0.103754	+	0.0753820i	0.534698	+	0.845043i	$0.320425\pi$
$380$	13.0573	+	7.18685i	0.669826	+	0.368678i
$381$		0			0
$382$		−	21.7670i		−	1.11370i
$383$	18.0171	−	24.7984i	0.920629	−	1.26714i	−0.0427747	−	0.999085i	$-0.513620\pi$
$383$	18.0171	−	24.7984i	0.920629	−	1.26714i	0.963404	−	0.268053i	$-0.0863802\pi$
$384$		0			0
$385$	−17.0747	−	3.26605i	−0.870206	−	0.166453i
$386$	−1.08981	−	3.35410i	−0.0554701	−	0.170719i
$387$		0			0
$388$	−1.35260	−	0.439486i	−0.0686678	−	0.0223115i
$389$	6.41169	+	19.7332i	0.325086	+	1.00051i	0.971402	+	0.237441i	$0.0763087\pi$
$389$	6.41169	+	19.7332i	0.325086	+	1.00051i	−0.646316	+	0.763070i	$0.723691\pi$
$390$		0			0
$391$	−1.79796	+	5.53355i	−0.0909268	+	0.279844i
$392$	1.30264	−	1.79293i	0.0657933	−	0.0905567i
$393$		0			0
$394$	14.4069	+	10.4672i	0.725808	+	0.527331i
$395$	33.8050	−	4.25334i	1.70091	−	0.214009i
$396$		0			0
$397$	−13.9737	−	19.2332i	−0.701320	−	0.965285i	−0.999940	−	0.0109127i	$-0.996526\pi$
$397$	−13.9737	−	19.2332i	−0.701320	−	0.965285i	0.298620	−	0.954372i	$-0.403474\pi$
$398$	2.79364	−	0.907710i	0.140033	−	0.0454994i
$399$		0			0
$400$	4.84416	−	1.23859i	0.242208	−	0.0619295i
$401$	23.5386			1.17546			0.587730	−	0.809057i	$-0.300022\pi$
$401$	23.5386			1.17546			0.587730	+	0.809057i	$0.300022\pi$
$402$		0			0
$403$	4.08506	+	5.62261i	0.203491	+	0.280082i
$404$	14.8278	−	10.7730i	0.737709	−	0.535977i
$405$		0			0
$406$	23.7463	+	17.2527i	1.17851	+	0.856238i
$407$			7.92264i			0.392711i
$408$		0			0
$409$	−0.925581	+	2.84864i	−0.0457670	+	0.140856i	−0.971329	−	0.237740i	$-0.923593\pi$
$409$	−0.925581	+	2.84864i	−0.0457670	+	0.140856i	0.925562	+	0.378597i	$0.123593\pi$
$410$	−0.585088	+	1.06301i	−0.0288954	+	0.0524982i
$411$		0			0
$412$	10.7612	+	3.49653i	0.530167	+	0.172262i
$413$	9.33056	+	3.03168i	0.459127	+	0.149179i
$414$		0			0
$415$	17.9955	−	8.45700i	0.883363	−	0.415138i
$416$	0.307217	−	0.945515i	0.0150625	−	0.0463577i
$417$		0			0
$418$		−	17.0698i		−	0.834910i
$419$	1.84898	+	1.34336i	0.0903284	+	0.0656274i	0.632033	−	0.774942i	$-0.282221\pi$
$419$	1.84898	+	1.34336i	0.0903284	+	0.0656274i	−0.541704	+	0.840569i	$0.682221\pi$
$420$		0			0
$421$	−7.15400	+	5.19769i	−0.348665	+	0.253320i	−0.748309	−	0.663351i	$-0.769134\pi$
$421$	−7.15400	+	5.19769i	−0.348665	+	0.253320i	0.399644	+	0.916670i	$0.369134\pi$
$422$	0.632926	+	0.871148i	0.0308104	+	0.0424068i
$423$		0			0
$424$	1.84357			0.0895315
$425$	4.74423	+	0.303260i	0.230129	+	0.0147103i
$426$		0			0
$427$	34.4118	−	11.1811i	1.66530	−	0.541090i
$428$	−3.92957	−	5.40859i	−0.189943	−	0.261434i
$429$		0			0
$430$	1.29463	−	6.76825i	0.0624327	−	0.326394i
$431$	−3.32277	−	2.41414i	−0.160052	−	0.116285i	0.504876	−	0.863192i	$-0.331538\pi$
$431$	−3.32277	−	2.41414i	−0.160052	−	0.116285i	−0.664929	+	0.746907i	$0.731538\pi$
$432$		0			0
$433$	−18.6835	+	25.7157i	−0.897874	+	1.23582i	0.0732677	+	0.997312i	$0.476657\pi$
$433$	−18.6835	+	25.7157i	−0.897874	+	1.23582i	−0.971141	+	0.238505i	$0.923343\pi$
$434$	−6.55806	+	20.1836i	−0.314797	+	0.968846i
$435$		0			0
$436$	−1.44405	−	4.44431i	−0.0691572	−	0.212844i
$437$	38.7932	+	12.6047i	1.85573	+	0.602963i
$438$		0			0
$439$	−1.40267	−	4.31697i	−0.0669458	−	0.206038i	0.911988	−	0.410218i	$-0.134547\pi$
$439$	−1.40267	−	4.31697i	−0.0669458	−	0.206038i	−0.978933	+	0.204180i	$0.934547\pi$
$440$	−3.91788	−	4.17632i	−0.186778	−	0.199098i
$441$		0			0
$442$	0.555600	−	0.764718i	0.0264272	−	0.0363739i
$443$			34.8279i			1.65472i	0.561670	+	0.827361i	$0.310159\pi$
$443$			34.8279i			1.65472i	−0.561670	+	0.827361i	$0.689841\pi$
$444$		0			0
$445$	3.75824	−	19.6479i	0.178158	−	0.931398i
$446$	5.55667	−	4.03716i	0.263116	−	0.191165i
$447$		0			0
$448$	2.88723	−	0.938119i	0.136409	−	0.0443220i
$449$	−10.9141			−0.515070			−0.257535	−	0.966269i	$-0.582910\pi$
$449$	−10.9141			−0.515070			−0.257535	+	0.966269i	$0.582910\pi$
$450$		0			0
$451$	1.38967			0.0654368
$452$	13.6062	−	4.42091i	0.639980	−	0.207942i
$453$		0			0
$454$	13.4040	−	9.73857i	0.629081	−	0.457054i
$455$	−4.92194	+	4.61736i	−0.230744	+	0.216465i
$456$		0			0
$457$			5.40224i			0.252706i	0.991985	+	0.126353i	$0.0403272\pi$
$457$			5.40224i			0.252706i	−0.991985	+	0.126353i	$0.959673\pi$
$458$	−4.40376	+	6.06125i	−0.205774	+	0.283224i
$459$		0			0
$460$	12.3842	−	5.81999i	0.577418	−	0.271359i
$461$	−9.56448	−	29.4364i	−0.445462	−	1.37099i	−0.881976	−	0.471294i	$-0.843787\pi$
$461$	−9.56448	−	29.4364i	−0.445462	−	1.37099i	0.436514	−	0.899697i	$-0.356213\pi$
$462$		0			0
$463$	−33.8565	−	11.0006i	−1.57344	−	0.511243i	−0.613087	−	0.790016i	$-0.710072\pi$
$463$	−33.8565	−	11.0006i	−1.57344	−	0.511243i	−0.960357	+	0.278773i	$0.910072\pi$
$464$	2.98776	+	9.19537i	0.138703	+	0.426885i
$465$		0			0
$466$	−7.44699	+	22.9195i	−0.344975	+	1.06172i
$467$	−17.7514	+	24.4327i	−0.821435	+	1.13061i	0.168022	+	0.985783i	$0.446262\pi$
$467$	−17.7514	+	24.4327i	−0.821435	+	1.13061i	−0.989457	+	0.144826i	$0.953738\pi$
$468$		0			0
$469$	−30.5881	−	22.2236i	−1.41243	−	1.02619i
$470$	2.62866	+	5.59346i	0.121251	+	0.258007i
$471$		0			0
$472$	1.89952	+	2.61447i	0.0874326	+	0.120341i
$473$	−7.50579	+	2.43878i	−0.345116	+	0.112135i
$474$		0			0
$475$	2.12602	−	33.2596i	0.0975483	−	1.52606i
$476$	2.88640			0.132298
$477$		0			0
$478$	9.93492	+	13.6743i	0.454413	+	0.625446i
$479$	23.3347	−	16.9537i	1.06619	−	0.774634i	0.0909678	−	0.995854i	$-0.471004\pi$
$479$	23.3347	−	16.9537i	1.06619	−	0.774634i	0.975224	+	0.221220i	$0.0710040\pi$
$480$		0			0
$481$	2.48825	+	1.80782i	0.113455	+	0.0824296i
$482$			13.3368i			0.607473i
$483$		0			0
$484$	1.37257	−	4.22433i	0.0623894	−	0.192015i
$485$	0.396996	+	3.15527i	0.0180267	+	0.143274i
$486$		0			0
$487$	−19.7619	−	6.42104i	−0.895498	−	0.290965i	−0.175120	−	0.984547i	$-0.556031\pi$
$487$	−19.7619	−	6.42104i	−0.895498	−	0.290965i	−0.720378	+	0.693582i	$0.756031\pi$
$488$	11.3353	+	3.68305i	0.513124	+	0.166724i
$489$		0			0
$490$	−4.86730	−	0.931017i	−0.219882	−	0.0420591i
$491$	−10.3097	+	31.7301i	−0.465272	+	1.43196i	0.393368	+	0.919381i	$0.371310\pi$
$491$	−10.3097	+	31.7301i	−0.465272	+	1.43196i	−0.858640	+	0.512579i	$0.828690\pi$
$492$		0			0
$493$			9.19273i			0.414020i
$494$	−5.36108	−	3.89505i	−0.241207	−	0.175247i
$495$		0			0
$496$	−5.65556	+	4.10900i	−0.253942	+	0.184500i
$497$	19.0757	+	26.2554i	0.855660	+	1.17772i
$498$		0			0
$499$	15.1320			0.677400			0.338700	−	0.940894i	$-0.390013\pi$
$499$	15.1320			0.677400			0.338700	+	0.940894i	$0.390013\pi$
$500$	−7.11365	−	8.62531i	−0.318132	−	0.385736i
$501$		0			0
$502$	−17.3594	+	5.64040i	−0.774787	+	0.251743i
$503$	−11.6400	−	16.0211i	−0.519001	−	0.714344i	0.466403	−	0.884572i	$-0.345550\pi$
$503$	−11.6400	−	16.0211i	−0.519001	−	0.714344i	−0.985405	+	0.170228i	$0.945550\pi$
$504$		0			0
$505$	−35.9037	−	19.7617i	−1.59769	−	0.879383i
$506$	−12.6785	−	9.21149i	−0.563629	−	0.409501i
$507$		0			0
$508$	−3.15264	+	4.33923i	−0.139876	+	0.192522i
$509$	3.57923	−	11.0158i	0.158647	−	0.488265i	−0.839865	−	0.542795i	$-0.817366\pi$
$509$	3.57923	−	11.0158i	0.158647	−	0.488265i	0.998512	+	0.0545302i	$0.0173661\pi$
$510$		0			0
$511$	13.5906	+	41.8274i	0.601211	+	1.85034i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$		0			0
$514$	3.04622	+	9.37530i	0.134363	+	0.413527i
$515$	−3.15848	−	25.1032i	−0.139179	−	1.10618i
$516$		0			0
$517$	4.16046	−	5.72638i	0.182977	−	0.251846i
$518$			9.39183i			0.412653i
$519$		0			0
$520$	−2.20565	+	0.277515i	−0.0967242	+	0.0121698i
$521$	17.1151	−	12.4349i	0.749826	−	0.544781i	−0.145947	−	0.989292i	$-0.546623\pi$
$521$	17.1151	−	12.4349i	0.749826	−	0.544781i	0.895773	+	0.444512i	$0.146623\pi$
$522$		0			0
$523$	−6.98471	+	2.26947i	−0.305420	+	0.0992369i	−0.457717	−	0.889098i	$-0.651333\pi$
$523$	−6.98471	+	2.26947i	−0.305420	+	0.0992369i	0.152297	+	0.988335i	$0.451333\pi$
$524$	−5.34104			−0.233325
$525$		0			0
$526$	23.6404			1.03077
$527$	−6.32129	+	2.05391i	−0.275360	+	0.0894697i
$528$		0			0
$529$	11.6889	−	8.49252i	0.508215	−	0.369240i
$530$	−1.75334	−	3.73089i	−0.0761601	−	0.162059i
$531$		0			0
$532$		−	20.2352i		−	0.877309i
$533$	0.317100	−	0.436451i	0.0137351	−	0.0189048i
$534$		0			0
$535$	−7.20829	+	13.0963i	−0.311641	+	0.566201i
$536$	−3.84859	−	11.8448i	−0.166234	−	0.511615i
$537$		0			0
$538$	−18.5896	−	6.04013i	−0.801455	−	0.260408i
$539$	1.75381	+	5.39768i	0.0755421	+	0.232495i
$540$		0			0
$541$	−10.3558	+	31.8720i	−0.445232	+	1.37028i	0.436997	+	0.899463i	$0.356042\pi$
$541$	−10.3558	+	31.8720i	−0.445232	+	1.37028i	−0.882229	+	0.470820i	$0.843958\pi$
$542$	15.9563	−	21.9619i	0.685380	−	0.943345i
$543$		0			0
$544$	0.769200	+	0.558856i	0.0329792	+	0.0239608i
$545$	−7.62073	+	7.14915i	−0.326436	+	0.306236i
$546$		0			0
$547$	−14.0268	−	19.3063i	−0.599745	−	0.825478i	0.395940	−	0.918276i	$-0.370419\pi$
$547$	−14.0268	−	19.3063i	−0.599745	−	0.825478i	−0.995685	+	0.0927985i	$0.970419\pi$
$548$	−16.8199	+	5.46512i	−0.718510	+	0.233458i
$549$		0			0
$550$	−4.72562	+	11.9007i	−0.201501	+	0.507446i
$551$	64.4460			2.74549
$552$		0			0
$553$	−27.1895	−	37.4231i	−1.15621	−	1.59139i
$554$	−14.3846	+	10.4510i	−0.611142	+	0.444021i
$555$		0			0
$556$	−0.823684	−	0.598442i	−0.0349320	−	0.0253796i
$557$		−	29.0734i		−	1.23188i	−0.787793	−	0.615940i	$-0.788776\pi$
$557$		−	29.0734i		−	1.23188i	0.787793	−	0.615940i	$-0.211224\pi$
$558$		0			0
$559$	−0.946759	+	2.91382i	−0.0400436	+	0.123242i
$560$	−4.64442	−	4.95078i	−0.196263	−	0.209209i
$561$		0			0
$562$	30.1933	+	9.81040i	1.27363	+	0.413827i
$563$	28.3204	+	9.20185i	1.19356	+	0.387812i	0.837389	−	0.546608i	$-0.184081\pi$
$563$	28.3204	+	9.20185i	1.19356	+	0.387812i	0.356174	+	0.934420i	$0.384081\pi$
$564$		0			0
$565$	−21.8870	−	23.3307i	−0.920791	−	0.981529i
$566$	−5.56681	+	17.1329i	−0.233990	+	0.720148i
$567$		0			0
$568$			10.6902i			0.448550i
$569$	−34.4433	−	25.0245i	−1.44394	−	1.04908i	−0.987201	−	0.159481i	$-0.949018\pi$
$569$	−34.4433	−	25.0245i	−1.44394	−	1.04908i	−0.456737	−	0.889602i	$-0.650982\pi$
$570$		0			0
$571$	17.3141	−	12.5794i	0.724571	−	0.526431i	−0.163271	−	0.986581i	$-0.552204\pi$
$571$	17.3141	−	12.5794i	0.724571	−	0.526431i	0.887841	+	0.460150i	$0.152204\pi$
$572$	1.49650	+	2.05975i	0.0625717	+	0.0861226i
$573$		0			0
$574$	1.64737			0.0687598
$575$	−23.5562	−	19.5272i	−0.982362	−	0.814342i
$576$		0			0
$577$	−1.72915	+	0.561836i	−0.0719856	+	0.0233895i	−0.344788	−	0.938680i	$-0.612049\pi$
$577$	−1.72915	+	0.561836i	−0.0719856	+	0.0233895i	0.272803	+	0.962070i	$0.412049\pi$
$578$	−9.46100	−	13.0219i	−0.393526	−	0.541642i
$579$		0			0
$580$	15.7674	−	14.7917i	0.654708	−	0.614194i
$581$	−21.8395	−	15.8674i	−0.906057	−	0.658289i
$582$		0			0
$583$	−2.77506	+	3.81954i	−0.114931	+	0.158189i
$584$	−4.47674	+	13.7780i	−0.185249	+	0.570137i
$585$		0			0
$586$	−7.42705	−	22.8581i	−0.306809	−	0.944260i
$587$	−33.0657	−	10.7437i	−1.36477	−	0.443439i	−0.467134	−	0.884186i	$-0.654714\pi$
$587$	−33.0657	−	10.7437i	−1.36477	−	0.443439i	−0.897631	+	0.440747i	$0.854714\pi$
$588$		0			0
$589$	14.3990	+	44.3156i	0.593301	+	1.82599i
$590$	3.48443	−	6.33063i	0.143452	−	0.260628i
$591$		0			0
$592$	−1.81842	+	2.50284i	−0.0747365	+	0.102866i
$593$			15.7263i			0.645800i	0.946433	+	0.322900i	$0.104658\pi$
$593$			15.7263i			0.645800i	−0.946433	+	0.322900i	$0.895342\pi$
$594$		0			0
$595$	−2.74513	−	5.84131i	−0.112539	−	0.239470i
$596$	0.343589	−	0.249632i	0.0140739	−	0.0102253i
$597$		0			0
$598$	−5.78609	+	1.88001i	−0.236611	+	0.0768795i
$599$	−39.2177			−1.60239			−0.801196	−	0.598402i	$-0.795803\pi$
$599$	−39.2177			−1.60239			−0.801196	+	0.598402i	$0.795803\pi$
$600$		0			0
$601$	−7.68430			−0.313449			−0.156725	−	0.987642i	$-0.550093\pi$
$601$	−7.68430			−0.313449			−0.156725	+	0.987642i	$0.550093\pi$
$602$	−8.89768	+	2.89103i	−0.362642	+	0.117830i
$603$		0			0
$604$	8.68773	−	6.31200i	0.353499	−	0.256832i
$605$	−9.85429	+	1.23987i	−0.400634	+	0.0504077i
$606$		0			0
$607$			18.4288i			0.748002i	0.927428	+	0.374001i	$0.122014\pi$
$607$			18.4288i			0.748002i	−0.927428	+	0.374001i	$0.877986\pi$
$608$	3.91788	−	5.39250i	0.158891	−	0.218695i
$609$		0			0
$610$	−3.32697	−	26.4424i	−0.134705	−	1.07062i
$611$	−0.849126	−	2.61334i	−0.0343520	−	0.105724i
$612$		0			0
$613$	34.8368	+	11.3191i	1.40704	+	0.457176i	0.911462	−	0.411385i	$-0.134955\pi$
$613$	34.8368	+	11.3191i	1.40704	+	0.457176i	0.495582	+	0.868561i	$0.334955\pi$
$614$	5.65098	+	17.3919i	0.228055	+	0.701881i
$615$		0			0
$616$	−2.40244	+	7.39396i	−0.0967972	+	0.297911i
$617$	9.38150	−	12.9125i	0.377685	−	0.519839i	−0.577285	−	0.816543i	$-0.695888\pi$
$617$	9.38150	−	12.9125i	0.377685	−	0.519839i	0.954969	+	0.296705i	$0.0958877\pi$
$618$		0			0
$619$	32.3427	+	23.4984i	1.29996	+	0.944479i	0.999955	−	0.00945769i	$-0.00301052\pi$
$619$	32.3427	+	23.4984i	1.29996	+	0.944479i	0.300008	+	0.953937i	$0.403011\pi$
$620$	13.6943	+	7.53744i	0.549975	+	0.302711i
$621$		0			0
$622$	−3.68657	−	5.07413i	−0.147818	−	0.203454i
$623$	−25.8295	+	8.39250i	−1.03484	+	0.336238i
$624$		0			0
$625$	−10.6898	+	22.5993i	−0.427594	+	0.903971i
$626$	19.0067			0.759660
$627$		0			0
$628$	13.8272	+	19.0315i	0.551765	+	0.759440i
$629$	−2.37965	+	1.72892i	−0.0948830	+	0.0689365i
$630$		0			0
$631$	4.44942	+	3.23269i	0.177129	+	0.128691i	0.672817	−	0.739809i	$-0.265084\pi$
$631$	4.44942	+	3.23269i	0.177129	+	0.128691i	−0.495688	+	0.868500i	$0.665084\pi$
$632$		−	15.2373i		−	0.606106i
$633$		0			0
$634$	−5.33420	+	16.4170i	−0.211848	+	0.652001i
$635$	11.7798	+	2.25324i	0.467466	+	0.0894170i
$636$		0			0
$637$	2.09544	+	0.680849i	0.0830243	+	0.0269762i
$638$	−23.5486	−	7.65139i	−0.932297	−	0.302922i
$639$		0			0
$640$	−0.279141	−	2.21858i	−0.0110340	−	0.0876969i
$641$	0.842700	−	2.59356i	0.0332846	−	0.102440i	−0.933034	−	0.359788i	$-0.882849\pi$
$641$	0.842700	−	2.59356i	0.0332846	−	0.102440i	0.966319	+	0.257349i	$0.0828489\pi$
$642$		0			0
$643$		−	6.26799i		−	0.247185i	−0.992333	−	0.123593i	$-0.960558\pi$
$643$		−	6.26799i		−	0.247185i	0.992333	−	0.123593i	$-0.0394416\pi$
$644$	−15.0297	−	10.9197i	−0.592252	−	0.430296i
$645$		0			0
$646$	5.12710	−	3.72506i	0.201723	−	0.146560i
$647$	−1.33178	−	1.83303i	−0.0523575	−	0.0720639i	0.782035	−	0.623234i	$-0.214182\pi$
$647$	−1.33178	−	1.83303i	−0.0523575	−	0.0720639i	−0.834393	+	0.551170i	$0.814182\pi$
$648$		0			0
$649$	−8.27600			−0.324862
$650$	2.65931	+	4.19971i	0.104307	+	0.164726i
$651$		0			0
$652$	−7.01988	+	2.28090i	−0.274920	+	0.0893269i
$653$	9.10501	+	12.5320i	0.356307	+	0.490414i	0.949115	−	0.314930i	$-0.101981\pi$
$653$	9.10501	+	12.5320i	0.356307	+	0.490414i	−0.592808	+	0.805343i	$0.701981\pi$
$654$		0			0
$655$	5.07963	+	10.8088i	0.198478	+	0.422336i
$656$	0.439008	+	0.318958i	0.0171404	+	0.0124532i
$657$		0			0
$658$	4.93198	−	6.78829i	0.192269	−	0.264635i
$659$	5.77728	−	17.7806i	0.225051	−	0.692635i	−0.773236	−	0.634119i	$-0.781363\pi$
$659$	5.77728	−	17.7806i	0.225051	−	0.692635i	0.998286	−	0.0585165i	$-0.0186370\pi$
$660$		0			0
$661$	4.59272	+	14.1349i	0.178636	+	0.549786i	0.999781	−	0.0209344i	$-0.00666410\pi$
$661$	4.59272	+	14.1349i	0.178636	+	0.549786i	−0.821145	+	0.570720i	$0.806664\pi$
$662$	10.4588	+	3.39828i	0.406494	+	0.132078i
$663$		0			0
$664$	−2.74785	−	8.45700i	−0.106637	−	0.328195i
$665$	−40.9507	+	19.2449i	−1.58800	+	0.746283i
$666$		0			0
$667$	34.7775	−	47.8671i	1.34659	−	1.85342i
$668$			0.837790i			0.0324151i
$669$		0			0
$670$	−20.3104	+	19.0536i	−0.784658	+	0.736103i
$671$	−24.6933	+	17.9407i	−0.953273	+	0.692593i
$672$		0			0
$673$	17.0778	−	5.54893i	0.658303	−	0.213896i	0.0392312	−	0.999230i	$-0.487509\pi$
$673$	17.0778	−	5.54893i	0.658303	−	0.213896i	0.619071	+	0.785335i	$0.287509\pi$
$674$	7.77008			0.299292
$675$		0			0
$676$	−12.0116			−0.461985
$677$	4.67961	−	1.52050i	0.179852	−	0.0584374i	−0.217707	−	0.976014i	$-0.569858\pi$
$677$	4.67961	−	1.52050i	0.179852	−	0.0584374i	0.397558	+	0.917577i	$0.369858\pi$
$678$		0			0
$679$	3.49298	−	2.53780i	0.134048	−	0.0973918i
$680$	0.399423	−	2.08816i	0.0153172	−	0.0800772i
$681$		0			0
$682$		−	17.9025i		−	0.685521i
$683$	−10.7468	+	14.7917i	−0.411216	+	0.565990i	−0.963514	−	0.267656i	$-0.913751\pi$
$683$	−10.7468	+	14.7917i	−0.411216	+	0.565990i	0.552299	+	0.833646i	$0.313751\pi$
$684$		0			0
$685$	27.0566	+	28.8413i	1.03378	+	1.10197i
$686$	−4.48779	−	13.8120i	−0.171345	−	0.527344i
$687$		0			0
$688$	−2.93090	−	0.952307i	−0.111740	−	0.0363064i
$689$	0.566374	+	1.74312i	0.0215771	+	0.0664076i
$690$		0			0
$691$	8.76796	−	26.9850i	0.333549	−	1.02656i	−0.633884	−	0.773428i	$-0.718540\pi$
$691$	8.76796	−	26.9850i	0.333549	−	1.02656i	0.967432	−	0.253129i	$-0.0814598\pi$
$692$	−11.0739	+	15.2419i	−0.420967	+	0.579411i
$693$		0			0
$694$	8.95458	+	6.50588i	0.339911	+	0.246960i
$695$	−0.427715	+	2.23607i	−0.0162242	+	0.0848189i
$696$		0			0
$697$	0.303260	+	0.417402i	0.0114868	+	0.0158102i
$698$	−26.5120	+	8.61427i	−1.00349	+	0.326055i
$699$		0			0
$700$	−5.60195	+	14.1075i	−0.211734	+	0.533215i
$701$	−34.4224			−1.30012			−0.650058	−	0.759884i	$-0.725255\pi$
$701$	−34.4224			−1.30012			−0.650058	+	0.759884i	$0.725255\pi$
$702$		0			0
$703$	12.1207	+	16.6826i	0.457139	+	0.629198i
$704$	−2.07182	+	1.50527i	−0.0780848	+	0.0567319i
$705$		0			0
$706$	−2.24377	−	1.63019i	−0.0844453	−	0.0613531i
$707$			55.6408i			2.09259i
$708$		0			0
$709$	2.97485	−	9.15565i	0.111723	−	0.343848i	−0.879527	−	0.475850i	$-0.842141\pi$
$709$	2.97485	−	9.15565i	0.111723	−	0.343848i	0.991249	+	0.132002i	$0.0421406\pi$
$710$	21.6341	−	10.1670i	0.811912	−	0.381560i
$711$		0			0
$712$	−8.50824	−	2.76450i	−0.318860	−	0.103604i
$713$	40.6856	+	13.2195i	1.52369	+	0.495076i
$714$		0			0
$715$	2.74513	−	4.98745i	0.102662	−	0.186520i
$716$	0.275711	−	0.848552i	0.0103038	−	0.0317119i
$717$		0			0
$718$		−	10.1549i		−	0.378978i
$719$	−24.2693	−	17.6327i	−0.905091	−	0.657587i	0.0346775	−	0.999399i	$-0.488960\pi$
$719$	−24.2693	−	17.6327i	−0.905091	−	0.657587i	−0.939769	+	0.341811i	$0.888960\pi$
$720$		0			0
$721$	−27.7900	+	20.1906i	−1.03495	+	0.751938i
$722$	−14.9467	−	20.5724i	−0.556259	−	0.765625i
$723$		0			0
$724$	2.19987			0.0817576
$725$	−44.9303	−	17.8413i	−1.66867	−	0.662609i
$726$		0			0
$727$	41.6547	−	13.5344i	1.54489	−	0.501965i	0.592169	−	0.805814i	$-0.298272\pi$
$727$	41.6547	−	13.5344i	1.54489	−	0.501965i	0.952720	+	0.303849i	$0.0982718\pi$
$728$	1.77401	+	2.44172i	0.0657493	+	0.0904961i
$729$		0			0
$730$	32.1406	−	4.04392i	1.18958	−	0.149672i
$731$	−2.37047	−	1.72224i	−0.0876749	−	0.0636995i
$732$		0			0
$733$	−15.1786	+	20.8915i	−0.560634	+	0.771646i	−0.991407	−	0.130814i	$-0.958241\pi$
$733$	−15.1786	+	20.8915i	−0.560634	+	0.771646i	0.430773	+	0.902460i	$0.358241\pi$
$734$	3.17715	−	9.77826i	0.117271	−	0.360922i
$735$		0			0
$736$	−1.89103	−	5.81999i	−0.0697043	−	0.214528i
$737$	30.3334	+	9.85592i	1.11735	+	0.363047i
$738$		0			0
$739$	−13.9765	−	43.0153i	−0.514134	−	1.58234i	−0.784852	−	0.619683i	$-0.787261\pi$
$739$	−13.9765	−	43.0153i	−0.514134	−	1.58234i	0.270718	−	0.962659i	$-0.412739\pi$
$740$	6.79449	+	1.29965i	0.249770	+	0.0477761i
$741$		0			0
$742$	−3.28968	+	4.52785i	−0.120768	+	0.166223i
$743$		−	37.5854i		−	1.37887i	−0.724345	−	0.689437i	$-0.757858\pi$
$743$		−	37.5854i		−	1.37887i	0.724345	−	0.689437i	$-0.242142\pi$
$744$		0			0
$745$	−0.831961	−	0.457918i	−0.0304807	−	0.0167768i
$746$	23.1211	−	16.7985i	0.846524	−	0.615036i
$747$		0			0
$748$	−2.31570	+	0.752417i	−0.0846705	+	0.0275111i
$749$	20.2956			0.741585
$750$		0			0
$751$	5.71461			0.208529			0.104265	−	0.994550i	$-0.466751\pi$
$751$	5.71461			0.208529			0.104265	+	0.994550i	$0.466751\pi$
$752$	2.62866	−	0.854102i	0.0958572	−	0.0311459i
$753$		0			0
$754$	−7.77648	+	5.64994i	−0.283203	+	0.205759i
$755$	−21.0363	−	11.5786i	−0.765590	−	0.421387i
$756$		0			0
$757$			16.7444i			0.608587i	0.952578	+	0.304293i	$0.0984203\pi$
$757$			16.7444i			0.608587i	−0.952578	+	0.304293i	$0.901580\pi$
$758$	1.46753	−	2.01988i	0.0533031	−	0.0733654i
$759$		0			0
$760$	−14.6391	−	2.80017i	−0.531016	−	0.101573i
$761$	−9.11807	−	28.0625i	−0.330530	−	1.01727i	−0.968882	−	0.247522i	$-0.920384\pi$
$761$	−9.11807	−	28.0625i	−0.330530	−	1.01727i	0.638353	−	0.769744i	$-0.279616\pi$
$762$		0			0
$763$	13.4921	+	4.38386i	0.488448	+	0.158706i
$764$	6.72639	+	20.7017i	0.243352	+	0.748961i
$765$		0			0
$766$	−9.47214	+	29.1522i	−0.342242	+	1.05331i
$767$	−1.88845	+	2.59923i	−0.0681881	+	0.0938529i
$768$		0			0
$769$	19.7088	+	14.3193i	0.710717	+	0.516366i	0.883405	−	0.468610i	$-0.155245\pi$
$769$	19.7088	+	14.3193i	0.710717	+	0.516366i	−0.172688	+	0.984977i	$0.555245\pi$
$770$	17.2482	−	2.17017i	0.621584	−	0.0782076i
$771$		0			0
$772$	2.07295	+	2.85317i	0.0746071	+	0.102688i
$773$	11.5292	−	3.74607i	0.414678	−	0.134737i	−0.0942453	−	0.995549i	$-0.530044\pi$
$773$	11.5292	−	3.74607i	0.414678	−	0.134737i	0.508923	+	0.860812i	$0.330044\pi$
$774$		0			0
$775$	2.22973	−	34.8821i	0.0800941	−	1.25300i
$776$	1.42221			0.0510543
$777$		0			0
$778$	−12.1958	−	16.7860i	−0.437239	−	0.601808i
$779$	2.92621	−	2.12602i	0.104842	−	0.0761724i
$780$		0			0
$781$	−22.1482	−	16.0916i	−0.792524	−	0.575802i
$782$		−	5.81832i		−	0.208063i
$783$		0			0
$784$	−0.684839	+	2.10772i	−0.0244585	+	0.0752756i
$785$	25.3642	−	46.0826i	0.905288	−	1.64476i
$786$		0			0
$787$	−22.2588	−	7.23232i	−0.793440	−	0.257804i	−0.115872	−	0.993264i	$-0.536966\pi$
$787$	−22.2588	−	7.23232i	−0.793440	−	0.257804i	−0.677568	+	0.735460i	$0.736966\pi$
$788$	−16.9363	−	5.50294i	−0.603331	−	0.196034i
$789$		0			0
$790$	−30.8361	+	14.4915i	−1.09710	+	0.515584i
$791$	−13.4211	+	41.3058i	−0.477198	+	1.46866i
$792$		0			0
$793$			11.8492i			0.420776i
$794$	19.2332	+	13.9737i	0.682559	+	0.495908i
$795$		0			0
$796$	−2.37642	+	1.72657i	−0.0842298	+	0.0611966i
$797$	−9.86558	−	13.5788i	−0.349457	−	0.480986i	0.597717	−	0.801707i	$-0.296075\pi$
$797$	−9.86558	−	13.5788i	−0.349457	−	0.480986i	−0.947174	+	0.320721i	$0.896075\pi$
$798$		0			0
$799$	2.62790			0.0929684
$800$	−4.22433	+	2.67490i	−0.149352	+	0.0945719i
$801$		0			0
$802$	−22.3865	+	7.27381i	−0.790495	+	0.256847i
$803$	−21.8069	−	30.0146i	−0.769547	−	1.05919i
$804$		0			0
$805$	−7.80447	+	40.8013i	−0.275071	+	1.43806i
$806$	−5.62261	−	4.08506i	−0.198048	−	0.143890i
$807$		0			0
$808$	−10.7730	+	14.8278i	−0.378993	+	0.521639i
$809$	−8.80775	+	27.1075i	−0.309664	+	0.953048i	0.668231	+	0.743954i	$0.267052\pi$
$809$	−8.80775	+	27.1075i	−0.309664	+	0.953048i	−0.977895	+	0.209095i	$0.932948\pi$
$810$		0			0
$811$	−2.87108	−	8.83629i	−0.100817	−	0.310284i	0.887909	−	0.460020i	$-0.152158\pi$
$811$	−2.87108	−	8.83629i	−0.100817	−	0.310284i	−0.988726	+	0.149736i	$0.952158\pi$
$812$	−27.9155	−	9.07029i	−0.979641	−	0.318305i
$813$		0			0
$814$	−2.44823	−	7.53488i	−0.0858104	−	0.264097i
$815$	11.2922	+	12.0371i	0.395550	+	0.421641i
$816$		0			0
$817$	−12.0739	+	16.6182i	−0.422411	+	0.581399i
$818$		−	2.99524i		−	0.104726i
$819$		0			0
$820$	0.227964	−	1.19178i	0.00796086	−	0.0416189i
$821$	8.94831	−	6.50133i	0.312298	−	0.226898i	−0.420584	−	0.907254i	$-0.638175\pi$
$821$	8.94831	−	6.50133i	0.312298	−	0.226898i	0.732882	+	0.680356i	$0.238175\pi$
$822$		0			0
$823$	−12.4591	+	4.04822i	−0.434298	+	0.141112i	−0.518003	−	0.855379i	$-0.673325\pi$
$823$	−12.4591	+	4.04822i	−0.434298	+	0.141112i	0.0837054	+	0.996491i	$0.473325\pi$
$824$	−11.3150			−0.394177
$825$		0			0
$826$	−9.81073			−0.341359
$827$	−10.5932	+	3.44195i	−0.368362	+	0.119688i	−0.487348	−	0.873208i	$-0.662036\pi$
$827$	−10.5932	+	3.44195i	−0.368362	+	0.119688i	0.118986	+	0.992896i	$0.462036\pi$
$828$		0			0
$829$	−22.0379	+	16.0114i	−0.765407	+	0.556101i	−0.900564	−	0.434724i	$-0.856846\pi$
$829$	−22.0379	+	16.0114i	−0.765407	+	0.556101i	0.135157	+	0.990824i	$0.456846\pi$
$830$	−14.5014	+	13.6040i	−0.503349	+	0.472201i
$831$		0			0
$832$			0.994174i			0.0344668i
$833$	−1.23853	+	1.70469i	−0.0429125	+	0.0590640i
$834$		0			0
$835$	1.69546	−	0.796785i	0.0586739	−	0.0275739i
$836$	5.27485	+	16.2343i	0.182434	+	0.561476i
$837$		0			0
$838$	−2.17360	−	0.706246i	−0.0750858	−	0.0243969i
$839$	−13.3219	−	41.0007i	−0.459924	−	1.41550i	−0.865256	−	0.501331i	$-0.832844\pi$
$839$	−13.3219	−	41.0007i	−0.459924	−	1.41550i	0.405331	−	0.914170i	$-0.367156\pi$
$840$		0			0
$841$	19.9259	−	61.3257i	0.687100	−	2.11468i
$842$	5.19769	−	7.15400i	0.179124	−	0.246543i
$843$		0			0
$844$	−0.871148	−	0.632926i	−0.0299862	−	0.0217862i
$845$	11.4237	+	24.3083i	0.392988	+	0.836231i
$846$		0			0
$847$	7.92584	+	10.9090i	0.272335	+	0.374837i
$848$	−1.75334	+	0.569693i	−0.0602098	+	0.0195634i
$849$		0			0
$850$	−4.60575	+	1.17763i	−0.157976	+	0.0403924i
$851$	18.9318			0.648972
$852$		0			0
$853$	−20.6992	−	28.4900i	−0.708726	−	0.975478i	−0.999824	−	0.0187844i	$-0.994020\pi$
$853$	−20.6992	−	28.4900i	−0.708726	−	0.975478i	0.291097	−	0.956693i	$-0.405980\pi$
$854$	−29.2724	+	21.2677i	−1.00168	+	0.727765i
$855$		0			0
$856$	5.40859	+	3.92957i	0.184862	+	0.134310i
$857$			21.8959i			0.747949i	0.927439	+	0.373975i	$0.122005\pi$
$857$			21.8959i			0.747949i	−0.927439	+	0.373975i	$0.877995\pi$
$858$		0			0
$859$	6.94501	−	21.3745i	0.236961	−	0.729290i	−0.759895	−	0.650046i	$-0.774750\pi$
$859$	6.94501	−	21.3745i	0.236961	−	0.729290i	0.996855	−	0.0792435i	$-0.0252504\pi$
$860$	0.860237	+	6.83706i	0.0293338	+	0.233142i
$861$		0			0
$862$	3.90615	+	1.26919i	0.133044	+	0.0432287i
$863$	27.3514	+	8.88701i	0.931052	+	0.302517i	0.734993	−	0.678075i	$-0.237185\pi$
$863$	27.3514	+	8.88701i	0.931052	+	0.302517i	0.196059	+	0.980592i	$0.437185\pi$
$864$		0			0
$865$	41.3775	+	7.91469i	1.40688	+	0.269108i
$866$	9.82252	−	30.2306i	0.333783	−	1.02728i
$867$		0			0
$868$		−	21.2223i		−	0.720333i
$869$	31.5689	+	22.9361i	1.07090	+	0.778056i
$870$		0			0
$871$	10.0170	−	7.27781i	0.339415	−	0.246599i
$872$	2.74674	+	3.78056i	0.0930162	+	0.128026i
$873$		0			0
$874$	−40.7895			−1.37973
$875$	33.8777	−	2.08023i	1.14527	−	0.0703246i
$876$		0			0
$877$	−1.61861	+	0.525918i	−0.0546565	+	0.0177590i	−0.336218	−	0.941784i	$-0.609148\pi$
$877$	−1.61861	+	0.525918i	−0.0546565	+	0.0177590i	0.281561	+	0.959543i	$0.409148\pi$
$878$	2.66804	+	3.67224i	0.0900418	+	0.123932i
$879$		0			0
$880$	5.01668	+	2.76122i	0.169112	+	0.0930807i
$881$	−33.1469	−	24.0826i	−1.11675	−	0.811365i	−0.133035	−	0.991111i	$-0.542472\pi$
$881$	−33.1469	−	24.0826i	−1.11675	−	0.811365i	−0.983713	+	0.179747i	$0.942472\pi$
$882$		0			0
$883$	27.0705	−	37.2593i	0.910993	−	1.25387i	−0.0558329	−	0.998440i	$-0.517781\pi$
$883$	27.0705	−	37.2593i	0.910993	−	1.25387i	0.966826	−	0.255435i	$-0.0822186\pi$
$884$	−0.292096	+	0.898980i	−0.00982426	+	0.0302360i
$885$		0			0
$886$	−10.7624	−	33.1233i	−0.361570	−	1.11280i
$887$	22.9233	+	7.44823i	0.769689	+	0.250087i	0.667432	−	0.744671i	$-0.267394\pi$
$887$	22.9233	+	7.44823i	0.769689	+	0.250087i	0.102257	+	0.994758i	$0.467394\pi$
$888$		0			0
$889$	−5.03168	−	15.4859i	−0.168757	−	0.519381i
$890$	2.49722	+	19.8476i	0.0837070	+	0.665293i
$891$		0			0
$892$	−4.03716	+	5.55667i	−0.135174	+	0.186051i
$893$		−	18.4230i		−	0.616502i
$894$		0			0
$895$	−1.97946	+	0.249055i	−0.0661660	+	0.00832500i
$896$	−2.45603	+	1.78441i	−0.0820501	+	0.0596129i
$897$		0			0
$898$	10.3800	−	3.37265i	0.346384	−	0.112547i
$899$	67.5897			2.25424
$900$		0			0
$901$	−1.75283			−0.0583953
$902$	−1.32165	+	0.429430i	−0.0440061	+	0.0142985i
$903$		0			0
$904$	−11.5741	+	8.40906i	−0.384948	+	0.279681i
$905$	−2.09220	−	4.45195i	−0.0695472	−	0.147988i
$906$		0			0
$907$			58.9644i			1.95788i	0.204144	+	0.978941i	$0.434559\pi$
$907$			58.9644i			1.95788i	−0.204144	+	0.978941i	$0.565441\pi$
$908$	−9.73857	+	13.4040i	−0.323186	+	0.444827i
$909$		0			0
$910$	3.25420	−	5.91234i	0.107876	−	0.195992i
$911$	14.8561	+	45.7224i	0.492204	+	1.51485i	0.821268	+	0.570542i	$0.193267\pi$
$911$	14.8561	+	45.7224i	0.492204	+	1.51485i	−0.329064	+	0.944308i	$0.606733\pi$
$912$		0			0
$913$	21.6577	+	7.03700i	0.716764	+	0.232891i
$914$	−1.66938	−	5.13783i	−0.0552183	−	0.169944i
$915$		0			0
$916$	2.31519	−	7.12543i	0.0764961	−	0.235431i
$917$	9.53060	−	13.1178i	0.314728	−	0.433186i
$918$		0			0
$919$	−1.67495	−	1.21692i	−0.0552515	−	0.0401426i	0.559817	−	0.828616i	$-0.310872\pi$
$919$	−1.67495	−	1.21692i	−0.0552515	−	0.0401426i	−0.615068	+	0.788474i	$0.710872\pi$
$920$	−9.97963	+	9.36208i	−0.329019	+	0.308659i
$921$		0			0
$922$	18.1927	+	25.0401i	0.599145	+	0.824652i
$923$	−10.1077	+	3.28420i	−0.332700	+	0.108101i
$924$		0			0
$925$	−3.83180	−	14.9863i	−0.125989	−	0.492745i
$926$	35.5988			1.16985
$927$		0			0
$928$	−5.68305	−	7.82205i	−0.186555	−	0.256771i
$929$	0.0530753	−	0.0385615i	0.00174134	−	0.00126516i	−0.586914	−	0.809649i	$-0.699657\pi$
$929$	0.0530753	−	0.0385615i	0.00174134	−	0.00126516i	0.588656	+	0.808384i	$0.299657\pi$
$930$		0			0
$931$	11.9508	+	8.68275i	0.391671	+	0.284566i
$932$		−	24.0990i		−	0.789387i
$933$		0			0
$934$	9.33245	−	28.7223i	0.305367	−	0.939823i
$935$	3.72506	+	3.97077i	0.121822	+	0.129858i
$936$		0			0
$937$	2.72528	+	0.885498i	0.0890311	+	0.0289280i	0.353194	−	0.935550i	$-0.385096\pi$
$937$	2.72528	+	0.885498i	0.0890311	+	0.0289280i	−0.264163	+	0.964478i	$0.585096\pi$
$938$	35.9585	+	11.6836i	1.17409	+	0.381484i
$939$		0			0
$940$	−4.22847	−	4.50740i	−0.137918	−	0.147015i
$941$	−14.8230	+	45.6205i	−0.483216	+	1.48719i	0.351331	+	0.936251i	$0.385729\pi$
$941$	−14.8230	+	45.6205i	−0.483216	+	1.48719i	−0.834547	+	0.550936i	$0.814271\pi$
$942$		0			0
$943$		−	3.32071i		−	0.108137i
$944$	−2.61447	−	1.89952i	−0.0850937	−	0.0618242i
$945$		0			0
$946$	6.38480	−	4.63883i	0.207588	−	0.150821i
$947$	9.72732	+	13.3885i	0.316095	+	0.435068i	0.937270	−	0.348604i	$-0.113344\pi$
$947$	9.72732	+	13.3885i	0.316095	+	0.435068i	−0.621175	+	0.783672i	$0.713344\pi$
$948$		0			0
$949$	−14.4026			−0.467529
$950$	8.25582	+	32.2887i	0.267854	+	1.04759i
$951$		0			0
$952$	−2.74513	+	0.891948i	−0.0889703	+	0.0289082i
$953$	12.7070	+	17.4897i	0.411620	+	0.566547i	0.963613	−	0.267302i	$-0.0861323\pi$
$953$	12.7070	+	17.4897i	0.411620	+	0.566547i	−0.551992	+	0.833849i	$0.686132\pi$
$954$		0			0
$955$	35.4975	−	33.3009i	1.14867	−	1.07759i
$956$	−13.6743	−	9.93492i	−0.442257	−	0.321318i
$957$		0			0
$958$	−16.9537	+	23.3347i	−0.547749	+	0.753911i
$959$	16.5911	−	51.0621i	0.535754	−	1.64888i
$960$		0			0
$961$	5.52189	+	16.9946i	0.178126	+	0.548214i
$962$	−2.92512	−	0.950428i	−0.0943096	−	0.0306430i
$963$		0			0
$964$	−4.12129	−	12.6840i	−0.132738	−	0.408525i
$965$	3.80256	−	6.90862i	0.122409	−	0.222396i
$966$		0			0
$967$	−31.5576	+	43.4354i	−1.01483	+	1.39679i	−0.0990564	+	0.995082i	$0.531582\pi$
$967$	−31.5576	+	43.4354i	−1.01483	+	1.39679i	−0.915769	+	0.401705i	$0.868418\pi$
$968$			4.44172i			0.142762i
$969$		0			0
$970$	−1.35260	−	2.87817i	−0.0434293	−	0.0924123i
$971$	−26.9231	+	19.5608i	−0.864004	+	0.627736i	−0.928971	−	0.370152i	$-0.879306\pi$
$971$	−26.9231	+	19.5608i	−0.864004	+	0.627736i	0.0649671	+	0.997887i	$0.479306\pi$
$972$		0			0
$973$	2.93958	−	0.955127i	0.0942386	−	0.0306200i
$974$	20.7789			0.665799
$975$		0			0
$976$	−11.9186			−0.381505
$977$	2.77297	−	0.900992i	0.0887151	−	0.0288253i	−0.264323	−	0.964434i	$-0.585149\pi$
$977$	2.77297	−	0.900992i	0.0887151	−	0.0288253i	0.353038	+	0.935609i	$0.385149\pi$
$978$		0			0
$979$	18.5347	−	13.4663i	0.592372	−	0.430384i
$980$	4.91678	−	0.618628i	0.157061	−	0.0197613i
$981$		0			0
$982$		−	33.3630i		−	1.06466i
$983$	29.0173	−	39.9389i	0.925510	−	1.27385i	−0.0360759	−	0.999349i	$-0.511486\pi$
$983$	29.0173	−	39.9389i	0.925510	−	1.27385i	0.961586	−	0.274506i	$-0.0885142\pi$
$984$		0			0
$985$	4.97091	+	39.5082i	0.158386	+	1.25883i
$986$	−2.84071	−	8.74281i	−0.0904666	−	0.278428i
$987$		0			0
$988$	6.30233	+	2.04775i	0.200504	+	0.0651477i
$989$	5.82765	+	17.9357i	0.185308	+	0.570321i
$990$		0			0
$991$	3.48465	−	10.7247i	0.110694	−	0.340680i	−0.880331	−	0.474360i	$-0.842679\pi$
$991$	3.48465	−	10.7247i	0.110694	−	0.340680i	0.991025	+	0.133680i	$0.0426795\pi$
$992$	4.10900	−	5.65556i	0.130461	−	0.179564i
$993$		0			0
$994$	−26.2554	−	19.0757i	−0.832770	−	0.605043i
$995$	5.75422	+	3.16717i	0.182421	+	0.100406i
$996$		0			0
$997$	−26.0485	−	35.8527i	−0.824966	−	1.13547i	−0.988839	−	0.148987i	$-0.952399\pi$
$997$	−26.0485	−	35.8527i	−0.824966	−	1.13547i	0.163873	−	0.986481i	$-0.447601\pi$
$998$	−14.3914	+	4.67603i	−0.455550	+	0.148017i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.d.19.1	✓	16
3.2	odd	2	inner	450.2.l.d.19.4	yes	16
25.4	even	10	inner	450.2.l.d.379.1	yes	16
75.29	odd	10	inner	450.2.l.d.379.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.l.d.19.1	✓	16	1.1	even	1	trivial
450.2.l.d.19.4	yes	16	3.2	odd	2	inner
450.2.l.d.379.1	yes	16	25.4	even	10	inner
450.2.l.d.379.4	yes	16	75.29	odd	10	inner

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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-1.95894 - 1.07822i) q^{5} +3.03582i q^{7} +(-0.587785 + 0.809017i) q^{8} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-1.95894 - 1.07822i) q^{5} +3.03582i q^{7} +(-0.587785 + 0.809017i) q^{8} +(2.19625 + 0.420099i) q^{10} +(-0.791366 - 2.43557i) q^{11} +(-0.945515 - 0.307217i) q^{13} +(-0.938119 - 2.88723i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.558856 - 0.769200i) q^{17} +(-5.39250 - 3.91788i) q^{19} +(-2.21858 + 0.279141i) q^{20} +(1.50527 + 2.07182i) q^{22} +(-5.81999 + 1.89103i) q^{23} +(2.67490 + 4.22433i) q^{25} +0.994174 q^{26} +(1.78441 + 2.45603i) q^{28} +(-7.82205 + 5.68305i) q^{29} +(-5.65556 - 4.10900i) q^{31} +1.00000i q^{32} +(-0.293808 + 0.904248i) q^{34} +(3.27327 - 5.94699i) q^{35} +(-2.94226 - 0.955998i) q^{37} +(6.33927 + 2.05975i) q^{38} +(2.02373 - 0.951057i) q^{40} +(-0.167686 + 0.516085i) q^{41} -3.08173i q^{43} +(-2.07182 - 1.50527i) q^{44} +(4.95078 - 3.59695i) q^{46} +(1.62460 + 2.23607i) q^{47} -2.21619 q^{49} +(-3.84937 - 3.19098i) q^{50} +(-0.945515 + 0.307217i) q^{52} +(-1.08362 - 1.49148i) q^{53} +(-1.07584 + 5.62441i) q^{55} +(-2.45603 - 1.78441i) q^{56} +(5.68305 - 7.82205i) q^{58} +(0.998638 - 3.07349i) q^{59} +(-3.68305 - 11.3353i) q^{61} +(6.64851 + 2.16023i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(1.52096 + 1.62129i) q^{65} +(-7.32046 + 10.0758i) q^{67} -0.950783i q^{68} +(-1.27534 + 6.66742i) q^{70} +(8.64854 - 6.28353i) q^{71} +(13.7780 - 4.47674i) q^{73} +3.09368 q^{74} -6.66550 q^{76} +(7.39396 - 2.40244i) q^{77} +(-12.3272 + 8.95623i) q^{79} +(-1.63079 + 1.52988i) q^{80} -0.542644i q^{82} +(-5.22672 + 7.19396i) q^{83} +(-1.92413 + 0.904248i) q^{85} +(0.952307 + 2.93090i) q^{86} +(2.43557 + 0.791366i) q^{88} +(2.76450 + 8.50824i) q^{89} +(0.932653 - 2.87041i) q^{91} +(-3.59695 + 4.95078i) q^{92} +(-2.23607 - 1.62460i) q^{94} +(6.33927 + 13.4892i) q^{95} +(-0.835952 - 1.15059i) q^{97} +(2.10772 - 0.684839i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4}+O(q^{10}) \) 16 * q + 4 * q^4	\( 16 q + 4 q^{4} - 4 q^{16} - 16 q^{19} - 20 q^{22} + 20 q^{25} - 10 q^{28} + 6 q^{31} - 26 q^{34} + 10 q^{37} + 20 q^{46} + 28 q^{49} - 20 q^{55} + 32 q^{61} + 4 q^{64} - 40 q^{67} - 30 q^{70} - 24 q^{76} - 36 q^{79} - 70 q^{85} + 10 q^{88} + 52 q^{91} - 70 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 - 4 * q^16 - 16 * q^19 - 20 * q^22 + 20 * q^25 - 10 * q^28 + 6 * q^31 - 26 * q^34 + 10 * q^37 + 20 * q^46 + 28 * q^49 - 20 * q^55 + 32 * q^61 + 4 * q^64 - 40 * q^67 - 30 * q^70 - 24 * q^76 - 36 * q^79 - 70 * q^85 + 10 * q^88 + 52 * q^91 - 70 * q^97

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