LMFDB - Embedded newform 450.2.l.b.19.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.2
Root			$0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	450.19
Dual form			450.2.l.b.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-0.847859 + 2.06909i) q^{5} +1.07768i q^{7} +(0.587785 - 0.809017i) q^{8} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-0.847859 + 2.06909i) q^{5} +1.07768i q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.166977 + 2.22982i) q^{10} +(0.638757 + 1.96589i) q^{11} +(5.51005 + 1.79032i) q^{13} +(0.333023 + 1.02494i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.484587 - 0.666977i) q^{17} +(2.76007 + 2.00531i) q^{19} +(0.530249 + 2.17229i) q^{20} +(1.21499 + 1.67229i) q^{22} +(-1.86655 + 0.606480i) q^{23} +(-3.56227 - 3.50859i) q^{25} +5.79360 q^{26} +(0.633446 + 0.871864i) q^{28} +(0.847859 - 0.616005i) q^{29} +(-1.71113 - 1.24321i) q^{31} -1.00000i q^{32} +(0.254763 - 0.784079i) q^{34} +(-2.22982 - 0.913723i) q^{35} +(-8.27012 - 2.68712i) q^{37} +(3.24466 + 1.05425i) q^{38} +(1.17557 + 1.90211i) q^{40} +(2.03150 - 6.25232i) q^{41} +7.47684i q^{43} +(1.67229 + 1.21499i) q^{44} +(-1.58779 + 1.15359i) q^{46} +(-5.08538 - 6.99942i) q^{47} +5.83860 q^{49} +(-4.47214 - 2.23607i) q^{50} +(5.51005 - 1.79032i) q^{52} +(1.50953 + 2.07768i) q^{53} +(-4.60919 - 0.345153i) q^{55} +(0.871864 + 0.633446i) q^{56} +(0.616005 - 0.847859i) q^{58} +(1.45309 - 4.47214i) q^{59} +(-2.86858 - 8.82859i) q^{61} +(-2.01155 - 0.653594i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(-8.37608 + 9.88284i) q^{65} +(2.56378 - 3.52874i) q^{67} -0.824429i q^{68} +(-2.40305 - 0.179949i) q^{70} +(3.96740 - 2.88249i) q^{71} +(-1.23420 + 0.401017i) q^{73} -8.69572 q^{74} +3.41164 q^{76} +(-2.11861 + 0.688378i) q^{77} +(-5.82141 + 4.22950i) q^{79} +(1.70582 + 1.44575i) q^{80} -6.57408i q^{82} +(-8.79798 + 12.1094i) q^{83} +(0.969175 + 1.56816i) q^{85} +(2.31047 + 7.11089i) q^{86} +(1.96589 + 0.638757i) q^{88} +(-3.61803 - 11.1352i) q^{89} +(-1.92940 + 5.93809i) q^{91} +(-1.15359 + 1.58779i) q^{92} +(-6.99942 - 5.08538i) q^{94} +(-6.48932 + 4.01062i) q^{95} +(0.300169 + 0.413147i) q^{97} +(5.55284 - 1.80423i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 10 q^{5}+O(q^{10}) $ 8 * q + 2 * q^4 + 10 * q^5	$ 8 q + 2 q^{4} + 10 q^{5} + 4 q^{11} + 4 q^{14} - 2 q^{16} - 10 q^{17} + 10 q^{19} + 20 q^{22} - 10 q^{23} + 10 q^{25} + 28 q^{26} + 10 q^{28} - 10 q^{29} + 6 q^{31} - 4 q^{34} - 10 q^{35} - 10 q^{37} + 14 q^{41} + 6 q^{44} - 8 q^{46} + 30 q^{47} - 16 q^{49} - 10 q^{55} - 4 q^{56} - 14 q^{61} + 2 q^{64} - 50 q^{65} + 10 q^{67} + 34 q^{71} - 36 q^{74} - 40 q^{77} - 50 q^{83} - 20 q^{85} - 22 q^{86} - 10 q^{88} - 20 q^{89} - 4 q^{91} + 10 q^{92} - 24 q^{94} - 20 q^{97} + 40 q^{98}+O(q^{100}) $ 8 * q + 2 * q^4 + 10 * q^5 + 4 * q^11 + 4 * q^14 - 2 * q^16 - 10 * q^17 + 10 * q^19 + 20 * q^22 - 10 * q^23 + 10 * q^25 + 28 * q^26 + 10 * q^28 - 10 * q^29 + 6 * q^31 - 4 * q^34 - 10 * q^35 - 10 * q^37 + 14 * q^41 + 6 * q^44 - 8 * q^46 + 30 * q^47 - 16 * q^49 - 10 * q^55 - 4 * q^56 - 14 * q^61 + 2 * q^64 - 50 * q^65 + 10 * q^67 + 34 * q^71 - 36 * q^74 - 40 * q^77 - 50 * q^83 - 20 * q^85 - 22 * q^86 - 10 * q^88 - 20 * q^89 - 4 * q^91 + 10 * q^92 - 24 * q^94 - 20 * q^97 + 40 * q^98

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
$5$	−0.847859	+	2.06909i	−0.379174	+	0.925325i
$5$	−0.847859	+	2.06909i	−0.379174	+	0.925325i
$6$		0			0
$7$			1.07768i			0.407326i	0.979041	+	0.203663i	$0.0652847\pi$
$7$			1.07768i			0.407326i	−0.979041	+	0.203663i	$0.934715\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$		0			0
$10$	−0.166977	+	2.22982i	−0.0528029	+	0.705133i
$11$	0.638757	+	1.96589i	0.192593	+	0.592739i	0.999996	+	0.00273957i	$0.000872032\pi$
$11$	0.638757	+	1.96589i	0.192593	+	0.592739i	−0.807404	+	0.589999i	$0.799128\pi$
$12$		0			0
$13$	5.51005	+	1.79032i	1.52821	+	0.496546i	0.948095	−	0.317987i	$-0.103007\pi$
$13$	5.51005	+	1.79032i	1.52821	+	0.496546i	0.580117	+	0.814533i	$0.303007\pi$
$14$	0.333023	+	1.02494i	0.0890040	+	0.273926i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.484587	−	0.666977i	0.117530	−	0.161766i	−0.746199	−	0.665723i	$-0.768123\pi$
$17$	0.484587	−	0.666977i	0.117530	−	0.161766i	0.863729	+	0.503957i	$0.168123\pi$
$18$		0			0
$19$	2.76007	+	2.00531i	0.633204	+	0.460050i	0.857509	−	0.514469i	$-0.172011\pi$
$19$	2.76007	+	2.00531i	0.633204	+	0.460050i	−0.224305	+	0.974519i	$0.572011\pi$
$20$	0.530249	+	2.17229i	0.118567	+	0.485738i
$21$		0			0
$22$	1.21499	+	1.67229i	0.259036	+	0.356533i
$23$	−1.86655	+	0.606480i	−0.389203	+	0.126460i	−0.497081	−	0.867704i	$-0.665595\pi$
$23$	−1.86655	+	0.606480i	−0.389203	+	0.126460i	0.107877	+	0.994164i	$0.465595\pi$
$24$		0			0
$25$	−3.56227	−	3.50859i	−0.712454	−	0.701719i
$26$	5.79360			1.13622
$27$		0			0
$28$	0.633446	+	0.871864i	0.119710	+	0.164767i
$29$	0.847859	−	0.616005i	0.157443	−	0.114389i	−0.506274	−	0.862373i	$-0.668978\pi$
$29$	0.847859	−	0.616005i	0.157443	−	0.114389i	0.663718	+	0.747983i	$0.268978\pi$
$30$		0			0
$31$	−1.71113	−	1.24321i	−0.307328	−	0.223287i	0.423421	−	0.905933i	$-0.360829\pi$
$31$	−1.71113	−	1.24321i	−0.307328	−	0.223287i	−0.730749	+	0.682646i	$0.760829\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	0.254763	−	0.784079i	0.0436914	−	0.134468i
$35$	−2.22982	−	0.913723i	−0.376909	−	0.154447i
$36$		0			0
$37$	−8.27012	−	2.68712i	−1.35960	−	0.441761i	−0.463690	−	0.885998i	$-0.653475\pi$
$37$	−8.27012	−	2.68712i	−1.35960	−	0.441761i	−0.895909	+	0.444237i	$0.853475\pi$
$38$	3.24466	+	1.05425i	0.526354	+	0.171023i
$39$		0			0
$40$	1.17557	+	1.90211i	0.185874	+	0.300750i
$41$	2.03150	−	6.25232i	0.317267	−	0.976449i	−0.657544	−	0.753416i	$-0.728404\pi$
$41$	2.03150	−	6.25232i	0.317267	−	0.976449i	0.974811	−	0.223032i	$-0.0715955\pi$
$42$		0			0
$43$			7.47684i			1.14021i	0.821573	+	0.570103i	$0.193097\pi$
$43$			7.47684i			1.14021i	−0.821573	+	0.570103i	$0.806903\pi$
$44$	1.67229	+	1.21499i	0.252107	+	0.183166i
$45$		0			0
$46$	−1.58779	+	1.15359i	−0.234106	+	0.170088i
$47$	−5.08538	−	6.99942i	−0.741779	−	1.02097i	−0.998514	−	0.0544892i	$-0.982647\pi$
$47$	−5.08538	−	6.99942i	−0.741779	−	1.02097i	0.256736	−	0.966482i	$-0.417353\pi$
$48$		0			0
$49$	5.83860			0.834085
$50$	−4.47214	−	2.23607i	−0.632456	−	0.316228i
$51$		0			0
$52$	5.51005	−	1.79032i	0.764106	−	0.248273i
$53$	1.50953	+	2.07768i	0.207349	+	0.285392i	0.900008	−	0.435874i	$-0.143561\pi$
$53$	1.50953	+	2.07768i	0.207349	+	0.285392i	−0.692658	+	0.721266i	$0.743561\pi$
$54$		0			0
$55$	−4.60919	−	0.345153i	−0.621503	−	0.0465404i
$56$	0.871864	+	0.633446i	0.116508	+	0.0846478i
$57$		0			0
$58$	0.616005	−	0.847859i	0.0808855	−	0.111329i
$59$	1.45309	−	4.47214i	0.189176	−	0.582223i	−0.810820	−	0.585296i	$-0.800978\pi$
$59$	1.45309	−	4.47214i	0.189176	−	0.582223i	0.999995	+	0.00307347i	$0.000978319\pi$
$60$		0			0
$61$	−2.86858	−	8.82859i	−0.367284	−	1.13038i	−0.948538	−	0.316663i	$-0.897438\pi$
$61$	−2.86858	−	8.82859i	−0.367284	−	1.13038i	0.581254	−	0.813722i	$-0.302562\pi$
$62$	−2.01155	−	0.653594i	−0.255468	−	0.0830065i
$63$		0			0
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−8.37608	+	9.88284i	−1.03892	+	1.22582i
$66$		0			0
$67$	2.56378	−	3.52874i	0.313216	−	0.431104i	−0.623165	−	0.782090i	$-0.714154\pi$
$67$	2.56378	−	3.52874i	0.313216	−	0.431104i	0.936381	+	0.350986i	$0.114154\pi$
$68$		−	0.824429i		−	0.0999768i
$69$		0			0
$70$	−2.40305	−	0.179949i	−0.287219	−	0.0215080i
$71$	3.96740	−	2.88249i	0.470844	−	0.342088i	−0.326926	−	0.945050i	$-0.606013\pi$
$71$	3.96740	−	2.88249i	0.470844	−	0.342088i	0.797770	+	0.602962i	$0.206013\pi$
$72$		0			0
$73$	−1.23420	+	0.401017i	−0.144453	+	0.0469355i	−0.380351	−	0.924842i	$-0.624197\pi$
$73$	−1.23420	+	0.401017i	−0.144453	+	0.0469355i	0.235898	+	0.971778i	$0.424197\pi$
$74$	−8.69572			−1.01086
$75$		0			0
$76$	3.41164			0.391342
$77$	−2.11861	+	0.688378i	−0.241438	+	0.0784480i
$78$		0			0
$79$	−5.82141	+	4.22950i	−0.654960	+	0.475856i	−0.864957	−	0.501846i	$-0.832655\pi$
$79$	−5.82141	+	4.22950i	−0.654960	+	0.475856i	0.209997	+	0.977702i	$0.432655\pi$
$80$	1.70582	+	1.44575i	0.190716	+	0.161639i
$81$		0			0
$82$		−	6.57408i		−	0.725986i
$83$	−8.79798	+	12.1094i	−0.965704	+	1.32918i	−0.0215168	+	0.999768i	$0.506850\pi$
$83$	−8.79798	+	12.1094i	−0.965704	+	1.32918i	−0.944187	+	0.329409i	$0.893150\pi$
$84$		0			0
$85$	0.969175	+	1.56816i	0.105122	+	0.170091i
$86$	2.31047	+	7.11089i	0.249144	+	0.766787i
$87$		0			0
$88$	1.96589	+	0.638757i	0.209565	+	0.0680918i
$89$	−3.61803	−	11.1352i	−0.383511	−	1.18032i	−0.937555	−	0.347838i	$-0.886916\pi$
$89$	−3.61803	−	11.1352i	−0.383511	−	1.18032i	0.554044	−	0.832487i	$-0.313084\pi$
$90$		0			0
$91$	−1.92940	+	5.93809i	−0.202256	+	0.622480i
$92$	−1.15359	+	1.58779i	−0.120270	+	0.165538i
$93$		0			0
$94$	−6.99942	−	5.08538i	−0.721935	−	0.524517i
$95$	−6.48932	+	4.01062i	−0.665790	+	0.411481i
$96$		0			0
$97$	0.300169	+	0.413147i	0.0304775	+	0.0419487i	0.823984	−	0.566613i	$-0.191747\pi$
$97$	0.300169	+	0.413147i	0.0304775	+	0.0419487i	−0.793506	+	0.608562i	$0.791747\pi$
$98$	5.55284	−	1.80423i	0.560921	−	0.182254i
$99$		0			0
$100$	−4.94424	−	0.744661i	−0.494424	−	0.0744661i
$101$	3.50766			0.349025			0.174513	−	0.984655i	$-0.444165\pi$
$101$	3.50766			0.349025			0.174513	+	0.984655i	$0.444165\pi$
$102$		0			0
$103$	−2.72837	−	3.75528i	−0.268835	−	0.370019i	0.653161	−	0.757219i	$-0.273442\pi$
$103$	−2.72837	−	3.75528i	−0.268835	−	0.370019i	−0.921996	+	0.387200i	$0.873442\pi$
$104$	4.68712	−	3.40540i	0.459610	−	0.333926i
$105$		0			0
$106$	2.07768	+	1.50953i	0.201802	+	0.146618i
$107$		−	7.60189i		−	0.734902i	−0.930043	−	0.367451i	$-0.880231\pi$
$107$		−	7.60189i		−	0.734902i	0.930043	−	0.367451i	$-0.119769\pi$
$108$		0			0
$109$	0.922836	−	2.84020i	0.0883917	−	0.272042i	−0.897084	−	0.441861i	$-0.854318\pi$
$109$	0.922836	−	2.84020i	0.0883917	−	0.272042i	0.985475	+	0.169819i	$0.0543184\pi$
$110$	−4.49025	+	1.09606i	−0.428129	+	0.104505i
$111$		0			0
$112$	1.02494	+	0.333023i	0.0968475	+	0.0314677i
$113$	19.2100	+	6.24170i	1.80712	+	0.587170i	0.999995	−	0.00320699i	$-0.00102082\pi$
$113$	19.2100	+	6.24170i	1.80712	+	0.587170i	0.807128	+	0.590377i	$0.201021\pi$
$114$		0			0
$115$	0.327712	−	4.37628i	0.0305593	−	0.408090i
$116$	0.323853	−	0.996718i	0.0300690	−	0.0925429i
$117$		0			0
$118$		−	4.70228i		−	0.432880i
$119$	0.718791	+	0.522232i	0.0658914	+	0.0478729i
$120$		0			0
$121$	5.44246	−	3.95418i	0.494769	−	0.359471i
$122$	−5.45637	−	7.51005i	−0.493996	−	0.679928i
$123$		0			0
$124$	−2.11507			−0.189939
$125$	10.2799	−	4.39587i	0.919462	−	0.393179i
$126$		0			0
$127$	−20.3060	+	6.59783i	−1.80187	+	0.585463i	−0.999929	−	0.0119411i	$-0.996199\pi$
$127$	−20.3060	+	6.59783i	−1.80187	+	0.585463i	−0.801940	+	0.597404i	$0.796199\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$		0			0
$130$	−4.91216	+	11.9875i	−0.430825	+	1.05137i
$131$	−7.28730	−	5.29454i	−0.636695	−	0.462586i	0.222018	−	0.975042i	$-0.428736\pi$
$131$	−7.28730	−	5.29454i	−0.636695	−	0.462586i	−0.858713	+	0.512457i	$0.828736\pi$
$132$		0			0
$133$	−2.16109	+	2.97449i	−0.187390	+	0.257921i
$134$	1.34786	−	4.14828i	0.116437	−	0.358357i
$135$		0			0
$136$	−0.254763	−	0.784079i	−0.0218457	−	0.0672342i
$137$	−4.27168	−	1.38795i	−0.364955	−	0.118581i	0.120798	−	0.992677i	$-0.461455\pi$
$137$	−4.27168	−	1.38795i	−0.364955	−	0.118581i	−0.485753	+	0.874096i	$0.661455\pi$
$138$		0			0
$139$	−4.14204	−	12.7479i	−0.351323	−	1.08126i	−0.958111	−	0.286398i	$-0.907542\pi$
$139$	−4.14204	−	12.7479i	−0.351323	−	1.08126i	0.606788	−	0.794864i	$-0.292458\pi$
$140$	−2.34104	+	0.571440i	−0.197854	+	0.0482955i
$141$		0			0
$142$	2.88249	−	3.96740i	0.241893	−	0.332937i
$143$			11.9757i			1.00146i
$144$		0			0
$145$	0.555707	+	2.27658i	0.0461489	+	0.189060i
$146$	−1.04988	+	0.762779i	−0.0868883	+	0.0631281i
$147$		0			0
$148$	−8.27012	+	2.68712i	−0.679800	+	0.220880i
$149$	13.6139			1.11529			0.557646	−	0.830079i	$-0.311705\pi$
$149$	13.6139			1.11529			0.557646	+	0.830079i	$0.311705\pi$
$150$		0			0
$151$	8.79830			0.715996			0.357998	−	0.933722i	$-0.383459\pi$
$151$	8.79830			0.715996			0.357998	+	0.933722i	$0.383459\pi$
$152$	3.24466	−	1.05425i	0.263177	−	0.0855113i
$153$		0			0
$154$	−1.80220	+	1.30937i	−0.145225	+	0.105512i
$155$	4.02311	−	2.48642i	0.323144	−	0.199714i
$156$		0			0
$157$		−	11.8558i		−	0.946195i	−0.881010	−	0.473097i	$-0.843136\pi$
$157$		−	11.8558i		−	0.946195i	0.881010	−	0.473097i	$-0.156864\pi$
$158$	−4.22950	+	5.82141i	−0.336481	+	0.463127i
$159$		0			0
$160$	2.06909	+	0.847859i	0.163576	+	0.0670291i
$161$	−0.653594	−	2.01155i	−0.0515104	−	0.158533i
$162$		0			0
$163$	14.2268	+	4.62257i	1.11433	+	0.362068i	0.807601	−	0.589729i	$-0.200766\pi$
$163$	14.2268	+	4.62257i	1.11433	+	0.362068i	0.306729	+	0.951797i	$0.400766\pi$
$164$	−2.03150	−	6.25232i	−0.158634	−	0.488224i
$165$		0			0
$166$	−4.62537	+	14.2354i	−0.358999	+	1.10488i
$167$	−12.6785	+	17.4504i	−0.981090	+	1.35035i	−0.0448496	+	0.998994i	$0.514281\pi$
$167$	−12.6785	+	17.4504i	−0.981090	+	1.35035i	−0.936240	+	0.351361i	$0.885719\pi$
$168$		0			0
$169$	16.6381	+	12.0883i	1.27986	+	0.929870i
$170$	1.40633	+	1.19192i	0.107860	+	0.0914157i
$171$		0			0
$172$	4.39477	+	6.04889i	0.335098	+	0.461223i
$173$	−4.26574	+	1.38602i	−0.324318	+	0.105377i	−0.466651	−	0.884441i	$-0.654540\pi$
$173$	−4.26574	+	1.38602i	−0.324318	+	0.105377i	0.142333	+	0.989819i	$0.454540\pi$
$174$		0			0
$175$	3.78115	−	3.83900i	0.285828	−	0.290201i
$176$	2.06706			0.155811
$177$		0			0
$178$	−6.88191	−	9.47214i	−0.515821	−	0.709967i
$179$	12.2423	−	8.89456i	0.915033	−	0.664811i	−0.0272495	−	0.999629i	$-0.508675\pi$
$179$	12.2423	−	8.89456i	0.915033	−	0.664811i	0.942283	+	0.334818i	$0.108675\pi$
$180$		0			0
$181$	7.94542	+	5.77269i	0.590579	+	0.429081i	0.842522	−	0.538661i	$-0.181070\pi$
$181$	7.94542	+	5.77269i	0.590579	+	0.429081i	−0.251944	+	0.967742i	$0.581070\pi$
$182$			6.24367i			0.462812i
$183$		0			0
$184$	−0.606480	+	1.86655i	−0.0447103	+	0.137604i
$185$	12.5718	−	14.8333i	0.924297	−	1.09057i
$186$		0			0
$187$	1.62074	+	0.526610i	0.118520	+	0.0385096i
$188$	−8.22832	−	2.67354i	−0.600112	−	0.194988i
$189$		0			0
$190$	−4.93236	+	5.81964i	−0.357831	+	0.422201i
$191$	−6.01130	+	18.5009i	−0.434962	+	1.33868i	0.458163	+	0.888868i	$0.348508\pi$
$191$	−6.01130	+	18.5009i	−0.434962	+	1.33868i	−0.893125	+	0.449808i	$0.851492\pi$
$192$		0			0
$193$			6.00000i			0.431889i	0.976406	+	0.215945i	$0.0692831\pi$
$193$			6.00000i			0.431889i	−0.976406	+	0.215945i	$0.930717\pi$
$194$	0.413147	+	0.300169i	0.0296622	+	0.0215509i
$195$		0			0
$196$	4.72353	−	3.43184i	0.337395	−	0.245132i
$197$	0.826937	+	1.13818i	0.0589168	+	0.0810920i	0.837459	−	0.546501i	$-0.184040\pi$
$197$	0.826937	+	1.13818i	0.0589168	+	0.0810920i	−0.778542	+	0.627593i	$0.784040\pi$
$198$		0			0
$199$	−13.7199			−0.972575			−0.486288	−	0.873799i	$-0.661649\pi$
$199$	−13.7199			−0.972575			−0.486288	+	0.873799i	$0.661649\pi$
$200$	−4.93236	+	0.819639i	−0.348771	+	0.0579572i
$201$		0			0
$202$	3.33598	−	1.08393i	0.234719	−	0.0762648i
$203$	0.663859	+	0.913723i	0.0465938	+	0.0641308i
$204$		0			0
$205$	11.2142	+	9.50445i	0.783233	+	0.663819i
$206$	−3.75528	−	2.72837i	−0.261643	−	0.190095i
$207$		0			0
$208$	3.40540	−	4.68712i	0.236122	−	0.324994i
$209$	−2.17921	+	6.70692i	−0.150739	+	0.463927i
$210$		0			0
$211$	−5.18484	−	15.9573i	−0.356939	−	1.09855i	−0.954877	−	0.297003i	$-0.904013\pi$
$211$	−5.18484	−	15.9573i	−0.356939	−	1.09855i	0.597937	−	0.801543i	$-0.295987\pi$
$212$	2.44246	+	0.793604i	0.167749	+	0.0545050i
$213$		0			0
$214$	−2.34911	−	7.22982i	−0.160582	−	0.494221i
$215$	−15.4702	−	6.33930i	−1.05506	−	0.432337i
$216$		0			0
$217$	1.33979	−	1.84406i	0.0909506	−	0.125183i
$218$		−	2.98636i		−	0.202262i
$219$		0			0
$220$	−3.93179	+	2.42998i	−0.265081	+	0.163829i
$221$	3.86420	−	2.80751i	0.259934	−	0.188853i
$222$		0			0
$223$	−11.1121	+	3.61054i	−0.744121	+	0.241779i	−0.656449	−	0.754370i	$-0.727942\pi$
$223$	−11.1121	+	3.61054i	−0.744121	+	0.241779i	−0.0876712	+	0.996149i	$0.527942\pi$
$224$	1.07768			0.0720058
$225$		0			0
$226$	20.1986			1.34359
$227$	−0.678012	+	0.220299i	−0.0450012	+	0.0146218i	−0.331431	−	0.943479i	$-0.607531\pi$
$227$	−0.678012	+	0.220299i	−0.0450012	+	0.0146218i	0.286430	+	0.958101i	$0.407531\pi$
$228$		0			0
$229$	16.5176	−	12.0008i	1.09152	−	0.793034i	0.111862	−	0.993724i	$-0.464318\pi$
$229$	16.5176	−	12.0008i	1.09152	−	0.793034i	0.979655	+	0.200690i	$0.0643185\pi$
$230$	−1.04067	−	4.26336i	−0.0686199	−	0.281117i
$231$		0			0
$232$		−	1.04801i		−	0.0688053i
$233$	8.84046	−	12.1679i	0.579158	−	0.797143i	−0.414445	−	0.910074i	$-0.636024\pi$
$233$	8.84046	−	12.1679i	0.579158	−	0.797143i	0.993603	+	0.112932i	$0.0360242\pi$
$234$		0			0
$235$	18.7941	−	4.58759i	1.22599	−	0.299261i
$236$	−1.45309	−	4.47214i	−0.0945878	−	0.291111i
$237$		0			0
$238$	0.844989	+	0.274554i	0.0547725	+	0.0177967i
$239$	1.29364	+	3.98141i	0.0836786	+	0.257536i	0.984138	−	0.177403i	$-0.0567697\pi$
$239$	1.29364	+	3.98141i	0.0836786	+	0.257536i	−0.900460	+	0.434940i	$0.856770\pi$
$240$		0			0
$241$	−9.09011	+	27.9765i	−0.585546	+	1.80212i	0.0115222	+	0.999934i	$0.496332\pi$
$241$	−9.09011	+	27.9765i	−0.585546	+	1.80212i	−0.597068	+	0.802191i	$0.703668\pi$
$242$	3.95418	−	5.44246i	0.254184	−	0.349855i
$243$		0			0
$244$	−7.51005	−	5.45637i	−0.480781	−	0.349308i
$245$	−4.95031	+	12.0806i	−0.316263	+	0.771800i
$246$		0			0
$247$	11.6180	+	15.9908i	0.739234	+	1.01747i
$248$	−2.01155	+	0.653594i	−0.127734	+	0.0415032i
$249$		0			0
$250$	8.41837	−	7.35738i	0.532424	−	0.465322i
$251$	23.6695			1.49400			0.747002	−	0.664822i	$-0.231492\pi$
$251$	23.6695			1.49400			0.747002	+	0.664822i	$0.231492\pi$
$252$		0			0
$253$	−2.38455	−	3.28205i	−0.149915	−	0.206341i
$254$	−17.2733	+	12.5498i	−1.08383	+	0.787446i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$		−	4.34928i		−	0.271300i	−0.990757	−	0.135650i	$-0.956688\pi$
$257$		−	4.34928i		−	0.271300i	0.990757	−	0.135650i	$-0.0433123\pi$
$258$		0			0
$259$	2.89587	−	8.91257i	0.179941	−	0.553800i
$260$	−0.967401	+	12.9187i	−0.0599957	+	0.801185i
$261$		0			0
$262$	−8.56674	−	2.78350i	−0.529255	−	0.171965i
$263$	−2.14652	−	0.697446i	−0.132360	−	0.0430064i	0.242088	−	0.970254i	$-0.422168\pi$
$263$	−2.14652	−	0.697446i	−0.132360	−	0.0430064i	−0.374448	+	0.927248i	$0.622168\pi$
$264$		0			0
$265$	−5.57878	+	1.36176i	−0.342702	+	0.0836524i
$266$	−1.13615	+	3.49672i	−0.0696620	+	0.214398i
$267$		0			0
$268$		−	4.36176i		−	0.266437i
$269$	6.92470	+	5.03109i	0.422206	+	0.306751i	0.778525	−	0.627614i	$-0.215968\pi$
$269$	6.92470	+	5.03109i	0.422206	+	0.306751i	−0.356319	+	0.934365i	$0.615968\pi$
$270$		0			0
$271$	19.3808	−	14.0809i	1.17730	−	0.855356i	0.185433	−	0.982657i	$-0.440631\pi$
$271$	19.3808	−	14.0809i	1.17730	−	0.855356i	0.991864	+	0.127300i	$0.0406312\pi$
$272$	−0.484587	−	0.666977i	−0.0293824	−	0.0404414i
$273$		0			0
$274$	−4.49151			−0.271342
$275$	4.62209	−	9.24418i	0.278723	−	0.557445i
$276$		0			0
$277$	−6.77810	+	2.20234i	−0.407257	+	0.132326i	−0.505479	−	0.862839i	$-0.668684\pi$
$277$	−6.77810	+	2.20234i	−0.407257	+	0.132326i	0.0982226	+	0.995164i	$0.468684\pi$
$278$	−7.87863	−	10.8440i	−0.472529	−	0.650380i
$279$		0			0
$280$	−2.04988	+	1.26689i	−0.122504	+	0.0757113i
$281$	1.82620	+	1.32681i	0.108942	+	0.0791511i	0.640922	−	0.767606i	$-0.278552\pi$
$281$	1.82620	+	1.32681i	0.108942	+	0.0791511i	−0.531980	+	0.846757i	$0.678552\pi$
$282$		0			0
$283$	−5.71186	+	7.86171i	−0.339535	+	0.467330i	−0.944306	−	0.329070i	$-0.893265\pi$
$283$	−5.71186	+	7.86171i	−0.339535	+	0.467330i	0.604771	+	0.796400i	$0.293265\pi$
$284$	1.51541	−	4.66396i	0.0899232	−	0.276755i
$285$		0			0
$286$	3.70071	+	11.3896i	0.218827	+	0.673481i
$287$	6.73802	+	2.18932i	0.397733	+	0.129231i
$288$		0			0
$289$	5.04325	+	15.5215i	0.296662	+	0.913032i
$290$	1.23201	+	1.99344i	0.0723462	+	0.117059i
$291$		0			0
$292$	−0.762779	+	1.04988i	−0.0446383	+	0.0614393i
$293$		−	6.52369i		−	0.381118i	−0.981676	−	0.190559i	$-0.938970\pi$
$293$		−	6.52369i		−	0.381118i	0.981676	−	0.190559i	$-0.0610301\pi$
$294$		0			0
$295$	8.02124	+	6.79830i	0.467015	+	0.395813i
$296$	−7.03498	+	5.11121i	−0.408900	+	0.297083i
$297$		0			0
$298$	12.9476	−	4.20692i	0.750032	−	0.243700i
$299$	−11.3706			−0.657578
$300$		0			0
$301$	−8.05766			−0.464436
$302$	8.36768	−	2.71883i	0.481506	−	0.156451i
$303$		0			0
$304$	2.76007	−	2.00531i	0.158301	−	0.115012i
$305$	20.6993	+	1.55004i	1.18524	+	0.0887550i
$306$		0			0
$307$			20.7081i			1.18187i	0.806718	+	0.590937i	$0.201242\pi$
$307$			20.7081i			1.18187i	−0.806718	+	0.590937i	$0.798758\pi$
$308$	−1.30937	+	1.80220i	−0.0746085	+	0.102690i
$309$		0			0
$310$	3.05786	−	3.60793i	0.173675	−	0.204917i
$311$	−2.46261	−	7.57914i	−0.139642	−	0.429773i	0.856641	−	0.515912i	$-0.172547\pi$
$311$	−2.46261	−	7.57914i	−0.139642	−	0.429773i	−0.996283	+	0.0861391i	$0.972547\pi$
$312$		0			0
$313$	−4.46075	−	1.44938i	−0.252136	−	0.0819240i	0.180222	−	0.983626i	$-0.442318\pi$
$313$	−4.46075	−	1.44938i	−0.252136	−	0.0819240i	−0.432358	+	0.901702i	$0.642318\pi$
$314$	−3.66364	−	11.2755i	−0.206751	−	0.636314i
$315$		0			0
$316$	−2.22358	+	6.84348i	−0.125086	+	0.384976i
$317$	−8.40508	+	11.5686i	−0.472077	+	0.649758i	−0.976958	−	0.213431i	$-0.931536\pi$
$317$	−8.40508	+	11.5686i	−0.472077	+	0.649758i	0.504882	+	0.863189i	$0.331536\pi$
$318$		0			0
$319$	1.75258	+	1.27332i	0.0981255	+	0.0712923i
$320$	2.22982	+	0.166977i	0.124651	+	0.00933432i
$321$		0			0
$322$	−1.24321	−	1.71113i	−0.0692813	−	0.0953575i
$323$	2.67499	−	0.869158i	0.148841	−	0.0483613i
$324$		0			0
$325$	−13.3468	−	25.7101i	−0.740345	−	1.42614i
$326$	14.9590			0.828500
$327$		0			0
$328$	−3.86415	−	5.31854i	−0.213362	−	0.293667i
$329$	7.54316	−	5.48043i	0.415868	−	0.302146i
$330$		0			0
$331$	−28.7771	−	20.9078i	−1.58174	−	1.14920i	−0.914672	−	0.404196i	$-0.867551\pi$
$331$	−28.7771	−	20.9078i	−1.58174	−	1.14920i	−0.667063	−	0.745002i	$-0.732449\pi$
$332$			14.9680i			0.821477i
$333$		0			0
$334$	−6.66547	+	20.5142i	−0.364718	+	1.12249i
$335$	5.12756	+	8.29657i	0.280148	+	0.453290i
$336$		0			0
$337$	7.19211	+	2.33686i	0.391779	+	0.127297i	0.498281	−	0.867016i	$-0.333965\pi$
$337$	7.19211	+	2.33686i	0.391779	+	0.127297i	−0.106501	+	0.994313i	$0.533965\pi$
$338$	19.5593	+	6.35520i	1.06389	+	0.345677i
$339$		0			0
$340$	1.70582	+	0.699000i	0.0925110	+	0.0379086i
$341$	1.35102	−	4.15801i	0.0731617	−	0.225169i
$342$		0			0
$343$			13.8359i			0.747071i
$344$	6.04889	+	4.39477i	0.326134	+	0.236950i
$345$		0			0
$346$	−3.62866	+	2.63637i	−0.195078	+	0.141732i
$347$	8.66728	+	11.9295i	0.465284	+	0.640409i	0.975594	−	0.219582i	$-0.0704693\pi$
$347$	8.66728	+	11.9295i	0.465284	+	0.640409i	−0.510310	+	0.859991i	$0.670469\pi$
$348$		0			0
$349$	7.61178			0.407449			0.203725	−	0.979028i	$-0.434695\pi$
$349$	7.61178			0.407449			0.203725	+	0.979028i	$0.434695\pi$
$350$	2.40977	−	4.81955i	0.128808	−	0.257616i
$351$		0			0
$352$	1.96589	−	0.638757i	0.104782	−	0.0340459i
$353$	−18.9068	−	26.0230i	−1.00631	−	1.38506i	−0.921374	−	0.388678i	$-0.872932\pi$
$353$	−18.9068	−	26.0230i	−1.00631	−	1.38506i	−0.0849343	−	0.996387i	$-0.527068\pi$
$354$		0			0
$355$	2.60033	+	10.6529i	0.138011	+	0.565395i
$356$	−9.47214	−	6.88191i	−0.502022	−	0.364740i
$357$		0			0
$358$	8.89456	−	12.2423i	0.470092	−	0.647026i
$359$	−10.7988	+	33.2352i	−0.569937	+	1.75408i	0.0828704	+	0.996560i	$0.473591\pi$
$359$	−10.7988	+	33.2352i	−0.569937	+	1.75408i	−0.652807	+	0.757524i	$0.726409\pi$
$360$		0			0
$361$	−2.27459	−	7.00046i	−0.119715	−	0.368445i
$362$	9.34041	+	3.03488i	0.490921	+	0.159510i
$363$		0			0
$364$	1.92940	+	5.93809i	0.101128	+	0.311240i
$365$	0.216690	−	2.89368i	0.0113421	−	0.151462i
$366$		0			0
$367$	−6.49110	+	8.93423i	−0.338832	+	0.466363i	−0.944100	−	0.329659i	$-0.893066\pi$
$367$	−6.49110	+	8.93423i	−0.338832	+	0.466363i	0.605268	+	0.796022i	$0.293066\pi$
$368$			1.96261i			0.102308i
$369$		0			0
$370$	7.37274	−	17.9922i	0.383291	−	0.935371i
$371$	−2.23909	+	1.62679i	−0.116248	+	0.0844588i
$372$		0			0
$373$	−19.4396	+	6.31632i	−1.00655	+	0.327047i	−0.765478	−	0.643462i	$-0.777498\pi$
$373$	−19.4396	+	6.31632i	−1.00655	+	0.327047i	−0.241068	+	0.970508i	$0.577498\pi$
$374$	1.70415			0.0881193
$375$		0			0
$376$	−8.65176			−0.446181
$377$	5.77459	−	1.87628i	0.297406	−	0.0966332i
$378$		0			0
$379$	−2.82662	+	2.05366i	−0.145193	+	0.105489i	−0.658011	−	0.753009i	$-0.728602\pi$
$379$	−2.82662	+	2.05366i	−0.145193	+	0.105489i	0.512817	+	0.858498i	$0.328602\pi$
$380$	−2.89259	+	7.05899i	−0.148387	+	0.362118i
$381$		0			0
$382$			19.4530i			0.995301i
$383$	−11.5136	+	15.8471i	−0.588318	+	0.809751i	−0.994577	−	0.104008i	$-0.966833\pi$
$383$	−11.5136	+	15.8471i	−0.588318	+	0.809751i	0.406258	+	0.913758i	$0.366833\pi$
$384$		0			0
$385$	0.371965	−	4.96724i	0.0189571	−	0.253154i
$386$	1.85410	+	5.70634i	0.0943713	+	0.290445i
$387$		0			0
$388$	0.485684	+	0.157808i	0.0246569	+	0.00801150i
$389$	3.15799	+	9.71930i	0.160117	+	0.492788i	0.998643	−	0.0520722i	$-0.0165826\pi$
$389$	3.15799	+	9.71930i	0.160117	+	0.492788i	−0.838527	+	0.544861i	$0.816583\pi$
$390$		0			0
$391$	−0.500000	+	1.53884i	−0.0252861	+	0.0778226i
$392$	3.43184	−	4.72353i	0.173334	−	0.238574i
$393$		0			0
$394$	1.13818	+	0.826937i	0.0573407	+	0.0416605i
$395$	−3.81549	−	15.6311i	−0.191978	−	0.786483i
$396$		0			0
$397$	−13.2284	−	18.2073i	−0.663912	−	0.913797i	0.335691	−	0.941972i	$-0.391030\pi$
$397$	−13.2284	−	18.2073i	−0.663912	−	0.913797i	−0.999603	+	0.0281755i	$0.991030\pi$
$398$	−13.0484	+	4.23967i	−0.654056	+	0.212516i
$399$		0			0
$400$	−4.43767	+	2.30371i	−0.221884	+	0.115185i
$401$	−30.3084			−1.51353			−0.756765	−	0.653687i	$-0.773221\pi$
$401$	−30.3084			−1.51353			−0.756765	+	0.653687i	$0.773221\pi$
$402$		0			0
$403$	−7.20266	−	9.91361i	−0.358790	−	0.493832i
$404$	2.83776	−	2.06175i	0.141184	−	0.102576i
$405$		0			0
$406$	0.913723	+	0.663859i	0.0453473	+	0.0329468i
$407$		−	17.9746i		−	0.890967i
$408$		0			0
$409$	4.76281	−	14.6584i	0.235506	−	0.724813i	−0.761548	−	0.648109i	$-0.775560\pi$
$409$	4.76281	−	14.6584i	0.235506	−	0.724813i	0.997054	−	0.0767043i	$-0.0244397\pi$
$410$	13.6024	+	5.57389i	0.671773	+	0.275275i
$411$		0			0
$412$	−4.41460	−	1.43439i	−0.217492	−	0.0706673i
$413$	4.81955	+	1.56597i	0.237154	+	0.0770561i
$414$		0			0
$415$	−17.5960	−	28.4709i	−0.863752	−	1.39758i
$416$	1.79032	−	5.51005i	0.0877778	−	0.270152i
$417$		0			0
$418$			7.05207i			0.344928i
$419$	−17.1755	−	12.4787i	−0.839076	−	0.609624i	0.0830364	−	0.996547i	$-0.473538\pi$
$419$	−17.1755	−	12.4787i	−0.839076	−	0.609624i	−0.922112	+	0.386922i	$0.873538\pi$
$420$		0			0
$421$	−26.5536	+	19.2923i	−1.29414	+	0.940249i	−0.999880	−	0.0154761i	$-0.995074\pi$
$421$	−26.5536	+	19.2923i	−1.29414	+	0.940249i	−0.294261	+	0.955725i	$0.595074\pi$
$422$	−9.86215	−	13.5741i	−0.480082	−	0.660776i
$423$		0			0
$424$	2.56816			0.124721
$425$	−4.06638	+	0.675734i	−0.197249	+	0.0327779i
$426$		0			0
$427$	9.51442	−	3.09142i	0.460435	−	0.149604i
$428$	−4.46828	−	6.15006i	−0.215982	−	0.297274i
$429$		0			0
$430$	−16.6720	−	1.24846i	−0.803997	−	0.0602062i
$431$	−0.680214	−	0.494204i	−0.0327647	−	0.0238050i	0.571282	−	0.820754i	$-0.306446\pi$
$431$	−0.680214	−	0.494204i	−0.0327647	−	0.0238050i	−0.604047	+	0.796949i	$0.706446\pi$
$432$		0			0
$433$	20.0053	−	27.5350i	0.961394	−	1.32325i	0.0151184	−	0.999886i	$-0.495187\pi$
$433$	20.0053	−	27.5350i	0.961394	−	1.32325i	0.946276	−	0.323360i	$-0.104813\pi$
$434$	0.704367	−	2.16782i	0.0338107	−	0.104059i
$435$		0			0
$436$	−0.922836	−	2.84020i	−0.0441958	−	0.136021i
$437$	−6.36801	−	2.06909i	−0.304623	−	0.0989780i
$438$		0			0
$439$	0.492305	+	1.51516i	0.0234964	+	0.0723145i	0.962117	−	0.272636i	$-0.0878956\pi$
$439$	0.492305	+	1.51516i	0.0234964	+	0.0723145i	−0.938621	+	0.344951i	$0.887896\pi$
$440$	−2.98845	+	3.52603i	−0.142469	+	0.168097i
$441$		0			0
$442$	2.80751	−	3.86420i	0.133540	−	0.183801i
$443$		−	24.6238i		−	1.16991i	−0.811065	−	0.584955i	$-0.801112\pi$
$443$		−	24.6238i		−	1.16991i	0.811065	−	0.584955i	$-0.198888\pi$
$444$		0			0
$445$	26.1072	+	1.95501i	1.23760	+	0.0926762i
$446$	−9.45251	+	6.86765i	−0.447589	+	0.325193i
$447$		0			0
$448$	1.02494	−	0.333023i	0.0484238	−	0.0157338i
$449$	−34.1186			−1.61016			−0.805078	−	0.593169i	$-0.797876\pi$
$449$	−34.1186			−1.61016			−0.805078	+	0.593169i	$0.797876\pi$
$450$		0			0
$451$	13.5890			0.639882
$452$	19.2100	−	6.24170i	0.903561	−	0.293585i
$453$		0			0
$454$	−0.576751	+	0.419034i	−0.0270683	+	0.0196663i
$455$	−10.6506	−	9.02676i	−0.499307	−	0.423181i
$456$		0			0
$457$		−	3.48932i		−	0.163224i	−0.996664	−	0.0816118i	$-0.973993\pi$
$457$		−	3.48932i		−	0.163224i	0.996664	−	0.0816118i	$-0.0260068\pi$
$458$	12.0008	−	16.5176i	0.560759	−	0.771819i
$459$		0			0
$460$	−2.30719	−	3.73311i	−0.107573	−	0.174057i
$461$	−4.16714	−	12.8251i	−0.194083	−	0.597326i	−0.999986	−	0.00527875i	$-0.998320\pi$
$461$	−4.16714	−	12.8251i	−0.194083	−	0.597326i	0.805903	−	0.592048i	$-0.201680\pi$
$462$		0			0
$463$	1.77278	+	0.576011i	0.0823881	+	0.0267695i	0.349921	−	0.936779i	$-0.386208\pi$
$463$	1.77278	+	0.576011i	0.0823881	+	0.0267695i	−0.267533	+	0.963549i	$0.586208\pi$
$464$	−0.323853	−	0.996718i	−0.0150345	−	0.0462715i
$465$		0			0
$466$	4.64771	−	14.3042i	0.215301	−	0.662628i
$467$	7.66561	−	10.5508i	0.354722	−	0.488233i	−0.593947	−	0.804504i	$-0.702431\pi$
$467$	7.66561	−	10.5508i	0.354722	−	0.488233i	0.948669	+	0.316271i	$0.102431\pi$
$468$		0			0
$469$	3.80287	+	2.76294i	0.175600	+	0.127581i
$470$	16.4566	−	10.1708i	0.759088	−	0.469142i
$471$		0			0
$472$	−2.76393	−	3.80423i	−0.127220	−	0.175104i
$473$	−14.6987	+	4.77588i	−0.675845	+	0.219595i
$474$		0			0
$475$	−2.79631	−	16.8274i	−0.128304	−	0.772096i
$476$	0.888474			0.0407231
$477$		0			0
$478$	2.46065	+	3.38679i	0.112547	+	0.154908i
$479$	−10.0171	+	7.27787i	−0.457694	+	0.332534i	−0.792626	−	0.609708i	$-0.791287\pi$
$479$	−10.0171	+	7.27787i	−0.457694	+	0.332534i	0.334932	+	0.942242i	$0.391287\pi$
$480$		0			0
$481$	−40.7579	−	29.6124i	−1.85840	−	1.35021i
$482$			29.4162i			1.33987i
$483$		0			0
$484$	2.07884	−	6.39800i	0.0944925	−	0.290818i
$485$	−1.10934	+	0.270786i	−0.0503725	+	0.0122958i
$486$		0			0
$487$	4.29789	+	1.39647i	0.194756	+	0.0632800i	0.404771	−	0.914418i	$-0.367351\pi$
$487$	4.29789	+	1.39647i	0.194756	+	0.0632800i	−0.210015	+	0.977698i	$0.567351\pi$
$488$	−8.82859	−	2.86858i	−0.399651	−	0.129855i
$489$		0			0
$490$	−0.974914	+	13.0191i	−0.0440421	+	0.588141i
$491$	−8.48797	+	26.1233i	−0.383057	+	1.17893i	0.554824	+	0.831968i	$0.312786\pi$
$491$	−8.48797	+	26.1233i	−0.383057	+	1.17893i	−0.937880	+	0.346959i	$0.887214\pi$
$492$		0			0
$493$		−	0.864011i		−	0.0389131i
$494$	15.9908	+	11.6180i	0.719459	+	0.522718i
$495$		0			0
$496$	−1.71113	+	1.24321i	−0.0768320	+	0.0558217i
$497$	3.10641	+	4.27560i	0.139341	+	0.191787i
$498$		0			0
$499$	−13.4814			−0.603510			−0.301755	−	0.953385i	$-0.597573\pi$
$499$	−13.4814			−0.603510			−0.301755	+	0.953385i	$0.597573\pi$
$500$	5.73279	−	9.59871i	0.256378	−	0.429267i
$501$		0			0
$502$	22.5110	−	7.31427i	1.00472	−	0.326452i
$503$	−16.3577	−	22.5145i	−0.729355	−	1.00387i	−0.999161	−	0.0409559i	$-0.986960\pi$
$503$	−16.3577	−	22.5145i	−0.729355	−	1.00387i	0.269806	−	0.962915i	$-0.413040\pi$
$504$		0			0
$505$	−2.97400	+	7.25767i	−0.132341	+	0.322962i
$506$	−3.28205	−	2.38455i	−0.145905	−	0.106006i
$507$		0			0
$508$	−12.5498	+	17.2733i	−0.556808	+	0.766381i
$509$	−6.20182	+	19.0873i	−0.274891	+	0.846028i	0.714357	+	0.699781i	$0.246719\pi$
$509$	−6.20182	+	19.0873i	−0.274891	+	0.846028i	−0.989248	+	0.146246i	$0.953281\pi$
$510$		0			0
$511$	−0.432169	−	1.33008i	−0.0191180	−	0.0588393i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$		0			0
$514$	−1.34400	−	4.13641i	−0.0592813	−	0.182449i
$515$	10.0833	−	2.46130i	0.444323	−	0.108458i
$516$		0			0
$517$	10.5118	−	14.4682i	0.462308	−	0.636313i
$518$		−	9.37123i		−	0.411748i
$519$		0			0
$520$	3.07205	+	12.5854i	0.134718	+	0.551905i
$521$	−23.5901	+	17.1392i	−1.03350	+	0.750881i	−0.969006	−	0.247037i	$-0.920543\pi$
$521$	−23.5901	+	17.1392i	−1.03350	+	0.750881i	−0.0644931	+	0.997918i	$0.520543\pi$
$522$		0			0
$523$	11.1330	−	3.61732i	0.486811	−	0.158174i	−0.0553197	−	0.998469i	$-0.517618\pi$
$523$	11.1330	−	3.61732i	0.486811	−	0.158174i	0.542131	+	0.840294i	$0.317618\pi$
$524$	−9.00760			−0.393499
$525$		0			0
$526$	−2.25698			−0.0984092
$527$	−1.65838	+	0.538842i	−0.0722404	+	0.0234723i
$528$		0			0
$529$	−15.4912	+	11.2550i	−0.673530	+	0.489348i
$530$	−4.88493	+	3.01905i	−0.212188	+	0.131139i
$531$		0			0
$532$			3.67667i			0.159404i
$533$	22.3873	−	30.8135i	0.969703	−	1.33468i
$534$		0			0
$535$	15.7290	+	6.44533i	0.680024	+	0.278656i
$536$	−1.34786	−	4.14828i	−0.0582186	−	0.179179i
$537$		0			0
$538$	8.14047	+	2.64500i	0.350961	+	0.114034i
$539$	3.72945	+	11.4781i	0.160639	+	0.494395i
$540$		0			0
$541$	−9.24566	+	28.4552i	−0.397502	+	1.22339i	0.529494	+	0.848314i	$0.322382\pi$
$541$	−9.24566	+	28.4552i	−0.397502	+	1.22339i	−0.926996	+	0.375072i	$0.877618\pi$
$542$	14.0809	−	19.3808i	0.604828	−	0.832475i
$543$		0			0
$544$	−0.666977	−	0.484587i	−0.0285964	−	0.0207765i
$545$	5.09419	+	4.31752i	0.218211	+	0.184942i
$546$		0			0
$547$	1.11198	+	1.53050i	0.0475447	+	0.0654396i	0.832127	−	0.554585i	$-0.187123\pi$
$547$	1.11198	+	1.53050i	0.0475447	+	0.0654396i	−0.784583	+	0.620024i	$0.787123\pi$
$548$	−4.27168	+	1.38795i	−0.182477	+	0.0592905i
$549$		0			0
$550$	1.53926	−	10.2200i	0.0656343	−	0.435784i
$551$	3.57543			0.152319
$552$		0			0
$553$	−4.55807	−	6.27364i	−0.193829	−	0.266782i
$554$	−5.76580	+	4.18910i	−0.244965	+	0.177978i
$555$		0			0
$556$	−10.8440	−	7.87863i	−0.459888	−	0.334128i
$557$		−	2.95618i		−	0.125257i	−0.998037	−	0.0626287i	$-0.980052\pi$
$557$		−	2.95618i		−	0.125257i	0.998037	−	0.0626287i	$-0.0199484\pi$
$558$		0			0
$559$	−13.3859	+	41.1977i	−0.566165	+	1.74248i
$560$	−1.55806	+	1.83833i	−0.0658399	+	0.0776838i
$561$		0			0
$562$	2.14683	+	0.697547i	0.0905586	+	0.0294243i
$563$	8.82870	+	2.86862i	0.372085	+	0.120898i	0.489089	−	0.872234i	$-0.337329\pi$
$563$	8.82870	+	2.86862i	0.372085	+	0.120898i	−0.117004	+	0.993131i	$0.537329\pi$
$564$		0			0
$565$	−29.2020	+	34.4551i	−1.22854	+	1.44954i
$566$	−3.00290	+	9.24199i	−0.126221	+	0.388470i
$567$		0			0
$568$		−	4.90398i		−	0.205766i
$569$	11.7064	+	8.50522i	0.490759	+	0.356557i	0.805476	−	0.592628i	$-0.201910\pi$
$569$	11.7064	+	8.50522i	0.490759	+	0.356557i	−0.314717	+	0.949186i	$0.601910\pi$
$570$		0			0
$571$	4.11663	−	2.99091i	0.172276	−	0.125166i	−0.498306	−	0.867001i	$-0.666044\pi$
$571$	4.11663	−	2.99091i	0.172276	−	0.125166i	0.670582	+	0.741835i	$0.266044\pi$
$572$	7.03916	+	9.68858i	0.294322	+	0.405100i
$573$		0			0
$574$	7.08478			0.295713
$575$	8.77706	+	4.38853i	0.366029	+	0.183014i
$576$		0			0
$577$	−16.0487	+	5.21453i	−0.668116	+	0.217084i	−0.623385	−	0.781915i	$-0.714243\pi$
$577$	−16.0487	+	5.21453i	−0.668116	+	0.217084i	−0.0447308	+	0.998999i	$0.514243\pi$
$578$	9.59284	+	13.2034i	0.399010	+	0.549190i
$579$		0			0
$580$	1.78772	+	1.51516i	0.0742309	+	0.0629135i
$581$	−13.0501	−	9.48144i	−0.541409	−	0.393356i
$582$		0			0
$583$	−3.12028	+	4.29470i	−0.129229	+	0.177868i
$584$	−0.401017	+	1.23420i	−0.0165942	+	0.0510717i
$585$		0			0
$586$	−2.01593	−	6.20440i	−0.0832774	−	0.256301i
$587$	41.9364	+	13.6260i	1.73090	+	0.562403i	0.993579	−	0.113140i	$-0.0360909\pi$
$587$	41.9364	+	13.6260i	1.73090	+	0.562403i	0.737320	+	0.675543i	$0.236091\pi$
$588$		0			0
$589$	−2.22982	−	6.86269i	−0.0918783	−	0.282772i
$590$	9.72945	+	3.98687i	0.400555	+	0.164137i
$591$		0			0
$592$	−5.11121	+	7.03498i	−0.210070	+	0.289136i
$593$			31.1398i			1.27876i	0.768891	+	0.639380i	$0.220809\pi$
$593$			31.1398i			1.27876i	−0.768891	+	0.639380i	$0.779191\pi$
$594$		0			0
$595$	−1.68998	+	1.04446i	−0.0692823	+	0.0428188i
$596$	11.0138	−	8.00203i	0.451145	−	0.327776i
$597$		0			0
$598$	−10.8141	+	3.51371i	−0.442220	+	0.143686i
$599$	28.6194			1.16936			0.584678	−	0.811265i	$-0.301221\pi$
$599$	28.6194			1.16936			0.584678	+	0.811265i	$0.301221\pi$
$600$		0			0
$601$	38.8122			1.58318			0.791592	−	0.611050i	$-0.209253\pi$
$601$	38.8122			1.58318			0.791592	+	0.611050i	$0.209253\pi$
$602$	−7.66329	+	2.48995i	−0.312332	+	0.101483i
$603$		0			0
$604$	7.11798	−	5.17151i	0.289626	−	0.210426i
$605$	3.56712	+	14.6135i	0.145024	+	0.594125i
$606$		0			0
$607$		−	6.78331i		−	0.275326i	−0.990479	−	0.137663i	$-0.956041\pi$
$607$		−	6.78331i		−	0.275326i	0.990479	−	0.137663i	$-0.0439591\pi$
$608$	2.00531	−	2.76007i	0.0813261	−	0.111936i
$609$		0			0
$610$	20.1652	−	4.92226i	0.816465	−	0.199296i
$611$	−15.4894	−	47.6716i	−0.626636	−	1.92859i
$612$		0			0
$613$	32.1696	+	10.4525i	1.29932	+	0.422174i	0.875344	−	0.483500i	$-0.160635\pi$
$613$	32.1696	+	10.4525i	1.29932	+	0.422174i	0.423974	+	0.905674i	$0.360635\pi$
$614$	6.39915	+	19.6946i	0.258249	+	0.794808i
$615$		0			0
$616$	−0.688378	+	2.11861i	−0.0277355	+	0.0853612i
$617$	7.72217	−	10.6287i	0.310883	−	0.427894i	−0.624773	−	0.780806i	$-0.714809\pi$
$617$	7.72217	−	10.6287i	0.310883	−	0.427894i	0.935656	+	0.352913i	$0.114809\pi$
$618$		0			0
$619$	−22.6836	−	16.4806i	−0.911732	−	0.662412i	0.0297205	−	0.999558i	$-0.490538\pi$
$619$	−22.6836	−	16.4806i	−0.911732	−	0.662412i	−0.941452	+	0.337146i	$0.890538\pi$
$620$	1.79328	−	4.37628i	0.0720200	−	0.175756i
$621$		0			0
$622$	−4.68416	−	6.44720i	−0.187818	−	0.258509i
$623$	12.0002	−	3.89910i	0.480777	−	0.156214i
$624$		0			0
$625$	0.379550	+	24.9971i	0.0151820	+	0.999885i
$626$	−4.69031			−0.187462
$627$		0			0
$628$	−6.96866	−	9.59153i	−0.278080	−	0.382744i
$629$	−5.79985	+	4.21384i	−0.231255	+	0.168017i
$630$		0			0
$631$	23.0144	+	16.7209i	0.916187	+	0.665649i	0.942572	−	0.334003i	$-0.108400\pi$
$631$	23.0144	+	16.7209i	0.916187	+	0.665649i	−0.0263851	+	0.999652i	$0.508400\pi$
$632$			7.19566i			0.286228i
$633$		0			0
$634$	−4.41881	+	13.5997i	−0.175494	+	0.540114i
$635$	3.56514	−	47.6091i	0.141478	−	1.88931i
$636$		0			0
$637$	32.1709	+	10.4530i	1.27466	+	0.414162i
$638$	2.06028	+	0.669425i	0.0815672	+	0.0265028i
$639$		0			0
$640$	2.17229	−	0.530249i	0.0858672	−	0.0209599i
$641$	−7.87785	+	24.2455i	−0.311156	+	0.957641i	0.666151	+	0.745817i	$0.267941\pi$
$641$	−7.87785	+	24.2455i	−0.311156	+	0.957641i	−0.977308	+	0.211824i	$0.932059\pi$
$642$		0			0
$643$			13.7340i			0.541617i	0.962633	+	0.270809i	$0.0872911\pi$
$643$			13.7340i			0.541617i	−0.962633	+	0.270809i	$0.912709\pi$
$644$	−1.71113	−	1.24321i	−0.0674280	−	0.0489893i
$645$		0			0
$646$	2.27549	−	1.65324i	0.0895278	−	0.0650458i
$647$	22.6465	+	31.1702i	0.890324	+	1.22543i	0.973453	+	0.228887i	$0.0735088\pi$
$647$	22.6465	+	31.1702i	0.890324	+	1.22543i	−0.0831286	+	0.996539i	$0.526491\pi$
$648$		0			0
$649$	9.71991			0.381540
$650$	−20.6384	−	20.3274i	−0.809504	−	0.797306i
$651$		0			0
$652$	14.2268	−	4.62257i	0.557165	−	0.181034i
$653$	8.14808	+	11.2149i	0.318859	+	0.438872i	0.938118	−	0.346315i	$-0.112567\pi$
$653$	8.14808	+	11.2149i	0.318859	+	0.438872i	−0.619259	+	0.785187i	$0.712567\pi$
$654$		0			0
$655$	17.1335	−	10.5891i	0.669461	−	0.413749i
$656$	−5.31854	−	3.86415i	−0.207654	−	0.150870i
$657$		0			0
$658$	5.48043	−	7.54316i	0.213649	−	0.294063i
$659$	8.36885	−	25.7567i	0.326004	−	1.00334i	−0.644981	−	0.764198i	$-0.723135\pi$
$659$	8.36885	−	25.7567i	0.326004	−	1.00334i	0.970985	−	0.239139i	$-0.0768651\pi$
$660$		0			0
$661$	−7.25043	−	22.3145i	−0.282009	−	0.867934i	−0.987279	−	0.158996i	$-0.949174\pi$
$661$	−7.25043	−	22.3145i	−0.282009	−	0.867934i	0.705270	−	0.708938i	$-0.250826\pi$
$662$	−33.8296	−	10.9919i	−1.31482	−	0.427212i
$663$		0			0
$664$	4.62537	+	14.2354i	0.179499	+	0.552442i
$665$	−4.32218	−	6.99344i	−0.167607	−	0.271194i
$666$		0			0
$667$	−1.20898	+	1.66402i	−0.0468118	+	0.0644310i
$668$			21.5699i			0.834565i
$669$		0			0
$670$	7.44038	+	6.30600i	0.287447	+	0.243622i
$671$	15.5237	−	11.2786i	0.599287	−	0.435407i
$672$		0			0
$673$	10.4567	−	3.39760i	0.403078	−	0.130968i	−0.100460	−	0.994941i	$-0.532031\pi$
$673$	10.4567	−	3.39760i	0.403078	−	0.130968i	0.503538	+	0.863973i	$0.332031\pi$
$674$	7.56224			0.291286
$675$		0			0
$676$	20.5659			0.790994
$677$	−34.8638	+	11.3279i	−1.33992	+	0.435368i	−0.889291	−	0.457341i	$-0.848802\pi$
$677$	−34.8638	+	11.3279i	−1.33992	+	0.435368i	−0.450633	+	0.892709i	$0.648802\pi$
$678$		0			0
$679$	−0.445242	+	0.323487i	−0.0170868	+	0.0124143i
$680$	1.83833	+	0.137661i	0.0704969	+	0.00527906i
$681$		0			0
$682$		−	4.37199i		−	0.167412i
$683$	−6.00469	+	8.26475i	−0.229763	+	0.316242i	−0.908296	−	0.418328i	$-0.862616\pi$
$683$	−6.00469	+	8.26475i	−0.229763	+	0.316242i	0.678533	+	0.734570i	$0.262616\pi$
$684$		0			0
$685$	6.49359	−	7.66171i	0.248107	−	0.292739i
$686$	4.27554	+	13.1588i	0.163241	+	0.502404i
$687$		0			0
$688$	7.11089	+	2.31047i	0.271100	+	0.0880858i
$689$	4.59783	+	14.1507i	0.175163	+	0.539097i
$690$		0			0
$691$	1.68239	−	5.17786i	0.0640011	−	0.196975i	−0.913943	−	0.405843i	$-0.866978\pi$
$691$	1.68239	−	5.17786i	0.0640011	−	0.196975i	0.977944	+	0.208868i	$0.0669779\pi$
$692$	−2.63637	+	3.62866i	−0.100220	+	0.137941i
$693$		0			0
$694$	11.9295	+	8.66728i	0.452837	+	0.329006i
$695$	29.8884	+	2.23815i	1.13373	+	0.0848980i
$696$		0			0
$697$	−3.18572	−	4.38476i	−0.120668	−	0.166085i
$698$	7.23924	−	2.35217i	0.274009	−	0.0890310i
$699$		0			0
$700$	0.802509	−	5.32832i	0.0303320	−	0.201392i
$701$	−13.9633			−0.527387			−0.263694	−	0.964606i	$-0.584941\pi$
$701$	−13.9633			−0.527387			−0.263694	+	0.964606i	$0.584941\pi$
$702$		0			0
$703$	−17.4376	−	24.0008i	−0.657672	−	0.905208i
$704$	1.67229	−	1.21499i	0.0630267	−	0.0457916i
$705$		0			0
$706$	−26.0230	−	18.9068i	−0.979388	−	0.711567i
$707$			3.78015i			0.142167i
$708$		0			0
$709$	−5.98835	+	18.4302i	−0.224897	+	0.692162i	0.773405	+	0.633912i	$0.218552\pi$
$709$	−5.98835	+	18.4302i	−0.224897	+	0.692162i	−0.998302	+	0.0582499i	$0.981448\pi$
$710$	5.76497	+	9.32792i	0.216356	+	0.350071i
$711$		0			0
$712$	−11.1352	−	3.61803i	−0.417308	−	0.135592i
$713$	3.94790	+	1.28275i	0.147850	+	0.0480393i
$714$		0			0
$715$	−24.7789	−	10.1537i	−0.926678	−	0.379728i
$716$	4.67615	−	14.3917i	0.174756	−	0.537843i
$717$		0			0
$718$			34.9455i			1.30415i
$719$	−7.97223	−	5.79216i	−0.297314	−	0.216011i	0.429120	−	0.903247i	$-0.358824\pi$
$719$	−7.97223	−	5.79216i	−0.297314	−	0.216011i	−0.726434	+	0.687236i	$0.758824\pi$
$720$		0			0
$721$	4.04701	−	2.94032i	0.150718	−	0.109503i
$722$	−4.32652	−	5.95495i	−0.161017	−	0.221620i
$723$		0			0
$724$	9.82108			0.364998
$725$	−5.18162	−	0.780413i	−0.192440	−	0.0289838i
$726$		0			0
$727$	33.7494	−	10.9658i	1.25169	−	0.406700i	0.393167	−	0.919467i	$-0.371380\pi$
$727$	33.7494	−	10.9658i	1.25169	−	0.406700i	0.858528	+	0.512767i	$0.171380\pi$
$728$	3.66994	+	5.05124i	0.136017	+	0.187211i
$729$		0			0
$730$	−0.688113	−	2.81902i	−0.0254682	−	0.104337i
$731$	4.98688	+	3.62318i	0.184446	+	0.134008i
$732$		0			0
$733$	16.2111	−	22.3126i	0.598769	−	0.824135i	−0.396826	−	0.917894i	$-0.629888\pi$
$733$	16.2111	−	22.3126i	0.598769	−	0.824135i	0.995595	+	0.0937592i	$0.0298884\pi$
$734$	−3.41257	+	10.5028i	−0.125960	+	0.387666i
$735$		0			0
$736$	0.606480	+	1.86655i	0.0223551	+	0.0688021i
$737$	8.57476	+	2.78611i	0.315855	+	0.102628i
$738$		0			0
$739$	11.9642	+	36.8219i	0.440109	+	1.35452i	0.887760	+	0.460307i	$0.152261\pi$
$739$	11.9642	+	36.8219i	0.440109	+	1.35452i	−0.447651	+	0.894208i	$0.647739\pi$
$740$	1.45199	−	19.3899i	0.0533762	−	0.712788i
$741$		0			0
$742$	−1.62679	+	2.23909i	−0.0597214	+	0.0821994i
$743$			13.3434i			0.489520i	0.969584	+	0.244760i	$0.0787092\pi$
$743$			13.3434i			0.489520i	−0.969584	+	0.244760i	$0.921291\pi$
$744$		0			0
$745$	−11.5426	+	28.1683i	−0.422889	+	1.03201i
$746$	−16.5363	+	12.0144i	−0.605439	+	0.439877i
$747$		0			0
$748$	1.62074	−	0.526610i	0.0592601	−	0.0192548i
$749$	8.19243			0.299345
$750$		0			0
$751$	13.3487			0.487099			0.243550	−	0.969888i	$-0.421688\pi$
$751$	13.3487			0.487099			0.243550	+	0.969888i	$0.421688\pi$
$752$	−8.22832	+	2.67354i	−0.300056	+	0.0974940i
$753$		0			0
$754$	4.91216	−	3.56889i	0.178890	−	0.129971i
$755$	−7.45972	+	18.2045i	−0.271487	+	0.662529i
$756$		0			0
$757$		−	33.3735i		−	1.21298i	−0.795091	−	0.606490i	$-0.792577\pi$
$757$		−	33.3735i		−	1.21298i	0.795091	−	0.606490i	$-0.207423\pi$
$758$	−2.05366	+	2.82662i	−0.0745922	+	0.102667i
$759$		0			0
$760$	−0.569667	+	7.60736i	−0.0206640	+	0.275948i
$761$	0.678475	+	2.08813i	0.0245947	+	0.0756947i	0.962600	−	0.270925i	$-0.0873295\pi$
$761$	0.678475	+	2.08813i	0.0245947	+	0.0756947i	−0.938006	+	0.346620i	$0.887329\pi$
$762$		0			0
$763$	3.06083	+	0.994526i	0.110810	+	0.0360042i
$764$	6.01130	+	18.5009i	0.217481	+	0.669338i
$765$		0			0
$766$	−6.05307	+	18.6294i	−0.218706	+	0.673108i
$767$	16.0131	−	22.0402i	0.578201	−	0.795825i
$768$		0			0
$769$	14.0154	+	10.1828i	0.505408	+	0.367200i	0.811079	−	0.584937i	$-0.198881\pi$
$769$	14.0154	+	10.1828i	0.505408	+	0.367200i	−0.305671	+	0.952137i	$0.598881\pi$
$770$	−1.18120	−	4.83907i	−0.0425676	−	0.174388i
$771$		0			0
$772$	3.52671	+	4.85410i	0.126929	+	0.174703i
$773$	−15.5460	+	5.05119i	−0.559150	+	0.181679i	−0.574939	−	0.818197i	$-0.694974\pi$
$773$	−15.5460	+	5.05119i	−0.559150	+	0.181679i	0.0157888	+	0.999875i	$0.494974\pi$
$774$		0			0
$775$	1.73360	+	10.4323i	0.0622726	+	0.374739i
$776$	0.510678			0.0183323
$777$		0			0
$778$	6.00686	+	8.26773i	0.215356	+	0.296413i
$779$	18.1449	−	13.1831i	0.650110	−	0.472333i
$780$		0			0
$781$	8.20086	+	5.95828i	0.293450	+	0.213204i
$782$			1.61803i			0.0578608i
$783$		0			0
$784$	1.80423	−	5.55284i	0.0644366	−	0.198316i
$785$	24.5307	+	10.0520i	0.875538	+	0.358772i
$786$		0			0
$787$	46.6492	+	15.1572i	1.66286	+	0.540297i	0.981469	−	0.191620i	$-0.0613741\pi$
$787$	46.6492	+	15.1572i	1.66286	+	0.540297i	0.681394	+	0.731917i	$0.261374\pi$
$788$	1.33801	+	0.434746i	0.0476647	+	0.0154872i
$789$		0			0
$790$	−8.45901	−	13.6870i	−0.300958	−	0.486960i
$791$	−6.72658	+	20.7023i	−0.239170	+	0.736088i
$792$		0			0
$793$		−	53.7816i		−	1.90984i
$794$	−18.2073	−	13.2284i	−0.646152	−	0.469457i
$795$		0			0
$796$	−11.0996	+	8.06433i	−0.393415	+	0.285833i
$797$	22.7780	+	31.3513i	0.806840	+	1.11052i	0.991803	+	0.127774i	$0.0407833\pi$
$797$	22.7780	+	31.3513i	0.806840	+	1.11052i	−0.184963	+	0.982745i	$0.559217\pi$
$798$		0			0
$799$	−7.13277			−0.252339
$800$	−3.50859	+	3.56227i	−0.124047	+	0.125945i
$801$		0			0
$802$	−28.8250	+	9.36582i	−1.01785	+	0.330719i
$803$	−1.57671	−	2.17016i	−0.0556410	−	0.0765832i
$804$		0			0
$805$	4.71624	+	0.353170i	0.166226	+	0.0124476i
$806$	−9.91361	−	7.20266i	−0.349192	−	0.253703i
$807$		0			0
$808$	2.06175	−	2.83776i	0.0725322	−	0.0998319i
$809$	3.57476	−	11.0020i	0.125682	−	0.386809i	−0.868343	−	0.495964i	$-0.834815\pi$
$809$	3.57476	−	11.0020i	0.125682	−	0.386809i	0.994025	+	0.109156i	$0.0348147\pi$
$810$		0			0
$811$	13.7829	+	42.4193i	0.483982	+	1.48954i	0.833450	+	0.552595i	$0.186362\pi$
$811$	13.7829	+	42.4193i	0.483982	+	1.48954i	−0.349468	+	0.936948i	$0.613638\pi$
$812$	1.07415	+	0.349011i	0.0376951	+	0.0122479i
$813$		0			0
$814$	−5.55445	−	17.0948i	−0.194683	−	0.599174i
$815$	−21.6268	+	25.5173i	−0.757555	+	0.893831i
$816$		0			0
$817$	−14.9934	+	20.6366i	−0.524552	+	0.721984i
$818$		−	15.4128i		−	0.538896i
$819$		0			0
$820$	14.6590	+	1.09772i	0.511916	+	0.0383342i
$821$	30.8655	−	22.4251i	1.07721	−	0.782640i	0.100017	−	0.994986i	$-0.468110\pi$
$821$	30.8655	−	22.4251i	1.07721	−	0.782640i	0.977195	+	0.212346i	$0.0681103\pi$
$822$		0			0
$823$	−48.4340	+	15.7372i	−1.68830	+	0.548563i	−0.986493	−	0.163801i	$-0.947624\pi$
$823$	−48.4340	+	15.7372i	−1.68830	+	0.548563i	−0.701810	+	0.712364i	$0.747624\pi$
$824$	−4.64178			−0.161704
$825$		0			0
$826$	5.06757			0.176323
$827$	−30.3723	+	9.86857i	−1.05615	+	0.343164i	−0.785079	−	0.619396i	$-0.787378\pi$
$827$	−30.3723	+	9.86857i	−1.05615	+	0.343164i	−0.271070	+	0.962560i	$0.587378\pi$
$828$		0			0
$829$	−26.0284	+	18.9107i	−0.904004	+	0.656797i	−0.939491	−	0.342573i	$-0.888702\pi$
$829$	−26.0284	+	18.9107i	−0.904004	+	0.656797i	0.0354873	+	0.999370i	$0.488702\pi$
$830$	−25.5327	−	21.6400i	−0.886254	−	0.751134i
$831$		0			0
$832$		−	5.79360i		−	0.200857i
$833$	2.82931	−	3.89421i	0.0980298	−	0.134926i
$834$		0			0
$835$	−25.3570	−	41.0284i	−0.877513	−	1.41985i
$836$	2.17921	+	6.70692i	0.0753695	+	0.231964i
$837$		0			0
$838$	−20.1910	−	6.56044i	−0.697485	−	0.226627i
$839$	−9.31121	−	28.6570i	−0.321459	−	0.989348i	−0.973014	−	0.230747i	$-0.925883\pi$
$839$	−9.31121	−	28.6570i	−0.321459	−	0.989348i	0.651555	−	0.758601i	$-0.274117\pi$
$840$		0			0
$841$	−8.62209	+	26.5361i	−0.297313	+	0.915037i
$842$	−19.2923	+	26.5536i	−0.664856	+	0.915096i
$843$		0			0
$844$	−13.5741	−	9.86215i	−0.467239	−	0.339469i
$845$	−39.1186	+	24.1766i	−1.34572	+	0.831701i
$846$		0			0
$847$	4.26136	+	5.86525i	0.146422	+	0.201532i
$848$	2.44246	−	0.793604i	0.0838745	−	0.0272525i
$849$		0			0
$850$	−3.65855	+	1.89924i	−0.125487	+	0.0651435i
$851$	17.0663			0.585025
$852$		0			0
$853$	12.6394	+	17.3966i	0.432765	+	0.595649i	0.968585	−	0.248683i	$-0.0799976\pi$
$853$	12.6394	+	17.3966i	0.432765	+	0.595649i	−0.535820	+	0.844332i	$0.679998\pi$
$854$	8.09345	−	5.88024i	0.276952	−	0.201218i
$855$		0			0
$856$	−6.15006	−	4.46828i	−0.210205	−	0.152723i
$857$		−	40.1894i		−	1.37284i	−0.727204	−	0.686422i	$-0.759181\pi$
$857$		−	40.1894i		−	1.37284i	0.727204	−	0.686422i	$-0.240819\pi$
$858$		0			0
$859$	16.4439	−	50.6091i	0.561058	−	1.72676i	−0.118323	−	0.992975i	$-0.537752\pi$
$859$	16.4439	−	50.6091i	0.561058	−	1.72676i	0.679382	−	0.733785i	$-0.262248\pi$
$860$	−16.2418	+	3.96458i	−0.553842	+	0.135191i
$861$		0			0
$862$	−0.799639	−	0.259819i	−0.0272358	−	0.00884945i
$863$	−10.3778	−	3.37194i	−0.353264	−	0.114782i	0.127009	−	0.991902i	$-0.459462\pi$
$863$	−10.3778	−	3.37194i	−0.353264	−	0.114782i	−0.480273	+	0.877119i	$0.659462\pi$
$864$		0			0
$865$	0.748938	−	10.0014i	0.0254647	−	0.340056i
$866$	10.5174	−	32.3693i	0.357396	−	1.09995i
$867$		0			0
$868$		−	2.27938i		−	0.0773672i
$869$	−12.0332	−	8.74265i	−0.408199	−	0.296574i
$870$		0			0
$871$	20.4441	−	14.8535i	0.692723	−	0.503293i
$872$	−1.75534	−	2.41602i	−0.0594433	−	0.0818167i
$873$		0			0
$874$	−6.69572			−0.226486
$875$	4.73736	+	11.0785i	0.160152	+	0.374521i
$876$		0			0
$877$	−5.38217	+	1.74877i	−0.181743	+	0.0590519i	−0.398475	−	0.917179i	$-0.630460\pi$
$877$	−5.38217	+	1.74877i	−0.181743	+	0.0590519i	0.216732	+	0.976231i	$0.430460\pi$
$878$	0.936419	+	1.28887i	0.0316026	+	0.0434973i
$879$		0			0
$880$	−1.75258	+	4.27694i	−0.0590793	+	0.144176i
$881$	12.3606	+	8.98051i	0.416440	+	0.302561i	0.776204	−	0.630482i	$-0.217143\pi$
$881$	12.3606	+	8.98051i	0.416440	+	0.302561i	−0.359764	+	0.933043i	$0.617143\pi$
$882$		0			0
$883$	15.0149	−	20.6662i	0.505291	−	0.695473i	−0.477826	−	0.878455i	$-0.658575\pi$
$883$	15.0149	−	20.6662i	0.505291	−	0.695473i	0.983116	+	0.182982i	$0.0585749\pi$
$884$	1.47599	−	4.54264i	0.0496431	−	0.152786i
$885$		0			0
$886$	−7.60916	−	23.4186i	−0.255635	−	0.786763i
$887$	−1.60591	−	0.521792i	−0.0539212	−	0.0175201i	0.281932	−	0.959434i	$-0.409025\pi$
$887$	−1.60591	−	0.521792i	−0.0539212	−	0.0175201i	−0.335853	+	0.941914i	$0.609025\pi$
$888$		0			0
$889$	−7.11037	−	21.8835i	−0.238474	−	0.733948i
$890$	25.4336	−	6.20826i	0.852536	−	0.208101i
$891$		0			0
$892$	−6.86765	+	9.45251i	−0.229946	+	0.316493i
$893$		−	29.5167i		−	0.987738i
$894$		0			0
$895$	8.02390	+	32.8718i	0.268209	+	1.09878i
$896$	0.871864	−	0.633446i	0.0291269	−	0.0211620i
$897$		0			0
$898$	−32.4487	+	10.5432i	−1.08283	+	0.351832i
$899$	−2.21662			−0.0739284
$900$		0			0
$901$	2.11727			0.0705363
$902$	12.9239	−	4.19924i	0.430320	−	0.139819i
$903$		0			0
$904$	16.3410	−	11.8724i	0.543493	−	0.394871i
$905$	−18.6808	+	11.5454i	−0.620971	+	0.383781i
$906$		0			0
$907$			1.58315i			0.0525677i	0.999655	+	0.0262838i	$0.00836737\pi$
$907$			1.58315i			0.0525677i	−0.999655	+	0.0262838i	$0.991633\pi$
$908$	−0.419034	+	0.576751i	−0.0139061	+	0.0191402i
$909$		0			0
$910$	−12.9187	−	5.29375i	−0.428251	−	0.175486i
$911$	1.28770	+	3.96315i	0.0426635	+	0.131305i	0.970120	−	0.242627i	$-0.0780092\pi$
$911$	1.28770	+	3.96315i	0.0426635	+	0.131305i	−0.927456	+	0.373932i	$0.878009\pi$
$912$		0			0
$913$	−29.4255	−	9.56093i	−0.973843	−	0.316421i
$914$	−1.07826	−	3.31854i	−0.0356657	−	0.109768i
$915$		0			0
$916$	6.30918	−	19.4177i	0.208461	−	0.641578i
$917$	5.70584	−	7.85341i	0.188423	−	0.259342i
$918$		0			0
$919$	−29.8895	−	21.7160i	−0.985963	−	0.716344i	−0.0269300	−	0.999637i	$-0.508573\pi$
$919$	−29.8895	−	21.7160i	−0.985963	−	0.716344i	−0.959033	+	0.283293i	$0.908573\pi$
$920$	−3.34786	−	2.83744i	−0.110376	−	0.0935475i
$921$		0			0
$922$	−7.92637	−	10.9097i	−0.261041	−	0.359292i
$923$	27.0211	−	8.77970i	0.889412	−	0.288987i
$924$		0			0
$925$	20.0324	+	38.5887i	0.658661	+	1.26879i
$926$	1.86401			0.0612552
$927$		0			0
$928$	−0.616005	−	0.847859i	−0.0202214	−	0.0278323i
$929$	10.7812	−	7.83301i	0.353720	−	0.256993i	−0.396708	−	0.917945i	$-0.629847\pi$
$929$	10.7812	−	7.83301i	0.353720	−	0.256993i	0.750428	+	0.660952i	$0.229847\pi$
$930$		0			0
$931$	16.1150	+	11.7082i	0.528146	+	0.383721i
$932$		−	15.0403i		−	0.492661i
$933$		0			0
$934$	4.03005	−	12.4032i	0.131867	−	0.405846i
$935$	−2.46376	+	2.90697i	−0.0805737	+	0.0950680i
$936$		0			0
$937$	−44.9856	−	14.6167i	−1.46961	−	0.477507i	−0.538623	−	0.842547i	$-0.681055\pi$
$937$	−44.9856	−	14.6167i	−1.46961	−	0.477507i	−0.930992	+	0.365040i	$0.881055\pi$
$938$	4.47054	+	1.45257i	0.145968	+	0.0474279i
$939$		0			0
$940$	12.5083	−	14.7583i	0.407974	−	0.481364i
$941$	−6.21002	+	19.1125i	−0.202441	+	0.623049i	0.797368	+	0.603493i	$0.206225\pi$
$941$	−6.21002	+	19.1125i	−0.202441	+	0.623049i	−0.999809	+	0.0195553i	$0.993775\pi$
$942$		0			0
$943$			12.9024i			0.420159i
$944$	−3.80423	−	2.76393i	−0.123817	−	0.0899583i
$945$		0			0
$946$	−12.5034	+	9.08427i	−0.406521	+	0.295355i
$947$	−18.5807	−	25.5742i	−0.603793	−	0.831049i	0.392256	−	0.919856i	$-0.371695\pi$
$947$	−18.5807	−	25.5742i	−0.603793	−	0.831049i	−0.996049	+	0.0888068i	$0.971695\pi$
$948$		0			0
$949$	−7.51846			−0.244060
$950$	−7.85941	−	15.1397i	−0.254993	−	0.491198i
$951$		0			0
$952$	0.844989	−	0.274554i	0.0273863	−	0.00889833i
$953$	18.0111	+	24.7901i	0.583436	+	0.803031i	0.994067	−	0.108771i	$-0.0346915\pi$
$953$	18.0111	+	24.7901i	0.583436	+	0.803031i	−0.410631	+	0.911802i	$0.634692\pi$
$954$		0			0
$955$	−33.1833	−	28.1241i	−1.07378	−	0.910073i
$956$	3.38679	+	2.46065i	0.109537	+	0.0795831i
$957$		0			0
$958$	−7.27787	+	10.0171i	−0.235137	+	0.323639i
$959$	1.49578	−	4.60352i	0.0483011	−	0.148656i
$960$		0			0
$961$	−8.19713	−	25.2282i	−0.264424	−	0.813812i
$962$	−47.9138	−	15.5681i	−1.54480	−	0.501937i
$963$		0			0
$964$	9.09011	+	27.9765i	0.292773	+	0.901062i
$965$	−12.4145	−	5.08715i	−0.399638	−	0.163761i
$966$		0			0
$967$	9.35631	−	12.8779i	0.300879	−	0.414124i	−0.631631	−	0.775269i	$-0.717614\pi$
$967$	9.35631	−	12.8779i	0.300879	−	0.414124i	0.932510	+	0.361145i	$0.117614\pi$
$968$		−	6.72725i		−	0.216222i
$969$		0			0
$970$	−0.971367	+	0.600338i	−0.0311887	+	0.0192757i
$971$	41.1459	−	29.8942i	1.32043	−	0.959351i	0.320507	−	0.947246i	$-0.396147\pi$
$971$	41.1459	−	29.8942i	1.32043	−	0.959351i	0.999927	−	0.0121047i	$-0.00385313\pi$
$972$		0			0
$973$	13.7382	−	4.46381i	0.440426	−	0.143103i
$974$	4.51906			0.144800
$975$		0			0
$976$	−9.28293			−0.297139
$977$	−15.7710	+	5.12432i	−0.504560	+	0.163942i	−0.550227	−	0.835015i	$-0.685459\pi$
$977$	−15.7710	+	5.12432i	−0.504560	+	0.163942i	0.0456666	+	0.998957i	$0.485459\pi$
$978$		0			0
$979$	19.5795	−	14.2253i	0.625763	−	0.454644i
$980$	3.09591	+	12.6831i	0.0988952	+	0.405147i
$981$		0			0
$982$			27.4676i			0.876528i
$983$	−1.57984	+	2.17446i	−0.0503891	+	0.0693546i	−0.833468	−	0.552568i	$-0.813648\pi$
$983$	−1.57984	+	2.17446i	−0.0503891	+	0.0693546i	0.783079	+	0.621922i	$0.213648\pi$
$984$		0			0
$985$	−3.05613	+	0.745991i	−0.0973762	+	0.0237692i
$986$	−0.266994	−	0.821724i	−0.00850283	−	0.0261690i
$987$		0			0
$988$	18.7983	+	6.10793i	0.598053	+	0.194319i
$989$	−4.53455	−	13.9559i	−0.144190	−	0.443772i
$990$		0			0
$991$	−5.94835	+	18.3071i	−0.188956	+	0.581545i	−0.999994	−	0.00344733i	$-0.998903\pi$
$991$	−5.94835	+	18.3071i	−0.188956	+	0.581545i	0.811038	+	0.584993i	$0.198903\pi$
$992$	−1.24321	+	1.71113i	−0.0394719	+	0.0543284i
$993$		0			0
$994$	4.27560	+	3.10641i	0.135614	+	0.0985293i
$995$	11.6325	−	28.3876i	0.368775	−	0.899949i
$996$		0			0
$997$	−25.2441	−	34.7455i	−0.799489	−	1.10040i	−0.992861	−	0.119277i	$-0.961942\pi$
$997$	−25.2441	−	34.7455i	−0.799489	−	1.10040i	0.193372	−	0.981125i	$-0.438058\pi$
$998$	−12.8216	+	4.16598i	−0.405860	+	0.131872i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.l.b.19.2		8
3.2	odd	2		50.2.e.a.19.1	✓	8
12.11	even	2		400.2.y.a.369.2		8
15.2	even	4		250.2.d.c.151.1		8
15.8	even	4		250.2.d.b.151.2		8
15.14	odd	2		250.2.e.a.99.2		8
25.4	even	10	inner	450.2.l.b.379.2		8
75.2	even	20		1250.2.a.h.1.4		4
75.11	odd	10		1250.2.b.c.1249.8		8
75.14	odd	10		1250.2.b.c.1249.1		8
75.23	even	20		1250.2.a.i.1.1		4
75.29	odd	10		50.2.e.a.29.1	yes	8
75.47	even	20		250.2.d.c.101.1		8
75.53	even	20		250.2.d.b.101.2		8
75.71	odd	10		250.2.e.a.149.2		8
300.23	odd	20		10000.2.a.bb.1.4		4
300.179	even	10		400.2.y.a.129.2		8
300.227	odd	20		10000.2.a.o.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.e.a.19.1	✓	8	3.2	odd	2
50.2.e.a.29.1	yes	8	75.29	odd	10
250.2.d.b.101.2		8	75.53	even	20
250.2.d.b.151.2		8	15.8	even	4
250.2.d.c.101.1		8	75.47	even	20
250.2.d.c.151.1		8	15.2	even	4
250.2.e.a.99.2		8	15.14	odd	2
250.2.e.a.149.2		8	75.71	odd	10
400.2.y.a.129.2		8	300.179	even	10
400.2.y.a.369.2		8	12.11	even	2
450.2.l.b.19.2		8	1.1	even	1	trivial
450.2.l.b.379.2		8	25.4	even	10	inner
1250.2.a.h.1.4		4	75.2	even	20
1250.2.a.i.1.1		4	75.23	even	20
1250.2.b.c.1249.1		8	75.14	odd	10
1250.2.b.c.1249.8		8	75.11	odd	10
10000.2.a.o.1.1		4	300.227	odd	20
10000.2.a.bb.1.4		4	300.23	odd	20

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)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-0.847859 + 2.06909i) q^{5} +1.07768i q^{7} +(0.587785 - 0.809017i) q^{8} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-0.847859 + 2.06909i) q^{5} +1.07768i q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.166977 + 2.22982i) q^{10} +(0.638757 + 1.96589i) q^{11} +(5.51005 + 1.79032i) q^{13} +(0.333023 + 1.02494i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.484587 - 0.666977i) q^{17} +(2.76007 + 2.00531i) q^{19} +(0.530249 + 2.17229i) q^{20} +(1.21499 + 1.67229i) q^{22} +(-1.86655 + 0.606480i) q^{23} +(-3.56227 - 3.50859i) q^{25} +5.79360 q^{26} +(0.633446 + 0.871864i) q^{28} +(0.847859 - 0.616005i) q^{29} +(-1.71113 - 1.24321i) q^{31} -1.00000i q^{32} +(0.254763 - 0.784079i) q^{34} +(-2.22982 - 0.913723i) q^{35} +(-8.27012 - 2.68712i) q^{37} +(3.24466 + 1.05425i) q^{38} +(1.17557 + 1.90211i) q^{40} +(2.03150 - 6.25232i) q^{41} +7.47684i q^{43} +(1.67229 + 1.21499i) q^{44} +(-1.58779 + 1.15359i) q^{46} +(-5.08538 - 6.99942i) q^{47} +5.83860 q^{49} +(-4.47214 - 2.23607i) q^{50} +(5.51005 - 1.79032i) q^{52} +(1.50953 + 2.07768i) q^{53} +(-4.60919 - 0.345153i) q^{55} +(0.871864 + 0.633446i) q^{56} +(0.616005 - 0.847859i) q^{58} +(1.45309 - 4.47214i) q^{59} +(-2.86858 - 8.82859i) q^{61} +(-2.01155 - 0.653594i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(-8.37608 + 9.88284i) q^{65} +(2.56378 - 3.52874i) q^{67} -0.824429i q^{68} +(-2.40305 - 0.179949i) q^{70} +(3.96740 - 2.88249i) q^{71} +(-1.23420 + 0.401017i) q^{73} -8.69572 q^{74} +3.41164 q^{76} +(-2.11861 + 0.688378i) q^{77} +(-5.82141 + 4.22950i) q^{79} +(1.70582 + 1.44575i) q^{80} -6.57408i q^{82} +(-8.79798 + 12.1094i) q^{83} +(0.969175 + 1.56816i) q^{85} +(2.31047 + 7.11089i) q^{86} +(1.96589 + 0.638757i) q^{88} +(-3.61803 - 11.1352i) q^{89} +(-1.92940 + 5.93809i) q^{91} +(-1.15359 + 1.58779i) q^{92} +(-6.99942 - 5.08538i) q^{94} +(-6.48932 + 4.01062i) q^{95} +(0.300169 + 0.413147i) q^{97} +(5.55284 - 1.80423i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 10 q^{5}+O(q^{10}) \) 8 * q + 2 * q^4 + 10 * q^5	\( 8 q + 2 q^{4} + 10 q^{5} + 4 q^{11} + 4 q^{14} - 2 q^{16} - 10 q^{17} + 10 q^{19} + 20 q^{22} - 10 q^{23} + 10 q^{25} + 28 q^{26} + 10 q^{28} - 10 q^{29} + 6 q^{31} - 4 q^{34} - 10 q^{35} - 10 q^{37} + 14 q^{41} + 6 q^{44} - 8 q^{46} + 30 q^{47} - 16 q^{49} - 10 q^{55} - 4 q^{56} - 14 q^{61} + 2 q^{64} - 50 q^{65} + 10 q^{67} + 34 q^{71} - 36 q^{74} - 40 q^{77} - 50 q^{83} - 20 q^{85} - 22 q^{86} - 10 q^{88} - 20 q^{89} - 4 q^{91} + 10 q^{92} - 24 q^{94} - 20 q^{97} + 40 q^{98}+O(q^{100}) \) 8 * q + 2 * q^4 + 10 * q^5 + 4 * q^11 + 4 * q^14 - 2 * q^16 - 10 * q^17 + 10 * q^19 + 20 * q^22 - 10 * q^23 + 10 * q^25 + 28 * q^26 + 10 * q^28 - 10 * q^29 + 6 * q^31 - 4 * q^34 - 10 * q^35 - 10 * q^37 + 14 * q^41 + 6 * q^44 - 8 * q^46 + 30 * q^47 - 16 * q^49 - 10 * q^55 - 4 * q^56 - 14 * q^61 + 2 * q^64 - 50 * q^65 + 10 * q^67 + 34 * q^71 - 36 * q^74 - 40 * q^77 - 50 * q^83 - 20 * q^85 - 22 * q^86 - 10 * q^88 - 20 * q^89 - 4 * q^91 + 10 * q^92 - 24 * q^94 - 20 * q^97 + 40 * q^98

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