LMFDB - Embedded newform 351.2.bd.e.323.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(80,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("351.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 88 x^{16} - 6 x^{15} + 48 x^{13} + 1980 x^{12} - 204 x^{11} + 18 x^{10} + 2076 x^{9} + \cdots + 81 $ x^20 + 88x^16 - 6x^15 + 48x^13 + 1980x^12 - 204x^11 + 18x^10 + 2076x^9 + 8020x^8 + 2220x^7 + 792x^6 + 4350x^5 + 10936x^4 + 6648x^3 + 1800x^2 - 540*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			323.5
Root			$1.59384 - 1.59384i$ of defining polynomial
Character	$\chi$	$=$	351.323
Dual form			351.2.bd.e.188.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17722 + 0.583384i) q^{2} +(2.66790 + 1.54031i) q^{4} +(1.66769 - 1.66769i) q^{5} +(-0.0615804 - 0.229821i) q^{7} +(1.72233 + 1.72233i) q^{8} +O(q^{10})$	\(q+(2.17722 + 0.583384i) q^{2} +(2.66790 + 1.54031i) q^{4} +(1.66769 - 1.66769i) q^{5} +(-0.0615804 - 0.229821i) q^{7} +(1.72233 + 1.72233i) q^{8} +(4.60382 - 2.65802i) q^{10} +(0.174313 - 0.650544i) q^{11} +(-3.51964 + 0.782400i) q^{13} -0.536296i q^{14} +(-0.335505 - 0.581113i) q^{16} +(-3.30309 + 5.72112i) q^{17} +(-0.752989 + 0.201763i) q^{19} +(7.01797 - 1.88046i) q^{20} +(0.759034 - 1.31469i) q^{22} +(3.22139 + 5.57962i) q^{23} -0.562360i q^{25} +(-8.11946 - 0.349845i) q^{26} +(0.189706 - 0.707992i) q^{28} +(4.06150 - 2.34491i) q^{29} +(-1.22640 - 1.22640i) q^{31} +(-1.65229 - 6.16644i) q^{32} +(-10.5292 + 10.5292i) q^{34} +(-0.485967 - 0.280573i) q^{35} +(-9.00279 - 2.41229i) q^{37} -1.75713 q^{38} +5.74463 q^{40} +(8.51967 + 2.28284i) q^{41} +(-8.68411 - 5.01378i) q^{43} +(1.46709 - 1.46709i) q^{44} +(3.75862 + 14.0274i) q^{46} +(-2.19216 - 2.19216i) q^{47} +(6.01315 - 3.47170i) q^{49} +(0.328072 - 1.22438i) q^{50} +(-10.5952 - 3.33398i) q^{52} +3.84476i q^{53} +(-0.794205 - 1.37560i) q^{55} +(0.289767 - 0.501891i) q^{56} +(10.2108 - 2.73596i) q^{58} +(5.65848 - 1.51618i) q^{59} +(-4.48825 + 7.77387i) q^{61} +(-1.95468 - 3.38561i) q^{62} -13.0476i q^{64} +(-4.56486 + 7.17445i) q^{65} +(3.26768 - 12.1951i) q^{67} +(-17.6246 + 10.1756i) q^{68} +(-0.894374 - 0.894374i) q^{70} +(-3.63119 - 13.5518i) q^{71} +(-1.87687 + 1.87687i) q^{73} +(-18.1938 - 10.5042i) q^{74} +(-2.31967 - 0.621555i) q^{76} -0.160243 q^{77} +15.5674 q^{79} +(-1.52863 - 0.409596i) q^{80} +(17.2174 + 9.94049i) q^{82} +(-4.09212 + 4.09212i) q^{83} +(4.03252 + 15.0496i) q^{85} +(-15.9823 - 15.9823i) q^{86} +(1.42068 - 0.820229i) q^{88} +(-2.19574 + 8.19460i) q^{89} +(0.396553 + 0.760707i) q^{91} +19.8478i q^{92} +(-3.49394 - 6.05169i) q^{94} +(-0.919273 + 1.59223i) q^{95} +(5.37012 - 1.43892i) q^{97} +(15.1173 - 4.05066i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{5}+O(q^{10}) $ 20 * q + 6 * q^5	$ 20 q + 6 q^{5} - 12 q^{10} - 8 q^{13} + 24 q^{16} - 12 q^{17} - 12 q^{19} + 36 q^{20} + 8 q^{22} - 42 q^{26} + 2 q^{28} - 6 q^{29} - 22 q^{31} - 36 q^{32} - 6 q^{34} - 36 q^{35} + 8 q^{37} + 72 q^{38} - 36 q^{40} + 30 q^{41} - 30 q^{43} + 36 q^{44} - 48 q^{46} + 6 q^{47} + 30 q^{49} + 54 q^{50} + 4 q^{52} - 28 q^{55} - 60 q^{56} + 44 q^{58} + 30 q^{59} - 16 q^{61} - 30 q^{62} - 78 q^{65} + 18 q^{67} + 6 q^{68} + 38 q^{70} - 60 q^{71} - 72 q^{74} - 8 q^{76} - 12 q^{77} - 16 q^{79} + 126 q^{80} + 78 q^{82} + 12 q^{83} + 12 q^{85} + 18 q^{86} + 84 q^{89} + 30 q^{91} - 22 q^{94} - 66 q^{95} + 26 q^{97} + 42 q^{98}+O(q^{100}) $ 20 * q + 6 * q^5 - 12 * q^10 - 8 * q^13 + 24 * q^16 - 12 * q^17 - 12 * q^19 + 36 * q^20 + 8 * q^22 - 42 * q^26 + 2 * q^28 - 6 * q^29 - 22 * q^31 - 36 * q^32 - 6 * q^34 - 36 * q^35 + 8 * q^37 + 72 * q^38 - 36 * q^40 + 30 * q^41 - 30 * q^43 + 36 * q^44 - 48 * q^46 + 6 * q^47 + 30 * q^49 + 54 * q^50 + 4 * q^52 - 28 * q^55 - 60 * q^56 + 44 * q^58 + 30 * q^59 - 16 * q^61 - 30 * q^62 - 78 * q^65 + 18 * q^67 + 6 * q^68 + 38 * q^70 - 60 * q^71 - 72 * q^74 - 8 * q^76 - 12 * q^77 - 16 * q^79 + 126 * q^80 + 78 * q^82 + 12 * q^83 + 12 * q^85 + 18 * q^86 + 84 * q^89 + 30 * q^91 - 22 * q^94 - 66 * q^95 + 26 * q^97 + 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.17722	+	0.583384i	1.53953	+	0.412515i	0.926113	−	0.377247i	$-0.123129\pi$
$2$	2.17722	+	0.583384i	1.53953	+	0.412515i	0.613414	+	0.789762i	$0.289796\pi$
$3$		0			0
$3$		0			0
$4$	2.66790	+	1.54031i	1.33395	+	0.770156i
$5$	1.66769	−	1.66769i	0.745812	−	0.745812i	−0.227877	−	0.973690i	$-0.573179\pi$
$5$	1.66769	−	1.66769i	0.745812	−	0.745812i	0.973690	+	0.227877i	$0.0731786\pi$
$6$		0			0
$7$	−0.0615804	−	0.229821i	−0.0232752	−	0.0868642i	0.953311	−	0.301989i	$-0.0976507\pi$
$7$	−0.0615804	−	0.229821i	−0.0232752	−	0.0868642i	−0.976586	+	0.215125i	$0.930984\pi$
$8$	1.72233	+	1.72233i	0.608937	+	0.608937i
$9$		0			0
$10$	4.60382	−	2.65802i	1.45586	−	0.840539i
$11$	0.174313	−	0.650544i	0.0525573	−	0.196146i	−0.934655	−	0.355555i	$-0.884292\pi$
$11$	0.174313	−	0.650544i	0.0525573	−	0.196146i	0.987213	+	0.159408i	$0.0509586\pi$
$12$		0			0
$13$	−3.51964	+	0.782400i	−0.976172	+	0.216999i
$13$	−3.51964	+	0.782400i	−0.976172	+	0.216999i
$14$		−	0.536296i		−	0.143331i
$15$		0			0
$16$	−0.335505	−	0.581113i	−0.0838764	−	0.145278i
$17$	−3.30309	+	5.72112i	−0.801117	+	1.38758i	0.117764	+	0.993042i	$0.462427\pi$
$17$	−3.30309	+	5.72112i	−0.801117	+	1.38758i	−0.918881	+	0.394534i	$0.870906\pi$
$18$		0			0
$19$	−0.752989	+	0.201763i	−0.172748	+	0.0462876i	−0.344156	−	0.938912i	$-0.611835\pi$
$19$	−0.752989	+	0.201763i	−0.172748	+	0.0462876i	0.171408	+	0.985200i	$0.445168\pi$
$20$	7.01797	−	1.88046i	1.56927	−	0.420484i
$21$		0			0
$22$	0.759034	−	1.31469i	0.161827	−	0.280292i
$23$	3.22139	+	5.57962i	0.671707	+	1.16343i	0.977420	+	0.211307i	$0.0677720\pi$
$23$	3.22139	+	5.57962i	0.671707	+	1.16343i	−0.305713	+	0.952124i	$0.598895\pi$
$24$		0			0
$25$		−	0.562360i		−	0.112472i
$26$	−8.11946	−	0.349845i	−1.59236	−	0.0686103i
$27$		0			0
$28$	0.189706	−	0.707992i	0.0358510	−	0.133798i
$29$	4.06150	−	2.34491i	0.754201	−	0.435438i	−0.0730087	−	0.997331i	$-0.523260\pi$
$29$	4.06150	−	2.34491i	0.754201	−	0.435438i	0.827210	+	0.561893i	$0.189927\pi$
$30$		0			0
$31$	−1.22640	−	1.22640i	−0.220268	−	0.220268i	0.588343	−	0.808611i	$-0.299780\pi$
$31$	−1.22640	−	1.22640i	−0.220268	−	0.220268i	−0.808611	+	0.588343i	$0.799780\pi$
$32$	−1.65229	−	6.16644i	−0.292087	−	1.09008i
$33$		0			0
$34$	−10.5292	+	10.5292i	−1.80574	+	1.80574i
$35$	−0.485967	−	0.280573i	−0.0821433	−	0.0474255i
$36$		0			0
$37$	−9.00279	−	2.41229i	−1.48005	−	0.396578i	−0.573686	−	0.819075i	$-0.694487\pi$
$37$	−9.00279	−	2.41229i	−1.48005	−	0.396578i	−0.906364	+	0.422497i	$0.861154\pi$
$38$	−1.75713			−0.285044
$39$		0			0
$40$	5.74463			0.908305
$41$	8.51967	+	2.28284i	1.33055	+	0.356520i	0.852920	−	0.522042i	$-0.174829\pi$
$41$	8.51967	+	2.28284i	1.33055	+	0.356520i	0.477630	+	0.878561i	$0.341496\pi$
$42$		0			0
$43$	−8.68411	−	5.01378i	−1.32432	−	0.764594i	−0.339901	−	0.940461i	$-0.610394\pi$
$43$	−8.68411	−	5.01378i	−1.32432	−	0.764594i	−0.984414	+	0.175867i	$0.943727\pi$
$44$	1.46709	−	1.46709i	0.221172	−	0.221172i
$45$		0			0
$46$	3.75862	+	14.0274i	0.554178	+	2.06822i
$47$	−2.19216	−	2.19216i	−0.319760	−	0.319760i	0.528915	−	0.848675i	$-0.322599\pi$
$47$	−2.19216	−	2.19216i	−0.319760	−	0.319760i	−0.848675	+	0.528915i	$0.822599\pi$
$48$		0			0
$49$	6.01315	−	3.47170i	0.859022	−	0.495956i
$50$	0.328072	−	1.22438i	0.0463964	−	0.173154i
$51$		0			0
$52$	−10.5952	−	3.33398i	−1.46929	−	0.462339i
$53$			3.84476i			0.528119i	0.964506	+	0.264059i	$0.0850615\pi$
$53$			3.84476i			0.528119i	−0.964506	+	0.264059i	$0.914938\pi$
$54$		0			0
$55$	−0.794205	−	1.37560i	−0.107091	−	0.185486i
$56$	0.289767	−	0.501891i	0.0387217	−	0.0670680i
$57$		0			0
$58$	10.2108	−	2.73596i	1.34074	−	0.359250i
$59$	5.65848	−	1.51618i	0.736671	−	0.197390i	0.129073	−	0.991635i	$-0.458800\pi$
$59$	5.65848	−	1.51618i	0.736671	−	0.197390i	0.607598	+	0.794245i	$0.292133\pi$
$60$		0			0
$61$	−4.48825	+	7.77387i	−0.574661	+	0.995343i	0.421417	+	0.906867i	$0.361533\pi$
$61$	−4.48825	+	7.77387i	−0.574661	+	0.995343i	−0.996078	+	0.0884757i	$0.971800\pi$
$62$	−1.95468	−	3.38561i	−0.248245	−	0.429973i
$63$		0			0
$64$		−	13.0476i		−	1.63095i
$65$	−4.56486	+	7.17445i	−0.566201	+	0.889881i
$66$		0			0
$67$	3.26768	−	12.1951i	0.399211	−	1.48987i	−0.415278	−	0.909695i	$-0.636316\pi$
$67$	3.26768	−	12.1951i	0.399211	−	1.48987i	0.814489	−	0.580180i	$-0.197018\pi$
$68$	−17.6246	+	10.1756i	−2.13730	+	1.23397i
$69$		0			0
$70$	−0.894374	−	0.894374i	−0.106898	−	0.106898i
$71$	−3.63119	−	13.5518i	−0.430943	−	1.60830i	−0.750592	−	0.660766i	$-0.770232\pi$
$71$	−3.63119	−	13.5518i	−0.430943	−	1.60830i	0.319649	−	0.947536i	$-0.396435\pi$
$72$		0			0
$73$	−1.87687	+	1.87687i	−0.219671	+	0.219671i	−0.808360	−	0.588689i	$-0.799644\pi$
$73$	−1.87687	+	1.87687i	−0.219671	+	0.219671i	0.588689	+	0.808360i	$0.299644\pi$
$74$	−18.1938	−	10.5042i	−2.11498	−	1.22109i
$75$		0			0
$76$	−2.31967	−	0.621555i	−0.266085	−	0.0712972i
$77$	−0.160243			−0.0182614
$78$		0			0
$79$	15.5674			1.75147			0.875736	−	0.482791i	$-0.160377\pi$
$79$	15.5674			1.75147			0.875736	+	0.482791i	$0.160377\pi$
$80$	−1.52863	−	0.409596i	−0.170906	−	0.0457942i
$81$		0			0
$82$	17.2174	+	9.94049i	1.90135	+	1.09774i
$83$	−4.09212	+	4.09212i	−0.449169	+	0.449169i	−0.895078	−	0.445909i	$-0.852880\pi$
$83$	−4.09212	+	4.09212i	−0.449169	+	0.449169i	0.445909	+	0.895078i	$0.352880\pi$
$84$		0			0
$85$	4.03252	+	15.0496i	0.437388	+	1.63235i
$86$	−15.9823	−	15.9823i	−1.72341	−	1.72341i
$87$		0			0
$88$	1.42068	−	0.820229i	0.151445	−	0.0874367i
$89$	−2.19574	+	8.19460i	−0.232748	+	0.868626i	0.746404	+	0.665494i	$0.231779\pi$
$89$	−2.19574	+	8.19460i	−0.232748	+	0.868626i	−0.979151	+	0.203133i	$0.934888\pi$
$90$		0			0
$91$	0.396553	+	0.760707i	0.0415700	+	0.0797437i
$92$			19.8478i			2.06928i
$93$		0			0
$94$	−3.49394	−	6.05169i	−0.360373	−	0.624184i
$95$	−0.919273	+	1.59223i	−0.0943154	+	0.163359i
$96$		0			0
$97$	5.37012	−	1.43892i	0.545253	−	0.146100i	0.0243302	−	0.999704i	$-0.492255\pi$
$97$	5.37012	−	1.43892i	0.545253	−	0.146100i	0.520923	+	0.853604i	$0.325588\pi$
$98$	15.1173	−	4.05066i	1.52708	−	0.409179i
$99$		0			0
$100$	0.866210	−	1.50032i	0.0866210	−	0.150032i
$101$	−0.280506	−	0.485851i	−0.0279114	−	0.0483440i	0.851732	−	0.523977i	$-0.175552\pi$
$101$	−0.280506	−	0.485851i	−0.0279114	−	0.0483440i	−0.879644	+	0.475633i	$0.842219\pi$
$102$		0			0
$103$			1.45647i			0.143510i	0.997422	+	0.0717551i	$0.0228600\pi$
$103$			1.45647i			0.143510i	−0.997422	+	0.0717551i	$0.977140\pi$
$104$	−7.40955	−	4.71444i	−0.726566	−	0.462289i
$105$		0			0
$106$	−2.24297	+	8.37089i	−0.217857	+	0.813053i
$107$	5.78045	−	3.33734i	0.558817	−	0.322633i	−0.193853	−	0.981030i	$-0.562099\pi$
$107$	5.78045	−	3.33734i	0.558817	−	0.322633i	0.752671	+	0.658397i	$0.228765\pi$
$108$		0			0
$109$	−9.95101	−	9.95101i	−0.953133	−	0.953133i	0.0458165	−	0.998950i	$-0.485411\pi$
$109$	−9.95101	−	9.95101i	−0.953133	−	0.953133i	−0.998950	+	0.0458165i	$0.985411\pi$
$110$	−0.926653	−	3.45832i	−0.0883529	−	0.329737i
$111$		0			0
$112$	−0.112891	+	0.112891i	−0.0106672	+	0.0106672i
$113$	10.4207	+	6.01638i	0.980295	+	0.565974i	0.902359	−	0.430985i	$-0.141834\pi$
$113$	10.4207	+	6.01638i	0.980295	+	0.565974i	0.0779360	+	0.996958i	$0.475167\pi$
$114$		0			0
$115$	14.6773	+	3.93278i	1.36867	+	0.366734i
$116$	14.4475			1.34142
$117$		0			0
$118$	13.2043			1.21555
$119$	1.51824	+	0.406811i	0.139177	+	0.0372923i
$120$		0			0
$121$	9.13346	+	5.27320i	0.830314	+	0.479382i
$122$	−14.3071	+	14.3071i	−1.29530	+	1.29530i
$123$		0			0
$124$	−1.38287	−	5.16095i	−0.124186	−	0.463467i
$125$	7.40059	+	7.40059i	0.661929	+	0.661929i
$126$		0			0
$127$	3.20694	−	1.85153i	0.284570	−	0.164296i	−0.350921	−	0.936405i	$-0.614131\pi$
$127$	3.20694	−	1.85153i	0.284570	−	0.164296i	0.635490	+	0.772109i	$0.280798\pi$
$128$	4.30718	−	16.0746i	0.380704	−	1.42081i
$129$		0			0
$130$	−14.1242	+	12.9573i	−1.23877	+	1.13643i
$131$		−	5.54828i		−	0.484756i	−0.970182	−	0.242378i	$-0.922073\pi$
$131$		−	5.54828i		−	0.484756i	0.970182	−	0.242378i	$-0.0779274\pi$
$132$		0			0
$133$	0.0927387	+	0.160628i	0.00804147	+	0.0139282i
$134$	14.2289	−	24.6452i	1.22919	−	2.12902i
$135$		0			0
$136$	−15.5427	+	4.16466i	−1.33278	+	0.357116i
$137$	−1.17804	+	0.315655i	−0.100647	+	0.0269682i	−0.308791	−	0.951130i	$-0.599924\pi$
$137$	−1.17804	+	0.315655i	−0.100647	+	0.0269682i	0.208144	+	0.978098i	$0.433258\pi$
$138$		0			0
$139$	−7.12594	+	12.3425i	−0.604414	+	1.04688i	0.387730	+	0.921773i	$0.373259\pi$
$139$	−7.12594	+	12.3425i	−0.604414	+	1.04688i	−0.992144	+	0.125103i	$0.960074\pi$
$140$	−0.864339	−	1.49708i	−0.0730500	−	0.126526i
$141$		0			0
$142$		−	31.6236i		−	2.65379i
$143$	−0.104532	+	2.42606i	−0.00874142	+	0.202877i
$144$		0			0
$145$	2.86274	−	10.6839i	0.237737	−	0.887248i
$146$	−5.18130	+	2.99143i	−0.428808	+	0.247572i
$147$		0			0
$148$	−20.3028	−	20.3028i	−1.66888	−	1.66888i
$149$	2.18961	+	8.17175i	0.179380	+	0.669456i	0.995764	+	0.0919461i	$0.0293088\pi$
$149$	2.18961	+	8.17175i	0.179380	+	0.669456i	−0.816384	+	0.577510i	$0.804025\pi$
$150$		0			0
$151$	−12.6697	+	12.6697i	−1.03105	+	1.03105i	−0.0315431	+	0.999502i	$0.510042\pi$
$151$	−12.6697	+	12.6697i	−1.03105	+	1.03105i	−0.999502	+	0.0315431i	$0.989958\pi$
$152$	−1.64440	−	0.949396i	−0.133379	−	0.0770062i
$153$		0			0
$154$	−0.348884	−	0.0934832i	−0.0281139	−	0.00753309i
$155$	−4.09051			−0.328558
$156$		0			0
$157$	−2.97189			−0.237183			−0.118591	−	0.992943i	$-0.537838\pi$
$157$	−2.97189			−0.237183			−0.118591	+	0.992943i	$0.537838\pi$
$158$	33.8937	+	9.08179i	2.69644	+	0.722508i
$159$		0			0
$160$	−13.0392	−	7.52819i	−1.03084	−	0.595156i
$161$	1.08394	−	1.08394i	0.0854264	−	0.0854264i
$162$		0			0
$163$	4.47749	+	16.7102i	0.350704	+	1.30884i	0.885805	+	0.464057i	$0.153607\pi$
$163$	4.47749	+	16.7102i	0.350704	+	1.30884i	−0.535101	+	0.844788i	$0.679727\pi$
$164$	19.2133	+	19.2133i	1.50031	+	1.50031i
$165$		0			0
$166$	−11.2967	+	6.52217i	−0.876796	+	0.506218i
$167$	5.31133	−	19.8221i	0.411003	−	1.53388i	−0.381706	−	0.924284i	$-0.624663\pi$
$167$	5.31133	−	19.8221i	0.411003	−	1.53388i	0.792709	−	0.609600i	$-0.208670\pi$
$168$		0			0
$169$	11.7757	−	5.50753i	0.905823	−	0.423656i
$170$			35.1187i			2.69348i
$171$		0			0
$172$	−15.4455	−	26.7525i	−1.17771	−	2.03986i
$173$	−2.44888	+	4.24159i	−0.186185	+	0.322482i	−0.943975	−	0.330016i	$-0.892946\pi$
$173$	−2.44888	+	4.24159i	−0.186185	+	0.322482i	0.757790	+	0.652498i	$0.226279\pi$
$174$		0			0
$175$	−0.129242	+	0.0346304i	−0.00976980	+	0.00261781i
$176$	−0.436522	+	0.116966i	−0.0329041	+	0.00881662i
$177$		0			0
$178$	−9.56120	+	16.5605i	−0.716642	+	1.24126i
$179$	−11.6679	−	20.2095i	−0.872103	−	1.51053i	−0.859817	−	0.510602i	$-0.829422\pi$
$179$	−11.6679	−	20.2095i	−0.872103	−	1.51053i	−0.0122863	−	0.999925i	$-0.503911\pi$
$180$		0			0
$181$			20.4154i			1.51747i	0.651401	+	0.758733i	$0.274181\pi$
$181$			20.4154i			1.51747i	−0.651401	+	0.758733i	$0.725819\pi$
$182$	0.419598	+	1.88757i	0.0311027	+	0.139916i
$183$		0			0
$184$	−4.06165	+	15.1583i	−0.299429	+	1.11748i
$185$	−19.0368	+	10.9909i	−1.39961	+	0.808067i
$186$		0			0
$187$	3.14607	+	3.14607i	0.230063	+	0.230063i
$188$	−2.47185	−	9.22507i	−0.180278	−	0.672807i
$189$		0			0
$190$	−2.93034	+	2.93034i	−0.212589	+	0.212589i
$191$	4.26929	+	2.46488i	0.308915	+	0.178352i	0.646441	−	0.762964i	$-0.276257\pi$
$191$	4.26929	+	2.46488i	0.308915	+	0.178352i	−0.337526	+	0.941316i	$0.609590\pi$
$192$		0			0
$193$	−7.31479	−	1.95999i	−0.526530	−	0.141083i	−0.0142447	−	0.999899i	$-0.504534\pi$
$193$	−7.31479	−	1.95999i	−0.526530	−	0.141083i	−0.512286	+	0.858815i	$0.671201\pi$
$194$	12.5314			0.899700
$195$		0			0
$196$	21.3900			1.52785
$197$	6.95565	+	1.86376i	0.495569	+	0.132787i	0.497943	−	0.867210i	$-0.334089\pi$
$197$	6.95565	+	1.86376i	0.495569	+	0.132787i	−0.00237364	+	0.999997i	$0.500756\pi$
$198$		0			0
$199$	−16.6847	−	9.63289i	−1.18274	−	0.682857i	−0.226096	−	0.974105i	$-0.572596\pi$
$199$	−16.6847	−	9.63289i	−1.18274	−	0.682857i	−0.956648	+	0.291248i	$0.905930\pi$
$200$	0.968572	−	0.968572i	0.0684884	−	0.0684884i
$201$		0			0
$202$	−0.327286	−	1.22145i	−0.0230278	−	0.0859408i
$203$	−0.789018	−	0.789018i	−0.0553782	−	0.0553782i
$204$		0			0
$205$	18.0152	−	10.4011i	1.25824	−	0.726444i
$206$	−0.849681	+	3.17105i	−0.0592001	+	0.220938i
$207$		0			0
$208$	1.63552	+	1.78281i	0.113403	+	0.123615i
$209$			0.525022i			0.0363165i
$210$		0			0
$211$	−1.48403	−	2.57041i	−0.102165	−	0.176954i	0.810412	−	0.585861i	$-0.199244\pi$
$211$	−1.48403	−	2.57041i	−0.102165	−	0.176954i	−0.912576	+	0.408907i	$0.865910\pi$
$212$	−5.92213	+	10.2574i	−0.406734	+	0.704483i
$213$		0			0
$214$	14.5323	−	3.89391i	0.993405	−	0.266182i
$215$	−22.8438	+	6.12098i	−1.55793	+	0.417447i
$216$		0			0
$217$	−0.206331	+	0.357375i	−0.0140066	+	0.0242602i
$218$	−15.8603	−	27.4708i	−1.07419	−	1.86056i
$219$		0			0
$220$		−	4.89329i		−	0.329905i
$221$	7.14948	−	22.7206i	0.480926	−	1.52835i
$222$		0			0
$223$	−0.386884	+	1.44387i	−0.0259077	+	0.0966887i	−0.977669	−	0.210150i	$-0.932605\pi$
$223$	−0.386884	+	1.44387i	−0.0259077	+	0.0966887i	0.951761	+	0.306839i	$0.0992713\pi$
$224$	−1.31543	+	0.759464i	−0.0878909	+	0.0507438i
$225$		0			0
$226$	19.1782	+	19.1782i	1.27572	+	1.27572i
$227$	2.32108	+	8.66239i	0.154056	+	0.574943i	0.999184	+	0.0403804i	$0.0128570\pi$
$227$	2.32108	+	8.66239i	0.154056	+	0.574943i	−0.845129	+	0.534563i	$0.820476\pi$
$228$		0			0
$229$	20.2045	−	20.2045i	1.33515	−	1.33515i	0.434461	−	0.900691i	$-0.356939\pi$
$229$	20.2045	−	20.2045i	1.33515	−	1.33515i	0.900691	−	0.434461i	$-0.143061\pi$
$230$	29.6615	+	17.1251i	1.95582	+	1.12919i
$231$		0			0
$232$	11.0340	+	2.95654i	0.724415	+	0.194107i
$233$	−4.12555			−0.270274			−0.135137	−	0.990827i	$-0.543147\pi$
$233$	−4.12555			−0.270274			−0.135137	+	0.990827i	$0.543147\pi$
$234$		0			0
$235$	−7.31168			−0.476961
$236$	17.4316	+	4.67079i	1.13470	+	0.304043i
$237$		0			0
$238$	3.06822	+	1.77144i	0.198883	+	0.114825i
$239$	4.10101	−	4.10101i	0.265272	−	0.265272i	−0.561920	−	0.827192i	$-0.689937\pi$
$239$	4.10101	−	4.10101i	0.265272	−	0.265272i	0.827192	+	0.561920i	$0.189937\pi$
$240$		0			0
$241$	1.89114	+	7.05783i	0.121819	+	0.454635i	0.999706	−	0.0242323i	$-0.00771415\pi$
$241$	1.89114	+	7.05783i	0.121819	+	0.454635i	−0.877887	+	0.478867i	$0.841047\pi$
$242$	16.8092	+	16.8092i	1.08054	+	1.08054i
$243$		0			0
$244$	−23.9484	+	13.8266i	−1.53314	+	0.885157i
$245$	4.23836	−	15.8178i	0.270779	−	1.01056i
$246$		0			0
$247$	2.49239	−	1.29927i	0.158587	−	0.0826706i
$248$		−	4.22455i		−	0.268259i
$249$		0			0
$250$	11.7953	+	20.4301i	0.746002	+	1.29211i
$251$	2.23631	−	3.87341i	0.141155	−	0.244487i	−0.786777	−	0.617237i	$-0.788252\pi$
$251$	2.23631	−	3.87341i	0.141155	−	0.244487i	0.927932	+	0.372750i	$0.121585\pi$
$252$		0			0
$253$	4.19132	−	1.12306i	0.263506	−	0.0706062i
$254$	8.06236	−	2.16030i	0.505877	−	0.135549i
$255$		0			0
$256$	5.70774	−	9.88610i	0.356734	−	0.617881i
$257$	4.98235	+	8.62968i	0.310790	+	0.538305i	0.978534	−	0.206087i	$-0.0660729\pi$
$257$	4.98235	+	8.62968i	0.310790	+	0.538305i	−0.667743	+	0.744392i	$0.732740\pi$
$258$		0			0
$259$			2.21758i			0.137794i
$260$	−23.2295	+	12.1094i	−1.44063	+	0.750993i
$261$		0			0
$262$	3.23678	−	12.0798i	0.199969	−	0.746295i
$263$	14.2182	−	8.20889i	0.876733	−	0.506182i	0.00715325	−	0.999974i	$-0.497723\pi$
$263$	14.2182	−	8.20889i	0.876733	−	0.506182i	0.869580	+	0.493792i	$0.164390\pi$
$264$		0			0
$265$	6.41186	+	6.41186i	0.393878	+	0.393878i
$266$	0.108205	+	0.403825i	0.00663445	+	0.0247601i
$267$		0			0
$268$	27.5021	−	27.5021i	1.67996	−	1.67996i
$269$	−13.9040	−	8.02750i	−0.847744	−	0.489445i	0.0121449	−	0.999926i	$-0.496134\pi$
$269$	−13.9040	−	8.02750i	−0.847744	−	0.489445i	−0.859889	+	0.510481i	$0.829467\pi$
$270$		0			0
$271$	4.96792	+	1.33115i	0.301780	+	0.0808616i	0.406532	−	0.913637i	$-0.366738\pi$
$271$	4.96792	+	1.33115i	0.301780	+	0.0808616i	−0.104752	+	0.994498i	$0.533405\pi$
$272$	4.43282			0.268779
$273$		0			0
$274$	−2.74900			−0.166073
$275$	−0.365840	−	0.0980265i	−0.0220610	−	0.00591122i
$276$		0			0
$277$	−17.1244	−	9.88678i	−1.02891	−	0.594039i	−0.112235	−	0.993682i	$-0.535801\pi$
$277$	−17.1244	−	9.88678i	−1.02891	−	0.594039i	−0.916671	+	0.399643i	$0.869134\pi$
$278$	−22.7151	+	22.7151i	−1.36236	+	1.36236i
$279$		0			0
$280$	−0.353756	−	1.32024i	−0.0211410	−	0.0788992i
$281$	16.0685	+	16.0685i	0.958566	+	0.958566i	0.999175	−	0.0406087i	$-0.0129297\pi$
$281$	16.0685	+	16.0685i	0.958566	+	0.958566i	−0.0406087	+	0.999175i	$0.512930\pi$
$282$		0			0
$283$	11.0985	−	6.40775i	0.659740	−	0.380901i	−0.132438	−	0.991191i	$-0.542281\pi$
$283$	11.0985	−	6.40775i	0.659740	−	0.380901i	0.792178	+	0.610290i	$0.208947\pi$
$284$	11.1863	−	41.7480i	0.663787	−	2.47729i
$285$		0			0
$286$	−1.64292	+	5.22108i	−0.0971476	+	0.308729i
$287$		−	2.09858i		−	0.123875i
$288$		0			0
$289$	−13.3208	−	23.0723i	−0.783578	−	1.35720i
$290$	12.4656	−	21.5911i	0.732006	−	1.26787i
$291$		0			0
$292$	−7.89827	+	2.11634i	−0.462212	+	0.123849i
$293$	−16.1677	+	4.33213i	−0.944529	+	0.253086i	−0.698039	−	0.716060i	$-0.745944\pi$
$293$	−16.1677	+	4.33213i	−0.944529	+	0.253086i	−0.246490	+	0.969145i	$0.579277\pi$
$294$		0			0
$295$	6.90805	−	11.9651i	0.402202	−	0.696634i
$296$	−11.3510	−	19.6606i	−0.659766	−	1.14275i
$297$		0			0
$298$			19.0691i			1.10464i
$299$	−15.7036	−	17.1178i	−0.908165	−	0.989949i
$300$		0			0
$301$	−0.617501	+	2.30454i	−0.0355921	+	0.132832i
$302$	−34.9760	+	20.1934i	−2.01264	+	1.16200i
$303$		0			0
$304$	0.369879	+	0.369879i	0.0212140	+	0.0212140i
$305$	5.47940	+	20.4494i	0.313749	+	1.17093i
$306$		0			0
$307$	−9.36801	+	9.36801i	−0.534661	+	0.534661i	−0.921956	−	0.387295i	$-0.873409\pi$
$307$	−9.36801	+	9.36801i	−0.534661	+	0.534661i	0.387295	+	0.921956i	$0.373409\pi$
$308$	−0.427512	−	0.246824i	−0.0243597	−	0.0140641i
$309$		0			0
$310$	−8.90593	−	2.38634i	−0.505823	−	0.135535i
$311$	−25.6526			−1.45462			−0.727312	−	0.686307i	$-0.759231\pi$
$311$	−25.6526			−1.45462			−0.727312	+	0.686307i	$0.759231\pi$
$312$		0			0
$313$	−10.8773			−0.614823			−0.307411	−	0.951577i	$-0.599463\pi$
$313$	−10.8773			−0.614823			−0.307411	+	0.951577i	$0.599463\pi$
$314$	−6.47045	−	1.73375i	−0.365149	−	0.0978413i
$315$		0			0
$316$	41.5323	+	23.9787i	2.33637	+	1.34891i
$317$	−5.53137	+	5.53137i	−0.310672	+	0.310672i	−0.845170	−	0.534498i	$-0.820501\pi$
$317$	−5.53137	+	5.53137i	−0.310672	+	0.310672i	0.534498	+	0.845170i	$0.320501\pi$
$318$		0			0
$319$	−0.817494	−	3.05093i	−0.0457709	−	0.170819i
$320$	−21.7593	−	21.7593i	−1.21638	−	1.21638i
$321$		0			0
$322$	2.99233	−	1.72762i	0.166756	−	0.0962766i
$323$	1.33288	−	4.97438i	0.0741635	−	0.276782i
$324$		0			0
$325$	0.439991	+	1.97930i	0.0244063	+	0.109792i
$326$			38.9939i			2.15967i
$327$		0			0
$328$	10.7419	+	18.6055i	0.593123	+	1.02732i
$329$	−0.368811	+	0.638799i	−0.0203332	+	0.0352181i
$330$		0			0
$331$	5.36167	−	1.43666i	0.294704	−	0.0789658i	−0.108438	−	0.994103i	$-0.534585\pi$
$331$	5.36167	−	1.43666i	0.294704	−	0.0789658i	0.403142	+	0.915137i	$0.367918\pi$
$332$	−17.2205	+	4.61422i	−0.945098	+	0.253238i
$333$		0			0
$334$	23.1279	−	40.0586i	1.26550	−	2.19191i
$335$	−14.8882	−	25.7872i	−0.813430	−	1.40890i
$336$		0			0
$337$			9.38139i			0.511037i	0.966804	+	0.255518i	$0.0822461\pi$
$337$			9.38139i			0.511037i	−0.966804	+	0.255518i	$0.917754\pi$
$338$	28.8513	−	5.12134i	1.56930	−	0.278564i
$339$		0			0
$340$	−12.4227	+	46.3620i	−0.673714	+	2.51433i
$341$	−1.01161	+	0.584051i	−0.0547815	+	0.0316281i
$342$		0			0
$343$	−2.34585	−	2.34585i	−0.126664	−	0.126664i
$344$	−6.32155	−	23.5923i	−0.340835	−	1.27201i
$345$		0			0
$346$	−7.80622	+	7.80622i	−0.419665	+	0.419665i
$347$	−7.17753	−	4.14395i	−0.385310	−	0.222459i	0.294816	−	0.955554i	$-0.404742\pi$
$347$	−7.17753	−	4.14395i	−0.385310	−	0.222459i	−0.680126	+	0.733095i	$0.738075\pi$
$348$		0			0
$349$	−20.9733	−	5.61979i	−1.12268	−	0.300820i	−0.350711	−	0.936484i	$-0.614060\pi$
$349$	−20.9733	−	5.61979i	−1.12268	−	0.300820i	−0.771966	+	0.635664i	$0.780727\pi$
$350$	−0.301592			−0.0161207
$351$		0			0
$352$	−4.29956			−0.229167
$353$	−20.9614	−	5.61660i	−1.11566	−	0.298941i	−0.346537	−	0.938036i	$-0.612642\pi$
$353$	−20.9614	−	5.61660i	−1.11566	−	0.298941i	−0.769128	+	0.639095i	$0.779309\pi$
$354$		0			0
$355$	−28.6558	−	16.5445i	−1.52089	−	0.878089i
$356$	−18.4802	+	18.4802i	−0.979451	+	0.979451i
$357$		0			0
$358$	−13.6138	−	50.8074i	−0.719511	−	2.68525i
$359$	9.11021	+	9.11021i	0.480819	+	0.480819i	0.905393	−	0.424574i	$-0.139576\pi$
$359$	9.11021	+	9.11021i	0.480819	+	0.480819i	−0.424574	+	0.905393i	$0.639576\pi$
$360$		0			0
$361$	−15.9282	+	9.19615i	−0.838326	+	0.484008i
$362$	−11.9100	+	44.4489i	−0.625978	+	2.33618i
$363$		0			0
$364$	−0.113763	+	2.64030i	−0.00596281	+	0.138389i
$365$			6.26007i			0.327667i
$366$		0			0
$367$	11.5803	+	20.0576i	0.604486	+	1.04700i	0.992133	+	0.125192i	$0.0399546\pi$
$367$	11.5803	+	20.0576i	0.604486	+	1.04700i	−0.387647	+	0.921808i	$0.626712\pi$
$368$	2.16159	−	3.74399i	0.112681	−	0.195169i
$369$		0			0
$370$	−47.8592	+	12.8238i	−2.48808	+	0.666679i
$371$	0.883608	−	0.236762i	0.0458746	−	0.0122921i
$372$		0			0
$373$	−13.8169	+	23.9316i	−0.715414	+	1.23913i	0.247386	+	0.968917i	$0.420428\pi$
$373$	−13.8169	+	23.9316i	−0.715414	+	1.23913i	−0.962800	+	0.270216i	$0.912905\pi$
$374$	5.01432	+	8.68505i	0.259284	+	0.449093i
$375$		0			0
$376$		−	7.55127i		−	0.389427i
$377$	−12.4603	+	11.4309i	−0.641740	+	0.588723i
$378$		0			0
$379$	4.53442	−	16.9227i	0.232917	−	0.869259i	−0.746159	−	0.665768i	$-0.768104\pi$
$379$	4.53442	−	16.9227i	0.232917	−	0.869259i	0.979077	−	0.203492i	$-0.0652291\pi$
$380$	−4.90505	+	2.83193i	−0.251624	+	0.145275i
$381$		0			0
$382$	7.85722	+	7.85722i	0.402010	+	0.402010i
$383$	−7.10970	−	26.5338i	−0.363289	−	1.35581i	−0.869726	−	0.493535i	$-0.835705\pi$
$383$	−7.10970	−	26.5338i	−0.363289	−	1.35581i	0.506437	−	0.862277i	$-0.330962\pi$
$384$		0			0
$385$	−0.267235	+	0.267235i	−0.0136196	+	0.0136196i
$386$	−14.7825	−	8.53467i	−0.752408	−	0.434403i
$387$		0			0
$388$	16.5433	+	4.43276i	0.839859	+	0.225040i
$389$	25.4722			1.29149			0.645746	−	0.763552i	$-0.276547\pi$
$389$	25.4722			1.29149			0.645746	+	0.763552i	$0.276547\pi$
$390$		0			0
$391$	−42.5622			−2.15247
$392$	16.3361	+	4.37724i	0.825096	+	0.221084i
$393$		0			0
$394$	14.0567	+	8.11563i	0.708165	+	0.408860i
$395$	25.9616	−	25.9616i	1.30627	−	1.30627i
$396$		0			0
$397$	−7.06772	−	26.3771i	−0.354719	−	1.32383i	−0.880838	−	0.473418i	$-0.843020\pi$
$397$	−7.06772	−	26.3771i	−0.354719	−	1.32383i	0.526119	−	0.850411i	$-0.323647\pi$
$398$	−30.7065	−	30.7065i	−1.53918	−	1.53918i
$399$		0			0
$400$	−0.326795	+	0.188675i	−0.0163397	+	0.00943375i
$401$	−0.294362	+	1.09857i	−0.0146997	+	0.0548602i	−0.972886	−	0.231285i	$-0.925707\pi$
$401$	−0.294362	+	1.09857i	−0.0146997	+	0.0548602i	0.958186	+	0.286145i	$0.0923738\pi$
$402$		0			0
$403$	5.27603	+	3.35695i	0.262818	+	0.167222i
$404$		−	1.72827i		−	0.0859846i
$405$		0			0
$406$	−1.25756	−	2.17817i	−0.0624119	−	0.108101i
$407$	−3.13860	+	5.43622i	−0.155575	+	0.269463i
$408$		0			0
$409$	9.21571	−	2.46934i	0.455688	−	0.122101i	−0.0236719	−	0.999720i	$-0.507536\pi$
$409$	9.21571	−	2.46934i	0.455688	−	0.122101i	0.479359	+	0.877619i	$0.340869\pi$
$410$	45.2909	−	12.1357i	2.23676	−	0.599338i
$411$		0			0
$412$	−2.24342	+	3.88571i	−0.110525	+	0.191435i
$413$	−0.696902	−	1.20707i	−0.0342923	−	0.0593960i
$414$		0			0
$415$			13.6488i			0.669991i
$416$	10.6401	+	20.4109i	0.521674	+	1.00073i
$417$		0			0
$418$	−0.306290	+	1.14309i	−0.0149811	+	0.0559103i
$419$	−30.0498	+	17.3492i	−1.46803	+	0.847566i	−0.999359	−	0.0358083i	$-0.988599\pi$
$419$	−30.0498	+	17.3492i	−1.46803	+	0.847566i	−0.468668	+	0.883374i	$0.655266\pi$
$420$		0			0
$421$	1.55485	+	1.55485i	0.0757785	+	0.0757785i	0.743980	−	0.668202i	$-0.232936\pi$
$421$	1.55485	+	1.55485i	0.0757785	+	0.0757785i	−0.668202	+	0.743980i	$0.732936\pi$
$422$	−1.73152	−	6.46210i	−0.0842889	−	0.314570i
$423$		0			0
$424$	−6.62197	+	6.62197i	−0.321591	+	0.321591i
$425$	3.21733	+	1.85753i	0.156064	+	0.0901033i
$426$		0			0
$427$	2.06299	+	0.552776i	0.0998350	+	0.0267507i
$428$	20.5622			0.993911
$429$		0			0
$430$	−53.3068			−2.57068
$431$	14.5930	+	3.91019i	0.702921	+	0.188347i	0.592538	−	0.805542i	$-0.298126\pi$
$431$	14.5930	+	3.91019i	0.702921	+	0.188347i	0.110382	+	0.993889i	$0.464792\pi$
$432$		0			0
$433$	−12.7498	−	7.36109i	−0.612715	−	0.353751i	0.161312	−	0.986903i	$-0.448427\pi$
$433$	−12.7498	−	7.36109i	−0.612715	−	0.353751i	−0.774027	+	0.633152i	$0.781761\pi$
$434$	−0.657714	+	0.657714i	−0.0315713	+	0.0315713i
$435$		0			0
$436$	−11.2206	−	41.8759i	−0.537370	−	2.00549i
$437$	−3.55143	−	3.55143i	−0.169888	−	0.169888i
$438$		0			0
$439$	−2.61711	+	1.51099i	−0.124908	+	0.0721156i	−0.561152	−	0.827713i	$-0.689642\pi$
$439$	−2.61711	+	1.51099i	−0.124908	+	0.0721156i	0.436244	+	0.899828i	$0.356308\pi$
$440$	1.00136	−	3.73713i	0.0477380	−	0.178161i
$441$		0			0
$442$	28.8208	−	45.2969i	1.37087	−	2.15455i
$443$		−	23.2321i		−	1.10379i	−0.833913	−	0.551896i	$-0.813905\pi$
$443$		−	23.2321i		−	1.10379i	0.833913	−	0.551896i	$-0.186095\pi$
$444$		0			0
$445$	10.0042	+	17.3278i	0.474246	+	0.821418i
$446$	−1.68466	+	2.91792i	−0.0797711	+	0.138168i
$447$		0			0
$448$	−2.99861	+	0.803476i	−0.141671	+	0.0379607i
$449$	29.7926	−	7.98291i	1.40600	−	0.376737i	0.525505	−	0.850791i	$-0.323877\pi$
$449$	29.7926	−	7.98291i	1.40600	−	0.376737i	0.880496	+	0.474054i	$0.157210\pi$
$450$		0			0
$451$	2.97018	−	5.14449i	0.139860	−	0.242245i
$452$	18.5342	+	32.1022i	0.871776	+	1.50996i
$453$		0			0
$454$			20.2140i			0.948690i
$455$	1.92995	+	0.607295i	0.0904773	+	0.0284704i
$456$		0			0
$457$	8.47866	−	31.6428i	0.396615	−	1.48019i	−0.422398	−	0.906411i	$-0.638811\pi$
$457$	8.47866	−	31.6428i	0.396615	−	1.48019i	0.819012	−	0.573776i	$-0.194522\pi$
$458$	55.7766	−	32.2027i	2.60627	−	1.50473i
$459$		0			0
$460$	33.0999	+	33.0999i	1.54329	+	1.54329i
$461$	2.53963	+	9.47804i	0.118282	+	0.441436i	0.999511	−	0.0312534i	$-0.00994988\pi$
$461$	2.53963	+	9.47804i	0.118282	+	0.441436i	−0.881229	+	0.472690i	$0.843283\pi$
$462$		0			0
$463$	5.87241	−	5.87241i	0.272914	−	0.272914i	−0.557358	−	0.830272i	$-0.688185\pi$
$463$	5.87241	−	5.87241i	0.272914	−	0.272914i	0.830272	+	0.557358i	$0.188185\pi$
$464$	−2.72531	−	1.57346i	−0.126519	−	0.0730460i
$465$		0			0
$466$	−8.98223	−	2.40678i	−0.416094	−	0.111492i
$467$	2.32585			0.107627			0.0538137	−	0.998551i	$-0.482862\pi$
$467$	2.32585			0.107627			0.0538137	+	0.998551i	$0.482862\pi$
$468$		0			0
$469$	−3.00393			−0.138708
$470$	−15.9191	−	4.26552i	−0.734294	−	0.196754i
$471$		0			0
$472$	12.3572	+	7.13441i	0.568784	+	0.328388i
$473$	−4.77543	+	4.77543i	−0.219575	+	0.219575i
$474$		0			0
$475$	0.113463	+	0.423451i	0.00520606	+	0.0194293i
$476$	3.42389	+	3.42389i	0.156934	+	0.156934i
$477$		0			0
$478$	11.3213	−	6.53633i	0.517822	−	0.298965i
$479$	−2.22109	+	8.28922i	−0.101484	+	0.378744i	−0.997923	−	0.0644243i	$-0.979479\pi$
$479$	−2.22109	+	8.28922i	−0.101484	+	0.378744i	0.896438	+	0.443168i	$0.146146\pi$
$480$		0			0
$481$	33.5739	+	1.44661i	1.53084	+	0.0659596i
$482$			16.4697i			0.750175i
$483$		0			0
$484$	16.2447	+	28.1367i	0.738398	+	1.27894i
$485$	6.55601	−	11.3553i	0.297693	−	0.515619i
$486$		0			0
$487$	9.43310	−	2.52759i	0.427455	−	0.114536i	−0.0386764	−	0.999252i	$-0.512314\pi$
$487$	9.43310	−	2.52759i	0.427455	−	0.114536i	0.466131	+	0.884716i	$0.345647\pi$
$488$	−21.1195	+	5.65895i	−0.956034	+	0.256168i
$489$		0			0
$490$	18.4557	−	31.9661i	0.833742	−	1.44408i
$491$	11.3589	+	19.6742i	0.512620	+	0.887884i	0.999893	+	0.0146340i	$0.00465833\pi$
$491$	11.3589	+	19.6742i	0.512620	+	0.887884i	−0.487273	+	0.873250i	$0.662008\pi$
$492$		0			0
$493$			30.9818i			1.39535i
$494$	6.18445	−	1.37478i	0.278252	−	0.0618541i
$495$		0			0
$496$	−0.301213	+	1.12414i	−0.0135249	+	0.0504755i
$497$	−2.89088	+	1.66905i	−0.129674	+	0.0748671i
$498$		0			0
$499$	6.65780	+	6.65780i	0.298044	+	0.298044i	0.840247	−	0.542203i	$-0.182410\pi$
$499$	6.65780	+	6.65780i	0.298044	+	0.298044i	−0.542203	+	0.840247i	$0.682410\pi$
$500$	8.34481	+	31.1432i	0.373191	+	1.39277i
$501$		0			0
$502$	7.12863	−	7.12863i	0.318166	−	0.318166i
$503$	−1.29978	−	0.750431i	−0.0579545	−	0.0334601i	0.470743	−	0.882271i	$-0.343986\pi$
$503$	−1.29978	−	0.750431i	−0.0579545	−	0.0334601i	−0.528697	+	0.848810i	$0.677319\pi$
$504$		0			0
$505$	−1.27805	−	0.342451i	−0.0568723	−	0.0152389i
$506$	9.78059			0.434800
$507$		0			0
$508$	11.4077			0.506135
$509$	6.23222	+	1.66992i	0.276238	+	0.0740178i	0.394279	−	0.918991i	$-0.370995\pi$
$509$	6.23222	+	1.66992i	0.276238	+	0.0740178i	−0.118040	+	0.993009i	$0.537661\pi$
$510$		0			0
$511$	0.546924	+	0.315767i	0.0241945	+	0.0139687i
$512$	−5.34045	+	5.34045i	−0.236017	+	0.236017i
$513$		0			0
$514$	5.81325	+	21.6953i	0.256411	+	0.956941i
$515$	2.42893	+	2.42893i	0.107032	+	0.107032i
$516$		0			0
$517$	−1.80822	+	1.04398i	−0.0795253	+	0.0459140i
$518$	−1.29370	+	4.82816i	−0.0568420	+	0.212137i
$519$		0			0
$520$	−20.2190	+	4.49460i	−0.886662	+	0.197101i
$521$		−	5.41790i		−	0.237363i	−0.992932	−	0.118681i	$-0.962133\pi$
$521$		−	5.41790i		−	0.237363i	0.992932	−	0.118681i	$-0.0378667\pi$
$522$		0			0
$523$	12.5509	+	21.7388i	0.548812	+	0.950570i	0.998356	+	0.0573118i	$0.0182529\pi$
$523$	12.5509	+	21.7388i	0.548812	+	0.950570i	−0.449545	+	0.893258i	$0.648414\pi$
$524$	8.54608	−	14.8023i	0.373337	−	0.646639i
$525$		0			0
$526$	35.7451	−	9.57788i	1.55856	−	0.417615i
$527$	11.0673	−	2.96548i	0.482100	−	0.129178i
$528$		0			0
$529$	−9.25476	+	16.0297i	−0.402381	+	0.696944i
$530$	10.2195	+	17.7006i	0.443905	+	0.768865i
$531$		0			0
$532$			0.571386i			0.0247727i
$533$	−31.7723	−	1.36898i	−1.37621	−	0.0592970i
$534$		0			0
$535$	4.07434	−	15.2056i	0.176149	−	0.657397i
$536$	26.6321	−	15.3761i	1.15033	−	0.664145i
$537$		0			0
$538$	−25.5890	−	25.5890i	−1.10322	−	1.10322i
$539$	−1.21032	−	4.51698i	−0.0521322	−	0.194560i
$540$		0			0
$541$	−2.49447	+	2.49447i	−0.107245	+	0.107245i	−0.758693	−	0.651448i	$-0.774162\pi$
$541$	−2.49447	+	2.49447i	−0.107245	+	0.107245i	0.651448	+	0.758693i	$0.274162\pi$
$542$	10.0397	+	5.79641i	0.431241	+	0.248977i
$543$		0			0
$544$	40.7366	+	10.9154i	1.74657	+	0.467992i
$545$	−33.1903			−1.42172
$546$		0			0
$547$	−37.0386			−1.58366			−0.791828	−	0.610744i	$-0.790871\pi$
$547$	−37.0386			−1.58366			−0.791828	+	0.610744i	$0.790871\pi$
$548$	−3.62910	−	0.972413i	−0.155027	−	0.0415394i
$549$		0			0
$550$	−0.739327	−	0.426851i	−0.0315250	−	0.0182010i
$551$	−2.58515	+	2.58515i	−0.110131	+	0.110131i
$552$		0			0
$553$	−0.958648	−	3.57772i	−0.0407658	−	0.152140i
$554$	−31.5158	−	31.5158i	−1.33898	−	1.33898i
$555$		0			0
$556$	−38.0225	+	21.9523i	−1.61251	+	0.930986i
$557$	−3.59545	+	13.4184i	−0.152344	+	0.568555i	0.846974	+	0.531634i	$0.178422\pi$
$557$	−3.59545	+	13.4184i	−0.152344	+	0.568555i	−0.999318	+	0.0369214i	$0.988245\pi$
$558$		0			0
$559$	34.4877	+	10.8522i	1.45867	+	0.459000i
$560$			0.376535i			0.0159115i
$561$		0			0
$562$	25.6105	+	44.3588i	1.08032	+	1.87116i
$563$	−21.6847	+	37.5590i	−0.913901	+	1.58292i	−0.105399	+	0.994430i	$0.533612\pi$
$563$	−21.6847	+	37.5590i	−0.913901	+	1.58292i	−0.808502	+	0.588493i	$0.799721\pi$
$564$		0			0
$565$	27.4119	−	7.34499i	1.15323	−	0.309006i
$566$	27.9021	−	7.47636i	1.17281	−	0.314255i
$567$		0			0
$568$	17.0866	−	29.5948i	0.716937	−	1.24177i
$569$	15.5975	+	27.0157i	0.653882	+	1.13256i	0.982173	+	0.187981i	$0.0601942\pi$
$569$	15.5975	+	27.0157i	0.653882	+	1.13256i	−0.328290	+	0.944577i	$0.606472\pi$
$570$		0			0
$571$		−	35.4985i		−	1.48557i	−0.669532	−	0.742783i	$-0.733505\pi$
$571$		−	35.4985i		−	1.48557i	0.669532	−	0.742783i	$-0.266495\pi$
$572$	−4.01577	+	6.31147i	−0.167908	+	0.263896i
$573$		0			0
$574$	1.22428	−	4.56907i	0.0511004	−	0.190709i
$575$	3.13776	−	1.81158i	0.130853	−	0.0755483i
$576$		0			0
$577$	21.5580	+	21.5580i	0.897471	+	0.897471i	0.995212	−	0.0977407i	$-0.0311616\pi$
$577$	21.5580	+	21.5580i	0.897471	+	0.897471i	−0.0977407	+	0.995212i	$0.531162\pi$
$578$	−15.5423	−	58.0047i	−0.646475	−	2.41268i
$579$		0			0
$580$	24.0940	−	24.0940i	1.00045	−	1.00045i
$581$	1.19245	+	0.688462i	0.0494712	+	0.0285622i
$582$		0			0
$583$	2.50119	+	0.670191i	0.103589	+	0.0277565i
$584$	−6.46521			−0.267532
$585$		0			0
$586$	−37.7280			−1.55853
$587$	17.2095	+	4.61128i	0.710313	+	0.190328i	0.595846	−	0.803099i	$-0.296817\pi$
$587$	17.2095	+	4.61128i	0.710313	+	0.190328i	0.114468	+	0.993427i	$0.463484\pi$
$588$		0			0
$589$	1.17091	+	0.676025i	0.0482465	+	0.0278551i
$590$	22.0206	−	22.0206i	0.906573	−	0.906573i
$591$		0			0
$592$	1.61867	+	6.04097i	0.0665271	+	0.248282i
$593$	23.3200	+	23.3200i	0.957638	+	0.957638i	0.999138	−	0.0415003i	$-0.0132138\pi$
$593$	23.3200	+	23.3200i	0.957638	+	0.957638i	−0.0415003	+	0.999138i	$0.513214\pi$
$594$		0			0
$595$	3.21038	−	1.85352i	0.131613	−	0.0759867i
$596$	−6.74537	+	25.1741i	−0.276301	+	1.03117i
$597$		0			0
$598$	−24.2040	−	46.4305i	−0.989775	−	1.89868i
$599$		−	26.9090i		−	1.09947i	−0.835339	−	0.549735i	$-0.814729\pi$
$599$		−	26.9090i		−	1.09947i	0.835339	−	0.549735i	$-0.185271\pi$
$600$		0			0
$601$	−6.35877	−	11.0137i	−0.259379	−	0.449258i	0.706696	−	0.707517i	$-0.250185\pi$
$601$	−6.35877	−	11.0137i	−0.259379	−	0.449258i	−0.966076	+	0.258259i	$0.916851\pi$
$602$	−2.68887	+	4.65726i	−0.109590	+	0.189816i
$603$		0			0
$604$	−53.3167	+	14.2862i	−2.16943	+	0.581296i
$605$	24.0258	−	6.43769i	0.976788	−	0.261729i
$606$		0			0
$607$	12.1988	−	21.1290i	0.495134	−	0.857598i	−0.504850	−	0.863207i	$-0.668452\pi$
$607$	12.1988	−	21.1290i	0.495134	−	0.857598i	0.999984	+	0.00560918i	$0.00178547\pi$
$608$	2.48832	+	4.30989i	0.100915	+	0.174789i
$609$		0			0
$610$			47.7194i			1.93210i
$611$	9.43076	+	6.00047i	0.381528	+	0.242753i
$612$		0			0
$613$	0.330916	−	1.23499i	0.0133656	−	0.0498809i	−0.958921	−	0.283673i	$-0.908447\pi$
$613$	0.330916	−	1.23499i	0.0133656	−	0.0498809i	0.972287	+	0.233792i	$0.0751136\pi$
$614$	−25.8614	+	14.9311i	−1.04368	+	0.602569i
$615$		0			0
$616$	−0.275992	−	0.275992i	−0.0111200	−	0.0111200i
$617$	2.36326	+	8.81982i	0.0951414	+	0.355073i	0.997041	−	0.0768734i	$-0.0244937\pi$
$617$	2.36326	+	8.81982i	0.0951414	+	0.355073i	−0.901899	+	0.431946i	$0.857827\pi$
$618$		0			0
$619$	28.2007	−	28.2007i	1.13348	−	1.13348i	0.143888	−	0.989594i	$-0.454039\pi$
$619$	28.2007	−	28.2007i	1.13348	−	1.13348i	0.989594	−	0.143888i	$-0.0459606\pi$
$620$	−10.9131	−	6.30066i	−0.438279	−	0.253040i
$621$		0			0
$622$	−55.8513	−	14.9653i	−2.23943	−	0.600054i
$623$	2.01851			0.0808698
$624$		0			0
$625$	27.4956			1.09982
$626$	−23.6823	−	6.34566i	−0.946536	−	0.253624i
$627$		0			0
$628$	−7.92869	−	4.57763i	−0.316389	−	0.182667i
$629$	43.5381	−	43.5381i	1.73598	−	1.73598i
$630$		0			0
$631$	2.14296	+	7.99762i	0.0853097	+	0.318380i	0.995373	−	0.0960899i	$-0.0306336\pi$
$631$	2.14296	+	7.99762i	0.0853097	+	0.318380i	−0.910063	+	0.414470i	$0.863967\pi$
$632$	26.8123	+	26.8123i	1.06654	+	1.06654i
$633$		0			0
$634$	−15.2699	+	8.81609i	−0.606446	+	0.350131i
$635$	2.26040	−	8.43593i	0.0897013	−	0.334770i
$636$		0			0
$637$	−18.4479	+	16.9238i	−0.730931	+	0.670545i
$638$		−	7.11946i		−	0.281862i
$639$		0			0
$640$	−19.6244	−	33.9904i	−0.775722	−	1.34359i
$641$	−20.4651	+	35.4467i	−0.808324	+	1.40006i	0.105699	+	0.994398i	$0.466292\pi$
$641$	−20.4651	+	35.4467i	−0.808324	+	1.40006i	−0.914024	+	0.405661i	$0.867041\pi$
$642$		0			0
$643$	−28.2318	+	7.56469i	−1.11335	+	0.298322i	−0.768191	−	0.640221i	$-0.778843\pi$
$643$	−28.2318	+	7.56469i	−1.11335	+	0.298322i	−0.345163	+	0.938543i	$0.612176\pi$
$644$	4.56144	−	1.22224i	0.179746	−	0.0481628i
$645$		0			0
$646$	5.80395	−	10.0527i	0.228354	−	0.395520i
$647$	10.0324	+	17.3766i	0.394413	+	0.683144i	0.993026	−	0.117895i	$-0.0376145\pi$
$647$	10.0324	+	17.3766i	0.394413	+	0.683144i	−0.598613	+	0.801039i	$0.704281\pi$
$648$		0			0
$649$		−	3.94538i		−	0.154870i
$650$	−0.196739	+	4.56606i	−0.00771674	+	0.179096i
$651$		0			0
$652$	−13.7934	+	51.4779i	−0.540193	+	2.01603i
$653$	28.9476	−	16.7129i	1.13281	−	0.654027i	0.188168	−	0.982137i	$-0.439745\pi$
$653$	28.9476	−	16.7129i	1.13281	−	0.654027i	0.944639	+	0.328110i	$0.106412\pi$
$654$		0			0
$655$	−9.25280	−	9.25280i	−0.361537	−	0.361537i
$656$	−1.53181	−	5.71680i	−0.0598072	−	0.223203i
$657$		0			0
$658$	−1.17565	+	1.17565i	−0.0458315	+	0.0458315i
$659$	4.13242	+	2.38586i	0.160976	+	0.0929397i	0.578324	−	0.815807i	$-0.303707\pi$
$659$	4.13242	+	2.38586i	0.160976	+	0.0929397i	−0.417348	+	0.908747i	$0.637040\pi$
$660$		0			0
$661$	−4.13649	−	1.10837i	−0.160891	−	0.0431106i	0.177475	−	0.984125i	$-0.443207\pi$
$661$	−4.13649	−	1.10837i	−0.160891	−	0.0431106i	−0.338365	+	0.941015i	$0.609874\pi$
$662$	12.5117			0.486280
$663$		0			0
$664$	−14.0960			−0.547031
$665$	0.422537	+	0.113218i	0.0163853	+	0.00439042i
$666$		0			0
$667$	26.1674	+	15.1077i	1.01320	+	0.584974i
$668$	44.7023	−	44.7023i	1.72959	−	1.72959i
$669$		0			0
$670$	−17.3711	−	64.8298i	−0.671104	−	2.50460i
$671$	4.27489	+	4.27489i	0.165030	+	0.165030i
$672$		0			0
$673$	−38.3246	+	22.1267i	−1.47730	+	0.852922i	−0.999671	−	0.0256376i	$-0.991838\pi$
$673$	−38.3246	+	22.1267i	−1.47730	+	0.852922i	−0.477633	+	0.878560i	$0.658505\pi$
$674$	−5.47295	+	20.4253i	−0.210810	+	0.786755i
$675$		0			0
$676$	39.8997	+	3.44473i	1.53460	+	0.132489i
$677$		−	41.9253i		−	1.61132i	−0.592378	−	0.805660i	$-0.701811\pi$
$677$		−	41.9253i		−	1.61132i	0.592378	−	0.805660i	$-0.298189\pi$
$678$		0			0
$679$	−0.661388	−	1.14556i	−0.0253817	−	0.0439625i
$680$	−18.9750	+	32.8657i	−0.727659	+	1.26034i
$681$		0			0
$682$	−2.54321	+	0.681452i	−0.0973847	+	0.0260941i
$683$	−27.5892	+	7.39251i	−1.05567	+	0.282867i	−0.744594	−	0.667518i	$-0.767357\pi$
$683$	−27.5892	+	7.39251i	−1.05567	+	0.282867i	−0.311078	+	0.950384i	$0.600690\pi$
$684$		0			0
$685$	−1.43819	+	2.49102i	−0.0549504	+	0.0951768i
$686$	−3.73889	−	6.47595i	−0.142752	−	0.247253i
$687$		0			0
$688$			6.72860i			0.256525i
$689$	−3.00814	−	13.5322i	−0.114601	−	0.515535i
$690$		0			0
$691$	1.73441	−	6.47289i	0.0659799	−	0.246240i	−0.925057	−	0.379828i	$-0.875983\pi$
$691$	1.73441	−	6.47289i	0.0659799	−	0.246240i	0.991037	+	0.133588i	$0.0426498\pi$
$692$	−13.0667	+	7.54408i	−0.496722	+	0.286783i
$693$		0			0
$694$	−13.2095	−	13.2095i	−0.501427	−	0.501427i
$695$	8.69957	+	32.4672i	0.329993	+	1.23155i
$696$		0			0
$697$	−41.2017	+	41.2017i	−1.56062	+	1.56062i
$698$	−42.3851	−	24.4710i	−1.60430	−	0.926242i
$699$		0			0
$700$	−0.398147	−	0.106683i	−0.0150485	−	0.00403224i
$701$	−35.8548			−1.35422			−0.677108	−	0.735884i	$-0.736767\pi$
$701$	−35.8548			−1.35422			−0.677108	+	0.735884i	$0.736767\pi$
$702$		0			0
$703$	7.26572			0.274032
$704$	−8.48803	−	2.27436i	−0.319905	−	0.0857182i
$705$		0			0
$706$	−42.3610	−	24.4571i	−1.59428	−	0.920457i
$707$	−0.0943852	+	0.0943852i	−0.00354972	+	0.00354972i
$708$		0			0
$709$	−8.95978	−	33.4384i	−0.336492	−	1.25580i	−0.902243	−	0.431228i	$-0.858080\pi$
$709$	−8.95978	−	33.4384i	−0.336492	−	1.25580i	0.565751	−	0.824576i	$-0.308586\pi$
$710$	−52.7383	−	52.7383i	−1.97923	−	1.97923i
$711$		0			0
$712$	−17.8956	+	10.3320i	−0.670667	+	0.387210i
$713$	2.89213	−	10.7936i	0.108311	−	0.404223i
$714$		0			0
$715$	3.87158	+	4.22024i	0.144789	+	0.157828i
$716$		−	71.8891i		−	2.68662i
$717$		0			0
$718$	14.5202	+	25.1497i	0.541888	+	0.938578i
$719$	−20.7242	+	35.8953i	−0.772881	+	1.33867i	0.163097	+	0.986610i	$0.447852\pi$
$719$	−20.7242	+	35.8953i	−0.772881	+	1.33867i	−0.935978	+	0.352059i	$0.885482\pi$
$720$		0			0
$721$	0.334727	−	0.0896899i	0.0124659	−	0.00334023i
$722$	−40.0441	+	10.7298i	−1.49029	+	0.399321i
$723$		0			0
$724$	−31.4461	+	54.4663i	−1.16869	+	2.02422i
$725$	−1.31868	−	2.28402i	−0.0489746	−	0.0848265i
$726$		0			0
$727$			23.6750i			0.878056i	0.898473	+	0.439028i	$0.144677\pi$
$727$			23.6750i			0.878056i	−0.898473	+	0.439028i	$0.855323\pi$
$728$	−0.627195	+	1.99319i	−0.0232454	+	0.0738724i
$729$		0			0
$730$	−3.65203	+	13.6296i	−0.135168	+	0.504453i
$731$	57.3688	−	33.1219i	2.12186	−	1.22506i
$732$		0			0
$733$	19.9861	+	19.9861i	0.738202	+	0.738202i	0.972230	−	0.234028i	$-0.0751907\pi$
$733$	19.9861	+	19.9861i	0.738202	+	0.738202i	−0.234028	+	0.972230i	$0.575191\pi$
$734$	13.5115	+	50.4256i	0.498719	+	1.86124i
$735$		0			0
$736$	29.0837	−	29.0837i	1.07204	−	1.07204i
$737$	−7.36388	−	4.25154i	−0.271252	−	0.156607i
$738$		0			0
$739$	17.5067	+	4.69092i	0.643996	+	0.172558i	0.566013	−	0.824397i	$-0.308485\pi$
$739$	17.5067	+	4.69092i	0.643996	+	0.172558i	0.0779831	+	0.996955i	$0.475152\pi$
$740$	−67.7176			−2.48935
$741$		0			0
$742$	2.06193			0.0756959
$743$	20.2036	+	5.41355i	0.741199	+	0.198604i	0.609611	−	0.792701i	$-0.291326\pi$
$743$	20.2036	+	5.41355i	0.741199	+	0.198604i	0.131588	+	0.991304i	$0.457992\pi$
$744$		0			0
$745$	17.2795	+	9.97633i	0.633072	+	0.365504i
$746$	−44.0438	+	44.0438i	−1.61256	+	1.61256i
$747$		0			0
$748$	3.54746	+	13.2393i	0.129708	+	0.484077i
$749$	−1.12295	−	1.12295i	−0.0410319	−	0.0410319i
$750$		0			0
$751$	15.0196	−	8.67155i	0.548071	−	0.316429i	−0.200272	−	0.979740i	$-0.564183\pi$
$751$	15.0196	−	8.67155i	0.548071	−	0.316429i	0.748344	+	0.663311i	$0.230849\pi$
$752$	−0.538410	+	2.00937i	−0.0196338	+	0.0732743i
$753$		0			0
$754$	−33.7975	+	17.6185i	−1.23083	+	0.641628i
$755$			42.2582i			1.53793i
$756$		0			0
$757$	−4.09818	−	7.09826i	−0.148951	−	0.257990i	0.781889	−	0.623418i	$-0.214256\pi$
$757$	−4.09818	−	7.09826i	−0.148951	−	0.257990i	−0.930840	+	0.365427i	$0.880923\pi$
$758$	19.7448	−	34.1991i	0.717165	−	1.24217i
$759$		0			0
$760$	−4.32564	+	1.15905i	−0.156908	+	0.0420432i
$761$	−25.5197	+	6.83798i	−0.925088	+	0.247876i	−0.689759	−	0.724039i	$-0.742283\pi$
$761$	−25.5197	+	6.83798i	−0.925088	+	0.247876i	−0.235329	+	0.971916i	$0.575617\pi$
$762$		0			0
$763$	−1.67416	+	2.89974i	−0.0606088	+	0.104978i
$764$	7.59335	+	13.1521i	0.274718	+	0.475825i
$765$		0			0
$766$		−	61.9175i		−	2.23717i
$767$	−18.7295	+	9.76361i	−0.676284	+	0.352543i
$768$		0			0
$769$	−4.87979	+	18.2116i	−0.175970	+	0.656728i	0.820415	+	0.571769i	$0.193743\pi$
$769$	−4.87979	+	18.2116i	−0.175970	+	0.656728i	−0.996384	+	0.0849589i	$0.972924\pi$
$770$	−0.737730	+	0.425929i	−0.0265860	+	0.0153494i
$771$		0			0
$772$	−16.4961	−	16.4961i	−0.593708	−	0.593708i
$773$	−4.88766	−	18.2410i	−0.175797	−	0.656083i	−0.996415	−	0.0846053i	$-0.973037\pi$
$773$	−4.88766	−	18.2410i	−0.175797	−	0.656083i	0.820618	−	0.571478i	$-0.193630\pi$
$774$		0			0
$775$	−0.689679	+	0.689679i	−0.0247740	+	0.0247740i
$776$	11.7274	+	6.77084i	0.420990	+	0.243059i
$777$		0			0
$778$	55.4586	+	14.8601i	1.98829	+	0.532760i
$779$	−6.87581			−0.246352
$780$		0			0
$781$	−9.44900			−0.338112
$782$	−92.6673	−	24.8301i	−3.31378	−	0.887924i
$783$		0			0
$784$	−4.03489	−	2.32955i	−0.144103	−	0.0831981i
$785$	−4.95618	+	4.95618i	−0.176894	+	0.176894i
$786$		0			0
$787$	7.73262	+	28.8585i	0.275638	+	1.02870i	0.955413	+	0.295274i	$0.0954110\pi$
$787$	7.73262	+	28.8585i	0.275638	+	1.02870i	−0.679774	+	0.733421i	$0.737922\pi$
$788$	15.6862	+	15.6862i	0.558797	+	0.558797i
$789$		0			0
$790$	71.6696	−	41.3785i	2.54989	−	1.47218i
$791$	0.740982	−	2.76538i	0.0263463	−	0.0983257i
$792$		0			0
$793$	9.71473	−	30.8728i	0.344980	−	1.09633i
$794$		−	61.5519i		−	2.18440i
$795$		0			0
$796$	−29.6753	−	51.3991i	−1.05181	−	1.82179i
$797$	3.01276	−	5.21825i	0.106717	−	0.184840i	−0.807721	−	0.589565i	$-0.799299\pi$
$797$	3.01276	−	5.21825i	0.106717	−	0.184840i	0.914439	+	0.404725i	$0.132633\pi$
$798$		0			0
$799$	19.7825	−	5.30071i	0.699855	−	0.187526i
$800$	−3.46776	+	0.929184i	−0.122604	+	0.0328516i
$801$		0			0
$802$	−1.28178	+	2.22011i	−0.0452613	+	0.0783948i
$803$	0.893826	+	1.54815i	0.0315424	+	0.0546331i
$804$		0			0
$805$		−	3.61534i		−	0.127424i
$806$	9.52867	+	10.3868i	0.335633	+	0.365859i
$807$		0			0
$808$	0.353673	−	1.31992i	0.0124422	−	0.0464348i
$809$	−33.4265	+	19.2988i	−1.17521	+	0.678509i	−0.954902	−	0.296921i	$-0.904040\pi$
$809$	−33.4265	+	19.2988i	−1.17521	+	0.678509i	−0.220310	+	0.975430i	$0.570707\pi$
$810$		0			0
$811$	28.3827	+	28.3827i	0.996651	+	0.996651i	0.999994	−	0.00334338i	$-0.00106423\pi$
$811$	28.3827	+	28.3827i	0.996651	+	0.996651i	−0.00334338	+	0.999994i	$0.501064\pi$
$812$	−0.889685	−	3.32035i	−0.0312218	−	0.116521i
$813$		0			0
$814$	−10.0048	+	10.0048i	−0.350669	+	0.350669i
$815$	35.3345	+	20.4004i	1.23771	+	0.714593i
$816$		0			0
$817$	7.55064	+	2.02319i	0.264163	+	0.0707824i
$818$	21.5052			0.751912
$819$		0			0
$820$	64.0837			2.23790
$821$	10.6825	+	2.86237i	0.372822	+	0.0998973i	0.440364	−	0.897819i	$-0.354849\pi$
$821$	10.6825	+	2.86237i	0.372822	+	0.0998973i	−0.0675428	+	0.997716i	$0.521516\pi$
$822$		0			0
$823$	−28.8982	−	16.6844i	−1.00733	−	0.581582i	−0.0969209	−	0.995292i	$-0.530899\pi$
$823$	−28.8982	−	16.6844i	−1.00733	−	0.581582i	−0.910409	+	0.413710i	$0.864233\pi$
$824$	−2.50853	+	2.50853i	−0.0873886	+	0.0873886i
$825$		0			0
$826$	−0.813124	−	3.03462i	−0.0282922	−	0.105588i
$827$	3.25128	+	3.25128i	0.113058	+	0.113058i	0.761373	−	0.648315i	$-0.224526\pi$
$827$	3.25128	+	3.25128i	0.113058	+	0.113058i	−0.648315	+	0.761373i	$0.724526\pi$
$828$		0			0
$829$	27.4013	−	15.8202i	0.951687	−	0.549457i	0.0580822	−	0.998312i	$-0.481501\pi$
$829$	27.4013	−	15.8202i	0.951687	−	0.549457i	0.893604	+	0.448855i	$0.148168\pi$
$830$	−7.96247	+	29.7163i	−0.276381	+	1.03147i
$831$		0			0
$832$	10.2084	+	45.9228i	0.353914	+	1.59209i
$833$			45.8693i			1.58928i
$834$		0			0
$835$	−24.1995	−	41.9148i	−0.837458	−	1.45052i
$836$	−0.808698	+	1.40071i	−0.0279694	+	0.0484444i
$837$		0			0
$838$	−75.5462	+	20.2425i	−2.60970	+	0.699267i
$839$	−16.9740	+	4.54816i	−0.586006	+	0.157020i	−0.539627	−	0.841904i	$-0.681435\pi$
$839$	−16.9740	+	4.54816i	−0.586006	+	0.157020i	−0.0463789	+	0.998924i	$0.514768\pi$
$840$		0			0
$841$	−3.50283	+	6.06707i	−0.120787	+	0.209209i
$842$	2.47817	+	4.29231i	0.0854033	+	0.147923i
$843$		0			0
$844$		−	9.14345i		−	0.314731i
$845$	10.4534	−	28.8230i	0.359606	−	0.991542i
$846$		0			0
$847$	0.649452	−	2.42379i	0.0223154	−	0.0832823i
$848$	2.23424	−	1.28994i	0.0767241	−	0.0442967i
$849$		0			0
$850$	5.92119	+	5.92119i	0.203095	+	0.203095i
$851$	−15.5419	−	58.0031i	−0.532769	−	1.98832i
$852$		0			0
$853$	13.7462	−	13.7462i	0.470661	−	0.470661i	−0.431467	−	0.902129i	$-0.642004\pi$
$853$	13.7462	−	13.7462i	0.470661	−	0.470661i	0.902129	+	0.431467i	$0.142004\pi$
$854$	4.16910	+	2.40703i	0.142664	+	0.0823669i
$855$		0			0
$856$	15.7039	+	4.20784i	0.536748	+	0.143821i
$857$	31.3861			1.07213			0.536064	−	0.844177i	$-0.319911\pi$
$857$	31.3861			1.07213			0.536064	+	0.844177i	$0.319911\pi$
$858$		0			0
$859$	−9.42683			−0.321639			−0.160820	−	0.986984i	$-0.551414\pi$
$859$	−9.42683			−0.321639			−0.160820	+	0.986984i	$0.551414\pi$
$860$	−70.3731	−	18.8564i	−2.39970	−	0.642998i
$861$		0			0
$862$	29.4911	+	17.0267i	1.00447	+	0.579931i
$863$	−22.1901	+	22.1901i	−0.755361	+	0.755361i	−0.975474	−	0.220113i	$-0.929357\pi$
$863$	−22.1901	+	22.1901i	−0.755361	+	0.755361i	0.220113	+	0.975474i	$0.429357\pi$
$864$		0			0
$865$	2.98967	+	11.1576i	0.101652	+	0.379370i
$866$	−23.4647	−	23.4647i	−0.797364	−	0.797364i
$867$		0			0
$868$	−1.10094	+	0.635627i	−0.0373683	+	0.0215746i
$869$	2.71360	−	10.1273i	0.0920525	−	0.343545i
$870$		0			0
$871$	−1.95957	+	45.4791i	−0.0663975	+	1.54100i
$872$		−	34.2779i		−	1.16080i
$873$		0			0
$874$	−5.66040	−	9.80410i	−0.191466	−	0.331629i
$875$	1.24508	−	2.15654i	0.0420914	−	0.0729045i
$876$		0			0
$877$	44.9923	−	12.0556i	1.51928	−	0.407090i	0.599776	−	0.800168i	$-0.295256\pi$
$877$	44.9923	−	12.0556i	1.51928	−	0.407090i	0.919505	+	0.393077i	$0.128590\pi$
$878$	−6.57951	+	1.76297i	−0.222048	+	0.0594975i
$879$		0			0
$880$	−0.532920	+	0.923044i	−0.0179647	+	0.0311158i
$881$	−15.0620	−	26.0881i	−0.507451	−	0.878930i	−0.999963	−	0.00862470i	$-0.997255\pi$
$881$	−15.0620	−	26.0881i	−0.507451	−	0.878930i	0.492512	−	0.870306i	$-0.336079\pi$
$882$		0			0
$883$			10.8871i			0.366381i	0.983077	+	0.183191i	$0.0586425\pi$
$883$			10.8871i			0.366381i	−0.983077	+	0.183191i	$0.941357\pi$
$884$	54.0709	−	49.6038i	1.81860	−	1.66836i
$885$		0			0
$886$	13.5532	−	50.5814i	0.455330	−	1.69932i
$887$	38.2317	−	22.0731i	1.28369	−	0.741141i	0.306173	−	0.951976i	$-0.400952\pi$
$887$	38.2317	−	22.0731i	1.28369	−	0.741141i	0.977522	+	0.210835i	$0.0676182\pi$
$888$		0			0
$889$	−0.623004	−	0.623004i	−0.0208949	−	0.0208949i
$890$	11.6726	+	43.5628i	0.391267	+	1.46023i
$891$		0			0
$892$	−3.25618	+	3.25618i	−0.109025	+	0.109025i
$893$	2.09297	+	1.20838i	0.0700386	+	0.0404368i
$894$		0			0
$895$	−53.1616	−	14.2446i	−1.77699	−	0.476144i
$896$	−3.95952			−0.132278
$897$		0			0
$898$	69.5222			2.31998
$899$	−7.85682	−	2.10523i	−0.262040	−	0.0702133i
$900$		0			0
$901$	−21.9964	−	12.6996i	−0.732805	−	0.423085i
$902$	9.46794	−	9.46794i	0.315248	−	0.315248i
$903$		0			0
$904$	7.58567	+	28.3101i	0.252296	+	0.941580i
$905$	34.0465	+	34.0465i	1.13175	+	1.13175i
$906$		0			0
$907$	7.47401	−	4.31512i	0.248170	−	0.143281i	−0.370756	−	0.928730i	$-0.620901\pi$
$907$	7.47401	−	4.31512i	0.248170	−	0.143281i	0.618926	+	0.785449i	$0.287568\pi$
$908$	−7.15037	+	26.6856i	−0.237293	+	0.885591i
$909$		0			0
$910$	3.84763	+	2.44811i	0.127548	+	0.0811542i
$911$			24.2976i			0.805014i	0.915417	+	0.402507i	$0.131861\pi$
$911$			24.2976i			0.805014i	−0.915417	+	0.402507i	$0.868139\pi$
$912$		0			0
$913$	1.94880	+	3.37541i	0.0644957	+	0.111710i
$914$	36.9198	−	63.9470i	1.22120	−	2.11518i
$915$		0			0
$916$	85.0248	−	22.7823i	2.80930	−	0.752749i
$917$	−1.27511	+	0.341665i	−0.0421079	+	0.0112828i
$918$		0			0
$919$	−0.373771	+	0.647390i	−0.0123296	+	0.0213554i	−0.872124	−	0.489284i	$-0.837258\pi$
$919$	−0.373771	+	0.647390i	−0.0123296	+	0.0213554i	0.859795	+	0.510640i	$0.170591\pi$
$920$	18.5057	+	32.0528i	0.610115	+	1.05675i
$921$		0			0
$922$			22.1173i			0.728396i
$923$	23.3834	+	44.8564i	0.769674	+	1.47647i
$924$		0			0
$925$	−1.35658	+	5.06281i	−0.0446040	+	0.166464i
$926$	16.2114	−	9.35966i	0.532740	−	0.307577i
$927$		0			0
$928$	−21.1705	−	21.1705i	−0.694956	−	0.694956i
$929$	14.4585	+	53.9597i	0.474366	+	1.77036i	0.623796	+	0.781587i	$0.285590\pi$
$929$	14.4585	+	53.9597i	0.474366	+	1.77036i	−0.149430	+	0.988772i	$0.547744\pi$
$930$		0			0
$931$	−3.82738	+	3.82738i	−0.125437	+	0.125437i
$932$	−11.0066	−	6.35464i	−0.360532	−	0.208153i
$933$		0			0
$934$	5.06388	+	1.35686i	0.165695	+	0.0443979i
$935$	10.4933			0.343168
$936$		0			0
$937$	−10.2614			−0.335224			−0.167612	−	0.985853i	$-0.553606\pi$
$937$	−10.2614			−0.335224			−0.167612	+	0.985853i	$0.553606\pi$
$938$	−6.54021	−	1.75244i	−0.213545	−	0.0572193i
$939$		0			0
$940$	−19.5068	−	11.2623i	−0.636242	−	0.367334i
$941$	41.7409	−	41.7409i	1.36071	−	1.36071i	0.487707	−	0.873007i	$-0.337833\pi$
$941$	41.7409	−	41.7409i	1.36071	−	1.36071i	0.873007	−	0.487707i	$-0.162167\pi$
$942$		0			0
$943$	14.7079	+	54.8905i	0.478954	+	1.78748i
$944$	−2.77952	−	2.77952i	−0.0904658	−	0.0904658i
$945$		0			0
$946$	−13.1831	+	7.61125i	−0.428619	+	0.247463i
$947$	3.35951	−	12.5379i	0.109169	−	0.407426i	−0.889615	−	0.456710i	$-0.849028\pi$
$947$	3.35951	−	12.5379i	0.109169	−	0.407426i	0.998785	+	0.0492848i	$0.0156942\pi$
$948$		0			0
$949$	5.13745	−	8.07438i	0.166769	−	0.262105i
$950$			0.988139i			0.0320595i
$951$		0			0
$952$	1.91425	+	3.31558i	0.0620413	+	0.107459i
$953$	−9.48459	+	16.4278i	−0.307236	+	0.532148i	−0.977757	−	0.209743i	$-0.932737\pi$
$953$	−9.48459	+	16.4278i	−0.307236	+	0.532148i	0.670521	+	0.741891i	$0.266071\pi$
$954$		0			0
$955$	11.2305	−	3.00920i	0.363410	−	0.0973754i
$956$	17.2579	−	4.62424i	0.558160	−	0.149559i
$957$		0			0
$958$	−9.67160	+	16.7517i	−0.312475	+	0.541223i
$959$	0.145088	+	0.251300i	0.00468515	+	0.00811491i
$960$		0			0
$961$		−	27.9919i		−	0.902964i
$962$	72.2539	+	22.7361i	2.32956	+	0.733041i
$963$		0			0
$964$	−5.82589	+	21.7425i	−0.187639	+	0.700279i
$965$	−15.4674	+	8.93013i	−0.497914	+	0.287471i
$966$		0			0
$967$	−37.7344	−	37.7344i	−1.21346	−	1.21346i	−0.969882	−	0.243575i	$-0.921680\pi$
$967$	−37.7344	−	37.7344i	−1.21346	−	1.21346i	−0.243575	−	0.969882i	$-0.578320\pi$
$968$	6.64865	+	24.8131i	0.213696	+	0.797523i
$969$		0			0
$970$	20.8984	−	20.8984i	0.671007	−	0.671007i
$971$	32.9176	+	19.0050i	1.05637	+	0.609898i	0.924427	−	0.381359i	$-0.124544\pi$
$971$	32.9176	+	19.0050i	1.05637	+	0.609898i	0.131947	+	0.991257i	$0.457877\pi$
$972$		0			0
$973$	3.27538	+	0.877636i	0.105004	+	0.0281357i
$974$	22.0125			0.705326
$975$		0			0
$976$	6.02333			0.192802
$977$	13.1888	+	3.53392i	0.421946	+	0.113060i	0.463543	−	0.886074i	$-0.346578\pi$
$977$	13.1888	+	3.53392i	0.421946	+	0.113060i	−0.0415973	+	0.999134i	$0.513245\pi$
$978$		0			0
$979$	4.94820	+	2.85685i	0.158145	+	0.0913052i
$980$	35.6718	−	35.6718i	1.13949	−	1.13949i
$981$		0			0
$982$	13.2532	+	49.4616i	0.422927	+	1.57838i
$983$	−23.6306	−	23.6306i	−0.753701	−	0.753701i	0.221467	−	0.975168i	$-0.428915\pi$
$983$	−23.6306	−	23.6306i	−0.753701	−	0.753701i	−0.975168	+	0.221467i	$0.928915\pi$
$984$		0			0
$985$	14.7080	−	8.49167i	0.468636	−	0.270567i
$986$	−18.0743	+	67.4541i	−0.575602	+	2.14818i
$987$		0			0
$988$	8.65072	+	0.372735i	0.275216	+	0.0118583i
$989$		−	64.6054i		−	2.05433i
$990$		0			0
$991$	−18.7056	−	32.3991i	−0.594204	−	1.02919i	−0.993659	−	0.112439i	$-0.964134\pi$
$991$	−18.7056	−	32.3991i	−0.594204	−	1.02919i	0.399454	−	0.916753i	$-0.369200\pi$
$992$	−5.53616	+	9.58891i	−0.175773	+	0.304448i
$993$		0			0
$994$	−7.26777	+	1.94739i	−0.230520	+	0.0617676i
$995$	−43.8894	+	11.7601i	−1.39139	+	0.372821i
$996$		0			0
$997$	2.58083	−	4.47014i	0.0817359	−	0.141571i	−0.822260	−	0.569112i	$-0.807287\pi$
$997$	2.58083	−	4.47014i	0.0817359	−	0.141571i	0.903996	+	0.427542i	$0.140620\pi$
$998$	10.6114	+	18.3795i	0.335899	+	0.581794i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.bd.e.323.5	yes	20
3.2	odd	2		351.2.bd.d.323.1	yes	20
13.6	odd	12		351.2.bd.d.188.1	✓	20
39.32	even	12	inner	351.2.bd.e.188.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.bd.d.188.1	✓	20	13.6	odd	12
351.2.bd.d.323.1	yes	20	3.2	odd	2
351.2.bd.e.188.5	yes	20	39.32	even	12	inner
351.2.bd.e.323.5	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.17722 + 0.583384i) q^{2} +(2.66790 + 1.54031i) q^{4} +(1.66769 - 1.66769i) q^{5} +(-0.0615804 - 0.229821i) q^{7} +(1.72233 + 1.72233i) q^{8} +O(q^{10})\)	\(q+(2.17722 + 0.583384i) q^{2} +(2.66790 + 1.54031i) q^{4} +(1.66769 - 1.66769i) q^{5} +(-0.0615804 - 0.229821i) q^{7} +(1.72233 + 1.72233i) q^{8} +(4.60382 - 2.65802i) q^{10} +(0.174313 - 0.650544i) q^{11} +(-3.51964 + 0.782400i) q^{13} -0.536296i q^{14} +(-0.335505 - 0.581113i) q^{16} +(-3.30309 + 5.72112i) q^{17} +(-0.752989 + 0.201763i) q^{19} +(7.01797 - 1.88046i) q^{20} +(0.759034 - 1.31469i) q^{22} +(3.22139 + 5.57962i) q^{23} -0.562360i q^{25} +(-8.11946 - 0.349845i) q^{26} +(0.189706 - 0.707992i) q^{28} +(4.06150 - 2.34491i) q^{29} +(-1.22640 - 1.22640i) q^{31} +(-1.65229 - 6.16644i) q^{32} +(-10.5292 + 10.5292i) q^{34} +(-0.485967 - 0.280573i) q^{35} +(-9.00279 - 2.41229i) q^{37} -1.75713 q^{38} +5.74463 q^{40} +(8.51967 + 2.28284i) q^{41} +(-8.68411 - 5.01378i) q^{43} +(1.46709 - 1.46709i) q^{44} +(3.75862 + 14.0274i) q^{46} +(-2.19216 - 2.19216i) q^{47} +(6.01315 - 3.47170i) q^{49} +(0.328072 - 1.22438i) q^{50} +(-10.5952 - 3.33398i) q^{52} +3.84476i q^{53} +(-0.794205 - 1.37560i) q^{55} +(0.289767 - 0.501891i) q^{56} +(10.2108 - 2.73596i) q^{58} +(5.65848 - 1.51618i) q^{59} +(-4.48825 + 7.77387i) q^{61} +(-1.95468 - 3.38561i) q^{62} -13.0476i q^{64} +(-4.56486 + 7.17445i) q^{65} +(3.26768 - 12.1951i) q^{67} +(-17.6246 + 10.1756i) q^{68} +(-0.894374 - 0.894374i) q^{70} +(-3.63119 - 13.5518i) q^{71} +(-1.87687 + 1.87687i) q^{73} +(-18.1938 - 10.5042i) q^{74} +(-2.31967 - 0.621555i) q^{76} -0.160243 q^{77} +15.5674 q^{79} +(-1.52863 - 0.409596i) q^{80} +(17.2174 + 9.94049i) q^{82} +(-4.09212 + 4.09212i) q^{83} +(4.03252 + 15.0496i) q^{85} +(-15.9823 - 15.9823i) q^{86} +(1.42068 - 0.820229i) q^{88} +(-2.19574 + 8.19460i) q^{89} +(0.396553 + 0.760707i) q^{91} +19.8478i q^{92} +(-3.49394 - 6.05169i) q^{94} +(-0.919273 + 1.59223i) q^{95} +(5.37012 - 1.43892i) q^{97} +(15.1173 - 4.05066i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{5}+O(q^{10}) \) 20 * q + 6 * q^5	\( 20 q + 6 q^{5} - 12 q^{10} - 8 q^{13} + 24 q^{16} - 12 q^{17} - 12 q^{19} + 36 q^{20} + 8 q^{22} - 42 q^{26} + 2 q^{28} - 6 q^{29} - 22 q^{31} - 36 q^{32} - 6 q^{34} - 36 q^{35} + 8 q^{37} + 72 q^{38} - 36 q^{40} + 30 q^{41} - 30 q^{43} + 36 q^{44} - 48 q^{46} + 6 q^{47} + 30 q^{49} + 54 q^{50} + 4 q^{52} - 28 q^{55} - 60 q^{56} + 44 q^{58} + 30 q^{59} - 16 q^{61} - 30 q^{62} - 78 q^{65} + 18 q^{67} + 6 q^{68} + 38 q^{70} - 60 q^{71} - 72 q^{74} - 8 q^{76} - 12 q^{77} - 16 q^{79} + 126 q^{80} + 78 q^{82} + 12 q^{83} + 12 q^{85} + 18 q^{86} + 84 q^{89} + 30 q^{91} - 22 q^{94} - 66 q^{95} + 26 q^{97} + 42 q^{98}+O(q^{100}) \) 20 * q + 6 * q^5 - 12 * q^10 - 8 * q^13 + 24 * q^16 - 12 * q^17 - 12 * q^19 + 36 * q^20 + 8 * q^22 - 42 * q^26 + 2 * q^28 - 6 * q^29 - 22 * q^31 - 36 * q^32 - 6 * q^34 - 36 * q^35 + 8 * q^37 + 72 * q^38 - 36 * q^40 + 30 * q^41 - 30 * q^43 + 36 * q^44 - 48 * q^46 + 6 * q^47 + 30 * q^49 + 54 * q^50 + 4 * q^52 - 28 * q^55 - 60 * q^56 + 44 * q^58 + 30 * q^59 - 16 * q^61 - 30 * q^62 - 78 * q^65 + 18 * q^67 + 6 * q^68 + 38 * q^70 - 60 * q^71 - 72 * q^74 - 8 * q^76 - 12 * q^77 - 16 * q^79 + 126 * q^80 + 78 * q^82 + 12 * q^83 + 12 * q^85 + 18 * q^86 + 84 * q^89 + 30 * q^91 - 22 * q^94 - 66 * q^95 + 26 * q^97 + 42 * q^98

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