LMFDB - Embedded newform 351.2.bd.e.323.3

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			323.3
Root			$0.107781 - 0.107781i$ of defining polynomial
Character	$\chi$	$=$	351.323
Dual form			351.2.bd.e.188.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.147232 + 0.0394506i) q^{2} +(-1.71193 - 0.988383i) q^{4} +(0.671392 - 0.671392i) q^{5} +(0.383498 + 1.43124i) q^{7} +(-0.428620 - 0.428620i) q^{8} +O(q^{10})$	\(q+(0.147232 + 0.0394506i) q^{2} +(-1.71193 - 0.988383i) q^{4} +(0.671392 - 0.671392i) q^{5} +(0.383498 + 1.43124i) q^{7} +(-0.428620 - 0.428620i) q^{8} +(0.125337 - 0.0723632i) q^{10} +(1.27929 - 4.77439i) q^{11} +(-0.563387 - 3.56126i) q^{13} +0.225852i q^{14} +(1.93057 + 3.34384i) q^{16} +(3.08999 - 5.35201i) q^{17} +(-1.68338 + 0.451059i) q^{19} +(-1.81297 + 0.485783i) q^{20} +(0.376704 - 0.652471i) q^{22} +(-3.74947 - 6.49427i) q^{23} +4.09847i q^{25} +(0.0575456 - 0.546556i) q^{26} +(0.758087 - 2.82922i) q^{28} +(-1.18018 + 0.681377i) q^{29} +(-2.06505 - 2.06505i) q^{31} +(0.466095 + 1.73949i) q^{32} +(0.666083 - 0.666083i) q^{34} +(1.21840 + 0.703442i) q^{35} +(-1.85655 - 0.497461i) q^{37} -0.265641 q^{38} -0.575543 q^{40} +(9.12748 + 2.44570i) q^{41} +(6.31673 + 3.64696i) q^{43} +(-6.90898 + 6.90898i) q^{44} +(-0.295837 - 1.10408i) q^{46} +(5.42720 + 5.42720i) q^{47} +(4.16081 - 2.40225i) q^{49} +(-0.161687 + 0.603423i) q^{50} +(-2.55541 + 6.65348i) q^{52} +8.05770i q^{53} +(-2.34658 - 4.06439i) q^{55} +(0.449081 - 0.777831i) q^{56} +(-0.200640 + 0.0537614i) q^{58} +(-4.49411 + 1.20419i) q^{59} +(-1.54373 + 2.67382i) q^{61} +(-0.222573 - 0.385507i) q^{62} -7.44778i q^{64} +(-2.76926 - 2.01275i) q^{65} +(-0.516129 + 1.92622i) q^{67} +(-10.5797 + 6.10818i) q^{68} +(0.151635 + 0.151635i) q^{70} +(-0.385189 - 1.43754i) q^{71} +(-7.05012 + 7.05012i) q^{73} +(-0.253718 - 0.146484i) q^{74} +(3.32764 + 0.891639i) q^{76} +7.32388 q^{77} -4.39155 q^{79} +(3.54120 + 0.948861i) q^{80} +(1.24737 + 0.720168i) q^{82} +(-6.90303 + 6.90303i) q^{83} +(-1.51871 - 5.66789i) q^{85} +(0.786147 + 0.786147i) q^{86} +(-2.59473 + 1.49807i) q^{88} +(2.33371 - 8.70954i) q^{89} +(4.88095 - 2.17208i) q^{91} +14.8236i q^{92} +(0.584948 + 1.01316i) q^{94} +(-0.827367 + 1.43304i) q^{95} +(12.5248 - 3.35601i) q^{97} +(0.707373 - 0.189540i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.147232	+	0.0394506i	0.104108	+	0.0278958i	0.310497	−	0.950574i	$-0.399504\pi$
$2$	0.147232	+	0.0394506i	0.104108	+	0.0278958i	−0.206389	+	0.978470i	$0.566171\pi$
$3$		0			0
$3$		0			0
$4$	−1.71193	−	0.988383i	−0.855965	−	0.494192i
$5$	0.671392	−	0.671392i	0.300255	−	0.300255i	−0.540858	−	0.841114i	$-0.681900\pi$
$5$	0.671392	−	0.671392i	0.300255	−	0.300255i	0.841114	+	0.540858i	$0.181900\pi$
$6$		0			0
$7$	0.383498	+	1.43124i	0.144949	+	0.540956i	0.999758	+	0.0220132i	$0.00700760\pi$
$7$	0.383498	+	1.43124i	0.144949	+	0.540956i	−0.854809	+	0.518943i	$0.826326\pi$
$8$	−0.428620	−	0.428620i	−0.151540	−	0.151540i
$9$		0			0
$10$	0.125337	−	0.0723632i	0.0396350	−	0.0228833i
$11$	1.27929	−	4.77439i	0.385721	−	1.43953i	−0.451305	−	0.892370i	$-0.649041\pi$
$11$	1.27929	−	4.77439i	0.385721	−	1.43953i	0.837027	−	0.547162i	$-0.184292\pi$
$12$		0			0
$13$	−0.563387	−	3.56126i	−0.156255	−	0.987717i
$13$	−0.563387	−	3.56126i	−0.156255	−	0.987717i
$14$			0.225852i			0.0603615i
$15$		0			0
$16$	1.93057	+	3.34384i	0.482642	+	0.835961i
$17$	3.08999	−	5.35201i	0.749432	−	1.29805i	−0.198664	−	0.980068i	$-0.563660\pi$
$17$	3.08999	−	5.35201i	0.749432	−	1.29805i	0.948095	−	0.317986i	$-0.103006\pi$
$18$		0			0
$19$	−1.68338	+	0.451059i	−0.386193	+	0.103480i	−0.446691	−	0.894688i	$-0.647398\pi$
$19$	−1.68338	+	0.451059i	−0.386193	+	0.103480i	0.0604982	+	0.998168i	$0.480731\pi$
$20$	−1.81297	+	0.485783i	−0.405392	+	0.108624i
$21$		0			0
$22$	0.376704	−	0.652471i	0.0803137	−	0.139107i
$23$	−3.74947	−	6.49427i	−0.781818	−	1.35415i	−0.930882	−	0.365321i	$-0.880959\pi$
$23$	−3.74947	−	6.49427i	−0.781818	−	1.35415i	0.149064	−	0.988828i	$-0.452374\pi$
$24$		0			0
$25$			4.09847i			0.819693i
$26$	0.0575456	−	0.546556i	0.0112856	−	0.107188i
$27$		0			0
$28$	0.758087	−	2.82922i	0.143265	−	0.534672i
$29$	−1.18018	+	0.681377i	−0.219154	+	0.126529i	−0.605558	−	0.795801i	$-0.707050\pi$
$29$	−1.18018	+	0.681377i	−0.219154	+	0.126529i	0.386405	+	0.922329i	$0.373717\pi$
$30$		0			0
$31$	−2.06505	−	2.06505i	−0.370893	−	0.370893i	0.496909	−	0.867803i	$-0.334468\pi$
$31$	−2.06505	−	2.06505i	−0.370893	−	0.370893i	−0.867803	+	0.496909i	$0.834468\pi$
$32$	0.466095	+	1.73949i	0.0823948	+	0.307502i
$33$		0			0
$34$	0.666083	−	0.666083i	0.114232	−	0.114232i
$35$	1.21840	+	0.703442i	0.205947	+	0.118903i
$36$		0			0
$37$	−1.85655	−	0.497461i	−0.305215	−	0.0817822i	0.102961	−	0.994685i	$-0.467168\pi$
$37$	−1.85655	−	0.497461i	−0.305215	−	0.0817822i	−0.408176	+	0.912903i	$0.633835\pi$
$38$	−0.265641			−0.0430926
$39$		0			0
$40$	−0.575543			−0.0910014
$41$	9.12748	+	2.44570i	1.42547	+	0.381954i	0.887422	−	0.460959i	$-0.152494\pi$
$41$	9.12748	+	2.44570i	1.42547	+	0.381954i	0.538050	+	0.842913i	$0.319161\pi$
$42$		0			0
$43$	6.31673	+	3.64696i	0.963292	+	0.556157i	0.897185	−	0.441656i	$-0.145609\pi$
$43$	6.31673	+	3.64696i	0.963292	+	0.556157i	0.0661074	+	0.997813i	$0.478942\pi$
$44$	−6.90898	+	6.90898i	−1.04157	+	1.04157i
$45$		0			0
$46$	−0.295837	−	1.10408i	−0.0436188	−	0.162788i
$47$	5.42720	+	5.42720i	0.791638	+	0.791638i	0.981760	−	0.190123i	$-0.0608885\pi$
$47$	5.42720	+	5.42720i	0.791638	+	0.791638i	−0.190123	+	0.981760i	$0.560889\pi$
$48$		0			0
$49$	4.16081	−	2.40225i	0.594402	−	0.343178i
$50$	−0.161687	+	0.603423i	−0.0228660	+	0.0853370i
$51$		0			0
$52$	−2.55541	+	6.65348i	−0.354372	+	0.922671i
$53$			8.05770i			1.10681i	0.832912	+	0.553405i	$0.186672\pi$
$53$			8.05770i			1.10681i	−0.832912	+	0.553405i	$0.813328\pi$
$54$		0			0
$55$	−2.34658	−	4.06439i	−0.316412	−	0.548042i
$56$	0.449081	−	0.777831i	0.0600109	−	0.103942i
$57$		0			0
$58$	−0.200640	+	0.0537614i	−0.0263454	+	0.00705922i
$59$	−4.49411	+	1.20419i	−0.585083	+	0.156773i	−0.539205	−	0.842175i	$-0.681275\pi$
$59$	−4.49411	+	1.20419i	−0.585083	+	0.156773i	−0.0458780	+	0.998947i	$0.514609\pi$
$60$		0			0
$61$	−1.54373	+	2.67382i	−0.197654	+	0.342348i	−0.947767	−	0.318962i	$-0.896666\pi$
$61$	−1.54373	+	2.67382i	−0.197654	+	0.342348i	0.750113	+	0.661310i	$0.229999\pi$
$62$	−0.222573	−	0.385507i	−0.0282668	−	0.0489595i
$63$		0			0
$64$		−	7.44778i		−	0.930973i
$65$	−2.76926	−	2.01275i	−0.343484	−	0.249651i
$66$		0			0
$67$	−0.516129	+	1.92622i	−0.0630552	+	0.235325i	−0.990260	−	0.139229i	$-0.955538\pi$
$67$	−0.516129	+	1.92622i	−0.0630552	+	0.235325i	0.927205	+	0.374554i	$0.122204\pi$
$68$	−10.5797	+	6.10818i	−1.28297	+	0.740726i
$69$		0			0
$70$	0.151635	+	0.151635i	0.0181239	+	0.0181239i
$71$	−0.385189	−	1.43754i	−0.0457135	−	0.170605i	0.939295	−	0.343110i	$-0.111481\pi$
$71$	−0.385189	−	1.43754i	−0.0457135	−	0.170605i	−0.985009	+	0.172505i	$0.944814\pi$
$72$		0			0
$73$	−7.05012	+	7.05012i	−0.825154	+	0.825154i	−0.986842	−	0.161688i	$-0.948306\pi$
$73$	−7.05012	+	7.05012i	−0.825154	+	0.825154i	0.161688	+	0.986842i	$0.448306\pi$
$74$	−0.253718	−	0.146484i	−0.0294941	−	0.0170284i
$75$		0			0
$76$	3.32764	+	0.891639i	0.381707	+	0.102278i
$77$	7.32388			0.834633
$78$		0			0
$79$	−4.39155			−0.494088			−0.247044	−	0.969004i	$-0.579459\pi$
$79$	−4.39155			−0.494088			−0.247044	+	0.969004i	$0.579459\pi$
$80$	3.54120	+	0.948861i	0.395918	+	0.106086i
$81$		0			0
$82$	1.24737	+	0.720168i	0.137749	+	0.0795293i
$83$	−6.90303	+	6.90303i	−0.757706	+	0.757706i	−0.975905	−	0.218198i	$-0.929982\pi$
$83$	−6.90303	+	6.90303i	−0.757706	+	0.757706i	0.218198	+	0.975905i	$0.429982\pi$
$84$		0			0
$85$	−1.51871	−	5.66789i	−0.164727	−	0.614768i
$86$	0.786147	+	0.786147i	0.0847724	+	0.0847724i
$87$		0			0
$88$	−2.59473	+	1.49807i	−0.276599	+	0.159694i
$89$	2.33371	−	8.70954i	0.247373	−	0.923209i	−0.724803	−	0.688957i	$-0.758069\pi$
$89$	2.33371	−	8.70954i	0.247373	−	0.923209i	0.972176	−	0.234253i	$-0.0752643\pi$
$90$		0			0
$91$	4.88095	−	2.17208i	0.511662	−	0.227696i
$92$			14.8236i			1.54547i
$93$		0			0
$94$	0.584948	+	1.01316i	0.0603328	+	0.104499i
$95$	−0.827367	+	1.43304i	−0.0848861	+	0.147027i
$96$		0			0
$97$	12.5248	−	3.35601i	1.27170	−	0.340751i	0.441018	−	0.897498i	$-0.354618\pi$
$97$	12.5248	−	3.35601i	1.27170	−	0.340751i	0.830682	+	0.556747i	$0.187951\pi$
$98$	0.707373	−	0.189540i	0.0714555	−	0.0191464i
$99$		0			0
$100$	4.05086	−	7.01629i	0.405086	−	0.701629i
$101$	−5.57578	−	9.65754i	−0.554811	−	0.960961i	−0.997918	−	0.0644926i	$-0.979457\pi$
$101$	−5.57578	−	9.65754i	−0.554811	−	0.960961i	0.443107	−	0.896469i	$-0.353876\pi$
$102$		0			0
$103$		−	5.77486i		−	0.569014i	−0.958674	−	0.284507i	$-0.908170\pi$
$103$		−	5.77486i		−	0.569014i	0.958674	−	0.284507i	$-0.0918299\pi$
$104$	−1.28495	+	1.76791i	−0.126000	+	0.173357i
$105$		0			0
$106$	−0.317881	+	1.18635i	−0.0308753	+	0.115228i
$107$	−5.94954	+	3.43497i	−0.575163	+	0.332071i	−0.759209	−	0.650847i	$-0.774414\pi$
$107$	−5.94954	+	3.43497i	−0.575163	+	0.332071i	0.184046	+	0.982918i	$0.441081\pi$
$108$		0			0
$109$	9.23765	+	9.23765i	0.884807	+	0.884807i	0.994019	−	0.109212i	$-0.0348326\pi$
$109$	9.23765	+	9.23765i	0.884807	+	0.884807i	−0.109212	+	0.994019i	$0.534833\pi$
$110$	−0.185148	−	0.690980i	−0.0176531	−	0.0658824i
$111$		0			0
$112$	−4.04546	+	4.04546i	−0.382260	+	0.382260i
$113$	1.55135	+	0.895672i	0.145939	+	0.0842577i	0.571191	−	0.820817i	$-0.306481\pi$
$113$	1.55135	+	0.895672i	0.145939	+	0.0842577i	−0.425253	+	0.905075i	$0.639815\pi$
$114$		0			0
$115$	−6.87756	−	1.84284i	−0.641336	−	0.171845i
$116$	2.69385			0.250117
$117$		0			0
$118$	−0.709180			−0.0652853
$119$	8.84499	+	2.37001i	0.810819	+	0.217258i
$120$		0			0
$121$	−11.6319	−	6.71568i	−1.05744	−	0.610516i
$122$	−0.332770	+	0.332770i	−0.0301275	+	0.0301275i
$123$		0			0
$124$	1.49416	+	5.57628i	0.134179	+	0.500764i
$125$	6.10863	+	6.10863i	0.546373	+	0.546373i
$126$		0			0
$127$	−5.78053	+	3.33739i	−0.512939	+	0.296145i	−0.734041	−	0.679105i	$-0.762368\pi$
$127$	−5.78053	+	3.33739i	−0.512939	+	0.296145i	0.221102	+	0.975251i	$0.429035\pi$
$128$	1.22601	−	4.57553i	0.108365	−	0.404424i
$129$		0			0
$130$	−0.328318	−	0.405589i	−0.0287954	−	0.0355725i
$131$			13.8121i			1.20677i	0.797451	+	0.603383i	$0.206181\pi$
$131$			13.8121i			1.20677i	−0.797451	+	0.603383i	$0.793819\pi$
$132$		0			0
$133$	−1.29114	−	2.23633i	−0.111956	−	0.193914i
$134$	−0.151981	+	0.263239i	−0.0131292	+	0.0227404i
$135$		0			0
$136$	−3.61841	+	0.969549i	−0.310276	+	0.0831381i
$137$	20.1653	−	5.40329i	1.72284	−	0.461634i	0.744328	−	0.667815i	$-0.232770\pi$
$137$	20.1653	−	5.40329i	1.72284	−	0.461634i	0.978514	+	0.206180i	$0.0661034\pi$
$138$		0			0
$139$	−4.33206	+	7.50334i	−0.367440	+	0.636425i	−0.989165	−	0.146811i	$-0.953099\pi$
$139$	−4.33206	+	7.50334i	−0.367440	+	0.636425i	0.621724	+	0.783236i	$0.286432\pi$
$140$	−1.39054	−	2.40849i	−0.117522	−	0.203554i
$141$		0			0
$142$		−	0.226848i		−	0.0190366i
$143$	−17.7236	−	1.86607i	−1.48212	−	0.156049i
$144$		0			0
$145$	−0.334892	+	1.24983i	−0.0278113	+	0.103793i
$146$	−1.31613	+	0.759869i	−0.108924	+	0.0628872i
$147$		0			0
$148$	2.68660	+	2.68660i	0.220837	+	0.220837i
$149$	−5.09679	−	19.0215i	−0.417545	−	1.55830i	−0.779682	−	0.626176i	$-0.784619\pi$
$149$	−5.09679	−	19.0215i	−0.417545	−	1.55830i	0.362136	−	0.932125i	$-0.382047\pi$
$150$		0			0
$151$	17.2304	−	17.2304i	1.40219	−	1.40219i	0.609099	−	0.793094i	$-0.291531\pi$
$151$	17.2304	−	17.2304i	1.40219	−	1.40219i	0.793094	−	0.609099i	$-0.208469\pi$
$152$	0.914861	+	0.528195i	0.0742050	+	0.0428423i
$153$		0			0
$154$	1.07831	+	0.288931i	0.0868923	+	0.0232827i
$155$	−2.77291			−0.222726
$156$		0			0
$157$	16.8427			1.34419			0.672097	−	0.740463i	$-0.265394\pi$
$157$	16.8427			1.34419			0.672097	+	0.740463i	$0.265394\pi$
$158$	−0.646575	−	0.173249i	−0.0514388	−	0.0137830i
$159$		0			0
$160$	1.48081	+	0.854948i	0.117069	+	0.0675896i
$161$	7.85691	−	7.85691i	0.619211	−	0.619211i
$162$		0			0
$163$	4.03723	+	15.0672i	0.316220	+	1.18015i	0.922848	+	0.385164i	$0.125855\pi$
$163$	4.03723	+	15.0672i	0.316220	+	1.18015i	−0.606628	+	0.794986i	$0.707478\pi$
$164$	−13.2083	−	13.2083i	−1.03140	−	1.03140i
$165$		0			0
$166$	−1.28867	+	0.744016i	−0.100020	+	0.0577468i
$167$	3.29146	−	12.2839i	0.254701	−	0.950556i	−0.713556	−	0.700598i	$-0.752917\pi$
$167$	3.29146	−	12.2839i	0.254701	−	0.950556i	0.968257	−	0.249958i	$-0.0804168\pi$
$168$		0			0
$169$	−12.3652	+	4.01274i	−0.951169	+	0.308672i
$170$		−	0.894405i		−	0.0685977i
$171$		0			0
$172$	−7.20920	−	12.4867i	−0.549696	−	0.952102i
$173$	−0.245830	+	0.425790i	−0.0186901	+	0.0323722i	−0.875219	−	0.483727i	$-0.839283\pi$
$173$	−0.245830	+	0.425790i	−0.0186901	+	0.0323722i	0.856529	+	0.516099i	$0.172616\pi$
$174$		0			0
$175$	−5.86587	+	1.57176i	−0.443418	+	0.118814i
$176$	18.4346	−	4.93953i	1.38956	−	0.372331i
$177$		0			0
$178$	0.687192	−	1.19025i	0.0515073	−	0.0892132i
$179$	−6.95866	−	12.0527i	−0.520114	−	0.900865i	−0.999727	−	0.0233840i	$-0.992556\pi$
$179$	−6.95866	−	12.0527i	−0.520114	−	0.900865i	0.479612	−	0.877481i	$-0.340777\pi$
$180$		0			0
$181$			13.3724i			0.993962i	0.867761	+	0.496981i	$0.165558\pi$
$181$			13.3724i			0.993962i	−0.867761	+	0.496981i	$0.834442\pi$
$182$	0.804319	−	0.127242i	0.0596201	−	0.00943181i
$183$		0			0
$184$	−1.17648	+	4.39067i	−0.0867309	+	0.323684i
$185$	−1.58046	+	0.912482i	−0.116198	+	0.0670870i
$186$		0			0
$187$	−21.5996	−	21.5996i	−1.57952	−	1.57952i
$188$	−3.92683	−	14.6551i	−0.286394	−	1.06884i
$189$		0			0
$190$	−0.178349	+	0.178349i	−0.0129388	+	0.0129388i
$191$	−8.79870	−	5.07993i	−0.636652	−	0.367571i	0.146672	−	0.989185i	$-0.453144\pi$
$191$	−8.79870	−	5.07993i	−0.636652	−	0.367571i	−0.783324	+	0.621614i	$0.786477\pi$
$192$		0			0
$193$	5.74909	+	1.54046i	0.413828	+	0.110885i	0.459725	−	0.888061i	$-0.347948\pi$
$193$	5.74909	+	1.54046i	0.413828	+	0.110885i	−0.0458969	+	0.998946i	$0.514615\pi$
$194$	1.97644			0.141900
$195$		0			0
$196$	−9.49736			−0.678383
$197$	23.0047	+	6.16408i	1.63901	+	0.439173i	0.956508	−	0.291707i	$-0.0942231\pi$
$197$	23.0047	+	6.16408i	1.63901	+	0.439173i	0.682507	+	0.730879i	$0.260890\pi$
$198$		0			0
$199$	5.76012	+	3.32561i	0.408324	+	0.235746i	0.690069	−	0.723743i	$-0.257580\pi$
$199$	5.76012	+	3.32561i	0.408324	+	0.235746i	−0.281745	+	0.959489i	$0.590913\pi$
$200$	1.75668	−	1.75668i	0.124216	−	0.124216i
$201$		0			0
$202$	−0.439936	−	1.64186i	−0.0309538	−	0.115521i
$203$	−1.42781	−	1.42781i	−0.100212	−	0.100212i
$204$		0			0
$205$	7.77013	−	4.48609i	0.542690	−	0.313322i
$206$	0.227821	−	0.850241i	0.0158731	−	0.0592391i
$207$		0			0
$208$	10.8207	−	8.75914i	0.750277	−	0.607337i
$209$			8.61413i			0.595851i
$210$		0			0
$211$	11.5311	+	19.9725i	0.793834	+	1.37496i	0.923577	+	0.383413i	$0.125251\pi$
$211$	11.5311	+	19.9725i	0.793834	+	1.37496i	−0.129743	+	0.991548i	$0.541415\pi$
$212$	7.96410	−	13.7942i	0.546976	−	0.947391i
$213$		0			0
$214$	−1.01147	+	0.271023i	−0.0691427	+	0.0185267i
$215$	6.68954	−	1.79246i	0.456223	−	0.122245i
$216$		0			0
$217$	2.16363	−	3.74751i	0.146877	−	0.254398i
$218$	0.995643	+	1.72450i	0.0674335	+	0.116798i
$219$		0			0
$220$			9.27727i			0.625473i
$221$	−20.8008	−	7.98900i	−1.39921	−	0.537398i
$222$		0			0
$223$	2.99432	−	11.1749i	0.200514	−	0.748329i	−0.790256	−	0.612777i	$-0.790052\pi$
$223$	2.99432	−	11.1749i	0.200514	−	0.748329i	0.990770	−	0.135552i	$-0.0432809\pi$
$224$	−2.31088	+	1.33418i	−0.154402	+	0.0891440i
$225$		0			0
$226$	0.193073	+	0.193073i	0.0128430	+	0.0128430i
$227$	−3.94608	−	14.7270i	−0.261911	−	0.977464i	−0.964114	−	0.265488i	$-0.914467\pi$
$227$	−3.94608	−	14.7270i	−0.261911	−	0.977464i	0.702204	−	0.711976i	$-0.252200\pi$
$228$		0			0
$229$	1.27649	−	1.27649i	0.0843528	−	0.0843528i	−0.663671	−	0.748024i	$-0.731003\pi$
$229$	1.27649	−	1.27649i	0.0843528	−	0.0843528i	0.748024	+	0.663671i	$0.231003\pi$
$230$	−0.939892	−	0.542647i	−0.0619747	−	0.0357811i
$231$		0			0
$232$	0.797900	+	0.213797i	0.0523847	+	0.0140364i
$233$	3.28492			0.215202			0.107601	−	0.994194i	$-0.465683\pi$
$233$	3.28492			0.215202			0.107601	+	0.994194i	$0.465683\pi$
$234$		0			0
$235$	7.28755			0.475387
$236$	8.88380	+	2.38041i	0.578286	+	0.154951i
$237$		0			0
$238$	1.20876	+	0.697880i	0.0783525	+	0.0452368i
$239$	−14.0261	+	14.0261i	−0.907273	+	0.907273i	−0.996051	−	0.0887785i	$-0.971704\pi$
$239$	−14.0261	+	14.0261i	−0.907273	+	0.907273i	0.0887785	+	0.996051i	$0.471704\pi$
$240$		0			0
$241$	−5.78824	−	21.6020i	−0.372853	−	1.39151i	−0.856456	−	0.516220i	$-0.827339\pi$
$241$	−5.78824	−	21.6020i	−0.372853	−	1.39151i	0.483603	−	0.875288i	$-0.339328\pi$
$242$	−1.44764	−	1.44764i	−0.0930581	−	0.0930581i
$243$		0			0
$244$	5.28552	−	3.05160i	0.338371	−	0.195358i
$245$	1.18069	−	4.40638i	0.0754313	−	0.281514i
$246$		0			0
$247$	2.55473	+	5.74082i	0.162554	+	0.365280i
$248$			1.77024i			0.112410i
$249$		0			0
$250$	0.658394	+	1.14037i	0.0416405	+	0.0721235i
$251$	−12.0369	+	20.8485i	−0.759762	+	1.31595i	0.183210	+	0.983074i	$0.441351\pi$
$251$	−12.0369	+	20.8485i	−0.759762	+	1.31595i	−0.942972	+	0.332873i	$0.891982\pi$
$252$		0			0
$253$	−35.8028	+	9.59333i	−2.25090	+	0.603128i
$254$	−0.982738	+	0.263324i	−0.0616624	+	0.0165224i
$255$		0			0
$256$	−7.08677	+	12.2746i	−0.442923	+	0.767165i
$257$	11.7973	+	20.4336i	0.735898	+	1.27461i	0.954328	+	0.298760i	$0.0965729\pi$
$257$	11.7973	+	20.4336i	0.735898	+	1.27461i	−0.218431	+	0.975852i	$0.570094\pi$
$258$		0			0
$259$		−	2.84794i		−	0.176962i
$260$	2.75140	+	6.18277i	0.170635	+	0.383439i
$261$		0			0
$262$	−0.544894	+	2.03357i	−0.0336637	+	0.125634i
$263$	−13.7544	+	7.94113i	−0.848136	+	0.489671i	−0.860021	−	0.510258i	$-0.829550\pi$
$263$	−13.7544	+	7.94113i	−0.848136	+	0.489671i	0.0118858	+	0.999929i	$0.496217\pi$
$264$		0			0
$265$	5.40987	+	5.40987i	0.332326	+	0.332326i
$266$	−0.101873	−	0.380194i	−0.00624622	−	0.0233112i
$267$		0			0
$268$	2.78742	−	2.78742i	0.170269	−	0.170269i
$269$	−14.3355	−	8.27660i	−0.874050	−	0.504633i	−0.00535797	−	0.999986i	$-0.501706\pi$
$269$	−14.3355	−	8.27660i	−0.874050	−	0.504633i	−0.868692	+	0.495353i	$0.835039\pi$
$270$		0			0
$271$	13.5663	+	3.63509i	0.824097	+	0.220816i	0.646137	−	0.763222i	$-0.276384\pi$
$271$	13.5663	+	3.63509i	0.824097	+	0.220816i	0.177960	+	0.984038i	$0.443050\pi$
$272$	23.8617			1.44683
$273$		0			0
$274$	3.18214			0.192240
$275$	19.5677	+	5.24314i	1.17997	+	0.316173i
$276$		0			0
$277$	−13.8085	−	7.97233i	−0.829672	−	0.479011i	0.0240686	−	0.999710i	$-0.492338\pi$
$277$	−13.8085	−	7.97233i	−0.829672	−	0.479011i	−0.853740	+	0.520699i	$0.825671\pi$
$278$	−0.933826	+	0.933826i	−0.0560072	+	0.0560072i
$279$		0			0
$280$	−0.220720	−	0.823738i	−0.0131905	−	0.0492278i
$281$	14.6040	+	14.6040i	0.871200	+	0.871200i	0.992603	−	0.121403i	$-0.0387395\pi$
$281$	14.6040	+	14.6040i	0.871200	+	0.871200i	−0.121403	+	0.992603i	$0.538739\pi$
$282$		0			0
$283$	−0.433494	+	0.250278i	−0.0257685	+	0.0148775i	−0.512829	−	0.858491i	$-0.671402\pi$
$283$	−0.433494	+	0.250278i	−0.0257685	+	0.0148775i	0.487060	+	0.873368i	$0.338069\pi$
$284$	−0.761429	+	2.84169i	−0.0451825	+	0.168623i
$285$		0			0
$286$	−2.53585	−	0.973950i	−0.149948	−	0.0575909i
$287$			14.0015i			0.826482i
$288$		0			0
$289$	−10.5960	−	18.3528i	−0.623295	−	1.07958i
$290$	−0.0986133	+	0.170803i	−0.00579077	+	0.0100299i
$291$		0			0
$292$	19.0375	−	5.10109i	1.11409	−	0.298519i
$293$	5.34411	−	1.43195i	0.312206	−	0.0836554i	−0.0993136	−	0.995056i	$-0.531665\pi$
$293$	5.34411	−	1.43195i	0.312206	−	0.0836554i	0.411520	+	0.911401i	$0.364998\pi$
$294$		0			0
$295$	−2.20882	+	3.82579i	−0.128603	+	0.222746i
$296$	0.582533	+	1.00898i	0.0338590	+	0.0586456i
$297$		0			0
$298$		−	3.00163i		−	0.173880i
$299$	−21.0154	+	17.0116i	−1.21535	+	0.983808i
$300$		0			0
$301$	−2.79721	+	10.4393i	−0.161229	+	0.601713i
$302$	3.21661	−	1.85711i	0.185095	−	0.106865i
$303$		0			0
$304$	−4.75815	−	4.75815i	−0.272898	−	0.272898i
$305$	0.758732	+	2.83163i	0.0434449	+	0.162139i
$306$		0			0
$307$	−17.8744	+	17.8744i	−1.02015	+	1.02015i	−0.0203530	+	0.999793i	$0.506479\pi$
$307$	−17.8744	+	17.8744i	−1.02015	+	1.02015i	−0.999793	+	0.0203530i	$0.993521\pi$
$308$	−12.5380	−	7.23880i	−0.714417	−	0.412469i
$309$		0			0
$310$	−0.408260	−	0.109393i	−0.0231876	−	0.00621310i
$311$	−23.3691			−1.32514			−0.662569	−	0.749001i	$-0.730534\pi$
$311$	−23.3691			−1.32514			−0.662569	+	0.749001i	$0.730534\pi$
$312$		0			0
$313$	−2.54165			−0.143662			−0.0718312	−	0.997417i	$-0.522884\pi$
$313$	−2.54165			−0.143662			−0.0718312	+	0.997417i	$0.522884\pi$
$314$	2.47978	+	0.664454i	0.139942	+	0.0374973i
$315$		0			0
$316$	7.51803	+	4.34054i	0.422922	+	0.244174i
$317$	2.12744	−	2.12744i	0.119489	−	0.119489i	−0.644834	−	0.764323i	$-0.723073\pi$
$317$	2.12744	−	2.12744i	0.119489	−	0.119489i	0.764323	+	0.644834i	$0.223073\pi$
$318$		0			0
$319$	1.74336	+	6.50631i	0.0976095	+	0.364284i
$320$	−5.00038	−	5.00038i	−0.279530	−	0.279530i
$321$		0			0
$322$	1.46674	−	0.846825i	0.0817385	−	0.0471917i
$323$	−2.78753	+	10.4032i	−0.155102	+	0.578850i
$324$		0			0
$325$	14.5957	−	2.30902i	0.809625	−	0.128081i
$326$			2.37763i			0.131685i
$327$		0			0
$328$	−2.86394	−	4.96049i	−0.158135	−	0.273897i
$329$	−5.68627	+	9.84891i	−0.313494	+	0.542988i
$330$		0			0
$331$	22.2635	−	5.96549i	1.22371	−	0.327893i	0.411584	−	0.911372i	$-0.364976\pi$
$331$	22.2635	−	5.96549i	1.22371	−	0.327893i	0.812128	+	0.583479i	$0.198309\pi$
$332$	18.6404	−	4.99467i	1.02302	−	0.274118i
$333$		0			0
$334$	0.969213	−	1.67873i	0.0530330	−	0.0918558i
$335$	0.946724	+	1.63977i	0.0517250	+	0.0895904i
$336$		0			0
$337$		−	21.1502i		−	1.15212i	−0.817406	−	0.576062i	$-0.804589\pi$
$337$		−	21.1502i		−	1.15212i	0.817406	−	0.576062i	$-0.195411\pi$
$338$	−1.97885	+	0.102987i	−0.107635	+	0.00560177i
$339$		0			0
$340$	−3.00213	+	11.2041i	−0.162813	+	0.607627i
$341$	−12.5011	+	7.21753i	−0.676974	+	0.390851i
$342$		0			0
$343$	12.3680	+	12.3680i	0.667810	+	0.667810i
$344$	−1.14431	−	4.27064i	−0.0616972	−	0.230257i
$345$		0			0
$346$	−0.0529916	+	0.0529916i	−0.00284885	+	0.00284885i
$347$	5.66522	+	3.27082i	0.304125	+	0.175587i	0.644295	−	0.764777i	$-0.277151\pi$
$347$	5.66522	+	3.27082i	0.304125	+	0.175587i	−0.340169	+	0.940364i	$0.610484\pi$
$348$		0			0
$349$	−2.20510	−	0.590855i	−0.118036	−	0.0316278i	0.199317	−	0.979935i	$-0.436128\pi$
$349$	−2.20510	−	0.590855i	−0.118036	−	0.0316278i	−0.317354	+	0.948307i	$0.602794\pi$
$350$	−0.925648			−0.0494779
$351$		0			0
$352$	8.90128			0.474440
$353$	12.0525	+	3.22946i	0.641490	+	0.171887i	0.564878	−	0.825174i	$-0.308923\pi$
$353$	12.0525	+	3.22946i	0.641490	+	0.171887i	0.0766119	+	0.997061i	$0.475590\pi$
$354$		0			0
$355$	−1.22377	−	0.706543i	−0.0649509	−	0.0374994i
$356$	−12.6035	+	12.6035i	−0.667985	+	0.667985i
$357$		0			0
$358$	−0.549046	−	2.04907i	−0.0290180	−	0.108297i
$359$	−5.21156	−	5.21156i	−0.275056	−	0.275056i	0.556076	−	0.831132i	$-0.312306\pi$
$359$	−5.21156	−	5.21156i	−0.275056	−	0.275056i	−0.831132	+	0.556076i	$0.812306\pi$
$360$		0			0
$361$	−13.8242	+	7.98140i	−0.727589	+	0.420073i
$362$	−0.527549	+	1.96884i	−0.0277273	+	0.103480i
$363$		0			0
$364$	−10.5027	−	1.10580i	−0.550490	−	0.0579598i
$365$			9.46678i			0.495514i
$366$		0			0
$367$	12.6719	+	21.9484i	0.661469	+	1.14570i	0.980230	+	0.197862i	$0.0633999\pi$
$367$	12.6719	+	21.9484i	0.661469	+	1.14570i	−0.318761	+	0.947835i	$0.603267\pi$
$368$	14.4772	−	25.0753i	0.754677	−	1.30714i
$369$		0			0
$370$	−0.268692	+	0.0719958i	−0.0139686	+	0.00374288i
$371$	−11.5325	+	3.09012i	−0.598736	+	0.160431i
$372$		0			0
$373$	8.02752	−	13.9041i	0.415649	−	0.719925i	−0.579847	−	0.814725i	$-0.696888\pi$
$373$	8.02752	−	13.9041i	0.415649	−	0.719925i	0.995496	+	0.0947999i	$0.0302211\pi$
$374$	−2.32802	−	4.03225i	−0.120379	−	0.208503i
$375$		0			0
$376$		−	4.65241i		−	0.239929i
$377$	3.09146	+	3.81905i	0.159218	+	0.196691i
$378$		0			0
$379$	9.20617	−	34.3579i	0.472889	−	1.76485i	−0.156420	−	0.987691i	$-0.549995\pi$
$379$	9.20617	−	34.3579i	0.472889	−	1.76485i	0.629309	−	0.777155i	$-0.283338\pi$
$380$	2.83279	−	1.63551i	0.145319	−	0.0839000i
$381$		0			0
$382$	−1.09504	−	1.09504i	−0.0560271	−	0.0560271i
$383$	4.21084	+	15.7151i	0.215164	+	0.803003i	0.986109	+	0.166101i	$0.0531177\pi$
$383$	4.21084	+	15.7151i	0.215164	+	0.803003i	−0.770945	+	0.636902i	$0.780216\pi$
$384$		0			0
$385$	4.91719	−	4.91719i	0.250603	−	0.250603i
$386$	0.785675	+	0.453609i	0.0399898	+	0.0230881i
$387$		0			0
$388$	−24.7586	−	6.63404i	−1.25693	−	0.336793i
$389$	−22.6947			−1.15067			−0.575334	−	0.817919i	$-0.695128\pi$
$389$	−22.6947			−1.15067			−0.575334	+	0.817919i	$0.695128\pi$
$390$		0			0
$391$	−46.3432			−2.34368
$392$	−2.81306	−	0.753756i	−0.142081	−	0.0380704i
$393$		0			0
$394$	3.14384	+	1.81509i	0.158384	+	0.0914431i
$395$	−2.94845	+	2.94845i	−0.148353	+	0.148353i
$396$		0			0
$397$	8.05845	+	30.0745i	0.404442	+	1.50940i	0.805083	+	0.593162i	$0.202121\pi$
$397$	8.05845	+	30.0745i	0.404442	+	1.50940i	−0.400641	+	0.916235i	$0.631213\pi$
$398$	0.716874	+	0.716874i	0.0359337	+	0.0359337i
$399$		0			0
$400$	−13.7046	+	7.91237i	−0.685232	+	0.395619i
$401$	4.99334	−	18.6354i	0.249355	−	0.930607i	−0.721789	−	0.692113i	$-0.756680\pi$
$401$	4.99334	−	18.6354i	0.249355	−	0.930607i	0.971144	−	0.238493i	$-0.0766535\pi$
$402$		0			0
$403$	−6.19076	+	8.51760i	−0.308384	+	0.424292i
$404$			22.0440i			1.09673i
$405$		0			0
$406$	−0.153890	−	0.266546i	−0.00763746	−	0.0132285i
$407$	−4.75015	+	8.22749i	−0.235456	+	0.407822i
$408$		0			0
$409$	23.8954	−	6.40275i	1.18155	−	0.316596i	0.386010	−	0.922495i	$-0.373853\pi$
$409$	23.8954	−	6.40275i	1.18155	−	0.316596i	0.795542	+	0.605899i	$0.207186\pi$
$410$	1.32099	−	0.353957i	0.0652389	−	0.0174807i
$411$		0			0
$412$	−5.70777	+	9.88616i	−0.281202	+	0.487056i
$413$	−3.44697	−	5.97032i	−0.169614	−	0.293780i
$414$		0			0
$415$			9.26928i			0.455011i
$416$	5.93220	−	2.63990i	0.290850	−	0.129432i
$417$		0			0
$418$	−0.339832	+	1.26827i	−0.0166217	+	0.0620331i
$419$	−0.358895	+	0.207208i	−0.0175332	+	0.0101228i	−0.508741	−	0.860920i	$-0.669889\pi$
$419$	−0.358895	+	0.207208i	−0.0175332	+	0.0101228i	0.491208	+	0.871042i	$0.336556\pi$
$420$		0			0
$421$	13.1801	+	13.1801i	0.642360	+	0.642360i	0.951135	−	0.308775i	$-0.0999190\pi$
$421$	13.1801	+	13.1801i	0.642360	+	0.642360i	−0.308775	+	0.951135i	$0.599919\pi$
$422$	0.909817	+	3.39548i	0.0442892	+	0.165290i
$423$		0			0
$424$	3.45369	−	3.45369i	0.167726	−	0.167726i
$425$	21.9350	+	12.6642i	1.06401	+	0.614304i
$426$		0			0
$427$	−4.41888	−	1.18404i	−0.213845	−	0.0572995i
$428$	13.5803			0.656426
$429$		0			0
$430$	1.05562			0.0509067
$431$	−0.208658	−	0.0559098i	−0.0100507	−	0.00269308i	0.253790	−	0.967259i	$-0.418323\pi$
$431$	−0.208658	−	0.0559098i	−0.0100507	−	0.00269308i	−0.263841	+	0.964566i	$0.584989\pi$
$432$		0			0
$433$	16.6783	+	9.62921i	0.801507	+	0.462750i	0.843998	−	0.536347i	$-0.180196\pi$
$433$	16.6783	+	9.62921i	0.801507	+	0.462750i	−0.0424908	+	0.999097i	$0.513529\pi$
$434$	0.466395	−	0.466395i	0.0223877	−	0.0223877i
$435$		0			0
$436$	−6.68387	−	24.9446i	−0.320100	−	1.19463i
$437$	9.24106	+	9.24106i	0.442060	+	0.442060i
$438$		0			0
$439$	−7.10282	+	4.10081i	−0.338999	+	0.195721i	−0.659829	−	0.751416i	$-0.729371\pi$
$439$	−7.10282	+	4.10081i	−0.338999	+	0.195721i	0.320830	+	0.947137i	$0.396038\pi$
$440$	−0.736288	+	2.74787i	−0.0351012	+	0.130999i
$441$		0			0
$442$	−2.74736	−	1.99683i	−0.130679	−	0.0949798i
$443$		−	15.3245i		−	0.728088i	−0.931382	−	0.364044i	$-0.881396\pi$
$443$		−	15.3245i		−	0.728088i	0.931382	−	0.364044i	$-0.118604\pi$
$444$		0			0
$445$	−4.28068	−	7.41435i	−0.202923	−	0.351474i
$446$	0.881715	−	1.52718i	0.0417504	−	0.0723139i
$447$		0			0
$448$	10.6595	−	2.85621i	0.503615	−	0.134943i
$449$	−16.2566	+	4.35595i	−0.767197	+	0.205570i	−0.621133	−	0.783705i	$-0.713327\pi$
$449$	−16.2566	+	4.35595i	−0.767197	+	0.205570i	−0.146064	+	0.989275i	$0.546661\pi$
$450$		0			0
$451$	23.3534	−	40.4493i	1.09967	−	1.90468i
$452$	−1.77053	−	3.06665i	−0.0832789	−	0.144243i
$453$		0			0
$454$		−	2.32395i		−	0.109068i
$455$	1.81871	−	4.73534i	0.0852626	−	0.221996i
$456$		0			0
$457$	−6.38172	+	23.8169i	−0.298524	+	1.11411i	0.639853	+	0.768497i	$0.278995\pi$
$457$	−6.38172	+	23.8169i	−0.298524	+	1.11411i	−0.938378	+	0.345611i	$0.887672\pi$
$458$	0.238298	−	0.137581i	0.0111349	−	0.00642875i
$459$		0			0
$460$	9.95247	+	9.95247i	0.464036	+	0.464036i
$461$	4.21645	+	15.7360i	0.196380	+	0.732899i	0.991905	+	0.126979i	$0.0405281\pi$
$461$	4.21645	+	15.7360i	0.196380	+	0.732899i	−0.795526	+	0.605920i	$0.792805\pi$
$462$		0			0
$463$	1.27663	−	1.27663i	0.0593302	−	0.0593302i	−0.676819	−	0.736149i	$-0.736642\pi$
$463$	1.27663	−	1.27663i	0.0593302	−	0.0593302i	0.736149	+	0.676819i	$0.236642\pi$
$464$	−4.55684	−	2.63089i	−0.211546	−	0.122136i
$465$		0			0
$466$	0.483644	+	0.129592i	0.0224044	+	0.00600324i
$467$	14.3428			0.663704			0.331852	−	0.943331i	$-0.392327\pi$
$467$	14.3428			0.663704			0.331852	+	0.943331i	$0.392327\pi$
$468$		0			0
$469$	−2.95481			−0.136440
$470$	1.07296	+	0.287498i	0.0494918	+	0.0132613i
$471$		0			0
$472$	2.44240	+	1.41012i	0.112421	+	0.0649061i
$473$	25.4930	−	25.4930i	1.17217	−	1.17217i
$474$		0			0
$475$	−1.84865	−	6.89926i	−0.0848219	−	0.316560i
$476$	−12.7995	−	12.7995i	−0.586666	−	0.586666i
$477$		0			0
$478$	−2.61842	+	1.51175i	−0.119764	+	0.0691457i
$479$	4.87032	−	18.1763i	0.222530	−	0.830495i	−0.760848	−	0.648930i	$-0.775217\pi$
$479$	4.87032	−	18.1763i	0.222530	−	0.830495i	0.983379	−	0.181565i	$-0.0581164\pi$
$480$		0			0
$481$	−0.725635	+	6.89193i	−0.0330861	+	0.314245i
$482$		−	3.40885i		−	0.155269i
$483$		0			0
$484$	13.2753	+	22.9935i	0.603424	+	1.04516i
$485$	6.15584	−	10.6622i	0.279522	−	0.484147i
$486$		0			0
$487$	−31.6441	+	8.47901i	−1.43393	+	0.384220i	−0.890404	−	0.455172i	$-0.849578\pi$
$487$	−31.6441	+	8.47901i	−1.43393	+	0.384220i	−0.543526	+	0.839392i	$0.682911\pi$
$488$	1.80773	−	0.484379i	0.0818319	−	0.0219268i
$489$		0			0
$490$	0.347669	−	0.602180i	0.0157061	−	0.0272037i
$491$	−13.9147	−	24.1009i	−0.627960	−	1.08766i	−0.987960	−	0.154707i	$-0.950557\pi$
$491$	−13.9147	−	24.1009i	−0.627960	−	1.08766i	0.360000	−	0.932952i	$-0.382777\pi$
$492$		0			0
$493$			8.42178i			0.379298i
$494$	0.149658	+	0.946016i	0.00673345	+	0.0425633i
$495$		0			0
$496$	2.91848	−	10.8919i	0.131044	−	0.489061i
$497$	1.90975	−	1.10259i	0.0856638	−	0.0494580i
$498$		0			0
$499$	−18.7743	−	18.7743i	−0.840452	−	0.840452i	0.148466	−	0.988918i	$-0.452567\pi$
$499$	−18.7743	−	18.7743i	−0.840452	−	0.840452i	−0.988918	+	0.148466i	$0.952567\pi$
$500$	−4.41988	−	16.4952i	−0.197663	−	0.737689i
$501$		0			0
$502$	−2.59470	+	2.59470i	−0.115807	+	0.115807i
$503$	9.08536	+	5.24543i	0.405096	+	0.233882i	0.688680	−	0.725065i	$-0.258190\pi$
$503$	9.08536	+	5.24543i	0.405096	+	0.233882i	−0.283584	+	0.958947i	$0.591524\pi$
$504$		0			0
$505$	−10.2275	−	2.74046i	−0.455119	−	0.121949i
$506$	−5.64976			−0.251163
$507$		0			0
$508$	13.1945			0.585410
$509$	−9.15495	−	2.45306i	−0.405786	−	0.108730i	0.0501520	−	0.998742i	$-0.484029\pi$
$509$	−9.15495	−	2.45306i	−0.405786	−	0.108730i	−0.455938	+	0.890012i	$0.650696\pi$
$510$		0			0
$511$	−12.7941	−	7.38667i	−0.565977	−	0.326767i
$512$	−8.22668	+	8.22668i	−0.363571	+	0.363571i
$513$		0			0
$514$	0.930823	+	3.47388i	0.0410569	+	0.153226i
$515$	−3.87719	−	3.87719i	−0.170849	−	0.170849i
$516$		0			0
$517$	32.8545	−	18.9686i	1.44494	−	0.834236i
$518$	0.112353	−	0.419306i	0.00493650	−	0.0184233i
$519$		0			0
$520$	0.324253	+	2.04966i	0.0142194	+	0.0898836i
$521$		−	24.9228i		−	1.09189i	−0.837822	−	0.545943i	$-0.816172\pi$
$521$		−	24.9228i		−	1.09189i	0.837822	−	0.545943i	$-0.183828\pi$
$522$		0			0
$523$	−19.3068	−	33.4403i	−0.844226	−	1.46224i	−0.886292	−	0.463127i	$-0.846727\pi$
$523$	−19.3068	−	33.4403i	−0.844226	−	1.46224i	0.0420665	−	0.999115i	$-0.486606\pi$
$524$	13.6516	−	23.6453i	0.596374	−	1.03295i
$525$		0			0
$526$	−2.33837	+	0.626564i	−0.101958	+	0.0273195i
$527$	−17.4331	+	4.67119i	−0.759399	+	0.203480i
$528$		0			0
$529$	−16.6170	+	28.7815i	−0.722479	+	1.25137i
$530$	0.583081	+	1.00993i	0.0253274	+	0.0438684i
$531$		0			0
$532$			5.10458i			0.221312i
$533$	3.56748	−	33.8832i	0.154525	−	1.46764i
$534$		0			0
$535$	−1.68826	+	6.30068i	−0.0729899	+	0.272402i
$536$	1.04684	−	0.604393i	0.0452166	−	0.0261058i
$537$		0			0
$538$	−1.78412	−	1.78412i	−0.0769188	−	0.0769188i
$539$	−6.14636	−	22.9385i	−0.264742	−	0.988032i
$540$		0			0
$541$	−4.93114	+	4.93114i	−0.212006	+	0.212006i	−0.805119	−	0.593113i	$-0.797899\pi$
$541$	−4.93114	+	4.93114i	−0.212006	+	0.212006i	0.593113	+	0.805119i	$0.297899\pi$
$542$	1.85399	+	1.07040i	0.0796355	+	0.0459776i
$543$		0			0
$544$	10.7500	+	2.88046i	0.460903	+	0.123499i
$545$	12.4042			0.531336
$546$		0			0
$547$	21.3170			0.911450			0.455725	−	0.890121i	$-0.349380\pi$
$547$	21.3170			0.911450			0.455725	+	0.890121i	$0.349380\pi$
$548$	−39.8622	−	10.6810i	−1.70283	−	0.456271i
$549$		0			0
$550$	2.67413	+	1.54391i	0.114025	+	0.0658326i
$551$	1.67934	−	1.67934i	0.0715425	−	0.0715425i
$552$		0			0
$553$	−1.68415	−	6.28535i	−0.0716175	−	0.267280i
$554$	−1.71853	−	1.71853i	−0.0730134	−	0.0730134i
$555$		0			0
$556$	14.8324	−	8.56347i	0.629032	−	0.363172i
$557$	6.81633	−	25.4389i	0.288817	−	1.07788i	−0.657188	−	0.753727i	$-0.728254\pi$
$557$	6.81633	−	25.4389i	0.288817	−	1.07788i	0.946005	−	0.324153i	$-0.105079\pi$
$558$		0			0
$559$	9.42904	−	24.5502i	0.398806	−	1.03836i
$560$			5.43217i			0.229551i
$561$		0			0
$562$	1.57403	+	2.72630i	0.0663964	+	0.115002i
$563$	−4.55796	+	7.89461i	−0.192095	+	0.332718i	−0.945944	−	0.324329i	$-0.894861\pi$
$563$	−4.55796	+	7.89461i	−0.192095	+	0.332718i	0.753849	+	0.657047i	$0.228195\pi$
$564$		0			0
$565$	1.64291	−	0.440216i	0.0691177	−	0.0185200i
$566$	−0.0736976	+	0.0197472i	−0.00309774	+	0.000830037i
$567$		0			0
$568$	−0.451060	+	0.781260i	−0.0189261	+	0.0327809i
$569$	−7.76549	−	13.4502i	−0.325546	−	0.563863i	0.656077	−	0.754694i	$-0.272215\pi$
$569$	−7.76549	−	13.4502i	−0.325546	−	0.563863i	−0.981623	+	0.190832i	$0.938881\pi$
$570$		0			0
$571$		−	0.678357i		−	0.0283884i	−0.999899	−	0.0141942i	$-0.995482\pi$
$571$		−	0.678357i		−	0.0283884i	0.999899	−	0.0141942i	$-0.00451830\pi$
$572$	28.4971	+	20.7123i	1.19153	+	0.866024i
$573$		0			0
$574$	−0.552367	+	2.06146i	−0.0230553	+	0.0860437i
$575$	26.6165	−	15.3671i	1.10999	−	0.640851i
$576$		0			0
$577$	−4.73750	−	4.73750i	−0.197225	−	0.197225i	0.601584	−	0.798809i	$-0.294536\pi$
$577$	−4.73750	−	4.73750i	−0.197225	−	0.197225i	−0.798809	+	0.601584i	$0.794536\pi$
$578$	−0.836038	−	3.12014i	−0.0347746	−	0.129781i
$579$		0			0
$580$	1.80863	−	1.80863i	0.0750991	−	0.0750991i
$581$	−12.5272	−	7.23256i	−0.519715	−	0.300057i
$582$		0			0
$583$	38.4706	+	10.3082i	1.59329	+	0.426920i
$584$	6.04364			0.250088
$585$		0			0
$586$	0.843313			0.0348369
$587$	−5.51125	−	1.47673i	−0.227474	−	0.0609514i	0.143282	−	0.989682i	$-0.454234\pi$
$587$	−5.51125	−	1.47673i	−0.227474	−	0.0609514i	−0.370755	+	0.928731i	$0.620901\pi$
$588$		0			0
$589$	4.40771	+	2.54479i	0.181617	+	0.104856i
$590$	−0.476138	+	0.476138i	−0.0196023	+	0.0196023i
$591$		0			0
$592$	−1.92077	−	7.16840i	−0.0789431	−	0.294620i
$593$	31.2873	+	31.2873i	1.28481	+	1.28481i	0.937895	+	0.346920i	$0.112773\pi$
$593$	31.2873	+	31.2873i	1.28481	+	1.28481i	0.346920	+	0.937895i	$0.387227\pi$
$594$		0			0
$595$	7.52966	−	4.34725i	0.308686	−	0.178220i
$596$	−10.0752	+	37.6010i	−0.412695	+	1.54020i
$597$		0			0
$598$	−3.76525	+	1.67558i	−0.153972	+	0.0685195i
$599$		−	29.1093i		−	1.18937i	−0.803958	−	0.594686i	$-0.797276\pi$
$599$		−	29.1093i		−	1.18937i	0.803958	−	0.594686i	$-0.202724\pi$
$600$		0			0
$601$	20.8551	+	36.1221i	0.850698	+	1.47345i	0.880580	+	0.473898i	$0.157154\pi$
$601$	20.8551	+	36.1221i	0.850698	+	1.47345i	−0.0298819	+	0.999553i	$0.509513\pi$
$602$	−0.823675	+	1.42665i	−0.0335705	+	0.0581458i
$603$		0			0
$604$	−46.5276	+	12.4670i	−1.89318	+	0.507276i
$605$	−12.3184	+	3.30071i	−0.500814	+	0.134193i
$606$		0			0
$607$	−10.8312	+	18.7601i	−0.439624	+	0.761451i	−0.997660	−	0.0683656i	$-0.978222\pi$
$607$	−10.8312	+	18.7601i	−0.439624	+	0.761451i	0.558036	+	0.829816i	$0.311555\pi$
$608$	−1.56923	−	2.71798i	−0.0636406	−	0.110229i
$609$		0			0
$610$			0.446837i			0.0180919i
$611$	16.2701	−	22.3853i	0.658216	−	0.905612i
$612$		0			0
$613$	2.67825	−	9.99538i	0.108174	−	0.403710i	−0.890512	−	0.454959i	$-0.849654\pi$
$613$	2.67825	−	9.99538i	0.108174	−	0.403710i	0.998686	+	0.0512497i	$0.0163204\pi$
$614$	−3.33683	+	1.92652i	−0.134663	+	0.0777480i
$615$		0			0
$616$	−3.13916	−	3.13916i	−0.126480	−	0.126480i
$617$	6.69506	+	24.9863i	0.269533	+	1.00591i	0.959417	+	0.281991i	$0.0909949\pi$
$617$	6.69506	+	24.9863i	0.269533	+	1.00591i	−0.689884	+	0.723920i	$0.742338\pi$
$618$		0			0
$619$	−23.6003	+	23.6003i	−0.948574	+	0.948574i	−0.998741	−	0.0501664i	$-0.984025\pi$
$619$	−23.6003	+	23.6003i	−0.948574	+	0.948574i	0.0501664	+	0.998741i	$0.484025\pi$
$620$	4.74703	+	2.74070i	0.190645	+	0.110069i
$621$		0			0
$622$	−3.44066	−	0.921922i	−0.137958	−	0.0369657i
$623$	13.3604			0.535272
$624$		0			0
$625$	−12.2898			−0.491591
$626$	−0.374210	−	0.100269i	−0.0149565	−	0.00400757i
$627$		0			0
$628$	−28.8335	−	16.6470i	−1.15058	−	0.664289i
$629$	−8.39914	+	8.39914i	−0.334895	+	0.334895i
$630$		0			0
$631$	−3.78942	−	14.1423i	−0.150854	−	0.562996i	−0.999425	−	0.0339135i	$-0.989203\pi$
$631$	−3.78942	−	14.1423i	−0.150854	−	0.562996i	0.848570	−	0.529082i	$-0.177464\pi$
$632$	1.88231	+	1.88231i	0.0748741	+	0.0748741i
$633$		0			0
$634$	0.397155	−	0.229297i	0.0157730	−	0.00910656i
$635$	−1.64030	+	6.12169i	−0.0650934	+	0.242932i
$636$		0			0
$637$	−10.8992	−	13.4644i	−0.431841	−	0.533477i
$638$			1.02671i			0.0406479i
$639$		0			0
$640$	−2.24884	−	3.89511i	−0.0888932	−	0.153968i
$641$	1.25270	−	2.16975i	0.0494788	−	0.0856998i	−0.840225	−	0.542237i	$-0.817577\pi$
$641$	1.25270	−	2.16975i	0.0494788	−	0.0856998i	0.889704	+	0.456538i	$0.150911\pi$
$642$		0			0
$643$	4.82626	−	1.29319i	0.190329	−	0.0509985i	−0.162395	−	0.986726i	$-0.551922\pi$
$643$	4.82626	−	1.29319i	0.190329	−	0.0509985i	0.352724	+	0.935727i	$0.385255\pi$
$644$	−21.2161	+	5.68484i	−0.836032	+	0.224014i
$645$		0			0
$646$	−0.820825	+	1.42171i	−0.0322949	+	0.0559365i
$647$	2.98289	+	5.16652i	0.117270	+	0.203117i	0.918685	−	0.394992i	$-0.129252\pi$
$647$	2.98289	+	5.16652i	0.117270	+	0.203117i	−0.801415	+	0.598109i	$0.795919\pi$
$648$		0			0
$649$			22.9971i			0.902716i
$650$	2.24004	+	0.235849i	0.0878617	+	0.00925075i
$651$		0			0
$652$	7.98066	−	29.7842i	0.312547	−	1.16644i
$653$	−24.2072	+	13.9760i	−0.947300	+	0.546924i	−0.892241	−	0.451559i	$-0.850868\pi$
$653$	−24.2072	+	13.9760i	−0.947300	+	0.546924i	−0.0550589	+	0.998483i	$0.517535\pi$
$654$		0			0
$655$	9.27331	+	9.27331i	0.362338	+	0.362338i
$656$	9.44319	+	35.2424i	0.368694	+	1.37599i
$657$		0			0
$658$	−1.22574	+	1.22574i	−0.0477845	+	0.0477845i
$659$	26.8351	+	15.4933i	1.04535	+	0.603532i	0.921344	−	0.388749i	$-0.127093\pi$
$659$	26.8351	+	15.4933i	1.04535	+	0.603532i	0.124005	+	0.992282i	$0.460426\pi$
$660$		0			0
$661$	−31.6260	−	8.47417i	−1.23011	−	0.329607i	−0.415488	−	0.909599i	$-0.636389\pi$
$661$	−31.6260	−	8.47417i	−1.23011	−	0.329607i	−0.814622	+	0.579992i	$0.803056\pi$
$662$	3.51323			0.136546
$663$		0			0
$664$	5.91755			0.229646
$665$	−2.36831	−	0.634588i	−0.0918393	−	0.0246083i
$666$		0			0
$667$	8.85009	+	5.10960i	0.342677	+	0.197845i
$668$	−17.7759	+	17.7759i	−0.687772	+	0.687772i
$669$		0			0
$670$	0.0746976	+	0.278775i	0.00288582	+	0.0107700i
$671$	10.7910	+	10.7910i	0.416581	+	0.416581i
$672$		0			0
$673$	10.4892	−	6.05594i	0.404329	−	0.233439i	−0.284021	−	0.958818i	$-0.591669\pi$
$673$	10.4892	−	6.05594i	0.404329	−	0.233439i	0.688350	+	0.725379i	$0.258335\pi$
$674$	0.834387	−	3.11398i	0.0321394	−	0.119946i
$675$		0			0
$676$	25.1345	+	5.35203i	0.966710	+	0.205847i
$677$		−	14.4287i		−	0.554539i	−0.960792	−	0.277269i	$-0.910571\pi$
$677$		−	14.4287i		−	0.554539i	0.960792	−	0.277269i	$-0.0894294\pi$
$678$		0			0
$679$	9.60647	+	16.6389i	0.368663	+	0.638542i
$680$	−1.77842	+	3.08031i	−0.0681993	+	0.118125i
$681$		0			0
$682$	−2.12530	+	0.569472i	−0.0813818	+	0.0218062i
$683$	−15.1105	+	4.04885i	−0.578187	+	0.154925i	−0.536049	−	0.844187i	$-0.680084\pi$
$683$	−15.1105	+	4.04885i	−0.578187	+	0.154925i	−0.0421385	+	0.999112i	$0.513417\pi$
$684$		0			0
$685$	9.91112	−	17.1666i	0.378684	−	0.655901i
$686$	1.33304	+	2.30888i	0.0508955	+	0.0881536i
$687$		0			0
$688$			28.1629i			1.07370i
$689$	28.6956	−	4.53960i	1.09322	−	0.172945i
$690$		0			0
$691$	−9.29933	+	34.7056i	−0.353763	+	1.32026i	0.528271	+	0.849076i	$0.322841\pi$
$691$	−9.29933	+	34.7056i	−0.353763	+	1.32026i	−0.882034	+	0.471186i	$0.843826\pi$
$692$	0.841688	−	0.485949i	0.0319962	−	0.0184730i
$693$		0			0
$694$	0.705064	+	0.705064i	0.0267639	+	0.0267639i
$695$	2.12917	+	7.94619i	0.0807642	+	0.301416i
$696$		0			0
$697$	41.2932	−	41.2932i	1.56409	−	1.56409i
$698$	−0.301351	−	0.173985i	−0.0114063	−	0.00658543i
$699$		0			0
$700$	11.5955	+	3.10699i	0.438267	+	0.117433i
$701$	−48.6512			−1.83753			−0.918764	−	0.394806i	$-0.870812\pi$
$701$	−48.6512			−1.83753			−0.918764	+	0.394806i	$0.870812\pi$
$702$		0			0
$703$	3.34966			0.126335
$704$	−35.5586	−	9.52790i	−1.34016	−	0.359096i
$705$		0			0
$706$	1.64711	+	0.950957i	0.0619896	+	0.0357897i
$707$	11.6839	−	11.6839i	0.439419	−	0.439419i
$708$		0			0
$709$	−2.87875	−	10.7437i	−0.108114	−	0.403487i	0.890566	−	0.454854i	$-0.150309\pi$
$709$	−2.87875	−	10.7437i	−0.108114	−	0.403487i	−0.998680	+	0.0513677i	$0.983642\pi$
$710$	−0.152304	−	0.152304i	−0.00571586	−	0.00571586i
$711$		0			0
$712$	−4.73336	+	2.73280i	−0.177390	+	0.102416i
$713$	−5.66814	+	21.1538i	−0.212274	+	0.792216i
$714$		0			0
$715$	−13.1523	+	10.6466i	−0.491869	+	0.398160i
$716$			27.5113i			1.02814i
$717$		0			0
$718$	−0.561707	−	0.972906i	−0.0209627	−	0.0363085i
$719$	−24.3322	+	42.1446i	−0.907438	+	1.57173i	−0.0898263	+	0.995957i	$0.528631\pi$
$719$	−24.3322	+	42.1446i	−0.907438	+	1.57173i	−0.817611	+	0.575771i	$0.804702\pi$
$720$		0			0
$721$	8.26518	−	2.21465i	0.307811	−	0.0824778i
$722$	−2.35023	+	0.629741i	−0.0874663	+	0.0234365i
$723$		0			0
$724$	13.2171	−	22.8926i	0.491208	−	0.850797i
$725$	−2.79260	−	4.83693i	−0.103715	−	0.179639i
$726$		0			0
$727$		−	15.4306i		−	0.572289i	−0.958186	−	0.286145i	$-0.907626\pi$
$727$		−	15.4306i		−	0.572289i	0.958186	−	0.286145i	$-0.0923738\pi$
$728$	−3.02307	−	1.16108i	−0.112042	−	0.0430323i
$729$		0			0
$730$	−0.373470	+	1.39381i	−0.0138227	+	0.0515872i
$731$	39.0372	−	22.5381i	1.44384	−	0.833603i
$732$		0			0
$733$	−16.9955	−	16.9955i	−0.627743	−	0.627743i	0.319756	−	0.947500i	$-0.396399\pi$
$733$	−16.9955	−	16.9955i	−0.627743	−	0.627743i	−0.947500	+	0.319756i	$0.896399\pi$
$734$	0.999829	+	3.73141i	0.0369043	+	0.137729i
$735$		0			0
$736$	9.54912	−	9.54912i	0.351985	−	0.351985i
$737$	8.53624	+	4.92840i	0.314437	+	0.181540i
$738$		0			0
$739$	9.04957	+	2.42482i	0.332894	+	0.0891986i	0.421394	−	0.906878i	$-0.361541\pi$
$739$	9.04957	+	2.42482i	0.332894	+	0.0891986i	−0.0885006	+	0.996076i	$0.528208\pi$
$740$	3.60753			0.132615
$741$		0			0
$742$	−1.81985			−0.0668088
$743$	−2.47489	−	0.663145i	−0.0907949	−	0.0243284i	0.213136	−	0.977023i	$-0.431632\pi$
$743$	−2.47489	−	0.663145i	−0.0907949	−	0.0243284i	−0.303930	+	0.952694i	$0.598299\pi$
$744$		0			0
$745$	−16.1928	−	9.34892i	−0.593259	−	0.342518i
$746$	1.73043	−	1.73043i	0.0633554	−	0.0633554i
$747$		0			0
$748$	15.6283	+	58.3256i	0.571427	+	2.13260i
$749$	−7.19788	−	7.19788i	−0.263005	−	0.263005i
$750$		0			0
$751$	−33.4720	+	19.3250i	−1.22141	+	0.705181i	−0.965218	−	0.261445i	$-0.915801\pi$
$751$	−33.4720	+	19.3250i	−1.22141	+	0.705181i	−0.256191	+	0.966626i	$0.582468\pi$
$752$	−7.67012	+	28.6253i	−0.279700	+	1.04386i
$753$		0			0
$754$	0.304497	+	0.684245i	0.0110891	+	0.0249187i
$755$		−	23.1367i		−	0.842032i
$756$		0			0
$757$	−23.9936	−	41.5582i	−0.872063	−	1.51046i	−0.859858	−	0.510532i	$-0.829448\pi$
$757$	−23.9936	−	41.5582i	−0.872063	−	1.51046i	−0.0122049	−	0.999926i	$-0.503885\pi$
$758$	2.71088	−	4.69537i	0.0984634	−	0.170544i
$759$		0			0
$760$	0.968856	−	0.259604i	0.0351441	−	0.00941683i
$761$	12.5377	−	3.35947i	0.454492	−	0.121781i	−0.0243083	−	0.999705i	$-0.507738\pi$
$761$	12.5377	−	3.35947i	0.454492	−	0.121781i	0.478801	+	0.877924i	$0.341072\pi$
$762$		0			0
$763$	−9.67863	+	16.7639i	−0.350390	+	0.606893i
$764$	10.0418	+	17.3930i	0.363301	+	0.629256i
$765$		0			0
$766$			2.47987i			0.0896015i
$767$	6.82037	+	15.3263i	0.246269	+	0.553400i
$768$		0			0
$769$	−0.735475	+	2.74483i	−0.0265219	+	0.0989811i	−0.977918	−	0.208989i	$-0.932983\pi$
$769$	−0.735475	+	2.74483i	−0.0265219	+	0.0989811i	0.951396	+	0.307970i	$0.0996495\pi$
$770$	0.917951	−	0.529979i	0.0330807	−	0.0190991i
$771$		0			0
$772$	−8.31947	−	8.31947i	−0.299424	−	0.299424i
$773$	8.82250	+	32.9260i	0.317323	+	1.18427i	0.921807	+	0.387649i	$0.126713\pi$
$773$	8.82250	+	32.9260i	0.317323	+	1.18427i	−0.604484	+	0.796617i	$0.706621\pi$
$774$		0			0
$775$	8.46353	−	8.46353i	0.304019	−	0.304019i
$776$	−6.80682	−	3.92992i	−0.244351	−	0.141076i
$777$		0			0
$778$	−3.34138	−	0.895319i	−0.119794	−	0.0320988i
$779$	−16.4681			−0.590032
$780$		0			0
$781$	−7.35616			−0.263224
$782$	−6.82318	−	1.82827i	−0.243996	−	0.0653786i
$783$		0			0
$784$	16.0655	+	9.27541i	0.573767	+	0.331265i
$785$	11.3080	−	11.3080i	0.403601	−	0.403601i
$786$		0			0
$787$	4.84557	+	18.0839i	0.172726	+	0.644622i	0.996928	+	0.0783261i	$0.0249575\pi$
$787$	4.84557	+	18.0839i	0.172726	+	0.644622i	−0.824202	+	0.566296i	$0.808376\pi$
$788$	−33.2899	−	33.2899i	−1.18590	−	1.18590i
$789$		0			0
$790$	−0.550423	+	0.317787i	−0.0195832	+	0.0113064i
$791$	−0.686977	+	2.56383i	−0.0244261	+	0.0911594i
$792$		0			0
$793$	10.3919	+	3.99124i	0.369027	+	0.141733i
$794$			4.74583i			0.168423i
$795$		0			0
$796$	−6.57395	−	11.3864i	−0.233008	−	0.403581i
$797$	−6.29804	+	10.9085i	−0.223088	+	0.386400i	−0.955744	−	0.294199i	$-0.904947\pi$
$797$	−6.29804	+	10.9085i	−0.223088	+	0.386400i	0.732656	+	0.680599i	$0.238280\pi$
$798$		0			0
$799$	45.8164	−	12.2765i	1.62087	−	0.434310i
$800$	−7.12925	+	1.91028i	−0.252057	+	0.0675385i
$801$		0			0
$802$	1.47035	−	2.54673i	0.0519200	−	0.0899280i
$803$	24.6408	+	42.6792i	0.869556	+	1.50611i
$804$		0			0
$805$		−	10.5501i		−	0.371843i
$806$	−1.24750	+	1.00983i	−0.0439413	+	0.0355697i
$807$		0			0
$808$	−1.74952	+	6.52930i	−0.0615480	+	0.229700i
$809$	14.4342	−	8.33357i	0.507478	−	0.292993i	−0.224318	−	0.974516i	$-0.572016\pi$
$809$	14.4342	−	8.33357i	0.507478	−	0.292993i	0.731796	+	0.681523i	$0.238682\pi$
$810$		0			0
$811$	21.9255	+	21.9255i	0.769910	+	0.769910i	0.978090	−	0.208180i	$-0.0667541\pi$
$811$	21.9255	+	21.9255i	0.769910	+	0.769910i	−0.208180	+	0.978090i	$0.566754\pi$
$812$	1.03309	+	3.85553i	0.0362542	+	0.135303i
$813$		0			0
$814$	−1.02395	+	1.02395i	−0.0358894	+	0.0358894i
$815$	12.8265	+	7.40540i	0.449294	+	0.259400i
$816$		0			0
$817$	−12.2784	−	3.28999i	−0.429568	−	0.115102i
$818$	3.77075			0.131841
$819$		0			0
$820$	−17.7359			−0.619364
$821$	−36.9934	−	9.91235i	−1.29108	−	0.345943i	−0.453008	−	0.891506i	$-0.649649\pi$
$821$	−36.9934	−	9.91235i	−1.29108	−	0.345943i	−0.838070	+	0.545563i	$0.816316\pi$
$822$		0			0
$823$	−1.44876	−	0.836444i	−0.0505007	−	0.0291566i	0.474537	−	0.880236i	$-0.342615\pi$
$823$	−1.44876	−	0.836444i	−0.0505007	−	0.0291566i	−0.525038	+	0.851079i	$0.675949\pi$
$824$	−2.47522	+	2.47522i	−0.0862283	+	0.0862283i
$825$		0			0
$826$	−0.271970	−	1.01500i	−0.00946303	−	0.0353165i
$827$	4.77029	+	4.77029i	0.165879	+	0.165879i	0.785165	−	0.619286i	$-0.212578\pi$
$827$	4.77029	+	4.77029i	0.165879	+	0.165879i	−0.619286	+	0.785165i	$0.712578\pi$
$828$		0			0
$829$	−34.5519	+	19.9485i	−1.20004	+	0.692842i	−0.960563	−	0.278061i	$-0.910308\pi$
$829$	−34.5519	+	19.9485i	−1.20004	+	0.692842i	−0.239473	+	0.970903i	$0.576975\pi$
$830$	−0.365678	+	1.36473i	−0.0126929	+	0.0473705i
$831$		0			0
$832$	−26.5235	+	4.19598i	−0.919537	+	0.145469i
$833$		−	29.6916i		−	1.02875i
$834$		0			0
$835$	−6.03744	−	10.4572i	−0.208934	−	0.361885i
$836$	8.51406	−	14.7468i	0.294465	−	0.510028i
$837$		0			0
$838$	−0.0610151	+	0.0163490i	−0.00210773	+	0.000564765i
$839$	−40.7025	+	10.9062i	−1.40521	+	0.376524i	−0.880211	−	0.474582i	$-0.842599\pi$
$839$	−40.7025	+	10.9062i	−1.40521	+	0.376524i	−0.524995	+	0.851106i	$0.675933\pi$
$840$		0			0
$841$	−13.5715	+	23.5064i	−0.467981	+	0.810567i
$842$	1.42057	+	2.46049i	0.0489560	+	0.0847942i
$843$		0			0
$844$		−	45.5886i		−	1.56922i
$845$	−5.60777	+	10.9960i	−0.192913	+	0.378274i
$846$		0			0
$847$	5.15090	−	19.2234i	0.176987	−	0.660525i
$848$	−26.9437	+	15.5560i	−0.925250	+	0.534194i
$849$		0			0
$850$	2.72992	+	2.72992i	0.0936355	+	0.0936355i
$851$	3.73043	+	13.9222i	0.127878	+	0.477245i
$852$		0			0
$853$	−8.52203	+	8.52203i	−0.291789	+	0.291789i	−0.837787	−	0.545998i	$-0.816151\pi$
$853$	−8.52203	+	8.52203i	−0.291789	+	0.291789i	0.545998	+	0.837787i	$0.316151\pi$
$854$	−0.603888	−	0.348655i	−0.0206646	−	0.0119307i
$855$		0			0
$856$	4.02238	+	1.07779i	0.137482	+	0.0368382i
$857$	7.32839			0.250333			0.125166	−	0.992136i	$-0.460053\pi$
$857$	7.32839			0.250333			0.125166	+	0.992136i	$0.460053\pi$
$858$		0			0
$859$	34.4710			1.17614			0.588068	−	0.808811i	$-0.299889\pi$
$859$	34.4710			1.17614			0.588068	+	0.808811i	$0.299889\pi$
$860$	−13.2237	−	3.54327i	−0.450923	−	0.120824i
$861$		0			0
$862$	−0.0285154	−	0.0164634i	−0.000971237	−	0.000560744i
$863$	34.8272	−	34.8272i	1.18553	−	1.18553i	0.207240	−	0.978290i	$-0.433552\pi$
$863$	34.8272	−	34.8272i	1.18553	−	1.18553i	0.978290	−	0.207240i	$-0.0664482\pi$
$864$		0			0
$865$	0.120824	+	0.450920i	0.00410813	+	0.0153317i
$866$	2.07569	+	2.07569i	0.0705349	+	0.0705349i
$867$		0			0
$868$	−7.40795	+	4.27698i	−0.251442	+	0.145170i
$869$	−5.61808	+	20.9670i	−0.190580	+	0.711256i
$870$		0			0
$871$	7.15056	+	0.752865i	0.242287	+	0.0255099i
$872$		−	7.91888i		−	0.268167i
$873$		0			0
$874$	0.996011	+	1.72514i	0.0336906	+	0.0583538i
$875$	−6.40024	+	11.0855i	−0.216368	+	0.374760i
$876$		0			0
$877$	13.8842	−	3.72027i	0.468837	−	0.125625i	−0.0166629	−	0.999861i	$-0.505304\pi$
$877$	13.8842	−	3.72027i	0.468837	−	0.125625i	0.485500	+	0.874237i	$0.338638\pi$
$878$	−1.20754	+	0.323559i	−0.0407524	+	0.0109196i
$879$		0			0
$880$	9.06046	−	15.6932i	0.305428	−	0.529017i
$881$	12.6911	+	21.9816i	0.427574	+	0.740580i	0.996657	−	0.0817002i	$-0.0260350\pi$
$881$	12.6911	+	21.9816i	0.427574	+	0.740580i	−0.569083	+	0.822280i	$0.692702\pi$
$882$		0			0
$883$		−	16.0718i		−	0.540860i	−0.962740	−	0.270430i	$-0.912834\pi$
$883$		−	16.0718i		−	0.540860i	0.962740	−	0.270430i	$-0.0871658\pi$
$884$	27.7133	+	34.2357i	0.932099	+	1.15147i
$885$		0			0
$886$	0.604560	−	2.25625i	0.0203106	−	0.0758001i
$887$	41.4102	−	23.9082i	1.39042	−	0.802758i	0.397057	−	0.917794i	$-0.370032\pi$
$887$	41.4102	−	23.9082i	1.39042	−	0.802758i	0.993361	+	0.115036i	$0.0366983\pi$
$888$		0			0
$889$	−6.99341	−	6.99341i	−0.234551	−	0.234551i
$890$	−0.337750	−	1.26050i	−0.0113214	−	0.0422521i
$891$		0			0
$892$	−16.1712	+	16.1712i	−0.541451	+	0.541451i
$893$	−11.5840	−	6.68802i	−0.387644	−	0.223806i
$894$		0			0
$895$	−12.7641	−	3.42013i	−0.426657	−	0.114322i
$896$	7.01884			0.234483
$897$		0			0
$898$	−2.56533			−0.0856062
$899$	3.84420	+	1.03005i	0.128211	+	0.0343541i
$900$		0			0
$901$	43.1249	+	24.8982i	1.43670	+	0.829479i
$902$	5.03411	−	5.03411i	0.167618	−	0.167618i
$903$		0			0
$904$	−0.281036	−	1.04884i	−0.00934712	−	0.0348839i
$905$	8.97811	+	8.97811i	0.298443	+	0.298443i
$906$		0			0
$907$	−12.0722	+	6.96988i	−0.400850	+	0.231431i	−0.686851	−	0.726798i	$-0.741007\pi$
$907$	−12.0722	+	6.96988i	−0.400850	+	0.231431i	0.286001	+	0.958229i	$0.407674\pi$
$908$	−7.80048	+	29.1118i	−0.258868	+	0.966109i
$909$		0			0
$910$	0.454584	−	0.625442i	0.0150693	−	0.0207332i
$911$		−	31.5432i		−	1.04507i	−0.852617	−	0.522537i	$-0.824986\pi$
$911$		−	31.5432i		−	1.04507i	0.852617	−	0.522537i	$-0.175014\pi$
$912$		0			0
$913$	24.1268	+	41.7888i	0.798479	+	1.38301i
$914$	−1.87918	+	3.25484i	−0.0621578	+	0.107660i
$915$		0			0
$916$	−3.44692	+	0.923600i	−0.113890	+	0.0305166i
$917$	−19.7683	+	5.29691i	−0.652808	+	0.174919i
$918$		0			0
$919$	7.99043	−	13.8398i	0.263580	−	0.456534i	−0.703611	−	0.710586i	$-0.748430\pi$
$919$	7.99043	−	13.8398i	0.263580	−	0.456534i	0.967191	+	0.254052i	$0.0817633\pi$
$920$	2.15798	+	3.73773i	0.0711465	+	0.123229i
$921$		0			0
$922$			2.48318i			0.0817791i
$923$	−4.90247	+	2.18165i	−0.161367	+	0.0718100i
$924$		0			0
$925$	2.03883	−	7.60901i	0.0670363	−	0.250183i
$926$	0.238325	−	0.137597i	0.00783183	−	0.00452171i
$927$		0			0
$928$	−1.73533	−	1.73533i	−0.0569649	−	0.0569649i
$929$	−1.12894	−	4.21325i	−0.0370392	−	0.138232i	0.944930	−	0.327272i	$-0.106129\pi$
$929$	−1.12894	−	4.21325i	−0.0370392	−	0.138232i	−0.981969	+	0.189039i	$0.939463\pi$
$930$		0			0
$931$	−5.92066	+	5.92066i	−0.194042	+	0.194042i
$932$	−5.62356	−	3.24676i	−0.184206	−	0.106351i
$933$		0			0
$934$	2.11171	+	0.565830i	0.0690972	+	0.0185145i
$935$	−29.0035			−0.948517
$936$		0			0
$937$	−10.2822			−0.335905			−0.167952	−	0.985795i	$-0.553715\pi$
$937$	−10.2822			−0.335905			−0.167952	+	0.985795i	$0.553715\pi$
$938$	−0.435041	−	0.116569i	−0.0142046	−	0.00380611i
$939$		0			0
$940$	−12.4758	−	7.20289i	−0.406915	−	0.234932i
$941$	14.5097	−	14.5097i	0.473004	−	0.473004i	−0.429881	−	0.902885i	$-0.641445\pi$
$941$	14.5097	−	14.5097i	0.473004	−	0.473004i	0.902885	+	0.429881i	$0.141445\pi$
$942$		0			0
$943$	−18.3401	−	68.4463i	−0.597237	−	2.22892i
$944$	−12.7028	−	12.7028i	−0.413442	−	0.413442i
$945$		0			0
$946$	4.75908	−	2.74766i	0.154731	−	0.0893340i
$947$	7.71523	−	28.7936i	0.250711	−	0.935667i	−0.719715	−	0.694269i	$-0.755728\pi$
$947$	7.71523	−	28.7936i	0.250711	−	0.935667i	0.970426	−	0.241397i	$-0.0776057\pi$
$948$		0			0
$949$	29.0793	+	21.1354i	0.943953	+	0.686084i
$950$		−	1.08872i		−	0.0353227i
$951$		0			0
$952$	−2.77531	−	4.80697i	−0.0899482	−	0.155795i
$953$	9.00065	−	15.5896i	0.291560	−	0.504996i	−0.682619	−	0.730774i	$-0.739159\pi$
$953$	9.00065	−	15.5896i	0.291560	−	0.504996i	0.974179	+	0.225778i	$0.0724924\pi$
$954$		0			0
$955$	−9.31800	+	2.49675i	−0.301523	+	0.0807929i
$956$	37.8749	−	10.1485i	1.22496	−	0.328227i
$957$		0			0
$958$	1.43413	−	2.48398i	0.0463346	−	0.0802538i
$959$	15.4668	+	26.7892i	0.499448	+	0.865068i
$960$		0			0
$961$		−	22.4712i		−	0.724876i
$962$	−0.378727	+	0.986083i	−0.0122106	+	0.0317926i
$963$		0			0
$964$	−11.4420	+	42.7021i	−0.368522	+	1.37534i
$965$	4.89414	−	2.82563i	0.157548	−	0.0909604i
$966$		0			0
$967$	28.6465	+	28.6465i	0.921208	+	0.921208i	0.997115	−	0.0759068i	$-0.0241851\pi$
$967$	28.6465	+	28.6465i	0.921208	+	0.921208i	−0.0759068	+	0.997115i	$0.524185\pi$
$968$	2.10719	+	7.86413i	0.0677276	+	0.252763i
$969$		0			0
$970$	1.32697	−	1.32697i	0.0426063	−	0.0426063i
$971$	8.62921	+	4.98208i	0.276925	+	0.159883i	0.632030	−	0.774944i	$-0.282222\pi$
$971$	8.62921	+	4.98208i	0.276925	+	0.159883i	−0.355106	+	0.934826i	$0.615555\pi$
$972$		0			0
$973$	−12.4004	−	3.32267i	−0.397538	−	0.106520i
$974$	−4.99351			−0.160002
$975$		0			0
$976$	−11.9211			−0.381586
$977$	−53.7209	−	14.3945i	−1.71869	−	0.460520i	−0.741158	−	0.671330i	$-0.765723\pi$
$977$	−53.7209	−	14.3945i	−1.71869	−	0.460520i	−0.977527	+	0.210810i	$0.932390\pi$
$978$		0			0
$979$	−38.5972	−	22.2841i	−1.23357	−	0.712203i
$980$	−6.37645	+	6.37645i	−0.203688	+	0.203688i
$981$		0			0
$982$	−1.09788	−	4.09735i	−0.0350348	−	0.130752i
$983$	−4.17351	−	4.17351i	−0.133114	−	0.133114i	0.637410	−	0.770525i	$-0.280006\pi$
$983$	−4.17351	−	4.17351i	−0.133114	−	0.133114i	−0.770525	+	0.637410i	$0.780006\pi$
$984$		0			0
$985$	19.5837	−	11.3066i	0.623987	−	0.360259i
$986$	−0.332244	+	1.23995i	−0.0105808	+	0.0394881i
$987$		0			0
$988$	1.30061	−	12.3529i	0.0413780	−	0.393000i
$989$		−	54.6967i		−	1.73925i
$990$		0			0
$991$	−27.1227	−	46.9780i	−0.861582	−	1.49230i	−0.870401	−	0.492343i	$-0.836140\pi$
$991$	−27.1227	−	46.9780i	−0.861582	−	1.49230i	0.00881858	−	0.999961i	$-0.497193\pi$
$992$	2.62962	−	4.55464i	0.0834907	−	0.144610i
$993$		0			0
$994$	0.324673	−	0.0869958i	0.0102980	−	0.00275934i
$995$	6.10008	−	1.63451i	0.193386	−	0.0518175i
$996$		0			0
$997$	−13.9771	+	24.2090i	−0.442659	+	0.766708i	−0.997886	−	0.0649911i	$-0.979298\pi$
$997$	−13.9771	+	24.2090i	−0.442659	+	0.766708i	0.555227	+	0.831699i	$0.312631\pi$
$998$	−2.02351	−	3.50482i	−0.0640530	−	0.110943i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.bd.e.323.3	yes	20
3.2	odd	2		351.2.bd.d.323.3	yes	20
13.6	odd	12		351.2.bd.d.188.3	✓	20
39.32	even	12	inner	351.2.bd.e.188.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.bd.d.188.3	✓	20	13.6	odd	12
351.2.bd.d.323.3	yes	20	3.2	odd	2
351.2.bd.e.188.3	yes	20	39.32	even	12	inner
351.2.bd.e.323.3	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)

\(f(q)\)	\(=\)	\(q+(0.147232 + 0.0394506i) q^{2} +(-1.71193 - 0.988383i) q^{4} +(0.671392 - 0.671392i) q^{5} +(0.383498 + 1.43124i) q^{7} +(-0.428620 - 0.428620i) q^{8} +O(q^{10})\)	\(q+(0.147232 + 0.0394506i) q^{2} +(-1.71193 - 0.988383i) q^{4} +(0.671392 - 0.671392i) q^{5} +(0.383498 + 1.43124i) q^{7} +(-0.428620 - 0.428620i) q^{8} +(0.125337 - 0.0723632i) q^{10} +(1.27929 - 4.77439i) q^{11} +(-0.563387 - 3.56126i) q^{13} +0.225852i q^{14} +(1.93057 + 3.34384i) q^{16} +(3.08999 - 5.35201i) q^{17} +(-1.68338 + 0.451059i) q^{19} +(-1.81297 + 0.485783i) q^{20} +(0.376704 - 0.652471i) q^{22} +(-3.74947 - 6.49427i) q^{23} +4.09847i q^{25} +(0.0575456 - 0.546556i) q^{26} +(0.758087 - 2.82922i) q^{28} +(-1.18018 + 0.681377i) q^{29} +(-2.06505 - 2.06505i) q^{31} +(0.466095 + 1.73949i) q^{32} +(0.666083 - 0.666083i) q^{34} +(1.21840 + 0.703442i) q^{35} +(-1.85655 - 0.497461i) q^{37} -0.265641 q^{38} -0.575543 q^{40} +(9.12748 + 2.44570i) q^{41} +(6.31673 + 3.64696i) q^{43} +(-6.90898 + 6.90898i) q^{44} +(-0.295837 - 1.10408i) q^{46} +(5.42720 + 5.42720i) q^{47} +(4.16081 - 2.40225i) q^{49} +(-0.161687 + 0.603423i) q^{50} +(-2.55541 + 6.65348i) q^{52} +8.05770i q^{53} +(-2.34658 - 4.06439i) q^{55} +(0.449081 - 0.777831i) q^{56} +(-0.200640 + 0.0537614i) q^{58} +(-4.49411 + 1.20419i) q^{59} +(-1.54373 + 2.67382i) q^{61} +(-0.222573 - 0.385507i) q^{62} -7.44778i q^{64} +(-2.76926 - 2.01275i) q^{65} +(-0.516129 + 1.92622i) q^{67} +(-10.5797 + 6.10818i) q^{68} +(0.151635 + 0.151635i) q^{70} +(-0.385189 - 1.43754i) q^{71} +(-7.05012 + 7.05012i) q^{73} +(-0.253718 - 0.146484i) q^{74} +(3.32764 + 0.891639i) q^{76} +7.32388 q^{77} -4.39155 q^{79} +(3.54120 + 0.948861i) q^{80} +(1.24737 + 0.720168i) q^{82} +(-6.90303 + 6.90303i) q^{83} +(-1.51871 - 5.66789i) q^{85} +(0.786147 + 0.786147i) q^{86} +(-2.59473 + 1.49807i) q^{88} +(2.33371 - 8.70954i) q^{89} +(4.88095 - 2.17208i) q^{91} +14.8236i q^{92} +(0.584948 + 1.01316i) q^{94} +(-0.827367 + 1.43304i) q^{95} +(12.5248 - 3.35601i) q^{97} +(0.707373 - 0.189540i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{5}+O(q^{10}) \) 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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