LMFDB - Embedded newform 2064.2.bg.e.1039.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2064,2,Mod(1039,2064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2064, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 5]))

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

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

chi := DirichletCharacter("2064.1039");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2064 = 2^{4} \cdot 3 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2064.bg (of order $6$, degree $2$, 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:	$16.4811229772$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1039.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2064.1039
Dual form			2064.2.bg.e.1327.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +1.73205i q^{11} +(2.00000 - 3.46410i) q^{13} +(1.50000 - 2.59808i) q^{17} +(2.50000 + 4.33013i) q^{19} -2.00000 q^{21} +(-2.50000 + 4.33013i) q^{25} -1.00000 q^{27} +(6.00000 + 3.46410i) q^{29} +(6.00000 - 3.46410i) q^{31} +(-1.50000 + 0.866025i) q^{33} +(-9.00000 + 5.19615i) q^{37} +4.00000 q^{39} +3.00000 q^{41} +(-6.50000 + 0.866025i) q^{43} +10.3923i q^{47} +(1.50000 + 2.59808i) q^{49} +3.00000 q^{51} +(-6.00000 - 10.3923i) q^{53} +(-2.50000 + 4.33013i) q^{57} +12.1244i q^{59} +(6.00000 + 3.46410i) q^{61} +(-1.00000 - 1.73205i) q^{63} +(-7.50000 + 4.33013i) q^{67} +(-3.00000 + 5.19615i) q^{71} +(-7.50000 - 4.33013i) q^{73} -5.00000 q^{75} +(-3.00000 - 1.73205i) q^{77} +(-0.500000 - 0.866025i) q^{81} +(9.00000 - 5.19615i) q^{83} +6.92820i q^{87} +(-13.5000 + 7.79423i) q^{89} +(4.00000 + 6.92820i) q^{91} +(6.00000 + 3.46410i) q^{93} -17.0000 q^{97} +(-1.50000 - 0.866025i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} - 2 q^{7} - q^{9}+O(q^{10}) $ 2 * q + q^3 - 2 * q^7 - q^9	$ 2 q + q^{3} - 2 q^{7} - q^{9} + 4 q^{13} + 3 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{25} - 2 q^{27} + 12 q^{29} + 12 q^{31} - 3 q^{33} - 18 q^{37} + 8 q^{39} + 6 q^{41} - 13 q^{43} + 3 q^{49} + 6 q^{51} - 12 q^{53} - 5 q^{57} + 12 q^{61} - 2 q^{63} - 15 q^{67} - 6 q^{71} - 15 q^{73} - 10 q^{75} - 6 q^{77} - q^{81} + 18 q^{83} - 27 q^{89} + 8 q^{91} + 12 q^{93} - 34 q^{97} - 3 q^{99}+O(q^{100}) $ 2 * q + q^3 - 2 * q^7 - q^9 + 4 * q^13 + 3 * q^17 + 5 * q^19 - 4 * q^21 - 5 * q^25 - 2 * q^27 + 12 * q^29 + 12 * q^31 - 3 * q^33 - 18 * q^37 + 8 * q^39 + 6 * q^41 - 13 * q^43 + 3 * q^49 + 6 * q^51 - 12 * q^53 - 5 * q^57 + 12 * q^61 - 2 * q^63 - 15 * q^67 - 6 * q^71 - 15 * q^73 - 10 * q^75 - 6 * q^77 - q^81 + 18 * q^83 - 27 * q^89 + 8 * q^91 + 12 * q^93 - 34 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2064\mathbb{Z}\right)^\times$.

$n$	$433$	$517$	$689$	$1807$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$-1$

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			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$5$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$6$		0			0
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$			1.73205i			0.522233i	0.965307	+	0.261116i	$0.0840907\pi$
$11$			1.73205i			0.522233i	−0.965307	+	0.261116i	$0.915909\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$		0			0
$21$	−2.00000			−0.436436
$22$		0			0
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$		0			0
$25$	−2.50000	+	4.33013i	−0.500000	+	0.866025i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	6.00000	+	3.46410i	1.11417	+	0.643268i	0.939907	−	0.341431i	$-0.110912\pi$
$29$	6.00000	+	3.46410i	1.11417	+	0.643268i	0.174265	+	0.984699i	$0.444245\pi$
$30$		0			0
$31$	6.00000	−	3.46410i	1.07763	−	0.622171i	0.147375	−	0.989081i	$-0.452918\pi$
$31$	6.00000	−	3.46410i	1.07763	−	0.622171i	0.930257	+	0.366910i	$0.119584\pi$
$32$		0			0
$33$	−1.50000	+	0.866025i	−0.261116	+	0.150756i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−9.00000	+	5.19615i	−1.47959	+	0.854242i	−0.999733	−	0.0231041i	$-0.992645\pi$
$37$	−9.00000	+	5.19615i	−1.47959	+	0.854242i	−0.479858	+	0.877346i	$0.659312\pi$
$38$		0			0
$39$	4.00000			0.640513
$40$		0			0
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$		0			0
$43$	−6.50000	+	0.866025i	−0.991241	+	0.132068i
$43$	−6.50000	+	0.866025i	−0.991241	+	0.132068i
$44$		0			0
$45$		0			0
$46$		0			0
$47$			10.3923i			1.51587i	0.652328	+	0.757937i	$0.273792\pi$
$47$			10.3923i			1.51587i	−0.652328	+	0.757937i	$0.726208\pi$
$48$		0			0
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$		0			0
$51$	3.00000			0.420084
$52$		0			0
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	−0.902557	−	0.430570i	$-0.858312\pi$
$53$	−6.00000	−	10.3923i	−0.824163	−	1.42749i	0.0783936	−	0.996922i	$-0.475021\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.50000	+	4.33013i	−0.331133	+	0.573539i
$58$		0			0
$59$			12.1244i			1.57846i	0.614100	+	0.789228i	$0.289519\pi$
$59$			12.1244i			1.57846i	−0.614100	+	0.789228i	$0.710481\pi$
$60$		0			0
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	6.00000	+	3.46410i	0.768221	+	0.443533i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$		0			0
$63$	−1.00000	−	1.73205i	−0.125988	−	0.218218i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.50000	+	4.33013i	−0.916271	+	0.529009i	−0.882443	−	0.470418i	$-0.844103\pi$
$67$	−7.50000	+	4.33013i	−0.916271	+	0.529009i	−0.0338274	+	0.999428i	$0.510770\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$		0			0
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.00787336	−	0.999969i	$-0.502506\pi$
$73$	−7.50000	−	4.33013i	−0.877809	−	0.506803i	−0.869935	+	0.493166i	$0.835840\pi$
$74$		0			0
$75$	−5.00000			−0.577350
$76$		0			0
$77$	−3.00000	−	1.73205i	−0.341882	−	0.197386i
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	9.00000	−	5.19615i	0.987878	−	0.570352i	0.0832389	−	0.996530i	$-0.473474\pi$
$83$	9.00000	−	5.19615i	0.987878	−	0.570352i	0.904639	+	0.426178i	$0.140140\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			6.92820i			0.742781i
$88$		0			0
$89$	−13.5000	+	7.79423i	−1.43100	+	0.826187i	−0.997197	−	0.0748225i	$-0.976161\pi$
$89$	−13.5000	+	7.79423i	−1.43100	+	0.826187i	−0.433800	+	0.901009i	$0.642828\pi$
$90$		0			0
$91$	4.00000	+	6.92820i	0.419314	+	0.726273i
$92$		0			0
$93$	6.00000	+	3.46410i	0.622171	+	0.359211i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−17.0000			−1.72609			−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000			−1.72609			−0.863044	+	0.505128i	$0.831445\pi$
$98$		0			0
$99$	−1.50000	−	0.866025i	−0.150756	−	0.0870388i
$100$		0			0
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	15.0000	+	8.66025i	1.47799	+	0.853320i	0.999691	−	0.0248745i	$-0.00791862\pi$
$103$	15.0000	+	8.66025i	1.47799	+	0.853320i	0.478303	+	0.878195i	$0.341252\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	5.19615i		−	0.502331i	−0.967944	−	0.251166i	$-0.919186\pi$
$107$		−	5.19615i		−	0.502331i	0.967944	−	0.251166i	$-0.0808138\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$	−9.00000	−	5.19615i	−0.854242	−	0.493197i
$112$		0			0
$113$			8.66025i			0.814688i	0.913275	+	0.407344i	$0.133545\pi$
$113$			8.66025i			0.814688i	−0.913275	+	0.407344i	$0.866455\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.00000	+	3.46410i	0.184900	+	0.320256i
$118$		0			0
$119$	3.00000	+	5.19615i	0.275010	+	0.476331i
$120$		0			0
$121$	8.00000			0.727273
$122$		0			0
$123$	1.50000	+	2.59808i	0.135250	+	0.234261i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$		0			0
$129$	−4.00000	−	5.19615i	−0.352180	−	0.457496i
$130$		0			0
$131$	15.0000			1.31056			0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000			1.31056			0.655278	+	0.755388i	$0.272551\pi$
$132$		0			0
$133$	−10.0000			−0.867110
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	20.7846i		−	1.77575i	−0.460086	−	0.887875i	$-0.652181\pi$
$137$		−	20.7846i		−	1.77575i	0.460086	−	0.887875i	$-0.347819\pi$
$138$		0			0
$139$	10.5000	−	6.06218i	0.890598	−	0.514187i	0.0164602	−	0.999865i	$-0.494760\pi$
$139$	10.5000	−	6.06218i	0.890598	−	0.514187i	0.874138	+	0.485677i	$0.161427\pi$
$140$		0			0
$141$	−9.00000	+	5.19615i	−0.757937	+	0.437595i
$142$		0			0
$143$	6.00000	+	3.46410i	0.501745	+	0.289683i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$		0			0
$149$	15.0000	−	8.66025i	1.22885	−	0.709476i	0.262059	−	0.965052i	$-0.415599\pi$
$149$	15.0000	−	8.66025i	1.22885	−	0.709476i	0.966789	+	0.255576i	$0.0822652\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$		0			0
$153$	1.50000	+	2.59808i	0.121268	+	0.210042i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.00000	+	5.19615i	0.718278	+	0.414698i	0.814119	−	0.580699i	$-0.197221\pi$
$157$	9.00000	+	5.19615i	0.718278	+	0.414698i	−0.0958404	+	0.995397i	$0.530554\pi$
$158$		0			0
$159$	6.00000	−	10.3923i	0.475831	−	0.824163i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	−0.996942	−	0.0781474i	$-0.975100\pi$
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	0.566149	+	0.824303i	$0.308433\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	15.0000	−	8.66025i	1.16073	−	0.670151i	0.209255	−	0.977861i	$-0.432896\pi$
$167$	15.0000	−	8.66025i	1.16073	−	0.670151i	0.951480	+	0.307711i	$0.0995628\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$		0			0
$171$	−5.00000			−0.382360
$172$		0			0
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$		0			0
$175$	−5.00000	−	8.66025i	−0.377964	−	0.654654i
$176$		0			0
$177$	−10.5000	+	6.06218i	−0.789228	+	0.455661i
$178$		0			0
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	0.436870	+	0.899525i	$0.356087\pi$
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	−0.997446	+	0.0714220i	$0.977246\pi$
$180$		0			0
$181$	−10.0000	+	17.3205i	−0.743294	+	1.28742i	0.207693	+	0.978194i	$0.433404\pi$
$181$	−10.0000	+	17.3205i	−0.743294	+	1.28742i	−0.950988	+	0.309229i	$0.899929\pi$
$182$		0			0
$183$			6.92820i			0.512148i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.50000	+	2.59808i	0.329073	+	0.189990i
$188$		0			0
$189$	1.00000	−	1.73205i	0.0727393	−	0.125988i
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	−14.0000			−1.00774			−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000			−1.00774			−0.503871	+	0.863779i	$0.668091\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.00000	−	15.5885i	0.641223	−	1.11063i	−0.343937	−	0.938993i	$-0.611761\pi$
$197$	9.00000	−	15.5885i	0.641223	−	1.11063i	0.985160	−	0.171639i	$-0.0549062\pi$
$198$		0			0
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$		0			0
$201$	−7.50000	−	4.33013i	−0.529009	−	0.305424i
$202$		0			0
$203$	−12.0000	+	6.92820i	−0.842235	+	0.486265i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.50000	+	4.33013i	−0.518786	+	0.299521i
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	−6.00000			−0.411113
$214$		0			0
$215$		0			0
$216$		0			0
$217$			13.8564i			0.940634i
$218$		0			0
$219$		−	8.66025i		−	0.585206i
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$		0			0
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$		0			0
$225$	−2.50000	−	4.33013i	−0.166667	−	0.288675i
$226$		0			0
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.832529	+	0.553981i	$0.186892\pi$
$227$	13.5000	+	23.3827i	0.896026	+	1.55196i	0.0634974	+	0.997982i	$0.479775\pi$
$228$		0			0
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$		0			0
$231$		−	3.46410i		−	0.227921i
$232$		0			0
$233$	7.50000	+	4.33013i	0.491341	+	0.283676i	0.725131	−	0.688611i	$-0.241779\pi$
$233$	7.50000	+	4.33013i	0.491341	+	0.283676i	−0.233789	+	0.972287i	$0.575113\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$		0			0
$241$	−18.0000	−	10.3923i	−1.15948	−	0.669427i	−0.208302	−	0.978065i	$-0.566794\pi$
$241$	−18.0000	−	10.3923i	−1.15948	−	0.669427i	−0.951180	+	0.308637i	$0.900127\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	20.0000			1.27257
$248$		0			0
$249$	9.00000	+	5.19615i	0.570352	+	0.329293i
$250$		0			0
$251$	16.5000	+	9.52628i	1.04147	+	0.601293i	0.920250	−	0.391332i	$-0.127986\pi$
$251$	16.5000	+	9.52628i	1.04147	+	0.601293i	0.121221	+	0.992626i	$0.461319\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$			15.5885i			0.972381i	0.873853	+	0.486191i	$0.161614\pi$
$257$			15.5885i			0.972381i	−0.873853	+	0.486191i	$0.838386\pi$
$258$		0			0
$259$		−	20.7846i		−	1.29149i
$260$		0			0
$261$	−6.00000	+	3.46410i	−0.371391	+	0.214423i
$262$		0			0
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−13.5000	−	7.79423i	−0.826187	−	0.476999i
$268$		0			0
$269$	30.0000			1.82913			0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000			1.82913			0.914566	+	0.404436i	$0.132532\pi$
$270$		0			0
$271$	−18.0000	−	10.3923i	−1.09342	−	0.631288i	−0.158937	−	0.987289i	$-0.550807\pi$
$271$	−18.0000	−	10.3923i	−1.09342	−	0.631288i	−0.934485	+	0.356001i	$0.884140\pi$
$272$		0			0
$273$	−4.00000	+	6.92820i	−0.242091	+	0.419314i
$274$		0			0
$275$	−7.50000	−	4.33013i	−0.452267	−	0.261116i
$276$		0			0
$277$	9.00000	−	5.19615i	0.540758	−	0.312207i	−0.204628	−	0.978840i	$-0.565599\pi$
$277$	9.00000	−	5.19615i	0.540758	−	0.312207i	0.745386	+	0.666633i	$0.232265\pi$
$278$		0			0
$279$			6.92820i			0.414781i
$280$		0			0
$281$	−4.50000	−	7.79423i	−0.268447	−	0.464965i	0.700014	−	0.714130i	$-0.253177\pi$
$281$	−4.50000	−	7.79423i	−0.268447	−	0.464965i	−0.968461	+	0.249165i	$0.919844\pi$
$282$		0			0
$283$	−19.5000	−	11.2583i	−1.15915	−	0.669238i	−0.208053	−	0.978117i	$-0.566713\pi$
$283$	−19.5000	−	11.2583i	−1.15915	−	0.669238i	−0.951101	+	0.308879i	$0.900046\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.00000	+	5.19615i	−0.177084	+	0.306719i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−8.50000	−	14.7224i	−0.498279	−	0.863044i
$292$		0			0
$293$	24.0000			1.40209			0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000			1.40209			0.701047	+	0.713115i	$0.252716\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	1.73205i		−	0.100504i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	5.00000	−	12.1244i	0.288195	−	0.698836i
$302$		0			0
$303$	6.00000			0.344691
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.50000	−	0.866025i	0.0856095	−	0.0494267i	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	1.50000	−	0.866025i	0.0856095	−	0.0494267i	0.542194	+	0.840254i	$0.317594\pi$
$308$		0			0
$309$			17.3205i			0.985329i
$310$		0			0
$311$	15.0000	−	8.66025i	0.850572	−	0.491078i	−0.0102718	−	0.999947i	$-0.503270\pi$
$311$	15.0000	−	8.66025i	0.850572	−	0.491078i	0.860844	+	0.508869i	$0.169936\pi$
$312$		0			0
$313$	6.00000	−	3.46410i	0.339140	−	0.195803i	−0.320752	−	0.947163i	$-0.603935\pi$
$313$	6.00000	−	3.46410i	0.339140	−	0.195803i	0.659892	+	0.751361i	$0.270602\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	24.0000			1.34797			0.673987	−	0.738743i	$-0.264580\pi$
$317$	24.0000			1.34797			0.673987	+	0.738743i	$0.264580\pi$
$318$		0			0
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$		0			0
$321$	4.50000	−	2.59808i	0.251166	−	0.145010i
$322$		0			0
$323$	15.0000			0.834622
$324$		0			0
$325$	10.0000	+	17.3205i	0.554700	+	0.960769i
$326$		0			0
$327$	−1.00000	+	1.73205i	−0.0553001	+	0.0957826i
$328$		0			0
$329$	−18.0000	−	10.3923i	−0.992372	−	0.572946i
$330$		0			0
$331$	5.50000	−	9.52628i	0.302307	−	0.523612i	−0.674351	−	0.738411i	$-0.735576\pi$
$331$	5.50000	−	9.52628i	0.302307	−	0.523612i	0.976658	+	0.214799i	$0.0689098\pi$
$332$		0			0
$333$		−	10.3923i		−	0.569495i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	0.482295	+	0.876009i	$0.339803\pi$
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	−0.999793	+	0.0203242i	$0.993530\pi$
$338$		0			0
$339$	−7.50000	+	4.33013i	−0.407344	+	0.235180i
$340$		0			0
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$		0			0
$343$	−20.0000			−1.07990
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16.5000	+	28.5788i	0.885766	+	1.53419i	0.844833	+	0.535031i	$0.179700\pi$
$347$	16.5000	+	28.5788i	0.885766	+	1.53419i	0.0409337	+	0.999162i	$0.486967\pi$
$348$		0			0
$349$	6.00000	−	3.46410i	0.321173	−	0.185429i	−0.330743	−	0.943721i	$-0.607299\pi$
$349$	6.00000	−	3.46410i	0.321173	−	0.185429i	0.651915	+	0.758292i	$0.273966\pi$
$350$		0			0
$351$	−2.00000	+	3.46410i	−0.106752	+	0.184900i
$352$		0			0
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	−0.823343	−	0.567545i	$-0.807893\pi$
$353$	1.50000	−	2.59808i	0.0798369	−	0.138282i	0.903179	+	0.429263i	$0.141227\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−3.00000	+	5.19615i	−0.158777	+	0.275010i
$358$		0			0
$359$	−21.0000	−	12.1244i	−1.10834	−	0.639899i	−0.169939	−	0.985455i	$-0.554357\pi$
$359$	−21.0000	−	12.1244i	−1.10834	−	0.639899i	−0.938398	+	0.345556i	$0.887690\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$		0			0
$363$	4.00000	+	6.92820i	0.209946	+	0.363636i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	18.0000	−	10.3923i	0.939592	−	0.542474i	0.0497598	−	0.998761i	$-0.484154\pi$
$367$	18.0000	−	10.3923i	0.939592	−	0.542474i	0.889833	+	0.456287i	$0.150821\pi$
$368$		0			0
$369$	−1.50000	+	2.59808i	−0.0780869	+	0.135250i
$370$		0			0
$371$	24.0000			1.24602
$372$		0			0
$373$	3.00000	+	1.73205i	0.155334	+	0.0896822i	0.575652	−	0.817695i	$-0.304748\pi$
$373$	3.00000	+	1.73205i	0.155334	+	0.0896822i	−0.420318	+	0.907377i	$0.638082\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	24.0000	−	13.8564i	1.23606	−	0.713641i
$378$		0			0
$379$		−	22.5167i		−	1.15660i	−0.815823	−	0.578302i	$-0.803716\pi$
$379$		−	22.5167i		−	1.15660i	0.815823	−	0.578302i	$-0.196284\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−18.0000			−0.919757			−0.459879	−	0.887982i	$-0.652107\pi$
$383$	−18.0000			−0.919757			−0.459879	+	0.887982i	$0.652107\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.50000	−	6.06218i	0.127082	−	0.308158i
$388$		0			0
$389$		−	24.2487i		−	1.22946i	−0.788738	−	0.614729i	$-0.789265\pi$
$389$		−	24.2487i		−	1.22946i	0.788738	−	0.614729i	$-0.210735\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	7.50000	+	12.9904i	0.378325	+	0.655278i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.00000	−	13.8564i	−0.401508	−	0.695433i	0.592400	−	0.805644i	$-0.298181\pi$
$397$	−8.00000	−	13.8564i	−0.401508	−	0.695433i	−0.993908	+	0.110211i	$0.964847\pi$
$398$		0			0
$399$	−5.00000	−	8.66025i	−0.250313	−	0.433555i
$400$		0			0
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	−0.199207	−	0.979957i	$-0.563837\pi$
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	0.948272	−	0.317460i	$-0.102830\pi$
$402$		0			0
$403$		−	27.7128i		−	1.38047i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−9.00000	−	15.5885i	−0.446113	−	0.772691i
$408$		0			0
$409$			15.5885i			0.770800i	0.922750	+	0.385400i	$0.125936\pi$
$409$			15.5885i			0.770800i	−0.922750	+	0.385400i	$0.874064\pi$
$410$		0			0
$411$	18.0000	−	10.3923i	0.887875	−	0.512615i
$412$		0			0
$413$	−21.0000	−	12.1244i	−1.03334	−	0.596601i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	10.5000	+	6.06218i	0.514187	+	0.296866i
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	12.0000	+	6.92820i	0.584844	+	0.337660i	0.763056	−	0.646332i	$-0.223698\pi$
$421$	12.0000	+	6.92820i	0.584844	+	0.337660i	−0.178212	+	0.983992i	$0.557031\pi$
$422$		0			0
$423$	−9.00000	−	5.19615i	−0.437595	−	0.252646i
$424$		0			0
$425$	7.50000	+	12.9904i	0.363803	+	0.630126i
$426$		0			0
$427$	−12.0000	+	6.92820i	−0.580721	+	0.335279i
$428$		0			0
$429$			6.92820i			0.334497i
$430$		0			0
$431$		−	38.1051i		−	1.83546i	−0.397206	−	0.917729i	$-0.630020\pi$
$431$		−	38.1051i		−	1.83546i	0.397206	−	0.917729i	$-0.369980\pi$
$432$		0			0
$433$	24.0000	−	13.8564i	1.15337	−	0.665896i	0.203661	−	0.979041i	$-0.434716\pi$
$433$	24.0000	−	13.8564i	1.15337	−	0.665896i	0.949705	+	0.313145i	$0.101383\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	21.0000	+	12.1244i	1.00228	+	0.578664i	0.908921	−	0.416969i	$-0.136908\pi$
$439$	21.0000	+	12.1244i	1.00228	+	0.578664i	0.0933546	+	0.995633i	$0.470241\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$		0			0
$443$	−15.0000	−	8.66025i	−0.712672	−	0.411461i	0.0993779	−	0.995050i	$-0.468315\pi$
$443$	−15.0000	−	8.66025i	−0.712672	−	0.411461i	−0.812049	+	0.583589i	$0.801648\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	15.0000	+	8.66025i	0.709476	+	0.409616i
$448$		0			0
$449$	−1.50000	+	0.866025i	−0.0707894	+	0.0408703i	−0.534977	−	0.844867i	$-0.679680\pi$
$449$	−1.50000	+	0.866025i	−0.0707894	+	0.0408703i	0.464188	+	0.885737i	$0.346346\pi$
$450$		0			0
$451$			5.19615i			0.244677i
$452$		0			0
$453$	−8.00000	−	13.8564i	−0.375873	−	0.651031i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	12.1244i		−	0.567153i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$		−	12.1244i		−	0.567153i	0.958950	−	0.283577i	$-0.0915211\pi$
$458$		0			0
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$		0			0
$461$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$461$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$462$		0			0
$463$	10.0000	+	17.3205i	0.464739	+	0.804952i	0.999190	−	0.0402476i	$-0.0128147\pi$
$463$	10.0000	+	17.3205i	0.464739	+	0.804952i	−0.534450	+	0.845200i	$0.679481\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.50000	−	12.9904i	−0.347059	−	0.601123i	0.638667	−	0.769483i	$-0.279486\pi$
$467$	−7.50000	−	12.9904i	−0.347059	−	0.601123i	−0.985726	+	0.168360i	$0.946153\pi$
$468$		0			0
$469$		−	17.3205i		−	0.799787i
$470$		0			0
$471$			10.3923i			0.478852i
$472$		0			0
$473$	−1.50000	−	11.2583i	−0.0689701	−	0.517659i
$474$		0			0
$475$	−25.0000			−1.14708
$476$		0			0
$477$	12.0000			0.549442
$478$		0			0
$479$	−9.00000	+	5.19615i	−0.411220	+	0.237418i	−0.691314	−	0.722554i	$-0.742968\pi$
$479$	−9.00000	+	5.19615i	−0.411220	+	0.237418i	0.280094	+	0.959973i	$0.409635\pi$
$480$		0			0
$481$			41.5692i			1.89539i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−3.00000	−	1.73205i	−0.135943	−	0.0784867i	0.430486	−	0.902597i	$-0.358342\pi$
$487$	−3.00000	−	1.73205i	−0.135943	−	0.0784867i	−0.566429	+	0.824110i	$0.691675\pi$
$488$		0			0
$489$	−11.0000			−0.497437
$490$		0			0
$491$	10.5000	−	18.1865i	0.473858	−	0.820747i	−0.525694	−	0.850674i	$-0.676194\pi$
$491$	10.5000	−	18.1865i	0.473858	−	0.820747i	0.999552	+	0.0299272i	$0.00952753\pi$
$492$		0			0
$493$	18.0000	−	10.3923i	0.810679	−	0.468046i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.00000	−	10.3923i	−0.269137	−	0.466159i
$498$		0			0
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	−0.804627	−	0.593780i	$-0.797635\pi$
$499$	2.50000	−	4.33013i	0.111915	−	0.193843i	0.916542	+	0.399937i	$0.130968\pi$
$500$		0			0
$501$	15.0000	+	8.66025i	0.670151	+	0.386912i
$502$		0			0
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	0.464107	+	0.885779i	$0.346375\pi$
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	−0.999161	+	0.0409609i	$0.986958\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.50000	−	2.59808i	0.0666173	−	0.115385i
$508$		0			0
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	−0.467416	−	0.884037i	$-0.654815\pi$
$509$	12.0000	−	20.7846i	0.531891	−	0.921262i	0.999307	−	0.0372243i	$-0.0118516\pi$
$510$		0			0
$511$	15.0000	−	8.66025i	0.663561	−	0.383107i
$512$		0			0
$513$	−2.50000	−	4.33013i	−0.110378	−	0.191180i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−18.0000			−0.791639
$518$		0			0
$519$	3.00000	+	5.19615i	0.131685	+	0.228086i
$520$		0			0
$521$	7.50000	−	4.33013i	0.328581	−	0.189706i	−0.326630	−	0.945152i	$-0.605913\pi$
$521$	7.50000	−	4.33013i	0.328581	−	0.189706i	0.655211	+	0.755446i	$0.272580\pi$
$522$		0			0
$523$	−3.50000	+	6.06218i	−0.153044	+	0.265081i	−0.932345	−	0.361569i	$-0.882241\pi$
$523$	−3.50000	+	6.06218i	−0.153044	+	0.265081i	0.779301	+	0.626650i	$0.215574\pi$
$524$		0			0
$525$	5.00000	−	8.66025i	0.218218	−	0.377964i
$526$		0			0
$527$		−	20.7846i		−	0.905392i
$528$		0			0
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$		0			0
$531$	−10.5000	−	6.06218i	−0.455661	−	0.263076i
$532$		0			0
$533$	6.00000	−	10.3923i	0.259889	−	0.450141i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−15.0000			−0.647298
$538$		0			0
$539$	−4.50000	+	2.59808i	−0.193829	+	0.111907i
$540$		0			0
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$		0			0
$543$	−20.0000			−0.858282
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−3.00000	+	1.73205i	−0.128271	+	0.0740571i	−0.562762	−	0.826619i	$-0.690261\pi$
$547$	−3.00000	+	1.73205i	−0.128271	+	0.0740571i	0.434492	+	0.900676i	$0.356928\pi$
$548$		0			0
$549$	−6.00000	+	3.46410i	−0.256074	+	0.147844i
$550$		0			0
$551$			34.6410i			1.47576i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.0000			1.01691			0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000			1.01691			0.508456	+	0.861088i	$0.330216\pi$
$558$		0			0
$559$	−10.0000	+	24.2487i	−0.422955	+	1.02561i
$560$		0			0
$561$			5.19615i			0.219382i
$562$		0			0
$563$		−	31.1769i		−	1.31395i	−0.753912	−	0.656975i	$-0.771836\pi$
$563$		−	31.1769i		−	1.31395i	0.753912	−	0.656975i	$-0.228164\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.00000			0.0839921
$568$		0			0
$569$	16.5000	+	28.5788i	0.691716	+	1.19809i	0.971275	+	0.237959i	$0.0764783\pi$
$569$	16.5000	+	28.5788i	0.691716	+	1.19809i	−0.279559	+	0.960128i	$0.590188\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−18.0000	−	10.3923i	−0.749350	−	0.432637i	0.0761091	−	0.997099i	$-0.475750\pi$
$577$	−18.0000	−	10.3923i	−0.749350	−	0.432637i	−0.825459	+	0.564462i	$0.809084\pi$
$578$		0			0
$579$	−7.00000	−	12.1244i	−0.290910	−	0.503871i
$580$		0			0
$581$			20.7846i			0.862291i
$582$		0			0
$583$	18.0000	−	10.3923i	0.745484	−	0.430405i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.5000	−	23.3827i	0.557205	−	0.965107i	−0.440524	−	0.897741i	$-0.645207\pi$
$587$	13.5000	−	23.3827i	0.557205	−	0.965107i	0.997728	−	0.0673658i	$-0.0214594\pi$
$588$		0			0
$589$	30.0000	+	17.3205i	1.23613	+	0.713679i
$590$		0			0
$591$	18.0000			0.740421
$592$		0			0
$593$	−28.5000	−	16.4545i	−1.17035	−	0.675705i	−0.216591	−	0.976262i	$-0.569494\pi$
$593$	−28.5000	−	16.4545i	−1.17035	−	0.675705i	−0.953764	+	0.300558i	$0.902827\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−7.00000	−	12.1244i	−0.286491	−	0.496217i
$598$		0			0
$599$	18.0000	−	10.3923i	0.735460	−	0.424618i	−0.0849563	−	0.996385i	$-0.527075\pi$
$599$	18.0000	−	10.3923i	0.735460	−	0.424618i	0.820416	+	0.571767i	$0.193742\pi$
$600$		0			0
$601$		−	15.5885i		−	0.635866i	−0.948113	−	0.317933i	$-0.897011\pi$
$601$		−	15.5885i		−	0.635866i	0.948113	−	0.317933i	$-0.102989\pi$
$602$		0			0
$603$		−	8.66025i		−	0.352673i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.0000	−	19.0526i	−0.446476	−	0.773320i	0.551678	−	0.834058i	$-0.313988\pi$
$607$	−11.0000	−	19.0526i	−0.446476	−	0.773320i	−0.998154	+	0.0607380i	$0.980655\pi$
$608$		0			0
$609$	−12.0000	−	6.92820i	−0.486265	−	0.280745i
$610$		0			0
$611$	36.0000	+	20.7846i	1.45640	+	0.840855i
$612$		0			0
$613$	34.0000			1.37325			0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000			1.37325			0.686624	+	0.727013i	$0.259092\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	−0.626017	−	0.779809i	$-0.715316\pi$
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	0.988343	+	0.152242i	$0.0486493\pi$
$618$		0			0
$619$	21.0000	+	12.1244i	0.844061	+	0.487319i	0.858643	−	0.512575i	$-0.171308\pi$
$619$	21.0000	+	12.1244i	0.844061	+	0.487319i	−0.0145814	+	0.999894i	$0.504642\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	31.1769i		−	1.24908i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$		0			0
$627$	−7.50000	−	4.33013i	−0.299521	−	0.172929i
$628$		0			0
$629$			31.1769i			1.24310i
$630$		0			0
$631$	−7.00000	+	12.1244i	−0.278666	+	0.482663i	−0.971053	−	0.238863i	$-0.923225\pi$
$631$	−7.00000	+	12.1244i	−0.278666	+	0.482663i	0.692388	+	0.721526i	$0.256559\pi$
$632$		0			0
$633$	−2.00000	−	3.46410i	−0.0794929	−	0.137686i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	12.0000			0.475457
$638$		0			0
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$		0			0
$641$			19.0526i			0.752531i	0.926512	+	0.376265i	$0.122792\pi$
$641$			19.0526i			0.752531i	−0.926512	+	0.376265i	$0.877208\pi$
$642$		0			0
$643$		−	25.9808i		−	1.02458i	−0.858812	−	0.512291i	$-0.828797\pi$
$643$		−	25.9808i		−	1.02458i	0.858812	−	0.512291i	$-0.171203\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$		0			0
$649$	−21.0000			−0.824322
$650$		0			0
$651$	−12.0000	+	6.92820i	−0.470317	+	0.271538i
$652$		0			0
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	7.50000	−	4.33013i	0.292603	−	0.168934i
$658$		0			0
$659$	−9.00000	−	5.19615i	−0.350590	−	0.202413i	0.314355	−	0.949306i	$-0.398212\pi$
$659$	−9.00000	−	5.19615i	−0.350590	−	0.202413i	−0.664945	+	0.746892i	$0.731545\pi$
$660$		0			0
$661$	−26.0000			−1.01128			−0.505641	−	0.862744i	$-0.668744\pi$
$661$	−26.0000			−1.01128			−0.505641	+	0.862744i	$0.668744\pi$
$662$		0			0
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	2.00000	+	3.46410i	0.0773245	+	0.133930i
$670$		0			0
$671$	−6.00000	+	10.3923i	−0.231627	+	0.401190i
$672$		0			0
$673$	−16.5000	−	9.52628i	−0.636028	−	0.367211i	0.147055	−	0.989128i	$-0.453021\pi$
$673$	−16.5000	−	9.52628i	−0.636028	−	0.367211i	−0.783083	+	0.621917i	$0.786354\pi$
$674$		0			0
$675$	2.50000	−	4.33013i	0.0962250	−	0.166667i
$676$		0			0
$677$			3.46410i			0.133136i	0.997782	+	0.0665681i	$0.0212050\pi$
$677$			3.46410i			0.133136i	−0.997782	+	0.0665681i	$0.978795\pi$
$678$		0			0
$679$	17.0000	−	29.4449i	0.652400	−	1.12999i
$680$		0			0
$681$	−13.5000	+	23.3827i	−0.517321	+	0.896026i
$682$		0			0
$683$	−33.0000	+	19.0526i	−1.26271	+	0.729026i	−0.973598	−	0.228269i	$-0.926693\pi$
$683$	−33.0000	+	19.0526i	−1.26271	+	0.729026i	−0.289112	+	0.957295i	$0.593360\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	14.0000			0.534133
$688$		0			0
$689$	−48.0000			−1.82865
$690$		0			0
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	0.856358	−	0.516382i	$-0.172722\pi$
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	−0.875379	+	0.483437i	$0.839388\pi$
$692$		0			0
$693$	3.00000	−	1.73205i	0.113961	−	0.0657952i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.50000	−	7.79423i	0.170450	−	0.295227i
$698$		0			0
$699$			8.66025i			0.327561i
$700$		0			0
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	−0.917102	−	0.398652i	$-0.869478\pi$
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	0.803794	+	0.594908i	$0.202811\pi$
$702$		0			0
$703$	−45.0000	−	25.9808i	−1.69721	−	0.979883i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.00000	+	10.3923i	0.225653	+	0.390843i
$708$		0			0
$709$	−34.0000			−1.27690			−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000			−1.27690			−0.638448	+	0.769665i	$0.720423\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−12.0000	+	6.92820i	−0.447524	+	0.258378i	−0.706784	−	0.707429i	$-0.749855\pi$
$719$	−12.0000	+	6.92820i	−0.447524	+	0.258378i	0.259260	+	0.965808i	$0.416521\pi$
$720$		0			0
$721$	−30.0000	+	17.3205i	−1.11726	+	0.645049i
$722$		0			0
$723$		−	20.7846i		−	0.772988i
$724$		0			0
$725$	−30.0000	+	17.3205i	−1.11417	+	0.643268i
$726$		0			0
$727$	26.0000			0.964287			0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000			0.964287			0.482143	+	0.876092i	$0.339858\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−7.50000	+	18.1865i	−0.277398	+	0.672653i
$732$		0			0
$733$		−	31.1769i		−	1.15155i	−0.817610	−	0.575773i	$-0.804701\pi$
$733$		−	31.1769i		−	1.15155i	0.817610	−	0.575773i	$-0.195299\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.50000	−	12.9904i	−0.276266	−	0.478507i
$738$		0			0
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$		0			0
$741$	10.0000	+	17.3205i	0.367359	+	0.636285i
$742$		0			0
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	0.997707	−	0.0676840i	$-0.0215610\pi$
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	−0.557470	+	0.830197i	$0.688228\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			10.3923i			0.380235i
$748$		0			0
$749$	9.00000	+	5.19615i	0.328853	+	0.189863i
$750$		0			0
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$		0			0
$753$			19.0526i			0.694314i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	42.0000	+	24.2487i	1.52652	+	0.881334i	0.999505	+	0.0314762i	$0.0100208\pi$
$757$	42.0000	+	24.2487i	1.52652	+	0.881334i	0.527011	+	0.849858i	$0.323312\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	30.0000	+	17.3205i	1.08750	+	0.627868i	0.932910	−	0.360111i	$-0.117261\pi$
$761$	30.0000	+	17.3205i	1.08750	+	0.627868i	0.154590	+	0.987979i	$0.450594\pi$
$762$		0			0
$763$	−4.00000			−0.144810
$764$		0			0
$765$		0			0
$766$		0			0
$767$	42.0000	+	24.2487i	1.51653	+	0.875570i
$768$		0			0
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	0.995397	−	0.0958377i	$-0.0305530\pi$
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	−0.580696	+	0.814120i	$0.697220\pi$
$770$		0			0
$771$	−13.5000	+	7.79423i	−0.486191	+	0.280702i
$772$		0			0
$773$		−	38.1051i		−	1.37055i	−0.728286	−	0.685273i	$-0.759683\pi$
$773$		−	38.1051i		−	1.37055i	0.728286	−	0.685273i	$-0.240317\pi$
$774$		0			0
$775$			34.6410i			1.24434i
$776$		0			0
$777$	18.0000	−	10.3923i	0.645746	−	0.372822i
$778$		0			0
$779$	7.50000	+	12.9904i	0.268715	+	0.465429i
$780$		0			0
$781$	−9.00000	−	5.19615i	−0.322045	−	0.185933i
$782$		0			0
$783$	−6.00000	−	3.46410i	−0.214423	−	0.123797i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−21.0000	−	12.1244i	−0.748569	−	0.432187i	0.0766075	−	0.997061i	$-0.475591\pi$
$787$	−21.0000	−	12.1244i	−0.748569	−	0.432187i	−0.825177	+	0.564875i	$0.808924\pi$
$788$		0			0
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$		0			0
$791$	−15.0000	−	8.66025i	−0.533339	−	0.307923i
$792$		0			0
$793$	24.0000	−	13.8564i	0.852265	−	0.492055i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.0000	+	25.9808i	0.531327	+	0.920286i	0.999331	+	0.0365596i	$0.0116399\pi$
$797$	15.0000	+	25.9808i	0.531327	+	0.920286i	−0.468004	+	0.883726i	$0.655027\pi$
$798$		0			0
$799$	27.0000	+	15.5885i	0.955191	+	0.551480i
$800$		0			0
$801$		−	15.5885i		−	0.550791i
$802$		0			0
$803$	7.50000	−	12.9904i	0.264669	−	0.458421i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	15.0000	+	25.9808i	0.528025	+	0.914566i
$808$		0			0
$809$	−6.00000			−0.210949			−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000			−0.210949			−0.105474	+	0.994422i	$0.533636\pi$
$810$		0			0
$811$	3.50000	+	6.06218i	0.122902	+	0.212872i	0.920911	−	0.389774i	$-0.127447\pi$
$811$	3.50000	+	6.06218i	0.122902	+	0.212872i	−0.798009	+	0.602645i	$0.794113\pi$
$812$		0			0
$813$		−	20.7846i		−	0.728948i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−20.0000	−	25.9808i	−0.699711	−	0.908952i
$818$		0			0
$819$	−8.00000			−0.279543
$820$		0			0
$821$	−54.0000			−1.88461			−0.942306	−	0.334751i	$-0.891348\pi$
$821$	−54.0000			−1.88461			−0.942306	+	0.334751i	$0.891348\pi$
$822$		0			0
$823$	−21.0000	+	12.1244i	−0.732014	+	0.422628i	−0.819159	−	0.573567i	$-0.805559\pi$
$823$	−21.0000	+	12.1244i	−0.732014	+	0.422628i	0.0871445	+	0.996196i	$0.472226\pi$
$824$		0			0
$825$		−	8.66025i		−	0.301511i
$826$		0			0
$827$	28.5000	−	16.4545i	0.991042	−	0.572178i	0.0854565	−	0.996342i	$-0.472765\pi$
$827$	28.5000	−	16.4545i	0.991042	−	0.572178i	0.905586	+	0.424163i	$0.139432\pi$
$828$		0			0
$829$	21.0000	−	12.1244i	0.729360	−	0.421096i	−0.0888279	−	0.996047i	$-0.528312\pi$
$829$	21.0000	−	12.1244i	0.729360	−	0.421096i	0.818188	+	0.574951i	$0.194979\pi$
$830$		0			0
$831$	9.00000	+	5.19615i	0.312207	+	0.180253i
$832$		0			0
$833$	9.00000			0.311832
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−6.00000	+	3.46410i	−0.207390	+	0.119737i
$838$		0			0
$839$	−30.0000			−1.03572			−0.517858	−	0.855467i	$-0.673270\pi$
$839$	−30.0000			−1.03572			−0.517858	+	0.855467i	$0.673270\pi$
$840$		0			0
$841$	9.50000	+	16.4545i	0.327586	+	0.567396i
$842$		0			0
$843$	4.50000	−	7.79423i	0.154988	−	0.268447i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−8.00000	+	13.8564i	−0.274883	+	0.476112i
$848$		0			0
$849$		−	22.5167i		−	0.772770i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−4.00000	+	6.92820i	−0.136957	+	0.237217i	−0.926343	−	0.376680i	$-0.877066\pi$
$853$	−4.00000	+	6.92820i	−0.136957	+	0.237217i	0.789386	+	0.613897i	$0.210399\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	0.810227	−	0.586116i	$-0.199344\pi$
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	−0.912705	+	0.408619i	$0.866010\pi$
$858$		0			0
$859$	23.0000			0.784750			0.392375	−	0.919805i	$-0.371654\pi$
$859$	23.0000			0.784750			0.392375	+	0.919805i	$0.371654\pi$
$860$		0			0
$861$	−6.00000			−0.204479
$862$		0			0
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	0.912558	−	0.408946i	$-0.134104\pi$
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	−0.810437	+	0.585826i	$0.800770\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.00000	+	6.92820i	−0.135847	+	0.235294i
$868$		0			0
$869$		0			0
$870$		0			0
$871$			34.6410i			1.17377i
$872$		0			0
$873$	8.50000	−	14.7224i	0.287681	−	0.498279i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	5.00000	−	8.66025i	0.168838	−	0.292436i	−0.769174	−	0.639040i	$-0.779332\pi$
$877$	5.00000	−	8.66025i	0.168838	−	0.292436i	0.938012	+	0.346604i	$0.112665\pi$
$878$		0			0
$879$	12.0000	+	20.7846i	0.404750	+	0.701047i
$880$		0			0
$881$	−3.00000			−0.101073			−0.0505363	−	0.998722i	$-0.516093\pi$
$881$	−3.00000			−0.101073			−0.0505363	+	0.998722i	$0.516093\pi$
$882$		0			0
$883$	−39.0000	+	22.5167i	−1.31245	+	0.757746i	−0.982502	−	0.186252i	$-0.940366\pi$
$883$	−39.0000	+	22.5167i	−1.31245	+	0.757746i	−0.329952	+	0.943998i	$0.607033\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−42.0000			−1.41022			−0.705111	−	0.709097i	$-0.749103\pi$
$887$	−42.0000			−1.41022			−0.705111	+	0.709097i	$0.749103\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.50000	−	0.866025i	0.0502519	−	0.0290129i
$892$		0			0
$893$	−45.0000	+	25.9808i	−1.50587	+	0.869413i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$	48.0000			1.60089
$900$		0			0
$901$	−36.0000			−1.19933
$902$		0			0
$903$	13.0000	−	1.73205i	0.432613	−	0.0576390i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			22.5167i			0.747653i	0.927499	+	0.373827i	$0.121955\pi$
$907$			22.5167i			0.747653i	−0.927499	+	0.373827i	$0.878045\pi$
$908$		0			0
$909$	3.00000	+	5.19615i	0.0995037	+	0.172345i
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$		0			0
$913$	9.00000	+	15.5885i	0.297857	+	0.515903i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−15.0000	+	25.9808i	−0.495344	+	0.857960i
$918$		0			0
$919$		−	6.92820i		−	0.228540i	−0.993450	−	0.114270i	$-0.963547\pi$
$919$		−	6.92820i		−	0.228540i	0.993450	−	0.114270i	$-0.0364530\pi$
$920$		0			0
$921$	1.50000	+	0.866025i	0.0494267	+	0.0285365i
$922$		0			0
$923$	12.0000	+	20.7846i	0.394985	+	0.684134i
$924$		0			0
$925$		−	51.9615i		−	1.70848i
$926$		0			0
$927$	−15.0000	+	8.66025i	−0.492665	+	0.284440i
$928$		0			0
$929$	43.5000	+	25.1147i	1.42719	+	0.823988i	0.996898	−	0.0787027i	$-0.0250778\pi$
$929$	43.5000	+	25.1147i	1.42719	+	0.823988i	0.430291	+	0.902690i	$0.358411\pi$
$930$		0			0
$931$	−7.50000	+	12.9904i	−0.245803	+	0.425743i
$932$		0			0
$933$	15.0000	+	8.66025i	0.491078	+	0.283524i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	34.5000	+	19.9186i	1.12707	+	0.650712i	0.943195	−	0.332239i	$-0.107804\pi$
$937$	34.5000	+	19.9186i	1.12707	+	0.650712i	0.183871	+	0.982950i	$0.441137\pi$
$938$		0			0
$939$	6.00000	+	3.46410i	0.195803	+	0.113047i
$940$		0			0
$941$	6.00000	+	10.3923i	0.195594	+	0.338779i	0.947095	−	0.320953i	$-0.104003\pi$
$941$	6.00000	+	10.3923i	0.195594	+	0.338779i	−0.751501	+	0.659732i	$0.770670\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$			12.1244i			0.393989i	0.980405	+	0.196994i	$0.0631181\pi$
$947$			12.1244i			0.393989i	−0.980405	+	0.196994i	$0.936882\pi$
$948$		0			0
$949$	−30.0000	+	17.3205i	−0.973841	+	0.562247i
$950$		0			0
$951$	12.0000	+	20.7846i	0.389127	+	0.673987i
$952$		0			0
$953$	6.00000	+	3.46410i	0.194359	+	0.112213i	0.594022	−	0.804449i	$-0.297539\pi$
$953$	6.00000	+	3.46410i	0.194359	+	0.112213i	−0.399663	+	0.916662i	$0.630873\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−12.0000			−0.387905
$958$		0			0
$959$	36.0000	+	20.7846i	1.16250	+	0.671170i
$960$		0			0
$961$	8.50000	−	14.7224i	0.274194	−	0.474917i
$962$		0			0
$963$	4.50000	+	2.59808i	0.145010	+	0.0837218i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			17.3205i			0.556990i	0.960438	+	0.278495i	$0.0898356\pi$
$967$			17.3205i			0.556990i	−0.960438	+	0.278495i	$0.910164\pi$
$968$		0			0
$969$	7.50000	+	12.9904i	0.240935	+	0.417311i
$970$		0			0
$971$	39.0000	+	22.5167i	1.25157	+	0.722594i	0.971421	−	0.237363i	$-0.0762830\pi$
$971$	39.0000	+	22.5167i	1.25157	+	0.722594i	0.280148	+	0.959957i	$0.409616\pi$
$972$		0			0
$973$			24.2487i			0.777378i
$974$		0			0
$975$	−10.0000	+	17.3205i	−0.320256	+	0.554700i
$976$		0			0
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	0.785020	−	0.619471i	$-0.212653\pi$
$977$	−4.50000	−	7.79423i	−0.143968	−	0.249359i	−0.928987	+	0.370111i	$0.879319\pi$
$978$		0			0
$979$	−13.5000	−	23.3827i	−0.431462	−	0.747314i
$980$		0			0
$981$	−2.00000			−0.0638551
$982$		0			0
$983$	−21.0000	−	36.3731i	−0.669796	−	1.16012i	−0.977961	−	0.208788i	$-0.933048\pi$
$983$	−21.0000	−	36.3731i	−0.669796	−	1.16012i	0.308165	−	0.951333i	$-0.400285\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	20.7846i		−	0.661581i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	58.0000			1.84243			0.921215	−	0.389053i	$-0.127198\pi$
$991$	58.0000			1.84243			0.921215	+	0.389053i	$0.127198\pi$
$992$		0			0
$993$	11.0000			0.349074
$994$		0			0
$995$		0			0
$996$		0			0
$997$		−	27.7128i		−	0.877674i	−0.898567	−	0.438837i	$-0.855391\pi$
$997$		−	27.7128i		−	0.877674i	0.898567	−	0.438837i	$-0.144609\pi$
$998$		0			0
$999$	9.00000	−	5.19615i	0.284747	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2064.2.bg.e.1039.1	yes	2
4.3	odd	2		2064.2.bg.b.1039.1	✓	2
43.37	odd	6		2064.2.bg.b.1327.1	yes	2
172.123	even	6	inner	2064.2.bg.e.1327.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2064.2.bg.b.1039.1	✓	2	4.3	odd	2
2064.2.bg.b.1327.1	yes	2	43.37	odd	6
2064.2.bg.e.1039.1	yes	2	1.1	even	1	trivial
2064.2.bg.e.1327.1	yes	2	172.123	even	6	inner

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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:	\( N \)	\(=\)	\( 2064 = 2^{4} \cdot 3 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2064.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +1.73205i q^{11} +(2.00000 - 3.46410i) q^{13} +(1.50000 - 2.59808i) q^{17} +(2.50000 + 4.33013i) q^{19} -2.00000 q^{21} +(-2.50000 + 4.33013i) q^{25} -1.00000 q^{27} +(6.00000 + 3.46410i) q^{29} +(6.00000 - 3.46410i) q^{31} +(-1.50000 + 0.866025i) q^{33} +(-9.00000 + 5.19615i) q^{37} +4.00000 q^{39} +3.00000 q^{41} +(-6.50000 + 0.866025i) q^{43} +10.3923i q^{47} +(1.50000 + 2.59808i) q^{49} +3.00000 q^{51} +(-6.00000 - 10.3923i) q^{53} +(-2.50000 + 4.33013i) q^{57} +12.1244i q^{59} +(6.00000 + 3.46410i) q^{61} +(-1.00000 - 1.73205i) q^{63} +(-7.50000 + 4.33013i) q^{67} +(-3.00000 + 5.19615i) q^{71} +(-7.50000 - 4.33013i) q^{73} -5.00000 q^{75} +(-3.00000 - 1.73205i) q^{77} +(-0.500000 - 0.866025i) q^{81} +(9.00000 - 5.19615i) q^{83} +6.92820i q^{87} +(-13.5000 + 7.79423i) q^{89} +(4.00000 + 6.92820i) q^{91} +(6.00000 + 3.46410i) q^{93} -17.0000 q^{97} +(-1.50000 - 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - 2 q^{7} - q^{9}+O(q^{10}) \) 2 * q + q^3 - 2 * q^7 - q^9	\( 2 q + q^{3} - 2 q^{7} - q^{9} + 4 q^{13} + 3 q^{17} + 5 q^{19} - 4 q^{21} - 5 q^{25} - 2 q^{27} + 12 q^{29} + 12 q^{31} - 3 q^{33} - 18 q^{37} + 8 q^{39} + 6 q^{41} - 13 q^{43} + 3 q^{49} + 6 q^{51} - 12 q^{53} - 5 q^{57} + 12 q^{61} - 2 q^{63} - 15 q^{67} - 6 q^{71} - 15 q^{73} - 10 q^{75} - 6 q^{77} - q^{81} + 18 q^{83} - 27 q^{89} + 8 q^{91} + 12 q^{93} - 34 q^{97} - 3 q^{99}+O(q^{100}) \) 2 * q + q^3 - 2 * q^7 - q^9 + 4 * q^13 + 3 * q^17 + 5 * q^19 - 4 * q^21 - 5 * q^25 - 2 * q^27 + 12 * q^29 + 12 * q^31 - 3 * q^33 - 18 * q^37 + 8 * q^39 + 6 * q^41 - 13 * q^43 + 3 * q^49 + 6 * q^51 - 12 * q^53 - 5 * q^57 + 12 * q^61 - 2 * q^63 - 15 * q^67 - 6 * q^71 - 15 * q^73 - 10 * q^75 - 6 * q^77 - q^81 + 18 * q^83 - 27 * q^89 + 8 * q^91 + 12 * q^93 - 34 * q^97 - 3 * q^99

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