LMFDB - Embedded newform 600.2.r.f.257.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(257,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))

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

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

chi := DirichletCharacter("600.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.r (of order $4$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.6040479020157644046336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 $ x^16 - 7x^12 - 32x^8 - 567*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.5
Root			$-1.47240 + 0.912166i$ of defining polynomial
Character	$\chi$	$=$	600.257
Dual form			600.2.r.f.593.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0537601 - 1.73122i) q^{3} +(0.560232 + 0.560232i) q^{7} +(-2.99422 - 0.186141i) q^{9} +O(q^{10})$	$q+(0.0537601 - 1.73122i) q^{3} +(0.560232 + 0.560232i) q^{7} +(-2.99422 - 0.186141i) q^{9} +0.939764i q^{11} +(4.13018 - 4.13018i) q^{13} +(4.50588 - 4.50588i) q^{17} -3.74456i q^{19} +(1.00000 - 0.939764i) q^{21} +(-6.18334 - 6.18334i) q^{23} +(-0.483219 + 5.17364i) q^{27} -3.16915 q^{29} -5.37228 q^{31} +(1.62693 + 0.0505218i) q^{33} +(3.56995 + 3.56995i) q^{37} +(-6.92820 - 7.37228i) q^{39} +9.15759i q^{41} +(-4.33875 + 4.33875i) q^{43} +(5.65685 - 5.65685i) q^{47} -6.37228i q^{49} +(-7.55842 - 8.04290i) q^{51} +(0.526485 + 0.526485i) q^{53} +(-6.48265 - 0.201308i) q^{57} +11.9769 q^{59} +1.37228 q^{61} +(-1.57317 - 1.78174i) q^{63} +(-1.22474 - 1.22474i) q^{67} +(-11.0371 + 10.3723i) q^{69} -3.16915i q^{71} +(5.56349 - 5.56349i) q^{73} +(-0.526485 + 0.526485i) q^{77} +8.74456i q^{79} +(8.93070 + 1.11469i) q^{81} +(3.97940 + 3.97940i) q^{83} +(-0.170374 + 5.48648i) q^{87} +16.0858 q^{89} +4.62772 q^{91} +(-0.288814 + 9.30058i) q^{93} +(-5.25065 - 5.25065i) q^{97} +(0.174928 - 2.81386i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 16 q^{21} - 40 q^{31} - 52 q^{51} - 24 q^{61} + 28 q^{81} + 120 q^{91}+O(q^{100}) $ 16 * q + 16 * q^21 - 40 * q^31 - 52 * q^51 - 24 * q^61 + 28 * q^81 + 120 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0537601	−	1.73122i	0.0310384	−	0.999518i
$3$	0.0537601	−	1.73122i	0.0310384	−	0.999518i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.560232	+	0.560232i	0.211748	+	0.211748i	0.805010	−	0.593262i	$-0.202160\pi$
$7$	0.560232	+	0.560232i	0.211748	+	0.211748i	−0.593262	+	0.805010i	$0.702160\pi$
$8$		0			0
$9$	−2.99422	−	0.186141i	−0.998073	−	0.0620469i
$10$		0			0
$11$			0.939764i			0.283349i	0.989913	+	0.141675i	$0.0452487\pi$
$11$			0.939764i			0.283349i	−0.989913	+	0.141675i	$0.954751\pi$
$12$		0			0
$13$	4.13018	−	4.13018i	1.14551	−	1.14551i	0.158081	−	0.987426i	$-0.449469\pi$
$13$	4.13018	−	4.13018i	1.14551	−	1.14551i	0.987426	−	0.158081i	$-0.0505307\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.50588	−	4.50588i	1.09284	−	1.09284i	0.0976128	−	0.995224i	$-0.468879\pi$
$17$	4.50588	−	4.50588i	1.09284	−	1.09284i	0.995224	−	0.0976128i	$-0.0311207\pi$
$18$		0			0
$19$		−	3.74456i		−	0.859062i	−0.903052	−	0.429531i	$-0.858679\pi$
$19$		−	3.74456i		−	0.859062i	0.903052	−	0.429531i	$-0.141321\pi$
$20$		0			0
$21$	1.00000	−	0.939764i	0.218218	−	0.205073i
$22$		0			0
$23$	−6.18334	−	6.18334i	−1.28932	−	1.28932i	−0.935203	−	0.354113i	$-0.884783\pi$
$23$	−6.18334	−	6.18334i	−1.28932	−	1.28932i	−0.354113	−	0.935203i	$-0.615217\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.483219	+	5.17364i	−0.0929956	+	0.995667i
$28$		0			0
$29$	−3.16915			−0.588496			−0.294248	−	0.955729i	$-0.595069\pi$
$29$	−3.16915			−0.588496			−0.294248	+	0.955729i	$0.595069\pi$
$30$		0			0
$31$	−5.37228			−0.964890			−0.482445	−	0.875926i	$-0.660251\pi$
$31$	−5.37228			−0.964890			−0.482445	+	0.875926i	$0.660251\pi$
$32$		0			0
$33$	1.62693	+	0.0505218i	0.283213	+	0.00879471i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.56995	+	3.56995i	0.586897	+	0.586897i	0.936790	−	0.349893i	$-0.113782\pi$
$37$	3.56995	+	3.56995i	0.586897	+	0.586897i	−0.349893	+	0.936790i	$0.613782\pi$
$38$		0			0
$39$	−6.92820	−	7.37228i	−1.10940	−	1.18051i
$40$		0			0
$41$			9.15759i			1.43017i	0.699035	+	0.715087i	$0.253613\pi$
$41$			9.15759i			1.43017i	−0.699035	+	0.715087i	$0.746387\pi$
$42$		0			0
$43$	−4.33875	+	4.33875i	−0.661653	+	0.661653i	−0.955770	−	0.294117i	$-0.904975\pi$
$43$	−4.33875	+	4.33875i	−0.661653	+	0.661653i	0.294117	+	0.955770i	$0.404975\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.65685	−	5.65685i	0.825137	−	0.825137i	−0.161703	−	0.986840i	$-0.551699\pi$
$47$	5.65685	−	5.65685i	0.825137	−	0.825137i	0.986840	+	0.161703i	$0.0516985\pi$
$48$		0			0
$49$		−	6.37228i		−	0.910326i
$50$		0			0
$51$	−7.55842	−	8.04290i	−1.05839	−	1.12623i
$52$		0			0
$53$	0.526485	+	0.526485i	0.0723183	+	0.0723183i	0.742341	−	0.670022i	$-0.233716\pi$
$53$	0.526485	+	0.526485i	0.0723183	+	0.0723183i	−0.670022	+	0.742341i	$0.733716\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−6.48265	−	0.201308i	−0.858648	−	0.0266639i
$58$		0			0
$59$	11.9769			1.55926			0.779628	−	0.626242i	$-0.215408\pi$
$59$	11.9769			1.55926			0.779628	+	0.626242i	$0.215408\pi$
$60$		0			0
$61$	1.37228			0.175703			0.0878513	−	0.996134i	$-0.472000\pi$
$61$	1.37228			0.175703			0.0878513	+	0.996134i	$0.472000\pi$
$62$		0			0
$63$	−1.57317	−	1.78174i	−0.198201	−	0.224478i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.22474	−	1.22474i	−0.149626	−	0.149626i	0.628325	−	0.777951i	$-0.283741\pi$
$67$	−1.22474	−	1.22474i	−0.149626	−	0.149626i	−0.777951	+	0.628325i	$0.783741\pi$
$68$		0			0
$69$	−11.0371	+	10.3723i	−1.32871	+	1.24868i
$70$		0			0
$71$		−	3.16915i		−	0.376109i	−0.982159	−	0.188054i	$-0.939782\pi$
$71$		−	3.16915i		−	0.376109i	0.982159	−	0.188054i	$-0.0602181\pi$
$72$		0			0
$73$	5.56349	−	5.56349i	0.651158	−	0.651158i	−0.302114	−	0.953272i	$-0.597692\pi$
$73$	5.56349	−	5.56349i	0.651158	−	0.651158i	0.953272	+	0.302114i	$0.0976924\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.526485	+	0.526485i	−0.0599986	+	0.0599986i
$78$		0			0
$79$			8.74456i			0.983840i	0.870640	+	0.491920i	$0.163705\pi$
$79$			8.74456i			0.983840i	−0.870640	+	0.491920i	$0.836295\pi$
$80$		0			0
$81$	8.93070	+	1.11469i	0.992300	+	0.123855i
$82$		0			0
$83$	3.97940	+	3.97940i	0.436796	+	0.436796i	0.890932	−	0.454136i	$-0.150052\pi$
$83$	3.97940	+	3.97940i	0.436796	+	0.436796i	−0.454136	+	0.890932i	$0.650052\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.170374	+	5.48648i	−0.0182660	+	0.588212i
$88$		0			0
$89$	16.0858			1.70509			0.852545	−	0.522654i	$-0.175058\pi$
$89$	16.0858			1.70509			0.852545	+	0.522654i	$0.175058\pi$
$90$		0			0
$91$	4.62772			0.485117
$92$		0			0
$93$	−0.288814	+	9.30058i	−0.0299486	+	0.964425i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.25065	−	5.25065i	−0.533122	−	0.533122i	0.388378	−	0.921500i	$-0.373036\pi$
$97$	−5.25065	−	5.25065i	−0.533122	−	0.533122i	−0.921500	+	0.388378i	$0.873036\pi$
$98$		0			0
$99$	0.174928	−	2.81386i	0.0175810	−	0.282804i
$100$		0			0
$101$			8.80773i			0.876402i	0.898877	+	0.438201i	$0.144384\pi$
$101$			8.80773i			0.876402i	−0.898877	+	0.438201i	$0.855616\pi$
$102$		0			0
$103$	−8.26037	+	8.26037i	−0.813918	+	0.813918i	−0.985219	−	0.171301i	$-0.945203\pi$
$103$	−8.26037	+	8.26037i	−0.813918	+	0.813918i	0.171301	+	0.985219i	$0.445203\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.15097	−	1.15097i	0.111269	−	0.111269i	−0.649280	−	0.760549i	$-0.724930\pi$
$107$	1.15097	−	1.15097i	0.111269	−	0.111269i	0.760549	+	0.649280i	$0.224930\pi$
$108$		0			0
$109$			10.8614i			1.04033i	0.854065	+	0.520167i	$0.174130\pi$
$109$			10.8614i			1.04033i	−0.854065	+	0.520167i	$0.825870\pi$
$110$		0			0
$111$	6.37228	−	5.98844i	0.604830	−	0.568398i
$112$		0			0
$113$	1.67746	+	1.67746i	0.157802	+	0.157802i	0.781592	−	0.623790i	$-0.214408\pi$
$113$	1.67746	+	1.67746i	0.157802	+	0.157802i	−0.623790	+	0.781592i	$0.714408\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−13.1355	+	11.5979i	−1.21438	+	1.07222i
$118$		0			0
$119$	5.04868			0.462811
$120$		0			0
$121$	10.1168			0.919713
$122$		0			0
$123$	15.8538	+	0.492313i	1.42949	+	0.0443903i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−9.58940	−	9.58940i	−0.850921	−	0.850921i	0.139325	−	0.990247i	$-0.455507\pi$
$127$	−9.58940	−	9.58940i	−0.850921	−	0.850921i	−0.990247	+	0.139325i	$0.955507\pi$
$128$		0			0
$129$	7.27806	+	7.74456i	0.640797	+	0.681871i
$130$		0			0
$131$		−	5.04868i		−	0.441105i	−0.975375	−	0.220552i	$-0.929214\pi$
$131$		−	5.04868i		−	0.441105i	0.975375	−	0.220552i	$-0.0707860\pi$
$132$		0			0
$133$	2.09782	−	2.09782i	0.181904	−	0.181904i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.03237	−	5.03237i	0.429944	−	0.429944i	−0.458665	−	0.888609i	$-0.651672\pi$
$137$	5.03237	−	5.03237i	0.429944	−	0.429944i	0.888609	+	0.458665i	$0.151672\pi$
$138$		0			0
$139$			15.1168i			1.28219i	0.767460	+	0.641097i	$0.221520\pi$
$139$			15.1168i			1.28219i	−0.767460	+	0.641097i	$0.778480\pi$
$140$		0			0
$141$	−9.48913	−	10.0974i	−0.799129	−	0.850350i
$142$		0			0
$143$	3.88140	+	3.88140i	0.324579	+	0.324579i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−11.0318	−	0.342574i	−0.909887	−	0.0282551i
$148$		0			0
$149$	3.75906			0.307954			0.153977	−	0.988074i	$-0.450792\pi$
$149$	3.75906			0.307954			0.153977	+	0.988074i	$0.450792\pi$
$150$		0			0
$151$	−2.62772			−0.213841			−0.106920	−	0.994268i	$-0.534099\pi$
$151$	−2.62772			−0.213841			−0.106920	+	0.994268i	$0.534099\pi$
$152$		0			0
$153$	−14.3303	+	12.6529i	−1.15854	+	1.02292i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.23773	+	9.23773i	0.737251	+	0.737251i	0.972045	−	0.234794i	$-0.0754416\pi$
$157$	9.23773	+	9.23773i	0.737251	+	0.737251i	−0.234794	+	0.972045i	$0.575442\pi$
$158$		0			0
$159$	0.939764	−	0.883156i	0.0745281	−	0.0700388i
$160$		0			0
$161$		−	6.92820i		−	0.546019i
$162$		0			0
$163$	−13.2636	+	13.2636i	−1.03889	+	1.03889i	−0.0396750	+	0.999213i	$0.512632\pi$
$163$	−13.2636	+	13.2636i	−1.03889	+	1.03889i	−0.999213	+	0.0396750i	$0.987368\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.82843	+	2.82843i	−0.218870	+	0.218870i	−0.808022	−	0.589152i	$-0.799462\pi$
$167$	−2.82843	+	2.82843i	−0.218870	+	0.218870i	0.589152	+	0.808022i	$0.299462\pi$
$168$		0			0
$169$		−	21.1168i		−	1.62437i
$170$		0			0
$171$	−0.697015	+	11.2120i	−0.0533021	+	0.857406i
$172$		0			0
$173$	8.48528	+	8.48528i	0.645124	+	0.645124i	0.951811	−	0.306687i	$-0.0992203\pi$
$173$	8.48528	+	8.48528i	0.645124	+	0.645124i	−0.306687	+	0.951811i	$0.599220\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.643878	−	20.7346i	0.0483968	−	1.55851i
$178$		0			0
$179$	5.98844			0.447597			0.223798	−	0.974635i	$-0.428154\pi$
$179$	5.98844			0.447597			0.223798	+	0.974635i	$0.428154\pi$
$180$		0			0
$181$	−20.1168			−1.49527			−0.747637	−	0.664108i	$-0.768811\pi$
$181$	−20.1168			−1.49527			−0.747637	+	0.664108i	$0.768811\pi$
$182$		0			0
$183$	0.0737740	−	2.37572i	0.00545353	−	0.175618i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.23447	+	4.23447i	0.309655	+	0.309655i
$188$		0			0
$189$	−3.16915	+	2.62772i	−0.230522	+	0.191138i
$190$		0			0
$191$			25.2434i			1.82655i	0.407347	+	0.913273i	$0.366454\pi$
$191$			25.2434i			1.82655i	−0.407347	+	0.913273i	$0.633546\pi$
$192$		0			0
$193$	−8.36465	+	8.36465i	−0.602101	+	0.602101i	−0.940870	−	0.338769i	$-0.889990\pi$
$193$	−8.36465	+	8.36465i	−0.602101	+	0.602101i	0.338769	+	0.940870i	$0.389990\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.0647	+	10.0647i	−0.717083	+	0.717083i	−0.968007	−	0.250924i	$-0.919266\pi$
$197$	−10.0647	+	10.0647i	−0.717083	+	0.717083i	0.250924	+	0.968007i	$0.419266\pi$
$198$		0			0
$199$			4.62772i			0.328050i	0.986456	+	0.164025i	$0.0524478\pi$
$199$			4.62772i			0.328050i	−0.986456	+	0.164025i	$0.947552\pi$
$200$		0			0
$201$	−2.18614	+	2.05446i	−0.154198	+	0.144910i
$202$		0			0
$203$	−1.77546	−	1.77546i	−0.124613	−	0.124613i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	17.3633	+	19.6652i	1.20683	+	1.36683i
$208$		0			0
$209$	3.51900			0.243415
$210$		0			0
$211$	9.74456			0.670843			0.335422	−	0.942068i	$-0.391121\pi$
$211$	9.74456			0.670843			0.335422	+	0.942068i	$0.391121\pi$
$212$		0			0
$213$	−5.48648	−	0.170374i	−0.375927	−	0.0116738i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.00972	−	3.00972i	−0.204313	−	0.204313i
$218$		0			0
$219$	−9.33252	−	9.93070i	−0.630633	−	0.671055i
$220$		0			0
$221$		−	37.2203i		−	2.50371i
$222$		0			0
$223$	12.3906	−	12.3906i	0.829733	−	0.829733i	−0.157747	−	0.987480i	$-0.550423\pi$
$223$	12.3906	−	12.3906i	0.829733	−	0.829733i	0.987480	+	0.157747i	$0.0504230\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.82843	+	2.82843i	−0.187729	+	0.187729i	−0.794714	−	0.606984i	$-0.792379\pi$
$227$	−2.82843	+	2.82843i	−0.187729	+	0.187729i	0.606984	+	0.794714i	$0.292379\pi$
$228$		0			0
$229$		−	4.62772i		−	0.305808i	−0.988241	−	0.152904i	$-0.951137\pi$
$229$		−	4.62772i		−	0.305808i	0.988241	−	0.152904i	$-0.0488626\pi$
$230$		0			0
$231$	0.883156	+	0.939764i	0.0581074	+	0.0618319i
$232$		0			0
$233$	−12.8932	−	12.8932i	−0.844659	−	0.844659i	0.144801	−	0.989461i	$-0.453746\pi$
$233$	−12.8932	−	12.8932i	−0.844659	−	0.844659i	−0.989461	+	0.144801i	$0.953746\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	15.1387	+	0.470108i	0.983366	+	0.0305368i
$238$		0			0
$239$	−13.2665			−0.858138			−0.429069	−	0.903272i	$-0.641158\pi$
$239$	−13.2665			−0.858138			−0.429069	+	0.903272i	$0.641158\pi$
$240$		0			0
$241$	−13.2337			−0.852457			−0.426228	−	0.904616i	$-0.640158\pi$
$241$	−13.2337			−0.852457			−0.426228	+	0.904616i	$0.640158\pi$
$242$		0			0
$243$	2.40989	−	15.4011i	0.154594	−	0.987978i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−15.4657	−	15.4657i	−0.984061	−	0.984061i
$248$		0			0
$249$	7.10313	−	6.67527i	0.450143	−	0.423028i
$250$		0			0
$251$			10.4472i			0.659422i	0.944082	+	0.329711i	$0.106951\pi$
$251$			10.4472i			0.659422i	−0.944082	+	0.329711i	$0.893049\pi$
$252$		0			0
$253$	5.81088	−	5.81088i	0.365327	−	0.365327i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.0647	−	10.0647i	0.627821	−	0.627821i	−0.319698	−	0.947519i	$-0.603582\pi$
$257$	10.0647	−	10.0647i	0.627821	−	0.627821i	0.947519	+	0.319698i	$0.103582\pi$
$258$		0			0
$259$			4.00000i			0.248548i
$260$		0			0
$261$	9.48913	+	0.589907i	0.587362	+	0.0365143i
$262$		0			0
$263$	10.7872	+	10.7872i	0.665169	+	0.665169i	0.956594	−	0.291425i	$-0.0941294\pi$
$263$	10.7872	+	10.7872i	0.665169	+	0.665169i	−0.291425	+	0.956594i	$0.594129\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.864773	−	27.8480i	0.0529233	−	1.70427i
$268$		0			0
$269$	−27.1229			−1.65371			−0.826856	−	0.562413i	$-0.809873\pi$
$269$	−27.1229			−1.65371			−0.826856	+	0.562413i	$0.809873\pi$
$270$		0			0
$271$	18.2337			1.10762			0.553809	−	0.832644i	$-0.313174\pi$
$271$	18.2337			1.10762			0.553809	+	0.832644i	$0.313174\pi$
$272$		0			0
$273$	0.248787	−	8.01158i	0.0150572	−	0.484883i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	14.6315	+	14.6315i	0.879120	+	0.879120i	0.993444	−	0.114323i	$-0.0364700\pi$
$277$	14.6315	+	14.6315i	0.879120	+	0.879120i	−0.114323	+	0.993444i	$0.536470\pi$
$278$		0			0
$279$	16.0858	+	1.00000i	0.963031	+	0.0598684i
$280$		0			0
$281$			20.7846i			1.23991i	0.784639	+	0.619953i	$0.212848\pi$
$281$			20.7846i			1.23991i	−0.784639	+	0.619953i	$0.787152\pi$
$282$		0			0
$283$	17.7455	−	17.7455i	1.05486	−	1.05486i	0.0564542	−	0.998405i	$-0.482021\pi$
$283$	17.7455	−	17.7455i	1.05486	−	1.05486i	0.998405	−	0.0564542i	$-0.0179795\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.13037	+	5.13037i	−0.302836	+	0.302836i
$288$		0			0
$289$		−	23.6060i		−	1.38859i
$290$		0			0
$291$	−9.37228	+	8.80773i	−0.549413	+	0.516318i
$292$		0			0
$293$	−21.3784	−	21.3784i	−1.24894	−	1.24894i	−0.956188	−	0.292754i	$-0.905428\pi$
$293$	−21.3784	−	21.3784i	−1.24894	−	1.24894i	−0.292754	−	0.956188i	$-0.594572\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.86199	−	0.454112i	−0.282122	−	0.0263502i
$298$		0			0
$299$	−51.0767			−2.95384
$300$		0			0
$301$	−4.86141			−0.280207
$302$		0			0
$303$	15.2481	+	0.473504i	0.875980	+	0.0272021i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	19.4916	+	19.4916i	1.11245	+	1.11245i	0.992819	+	0.119628i	$0.0381701\pi$
$307$	19.4916	+	19.4916i	1.11245	+	1.11245i	0.119628	+	0.992819i	$0.461830\pi$
$308$		0			0
$309$	13.8564	+	14.7446i	0.788263	+	0.838789i
$310$		0			0
$311$		−	25.8333i		−	1.46487i	−0.680836	−	0.732436i	$-0.738383\pi$
$311$		−	25.8333i		−	1.46487i	0.680836	−	0.732436i	$-0.261617\pi$
$312$		0			0
$313$	9.02916	−	9.02916i	0.510359	−	0.510359i	−0.404278	−	0.914636i	$-0.632477\pi$
$313$	9.02916	−	9.02916i	0.510359	−	0.510359i	0.914636	+	0.404278i	$0.132477\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.70982	+	6.70982i	−0.376861	+	0.376861i	−0.869969	−	0.493107i	$-0.835861\pi$
$317$	−6.70982	+	6.70982i	−0.376861	+	0.376861i	0.493107	+	0.869969i	$0.335861\pi$
$318$		0			0
$319$		−	2.97825i		−	0.166750i
$320$		0			0
$321$	−1.93070	−	2.05446i	−0.107761	−	0.114669i
$322$		0			0
$323$	−16.8726	−	16.8726i	−0.938814	−	0.938814i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	18.8034	+	0.583910i	1.03983	+	0.0322903i
$328$		0			0
$329$	6.33830			0.349442
$330$		0			0
$331$	26.3723			1.44955			0.724776	−	0.688985i	$-0.241943\pi$
$331$	26.3723			1.44955			0.724776	+	0.688985i	$0.241943\pi$
$332$		0			0
$333$	−10.0247	−	11.3537i	−0.549351	−	0.622181i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	3.67423	+	3.67423i	0.200148	+	0.200148i	0.800064	−	0.599915i	$-0.204799\pi$
$337$	3.67423	+	3.67423i	0.200148	+	0.200148i	−0.599915	+	0.800064i	$0.704799\pi$
$338$		0			0
$339$	2.99422	−	2.81386i	0.162624	−	0.152828i
$340$		0			0
$341$		−	5.04868i		−	0.273401i
$342$		0			0
$343$	7.49157	−	7.49157i	0.404507	−	0.404507i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.38728	−	8.38728i	0.450253	−	0.450253i	−0.445186	−	0.895438i	$-0.646862\pi$
$347$	8.38728	−	8.38728i	0.450253	−	0.450253i	0.895438	+	0.445186i	$0.146862\pi$
$348$		0			0
$349$			4.51087i			0.241462i	0.992685	+	0.120731i	$0.0385238\pi$
$349$			4.51087i			0.241462i	−0.992685	+	0.120731i	$0.961476\pi$
$350$		0			0
$351$	19.3723	+	23.3639i	1.03402	+	1.24707i
$352$		0			0
$353$	5.13037	+	5.13037i	0.273062	+	0.273062i	0.830332	−	0.557270i	$-0.188151\pi$
$353$	5.13037	+	5.13037i	0.273062	+	0.273062i	−0.557270	+	0.830332i	$0.688151\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.271417	−	8.74035i	0.0143649	−	0.462588i
$358$		0			0
$359$	5.04868			0.266459			0.133229	−	0.991085i	$-0.457465\pi$
$359$	5.04868			0.266459			0.133229	+	0.991085i	$0.457465\pi$
$360$		0			0
$361$	4.97825			0.262013
$362$		0			0
$363$	0.543882	−	17.5144i	0.0285464	−	0.919270i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−9.02916	−	9.02916i	−0.471319	−	0.471319i	0.431023	−	0.902341i	$-0.358153\pi$
$367$	−9.02916	−	9.02916i	−0.471319	−	0.471319i	−0.902341	+	0.431023i	$0.858153\pi$
$368$		0			0
$369$	1.70460	−	27.4198i	0.0887379	−	1.42742i
$370$		0			0
$371$			0.589907i			0.0306265i
$372$		0			0
$373$	0.560232	−	0.560232i	0.0290077	−	0.0290077i	−0.692454	−	0.721462i	$-0.743471\pi$
$373$	0.560232	−	0.560232i	0.0290077	−	0.0290077i	0.721462	+	0.692454i	$0.243471\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−13.0892	+	13.0892i	−0.674126	+	0.674126i
$378$		0			0
$379$		−	3.51087i		−	0.180342i	−0.995926	−	0.0901708i	$-0.971259\pi$
$379$		−	3.51087i		−	0.180342i	0.995926	−	0.0901708i	$-0.0287413\pi$
$380$		0			0
$381$	−17.1168	+	16.0858i	−0.876922	+	0.824100i
$382$		0			0
$383$	10.0647	+	10.0647i	0.514284	+	0.514284i	0.915836	−	0.401552i	$-0.131529\pi$
$383$	10.0647	+	10.0647i	0.514284	+	0.514284i	−0.401552	+	0.915836i	$0.631529\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	13.7988	−	12.1835i	0.701432	−	0.619325i
$388$		0			0
$389$	−29.0024			−1.47048			−0.735241	−	0.677806i	$-0.762931\pi$
$389$	−29.0024			−1.47048			−0.735241	+	0.677806i	$0.762931\pi$
$390$		0			0
$391$	−55.7228			−2.81802
$392$		0			0
$393$	−8.74035	−	0.271417i	−0.440892	−	0.0136912i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−5.66777	−	5.66777i	−0.284457	−	0.284457i	0.550426	−	0.834884i	$-0.314465\pi$
$397$	−5.66777	−	5.66777i	−0.284457	−	0.284457i	−0.834884	+	0.550426i	$0.814465\pi$
$398$		0			0
$399$	−3.51900	−	3.74456i	−0.176171	−	0.187463i
$400$		0			0
$401$		−	16.6757i		−	0.832745i	−0.909194	−	0.416372i	$-0.863301\pi$
$401$		−	16.6757i		−	0.832745i	0.909194	−	0.416372i	$-0.136699\pi$
$402$		0			0
$403$	−22.1885	+	22.1885i	−1.10529	+	1.10529i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.35491	+	3.35491i	−0.166297	+	0.166297i
$408$		0			0
$409$			2.48913i			0.123079i	0.998105	+	0.0615397i	$0.0196011\pi$
$409$			2.48913i			0.123079i	−0.998105	+	0.0615397i	$0.980399\pi$
$410$		0			0
$411$	−8.44158	−	8.98266i	−0.416392	−	0.443082i
$412$		0			0
$413$	6.70982	+	6.70982i	0.330169	+	0.330169i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	26.1705	+	0.812683i	1.28158	+	0.0397972i
$418$		0			0
$419$	−2.81929			−0.137731			−0.0688657	−	0.997626i	$-0.521938\pi$
$419$	−2.81929			−0.137731			−0.0688657	+	0.997626i	$0.521938\pi$
$420$		0			0
$421$	−5.25544			−0.256134			−0.128067	−	0.991765i	$-0.540877\pi$
$421$	−5.25544			−0.256134			−0.128067	+	0.991765i	$0.540877\pi$
$422$		0			0
$423$	−17.9908	+	15.8849i	−0.874744	+	0.772350i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.768795	+	0.768795i	0.0372046	+	0.0372046i
$428$		0			0
$429$	6.92820	−	6.51087i	0.334497	−	0.314348i
$430$		0			0
$431$		−	22.6641i		−	1.09169i	−0.837885	−	0.545847i	$-0.816208\pi$
$431$		−	22.6641i		−	1.09169i	0.837885	−	0.545847i	$-0.183792\pi$
$432$		0			0
$433$	−6.12372	+	6.12372i	−0.294287	+	0.294287i	−0.838771	−	0.544484i	$-0.816726\pi$
$433$	−6.12372	+	6.12372i	−0.294287	+	0.294287i	0.544484	+	0.838771i	$0.316726\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−23.1539	+	23.1539i	−1.10760	+	1.10760i
$438$		0			0
$439$		−	8.62772i		−	0.411779i	−0.978575	−	0.205889i	$-0.933991\pi$
$439$		−	8.62772i		−	0.411779i	0.978575	−	0.205889i	$-0.0660087\pi$
$440$		0			0
$441$	−1.18614	+	19.0800i	−0.0564829	+	0.908572i
$442$		0			0
$443$	23.0559	+	23.0559i	1.09542	+	1.09542i	0.994939	+	0.100480i	$0.0320378\pi$
$443$	23.0559	+	23.0559i	1.09542	+	1.09542i	0.100480	+	0.994939i	$0.467962\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.202087	−	6.50774i	0.00955839	−	0.307805i
$448$		0			0
$449$	−2.22938			−0.105211			−0.0526056	−	0.998615i	$-0.516753\pi$
$449$	−2.22938			−0.105211			−0.0526056	+	0.998615i	$0.516753\pi$
$450$		0			0
$451$	−8.60597			−0.405239
$452$		0			0
$453$	−0.141266	+	4.54915i	−0.00663727	+	0.213738i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−11.3744	−	11.3744i	−0.532071	−	0.532071i	0.389117	−	0.921188i	$-0.372780\pi$
$457$	−11.3744	−	11.3744i	−0.532071	−	0.532071i	−0.921188	+	0.389117i	$0.872780\pi$
$458$		0			0
$459$	21.1345	+	25.4891i	0.986472	+	1.18973i
$460$		0			0
$461$			17.0256i			0.792959i	0.918044	+	0.396480i	$0.129768\pi$
$461$			17.0256i			0.792959i	−0.918044	+	0.396480i	$0.870232\pi$
$462$		0			0
$463$	6.43657	−	6.43657i	0.299133	−	0.299133i	−0.541541	−	0.840674i	$-0.682159\pi$
$463$	6.43657	−	6.43657i	0.299133	−	0.299133i	0.840674	+	0.541541i	$0.182159\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.82843	+	2.82843i	−0.130884	+	0.130884i	−0.769514	−	0.638630i	$-0.779501\pi$
$467$	−2.82843	+	2.82843i	−0.130884	+	0.130884i	0.638630	+	0.769514i	$0.279501\pi$
$468$		0			0
$469$		−	1.37228i		−	0.0633661i
$470$		0			0
$471$	16.4891	−	15.4959i	0.759779	−	0.714013i
$472$		0			0
$473$	−4.07740	−	4.07740i	−0.187479	−	0.187479i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.47841	−	1.67441i	−0.0676919	−	0.0766661i
$478$		0			0
$479$	4.45877			0.203726			0.101863	−	0.994798i	$-0.467520\pi$
$479$	4.45877			0.203726			0.101863	+	0.994798i	$0.467520\pi$
$480$		0			0
$481$	29.4891			1.34459
$482$		0			0
$483$	−11.9942	−	0.372461i	−0.545756	−	0.0169476i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	9.94106	+	9.94106i	0.450473	+	0.450473i	0.895511	−	0.445039i	$-0.146810\pi$
$487$	9.94106	+	9.94106i	0.450473	+	0.450473i	−0.445039	+	0.895511i	$0.646810\pi$
$488$		0			0
$489$	22.2492	+	23.6753i	1.00614	+	1.07063i
$490$		0			0
$491$			4.45877i			0.201221i	0.994926	+	0.100611i	$0.0320797\pi$
$491$			4.45877i			0.201221i	−0.994926	+	0.100611i	$0.967920\pi$
$492$		0			0
$493$	−14.2798	+	14.2798i	−0.643130	+	0.643130i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.77546	−	1.77546i	0.0796401	−	0.0796401i
$498$		0			0
$499$		−	23.3723i		−	1.04629i	−0.852245	−	0.523144i	$-0.824759\pi$
$499$		−	23.3723i		−	1.04629i	0.852245	−	0.523144i	$-0.175241\pi$
$500$		0			0
$501$	4.74456	+	5.04868i	0.211971	+	0.225558i
$502$		0			0
$503$	−16.2481	−	16.2481i	−0.724466	−	0.724466i	0.245046	−	0.969512i	$-0.421197\pi$
$503$	−16.2481	−	16.2481i	−0.724466	−	0.724466i	−0.969512	+	0.245046i	$0.921197\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−36.5578	−	1.13524i	−1.62359	−	0.0504179i
$508$		0			0
$509$	22.0742			0.978423			0.489212	−	0.872165i	$-0.337285\pi$
$509$	22.0742			0.978423			0.489212	+	0.872165i	$0.337285\pi$
$510$		0			0
$511$	6.23369			0.275762
$512$		0			0
$513$	19.3730	+	1.80944i	0.855339	+	0.0798889i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.31611	+	5.31611i	0.233802	+	0.233802i
$518$		0			0
$519$	15.1460	−	14.2337i	0.664837	−	0.624790i
$520$		0			0
$521$		−	16.6757i		−	0.730576i	−0.930895	−	0.365288i	$-0.880971\pi$
$521$		−	16.6757i		−	0.730576i	0.930895	−	0.365288i	$-0.119029\pi$
$522$		0			0
$523$	−12.8465	+	12.8465i	−0.561738	+	0.561738i	−0.929801	−	0.368063i	$-0.880021\pi$
$523$	−12.8465	+	12.8465i	−0.561738	+	0.561738i	0.368063	+	0.929801i	$0.380021\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−24.2069	+	24.2069i	−1.05447	+	1.05447i
$528$		0			0
$529$			53.4674i			2.32467i
$530$		0			0
$531$	−35.8614	−	2.22938i	−1.55625	−	0.0967470i
$532$		0			0
$533$	37.8225	+	37.8225i	1.63828	+	1.63828i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.321939	−	10.3673i	0.0138927	−	0.447381i
$538$		0			0
$539$	5.98844			0.257940
$540$		0			0
$541$	5.88316			0.252937			0.126468	−	0.991971i	$-0.459636\pi$
$541$	5.88316			0.252937			0.126468	+	0.991971i	$0.459636\pi$
$542$		0			0
$543$	−1.08148	+	34.8266i	−0.0464109	+	1.49455i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	3.53113	+	3.53113i	0.150980	+	0.150980i	0.778556	−	0.627575i	$-0.215953\pi$
$547$	3.53113	+	3.53113i	0.150980	+	0.150980i	−0.627575	+	0.778556i	$0.715953\pi$
$548$		0			0
$549$	−4.10891	−	0.255437i	−0.175364	−	0.0109018i
$550$		0			0
$551$			11.8671i			0.505554i
$552$		0			0
$553$	−4.89898	+	4.89898i	−0.208326	+	0.208326i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	24.7334	−	24.7334i	1.04799	−	1.04799i	0.0491969	−	0.998789i	$-0.484334\pi$
$557$	24.7334	−	24.7334i	1.04799	−	1.04799i	0.998789	−	0.0491969i	$-0.0156662\pi$
$558$		0			0
$559$			35.8397i			1.51586i
$560$		0			0
$561$	7.55842	−	7.10313i	0.319117	−	0.299894i
$562$		0			0
$563$	−22.9579	−	22.9579i	−0.967560	−	0.967560i	0.0319299	−	0.999490i	$-0.489835\pi$
$563$	−22.9579	−	22.9579i	−0.967560	−	0.967560i	−0.999490	+	0.0319299i	$0.989835\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	4.37878	+	5.62775i	0.183891	+	0.236343i
$568$		0			0
$569$	−34.9909			−1.46689			−0.733447	−	0.679747i	$-0.762090\pi$
$569$	−34.9909			−1.46689			−0.733447	+	0.679747i	$0.762090\pi$
$570$		0			0
$571$	31.8397			1.33245			0.666224	−	0.745752i	$-0.267909\pi$
$571$	31.8397			1.33245			0.666224	+	0.745752i	$0.267909\pi$
$572$		0			0
$573$	43.7017	+	1.35709i	1.82567	+	0.0566931i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−26.2144	−	26.2144i	−1.09132	−	1.09132i	−0.995388	−	0.0959325i	$-0.969417\pi$
$577$	−26.2144	−	26.2144i	−1.09132	−	1.09132i	−0.0959325	−	0.995388i	$-0.530583\pi$
$578$		0			0
$579$	14.0313	+	14.9307i	0.583122	+	0.620499i
$580$		0			0
$581$			4.45877i			0.184981i
$582$		0			0
$583$	−0.494772	+	0.494772i	−0.0204914	+	0.0204914i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−16.8726	+	16.8726i	−0.696405	+	0.696405i	−0.963633	−	0.267228i	$-0.913892\pi$
$587$	−16.8726	+	16.8726i	−0.696405	+	0.696405i	0.267228	+	0.963633i	$0.413892\pi$
$588$		0			0
$589$			20.1168i			0.828900i
$590$		0			0
$591$	16.8832	+	17.9653i	0.694480	+	0.738994i
$592$		0			0
$593$	13.5177	+	13.5177i	0.555103	+	0.555103i	0.927909	−	0.372806i	$-0.121604\pi$
$593$	13.5177	+	13.5177i	0.555103	+	0.555103i	−0.372806	+	0.927909i	$0.621604\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.01158	+	0.248787i	0.327892	+	0.0101822i
$598$		0			0
$599$	28.4125			1.16090			0.580452	−	0.814294i	$-0.302876\pi$
$599$	28.4125			1.16090			0.580452	+	0.814294i	$0.302876\pi$
$600$		0			0
$601$	−3.74456			−0.152744			−0.0763719	−	0.997079i	$-0.524334\pi$
$601$	−3.74456			−0.152744			−0.0763719	+	0.997079i	$0.524334\pi$
$602$		0			0
$603$	3.43918	+	3.89513i	0.140054	+	0.158622i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−18.4755	−	18.4755i	−0.749896	−	0.749896i	0.224564	−	0.974459i	$-0.427904\pi$
$607$	−18.4755	−	18.4755i	−0.749896	−	0.749896i	−0.974459	+	0.224564i	$0.927904\pi$
$608$		0			0
$609$	−3.16915	+	2.97825i	−0.128420	+	0.120685i
$610$		0			0
$611$		−	46.7277i		−	1.89040i
$612$		0			0
$613$	8.88606	−	8.88606i	0.358905	−	0.358905i	−0.504504	−	0.863409i	$-0.668325\pi$
$613$	8.88606	−	8.88606i	0.358905	−	0.358905i	0.863409	+	0.504504i	$0.168325\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.9461	+	13.9461i	−0.561450	+	0.561450i	−0.929719	−	0.368269i	$-0.879951\pi$
$617$	−13.9461	+	13.9461i	−0.561450	+	0.561450i	0.368269	+	0.929719i	$0.379951\pi$
$618$		0			0
$619$		−	12.8614i		−	0.516944i	−0.966019	−	0.258472i	$-0.916781\pi$
$619$		−	12.8614i		−	0.516944i	0.966019	−	0.258472i	$-0.0832189\pi$
$620$		0			0
$621$	34.9783	−	29.0024i	1.40363	−	1.16383i
$622$		0			0
$623$	9.01177	+	9.01177i	0.361049	+	0.361049i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.189182	−	6.09216i	0.00755520	−	0.243297i
$628$		0			0
$629$	32.1716			1.28276
$630$		0			0
$631$	−25.6060			−1.01936			−0.509679	−	0.860365i	$-0.670236\pi$
$631$	−25.6060			−1.01936			−0.509679	+	0.860365i	$0.670236\pi$
$632$		0			0
$633$	0.523868	−	16.8699i	0.0208219	−	0.670520i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−26.3187	−	26.3187i	−1.04278	−	1.04278i
$638$		0			0
$639$	−0.589907	+	9.48913i	−0.0233364	+	0.375384i
$640$		0			0
$641$			23.9538i			0.946117i	0.881031	+	0.473058i	$0.156850\pi$
$641$			23.9538i			0.946117i	−0.881031	+	0.473058i	$0.843150\pi$
$642$		0			0
$643$	5.10754	−	5.10754i	0.201422	−	0.201422i	−0.599187	−	0.800609i	$-0.704509\pi$
$643$	5.10754	−	5.10754i	0.201422	−	0.201422i	0.800609	+	0.599187i	$0.204509\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$647$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$648$		0			0
$649$			11.2554i			0.441815i
$650$		0			0
$651$	−5.37228	+	5.04868i	−0.210556	+	0.197873i
$652$		0			0
$653$	−6.90583	−	6.90583i	−0.270246	−	0.270246i	0.558953	−	0.829199i	$-0.311203\pi$
$653$	−6.90583	−	6.90583i	−0.270246	−	0.270246i	−0.829199	+	0.558953i	$0.811203\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−17.6939	+	15.6227i	−0.690305	+	0.609501i
$658$		0			0
$659$	35.6906			1.39031			0.695154	−	0.718861i	$-0.255336\pi$
$659$	35.6906			1.39031			0.695154	+	0.718861i	$0.255336\pi$
$660$		0			0
$661$	40.2337			1.56491			0.782455	−	0.622708i	$-0.213967\pi$
$661$	40.2337			1.56491			0.782455	+	0.622708i	$0.213967\pi$
$662$		0			0
$663$	−64.4363	−	2.00096i	−2.50250	−	0.0777110i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	19.5959	+	19.5959i	0.758757	+	0.758757i
$668$		0			0
$669$	−20.7846	−	22.1168i	−0.803579	−	0.855087i
$670$		0			0
$671$			1.28962i			0.0497852i
$672$		0			0
$673$	1.82380	−	1.82380i	0.0703023	−	0.0703023i	−0.671081	−	0.741384i	$-0.734170\pi$
$673$	1.82380	−	1.82380i	0.0703023	−	0.0703023i	0.741384	+	0.671081i	$0.234170\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.2481	−	16.2481i	0.624464	−	0.624464i	−0.322205	−	0.946670i	$-0.604424\pi$
$677$	16.2481	−	16.2481i	0.624464	−	0.624464i	0.946670	+	0.322205i	$0.104424\pi$
$678$		0			0
$679$		−	5.88316i		−	0.225775i
$680$		0			0
$681$	4.74456	+	5.04868i	0.181812	+	0.193466i
$682$		0			0
$683$	17.3990	+	17.3990i	0.665756	+	0.665756i	0.956731	−	0.290975i	$-0.0939795\pi$
$683$	17.3990	+	17.3990i	0.665756	+	0.665756i	−0.290975	+	0.956731i	$0.593980\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−8.01158	−	0.248787i	−0.305661	−	0.00949180i
$688$		0			0
$689$	4.34896			0.165682
$690$		0			0
$691$	−21.3505			−0.812213			−0.406106	−	0.913826i	$-0.633114\pi$
$691$	−21.3505			−0.812213			−0.406106	+	0.913826i	$0.633114\pi$
$692$		0			0
$693$	1.67441	−	1.47841i	0.0636057	−	0.0561602i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	41.2630	+	41.2630i	1.56295	+	1.56295i
$698$		0			0
$699$	−23.0140	+	21.6277i	−0.870469	+	0.818035i
$700$		0			0
$701$			13.2665i			0.501069i	0.968108	+	0.250534i	$0.0806063\pi$
$701$			13.2665i			0.501069i	−0.968108	+	0.250534i	$0.919394\pi$
$702$		0			0
$703$	13.3679	−	13.3679i	0.504180	−	0.504180i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.93437	+	4.93437i	−0.185576	+	0.185576i
$708$		0			0
$709$			0.861407i			0.0323508i	0.999869	+	0.0161754i	$0.00514902\pi$
$709$			0.861407i			0.0323508i	−0.999869	+	0.0161754i	$0.994851\pi$
$710$		0			0
$711$	1.62772	−	26.1831i	0.0610442	−	0.981945i
$712$		0			0
$713$	33.2186	+	33.2186i	1.24405	+	1.24405i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.713208	+	22.9672i	−0.0266352	+	0.857725i
$718$		0			0
$719$	−27.8226			−1.03761			−0.518804	−	0.854893i	$-0.673623\pi$
$719$	−27.8226			−1.03761			−0.518804	+	0.854893i	$0.673623\pi$
$720$		0			0
$721$	−9.25544			−0.344690
$722$		0			0
$723$	−0.711444	+	22.9104i	−0.0264589	+	0.852046i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	10.5668	+	10.5668i	0.391899	+	0.391899i	0.875364	−	0.483465i	$-0.160622\pi$
$727$	10.5668	+	10.5668i	0.391899	+	0.391899i	−0.483465	+	0.875364i	$0.660622\pi$
$728$		0			0
$729$	−26.5330	−	5.00000i	−0.982704	−	0.185185i
$730$		0			0
$731$			39.0998i			1.44616i
$732$		0			0
$733$	−34.2929	+	34.2929i	−1.26664	+	1.26664i	−0.318820	+	0.947815i	$0.603287\pi$
$733$	−34.2929	+	34.2929i	−1.26664	+	1.26664i	−0.947815	+	0.318820i	$0.896713\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.15097	−	1.15097i	0.0423966	−	0.0423966i
$738$		0			0
$739$		−	44.4674i		−	1.63576i	−0.575390	−	0.817879i	$-0.695150\pi$
$739$		−	44.4674i		−	1.63576i	0.575390	−	0.817879i	$-0.304850\pi$
$740$		0			0
$741$	−27.6060	+	25.9431i	−1.01413	+	0.953043i
$742$		0			0
$743$	−32.6922	−	32.6922i	−1.19936	−	1.19936i	−0.974359	−	0.225000i	$-0.927762\pi$
$743$	−32.6922	−	32.6922i	−1.19936	−	1.19936i	−0.225000	−	0.974359i	$-0.572238\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−11.1745	−	12.6559i	−0.408852	−	0.463056i
$748$		0			0
$749$	1.28962			0.0471217
$750$		0			0
$751$	−44.0000			−1.60558			−0.802791	−	0.596260i	$-0.796653\pi$
$751$	−44.0000			−1.60558			−0.802791	+	0.596260i	$0.796653\pi$
$752$		0			0
$753$	18.0864	+	0.561643i	0.659104	+	0.0204674i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−28.6251	−	28.6251i	−1.04040	−	1.04040i	−0.999149	−	0.0412473i	$-0.986867\pi$
$757$	−28.6251	−	28.6251i	−1.04040	−	1.04040i	−0.0412473	−	0.999149i	$-0.513133\pi$
$758$		0			0
$759$	−9.74749	−	10.3723i	−0.353812	−	0.376490i
$760$		0			0
$761$		−	14.2063i		−	0.514977i	−0.966281	−	0.257488i	$-0.917105\pi$
$761$		−	14.2063i		−	0.514977i	0.966281	−	0.257488i	$-0.0828949\pi$
$762$		0			0
$763$	−6.08490	+	6.08490i	−0.220288	+	0.220288i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	49.4667	−	49.4667i	1.78614	−	1.78614i
$768$		0			0
$769$			7.51087i			0.270849i	0.990788	+	0.135425i	$0.0432398\pi$
$769$			7.51087i			0.270849i	−0.990788	+	0.135425i	$0.956760\pi$
$770$		0			0
$771$	−16.8832	−	17.9653i	−0.608032	−	0.647005i
$772$		0			0
$773$	−36.7696	−	36.7696i	−1.32251	−	1.32251i	−0.911739	−	0.410770i	$-0.865260\pi$
$773$	−36.7696	−	36.7696i	−1.32251	−	1.32251i	−0.410770	−	0.911739i	$-0.634740\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	6.92487	+	0.215040i	0.248428	+	0.00771453i
$778$		0			0
$779$	34.2912			1.22861
$780$		0			0
$781$	2.97825			0.106570
$782$		0			0
$783$	1.53139	−	16.3960i	0.0547275	−	0.585946i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−0.560232	−	0.560232i	−0.0199701	−	0.0199701i	0.697051	−	0.717021i	$-0.254495\pi$
$787$	−0.560232	−	0.560232i	−0.0199701	−	0.0199701i	−0.717021	+	0.697051i	$0.754495\pi$
$788$		0			0
$789$	19.2549	−	18.0951i	0.685494	−	0.644202i
$790$		0			0
$791$			1.87953i			0.0668283i
$792$		0			0
$793$	5.66777	−	5.66777i	0.201269	−	0.201269i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.0647	−	10.0647i	0.356511	−	0.356511i	−0.506014	−	0.862525i	$-0.668882\pi$
$797$	10.0647	−	10.0647i	0.356511	−	0.356511i	0.862525	+	0.506014i	$0.168882\pi$
$798$		0			0
$799$		−	50.9783i		−	1.80348i
$800$		0			0
$801$	−48.1644	−	2.99422i	−1.70181	−	0.105796i
$802$		0			0
$803$	5.22837	+	5.22837i	0.184505	+	0.184505i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.45813	+	46.9556i	−0.0513286	+	1.65292i
$808$		0			0
$809$	−5.74839			−0.202103			−0.101051	−	0.994881i	$-0.532221\pi$
$809$	−5.74839			−0.202103			−0.101051	+	0.994881i	$0.532221\pi$
$810$		0			0
$811$	32.6277			1.14571			0.572857	−	0.819655i	$-0.305835\pi$
$811$	32.6277			1.14571			0.572857	+	0.819655i	$0.305835\pi$
$812$		0			0
$813$	0.980245	−	31.5665i	0.0343787	−	1.10708i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	16.2467	+	16.2467i	0.568401	+	0.568401i
$818$		0			0
$819$	−13.8564	−	0.861407i	−0.484182	−	0.0301000i
$820$		0			0
$821$			25.8333i			0.901588i	0.892628	+	0.450794i	$0.148859\pi$
$821$			25.8333i			0.901588i	−0.892628	+	0.450794i	$0.851141\pi$
$822$		0			0
$823$	−2.59259	+	2.59259i	−0.0903721	+	0.0903721i	−0.750848	−	0.660475i	$-0.770355\pi$
$823$	−2.59259	+	2.59259i	−0.0903721	+	0.0903721i	0.660475	+	0.750848i	$0.270355\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.2157	−	11.2157i	0.390008	−	0.390008i	−0.484682	−	0.874690i	$-0.661065\pi$
$827$	11.2157	−	11.2157i	0.390008	−	0.390008i	0.874690	+	0.484682i	$0.161065\pi$
$828$		0			0
$829$			13.2554i			0.460380i	0.973146	+	0.230190i	$0.0739348\pi$
$829$			13.2554i			0.460380i	−0.973146	+	0.230190i	$0.926065\pi$
$830$		0			0
$831$	26.1168	−	24.5437i	0.905983	−	0.851410i
$832$		0			0
$833$	−28.7128	−	28.7128i	−0.994838	−	0.994838i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.59599	−	27.7942i	0.0897305	−	0.960709i
$838$		0			0
$839$	−40.9793			−1.41476			−0.707381	−	0.706832i	$-0.750124\pi$
$839$	−40.9793			−1.41476			−0.707381	+	0.706832i	$0.750124\pi$
$840$		0			0
$841$	−18.9565			−0.653672
$842$		0			0
$843$	35.9827	+	1.11738i	1.23931	+	0.0384847i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.66777	+	5.66777i	0.194747	+	0.194747i
$848$		0			0
$849$	−29.7673	−	31.6753i	−1.02161	−	1.08709i
$850$		0			0
$851$		−	44.1485i		−	1.51339i
$852$		0			0
$853$	27.5823	−	27.5823i	0.944399	−	0.944399i	−0.0541349	−	0.998534i	$-0.517240\pi$
$853$	27.5823	−	27.5823i	0.944399	−	0.944399i	0.998534	+	0.0541349i	$0.0172401\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.2401	−	14.2401i	0.486434	−	0.486434i	−0.420745	−	0.907179i	$-0.638231\pi$
$857$	14.2401	−	14.2401i	0.486434	−	0.486434i	0.907179	+	0.420745i	$0.138231\pi$
$858$		0			0
$859$			11.8614i			0.404706i	0.979313	+	0.202353i	$0.0648588\pi$
$859$			11.8614i			0.404706i	−0.979313	+	0.202353i	$0.935141\pi$
$860$		0			0
$861$	8.60597	+	9.15759i	0.293291	+	0.312090i
$862$		0			0
$863$	−5.65685	−	5.65685i	−0.192562	−	0.192562i	0.604240	−	0.796802i	$-0.293477\pi$
$863$	−5.65685	−	5.65685i	−0.192562	−	0.192562i	−0.796802	+	0.604240i	$0.793477\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−40.8670	−	1.26906i	−1.38792	−	0.0430995i
$868$		0			0
$869$	−8.21782			−0.278771
$870$		0			0
$871$	−10.1168			−0.342796
$872$		0			0
$873$	14.7442	+	16.6990i	0.499017	+	0.565174i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.768795	−	0.768795i	−0.0259604	−	0.0259604i	0.694007	−	0.719968i	$-0.255843\pi$
$877$	−0.768795	−	0.768795i	−0.0259604	−	0.0259604i	−0.719968	+	0.694007i	$0.755843\pi$
$878$		0			0
$879$	−38.1600	+	35.8614i	−1.28711	+	1.20958i
$880$		0			0
$881$			17.6155i			0.593480i	0.954958	+	0.296740i	$0.0958995\pi$
$881$			17.6155i			0.593480i	−0.954958	+	0.296740i	$0.904101\pi$
$882$		0			0
$883$	5.28947	−	5.28947i	0.178005	−	0.178005i	−0.612481	−	0.790486i	$-0.709828\pi$
$883$	5.28947	−	5.28947i	0.178005	−	0.178005i	0.790486	+	0.612481i	$0.209828\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.6274	−	22.6274i	0.759754	−	0.759754i	−0.216523	−	0.976277i	$-0.569472\pi$
$887$	22.6274	−	22.6274i	0.759754	−	0.759754i	0.976277	+	0.216523i	$0.0694717\pi$
$888$		0			0
$889$		−	10.7446i		−	0.360361i
$890$		0			0
$891$	−1.04755	+	8.39275i	−0.0350942	+	0.281168i
$892$		0			0
$893$	−21.1824	−	21.1824i	−0.708843	−	0.708843i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−2.74589	+	88.4248i	−0.0916825	+	2.95242i
$898$		0			0
$899$	17.0256			0.567834
$900$		0			0
$901$	4.74456			0.158064
$902$		0			0
$903$	−0.261350	+	8.41615i	−0.00869717	+	0.280072i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	35.4910	+	35.4910i	1.17846	+	1.17846i	0.980137	+	0.198321i	$0.0635488\pi$
$907$	35.4910	+	35.4910i	1.17846	+	1.17846i	0.198321	+	0.980137i	$0.436451\pi$
$908$		0			0
$909$	1.63948	−	26.3723i	0.0543780	−	0.874713i
$910$		0			0
$911$			54.2458i			1.79724i	0.438724	+	0.898622i	$0.355431\pi$
$911$			54.2458i			1.79724i	−0.438724	+	0.898622i	$0.644569\pi$
$912$		0			0
$913$	−3.73969	+	3.73969i	−0.123766	+	0.123766i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.82843	−	2.82843i	0.0934029	−	0.0934029i
$918$		0			0
$919$		−	33.8397i		−	1.11627i	−0.829751	−	0.558134i	$-0.811518\pi$
$919$		−	33.8397i		−	1.11627i	0.829751	−	0.558134i	$-0.188482\pi$
$920$		0			0
$921$	34.7921	−	32.6964i	1.14644	−	1.07738i
$922$		0			0
$923$	−13.0892	−	13.0892i	−0.430835	−	0.430835i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	26.2709	−	23.1958i	0.862851	−	0.761849i
$928$		0			0
$929$	−3.16915			−0.103976			−0.0519882	−	0.998648i	$-0.516556\pi$
$929$	−3.16915			−0.103976			−0.0519882	+	0.998648i	$0.516556\pi$
$930$		0			0
$931$	−23.8614			−0.782026
$932$		0			0
$933$	−44.7230	−	1.38880i	−1.46417	−	0.0454673i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−3.67423	−	3.67423i	−0.120032	−	0.120032i	0.644539	−	0.764571i	$-0.277049\pi$
$937$	−3.67423	−	3.67423i	−0.120032	−	0.120032i	−0.764571	+	0.644539i	$0.777049\pi$
$938$		0			0
$939$	−15.1460	−	16.1168i	−0.494272	−	0.525953i
$940$		0			0
$941$			30.2921i			0.987493i	0.869606	+	0.493746i	$0.164373\pi$
$941$			30.2921i			0.987493i	−0.869606	+	0.493746i	$0.835627\pi$
$942$		0			0
$943$	56.6245	−	56.6245i	1.84395	−	1.84395i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.8520	−	20.8520i	0.677598	−	0.677598i	−0.281858	−	0.959456i	$-0.590951\pi$
$947$	20.8520	−	20.8520i	0.677598	−	0.677598i	0.959456	+	0.281858i	$0.0909508\pi$
$948$		0			0
$949$		−	45.9565i		−	1.49181i
$950$		0			0
$951$	11.2554	+	11.9769i	0.364983	+	0.388377i
$952$		0			0
$953$	−17.3990	−	17.3990i	−0.563610	−	0.563610i	0.366721	−	0.930331i	$-0.380480\pi$
$953$	−17.3990	−	17.3990i	−0.563610	−	0.563610i	−0.930331	+	0.366721i	$0.880480\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−5.15600	−	0.160111i	−0.166670	−	0.00517565i
$958$		0			0
$959$	5.63858			0.182079
$960$		0			0
$961$	−2.13859			−0.0689869
$962$		0			0
$963$	−3.66050	+	3.23202i	−0.117958	+	0.104150i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−42.1361	−	42.1361i	−1.35501	−	1.35501i	−0.879963	−	0.475043i	$-0.842433\pi$
$967$	−42.1361	−	42.1361i	−1.35501	−	1.35501i	−0.475043	−	0.879963i	$-0.657567\pi$
$968$		0			0
$969$	−30.1171	+	28.3030i	−0.967501	+	0.909223i
$970$		0			0
$971$			22.4241i			0.719623i	0.933025	+	0.359812i	$0.117159\pi$
$971$			22.4241i			0.719623i	−0.933025	+	0.359812i	$0.882841\pi$
$972$		0			0
$973$	−8.46893	+	8.46893i	−0.271502	+	0.271502i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.33431	+	7.33431i	−0.234645	+	0.234645i	−0.814628	−	0.579983i	$-0.803059\pi$
$977$	−7.33431	+	7.33431i	−0.234645	+	0.234645i	0.579983	+	0.814628i	$0.303059\pi$
$978$		0			0
$979$			15.1168i			0.483136i
$980$		0			0
$981$	2.02175	−	32.5214i	0.0645495	−	1.03833i
$982$		0			0
$983$	7.95880	+	7.95880i	0.253846	+	0.253846i	0.822545	−	0.568699i	$-0.192553\pi$
$983$	7.95880	+	7.95880i	0.253846	+	0.253846i	−0.568699	+	0.822545i	$0.692553\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.340747	−	10.9730i	0.0108461	−	0.349273i
$988$		0			0
$989$	53.6559			1.70616
$990$		0			0
$991$	57.8397			1.83734			0.918669	−	0.395029i	$-0.129265\pi$
$991$	57.8397			1.83734			0.918669	+	0.395029i	$0.129265\pi$
$992$		0			0
$993$	1.41778	−	45.6561i	0.0449918	−	1.44885i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−4.06472	−	4.06472i	−0.128731	−	0.128731i	0.639806	−	0.768537i	$-0.279015\pi$
$997$	−4.06472	−	4.06472i	−0.128731	−	0.128731i	−0.768537	+	0.639806i	$0.779015\pi$
$998$		0			0
$999$	−20.1947	+	16.7446i	−0.638932	+	0.529775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.r.f.257.5	yes	16
3.2	odd	2	inner	600.2.r.f.257.8	yes	16
4.3	odd	2		1200.2.v.m.257.4		16
5.2	odd	4	inner	600.2.r.f.593.1	yes	16
5.3	odd	4	inner	600.2.r.f.593.8	yes	16
5.4	even	2	inner	600.2.r.f.257.4	yes	16
12.11	even	2		1200.2.v.m.257.1		16
15.2	even	4	inner	600.2.r.f.593.4	yes	16
15.8	even	4	inner	600.2.r.f.593.5	yes	16
15.14	odd	2	inner	600.2.r.f.257.1	✓	16
20.3	even	4		1200.2.v.m.593.1		16
20.7	even	4		1200.2.v.m.593.8		16
20.19	odd	2		1200.2.v.m.257.5		16
60.23	odd	4		1200.2.v.m.593.4		16
60.47	odd	4		1200.2.v.m.593.5		16
60.59	even	2		1200.2.v.m.257.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.r.f.257.1	✓	16	15.14	odd	2	inner
600.2.r.f.257.4	yes	16	5.4	even	2	inner
600.2.r.f.257.5	yes	16	1.1	even	1	trivial
600.2.r.f.257.8	yes	16	3.2	odd	2	inner
600.2.r.f.593.1	yes	16	5.2	odd	4	inner
600.2.r.f.593.4	yes	16	15.2	even	4	inner
600.2.r.f.593.5	yes	16	15.8	even	4	inner
600.2.r.f.593.8	yes	16	5.3	odd	4	inner
1200.2.v.m.257.1		16	12.11	even	2
1200.2.v.m.257.4		16	4.3	odd	2
1200.2.v.m.257.5		16	20.19	odd	2
1200.2.v.m.257.8		16	60.59	even	2
1200.2.v.m.593.1		16	20.3	even	4
1200.2.v.m.593.4		16	60.23	odd	4
1200.2.v.m.593.5		16	60.47	odd	4
1200.2.v.m.593.8		16	20.7	even	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0537601 - 1.73122i) q^{3} +(0.560232 + 0.560232i) q^{7} +(-2.99422 - 0.186141i) q^{9} +O(q^{10})\)	\(q+(0.0537601 - 1.73122i) q^{3} +(0.560232 + 0.560232i) q^{7} +(-2.99422 - 0.186141i) q^{9} +0.939764i q^{11} +(4.13018 - 4.13018i) q^{13} +(4.50588 - 4.50588i) q^{17} -3.74456i q^{19} +(1.00000 - 0.939764i) q^{21} +(-6.18334 - 6.18334i) q^{23} +(-0.483219 + 5.17364i) q^{27} -3.16915 q^{29} -5.37228 q^{31} +(1.62693 + 0.0505218i) q^{33} +(3.56995 + 3.56995i) q^{37} +(-6.92820 - 7.37228i) q^{39} +9.15759i q^{41} +(-4.33875 + 4.33875i) q^{43} +(5.65685 - 5.65685i) q^{47} -6.37228i q^{49} +(-7.55842 - 8.04290i) q^{51} +(0.526485 + 0.526485i) q^{53} +(-6.48265 - 0.201308i) q^{57} +11.9769 q^{59} +1.37228 q^{61} +(-1.57317 - 1.78174i) q^{63} +(-1.22474 - 1.22474i) q^{67} +(-11.0371 + 10.3723i) q^{69} -3.16915i q^{71} +(5.56349 - 5.56349i) q^{73} +(-0.526485 + 0.526485i) q^{77} +8.74456i q^{79} +(8.93070 + 1.11469i) q^{81} +(3.97940 + 3.97940i) q^{83} +(-0.170374 + 5.48648i) q^{87} +16.0858 q^{89} +4.62772 q^{91} +(-0.288814 + 9.30058i) q^{93} +(-5.25065 - 5.25065i) q^{97} +(0.174928 - 2.81386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 16 q^{21} - 40 q^{31} - 52 q^{51} - 24 q^{61} + 28 q^{81} + 120 q^{91}+O(q^{100}) \) 16 * q + 16 * q^21 - 40 * q^31 - 52 * q^51 - 24 * q^61 + 28 * q^81 + 120 * q^91

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