LMFDB - Embedded newform 600.2.r.f.257.1

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			257.1
Root			$-0.912166 + 1.47240i$ of defining polynomial
Character	$\chi$	$=$	600.257
Dual form			600.2.r.f.593.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73122 + 0.0537601i) q^{3} +(-0.560232 - 0.560232i) q^{7} +(2.99422 - 0.186141i) q^{9} +O(q^{10})$	$q+(-1.73122 + 0.0537601i) q^{3} +(-0.560232 - 0.560232i) q^{7} +(2.99422 - 0.186141i) q^{9} -0.939764i q^{11} +(-4.13018 + 4.13018i) q^{13} +(4.50588 - 4.50588i) q^{17} -3.74456i q^{19} +(1.00000 + 0.939764i) q^{21} +(-6.18334 - 6.18334i) q^{23} +(-5.17364 + 0.483219i) q^{27} +3.16915 q^{29} -5.37228 q^{31} +(0.0505218 + 1.62693i) q^{33} +(-3.56995 - 3.56995i) q^{37} +(6.92820 - 7.37228i) q^{39} -9.15759i q^{41} +(4.33875 - 4.33875i) q^{43} +(5.65685 - 5.65685i) q^{47} -6.37228i q^{49} +(-7.55842 + 8.04290i) q^{51} +(0.526485 + 0.526485i) q^{53} +(0.201308 + 6.48265i) q^{57} -11.9769 q^{59} +1.37228 q^{61} +(-1.78174 - 1.57317i) q^{63} +(1.22474 + 1.22474i) q^{67} +(11.0371 + 10.3723i) q^{69} +3.16915i q^{71} +(-5.56349 + 5.56349i) q^{73} +(-0.526485 + 0.526485i) q^{77} +8.74456i q^{79} +(8.93070 - 1.11469i) q^{81} +(3.97940 + 3.97940i) q^{83} +(-5.48648 + 0.170374i) q^{87} -16.0858 q^{89} +4.62772 q^{91} +(9.30058 - 0.288814i) q^{93} +(5.25065 + 5.25065i) q^{97} +(-0.174928 - 2.81386i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.73122	+	0.0537601i	−0.999518	+	0.0310384i
$3$	−1.73122	+	0.0537601i	−0.999518	+	0.0310384i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.560232	−	0.560232i	−0.211748	−	0.211748i	0.593262	−	0.805010i	$-0.297840\pi$
$7$	−0.560232	−	0.560232i	−0.211748	−	0.211748i	−0.805010	+	0.593262i	$0.797840\pi$
$8$		0			0
$9$	2.99422	−	0.186141i	0.998073	−	0.0620469i
$10$		0			0
$11$		−	0.939764i		−	0.283349i	−0.989913	−	0.141675i	$-0.954751\pi$
$11$		−	0.939764i		−	0.283349i	0.989913	−	0.141675i	$-0.0452487\pi$
$12$		0			0
$13$	−4.13018	+	4.13018i	−1.14551	+	1.14551i	−0.158081	+	0.987426i	$0.550531\pi$
$13$	−4.13018	+	4.13018i	−1.14551	+	1.14551i	−0.987426	+	0.158081i	$0.949469\pi$
$14$		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
$27$	−5.17364	+	0.483219i	−0.995667	+	0.0929956i
$28$		0			0
$29$	3.16915			0.588496			0.294248	−	0.955729i	$-0.404931\pi$
$29$	3.16915			0.588496			0.294248	+	0.955729i	$0.404931\pi$
$30$		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
$33$	0.0505218	+	1.62693i	0.00879471	+	0.283213i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.56995	−	3.56995i	−0.586897	−	0.586897i	0.349893	−	0.936790i	$-0.386218\pi$
$37$	−3.56995	−	3.56995i	−0.586897	−	0.586897i	−0.936790	+	0.349893i	$0.886218\pi$
$38$		0			0
$39$	6.92820	−	7.37228i	1.10940	−	1.18051i
$40$		0			0
$41$		−	9.15759i		−	1.43017i	−0.699035	−	0.715087i	$-0.746387\pi$
$41$		−	9.15759i		−	1.43017i	0.699035	−	0.715087i	$-0.253613\pi$
$42$		0			0
$43$	4.33875	−	4.33875i	0.661653	−	0.661653i	−0.294117	−	0.955770i	$-0.595025\pi$
$43$	4.33875	−	4.33875i	0.661653	−	0.661653i	0.955770	+	0.294117i	$0.0950254\pi$
$44$		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
$57$	0.201308	+	6.48265i	0.0266639	+	0.858648i
$58$		0			0
$59$	−11.9769			−1.55926			−0.779628	−	0.626242i	$-0.784592\pi$
$59$	−11.9769			−1.55926			−0.779628	+	0.626242i	$0.784592\pi$
$60$		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
$63$	−1.78174	−	1.57317i	−0.224478	−	0.198201i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.22474	+	1.22474i	0.149626	+	0.149626i	0.777951	−	0.628325i	$-0.216259\pi$
$67$	1.22474	+	1.22474i	0.149626	+	0.149626i	−0.628325	+	0.777951i	$0.716259\pi$
$68$		0			0
$69$	11.0371	+	10.3723i	1.32871	+	1.24868i
$70$		0			0
$71$			3.16915i			0.376109i	0.982159	+	0.188054i	$0.0602181\pi$
$71$			3.16915i			0.376109i	−0.982159	+	0.188054i	$0.939782\pi$
$72$		0			0
$73$	−5.56349	+	5.56349i	−0.651158	+	0.651158i	−0.953272	−	0.302114i	$-0.902308\pi$
$73$	−5.56349	+	5.56349i	−0.651158	+	0.651158i	0.302114	+	0.953272i	$0.402308\pi$
$74$		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
$87$	−5.48648	+	0.170374i	−0.588212	+	0.0182660i
$88$		0			0
$89$	−16.0858			−1.70509			−0.852545	−	0.522654i	$-0.824942\pi$
$89$	−16.0858			−1.70509			−0.852545	+	0.522654i	$0.824942\pi$
$90$		0			0
$91$	4.62772			0.485117
$92$		0			0
$93$	9.30058	−	0.288814i	0.964425	−	0.0299486i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	5.25065	+	5.25065i	0.533122	+	0.533122i	0.921500	−	0.388378i	$-0.126964\pi$
$97$	5.25065	+	5.25065i	0.533122	+	0.533122i	−0.388378	+	0.921500i	$0.626964\pi$
$98$		0			0
$99$	−0.174928	−	2.81386i	−0.0175810	−	0.282804i
$100$		0			0
$101$		−	8.80773i		−	0.876402i	−0.898877	−	0.438201i	$-0.855616\pi$
$101$		−	8.80773i		−	0.876402i	0.898877	−	0.438201i	$-0.144384\pi$
$102$		0			0
$103$	8.26037	−	8.26037i	0.813918	−	0.813918i	−0.171301	−	0.985219i	$-0.554797\pi$
$103$	8.26037	−	8.26037i	0.813918	−	0.813918i	0.985219	+	0.171301i	$0.0547969\pi$
$104$		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
$117$	−11.5979	+	13.1355i	−1.07222	+	1.21438i
$118$		0			0
$119$	−5.04868			−0.462811
$120$		0			0
$121$	10.1168			0.919713
$122$		0			0
$123$	0.492313	+	15.8538i	0.0443903	+	1.42949i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	9.58940	+	9.58940i	0.850921	+	0.850921i	0.990247	−	0.139325i	$-0.0444934\pi$
$127$	9.58940	+	9.58940i	0.850921	+	0.850921i	−0.139325	+	0.990247i	$0.544493\pi$
$128$		0			0
$129$	−7.27806	+	7.74456i	−0.640797	+	0.681871i
$130$		0			0
$131$			5.04868i			0.441105i	0.975375	+	0.220552i	$0.0707860\pi$
$131$			5.04868i			0.441105i	−0.975375	+	0.220552i	$0.929214\pi$
$132$		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
$147$	0.342574	+	11.0318i	0.0282551	+	0.909887i
$148$		0			0
$149$	−3.75906			−0.307954			−0.153977	−	0.988074i	$-0.549208\pi$
$149$	−3.75906			−0.307954			−0.153977	+	0.988074i	$0.549208\pi$
$150$		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
$153$	12.6529	−	14.3303i	1.02292	−	1.15854i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.23773	−	9.23773i	−0.737251	−	0.737251i	0.234794	−	0.972045i	$-0.424558\pi$
$157$	−9.23773	−	9.23773i	−0.737251	−	0.737251i	−0.972045	+	0.234794i	$0.924558\pi$
$158$		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	$-0.487368\pi$
$163$	13.2636	−	13.2636i	1.03889	−	1.03889i	0.999213	−	0.0396750i	$-0.0126323\pi$
$164$		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
$177$	20.7346	−	0.643878i	1.55851	−	0.0483968i
$178$		0			0
$179$	−5.98844			−0.447597			−0.223798	−	0.974635i	$-0.571846\pi$
$179$	−5.98844			−0.447597			−0.223798	+	0.974635i	$0.571846\pi$
$180$		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
$183$	−2.37572	+	0.0737740i	−0.175618	+	0.00545353i
$184$		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	$-0.633546\pi$
$191$		−	25.2434i		−	1.82655i	0.407347	−	0.913273i	$-0.366454\pi$
$192$		0			0
$193$	8.36465	−	8.36465i	0.602101	−	0.602101i	−0.338769	−	0.940870i	$-0.610010\pi$
$193$	8.36465	−	8.36465i	0.602101	−	0.602101i	0.940870	+	0.338769i	$0.110010\pi$
$194$		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
$207$	−19.6652	−	17.3633i	−1.36683	−	1.20683i
$208$		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
$213$	−0.170374	−	5.48648i	−0.0116738	−	0.375927i
$214$		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	−0.987480	−	0.157747i	$-0.949577\pi$
$223$	−12.3906	+	12.3906i	−0.829733	+	0.829733i	0.157747	+	0.987480i	$0.449577\pi$
$224$		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
$237$	−0.470108	−	15.1387i	−0.0305368	−	0.983366i
$238$		0			0
$239$	13.2665			0.858138			0.429069	−	0.903272i	$-0.358842\pi$
$239$	13.2665			0.858138			0.429069	+	0.903272i	$0.358842\pi$
$240$		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
$243$	−15.4011	+	2.40989i	−0.987978	+	0.154594i
$244$		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	$-0.893049\pi$
$251$		−	10.4472i		−	0.659422i	0.944082	−	0.329711i	$-0.106951\pi$
$252$		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
$267$	27.8480	−	0.864773i	1.70427	−	0.0529233i
$268$		0			0
$269$	27.1229			1.65371			0.826856	−	0.562413i	$-0.190127\pi$
$269$	27.1229			1.65371			0.826856	+	0.562413i	$0.190127\pi$
$270$		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
$273$	−8.01158	+	0.248787i	−0.484883	+	0.0150572i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−14.6315	−	14.6315i	−0.879120	−	0.879120i	0.114323	−	0.993444i	$-0.463530\pi$
$277$	−14.6315	−	14.6315i	−0.879120	−	0.879120i	−0.993444	+	0.114323i	$0.963530\pi$
$278$		0			0
$279$	−16.0858	+	1.00000i	−0.963031	+	0.0598684i
$280$		0			0
$281$		−	20.7846i		−	1.23991i	−0.784639	−	0.619953i	$-0.787152\pi$
$281$		−	20.7846i		−	1.23991i	0.784639	−	0.619953i	$-0.212848\pi$
$282$		0			0
$283$	−17.7455	+	17.7455i	−1.05486	+	1.05486i	−0.0564542	+	0.998405i	$0.517979\pi$
$283$	−17.7455	+	17.7455i	−1.05486	+	1.05486i	−0.998405	+	0.0564542i	$0.982021\pi$
$284$		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
$297$	0.454112	+	4.86199i	0.0263502	+	0.282122i
$298$		0			0
$299$	51.0767			2.95384
$300$		0			0
$301$	−4.86141			−0.280207
$302$		0			0
$303$	0.473504	+	15.2481i	0.0272021	+	0.875980i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−19.4916	−	19.4916i	−1.11245	−	1.11245i	−0.992819	−	0.119628i	$-0.961830\pi$
$307$	−19.4916	−	19.4916i	−1.11245	−	1.11245i	−0.119628	−	0.992819i	$-0.538170\pi$
$308$		0			0
$309$	−13.8564	+	14.7446i	−0.788263	+	0.838789i
$310$		0			0
$311$			25.8333i			1.46487i	0.680836	+	0.732436i	$0.261617\pi$
$311$			25.8333i			1.46487i	−0.680836	+	0.732436i	$0.738383\pi$
$312$		0			0
$313$	−9.02916	+	9.02916i	−0.510359	+	0.510359i	−0.914636	−	0.404278i	$-0.867523\pi$
$313$	−9.02916	+	9.02916i	−0.510359	+	0.510359i	0.404278	+	0.914636i	$0.367523\pi$
$314$		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
$327$	−0.583910	−	18.8034i	−0.0322903	−	1.03983i
$328$		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
$333$	−11.3537	−	10.0247i	−0.622181	−	0.549351i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−3.67423	−	3.67423i	−0.200148	−	0.200148i	0.599915	−	0.800064i	$-0.295201\pi$
$337$	−3.67423	−	3.67423i	−0.200148	−	0.200148i	−0.800064	+	0.599915i	$0.795201\pi$
$338$		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
$357$	8.74035	−	0.271417i	0.462588	−	0.0143649i
$358$		0			0
$359$	−5.04868			−0.266459			−0.133229	−	0.991085i	$-0.542535\pi$
$359$	−5.04868			−0.266459			−0.133229	+	0.991085i	$0.542535\pi$
$360$		0			0
$361$	4.97825			0.262013
$362$		0			0
$363$	−17.5144	+	0.543882i	−0.919270	+	0.0285464i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	9.02916	+	9.02916i	0.471319	+	0.471319i	0.902341	−	0.431023i	$-0.141847\pi$
$367$	9.02916	+	9.02916i	0.471319	+	0.471319i	−0.431023	+	0.902341i	$0.641847\pi$
$368$		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	−0.721462	−	0.692454i	$-0.756529\pi$
$373$	−0.560232	+	0.560232i	−0.0290077	+	0.0290077i	0.692454	+	0.721462i	$0.256529\pi$
$374$		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
$387$	12.1835	−	13.7988i	0.619325	−	0.701432i
$388$		0			0
$389$	29.0024			1.47048			0.735241	−	0.677806i	$-0.237069\pi$
$389$	29.0024			1.47048			0.735241	+	0.677806i	$0.237069\pi$
$390$		0			0
$391$	−55.7228			−2.81802
$392$		0			0
$393$	−0.271417	−	8.74035i	−0.0136912	−	0.440892i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	5.66777	+	5.66777i	0.284457	+	0.284457i	0.834884	−	0.550426i	$-0.185535\pi$
$397$	5.66777	+	5.66777i	0.284457	+	0.284457i	−0.550426	+	0.834884i	$0.685535\pi$
$398$		0			0
$399$	3.51900	−	3.74456i	0.176171	−	0.187463i
$400$		0			0
$401$			16.6757i			0.832745i	0.909194	+	0.416372i	$0.136699\pi$
$401$			16.6757i			0.832745i	−0.909194	+	0.416372i	$0.863301\pi$
$402$		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
$417$	−0.812683	−	26.1705i	−0.0397972	−	1.28158i
$418$		0			0
$419$	2.81929			0.137731			0.0688657	−	0.997626i	$-0.478062\pi$
$419$	2.81929			0.137731			0.0688657	+	0.997626i	$0.478062\pi$
$420$		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
$423$	15.8849	−	17.9908i	0.772350	−	0.874744i
$424$		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	$0.183792\pi$
$431$			22.6641i			1.09169i	−0.837885	+	0.545847i	$0.816208\pi$
$432$		0			0
$433$	6.12372	−	6.12372i	0.294287	−	0.294287i	−0.544484	−	0.838771i	$-0.683274\pi$
$433$	6.12372	−	6.12372i	0.294287	−	0.294287i	0.838771	+	0.544484i	$0.183274\pi$
$434$		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
$447$	6.50774	−	0.202087i	0.307805	−	0.00955839i
$448$		0			0
$449$	2.22938			0.105211			0.0526056	−	0.998615i	$-0.483247\pi$
$449$	2.22938			0.105211			0.0526056	+	0.998615i	$0.483247\pi$
$450$		0			0
$451$	−8.60597			−0.405239
$452$		0			0
$453$	4.54915	−	0.141266i	0.213738	−	0.00663727i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.3744	+	11.3744i	0.532071	+	0.532071i	0.921188	−	0.389117i	$-0.127220\pi$
$457$	11.3744	+	11.3744i	0.532071	+	0.532071i	−0.389117	+	0.921188i	$0.627220\pi$
$458$		0			0
$459$	−21.1345	+	25.4891i	−0.986472	+	1.18973i
$460$		0			0
$461$		−	17.0256i		−	0.792959i	−0.918044	−	0.396480i	$-0.870232\pi$
$461$		−	17.0256i		−	0.792959i	0.918044	−	0.396480i	$-0.129768\pi$
$462$		0			0
$463$	−6.43657	+	6.43657i	−0.299133	+	0.299133i	−0.840674	−	0.541541i	$-0.817841\pi$
$463$	−6.43657	+	6.43657i	−0.299133	+	0.299133i	0.541541	+	0.840674i	$0.317841\pi$
$464$		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
$477$	1.67441	+	1.47841i	0.0766661	+	0.0676919i
$478$		0			0
$479$	−4.45877			−0.203726			−0.101863	−	0.994798i	$-0.532480\pi$
$479$	−4.45877			−0.203726			−0.101863	+	0.994798i	$0.532480\pi$
$480$		0			0
$481$	29.4891			1.34459
$482$		0			0
$483$	−0.372461	−	11.9942i	−0.0169476	−	0.545756i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−9.94106	−	9.94106i	−0.450473	−	0.450473i	0.445039	−	0.895511i	$-0.353190\pi$
$487$	−9.94106	−	9.94106i	−0.450473	−	0.450473i	−0.895511	+	0.445039i	$0.853190\pi$
$488$		0			0
$489$	−22.2492	+	23.6753i	−1.00614	+	1.07063i
$490$		0			0
$491$		−	4.45877i		−	0.201221i	−0.994926	−	0.100611i	$-0.967920\pi$
$491$		−	4.45877i		−	0.201221i	0.994926	−	0.100611i	$-0.0320797\pi$
$492$		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
$507$	1.13524	+	36.5578i	0.0504179	+	1.62359i
$508$		0			0
$509$	−22.0742			−0.978423			−0.489212	−	0.872165i	$-0.662715\pi$
$509$	−22.0742			−0.978423			−0.489212	+	0.872165i	$0.662715\pi$
$510$		0			0
$511$	6.23369			0.275762
$512$		0			0
$513$	1.80944	+	19.3730i	0.0798889	+	0.855339i
$514$		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	$0.119029\pi$
$521$			16.6757i			0.730576i	−0.930895	+	0.365288i	$0.880971\pi$
$522$		0			0
$523$	12.8465	−	12.8465i	0.561738	−	0.561738i	−0.368063	−	0.929801i	$-0.619979\pi$
$523$	12.8465	−	12.8465i	0.561738	−	0.561738i	0.929801	+	0.368063i	$0.119979\pi$
$524$		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
$537$	10.3673	−	0.321939i	0.447381	−	0.0138927i
$538$		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
$543$	34.8266	−	1.08148i	1.49455	−	0.0464109i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−3.53113	−	3.53113i	−0.150980	−	0.150980i	0.627575	−	0.778556i	$-0.284047\pi$
$547$	−3.53113	−	3.53113i	−0.150980	−	0.150980i	−0.778556	+	0.627575i	$0.784047\pi$
$548$		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
$567$	−5.62775	−	4.37878i	−0.236343	−	0.183891i
$568$		0			0
$569$	34.9909			1.46689			0.733447	−	0.679747i	$-0.237910\pi$
$569$	34.9909			1.46689			0.733447	+	0.679747i	$0.237910\pi$
$570$		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
$573$	1.35709	+	43.7017i	0.0566931	+	1.82567i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	26.2144	+	26.2144i	1.09132	+	1.09132i	0.995388	+	0.0959325i	$0.0305833\pi$
$577$	26.2144	+	26.2144i	1.09132	+	1.09132i	0.0959325	+	0.995388i	$0.469417\pi$
$578$		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
$597$	−0.248787	−	8.01158i	−0.0101822	−	0.327892i
$598$		0			0
$599$	−28.4125			−1.16090			−0.580452	−	0.814294i	$-0.697124\pi$
$599$	−28.4125			−1.16090			−0.580452	+	0.814294i	$0.697124\pi$
$600$		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
$603$	3.89513	+	3.43918i	0.158622	+	0.140054i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	18.4755	+	18.4755i	0.749896	+	0.749896i	0.974459	−	0.224564i	$-0.0720957\pi$
$607$	18.4755	+	18.4755i	0.749896	+	0.749896i	−0.224564	+	0.974459i	$0.572096\pi$
$608$		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	−0.863409	−	0.504504i	$-0.831675\pi$
$613$	−8.88606	+	8.88606i	−0.358905	+	0.358905i	0.504504	+	0.863409i	$0.331675\pi$
$614$		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
$627$	6.09216	−	0.189182i	0.243297	−	0.00755520i
$628$		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
$633$	−16.8699	+	0.523868i	−0.670520	+	0.0208219i
$634$		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	$-0.843150\pi$
$641$		−	23.9538i		−	0.946117i	0.881031	−	0.473058i	$-0.156850\pi$
$642$		0			0
$643$	−5.10754	+	5.10754i	−0.201422	+	0.201422i	−0.800609	−	0.599187i	$-0.795491\pi$
$643$	−5.10754	+	5.10754i	−0.201422	+	0.201422i	0.599187	+	0.800609i	$0.295491\pi$
$644$		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
$657$	−15.6227	+	17.6939i	−0.609501	+	0.690305i
$658$		0			0
$659$	−35.6906			−1.39031			−0.695154	−	0.718861i	$-0.744664\pi$
$659$	−35.6906			−1.39031			−0.695154	+	0.718861i	$0.744664\pi$
$660$		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
$663$	−2.00096	−	64.4363i	−0.0777110	−	2.50250i
$664$		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	−0.741384	−	0.671081i	$-0.765830\pi$
$673$	−1.82380	+	1.82380i	−0.0703023	+	0.0703023i	0.671081	+	0.741384i	$0.265830\pi$
$674$		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
$687$	0.248787	+	8.01158i	0.00949180	+	0.305661i
$688$		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
$693$	−1.47841	+	1.67441i	−0.0561602	+	0.0636057i
$694$		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	$-0.919394\pi$
$701$		−	13.2665i		−	0.501069i	0.968108	−	0.250534i	$-0.0806063\pi$
$702$		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
$717$	−22.9672	+	0.713208i	−0.857725	+	0.0266352i
$718$		0			0
$719$	27.8226			1.03761			0.518804	−	0.854893i	$-0.326377\pi$
$719$	27.8226			1.03761			0.518804	+	0.854893i	$0.326377\pi$
$720$		0			0
$721$	−9.25544			−0.344690
$722$		0			0
$723$	22.9104	−	0.711444i	0.852046	−	0.0264589i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−10.5668	−	10.5668i	−0.391899	−	0.391899i	0.483465	−	0.875364i	$-0.339378\pi$
$727$	−10.5668	−	10.5668i	−0.391899	−	0.391899i	−0.875364	+	0.483465i	$0.839378\pi$
$728$		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	$-0.396713\pi$
$733$	34.2929	−	34.2929i	1.26664	−	1.26664i	0.947815	−	0.318820i	$-0.103287\pi$
$734$		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
$747$	12.6559	+	11.1745i	0.463056	+	0.408852i
$748$		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
$753$	0.561643	+	18.0864i	0.0204674	+	0.659104i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	28.6251	+	28.6251i	1.04040	+	1.04040i	0.999149	+	0.0412473i	$0.0131332\pi$
$757$	28.6251	+	28.6251i	1.04040	+	1.04040i	0.0412473	+	0.999149i	$0.486867\pi$
$758$		0			0
$759$	9.74749	−	10.3723i	0.353812	−	0.376490i
$760$		0			0
$761$			14.2063i			0.514977i	0.966281	+	0.257488i	$0.0828949\pi$
$761$			14.2063i			0.514977i	−0.966281	+	0.257488i	$0.917105\pi$
$762$		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
$777$	−0.215040	−	6.92487i	−0.00771453	−	0.248428i
$778$		0			0
$779$	−34.2912			−1.22861
$780$		0			0
$781$	2.97825			0.106570
$782$		0			0
$783$	−16.3960	+	1.53139i	−0.585946	+	0.0547275i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.560232	+	0.560232i	0.0199701	+	0.0199701i	0.717021	−	0.697051i	$-0.245505\pi$
$787$	0.560232	+	0.560232i	0.0199701	+	0.0199701i	−0.697051	+	0.717021i	$0.745505\pi$
$788$		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
$807$	−46.9556	+	1.45813i	−1.65292	+	0.0513286i
$808$		0			0
$809$	5.74839			0.202103			0.101051	−	0.994881i	$-0.467779\pi$
$809$	5.74839			0.202103			0.101051	+	0.994881i	$0.467779\pi$
$810$		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
$813$	−31.5665	+	0.980245i	−1.10708	+	0.0343787i
$814$		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	$-0.851141\pi$
$821$		−	25.8333i		−	0.901588i	0.892628	−	0.450794i	$-0.148859\pi$
$822$		0			0
$823$	2.59259	−	2.59259i	0.0903721	−	0.0903721i	−0.660475	−	0.750848i	$-0.729645\pi$
$823$	2.59259	−	2.59259i	0.0903721	−	0.0903721i	0.750848	+	0.660475i	$0.229645\pi$
$824$		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
$837$	27.7942	−	2.59599i	0.960709	−	0.0897305i
$838$		0			0
$839$	40.9793			1.41476			0.707381	−	0.706832i	$-0.249876\pi$
$839$	40.9793			1.41476			0.707381	+	0.706832i	$0.249876\pi$
$840$		0			0
$841$	−18.9565			−0.653672
$842$		0			0
$843$	1.11738	+	35.9827i	0.0384847	+	1.23931i
$844$		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	−0.998534	−	0.0541349i	$-0.982760\pi$
$853$	−27.5823	+	27.5823i	−0.944399	+	0.944399i	0.0541349	+	0.998534i	$0.482760\pi$
$854$		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
$867$	1.26906	+	40.8670i	0.0430995	+	1.38792i
$868$		0			0
$869$	8.21782			0.278771
$870$		0			0
$871$	−10.1168			−0.342796
$872$		0			0
$873$	16.6990	+	14.7442i	0.565174	+	0.499017i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.768795	+	0.768795i	0.0259604	+	0.0259604i	0.719968	−	0.694007i	$-0.244157\pi$
$877$	0.768795	+	0.768795i	0.0259604	+	0.0259604i	−0.694007	+	0.719968i	$0.744157\pi$
$878$		0			0
$879$	38.1600	+	35.8614i	1.28711	+	1.20958i
$880$		0			0
$881$		−	17.6155i		−	0.593480i	−0.954958	−	0.296740i	$-0.904101\pi$
$881$		−	17.6155i		−	0.593480i	0.954958	−	0.296740i	$-0.0958995\pi$
$882$		0			0
$883$	−5.28947	+	5.28947i	−0.178005	+	0.178005i	−0.790486	−	0.612481i	$-0.790172\pi$
$883$	−5.28947	+	5.28947i	−0.178005	+	0.178005i	0.612481	+	0.790486i	$0.290172\pi$
$884$		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
$897$	−88.4248	+	2.74589i	−2.95242	+	0.0916825i
$898$		0			0
$899$	−17.0256			−0.567834
$900$		0			0
$901$	4.74456			0.158064
$902$		0			0
$903$	8.41615	−	0.261350i	0.280072	−	0.00869717i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−35.4910	−	35.4910i	−1.17846	−	1.17846i	−0.980137	−	0.198321i	$-0.936451\pi$
$907$	−35.4910	−	35.4910i	−1.17846	−	1.17846i	−0.198321	−	0.980137i	$-0.563549\pi$
$908$		0			0
$909$	−1.63948	−	26.3723i	−0.0543780	−	0.874713i
$910$		0			0
$911$		−	54.2458i		−	1.79724i	−0.438724	−	0.898622i	$-0.644569\pi$
$911$		−	54.2458i		−	1.79724i	0.438724	−	0.898622i	$-0.355431\pi$
$912$		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
$927$	23.1958	−	26.2709i	0.761849	−	0.862851i
$928$		0			0
$929$	3.16915			0.103976			0.0519882	−	0.998648i	$-0.483444\pi$
$929$	3.16915			0.103976			0.0519882	+	0.998648i	$0.483444\pi$
$930$		0			0
$931$	−23.8614			−0.782026
$932$		0			0
$933$	−1.38880	−	44.7230i	−0.0454673	−	1.46417i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	3.67423	+	3.67423i	0.120032	+	0.120032i	0.764571	−	0.644539i	$-0.222951\pi$
$937$	3.67423	+	3.67423i	0.120032	+	0.120032i	−0.644539	+	0.764571i	$0.722951\pi$
$938$		0			0
$939$	15.1460	−	16.1168i	0.494272	−	0.525953i
$940$		0			0
$941$		−	30.2921i		−	0.987493i	−0.869606	−	0.493746i	$-0.835627\pi$
$941$		−	30.2921i		−	0.987493i	0.869606	−	0.493746i	$-0.164373\pi$
$942$		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
$957$	0.160111	+	5.15600i	0.00517565	+	0.166670i
$958$		0			0
$959$	−5.63858			−0.182079
$960$		0			0
$961$	−2.13859			−0.0689869
$962$		0			0
$963$	3.23202	−	3.66050i	0.104150	−	0.117958i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	42.1361	+	42.1361i	1.35501	+	1.35501i	0.879963	+	0.475043i	$0.157567\pi$
$967$	42.1361	+	42.1361i	1.35501	+	1.35501i	0.475043	+	0.879963i	$0.342433\pi$
$968$		0			0
$969$	30.1171	+	28.3030i	0.967501	+	0.909223i
$970$		0			0
$971$		−	22.4241i		−	0.719623i	−0.933025	−	0.359812i	$-0.882841\pi$
$971$		−	22.4241i		−	0.719623i	0.933025	−	0.359812i	$-0.117159\pi$
$972$		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
$987$	10.9730	−	0.340747i	0.349273	−	0.0108461i
$988$		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
$993$	−45.6561	+	1.41778i	−1.44885	+	0.0449918i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	4.06472	+	4.06472i	0.128731	+	0.128731i	0.768537	−	0.639806i	$-0.220985\pi$
$997$	4.06472	+	4.06472i	0.128731	+	0.128731i	−0.639806	+	0.768537i	$0.720985\pi$
$998$		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.257.1	✓	16
3.2	odd	2	inner	600.2.r.f.257.4	yes	16
4.3	odd	2		1200.2.v.m.257.8		16
5.2	odd	4	inner	600.2.r.f.593.5	yes	16
5.3	odd	4	inner	600.2.r.f.593.4	yes	16
5.4	even	2	inner	600.2.r.f.257.8	yes	16
12.11	even	2		1200.2.v.m.257.5		16
15.2	even	4	inner	600.2.r.f.593.8	yes	16
15.8	even	4	inner	600.2.r.f.593.1	yes	16
15.14	odd	2	inner	600.2.r.f.257.5	yes	16
20.3	even	4		1200.2.v.m.593.5		16
20.7	even	4		1200.2.v.m.593.4		16
20.19	odd	2		1200.2.v.m.257.1		16
60.23	odd	4		1200.2.v.m.593.8		16
60.47	odd	4		1200.2.v.m.593.1		16
60.59	even	2		1200.2.v.m.257.4		16

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

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

Introduction

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