LMFDB - Embedded newform 3024.2.cc.d.881.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(881,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3024.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cc (of order $6$, degree $2$, not 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.14
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.d.2897.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0868503 - 0.150429i) q^{5} +(2.60056 - 0.486915i) q^{7} +O(q^{10})$	$q+(0.0868503 - 0.150429i) q^{5} +(2.60056 - 0.486915i) q^{7} +(3.25192 - 1.87750i) q^{11} +(-3.54137 - 2.04461i) q^{13} +6.00535 q^{17} +6.26182i q^{19} +(-6.37812 - 3.68241i) q^{23} +(2.48491 + 4.30400i) q^{25} +(8.58300 - 4.95540i) q^{29} +(-3.76792 - 2.17541i) q^{31} +(0.152613 - 0.433489i) q^{35} +7.23702 q^{37} +(0.489900 - 0.848533i) q^{41} +(-0.0468552 - 0.0811557i) q^{43} +(-1.86055 - 3.22257i) q^{47} +(6.52583 - 2.53251i) q^{49} +5.61363i q^{53} -0.652244i q^{55} +(0.620738 - 1.07515i) q^{59} +(-7.45935 + 4.30666i) q^{61} +(-0.615138 + 0.355150i) q^{65} +(-4.21946 + 7.30831i) q^{67} -12.9874i q^{71} -15.4606i q^{73} +(7.54263 - 6.46595i) q^{77} +(1.21466 + 2.10385i) q^{79} +(3.16176 + 5.47633i) q^{83} +(0.521567 - 0.903380i) q^{85} -11.8093 q^{89} +(-10.2051 - 3.59278i) q^{91} +(0.941960 + 0.543841i) q^{95} +(5.02479 - 2.90106i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) $ 48 * q + 12 * q^23 - 24 * q^25 + 36 * q^29 - 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 + 12 * q^79 + 12 * q^91 - 108 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.0868503	−	0.150429i	0.0388406	−	0.0672740i	−0.845952	−	0.533260i	$-0.820967\pi$
$5$	0.0868503	−	0.150429i	0.0388406	−	0.0672740i	0.884792	+	0.465986i	$0.154300\pi$
$6$		0			0
$7$	2.60056	−	0.486915i	0.982919	−	0.184037i
$7$	2.60056	−	0.486915i	0.982919	−	0.184037i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.25192	−	1.87750i	0.980490	−	0.566086i	0.0780721	−	0.996948i	$-0.475124\pi$
$11$	3.25192	−	1.87750i	0.980490	−	0.566086i	0.902418	+	0.430861i	$0.141790\pi$
$12$		0			0
$13$	−3.54137	−	2.04461i	−0.982199	−	0.567073i	−0.0792654	−	0.996854i	$-0.525257\pi$
$13$	−3.54137	−	2.04461i	−0.982199	−	0.567073i	−0.902933	+	0.429781i	$0.858591\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.00535			1.45651			0.728256	−	0.685305i	$-0.240331\pi$
$17$	6.00535			1.45651			0.728256	+	0.685305i	$0.240331\pi$
$18$		0			0
$19$			6.26182i			1.43656i	0.695754	+	0.718280i	$0.255070\pi$
$19$			6.26182i			1.43656i	−0.695754	+	0.718280i	$0.744930\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.37812	−	3.68241i	−1.32993	−	0.767836i	−0.344642	−	0.938734i	$-0.612000\pi$
$23$	−6.37812	−	3.68241i	−1.32993	−	0.767836i	−0.985289	+	0.170898i	$0.945333\pi$
$24$		0			0
$25$	2.48491	+	4.30400i	0.496983	+	0.860799i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	8.58300	−	4.95540i	1.59382	−	0.920194i	0.601181	−	0.799113i	$-0.294697\pi$
$29$	8.58300	−	4.95540i	1.59382	−	0.920194i	0.992643	−	0.121081i	$-0.0386361\pi$
$30$		0			0
$31$	−3.76792	−	2.17541i	−0.676738	−	0.390715i	0.121887	−	0.992544i	$-0.461105\pi$
$31$	−3.76792	−	2.17541i	−0.676738	−	0.390715i	−0.798625	+	0.601829i	$0.794439\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.152613	−	0.433489i	0.0257963	−	0.0732730i
$36$		0			0
$37$	7.23702			1.18976			0.594880	−	0.803815i	$-0.297200\pi$
$37$	7.23702			1.18976			0.594880	+	0.803815i	$0.297200\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.489900	−	0.848533i	0.0765096	−	0.132519i	−0.825232	−	0.564794i	$-0.808956\pi$
$41$	0.489900	−	0.848533i	0.0765096	−	0.132519i	0.901742	+	0.432275i	$0.142289\pi$
$42$		0			0
$43$	−0.0468552	−	0.0811557i	−0.00714536	−	0.0123761i	0.862431	−	0.506175i	$-0.168941\pi$
$43$	−0.0468552	−	0.0811557i	−0.00714536	−	0.0123761i	−0.869576	+	0.493799i	$0.835608\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.86055	−	3.22257i	−0.271389	−	0.470060i	0.697829	−	0.716265i	$-0.254150\pi$
$47$	−1.86055	−	3.22257i	−0.271389	−	0.470060i	−0.969218	+	0.246205i	$0.920816\pi$
$48$		0			0
$49$	6.52583	−	2.53251i	0.932261	−	0.361786i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			5.61363i			0.771091i	0.922689	+	0.385545i	$0.125987\pi$
$53$			5.61363i			0.771091i	−0.922689	+	0.385545i	$0.874013\pi$
$54$		0			0
$55$		−	0.652244i		−	0.0879486i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.620738	−	1.07515i	0.0808131	−	0.139972i	−0.822786	−	0.568351i	$-0.807582\pi$
$59$	0.620738	−	1.07515i	0.0808131	−	0.139972i	0.903599	+	0.428378i	$0.140915\pi$
$60$		0			0
$61$	−7.45935	+	4.30666i	−0.955072	+	0.551411i	−0.894653	−	0.446762i	$-0.852577\pi$
$61$	−7.45935	+	4.30666i	−0.955072	+	0.551411i	−0.0604191	+	0.998173i	$0.519244\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.615138	+	0.355150i	−0.0762984	+	0.0440509i
$66$		0			0
$67$	−4.21946	+	7.30831i	−0.515489	+	0.892852i	0.484350	+	0.874874i	$0.339056\pi$
$67$	−4.21946	+	7.30831i	−0.515489	+	0.892852i	−0.999838	+	0.0179779i	$0.994277\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	12.9874i		−	1.54133i	−0.637243	−	0.770663i	$-0.719925\pi$
$71$		−	12.9874i		−	1.54133i	0.637243	−	0.770663i	$-0.280075\pi$
$72$		0			0
$73$		−	15.4606i		−	1.80953i	−0.425912	−	0.904765i	$-0.640047\pi$
$73$		−	15.4606i		−	1.80953i	0.425912	−	0.904765i	$-0.359953\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.54263	−	6.46595i	0.859562	−	0.736863i
$78$		0			0
$79$	1.21466	+	2.10385i	0.136660	+	0.236701i	0.926230	−	0.376958i	$-0.123030\pi$
$79$	1.21466	+	2.10385i	0.136660	+	0.236701i	−0.789571	+	0.613660i	$0.789697\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.16176	+	5.47633i	0.347048	+	0.601106i	0.985724	−	0.168371i	$-0.0538506\pi$
$83$	3.16176	+	5.47633i	0.347048	+	0.601106i	−0.638675	+	0.769476i	$0.720517\pi$
$84$		0			0
$85$	0.521567	−	0.903380i	0.0565719	−	0.0979854i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−11.8093			−1.25179			−0.625894	−	0.779908i	$-0.715266\pi$
$89$	−11.8093			−1.25179			−0.625894	+	0.779908i	$0.715266\pi$
$90$		0			0
$91$	−10.2051	−	3.59278i	−1.06978	−	0.376626i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.941960	+	0.543841i	0.0966431	+	0.0557969i
$96$		0			0
$97$	5.02479	−	2.90106i	0.510190	−	0.294558i	−0.222722	−	0.974882i	$-0.571494\pi$
$97$	5.02479	−	2.90106i	0.510190	−	0.294558i	0.732912	+	0.680324i	$0.238161\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.420935	+	0.729081i	0.0418846	+	0.0725462i	0.886208	−	0.463288i	$-0.153330\pi$
$101$	0.420935	+	0.729081i	0.0418846	+	0.0725462i	−0.844323	+	0.535834i	$0.819997\pi$
$102$		0			0
$103$	−4.90770	−	2.83346i	−0.483571	−	0.279190i	0.238333	−	0.971184i	$-0.423399\pi$
$103$	−4.90770	−	2.83346i	−0.483571	−	0.279190i	−0.721903	+	0.691994i	$0.756732\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			2.20771i			0.213427i	0.994290	+	0.106714i	$0.0340328\pi$
$107$			2.20771i			0.213427i	−0.994290	+	0.106714i	$0.965967\pi$
$108$		0			0
$109$	14.3263			1.37221			0.686106	−	0.727502i	$-0.259319\pi$
$109$	14.3263			1.37221			0.686106	+	0.727502i	$0.259319\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.85839	+	5.11439i	0.833327	+	0.481122i	0.854990	−	0.518644i	$-0.173563\pi$
$113$	8.85839	+	5.11439i	0.833327	+	0.481122i	−0.0216633	+	0.999765i	$0.506896\pi$
$114$		0			0
$115$	−1.10788	+	0.639637i	−0.103311	+	0.0596465i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	15.6173	−	2.92410i	1.43163	−	0.268052i
$120$		0			0
$121$	1.54998	−	2.68465i	0.140907	−	0.244059i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.73177			0.154894
$126$		0			0
$127$	19.2886			1.71159			0.855793	−	0.517318i	$-0.173070\pi$
$127$	19.2886			1.71159			0.855793	+	0.517318i	$0.173070\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.139440	−	0.241517i	0.0121829	−	0.0211014i	−0.859870	−	0.510514i	$-0.829455\pi$
$131$	0.139440	−	0.241517i	0.0121829	−	0.0211014i	0.872053	+	0.489412i	$0.162789\pi$
$132$		0			0
$133$	3.04897	+	16.2842i	0.264380	+	1.41202i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.44020	−	4.87295i	0.721095	−	0.416324i	−0.0940607	−	0.995566i	$-0.529985\pi$
$137$	8.44020	−	4.87295i	0.721095	−	0.416324i	0.815155	+	0.579242i	$0.196651\pi$
$138$		0			0
$139$	−8.71086	−	5.02922i	−0.738846	−	0.426573i	0.0828037	−	0.996566i	$-0.473613\pi$
$139$	−8.71086	−	5.02922i	−0.738846	−	0.426573i	−0.821650	+	0.569993i	$0.806946\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−15.3550			−1.28405
$144$		0			0
$145$		−	1.72151i		−	0.142964i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.61846	+	2.66647i	0.378359	+	0.218446i	0.677104	−	0.735887i	$-0.263235\pi$
$149$	4.61846	+	2.66647i	0.378359	+	0.218446i	−0.298745	+	0.954333i	$0.596568\pi$
$150$		0			0
$151$	−1.32219	−	2.29010i	−0.107598	−	0.186365i	0.807199	−	0.590280i	$-0.200983\pi$
$151$	−1.32219	−	2.29010i	−0.107598	−	0.186365i	−0.914797	+	0.403914i	$0.867649\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.654489	+	0.377870i	−0.0525699	+	0.0303512i
$156$		0			0
$157$	14.0098	+	8.08854i	1.11810	+	0.645535i	0.940915	−	0.338642i	$-0.109968\pi$
$157$	14.0098	+	8.08854i	1.11810	+	0.645535i	0.177185	+	0.984178i	$0.443301\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−18.3797	−	6.47073i	−1.44852	−	0.509965i
$162$		0			0
$163$	17.8942			1.40158			0.700791	−	0.713367i	$-0.252831\pi$
$163$	17.8942			1.40158			0.700791	+	0.713367i	$0.252831\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.97390	+	3.41889i	−0.152745	+	0.264562i	−0.932236	−	0.361852i	$-0.882145\pi$
$167$	−1.97390	+	3.41889i	−0.152745	+	0.264562i	0.779491	+	0.626414i	$0.215478\pi$
$168$		0			0
$169$	1.86085	+	3.22309i	0.143143	+	0.247930i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.45755	−	11.1848i	−0.490959	−	0.850365i	0.508987	−	0.860774i	$-0.330020\pi$
$173$	−6.45755	−	11.1848i	−0.490959	−	0.850365i	−0.999946	+	0.0104087i	$0.996687\pi$
$174$		0			0
$175$	8.55785	+	9.98286i	0.646913	+	0.754633i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	2.58227i		−	0.193008i	−0.995333	−	0.0965040i	$-0.969234\pi$
$179$		−	2.58227i		−	0.193008i	0.995333	−	0.0965040i	$-0.0307660\pi$
$180$		0			0
$181$		−	2.28359i		−	0.169738i	−0.996392	−	0.0848691i	$-0.972953\pi$
$181$		−	2.28359i		−	0.169738i	0.996392	−	0.0848691i	$-0.0270472\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.628538	−	1.08866i	0.0462110	−	0.0800398i
$186$		0			0
$187$	19.5289	−	11.2750i	1.42810	−	0.824512i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.15049	+	0.664237i	−0.0832467	+	0.0480625i	−0.541046	−	0.840993i	$-0.681971\pi$
$191$	−1.15049	+	0.664237i	−0.0832467	+	0.0480625i	0.457799	+	0.889056i	$0.348638\pi$
$192$		0			0
$193$	5.44766	−	9.43563i	0.392131	−	0.679191i	−0.600599	−	0.799550i	$-0.705071\pi$
$193$	5.44766	−	9.43563i	0.392131	−	0.679191i	0.992730	+	0.120359i	$0.0384046\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	14.2922i		−	1.01827i	−0.860685	−	0.509137i	$-0.829964\pi$
$197$		−	14.2922i		−	1.01827i	0.860685	−	0.509137i	$-0.170036\pi$
$198$		0			0
$199$			12.9598i			0.918694i	0.888257	+	0.459347i	$0.151917\pi$
$199$			12.9598i			0.918694i	−0.888257	+	0.459347i	$0.848083\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	19.9078	−	17.0660i	1.39725	−	1.19780i
$204$		0			0
$205$	−0.0850960	−	0.147391i	−0.00594336	−	0.0102942i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	11.7565	+	20.3629i	0.813217	+	1.40853i
$210$		0			0
$211$	−5.25659	+	9.10469i	−0.361879	+	0.626793i	−0.988270	−	0.152716i	$-0.951198\pi$
$211$	−5.25659	+	9.10469i	−0.361879	+	0.626793i	0.626391	+	0.779509i	$0.284531\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.0162776			−0.00111012
$216$		0			0
$217$	−10.8579	−	3.82262i	−0.737084	−	0.259496i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−21.2672	−	12.2786i	−1.43058	−	0.825948i
$222$		0			0
$223$	1.64141	−	0.947666i	0.109917	−	0.0634604i	−0.444034	−	0.896010i	$-0.646453\pi$
$223$	1.64141	−	0.947666i	0.109917	−	0.0634604i	0.553950	+	0.832550i	$0.313120\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.45673	−	14.6475i	−0.561293	−	0.972188i	−0.997384	−	0.0722857i	$-0.976971\pi$
$227$	−8.45673	−	14.6475i	−0.561293	−	0.972188i	0.436091	−	0.899903i	$-0.356363\pi$
$228$		0			0
$229$	9.13120	+	5.27190i	0.603406	+	0.348377i	0.770380	−	0.637584i	$-0.220066\pi$
$229$	9.13120	+	5.27190i	0.603406	+	0.348377i	−0.166974	+	0.985961i	$0.553400\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			0.327782i			0.0214737i	0.999942	+	0.0107369i	$0.00341771\pi$
$233$			0.327782i			0.0214737i	−0.999942	+	0.0107369i	$0.996582\pi$
$234$		0			0
$235$	−0.646357			−0.0421637
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.46268	−	4.30858i	−0.482721	−	0.278699i	0.238829	−	0.971062i	$-0.423236\pi$
$239$	−7.46268	−	4.30858i	−0.482721	−	0.278699i	−0.721550	+	0.692363i	$0.756570\pi$
$240$		0			0
$241$	11.4421	−	6.60608i	0.737049	−	0.425535i	−0.0839465	−	0.996470i	$-0.526752\pi$
$241$	11.4421	−	6.60608i	0.737049	−	0.425535i	0.820995	+	0.570935i	$0.193419\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.185808	−	1.20162i	0.0118708	−	0.0767689i
$246$		0			0
$247$	12.8030	−	22.1754i	0.814634	−	1.41099i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−26.6383			−1.68140			−0.840698	−	0.541504i	$-0.817855\pi$
$251$	−26.6383			−1.68140			−0.840698	+	0.541504i	$0.817855\pi$
$252$		0			0
$253$	−27.6548			−1.73865
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.45554	−	7.71722i	0.277929	−	0.481387i	−0.692941	−	0.720994i	$-0.743685\pi$
$257$	4.45554	−	7.71722i	0.277929	−	0.481387i	0.970870	+	0.239607i	$0.0770187\pi$
$258$		0			0
$259$	18.8203	−	3.52382i	1.16944	−	0.218959i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.49185	−	3.74807i	0.400304	−	0.231116i	−0.286311	−	0.958137i	$-0.592429\pi$
$263$	6.49185	−	3.74807i	0.400304	−	0.231116i	0.686615	+	0.727021i	$0.259096\pi$
$264$		0			0
$265$	0.844453	+	0.487545i	0.0518743	+	0.0299497i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	9.03823			0.551071			0.275535	−	0.961291i	$-0.411145\pi$
$269$	9.03823			0.551071			0.275535	+	0.961291i	$0.411145\pi$
$270$		0			0
$271$		−	17.8997i		−	1.08733i	−0.839302	−	0.543666i	$-0.817036\pi$
$271$		−	17.8997i		−	1.08733i	0.839302	−	0.543666i	$-0.182964\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	16.1615	+	9.33083i	0.974574	+	0.562670i
$276$		0			0
$277$	−4.07950	−	7.06590i	−0.245113	−	0.424549i	0.717050	−	0.697022i	$-0.245492\pi$
$277$	−4.07950	−	7.06590i	−0.245113	−	0.424549i	−0.962164	+	0.272473i	$0.912159\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.54874	−	5.51297i	0.569630	−	0.328876i	−0.187371	−	0.982289i	$-0.559997\pi$
$281$	9.54874	−	5.51297i	0.569630	−	0.328876i	0.757002	+	0.653413i	$0.226663\pi$
$282$		0			0
$283$	3.59197	+	2.07382i	0.213520	+	0.123276i	0.602946	−	0.797782i	$-0.293993\pi$
$283$	3.59197	+	2.07382i	0.213520	+	0.123276i	−0.389426	+	0.921058i	$0.627327\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.860852	−	2.44520i	0.0508145	−	0.144336i
$288$		0			0
$289$	19.0643			1.12143
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.29441	+	7.43814i	−0.250882	+	0.434541i	−0.963769	−	0.266738i	$-0.914054\pi$
$293$	−4.29441	+	7.43814i	−0.250882	+	0.434541i	0.712887	+	0.701279i	$0.247387\pi$
$294$		0			0
$295$	−0.107823	−	0.186754i	−0.00627767	−	0.0108732i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	15.0582	+	26.0815i	0.870837	+	1.50833i
$300$		0			0
$301$	−0.161366	−	0.188236i	−0.00930097	−	0.0108497i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			1.49614i			0.0856686i
$306$		0			0
$307$			32.6161i			1.86150i	0.365657	+	0.930750i	$0.380844\pi$
$307$			32.6161i			1.86150i	−0.365657	+	0.930750i	$0.619156\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.978823	−	1.69537i	0.0555039	−	0.0961356i	−0.836938	−	0.547297i	$-0.815657\pi$
$311$	0.978823	−	1.69537i	0.0555039	−	0.0961356i	0.892442	+	0.451161i	$0.148990\pi$
$312$		0			0
$313$	−20.0759	+	11.5909i	−1.13476	+	0.655154i	−0.945128	−	0.326702i	$-0.894063\pi$
$313$	−20.0759	+	11.5909i	−1.13476	+	0.655154i	−0.189632	+	0.981855i	$0.560729\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.60905	+	4.39309i	−0.427367	+	0.246740i	−0.698224	−	0.715879i	$-0.746026\pi$
$317$	−7.60905	+	4.39309i	−0.427367	+	0.246740i	0.270857	+	0.962620i	$0.412693\pi$
$318$		0			0
$319$	18.6075	−	32.2291i	1.04182	−	1.80448i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			37.6044i			2.09237i
$324$		0			0
$325$		−	20.3227i		−	1.12730i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.40759	−	7.47455i	−0.353262	−	0.412085i
$330$		0			0
$331$	1.12187	+	1.94314i	0.0616637	+	0.106805i	0.895209	−	0.445646i	$-0.147026\pi$
$331$	1.12187	+	1.94314i	0.0616637	+	0.106805i	−0.833545	+	0.552451i	$0.813693\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.732922	+	1.26946i	0.0400438	+	0.0693579i
$336$		0			0
$337$	−15.4124	+	26.6951i	−0.839569	+	1.45418i	0.0506868	+	0.998715i	$0.483859\pi$
$337$	−15.4124	+	26.6951i	−0.839569	+	1.45418i	−0.890256	+	0.455461i	$0.849474\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−16.3373			−0.884713
$342$		0			0
$343$	15.7377	−	9.76346i	0.849755	−	0.527177i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.65066	+	2.68506i	0.249660	+	0.144142i	0.619609	−	0.784911i	$-0.287291\pi$
$347$	4.65066	+	2.68506i	0.249660	+	0.144142i	−0.369948	+	0.929052i	$0.620625\pi$
$348$		0			0
$349$	−25.3572	+	14.6400i	−1.35734	+	0.783660i	−0.989264	−	0.146136i	$-0.953316\pi$
$349$	−25.3572	+	14.6400i	−1.35734	+	0.783660i	−0.368075	+	0.929796i	$0.619983\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.84978	+	17.0603i	0.524251	+	0.908029i	0.999601	+	0.0282324i	$0.00898783\pi$
$353$	9.84978	+	17.0603i	0.524251	+	0.908029i	−0.475351	+	0.879796i	$0.657679\pi$
$354$		0			0
$355$	−1.95369	−	1.12796i	−0.103691	−	0.0598661i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			5.24810i			0.276984i	0.990364	+	0.138492i	$0.0442255\pi$
$359$			5.24810i			0.276984i	−0.990364	+	0.138492i	$0.955774\pi$
$360$		0			0
$361$	−20.2104			−1.06370
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.32573	−	1.34276i	−0.121734	−	0.0702833i
$366$		0			0
$367$	−5.73229	+	3.30954i	−0.299223	+	0.172757i	−0.642094	−	0.766626i	$-0.721934\pi$
$367$	−5.73229	+	3.30954i	−0.299223	+	0.172757i	0.342871	+	0.939383i	$0.388601\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.73336	+	14.5986i	0.141909	+	0.757920i
$372$		0			0
$373$	−0.420263	+	0.727917i	−0.0217604	+	0.0376901i	−0.876701	−	0.481037i	$-0.840260\pi$
$373$	−0.420263	+	0.727917i	−0.0217604	+	0.0376901i	0.854940	+	0.518727i	$0.173594\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−40.5274			−2.08727
$378$		0			0
$379$	−12.1366			−0.623415			−0.311707	−	0.950178i	$-0.600901\pi$
$379$	−12.1366			−0.623415			−0.311707	+	0.950178i	$0.600901\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.94973	−	17.2334i	0.508408	−	0.880588i	−0.491545	−	0.870852i	$-0.663568\pi$
$383$	9.94973	−	17.2334i	0.508408	−	0.880588i	0.999953	−	0.00973571i	$-0.00309902\pi$
$384$		0			0
$385$	−0.317588	−	1.69620i	−0.0161858	−	0.0864464i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.0098	+	6.93387i	−0.608921	+	0.351561i	−0.772543	−	0.634962i	$-0.781016\pi$
$389$	−12.0098	+	6.93387i	−0.608921	+	0.351561i	0.163622	+	0.986523i	$0.447682\pi$
$390$		0			0
$391$	−38.3029	−	22.1142i	−1.93706	−	1.11836i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.421973			0.0212318
$396$		0			0
$397$			15.9421i			0.800110i	0.916491	+	0.400055i	$0.131009\pi$
$397$			15.9421i			0.800110i	−0.916491	+	0.400055i	$0.868991\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.1057	−	5.83454i	−0.504655	−	0.291363i	0.225979	−	0.974132i	$-0.427442\pi$
$401$	−10.1057	−	5.83454i	−0.504655	−	0.291363i	−0.730634	+	0.682769i	$0.760775\pi$
$402$		0			0
$403$	8.89572	+	15.4078i	0.443127	+	0.767519i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	23.5342	−	13.5875i	1.16655	−	0.673506i
$408$		0			0
$409$	18.0845	+	10.4411i	0.894222	+	0.516279i	0.875321	−	0.483542i	$-0.160650\pi$
$409$	18.0845	+	10.4411i	0.894222	+	0.516279i	0.0189007	+	0.999821i	$0.493983\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.09076	−	3.09824i	0.0536727	−	0.152454i
$414$		0			0
$415$	1.09840			0.0539183
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.27039	+	2.20038i	−0.0620626	+	0.107496i	−0.895387	−	0.445288i	$-0.853101\pi$
$419$	−1.27039	+	2.20038i	−0.0620626	+	0.107496i	0.833325	+	0.552784i	$0.186434\pi$
$420$		0			0
$421$	0.363861	+	0.630226i	0.0177335	+	0.0307153i	0.874756	−	0.484564i	$-0.161022\pi$
$421$	0.363861	+	0.630226i	0.0177335	+	0.0307153i	−0.857022	+	0.515279i	$0.827688\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	14.9228	+	25.8470i	0.723862	+	1.25377i
$426$		0			0
$427$	−17.3015	+	14.8318i	−0.837279	+	0.717761i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			11.9157i			0.573959i	0.957937	+	0.286979i	$0.0926511\pi$
$431$			11.9157i			0.573959i	−0.957937	+	0.286979i	$0.907349\pi$
$432$		0			0
$433$		−	2.17537i		−	0.104541i	−0.998633	−	0.0522707i	$-0.983354\pi$
$433$		−	2.17537i		−	0.104541i	0.998633	−	0.0522707i	$-0.0166459\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	23.0586	−	39.9386i	1.10304	−	1.91052i
$438$		0			0
$439$	2.96411	−	1.71133i	0.141469	−	0.0816774i	−0.427595	−	0.903971i	$-0.640639\pi$
$439$	2.96411	−	1.71133i	0.141469	−	0.0816774i	0.569064	+	0.822293i	$0.307306\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−27.7665	+	16.0310i	−1.31923	+	0.761656i	−0.983604	−	0.180340i	$-0.942280\pi$
$443$	−27.7665	+	16.0310i	−1.31923	+	0.761656i	−0.335623	+	0.941996i	$0.608947\pi$
$444$		0			0
$445$	−1.02565	+	1.77647i	−0.0486203	+	0.0842128i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			22.2281i			1.04901i	0.851408	+	0.524504i	$0.175749\pi$
$449$			22.2281i			1.04901i	−0.851408	+	0.524504i	$0.824251\pi$
$450$		0			0
$451$		−	3.67914i		−	0.173244i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.42677	+	1.22311i	−0.0668882	+	0.0573402i
$456$		0			0
$457$	−19.8319	−	34.3499i	−0.927698	−	1.60682i	−0.787163	−	0.616745i	$-0.788451\pi$
$457$	−19.8319	−	34.3499i	−0.927698	−	1.60682i	−0.140535	−	0.990076i	$-0.544882\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.83439	+	4.90930i	0.132010	+	0.228649i	0.924451	−	0.381300i	$-0.124523\pi$
$461$	2.83439	+	4.90930i	0.132010	+	0.228649i	−0.792441	+	0.609949i	$0.791190\pi$
$462$		0			0
$463$	−16.5927	+	28.7393i	−0.771127	+	1.33563i	0.165819	+	0.986156i	$0.446973\pi$
$463$	−16.5927	+	28.7393i	−0.771127	+	1.33563i	−0.936946	+	0.349474i	$0.886360\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.5710			0.905639			0.452820	−	0.891602i	$-0.350418\pi$
$467$	19.5710			0.905639			0.452820	+	0.891602i	$0.350418\pi$
$468$		0			0
$469$	−7.41442	+	21.0602i	−0.342366	+	0.972471i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.304739	−	0.175941i	−0.0140119	−	0.00808978i
$474$		0			0
$475$	−26.9508	+	15.5601i	−1.23659	+	0.713945i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.2742	−	29.9198i	−0.789277	−	1.36707i	−0.926410	−	0.376516i	$-0.877122\pi$
$479$	−17.2742	−	29.9198i	−0.789277	−	1.36707i	0.137133	−	0.990553i	$-0.456211\pi$
$480$		0			0
$481$	−25.6290	−	14.7969i	−1.16858	−	0.674680i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	1.00783i		−	0.0457633i
$486$		0			0
$487$	−2.11458			−0.0958208			−0.0479104	−	0.998852i	$-0.515256\pi$
$487$	−2.11458			−0.0958208			−0.0479104	+	0.998852i	$0.515256\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.1214	+	7.57564i	0.592160	+	0.341884i	0.765951	−	0.642899i	$-0.222268\pi$
$491$	13.1214	+	7.57564i	0.592160	+	0.341884i	−0.173791	+	0.984783i	$0.555602\pi$
$492$		0			0
$493$	51.5440	−	29.7589i	2.32142	−	1.34027i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.32379	−	33.7746i	−0.283661	−	1.51500i
$498$		0			0
$499$	−2.08304	+	3.60793i	−0.0932496	+	0.161513i	−0.908877	−	0.417065i	$-0.863059\pi$
$499$	−2.08304	+	3.60793i	−0.0932496	+	0.161513i	0.815627	+	0.578578i	$0.196392\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.80385			0.0804296			0.0402148	−	0.999191i	$-0.487196\pi$
$503$	1.80385			0.0804296			0.0402148	+	0.999191i	$0.487196\pi$
$504$		0			0
$505$	0.146233			0.00650730
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−14.8129	+	25.6567i	−0.656570	+	1.13721i	0.324928	+	0.945739i	$0.394660\pi$
$509$	−14.8129	+	25.6567i	−0.656570	+	1.13721i	−0.981498	+	0.191474i	$0.938673\pi$
$510$		0			0
$511$	−7.52802	−	40.2063i	−0.333020	−	1.77862i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.852471	+	0.492175i	−0.0375644	+	0.0216878i
$516$		0			0
$517$	−12.1007	−	6.98635i	−0.532189	−	0.307259i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	37.7462			1.65369			0.826845	−	0.562430i	$-0.190134\pi$
$521$	37.7462			1.65369			0.826845	+	0.562430i	$0.190134\pi$
$522$		0			0
$523$		−	2.50718i		−	0.109631i	−0.998496	−	0.0548157i	$-0.982543\pi$
$523$		−	2.50718i		−	0.109631i	0.998496	−	0.0548157i	$-0.0174571\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−22.6277	−	13.0641i	−0.985677	−	0.569081i
$528$		0			0
$529$	15.6203	+	27.0552i	0.679144	+	1.17631i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.46984	+	2.00331i	−0.150295	+	0.0867730i
$534$		0			0
$535$	0.332104	+	0.191740i	0.0143581	+	0.00828965i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	16.4667	−	20.4877i	0.709270	−	0.882468i
$540$		0			0
$541$	−4.54144			−0.195252			−0.0976259	−	0.995223i	$-0.531125\pi$
$541$	−4.54144			−0.195252			−0.0976259	+	0.995223i	$0.531125\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.24424	−	2.15509i	0.0532976	−	0.0923141i
$546$		0			0
$547$	−19.2147	−	33.2809i	−0.821563	−	1.42299i	−0.904518	−	0.426435i	$-0.859769\pi$
$547$	−19.2147	−	33.2809i	−0.821563	−	1.42299i	0.0829555	−	0.996553i	$-0.473564\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	31.0298	+	53.7452i	1.32191	+	2.28962i
$552$		0			0
$553$	4.18318	+	4.87975i	0.177887	+	0.207508i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	2.36437i		−	0.100182i	−0.998745	−	0.0500908i	$-0.984049\pi$
$557$		−	2.36437i		−	0.100182i	0.998745	−	0.0500908i	$-0.0159511\pi$
$558$		0			0
$559$			0.383203i			0.0162077i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	16.7687	−	29.0442i	0.706715	−	1.22407i	−0.259354	−	0.965782i	$-0.583510\pi$
$563$	16.7687	−	29.0442i	0.706715	−	1.22407i	0.966069	−	0.258284i	$-0.0831571\pi$
$564$		0			0
$565$	1.53871	−	0.888373i	0.0647339	−	0.0373741i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−29.3733	+	16.9587i	−1.23139	+	0.710944i	−0.967320	−	0.253559i	$-0.918399\pi$
$569$	−29.3733	+	16.9587i	−1.23139	+	0.710944i	−0.264072	+	0.964503i	$0.585066\pi$
$570$		0			0
$571$	−8.69836	+	15.0660i	−0.364015	+	0.630492i	−0.988618	−	0.150450i	$-0.951928\pi$
$571$	−8.69836	+	15.0660i	−0.364015	+	0.630492i	0.624603	+	0.780943i	$0.285261\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	36.6019i		−	1.52640i
$576$		0			0
$577$			32.7477i			1.36330i	0.731676	+	0.681652i	$0.238738\pi$
$577$			32.7477i			1.36330i	−0.731676	+	0.681652i	$0.761262\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	10.8889	+	12.7020i	0.451746	+	0.526969i
$582$		0			0
$583$	10.5396	+	18.2551i	0.436504	+	0.756047i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.8495	+	27.4522i	0.654179	+	1.13307i	0.982099	+	0.188366i	$0.0603192\pi$
$587$	15.8495	+	27.4522i	0.654179	+	1.13307i	−0.327920	+	0.944706i	$0.606347\pi$
$588$		0			0
$589$	13.6220	−	23.5940i	0.561285	−	0.972174i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.9802			−0.615164			−0.307582	−	0.951522i	$-0.599520\pi$
$593$	−14.9802			−0.615164			−0.307582	+	0.951522i	$0.599520\pi$
$594$		0			0
$595$	0.916496	−	2.60325i	0.0375727	−	0.106723i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−39.0125	−	22.5239i	−1.59401	−	0.920301i	−0.992610	−	0.121352i	$-0.961277\pi$
$599$	−39.0125	−	22.5239i	−1.59401	−	0.920301i	−0.601399	−	0.798949i	$-0.705390\pi$
$600$		0			0
$601$	−27.6942	+	15.9892i	−1.12967	+	0.652214i	−0.943851	−	0.330370i	$-0.892826\pi$
$601$	−27.6942	+	15.9892i	−1.12967	+	0.652214i	−0.185817	+	0.982584i	$0.559493\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.269233	−	0.466325i	−0.0109459	−	0.0189588i
$606$		0			0
$607$	16.0165	+	9.24714i	0.650090	+	0.375330i	0.788491	−	0.615047i	$-0.210863\pi$
$607$	16.0165	+	9.24714i	0.650090	+	0.375330i	−0.138401	+	0.990376i	$0.544196\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			15.2164i			0.615589i
$612$		0			0
$613$	−11.7894			−0.476170			−0.238085	−	0.971244i	$-0.576520\pi$
$613$	−11.7894			−0.476170			−0.238085	+	0.971244i	$0.576520\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−34.5770	−	19.9630i	−1.39202	−	0.803681i	−0.398478	−	0.917178i	$-0.630462\pi$
$617$	−34.5770	−	19.9630i	−1.39202	−	0.803681i	−0.993538	+	0.113497i	$0.963795\pi$
$618$		0			0
$619$	−24.9967	+	14.4319i	−1.00470	+	0.580065i	−0.909636	−	0.415406i	$-0.863640\pi$
$619$	−24.9967	+	14.4319i	−1.00470	+	0.580065i	−0.0950661	+	0.995471i	$0.530306\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−30.7109	+	5.75015i	−1.23041	+	0.230375i
$624$		0			0
$625$	−12.2742	+	21.2595i	−0.490967	+	0.850379i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	43.4609			1.73290
$630$		0			0
$631$	6.75385			0.268866			0.134433	−	0.990923i	$-0.457079\pi$
$631$	6.75385			0.268866			0.134433	+	0.990923i	$0.457079\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.67522	−	2.90157i	0.0664791	−	0.115145i
$636$		0			0
$637$	−28.2883	−	4.37424i	−1.12082	−	0.173314i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.49123	−	5.47976i	0.374881	−	0.216438i	−0.300708	−	0.953716i	$-0.597223\pi$
$641$	9.49123	−	5.47976i	0.374881	−	0.216438i	0.675589	+	0.737279i	$0.263890\pi$
$642$		0			0
$643$	32.3924	+	18.7017i	1.27743	+	0.737525i	0.976375	−	0.216082i	$-0.0693278\pi$
$643$	32.3924	+	18.7017i	1.27743	+	0.737525i	0.301055	+	0.953607i	$0.402661\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−32.8051			−1.28970			−0.644851	−	0.764308i	$-0.723080\pi$
$647$	−32.8051			−1.28970			−0.644851	+	0.764308i	$0.723080\pi$
$648$		0			0
$649$		−	4.66173i		−	0.182989i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−8.73185	−	5.04134i	−0.341704	−	0.197283i	0.319321	−	0.947646i	$-0.396545\pi$
$653$	−8.73185	−	5.04134i	−0.341704	−	0.197283i	−0.661025	+	0.750364i	$0.729878\pi$
$654$		0			0
$655$	−0.0242208	−	0.0419517i	−0.000946385	−	0.00163919i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.61256	−	2.08571i	0.140725	−	0.0812478i	−0.427984	−	0.903786i	$-0.640776\pi$
$659$	3.61256	−	2.08571i	0.140725	−	0.0812478i	0.568710	+	0.822538i	$0.307443\pi$
$660$		0			0
$661$	−11.2303	−	6.48380i	−0.436807	−	0.252190i	0.265435	−	0.964129i	$-0.414484\pi$
$661$	−11.2303	−	6.48380i	−0.436807	−	0.252190i	−0.702242	+	0.711938i	$0.747818\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.71443	+	0.955636i	0.105261	+	0.0370580i
$666$		0			0
$667$	−72.9913			−2.82623
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−16.1715	+	28.0098i	−0.624292	+	1.08131i
$672$		0			0
$673$	−0.494352	−	0.856243i	−0.0190559	−	0.0330057i	0.856340	−	0.516412i	$-0.172733\pi$
$673$	−0.494352	−	0.856243i	−0.0190559	−	0.0330057i	−0.875396	+	0.483406i	$0.839399\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.07575	+	10.5235i	0.233510	+	0.404451i	0.958839	−	0.283952i	$-0.0916455\pi$
$677$	6.07575	+	10.5235i	0.233510	+	0.404451i	−0.725329	+	0.688403i	$0.758312\pi$
$678$		0			0
$679$	11.6547	−	9.99103i	0.447266	−	0.383421i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			51.6772i			1.97737i	0.149991	+	0.988687i	$0.452076\pi$
$683$			51.6772i			1.97737i	−0.149991	+	0.988687i	$0.547924\pi$
$684$		0			0
$685$		−	1.69287i		−	0.0646812i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	11.4777	−	19.8799i	0.437264	−	0.757364i
$690$		0			0
$691$	−22.0325	+	12.7205i	−0.838156	+	0.483910i	−0.856637	−	0.515919i	$-0.827450\pi$
$691$	−22.0325	+	12.7205i	−0.838156	+	0.483910i	0.0184807	+	0.999829i	$0.494117\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.51308	+	0.873579i	−0.0573945	+	0.0331367i
$696$		0			0
$697$	2.94203	−	5.09574i	0.111437	−	0.193015i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			28.3599i			1.07114i	0.844491	+	0.535570i	$0.179903\pi$
$701$			28.3599i			1.07114i	−0.844491	+	0.535570i	$0.820097\pi$
$702$		0			0
$703$			45.3169i			1.70916i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.44967	+	1.69106i	0.0545203	+	0.0635988i
$708$		0			0
$709$	6.51347	+	11.2817i	0.244619	+	0.423692i	0.962024	−	0.272964i	$-0.0880039\pi$
$709$	6.51347	+	11.2817i	0.244619	+	0.423692i	−0.717406	+	0.696656i	$0.754671\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	16.0215	+	27.7500i	0.600009	+	1.03925i
$714$		0			0
$715$	−1.33359	+	2.30984i	−0.0498733	+	0.0863830i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−19.3881			−0.723054			−0.361527	−	0.932362i	$-0.617745\pi$
$719$	−19.3881			−0.723054			−0.361527	+	0.932362i	$0.617745\pi$
$720$		0			0
$721$	−14.1424	−	4.97896i	−0.526692	−	0.185426i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	42.6560	+	24.6275i	1.58421	+	0.914641i
$726$		0			0
$727$	−36.8758	+	21.2903i	−1.36765	+	0.789612i	−0.990627	−	0.136592i	$-0.956385\pi$
$727$	−36.8758	+	21.2903i	−1.36765	+	0.789612i	−0.377021	+	0.926205i	$0.623052\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.281382	−	0.487368i	−0.0104073	−	0.0180260i
$732$		0			0
$733$	−15.9811	−	9.22669i	−0.590275	−	0.340795i	0.174931	−	0.984581i	$-0.444030\pi$
$733$	−15.9811	−	9.22669i	−0.590275	−	0.340795i	−0.765206	+	0.643785i	$0.777363\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			31.6880i			1.16724i
$738$		0			0
$739$	−36.5334			−1.34390			−0.671952	−	0.740595i	$-0.734544\pi$
$739$	−36.5334			−1.34390			−0.671952	+	0.740595i	$0.734544\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−14.5665	−	8.41000i	−0.534395	−	0.308533i	0.208409	−	0.978042i	$-0.433171\pi$
$743$	−14.5665	−	8.41000i	−0.534395	−	0.308533i	−0.742804	+	0.669509i	$0.766505\pi$
$744$		0			0
$745$	0.802230	−	0.463167i	0.0293914	−	0.0169691i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.07497	+	5.74128i	0.0392784	+	0.209782i
$750$		0			0
$751$	18.3761	−	31.8283i	0.670554	−	1.16143i	−0.307194	−	0.951647i	$-0.599390\pi$
$751$	18.3761	−	31.8283i	0.670554	−	1.16143i	0.977747	−	0.209786i	$-0.0672767\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.459330			−0.0167167
$756$		0			0
$757$	27.4501			0.997692			0.498846	−	0.866691i	$-0.333757\pi$
$757$	27.4501			0.997692			0.498846	+	0.866691i	$0.333757\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	22.4566	−	38.8960i	0.814053	−	1.40998i	−0.0959536	−	0.995386i	$-0.530590\pi$
$761$	22.4566	−	38.8960i	0.814053	−	1.40998i	0.910006	−	0.414595i	$-0.136077\pi$
$762$		0			0
$763$	37.2564	−	6.97570i	1.34877	−	0.252537i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.39652	+	2.53833i	−0.158749	+	0.0916538i
$768$		0			0
$769$	−7.93860	−	4.58335i	−0.286273	−	0.165280i	0.349987	−	0.936755i	$-0.386186\pi$
$769$	−7.93860	−	4.58335i	−0.286273	−	0.165280i	−0.636260	+	0.771475i	$0.719519\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−25.8694			−0.930457			−0.465229	−	0.885191i	$-0.654028\pi$
$773$	−25.8694			−0.930457			−0.465229	+	0.885191i	$0.654028\pi$
$774$		0			0
$775$		−	21.6228i		−	0.776714i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.31336	+	3.06767i	0.190371	+	0.109911i
$780$		0			0
$781$	−24.3839	−	42.2341i	−0.872523	−	1.51126i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.43350	−	1.40498i	0.0868555	−	0.0501460i
$786$		0			0
$787$	31.5865	+	18.2365i	1.12594	+	0.650060i	0.942910	−	0.333048i	$-0.108077\pi$
$787$	31.5865	+	18.2365i	1.12594	+	0.650060i	0.183027	+	0.983108i	$0.441410\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	25.5271	+	8.98700i	0.907637	+	0.319541i
$792$		0			0
$793$	35.2217			1.25076
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−26.3073	+	45.5656i	−0.931853	+	1.61402i	−0.151702	+	0.988426i	$0.548475\pi$
$797$	−26.3073	+	45.5656i	−0.931853	+	1.61402i	−0.780151	+	0.625591i	$0.784858\pi$
$798$		0			0
$799$	−11.1733	−	19.3527i	−0.395281	−	0.684648i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−29.0273	−	50.2767i	−1.02435	−	1.77423i
$804$		0			0
$805$	−2.56967	+	2.20286i	−0.0905690	+	0.0776406i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			46.9491i			1.65064i	0.564664	+	0.825321i	$0.309006\pi$
$809$			46.9491i			1.65064i	−0.564664	+	0.825321i	$0.690994\pi$
$810$		0			0
$811$		−	42.7359i		−	1.50066i	−0.661063	−	0.750330i	$-0.729895\pi$
$811$		−	42.7359i		−	1.50066i	0.661063	−	0.750330i	$-0.270105\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.55412	−	2.69181i	0.0544383	−	0.0942900i
$816$		0			0
$817$	0.508182	−	0.293399i	0.0177790	−	0.0102647i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.36444	+	4.25186i	−0.257021	+	0.148391i	−0.622975	−	0.782242i	$-0.714076\pi$
$821$	−7.36444	+	4.25186i	−0.257021	+	0.148391i	0.365954	+	0.930633i	$0.380743\pi$
$822$		0			0
$823$	−1.70687	+	2.95638i	−0.0594977	+	0.103053i	−0.894240	−	0.447588i	$-0.852283\pi$
$823$	−1.70687	+	2.95638i	−0.0594977	+	0.103053i	0.834742	+	0.550641i	$0.185617\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			32.0029i			1.11285i	0.830898	+	0.556425i	$0.187827\pi$
$827$			32.0029i			1.11285i	−0.830898	+	0.556425i	$0.812173\pi$
$828$		0			0
$829$		−	44.9590i		−	1.56149i	−0.624849	−	0.780746i	$-0.714839\pi$
$829$		−	44.9590i		−	1.56149i	0.624849	−	0.780746i	$-0.285161\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	39.1899	−	15.2086i	1.35785	−	0.526946i
$834$		0			0
$835$	0.342867	+	0.593864i	0.0118654	+	0.0205515i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.359076	−	0.621938i	−0.0123967	−	0.0214717i	0.859761	−	0.510697i	$-0.170613\pi$
$839$	−0.359076	−	0.621938i	−0.0123967	−	0.0214717i	−0.872157	+	0.489226i	$0.837279\pi$
$840$		0			0
$841$	34.6119	−	59.9496i	1.19352	−	2.06723i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.646463			0.0222390
$846$		0			0
$847$	2.72362	−	7.73629i	0.0935848	−	0.265822i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−46.1586	−	26.6497i	−1.58230	−	0.913540i
$852$		0			0
$853$	19.4916	−	11.2535i	0.667380	−	0.385312i	−0.127703	−	0.991812i	$-0.540760\pi$
$853$	19.4916	−	11.2535i	0.667380	−	0.385312i	0.795083	+	0.606500i	$0.207427\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.0401	+	19.1221i	0.377124	+	0.653198i	0.990643	−	0.136482i	$-0.0435797\pi$
$857$	11.0401	+	19.1221i	0.377124	+	0.653198i	−0.613518	+	0.789680i	$0.710246\pi$
$858$		0			0
$859$	7.67558	+	4.43150i	0.261887	+	0.151201i	0.625195	−	0.780468i	$-0.285019\pi$
$859$	7.67558	+	4.43150i	0.261887	+	0.151201i	−0.363308	+	0.931669i	$0.618353\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	51.9364i		−	1.76793i	−0.467548	−	0.883967i	$-0.654863\pi$
$863$		−	51.9364i		−	1.76793i	0.467548	−	0.883967i	$-0.345137\pi$
$864$		0			0
$865$	−2.24336			−0.0762766
$866$		0			0
$867$		0			0
$868$		0			0
$869$	7.89993	+	4.56103i	0.267987	+	0.154722i
$870$		0			0
$871$	29.8853	−	17.2543i	1.01262	−	0.584639i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.50356	−	0.843223i	0.152248	−	0.0285061i
$876$		0			0
$877$	0.665639	−	1.15292i	0.0224770	−	0.0389314i	−0.854568	−	0.519339i	$-0.826178\pi$
$877$	0.665639	−	1.15292i	0.0224770	−	0.0389314i	0.877045	+	0.480408i	$0.159511\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.54305			−0.0856776			−0.0428388	−	0.999082i	$-0.513640\pi$
$881$	−2.54305			−0.0856776			−0.0428388	+	0.999082i	$0.513640\pi$
$882$		0			0
$883$	−32.5186			−1.09434			−0.547169	−	0.837022i	$-0.684295\pi$
$883$	−32.5186			−1.09434			−0.547169	+	0.837022i	$0.684295\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.57415	+	13.1188i	−0.254315	+	0.440486i	−0.964709	−	0.263318i	$-0.915183\pi$
$887$	−7.57415	+	13.1188i	−0.254315	+	0.440486i	0.710394	+	0.703804i	$0.248517\pi$
$888$		0			0
$889$	50.1612	−	9.39191i	1.68235	−	0.314995i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	20.1791	−	11.6504i	0.675269	−	0.389867i
$894$		0			0
$895$	−0.388449	−	0.224271i	−0.0129844	−	0.00749655i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−43.1200			−1.43813
$900$		0			0
$901$			33.7118i			1.12310i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.343519	−	0.198331i	−0.0114190	−	0.00659274i
$906$		0			0
$907$	4.07650	+	7.06071i	0.135358	+	0.234447i	0.925734	−	0.378175i	$-0.123448\pi$
$907$	4.07650	+	7.06071i	0.135358	+	0.234447i	−0.790376	+	0.612622i	$0.790115\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−18.5370	+	10.7023i	−0.614157	+	0.354584i	−0.774591	−	0.632463i	$-0.782044\pi$
$911$	−18.5370	+	10.7023i	−0.614157	+	0.354584i	0.160434	+	0.987047i	$0.448711\pi$
$912$		0			0
$913$	20.5636	+	11.8724i	0.680555	+	0.392919i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.245024	−	0.695975i	0.00809139	−	0.0229831i
$918$		0			0
$919$	−35.4665			−1.16993			−0.584966	−	0.811058i	$-0.698892\pi$
$919$	−35.4665			−1.16993			−0.584966	+	0.811058i	$0.698892\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−26.5542	+	45.9933i	−0.874044	+	1.51389i
$924$		0			0
$925$	17.9834	+	31.1481i	0.591290	+	1.02414i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−22.4162	−	38.8260i	−0.735452	−	1.27384i	−0.954525	−	0.298132i	$-0.903636\pi$
$929$	−22.4162	−	38.8260i	−0.735452	−	1.27384i	0.219072	−	0.975709i	$-0.429697\pi$
$930$		0			0
$931$	15.8581	+	40.8635i	0.519728	+	1.33925i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	3.91696i		−	0.128098i
$936$		0			0
$937$			31.7907i			1.03856i	0.854605	+	0.519279i	$0.173800\pi$
$937$			31.7907i			1.03856i	−0.854605	+	0.519279i	$0.826200\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.4585	+	23.3109i	−0.438736	+	0.759913i	−0.997592	−	0.0693513i	$-0.977907\pi$
$941$	−13.4585	+	23.3109i	−0.438736	+	0.759913i	0.558856	+	0.829265i	$0.311240\pi$
$942$		0			0
$943$	−6.24929	+	3.60803i	−0.203505	+	0.117494i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−14.5020	+	8.37275i	−0.471252	+	0.272078i	−0.716764	−	0.697316i	$-0.754377\pi$
$947$	−14.5020	+	8.37275i	−0.471252	+	0.272078i	0.245511	+	0.969394i	$0.421044\pi$
$948$		0			0
$949$	−31.6109	+	54.7518i	−1.02613	+	1.77732i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	34.1919i		−	1.10758i	−0.832655	−	0.553791i	$-0.813180\pi$
$953$		−	34.1919i		−	1.10758i	0.832655	−	0.553791i	$-0.186820\pi$
$954$		0			0
$955$			0.230757i			0.00746712i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	19.5765	−	16.7821i	0.632159	−	0.541921i
$960$		0			0
$961$	−6.03521	−	10.4533i	−0.194684	−	0.337203i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.946262	−	1.63897i	−0.0304613	−	0.0527605i
$966$		0			0
$967$	−8.23331	+	14.2605i	−0.264765	+	0.458587i	−0.967502	−	0.252863i	$-0.918628\pi$
$967$	−8.23331	+	14.2605i	−0.264765	+	0.458587i	0.702737	+	0.711450i	$0.251961\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	23.9361			0.768145			0.384072	−	0.923303i	$-0.374521\pi$
$971$	23.9361			0.768145			0.384072	+	0.923303i	$0.374521\pi$
$972$		0			0
$973$	−25.1019	−	8.83734i	−0.804731	−	0.283312i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−29.6914	−	17.1423i	−0.949911	−	0.548431i	−0.0568577	−	0.998382i	$-0.518108\pi$
$977$	−29.6914	−	17.1423i	−0.949911	−	0.548431i	−0.893053	+	0.449951i	$0.851441\pi$
$978$		0			0
$979$	−38.4030	+	22.1720i	−1.22737	+	0.708620i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.4725	+	31.9952i	0.589180	+	1.02049i	0.994340	+	0.106244i	$0.0338824\pi$
$983$	18.4725	+	31.9952i	0.589180	+	1.02049i	−0.405160	+	0.914246i	$0.632784\pi$
$984$		0			0
$985$	−2.14996	−	1.24128i	−0.0685034	−	0.0395505i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			0.690161i			0.0219458i
$990$		0			0
$991$	23.6495			0.751251			0.375626	−	0.926771i	$-0.377428\pi$
$991$	23.6495			0.751251			0.375626	+	0.926771i	$0.377428\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.94953	+	1.12556i	0.0618042	+	0.0356827i
$996$		0			0
$997$	31.1468	−	17.9826i	0.986428	−	0.569515i	0.0822235	−	0.996614i	$-0.473798\pi$
$997$	31.1468	−	17.9826i	0.986428	−	0.569515i	0.904205	+	0.427099i	$0.140465\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.d.881.14		48
3.2	odd	2		1008.2.cc.d.545.14		48
4.3	odd	2		1512.2.bu.a.881.14		48
7.6	odd	2	inner	3024.2.cc.d.881.11		48
9.2	odd	6	inner	3024.2.cc.d.2897.11		48
9.7	even	3		1008.2.cc.d.209.11		48
12.11	even	2		504.2.bu.a.41.11	✓	48
21.20	even	2		1008.2.cc.d.545.11		48
28.27	even	2		1512.2.bu.a.881.11		48
36.7	odd	6		504.2.bu.a.209.14	yes	48
36.11	even	6		1512.2.bu.a.1385.11		48
36.23	even	6		4536.2.k.a.3401.28		48
36.31	odd	6		4536.2.k.a.3401.21		48
63.20	even	6	inner	3024.2.cc.d.2897.14		48
63.34	odd	6		1008.2.cc.d.209.14		48
84.83	odd	2		504.2.bu.a.41.14	yes	48
252.83	odd	6		1512.2.bu.a.1385.14		48
252.139	even	6		4536.2.k.a.3401.27		48
252.167	odd	6		4536.2.k.a.3401.22		48
252.223	even	6		504.2.bu.a.209.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bu.a.41.11	✓	48	12.11	even	2
504.2.bu.a.41.14	yes	48	84.83	odd	2
504.2.bu.a.209.11	yes	48	252.223	even	6
504.2.bu.a.209.14	yes	48	36.7	odd	6
1008.2.cc.d.209.11		48	9.7	even	3
1008.2.cc.d.209.14		48	63.34	odd	6
1008.2.cc.d.545.11		48	21.20	even	2
1008.2.cc.d.545.14		48	3.2	odd	2
1512.2.bu.a.881.11		48	28.27	even	2
1512.2.bu.a.881.14		48	4.3	odd	2
1512.2.bu.a.1385.11		48	36.11	even	6
1512.2.bu.a.1385.14		48	252.83	odd	6
3024.2.cc.d.881.11		48	7.6	odd	2	inner
3024.2.cc.d.881.14		48	1.1	even	1	trivial
3024.2.cc.d.2897.11		48	9.2	odd	6	inner
3024.2.cc.d.2897.14		48	63.20	even	6	inner
4536.2.k.a.3401.21		48	36.31	odd	6
4536.2.k.a.3401.22		48	252.167	odd	6
4536.2.k.a.3401.27		48	252.139	even	6
4536.2.k.a.3401.28		48	36.23	even	6

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0868503 - 0.150429i) q^{5} +(2.60056 - 0.486915i) q^{7} +O(q^{10})\)	\(q+(0.0868503 - 0.150429i) q^{5} +(2.60056 - 0.486915i) q^{7} +(3.25192 - 1.87750i) q^{11} +(-3.54137 - 2.04461i) q^{13} +6.00535 q^{17} +6.26182i q^{19} +(-6.37812 - 3.68241i) q^{23} +(2.48491 + 4.30400i) q^{25} +(8.58300 - 4.95540i) q^{29} +(-3.76792 - 2.17541i) q^{31} +(0.152613 - 0.433489i) q^{35} +7.23702 q^{37} +(0.489900 - 0.848533i) q^{41} +(-0.0468552 - 0.0811557i) q^{43} +(-1.86055 - 3.22257i) q^{47} +(6.52583 - 2.53251i) q^{49} +5.61363i q^{53} -0.652244i q^{55} +(0.620738 - 1.07515i) q^{59} +(-7.45935 + 4.30666i) q^{61} +(-0.615138 + 0.355150i) q^{65} +(-4.21946 + 7.30831i) q^{67} -12.9874i q^{71} -15.4606i q^{73} +(7.54263 - 6.46595i) q^{77} +(1.21466 + 2.10385i) q^{79} +(3.16176 + 5.47633i) q^{83} +(0.521567 - 0.903380i) q^{85} -11.8093 q^{89} +(-10.2051 - 3.59278i) q^{91} +(0.941960 + 0.543841i) q^{95} +(5.02479 - 2.90106i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) \) 48 * q + 12 * q^23 - 24 * q^25 + 36 * q^29 - 12 * q^43 + 6 * q^49 - 36 * q^65 + 60 * q^77 + 12 * q^79 + 12 * q^91 - 108 * q^95

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