LMFDB - Embedded newform 1300.2.m.c.593.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1300,2,Mod(57,1300)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1300, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1300.57"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2,0,0,0,0,0,0,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.31678304256.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 8x^{5} + 32x^{4} - 20x^{3} + 8x^{2} + 8x + 4 $ x^8 - 2x^7 + 2x^6 + 8x^5 + 32x^4 - 20x^3 + 8x^2 + 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			593.3
Root			$-0.285451 + 0.285451i$ of defining polynomial
Character	$\chi$	$=$	1300.593
Dual form			1300.2.m.c.57.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.285451 + 0.285451i) q^{3} +1.26613i q^{7} -2.83704i q^{9} +(4.21777 - 4.21777i) q^{11} +(-2.28545 + 2.78868i) q^{13} +(1.93232 + 1.93232i) q^{17} +(-2.55158 + 2.55158i) q^{19} +(-0.361419 + 0.361419i) q^{21} +(5.21777 - 5.21777i) q^{23} +(1.66619 - 1.66619i) q^{27} -7.16941i q^{29} +(2.78868 + 2.78868i) q^{31} +2.40794 q^{33} -5.83704i q^{37} +(-1.44842 + 0.143646i) q^{39} +(-1.33381 - 1.33381i) q^{41} +(-5.65332 + 5.65332i) q^{43} -10.8048i q^{47} +5.39691 q^{49} +1.10317i q^{51} +(9.27258 + 9.27258i) q^{53} -1.45671 q^{57} +(-2.55158 - 2.55158i) q^{59} +13.8499 q^{61} +3.59206 q^{63} -1.30477 q^{67} +2.97884 q^{69} +(8.72745 + 8.72745i) q^{71} +7.64360 q^{73} +(5.34026 + 5.34026i) q^{77} +0.954914i q^{79} -7.55987 q^{81} -5.13078i q^{83} +(2.04652 - 2.04652i) q^{87} +(5.31122 + 5.31122i) q^{89} +(-3.53083 - 2.89368i) q^{91} +1.59206i q^{93} -2.81956 q^{97} +(-11.9660 - 11.9660i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 14 q^{11} - 14 q^{13} + 2 q^{19} + 4 q^{21} + 22 q^{23} + 16 q^{27} - 6 q^{31} - 16 q^{33} - 34 q^{39} - 8 q^{41} + 14 q^{43} - 24 q^{49} + 8 q^{53} - 16 q^{57} + 2 q^{59} - 12 q^{61} + 64 q^{63}+ \cdots + 10 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 14 * q^11 - 14 * q^13 + 2 * q^19 + 4 * q^21 + 22 * q^23 + 16 * q^27 - 6 * q^31 - 16 * q^33 - 34 * q^39 - 8 * q^41 + 14 * q^43 - 24 * q^49 + 8 * q^53 - 16 * q^57 + 2 * q^59 - 12 * q^61 + 64 * q^63 - 20 * q^67 - 20 * q^69 - 22 * q^71 + 28 * q^73 - 8 * q^77 - 20 * q^81 - 12 * q^87 + 4 * q^89 - 12 * q^97 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.285451	+	0.285451i	0.164805	+	0.164805i	0.784692	−	0.619886i	$-0.212821\pi$
$3$	0.285451	+	0.285451i	0.164805	+	0.164805i	−0.619886	+	0.784692i	$0.712821\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			1.26613i			0.478553i	0.970951	+	0.239277i	$0.0769103\pi$
$7$			1.26613i			0.478553i	−0.970951	+	0.239277i	$0.923090\pi$
$8$		0			0
$9$		−	2.83704i		−	0.945678i
$10$		0			0
$11$	4.21777	−	4.21777i	1.27171	−	1.27171i	0.326514	−	0.945192i	$-0.394126\pi$
$11$	4.21777	−	4.21777i	1.27171	−	1.27171i	0.945192	−	0.326514i	$-0.105874\pi$
$12$		0			0
$13$	−2.28545	+	2.78868i	−0.633870	+	0.773439i
$13$	−2.28545	+	2.78868i	−0.633870	+	0.773439i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.93232	+	1.93232i	0.468657	+	0.468657i	0.901479	−	0.432822i	$-0.142482\pi$
$17$	1.93232	+	1.93232i	0.468657	+	0.468657i	−0.432822	+	0.901479i	$0.642482\pi$
$18$		0			0
$19$	−2.55158	+	2.55158i	−0.585373	+	0.585373i	−0.936375	−	0.351001i	$-0.885841\pi$
$19$	−2.55158	+	2.55158i	−0.585373	+	0.585373i	0.351001	+	0.936375i	$0.385841\pi$
$20$		0			0
$21$	−0.361419	+	0.361419i	−0.0788681	+	0.0788681i
$22$		0			0
$23$	5.21777	−	5.21777i	1.08798	−	1.08798i	0.0922445	−	0.995736i	$-0.470596\pi$
$23$	5.21777	−	5.21777i	1.08798	−	1.08798i	0.995736	−	0.0922445i	$-0.0294041\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.66619	−	1.66619i	0.320658	−	0.320658i
$28$		0			0
$29$		−	7.16941i		−	1.33133i	−0.746252	−	0.665663i	$-0.768149\pi$
$29$		−	7.16941i		−	1.33133i	0.746252	−	0.665663i	$-0.231851\pi$
$30$		0			0
$31$	2.78868	+	2.78868i	0.500861	+	0.500861i	0.911705	−	0.410844i	$-0.134766\pi$
$31$	2.78868	+	2.78868i	0.500861	+	0.500861i	−0.410844	+	0.911705i	$0.634766\pi$
$32$		0			0
$33$	2.40794			0.419168
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	5.83704i		−	0.959603i	−0.877377	−	0.479801i	$-0.840709\pi$
$37$		−	5.83704i		−	0.959603i	0.877377	−	0.479801i	$-0.159291\pi$
$38$		0			0
$39$	−1.44842	+	0.143646i	−0.231932	+	0.0230018i
$40$		0			0
$41$	−1.33381	−	1.33381i	−0.208306	−	0.208306i	0.595241	−	0.803547i	$-0.297057\pi$
$41$	−1.33381	−	1.33381i	−0.208306	−	0.208306i	−0.803547	+	0.595241i	$0.797057\pi$
$42$		0			0
$43$	−5.65332	+	5.65332i	−0.862123	+	0.862123i	−0.991584	−	0.129461i	$-0.958675\pi$
$43$	−5.65332	+	5.65332i	−0.862123	+	0.862123i	0.129461	+	0.991584i	$0.458675\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	10.8048i		−	1.57605i	−0.615644	−	0.788024i	$-0.711104\pi$
$47$		−	10.8048i		−	1.57605i	0.615644	−	0.788024i	$-0.288896\pi$
$48$		0			0
$49$	5.39691			0.770987
$50$		0			0
$51$			1.10317i			0.154474i
$52$		0			0
$53$	9.27258	+	9.27258i	1.27369	+	1.27369i	0.944139	+	0.329548i	$0.106896\pi$
$53$	9.27258	+	9.27258i	1.27369	+	1.27369i	0.329548	+	0.944139i	$0.393104\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.45671			−0.192945
$58$		0			0
$59$	−2.55158	−	2.55158i	−0.332188	−	0.332188i	0.521229	−	0.853417i	$-0.325474\pi$
$59$	−2.55158	−	2.55158i	−0.332188	−	0.332188i	−0.853417	+	0.521229i	$0.825474\pi$
$60$		0			0
$61$	13.8499			1.77330			0.886651	−	0.462439i	$-0.153026\pi$
$61$	13.8499			1.77330			0.886651	+	0.462439i	$0.153026\pi$
$62$		0			0
$63$	3.59206			0.452557
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.30477			−0.159403			−0.0797015	−	0.996819i	$-0.525397\pi$
$67$	−1.30477			−0.159403			−0.0797015	+	0.996819i	$0.525397\pi$
$68$		0			0
$69$	2.97884			0.358610
$70$		0			0
$71$	8.72745	+	8.72745i	1.03576	+	1.03576i	0.999337	+	0.0364208i	$0.0115957\pi$
$71$	8.72745	+	8.72745i	1.03576	+	1.03576i	0.0364208	+	0.999337i	$0.488404\pi$
$72$		0			0
$73$	7.64360			0.894615			0.447308	−	0.894380i	$-0.352383\pi$
$73$	7.64360			0.894615			0.447308	+	0.894380i	$0.352383\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.34026	+	5.34026i	0.608579	+	0.608579i
$78$		0			0
$79$			0.954914i			0.107436i	0.998556	+	0.0537181i	$0.0171072\pi$
$79$			0.954914i			0.107436i	−0.998556	+	0.0537181i	$0.982893\pi$
$80$		0			0
$81$	−7.55987			−0.839986
$82$		0			0
$83$		−	5.13078i		−	0.563176i	−0.959535	−	0.281588i	$-0.909139\pi$
$83$		−	5.13078i		−	0.563176i	0.959535	−	0.281588i	$-0.0908611\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.04652	−	2.04652i	0.219410	−	0.219410i
$88$		0			0
$89$	5.31122	+	5.31122i	0.562988	+	0.562988i	0.930155	−	0.367167i	$-0.119672\pi$
$89$	5.31122	+	5.31122i	0.562988	+	0.562988i	−0.367167	+	0.930155i	$0.619672\pi$
$90$		0			0
$91$	−3.53083	−	2.89368i	−0.370132	−	0.303341i
$92$		0			0
$93$			1.59206i			0.165089i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.81956			−0.286283			−0.143141	−	0.989702i	$-0.545720\pi$
$97$	−2.81956			−0.286283			−0.143141	+	0.989702i	$0.545720\pi$
$98$		0			0
$99$	−11.9660	−	11.9660i	−1.20263	−	1.20263i
$100$		0			0
$101$		−	1.27716i		−	0.127082i	−0.997979	−	0.0635412i	$-0.979761\pi$
$101$		−	1.27716i		−	0.127082i	0.997979	−	0.0635412i	$-0.0202394\pi$
$102$		0			0
$103$	−0.313060	+	0.313060i	−0.0308467	+	0.0308467i	−0.722362	−	0.691515i	$-0.756943\pi$
$103$	−0.313060	+	0.313060i	−0.0308467	+	0.0308467i	0.691515	+	0.722362i	$0.256943\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.19016	+	7.19016i	−0.695099	+	0.695099i	−0.963349	−	0.268250i	$-0.913555\pi$
$107$	−7.19016	+	7.19016i	−0.695099	+	0.695099i	0.268250	+	0.963349i	$0.413555\pi$
$108$		0			0
$109$	3.07413	−	3.07413i	0.294448	−	0.294448i	−0.544387	−	0.838834i	$-0.683238\pi$
$109$	3.07413	−	3.07413i	0.294448	−	0.294448i	0.838834	+	0.544387i	$0.183238\pi$
$110$		0			0
$111$	1.66619	−	1.66619i	0.158148	−	0.158148i
$112$		0			0
$113$	−9.06310	−	9.06310i	−0.852585	−	0.852585i	0.137866	−	0.990451i	$-0.455976\pi$
$113$	−9.06310	−	9.06310i	−0.852585	−	0.852585i	−0.990451	+	0.137866i	$0.955976\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	7.91157	+	6.48391i	0.731425	+	0.599437i
$118$		0			0
$119$	−2.44658	+	2.44658i	−0.224277	+	0.224277i
$120$		0			0
$121$		−	24.5792i		−	2.23447i
$122$		0			0
$123$		−	0.761476i		−	0.0686600i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−6.88396	−	6.88396i	−0.610853	−	0.610853i	0.332315	−	0.943168i	$-0.392170\pi$
$127$	−6.88396	−	6.88396i	−0.610853	−	0.610853i	−0.943168	+	0.332315i	$0.892170\pi$
$128$		0			0
$129$	−3.22749			−0.284165
$130$		0			0
$131$	0.193437			0.0169007			0.00845036	−	0.999964i	$-0.497310\pi$
$131$	0.193437			0.0169007			0.00845036	+	0.999964i	$0.497310\pi$
$132$		0			0
$133$	−3.23064	−	3.23064i	−0.280132	−	0.280132i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			4.03864i			0.345044i	0.985006	+	0.172522i	$0.0551916\pi$
$137$			4.03864i			0.345044i	−0.985006	+	0.172522i	$0.944808\pi$
$138$		0			0
$139$			2.57090i			0.218061i	0.994038	+	0.109031i	$0.0347746\pi$
$139$			2.57090i			0.218061i	−0.994038	+	0.109031i	$0.965225\pi$
$140$		0			0
$141$	3.08426	−	3.08426i	0.259741	−	0.259741i
$142$		0			0
$143$	2.12249	+	21.4015i	0.177491	+	1.78968i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.54055	+	1.54055i	0.127063	+	0.127063i
$148$		0			0
$149$	0.898264	−	0.898264i	0.0735887	−	0.0735887i	−0.669354	−	0.742943i	$-0.733429\pi$
$149$	0.898264	−	0.898264i	0.0735887	−	0.0735887i	0.742943	+	0.669354i	$0.233429\pi$
$150$		0			0
$151$	−7.58564	+	7.58564i	−0.617311	+	0.617311i	−0.944841	−	0.327530i	$-0.893784\pi$
$151$	−7.58564	+	7.58564i	−0.617311	+	0.617311i	0.327530	+	0.944841i	$0.393784\pi$
$152$		0			0
$153$	5.48206	−	5.48206i	0.443199	−	0.443199i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	5.36142	−	5.36142i	0.427888	−	0.427888i	−0.460020	−	0.887908i	$-0.652158\pi$
$157$	5.36142	−	5.36142i	0.427888	−	0.427888i	0.887908	+	0.460020i	$0.152158\pi$
$158$		0			0
$159$			5.29374i			0.419821i
$160$		0			0
$161$	6.60639	+	6.60639i	0.520657	+	0.520657i
$162$		0			0
$163$	−16.7883			−1.31496			−0.657479	−	0.753473i	$-0.728377\pi$
$163$	−16.7883			−1.31496			−0.657479	+	0.753473i	$0.728377\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			17.2790i			1.33709i	0.743671	+	0.668546i	$0.233083\pi$
$167$			17.2790i			1.33709i	−0.743671	+	0.668546i	$0.766917\pi$
$168$		0			0
$169$	−2.55342	−	12.7468i	−0.196417	−	0.980520i
$170$		0			0
$171$	7.23893	+	7.23893i	0.553575	+	0.553575i
$172$		0			0
$173$	4.52582	−	4.52582i	0.344091	−	0.344091i	−0.513812	−	0.857903i	$-0.671767\pi$
$173$	4.52582	−	4.52582i	0.344091	−	0.344091i	0.857903	+	0.513812i	$0.171767\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	1.45671i		−	0.109493i
$178$		0			0
$179$	−7.01935			−0.524651			−0.262325	−	0.964980i	$-0.584489\pi$
$179$	−7.01935			−0.524651			−0.262325	+	0.964980i	$0.584489\pi$
$180$		0			0
$181$			3.02116i			0.224561i	0.993677	+	0.112281i	$0.0358155\pi$
$181$			3.02116i			0.224561i	−0.993677	+	0.112281i	$0.964184\pi$
$182$		0			0
$183$	3.95348	+	3.95348i	0.292250	+	0.292250i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	16.3002			1.19199
$188$		0			0
$189$	2.10962	+	2.10962i	0.153452	+	0.153452i
$190$		0			0
$191$	−0.916276			−0.0662994			−0.0331497	−	0.999450i	$-0.510554\pi$
$191$	−0.916276			−0.0662994			−0.0331497	+	0.999450i	$0.510554\pi$
$192$		0			0
$193$	−15.0580			−1.08390			−0.541949	−	0.840412i	$-0.682313\pi$
$193$	−15.0580			−1.08390			−0.541949	+	0.840412i	$0.682313\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.56445			0.396451			0.198225	−	0.980156i	$-0.436482\pi$
$197$	5.56445			0.396451			0.198225	+	0.980156i	$0.436482\pi$
$198$		0			0
$199$	16.2616			1.15275			0.576375	−	0.817185i	$-0.304467\pi$
$199$	16.2616			1.15275			0.576375	+	0.817185i	$0.304467\pi$
$200$		0			0
$201$	−0.372448	−	0.372448i	−0.0262705	−	0.0262705i
$202$		0			0
$203$	9.07743			0.637111
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−14.8030	−	14.8030i	−1.02888	−	1.02888i
$208$		0			0
$209$			21.5240i			1.48885i
$210$		0			0
$211$	−19.4383			−1.33819			−0.669094	−	0.743177i	$-0.733318\pi$
$211$	−19.4383			−1.33819			−0.669094	+	0.743177i	$0.733318\pi$
$212$		0			0
$213$			4.98252i			0.341397i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.53083	+	3.53083i	−0.239689	+	0.239689i
$218$		0			0
$219$	2.18187	+	2.18187i	0.147437	+	0.147437i
$220$		0			0
$221$	−9.80485	+	0.972392i	−0.659545	+	0.0654101i
$222$		0			0
$223$		−	3.60496i		−	0.241406i	−0.992689	−	0.120703i	$-0.961485\pi$
$223$		−	3.60496i		−	0.241406i	0.992689	−	0.120703i	$-0.0385149\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−24.4374			−1.62197			−0.810984	−	0.585068i	$-0.801068\pi$
$227$	−24.4374			−1.62197			−0.810984	+	0.585068i	$0.801068\pi$
$228$		0			0
$229$	9.46315	+	9.46315i	0.625343	+	0.625343i	0.946893	−	0.321550i	$-0.104204\pi$
$229$	9.46315	+	9.46315i	0.625343	+	0.625343i	−0.321550	+	0.946893i	$0.604204\pi$
$230$		0			0
$231$			3.04877i			0.200594i
$232$		0			0
$233$	1.80011	−	1.80011i	0.117929	−	0.117929i	−0.645679	−	0.763609i	$-0.723426\pi$
$233$	1.80011	−	1.80011i	0.117929	−	0.117929i	0.763609	+	0.645679i	$0.223426\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.272581	+	0.272581i	−0.0177061	+	0.0177061i
$238$		0			0
$239$	−13.0999	+	13.0999i	−0.847362	+	0.847362i	−0.989803	−	0.142441i	$-0.954505\pi$
$239$	−13.0999	+	13.0999i	−0.847362	+	0.847362i	0.142441	+	0.989803i	$0.454505\pi$
$240$		0			0
$241$	−13.2371	+	13.2371i	−0.852676	+	0.852676i	−0.990462	−	0.137786i	$-0.956001\pi$
$241$	−13.2371	+	13.2371i	−0.852676	+	0.852676i	0.137786	+	0.990462i	$0.456001\pi$
$242$		0			0
$243$	−7.15654	−	7.15654i	−0.459092	−	0.459092i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.28402	−	12.9471i	−0.0817002	−	0.823802i
$248$		0			0
$249$	1.46459	−	1.46459i	0.0928144	−	0.0928144i
$250$		0			0
$251$		−	4.62612i		−	0.291998i	−0.989285	−	0.145999i	$-0.953360\pi$
$251$		−	4.62612i		−	0.291998i	0.989285	−	0.145999i	$-0.0466396\pi$
$252$		0			0
$253$		−	44.0148i		−	2.76718i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.55342	+	4.55342i	0.284035	+	0.284035i	0.834716	−	0.550681i	$-0.185632\pi$
$257$	4.55342	+	4.55342i	0.284035	+	0.284035i	−0.550681	+	0.834716i	$0.685632\pi$
$258$		0			0
$259$	7.39046			0.459221
$260$		0			0
$261$	−20.3399			−1.25901
$262$		0			0
$263$	2.72100	+	2.72100i	0.167784	+	0.167784i	0.786005	−	0.618221i	$-0.212146\pi$
$263$	2.72100	+	2.72100i	0.167784	+	0.167784i	−0.618221	+	0.786005i	$0.712146\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			3.03219i			0.185567i
$268$		0			0
$269$			11.6870i			0.712567i	0.934378	+	0.356284i	$0.115956\pi$
$269$			11.6870i			0.712567i	−0.934378	+	0.356284i	$0.884044\pi$
$270$		0			0
$271$	−13.9660	+	13.9660i	−0.848372	+	0.848372i	−0.989930	−	0.141558i	$-0.954789\pi$
$271$	−13.9660	+	13.9660i	−0.848372	+	0.848372i	0.141558	+	0.989930i	$0.454789\pi$
$272$		0			0
$273$	−0.181875	−	1.83389i	−0.0110076	−	0.110992i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.09672	−	1.09672i	−0.0658954	−	0.0658954i	0.673391	−	0.739286i	$-0.264837\pi$
$277$	−1.09672	−	1.09672i	−0.0658954	−	0.0658954i	−0.739286	+	0.673391i	$0.764837\pi$
$278$		0			0
$279$	7.91157	−	7.91157i	0.473653	−	0.473653i
$280$		0			0
$281$	−8.62755	+	8.62755i	−0.514677	+	0.514677i	−0.915956	−	0.401279i	$-0.868566\pi$
$281$	−8.62755	+	8.62755i	−0.514677	+	0.514677i	0.401279	+	0.915956i	$0.368566\pi$
$282$		0			0
$283$	−7.50507	+	7.50507i	−0.446130	+	0.446130i	−0.894066	−	0.447936i	$-0.852159\pi$
$283$	−7.50507	+	7.50507i	−0.446130	+	0.446130i	0.447936	+	0.894066i	$0.352159\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.68878	−	1.68878i	0.0996856	−	0.0996856i
$288$		0			0
$289$		−	9.53226i		−	0.560721i
$290$		0			0
$291$	−0.804846	−	0.804846i	−0.0471809	−	0.0471809i
$292$		0			0
$293$	−21.0341			−1.22882			−0.614411	−	0.788986i	$-0.710606\pi$
$293$	−21.0341			−1.22882			−0.614411	+	0.788986i	$0.710606\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	14.0552i		−	0.815566i
$298$		0			0
$299$	2.62571	+	26.4756i	0.151849	+	1.53113i
$300$		0			0
$301$	−7.15785	−	7.15785i	−0.412572	−	0.412572i
$302$		0			0
$303$	0.364567	−	0.364567i	0.0209439	−	0.0209439i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			13.7984i			0.787516i	0.919214	+	0.393758i	$0.128825\pi$
$307$			13.7984i			0.787516i	−0.919214	+	0.393758i	$0.871175\pi$
$308$		0			0
$309$	−0.178727			−0.0101674
$310$		0			0
$311$		−	19.9743i		−	1.13264i	−0.824187	−	0.566318i	$-0.808367\pi$
$311$		−	19.9743i		−	1.13264i	0.824187	−	0.566318i	$-0.191633\pi$
$312$		0			0
$313$	4.92587	+	4.92587i	0.278427	+	0.278427i	0.832481	−	0.554054i	$-0.186920\pi$
$313$	4.92587	+	4.92587i	0.278427	+	0.278427i	−0.554054	+	0.832481i	$0.686920\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.7146			−0.657956			−0.328978	−	0.944338i	$-0.606704\pi$
$317$	−11.7146			−0.657956			−0.328978	+	0.944338i	$0.606704\pi$
$318$		0			0
$319$	−30.2390	−	30.2390i	−1.69306	−	1.69306i
$320$		0			0
$321$	−4.10488			−0.229112
$322$		0			0
$323$	−9.86096			−0.548679
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.75503			0.0970532
$328$		0			0
$329$	13.6804			0.754223
$330$		0			0
$331$	−4.94061	−	4.94061i	−0.271561	−	0.271561i	0.558168	−	0.829728i	$-0.311505\pi$
$331$	−4.94061	−	4.94061i	−0.271561	−	0.271561i	−0.829728	+	0.558168i	$0.811505\pi$
$332$		0			0
$333$	−16.5599			−0.907475
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.67909	+	8.67909i	0.472780	+	0.472780i	0.902813	−	0.430033i	$-0.141498\pi$
$337$	8.67909	+	8.67909i	0.472780	+	0.472780i	−0.430033	+	0.902813i	$0.641498\pi$
$338$		0			0
$339$		−	5.17415i		−	0.281021i
$340$		0			0
$341$	23.5240			1.27390
$342$		0			0
$343$			15.6961i			0.847511i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−19.0627	+	19.0627i	−1.02334	+	1.02334i	−0.0236177	+	0.999721i	$0.507518\pi$
$347$	−19.0627	+	19.0627i	−1.02334	+	1.02334i	−0.999721	+	0.0236177i	$0.992482\pi$
$348$		0			0
$349$	2.00645	+	2.00645i	0.107403	+	0.107403i	0.758766	−	0.651363i	$-0.225803\pi$
$349$	2.00645	+	2.00645i	0.107403	+	0.107403i	−0.651363	+	0.758766i	$0.725803\pi$
$350$		0			0
$351$	0.838467	+	8.45446i	0.0447541	+	0.451265i
$352$		0			0
$353$			2.41162i			0.128358i	0.997938	+	0.0641788i	$0.0204428\pi$
$353$			2.41162i			0.128358i	−0.997938	+	0.0641788i	$0.979557\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−1.39676			−0.0739242
$358$		0			0
$359$	1.92546	+	1.92546i	0.101622	+	0.101622i	0.756090	−	0.654468i	$-0.227107\pi$
$359$	1.92546	+	1.92546i	0.101622	+	0.101622i	−0.654468	+	0.756090i	$0.727107\pi$
$360$		0			0
$361$			5.97884i			0.314676i
$362$		0			0
$363$	7.01617	−	7.01617i	0.368253	−	0.368253i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	16.8435	−	16.8435i	0.879224	−	0.879224i	−0.114230	−	0.993454i	$-0.536440\pi$
$367$	16.8435	−	16.8435i	0.879224	−	0.879224i	0.993454	+	0.114230i	$0.0364401\pi$
$368$		0			0
$369$	−3.78407	+	3.78407i	−0.196991	+	0.196991i
$370$		0			0
$371$	−11.7403	+	11.7403i	−0.609527	+	0.609527i
$372$		0			0
$373$	20.4388	+	20.4388i	1.05828	+	1.05828i	0.998193	+	0.0600904i	$0.0191389\pi$
$373$	20.4388	+	20.4388i	1.05828	+	1.05828i	0.0600904	+	0.998193i	$0.480861\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	19.9932	+	16.3853i	1.02970	+	0.843888i
$378$		0			0
$379$	−15.7841	+	15.7841i	−0.810775	+	0.810775i	−0.984750	−	0.173975i	$-0.944339\pi$
$379$	−15.7841	+	15.7841i	−0.810775	+	0.810775i	0.173975	+	0.984750i	$0.444339\pi$
$380$		0			0
$381$		−	3.93007i		−	0.201344i
$382$		0			0
$383$		−	21.7432i		−	1.11102i	−0.831508	−	0.555512i	$-0.812522\pi$
$383$		−	21.7432i		−	1.11102i	0.831508	−	0.555512i	$-0.187478\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	16.0387	+	16.0387i	0.815291	+	0.815291i
$388$		0			0
$389$	17.9227			0.908718			0.454359	−	0.890819i	$-0.349868\pi$
$389$	17.9227			0.908718			0.454359	+	0.890819i	$0.349868\pi$
$390$		0			0
$391$	20.1648			1.01978
$392$		0			0
$393$	0.0552170	+	0.0552170i	0.00278533	+	0.00278533i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			33.9632i			1.70457i	0.523081	+	0.852283i	$0.324782\pi$
$397$			33.9632i			1.70457i	−0.523081	+	0.852283i	$0.675218\pi$
$398$		0			0
$399$		−	1.84438i		−	0.0923346i
$400$		0			0
$401$	15.0857	−	15.0857i	0.753343	−	0.753343i	−0.221758	−	0.975102i	$-0.571180\pi$
$401$	15.0857	−	15.0857i	0.753343	−	0.753343i	0.975102	+	0.221758i	$0.0711796\pi$
$402$		0			0
$403$	−14.1501	+	1.40333i	−0.704866	+	0.0699048i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−24.6193	−	24.6193i	−1.22033	−	1.22033i
$408$		0			0
$409$	11.7141	−	11.7141i	0.579227	−	0.579227i	−0.355463	−	0.934690i	$-0.615677\pi$
$409$	11.7141	−	11.7141i	0.579227	−	0.579227i	0.934690	+	0.355463i	$0.115677\pi$
$410$		0			0
$411$	−1.15283	+	1.15283i	−0.0568651	+	0.0568651i
$412$		0			0
$413$	3.23064	−	3.23064i	0.158970	−	0.158970i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.733868	+	0.733868i	−0.0359376	+	0.0359376i
$418$		0			0
$419$			13.2486i			0.647234i	0.946188	+	0.323617i	$0.104899\pi$
$419$			13.2486i			0.647234i	−0.946188	+	0.323617i	$0.895101\pi$
$420$		0			0
$421$	−6.17729	−	6.17729i	−0.301063	−	0.301063i	0.540367	−	0.841430i	$-0.318286\pi$
$421$	−6.17729	−	6.17729i	−0.301063	−	0.301063i	−0.841430	+	0.540367i	$0.818286\pi$
$422$		0			0
$423$	−30.6537			−1.49044
$424$		0			0
$425$		0			0
$426$		0			0
$427$			17.5358i			0.848619i
$428$		0			0
$429$	−5.50322	+	6.71496i	−0.265698	+	0.324201i
$430$		0			0
$431$	4.25641	+	4.25641i	0.205024	+	0.205024i	0.802149	−	0.597124i	$-0.203690\pi$
$431$	4.25641	+	4.25641i	0.205024	+	0.205024i	−0.597124	+	0.802149i	$0.703690\pi$
$432$		0			0
$433$	27.2579	−	27.2579i	1.30993	−	1.30993i	0.388467	−	0.921463i	$-0.373005\pi$
$433$	27.2579	−	27.2579i	1.30993	−	1.30993i	0.921463	−	0.388467i	$-0.126995\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			26.6272i			1.27375i
$438$		0			0
$439$	−24.2063			−1.15531			−0.577653	−	0.816283i	$-0.696031\pi$
$439$	−24.2063			−1.15531			−0.577653	+	0.816283i	$0.696031\pi$
$440$		0			0
$441$		−	15.3112i		−	0.729106i
$442$		0			0
$443$	9.84991	+	9.84991i	0.467983	+	0.467983i	0.901261	−	0.433277i	$-0.142643\pi$
$443$	9.84991	+	9.84991i	0.467983	+	0.467983i	−0.433277	+	0.901261i	$0.642643\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.512822			0.0242556
$448$		0			0
$449$	12.7067	+	12.7067i	0.599666	+	0.599666i	0.940224	−	0.340558i	$-0.110616\pi$
$449$	12.7067	+	12.7067i	0.599666	+	0.599666i	−0.340558	+	0.940224i	$0.610616\pi$
$450$		0			0
$451$	−11.2514			−0.529809
$452$		0			0
$453$	−4.33066			−0.203472
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−10.4226			−0.487551			−0.243775	−	0.969832i	$-0.578386\pi$
$457$	−10.4226			−0.487551			−0.243775	+	0.969832i	$0.578386\pi$
$458$		0			0
$459$	6.43923			0.300557
$460$		0			0
$461$	−23.2616	−	23.2616i	−1.08340	−	1.08340i	−0.996190	−	0.0872084i	$-0.972205\pi$
$461$	−23.2616	−	23.2616i	−1.08340	−	1.08340i	−0.0872084	−	0.996190i	$-0.527795\pi$
$462$		0			0
$463$	−2.36644			−0.109978			−0.0549888	−	0.998487i	$-0.517512\pi$
$463$	−2.36644			−0.109978			−0.0549888	+	0.998487i	$0.517512\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−22.6648	−	22.6648i	−1.04880	−	1.04880i	−0.998746	−	0.0500547i	$-0.984060\pi$
$467$	−22.6648	−	22.6648i	−1.04880	−	1.04880i	−0.0500547	−	0.998746i	$-0.515940\pi$
$468$		0			0
$469$		−	1.65201i		−	0.0762828i
$470$		0			0
$471$	3.06085			0.141036
$472$		0			0
$473$			47.6888i			2.19274i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	26.3066	−	26.3066i	1.20450	−	1.20450i
$478$		0			0
$479$	−1.74861	−	1.74861i	−0.0798958	−	0.0798958i	0.666030	−	0.745925i	$-0.267992\pi$
$479$	−1.74861	−	1.74861i	−0.0798958	−	0.0798958i	−0.745925	+	0.666030i	$0.767992\pi$
$480$		0			0
$481$	16.2776	+	13.3403i	0.742195	+	0.608263i
$482$		0			0
$483$			3.77161i			0.171614i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	14.3822			0.651720			0.325860	−	0.945418i	$-0.394346\pi$
$487$	14.3822			0.651720			0.325860	+	0.945418i	$0.394346\pi$
$488$		0			0
$489$	−4.79223	−	4.79223i	−0.216712	−	0.216712i
$490$		0			0
$491$		−	13.4770i		−	0.608206i	−0.952639	−	0.304103i	$-0.901643\pi$
$491$		−	13.4770i		−	0.608206i	0.952639	−	0.304103i	$-0.0983568\pi$
$492$		0			0
$493$	13.8536	−	13.8536i	0.623935	−	0.623935i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−11.0501	+	11.0501i	−0.495665	+	0.495665i
$498$		0			0
$499$	−19.7644	+	19.7644i	−0.884775	+	0.884775i	−0.994015	−	0.109241i	$-0.965158\pi$
$499$	−19.7644	+	19.7644i	−0.884775	+	0.884775i	0.109241	+	0.994015i	$0.465158\pi$
$500$		0			0
$501$	−4.93232	+	4.93232i	−0.220360	+	0.220360i
$502$		0			0
$503$	6.04181	+	6.04181i	0.269391	+	0.269391i	0.828855	−	0.559464i	$-0.188993\pi$
$503$	6.04181	+	6.04181i	0.269391	+	0.269391i	−0.559464	+	0.828855i	$0.688993\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.90970	−	4.36746i	0.129224	−	0.193966i
$508$		0			0
$509$	−13.1677	+	13.1677i	−0.583648	+	0.583648i	−0.935904	−	0.352256i	$-0.885415\pi$
$509$	−13.1677	+	13.1677i	−0.583648	+	0.583648i	0.352256	+	0.935904i	$0.385415\pi$
$510$		0			0
$511$			9.67781i			0.428121i
$512$		0			0
$513$			8.50284i			0.375410i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−45.5724	−	45.5724i	−2.00427	−	2.00427i
$518$		0			0
$519$	2.58380			0.113416
$520$		0			0
$521$	11.8720			0.520121			0.260061	−	0.965592i	$-0.416257\pi$
$521$	11.8720			0.520121			0.260061	+	0.965592i	$0.416257\pi$
$522$		0			0
$523$	−28.9954	−	28.9954i	−1.26788	−	1.26788i	−0.947180	−	0.320702i	$-0.896081\pi$
$523$	−28.9954	−	28.9954i	−1.26788	−	1.26788i	−0.320702	−	0.947180i	$-0.603919\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			10.7772i			0.469464i
$528$		0			0
$529$		−	31.4503i		−	1.36740i
$530$		0			0
$531$	−7.23893	+	7.23893i	−0.314143	+	0.314143i
$532$		0			0
$533$	6.76792	−	0.671206i	0.293151	−	0.0290732i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−2.00368	−	2.00368i	−0.0864652	−	0.0864652i
$538$		0			0
$539$	22.7629	−	22.7629i	0.980469	−	0.980469i
$540$		0			0
$541$	−4.93375	+	4.93375i	−0.212119	+	0.212119i	−0.805167	−	0.593048i	$-0.797924\pi$
$541$	−4.93375	+	4.93375i	−0.212119	+	0.212119i	0.593048	+	0.805167i	$0.297924\pi$
$542$		0			0
$543$	−0.862394	+	0.862394i	−0.0370089	+	0.0370089i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	19.6257	−	19.6257i	0.839135	−	0.839135i	−0.149610	−	0.988745i	$-0.547802\pi$
$547$	19.6257	−	19.6257i	0.839135	−	0.839135i	0.988745	+	0.149610i	$0.0478019\pi$
$548$		0			0
$549$		−	39.2927i		−	1.67697i
$550$		0			0
$551$	18.2934	+	18.2934i	0.779323	+	0.779323i
$552$		0			0
$553$	−1.20905			−0.0514139
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	31.5792i		−	1.33805i	−0.743238	−	0.669027i	$-0.766711\pi$
$557$		−	31.5792i		−	1.33805i	0.743238	−	0.669027i	$-0.233289\pi$
$558$		0			0
$559$	−2.84489	−	28.6857i	−0.120326	−	1.21327i
$560$		0			0
$561$	4.65291	+	4.65291i	0.196446	+	0.196446i
$562$		0			0
$563$	21.3660	−	21.3660i	0.900471	−	0.900471i	−0.0950060	−	0.995477i	$-0.530287\pi$
$563$	21.3660	−	21.3660i	0.900471	−	0.900471i	0.995477	+	0.0950060i	$0.0302870\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	9.57180i		−	0.401978i
$568$		0			0
$569$	41.8436			1.75418			0.877088	−	0.480329i	$-0.159483\pi$
$569$	41.8436			1.75418			0.877088	+	0.480329i	$0.159483\pi$
$570$		0			0
$571$			22.5809i			0.944983i	0.881335	+	0.472491i	$0.156645\pi$
$571$			22.5809i			0.944983i	−0.881335	+	0.472491i	$0.843355\pi$
$572$		0			0
$573$	−0.261552	−	0.261552i	−0.0109265	−	0.0109265i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	23.6436			0.984296			0.492148	−	0.870512i	$-0.336212\pi$
$577$	23.6436			0.984296			0.492148	+	0.870512i	$0.336212\pi$
$578$		0			0
$579$	−4.29832	−	4.29832i	−0.178632	−	0.178632i
$580$		0			0
$581$	6.49624			0.269510
$582$		0			0
$583$	78.2193			3.23951
$584$		0			0
$585$		0			0
$586$		0			0
$587$	37.8370			1.56170			0.780851	−	0.624718i	$-0.214786\pi$
$587$	37.8370			1.56170			0.780851	+	0.624718i	$0.214786\pi$
$588$		0			0
$589$	−14.2311			−0.586381
$590$		0			0
$591$	1.58838	+	1.58838i	0.0653372	+	0.0653372i
$592$		0			0
$593$	−3.64547			−0.149701			−0.0748507	−	0.997195i	$-0.523848\pi$
$593$	−3.64547			−0.149701			−0.0748507	+	0.997195i	$0.523848\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.64188	+	4.64188i	0.189980	+	0.189980i
$598$		0			0
$599$			25.0451i			1.02331i	0.859190	+	0.511657i	$0.170968\pi$
$599$			25.0451i			1.02331i	−0.859190	+	0.511657i	$0.829032\pi$
$600$		0			0
$601$	4.47132			0.182389			0.0911945	−	0.995833i	$-0.470932\pi$
$601$	4.47132			0.182389			0.0911945	+	0.995833i	$0.470932\pi$
$602$		0			0
$603$			3.70168i			0.150744i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	3.24538	−	3.24538i	0.131726	−	0.131726i	−0.638170	−	0.769896i	$-0.720308\pi$
$607$	3.24538	−	3.24538i	0.131726	−	0.131726i	0.769896	+	0.638170i	$0.220308\pi$
$608$		0			0
$609$	2.59116	+	2.59116i	0.104999	+	0.104999i
$610$		0			0
$611$	30.1312	+	24.6940i	1.21898	+	0.999010i
$612$		0			0
$613$			47.3997i			1.91445i	0.289337	+	0.957227i	$0.406565\pi$
$613$			47.3997i			1.91445i	−0.289337	+	0.957227i	$0.593435\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.45402			−0.0585366			−0.0292683	−	0.999572i	$-0.509318\pi$
$617$	−1.45402			−0.0585366			−0.0292683	+	0.999572i	$0.509318\pi$
$618$		0			0
$619$	11.7229	+	11.7229i	0.471182	+	0.471182i	0.902297	−	0.431115i	$-0.141880\pi$
$619$	11.7229	+	11.7229i	0.471182	+	0.471182i	−0.431115	+	0.902297i	$0.641880\pi$
$620$		0			0
$621$		−	17.3876i		−	0.697740i
$622$		0			0
$623$	−6.72471	+	6.72471i	−0.269420	+	0.269420i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−6.14405	+	6.14405i	−0.245370	+	0.245370i
$628$		0			0
$629$	11.2790	−	11.2790i	0.449724	−	0.449724i
$630$		0			0
$631$	21.2758	−	21.2758i	0.846975	−	0.846975i	−0.142780	−	0.989754i	$-0.545604\pi$
$631$	21.2758	−	21.2758i	0.846975	−	0.846975i	0.989754	+	0.142780i	$0.0456041\pi$
$632$		0			0
$633$	−5.54869	−	5.54869i	−0.220541	−	0.220541i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−12.3344	+	15.0502i	−0.488706	+	0.596312i
$638$		0			0
$639$	24.7601	−	24.7601i	0.979493	−	0.979493i
$640$		0			0
$641$			18.2716i			0.721684i	0.932627	+	0.360842i	$0.117511\pi$
$641$			18.2716i			0.721684i	−0.932627	+	0.360842i	$0.882489\pi$
$642$		0			0
$643$			27.6308i			1.08965i	0.838550	+	0.544825i	$0.183404\pi$
$643$			27.6308i			1.08965i	−0.838550	+	0.544825i	$0.816596\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.6648	+	22.6648i	0.891045	+	0.891045i	0.994621	−	0.103577i	$-0.0330288\pi$
$647$	22.6648	+	22.6648i	0.891045	+	0.891045i	−0.103577	+	0.994621i	$0.533029\pi$
$648$		0			0
$649$	−21.5240			−0.844891
$650$		0			0
$651$	−2.01576			−0.0790039
$652$		0			0
$653$	−17.3338	−	17.3338i	−0.678324	−	0.678324i	0.281296	−	0.959621i	$-0.409236\pi$
$653$	−17.3338	−	17.3338i	−0.678324	−	0.678324i	−0.959621	+	0.281296i	$0.909236\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	21.6852i		−	0.846018i
$658$		0			0
$659$			22.5065i			0.876730i	0.898797	+	0.438365i	$0.144442\pi$
$659$			22.5065i			0.876730i	−0.898797	+	0.438365i	$0.855558\pi$
$660$		0			0
$661$	−8.66806	+	8.66806i	−0.337148	+	0.337148i	−0.855293	−	0.518145i	$-0.826623\pi$
$661$	−8.66806	+	8.66806i	−0.337148	+	0.337148i	0.518145	+	0.855293i	$0.326623\pi$
$662$		0			0
$663$	−3.07638	−	2.52124i	−0.119477	−	0.0979167i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−37.4084	−	37.4084i	−1.44846	−	1.44846i
$668$		0			0
$669$	1.02904	−	1.02904i	0.0397850	−	0.0397850i
$670$		0			0
$671$	58.4159	−	58.4159i	2.25512	−	2.25512i
$672$		0			0
$673$	−9.10360	+	9.10360i	−0.350918	+	0.350918i	−0.860451	−	0.509533i	$-0.829818\pi$
$673$	−9.10360	+	9.10360i	−0.350918	+	0.350918i	0.509533	+	0.860451i	$0.329818\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	9.29832	−	9.29832i	0.357364	−	0.357364i	−0.505477	−	0.862840i	$-0.668683\pi$
$677$	9.29832	−	9.29832i	0.357364	−	0.357364i	0.862840	+	0.505477i	$0.168683\pi$
$678$		0			0
$679$		−	3.56993i		−	0.137001i
$680$		0			0
$681$	−6.97569	−	6.97569i	−0.267309	−	0.267309i
$682$		0			0
$683$	−10.8177			−0.413927			−0.206964	−	0.978349i	$-0.566358\pi$
$683$	−10.8177			−0.413927			−0.206964	+	0.978349i	$0.566358\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			5.40254i			0.206120i
$688$		0			0
$689$	−47.0503	+	4.66619i	−1.79247	+	0.177768i
$690$		0			0
$691$	−0.121054	−	0.121054i	−0.00460512	−	0.00460512i	0.704800	−	0.709406i	$-0.251037\pi$
$691$	−0.121054	−	0.121054i	−0.00460512	−	0.00460512i	−0.709406	+	0.704800i	$0.751037\pi$
$692$		0			0
$693$	15.1505	−	15.1505i	0.575520	−	0.575520i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	5.15470i		−	0.195248i
$698$		0			0
$699$	1.02769			0.0388708
$700$		0			0
$701$			1.15470i			0.0436125i	0.999762	+	0.0218063i	$0.00694170\pi$
$701$			1.15470i			0.0436125i	−0.999762	+	0.0218063i	$0.993058\pi$
$702$		0			0
$703$	14.8937	+	14.8937i	0.561726	+	0.561726i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.61706			0.0608156
$708$		0			0
$709$	−37.1464	−	37.1464i	−1.39506	−	1.39506i	−0.813503	−	0.581561i	$-0.802442\pi$
$709$	−37.1464	−	37.1464i	−1.39506	−	1.39506i	−0.581561	−	0.813503i	$-0.697558\pi$
$710$		0			0
$711$	2.70912			0.101600
$712$		0			0
$713$	29.1014			1.08985
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−7.47876			−0.279300
$718$		0			0
$719$	−13.4383			−0.501165			−0.250582	−	0.968095i	$-0.580622\pi$
$719$	−13.4383			−0.501165			−0.250582	+	0.968095i	$0.580622\pi$
$720$		0			0
$721$	−0.396375	−	0.396375i	−0.0147618	−	0.0147618i
$722$		0			0
$723$	−7.55709			−0.281051
$724$		0			0
$725$		0			0
$726$		0			0
$727$	28.7860	+	28.7860i	1.06761	+	1.06761i	0.997542	+	0.0700702i	$0.0223223\pi$
$727$	28.7860	+	28.7860i	1.06761	+	1.06761i	0.0700702	+	0.997542i	$0.477678\pi$
$728$		0			0
$729$			18.5939i			0.688664i
$730$		0			0
$731$	−21.8481			−0.808080
$732$		0			0
$733$		−	28.5996i		−	1.05635i	−0.849136	−	0.528174i	$-0.822877\pi$
$733$		−	28.5996i		−	1.05635i	0.849136	−	0.528174i	$-0.177123\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.50322	+	5.50322i	−0.202714	+	0.202714i
$738$		0			0
$739$	11.0484	+	11.0484i	0.406420	+	0.406420i	0.880488	−	0.474068i	$-0.157215\pi$
$739$	11.0484	+	11.0484i	0.406420	+	0.406420i	−0.474068	+	0.880488i	$0.657215\pi$
$740$		0			0
$741$	3.32923	−	4.06228i	0.122302	−	0.149232i
$742$		0			0
$743$			11.7882i			0.432466i	0.976342	+	0.216233i	$0.0693771\pi$
$743$			11.7882i			0.432466i	−0.976342	+	0.216233i	$0.930623\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−14.5562			−0.532583
$748$		0			0
$749$	−9.10370	−	9.10370i	−0.332642	−	0.332642i
$750$		0			0
$751$		−	30.3583i		−	1.10779i	−0.832587	−	0.553895i	$-0.813141\pi$
$751$		−	30.3583i		−	1.10779i	0.832587	−	0.553895i	$-0.186859\pi$
$752$		0			0
$753$	1.32053	−	1.32053i	0.0481229	−	0.0481229i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−19.1677	+	19.1677i	−0.696662	+	0.696662i	−0.963689	−	0.267027i	$-0.913959\pi$
$757$	−19.1677	+	19.1677i	−0.696662	+	0.696662i	0.267027	+	0.963689i	$0.413959\pi$
$758$		0			0
$759$	12.5641	−	12.5641i	0.456047	−	0.456047i
$760$		0			0
$761$	12.2165	−	12.2165i	0.442847	−	0.442847i	−0.450121	−	0.892968i	$-0.648619\pi$
$761$	12.2165	−	12.2165i	0.442847	−	0.442847i	0.892968	+	0.450121i	$0.148619\pi$
$762$		0			0
$763$	3.89225	+	3.89225i	0.140909	+	0.140909i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.9471	−	1.28402i	0.467491	−	0.0463632i
$768$		0			0
$769$	−23.5875	+	23.5875i	−0.850586	+	0.850586i	−0.990205	−	0.139619i	$-0.955412\pi$
$769$	−23.5875	+	23.5875i	−0.850586	+	0.850586i	0.139619	+	0.990205i	$0.455412\pi$
$770$		0			0
$771$			2.59956i			0.0936209i
$772$		0			0
$773$			31.8600i			1.14592i	0.819582	+	0.572962i	$0.194206\pi$
$773$			31.8600i			1.14592i	−0.819582	+	0.572962i	$0.805794\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	2.10962	+	2.10962i	0.0756821	+	0.0756821i
$778$		0			0
$779$	6.80666			0.243874
$780$		0			0
$781$	73.6208			2.63436
$782$		0			0
$783$	−11.9456	−	11.9456i	−0.426901	−	0.426901i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			28.3333i			1.00997i	0.863127	+	0.504987i	$0.168503\pi$
$787$			28.3333i			1.00997i	−0.863127	+	0.504987i	$0.831497\pi$
$788$		0			0
$789$			1.55342i			0.0553034i
$790$		0			0
$791$	11.4751	−	11.4751i	0.408007	−	0.408007i
$792$		0			0
$793$	−31.6533	+	38.6230i	−1.12404	+	1.37154i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	21.2610	+	21.2610i	0.753104	+	0.753104i	0.975057	−	0.221953i	$-0.0712433\pi$
$797$	21.2610	+	21.2610i	0.753104	+	0.753104i	−0.221953	+	0.975057i	$0.571243\pi$
$798$		0			0
$799$	20.8784	−	20.8784i	0.738626	−	0.738626i
$800$		0			0
$801$	15.0681	−	15.0681i	0.532406	−	0.532406i
$802$		0			0
$803$	32.2390	−	32.2390i	1.13769	−	1.13769i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.33606	+	3.33606i	−0.117435	+	0.117435i
$808$		0			0
$809$		−	22.8766i		−	0.804300i	−0.915574	−	0.402150i	$-0.868263\pi$
$809$		−	22.8766i		−	0.804300i	0.915574	−	0.402150i	$-0.131737\pi$
$810$		0			0
$811$	−20.7214	−	20.7214i	−0.727628	−	0.727628i	0.242519	−	0.970147i	$-0.422026\pi$
$811$	−20.7214	−	20.7214i	−0.727628	−	0.727628i	−0.970147	+	0.242519i	$0.922026\pi$
$812$		0			0
$813$	−7.97321			−0.279633
$814$		0			0
$815$		0			0
$816$		0			0
$817$		−	28.8498i		−	1.00933i
$818$		0			0
$819$	−8.20948	+	10.0171i	−0.286863	+	0.350026i
$820$		0			0
$821$	28.2951	+	28.2951i	0.987505	+	0.987505i	0.999923	−	0.0124179i	$-0.00395285\pi$
$821$	28.2951	+	28.2951i	0.987505	+	0.987505i	−0.0124179	+	0.999923i	$0.503953\pi$
$822$		0			0
$823$	13.8518	−	13.8518i	0.482842	−	0.482842i	−0.423196	−	0.906038i	$-0.639092\pi$
$823$	13.8518	−	13.8518i	0.482842	−	0.482842i	0.906038	+	0.423196i	$0.139092\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			10.5533i			0.366975i	0.983022	+	0.183488i	$0.0587387\pi$
$827$			10.5533i			0.366975i	−0.983022	+	0.183488i	$0.941261\pi$
$828$		0			0
$829$	35.3056			1.22622			0.613108	−	0.789999i	$-0.289919\pi$
$829$	35.3056			1.22622			0.613108	+	0.789999i	$0.289919\pi$
$830$		0			0
$831$		−	0.626120i		−	0.0217198i
$832$		0			0
$833$	10.4286	+	10.4286i	0.361328	+	0.361328i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	9.29292			0.321210
$838$		0			0
$839$	−2.46456	−	2.46456i	−0.0850860	−	0.0850860i	0.663283	−	0.748369i	$-0.269163\pi$
$839$	−2.46456	−	2.46456i	−0.0850860	−	0.0850860i	−0.748369	+	0.663283i	$0.769163\pi$
$840$		0			0
$841$	−22.4005			−0.772431
$842$		0			0
$843$	−4.92549			−0.169643
$844$		0			0
$845$		0			0
$846$		0			0
$847$	31.1205			1.06931
$848$		0			0
$849$	−4.28466			−0.147049
$850$		0			0
$851$	−30.4563	−	30.4563i	−1.04403	−	1.04403i
$852$		0			0
$853$	−26.8214			−0.918348			−0.459174	−	0.888346i	$-0.651855\pi$
$853$	−26.8214			−0.918348			−0.459174	+	0.888346i	$0.651855\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−20.6207	−	20.6207i	−0.704390	−	0.704390i	0.260959	−	0.965350i	$-0.415961\pi$
$857$	−20.6207	−	20.6207i	−0.704390	−	0.704390i	−0.965350	+	0.260959i	$0.915961\pi$
$858$		0			0
$859$		−	15.3195i		−	0.522696i	−0.965245	−	0.261348i	$-0.915833\pi$
$859$		−	15.3195i		−	0.522696i	0.965245	−	0.261348i	$-0.0841670\pi$
$860$		0			0
$861$	0.964130			0.0328574
$862$		0			0
$863$			19.7984i			0.673945i	0.941514	+	0.336973i	$0.109403\pi$
$863$			19.7984i			0.673945i	−0.941514	+	0.336973i	$0.890597\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	2.72100	−	2.72100i	0.0924099	−	0.0924099i
$868$		0			0
$869$	4.02761	+	4.02761i	0.136627	+	0.136627i
$870$		0			0
$871$	2.98199	−	3.63858i	0.101041	−	0.123289i
$872$		0			0
$873$			7.99918i			0.270731i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	36.4393			1.23047			0.615234	−	0.788345i	$-0.289062\pi$
$877$	36.4393			1.23047			0.615234	+	0.788345i	$0.289062\pi$
$878$		0			0
$879$	−6.00420	−	6.00420i	−0.202517	−	0.202517i
$880$		0			0
$881$			39.4236i			1.32821i	0.747637	+	0.664107i	$0.231188\pi$
$881$			39.4236i			1.32821i	−0.747637	+	0.664107i	$0.768812\pi$
$882$		0			0
$883$	23.9341	−	23.9341i	0.805445	−	0.805445i	−0.178495	−	0.983941i	$-0.557123\pi$
$883$	23.9341	−	23.9341i	0.805445	−	0.805445i	0.983941	+	0.178495i	$0.0571229\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−28.8887	+	28.8887i	−0.969987	+	0.969987i	−0.999563	−	0.0295751i	$-0.990585\pi$
$887$	−28.8887	+	28.8887i	−0.969987	+	0.969987i	0.0295751	+	0.999563i	$0.490585\pi$
$888$		0			0
$889$	8.71601	−	8.71601i	0.292326	−	0.292326i
$890$		0			0
$891$	−31.8858	+	31.8858i	−1.06822	+	1.06822i
$892$		0			0
$893$	27.5695	+	27.5695i	0.922577	+	0.922577i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−6.80799	+	8.30702i	−0.227312	+	0.277363i
$898$		0			0
$899$	19.9932	−	19.9932i	0.666810	−	0.666810i
$900$		0			0
$901$			35.8352i			1.19384i
$902$		0			0
$903$		−	4.08644i		−	0.135988i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−22.9907	−	22.9907i	−0.763394	−	0.763394i	0.213540	−	0.976934i	$-0.431501\pi$
$907$	−22.9907	−	22.9907i	−0.763394	−	0.763394i	−0.976934	+	0.213540i	$0.931501\pi$
$908$		0			0
$909$	−3.62335			−0.120179
$910$		0			0
$911$	37.1427			1.23059			0.615296	−	0.788296i	$-0.289037\pi$
$911$	37.1427			1.23059			0.615296	+	0.788296i	$0.289037\pi$
$912$		0			0
$913$	−21.6404	−	21.6404i	−0.716194	−	0.716194i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			0.244917i			0.00808789i
$918$		0			0
$919$		−	46.7810i		−	1.54316i	−0.636131	−	0.771581i	$-0.719466\pi$
$919$		−	46.7810i		−	1.54316i	0.636131	−	0.771581i	$-0.280534\pi$
$920$		0			0
$921$	−3.93877	+	3.93877i	−0.129787	+	0.129787i
$922$		0			0
$923$	−44.2842	+	4.39186i	−1.45763	+	0.144560i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.888162	+	0.888162i	0.0291711	+	0.0291711i
$928$		0			0
$929$	−29.4287	+	29.4287i	−0.965525	+	0.965525i	−0.999425	−	0.0339004i	$-0.989207\pi$
$929$	−29.4287	+	29.4287i	−0.965525	+	0.965525i	0.0339004	+	0.999425i	$0.489207\pi$
$930$		0			0
$931$	−13.7707	+	13.7707i	−0.451315	+	0.451315i
$932$		0			0
$933$	5.70168	−	5.70168i	0.186665	−	0.186665i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	29.2450	−	29.2450i	0.955392	−	0.955392i	−0.0436550	−	0.999047i	$-0.513900\pi$
$937$	29.2450	−	29.2450i	0.955392	−	0.955392i	0.999047	+	0.0436550i	$0.0139003\pi$
$938$		0			0
$939$			2.81219i			0.0917725i
$940$		0			0
$941$	15.1015	+	15.1015i	0.492293	+	0.492293i	0.909028	−	0.416735i	$-0.136826\pi$
$941$	15.1015	+	15.1015i	0.492293	+	0.492293i	−0.416735	+	0.909028i	$0.636826\pi$
$942$		0			0
$943$	−13.9190			−0.453266
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	38.1180i		−	1.23867i	−0.785127	−	0.619335i	$-0.787402\pi$
$947$		−	38.1180i		−	1.23867i	0.785127	−	0.619335i	$-0.212598\pi$
$948$		0			0
$949$	−17.4691	+	21.3155i	−0.567070	+	0.691931i
$950$		0			0
$951$	−3.34394	−	3.34394i	−0.108435	−	0.108435i
$952$		0			0
$953$	35.8177	−	35.8177i	1.16025	−	1.16025i	0.175830	−	0.984421i	$-0.443739\pi$
$953$	35.8177	−	35.8177i	1.16025	−	1.16025i	0.984421	−	0.175830i	$-0.0562609\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	17.2635i		−	0.558050i
$958$		0			0
$959$	−5.11345			−0.165122
$960$		0			0
$961$		−	15.4466i		−	0.498277i
$962$		0			0
$963$	20.3987	+	20.3987i	0.657341	+	0.657341i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	15.1852			0.488322			0.244161	−	0.969735i	$-0.421487\pi$
$967$	15.1852			0.488322			0.244161	+	0.969735i	$0.421487\pi$
$968$		0			0
$969$	−2.81482	−	2.81482i	−0.0904252	−	0.0904252i
$970$		0			0
$971$	−52.5959			−1.68788			−0.843941	−	0.536436i	$-0.819770\pi$
$971$	−52.5959			−1.68788			−0.843941	+	0.536436i	$0.819770\pi$
$972$		0			0
$973$	−3.25510			−0.104354
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−40.6014			−1.29895			−0.649477	−	0.760381i	$-0.725012\pi$
$977$	−40.6014			−1.29895			−0.649477	+	0.760381i	$0.725012\pi$
$978$		0			0
$979$	44.8030			1.43191
$980$		0			0
$981$	−8.72141	−	8.72141i	−0.278453	−	0.278453i
$982$		0			0
$983$	−12.2368			−0.390294			−0.195147	−	0.980774i	$-0.562518\pi$
$983$	−12.2368			−0.390294			−0.195147	+	0.980774i	$0.562518\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	3.90508	+	3.90508i	0.124300	+	0.124300i
$988$		0			0
$989$			58.9955i			1.87595i
$990$		0			0
$991$	−20.9218			−0.664603			−0.332302	−	0.943173i	$-0.607825\pi$
$991$	−20.9218			−0.664603			−0.332302	+	0.943173i	$0.607825\pi$
$992$		0			0
$993$		−	2.82061i		−	0.0895093i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−9.72732	+	9.72732i	−0.308067	+	0.308067i	−0.844159	−	0.536092i	$-0.819900\pi$
$997$	−9.72732	+	9.72732i	−0.308067	+	0.308067i	0.536092	+	0.844159i	$0.319900\pi$
$998$		0			0
$999$	−9.72561	−	9.72561i	−0.307705	−	0.307705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.m.c.593.3		8
5.2	odd	4		1300.2.r.c.957.3		8
5.3	odd	4		260.2.r.c.177.2	yes	8
5.4	even	2		260.2.m.c.73.2	yes	8
13.5	odd	4		1300.2.r.c.993.3		8
15.8	even	4		2340.2.bp.g.1477.2		8
15.14	odd	2		2340.2.u.g.73.4		8
20.3	even	4		1040.2.cd.m.177.3		8
20.19	odd	2		1040.2.bg.m.593.3		8
65.18	even	4		260.2.m.c.57.2	✓	8
65.44	odd	4		260.2.r.c.213.2	yes	8
65.57	even	4	inner	1300.2.m.c.57.3		8
195.44	even	4		2340.2.bp.g.1513.2		8
195.83	odd	4		2340.2.u.g.577.4		8
260.83	odd	4		1040.2.bg.m.577.3		8
260.239	even	4		1040.2.cd.m.993.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.m.c.57.2	✓	8	65.18	even	4
260.2.m.c.73.2	yes	8	5.4	even	2
260.2.r.c.177.2	yes	8	5.3	odd	4
260.2.r.c.213.2	yes	8	65.44	odd	4
1040.2.bg.m.577.3		8	260.83	odd	4
1040.2.bg.m.593.3		8	20.19	odd	2
1040.2.cd.m.177.3		8	20.3	even	4
1040.2.cd.m.993.3		8	260.239	even	4
1300.2.m.c.57.3		8	65.57	even	4	inner
1300.2.m.c.593.3		8	1.1	even	1	trivial
1300.2.r.c.957.3		8	5.2	odd	4
1300.2.r.c.993.3		8	13.5	odd	4
2340.2.u.g.73.4		8	15.14	odd	2
2340.2.u.g.577.4		8	195.83	odd	4
2340.2.bp.g.1477.2		8	15.8	even	4
2340.2.bp.g.1513.2		8	195.44	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.285451 + 0.285451i) q^{3} +1.26613i q^{7} -2.83704i q^{9} +(4.21777 - 4.21777i) q^{11} +(-2.28545 + 2.78868i) q^{13} +(1.93232 + 1.93232i) q^{17} +(-2.55158 + 2.55158i) q^{19} +(-0.361419 + 0.361419i) q^{21} +(5.21777 - 5.21777i) q^{23} +(1.66619 - 1.66619i) q^{27} -7.16941i q^{29} +(2.78868 + 2.78868i) q^{31} +2.40794 q^{33} -5.83704i q^{37} +(-1.44842 + 0.143646i) q^{39} +(-1.33381 - 1.33381i) q^{41} +(-5.65332 + 5.65332i) q^{43} -10.8048i q^{47} +5.39691 q^{49} +1.10317i q^{51} +(9.27258 + 9.27258i) q^{53} -1.45671 q^{57} +(-2.55158 - 2.55158i) q^{59} +13.8499 q^{61} +3.59206 q^{63} -1.30477 q^{67} +2.97884 q^{69} +(8.72745 + 8.72745i) q^{71} +7.64360 q^{73} +(5.34026 + 5.34026i) q^{77} +0.954914i q^{79} -7.55987 q^{81} -5.13078i q^{83} +(2.04652 - 2.04652i) q^{87} +(5.31122 + 5.31122i) q^{89} +(-3.53083 - 2.89368i) q^{91} +1.59206i q^{93} -2.81956 q^{97} +(-11.9660 - 11.9660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 14 q^{11} - 14 q^{13} + 2 q^{19} + 4 q^{21} + 22 q^{23} + 16 q^{27} - 6 q^{31} - 16 q^{33} - 34 q^{39} - 8 q^{41} + 14 q^{43} - 24 q^{49} + 8 q^{53} - 16 q^{57} + 2 q^{59} - 12 q^{61} + 64 q^{63}+ \cdots + 10 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 14 * q^11 - 14 * q^13 + 2 * q^19 + 4 * q^21 + 22 * q^23 + 16 * q^27 - 6 * q^31 - 16 * q^33 - 34 * q^39 - 8 * q^41 + 14 * q^43 - 24 * q^49 + 8 * q^53 - 16 * q^57 + 2 * q^59 - 12 * q^61 + 64 * q^63 - 20 * q^67 - 20 * q^69 - 22 * q^71 + 28 * q^73 - 8 * q^77 - 20 * q^81 - 12 * q^87 + 4 * q^89 - 12 * q^97 + 10 * q^99

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