LMFDB - Embedded newform 2268.2.l.j.541.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(109,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("2268.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.l (of order $3$, 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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 756)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.3
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	2268.541
Dual form			2268.2.l.j.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.42107 q^{5} +(0.710533 + 2.54856i) q^{7} +O(q^{10})$	$q+2.42107 q^{5} +(0.710533 + 2.54856i) q^{7} -4.70370 q^{11} +(1.71053 + 2.96273i) q^{13} +(0.851848 + 1.47544i) q^{17} +(-0.641315 + 1.11079i) q^{19} +1.12476 q^{23} +0.861564 q^{25} +(-2.35185 + 4.07352i) q^{29} +(1.71053 - 2.96273i) q^{31} +(1.72025 + 6.17023i) q^{35} +(-4.27292 + 7.40091i) q^{37} +(1.85868 + 3.21934i) q^{41} +(-2.77292 + 4.80283i) q^{43} +(-5.91423 - 10.2437i) q^{47} +(-5.99028 + 3.62167i) q^{49} +(5.13160 + 8.88819i) q^{53} -11.3880 q^{55} +(2.06238 - 3.57215i) q^{59} +(4.62476 + 8.01033i) q^{61} +(4.14132 + 7.17297i) q^{65} +(5.56238 - 9.63433i) q^{67} -14.9669 q^{71} +(-1.06922 - 1.85194i) q^{73} +(-3.34213 - 11.9876i) q^{77} +(7.26608 + 12.5852i) q^{79} +(4.21053 - 7.29286i) q^{83} +(2.06238 + 3.57215i) q^{85} +(8.04583 - 13.9358i) q^{89} +(-6.33530 + 6.46451i) q^{91} +(-1.55267 + 2.68930i) q^{95} +(-8.12476 + 14.0725i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{5} - 4 q^{7}+O(q^{10}) $ 6 * q - 2 * q^5 - 4 * q^7	$ 6 q - 2 q^{5} - 4 q^{7} - 10 q^{11} + 2 q^{13} - 4 q^{17} - 3 q^{19} - 28 q^{23} + 20 q^{25} - 5 q^{29} + 2 q^{31} + 26 q^{35} + 12 q^{41} + 9 q^{43} - 9 q^{47} - 12 q^{49} + 6 q^{53} + 16 q^{55} - 5 q^{59} - 7 q^{61} + 24 q^{65} + 16 q^{67} - 22 q^{71} + q^{73} + 13 q^{77} + 8 q^{79} + 17 q^{83} - 5 q^{85} - 3 q^{89} + 5 q^{91} + 32 q^{95} - 14 q^{97}+O(q^{100}) $ 6 * q - 2 * q^5 - 4 * q^7 - 10 * q^11 + 2 * q^13 - 4 * q^17 - 3 * q^19 - 28 * q^23 + 20 * q^25 - 5 * q^29 + 2 * q^31 + 26 * q^35 + 12 * q^41 + 9 * q^43 - 9 * q^47 - 12 * q^49 + 6 * q^53 + 16 * q^55 - 5 * q^59 - 7 * q^61 + 24 * q^65 + 16 * q^67 - 22 * q^71 + q^73 + 13 * q^77 + 8 * q^79 + 17 * q^83 - 5 * q^85 - 3 * q^89 + 5 * q^91 + 32 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$3$		0			0
$4$		0			0
$5$	2.42107			1.08273			0.541367	−	0.840786i	$-0.317907\pi$
$5$	2.42107			1.08273			0.541367	+	0.840786i	$0.317907\pi$
$6$		0			0
$7$	0.710533	+	2.54856i	0.268556	+	0.963264i
$7$	0.710533	+	2.54856i	0.268556	+	0.963264i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.70370			−1.41822			−0.709109	−	0.705099i	$-0.750903\pi$
$11$	−4.70370			−1.41822			−0.709109	+	0.705099i	$0.750903\pi$
$12$		0			0
$13$	1.71053	+	2.96273i	0.474417	+	0.821714i	0.999571	−	0.0292934i	$-0.00932572\pi$
$13$	1.71053	+	2.96273i	0.474417	+	0.821714i	−0.525154	+	0.851007i	$0.675992\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.851848	+	1.47544i	0.206604	+	0.357848i	0.950642	−	0.310288i	$-0.100426\pi$
$17$	0.851848	+	1.47544i	0.206604	+	0.357848i	−0.744039	+	0.668136i	$0.767092\pi$
$18$		0			0
$19$	−0.641315	+	1.11079i	−0.147128	+	0.254833i	−0.930165	−	0.367142i	$-0.880336\pi$
$19$	−0.641315	+	1.11079i	−0.147128	+	0.254833i	0.783037	+	0.621975i	$0.213670\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.12476			0.234529			0.117265	−	0.993101i	$-0.462587\pi$
$23$	1.12476			0.234529			0.117265	+	0.993101i	$0.462587\pi$
$24$		0			0
$25$	0.861564			0.172313
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.35185	+	4.07352i	−0.436727	+	0.756434i	−0.997435	−	0.0715801i	$-0.977196\pi$
$29$	−2.35185	+	4.07352i	−0.436727	+	0.756434i	0.560708	+	0.828014i	$0.310529\pi$
$30$		0			0
$31$	1.71053	−	2.96273i	0.307221	−	0.532122i	−0.670532	−	0.741880i	$-0.733934\pi$
$31$	1.71053	−	2.96273i	0.307221	−	0.532122i	0.977753	+	0.209758i	$0.0672676\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.72025	+	6.17023i	0.290775	+	1.04296i
$36$		0			0
$37$	−4.27292	+	7.40091i	−0.702463	+	1.21670i	0.265136	+	0.964211i	$0.414583\pi$
$37$	−4.27292	+	7.40091i	−0.702463	+	1.21670i	−0.967599	+	0.252491i	$0.918750\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.85868	+	3.21934i	0.290278	+	0.502776i	0.973875	−	0.227083i	$-0.0729189\pi$
$41$	1.85868	+	3.21934i	0.290278	+	0.502776i	−0.683598	+	0.729859i	$0.739586\pi$
$42$		0			0
$43$	−2.77292	+	4.80283i	−0.422866	+	0.732425i	−0.996218	−	0.0868839i	$-0.972309\pi$
$43$	−2.77292	+	4.80283i	−0.422866	+	0.732425i	0.573353	+	0.819309i	$0.305642\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.91423	−	10.2437i	−0.862679	−	1.49420i	−0.869333	−	0.494226i	$-0.835451\pi$
$47$	−5.91423	−	10.2437i	−0.862679	−	1.49420i	0.00665422	−	0.999978i	$-0.497882\pi$
$48$		0			0
$49$	−5.99028	+	3.62167i	−0.855755	+	0.517381i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.13160	+	8.88819i	0.704879	+	1.22089i	0.966735	+	0.255780i	$0.0823323\pi$
$53$	5.13160	+	8.88819i	0.704879	+	1.22089i	−0.261856	+	0.965107i	$0.584334\pi$
$54$		0			0
$55$	−11.3880			−1.53555
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.06238	−	3.57215i	0.268499	−	0.465054i	−0.699975	−	0.714167i	$-0.746806\pi$
$59$	2.06238	−	3.57215i	0.268499	−	0.465054i	0.968474	+	0.249113i	$0.0801390\pi$
$60$		0			0
$61$	4.62476	+	8.01033i	0.592140	+	1.02562i	0.993944	+	0.109891i	$0.0350502\pi$
$61$	4.62476	+	8.01033i	0.592140	+	1.02562i	−0.401803	+	0.915726i	$0.631616\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.14132	+	7.17297i	0.513667	+	0.889697i
$66$		0			0
$67$	5.56238	−	9.63433i	0.679553	−	1.17702i	−0.295563	−	0.955323i	$-0.595507\pi$
$67$	5.56238	−	9.63433i	0.679553	−	1.17702i	0.975116	−	0.221697i	$-0.0711596\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−14.9669			−1.77624			−0.888122	−	0.459608i	$-0.847990\pi$
$71$	−14.9669			−1.77624			−0.888122	+	0.459608i	$0.847990\pi$
$72$		0			0
$73$	−1.06922	−	1.85194i	−0.125143	−	0.216753i	0.796646	−	0.604446i	$-0.206605\pi$
$73$	−1.06922	−	1.85194i	−0.125143	−	0.216753i	−0.921789	+	0.387693i	$0.873272\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.34213	−	11.9876i	−0.380871	−	1.36612i
$78$		0			0
$79$	7.26608	+	12.5852i	0.817498	+	1.41595i	0.907520	+	0.420008i	$0.137973\pi$
$79$	7.26608	+	12.5852i	0.817498	+	1.41595i	−0.0900228	+	0.995940i	$0.528694\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.21053	−	7.29286i	0.462166	−	0.800495i	−0.536903	−	0.843644i	$-0.680406\pi$
$83$	4.21053	−	7.29286i	0.462166	−	0.800495i	0.999069	+	0.0431491i	$0.0137391\pi$
$84$		0			0
$85$	2.06238	+	3.57215i	0.223697	+	0.387454i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8.04583	−	13.9358i	0.852856	−	1.47719i	−0.0257633	−	0.999668i	$-0.508202\pi$
$89$	8.04583	−	13.9358i	0.852856	−	1.47719i	0.878620	−	0.477522i	$-0.158465\pi$
$90$		0			0
$91$	−6.33530	+	6.46451i	−0.664120	+	0.677665i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.55267	+	2.68930i	−0.159300	+	0.275916i
$96$		0			0
$97$	−8.12476	+	14.0725i	−0.824945	+	1.42885i	0.0770168	+	0.997030i	$0.475460\pi$
$97$	−8.12476	+	14.0725i	−0.824945	+	1.42885i	−0.901962	+	0.431816i	$0.857873\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	12.9863			1.29219			0.646094	−	0.763258i	$-0.276401\pi$
$101$	12.9863			1.29219			0.646094	+	0.763258i	$0.276401\pi$
$102$		0			0
$103$	−7.00000			−0.689730			−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000			−0.689730			−0.344865	+	0.938652i	$0.612075\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.35868	−	11.0136i	0.614717	−	1.06472i	−0.375717	−	0.926735i	$-0.622603\pi$
$107$	6.35868	−	11.0136i	0.614717	−	1.06472i	0.990434	−	0.137987i	$-0.0440632\pi$
$108$		0			0
$109$	3.70370	+	6.41499i	0.354750	+	0.614445i	0.987075	−	0.160258i	$-0.0512327\pi$
$109$	3.70370	+	6.41499i	0.354750	+	0.614445i	−0.632325	+	0.774703i	$0.717899\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.34213	−	5.78874i	−0.314401	−	0.544559i	0.664909	−	0.746925i	$-0.268470\pi$
$113$	−3.34213	−	5.78874i	−0.314401	−	0.544559i	−0.979310	+	0.202365i	$0.935137\pi$
$114$		0			0
$115$	2.72313			0.253933
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.15499	+	3.21934i	−0.289217	+	0.295116i
$120$		0			0
$121$	11.1248			1.01134
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.0194			−0.896165
$126$		0			0
$127$	−11.5322			−1.02331			−0.511657	−	0.859190i	$-0.670968\pi$
$127$	−11.5322			−1.02331			−0.511657	+	0.859190i	$0.670968\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.13844			0.798429			0.399214	−	0.916858i	$-0.369283\pi$
$131$	9.13844			0.798429			0.399214	+	0.916858i	$0.369283\pi$
$132$		0			0
$133$	−3.28659	−	0.845174i	−0.284983	−	0.0732859i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.24953			0.192190			0.0960950	−	0.995372i	$-0.469365\pi$
$137$	2.24953			0.192190			0.0960950	+	0.995372i	$0.469365\pi$
$138$		0			0
$139$	5.28947	+	9.16163i	0.448647	+	0.777079i	0.998298	−	0.0583152i	$-0.0185728\pi$
$139$	5.28947	+	9.16163i	0.448647	+	0.777079i	−0.549652	+	0.835394i	$0.685239\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.04583	−	13.9358i	−0.672826	−	1.16537i
$144$		0			0
$145$	−5.69398	+	9.86227i	−0.472859	+	0.819017i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−24.3743			−1.99682			−0.998410	−	0.0563721i	$-0.982047\pi$
$149$	−24.3743			−1.99682			−0.998410	+	0.0563721i	$0.982047\pi$
$150$		0			0
$151$	11.1384			0.906433			0.453217	−	0.891400i	$-0.350276\pi$
$151$	11.1384			0.906433			0.453217	+	0.891400i	$0.350276\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.14132	−	7.17297i	0.332638	−	0.576147i
$156$		0			0
$157$	−1.63160	+	2.82601i	−0.130216	+	0.225540i	−0.923760	−	0.382973i	$-0.874900\pi$
$157$	−1.63160	+	2.82601i	−0.130216	+	0.225540i	0.793544	+	0.608513i	$0.208234\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.799182	+	2.86652i	0.0629844	+	0.225914i
$162$		0			0
$163$	0.0760548	−	0.131731i	0.00595707	−	0.0103179i	−0.863032	−	0.505150i	$-0.831437\pi$
$163$	0.0760548	−	0.131731i	0.00595707	−	0.0103179i	0.868989	+	0.494832i	$0.164770\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.1179	+	20.9889i	0.937713	+	1.62417i	0.769723	+	0.638379i	$0.220395\pi$
$167$	12.1179	+	20.9889i	0.937713	+	1.62417i	0.167991	+	0.985789i	$0.446272\pi$
$168$		0			0
$169$	0.648152	−	1.12263i	0.0498578	−	0.0863563i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.47661	+	6.02167i	0.264322	+	0.457819i	0.967386	−	0.253308i	$-0.0815185\pi$
$173$	3.47661	+	6.02167i	0.264322	+	0.457819i	−0.703064	+	0.711127i	$0.748185\pi$
$174$		0			0
$175$	0.612170	+	2.19574i	0.0462757	+	0.165983i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.34897	+	12.7288i	0.549288	+	0.951394i	0.998324	+	0.0578806i	$0.0184343\pi$
$179$	7.34897	+	12.7288i	0.549288	+	0.951394i	−0.449036	+	0.893514i	$0.648232\pi$
$180$		0			0
$181$	17.1053			1.27143			0.635715	−	0.771924i	$-0.280705\pi$
$181$	17.1053			1.27143			0.635715	+	0.771924i	$0.280705\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10.3450	+	17.9181i	−0.760580	+	1.31736i
$186$		0			0
$187$	−4.00684	−	6.94004i	−0.293009	−	0.507506i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.4903	+	19.9018i	0.831408	+	1.44004i	0.896922	+	0.442189i	$0.145798\pi$
$191$	11.4903	+	19.9018i	0.831408	+	1.44004i	−0.0655141	+	0.997852i	$0.520869\pi$
$192$		0			0
$193$	−2.68715	+	4.65427i	−0.193425	+	0.335022i	−0.946383	−	0.323047i	$-0.895293\pi$
$193$	−2.68715	+	4.65427i	−0.193425	+	0.335022i	0.752958	+	0.658068i	$0.228626\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.57893			0.254988			0.127494	−	0.991839i	$-0.459307\pi$
$197$	3.57893			0.254988			0.127494	+	0.991839i	$0.459307\pi$
$198$		0			0
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−12.0527	−	3.09945i	−0.845931	−	0.217539i
$204$		0			0
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.01655	−	5.22482i	0.208659	−	0.361408i
$210$		0			0
$211$	−9.55555	−	16.5507i	−0.657831	−	1.13940i	−0.981176	−	0.193115i	$-0.938141\pi$
$211$	−9.55555	−	16.5507i	−0.657831	−	1.13940i	0.323345	−	0.946281i	$-0.395193\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.71341	+	11.6280i	−0.457851	+	0.793021i
$216$		0			0
$217$	8.76608	+	2.25427i	0.595080	+	0.153030i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.91423	+	5.04759i	−0.196032	+	0.339538i
$222$		0			0
$223$	−12.1316	+	21.0125i	−0.812392	+	1.40710i	0.0987935	+	0.995108i	$0.468502\pi$
$223$	−12.1316	+	21.0125i	−0.812392	+	1.40710i	−0.911186	+	0.411996i	$0.864832\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.84789			−0.255393			−0.127697	−	0.991813i	$-0.540758\pi$
$227$	−3.84789			−0.255393			−0.127697	+	0.991813i	$0.540758\pi$
$228$		0			0
$229$	3.53216			0.233412			0.116706	−	0.993167i	$-0.462767\pi$
$229$	3.53216			0.233412			0.116706	+	0.993167i	$0.462767\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.6248	−	20.1347i	0.761564	−	1.31907i	−0.180481	−	0.983579i	$-0.557765\pi$
$233$	11.6248	−	20.1347i	0.761564	−	1.31907i	0.942044	−	0.335488i	$-0.108901\pi$
$234$		0			0
$235$	−14.3187	−	24.8008i	−0.934052	−	1.61783i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.14132	+	7.17297i	0.267879	+	0.463981i	0.968314	−	0.249736i	$-0.0803438\pi$
$239$	4.14132	+	7.17297i	0.267879	+	0.463981i	−0.700435	+	0.713717i	$0.747010\pi$
$240$		0			0
$241$	13.5264			0.871312			0.435656	−	0.900113i	$-0.356516\pi$
$241$	13.5264			0.871312			0.435656	+	0.900113i	$0.356516\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−14.5029	+	8.76830i	−0.926555	+	0.560186i
$246$		0			0
$247$	−4.38796			−0.279199
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5.11109			0.322609			0.161305	−	0.986905i	$-0.448430\pi$
$251$	5.11109			0.322609			0.161305	+	0.986905i	$0.448430\pi$
$252$		0			0
$253$	−5.29055			−0.332614
$254$		0			0
$255$		0			0
$256$		0			0
$257$	16.0917			1.00377			0.501885	−	0.864934i	$-0.332640\pi$
$257$	16.0917			1.00377			0.501885	+	0.864934i	$0.332640\pi$
$258$		0			0
$259$	−21.8977	−	5.63118i	−1.36066	−	0.349904i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.7174			−0.784187			−0.392093	−	0.919925i	$-0.628249\pi$
$263$	−12.7174			−0.784187			−0.392093	+	0.919925i	$0.628249\pi$
$264$		0			0
$265$	12.4239	+	21.5189i	0.763197	+	1.32190i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−11.3518	−	19.6620i	−0.692134	−	1.19881i	−0.971137	−	0.238522i	$-0.923337\pi$
$269$	−11.3518	−	19.6620i	−0.692134	−	1.19881i	0.279003	−	0.960290i	$-0.409996\pi$
$270$		0			0
$271$	−7.56238	+	13.0984i	−0.459382	+	0.795673i	−0.998928	−	0.0462830i	$-0.985262\pi$
$271$	−7.56238	+	13.0984i	−0.459382	+	0.795673i	0.539546	+	0.841956i	$0.318596\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.05253			−0.244377
$276$		0			0
$277$	23.5458			1.41473			0.707366	−	0.706848i	$-0.249883\pi$
$277$	23.5458			1.41473			0.707366	+	0.706848i	$0.249883\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−2.77975	+	4.81467i	−0.165826	+	0.287219i	−0.936948	−	0.349468i	$-0.886362\pi$
$281$	−2.77975	+	4.81467i	−0.165826	+	0.287219i	0.771122	+	0.636687i	$0.219696\pi$
$282$		0			0
$283$	6.97661	−	12.0838i	0.414717	−	0.718310i	−0.580682	−	0.814130i	$-0.697214\pi$
$283$	6.97661	−	12.0838i	0.414717	−	0.718310i	0.995399	+	0.0958203i	$0.0305474\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.88401	+	7.02441i	−0.406350	+	0.414638i
$288$		0			0
$289$	7.04871	−	12.2087i	0.414630	−	0.718160i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.07605	+	7.05993i	0.238126	+	0.412446i	0.960176	−	0.279394i	$-0.0901337\pi$
$293$	4.07605	+	7.05993i	0.238126	+	0.412446i	−0.722051	+	0.691840i	$0.756800\pi$
$294$		0			0
$295$	4.99316	−	8.64841i	0.290713	−	0.503530i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.92395	+	3.33237i	0.111265	+	0.192716i
$300$		0			0
$301$	−14.2105	−	3.65436i	−0.819082	−	0.210634i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	11.1969	+	19.3935i	0.641130	+	1.11047i
$306$		0			0
$307$	2.13844			0.122047			0.0610235	−	0.998136i	$-0.480564\pi$
$307$	2.13844			0.122047			0.0610235	+	0.998136i	$0.480564\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.42107	−	9.38956i	0.307400	−	0.532433i	−0.670392	−	0.742007i	$-0.733874\pi$
$311$	5.42107	−	9.38956i	0.307400	−	0.532433i	0.977793	+	0.209573i	$0.0672075\pi$
$312$		0			0
$313$	−16.1706	−	28.0083i	−0.914016	−	1.58312i	−0.808336	−	0.588722i	$-0.799631\pi$
$313$	−16.1706	−	28.0083i	−0.914016	−	1.58312i	−0.105680	−	0.994400i	$-0.533702\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.9601	−	18.9834i	−0.615578	−	1.06621i	−0.990283	−	0.139069i	$-0.955589\pi$
$317$	−10.9601	−	18.9834i	−0.615578	−	1.06621i	0.374704	−	0.927144i	$-0.377744\pi$
$318$		0			0
$319$	11.0624	−	19.1606i	0.619374	−	1.07279i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2.18521			−0.121588
$324$		0			0
$325$	1.47373	+	2.55258i	0.0817480	+	0.141592i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	21.9045	−	22.3513i	1.20763	−	1.23227i
$330$		0			0
$331$	−6.19686	−	10.7333i	−0.340610	−	0.589954i	0.643936	−	0.765079i	$-0.277300\pi$
$331$	−6.19686	−	10.7333i	−0.340610	−	0.589954i	−0.984546	+	0.175125i	$0.943967\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	13.4669	−	23.3253i	0.735775	−	1.27440i
$336$		0			0
$337$	−3.86552	−	6.69528i	−0.210568	−	0.364715i	0.741324	−	0.671147i	$-0.234198\pi$
$337$	−3.86552	−	6.69528i	−0.210568	−	0.364715i	−0.951893	+	0.306432i	$0.900865\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.04583	+	13.9358i	−0.435706	+	0.754665i
$342$		0			0
$343$	−13.4863	−	12.6933i	−0.728193	−	0.685372i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	14.1111	−	24.4411i	0.757523	−	1.31207i	−0.186587	−	0.982438i	$-0.559743\pi$
$347$	14.1111	−	24.4411i	0.757523	−	1.31207i	0.944110	−	0.329630i	$-0.106924\pi$
$348$		0			0
$349$	0.617927	−	1.07028i	0.0330769	−	0.0572908i	−0.849013	−	0.528372i	$-0.822803\pi$
$349$	0.617927	−	1.07028i	0.0330769	−	0.0572908i	0.882090	+	0.471081i	$0.156136\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−18.9201			−1.00702			−0.503508	−	0.863990i	$-0.667958\pi$
$353$	−18.9201			−1.00702			−0.503508	+	0.863990i	$0.667958\pi$
$354$		0			0
$355$	−36.2359			−1.92320
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.93078	−	10.2724i	0.313015	−	0.542157i	−0.665999	−	0.745953i	$-0.731994\pi$
$359$	5.93078	−	10.2724i	0.313015	−	0.542157i	0.979013	+	0.203795i	$0.0653278\pi$
$360$		0			0
$361$	8.67743	+	15.0297i	0.456707	+	0.791039i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.58865	−	4.48367i	−0.135496	−	0.234686i
$366$		0			0
$367$	−14.2222			−0.742392			−0.371196	−	0.928555i	$-0.621052\pi$
$367$	−14.2222			−0.742392			−0.371196	+	0.928555i	$0.621052\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−19.0059	+	19.3935i	−0.986737	+	1.00686i
$372$		0			0
$373$	23.6843			1.22632			0.613162	−	0.789957i	$-0.289897\pi$
$373$	23.6843			1.22632			0.613162	+	0.789957i	$0.289897\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−16.0917			−0.828763
$378$		0			0
$379$	4.42107			0.227095			0.113547	−	0.993533i	$-0.463779\pi$
$379$	4.42107			0.227095			0.113547	+	0.993533i	$0.463779\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.40164			−0.224913			−0.112457	−	0.993657i	$-0.535872\pi$
$383$	−4.40164			−0.224913			−0.112457	+	0.993657i	$0.535872\pi$
$384$		0			0
$385$	−8.09153	−	29.0229i	−0.412382	−	1.47914i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.30998			0.167822			0.0839112	−	0.996473i	$-0.473259\pi$
$389$	3.30998			0.167822			0.0839112	+	0.996473i	$0.473259\pi$
$390$		0			0
$391$	0.958128	+	1.65953i	0.0484546	+	0.0839258i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	17.5917	+	30.4696i	0.885132	+	1.53309i
$396$		0			0
$397$	15.5848	−	26.9937i	0.782180	−	1.35478i	−0.148490	−	0.988914i	$-0.547441\pi$
$397$	15.5848	−	26.9937i	0.782180	−	1.35478i	0.930669	−	0.365861i	$-0.119226\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.586849			−0.0293058			−0.0146529	−	0.999893i	$-0.504664\pi$
$401$	−0.586849			−0.0293058			−0.0146529	+	0.999893i	$0.504664\pi$
$402$		0			0
$403$	11.7037			0.583003
$404$		0			0
$405$		0			0
$406$		0			0
$407$	20.0985	−	34.8116i	0.996245	−	1.72555i
$408$		0			0
$409$	−14.5156	+	25.1418i	−0.717750	+	1.24318i	0.244139	+	0.969740i	$0.421495\pi$
$409$	−14.5156	+	25.1418i	−0.717750	+	1.24318i	−0.961889	+	0.273440i	$0.911839\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.5692	+	2.71797i	0.520077	+	0.133742i
$414$		0			0
$415$	10.1940	−	17.6565i	0.500403	−	0.866723i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−11.5917	−	20.0773i	−0.566290	−	0.980842i	−0.996928	−	0.0783181i	$-0.975045\pi$
$419$	−11.5917	−	20.0773i	−0.566290	−	0.980842i	0.430639	−	0.902524i	$-0.358288\pi$
$420$		0			0
$421$	14.5293	−	25.1654i	0.708114	−	1.22649i	−0.257442	−	0.966294i	$-0.582880\pi$
$421$	14.5293	−	25.1654i	0.708114	−	1.22649i	0.965556	−	0.260195i	$-0.0837869\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.733922	+	1.27119i	0.0356004	+	0.0616617i
$426$		0			0
$427$	−17.1287	+	17.4781i	−0.828917	+	0.845823i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.990285	−	1.71522i	−0.0477003	−	0.0826194i	0.841189	−	0.540741i	$-0.181856\pi$
$431$	−0.990285	−	1.71522i	−0.0477003	−	0.0826194i	−0.888890	+	0.458121i	$0.848523\pi$
$432$		0			0
$433$	29.5048			1.41791			0.708955	−	0.705253i	$-0.249167\pi$
$433$	29.5048			1.41791			0.708955	+	0.705253i	$0.249167\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.721328	+	1.24938i	−0.0345058	+	0.0597658i
$438$		0			0
$439$	−9.48633	−	16.4308i	−0.452758	−	0.784199i	0.545799	−	0.837916i	$-0.316226\pi$
$439$	−9.48633	−	16.4308i	−0.452758	−	0.784199i	−0.998556	+	0.0537171i	$0.982893\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.6345	+	18.4195i	0.505259	+	0.875135i	0.999981	+	0.00608363i	$0.00193649\pi$
$443$	10.6345	+	18.4195i	0.505259	+	0.875135i	−0.494722	+	0.869051i	$0.664730\pi$
$444$		0			0
$445$	19.4795	−	33.7395i	0.923416	−	1.59940i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	21.2690			1.00374			0.501872	−	0.864942i	$-0.332645\pi$
$449$	21.2690			1.00374			0.501872	+	0.864942i	$0.332645\pi$
$450$		0			0
$451$	−8.74269	−	15.1428i	−0.411677	−	0.713046i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−15.3382	+	15.6510i	−0.719065	+	0.733731i
$456$		0			0
$457$	5.73392	+	9.93144i	0.268222	+	0.464573i	0.968403	−	0.249392i	$-0.0802307\pi$
$457$	5.73392	+	9.93144i	0.268222	+	0.464573i	−0.700181	+	0.713965i	$0.746897\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.70082	+	6.41001i	−0.172364	+	0.298544i	−0.939246	−	0.343245i	$-0.888474\pi$
$461$	−3.70082	+	6.41001i	−0.172364	+	0.298544i	0.766882	+	0.641788i	$0.221807\pi$
$462$		0			0
$463$	−2.84213	−	4.92272i	−0.132085	−	0.228778i	0.792395	−	0.610008i	$-0.208834\pi$
$463$	−2.84213	−	4.92272i	−0.132085	−	0.228778i	−0.924480	+	0.381230i	$0.875501\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−12.6150	+	21.8499i	−0.583755	+	1.01109i	0.411275	+	0.911511i	$0.365084\pi$
$467$	−12.6150	+	21.8499i	−0.583755	+	1.01109i	−0.995029	+	0.0995815i	$0.968250\pi$
$468$		0			0
$469$	28.5059	+	7.33054i	1.31628	+	0.338493i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	13.0430	−	22.5911i	0.599716	−	1.03874i
$474$		0			0
$475$	−0.552534	+	0.957016i	−0.0253520	+	0.0439109i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	12.2359			0.559070			0.279535	−	0.960135i	$-0.409820\pi$
$479$	12.2359			0.559070			0.279535	+	0.960135i	$0.409820\pi$
$480$		0			0
$481$	−29.2359			−1.33304
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−19.6706	+	34.0705i	−0.893196	+	1.54706i
$486$		0			0
$487$	2.99028	+	5.17933i	0.135503	+	0.234698i	0.925789	−	0.378040i	$-0.123402\pi$
$487$	2.99028	+	5.17933i	0.135503	+	0.234698i	−0.790287	+	0.612737i	$0.790068\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.60138	−	7.96982i	−0.207657	−	0.359673i	0.743319	−	0.668937i	$-0.233251\pi$
$491$	−4.60138	−	7.96982i	−0.207657	−	0.359673i	−0.950976	+	0.309264i	$0.899917\pi$
$492$		0			0
$493$	−8.01367			−0.360918
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.6345	−	38.1440i	−0.477022	−	1.71099i
$498$		0			0
$499$	19.6648			0.880319			0.440159	−	0.897920i	$-0.354922\pi$
$499$	19.6648			0.880319			0.440159	+	0.897920i	$0.354922\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−9.54583			−0.425628			−0.212814	−	0.977093i	$-0.568263\pi$
$503$	−9.54583			−0.425628			−0.212814	+	0.977093i	$0.568263\pi$
$504$		0			0
$505$	31.4408			1.39910
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.54583			−0.157166			−0.0785831	−	0.996908i	$-0.525040\pi$
$509$	−3.54583			−0.157166			−0.0785831	+	0.996908i	$0.525040\pi$
$510$		0			0
$511$	3.96006	−	4.04083i	0.175183	−	0.178756i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−16.9475			−0.746795
$516$		0			0
$517$	27.8187	+	48.1835i	1.22347	+	2.11911i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.77292	−	13.4631i	−0.340538	−	0.589828i	0.643995	−	0.765030i	$-0.277276\pi$
$521$	−7.77292	−	13.4631i	−0.340538	−	0.589828i	−0.984533	+	0.175201i	$0.943942\pi$
$522$		0			0
$523$	15.6871	−	27.1709i	0.685951	−	1.18810i	−0.287186	−	0.957875i	$-0.592720\pi$
$523$	15.6871	−	27.1709i	0.685951	−	1.18810i	0.973137	−	0.230227i	$-0.0739469\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.82846			0.253892
$528$		0			0
$529$	−21.7349			−0.944996
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.35868	+	11.0136i	−0.275425	+	0.477050i
$534$		0			0
$535$	15.3948	−	26.6646i	0.665575	−	1.15281i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	28.1765	−	17.0352i	1.21365	−	0.733759i
$540$		0			0
$541$	2.13448	−	3.69703i	0.0917684	−	0.158948i	−0.816487	−	0.577364i	$-0.804081\pi$
$541$	2.13448	−	3.69703i	0.0917684	−	0.158948i	0.908255	+	0.418416i	$0.137415\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.96690	+	15.5311i	0.384100	+	0.665280i
$546$		0			0
$547$	10.2008	−	17.6683i	0.436155	−	0.755443i	−0.561234	−	0.827657i	$-0.689673\pi$
$547$	10.2008	−	17.6683i	0.436155	−	0.755443i	0.997389	+	0.0722139i	$0.0230064\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.01655	−	5.22482i	−0.128509	−	0.222585i
$552$		0			0
$553$	−26.9114	+	27.4602i	−1.14439	+	1.16773i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.7466	−	30.7381i	−0.751950	−	1.30241i	−0.946877	−	0.321597i	$-0.895780\pi$
$557$	−17.7466	−	30.7381i	−0.751950	−	1.30241i	0.194927	−	0.980818i	$-0.437553\pi$
$558$		0			0
$559$	−18.9727			−0.802458
$560$		0			0
$561$		0			0
$562$		0			0
$563$	2.64527	−	4.58175i	0.111485	−	0.193098i	−0.804884	−	0.593432i	$-0.797773\pi$
$563$	2.64527	−	4.58175i	0.111485	−	0.193098i	0.916369	+	0.400334i	$0.131106\pi$
$564$		0			0
$565$	−8.09153	−	14.0149i	−0.340413	−	0.589613i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.530225	−	0.918376i	−0.0222282	−	0.0385003i	0.854697	−	0.519127i	$-0.173743\pi$
$569$	−0.530225	−	0.918376i	−0.0222282	−	0.0385003i	−0.876926	+	0.480626i	$0.840409\pi$
$570$		0			0
$571$	14.5498	−	25.2010i	0.608890	−	1.05463i	−0.382534	−	0.923941i	$-0.624949\pi$
$571$	14.5498	−	25.2010i	0.608890	−	1.05463i	0.991424	−	0.130686i	$-0.0417181\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.969055			0.0404124
$576$		0			0
$577$	0.617927	+	1.07028i	0.0257246	+	0.0445564i	0.878601	−	0.477556i	$-0.158477\pi$
$577$	0.617927	+	1.07028i	0.0257246	+	0.0445564i	−0.852876	+	0.522113i	$0.825144\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	21.5780	+	5.54897i	0.895206	+	0.230210i
$582$		0			0
$583$	−24.1375	−	41.8074i	−0.999673	−	1.73148i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.9863	+	22.4930i	−0.536003	+	0.928385i	0.463111	+	0.886300i	$0.346733\pi$
$587$	−12.9863	+	22.4930i	−0.536003	+	0.928385i	−0.999114	+	0.0420843i	$0.986600\pi$
$588$		0			0
$589$	2.19398	+	3.80009i	0.0904014	+	0.156580i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.15103	−	10.6539i	0.252593	−	0.437503i	−0.711646	−	0.702538i	$-0.752050\pi$
$593$	6.15103	−	10.6539i	0.252593	−	0.437503i	0.964239	+	0.265035i	$0.0853835\pi$
$594$		0			0
$595$	−7.63844	+	7.79423i	−0.313145	+	0.319532i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−11.8937	+	20.6005i	−0.485964	+	0.841715i	−0.999870	−	0.0161320i	$-0.994865\pi$
$599$	−11.8937	+	20.6005i	−0.485964	+	0.841715i	0.513906	+	0.857847i	$0.328198\pi$
$600$		0			0
$601$	3.96006	−	6.85903i	0.161534	−	0.279785i	−0.773885	−	0.633326i	$-0.781689\pi$
$601$	3.96006	−	6.85903i	0.161534	−	0.279785i	0.935419	+	0.353541i	$0.115022\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	26.9338			1.09501
$606$		0			0
$607$	−0.0467764			−0.00189860			−0.000949298	−	1.00000i	$-0.500302\pi$
$607$	−0.0467764			−0.00189860			−0.000949298		1.00000i	$0.500302\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	20.2330	−	35.0445i	0.818539	−	1.41775i
$612$		0			0
$613$	−9.91027	−	17.1651i	−0.400272	−	0.693292i	0.593486	−	0.804844i	$-0.297751\pi$
$613$	−9.91027	−	17.1651i	−0.400272	−	0.693292i	−0.993759	+	0.111552i	$0.964418\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	17.2164	+	29.8197i	0.693107	+	1.20050i	0.970815	+	0.239831i	$0.0770921\pi$
$617$	17.2164	+	29.8197i	0.693107	+	1.20050i	−0.277708	+	0.960666i	$0.589575\pi$
$618$		0			0
$619$	47.5127			1.90970			0.954849	−	0.297092i	$-0.0960168\pi$
$619$	47.5127			1.90970			0.954849	+	0.297092i	$0.0960168\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	41.2330	+	10.6034i	1.65196	+	0.424817i
$624$		0			0
$625$	−28.5655			−1.14262
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−14.5595			−0.580525
$630$		0			0
$631$	9.26320			0.368762			0.184381	−	0.982855i	$-0.440972\pi$
$631$	9.26320			0.368762			0.184381	+	0.982855i	$0.440972\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−27.9201			−1.10798
$636$		0			0
$637$	−20.9766	−	11.5526i	−0.831124	−	0.457731i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	3.10533			0.122653			0.0613266	−	0.998118i	$-0.480467\pi$
$641$	3.10533			0.122653			0.0613266	+	0.998118i	$0.480467\pi$
$642$		0			0
$643$	8.86840	+	15.3605i	0.349736	+	0.605760i	0.986202	−	0.165544i	$-0.0529381\pi$
$643$	8.86840	+	15.3605i	0.349736	+	0.605760i	−0.636467	+	0.771304i	$0.719605\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.460060	−	0.796847i	−0.0180868	−	0.0313273i	0.856840	−	0.515582i	$-0.172424\pi$
$647$	−0.460060	−	0.796847i	−0.0180868	−	0.0313273i	−0.874927	+	0.484255i	$0.839091\pi$
$648$		0			0
$649$	−9.70082	+	16.8023i	−0.380790	+	0.659548i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.20275			−0.360131			−0.180066	−	0.983655i	$-0.557631\pi$
$653$	−9.20275			−0.360131			−0.180066	+	0.983655i	$0.557631\pi$
$654$		0			0
$655$	22.1248			0.864486
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−24.6999	+	42.7814i	−0.962170	+	1.66653i	−0.245138	+	0.969488i	$0.578833\pi$
$659$	−24.6999	+	42.7814i	−0.962170	+	1.66653i	−0.717032	+	0.697040i	$0.754500\pi$
$660$		0			0
$661$	24.9922	−	43.2878i	0.972085	−	1.68370i	0.282846	−	0.959165i	$-0.408721\pi$
$661$	24.9922	−	43.2878i	0.972085	−	1.68370i	0.689238	−	0.724535i	$-0.257945\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−7.95705	−	2.04622i	−0.308561	−	0.0793492i
$666$		0			0
$667$	−2.64527	+	4.58175i	−0.102425	+	0.177406i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−21.7535	−	37.6781i	−0.839784	−	1.45455i
$672$		0			0
$673$	−4.71737	+	8.17072i	−0.181841	+	0.314958i	−0.942508	−	0.334185i	$-0.891539\pi$
$673$	−4.71737	+	8.17072i	−0.181841	+	0.314958i	0.760666	+	0.649143i	$0.224872\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.8937	−	20.6005i	−0.457113	−	0.791743i	0.541694	−	0.840576i	$-0.317783\pi$
$677$	−11.8937	−	20.6005i	−0.457113	−	0.791743i	−0.998807	+	0.0488331i	$0.984450\pi$
$678$		0			0
$679$	−41.6375	−	10.7074i	−1.59790	−	0.410914i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−17.3187	−	29.9969i	−0.662683	−	1.14780i	−0.979908	−	0.199451i	$-0.936084\pi$
$683$	−17.3187	−	29.9969i	−0.662683	−	1.14780i	0.317224	−	0.948350i	$-0.397249\pi$
$684$		0			0
$685$	5.44625			0.208091
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−17.5555	+	30.4071i	−0.668813	+	1.15842i
$690$		0			0
$691$	−17.9601	−	31.1077i	−0.683233	−	1.18339i	−0.973989	−	0.226597i	$-0.927240\pi$
$691$	−17.9601	−	31.1077i	−0.683233	−	1.18339i	0.290756	−	0.956797i	$-0.406093\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.8062	+	22.1809i	0.485765	+	0.841370i
$696$		0			0
$697$	−3.16664	+	5.48477i	−0.119945	+	0.207751i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	9.72529			0.367319			0.183659	−	0.982990i	$-0.441206\pi$
$701$	9.72529			0.367319			0.183659	+	0.982990i	$0.441206\pi$
$702$		0			0
$703$	−5.48057	−	9.49263i	−0.206704	−	0.358021i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.22722	+	33.0964i	0.347025	+	1.24472i
$708$		0			0
$709$	12.0555	+	20.8808i	0.452756	+	0.784196i	0.998556	−	0.0537196i	$-0.0171077\pi$
$709$	12.0555	+	20.8808i	0.452756	+	0.784196i	−0.545801	+	0.837915i	$0.683774\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.92395	−	3.33237i	0.0720523	−	0.124798i
$714$		0			0
$715$	−19.4795	−	33.7395i	−0.728492	−	1.26178i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	12.6764	−	21.9561i	0.472748	−	0.818824i	−0.526765	−	0.850011i	$-0.676595\pi$
$719$	12.6764	−	21.9561i	0.472748	−	0.818824i	0.999514	+	0.0311869i	$0.00992872\pi$
$720$		0			0
$721$	−4.97373	−	17.8399i	−0.185232	−	0.664393i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.02627	+	3.50960i	−0.0752537	+	0.130343i
$726$		0			0
$727$	−23.7564	+	41.1472i	−0.881075	+	1.52607i	−0.0309272	+	0.999522i	$0.509846\pi$
$727$	−23.7564	+	41.1472i	−0.881075	+	1.52607i	−0.850148	+	0.526545i	$0.823487\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−9.44841			−0.349462
$732$		0			0
$733$	−30.8364			−1.13897			−0.569484	−	0.822003i	$-0.692857\pi$
$733$	−30.8364			−1.13897			−0.569484	+	0.822003i	$0.692857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−26.1638	+	45.3170i	−0.963754	+	1.66927i
$738$		0			0
$739$	−10.4971	−	18.1815i	−0.386143	−	0.668819i	0.605784	−	0.795629i	$-0.292859\pi$
$739$	−10.4971	−	18.1815i	−0.386143	−	0.668819i	−0.991927	+	0.126810i	$0.959526\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	22.6871	+	39.2953i	0.832311	+	1.44160i	0.896201	+	0.443647i	$0.146316\pi$
$743$	22.6871	+	39.2953i	0.832311	+	1.44160i	−0.0638908	+	0.997957i	$0.520351\pi$
$744$		0			0
$745$	−59.0118			−2.16202
$746$		0			0
$747$		0			0
$748$		0			0
$749$	32.5868	+	8.37997i	1.19069	+	0.306197i
$750$		0			0
$751$	12.8421			0.468616			0.234308	−	0.972162i	$-0.424718\pi$
$751$	12.8421			0.468616			0.234308	+	0.972162i	$0.424718\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	26.9669			0.981426
$756$		0			0
$757$	12.9727			0.471499			0.235750	−	0.971814i	$-0.424245\pi$
$757$	12.9727			0.471499			0.235750	+	0.971814i	$0.424245\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−41.4933			−1.50413			−0.752065	−	0.659088i	$-0.770942\pi$
$761$	−41.4933			−1.50413			−0.752065	+	0.659088i	$0.770942\pi$
$762$		0			0
$763$	−13.7174	+	13.9971i	−0.496602	+	0.506731i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	14.1111			0.509522
$768$		0			0
$769$	12.3450	+	21.3822i	0.445173	+	0.771061i	0.998064	−	0.0621917i	$-0.0198090\pi$
$769$	12.3450	+	21.3822i	0.445173	+	0.771061i	−0.552892	+	0.833253i	$0.686476\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	19.8256	+	34.3389i	0.713077	+	1.23508i	0.963697	+	0.266999i	$0.0860322\pi$
$773$	19.8256	+	34.3389i	0.713077	+	1.23508i	−0.250620	+	0.968086i	$0.580634\pi$
$774$		0			0
$775$	1.47373	−	2.55258i	0.0529381	−	0.0916914i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.76801			−0.170832
$780$		0			0
$781$	70.3997			2.51910
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.95021	+	6.84197i	−0.140989	+	0.244200i
$786$		0			0
$787$	−9.01273	+	15.6105i	−0.321269	+	0.556454i	−0.980750	−	0.195267i	$-0.937443\pi$
$787$	−9.01273	+	15.6105i	−0.321269	+	0.556454i	0.659481	+	0.751721i	$0.270776\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	12.3782	−	12.6307i	0.440120	−	0.449096i
$792$		0			0
$793$	−15.8216	+	27.4039i	−0.561842	+	0.973139i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	19.9396	+	34.5363i	0.706295	+	1.22334i	0.966222	+	0.257711i	$0.0829682\pi$
$797$	19.9396	+	34.5363i	0.706295	+	1.22334i	−0.259927	+	0.965628i	$0.583699\pi$
$798$		0			0
$799$	10.0761	−	17.4522i	0.356465	−	0.617416i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	5.02928	+	8.71097i	0.177479	+	0.307403i
$804$		0			0
$805$	1.93487	+	6.94004i	0.0681953	+	0.244604i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−22.5848	−	39.1181i	−0.794040	−	1.37532i	−0.923447	−	0.383726i	$-0.874641\pi$
$809$	−22.5848	−	39.1181i	−0.794040	−	1.37532i	0.129407	−	0.991592i	$-0.458693\pi$
$810$		0			0
$811$	−1.70945			−0.0600271			−0.0300135	−	0.999549i	$-0.509555\pi$
$811$	−1.70945			−0.0600271			−0.0300135	+	0.999549i	$0.509555\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.184134	−	0.318929i	0.00644992	−	0.0111716i
$816$		0			0
$817$	−3.55662	−	6.16025i	−0.124431	−	0.215520i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−26.4572	−	45.8252i	−0.923362	−	1.59931i	−0.794175	−	0.607690i	$-0.792096\pi$
$821$	−26.4572	−	45.8252i	−0.923362	−	1.59931i	−0.129187	−	0.991620i	$-0.541237\pi$
$822$		0			0
$823$	15.6179	−	27.0510i	0.544407	−	0.942940i	−0.454237	−	0.890881i	$-0.650088\pi$
$823$	15.6179	−	27.0510i	0.544407	−	0.942940i	0.998644	−	0.0520593i	$-0.0165785\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−35.2243			−1.22487			−0.612435	−	0.790521i	$-0.709810\pi$
$827$	−35.2243			−1.22487			−0.612435	+	0.790521i	$0.709810\pi$
$828$		0			0
$829$	−9.05842	−	15.6897i	−0.314612	−	0.544924i	0.664743	−	0.747072i	$-0.268541\pi$
$829$	−9.05842	−	15.6897i	−0.314612	−	0.544924i	−0.979355	+	0.202148i	$0.935208\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−10.4464	−	5.75322i	−0.361946	−	0.199337i
$834$		0			0
$835$	29.3383	+	50.8154i	1.01529	+	1.75854i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−9.77004	+	16.9222i	−0.337299	+	0.584219i	−0.983924	−	0.178589i	$-0.942847\pi$
$839$	−9.77004	+	16.9222i	−0.337299	+	0.584219i	0.646625	+	0.762808i	$0.276180\pi$
$840$		0			0
$841$	3.43762	+	5.95413i	0.118539	+	0.205315i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.56922	−	2.71797i	0.0539827	−	0.0935009i
$846$		0			0
$847$	7.90451	+	28.3521i	0.271602	+	0.974189i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.80602	+	8.32427i	−0.164748	+	0.285352i
$852$		0			0
$853$	−8.68715	+	15.0466i	−0.297442	+	0.515185i	−0.975550	−	0.219777i	$-0.929467\pi$
$853$	−8.68715	+	15.0466i	−0.297442	+	0.515185i	0.678108	+	0.734962i	$0.262800\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.5458			0.735992			0.367996	−	0.929827i	$-0.380044\pi$
$857$	21.5458			0.735992			0.367996	+	0.929827i	$0.380044\pi$
$858$		0			0
$859$	17.3743			0.592803			0.296402	−	0.955063i	$-0.404213\pi$
$859$	17.3743			0.592803			0.296402	+	0.955063i	$0.404213\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−8.71053	+	15.0871i	−0.296510	+	0.513570i	−0.975335	−	0.220730i	$-0.929156\pi$
$863$	−8.71053	+	15.0871i	−0.296510	+	0.513570i	0.678825	+	0.734300i	$0.262489\pi$
$864$		0			0
$865$	8.41711	+	14.5789i	0.286190	+	0.495696i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−34.1774	−	59.1970i	−1.15939	−	2.00812i
$870$		0			0
$871$	38.0586			1.28956
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.11914	−	25.5351i	−0.240671	−	0.863244i
$876$		0			0
$877$	46.9981			1.58701			0.793507	−	0.608562i	$-0.208253\pi$
$877$	46.9981			1.58701			0.793507	+	0.608562i	$0.208253\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	15.1715			0.511142			0.255571	−	0.966790i	$-0.417737\pi$
$881$	15.1715			0.511142			0.255571	+	0.966790i	$0.417737\pi$
$882$		0			0
$883$	−32.4660			−1.09257			−0.546283	−	0.837601i	$-0.683958\pi$
$883$	−32.4660			−1.09257			−0.546283	+	0.837601i	$0.683958\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.86948			−0.0963477			−0.0481738	−	0.998839i	$-0.515340\pi$
$887$	−2.86948			−0.0963477			−0.0481738	+	0.998839i	$0.515340\pi$
$888$		0			0
$889$	−8.19398	−	29.3904i	−0.274817	−	0.985721i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	15.1715			0.507696
$894$		0			0
$895$	17.7923	+	30.8172i	0.594733	+	1.03011i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	8.04583	+	13.9358i	0.268343	+	0.464784i
$900$		0			0
$901$	−8.74269	+	15.1428i	−0.291261	+	0.504479i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	41.4132			1.37662
$906$		0			0
$907$	−32.4328			−1.07692			−0.538458	−	0.842653i	$-0.680993\pi$
$907$	−32.4328			−1.07692			−0.538458	+	0.842653i	$0.680993\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	16.6219	−	28.7899i	0.550708	−	0.953854i	−0.447516	−	0.894276i	$-0.647691\pi$
$911$	16.6219	−	28.7899i	0.550708	−	0.953854i	0.998224	−	0.0595777i	$-0.0189754\pi$
$912$		0			0
$913$	−19.8051	+	34.3034i	−0.655452	+	1.13528i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.49316	+	23.2898i	0.214423	+	0.769098i
$918$		0			0
$919$	14.3752	−	24.8986i	0.474195	−	0.821330i	−0.525368	−	0.850875i	$-0.676072\pi$
$919$	14.3752	−	24.8986i	0.474195	−	0.821330i	0.999563	+	0.0295447i	$0.00940573\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−25.6014	−	44.3429i	−0.842680	−	1.45956i
$924$		0			0
$925$	−3.68139	+	6.37635i	−0.121043	+	0.209653i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	27.2729	+	47.2381i	0.894795	+	1.54983i	0.834058	+	0.551677i	$0.186012\pi$
$929$	27.2729	+	47.2381i	0.894795	+	1.54983i	0.0607376	+	0.998154i	$0.480655\pi$
$930$		0			0
$931$	−0.181255	−	8.97658i	−0.00594039	−	0.294196i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−9.70082	−	16.8023i	−0.317251	−	0.549494i
$936$		0			0
$937$	28.6979			0.937521			0.468760	−	0.883325i	$-0.344701\pi$
$937$	28.6979			0.937521			0.468760	+	0.883325i	$0.344701\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.64815	−	16.7111i	0.314521	−	0.544766i	−0.664815	−	0.747008i	$-0.731490\pi$
$941$	9.64815	−	16.7111i	0.314521	−	0.544766i	0.979336	+	0.202242i	$0.0648229\pi$
$942$		0			0
$943$	2.09058	+	3.62099i	0.0680787	+	0.117916i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.26608	−	9.12112i	−0.171125	−	0.296396i	0.767689	−	0.640823i	$-0.221407\pi$
$947$	−5.26608	−	9.12112i	−0.171125	−	0.296396i	−0.938813	+	0.344426i	$0.888073\pi$
$948$		0			0
$949$	3.65787	−	6.33561i	0.118739	−	0.205663i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	19.1970			0.621852			0.310926	−	0.950434i	$-0.399361\pi$
$953$	19.1970			0.621852			0.310926	+	0.950434i	$0.399361\pi$
$954$		0			0
$955$	27.8187	+	48.1835i	0.900193	+	1.55918i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.59836	+	5.73305i	0.0516139	+	0.185130i
$960$		0			0
$961$	9.64815	+	16.7111i	0.311231	+	0.539067i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.50576	+	11.2683i	−0.209428	+	0.362739i
$966$		0			0
$967$	7.74269	+	13.4107i	0.248988	+	0.431260i	0.963245	−	0.268623i	$-0.0865686\pi$
$967$	7.74269	+	13.4107i	0.248988	+	0.431260i	−0.714257	+	0.699883i	$0.753235\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.904515	+	1.56667i	−0.0290273	+	0.0502767i	−0.880174	−	0.474651i	$-0.842574\pi$
$971$	−0.904515	+	1.56667i	−0.0290273	+	0.0502767i	0.851147	+	0.524928i	$0.175908\pi$
$972$		0			0
$973$	−19.5906	+	19.9901i	−0.628045	+	0.640855i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.9493	−	32.8211i	0.606241	−	1.05004i	−0.385613	−	0.922660i	$-0.626010\pi$
$977$	18.9493	−	32.8211i	0.606241	−	1.05004i	0.991854	−	0.127379i	$-0.0406565\pi$
$978$		0			0
$979$	−37.8451	+	65.5497i	−1.20954	+	2.09498i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−38.1111			−1.21556			−0.607778	−	0.794107i	$-0.707939\pi$
$983$	−38.1111			−1.21556			−0.607778	+	0.794107i	$0.707939\pi$
$984$		0			0
$985$	8.66484			0.276085
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.11887	+	5.40205i	−0.0991744	+	0.171775i
$990$		0			0
$991$	−5.89480	−	10.2101i	−0.187254	−	0.324334i	0.757079	−	0.653323i	$-0.226626\pi$
$991$	−5.89480	−	10.2101i	−0.187254	−	0.324334i	−0.944334	+	0.328989i	$0.893292\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8.47373	+	14.6769i	0.268635	+	0.465290i
$996$		0			0
$997$	14.8069			0.468938			0.234469	−	0.972124i	$-0.424665\pi$
$997$	14.8069			0.468938			0.234469	+	0.972124i	$0.424665\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.l.j.541.3		6
3.2	odd	2		2268.2.l.k.541.1		6
7.4	even	3		2268.2.i.k.865.1		6
9.2	odd	6		756.2.k.e.541.3	yes	6
9.4	even	3		2268.2.i.k.2053.1		6
9.5	odd	6		2268.2.i.j.2053.3		6
9.7	even	3		756.2.k.f.541.1	yes	6
21.11	odd	6		2268.2.i.j.865.3		6
63.2	odd	6		5292.2.a.x.1.1		3
63.4	even	3	inner	2268.2.l.j.109.3		6
63.11	odd	6		756.2.k.e.109.3	✓	6
63.16	even	3		5292.2.a.u.1.3		3
63.25	even	3		756.2.k.f.109.1	yes	6
63.32	odd	6		2268.2.l.k.109.1		6
63.47	even	6		5292.2.a.v.1.3		3
63.61	odd	6		5292.2.a.w.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.k.e.109.3	✓	6	63.11	odd	6
756.2.k.e.541.3	yes	6	9.2	odd	6
756.2.k.f.109.1	yes	6	63.25	even	3
756.2.k.f.541.1	yes	6	9.7	even	3
2268.2.i.j.865.3		6	21.11	odd	6
2268.2.i.j.2053.3		6	9.5	odd	6
2268.2.i.k.865.1		6	7.4	even	3
2268.2.i.k.2053.1		6	9.4	even	3
2268.2.l.j.109.3		6	63.4	even	3	inner
2268.2.l.j.541.3		6	1.1	even	1	trivial
2268.2.l.k.109.1		6	63.32	odd	6
2268.2.l.k.541.1		6	3.2	odd	2
5292.2.a.u.1.3		3	63.16	even	3
5292.2.a.v.1.3		3	63.47	even	6
5292.2.a.w.1.1		3	63.61	odd	6
5292.2.a.x.1.1		3	63.2	odd	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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.42107 q^{5} +(0.710533 + 2.54856i) q^{7} +O(q^{10})\)	\(q+2.42107 q^{5} +(0.710533 + 2.54856i) q^{7} -4.70370 q^{11} +(1.71053 + 2.96273i) q^{13} +(0.851848 + 1.47544i) q^{17} +(-0.641315 + 1.11079i) q^{19} +1.12476 q^{23} +0.861564 q^{25} +(-2.35185 + 4.07352i) q^{29} +(1.71053 - 2.96273i) q^{31} +(1.72025 + 6.17023i) q^{35} +(-4.27292 + 7.40091i) q^{37} +(1.85868 + 3.21934i) q^{41} +(-2.77292 + 4.80283i) q^{43} +(-5.91423 - 10.2437i) q^{47} +(-5.99028 + 3.62167i) q^{49} +(5.13160 + 8.88819i) q^{53} -11.3880 q^{55} +(2.06238 - 3.57215i) q^{59} +(4.62476 + 8.01033i) q^{61} +(4.14132 + 7.17297i) q^{65} +(5.56238 - 9.63433i) q^{67} -14.9669 q^{71} +(-1.06922 - 1.85194i) q^{73} +(-3.34213 - 11.9876i) q^{77} +(7.26608 + 12.5852i) q^{79} +(4.21053 - 7.29286i) q^{83} +(2.06238 + 3.57215i) q^{85} +(8.04583 - 13.9358i) q^{89} +(-6.33530 + 6.46451i) q^{91} +(-1.55267 + 2.68930i) q^{95} +(-8.12476 + 14.0725i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{5} - 4 q^{7}+O(q^{10}) \) 6 * q - 2 * q^5 - 4 * q^7	\( 6 q - 2 q^{5} - 4 q^{7} - 10 q^{11} + 2 q^{13} - 4 q^{17} - 3 q^{19} - 28 q^{23} + 20 q^{25} - 5 q^{29} + 2 q^{31} + 26 q^{35} + 12 q^{41} + 9 q^{43} - 9 q^{47} - 12 q^{49} + 6 q^{53} + 16 q^{55} - 5 q^{59} - 7 q^{61} + 24 q^{65} + 16 q^{67} - 22 q^{71} + q^{73} + 13 q^{77} + 8 q^{79} + 17 q^{83} - 5 q^{85} - 3 q^{89} + 5 q^{91} + 32 q^{95} - 14 q^{97}+O(q^{100}) \) 6 * q - 2 * q^5 - 4 * q^7 - 10 * q^11 + 2 * q^13 - 4 * q^17 - 3 * q^19 - 28 * q^23 + 20 * q^25 - 5 * q^29 + 2 * q^31 + 26 * q^35 + 12 * q^41 + 9 * q^43 - 9 * q^47 - 12 * q^49 + 6 * q^53 + 16 * q^55 - 5 * q^59 - 7 * q^61 + 24 * q^65 + 16 * q^67 - 22 * q^71 + q^73 + 13 * q^77 + 8 * q^79 + 17 * q^83 - 5 * q^85 - 3 * q^89 + 5 * q^91 + 32 * q^95 - 14 * q^97

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