LMFDB - Embedded newform 756.2.k.f.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(109,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("756.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.03669039281$
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:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	756.541
Dual form			756.2.k.f.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21053 + 2.09671i) q^{5} +(1.85185 - 1.88962i) q^{7} +O(q^{10})$	$q+(-1.21053 + 2.09671i) q^{5} +(1.85185 - 1.88962i) q^{7} +(2.35185 + 4.07352i) q^{11} -3.42107 q^{13} +(0.851848 + 1.47544i) q^{17} +(-0.641315 + 1.11079i) q^{19} +(-0.562382 + 0.974074i) q^{23} +(-0.430782 - 0.746136i) q^{25} +4.70370 q^{29} +(1.71053 + 2.96273i) q^{31} +(1.72025 + 6.17023i) q^{35} +(-4.27292 + 7.40091i) q^{37} -3.71737 q^{41} +5.54583 q^{43} +(-5.91423 + 10.2437i) q^{47} +(-0.141315 - 6.99857i) q^{49} +(5.13160 + 8.88819i) q^{53} -11.3880 q^{55} +(2.06238 + 3.57215i) q^{59} +(4.62476 - 8.01033i) q^{61} +(4.14132 - 7.17297i) q^{65} +(5.56238 + 9.63433i) q^{67} -14.9669 q^{71} +(-1.06922 - 1.85194i) q^{73} +(12.0527 + 3.09945i) q^{77} +(7.26608 - 12.5852i) q^{79} -8.42107 q^{83} -4.12476 q^{85} +(8.04583 - 13.9358i) q^{89} +(-6.33530 + 6.46451i) q^{91} +(-1.55267 - 2.68930i) q^{95} +16.2495 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{5} + 2 q^{7}+O(q^{10}) $ 6 * q + q^5 + 2 * q^7	$ 6 q + q^{5} + 2 q^{7} + 5 q^{11} - 4 q^{13} - 4 q^{17} - 3 q^{19} + 14 q^{23} - 10 q^{25} + 10 q^{29} + 2 q^{31} + 26 q^{35} - 24 q^{41} - 18 q^{43} - 9 q^{47} + 6 q^{53} + 16 q^{55} - 5 q^{59} - 7 q^{61} + 24 q^{65} + 16 q^{67} - 22 q^{71} + q^{73} + 31 q^{77} + 8 q^{79} - 34 q^{83} + 10 q^{85} - 3 q^{89} + 5 q^{91} + 32 q^{95} + 28 q^{97}+O(q^{100}) $ 6 * q + q^5 + 2 * q^7 + 5 * q^11 - 4 * q^13 - 4 * q^17 - 3 * q^19 + 14 * q^23 - 10 * q^25 + 10 * q^29 + 2 * q^31 + 26 * q^35 - 24 * q^41 - 18 * q^43 - 9 * q^47 + 6 * q^53 + 16 * q^55 - 5 * q^59 - 7 * q^61 + 24 * q^65 + 16 * q^67 - 22 * q^71 + q^73 + 31 * q^77 + 8 * q^79 - 34 * q^83 + 10 * q^85 - 3 * q^89 + 5 * q^91 + 32 * q^95 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.21053	+	2.09671i	−0.541367	+	0.937675i	0.457459	+	0.889231i	$0.348760\pi$
$5$	−1.21053	+	2.09671i	−0.541367	+	0.937675i	−0.998826	+	0.0484443i	$0.984574\pi$
$6$		0			0
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$7$	1.85185	−	1.88962i	0.699933	−	0.714209i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.35185	+	4.07352i	0.709109	+	1.22821i	0.965188	+	0.261557i	$0.0842359\pi$
$11$	2.35185	+	4.07352i	0.709109	+	1.22821i	−0.256079	+	0.966656i	$0.582431\pi$
$12$		0			0
$13$	−3.42107			−0.948833			−0.474417	−	0.880300i	$-0.657341\pi$
$13$	−3.42107			−0.948833			−0.474417	+	0.880300i	$0.657341\pi$
$14$		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
$23$	−0.562382	+	0.974074i	−0.117265	+	0.203108i	−0.918683	−	0.394996i	$-0.870746\pi$
$23$	−0.562382	+	0.974074i	−0.117265	+	0.203108i	0.801418	+	0.598105i	$0.204079\pi$
$24$		0			0
$25$	−0.430782	−	0.746136i	−0.0861564	−	0.149227i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.70370			0.873455			0.436727	−	0.899594i	$-0.356137\pi$
$29$	4.70370			0.873455			0.436727	+	0.899594i	$0.356137\pi$
$30$		0			0
$31$	1.71053	+	2.96273i	0.307221	+	0.532122i	0.977753	−	0.209758i	$-0.0672676\pi$
$31$	1.71053	+	2.96273i	0.307221	+	0.532122i	−0.670532	+	0.741880i	$0.733934\pi$
$32$		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
$41$	−3.71737			−0.580556			−0.290278	−	0.956942i	$-0.593748\pi$
$41$	−3.71737			−0.580556			−0.290278	+	0.956942i	$0.593748\pi$
$42$		0			0
$43$	5.54583			0.845731			0.422866	−	0.906192i	$-0.361024\pi$
$43$	5.54583			0.845731			0.422866	+	0.906192i	$0.361024\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.91423	+	10.2437i	−0.862679	+	1.49420i	0.00665422	+	0.999978i	$0.497882\pi$
$47$	−5.91423	+	10.2437i	−0.862679	+	1.49420i	−0.869333	+	0.494226i	$0.835451\pi$
$48$		0			0
$49$	−0.141315	−	6.99857i	−0.0201879	−	0.999796i
$50$		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	0.968474	−	0.249113i	$-0.0801390\pi$
$59$	2.06238	+	3.57215i	0.268499	+	0.465054i	−0.699975	+	0.714167i	$0.746806\pi$
$60$		0			0
$61$	4.62476	−	8.01033i	0.592140	−	1.02562i	−0.401803	−	0.915726i	$-0.631616\pi$
$61$	4.62476	−	8.01033i	0.592140	−	1.02562i	0.993944	−	0.109891i	$-0.0350502\pi$
$62$		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	0.975116	+	0.221697i	$0.0711596\pi$
$67$	5.56238	+	9.63433i	0.679553	+	1.17702i	−0.295563	+	0.955323i	$0.595507\pi$
$68$		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
$77$	12.0527	+	3.09945i	1.37353	+	0.353215i
$78$		0			0
$79$	7.26608	−	12.5852i	0.817498	−	1.41595i	−0.0900228	−	0.995940i	$-0.528694\pi$
$79$	7.26608	−	12.5852i	0.817498	−	1.41595i	0.907520	−	0.420008i	$-0.137973\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.42107			−0.924332			−0.462166	−	0.886793i	$-0.652928\pi$
$83$	−8.42107			−0.924332			−0.462166	+	0.886793i	$0.652928\pi$
$84$		0			0
$85$	−4.12476			−0.447393
$86$		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
$97$	16.2495			1.64989			0.824945	−	0.565213i	$-0.191206\pi$
$97$	16.2495			1.64989			0.824945	+	0.565213i	$0.191206\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.49316	−	11.2465i	−0.646094	−	1.11907i	−0.984048	−	0.177905i	$-0.943068\pi$
$101$	−6.49316	−	11.2465i	−0.646094	−	1.11907i	0.337954	−	0.941163i	$-0.390265\pi$
$102$		0			0
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	0.985329	+	0.170664i	$0.0545913\pi$
$104$		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
$113$	6.68427			0.628803			0.314401	−	0.949290i	$-0.398196\pi$
$113$	6.68427			0.628803			0.314401	+	0.949290i	$0.398196\pi$
$114$		0			0
$115$	−1.36156	−	2.35830i	−0.126966	−	0.219912i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.36552	+	1.12263i	0.400187	+	0.102911i
$120$		0			0
$121$	−5.56238	+	9.63433i	−0.505671	+	0.875848i
$122$		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
$131$	−4.56922	+	7.91412i	−0.399214	+	0.691460i	−0.993629	−	0.112699i	$-0.964050\pi$
$131$	−4.56922	+	7.91412i	−0.399214	+	0.691460i	0.594415	+	0.804159i	$0.297384\pi$
$132$		0			0
$133$	0.911351	+	3.26886i	0.0790242	+	0.283446i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.12476	−	1.94815i	−0.0960950	−	0.166441i	0.813970	−	0.580907i	$-0.197302\pi$
$137$	−1.12476	−	1.94815i	−0.0960950	−	0.166441i	−0.910065	+	0.414465i	$0.863969\pi$
$138$		0			0
$139$	−10.5789			−0.897293			−0.448647	−	0.893709i	$-0.648094\pi$
$139$	−10.5789			−0.897293			−0.448647	+	0.893709i	$0.648094\pi$
$140$		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
$149$	12.1871	−	21.1088i	0.998410	−	1.72930i	0.450385	−	0.892834i	$-0.351287\pi$
$149$	12.1871	−	21.1088i	0.998410	−	1.72930i	0.548025	−	0.836462i	$-0.315380\pi$
$150$		0			0
$151$	−5.56922	−	9.64617i	−0.453217	−	0.784994i	0.545367	−	0.838197i	$-0.316390\pi$
$151$	−5.56922	−	9.64617i	−0.453217	−	0.784994i	−0.998584	+	0.0532032i	$0.983057\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−8.28263			−0.665277
$156$		0			0
$157$	−1.63160	−	2.82601i	−0.130216	−	0.225540i	0.793544	−	0.608513i	$-0.208234\pi$
$157$	−1.63160	−	2.82601i	−0.130216	−	0.225540i	−0.923760	+	0.382973i	$0.874900\pi$
$158$		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
$167$	−24.2359			−1.87543			−0.937713	−	0.347410i	$-0.887061\pi$
$167$	−24.2359			−1.87543			−0.937713	+	0.347410i	$0.887061\pi$
$168$		0			0
$169$	−1.29630			−0.0997156
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.47661	−	6.02167i	0.264322	−	0.457819i	−0.703064	−	0.711127i	$-0.748185\pi$
$173$	3.47661	−	6.02167i	0.264322	−	0.457819i	0.967386	+	0.253308i	$0.0815185\pi$
$174$		0			0
$175$	−2.20765	−	0.567717i	−0.166883	−	0.0429154i
$176$		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	−0.0655141	−	0.997852i	$-0.520869\pi$
$191$	11.4903	−	19.9018i	0.831408	−	1.44004i	0.896922	−	0.442189i	$-0.145798\pi$
$192$		0			0
$193$	−2.68715	−	4.65427i	−0.193425	−	0.335022i	0.752958	−	0.658068i	$-0.228626\pi$
$193$	−2.68715	−	4.65427i	−0.193425	−	0.335022i	−0.946383	+	0.323047i	$0.895293\pi$
$194$		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
$203$	8.71053	−	8.88819i	0.611360	−	0.623829i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.03310			−0.417318
$210$		0			0
$211$	19.1111			1.31566			0.657831	−	0.753166i	$-0.271474\pi$
$211$	19.1111			1.31566			0.657831	+	0.753166i	$0.271474\pi$
$212$		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
$223$	24.2632			1.62478			0.812392	−	0.583112i	$-0.198165\pi$
$223$	24.2632			1.62478			0.812392	+	0.583112i	$0.198165\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.92395	+	3.33237i	0.127697	+	0.221177i	0.922784	−	0.385318i	$-0.125908\pi$
$227$	1.92395	+	3.33237i	0.127697	+	0.221177i	−0.795087	+	0.606495i	$0.792575\pi$
$228$		0			0
$229$	−1.76608	+	3.05894i	−0.116706	+	0.202140i	−0.918460	−	0.395513i	$-0.870567\pi$
$229$	−1.76608	+	3.05894i	−0.116706	+	0.202140i	0.801755	+	0.597653i	$0.203900\pi$
$230$		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
$239$	−8.28263			−0.535759			−0.267879	−	0.963452i	$-0.586323\pi$
$239$	−8.28263			−0.535759			−0.267879	+	0.963452i	$0.586323\pi$
$240$		0			0
$241$	−6.76320	−	11.7142i	−0.435656	−	0.754578i	0.561693	−	0.827346i	$-0.310150\pi$
$241$	−6.76320	−	11.7142i	−0.435656	−	0.754578i	−0.997349	+	0.0727675i	$0.976817\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	14.8450	+	8.17571i	0.948413	+	0.522327i
$246$		0			0
$247$	2.19398	−	3.80009i	0.139600	−	0.241794i
$248$		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
$257$	−8.04583	+	13.9358i	−0.501885	+	0.869290i	0.498113	+	0.867112i	$0.334027\pi$
$257$	−8.04583	+	13.9358i	−0.501885	+	0.869290i	−0.999998	+	0.00217808i	$0.999307\pi$
$258$		0			0
$259$	6.07210	+	21.7795i	0.377302	+	1.35331i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.35868	+	11.0136i	0.392093	+	0.679126i	0.992725	−	0.120400i	$-0.0384177\pi$
$263$	6.35868	+	11.0136i	0.392093	+	0.679126i	−0.600632	+	0.799525i	$0.705084\pi$
$264$		0			0
$265$	−24.8479			−1.52639
$266$		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
$275$	2.02627	−	3.50960i	0.122188	−	0.211637i
$276$		0			0
$277$	−11.7729	−	20.3913i	−0.707366	−	1.22519i	−0.965831	−	0.259173i	$-0.916550\pi$
$277$	−11.7729	−	20.3913i	−0.707366	−	1.22519i	0.258465	−	0.966021i	$-0.416783\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.55950			0.331652			0.165826	−	0.986155i	$-0.446971\pi$
$281$	5.55950			0.331652			0.165826	+	0.986155i	$0.446971\pi$
$282$		0			0
$283$	6.97661	+	12.0838i	0.414717	+	0.718310i	0.995399	−	0.0958203i	$-0.0305474\pi$
$283$	6.97661	+	12.0838i	0.414717	+	0.718310i	−0.580682	+	0.814130i	$0.697214\pi$
$284$		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
$293$	−8.15211			−0.476251			−0.238126	−	0.971234i	$-0.576533\pi$
$293$	−8.15211			−0.476251			−0.238126	+	0.971234i	$0.576533\pi$
$294$		0			0
$295$	−9.98633			−0.581426
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.92395	−	3.33237i	0.111265	−	0.192716i
$300$		0			0
$301$	10.2700	−	10.4795i	0.591955	−	0.604028i
$302$		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	0.977793	−	0.209573i	$-0.0672075\pi$
$311$	5.42107	+	9.38956i	0.307400	+	0.532433i	−0.670392	+	0.742007i	$0.733874\pi$
$312$		0			0
$313$	−16.1706	+	28.0083i	−0.914016	+	1.58312i	−0.105680	+	0.994400i	$0.533702\pi$
$313$	−16.1706	+	28.0083i	−0.914016	+	1.58312i	−0.808336	+	0.588722i	$0.799631\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.9601	+	18.9834i	−0.615578	+	1.06621i	0.374704	+	0.927144i	$0.377744\pi$
$317$	−10.9601	+	18.9834i	−0.615578	+	1.06621i	−0.990283	+	0.139069i	$0.955589\pi$
$318$		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
$329$	8.40451	+	30.1455i	0.463356	+	1.66198i
$330$		0			0
$331$	−6.19686	+	10.7333i	−0.340610	+	0.589954i	−0.984546	−	0.175125i	$-0.943967\pi$
$331$	−6.19686	+	10.7333i	−0.340610	+	0.589954i	0.643936	+	0.765079i	$0.277300\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−26.9338			−1.47155
$336$		0			0
$337$	7.73104			0.421137			0.210568	−	0.977579i	$-0.432469\pi$
$337$	7.73104			0.421137			0.210568	+	0.977579i	$0.432469\pi$
$338$		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	0.944110	+	0.329630i	$0.106924\pi$
$347$	14.1111	+	24.4411i	0.757523	+	1.31207i	−0.186587	+	0.982438i	$0.559743\pi$
$348$		0			0
$349$	−1.23585			−0.0661537			−0.0330769	−	0.999453i	$-0.510531\pi$
$349$	−1.23585			−0.0661537			−0.0330769	+	0.999453i	$0.510531\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.46006	+	16.3853i	0.503508	+	0.872102i	0.999992	+	0.00405566i	$0.00129096\pi$
$353$	9.46006	+	16.3853i	0.503508	+	0.872102i	−0.496484	+	0.868046i	$0.665376\pi$
$354$		0			0
$355$	18.1179	−	31.3812i	0.961600	−	1.66554i
$356$		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
$365$	5.17730			0.270992
$366$		0			0
$367$	7.11109	+	12.3168i	0.371196	+	0.642930i	0.989750	−	0.142812i	$-0.0456145\pi$
$367$	7.11109	+	12.3168i	0.371196	+	0.642930i	−0.618554	+	0.785742i	$0.712281\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	26.2982	+	6.76282i	1.36534	+	0.351108i
$372$		0			0
$373$	−11.8421	+	20.5112i	−0.613162	+	1.06203i	0.377542	+	0.925993i	$0.376770\pi$
$373$	−11.8421	+	20.5112i	−0.613162	+	1.06203i	−0.990704	+	0.136036i	$0.956564\pi$
$374$		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
$383$	2.20082	−	3.81193i	0.112457	−	0.194780i	−0.804304	−	0.594219i	$-0.797461\pi$
$383$	2.20082	−	3.81193i	0.112457	−	0.194780i	0.916760	+	0.399438i	$0.130795\pi$
$384$		0			0
$385$	−21.0888	+	21.5189i	−1.07478	+	1.09670i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.65499	−	2.86652i	−0.0839112	−	0.145339i	0.821016	−	0.570906i	$-0.193408\pi$
$389$	−1.65499	−	2.86652i	−0.0839112	−	0.145339i	−0.904927	+	0.425567i	$0.860075\pi$
$390$		0			0
$391$	−1.91626			−0.0969092
$392$		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
$401$	0.293425	−	0.508226i	0.0146529	−	0.0253796i	−0.858606	−	0.512636i	$-0.828669\pi$
$401$	0.293425	−	0.508226i	0.0146529	−	0.0253796i	0.873259	+	0.487257i	$0.162002\pi$
$402$		0			0
$403$	−5.85185	−	10.1357i	−0.291501	−	0.504895i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−40.1970			−1.99249
$408$		0			0
$409$	−14.5156	−	25.1418i	−0.717750	−	1.24318i	−0.961889	−	0.273440i	$-0.911839\pi$
$409$	−14.5156	−	25.1418i	−0.717750	−	1.24318i	0.244139	−	0.969740i	$-0.421495\pi$
$410$		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
$419$	23.1833			1.13258			0.566290	−	0.824206i	$-0.308378\pi$
$419$	23.1833			1.13258			0.566290	+	0.824206i	$0.308378\pi$
$420$		0			0
$421$	−29.0586			−1.41623			−0.708114	−	0.706098i	$-0.750454\pi$
$421$	−29.0586			−1.41623			−0.708114	+	0.706098i	$0.750454\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.733922	−	1.27119i	0.0356004	−	0.0616617i
$426$		0			0
$427$	−6.57210	−	23.5729i	−0.318046	−	1.14077i
$428$		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	−0.998556	−	0.0537171i	$-0.982893\pi$
$439$	−9.48633	+	16.4308i	−0.452758	+	0.784199i	0.545799	+	0.837916i	$0.316226\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.6345	−	18.4195i	0.505259	−	0.875135i	−0.494722	−	0.869051i	$-0.664730\pi$
$443$	10.6345	−	18.4195i	0.505259	−	0.875135i	0.999981	−	0.00608363i	$-0.00193649\pi$
$444$		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
$455$	−5.88508	−	21.1088i	−0.275897	−	0.989594i
$456$		0			0
$457$	5.73392	−	9.93144i	0.268222	−	0.464573i	−0.700181	−	0.713965i	$-0.746897\pi$
$457$	5.73392	−	9.93144i	0.268222	−	0.464573i	0.968403	+	0.249392i	$0.0802307\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.40164			0.344729			0.172364	−	0.985033i	$-0.444859\pi$
$461$	7.40164			0.344729			0.172364	+	0.985033i	$0.444859\pi$
$462$		0			0
$463$	5.68427			0.264170			0.132085	−	0.991238i	$-0.457833\pi$
$463$	5.68427			0.264170			0.132085	+	0.991238i	$0.457833\pi$
$464$		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
$475$	1.10507			0.0507040
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.11793	−	10.5966i	−0.279535	−	0.484169i	0.691734	−	0.722152i	$-0.256847\pi$
$479$	−6.11793	−	10.5966i	−0.279535	−	0.484169i	−0.971269	+	0.237983i	$0.923514\pi$
$480$		0			0
$481$	14.6179	−	25.3190i	0.666520	−	1.15445i
$482$		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
$491$	9.20275			0.415314			0.207657	−	0.978202i	$-0.433416\pi$
$491$	9.20275			0.415314			0.207657	+	0.978202i	$0.433416\pi$
$492$		0			0
$493$	4.00684	+	6.94004i	0.180459	+	0.312564i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−27.7164	+	28.2817i	−1.24325	+	1.26861i
$498$		0			0
$499$	−9.83242	+	17.0302i	−0.440159	+	0.762379i	−0.997701	−	0.0677705i	$-0.978411\pi$
$499$	−9.83242	+	17.0302i	−0.440159	+	0.762379i	0.557541	+	0.830149i	$0.311745\pi$
$500$		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
$509$	1.77292	−	3.07078i	0.0785831	−	0.136110i	−0.824056	−	0.566509i	$-0.808294\pi$
$509$	1.77292	−	3.07078i	0.0785831	−	0.136110i	0.902639	+	0.430399i	$0.141627\pi$
$510$		0			0
$511$	−5.47949	−	1.40910i	−0.242398	−	0.0623348i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.47373	+	14.6769i	0.373397	+	0.646743i
$516$		0			0
$517$	−55.6375			−2.44693
$518$		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
$527$	−2.91423	+	5.04759i	−0.126946	+	0.219877i
$528$		0			0
$529$	10.8675	+	18.8230i	0.472498	+	0.818391i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.7174			0.550850
$534$		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
$545$	−17.9338			−0.768199
$546$		0			0
$547$	−20.4016			−0.872311			−0.436155	−	0.899871i	$-0.643660\pi$
$547$	−20.4016			−0.872311			−0.436155	+	0.899871i	$0.643660\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.01655	+	5.22482i	−0.128509	+	0.222585i
$552$		0			0
$553$	−10.3256	−	37.0360i	−0.439088	−	1.57493i
$554$		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	0.916369	−	0.400334i	$-0.131106\pi$
$563$	2.64527	+	4.58175i	0.111485	+	0.193098i	−0.804884	+	0.593432i	$0.797773\pi$
$564$		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	−0.876926	−	0.480626i	$-0.840409\pi$
$569$	−0.530225	+	0.918376i	−0.0222282	+	0.0385003i	0.854697	+	0.519127i	$0.173743\pi$
$570$		0			0
$571$	14.5498	+	25.2010i	0.608890	+	1.05463i	0.991424	+	0.130686i	$0.0417181\pi$
$571$	14.5498	+	25.2010i	0.608890	+	1.05463i	−0.382534	+	0.923941i	$0.624949\pi$
$572$		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
$581$	−15.5945	+	15.9126i	−0.646970	+	0.660166i
$582$		0			0
$583$	−24.1375	+	41.8074i	−0.999673	+	1.73148i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	25.9727			1.07201			0.536003	−	0.844216i	$-0.319934\pi$
$587$	25.9727			1.07201			0.536003	+	0.844216i	$0.319934\pi$
$588$		0			0
$589$	−4.38796			−0.180803
$590$		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	0.513906	−	0.857847i	$-0.328198\pi$
$599$	−11.8937	−	20.6005i	−0.485964	−	0.841715i	−0.999870	+	0.0161320i	$0.994865\pi$
$600$		0			0
$601$	−7.92012			−0.323068			−0.161534	−	0.986867i	$-0.551644\pi$
$601$	−7.92012			−0.323068			−0.161534	+	0.986867i	$0.551644\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−13.4669	−	23.3253i	−0.547507	−	0.948310i
$606$		0			0
$607$	0.0233882	−	0.0405096i	0.000949298	−	0.00164423i	−0.865550	−	0.500822i	$-0.833031\pi$
$607$	0.0233882	−	0.0405096i	0.000949298	−	0.00164423i	0.866500	+	0.499178i	$0.166364\pi$
$608$		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
$617$	−34.4328			−1.38621			−0.693107	−	0.720835i	$-0.743759\pi$
$617$	−34.4328			−1.38621			−0.693107	+	0.720835i	$0.743759\pi$
$618$		0			0
$619$	−23.7564	−	41.1472i	−0.954849	−	1.65385i	−0.734714	−	0.678377i	$-0.762683\pi$
$619$	−23.7564	−	41.1472i	−0.954849	−	1.65385i	−0.220135	−	0.975469i	$-0.570650\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−11.4337	−	41.0105i	−0.458080	−	1.64305i
$624$		0			0
$625$	14.2828	−	24.7385i	0.571311	−	0.989539i
$626$		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
$635$	13.9601	−	24.1795i	0.553988	−	0.959536i
$636$		0			0
$637$	0.483448	+	23.9426i	0.0191549	+	0.948640i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.55267	−	2.68930i	−0.0613266	−	0.106221i	0.833732	−	0.552169i	$-0.186200\pi$
$641$	−1.55267	−	2.68930i	−0.0613266	−	0.106221i	−0.895059	+	0.445948i	$0.852866\pi$
$642$		0			0
$643$	−17.7368			−0.699471			−0.349736	−	0.936848i	$-0.613729\pi$
$643$	−17.7368			−0.699471			−0.349736	+	0.936848i	$0.613729\pi$
$644$		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
$653$	4.60138	−	7.96982i	0.180066	−	0.311883i	−0.761837	−	0.647769i	$-0.775702\pi$
$653$	4.60138	−	7.96982i	0.180066	−	0.311883i	0.941903	+	0.335886i	$0.109036\pi$
$654$		0			0
$655$	−11.0624	−	19.1606i	−0.432243	−	0.748667i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	49.3997			1.92434			0.962170	−	0.272448i	$-0.0878334\pi$
$659$	49.3997			1.92434			0.962170	+	0.272448i	$0.0878334\pi$
$660$		0			0
$661$	24.9922	+	43.2878i	0.972085	+	1.68370i	0.689238	+	0.724535i	$0.257945\pi$
$661$	24.9922	+	43.2878i	0.972085	+	1.68370i	0.282846	+	0.959165i	$0.408721\pi$
$662$		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
$671$	43.5070			1.67957
$672$		0			0
$673$	9.43474			0.363682			0.181841	−	0.983328i	$-0.441794\pi$
$673$	9.43474			0.363682			0.181841	+	0.983328i	$0.441794\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.8937	+	20.6005i	−0.457113	+	0.791743i	−0.998807	−	0.0488331i	$-0.984450\pi$
$677$	−11.8937	+	20.6005i	−0.457113	+	0.791743i	0.541694	+	0.840576i	$0.317783\pi$
$678$		0			0
$679$	30.0917	−	30.7054i	1.15481	−	1.17837i
$680$		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	0.290756	+	0.956797i	$0.406093\pi$
$691$	−17.9601	+	31.1077i	−0.683233	+	1.18339i	−0.973989	+	0.226597i	$0.927240\pi$
$692$		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
$707$	−33.2759	−	8.55719i	−1.25147	−	0.321826i
$708$		0			0
$709$	12.0555	−	20.8808i	0.452756	−	0.784196i	−0.545801	−	0.837915i	$-0.683774\pi$
$709$	12.0555	−	20.8808i	0.452756	−	0.784196i	0.998556	+	0.0537196i	$0.0171077\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.84789			−0.144105
$714$		0			0
$715$	38.9590			1.45698
$716$		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
$727$	47.5127			1.76215			0.881075	−	0.472977i	$-0.156821\pi$
$727$	47.5127			1.76215			0.881075	+	0.472977i	$0.156821\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.72421	+	8.18257i	0.174731	+	0.302643i
$732$		0			0
$733$	15.4182	−	26.7051i	0.569484	−	0.986375i	−0.427133	−	0.904189i	$-0.640476\pi$
$733$	15.4182	−	26.7051i	0.569484	−	0.986375i	0.996617	−	0.0821861i	$-0.0261902\pi$
$734$		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
$743$	−45.3743			−1.66462			−0.832311	−	0.554309i	$-0.812982\pi$
$743$	−45.3743			−1.66462			−0.832311	+	0.554309i	$0.812982\pi$
$744$		0			0
$745$	29.5059	+	51.1057i	1.08101	+	1.87237i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−9.03611	−	32.4109i	−0.330172	−	1.18427i
$750$		0			0
$751$	−6.42107	+	11.1216i	−0.234308	+	0.405833i	−0.959071	−	0.283164i	$-0.908616\pi$
$751$	−6.42107	+	11.1216i	−0.234308	+	0.405833i	0.724763	+	0.688998i	$0.241949\pi$
$752$		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
$761$	20.7466	−	35.9342i	0.752065	−	1.30262i	−0.194755	−	0.980852i	$-0.562391\pi$
$761$	20.7466	−	35.9342i	0.752065	−	1.30262i	0.946820	−	0.321764i	$-0.104276\pi$
$762$		0			0
$763$	18.9806	+	4.88102i	0.687143	+	0.176705i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.05555	−	12.2206i	−0.254761	−	0.441259i
$768$		0			0
$769$	−24.6900			−0.890345			−0.445173	−	0.895445i	$-0.646858\pi$
$769$	−24.6900			−0.890345			−0.445173	+	0.895445i	$0.646858\pi$
$770$		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
$779$	2.38401	−	4.12922i	0.0854159	−	0.147945i
$780$		0			0
$781$	−35.1999	−	60.9680i	−1.25955	−	2.18161i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	7.90042			0.281978
$786$		0			0
$787$	−9.01273	−	15.6105i	−0.321269	−	0.556454i	0.659481	−	0.751721i	$-0.270776\pi$
$787$	−9.01273	−	15.6105i	−0.321269	−	0.556454i	−0.980750	+	0.195267i	$0.937443\pi$
$788$		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
$797$	−39.8791			−1.41259			−0.706295	−	0.707918i	$-0.749635\pi$
$797$	−39.8791			−1.41259			−0.706295	+	0.707918i	$0.749635\pi$
$798$		0			0
$799$	−20.1521			−0.712930
$800$		0			0
$801$		0			0
$802$		0			0
$803$	5.02928	−	8.71097i	0.177479	−	0.307403i
$804$		0			0
$805$	−6.97769	−	1.79437i	−0.245931	−	0.0632434i
$806$		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	−0.129187	+	0.991620i	$0.541237\pi$
$821$	−26.4572	+	45.8252i	−0.923362	+	1.59931i	−0.794175	+	0.607690i	$0.792096\pi$
$822$		0			0
$823$	15.6179	+	27.0510i	0.544407	+	0.942940i	0.998644	+	0.0520593i	$0.0165785\pi$
$823$	15.6179	+	27.0510i	0.544407	+	0.942940i	−0.454237	+	0.890881i	$0.650088\pi$
$824$		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
$833$	10.2056	−	6.17023i	0.353604	−	0.213786i
$834$		0			0
$835$	29.3383	−	50.8154i	1.01529	−	1.75854i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	19.5401			0.674598			0.337299	−	0.941398i	$-0.390487\pi$
$839$	19.5401			0.674598			0.337299	+	0.941398i	$0.390487\pi$
$840$		0			0
$841$	−6.87524			−0.237077
$842$		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
$853$	17.3743			0.594884			0.297442	−	0.954740i	$-0.403866\pi$
$853$	17.3743			0.594884			0.297442	+	0.954740i	$0.403866\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−10.7729	−	18.6592i	−0.367996	−	0.637387i	0.621256	−	0.783607i	$-0.286623\pi$
$857$	−10.7729	−	18.6592i	−0.367996	−	0.637387i	−0.989252	+	0.146220i	$0.953289\pi$
$858$		0			0
$859$	−8.68715	+	15.0466i	−0.296402	+	0.513383i	−0.975310	−	0.220840i	$-0.929120\pi$
$859$	−8.68715	+	15.0466i	−0.296402	+	0.513383i	0.678908	+	0.734223i	$0.262453\pi$
$860$		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
$869$	68.3549			2.31878
$870$		0			0
$871$	−19.0293	−	32.9597i	−0.644782	−	1.11680i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−18.5545	+	18.9329i	−0.627255	+	0.640049i
$876$		0			0
$877$	−23.4991	+	40.7016i	−0.793507	+	1.37439i	0.130276	+	0.991478i	$0.458414\pi$
$877$	−23.4991	+	40.7016i	−0.793507	+	1.37439i	−0.923783	+	0.382916i	$0.874920\pi$
$878$		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
$887$	1.43474	−	2.48504i	0.0481738	−	0.0834395i	−0.840933	−	0.541139i	$-0.817993\pi$
$887$	1.43474	−	2.48504i	0.0481738	−	0.0834395i	0.889107	+	0.457700i	$0.151327\pi$
$888$		0			0
$889$	−21.3558	+	21.7914i	−0.716251	+	0.730859i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−7.58577	−	13.1389i	−0.253848	−	0.439678i
$894$		0			0
$895$	−35.5847			−1.18947
$896$		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
$905$	−20.7066	+	35.8648i	−0.688310	+	1.19219i
$906$		0			0
$907$	16.2164	+	28.0877i	0.538458	+	0.932636i	0.998987	+	0.0449915i	$0.0143261\pi$
$907$	16.2164	+	28.0877i	0.538458	+	0.932636i	−0.460530	+	0.887644i	$0.652341\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−33.2438			−1.10142			−0.550708	−	0.834698i	$-0.685642\pi$
$911$	−33.2438			−1.10142			−0.550708	+	0.834698i	$0.685642\pi$
$912$		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
$923$	51.2028			1.68536
$924$		0			0
$925$	7.36278			0.242087
$926$		0			0
$927$		0			0
$928$		0			0
$929$	27.2729	−	47.2381i	0.894795	−	1.54983i	0.0607376	−	0.998154i	$-0.480655\pi$
$929$	27.2729	−	47.2381i	0.894795	−	1.54983i	0.834058	−	0.551677i	$-0.186012\pi$
$930$		0			0
$931$	7.86458	+	4.33132i	0.257751	+	0.141953i
$932$		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	0.979336	−	0.202242i	$-0.0648229\pi$
$941$	9.64815	+	16.7111i	0.314521	+	0.544766i	−0.664815	+	0.747008i	$0.731490\pi$
$942$		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	−0.938813	−	0.344426i	$-0.888073\pi$
$947$	−5.26608	+	9.12112i	−0.171125	+	0.296396i	0.767689	+	0.640823i	$0.221407\pi$
$948$		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
$959$	−5.76415	−	1.48230i	−0.186134	−	0.0478660i
$960$		0			0
$961$	9.64815	−	16.7111i	0.311231	−	0.539067i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	13.0115			0.418855
$966$		0			0
$967$	−15.4854			−0.497976			−0.248988	−	0.968507i	$-0.580098\pi$
$967$	−15.4854			−0.497976			−0.248988	+	0.968507i	$0.580098\pi$
$968$		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	0.991854	+	0.127379i	$0.0406565\pi$
$977$	18.9493	+	32.8211i	0.606241	+	1.05004i	−0.385613	+	0.922660i	$0.626010\pi$
$978$		0			0
$979$	75.6903			2.41907
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.0555	+	33.0052i	0.607778	+	1.05270i	0.991606	+	0.129297i	$0.0412721\pi$
$983$	19.0555	+	33.0052i	0.607778	+	1.05270i	−0.383828	+	0.923404i	$0.625395\pi$
$984$		0			0
$985$	−4.33242	+	7.50397i	−0.138042	+	0.239096i
$986$		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
$995$	−16.9475			−0.537271
$996$		0			0
$997$	−7.40344	−	12.8231i	−0.234469	−	0.406112i	0.724649	−	0.689118i	$-0.242002\pi$
$997$	−7.40344	−	12.8231i	−0.234469	−	0.406112i	−0.959118	+	0.283006i	$0.908669\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.k.e.109.3	✓	6	21.11	odd	6
756.2.k.e.541.3	yes	6	3.2	odd	2
756.2.k.f.109.1	yes	6	7.4	even	3	inner
756.2.k.f.541.1	yes	6	1.1	even	1	trivial
2268.2.i.j.865.3		6	63.32	odd	6
2268.2.i.j.2053.3		6	9.2	odd	6
2268.2.i.k.865.1		6	63.4	even	3
2268.2.i.k.2053.1		6	9.7	even	3
2268.2.l.j.109.3		6	63.25	even	3
2268.2.l.j.541.3		6	9.4	even	3
2268.2.l.k.109.1		6	63.11	odd	6
2268.2.l.k.541.1		6	9.5	odd	6
5292.2.a.u.1.3		3	7.2	even	3
5292.2.a.v.1.3		3	21.5	even	6
5292.2.a.w.1.1		3	7.5	odd	6
5292.2.a.x.1.1		3	21.2	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21053 + 2.09671i) q^{5} +(1.85185 - 1.88962i) q^{7} +O(q^{10})\)	\(q+(-1.21053 + 2.09671i) q^{5} +(1.85185 - 1.88962i) q^{7} +(2.35185 + 4.07352i) q^{11} -3.42107 q^{13} +(0.851848 + 1.47544i) q^{17} +(-0.641315 + 1.11079i) q^{19} +(-0.562382 + 0.974074i) q^{23} +(-0.430782 - 0.746136i) q^{25} +4.70370 q^{29} +(1.71053 + 2.96273i) q^{31} +(1.72025 + 6.17023i) q^{35} +(-4.27292 + 7.40091i) q^{37} -3.71737 q^{41} +5.54583 q^{43} +(-5.91423 + 10.2437i) q^{47} +(-0.141315 - 6.99857i) q^{49} +(5.13160 + 8.88819i) q^{53} -11.3880 q^{55} +(2.06238 + 3.57215i) q^{59} +(4.62476 - 8.01033i) q^{61} +(4.14132 - 7.17297i) q^{65} +(5.56238 + 9.63433i) q^{67} -14.9669 q^{71} +(-1.06922 - 1.85194i) q^{73} +(12.0527 + 3.09945i) q^{77} +(7.26608 - 12.5852i) q^{79} -8.42107 q^{83} -4.12476 q^{85} +(8.04583 - 13.9358i) q^{89} +(-6.33530 + 6.46451i) q^{91} +(-1.55267 - 2.68930i) q^{95} +16.2495 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5} + 2 q^{7}+O(q^{10}) \) 6 * q + q^5 + 2 * q^7	\( 6 q + q^{5} + 2 q^{7} + 5 q^{11} - 4 q^{13} - 4 q^{17} - 3 q^{19} + 14 q^{23} - 10 q^{25} + 10 q^{29} + 2 q^{31} + 26 q^{35} - 24 q^{41} - 18 q^{43} - 9 q^{47} + 6 q^{53} + 16 q^{55} - 5 q^{59} - 7 q^{61} + 24 q^{65} + 16 q^{67} - 22 q^{71} + q^{73} + 31 q^{77} + 8 q^{79} - 34 q^{83} + 10 q^{85} - 3 q^{89} + 5 q^{91} + 32 q^{95} + 28 q^{97}+O(q^{100}) \) 6 * q + q^5 + 2 * q^7 + 5 * q^11 - 4 * q^13 - 4 * q^17 - 3 * q^19 + 14 * q^23 - 10 * q^25 + 10 * q^29 + 2 * q^31 + 26 * q^35 - 24 * q^41 - 18 * q^43 - 9 * q^47 + 6 * q^53 + 16 * q^55 - 5 * q^59 - 7 * q^61 + 24 * q^65 + 16 * q^67 - 22 * q^71 + q^73 + 31 * q^77 + 8 * q^79 - 34 * q^83 + 10 * q^85 - 3 * q^89 + 5 * q^91 + 32 * q^95 + 28 * q^97

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