LMFDB - Embedded newform 2268.2.i.k.865.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(865,2268)]

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, 4, 4]))

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

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

chi := DirichletCharacter("2268.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.i (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			865.1
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	2268.865
Dual form			2268.2.i.k.2053.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21053 + 2.09671i) q^{5} +(-2.56238 + 0.658939i) q^{7} +O(q^{10})$	$q+(-1.21053 + 2.09671i) q^{5} +(-2.56238 + 0.658939i) q^{7} +(2.35185 + 4.07352i) q^{11} +(1.71053 + 2.96273i) q^{13} +(0.851848 - 1.47544i) q^{17} +(-0.641315 - 1.11079i) q^{19} +(-0.562382 + 0.974074i) q^{23} +(-0.430782 - 0.746136i) q^{25} +(-2.35185 + 4.07352i) q^{29} -3.42107 q^{31} +(1.72025 - 6.17023i) q^{35} +(-4.27292 - 7.40091i) q^{37} +(1.85868 + 3.21934i) q^{41} +(-2.77292 + 4.80283i) q^{43} +11.8285 q^{47} +(6.13160 - 3.37690i) q^{49} +(5.13160 - 8.88819i) q^{53} -11.3880 q^{55} -4.12476 q^{59} -9.24953 q^{61} -8.28263 q^{65} -11.1248 q^{67} -14.9669 q^{71} +(-1.06922 + 1.85194i) q^{73} +(-8.71053 - 8.88819i) q^{77} -14.5322 q^{79} +(4.21053 - 7.29286i) q^{83} +(2.06238 + 3.57215i) q^{85} +(8.04583 + 13.9358i) q^{89} +(-6.33530 - 6.46451i) q^{91} +3.10533 q^{95} +(-8.12476 + 14.0725i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 2 q^{13} - 4 q^{17} - 3 q^{19} + 14 q^{23} - 10 q^{25} - 5 q^{29} - 4 q^{31} + 26 q^{35} + 12 q^{41} + 9 q^{43} + 18 q^{47} + 12 q^{49} + 6 q^{53} + 16 q^{55} + 10 q^{59} + 14 q^{61} - 48 q^{65} - 32 q^{67} - 22 q^{71} + q^{73} - 44 q^{77} - 16 q^{79} + 17 q^{83} - 5 q^{85} - 3 q^{89} + 5 q^{91} - 64 q^{95} - 14 q^{97}+O(q^{100}) $ 6 * q + q^5 + 2 * q^7 + 5 * q^11 + 2 * q^13 - 4 * q^17 - 3 * q^19 + 14 * q^23 - 10 * q^25 - 5 * q^29 - 4 * q^31 + 26 * q^35 + 12 * q^41 + 9 * q^43 + 18 * q^47 + 12 * q^49 + 6 * q^53 + 16 * q^55 + 10 * q^59 + 14 * q^61 - 48 * q^65 - 32 * q^67 - 22 * q^71 + q^73 - 44 * q^77 - 16 * q^79 + 17 * q^83 - 5 * q^85 - 3 * q^89 + 5 * q^91 - 64 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−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
$7$	−2.56238	+	0.658939i	−0.968489	+	0.249055i
$7$	−2.56238	+	0.658939i	−0.968489	+	0.249055i
$8$		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
$13$	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	−0.744039	−	0.668136i	$-0.767092\pi$
$17$	0.851848	−	1.47544i	0.206604	−	0.357848i	0.950642	+	0.310288i	$0.100426\pi$
$18$		0			0
$19$	−0.641315	−	1.11079i	−0.147128	−	0.254833i	0.783037	−	0.621975i	$-0.213670\pi$
$19$	−0.641315	−	1.11079i	−0.147128	−	0.254833i	−0.930165	+	0.367142i	$0.880336\pi$
$20$		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
$29$	−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
$31$	−3.42107			−0.614442			−0.307221	−	0.951638i	$-0.599399\pi$
$31$	−3.42107			−0.614442			−0.307221	+	0.951638i	$0.599399\pi$
$32$		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	−0.967599	−	0.252491i	$-0.918750\pi$
$37$	−4.27292	−	7.40091i	−0.702463	−	1.21670i	0.265136	−	0.964211i	$-0.414583\pi$
$38$		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
$47$	11.8285			1.72536			0.862679	−	0.505752i	$-0.168785\pi$
$47$	11.8285			1.72536			0.862679	+	0.505752i	$0.168785\pi$
$48$		0			0
$49$	6.13160	−	3.37690i	0.875943	−	0.482415i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.13160	−	8.88819i	0.704879	−	1.22089i	−0.261856	−	0.965107i	$-0.584334\pi$
$53$	5.13160	−	8.88819i	0.704879	−	1.22089i	0.966735	−	0.255780i	$-0.0823323\pi$
$54$		0			0
$55$	−11.3880			−1.53555
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.12476			−0.536998			−0.268499	−	0.963280i	$-0.586528\pi$
$59$	−4.12476			−0.536998			−0.268499	+	0.963280i	$0.586528\pi$
$60$		0			0
$61$	−9.24953			−1.18428			−0.592140	−	0.805835i	$-0.701717\pi$
$61$	−9.24953			−1.18428			−0.592140	+	0.805835i	$0.701717\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.28263			−1.02733
$66$		0			0
$67$	−11.1248			−1.35911			−0.679553	−	0.733626i	$-0.737826\pi$
$67$	−11.1248			−1.35911			−0.679553	+	0.733626i	$0.737826\pi$
$68$		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	−0.921789	−	0.387693i	$-0.873272\pi$
$73$	−1.06922	+	1.85194i	−0.125143	+	0.216753i	0.796646	+	0.604446i	$0.206605\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.71053	−	8.88819i	−0.992657	−	1.01290i
$78$		0			0
$79$	−14.5322			−1.63500			−0.817498	−	0.575932i	$-0.804639\pi$
$79$	−14.5322			−1.63500			−0.817498	+	0.575932i	$0.804639\pi$
$80$		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	0.878620	+	0.477522i	$0.158465\pi$
$89$	8.04583	+	13.9358i	0.852856	+	1.47719i	−0.0257633	+	0.999668i	$0.508202\pi$
$90$		0			0
$91$	−6.33530	−	6.46451i	−0.664120	−	0.677665i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.10533			0.318600
$96$		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
$101$	−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	0.990434	+	0.137987i	$0.0440632\pi$
$107$	6.35868	+	11.0136i	0.614717	+	1.06472i	−0.375717	+	0.926735i	$0.622603\pi$
$108$		0			0
$109$	3.70370	−	6.41499i	0.354750	−	0.614445i	−0.632325	−	0.774703i	$-0.717899\pi$
$109$	3.70370	−	6.41499i	0.354750	−	0.614445i	0.987075	+	0.160258i	$0.0512327\pi$
$110$		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
$115$	−1.36156	−	2.35830i	−0.126966	−	0.219912i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.21053	+	4.34197i	−0.110969	+	0.398028i
$120$		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
$133$	2.37524	+	2.42368i	0.205959	+	0.210160i
$134$		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
$139$	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
$149$	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
$155$	4.14132	−	7.17297i	0.332638	−	0.576147i
$156$		0			0
$157$	3.26320			0.260432			0.130216	−	0.991486i	$-0.458433\pi$
$157$	3.26320			0.260432			0.130216	+	0.991486i	$0.458433\pi$
$158$		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	0.868989	−	0.494832i	$-0.164770\pi$
$163$	0.0760548	+	0.131731i	0.00595707	+	0.0103179i	−0.863032	+	0.505150i	$0.831437\pi$
$164$		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
$173$	−6.95322			−0.528644			−0.264322	−	0.964435i	$-0.585148\pi$
$173$	−6.95322			−0.528644			−0.264322	+	0.964435i	$0.585148\pi$
$174$		0			0
$175$	1.59549	+	1.62803i	0.120607	+	0.123067i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.34897	−	12.7288i	0.549288	−	0.951394i	−0.449036	−	0.893514i	$-0.648232\pi$
$179$	7.34897	−	12.7288i	0.549288	−	0.951394i	0.998324	−	0.0578806i	$-0.0184343\pi$
$180$		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
$185$	20.6900			1.52116
$186$		0			0
$187$	8.01367			0.586018
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−22.9806			−1.66282			−0.831408	−	0.555663i	$-0.812465\pi$
$191$	−22.9806			−1.66282			−0.831408	+	0.555663i	$0.812465\pi$
$192$		0			0
$193$	5.37429			0.386850			0.193425	−	0.981115i	$-0.438040\pi$
$193$	5.37429			0.386850			0.193425	+	0.981115i	$0.438040\pi$
$194$		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	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.34213	−	11.9876i	0.234572	−	0.841367i
$204$		0			0
$205$	−9.00000			−0.628587
$206$		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
$221$	5.82846			0.392065
$222$		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
$227$	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	0.942044	+	0.335488i	$0.108901\pi$
$233$	11.6248	+	20.1347i	0.761564	+	1.31907i	−0.180481	+	0.983579i	$0.557765\pi$
$234$		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
$241$	−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
$245$	−0.342133	+	16.9440i	−0.0218581	+	1.08251i
$246$		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
$259$	15.8256	+	16.1484i	0.983354	+	1.00341i
$260$		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
$265$	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	0.279003	+	0.960290i	$0.409996\pi$
$269$	−11.3518	+	19.6620i	−0.692134	+	1.19881i	−0.971137	+	0.238522i	$0.923337\pi$
$270$		0			0
$271$	−7.56238	−	13.0984i	−0.459382	−	0.795673i	0.539546	−	0.841956i	$-0.318596\pi$
$271$	−7.56238	−	13.0984i	−0.459382	−	0.795673i	−0.998928	+	0.0462830i	$0.985262\pi$
$272$		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
$281$	−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
$283$	−13.9532			−0.829433			−0.414717	−	0.909951i	$-0.636119\pi$
$283$	−13.9532			−0.829433			−0.414717	+	0.909951i	$0.636119\pi$
$284$		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
$299$	−3.84789			−0.222529
$300$		0			0
$301$	3.94050	−	14.1339i	0.227126	−	0.814662i
$302$		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
$311$	−10.8421			−0.614801			−0.307400	−	0.951580i	$-0.599459\pi$
$311$	−10.8421			−0.614801			−0.307400	+	0.951580i	$0.599459\pi$
$312$		0			0
$313$	32.3412			1.82803			0.914016	−	0.405678i	$-0.132965\pi$
$313$	32.3412			1.82803			0.914016	+	0.405678i	$0.132965\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.9201			1.23116			0.615578	−	0.788076i	$-0.288922\pi$
$317$	21.9201			1.23116			0.615578	+	0.788076i	$0.288922\pi$
$318$		0			0
$319$	−22.1248			−1.23875
$320$		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
$329$	−30.3090	+	7.79423i	−1.67099	+	0.429710i
$330$		0			0
$331$	12.3937			0.681220			0.340610	−	0.940205i	$-0.389366\pi$
$331$	12.3937			0.681220			0.340610	+	0.940205i	$0.389366\pi$
$332$		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
$347$	−28.2222			−1.51505			−0.757523	−	0.652808i	$-0.773591\pi$
$347$	−28.2222			−1.51505			−0.757523	+	0.652808i	$0.773591\pi$
$348$		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
$353$	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	0.979013	−	0.203795i	$-0.0653278\pi$
$359$	5.93078	+	10.2724i	0.313015	+	0.542157i	−0.665999	+	0.745953i	$0.731994\pi$
$360$		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
$367$	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
$371$	−7.29235	+	26.1563i	−0.378600	+	1.35797i
$372$		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
$385$	29.1803	−	7.50397i	1.48717	−	0.382438i
$386$		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
$391$	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	0.930669	+	0.365861i	$0.119226\pi$
$397$	15.5848	+	26.9937i	0.782180	+	1.35478i	−0.148490	+	0.988914i	$0.547441\pi$
$398$		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
$407$	20.0985	−	34.8116i	0.996245	−	1.72555i
$408$		0			0
$409$	29.0312			1.43550			0.717750	−	0.696300i	$-0.245172\pi$
$409$	29.0312			1.43550			0.717750	+	0.696300i	$0.245172\pi$
$410$		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
$425$	−1.46784			−0.0712008
$426$		0			0
$427$	23.7008	−	6.09487i	1.14696	−	0.294951i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.990285	+	1.71522i	−0.0477003	+	0.0826194i	−0.888890	−	0.458121i	$-0.848523\pi$
$431$	−0.990285	+	1.71522i	−0.0477003	+	0.0826194i	0.841189	+	0.540741i	$0.181856\pi$
$432$		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
$437$	1.44266			0.0690116
$438$		0			0
$439$	18.9727			0.905515			0.452758	−	0.891634i	$-0.350440\pi$
$439$	18.9727			0.905515			0.452758	+	0.891634i	$0.350440\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−21.2690			−1.01052			−0.505259	−	0.862968i	$-0.668603\pi$
$443$	−21.2690			−1.01052			−0.505259	+	0.862968i	$0.668603\pi$
$444$		0			0
$445$	−38.9590			−1.84683
$446$		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
$455$	21.2233	−	5.45774i	0.994962	−	0.255863i
$456$		0			0
$457$	−11.4678			−0.536443			−0.268222	−	0.963357i	$-0.586436\pi$
$457$	−11.4678			−0.536443			−0.268222	+	0.963357i	$0.586436\pi$
$458$		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	−0.995029	−	0.0995815i	$-0.968250\pi$
$467$	−12.6150	−	21.8499i	−0.583755	−	1.01109i	0.411275	−	0.911511i	$-0.365084\pi$
$468$		0			0
$469$	28.5059	−	7.33054i	1.31628	−	0.338493i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−26.0859			−1.19943
$474$		0			0
$475$	−0.552534	+	0.957016i	−0.0253520	+	0.0439109i
$476$		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	−0.790287	−	0.612737i	$-0.790068\pi$
$487$	2.99028	−	5.17933i	0.135503	−	0.234698i	0.925789	+	0.378040i	$0.123402\pi$
$488$		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
$493$	4.00684	+	6.94004i	0.180459	+	0.312564i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	38.3509	−	9.86227i	1.72027	−	0.442383i
$498$		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
$511$	1.51943	−	5.44993i	0.0672156	−	0.241091i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.47373	+	14.6769i	0.373397	+	0.646743i
$516$		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	−0.984533	−	0.175201i	$-0.943942\pi$
$521$	−7.77292	+	13.4631i	−0.340538	+	0.589828i	0.643995	+	0.765030i	$0.277276\pi$
$522$		0			0
$523$	15.6871	+	27.1709i	0.685951	+	1.18810i	0.973137	+	0.230227i	$0.0739469\pi$
$523$	15.6871	+	27.1709i	0.685951	+	1.18810i	−0.287186	+	0.957875i	$0.592720\pi$
$524$		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
$533$	−6.35868	+	11.0136i	−0.275425	+	0.477050i
$534$		0			0
$535$	−30.7896			−1.33115
$536$		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	0.908255	−	0.418416i	$-0.137415\pi$
$541$	2.13448	+	3.69703i	0.0917684	+	0.158948i	−0.816487	+	0.577364i	$0.804081\pi$
$542$		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
$551$	6.03310			0.257019
$552$		0			0
$553$	37.2369	−	9.57580i	1.58348	−	0.407204i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.7466	+	30.7381i	−0.751950	+	1.30241i	0.194927	+	0.980818i	$0.437553\pi$
$557$	−17.7466	+	30.7381i	−0.751950	+	1.30241i	−0.946877	+	0.321597i	$0.895780\pi$
$558$		0			0
$559$	−18.9727			−0.802458
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5.29055			−0.222970			−0.111485	−	0.993766i	$-0.535561\pi$
$563$	−5.29055			−0.222970			−0.111485	+	0.993766i	$0.535561\pi$
$564$		0			0
$565$	16.1831			0.680826
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.06045			0.0444564			0.0222282	−	0.999753i	$-0.492924\pi$
$569$	1.06045			0.0444564			0.0222282	+	0.999753i	$0.492924\pi$
$570$		0			0
$571$	−29.0996			−1.21778			−0.608890	−	0.793255i	$-0.708385\pi$
$571$	−29.0996			−1.21778			−0.608890	+	0.793255i	$0.708385\pi$
$572$		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	−0.852876	−	0.522113i	$-0.825144\pi$
$577$	0.617927	−	1.07028i	0.0257246	−	0.0445564i	0.878601	+	0.477556i	$0.158477\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.98345	+	21.4616i	−0.248235	+	0.890376i
$582$		0			0
$583$	48.2750			1.99935
$584$		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	0.964239	−	0.265035i	$-0.0853835\pi$
$593$	6.15103	+	10.6539i	0.252593	+	0.437503i	−0.711646	+	0.702538i	$0.752050\pi$
$594$		0			0
$595$	−7.63844	−	7.79423i	−0.313145	−	0.319532i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	23.7874			0.971928			0.485964	−	0.873979i	$-0.338469\pi$
$599$	23.7874			0.971928			0.485964	+	0.873979i	$0.338469\pi$
$600$		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
$605$	−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	−0.993759	−	0.111552i	$-0.964418\pi$
$613$	−9.91027	+	17.1651i	−0.400272	+	0.693292i	0.593486	+	0.804844i	$0.297751\pi$
$614$		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
$619$	−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
$623$	−29.7993	−	30.4071i	−1.19388	−	1.21823i
$624$		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
$637$	20.4932	+	12.3900i	0.811969	+	0.490909i
$638$		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
$643$	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	−0.874927	−	0.484255i	$-0.839091\pi$
$647$	−0.460060	+	0.796847i	−0.0180868	+	0.0313273i	0.856840	+	0.515582i	$0.172424\pi$
$648$		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
$659$	−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
$661$	−49.9844			−1.94417			−0.972085	−	0.234631i	$-0.924612\pi$
$661$	−49.9844			−1.94417			−0.972085	+	0.234631i	$0.924612\pi$
$662$		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
$677$	23.7874			0.914226			0.457113	−	0.889409i	$-0.348884\pi$
$677$	23.7874			0.914226			0.457113	+	0.889409i	$0.348884\pi$
$678$		0			0
$679$	11.5458	−	41.4128i	0.443088	−	1.58928i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−17.3187	+	29.9969i	−0.662683	+	1.14780i	0.317224	+	0.948350i	$0.397249\pi$
$683$	−17.3187	+	29.9969i	−0.662683	+	1.14780i	−0.979908	+	0.199451i	$0.936084\pi$
$684$		0			0
$685$	5.44625			0.208091
$686$		0			0
$687$		0			0
$688$		0			0
$689$	35.1111			1.33763
$690$		0			0
$691$	35.9201			1.36647			0.683233	−	0.730201i	$-0.260573\pi$
$691$	35.9201			1.36647			0.683233	+	0.730201i	$0.260573\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−25.6123			−0.971530
$696$		0			0
$697$	6.33327			0.239890
$698$		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
$707$	24.0487	+	24.5392i	0.904445	+	0.922892i
$708$		0			0
$709$	−24.1111			−0.905511			−0.452756	−	0.891635i	$-0.649559\pi$
$709$	−24.1111			−0.905511			−0.452756	+	0.891635i	$0.649559\pi$
$710$		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	0.999514	−	0.0311869i	$-0.00992872\pi$
$719$	12.6764	+	21.9561i	0.472748	+	0.818824i	−0.526765	+	0.850011i	$0.676595\pi$
$720$		0			0
$721$	−4.97373	+	17.8399i	−0.185232	+	0.664393i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.05253			0.150507
$726$		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
$731$	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	−0.991927	−	0.126810i	$-0.959526\pi$
$739$	−10.4971	+	18.1815i	−0.386143	+	0.668819i	0.605784	+	0.795629i	$0.292859\pi$
$740$		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
$745$	29.5059	+	51.1057i	1.08101	+	1.87237i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−23.5506	−	24.0310i	−0.860522	−	0.878073i
$750$		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
$763$	−5.26320	+	18.8782i	−0.190541	+	0.683435i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.05555	−	12.2206i	−0.254761	−	0.441259i
$768$		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	−0.250620	−	0.968086i	$-0.580634\pi$
$773$	19.8256	−	34.3389i	0.713077	−	1.23508i	0.963697	−	0.266999i	$-0.0860322\pi$
$774$		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
$785$	−3.95021	+	6.84197i	−0.140989	+	0.244200i
$786$		0			0
$787$	18.0255			0.642538			0.321269	−	0.946988i	$-0.395891\pi$
$787$	18.0255			0.642538			0.321269	+	0.946988i	$0.395891\pi$
$788$		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
$803$	−10.0586			−0.354959
$804$		0			0
$805$	5.04282	+	5.14567i	0.177736	+	0.181361i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−22.5848	+	39.1181i	−0.794040	+	1.37532i	0.129407	+	0.991592i	$0.458693\pi$
$809$	−22.5848	+	39.1181i	−0.794040	+	1.37532i	−0.923447	+	0.383726i	$0.874641\pi$
$810$		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
$815$	−0.368267			−0.0128998
$816$		0			0
$817$	7.11325			0.248861
$818$		0			0
$819$		0			0
$820$		0			0
$821$	52.9144			1.84672			0.923362	−	0.383930i	$-0.125430\pi$
$821$	52.9144			1.84672			0.923362	+	0.383930i	$0.125430\pi$
$822$		0			0
$823$	−31.2359			−1.08881			−0.544407	−	0.838821i	$-0.683245\pi$
$823$	−31.2359			−1.08881			−0.544407	+	0.838821i	$0.683245\pi$
$824$		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	−0.979355	−	0.202148i	$-0.935208\pi$
$829$	−9.05842	+	15.6897i	−0.314612	+	0.544924i	0.664743	+	0.747072i	$0.268541\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.240758	−	11.9234i	0.00834177	−	0.413123i
$834$		0			0
$835$	−58.6766			−2.03059
$836$		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
$851$	9.61204			0.329496
$852$		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
$857$	−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	0.678825	−	0.734300i	$-0.262489\pi$
$863$	−8.71053	−	15.0871i	−0.296510	−	0.513570i	−0.975335	+	0.220730i	$0.929156\pi$
$864$		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
$871$	−19.0293	−	32.9597i	−0.644782	−	1.11680i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	25.6736	−	6.60219i	0.867926	−	0.223195i
$876$		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
$889$	29.5498	−	7.59898i	0.991068	−	0.254862i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−7.58577	−	13.1389i	−0.253848	−	0.439678i
$894$		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
$905$	−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
$911$	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
$913$	39.6101			1.31090
$914$		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	0.999563	−	0.0295447i	$-0.00940573\pi$
$919$	14.3752	+	24.8986i	0.474195	+	0.821330i	−0.525368	+	0.850875i	$0.676072\pi$
$920$		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
$929$	−54.5458			−1.78959			−0.894795	−	0.446477i	$-0.852679\pi$
$929$	−54.5458			−1.78959			−0.894795	+	0.446477i	$0.852679\pi$
$930$		0			0
$931$	−7.68332	−	4.64526i	−0.251811	−	0.152242i
$932$		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
$941$	−19.2963			−0.629042			−0.314521	−	0.949251i	$-0.601844\pi$
$941$	−19.2963			−0.629042			−0.314521	+	0.949251i	$0.601844\pi$
$942$		0			0
$943$	−4.18116			−0.136157
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.5322			0.342249			0.171125	−	0.985249i	$-0.445260\pi$
$947$	10.5322			0.342249			0.171125	+	0.985249i	$0.445260\pi$
$948$		0			0
$949$	−7.31573			−0.237479
$950$		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
$959$	4.16578	+	4.25075i	0.134520	+	0.137264i
$960$		0			0
$961$	−19.2963			−0.622461
$962$		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	0.851147	−	0.524928i	$-0.175908\pi$
$971$	−0.904515	−	1.56667i	−0.0290273	−	0.0502767i	−0.880174	+	0.474651i	$0.842574\pi$
$972$		0			0
$973$	−19.5906	−	19.9901i	−0.628045	−	0.640855i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−37.8985			−1.21248			−0.606241	−	0.795281i	$-0.707323\pi$
$977$	−37.8985			−1.21248			−0.606241	+	0.795281i	$0.707323\pi$
$978$		0			0
$979$	−37.8451	+	65.5497i	−1.20954	+	2.09498i
$980$		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	−0.944334	−	0.328989i	$-0.893292\pi$
$991$	−5.89480	+	10.2101i	−0.187254	+	0.324334i	0.757079	+	0.653323i	$0.226626\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8.47373	+	14.6769i	0.268635	+	0.465290i
$996$		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	2268.2.i.k.865.1		6
3.2	odd	2		2268.2.i.j.865.3		6
7.2	even	3		2268.2.l.j.541.3		6
9.2	odd	6		756.2.k.e.109.3	✓	6
9.4	even	3		2268.2.l.j.109.3		6
9.5	odd	6		2268.2.l.k.109.1		6
9.7	even	3		756.2.k.f.109.1	yes	6
21.2	odd	6		2268.2.l.k.541.1		6
63.2	odd	6		756.2.k.e.541.3	yes	6
63.11	odd	6		5292.2.a.x.1.1		3
63.16	even	3		756.2.k.f.541.1	yes	6
63.23	odd	6		2268.2.i.j.2053.3		6
63.25	even	3		5292.2.a.u.1.3		3
63.38	even	6		5292.2.a.v.1.3		3
63.52	odd	6		5292.2.a.w.1.1		3
63.58	even	3	inner	2268.2.i.k.2053.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.k.e.109.3	✓	6	9.2	odd	6
756.2.k.e.541.3	yes	6	63.2	odd	6
756.2.k.f.109.1	yes	6	9.7	even	3
756.2.k.f.541.1	yes	6	63.16	even	3
2268.2.i.j.865.3		6	3.2	odd	2
2268.2.i.j.2053.3		6	63.23	odd	6
2268.2.i.k.865.1		6	1.1	even	1	trivial
2268.2.i.k.2053.1		6	63.58	even	3	inner
2268.2.l.j.109.3		6	9.4	even	3
2268.2.l.j.541.3		6	7.2	even	3
2268.2.l.k.109.1		6	9.5	odd	6
2268.2.l.k.541.1		6	21.2	odd	6
5292.2.a.u.1.3		3	63.25	even	3
5292.2.a.v.1.3		3	63.38	even	6
5292.2.a.w.1.1		3	63.52	odd	6
5292.2.a.x.1.1		3	63.11	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.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.21053 + 2.09671i) q^{5} +(-2.56238 + 0.658939i) q^{7} +O(q^{10})\)	\(q+(-1.21053 + 2.09671i) q^{5} +(-2.56238 + 0.658939i) q^{7} +(2.35185 + 4.07352i) q^{11} +(1.71053 + 2.96273i) q^{13} +(0.851848 - 1.47544i) q^{17} +(-0.641315 - 1.11079i) q^{19} +(-0.562382 + 0.974074i) q^{23} +(-0.430782 - 0.746136i) q^{25} +(-2.35185 + 4.07352i) q^{29} -3.42107 q^{31} +(1.72025 - 6.17023i) q^{35} +(-4.27292 - 7.40091i) q^{37} +(1.85868 + 3.21934i) q^{41} +(-2.77292 + 4.80283i) q^{43} +11.8285 q^{47} +(6.13160 - 3.37690i) q^{49} +(5.13160 - 8.88819i) q^{53} -11.3880 q^{55} -4.12476 q^{59} -9.24953 q^{61} -8.28263 q^{65} -11.1248 q^{67} -14.9669 q^{71} +(-1.06922 + 1.85194i) q^{73} +(-8.71053 - 8.88819i) q^{77} -14.5322 q^{79} +(4.21053 - 7.29286i) q^{83} +(2.06238 + 3.57215i) q^{85} +(8.04583 + 13.9358i) q^{89} +(-6.33530 - 6.46451i) q^{91} +3.10533 q^{95} +(-8.12476 + 14.0725i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5} + 2 q^{7}+O(q^{10}) \) 6 * q + q^5 + 2 * q^7	\( 6 q + q^{5} + 2 q^{7} + 5 q^{11} + 2 q^{13} - 4 q^{17} - 3 q^{19} + 14 q^{23} - 10 q^{25} - 5 q^{29} - 4 q^{31} + 26 q^{35} + 12 q^{41} + 9 q^{43} + 18 q^{47} + 12 q^{49} + 6 q^{53} + 16 q^{55} + 10 q^{59} + 14 q^{61} - 48 q^{65} - 32 q^{67} - 22 q^{71} + q^{73} - 44 q^{77} - 16 q^{79} + 17 q^{83} - 5 q^{85} - 3 q^{89} + 5 q^{91} - 64 q^{95} - 14 q^{97}+O(q^{100}) \) 6 * q + q^5 + 2 * q^7 + 5 * q^11 + 2 * q^13 - 4 * q^17 - 3 * q^19 + 14 * q^23 - 10 * q^25 - 5 * q^29 - 4 * q^31 + 26 * q^35 + 12 * q^41 + 9 * q^43 + 18 * q^47 + 12 * q^49 + 6 * q^53 + 16 * q^55 + 10 * q^59 + 14 * q^61 - 48 * q^65 - 32 * q^67 - 22 * q^71 + q^73 - 44 * q^77 - 16 * q^79 + 17 * q^83 - 5 * q^85 - 3 * q^89 + 5 * q^91 - 64 * q^95 - 14 * q^97

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