LMFDB - Embedded newform 756.2.t.e.269.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(269,756)]

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, 3, 1]))

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

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

chi := DirichletCharacter("756.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.t (of order $6$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.4
Root			$-0.385418 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	756.269
Dual form			756.2.t.e.593.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.385418 + 0.667563i) q^{5} +(-2.20291 - 1.46533i) q^{7} +O(q^{10})$	$q+(0.385418 + 0.667563i) q^{5} +(-2.20291 - 1.46533i) q^{7} +(-4.68157 - 2.70291i) q^{11} +5.28088i q^{13} +(-2.85433 + 4.94385i) q^{17} +(0.535344 - 0.309081i) q^{19} +(-5.83782 + 3.37047i) q^{23} +(2.20291 - 3.81555i) q^{25} +8.07606i q^{29} +(0.502688 + 0.290227i) q^{31} +(0.129163 - 2.03534i) q^{35} +(-4.53803 - 7.86010i) q^{37} -8.59231 q^{41} +3.40581 q^{43} +(0.385418 + 0.667563i) q^{47} +(2.70560 + 6.45599i) q^{49} +(-6.63798 - 3.83244i) q^{53} -4.16699i q^{55} +(6.89423 - 11.9412i) q^{59} +(-3.57606 + 2.06464i) q^{61} +(-3.52532 + 2.03534i) q^{65} +(-6.77628 + 11.7369i) q^{67} +2.25906i q^{71} +(1.96197 + 1.13274i) q^{73} +(6.35241 + 12.8143i) q^{77} +(4.03534 + 6.98942i) q^{79} -3.85418 q^{83} -4.40044 q^{85} +(2.59808 + 4.50000i) q^{89} +(7.73825 - 11.6333i) q^{91} +(0.412662 + 0.238250i) q^{95} -14.0259i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q - 18 q^{19} - 24 q^{37} - 12 q^{43} + 18 q^{61} + 54 q^{73} + 24 q^{79} - 12 q^{85} + 42 q^{91}+O(q^{100}) $ 12 * q - 18 * q^19 - 24 * q^37 - 12 * q^43 + 18 * q^61 + 54 * q^73 + 24 * q^79 - 12 * q^85 + 42 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$5$	0.385418	+	0.667563i	0.172364	+	0.298543i	0.939246	−	0.343245i	$-0.111526\pi$
$5$	0.385418	+	0.667563i	0.172364	+	0.298543i	−0.766882	+	0.641788i	$0.778193\pi$
$6$		0			0
$7$	−2.20291	−	1.46533i	−0.832620	−	0.553844i
$7$	−2.20291	−	1.46533i	−0.832620	−	0.553844i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.68157	−	2.70291i	−1.41155	−	0.814957i	−0.416013	−	0.909359i	$-0.636573\pi$
$11$	−4.68157	−	2.70291i	−1.41155	−	0.814957i	−0.995534	+	0.0944018i	$0.969906\pi$
$12$		0			0
$13$			5.28088i			1.46465i	0.680954	+	0.732326i	$0.261565\pi$
$13$			5.28088i			1.46465i	−0.680954	+	0.732326i	$0.738435\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.85433	+	4.94385i	−0.692277	+	1.19906i	0.278813	+	0.960345i	$0.410059\pi$
$17$	−2.85433	+	4.94385i	−0.692277	+	1.19906i	−0.971090	+	0.238713i	$0.923274\pi$
$18$		0			0
$19$	0.535344	−	0.309081i	0.122816	−	0.0709080i	−0.437333	−	0.899300i	$-0.644077\pi$
$19$	0.535344	−	0.309081i	0.122816	−	0.0709080i	0.560150	+	0.828391i	$0.310744\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.83782	+	3.37047i	−1.21727	+	0.702791i	−0.964333	−	0.264691i	$-0.914730\pi$
$23$	−5.83782	+	3.37047i	−1.21727	+	0.702791i	−0.252937	+	0.967483i	$0.581397\pi$
$24$		0			0
$25$	2.20291	−	3.81555i	0.440581	−	0.763109i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			8.07606i			1.49969i	0.661615	+	0.749844i	$0.269871\pi$
$29$			8.07606i			1.49969i	−0.661615	+	0.749844i	$0.730129\pi$
$30$		0			0
$31$	0.502688	+	0.290227i	0.0902855	+	0.0521264i	0.544463	−	0.838785i	$-0.316733\pi$
$31$	0.502688	+	0.290227i	0.0902855	+	0.0521264i	−0.454177	+	0.890911i	$0.650067\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.129163	−	2.03534i	0.0218326	−	0.344036i
$36$		0			0
$37$	−4.53803	−	7.86010i	−0.746048	−	1.29219i	−0.949704	−	0.313150i	$-0.898616\pi$
$37$	−4.53803	−	7.86010i	−0.746048	−	1.29219i	0.203656	−	0.979043i	$-0.434718\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.59231			−1.34189			−0.670947	−	0.741506i	$-0.734112\pi$
$41$	−8.59231			−1.34189			−0.670947	+	0.741506i	$0.734112\pi$
$42$		0			0
$43$	3.40581			0.519382			0.259691	−	0.965692i	$-0.416379\pi$
$43$	3.40581			0.519382			0.259691	+	0.965692i	$0.416379\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.385418	+	0.667563i	0.0562189	+	0.0973740i	0.892765	−	0.450522i	$-0.148762\pi$
$47$	0.385418	+	0.667563i	0.0562189	+	0.0973740i	−0.836546	+	0.547896i	$0.815429\pi$
$48$		0			0
$49$	2.70560	+	6.45599i	0.386514	+	0.922284i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.63798	−	3.83244i	−0.911796	−	0.526426i	−0.0307875	−	0.999526i	$-0.509802\pi$
$53$	−6.63798	−	3.83244i	−0.911796	−	0.526426i	−0.881009	+	0.473100i	$0.843135\pi$
$54$		0			0
$55$		−	4.16699i		−	0.561877i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.89423	−	11.9412i	0.897552	−	1.55461i	0.0669387	−	0.997757i	$-0.478677\pi$
$59$	6.89423	−	11.9412i	0.897552	−	1.55461i	0.830614	−	0.556849i	$-0.187990\pi$
$60$		0			0
$61$	−3.57606	+	2.06464i	−0.457868	+	0.264350i	−0.711147	−	0.703043i	$-0.751824\pi$
$61$	−3.57606	+	2.06464i	−0.457868	+	0.264350i	0.253279	+	0.967393i	$0.418491\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.52532	+	2.03534i	−0.437262	+	0.252453i
$66$		0			0
$67$	−6.77628	+	11.7369i	−0.827855	+	1.43389i	0.0718632	+	0.997414i	$0.477105\pi$
$67$	−6.77628	+	11.7369i	−0.827855	+	1.43389i	−0.899718	+	0.436472i	$0.856228\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			2.25906i			0.268101i	0.990974	+	0.134051i	$0.0427985\pi$
$71$			2.25906i			0.268101i	−0.990974	+	0.134051i	$0.957202\pi$
$72$		0			0
$73$	1.96197	+	1.13274i	0.229631	+	0.132577i	0.610402	−	0.792092i	$-0.291008\pi$
$73$	1.96197	+	1.13274i	0.229631	+	0.132577i	−0.380771	+	0.924669i	$0.624341\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.35241	+	12.8143i	0.723924	+	1.46033i
$78$		0			0
$79$	4.03534	+	6.98942i	0.454012	+	0.786371i	0.998631	−	0.0523123i	$-0.0166591\pi$
$79$	4.03534	+	6.98942i	0.454012	+	0.786371i	−0.544619	+	0.838683i	$0.683326\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.85418			−0.423051			−0.211525	−	0.977373i	$-0.567843\pi$
$83$	−3.85418			−0.423051			−0.211525	+	0.977373i	$0.567843\pi$
$84$		0			0
$85$	−4.40044			−0.477294
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.59808	+	4.50000i	0.275396	+	0.476999i	0.970235	−	0.242166i	$-0.0778579\pi$
$89$	2.59808	+	4.50000i	0.275396	+	0.476999i	−0.694839	+	0.719165i	$0.744525\pi$
$90$		0			0
$91$	7.73825	−	11.6333i	0.811189	−	1.21950i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.412662	+	0.238250i	0.0423382	+	0.0244440i
$96$		0			0
$97$		−	14.0259i		−	1.42411i	−0.702123	−	0.712055i	$-0.747765\pi$
$97$		−	14.0259i		−	1.42411i	0.702123	−	0.712055i	$-0.252235\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.35241	−	11.0027i	0.632088	−	1.09481i	−0.355036	−	0.934853i	$-0.615531\pi$
$101$	6.35241	−	11.0027i	0.632088	−	1.09481i	0.987124	−	0.159956i	$-0.0511352\pi$
$102$		0			0
$103$	−2.57069	+	1.48419i	−0.253297	+	0.146241i	−0.621273	−	0.783594i	$-0.713384\pi$
$103$	−2.57069	+	1.48419i	−0.253297	+	0.146241i	0.367976	+	0.929835i	$0.380051\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.26891	+	2.46466i	−0.412691	+	0.238267i	−0.691945	−	0.721950i	$-0.743246\pi$
$107$	−4.26891	+	2.46466i	−0.412691	+	0.238267i	0.279254	+	0.960217i	$0.409913\pi$
$108$		0			0
$109$	3.40581	−	5.89904i	0.326218	−	0.565026i	−0.655540	−	0.755160i	$-0.727559\pi$
$109$	3.40581	−	5.89904i	0.326218	−	0.565026i	0.981758	+	0.190134i	$0.0608924\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			6.32975i			0.595453i	0.954651	+	0.297726i	$0.0962283\pi$
$113$			6.32975i			0.595453i	−0.954651	+	0.297726i	$0.903772\pi$
$114$		0			0
$115$	−4.50000	−	2.59808i	−0.419627	−	0.242272i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	13.5322	−	6.70828i	1.24050	−	0.614947i
$120$		0			0
$121$	9.11141	+	15.7814i	0.828310	+	1.43467i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	7.25033			0.648489
$126$		0			0
$127$	−4.41119			−0.391430			−0.195715	−	0.980661i	$-0.562703\pi$
$127$	−4.41119			−0.391430			−0.195715	+	0.980661i	$0.562703\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.39600	−	7.61410i	−0.384080	−	0.665247i	0.607561	−	0.794273i	$-0.292148\pi$
$131$	−4.39600	−	7.61410i	−0.384080	−	0.665247i	−0.991641	+	0.129026i	$0.958815\pi$
$132$		0			0
$133$	−1.63222	−	0.103581i	−0.141531	−	0.00898160i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.91281	−	2.25906i	−0.334294	−	0.193005i	0.323452	−	0.946245i	$-0.395157\pi$
$137$	−3.91281	−	2.25906i	−0.334294	−	0.193005i	−0.657746	+	0.753240i	$0.728490\pi$
$138$		0			0
$139$			7.67811i			0.651249i	0.945499	+	0.325624i	$0.105575\pi$
$139$			7.67811i			0.651249i	−0.945499	+	0.325624i	$0.894425\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	14.2737	−	24.7228i	1.19363	−	2.06743i
$144$		0			0
$145$	−5.39128	+	3.11266i	−0.447721	+	0.258492i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.40674	−	4.27628i	0.606784	−	0.350327i	−0.164922	−	0.986307i	$-0.552737\pi$
$149$	7.40674	−	4.27628i	0.606784	−	0.350327i	0.771706	+	0.635980i	$0.219404\pi$
$150$		0			0
$151$	3.53803	−	6.12805i	0.287921	−	0.498694i	−0.685392	−	0.728174i	$-0.740369\pi$
$151$	3.53803	−	6.12805i	0.287921	−	0.498694i	0.973313	+	0.229480i	$0.0737026\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			0.447435i			0.0359388i
$156$		0			0
$157$	9.22013	+	5.32324i	0.735846	+	0.424841i	0.820557	−	0.571565i	$-0.193663\pi$
$157$	9.22013	+	5.32324i	0.735846	+	0.424841i	−0.0847108	+	0.996406i	$0.526997\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	17.7990	+	1.12953i	1.40276	+	0.0890195i
$162$		0			0
$163$	−7.53534	−	13.0516i	−0.590214	−	1.02228i	−0.994203	−	0.107517i	$-0.965710\pi$
$163$	−7.53534	−	13.0516i	−0.590214	−	1.02228i	0.403990	−	0.914764i	$-0.367623\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	17.3843			1.34524			0.672619	−	0.739989i	$-0.265169\pi$
$167$	17.3843			1.34524			0.672619	+	0.739989i	$0.265169\pi$
$168$		0			0
$169$	−14.8877			−1.14521
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.87772	+	17.1087i	0.750989	+	1.30075i	0.947344	+	0.320219i	$0.103756\pi$
$173$	9.87772	+	17.1087i	0.750989	+	1.30075i	−0.196354	+	0.980533i	$0.562910\pi$
$174$		0			0
$175$	−10.4438	+	5.17730i	−0.789481	+	0.391367i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−15.1444	−	8.74363i	−1.13195	−	0.653529i	−0.187522	−	0.982260i	$-0.560046\pi$
$179$	−15.1444	−	8.74363i	−1.13195	−	0.653529i	−0.944424	+	0.328731i	$0.893379\pi$
$180$		0			0
$181$			4.11997i			0.306235i	0.988208	+	0.153118i	$0.0489313\pi$
$181$			4.11997i			0.306235i	−0.988208	+	0.153118i	$0.951069\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.49807	−	6.05884i	0.257184	−	0.445455i
$186$		0			0
$187$	26.7255	−	15.4300i	1.95436	−	1.12835i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.4444	−	7.18478i	0.900446	−	0.519873i	0.0231011	−	0.999733i	$-0.492646\pi$
$191$	12.4444	−	7.18478i	0.900446	−	0.519873i	0.877345	+	0.479860i	$0.159313\pi$
$192$		0			0
$193$	−1.03534	+	1.79327i	−0.0745257	+	0.129082i	−0.900880	−	0.434068i	$-0.857078\pi$
$193$	−1.03534	+	1.79327i	−0.0745257	+	0.129082i	0.826354	+	0.563151i	$0.190411\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			20.2881i			1.44547i	0.691126	+	0.722735i	$0.257115\pi$
$197$			20.2881i			1.44547i	−0.691126	+	0.722735i	$0.742885\pi$
$198$		0			0
$199$	5.42394	+	3.13151i	0.384493	+	0.221987i	0.679771	−	0.733424i	$-0.262079\pi$
$199$	5.42394	+	3.13151i	0.384493	+	0.221987i	−0.295279	+	0.955411i	$0.595412\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	11.8341	−	17.7908i	0.830593	−	1.24867i
$204$		0			0
$205$	−3.31163	−	5.73591i	−0.231294	−	0.400613i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.34167			−0.231148
$210$		0			0
$211$	3.73556			0.257167			0.128583	−	0.991699i	$-0.458957\pi$
$211$	3.73556			0.257167			0.128583	+	0.991699i	$0.458957\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.31266	+	2.27359i	0.0895227	+	0.155058i
$216$		0			0
$217$	−0.682096	−	1.37595i	−0.0463037	−	0.0934056i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−26.1079	−	15.0734i	−1.75620	−	1.01394i
$222$		0			0
$223$			15.8426i			1.06090i	0.847716	+	0.530451i	$0.177977\pi$
$223$			15.8426i			1.06090i	−0.847716	+	0.530451i	$0.822023\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.95640	−	3.38859i	0.129851	−	0.224909i	−0.793768	−	0.608221i	$-0.791883\pi$
$227$	1.95640	−	3.38859i	0.129851	−	0.224909i	0.923619	+	0.383312i	$0.125217\pi$
$228$		0			0
$229$	4.39397	−	2.53686i	0.290362	−	0.167640i	−0.347743	−	0.937590i	$-0.613052\pi$
$229$	4.39397	−	2.53686i	0.290362	−	0.167640i	0.638105	+	0.769949i	$0.279719\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.56891	+	0.905813i	−0.102783	+	0.0593418i	−0.550510	−	0.834828i	$-0.685567\pi$
$233$	−1.56891	+	0.905813i	−0.102783	+	0.0593418i	0.447727	+	0.894170i	$0.352234\pi$
$234$		0			0
$235$	−0.297093	+	0.514581i	−0.0193802	+	0.0335676i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			8.58881i			0.555564i	0.960644	+	0.277782i	$0.0895993\pi$
$239$			8.58881i			0.555564i	−0.960644	+	0.277782i	$0.910401\pi$
$240$		0			0
$241$	−20.6521	−	11.9235i	−1.33032	−	0.768061i	−0.344972	−	0.938613i	$-0.612112\pi$
$241$	−20.6521	−	11.9235i	−1.33032	−	0.768061i	−0.985349	+	0.170552i	$0.945445\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.26699	+	4.29440i	−0.208720	+	0.274359i
$246$		0			0
$247$	1.63222	+	2.82709i	0.103856	+	0.179883i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.25033			−0.457637			−0.228818	−	0.973469i	$-0.573486\pi$
$251$	−7.25033			−0.457637			−0.228818	+	0.973469i	$0.573486\pi$
$252$		0			0
$253$	36.4403			2.29098
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.2737	+	24.7228i	0.890370	+	1.54217i	0.839432	+	0.543465i	$0.182888\pi$
$257$	14.2737	+	24.7228i	0.890370	+	1.54217i	0.0509387	+	0.998702i	$0.483779\pi$
$258$		0			0
$259$	−1.52081	+	23.9648i	−0.0944986	+	1.48910i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.95640	−	1.12953i	−0.120637	−	0.0696498i	0.438467	−	0.898747i	$-0.355522\pi$
$263$	−1.95640	−	1.12953i	−0.120637	−	0.0696498i	−0.559104	+	0.829097i	$0.688855\pi$
$264$		0			0
$265$		−	5.90835i		−	0.362947i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.33605	−	14.4385i	0.508258	−	0.880329i	−0.491696	−	0.870767i	$-0.663623\pi$
$269$	8.33605	−	14.4385i	0.508258	−	0.880329i	0.999954	−	0.00956210i	$-0.00304376\pi$
$270$		0			0
$271$	−27.2528	+	15.7344i	−1.65549	+	0.955797i	−0.680730	+	0.732534i	$0.738337\pi$
$271$	−27.2528	+	15.7344i	−1.65549	+	0.955797i	−0.974758	+	0.223263i	$0.928329\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−20.6261	+	11.9085i	−1.24380	+	0.718110i
$276$		0			0
$277$	−9.51991	+	16.4890i	−0.571996	+	0.990726i	0.424365	+	0.905491i	$0.360497\pi$
$277$	−9.51991	+	16.4890i	−0.571996	+	0.990726i	−0.996361	+	0.0852348i	$0.972836\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			7.59956i			0.453352i	0.973970	+	0.226676i	$0.0727858\pi$
$281$			7.59956i			0.453352i	−0.973970	+	0.226676i	$0.927214\pi$
$282$		0			0
$283$	−26.8315	−	15.4912i	−1.59497	−	0.920856i	−0.992436	−	0.122762i	$-0.960825\pi$
$283$	−26.8315	−	15.4912i	−1.59497	−	0.920856i	−0.602533	−	0.798094i	$-0.705842\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	18.9281	+	12.5906i	1.11729	+	0.743199i
$288$		0			0
$289$	−7.79440	−	13.5003i	−0.458494	−	0.794136i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.93783			0.288471			0.144235	−	0.989543i	$-0.453928\pi$
$293$	4.93783			0.288471			0.144235	+	0.989543i	$0.453928\pi$
$294$		0			0
$295$	10.6286			0.618823
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−17.7990	−	30.8288i	−1.02935	−	1.78288i
$300$		0			0
$301$	−7.50269	−	4.99065i	−0.432448	−	0.287656i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.75656	−	1.59150i	−0.157840	−	0.0911289i
$306$		0			0
$307$			7.95736i			0.454151i	0.973877	+	0.227075i	$0.0729164\pi$
$307$			7.95736i			0.454151i	−0.973877	+	0.227075i	$0.927084\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.93783	+	8.55257i	−0.279998	+	0.484971i	−0.971384	−	0.237514i	$-0.923667\pi$
$311$	−4.93783	+	8.55257i	−0.279998	+	0.484971i	0.691386	+	0.722486i	$0.257001\pi$
$312$		0			0
$313$	14.5707	−	8.41239i	0.823584	−	0.475496i	−0.0280668	−	0.999606i	$-0.508935\pi$
$313$	14.5707	−	8.41239i	0.823584	−	0.475496i	0.851651	+	0.524110i	$0.175602\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.4515	+	12.3850i	−1.20483	+	0.695611i	−0.961626	−	0.274363i	$-0.911533\pi$
$317$	−21.4515	+	12.3850i	−1.20483	+	0.695611i	−0.243208	+	0.969974i	$0.578200\pi$
$318$		0			0
$319$	21.8288	−	37.8087i	1.22218	−	2.11688i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			3.52888i			0.196352i
$324$		0			0
$325$	20.1494	+	11.6333i	1.11769	+	0.645299i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.129163	−	2.03534i	0.00712100	−	0.112212i
$330$		0			0
$331$	9.00269	+	15.5931i	0.494833	+	0.857075i	0.999982	−	0.00595666i	$-0.00189608\pi$
$331$	9.00269	+	15.5931i	0.494833	+	0.857075i	−0.505150	+	0.863032i	$0.668563\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−10.4468			−0.570769
$336$		0			0
$337$	5.21744			0.284212			0.142106	−	0.989851i	$-0.454613\pi$
$337$	5.21744			0.284212			0.142106	+	0.989851i	$0.454613\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.56891	−	2.71744i	−0.0849615	−	0.147158i
$342$		0			0
$343$	3.50000	−	18.1865i	0.188982	−	0.981981i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−14.1013	−	8.14138i	−0.756996	−	0.437052i	0.0712201	−	0.997461i	$-0.477311\pi$
$347$	−14.1013	−	8.14138i	−0.756996	−	0.437052i	−0.828216	+	0.560409i	$0.810644\pi$
$348$		0			0
$349$		−	17.4052i		−	0.931681i	−0.884869	−	0.465840i	$-0.845752\pi$
$349$		−	17.4052i		−	0.931681i	0.884869	−	0.465840i	$-0.154248\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	14.9447	−	25.8850i	0.795427	−	1.37772i	−0.127141	−	0.991885i	$-0.540580\pi$
$353$	14.9447	−	25.8850i	0.795427	−	1.37772i	0.922568	−	0.385835i	$-0.126087\pi$
$354$		0			0
$355$	−1.50807	+	0.870682i	−0.0800398	+	0.0462110i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−20.2700	+	11.7029i	−1.06981	+	0.617656i	−0.928130	−	0.372257i	$-0.878584\pi$
$359$	−20.2700	+	11.7029i	−1.06981	+	0.617656i	−0.141681	+	0.989912i	$0.545251\pi$
$360$		0			0
$361$	−9.30894	+	16.1236i	−0.489944	+	0.848608i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			1.74632i			0.0914063i
$366$		0			0
$367$	17.3696	+	10.0283i	0.906684	+	0.523474i	0.879363	−	0.476152i	$-0.157969\pi$
$367$	17.3696	+	10.0283i	0.906684	+	0.523474i	0.0273213	+	0.999627i	$0.491302\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9.00704	+	18.1694i	0.467622	+	0.943306i
$372$		0			0
$373$	3.99462	+	6.91889i	0.206834	+	0.358247i	0.950715	−	0.310065i	$-0.100351\pi$
$373$	3.99462	+	6.91889i	0.206834	+	0.358247i	−0.743882	+	0.668311i	$0.767017\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−42.6487			−2.19652
$378$		0			0
$379$	−34.5816			−1.77634			−0.888170	−	0.459516i	$-0.848023\pi$
$379$	−34.5816			−1.77634			−0.888170	+	0.459516i	$0.848023\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.01058	+	6.94653i	0.204931	+	0.354951i	0.950111	−	0.311913i	$-0.100970\pi$
$383$	4.01058	+	6.94653i	0.204931	+	0.354951i	−0.745180	+	0.666864i	$0.767636\pi$
$384$		0			0
$385$	−6.10603	+	9.17949i	−0.311192	+	0.467830i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−15.9446	−	9.20560i	−0.808421	−	0.466742i	0.0379861	−	0.999278i	$-0.487906\pi$
$389$	−15.9446	−	9.20560i	−0.808421	−	0.466742i	−0.846407	+	0.532536i	$0.821239\pi$
$390$		0			0
$391$		−	38.4817i		−	1.94610i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.11058	+	5.38769i	−0.156511	+	0.271084i
$396$		0			0
$397$	−21.9973	+	12.7002i	−1.10401	+	0.637402i	−0.937272	−	0.348598i	$-0.886658\pi$
$397$	−21.9973	+	12.7002i	−1.10401	+	0.637402i	−0.166741	+	0.986001i	$0.553324\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.43813	−	4.29440i	0.371442	−	0.214452i	−0.302646	−	0.953103i	$-0.597870\pi$
$401$	7.43813	−	4.29440i	0.371442	−	0.214452i	0.674088	+	0.738651i	$0.264537\pi$
$402$		0			0
$403$	−1.53266	+	2.65464i	−0.0763470	+	0.132237i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			49.0635i			2.43199i
$408$		0			0
$409$	−3.04072	−	1.75556i	−0.150354	−	0.0868069i	0.422936	−	0.906160i	$-0.361000\pi$
$409$	−3.04072	−	1.75556i	−0.150354	−	0.0868069i	−0.573290	+	0.819353i	$0.694333\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−32.6851	+	16.2029i	−1.60833	+	0.797293i
$414$		0			0
$415$	−1.48547	−	2.57290i	−0.0729187	−	0.126299i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−29.5725			−1.44471			−0.722355	−	0.691523i	$-0.756940\pi$
$419$	−29.5725			−1.44471			−0.722355	+	0.691523i	$0.756940\pi$
$420$		0			0
$421$	−23.0344			−1.12263			−0.561315	−	0.827602i	$-0.689704\pi$
$421$	−23.0344			−1.12263			−0.561315	+	0.827602i	$0.689704\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	12.5756	+	21.7817i	0.610008	+	1.05657i
$426$		0			0
$427$	10.9031	+	0.691914i	0.527639	+	0.0334841i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	20.2386	+	11.6848i	0.974861	+	0.562836i	0.900715	−	0.434411i	$-0.143043\pi$
$431$	20.2386	+	11.6848i	0.974861	+	0.562836i	0.0741463	+	0.997247i	$0.476377\pi$
$432$		0			0
$433$			37.9199i			1.82231i	0.412059	+	0.911157i	$0.364810\pi$
$433$			37.9199i			1.82231i	−0.412059	+	0.911157i	$0.635190\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.08350	+	3.60872i	−0.0996671	+	0.172628i
$438$		0			0
$439$	−2.71744	+	1.56891i	−0.129696	+	0.0748802i	−0.563444	−	0.826154i	$-0.690524\pi$
$439$	−2.71744	+	1.56891i	−0.129696	+	0.0748802i	0.433748	+	0.901034i	$0.357191\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−20.9822	+	12.1141i	−0.996896	+	0.575558i	−0.907328	−	0.420423i	$-0.861882\pi$
$443$	−20.9822	+	12.1141i	−0.996896	+	0.575558i	−0.0895675	+	0.995981i	$0.528548\pi$
$444$		0			0
$445$	−2.00269	+	3.46876i	−0.0949365	+	0.164435i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	25.1812i		−	1.18837i	−0.804327	−	0.594187i	$-0.797474\pi$
$449$		−	25.1812i		−	1.18837i	0.804327	−	0.594187i	$-0.202526\pi$
$450$		0			0
$451$	40.2255	+	23.2242i	1.89415	+	1.09359i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.7484	+	0.682096i	0.503893	+	0.0319771i
$456$		0			0
$457$	13.1060	+	22.7003i	0.613074	+	1.06188i	0.990719	+	0.135925i	$0.0434007\pi$
$457$	13.1060	+	22.7003i	0.613074	+	1.06188i	−0.377645	+	0.925951i	$0.623266\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.80000			0.0838342			0.0419171	−	0.999121i	$-0.486653\pi$
$461$	1.80000			0.0838342			0.0419171	+	0.999121i	$0.486653\pi$
$462$		0			0
$463$	−20.4456			−0.950189			−0.475095	−	0.879935i	$-0.657586\pi$
$463$	−20.4456			−0.950189			−0.475095	+	0.879935i	$0.657586\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.25271	−	9.09797i	−0.243067	−	0.421004i	0.718520	−	0.695507i	$-0.244820\pi$
$467$	−5.25271	−	9.09797i	−0.243067	−	0.421004i	−0.961586	+	0.274503i	$0.911487\pi$
$468$		0			0
$469$	32.1259	−	15.9257i	1.48344	−	0.735381i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−15.9446	−	9.20560i	−0.733132	−	0.423274i
$474$		0			0
$475$		−	2.72351i		−	0.124963i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.98349	+	5.16756i	−0.136319	+	0.236112i	−0.926101	−	0.377276i	$-0.876861\pi$
$479$	−2.98349	+	5.16756i	−0.136319	+	0.236112i	0.789781	+	0.613388i	$0.210194\pi$
$480$		0			0
$481$	41.5083	−	23.9648i	1.89261	−	1.09270i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	9.36314	−	5.40581i	0.425158	−	0.245465i
$486$		0			0
$487$	−12.0199	+	20.8191i	−0.544674	+	0.943403i	0.453953	+	0.891026i	$0.350013\pi$
$487$	−12.0199	+	20.8191i	−0.544674	+	0.943403i	−0.998627	+	0.0523777i	$0.983320\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			21.5579i			0.972896i	0.873709	+	0.486448i	$0.161708\pi$
$491$			21.5579i			0.972896i	−0.873709	+	0.486448i	$0.838292\pi$
$492$		0			0
$493$	−39.9268	−	23.0518i	−1.79821	−	1.03820i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.31028	−	4.97650i	0.148486	−	0.223227i
$498$		0			0
$499$	−14.4257	−	24.9861i	−0.645784	−	1.11853i	−0.984120	−	0.177505i	$-0.943197\pi$
$499$	−14.4257	−	24.9861i	−0.645784	−	1.11853i	0.338336	−	0.941025i	$-0.390136\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	20.7805			0.926555			0.463278	−	0.886213i	$-0.346673\pi$
$503$	20.7805			0.926555			0.463278	+	0.886213i	$0.346673\pi$
$504$		0			0
$505$	9.79331			0.435797
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.7027	−	22.0018i	−0.563039	−	0.975212i	−0.997229	−	0.0743909i	$-0.976299\pi$
$509$	−12.7027	−	22.0018i	−0.563039	−	0.975212i	0.434190	−	0.900821i	$-0.357035\pi$
$510$		0			0
$511$	−2.66219	−	5.37026i	−0.117768	−	0.237566i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.98158	−	1.14406i	−0.0873187	−	0.0504135i
$516$		0			0
$517$		−	4.16699i		−	0.183264i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.02709	+	1.77897i	−0.0449976	+	0.0779381i	−0.887647	−	0.460524i	$-0.847661\pi$
$521$	−1.02709	+	1.77897i	−0.0449976	+	0.0779381i	0.842649	+	0.538463i	$0.180995\pi$
$522$		0			0
$523$	−9.81790	+	5.66837i	−0.429307	+	0.247860i	−0.699051	−	0.715071i	$-0.746394\pi$
$523$	−9.81790	+	5.66837i	−0.429307	+	0.247860i	0.269744	+	0.962932i	$0.413061\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.86968	+	1.65681i	−0.125005	+	0.0721717i
$528$		0			0
$529$	11.2201	−	19.4338i	0.487832	−	0.844949i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	45.3749i		−	1.96541i
$534$		0			0
$535$	−3.29063	−	1.89984i	−0.142266	−	0.0821374i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.78349	−	37.5371i	0.206040	−	1.61684i
$540$		0			0
$541$	−9.39128	−	16.2662i	−0.403763	−	0.699337i	0.590414	−	0.807101i	$-0.298965\pi$
$541$	−9.39128	−	16.2662i	−0.403763	−	0.699337i	−0.994177	+	0.107763i	$0.965631\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.25064			0.224913
$546$		0			0
$547$	−6.91856			−0.295816			−0.147908	−	0.989001i	$-0.547254\pi$
$547$	−6.91856			−0.295816			−0.147908	+	0.989001i	$0.547254\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.49616	+	4.32347i	0.106340	+	0.184186i
$552$		0			0
$553$	1.35235	−	21.3102i	0.0575076	−	0.906200i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.00704	−	5.20022i	−0.381641	−	0.220340i	0.296891	−	0.954911i	$-0.404050\pi$
$557$	−9.00704	−	5.20022i	−0.381641	−	0.220340i	−0.678532	+	0.734571i	$0.737383\pi$
$558$		0			0
$559$			17.9857i			0.760714i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.01074	−	5.21475i	0.126887	−	0.219776i	−0.795582	−	0.605846i	$-0.792835\pi$
$563$	3.01074	−	5.21475i	0.126887	−	0.219776i	0.922469	+	0.386071i	$0.126168\pi$
$564$		0			0
$565$	−4.22550	+	2.43960i	−0.177768	+	0.102635i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	25.4208	−	14.6767i	1.06570	−	0.615280i	0.138694	−	0.990335i	$-0.455710\pi$
$569$	25.4208	−	14.6767i	1.06570	−	0.615280i	0.927002	+	0.375055i	$0.122376\pi$
$570$		0			0
$571$	−8.61410	+	14.9201i	−0.360489	+	0.624385i	−0.988041	−	0.154189i	$-0.950723\pi$
$571$	−8.61410	+	14.9201i	−0.360489	+	0.624385i	0.627553	+	0.778574i	$0.284057\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			29.6993i			1.23855i
$576$		0			0
$577$	1.85594	+	1.07153i	0.0772636	+	0.0446082i	0.538134	−	0.842859i	$-0.319129\pi$
$577$	1.85594	+	1.07153i	0.0772636	+	0.0446082i	−0.460870	+	0.887467i	$0.652463\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	8.49039	+	5.64765i	0.352241	+	0.234304i
$582$		0			0
$583$	20.7174	+	35.8837i	0.858029	+	1.48615i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.5840			0.725769			0.362885	−	0.931834i	$-0.381792\pi$
$587$	17.5840			0.725769			0.362885	+	0.931834i	$0.381792\pi$
$588$		0			0
$589$	0.358815			0.0147847
$590$		0			0
$591$		0			0
$592$		0			0
$593$	12.1469	+	21.0391i	0.498815	+	0.863973i	0.999999	−	0.00136757i	$-0.000435311\pi$
$593$	12.1469	+	21.0391i	0.498815	+	0.863973i	−0.501184	+	0.865341i	$0.667102\pi$
$594$		0			0
$595$	9.69375	+	6.44811i	0.397405	+	0.264347i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	32.7458	+	18.9058i	1.33796	+	0.772471i	0.986504	−	0.163735i	$-0.0523541\pi$
$599$	32.7458	+	18.9058i	1.33796	+	0.772471i	0.351454	+	0.936205i	$0.385687\pi$
$600$		0			0
$601$			2.90227i			0.118386i	0.998247	+	0.0591931i	$0.0188528\pi$
$601$			2.90227i			0.118386i	−0.998247	+	0.0591931i	$0.981147\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.02339	+	12.1649i	−0.285542	+	0.494572i
$606$		0			0
$607$	9.67403	−	5.58530i	0.392657	−	0.226701i	−0.290654	−	0.956828i	$-0.593873\pi$
$607$	9.67403	−	5.58530i	0.392657	−	0.226701i	0.683311	+	0.730128i	$0.260539\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.52532	+	2.03534i	−0.142619	+	0.0823412i
$612$		0			0
$613$	−8.12953	+	14.0808i	−0.328349	+	0.568717i	−0.982184	−	0.187920i	$-0.939825\pi$
$613$	−8.12953	+	14.0808i	−0.328349	+	0.568717i	0.653836	+	0.756637i	$0.273159\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			5.34050i			0.215001i	0.994205	+	0.107500i	$0.0342846\pi$
$617$			5.34050i			0.215001i	−0.994205	+	0.107500i	$0.965715\pi$
$618$		0			0
$619$	18.3669	+	10.6041i	0.738227	+	0.426216i	0.821424	−	0.570317i	$-0.193180\pi$
$619$	18.3669	+	10.6041i	0.738227	+	0.426216i	−0.0831972	+	0.996533i	$0.526513\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.870682	−	13.7201i	0.0348831	−	0.549685i
$624$		0			0
$625$	−8.22013	−	14.2377i	−0.328805	−	0.569507i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	51.8122			2.06589
$630$		0			0
$631$	44.7338			1.78082			0.890411	−	0.455157i	$-0.150417\pi$
$631$	44.7338			1.78082			0.890411	+	0.455157i	$0.150417\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.70015	−	2.94475i	−0.0674684	−	0.116859i
$636$		0			0
$637$	−34.0933	+	14.2879i	−1.35083	+	0.566108i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−23.6508	−	13.6548i	−0.934152	−	0.539333i	−0.0460296	−	0.998940i	$-0.514657\pi$
$641$	−23.6508	−	13.6548i	−0.934152	−	0.539333i	−0.888122	+	0.459607i	$0.847990\pi$
$642$		0			0
$643$		−	35.7298i		−	1.40905i	−0.709681	−	0.704524i	$-0.751161\pi$
$643$		−	35.7298i		−	1.40905i	0.709681	−	0.704524i	$-0.248839\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−20.4537	+	35.4268i	−0.804117	+	1.39277i	0.112768	+	0.993621i	$0.464028\pi$
$647$	−20.4537	+	35.4268i	−0.804117	+	1.39277i	−0.916885	+	0.399150i	$0.869305\pi$
$648$		0			0
$649$	−64.5517	+	37.2689i	−2.53387	+	1.46293i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	22.5825	−	13.0380i	0.883723	−	0.510218i	0.0118388	−	0.999930i	$-0.496232\pi$
$653$	22.5825	−	13.0380i	0.883723	−	0.510218i	0.871884	+	0.489712i	$0.162898\pi$
$654$		0			0
$655$	3.38859	−	5.86921i	0.132403	−	0.229329i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	40.8568i		−	1.59156i	−0.605589	−	0.795778i	$-0.707062\pi$
$659$		−	40.8568i		−	1.59156i	0.605589	−	0.795778i	$-0.292938\pi$
$660$		0			0
$661$	−6.28544	−	3.62890i	−0.244475	−	0.141148i	0.372757	−	0.927929i	$-0.378413\pi$
$661$	−6.28544	−	3.62890i	−0.244475	−	0.141148i	−0.617232	+	0.786781i	$0.711746\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.559939	−	1.12953i	−0.0217135	−	0.0438013i
$666$		0			0
$667$	−27.2201	−	47.1466i	−1.05397	−	1.82553i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	22.3221			0.861736
$672$		0			0
$673$	35.2465			1.35865			0.679326	−	0.733836i	$-0.262272\pi$
$673$	35.2465			1.35865			0.679326	+	0.733836i	$0.262272\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	5.48172	+	9.49462i	0.210680	+	0.364908i	0.951927	−	0.306324i	$-0.0990989\pi$
$677$	5.48172	+	9.49462i	0.210680	+	0.364908i	−0.741248	+	0.671232i	$0.765766\pi$
$678$		0			0
$679$	−20.5526	+	30.8977i	−0.788735	+	1.18574i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7.70628	−	4.44922i	−0.294873	−	0.170245i	0.345265	−	0.938505i	$-0.387789\pi$
$683$	−7.70628	−	4.44922i	−0.294873	−	0.170245i	−0.640137	+	0.768261i	$0.721123\pi$
$684$		0			0
$685$		−	3.48273i		−	0.133068i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	20.2386	−	35.0544i	0.771031	−	1.33546i
$690$		0			0
$691$	7.27987	−	4.20304i	0.276939	−	0.159891i	−0.355098	−	0.934829i	$-0.615552\pi$
$691$	7.27987	−	4.20304i	0.276939	−	0.159891i	0.632037	+	0.774938i	$0.282219\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.12562	+	2.95928i	−0.194426	+	0.112252i
$696$		0			0
$697$	24.5253	−	42.4790i	0.928961	−	1.60901i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	28.3351i		−	1.07020i	−0.844788	−	0.535101i	$-0.820273\pi$
$701$		−	28.3351i		−	1.07020i	0.844788	−	0.535101i	$-0.179727\pi$
$702$		0			0
$703$	−4.85881	−	2.80524i	−0.183254	−	0.105802i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−30.1164	+	14.9295i	−1.13264	+	0.561482i
$708$		0			0
$709$	12.0434	+	20.8598i	0.452300	+	0.783406i	0.998528	−	0.0542300i	$-0.0172704\pi$
$709$	12.0434	+	20.8598i	0.452300	+	0.783406i	−0.546229	+	0.837636i	$0.683937\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.91281			−0.146536
$714$		0			0
$715$	22.0054			0.822954
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.57083	−	4.45281i	−0.0958759	−	0.166062i	0.814098	−	0.580728i	$-0.197232\pi$
$719$	−2.57083	−	4.45281i	−0.0958759	−	0.166062i	−0.909974	+	0.414666i	$0.863899\pi$
$720$		0			0
$721$	7.83781	+	0.497389i	0.291895	+	0.0185237i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	30.8146	+	17.7908i	1.14443	+	0.660734i
$726$		0			0
$727$			6.91889i			0.256607i	0.991735	+	0.128304i	$0.0409532\pi$
$727$			6.91889i			0.256607i	−0.991735	+	0.128304i	$0.959047\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−9.72132	+	16.8378i	−0.359556	+	0.622769i
$732$		0			0
$733$	14.8940	−	8.59904i	0.550121	−	0.317613i	−0.199050	−	0.979989i	$-0.563785\pi$
$733$	14.8940	−	8.59904i	0.550121	−	0.317613i	0.749171	+	0.662377i	$0.230452\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	63.4473	−	36.6313i	2.33711	−	1.34933i
$738$		0			0
$739$	10.6114	−	18.3795i	0.390347	−	0.676101i	−0.602148	−	0.798384i	$-0.705688\pi$
$739$	10.6114	−	18.3795i	0.390347	−	0.676101i	0.992495	+	0.122284i	$0.0390217\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	33.7047i		−	1.23651i	−0.785979	−	0.618253i	$-0.787841\pi$
$743$		−	33.7047i		−	1.23651i	0.785979	−	0.618253i	$-0.212159\pi$
$744$		0			0
$745$	5.70937	+	3.29631i	0.209175	+	0.120767i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	13.0156	+	0.825969i	0.475578	+	0.0301803i
$750$		0			0
$751$	−2.41119	−	4.17630i	−0.0879856	−	0.152395i	0.818674	−	0.574259i	$-0.194710\pi$
$751$	−2.41119	−	4.17630i	−0.0879856	−	0.152395i	−0.906660	+	0.421863i	$0.861376\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.45448			0.198509
$756$		0			0
$757$	−7.30426			−0.265478			−0.132739	−	0.991151i	$-0.542377\pi$
$757$	−7.30426			−0.265478			−0.132739	+	0.991151i	$0.542377\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−7.91925	−	13.7165i	−0.287072	−	0.497224i	0.686037	−	0.727566i	$-0.259349\pi$
$761$	−7.91925	−	13.7165i	−0.287072	−	0.497224i	−0.973110	+	0.230342i	$0.926015\pi$
$762$		0			0
$763$	−16.1468	+	8.00439i	−0.584552	+	0.289778i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	63.0598	+	36.4076i	2.27696	+	1.31460i
$768$		0			0
$769$			47.3208i			1.70643i	0.521559	+	0.853215i	$0.325351\pi$
$769$			47.3208i			1.70643i	−0.521559	+	0.853215i	$0.674649\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	10.5173	−	18.2165i	0.378282	−	0.655203i	−0.612531	−	0.790447i	$-0.709848\pi$
$773$	10.5173	−	18.2165i	0.378282	−	0.655203i	0.990812	+	0.135244i	$0.0431817\pi$
$774$		0			0
$775$	2.21475	−	1.27869i	0.0795562	−	0.0459318i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.59984	+	2.65572i	−0.164806	+	0.0951510i
$780$		0			0
$781$	6.10603	−	10.5760i	0.218491	−	0.378437i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			8.20669i			0.292909i
$786$		0			0
$787$	−33.7881	−	19.5076i	−1.20442	−	0.695370i	−0.242883	−	0.970056i	$-0.578093\pi$
$787$	−33.7881	−	19.5076i	−1.20442	−	0.695370i	−0.961534	+	0.274685i	$0.911426\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	9.27519	−	13.9438i	0.329788	−	0.495786i
$792$		0			0
$793$	−10.9031	−	18.8848i	−0.387181	−	0.670618i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−31.6853			−1.12235			−0.561175	−	0.827697i	$-0.689651\pi$
$797$	−31.6853			−1.12235			−0.561175	+	0.827697i	$0.689651\pi$
$798$		0			0
$799$	−4.40044			−0.155676
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.12340	−	10.6060i	−0.216090	−	0.374279i
$804$		0			0
$805$	6.10603	+	12.3173i	0.215209	+	0.434128i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.93123	+	1.11500i	0.0678985	+	0.0392012i	0.533565	−	0.845759i	$-0.320852\pi$
$809$	1.93123	+	1.11500i	0.0678985	+	0.0392012i	−0.465666	+	0.884960i	$0.654185\pi$
$810$		0			0
$811$			55.3535i			1.94373i	0.235548	+	0.971863i	$0.424312\pi$
$811$			55.3535i			1.94373i	−0.235548	+	0.971863i	$0.575688\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.80851	−	10.0606i	0.203463	−	0.352409i
$816$		0			0
$817$	1.82328	−	1.05267i	0.0637885	−	0.0368283i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	39.8216	−	22.9910i	1.38978	−	0.802393i	0.396494	−	0.918037i	$-0.370227\pi$
$821$	39.8216	−	22.9910i	1.38978	−	0.802393i	0.993291	+	0.115645i	$0.0368934\pi$
$822$		0			0
$823$	−21.1494	+	36.6319i	−0.737223	+	1.27691i	0.216518	+	0.976279i	$0.430530\pi$
$823$	−21.1494	+	36.6319i	−0.737223	+	1.27691i	−0.953741	+	0.300629i	$0.902803\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			21.1105i			0.734084i	0.930204	+	0.367042i	$0.119630\pi$
$827$			21.1105i			0.734084i	−0.930204	+	0.367042i	$0.880370\pi$
$828$		0			0
$829$	47.3615	+	27.3442i	1.64493	+	0.949703i	0.979043	+	0.203652i	$0.0652812\pi$
$829$	47.3615	+	27.3442i	1.64493	+	0.949703i	0.665890	+	0.746050i	$0.268052\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−39.6401	−	5.05147i	−1.37345	−	0.175023i
$834$		0			0
$835$	6.70022	+	11.6051i	0.231871	+	0.401612i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	43.3651			1.49713			0.748564	−	0.663062i	$-0.230744\pi$
$839$	43.3651			1.49713			0.748564	+	0.663062i	$0.230744\pi$
$840$		0			0
$841$	−36.2228			−1.24906
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5.73798	−	9.93847i	−0.197392	−	0.341894i
$846$		0			0
$847$	3.05347	−	48.1163i	0.104918	−	1.65329i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	52.9845	+	30.5906i	1.81628	+	1.04863i
$852$		0			0
$853$		−	26.5989i		−	0.910730i	−0.890305	−	0.455365i	$-0.849509\pi$
$853$		−	26.5989i		−	0.910730i	0.890305	−	0.455365i	$-0.150491\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−14.8155	+	25.6613i	−0.506090	+	0.876573i	0.493886	+	0.869527i	$0.335576\pi$
$857$	−14.8155	+	25.6613i	−0.506090	+	0.876573i	−0.999975	+	0.00704593i	$0.997757\pi$
$858$		0			0
$859$	4.19285	−	2.42074i	0.143058	−	0.0825947i	−0.426763	−	0.904364i	$-0.640346\pi$
$859$	4.19285	−	2.42074i	0.143058	−	0.0825947i	0.569821	+	0.821769i	$0.307013\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−19.0258	+	10.9846i	−0.647647	+	0.373919i	−0.787554	−	0.616246i	$-0.788653\pi$
$863$	−19.0258	+	10.9846i	−0.647647	+	0.373919i	0.139907	+	0.990165i	$0.455320\pi$
$864$		0			0
$865$	−7.61410	+	13.1880i	−0.258887	+	0.448406i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	43.6286i		−	1.48000i
$870$		0			0
$871$	−61.9810	−	35.7847i	−2.10015	−	1.21252i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−15.9718	−	10.6242i	−0.539945	−	0.359162i
$876$		0			0
$877$	21.2989	+	36.8907i	0.719212	+	1.24571i	0.961312	+	0.275461i	$0.0888304\pi$
$877$	21.2989	+	36.8907i	0.719212	+	1.24571i	−0.242100	+	0.970251i	$0.577836\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−41.2523			−1.38982			−0.694912	−	0.719095i	$-0.744557\pi$
$881$	−41.2523			−1.38982			−0.694912	+	0.719095i	$0.744557\pi$
$882$		0			0
$883$	4.21206			0.141747			0.0708736	−	0.997485i	$-0.477421\pi$
$883$	4.21206			0.141747			0.0708736	+	0.997485i	$0.477421\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.79585	+	3.11051i	0.0602988	+	0.104441i	0.894599	−	0.446870i	$-0.147461\pi$
$887$	1.79585	+	3.11051i	0.0602988	+	0.104441i	−0.834300	+	0.551310i	$0.814128\pi$
$888$		0			0
$889$	9.71744	+	6.46386i	0.325912	+	0.216791i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.412662	+	0.238250i	0.0138092	+	0.00797275i
$894$		0			0
$895$		−	13.4798i		−	0.450580i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.34389	+	4.05974i	−0.0781733	+	0.135400i
$900$		0			0
$901$	37.8940	−	21.8781i	1.26243	−	0.728865i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.75034	+	1.58791i	−0.0914244	+	0.0527839i
$906$		0			0
$907$	−2.92394	+	5.06440i	−0.0970877	+	0.168161i	−0.910478	−	0.413558i	$-0.864286\pi$
$907$	−2.92394	+	5.06440i	−0.0970877	+	0.168161i	0.813390	+	0.581718i	$0.197619\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	7.59956i		−	0.251785i	−0.992044	−	0.125892i	$-0.959821\pi$
$911$		−	7.59956i		−	0.251785i	0.992044	−	0.125892i	$-0.0401794\pi$
$912$		0			0
$913$	18.0436	+	10.4175i	0.597156	+	0.344768i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.47321	+	23.2148i	−0.0486498	+	0.766619i
$918$		0			0
$919$	−13.3062	−	23.0471i	−0.438933	−	0.760254i	0.558675	−	0.829387i	$-0.311310\pi$
$919$	−13.3062	−	23.0471i	−0.438933	−	0.760254i	−0.997607	+	0.0691331i	$0.977977\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−11.9298			−0.392675
$924$		0			0
$925$	−39.9874			−1.31478
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−26.2056	−	45.3895i	−0.859779	−	1.48918i	−0.872140	−	0.489257i	$-0.837268\pi$
$929$	−26.2056	−	45.3895i	−0.859779	−	1.48918i	0.0123610	−	0.999924i	$-0.496065\pi$
$930$		0			0
$931$	3.44385	+	2.61992i	0.112867	+	0.0858646i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	20.6010	+	11.8940i	0.673723	+	0.388974i
$936$		0			0
$937$		−	49.0719i		−	1.60311i	−0.597922	−	0.801554i	$-0.704007\pi$
$937$		−	49.0719i		−	1.60311i	0.597922	−	0.801554i	$-0.295993\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.7319	+	23.7843i	−0.447647	+	0.775348i	−0.998232	−	0.0594314i	$-0.981071\pi$
$941$	−13.7319	+	23.7843i	−0.447647	+	0.775348i	0.550585	+	0.834779i	$0.314405\pi$
$942$		0			0
$943$	50.1604	−	28.9601i	1.63345	−	0.943071i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−51.0532	+	29.4756i	−1.65901	+	0.957828i	−0.685833	+	0.727759i	$0.740562\pi$
$947$	−51.0532	+	29.4756i	−1.65901	+	0.957828i	−0.973174	+	0.230069i	$0.926105\pi$
$948$		0			0
$949$	−5.98188	+	10.3609i	−0.194180	+	0.336330i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	16.6649i		−	0.539828i	−0.962884	−	0.269914i	$-0.913005\pi$
$953$		−	16.6649i		−	0.539828i	0.962884	−	0.269914i	$-0.0869953\pi$
$954$		0			0
$955$	9.59259	+	5.53828i	0.310409	+	0.179215i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	5.30927	+	10.7101i	0.171445	+	0.345846i
$960$		0			0
$961$	−15.3315	−	26.5550i	−0.494566	−	0.856613i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.59616			−0.0513822
$966$		0			0
$967$	23.3459			0.750753			0.375376	−	0.926872i	$-0.377513\pi$
$967$	23.3459			0.750753			0.375376	+	0.926872i	$0.377513\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.66507	−	13.2763i	−0.245984	−	0.426056i	0.716424	−	0.697665i	$-0.245778\pi$
$971$	−7.66507	−	13.2763i	−0.245984	−	0.426056i	−0.962408	+	0.271609i	$0.912444\pi$
$972$		0			0
$973$	11.2510	−	16.9142i	0.360690	−	0.542243i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	17.1008	+	9.87316i	0.547103	+	0.315870i	0.747953	−	0.663752i	$-0.231037\pi$
$977$	17.1008	+	9.87316i	0.547103	+	0.315870i	−0.200849	+	0.979622i	$0.564370\pi$
$978$		0			0
$979$		−	28.0894i		−	0.897742i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−11.4194	+	19.7790i	−0.364222	+	0.630851i	−0.988651	−	0.150230i	$-0.951998\pi$
$983$	−11.4194	+	19.7790i	−0.364222	+	0.630851i	0.624429	+	0.781082i	$0.285332\pi$
$984$		0			0
$985$	−13.5436	+	7.81940i	−0.431535	+	0.249147i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−19.8825	+	11.4792i	−0.632228	+	0.365017i
$990$		0			0
$991$	−3.92125	+	6.79180i	−0.124563	+	0.215749i	−0.921562	−	0.388232i	$-0.873086\pi$
$991$	−3.92125	+	6.79180i	−0.124563	+	0.215749i	0.796999	+	0.603980i	$0.206419\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			4.82776i			0.153050i
$996$		0			0
$997$	0.608720	+	0.351445i	0.0192783	+	0.0111304i	0.509608	−	0.860407i	$-0.329790\pi$
$997$	0.608720	+	0.351445i	0.0192783	+	0.0111304i	−0.490330	+	0.871537i	$0.663124\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.t.e.269.4	yes	12
3.2	odd	2	inner	756.2.t.e.269.3	✓	12
7.3	odd	6		5292.2.f.e.2645.8		12
7.4	even	3		5292.2.f.e.2645.6		12
7.5	odd	6	inner	756.2.t.e.593.3	yes	12
9.2	odd	6		2268.2.bm.i.1025.4		12
9.4	even	3		2268.2.w.i.269.4		12
9.5	odd	6		2268.2.w.i.269.3		12
9.7	even	3		2268.2.bm.i.1025.3		12
21.5	even	6	inner	756.2.t.e.593.4	yes	12
21.11	odd	6		5292.2.f.e.2645.7		12
21.17	even	6		5292.2.f.e.2645.5		12
63.5	even	6		2268.2.bm.i.593.3		12
63.40	odd	6		2268.2.bm.i.593.4		12
63.47	even	6		2268.2.w.i.1349.4		12
63.61	odd	6		2268.2.w.i.1349.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.t.e.269.3	✓	12	3.2	odd	2	inner
756.2.t.e.269.4	yes	12	1.1	even	1	trivial
756.2.t.e.593.3	yes	12	7.5	odd	6	inner
756.2.t.e.593.4	yes	12	21.5	even	6	inner
2268.2.w.i.269.3		12	9.5	odd	6
2268.2.w.i.269.4		12	9.4	even	3
2268.2.w.i.1349.3		12	63.61	odd	6
2268.2.w.i.1349.4		12	63.47	even	6
2268.2.bm.i.593.3		12	63.5	even	6
2268.2.bm.i.593.4		12	63.40	odd	6
2268.2.bm.i.1025.3		12	9.7	even	3
2268.2.bm.i.1025.4		12	9.2	odd	6
5292.2.f.e.2645.5		12	21.17	even	6
5292.2.f.e.2645.6		12	7.4	even	3
5292.2.f.e.2645.7		12	21.11	odd	6
5292.2.f.e.2645.8		12	7.3	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.385418 + 0.667563i) q^{5} +(-2.20291 - 1.46533i) q^{7} +O(q^{10})\)	\(q+(0.385418 + 0.667563i) q^{5} +(-2.20291 - 1.46533i) q^{7} +(-4.68157 - 2.70291i) q^{11} +5.28088i q^{13} +(-2.85433 + 4.94385i) q^{17} +(0.535344 - 0.309081i) q^{19} +(-5.83782 + 3.37047i) q^{23} +(2.20291 - 3.81555i) q^{25} +8.07606i q^{29} +(0.502688 + 0.290227i) q^{31} +(0.129163 - 2.03534i) q^{35} +(-4.53803 - 7.86010i) q^{37} -8.59231 q^{41} +3.40581 q^{43} +(0.385418 + 0.667563i) q^{47} +(2.70560 + 6.45599i) q^{49} +(-6.63798 - 3.83244i) q^{53} -4.16699i q^{55} +(6.89423 - 11.9412i) q^{59} +(-3.57606 + 2.06464i) q^{61} +(-3.52532 + 2.03534i) q^{65} +(-6.77628 + 11.7369i) q^{67} +2.25906i q^{71} +(1.96197 + 1.13274i) q^{73} +(6.35241 + 12.8143i) q^{77} +(4.03534 + 6.98942i) q^{79} -3.85418 q^{83} -4.40044 q^{85} +(2.59808 + 4.50000i) q^{89} +(7.73825 - 11.6333i) q^{91} +(0.412662 + 0.238250i) q^{95} -14.0259i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q - 18 q^{19} - 24 q^{37} - 12 q^{43} + 18 q^{61} + 54 q^{73} + 24 q^{79} - 12 q^{85} + 42 q^{91}+O(q^{100}) \) 12 * q - 18 * q^19 - 24 * q^37 - 12 * q^43 + 18 * q^61 + 54 * q^73 + 24 * q^79 - 12 * q^85 + 42 * q^91

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