LMFDB - Embedded newform 2268.2.l.m.541.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2268,2,Mod(109,2268)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2268, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2268.109"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.l (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,4,0,-2,0,0,0,-10,0,-3,0,0,0,2,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.3
Root			$-1.03075 - 1.78531i$ of defining polynomial
Character	$\chi$	$=$	2268.541
Dual form			2268.2.l.m.109.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.90305 q^{5} +(-2.64072 - 0.163054i) q^{7} +2.82619 q^{11} +(-2.41310 - 4.17961i) q^{13} +(-2.14072 - 3.70784i) q^{17} +(2.37467 - 4.11304i) q^{19} -2.46789 q^{23} -1.37839 q^{25} +(-4.32619 + 7.49319i) q^{29} +(-1.68547 + 2.91932i) q^{31} +(-5.02543 - 0.310300i) q^{35} +(-2.59225 + 4.48991i) q^{37} +(-4.10229 - 7.10538i) q^{41} +(-3.36462 + 5.82770i) q^{43} +(-0.864622 - 1.49757i) q^{47} +(6.94683 + 0.861161i) q^{49} +(-5.80983 - 10.0629i) q^{53} +5.37839 q^{55} +(6.73297 - 11.6618i) q^{59} +(-2.62063 - 4.53907i) q^{61} +(-4.59225 - 7.95401i) q^{65} +(6.35992 - 11.0157i) q^{67} -7.39848 q^{71} +(4.23297 + 7.33172i) q^{73} +(-7.46319 - 0.460822i) q^{77} +(1.97161 + 3.41494i) q^{79} +(4.72390 - 8.18204i) q^{83} +(-4.07391 - 7.05621i) q^{85} +(-4.91941 + 8.52068i) q^{89} +(5.69081 + 11.4306i) q^{91} +(4.51911 - 7.82734i) q^{95} +(-1.60699 + 2.78339i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} - 2 q^{7} - 10 q^{11} - 3 q^{13} + 2 q^{17} - 8 q^{19} - 4 q^{23} + 16 q^{25} - 2 q^{29} + 11 q^{35} + 4 q^{37} - 3 q^{41} - 5 q^{43} + 15 q^{47} + 14 q^{49} - 24 q^{53} + 16 q^{55} + 10 q^{59}+ \cdots - 19 q^{97}+O(q^{100}) $ 8 * q + 4 * q^5 - 2 * q^7 - 10 * q^11 - 3 * q^13 + 2 * q^17 - 8 * q^19 - 4 * q^23 + 16 * q^25 - 2 * q^29 + 11 * q^35 + 4 * q^37 - 3 * q^41 - 5 * q^43 + 15 * q^47 + 14 * q^49 - 24 * q^53 + 16 * q^55 + 10 * q^59 - 12 * q^61 - 12 * q^65 - 7 * q^67 - 22 * q^71 - 10 * q^73 - 8 * q^77 + 35 * q^83 + 13 * q^85 - 18 * q^89 - 9 * q^91 - 10 * q^95 - 19 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.90305			0.851071			0.425535	−	0.904942i	$-0.360086\pi$
$5$	1.90305			0.851071			0.425535	+	0.904942i	$0.360086\pi$
$6$		0			0
$7$	−2.64072	−	0.163054i	−0.998099	−	0.0616287i
$7$	−2.64072	−	0.163054i	−0.998099	−	0.0616287i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.82619			0.852129			0.426065	−	0.904693i	$-0.359900\pi$
$11$	2.82619			0.852129			0.426065	+	0.904693i	$0.359900\pi$
$12$		0			0
$13$	−2.41310	−	4.17961i	−0.669272	−	1.15921i	−0.978108	−	0.208098i	$-0.933273\pi$
$13$	−2.41310	−	4.17961i	−0.669272	−	1.15921i	0.308835	−	0.951115i	$-0.400061\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.14072	−	3.70784i	−0.519201	−	0.899283i	−0.999751	−	0.0223156i	$-0.992896\pi$
$17$	−2.14072	−	3.70784i	−0.519201	−	0.899283i	0.480550	−	0.876968i	$-0.340437\pi$
$18$		0			0
$19$	2.37467	−	4.11304i	0.544786	−	0.943597i	−0.453835	−	0.891086i	$-0.649944\pi$
$19$	2.37467	−	4.11304i	0.544786	−	0.943597i	0.998620	−	0.0525107i	$-0.0167224\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.46789			−0.514590			−0.257295	−	0.966333i	$-0.582831\pi$
$23$	−2.46789			−0.514590			−0.257295	+	0.966333i	$0.582831\pi$
$24$		0			0
$25$	−1.37839			−0.275678
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.32619	+	7.49319i	−0.803354	+	1.39145i	0.114043	+	0.993476i	$0.463620\pi$
$29$	−4.32619	+	7.49319i	−0.803354	+	1.39145i	−0.917397	+	0.397974i	$0.869714\pi$
$30$		0			0
$31$	−1.68547	+	2.91932i	−0.302719	+	0.524325i	−0.976751	−	0.214377i	$-0.931228\pi$
$31$	−1.68547	+	2.91932i	−0.302719	+	0.524325i	0.674032	+	0.738703i	$0.264561\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.02543	−	0.310300i	−0.849453	−	0.0524504i
$36$		0			0
$37$	−2.59225	+	4.48991i	−0.426163	+	0.738136i	−0.996528	−	0.0832552i	$-0.973468\pi$
$37$	−2.59225	+	4.48991i	−0.426163	+	0.738136i	0.570365	+	0.821391i	$0.306802\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.10229	−	7.10538i	−0.640670	−	1.10967i	−0.985283	−	0.170929i	$-0.945323\pi$
$41$	−4.10229	−	7.10538i	−0.640670	−	1.10967i	0.344613	−	0.938745i	$-0.388010\pi$
$42$		0			0
$43$	−3.36462	+	5.82770i	−0.513100	+	0.888715i	0.486784	+	0.873522i	$0.338170\pi$
$43$	−3.36462	+	5.82770i	−0.513100	+	0.888715i	−0.999885	+	0.0151933i	$0.995164\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.864622	−	1.49757i	−0.126118	−	0.218443i	0.796051	−	0.605229i	$-0.206919\pi$
$47$	−0.864622	−	1.49757i	−0.126118	−	0.218443i	−0.922169	+	0.386786i	$0.873585\pi$
$48$		0			0
$49$	6.94683	+	0.861161i	0.992404	+	0.123023i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.80983	−	10.0629i	−0.798042	−	1.38225i	−0.920890	−	0.389823i	$-0.872536\pi$
$53$	−5.80983	−	10.0629i	−0.798042	−	1.38225i	0.122848	−	0.992425i	$-0.460797\pi$
$54$		0			0
$55$	5.37839			0.725222
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.73297	−	11.6618i	0.876558	−	1.51824i	0.0214644	−	0.999770i	$-0.493167\pi$
$59$	6.73297	−	11.6618i	0.876558	−	1.51824i	0.855094	−	0.518474i	$-0.173500\pi$
$60$		0			0
$61$	−2.62063	−	4.53907i	−0.335538	−	0.581169i	0.648050	−	0.761598i	$-0.275585\pi$
$61$	−2.62063	−	4.53907i	−0.335538	−	0.581169i	−0.983588	+	0.180429i	$0.942251\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.59225	−	7.95401i	−0.569598	−	0.986573i
$66$		0			0
$67$	6.35992	−	11.0157i	0.776988	−	1.34578i	−0.156682	−	0.987649i	$-0.550080\pi$
$67$	6.35992	−	11.0157i	0.776988	−	1.34578i	0.933670	−	0.358134i	$-0.116587\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.39848			−0.878038			−0.439019	−	0.898478i	$-0.644674\pi$
$71$	−7.39848			−0.878038			−0.439019	+	0.898478i	$0.644674\pi$
$72$		0			0
$73$	4.23297	+	7.33172i	0.495432	+	0.858113i	0.999986	−	0.00526700i	$-0.00167654\pi$
$73$	4.23297	+	7.33172i	0.495432	+	0.858113i	−0.504554	+	0.863380i	$0.668343\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.46319	−	0.460822i	−0.850509	−	0.0525156i
$78$		0			0
$79$	1.97161	+	3.41494i	0.221824	+	0.384210i	0.955362	−	0.295438i	$-0.0954657\pi$
$79$	1.97161	+	3.41494i	0.221824	+	0.384210i	−0.733538	+	0.679649i	$0.762132\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.72390	−	8.18204i	0.518515	−	0.898095i	−0.481253	−	0.876582i	$-0.659818\pi$
$83$	4.72390	−	8.18204i	0.518515	−	0.898095i	0.999769	−	0.0215134i	$-0.00684845\pi$
$84$		0			0
$85$	−4.07391	−	7.05621i	−0.441877	−	0.765354i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.91941	+	8.52068i	−0.521457	+	0.903190i	0.478232	+	0.878234i	$0.341278\pi$
$89$	−4.91941	+	8.52068i	−0.521457	+	0.903190i	−0.999689	+	0.0249561i	$0.992055\pi$
$90$		0			0
$91$	5.69081	+	11.4306i	0.596559	+	1.19826i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.51911	−	7.82734i	0.463651	−	0.803068i
$96$		0			0
$97$	−1.60699	+	2.78339i	−0.163165	+	0.282611i	−0.936002	−	0.351994i	$-0.885504\pi$
$97$	−1.60699	+	2.78339i	−0.163165	+	0.282611i	0.772837	+	0.634605i	$0.218837\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.532112			−0.0529471			−0.0264735	−	0.999650i	$-0.508428\pi$
$101$	−0.532112			−0.0529471			−0.0264735	+	0.999650i	$0.508428\pi$
$102$		0			0
$103$	−5.25391			−0.517683			−0.258841	−	0.965920i	$-0.583341\pi$
$103$	−5.25391			−0.517683			−0.258841	+	0.965920i	$0.583341\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.935164	−	1.61975i	0.0904057	−	0.156587i	−0.817276	−	0.576246i	$-0.804517\pi$
$107$	0.935164	−	1.61975i	0.0904057	−	0.156587i	0.907682	+	0.419659i	$0.137850\pi$
$108$		0			0
$109$	−1.99627	−	3.45765i	−0.191208	−	0.331183i	0.754443	−	0.656366i	$-0.227907\pi$
$109$	−1.99627	−	3.45765i	−0.191208	−	0.331183i	−0.945651	+	0.325183i	$0.894574\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.64607	−	11.5113i	−0.625209	−	1.08289i	−0.988500	−	0.151219i	$-0.951680\pi$
$113$	−6.64607	−	11.5113i	−0.625209	−	1.08289i	0.363291	−	0.931676i	$-0.381653\pi$
$114$		0			0
$115$	−4.69652			−0.437953
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.04847	+	10.1404i	0.462793	+	0.929571i
$120$		0			0
$121$	−3.01264			−0.273876
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.1384			−1.08569
$126$		0			0
$127$	4.73670			0.420314			0.210157	−	0.977668i	$-0.432603\pi$
$127$	4.73670			0.420314			0.210157	+	0.977668i	$0.432603\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	13.7072			1.19760			0.598802	−	0.800897i	$-0.295644\pi$
$131$	13.7072			1.19760			0.598802	+	0.800897i	$0.295644\pi$
$132$		0			0
$133$	−6.94148	+	10.4742i	−0.601903	+	0.908229i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−21.0710			−1.80021			−0.900106	−	0.435670i	$-0.856511\pi$
$137$	−21.0710			−1.80021			−0.900106	+	0.435670i	$0.856511\pi$
$138$		0			0
$139$	−5.39673	−	9.34742i	−0.457745	−	0.792838i	0.541096	−	0.840961i	$-0.318009\pi$
$139$	−5.39673	−	9.34742i	−0.457745	−	0.792838i	−0.998841	+	0.0481230i	$0.984676\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.81987	−	11.8124i	−0.570307	−	0.987800i
$144$		0			0
$145$	−8.23297	+	14.2599i	−0.683711	+	1.18422i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.25391			0.348493			0.174247	−	0.984702i	$-0.444251\pi$
$149$	4.25391			0.348493			0.174247	+	0.984702i	$0.444251\pi$
$150$		0			0
$151$	17.3415			1.41123			0.705614	−	0.708597i	$-0.250671\pi$
$151$	17.3415			1.41123			0.705614	+	0.708597i	$0.250671\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.20754	+	5.55562i	−0.257636	+	0.446238i
$156$		0			0
$157$	3.38471	−	5.86249i	0.270129	−	0.467878i	−0.698765	−	0.715351i	$-0.746267\pi$
$157$	3.38471	−	5.86249i	0.270129	−	0.467878i	0.968895	+	0.247473i	$0.0796002\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.51701	+	0.402399i	0.513612	+	0.0317135i
$162$		0			0
$163$	8.46691	−	14.6651i	0.663180	−	1.14866i	−0.316595	−	0.948561i	$-0.602540\pi$
$163$	8.46691	−	14.6651i	0.663180	−	1.14866i	0.979775	−	0.200101i	$-0.0641269\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.120634	+	0.208945i	0.00933496	+	0.0161686i	0.870655	−	0.491894i	$-0.163695\pi$
$167$	0.120634	+	0.208945i	0.00933496	+	0.0161686i	−0.861320	+	0.508063i	$0.830362\pi$
$168$		0			0
$169$	−5.14607	+	8.91325i	−0.395851	+	0.685635i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.70556	+	9.88232i	0.433786	+	0.751339i	0.997196	−	0.0748388i	$-0.0238442\pi$
$173$	5.70556	+	9.88232i	0.433786	+	0.751339i	−0.563410	+	0.826177i	$0.690511\pi$
$174$		0			0
$175$	3.63995	+	0.224752i	0.275154	+	0.0169897i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.5592	−	21.7531i	−0.938716	−	1.62590i	−0.767870	−	0.640606i	$-0.778683\pi$
$179$	−12.5592	−	21.7531i	−0.938716	−	1.62590i	−0.170846	−	0.985298i	$-0.554650\pi$
$180$		0			0
$181$	15.3709			1.14251			0.571257	−	0.820772i	$-0.306456\pi$
$181$	15.3709			1.14251			0.571257	+	0.820772i	$0.306456\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.93318	+	8.54453i	−0.362695	+	0.628206i
$186$		0			0
$187$	−6.05009	−	10.4791i	−0.442427	−	0.766305i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.78679	+	10.0230i	0.418717	+	0.725240i	0.995811	−	0.0914385i	$-0.0291465\pi$
$191$	5.78679	+	10.0230i	0.418717	+	0.725240i	−0.577093	+	0.816678i	$0.695813\pi$
$192$		0			0
$193$	−1.07488	+	1.86175i	−0.0773715	+	0.134011i	−0.902115	−	0.431495i	$-0.857986\pi$
$193$	−1.07488	+	1.86175i	−0.0773715	+	0.134011i	0.824744	+	0.565507i	$0.191319\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.649147			−0.0462498			−0.0231249	−	0.999733i	$-0.507362\pi$
$197$	−0.649147			−0.0462498			−0.0231249	+	0.999733i	$0.507362\pi$
$198$		0			0
$199$	−5.19454	−	8.99721i	−0.368231	−	0.637795i	0.621058	−	0.783765i	$-0.286703\pi$
$199$	−5.19454	−	8.99721i	−0.368231	−	0.637795i	−0.989289	+	0.145970i	$0.953370\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	12.6461	−	19.0820i	0.887580	−	1.33929i
$204$		0			0
$205$	−7.80688	−	13.5219i	−0.545256	−	0.944411i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.71126	−	11.6242i	0.464228	−	0.804066i
$210$		0			0
$211$	11.3215	+	19.6094i	0.779404	+	1.34997i	0.932286	+	0.361722i	$0.117811\pi$
$211$	11.3215	+	19.6094i	0.779404	+	1.34997i	−0.152882	+	0.988244i	$0.548855\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.40305	+	11.0904i	−0.436685	+	0.756360i
$216$		0			0
$217$	4.92687	−	7.43429i	0.334457	−	0.504673i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−10.3315	+	17.8947i	−0.694974	+	1.20373i
$222$		0			0
$223$	−13.2767	+	22.9960i	−0.889077	+	1.53993i	−0.0481078	+	0.998842i	$0.515319\pi$
$223$	−13.2767	+	22.9960i	−0.889077	+	1.53993i	−0.840969	+	0.541084i	$0.818014\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.2539			−0.680576			−0.340288	−	0.940321i	$-0.610524\pi$
$227$	−10.2539			−0.680576			−0.340288	+	0.940321i	$0.610524\pi$
$228$		0			0
$229$	12.3985			0.819315			0.409657	−	0.912239i	$-0.365648\pi$
$229$	12.3985			0.819315			0.409657	+	0.912239i	$0.365648\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.60699	−	6.24749i	0.236302	−	0.409287i	−0.723348	−	0.690483i	$-0.757398\pi$
$233$	3.60699	−	6.24749i	0.236302	−	0.409287i	0.959650	+	0.281196i	$0.0907312\pi$
$234$		0			0
$235$	−1.64542	−	2.84995i	−0.107335	−	0.185910i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.55479	−	4.42503i	−0.165256	−	0.286231i	0.771490	−	0.636241i	$-0.219512\pi$
$239$	−2.55479	−	4.42503i	−0.165256	−	0.286231i	−0.936746	+	0.350010i	$0.886178\pi$
$240$		0			0
$241$	−13.7032			−0.882704			−0.441352	−	0.897334i	$-0.645501\pi$
$241$	−13.7032			−0.882704			−0.441352	+	0.897334i	$0.645501\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	13.2202	+	1.63883i	0.844606	+	0.104701i
$246$		0			0
$247$	−22.9212			−1.45844
$248$		0			0
$249$		0			0
$250$		0			0
$251$	26.7694			1.68967			0.844835	−	0.535026i	$-0.179698\pi$
$251$	26.7694			1.68967			0.844835	+	0.535026i	$0.179698\pi$
$252$		0			0
$253$	−6.97473			−0.438497
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−20.7581			−1.29485			−0.647427	−	0.762128i	$-0.724155\pi$
$257$	−20.7581			−1.29485			−0.647427	+	0.762128i	$0.724155\pi$
$258$		0			0
$259$	7.57750	−	11.4339i	0.470843	−	0.710469i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.68316			0.288776			0.144388	−	0.989521i	$-0.453879\pi$
$263$	4.68316			0.288776			0.144388	+	0.989521i	$0.453879\pi$
$264$		0			0
$265$	−11.0564	−	19.1503i	−0.679190	−	1.17639i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.26767	+	12.5880i	0.443118	+	0.767503i	0.997919	−	0.0644803i	$-0.0205390\pi$
$269$	7.26767	+	12.5880i	0.443118	+	0.767503i	−0.554801	+	0.831983i	$0.687206\pi$
$270$		0			0
$271$	−3.32247	+	5.75468i	−0.201825	+	0.349572i	−0.949117	−	0.314925i	$-0.898021\pi$
$271$	−3.32247	+	5.75468i	−0.201825	+	0.349572i	0.747291	+	0.664497i	$0.231354\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.89560			−0.234914
$276$		0			0
$277$	10.0201			0.602049			0.301024	−	0.953616i	$-0.402671\pi$
$277$	10.0201			0.602049			0.301024	+	0.953616i	$0.402671\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.87531	−	17.1045i	0.589112	−	1.02037i	−0.405237	−	0.914211i	$-0.632811\pi$
$281$	9.87531	−	17.1045i	0.589112	−	1.02037i	0.994349	−	0.106160i	$-0.0338555\pi$
$282$		0			0
$283$	−0.314530	+	0.544781i	−0.0186969	+	0.0323839i	−0.875222	−	0.483721i	$-0.839285\pi$
$283$	−0.314530	+	0.544781i	−0.0186969	+	0.0323839i	0.856526	+	0.516105i	$0.172618\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.67445	+	19.4322i	0.571065	+	1.14705i
$288$		0			0
$289$	−0.665382	+	1.15248i	−0.0391401	+	0.0677927i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.54179	+	6.13457i	0.206914	+	0.358385i	0.950741	−	0.309987i	$-0.100325\pi$
$293$	3.54179	+	6.13457i	0.206914	+	0.358385i	−0.743827	+	0.668372i	$0.766991\pi$
$294$		0			0
$295$	12.8132	−	22.1931i	0.746013	−	1.29213i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.95525	+	10.3148i	0.344401	+	0.596520i
$300$		0			0
$301$	9.83526	−	14.8407i	0.566895	−	0.855404i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.98720	−	8.63809i	−0.285566	−	0.494616i
$306$		0			0
$307$	−16.9445			−0.967075			−0.483537	−	0.875324i	$-0.660648\pi$
$307$	−16.9445			−0.967075			−0.483537	+	0.875324i	$0.660648\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.38831	+	7.60077i	−0.248838	+	0.431000i	−0.963204	−	0.268772i	$-0.913382\pi$
$311$	−4.38831	+	7.60077i	−0.248838	+	0.431000i	0.714366	+	0.699773i	$0.246715\pi$
$312$		0			0
$313$	−10.1792	−	17.6308i	−0.575360	−	0.996552i	−0.996002	−	0.0893259i	$-0.971529\pi$
$313$	−10.1792	−	17.6308i	−0.575360	−	0.996552i	0.420643	−	0.907226i	$-0.361805\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.7667	−	22.1126i	−0.717049	−	1.24197i	−0.962164	−	0.272472i	$-0.912159\pi$
$317$	−12.7667	−	22.1126i	−0.717049	−	1.24197i	0.245114	−	0.969494i	$-0.421174\pi$
$318$		0			0
$319$	−12.2267	+	21.1772i	−0.684561	+	1.18569i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−20.3340			−1.13141
$324$		0			0
$325$	3.32619	+	5.76113i	0.184504	+	0.319570i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.03904	+	4.09565i	0.112416	+	0.225800i
$330$		0			0
$331$	11.9423	+	20.6846i	0.656406	+	1.13693i	0.981539	+	0.191260i	$0.0612573\pi$
$331$	11.9423	+	20.6846i	0.656406	+	1.13693i	−0.325134	+	0.945668i	$0.605409\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	12.1033	−	20.9635i	0.661272	−	1.14536i
$336$		0			0
$337$	14.1778	+	24.5567i	0.772315	+	1.33769i	0.936291	+	0.351224i	$0.114235\pi$
$337$	14.1778	+	24.5567i	0.772315	+	1.33769i	−0.163976	+	0.986464i	$0.552432\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.76346	+	8.25056i	−0.257956	+	0.446793i
$342$		0			0
$343$	−18.2042	−	3.40680i	−0.982936	−	0.183950i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.18288	+	3.78086i	−0.117183	+	0.202967i	−0.918650	−	0.395072i	$-0.870720\pi$
$347$	−2.18288	+	3.78086i	−0.117183	+	0.202967i	0.801467	+	0.598039i	$0.204053\pi$
$348$		0			0
$349$	7.55446	−	13.0847i	0.404381	−	0.700409i	−0.589868	−	0.807500i	$-0.700820\pi$
$349$	7.55446	−	13.0847i	0.404381	−	0.700409i	0.994249	+	0.107091i	$0.0341536\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−25.5421			−1.35947			−0.679734	−	0.733459i	$-0.737905\pi$
$353$	−25.5421			−1.35947			−0.679734	+	0.733459i	$0.737905\pi$
$354$		0			0
$355$	−14.0797			−0.747273
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.70718	−	16.8133i	0.512325	−	0.887373i	−0.487573	−	0.873082i	$-0.662118\pi$
$359$	9.70718	−	16.8133i	0.512325	−	0.887373i	0.999898	−	0.0142909i	$-0.00454908\pi$
$360$		0			0
$361$	−1.77808	−	3.07972i	−0.0935831	−	0.162091i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	8.05556	+	13.9526i	0.421647	+	0.730315i
$366$		0			0
$367$	13.2101			0.689561			0.344780	−	0.938683i	$-0.387953\pi$
$367$	13.2101			0.689561			0.344780	+	0.938683i	$0.387953\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	13.7013	+	27.5207i	0.711338	+	1.42880i
$372$		0			0
$373$	32.3556			1.67531			0.837656	−	0.546199i	$-0.183926\pi$
$373$	32.3556			1.67531			0.837656	+	0.546199i	$0.183926\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	41.7581			2.15065
$378$		0			0
$379$	−12.9760			−0.666530			−0.333265	−	0.942833i	$-0.608150\pi$
$379$	−12.9760			−0.666530			−0.333265	+	0.942833i	$0.608150\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.3015			0.628579			0.314289	−	0.949327i	$-0.398234\pi$
$383$	12.3015			0.628579			0.314289	+	0.949327i	$0.398234\pi$
$384$		0			0
$385$	−14.2028	−	0.876969i	−0.723844	−	0.0446945i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−29.2614			−1.48361			−0.741805	−	0.670616i	$-0.766030\pi$
$389$	−29.2614			−1.48361			−0.741805	+	0.670616i	$0.766030\pi$
$390$		0			0
$391$	5.28306	+	9.15053i	0.267176	+	0.462762i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.75208	+	6.49880i	0.188788	+	0.326990i
$396$		0			0
$397$	−6.33089	+	10.9654i	−0.317738	+	0.550339i	−0.980016	−	0.198920i	$-0.936257\pi$
$397$	−6.33089	+	10.9654i	−0.317738	+	0.550339i	0.662277	+	0.749259i	$0.269590\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.96850			0.248115			0.124058	−	0.992275i	$-0.460409\pi$
$401$	4.96850			0.248115			0.124058	+	0.992275i	$0.460409\pi$
$402$		0			0
$403$	16.2688			0.810407
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.32619	+	12.6893i	−0.363146	+	0.628987i
$408$		0			0
$409$	−9.43950	+	16.3497i	−0.466753	+	0.808441i	−0.999279	−	0.0379735i	$-0.987910\pi$
$409$	−9.43950	+	16.3497i	−0.466753	+	0.808441i	0.532525	+	0.846414i	$0.321243\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−19.6814	+	29.6979i	−0.968459	+	1.46134i
$414$		0			0
$415$	8.98983	−	15.5708i	0.441293	−	0.764343i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.93516	+	6.81590i	0.192245	+	0.332979i	0.945994	−	0.324184i	$-0.105090\pi$
$419$	3.93516	+	6.81590i	0.192245	+	0.332979i	−0.753749	+	0.657163i	$0.771756\pi$
$420$		0			0
$421$	12.6287	−	21.8736i	0.615487	−	1.06605i	−0.374812	−	0.927101i	$-0.622293\pi$
$421$	12.6287	−	21.8736i	0.615487	−	1.06605i	0.990299	−	0.138953i	$-0.0443738\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.95075	+	5.11086i	0.143133	+	0.247913i
$426$		0			0
$427$	6.18025	+	12.4137i	0.299083	+	0.600743i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	15.9729	+	27.6659i	0.769388	+	1.33262i	0.937895	+	0.346918i	$0.112772\pi$
$431$	15.9729	+	27.6659i	0.769388	+	1.33262i	−0.168508	+	0.985700i	$0.553895\pi$
$432$		0			0
$433$	37.2827			1.79169			0.895847	−	0.444363i	$-0.146570\pi$
$433$	37.2827			1.79169			0.895847	+	0.444363i	$0.146570\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.86041	+	10.1505i	−0.280341	+	0.485566i
$438$		0			0
$439$	19.5598	+	33.8786i	0.933539	+	1.61694i	0.777219	+	0.629230i	$0.216630\pi$
$439$	19.5598	+	33.8786i	0.933539	+	1.61694i	0.156319	+	0.987707i	$0.450037\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.00359878	+	0.00623326i	0.000170983	+	0.000296151i	0.866111	−	0.499852i	$-0.166612\pi$
$443$	0.00359878	+	0.00623326i	0.000170983	+	0.000296151i	−0.865940	+	0.500148i	$0.833279\pi$
$444$		0			0
$445$	−9.36190	+	16.2153i	−0.443797	+	0.768679i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	30.6812			1.44794			0.723968	−	0.689834i	$-0.242316\pi$
$449$	30.6812			1.44794			0.723968	+	0.689834i	$0.242316\pi$
$450$		0			0
$451$	−11.5939	−	20.0812i	−0.545934	−	0.945585i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	10.8299	+	21.7531i	0.507714	+	1.01980i
$456$		0			0
$457$	19.0561	+	33.0061i	0.891406	+	1.54396i	0.838191	+	0.545377i	$0.183614\pi$
$457$	19.0561	+	33.0061i	0.891406	+	1.54396i	0.0532152	+	0.998583i	$0.483053\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	15.1250	−	26.1972i	0.704440	−	1.22013i	−0.262453	−	0.964945i	$-0.584531\pi$
$461$	15.1250	−	26.1972i	0.704440	−	1.22013i	0.966893	−	0.255181i	$-0.0821352\pi$
$462$		0			0
$463$	−12.3004	−	21.3050i	−0.571650	−	0.990126i	−0.996397	−	0.0848141i	$-0.972970\pi$
$463$	−12.3004	−	21.3050i	−0.571650	−	0.990126i	0.424747	−	0.905312i	$-0.360363\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.26472	−	5.65466i	0.151073	−	0.261667i	−0.780549	−	0.625095i	$-0.785060\pi$
$467$	3.26472	−	5.65466i	0.151073	−	0.261667i	0.931622	+	0.363428i	$0.118394\pi$
$468$		0			0
$469$	−18.5909	+	28.0524i	−0.858450	+	1.29534i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−9.50907	+	16.4702i	−0.437228	+	0.757300i
$474$		0			0
$475$	−3.27322	+	5.66938i	−0.150186	+	0.260129i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	27.4523			1.25433			0.627164	−	0.778887i	$-0.284215\pi$
$479$	27.4523			1.25433			0.627164	+	0.778887i	$0.284215\pi$
$480$		0			0
$481$	25.0214			1.14088
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.05819	+	5.29694i	−0.138865	+	0.240522i
$486$		0			0
$487$	−16.0776	−	27.8473i	−0.728547	−	1.26188i	−0.957497	−	0.288442i	$-0.906863\pi$
$487$	−16.0776	−	27.8473i	−0.728547	−	1.26188i	0.228950	−	0.973438i	$-0.426471\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	14.8937	+	25.7966i	0.672141	+	1.16418i	0.977296	+	0.211880i	$0.0679585\pi$
$491$	14.8937	+	25.7966i	0.672141	+	1.16418i	−0.305155	+	0.952303i	$0.598708\pi$
$492$		0			0
$493$	37.0447			1.66841
$494$		0			0
$495$		0			0
$496$		0			0
$497$	19.5373	+	1.20635i	0.876369	+	0.0541123i
$498$		0			0
$499$	−29.1751			−1.30606			−0.653028	−	0.757333i	$-0.726502\pi$
$499$	−29.1751			−1.30606			−0.653028	+	0.757333i	$0.726502\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	39.1553			1.74585			0.872923	−	0.487857i	$-0.162221\pi$
$503$	39.1553			1.74585			0.872923	+	0.487857i	$0.162221\pi$
$504$		0			0
$505$	−1.01264			−0.0450617
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−9.21923			−0.408635			−0.204318	−	0.978905i	$-0.565498\pi$
$509$	−9.21923			−0.408635			−0.204318	+	0.978905i	$0.565498\pi$
$510$		0			0
$511$	−9.98263	−	20.0512i	−0.441606	−	0.887015i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−9.99846			−0.440585
$516$		0			0
$517$	−2.44359	−	4.23242i	−0.107469	−	0.186142i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	14.6973	+	25.4565i	0.643900	+	1.11527i	0.984554	+	0.175079i	$0.0560181\pi$
$521$	14.6973	+	25.4565i	0.643900	+	1.11527i	−0.340654	+	0.940189i	$0.610649\pi$
$522$		0			0
$523$	−8.57488	+	14.8521i	−0.374953	+	0.649438i	−0.990320	−	0.138803i	$-0.955675\pi$
$523$	−8.57488	+	14.8521i	−0.374953	+	0.649438i	0.615367	+	0.788241i	$0.289008\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	14.4325			0.628689
$528$		0			0
$529$	−16.9095			−0.735197
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−19.7985	+	34.2919i	−0.857566	+	1.48535i
$534$		0			0
$535$	1.77967	−	3.08247i	0.0769417	−	0.133267i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	19.6331	+	2.43381i	0.845656	+	0.104831i
$540$		0			0
$541$	−11.0775	+	19.1868i	−0.476259	+	0.824905i	−0.999630	−	0.0272000i	$-0.991341\pi$
$541$	−11.0775	+	19.1868i	−0.476259	+	0.824905i	0.523371	+	0.852105i	$0.324674\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.79901	−	6.58009i	−0.162732	−	0.281860i
$546$		0			0
$547$	−3.87110	+	6.70494i	−0.165516	+	0.286683i	−0.936839	−	0.349762i	$-0.886262\pi$
$547$	−3.87110	+	6.70494i	−0.165516	+	0.286683i	0.771322	+	0.636445i	$0.219596\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	20.5465	+	35.5876i	0.875311	+	1.51608i
$552$		0			0
$553$	−4.64967	−	9.33938i	−0.197724	−	0.397151i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.73233	−	8.19663i	−0.200515	−	0.347302i	0.748179	−	0.663496i	$-0.230928\pi$
$557$	−4.73233	−	8.19663i	−0.200515	−	0.347302i	−0.948694	+	0.316194i	$0.897595\pi$
$558$		0			0
$559$	32.4766			1.37362
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.50632	−	16.4654i	0.400644	−	0.693935i	−0.593160	−	0.805084i	$-0.702120\pi$
$563$	9.50632	−	16.4654i	0.400644	−	0.693935i	0.993804	+	0.111150i	$0.0354532\pi$
$564$		0			0
$565$	−12.6478	−	21.9067i	−0.532097	−	0.921620i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−18.9121	−	32.7568i	−0.792837	−	1.37323i	−0.924203	−	0.381901i	$-0.875270\pi$
$569$	−18.9121	−	32.7568i	−0.792837	−	1.37323i	0.131366	−	0.991334i	$-0.458064\pi$
$570$		0			0
$571$	−12.0400	+	20.8540i	−0.503860	+	0.872712i	0.496130	+	0.868248i	$0.334754\pi$
$571$	−12.0400	+	20.8540i	−0.503860	+	0.872712i	−0.999990	+	0.00446331i	$0.998579\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	3.40172			0.141861
$576$		0			0
$577$	−15.1936	−	26.3160i	−0.632516	−	1.09555i	−0.987036	−	0.160502i	$-0.948689\pi$
$577$	−15.1936	−	26.3160i	−0.632516	−	1.09555i	0.354519	−	0.935049i	$-0.384645\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−13.8086	+	20.8362i	−0.572878	+	0.864432i
$582$		0			0
$583$	−16.4197	−	28.4398i	−0.680034	−	1.17785i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.7714	−	34.2451i	0.816053	−	1.41345i	−0.0925163	−	0.995711i	$-0.529491\pi$
$587$	19.7714	−	34.2451i	0.816053	−	1.41345i	0.908569	−	0.417734i	$-0.137176\pi$
$588$		0			0
$589$	8.00486	+	13.8648i	0.329834	+	0.571290i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.167128	−	0.289474i	0.00686313	−	0.0118873i	−0.862573	−	0.505932i	$-0.831149\pi$
$593$	0.167128	−	0.289474i	0.00686313	−	0.0118873i	0.869437	+	0.494045i	$0.164482\pi$
$594$		0			0
$595$	9.60751	+	19.2978i	0.393869	+	0.791131i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.16166	−	2.01205i	0.0474640	−	0.0822101i	−0.841317	−	0.540542i	$-0.818219\pi$
$599$	1.16166	−	2.01205i	0.0474640	−	0.0822101i	0.888781	+	0.458331i	$0.151553\pi$
$600$		0			0
$601$	−8.31826	+	14.4076i	−0.339309	+	0.587700i	−0.984303	−	0.176488i	$-0.943526\pi$
$601$	−8.31826	+	14.4076i	−0.339309	+	0.587700i	0.644994	+	0.764188i	$0.276860\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.73320			−0.233088
$606$		0			0
$607$	23.5587			0.956217			0.478109	−	0.878301i	$-0.341323\pi$
$607$	23.5587			0.956217			0.478109	+	0.878301i	$0.341323\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.17283	+	7.22756i	−0.168815	+	0.292396i
$612$		0			0
$613$	−18.4839	−	32.0151i	−0.746559	−	1.29308i	−0.949463	−	0.313879i	$-0.898371\pi$
$613$	−18.4839	−	32.0151i	−0.746559	−	1.29308i	0.202904	−	0.979199i	$-0.434962\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	17.8625	+	30.9388i	0.719118	+	1.24555i	0.961350	+	0.275330i	$0.0887872\pi$
$617$	17.8625	+	30.9388i	0.719118	+	1.24555i	−0.242232	+	0.970218i	$0.577879\pi$
$618$		0			0
$619$	23.0214			0.925307			0.462654	−	0.886539i	$-0.346897\pi$
$619$	23.0214			0.925307			0.462654	+	0.886539i	$0.346897\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	14.3801	−	21.6986i	0.576128	−	0.869336i
$624$		0			0
$625$	−16.2081			−0.648323
$626$		0			0
$627$		0			0
$628$		0			0
$629$	22.1971			0.885058
$630$		0			0
$631$	−33.7928			−1.34527			−0.672635	−	0.739974i	$-0.734838\pi$
$631$	−33.7928			−1.34527			−0.672635	+	0.739974i	$0.734838\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	9.01418			0.357717
$636$		0			0
$637$	−13.1640	−	31.1131i	−0.521579	−	1.23274i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−24.3067			−0.960058			−0.480029	−	0.877253i	$-0.659374\pi$
$641$	−24.3067			−0.960058			−0.480029	+	0.877253i	$0.659374\pi$
$642$		0			0
$643$	8.27674	+	14.3357i	0.326403	+	0.565346i	0.981795	−	0.189942i	$-0.0608300\pi$
$643$	8.27674	+	14.3357i	0.326403	+	0.565346i	−0.655392	+	0.755289i	$0.727497\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−24.5103	−	42.4531i	−0.963600	−	1.66900i	−0.713329	−	0.700829i	$-0.752814\pi$
$647$	−24.5103	−	42.4531i	−0.963600	−	1.66900i	−0.250271	−	0.968176i	$-0.580520\pi$
$648$		0			0
$649$	19.0287	−	32.9586i	0.746941	−	1.29374i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−41.4646			−1.62263			−0.811317	−	0.584607i	$-0.801249\pi$
$653$	−41.4646			−1.62263			−0.811317	+	0.584607i	$0.801249\pi$
$654$		0			0
$655$	26.0855			1.01925
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.587031	+	1.01677i	−0.0228675	+	0.0396076i	−0.877233	−	0.480065i	$-0.840613\pi$
$659$	−0.587031	+	1.01677i	−0.0228675	+	0.0396076i	0.854365	+	0.519673i	$0.173946\pi$
$660$		0			0
$661$	−8.72665	+	15.1150i	−0.339427	+	0.587906i	−0.984325	−	0.176363i	$-0.943567\pi$
$661$	−8.72665	+	15.1150i	−0.339427	+	0.587906i	0.644898	+	0.764269i	$0.276900\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−13.2100	+	19.9330i	−0.512262	+	0.772967i
$666$		0			0
$667$	10.6766	−	18.4923i	0.413398	−	0.716026i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−7.40642	−	12.8283i	−0.285922	−	0.495231i
$672$		0			0
$673$	9.84453	−	17.0512i	0.379479	−	0.657277i	−0.611508	−	0.791239i	$-0.709437\pi$
$673$	9.84453	−	17.0512i	0.379479	−	0.657277i	0.990986	+	0.133962i	$0.0427699\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.4311	+	30.1915i	0.669931	+	1.16035i	0.977923	+	0.208965i	$0.0670095\pi$
$677$	17.4311	+	30.1915i	0.669931	+	1.16035i	−0.307992	+	0.951389i	$0.599657\pi$
$678$		0			0
$679$	4.69746	−	7.08814i	0.180272	−	0.272018i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−2.44793	−	4.23993i	−0.0936673	−	0.162237i	0.815384	−	0.578920i	$-0.196526\pi$
$683$	−2.44793	−	4.23993i	−0.0936673	−	0.162237i	−0.909052	+	0.416683i	$0.863192\pi$
$684$		0			0
$685$	−40.0991			−1.53211
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−28.0394	+	48.5656i	−1.06821	+	1.85020i
$690$		0			0
$691$	−16.1078	−	27.8995i	−0.612768	−	1.06135i	−0.990772	−	0.135541i	$-0.956723\pi$
$691$	−16.1078	−	27.8995i	−0.612768	−	1.06135i	0.378003	−	0.925804i	$-0.376611\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−10.2703	−	17.7886i	−0.389573	−	0.674761i
$696$		0			0
$697$	−17.5637	+	30.4213i	−0.665274	+	1.15229i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−30.9190			−1.16779			−0.583897	−	0.811828i	$-0.698473\pi$
$701$	−30.9190			−1.16779			−0.583897	+	0.811828i	$0.698473\pi$
$702$		0			0
$703$	12.3114	+	21.3241i	0.464335	+	0.804252i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.40516	+	0.0867630i	0.0528465	+	0.00326306i
$708$		0			0
$709$	−0.302506	−	0.523955i	−0.0113608	−	0.0196776i	0.860289	−	0.509807i	$-0.170283\pi$
$709$	−0.302506	−	0.523955i	−0.0113608	−	0.0196776i	−0.871650	+	0.490129i	$0.836950\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.15955	−	7.20456i	0.155776	−	0.269813i
$714$		0			0
$715$	−12.9786	−	22.4796i	−0.485371	−	0.840688i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.5635	+	32.1529i	−0.692302	+	1.19910i	0.278780	+	0.960355i	$0.410070\pi$
$719$	−18.5635	+	32.1529i	−0.692302	+	1.19910i	−0.971082	+	0.238747i	$0.923263\pi$
$720$		0			0
$721$	13.8741	+	0.856671i	0.516699	+	0.0319041i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	5.96319	−	10.3285i	0.221467	−	0.383593i
$726$		0			0
$727$	−9.25293	+	16.0265i	−0.343172	+	0.594392i	−0.985020	−	0.172440i	$-0.944835\pi$
$727$	−9.25293	+	16.0265i	−0.343172	+	0.594392i	0.641848	+	0.766832i	$0.278168\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	28.8109			1.06561
$732$		0			0
$733$	33.8642			1.25080			0.625401	−	0.780304i	$-0.284936\pi$
$733$	33.8642			1.25080			0.625401	+	0.780304i	$0.284936\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	17.9744	−	31.1325i	0.662094	−	1.14678i
$738$		0			0
$739$	−2.36835	−	4.10210i	−0.0871211	−	0.150898i	0.819172	−	0.573548i	$-0.194433\pi$
$739$	−2.36835	−	4.10210i	−0.0871211	−	0.150898i	−0.906293	+	0.422650i	$0.861100\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.2539	−	17.7603i	−0.376179	−	0.651562i	0.614323	−	0.789054i	$-0.289429\pi$
$743$	−10.2539	−	17.7603i	−0.376179	−	0.651562i	−0.990503	+	0.137493i	$0.956096\pi$
$744$		0			0
$745$	8.09540			0.296593
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.73362	+	4.12483i	−0.0998841	+	0.150718i
$750$		0			0
$751$	43.5382			1.58873			0.794365	−	0.607440i	$-0.207804\pi$
$751$	43.5382			1.58873			0.794365	+	0.607440i	$0.207804\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	33.0017			1.20105
$756$		0			0
$757$	−2.62356			−0.0953547			−0.0476774	−	0.998863i	$-0.515182\pi$
$757$	−2.62356			−0.0953547			−0.0476774	+	0.998863i	$0.515182\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	18.7600			0.680050			0.340025	−	0.940416i	$-0.389564\pi$
$761$	18.7600			0.680050			0.340025	+	0.940416i	$0.389564\pi$
$762$		0			0
$763$	4.70782	+	9.45619i	0.170435	+	0.342337i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−64.9892			−2.34662
$768$		0			0
$769$	−12.1992	−	21.1297i	−0.439916	−	0.761957i	0.557767	−	0.829998i	$-0.311658\pi$
$769$	−12.1992	−	21.1297i	−0.439916	−	0.761957i	−0.997683	+	0.0680412i	$0.978325\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.41582	+	5.91637i	0.122858	+	0.212797i	0.920894	−	0.389814i	$-0.127461\pi$
$773$	3.41582	+	5.91637i	0.122858	+	0.212797i	−0.798035	+	0.602611i	$0.794127\pi$
$774$		0			0
$775$	2.32324	−	4.02397i	0.0834532	−	0.144545i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−38.9663			−1.39611
$780$		0			0
$781$	−20.9095			−0.748202
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.44128	−	11.1566i	0.229899	−	0.398197i
$786$		0			0
$787$	−6.38273	+	11.0552i	−0.227520	+	0.394076i	−0.957072	−	0.289849i	$-0.906395\pi$
$787$	−6.38273	+	11.0552i	−0.227520	+	0.394076i	0.729553	+	0.683925i	$0.239728\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	15.6734	+	31.4819i	0.557284	+	1.11937i
$792$		0			0
$793$	−12.6477	+	21.9064i	−0.449132	+	0.777920i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.0922	−	20.9444i	−0.428329	−	0.741888i	0.568395	−	0.822755i	$-0.307564\pi$
$797$	−12.0922	−	20.9444i	−0.428329	−	0.741888i	−0.996725	+	0.0808672i	$0.974231\pi$
$798$		0			0
$799$	−3.70183	+	6.41176i	−0.130961	+	0.226832i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	11.9632	+	20.7209i	0.422172	+	0.731223i
$804$		0			0
$805$	12.4022	+	0.765787i	0.437120	+	0.0269904i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−21.6057	−	37.4221i	−0.759614	−	1.31569i	−0.943047	−	0.332659i	$-0.892054\pi$
$809$	−21.6057	−	37.4221i	−0.759614	−	1.31569i	0.183433	−	0.983032i	$-0.441279\pi$
$810$		0			0
$811$	−6.80934			−0.239108			−0.119554	−	0.992828i	$-0.538147\pi$
$811$	−6.80934			−0.239108			−0.119554	+	0.992828i	$0.538147\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	16.1130	−	27.9085i	0.564413	−	0.977592i
$816$		0			0
$817$	15.9797	+	27.6777i	0.559059	+	0.968319i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.6274	+	28.7995i	0.580300	+	1.00511i	0.995443	+	0.0953533i	$0.0303981\pi$
$821$	16.6274	+	28.7995i	0.580300	+	1.00511i	−0.415143	+	0.909756i	$0.636269\pi$
$822$		0			0
$823$	−27.5340	+	47.6903i	−0.959775	+	1.66238i	−0.236735	+	0.971574i	$0.576077\pi$
$823$	−27.5340	+	47.6903i	−0.959775	+	1.66238i	−0.723041	+	0.690805i	$0.757256\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.7613			0.478528			0.239264	−	0.970955i	$-0.423094\pi$
$827$	13.7613			0.478528			0.239264	+	0.970955i	$0.423094\pi$
$828$		0			0
$829$	−2.22066	−	3.84630i	−0.0771268	−	0.133588i	0.824882	−	0.565304i	$-0.191241\pi$
$829$	−2.22066	−	3.84630i	−0.0771268	−	0.133588i	−0.902009	+	0.431717i	$0.857908\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−11.6782	−	27.6012i	−0.404625	−	0.956326i
$834$		0			0
$835$	0.229573	+	0.397633i	0.00794471	+	0.0137606i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.03211	−	13.9120i	0.277299	−	0.480296i	−0.693413	−	0.720540i	$-0.743894\pi$
$839$	8.03211	−	13.9120i	0.277299	−	0.480296i	0.970713	+	0.240244i	$0.0772273\pi$
$840$		0			0
$841$	−22.9319	−	39.7192i	−0.790755	−	1.36963i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−9.79323	+	16.9624i	−0.336897	+	0.583524i
$846$		0			0
$847$	7.95554	+	0.491223i	0.273355	+	0.0168786i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6.39738	−	11.0806i	0.219299	−	0.379838i
$852$		0			0
$853$	−16.5865	+	28.7287i	−0.567912	+	0.983653i	0.428860	+	0.903371i	$0.358915\pi$
$853$	−16.5865	+	28.7287i	−0.567912	+	0.983653i	−0.996772	+	0.0802821i	$0.974418\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.27179			0.145922			0.0729608	−	0.997335i	$-0.476755\pi$
$857$	4.27179			0.145922			0.0729608	+	0.997335i	$0.476755\pi$
$858$		0			0
$859$	34.6896			1.18360			0.591798	−	0.806087i	$-0.298418\pi$
$859$	34.6896			1.18360			0.591798	+	0.806087i	$0.298418\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.1166	−	27.9147i	0.548615	−	0.950229i	−0.449755	−	0.893152i	$-0.648489\pi$
$863$	16.1166	−	27.9147i	0.548615	−	0.950229i	0.998370	−	0.0570767i	$-0.0181780\pi$
$864$		0			0
$865$	10.8580	+	18.8066i	0.369182	+	0.639442i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	5.57216	+	9.65127i	0.189023	+	0.327397i
$870$		0			0
$871$	−61.3884			−2.08007
$872$		0			0
$873$		0			0
$874$		0			0
$875$	32.0542	+	1.97922i	1.08363	+	0.0669098i
$876$		0			0
$877$	−21.3998			−0.722619			−0.361309	−	0.932446i	$-0.617670\pi$
$877$	−21.3998			−0.722619			−0.361309	+	0.932446i	$0.617670\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	21.2279			0.715186			0.357593	−	0.933877i	$-0.383597\pi$
$881$	21.2279			0.715186			0.357593	+	0.933877i	$0.383597\pi$
$882$		0			0
$883$	44.9170			1.51158			0.755788	−	0.654816i	$-0.227254\pi$
$883$	44.9170			1.51158			0.755788	+	0.654816i	$0.227254\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2.75524			0.0925119			0.0462560	−	0.998930i	$-0.485271\pi$
$887$	2.75524			0.0925119			0.0462560	+	0.998930i	$0.485271\pi$
$888$		0			0
$889$	−12.5083	−	0.772338i	−0.419515	−	0.0259034i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−8.21276			−0.274829
$894$		0			0
$895$	−23.9007	−	41.3973i	−0.798914	−	1.38376i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−14.5833	−	25.2591i	−0.486382	−	0.842438i
$900$		0			0
$901$	−24.8745	+	43.0838i	−0.828689	+	1.43533i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	29.2517			0.972360
$906$		0			0
$907$	41.9934			1.39437			0.697185	−	0.716892i	$-0.254436\pi$
$907$	41.9934			1.39437			0.697185	+	0.716892i	$0.254436\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.384944	+	0.666743i	−0.0127538	+	0.0220902i	−0.872332	−	0.488914i	$-0.837393\pi$
$911$	−0.384944	+	0.666743i	−0.0127538	+	0.0220902i	0.859578	+	0.511004i	$0.170726\pi$
$912$		0			0
$913$	13.3507	−	23.1240i	0.441842	−	0.765293i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−36.1969	−	2.23502i	−1.19533	−	0.0738068i
$918$		0			0
$919$	18.0097	−	31.1937i	0.594086	−	1.02899i	−0.399590	−	0.916694i	$-0.630847\pi$
$919$	18.0097	−	31.1937i	0.594086	−	1.02899i	0.993675	−	0.112292i	$-0.0358193\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	17.8532	+	30.9227i	0.587647	+	1.01783i
$924$		0			0
$925$	3.57313	−	6.18885i	0.117484	−	0.203488i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−24.5047	−	42.4433i	−0.803972	−	1.39252i	−0.916983	−	0.398926i	$-0.869383\pi$
$929$	−24.5047	−	42.4433i	−0.803972	−	1.39252i	0.113011	−	0.993594i	$-0.463950\pi$
$930$		0			0
$931$	20.0384	−	26.5276i	0.656732	−	0.869408i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−11.5136	−	19.9422i	−0.376536	−	0.652180i
$936$		0			0
$937$	49.0435			1.60218			0.801090	−	0.598544i	$-0.204254\pi$
$937$	49.0435			1.60218			0.801090	+	0.598544i	$0.204254\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	11.7691	−	20.3847i	0.383661	−	0.664521i	−0.607921	−	0.793997i	$-0.707996\pi$
$941$	11.7691	−	20.3847i	0.383661	−	0.664521i	0.991583	+	0.129476i	$0.0413296\pi$
$942$		0			0
$943$	10.1240	+	17.5353i	0.329683	+	0.571027i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.04896	+	12.2092i	0.229060	+	0.396744i	0.957530	−	0.288334i	$-0.0931013\pi$
$947$	7.04896	+	12.2092i	0.229060	+	0.396744i	−0.728469	+	0.685078i	$0.759768\pi$
$948$		0			0
$949$	20.4291	−	35.3843i	0.663158	−	1.14862i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−26.2807			−0.851316			−0.425658	−	0.904884i	$-0.639957\pi$
$953$	−26.2807			−0.851316			−0.425658	+	0.904884i	$0.639957\pi$
$954$		0			0
$955$	11.0126	+	19.0743i	0.356358	+	0.617230i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	55.6425	+	3.43571i	1.79679	+	0.110945i
$960$		0			0
$961$	9.81838	+	17.0059i	0.316722	+	0.548578i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.04555	+	3.54300i	−0.0658487	+	0.114053i
$966$		0			0
$967$	9.48538	+	16.4292i	0.305029	+	0.528326i	0.977268	−	0.212008i	$-0.0680004\pi$
$967$	9.48538	+	16.4292i	0.305029	+	0.528326i	−0.672238	+	0.740335i	$0.734667\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−29.5030	+	51.1008i	−0.946797	+	1.63990i	−0.194686	+	0.980866i	$0.562369\pi$
$971$	−29.5030	+	51.1008i	−0.946797	+	1.63990i	−0.752112	+	0.659036i	$0.770965\pi$
$972$		0			0
$973$	12.7271	+	25.5639i	0.408013	+	0.819541i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.0850	−	19.1997i	0.354639	−	0.614253i	−0.632417	−	0.774628i	$-0.717937\pi$
$977$	11.0850	−	19.1997i	0.354639	−	0.614253i	0.987056	+	0.160375i	$0.0512704\pi$
$978$		0			0
$979$	−13.9032	+	24.0811i	−0.444349	+	0.769634i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−36.5019			−1.16423			−0.582115	−	0.813107i	$-0.697775\pi$
$983$	−36.5019			−1.16423			−0.582115	+	0.813107i	$0.697775\pi$
$984$		0			0
$985$	−1.23536			−0.0393619
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.30351	−	14.3821i	0.264036	−	0.457324i
$990$		0			0
$991$	5.91487	+	10.2449i	0.187892	+	0.325439i	0.944547	−	0.328375i	$-0.106501\pi$
$991$	5.91487	+	10.2449i	0.187892	+	0.325439i	−0.756655	+	0.653814i	$0.773168\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−9.88548	−	17.1222i	−0.313391	−	0.542809i
$996$		0			0
$997$	23.0321			0.729433			0.364716	−	0.931119i	$-0.381166\pi$
$997$	23.0321			0.729433			0.364716	+	0.931119i	$0.381166\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.l.m.541.3		8
3.2	odd	2		2268.2.l.l.541.2		8
7.4	even	3		2268.2.i.l.865.2		8
9.2	odd	6		2268.2.k.d.1297.3	yes	8
9.4	even	3		2268.2.i.l.2053.2		8
9.5	odd	6		2268.2.i.m.2053.3		8
9.7	even	3		2268.2.k.c.1297.2	✓	8
21.11	odd	6		2268.2.i.m.865.3		8
63.4	even	3	inner	2268.2.l.m.109.3		8
63.11	odd	6		2268.2.k.d.1621.3	yes	8
63.25	even	3		2268.2.k.c.1621.2	yes	8
63.32	odd	6		2268.2.l.l.109.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.l.865.2		8	7.4	even	3
2268.2.i.l.2053.2		8	9.4	even	3
2268.2.i.m.865.3		8	21.11	odd	6
2268.2.i.m.2053.3		8	9.5	odd	6
2268.2.k.c.1297.2	✓	8	9.7	even	3
2268.2.k.c.1621.2	yes	8	63.25	even	3
2268.2.k.d.1297.3	yes	8	9.2	odd	6
2268.2.k.d.1621.3	yes	8	63.11	odd	6
2268.2.l.l.109.2		8	63.32	odd	6
2268.2.l.l.541.2		8	3.2	odd	2
2268.2.l.m.109.3		8	63.4	even	3	inner
2268.2.l.m.541.3		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.90305 q^{5} +(-2.64072 - 0.163054i) q^{7} +2.82619 q^{11} +(-2.41310 - 4.17961i) q^{13} +(-2.14072 - 3.70784i) q^{17} +(2.37467 - 4.11304i) q^{19} -2.46789 q^{23} -1.37839 q^{25} +(-4.32619 + 7.49319i) q^{29} +(-1.68547 + 2.91932i) q^{31} +(-5.02543 - 0.310300i) q^{35} +(-2.59225 + 4.48991i) q^{37} +(-4.10229 - 7.10538i) q^{41} +(-3.36462 + 5.82770i) q^{43} +(-0.864622 - 1.49757i) q^{47} +(6.94683 + 0.861161i) q^{49} +(-5.80983 - 10.0629i) q^{53} +5.37839 q^{55} +(6.73297 - 11.6618i) q^{59} +(-2.62063 - 4.53907i) q^{61} +(-4.59225 - 7.95401i) q^{65} +(6.35992 - 11.0157i) q^{67} -7.39848 q^{71} +(4.23297 + 7.33172i) q^{73} +(-7.46319 - 0.460822i) q^{77} +(1.97161 + 3.41494i) q^{79} +(4.72390 - 8.18204i) q^{83} +(-4.07391 - 7.05621i) q^{85} +(-4.91941 + 8.52068i) q^{89} +(5.69081 + 11.4306i) q^{91} +(4.51911 - 7.82734i) q^{95} +(-1.60699 + 2.78339i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} - 2 q^{7} - 10 q^{11} - 3 q^{13} + 2 q^{17} - 8 q^{19} - 4 q^{23} + 16 q^{25} - 2 q^{29} + 11 q^{35} + 4 q^{37} - 3 q^{41} - 5 q^{43} + 15 q^{47} + 14 q^{49} - 24 q^{53} + 16 q^{55} + 10 q^{59}+ \cdots - 19 q^{97}+O(q^{100}) \) 8 * q + 4 * q^5 - 2 * q^7 - 10 * q^11 - 3 * q^13 + 2 * q^17 - 8 * q^19 - 4 * q^23 + 16 * q^25 - 2 * q^29 + 11 * q^35 + 4 * q^37 - 3 * q^41 - 5 * q^43 + 15 * q^47 + 14 * q^49 - 24 * q^53 + 16 * q^55 + 10 * q^59 - 12 * q^61 - 12 * q^65 - 7 * q^67 - 22 * q^71 - 10 * q^73 - 8 * q^77 + 35 * q^83 + 13 * q^85 - 18 * q^89 - 9 * q^91 - 10 * q^95 - 19 * q^97

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