LMFDB - Embedded newform 2268.2.i.m.865.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2268.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$8$
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			865.3
Root			$-1.03075 + 1.78531i$ of defining polynomial
Character	$\chi$	$=$	2268.865
Dual form			2268.2.i.m.2053.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951526 - 1.64809i) q^{5} +(1.46157 + 2.20541i) q^{7} +O(q^{10})$	$q+(0.951526 - 1.64809i) q^{5} +(1.46157 + 2.20541i) q^{7} +(1.41310 + 2.44755i) q^{11} +(-2.41310 - 4.17961i) q^{13} +(2.14072 - 3.70784i) q^{17} +(2.37467 + 4.11304i) q^{19} +(-1.23394 + 2.13725i) q^{23} +(0.689196 + 1.19372i) q^{25} +(4.32619 - 7.49319i) q^{29} +3.37094 q^{31} +(5.02543 - 0.310300i) q^{35} +(-2.59225 - 4.48991i) q^{37} +(4.10229 + 7.10538i) q^{41} +(-3.36462 + 5.82770i) q^{43} -1.72924 q^{47} +(-2.72763 + 6.44671i) q^{49} +(5.80983 - 10.0629i) q^{53} +5.37839 q^{55} +13.4659 q^{59} +5.24127 q^{61} -9.18450 q^{65} -12.7198 q^{67} +7.39848 q^{71} +(4.23297 - 7.33172i) q^{73} +(-3.33251 + 6.69372i) q^{77} -3.94323 q^{79} +(-4.72390 + 8.18204i) q^{83} +(-4.07391 - 7.05621i) q^{85} +(4.91941 + 8.52068i) q^{89} +(5.69081 - 11.4306i) q^{91} +9.03823 q^{95} +(-1.60699 + 2.78339i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{5} + q^{7}+O(q^{10}) $ 8 * q + 2 * q^5 + q^7	$ 8 q + 2 q^{5} + q^{7} - 5 q^{11} - 3 q^{13} - 2 q^{17} - 8 q^{19} - 2 q^{23} - 8 q^{25} + 2 q^{29} - 11 q^{35} + 4 q^{37} + 3 q^{41} - 5 q^{43} + 30 q^{47} - 19 q^{49} + 24 q^{53} + 16 q^{55} + 20 q^{59} + 24 q^{61} - 24 q^{65} + 14 q^{67} + 22 q^{71} - 10 q^{73} + 11 q^{77} - 35 q^{83} + 13 q^{85} + 18 q^{89} - 9 q^{91} - 20 q^{95} - 19 q^{97}+O(q^{100}) $ 8 * q + 2 * q^5 + q^7 - 5 * q^11 - 3 * q^13 - 2 * q^17 - 8 * q^19 - 2 * q^23 - 8 * q^25 + 2 * q^29 - 11 * q^35 + 4 * q^37 + 3 * q^41 - 5 * q^43 + 30 * q^47 - 19 * q^49 + 24 * q^53 + 16 * q^55 + 20 * q^59 + 24 * q^61 - 24 * q^65 + 14 * q^67 + 22 * q^71 - 10 * q^73 + 11 * q^77 - 35 * q^83 + 13 * q^85 + 18 * q^89 - 9 * q^91 - 20 * q^95 - 19 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.951526	−	1.64809i	0.425535	−	0.737049i	−0.570935	−	0.820995i	$-0.693419\pi$
$5$	0.951526	−	1.64809i	0.425535	−	0.737049i	0.996470	+	0.0839464i	$0.0267524\pi$
$6$		0			0
$7$	1.46157	+	2.20541i	0.552422	+	0.833565i
$7$	1.46157	+	2.20541i	0.552422	+	0.833565i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.41310	+	2.44755i	0.426065	+	0.737965i	0.996519	−	0.0833637i	$-0.0265663\pi$
$11$	1.41310	+	2.44755i	0.426065	+	0.737965i	−0.570455	+	0.821329i	$0.693233\pi$
$12$		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	−0.480550	−	0.876968i	$-0.659563\pi$
$17$	2.14072	−	3.70784i	0.519201	−	0.899283i	0.999751	−	0.0223156i	$-0.00710387\pi$
$18$		0			0
$19$	2.37467	+	4.11304i	0.544786	+	0.943597i	0.998620	+	0.0525107i	$0.0167224\pi$
$19$	2.37467	+	4.11304i	0.544786	+	0.943597i	−0.453835	+	0.891086i	$0.649944\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.23394	+	2.13725i	−0.257295	+	0.445648i	−0.965516	−	0.260342i	$-0.916165\pi$
$23$	−1.23394	+	2.13725i	−0.257295	+	0.445648i	0.708221	+	0.705991i	$0.249498\pi$
$24$		0			0
$25$	0.689196	+	1.19372i	0.137839	+	0.238744i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.32619	−	7.49319i	0.803354	−	1.39145i	−0.114043	−	0.993476i	$-0.536380\pi$
$29$	4.32619	−	7.49319i	0.803354	−	1.39145i	0.917397	−	0.397974i	$-0.130286\pi$
$30$		0			0
$31$	3.37094			0.605439			0.302719	−	0.953080i	$-0.402105\pi$
$31$	3.37094			0.605439			0.302719	+	0.953080i	$0.402105\pi$
$32$		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	0.570365	−	0.821391i	$-0.306802\pi$
$37$	−2.59225	−	4.48991i	−0.426163	−	0.738136i	−0.996528	+	0.0832552i	$0.973468\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.10229	+	7.10538i	0.640670	+	1.10967i	0.985283	+	0.170929i	$0.0546768\pi$
$41$	4.10229	+	7.10538i	0.640670	+	1.10967i	−0.344613	+	0.938745i	$0.611990\pi$
$42$		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
$47$	−1.72924			−0.252236			−0.126118	−	0.992015i	$-0.540252\pi$
$47$	−1.72924			−0.252236			−0.126118	+	0.992015i	$0.540252\pi$
$48$		0			0
$49$	−2.72763	+	6.44671i	−0.389661	+	0.920958i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.80983	−	10.0629i	0.798042	−	1.38225i	−0.122848	−	0.992425i	$-0.539203\pi$
$53$	5.80983	−	10.0629i	0.798042	−	1.38225i	0.920890	−	0.389823i	$-0.127464\pi$
$54$		0			0
$55$	5.37839			0.725222
$56$		0			0
$57$		0			0
$58$		0			0
$59$	13.4659			1.75312			0.876558	−	0.481296i	$-0.159834\pi$
$59$	13.4659			1.75312			0.876558	+	0.481296i	$0.159834\pi$
$60$		0			0
$61$	5.24127			0.671076			0.335538	−	0.942027i	$-0.391082\pi$
$61$	5.24127			0.671076			0.335538	+	0.942027i	$0.391082\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.18450			−1.13920
$66$		0			0
$67$	−12.7198			−1.55398			−0.776988	−	0.629515i	$-0.783254\pi$
$67$	−12.7198			−1.55398			−0.776988	+	0.629515i	$0.783254\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	7.39848			0.878038			0.439019	−	0.898478i	$-0.355326\pi$
$71$	7.39848			0.878038			0.439019	+	0.898478i	$0.355326\pi$
$72$		0			0
$73$	4.23297	−	7.33172i	0.495432	−	0.858113i	−0.504554	−	0.863380i	$-0.668343\pi$
$73$	4.23297	−	7.33172i	0.495432	−	0.858113i	0.999986	+	0.00526700i	$0.00167654\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.33251	+	6.69372i	−0.379775	+	0.762820i
$78$		0			0
$79$	−3.94323			−0.443648			−0.221824	−	0.975087i	$-0.571201\pi$
$79$	−3.94323			−0.443648			−0.221824	+	0.975087i	$0.571201\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.72390	+	8.18204i	−0.518515	+	0.898095i	0.481253	+	0.876582i	$0.340182\pi$
$83$	−4.72390	+	8.18204i	−0.518515	+	0.898095i	−0.999769	+	0.0215134i	$0.993152\pi$
$84$		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	0.999689	+	0.0249561i	$0.00794460\pi$
$89$	4.91941	+	8.52068i	0.521457	+	0.903190i	−0.478232	+	0.878234i	$0.658722\pi$
$90$		0			0
$91$	5.69081	−	11.4306i	0.596559	−	1.19826i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	9.03823			0.927303
$96$		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
$101$	−0.266056	−	0.460822i	−0.0264735	−	0.0458535i	0.852485	−	0.522752i	$-0.175094\pi$
$101$	−0.266056	−	0.460822i	−0.0264735	−	0.0458535i	−0.878959	+	0.476898i	$0.841761\pi$
$102$		0			0
$103$	2.62695	−	4.55002i	0.258841	−	0.448326i	−0.707090	−	0.707123i	$-0.749993\pi$
$103$	2.62695	−	4.55002i	0.258841	−	0.448326i	0.965932	+	0.258797i	$0.0833260\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.935164	−	1.61975i	−0.0904057	−	0.156587i	0.817276	−	0.576246i	$-0.195483\pi$
$107$	−0.935164	−	1.61975i	−0.0904057	−	0.156587i	−0.907682	+	0.419659i	$0.862150\pi$
$108$		0			0
$109$	−1.99627	+	3.45765i	−0.191208	+	0.331183i	−0.945651	−	0.325183i	$-0.894574\pi$
$109$	−1.99627	+	3.45765i	−0.191208	+	0.331183i	0.754443	+	0.656366i	$0.227907\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.64607	+	11.5113i	0.625209	+	1.08289i	0.988500	+	0.151219i	$0.0483198\pi$
$113$	6.64607	+	11.5113i	0.625209	+	1.08289i	−0.363291	+	0.931676i	$0.618347\pi$
$114$		0			0
$115$	2.34826	+	4.06731i	0.218976	+	0.379278i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	11.3061	−	0.698107i	1.03643	−	0.0639954i
$120$		0			0
$121$	1.50632	−	2.60902i	0.136938	−	0.237184i
$122$		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
$131$	6.85360	−	11.8708i	0.598802	−	1.03716i	−0.394196	−	0.919026i	$-0.628977\pi$
$131$	6.85360	−	11.8708i	0.598802	−	1.03716i	0.992998	−	0.118129i	$-0.0376898\pi$
$132$		0			0
$133$	−5.60019	+	11.2486i	−0.485598	+	0.975377i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.5355	−	18.2480i	−0.900106	−	1.55903i	−0.827355	−	0.561680i	$-0.810155\pi$
$137$	−10.5355	−	18.2480i	−0.900106	−	1.55903i	−0.0727520	−	0.997350i	$-0.523178\pi$
$138$		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
$149$	2.12695	−	3.68399i	0.174247	−	0.301804i	−0.765654	−	0.643253i	$-0.777584\pi$
$149$	2.12695	−	3.68399i	0.174247	−	0.301804i	0.939900	+	0.341449i	$0.110918\pi$
$150$		0			0
$151$	−8.67073	−	15.0181i	−0.705614	−	1.22216i	−0.966470	−	0.256781i	$-0.917338\pi$
$151$	−8.67073	−	15.0181i	−0.705614	−	1.22216i	0.260856	−	0.965378i	$-0.415995\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.20754	−	5.55562i	0.257636	−	0.446238i
$156$		0			0
$157$	−6.76942			−0.540259			−0.270129	−	0.962824i	$-0.587066\pi$
$157$	−6.76942			−0.540259			−0.270129	+	0.962824i	$0.587066\pi$
$158$		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	0.979775	+	0.200101i	$0.0641269\pi$
$163$	8.46691	+	14.6651i	0.663180	+	1.14866i	−0.316595	+	0.948561i	$0.602540\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.120634	−	0.208945i	−0.00933496	−	0.0161686i	0.861320	−	0.508063i	$-0.169638\pi$
$167$	−0.120634	−	0.208945i	−0.00933496	−	0.0161686i	−0.870655	+	0.491894i	$0.836305\pi$
$168$		0			0
$169$	−5.14607	+	8.91325i	−0.395851	+	0.685635i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.4111			0.867571			0.433786	−	0.901016i	$-0.357178\pi$
$173$	11.4111			0.867571			0.433786	+	0.901016i	$0.357178\pi$
$174$		0			0
$175$	−1.62533	+	3.26467i	−0.122864	+	0.246786i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.5592	−	21.7531i	0.938716	−	1.62590i	0.170846	−	0.985298i	$-0.445350\pi$
$179$	12.5592	−	21.7531i	0.938716	−	1.62590i	0.767870	−	0.640606i	$-0.221317\pi$
$180$		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
$185$	−9.86637			−0.725390
$186$		0			0
$187$	12.1002			0.884853
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.5736			0.837435			0.418717	−	0.908117i	$-0.362480\pi$
$191$	11.5736			0.837435			0.418717	+	0.908117i	$0.362480\pi$
$192$		0			0
$193$	2.14976			0.154743			0.0773715	−	0.997002i	$-0.475347\pi$
$193$	2.14976			0.154743			0.0773715	+	0.997002i	$0.475347\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.649147			0.0462498			0.0231249	−	0.999733i	$-0.492638\pi$
$197$	0.649147			0.0462498			0.0231249	+	0.999733i	$0.492638\pi$
$198$		0			0
$199$	−5.19454	+	8.99721i	−0.368231	+	0.637795i	−0.989289	−	0.145970i	$-0.953370\pi$
$199$	−5.19454	+	8.99721i	−0.368231	+	0.637795i	0.621058	+	0.783765i	$0.286703\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	22.8485	−	1.41081i	1.60365	−	0.0990192i
$204$		0			0
$205$	15.6138			1.09051
$206$		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
$221$	−20.6631			−1.38995
$222$		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
$227$	−5.12695	−	8.88014i	−0.340288	−	0.589396i	0.644198	−	0.764859i	$-0.277191\pi$
$227$	−5.12695	−	8.88014i	−0.340288	−	0.589396i	−0.984486	+	0.175463i	$0.943858\pi$
$228$		0			0
$229$	−6.19924	+	10.7374i	−0.409657	+	0.709547i	−0.994851	−	0.101346i	$-0.967685\pi$
$229$	−6.19924	+	10.7374i	−0.409657	+	0.709547i	0.585194	+	0.810893i	$0.301018\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.60699	−	6.24749i	−0.236302	−	0.409287i	0.723348	−	0.690483i	$-0.242602\pi$
$233$	−3.60699	−	6.24749i	−0.236302	−	0.409287i	−0.959650	+	0.281196i	$0.909269\pi$
$234$		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	0.936746	−	0.350010i	$-0.113822\pi$
$239$	2.55479	+	4.42503i	0.165256	+	0.286231i	−0.771490	+	0.636241i	$0.780488\pi$
$240$		0			0
$241$	6.85162	+	11.8674i	0.441352	+	0.764444i	0.997790	−	0.0664450i	$-0.0211657\pi$
$241$	6.85162	+	11.8674i	0.441352	+	0.764444i	−0.556438	+	0.830889i	$0.687832\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.02936	+	10.6296i	0.512977	+	0.679100i
$246$		0			0
$247$	11.4606	−	19.8503i	0.729220	−	1.26305i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−26.7694			−1.68967			−0.844835	−	0.535026i	$-0.820302\pi$
$251$	−26.7694			−1.68967			−0.844835	+	0.535026i	$0.820302\pi$
$252$		0			0
$253$	−6.97473			−0.438497
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.3790	+	17.9770i	−0.647427	+	1.12138i	0.336309	+	0.941752i	$0.390821\pi$
$257$	−10.3790	+	17.9770i	−0.647427	+	1.12138i	−0.983735	+	0.179624i	$0.942512\pi$
$258$		0			0
$259$	6.11331	−	12.2793i	0.379863	−	0.762997i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.34158	+	4.05574i	0.144388	+	0.250087i	0.929144	−	0.369717i	$-0.120545\pi$
$263$	2.34158	+	4.05574i	0.144388	+	0.250087i	−0.784756	+	0.619804i	$0.787212\pi$
$264$		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	$-0.979461\pi$
$269$	−7.26767	+	12.5880i	−0.443118	+	0.767503i	0.554801	+	0.831983i	$0.312794\pi$
$270$		0			0
$271$	−3.32247	−	5.75468i	−0.201825	−	0.349572i	0.747291	−	0.664497i	$-0.231354\pi$
$271$	−3.32247	−	5.75468i	−0.201825	−	0.349572i	−0.949117	+	0.314925i	$0.898021\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.94780	+	3.37369i	−0.117457	+	0.203441i
$276$		0			0
$277$	−5.01004	−	8.67765i	−0.301024	−	0.521389i	0.675344	−	0.737503i	$-0.263995\pi$
$277$	−5.01004	−	8.67765i	−0.301024	−	0.521389i	−0.976368	+	0.216113i	$0.930662\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.87531	+	17.1045i	−0.589112	+	1.02037i	0.405237	+	0.914211i	$0.367189\pi$
$281$	−9.87531	+	17.1045i	−0.589112	+	1.02037i	−0.994349	+	0.106160i	$0.966144\pi$
$282$		0			0
$283$	0.629059			0.0373937			0.0186969	−	0.999825i	$-0.494048\pi$
$283$	0.629059			0.0373937			0.0186969	+	0.999825i	$0.494048\pi$
$284$		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	0.743827	−	0.668372i	$-0.233009\pi$
$293$	−3.54179	−	6.13457i	−0.206914	−	0.358385i	−0.950741	+	0.309987i	$0.899675\pi$
$294$		0			0
$295$	12.8132	−	22.1931i	0.746013	−	1.29213i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	11.9105			0.688802
$300$		0			0
$301$	−17.7701	+	1.09723i	−1.02425	+	0.0632433i
$302$		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
$311$	−8.77662			−0.497676			−0.248838	−	0.968545i	$-0.580049\pi$
$311$	−8.77662			−0.497676			−0.248838	+	0.968545i	$0.580049\pi$
$312$		0			0
$313$	20.3583			1.15072			0.575360	−	0.817900i	$-0.304862\pi$
$313$	20.3583			1.15072			0.575360	+	0.817900i	$0.304862\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−25.5334			−1.43410			−0.717049	−	0.697022i	$-0.754508\pi$
$317$	−25.5334			−1.43410			−0.717049	+	0.697022i	$0.754508\pi$
$318$		0			0
$319$	24.4533			1.36912
$320$		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
$329$	−2.52741	−	3.81369i	−0.139341	−	0.210255i
$330$		0			0
$331$	−23.8845			−1.31281			−0.656406	−	0.754408i	$-0.727924\pi$
$331$	−23.8845			−1.31281			−0.656406	+	0.754408i	$0.727924\pi$
$332$		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
$347$	−4.36576			−0.234366			−0.117183	−	0.993110i	$-0.537386\pi$
$347$	−4.36576			−0.234366			−0.117183	+	0.993110i	$0.537386\pi$
$348$		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
$353$	−12.7710	−	22.1201i	−0.679734	−	1.17733i	−0.975061	−	0.221937i	$-0.928762\pi$
$353$	−12.7710	−	22.1201i	−0.679734	−	1.17733i	0.295327	−	0.955396i	$-0.404571\pi$
$354$		0			0
$355$	7.03985	−	12.1934i	0.373636	−	0.647157i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.70718	−	16.8133i	−0.512325	−	0.887373i	−0.999898	−	0.0142909i	$-0.995451\pi$
$359$	−9.70718	−	16.8133i	−0.512325	−	0.887373i	0.487573	−	0.873082i	$-0.337882\pi$
$360$		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
$367$	−6.60504	−	11.4403i	−0.344780	−	0.597177i	0.640533	−	0.767930i	$-0.278713\pi$
$367$	−6.60504	−	11.4403i	−0.344780	−	0.597177i	−0.985314	+	0.170753i	$0.945380\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	30.6843	−	1.89463i	1.59305	−	0.0983645i
$372$		0			0
$373$	−16.1778	+	28.0208i	−0.837656	+	1.45086i	0.0541942	+	0.998530i	$0.482741\pi$
$373$	−16.1778	+	28.0208i	−0.837656	+	1.45086i	−0.891850	+	0.452332i	$0.850592\pi$
$374$		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
$383$	6.15077	−	10.6534i	0.314289	−	0.544365i	−0.664997	−	0.746846i	$-0.731567\pi$
$383$	6.15077	−	10.6534i	0.314289	−	0.544365i	0.979286	+	0.202481i	$0.0649004\pi$
$384$		0			0
$385$	7.86090	+	11.8615i	0.400628	+	0.604520i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−14.6307	−	25.3411i	−0.741805	−	1.28484i	−0.951673	−	0.307114i	$-0.900637\pi$
$389$	−14.6307	−	25.3411i	−0.741805	−	1.28484i	0.209868	−	0.977730i	$-0.432697\pi$
$390$		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	0.662277	−	0.749259i	$-0.269590\pi$
$397$	−6.33089	−	10.9654i	−0.317738	−	0.550339i	−0.980016	+	0.198920i	$0.936257\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.48425	−	4.30285i	0.124058	−	0.214874i	−0.797307	−	0.603574i	$-0.793743\pi$
$401$	2.48425	−	4.30285i	0.124058	−	0.214874i	0.921364	+	0.388701i	$0.127076\pi$
$402$		0			0
$403$	−8.13440	−	14.0892i	−0.405204	−	0.701833i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.32619	−	12.6893i	0.363146	−	0.628987i
$408$		0			0
$409$	18.8790			0.933507			0.466753	−	0.884388i	$-0.345424\pi$
$409$	18.8790			0.933507			0.466753	+	0.884388i	$0.345424\pi$
$410$		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	0.753749	−	0.657163i	$-0.228244\pi$
$419$	−3.93516	−	6.81590i	−0.192245	−	0.332979i	−0.945994	+	0.324184i	$0.894910\pi$
$420$		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
$425$	5.90151			0.286265
$426$		0			0
$427$	7.66048	+	11.5591i	0.370717	+	0.559385i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.9729	+	27.6659i	−0.769388	+	1.33262i	0.168508	+	0.985700i	$0.446105\pi$
$431$	−15.9729	+	27.6659i	−0.769388	+	1.33262i	−0.937895	+	0.346918i	$0.887228\pi$
$432$		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
$437$	−11.7208			−0.560683
$438$		0			0
$439$	−39.1196			−1.86708			−0.933539	−	0.358477i	$-0.883296\pi$
$439$	−39.1196			−1.86708			−0.933539	+	0.358477i	$0.883296\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	0.00719755			0.000341966			0.000170983	−	1.00000i	$-0.499946\pi$
$443$	0.00719755			0.000341966			0.000170983		1.00000i	$0.499946\pi$
$444$		0			0
$445$	18.7238			0.887594
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−30.6812			−1.44794			−0.723968	−	0.689834i	$-0.757684\pi$
$449$	−30.6812			−1.44794			−0.723968	+	0.689834i	$0.757684\pi$
$450$		0			0
$451$	−11.5939	+	20.0812i	−0.545934	+	0.945585i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−13.4238	−	20.2555i	−0.629317	−	0.949594i
$456$		0			0
$457$	−38.1122			−1.78281			−0.891406	−	0.453206i	$-0.850280\pi$
$457$	−38.1122			−1.78281			−0.891406	+	0.453206i	$0.850280\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−15.1250	+	26.1972i	−0.704440	+	1.22013i	0.262453	+	0.964945i	$0.415469\pi$
$461$	−15.1250	+	26.1972i	−0.704440	+	1.22013i	−0.966893	+	0.255181i	$0.917865\pi$
$462$		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	$-0.214940\pi$
$467$	−3.26472	−	5.65466i	−0.151073	−	0.261667i	−0.931622	+	0.363428i	$0.881606\pi$
$468$		0			0
$469$	−18.5909	−	28.0524i	−0.858450	−	1.29534i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−19.0181			−0.874455
$474$		0			0
$475$	−3.27322	+	5.66938i	−0.150186	+	0.260129i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.7262	+	23.7744i	0.627164	+	1.08628i	0.988118	+	0.153697i	$0.0491179\pi$
$479$	13.7262	+	23.7744i	0.627164	+	1.08628i	−0.360954	+	0.932584i	$0.617549\pi$
$480$		0			0
$481$	−12.5107	+	21.6691i	−0.570438	+	0.988028i
$482$		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	0.228950	+	0.973438i	$0.426471\pi$
$487$	−16.0776	+	27.8473i	−0.728547	+	1.26188i	−0.957497	+	0.288442i	$0.906863\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−14.8937	−	25.7966i	−0.672141	−	1.16418i	−0.977296	−	0.211880i	$-0.932041\pi$
$491$	−14.8937	−	25.7966i	−0.672141	−	1.16418i	0.305155	−	0.952303i	$-0.401292\pi$
$492$		0			0
$493$	−18.5224	−	32.0817i	−0.834205	−	1.44489i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.8134	+	16.3166i	0.485047	+	0.731902i
$498$		0			0
$499$	14.5875	−	25.2664i	0.653028	−	1.13108i	−0.329356	−	0.944206i	$-0.606832\pi$
$499$	14.5875	−	25.2664i	0.653028	−	1.13108i	0.982384	−	0.186872i	$-0.0598351\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−39.1553			−1.74585			−0.872923	−	0.487857i	$-0.837779\pi$
$503$	−39.1553			−1.74585			−0.872923	+	0.487857i	$0.837779\pi$
$504$		0			0
$505$	−1.01264			−0.0450617
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.60962	+	7.98409i	−0.204318	+	0.353889i	−0.949915	−	0.312508i	$-0.898831\pi$
$509$	−4.60962	+	7.98409i	−0.204318	+	0.353889i	0.745597	+	0.666397i	$0.232164\pi$
$510$		0			0
$511$	22.3562	−	1.38041i	0.988980	−	0.0610656i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−4.99923	−	8.65892i	−0.220292	−	0.381557i
$516$		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	0.340654	+	0.940189i	$0.389351\pi$
$521$	−14.6973	+	25.4565i	−0.643900	+	1.11527i	−0.984554	+	0.175079i	$0.943982\pi$
$522$		0			0
$523$	−8.57488	−	14.8521i	−0.374953	−	0.649438i	0.615367	−	0.788241i	$-0.289008\pi$
$523$	−8.57488	−	14.8521i	−0.374953	−	0.649438i	−0.990320	+	0.138803i	$0.955675\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.21625	−	12.4989i	0.314345	−	0.544461i
$528$		0			0
$529$	8.45476	+	14.6441i	0.367598	+	0.636699i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	19.7985	−	34.2919i	0.857566	−	1.48535i
$534$		0			0
$535$	−3.55933			−0.153883
$536$		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	0.523371	−	0.852105i	$-0.324674\pi$
$541$	−11.0775	−	19.1868i	−0.476259	−	0.824905i	−0.999630	+	0.0272000i	$0.991341\pi$
$542$		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
$551$	41.0931			1.75062
$552$		0			0
$553$	−5.76330	−	8.69642i	−0.245081	−	0.369809i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.73233	−	8.19663i	0.200515	−	0.347302i	−0.748179	−	0.663496i	$-0.769072\pi$
$557$	4.73233	−	8.19663i	0.200515	−	0.347302i	0.948694	+	0.316194i	$0.102405\pi$
$558$		0			0
$559$	32.4766			1.37362
$560$		0			0
$561$		0			0
$562$		0			0
$563$	19.0126			0.801287			0.400644	−	0.916234i	$-0.368787\pi$
$563$	19.0126			0.801287			0.400644	+	0.916234i	$0.368787\pi$
$564$		0			0
$565$	25.2956			1.06419
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−37.8242			−1.58567			−0.792837	−	0.609433i	$-0.791397\pi$
$569$	−37.8242			−1.58567			−0.792837	+	0.609433i	$0.791397\pi$
$570$		0			0
$571$	24.0801			1.00772			0.503860	−	0.863785i	$-0.331913\pi$
$571$	24.0801			1.00772			0.503860	+	0.863785i	$0.331913\pi$
$572$		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	0.354519	+	0.935049i	$0.384645\pi$
$577$	−15.1936	+	26.3160i	−0.632516	+	1.09555i	−0.987036	+	0.160502i	$0.948689\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−24.9490	+	1.54050i	−1.03506	+	0.0639108i
$582$		0			0
$583$	32.8394			1.36007
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−19.7714	+	34.2451i	−0.816053	+	1.41345i	0.0925163	+	0.995711i	$0.470509\pi$
$587$	−19.7714	+	34.2451i	−0.816053	+	1.41345i	−0.908569	+	0.417734i	$0.862824\pi$
$588$		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	$-0.168851\pi$
$593$	−0.167128	−	0.289474i	−0.00686313	−	0.0118873i	−0.869437	+	0.494045i	$0.835518\pi$
$594$		0			0
$595$	9.60751	−	19.2978i	0.393869	−	0.791131i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.32331			0.0949280			0.0474640	−	0.998873i	$-0.484886\pi$
$599$	2.32331			0.0949280			0.0474640	+	0.998873i	$0.484886\pi$
$600$		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
$605$	−2.86660	−	4.96510i	−0.116544	−	0.201860i
$606$		0			0
$607$	−11.7793	+	20.4024i	−0.478109	+	0.828108i	−0.999685	−	0.0250962i	$-0.992011\pi$
$607$	−11.7793	+	20.4024i	−0.478109	+	0.828108i	0.521576	+	0.853205i	$0.325344\pi$
$608$		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	0.202904	+	0.979199i	$0.434962\pi$
$613$	−18.4839	+	32.0151i	−0.746559	+	1.29308i	−0.949463	+	0.313879i	$0.898371\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.8625	−	30.9388i	−0.719118	−	1.24555i	−0.961350	−	0.275330i	$-0.911213\pi$
$617$	−17.8625	−	30.9388i	−0.719118	−	1.24555i	0.242232	−	0.970218i	$-0.422121\pi$
$618$		0			0
$619$	−11.5107	−	19.9371i	−0.462654	−	0.801340i	0.536439	−	0.843939i	$-0.319769\pi$
$619$	−11.5107	−	19.9371i	−0.462654	−	0.801340i	−0.999092	+	0.0425997i	$0.986436\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−11.6015	+	23.3029i	−0.464803	+	0.933610i
$624$		0			0
$625$	8.10404	−	14.0366i	0.324162	−	0.561464i
$626$		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
$635$	4.50709	−	7.80651i	0.178858	−	0.309792i
$636$		0			0
$637$	33.5267	−	4.15613i	1.32838	−	0.164672i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.1534	−	21.0502i	−0.480029	−	0.831434i	0.519709	−	0.854344i	$-0.326040\pi$
$641$	−12.1534	−	21.0502i	−0.480029	−	0.831434i	−0.999738	+	0.0229092i	$0.992707\pi$
$642$		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	0.250271	−	0.968176i	$-0.419480\pi$
$647$	24.5103	−	42.4531i	0.963600	−	1.66900i	0.713329	−	0.700829i	$-0.247186\pi$
$648$		0			0
$649$	19.0287	+	32.9586i	0.746941	+	1.29374i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−20.7323	+	35.9094i	−0.811317	+	1.40524i	0.100626	+	0.994924i	$0.467915\pi$
$653$	−20.7323	+	35.9094i	−0.811317	+	1.40524i	−0.911943	+	0.410318i	$0.865418\pi$
$654$		0			0
$655$	−13.0428	−	22.5907i	−0.509623	−	0.882693i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.587031	−	1.01677i	0.0228675	−	0.0396076i	−0.854365	−	0.519673i	$-0.826054\pi$
$659$	0.587031	−	1.01677i	0.0228675	−	0.0396076i	0.877233	+	0.480065i	$0.159387\pi$
$660$		0			0
$661$	17.4533			0.678855			0.339427	−	0.940632i	$-0.389767\pi$
$661$	17.4533			0.678855			0.339427	+	0.940632i	$0.389767\pi$
$662$		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
$677$	34.8622			1.33986			0.669931	−	0.742424i	$-0.266324\pi$
$677$	34.8622			1.33986			0.669931	+	0.742424i	$0.266324\pi$
$678$		0			0
$679$	−8.48724	+	0.524053i	−0.325710	+	0.0201113i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	2.44793	−	4.23993i	0.0936673	−	0.162237i	−0.815384	−	0.578920i	$-0.803474\pi$
$683$	2.44793	−	4.23993i	0.0936673	−	0.162237i	0.909052	+	0.416683i	$0.136808\pi$
$684$		0			0
$685$	−40.0991			−1.53211
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−56.0787			−2.13643
$690$		0			0
$691$	32.2155			1.22554			0.612768	−	0.790263i	$-0.290056\pi$
$691$	32.2155			1.22554			0.612768	+	0.790263i	$0.290056\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−20.5405			−0.779147
$696$		0			0
$697$	35.1275			1.33055
$698$		0			0
$699$		0			0
$700$		0			0
$701$	30.9190			1.16779			0.583897	−	0.811828i	$-0.301527\pi$
$701$	30.9190			1.16779			0.583897	+	0.811828i	$0.301527\pi$
$702$		0			0
$703$	12.3114	−	21.3241i	0.464335	−	0.804252i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.627441	−	1.26029i	0.0235973	−	0.0473979i
$708$		0			0
$709$	0.605012			0.0227217			0.0113608	−	0.999935i	$-0.496384\pi$
$709$	0.605012			0.0227217			0.0113608	+	0.999935i	$0.496384\pi$
$710$		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	0.971082	+	0.238747i	$0.0767366\pi$
$719$	18.5635	+	32.1529i	0.692302	+	1.19910i	−0.278780	+	0.960355i	$0.589930\pi$
$720$		0			0
$721$	13.8741	−	0.856671i	0.516699	−	0.0319041i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	11.9264			0.442935
$726$		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
$731$	14.4054	+	24.9510i	0.532805	+	0.922845i
$732$		0			0
$733$	−16.9321	+	29.3272i	−0.625401	+	1.08323i	0.363062	+	0.931765i	$0.381731\pi$
$733$	−16.9321	+	29.3272i	−0.625401	+	1.08323i	−0.988463	+	0.151461i	$0.951602\pi$
$734$		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	−0.906293	−	0.422650i	$-0.861100\pi$
$739$	−2.36835	+	4.10210i	−0.0871211	+	0.150898i	0.819172	+	0.573548i	$0.194433\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.2539	+	17.7603i	0.376179	+	0.651562i	0.990503	−	0.137493i	$-0.0439043\pi$
$743$	10.2539	+	17.7603i	0.376179	+	0.651562i	−0.614323	+	0.789054i	$0.710571\pi$
$744$		0			0
$745$	−4.04770	−	7.01083i	−0.148296	−	0.256857i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.20540	−	4.42980i	0.0805836	−	0.161861i
$750$		0			0
$751$	−21.7691	+	37.7052i	−0.794365	+	1.37588i	0.128876	+	0.991661i	$0.458863\pi$
$751$	−21.7691	+	37.7052i	−0.794365	+	1.37588i	−0.923241	+	0.384221i	$0.874470\pi$
$752$		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
$761$	9.38001	−	16.2467i	0.340025	−	0.588941i	−0.644412	−	0.764679i	$-0.722898\pi$
$761$	9.38001	−	16.2467i	0.340025	−	0.588941i	0.984437	+	0.175738i	$0.0562311\pi$
$762$		0			0
$763$	−10.5432	+	0.651001i	−0.381690	+	0.0235678i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−32.4946	−	56.2823i	−1.17331	−	2.03224i
$768$		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	$-0.872539\pi$
$773$	−3.41582	+	5.91637i	−0.122858	+	0.212797i	0.798035	+	0.602611i	$0.205873\pi$
$774$		0			0
$775$	2.32324	+	4.02397i	0.0834532	+	0.144545i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−19.4831	+	33.7458i	−0.698056	+	1.20907i
$780$		0			0
$781$	10.4548	+	18.1082i	0.374101	+	0.647962i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−6.44128	+	11.1566i	−0.229899	+	0.398197i
$786$		0			0
$787$	12.7655			0.455040			0.227520	−	0.973773i	$-0.426938\pi$
$787$	12.7655			0.455040			0.227520	+	0.973773i	$0.426938\pi$
$788$		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	0.996725	−	0.0808672i	$-0.0257690\pi$
$797$	12.0922	+	20.9444i	0.428329	+	0.741888i	−0.568395	+	0.822755i	$0.692436\pi$
$798$		0			0
$799$	−3.70183	+	6.41176i	−0.130961	+	0.226832i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	23.9264			0.844344
$804$		0			0
$805$	−5.53791	+	11.1235i	−0.195186	+	0.392053i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	21.6057	−	37.4221i	0.759614	−	1.31569i	−0.183433	−	0.983032i	$-0.558721\pi$
$809$	21.6057	−	37.4221i	0.759614	−	1.31569i	0.943047	−	0.332659i	$-0.107946\pi$
$810$		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
$815$	32.2260			1.12883
$816$		0			0
$817$	−31.9594			−1.11812
$818$		0			0
$819$		0			0
$820$		0			0
$821$	33.2548			1.16060			0.580300	−	0.814403i	$-0.302935\pi$
$821$	33.2548			1.16060			0.580300	+	0.814403i	$0.302935\pi$
$822$		0			0
$823$	55.0680			1.91955			0.959775	−	0.280769i	$-0.0905894\pi$
$823$	55.0680			1.91955			0.959775	+	0.280769i	$0.0905894\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−13.7613			−0.478528			−0.239264	−	0.970955i	$-0.576906\pi$
$827$	−13.7613			−0.478528			−0.239264	+	0.970955i	$0.576906\pi$
$828$		0			0
$829$	−2.22066	+	3.84630i	−0.0771268	+	0.133588i	−0.902009	−	0.431717i	$-0.857908\pi$
$829$	−2.22066	+	3.84630i	−0.0771268	+	0.133588i	0.824882	+	0.565304i	$0.191241\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	18.0643	+	23.9142i	0.625890	+	0.828578i
$834$		0			0
$835$	−0.459147			−0.0158894
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−8.03211	+	13.9120i	−0.277299	+	0.480296i	−0.970713	−	0.240244i	$-0.922773\pi$
$839$	−8.03211	+	13.9120i	−0.277299	+	0.480296i	0.693413	+	0.720540i	$0.256106\pi$
$840$		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
$851$	12.7948			0.438599
$852$		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
$857$	2.13590	+	3.69948i	0.0729608	+	0.126372i	0.900198	−	0.435481i	$-0.143422\pi$
$857$	2.13590	+	3.69948i	0.0729608	+	0.126372i	−0.827237	+	0.561853i	$0.810089\pi$
$858$		0			0
$859$	−17.3448	+	30.0421i	−0.591798	+	1.02502i	0.402193	+	0.915555i	$0.368248\pi$
$859$	−17.3448	+	30.0421i	−0.591798	+	1.02502i	−0.993990	+	0.109468i	$0.965085\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−16.1166	−	27.9147i	−0.548615	−	0.950229i	−0.998370	−	0.0570767i	$-0.981822\pi$
$863$	−16.1166	−	27.9147i	−0.548615	−	0.950229i	0.449755	−	0.893152i	$-0.351511\pi$
$864$		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
$871$	30.6942	+	53.1639i	1.04003	+	1.80139i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	17.7411	+	26.7701i	0.599760	+	0.904995i
$876$		0			0
$877$	10.6999	−	18.5327i	0.361309	−	0.625806i	−0.626867	−	0.779126i	$-0.715663\pi$
$877$	10.6999	−	18.5327i	0.361309	−	0.625806i	0.988177	+	0.153320i	$0.0489965\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−21.2279			−0.715186			−0.357593	−	0.933877i	$-0.616403\pi$
$881$	−21.2279			−0.715186			−0.357593	+	0.933877i	$0.616403\pi$
$882$		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
$887$	1.37762	−	2.38611i	0.0462560	−	0.0801177i	−0.841970	−	0.539524i	$-0.818604\pi$
$887$	1.37762	−	2.38611i	0.0462560	−	0.0801177i	0.888226	+	0.459406i	$0.151938\pi$
$888$		0			0
$889$	6.92301	+	10.4463i	0.232190	+	0.350359i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.10638	−	7.11246i	−0.137415	−	0.238009i
$894$		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
$905$	14.6259	−	25.3327i	0.486180	−	0.842088i
$906$		0			0
$907$	−20.9967	−	36.3674i	−0.697185	−	1.20756i	−0.969439	−	0.245334i	$-0.921102\pi$
$907$	−20.9967	−	36.3674i	−0.697185	−	1.20756i	0.272254	−	0.962225i	$-0.412231\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.384944	−	0.666743i	0.0127538	−	0.0220902i	−0.859578	−	0.511004i	$-0.829274\pi$
$911$	0.384944	−	0.666743i	0.0127538	−	0.0220902i	0.872332	+	0.488914i	$0.162607\pi$
$912$		0			0
$913$	−26.7013			−0.883684
$914$		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	0.993675	+	0.112292i	$0.0358193\pi$
$919$	18.0097	+	31.1937i	0.594086	+	1.02899i	−0.399590	+	0.916694i	$0.630847\pi$
$920$		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
$929$	−49.0093			−1.60794			−0.803972	−	0.594668i	$-0.797284\pi$
$929$	−49.0093			−1.60794			−0.803972	+	0.594668i	$0.797284\pi$
$930$		0			0
$931$	−32.9928	+	4.08994i	−1.08130	+	0.134042i
$932$		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
$941$	23.5382			0.767323			0.383661	−	0.923474i	$-0.374663\pi$
$941$	23.5382			0.767323			0.383661	+	0.923474i	$0.374663\pi$
$942$		0			0
$943$	−20.2480			−0.659366
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.0979			0.458121			0.229060	−	0.973412i	$-0.426435\pi$
$947$	14.0979			0.458121			0.229060	+	0.973412i	$0.426435\pi$
$948$		0			0
$949$	−40.8583			−1.32632
$950$		0			0
$951$		0			0
$952$		0			0
$953$	26.2807			0.851316			0.425658	−	0.904884i	$-0.360043\pi$
$953$	26.2807			0.851316			0.425658	+	0.904884i	$0.360043\pi$
$954$		0			0
$955$	11.0126	−	19.0743i	0.356358	−	0.617230i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	24.8459	−	49.9057i	0.802315	−	1.61154i
$960$		0			0
$961$	−19.6368			−0.633444
$962$		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	0.752112	+	0.659036i	$0.229035\pi$
$971$	29.5030	+	51.1008i	0.946797	+	1.63990i	0.194686	+	0.980866i	$0.437631\pi$
$972$		0			0
$973$	12.7271	−	25.5639i	0.408013	−	0.819541i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.1699			0.709278			0.354639	−	0.935003i	$-0.384604\pi$
$977$	22.1699			0.709278			0.354639	+	0.935003i	$0.384604\pi$
$978$		0			0
$979$	−13.9032	+	24.0811i	−0.444349	+	0.769634i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.2510	−	31.6116i	−0.582115	−	1.00825i	−0.995228	−	0.0975731i	$-0.968892\pi$
$983$	−18.2510	−	31.6116i	−0.582115	−	1.00825i	0.413113	−	0.910680i	$-0.364441\pi$
$984$		0			0
$985$	0.617681	−	1.06985i	0.0196809	−	0.0340884i
$986$		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	−0.756655	−	0.653814i	$-0.773168\pi$
$991$	5.91487	−	10.2449i	0.187892	−	0.325439i	0.944547	+	0.328375i	$0.106501\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.88548	+	17.1222i	0.313391	+	0.542809i
$996$		0			0
$997$	−11.5160	−	19.9464i	−0.364716	−	0.631707i	0.624014	−	0.781413i	$-0.285501\pi$
$997$	−11.5160	−	19.9464i	−0.364716	−	0.631707i	−0.988731	+	0.149706i	$0.952167\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.i.m.865.3		8
3.2	odd	2		2268.2.i.l.865.2		8
7.2	even	3		2268.2.l.l.541.2		8
9.2	odd	6		2268.2.k.c.1621.2	yes	8
9.4	even	3		2268.2.l.l.109.2		8
9.5	odd	6		2268.2.l.m.109.3		8
9.7	even	3		2268.2.k.d.1621.3	yes	8
21.2	odd	6		2268.2.l.m.541.3		8
63.2	odd	6		2268.2.k.c.1297.2	✓	8
63.16	even	3		2268.2.k.d.1297.3	yes	8
63.23	odd	6		2268.2.i.l.2053.2		8
63.58	even	3	inner	2268.2.i.m.2053.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.l.865.2		8	3.2	odd	2
2268.2.i.l.2053.2		8	63.23	odd	6
2268.2.i.m.865.3		8	1.1	even	1	trivial
2268.2.i.m.2053.3		8	63.58	even	3	inner
2268.2.k.c.1297.2	✓	8	63.2	odd	6
2268.2.k.c.1621.2	yes	8	9.2	odd	6
2268.2.k.d.1297.3	yes	8	63.16	even	3
2268.2.k.d.1621.3	yes	8	9.7	even	3
2268.2.l.l.109.2		8	9.4	even	3
2268.2.l.l.541.2		8	7.2	even	3
2268.2.l.m.109.3		8	9.5	odd	6
2268.2.l.m.541.3		8	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.951526 - 1.64809i) q^{5} +(1.46157 + 2.20541i) q^{7} +O(q^{10})\)	\(q+(0.951526 - 1.64809i) q^{5} +(1.46157 + 2.20541i) q^{7} +(1.41310 + 2.44755i) q^{11} +(-2.41310 - 4.17961i) q^{13} +(2.14072 - 3.70784i) q^{17} +(2.37467 + 4.11304i) q^{19} +(-1.23394 + 2.13725i) q^{23} +(0.689196 + 1.19372i) q^{25} +(4.32619 - 7.49319i) q^{29} +3.37094 q^{31} +(5.02543 - 0.310300i) q^{35} +(-2.59225 - 4.48991i) q^{37} +(4.10229 + 7.10538i) q^{41} +(-3.36462 + 5.82770i) q^{43} -1.72924 q^{47} +(-2.72763 + 6.44671i) q^{49} +(5.80983 - 10.0629i) q^{53} +5.37839 q^{55} +13.4659 q^{59} +5.24127 q^{61} -9.18450 q^{65} -12.7198 q^{67} +7.39848 q^{71} +(4.23297 - 7.33172i) q^{73} +(-3.33251 + 6.69372i) q^{77} -3.94323 q^{79} +(-4.72390 + 8.18204i) q^{83} +(-4.07391 - 7.05621i) q^{85} +(4.91941 + 8.52068i) q^{89} +(5.69081 - 11.4306i) q^{91} +9.03823 q^{95} +(-1.60699 + 2.78339i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{5} + q^{7}+O(q^{10}) \) 8 * q + 2 * q^5 + q^7	\( 8 q + 2 q^{5} + q^{7} - 5 q^{11} - 3 q^{13} - 2 q^{17} - 8 q^{19} - 2 q^{23} - 8 q^{25} + 2 q^{29} - 11 q^{35} + 4 q^{37} + 3 q^{41} - 5 q^{43} + 30 q^{47} - 19 q^{49} + 24 q^{53} + 16 q^{55} + 20 q^{59} + 24 q^{61} - 24 q^{65} + 14 q^{67} + 22 q^{71} - 10 q^{73} + 11 q^{77} - 35 q^{83} + 13 q^{85} + 18 q^{89} - 9 q^{91} - 20 q^{95} - 19 q^{97}+O(q^{100}) \) 8 * q + 2 * q^5 + q^7 - 5 * q^11 - 3 * q^13 - 2 * q^17 - 8 * q^19 - 2 * q^23 - 8 * q^25 + 2 * q^29 - 11 * q^35 + 4 * q^37 + 3 * q^41 - 5 * q^43 + 30 * q^47 - 19 * q^49 + 24 * q^53 + 16 * q^55 + 20 * q^59 + 24 * q^61 - 24 * q^65 + 14 * q^67 + 22 * q^71 - 10 * q^73 + 11 * q^77 - 35 * q^83 + 13 * q^85 + 18 * q^89 - 9 * q^91 - 20 * q^95 - 19 * q^97

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