LMFDB - Embedded newform 2268.2.i.m.2053.3

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			2053.3
Root			$-1.03075 - 1.78531i$ of defining polynomial
Character	$\chi$	$=$	2268.2053
Dual form			2268.2.i.m.865.3

$q$-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 $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

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

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	0.996470	−	0.0839464i	$-0.0267524\pi$
$5$	0.951526	+	1.64809i	0.425535	+	0.737049i	−0.570935	+	0.820995i	$0.693419\pi$
$6$		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	−0.570455	−	0.821329i	$-0.693233\pi$
$11$	1.41310	−	2.44755i	0.426065	−	0.737965i	0.996519	+	0.0833637i	$0.0265663\pi$
$12$		0			0
$13$	−2.41310	+	4.17961i	−0.669272	+	1.15921i	0.308835	+	0.951115i	$0.400061\pi$
$13$	−2.41310	+	4.17961i	−0.669272	+	1.15921i	−0.978108	+	0.208098i	$0.933273\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.14072	+	3.70784i	0.519201	+	0.899283i	0.999751	+	0.0223156i	$0.00710387\pi$
$17$	2.14072	+	3.70784i	0.519201	+	0.899283i	−0.480550	+	0.876968i	$0.659563\pi$
$18$		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
$23$	−1.23394	−	2.13725i	−0.257295	−	0.445648i	0.708221	−	0.705991i	$-0.249498\pi$
$23$	−1.23394	−	2.13725i	−0.257295	−	0.445648i	−0.965516	+	0.260342i	$0.916165\pi$
$24$		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	0.917397	+	0.397974i	$0.130286\pi$
$29$	4.32619	+	7.49319i	0.803354	+	1.39145i	−0.114043	+	0.993476i	$0.536380\pi$
$30$		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	−0.996528	−	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	−0.344613	−	0.938745i	$-0.611990\pi$
$41$	4.10229	−	7.10538i	0.640670	−	1.10967i	0.985283	−	0.170929i	$-0.0546768\pi$
$42$		0			0
$43$	−3.36462	−	5.82770i	−0.513100	−	0.888715i	−0.999885	−	0.0151933i	$-0.995164\pi$
$43$	−3.36462	−	5.82770i	−0.513100	−	0.888715i	0.486784	−	0.873522i	$-0.338170\pi$
$44$		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	0.920890	+	0.389823i	$0.127464\pi$
$53$	5.80983	+	10.0629i	0.798042	+	1.38225i	−0.122848	+	0.992425i	$0.539203\pi$
$54$		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	0.999986	−	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
$77$	−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	−0.999769	−	0.0215134i	$-0.993152\pi$
$83$	−4.72390	−	8.18204i	−0.518515	−	0.898095i	0.481253	−	0.876582i	$-0.340182\pi$
$84$		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	$-0.658722\pi$
$89$	4.91941	−	8.52068i	0.521457	−	0.903190i	0.999689	−	0.0249561i	$-0.00794460\pi$
$90$		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	0.772837	−	0.634605i	$-0.218837\pi$
$97$	−1.60699	−	2.78339i	−0.163165	−	0.282611i	−0.936002	+	0.351994i	$0.885504\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.266056	+	0.460822i	−0.0264735	+	0.0458535i	−0.878959	−	0.476898i	$-0.841761\pi$
$101$	−0.266056	+	0.460822i	−0.0264735	+	0.0458535i	0.852485	+	0.522752i	$0.175094\pi$
$102$		0			0
$103$	2.62695	+	4.55002i	0.258841	+	0.448326i	0.965932	−	0.258797i	$-0.0833260\pi$
$103$	2.62695	+	4.55002i	0.258841	+	0.448326i	−0.707090	+	0.707123i	$0.749993\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.935164	+	1.61975i	−0.0904057	+	0.156587i	−0.907682	−	0.419659i	$-0.862150\pi$
$107$	−0.935164	+	1.61975i	−0.0904057	+	0.156587i	0.817276	+	0.576246i	$0.195483\pi$
$108$		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	−0.363291	−	0.931676i	$-0.618347\pi$
$113$	6.64607	−	11.5113i	0.625209	−	1.08289i	0.988500	−	0.151219i	$-0.0483198\pi$
$114$		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	0.992998	+	0.118129i	$0.0376898\pi$
$131$	6.85360	+	11.8708i	0.598802	+	1.03716i	−0.394196	+	0.919026i	$0.628977\pi$
$132$		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	−0.0727520	+	0.997350i	$0.523178\pi$
$137$	−10.5355	+	18.2480i	−0.900106	+	1.55903i	−0.827355	+	0.561680i	$0.810155\pi$
$138$		0			0
$139$	−5.39673	+	9.34742i	−0.457745	+	0.792838i	−0.998841	−	0.0481230i	$-0.984676\pi$
$139$	−5.39673	+	9.34742i	−0.457745	+	0.792838i	0.541096	+	0.840961i	$0.318009\pi$
$140$		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	0.939900	−	0.341449i	$-0.110918\pi$
$149$	2.12695	+	3.68399i	0.174247	+	0.301804i	−0.765654	+	0.643253i	$0.777584\pi$
$150$		0			0
$151$	−8.67073	+	15.0181i	−0.705614	+	1.22216i	0.260856	+	0.965378i	$0.415995\pi$
$151$	−8.67073	+	15.0181i	−0.705614	+	1.22216i	−0.966470	+	0.256781i	$0.917338\pi$
$152$		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	−0.316595	−	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	$-0.836305\pi$
$167$	−0.120634	+	0.208945i	−0.00933496	+	0.0161686i	0.861320	+	0.508063i	$0.169638\pi$
$168$		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	0.767870	+	0.640606i	$0.221317\pi$
$179$	12.5592	+	21.7531i	0.938716	+	1.62590i	0.170846	+	0.985298i	$0.445350\pi$
$180$		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	0.621058	−	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
$203$	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	−0.152882	−	0.988244i	$-0.548855\pi$
$211$	11.3215	−	19.6094i	0.779404	−	1.34997i	0.932286	−	0.361722i	$-0.117811\pi$
$212$		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	−0.840969	−	0.541084i	$-0.818014\pi$
$223$	−13.2767	−	22.9960i	−0.889077	−	1.53993i	−0.0481078	−	0.998842i	$-0.515319\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.12695	+	8.88014i	−0.340288	+	0.589396i	−0.984486	−	0.175463i	$-0.943858\pi$
$227$	−5.12695	+	8.88014i	−0.340288	+	0.589396i	0.644198	+	0.764859i	$0.277191\pi$
$228$		0			0
$229$	−6.19924	−	10.7374i	−0.409657	−	0.709547i	0.585194	−	0.810893i	$-0.301018\pi$
$229$	−6.19924	−	10.7374i	−0.409657	−	0.709547i	−0.994851	+	0.101346i	$0.967685\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.60699	+	6.24749i	−0.236302	+	0.409287i	−0.959650	−	0.281196i	$-0.909269\pi$
$233$	−3.60699	+	6.24749i	−0.236302	+	0.409287i	0.723348	+	0.690483i	$0.242602\pi$
$234$		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	$-0.780488\pi$
$239$	2.55479	−	4.42503i	0.165256	−	0.286231i	0.936746	+	0.350010i	$0.113822\pi$
$240$		0			0
$241$	6.85162	−	11.8674i	0.441352	−	0.764444i	−0.556438	−	0.830889i	$-0.687832\pi$
$241$	6.85162	−	11.8674i	0.441352	−	0.764444i	0.997790	+	0.0664450i	$0.0211657\pi$
$242$		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	−0.983735	−	0.179624i	$-0.942512\pi$
$257$	−10.3790	−	17.9770i	−0.647427	−	1.12138i	0.336309	−	0.941752i	$-0.390821\pi$
$258$		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	−0.784756	−	0.619804i	$-0.787212\pi$
$263$	2.34158	−	4.05574i	0.144388	−	0.250087i	0.929144	+	0.369717i	$0.120545\pi$
$264$		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	0.554801	−	0.831983i	$-0.312794\pi$
$269$	−7.26767	−	12.5880i	−0.443118	−	0.767503i	−0.997919	+	0.0644803i	$0.979461\pi$
$270$		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
$275$	−1.94780	−	3.37369i	−0.117457	−	0.203441i
$276$		0			0
$277$	−5.01004	+	8.67765i	−0.301024	+	0.521389i	−0.976368	−	0.216113i	$-0.930662\pi$
$277$	−5.01004	+	8.67765i	−0.301024	+	0.521389i	0.675344	+	0.737503i	$0.263995\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.87531	−	17.1045i	−0.589112	−	1.02037i	−0.994349	−	0.106160i	$-0.966144\pi$
$281$	−9.87531	−	17.1045i	−0.589112	−	1.02037i	0.405237	−	0.914211i	$-0.367189\pi$
$282$		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	−0.950741	−	0.309987i	$-0.899675\pi$
$293$	−3.54179	+	6.13457i	−0.206914	+	0.358385i	0.743827	+	0.668372i	$0.233009\pi$
$294$		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	−0.163976	−	0.986464i	$-0.552432\pi$
$337$	14.1778	−	24.5567i	0.772315	−	1.33769i	0.936291	−	0.351224i	$-0.114235\pi$
$338$		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	0.994249	−	0.107091i	$-0.0341536\pi$
$349$	7.55446	+	13.0847i	0.404381	+	0.700409i	−0.589868	+	0.807500i	$0.700820\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.7710	+	22.1201i	−0.679734	+	1.17733i	0.295327	+	0.955396i	$0.404571\pi$
$353$	−12.7710	+	22.1201i	−0.679734	+	1.17733i	−0.975061	+	0.221937i	$0.928762\pi$
$354$		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	0.487573	+	0.873082i	$0.337882\pi$
$359$	−9.70718	+	16.8133i	−0.512325	+	0.887373i	−0.999898	+	0.0142909i	$0.995451\pi$
$360$		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	−0.985314	−	0.170753i	$-0.945380\pi$
$367$	−6.60504	+	11.4403i	−0.344780	+	0.597177i	0.640533	+	0.767930i	$0.278713\pi$
$368$		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	−0.891850	−	0.452332i	$-0.850592\pi$
$373$	−16.1778	−	28.0208i	−0.837656	−	1.45086i	0.0541942	−	0.998530i	$-0.482741\pi$
$374$		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	0.979286	−	0.202481i	$-0.0649004\pi$
$383$	6.15077	+	10.6534i	0.314289	+	0.544365i	−0.664997	+	0.746846i	$0.731567\pi$
$384$		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	0.209868	+	0.977730i	$0.432697\pi$
$389$	−14.6307	+	25.3411i	−0.741805	+	1.28484i	−0.951673	+	0.307114i	$0.900637\pi$
$390$		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
$401$	2.48425	+	4.30285i	0.124058	+	0.214874i	0.921364	−	0.388701i	$-0.127076\pi$
$401$	2.48425	+	4.30285i	0.124058	+	0.214874i	−0.797307	+	0.603574i	$0.793743\pi$
$402$		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	−0.945994	−	0.324184i	$-0.894910\pi$
$419$	−3.93516	+	6.81590i	−0.192245	+	0.332979i	0.753749	+	0.657163i	$0.228244\pi$
$420$		0			0
$421$	12.6287	+	21.8736i	0.615487	+	1.06605i	0.990299	+	0.138953i	$0.0443738\pi$
$421$	12.6287	+	21.8736i	0.615487	+	1.06605i	−0.374812	+	0.927101i	$0.622293\pi$
$422$		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	−0.937895	−	0.346918i	$-0.887228\pi$
$431$	−15.9729	−	27.6659i	−0.769388	−	1.33262i	0.168508	−	0.985700i	$-0.446105\pi$
$432$		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	−0.966893	−	0.255181i	$-0.917865\pi$
$461$	−15.1250	−	26.1972i	−0.704440	−	1.22013i	0.262453	−	0.964945i	$-0.415469\pi$
$462$		0			0
$463$	−12.3004	+	21.3050i	−0.571650	+	0.990126i	0.424747	+	0.905312i	$0.360363\pi$
$463$	−12.3004	+	21.3050i	−0.571650	+	0.990126i	−0.996397	+	0.0848141i	$0.972970\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.26472	+	5.65466i	−0.151073	+	0.261667i	−0.931622	−	0.363428i	$-0.881606\pi$
$467$	−3.26472	+	5.65466i	−0.151073	+	0.261667i	0.780549	+	0.625095i	$0.214940\pi$
$468$		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	−0.360954	−	0.932584i	$-0.617549\pi$
$479$	13.7262	−	23.7744i	0.627164	−	1.08628i	0.988118	−	0.153697i	$-0.0491179\pi$
$480$		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	−0.957497	−	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	0.305155	+	0.952303i	$0.401292\pi$
$491$	−14.8937	+	25.7966i	−0.672141	+	1.16418i	−0.977296	+	0.211880i	$0.932041\pi$
$492$		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	0.982384	+	0.186872i	$0.0598351\pi$
$499$	14.5875	+	25.2664i	0.653028	+	1.13108i	−0.329356	+	0.944206i	$0.606832\pi$
$500$		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	0.745597	−	0.666397i	$-0.232164\pi$
$509$	−4.60962	−	7.98409i	−0.204318	−	0.353889i	−0.949915	+	0.312508i	$0.898831\pi$
$510$		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	−0.984554	−	0.175079i	$-0.943982\pi$
$521$	−14.6973	−	25.4565i	−0.643900	−	1.11527i	0.340654	−	0.940189i	$-0.389351\pi$
$522$		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
$527$	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	−0.999630	−	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	0.771322	−	0.636445i	$-0.219596\pi$
$547$	−3.87110	−	6.70494i	−0.165516	−	0.286683i	−0.936839	+	0.349762i	$0.886262\pi$
$548$		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	0.948694	−	0.316194i	$-0.102405\pi$
$557$	4.73233	+	8.19663i	0.200515	+	0.347302i	−0.748179	+	0.663496i	$0.769072\pi$
$558$		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	−0.987036	−	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
$581$	−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	−0.908569	−	0.417734i	$-0.862824\pi$
$587$	−19.7714	−	34.2451i	−0.816053	−	1.41345i	0.0925163	−	0.995711i	$-0.470509\pi$
$588$		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	−0.869437	−	0.494045i	$-0.835518\pi$
$593$	−0.167128	+	0.289474i	−0.00686313	+	0.0118873i	0.862573	+	0.505932i	$0.168851\pi$
$594$		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	0.644994	−	0.764188i	$-0.276860\pi$
$601$	−8.31826	−	14.4076i	−0.339309	−	0.587700i	−0.984303	+	0.176488i	$0.943526\pi$
$602$		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	0.521576	−	0.853205i	$-0.325344\pi$
$607$	−11.7793	−	20.4024i	−0.478109	−	0.828108i	−0.999685	+	0.0250962i	$0.992011\pi$
$608$		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	0.242232	+	0.970218i	$0.422121\pi$
$617$	−17.8625	+	30.9388i	−0.719118	+	1.24555i	−0.961350	+	0.275330i	$0.911213\pi$
$618$		0			0
$619$	−11.5107	+	19.9371i	−0.462654	+	0.801340i	−0.999092	−	0.0425997i	$-0.986436\pi$
$619$	−11.5107	+	19.9371i	−0.462654	+	0.801340i	0.536439	+	0.843939i	$0.319769\pi$
$620$		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	−0.999738	−	0.0229092i	$-0.992707\pi$
$641$	−12.1534	+	21.0502i	−0.480029	+	0.831434i	0.519709	+	0.854344i	$0.326040\pi$
$642$		0			0
$643$	8.27674	−	14.3357i	0.326403	−	0.565346i	−0.655392	−	0.755289i	$-0.727497\pi$
$643$	8.27674	−	14.3357i	0.326403	−	0.565346i	0.981795	+	0.189942i	$0.0608300\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.5103	+	42.4531i	0.963600	+	1.66900i	0.713329	+	0.700829i	$0.247186\pi$
$647$	24.5103	+	42.4531i	0.963600	+	1.66900i	0.250271	+	0.968176i	$0.419480\pi$
$648$		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	−0.911943	−	0.410318i	$-0.865418\pi$
$653$	−20.7323	−	35.9094i	−0.811317	−	1.40524i	0.100626	−	0.994924i	$-0.467915\pi$
$654$		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	0.877233	−	0.480065i	$-0.159387\pi$
$659$	0.587031	+	1.01677i	0.0228675	+	0.0396076i	−0.854365	+	0.519673i	$0.826054\pi$
$660$		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	0.990986	−	0.133962i	$-0.0427699\pi$
$673$	9.84453	+	17.0512i	0.379479	+	0.657277i	−0.611508	+	0.791239i	$0.709437\pi$
$674$		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	0.909052	−	0.416683i	$-0.136808\pi$
$683$	2.44793	+	4.23993i	0.0936673	+	0.162237i	−0.815384	+	0.578920i	$0.803474\pi$
$684$		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	−0.278780	−	0.960355i	$-0.589930\pi$
$719$	18.5635	−	32.1529i	0.692302	−	1.19910i	0.971082	−	0.238747i	$-0.0767366\pi$
$720$		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	0.641848	−	0.766832i	$-0.278168\pi$
$727$	−9.25293	−	16.0265i	−0.343172	−	0.594392i	−0.985020	+	0.172440i	$0.944835\pi$
$728$		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	−0.988463	−	0.151461i	$-0.951602\pi$
$733$	−16.9321	−	29.3272i	−0.625401	−	1.08323i	0.363062	−	0.931765i	$-0.381731\pi$
$734$		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	$-0.710571\pi$
$743$	10.2539	−	17.7603i	0.376179	−	0.651562i	0.990503	+	0.137493i	$0.0439043\pi$
$744$		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	−0.923241	−	0.384221i	$-0.874470\pi$
$751$	−21.7691	−	37.7052i	−0.794365	−	1.37588i	0.128876	−	0.991661i	$-0.458863\pi$
$752$		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	0.984437	−	0.175738i	$-0.0562311\pi$
$761$	9.38001	+	16.2467i	0.340025	+	0.588941i	−0.644412	+	0.764679i	$0.722898\pi$
$762$		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	−0.997683	−	0.0680412i	$-0.978325\pi$
$769$	−12.1992	+	21.1297i	−0.439916	+	0.761957i	0.557767	+	0.829998i	$0.311658\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.41582	−	5.91637i	−0.122858	−	0.212797i	0.798035	−	0.602611i	$-0.205873\pi$
$773$	−3.41582	−	5.91637i	−0.122858	−	0.212797i	−0.920894	+	0.389814i	$0.872539\pi$
$774$		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	−0.568395	−	0.822755i	$-0.692436\pi$
$797$	12.0922	−	20.9444i	0.428329	−	0.741888i	0.996725	+	0.0808672i	$0.0257690\pi$
$798$		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	0.943047	+	0.332659i	$0.107946\pi$
$809$	21.6057	+	37.4221i	0.759614	+	1.31569i	−0.183433	+	0.983032i	$0.558721\pi$
$810$		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	0.824882	−	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
$833$	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	0.693413	−	0.720540i	$-0.256106\pi$
$839$	−8.03211	−	13.9120i	−0.277299	−	0.480296i	−0.970713	+	0.240244i	$0.922773\pi$
$840$		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	−0.996772	−	0.0802821i	$-0.974418\pi$
$853$	−16.5865	−	28.7287i	−0.567912	−	0.983653i	0.428860	−	0.903371i	$-0.358915\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.13590	−	3.69948i	0.0729608	−	0.126372i	−0.827237	−	0.561853i	$-0.810089\pi$
$857$	2.13590	−	3.69948i	0.0729608	−	0.126372i	0.900198	+	0.435481i	$0.143422\pi$
$858$		0			0
$859$	−17.3448	−	30.0421i	−0.591798	−	1.02502i	−0.993990	−	0.109468i	$-0.965085\pi$
$859$	−17.3448	−	30.0421i	−0.591798	−	1.02502i	0.402193	−	0.915555i	$-0.368248\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−16.1166	+	27.9147i	−0.548615	+	0.950229i	0.449755	+	0.893152i	$0.351511\pi$
$863$	−16.1166	+	27.9147i	−0.548615	+	0.950229i	−0.998370	+	0.0570767i	$0.981822\pi$
$864$		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	0.988177	−	0.153320i	$-0.0489965\pi$
$877$	10.6999	+	18.5327i	0.361309	+	0.625806i	−0.626867	+	0.779126i	$0.715663\pi$
$878$		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	0.888226	−	0.459406i	$-0.151938\pi$
$887$	1.37762	+	2.38611i	0.0462560	+	0.0801177i	−0.841970	+	0.539524i	$0.818604\pi$
$888$		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	0.272254	+	0.962225i	$0.412231\pi$
$907$	−20.9967	+	36.3674i	−0.697185	+	1.20756i	−0.969439	+	0.245334i	$0.921102\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.384944	+	0.666743i	0.0127538	+	0.0220902i	0.872332	−	0.488914i	$-0.162607\pi$
$911$	0.384944	+	0.666743i	0.0127538	+	0.0220902i	−0.859578	+	0.511004i	$0.829274\pi$
$912$		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	−0.399590	−	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
$929$	−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	−0.672238	−	0.740335i	$-0.734667\pi$
$967$	9.48538	−	16.4292i	0.305029	−	0.528326i	0.977268	+	0.212008i	$0.0680004\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	29.5030	−	51.1008i	0.946797	−	1.63990i	0.194686	−	0.980866i	$-0.437631\pi$
$971$	29.5030	−	51.1008i	0.946797	−	1.63990i	0.752112	−	0.659036i	$-0.229035\pi$
$972$		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	0.413113	+	0.910680i	$0.364441\pi$
$983$	−18.2510	+	31.6116i	−0.582115	+	1.00825i	−0.995228	+	0.0975731i	$0.968892\pi$
$984$		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	0.944547	−	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
$997$	−11.5160	+	19.9464i	−0.364716	+	0.631707i	−0.988731	−	0.149706i	$-0.952167\pi$
$997$	−11.5160	+	19.9464i	−0.364716	+	0.631707i	0.624014	+	0.781413i	$0.285501\pi$
$998$		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.2053.3		8
3.2	odd	2		2268.2.i.l.2053.2		8
7.4	even	3		2268.2.l.l.109.2		8
9.2	odd	6		2268.2.l.m.541.3		8
9.4	even	3		2268.2.k.d.1297.3	yes	8
9.5	odd	6		2268.2.k.c.1297.2	✓	8
9.7	even	3		2268.2.l.l.541.2		8
21.11	odd	6		2268.2.l.m.109.3		8
63.4	even	3		2268.2.k.d.1621.3	yes	8
63.11	odd	6		2268.2.i.l.865.2		8
63.25	even	3	inner	2268.2.i.m.865.3		8
63.32	odd	6		2268.2.k.c.1621.2	yes	8

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