LMFDB - Embedded newform 2736.2.dc.f.449.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2736,2,Mod(449,2736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2736, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))

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

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

chi := DirichletCharacter("2736.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2736 = 2^{4} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2736.dc (of order $6$, 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:	$21.8470699930$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} - 18 x^{18} + 232 x^{17} + 208 x^{16} - 3152 x^{15} - 2732 x^{14} + 24552 x^{13} + \cdots + 414864 $ x^20 - 8x^19 - 18x^18 + 232x^17 + 208x^16 - 3152x^15 - 2732x^14 + 24552x^13 + 30728x^12 - 110512x^11 - 211368x^10 + 231024x^9 + 827916x^8 + 179664x^7 - 1551960x^6 - 1894880x^5 + 305564x^4 + 2772832x^3 + 3072904x^2 + 1645728*x + 414864
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 1368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.7
Root			$-0.561107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2736.449
Dual form			2736.2.dc.f.1889.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.524572 - 0.302862i) q^{5} -4.37361 q^{7} +O(q^{10})$	$q+(0.524572 - 0.302862i) q^{5} -4.37361 q^{7} -4.96560i q^{11} +(1.91196 + 1.10387i) q^{13} +(-2.80061 + 1.61693i) q^{17} +(0.965553 - 4.25061i) q^{19} +(-1.27590 - 0.736640i) q^{23} +(-2.31655 + 4.01238i) q^{25} +(-1.05366 + 1.82499i) q^{29} +9.85749i q^{31} +(-2.29427 + 1.32460i) q^{35} -5.03086i q^{37} +(3.79948 + 6.58090i) q^{41} +(-1.50446 - 2.60580i) q^{43} +(9.40077 + 5.42754i) q^{47} +12.1285 q^{49} +(1.08442 - 1.87827i) q^{53} +(-1.50389 - 2.60481i) q^{55} +(0.306301 + 0.530529i) q^{59} +(-4.45845 + 7.72227i) q^{61} +1.33728 q^{65} +(-11.7394 - 6.77776i) q^{67} +(1.90222 + 3.29475i) q^{71} +(-1.75981 - 3.04808i) q^{73} +21.7176i q^{77} +(-13.7950 + 7.96456i) q^{79} +14.1763i q^{83} +(-0.979412 + 1.69639i) q^{85} +(-6.78655 + 11.7546i) q^{89} +(-8.36216 - 4.82790i) q^{91} +(-0.780846 - 2.52218i) q^{95} +(3.12989 - 1.80704i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{7}+O(q^{10}) $ 20 * q + 4 * q^7	$ 20 q + 4 q^{7} + 6 q^{13} + 12 q^{17} - 4 q^{19} + 14 q^{25} + 12 q^{35} + 8 q^{41} + 2 q^{43} + 36 q^{47} + 32 q^{49} - 8 q^{53} - 12 q^{55} - 8 q^{59} - 2 q^{61} + 8 q^{65} - 30 q^{67} + 4 q^{71} - 22 q^{73} - 54 q^{79} - 4 q^{85} - 32 q^{89} - 18 q^{91} + 32 q^{95} + 12 q^{97}+O(q^{100}) $ 20 * q + 4 * q^7 + 6 * q^13 + 12 * q^17 - 4 * q^19 + 14 * q^25 + 12 * q^35 + 8 * q^41 + 2 * q^43 + 36 * q^47 + 32 * q^49 - 8 * q^53 - 12 * q^55 - 8 * q^59 - 2 * q^61 + 8 * q^65 - 30 * q^67 + 4 * q^71 - 22 * q^73 - 54 * q^79 - 4 * q^85 - 32 * q^89 - 18 * q^91 + 32 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.524572	−	0.302862i	0.234596	−	0.135444i	−0.378095	−	0.925767i	$-0.623421\pi$
$5$	0.524572	−	0.302862i	0.234596	−	0.135444i	0.612690	+	0.790323i	$0.290087\pi$
$6$		0			0
$7$	−4.37361			−1.65307			−0.826535	−	0.562885i	$-0.809691\pi$
$7$	−4.37361			−1.65307			−0.826535	+	0.562885i	$0.809691\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	4.96560i		−	1.49718i	−0.663031	−	0.748592i	$-0.730730\pi$
$11$		−	4.96560i		−	1.49718i	0.663031	−	0.748592i	$-0.269270\pi$
$12$		0			0
$13$	1.91196	+	1.10387i	0.530282	+	0.306158i	0.741131	−	0.671360i	$-0.234290\pi$
$13$	1.91196	+	1.10387i	0.530282	+	0.306158i	−0.210850	+	0.977519i	$0.567623\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.80061	+	1.61693i	−0.679247	+	0.392163i	−0.799571	−	0.600571i	$-0.794940\pi$
$17$	−2.80061	+	1.61693i	−0.679247	+	0.392163i	0.120325	+	0.992735i	$0.461606\pi$
$18$		0			0
$19$	0.965553	−	4.25061i	0.221513	−	0.975157i
$19$	0.965553	−	4.25061i	0.221513	−	0.975157i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.27590	−	0.736640i	−0.266043	−	0.153600i	0.361045	−	0.932548i	$-0.382420\pi$
$23$	−1.27590	−	0.736640i	−0.266043	−	0.153600i	−0.627088	+	0.778948i	$0.715753\pi$
$24$		0			0
$25$	−2.31655	+	4.01238i	−0.463310	+	0.802476i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.05366	+	1.82499i	−0.195660	+	0.338893i	−0.947117	−	0.320889i	$-0.896018\pi$
$29$	−1.05366	+	1.82499i	−0.195660	+	0.338893i	0.751457	+	0.659782i	$0.229352\pi$
$30$		0			0
$31$			9.85749i			1.77046i	0.465157	+	0.885228i	$0.345998\pi$
$31$			9.85749i			1.77046i	−0.465157	+	0.885228i	$0.654002\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.29427	+	1.32460i	−0.387803	+	0.223898i
$36$		0			0
$37$		−	5.03086i		−	0.827069i	−0.910488	−	0.413534i	$-0.864294\pi$
$37$		−	5.03086i		−	0.827069i	0.910488	−	0.413534i	$-0.135706\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.79948	+	6.58090i	0.593379	+	1.02776i	0.993773	+	0.111420i	$0.0355399\pi$
$41$	3.79948	+	6.58090i	0.593379	+	1.02776i	−0.400394	+	0.916343i	$0.631127\pi$
$42$		0			0
$43$	−1.50446	−	2.60580i	−0.229428	−	0.397381i	0.728211	−	0.685353i	$-0.240352\pi$
$43$	−1.50446	−	2.60580i	−0.229428	−	0.397381i	−0.957639	+	0.287972i	$0.907019\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	9.40077	+	5.42754i	1.37124	+	0.791687i	0.991085	−	0.133234i	$-0.0425362\pi$
$47$	9.40077	+	5.42754i	1.37124	+	0.791687i	0.380158	+	0.924921i	$0.375870\pi$
$48$		0			0
$49$	12.1285			1.73264
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.08442	−	1.87827i	0.148957	−	0.258000i	−0.781885	−	0.623422i	$-0.785742\pi$
$53$	1.08442	−	1.87827i	0.148957	−	0.258000i	0.930842	+	0.365422i	$0.119075\pi$
$54$		0			0
$55$	−1.50389	−	2.60481i	−0.202784	−	0.351233i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.306301	+	0.530529i	0.0398770	+	0.0690690i	0.885275	−	0.465068i	$-0.153970\pi$
$59$	0.306301	+	0.530529i	0.0398770	+	0.0690690i	−0.845398	+	0.534137i	$0.820637\pi$
$60$		0			0
$61$	−4.45845	+	7.72227i	−0.570846	+	0.988735i	0.425633	+	0.904896i	$0.360051\pi$
$61$	−4.45845	+	7.72227i	−0.570846	+	0.988735i	−0.996479	+	0.0838390i	$0.973282\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.33728			0.165869
$66$		0			0
$67$	−11.7394	−	6.77776i	−1.43420	−	0.828035i	−0.436761	−	0.899578i	$-0.643874\pi$
$67$	−11.7394	−	6.77776i	−1.43420	−	0.828035i	−0.997438	+	0.0715426i	$0.977208\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.90222	+	3.29475i	0.225752	+	0.391014i	0.956545	−	0.291585i	$-0.0941827\pi$
$71$	1.90222	+	3.29475i	0.225752	+	0.391014i	−0.730793	+	0.682600i	$0.760849\pi$
$72$		0			0
$73$	−1.75981	−	3.04808i	−0.205970	−	0.356751i	0.744471	−	0.667655i	$-0.232702\pi$
$73$	−1.75981	−	3.04808i	−0.205970	−	0.356751i	−0.950441	+	0.310904i	$0.899368\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			21.7176i			2.47495i
$78$		0			0
$79$	−13.7950	+	7.96456i	−1.55206	+	0.896083i	−0.554087	+	0.832458i	$0.686933\pi$
$79$	−13.7950	+	7.96456i	−1.55206	+	0.896083i	−0.997974	+	0.0636245i	$0.979734\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			14.1763i			1.55606i	0.628230	+	0.778028i	$0.283780\pi$
$83$			14.1763i			1.55606i	−0.628230	+	0.778028i	$0.716220\pi$
$84$		0			0
$85$	−0.979412	+	1.69639i	−0.106232	+	0.183999i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.78655	+	11.7546i	−0.719373	+	1.24599i	0.241876	+	0.970307i	$0.422237\pi$
$89$	−6.78655	+	11.7546i	−0.719373	+	1.24599i	−0.961249	+	0.275683i	$0.911096\pi$
$90$		0			0
$91$	−8.36216	−	4.82790i	−0.876593	−	0.506101i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.780846	−	2.52218i	−0.0801131	−	0.258770i
$96$		0			0
$97$	3.12989	−	1.80704i	0.317792	−	0.183478i	−0.332616	−	0.943062i	$-0.607931\pi$
$97$	3.12989	−	1.80704i	0.317792	−	0.183478i	0.650408	+	0.759585i	$0.274598\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	16.6728	+	9.62603i	1.65900	+	0.957826i	0.973176	+	0.230060i	$0.0738923\pi$
$101$	16.6728	+	9.62603i	1.65900	+	0.957826i	0.685826	+	0.727765i	$0.259441\pi$
$102$		0			0
$103$			3.29310i			0.324479i	0.986751	+	0.162239i	$0.0518717\pi$
$103$			3.29310i			0.324479i	−0.986751	+	0.162239i	$0.948128\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.00308			−0.193645			−0.0968224	−	0.995302i	$-0.530868\pi$
$107$	−2.00308			−0.193645			−0.0968224	+	0.995302i	$0.530868\pi$
$108$		0			0
$109$	0.514531	−	0.297065i	0.0492832	−	0.0284536i	−0.475156	−	0.879902i	$-0.657608\pi$
$109$	0.514531	−	0.297065i	0.0492832	−	0.0284536i	0.524439	+	0.851448i	$0.324275\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.13975			−0.671651			−0.335825	−	0.941924i	$-0.609015\pi$
$113$	−7.13975			−0.671651			−0.335825	+	0.941924i	$0.609015\pi$
$114$		0			0
$115$	−0.892400			−0.0832167
$116$		0			0
$117$		0			0
$118$		0			0
$119$	12.2488	−	7.07183i	1.12284	−	0.648273i
$120$		0			0
$121$	−13.6572			−1.24156
$122$		0			0
$123$		0			0
$124$		0			0
$125$			5.83499i			0.521898i
$126$		0			0
$127$	−9.79592	−	5.65568i	−0.869247	−	0.501860i	−0.00214915	−	0.999998i	$-0.500684\pi$
$127$	−9.79592	−	5.65568i	−0.869247	−	0.501860i	−0.867098	+	0.498138i	$0.834017\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.84637	−	2.79805i	0.423430	−	0.244467i	−0.273114	−	0.961982i	$-0.588054\pi$
$131$	4.84637	−	2.79805i	0.423430	−	0.244467i	0.696544	+	0.717515i	$0.254720\pi$
$132$		0			0
$133$	−4.22295	+	18.5905i	−0.366176	+	1.61200i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.97602	−	4.02761i	−0.596002	−	0.344102i	0.171465	−	0.985190i	$-0.445150\pi$
$137$	−6.97602	−	4.02761i	−0.596002	−	0.344102i	−0.767467	+	0.641088i	$0.778483\pi$
$138$		0			0
$139$	−6.58012	+	11.3971i	−0.558118	+	0.966689i	0.439535	+	0.898225i	$0.355143\pi$
$139$	−6.58012	+	11.3971i	−0.558118	+	0.966689i	−0.997654	+	0.0684640i	$0.978190\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.48137	−	9.49401i	0.458375	−	0.793929i
$144$		0			0
$145$			1.27645i			0.106004i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	19.6556	−	11.3482i	1.61025	−	0.929679i	0.620939	−	0.783859i	$-0.286751\pi$
$149$	19.6556	−	11.3482i	1.61025	−	0.929679i	0.989311	−	0.145820i	$-0.0465820\pi$
$150$		0			0
$151$			11.4226i			0.929556i	0.885427	+	0.464778i	$0.153866\pi$
$151$			11.4226i			0.929556i	−0.885427	+	0.464778i	$0.846134\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.98545	+	5.17096i	0.239797	+	0.415341i
$156$		0			0
$157$	−4.15228	−	7.19197i	−0.331388	−	0.573981i	0.651396	−	0.758738i	$-0.274184\pi$
$157$	−4.15228	−	7.19197i	−0.331388	−	0.573981i	−0.982784	+	0.184757i	$0.940850\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.58028	+	3.22178i	0.439788	+	0.253912i
$162$		0			0
$163$	13.1546			1.03035			0.515173	−	0.857086i	$-0.327728\pi$
$163$	13.1546			1.03035			0.515173	+	0.857086i	$0.327728\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−11.1178	+	19.2567i	−0.860324	+	1.49013i	0.0112920	+	0.999936i	$0.496406\pi$
$167$	−11.1178	+	19.2567i	−0.860324	+	1.49013i	−0.871616	+	0.490189i	$0.836928\pi$
$168$		0			0
$169$	−4.06295	−	7.03723i	−0.312534	−	0.541325i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−5.63651	−	9.76272i	−0.428536	−	0.742246i	0.568208	−	0.822885i	$-0.307637\pi$
$173$	−5.63651	−	9.76272i	−0.428536	−	0.742246i	−0.996743	+	0.0806396i	$0.974304\pi$
$174$		0			0
$175$	10.1317	−	17.5486i	0.765884	−	1.32655i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−25.0361			−1.87128			−0.935642	−	0.352951i	$-0.885178\pi$
$179$	−25.0361			−1.87128			−0.935642	+	0.352951i	$0.885178\pi$
$180$		0			0
$181$	6.39225	+	3.69057i	0.475132	+	0.274318i	0.718386	−	0.695645i	$-0.244881\pi$
$181$	6.39225	+	3.69057i	0.475132	+	0.274318i	−0.243254	+	0.969963i	$0.578215\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.52366	−	2.63905i	−0.112021	−	0.194027i
$186$		0			0
$187$	8.02903	+	13.9067i	0.587141	+	1.01696i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			18.4138i			1.33237i	0.745785	+	0.666187i	$0.232075\pi$
$191$			18.4138i			1.33237i	−0.745785	+	0.666187i	$0.767925\pi$
$192$		0			0
$193$	−12.0421	+	6.95252i	−0.866811	+	0.500454i	−0.866287	−	0.499546i	$-0.833500\pi$
$193$	−12.0421	+	6.95252i	−0.866811	+	0.500454i	−0.000523893		1.00000i	$0.500167\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	9.26259i		−	0.659932i	−0.943993	−	0.329966i	$-0.892963\pi$
$197$		−	9.26259i		−	0.659932i	0.943993	−	0.329966i	$-0.107037\pi$
$198$		0			0
$199$	6.97107	−	12.0743i	0.494166	−	0.855921i	−0.505811	−	0.862644i	$-0.668807\pi$
$199$	6.97107	−	12.0743i	0.494166	−	0.855921i	0.999977	+	0.00672315i	$0.00214006\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.60830	−	7.98181i	0.323439	−	0.560214i
$204$		0			0
$205$	3.98620	+	2.30143i	0.278408	+	0.160739i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−21.1068	−	4.79455i	−1.45999	−	0.331646i
$210$		0			0
$211$	0.223008	−	0.128754i	0.0153525	−	0.00886378i	−0.492304	−	0.870423i	$-0.663845\pi$
$211$	0.223008	−	0.128754i	0.0153525	−	0.00886378i	0.507657	+	0.861559i	$0.330512\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.57839	−	0.911286i	−0.107646	−	0.0621492i
$216$		0			0
$217$		−	43.1128i		−	2.92669i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−7.13952			−0.480256
$222$		0			0
$223$	13.3860	−	7.72842i	0.896394	−	0.517533i	0.0203653	−	0.999793i	$-0.493517\pi$
$223$	13.3860	−	7.72842i	0.896394	−	0.517533i	0.876028	+	0.482259i	$0.160184\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.51731			0.233452			0.116726	−	0.993164i	$-0.462760\pi$
$227$	3.51731			0.233452			0.116726	+	0.993164i	$0.462760\pi$
$228$		0			0
$229$	−15.1834			−1.00335			−0.501674	−	0.865057i	$-0.667282\pi$
$229$	−15.1834			−1.00335			−0.501674	+	0.865057i	$0.667282\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.6888	−	6.17117i	0.700246	−	0.404287i	−0.107193	−	0.994238i	$-0.534186\pi$
$233$	10.6888	−	6.17117i	0.700246	−	0.404287i	0.807439	+	0.589951i	$0.200853\pi$
$234$		0			0
$235$	6.57517			0.428917
$236$		0			0
$237$		0			0
$238$		0			0
$239$			19.8027i			1.28093i	0.767986	+	0.640466i	$0.221259\pi$
$239$			19.8027i			1.28093i	−0.767986	+	0.640466i	$0.778741\pi$
$240$		0			0
$241$	12.7113	+	7.33884i	0.818804	+	0.472737i	0.850004	−	0.526777i	$-0.176600\pi$
$241$	12.7113	+	7.33884i	0.818804	+	0.472737i	−0.0312001	+	0.999513i	$0.509933\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.36226	−	3.67325i	0.406470	−	0.234675i
$246$		0			0
$247$	6.53822	−	7.06115i	0.416017	−	0.449290i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	3.82239	+	2.20686i	0.241267	+	0.139296i	0.615759	−	0.787935i	$-0.288850\pi$
$251$	3.82239	+	2.20686i	0.241267	+	0.139296i	−0.374492	+	0.927230i	$0.622183\pi$
$252$		0			0
$253$	−3.65786	+	6.33560i	−0.229968	+	0.398316i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.90044	−	10.2199i	0.368059	−	0.637497i	−0.621203	−	0.783650i	$-0.713356\pi$
$257$	5.90044	−	10.2199i	0.368059	−	0.637497i	0.989262	+	0.146153i	$0.0466890\pi$
$258$		0			0
$259$			22.0030i			1.36720i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.83830	−	3.94810i	0.421668	−	0.243450i	−0.274123	−	0.961695i	$-0.588387\pi$
$263$	6.83830	−	3.94810i	0.421668	−	0.243450i	0.695791	+	0.718245i	$0.255054\pi$
$264$		0			0
$265$		−	1.31372i		−	0.0807010i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	14.3294	+	24.8193i	0.873681	+	1.51326i	0.858161	+	0.513381i	$0.171607\pi$
$269$	14.3294	+	24.8193i	0.873681	+	1.51326i	0.0155207	+	0.999880i	$0.495059\pi$
$270$		0			0
$271$	3.13683	+	5.43315i	0.190549	+	0.330040i	0.945432	−	0.325819i	$-0.105640\pi$
$271$	3.13683	+	5.43315i	0.190549	+	0.330040i	−0.754883	+	0.655859i	$0.772307\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	19.9239	+	11.5031i	1.20146	+	0.693660i
$276$		0			0
$277$	−7.56534			−0.454557			−0.227279	−	0.973830i	$-0.572983\pi$
$277$	−7.56534			−0.454557			−0.227279	+	0.973830i	$0.572983\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−12.1342	+	21.0171i	−0.723867	+	1.25377i	0.235572	+	0.971857i	$0.424304\pi$
$281$	−12.1342	+	21.0171i	−0.723867	+	1.25377i	−0.959439	+	0.281917i	$0.909030\pi$
$282$		0			0
$283$	0.151128	+	0.261761i	0.00898362	+	0.0155601i	0.870482	−	0.492200i	$-0.163807\pi$
$283$	0.151128	+	0.261761i	0.00898362	+	0.0155601i	−0.861499	+	0.507760i	$0.830474\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−16.6175	−	28.7823i	−0.980898	−	1.69896i
$288$		0			0
$289$	−3.27107	+	5.66567i	−0.192416	+	0.333274i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.09526			−0.0639860			−0.0319930	−	0.999488i	$-0.510185\pi$
$293$	−1.09526			−0.0639860			−0.0319930	+	0.999488i	$0.510185\pi$
$294$		0			0
$295$	0.321354	+	0.185534i	0.0187099	+	0.0108022i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.62631	−	2.81685i	−0.0940519	−	0.162903i
$300$		0			0
$301$	6.57992	+	11.3968i	0.379260	+	0.656898i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			5.40118i			0.309270i
$306$		0			0
$307$	−6.19400	+	3.57611i	−0.353510	+	0.204099i	−0.666230	−	0.745746i	$-0.732093\pi$
$307$	−6.19400	+	3.57611i	−0.353510	+	0.204099i	0.312720	+	0.949845i	$0.398760\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			2.76798i			0.156958i	0.996916	+	0.0784789i	$0.0250063\pi$
$311$			2.76798i			0.156958i	−0.996916	+	0.0784789i	$0.974994\pi$
$312$		0			0
$313$	−5.28875	+	9.16039i	−0.298938	+	0.517776i	−0.975893	−	0.218248i	$-0.929966\pi$
$313$	−5.28875	+	9.16039i	−0.298938	+	0.517776i	0.676955	+	0.736024i	$0.263299\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.32100	−	16.1444i	0.523519	−	0.906762i	−0.476106	−	0.879388i	$-0.657952\pi$
$317$	9.32100	−	16.1444i	0.523519	−	0.906762i	0.999625	−	0.0273741i	$-0.00871453\pi$
$318$		0			0
$319$	9.06219	+	5.23206i	0.507385	+	0.292939i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.16881	+	13.4655i	0.231959	+	0.749242i
$324$		0			0
$325$	−8.85829	+	5.11434i	−0.491369	+	0.283692i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−41.1153	−	23.7379i	−2.26676	−	1.30871i
$330$		0			0
$331$		−	1.01912i		−	0.0560161i	−0.999608	−	0.0280081i	$-0.991084\pi$
$331$		−	1.01912i		−	0.0560161i	0.999608	−	0.0280081i	$-0.00891641\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−8.21089			−0.448609
$336$		0			0
$337$	14.2415	−	8.22233i	0.775784	−	0.447899i	−0.0591502	−	0.998249i	$-0.518839\pi$
$337$	14.2415	−	8.22233i	0.775784	−	0.447899i	0.834934	+	0.550350i	$0.185506\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	48.9483			2.65070
$342$		0			0
$343$	−22.4300			−1.21111
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.18410	−	4.72509i	0.439346	−	0.253656i	−0.263974	−	0.964530i	$-0.585033\pi$
$347$	8.18410	−	4.72509i	0.439346	−	0.253656i	0.703320	+	0.710873i	$0.251700\pi$
$348$		0			0
$349$	−22.6715			−1.21358			−0.606790	−	0.794863i	$-0.707543\pi$
$349$	−22.6715			−1.21358			−0.606790	+	0.794863i	$0.707543\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	12.5827i		−	0.669708i	−0.942270	−	0.334854i	$-0.891313\pi$
$353$		−	12.5827i		−	0.669708i	0.942270	−	0.334854i	$-0.108687\pi$
$354$		0			0
$355$	1.99570	+	1.15222i	0.105921	+	0.0611535i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−17.4835	+	10.0941i	−0.922743	+	0.532746i	−0.884509	−	0.466523i	$-0.845506\pi$
$359$	−17.4835	+	10.0941i	−0.922743	+	0.532746i	−0.0382336	+	0.999269i	$0.512173\pi$
$360$		0			0
$361$	−17.1354	−	8.20838i	−0.901864	−	0.432020i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.84629	−	1.06596i	−0.0966394	−	0.0557948i
$366$		0			0
$367$	4.61388	−	7.99148i	0.240843	−	0.417152i	−0.720112	−	0.693858i	$-0.755910\pi$
$367$	4.61388	−	7.99148i	0.240843	−	0.417152i	0.960955	+	0.276706i	$0.0892429\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.74283	+	8.21483i	−0.246236	+	0.426493i
$372$		0			0
$373$			2.81744i			0.145881i	0.997336	+	0.0729407i	$0.0232384\pi$
$373$			2.81744i			0.145881i	−0.997336	+	0.0729407i	$0.976762\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.02911	+	2.32621i	−0.207510	+	0.119806i
$378$		0			0
$379$			12.9290i			0.664116i	0.943259	+	0.332058i	$0.107743\pi$
$379$			12.9290i			0.664116i	−0.943259	+	0.332058i	$0.892257\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.52287	+	13.0300i	0.384401	+	0.665801i	0.991686	−	0.128683i	$-0.0410748\pi$
$383$	7.52287	+	13.0300i	0.384401	+	0.665801i	−0.607285	+	0.794484i	$0.707741\pi$
$384$		0			0
$385$	6.57743	+	11.3924i	0.335217	+	0.580612i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.0322	−	6.94677i	−0.610054	−	0.352215i	0.162932	−	0.986637i	$-0.447905\pi$
$389$	−12.0322	−	6.94677i	−0.610054	−	0.352215i	−0.772987	+	0.634422i	$0.781238\pi$
$390$		0			0
$391$	4.76438			0.240945
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.82432	+	8.35597i	−0.242738	+	0.420434i
$396$		0			0
$397$	−10.0494	−	17.4060i	−0.504364	−	0.873585i	−0.999987	−	0.00504676i	$-0.998394\pi$
$397$	−10.0494	−	17.4060i	−0.504364	−	0.873585i	0.495623	−	0.868538i	$-0.334940\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.20805	−	14.2168i	−0.409890	−	0.709951i	0.584987	−	0.811043i	$-0.301100\pi$
$401$	−8.20805	−	14.2168i	−0.409890	−	0.709951i	−0.994877	+	0.101092i	$0.967766\pi$
$402$		0			0
$403$	−10.8814	+	18.8471i	−0.542040	+	0.938841i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−24.9812			−1.23827
$408$		0			0
$409$	−30.3916	−	17.5466i	−1.50277	−	0.867623i	−0.999995	−	0.00320474i	$-0.998980\pi$
$409$	−30.3916	−	17.5466i	−1.50277	−	0.867623i	−0.502773	−	0.864419i	$-0.667687\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.33964	−	2.32033i	−0.0659195	−	0.114176i
$414$		0			0
$415$	4.29347	+	7.43650i	0.210758	+	0.365044i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			9.77786i			0.477680i	0.971059	+	0.238840i	$0.0767671\pi$
$419$			9.77786i			0.477680i	−0.971059	+	0.238840i	$0.923233\pi$
$420$		0			0
$421$	−18.1421	+	10.4744i	−0.884192	+	0.510489i	−0.872038	−	0.489437i	$-0.837202\pi$
$421$	−18.1421	+	10.4744i	−0.884192	+	0.510489i	−0.0121540	+	0.999926i	$0.503869\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		−	14.9828i		−	0.726772i
$426$		0			0
$427$	19.4995	−	33.7742i	0.943649	−	1.63445i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	12.2100	−	21.1484i	0.588137	−	1.01868i	−0.406339	−	0.913722i	$-0.633195\pi$
$431$	12.2100	−	21.1484i	0.588137	−	1.01868i	0.994476	−	0.104961i	$-0.0334718\pi$
$432$		0			0
$433$	−19.1998	−	11.0850i	−0.922685	−	0.532712i	−0.0381943	−	0.999270i	$-0.512161\pi$
$433$	−19.1998	−	11.0850i	−0.922685	−	0.532712i	−0.884491	+	0.466558i	$0.845494\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.36312	+	4.71208i	−0.208716	+	0.225410i
$438$		0			0
$439$	−3.89573	+	2.24920i	−0.185933	+	0.107349i	−0.590077	−	0.807347i	$-0.700903\pi$
$439$	−3.89573	+	2.24920i	−0.185933	+	0.107349i	0.404144	+	0.914695i	$0.367569\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	15.6836	+	9.05495i	0.745152	+	0.430214i	0.823940	−	0.566678i	$-0.191772\pi$
$443$	15.6836	+	9.05495i	0.745152	+	0.430214i	−0.0787875	+	0.996891i	$0.525105\pi$
$444$		0			0
$445$			8.22154i			0.389738i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	33.9207			1.60082			0.800409	−	0.599454i	$-0.204615\pi$
$449$	33.9207			1.60082			0.800409	+	0.599454i	$0.204615\pi$
$450$		0			0
$451$	32.6781	−	18.8667i	1.53875	−	0.888398i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5.84874			−0.274193
$456$		0			0
$457$	31.7160			1.48361			0.741807	−	0.670614i	$-0.233969\pi$
$457$	31.7160			1.48361			0.741807	+	0.670614i	$0.233969\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.65156	+	3.26293i	−0.263219	+	0.151970i	−0.625802	−	0.779982i	$-0.715228\pi$
$461$	−5.65156	+	3.26293i	−0.263219	+	0.151970i	0.362583	+	0.931952i	$0.381895\pi$
$462$		0			0
$463$	23.5365			1.09383			0.546916	−	0.837187i	$-0.315802\pi$
$463$	23.5365			1.09383			0.546916	+	0.837187i	$0.315802\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	27.7992i		−	1.28639i	−0.765701	−	0.643196i	$-0.777608\pi$
$467$		−	27.7992i		−	1.28639i	0.765701	−	0.643196i	$-0.222392\pi$
$468$		0			0
$469$	51.3437	+	29.6433i	2.37083	+	1.36880i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−12.9394	+	7.47054i	−0.594952	+	0.343496i
$474$		0			0
$475$	14.8183	+	13.7209i	0.679912	+	0.629559i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−10.7896	−	6.22939i	−0.492991	−	0.284628i	0.232824	−	0.972519i	$-0.425203\pi$
$479$	−10.7896	−	6.22939i	−0.492991	−	0.284628i	−0.725814	+	0.687891i	$0.758537\pi$
$480$		0			0
$481$	5.55342	−	9.61880i	0.253214	−	0.438579i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.09457	−	1.89585i	0.0497018	−	0.0860860i
$486$		0			0
$487$		−	19.2572i		−	0.872628i	−0.899794	−	0.436314i	$-0.856284\pi$
$487$		−	19.2572i		−	0.872628i	0.899794	−	0.436314i	$-0.143716\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	24.6394	−	14.2256i	1.11196	−	0.641991i	0.172624	−	0.984988i	$-0.444775\pi$
$491$	24.6394	−	14.2256i	1.11196	−	0.641991i	0.939337	+	0.342997i	$0.111442\pi$
$492$		0			0
$493$		−	6.81478i		−	0.306922i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.31958	−	14.4099i	−0.373184	−	0.646374i
$498$		0			0
$499$	−17.1417	−	29.6903i	−0.767367	−	1.32912i	−0.938986	−	0.343956i	$-0.888233\pi$
$499$	−17.1417	−	29.6903i	−0.767367	−	1.32912i	0.171618	−	0.985164i	$-0.445100\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−15.7949	−	9.11919i	−0.704260	−	0.406605i	0.104672	−	0.994507i	$-0.466621\pi$
$503$	−15.7949	−	9.11919i	−0.704260	−	0.406605i	−0.808932	+	0.587902i	$0.799954\pi$
$504$		0			0
$505$	11.6614			0.518926
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.00706242	−	0.0122325i	0.000313036	−	0.000542195i	−0.865869	−	0.500271i	$-0.833234\pi$
$509$	0.00706242	−	0.0122325i	0.000313036	−	0.000542195i	0.866182	+	0.499729i	$0.166567\pi$
$510$		0			0
$511$	7.69673	+	13.3311i	0.340483	+	0.589734i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.997353	+	1.72747i	0.0439486	+	0.0761213i
$516$		0			0
$517$	26.9510	−	46.6804i	1.18530	−	2.05300i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−23.7469			−1.04037			−0.520186	−	0.854053i	$-0.674137\pi$
$521$	−23.7469			−1.04037			−0.520186	+	0.854053i	$0.674137\pi$
$522$		0			0
$523$	26.6145	+	15.3659i	1.16377	+	0.671905i	0.952205	−	0.305459i	$-0.0988099\pi$
$523$	26.6145	+	15.3659i	1.16377	+	0.671905i	0.211567	+	0.977363i	$0.432143\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−15.9389	−	27.6069i	−0.694308	−	1.20258i
$528$		0			0
$529$	−10.4147	−	18.0388i	−0.452814	−	0.784297i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			16.7765i			0.726672i
$534$		0			0
$535$	−1.05076	+	0.606655i	−0.0454282	+	0.0262280i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	60.2252i		−	2.59408i
$540$		0			0
$541$	−13.1670	+	22.8060i	−0.566096	+	0.980506i	0.430851	+	0.902423i	$0.358213\pi$
$541$	−13.1670	+	22.8060i	−0.566096	+	0.980506i	−0.996947	+	0.0780835i	$0.975120\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.179939	−	0.311663i	0.00770774	−	0.0133502i
$546$		0			0
$547$	−22.7124	−	13.1130i	−0.971113	−	0.560672i	−0.0715375	−	0.997438i	$-0.522791\pi$
$547$	−22.7124	−	13.1130i	−0.971113	−	0.560672i	−0.899575	+	0.436766i	$0.856124\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.73998	+	6.24083i	0.287133	+	0.265868i
$552$		0			0
$553$	60.3341	−	34.8339i	2.56567	−	1.48129i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	25.8083	+	14.9004i	1.09353	+	0.631352i	0.934515	−	0.355924i	$-0.115834\pi$
$557$	25.8083	+	14.9004i	1.09353	+	0.631352i	0.159018	+	0.987276i	$0.449167\pi$
$558$		0			0
$559$		−	6.64291i		−	0.280965i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5.09466			−0.214714			−0.107357	−	0.994221i	$-0.534239\pi$
$563$	−5.09466			−0.214714			−0.107357	+	0.994221i	$0.534239\pi$
$564$		0			0
$565$	−3.74531	+	2.16236i	−0.157566	+	0.0909710i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.90540			−0.121801			−0.0609003	−	0.998144i	$-0.519397\pi$
$569$	−2.90540			−0.121801			−0.0609003	+	0.998144i	$0.519397\pi$
$570$		0			0
$571$	−36.5319			−1.52881			−0.764406	−	0.644735i	$-0.776968\pi$
$571$	−36.5319			−1.52881			−0.764406	+	0.644735i	$0.776968\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	5.91136	−	3.41293i	0.246521	−	0.142329i
$576$		0			0
$577$	40.6393			1.69184			0.845919	−	0.533312i	$-0.179053\pi$
$577$	40.6393			1.69184			0.845919	+	0.533312i	$0.179053\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		−	62.0018i		−	2.57227i
$582$		0			0
$583$	−9.32674	−	5.38480i	−0.386274	−	0.223016i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17.1443	+	9.89826i	−0.707620	+	0.408545i	−0.810179	−	0.586182i	$-0.800630\pi$
$587$	−17.1443	+	9.89826i	−0.707620	+	0.408545i	0.102559	+	0.994727i	$0.467297\pi$
$588$		0			0
$589$	41.9004	+	9.51792i	1.72647	+	0.392179i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.51318	−	0.873633i	−0.0621387	−	0.0358758i	0.468609	−	0.883406i	$-0.344755\pi$
$593$	−1.51318	−	0.873633i	−0.0621387	−	0.0358758i	−0.530747	+	0.847530i	$0.678089\pi$
$594$		0			0
$595$	4.28357	−	7.41936i	0.175609	−	0.304164i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.607867	+	1.05286i	−0.0248368	+	0.0430186i	−0.878177	−	0.478336i	$-0.841240\pi$
$599$	−0.607867	+	1.05286i	−0.0248368	+	0.0430186i	0.853340	+	0.521355i	$0.174573\pi$
$600$		0			0
$601$			39.9166i			1.62823i	0.580703	+	0.814116i	$0.302778\pi$
$601$			39.9166i			1.62823i	−0.580703	+	0.814116i	$0.697222\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.16417	+	4.13623i	−0.291265	+	0.168162i
$606$		0			0
$607$			23.1840i			0.941008i	0.882398	+	0.470504i	$0.155928\pi$
$607$			23.1840i			0.941008i	−0.882398	+	0.470504i	$0.844072\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	11.9826	+	20.7544i	0.484763	+	0.839635i
$612$		0			0
$613$	18.7145	+	32.4145i	0.755872	+	1.30921i	0.944940	+	0.327244i	$0.106120\pi$
$613$	18.7145	+	32.4145i	0.755872	+	1.30921i	−0.189068	+	0.981964i	$0.560547\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−24.1965	−	13.9699i	−0.974115	−	0.562406i	−0.0736271	−	0.997286i	$-0.523457\pi$
$617$	−24.1965	−	13.9699i	−0.974115	−	0.562406i	−0.900488	+	0.434880i	$0.856791\pi$
$618$		0			0
$619$	20.3728			0.818850			0.409425	−	0.912344i	$-0.365729\pi$
$619$	20.3728			0.818850			0.409425	+	0.912344i	$0.365729\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	29.6817	−	51.4103i	1.18917	−	2.05971i
$624$		0			0
$625$	−9.81555	−	17.0010i	−0.392622	−	0.680042i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	8.13455	+	14.0895i	0.324346	+	0.561784i
$630$		0			0
$631$	−7.12585	+	12.3423i	−0.283676	+	0.491341i	−0.972287	−	0.233790i	$-0.924887\pi$
$631$	−7.12585	+	12.3423i	−0.283676	+	0.491341i	0.688611	+	0.725130i	$0.258221\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.85155			−0.271895
$636$		0			0
$637$	23.1891	+	13.3883i	0.918787	+	0.530462i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−20.7247	−	35.8962i	−0.818575	−	1.41781i	−0.906732	−	0.421707i	$-0.861431\pi$
$641$	−20.7247	−	35.8962i	−0.818575	−	1.41781i	0.0881571	−	0.996107i	$-0.471902\pi$
$642$		0			0
$643$	−24.3938	−	42.2512i	−0.961996	−	1.66623i	−0.717477	−	0.696582i	$-0.754703\pi$
$643$	−24.3938	−	42.2512i	−0.961996	−	1.66623i	−0.244519	−	0.969644i	$-0.578630\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	24.1855i		−	0.950829i	−0.879762	−	0.475414i	$-0.842298\pi$
$647$		−	24.1855i		−	0.950829i	0.879762	−	0.475414i	$-0.157702\pi$
$648$		0			0
$649$	2.63440	−	1.52097i	0.103409	−	0.0597032i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			19.3902i			0.758797i	0.925233	+	0.379399i	$0.123869\pi$
$653$			19.3902i			0.758797i	−0.925233	+	0.379399i	$0.876131\pi$
$654$		0			0
$655$	1.69485	−	2.93556i	0.0662231	−	0.114702i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.1706	−	28.0083i	0.629918	−	1.09105i	−0.357650	−	0.933856i	$-0.616422\pi$
$659$	16.1706	−	28.0083i	0.629918	−	1.09105i	0.987568	−	0.157194i	$-0.0502448\pi$
$660$		0			0
$661$	17.2738	+	9.97301i	0.671872	+	0.387905i	0.796785	−	0.604262i	$-0.206532\pi$
$661$	17.2738	+	9.97301i	0.671872	+	0.387905i	−0.124914	+	0.992168i	$0.539865\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.41512	+	11.0310i	0.132433	+	0.427765i
$666$		0			0
$667$	2.68873	−	1.55234i	0.104108	−	0.0601068i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	38.3457	+	22.1389i	1.48032	+	0.854662i
$672$		0			0
$673$		−	15.5000i		−	0.597480i	−0.954335	−	0.298740i	$-0.903434\pi$
$673$		−	15.5000i		−	0.597480i	0.954335	−	0.298740i	$-0.0965663\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−25.6896			−0.987332			−0.493666	−	0.869652i	$-0.664343\pi$
$677$	−25.6896			−0.987332			−0.493666	+	0.869652i	$0.664343\pi$
$678$		0			0
$679$	−13.6889	+	7.90331i	−0.525333	+	0.303301i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−38.9201			−1.48924			−0.744618	−	0.667491i	$-0.767368\pi$
$683$	−38.9201			−1.48924			−0.744618	+	0.667491i	$0.767368\pi$
$684$		0			0
$685$	−4.87923			−0.186426
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.14673	−	2.39412i	0.157978	−	0.0912086i
$690$		0			0
$691$	6.29825			0.239597			0.119798	−	0.992798i	$-0.461775\pi$
$691$	6.29825			0.239597			0.119798	+	0.992798i	$0.461775\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			7.97146i			0.302375i
$696$		0			0
$697$	−21.2817	−	12.2870i	−0.806102	−	0.465403i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	26.2523	−	15.1568i	0.991537	−	0.572464i	0.0858038	−	0.996312i	$-0.472654\pi$
$701$	26.2523	−	15.1568i	0.991537	−	0.572464i	0.905733	+	0.423848i	$0.139321\pi$
$702$		0			0
$703$	−21.3843	−	4.85756i	−0.806522	−	0.183206i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−72.9202	−	42.1005i	−2.74245	−	1.58335i
$708$		0			0
$709$	−0.526628	+	0.912146i	−0.0197779	+	0.0342564i	−0.875745	−	0.482774i	$-0.839629\pi$
$709$	−0.526628	+	0.912146i	−0.0197779	+	0.0342564i	0.855967	+	0.517030i	$0.172963\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	7.26142	−	12.5772i	0.271942	−	0.471018i
$714$		0			0
$715$		−	6.64039i		−	0.248336i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.0751	+	10.4356i	−0.674086	+	0.389184i	−0.797623	−	0.603156i	$-0.793910\pi$
$719$	−18.0751	+	10.4356i	−0.674086	+	0.389184i	0.123537	+	0.992340i	$0.460576\pi$
$720$		0			0
$721$		−	14.4027i		−	0.536386i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.88171	−	8.45538i	−0.181302	−	0.314025i
$726$		0			0
$727$	6.50923	+	11.2743i	0.241414	+	0.418141i	0.961117	−	0.276141i	$-0.0890555\pi$
$727$	6.50923	+	11.2743i	0.241414	+	0.418141i	−0.719703	+	0.694282i	$0.755722\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.42679	+	4.86521i	0.311676	+	0.179946i
$732$		0			0
$733$	−52.1956			−1.92789			−0.963944	−	0.266104i	$-0.914263\pi$
$733$	−52.1956			−1.92789			−0.963944	+	0.266104i	$0.914263\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−33.6556	+	58.2933i	−1.23972	+	2.14726i
$738$		0			0
$739$	5.41460	+	9.37837i	0.199179	+	0.344989i	0.948263	−	0.317487i	$-0.102839\pi$
$739$	5.41460	+	9.37837i	0.199179	+	0.344989i	−0.749083	+	0.662476i	$0.769506\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−18.7477	−	32.4720i	−0.687786	−	1.19128i	−0.972552	−	0.232684i	$-0.925249\pi$
$743$	−18.7477	−	32.4720i	−0.687786	−	1.19128i	0.284766	−	0.958597i	$-0.408084\pi$
$744$		0			0
$745$	6.87385	−	11.9059i	0.251838	−	0.436197i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	8.76068			0.320108
$750$		0			0
$751$	41.3564	+	23.8771i	1.50912	+	0.871289i	0.999944	+	0.0106254i	$0.00338223\pi$
$751$	41.3564	+	23.8771i	1.50912	+	0.871289i	0.509174	+	0.860664i	$0.329951\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.45946	+	5.99196i	0.125903	+	0.218070i
$756$		0			0
$757$	5.28153	+	9.14788i	0.191960	+	0.332485i	0.945900	−	0.324459i	$-0.105182\pi$
$757$	5.28153	+	9.14788i	0.191960	+	0.332485i	−0.753939	+	0.656944i	$0.771849\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			17.4566i			0.632801i	0.948626	+	0.316400i	$0.102474\pi$
$761$			17.4566i			0.632801i	−0.948626	+	0.316400i	$0.897526\pi$
$762$		0			0
$763$	−2.25036	+	1.29925i	−0.0814685	+	0.0470359i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			1.35247i			0.0488347i
$768$		0			0
$769$	−2.34837	+	4.06750i	−0.0846844	+	0.146678i	−0.905257	−	0.424865i	$-0.860322\pi$
$769$	−2.34837	+	4.06750i	−0.0846844	+	0.146678i	0.820572	+	0.571543i	$0.193655\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.20124	+	10.7409i	−0.223043	+	0.386322i	−0.955731	−	0.294243i	$-0.904932\pi$
$773$	−6.20124	+	10.7409i	−0.223043	+	0.386322i	0.732687	+	0.680565i	$0.238266\pi$
$774$		0			0
$775$	−39.5520	−	22.8354i	−1.42075	−	0.820270i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	31.6414	−	9.79592i	1.13367	−	0.350975i
$780$		0			0
$781$	16.3604	−	9.44567i	0.585421	−	0.337993i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−4.35634	−	2.51513i	−0.155484	−	0.0897690i
$786$		0			0
$787$			0.833723i			0.0297190i	0.999890	+	0.0148595i	$0.00473010\pi$
$787$			0.833723i			0.0297190i	−0.999890	+	0.0148595i	$0.995270\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	31.2265			1.11029
$792$		0			0
$793$	−17.0487	+	9.84310i	−0.605419	+	0.349539i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	39.8381			1.41114			0.705569	−	0.708641i	$-0.250691\pi$
$797$	39.8381			1.41114			0.705569	+	0.708641i	$0.250691\pi$
$798$		0			0
$799$	−35.1038			−1.24188
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−15.1355	+	8.73851i	−0.534122	+	0.308375i
$804$		0			0
$805$	3.90301			0.137563
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	29.2719i		−	1.02914i	−0.857447	−	0.514572i	$-0.827951\pi$
$809$		−	29.2719i		−	1.02914i	0.857447	−	0.514572i	$-0.172049\pi$
$810$		0			0
$811$	−16.6197	−	9.59539i	−0.583597	−	0.336940i	0.178965	−	0.983856i	$-0.442725\pi$
$811$	−16.6197	−	9.59539i	−0.583597	−	0.336940i	−0.762562	+	0.646916i	$0.776059\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.90052	−	3.98402i	0.241715	−	0.139554i
$816$		0			0
$817$	−12.5289	+	3.87884i	−0.438330	+	0.135703i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19.0207	−	10.9816i	−0.663828	−	0.383261i	0.129906	−	0.991526i	$-0.458532\pi$
$821$	−19.0207	−	10.9816i	−0.663828	−	0.383261i	−0.793734	+	0.608265i	$0.791866\pi$
$822$		0			0
$823$	3.18570	−	5.51779i	0.111046	−	0.192338i	−0.805146	−	0.593077i	$-0.797913\pi$
$823$	3.18570	−	5.51779i	0.111046	−	0.192338i	0.916192	+	0.400739i	$0.131246\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.935401	+	1.62016i	−0.0325271	+	0.0563386i	−0.881831	−	0.471566i	$-0.843689\pi$
$827$	−0.935401	+	1.62016i	−0.0325271	+	0.0563386i	0.849304	+	0.527905i	$0.177022\pi$
$828$		0			0
$829$		−	2.41224i		−	0.0837806i	−0.999122	−	0.0418903i	$-0.986662\pi$
$829$		−	2.41224i		−	0.0837806i	0.999122	−	0.0418903i	$-0.0133380\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−33.9671	+	19.6109i	−1.17689	+	0.679478i
$834$		0			0
$835$			13.4687i			0.466102i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.12136	+	15.7987i	0.314904	+	0.545430i	0.979417	−	0.201847i	$-0.0646943\pi$
$839$	9.12136	+	15.7987i	0.314904	+	0.545430i	−0.664513	+	0.747277i	$0.731361\pi$
$840$		0			0
$841$	12.2796	+	21.2689i	0.423434	+	0.733410i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.26261	−	2.46102i	−0.146638	−	0.0846617i
$846$		0			0
$847$	59.7312			2.05239
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.70594	+	6.41887i	−0.127038	+	0.220036i
$852$		0			0
$853$	−6.34815	−	10.9953i	−0.217357	−	0.376473i	0.736642	−	0.676283i	$-0.236410\pi$
$853$	−6.34815	−	10.9953i	−0.217357	−	0.376473i	−0.953999	+	0.299810i	$0.903077\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.78818	+	10.0254i	0.197720	+	0.342462i	0.947789	−	0.318898i	$-0.103313\pi$
$857$	5.78818	+	10.0254i	0.197720	+	0.342462i	−0.750069	+	0.661360i	$0.769980\pi$
$858$		0			0
$859$	11.8563	−	20.5357i	0.404532	−	0.700669i	−0.589735	−	0.807597i	$-0.700768\pi$
$859$	11.8563	−	20.5357i	0.404532	−	0.700669i	0.994267	+	0.106927i	$0.0341012\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.59563			0.258558			0.129279	−	0.991608i	$-0.458734\pi$
$863$	7.59563			0.258558			0.129279	+	0.991608i	$0.458734\pi$
$864$		0			0
$865$	−5.91350	−	3.41416i	−0.201065	−	0.116085i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	39.5488	+	68.5005i	1.34160	+	2.32372i
$870$		0			0
$871$	−14.9635	−	25.9176i	−0.507019	−	0.878183i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		−	25.5200i		−	0.862733i
$876$		0			0
$877$	−9.21952	+	5.32289i	−0.311321	+	0.179741i	−0.647518	−	0.762051i	$-0.724193\pi$
$877$	−9.21952	+	5.32289i	−0.311321	+	0.179741i	0.336196	+	0.941792i	$0.390859\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	47.9276i		−	1.61472i	−0.590058	−	0.807361i	$-0.700895\pi$
$881$		−	47.9276i		−	1.61472i	0.590058	−	0.807361i	$-0.299105\pi$
$882$		0			0
$883$	−24.9331	+	43.1854i	−0.839067	+	1.45331i	0.0516094	+	0.998667i	$0.483565\pi$
$883$	−24.9331	+	43.1854i	−0.839067	+	1.45331i	−0.890676	+	0.454639i	$0.849768\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.4328	+	23.2663i	−0.451030	+	0.781206i	−0.998450	−	0.0556514i	$-0.982276\pi$
$887$	−13.4328	+	23.2663i	−0.451030	+	0.781206i	0.547421	+	0.836858i	$0.315610\pi$
$888$		0			0
$889$	42.8435	+	24.7357i	1.43693	+	0.829610i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	32.1473	−	34.7184i	1.07577	−	1.16181i
$894$		0			0
$895$	−13.1332	+	7.58246i	−0.438995	+	0.253454i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−17.9899	−	10.3864i	−0.599995	−	0.346407i
$900$		0			0
$901$			7.01373i			0.233661i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.47092			0.148619
$906$		0			0
$907$	−49.3174	+	28.4734i	−1.63756	+	0.945444i	−0.655887	+	0.754859i	$0.727705\pi$
$907$	−49.3174	+	28.4734i	−1.63756	+	0.945444i	−0.981671	+	0.190585i	$0.938962\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	47.3317			1.56817			0.784084	−	0.620655i	$-0.213133\pi$
$911$	47.3317			1.56817			0.784084	+	0.620655i	$0.213133\pi$
$912$		0			0
$913$	70.3940			2.32970
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21.1962	+	12.2376i	−0.699959	+	0.404121i
$918$		0			0
$919$	−25.8656			−0.853229			−0.426614	−	0.904434i	$-0.640294\pi$
$919$	−25.8656			−0.853229			−0.426614	+	0.904434i	$0.640294\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			8.39922i			0.276464i
$924$		0			0
$925$	20.1857	+	11.6542i	0.663703	+	0.383189i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−11.6190	+	6.70826i	−0.381209	+	0.220091i	−0.678344	−	0.734744i	$-0.737302\pi$
$929$	−11.6190	+	6.70826i	−0.381209	+	0.220091i	0.297135	+	0.954835i	$0.403969\pi$
$930$		0			0
$931$	11.7107	−	51.5535i	0.383802	−	1.68960i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	8.42360	+	4.86337i	0.275481	+	0.159049i
$936$		0			0
$937$	−10.5622	+	18.2943i	−0.345053	+	0.597649i	−0.985363	−	0.170467i	$-0.945472\pi$
$937$	−10.5622	+	18.2943i	−0.345053	+	0.597649i	0.640310	+	0.768116i	$0.278806\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.45798	−	7.72145i	0.145326	−	0.251712i	−0.784168	−	0.620548i	$-0.786910\pi$
$941$	4.45798	−	7.72145i	0.145326	−	0.251712i	0.929495	+	0.368836i	$0.120244\pi$
$942$		0			0
$943$		−	11.1954i		−	0.364573i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−38.3309	+	22.1303i	−1.24559	+	0.719139i	−0.970226	−	0.242202i	$-0.922130\pi$
$947$	−38.3309	+	22.1303i	−1.24559	+	0.719139i	−0.275360	+	0.961341i	$0.588797\pi$
$948$		0			0
$949$		−	7.77040i		−	0.252238i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	21.4711	+	37.1890i	0.695517	+	1.20467i	0.970006	+	0.243080i	$0.0781577\pi$
$953$	21.4711	+	37.1890i	0.695517	+	1.20467i	−0.274490	+	0.961590i	$0.588509\pi$
$954$		0			0
$955$	5.57683	+	9.65935i	0.180462	+	0.312569i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	30.5104	+	17.6152i	0.985233	+	0.568824i
$960$		0			0
$961$	−66.1700			−2.13452
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.21130	+	7.29419i	−0.135567	+	0.234808i
$966$		0			0
$967$	6.84907	+	11.8629i	0.220251	+	0.381486i	0.954884	−	0.296978i	$-0.0959790\pi$
$967$	6.84907	+	11.8629i	0.220251	+	0.381486i	−0.734633	+	0.678465i	$0.762646\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−15.0241	−	26.0224i	−0.482145	−	0.835100i	0.517645	−	0.855596i	$-0.326809\pi$
$971$	−15.0241	−	26.0224i	−0.482145	−	0.835100i	−0.999790	+	0.0204959i	$0.993475\pi$
$972$		0			0
$973$	28.7789	−	49.8465i	0.922609	−	1.59801i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.06375			0.257982			0.128991	−	0.991646i	$-0.458826\pi$
$977$	8.06375			0.257982			0.128991	+	0.991646i	$0.458826\pi$
$978$		0			0
$979$	58.3689	+	33.6993i	1.86548	+	1.07703i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	30.7029	+	53.1790i	0.979271	+	1.69615i	0.665055	+	0.746795i	$0.268408\pi$
$983$	30.7029	+	53.1790i	0.979271	+	1.69615i	0.314216	+	0.949352i	$0.398258\pi$
$984$		0			0
$985$	−2.80528	−	4.85889i	−0.0893838	−	0.154817i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			4.43298i			0.140961i
$990$		0			0
$991$	9.12690	−	5.26942i	0.289926	−	0.167389i	−0.347983	−	0.937501i	$-0.613133\pi$
$991$	9.12690	−	5.26942i	0.289926	−	0.167389i	0.637908	+	0.770112i	$0.279800\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	8.44508i		−	0.267727i
$996$		0			0
$997$	−16.1468	+	27.9670i	−0.511373	+	0.885724i	0.488540	+	0.872541i	$0.337530\pi$
$997$	−16.1468	+	27.9670i	−0.511373	+	0.885724i	−0.999913	+	0.0131823i	$0.995804\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.dc.f.449.7		20
3.2	odd	2		2736.2.dc.e.449.4		20
4.3	odd	2		1368.2.cu.b.449.7	yes	20
12.11	even	2		1368.2.cu.a.449.4	✓	20
19.8	odd	6		2736.2.dc.e.1889.4		20
57.8	even	6	inner	2736.2.dc.f.1889.7		20
76.27	even	6		1368.2.cu.a.521.4	yes	20
228.179	odd	6		1368.2.cu.b.521.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.cu.a.449.4	✓	20	12.11	even	2
1368.2.cu.a.521.4	yes	20	76.27	even	6
1368.2.cu.b.449.7	yes	20	4.3	odd	2
1368.2.cu.b.521.7	yes	20	228.179	odd	6
2736.2.dc.e.449.4		20	3.2	odd	2
2736.2.dc.e.1889.4		20	19.8	odd	6
2736.2.dc.f.449.7		20	1.1	even	1	trivial
2736.2.dc.f.1889.7		20	57.8	even	6	inner

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:	\( N \)	\(=\)	\( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2736.dc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.524572 - 0.302862i) q^{5} -4.37361 q^{7} +O(q^{10})\)	\(q+(0.524572 - 0.302862i) q^{5} -4.37361 q^{7} -4.96560i q^{11} +(1.91196 + 1.10387i) q^{13} +(-2.80061 + 1.61693i) q^{17} +(0.965553 - 4.25061i) q^{19} +(-1.27590 - 0.736640i) q^{23} +(-2.31655 + 4.01238i) q^{25} +(-1.05366 + 1.82499i) q^{29} +9.85749i q^{31} +(-2.29427 + 1.32460i) q^{35} -5.03086i q^{37} +(3.79948 + 6.58090i) q^{41} +(-1.50446 - 2.60580i) q^{43} +(9.40077 + 5.42754i) q^{47} +12.1285 q^{49} +(1.08442 - 1.87827i) q^{53} +(-1.50389 - 2.60481i) q^{55} +(0.306301 + 0.530529i) q^{59} +(-4.45845 + 7.72227i) q^{61} +1.33728 q^{65} +(-11.7394 - 6.77776i) q^{67} +(1.90222 + 3.29475i) q^{71} +(-1.75981 - 3.04808i) q^{73} +21.7176i q^{77} +(-13.7950 + 7.96456i) q^{79} +14.1763i q^{83} +(-0.979412 + 1.69639i) q^{85} +(-6.78655 + 11.7546i) q^{89} +(-8.36216 - 4.82790i) q^{91} +(-0.780846 - 2.52218i) q^{95} +(3.12989 - 1.80704i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^7	\( 20 q + 4 q^{7} + 6 q^{13} + 12 q^{17} - 4 q^{19} + 14 q^{25} + 12 q^{35} + 8 q^{41} + 2 q^{43} + 36 q^{47} + 32 q^{49} - 8 q^{53} - 12 q^{55} - 8 q^{59} - 2 q^{61} + 8 q^{65} - 30 q^{67} + 4 q^{71} - 22 q^{73} - 54 q^{79} - 4 q^{85} - 32 q^{89} - 18 q^{91} + 32 q^{95} + 12 q^{97}+O(q^{100}) \) 20 * q + 4 * q^7 + 6 * q^13 + 12 * q^17 - 4 * q^19 + 14 * q^25 + 12 * q^35 + 8 * q^41 + 2 * q^43 + 36 * q^47 + 32 * q^49 - 8 * q^53 - 12 * q^55 - 8 * q^59 - 2 * q^61 + 8 * q^65 - 30 * q^67 + 4 * q^71 - 22 * q^73 - 54 * q^79 - 4 * q^85 - 32 * q^89 - 18 * q^91 + 32 * q^95 + 12 * q^97

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