LMFDB - Embedded newform 2736.2.dc.e.1889.2

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			1889.2
Root			$-0.476437 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2736.1889
Dual form			2736.2.dc.e.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.20539 - 1.85063i) q^{5} +4.57072 q^{7} +O(q^{10})$	$q+(-3.20539 - 1.85063i) q^{5} +4.57072 q^{7} -0.467805i q^{11} +(-1.80826 + 1.04400i) q^{13} +(-1.39674 - 0.806410i) q^{17} +(-4.34896 + 0.294192i) q^{19} +(-3.86093 + 2.22911i) q^{23} +(4.34968 + 7.53386i) q^{25} +(-3.12596 - 5.41433i) q^{29} -5.77041i q^{31} +(-14.6509 - 8.45871i) q^{35} +8.44836i q^{37} +(2.87603 - 4.98143i) q^{41} +(2.14080 - 3.70798i) q^{43} +(-6.43852 + 3.71728i) q^{47} +13.8914 q^{49} +(5.22137 + 9.04368i) q^{53} +(-0.865736 + 1.49950i) q^{55} +(1.70945 - 2.96085i) q^{59} +(-4.52498 - 7.83749i) q^{61} +7.72823 q^{65} +(-9.15010 + 5.28281i) q^{67} +(-3.31319 + 5.73861i) q^{71} +(-6.69280 + 11.5923i) q^{73} -2.13821i q^{77} +(-2.02759 - 1.17063i) q^{79} -3.13477i q^{83} +(2.98474 + 5.16972i) q^{85} +(4.20111 + 7.27653i) q^{89} +(-8.26504 + 4.77182i) q^{91} +(14.4845 + 7.10532i) q^{95} +(-2.11693 - 1.22221i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

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

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
$5$	−3.20539	−	1.85063i	−1.43349	−	0.827628i	−0.436108	−	0.899894i	$-0.643643\pi$
$5$	−3.20539	−	1.85063i	−1.43349	−	0.827628i	−0.997385	+	0.0722668i	$0.976977\pi$
$6$		0			0
$7$	4.57072			1.72757			0.863784	−	0.503862i	$-0.168088\pi$
$7$	4.57072			1.72757			0.863784	+	0.503862i	$0.168088\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	0.467805i		−	0.141049i	−0.997510	−	0.0705243i	$-0.977533\pi$
$11$		−	0.467805i		−	0.141049i	0.997510	−	0.0705243i	$-0.0224672\pi$
$12$		0			0
$13$	−1.80826	+	1.04400i	−0.501521	+	0.289553i	−0.729341	−	0.684150i	$-0.760173\pi$
$13$	−1.80826	+	1.04400i	−0.501521	+	0.289553i	0.227821	+	0.973703i	$0.426840\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.39674	−	0.806410i	−0.338760	−	0.195583i	0.320963	−	0.947092i	$-0.395993\pi$
$17$	−1.39674	−	0.806410i	−0.338760	−	0.195583i	−0.659724	+	0.751508i	$0.729327\pi$
$18$		0			0
$19$	−4.34896	+	0.294192i	−0.997720	+	0.0674923i
$19$	−4.34896	+	0.294192i	−0.997720	+	0.0674923i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.86093	+	2.22911i	−0.805059	+	0.464801i	−0.845237	−	0.534391i	$-0.820541\pi$
$23$	−3.86093	+	2.22911i	−0.805059	+	0.464801i	0.0401778	+	0.999193i	$0.487208\pi$
$24$		0			0
$25$	4.34968	+	7.53386i	0.869935	+	1.50677i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.12596	−	5.41433i	−0.580477	−	1.00542i	−0.995423	−	0.0955693i	$-0.969533\pi$
$29$	−3.12596	−	5.41433i	−0.580477	−	1.00542i	0.414946	−	0.909846i	$-0.363800\pi$
$30$		0			0
$31$		−	5.77041i		−	1.03640i	−0.855261	−	0.518198i	$-0.826603\pi$
$31$		−	5.77041i		−	1.03640i	0.855261	−	0.518198i	$-0.173397\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−14.6509	−	8.45871i	−2.47646	−	1.42978i
$36$		0			0
$37$			8.44836i			1.38890i	0.719540	+	0.694451i	$0.244353\pi$
$37$			8.44836i			1.38890i	−0.719540	+	0.694451i	$0.755647\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.87603	−	4.98143i	0.449160	−	0.777968i	−0.549171	−	0.835710i	$-0.685057\pi$
$41$	2.87603	−	4.98143i	0.449160	−	0.777968i	0.998332	+	0.0577415i	$0.0183899\pi$
$42$		0			0
$43$	2.14080	−	3.70798i	0.326470	−	0.565462i	−0.655339	−	0.755335i	$-0.727474\pi$
$43$	2.14080	−	3.70798i	0.326470	−	0.565462i	0.981809	+	0.189873i	$0.0608076\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.43852	+	3.71728i	−0.939155	+	0.542221i	−0.889695	−	0.456555i	$-0.849083\pi$
$47$	−6.43852	+	3.71728i	−0.939155	+	0.542221i	−0.0494595	+	0.998776i	$0.515750\pi$
$48$		0			0
$49$	13.8914			1.98449
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.22137	+	9.04368i	0.717211	+	1.24225i	0.962101	+	0.272695i	$0.0879149\pi$
$53$	5.22137	+	9.04368i	0.717211	+	1.24225i	−0.244890	+	0.969551i	$0.578752\pi$
$54$		0			0
$55$	−0.865736	+	1.49950i	−0.116736	+	0.202192i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.70945	−	2.96085i	0.222551	−	0.385470i	−0.733031	−	0.680195i	$-0.761895\pi$
$59$	1.70945	−	2.96085i	0.222551	−	0.385470i	0.955582	+	0.294726i	$0.0952282\pi$
$60$		0			0
$61$	−4.52498	−	7.83749i	−0.579364	−	1.00349i	−0.995552	−	0.0942098i	$-0.969968\pi$
$61$	−4.52498	−	7.83749i	−0.579364	−	1.00349i	0.416188	−	0.909279i	$-0.363366\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.72823			0.958569
$66$		0			0
$67$	−9.15010	+	5.28281i	−1.11786	+	0.645398i	−0.940854	−	0.338811i	$-0.889975\pi$
$67$	−9.15010	+	5.28281i	−1.11786	+	0.645398i	−0.177008	+	0.984209i	$0.556642\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.31319	+	5.73861i	−0.393203	+	0.681048i	−0.992870	−	0.119202i	$-0.961966\pi$
$71$	−3.31319	+	5.73861i	−0.393203	+	0.681048i	0.599667	+	0.800250i	$0.295300\pi$
$72$		0			0
$73$	−6.69280	+	11.5923i	−0.783333	+	1.35677i	0.146657	+	0.989187i	$0.453149\pi$
$73$	−6.69280	+	11.5923i	−0.783333	+	1.35677i	−0.929990	+	0.367585i	$0.880185\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	2.13821i		−	0.243671i
$78$		0			0
$79$	−2.02759	−	1.17063i	−0.228122	−	0.131706i	0.381583	−	0.924334i	$-0.375379\pi$
$79$	−2.02759	−	1.17063i	−0.228122	−	0.131706i	−0.609705	+	0.792628i	$0.708712\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	3.13477i		−	0.344086i	−0.985089	−	0.172043i	$-0.944963\pi$
$83$		−	3.13477i		−	0.344086i	0.985089	−	0.172043i	$-0.0550368\pi$
$84$		0			0
$85$	2.98474	+	5.16972i	0.323740	+	0.560734i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.20111	+	7.27653i	0.445317	+	0.771311i	0.998074	−	0.0620310i	$-0.0197578\pi$
$89$	4.20111	+	7.27653i	0.445317	+	0.771311i	−0.552758	+	0.833342i	$0.686424\pi$
$90$		0			0
$91$	−8.26504	+	4.77182i	−0.866411	+	0.500223i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	14.4845	+	7.10532i	1.48608	+	0.728991i
$96$		0			0
$97$	−2.11693	−	1.22221i	−0.214942	−	0.124097i	0.388664	−	0.921380i	$-0.372937\pi$
$97$	−2.11693	−	1.22221i	−0.214942	−	0.124097i	−0.603606	+	0.797283i	$0.706270\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.07795	+	4.66381i	−0.803786	+	0.464066i	−0.844793	−	0.535093i	$-0.820277\pi$
$101$	−8.07795	+	4.66381i	−0.803786	+	0.464066i	0.0410074	+	0.999159i	$0.486943\pi$
$102$		0			0
$103$		−	9.71707i		−	0.957452i	−0.877964	−	0.478726i	$-0.841099\pi$
$103$		−	9.71707i		−	0.957452i	0.877964	−	0.478726i	$-0.158901\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.0894			−1.26540			−0.632698	−	0.774398i	$-0.718053\pi$
$107$	−13.0894			−1.26540			−0.632698	+	0.774398i	$0.718053\pi$
$108$		0			0
$109$	−13.6879	−	7.90270i	−1.31106	−	0.756941i	−0.328789	−	0.944404i	$-0.606640\pi$
$109$	−13.6879	−	7.90270i	−1.31106	−	0.756941i	−0.982272	+	0.187462i	$0.939974\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.89967			−0.272778			−0.136389	−	0.990655i	$-0.543550\pi$
$113$	−2.89967			−0.272778			−0.136389	+	0.990655i	$0.543550\pi$
$114$		0			0
$115$	16.5010			1.53873
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.38412	−	3.68587i	−0.585231	−	0.337883i
$120$		0			0
$121$	10.7812			0.980105
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	13.6923i		−	1.22467i
$126$		0			0
$127$	−9.29852	+	5.36850i	−0.825110	+	0.476378i	−0.852175	−	0.523256i	$-0.824717\pi$
$127$	−9.29852	+	5.36850i	−0.825110	+	0.476378i	0.0270654	+	0.999634i	$0.491384\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	17.6071	+	10.1654i	1.53834	+	0.888159i	0.998936	+	0.0461084i	$0.0146820\pi$
$131$	17.6071	+	10.1654i	1.53834	+	0.888159i	0.539399	+	0.842050i	$0.318651\pi$
$132$		0			0
$133$	−19.8779	+	1.34467i	−1.72363	+	0.116598i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.72457	+	4.45978i	−0.659954	+	0.381025i	−0.792260	−	0.610184i	$-0.791095\pi$
$137$	−7.72457	+	4.45978i	−0.659954	+	0.381025i	0.132305	+	0.991209i	$0.457762\pi$
$138$		0			0
$139$	−4.09089	−	7.08563i	−0.346985	−	0.600995i	0.638728	−	0.769433i	$-0.279461\pi$
$139$	−4.09089	−	7.08563i	−0.346985	−	0.600995i	−0.985712	+	0.168438i	$0.946128\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.488388	+	0.845913i	0.0408411	+	0.0707388i
$144$		0			0
$145$			23.1400i			1.92167i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−19.7461	−	11.4004i	−1.61766	−	0.933959i	−0.987522	−	0.157479i	$-0.949663\pi$
$149$	−19.7461	−	11.4004i	−1.61766	−	0.933959i	−0.630142	−	0.776480i	$-0.717003\pi$
$150$		0			0
$151$			10.3753i			0.844327i	0.906520	+	0.422163i	$0.138729\pi$
$151$			10.3753i			0.844327i	−0.906520	+	0.422163i	$0.861271\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.6789	+	18.4964i	−0.857750	+	1.48567i
$156$		0			0
$157$	−8.75398	+	15.1623i	−0.698644	+	1.21009i	0.270293	+	0.962778i	$0.412879\pi$
$157$	−8.75398	+	15.1623i	−0.698644	+	1.21009i	−0.968937	+	0.247308i	$0.920454\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−17.6472	+	10.1886i	−1.39080	+	0.802976i
$162$		0			0
$163$	−20.6462			−1.61714			−0.808568	−	0.588403i	$-0.799757\pi$
$163$	−20.6462			−1.61714			−0.808568	+	0.588403i	$0.799757\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.14132	−	14.1012i	−0.629995	−	1.09118i	−0.987552	−	0.157292i	$-0.949724\pi$
$167$	−8.14132	−	14.1012i	−0.629995	−	1.09118i	0.357558	−	0.933891i	$-0.383610\pi$
$168$		0			0
$169$	−4.32013	+	7.48269i	−0.332318	+	0.575592i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.86811	+	8.43181i	−0.370115	+	0.641058i	−0.989583	−	0.143964i	$-0.954015\pi$
$173$	−4.86811	+	8.43181i	−0.370115	+	0.641058i	0.619468	+	0.785022i	$0.287348\pi$
$174$		0			0
$175$	19.8811	+	34.4351i	1.50287	+	2.60305i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.5360			−1.01173			−0.505866	−	0.862612i	$-0.668827\pi$
$179$	−13.5360			−1.01173			−0.505866	+	0.862612i	$0.668827\pi$
$180$		0			0
$181$	17.7121	−	10.2261i	1.31653	−	0.760098i	0.333360	−	0.942799i	$-0.391817\pi$
$181$	17.7121	−	10.2261i	1.31653	−	0.760098i	0.983168	+	0.182701i	$0.0584841\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	15.6348	−	27.0803i	1.14949	−	1.99098i
$186$		0			0
$187$	−0.377243	+	0.653404i	−0.0275868	+	0.0477817i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			7.68940i			0.556385i	0.960525	+	0.278193i	$0.0897353\pi$
$191$			7.68940i			0.556385i	−0.960525	+	0.278193i	$0.910265\pi$
$192$		0			0
$193$	16.6120	+	9.59093i	1.19576	+	0.690370i	0.959606	−	0.281346i	$-0.0907809\pi$
$193$	16.6120	+	9.59093i	1.19576	+	0.690370i	0.236150	+	0.971717i	$0.424114\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			21.6086i			1.53955i	0.638315	+	0.769776i	$0.279632\pi$
$197$			21.6086i			1.53955i	−0.638315	+	0.769776i	$0.720368\pi$
$198$		0			0
$199$	−9.06420	−	15.6997i	−0.642544	−	1.11292i	−0.984863	−	0.173336i	$-0.944546\pi$
$199$	−9.06420	−	15.6997i	−0.642544	−	1.11292i	0.342318	−	0.939584i	$-0.388788\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−14.2879	−	24.7474i	−1.00281	−	1.73692i
$204$		0			0
$205$	−18.4376	+	10.6449i	−1.28774	+	0.743475i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.137625	+	2.03447i	0.00951970	+	0.140727i
$210$		0			0
$211$	4.11166	+	2.37387i	0.283058	+	0.163424i	0.634807	−	0.772671i	$-0.281080\pi$
$211$	4.11166	+	2.37387i	0.283058	+	0.163424i	−0.351749	+	0.936094i	$0.614413\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−13.7242	+	7.92368i	−0.935984	+	0.540390i
$216$		0			0
$217$		−	26.3749i		−	1.79044i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.36756			0.226527
$222$		0			0
$223$	−3.61166	−	2.08519i	−0.241855	−	0.139635i	0.374174	−	0.927358i	$-0.377926\pi$
$223$	−3.61166	−	2.08519i	−0.241855	−	0.139635i	−0.616029	+	0.787724i	$0.711260\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	23.7912			1.57908			0.789539	−	0.613700i	$-0.210320\pi$
$227$	23.7912			1.57908			0.789539	+	0.613700i	$0.210320\pi$
$228$		0			0
$229$	−7.51856			−0.496840			−0.248420	−	0.968652i	$-0.579911\pi$
$229$	−7.51856			−0.496840			−0.248420	+	0.968652i	$0.579911\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.232592	+	0.134287i	0.0152376	+	0.00879744i	0.507599	−	0.861593i	$-0.330533\pi$
$233$	0.232592	+	0.134287i	0.0152376	+	0.00879744i	−0.492362	+	0.870391i	$0.663866\pi$
$234$		0			0
$235$	27.5173			1.79503
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	22.2511i		−	1.43930i	−0.694337	−	0.719650i	$-0.744302\pi$
$239$		−	22.2511i		−	1.43930i	0.694337	−	0.719650i	$-0.255698\pi$
$240$		0			0
$241$	15.7653	−	9.10209i	1.01553	−	0.586317i	0.102724	−	0.994710i	$-0.467244\pi$
$241$	15.7653	−	9.10209i	1.01553	−	0.586317i	0.912806	+	0.408393i	$0.133911\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−44.5275	−	25.7080i	−2.84476	−	1.64242i
$246$		0			0
$247$	7.55691	−	5.07228i	0.480834	−	0.322742i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.83337	−	4.52260i	0.494438	−	0.285464i	−0.231976	−	0.972722i	$-0.574519\pi$
$251$	7.83337	−	4.52260i	0.494438	−	0.285464i	0.726414	+	0.687258i	$0.241186\pi$
$252$		0			0
$253$	1.04279	+	1.80616i	0.0655596	+	0.113553i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.60355	+	2.77742i	0.100026	+	0.173251i	0.911695	−	0.410867i	$-0.134774\pi$
$257$	1.60355	+	2.77742i	0.100026	+	0.173251i	−0.811669	+	0.584118i	$0.801441\pi$
$258$		0			0
$259$			38.6150i			2.39942i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−21.8434	−	12.6113i	−1.34692	−	0.777644i	−0.359108	−	0.933296i	$-0.616919\pi$
$263$	−21.8434	−	12.6113i	−1.34692	−	0.777644i	−0.987812	+	0.155652i	$0.950252\pi$
$264$		0			0
$265$		−	38.6514i		−	2.37433i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.77754	−	10.0070i	0.352263	−	0.610137i	−0.634383	−	0.773019i	$-0.718746\pi$
$269$	5.77754	−	10.0070i	0.352263	−	0.610137i	0.986646	+	0.162882i	$0.0520791\pi$
$270$		0			0
$271$	−8.54880	+	14.8070i	−0.519303	+	0.899458i	0.480446	+	0.877024i	$0.340475\pi$
$271$	−8.54880	+	14.8070i	−0.519303	+	0.899458i	−0.999748	+	0.0224339i	$0.992858\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.52438	−	2.03480i	0.212528	−	0.122703i
$276$		0			0
$277$	20.0855			1.20682			0.603410	−	0.797431i	$-0.293808\pi$
$277$	20.0855			1.20682			0.603410	+	0.797431i	$0.293808\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	15.3862	+	26.6496i	0.917861	+	1.58978i	0.802658	+	0.596440i	$0.203419\pi$
$281$	15.3862	+	26.6496i	0.917861	+	1.58978i	0.115203	+	0.993342i	$0.463248\pi$
$282$		0			0
$283$	−0.494369	+	0.856272i	−0.0293872	+	0.0509001i	−0.880345	−	0.474334i	$-0.842689\pi$
$283$	−0.494369	+	0.856272i	−0.0293872	+	0.0509001i	0.850958	+	0.525234i	$0.176022\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	13.1455	−	22.7687i	0.775955	−	1.34399i
$288$		0			0
$289$	−7.19940	−	12.4697i	−0.423494	−	0.733514i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.48745			0.262160			0.131080	−	0.991372i	$-0.458156\pi$
$293$	4.48745			0.262160			0.131080	+	0.991372i	$0.458156\pi$
$294$		0			0
$295$	−10.9589	+	6.32712i	−0.638051	+	0.368379i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.65437	−	8.06161i	0.269169	−	0.466215i
$300$		0			0
$301$	9.78501	−	16.9481i	0.563999	−	0.976874i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			33.4963i			1.91799i
$306$		0			0
$307$	26.7838	+	15.4637i	1.52863	+	0.882558i	0.999419	+	0.0340701i	$0.0108470\pi$
$307$	26.7838	+	15.4637i	1.52863	+	0.882558i	0.529215	+	0.848488i	$0.322486\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			23.0441i			1.30671i	0.757052	+	0.653354i	$0.226639\pi$
$311$			23.0441i			1.30671i	−0.757052	+	0.653354i	$0.773361\pi$
$312$		0			0
$313$	−8.50521	−	14.7315i	−0.480743	−	0.832671i	0.519013	−	0.854766i	$-0.326300\pi$
$313$	−8.50521	−	14.7315i	−0.480743	−	0.832671i	−0.999756	+	0.0220954i	$0.992966\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.8317	−	25.6893i	−0.833032	−	1.44285i	−0.895623	−	0.444814i	$-0.853270\pi$
$317$	−14.8317	−	25.6893i	−0.833032	−	1.44285i	0.0625908	−	0.998039i	$-0.480064\pi$
$318$		0			0
$319$	−2.53285	+	1.46234i	−0.141812	+	0.0818755i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	6.31162	+	3.09614i	0.351188	+	0.172274i
$324$		0			0
$325$	−15.7307	−	9.08211i	−0.872581	−	0.503785i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−29.4287	+	16.9906i	−1.62245	+	0.936724i
$330$		0			0
$331$		−	8.35916i		−	0.459461i	−0.973254	−	0.229731i	$-0.926216\pi$
$331$		−	8.35916i		−	0.459461i	0.973254	−	0.229731i	$-0.0737845\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	39.1062			2.13660
$336$		0			0
$337$	−7.39035	−	4.26682i	−0.402578	−	0.232428i	0.285018	−	0.958522i	$-0.408000\pi$
$337$	−7.39035	−	4.26682i	−0.402578	−	0.232428i	−0.687596	+	0.726094i	$0.741334\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.69943			−0.146182
$342$		0			0
$343$	31.4988			1.70078
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.25588	+	0.725083i	0.0674192	+	0.0389245i	0.533331	−	0.845907i	$-0.320940\pi$
$347$	1.25588	+	0.725083i	0.0674192	+	0.0389245i	−0.465911	+	0.884831i	$0.654273\pi$
$348$		0			0
$349$	7.18080			0.384379			0.192190	−	0.981358i	$-0.438441\pi$
$349$	7.18080			0.384379			0.192190	+	0.981358i	$0.438441\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	3.58785i		−	0.190962i	−0.995431	−	0.0954811i	$-0.969561\pi$
$353$		−	3.58785i		−	0.190962i	0.995431	−	0.0954811i	$-0.0304389\pi$
$354$		0			0
$355$	21.2401	−	12.2630i	1.12731	−	0.650851i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.247255	−	0.142753i	−0.0130496	−	0.00753419i	0.493461	−	0.869768i	$-0.335732\pi$
$359$	−0.247255	−	0.142753i	−0.0130496	−	0.00753419i	−0.506511	+	0.862234i	$0.669065\pi$
$360$		0			0
$361$	18.8269	−	2.55886i	0.990890	−	0.134677i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	42.9061	−	24.7718i	2.24581	−	1.29662i
$366$		0			0
$367$	−17.9009	−	31.0053i	−0.934420	−	1.61846i	−0.775664	−	0.631146i	$-0.782585\pi$
$367$	−17.9009	−	31.0053i	−0.934420	−	1.61846i	−0.158756	−	0.987318i	$-0.550748\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	23.8654	+	41.3361i	1.23903	+	2.14606i
$372$		0			0
$373$			12.2239i			0.632929i	0.948604	+	0.316464i	$0.102496\pi$
$373$			12.2239i			0.632929i	−0.948604	+	0.316464i	$0.897504\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	11.3051	+	6.52700i	0.582242	+	0.336158i
$378$		0			0
$379$		−	16.4191i		−	0.843393i	−0.906737	−	0.421697i	$-0.861435\pi$
$379$		−	16.4191i		−	0.843393i	0.906737	−	0.421697i	$-0.138565\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.62316	−	13.2037i	0.389525	−	0.674678i	−0.602860	−	0.797847i	$-0.705972\pi$
$383$	7.62316	−	13.2037i	0.389525	−	0.674678i	0.992386	+	0.123169i	$0.0393058\pi$
$384$		0			0
$385$	−3.95703	+	6.85378i	−0.201669	+	0.349301i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	21.5712	−	12.4541i	1.09370	−	0.631450i	0.159143	−	0.987255i	$-0.449127\pi$
$389$	21.5712	−	12.4541i	1.09370	−	0.631450i	0.934560	+	0.355805i	$0.115793\pi$
$390$		0			0
$391$	7.19031			0.363629
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.33282	+	7.50466i	0.218008	+	0.377600i
$396$		0			0
$397$	−2.04833	+	3.54782i	−0.102803	+	0.178060i	−0.912838	−	0.408321i	$-0.866114\pi$
$397$	−2.04833	+	3.54782i	−0.102803	+	0.178060i	0.810036	+	0.586381i	$0.199448\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.3901	+	30.1205i	−0.868420	+	1.50415i	−0.00480879	+	0.999988i	$0.501531\pi$
$401$	−17.3901	+	30.1205i	−0.868420	+	1.50415i	−0.863611	+	0.504159i	$0.831803\pi$
$402$		0			0
$403$	6.02430	+	10.4344i	0.300092	+	0.519774i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.95219			0.195903
$408$		0			0
$409$	−3.12394	+	1.80361i	−0.154469	+	0.0891828i	−0.575242	−	0.817983i	$-0.695092\pi$
$409$	−3.12394	+	1.80361i	−0.154469	+	0.0891828i	0.420773	+	0.907166i	$0.361759\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.81340	−	13.5332i	0.384472	−	0.665925i
$414$		0			0
$415$	−5.80131	+	10.0482i	−0.284775	+	0.493245i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			10.0710i			0.492003i	0.969269	+	0.246001i	$0.0791168\pi$
$419$			10.0710i			0.492003i	−0.969269	+	0.246001i	$0.920883\pi$
$420$		0			0
$421$	10.8720	+	6.27693i	0.529867	+	0.305919i	0.740962	−	0.671547i	$-0.234370\pi$
$421$	10.8720	+	6.27693i	0.529867	+	0.305919i	−0.211095	+	0.977465i	$0.567703\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		−	14.0305i		−	0.680579i
$426$		0			0
$427$	−20.6824	−	35.8230i	−1.00089	−	1.73359i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.21505	−	14.2289i	−0.395705	−	0.685381i	0.597486	−	0.801879i	$-0.296166\pi$
$431$	−8.21505	−	14.2289i	−0.395705	−	0.685381i	−0.993191	+	0.116498i	$0.962833\pi$
$432$		0			0
$433$	−1.60283	+	0.925397i	−0.0770273	+	0.0444717i	−0.538019	−	0.842933i	$-0.680827\pi$
$433$	−1.60283	+	0.925397i	−0.0770273	+	0.0444717i	0.460992	+	0.887404i	$0.347494\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	16.1352	−	10.8302i	0.771853	−	0.518077i
$438$		0			0
$439$	−18.2488	−	10.5360i	−0.870969	−	0.502854i	−0.00329878	−	0.999995i	$-0.501050\pi$
$439$	−18.2488	−	10.5360i	−0.870969	−	0.502854i	−0.867670	+	0.497140i	$0.834383\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.1762	−	9.33933i	0.768554	−	0.443725i	−0.0638045	−	0.997962i	$-0.520323\pi$
$443$	16.1762	−	9.33933i	0.768554	−	0.443725i	0.832359	+	0.554238i	$0.186990\pi$
$444$		0			0
$445$		−	31.0988i		−	1.47423i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	20.4689			0.965989			0.482994	−	0.875623i	$-0.339549\pi$
$449$	20.4689			0.965989			0.482994	+	0.875623i	$0.339549\pi$
$450$		0			0
$451$	−2.33034	−	1.34542i	−0.109731	−	0.0633534i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	35.3235			1.65599
$456$		0			0
$457$	−36.4364			−1.70442			−0.852210	−	0.523199i	$-0.824738\pi$
$457$	−36.4364			−1.70442			−0.852210	+	0.523199i	$0.824738\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−15.4134	−	8.89895i	−0.717875	−	0.414466i	0.0960948	−	0.995372i	$-0.469365\pi$
$461$	−15.4134	−	8.89895i	−0.717875	−	0.414466i	−0.813970	+	0.580907i	$0.802698\pi$
$462$		0			0
$463$	3.39051			0.157570			0.0787851	−	0.996892i	$-0.474896\pi$
$463$	3.39051			0.157570			0.0787851	+	0.996892i	$0.474896\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			12.0875i			0.559341i	0.960096	+	0.279670i	$0.0902252\pi$
$467$			12.0875i			0.559341i	−0.960096	+	0.279670i	$0.909775\pi$
$468$		0			0
$469$	−41.8225	+	24.1462i	−1.93118	+	1.11497i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.73461	−	1.00148i	−0.0797576	−	0.0460481i
$474$		0			0
$475$	−21.1330	−	31.4848i	−0.969647	−	1.44462i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.5409	−	7.81786i	0.618701	−	0.357207i	−0.157662	−	0.987493i	$-0.550396\pi$
$479$	13.5409	−	7.81786i	0.618701	−	0.357207i	0.776363	+	0.630286i	$0.217062\pi$
$480$		0			0
$481$	−8.82007	−	15.2768i	−0.402161	−	0.696563i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.52373	+	7.83532i	0.205412	+	0.355784i
$486$		0			0
$487$		−	15.7389i		−	0.713197i	−0.934258	−	0.356598i	$-0.883936\pi$
$487$		−	15.7389i		−	0.713197i	0.934258	−	0.356598i	$-0.116064\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.61258	−	1.50838i	−0.117904	−	0.0680720i	0.439888	−	0.898053i	$-0.355018\pi$
$491$	−2.61258	−	1.50838i	−0.117904	−	0.0680720i	−0.557792	+	0.829981i	$0.688351\pi$
$492$		0			0
$493$			10.0832i			0.454126i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−15.1436	+	26.2296i	−0.679285	+	1.17656i
$498$		0			0
$499$	5.86305	−	10.1551i	0.262466	−	0.454604i	−0.704431	−	0.709773i	$-0.748798\pi$
$499$	5.86305	−	10.1551i	0.262466	−	0.454604i	0.966897	+	0.255168i	$0.0821309\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−33.0348	+	19.0726i	−1.47295	+	0.850407i	−0.999537	−	0.0304338i	$-0.990311\pi$
$503$	−33.0348	+	19.0726i	−1.47295	+	0.850407i	−0.473412	+	0.880841i	$0.656978\pi$
$504$		0			0
$505$	34.5239			1.53630
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.57499	+	13.1203i	0.335756	+	0.581546i	0.983630	−	0.180202i	$-0.0576750\pi$
$509$	7.57499	+	13.1203i	0.335756	+	0.581546i	−0.647874	+	0.761747i	$0.724342\pi$
$510$		0			0
$511$	−30.5909	+	52.9850i	−1.35326	+	2.34392i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−17.9827	+	31.1470i	−0.792414	+	1.37250i
$516$		0			0
$517$	1.73896	+	3.01197i	0.0764796	+	0.132467i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4.46456			−0.195596			−0.0977980	−	0.995206i	$-0.531180\pi$
$521$	−4.46456			−0.195596			−0.0977980	+	0.995206i	$0.531180\pi$
$522$		0			0
$523$	2.10981	−	1.21810i	0.0922557	−	0.0532639i	−0.453162	−	0.891428i	$-0.649704\pi$
$523$	2.10981	−	1.21810i	0.0922557	−	0.0532639i	0.545418	+	0.838164i	$0.316371\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.65332	+	8.05978i	−0.202702	+	0.351090i
$528$		0			0
$529$	−1.56215	+	2.70572i	−0.0679195	+	0.117640i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			12.0103i			0.520223i
$534$		0			0
$535$	41.9565	+	24.2236i	1.81394	+	1.04728i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	6.49849i		−	0.279910i
$540$		0			0
$541$	3.14078	+	5.44000i	0.135033	+	0.233884i	0.925610	−	0.378479i	$-0.123553\pi$
$541$	3.14078	+	5.44000i	0.135033	+	0.233884i	−0.790577	+	0.612362i	$0.790219\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	29.2500	+	50.6624i	1.25293	+	2.17014i
$546$		0			0
$547$	−33.9435	+	19.5973i	−1.45132	+	0.837919i	−0.998556	−	0.0537123i	$-0.982895\pi$
$547$	−33.9435	+	19.5973i	−1.45132	+	0.837919i	−0.452762	+	0.891631i	$0.649561\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	15.1875	+	22.6271i	0.647011	+	0.963945i
$552$		0			0
$553$	−9.26756	−	5.35063i	−0.394097	−	0.227532i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.65383	−	5.57364i	0.409046	−	0.236163i	−0.281334	−	0.959610i	$-0.590777\pi$
$557$	9.65383	−	5.57364i	0.409046	−	0.236163i	0.690380	+	0.723447i	$0.257444\pi$
$558$		0			0
$559$			8.93998i			0.378121i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.7451			0.494997			0.247499	−	0.968888i	$-0.420391\pi$
$563$	11.7451			0.494997			0.247499	+	0.968888i	$0.420391\pi$
$564$		0			0
$565$	9.29457	+	5.36622i	0.391025	+	0.225759i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	38.9553			1.63309			0.816545	−	0.577282i	$-0.195887\pi$
$569$	38.9553			1.63309			0.816545	+	0.577282i	$0.195887\pi$
$570$		0			0
$571$	−7.90186			−0.330683			−0.165341	−	0.986236i	$-0.552873\pi$
$571$	−7.90186			−0.330683			−0.165341	+	0.986236i	$0.552873\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−33.5876	−	19.3918i	−1.40070	−	0.808694i
$576$		0			0
$577$	41.8337			1.74156			0.870780	−	0.491673i	$-0.163614\pi$
$577$	41.8337			1.74156			0.870780	+	0.491673i	$0.163614\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		−	14.3282i		−	0.594432i
$582$		0			0
$583$	4.23068	−	2.44259i	0.175217	−	0.101162i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−28.2507	−	16.3106i	−1.16603	−	0.673209i	−0.213290	−	0.976989i	$-0.568418\pi$
$587$	−28.2507	−	16.3106i	−1.16603	−	0.673209i	−0.952742	+	0.303780i	$0.901751\pi$
$588$		0			0
$589$	1.69761	+	25.0953i	0.0699487	+	1.03403i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−18.2109	+	10.5140i	−0.747830	+	0.431760i	−0.824909	−	0.565265i	$-0.808774\pi$
$593$	−18.2109	+	10.5140i	−0.747830	+	0.431760i	0.0770792	+	0.997025i	$0.475441\pi$
$594$		0			0
$595$	13.6424	+	23.6293i	0.559283	+	0.968707i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−12.7533	−	22.0894i	−0.521087	−	0.902550i	−0.999699	−	0.0245231i	$-0.992193\pi$
$599$	−12.7533	−	22.0894i	−0.521087	−	0.902550i	0.478612	−	0.878027i	$-0.341140\pi$
$600$		0			0
$601$		−	28.4992i		−	1.16251i	−0.813722	−	0.581254i	$-0.802562\pi$
$601$		−	28.4992i		−	1.16251i	0.813722	−	0.581254i	$-0.197438\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−34.5578	−	19.9520i	−1.40497	−	0.811162i
$606$		0			0
$607$		−	0.739247i		−	0.0300051i	−0.999887	−	0.0150025i	$-0.995224\pi$
$607$		−	0.739247i		−	0.0300051i	0.999887	−	0.0150025i	$-0.00477564\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.76167	−	13.4436i	0.314004	−	0.543870i
$612$		0			0
$613$	3.29782	−	5.71199i	0.133198	−	0.230705i	−0.791710	−	0.610897i	$-0.790809\pi$
$613$	3.29782	−	5.71199i	0.133198	−	0.230705i	0.924908	+	0.380192i	$0.124142\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6.07286	−	3.50617i	0.244484	−	0.141153i	−0.372752	−	0.927931i	$-0.621586\pi$
$617$	6.07286	−	3.50617i	0.244484	−	0.141153i	0.617236	+	0.786778i	$0.288252\pi$
$618$		0			0
$619$	−0.217266			−0.00873264			−0.00436632	−	0.999990i	$-0.501390\pi$
$619$	−0.217266			−0.00873264			−0.00436632	+	0.999990i	$0.501390\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	19.2021	+	33.2590i	0.769315	+	1.33249i
$624$		0			0
$625$	−3.59097	+	6.21975i	−0.143639	+	0.248790i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	6.81284	−	11.8002i	0.271646	−	0.470504i
$630$		0			0
$631$	−22.2465	−	38.5321i	−0.885621	−	1.53394i	−0.845001	−	0.534765i	$-0.820400\pi$
$631$	−22.2465	−	38.5321i	−0.885621	−	1.53394i	−0.0406200	−	0.999175i	$-0.512933\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	39.7405			1.57705
$636$		0			0
$637$	−25.1193	+	14.5026i	−0.995264	+	0.574616i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.0772	−	17.4542i	0.398025	−	0.689399i	−0.595457	−	0.803387i	$-0.703029\pi$
$641$	10.0772	−	17.4542i	0.398025	−	0.689399i	0.993482	+	0.113988i	$0.0363624\pi$
$642$		0			0
$643$	−1.34203	+	2.32447i	−0.0529246	+	0.0916681i	−0.891274	−	0.453465i	$-0.850188\pi$
$643$	−1.34203	+	2.32447i	−0.0529246	+	0.0916681i	0.838349	+	0.545133i	$0.183521\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	18.7684i		−	0.737862i	−0.929457	−	0.368931i	$-0.879724\pi$
$647$		−	18.7684i		−	0.737862i	0.929457	−	0.368931i	$-0.120276\pi$
$648$		0			0
$649$	−1.38510	−	0.799689i	−0.0543700	−	0.0313905i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	1.34256i		−	0.0525383i	−0.999655	−	0.0262691i	$-0.991637\pi$
$653$		−	1.34256i		−	0.0525383i	0.999655	−	0.0262691i	$-0.00836269\pi$
$654$		0			0
$655$	−37.6250	−	65.1684i	−1.47013	−	2.54634i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−22.7316	−	39.3723i	−0.885498	−	1.53373i	−0.845141	−	0.534543i	$-0.820484\pi$
$659$	−22.7316	−	39.3723i	−0.885498	−	1.53373i	−0.0403571	−	0.999185i	$-0.512850\pi$
$660$		0			0
$661$	−26.3005	+	15.1846i	−1.02297	+	0.590613i	−0.914963	−	0.403537i	$-0.867781\pi$
$661$	−26.3005	+	15.1846i	−1.02297	+	0.590613i	−0.108009	+	0.994150i	$0.534447\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	66.2047	+	32.4764i	2.56731	+	1.25938i
$666$		0			0
$667$	24.1383	+	13.9362i	0.934637	+	0.539613i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.66642	+	2.11681i	−0.141541	+	0.0817185i
$672$		0			0
$673$		−	40.1599i		−	1.54805i	−0.633154	−	0.774026i	$-0.718240\pi$
$673$		−	40.1599i		−	1.54805i	0.633154	−	0.774026i	$-0.281760\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	37.3822			1.43671			0.718357	−	0.695675i	$-0.244895\pi$
$677$	37.3822			1.43671			0.718357	+	0.695675i	$0.244895\pi$
$678$		0			0
$679$	−9.67590	−	5.58638i	−0.371327	−	0.214386i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	25.0486			0.958459			0.479229	−	0.877690i	$-0.340916\pi$
$683$	25.0486			0.958459			0.479229	+	0.877690i	$0.340916\pi$
$684$		0			0
$685$	33.0137			1.26139
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−18.8832	−	10.9022i	−0.719392	−	0.415341i
$690$		0			0
$691$	−2.95898			−0.112565			−0.0562824	−	0.998415i	$-0.517925\pi$
$691$	−2.95898			−0.112565			−0.0562824	+	0.998415i	$0.517925\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			30.2829i			1.14870i
$696$		0			0
$697$	−8.03415	+	4.63852i	−0.304315	+	0.175696i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	27.3853	+	15.8109i	1.03433	+	0.597171i	0.918222	−	0.396066i	$-0.129625\pi$
$701$	27.3853	+	15.8109i	1.03433	+	0.597171i	0.116108	+	0.993237i	$0.462958\pi$
$702$		0			0
$703$	−2.48544	−	36.7416i	−0.0937402	−	1.38573i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−36.9220	+	21.3169i	−1.38859	+	0.801706i
$708$		0			0
$709$	2.09318	+	3.62550i	0.0786111	+	0.136158i	0.902651	−	0.430373i	$-0.141618\pi$
$709$	2.09318	+	3.62550i	0.0786111	+	0.136158i	−0.824040	+	0.566532i	$0.808285\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	12.8629	+	22.2791i	0.481718	+	0.834360i
$714$		0			0
$715$		−	3.61531i		−	0.135205i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.54736	+	3.78012i	0.244175	+	0.140975i	0.617094	−	0.786889i	$-0.288310\pi$
$719$	6.54736	+	3.78012i	0.244175	+	0.140975i	−0.372919	+	0.927864i	$0.621643\pi$
$720$		0			0
$721$		−	44.4140i		−	1.65406i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	27.1939	−	47.1011i	1.00995	−	1.74929i
$726$		0			0
$727$	13.1786	−	22.8260i	0.488767	−	0.846570i	−0.511149	−	0.859492i	$-0.670780\pi$
$727$	13.1786	−	22.8260i	0.488767	−	0.846570i	0.999917	+	0.0129222i	$0.00411337\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−5.98031	+	3.45273i	−0.221190	+	0.127704i
$732$		0			0
$733$	14.7410			0.544472			0.272236	−	0.962231i	$-0.412237\pi$
$733$	14.7410			0.544472			0.272236	+	0.962231i	$0.412237\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.47133	+	4.28047i	0.0910325	+	0.157673i
$738$		0			0
$739$	12.9297	−	22.3948i	0.475625	−	0.823807i	−0.523985	−	0.851727i	$-0.675555\pi$
$739$	12.9297	−	22.3948i	0.475625	−	0.823807i	0.999610	+	0.0279206i	$0.00888855\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−22.4098	+	38.8149i	−0.822135	+	1.42398i	0.0819537	+	0.996636i	$0.473884\pi$
$743$	−22.4098	+	38.8149i	−0.822135	+	1.42398i	−0.904089	+	0.427344i	$0.859449\pi$
$744$		0			0
$745$	42.1960	+	73.0856i	1.54594	+	2.67765i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−59.8278			−2.18606
$750$		0			0
$751$	25.9931	−	15.0071i	0.948503	−	0.547618i	0.0558871	−	0.998437i	$-0.482201\pi$
$751$	25.9931	−	15.0071i	0.948503	−	0.547618i	0.892615	+	0.450819i	$0.148868\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	19.2008	−	33.2567i	0.698788	−	1.21034i
$756$		0			0
$757$	−13.6039	+	23.5626i	−0.494440	+	0.856396i	−0.999979	−	0.00640787i	$-0.997960\pi$
$757$	−13.6039	+	23.5626i	−0.494440	+	0.856396i	0.505539	+	0.862804i	$0.331294\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	28.5632i		−	1.03541i	−0.855558	−	0.517707i	$-0.826786\pi$
$761$		−	28.5632i		−	1.03541i	0.855558	−	0.517707i	$-0.173214\pi$
$762$		0			0
$763$	−62.5634	−	36.1210i	−2.26495	−	1.30767i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			7.13864i			0.257761i
$768$		0			0
$769$	10.6797	+	18.4978i	0.385120	+	0.667047i	0.991786	−	0.127910i	$-0.0408269\pi$
$769$	10.6797	+	18.4978i	0.385120	+	0.667047i	−0.606666	+	0.794957i	$0.707494\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−9.23746	−	15.9997i	−0.332248	−	0.575471i	0.650704	−	0.759331i	$-0.274474\pi$
$773$	−9.23746	−	15.9997i	−0.332248	−	0.575471i	−0.982952	+	0.183861i	$0.941141\pi$
$774$		0			0
$775$	43.4734	−	25.0994i	1.56161	−	0.901597i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−11.0422	+	22.5101i	−0.395629	+	0.806509i
$780$		0			0
$781$	2.68455	+	1.54993i	0.0960608	+	0.0554608i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	56.1198	−	32.4008i	2.00300	−	1.15643i
$786$		0			0
$787$		−	34.0202i		−	1.21269i	−0.795202	−	0.606345i	$-0.792635\pi$
$787$		−	34.0202i		−	1.21269i	0.795202	−	0.606345i	$-0.207365\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−13.2536			−0.471243
$792$		0			0
$793$	16.3647	+	9.44814i	0.581126	+	0.335513i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.5901			−0.481386			−0.240693	−	0.970601i	$-0.577375\pi$
$797$	−13.5901			−0.481386			−0.240693	+	0.970601i	$0.577375\pi$
$798$		0			0
$799$	11.9906			0.424198
$800$		0			0
$801$		0			0
$802$		0			0
$803$	5.42293	+	3.13093i	0.191371	+	0.110488i
$804$		0			0
$805$	75.4216			2.65826
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	6.77087i		−	0.238051i	−0.992891	−	0.119026i	$-0.962023\pi$
$809$		−	6.77087i		−	0.238051i	0.992891	−	0.119026i	$-0.0379771\pi$
$810$		0			0
$811$	41.8928	−	24.1868i	1.47106	−	0.849314i	0.471584	−	0.881821i	$-0.343683\pi$
$811$	41.8928	−	24.1868i	1.47106	−	0.849314i	0.999472	+	0.0325071i	$0.0103492\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	66.1791	+	38.2085i	2.31815	+	1.33839i
$816$		0			0
$817$	−8.21941	+	16.7557i	−0.287561	+	0.586207i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−31.2403	+	18.0366i	−1.09030	+	0.629482i	−0.933655	−	0.358174i	$-0.883400\pi$
$821$	−31.2403	+	18.0366i	−1.09030	+	0.629482i	−0.156640	+	0.987656i	$0.550066\pi$
$822$		0			0
$823$	−0.179013	−	0.310060i	−0.00624001	−	0.0108080i	0.862889	−	0.505394i	$-0.168653\pi$
$823$	−0.179013	−	0.310060i	−0.00624001	−	0.0108080i	−0.869129	+	0.494586i	$0.835320\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.06847	−	3.58270i	−0.0719279	−	0.124583i	0.827818	−	0.560996i	$-0.189582\pi$
$827$	−2.06847	−	3.58270i	−0.0719279	−	0.124583i	−0.899746	+	0.436414i	$0.856248\pi$
$828$		0			0
$829$		−	34.6645i		−	1.20395i	−0.798516	−	0.601973i	$-0.794381\pi$
$829$		−	34.6645i		−	1.20395i	0.798516	−	0.601973i	$-0.205619\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−19.4028	−	11.2022i	−0.672267	−	0.388133i
$834$		0			0
$835$			60.2664i			2.08560i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	17.4451	−	30.2157i	0.602271	−	1.04316i	−0.390206	−	0.920728i	$-0.627596\pi$
$839$	17.4451	−	30.2157i	0.602271	−	1.04316i	0.992476	−	0.122436i	$-0.0390705\pi$
$840$		0			0
$841$	−5.04330	+	8.73525i	−0.173907	+	0.301215i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	27.6954	−	15.9900i	0.952751	−	0.550071i
$846$		0			0
$847$	49.2776			1.69320
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−18.8323	−	32.6185i	−0.645563	−	1.11815i
$852$		0			0
$853$	8.09670	−	14.0239i	0.277226	−	0.480169i	−0.693469	−	0.720487i	$-0.743918\pi$
$853$	8.09670	−	14.0239i	0.277226	−	0.480169i	0.970694	+	0.240318i	$0.0772517\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.54801	+	9.60944i	−0.189516	+	0.328252i	−0.945089	−	0.326813i	$-0.894025\pi$
$857$	−5.54801	+	9.60944i	−0.189516	+	0.328252i	0.755573	+	0.655065i	$0.227359\pi$
$858$		0			0
$859$	−4.73033	−	8.19318i	−0.161397	−	0.279548i	0.773973	−	0.633219i	$-0.218267\pi$
$859$	−4.73033	−	8.19318i	−0.161397	−	0.279548i	−0.935370	+	0.353671i	$0.884933\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	15.8335			0.538979			0.269490	−	0.963003i	$-0.413145\pi$
$863$	15.8335			0.538979			0.269490	+	0.963003i	$0.413145\pi$
$864$		0			0
$865$	31.2083	−	18.0181i	1.06112	−	0.612635i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.547628	+	0.948520i	−0.0185770	+	0.0321763i
$870$		0			0
$871$	11.0305	−	19.1054i	0.373754	−	0.647361i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		−	62.5835i		−	2.11571i
$876$		0			0
$877$	−36.7139	−	21.1968i	−1.23974	−	0.715765i	−0.270700	−	0.962664i	$-0.587255\pi$
$877$	−36.7139	−	21.1968i	−1.23974	−	0.715765i	−0.969041	+	0.246898i	$0.920589\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	27.1415i		−	0.914420i	−0.889359	−	0.457210i	$-0.848849\pi$
$881$		−	27.1415i		−	0.914420i	0.889359	−	0.457210i	$-0.151151\pi$
$882$		0			0
$883$	−6.14070	−	10.6360i	−0.206651	−	0.357930i	0.744006	−	0.668173i	$-0.232923\pi$
$883$	−6.14070	−	10.6360i	−0.206651	−	0.357930i	−0.950658	+	0.310242i	$0.899590\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.7062	+	22.0079i	0.426634	+	0.738951i	0.996571	−	0.0827366i	$-0.0263660\pi$
$887$	12.7062	+	22.0079i	0.426634	+	0.738951i	−0.569938	+	0.821688i	$0.693033\pi$
$888$		0			0
$889$	−42.5009	+	24.5379i	−1.42543	+	0.822975i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	26.9073	−	18.0605i	0.900418	−	0.604371i
$894$		0			0
$895$	43.3883	+	25.0502i	1.45031	+	0.837337i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−31.2429	+	18.0381i	−1.04201	+	0.601604i
$900$		0			0
$901$		−	16.8423i		−	0.561098i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−75.6988			−2.51631
$906$		0			0
$907$	−14.1039	−	8.14290i	−0.468313	−	0.270381i	0.247220	−	0.968959i	$-0.420483\pi$
$907$	−14.1039	−	8.14290i	−0.468313	−	0.270381i	−0.715533	+	0.698579i	$0.753816\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	20.1499			0.667596			0.333798	−	0.942645i	$-0.391670\pi$
$911$	20.1499			0.667596			0.333798	+	0.942645i	$0.391670\pi$
$912$		0			0
$913$	−1.46646			−0.0485329
$914$		0			0
$915$		0			0
$916$		0			0
$917$	80.4769	+	46.4633i	2.65758	+	1.53435i
$918$		0			0
$919$	−37.3088			−1.23070			−0.615352	−	0.788252i	$-0.710986\pi$
$919$	−37.3088			−1.23070			−0.615352	+	0.788252i	$0.710986\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	13.8359i		−	0.455413i
$924$		0			0
$925$	−63.6487	+	36.7476i	−2.09276	+	1.20825i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	20.9287	+	12.0832i	0.686648	+	0.396437i	0.802355	−	0.596847i	$-0.203580\pi$
$929$	20.9287	+	12.0832i	0.686648	+	0.396437i	−0.115707	+	0.993283i	$0.536913\pi$
$930$		0			0
$931$	−60.4133	+	4.08675i	−1.97997	+	0.133938i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.41842	−	1.39628i	0.0790908	−	0.0456631i
$936$		0			0
$937$	10.6733	+	18.4867i	0.348681	+	0.603934i	0.986015	−	0.166654i	$-0.0532962\pi$
$937$	10.6733	+	18.4867i	0.348681	+	0.603934i	−0.637334	+	0.770588i	$0.719963\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6.82655	+	11.8239i	0.222539	+	0.385449i	0.955578	−	0.294737i	$-0.0952322\pi$
$941$	6.82655	+	11.8239i	0.222539	+	0.385449i	−0.733039	+	0.680186i	$0.761899\pi$
$942$		0			0
$943$			25.6439i			0.835081i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.9512	+	16.1376i	0.908293	+	0.524403i	0.879881	−	0.475193i	$-0.157622\pi$
$947$	27.9512	+	16.1376i	0.908293	+	0.524403i	0.0284114	+	0.999596i	$0.490955\pi$
$948$		0			0
$949$		−	27.9491i		−	0.907266i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−4.08154	+	7.06943i	−0.132214	+	0.229001i	−0.924530	−	0.381110i	$-0.875542\pi$
$953$	−4.08154	+	7.06943i	−0.132214	+	0.229001i	0.792316	+	0.610111i	$0.208875\pi$
$954$		0			0
$955$	14.2302	−	24.6475i	0.460480	−	0.797574i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−35.3068	+	20.3844i	−1.14012	+	0.658247i
$960$		0			0
$961$	−2.29760			−0.0741161
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−35.4986	−	61.4853i	−1.14274	−	1.97928i
$966$		0			0
$967$	−12.6054	+	21.8331i	−0.405361	+	0.702107i	−0.994363	−	0.106025i	$-0.966188\pi$
$967$	−12.6054	+	21.8331i	−0.405361	+	0.702107i	0.589002	+	0.808132i	$0.299521\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	11.3118	−	19.5927i	0.363014	−	0.628760i	−0.625441	−	0.780272i	$-0.715081\pi$
$971$	11.3118	−	19.5927i	0.363014	−	0.628760i	0.988455	+	0.151512i	$0.0484142\pi$
$972$		0			0
$973$	−18.6983	−	32.3864i	−0.599440	−	1.03826i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−19.1861			−0.613818			−0.306909	−	0.951739i	$-0.599295\pi$
$977$	−19.1861			−0.613818			−0.306909	+	0.951739i	$0.599295\pi$
$978$		0			0
$979$	3.40400	−	1.96530i	0.108792	−	0.0628113i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.5342	−	18.2457i	0.335988	−	0.581949i	−0.647686	−	0.761908i	$-0.724263\pi$
$983$	10.5342	−	18.2457i	0.335988	−	0.581949i	0.983674	+	0.179959i	$0.0575964\pi$
$984$		0			0
$985$	39.9896	−	69.2640i	1.27418	−	2.20694i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			19.0883i			0.606974i
$990$		0			0
$991$	−24.7719	−	14.3020i	−0.786904	−	0.454319i	0.0519674	−	0.998649i	$-0.483451\pi$
$991$	−24.7719	−	14.3020i	−0.786904	−	0.454319i	−0.838872	+	0.544329i	$0.816784\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			67.0980i			2.12715i
$996$		0			0
$997$	−23.4801	−	40.6687i	−0.743622	−	1.28799i	−0.950836	−	0.309695i	$-0.899773\pi$
$997$	−23.4801	−	40.6687i	−0.743622	−	1.28799i	0.207214	−	0.978296i	$-0.433560\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2736.2.dc.e.1889.2		20
3.2	odd	2		2736.2.dc.f.1889.9		20
4.3	odd	2		1368.2.cu.a.521.2	yes	20
12.11	even	2		1368.2.cu.b.521.9	yes	20
19.12	odd	6		2736.2.dc.f.449.9		20
57.50	even	6	inner	2736.2.dc.e.449.2		20
76.31	even	6		1368.2.cu.b.449.9	yes	20
228.107	odd	6		1368.2.cu.a.449.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1368.2.cu.a.449.2	✓	20	228.107	odd	6
1368.2.cu.a.521.2	yes	20	4.3	odd	2
1368.2.cu.b.449.9	yes	20	76.31	even	6
1368.2.cu.b.521.9	yes	20	12.11	even	2
2736.2.dc.e.449.2		20	57.50	even	6	inner
2736.2.dc.e.1889.2		20	1.1	even	1	trivial
2736.2.dc.f.449.9		20	19.12	odd	6
2736.2.dc.f.1889.9		20	3.2	odd	2

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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)

\(f(q)\)	\(=\)	\(q+(-3.20539 - 1.85063i) q^{5} +4.57072 q^{7} +O(q^{10})\)	\(q+(-3.20539 - 1.85063i) q^{5} +4.57072 q^{7} -0.467805i q^{11} +(-1.80826 + 1.04400i) q^{13} +(-1.39674 - 0.806410i) q^{17} +(-4.34896 + 0.294192i) q^{19} +(-3.86093 + 2.22911i) q^{23} +(4.34968 + 7.53386i) q^{25} +(-3.12596 - 5.41433i) q^{29} -5.77041i q^{31} +(-14.6509 - 8.45871i) q^{35} +8.44836i q^{37} +(2.87603 - 4.98143i) q^{41} +(2.14080 - 3.70798i) q^{43} +(-6.43852 + 3.71728i) q^{47} +13.8914 q^{49} +(5.22137 + 9.04368i) q^{53} +(-0.865736 + 1.49950i) q^{55} +(1.70945 - 2.96085i) q^{59} +(-4.52498 - 7.83749i) q^{61} +7.72823 q^{65} +(-9.15010 + 5.28281i) q^{67} +(-3.31319 + 5.73861i) q^{71} +(-6.69280 + 11.5923i) q^{73} -2.13821i q^{77} +(-2.02759 - 1.17063i) q^{79} -3.13477i q^{83} +(2.98474 + 5.16972i) q^{85} +(4.20111 + 7.27653i) q^{89} +(-8.26504 + 4.77182i) q^{91} +(14.4845 + 7.10532i) q^{95} +(-2.11693 - 1.22221i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{7}+O(q^{10}) \) 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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