LMFDB - Embedded newform 1600.2.q.f.849.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(49,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1600.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.q (of order $4$, 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			849.2
Root			$1.22306 + 0.710021i$ of defining polynomial
Character	$\chi$	$=$	1600.849
Dual form			1600.2.q.f.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09156 + 1.09156i) q^{3} -0.973926 q^{7} +0.616985i q^{9} +O(q^{10})$	$q+(-1.09156 + 1.09156i) q^{3} -0.973926 q^{7} +0.616985i q^{9} +(-1.40810 + 1.40810i) q^{11} +(4.60317 - 4.60317i) q^{13} -0.490104i q^{17} +(4.54863 + 4.54863i) q^{19} +(1.06310 - 1.06310i) q^{21} +1.94308 q^{23} +(-3.94816 - 3.94816i) q^{27} +(3.74613 + 3.74613i) q^{29} -4.29021 q^{31} -3.07405i q^{33} +(-4.55320 - 4.55320i) q^{37} +10.0493i q^{39} +10.1542i q^{41} +(1.79055 + 1.79055i) q^{43} +10.0162i q^{47} -6.05147 q^{49} +(0.534979 + 0.534979i) q^{51} +(5.61412 + 5.61412i) q^{53} -9.93022 q^{57} +(8.44185 - 8.44185i) q^{59} +(3.01095 + 3.01095i) q^{61} -0.600897i q^{63} +(-7.07504 + 7.07504i) q^{67} +(-2.12099 + 2.12099i) q^{69} +0.897891i q^{71} -9.71555 q^{73} +(1.37138 - 1.37138i) q^{77} -14.7857 q^{79} +6.76838 q^{81} +(0.815000 - 0.815000i) q^{83} -8.17827 q^{87} +1.12404i q^{89} +(-4.48314 + 4.48314i) q^{91} +(4.68303 - 4.68303i) q^{93} +7.54442i q^{97} +(-0.868775 - 0.868775i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3} - 12 q^{7}+O(q^{10}) $ 12 * q + 2 * q^3 - 12 * q^7	$ 12 q + 2 q^{3} - 12 q^{7} + 2 q^{11} + 4 q^{13} - 14 q^{19} - 20 q^{21} - 12 q^{23} - 10 q^{27} + 4 q^{31} - 8 q^{37} - 4 q^{49} - 10 q^{51} - 16 q^{53} - 16 q^{57} + 20 q^{59} + 4 q^{61} - 50 q^{67} + 40 q^{73} - 8 q^{77} + 12 q^{79} - 8 q^{81} - 2 q^{83} + 64 q^{87} + 44 q^{93} + 12 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 - 12 * q^7 + 2 * q^11 + 4 * q^13 - 14 * q^19 - 20 * q^21 - 12 * q^23 - 10 * q^27 + 4 * q^31 - 8 * q^37 - 4 * q^49 - 10 * q^51 - 16 * q^53 - 16 * q^57 + 20 * q^59 + 4 * q^61 - 50 * q^67 + 40 * q^73 - 8 * q^77 + 12 * q^79 - 8 * q^81 - 2 * q^83 + 64 * q^87 + 44 * q^93 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−1.09156	+	1.09156i	−0.630214	+	0.630214i	−0.948122	−	0.317908i	$-0.897020\pi$
$3$	−1.09156	+	1.09156i	−0.630214	+	0.630214i	0.317908	+	0.948122i	$0.397020\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.973926			−0.368109			−0.184055	−	0.982916i	$-0.558922\pi$
$7$	−0.973926			−0.368109			−0.184055	+	0.982916i	$0.558922\pi$
$8$		0			0
$9$			0.616985i			0.205662i
$10$		0			0
$11$	−1.40810	+	1.40810i	−0.424558	+	0.424558i	−0.886769	−	0.462212i	$-0.847056\pi$
$11$	−1.40810	+	1.40810i	−0.424558	+	0.424558i	0.462212	+	0.886769i	$0.347056\pi$
$12$		0			0
$13$	4.60317	−	4.60317i	1.27669	−	1.27669i	0.334179	−	0.942510i	$-0.391541\pi$
$13$	4.60317	−	4.60317i	1.27669	−	1.27669i	0.942510	−	0.334179i	$-0.108459\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	0.490104i		−	0.118868i	−0.998232	−	0.0594338i	$-0.981070\pi$
$17$		−	0.490104i		−	0.118868i	0.998232	−	0.0594338i	$-0.0189295\pi$
$18$		0			0
$19$	4.54863	+	4.54863i	1.04353	+	1.04353i	0.999009	+	0.0445187i	$0.0141754\pi$
$19$	4.54863	+	4.54863i	1.04353	+	1.04353i	0.0445187	+	0.999009i	$0.485825\pi$
$20$		0			0
$21$	1.06310	−	1.06310i	0.231988	−	0.231988i
$22$		0			0
$23$	1.94308			0.405160			0.202580	−	0.979266i	$-0.435067\pi$
$23$	1.94308			0.405160			0.202580	+	0.979266i	$0.435067\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.94816	−	3.94816i	−0.759824	−	0.759824i
$28$		0			0
$29$	3.74613	+	3.74613i	0.695640	+	0.695640i	0.963467	−	0.267827i	$-0.0863057\pi$
$29$	3.74613	+	3.74613i	0.695640	+	0.695640i	−0.267827	+	0.963467i	$0.586306\pi$
$30$		0			0
$31$	−4.29021			−0.770545			−0.385272	−	0.922803i	$-0.625893\pi$
$31$	−4.29021			−0.770545			−0.385272	+	0.922803i	$0.625893\pi$
$32$		0			0
$33$		−	3.07405i		−	0.535124i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.55320	−	4.55320i	−0.748542	−	0.748542i	0.225663	−	0.974205i	$-0.427545\pi$
$37$	−4.55320	−	4.55320i	−0.748542	−	0.748542i	−0.974205	+	0.225663i	$0.927545\pi$
$38$		0			0
$39$			10.0493i			1.60917i
$40$		0			0
$41$			10.1542i			1.58582i	0.609341	+	0.792908i	$0.291434\pi$
$41$			10.1542i			1.58582i	−0.609341	+	0.792908i	$0.708566\pi$
$42$		0			0
$43$	1.79055	+	1.79055i	0.273057	+	0.273057i	0.830329	−	0.557273i	$-0.188152\pi$
$43$	1.79055	+	1.79055i	0.273057	+	0.273057i	−0.557273	+	0.830329i	$0.688152\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			10.0162i			1.46102i	0.682902	+	0.730510i	$0.260717\pi$
$47$			10.0162i			1.46102i	−0.682902	+	0.730510i	$0.739283\pi$
$48$		0			0
$49$	−6.05147			−0.864495
$50$		0			0
$51$	0.534979	+	0.534979i	0.0749120	+	0.0749120i
$52$		0			0
$53$	5.61412	+	5.61412i	0.771158	+	0.771158i	0.978309	−	0.207151i	$-0.0664190\pi$
$53$	5.61412	+	5.61412i	0.771158	+	0.771158i	−0.207151	+	0.978309i	$0.566419\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−9.93022			−1.31529
$58$		0			0
$59$	8.44185	−	8.44185i	1.09904	−	1.09904i	0.104512	−	0.994524i	$-0.466672\pi$
$59$	8.44185	−	8.44185i	1.09904	−	1.09904i	0.994524	−	0.104512i	$-0.0333281\pi$
$60$		0			0
$61$	3.01095	+	3.01095i	0.385513	+	0.385513i	0.873084	−	0.487571i	$-0.162117\pi$
$61$	3.01095	+	3.01095i	0.385513	+	0.385513i	−0.487571	+	0.873084i	$0.662117\pi$
$62$		0			0
$63$		−	0.600897i		−	0.0757060i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.07504	+	7.07504i	−0.864354	+	0.864354i	−0.991840	−	0.127486i	$-0.959309\pi$
$67$	−7.07504	+	7.07504i	−0.864354	+	0.864354i	0.127486	+	0.991840i	$0.459309\pi$
$68$		0			0
$69$	−2.12099	+	2.12099i	−0.255337	+	0.255337i
$70$		0			0
$71$			0.897891i			0.106560i	0.998580	+	0.0532800i	$0.0169676\pi$
$71$			0.897891i			0.106560i	−0.998580	+	0.0532800i	$0.983032\pi$
$72$		0			0
$73$	−9.71555			−1.13712			−0.568559	−	0.822642i	$-0.692499\pi$
$73$	−9.71555			−1.13712			−0.568559	+	0.822642i	$0.692499\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.37138	−	1.37138i	0.156284	−	0.156284i
$78$		0			0
$79$	−14.7857			−1.66352			−0.831760	−	0.555135i	$-0.812666\pi$
$79$	−14.7857			−1.66352			−0.831760	+	0.555135i	$0.812666\pi$
$80$		0			0
$81$	6.76838			0.752042
$82$		0			0
$83$	0.815000	−	0.815000i	0.0894579	−	0.0894579i	−0.660962	−	0.750420i	$-0.729851\pi$
$83$	0.815000	−	0.815000i	0.0894579	−	0.0894579i	0.750420	+	0.660962i	$0.229851\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−8.17827			−0.876803
$88$		0			0
$89$			1.12404i			0.119148i	0.998224	+	0.0595739i	$0.0189742\pi$
$89$			1.12404i			0.119148i	−0.998224	+	0.0595739i	$0.981026\pi$
$90$		0			0
$91$	−4.48314	+	4.48314i	−0.469961	+	0.469961i
$92$		0			0
$93$	4.68303	−	4.68303i	0.485608	−	0.485608i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			7.54442i			0.766019i	0.923744	+	0.383010i	$0.125112\pi$
$97$			7.54442i			0.766019i	−0.923744	+	0.383010i	$0.874888\pi$
$98$		0			0
$99$	−0.868775	−	0.868775i	−0.0873152	−	0.0873152i
$100$		0			0
$101$	−2.60535	+	2.60535i	−0.259242	+	0.259242i	−0.824746	−	0.565504i	$-0.808682\pi$
$101$	−2.60535	+	2.60535i	−0.259242	+	0.259242i	0.565504	+	0.824746i	$0.308682\pi$
$102$		0			0
$103$	13.8146			1.36120			0.680598	−	0.732657i	$-0.261720\pi$
$103$	13.8146			1.36120			0.680598	+	0.732657i	$0.261720\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.89124	−	9.89124i	−0.956222	−	0.956222i	0.0428589	−	0.999081i	$-0.486353\pi$
$107$	−9.89124	−	9.89124i	−0.956222	−	0.956222i	−0.999081	+	0.0428589i	$0.986353\pi$
$108$		0			0
$109$	11.5454	+	11.5454i	1.10584	+	1.10584i	0.993691	+	0.112154i	$0.0357750\pi$
$109$	11.5454	+	11.5454i	1.10584	+	1.10584i	0.112154	+	0.993691i	$0.464225\pi$
$110$		0			0
$111$	9.94021			0.943483
$112$		0			0
$113$			17.2057i			1.61857i	0.587415	+	0.809286i	$0.300146\pi$
$113$			17.2057i			1.61857i	−0.587415	+	0.809286i	$0.699854\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.84008	+	2.84008i	0.262566	+	0.262566i
$118$		0			0
$119$			0.477325i			0.0437563i
$120$		0			0
$121$			7.03452i			0.639502i
$122$		0			0
$123$	−11.0839	−	11.0839i	−0.999403	−	0.999403i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	1.37608i		−	0.122107i	−0.998134	−	0.0610535i	$-0.980554\pi$
$127$		−	1.37608i		−	0.122107i	0.998134	−	0.0610535i	$-0.0194460\pi$
$128$		0			0
$129$	−3.90900			−0.344168
$130$		0			0
$131$	9.03973	+	9.03973i	0.789804	+	0.789804i	0.981462	−	0.191657i	$-0.0613863\pi$
$131$	9.03973	+	9.03973i	0.789804	+	0.789804i	−0.191657	+	0.981462i	$0.561386\pi$
$132$		0			0
$133$	−4.43003	−	4.43003i	−0.384132	−	0.384132i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−15.3056			−1.30764			−0.653822	−	0.756649i	$-0.726835\pi$
$137$	−15.3056			−1.30764			−0.653822	+	0.756649i	$0.726835\pi$
$138$		0			0
$139$	−0.346824	+	0.346824i	−0.0294173	+	0.0294173i	−0.721662	−	0.692245i	$-0.756622\pi$
$139$	−0.346824	+	0.346824i	−0.0294173	+	0.0294173i	0.692245	+	0.721662i	$0.256622\pi$
$140$		0			0
$141$	−10.9334	−	10.9334i	−0.920754	−	0.920754i
$142$		0			0
$143$			12.9634i			1.08406i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.60555	−	6.60555i	0.544817	−	0.544817i
$148$		0			0
$149$	−4.30028	+	4.30028i	−0.352293	+	0.352293i	−0.860962	−	0.508669i	$-0.830138\pi$
$149$	−4.30028	+	4.30028i	−0.352293	+	0.352293i	0.508669	+	0.860962i	$0.330138\pi$
$150$		0			0
$151$			2.02102i			0.164468i	0.996613	+	0.0822341i	$0.0262055\pi$
$151$			2.02102i			0.164468i	−0.996613	+	0.0822341i	$0.973794\pi$
$152$		0			0
$153$	0.302387			0.0244465
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−2.93327	+	2.93327i	−0.234101	+	0.234101i	−0.814402	−	0.580301i	$-0.802935\pi$
$157$	−2.93327	+	2.93327i	−0.234101	+	0.234101i	0.580301	+	0.814402i	$0.302935\pi$
$158$		0			0
$159$	−12.2563			−0.971989
$160$		0			0
$161$	−1.89241			−0.149143
$162$		0			0
$163$	5.74697	−	5.74697i	0.450137	−	0.450137i	−0.445263	−	0.895400i	$-0.646890\pi$
$163$	5.74697	−	5.74697i	0.450137	−	0.450137i	0.895400	+	0.445263i	$0.146890\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.41553			0.496449			0.248224	−	0.968703i	$-0.420153\pi$
$167$	6.41553			0.496449			0.248224	+	0.968703i	$0.420153\pi$
$168$		0			0
$169$		−	29.3783i		−	2.25987i
$170$		0			0
$171$	−2.80644	+	2.80644i	−0.214613	+	0.214613i
$172$		0			0
$173$	−0.545724	+	0.545724i	−0.0414907	+	0.0414907i	−0.727548	−	0.686057i	$-0.759340\pi$
$173$	−0.545724	+	0.545724i	−0.0414907	+	0.0414907i	0.686057	+	0.727548i	$0.259340\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			18.4296i			1.38525i
$178$		0			0
$179$	−3.57757	−	3.57757i	−0.267400	−	0.267400i	0.560652	−	0.828052i	$-0.310551\pi$
$179$	−3.57757	−	3.57757i	−0.267400	−	0.267400i	−0.828052	+	0.560652i	$0.810551\pi$
$180$		0			0
$181$	−1.64176	+	1.64176i	−0.122031	+	0.122031i	−0.765485	−	0.643454i	$-0.777501\pi$
$181$	−1.64176	+	1.64176i	−0.122031	+	0.122031i	0.643454	+	0.765485i	$0.277501\pi$
$182$		0			0
$183$	−6.57328			−0.485911
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.690114	+	0.690114i	0.0504662	+	0.0504662i
$188$		0			0
$189$	3.84522	+	3.84522i	0.279698	+	0.279698i
$190$		0			0
$191$	15.3359			1.10967			0.554835	−	0.831960i	$-0.312781\pi$
$191$	15.3359			1.10967			0.554835	+	0.831960i	$0.312781\pi$
$192$		0			0
$193$			0.0812703i			0.00584996i	0.999996	+	0.00292498i	$0.000931052\pi$
$193$			0.0812703i			0.00584996i	−0.999996	+	0.00292498i	$0.999069\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.40711	+	1.40711i	0.100252	+	0.100252i	0.755454	−	0.655202i	$-0.227416\pi$
$197$	1.40711	+	1.40711i	0.100252	+	0.100252i	−0.655202	+	0.755454i	$0.727416\pi$
$198$		0			0
$199$			14.3046i			1.01402i	0.861939	+	0.507011i	$0.169250\pi$
$199$			14.3046i			1.01402i	−0.861939	+	0.507011i	$0.830750\pi$
$200$		0			0
$201$		−	15.4457i		−	1.08946i
$202$		0			0
$203$	−3.64846	−	3.64846i	−0.256071	−	0.256071i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			1.19885i			0.0833258i
$208$		0			0
$209$	−12.8098			−0.886075
$210$		0			0
$211$	−8.70115	−	8.70115i	−0.599012	−	0.599012i	0.341038	−	0.940050i	$-0.389222\pi$
$211$	−8.70115	−	8.70115i	−0.599012	−	0.599012i	−0.940050	+	0.341038i	$0.889222\pi$
$212$		0			0
$213$	−0.980103	−	0.980103i	−0.0671556	−	0.0671556i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	4.17835			0.283645
$218$		0			0
$219$	10.6051	−	10.6051i	0.716628	−	0.716628i
$220$		0			0
$221$	−2.25603	−	2.25603i	−0.151757	−	0.151757i
$222$		0			0
$223$			7.78095i			0.521051i	0.965467	+	0.260525i	$0.0838958\pi$
$223$			7.78095i			0.521051i	−0.965467	+	0.260525i	$0.916104\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.15443	−	2.15443i	0.142995	−	0.142995i	−0.631986	−	0.774980i	$-0.717760\pi$
$227$	2.15443	−	2.15443i	0.142995	−	0.142995i	0.774980	+	0.631986i	$0.217760\pi$
$228$		0			0
$229$	7.63865	−	7.63865i	0.504776	−	0.504776i	−0.408142	−	0.912918i	$-0.633823\pi$
$229$	7.63865	−	7.63865i	0.504776	−	0.504776i	0.912918	+	0.408142i	$0.133823\pi$
$230$		0			0
$231$			2.99390i			0.196984i
$232$		0			0
$233$	7.51503			0.492326			0.246163	−	0.969228i	$-0.420830\pi$
$233$	7.51503			0.492326			0.246163	+	0.969228i	$0.420830\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	16.1395	−	16.1395i	1.04837	−	1.04837i
$238$		0			0
$239$	20.5776			1.33105			0.665526	−	0.746375i	$-0.268207\pi$
$239$	20.5776			1.33105			0.665526	+	0.746375i	$0.268207\pi$
$240$		0			0
$241$	−23.2914			−1.50033			−0.750166	−	0.661250i	$-0.770026\pi$
$241$	−23.2914			−1.50033			−0.750166	+	0.661250i	$0.770026\pi$
$242$		0			0
$243$	4.45639	−	4.45639i	0.285877	−	0.285877i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	41.8762			2.66452
$248$		0			0
$249$			1.77925i			0.112755i
$250$		0			0
$251$	3.34230	−	3.34230i	0.210964	−	0.210964i	−0.593713	−	0.804677i	$-0.702339\pi$
$251$	3.34230	−	3.34230i	0.210964	−	0.210964i	0.804677	+	0.593713i	$0.202339\pi$
$252$		0			0
$253$	−2.73604	+	2.73604i	−0.172014	+	0.172014i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	22.4537i		−	1.40062i	−0.713838	−	0.700311i	$-0.753045\pi$
$257$		−	22.4537i		−	1.40062i	0.713838	−	0.700311i	$-0.246955\pi$
$258$		0			0
$259$	4.43448	+	4.43448i	0.275545	+	0.275545i
$260$		0			0
$261$	−2.31131	+	2.31131i	−0.143066	+	0.143066i
$262$		0			0
$263$	−8.23670			−0.507897			−0.253948	−	0.967218i	$-0.581729\pi$
$263$	−8.23670			−0.507897			−0.253948	+	0.967218i	$0.581729\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.22696	−	1.22696i	−0.0750885	−	0.0750885i
$268$		0			0
$269$	17.2960	+	17.2960i	1.05455	+	1.05455i	0.998423	+	0.0561306i	$0.0178763\pi$
$269$	17.2960	+	17.2960i	1.05455	+	1.05455i	0.0561306	+	0.998423i	$0.482124\pi$
$270$		0			0
$271$	12.4753			0.757822			0.378911	−	0.925433i	$-0.376299\pi$
$271$	12.4753			0.757822			0.378911	+	0.925433i	$0.376299\pi$
$272$		0			0
$273$		−	9.78726i		−	0.592352i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.2583	+	10.2583i	0.616363	+	0.616363i	0.944597	−	0.328234i	$-0.106453\pi$
$277$	10.2583	+	10.2583i	0.616363	+	0.616363i	−0.328234	+	0.944597i	$0.606453\pi$
$278$		0			0
$279$		−	2.64700i		−	0.158472i
$280$		0			0
$281$		−	21.4066i		−	1.27701i	−0.769618	−	0.638505i	$-0.779553\pi$
$281$		−	21.4066i		−	1.27701i	0.769618	−	0.638505i	$-0.220447\pi$
$282$		0			0
$283$	−7.39635	−	7.39635i	−0.439668	−	0.439668i	0.452232	−	0.891900i	$-0.350628\pi$
$283$	−7.39635	−	7.39635i	−0.439668	−	0.439668i	−0.891900	+	0.452232i	$0.850628\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	9.88942i		−	0.583754i
$288$		0			0
$289$	16.7598			0.985870
$290$		0			0
$291$	−8.23520	−	8.23520i	−0.482756	−	0.482756i
$292$		0			0
$293$	0.556728	+	0.556728i	0.0325244	+	0.0325244i	0.723182	−	0.690658i	$-0.242679\pi$
$293$	0.556728	+	0.556728i	0.0325244	+	0.0325244i	−0.690658	+	0.723182i	$0.742679\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	11.1188			0.645178
$298$		0			0
$299$	8.94430	−	8.94430i	0.517263	−	0.517263i
$300$		0			0
$301$	−1.74387	−	1.74387i	−0.100515	−	0.100515i
$302$		0			0
$303$		−	5.68781i		−	0.326756i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	9.76852	−	9.76852i	0.557519	−	0.557519i	−0.371082	−	0.928600i	$-0.621013\pi$
$307$	9.76852	−	9.76852i	0.557519	−	0.557519i	0.928600	+	0.371082i	$0.121013\pi$
$308$		0			0
$309$	−15.0795	+	15.0795i	−0.857844	+	0.857844i
$310$		0			0
$311$		−	30.6874i		−	1.74013i	−0.492941	−	0.870063i	$-0.664078\pi$
$311$		−	30.6874i		−	1.74013i	0.492941	−	0.870063i	$-0.335922\pi$
$312$		0			0
$313$	1.71127			0.0967268			0.0483634	−	0.998830i	$-0.484599\pi$
$313$	1.71127			0.0967268			0.0483634	+	0.998830i	$0.484599\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.0380	−	10.0380i	0.563790	−	0.563790i	−0.366592	−	0.930382i	$-0.619476\pi$
$317$	10.0380	−	10.0380i	0.563790	−	0.563790i	0.930382	+	0.366592i	$0.119476\pi$
$318$		0			0
$319$	−10.5498			−0.590678
$320$		0			0
$321$	21.5938			1.20525
$322$		0			0
$323$	2.22930	−	2.22930i	0.124042	−	0.124042i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−25.2049			−1.39384
$328$		0			0
$329$		−	9.75508i		−	0.537815i
$330$		0			0
$331$	−7.89713	+	7.89713i	−0.434066	+	0.434066i	−0.890009	−	0.455943i	$-0.849302\pi$
$331$	−7.89713	+	7.89713i	−0.434066	+	0.434066i	0.455943	+	0.890009i	$0.349302\pi$
$332$		0			0
$333$	2.80926	−	2.80926i	0.153946	−	0.153946i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	3.46077i		−	0.188520i	−0.995548	−	0.0942601i	$-0.969951\pi$
$337$		−	3.46077i		−	0.188520i	0.995548	−	0.0942601i	$-0.0300485\pi$
$338$		0			0
$339$	−18.7810	−	18.7810i	−1.02005	−	1.02005i
$340$		0			0
$341$	6.04104	−	6.04104i	0.327141	−	0.327141i
$342$		0			0
$343$	12.7112			0.686338
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.4637	+	17.4637i	0.937498	+	0.937498i	0.998158	−	0.0606600i	$-0.0193205\pi$
$347$	17.4637	+	17.4637i	0.937498	+	0.937498i	−0.0606600	+	0.998158i	$0.519321\pi$
$348$		0			0
$349$	−24.2159	−	24.2159i	−1.29625	−	1.29625i	−0.930852	−	0.365397i	$-0.880933\pi$
$349$	−24.2159	−	24.2159i	−1.29625	−	1.29625i	−0.365397	−	0.930852i	$-0.619067\pi$
$350$		0			0
$351$	−36.3481			−1.94012
$352$		0			0
$353$			10.7028i			0.569650i	0.958580	+	0.284825i	$0.0919355\pi$
$353$			10.7028i			0.569650i	−0.958580	+	0.284825i	$0.908065\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.521030	−	0.521030i	−0.0275758	−	0.0275758i
$358$		0			0
$359$		−	23.6390i		−	1.24762i	−0.781577	−	0.623809i	$-0.785584\pi$
$359$		−	23.6390i		−	1.24762i	0.781577	−	0.623809i	$-0.214416\pi$
$360$		0			0
$361$			22.3801i			1.17790i
$362$		0			0
$363$	−7.67861	−	7.67861i	−0.403023	−	0.403023i
$364$		0			0
$365$		0			0
$366$		0			0
$367$			13.7431i			0.717386i	0.933456	+	0.358693i	$0.116777\pi$
$367$			13.7431i			0.717386i	−0.933456	+	0.358693i	$0.883223\pi$
$368$		0			0
$369$	−6.26498			−0.326142
$370$		0			0
$371$	−5.46773	−	5.46773i	−0.283871	−	0.283871i
$372$		0			0
$373$	−18.4703	−	18.4703i	−0.956355	−	0.956355i	0.0427313	−	0.999087i	$-0.486394\pi$
$373$	−18.4703	−	18.4703i	−0.956355	−	0.956355i	−0.999087	+	0.0427313i	$0.986394\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	34.4881			1.77623
$378$		0			0
$379$	−16.1028	+	16.1028i	−0.827143	+	0.827143i	−0.987121	−	0.159978i	$-0.948858\pi$
$379$	−16.1028	+	16.1028i	−0.827143	+	0.827143i	0.159978	+	0.987121i	$0.448858\pi$
$380$		0			0
$381$	1.50207	+	1.50207i	0.0769535	+	0.0769535i
$382$		0			0
$383$			23.1255i			1.18166i	0.806796	+	0.590830i	$0.201200\pi$
$383$			23.1255i			1.18166i	−0.806796	+	0.590830i	$0.798800\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.10474	+	1.10474i	−0.0561573	+	0.0561573i
$388$		0			0
$389$	19.4044	−	19.4044i	0.983842	−	0.983842i	−0.0160295	−	0.999872i	$-0.505103\pi$
$389$	19.4044	−	19.4044i	0.983842	−	0.983842i	0.999872	+	0.0160295i	$0.00510257\pi$
$390$		0			0
$391$		−	0.952310i		−	0.0481604i
$392$		0			0
$393$	−19.7348			−0.995491
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.00102	−	4.00102i	0.200806	−	0.200806i	−0.599540	−	0.800345i	$-0.704650\pi$
$397$	4.00102	−	4.00102i	0.200806	−	0.200806i	0.800345	+	0.599540i	$0.204650\pi$
$398$		0			0
$399$	9.67130			0.484171
$400$		0			0
$401$	38.9287			1.94401			0.972003	−	0.234967i	$-0.0754980\pi$
$401$	38.9287			1.94401			0.972003	+	0.234967i	$0.0754980\pi$
$402$		0			0
$403$	−19.7486	+	19.7486i	−0.983746	+	0.983746i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	12.8227			0.635598
$408$		0			0
$409$			4.59845i			0.227379i	0.993516	+	0.113689i	$0.0362669\pi$
$409$			4.59845i			0.227379i	−0.993516	+	0.113689i	$0.963733\pi$
$410$		0			0
$411$	16.7070	−	16.7070i	0.824095	−	0.824095i
$412$		0			0
$413$	−8.22174	+	8.22174i	−0.404565	+	0.404565i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	0.757161i		−	0.0370783i
$418$		0			0
$419$	16.6774	+	16.6774i	0.814746	+	0.814746i	0.985341	−	0.170595i	$-0.0545689\pi$
$419$	16.6774	+	16.6774i	0.814746	+	0.814746i	−0.170595	+	0.985341i	$0.554569\pi$
$420$		0			0
$421$	15.4169	−	15.4169i	0.751372	−	0.751372i	−0.223364	−	0.974735i	$-0.571704\pi$
$421$	15.4169	−	15.4169i	0.751372	−	0.751372i	0.974735	+	0.223364i	$0.0717037\pi$
$422$		0			0
$423$	−6.17987			−0.300476
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−2.93244	−	2.93244i	−0.141911	−	0.141911i
$428$		0			0
$429$	−14.1504	−	14.1504i	−0.683186	−	0.683186i
$430$		0			0
$431$	−20.2234			−0.974126			−0.487063	−	0.873367i	$-0.661932\pi$
$431$	−20.2234			−0.974126			−0.487063	+	0.873367i	$0.661932\pi$
$432$		0			0
$433$		−	0.676118i		−	0.0324922i	−0.999868	−	0.0162461i	$-0.994828\pi$
$433$		−	0.676118i		−	0.0324922i	0.999868	−	0.0162461i	$-0.00517152\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.83834	+	8.83834i	0.422795	+	0.422795i
$438$		0			0
$439$		−	13.3550i		−	0.637400i	−0.947856	−	0.318700i	$-0.896754\pi$
$439$		−	13.3550i		−	0.637400i	0.947856	−	0.318700i	$-0.103246\pi$
$440$		0			0
$441$		−	3.73366i		−	0.177794i
$442$		0			0
$443$	28.1262	+	28.1262i	1.33631	+	1.33631i	0.899600	+	0.436714i	$0.143858\pi$
$443$	28.1262	+	28.1262i	1.33631	+	1.33631i	0.436714	+	0.899600i	$0.356142\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	9.38805i		−	0.444039i
$448$		0			0
$449$	8.37972			0.395464			0.197732	−	0.980256i	$-0.436642\pi$
$449$	8.37972			0.395464			0.197732	+	0.980256i	$0.436642\pi$
$450$		0			0
$451$	−14.2981	−	14.2981i	−0.673271	−	0.673271i
$452$		0			0
$453$	−2.20607	−	2.20607i	−0.103650	−	0.103650i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.66561			−0.265026			−0.132513	−	0.991181i	$-0.542305\pi$
$457$	−5.66561			−0.265026			−0.132513	+	0.991181i	$0.542305\pi$
$458$		0			0
$459$	−1.93501	+	1.93501i	−0.0903186	+	0.0903186i
$460$		0			0
$461$	16.6375	+	16.6375i	0.774887	+	0.774887i	0.978956	−	0.204069i	$-0.0654168\pi$
$461$	16.6375	+	16.6375i	0.774887	+	0.774887i	−0.204069	+	0.978956i	$0.565417\pi$
$462$		0			0
$463$		−	41.6835i		−	1.93720i	−0.248631	−	0.968598i	$-0.579981\pi$
$463$		−	41.6835i		−	1.93720i	0.248631	−	0.968598i	$-0.420019\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.11020	−	3.11020i	0.143923	−	0.143923i	−0.631474	−	0.775397i	$-0.717550\pi$
$467$	3.11020	−	3.11020i	0.143923	−	0.143923i	0.775397	+	0.631474i	$0.217550\pi$
$468$		0			0
$469$	6.89057	−	6.89057i	0.318177	−	0.318177i
$470$		0			0
$471$		−	6.40370i		−	0.295067i
$472$		0			0
$473$	−5.04255			−0.231857
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−3.46383	+	3.46383i	−0.158598	+	0.158598i
$478$		0			0
$479$	−8.32325			−0.380299			−0.190149	−	0.981755i	$-0.560897\pi$
$479$	−8.32325			−0.380299			−0.190149	+	0.981755i	$0.560897\pi$
$480$		0			0
$481$	−41.9183			−1.91131
$482$		0			0
$483$	2.06569	−	2.06569i	0.0939920	−	0.0939920i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−7.29577			−0.330603			−0.165301	−	0.986243i	$-0.552860\pi$
$487$	−7.29577			−0.330603			−0.165301	+	0.986243i	$0.552860\pi$
$488$		0			0
$489$			12.5463i			0.567365i
$490$		0			0
$491$	−3.57528	+	3.57528i	−0.161350	+	0.161350i	−0.783165	−	0.621815i	$-0.786396\pi$
$491$	−3.57528	+	3.57528i	−0.161350	+	0.161350i	0.621815	+	0.783165i	$0.286396\pi$
$492$		0			0
$493$	1.83600	−	1.83600i	0.0826891	−	0.0826891i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		−	0.874479i		−	0.0392257i
$498$		0			0
$499$	−10.8833	−	10.8833i	−0.487203	−	0.487203i	0.420220	−	0.907422i	$-0.361953\pi$
$499$	−10.8833	−	10.8833i	−0.487203	−	0.487203i	−0.907422	+	0.420220i	$0.861953\pi$
$500$		0			0
$501$	−7.00295	+	7.00295i	−0.312869	+	0.312869i
$502$		0			0
$503$	−29.3781			−1.30991			−0.654953	−	0.755670i	$-0.727312\pi$
$503$	−29.3781			−1.30991			−0.654953	+	0.755670i	$0.727312\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	32.0682	+	32.0682i	1.42420	+	1.42420i
$508$		0			0
$509$	−17.4592	−	17.4592i	−0.773863	−	0.773863i	0.204916	−	0.978780i	$-0.434308\pi$
$509$	−17.4592	−	17.4592i	−0.773863	−	0.773863i	−0.978780	+	0.204916i	$0.934308\pi$
$510$		0			0
$511$	9.46222			0.418584
$512$		0			0
$513$		−	35.9175i		−	1.58579i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−14.1039	−	14.1039i	−0.620287	−	0.620287i
$518$		0			0
$519$		−	1.19138i		−	0.0522959i
$520$		0			0
$521$		−	9.48578i		−	0.415580i	−0.978174	−	0.207790i	$-0.933373\pi$
$521$		−	9.48578i		−	0.415580i	0.978174	−	0.207790i	$-0.0666270\pi$
$522$		0			0
$523$	16.2705	+	16.2705i	0.711460	+	0.711460i	0.966841	−	0.255380i	$-0.0822006\pi$
$523$	16.2705	+	16.2705i	0.711460	+	0.711460i	−0.255380	+	0.966841i	$0.582201\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			2.10265i			0.0915929i
$528$		0			0
$529$	−19.2245			−0.835846
$530$		0			0
$531$	5.20849	+	5.20849i	0.226029	+	0.226029i
$532$		0			0
$533$	46.7414	+	46.7414i	2.02459	+	2.02459i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	7.81028			0.337039
$538$		0			0
$539$	8.52106	−	8.52106i	0.367028	−	0.367028i
$540$		0			0
$541$	−2.55686	−	2.55686i	−0.109928	−	0.109928i	0.650003	−	0.759931i	$-0.274767\pi$
$541$	−2.55686	−	2.55686i	−0.109928	−	0.109928i	−0.759931	+	0.650003i	$0.774767\pi$
$542$		0			0
$543$		−	3.58416i		−	0.153811i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−21.9660	+	21.9660i	−0.939197	+	0.939197i	−0.998255	−	0.0590579i	$-0.981190\pi$
$547$	−21.9660	+	21.9660i	−0.939197	+	0.939197i	0.0590579	+	0.998255i	$0.481190\pi$
$548$		0			0
$549$	−1.85771	+	1.85771i	−0.0792852	+	0.0792852i
$550$		0			0
$551$			34.0796i			1.45184i
$552$		0			0
$553$	14.4002			0.612357
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−17.5409	+	17.5409i	−0.743234	+	0.743234i	−0.973199	−	0.229965i	$-0.926139\pi$
$557$	−17.5409	+	17.5409i	−0.743234	+	0.743234i	0.229965	+	0.973199i	$0.426139\pi$
$558$		0			0
$559$	16.4844			0.697217
$560$		0			0
$561$	−1.50661			−0.0636089
$562$		0			0
$563$	−27.5975	+	27.5975i	−1.16309	+	1.16309i	−0.179300	+	0.983794i	$0.557383\pi$
$563$	−27.5975	+	27.5975i	−1.16309	+	1.16309i	−0.983794	+	0.179300i	$0.942617\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−6.59190			−0.276834
$568$		0			0
$569$			23.6390i			0.990998i	0.868608	+	0.495499i	$0.165015\pi$
$569$			23.6390i			0.990998i	−0.868608	+	0.495499i	$0.834985\pi$
$570$		0			0
$571$	21.7518	−	21.7518i	0.910284	−	0.910284i	−0.0860105	−	0.996294i	$-0.527412\pi$
$571$	21.7518	−	21.7518i	0.910284	−	0.910284i	0.996294	+	0.0860105i	$0.0274118\pi$
$572$		0			0
$573$	−16.7401	+	16.7401i	−0.699329	+	0.699329i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	3.69585i		−	0.153860i	−0.997036	−	0.0769302i	$-0.975488\pi$
$577$		−	3.69585i		−	0.153860i	0.997036	−	0.0769302i	$-0.0245119\pi$
$578$		0			0
$579$	−0.0887116	−	0.0887116i	−0.00368673	−	0.00368673i
$580$		0			0
$581$	−0.793750	+	0.793750i	−0.0329303	+	0.0329303i
$582$		0			0
$583$	−15.8105			−0.654802
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−27.0313	−	27.0313i	−1.11570	−	1.11570i	−0.992365	−	0.123335i	$-0.960641\pi$
$587$	−27.0313	−	27.0313i	−1.11570	−	1.11570i	−0.123335	−	0.992365i	$-0.539359\pi$
$588$		0			0
$589$	−19.5146	−	19.5146i	−0.804085	−	0.804085i
$590$		0			0
$591$	−3.07189			−0.126361
$592$		0			0
$593$			4.55524i			0.187061i	0.995616	+	0.0935306i	$0.0298153\pi$
$593$			4.55524i			0.187061i	−0.995616	+	0.0935306i	$0.970185\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−15.6143	−	15.6143i	−0.639051	−	0.639051i
$598$		0			0
$599$		−	7.46846i		−	0.305153i	−0.988292	−	0.152576i	$-0.951243\pi$
$599$		−	7.46846i		−	0.305153i	0.988292	−	0.152576i	$-0.0487570\pi$
$600$		0			0
$601$			12.2638i			0.500250i	0.968214	+	0.250125i	$0.0804717\pi$
$601$			12.2638i			0.500250i	−0.968214	+	0.250125i	$0.919528\pi$
$602$		0			0
$603$	−4.36519	−	4.36519i	−0.177764	−	0.177764i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	5.23884i		−	0.212638i	−0.994332	−	0.106319i	$-0.966094\pi$
$607$		−	5.23884i		−	0.212638i	0.994332	−	0.106319i	$-0.0339065\pi$
$608$		0			0
$609$	7.96503			0.322759
$610$		0			0
$611$	46.1064	+	46.1064i	1.86527	+	1.86527i
$612$		0			0
$613$	−20.7209	−	20.7209i	−0.836910	−	0.836910i	0.151541	−	0.988451i	$-0.451576\pi$
$613$	−20.7209	−	20.7209i	−0.836910	−	0.836910i	−0.988451	+	0.151541i	$0.951576\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.20286			0.0886838			0.0443419	−	0.999016i	$-0.485881\pi$
$617$	2.20286			0.0886838			0.0443419	+	0.999016i	$0.485881\pi$
$618$		0			0
$619$	−31.4569	+	31.4569i	−1.26436	+	1.26436i	−0.315404	+	0.948958i	$0.602140\pi$
$619$	−31.4569	+	31.4569i	−1.26436	+	1.26436i	−0.948958	+	0.315404i	$0.897860\pi$
$620$		0			0
$621$	−7.67158	−	7.67158i	−0.307850	−	0.307850i
$622$		0			0
$623$		−	1.09473i		−	0.0438594i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	13.9827	−	13.9827i	0.558416	−	0.558416i
$628$		0			0
$629$	−2.23154	+	2.23154i	−0.0889775	+	0.0889775i
$630$		0			0
$631$			16.8215i			0.669655i	0.942279	+	0.334828i	$0.108678\pi$
$631$			16.8215i			0.669655i	−0.942279	+	0.334828i	$0.891322\pi$
$632$		0			0
$633$	18.9957			0.755011
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−27.8559	+	27.8559i	−1.10369	+	1.10369i
$638$		0			0
$639$	−0.553985			−0.0219153
$640$		0			0
$641$	−14.9208			−0.589336			−0.294668	−	0.955600i	$-0.595209\pi$
$641$	−14.9208			−0.589336			−0.294668	+	0.955600i	$0.595209\pi$
$642$		0			0
$643$	0.541845	−	0.541845i	0.0213683	−	0.0213683i	−0.696342	−	0.717710i	$-0.745190\pi$
$643$	0.541845	−	0.541845i	0.0213683	−	0.0213683i	0.717710	+	0.696342i	$0.245190\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−32.6391			−1.28318			−0.641588	−	0.767049i	$-0.721724\pi$
$647$	−32.6391			−1.28318			−0.641588	+	0.767049i	$0.721724\pi$
$648$		0			0
$649$			23.7739i			0.933208i
$650$		0			0
$651$	−4.56093	+	4.56093i	−0.178757	+	0.178757i
$652$		0			0
$653$	9.73805	−	9.73805i	0.381079	−	0.381079i	−0.490412	−	0.871491i	$-0.663154\pi$
$653$	9.73805	−	9.73805i	0.381079	−	0.381079i	0.871491	+	0.490412i	$0.163154\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	5.99434i		−	0.233862i
$658$		0			0
$659$	1.26445	+	1.26445i	0.0492560	+	0.0492560i	0.731306	−	0.682050i	$-0.238911\pi$
$659$	1.26445	+	1.26445i	0.0492560	+	0.0492560i	−0.682050	+	0.731306i	$0.738911\pi$
$660$		0			0
$661$	22.6701	−	22.6701i	0.881763	−	0.881763i	−0.111951	−	0.993714i	$-0.535710\pi$
$661$	22.6701	−	22.6701i	0.881763	−	0.881763i	0.993714	+	0.111951i	$0.0357099\pi$
$662$		0			0
$663$	4.92519			0.191279
$664$		0			0
$665$		0			0
$666$		0			0
$667$	7.27903	+	7.27903i	0.281845	+	0.281845i
$668$		0			0
$669$	−8.49339	−	8.49339i	−0.328373	−	0.328373i
$670$		0			0
$671$	−8.47943			−0.327345
$672$		0			0
$673$		−	3.58765i		−	0.138294i	−0.997606	−	0.0691469i	$-0.977972\pi$
$673$		−	3.58765i		−	0.138294i	0.997606	−	0.0691469i	$-0.0220277\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.1507	+	10.1507i	0.390124	+	0.390124i	0.874731	−	0.484608i	$-0.161038\pi$
$677$	10.1507	+	10.1507i	0.390124	+	0.390124i	−0.484608	+	0.874731i	$0.661038\pi$
$678$		0			0
$679$		−	7.34770i		−	0.281979i
$680$		0			0
$681$			4.70339i			0.180234i
$682$		0			0
$683$	16.6805	+	16.6805i	0.638260	+	0.638260i	0.950126	−	0.311866i	$-0.100954\pi$
$683$	16.6805	+	16.6805i	0.638260	+	0.638260i	−0.311866	+	0.950126i	$0.600954\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			16.6761i			0.636234i
$688$		0			0
$689$	51.6854			1.96906
$690$		0			0
$691$	−12.4781	−	12.4781i	−0.474689	−	0.474689i	0.428739	−	0.903428i	$-0.358958\pi$
$691$	−12.4781	−	12.4781i	−0.474689	−	0.474689i	−0.903428	+	0.428739i	$0.858958\pi$
$692$		0			0
$693$	0.846123	+	0.846123i	0.0321415	+	0.0321415i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.97661			0.188502
$698$		0			0
$699$	−8.20312	+	8.20312i	−0.310271	+	0.310271i
$700$		0			0
$701$	6.40945	+	6.40945i	0.242082	+	0.242082i	0.817711	−	0.575629i	$-0.195243\pi$
$701$	6.40945	+	6.40945i	0.242082	+	0.242082i	−0.575629	+	0.817711i	$0.695243\pi$
$702$		0			0
$703$		−	41.4217i		−	1.56225i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.53742	−	2.53742i	0.0954295	−	0.0954295i
$708$		0			0
$709$	−8.78514	+	8.78514i	−0.329933	+	0.329933i	−0.852561	−	0.522628i	$-0.824952\pi$
$709$	−8.78514	+	8.78514i	−0.329933	+	0.329933i	0.522628	+	0.852561i	$0.324952\pi$
$710$		0			0
$711$		−	9.12255i		−	0.342122i
$712$		0			0
$713$	−8.33621			−0.312194
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−22.4617	+	22.4617i	−0.838847	+	0.838847i
$718$		0			0
$719$	46.2329			1.72420			0.862099	−	0.506740i	$-0.169150\pi$
$719$	46.2329			1.72420			0.862099	+	0.506740i	$0.169150\pi$
$720$		0			0
$721$	−13.4544			−0.501069
$722$		0			0
$723$	25.4240	−	25.4240i	0.945530	−	0.945530i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	17.4640			0.647703			0.323852	−	0.946108i	$-0.395022\pi$
$727$	17.4640			0.647703			0.323852	+	0.946108i	$0.395022\pi$
$728$		0			0
$729$			30.0340i			1.11237i
$730$		0			0
$731$	0.877557	−	0.877557i	0.0324576	−	0.0324576i
$732$		0			0
$733$	7.89695	−	7.89695i	0.291680	−	0.291680i	−0.546063	−	0.837744i	$-0.683874\pi$
$733$	7.89695	−	7.89695i	0.291680	−	0.291680i	0.837744	+	0.546063i	$0.183874\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	19.9247i		−	0.733936i
$738$		0			0
$739$	26.1724	+	26.1724i	0.962769	+	0.962769i	0.999331	−	0.0365624i	$-0.0116408\pi$
$739$	26.1724	+	26.1724i	0.962769	+	0.962769i	−0.0365624	+	0.999331i	$0.511641\pi$
$740$		0			0
$741$	−45.7105	+	45.7105i	−1.67922	+	1.67922i
$742$		0			0
$743$	49.7660			1.82574			0.912868	−	0.408254i	$-0.133862\pi$
$743$	49.7660			1.82574			0.912868	+	0.408254i	$0.133862\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.502843	+	0.502843i	0.0183981	+	0.0183981i
$748$		0			0
$749$	9.63333	+	9.63333i	0.351994	+	0.351994i
$750$		0			0
$751$	24.2379			0.884454			0.442227	−	0.896903i	$-0.354189\pi$
$751$	24.2379			0.884454			0.442227	+	0.896903i	$0.354189\pi$
$752$		0			0
$753$			7.29665i			0.265905i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−15.4872	−	15.4872i	−0.562890	−	0.562890i	0.367237	−	0.930127i	$-0.380304\pi$
$757$	−15.4872	−	15.4872i	−0.562890	−	0.562890i	−0.930127	+	0.367237i	$0.880304\pi$
$758$		0			0
$759$		−	5.97312i		−	0.216811i
$760$		0			0
$761$		−	25.9821i		−	0.941849i	−0.882174	−	0.470924i	$-0.843920\pi$
$761$		−	25.9821i		−	0.941849i	0.882174	−	0.470924i	$-0.156080\pi$
$762$		0			0
$763$	−11.2443	−	11.2443i	−0.407072	−	0.407072i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	77.7185i		−	2.80625i
$768$		0			0
$769$	24.9737			0.900573			0.450287	−	0.892884i	$-0.351322\pi$
$769$	24.9737			0.900573			0.450287	+	0.892884i	$0.351322\pi$
$770$		0			0
$771$	24.5096	+	24.5096i	0.882691	+	0.882691i
$772$		0			0
$773$	1.32495	+	1.32495i	0.0476550	+	0.0476550i	0.730533	−	0.682878i	$-0.239272\pi$
$773$	1.32495	+	1.32495i	0.0476550	+	0.0476550i	−0.682878	+	0.730533i	$0.739272\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−9.68103			−0.347305
$778$		0			0
$779$	−46.1876	+	46.1876i	−1.65484	+	1.65484i
$780$		0			0
$781$	−1.26432	−	1.26432i	−0.0452409	−	0.0452409i
$782$		0			0
$783$		−	29.5807i		−	1.05713i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.647036	−	0.647036i	0.0230644	−	0.0230644i	−0.695481	−	0.718545i	$-0.744808\pi$
$787$	0.647036	−	0.647036i	0.0230644	−	0.0230644i	0.718545	+	0.695481i	$0.244808\pi$
$788$		0			0
$789$	8.99087	−	8.99087i	0.320084	−	0.320084i
$790$		0			0
$791$		−	16.7570i		−	0.595811i
$792$		0			0
$793$	27.7198			0.984360
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−18.3024	+	18.3024i	−0.648303	+	0.648303i	−0.952583	−	0.304280i	$-0.901584\pi$
$797$	−18.3024	+	18.3024i	−0.648303	+	0.648303i	0.304280	+	0.952583i	$0.401584\pi$
$798$		0			0
$799$	4.90900			0.173668
$800$		0			0
$801$	−0.693514			−0.0245041
$802$		0			0
$803$	13.6804	−	13.6804i	0.482772	−	0.482772i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−37.7593			−1.32919
$808$		0			0
$809$			32.4845i			1.14209i	0.820917	+	0.571047i	$0.193463\pi$
$809$			32.4845i			1.14209i	−0.820917	+	0.571047i	$0.806537\pi$
$810$		0			0
$811$	−7.69149	+	7.69149i	−0.270085	+	0.270085i	−0.829134	−	0.559049i	$-0.811166\pi$
$811$	−7.69149	+	7.69149i	−0.270085	+	0.270085i	0.559049	+	0.829134i	$0.311166\pi$
$812$		0			0
$813$	−13.6176	+	13.6176i	−0.477590	+	0.477590i
$814$		0			0
$815$		0			0
$816$		0			0
$817$			16.2891i			0.569884i
$818$		0			0
$819$	−2.76603	−	2.76603i	−0.0966529	−	0.0966529i
$820$		0			0
$821$	−10.5798	+	10.5798i	−0.369238	+	0.369238i	−0.867199	−	0.497961i	$-0.834082\pi$
$821$	−10.5798	+	10.5798i	−0.369238	+	0.369238i	0.497961	+	0.867199i	$0.334082\pi$
$822$		0			0
$823$	−4.85817			−0.169345			−0.0846726	−	0.996409i	$-0.526984\pi$
$823$	−4.85817			−0.169345			−0.0846726	+	0.996409i	$0.526984\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−8.02757	−	8.02757i	−0.279146	−	0.279146i	0.553622	−	0.832768i	$-0.313245\pi$
$827$	−8.02757	−	8.02757i	−0.279146	−	0.279146i	−0.832768	+	0.553622i	$0.813245\pi$
$828$		0			0
$829$	24.3613	+	24.3613i	0.846102	+	0.846102i	0.989644	−	0.143542i	$-0.0458493\pi$
$829$	24.3613	+	24.3613i	0.846102	+	0.846102i	−0.143542	+	0.989644i	$0.545849\pi$
$830$		0			0
$831$	−22.3952			−0.776881
$832$		0			0
$833$			2.96585i			0.102761i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	16.9385	+	16.9385i	0.585479	+	0.585479i
$838$		0			0
$839$			43.1207i			1.48869i	0.667794	+	0.744346i	$0.267239\pi$
$839$			43.1207i			1.48869i	−0.667794	+	0.744346i	$0.732761\pi$
$840$		0			0
$841$		−	0.932964i		−	0.0321712i
$842$		0			0
$843$	23.3666	+	23.3666i	0.804789	+	0.804789i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	6.85110i		−	0.235407i
$848$		0			0
$849$	16.1472			0.554169
$850$		0			0
$851$	−8.84723	−	8.84723i	−0.303279	−	0.303279i
$852$		0			0
$853$	−18.0611	−	18.0611i	−0.618401	−	0.618401i	0.326720	−	0.945121i	$-0.394057\pi$
$853$	−18.0611	−	18.0611i	−0.618401	−	0.618401i	−0.945121	+	0.326720i	$0.894057\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−35.8346			−1.22409			−0.612043	−	0.790825i	$-0.709652\pi$
$857$	−35.8346			−1.22409			−0.612043	+	0.790825i	$0.709652\pi$
$858$		0			0
$859$	−0.619460	+	0.619460i	−0.0211357	+	0.0211357i	−0.717596	−	0.696460i	$-0.754757\pi$
$859$	−0.619460	+	0.619460i	−0.0211357	+	0.0211357i	0.696460	+	0.717596i	$0.254757\pi$
$860$		0			0
$861$	10.7949	+	10.7949i	0.367890	+	0.367890i
$862$		0			0
$863$			18.8270i			0.640878i	0.947269	+	0.320439i	$0.103830\pi$
$863$			18.8270i			0.640878i	−0.947269	+	0.320439i	$0.896170\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−18.2944	+	18.2944i	−0.621309	+	0.621309i
$868$		0			0
$869$	20.8197	−	20.8197i	0.706260	−	0.706260i
$870$		0			0
$871$			65.1352i			2.20702i
$872$		0			0
$873$	−4.65479			−0.157541
$874$		0			0
$875$		0			0
$876$		0			0
$877$	7.77833	−	7.77833i	0.262656	−	0.262656i	−0.563476	−	0.826132i	$-0.690536\pi$
$877$	7.77833	−	7.77833i	0.262656	−	0.262656i	0.826132	+	0.563476i	$0.190536\pi$
$878$		0			0
$879$	−1.21541			−0.0409946
$880$		0			0
$881$	13.6551			0.460052			0.230026	−	0.973184i	$-0.426119\pi$
$881$	13.6551			0.460052			0.230026	+	0.973184i	$0.426119\pi$
$882$		0			0
$883$	25.7585	−	25.7585i	0.866844	−	0.866844i	−0.125278	−	0.992122i	$-0.539982\pi$
$883$	25.7585	−	25.7585i	0.866844	−	0.866844i	0.992122	+	0.125278i	$0.0399823\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−38.8982			−1.30607			−0.653037	−	0.757326i	$-0.726505\pi$
$887$	−38.8982			−1.30607			−0.653037	+	0.757326i	$0.726505\pi$
$888$		0			0
$889$			1.34020i			0.0449488i
$890$		0			0
$891$	−9.53054	+	9.53054i	−0.319285	+	0.319285i
$892$		0			0
$893$	−45.5602	+	45.5602i	−1.52461	+	1.52461i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			19.5265i			0.651972i
$898$		0			0
$899$	−16.0717	−	16.0717i	−0.536022	−	0.536022i
$900$		0			0
$901$	2.75150	−	2.75150i	0.0916658	−	0.0916658i
$902$		0			0
$903$	3.80707			0.126692
$904$		0			0
$905$		0			0
$906$		0			0
$907$	5.10220	+	5.10220i	0.169416	+	0.169416i	0.786723	−	0.617307i	$-0.211776\pi$
$907$	5.10220	+	5.10220i	0.169416	+	0.169416i	−0.617307	+	0.786723i	$0.711776\pi$
$908$		0			0
$909$	−1.60746	−	1.60746i	−0.0533162	−	0.0533162i
$910$		0			0
$911$	46.7058			1.54743			0.773716	−	0.633533i	$-0.218396\pi$
$911$	46.7058			1.54743			0.773716	+	0.633533i	$0.218396\pi$
$912$		0			0
$913$			2.29520i			0.0759601i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.80402	−	8.80402i	−0.290734	−	0.290734i
$918$		0			0
$919$		−	53.4692i		−	1.76379i	−0.471449	−	0.881893i	$-0.656269\pi$
$919$		−	53.4692i		−	1.76379i	0.471449	−	0.881893i	$-0.343731\pi$
$920$		0			0
$921$			21.3259i			0.702712i
$922$		0			0
$923$	4.13314	+	4.13314i	0.136044	+	0.136044i
$924$		0			0
$925$		0			0
$926$		0			0
$927$			8.52342i			0.279946i
$928$		0			0
$929$	−14.2098			−0.466209			−0.233104	−	0.972452i	$-0.574888\pi$
$929$	−14.2098			−0.466209			−0.233104	+	0.972452i	$0.574888\pi$
$930$		0			0
$931$	−27.5259	−	27.5259i	−0.902125	−	0.902125i
$932$		0			0
$933$	33.4972	+	33.4972i	1.09665	+	1.09665i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	5.26656			0.172051			0.0860255	−	0.996293i	$-0.472583\pi$
$937$	5.26656			0.172051			0.0860255	+	0.996293i	$0.472583\pi$
$938$		0			0
$939$	−1.86796	+	1.86796i	−0.0609585	+	0.0609585i
$940$		0			0
$941$	18.7780	+	18.7780i	0.612145	+	0.612145i	0.943505	−	0.331359i	$-0.107507\pi$
$941$	18.7780	+	18.7780i	0.612145	+	0.612145i	−0.331359	+	0.943505i	$0.607507\pi$
$942$		0			0
$943$			19.7304i			0.642509i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.27572	−	3.27572i	0.106447	−	0.106447i	−0.651878	−	0.758324i	$-0.726018\pi$
$947$	3.27572	−	3.27572i	0.106447	−	0.106447i	0.758324	+	0.651878i	$0.226018\pi$
$948$		0			0
$949$	−44.7223	+	44.7223i	−1.45175	+	1.45175i
$950$		0			0
$951$			21.9142i			0.710616i
$952$		0			0
$953$	30.0292			0.972741			0.486371	−	0.873753i	$-0.338320\pi$
$953$	30.0292			0.972741			0.486371	+	0.873753i	$0.338320\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	11.5158	−	11.5158i	0.372253	−	0.372253i
$958$		0			0
$959$	14.9065			0.481356
$960$		0			0
$961$	−12.5941			−0.406260
$962$		0			0
$963$	6.10274	−	6.10274i	0.196658	−	0.196658i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−15.2196			−0.489429			−0.244715	−	0.969595i	$-0.578694\pi$
$967$	−15.2196			−0.489429			−0.244715	+	0.969595i	$0.578694\pi$
$968$		0			0
$969$			4.86684i			0.156345i
$970$		0			0
$971$	18.4838	−	18.4838i	0.593173	−	0.593173i	−0.345314	−	0.938487i	$-0.612228\pi$
$971$	18.4838	−	18.4838i	0.593173	−	0.593173i	0.938487	+	0.345314i	$0.112228\pi$
$972$		0			0
$973$	0.337781	−	0.337781i	0.0108288	−	0.0108288i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	18.7912i		−	0.601183i	−0.953753	−	0.300592i	$-0.902816\pi$
$977$		−	18.7912i		−	0.601183i	0.953753	−	0.300592i	$-0.0971841\pi$
$978$		0			0
$979$	−1.58276	−	1.58276i	−0.0505851	−	0.0505851i
$980$		0			0
$981$	−7.12331	+	7.12331i	−0.227430	+	0.227430i
$982$		0			0
$983$	−56.5605			−1.80400			−0.901999	−	0.431738i	$-0.857901\pi$
$983$	−56.5605			−1.80400			−0.901999	+	0.431738i	$0.857901\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	10.6483	+	10.6483i	0.338938	+	0.338938i
$988$		0			0
$989$	3.47918	+	3.47918i	0.110632	+	0.110632i
$990$		0			0
$991$	−45.0866			−1.43222			−0.716112	−	0.697985i	$-0.754080\pi$
$991$	−45.0866			−1.43222			−0.716112	+	0.697985i	$0.754080\pi$
$992$		0			0
$993$		−	17.2404i		−	0.547108i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−35.1508	−	35.1508i	−1.11324	−	1.11324i	−0.992710	−	0.120528i	$-0.961541\pi$
$997$	−35.1508	−	35.1508i	−1.11324	−	1.11324i	−0.120528	−	0.992710i	$-0.538459\pi$
$998$		0			0
$999$			35.9536i			1.13752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.q.f.849.2		12
4.3	odd	2		400.2.q.f.349.2		12
5.2	odd	4		1600.2.l.f.401.5		12
5.3	odd	4		1600.2.l.g.401.2		12
5.4	even	2		1600.2.q.e.849.5		12
16.5	even	4		1600.2.q.e.49.5		12
16.11	odd	4		400.2.q.e.149.5		12
20.3	even	4		400.2.l.f.301.2	yes	12
20.7	even	4		400.2.l.g.301.5	yes	12
20.19	odd	2		400.2.q.e.349.5		12
80.27	even	4		400.2.l.g.101.5	yes	12
80.37	odd	4		1600.2.l.f.1201.5		12
80.43	even	4		400.2.l.f.101.2	✓	12
80.53	odd	4		1600.2.l.g.1201.2		12
80.59	odd	4		400.2.q.f.149.2		12
80.69	even	4	inner	1600.2.q.f.49.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.2	✓	12	80.43	even	4
400.2.l.f.301.2	yes	12	20.3	even	4
400.2.l.g.101.5	yes	12	80.27	even	4
400.2.l.g.301.5	yes	12	20.7	even	4
400.2.q.e.149.5		12	16.11	odd	4
400.2.q.e.349.5		12	20.19	odd	2
400.2.q.f.149.2		12	80.59	odd	4
400.2.q.f.349.2		12	4.3	odd	2
1600.2.l.f.401.5		12	5.2	odd	4
1600.2.l.f.1201.5		12	80.37	odd	4
1600.2.l.g.401.2		12	5.3	odd	4
1600.2.l.g.1201.2		12	80.53	odd	4
1600.2.q.e.49.5		12	16.5	even	4
1600.2.q.e.849.5		12	5.4	even	2
1600.2.q.f.49.2		12	80.69	even	4	inner
1600.2.q.f.849.2		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09156 + 1.09156i) q^{3} -0.973926 q^{7} +0.616985i q^{9} +O(q^{10})\)	\(q+(-1.09156 + 1.09156i) q^{3} -0.973926 q^{7} +0.616985i q^{9} +(-1.40810 + 1.40810i) q^{11} +(4.60317 - 4.60317i) q^{13} -0.490104i q^{17} +(4.54863 + 4.54863i) q^{19} +(1.06310 - 1.06310i) q^{21} +1.94308 q^{23} +(-3.94816 - 3.94816i) q^{27} +(3.74613 + 3.74613i) q^{29} -4.29021 q^{31} -3.07405i q^{33} +(-4.55320 - 4.55320i) q^{37} +10.0493i q^{39} +10.1542i q^{41} +(1.79055 + 1.79055i) q^{43} +10.0162i q^{47} -6.05147 q^{49} +(0.534979 + 0.534979i) q^{51} +(5.61412 + 5.61412i) q^{53} -9.93022 q^{57} +(8.44185 - 8.44185i) q^{59} +(3.01095 + 3.01095i) q^{61} -0.600897i q^{63} +(-7.07504 + 7.07504i) q^{67} +(-2.12099 + 2.12099i) q^{69} +0.897891i q^{71} -9.71555 q^{73} +(1.37138 - 1.37138i) q^{77} -14.7857 q^{79} +6.76838 q^{81} +(0.815000 - 0.815000i) q^{83} -8.17827 q^{87} +1.12404i q^{89} +(-4.48314 + 4.48314i) q^{91} +(4.68303 - 4.68303i) q^{93} +7.54442i q^{97} +(-0.868775 - 0.868775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3} - 12 q^{7}+O(q^{10}) \) 12 * q + 2 * q^3 - 12 * q^7	\( 12 q + 2 q^{3} - 12 q^{7} + 2 q^{11} + 4 q^{13} - 14 q^{19} - 20 q^{21} - 12 q^{23} - 10 q^{27} + 4 q^{31} - 8 q^{37} - 4 q^{49} - 10 q^{51} - 16 q^{53} - 16 q^{57} + 20 q^{59} + 4 q^{61} - 50 q^{67} + 40 q^{73} - 8 q^{77} + 12 q^{79} - 8 q^{81} - 2 q^{83} + 64 q^{87} + 44 q^{93} + 12 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 - 12 * q^7 + 2 * q^11 + 4 * q^13 - 14 * q^19 - 20 * q^21 - 12 * q^23 - 10 * q^27 + 4 * q^31 - 8 * q^37 - 4 * q^49 - 10 * q^51 - 16 * q^53 - 16 * q^57 + 20 * q^59 + 4 * q^61 - 50 * q^67 + 40 * q^73 - 8 * q^77 + 12 * q^79 - 8 * q^81 - 2 * q^83 + 64 * q^87 + 44 * q^93 + 12 * q^99

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