LMFDB - Embedded newform 1600.2.l.g.401.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(401,1600)]

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, 3, 0]))

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

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

chi := DirichletCharacter("1600.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.l (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			401.2
Root			$1.22306 - 0.710021i$ of defining polynomial
Character	$\chi$	$=$	1600.401
Dual form			1600.2.l.g.1201.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09156 - 1.09156i) q^{3} +0.973926i q^{7} -0.616985i q^{9} +O(q^{10})$	$q+(-1.09156 - 1.09156i) q^{3} +0.973926i q^{7} -0.616985i q^{9} +(-1.40810 + 1.40810i) q^{11} +(4.60317 + 4.60317i) q^{13} -0.490104 q^{17} +(-4.54863 - 4.54863i) q^{19} +(1.06310 - 1.06310i) q^{21} +1.94308i q^{23} +(-3.94816 + 3.94816i) q^{27} +(-3.74613 - 3.74613i) q^{29} -4.29021 q^{31} +3.07405 q^{33} +(-4.55320 + 4.55320i) q^{37} -10.0493i q^{39} +10.1542i q^{41} +(-1.79055 + 1.79055i) q^{43} +10.0162 q^{47} +6.05147 q^{49} +(0.534979 + 0.534979i) q^{51} +(-5.61412 + 5.61412i) q^{53} +9.93022i q^{57} +(-8.44185 + 8.44185i) q^{59} +(3.01095 + 3.01095i) q^{61} +0.600897 q^{63} +(7.07504 + 7.07504i) q^{67} +(2.12099 - 2.12099i) q^{69} +0.897891i q^{71} -9.71555i q^{73} +(-1.37138 - 1.37138i) q^{77} +14.7857 q^{79} +6.76838 q^{81} +(0.815000 + 0.815000i) q^{83} +8.17827i q^{87} -1.12404i q^{89} +(-4.48314 + 4.48314i) q^{91} +(4.68303 + 4.68303i) q^{93} +7.54442 q^{97} +(0.868775 + 0.868775i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3}+O(q^{10}) $ 12 * q + 2 * q^3	$ 12 q + 2 q^{3} + 2 q^{11} + 4 q^{13} + 8 q^{17} + 14 q^{19} - 20 q^{21} - 10 q^{27} + 4 q^{31} - 28 q^{33} - 8 q^{37} + 8 q^{47} + 4 q^{49} - 10 q^{51} + 16 q^{53} - 20 q^{59} + 4 q^{61} - 8 q^{63} + 50 q^{67} + 8 q^{77} - 12 q^{79} - 8 q^{81} - 2 q^{83} + 44 q^{93} - 12 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 + 2 * q^11 + 4 * q^13 + 8 * q^17 + 14 * q^19 - 20 * q^21 - 10 * q^27 + 4 * q^31 - 28 * q^33 - 8 * q^37 + 8 * q^47 + 4 * q^49 - 10 * q^51 + 16 * q^53 - 20 * q^59 + 4 * q^61 - 8 * q^63 + 50 * q^67 + 8 * q^77 - 12 * q^79 - 8 * q^81 - 2 * q^83 + 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	0.317908	−	0.948122i	$-0.397020\pi$
$3$	−1.09156	−	1.09156i	−0.630214	−	0.630214i	−0.948122	+	0.317908i	$0.897020\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			0.973926i			0.368109i	0.982916	+	0.184055i	$0.0589224\pi$
$7$			0.973926i			0.368109i	−0.982916	+	0.184055i	$0.941078\pi$
$8$		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	0.942510	+	0.334179i	$0.108459\pi$
$13$	4.60317	+	4.60317i	1.27669	+	1.27669i	0.334179	+	0.942510i	$0.391541\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.490104			−0.118868			−0.0594338	−	0.998232i	$-0.518930\pi$
$17$	−0.490104			−0.118868			−0.0594338	+	0.998232i	$0.518930\pi$
$18$		0			0
$19$	−4.54863	−	4.54863i	−1.04353	−	1.04353i	−0.999009	−	0.0445187i	$-0.985825\pi$
$19$	−4.54863	−	4.54863i	−1.04353	−	1.04353i	−0.0445187	−	0.999009i	$-0.514175\pi$
$20$		0			0
$21$	1.06310	−	1.06310i	0.231988	−	0.231988i
$22$		0			0
$23$			1.94308i			0.405160i	0.979266	+	0.202580i	$0.0649325\pi$
$23$			1.94308i			0.405160i	−0.979266	+	0.202580i	$0.935067\pi$
$24$		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	0.267827	−	0.963467i	$-0.413694\pi$
$29$	−3.74613	−	3.74613i	−0.695640	−	0.695640i	−0.963467	+	0.267827i	$0.913694\pi$
$30$		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
$33$	3.07405			0.535124
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.55320	+	4.55320i	−0.748542	+	0.748542i	−0.974205	−	0.225663i	$-0.927545\pi$
$37$	−4.55320	+	4.55320i	−0.748542	+	0.748542i	0.225663	+	0.974205i	$0.427545\pi$
$38$		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	$-0.811848\pi$
$43$	−1.79055	+	1.79055i	−0.273057	+	0.273057i	0.557273	+	0.830329i	$0.311848\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	10.0162			1.46102			0.730510	−	0.682902i	$-0.239283\pi$
$47$	10.0162			1.46102			0.730510	+	0.682902i	$0.239283\pi$
$48$		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	$-0.933581\pi$
$53$	−5.61412	+	5.61412i	−0.771158	+	0.771158i	0.207151	+	0.978309i	$0.433581\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			9.93022i			1.31529i
$58$		0			0
$59$	−8.44185	+	8.44185i	−1.09904	+	1.09904i	−0.104512	+	0.994524i	$0.533328\pi$
$59$	−8.44185	+	8.44185i	−1.09904	+	1.09904i	−0.994524	+	0.104512i	$0.966672\pi$
$60$		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
$63$	0.600897			0.0757060
$64$		0			0
$65$		0			0
$66$		0			0
$67$	7.07504	+	7.07504i	0.864354	+	0.864354i	0.991840	−	0.127486i	$-0.0406908\pi$
$67$	7.07504	+	7.07504i	0.864354	+	0.864354i	−0.127486	+	0.991840i	$0.540691\pi$
$68$		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
$73$		−	9.71555i		−	1.13712i	−0.822642	−	0.568559i	$-0.807501\pi$
$73$		−	9.71555i		−	1.13712i	0.822642	−	0.568559i	$-0.192499\pi$
$74$		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	$-0.187334\pi$
$79$	14.7857			1.66352			0.831760	+	0.555135i	$0.187334\pi$
$80$		0			0
$81$	6.76838			0.752042
$82$		0			0
$83$	0.815000	+	0.815000i	0.0894579	+	0.0894579i	0.750420	−	0.660962i	$-0.229851\pi$
$83$	0.815000	+	0.815000i	0.0894579	+	0.0894579i	−0.660962	+	0.750420i	$0.729851\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			8.17827i			0.876803i
$88$		0			0
$89$		−	1.12404i		−	0.119148i	−0.998224	−	0.0595739i	$-0.981026\pi$
$89$		−	1.12404i		−	0.119148i	0.998224	−	0.0595739i	$-0.0189742\pi$
$90$		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
$97$	7.54442			0.766019			0.383010	−	0.923744i	$-0.374888\pi$
$97$	7.54442			0.766019			0.383010	+	0.923744i	$0.374888\pi$
$98$		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
$103$			13.8146i			1.36120i	0.732657	+	0.680598i	$0.238280\pi$
$103$			13.8146i			1.36120i	−0.732657	+	0.680598i	$0.761720\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.89124	+	9.89124i	−0.956222	+	0.956222i	−0.999081	−	0.0428589i	$-0.986353\pi$
$107$	−9.89124	+	9.89124i	−0.956222	+	0.956222i	0.0428589	+	0.999081i	$0.486353\pi$
$108$		0			0
$109$	−11.5454	−	11.5454i	−1.10584	−	1.10584i	−0.993691	−	0.112154i	$-0.964225\pi$
$109$	−11.5454	−	11.5454i	−1.10584	−	1.10584i	−0.112154	−	0.993691i	$-0.535775\pi$
$110$		0			0
$111$	9.94021			0.943483
$112$		0			0
$113$	−17.2057			−1.61857			−0.809286	−	0.587415i	$-0.800146\pi$
$113$	−17.2057			−1.61857			−0.809286	+	0.587415i	$0.800146\pi$
$114$		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
$127$	−1.37608			−0.122107			−0.0610535	−	0.998134i	$-0.519446\pi$
$127$	−1.37608			−0.122107			−0.0610535	+	0.998134i	$0.519446\pi$
$128$		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
$137$			15.3056i			1.30764i	0.756649	+	0.653822i	$0.226835\pi$
$137$			15.3056i			1.30764i	−0.756649	+	0.653822i	$0.773165\pi$
$138$		0			0
$139$	0.346824	−	0.346824i	0.0294173	−	0.0294173i	−0.692245	−	0.721662i	$-0.743378\pi$
$139$	0.346824	−	0.346824i	0.0294173	−	0.0294173i	0.721662	+	0.692245i	$0.243378\pi$
$140$		0			0
$141$	−10.9334	−	10.9334i	−0.920754	−	0.920754i
$142$		0			0
$143$	−12.9634			−1.08406
$144$		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	−0.508669	−	0.860962i	$-0.669862\pi$
$149$	4.30028	−	4.30028i	0.352293	−	0.352293i	0.860962	+	0.508669i	$0.169862\pi$
$150$		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
$153$			0.302387i			0.0244465i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.93327	+	2.93327i	0.234101	+	0.234101i	0.814402	−	0.580301i	$-0.197065\pi$
$157$	2.93327	+	2.93327i	0.234101	+	0.234101i	−0.580301	+	0.814402i	$0.697065\pi$
$158$		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	0.895400	−	0.445263i	$-0.146890\pi$
$163$	5.74697	+	5.74697i	0.450137	+	0.450137i	−0.445263	+	0.895400i	$0.646890\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	6.41553i		−	0.496449i	−0.968703	−	0.248224i	$-0.920153\pi$
$167$		−	6.41553i		−	0.496449i	0.968703	−	0.248224i	$-0.0798470\pi$
$168$		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	0.686057	−	0.727548i	$-0.259340\pi$
$173$	−0.545724	−	0.545724i	−0.0414907	−	0.0414907i	−0.727548	+	0.686057i	$0.759340\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	18.4296			1.38525
$178$		0			0
$179$	3.57757	+	3.57757i	0.267400	+	0.267400i	0.828052	−	0.560652i	$-0.189449\pi$
$179$	3.57757	+	3.57757i	0.267400	+	0.267400i	−0.560652	+	0.828052i	$0.689449\pi$
$180$		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
$183$		−	6.57328i		−	0.485911i
$184$		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
$193$	−0.0812703			−0.00584996			−0.00292498	−	0.999996i	$-0.500931\pi$
$193$	−0.0812703			−0.00584996			−0.00292498	+	0.999996i	$0.500931\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.40711	−	1.40711i	0.100252	−	0.100252i	−0.655202	−	0.755454i	$-0.727416\pi$
$197$	1.40711	−	1.40711i	0.100252	−	0.100252i	0.755454	+	0.655202i	$0.227416\pi$
$198$		0			0
$199$		−	14.3046i		−	1.01402i	−0.861939	−	0.507011i	$-0.830750\pi$
$199$		−	14.3046i		−	1.01402i	0.861939	−	0.507011i	$-0.169250\pi$
$200$		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
$207$	1.19885			0.0833258
$208$		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
$217$		−	4.17835i		−	0.283645i
$218$		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
$223$	−7.78095			−0.521051			−0.260525	−	0.965467i	$-0.583896\pi$
$223$	−7.78095			−0.521051			−0.260525	+	0.965467i	$0.583896\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.15443	−	2.15443i	−0.142995	−	0.142995i	0.631986	−	0.774980i	$-0.282240\pi$
$227$	−2.15443	−	2.15443i	−0.142995	−	0.142995i	−0.774980	+	0.631986i	$0.782240\pi$
$228$		0			0
$229$	−7.63865	+	7.63865i	−0.504776	+	0.504776i	−0.912918	−	0.408142i	$-0.866177\pi$
$229$	−7.63865	+	7.63865i	−0.504776	+	0.504776i	0.408142	+	0.912918i	$0.366177\pi$
$230$		0			0
$231$			2.99390i			0.196984i
$232$		0			0
$233$			7.51503i			0.492326i	0.969228	+	0.246163i	$0.0791699\pi$
$233$			7.51503i			0.492326i	−0.969228	+	0.246163i	$0.920830\pi$
$234$		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	$-0.731793\pi$
$239$	−20.5776			−1.33105			−0.665526	+	0.746375i	$0.731793\pi$
$240$		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
$247$		−	41.8762i		−	2.66452i
$248$		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
$257$	−22.4537			−1.40062			−0.700311	−	0.713838i	$-0.746955\pi$
$257$	−22.4537			−1.40062			−0.700311	+	0.713838i	$0.746955\pi$
$258$		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
$263$		−	8.23670i		−	0.507897i	−0.967218	−	0.253948i	$-0.918271\pi$
$263$		−	8.23670i		−	0.507897i	0.967218	−	0.253948i	$-0.0817294\pi$
$264$		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	$-0.982124\pi$
$269$	−17.2960	−	17.2960i	−1.05455	−	1.05455i	−0.0561306	−	0.998423i	$-0.517876\pi$
$270$		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
$273$	9.78726			0.592352
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.2583	−	10.2583i	0.616363	−	0.616363i	−0.328234	−	0.944597i	$-0.606453\pi$
$277$	10.2583	−	10.2583i	0.616363	−	0.616363i	0.944597	+	0.328234i	$0.106453\pi$
$278$		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	$-0.649372\pi$
$283$	7.39635	−	7.39635i	0.439668	−	0.439668i	0.891900	+	0.452232i	$0.149372\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.88942			−0.583754
$288$		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	$-0.757321\pi$
$293$	−0.556728	+	0.556728i	−0.0325244	+	0.0325244i	0.690658	+	0.723182i	$0.257321\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	11.1188i		−	0.645178i
$298$		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
$303$	5.68781			0.326756
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−9.76852	−	9.76852i	−0.557519	−	0.557519i	0.371082	−	0.928600i	$-0.378987\pi$
$307$	−9.76852	−	9.76852i	−0.557519	−	0.557519i	−0.928600	+	0.371082i	$0.878987\pi$
$308$		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
$313$			1.71127i			0.0967268i	0.998830	+	0.0483634i	$0.0154006\pi$
$313$			1.71127i			0.0967268i	−0.998830	+	0.0483634i	$0.984599\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.0380	−	10.0380i	−0.563790	−	0.563790i	0.366592	−	0.930382i	$-0.380524\pi$
$317$	−10.0380	−	10.0380i	−0.563790	−	0.563790i	−0.930382	+	0.366592i	$0.880524\pi$
$318$		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
$327$			25.2049i			1.39384i
$328$		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
$337$	−3.46077			−0.188520			−0.0942601	−	0.995548i	$-0.530049\pi$
$337$	−3.46077			−0.188520			−0.0942601	+	0.995548i	$0.530049\pi$
$338$		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
$343$			12.7112i			0.686338i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.4637	−	17.4637i	0.937498	−	0.937498i	−0.0606600	−	0.998158i	$-0.519321\pi$
$347$	17.4637	−	17.4637i	0.937498	−	0.937498i	0.998158	+	0.0606600i	$0.0193205\pi$
$348$		0			0
$349$	24.2159	+	24.2159i	1.29625	+	1.29625i	0.930852	+	0.365397i	$0.119067\pi$
$349$	24.2159	+	24.2159i	1.29625	+	1.29625i	0.365397	+	0.930852i	$0.380933\pi$
$350$		0			0
$351$	−36.3481			−1.94012
$352$		0			0
$353$	−10.7028			−0.569650			−0.284825	−	0.958580i	$-0.591935\pi$
$353$	−10.7028			−0.569650			−0.284825	+	0.958580i	$0.591935\pi$
$354$		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	$0.214416\pi$
$359$			23.6390i			1.24762i	−0.781577	+	0.623809i	$0.785584\pi$
$360$		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
$367$	13.7431			0.717386			0.358693	−	0.933456i	$-0.383223\pi$
$367$	13.7431			0.717386			0.358693	+	0.933456i	$0.383223\pi$
$368$		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	$-0.513606\pi$
$373$	18.4703	−	18.4703i	0.956355	−	0.956355i	0.999087	+	0.0427313i	$0.0136059\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	34.4881i		−	1.77623i
$378$		0			0
$379$	16.1028	−	16.1028i	0.827143	−	0.827143i	−0.159978	−	0.987121i	$-0.551142\pi$
$379$	16.1028	−	16.1028i	0.827143	−	0.827143i	0.987121	+	0.159978i	$0.0511423\pi$
$380$		0			0
$381$	1.50207	+	1.50207i	0.0769535	+	0.0769535i
$382$		0			0
$383$	−23.1255			−1.18166			−0.590830	−	0.806796i	$-0.701200\pi$
$383$	−23.1255			−1.18166			−0.590830	+	0.806796i	$0.701200\pi$
$384$		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	−0.999872	−	0.0160295i	$-0.994897\pi$
$389$	−19.4044	+	19.4044i	−0.983842	+	0.983842i	0.0160295	+	0.999872i	$0.494897\pi$
$390$		0			0
$391$		−	0.952310i		−	0.0481604i
$392$		0			0
$393$		−	19.7348i		−	0.995491i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−4.00102	−	4.00102i	−0.200806	−	0.200806i	0.599540	−	0.800345i	$-0.295350\pi$
$397$	−4.00102	−	4.00102i	−0.200806	−	0.200806i	−0.800345	+	0.599540i	$0.795350\pi$
$398$		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
$407$		−	12.8227i		−	0.635598i
$408$		0			0
$409$		−	4.59845i		−	0.227379i	−0.993516	−	0.113689i	$-0.963733\pi$
$409$		−	4.59845i		−	0.227379i	0.993516	−	0.113689i	$-0.0362669\pi$
$410$		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
$417$	−0.757161			−0.0370783
$418$		0			0
$419$	−16.6774	−	16.6774i	−0.814746	−	0.814746i	0.170595	−	0.985341i	$-0.445431\pi$
$419$	−16.6774	−	16.6774i	−0.814746	−	0.814746i	−0.985341	+	0.170595i	$0.945431\pi$
$420$		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
$423$		−	6.17987i		−	0.300476i
$424$		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
$433$	0.676118			0.0324922			0.0162461	−	0.999868i	$-0.494828\pi$
$433$	0.676118			0.0324922			0.0162461	+	0.999868i	$0.494828\pi$
$434$		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	$0.103246\pi$
$439$			13.3550i			0.637400i	−0.947856	+	0.318700i	$0.896754\pi$
$440$		0			0
$441$		−	3.73366i		−	0.177794i
$442$		0			0
$443$	−28.1262	+	28.1262i	−1.33631	+	1.33631i	−0.436714	+	0.899600i	$0.643858\pi$
$443$	−28.1262	+	28.1262i	−1.33631	+	1.33631i	−0.899600	+	0.436714i	$0.856142\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−9.38805			−0.444039
$448$		0			0
$449$	−8.37972			−0.395464			−0.197732	−	0.980256i	$-0.563358\pi$
$449$	−8.37972			−0.395464			−0.197732	+	0.980256i	$0.563358\pi$
$450$		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
$457$			5.66561i			0.265026i	0.991181	+	0.132513i	$0.0423046\pi$
$457$			5.66561i			0.265026i	−0.991181	+	0.132513i	$0.957695\pi$
$458$		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
$463$	41.6835			1.93720			0.968598	−	0.248631i	$-0.0799808\pi$
$463$	41.6835			1.93720			0.968598	+	0.248631i	$0.0799808\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.11020	−	3.11020i	−0.143923	−	0.143923i	0.631474	−	0.775397i	$-0.282450\pi$
$467$	−3.11020	−	3.11020i	−0.143923	−	0.143923i	−0.775397	+	0.631474i	$0.782450\pi$
$468$		0			0
$469$	−6.89057	+	6.89057i	−0.318177	+	0.318177i
$470$		0			0
$471$		−	6.40370i		−	0.295067i
$472$		0			0
$473$		−	5.04255i		−	0.231857i
$474$		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	$-0.439103\pi$
$479$	8.32325			0.380299			0.190149	+	0.981755i	$0.439103\pi$
$480$		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
$487$			7.29577i			0.330603i	0.986243	+	0.165301i	$0.0528597\pi$
$487$			7.29577i			0.330603i	−0.986243	+	0.165301i	$0.947140\pi$
$488$		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
$497$	−0.874479			−0.0392257
$498$		0			0
$499$	10.8833	+	10.8833i	0.487203	+	0.487203i	0.907422	−	0.420220i	$-0.138047\pi$
$499$	10.8833	+	10.8833i	0.487203	+	0.487203i	−0.420220	+	0.907422i	$0.638047\pi$
$500$		0			0
$501$	−7.00295	+	7.00295i	−0.312869	+	0.312869i
$502$		0			0
$503$		−	29.3781i		−	1.30991i	−0.755670	−	0.654953i	$-0.772688\pi$
$503$		−	29.3781i		−	1.30991i	0.755670	−	0.654953i	$-0.227312\pi$
$504$		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	0.978780	−	0.204916i	$-0.0656922\pi$
$509$	17.4592	+	17.4592i	0.773863	+	0.773863i	−0.204916	+	0.978780i	$0.565692\pi$
$510$		0			0
$511$	9.46222			0.418584
$512$		0			0
$513$	35.9175			1.58579
$514$		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	$-0.917799\pi$
$523$	−16.2705	+	16.2705i	−0.711460	+	0.711460i	0.255380	+	0.966841i	$0.417799\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.10265			0.0915929
$528$		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
$537$		−	7.81028i		−	0.337039i
$538$		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
$543$	3.58416			0.153811
$544$		0			0
$545$		0			0
$546$		0			0
$547$	21.9660	+	21.9660i	0.939197	+	0.939197i	0.998255	−	0.0590579i	$-0.0188097\pi$
$547$	21.9660	+	21.9660i	0.939197	+	0.939197i	−0.0590579	+	0.998255i	$0.518810\pi$
$548$		0			0
$549$	1.85771	−	1.85771i	0.0792852	−	0.0792852i
$550$		0			0
$551$			34.0796i			1.45184i
$552$		0			0
$553$			14.4002i			0.612357i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	17.5409	+	17.5409i	0.743234	+	0.743234i	0.973199	−	0.229965i	$-0.0738612\pi$
$557$	17.5409	+	17.5409i	0.743234	+	0.743234i	−0.229965	+	0.973199i	$0.573861\pi$
$558$		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	−0.983794	−	0.179300i	$-0.942617\pi$
$563$	−27.5975	−	27.5975i	−1.16309	−	1.16309i	−0.179300	−	0.983794i	$-0.557383\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			6.59190i			0.276834i
$568$		0			0
$569$		−	23.6390i		−	0.990998i	−0.868608	−	0.495499i	$-0.834985\pi$
$569$		−	23.6390i		−	0.990998i	0.868608	−	0.495499i	$-0.165015\pi$
$570$		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
$577$	−3.69585			−0.153860			−0.0769302	−	0.997036i	$-0.524512\pi$
$577$	−3.69585			−0.153860			−0.0769302	+	0.997036i	$0.524512\pi$
$578$		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
$583$		−	15.8105i		−	0.654802i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−27.0313	+	27.0313i	−1.11570	+	1.11570i	−0.123335	+	0.992365i	$0.539359\pi$
$587$	−27.0313	+	27.0313i	−1.11570	+	1.11570i	−0.992365	+	0.123335i	$0.960641\pi$
$588$		0			0
$589$	19.5146	+	19.5146i	0.804085	+	0.804085i
$590$		0			0
$591$	−3.07189			−0.126361
$592$		0			0
$593$	−4.55524			−0.187061			−0.0935306	−	0.995616i	$-0.529815\pi$
$593$	−4.55524			−0.187061			−0.0935306	+	0.995616i	$0.529815\pi$
$594$		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	$0.0487570\pi$
$599$			7.46846i			0.305153i	−0.988292	+	0.152576i	$0.951243\pi$
$600$		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
$607$	−5.23884			−0.212638			−0.106319	−	0.994332i	$-0.533906\pi$
$607$	−5.23884			−0.212638			−0.106319	+	0.994332i	$0.533906\pi$
$608$		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	$-0.548424\pi$
$613$	20.7209	−	20.7209i	0.836910	−	0.836910i	0.988451	+	0.151541i	$0.0484235\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	2.20286i		−	0.0886838i	−0.999016	−	0.0443419i	$-0.985881\pi$
$617$		−	2.20286i		−	0.0886838i	0.999016	−	0.0443419i	$-0.0141191\pi$
$618$		0			0
$619$	31.4569	−	31.4569i	1.26436	−	1.26436i	0.315404	−	0.948958i	$-0.397860\pi$
$619$	31.4569	−	31.4569i	1.26436	−	1.26436i	0.948958	−	0.315404i	$-0.102140\pi$
$620$		0			0
$621$	−7.67158	−	7.67158i	−0.307850	−	0.307850i
$622$		0			0
$623$	1.09473			0.0438594
$624$		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
$633$			18.9957i			0.755011i
$634$		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	0.717710	−	0.696342i	$-0.245190\pi$
$643$	0.541845	+	0.541845i	0.0213683	+	0.0213683i	−0.696342	+	0.717710i	$0.745190\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			32.6391i			1.28318i	0.767049	+	0.641588i	$0.221724\pi$
$647$			32.6391i			1.28318i	−0.767049	+	0.641588i	$0.778276\pi$
$648$		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	0.871491	−	0.490412i	$-0.163154\pi$
$653$	9.73805	+	9.73805i	0.381079	+	0.381079i	−0.490412	+	0.871491i	$0.663154\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−5.99434			−0.233862
$658$		0			0
$659$	−1.26445	−	1.26445i	−0.0492560	−	0.0492560i	0.682050	−	0.731306i	$-0.261089\pi$
$659$	−1.26445	−	1.26445i	−0.0492560	−	0.0492560i	−0.731306	+	0.682050i	$0.761089\pi$
$660$		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
$663$			4.92519i			0.191279i
$664$		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
$673$	3.58765			0.138294			0.0691469	−	0.997606i	$-0.477972\pi$
$673$	3.58765			0.138294			0.0691469	+	0.997606i	$0.477972\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.1507	−	10.1507i	0.390124	−	0.390124i	−0.484608	−	0.874731i	$-0.661038\pi$
$677$	10.1507	−	10.1507i	0.390124	−	0.390124i	0.874731	+	0.484608i	$0.161038\pi$
$678$		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	$-0.899046\pi$
$683$	−16.6805	+	16.6805i	−0.638260	+	0.638260i	0.311866	+	0.950126i	$0.399046\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	16.6761			0.636234
$688$		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
$697$		−	4.97661i		−	0.188502i
$698$		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
$703$	41.4217			1.56225
$704$		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	−0.522628	−	0.852561i	$-0.675048\pi$
$709$	8.78514	−	8.78514i	0.329933	−	0.329933i	0.852561	+	0.522628i	$0.175048\pi$
$710$		0			0
$711$		−	9.12255i		−	0.342122i
$712$		0			0
$713$		−	8.33621i		−	0.312194i
$714$		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	$-0.830850\pi$
$719$	−46.2329			−1.72420			−0.862099	+	0.506740i	$0.830850\pi$
$720$		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
$727$		−	17.4640i		−	0.647703i	−0.946108	−	0.323852i	$-0.895022\pi$
$727$		−	17.4640i		−	0.647703i	0.946108	−	0.323852i	$-0.104978\pi$
$728$		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	0.837744	−	0.546063i	$-0.183874\pi$
$733$	7.89695	+	7.89695i	0.291680	+	0.291680i	−0.546063	+	0.837744i	$0.683874\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−19.9247			−0.733936
$738$		0			0
$739$	−26.1724	−	26.1724i	−0.962769	−	0.962769i	0.0365624	−	0.999331i	$-0.488359\pi$
$739$	−26.1724	−	26.1724i	−0.962769	−	0.962769i	−0.999331	+	0.0365624i	$0.988359\pi$
$740$		0			0
$741$	−45.7105	+	45.7105i	−1.67922	+	1.67922i
$742$		0			0
$743$			49.7660i			1.82574i	0.408254	+	0.912868i	$0.366138\pi$
$743$			49.7660i			1.82574i	−0.408254	+	0.912868i	$0.633862\pi$
$744$		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
$753$	−7.29665			−0.265905
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−15.4872	+	15.4872i	−0.562890	+	0.562890i	−0.930127	−	0.367237i	$-0.880304\pi$
$757$	−15.4872	+	15.4872i	−0.562890	+	0.562890i	0.367237	+	0.930127i	$0.380304\pi$
$758$		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
$767$	−77.7185			−2.80625
$768$		0			0
$769$	−24.9737			−0.900573			−0.450287	−	0.892884i	$-0.648678\pi$
$769$	−24.9737			−0.900573			−0.450287	+	0.892884i	$0.648678\pi$
$770$		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	$-0.760728\pi$
$773$	−1.32495	+	1.32495i	−0.0476550	+	0.0476550i	0.682878	+	0.730533i	$0.260728\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$			9.68103i			0.347305i
$778$		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
$783$	29.5807			1.05713
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−0.647036	−	0.647036i	−0.0230644	−	0.0230644i	0.695481	−	0.718545i	$-0.255192\pi$
$787$	−0.647036	−	0.647036i	−0.0230644	−	0.0230644i	−0.718545	+	0.695481i	$0.755192\pi$
$788$		0			0
$789$	−8.99087	+	8.99087i	−0.320084	+	0.320084i
$790$		0			0
$791$		−	16.7570i		−	0.595811i
$792$		0			0
$793$			27.7198i			0.984360i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	18.3024	+	18.3024i	0.648303	+	0.648303i	0.952583	−	0.304280i	$-0.0984158\pi$
$797$	18.3024	+	18.3024i	0.648303	+	0.648303i	−0.304280	+	0.952583i	$0.598416\pi$
$798$		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
$807$			37.7593i			1.32919i
$808$		0			0
$809$		−	32.4845i		−	1.14209i	−0.820917	−	0.571047i	$-0.806537\pi$
$809$		−	32.4845i		−	1.14209i	0.820917	−	0.571047i	$-0.193463\pi$
$810$		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
$817$	16.2891			0.569884
$818$		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
$823$		−	4.85817i		−	0.169345i	−0.996409	−	0.0846726i	$-0.973016\pi$
$823$		−	4.85817i		−	0.169345i	0.996409	−	0.0846726i	$-0.0269844\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−8.02757	+	8.02757i	−0.279146	+	0.279146i	−0.832768	−	0.553622i	$-0.813245\pi$
$827$	−8.02757	+	8.02757i	−0.279146	+	0.279146i	0.553622	+	0.832768i	$0.313245\pi$
$828$		0			0
$829$	−24.3613	−	24.3613i	−0.846102	−	0.846102i	0.143542	−	0.989644i	$-0.454151\pi$
$829$	−24.3613	−	24.3613i	−0.846102	−	0.846102i	−0.989644	+	0.143542i	$0.954151\pi$
$830$		0			0
$831$	−22.3952			−0.776881
$832$		0			0
$833$	−2.96585			−0.102761
$834$		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	$-0.732761\pi$
$839$		−	43.1207i		−	1.48869i	0.667794	−	0.744346i	$-0.267239\pi$
$840$		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
$847$	−6.85110			−0.235407
$848$		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	$-0.605943\pi$
$853$	18.0611	−	18.0611i	0.618401	−	0.618401i	0.945121	+	0.326720i	$0.105943\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			35.8346i			1.22409i	0.790825	+	0.612043i	$0.209652\pi$
$857$			35.8346i			1.22409i	−0.790825	+	0.612043i	$0.790348\pi$
$858$		0			0
$859$	0.619460	−	0.619460i	0.0211357	−	0.0211357i	−0.696460	−	0.717596i	$-0.745243\pi$
$859$	0.619460	−	0.619460i	0.0211357	−	0.0211357i	0.717596	+	0.696460i	$0.245243\pi$
$860$		0			0
$861$	10.7949	+	10.7949i	0.367890	+	0.367890i
$862$		0			0
$863$	−18.8270			−0.640878			−0.320439	−	0.947269i	$-0.603830\pi$
$863$	−18.8270			−0.640878			−0.320439	+	0.947269i	$0.603830\pi$
$864$		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
$873$		−	4.65479i		−	0.157541i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7.77833	−	7.77833i	−0.262656	−	0.262656i	0.563476	−	0.826132i	$-0.309464\pi$
$877$	−7.77833	−	7.77833i	−0.262656	−	0.262656i	−0.826132	+	0.563476i	$0.809464\pi$
$878$		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	0.992122	−	0.125278i	$-0.0399823\pi$
$883$	25.7585	+	25.7585i	0.866844	+	0.866844i	−0.125278	+	0.992122i	$0.539982\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			38.8982i			1.30607i	0.757326	+	0.653037i	$0.226505\pi$
$887$			38.8982i			1.30607i	−0.757326	+	0.653037i	$0.773495\pi$
$888$		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
$897$	19.5265			0.651972
$898$		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
$903$			3.80707i			0.126692i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	5.10220	−	5.10220i	0.169416	−	0.169416i	−0.617307	−	0.786723i	$-0.711776\pi$
$907$	5.10220	−	5.10220i	0.169416	−	0.169416i	0.786723	+	0.617307i	$0.211776\pi$
$908$		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
$913$	−2.29520			−0.0759601
$914$		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	$0.343731\pi$
$919$			53.4692i			1.76379i	−0.471449	+	0.881893i	$0.656269\pi$
$920$		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
$927$	8.52342			0.279946
$928$		0			0
$929$	14.2098			0.466209			0.233104	−	0.972452i	$-0.425112\pi$
$929$	14.2098			0.466209			0.233104	+	0.972452i	$0.425112\pi$
$930$		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
$937$		−	5.26656i		−	0.172051i	−0.996293	−	0.0860255i	$-0.972583\pi$
$937$		−	5.26656i		−	0.172051i	0.996293	−	0.0860255i	$-0.0274166\pi$
$938$		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
$943$	−19.7304			−0.642509
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.27572	−	3.27572i	−0.106447	−	0.106447i	0.651878	−	0.758324i	$-0.273982\pi$
$947$	−3.27572	−	3.27572i	−0.106447	−	0.106447i	−0.758324	+	0.651878i	$0.773982\pi$
$948$		0			0
$949$	44.7223	−	44.7223i	1.45175	−	1.45175i
$950$		0			0
$951$			21.9142i			0.710616i
$952$		0			0
$953$			30.0292i			0.972741i	0.873753	+	0.486371i	$0.161680\pi$
$953$			30.0292i			0.972741i	−0.873753	+	0.486371i	$0.838320\pi$
$954$		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
$967$			15.2196i			0.489429i	0.969595	+	0.244715i	$0.0786943\pi$
$967$			15.2196i			0.489429i	−0.969595	+	0.244715i	$0.921306\pi$
$968$		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
$977$	−18.7912			−0.601183			−0.300592	−	0.953753i	$-0.597184\pi$
$977$	−18.7912			−0.601183			−0.300592	+	0.953753i	$0.597184\pi$
$978$		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
$983$		−	56.5605i		−	1.80400i	−0.431738	−	0.901999i	$-0.642099\pi$
$983$		−	56.5605i		−	1.80400i	0.431738	−	0.901999i	$-0.357901\pi$
$984$		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
$993$	17.2404			0.547108
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−35.1508	+	35.1508i	−1.11324	+	1.11324i	−0.120528	+	0.992710i	$0.538459\pi$
$997$	−35.1508	+	35.1508i	−1.11324	+	1.11324i	−0.992710	+	0.120528i	$0.961541\pi$
$998$		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.l.g.401.2		12
4.3	odd	2		400.2.l.f.301.2	yes	12
5.2	odd	4		1600.2.q.f.849.2		12
5.3	odd	4		1600.2.q.e.849.5		12
5.4	even	2		1600.2.l.f.401.5		12
16.5	even	4	inner	1600.2.l.g.1201.2		12
16.11	odd	4		400.2.l.f.101.2	✓	12
20.3	even	4		400.2.q.e.349.5		12
20.7	even	4		400.2.q.f.349.2		12
20.19	odd	2		400.2.l.g.301.5	yes	12
80.27	even	4		400.2.q.e.149.5		12
80.37	odd	4		1600.2.q.e.49.5		12
80.43	even	4		400.2.q.f.149.2		12
80.53	odd	4		1600.2.q.f.49.2		12
80.59	odd	4		400.2.l.g.101.5	yes	12
80.69	even	4		1600.2.l.f.1201.5		12

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

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.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09156 - 1.09156i) q^{3} +0.973926i q^{7} -0.616985i q^{9} +O(q^{10})\)	\(q+(-1.09156 - 1.09156i) q^{3} +0.973926i q^{7} -0.616985i q^{9} +(-1.40810 + 1.40810i) q^{11} +(4.60317 + 4.60317i) q^{13} -0.490104 q^{17} +(-4.54863 - 4.54863i) q^{19} +(1.06310 - 1.06310i) q^{21} +1.94308i q^{23} +(-3.94816 + 3.94816i) q^{27} +(-3.74613 - 3.74613i) q^{29} -4.29021 q^{31} +3.07405 q^{33} +(-4.55320 + 4.55320i) q^{37} -10.0493i q^{39} +10.1542i q^{41} +(-1.79055 + 1.79055i) q^{43} +10.0162 q^{47} +6.05147 q^{49} +(0.534979 + 0.534979i) q^{51} +(-5.61412 + 5.61412i) q^{53} +9.93022i q^{57} +(-8.44185 + 8.44185i) q^{59} +(3.01095 + 3.01095i) q^{61} +0.600897 q^{63} +(7.07504 + 7.07504i) q^{67} +(2.12099 - 2.12099i) q^{69} +0.897891i q^{71} -9.71555i q^{73} +(-1.37138 - 1.37138i) q^{77} +14.7857 q^{79} +6.76838 q^{81} +(0.815000 + 0.815000i) q^{83} +8.17827i q^{87} -1.12404i q^{89} +(-4.48314 + 4.48314i) q^{91} +(4.68303 + 4.68303i) q^{93} +7.54442 q^{97} +(0.868775 + 0.868775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3}+O(q^{10}) \) 12 * q + 2 * q^3	\( 12 q + 2 q^{3} + 2 q^{11} + 4 q^{13} + 8 q^{17} + 14 q^{19} - 20 q^{21} - 10 q^{27} + 4 q^{31} - 28 q^{33} - 8 q^{37} + 8 q^{47} + 4 q^{49} - 10 q^{51} + 16 q^{53} - 20 q^{59} + 4 q^{61} - 8 q^{63} + 50 q^{67} + 8 q^{77} - 12 q^{79} - 8 q^{81} - 2 q^{83} + 44 q^{93} - 12 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 + 2 * q^11 + 4 * q^13 + 8 * q^17 + 14 * q^19 - 20 * q^21 - 10 * q^27 + 4 * q^31 - 28 * q^33 - 8 * q^37 + 8 * q^47 + 4 * q^49 - 10 * q^51 + 16 * q^53 - 20 * q^59 + 4 * q^61 - 8 * q^63 + 50 * q^67 + 8 * q^77 - 12 * q^79 - 8 * q^81 - 2 * q^83 + 44 * q^93 - 12 * q^99

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