LMFDB - Embedded newform 2100.2.s.b.1457.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1457,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("2100.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.s (of order $4$, degree $2$, 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.11
Character	$\chi$	$=$	2100.1457
Dual form			2100.2.s.b.1793.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62919 + 0.587996i) q^{3} +(0.707107 + 0.707107i) q^{7} +(2.30852 + 1.91591i) q^{9} +O(q^{10})$	$q+(1.62919 + 0.587996i) q^{3} +(0.707107 + 0.707107i) q^{7} +(2.30852 + 1.91591i) q^{9} -2.43430i q^{11} +(2.98864 - 2.98864i) q^{13} +(4.94659 - 4.94659i) q^{17} -1.61006i q^{19} +(0.736236 + 1.56779i) q^{21} +(2.57981 + 2.57981i) q^{23} +(2.63447 + 4.47879i) q^{27} -1.41040 q^{29} -8.99675 q^{31} +(1.43136 - 3.96593i) q^{33} +(-7.11006 - 7.11006i) q^{37} +(6.62637 - 3.11176i) q^{39} -4.49343i q^{41} +(-4.69565 + 4.69565i) q^{43} +(6.89003 - 6.89003i) q^{47} +1.00000i q^{49} +(10.9675 - 5.15037i) q^{51} +(8.78938 + 8.78938i) q^{53} +(0.946707 - 2.62309i) q^{57} +3.56655 q^{59} +8.83984 q^{61} +(0.277616 + 2.98713i) q^{63} +(6.03073 + 6.03073i) q^{67} +(2.68609 + 5.71992i) q^{69} +4.71253i q^{71} +(-7.52517 + 7.52517i) q^{73} +(1.72131 - 1.72131i) q^{77} -1.16138i q^{79} +(1.65855 + 8.84586i) q^{81} +(2.94830 + 2.94830i) q^{83} +(-2.29781 - 0.829310i) q^{87} +0.172323 q^{89} +4.22658 q^{91} +(-14.6574 - 5.29005i) q^{93} +(9.38212 + 9.38212i) q^{97} +(4.66390 - 5.61963i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3}+O(q^{10}) $ 24 * q + 4 * q^3	$ 24 q + 4 q^{3} - 24 q^{13} + 4 q^{21} - 8 q^{27} - 16 q^{31} + 20 q^{33} - 32 q^{37} + 8 q^{43} + 52 q^{51} + 28 q^{57} - 8 q^{63} + 24 q^{67} - 12 q^{81} + 20 q^{87} - 24 q^{91} - 20 q^{93} + 104 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^13 + 4 * q^21 - 8 * q^27 - 16 * q^31 + 20 * q^33 - 32 * q^37 + 8 * q^43 + 52 * q^51 + 28 * q^57 - 8 * q^63 + 24 * q^67 - 12 * q^81 + 20 * q^87 - 24 * q^91 - 20 * q^93 + 104 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	1.62919	+	0.587996i	0.940613	+	0.339479i
$3$	1.62919	+	0.587996i	0.940613	+	0.339479i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$	2.30852	+	1.91591i	0.769507	+	0.638638i
$10$		0			0
$11$		−	2.43430i		−	0.733968i	−0.930227	−	0.366984i	$-0.880390\pi$
$11$		−	2.43430i		−	0.733968i	0.930227	−	0.366984i	$-0.119610\pi$
$12$		0			0
$13$	2.98864	−	2.98864i	0.828900	−	0.828900i	−0.158465	−	0.987365i	$-0.550654\pi$
$13$	2.98864	−	2.98864i	0.828900	−	0.828900i	0.987365	+	0.158465i	$0.0506544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.94659	−	4.94659i	1.19973	−	1.19973i	0.225477	−	0.974249i	$-0.427606\pi$
$17$	4.94659	−	4.94659i	1.19973	−	1.19973i	0.974249	−	0.225477i	$-0.0723939\pi$
$18$		0			0
$19$		−	1.61006i		−	0.369373i	−0.982798	−	0.184686i	$-0.940873\pi$
$19$		−	1.61006i		−	0.369373i	0.982798	−	0.184686i	$-0.0591269\pi$
$20$		0			0
$21$	0.736236	+	1.56779i	0.160660	+	0.342119i
$22$		0			0
$23$	2.57981	+	2.57981i	0.537928	+	0.537928i	0.922920	−	0.384992i	$-0.125796\pi$
$23$	2.57981	+	2.57981i	0.537928	+	0.537928i	−0.384992	+	0.922920i	$0.625796\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.63447	+	4.47879i	0.507005	+	0.861943i
$28$		0			0
$29$	−1.41040			−0.261905			−0.130953	−	0.991389i	$-0.541804\pi$
$29$	−1.41040			−0.261905			−0.130953	+	0.991389i	$0.541804\pi$
$30$		0			0
$31$	−8.99675			−1.61586			−0.807932	−	0.589276i	$-0.799413\pi$
$31$	−8.99675			−1.61586			−0.807932	+	0.589276i	$0.799413\pi$
$32$		0			0
$33$	1.43136	−	3.96593i	0.249167	−	0.690380i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.11006	−	7.11006i	−1.16889	−	1.16889i	−0.982471	−	0.186416i	$-0.940313\pi$
$37$	−7.11006	−	7.11006i	−1.16889	−	1.16889i	−0.186416	−	0.982471i	$-0.559687\pi$
$38$		0			0
$39$	6.62637	−	3.11176i	1.06107	−	0.498280i
$40$		0			0
$41$		−	4.49343i		−	0.701755i	−0.936421	−	0.350878i	$-0.885883\pi$
$41$		−	4.49343i		−	0.701755i	0.936421	−	0.350878i	$-0.114117\pi$
$42$		0			0
$43$	−4.69565	+	4.69565i	−0.716080	+	0.716080i	−0.967800	−	0.251720i	$-0.919004\pi$
$43$	−4.69565	+	4.69565i	−0.716080	+	0.716080i	0.251720	+	0.967800i	$0.419004\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.89003	−	6.89003i	1.00501	−	1.00501i	0.00502726	−	0.999987i	$-0.498400\pi$
$47$	6.89003	−	6.89003i	1.00501	−	1.00501i	0.999987	−	0.00502726i	$-0.00160023\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	10.9675	−	5.15037i	1.53576	−	0.721196i
$52$		0			0
$53$	8.78938	+	8.78938i	1.20731	+	1.20731i	0.971893	+	0.235421i	$0.0756469\pi$
$53$	8.78938	+	8.78938i	1.20731	+	1.20731i	0.235421	+	0.971893i	$0.424353\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.946707	−	2.62309i	0.125394	−	0.347437i
$58$		0			0
$59$	3.56655			0.464325			0.232162	−	0.972677i	$-0.425420\pi$
$59$	3.56655			0.464325			0.232162	+	0.972677i	$0.425420\pi$
$60$		0			0
$61$	8.83984			1.13183			0.565913	−	0.824465i	$-0.308524\pi$
$61$	8.83984			1.13183			0.565913	+	0.824465i	$0.308524\pi$
$62$		0			0
$63$	0.277616	+	2.98713i	0.0349764	+	0.376343i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.03073	+	6.03073i	0.736771	+	0.736771i	0.971952	−	0.235180i	$-0.0755681\pi$
$67$	6.03073	+	6.03073i	0.736771	+	0.736771i	−0.235180	+	0.971952i	$0.575568\pi$
$68$		0			0
$69$	2.68609	+	5.71992i	0.323367	+	0.688598i
$70$		0			0
$71$			4.71253i			0.559274i	0.960106	+	0.279637i	$0.0902141\pi$
$71$			4.71253i			0.559274i	−0.960106	+	0.279637i	$0.909786\pi$
$72$		0			0
$73$	−7.52517	+	7.52517i	−0.880755	+	0.880755i	−0.993611	−	0.112857i	$-0.964000\pi$
$73$	−7.52517	+	7.52517i	−0.880755	+	0.880755i	0.112857	+	0.993611i	$0.464000\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.72131	−	1.72131i	0.196161	−	0.196161i
$78$		0			0
$79$		−	1.16138i		−	0.130665i	−0.997864	−	0.0653327i	$-0.979189\pi$
$79$		−	1.16138i		−	0.130665i	0.997864	−	0.0653327i	$-0.0208109\pi$
$80$		0			0
$81$	1.65855	+	8.84586i	0.184283	+	0.982873i
$82$		0			0
$83$	2.94830	+	2.94830i	0.323618	+	0.323618i	0.850153	−	0.526535i	$-0.176509\pi$
$83$	2.94830	+	2.94830i	0.323618	+	0.323618i	−0.526535	+	0.850153i	$0.676509\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.29781	−	0.829310i	−0.246351	−	0.0889114i
$88$		0			0
$89$	0.172323			0.0182662			0.00913311	−	0.999958i	$-0.497093\pi$
$89$	0.172323			0.0182662			0.00913311	+	0.999958i	$0.497093\pi$
$90$		0			0
$91$	4.22658			0.443066
$92$		0			0
$93$	−14.6574	−	5.29005i	−1.51990	−	0.548552i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	9.38212	+	9.38212i	0.952610	+	0.952610i	0.998927	−	0.0463165i	$-0.0147483\pi$
$97$	9.38212	+	9.38212i	0.952610	+	0.952610i	−0.0463165	+	0.998927i	$0.514748\pi$
$98$		0			0
$99$	4.66390	−	5.61963i	0.468740	−	0.564794i
$100$		0			0
$101$		−	7.13144i		−	0.709604i	−0.934941	−	0.354802i	$-0.884548\pi$
$101$		−	7.13144i		−	0.709604i	0.934941	−	0.354802i	$-0.115452\pi$
$102$		0			0
$103$	−8.42462	+	8.42462i	−0.830103	+	0.830103i	−0.987531	−	0.157428i	$-0.949680\pi$
$103$	−8.42462	+	8.42462i	−0.830103	+	0.830103i	0.157428	+	0.987531i	$0.449680\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.58306	−	2.58306i	0.249714	−	0.249714i	−0.571139	−	0.820853i	$-0.693498\pi$
$107$	2.58306	−	2.58306i	0.249714	−	0.249714i	0.820853	+	0.571139i	$0.193498\pi$
$108$		0			0
$109$		−	1.15884i		−	0.110997i	−0.998459	−	0.0554985i	$-0.982325\pi$
$109$		−	1.15884i		−	0.110997i	0.998459	−	0.0554985i	$-0.0176748\pi$
$110$		0			0
$111$	−7.40296	−	15.7643i	−0.702658	−	1.49628i
$112$		0			0
$113$	1.85511	+	1.85511i	0.174514	+	0.174514i	0.788959	−	0.614445i	$-0.210620\pi$
$113$	1.85511	+	1.85511i	0.174514	+	0.174514i	−0.614445	+	0.788959i	$0.710620\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	12.6253	−	1.17337i	1.16721	−	0.108478i
$118$		0			0
$119$	6.99554			0.641280
$120$		0			0
$121$	5.07420			0.461291
$122$		0			0
$123$	2.64211	−	7.32065i	0.238231	−	0.660080i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.33168	−	2.33168i	−0.206903	−	0.206903i	0.596046	−	0.802950i	$-0.296737\pi$
$127$	−2.33168	−	2.33168i	−0.206903	−	0.206903i	−0.802950	+	0.596046i	$0.796737\pi$
$128$		0			0
$129$	−10.4111	+	4.88909i	−0.916649	+	0.430460i
$130$		0			0
$131$		−	6.20687i		−	0.542297i	−0.962538	−	0.271148i	$-0.912597\pi$
$131$		−	6.20687i		−	0.542297i	0.962538	−	0.271148i	$-0.0874034\pi$
$132$		0			0
$133$	1.13848	−	1.13848i	0.0987190	−	0.0987190i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.32888	−	5.32888i	0.455277	−	0.455277i	−0.441825	−	0.897101i	$-0.645669\pi$
$137$	5.32888	−	5.32888i	0.455277	−	0.455277i	0.897101	+	0.441825i	$0.145669\pi$
$138$		0			0
$139$		−	10.1410i		−	0.860148i	−0.902794	−	0.430074i	$-0.858488\pi$
$139$		−	10.1410i		−	0.860148i	0.902794	−	0.430074i	$-0.141512\pi$
$140$		0			0
$141$	15.2765	−	7.17387i	1.28651	−	0.604149i
$142$		0			0
$143$	−7.27524	−	7.27524i	−0.608386	−	0.608386i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.587996	+	1.62919i	−0.0484971	+	0.134373i
$148$		0			0
$149$	−23.9444			−1.96160			−0.980799	−	0.195021i	$-0.937522\pi$
$149$	−23.9444			−1.96160			−0.980799	+	0.195021i	$0.937522\pi$
$150$		0			0
$151$	−18.6080			−1.51430			−0.757150	−	0.653242i	$-0.773409\pi$
$151$	−18.6080			−1.51430			−0.757150	+	0.653242i	$0.773409\pi$
$152$		0			0
$153$	20.8966	−	1.94208i	1.68939	−	0.157008i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	7.47944	+	7.47944i	0.596925	+	0.596925i	0.939493	−	0.342568i	$-0.111297\pi$
$157$	7.47944	+	7.47944i	0.596925	+	0.596925i	−0.342568	+	0.939493i	$0.611297\pi$
$158$		0			0
$159$	9.15146	+	19.4877i	0.725758	+	1.54547i
$160$		0			0
$161$			3.64840i			0.287534i
$162$		0			0
$163$	−7.27351	+	7.27351i	−0.569706	+	0.569706i	−0.932046	−	0.362340i	$-0.881978\pi$
$163$	−7.27351	+	7.27351i	−0.569706	+	0.569706i	0.362340	+	0.932046i	$0.381978\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.9727	+	10.9727i	−0.849090	+	0.849090i	−0.990020	−	0.140930i	$-0.954991\pi$
$167$	−10.9727	+	10.9727i	−0.849090	+	0.849090i	0.140930	+	0.990020i	$0.454991\pi$
$168$		0			0
$169$		−	4.86395i		−	0.374150i
$170$		0			0
$171$	3.08473	−	3.71685i	0.235895	−	0.284235i
$172$		0			0
$173$	−0.631993	−	0.631993i	−0.0480496	−	0.0480496i	0.682674	−	0.730723i	$-0.260817\pi$
$173$	−0.631993	−	0.631993i	−0.0480496	−	0.0480496i	−0.730723	+	0.682674i	$0.760817\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.81058	+	2.09711i	0.436750	+	0.157629i
$178$		0			0
$179$	7.60854			0.568689			0.284344	−	0.958722i	$-0.408224\pi$
$179$	7.60854			0.568689			0.284344	+	0.958722i	$0.408224\pi$
$180$		0			0
$181$	−17.5290			−1.30292			−0.651461	−	0.758682i	$-0.725844\pi$
$181$	−17.5290			−1.30292			−0.651461	+	0.758682i	$0.725844\pi$
$182$		0			0
$183$	14.4018	+	5.19778i	1.06461	+	0.384231i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−12.0415	−	12.0415i	−0.880560	−	0.880560i
$188$		0			0
$189$	−1.30413	+	5.02984i	−0.0948613	+	0.365867i
$190$		0			0
$191$		−	5.61285i		−	0.406132i	−0.979165	−	0.203066i	$-0.934909\pi$
$191$		−	5.61285i		−	0.406132i	0.979165	−	0.203066i	$-0.0650905\pi$
$192$		0			0
$193$	5.70245	−	5.70245i	0.410471	−	0.410471i	−0.471431	−	0.881903i	$-0.656263\pi$
$193$	5.70245	−	5.70245i	0.410471	−	0.410471i	0.881903	+	0.471431i	$0.156263\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.94136	+	2.94136i	−0.209563	+	0.209563i	−0.804082	−	0.594519i	$-0.797343\pi$
$197$	−2.94136	+	2.94136i	−0.209563	+	0.209563i	0.594519	+	0.804082i	$0.297343\pi$
$198$		0			0
$199$			26.1729i			1.85535i	0.373388	+	0.927675i	$0.378196\pi$
$199$			26.1729i			1.85535i	−0.373388	+	0.927675i	$0.621804\pi$
$200$		0			0
$201$	6.27917	+	13.3713i	0.442898	+	0.943136i
$202$		0			0
$203$	−0.997305	−	0.997305i	−0.0699971	−	0.0699971i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.01286	+	10.8982i	0.0703984	+	0.757480i
$208$		0			0
$209$	−3.91936			−0.271108
$210$		0			0
$211$	−6.53694			−0.450021			−0.225011	−	0.974356i	$-0.572242\pi$
$211$	−6.53694			−0.450021			−0.225011	+	0.974356i	$0.572242\pi$
$212$		0			0
$213$	−2.77094	+	7.67760i	−0.189862	+	0.526061i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−6.36166	−	6.36166i	−0.431858	−	0.431858i
$218$		0			0
$219$	−16.6847	+	7.83517i	−1.12745	+	0.529452i
$220$		0			0
$221$		−	29.5672i		−	1.98890i
$222$		0			0
$223$	5.01848	−	5.01848i	0.336062	−	0.336062i	−0.518821	−	0.854883i	$-0.673629\pi$
$223$	5.01848	−	5.01848i	0.336062	−	0.336062i	0.854883	+	0.518821i	$0.173629\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	12.2157	−	12.2157i	0.810781	−	0.810781i	−0.173970	−	0.984751i	$-0.555659\pi$
$227$	12.2157	−	12.2157i	0.810781	−	0.810781i	0.984751	+	0.173970i	$0.0556594\pi$
$228$		0			0
$229$			2.46947i			0.163187i	0.996666	+	0.0815935i	$0.0260009\pi$
$229$			2.46947i			0.163187i	−0.996666	+	0.0815935i	$0.973999\pi$
$230$		0			0
$231$	3.81646	−	1.79222i	0.251105	−	0.117919i
$232$		0			0
$233$	−12.3358	−	12.3358i	−0.808142	−	0.808142i	0.176210	−	0.984353i	$-0.443616\pi$
$233$	−12.3358	−	12.3358i	−0.808142	−	0.808142i	−0.984353	+	0.176210i	$0.943616\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.682886	−	1.89211i	0.0443582	−	0.122906i
$238$		0			0
$239$	9.59397			0.620582			0.310291	−	0.950642i	$-0.399573\pi$
$239$	9.59397			0.620582			0.310291	+	0.950642i	$0.399573\pi$
$240$		0			0
$241$	−4.49641			−0.289639			−0.144820	−	0.989458i	$-0.546260\pi$
$241$	−4.49641			−0.289639			−0.144820	+	0.989458i	$0.546260\pi$
$242$		0			0
$243$	−2.49923	+	15.3868i	−0.160326	+	0.987064i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.81189	−	4.81189i	−0.306173	−	0.306173i
$248$		0			0
$249$	3.06976	+	6.53694i	0.194538	+	0.414262i
$250$		0			0
$251$			13.5516i			0.855371i	0.903928	+	0.427685i	$0.140671\pi$
$251$			13.5516i			0.855371i	−0.903928	+	0.427685i	$0.859329\pi$
$252$		0			0
$253$	6.28003	−	6.28003i	0.394822	−	0.394822i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.2974	+	15.2974i	−0.954228	+	0.954228i	−0.998997	−	0.0447692i	$-0.985745\pi$
$257$	−15.2974	+	15.2974i	−0.954228	+	0.954228i	0.0447692	+	0.998997i	$0.485745\pi$
$258$		0			0
$259$		−	10.0551i		−	0.624796i
$260$		0			0
$261$	−3.25595	−	2.70221i	−0.201538	−	0.167263i
$262$		0			0
$263$	17.8610	+	17.8610i	1.10135	+	1.10135i	0.994247	+	0.107107i	$0.0341588\pi$
$263$	17.8610	+	17.8610i	1.10135	+	1.10135i	0.107107	+	0.994247i	$0.465841\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.280747	+	0.101325i	0.0171815	+	0.00620100i
$268$		0			0
$269$	23.5710			1.43715			0.718575	−	0.695449i	$-0.244795\pi$
$269$	23.5710			1.43715			0.718575	+	0.695449i	$0.244795\pi$
$270$		0			0
$271$	−25.1730			−1.52915			−0.764576	−	0.644534i	$-0.777051\pi$
$271$	−25.1730			−1.52915			−0.764576	+	0.644534i	$0.777051\pi$
$272$		0			0
$273$	6.88590	+	2.48521i	0.416754	+	0.150412i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	0.894945	+	0.894945i	0.0537721	+	0.0537721i	0.733481	−	0.679709i	$-0.237894\pi$
$277$	0.894945	+	0.894945i	0.0537721	+	0.0537721i	−0.679709	+	0.733481i	$0.737894\pi$
$278$		0			0
$279$	−20.7692	−	17.2370i	−1.24342	−	1.03195i
$280$		0			0
$281$			11.4798i			0.684828i	0.939549	+	0.342414i	$0.111245\pi$
$281$			11.4798i			0.684828i	−0.939549	+	0.342414i	$0.888755\pi$
$282$		0			0
$283$	−6.10745	+	6.10745i	−0.363050	+	0.363050i	−0.864935	−	0.501884i	$-0.832640\pi$
$283$	−6.10745	+	6.10745i	−0.363050	+	0.363050i	0.501884	+	0.864935i	$0.332640\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.17733	−	3.17733i	0.187552	−	0.187552i
$288$		0			0
$289$		−	31.9376i		−	1.87868i
$290$		0			0
$291$	9.76862	+	20.8019i	0.572647	+	1.21943i
$292$		0			0
$293$	−10.9572	−	10.9572i	−0.640129	−	0.640129i	0.310458	−	0.950587i	$-0.399518\pi$
$293$	−10.9572	−	10.9572i	−0.640129	−	0.640129i	−0.950587	+	0.310458i	$0.899518\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	10.9027	−	6.41309i	0.632639	−	0.372125i
$298$		0			0
$299$	15.4203			0.891777
$300$		0			0
$301$	−6.64065			−0.382761
$302$		0			0
$303$	4.19325	−	11.6185i	0.240896	−	0.667463i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	0.403804	+	0.403804i	0.0230463	+	0.0230463i	0.718536	−	0.695490i	$-0.244813\pi$
$307$	0.403804	+	0.403804i	0.0230463	+	0.0230463i	−0.695490	+	0.718536i	$0.744813\pi$
$308$		0			0
$309$	−18.6790	+	8.77167i	−1.06261	+	0.499003i
$310$		0			0
$311$			23.8750i			1.35383i	0.736062	+	0.676914i	$0.236683\pi$
$311$			23.8750i			1.35383i	−0.736062	+	0.676914i	$0.763317\pi$
$312$		0			0
$313$	0.933579	−	0.933579i	0.0527690	−	0.0527690i	−0.680230	−	0.732999i	$-0.738120\pi$
$313$	0.933579	−	0.933579i	0.0527690	−	0.0527690i	0.732999	+	0.680230i	$0.238120\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.3618	+	10.3618i	−0.581974	+	0.581974i	−0.935445	−	0.353471i	$-0.885001\pi$
$317$	−10.3618	+	10.3618i	−0.581974	+	0.581974i	0.353471	+	0.935445i	$0.385001\pi$
$318$		0			0
$319$			3.43334i			0.192230i
$320$		0			0
$321$	5.72713	−	2.68947i	0.319657	−	0.150112i
$322$		0			0
$323$	−7.96430	−	7.96430i	−0.443146	−	0.443146i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.681395	−	1.88798i	0.0376812	−	0.104405i
$328$		0			0
$329$	9.74398			0.537203
$330$		0			0
$331$	1.77630			0.0976345			0.0488172	−	0.998808i	$-0.484455\pi$
$331$	1.77630			0.0976345			0.0488172	+	0.998808i	$0.484455\pi$
$332$		0			0
$333$	−2.79147	−	30.0360i	−0.152972	−	1.64596i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−4.85736	−	4.85736i	−0.264597	−	0.264597i	0.562321	−	0.826919i	$-0.309908\pi$
$337$	−4.85736	−	4.85736i	−0.264597	−	0.264597i	−0.826919	+	0.562321i	$0.809908\pi$
$338$		0			0
$339$	1.93153	+	4.11312i	0.104906	+	0.223394i
$340$		0			0
$341$			21.9008i			1.18599i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.0503	+	13.0503i	−0.700579	+	0.700579i	−0.964535	−	0.263956i	$-0.914973\pi$
$347$	−13.0503	+	13.0503i	−0.700579	+	0.700579i	0.263956	+	0.964535i	$0.414973\pi$
$348$		0			0
$349$		−	15.7209i		−	0.841522i	−0.907172	−	0.420761i	$-0.861763\pi$
$349$		−	15.7209i		−	0.841522i	0.907172	−	0.420761i	$-0.138237\pi$
$350$		0			0
$351$	21.2590	+	5.51200i	1.13472	+	0.294209i
$352$		0			0
$353$	−24.4258	−	24.4258i	−1.30005	−	1.30005i	−0.928353	−	0.371701i	$-0.878775\pi$
$353$	−24.4258	−	24.4258i	−1.30005	−	1.30005i	−0.371701	−	0.928353i	$-0.621225\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	11.3971	+	4.11335i	0.603197	+	0.217701i
$358$		0			0
$359$	−25.3763			−1.33931			−0.669655	−	0.742673i	$-0.733558\pi$
$359$	−25.3763			−1.33931			−0.669655	+	0.742673i	$0.733558\pi$
$360$		0			0
$361$	16.4077			0.863564
$362$		0			0
$363$	8.26683	+	2.98360i	0.433896	+	0.156599i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−22.5655	−	22.5655i	−1.17791	−	1.17791i	−0.980276	−	0.197633i	$-0.936674\pi$
$367$	−22.5655	−	22.5655i	−1.17791	−	1.17791i	−0.197633	−	0.980276i	$-0.563326\pi$
$368$		0			0
$369$	8.60901	−	10.3732i	0.448167	−	0.540006i
$370$		0			0
$371$			12.4301i			0.645337i
$372$		0			0
$373$	1.44947	−	1.44947i	0.0750506	−	0.0750506i	−0.668585	−	0.743636i	$-0.733100\pi$
$373$	1.44947	−	1.44947i	0.0750506	−	0.0750506i	0.743636	+	0.668585i	$0.233100\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.21519	+	4.21519i	−0.217093	+	0.217093i
$378$		0			0
$379$		−	14.4529i		−	0.742394i	−0.928554	−	0.371197i	$-0.878947\pi$
$379$		−	14.4529i		−	0.742394i	0.928554	−	0.371197i	$-0.121053\pi$
$380$		0			0
$381$	−2.42774	−	5.16978i	−0.124377	−	0.264856i
$382$		0			0
$383$	15.1020	+	15.1020i	0.771675	+	0.771675i	0.978399	−	0.206724i	$-0.0662803\pi$
$383$	15.1020	+	15.1020i	0.771675	+	0.771675i	−0.206724	+	0.978399i	$0.566280\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−19.8365	+	1.84355i	−1.00834	+	0.0937131i
$388$		0			0
$389$	−4.85986			−0.246405			−0.123202	−	0.992382i	$-0.539316\pi$
$389$	−4.85986			−0.246405			−0.123202	+	0.992382i	$0.539316\pi$
$390$		0			0
$391$	25.5226			1.29073
$392$		0			0
$393$	3.64961	−	10.1122i	0.184099	−	0.510092i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	5.43039	+	5.43039i	0.272543	+	0.272543i	0.830123	−	0.557580i	$-0.188270\pi$
$397$	5.43039	+	5.43039i	0.272543	+	0.272543i	−0.557580	+	0.830123i	$0.688270\pi$
$398$		0			0
$399$	2.52423	−	1.18538i	0.126369	−	0.0593433i
$400$		0			0
$401$		−	36.9608i		−	1.84573i	−0.385119	−	0.922867i	$-0.625840\pi$
$401$		−	36.9608i		−	1.84573i	0.385119	−	0.922867i	$-0.374160\pi$
$402$		0			0
$403$	−26.8880	+	26.8880i	−1.33939	+	1.33939i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−17.3080	+	17.3080i	−0.857926	+	0.857926i
$408$		0			0
$409$		−	29.4192i		−	1.45469i	−0.686274	−	0.727343i	$-0.740755\pi$
$409$		−	29.4192i		−	1.45469i	0.686274	−	0.727343i	$-0.259245\pi$
$410$		0			0
$411$	11.8151	−	5.54840i	0.582797	−	0.273682i
$412$		0			0
$413$	2.52193	+	2.52193i	0.124096	+	0.124096i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.96286	−	16.5216i	0.292002	−	0.809067i
$418$		0			0
$419$	28.7181			1.40297			0.701485	−	0.712684i	$-0.252521\pi$
$419$	28.7181			1.40297			0.701485	+	0.712684i	$0.252521\pi$
$420$		0			0
$421$	4.98981			0.243189			0.121594	−	0.992580i	$-0.461199\pi$
$421$	4.98981			0.243189			0.121594	+	0.992580i	$0.461199\pi$
$422$		0			0
$423$	29.1065	−	2.70509i	1.41521	−	0.131526i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	6.25071	+	6.25071i	0.302493	+	0.302493i
$428$		0			0
$429$	−7.57494	−	16.1306i	−0.365722	−	0.778791i
$430$		0			0
$431$			37.5003i			1.80632i	0.429300	+	0.903162i	$0.358760\pi$
$431$			37.5003i			1.80632i	−0.429300	+	0.903162i	$0.641240\pi$
$432$		0			0
$433$	−23.2740	+	23.2740i	−1.11848	+	1.11848i	−0.126514	+	0.991965i	$0.540379\pi$
$433$	−23.2740	+	23.2740i	−1.11848	+	1.11848i	−0.991965	+	0.126514i	$0.959621\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.15364	−	4.15364i	0.198696	−	0.198696i
$438$		0			0
$439$			0.591384i			0.0282252i	0.999900	+	0.0141126i	$0.00449234\pi$
$439$			0.591384i			0.0282252i	−0.999900	+	0.0141126i	$0.995508\pi$
$440$		0			0
$441$	−1.91591	+	2.30852i	−0.0912340	+	0.109930i
$442$		0			0
$443$	−12.5701	−	12.5701i	−0.597226	−	0.597226i	0.342348	−	0.939573i	$-0.388778\pi$
$443$	−12.5701	−	12.5701i	−0.597226	−	0.597226i	−0.939573	+	0.342348i	$0.888778\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−39.0099	−	14.0792i	−1.84511	−	0.665922i
$448$		0			0
$449$	9.79590			0.462297			0.231149	−	0.972918i	$-0.425752\pi$
$449$	9.79590			0.462297			0.231149	+	0.972918i	$0.425752\pi$
$450$		0			0
$451$	−10.9383			−0.515066
$452$		0			0
$453$	−30.3160	−	10.9414i	−1.42437	−	0.514073i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−27.1080	−	27.1080i	−1.26806	−	1.26806i	−0.947089	−	0.320970i	$-0.895991\pi$
$457$	−27.1080	−	27.1080i	−1.26806	−	1.26806i	−0.320970	−	0.947089i	$-0.604009\pi$
$458$		0			0
$459$	35.1864	+	9.12308i	1.64236	+	0.425829i
$460$		0			0
$461$			6.82113i			0.317692i	0.987303	+	0.158846i	$0.0507773\pi$
$461$			6.82113i			0.317692i	−0.987303	+	0.158846i	$0.949223\pi$
$462$		0			0
$463$	9.03568	−	9.03568i	0.419924	−	0.419924i	−0.465254	−	0.885177i	$-0.654037\pi$
$463$	9.03568	−	9.03568i	0.419924	−	0.419924i	0.885177	+	0.465254i	$0.154037\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	28.6718	−	28.6718i	1.32677	−	1.32677i	0.418603	−	0.908169i	$-0.362520\pi$
$467$	28.6718	−	28.6718i	1.32677	−	1.32677i	0.908169	−	0.418603i	$-0.137480\pi$
$468$		0			0
$469$			8.52874i			0.393821i
$470$		0			0
$471$	7.78756	+	16.5833i	0.358832	+	0.764119i
$472$		0			0
$473$	11.4306	+	11.4306i	0.525580	+	0.525580i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	3.45079	+	37.1302i	0.158001	+	1.70007i
$478$		0			0
$479$	−21.3227			−0.974261			−0.487130	−	0.873329i	$-0.661956\pi$
$479$	−21.3227			−0.974261			−0.487130	+	0.873329i	$0.661956\pi$
$480$		0			0
$481$	−42.4988			−1.93778
$482$		0			0
$483$	−2.14525	+	5.94394i	−0.0976120	+	0.270459i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	11.4319	+	11.4319i	0.518028	+	0.518028i	0.916974	−	0.398946i	$-0.130624\pi$
$487$	11.4319	+	11.4319i	0.518028	+	0.518028i	−0.398946	+	0.916974i	$0.630624\pi$
$488$		0			0
$489$	−16.1267	+	7.57314i	−0.729276	+	0.342469i
$490$		0			0
$491$		−	3.48805i		−	0.157413i	−0.996898	−	0.0787067i	$-0.974921\pi$
$491$		−	3.48805i		−	0.157413i	0.996898	−	0.0787067i	$-0.0250790\pi$
$492$		0			0
$493$	−6.97669	+	6.97669i	−0.314214	+	0.314214i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.33226	+	3.33226i	−0.149472	+	0.149472i
$498$		0			0
$499$			13.2787i			0.594438i	0.954809	+	0.297219i	$0.0960592\pi$
$499$			13.2787i			0.594438i	−0.954809	+	0.297219i	$0.903941\pi$
$500$		0			0
$501$	−24.3284	+	11.4247i	−1.08691	+	0.510417i
$502$		0			0
$503$	−23.9159	−	23.9159i	−1.06636	−	1.06636i	−0.997636	−	0.0687200i	$-0.978108\pi$
$503$	−23.9159	−	23.9159i	−1.06636	−	1.06636i	−0.0687200	−	0.997636i	$-0.521892\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.85998	−	7.92431i	0.127016	−	0.351931i
$508$		0			0
$509$	−26.8408			−1.18970			−0.594848	−	0.803838i	$-0.702788\pi$
$509$	−26.8408			−1.18970			−0.594848	+	0.803838i	$0.702788\pi$
$510$		0			0
$511$	−10.6422			−0.470783
$512$		0			0
$513$	7.21111	−	4.24166i	0.318378	−	0.187274i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−16.7724	−	16.7724i	−0.737649	−	0.737649i
$518$		0			0
$519$	−0.658028	−	1.40125i	−0.0288842	−	0.0615079i
$520$		0			0
$521$			18.5361i			0.812081i	0.913855	+	0.406040i	$0.133091\pi$
$521$			18.5361i			0.812081i	−0.913855	+	0.406040i	$0.866909\pi$
$522$		0			0
$523$	19.4744	−	19.4744i	0.851554	−	0.851554i	−0.138770	−	0.990325i	$-0.544315\pi$
$523$	19.4744	−	19.4744i	0.851554	−	0.851554i	0.990325	+	0.138770i	$0.0443149\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−44.5032	+	44.5032i	−1.93859	+	1.93859i
$528$		0			0
$529$		−	9.68915i		−	0.421267i
$530$		0			0
$531$	8.23345	+	6.83319i	0.357301	+	0.296535i
$532$		0			0
$533$	−13.4292	−	13.4292i	−0.581685	−	0.581685i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	12.3958	+	4.47379i	0.534916	+	0.193058i
$538$		0			0
$539$	2.43430			0.104853
$540$		0			0
$541$	−37.9743			−1.63264			−0.816321	−	0.577599i	$-0.803990\pi$
$541$	−37.9743			−1.63264			−0.816321	+	0.577599i	$0.803990\pi$
$542$		0			0
$543$	−28.5581	−	10.3070i	−1.22555	−	0.442315i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	4.67326	+	4.67326i	0.199814	+	0.199814i	0.799920	−	0.600106i	$-0.204875\pi$
$547$	4.67326	+	4.67326i	0.199814	+	0.199814i	−0.600106	+	0.799920i	$0.704875\pi$
$548$		0			0
$549$	20.4070	+	16.9364i	0.870948	+	0.722826i
$550$		0			0
$551$			2.27083i			0.0967406i
$552$		0			0
$553$	0.821219	−	0.821219i	0.0349218	−	0.0349218i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.6349	−	12.6349i	0.535360	−	0.535360i	−0.386803	−	0.922163i	$-0.626421\pi$
$557$	12.6349	−	12.6349i	0.535360	−	0.535360i	0.922163	+	0.386803i	$0.126421\pi$
$558$		0			0
$559$			28.0672i			1.18712i
$560$		0			0
$561$	−12.5375	−	26.6982i	−0.529335	−	1.12720i
$562$		0			0
$563$	28.5948	+	28.5948i	1.20513	+	1.20513i	0.972586	+	0.232543i	$0.0747045\pi$
$563$	28.5948	+	28.5948i	1.20513	+	1.20513i	0.232543	+	0.972586i	$0.425295\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−5.08219	+	7.42774i	−0.213432	+	0.311936i
$568$		0			0
$569$	−24.9168			−1.04457			−0.522283	−	0.852772i	$-0.674920\pi$
$569$	−24.9168			−1.04457			−0.522283	+	0.852772i	$0.674920\pi$
$570$		0			0
$571$	14.2337			0.595662			0.297831	−	0.954619i	$-0.403737\pi$
$571$	14.2337			0.595662			0.297831	+	0.954619i	$0.403737\pi$
$572$		0			0
$573$	3.30033	−	9.14440i	0.137873	−	0.382013i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	14.8426	+	14.8426i	0.617906	+	0.617906i	0.944994	−	0.327088i	$-0.106067\pi$
$577$	14.8426	+	14.8426i	0.617906	+	0.617906i	−0.327088	+	0.944994i	$0.606067\pi$
$578$		0			0
$579$	12.6434	−	5.93736i	0.525441	−	0.246748i
$580$		0			0
$581$			4.16953i			0.172981i
$582$		0			0
$583$	21.3960	−	21.3960i	0.886131	−	0.886131i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.26590	+	2.26590i	−0.0935238	+	0.0935238i	−0.752321	−	0.658797i	$-0.771066\pi$
$587$	−2.26590	+	2.26590i	−0.0935238	+	0.0935238i	0.658797	+	0.752321i	$0.271066\pi$
$588$		0			0
$589$			14.4853i			0.596856i
$590$		0			0
$591$	−6.52154	+	3.06253i	−0.268260	+	0.125975i
$592$		0			0
$593$	8.49972	+	8.49972i	0.349042	+	0.349042i	0.859753	−	0.510711i	$-0.170618\pi$
$593$	8.49972	+	8.49972i	0.349042	+	0.349042i	−0.510711	+	0.859753i	$0.670618\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−15.3896	+	42.6407i	−0.629853	+	1.74517i
$598$		0			0
$599$	−33.6550			−1.37511			−0.687553	−	0.726135i	$-0.741315\pi$
$599$	−33.6550			−1.37511			−0.687553	+	0.726135i	$0.741315\pi$
$600$		0			0
$601$	43.7503			1.78461			0.892305	−	0.451432i	$-0.149087\pi$
$601$	43.7503			1.78461			0.892305	+	0.451432i	$0.149087\pi$
$602$		0			0
$603$	2.36772	+	25.4764i	0.0964210	+	1.03748i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	12.2869	+	12.2869i	0.498708	+	0.498708i	0.911036	−	0.412328i	$-0.135284\pi$
$607$	12.2869	+	12.2869i	0.498708	+	0.498708i	−0.412328	+	0.911036i	$0.635284\pi$
$608$		0			0
$609$	−1.03839	−	2.21121i	−0.0420776	−	0.0896028i
$610$		0			0
$611$		−	41.1837i		−	1.66611i
$612$		0			0
$613$	19.8333	−	19.8333i	0.801061	−	0.801061i	−0.182201	−	0.983261i	$-0.558322\pi$
$613$	19.8333	−	19.8333i	0.801061	−	0.801061i	0.983261	+	0.182201i	$0.0583221\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	12.5403	−	12.5403i	0.504852	−	0.504852i	−0.408090	−	0.912942i	$-0.633805\pi$
$617$	12.5403	−	12.5403i	0.504852	−	0.504852i	0.912942	+	0.408090i	$0.133805\pi$
$618$		0			0
$619$			31.4704i			1.26490i	0.774600	+	0.632452i	$0.217951\pi$
$619$			31.4704i			1.26490i	−0.774600	+	0.632452i	$0.782049\pi$
$620$		0			0
$621$	−4.75798	+	18.3509i	−0.190931	+	0.736395i
$622$		0			0
$623$	0.121851	+	0.121851i	0.00488185	+	0.00488185i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−6.38538	−	2.30457i	−0.255008	−	0.0920355i
$628$		0			0
$629$	−70.3412			−2.80469
$630$		0			0
$631$	−31.7145			−1.26254			−0.631268	−	0.775565i	$-0.717465\pi$
$631$	−31.7145			−1.26254			−0.631268	+	0.775565i	$0.717465\pi$
$632$		0			0
$633$	−10.6499	−	3.84369i	−0.423296	−	0.152773i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	2.98864	+	2.98864i	0.118414	+	0.118414i
$638$		0			0
$639$	−9.02879	+	10.8790i	−0.357173	+	0.430365i
$640$		0			0
$641$			17.4067i			0.687525i	0.939057	+	0.343762i	$0.111701\pi$
$641$			17.4067i			0.687525i	−0.939057	+	0.343762i	$0.888299\pi$
$642$		0			0
$643$	−16.4684	+	16.4684i	−0.649449	+	0.649449i	−0.952860	−	0.303411i	$-0.901875\pi$
$643$	−16.4684	+	16.4684i	−0.649449	+	0.649449i	0.303411	+	0.952860i	$0.401875\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.9808	+	11.9808i	−0.471012	+	0.471012i	−0.902242	−	0.431230i	$-0.858080\pi$
$647$	−11.9808	+	11.9808i	−0.471012	+	0.471012i	0.431230	+	0.902242i	$0.358080\pi$
$648$		0			0
$649$		−	8.68204i		−	0.340800i
$650$		0			0
$651$	−6.62373	−	14.1050i	−0.259604	−	0.552818i
$652$		0			0
$653$	7.81877	+	7.81877i	0.305972	+	0.305972i	0.843345	−	0.537373i	$-0.180583\pi$
$653$	7.81877	+	7.81877i	0.305972	+	0.305972i	−0.537373	+	0.843345i	$0.680583\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−31.7896	+	2.95445i	−1.24023	+	0.115264i
$658$		0			0
$659$	−45.2957			−1.76447			−0.882235	−	0.470810i	$-0.843962\pi$
$659$	−45.2957			−1.76447			−0.882235	+	0.470810i	$0.843962\pi$
$660$		0			0
$661$	−0.836250			−0.0325263			−0.0162632	−	0.999868i	$-0.505177\pi$
$661$	−0.836250			−0.0325263			−0.0162632	+	0.999868i	$0.505177\pi$
$662$		0			0
$663$	17.3854	−	48.1706i	0.675192	−	1.87079i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.63857	−	3.63857i	−0.140886	−	0.140886i
$668$		0			0
$669$	11.1269	−	5.22521i	0.430191	−	0.202018i
$670$		0			0
$671$		−	21.5188i		−	0.830724i
$672$		0			0
$673$	27.4215	−	27.4215i	1.05702	−	1.05702i	0.0587488	−	0.998273i	$-0.481289\pi$
$673$	27.4215	−	27.4215i	1.05702	−	1.05702i	0.998273	−	0.0587488i	$-0.0187111\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.26276	+	7.26276i	−0.279131	+	0.279131i	−0.832762	−	0.553631i	$-0.813242\pi$
$677$	−7.26276	+	7.26276i	−0.279131	+	0.279131i	0.553631	+	0.832762i	$0.313242\pi$
$678$		0			0
$679$			13.2683i			0.509192i
$680$		0			0
$681$	27.0844	−	12.7189i	1.03788	−	0.487388i
$682$		0			0
$683$	13.6466	+	13.6466i	0.522171	+	0.522171i	0.918227	−	0.396055i	$-0.129621\pi$
$683$	13.6466	+	13.6466i	0.522171	+	0.522171i	−0.396055	+	0.918227i	$0.629621\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1.45204	+	4.02323i	−0.0553986	+	0.153496i
$688$		0			0
$689$	52.5366			2.00149
$690$		0			0
$691$	−10.1089			−0.384559			−0.192280	−	0.981340i	$-0.561588\pi$
$691$	−10.1089			−0.384559			−0.192280	+	0.981340i	$0.561588\pi$
$692$		0			0
$693$	7.27156	−	0.675801i	0.276224	−	0.0256716i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−22.2271	−	22.2271i	−0.841913	−	0.841913i
$698$		0			0
$699$	−12.8439	−	27.3507i	−0.485802	−	1.03450i
$700$		0			0
$701$		−	36.9379i		−	1.39512i	−0.716525	−	0.697562i	$-0.754268\pi$
$701$		−	36.9379i		−	1.39512i	0.716525	−	0.697562i	$-0.245732\pi$
$702$		0			0
$703$	−11.4476	+	11.4476i	−0.431755	+	0.431755i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.04269	−	5.04269i	0.189650	−	0.189650i
$708$		0			0
$709$		−	39.5205i		−	1.48423i	−0.670275	−	0.742113i	$-0.733824\pi$
$709$		−	39.5205i		−	1.48423i	0.670275	−	0.742113i	$-0.266176\pi$
$710$		0			0
$711$	2.22510	−	2.68107i	0.0834479	−	0.100548i
$712$		0			0
$713$	−23.2099	−	23.2099i	−0.869218	−	0.869218i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	15.6304	+	5.64121i	0.583728	+	0.210675i
$718$		0			0
$719$	17.8781			0.666740			0.333370	−	0.942796i	$-0.391814\pi$
$719$	17.8781			0.666740			0.333370	+	0.942796i	$0.391814\pi$
$720$		0			0
$721$	−11.9142			−0.443709
$722$		0			0
$723$	−7.32551	−	2.64387i	−0.272439	−	0.0983266i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	12.1939	+	12.1939i	0.452245	+	0.452245i	0.896099	−	0.443854i	$-0.146389\pi$
$727$	12.1939	+	12.1939i	0.452245	+	0.452245i	−0.443854	+	0.896099i	$0.646389\pi$
$728$		0			0
$729$	−13.1191	+	23.5985i	−0.485892	+	0.874019i
$730$		0			0
$731$			46.4549i			1.71820i
$732$		0			0
$733$	−21.7602	+	21.7602i	−0.803732	+	0.803732i	−0.983677	−	0.179945i	$-0.942408\pi$
$733$	−21.7602	+	21.7602i	−0.803732	+	0.803732i	0.179945	+	0.983677i	$0.442408\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	14.6806	−	14.6806i	0.540767	−	0.540767i
$738$		0			0
$739$			14.3075i			0.526310i	0.964754	+	0.263155i	$0.0847630\pi$
$739$			14.3075i			0.526310i	−0.964754	+	0.263155i	$0.915237\pi$
$740$		0			0
$741$	−5.01011	−	10.6688i	−0.184051	−	0.391930i
$742$		0			0
$743$	7.38543	+	7.38543i	0.270945	+	0.270945i	0.829481	−	0.558535i	$-0.188637\pi$
$743$	7.38543	+	7.38543i	0.270945	+	0.270945i	−0.558535	+	0.829481i	$0.688637\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.15753	+	12.4549i	0.0423518	+	0.455702i
$748$		0			0
$749$	3.65300			0.133478
$750$		0			0
$751$	−19.5508			−0.713419			−0.356710	−	0.934215i	$-0.616101\pi$
$751$	−19.5508			−0.713419			−0.356710	+	0.934215i	$0.616101\pi$
$752$		0			0
$753$	−7.96829	+	22.0782i	−0.290381	+	0.804573i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−28.2828	−	28.2828i	−1.02796	−	1.02796i	−0.999598	−	0.0283579i	$-0.990972\pi$
$757$	−28.2828	−	28.2828i	−1.02796	−	1.02796i	−0.0283579	−	0.999598i	$-0.509028\pi$
$758$		0			0
$759$	13.9240	−	6.53873i	0.505409	−	0.237341i
$760$		0			0
$761$		−	21.8245i		−	0.791138i	−0.918436	−	0.395569i	$-0.870547\pi$
$761$		−	21.8245i		−	0.791138i	0.918436	−	0.395569i	$-0.129453\pi$
$762$		0			0
$763$	0.819426	−	0.819426i	0.0296652	−	0.0296652i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	10.6591	−	10.6591i	0.384879	−	0.384879i
$768$		0			0
$769$			21.0365i			0.758595i	0.925275	+	0.379298i	$0.123834\pi$
$769$			21.0365i			0.758595i	−0.925275	+	0.379298i	$0.876166\pi$
$770$		0			0
$771$	−33.9173	+	15.9276i	−1.22150	+	0.573619i
$772$		0			0
$773$	11.4974	+	11.4974i	0.413533	+	0.413533i	0.882967	−	0.469434i	$-0.155542\pi$
$773$	11.4974	+	11.4974i	0.413533	+	0.413533i	−0.469434	+	0.882967i	$0.655542\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	5.91238	−	16.3817i	0.212105	−	0.587692i
$778$		0			0
$779$	−7.23467			−0.259209
$780$		0			0
$781$	11.4717			0.410489
$782$		0			0
$783$	−3.71567	−	6.31689i	−0.132787	−	0.225747i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	29.7791	+	29.7791i	1.06151	+	1.06151i	0.997980	+	0.0635285i	$0.0202354\pi$
$787$	29.7791	+	29.7791i	1.06151	+	1.06151i	0.0635285	+	0.997980i	$0.479765\pi$
$788$		0			0
$789$	18.5968	+	39.6011i	0.662062	+	1.40984i
$790$		0			0
$791$			2.62352i			0.0932817i
$792$		0			0
$793$	26.4191	−	26.4191i	0.938170	−	0.938170i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	18.2146	−	18.2146i	0.645194	−	0.645194i	−0.306634	−	0.951828i	$-0.599203\pi$
$797$	18.2146	−	18.2146i	0.645194	−	0.645194i	0.951828	+	0.306634i	$0.0992027\pi$
$798$		0			0
$799$		−	68.1644i		−	2.41148i
$800$		0			0
$801$	0.397812	+	0.330156i	0.0140560	+	0.0116655i
$802$		0			0
$803$	18.3185	+	18.3185i	0.646446	+	0.646446i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	38.4017	+	13.8597i	1.35180	+	0.487883i
$808$		0			0
$809$	32.6294			1.14719			0.573594	−	0.819140i	$-0.305549\pi$
$809$	32.6294			1.14719			0.573594	+	0.819140i	$0.305549\pi$
$810$		0			0
$811$	23.3733			0.820749			0.410375	−	0.911917i	$-0.365398\pi$
$811$	23.3733			0.820749			0.410375	+	0.911917i	$0.365398\pi$
$812$		0			0
$813$	−41.0116	−	14.8016i	−1.43834	−	0.519115i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	7.56027	+	7.56027i	0.264500	+	0.264500i
$818$		0			0
$819$	9.75715	+	8.09776i	0.340942	+	0.282958i
$820$		0			0
$821$			3.48918i			0.121773i	0.998145	+	0.0608867i	$0.0193928\pi$
$821$			3.48918i			0.121773i	−0.998145	+	0.0608867i	$0.980607\pi$
$822$		0			0
$823$	−23.0664	+	23.0664i	−0.804045	+	0.804045i	−0.983725	−	0.179680i	$-0.942494\pi$
$823$	−23.0664	+	23.0664i	−0.804045	+	0.804045i	0.179680	+	0.983725i	$0.442494\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.1289	+	18.1289i	−0.630404	+	0.630404i	−0.948169	−	0.317765i	$-0.897068\pi$
$827$	−18.1289	+	18.1289i	−0.630404	+	0.630404i	0.317765	+	0.948169i	$0.397068\pi$
$828$		0			0
$829$		−	7.54620i		−	0.262091i	−0.991376	−	0.131045i	$-0.958167\pi$
$829$		−	7.54620i		−	0.262091i	0.991376	−	0.131045i	$-0.0418333\pi$
$830$		0			0
$831$	0.931812	+	1.98426i	0.0323242	+	0.0688332i
$832$		0			0
$833$	4.94659	+	4.94659i	0.171389	+	0.171389i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−23.7017	−	40.2945i	−0.819250	−	1.39278i
$838$		0			0
$839$	17.3150			0.597780			0.298890	−	0.954288i	$-0.403384\pi$
$839$	17.3150			0.597780			0.298890	+	0.954288i	$0.403384\pi$
$840$		0			0
$841$	−27.0108			−0.931406
$842$		0			0
$843$	−6.75008	+	18.7028i	−0.232485	+	0.644159i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	3.58800	+	3.58800i	0.123285	+	0.123285i
$848$		0			0
$849$	−13.5414	+	6.35905i	−0.464738	+	0.218242i
$850$		0			0
$851$		−	36.6852i		−	1.25755i
$852$		0			0
$853$	−4.87944	+	4.87944i	−0.167069	+	0.167069i	−0.785690	−	0.618621i	$-0.787692\pi$
$853$	−4.87944	+	4.87944i	−0.167069	+	0.167069i	0.618621	+	0.785690i	$0.287692\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.1962	−	10.1962i	0.348296	−	0.348296i	−0.511178	−	0.859475i	$-0.670791\pi$
$857$	10.1962	−	10.1962i	0.348296	−	0.348296i	0.859475	+	0.511178i	$0.170791\pi$
$858$		0			0
$859$			43.7659i			1.49327i	0.665231	+	0.746637i	$0.268333\pi$
$859$			43.7659i			1.49327i	−0.665231	+	0.746637i	$0.731667\pi$
$860$		0			0
$861$	7.04473	−	3.30822i	0.240084	−	0.112744i
$862$		0			0
$863$	−9.65231	−	9.65231i	−0.328569	−	0.328569i	0.523473	−	0.852042i	$-0.324636\pi$
$863$	−9.65231	−	9.65231i	−0.328569	−	0.328569i	−0.852042	+	0.523473i	$0.824636\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	18.7792	−	52.0324i	0.637774	−	1.76711i
$868$		0			0
$869$	−2.82714			−0.0959042
$870$		0			0
$871$	36.0474			1.22142
$872$		0			0
$873$	3.68351	+	39.6342i	0.124668	+	1.34141i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	28.6620	+	28.6620i	0.967848	+	0.967848i	0.999499	−	0.0316508i	$-0.0100764\pi$
$877$	28.6620	+	28.6620i	0.967848	+	0.967848i	−0.0316508	+	0.999499i	$0.510076\pi$
$878$		0			0
$879$	−11.4086	−	24.2942i	−0.384803	−	0.819424i
$880$		0			0
$881$			28.5710i			0.962583i	0.876561	+	0.481291i	$0.159832\pi$
$881$			28.5710i			0.962583i	−0.876561	+	0.481291i	$0.840168\pi$
$882$		0			0
$883$	−21.9387	+	21.9387i	−0.738297	+	0.738297i	−0.972248	−	0.233952i	$-0.924834\pi$
$883$	−21.9387	+	21.9387i	−0.738297	+	0.738297i	0.233952	+	0.972248i	$0.424834\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.26720	−	5.26720i	0.176855	−	0.176855i	−0.613128	−	0.789983i	$-0.710089\pi$
$887$	5.26720	−	5.26720i	0.176855	−	0.176855i	0.789983	+	0.613128i	$0.210089\pi$
$888$		0			0
$889$		−	3.29750i		−	0.110595i
$890$		0			0
$891$	21.5335	−	4.03741i	0.721398	−	0.135258i
$892$		0			0
$893$	−11.0934	−	11.0934i	−0.371225	−	0.371225i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	25.1225	+	9.06704i	0.838817	+	0.302740i
$898$		0			0
$899$	12.6890			0.423203
$900$		0			0
$901$	86.9550			2.89689
$902$		0			0
$903$	−10.8189	−	3.90467i	−0.360030	−	0.129939i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	5.47086	+	5.47086i	0.181657	+	0.181657i	0.792077	−	0.610421i	$-0.209000\pi$
$907$	5.47086	+	5.47086i	0.181657	+	0.181657i	−0.610421	+	0.792077i	$0.709000\pi$
$908$		0			0
$909$	13.6632	−	16.4631i	0.453180	−	0.546046i
$910$		0			0
$911$			7.74155i			0.256489i	0.991743	+	0.128244i	$0.0409342\pi$
$911$			7.74155i			0.256489i	−0.991743	+	0.128244i	$0.959066\pi$
$912$		0			0
$913$	7.17705	−	7.17705i	0.237526	−	0.237526i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.38892	−	4.38892i	0.144935	−	0.144935i
$918$		0			0
$919$		−	25.4209i		−	0.838557i	−0.907858	−	0.419278i	$-0.862283\pi$
$919$		−	25.4209i		−	0.838557i	0.907858	−	0.419278i	$-0.137717\pi$
$920$		0			0
$921$	0.420438	+	0.895308i	0.0138539	+	0.0295014i
$922$		0			0
$923$	14.0840	+	14.0840i	0.463582	+	0.463582i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−35.5893	+	3.30758i	−1.16891	+	0.108635i
$928$		0			0
$929$	47.5656			1.56058			0.780289	−	0.625419i	$-0.215072\pi$
$929$	47.5656			1.56058			0.780289	+	0.625419i	$0.215072\pi$
$930$		0			0
$931$	1.61006			0.0527675
$932$		0			0
$933$	−14.0384	+	38.8969i	−0.459596	+	1.27343i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	9.39983	+	9.39983i	0.307079	+	0.307079i	0.843775	−	0.536696i	$-0.180328\pi$
$937$	9.39983	+	9.39983i	0.307079	+	0.307079i	−0.536696	+	0.843775i	$0.680328\pi$
$938$		0			0
$939$	2.06992	−	0.972038i	0.0675492	−	0.0317213i
$940$		0			0
$941$			7.36091i			0.239959i	0.992776	+	0.119979i	$0.0382828\pi$
$941$			7.36091i			0.239959i	−0.992776	+	0.119979i	$0.961717\pi$
$942$		0			0
$943$	11.5922	−	11.5922i	0.377494	−	0.377494i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.1921	+	15.1921i	−0.493678	+	0.493678i	−0.909463	−	0.415785i	$-0.863507\pi$
$947$	−15.1921	+	15.1921i	−0.493678	+	0.493678i	0.415785	+	0.909463i	$0.363507\pi$
$948$		0			0
$949$			44.9801i			1.46011i
$950$		0			0
$951$	−22.9739	+	10.7886i	−0.744981	+	0.349845i
$952$		0			0
$953$	−17.4626	−	17.4626i	−0.565670	−	0.565670i	0.365242	−	0.930913i	$-0.380986\pi$
$953$	−17.4626	−	17.4626i	−0.565670	−	0.565670i	−0.930913	+	0.365242i	$0.880986\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.01879	+	5.59356i	−0.0652581	+	0.180814i
$958$		0			0
$959$	7.53617			0.243356
$960$		0			0
$961$	49.9414			1.61101
$962$		0			0
$963$	10.9120	−	1.01413i	0.351634	−	0.0326800i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−23.0684	−	23.0684i	−0.741828	−	0.741828i	0.231101	−	0.972930i	$-0.425767\pi$
$967$	−23.0684	−	23.0684i	−0.741828	−	0.741828i	−0.972930	+	0.231101i	$0.925767\pi$
$968$		0			0
$969$	−8.29239	−	17.6583i	−0.266390	−	0.567268i
$970$		0			0
$971$			2.29785i			0.0737415i	0.999320	+	0.0368707i	$0.0117390\pi$
$971$			2.29785i			0.0737415i	−0.999320	+	0.0368707i	$0.988261\pi$
$972$		0			0
$973$	7.17076	−	7.17076i	0.229884	−	0.229884i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.29551	−	8.29551i	0.265397	−	0.265397i	−0.561845	−	0.827242i	$-0.689908\pi$
$977$	8.29551	−	8.29551i	0.265397	−	0.265397i	0.827242	+	0.561845i	$0.189908\pi$
$978$		0			0
$979$		−	0.419486i		−	0.0134068i
$980$		0			0
$981$	2.22024	−	2.67521i	0.0708869	−	0.0854130i
$982$		0			0
$983$	6.75732	+	6.75732i	0.215525	+	0.215525i	0.806610	−	0.591085i	$-0.201300\pi$
$983$	6.75732	+	6.75732i	0.215525	+	0.215525i	−0.591085	+	0.806610i	$0.701300\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	15.8748	+	5.72942i	0.505300	+	0.182369i
$988$		0			0
$989$	−24.2278			−0.770398
$990$		0			0
$991$	2.89708			0.0920287			0.0460143	−	0.998941i	$-0.485348\pi$
$991$	2.89708			0.0920287			0.0460143	+	0.998941i	$0.485348\pi$
$992$		0			0
$993$	2.89394	+	1.04446i	0.0918363	+	0.0331449i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.587263	+	0.587263i	0.0185988	+	0.0185988i	0.716345	−	0.697746i	$-0.245814\pi$
$997$	0.587263	+	0.587263i	0.0185988	+	0.0185988i	−0.697746	+	0.716345i	$0.745814\pi$
$998$		0			0
$999$	13.1132	−	50.5757i	0.414883	−	1.60015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.s.b.1457.11		24
3.2	odd	2	inner	2100.2.s.b.1457.5		24
5.2	odd	4		420.2.s.a.113.8	yes	24
5.3	odd	4	inner	2100.2.s.b.1793.5		24
5.4	even	2		420.2.s.a.197.2	yes	24
15.2	even	4		420.2.s.a.113.2	✓	24
15.8	even	4	inner	2100.2.s.b.1793.11		24
15.14	odd	2		420.2.s.a.197.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.s.a.113.2	✓	24	15.2	even	4
420.2.s.a.113.8	yes	24	5.2	odd	4
420.2.s.a.197.2	yes	24	5.4	even	2
420.2.s.a.197.8	yes	24	15.14	odd	2
2100.2.s.b.1457.5		24	3.2	odd	2	inner
2100.2.s.b.1457.11		24	1.1	even	1	trivial
2100.2.s.b.1793.5		24	5.3	odd	4	inner
2100.2.s.b.1793.11		24	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.62919 + 0.587996i) q^{3} +(0.707107 + 0.707107i) q^{7} +(2.30852 + 1.91591i) q^{9} +O(q^{10})\)	\(q+(1.62919 + 0.587996i) q^{3} +(0.707107 + 0.707107i) q^{7} +(2.30852 + 1.91591i) q^{9} -2.43430i q^{11} +(2.98864 - 2.98864i) q^{13} +(4.94659 - 4.94659i) q^{17} -1.61006i q^{19} +(0.736236 + 1.56779i) q^{21} +(2.57981 + 2.57981i) q^{23} +(2.63447 + 4.47879i) q^{27} -1.41040 q^{29} -8.99675 q^{31} +(1.43136 - 3.96593i) q^{33} +(-7.11006 - 7.11006i) q^{37} +(6.62637 - 3.11176i) q^{39} -4.49343i q^{41} +(-4.69565 + 4.69565i) q^{43} +(6.89003 - 6.89003i) q^{47} +1.00000i q^{49} +(10.9675 - 5.15037i) q^{51} +(8.78938 + 8.78938i) q^{53} +(0.946707 - 2.62309i) q^{57} +3.56655 q^{59} +8.83984 q^{61} +(0.277616 + 2.98713i) q^{63} +(6.03073 + 6.03073i) q^{67} +(2.68609 + 5.71992i) q^{69} +4.71253i q^{71} +(-7.52517 + 7.52517i) q^{73} +(1.72131 - 1.72131i) q^{77} -1.16138i q^{79} +(1.65855 + 8.84586i) q^{81} +(2.94830 + 2.94830i) q^{83} +(-2.29781 - 0.829310i) q^{87} +0.172323 q^{89} +4.22658 q^{91} +(-14.6574 - 5.29005i) q^{93} +(9.38212 + 9.38212i) q^{97} +(4.66390 - 5.61963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3}+O(q^{10}) \) 24 * q + 4 * q^3	\( 24 q + 4 q^{3} - 24 q^{13} + 4 q^{21} - 8 q^{27} - 16 q^{31} + 20 q^{33} - 32 q^{37} + 8 q^{43} + 52 q^{51} + 28 q^{57} - 8 q^{63} + 24 q^{67} - 12 q^{81} + 20 q^{87} - 24 q^{91} - 20 q^{93} + 104 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^13 + 4 * q^21 - 8 * q^27 - 16 * q^31 + 20 * q^33 - 32 * q^37 + 8 * q^43 + 52 * q^51 + 28 * q^57 - 8 * q^63 + 24 * q^67 - 12 * q^81 + 20 * q^87 - 24 * q^91 - 20 * q^93 + 104 * q^97

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