LMFDB - Embedded newform 5577.2.a.bf.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.a (trivial)

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:	yes
Analytic conductor:	$44.5325692073$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 5 x^{12} + 90 x^{11} - 84 x^{10} - 450 x^{9} + 761 x^{8} + 782 x^{7} - 2061 x^{6} + \cdots + 64 $ x^14 - 6x^13 - 5x^12 + 90x^11 - 84x^10 - 450x^9 + 761x^8 + 782x^7 - 2061x^6 - 92x^5 + 1921x^4 - 400x^3 - 635x^2 + 112*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.291537$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.291537 q^{2} +1.00000 q^{3} -1.91501 q^{4} -3.62473 q^{5} +0.291537 q^{6} -1.35287 q^{7} -1.14137 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.291537 q^{2} +1.00000 q^{3} -1.91501 q^{4} -3.62473 q^{5} +0.291537 q^{6} -1.35287 q^{7} -1.14137 q^{8} +1.00000 q^{9} -1.05674 q^{10} -1.00000 q^{11} -1.91501 q^{12} -0.394413 q^{14} -3.62473 q^{15} +3.49726 q^{16} -3.00389 q^{17} +0.291537 q^{18} +7.12475 q^{19} +6.94138 q^{20} -1.35287 q^{21} -0.291537 q^{22} -1.04717 q^{23} -1.14137 q^{24} +8.13867 q^{25} +1.00000 q^{27} +2.59076 q^{28} +8.54023 q^{29} -1.05674 q^{30} +6.40036 q^{31} +3.30232 q^{32} -1.00000 q^{33} -0.875744 q^{34} +4.90380 q^{35} -1.91501 q^{36} -9.77170 q^{37} +2.07713 q^{38} +4.13715 q^{40} +2.49920 q^{41} -0.394413 q^{42} +9.35075 q^{43} +1.91501 q^{44} -3.62473 q^{45} -0.305287 q^{46} -6.55910 q^{47} +3.49726 q^{48} -5.16973 q^{49} +2.37272 q^{50} -3.00389 q^{51} -1.69147 q^{53} +0.291537 q^{54} +3.62473 q^{55} +1.54413 q^{56} +7.12475 q^{57} +2.48979 q^{58} +1.88793 q^{59} +6.94138 q^{60} +6.08777 q^{61} +1.86594 q^{62} -1.35287 q^{63} -6.03178 q^{64} -0.291537 q^{66} -8.83689 q^{67} +5.75247 q^{68} -1.04717 q^{69} +1.42964 q^{70} -13.8980 q^{71} -1.14137 q^{72} +4.82119 q^{73} -2.84881 q^{74} +8.13867 q^{75} -13.6439 q^{76} +1.35287 q^{77} +7.17375 q^{79} -12.6766 q^{80} +1.00000 q^{81} +0.728609 q^{82} -2.66970 q^{83} +2.59076 q^{84} +10.8883 q^{85} +2.72609 q^{86} +8.54023 q^{87} +1.14137 q^{88} -15.6776 q^{89} -1.05674 q^{90} +2.00533 q^{92} +6.40036 q^{93} -1.91222 q^{94} -25.8253 q^{95} +3.30232 q^{96} -4.23268 q^{97} -1.50717 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 6 q^{2} + 14 q^{3} + 18 q^{4} - 12 q^{5} - 6 q^{6} - 12 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 6 * q^2 + 14 * q^3 + 18 * q^4 - 12 * q^5 - 6 * q^6 - 12 * q^7 - 12 * q^8 + 14 * q^9	$ 14 q - 6 q^{2} + 14 q^{3} + 18 q^{4} - 12 q^{5} - 6 q^{6} - 12 q^{7} - 12 q^{8} + 14 q^{9} - 14 q^{11} + 18 q^{12} - 2 q^{14} - 12 q^{15} + 22 q^{16} + 2 q^{17} - 6 q^{18} + 2 q^{19} - 44 q^{20} - 12 q^{21} + 6 q^{22} + 2 q^{23} - 12 q^{24} + 20 q^{25} + 14 q^{27} - 24 q^{28} - 28 q^{31} - 30 q^{32} - 14 q^{33} + 16 q^{34} - 2 q^{35} + 18 q^{36} - 10 q^{38} + 10 q^{40} - 40 q^{41} - 2 q^{42} - 2 q^{43} - 18 q^{44} - 12 q^{45} - 32 q^{46} - 48 q^{47} + 22 q^{48} + 10 q^{49} + 2 q^{51} + 8 q^{53} - 6 q^{54} + 12 q^{55} - 10 q^{56} + 2 q^{57} + 16 q^{58} - 40 q^{59} - 44 q^{60} + 4 q^{61} - 6 q^{62} - 12 q^{63} + 16 q^{64} + 6 q^{66} - 40 q^{67} + 22 q^{68} + 2 q^{69} + 40 q^{70} - 36 q^{71} - 12 q^{72} - 10 q^{73} - 48 q^{74} + 20 q^{75} + 4 q^{76} + 12 q^{77} - 24 q^{79} - 68 q^{80} + 14 q^{81} + 46 q^{82} - 12 q^{83} - 24 q^{84} - 34 q^{85} - 48 q^{86} + 12 q^{88} - 20 q^{89} + 36 q^{92} - 28 q^{93} - 50 q^{94} - 60 q^{95} - 30 q^{96} + 16 q^{97} - 44 q^{98} - 14 q^{99}+O(q^{100}) $ 14 * q - 6 * q^2 + 14 * q^3 + 18 * q^4 - 12 * q^5 - 6 * q^6 - 12 * q^7 - 12 * q^8 + 14 * q^9 - 14 * q^11 + 18 * q^12 - 2 * q^14 - 12 * q^15 + 22 * q^16 + 2 * q^17 - 6 * q^18 + 2 * q^19 - 44 * q^20 - 12 * q^21 + 6 * q^22 + 2 * q^23 - 12 * q^24 + 20 * q^25 + 14 * q^27 - 24 * q^28 - 28 * q^31 - 30 * q^32 - 14 * q^33 + 16 * q^34 - 2 * q^35 + 18 * q^36 - 10 * q^38 + 10 * q^40 - 40 * q^41 - 2 * q^42 - 2 * q^43 - 18 * q^44 - 12 * q^45 - 32 * q^46 - 48 * q^47 + 22 * q^48 + 10 * q^49 + 2 * q^51 + 8 * q^53 - 6 * q^54 + 12 * q^55 - 10 * q^56 + 2 * q^57 + 16 * q^58 - 40 * q^59 - 44 * q^60 + 4 * q^61 - 6 * q^62 - 12 * q^63 + 16 * q^64 + 6 * q^66 - 40 * q^67 + 22 * q^68 + 2 * q^69 + 40 * q^70 - 36 * q^71 - 12 * q^72 - 10 * q^73 - 48 * q^74 + 20 * q^75 + 4 * q^76 + 12 * q^77 - 24 * q^79 - 68 * q^80 + 14 * q^81 + 46 * q^82 - 12 * q^83 - 24 * q^84 - 34 * q^85 - 48 * q^86 + 12 * q^88 - 20 * q^89 + 36 * q^92 - 28 * q^93 - 50 * q^94 - 60 * q^95 - 30 * q^96 + 16 * q^97 - 44 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	0.291537	0.206148	0.103074	−	0.994674i	$-0.467132\pi$
$2$	0.291537	0.206148	0.103074	+	0.994674i	$0.467132\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.91501	−0.957503
$5$	−3.62473	−1.62103	−0.810514	−	0.585719i	$-0.800812\pi$
$5$	−3.62473	−1.62103	−0.810514	+	0.585719i	$0.800812\pi$
$6$	0.291537	0.119019
$7$	−1.35287	−0.511338	−0.255669	−	0.966764i	$-0.582296\pi$
$7$	−1.35287	−0.511338	−0.255669	+	0.966764i	$0.582296\pi$
$8$	−1.14137	−0.403535
$9$	1.00000	0.333333
$10$	−1.05674	−0.334171
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.91501	−0.552815
$13$	0	0
$13$	0	0
$14$	−0.394413	−0.105411
$15$	−3.62473	−0.935901
$16$	3.49726	0.874316
$17$	−3.00389	−0.728550	−0.364275	−	0.931291i	$-0.618683\pi$
$17$	−3.00389	−0.728550	−0.364275	+	0.931291i	$0.618683\pi$
$18$	0.291537	0.0687159
$19$	7.12475	1.63453	0.817265	−	0.576262i	$-0.195489\pi$
$19$	7.12475	1.63453	0.817265	+	0.576262i	$0.195489\pi$
$20$	6.94138	1.55214
$21$	−1.35287	−0.295221
$22$	−0.291537	−0.0621558
$23$	−1.04717	−0.218349	−0.109175	−	0.994023i	$-0.534821\pi$
$23$	−1.04717	−0.218349	−0.109175	+	0.994023i	$0.534821\pi$
$24$	−1.14137	−0.232981
$25$	8.13867	1.62773
$26$	0	0
$27$	1.00000	0.192450
$28$	2.59076	0.489608
$29$	8.54023	1.58588	0.792940	−	0.609299i	$-0.208549\pi$
$29$	8.54023	1.58588	0.792940	+	0.609299i	$0.208549\pi$
$30$	−1.05674	−0.192934
$31$	6.40036	1.14954	0.574769	−	0.818316i	$-0.305092\pi$
$31$	6.40036	1.14954	0.574769	+	0.818316i	$0.305092\pi$
$32$	3.30232	0.583773
$33$	−1.00000	−0.174078
$34$	−0.875744	−0.150189
$35$	4.90380	0.828894
$36$	−1.91501	−0.319168
$37$	−9.77170	−1.60646	−0.803229	−	0.595670i	$-0.796886\pi$
$37$	−9.77170	−1.60646	−0.803229	+	0.595670i	$0.796886\pi$
$38$	2.07713	0.336955
$39$	0	0
$40$	4.13715	0.654141
$41$	2.49920	0.390310	0.195155	−	0.980772i	$-0.437479\pi$
$41$	2.49920	0.390310	0.195155	+	0.980772i	$0.437479\pi$
$42$	−0.394413	−0.0608592
$43$	9.35075	1.42598	0.712988	−	0.701177i	$-0.247342\pi$
$43$	9.35075	1.42598	0.712988	+	0.701177i	$0.247342\pi$
$44$	1.91501	0.288698
$45$	−3.62473	−0.540343
$46$	−0.305287	−0.0450122
$47$	−6.55910	−0.956744	−0.478372	−	0.878157i	$-0.658773\pi$
$47$	−6.55910	−0.956744	−0.478372	+	0.878157i	$0.658773\pi$
$48$	3.49726	0.504786
$49$	−5.16973	−0.738533
$50$	2.37272	0.335553
$51$	−3.00389	−0.420629
$52$	0	0
$53$	−1.69147	−0.232342	−0.116171	−	0.993229i	$-0.537062\pi$
$53$	−1.69147	−0.232342	−0.116171	+	0.993229i	$0.537062\pi$
$54$	0.291537	0.0396731
$55$	3.62473	0.488758
$56$	1.54413	0.206343
$57$	7.12475	0.943697
$58$	2.48979	0.326925
$59$	1.88793	0.245787	0.122894	−	0.992420i	$-0.460783\pi$
$59$	1.88793	0.245787	0.122894	+	0.992420i	$0.460783\pi$
$60$	6.94138	0.896128
$61$	6.08777	0.779460	0.389730	−	0.920929i	$-0.372568\pi$
$61$	6.08777	0.779460	0.389730	+	0.920929i	$0.372568\pi$
$62$	1.86594	0.236975
$63$	−1.35287	−0.170446
$64$	−6.03178	−0.753972
$65$	0	0
$66$	−0.291537	−0.0358857
$67$	−8.83689	−1.07960	−0.539799	−	0.841794i	$-0.681500\pi$
$67$	−8.83689	−1.07960	−0.539799	+	0.841794i	$0.681500\pi$
$68$	5.75247	0.697589
$69$	−1.04717	−0.126064
$70$	1.42964	0.170875
$71$	−13.8980	−1.64939	−0.824693	−	0.565581i	$-0.808652\pi$
$71$	−13.8980	−1.64939	−0.824693	+	0.565581i	$0.808652\pi$
$72$	−1.14137	−0.134512
$73$	4.82119	0.564278	0.282139	−	0.959374i	$-0.408956\pi$
$73$	4.82119	0.564278	0.282139	+	0.959374i	$0.408956\pi$
$74$	−2.84881	−0.331167
$75$	8.13867	0.939772
$76$	−13.6439	−1.56507
$77$	1.35287	0.154174
$78$	0	0
$79$	7.17375	0.807110	0.403555	−	0.914955i	$-0.367774\pi$
$79$	7.17375	0.807110	0.403555	+	0.914955i	$0.367774\pi$
$80$	−12.6766	−1.41729
$81$	1.00000	0.111111
$82$	0.728609	0.0804614
$83$	−2.66970	−0.293038	−0.146519	−	0.989208i	$-0.546807\pi$
$83$	−2.66970	−0.293038	−0.146519	+	0.989208i	$0.546807\pi$
$84$	2.59076	0.282675
$85$	10.8883	1.18100
$86$	2.72609	0.293961
$87$	8.54023	0.915609
$88$	1.14137	0.121670
$89$	−15.6776	−1.66182	−0.830911	−	0.556405i	$-0.812180\pi$
$89$	−15.6776	−1.66182	−0.830911	+	0.556405i	$0.812180\pi$
$90$	−1.05674	−0.111390
$91$	0	0
$92$	2.00533	0.209070
$93$	6.40036	0.663686
$94$	−1.91222	−0.197230
$95$	−25.8253	−2.64962
$96$	3.30232	0.337041
$97$	−4.23268	−0.429763	−0.214882	−	0.976640i	$-0.568937\pi$
$97$	−4.23268	−0.429763	−0.214882	+	0.976640i	$0.568937\pi$
$98$	−1.50717	−0.152247
$99$	−1.00000	−0.100504
$100$	−15.5856	−1.55856
$101$	−12.5949	−1.25324	−0.626619	−	0.779326i	$-0.715562\pi$
$101$	−12.5949	−1.25324	−0.626619	+	0.779326i	$0.715562\pi$
$102$	−0.875744	−0.0867116
$103$	16.5972	1.63537	0.817685	−	0.575666i	$-0.195257\pi$
$103$	16.5972	1.63537	0.817685	+	0.575666i	$0.195257\pi$
$104$	0	0
$105$	4.90380	0.478562
$106$	−0.493126	−0.0478967
$107$	0.0137756	0.00133174	0.000665870	−	1.00000i	$-0.499788\pi$
$107$	0.0137756	0.00133174	0.000665870		1.00000i	$0.499788\pi$
$108$	−1.91501	−0.184272
$109$	−17.0753	−1.63551	−0.817756	−	0.575564i	$-0.804782\pi$
$109$	−17.0753	−1.63551	−0.817756	+	0.575564i	$0.804782\pi$
$110$	1.05674	0.100756
$111$	−9.77170	−0.927489
$112$	−4.73136	−0.447071
$113$	−12.6286	−1.18800	−0.594000	−	0.804465i	$-0.702452\pi$
$113$	−12.6286	−1.18800	−0.594000	+	0.804465i	$0.702452\pi$
$114$	2.07713	0.194541
$115$	3.79569	0.353950
$116$	−16.3546	−1.51849
$117$	0	0
$118$	0.550400	0.0506684
$119$	4.06388	0.372536
$120$	4.13715	0.377668
$121$	1.00000	0.0909091
$122$	1.77481	0.160684
$123$	2.49920	0.225345
$124$	−12.2567	−1.10069
$125$	−11.3768	−1.01757
$126$	−0.394413	−0.0351371
$127$	0.172249	0.0152846	0.00764231	−	0.999971i	$-0.497567\pi$
$127$	0.172249	0.0152846	0.00764231	+	0.999971i	$0.497567\pi$
$128$	−8.36312	−0.739202
$129$	9.35075	0.823287
$130$	0	0
$131$	6.69726	0.585142	0.292571	−	0.956244i	$-0.405489\pi$
$131$	6.69726	0.585142	0.292571	+	0.956244i	$0.405489\pi$
$132$	1.91501	0.166680
$133$	−9.63890	−0.835798
$134$	−2.57628	−0.222557
$135$	−3.62473	−0.311967
$136$	3.42854	0.293995
$137$	16.1504	1.37982	0.689909	−	0.723896i	$-0.257650\pi$
$137$	16.1504	1.37982	0.689909	+	0.723896i	$0.257650\pi$
$138$	−0.305287	−0.0259878
$139$	−6.94791	−0.589314	−0.294657	−	0.955603i	$-0.595205\pi$
$139$	−6.94791	−0.589314	−0.294657	+	0.955603i	$0.595205\pi$
$140$	−9.39082	−0.793669
$141$	−6.55910	−0.552376
$142$	−4.05177	−0.340017
$143$	0	0
$144$	3.49726	0.291439
$145$	−30.9560	−2.57076
$146$	1.40555	0.116324
$147$	−5.16973	−0.426392
$148$	18.7129	1.53819
$149$	12.6470	1.03608	0.518040	−	0.855356i	$-0.326662\pi$
$149$	12.6470	1.03608	0.518040	+	0.855356i	$0.326662\pi$
$150$	2.37272	0.193732
$151$	−0.705772	−0.0574349	−0.0287175	−	0.999588i	$-0.509142\pi$
$151$	−0.705772	−0.0574349	−0.0287175	+	0.999588i	$0.509142\pi$
$152$	−8.13197	−0.659590
$153$	−3.00389	−0.242850
$154$	0.394413	0.0317827
$155$	−23.1996	−1.86343
$156$	0	0
$157$	−16.4554	−1.31328	−0.656642	−	0.754203i	$-0.728024\pi$
$157$	−16.4554	−1.31328	−0.656642	+	0.754203i	$0.728024\pi$
$158$	2.09141	0.166384
$159$	−1.69147	−0.134142
$160$	−11.9700	−0.946312
$161$	1.41668	0.111650
$162$	0.291537	0.0229053
$163$	−10.8137	−0.846997	−0.423498	−	0.905897i	$-0.639198\pi$
$163$	−10.8137	−0.846997	−0.423498	+	0.905897i	$0.639198\pi$
$164$	−4.78599	−0.373723
$165$	3.62473	0.282185
$166$	−0.778316	−0.0604090
$167$	13.3304	1.03153	0.515767	−	0.856729i	$-0.327507\pi$
$167$	13.3304	1.03153	0.515767	+	0.856729i	$0.327507\pi$
$168$	1.54413	0.119132
$169$	0	0
$170$	3.17433	0.243460
$171$	7.12475	0.544844
$172$	−17.9067	−1.36538
$173$	−14.2482	−1.08327	−0.541634	−	0.840614i	$-0.682194\pi$
$173$	−14.2482	−1.08327	−0.541634	+	0.840614i	$0.682194\pi$
$174$	2.48979	0.188750
$175$	−11.0106	−0.832323
$176$	−3.49726	−0.263616
$177$	1.88793	0.141905
$178$	−4.57060	−0.342581
$179$	16.3217	1.21994	0.609969	−	0.792425i	$-0.291182\pi$
$179$	16.3217	1.21994	0.609969	+	0.792425i	$0.291182\pi$
$180$	6.94138	0.517380
$181$	7.14758	0.531275	0.265638	−	0.964073i	$-0.414418\pi$
$181$	7.14758	0.531275	0.265638	+	0.964073i	$0.414418\pi$
$182$	0	0
$183$	6.08777	0.450021
$184$	1.19520	0.0881114
$185$	35.4198	2.60411
$186$	1.86594	0.136817
$187$	3.00389	0.219666
$188$	12.5607	0.916085
$189$	−1.35287	−0.0984071
$190$	−7.52902	−0.546213
$191$	−4.05297	−0.293263	−0.146631	−	0.989191i	$-0.546843\pi$
$191$	−4.05297	−0.293263	−0.146631	+	0.989191i	$0.546843\pi$
$192$	−6.03178	−0.435306
$193$	20.1309	1.44905	0.724526	−	0.689247i	$-0.242058\pi$
$193$	20.1309	1.44905	0.724526	+	0.689247i	$0.242058\pi$
$194$	−1.23398	−0.0885946
$195$	0	0
$196$	9.90007	0.707148
$197$	−4.07901	−0.290618	−0.145309	−	0.989386i	$-0.546418\pi$
$197$	−4.07901	−0.290618	−0.145309	+	0.989386i	$0.546418\pi$
$198$	−0.291537	−0.0207186
$199$	−0.0747920	−0.00530186	−0.00265093	−	0.999996i	$-0.500844\pi$
$199$	−0.0747920	−0.00530186	−0.00265093	+	0.999996i	$0.500844\pi$
$200$	−9.28921	−0.656847
$201$	−8.83689	−0.623306
$202$	−3.67187	−0.258352
$203$	−11.5539	−0.810922
$204$	5.75247	0.402753
$205$	−9.05893	−0.632703
$206$	4.83869	0.337128
$207$	−1.04717	−0.0727831
$208$	0	0
$209$	−7.12475	−0.492830
$210$	1.42964	0.0986544
$211$	11.7288	0.807443	0.403721	−	0.914882i	$-0.367717\pi$
$211$	11.7288	0.807443	0.403721	+	0.914882i	$0.367717\pi$
$212$	3.23918	0.222468
$213$	−13.8980	−0.952273
$214$	0.00401610	0.000274535 0
$215$	−33.8939	−2.31155
$216$	−1.14137	−0.0776603
$217$	−8.65888	−0.587803
$218$	−4.97806	−0.337157
$219$	4.82119	0.325786
$220$	−6.94138	−0.467988
$221$	0	0
$222$	−2.84881	−0.191200
$223$	−16.8842	−1.13065	−0.565323	−	0.824869i	$-0.691249\pi$
$223$	−16.8842	−1.13065	−0.565323	+	0.824869i	$0.691249\pi$
$224$	−4.46762	−0.298505
$225$	8.13867	0.542578
$226$	−3.68171	−0.244904
$227$	−20.8289	−1.38246	−0.691230	−	0.722635i	$-0.742931\pi$
$227$	−20.8289	−1.38246	−0.691230	+	0.722635i	$0.742931\pi$
$228$	−13.6439	−0.903593
$229$	8.80483	0.581839	0.290920	−	0.956747i	$-0.406039\pi$
$229$	8.80483	0.581839	0.290920	+	0.956747i	$0.406039\pi$
$230$	1.10658	0.0729660
$231$	1.35287	0.0890126
$232$	−9.74754	−0.639958
$233$	11.2325	0.735866	0.367933	−	0.929852i	$-0.380066\pi$
$233$	11.2325	0.735866	0.367933	+	0.929852i	$0.380066\pi$
$234$	0	0
$235$	23.7750	1.55091
$236$	−3.61539	−0.235342
$237$	7.17375	0.465985
$238$	1.18477	0.0767973
$239$	14.7314	0.952892	0.476446	−	0.879204i	$-0.341925\pi$
$239$	14.7314	0.952892	0.476446	+	0.879204i	$0.341925\pi$
$240$	−12.6766	−0.818273
$241$	−2.58092	−0.166252	−0.0831259	−	0.996539i	$-0.526490\pi$
$241$	−2.58092	−0.166252	−0.0831259	+	0.996539i	$0.526490\pi$
$242$	0.291537	0.0187407
$243$	1.00000	0.0641500
$244$	−11.6581	−0.746335
$245$	18.7389	1.19718
$246$	0.728609	0.0464544
$247$	0	0
$248$	−7.30516	−0.463878
$249$	−2.66970	−0.169185
$250$	−3.31676	−0.209770
$251$	20.3491	1.28442	0.642211	−	0.766528i	$-0.278017\pi$
$251$	20.3491	1.28442	0.642211	+	0.766528i	$0.278017\pi$
$252$	2.59076	0.163203
$253$	1.04717	0.0658348
$254$	0.0502169	0.00315089
$255$	10.8883	0.681851
$256$	9.62540	0.601587
$257$	−26.9824	−1.68311	−0.841557	−	0.540169i	$-0.818360\pi$
$257$	−26.9824	−1.68311	−0.841557	+	0.540169i	$0.818360\pi$
$258$	2.72609	0.169719
$259$	13.2199	0.821444
$260$	0	0
$261$	8.54023	0.528627
$262$	1.95250	0.120626
$263$	1.84546	0.113796	0.0568980	−	0.998380i	$-0.481879\pi$
$263$	1.84546	0.113796	0.0568980	+	0.998380i	$0.481879\pi$
$264$	1.14137	0.0702463
$265$	6.13113	0.376632
$266$	−2.81009	−0.172298
$267$	−15.6776	−0.959454
$268$	16.9227	1.03372
$269$	−6.42846	−0.391950	−0.195975	−	0.980609i	$-0.562787\pi$
$269$	−6.42846	−0.391950	−0.195975	+	0.980609i	$0.562787\pi$
$270$	−1.05674	−0.0643113
$271$	−2.26323	−0.137481	−0.0687407	−	0.997635i	$-0.521898\pi$
$271$	−2.26323	−0.137481	−0.0687407	+	0.997635i	$0.521898\pi$
$272$	−10.5054	−0.636983
$273$	0	0
$274$	4.70842	0.284446
$275$	−8.13867	−0.490780
$276$	2.00533	0.120707
$277$	−21.8111	−1.31050	−0.655250	−	0.755412i	$-0.727437\pi$
$277$	−21.8111	−1.31050	−0.655250	+	0.755412i	$0.727437\pi$
$278$	−2.02557	−0.121486
$279$	6.40036	0.383179
$280$	−5.59704	−0.334487
$281$	7.10283	0.423719	0.211860	−	0.977300i	$-0.432048\pi$
$281$	7.10283	0.423719	0.211860	+	0.977300i	$0.432048\pi$
$282$	−1.91222	−0.113871
$283$	−2.36093	−0.140343	−0.0701715	−	0.997535i	$-0.522355\pi$
$283$	−2.36093	−0.140343	−0.0701715	+	0.997535i	$0.522355\pi$
$284$	26.6147	1.57929
$285$	−25.8253	−1.52976
$286$	0	0
$287$	−3.38111	−0.199580
$288$	3.30232	0.194591
$289$	−7.97665	−0.469215
$290$	−9.02482	−0.529955
$291$	−4.23268	−0.248124
$292$	−9.23261	−0.540298
$293$	−6.81218	−0.397972	−0.198986	−	0.980002i	$-0.563765\pi$
$293$	−6.81218	−0.397972	−0.198986	+	0.980002i	$0.563765\pi$
$294$	−1.50717	−0.0878997
$295$	−6.84322	−0.398428
$296$	11.1531	0.648261
$297$	−1.00000	−0.0580259
$298$	3.68706	0.213586
$299$	0	0
$300$	−15.5856	−0.899835
$301$	−12.6504	−0.729156
$302$	−0.205758	−0.0118401
$303$	−12.5949	−0.723557
$304$	24.9171	1.42910
$305$	−22.0665	−1.26353
$306$	−0.875744	−0.0500629
$307$	−21.5065	−1.22744	−0.613720	−	0.789524i	$-0.710327\pi$
$307$	−21.5065	−1.22744	−0.613720	+	0.789524i	$0.710327\pi$
$308$	−2.59076	−0.147622
$309$	16.5972	0.944181
$310$	−6.76353	−0.384142
$311$	−17.1520	−0.972602	−0.486301	−	0.873791i	$-0.661654\pi$
$311$	−17.1520	−0.972602	−0.486301	+	0.873791i	$0.661654\pi$
$312$	0	0
$313$	6.59696	0.372882	0.186441	−	0.982466i	$-0.440305\pi$
$313$	6.59696	0.372882	0.186441	+	0.982466i	$0.440305\pi$
$314$	−4.79735	−0.270730
$315$	4.90380	0.276298
$316$	−13.7378	−0.772810
$317$	−31.0269	−1.74264	−0.871321	−	0.490713i	$-0.836736\pi$
$317$	−31.0269	−1.74264	−0.871321	+	0.490713i	$0.836736\pi$
$318$	−0.493126	−0.0276531
$319$	−8.54023	−0.478161
$320$	21.8636	1.22221
$321$	0.0137756	0.000768880 0
$322$	0.413015	0.0230164
$323$	−21.4020	−1.19084
$324$	−1.91501	−0.106389
$325$	0	0
$326$	−3.15260	−0.174606
$327$	−17.0753	−0.944264
$328$	−2.85251	−0.157503
$329$	8.87364	0.489220
$330$	1.05674	0.0581717
$331$	−20.2735	−1.11433	−0.557166	−	0.830401i	$-0.688111\pi$
$331$	−20.2735	−1.11433	−0.557166	+	0.830401i	$0.688111\pi$
$332$	5.11249	0.280584
$333$	−9.77170	−0.535486
$334$	3.88629	0.212648
$335$	32.0313	1.75006
$336$	−4.73136	−0.258117
$337$	0.168823	0.00919636	0.00459818	−	0.999989i	$-0.498536\pi$
$337$	0.168823	0.00919636	0.00459818	+	0.999989i	$0.498536\pi$
$338$	0	0
$339$	−12.6286	−0.685893
$340$	−20.8511	−1.13081
$341$	−6.40036	−0.346599
$342$	2.07713	0.112318
$343$	16.4641	0.888979
$344$	−10.6726	−0.575430
$345$	3.79569	0.204353
$346$	−4.15386	−0.223313
$347$	11.3670	0.610211	0.305106	−	0.952318i	$-0.401308\pi$
$347$	11.3670	0.610211	0.305106	+	0.952318i	$0.401308\pi$
$348$	−16.3546	−0.876698
$349$	24.0656	1.28820	0.644100	−	0.764941i	$-0.277232\pi$
$349$	24.0656	1.28820	0.644100	+	0.764941i	$0.277232\pi$
$350$	−3.20999	−0.171581
$351$	0	0
$352$	−3.30232	−0.176014
$353$	−10.5415	−0.561065	−0.280533	−	0.959844i	$-0.590511\pi$
$353$	−10.5415	−0.561065	−0.280533	+	0.959844i	$0.590511\pi$
$354$	0.550400	0.0292534
$355$	50.3764	2.67370
$356$	30.0227	1.59120
$357$	4.06388	0.215084
$358$	4.75836	0.251487
$359$	10.0371	0.529739	0.264869	−	0.964284i	$-0.414671\pi$
$359$	10.0371	0.529739	0.264869	+	0.964284i	$0.414671\pi$
$360$	4.13715	0.218047
$361$	31.7621	1.67169
$362$	2.08378	0.109521
$363$	1.00000	0.0524864
$364$	0	0
$365$	−17.4755	−0.914710
$366$	1.77481	0.0927708
$367$	−2.70569	−0.141236	−0.0706178	−	0.997503i	$-0.522497\pi$
$367$	−2.70569	−0.141236	−0.0706178	+	0.997503i	$0.522497\pi$
$368$	−3.66221	−0.190906
$369$	2.49920	0.130103
$370$	10.3262	0.536832
$371$	2.28835	0.118805
$372$	−12.2567	−0.635482
$373$	−33.5735	−1.73837	−0.869184	−	0.494489i	$-0.835355\pi$
$373$	−33.5735	−1.73837	−0.869184	+	0.494489i	$0.835355\pi$
$374$	0.875744	0.0452836
$375$	−11.3768	−0.587496
$376$	7.48635	0.386079
$377$	0	0
$378$	−0.394413	−0.0202864
$379$	5.67326	0.291416	0.145708	−	0.989328i	$-0.453454\pi$
$379$	5.67326	0.291416	0.145708	+	0.989328i	$0.453454\pi$
$380$	49.4556	2.53702
$381$	0.172249	0.00882458
$382$	−1.18159	−0.0604554
$383$	−8.31352	−0.424801	−0.212400	−	0.977183i	$-0.568128\pi$
$383$	−8.31352	−0.424801	−0.212400	+	0.977183i	$0.568128\pi$
$384$	−8.36312	−0.426779
$385$	−4.90380	−0.249921
$386$	5.86889	0.298719
$387$	9.35075	0.475325
$388$	8.10560	0.411500
$389$	−16.5445	−0.838841	−0.419421	−	0.907792i	$-0.637767\pi$
$389$	−16.5445	−0.838841	−0.419421	+	0.907792i	$0.637767\pi$
$390$	0	0
$391$	3.14557	0.159078
$392$	5.90057	0.298024
$393$	6.69726	0.337832
$394$	−1.18918	−0.0599101
$395$	−26.0029	−1.30835
$396$	1.91501	0.0962327
$397$	2.14310	0.107559	0.0537795	−	0.998553i	$-0.482873\pi$
$397$	2.14310	0.107559	0.0537795	+	0.998553i	$0.482873\pi$
$398$	−0.0218046	−0.00109297
$399$	−9.63890	−0.482548
$400$	28.4630	1.42315
$401$	−33.0952	−1.65269	−0.826347	−	0.563161i	$-0.809585\pi$
$401$	−33.0952	−1.65269	−0.826347	+	0.563161i	$0.809585\pi$
$402$	−2.57628	−0.128493
$403$	0	0
$404$	24.1193	1.19998
$405$	−3.62473	−0.180114
$406$	−3.36837	−0.167170
$407$	9.77170	0.484365
$408$	3.42854	0.169738
$409$	17.2674	0.853818	0.426909	−	0.904295i	$-0.359602\pi$
$409$	17.2674	0.853818	0.426909	+	0.904295i	$0.359602\pi$
$410$	−2.64101	−0.130430
$411$	16.1504	0.796639
$412$	−31.7837	−1.56587
$413$	−2.55413	−0.125680
$414$	−0.305287	−0.0150041
$415$	9.67694	0.475022
$416$	0	0
$417$	−6.94791	−0.340241
$418$	−2.07713	−0.101596
$419$	−14.1080	−0.689220	−0.344610	−	0.938746i	$-0.611989\pi$
$419$	−14.1080	−0.689220	−0.344610	+	0.938746i	$0.611989\pi$
$420$	−9.39082	−0.458225
$421$	−1.67313	−0.0815433	−0.0407717	−	0.999168i	$-0.512982\pi$
$421$	−1.67313	−0.0815433	−0.0407717	+	0.999168i	$0.512982\pi$
$422$	3.41937	0.166452
$423$	−6.55910	−0.318915
$424$	1.93059	0.0937579
$425$	−24.4476	−1.18589
$426$	−4.05177	−0.196309
$427$	−8.23599	−0.398568
$428$	−0.0263804	−0.00127514
$429$	0	0
$430$	−9.88132	−0.476520
$431$	23.8926	1.15087	0.575433	−	0.817849i	$-0.304833\pi$
$431$	23.8926	1.15087	0.575433	+	0.817849i	$0.304833\pi$
$432$	3.49726	0.168262
$433$	−15.9289	−0.765494	−0.382747	−	0.923853i	$-0.625022\pi$
$433$	−15.9289	−0.765494	−0.382747	+	0.923853i	$0.625022\pi$
$434$	−2.52438	−0.121174
$435$	−30.9560	−1.48423
$436$	32.6992	1.56601
$437$	−7.46080	−0.356898
$438$	1.40555	0.0671600
$439$	−25.6751	−1.22541	−0.612704	−	0.790313i	$-0.709918\pi$
$439$	−25.6751	−1.22541	−0.612704	+	0.790313i	$0.709918\pi$
$440$	−4.13715	−0.197231
$441$	−5.16973	−0.246178
$442$	0	0
$443$	−10.2668	−0.487791	−0.243896	−	0.969801i	$-0.578425\pi$
$443$	−10.2668	−0.487791	−0.243896	+	0.969801i	$0.578425\pi$
$444$	18.7129	0.888074
$445$	56.8271	2.69386
$446$	−4.92235	−0.233080
$447$	12.6470	0.598182
$448$	8.16024	0.385535
$449$	9.87329	0.465950	0.232975	−	0.972483i	$-0.425154\pi$
$449$	9.87329	0.465950	0.232975	+	0.972483i	$0.425154\pi$
$450$	2.37272	0.111851
$451$	−2.49920	−0.117683
$452$	24.1839	1.13751
$453$	−0.705772	−0.0331601
$454$	−6.07238	−0.284991
$455$	0	0
$456$	−8.13197	−0.380814
$457$	0.411010	0.0192262	0.00961311	−	0.999954i	$-0.496940\pi$
$457$	0.411010	0.0192262	0.00961311	+	0.999954i	$0.496940\pi$
$458$	2.56693	0.119945
$459$	−3.00389	−0.140210
$460$	−7.26878	−0.338909
$461$	−37.0542	−1.72578	−0.862892	−	0.505388i	$-0.831349\pi$
$461$	−37.0542	−1.72578	−0.862892	+	0.505388i	$0.831349\pi$
$462$	0.394413	0.0183497
$463$	−25.1563	−1.16911	−0.584556	−	0.811354i	$-0.698731\pi$
$463$	−25.1563	−1.16911	−0.584556	+	0.811354i	$0.698731\pi$
$464$	29.8674	1.38656
$465$	−23.1996	−1.07585
$466$	3.27469	0.151697
$467$	25.8359	1.19554	0.597771	−	0.801667i	$-0.296053\pi$
$467$	25.8359	1.19554	0.597771	+	0.801667i	$0.296053\pi$
$468$	0	0
$469$	11.9552	0.552040
$470$	6.93128	0.319716
$471$	−16.4554	−0.758224
$472$	−2.15482	−0.0991835
$473$	−9.35075	−0.429948
$474$	2.09141	0.0960617
$475$	57.9860	2.66058
$476$	−7.78236	−0.356704
$477$	−1.69147	−0.0774472
$478$	4.29473	0.196436
$479$	−13.8674	−0.633620	−0.316810	−	0.948489i	$-0.602612\pi$
$479$	−13.8674	−0.633620	−0.316810	+	0.948489i	$0.602612\pi$
$480$	−11.9700	−0.546353
$481$	0	0
$482$	−0.752434	−0.0342724
$483$	1.41668	0.0644614
$484$	−1.91501	−0.0870457
$485$	15.3423	0.696658
$486$	0.291537	0.0132244
$487$	18.2607	0.827473	0.413736	−	0.910397i	$-0.364224\pi$
$487$	18.2607	0.827473	0.413736	+	0.910397i	$0.364224\pi$
$488$	−6.94839	−0.314539
$489$	−10.8137	−0.489014
$490$	5.46307	0.246796
$491$	−40.6739	−1.83559	−0.917793	−	0.397058i	$-0.870031\pi$
$491$	−40.6739	−1.83559	−0.917793	+	0.397058i	$0.870031\pi$
$492$	−4.78599	−0.215769
$493$	−25.6539	−1.15539
$494$	0	0
$495$	3.62473	0.162919
$496$	22.3837	1.00506
$497$	18.8022	0.843394
$498$	−0.778316	−0.0348772
$499$	1.90505	0.0852819	0.0426409	−	0.999090i	$-0.486423\pi$
$499$	1.90505	0.0852819	0.0426409	+	0.999090i	$0.486423\pi$
$500$	21.7867	0.974330
$501$	13.3304	0.595556
$502$	5.93250	0.264780
$503$	22.7648	1.01503	0.507516	−	0.861643i	$-0.330564\pi$
$503$	22.7648	1.01503	0.507516	+	0.861643i	$0.330564\pi$
$504$	1.54413	0.0687809
$505$	45.6530	2.03153
$506$	0.305287	0.0135717
$507$	0	0
$508$	−0.329858	−0.0146351
$509$	−30.2798	−1.34213	−0.671064	−	0.741400i	$-0.734162\pi$
$509$	−30.2798	−1.34213	−0.671064	+	0.741400i	$0.734162\pi$
$510$	3.17433	0.140562
$511$	−6.52247	−0.288537
$512$	19.5324	0.863218
$513$	7.12475	0.314566
$514$	−7.86635	−0.346970
$515$	−60.1603	−2.65098
$516$	−17.9067	−0.788300
$517$	6.55910	0.288469
$518$	3.85408	0.169339
$519$	−14.2482	−0.625425
$520$	0	0
$521$	10.2452	0.448849	0.224424	−	0.974491i	$-0.427950\pi$
$521$	10.2452	0.448849	0.224424	+	0.974491i	$0.427950\pi$
$522$	2.48979	0.108975
$523$	−36.2246	−1.58399	−0.791996	−	0.610527i	$-0.790958\pi$
$523$	−36.2246	−1.58399	−0.791996	+	0.610527i	$0.790958\pi$
$524$	−12.8253	−0.560275
$525$	−11.0106	−0.480542
$526$	0.538019	0.0234588
$527$	−19.2260	−0.837496
$528$	−3.49726	−0.152199
$529$	−21.9034	−0.952324
$530$	1.78745	0.0776418
$531$	1.88793	0.0819290
$532$	18.4585	0.800280
$533$	0	0
$534$	−4.57060	−0.197789
$535$	−0.0499329	−0.00215879
$536$	10.0861	0.435655
$537$	16.3217	0.704332
$538$	−1.87413	−0.0807995
$539$	5.16973	0.222676
$540$	6.94138	0.298709
$541$	−20.1300	−0.865457	−0.432728	−	0.901524i	$-0.642449\pi$
$541$	−20.1300	−0.865457	−0.432728	+	0.901524i	$0.642449\pi$
$542$	−0.659814	−0.0283414
$543$	7.14758	0.306732
$544$	−9.91979	−0.425308
$545$	61.8932	2.65121
$546$	0	0
$547$	36.6440	1.56678	0.783391	−	0.621529i	$-0.213488\pi$
$547$	36.6440	1.56678	0.783391	+	0.621529i	$0.213488\pi$
$548$	−30.9280	−1.32118
$549$	6.08777	0.259820
$550$	−2.37272	−0.101173
$551$	60.8470	2.59217
$552$	1.19520	0.0508712
$553$	−9.70518	−0.412706
$554$	−6.35873	−0.270156
$555$	35.4198	1.50349
$556$	13.3053	0.564270
$557$	−40.1467	−1.70107	−0.850536	−	0.525917i	$-0.823722\pi$
$557$	−40.1467	−1.70107	−0.850536	+	0.525917i	$0.823722\pi$
$558$	1.86594	0.0789915
$559$	0	0
$560$	17.1499	0.724715
$561$	3.00389	0.126824
$562$	2.07073	0.0873487
$563$	−11.2869	−0.475687	−0.237843	−	0.971304i	$-0.576441\pi$
$563$	−11.2869	−0.475687	−0.237843	+	0.971304i	$0.576441\pi$
$564$	12.5607	0.528902
$565$	45.7753	1.92578
$566$	−0.688299	−0.0289314
$567$	−1.35287	−0.0568154
$568$	15.8627	0.665584
$569$	−3.87351	−0.162386	−0.0811930	−	0.996698i	$-0.525873\pi$
$569$	−3.87351	−0.162386	−0.0811930	+	0.996698i	$0.525873\pi$
$570$	−7.52902	−0.315356
$571$	36.5724	1.53051	0.765254	−	0.643729i	$-0.222613\pi$
$571$	36.5724	1.53051	0.765254	+	0.643729i	$0.222613\pi$
$572$	0	0
$573$	−4.05297	−0.169315
$574$	−0.985716	−0.0411430
$575$	−8.52253	−0.355414
$576$	−6.03178	−0.251324
$577$	−4.08847	−0.170205	−0.0851027	−	0.996372i	$-0.527122\pi$
$577$	−4.08847	−0.170205	−0.0851027	+	0.996372i	$0.527122\pi$
$578$	−2.32549	−0.0967275
$579$	20.1309	0.836611
$580$	59.2810	2.46151
$581$	3.61177	0.149841
$582$	−1.23398	−0.0511501
$583$	1.69147	0.0700536
$584$	−5.50275	−0.227706
$585$	0	0
$586$	−1.98600	−0.0820409
$587$	12.8349	0.529751	0.264876	−	0.964283i	$-0.414669\pi$
$587$	12.8349	0.529751	0.264876	+	0.964283i	$0.414669\pi$
$588$	9.90007	0.408272
$589$	45.6010	1.87896
$590$	−1.99505	−0.0821349
$591$	−4.07901	−0.167788
$592$	−34.1742	−1.40455
$593$	31.7447	1.30360	0.651800	−	0.758391i	$-0.274014\pi$
$593$	31.7447	1.30360	0.651800	+	0.758391i	$0.274014\pi$
$594$	−0.291537	−0.0119619
$595$	−14.7305	−0.603891
$596$	−24.2190	−0.992051
$597$	−0.0747920	−0.00306103
$598$	0	0
$599$	−23.8296	−0.973650	−0.486825	−	0.873500i	$-0.661845\pi$
$599$	−23.8296	−0.973650	−0.486825	+	0.873500i	$0.661845\pi$
$600$	−9.28921	−0.379231
$601$	7.39409	0.301611	0.150806	−	0.988563i	$-0.451813\pi$
$601$	7.39409	0.301611	0.150806	+	0.988563i	$0.451813\pi$
$602$	−3.68805	−0.150314
$603$	−8.83689	−0.359866
$604$	1.35156	0.0549941
$605$	−3.62473	−0.147366
$606$	−3.67187	−0.149160
$607$	−28.8192	−1.16974	−0.584868	−	0.811129i	$-0.698854\pi$
$607$	−28.8192	−1.16974	−0.584868	+	0.811129i	$0.698854\pi$
$608$	23.5282	0.954194
$609$	−11.5539	−0.468186
$610$	−6.43320	−0.260473
$611$	0	0
$612$	5.75247	0.232530
$613$	9.69520	0.391586	0.195793	−	0.980645i	$-0.437272\pi$
$613$	9.69520	0.391586	0.195793	+	0.980645i	$0.437272\pi$
$614$	−6.26993	−0.253034
$615$	−9.05893	−0.365291
$616$	−1.54413	−0.0622147
$617$	9.85970	0.396936	0.198468	−	0.980107i	$-0.436403\pi$
$617$	9.85970	0.396936	0.198468	+	0.980107i	$0.436403\pi$
$618$	4.83869	0.194641
$619$	41.0190	1.64869	0.824347	−	0.566085i	$-0.191542\pi$
$619$	41.0190	1.64869	0.824347	+	0.566085i	$0.191542\pi$
$620$	44.4273	1.78424
$621$	−1.04717	−0.0420213
$622$	−5.00044	−0.200500
$623$	21.2098	0.849754
$624$	0	0
$625$	0.544553	0.0217821
$626$	1.92326	0.0768687
$627$	−7.12475	−0.284535
$628$	31.5122	1.25747
$629$	29.3531	1.17039
$630$	1.42964	0.0569582
$631$	−11.5909	−0.461428	−0.230714	−	0.973022i	$-0.574106\pi$
$631$	−11.5909	−0.461428	−0.230714	+	0.973022i	$0.574106\pi$
$632$	−8.18788	−0.325697
$633$	11.7288	0.466177
$634$	−9.04547	−0.359242
$635$	−0.624356	−0.0247768
$636$	3.23918	0.128442
$637$	0	0
$638$	−2.48979	−0.0985717
$639$	−13.8980	−0.549795
$640$	30.3140	1.19827
$641$	28.6964	1.13344	0.566719	−	0.823911i	$-0.308212\pi$
$641$	28.6964	1.13344	0.566719	+	0.823911i	$0.308212\pi$
$642$	0.00401610	0.000158503 0
$643$	35.0265	1.38131	0.690654	−	0.723185i	$-0.257323\pi$
$643$	35.0265	1.38131	0.690654	+	0.723185i	$0.257323\pi$
$644$	−2.71296	−0.106906
$645$	−33.8939	−1.33457
$646$	−6.23946	−0.245488
$647$	−47.7604	−1.87765	−0.938827	−	0.344390i	$-0.888086\pi$
$647$	−47.7604	−1.87765	−0.938827	+	0.344390i	$0.888086\pi$
$648$	−1.14137	−0.0448372
$649$	−1.88793	−0.0741076
$650$	0	0
$651$	−8.65888	−0.339368
$652$	20.7084	0.811002
$653$	−8.04673	−0.314893	−0.157446	−	0.987528i	$-0.550326\pi$
$653$	−8.04673	−0.314893	−0.157446	+	0.987528i	$0.550326\pi$
$654$	−4.97806	−0.194658
$655$	−24.2757	−0.948532
$656$	8.74036	0.341254
$657$	4.82119	0.188093
$658$	2.58699	0.100851
$659$	22.3668	0.871288	0.435644	−	0.900119i	$-0.356521\pi$
$659$	22.3668	0.871288	0.435644	+	0.900119i	$0.356521\pi$
$660$	−6.94138	−0.270193
$661$	−9.90190	−0.385139	−0.192570	−	0.981283i	$-0.561682\pi$
$661$	−9.90190	−0.385139	−0.192570	+	0.981283i	$0.561682\pi$
$662$	−5.91047	−0.229717
$663$	0	0
$664$	3.04711	0.118251
$665$	34.9384	1.35485
$666$	−2.84881	−0.110389
$667$	−8.94304	−0.346276
$668$	−25.5277	−0.987697
$669$	−16.8842	−0.652779
$670$	9.33831	0.360770
$671$	−6.08777	−0.235016
$672$	−4.46762	−0.172342
$673$	−3.32998	−0.128361	−0.0641806	−	0.997938i	$-0.520443\pi$
$673$	−3.32998	−0.128361	−0.0641806	+	0.997938i	$0.520443\pi$
$674$	0.0492180	0.00189581
$675$	8.13867	0.313257
$676$	0	0
$677$	15.1408	0.581906	0.290953	−	0.956737i	$-0.406028\pi$
$677$	15.1408	0.581906	0.290953	+	0.956737i	$0.406028\pi$
$678$	−3.68171	−0.141395
$679$	5.72628	0.219754
$680$	−12.4275	−0.476574
$681$	−20.8289	−0.798163
$682$	−1.86594	−0.0714505
$683$	−33.7146	−1.29005	−0.645026	−	0.764161i	$-0.723154\pi$
$683$	−33.7146	−1.29005	−0.645026	+	0.764161i	$0.723154\pi$
$684$	−13.6439	−0.521689
$685$	−58.5407	−2.23673
$686$	4.79989	0.183261
$687$	8.80483	0.335925
$688$	32.7020	1.24675
$689$	0	0
$690$	1.10658	0.0421269
$691$	2.25620	0.0858299	0.0429150	−	0.999079i	$-0.486336\pi$
$691$	2.25620	0.0858299	0.0429150	+	0.999079i	$0.486336\pi$
$692$	27.2853	1.03723
$693$	1.35287	0.0513914
$694$	3.31389	0.125794
$695$	25.1843	0.955295
$696$	−9.74754	−0.369480
$697$	−7.50732	−0.284360
$698$	7.01600	0.265559
$699$	11.2325	0.424852
$700$	21.0854	0.796951
$701$	41.5303	1.56858	0.784289	−	0.620395i	$-0.213028\pi$
$701$	41.5303	1.56858	0.784289	+	0.620395i	$0.213028\pi$
$702$	0	0
$703$	−69.6210	−2.62580
$704$	6.03178	0.227331
$705$	23.7750	0.895417
$706$	−3.07322	−0.115662
$707$	17.0393	0.640829
$708$	−3.61539	−0.135875
$709$	3.16919	0.119022	0.0595108	−	0.998228i	$-0.481046\pi$
$709$	3.16919	0.119022	0.0595108	+	0.998228i	$0.481046\pi$
$710$	14.6866	0.551177
$711$	7.17375	0.269037
$712$	17.8939	0.670603
$713$	−6.70224	−0.251001
$714$	1.18477	0.0443390
$715$	0	0
$716$	−31.2561	−1.16809
$717$	14.7314	0.550153
$718$	2.92619	0.109204
$719$	19.2432	0.717650	0.358825	−	0.933405i	$-0.383178\pi$
$719$	19.2432	0.717650	0.358825	+	0.933405i	$0.383178\pi$
$720$	−12.6766	−0.472430
$721$	−22.4539	−0.836227
$722$	9.25982	0.344615
$723$	−2.58092	−0.0959856
$724$	−13.6877	−0.508698
$725$	69.5061	2.58139
$726$	0.291537	0.0108199
$727$	9.70728	0.360023	0.180012	−	0.983664i	$-0.442386\pi$
$727$	9.70728	0.360023	0.180012	+	0.983664i	$0.442386\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−5.09475	−0.188565
$731$	−28.0886	−1.03889
$732$	−11.6581	−0.430897
$733$	31.3082	1.15639	0.578197	−	0.815897i	$-0.303756\pi$
$733$	31.3082	1.15639	0.578197	+	0.815897i	$0.303756\pi$
$734$	−0.788807	−0.0291154
$735$	18.7389	0.691194
$736$	−3.45807	−0.127466
$737$	8.83689	0.325511
$738$	0.728609	0.0268205
$739$	−15.9519	−0.586799	−0.293400	−	0.955990i	$-0.594787\pi$
$739$	−15.9519	−0.586799	−0.293400	+	0.955990i	$0.594787\pi$
$740$	−67.8291	−2.49345
$741$	0	0
$742$	0.667138	0.0244914
$743$	30.7410	1.12778	0.563889	−	0.825850i	$-0.309304\pi$
$743$	30.7410	1.12778	0.563889	+	0.825850i	$0.309304\pi$
$744$	−7.30516	−0.267820
$745$	−45.8419	−1.67952
$746$	−9.78790	−0.358360
$747$	−2.66970	−0.0976792
$748$	−5.75247	−0.210331
$749$	−0.0186367	−0.000680970 0
$750$	−3.31676	−0.121111
$751$	−4.93841	−0.180205	−0.0901025	−	0.995932i	$-0.528719\pi$
$751$	−4.93841	−0.180205	−0.0901025	+	0.995932i	$0.528719\pi$
$752$	−22.9389	−0.836496
$753$	20.3491	0.741561
$754$	0	0
$755$	2.55823	0.0931036
$756$	2.59076	0.0942251
$757$	−4.98207	−0.181077	−0.0905383	−	0.995893i	$-0.528859\pi$
$757$	−4.98207	−0.181077	−0.0905383	+	0.995893i	$0.528859\pi$
$758$	1.65396	0.0600747
$759$	1.04717	0.0380097
$760$	29.4762	1.06921
$761$	32.9804	1.19554	0.597769	−	0.801668i	$-0.296054\pi$
$761$	32.9804	1.19554	0.597769	+	0.801668i	$0.296054\pi$
$762$	0.0502169	0.00181917
$763$	23.1007	0.836301
$764$	7.76147	0.280800
$765$	10.8883	0.393667
$766$	−2.42370	−0.0875717
$767$	0	0
$768$	9.62540	0.347327
$769$	6.79073	0.244880	0.122440	−	0.992476i	$-0.460928\pi$
$769$	6.79073	0.244880	0.122440	+	0.992476i	$0.460928\pi$
$770$	−1.42964	−0.0515206
$771$	−26.9824	−0.971746
$772$	−38.5508	−1.38747
$773$	−30.6390	−1.10201	−0.551005	−	0.834502i	$-0.685755\pi$
$773$	−30.6390	−1.10201	−0.551005	+	0.834502i	$0.685755\pi$
$774$	2.72609	0.0979871
$775$	52.0904	1.87114
$776$	4.83104	0.173424
$777$	13.2199	0.474261
$778$	−4.82334	−0.172925
$779$	17.8062	0.637973
$780$	0	0
$781$	13.8980	0.497308
$782$	0.917049	0.0327936
$783$	8.54023	0.305203
$784$	−18.0799	−0.645711
$785$	59.6464	2.12887
$786$	1.95250	0.0696432
$787$	35.0701	1.25012	0.625058	−	0.780579i	$-0.285075\pi$
$787$	35.0701	1.25012	0.625058	+	0.780579i	$0.285075\pi$
$788$	7.81133	0.278267
$789$	1.84546	0.0657001
$790$	−7.58080	−0.269713
$791$	17.0849	0.607471
$792$	1.14137	0.0405567
$793$	0	0
$794$	0.624792	0.0221730
$795$	6.13113	0.217449
$796$	0.143227	0.00507655
$797$	−13.0984	−0.463969	−0.231985	−	0.972719i	$-0.574522\pi$
$797$	−13.0984	−0.463969	−0.231985	+	0.972719i	$0.574522\pi$
$798$	−2.81009	−0.0994762
$799$	19.7028	0.697036
$800$	26.8764	0.950226
$801$	−15.6776	−0.553941
$802$	−9.64846	−0.340699
$803$	−4.82119	−0.170136
$804$	16.9227	0.596818
$805$	−5.13510	−0.180988
$806$	0	0
$807$	−6.42846	−0.226292
$808$	14.3754	0.505725
$809$	−52.0917	−1.83145	−0.915724	−	0.401808i	$-0.868382\pi$
$809$	−52.0917	−1.83145	−0.915724	+	0.401808i	$0.868382\pi$
$810$	−1.05674	−0.0371301
$811$	−16.9990	−0.596916	−0.298458	−	0.954423i	$-0.596472\pi$
$811$	−16.9990	−0.596916	−0.298458	+	0.954423i	$0.596472\pi$
$812$	22.1257	0.776460
$813$	−2.26323	−0.0793749
$814$	2.84881	0.0998507
$815$	39.1969	1.37301
$816$	−10.5054	−0.367762
$817$	66.6218	2.33080
$818$	5.03408	0.176012
$819$	0	0
$820$	17.3479	0.605815
$821$	−21.0227	−0.733698	−0.366849	−	0.930280i	$-0.619564\pi$
$821$	−21.0227	−0.733698	−0.366849	+	0.930280i	$0.619564\pi$
$822$	4.70842	0.164225
$823$	−18.6055	−0.648548	−0.324274	−	0.945963i	$-0.605120\pi$
$823$	−18.6055	−0.648548	−0.324274	+	0.945963i	$0.605120\pi$
$824$	−18.9435	−0.659928
$825$	−8.13867	−0.283352
$826$	−0.744622	−0.0259087
$827$	−20.6881	−0.719396	−0.359698	−	0.933069i	$-0.617120\pi$
$827$	−20.6881	−0.719396	−0.359698	+	0.933069i	$0.617120\pi$
$828$	2.00533	0.0696900
$829$	−42.4447	−1.47416	−0.737082	−	0.675803i	$-0.763797\pi$
$829$	−42.4447	−1.47416	−0.737082	+	0.675803i	$0.763797\pi$
$830$	2.82118	0.0979247
$831$	−21.8111	−0.756618
$832$	0	0
$833$	15.5293	0.538058
$834$	−2.02557	−0.0701398
$835$	−48.3189	−1.67215
$836$	13.6439	0.471886
$837$	6.40036	0.221229
$838$	−4.11299	−0.142081
$839$	−27.3635	−0.944692	−0.472346	−	0.881413i	$-0.656593\pi$
$839$	−27.3635	−0.944692	−0.472346	+	0.881413i	$0.656593\pi$
$840$	−5.59704	−0.193116
$841$	43.9355	1.51502
$842$	−0.487779	−0.0168100
$843$	7.10283	0.244634
$844$	−22.4607	−0.773129
$845$	0	0
$846$	−1.91222	−0.0657435
$847$	−1.35287	−0.0464853
$848$	−5.91552	−0.203140
$849$	−2.36093	−0.0810270
$850$	−7.12739	−0.244467
$851$	10.2326	0.350769
$852$	26.6147	0.911804
$853$	7.41283	0.253811	0.126905	−	0.991915i	$-0.459496\pi$
$853$	7.41283	0.253811	0.126905	+	0.991915i	$0.459496\pi$
$854$	−2.40109	−0.0821637
$855$	−25.8253	−0.883207
$856$	−0.0157231	−0.000537403 0
$857$	−45.2655	−1.54624	−0.773121	−	0.634259i	$-0.781305\pi$
$857$	−45.2655	−1.54624	−0.773121	+	0.634259i	$0.781305\pi$
$858$	0	0
$859$	18.4545	0.629658	0.314829	−	0.949148i	$-0.398053\pi$
$859$	18.4545	0.629658	0.314829	+	0.949148i	$0.398053\pi$
$860$	64.9071	2.21331
$861$	−3.38111	−0.115228
$862$	6.96558	0.237248
$863$	−24.9328	−0.848724	−0.424362	−	0.905493i	$-0.639502\pi$
$863$	−24.9328	−0.848724	−0.424362	+	0.905493i	$0.639502\pi$
$864$	3.30232	0.112347
$865$	51.6457	1.75601
$866$	−4.64386	−0.157805
$867$	−7.97665	−0.270901
$868$	16.5818	0.562823
$869$	−7.17375	−0.243353
$870$	−9.02482	−0.305970
$871$	0	0
$872$	19.4892	0.659986
$873$	−4.23268	−0.143254
$874$	−2.17510	−0.0735738
$875$	15.3914	0.520324
$876$	−9.23261	−0.311941
$877$	40.4740	1.36671	0.683354	−	0.730087i	$-0.260520\pi$
$877$	40.4740	1.36671	0.683354	+	0.730087i	$0.260520\pi$
$878$	−7.48524	−0.252615
$879$	−6.81218	−0.229769
$880$	12.6766	0.427329
$881$	−39.2743	−1.32318	−0.661592	−	0.749864i	$-0.730119\pi$
$881$	−39.2743	−1.32318	−0.661592	+	0.749864i	$0.730119\pi$
$882$	−1.50717	−0.0507489
$883$	−56.5727	−1.90382	−0.951912	−	0.306371i	$-0.900885\pi$
$883$	−56.5727	−1.90382	−0.951912	+	0.306371i	$0.900885\pi$
$884$	0	0
$885$	−6.84322	−0.230032
$886$	−2.99315	−0.100557
$887$	−7.03598	−0.236245	−0.118122	−	0.992999i	$-0.537688\pi$
$887$	−7.03598	−0.236245	−0.118122	+	0.992999i	$0.537688\pi$
$888$	11.1531	0.374274
$889$	−0.233031	−0.00781561
$890$	16.5672	0.555333
$891$	−1.00000	−0.0335013
$892$	32.3333	1.08260
$893$	−46.7320	−1.56383
$894$	3.68706	0.123314
$895$	−59.1616	−1.97755
$896$	11.3142	0.377982
$897$	0	0
$898$	2.87843	0.0960544
$899$	54.6605	1.82303
$900$	−15.5856	−0.519520
$901$	5.08099	0.169272
$902$	−0.728609	−0.0242600
$903$	−12.6504	−0.420978
$904$	14.4139	0.479399
$905$	−25.9080	−0.861212
$906$	−0.205758	−0.00683587
$907$	36.9282	1.22618	0.613091	−	0.790012i	$-0.289926\pi$
$907$	36.9282	1.22618	0.613091	+	0.790012i	$0.289926\pi$
$908$	39.8874	1.32371
$909$	−12.5949	−0.417746
$910$	0	0
$911$	−33.9405	−1.12450	−0.562249	−	0.826968i	$-0.690064\pi$
$911$	−33.9405	−1.12450	−0.562249	+	0.826968i	$0.690064\pi$
$912$	24.9171	0.825089
$913$	2.66970	0.0883542
$914$	0.119824	0.00396344
$915$	−22.0665	−0.729497
$916$	−16.8613	−0.557113
$917$	−9.06054	−0.299206
$918$	−0.875744	−0.0289039
$919$	5.97855	0.197214	0.0986071	−	0.995126i	$-0.468561\pi$
$919$	5.97855	0.197214	0.0986071	+	0.995126i	$0.468561\pi$
$920$	−4.33228	−0.142831
$921$	−21.5065	−0.708662
$922$	−10.8026	−0.355766
$923$	0	0
$924$	−2.59076	−0.0852298
$925$	−79.5286	−2.61489
$926$	−7.33398	−0.241010
$927$	16.5972	0.545123
$928$	28.2025	0.925794
$929$	−27.0114	−0.886214	−0.443107	−	0.896469i	$-0.646124\pi$
$929$	−27.0114	−0.886214	−0.443107	+	0.896469i	$0.646124\pi$
$930$	−6.76353	−0.221785
$931$	−36.8331	−1.20715
$932$	−21.5103	−0.704594
$933$	−17.1520	−0.561532
$934$	7.53211	0.246458
$935$	−10.8883	−0.356085
$936$	0	0
$937$	10.5115	0.343394	0.171697	−	0.985150i	$-0.445075\pi$
$937$	10.5115	0.343394	0.171697	+	0.985150i	$0.445075\pi$
$938$	3.48538	0.113802
$939$	6.59696	0.215284
$940$	−45.5292	−1.48500
$941$	−37.9757	−1.23797	−0.618986	−	0.785402i	$-0.712456\pi$
$941$	−37.9757	−1.23797	−0.618986	+	0.785402i	$0.712456\pi$
$942$	−4.79735	−0.156306
$943$	−2.61708	−0.0852238
$944$	6.60257	0.214895
$945$	4.90380	0.159521
$946$	−2.72609	−0.0886327
$947$	6.27503	0.203911	0.101955	−	0.994789i	$-0.467490\pi$
$947$	6.27503	0.203911	0.101955	+	0.994789i	$0.467490\pi$
$948$	−13.7378	−0.446182
$949$	0	0
$950$	16.9050	0.548472
$951$	−31.0269	−1.00612
$952$	−4.63839	−0.150331
$953$	−20.3337	−0.658672	−0.329336	−	0.944213i	$-0.606825\pi$
$953$	−20.3337	−0.658672	−0.329336	+	0.944213i	$0.606825\pi$
$954$	−0.493126	−0.0159656
$955$	14.6909	0.475388
$956$	−28.2106	−0.912397
$957$	−8.54023	−0.276066
$958$	−4.04287	−0.130619
$959$	−21.8494	−0.705554
$960$	21.8636	0.705644
$961$	9.96459	0.321438
$962$	0	0
$963$	0.0137756	0.000443913 0
$964$	4.94248	0.159187
$965$	−72.9690	−2.34896
$966$	0.413015	0.0132886
$967$	−22.4521	−0.722012	−0.361006	−	0.932563i	$-0.617567\pi$
$967$	−22.4521	−0.722012	−0.361006	+	0.932563i	$0.617567\pi$
$968$	−1.14137	−0.0366850
$969$	−21.4020	−0.687530
$970$	4.47284	0.143614
$971$	41.9862	1.34740	0.673701	−	0.739004i	$-0.264704\pi$
$971$	41.9862	1.34740	0.673701	+	0.739004i	$0.264704\pi$
$972$	−1.91501	−0.0614239
$973$	9.39965	0.301339
$974$	5.32367	0.170581
$975$	0	0
$976$	21.2905	0.681494
$977$	−23.1730	−0.741369	−0.370685	−	0.928759i	$-0.620877\pi$
$977$	−23.1730	−0.741369	−0.370685	+	0.928759i	$0.620877\pi$
$978$	−3.15260	−0.100809
$979$	15.6776	0.501058
$980$	−35.8851	−1.14631
$981$	−17.0753	−0.545171
$982$	−11.8579	−0.378402
$983$	52.2582	1.66678	0.833388	−	0.552688i	$-0.186398\pi$
$983$	52.2582	1.66678	0.833388	+	0.552688i	$0.186398\pi$
$984$	−2.85251	−0.0909346
$985$	14.7853	0.471099
$986$	−7.47905	−0.238182
$987$	8.87364	0.282451
$988$	0	0
$989$	−9.79178	−0.311361
$990$	1.05674	0.0335855
$991$	−24.8490	−0.789355	−0.394678	−	0.918820i	$-0.629144\pi$
$991$	−24.8490	−0.789355	−0.394678	+	0.918820i	$0.629144\pi$
$992$	21.1360	0.671069
$993$	−20.2735	−0.643360
$994$	5.48153	0.173864
$995$	0.271101	0.00859447
$996$	5.11249	0.161996
$997$	−59.9011	−1.89709	−0.948543	−	0.316649i	$-0.897442\pi$
$997$	−59.9011	−1.89709	−0.948543	+	0.316649i	$0.897442\pi$
$998$	0.555393	0.0175807
$999$	−9.77170	−0.309163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.bf.1.9		14
13.2	odd	12		429.2.s.b.199.8	yes	28
13.7	odd	12		429.2.s.b.166.8	✓	28
13.12	even	2		5577.2.a.bg.1.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.s.b.166.8	✓	28	13.7	odd	12
429.2.s.b.199.8	yes	28	13.2	odd	12
5577.2.a.bf.1.9		14	1.1	even	1	trivial
5577.2.a.bg.1.6		14	13.12	even	2

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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q+0.291537 q^{2} +1.00000 q^{3} -1.91501 q^{4} -3.62473 q^{5} +0.291537 q^{6} -1.35287 q^{7} -1.14137 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.291537 q^{2} +1.00000 q^{3} -1.91501 q^{4} -3.62473 q^{5} +0.291537 q^{6} -1.35287 q^{7} -1.14137 q^{8} +1.00000 q^{9} -1.05674 q^{10} -1.00000 q^{11} -1.91501 q^{12} -0.394413 q^{14} -3.62473 q^{15} +3.49726 q^{16} -3.00389 q^{17} +0.291537 q^{18} +7.12475 q^{19} +6.94138 q^{20} -1.35287 q^{21} -0.291537 q^{22} -1.04717 q^{23} -1.14137 q^{24} +8.13867 q^{25} +1.00000 q^{27} +2.59076 q^{28} +8.54023 q^{29} -1.05674 q^{30} +6.40036 q^{31} +3.30232 q^{32} -1.00000 q^{33} -0.875744 q^{34} +4.90380 q^{35} -1.91501 q^{36} -9.77170 q^{37} +2.07713 q^{38} +4.13715 q^{40} +2.49920 q^{41} -0.394413 q^{42} +9.35075 q^{43} +1.91501 q^{44} -3.62473 q^{45} -0.305287 q^{46} -6.55910 q^{47} +3.49726 q^{48} -5.16973 q^{49} +2.37272 q^{50} -3.00389 q^{51} -1.69147 q^{53} +0.291537 q^{54} +3.62473 q^{55} +1.54413 q^{56} +7.12475 q^{57} +2.48979 q^{58} +1.88793 q^{59} +6.94138 q^{60} +6.08777 q^{61} +1.86594 q^{62} -1.35287 q^{63} -6.03178 q^{64} -0.291537 q^{66} -8.83689 q^{67} +5.75247 q^{68} -1.04717 q^{69} +1.42964 q^{70} -13.8980 q^{71} -1.14137 q^{72} +4.82119 q^{73} -2.84881 q^{74} +8.13867 q^{75} -13.6439 q^{76} +1.35287 q^{77} +7.17375 q^{79} -12.6766 q^{80} +1.00000 q^{81} +0.728609 q^{82} -2.66970 q^{83} +2.59076 q^{84} +10.8883 q^{85} +2.72609 q^{86} +8.54023 q^{87} +1.14137 q^{88} -15.6776 q^{89} -1.05674 q^{90} +2.00533 q^{92} +6.40036 q^{93} -1.91222 q^{94} -25.8253 q^{95} +3.30232 q^{96} -4.23268 q^{97} -1.50717 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 6 q^{2} + 14 q^{3} + 18 q^{4} - 12 q^{5} - 6 q^{6} - 12 q^{7} - 12 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 6 * q^2 + 14 * q^3 + 18 * q^4 - 12 * q^5 - 6 * q^6 - 12 * q^7 - 12 * q^8 + 14 * q^9	\( 14 q - 6 q^{2} + 14 q^{3} + 18 q^{4} - 12 q^{5} - 6 q^{6} - 12 q^{7} - 12 q^{8} + 14 q^{9} - 14 q^{11} + 18 q^{12} - 2 q^{14} - 12 q^{15} + 22 q^{16} + 2 q^{17} - 6 q^{18} + 2 q^{19} - 44 q^{20} - 12 q^{21} + 6 q^{22} + 2 q^{23} - 12 q^{24} + 20 q^{25} + 14 q^{27} - 24 q^{28} - 28 q^{31} - 30 q^{32} - 14 q^{33} + 16 q^{34} - 2 q^{35} + 18 q^{36} - 10 q^{38} + 10 q^{40} - 40 q^{41} - 2 q^{42} - 2 q^{43} - 18 q^{44} - 12 q^{45} - 32 q^{46} - 48 q^{47} + 22 q^{48} + 10 q^{49} + 2 q^{51} + 8 q^{53} - 6 q^{54} + 12 q^{55} - 10 q^{56} + 2 q^{57} + 16 q^{58} - 40 q^{59} - 44 q^{60} + 4 q^{61} - 6 q^{62} - 12 q^{63} + 16 q^{64} + 6 q^{66} - 40 q^{67} + 22 q^{68} + 2 q^{69} + 40 q^{70} - 36 q^{71} - 12 q^{72} - 10 q^{73} - 48 q^{74} + 20 q^{75} + 4 q^{76} + 12 q^{77} - 24 q^{79} - 68 q^{80} + 14 q^{81} + 46 q^{82} - 12 q^{83} - 24 q^{84} - 34 q^{85} - 48 q^{86} + 12 q^{88} - 20 q^{89} + 36 q^{92} - 28 q^{93} - 50 q^{94} - 60 q^{95} - 30 q^{96} + 16 q^{97} - 44 q^{98} - 14 q^{99}+O(q^{100}) \) 14 * q - 6 * q^2 + 14 * q^3 + 18 * q^4 - 12 * q^5 - 6 * q^6 - 12 * q^7 - 12 * q^8 + 14 * q^9 - 14 * q^11 + 18 * q^12 - 2 * q^14 - 12 * q^15 + 22 * q^16 + 2 * q^17 - 6 * q^18 + 2 * q^19 - 44 * q^20 - 12 * q^21 + 6 * q^22 + 2 * q^23 - 12 * q^24 + 20 * q^25 + 14 * q^27 - 24 * q^28 - 28 * q^31 - 30 * q^32 - 14 * q^33 + 16 * q^34 - 2 * q^35 + 18 * q^36 - 10 * q^38 + 10 * q^40 - 40 * q^41 - 2 * q^42 - 2 * q^43 - 18 * q^44 - 12 * q^45 - 32 * q^46 - 48 * q^47 + 22 * q^48 + 10 * q^49 + 2 * q^51 + 8 * q^53 - 6 * q^54 + 12 * q^55 - 10 * q^56 + 2 * q^57 + 16 * q^58 - 40 * q^59 - 44 * q^60 + 4 * q^61 - 6 * q^62 - 12 * q^63 + 16 * q^64 + 6 * q^66 - 40 * q^67 + 22 * q^68 + 2 * q^69 + 40 * q^70 - 36 * q^71 - 12 * q^72 - 10 * q^73 - 48 * q^74 + 20 * q^75 + 4 * q^76 + 12 * q^77 - 24 * q^79 - 68 * q^80 + 14 * q^81 + 46 * q^82 - 12 * q^83 - 24 * q^84 - 34 * q^85 - 48 * q^86 + 12 * q^88 - 20 * q^89 + 36 * q^92 - 28 * q^93 - 50 * q^94 - 60 * q^95 - 30 * q^96 + 16 * q^97 - 44 * q^98 - 14 * q^99

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