LMFDB - Embedded newform 4026.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.87939 q^{5} -1.00000 q^{6} -0.347296 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.87939 q^{5} -1.00000 q^{6} -0.347296 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.87939 q^{10} +1.00000 q^{11} +1.00000 q^{12} -2.53209 q^{13} +0.347296 q^{14} -2.87939 q^{15} +1.00000 q^{16} +4.75877 q^{17} -1.00000 q^{18} -2.83750 q^{19} -2.87939 q^{20} -0.347296 q^{21} -1.00000 q^{22} -3.53209 q^{23} -1.00000 q^{24} +3.29086 q^{25} +2.53209 q^{26} +1.00000 q^{27} -0.347296 q^{28} +8.47565 q^{29} +2.87939 q^{30} +2.17024 q^{31} -1.00000 q^{32} +1.00000 q^{33} -4.75877 q^{34} +1.00000 q^{35} +1.00000 q^{36} +1.90167 q^{37} +2.83750 q^{38} -2.53209 q^{39} +2.87939 q^{40} -1.24123 q^{41} +0.347296 q^{42} -10.0077 q^{43} +1.00000 q^{44} -2.87939 q^{45} +3.53209 q^{46} +13.0915 q^{47} +1.00000 q^{48} -6.87939 q^{49} -3.29086 q^{50} +4.75877 q^{51} -2.53209 q^{52} +2.20439 q^{53} -1.00000 q^{54} -2.87939 q^{55} +0.347296 q^{56} -2.83750 q^{57} -8.47565 q^{58} -10.8648 q^{59} -2.87939 q^{60} -1.00000 q^{61} -2.17024 q^{62} -0.347296 q^{63} +1.00000 q^{64} +7.29086 q^{65} -1.00000 q^{66} -14.0865 q^{67} +4.75877 q^{68} -3.53209 q^{69} -1.00000 q^{70} -0.781059 q^{71} -1.00000 q^{72} +10.8452 q^{73} -1.90167 q^{74} +3.29086 q^{75} -2.83750 q^{76} -0.347296 q^{77} +2.53209 q^{78} +0.532089 q^{79} -2.87939 q^{80} +1.00000 q^{81} +1.24123 q^{82} -9.62361 q^{83} -0.347296 q^{84} -13.7023 q^{85} +10.0077 q^{86} +8.47565 q^{87} -1.00000 q^{88} +12.7665 q^{89} +2.87939 q^{90} +0.879385 q^{91} -3.53209 q^{92} +2.17024 q^{93} -13.0915 q^{94} +8.17024 q^{95} -1.00000 q^{96} +7.80066 q^{97} +6.87939 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} - 6 q^{19} - 3 q^{20} - 3 q^{22} - 6 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{26} + 3 q^{27} + 6 q^{29} + 3 q^{30} - 15 q^{31} - 3 q^{32} + 3 q^{33} - 3 q^{34} + 3 q^{35} + 3 q^{36} - 6 q^{37} + 6 q^{38} - 3 q^{39} + 3 q^{40} - 15 q^{41} - 6 q^{43} + 3 q^{44} - 3 q^{45} + 6 q^{46} + 9 q^{47} + 3 q^{48} - 15 q^{49} + 6 q^{50} + 3 q^{51} - 3 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} - 6 q^{57} - 6 q^{58} - 9 q^{59} - 3 q^{60} - 3 q^{61} + 15 q^{62} + 3 q^{64} + 6 q^{65} - 3 q^{66} - 27 q^{67} + 3 q^{68} - 6 q^{69} - 3 q^{70} + 15 q^{71} - 3 q^{72} + 6 q^{73} + 6 q^{74} - 6 q^{75} - 6 q^{76} + 3 q^{78} - 3 q^{79} - 3 q^{80} + 3 q^{81} + 15 q^{82} + 6 q^{83} - 15 q^{85} + 6 q^{86} + 6 q^{87} - 3 q^{88} + 3 q^{89} + 3 q^{90} - 3 q^{91} - 6 q^{92} - 15 q^{93} - 9 q^{94} + 3 q^{95} - 3 q^{96} + 9 q^{97} + 15 q^{98} + 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 - 6 * q^19 - 3 * q^20 - 3 * q^22 - 6 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^26 + 3 * q^27 + 6 * q^29 + 3 * q^30 - 15 * q^31 - 3 * q^32 + 3 * q^33 - 3 * q^34 + 3 * q^35 + 3 * q^36 - 6 * q^37 + 6 * q^38 - 3 * q^39 + 3 * q^40 - 15 * q^41 - 6 * q^43 + 3 * q^44 - 3 * q^45 + 6 * q^46 + 9 * q^47 + 3 * q^48 - 15 * q^49 + 6 * q^50 + 3 * q^51 - 3 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 - 6 * q^57 - 6 * q^58 - 9 * q^59 - 3 * q^60 - 3 * q^61 + 15 * q^62 + 3 * q^64 + 6 * q^65 - 3 * q^66 - 27 * q^67 + 3 * q^68 - 6 * q^69 - 3 * q^70 + 15 * q^71 - 3 * q^72 + 6 * q^73 + 6 * q^74 - 6 * q^75 - 6 * q^76 + 3 * q^78 - 3 * q^79 - 3 * q^80 + 3 * q^81 + 15 * q^82 + 6 * q^83 - 15 * q^85 + 6 * q^86 + 6 * q^87 - 3 * q^88 + 3 * q^89 + 3 * q^90 - 3 * q^91 - 6 * q^92 - 15 * q^93 - 9 * q^94 + 3 * q^95 - 3 * q^96 + 9 * q^97 + 15 * q^98 + 3 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−2.87939	−1.28770	−0.643850	−	0.765152i	$-0.722664\pi$
$5$	−2.87939	−1.28770	−0.643850	+	0.765152i	$0.722664\pi$
$6$	−1.00000	−0.408248
$7$	−0.347296	−0.131266	−0.0656328	−	0.997844i	$-0.520907\pi$
$7$	−0.347296	−0.131266	−0.0656328	+	0.997844i	$0.520907\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.87939	0.910542
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−2.53209	−0.702275	−0.351138	−	0.936324i	$-0.614205\pi$
$13$	−2.53209	−0.702275	−0.351138	+	0.936324i	$0.614205\pi$
$14$	0.347296	0.0928189
$15$	−2.87939	−0.743454
$16$	1.00000	0.250000
$17$	4.75877	1.15417	0.577086	−	0.816684i	$-0.304190\pi$
$17$	4.75877	1.15417	0.577086	+	0.816684i	$0.304190\pi$
$18$	−1.00000	−0.235702
$19$	−2.83750	−0.650966	−0.325483	−	0.945548i	$-0.605527\pi$
$19$	−2.83750	−0.650966	−0.325483	+	0.945548i	$0.605527\pi$
$20$	−2.87939	−0.643850
$21$	−0.347296	−0.0757863
$22$	−1.00000	−0.213201
$23$	−3.53209	−0.736491	−0.368246	−	0.929729i	$-0.620041\pi$
$23$	−3.53209	−0.736491	−0.368246	+	0.929729i	$0.620041\pi$
$24$	−1.00000	−0.204124
$25$	3.29086	0.658172
$26$	2.53209	0.496583
$27$	1.00000	0.192450
$28$	−0.347296	−0.0656328
$29$	8.47565	1.57389	0.786945	−	0.617024i	$-0.211662\pi$
$29$	8.47565	1.57389	0.786945	+	0.617024i	$0.211662\pi$
$30$	2.87939	0.525701
$31$	2.17024	0.389787	0.194894	−	0.980824i	$-0.437564\pi$
$31$	2.17024	0.389787	0.194894	+	0.980824i	$0.437564\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−4.75877	−0.816122
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	1.90167	0.312633	0.156317	−	0.987707i	$-0.450038\pi$
$37$	1.90167	0.312633	0.156317	+	0.987707i	$0.450038\pi$
$38$	2.83750	0.460303
$39$	−2.53209	−0.405459
$40$	2.87939	0.455271
$41$	−1.24123	−0.193847	−0.0969237	−	0.995292i	$-0.530900\pi$
$41$	−1.24123	−0.193847	−0.0969237	+	0.995292i	$0.530900\pi$
$42$	0.347296	0.0535890
$43$	−10.0077	−1.52617	−0.763083	−	0.646300i	$-0.776315\pi$
$43$	−10.0077	−1.52617	−0.763083	+	0.646300i	$0.776315\pi$
$44$	1.00000	0.150756
$45$	−2.87939	−0.429233
$46$	3.53209	0.520778
$47$	13.0915	1.90959	0.954797	−	0.297258i	$-0.0960722\pi$
$47$	13.0915	1.90959	0.954797	+	0.297258i	$0.0960722\pi$
$48$	1.00000	0.144338
$49$	−6.87939	−0.982769
$50$	−3.29086	−0.465398
$51$	4.75877	0.666361
$52$	−2.53209	−0.351138
$53$	2.20439	0.302797	0.151398	−	0.988473i	$-0.451622\pi$
$53$	2.20439	0.302797	0.151398	+	0.988473i	$0.451622\pi$
$54$	−1.00000	−0.136083
$55$	−2.87939	−0.388256
$56$	0.347296	0.0464094
$57$	−2.83750	−0.375836
$58$	−8.47565	−1.11291
$59$	−10.8648	−1.41448	−0.707241	−	0.706973i	$-0.750060\pi$
$59$	−10.8648	−1.41448	−0.707241	+	0.706973i	$0.750060\pi$
$60$	−2.87939	−0.371727
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−2.17024	−0.275621
$63$	−0.347296	−0.0437552
$64$	1.00000	0.125000
$65$	7.29086	0.904320
$66$	−1.00000	−0.123091
$67$	−14.0865	−1.72094	−0.860468	−	0.509505i	$-0.829829\pi$
$67$	−14.0865	−1.72094	−0.860468	+	0.509505i	$0.829829\pi$
$68$	4.75877	0.577086
$69$	−3.53209	−0.425214
$70$	−1.00000	−0.119523
$71$	−0.781059	−0.0926947	−0.0463473	−	0.998925i	$-0.514758\pi$
$71$	−0.781059	−0.0926947	−0.0463473	+	0.998925i	$0.514758\pi$
$72$	−1.00000	−0.117851
$73$	10.8452	1.26934	0.634669	−	0.772784i	$-0.281136\pi$
$73$	10.8452	1.26934	0.634669	+	0.772784i	$0.281136\pi$
$74$	−1.90167	−0.221065
$75$	3.29086	0.379996
$76$	−2.83750	−0.325483
$77$	−0.347296	−0.0395781
$78$	2.53209	0.286703
$79$	0.532089	0.0598647	0.0299323	−	0.999552i	$-0.490471\pi$
$79$	0.532089	0.0598647	0.0299323	+	0.999552i	$0.490471\pi$
$80$	−2.87939	−0.321925
$81$	1.00000	0.111111
$82$	1.24123	0.137071
$83$	−9.62361	−1.05633	−0.528164	−	0.849142i	$-0.677119\pi$
$83$	−9.62361	−1.05633	−0.528164	+	0.849142i	$0.677119\pi$
$84$	−0.347296	−0.0378931
$85$	−13.7023	−1.48623
$86$	10.0077	1.07916
$87$	8.47565	0.908685
$88$	−1.00000	−0.106600
$89$	12.7665	1.35325	0.676624	−	0.736329i	$-0.263442\pi$
$89$	12.7665	1.35325	0.676624	+	0.736329i	$0.263442\pi$
$90$	2.87939	0.303514
$91$	0.879385	0.0921846
$92$	−3.53209	−0.368246
$93$	2.17024	0.225044
$94$	−13.0915	−1.35029
$95$	8.17024	0.838249
$96$	−1.00000	−0.102062
$97$	7.80066	0.792037	0.396018	−	0.918243i	$-0.370392\pi$
$97$	7.80066	0.792037	0.396018	+	0.918243i	$0.370392\pi$
$98$	6.87939	0.694923
$99$	1.00000	0.100504
$100$	3.29086	0.329086
$101$	−9.46110	−0.941415	−0.470708	−	0.882289i	$-0.656001\pi$
$101$	−9.46110	−0.941415	−0.470708	+	0.882289i	$0.656001\pi$
$102$	−4.75877	−0.471188
$103$	−9.49020	−0.935097	−0.467549	−	0.883967i	$-0.654863\pi$
$103$	−9.49020	−0.935097	−0.467549	+	0.883967i	$0.654863\pi$
$104$	2.53209	0.248292
$105$	1.00000	0.0975900
$106$	−2.20439	−0.214110
$107$	5.51249	0.532912	0.266456	−	0.963847i	$-0.414147\pi$
$107$	5.51249	0.532912	0.266456	+	0.963847i	$0.414147\pi$
$108$	1.00000	0.0962250
$109$	−17.2422	−1.65150	−0.825750	−	0.564037i	$-0.809248\pi$
$109$	−17.2422	−1.65150	−0.825750	+	0.564037i	$0.809248\pi$
$110$	2.87939	0.274539
$111$	1.90167	0.180499
$112$	−0.347296	−0.0328164
$113$	−8.89899	−0.837146	−0.418573	−	0.908183i	$-0.637470\pi$
$113$	−8.89899	−0.837146	−0.418573	+	0.908183i	$0.637470\pi$
$114$	2.83750	0.265756
$115$	10.1702	0.948380
$116$	8.47565	0.786945
$117$	−2.53209	−0.234092
$118$	10.8648	1.00019
$119$	−1.65270	−0.151503
$120$	2.87939	0.262851
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−1.24123	−0.111918
$124$	2.17024	0.194894
$125$	4.92127	0.440172
$126$	0.347296	0.0309396
$127$	3.49794	0.310392	0.155196	−	0.987884i	$-0.450399\pi$
$127$	3.49794	0.310392	0.155196	+	0.987884i	$0.450399\pi$
$128$	−1.00000	−0.0883883
$129$	−10.0077	−0.881132
$130$	−7.29086	−0.639451
$131$	−9.96316	−0.870486	−0.435243	−	0.900313i	$-0.643337\pi$
$131$	−9.96316	−0.870486	−0.435243	+	0.900313i	$0.643337\pi$
$132$	1.00000	0.0870388
$133$	0.985452	0.0854495
$134$	14.0865	1.21689
$135$	−2.87939	−0.247818
$136$	−4.75877	−0.408061
$137$	−8.14796	−0.696127	−0.348063	−	0.937471i	$-0.613161\pi$
$137$	−8.14796	−0.696127	−0.348063	+	0.937471i	$0.613161\pi$
$138$	3.53209	0.300671
$139$	−16.6604	−1.41312	−0.706560	−	0.707653i	$-0.749754\pi$
$139$	−16.6604	−1.41312	−0.706560	+	0.707653i	$0.749754\pi$
$140$	1.00000	0.0845154
$141$	13.0915	1.10250
$142$	0.781059	0.0655450
$143$	−2.53209	−0.211744
$144$	1.00000	0.0833333
$145$	−24.4047	−2.02670
$146$	−10.8452	−0.897558
$147$	−6.87939	−0.567402
$148$	1.90167	0.156317
$149$	−0.192533	−0.0157729	−0.00788647	−	0.999969i	$-0.502510\pi$
$149$	−0.192533	−0.0157729	−0.00788647	+	0.999969i	$0.502510\pi$
$150$	−3.29086	−0.268698
$151$	0.610815	0.0497074	0.0248537	−	0.999691i	$-0.492088\pi$
$151$	0.610815	0.0497074	0.0248537	+	0.999691i	$0.492088\pi$
$152$	2.83750	0.230151
$153$	4.75877	0.384724
$154$	0.347296	0.0279859
$155$	−6.24897	−0.501929
$156$	−2.53209	−0.202729
$157$	−15.2540	−1.21740	−0.608702	−	0.793399i	$-0.708309\pi$
$157$	−15.2540	−1.21740	−0.608702	+	0.793399i	$0.708309\pi$
$158$	−0.532089	−0.0423307
$159$	2.20439	0.174820
$160$	2.87939	0.227635
$161$	1.22668	0.0966761
$162$	−1.00000	−0.0785674
$163$	−7.73648	−0.605968	−0.302984	−	0.952996i	$-0.597983\pi$
$163$	−7.73648	−0.605968	−0.302984	+	0.952996i	$0.597983\pi$
$164$	−1.24123	−0.0969237
$165$	−2.87939	−0.224160
$166$	9.62361	0.746937
$167$	23.9786	1.85552	0.927762	−	0.373173i	$-0.121730\pi$
$167$	23.9786	1.85552	0.927762	+	0.373173i	$0.121730\pi$
$168$	0.347296	0.0267945
$169$	−6.58853	−0.506810
$170$	13.7023	1.05092
$171$	−2.83750	−0.216989
$172$	−10.0077	−0.763083
$173$	−5.78106	−0.439526	−0.219763	−	0.975553i	$-0.570528\pi$
$173$	−5.78106	−0.439526	−0.219763	+	0.975553i	$0.570528\pi$
$174$	−8.47565	−0.642538
$175$	−1.14290	−0.0863954
$176$	1.00000	0.0753778
$177$	−10.8648	−0.816651
$178$	−12.7665	−0.956890
$179$	−12.4807	−0.932852	−0.466426	−	0.884560i	$-0.654459\pi$
$179$	−12.4807	−0.932852	−0.466426	+	0.884560i	$0.654459\pi$
$180$	−2.87939	−0.214617
$181$	4.64590	0.345327	0.172663	−	0.984981i	$-0.444763\pi$
$181$	4.64590	0.345327	0.172663	+	0.984981i	$0.444763\pi$
$182$	−0.879385	−0.0651844
$183$	−1.00000	−0.0739221
$184$	3.53209	0.260389
$185$	−5.47565	−0.402578
$186$	−2.17024	−0.159130
$187$	4.75877	0.347996
$188$	13.0915	0.954797
$189$	−0.347296	−0.0252621
$190$	−8.17024	−0.592732
$191$	−19.1138	−1.38303	−0.691513	−	0.722364i	$-0.743056\pi$
$191$	−19.1138	−1.38303	−0.691513	+	0.722364i	$0.743056\pi$
$192$	1.00000	0.0721688
$193$	11.4757	0.826035	0.413018	−	0.910723i	$-0.364475\pi$
$193$	11.4757	0.826035	0.413018	+	0.910723i	$0.364475\pi$
$194$	−7.80066	−0.560055
$195$	7.29086	0.522109
$196$	−6.87939	−0.491385
$197$	−5.97771	−0.425894	−0.212947	−	0.977064i	$-0.568306\pi$
$197$	−5.97771	−0.425894	−0.212947	+	0.977064i	$0.568306\pi$
$198$	−1.00000	−0.0710669
$199$	−25.1189	−1.78063	−0.890314	−	0.455346i	$-0.849515\pi$
$199$	−25.1189	−1.78063	−0.890314	+	0.455346i	$0.849515\pi$
$200$	−3.29086	−0.232699
$201$	−14.0865	−0.993583
$202$	9.46110	0.665681
$203$	−2.94356	−0.206598
$204$	4.75877	0.333181
$205$	3.57398	0.249617
$206$	9.49020	0.661214
$207$	−3.53209	−0.245497
$208$	−2.53209	−0.175569
$209$	−2.83750	−0.196274
$210$	−1.00000	−0.0690066
$211$	6.82295	0.469711	0.234856	−	0.972030i	$-0.424538\pi$
$211$	6.82295	0.469711	0.234856	+	0.972030i	$0.424538\pi$
$212$	2.20439	0.151398
$213$	−0.781059	−0.0535173
$214$	−5.51249	−0.376826
$215$	28.8161	1.96524
$216$	−1.00000	−0.0680414
$217$	−0.753718	−0.0511657
$218$	17.2422	1.16779
$219$	10.8452	0.732853
$220$	−2.87939	−0.194128
$221$	−12.0496	−0.810546
$222$	−1.90167	−0.127632
$223$	−7.35235	−0.492350	−0.246175	−	0.969225i	$-0.579174\pi$
$223$	−7.35235	−0.492350	−0.246175	+	0.969225i	$0.579174\pi$
$224$	0.347296	0.0232047
$225$	3.29086	0.219391
$226$	8.89899	0.591952
$227$	5.41147	0.359172	0.179586	−	0.983742i	$-0.442524\pi$
$227$	5.41147	0.359172	0.179586	+	0.983742i	$0.442524\pi$
$228$	−2.83750	−0.187918
$229$	−10.5226	−0.695353	−0.347676	−	0.937615i	$-0.613029\pi$
$229$	−10.5226	−0.695353	−0.347676	+	0.937615i	$0.613029\pi$
$230$	−10.1702	−0.670606
$231$	−0.347296	−0.0228504
$232$	−8.47565	−0.556454
$233$	−6.98040	−0.457301	−0.228651	−	0.973509i	$-0.573431\pi$
$233$	−6.98040	−0.457301	−0.228651	+	0.973509i	$0.573431\pi$
$234$	2.53209	0.165528
$235$	−37.6955	−2.45899
$236$	−10.8648	−0.707241
$237$	0.532089	0.0345629
$238$	1.65270	0.107129
$239$	3.89899	0.252204	0.126102	−	0.992017i	$-0.459753\pi$
$239$	3.89899	0.252204	0.126102	+	0.992017i	$0.459753\pi$
$240$	−2.87939	−0.185864
$241$	−7.85710	−0.506120	−0.253060	−	0.967451i	$-0.581437\pi$
$241$	−7.85710	−0.506120	−0.253060	+	0.967451i	$0.581437\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	19.8084	1.26551
$246$	1.24123	0.0791379
$247$	7.18479	0.457157
$248$	−2.17024	−0.137811
$249$	−9.62361	−0.609871
$250$	−4.92127	−0.311249
$251$	14.2790	0.901282	0.450641	−	0.892705i	$-0.351195\pi$
$251$	14.2790	0.901282	0.450641	+	0.892705i	$0.351195\pi$
$252$	−0.347296	−0.0218776
$253$	−3.53209	−0.222061
$254$	−3.49794	−0.219480
$255$	−13.7023	−0.858073
$256$	1.00000	0.0625000
$257$	−23.7716	−1.48283	−0.741415	−	0.671047i	$-0.765845\pi$
$257$	−23.7716	−1.48283	−0.741415	+	0.671047i	$0.765845\pi$
$258$	10.0077	0.623055
$259$	−0.660444	−0.0410380
$260$	7.29086	0.452160
$261$	8.47565	0.524630
$262$	9.96316	0.615526
$263$	−15.9094	−0.981017	−0.490508	−	0.871437i	$-0.663189\pi$
$263$	−15.9094	−0.981017	−0.490508	+	0.871437i	$0.663189\pi$
$264$	−1.00000	−0.0615457
$265$	−6.34730	−0.389911
$266$	−0.985452	−0.0604219
$267$	12.7665	0.781298
$268$	−14.0865	−0.860468
$269$	−13.0000	−0.792624	−0.396312	−	0.918116i	$-0.629710\pi$
$269$	−13.0000	−0.792624	−0.396312	+	0.918116i	$0.629710\pi$
$270$	2.87939	0.175234
$271$	−4.22668	−0.256753	−0.128376	−	0.991726i	$-0.540977\pi$
$271$	−4.22668	−0.256753	−0.128376	+	0.991726i	$0.540977\pi$
$272$	4.75877	0.288543
$273$	0.879385	0.0532228
$274$	8.14796	0.492236
$275$	3.29086	0.198446
$276$	−3.53209	−0.212607
$277$	−3.64084	−0.218757	−0.109379	−	0.994000i	$-0.534886\pi$
$277$	−3.64084	−0.218757	−0.109379	+	0.994000i	$0.534886\pi$
$278$	16.6604	0.999227
$279$	2.17024	0.129929
$280$	−1.00000	−0.0597614
$281$	4.76146	0.284045	0.142022	−	0.989863i	$-0.454639\pi$
$281$	4.76146	0.284045	0.142022	+	0.989863i	$0.454639\pi$
$282$	−13.0915	−0.779589
$283$	10.3773	0.616868	0.308434	−	0.951246i	$-0.400195\pi$
$283$	10.3773	0.616868	0.308434	+	0.951246i	$0.400195\pi$
$284$	−0.781059	−0.0463473
$285$	8.17024	0.483964
$286$	2.53209	0.149726
$287$	0.431074	0.0254455
$288$	−1.00000	−0.0589256
$289$	5.64590	0.332112
$290$	24.4047	1.43309
$291$	7.80066	0.457283
$292$	10.8452	0.634669
$293$	29.4807	1.72228	0.861141	−	0.508367i	$-0.169751\pi$
$293$	29.4807	1.72228	0.861141	+	0.508367i	$0.169751\pi$
$294$	6.87939	0.401214
$295$	31.2841	1.82143
$296$	−1.90167	−0.110533
$297$	1.00000	0.0580259
$298$	0.192533	0.0111532
$299$	8.94356	0.517220
$300$	3.29086	0.189998
$301$	3.47565	0.200333
$302$	−0.610815	−0.0351484
$303$	−9.46110	−0.543526
$304$	−2.83750	−0.162742
$305$	2.87939	0.164873
$306$	−4.75877	−0.272041
$307$	−22.5381	−1.28632	−0.643158	−	0.765734i	$-0.722376\pi$
$307$	−22.5381	−1.28632	−0.643158	+	0.765734i	$0.722376\pi$
$308$	−0.347296	−0.0197890
$309$	−9.49020	−0.539879
$310$	6.24897	0.354918
$311$	−5.81790	−0.329903	−0.164951	−	0.986302i	$-0.552747\pi$
$311$	−5.81790	−0.329903	−0.164951	+	0.986302i	$0.552747\pi$
$312$	2.53209	0.143351
$313$	8.92127	0.504260	0.252130	−	0.967693i	$-0.418869\pi$
$313$	8.92127	0.504260	0.252130	+	0.967693i	$0.418869\pi$
$314$	15.2540	0.860834
$315$	1.00000	0.0563436
$316$	0.532089	0.0299323
$317$	9.38144	0.526914	0.263457	−	0.964671i	$-0.415137\pi$
$317$	9.38144	0.526914	0.263457	+	0.964671i	$0.415137\pi$
$318$	−2.20439	−0.123616
$319$	8.47565	0.474545
$320$	−2.87939	−0.160963
$321$	5.51249	0.307677
$322$	−1.22668	−0.0683603
$323$	−13.5030	−0.751327
$324$	1.00000	0.0555556
$325$	−8.33275	−0.462218
$326$	7.73648	0.428484
$327$	−17.2422	−0.953494
$328$	1.24123	0.0685354
$329$	−4.54664	−0.250664
$330$	2.87939	0.158505
$331$	26.3979	1.45096	0.725479	−	0.688245i	$-0.241618\pi$
$331$	26.3979	1.45096	0.725479	+	0.688245i	$0.241618\pi$
$332$	−9.62361	−0.528164
$333$	1.90167	0.104211
$334$	−23.9786	−1.31205
$335$	40.5604	2.21605
$336$	−0.347296	−0.0189466
$337$	−33.2918	−1.81352	−0.906760	−	0.421648i	$-0.861452\pi$
$337$	−33.2918	−1.81352	−0.906760	+	0.421648i	$0.861452\pi$
$338$	6.58853	0.358369
$339$	−8.89899	−0.483327
$340$	−13.7023	−0.743113
$341$	2.17024	0.117525
$342$	2.83750	0.153434
$343$	4.82026	0.260270
$344$	10.0077	0.539581
$345$	10.1702	0.547548
$346$	5.78106	0.310792
$347$	13.3327	0.715739	0.357870	−	0.933772i	$-0.383503\pi$
$347$	13.3327	0.715739	0.357870	+	0.933772i	$0.383503\pi$
$348$	8.47565	0.454343
$349$	10.2513	0.548741	0.274371	−	0.961624i	$-0.411530\pi$
$349$	10.2513	0.548741	0.274371	+	0.961624i	$0.411530\pi$
$350$	1.14290	0.0610908
$351$	−2.53209	−0.135153
$352$	−1.00000	−0.0533002
$353$	−23.6117	−1.25673	−0.628363	−	0.777920i	$-0.716275\pi$
$353$	−23.6117	−1.25673	−0.628363	+	0.777920i	$0.716275\pi$
$354$	10.8648	0.577460
$355$	2.24897	0.119363
$356$	12.7665	0.676624
$357$	−1.65270	−0.0874704
$358$	12.4807	0.659626
$359$	−16.4884	−0.870227	−0.435113	−	0.900376i	$-0.643292\pi$
$359$	−16.4884	−0.870227	−0.435113	+	0.900376i	$0.643292\pi$
$360$	2.87939	0.151757
$361$	−10.9486	−0.576243
$362$	−4.64590	−0.244183
$363$	1.00000	0.0524864
$364$	0.879385	0.0460923
$365$	−31.2276	−1.63453
$366$	1.00000	0.0522708
$367$	23.5681	1.23025	0.615123	−	0.788432i	$-0.289107\pi$
$367$	23.5681	1.23025	0.615123	+	0.788432i	$0.289107\pi$
$368$	−3.53209	−0.184123
$369$	−1.24123	−0.0646158
$370$	5.47565	0.284666
$371$	−0.765578	−0.0397468
$372$	2.17024	0.112522
$373$	17.6432	0.913531	0.456765	−	0.889587i	$-0.349008\pi$
$373$	17.6432	0.913531	0.456765	+	0.889587i	$0.349008\pi$
$374$	−4.75877	−0.246070
$375$	4.92127	0.254134
$376$	−13.0915	−0.675144
$377$	−21.4611	−1.10530
$378$	0.347296	0.0178630
$379$	29.5235	1.51652	0.758261	−	0.651951i	$-0.226049\pi$
$379$	29.5235	1.51652	0.758261	+	0.651951i	$0.226049\pi$
$380$	8.17024	0.419125
$381$	3.49794	0.179205
$382$	19.1138	0.977947
$383$	−17.1438	−0.876009	−0.438005	−	0.898973i	$-0.644315\pi$
$383$	−17.1438	−0.876009	−0.438005	+	0.898973i	$0.644315\pi$
$384$	−1.00000	−0.0510310
$385$	1.00000	0.0509647
$386$	−11.4757	−0.584095
$387$	−10.0077	−0.508722
$388$	7.80066	0.396018
$389$	−15.3824	−0.779918	−0.389959	−	0.920832i	$-0.627511\pi$
$389$	−15.3824	−0.779918	−0.389959	+	0.920832i	$0.627511\pi$
$390$	−7.29086	−0.369187
$391$	−16.8084	−0.850037
$392$	6.87939	0.347461
$393$	−9.96316	−0.502575
$394$	5.97771	0.301153
$395$	−1.53209	−0.0770878
$396$	1.00000	0.0502519
$397$	23.0087	1.15477	0.577386	−	0.816471i	$-0.304073\pi$
$397$	23.0087	1.15477	0.577386	+	0.816471i	$0.304073\pi$
$398$	25.1189	1.25909
$399$	0.985452	0.0493343
$400$	3.29086	0.164543
$401$	−15.7297	−0.785502	−0.392751	−	0.919645i	$-0.628477\pi$
$401$	−15.7297	−0.785502	−0.392751	+	0.919645i	$0.628477\pi$
$402$	14.0865	0.702569
$403$	−5.49525	−0.273738
$404$	−9.46110	−0.470708
$405$	−2.87939	−0.143078
$406$	2.94356	0.146087
$407$	1.90167	0.0942625
$408$	−4.75877	−0.235594
$409$	20.1857	0.998120	0.499060	−	0.866567i	$-0.333679\pi$
$409$	20.1857	0.998120	0.499060	+	0.866567i	$0.333679\pi$
$410$	−3.57398	−0.176506
$411$	−8.14796	−0.401909
$412$	−9.49020	−0.467549
$413$	3.77332	0.185673
$414$	3.53209	0.173593
$415$	27.7101	1.36023
$416$	2.53209	0.124146
$417$	−16.6604	−0.815865
$418$	2.83750	0.138786
$419$	−32.3455	−1.58018	−0.790092	−	0.612989i	$-0.789967\pi$
$419$	−32.3455	−1.58018	−0.790092	+	0.612989i	$0.789967\pi$
$420$	1.00000	0.0487950
$421$	−28.9522	−1.41105	−0.705523	−	0.708687i	$-0.749288\pi$
$421$	−28.9522	−1.41105	−0.705523	+	0.708687i	$0.749288\pi$
$422$	−6.82295	−0.332136
$423$	13.0915	0.636531
$424$	−2.20439	−0.107055
$425$	15.6604	0.759643
$426$	0.781059	0.0378424
$427$	0.347296	0.0168068
$428$	5.51249	0.266456
$429$	−2.53209	−0.122250
$430$	−28.8161	−1.38964
$431$	4.63579	0.223298	0.111649	−	0.993748i	$-0.464387\pi$
$431$	4.63579	0.223298	0.111649	+	0.993748i	$0.464387\pi$
$432$	1.00000	0.0481125
$433$	−29.9222	−1.43797	−0.718985	−	0.695026i	$-0.755393\pi$
$433$	−29.9222	−1.43797	−0.718985	+	0.695026i	$0.755393\pi$
$434$	0.753718	0.0361796
$435$	−24.4047	−1.17011
$436$	−17.2422	−0.825750
$437$	10.0223	0.479431
$438$	−10.8452	−0.518205
$439$	−14.2071	−0.678067	−0.339033	−	0.940774i	$-0.610100\pi$
$439$	−14.2071	−0.678067	−0.339033	+	0.940774i	$0.610100\pi$
$440$	2.87939	0.137269
$441$	−6.87939	−0.327590
$442$	12.0496	0.573142
$443$	9.31820	0.442721	0.221361	−	0.975192i	$-0.428950\pi$
$443$	9.31820	0.442721	0.221361	+	0.975192i	$0.428950\pi$
$444$	1.90167	0.0902495
$445$	−36.7597	−1.74258
$446$	7.35235	0.348144
$447$	−0.192533	−0.00910651
$448$	−0.347296	−0.0164082
$449$	28.8972	1.36374	0.681872	−	0.731471i	$-0.261166\pi$
$449$	28.8972	1.36374	0.681872	+	0.731471i	$0.261166\pi$
$450$	−3.29086	−0.155133
$451$	−1.24123	−0.0584472
$452$	−8.89899	−0.418573
$453$	0.610815	0.0286986
$454$	−5.41147	−0.253973
$455$	−2.53209	−0.118706
$456$	2.83750	0.132878
$457$	−24.8803	−1.16385	−0.581926	−	0.813242i	$-0.697701\pi$
$457$	−24.8803	−1.16385	−0.581926	+	0.813242i	$0.697701\pi$
$458$	10.5226	0.491688
$459$	4.75877	0.222120
$460$	10.1702	0.474190
$461$	−20.0547	−0.934040	−0.467020	−	0.884247i	$-0.654672\pi$
$461$	−20.0547	−0.934040	−0.467020	+	0.884247i	$0.654672\pi$
$462$	0.347296	0.0161577
$463$	21.6117	1.00438	0.502192	−	0.864756i	$-0.332527\pi$
$463$	21.6117	1.00438	0.502192	+	0.864756i	$0.332527\pi$
$464$	8.47565	0.393472
$465$	−6.24897	−0.289789
$466$	6.98040	0.323361
$467$	−9.57667	−0.443155	−0.221578	−	0.975143i	$-0.571121\pi$
$467$	−9.57667	−0.443155	−0.221578	+	0.975143i	$0.571121\pi$
$468$	−2.53209	−0.117046
$469$	4.89218	0.225900
$470$	37.6955	1.73876
$471$	−15.2540	−0.702868
$472$	10.8648	0.500095
$473$	−10.0077	−0.460156
$474$	−0.532089	−0.0244397
$475$	−9.33780	−0.428448
$476$	−1.65270	−0.0757515
$477$	2.20439	0.100932
$478$	−3.89899	−0.178335
$479$	0.445622	0.0203610	0.0101805	−	0.999948i	$-0.496759\pi$
$479$	0.445622	0.0203610	0.0101805	+	0.999948i	$0.496759\pi$
$480$	2.87939	0.131425
$481$	−4.81521	−0.219555
$482$	7.85710	0.357881
$483$	1.22668	0.0558159
$484$	1.00000	0.0454545
$485$	−22.4611	−1.01991
$486$	−1.00000	−0.0453609
$487$	42.3492	1.91902	0.959512	−	0.281668i	$-0.0908877\pi$
$487$	42.3492	1.91902	0.959512	+	0.281668i	$0.0908877\pi$
$488$	1.00000	0.0452679
$489$	−7.73648	−0.349856
$490$	−19.8084	−0.894852
$491$	15.6774	0.707509	0.353755	−	0.935338i	$-0.384905\pi$
$491$	15.6774	0.707509	0.353755	+	0.935338i	$0.384905\pi$
$492$	−1.24123	−0.0559589
$493$	40.3337	1.81654
$494$	−7.18479	−0.323259
$495$	−2.87939	−0.129419
$496$	2.17024	0.0974469
$497$	0.271259	0.0121676
$498$	9.62361	0.431244
$499$	2.87258	0.128594	0.0642971	−	0.997931i	$-0.479519\pi$
$499$	2.87258	0.128594	0.0642971	+	0.997931i	$0.479519\pi$
$500$	4.92127	0.220086
$501$	23.9786	1.07129
$502$	−14.2790	−0.637303
$503$	24.2094	1.07945	0.539723	−	0.841843i	$-0.318529\pi$
$503$	24.2094	1.07945	0.539723	+	0.841843i	$0.318529\pi$
$504$	0.347296	0.0154698
$505$	27.2422	1.21226
$506$	3.53209	0.157021
$507$	−6.58853	−0.292607
$508$	3.49794	0.155196
$509$	−24.5125	−1.08650	−0.543248	−	0.839572i	$-0.682806\pi$
$509$	−24.5125	−1.08650	−0.543248	+	0.839572i	$0.682806\pi$
$510$	13.7023	0.606750
$511$	−3.76651	−0.166621
$512$	−1.00000	−0.0441942
$513$	−2.83750	−0.125279
$514$	23.7716	1.04852
$515$	27.3259	1.20412
$516$	−10.0077	−0.440566
$517$	13.0915	0.575764
$518$	0.660444	0.0290183
$519$	−5.78106	−0.253760
$520$	−7.29086	−0.319725
$521$	−23.3378	−1.02245	−0.511224	−	0.859448i	$-0.670808\pi$
$521$	−23.3378	−1.02245	−0.511224	+	0.859448i	$0.670808\pi$
$522$	−8.47565	−0.370969
$523$	−32.1361	−1.40521	−0.702607	−	0.711578i	$-0.747981\pi$
$523$	−32.1361	−1.40521	−0.702607	+	0.711578i	$0.747981\pi$
$524$	−9.96316	−0.435243
$525$	−1.14290	−0.0498804
$526$	15.9094	0.693683
$527$	10.3277	0.449882
$528$	1.00000	0.0435194
$529$	−10.5243	−0.457580
$530$	6.34730	0.275709
$531$	−10.8648	−0.471494
$532$	0.985452	0.0427248
$533$	3.14290	0.136134
$534$	−12.7665	−0.552461
$535$	−15.8726	−0.686231
$536$	14.0865	0.608443
$537$	−12.4807	−0.538582
$538$	13.0000	0.560470
$539$	−6.87939	−0.296316
$540$	−2.87939	−0.123909
$541$	14.6578	0.630186	0.315093	−	0.949061i	$-0.397964\pi$
$541$	14.6578	0.630186	0.315093	+	0.949061i	$0.397964\pi$
$542$	4.22668	0.181552
$543$	4.64590	0.199375
$544$	−4.75877	−0.204031
$545$	49.6468	2.12664
$546$	−0.879385	−0.0376342
$547$	−35.9522	−1.53721	−0.768603	−	0.639726i	$-0.779048\pi$
$547$	−35.9522	−1.53721	−0.768603	+	0.639726i	$0.779048\pi$
$548$	−8.14796	−0.348063
$549$	−1.00000	−0.0426790
$550$	−3.29086	−0.140323
$551$	−24.0496	−1.02455
$552$	3.53209	0.150336
$553$	−0.184793	−0.00785818
$554$	3.64084	0.154685
$555$	−5.47565	−0.232428
$556$	−16.6604	−0.706560
$557$	39.9053	1.69084	0.845421	−	0.534101i	$-0.179350\pi$
$557$	39.9053	1.69084	0.845421	+	0.534101i	$0.179350\pi$
$558$	−2.17024	−0.0918738
$559$	25.3405	1.07179
$560$	1.00000	0.0422577
$561$	4.75877	0.200915
$562$	−4.76146	−0.200850
$563$	1.25133	0.0527375	0.0263687	−	0.999652i	$-0.491606\pi$
$563$	1.25133	0.0527375	0.0263687	+	0.999652i	$0.491606\pi$
$564$	13.0915	0.551252
$565$	25.6236	1.07799
$566$	−10.3773	−0.436192
$567$	−0.347296	−0.0145851
$568$	0.781059	0.0327725
$569$	19.0087	0.796885	0.398443	−	0.917193i	$-0.369551\pi$
$569$	19.0087	0.796885	0.398443	+	0.917193i	$0.369551\pi$
$570$	−8.17024	−0.342214
$571$	7.58946	0.317609	0.158804	−	0.987310i	$-0.449236\pi$
$571$	7.58946	0.317609	0.158804	+	0.987310i	$0.449236\pi$
$572$	−2.53209	−0.105872
$573$	−19.1138	−0.798491
$574$	−0.431074	−0.0179927
$575$	−11.6236	−0.484738
$576$	1.00000	0.0416667
$577$	29.1625	1.21405	0.607025	−	0.794682i	$-0.292363\pi$
$577$	29.1625	1.21405	0.607025	+	0.794682i	$0.292363\pi$
$578$	−5.64590	−0.234838
$579$	11.4757	0.476912
$580$	−24.4047	−1.01335
$581$	3.34224	0.138660
$582$	−7.80066	−0.323348
$583$	2.20439	0.0912966
$584$	−10.8452	−0.448779
$585$	7.29086	0.301440
$586$	−29.4807	−1.21784
$587$	8.05737	0.332563	0.166282	−	0.986078i	$-0.446824\pi$
$587$	8.05737	0.332563	0.166282	+	0.986078i	$0.446824\pi$
$588$	−6.87939	−0.283701
$589$	−6.15806	−0.253738
$590$	−31.2841	−1.28794
$591$	−5.97771	−0.245890
$592$	1.90167	0.0781583
$593$	−22.9145	−0.940984	−0.470492	−	0.882404i	$-0.655924\pi$
$593$	−22.9145	−0.940984	−0.470492	+	0.882404i	$0.655924\pi$
$594$	−1.00000	−0.0410305
$595$	4.75877	0.195091
$596$	−0.192533	−0.00788647
$597$	−25.1189	−1.02805
$598$	−8.94356	−0.365729
$599$	−26.9564	−1.10141	−0.550703	−	0.834701i	$-0.685640\pi$
$599$	−26.9564	−1.10141	−0.550703	+	0.834701i	$0.685640\pi$
$600$	−3.29086	−0.134349
$601$	27.8931	1.13778	0.568892	−	0.822412i	$-0.307372\pi$
$601$	27.8931	1.13778	0.568892	+	0.822412i	$0.307372\pi$
$602$	−3.47565	−0.141657
$603$	−14.0865	−0.573645
$604$	0.610815	0.0248537
$605$	−2.87939	−0.117064
$606$	9.46110	0.384331
$607$	−3.93819	−0.159846	−0.0799230	−	0.996801i	$-0.525467\pi$
$607$	−3.93819	−0.159846	−0.0799230	+	0.996801i	$0.525467\pi$
$608$	2.83750	0.115076
$609$	−2.94356	−0.119279
$610$	−2.87939	−0.116583
$611$	−33.1489	−1.34106
$612$	4.75877	0.192362
$613$	0.669940	0.0270586	0.0135293	−	0.999908i	$-0.495693\pi$
$613$	0.669940	0.0270586	0.0135293	+	0.999908i	$0.495693\pi$
$614$	22.5381	0.909563
$615$	3.57398	0.144117
$616$	0.347296	0.0139930
$617$	−27.1411	−1.09266	−0.546331	−	0.837570i	$-0.683976\pi$
$617$	−27.1411	−1.09266	−0.546331	+	0.837570i	$0.683976\pi$
$618$	9.49020	0.381752
$619$	−28.1165	−1.13010	−0.565049	−	0.825058i	$-0.691143\pi$
$619$	−28.1165	−1.13010	−0.565049	+	0.825058i	$0.691143\pi$
$620$	−6.24897	−0.250965
$621$	−3.53209	−0.141738
$622$	5.81790	0.233276
$623$	−4.43376	−0.177635
$624$	−2.53209	−0.101365
$625$	−30.6245	−1.22498
$626$	−8.92127	−0.356566
$627$	−2.83750	−0.113319
$628$	−15.2540	−0.608702
$629$	9.04963	0.360832
$630$	−1.00000	−0.0398410
$631$	−5.88981	−0.234470	−0.117235	−	0.993104i	$-0.537403\pi$
$631$	−5.88981	−0.234470	−0.117235	+	0.993104i	$0.537403\pi$
$632$	−0.532089	−0.0211654
$633$	6.82295	0.271188
$634$	−9.38144	−0.372585
$635$	−10.0719	−0.399692
$636$	2.20439	0.0874099
$637$	17.4192	0.690174
$638$	−8.47565	−0.335554
$639$	−0.781059	−0.0308982
$640$	2.87939	0.113818
$641$	−39.7897	−1.57160	−0.785800	−	0.618481i	$-0.787748\pi$
$641$	−39.7897	−1.57160	−0.785800	+	0.618481i	$0.787748\pi$
$642$	−5.51249	−0.217561
$643$	−36.8813	−1.45445	−0.727227	−	0.686397i	$-0.759191\pi$
$643$	−36.8813	−1.45445	−0.727227	+	0.686397i	$0.759191\pi$
$644$	1.22668	0.0483380
$645$	28.8161	1.13463
$646$	13.5030	0.531268
$647$	14.0077	0.550701	0.275351	−	0.961344i	$-0.411206\pi$
$647$	14.0077	0.550701	0.275351	+	0.961344i	$0.411206\pi$
$648$	−1.00000	−0.0392837
$649$	−10.8648	−0.426482
$650$	8.33275	0.326837
$651$	−0.753718	−0.0295405
$652$	−7.73648	−0.302984
$653$	15.0155	0.587601	0.293801	−	0.955867i	$-0.405080\pi$
$653$	15.0155	0.587601	0.293801	+	0.955867i	$0.405080\pi$
$654$	17.2422	0.674222
$655$	28.6878	1.12092
$656$	−1.24123	−0.0484619
$657$	10.8452	0.423113
$658$	4.54664	0.177246
$659$	23.6905	0.922850	0.461425	−	0.887179i	$-0.347338\pi$
$659$	23.6905	0.922850	0.461425	+	0.887179i	$0.347338\pi$
$660$	−2.87939	−0.112080
$661$	25.3847	0.987352	0.493676	−	0.869646i	$-0.335653\pi$
$661$	25.3847	0.987352	0.493676	+	0.869646i	$0.335653\pi$
$662$	−26.3979	−1.02598
$663$	−12.0496	−0.467969
$664$	9.62361	0.373468
$665$	−2.83750	−0.110033
$666$	−1.90167	−0.0736884
$667$	−29.9368	−1.15916
$668$	23.9786	0.927762
$669$	−7.35235	−0.284258
$670$	−40.5604	−1.56698
$671$	−1.00000	−0.0386046
$672$	0.347296	0.0133972
$673$	22.7956	0.878706	0.439353	−	0.898314i	$-0.355208\pi$
$673$	22.7956	0.878706	0.439353	+	0.898314i	$0.355208\pi$
$674$	33.2918	1.28235
$675$	3.29086	0.126665
$676$	−6.58853	−0.253405
$677$	17.8699	0.686796	0.343398	−	0.939190i	$-0.388422\pi$
$677$	17.8699	0.686796	0.343398	+	0.939190i	$0.388422\pi$
$678$	8.89899	0.341763
$679$	−2.70914	−0.103967
$680$	13.7023	0.525461
$681$	5.41147	0.207368
$682$	−2.17024	−0.0831030
$683$	−24.5817	−0.940593	−0.470297	−	0.882508i	$-0.655853\pi$
$683$	−24.5817	−0.940593	−0.470297	+	0.882508i	$0.655853\pi$
$684$	−2.83750	−0.108494
$685$	23.4611	0.896403
$686$	−4.82026	−0.184038
$687$	−10.5226	−0.401462
$688$	−10.0077	−0.381542
$689$	−5.58172	−0.212647
$690$	−10.1702	−0.387175
$691$	−38.4323	−1.46203	−0.731017	−	0.682359i	$-0.760954\pi$
$691$	−38.4323	−1.46203	−0.731017	+	0.682359i	$0.760954\pi$
$692$	−5.78106	−0.219763
$693$	−0.347296	−0.0131927
$694$	−13.3327	−0.506104
$695$	47.9718	1.81968
$696$	−8.47565	−0.321269
$697$	−5.90673	−0.223733
$698$	−10.2513	−0.388019
$699$	−6.98040	−0.264023
$700$	−1.14290	−0.0431977
$701$	24.5280	0.926409	0.463204	−	0.886252i	$-0.346700\pi$
$701$	24.5280	0.926409	0.463204	+	0.886252i	$0.346700\pi$
$702$	2.53209	0.0955675
$703$	−5.39599	−0.203514
$704$	1.00000	0.0376889
$705$	−37.6955	−1.41970
$706$	23.6117	0.888640
$707$	3.28581	0.123575
$708$	−10.8648	−0.408326
$709$	42.8776	1.61030	0.805152	−	0.593069i	$-0.202084\pi$
$709$	42.8776	1.61030	0.805152	+	0.593069i	$0.202084\pi$
$710$	−2.24897	−0.0844024
$711$	0.532089	0.0199549
$712$	−12.7665	−0.478445
$713$	−7.66550	−0.287075
$714$	1.65270	0.0618509
$715$	7.29086	0.272663
$716$	−12.4807	−0.466426
$717$	3.89899	0.145610
$718$	16.4884	0.615343
$719$	18.9118	0.705290	0.352645	−	0.935757i	$-0.385282\pi$
$719$	18.9118	0.705290	0.352645	+	0.935757i	$0.385282\pi$
$720$	−2.87939	−0.107308
$721$	3.29591	0.122746
$722$	10.9486	0.407465
$723$	−7.85710	−0.292209
$724$	4.64590	0.172663
$725$	27.8922	1.03589
$726$	−1.00000	−0.0371135
$727$	−45.1762	−1.67549	−0.837747	−	0.546059i	$-0.816127\pi$
$727$	−45.1762	−1.67549	−0.837747	+	0.546059i	$0.816127\pi$
$728$	−0.879385	−0.0325922
$729$	1.00000	0.0370370
$730$	31.2276	1.15579
$731$	−47.6245	−1.76146
$732$	−1.00000	−0.0369611
$733$	−33.4074	−1.23393	−0.616964	−	0.786991i	$-0.711638\pi$
$733$	−33.4074	−1.23393	−0.616964	+	0.786991i	$0.711638\pi$
$734$	−23.5681	−0.869915
$735$	19.8084	0.730644
$736$	3.53209	0.130195
$737$	−14.0865	−0.518882
$738$	1.24123	0.0456903
$739$	−30.9118	−1.13711	−0.568554	−	0.822646i	$-0.692497\pi$
$739$	−30.9118	−1.13711	−0.568554	+	0.822646i	$0.692497\pi$
$740$	−5.47565	−0.201289
$741$	7.18479	0.263940
$742$	0.765578	0.0281052
$743$	41.0951	1.50763	0.753817	−	0.657084i	$-0.228210\pi$
$743$	41.0951	1.50763	0.753817	+	0.657084i	$0.228210\pi$
$744$	−2.17024	−0.0795650
$745$	0.554378	0.0203108
$746$	−17.6432	−0.645964
$747$	−9.62361	−0.352109
$748$	4.75877	0.173998
$749$	−1.91447	−0.0699531
$750$	−4.92127	−0.179700
$751$	−5.07604	−0.185227	−0.0926136	−	0.995702i	$-0.529522\pi$
$751$	−5.07604	−0.185227	−0.0926136	+	0.995702i	$0.529522\pi$
$752$	13.0915	0.477399
$753$	14.2790	0.520356
$754$	21.4611	0.781567
$755$	−1.75877	−0.0640082
$756$	−0.347296	−0.0126310
$757$	−10.4175	−0.378629	−0.189315	−	0.981917i	$-0.560627\pi$
$757$	−10.4175	−0.378629	−0.189315	+	0.981917i	$0.560627\pi$
$758$	−29.5235	−1.07234
$759$	−3.53209	−0.128207
$760$	−8.17024	−0.296366
$761$	−4.13878	−0.150031	−0.0750154	−	0.997182i	$-0.523901\pi$
$761$	−4.13878	−0.150031	−0.0750154	+	0.997182i	$0.523901\pi$
$762$	−3.49794	−0.126717
$763$	5.98814	0.216785
$764$	−19.1138	−0.691513
$765$	−13.7023	−0.495409
$766$	17.1438	0.619432
$767$	27.5107	0.993355
$768$	1.00000	0.0360844
$769$	5.43283	0.195913	0.0979564	−	0.995191i	$-0.468769\pi$
$769$	5.43283	0.195913	0.0979564	+	0.995191i	$0.468769\pi$
$770$	−1.00000	−0.0360375
$771$	−23.7716	−0.856112
$772$	11.4757	0.413018
$773$	22.8144	0.820576	0.410288	−	0.911956i	$-0.365428\pi$
$773$	22.8144	0.820576	0.410288	+	0.911956i	$0.365428\pi$
$774$	10.0077	0.359721
$775$	7.14197	0.256547
$776$	−7.80066	−0.280027
$777$	−0.660444	−0.0236933
$778$	15.3824	0.551485
$779$	3.52198	0.126188
$780$	7.29086	0.261055
$781$	−0.781059	−0.0279485
$782$	16.8084	0.601067
$783$	8.47565	0.302895
$784$	−6.87939	−0.245692
$785$	43.9222	1.56765
$786$	9.96316	0.355374
$787$	−24.5307	−0.874424	−0.437212	−	0.899359i	$-0.644034\pi$
$787$	−24.5307	−0.874424	−0.437212	+	0.899359i	$0.644034\pi$
$788$	−5.97771	−0.212947
$789$	−15.9094	−0.566390
$790$	1.53209	0.0545093
$791$	3.09059	0.109889
$792$	−1.00000	−0.0355335
$793$	2.53209	0.0899171
$794$	−23.0087	−0.816547
$795$	−6.34730	−0.225115
$796$	−25.1189	−0.890314
$797$	17.8030	0.630615	0.315308	−	0.948989i	$-0.397892\pi$
$797$	17.8030	0.630615	0.315308	+	0.948989i	$0.397892\pi$
$798$	−0.985452	−0.0348846
$799$	62.2995	2.20400
$800$	−3.29086	−0.116349
$801$	12.7665	0.451082
$802$	15.7297	0.555434
$803$	10.8452	0.382720
$804$	−14.0865	−0.496791
$805$	−3.53209	−0.124490
$806$	5.49525	0.193562
$807$	−13.0000	−0.457622
$808$	9.46110	0.332840
$809$	46.3696	1.63027	0.815134	−	0.579273i	$-0.196663\pi$
$809$	46.3696	1.63027	0.815134	+	0.579273i	$0.196663\pi$
$810$	2.87939	0.101171
$811$	−42.6486	−1.49759	−0.748797	−	0.662799i	$-0.769368\pi$
$811$	−42.6486	−1.49759	−0.748797	+	0.662799i	$0.769368\pi$
$812$	−2.94356	−0.103299
$813$	−4.22668	−0.148236
$814$	−1.90167	−0.0666536
$815$	22.2763	0.780305
$816$	4.75877	0.166590
$817$	28.3969	0.993483
$818$	−20.1857	−0.705777
$819$	0.879385	0.0307282
$820$	3.57398	0.124809
$821$	10.4783	0.365697	0.182848	−	0.983141i	$-0.441468\pi$
$821$	10.4783	0.365697	0.182848	+	0.983141i	$0.441468\pi$
$822$	8.14796	0.284193
$823$	−41.1225	−1.43344	−0.716720	−	0.697361i	$-0.754357\pi$
$823$	−41.1225	−1.43344	−0.716720	+	0.697361i	$0.754357\pi$
$824$	9.49020	0.330607
$825$	3.29086	0.114573
$826$	−3.77332	−0.131291
$827$	−1.07461	−0.0373677	−0.0186839	−	0.999825i	$-0.505948\pi$
$827$	−1.07461	−0.0373677	−0.0186839	+	0.999825i	$0.505948\pi$
$828$	−3.53209	−0.122749
$829$	−35.2208	−1.22327	−0.611635	−	0.791140i	$-0.709488\pi$
$829$	−35.2208	−1.22327	−0.611635	+	0.791140i	$0.709488\pi$
$830$	−27.7101	−0.961831
$831$	−3.64084	−0.126299
$832$	−2.53209	−0.0877844
$833$	−32.7374	−1.13428
$834$	16.6604	0.576904
$835$	−69.0438	−2.38936
$836$	−2.83750	−0.0981369
$837$	2.17024	0.0750146
$838$	32.3455	1.11736
$839$	7.93170	0.273833	0.136916	−	0.990583i	$-0.456281\pi$
$839$	7.93170	0.273833	0.136916	+	0.990583i	$0.456281\pi$
$840$	−1.00000	−0.0345033
$841$	42.8367	1.47713
$842$	28.9522	0.997760
$843$	4.76146	0.163993
$844$	6.82295	0.234856
$845$	18.9709	0.652619
$846$	−13.0915	−0.450096
$847$	−0.347296	−0.0119332
$848$	2.20439	0.0756992
$849$	10.3773	0.356149
$850$	−15.6604	−0.537149
$851$	−6.71688	−0.230252
$852$	−0.781059	−0.0267586
$853$	33.0104	1.13026	0.565128	−	0.825003i	$-0.308827\pi$
$853$	33.0104	1.13026	0.565128	+	0.825003i	$0.308827\pi$
$854$	−0.347296	−0.0118842
$855$	8.17024	0.279416
$856$	−5.51249	−0.188413
$857$	7.18891	0.245569	0.122784	−	0.992433i	$-0.460818\pi$
$857$	7.18891	0.245569	0.122784	+	0.992433i	$0.460818\pi$
$858$	2.53209	0.0864441
$859$	−14.9617	−0.510488	−0.255244	−	0.966877i	$-0.582156\pi$
$859$	−14.9617	−0.510488	−0.255244	+	0.966877i	$0.582156\pi$
$860$	28.8161	0.982622
$861$	0.431074	0.0146910
$862$	−4.63579	−0.157896
$863$	6.23947	0.212394	0.106197	−	0.994345i	$-0.466133\pi$
$863$	6.23947	0.212394	0.106197	+	0.994345i	$0.466133\pi$
$864$	−1.00000	−0.0340207
$865$	16.6459	0.565977
$866$	29.9222	1.01680
$867$	5.64590	0.191745
$868$	−0.753718	−0.0255829
$869$	0.532089	0.0180499
$870$	24.4047	0.827396
$871$	35.6682	1.20857
$872$	17.2422	0.583893
$873$	7.80066	0.264012
$874$	−10.0223	−0.339009
$875$	−1.70914	−0.0577795
$876$	10.8452	0.366427
$877$	46.4725	1.56926	0.784632	−	0.619962i	$-0.212852\pi$
$877$	46.4725	1.56926	0.784632	+	0.619962i	$0.212852\pi$
$878$	14.2071	0.479466
$879$	29.4807	0.994359
$880$	−2.87939	−0.0970641
$881$	24.3441	0.820174	0.410087	−	0.912046i	$-0.365498\pi$
$881$	24.3441	0.820174	0.410087	+	0.912046i	$0.365498\pi$
$882$	6.87939	0.231641
$883$	21.0550	0.708557	0.354279	−	0.935140i	$-0.384726\pi$
$883$	21.0550	0.708557	0.354279	+	0.935140i	$0.384726\pi$
$884$	−12.0496	−0.405273
$885$	31.2841	1.05160
$886$	−9.31820	−0.313051
$887$	14.6212	0.490933	0.245467	−	0.969405i	$-0.421059\pi$
$887$	14.6212	0.490933	0.245467	+	0.969405i	$0.421059\pi$
$888$	−1.90167	−0.0638160
$889$	−1.21482	−0.0407438
$890$	36.7597	1.23219
$891$	1.00000	0.0335013
$892$	−7.35235	−0.246175
$893$	−37.1471	−1.24308
$894$	0.192533	0.00643928
$895$	35.9368	1.20123
$896$	0.347296	0.0116024
$897$	8.94356	0.298617
$898$	−28.8972	−0.964313
$899$	18.3942	0.613482
$900$	3.29086	0.109695
$901$	10.4902	0.349479
$902$	1.24123	0.0413284
$903$	3.47565	0.115662
$904$	8.89899	0.295976
$905$	−13.3773	−0.444677
$906$	−0.610815	−0.0202930
$907$	45.3705	1.50650	0.753252	−	0.657732i	$-0.228484\pi$
$907$	45.3705	1.50650	0.753252	+	0.657732i	$0.228484\pi$
$908$	5.41147	0.179586
$909$	−9.46110	−0.313805
$910$	2.53209	0.0839379
$911$	43.1949	1.43111	0.715555	−	0.698556i	$-0.246174\pi$
$911$	43.1949	1.43111	0.715555	+	0.698556i	$0.246174\pi$
$912$	−2.83750	−0.0939589
$913$	−9.62361	−0.318495
$914$	24.8803	0.822968
$915$	2.87939	0.0951895
$916$	−10.5226	−0.347676
$917$	3.46017	0.114265
$918$	−4.75877	−0.157063
$919$	21.6527	0.714257	0.357128	−	0.934055i	$-0.383756\pi$
$919$	21.6527	0.714257	0.357128	+	0.934055i	$0.383756\pi$
$920$	−10.1702	−0.335303
$921$	−22.5381	−0.742655
$922$	20.0547	0.660466
$923$	1.97771	0.0650972
$924$	−0.347296	−0.0114252
$925$	6.25814	0.205766
$926$	−21.6117	−0.710206
$927$	−9.49020	−0.311699
$928$	−8.47565	−0.278227
$929$	2.18243	0.0716032	0.0358016	−	0.999359i	$-0.488602\pi$
$929$	2.18243	0.0716032	0.0358016	+	0.999359i	$0.488602\pi$
$930$	6.24897	0.204912
$931$	19.5202	0.639750
$932$	−6.98040	−0.228651
$933$	−5.81790	−0.190469
$934$	9.57667	0.313358
$935$	−13.7023	−0.448114
$936$	2.53209	0.0827639
$937$	6.50299	0.212444	0.106222	−	0.994342i	$-0.466125\pi$
$937$	6.50299	0.212444	0.106222	+	0.994342i	$0.466125\pi$
$938$	−4.89218	−0.159735
$939$	8.92127	0.291135
$940$	−37.6955	−1.22949
$941$	2.01960	0.0658371	0.0329185	−	0.999458i	$-0.489520\pi$
$941$	2.01960	0.0658371	0.0329185	+	0.999458i	$0.489520\pi$
$942$	15.2540	0.497003
$943$	4.38413	0.142767
$944$	−10.8648	−0.353620
$945$	1.00000	0.0325300
$946$	10.0077	0.325380
$947$	41.1192	1.33619	0.668097	−	0.744074i	$-0.267109\pi$
$947$	41.1192	1.33619	0.668097	+	0.744074i	$0.267109\pi$
$948$	0.532089	0.0172814
$949$	−27.4611	−0.891425
$950$	9.33780	0.302958
$951$	9.38144	0.304214
$952$	1.65270	0.0535644
$953$	12.7074	0.411633	0.205816	−	0.978591i	$-0.434015\pi$
$953$	12.7074	0.411633	0.205816	+	0.978591i	$0.434015\pi$
$954$	−2.20439	−0.0713699
$955$	55.0360	1.78092
$956$	3.89899	0.126102
$957$	8.47565	0.273979
$958$	−0.445622	−0.0143974
$959$	2.82976	0.0913776
$960$	−2.87939	−0.0929318
$961$	−26.2900	−0.848066
$962$	4.81521	0.155249
$963$	5.51249	0.177637
$964$	−7.85710	−0.253060
$965$	−33.0428	−1.06369
$966$	−1.22668	−0.0394678
$967$	46.9837	1.51089	0.755447	−	0.655210i	$-0.227420\pi$
$967$	46.9837	1.51089	0.755447	+	0.655210i	$0.227420\pi$
$968$	−1.00000	−0.0321412
$969$	−13.5030	−0.433779
$970$	22.4611	0.721183
$971$	−23.2480	−0.746065	−0.373033	−	0.927818i	$-0.621682\pi$
$971$	−23.2480	−0.746065	−0.373033	+	0.927818i	$0.621682\pi$
$972$	1.00000	0.0320750
$973$	5.78611	0.185494
$974$	−42.3492	−1.35695
$975$	−8.33275	−0.266862
$976$	−1.00000	−0.0320092
$977$	−2.52528	−0.0807909	−0.0403955	−	0.999184i	$-0.512862\pi$
$977$	−2.52528	−0.0807909	−0.0403955	+	0.999184i	$0.512862\pi$
$978$	7.73648	0.247385
$979$	12.7665	0.408019
$980$	19.8084	0.632756
$981$	−17.2422	−0.550500
$982$	−15.6774	−0.500285
$983$	22.0443	0.703102	0.351551	−	0.936169i	$-0.385654\pi$
$983$	22.0443	0.703102	0.351551	+	0.936169i	$0.385654\pi$
$984$	1.24123	0.0395690
$985$	17.2121	0.548424
$986$	−40.3337	−1.28449
$987$	−4.54664	−0.144721
$988$	7.18479	0.228579
$989$	35.3482	1.12401
$990$	2.87939	0.0915129
$991$	−22.0496	−0.700430	−0.350215	−	0.936669i	$-0.613891\pi$
$991$	−22.0496	−0.700430	−0.350215	+	0.936669i	$0.613891\pi$
$992$	−2.17024	−0.0689053
$993$	26.3979	0.837711
$994$	−0.271259	−0.00860381
$995$	72.3269	2.29292
$996$	−9.62361	−0.304936
$997$	44.5844	1.41200	0.706001	−	0.708211i	$-0.250497\pi$
$997$	44.5844	1.41200	0.706001	+	0.708211i	$0.250497\pi$
$998$	−2.87258	−0.0909299
$999$	1.90167	0.0601663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.n.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.n.1.1	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.87939 q^{5} -1.00000 q^{6} -0.347296 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.87939 q^{5} -1.00000 q^{6} -0.347296 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.87939 q^{10} +1.00000 q^{11} +1.00000 q^{12} -2.53209 q^{13} +0.347296 q^{14} -2.87939 q^{15} +1.00000 q^{16} +4.75877 q^{17} -1.00000 q^{18} -2.83750 q^{19} -2.87939 q^{20} -0.347296 q^{21} -1.00000 q^{22} -3.53209 q^{23} -1.00000 q^{24} +3.29086 q^{25} +2.53209 q^{26} +1.00000 q^{27} -0.347296 q^{28} +8.47565 q^{29} +2.87939 q^{30} +2.17024 q^{31} -1.00000 q^{32} +1.00000 q^{33} -4.75877 q^{34} +1.00000 q^{35} +1.00000 q^{36} +1.90167 q^{37} +2.83750 q^{38} -2.53209 q^{39} +2.87939 q^{40} -1.24123 q^{41} +0.347296 q^{42} -10.0077 q^{43} +1.00000 q^{44} -2.87939 q^{45} +3.53209 q^{46} +13.0915 q^{47} +1.00000 q^{48} -6.87939 q^{49} -3.29086 q^{50} +4.75877 q^{51} -2.53209 q^{52} +2.20439 q^{53} -1.00000 q^{54} -2.87939 q^{55} +0.347296 q^{56} -2.83750 q^{57} -8.47565 q^{58} -10.8648 q^{59} -2.87939 q^{60} -1.00000 q^{61} -2.17024 q^{62} -0.347296 q^{63} +1.00000 q^{64} +7.29086 q^{65} -1.00000 q^{66} -14.0865 q^{67} +4.75877 q^{68} -3.53209 q^{69} -1.00000 q^{70} -0.781059 q^{71} -1.00000 q^{72} +10.8452 q^{73} -1.90167 q^{74} +3.29086 q^{75} -2.83750 q^{76} -0.347296 q^{77} +2.53209 q^{78} +0.532089 q^{79} -2.87939 q^{80} +1.00000 q^{81} +1.24123 q^{82} -9.62361 q^{83} -0.347296 q^{84} -13.7023 q^{85} +10.0077 q^{86} +8.47565 q^{87} -1.00000 q^{88} +12.7665 q^{89} +2.87939 q^{90} +0.879385 q^{91} -3.53209 q^{92} +2.17024 q^{93} -13.0915 q^{94} +8.17024 q^{95} -1.00000 q^{96} +7.80066 q^{97} +6.87939 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} - 6 q^{19} - 3 q^{20} - 3 q^{22} - 6 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{26} + 3 q^{27} + 6 q^{29} + 3 q^{30} - 15 q^{31} - 3 q^{32} + 3 q^{33} - 3 q^{34} + 3 q^{35} + 3 q^{36} - 6 q^{37} + 6 q^{38} - 3 q^{39} + 3 q^{40} - 15 q^{41} - 6 q^{43} + 3 q^{44} - 3 q^{45} + 6 q^{46} + 9 q^{47} + 3 q^{48} - 15 q^{49} + 6 q^{50} + 3 q^{51} - 3 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} - 6 q^{57} - 6 q^{58} - 9 q^{59} - 3 q^{60} - 3 q^{61} + 15 q^{62} + 3 q^{64} + 6 q^{65} - 3 q^{66} - 27 q^{67} + 3 q^{68} - 6 q^{69} - 3 q^{70} + 15 q^{71} - 3 q^{72} + 6 q^{73} + 6 q^{74} - 6 q^{75} - 6 q^{76} + 3 q^{78} - 3 q^{79} - 3 q^{80} + 3 q^{81} + 15 q^{82} + 6 q^{83} - 15 q^{85} + 6 q^{86} + 6 q^{87} - 3 q^{88} + 3 q^{89} + 3 q^{90} - 3 q^{91} - 6 q^{92} - 15 q^{93} - 9 q^{94} + 3 q^{95} - 3 q^{96} + 9 q^{97} + 15 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 - 6 * q^19 - 3 * q^20 - 3 * q^22 - 6 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^26 + 3 * q^27 + 6 * q^29 + 3 * q^30 - 15 * q^31 - 3 * q^32 + 3 * q^33 - 3 * q^34 + 3 * q^35 + 3 * q^36 - 6 * q^37 + 6 * q^38 - 3 * q^39 + 3 * q^40 - 15 * q^41 - 6 * q^43 + 3 * q^44 - 3 * q^45 + 6 * q^46 + 9 * q^47 + 3 * q^48 - 15 * q^49 + 6 * q^50 + 3 * q^51 - 3 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 - 6 * q^57 - 6 * q^58 - 9 * q^59 - 3 * q^60 - 3 * q^61 + 15 * q^62 + 3 * q^64 + 6 * q^65 - 3 * q^66 - 27 * q^67 + 3 * q^68 - 6 * q^69 - 3 * q^70 + 15 * q^71 - 3 * q^72 + 6 * q^73 + 6 * q^74 - 6 * q^75 - 6 * q^76 + 3 * q^78 - 3 * q^79 - 3 * q^80 + 3 * q^81 + 15 * q^82 + 6 * q^83 - 15 * q^85 + 6 * q^86 + 6 * q^87 - 3 * q^88 + 3 * q^89 + 3 * q^90 - 3 * q^91 - 6 * q^92 - 15 * q^93 - 9 * q^94 + 3 * q^95 - 3 * q^96 + 9 * q^97 + 15 * q^98 + 3 * q^99

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