LMFDB - Embedded newform 8022.2.a.ba.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, 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("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 39 x^{14} + 165 x^{13} + 711 x^{12} - 1949 x^{11} - 7497 x^{10} + 8238 x^{9} + \cdots + 30 $ x^16 - 5x^15 - 39x^14 + 165x^13 + 711x^12 - 1949x^11 - 7497x^10 + 8238x^9 + 42708x^8 + 7872x^7 - 97852x^6 - 109082x^5 - 6830x^4 + 49478x^3 + 28368x^2 + 4947*x + 30
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.518182$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.51818 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.51818 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.51818 q^{10} +1.68412 q^{11} +1.00000 q^{12} -4.53110 q^{13} +1.00000 q^{14} +1.51818 q^{15} +1.00000 q^{16} +6.66440 q^{17} +1.00000 q^{18} -3.29596 q^{19} +1.51818 q^{20} +1.00000 q^{21} +1.68412 q^{22} -7.43253 q^{23} +1.00000 q^{24} -2.69512 q^{25} -4.53110 q^{26} +1.00000 q^{27} +1.00000 q^{28} +9.88909 q^{29} +1.51818 q^{30} -1.03796 q^{31} +1.00000 q^{32} +1.68412 q^{33} +6.66440 q^{34} +1.51818 q^{35} +1.00000 q^{36} +5.18753 q^{37} -3.29596 q^{38} -4.53110 q^{39} +1.51818 q^{40} +4.36845 q^{41} +1.00000 q^{42} +10.9369 q^{43} +1.68412 q^{44} +1.51818 q^{45} -7.43253 q^{46} +1.09510 q^{47} +1.00000 q^{48} +1.00000 q^{49} -2.69512 q^{50} +6.66440 q^{51} -4.53110 q^{52} -10.6381 q^{53} +1.00000 q^{54} +2.55680 q^{55} +1.00000 q^{56} -3.29596 q^{57} +9.88909 q^{58} +6.86271 q^{59} +1.51818 q^{60} -1.76570 q^{61} -1.03796 q^{62} +1.00000 q^{63} +1.00000 q^{64} -6.87904 q^{65} +1.68412 q^{66} +6.13904 q^{67} +6.66440 q^{68} -7.43253 q^{69} +1.51818 q^{70} +12.7430 q^{71} +1.00000 q^{72} +14.5572 q^{73} +5.18753 q^{74} -2.69512 q^{75} -3.29596 q^{76} +1.68412 q^{77} -4.53110 q^{78} -12.4378 q^{79} +1.51818 q^{80} +1.00000 q^{81} +4.36845 q^{82} +14.1150 q^{83} +1.00000 q^{84} +10.1178 q^{85} +10.9369 q^{86} +9.88909 q^{87} +1.68412 q^{88} +10.7794 q^{89} +1.51818 q^{90} -4.53110 q^{91} -7.43253 q^{92} -1.03796 q^{93} +1.09510 q^{94} -5.00386 q^{95} +1.00000 q^{96} -16.7376 q^{97} +1.00000 q^{98} +1.68412 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 16 q^{12} + 6 q^{13} + 16 q^{14} + 11 q^{15} + 16 q^{16} + 14 q^{17} + 16 q^{18} + 29 q^{19} + 11 q^{20} + 16 q^{21} + 8 q^{22} + 9 q^{23} + 16 q^{24} + 29 q^{25} + 6 q^{26} + 16 q^{27} + 16 q^{28} + 11 q^{30} + 14 q^{31} + 16 q^{32} + 8 q^{33} + 14 q^{34} + 11 q^{35} + 16 q^{36} + 11 q^{37} + 29 q^{38} + 6 q^{39} + 11 q^{40} + 14 q^{41} + 16 q^{42} + 28 q^{43} + 8 q^{44} + 11 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 16 q^{49} + 29 q^{50} + 14 q^{51} + 6 q^{52} - 4 q^{53} + 16 q^{54} + 17 q^{55} + 16 q^{56} + 29 q^{57} + 25 q^{59} + 11 q^{60} + 16 q^{61} + 14 q^{62} + 16 q^{63} + 16 q^{64} + 6 q^{65} + 8 q^{66} + 26 q^{67} + 14 q^{68} + 9 q^{69} + 11 q^{70} + 9 q^{71} + 16 q^{72} + 31 q^{73} + 11 q^{74} + 29 q^{75} + 29 q^{76} + 8 q^{77} + 6 q^{78} + 9 q^{79} + 11 q^{80} + 16 q^{81} + 14 q^{82} + 13 q^{83} + 16 q^{84} + 20 q^{85} + 28 q^{86} + 8 q^{88} + 21 q^{89} + 11 q^{90} + 6 q^{91} + 9 q^{92} + 14 q^{93} - q^{94} - 37 q^{95} + 16 q^{96} + 18 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 16 * q^12 + 6 * q^13 + 16 * q^14 + 11 * q^15 + 16 * q^16 + 14 * q^17 + 16 * q^18 + 29 * q^19 + 11 * q^20 + 16 * q^21 + 8 * q^22 + 9 * q^23 + 16 * q^24 + 29 * q^25 + 6 * q^26 + 16 * q^27 + 16 * q^28 + 11 * q^30 + 14 * q^31 + 16 * q^32 + 8 * q^33 + 14 * q^34 + 11 * q^35 + 16 * q^36 + 11 * q^37 + 29 * q^38 + 6 * q^39 + 11 * q^40 + 14 * q^41 + 16 * q^42 + 28 * q^43 + 8 * q^44 + 11 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 16 * q^49 + 29 * q^50 + 14 * q^51 + 6 * q^52 - 4 * q^53 + 16 * q^54 + 17 * q^55 + 16 * q^56 + 29 * q^57 + 25 * q^59 + 11 * q^60 + 16 * q^61 + 14 * q^62 + 16 * q^63 + 16 * q^64 + 6 * q^65 + 8 * q^66 + 26 * q^67 + 14 * q^68 + 9 * q^69 + 11 * q^70 + 9 * q^71 + 16 * q^72 + 31 * q^73 + 11 * q^74 + 29 * q^75 + 29 * q^76 + 8 * q^77 + 6 * q^78 + 9 * q^79 + 11 * q^80 + 16 * q^81 + 14 * q^82 + 13 * q^83 + 16 * q^84 + 20 * q^85 + 28 * q^86 + 8 * q^88 + 21 * q^89 + 11 * q^90 + 6 * q^91 + 9 * q^92 + 14 * q^93 - q^94 - 37 * q^95 + 16 * q^96 + 18 * q^97 + 16 * q^98 + 8 * 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
$5$	1.51818	0.678952	0.339476	−	0.940615i	$-0.389750\pi$
$5$	1.51818	0.678952	0.339476	+	0.940615i	$0.389750\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.51818	0.480091
$11$	1.68412	0.507781	0.253890	−	0.967233i	$-0.418290\pi$
$11$	1.68412	0.507781	0.253890	+	0.967233i	$0.418290\pi$
$12$	1.00000	0.288675
$13$	−4.53110	−1.25670	−0.628351	−	0.777930i	$-0.716270\pi$
$13$	−4.53110	−1.25670	−0.628351	+	0.777930i	$0.716270\pi$
$14$	1.00000	0.267261
$15$	1.51818	0.391993
$16$	1.00000	0.250000
$17$	6.66440	1.61635	0.808177	−	0.588939i	$-0.200454\pi$
$17$	6.66440	1.61635	0.808177	+	0.588939i	$0.200454\pi$
$18$	1.00000	0.235702
$19$	−3.29596	−0.756144	−0.378072	−	0.925776i	$-0.623413\pi$
$19$	−3.29596	−0.756144	−0.378072	+	0.925776i	$0.623413\pi$
$20$	1.51818	0.339476
$21$	1.00000	0.218218
$22$	1.68412	0.359055
$23$	−7.43253	−1.54979	−0.774895	−	0.632091i	$-0.782197\pi$
$23$	−7.43253	−1.54979	−0.774895	+	0.632091i	$0.782197\pi$
$24$	1.00000	0.204124
$25$	−2.69512	−0.539025
$26$	−4.53110	−0.888623
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	9.88909	1.83636	0.918179	−	0.396166i	$-0.129660\pi$
$29$	9.88909	1.83636	0.918179	+	0.396166i	$0.129660\pi$
$30$	1.51818	0.277181
$31$	−1.03796	−0.186423	−0.0932114	−	0.995646i	$-0.529713\pi$
$31$	−1.03796	−0.186423	−0.0932114	+	0.995646i	$0.529713\pi$
$32$	1.00000	0.176777
$33$	1.68412	0.293167
$34$	6.66440	1.14294
$35$	1.51818	0.256620
$36$	1.00000	0.166667
$37$	5.18753	0.852825	0.426412	−	0.904529i	$-0.359777\pi$
$37$	5.18753	0.852825	0.426412	+	0.904529i	$0.359777\pi$
$38$	−3.29596	−0.534675
$39$	−4.53110	−0.725557
$40$	1.51818	0.240046
$41$	4.36845	0.682237	0.341119	−	0.940020i	$-0.389194\pi$
$41$	4.36845	0.682237	0.341119	+	0.940020i	$0.389194\pi$
$42$	1.00000	0.154303
$43$	10.9369	1.66787	0.833933	−	0.551866i	$-0.186084\pi$
$43$	10.9369	1.66787	0.833933	+	0.551866i	$0.186084\pi$
$44$	1.68412	0.253890
$45$	1.51818	0.226317
$46$	−7.43253	−1.09587
$47$	1.09510	0.159737	0.0798684	−	0.996805i	$-0.474550\pi$
$47$	1.09510	0.159737	0.0798684	+	0.996805i	$0.474550\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−2.69512	−0.381148
$51$	6.66440	0.933203
$52$	−4.53110	−0.628351
$53$	−10.6381	−1.46126	−0.730628	−	0.682775i	$-0.760773\pi$
$53$	−10.6381	−1.46126	−0.730628	+	0.682775i	$0.760773\pi$
$54$	1.00000	0.136083
$55$	2.55680	0.344758
$56$	1.00000	0.133631
$57$	−3.29596	−0.436560
$58$	9.88909	1.29850
$59$	6.86271	0.893449	0.446724	−	0.894672i	$-0.352590\pi$
$59$	6.86271	0.893449	0.446724	+	0.894672i	$0.352590\pi$
$60$	1.51818	0.195996
$61$	−1.76570	−0.226075	−0.113038	−	0.993591i	$-0.536058\pi$
$61$	−1.76570	−0.226075	−0.113038	+	0.993591i	$0.536058\pi$
$62$	−1.03796	−0.131821
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−6.87904	−0.853240
$66$	1.68412	0.207301
$67$	6.13904	0.750003	0.375002	−	0.927024i	$-0.377642\pi$
$67$	6.13904	0.750003	0.375002	+	0.927024i	$0.377642\pi$
$68$	6.66440	0.808177
$69$	−7.43253	−0.894771
$70$	1.51818	0.181457
$71$	12.7430	1.51231	0.756156	−	0.654391i	$-0.227075\pi$
$71$	12.7430	1.51231	0.756156	+	0.654391i	$0.227075\pi$
$72$	1.00000	0.117851
$73$	14.5572	1.70379	0.851896	−	0.523711i	$-0.175453\pi$
$73$	14.5572	1.70379	0.851896	+	0.523711i	$0.175453\pi$
$74$	5.18753	0.603038
$75$	−2.69512	−0.311206
$76$	−3.29596	−0.378072
$77$	1.68412	0.191923
$78$	−4.53110	−0.513047
$79$	−12.4378	−1.39936	−0.699680	−	0.714456i	$-0.746674\pi$
$79$	−12.4378	−1.39936	−0.699680	+	0.714456i	$0.746674\pi$
$80$	1.51818	0.169738
$81$	1.00000	0.111111
$82$	4.36845	0.482415
$83$	14.1150	1.54932	0.774659	−	0.632379i	$-0.217921\pi$
$83$	14.1150	1.54932	0.774659	+	0.632379i	$0.217921\pi$
$84$	1.00000	0.109109
$85$	10.1178	1.09743
$86$	10.9369	1.17936
$87$	9.88909	1.06022
$88$	1.68412	0.179528
$89$	10.7794	1.14261	0.571306	−	0.820737i	$-0.306437\pi$
$89$	10.7794	1.14261	0.571306	+	0.820737i	$0.306437\pi$
$90$	1.51818	0.160030
$91$	−4.53110	−0.474989
$92$	−7.43253	−0.774895
$93$	−1.03796	−0.107631
$94$	1.09510	0.112951
$95$	−5.00386	−0.513385
$96$	1.00000	0.102062
$97$	−16.7376	−1.69945	−0.849724	−	0.527228i	$-0.823231\pi$
$97$	−16.7376	−1.69945	−0.849724	+	0.527228i	$0.823231\pi$
$98$	1.00000	0.101015
$99$	1.68412	0.169260
$100$	−2.69512	−0.269512
$101$	−1.81874	−0.180971	−0.0904856	−	0.995898i	$-0.528842\pi$
$101$	−1.81874	−0.180971	−0.0904856	+	0.995898i	$0.528842\pi$
$102$	6.66440	0.659874
$103$	1.15681	0.113984	0.0569921	−	0.998375i	$-0.481849\pi$
$103$	1.15681	0.113984	0.0569921	+	0.998375i	$0.481849\pi$
$104$	−4.53110	−0.444311
$105$	1.51818	0.148159
$106$	−10.6381	−1.03326
$107$	0.201000	0.0194314	0.00971568	−	0.999953i	$-0.496907\pi$
$107$	0.201000	0.0194314	0.00971568	+	0.999953i	$0.496907\pi$
$108$	1.00000	0.0962250
$109$	−14.9673	−1.43361	−0.716804	−	0.697275i	$-0.754396\pi$
$109$	−14.9673	−1.43361	−0.716804	+	0.697275i	$0.754396\pi$
$110$	2.55680	0.243781
$111$	5.18753	0.492379
$112$	1.00000	0.0944911
$113$	19.1404	1.80058	0.900288	−	0.435295i	$-0.143356\pi$
$113$	19.1404	1.80058	0.900288	+	0.435295i	$0.143356\pi$
$114$	−3.29596	−0.308695
$115$	−11.2839	−1.05223
$116$	9.88909	0.918179
$117$	−4.53110	−0.418901
$118$	6.86271	0.631764
$119$	6.66440	0.610925
$120$	1.51818	0.138590
$121$	−8.16375	−0.742159
$122$	−1.76570	−0.159859
$123$	4.36845	0.393890
$124$	−1.03796	−0.0932114
$125$	−11.6826	−1.04492
$126$	1.00000	0.0890871
$127$	5.68647	0.504593	0.252296	−	0.967650i	$-0.418814\pi$
$127$	5.68647	0.504593	0.252296	+	0.967650i	$0.418814\pi$
$128$	1.00000	0.0883883
$129$	10.9369	0.962943
$130$	−6.87904	−0.603332
$131$	12.7076	1.11027	0.555136	−	0.831760i	$-0.312666\pi$
$131$	12.7076	1.11027	0.555136	+	0.831760i	$0.312666\pi$
$132$	1.68412	0.146584
$133$	−3.29596	−0.285796
$134$	6.13904	0.530332
$135$	1.51818	0.130664
$136$	6.66440	0.571468
$137$	5.24182	0.447839	0.223920	−	0.974608i	$-0.428115\pi$
$137$	5.24182	0.447839	0.223920	+	0.974608i	$0.428115\pi$
$138$	−7.43253	−0.632699
$139$	9.02717	0.765675	0.382837	−	0.923816i	$-0.374947\pi$
$139$	9.02717	0.765675	0.382837	+	0.923816i	$0.374947\pi$
$140$	1.51818	0.128310
$141$	1.09510	0.0922240
$142$	12.7430	1.06937
$143$	−7.63091	−0.638129
$144$	1.00000	0.0833333
$145$	15.0134	1.24680
$146$	14.5572	1.20476
$147$	1.00000	0.0824786
$148$	5.18753	0.426412
$149$	2.72440	0.223192	0.111596	−	0.993754i	$-0.464404\pi$
$149$	2.72440	0.223192	0.111596	+	0.993754i	$0.464404\pi$
$150$	−2.69512	−0.220056
$151$	−7.59623	−0.618173	−0.309086	−	0.951034i	$-0.600023\pi$
$151$	−7.59623	−0.618173	−0.309086	+	0.951034i	$0.600023\pi$
$152$	−3.29596	−0.267337
$153$	6.66440	0.538785
$154$	1.68412	0.135710
$155$	−1.57581	−0.126572
$156$	−4.53110	−0.362779
$157$	−15.3777	−1.22727	−0.613637	−	0.789588i	$-0.710294\pi$
$157$	−15.3777	−1.22727	−0.613637	+	0.789588i	$0.710294\pi$
$158$	−12.4378	−0.989497
$159$	−10.6381	−0.843657
$160$	1.51818	0.120023
$161$	−7.43253	−0.585765
$162$	1.00000	0.0785674
$163$	−5.43341	−0.425578	−0.212789	−	0.977098i	$-0.568255\pi$
$163$	−5.43341	−0.425578	−0.212789	+	0.977098i	$0.568255\pi$
$164$	4.36845	0.341119
$165$	2.55680	0.199046
$166$	14.1150	1.09553
$167$	4.89435	0.378736	0.189368	−	0.981906i	$-0.439356\pi$
$167$	4.89435	0.378736	0.189368	+	0.981906i	$0.439356\pi$
$168$	1.00000	0.0771517
$169$	7.53091	0.579301
$170$	10.1178	0.775998
$171$	−3.29596	−0.252048
$172$	10.9369	0.833933
$173$	−8.82793	−0.671175	−0.335588	−	0.942009i	$-0.608935\pi$
$173$	−8.82793	−0.671175	−0.335588	+	0.942009i	$0.608935\pi$
$174$	9.88909	0.749690
$175$	−2.69512	−0.203732
$176$	1.68412	0.126945
$177$	6.86271	0.515833
$178$	10.7794	0.807949
$179$	11.8545	0.886045	0.443022	−	0.896511i	$-0.353906\pi$
$179$	11.8545	0.886045	0.443022	+	0.896511i	$0.353906\pi$
$180$	1.51818	0.113159
$181$	−3.45602	−0.256884	−0.128442	−	0.991717i	$-0.540998\pi$
$181$	−3.45602	−0.256884	−0.128442	+	0.991717i	$0.540998\pi$
$182$	−4.53110	−0.335868
$183$	−1.76570	−0.130525
$184$	−7.43253	−0.547933
$185$	7.87561	0.579027
$186$	−1.03796	−0.0761068
$187$	11.2236	0.820754
$188$	1.09510	0.0798684
$189$	1.00000	0.0727393
$190$	−5.00386	−0.363018
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	1.00000	0.0721688
$193$	−22.3434	−1.60831	−0.804155	−	0.594420i	$-0.797382\pi$
$193$	−22.3434	−1.60831	−0.804155	+	0.594420i	$0.797382\pi$
$194$	−16.7376	−1.20169
$195$	−6.87904	−0.492618
$196$	1.00000	0.0714286
$197$	−20.3840	−1.45230	−0.726151	−	0.687536i	$-0.758692\pi$
$197$	−20.3840	−1.45230	−0.726151	+	0.687536i	$0.758692\pi$
$198$	1.68412	0.119685
$199$	−12.1717	−0.862827	−0.431414	−	0.902154i	$-0.641985\pi$
$199$	−12.1717	−0.862827	−0.431414	+	0.902154i	$0.641985\pi$
$200$	−2.69512	−0.190574
$201$	6.13904	0.433015
$202$	−1.81874	−0.127966
$203$	9.88909	0.694078
$204$	6.66440	0.466601
$205$	6.63210	0.463206
$206$	1.15681	0.0805990
$207$	−7.43253	−0.516596
$208$	−4.53110	−0.314176
$209$	−5.55078	−0.383956
$210$	1.51818	0.104764
$211$	−1.90300	−0.131008	−0.0655038	−	0.997852i	$-0.520865\pi$
$211$	−1.90300	−0.131008	−0.0655038	+	0.997852i	$0.520865\pi$
$212$	−10.6381	−0.730628
$213$	12.7430	0.873134
$214$	0.201000	0.0137400
$215$	16.6042	1.13240
$216$	1.00000	0.0680414
$217$	−1.03796	−0.0704612
$218$	−14.9673	−1.01371
$219$	14.5572	0.983685
$220$	2.55680	0.172379
$221$	−30.1971	−2.03128
$222$	5.18753	0.348164
$223$	−3.74781	−0.250972	−0.125486	−	0.992095i	$-0.540049\pi$
$223$	−3.74781	−0.250972	−0.125486	+	0.992095i	$0.540049\pi$
$224$	1.00000	0.0668153
$225$	−2.69512	−0.179675
$226$	19.1404	1.27320
$227$	−17.1056	−1.13534	−0.567671	−	0.823256i	$-0.692155\pi$
$227$	−17.1056	−1.13534	−0.567671	+	0.823256i	$0.692155\pi$
$228$	−3.29596	−0.218280
$229$	−4.56969	−0.301974	−0.150987	−	0.988536i	$-0.548245\pi$
$229$	−4.56969	−0.301974	−0.150987	+	0.988536i	$0.548245\pi$
$230$	−11.2839	−0.744040
$231$	1.68412	0.110807
$232$	9.88909	0.649250
$233$	−24.5304	−1.60704	−0.803521	−	0.595277i	$-0.797042\pi$
$233$	−24.5304	−1.60704	−0.803521	+	0.595277i	$0.797042\pi$
$234$	−4.53110	−0.296208
$235$	1.66256	0.108453
$236$	6.86271	0.446724
$237$	−12.4378	−0.807921
$238$	6.66440	0.431989
$239$	−10.9210	−0.706423	−0.353211	−	0.935544i	$-0.614910\pi$
$239$	−10.9210	−0.706423	−0.353211	+	0.935544i	$0.614910\pi$
$240$	1.51818	0.0979982
$241$	−1.24448	−0.0801642	−0.0400821	−	0.999196i	$-0.512762\pi$
$241$	−1.24448	−0.0801642	−0.0400821	+	0.999196i	$0.512762\pi$
$242$	−8.16375	−0.524786
$243$	1.00000	0.0641500
$244$	−1.76570	−0.113038
$245$	1.51818	0.0969931
$246$	4.36845	0.278522
$247$	14.9343	0.950248
$248$	−1.03796	−0.0659104
$249$	14.1150	0.894500
$250$	−11.6826	−0.738872
$251$	25.4349	1.60543	0.802717	−	0.596360i	$-0.203387\pi$
$251$	25.4349	1.60543	0.802717	+	0.596360i	$0.203387\pi$
$252$	1.00000	0.0629941
$253$	−12.5173	−0.786953
$254$	5.68647	0.356801
$255$	10.1178	0.633599
$256$	1.00000	0.0625000
$257$	−28.0420	−1.74921	−0.874606	−	0.484834i	$-0.838880\pi$
$257$	−28.0420	−1.74921	−0.874606	+	0.484834i	$0.838880\pi$
$258$	10.9369	0.680904
$259$	5.18753	0.322337
$260$	−6.87904	−0.426620
$261$	9.88909	0.612119
$262$	12.7076	0.785081
$263$	2.23470	0.137798	0.0688988	−	0.997624i	$-0.478051\pi$
$263$	2.23470	0.137798	0.0688988	+	0.997624i	$0.478051\pi$
$264$	1.68412	0.103650
$265$	−16.1506	−0.992123
$266$	−3.29596	−0.202088
$267$	10.7794	0.659687
$268$	6.13904	0.375002
$269$	6.06700	0.369912	0.184956	−	0.982747i	$-0.440786\pi$
$269$	6.06700	0.369912	0.184956	+	0.982747i	$0.440786\pi$
$270$	1.51818	0.0923936
$271$	−16.3732	−0.994599	−0.497299	−	0.867579i	$-0.665675\pi$
$271$	−16.3732	−0.994599	−0.497299	+	0.867579i	$0.665675\pi$
$272$	6.66440	0.404089
$273$	−4.53110	−0.274235
$274$	5.24182	0.316670
$275$	−4.53891	−0.273706
$276$	−7.43253	−0.447386
$277$	12.1527	0.730188	0.365094	−	0.930971i	$-0.381037\pi$
$277$	12.1527	0.730188	0.365094	+	0.930971i	$0.381037\pi$
$278$	9.02717	0.541414
$279$	−1.03796	−0.0621409
$280$	1.51818	0.0907287
$281$	−30.0646	−1.79350	−0.896751	−	0.442536i	$-0.854079\pi$
$281$	−30.0646	−1.79350	−0.896751	+	0.442536i	$0.854079\pi$
$282$	1.09510	0.0652122
$283$	−7.09061	−0.421493	−0.210746	−	0.977541i	$-0.567589\pi$
$283$	−7.09061	−0.421493	−0.210746	+	0.977541i	$0.567589\pi$
$284$	12.7430	0.756156
$285$	−5.00386	−0.296403
$286$	−7.63091	−0.451225
$287$	4.36845	0.257861
$288$	1.00000	0.0589256
$289$	27.4142	1.61260
$290$	15.0134	0.881619
$291$	−16.7376	−0.981177
$292$	14.5572	0.851896
$293$	18.2439	1.06582	0.532911	−	0.846171i	$-0.321098\pi$
$293$	18.2439	1.06582	0.532911	+	0.846171i	$0.321098\pi$
$294$	1.00000	0.0583212
$295$	10.4188	0.606608
$296$	5.18753	0.301519
$297$	1.68412	0.0977224
$298$	2.72440	0.157820
$299$	33.6776	1.94762
$300$	−2.69512	−0.155603
$301$	10.9369	0.630394
$302$	−7.59623	−0.437114
$303$	−1.81874	−0.104484
$304$	−3.29596	−0.189036
$305$	−2.68066	−0.153494
$306$	6.66440	0.380978
$307$	−2.23455	−0.127532	−0.0637662	−	0.997965i	$-0.520311\pi$
$307$	−2.23455	−0.127532	−0.0637662	+	0.997965i	$0.520311\pi$
$308$	1.68412	0.0959615
$309$	1.15681	0.0658088
$310$	−1.57581	−0.0895000
$311$	−3.20028	−0.181471	−0.0907356	−	0.995875i	$-0.528922\pi$
$311$	−3.20028	−0.181471	−0.0907356	+	0.995875i	$0.528922\pi$
$312$	−4.53110	−0.256523
$313$	28.9085	1.63400	0.817001	−	0.576636i	$-0.195635\pi$
$313$	28.9085	1.63400	0.817001	+	0.576636i	$0.195635\pi$
$314$	−15.3777	−0.867813
$315$	1.51818	0.0855399
$316$	−12.4378	−0.699680
$317$	22.6721	1.27339	0.636695	−	0.771115i	$-0.280301\pi$
$317$	22.6721	1.27339	0.636695	+	0.771115i	$0.280301\pi$
$318$	−10.6381	−0.596556
$319$	16.6544	0.932467
$320$	1.51818	0.0848689
$321$	0.201000	0.0112187
$322$	−7.43253	−0.414199
$323$	−21.9656	−1.22220
$324$	1.00000	0.0555556
$325$	12.2119	0.677394
$326$	−5.43341	−0.300929
$327$	−14.9673	−0.827694
$328$	4.36845	0.241207
$329$	1.09510	0.0603748
$330$	2.55680	0.140747
$331$	23.6486	1.29985	0.649924	−	0.759999i	$-0.274801\pi$
$331$	23.6486	1.29985	0.649924	+	0.759999i	$0.274801\pi$
$332$	14.1150	0.774659
$333$	5.18753	0.284275
$334$	4.89435	0.267807
$335$	9.32018	0.509216
$336$	1.00000	0.0545545
$337$	−0.0198882	−0.00108338	−0.000541689	−	1.00000i	$-0.500172\pi$
$337$	−0.0198882	−0.00108338	−0.000541689		1.00000i	$0.500172\pi$
$338$	7.53091	0.409627
$339$	19.1404	1.03956
$340$	10.1178	0.548713
$341$	−1.74804	−0.0946619
$342$	−3.29596	−0.178225
$343$	1.00000	0.0539949
$344$	10.9369	0.589680
$345$	−11.2839	−0.607506
$346$	−8.82793	−0.474593
$347$	−30.8038	−1.65364	−0.826818	−	0.562469i	$-0.809851\pi$
$347$	−30.8038	−1.65364	−0.826818	+	0.562469i	$0.809851\pi$
$348$	9.88909	0.530111
$349$	−19.2872	−1.03242	−0.516210	−	0.856462i	$-0.672657\pi$
$349$	−19.2872	−1.03242	−0.516210	+	0.856462i	$0.672657\pi$
$350$	−2.69512	−0.144060
$351$	−4.53110	−0.241852
$352$	1.68412	0.0897638
$353$	7.26466	0.386659	0.193329	−	0.981134i	$-0.438071\pi$
$353$	7.26466	0.386659	0.193329	+	0.981134i	$0.438071\pi$
$354$	6.86271	0.364749
$355$	19.3461	1.02679
$356$	10.7794	0.571306
$357$	6.66440	0.352717
$358$	11.8545	0.626528
$359$	−2.69740	−0.142363	−0.0711817	−	0.997463i	$-0.522677\pi$
$359$	−2.69740	−0.142363	−0.0711817	+	0.997463i	$0.522677\pi$
$360$	1.51818	0.0800152
$361$	−8.13667	−0.428246
$362$	−3.45602	−0.181644
$363$	−8.16375	−0.428486
$364$	−4.53110	−0.237494
$365$	22.1005	1.15679
$366$	−1.76570	−0.0922949
$367$	−27.4737	−1.43411	−0.717057	−	0.697015i	$-0.754511\pi$
$367$	−27.4737	−1.43411	−0.717057	+	0.697015i	$0.754511\pi$
$368$	−7.43253	−0.387447
$369$	4.36845	0.227412
$370$	7.87561	0.409434
$371$	−10.6381	−0.552303
$372$	−1.03796	−0.0538156
$373$	33.1406	1.71596	0.857978	−	0.513686i	$-0.171720\pi$
$373$	33.1406	1.71596	0.857978	+	0.513686i	$0.171720\pi$
$374$	11.2236	0.580360
$375$	−11.6826	−0.603287
$376$	1.09510	0.0564755
$377$	−44.8085	−2.30775
$378$	1.00000	0.0514344
$379$	−31.6535	−1.62593	−0.812965	−	0.582312i	$-0.802148\pi$
$379$	−31.6535	−1.62593	−0.812965	+	0.582312i	$0.802148\pi$
$380$	−5.00386	−0.256693
$381$	5.68647	0.291327
$382$	−1.00000	−0.0511645
$383$	29.8945	1.52754	0.763770	−	0.645489i	$-0.223346\pi$
$383$	29.8945	1.52754	0.763770	+	0.645489i	$0.223346\pi$
$384$	1.00000	0.0510310
$385$	2.55680	0.130306
$386$	−22.3434	−1.13725
$387$	10.9369	0.555955
$388$	−16.7376	−0.849724
$389$	11.0785	0.561703	0.280852	−	0.959751i	$-0.409383\pi$
$389$	11.0785	0.561703	0.280852	+	0.959751i	$0.409383\pi$
$390$	−6.87904	−0.348334
$391$	−49.5333	−2.50501
$392$	1.00000	0.0505076
$393$	12.7076	0.641016
$394$	−20.3840	−1.02693
$395$	−18.8828	−0.950098
$396$	1.68412	0.0846301
$397$	−4.80631	−0.241222	−0.120611	−	0.992700i	$-0.538485\pi$
$397$	−4.80631	−0.241222	−0.120611	+	0.992700i	$0.538485\pi$
$398$	−12.1717	−0.610111
$399$	−3.29596	−0.165004
$400$	−2.69512	−0.134756
$401$	1.49290	0.0745516	0.0372758	−	0.999305i	$-0.488132\pi$
$401$	1.49290	0.0745516	0.0372758	+	0.999305i	$0.488132\pi$
$402$	6.13904	0.306188
$403$	4.70310	0.234278
$404$	−1.81874	−0.0904856
$405$	1.51818	0.0754391
$406$	9.88909	0.490787
$407$	8.73641	0.433048
$408$	6.66440	0.329937
$409$	5.72077	0.282874	0.141437	−	0.989947i	$-0.454828\pi$
$409$	5.72077	0.282874	0.141437	+	0.989947i	$0.454828\pi$
$410$	6.63210	0.327536
$411$	5.24182	0.258560
$412$	1.15681	0.0569921
$413$	6.86271	0.337692
$414$	−7.43253	−0.365289
$415$	21.4291	1.05191
$416$	−4.53110	−0.222156
$417$	9.02717	0.442063
$418$	−5.55078	−0.271498
$419$	−4.41382	−0.215629	−0.107815	−	0.994171i	$-0.534385\pi$
$419$	−4.41382	−0.215629	−0.107815	+	0.994171i	$0.534385\pi$
$420$	1.51818	0.0740797
$421$	−11.9942	−0.584562	−0.292281	−	0.956332i	$-0.594414\pi$
$421$	−11.9942	−0.584562	−0.292281	+	0.956332i	$0.594414\pi$
$422$	−1.90300	−0.0926364
$423$	1.09510	0.0532456
$424$	−10.6381	−0.516632
$425$	−17.9614	−0.871255
$426$	12.7430	0.617399
$427$	−1.76570	−0.0854484
$428$	0.201000	0.00971568
$429$	−7.63091	−0.368424
$430$	16.6042	0.800728
$431$	−18.0119	−0.867602	−0.433801	−	0.901009i	$-0.642828\pi$
$431$	−18.0119	−0.867602	−0.433801	+	0.901009i	$0.642828\pi$
$432$	1.00000	0.0481125
$433$	25.5984	1.23018	0.615089	−	0.788457i	$-0.289120\pi$
$433$	25.5984	1.23018	0.615089	+	0.788457i	$0.289120\pi$
$434$	−1.03796	−0.0498236
$435$	15.0134	0.719839
$436$	−14.9673	−0.716804
$437$	24.4973	1.17186
$438$	14.5572	0.695570
$439$	−2.63532	−0.125777	−0.0628884	−	0.998021i	$-0.520031\pi$
$439$	−2.63532	−0.125777	−0.0628884	+	0.998021i	$0.520031\pi$
$440$	2.55680	0.121891
$441$	1.00000	0.0476190
$442$	−30.1971	−1.43633
$443$	−23.2689	−1.10554	−0.552770	−	0.833334i	$-0.686429\pi$
$443$	−23.2689	−1.10554	−0.552770	+	0.833334i	$0.686429\pi$
$444$	5.18753	0.246189
$445$	16.3651	0.775778
$446$	−3.74781	−0.177464
$447$	2.72440	0.128860
$448$	1.00000	0.0472456
$449$	−1.40183	−0.0661565	−0.0330783	−	0.999453i	$-0.510531\pi$
$449$	−1.40183	−0.0661565	−0.0330783	+	0.999453i	$0.510531\pi$
$450$	−2.69512	−0.127049
$451$	7.35699	0.346427
$452$	19.1404	0.900288
$453$	−7.59623	−0.356902
$454$	−17.1056	−0.802807
$455$	−6.87904	−0.322494
$456$	−3.29596	−0.154347
$457$	23.0409	1.07781	0.538905	−	0.842367i	$-0.318838\pi$
$457$	23.0409	1.07781	0.538905	+	0.842367i	$0.318838\pi$
$458$	−4.56969	−0.213528
$459$	6.66440	0.311068
$460$	−11.2839	−0.526116
$461$	−13.9442	−0.649448	−0.324724	−	0.945809i	$-0.605271\pi$
$461$	−13.9442	−0.649448	−0.324724	+	0.945809i	$0.605271\pi$
$462$	1.68412	0.0783523
$463$	34.4035	1.59887	0.799433	−	0.600755i	$-0.205133\pi$
$463$	34.4035	1.59887	0.799433	+	0.600755i	$0.205133\pi$
$464$	9.88909	0.459089
$465$	−1.57581	−0.0730764
$466$	−24.5304	−1.13635
$467$	−20.6342	−0.954835	−0.477417	−	0.878677i	$-0.658427\pi$
$467$	−20.6342	−0.954835	−0.477417	+	0.878677i	$0.658427\pi$
$468$	−4.53110	−0.209450
$469$	6.13904	0.283475
$470$	1.66256	0.0766882
$471$	−15.3777	−0.708567
$472$	6.86271	0.315882
$473$	18.4191	0.846910
$474$	−12.4378	−0.571286
$475$	8.88301	0.407581
$476$	6.66440	0.305462
$477$	−10.6381	−0.487086
$478$	−10.9210	−0.499516
$479$	8.99786	0.411123	0.205561	−	0.978644i	$-0.434098\pi$
$479$	8.99786	0.411123	0.205561	+	0.978644i	$0.434098\pi$
$480$	1.51818	0.0692952
$481$	−23.5052	−1.07175
$482$	−1.24448	−0.0566846
$483$	−7.43253	−0.338192
$484$	−8.16375	−0.371079
$485$	−25.4107	−1.15384
$486$	1.00000	0.0453609
$487$	−31.8800	−1.44462	−0.722311	−	0.691569i	$-0.756920\pi$
$487$	−31.8800	−1.44462	−0.722311	+	0.691569i	$0.756920\pi$
$488$	−1.76570	−0.0799297
$489$	−5.43341	−0.245707
$490$	1.51818	0.0685845
$491$	−22.1310	−0.998757	−0.499379	−	0.866384i	$-0.666438\pi$
$491$	−22.1310	−0.998757	−0.499379	+	0.866384i	$0.666438\pi$
$492$	4.36845	0.196945
$493$	65.9048	2.96820
$494$	14.9343	0.671927
$495$	2.55680	0.114919
$496$	−1.03796	−0.0466057
$497$	12.7430	0.571600
$498$	14.1150	0.632507
$499$	−3.81187	−0.170643	−0.0853215	−	0.996353i	$-0.527192\pi$
$499$	−3.81187	−0.170643	−0.0853215	+	0.996353i	$0.527192\pi$
$500$	−11.6826	−0.522462
$501$	4.89435	0.218663
$502$	25.4349	1.13521
$503$	−8.86340	−0.395200	−0.197600	−	0.980283i	$-0.563315\pi$
$503$	−8.86340	−0.395200	−0.197600	+	0.980283i	$0.563315\pi$
$504$	1.00000	0.0445435
$505$	−2.76118	−0.122871
$506$	−12.5173	−0.556460
$507$	7.53091	0.334459
$508$	5.68647	0.252296
$509$	3.40292	0.150832	0.0754159	−	0.997152i	$-0.475972\pi$
$509$	3.40292	0.150832	0.0754159	+	0.997152i	$0.475972\pi$
$510$	10.1178	0.448022
$511$	14.5572	0.643973
$512$	1.00000	0.0441942
$513$	−3.29596	−0.145520
$514$	−28.0420	−1.23688
$515$	1.75625	0.0773898
$516$	10.9369	0.481472
$517$	1.84428	0.0811112
$518$	5.18753	0.227927
$519$	−8.82793	−0.387503
$520$	−6.87904	−0.301666
$521$	−37.1615	−1.62807	−0.814037	−	0.580812i	$-0.802735\pi$
$521$	−37.1615	−1.62807	−0.814037	+	0.580812i	$0.802735\pi$
$522$	9.88909	0.432834
$523$	2.38474	0.104278	0.0521388	−	0.998640i	$-0.483396\pi$
$523$	2.38474	0.104278	0.0521388	+	0.998640i	$0.483396\pi$
$524$	12.7076	0.555136
$525$	−2.69512	−0.117625
$526$	2.23470	0.0974376
$527$	−6.91737	−0.301325
$528$	1.68412	0.0732918
$529$	32.2425	1.40185
$530$	−16.1506	−0.701537
$531$	6.86271	0.297816
$532$	−3.29596	−0.142898
$533$	−19.7939	−0.857369
$534$	10.7794	0.466469
$535$	0.305154	0.0131929
$536$	6.13904	0.265166
$537$	11.8545	0.511558
$538$	6.06700	0.261567
$539$	1.68412	0.0725401
$540$	1.51818	0.0653321
$541$	−7.22812	−0.310761	−0.155380	−	0.987855i	$-0.549660\pi$
$541$	−7.22812	−0.310761	−0.155380	+	0.987855i	$0.549660\pi$
$542$	−16.3732	−0.703287
$543$	−3.45602	−0.148312
$544$	6.66440	0.285734
$545$	−22.7231	−0.973350
$546$	−4.53110	−0.193913
$547$	−43.6445	−1.86610	−0.933052	−	0.359741i	$-0.882865\pi$
$547$	−43.6445	−1.86610	−0.933052	+	0.359741i	$0.882865\pi$
$548$	5.24182	0.223920
$549$	−1.76570	−0.0753584
$550$	−4.53891	−0.193540
$551$	−32.5940	−1.38855
$552$	−7.43253	−0.316349
$553$	−12.4378	−0.528908
$554$	12.1527	0.516321
$555$	7.87561	0.334301
$556$	9.02717	0.382837
$557$	−21.6227	−0.916183	−0.458091	−	0.888905i	$-0.651467\pi$
$557$	−21.6227	−0.916183	−0.458091	+	0.888905i	$0.651467\pi$
$558$	−1.03796	−0.0439403
$559$	−49.5564	−2.09601
$560$	1.51818	0.0641549
$561$	11.2236	0.473862
$562$	−30.0646	−1.26820
$563$	−6.41958	−0.270553	−0.135276	−	0.990808i	$-0.543192\pi$
$563$	−6.41958	−0.270553	−0.135276	+	0.990808i	$0.543192\pi$
$564$	1.09510	0.0461120
$565$	29.0586	1.22250
$566$	−7.09061	−0.298041
$567$	1.00000	0.0419961
$568$	12.7430	0.534683
$569$	−37.3317	−1.56503	−0.782513	−	0.622634i	$-0.786063\pi$
$569$	−37.3317	−1.56503	−0.782513	+	0.622634i	$0.786063\pi$
$570$	−5.00386	−0.209589
$571$	22.1557	0.927189	0.463594	−	0.886048i	$-0.346560\pi$
$571$	22.1557	0.927189	0.463594	+	0.886048i	$0.346560\pi$
$572$	−7.63091	−0.319065
$573$	−1.00000	−0.0417756
$574$	4.36845	0.182336
$575$	20.0316	0.835375
$576$	1.00000	0.0416667
$577$	−26.8240	−1.11670	−0.558349	−	0.829606i	$-0.688565\pi$
$577$	−26.8240	−1.11670	−0.558349	+	0.829606i	$0.688565\pi$
$578$	27.4142	1.14028
$579$	−22.3434	−0.928558
$580$	15.0134	0.623399
$581$	14.1150	0.585587
$582$	−16.7376	−0.693797
$583$	−17.9158	−0.741998
$584$	14.5572	0.602381
$585$	−6.87904	−0.284413
$586$	18.2439	0.753650
$587$	34.0272	1.40445	0.702227	−	0.711953i	$-0.252189\pi$
$587$	34.0272	1.40445	0.702227	+	0.711953i	$0.252189\pi$
$588$	1.00000	0.0412393
$589$	3.42107	0.140963
$590$	10.4188	0.428937
$591$	−20.3840	−0.838486
$592$	5.18753	0.213206
$593$	25.3146	1.03955	0.519773	−	0.854304i	$-0.326017\pi$
$593$	25.3146	1.03955	0.519773	+	0.854304i	$0.326017\pi$
$594$	1.68412	0.0691002
$595$	10.1178	0.414788
$596$	2.72440	0.111596
$597$	−12.1717	−0.498154
$598$	33.6776	1.37718
$599$	22.3350	0.912583	0.456291	−	0.889830i	$-0.349177\pi$
$599$	22.3350	0.912583	0.456291	+	0.889830i	$0.349177\pi$
$600$	−2.69512	−0.110028
$601$	15.1351	0.617373	0.308686	−	0.951164i	$-0.400111\pi$
$601$	15.1351	0.617373	0.308686	+	0.951164i	$0.400111\pi$
$602$	10.9369	0.445756
$603$	6.13904	0.250001
$604$	−7.59623	−0.309086
$605$	−12.3941	−0.503890
$606$	−1.81874	−0.0738812
$607$	−30.2739	−1.22878	−0.614391	−	0.789002i	$-0.710598\pi$
$607$	−30.2739	−1.22878	−0.614391	+	0.789002i	$0.710598\pi$
$608$	−3.29596	−0.133669
$609$	9.88909	0.400726
$610$	−2.68066	−0.108537
$611$	−4.96201	−0.200741
$612$	6.66440	0.269392
$613$	−36.2118	−1.46258	−0.731291	−	0.682065i	$-0.761082\pi$
$613$	−36.2118	−1.46258	−0.731291	+	0.682065i	$0.761082\pi$
$614$	−2.23455	−0.0901791
$615$	6.63210	0.267432
$616$	1.68412	0.0678550
$617$	16.0738	0.647108	0.323554	−	0.946210i	$-0.395122\pi$
$617$	16.0738	0.647108	0.323554	+	0.946210i	$0.395122\pi$
$618$	1.15681	0.0465339
$619$	29.8056	1.19799	0.598994	−	0.800754i	$-0.295567\pi$
$619$	29.8056	1.19799	0.598994	+	0.800754i	$0.295567\pi$
$620$	−1.57581	−0.0632860
$621$	−7.43253	−0.298257
$622$	−3.20028	−0.128320
$623$	10.7794	0.431867
$624$	−4.53110	−0.181389
$625$	−4.26069	−0.170427
$626$	28.9085	1.15541
$627$	−5.55078	−0.221677
$628$	−15.3777	−0.613637
$629$	34.5718	1.37847
$630$	1.51818	0.0604858
$631$	19.9387	0.793745	0.396873	−	0.917874i	$-0.370095\pi$
$631$	19.9387	0.793745	0.396873	+	0.917874i	$0.370095\pi$
$632$	−12.4378	−0.494749
$633$	−1.90300	−0.0756373
$634$	22.6721	0.900423
$635$	8.63310	0.342594
$636$	−10.6381	−0.421829
$637$	−4.53110	−0.179529
$638$	16.6544	0.659354
$639$	12.7430	0.504104
$640$	1.51818	0.0600114
$641$	−25.8182	−1.01976	−0.509879	−	0.860246i	$-0.670310\pi$
$641$	−25.8182	−1.01976	−0.509879	+	0.860246i	$0.670310\pi$
$642$	0.201000	0.00793282
$643$	34.7874	1.37188	0.685941	−	0.727657i	$-0.259391\pi$
$643$	34.7874	1.37188	0.685941	+	0.727657i	$0.259391\pi$
$644$	−7.43253	−0.292883
$645$	16.6042	0.653792
$646$	−21.9656	−0.864224
$647$	−21.0585	−0.827896	−0.413948	−	0.910300i	$-0.635851\pi$
$647$	−21.0585	−0.827896	−0.413948	+	0.910300i	$0.635851\pi$
$648$	1.00000	0.0392837
$649$	11.5576	0.453676
$650$	12.2119	0.478990
$651$	−1.03796	−0.0406808
$652$	−5.43341	−0.212789
$653$	−17.9408	−0.702076	−0.351038	−	0.936361i	$-0.614171\pi$
$653$	−17.9408	−0.702076	−0.351038	+	0.936361i	$0.614171\pi$
$654$	−14.9673	−0.585268
$655$	19.2925	0.753821
$656$	4.36845	0.170559
$657$	14.5572	0.567931
$658$	1.09510	0.0426914
$659$	30.0513	1.17063	0.585316	−	0.810806i	$-0.300971\pi$
$659$	30.0513	1.17063	0.585316	+	0.810806i	$0.300971\pi$
$660$	2.55680	0.0995232
$661$	−4.64932	−0.180838	−0.0904189	−	0.995904i	$-0.528821\pi$
$661$	−4.64932	−0.180838	−0.0904189	+	0.995904i	$0.528821\pi$
$662$	23.6486	0.919131
$663$	−30.1971	−1.17276
$664$	14.1150	0.547767
$665$	−5.00386	−0.194041
$666$	5.18753	0.201013
$667$	−73.5009	−2.84597
$668$	4.89435	0.189368
$669$	−3.74781	−0.144899
$670$	9.32018	0.360070
$671$	−2.97365	−0.114797
$672$	1.00000	0.0385758
$673$	37.9525	1.46296	0.731482	−	0.681861i	$-0.238829\pi$
$673$	37.9525	1.46296	0.731482	+	0.681861i	$0.238829\pi$
$674$	−0.0198882	−0.000766064 0
$675$	−2.69512	−0.103735
$676$	7.53091	0.289650
$677$	23.4936	0.902932	0.451466	−	0.892288i	$-0.350901\pi$
$677$	23.4936	0.902932	0.451466	+	0.892288i	$0.350901\pi$
$678$	19.1404	0.735082
$679$	−16.7376	−0.642331
$680$	10.1178	0.387999
$681$	−17.1056	−0.655490
$682$	−1.74804	−0.0669361
$683$	−1.20957	−0.0462830	−0.0231415	−	0.999732i	$-0.507367\pi$
$683$	−1.20957	−0.0462830	−0.0231415	+	0.999732i	$0.507367\pi$
$684$	−3.29596	−0.126024
$685$	7.95804	0.304061
$686$	1.00000	0.0381802
$687$	−4.56969	−0.174345
$688$	10.9369	0.416967
$689$	48.2024	1.83636
$690$	−11.2839	−0.429572
$691$	1.99079	0.0757332	0.0378666	−	0.999283i	$-0.487944\pi$
$691$	1.99079	0.0757332	0.0378666	+	0.999283i	$0.487944\pi$
$692$	−8.82793	−0.335588
$693$	1.68412	0.0639744
$694$	−30.8038	−1.16930
$695$	13.7049	0.519856
$696$	9.88909	0.374845
$697$	29.1131	1.10274
$698$	−19.2872	−0.730031
$699$	−24.5304	−0.927826
$700$	−2.69512	−0.101866
$701$	−38.2631	−1.44518	−0.722588	−	0.691279i	$-0.757047\pi$
$701$	−38.2631	−1.44518	−0.722588	+	0.691279i	$0.757047\pi$
$702$	−4.53110	−0.171016
$703$	−17.0979	−0.644859
$704$	1.68412	0.0634726
$705$	1.66256	0.0626157
$706$	7.26466	0.273409
$707$	−1.81874	−0.0684007
$708$	6.86271	0.257916
$709$	5.12560	0.192496	0.0962479	−	0.995357i	$-0.469316\pi$
$709$	5.12560	0.192496	0.0962479	+	0.995357i	$0.469316\pi$
$710$	19.3461	0.726048
$711$	−12.4378	−0.466453
$712$	10.7794	0.403974
$713$	7.71465	0.288916
$714$	6.66440	0.249409
$715$	−11.5851	−0.433259
$716$	11.8545	0.443022
$717$	−10.9210	−0.407853
$718$	−2.69740	−0.100666
$719$	−16.4593	−0.613830	−0.306915	−	0.951737i	$-0.599297\pi$
$719$	−16.4593	−0.613830	−0.306915	+	0.951737i	$0.599297\pi$
$720$	1.51818	0.0565793
$721$	1.15681	0.0430820
$722$	−8.13667	−0.302815
$723$	−1.24448	−0.0462828
$724$	−3.45602	−0.128442
$725$	−26.6523	−0.989842
$726$	−8.16375	−0.302985
$727$	35.9875	1.33470	0.667351	−	0.744743i	$-0.267428\pi$
$727$	35.9875	1.33470	0.667351	+	0.744743i	$0.267428\pi$
$728$	−4.53110	−0.167934
$729$	1.00000	0.0370370
$730$	22.1005	0.817975
$731$	72.8881	2.69586
$732$	−1.76570	−0.0652623
$733$	24.7453	0.913987	0.456993	−	0.889470i	$-0.348926\pi$
$733$	24.7453	0.913987	0.456993	+	0.889470i	$0.348926\pi$
$734$	−27.4737	−1.01407
$735$	1.51818	0.0559990
$736$	−7.43253	−0.273967
$737$	10.3389	0.380837
$738$	4.36845	0.160805
$739$	9.66608	0.355572	0.177786	−	0.984069i	$-0.443106\pi$
$739$	9.66608	0.355572	0.177786	+	0.984069i	$0.443106\pi$
$740$	7.87561	0.289513
$741$	14.9343	0.548626
$742$	−10.6381	−0.390537
$743$	34.9779	1.28321	0.641607	−	0.767034i	$-0.278268\pi$
$743$	34.9779	1.28321	0.641607	+	0.767034i	$0.278268\pi$
$744$	−1.03796	−0.0380534
$745$	4.13614	0.151536
$746$	33.1406	1.21336
$747$	14.1150	0.516440
$748$	11.2236	0.410377
$749$	0.201000	0.00734436
$750$	−11.6826	−0.426588
$751$	−31.5923	−1.15282	−0.576410	−	0.817161i	$-0.695547\pi$
$751$	−31.5923	−1.15282	−0.576410	+	0.817161i	$0.695547\pi$
$752$	1.09510	0.0399342
$753$	25.4349	0.926898
$754$	−44.8085	−1.63183
$755$	−11.5325	−0.419709
$756$	1.00000	0.0363696
$757$	17.3861	0.631910	0.315955	−	0.948774i	$-0.397675\pi$
$757$	17.3861	0.631910	0.315955	+	0.948774i	$0.397675\pi$
$758$	−31.6535	−1.14971
$759$	−12.5173	−0.454347
$760$	−5.00386	−0.181509
$761$	−38.7826	−1.40587	−0.702935	−	0.711254i	$-0.748128\pi$
$761$	−38.7826	−1.40587	−0.702935	+	0.711254i	$0.748128\pi$
$762$	5.68647	0.205999
$763$	−14.9673	−0.541853
$764$	−1.00000	−0.0361787
$765$	10.1178	0.365809
$766$	29.8945	1.08013
$767$	−31.0957	−1.12280
$768$	1.00000	0.0360844
$769$	−2.27017	−0.0818645	−0.0409323	−	0.999162i	$-0.513033\pi$
$769$	−2.27017	−0.0818645	−0.0409323	+	0.999162i	$0.513033\pi$
$770$	2.55680	0.0921406
$771$	−28.0420	−1.00991
$772$	−22.3434	−0.804155
$773$	2.35936	0.0848603	0.0424301	−	0.999099i	$-0.486490\pi$
$773$	2.35936	0.0848603	0.0424301	+	0.999099i	$0.486490\pi$
$774$	10.9369	0.393120
$775$	2.79743	0.100487
$776$	−16.7376	−0.600845
$777$	5.18753	0.186102
$778$	11.0785	0.397184
$779$	−14.3982	−0.515870
$780$	−6.87904	−0.246309
$781$	21.4607	0.767923
$782$	−49.5333	−1.77131
$783$	9.88909	0.353407
$784$	1.00000	0.0357143
$785$	−23.3461	−0.833259
$786$	12.7076	0.453267
$787$	45.7648	1.63134	0.815669	−	0.578518i	$-0.196369\pi$
$787$	45.7648	1.63134	0.815669	+	0.578518i	$0.196369\pi$
$788$	−20.3840	−0.726151
$789$	2.23470	0.0795575
$790$	−18.8828	−0.671821
$791$	19.1404	0.680554
$792$	1.68412	0.0598425
$793$	8.00059	0.284109
$794$	−4.80631	−0.170570
$795$	−16.1506	−0.572802
$796$	−12.1717	−0.431414
$797$	−13.5697	−0.480662	−0.240331	−	0.970691i	$-0.577256\pi$
$797$	−13.5697	−0.480662	−0.240331	+	0.970691i	$0.577256\pi$
$798$	−3.29596	−0.116676
$799$	7.29818	0.258191
$800$	−2.69512	−0.0952870
$801$	10.7794	0.380871
$802$	1.49290	0.0527160
$803$	24.5160	0.865153
$804$	6.13904	0.216507
$805$	−11.2839	−0.397706
$806$	4.70310	0.165660
$807$	6.06700	0.213569
$808$	−1.81874	−0.0639830
$809$	41.1114	1.44540	0.722700	−	0.691162i	$-0.242901\pi$
$809$	41.1114	1.44540	0.722700	+	0.691162i	$0.242901\pi$
$810$	1.51818	0.0533435
$811$	9.31624	0.327137	0.163569	−	0.986532i	$-0.447699\pi$
$811$	9.31624	0.327137	0.163569	+	0.986532i	$0.447699\pi$
$812$	9.88909	0.347039
$813$	−16.3732	−0.574232
$814$	8.73641	0.306211
$815$	−8.24890	−0.288947
$816$	6.66440	0.233301
$817$	−36.0477	−1.26115
$818$	5.72077	0.200022
$819$	−4.53110	−0.158330
$820$	6.63210	0.231603
$821$	−16.1715	−0.564389	−0.282195	−	0.959357i	$-0.591062\pi$
$821$	−16.1715	−0.564389	−0.282195	+	0.959357i	$0.591062\pi$
$822$	5.24182	0.182830
$823$	28.6720	0.999444	0.499722	−	0.866186i	$-0.333436\pi$
$823$	28.6720	0.999444	0.499722	+	0.866186i	$0.333436\pi$
$824$	1.15681	0.0402995
$825$	−4.53891	−0.158024
$826$	6.86271	0.238784
$827$	−0.119337	−0.00414976	−0.00207488	−	0.999998i	$-0.500660\pi$
$827$	−0.119337	−0.00414976	−0.00207488	+	0.999998i	$0.500660\pi$
$828$	−7.43253	−0.258298
$829$	4.62212	0.160533	0.0802664	−	0.996773i	$-0.474423\pi$
$829$	4.62212	0.160533	0.0802664	+	0.996773i	$0.474423\pi$
$830$	21.4291	0.743814
$831$	12.1527	0.421574
$832$	−4.53110	−0.157088
$833$	6.66440	0.230908
$834$	9.02717	0.312585
$835$	7.43051	0.257143
$836$	−5.55078	−0.191978
$837$	−1.03796	−0.0358771
$838$	−4.41382	−0.152473
$839$	14.4161	0.497700	0.248850	−	0.968542i	$-0.419947\pi$
$839$	14.4161	0.497700	0.248850	+	0.968542i	$0.419947\pi$
$840$	1.51818	0.0523822
$841$	68.7941	2.37221
$842$	−11.9942	−0.413348
$843$	−30.0646	−1.03548
$844$	−1.90300	−0.0655038
$845$	11.4333	0.393317
$846$	1.09510	0.0376503
$847$	−8.16375	−0.280510
$848$	−10.6381	−0.365314
$849$	−7.09061	−0.243349
$850$	−17.9614	−0.616070
$851$	−38.5565	−1.32170
$852$	12.7430	0.436567
$853$	−32.3895	−1.10900	−0.554498	−	0.832185i	$-0.687090\pi$
$853$	−32.3895	−1.10900	−0.554498	+	0.832185i	$0.687090\pi$
$854$	−1.76570	−0.0604212
$855$	−5.00386	−0.171128
$856$	0.201000	0.00687002
$857$	0.912809	0.0311810	0.0155905	−	0.999878i	$-0.495037\pi$
$857$	0.912809	0.0311810	0.0155905	+	0.999878i	$0.495037\pi$
$858$	−7.63091	−0.260515
$859$	−46.0217	−1.57024	−0.785119	−	0.619344i	$-0.787398\pi$
$859$	−46.0217	−1.57024	−0.785119	+	0.619344i	$0.787398\pi$
$860$	16.6042	0.566200
$861$	4.36845	0.148876
$862$	−18.0119	−0.613487
$863$	18.1204	0.616825	0.308412	−	0.951253i	$-0.400202\pi$
$863$	18.1204	0.616825	0.308412	+	0.951253i	$0.400202\pi$
$864$	1.00000	0.0340207
$865$	−13.4024	−0.455695
$866$	25.5984	0.869868
$867$	27.4142	0.931036
$868$	−1.03796	−0.0352306
$869$	−20.9467	−0.710568
$870$	15.0134	0.509003
$871$	−27.8166	−0.942531
$872$	−14.9673	−0.506857
$873$	−16.7376	−0.566483
$874$	24.4973	0.828633
$875$	−11.6826	−0.394944
$876$	14.5572	0.491842
$877$	−9.56239	−0.322899	−0.161450	−	0.986881i	$-0.551617\pi$
$877$	−9.56239	−0.322899	−0.161450	+	0.986881i	$0.551617\pi$
$878$	−2.63532	−0.0889376
$879$	18.2439	0.615353
$880$	2.55680	0.0861896
$881$	−41.2028	−1.38816	−0.694078	−	0.719900i	$-0.744188\pi$
$881$	−41.2028	−1.38816	−0.694078	+	0.719900i	$0.744188\pi$
$882$	1.00000	0.0336718
$883$	−45.0244	−1.51519	−0.757596	−	0.652724i	$-0.773626\pi$
$883$	−45.0244	−1.51519	−0.757596	+	0.652724i	$0.773626\pi$
$884$	−30.1971	−1.01564
$885$	10.4188	0.350226
$886$	−23.2689	−0.781735
$887$	4.79218	0.160906	0.0804528	−	0.996758i	$-0.474363\pi$
$887$	4.79218	0.160906	0.0804528	+	0.996758i	$0.474363\pi$
$888$	5.18753	0.174082
$889$	5.68647	0.190718
$890$	16.3651	0.548558
$891$	1.68412	0.0564201
$892$	−3.74781	−0.125486
$893$	−3.60940	−0.120784
$894$	2.72440	0.0911176
$895$	17.9972	0.601581
$896$	1.00000	0.0334077
$897$	33.6776	1.12446
$898$	−1.40183	−0.0467797
$899$	−10.2645	−0.342339
$900$	−2.69512	−0.0898375
$901$	−70.8966	−2.36191
$902$	7.35699	0.244961
$903$	10.9369	0.363958
$904$	19.1404	0.636600
$905$	−5.24687	−0.174412
$906$	−7.59623	−0.252368
$907$	−41.9863	−1.39413	−0.697067	−	0.717006i	$-0.745512\pi$
$907$	−41.9863	−1.39413	−0.697067	+	0.717006i	$0.745512\pi$
$908$	−17.1056	−0.567671
$909$	−1.81874	−0.0603238
$910$	−6.87904	−0.228038
$911$	13.0290	0.431671	0.215836	−	0.976430i	$-0.430752\pi$
$911$	13.0290	0.431671	0.215836	+	0.976430i	$0.430752\pi$
$912$	−3.29596	−0.109140
$913$	23.7713	0.786714
$914$	23.0409	0.762126
$915$	−2.68066	−0.0886199
$916$	−4.56969	−0.150987
$917$	12.7076	0.419643
$918$	6.66440	0.219958
$919$	−18.0609	−0.595775	−0.297887	−	0.954601i	$-0.596282\pi$
$919$	−18.0609	−0.595775	−0.297887	+	0.954601i	$0.596282\pi$
$920$	−11.2839	−0.372020
$921$	−2.23455	−0.0736309
$922$	−13.9442	−0.459229
$923$	−57.7397	−1.90053
$924$	1.68412	0.0554034
$925$	−13.9810	−0.459694
$926$	34.4035	1.13057
$927$	1.15681	0.0379947
$928$	9.88909	0.324625
$929$	55.6700	1.82647	0.913236	−	0.407431i	$-0.133575\pi$
$929$	55.6700	1.82647	0.913236	+	0.407431i	$0.133575\pi$
$930$	−1.57581	−0.0516728
$931$	−3.29596	−0.108021
$932$	−24.5304	−0.803521
$933$	−3.20028	−0.104772
$934$	−20.6342	−0.675170
$935$	17.0395	0.557252
$936$	−4.53110	−0.148104
$937$	3.40214	0.111143	0.0555715	−	0.998455i	$-0.482302\pi$
$937$	3.40214	0.111143	0.0555715	+	0.998455i	$0.482302\pi$
$938$	6.13904	0.200447
$939$	28.9085	0.943392
$940$	1.66256	0.0542267
$941$	−41.4165	−1.35014	−0.675069	−	0.737754i	$-0.735886\pi$
$941$	−41.4165	−1.35014	−0.675069	+	0.737754i	$0.735886\pi$
$942$	−15.3777	−0.501032
$943$	−32.4686	−1.05732
$944$	6.86271	0.223362
$945$	1.51818	0.0493865
$946$	18.4191	0.598856
$947$	42.1805	1.37068	0.685341	−	0.728223i	$-0.259653\pi$
$947$	42.1805	1.37068	0.685341	+	0.728223i	$0.259653\pi$
$948$	−12.4378	−0.403961
$949$	−65.9602	−2.14116
$950$	8.88301	0.288203
$951$	22.6721	0.735192
$952$	6.66440	0.215994
$953$	−21.6343	−0.700805	−0.350402	−	0.936599i	$-0.613955\pi$
$953$	−21.6343	−0.700805	−0.350402	+	0.936599i	$0.613955\pi$
$954$	−10.6381	−0.344422
$955$	−1.51818	−0.0491272
$956$	−10.9210	−0.353211
$957$	16.6544	0.538360
$958$	8.99786	0.290708
$959$	5.24182	0.169267
$960$	1.51818	0.0489991
$961$	−29.9226	−0.965247
$962$	−23.5052	−0.757839
$963$	0.201000	0.00647712
$964$	−1.24448	−0.0400821
$965$	−33.9213	−1.09196
$966$	−7.43253	−0.239138
$967$	20.5055	0.659411	0.329706	−	0.944084i	$-0.393050\pi$
$967$	20.5055	0.659411	0.329706	+	0.944084i	$0.393050\pi$
$968$	−8.16375	−0.262393
$969$	−21.9656	−0.705636
$970$	−25.4107	−0.815890
$971$	40.9980	1.31569	0.657845	−	0.753154i	$-0.271468\pi$
$971$	40.9980	1.31569	0.657845	+	0.753154i	$0.271468\pi$
$972$	1.00000	0.0320750
$973$	9.02717	0.289398
$974$	−31.8800	−1.02150
$975$	12.2119	0.391093
$976$	−1.76570	−0.0565188
$977$	−21.3860	−0.684199	−0.342099	−	0.939664i	$-0.611138\pi$
$977$	−21.3860	−0.684199	−0.342099	+	0.939664i	$0.611138\pi$
$978$	−5.43341	−0.173741
$979$	18.1537	0.580196
$980$	1.51818	0.0484965
$981$	−14.9673	−0.477869
$982$	−22.1310	−0.706228
$983$	−37.3080	−1.18994	−0.594969	−	0.803748i	$-0.702836\pi$
$983$	−37.3080	−1.18994	−0.594969	+	0.803748i	$0.702836\pi$
$984$	4.36845	0.139261
$985$	−30.9466	−0.986042
$986$	65.9048	2.09884
$987$	1.09510	0.0348574
$988$	14.9343	0.475124
$989$	−81.2890	−2.58484
$990$	2.55680	0.0812604
$991$	25.0574	0.795975	0.397987	−	0.917391i	$-0.369709\pi$
$991$	25.0574	0.795975	0.397987	+	0.917391i	$0.369709\pi$
$992$	−1.03796	−0.0329552
$993$	23.6486	0.750467
$994$	12.7430	0.404182
$995$	−18.4788	−0.585818
$996$	14.1150	0.447250
$997$	−15.0072	−0.475282	−0.237641	−	0.971353i	$-0.576374\pi$
$997$	−15.0072	−0.475282	−0.237641	+	0.971353i	$0.576374\pi$
$998$	−3.81187	−0.120663
$999$	5.18753	0.164126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.ba.1.9	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.ba.1.9	✓	16	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.51818 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.51818 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.51818 q^{10} +1.68412 q^{11} +1.00000 q^{12} -4.53110 q^{13} +1.00000 q^{14} +1.51818 q^{15} +1.00000 q^{16} +6.66440 q^{17} +1.00000 q^{18} -3.29596 q^{19} +1.51818 q^{20} +1.00000 q^{21} +1.68412 q^{22} -7.43253 q^{23} +1.00000 q^{24} -2.69512 q^{25} -4.53110 q^{26} +1.00000 q^{27} +1.00000 q^{28} +9.88909 q^{29} +1.51818 q^{30} -1.03796 q^{31} +1.00000 q^{32} +1.68412 q^{33} +6.66440 q^{34} +1.51818 q^{35} +1.00000 q^{36} +5.18753 q^{37} -3.29596 q^{38} -4.53110 q^{39} +1.51818 q^{40} +4.36845 q^{41} +1.00000 q^{42} +10.9369 q^{43} +1.68412 q^{44} +1.51818 q^{45} -7.43253 q^{46} +1.09510 q^{47} +1.00000 q^{48} +1.00000 q^{49} -2.69512 q^{50} +6.66440 q^{51} -4.53110 q^{52} -10.6381 q^{53} +1.00000 q^{54} +2.55680 q^{55} +1.00000 q^{56} -3.29596 q^{57} +9.88909 q^{58} +6.86271 q^{59} +1.51818 q^{60} -1.76570 q^{61} -1.03796 q^{62} +1.00000 q^{63} +1.00000 q^{64} -6.87904 q^{65} +1.68412 q^{66} +6.13904 q^{67} +6.66440 q^{68} -7.43253 q^{69} +1.51818 q^{70} +12.7430 q^{71} +1.00000 q^{72} +14.5572 q^{73} +5.18753 q^{74} -2.69512 q^{75} -3.29596 q^{76} +1.68412 q^{77} -4.53110 q^{78} -12.4378 q^{79} +1.51818 q^{80} +1.00000 q^{81} +4.36845 q^{82} +14.1150 q^{83} +1.00000 q^{84} +10.1178 q^{85} +10.9369 q^{86} +9.88909 q^{87} +1.68412 q^{88} +10.7794 q^{89} +1.51818 q^{90} -4.53110 q^{91} -7.43253 q^{92} -1.03796 q^{93} +1.09510 q^{94} -5.00386 q^{95} +1.00000 q^{96} -16.7376 q^{97} +1.00000 q^{98} +1.68412 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 16 q^{12} + 6 q^{13} + 16 q^{14} + 11 q^{15} + 16 q^{16} + 14 q^{17} + 16 q^{18} + 29 q^{19} + 11 q^{20} + 16 q^{21} + 8 q^{22} + 9 q^{23} + 16 q^{24} + 29 q^{25} + 6 q^{26} + 16 q^{27} + 16 q^{28} + 11 q^{30} + 14 q^{31} + 16 q^{32} + 8 q^{33} + 14 q^{34} + 11 q^{35} + 16 q^{36} + 11 q^{37} + 29 q^{38} + 6 q^{39} + 11 q^{40} + 14 q^{41} + 16 q^{42} + 28 q^{43} + 8 q^{44} + 11 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 16 q^{49} + 29 q^{50} + 14 q^{51} + 6 q^{52} - 4 q^{53} + 16 q^{54} + 17 q^{55} + 16 q^{56} + 29 q^{57} + 25 q^{59} + 11 q^{60} + 16 q^{61} + 14 q^{62} + 16 q^{63} + 16 q^{64} + 6 q^{65} + 8 q^{66} + 26 q^{67} + 14 q^{68} + 9 q^{69} + 11 q^{70} + 9 q^{71} + 16 q^{72} + 31 q^{73} + 11 q^{74} + 29 q^{75} + 29 q^{76} + 8 q^{77} + 6 q^{78} + 9 q^{79} + 11 q^{80} + 16 q^{81} + 14 q^{82} + 13 q^{83} + 16 q^{84} + 20 q^{85} + 28 q^{86} + 8 q^{88} + 21 q^{89} + 11 q^{90} + 6 q^{91} + 9 q^{92} + 14 q^{93} - q^{94} - 37 q^{95} + 16 q^{96} + 18 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 16 * q^12 + 6 * q^13 + 16 * q^14 + 11 * q^15 + 16 * q^16 + 14 * q^17 + 16 * q^18 + 29 * q^19 + 11 * q^20 + 16 * q^21 + 8 * q^22 + 9 * q^23 + 16 * q^24 + 29 * q^25 + 6 * q^26 + 16 * q^27 + 16 * q^28 + 11 * q^30 + 14 * q^31 + 16 * q^32 + 8 * q^33 + 14 * q^34 + 11 * q^35 + 16 * q^36 + 11 * q^37 + 29 * q^38 + 6 * q^39 + 11 * q^40 + 14 * q^41 + 16 * q^42 + 28 * q^43 + 8 * q^44 + 11 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 16 * q^49 + 29 * q^50 + 14 * q^51 + 6 * q^52 - 4 * q^53 + 16 * q^54 + 17 * q^55 + 16 * q^56 + 29 * q^57 + 25 * q^59 + 11 * q^60 + 16 * q^61 + 14 * q^62 + 16 * q^63 + 16 * q^64 + 6 * q^65 + 8 * q^66 + 26 * q^67 + 14 * q^68 + 9 * q^69 + 11 * q^70 + 9 * q^71 + 16 * q^72 + 31 * q^73 + 11 * q^74 + 29 * q^75 + 29 * q^76 + 8 * q^77 + 6 * q^78 + 9 * q^79 + 11 * q^80 + 16 * q^81 + 14 * q^82 + 13 * q^83 + 16 * q^84 + 20 * q^85 + 28 * q^86 + 8 * q^88 + 21 * q^89 + 11 * q^90 + 6 * q^91 + 9 * q^92 + 14 * q^93 - q^94 - 37 * q^95 + 16 * q^96 + 18 * q^97 + 16 * q^98 + 8 * q^99

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