LMFDB - Embedded newform 3174.2.a.bb.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3174,2,Mod(1,3174)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3174, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3174.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3174 = 2 \cdot 3 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3174.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:	$25.3445176016$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.284630$ of defining polynomial
Character	$\chi$	$=$	3174.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.194262 q^{5} -1.00000 q^{6} -1.95185 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.194262 q^{5} -1.00000 q^{6} -1.95185 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.194262 q^{10} -6.30195 q^{11} -1.00000 q^{12} +4.81288 q^{13} -1.95185 q^{14} -0.194262 q^{15} +1.00000 q^{16} +3.20786 q^{17} +1.00000 q^{18} -0.859449 q^{19} +0.194262 q^{20} +1.95185 q^{21} -6.30195 q^{22} -1.00000 q^{24} -4.96226 q^{25} +4.81288 q^{26} -1.00000 q^{27} -1.95185 q^{28} +5.41741 q^{29} -0.194262 q^{30} -1.01371 q^{31} +1.00000 q^{32} +6.30195 q^{33} +3.20786 q^{34} -0.379170 q^{35} +1.00000 q^{36} -6.89037 q^{37} -0.859449 q^{38} -4.81288 q^{39} +0.194262 q^{40} -0.972011 q^{41} +1.95185 q^{42} +5.14282 q^{43} -6.30195 q^{44} +0.194262 q^{45} -7.41216 q^{47} -1.00000 q^{48} -3.19028 q^{49} -4.96226 q^{50} -3.20786 q^{51} +4.81288 q^{52} -2.00797 q^{53} -1.00000 q^{54} -1.22423 q^{55} -1.95185 q^{56} +0.859449 q^{57} +5.41741 q^{58} -8.60221 q^{59} -0.194262 q^{60} -12.1201 q^{61} -1.01371 q^{62} -1.95185 q^{63} +1.00000 q^{64} +0.934959 q^{65} +6.30195 q^{66} -7.09327 q^{67} +3.20786 q^{68} -0.379170 q^{70} +1.10938 q^{71} +1.00000 q^{72} -13.1859 q^{73} -6.89037 q^{74} +4.96226 q^{75} -0.859449 q^{76} +12.3005 q^{77} -4.81288 q^{78} -1.12979 q^{79} +0.194262 q^{80} +1.00000 q^{81} -0.972011 q^{82} -4.00714 q^{83} +1.95185 q^{84} +0.623165 q^{85} +5.14282 q^{86} -5.41741 q^{87} -6.30195 q^{88} +9.55158 q^{89} +0.194262 q^{90} -9.39402 q^{91} +1.01371 q^{93} -7.41216 q^{94} -0.166958 q^{95} -1.00000 q^{96} +1.12094 q^{97} -3.19028 q^{98} -6.30195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9} + q^{10} - 11 q^{11} - 5 q^{12} + 12 q^{13} - 11 q^{14} - q^{15} + 5 q^{16} + q^{17} + 5 q^{18} - 15 q^{19} + q^{20} + 11 q^{21} - 11 q^{22} - 5 q^{24} + 6 q^{25} + 12 q^{26} - 5 q^{27} - 11 q^{28} + q^{29} - q^{30} - 18 q^{31} + 5 q^{32} + 11 q^{33} + q^{34} - 11 q^{35} + 5 q^{36} - 10 q^{37} - 15 q^{38} - 12 q^{39} + q^{40} - 16 q^{41} + 11 q^{42} - 18 q^{43} - 11 q^{44} + q^{45} - 4 q^{47} - 5 q^{48} + 20 q^{49} + 6 q^{50} - q^{51} + 12 q^{52} + q^{53} - 5 q^{54} - 22 q^{55} - 11 q^{56} + 15 q^{57} + q^{58} + 2 q^{59} - q^{60} + q^{61} - 18 q^{62} - 11 q^{63} + 5 q^{64} - 24 q^{65} + 11 q^{66} - 29 q^{67} + q^{68} - 11 q^{70} - 11 q^{71} + 5 q^{72} - 8 q^{73} - 10 q^{74} - 6 q^{75} - 15 q^{76} + 11 q^{77} - 12 q^{78} - 40 q^{79} + q^{80} + 5 q^{81} - 16 q^{82} - 8 q^{83} + 11 q^{84} - 13 q^{85} - 18 q^{86} - q^{87} - 11 q^{88} - 2 q^{89} + q^{90} - 33 q^{91} + 18 q^{93} - 4 q^{94} - 3 q^{95} - 5 q^{96} - 17 q^{97} + 20 q^{98} - 11 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9 + q^10 - 11 * q^11 - 5 * q^12 + 12 * q^13 - 11 * q^14 - q^15 + 5 * q^16 + q^17 + 5 * q^18 - 15 * q^19 + q^20 + 11 * q^21 - 11 * q^22 - 5 * q^24 + 6 * q^25 + 12 * q^26 - 5 * q^27 - 11 * q^28 + q^29 - q^30 - 18 * q^31 + 5 * q^32 + 11 * q^33 + q^34 - 11 * q^35 + 5 * q^36 - 10 * q^37 - 15 * q^38 - 12 * q^39 + q^40 - 16 * q^41 + 11 * q^42 - 18 * q^43 - 11 * q^44 + q^45 - 4 * q^47 - 5 * q^48 + 20 * q^49 + 6 * q^50 - q^51 + 12 * q^52 + q^53 - 5 * q^54 - 22 * q^55 - 11 * q^56 + 15 * q^57 + q^58 + 2 * q^59 - q^60 + q^61 - 18 * q^62 - 11 * q^63 + 5 * q^64 - 24 * q^65 + 11 * q^66 - 29 * q^67 + q^68 - 11 * q^70 - 11 * q^71 + 5 * q^72 - 8 * q^73 - 10 * q^74 - 6 * q^75 - 15 * q^76 + 11 * q^77 - 12 * q^78 - 40 * q^79 + q^80 + 5 * q^81 - 16 * q^82 - 8 * q^83 + 11 * q^84 - 13 * q^85 - 18 * q^86 - q^87 - 11 * q^88 - 2 * q^89 + q^90 - 33 * q^91 + 18 * q^93 - 4 * q^94 - 3 * q^95 - 5 * q^96 - 17 * q^97 + 20 * q^98 - 11 * 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
$5$	0.194262	0.0868765	0.0434383	−	0.999056i	$-0.486169\pi$
$5$	0.194262	0.0868765	0.0434383	+	0.999056i	$0.486169\pi$
$6$	−1.00000	−0.408248
$7$	−1.95185	−0.737730	−0.368865	−	0.929483i	$-0.620253\pi$
$7$	−1.95185	−0.737730	−0.368865	+	0.929483i	$0.620253\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.194262	0.0614310
$11$	−6.30195	−1.90011	−0.950055	−	0.312083i	$-0.898973\pi$
$11$	−6.30195	−1.90011	−0.950055	+	0.312083i	$0.898973\pi$
$12$	−1.00000	−0.288675
$13$	4.81288	1.33485	0.667426	−	0.744676i	$-0.267396\pi$
$13$	4.81288	1.33485	0.667426	+	0.744676i	$0.267396\pi$
$14$	−1.95185	−0.521654
$15$	−0.194262	−0.0501582
$16$	1.00000	0.250000
$17$	3.20786	0.778020	0.389010	−	0.921233i	$-0.372817\pi$
$17$	3.20786	0.778020	0.389010	+	0.921233i	$0.372817\pi$
$18$	1.00000	0.235702
$19$	−0.859449	−0.197171	−0.0985855	−	0.995129i	$-0.531432\pi$
$19$	−0.859449	−0.197171	−0.0985855	+	0.995129i	$0.531432\pi$
$20$	0.194262	0.0434383
$21$	1.95185	0.425928
$22$	−6.30195	−1.34358
$23$	0	0
$23$	0	0
$24$	−1.00000	−0.204124
$25$	−4.96226	−0.992452
$26$	4.81288	0.943883
$27$	−1.00000	−0.192450
$28$	−1.95185	−0.368865
$29$	5.41741	1.00599	0.502994	−	0.864290i	$-0.332232\pi$
$29$	5.41741	1.00599	0.502994	+	0.864290i	$0.332232\pi$
$30$	−0.194262	−0.0354672
$31$	−1.01371	−0.182067	−0.0910334	−	0.995848i	$-0.529017\pi$
$31$	−1.01371	−0.182067	−0.0910334	+	0.995848i	$0.529017\pi$
$32$	1.00000	0.176777
$33$	6.30195	1.09703
$34$	3.20786	0.550144
$35$	−0.379170	−0.0640914
$36$	1.00000	0.166667
$37$	−6.89037	−1.13277	−0.566385	−	0.824141i	$-0.691658\pi$
$37$	−6.89037	−1.13277	−0.566385	+	0.824141i	$0.691658\pi$
$38$	−0.859449	−0.139421
$39$	−4.81288	−0.770678
$40$	0.194262	0.0307155
$41$	−0.972011	−0.151803	−0.0759013	−	0.997115i	$-0.524183\pi$
$41$	−0.972011	−0.151803	−0.0759013	+	0.997115i	$0.524183\pi$
$42$	1.95185	0.301177
$43$	5.14282	0.784273	0.392136	−	0.919907i	$-0.371736\pi$
$43$	5.14282	0.784273	0.392136	+	0.919907i	$0.371736\pi$
$44$	−6.30195	−0.950055
$45$	0.194262	0.0289588
$46$	0	0
$47$	−7.41216	−1.08117	−0.540587	−	0.841288i	$-0.681798\pi$
$47$	−7.41216	−1.08117	−0.540587	+	0.841288i	$0.681798\pi$
$48$	−1.00000	−0.144338
$49$	−3.19028	−0.455755
$50$	−4.96226	−0.701770
$51$	−3.20786	−0.449190
$52$	4.81288	0.667426
$53$	−2.00797	−0.275815	−0.137908	−	0.990445i	$-0.544038\pi$
$53$	−2.00797	−0.275815	−0.137908	+	0.990445i	$0.544038\pi$
$54$	−1.00000	−0.136083
$55$	−1.22423	−0.165075
$56$	−1.95185	−0.260827
$57$	0.859449	0.113837
$58$	5.41741	0.711341
$59$	−8.60221	−1.11991	−0.559956	−	0.828522i	$-0.689182\pi$
$59$	−8.60221	−1.11991	−0.559956	+	0.828522i	$0.689182\pi$
$60$	−0.194262	−0.0250791
$61$	−12.1201	−1.55182	−0.775912	−	0.630841i	$-0.782710\pi$
$61$	−12.1201	−1.55182	−0.775912	+	0.630841i	$0.782710\pi$
$62$	−1.01371	−0.128741
$63$	−1.95185	−0.245910
$64$	1.00000	0.125000
$65$	0.934959	0.115967
$66$	6.30195	0.775716
$67$	−7.09327	−0.866580	−0.433290	−	0.901254i	$-0.642647\pi$
$67$	−7.09327	−0.866580	−0.433290	+	0.901254i	$0.642647\pi$
$68$	3.20786	0.389010
$69$	0	0
$70$	−0.379170	−0.0453194
$71$	1.10938	0.131659	0.0658294	−	0.997831i	$-0.479031\pi$
$71$	1.10938	0.131659	0.0658294	+	0.997831i	$0.479031\pi$
$72$	1.00000	0.117851
$73$	−13.1859	−1.54330	−0.771648	−	0.636049i	$-0.780567\pi$
$73$	−13.1859	−1.54330	−0.771648	+	0.636049i	$0.780567\pi$
$74$	−6.89037	−0.800989
$75$	4.96226	0.572993
$76$	−0.859449	−0.0985855
$77$	12.3005	1.40177
$78$	−4.81288	−0.544951
$79$	−1.12979	−0.127112	−0.0635559	−	0.997978i	$-0.520244\pi$
$79$	−1.12979	−0.127112	−0.0635559	+	0.997978i	$0.520244\pi$
$80$	0.194262	0.0217191
$81$	1.00000	0.111111
$82$	−0.972011	−0.107341
$83$	−4.00714	−0.439841	−0.219920	−	0.975518i	$-0.570580\pi$
$83$	−4.00714	−0.439841	−0.219920	+	0.975518i	$0.570580\pi$
$84$	1.95185	0.212964
$85$	0.623165	0.0675917
$86$	5.14282	0.554564
$87$	−5.41741	−0.580807
$88$	−6.30195	−0.671790
$89$	9.55158	1.01247	0.506233	−	0.862397i	$-0.331038\pi$
$89$	9.55158	1.01247	0.506233	+	0.862397i	$0.331038\pi$
$90$	0.194262	0.0204770
$91$	−9.39402	−0.984760
$92$	0	0
$93$	1.01371	0.105116
$94$	−7.41216	−0.764506
$95$	−0.166958	−0.0171295
$96$	−1.00000	−0.102062
$97$	1.12094	0.113815	0.0569073	−	0.998379i	$-0.481876\pi$
$97$	1.12094	0.113815	0.0569073	+	0.998379i	$0.481876\pi$
$98$	−3.19028	−0.322267
$99$	−6.30195	−0.633370
$100$	−4.96226	−0.496226
$101$	12.5714	1.25090	0.625451	−	0.780263i	$-0.284915\pi$
$101$	12.5714	1.25090	0.625451	+	0.780263i	$0.284915\pi$
$102$	−3.20786	−0.317626
$103$	−19.3963	−1.91117	−0.955587	−	0.294708i	$-0.904778\pi$
$103$	−19.3963	−1.91117	−0.955587	+	0.294708i	$0.904778\pi$
$104$	4.81288	0.471942
$105$	0.379170	0.0370032
$106$	−2.00797	−0.195031
$107$	−3.07594	−0.297363	−0.148681	−	0.988885i	$-0.547503\pi$
$107$	−3.07594	−0.297363	−0.148681	+	0.988885i	$0.547503\pi$
$108$	−1.00000	−0.0962250
$109$	−1.94929	−0.186708	−0.0933542	−	0.995633i	$-0.529759\pi$
$109$	−1.94929	−0.186708	−0.0933542	+	0.995633i	$0.529759\pi$
$110$	−1.22423	−0.116726
$111$	6.89037	0.654005
$112$	−1.95185	−0.184432
$113$	17.1492	1.61326	0.806632	−	0.591054i	$-0.201288\pi$
$113$	17.1492	1.61326	0.806632	+	0.591054i	$0.201288\pi$
$114$	0.859449	0.0804947
$115$	0	0
$116$	5.41741	0.502994
$117$	4.81288	0.444951
$118$	−8.60221	−0.791898
$119$	−6.26126	−0.573969
$120$	−0.194262	−0.0177336
$121$	28.7146	2.61042
$122$	−12.1201	−1.09731
$123$	0.972011	0.0876433
$124$	−1.01371	−0.0910334
$125$	−1.93529	−0.173097
$126$	−1.95185	−0.173885
$127$	−21.6118	−1.91774	−0.958869	−	0.283850i	$-0.908388\pi$
$127$	−21.6118	−1.91774	−0.958869	+	0.283850i	$0.908388\pi$
$128$	1.00000	0.0883883
$129$	−5.14282	−0.452800
$130$	0.934959	0.0820013
$131$	−14.9571	−1.30681	−0.653404	−	0.757009i	$-0.726660\pi$
$131$	−14.9571	−1.30681	−0.653404	+	0.757009i	$0.726660\pi$
$132$	6.30195	0.548514
$133$	1.67751	0.145459
$134$	−7.09327	−0.612765
$135$	−0.194262	−0.0167194
$136$	3.20786	0.275072
$137$	−18.1570	−1.55126	−0.775628	−	0.631190i	$-0.782567\pi$
$137$	−18.1570	−1.55126	−0.775628	+	0.631190i	$0.782567\pi$
$138$	0	0
$139$	−7.36718	−0.624876	−0.312438	−	0.949938i	$-0.601146\pi$
$139$	−7.36718	−0.624876	−0.312438	+	0.949938i	$0.601146\pi$
$140$	−0.379170	−0.0320457
$141$	7.41216	0.624217
$142$	1.10938	0.0930969
$143$	−30.3305	−2.53637
$144$	1.00000	0.0833333
$145$	1.05240	0.0873967
$146$	−13.1859	−1.09128
$147$	3.19028	0.263130
$148$	−6.89037	−0.566385
$149$	−15.6333	−1.28073	−0.640365	−	0.768070i	$-0.721217\pi$
$149$	−15.6333	−1.28073	−0.640365	+	0.768070i	$0.721217\pi$
$150$	4.96226	0.405167
$151$	20.7042	1.68488	0.842440	−	0.538790i	$-0.181118\pi$
$151$	20.7042	1.68488	0.842440	+	0.538790i	$0.181118\pi$
$152$	−0.859449	−0.0697105
$153$	3.20786	0.259340
$154$	12.3005	0.991199
$155$	−0.196924	−0.0158173
$156$	−4.81288	−0.385339
$157$	3.97631	0.317344	0.158672	−	0.987331i	$-0.449279\pi$
$157$	3.97631	0.317344	0.158672	+	0.987331i	$0.449279\pi$
$158$	−1.12979	−0.0898816
$159$	2.00797	0.159242
$160$	0.194262	0.0153577
$161$	0	0
$162$	1.00000	0.0785674
$163$	24.5129	1.91999	0.959997	−	0.280009i	$-0.0903375\pi$
$163$	24.5129	1.91999	0.959997	+	0.280009i	$0.0903375\pi$
$164$	−0.972011	−0.0759013
$165$	1.22423	0.0953060
$166$	−4.00714	−0.311015
$167$	−1.95444	−0.151239	−0.0756194	−	0.997137i	$-0.524093\pi$
$167$	−1.95444	−0.151239	−0.0756194	+	0.997137i	$0.524093\pi$
$168$	1.95185	0.150588
$169$	10.1638	0.781832
$170$	0.623165	0.0477945
$171$	−0.859449	−0.0657237
$172$	5.14282	0.392136
$173$	6.14165	0.466941	0.233471	−	0.972364i	$-0.424992\pi$
$173$	6.14165	0.466941	0.233471	+	0.972364i	$0.424992\pi$
$174$	−5.41741	−0.410693
$175$	9.68559	0.732162
$176$	−6.30195	−0.475027
$177$	8.60221	0.646582
$178$	9.55158	0.715921
$179$	6.47091	0.483658	0.241829	−	0.970319i	$-0.422253\pi$
$179$	6.47091	0.483658	0.241829	+	0.970319i	$0.422253\pi$
$180$	0.194262	0.0144794
$181$	−3.26146	−0.242423	−0.121211	−	0.992627i	$-0.538678\pi$
$181$	−3.26146	−0.242423	−0.121211	+	0.992627i	$0.538678\pi$
$182$	−9.39402	−0.696331
$183$	12.1201	0.895946
$184$	0	0
$185$	−1.33853	−0.0984110
$186$	1.01371	0.0743285
$187$	−20.2158	−1.47832
$188$	−7.41216	−0.540587
$189$	1.95185	0.141976
$190$	−0.166958	−0.0121124
$191$	22.8536	1.65363	0.826815	−	0.562474i	$-0.190150\pi$
$191$	22.8536	1.65363	0.826815	+	0.562474i	$0.190150\pi$
$192$	−1.00000	−0.0721688
$193$	−16.9414	−1.21947	−0.609734	−	0.792606i	$-0.708724\pi$
$193$	−16.9414	−1.21947	−0.609734	+	0.792606i	$0.708724\pi$
$194$	1.12094	0.0804790
$195$	−0.934959	−0.0669538
$196$	−3.19028	−0.227877
$197$	1.25480	0.0894010	0.0447005	−	0.999000i	$-0.485767\pi$
$197$	1.25480	0.0894010	0.0447005	+	0.999000i	$0.485767\pi$
$198$	−6.30195	−0.447860
$199$	−24.8140	−1.75902	−0.879509	−	0.475883i	$-0.842129\pi$
$199$	−24.8140	−1.75902	−0.879509	+	0.475883i	$0.842129\pi$
$200$	−4.96226	−0.350885
$201$	7.09327	0.500320
$202$	12.5714	0.884521
$203$	−10.5740	−0.742147
$204$	−3.20786	−0.224595
$205$	−0.188825	−0.0131881
$206$	−19.3963	−1.35140
$207$	0	0
$208$	4.81288	0.333713
$209$	5.41620	0.374646
$210$	0.379170	0.0261652
$211$	7.25827	0.499680	0.249840	−	0.968287i	$-0.419622\pi$
$211$	7.25827	0.499680	0.249840	+	0.968287i	$0.419622\pi$
$212$	−2.00797	−0.137908
$213$	−1.10938	−0.0760133
$214$	−3.07594	−0.210267
$215$	0.999053	0.0681349
$216$	−1.00000	−0.0680414
$217$	1.97860	0.134316
$218$	−1.94929	−0.132023
$219$	13.1859	0.891023
$220$	−1.22423	−0.0825374
$221$	15.4390	1.03854
$222$	6.89037	0.462451
$223$	20.7342	1.38846	0.694231	−	0.719752i	$-0.255745\pi$
$223$	20.7342	1.38846	0.694231	+	0.719752i	$0.255745\pi$
$224$	−1.95185	−0.130413
$225$	−4.96226	−0.330817
$226$	17.1492	1.14075
$227$	21.0504	1.39716	0.698581	−	0.715531i	$-0.253815\pi$
$227$	21.0504	1.39716	0.698581	+	0.715531i	$0.253815\pi$
$228$	0.859449	0.0569184
$229$	1.91595	0.126609	0.0633047	−	0.997994i	$-0.479836\pi$
$229$	1.91595	0.126609	0.0633047	+	0.997994i	$0.479836\pi$
$230$	0	0
$231$	−12.3005	−0.809311
$232$	5.41741	0.355670
$233$	−14.4306	−0.945378	−0.472689	−	0.881229i	$-0.656717\pi$
$233$	−14.4306	−0.945378	−0.472689	+	0.881229i	$0.656717\pi$
$234$	4.81288	0.314628
$235$	−1.43990	−0.0939287
$236$	−8.60221	−0.559956
$237$	1.12979	0.0733880
$238$	−6.26126	−0.405857
$239$	−9.81701	−0.635010	−0.317505	−	0.948257i	$-0.602845\pi$
$239$	−9.81701	−0.635010	−0.317505	+	0.948257i	$0.602845\pi$
$240$	−0.194262	−0.0125395
$241$	14.9039	0.960043	0.480022	−	0.877257i	$-0.340629\pi$
$241$	14.9039	0.960043	0.480022	+	0.877257i	$0.340629\pi$
$242$	28.7146	1.84584
$243$	−1.00000	−0.0641500
$244$	−12.1201	−0.775912
$245$	−0.619750	−0.0395944
$246$	0.972011	0.0619732
$247$	−4.13642	−0.263194
$248$	−1.01371	−0.0643703
$249$	4.00714	0.253942
$250$	−1.93529	−0.122398
$251$	2.14471	0.135373	0.0676864	−	0.997707i	$-0.478438\pi$
$251$	2.14471	0.135373	0.0676864	+	0.997707i	$0.478438\pi$
$252$	−1.95185	−0.122955
$253$	0	0
$254$	−21.6118	−1.35604
$255$	−0.623165	−0.0390241
$256$	1.00000	0.0625000
$257$	−15.8488	−0.988620	−0.494310	−	0.869286i	$-0.664579\pi$
$257$	−15.8488	−0.988620	−0.494310	+	0.869286i	$0.664579\pi$
$258$	−5.14282	−0.320178
$259$	13.4490	0.835678
$260$	0.934959	0.0579837
$261$	5.41741	0.335329
$262$	−14.9571	−0.924053
$263$	−0.130608	−0.00805362	−0.00402681	−	0.999992i	$-0.501282\pi$
$263$	−0.130608	−0.00805362	−0.00402681	+	0.999992i	$0.501282\pi$
$264$	6.30195	0.387858
$265$	−0.390071	−0.0239619
$266$	1.67751	0.102855
$267$	−9.55158	−0.584547
$268$	−7.09327	−0.433290
$269$	−23.9688	−1.46140	−0.730702	−	0.682697i	$-0.760807\pi$
$269$	−23.9688	−1.46140	−0.730702	+	0.682697i	$0.760807\pi$
$270$	−0.194262	−0.0118224
$271$	3.22188	0.195715	0.0978575	−	0.995200i	$-0.468801\pi$
$271$	3.22188	0.195715	0.0978575	+	0.995200i	$0.468801\pi$
$272$	3.20786	0.194505
$273$	9.39402	0.568552
$274$	−18.1570	−1.09690
$275$	31.2719	1.88577
$276$	0	0
$277$	−13.0026	−0.781250	−0.390625	−	0.920550i	$-0.627741\pi$
$277$	−13.0026	−0.781250	−0.390625	+	0.920550i	$0.627741\pi$
$278$	−7.36718	−0.441854
$279$	−1.01371	−0.0606889
$280$	−0.379170	−0.0226597
$281$	−9.71850	−0.579757	−0.289878	−	0.957063i	$-0.593615\pi$
$281$	−9.71850	−0.579757	−0.289878	+	0.957063i	$0.593615\pi$
$282$	7.41216	0.441388
$283$	−19.9847	−1.18797	−0.593985	−	0.804476i	$-0.702446\pi$
$283$	−19.9847	−1.18797	−0.593985	+	0.804476i	$0.702446\pi$
$284$	1.10938	0.0658294
$285$	0.166958	0.00988974
$286$	−30.3305	−1.79348
$287$	1.89722	0.111989
$288$	1.00000	0.0589256
$289$	−6.70963	−0.394684
$290$	1.05240	0.0617988
$291$	−1.12094	−0.0657108
$292$	−13.1859	−0.771648
$293$	17.8821	1.04468	0.522341	−	0.852737i	$-0.325059\pi$
$293$	17.8821	1.04468	0.522341	+	0.852737i	$0.325059\pi$
$294$	3.19028	0.186061
$295$	−1.67108	−0.0972941
$296$	−6.89037	−0.400494
$297$	6.30195	0.365676
$298$	−15.6333	−0.905613
$299$	0	0
$300$	4.96226	0.286496
$301$	−10.0380	−0.578581
$302$	20.7042	1.19139
$303$	−12.5714	−0.722209
$304$	−0.859449	−0.0492928
$305$	−2.35448	−0.134817
$306$	3.20786	0.183381
$307$	−12.5139	−0.714205	−0.357102	−	0.934065i	$-0.616235\pi$
$307$	−12.5139	−0.714205	−0.357102	+	0.934065i	$0.616235\pi$
$308$	12.3005	0.700884
$309$	19.3963	1.10342
$310$	−0.196924	−0.0111845
$311$	5.45773	0.309479	0.154740	−	0.987955i	$-0.450546\pi$
$311$	5.45773	0.309479	0.154740	+	0.987955i	$0.450546\pi$
$312$	−4.81288	−0.272476
$313$	23.9234	1.35223	0.676114	−	0.736797i	$-0.263663\pi$
$313$	23.9234	1.35223	0.676114	+	0.736797i	$0.263663\pi$
$314$	3.97631	0.224396
$315$	−0.379170	−0.0213638
$316$	−1.12979	−0.0635559
$317$	−16.1225	−0.905532	−0.452766	−	0.891629i	$-0.649563\pi$
$317$	−16.1225	−0.905532	−0.452766	+	0.891629i	$0.649563\pi$
$318$	2.00797	0.112601
$319$	−34.1402	−1.91149
$320$	0.194262	0.0108596
$321$	3.07594	0.171682
$322$	0	0
$323$	−2.75699	−0.153403
$324$	1.00000	0.0555556
$325$	−23.8828	−1.32478
$326$	24.5129	1.35764
$327$	1.94929	0.107796
$328$	−0.972011	−0.0536703
$329$	14.4674	0.797615
$330$	1.22423	0.0673915
$331$	−0.517893	−0.0284660	−0.0142330	−	0.999899i	$-0.504531\pi$
$331$	−0.517893	−0.0284660	−0.0142330	+	0.999899i	$0.504531\pi$
$332$	−4.00714	−0.219920
$333$	−6.89037	−0.377590
$334$	−1.95444	−0.106942
$335$	−1.37795	−0.0752855
$336$	1.95185	0.106482
$337$	0.530119	0.0288774	0.0144387	−	0.999896i	$-0.495404\pi$
$337$	0.530119	0.0288774	0.0144387	+	0.999896i	$0.495404\pi$
$338$	10.1638	0.552839
$339$	−17.1492	−0.931418
$340$	0.623165	0.0337958
$341$	6.38832	0.345947
$342$	−0.859449	−0.0464737
$343$	19.8899	1.07395
$344$	5.14282	0.277282
$345$	0	0
$346$	6.14165	0.330177
$347$	26.8126	1.43937	0.719687	−	0.694298i	$-0.244285\pi$
$347$	26.8126	1.43937	0.719687	+	0.694298i	$0.244285\pi$
$348$	−5.41741	−0.290404
$349$	1.45728	0.0780066	0.0390033	−	0.999239i	$-0.487582\pi$
$349$	1.45728	0.0780066	0.0390033	+	0.999239i	$0.487582\pi$
$350$	9.68559	0.517716
$351$	−4.81288	−0.256893
$352$	−6.30195	−0.335895
$353$	22.4537	1.19509	0.597545	−	0.801835i	$-0.296143\pi$
$353$	22.4537	1.19509	0.597545	+	0.801835i	$0.296143\pi$
$354$	8.60221	0.457202
$355$	0.215510	0.0114381
$356$	9.55158	0.506233
$357$	6.26126	0.331381
$358$	6.47091	0.341998
$359$	−0.168999	−0.00891940	−0.00445970	−	0.999990i	$-0.501420\pi$
$359$	−0.168999	−0.00891940	−0.00445970	+	0.999990i	$0.501420\pi$
$360$	0.194262	0.0102385
$361$	−18.2613	−0.961124
$362$	−3.26146	−0.171419
$363$	−28.7146	−1.50712
$364$	−9.39402	−0.492380
$365$	−2.56152	−0.134076
$366$	12.1201	0.633530
$367$	−17.8312	−0.930782	−0.465391	−	0.885105i	$-0.654086\pi$
$367$	−17.8312	−0.930782	−0.465391	+	0.885105i	$0.654086\pi$
$368$	0	0
$369$	−0.972011	−0.0506009
$370$	−1.33853	−0.0695871
$371$	3.91925	0.203477
$372$	1.01371	0.0525582
$373$	27.3884	1.41812	0.709058	−	0.705150i	$-0.249121\pi$
$373$	27.3884	1.41812	0.709058	+	0.705150i	$0.249121\pi$
$374$	−20.2158	−1.04533
$375$	1.93529	0.0999378
$376$	−7.41216	−0.382253
$377$	26.0733	1.34285
$378$	1.95185	0.100392
$379$	2.73604	0.140541	0.0702704	−	0.997528i	$-0.477614\pi$
$379$	2.73604	0.140541	0.0702704	+	0.997528i	$0.477614\pi$
$380$	−0.166958	−0.00856476
$381$	21.6118	1.10721
$382$	22.8536	1.16929
$383$	14.4109	0.736362	0.368181	−	0.929754i	$-0.379981\pi$
$383$	14.4109	0.736362	0.368181	+	0.929754i	$0.379981\pi$
$384$	−1.00000	−0.0510310
$385$	2.38951	0.121781
$386$	−16.9414	−0.862294
$387$	5.14282	0.261424
$388$	1.12094	0.0569073
$389$	−1.08404	−0.0549630	−0.0274815	−	0.999622i	$-0.508749\pi$
$389$	−1.08404	−0.0549630	−0.0274815	+	0.999622i	$0.508749\pi$
$390$	−0.934959	−0.0473435
$391$	0	0
$392$	−3.19028	−0.161134
$393$	14.9571	0.754486
$394$	1.25480	0.0632161
$395$	−0.219476	−0.0110430
$396$	−6.30195	−0.316685
$397$	−27.0241	−1.35630	−0.678149	−	0.734924i	$-0.737218\pi$
$397$	−27.0241	−1.35630	−0.678149	+	0.734924i	$0.737218\pi$
$398$	−24.8140	−1.24381
$399$	−1.67751	−0.0839807
$400$	−4.96226	−0.248113
$401$	−9.27409	−0.463126	−0.231563	−	0.972820i	$-0.574384\pi$
$401$	−9.27409	−0.463126	−0.231563	+	0.972820i	$0.574384\pi$
$402$	7.09327	0.353780
$403$	−4.87884	−0.243032
$404$	12.5714	0.625451
$405$	0.194262	0.00965294
$406$	−10.5740	−0.524777
$407$	43.4228	2.15239
$408$	−3.20786	−0.158813
$409$	36.7657	1.81795	0.908974	−	0.416852i	$-0.136867\pi$
$409$	36.7657	1.81795	0.908974	+	0.416852i	$0.136867\pi$
$410$	−0.188825	−0.00932538
$411$	18.1570	0.895619
$412$	−19.3963	−0.955587
$413$	16.7902	0.826193
$414$	0	0
$415$	−0.778434	−0.0382118
$416$	4.81288	0.235971
$417$	7.36718	0.360772
$418$	5.41620	0.264915
$419$	26.4958	1.29441	0.647203	−	0.762318i	$-0.275939\pi$
$419$	26.4958	1.29441	0.647203	+	0.762318i	$0.275939\pi$
$420$	0.379170	0.0185016
$421$	−9.95095	−0.484980	−0.242490	−	0.970154i	$-0.577964\pi$
$421$	−9.95095	−0.484980	−0.242490	+	0.970154i	$0.577964\pi$
$422$	7.25827	0.353327
$423$	−7.41216	−0.360392
$424$	−2.00797	−0.0975155
$425$	−15.9182	−0.772148
$426$	−1.10938	−0.0537495
$427$	23.6567	1.14483
$428$	−3.07594	−0.148681
$429$	30.3305	1.46437
$430$	0.999053	0.0481786
$431$	−8.77287	−0.422575	−0.211287	−	0.977424i	$-0.567766\pi$
$431$	−8.77287	−0.422575	−0.211287	+	0.977424i	$0.567766\pi$
$432$	−1.00000	−0.0481125
$433$	7.99061	0.384004	0.192002	−	0.981395i	$-0.438502\pi$
$433$	7.99061	0.384004	0.192002	+	0.981395i	$0.438502\pi$
$434$	1.97860	0.0949758
$435$	−1.05240	−0.0504585
$436$	−1.94929	−0.0933542
$437$	0	0
$438$	13.1859	0.630048
$439$	−1.41063	−0.0673257	−0.0336628	−	0.999433i	$-0.510717\pi$
$439$	−1.41063	−0.0673257	−0.0336628	+	0.999433i	$0.510717\pi$
$440$	−1.22423	−0.0583628
$441$	−3.19028	−0.151918
$442$	15.4390	0.734361
$443$	12.5935	0.598335	0.299167	−	0.954201i	$-0.403291\pi$
$443$	12.5935	0.598335	0.299167	+	0.954201i	$0.403291\pi$
$444$	6.89037	0.327002
$445$	1.85551	0.0879594
$446$	20.7342	0.981791
$447$	15.6333	0.739430
$448$	−1.95185	−0.0922162
$449$	−38.3533	−1.81000	−0.905002	−	0.425407i	$-0.860131\pi$
$449$	−38.3533	−1.81000	−0.905002	+	0.425407i	$0.860131\pi$
$450$	−4.96226	−0.233923
$451$	6.12557	0.288442
$452$	17.1492	0.806632
$453$	−20.7042	−0.972766
$454$	21.0504	0.987943
$455$	−1.82490	−0.0855525
$456$	0.859449	0.0402474
$457$	−26.6357	−1.24597	−0.622983	−	0.782235i	$-0.714079\pi$
$457$	−26.6357	−1.24597	−0.622983	+	0.782235i	$0.714079\pi$
$458$	1.91595	0.0895264
$459$	−3.20786	−0.149730
$460$	0	0
$461$	7.65301	0.356436	0.178218	−	0.983991i	$-0.442967\pi$
$461$	7.65301	0.356436	0.178218	+	0.983991i	$0.442967\pi$
$462$	−12.3005	−0.572269
$463$	−4.15149	−0.192936	−0.0964681	−	0.995336i	$-0.530755\pi$
$463$	−4.15149	−0.192936	−0.0964681	+	0.995336i	$0.530755\pi$
$464$	5.41741	0.251497
$465$	0.196924	0.00913214
$466$	−14.4306	−0.668483
$467$	32.1155	1.48613	0.743063	−	0.669221i	$-0.233372\pi$
$467$	32.1155	1.48613	0.743063	+	0.669221i	$0.233372\pi$
$468$	4.81288	0.222475
$469$	13.8450	0.639302
$470$	−1.43990	−0.0664176
$471$	−3.97631	−0.183219
$472$	−8.60221	−0.395949
$473$	−32.4098	−1.49020
$474$	1.12979	0.0518932
$475$	4.26481	0.195683
$476$	−6.26126	−0.286984
$477$	−2.00797	−0.0919385
$478$	−9.81701	−0.449020
$479$	−1.81509	−0.0829337	−0.0414668	−	0.999140i	$-0.513203\pi$
$479$	−1.81509	−0.0829337	−0.0414668	+	0.999140i	$0.513203\pi$
$480$	−0.194262	−0.00886680
$481$	−33.1625	−1.51208
$482$	14.9039	0.678853
$483$	0	0
$484$	28.7146	1.30521
$485$	0.217756	0.00988781
$486$	−1.00000	−0.0453609
$487$	−16.1873	−0.733515	−0.366758	−	0.930317i	$-0.619532\pi$
$487$	−16.1873	−0.733515	−0.366758	+	0.930317i	$0.619532\pi$
$488$	−12.1201	−0.548653
$489$	−24.5129	−1.10851
$490$	−0.619750	−0.0279975
$491$	−1.42155	−0.0641536	−0.0320768	−	0.999485i	$-0.510212\pi$
$491$	−1.42155	−0.0641536	−0.0320768	+	0.999485i	$0.510212\pi$
$492$	0.972011	0.0438216
$493$	17.3783	0.782679
$494$	−4.13642	−0.186106
$495$	−1.22423	−0.0550250
$496$	−1.01371	−0.0455167
$497$	−2.16534	−0.0971286
$498$	4.00714	0.179564
$499$	20.5750	0.921061	0.460531	−	0.887644i	$-0.347659\pi$
$499$	20.5750	0.921061	0.460531	+	0.887644i	$0.347659\pi$
$500$	−1.93529	−0.0865487
$501$	1.95444	0.0873177
$502$	2.14471	0.0957230
$503$	−14.7875	−0.659342	−0.329671	−	0.944096i	$-0.606938\pi$
$503$	−14.7875	−0.659342	−0.329671	+	0.944096i	$0.606938\pi$
$504$	−1.95185	−0.0869423
$505$	2.44214	0.108674
$506$	0	0
$507$	−10.1638	−0.451391
$508$	−21.6118	−0.958869
$509$	33.1496	1.46933	0.734666	−	0.678429i	$-0.237339\pi$
$509$	33.1496	1.46933	0.734666	+	0.678429i	$0.237339\pi$
$510$	−0.623165	−0.0275942
$511$	25.7370	1.13854
$512$	1.00000	0.0441942
$513$	0.859449	0.0379456
$514$	−15.8488	−0.699060
$515$	−3.76796	−0.166036
$516$	−5.14282	−0.226400
$517$	46.7111	2.05435
$518$	13.4490	0.590913
$519$	−6.14165	−0.269589
$520$	0.934959	0.0410006
$521$	28.9660	1.26902	0.634511	−	0.772913i	$-0.281201\pi$
$521$	28.9660	1.26902	0.634511	+	0.772913i	$0.281201\pi$
$522$	5.41741	0.237114
$523$	−33.6692	−1.47225	−0.736126	−	0.676845i	$-0.763347\pi$
$523$	−33.6692	−1.47225	−0.736126	+	0.676845i	$0.763347\pi$
$524$	−14.9571	−0.653404
$525$	−9.68559	−0.422714
$526$	−0.130608	−0.00569477
$527$	−3.25182	−0.141652
$528$	6.30195	0.274257
$529$	0	0
$530$	−0.390071	−0.0169436
$531$	−8.60221	−0.373304
$532$	1.67751	0.0727295
$533$	−4.67817	−0.202634
$534$	−9.55158	−0.413337
$535$	−0.597538	−0.0258338
$536$	−7.09327	−0.306382
$537$	−6.47091	−0.279240
$538$	−23.9688	−1.03337
$539$	20.1050	0.865984
$540$	−0.194262	−0.00835970
$541$	−40.1990	−1.72829	−0.864144	−	0.503245i	$-0.832139\pi$
$541$	−40.1990	−1.72829	−0.864144	+	0.503245i	$0.832139\pi$
$542$	3.22188	0.138391
$543$	3.26146	0.139963
$544$	3.20786	0.137536
$545$	−0.378673	−0.0162206
$546$	9.39402	0.402027
$547$	22.7001	0.970588	0.485294	−	0.874351i	$-0.338713\pi$
$547$	22.7001	0.970588	0.485294	+	0.874351i	$0.338713\pi$
$548$	−18.1570	−0.775628
$549$	−12.1201	−0.517275
$550$	31.2719	1.33344
$551$	−4.65598	−0.198352
$552$	0	0
$553$	2.20519	0.0937741
$554$	−13.0026	−0.552427
$555$	1.33853	0.0568176
$556$	−7.36718	−0.312438
$557$	−3.95623	−0.167631	−0.0838154	−	0.996481i	$-0.526711\pi$
$557$	−3.95623	−0.167631	−0.0838154	+	0.996481i	$0.526711\pi$
$558$	−1.01371	−0.0429136
$559$	24.7518	1.04689
$560$	−0.379170	−0.0160228
$561$	20.2158	0.853511
$562$	−9.71850	−0.409950
$563$	27.2143	1.14695	0.573473	−	0.819224i	$-0.305596\pi$
$563$	27.2143	1.14695	0.573473	+	0.819224i	$0.305596\pi$
$564$	7.41216	0.312108
$565$	3.33144	0.140155
$566$	−19.9847	−0.840022
$567$	−1.95185	−0.0819700
$568$	1.10938	0.0465484
$569$	20.6417	0.865344	0.432672	−	0.901551i	$-0.357571\pi$
$569$	20.6417	0.865344	0.432672	+	0.901551i	$0.357571\pi$
$570$	0.166958	0.00699310
$571$	−30.3575	−1.27042	−0.635212	−	0.772338i	$-0.719087\pi$
$571$	−30.3575	−1.27042	−0.635212	+	0.772338i	$0.719087\pi$
$572$	−30.3305	−1.26818
$573$	−22.8536	−0.954723
$574$	1.89722	0.0791884
$575$	0	0
$576$	1.00000	0.0416667
$577$	−14.1163	−0.587667	−0.293834	−	0.955857i	$-0.594931\pi$
$577$	−14.1163	−0.587667	−0.293834	+	0.955857i	$0.594931\pi$
$578$	−6.70963	−0.279084
$579$	16.9414	0.704060
$580$	1.05240	0.0436983
$581$	7.82134	0.324484
$582$	−1.12094	−0.0464646
$583$	12.6541	0.524079
$584$	−13.1859	−0.545638
$585$	0.934959	0.0386558
$586$	17.8821	0.738702
$587$	36.5538	1.50874	0.754369	−	0.656451i	$-0.227943\pi$
$587$	36.5538	1.50874	0.754369	+	0.656451i	$0.227943\pi$
$588$	3.19028	0.131565
$589$	0.871227	0.0358983
$590$	−1.67108	−0.0687973
$591$	−1.25480	−0.0516157
$592$	−6.89037	−0.283192
$593$	6.64351	0.272816	0.136408	−	0.990653i	$-0.456444\pi$
$593$	6.64351	0.272816	0.136408	+	0.990653i	$0.456444\pi$
$594$	6.30195	0.258572
$595$	−1.21632	−0.0498644
$596$	−15.6333	−0.640365
$597$	24.8140	1.01557
$598$	0	0
$599$	28.0099	1.14445	0.572226	−	0.820096i	$-0.306080\pi$
$599$	28.0099	1.14445	0.572226	+	0.820096i	$0.306080\pi$
$600$	4.96226	0.202584
$601$	17.5864	0.717363	0.358682	−	0.933460i	$-0.383226\pi$
$601$	17.5864	0.717363	0.358682	+	0.933460i	$0.383226\pi$
$602$	−10.0380	−0.409119
$603$	−7.09327	−0.288860
$604$	20.7042	0.842440
$605$	5.57814	0.226784
$606$	−12.5714	−0.510679
$607$	−23.5948	−0.957684	−0.478842	−	0.877901i	$-0.658943\pi$
$607$	−23.5948	−0.957684	−0.478842	+	0.877901i	$0.658943\pi$
$608$	−0.859449	−0.0348552
$609$	10.5740	0.428479
$610$	−2.35448	−0.0953301
$611$	−35.6738	−1.44321
$612$	3.20786	0.129670
$613$	−32.9938	−1.33261	−0.666303	−	0.745681i	$-0.732124\pi$
$613$	−32.9938	−1.33261	−0.666303	+	0.745681i	$0.732124\pi$
$614$	−12.5139	−0.505019
$615$	0.188825	0.00761414
$616$	12.3005	0.495599
$617$	38.0582	1.53216	0.766082	−	0.642743i	$-0.222204\pi$
$617$	38.0582	1.53216	0.766082	+	0.642743i	$0.222204\pi$
$618$	19.3963	0.780234
$619$	8.49110	0.341286	0.170643	−	0.985333i	$-0.445416\pi$
$619$	8.49110	0.341286	0.170643	+	0.985333i	$0.445416\pi$
$620$	−0.196924	−0.00790866
$621$	0	0
$622$	5.45773	0.218835
$623$	−18.6432	−0.746926
$624$	−4.81288	−0.192669
$625$	24.4354	0.977414
$626$	23.9234	0.956170
$627$	−5.41620	−0.216302
$628$	3.97631	0.158672
$629$	−22.1033	−0.881318
$630$	−0.379170	−0.0151065
$631$	−11.1468	−0.443747	−0.221874	−	0.975075i	$-0.571217\pi$
$631$	−11.1468	−0.443747	−0.221874	+	0.975075i	$0.571217\pi$
$632$	−1.12979	−0.0449408
$633$	−7.25827	−0.288490
$634$	−16.1225	−0.640308
$635$	−4.19835	−0.166606
$636$	2.00797	0.0796210
$637$	−15.3545	−0.608366
$638$	−34.1402	−1.35163
$639$	1.10938	0.0438863
$640$	0.194262	0.00767887
$641$	37.8358	1.49442	0.747212	−	0.664586i	$-0.231392\pi$
$641$	37.8358	1.49442	0.747212	+	0.664586i	$0.231392\pi$
$642$	3.07594	0.121398
$643$	22.3733	0.882317	0.441158	−	0.897429i	$-0.354568\pi$
$643$	22.3733	0.882317	0.441158	+	0.897429i	$0.354568\pi$
$644$	0	0
$645$	−0.999053	−0.0393377
$646$	−2.75699	−0.108472
$647$	−10.9467	−0.430359	−0.215180	−	0.976575i	$-0.569034\pi$
$647$	−10.9467	−0.430359	−0.215180	+	0.976575i	$0.569034\pi$
$648$	1.00000	0.0392837
$649$	54.2107	2.12796
$650$	−23.8828	−0.936759
$651$	−1.97860	−0.0775474
$652$	24.5129	0.959997
$653$	5.78807	0.226505	0.113252	−	0.993566i	$-0.463873\pi$
$653$	5.78807	0.226505	0.113252	+	0.993566i	$0.463873\pi$
$654$	1.94929	0.0762234
$655$	−2.90559	−0.113531
$656$	−0.972011	−0.0379507
$657$	−13.1859	−0.514432
$658$	14.4674	0.563999
$659$	8.31443	0.323884	0.161942	−	0.986800i	$-0.448224\pi$
$659$	8.31443	0.323884	0.161942	+	0.986800i	$0.448224\pi$
$660$	1.22423	0.0476530
$661$	12.1685	0.473301	0.236650	−	0.971595i	$-0.423950\pi$
$661$	12.1685	0.473301	0.236650	+	0.971595i	$0.423950\pi$
$662$	−0.517893	−0.0201285
$663$	−15.4390	−0.599603
$664$	−4.00714	−0.155507
$665$	0.325877	0.0126370
$666$	−6.89037	−0.266996
$667$	0	0
$668$	−1.95444	−0.0756194
$669$	−20.7342	−0.801629
$670$	−1.37795	−0.0532349
$671$	76.3805	2.94864
$672$	1.95185	0.0752942
$673$	4.87132	0.187775	0.0938877	−	0.995583i	$-0.470071\pi$
$673$	4.87132	0.187775	0.0938877	+	0.995583i	$0.470071\pi$
$674$	0.530119	0.0204194
$675$	4.96226	0.190998
$676$	10.1638	0.390916
$677$	20.0060	0.768892	0.384446	−	0.923147i	$-0.374392\pi$
$677$	20.0060	0.768892	0.384446	+	0.923147i	$0.374392\pi$
$678$	−17.1492	−0.658612
$679$	−2.18791	−0.0839643
$680$	0.623165	0.0238973
$681$	−21.0504	−0.806652
$682$	6.38832	0.244621
$683$	−23.9883	−0.917888	−0.458944	−	0.888465i	$-0.651772\pi$
$683$	−23.9883	−0.917888	−0.458944	+	0.888465i	$0.651772\pi$
$684$	−0.859449	−0.0328618
$685$	−3.52721	−0.134768
$686$	19.8899	0.759400
$687$	−1.91595	−0.0730980
$688$	5.14282	0.196068
$689$	−9.66410	−0.368173
$690$	0	0
$691$	16.5438	0.629356	0.314678	−	0.949199i	$-0.398104\pi$
$691$	16.5438	0.629356	0.314678	+	0.949199i	$0.398104\pi$
$692$	6.14165	0.233471
$693$	12.3005	0.467256
$694$	26.8126	1.01779
$695$	−1.43116	−0.0542870
$696$	−5.41741	−0.205346
$697$	−3.11808	−0.118106
$698$	1.45728	0.0551590
$699$	14.4306	0.545814
$700$	9.68559	0.366081
$701$	15.9822	0.603640	0.301820	−	0.953365i	$-0.402406\pi$
$701$	15.9822	0.603640	0.301820	+	0.953365i	$0.402406\pi$
$702$	−4.81288	−0.181650
$703$	5.92192	0.223349
$704$	−6.30195	−0.237514
$705$	1.43990	0.0542298
$706$	22.4537	0.845056
$707$	−24.5375	−0.922828
$708$	8.60221	0.323291
$709$	−6.40478	−0.240536	−0.120268	−	0.992741i	$-0.538375\pi$
$709$	−6.40478	−0.240536	−0.120268	+	0.992741i	$0.538375\pi$
$710$	0.215510	0.00808793
$711$	−1.12979	−0.0423706
$712$	9.55158	0.357960
$713$	0	0
$714$	6.26126	0.234322
$715$	−5.89206	−0.220351
$716$	6.47091	0.241829
$717$	9.81701	0.366623
$718$	−0.168999	−0.00630697
$719$	−41.6971	−1.55504	−0.777519	−	0.628859i	$-0.783522\pi$
$719$	−41.6971	−1.55504	−0.777519	+	0.628859i	$0.783522\pi$
$720$	0.194262	0.00723971
$721$	37.8587	1.40993
$722$	−18.2613	−0.679617
$723$	−14.9039	−0.554281
$724$	−3.26146	−0.121211
$725$	−26.8826	−0.998395
$726$	−28.7146	−1.06570
$727$	10.0060	0.371101	0.185551	−	0.982635i	$-0.440593\pi$
$727$	10.0060	0.371101	0.185551	+	0.982635i	$0.440593\pi$
$728$	−9.39402	−0.348165
$729$	1.00000	0.0370370
$730$	−2.56152	−0.0948062
$731$	16.4974	0.610180
$732$	12.1201	0.447973
$733$	23.3610	0.862858	0.431429	−	0.902147i	$-0.358009\pi$
$733$	23.3610	0.862858	0.431429	+	0.902147i	$0.358009\pi$
$734$	−17.8312	−0.658163
$735$	0.619750	0.0228598
$736$	0	0
$737$	44.7014	1.64660
$738$	−0.972011	−0.0357802
$739$	26.7250	0.983094	0.491547	−	0.870851i	$-0.336432\pi$
$739$	26.7250	0.983094	0.491547	+	0.870851i	$0.336432\pi$
$740$	−1.33853	−0.0492055
$741$	4.13642	0.151955
$742$	3.91925	0.143880
$743$	15.1711	0.556575	0.278288	−	0.960498i	$-0.410233\pi$
$743$	15.1711	0.556575	0.278288	+	0.960498i	$0.410233\pi$
$744$	1.01371	0.0371642
$745$	−3.03695	−0.111265
$746$	27.3884	1.00276
$747$	−4.00714	−0.146614
$748$	−20.2158	−0.739162
$749$	6.00378	0.219373
$750$	1.93529	0.0706667
$751$	−21.6684	−0.790691	−0.395346	−	0.918532i	$-0.629375\pi$
$751$	−21.6684	−0.790691	−0.395346	+	0.918532i	$0.629375\pi$
$752$	−7.41216	−0.270294
$753$	−2.14471	−0.0781575
$754$	26.0733	0.949535
$755$	4.02203	0.146377
$756$	1.95185	0.0709881
$757$	4.05195	0.147271	0.0736354	−	0.997285i	$-0.476540\pi$
$757$	4.05195	0.147271	0.0736354	+	0.997285i	$0.476540\pi$
$758$	2.73604	0.0993774
$759$	0	0
$760$	−0.166958	−0.00605620
$761$	−44.2112	−1.60266	−0.801328	−	0.598225i	$-0.795873\pi$
$761$	−44.2112	−1.60266	−0.801328	+	0.598225i	$0.795873\pi$
$762$	21.6118	0.782913
$763$	3.80473	0.137740
$764$	22.8536	0.826815
$765$	0.623165	0.0225306
$766$	14.4109	0.520687
$767$	−41.4014	−1.49492
$768$	−1.00000	−0.0360844
$769$	−8.81046	−0.317713	−0.158857	−	0.987302i	$-0.550781\pi$
$769$	−8.81046	−0.317713	−0.158857	+	0.987302i	$0.550781\pi$
$770$	2.38951	0.0861119
$771$	15.8488	0.570780
$772$	−16.9414	−0.609734
$773$	0.634119	0.0228077	0.0114038	−	0.999935i	$-0.496370\pi$
$773$	0.634119	0.0228077	0.0114038	+	0.999935i	$0.496370\pi$
$774$	5.14282	0.184855
$775$	5.03027	0.180693
$776$	1.12094	0.0402395
$777$	−13.4490	−0.482479
$778$	−1.08404	−0.0388647
$779$	0.835394	0.0299311
$780$	−0.934959	−0.0334769
$781$	−6.99124	−0.250166
$782$	0	0
$783$	−5.41741	−0.193602
$784$	−3.19028	−0.113939
$785$	0.772445	0.0275698
$786$	14.9571	0.533502
$787$	−15.9809	−0.569659	−0.284829	−	0.958578i	$-0.591937\pi$
$787$	−15.9809	−0.569659	−0.284829	+	0.958578i	$0.591937\pi$
$788$	1.25480	0.0447005
$789$	0.130608	0.00464976
$790$	−0.219476	−0.00780860
$791$	−33.4727	−1.19015
$792$	−6.30195	−0.223930
$793$	−58.3328	−2.07146
$794$	−27.0241	−0.959048
$795$	0.390071	0.0138344
$796$	−24.8140	−0.879509
$797$	40.9716	1.45129	0.725644	−	0.688070i	$-0.241542\pi$
$797$	40.9716	1.45129	0.725644	+	0.688070i	$0.241542\pi$
$798$	−1.67751	−0.0593833
$799$	−23.7772	−0.841176
$800$	−4.96226	−0.175442
$801$	9.55158	0.337488
$802$	−9.27409	−0.327479
$803$	83.0971	2.93243
$804$	7.09327	0.250160
$805$	0	0
$806$	−4.87884	−0.171850
$807$	23.9688	0.843742
$808$	12.5714	0.442261
$809$	−28.2257	−0.992363	−0.496181	−	0.868219i	$-0.665265\pi$
$809$	−28.2257	−0.992363	−0.496181	+	0.868219i	$0.665265\pi$
$810$	0.194262	0.00682566
$811$	−3.61726	−0.127019	−0.0635096	−	0.997981i	$-0.520229\pi$
$811$	−3.61726	−0.127019	−0.0635096	+	0.997981i	$0.520229\pi$
$812$	−10.5740	−0.371073
$813$	−3.22188	−0.112996
$814$	43.4228	1.52197
$815$	4.76191	0.166802
$816$	−3.20786	−0.112298
$817$	−4.41999	−0.154636
$818$	36.7657	1.28548
$819$	−9.39402	−0.328253
$820$	−0.188825	−0.00659404
$821$	30.8947	1.07823	0.539116	−	0.842231i	$-0.318758\pi$
$821$	30.8947	1.07823	0.539116	+	0.842231i	$0.318758\pi$
$822$	18.1570	0.633298
$823$	4.00604	0.139642	0.0698209	−	0.997560i	$-0.477757\pi$
$823$	4.00604	0.139642	0.0698209	+	0.997560i	$0.477757\pi$
$824$	−19.3963	−0.675702
$825$	−31.2719	−1.08875
$826$	16.7902	0.584206
$827$	26.0104	0.904469	0.452234	−	0.891899i	$-0.350627\pi$
$827$	26.0104	0.904469	0.452234	+	0.891899i	$0.350627\pi$
$828$	0	0
$829$	39.4460	1.37002	0.685008	−	0.728535i	$-0.259798\pi$
$829$	39.4460	1.37002	0.685008	+	0.728535i	$0.259798\pi$
$830$	−0.778434	−0.0270199
$831$	13.0026	0.451055
$832$	4.81288	0.166857
$833$	−10.2340	−0.354587
$834$	7.36718	0.255104
$835$	−0.379672	−0.0131391
$836$	5.41620	0.187323
$837$	1.01371	0.0350388
$838$	26.4958	0.915283
$839$	−3.26103	−0.112583	−0.0562916	−	0.998414i	$-0.517928\pi$
$839$	−3.26103	−0.112583	−0.0562916	+	0.998414i	$0.517928\pi$
$840$	0.379170	0.0130826
$841$	0.348328	0.0120113
$842$	−9.95095	−0.342932
$843$	9.71850	0.334723
$844$	7.25827	0.249840
$845$	1.97444	0.0679228
$846$	−7.41216	−0.254835
$847$	−56.0465	−1.92578
$848$	−2.00797	−0.0689539
$849$	19.9847	0.685875
$850$	−15.9182	−0.545991
$851$	0	0
$852$	−1.10938	−0.0380066
$853$	−7.71650	−0.264208	−0.132104	−	0.991236i	$-0.542173\pi$
$853$	−7.71650	−0.264208	−0.132104	+	0.991236i	$0.542173\pi$
$854$	23.6567	0.809515
$855$	−0.166958	−0.00570984
$856$	−3.07594	−0.105134
$857$	4.63538	0.158342	0.0791708	−	0.996861i	$-0.474773\pi$
$857$	4.63538	0.158342	0.0791708	+	0.996861i	$0.474773\pi$
$858$	30.3305	1.03547
$859$	−49.1319	−1.67636	−0.838179	−	0.545396i	$-0.816379\pi$
$859$	−49.1319	−1.67636	−0.838179	+	0.545396i	$0.816379\pi$
$860$	0.999053	0.0340674
$861$	−1.89722	−0.0646571
$862$	−8.77287	−0.298805
$863$	−40.8058	−1.38905	−0.694523	−	0.719470i	$-0.744385\pi$
$863$	−40.8058	−1.38905	−0.694523	+	0.719470i	$0.744385\pi$
$864$	−1.00000	−0.0340207
$865$	1.19309	0.0405662
$866$	7.99061	0.271532
$867$	6.70963	0.227871
$868$	1.97860	0.0671580
$869$	7.11991	0.241526
$870$	−1.05240	−0.0356796
$871$	−34.1390	−1.15676
$872$	−1.94929	−0.0660114
$873$	1.12094	0.0379382
$874$	0	0
$875$	3.77739	0.127699
$876$	13.1859	0.445511
$877$	25.6472	0.866043	0.433021	−	0.901384i	$-0.357447\pi$
$877$	25.6472	0.866043	0.433021	+	0.901384i	$0.357447\pi$
$878$	−1.41063	−0.0476064
$879$	−17.8821	−0.603147
$880$	−1.22423	−0.0412687
$881$	−43.0288	−1.44968	−0.724838	−	0.688919i	$-0.758085\pi$
$881$	−43.0288	−1.44968	−0.724838	+	0.688919i	$0.758085\pi$
$882$	−3.19028	−0.107422
$883$	−10.0370	−0.337771	−0.168885	−	0.985636i	$-0.554017\pi$
$883$	−10.0370	−0.337771	−0.168885	+	0.985636i	$0.554017\pi$
$884$	15.4390	0.519271
$885$	1.67108	0.0561728
$886$	12.5935	0.423087
$887$	−10.5222	−0.353300	−0.176650	−	0.984274i	$-0.556526\pi$
$887$	−10.5222	−0.353300	−0.176650	+	0.984274i	$0.556526\pi$
$888$	6.89037	0.231226
$889$	42.1830	1.41477
$890$	1.85551	0.0621967
$891$	−6.30195	−0.211123
$892$	20.7342	0.694231
$893$	6.37037	0.213176
$894$	15.6333	0.522856
$895$	1.25705	0.0420185
$896$	−1.95185	−0.0652067
$897$	0	0
$898$	−38.3533	−1.27987
$899$	−5.49166	−0.183157
$900$	−4.96226	−0.165409
$901$	−6.44128	−0.214590
$902$	6.12557	0.203959
$903$	10.0380	0.334044
$904$	17.1492	0.570375
$905$	−0.633578	−0.0210608
$906$	−20.7042	−0.687850
$907$	−39.0117	−1.29536	−0.647680	−	0.761912i	$-0.724261\pi$
$907$	−39.0117	−1.29536	−0.647680	+	0.761912i	$0.724261\pi$
$908$	21.0504	0.698581
$909$	12.5714	0.416967
$910$	−1.82490	−0.0604948
$911$	22.7667	0.754294	0.377147	−	0.926153i	$-0.376905\pi$
$911$	22.7667	0.754294	0.377147	+	0.926153i	$0.376905\pi$
$912$	0.859449	0.0284592
$913$	25.2528	0.835746
$914$	−26.6357	−0.881031
$915$	2.35448	0.0778367
$916$	1.91595	0.0633047
$917$	29.1940	0.964071
$918$	−3.20786	−0.105875
$919$	21.7361	0.717007	0.358504	−	0.933528i	$-0.383287\pi$
$919$	21.7361	0.717007	0.358504	+	0.933528i	$0.383287\pi$
$920$	0	0
$921$	12.5139	0.412346
$922$	7.65301	0.252039
$923$	5.33930	0.175745
$924$	−12.3005	−0.404655
$925$	34.1918	1.12422
$926$	−4.15149	−0.136426
$927$	−19.3963	−0.637058
$928$	5.41741	0.177835
$929$	−40.7826	−1.33803	−0.669016	−	0.743248i	$-0.733284\pi$
$929$	−40.7826	−1.33803	−0.669016	+	0.743248i	$0.733284\pi$
$930$	0.196924	0.00645740
$931$	2.74189	0.0898617
$932$	−14.4306	−0.472689
$933$	−5.45773	−0.178678
$934$	32.1155	1.05085
$935$	−3.92715	−0.128432
$936$	4.81288	0.157314
$937$	7.22235	0.235944	0.117972	−	0.993017i	$-0.462361\pi$
$937$	7.22235	0.235944	0.117972	+	0.993017i	$0.462361\pi$
$938$	13.8450	0.452055
$939$	−23.9234	−0.780710
$940$	−1.43990	−0.0469643
$941$	−13.2043	−0.430449	−0.215225	−	0.976565i	$-0.569048\pi$
$941$	−13.2043	−0.430449	−0.215225	+	0.976565i	$0.569048\pi$
$942$	−3.97631	−0.129555
$943$	0	0
$944$	−8.60221	−0.279978
$945$	0.379170	0.0123344
$946$	−32.4098	−1.05373
$947$	33.7912	1.09807	0.549034	−	0.835800i	$-0.314996\pi$
$947$	33.7912	1.09807	0.549034	+	0.835800i	$0.314996\pi$
$948$	1.12979	0.0366940
$949$	−63.4623	−2.06007
$950$	4.26481	0.138369
$951$	16.1225	0.522809
$952$	−6.26126	−0.202929
$953$	22.5608	0.730815	0.365407	−	0.930848i	$-0.380930\pi$
$953$	22.5608	0.730815	0.365407	+	0.930848i	$0.380930\pi$
$954$	−2.00797	−0.0650103
$955$	4.43958	0.143662
$956$	−9.81701	−0.317505
$957$	34.1402	1.10360
$958$	−1.81509	−0.0586430
$959$	35.4397	1.14441
$960$	−0.194262	−0.00626977
$961$	−29.9724	−0.966852
$962$	−33.1625	−1.06920
$963$	−3.07594	−0.0991209
$964$	14.9039	0.480022
$965$	−3.29107	−0.105943
$966$	0	0
$967$	−15.9309	−0.512303	−0.256152	−	0.966637i	$-0.582455\pi$
$967$	−15.9309	−0.512303	−0.256152	+	0.966637i	$0.582455\pi$
$968$	28.7146	0.922921
$969$	2.75699	0.0885673
$970$	0.217756	0.00699174
$971$	−42.1496	−1.35264	−0.676322	−	0.736606i	$-0.736427\pi$
$971$	−42.1496	−1.35264	−0.676322	+	0.736606i	$0.736427\pi$
$972$	−1.00000	−0.0320750
$973$	14.3796	0.460989
$974$	−16.1873	−0.518674
$975$	23.8828	0.764861
$976$	−12.1201	−0.387956
$977$	31.8104	1.01770	0.508852	−	0.860854i	$-0.330070\pi$
$977$	31.8104	1.01770	0.508852	+	0.860854i	$0.330070\pi$
$978$	−24.5129	−0.783835
$979$	−60.1936	−1.92379
$980$	−0.619750	−0.0197972
$981$	−1.94929	−0.0622361
$982$	−1.42155	−0.0453634
$983$	−19.8293	−0.632457	−0.316229	−	0.948683i	$-0.602417\pi$
$983$	−19.8293	−0.632457	−0.316229	+	0.948683i	$0.602417\pi$
$984$	0.972011	0.0309866
$985$	0.243760	0.00776685
$986$	17.3783	0.553438
$987$	−14.4674	−0.460503
$988$	−4.13642	−0.131597
$989$	0	0
$990$	−1.22423	−0.0389085
$991$	6.30934	0.200423	0.100211	−	0.994966i	$-0.468048\pi$
$991$	6.30934	0.200423	0.100211	+	0.994966i	$0.468048\pi$
$992$	−1.01371	−0.0321852
$993$	0.517893	0.0164348
$994$	−2.16534	−0.0686803
$995$	−4.82041	−0.152817
$996$	4.00714	0.126971
$997$	−44.5390	−1.41056	−0.705282	−	0.708927i	$-0.749180\pi$
$997$	−44.5390	−1.41056	−0.705282	+	0.708927i	$0.749180\pi$
$998$	20.5750	0.651289
$999$	6.89037	0.218002

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3174.2.a.bb.1.3		5
3.2	odd	2		9522.2.a.br.1.3		5
23.5	odd	22		138.2.e.b.25.1	✓	10
23.14	odd	22		138.2.e.b.127.1	yes	10
23.22	odd	2		3174.2.a.ba.1.3		5
69.5	even	22		414.2.i.e.163.1		10
69.14	even	22		414.2.i.e.127.1		10
69.68	even	2		9522.2.a.bs.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.b.25.1	✓	10	23.5	odd	22
138.2.e.b.127.1	yes	10	23.14	odd	22
414.2.i.e.127.1		10	69.14	even	22
414.2.i.e.163.1		10	69.5	even	22
3174.2.a.ba.1.3		5	23.22	odd	2
3174.2.a.bb.1.3		5	1.1	even	1	trivial
9522.2.a.br.1.3		5	3.2	odd	2
9522.2.a.bs.1.3		5	69.68	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3174 = 2 \cdot 3 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3174.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.194262 q^{5} -1.00000 q^{6} -1.95185 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.194262 q^{5} -1.00000 q^{6} -1.95185 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.194262 q^{10} -6.30195 q^{11} -1.00000 q^{12} +4.81288 q^{13} -1.95185 q^{14} -0.194262 q^{15} +1.00000 q^{16} +3.20786 q^{17} +1.00000 q^{18} -0.859449 q^{19} +0.194262 q^{20} +1.95185 q^{21} -6.30195 q^{22} -1.00000 q^{24} -4.96226 q^{25} +4.81288 q^{26} -1.00000 q^{27} -1.95185 q^{28} +5.41741 q^{29} -0.194262 q^{30} -1.01371 q^{31} +1.00000 q^{32} +6.30195 q^{33} +3.20786 q^{34} -0.379170 q^{35} +1.00000 q^{36} -6.89037 q^{37} -0.859449 q^{38} -4.81288 q^{39} +0.194262 q^{40} -0.972011 q^{41} +1.95185 q^{42} +5.14282 q^{43} -6.30195 q^{44} +0.194262 q^{45} -7.41216 q^{47} -1.00000 q^{48} -3.19028 q^{49} -4.96226 q^{50} -3.20786 q^{51} +4.81288 q^{52} -2.00797 q^{53} -1.00000 q^{54} -1.22423 q^{55} -1.95185 q^{56} +0.859449 q^{57} +5.41741 q^{58} -8.60221 q^{59} -0.194262 q^{60} -12.1201 q^{61} -1.01371 q^{62} -1.95185 q^{63} +1.00000 q^{64} +0.934959 q^{65} +6.30195 q^{66} -7.09327 q^{67} +3.20786 q^{68} -0.379170 q^{70} +1.10938 q^{71} +1.00000 q^{72} -13.1859 q^{73} -6.89037 q^{74} +4.96226 q^{75} -0.859449 q^{76} +12.3005 q^{77} -4.81288 q^{78} -1.12979 q^{79} +0.194262 q^{80} +1.00000 q^{81} -0.972011 q^{82} -4.00714 q^{83} +1.95185 q^{84} +0.623165 q^{85} +5.14282 q^{86} -5.41741 q^{87} -6.30195 q^{88} +9.55158 q^{89} +0.194262 q^{90} -9.39402 q^{91} +1.01371 q^{93} -7.41216 q^{94} -0.166958 q^{95} -1.00000 q^{96} +1.12094 q^{97} -3.19028 q^{98} -6.30195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9} + q^{10} - 11 q^{11} - 5 q^{12} + 12 q^{13} - 11 q^{14} - q^{15} + 5 q^{16} + q^{17} + 5 q^{18} - 15 q^{19} + q^{20} + 11 q^{21} - 11 q^{22} - 5 q^{24} + 6 q^{25} + 12 q^{26} - 5 q^{27} - 11 q^{28} + q^{29} - q^{30} - 18 q^{31} + 5 q^{32} + 11 q^{33} + q^{34} - 11 q^{35} + 5 q^{36} - 10 q^{37} - 15 q^{38} - 12 q^{39} + q^{40} - 16 q^{41} + 11 q^{42} - 18 q^{43} - 11 q^{44} + q^{45} - 4 q^{47} - 5 q^{48} + 20 q^{49} + 6 q^{50} - q^{51} + 12 q^{52} + q^{53} - 5 q^{54} - 22 q^{55} - 11 q^{56} + 15 q^{57} + q^{58} + 2 q^{59} - q^{60} + q^{61} - 18 q^{62} - 11 q^{63} + 5 q^{64} - 24 q^{65} + 11 q^{66} - 29 q^{67} + q^{68} - 11 q^{70} - 11 q^{71} + 5 q^{72} - 8 q^{73} - 10 q^{74} - 6 q^{75} - 15 q^{76} + 11 q^{77} - 12 q^{78} - 40 q^{79} + q^{80} + 5 q^{81} - 16 q^{82} - 8 q^{83} + 11 q^{84} - 13 q^{85} - 18 q^{86} - q^{87} - 11 q^{88} - 2 q^{89} + q^{90} - 33 q^{91} + 18 q^{93} - 4 q^{94} - 3 q^{95} - 5 q^{96} - 17 q^{97} + 20 q^{98} - 11 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9 + q^10 - 11 * q^11 - 5 * q^12 + 12 * q^13 - 11 * q^14 - q^15 + 5 * q^16 + q^17 + 5 * q^18 - 15 * q^19 + q^20 + 11 * q^21 - 11 * q^22 - 5 * q^24 + 6 * q^25 + 12 * q^26 - 5 * q^27 - 11 * q^28 + q^29 - q^30 - 18 * q^31 + 5 * q^32 + 11 * q^33 + q^34 - 11 * q^35 + 5 * q^36 - 10 * q^37 - 15 * q^38 - 12 * q^39 + q^40 - 16 * q^41 + 11 * q^42 - 18 * q^43 - 11 * q^44 + q^45 - 4 * q^47 - 5 * q^48 + 20 * q^49 + 6 * q^50 - q^51 + 12 * q^52 + q^53 - 5 * q^54 - 22 * q^55 - 11 * q^56 + 15 * q^57 + q^58 + 2 * q^59 - q^60 + q^61 - 18 * q^62 - 11 * q^63 + 5 * q^64 - 24 * q^65 + 11 * q^66 - 29 * q^67 + q^68 - 11 * q^70 - 11 * q^71 + 5 * q^72 - 8 * q^73 - 10 * q^74 - 6 * q^75 - 15 * q^76 + 11 * q^77 - 12 * q^78 - 40 * q^79 + q^80 + 5 * q^81 - 16 * q^82 - 8 * q^83 + 11 * q^84 - 13 * q^85 - 18 * q^86 - q^87 - 11 * q^88 - 2 * q^89 + q^90 - 33 * q^91 + 18 * q^93 - 4 * q^94 - 3 * q^95 - 5 * q^96 - 17 * q^97 + 20 * q^98 - 11 * q^99

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