LMFDB - Embedded newform 7935.2.a.bq.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 21x^{13} + 172x^{11} - 696x^{9} + 1466x^{7} - 1583x^{5} + 803x^{3} - 11x^{2} - 143x + 11 $ x^15 - 21x^13 + 172x^11 - 696x^9 + 1466x^7 - 1583x^5 + 803x^3 - 11x^2 - 143x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.910856$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.910856 q^{2} -1.00000 q^{3} -1.17034 q^{4} +1.00000 q^{5} +0.910856 q^{6} -2.43067 q^{7} +2.88772 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.910856 q^{2} -1.00000 q^{3} -1.17034 q^{4} +1.00000 q^{5} +0.910856 q^{6} -2.43067 q^{7} +2.88772 q^{8} +1.00000 q^{9} -0.910856 q^{10} -3.76274 q^{11} +1.17034 q^{12} -4.94931 q^{13} +2.21399 q^{14} -1.00000 q^{15} -0.289619 q^{16} +2.79498 q^{17} -0.910856 q^{18} -3.08967 q^{19} -1.17034 q^{20} +2.43067 q^{21} +3.42732 q^{22} -2.88772 q^{24} +1.00000 q^{25} +4.50811 q^{26} -1.00000 q^{27} +2.84472 q^{28} +3.02833 q^{29} +0.910856 q^{30} +7.55866 q^{31} -5.51165 q^{32} +3.76274 q^{33} -2.54582 q^{34} -2.43067 q^{35} -1.17034 q^{36} +0.0646330 q^{37} +2.81424 q^{38} +4.94931 q^{39} +2.88772 q^{40} -5.77566 q^{41} -2.21399 q^{42} +7.31352 q^{43} +4.40370 q^{44} +1.00000 q^{45} -2.31016 q^{47} +0.289619 q^{48} -1.09183 q^{49} -0.910856 q^{50} -2.79498 q^{51} +5.79239 q^{52} +3.16958 q^{53} +0.910856 q^{54} -3.76274 q^{55} -7.01911 q^{56} +3.08967 q^{57} -2.75837 q^{58} +11.6195 q^{59} +1.17034 q^{60} +6.33802 q^{61} -6.88486 q^{62} -2.43067 q^{63} +5.59956 q^{64} -4.94931 q^{65} -3.42732 q^{66} +12.6081 q^{67} -3.27108 q^{68} +2.21399 q^{70} -12.1241 q^{71} +2.88772 q^{72} -1.33182 q^{73} -0.0588714 q^{74} -1.00000 q^{75} +3.61596 q^{76} +9.14600 q^{77} -4.50811 q^{78} -7.35871 q^{79} -0.289619 q^{80} +1.00000 q^{81} +5.26079 q^{82} +2.04338 q^{83} -2.84472 q^{84} +2.79498 q^{85} -6.66156 q^{86} -3.02833 q^{87} -10.8658 q^{88} +7.99014 q^{89} -0.910856 q^{90} +12.0302 q^{91} -7.55866 q^{93} +2.10422 q^{94} -3.08967 q^{95} +5.51165 q^{96} -0.335046 q^{97} +0.994498 q^{98} -3.76274 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{3} + 12 q^{4} + 15 q^{5} + 5 q^{7} + 15 q^{9}+O(q^{10}) $ 15 * q - 15 * q^3 + 12 * q^4 + 15 * q^5 + 5 * q^7 + 15 * q^9	$ 15 q - 15 q^{3} + 12 q^{4} + 15 q^{5} + 5 q^{7} + 15 q^{9} - 13 q^{11} - 12 q^{12} - 24 q^{13} - 15 q^{14} - 15 q^{15} + 2 q^{16} - 2 q^{17} - 13 q^{19} + 12 q^{20} - 5 q^{21} + 9 q^{22} + 15 q^{25} - 9 q^{26} - 15 q^{27} - q^{28} - 3 q^{29} - 22 q^{31} + 13 q^{33} - q^{34} + 5 q^{35} + 12 q^{36} + 6 q^{37} + 17 q^{38} + 24 q^{39} - 20 q^{41} + 15 q^{42} + 4 q^{43} + 18 q^{44} + 15 q^{45} + 7 q^{47} - 2 q^{48} - 10 q^{49} + 2 q^{51} - 55 q^{52} - 4 q^{53} - 13 q^{55} - 25 q^{56} + 13 q^{57} + 2 q^{58} + 9 q^{59} - 12 q^{60} - 13 q^{61} - 7 q^{62} + 5 q^{63} - 26 q^{64} - 24 q^{65} - 9 q^{66} + 32 q^{67} - 27 q^{68} - 15 q^{70} + 14 q^{71} - 43 q^{73} + 11 q^{74} - 15 q^{75} - 88 q^{76} - 21 q^{77} + 9 q^{78} - 33 q^{79} + 2 q^{80} + 15 q^{81} - 35 q^{82} + 12 q^{83} + q^{84} - 2 q^{85} - 77 q^{86} + 3 q^{87} + 37 q^{88} - 29 q^{89} - 20 q^{91} + 22 q^{93} - 20 q^{94} - 13 q^{95} - 18 q^{97} - 19 q^{98} - 13 q^{99}+O(q^{100}) $ 15 * q - 15 * q^3 + 12 * q^4 + 15 * q^5 + 5 * q^7 + 15 * q^9 - 13 * q^11 - 12 * q^12 - 24 * q^13 - 15 * q^14 - 15 * q^15 + 2 * q^16 - 2 * q^17 - 13 * q^19 + 12 * q^20 - 5 * q^21 + 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 - q^28 - 3 * q^29 - 22 * q^31 + 13 * q^33 - q^34 + 5 * q^35 + 12 * q^36 + 6 * q^37 + 17 * q^38 + 24 * q^39 - 20 * q^41 + 15 * q^42 + 4 * q^43 + 18 * q^44 + 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 + 2 * q^51 - 55 * q^52 - 4 * q^53 - 13 * q^55 - 25 * q^56 + 13 * q^57 + 2 * q^58 + 9 * q^59 - 12 * q^60 - 13 * q^61 - 7 * q^62 + 5 * q^63 - 26 * q^64 - 24 * q^65 - 9 * q^66 + 32 * q^67 - 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 + 11 * q^74 - 15 * q^75 - 88 * q^76 - 21 * q^77 + 9 * q^78 - 33 * q^79 + 2 * q^80 + 15 * q^81 - 35 * q^82 + 12 * q^83 + q^84 - 2 * q^85 - 77 * q^86 + 3 * q^87 + 37 * q^88 - 29 * q^89 - 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 - 18 * q^97 - 19 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.910856	−0.644072	−0.322036	−	0.946727i	$-0.604367\pi$
$2$	−0.910856	−0.644072	−0.322036	+	0.946727i	$0.604367\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.17034	−0.585171
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.910856	0.371855
$7$	−2.43067	−0.918708	−0.459354	−	0.888253i	$-0.651919\pi$
$7$	−2.43067	−0.918708	−0.459354	+	0.888253i	$0.651919\pi$
$8$	2.88772	1.02096
$9$	1.00000	0.333333
$10$	−0.910856	−0.288038
$11$	−3.76274	−1.13451	−0.567255	−	0.823542i	$-0.691995\pi$
$11$	−3.76274	−1.13451	−0.567255	+	0.823542i	$0.691995\pi$
$12$	1.17034	0.337848
$13$	−4.94931	−1.37269	−0.686346	−	0.727275i	$-0.740787\pi$
$13$	−4.94931	−1.37269	−0.686346	+	0.727275i	$0.740787\pi$
$14$	2.21399	0.591715
$15$	−1.00000	−0.258199
$16$	−0.289619	−0.0724047
$17$	2.79498	0.677882	0.338941	−	0.940808i	$-0.389931\pi$
$17$	2.79498	0.677882	0.338941	+	0.940808i	$0.389931\pi$
$18$	−0.910856	−0.214691
$19$	−3.08967	−0.708818	−0.354409	−	0.935091i	$-0.615318\pi$
$19$	−3.08967	−0.708818	−0.354409	+	0.935091i	$0.615318\pi$
$20$	−1.17034	−0.261696
$21$	2.43067	0.530416
$22$	3.42732	0.730707
$23$	0	0
$23$	0	0
$24$	−2.88772	−0.589454
$25$	1.00000	0.200000
$26$	4.50811	0.884114
$27$	−1.00000	−0.192450
$28$	2.84472	0.537601
$29$	3.02833	0.562347	0.281173	−	0.959657i	$-0.409276\pi$
$29$	3.02833	0.562347	0.281173	+	0.959657i	$0.409276\pi$
$30$	0.910856	0.166299
$31$	7.55866	1.35758	0.678788	−	0.734334i	$-0.262505\pi$
$31$	7.55866	1.35758	0.678788	+	0.734334i	$0.262505\pi$
$32$	−5.51165	−0.974331
$33$	3.76274	0.655010
$34$	−2.54582	−0.436605
$35$	−2.43067	−0.410859
$36$	−1.17034	−0.195057
$37$	0.0646330	0.0106256	0.00531280	−	0.999986i	$-0.498309\pi$
$37$	0.0646330	0.0106256	0.00531280	+	0.999986i	$0.498309\pi$
$38$	2.81424	0.456530
$39$	4.94931	0.792525
$40$	2.88772	0.456589
$41$	−5.77566	−0.902006	−0.451003	−	0.892522i	$-0.648934\pi$
$41$	−5.77566	−0.902006	−0.451003	+	0.892522i	$0.648934\pi$
$42$	−2.21399	−0.341627
$43$	7.31352	1.11530	0.557651	−	0.830076i	$-0.311703\pi$
$43$	7.31352	1.11530	0.557651	+	0.830076i	$0.311703\pi$
$44$	4.40370	0.663882
$45$	1.00000	0.149071
$46$	0	0
$47$	−2.31016	−0.336972	−0.168486	−	0.985704i	$-0.553888\pi$
$47$	−2.31016	−0.336972	−0.168486	+	0.985704i	$0.553888\pi$
$48$	0.289619	0.0418029
$49$	−1.09183	−0.155975
$50$	−0.910856	−0.128814
$51$	−2.79498	−0.391375
$52$	5.79239	0.803260
$53$	3.16958	0.435375	0.217688	−	0.976018i	$-0.430149\pi$
$53$	3.16958	0.435375	0.217688	+	0.976018i	$0.430149\pi$
$54$	0.910856	0.123952
$55$	−3.76274	−0.507368
$56$	−7.01911	−0.937969
$57$	3.08967	0.409236
$58$	−2.75837	−0.362192
$59$	11.6195	1.51273	0.756367	−	0.654148i	$-0.226973\pi$
$59$	11.6195	1.51273	0.756367	+	0.654148i	$0.226973\pi$
$60$	1.17034	0.151090
$61$	6.33802	0.811500	0.405750	−	0.913984i	$-0.367010\pi$
$61$	6.33802	0.811500	0.405750	+	0.913984i	$0.367010\pi$
$62$	−6.88486	−0.874377
$63$	−2.43067	−0.306236
$64$	5.59956	0.699944
$65$	−4.94931	−0.613887
$66$	−3.42732	−0.421874
$67$	12.6081	1.54032	0.770162	−	0.637848i	$-0.220175\pi$
$67$	12.6081	1.54032	0.770162	+	0.637848i	$0.220175\pi$
$68$	−3.27108	−0.396677
$69$	0	0
$70$	2.21399	0.264623
$71$	−12.1241	−1.43886	−0.719432	−	0.694563i	$-0.755598\pi$
$71$	−12.1241	−1.43886	−0.719432	+	0.694563i	$0.755598\pi$
$72$	2.88772	0.340322
$73$	−1.33182	−0.155877	−0.0779386	−	0.996958i	$-0.524834\pi$
$73$	−1.33182	−0.155877	−0.0779386	+	0.996958i	$0.524834\pi$
$74$	−0.0588714	−0.00684366
$75$	−1.00000	−0.115470
$76$	3.61596	0.414779
$77$	9.14600	1.04228
$78$	−4.50811	−0.510443
$79$	−7.35871	−0.827920	−0.413960	−	0.910295i	$-0.635855\pi$
$79$	−7.35871	−0.827920	−0.413960	+	0.910295i	$0.635855\pi$
$80$	−0.289619	−0.0323804
$81$	1.00000	0.111111
$82$	5.26079	0.580958
$83$	2.04338	0.224290	0.112145	−	0.993692i	$-0.464228\pi$
$83$	2.04338	0.224290	0.112145	+	0.993692i	$0.464228\pi$
$84$	−2.84472	−0.310384
$85$	2.79498	0.303158
$86$	−6.66156	−0.718335
$87$	−3.02833	−0.324671
$88$	−10.8658	−1.15829
$89$	7.99014	0.846953	0.423477	−	0.905907i	$-0.360810\pi$
$89$	7.99014	0.846953	0.423477	+	0.905907i	$0.360810\pi$
$90$	−0.910856	−0.0960127
$91$	12.0302	1.26110
$92$	0	0
$93$	−7.55866	−0.783797
$94$	2.10422	0.217034
$95$	−3.08967	−0.316993
$96$	5.51165	0.562530
$97$	−0.335046	−0.0340188	−0.0170094	−	0.999855i	$-0.505415\pi$
$97$	−0.335046	−0.0340188	−0.0170094	+	0.999855i	$0.505415\pi$
$98$	0.994498	0.100460
$99$	−3.76274	−0.378170
$100$	−1.17034	−0.117034
$101$	1.60323	0.159527	0.0797637	−	0.996814i	$-0.474583\pi$
$101$	1.60323	0.159527	0.0797637	+	0.996814i	$0.474583\pi$
$102$	2.54582	0.252074
$103$	15.9684	1.57342	0.786709	−	0.617325i	$-0.211783\pi$
$103$	15.9684	1.57342	0.786709	+	0.617325i	$0.211783\pi$
$104$	−14.2923	−1.40147
$105$	2.43067	0.237209
$106$	−2.88703	−0.280413
$107$	6.45727	0.624248	0.312124	−	0.950041i	$-0.398960\pi$
$107$	6.45727	0.624248	0.312124	+	0.950041i	$0.398960\pi$
$108$	1.17034	0.112616
$109$	−18.9527	−1.81534	−0.907670	−	0.419685i	$-0.862141\pi$
$109$	−18.9527	−1.81534	−0.907670	+	0.419685i	$0.862141\pi$
$110$	3.42732	0.326782
$111$	−0.0646330	−0.00613470
$112$	0.703968	0.0665188
$113$	−12.8406	−1.20794	−0.603972	−	0.797006i	$-0.706416\pi$
$113$	−12.8406	−1.20794	−0.603972	+	0.797006i	$0.706416\pi$
$114$	−2.81424	−0.263578
$115$	0	0
$116$	−3.54418	−0.329069
$117$	−4.94931	−0.457564
$118$	−10.5837	−0.974310
$119$	−6.79368	−0.622776
$120$	−2.88772	−0.263612
$121$	3.15825	0.287113
$122$	−5.77302	−0.522665
$123$	5.77566	0.520774
$124$	−8.84622	−0.794414
$125$	1.00000	0.0894427
$126$	2.21399	0.197238
$127$	22.1233	1.96312	0.981561	−	0.191150i	$-0.0612216\pi$
$127$	22.1233	1.96312	0.981561	+	0.191150i	$0.0612216\pi$
$128$	5.92291	0.523516
$129$	−7.31352	−0.643920
$130$	4.50811	0.395388
$131$	5.90983	0.516344	0.258172	−	0.966099i	$-0.416880\pi$
$131$	5.90983	0.516344	0.258172	+	0.966099i	$0.416880\pi$
$132$	−4.40370	−0.383292
$133$	7.50997	0.651197
$134$	−11.4842	−0.992080
$135$	−1.00000	−0.0860663
$136$	8.07113	0.692094
$137$	−10.3638	−0.885443	−0.442722	−	0.896659i	$-0.645987\pi$
$137$	−10.3638	−0.885443	−0.442722	+	0.896659i	$0.645987\pi$
$138$	0	0
$139$	6.60670	0.560373	0.280186	−	0.959946i	$-0.409604\pi$
$139$	6.60670	0.560373	0.280186	+	0.959946i	$0.409604\pi$
$140$	2.84472	0.240422
$141$	2.31016	0.194551
$142$	11.0433	0.926732
$143$	18.6230	1.55733
$144$	−0.289619	−0.0241349
$145$	3.02833	0.251489
$146$	1.21309	0.100396
$147$	1.09183	0.0900525
$148$	−0.0756427	−0.00621779
$149$	−14.5844	−1.19480	−0.597400	−	0.801943i	$-0.703800\pi$
$149$	−14.5844	−1.19480	−0.597400	+	0.801943i	$0.703800\pi$
$150$	0.910856	0.0743711
$151$	−2.65827	−0.216327	−0.108164	−	0.994133i	$-0.534497\pi$
$151$	−2.65827	−0.216327	−0.108164	+	0.994133i	$0.534497\pi$
$152$	−8.92210	−0.723678
$153$	2.79498	0.225961
$154$	−8.33069	−0.671306
$155$	7.55866	0.607127
$156$	−5.79239	−0.463762
$157$	−5.37886	−0.429280	−0.214640	−	0.976693i	$-0.568858\pi$
$157$	−5.37886	−0.429280	−0.214640	+	0.976693i	$0.568858\pi$
$158$	6.70273	0.533240
$159$	−3.16958	−0.251364
$160$	−5.51165	−0.435734
$161$	0	0
$162$	−0.910856	−0.0715636
$163$	−21.9931	−1.72264	−0.861318	−	0.508067i	$-0.830360\pi$
$163$	−21.9931	−1.72264	−0.861318	+	0.508067i	$0.830360\pi$
$164$	6.75949	0.527828
$165$	3.76274	0.292929
$166$	−1.86122	−0.144459
$167$	−24.0688	−1.86250	−0.931251	−	0.364379i	$-0.881281\pi$
$167$	−24.0688	−1.86250	−0.931251	+	0.364379i	$0.881281\pi$
$168$	7.01911	0.541536
$169$	11.4957	0.884286
$170$	−2.54582	−0.195256
$171$	−3.08967	−0.236273
$172$	−8.55931	−0.652642
$173$	0.612805	0.0465907	0.0232954	−	0.999729i	$-0.492584\pi$
$173$	0.612805	0.0465907	0.0232954	+	0.999729i	$0.492584\pi$
$174$	2.75837	0.209112
$175$	−2.43067	−0.183742
$176$	1.08976	0.0821439
$177$	−11.6195	−0.873377
$178$	−7.27787	−0.545499
$179$	−16.2248	−1.21270	−0.606349	−	0.795199i	$-0.707366\pi$
$179$	−16.2248	−1.21270	−0.606349	+	0.795199i	$0.707366\pi$
$180$	−1.17034	−0.0872321
$181$	15.2452	1.13317	0.566583	−	0.824004i	$-0.308265\pi$
$181$	15.2452	1.13317	0.566583	+	0.824004i	$0.308265\pi$
$182$	−10.9577	−0.812242
$183$	−6.33802	−0.468520
$184$	0	0
$185$	0.0646330	0.00475191
$186$	6.88486	0.504822
$187$	−10.5168	−0.769064
$188$	2.70368	0.197186
$189$	2.43067	0.176805
$190$	2.81424	0.204167
$191$	20.7866	1.50406	0.752032	−	0.659127i	$-0.229074\pi$
$191$	20.7866	1.50406	0.752032	+	0.659127i	$0.229074\pi$
$192$	−5.59956	−0.404113
$193$	−3.80431	−0.273840	−0.136920	−	0.990582i	$-0.543720\pi$
$193$	−3.80431	−0.273840	−0.136920	+	0.990582i	$0.543720\pi$
$194$	0.305179	0.0219105
$195$	4.94931	0.354428
$196$	1.27781	0.0912723
$197$	17.7994	1.26816	0.634079	−	0.773268i	$-0.281379\pi$
$197$	17.7994	1.26816	0.634079	+	0.773268i	$0.281379\pi$
$198$	3.42732	0.243569
$199$	21.6834	1.53710	0.768548	−	0.639792i	$-0.220979\pi$
$199$	21.6834	1.53710	0.768548	+	0.639792i	$0.220979\pi$
$200$	2.88772	0.204193
$201$	−12.6081	−0.889307
$202$	−1.46031	−0.102747
$203$	−7.36088	−0.516632
$204$	3.27108	0.229021
$205$	−5.77566	−0.403390
$206$	−14.5450	−1.01339
$207$	0	0
$208$	1.43341	0.0993894
$209$	11.6256	0.804161
$210$	−2.21399	−0.152780
$211$	12.6185	0.868694	0.434347	−	0.900746i	$-0.356979\pi$
$211$	12.6185	0.868694	0.434347	+	0.900746i	$0.356979\pi$
$212$	−3.70949	−0.254769
$213$	12.1241	0.830728
$214$	−5.88164	−0.402061
$215$	7.31352	0.498778
$216$	−2.88772	−0.196485
$217$	−18.3726	−1.24722
$218$	17.2632	1.16921
$219$	1.33182	0.0899958
$220$	4.40370	0.296897
$221$	−13.8332	−0.930524
$222$	0.0588714	0.00395119
$223$	13.1736	0.882172	0.441086	−	0.897465i	$-0.354593\pi$
$223$	13.1736	0.882172	0.441086	+	0.897465i	$0.354593\pi$
$224$	13.3970	0.895126
$225$	1.00000	0.0666667
$226$	11.6960	0.778003
$227$	−9.94096	−0.659805	−0.329902	−	0.944015i	$-0.607016\pi$
$227$	−9.94096	−0.659805	−0.329902	+	0.944015i	$0.607016\pi$
$228$	−3.61596	−0.239473
$229$	−26.8893	−1.77690	−0.888449	−	0.458976i	$-0.848216\pi$
$229$	−26.8893	−1.77690	−0.888449	+	0.458976i	$0.848216\pi$
$230$	0	0
$231$	−9.14600	−0.601763
$232$	8.74498	0.574136
$233$	21.5646	1.41274	0.706371	−	0.707842i	$-0.250331\pi$
$233$	21.5646	1.41274	0.706371	+	0.707842i	$0.250331\pi$
$234$	4.50811	0.294705
$235$	−2.31016	−0.150698
$236$	−13.5988	−0.885207
$237$	7.35871	0.478000
$238$	6.18806	0.401113
$239$	19.6263	1.26952	0.634760	−	0.772709i	$-0.281099\pi$
$239$	19.6263	1.26952	0.634760	+	0.772709i	$0.281099\pi$
$240$	0.289619	0.0186948
$241$	2.15969	0.139118	0.0695588	−	0.997578i	$-0.477841\pi$
$241$	2.15969	0.139118	0.0695588	+	0.997578i	$0.477841\pi$
$242$	−2.87671	−0.184922
$243$	−1.00000	−0.0641500
$244$	−7.41764	−0.474866
$245$	−1.09183	−0.0697544
$246$	−5.26079	−0.335416
$247$	15.2917	0.972990
$248$	21.8273	1.38604
$249$	−2.04338	−0.129494
$250$	−0.910856	−0.0576076
$251$	12.9685	0.818567	0.409284	−	0.912407i	$-0.365779\pi$
$251$	12.9685	0.818567	0.409284	+	0.912407i	$0.365779\pi$
$252$	2.84472	0.179200
$253$	0	0
$254$	−20.1511	−1.26439
$255$	−2.79498	−0.175028
$256$	−16.5940	−1.03713
$257$	13.0232	0.812364	0.406182	−	0.913792i	$-0.366860\pi$
$257$	13.0232	0.812364	0.406182	+	0.913792i	$0.366860\pi$
$258$	6.66156	0.414731
$259$	−0.157102	−0.00976183
$260$	5.79239	0.359229
$261$	3.02833	0.187449
$262$	−5.38301	−0.332563
$263$	−29.0926	−1.79392	−0.896962	−	0.442107i	$-0.854231\pi$
$263$	−29.0926	−1.79392	−0.896962	+	0.442107i	$0.854231\pi$
$264$	10.8658	0.668742
$265$	3.16958	0.194706
$266$	−6.84050	−0.419418
$267$	−7.99014	−0.488989
$268$	−14.7558	−0.901352
$269$	−4.85359	−0.295928	−0.147964	−	0.988993i	$-0.547272\pi$
$269$	−4.85359	−0.295928	−0.147964	+	0.988993i	$0.547272\pi$
$270$	0.910856	0.0554329
$271$	−12.1017	−0.735126	−0.367563	−	0.929999i	$-0.619808\pi$
$271$	−12.1017	−0.735126	−0.367563	+	0.929999i	$0.619808\pi$
$272$	−0.809478	−0.0490818
$273$	−12.0302	−0.728099
$274$	9.43997	0.570289
$275$	−3.76274	−0.226902
$276$	0	0
$277$	−17.5494	−1.05444	−0.527220	−	0.849729i	$-0.676766\pi$
$277$	−17.5494	−1.05444	−0.527220	+	0.849729i	$0.676766\pi$
$278$	−6.01775	−0.360921
$279$	7.55866	0.452525
$280$	−7.01911	−0.419472
$281$	−0.614746	−0.0366726	−0.0183363	−	0.999832i	$-0.505837\pi$
$281$	−0.614746	−0.0366726	−0.0183363	+	0.999832i	$0.505837\pi$
$282$	−2.10422	−0.125305
$283$	11.4425	0.680187	0.340093	−	0.940392i	$-0.389541\pi$
$283$	11.4425	0.680187	0.340093	+	0.940392i	$0.389541\pi$
$284$	14.1893	0.841981
$285$	3.08967	0.183016
$286$	−16.9629	−1.00304
$287$	14.0387	0.828681
$288$	−5.51165	−0.324777
$289$	−9.18809	−0.540476
$290$	−2.75837	−0.161977
$291$	0.335046	0.0196407
$292$	1.55868	0.0912148
$293$	4.27941	0.250006	0.125003	−	0.992156i	$-0.460106\pi$
$293$	4.27941	0.250006	0.125003	+	0.992156i	$0.460106\pi$
$294$	−0.994498	−0.0580003
$295$	11.6195	0.676515
$296$	0.186642	0.0108484
$297$	3.76274	0.218337
$298$	13.2843	0.769538
$299$	0	0
$300$	1.17034	0.0675697
$301$	−17.7768	−1.02464
$302$	2.42130	0.139330
$303$	−1.60323	−0.0921032
$304$	0.894825	0.0513217
$305$	6.33802	0.362914
$306$	−2.54582	−0.145535
$307$	21.7773	1.24290	0.621448	−	0.783456i	$-0.286545\pi$
$307$	21.7773	1.24290	0.621448	+	0.783456i	$0.286545\pi$
$308$	−10.7039	−0.609914
$309$	−15.9684	−0.908413
$310$	−6.88486	−0.391033
$311$	16.4437	0.932435	0.466218	−	0.884670i	$-0.345616\pi$
$311$	16.4437	0.932435	0.466218	+	0.884670i	$0.345616\pi$
$312$	14.2923	0.809140
$313$	0.100245	0.00566620	0.00283310	−	0.999996i	$-0.499098\pi$
$313$	0.100245	0.00566620	0.00283310	+	0.999996i	$0.499098\pi$
$314$	4.89937	0.276487
$315$	−2.43067	−0.136953
$316$	8.61220	0.484474
$317$	−1.64980	−0.0926620	−0.0463310	−	0.998926i	$-0.514753\pi$
$317$	−1.64980	−0.0926620	−0.0463310	+	0.998926i	$0.514753\pi$
$318$	2.88703	0.161897
$319$	−11.3948	−0.637988
$320$	5.59956	0.313025
$321$	−6.45727	−0.360409
$322$	0	0
$323$	−8.63555	−0.480495
$324$	−1.17034	−0.0650190
$325$	−4.94931	−0.274539
$326$	20.0326	1.10950
$327$	18.9527	1.04809
$328$	−16.6785	−0.920917
$329$	5.61525	0.309579
$330$	−3.42732	−0.188668
$331$	−32.1255	−1.76578	−0.882888	−	0.469584i	$-0.844404\pi$
$331$	−32.1255	−1.76578	−0.882888	+	0.469584i	$0.844404\pi$
$332$	−2.39145	−0.131248
$333$	0.0646330	0.00354187
$334$	21.9232	1.19959
$335$	12.6081	0.688854
$336$	−0.703968	−0.0384046
$337$	−3.22410	−0.175628	−0.0878139	−	0.996137i	$-0.527988\pi$
$337$	−3.22410	−0.175628	−0.0878139	+	0.996137i	$0.527988\pi$
$338$	−10.4709	−0.569544
$339$	12.8406	0.697407
$340$	−3.27108	−0.177399
$341$	−28.4413	−1.54018
$342$	2.81424	0.152177
$343$	19.6686	1.06200
$344$	21.1194	1.13868
$345$	0	0
$346$	−0.558177	−0.0300078
$347$	26.8644	1.44216	0.721079	−	0.692853i	$-0.243646\pi$
$347$	26.8644	1.44216	0.721079	+	0.692853i	$0.243646\pi$
$348$	3.54418	0.189988
$349$	−33.7651	−1.80741	−0.903703	−	0.428160i	$-0.859162\pi$
$349$	−33.7651	−1.80741	−0.903703	+	0.428160i	$0.859162\pi$
$350$	2.21399	0.118343
$351$	4.94931	0.264175
$352$	20.7389	1.10539
$353$	−15.5685	−0.828625	−0.414313	−	0.910135i	$-0.635978\pi$
$353$	−15.5685	−0.828625	−0.414313	+	0.910135i	$0.635978\pi$
$354$	10.5837	0.562518
$355$	−12.1241	−0.643479
$356$	−9.35119	−0.495612
$357$	6.79368	0.359560
$358$	14.7784	0.781065
$359$	−11.5656	−0.610407	−0.305204	−	0.952287i	$-0.598725\pi$
$359$	−11.5656	−0.610407	−0.305204	+	0.952287i	$0.598725\pi$
$360$	2.88772	0.152196
$361$	−9.45396	−0.497577
$362$	−13.8862	−0.729842
$363$	−3.15825	−0.165765
$364$	−14.0794	−0.737961
$365$	−1.33182	−0.0697104
$366$	5.77302	0.301761
$367$	32.2417	1.68300	0.841501	−	0.540256i	$-0.181673\pi$
$367$	32.2417	1.68300	0.841501	+	0.540256i	$0.181673\pi$
$368$	0	0
$369$	−5.77566	−0.300669
$370$	−0.0588714	−0.00306058
$371$	−7.70421	−0.399983
$372$	8.84622	0.458655
$373$	21.4908	1.11275	0.556377	−	0.830930i	$-0.312191\pi$
$373$	21.4908	1.11275	0.556377	+	0.830930i	$0.312191\pi$
$374$	9.57928	0.495333
$375$	−1.00000	−0.0516398
$376$	−6.67111	−0.344036
$377$	−14.9882	−0.771929
$378$	−2.21399	−0.113876
$379$	−11.9256	−0.612579	−0.306289	−	0.951938i	$-0.599088\pi$
$379$	−11.9256	−0.612579	−0.306289	+	0.951938i	$0.599088\pi$
$380$	3.61596	0.185495
$381$	−22.1233	−1.13341
$382$	−18.9336	−0.968726
$383$	28.1911	1.44050	0.720249	−	0.693715i	$-0.244027\pi$
$383$	28.1911	1.44050	0.720249	+	0.693715i	$0.244027\pi$
$384$	−5.92291	−0.302252
$385$	9.14600	0.466123
$386$	3.46518	0.176373
$387$	7.31352	0.371767
$388$	0.392118	0.0199068
$389$	27.3092	1.38463	0.692316	−	0.721595i	$-0.256591\pi$
$389$	27.3092	1.38463	0.692316	+	0.721595i	$0.256591\pi$
$390$	−4.50811	−0.228277
$391$	0	0
$392$	−3.15290	−0.159245
$393$	−5.90983	−0.298112
$394$	−16.2127	−0.816786
$395$	−7.35871	−0.370257
$396$	4.40370	0.221294
$397$	−25.7256	−1.29113	−0.645566	−	0.763705i	$-0.723378\pi$
$397$	−25.7256	−1.29113	−0.645566	+	0.763705i	$0.723378\pi$
$398$	−19.7505	−0.990002
$399$	−7.50997	−0.375969
$400$	−0.289619	−0.0144809
$401$	−1.79450	−0.0896133	−0.0448066	−	0.998996i	$-0.514267\pi$
$401$	−1.79450	−0.0896133	−0.0448066	+	0.998996i	$0.514267\pi$
$402$	11.4842	0.572778
$403$	−37.4102	−1.86354
$404$	−1.87633	−0.0933507
$405$	1.00000	0.0496904
$406$	6.70470	0.332749
$407$	−0.243198	−0.0120549
$408$	−8.07113	−0.399580
$409$	−3.54580	−0.175328	−0.0876642	−	0.996150i	$-0.527940\pi$
$409$	−3.54580	−0.175328	−0.0876642	+	0.996150i	$0.527940\pi$
$410$	5.26079	0.259812
$411$	10.3638	0.511211
$412$	−18.6885	−0.920718
$413$	−28.2433	−1.38976
$414$	0	0
$415$	2.04338	0.100305
$416$	27.2789	1.33746
$417$	−6.60670	−0.323531
$418$	−10.5893	−0.517938
$419$	−15.0698	−0.736209	−0.368105	−	0.929784i	$-0.619993\pi$
$419$	−15.0698	−0.736209	−0.368105	+	0.929784i	$0.619993\pi$
$420$	−2.84472	−0.138808
$421$	−10.0268	−0.488675	−0.244337	−	0.969690i	$-0.578570\pi$
$421$	−10.0268	−0.488675	−0.244337	+	0.969690i	$0.578570\pi$
$422$	−11.4937	−0.559502
$423$	−2.31016	−0.112324
$424$	9.15287	0.444503
$425$	2.79498	0.135576
$426$	−11.0433	−0.535049
$427$	−15.4056	−0.745531
$428$	−7.55721	−0.365291
$429$	−18.6230	−0.899127
$430$	−6.66156	−0.321249
$431$	2.28394	0.110013	0.0550067	−	0.998486i	$-0.482482\pi$
$431$	2.28394	0.110013	0.0550067	+	0.998486i	$0.482482\pi$
$432$	0.289619	0.0139343
$433$	5.89581	0.283334	0.141667	−	0.989914i	$-0.454754\pi$
$433$	5.89581	0.283334	0.141667	+	0.989914i	$0.454754\pi$
$434$	16.7348	0.803298
$435$	−3.02833	−0.145197
$436$	22.1811	1.06228
$437$	0	0
$438$	−1.21309	−0.0579638
$439$	−37.9803	−1.81270	−0.906350	−	0.422527i	$-0.861143\pi$
$439$	−37.9803	−1.81270	−0.906350	+	0.422527i	$0.861143\pi$
$440$	−10.8658	−0.518005
$441$	−1.09183	−0.0519918
$442$	12.6001	0.599325
$443$	−15.0854	−0.716729	−0.358364	−	0.933582i	$-0.616665\pi$
$443$	−15.0854	−0.716729	−0.358364	+	0.933582i	$0.616665\pi$
$444$	0.0756427	0.00358984
$445$	7.99014	0.378769
$446$	−11.9993	−0.568183
$447$	14.5844	0.689818
$448$	−13.6107	−0.643045
$449$	−24.8722	−1.17379	−0.586897	−	0.809662i	$-0.699651\pi$
$449$	−24.8722	−1.17379	−0.586897	+	0.809662i	$0.699651\pi$
$450$	−0.910856	−0.0429382
$451$	21.7323	1.02334
$452$	15.0279	0.706853
$453$	2.65827	0.124897
$454$	9.05478	0.424962
$455$	12.0302	0.563983
$456$	8.92210	0.417816
$457$	−29.3337	−1.37217	−0.686086	−	0.727520i	$-0.740673\pi$
$457$	−29.3337	−1.37217	−0.686086	+	0.727520i	$0.740673\pi$
$458$	24.4923	1.14445
$459$	−2.79498	−0.130458
$460$	0	0
$461$	−8.11526	−0.377965	−0.188983	−	0.981980i	$-0.560519\pi$
$461$	−8.11526	−0.377965	−0.188983	+	0.981980i	$0.560519\pi$
$462$	8.33069	0.387579
$463$	−29.9720	−1.39292	−0.696458	−	0.717598i	$-0.745242\pi$
$463$	−29.9720	−1.39292	−0.696458	+	0.717598i	$0.745242\pi$
$464$	−0.877061	−0.0407165
$465$	−7.55866	−0.350525
$466$	−19.6422	−0.909908
$467$	11.9860	0.554644	0.277322	−	0.960777i	$-0.410553\pi$
$467$	11.9860	0.554644	0.277322	+	0.960777i	$0.410553\pi$
$468$	5.79239	0.267753
$469$	−30.6462	−1.41511
$470$	2.10422	0.0970607
$471$	5.37886	0.247845
$472$	33.5540	1.54445
$473$	−27.5189	−1.26532
$474$	−6.70273	−0.307866
$475$	−3.08967	−0.141764
$476$	7.95092	0.364430
$477$	3.16958	0.145125
$478$	−17.8767	−0.817663
$479$	−11.7272	−0.535830	−0.267915	−	0.963442i	$-0.586335\pi$
$479$	−11.7272	−0.535830	−0.267915	+	0.963442i	$0.586335\pi$
$480$	5.51165	0.251571
$481$	−0.319889	−0.0145857
$482$	−1.96716	−0.0896018
$483$	0	0
$484$	−3.69623	−0.168010
$485$	−0.335046	−0.0152137
$486$	0.910856	0.0413173
$487$	−9.09620	−0.412188	−0.206094	−	0.978532i	$-0.566075\pi$
$487$	−9.09620	−0.412188	−0.206094	+	0.978532i	$0.566075\pi$
$488$	18.3024	0.828513
$489$	21.9931	0.994564
$490$	0.994498	0.0449269
$491$	−5.71827	−0.258062	−0.129031	−	0.991641i	$-0.541187\pi$
$491$	−5.71827	−0.258062	−0.129031	+	0.991641i	$0.541187\pi$
$492$	−6.75949	−0.304741
$493$	8.46412	0.381205
$494$	−13.9286	−0.626676
$495$	−3.76274	−0.169123
$496$	−2.18913	−0.0982949
$497$	29.4697	1.32190
$498$	1.86122	0.0834034
$499$	2.65014	0.118637	0.0593184	−	0.998239i	$-0.481107\pi$
$499$	2.65014	0.118637	0.0593184	+	0.998239i	$0.481107\pi$
$500$	−1.17034	−0.0523393
$501$	24.0688	1.07532
$502$	−11.8125	−0.527217
$503$	−29.0015	−1.29311	−0.646556	−	0.762867i	$-0.723791\pi$
$503$	−29.0015	−1.29311	−0.646556	+	0.762867i	$0.723791\pi$
$504$	−7.01911	−0.312656
$505$	1.60323	0.0713428
$506$	0	0
$507$	−11.4957	−0.510543
$508$	−25.8918	−1.14876
$509$	−26.7739	−1.18673	−0.593366	−	0.804933i	$-0.702201\pi$
$509$	−26.7739	−1.18673	−0.593366	+	0.804933i	$0.702201\pi$
$510$	2.54582	0.112731
$511$	3.23721	0.143206
$512$	3.26895	0.144469
$513$	3.08967	0.136412
$514$	−11.8622	−0.523221
$515$	15.9684	0.703654
$516$	8.55931	0.376803
$517$	8.69255	0.382298
$518$	0.143097	0.00628732
$519$	−0.612805	−0.0268992
$520$	−14.2923	−0.626757
$521$	25.3591	1.11100	0.555500	−	0.831516i	$-0.312527\pi$
$521$	25.3591	1.11100	0.555500	+	0.831516i	$0.312527\pi$
$522$	−2.75837	−0.120731
$523$	−8.10366	−0.354348	−0.177174	−	0.984180i	$-0.556696\pi$
$523$	−8.10366	−0.354348	−0.177174	+	0.984180i	$0.556696\pi$
$524$	−6.91652	−0.302150
$525$	2.43067	0.106083
$526$	26.4991	1.15542
$527$	21.1263	0.920276
$528$	−1.08976	−0.0474258
$529$	0	0
$530$	−2.88703	−0.125405
$531$	11.6195	0.504244
$532$	−8.78923	−0.381061
$533$	28.5856	1.23818
$534$	7.27787	0.314944
$535$	6.45727	0.279172
$536$	36.4087	1.57262
$537$	16.2248	0.700151
$538$	4.42092	0.190599
$539$	4.10827	0.176956
$540$	1.17034	0.0503635
$541$	−22.4629	−0.965755	−0.482877	−	0.875688i	$-0.660408\pi$
$541$	−22.4629	−0.965755	−0.482877	+	0.875688i	$0.660408\pi$
$542$	11.0229	0.473475
$543$	−15.2452	−0.654234
$544$	−15.4049	−0.660481
$545$	−18.9527	−0.811845
$546$	10.9577	0.468948
$547$	−26.1319	−1.11732	−0.558659	−	0.829397i	$-0.688684\pi$
$547$	−26.1319	−1.11732	−0.558659	+	0.829397i	$0.688684\pi$
$548$	12.1292	0.518135
$549$	6.33802	0.270500
$550$	3.42732	0.146141
$551$	−9.35653	−0.398601
$552$	0	0
$553$	17.8866	0.760616
$554$	15.9850	0.679136
$555$	−0.0646330	−0.00274352
$556$	−7.73209	−0.327914
$557$	10.2812	0.435628	0.217814	−	0.975990i	$-0.430107\pi$
$557$	10.2812	0.435628	0.217814	+	0.975990i	$0.430107\pi$
$558$	−6.88486	−0.291459
$559$	−36.1969	−1.53097
$560$	0.703968	0.0297481
$561$	10.5168	0.444019
$562$	0.559945	0.0236198
$563$	−20.8475	−0.878617	−0.439309	−	0.898336i	$-0.644777\pi$
$563$	−20.8475	−0.878617	−0.439309	+	0.898336i	$0.644777\pi$
$564$	−2.70368	−0.113845
$565$	−12.8406	−0.540209
$566$	−10.4225	−0.438089
$567$	−2.43067	−0.102079
$568$	−35.0110	−1.46903
$569$	−43.6395	−1.82946	−0.914732	−	0.404060i	$-0.867599\pi$
$569$	−43.6395	−1.82946	−0.914732	+	0.404060i	$0.867599\pi$
$570$	−2.81424	−0.117876
$571$	−40.9849	−1.71516	−0.857582	−	0.514347i	$-0.828034\pi$
$571$	−40.9849	−1.71516	−0.857582	+	0.514347i	$0.828034\pi$
$572$	−21.7953	−0.911306
$573$	−20.7866	−0.868372
$574$	−12.7873	−0.533730
$575$	0	0
$576$	5.59956	0.233315
$577$	2.05812	0.0856808	0.0428404	−	0.999082i	$-0.486359\pi$
$577$	2.05812	0.0856808	0.0428404	+	0.999082i	$0.486359\pi$
$578$	8.36903	0.348106
$579$	3.80431	0.158102
$580$	−3.54418	−0.147164
$581$	−4.96678	−0.206057
$582$	−0.305179	−0.0126501
$583$	−11.9263	−0.493938
$584$	−3.84592	−0.159145
$585$	−4.94931	−0.204629
$586$	−3.89792	−0.161022
$587$	−28.1217	−1.16071	−0.580354	−	0.814365i	$-0.697086\pi$
$587$	−28.1217	−1.16071	−0.580354	+	0.814365i	$0.697086\pi$
$588$	−1.27781	−0.0526961
$589$	−23.3537	−0.962274
$590$	−10.5837	−0.435725
$591$	−17.7994	−0.732171
$592$	−0.0187189	−0.000769343 0
$593$	−25.1074	−1.03104	−0.515520	−	0.856878i	$-0.672401\pi$
$593$	−25.1074	−1.03104	−0.515520	+	0.856878i	$0.672401\pi$
$594$	−3.42732	−0.140625
$595$	−6.79368	−0.278514
$596$	17.0687	0.699162
$597$	−21.6834	−0.887443
$598$	0	0
$599$	−22.0286	−0.900065	−0.450032	−	0.893012i	$-0.648588\pi$
$599$	−22.0286	−0.900065	−0.450032	+	0.893012i	$0.648588\pi$
$600$	−2.88772	−0.117891
$601$	−21.9383	−0.894883	−0.447442	−	0.894313i	$-0.647665\pi$
$601$	−21.9383	−0.894883	−0.447442	+	0.894313i	$0.647665\pi$
$602$	16.1921	0.659940
$603$	12.6081	0.513441
$604$	3.11109	0.126588
$605$	3.15825	0.128401
$606$	1.46031	0.0593211
$607$	23.3987	0.949724	0.474862	−	0.880060i	$-0.342498\pi$
$607$	23.3987	0.949724	0.474862	+	0.880060i	$0.342498\pi$
$608$	17.0292	0.690623
$609$	7.36088	0.298278
$610$	−5.77302	−0.233743
$611$	11.4337	0.462559
$612$	−3.27108	−0.132226
$613$	43.5860	1.76042	0.880211	−	0.474583i	$-0.157401\pi$
$613$	43.5860	1.76042	0.880211	+	0.474583i	$0.157401\pi$
$614$	−19.8360	−0.800514
$615$	5.77566	0.232897
$616$	26.4111	1.06413
$617$	25.7970	1.03855	0.519275	−	0.854607i	$-0.326202\pi$
$617$	25.7970	1.03855	0.519275	+	0.854607i	$0.326202\pi$
$618$	14.5450	0.585084
$619$	−28.1339	−1.13080	−0.565399	−	0.824817i	$-0.691278\pi$
$619$	−28.1339	−1.13080	−0.565399	+	0.824817i	$0.691278\pi$
$620$	−8.84622	−0.355273
$621$	0	0
$622$	−14.9778	−0.600556
$623$	−19.4214	−0.778103
$624$	−1.43341	−0.0573825
$625$	1.00000	0.0400000
$626$	−0.0913091	−0.00364945
$627$	−11.6256	−0.464283
$628$	6.29510	0.251202
$629$	0.180648	0.00720291
$630$	2.21399	0.0882076
$631$	24.8136	0.987813	0.493906	−	0.869515i	$-0.335569\pi$
$631$	24.8136	0.987813	0.493906	+	0.869515i	$0.335569\pi$
$632$	−21.2499	−0.845277
$633$	−12.6185	−0.501541
$634$	1.50273	0.0596810
$635$	22.1233	0.877935
$636$	3.70949	0.147091
$637$	5.40380	0.214106
$638$	10.3791	0.410911
$639$	−12.1241	−0.479621
$640$	5.92291	0.234123
$641$	−9.33427	−0.368681	−0.184341	−	0.982862i	$-0.559015\pi$
$641$	−9.33427	−0.368681	−0.184341	+	0.982862i	$0.559015\pi$
$642$	5.88164	0.232130
$643$	36.1030	1.42376	0.711882	−	0.702299i	$-0.247843\pi$
$643$	36.1030	1.42376	0.711882	+	0.702299i	$0.247843\pi$
$644$	0	0
$645$	−7.31352	−0.287970
$646$	7.86574	0.309474
$647$	−33.5907	−1.32059	−0.660294	−	0.751007i	$-0.729568\pi$
$647$	−33.5907	−1.32059	−0.660294	+	0.751007i	$0.729568\pi$
$648$	2.88772	0.113441
$649$	−43.7213	−1.71621
$650$	4.50811	0.176823
$651$	18.3726	0.720081
$652$	25.7395	1.00804
$653$	29.0025	1.13496	0.567478	−	0.823389i	$-0.307919\pi$
$653$	29.0025	1.13496	0.567478	+	0.823389i	$0.307919\pi$
$654$	−17.2632	−0.675044
$655$	5.90983	0.230916
$656$	1.67274	0.0653095
$657$	−1.33182	−0.0519591
$658$	−5.11468	−0.199391
$659$	−19.4984	−0.759550	−0.379775	−	0.925079i	$-0.623999\pi$
$659$	−19.4984	−0.759550	−0.379775	+	0.925079i	$0.623999\pi$
$660$	−4.40370	−0.171414
$661$	−41.1925	−1.60220	−0.801101	−	0.598529i	$-0.795752\pi$
$661$	−41.1925	−1.60220	−0.801101	+	0.598529i	$0.795752\pi$
$662$	29.2617	1.13729
$663$	13.8332	0.537238
$664$	5.90071	0.228992
$665$	7.50997	0.291224
$666$	−0.0588714	−0.00228122
$667$	0	0
$668$	28.1687	1.08988
$669$	−13.1736	−0.509322
$670$	−11.4842	−0.443672
$671$	−23.8483	−0.920655
$672$	−13.3970	−0.516801
$673$	−37.0701	−1.42895	−0.714473	−	0.699663i	$-0.753334\pi$
$673$	−37.0701	−1.42895	−0.714473	+	0.699663i	$0.753334\pi$
$674$	2.93669	0.113117
$675$	−1.00000	−0.0384900
$676$	−13.4539	−0.517458
$677$	1.44434	0.0555104	0.0277552	−	0.999615i	$-0.491164\pi$
$677$	1.44434	0.0555104	0.0277552	+	0.999615i	$0.491164\pi$
$678$	−11.6960	−0.449180
$679$	0.814387	0.0312533
$680$	8.07113	0.309514
$681$	9.94096	0.380938
$682$	25.9060	0.991990
$683$	4.66816	0.178622	0.0893110	−	0.996004i	$-0.471533\pi$
$683$	4.66816	0.178622	0.0893110	+	0.996004i	$0.471533\pi$
$684$	3.61596	0.138260
$685$	−10.3638	−0.395982
$686$	−17.9153	−0.684008
$687$	26.8893	1.02589
$688$	−2.11813	−0.0807530
$689$	−15.6872	−0.597637
$690$	0	0
$691$	5.30553	0.201832	0.100916	−	0.994895i	$-0.467823\pi$
$691$	5.30553	0.201832	0.100916	+	0.994895i	$0.467823\pi$
$692$	−0.717191	−0.0272635
$693$	9.14600	0.347428
$694$	−24.4696	−0.928854
$695$	6.60670	0.250606
$696$	−8.74498	−0.331478
$697$	−16.1428	−0.611454
$698$	30.7552	1.16410
$699$	−21.5646	−0.815647
$700$	2.84472	0.107520
$701$	29.4099	1.11079	0.555397	−	0.831585i	$-0.312566\pi$
$701$	29.4099	1.11079	0.555397	+	0.831585i	$0.312566\pi$
$702$	−4.50811	−0.170148
$703$	−0.199694	−0.00753162
$704$	−21.0697	−0.794094
$705$	2.31016	0.0870057
$706$	14.1806	0.533695
$707$	−3.89693	−0.146559
$708$	13.5988	0.511075
$709$	−9.70304	−0.364405	−0.182203	−	0.983261i	$-0.558323\pi$
$709$	−9.70304	−0.364405	−0.182203	+	0.983261i	$0.558323\pi$
$710$	11.0433	0.414447
$711$	−7.35871	−0.275973
$712$	23.0733	0.864710
$713$	0	0
$714$	−6.18806	−0.231583
$715$	18.6230	0.696461
$716$	18.9885	0.709635
$717$	−19.6263	−0.732958
$718$	10.5346	0.393147
$719$	34.9462	1.30327	0.651636	−	0.758531i	$-0.274083\pi$
$719$	34.9462	1.30327	0.651636	+	0.758531i	$0.274083\pi$
$720$	−0.289619	−0.0107935
$721$	−38.8141	−1.44551
$722$	8.61120	0.320476
$723$	−2.15969	−0.0803196
$724$	−17.8421	−0.663096
$725$	3.02833	0.112469
$726$	2.87671	0.106765
$727$	41.0065	1.52085	0.760423	−	0.649428i	$-0.224992\pi$
$727$	41.0065	1.52085	0.760423	+	0.649428i	$0.224992\pi$
$728$	34.7398	1.28754
$729$	1.00000	0.0370370
$730$	1.21309	0.0448986
$731$	20.4411	0.756043
$732$	7.41764	0.274164
$733$	8.07063	0.298096	0.149048	−	0.988830i	$-0.452379\pi$
$733$	8.07063	0.298096	0.149048	+	0.988830i	$0.452379\pi$
$734$	−29.3675	−1.08397
$735$	1.09183	0.0402727
$736$	0	0
$737$	−47.4410	−1.74751
$738$	5.26079	0.193653
$739$	−28.8795	−1.06235	−0.531175	−	0.847262i	$-0.678249\pi$
$739$	−28.8795	−1.06235	−0.531175	+	0.847262i	$0.678249\pi$
$740$	−0.0756427	−0.00278068
$741$	−15.2917	−0.561756
$742$	7.01743	0.257618
$743$	−16.0255	−0.587917	−0.293959	−	0.955818i	$-0.594973\pi$
$743$	−16.0255	−0.587917	−0.293959	+	0.955818i	$0.594973\pi$
$744$	−21.8273	−0.800229
$745$	−14.5844	−0.534331
$746$	−19.5751	−0.716694
$747$	2.04338	0.0747633
$748$	12.3082	0.450034
$749$	−15.6955	−0.573501
$750$	0.910856	0.0332598
$751$	24.0228	0.876603	0.438302	−	0.898828i	$-0.355580\pi$
$751$	24.0228	0.876603	0.438302	+	0.898828i	$0.355580\pi$
$752$	0.669066	0.0243983
$753$	−12.9685	−0.472600
$754$	13.6521	0.497178
$755$	−2.65827	−0.0967445
$756$	−2.84472	−0.103461
$757$	9.76840	0.355039	0.177519	−	0.984117i	$-0.443193\pi$
$757$	9.76840	0.355039	0.177519	+	0.984117i	$0.443193\pi$
$758$	10.8625	0.394545
$759$	0	0
$760$	−8.92210	−0.323639
$761$	−19.9533	−0.723307	−0.361654	−	0.932313i	$-0.617788\pi$
$761$	−19.9533	−0.723307	−0.361654	+	0.932313i	$0.617788\pi$
$762$	20.1511	0.729997
$763$	46.0678	1.66777
$764$	−24.3274	−0.880134
$765$	2.79498	0.101053
$766$	−25.6780	−0.927785
$767$	−57.5087	−2.07652
$768$	16.5940	0.598785
$769$	−11.9831	−0.432121	−0.216061	−	0.976380i	$-0.569321\pi$
$769$	−11.9831	−0.432121	−0.216061	+	0.976380i	$0.569321\pi$
$770$	−8.33069	−0.300217
$771$	−13.0232	−0.469019
$772$	4.45234	0.160243
$773$	−23.5714	−0.847804	−0.423902	−	0.905708i	$-0.639340\pi$
$773$	−23.5714	−0.847804	−0.423902	+	0.905708i	$0.639340\pi$
$774$	−6.66156	−0.239445
$775$	7.55866	0.271515
$776$	−0.967520	−0.0347320
$777$	0.157102	0.00563599
$778$	−24.8747	−0.891803
$779$	17.8449	0.639358
$780$	−5.79239	−0.207401
$781$	45.6198	1.63241
$782$	0	0
$783$	−3.02833	−0.108224
$784$	0.316214	0.0112934
$785$	−5.37886	−0.191980
$786$	5.38301	0.192005
$787$	15.5156	0.553071	0.276536	−	0.961004i	$-0.410814\pi$
$787$	15.5156	0.553071	0.276536	+	0.961004i	$0.410814\pi$
$788$	−20.8314	−0.742089
$789$	29.0926	1.03572
$790$	6.70273	0.238472
$791$	31.2113	1.10975
$792$	−10.8658	−0.386098
$793$	−31.3688	−1.11394
$794$	23.4323	0.831582
$795$	−3.16958	−0.112413
$796$	−25.3770	−0.899464
$797$	−41.6781	−1.47631	−0.738157	−	0.674629i	$-0.764304\pi$
$797$	−41.6781	−1.47631	−0.738157	+	0.674629i	$0.764304\pi$
$798$	6.84050	0.242151
$799$	−6.45685	−0.228427
$800$	−5.51165	−0.194866
$801$	7.99014	0.282318
$802$	1.63453	0.0577174
$803$	5.01128	0.176844
$804$	14.7558	0.520396
$805$	0	0
$806$	34.0753	1.20025
$807$	4.85359	0.170854
$808$	4.62969	0.162872
$809$	13.4392	0.472498	0.236249	−	0.971693i	$-0.424082\pi$
$809$	13.4392	0.472498	0.236249	+	0.971693i	$0.424082\pi$
$810$	−0.910856	−0.0320042
$811$	21.6936	0.761767	0.380883	−	0.924623i	$-0.375620\pi$
$811$	21.6936	0.761767	0.380883	+	0.924623i	$0.375620\pi$
$812$	8.61474	0.302318
$813$	12.1017	0.424425
$814$	0.221518	0.00776420
$815$	−21.9931	−0.770386
$816$	0.809478	0.0283374
$817$	−22.5963	−0.790546
$818$	3.22971	0.112924
$819$	12.0302	0.420368
$820$	6.75949	0.236052
$821$	51.3387	1.79173	0.895867	−	0.444323i	$-0.146556\pi$
$821$	51.3387	1.79173	0.895867	+	0.444323i	$0.146556\pi$
$822$	−9.43997	−0.329257
$823$	−27.1516	−0.946446	−0.473223	−	0.880943i	$-0.656909\pi$
$823$	−27.1516	−0.946446	−0.473223	+	0.880943i	$0.656909\pi$
$824$	46.1125	1.60640
$825$	3.76274	0.131002
$826$	25.7255	0.895106
$827$	−15.2769	−0.531231	−0.265616	−	0.964079i	$-0.585575\pi$
$827$	−15.2769	−0.531231	−0.265616	+	0.964079i	$0.585575\pi$
$828$	0	0
$829$	−50.6337	−1.75858	−0.879290	−	0.476287i	$-0.841982\pi$
$829$	−50.6337	−1.75858	−0.879290	+	0.476287i	$0.841982\pi$
$830$	−1.86122	−0.0646040
$831$	17.5494	0.608782
$832$	−27.7140	−0.960809
$833$	−3.05164	−0.105733
$834$	6.01775	0.208378
$835$	−24.0688	−0.832936
$836$	−13.6059	−0.470572
$837$	−7.55866	−0.261266
$838$	13.7264	0.474172
$839$	−29.1431	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$839$	−29.1431	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$840$	7.01911	0.242182
$841$	−19.8292	−0.683766
$842$	9.13294	0.314742
$843$	0.614746	0.0211730
$844$	−14.7680	−0.508334
$845$	11.4957	0.395465
$846$	2.10422	0.0723447
$847$	−7.67667	−0.263773
$848$	−0.917970	−0.0315232
$849$	−11.4425	−0.392706
$850$	−2.54582	−0.0873210
$851$	0	0
$852$	−14.1893	−0.486118
$853$	−26.7518	−0.915963	−0.457981	−	0.888962i	$-0.651427\pi$
$853$	−26.7518	−0.915963	−0.457981	+	0.888962i	$0.651427\pi$
$854$	14.0323	0.480176
$855$	−3.08967	−0.105664
$856$	18.6468	0.637335
$857$	0.553217	0.0188975	0.00944877	−	0.999955i	$-0.496992\pi$
$857$	0.553217	0.0188975	0.00944877	+	0.999955i	$0.496992\pi$
$858$	16.9629	0.579103
$859$	21.1681	0.722247	0.361124	−	0.932518i	$-0.382393\pi$
$859$	21.1681	0.722247	0.361124	+	0.932518i	$0.382393\pi$
$860$	−8.55931	−0.291870
$861$	−14.0387	−0.478439
$862$	−2.08034	−0.0708567
$863$	−46.1790	−1.57195	−0.785975	−	0.618258i	$-0.787839\pi$
$863$	−46.1790	−1.57195	−0.785975	+	0.618258i	$0.787839\pi$
$864$	5.51165	0.187510
$865$	0.612805	0.0208360
$866$	−5.37023	−0.182488
$867$	9.18809	0.312044
$868$	21.5023	0.729834
$869$	27.6889	0.939283
$870$	2.75837	0.0935176
$871$	−62.4014	−2.11439
$872$	−54.7302	−1.85340
$873$	−0.335046	−0.0113396
$874$	0	0
$875$	−2.43067	−0.0821717
$876$	−1.55868	−0.0526629
$877$	17.6275	0.595237	0.297619	−	0.954685i	$-0.403808\pi$
$877$	17.6275	0.595237	0.297619	+	0.954685i	$0.403808\pi$
$878$	34.5946	1.16751
$879$	−4.27941	−0.144341
$880$	1.08976	0.0367358
$881$	−3.32664	−0.112077	−0.0560387	−	0.998429i	$-0.517847\pi$
$881$	−3.32664	−0.112077	−0.0560387	+	0.998429i	$0.517847\pi$
$882$	0.994498	0.0334865
$883$	31.3443	1.05482	0.527411	−	0.849610i	$-0.323163\pi$
$883$	31.3443	1.05482	0.527411	+	0.849610i	$0.323163\pi$
$884$	16.1896	0.544515
$885$	−11.6195	−0.390586
$886$	13.7406	0.461625
$887$	32.3599	1.08654	0.543269	−	0.839559i	$-0.317186\pi$
$887$	32.3599	1.08654	0.543269	+	0.839559i	$0.317186\pi$
$888$	−0.186642	−0.00626331
$889$	−53.7744	−1.80354
$890$	−7.27787	−0.243955
$891$	−3.76274	−0.126057
$892$	−15.4177	−0.516221
$893$	7.13763	0.238852
$894$	−13.2843	−0.444293
$895$	−16.2248	−0.542335
$896$	−14.3967	−0.480958
$897$	0	0
$898$	22.6550	0.756008
$899$	22.8901	0.763428
$900$	−1.17034	−0.0390114
$901$	8.85891	0.295133
$902$	−19.7950	−0.659102
$903$	17.7768	0.591574
$904$	−37.0802	−1.23327
$905$	15.2452	0.506768
$906$	−2.42130	−0.0804424
$907$	−17.2228	−0.571874	−0.285937	−	0.958248i	$-0.592305\pi$
$907$	−17.2228	−0.571874	−0.285937	+	0.958248i	$0.592305\pi$
$908$	11.6343	0.386098
$909$	1.60323	0.0531758
$910$	−10.9577	−0.363246
$911$	18.5224	0.613673	0.306837	−	0.951762i	$-0.400730\pi$
$911$	18.5224	0.613673	0.306837	+	0.951762i	$0.400730\pi$
$912$	−0.894825	−0.0296306
$913$	−7.68871	−0.254459
$914$	26.7188	0.883778
$915$	−6.33802	−0.209528
$916$	31.4697	1.03979
$917$	−14.3649	−0.474370
$918$	2.54582	0.0840247
$919$	−18.4406	−0.608300	−0.304150	−	0.952624i	$-0.598372\pi$
$919$	−18.4406	−0.608300	−0.304150	+	0.952624i	$0.598372\pi$
$920$	0	0
$921$	−21.7773	−0.717586
$922$	7.39183	0.243437
$923$	60.0059	1.97512
$924$	10.7039	0.352134
$925$	0.0646330	0.00212512
$926$	27.3001	0.897138
$927$	15.9684	0.524472
$928$	−16.6911	−0.547912
$929$	1.98622	0.0651657	0.0325828	−	0.999469i	$-0.489627\pi$
$929$	1.98622	0.0651657	0.0325828	+	0.999469i	$0.489627\pi$
$930$	6.88486	0.225763
$931$	3.37339	0.110558
$932$	−25.2379	−0.826695
$933$	−16.4437	−0.538342
$934$	−10.9175	−0.357231
$935$	−10.5168	−0.343936
$936$	−14.2923	−0.467157
$937$	1.92466	0.0628759	0.0314380	−	0.999506i	$-0.489991\pi$
$937$	1.92466	0.0628759	0.0314380	+	0.999506i	$0.489991\pi$
$938$	27.9142	0.911432
$939$	−0.100245	−0.00327138
$940$	2.70368	0.0881842
$941$	−13.5988	−0.443307	−0.221654	−	0.975125i	$-0.571145\pi$
$941$	−13.5988	−0.443307	−0.221654	+	0.975125i	$0.571145\pi$
$942$	−4.89937	−0.159630
$943$	0	0
$944$	−3.36523	−0.109529
$945$	2.43067	0.0790698
$946$	25.0658	0.814958
$947$	6.62497	0.215283	0.107641	−	0.994190i	$-0.465670\pi$
$947$	6.62497	0.215283	0.107641	+	0.994190i	$0.465670\pi$
$948$	−8.61220	−0.279711
$949$	6.59158	0.213972
$950$	2.81424	0.0913060
$951$	1.64980	0.0534984
$952$	−19.6183	−0.635832
$953$	54.6244	1.76946	0.884729	−	0.466106i	$-0.154343\pi$
$953$	54.6244	1.76946	0.884729	+	0.466106i	$0.154343\pi$
$954$	−2.88703	−0.0934711
$955$	20.7866	0.672638
$956$	−22.9695	−0.742886
$957$	11.3948	0.368343
$958$	10.6818	0.345114
$959$	25.1911	0.813464
$960$	−5.59956	−0.180725
$961$	26.1334	0.843013
$962$	0.291373	0.00939424
$963$	6.45727	0.208083
$964$	−2.52757	−0.0814076
$965$	−3.80431	−0.122465
$966$	0	0
$967$	19.4160	0.624377	0.312189	−	0.950020i	$-0.398938\pi$
$967$	19.4160	0.624377	0.312189	+	0.950020i	$0.398938\pi$
$968$	9.12015	0.293133
$969$	8.63555	0.277414
$970$	0.305179	0.00979870
$971$	23.0571	0.739937	0.369969	−	0.929044i	$-0.379368\pi$
$971$	23.0571	0.739937	0.369969	+	0.929044i	$0.379368\pi$
$972$	1.17034	0.0375387
$973$	−16.0587	−0.514819
$974$	8.28533	0.265479
$975$	4.94931	0.158505
$976$	−1.83561	−0.0587564
$977$	47.2125	1.51046	0.755231	−	0.655459i	$-0.227525\pi$
$977$	47.2125	1.51046	0.755231	+	0.655459i	$0.227525\pi$
$978$	−20.0326	−0.640571
$979$	−30.0649	−0.960877
$980$	1.27781	0.0408182
$981$	−18.9527	−0.605113
$982$	5.20852	0.166211
$983$	−3.64839	−0.116366	−0.0581828	−	0.998306i	$-0.518531\pi$
$983$	−3.64839	−0.116366	−0.0581828	+	0.998306i	$0.518531\pi$
$984$	16.6785	0.531692
$985$	17.7994	0.567138
$986$	−7.70959	−0.245523
$987$	−5.61525	−0.178735
$988$	−17.8965	−0.569365
$989$	0	0
$990$	3.42732	0.108927
$991$	31.7156	1.00748	0.503739	−	0.863856i	$-0.331957\pi$
$991$	31.7156	1.00748	0.503739	+	0.863856i	$0.331957\pi$
$992$	−41.6607	−1.32273
$993$	32.1255	1.01947
$994$	−26.8426	−0.851396
$995$	21.6834	0.687411
$996$	2.39145	0.0757760
$997$	−44.1481	−1.39818	−0.699092	−	0.715032i	$-0.746412\pi$
$997$	−44.1481	−1.39818	−0.699092	+	0.715032i	$0.746412\pi$
$998$	−2.41390	−0.0764107
$999$	−0.0646330	−0.00204490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bq.1.6		15
23.5	odd	22		345.2.m.a.301.2	yes	30
23.14	odd	22		345.2.m.a.196.2	✓	30
23.22	odd	2		7935.2.a.bp.1.6		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.196.2	✓	30	23.14	odd	22
345.2.m.a.301.2	yes	30	23.5	odd	22
7935.2.a.bp.1.6		15	23.22	odd	2
7935.2.a.bq.1.6		15	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-0.910856 q^{2} -1.00000 q^{3} -1.17034 q^{4} +1.00000 q^{5} +0.910856 q^{6} -2.43067 q^{7} +2.88772 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.910856 q^{2} -1.00000 q^{3} -1.17034 q^{4} +1.00000 q^{5} +0.910856 q^{6} -2.43067 q^{7} +2.88772 q^{8} +1.00000 q^{9} -0.910856 q^{10} -3.76274 q^{11} +1.17034 q^{12} -4.94931 q^{13} +2.21399 q^{14} -1.00000 q^{15} -0.289619 q^{16} +2.79498 q^{17} -0.910856 q^{18} -3.08967 q^{19} -1.17034 q^{20} +2.43067 q^{21} +3.42732 q^{22} -2.88772 q^{24} +1.00000 q^{25} +4.50811 q^{26} -1.00000 q^{27} +2.84472 q^{28} +3.02833 q^{29} +0.910856 q^{30} +7.55866 q^{31} -5.51165 q^{32} +3.76274 q^{33} -2.54582 q^{34} -2.43067 q^{35} -1.17034 q^{36} +0.0646330 q^{37} +2.81424 q^{38} +4.94931 q^{39} +2.88772 q^{40} -5.77566 q^{41} -2.21399 q^{42} +7.31352 q^{43} +4.40370 q^{44} +1.00000 q^{45} -2.31016 q^{47} +0.289619 q^{48} -1.09183 q^{49} -0.910856 q^{50} -2.79498 q^{51} +5.79239 q^{52} +3.16958 q^{53} +0.910856 q^{54} -3.76274 q^{55} -7.01911 q^{56} +3.08967 q^{57} -2.75837 q^{58} +11.6195 q^{59} +1.17034 q^{60} +6.33802 q^{61} -6.88486 q^{62} -2.43067 q^{63} +5.59956 q^{64} -4.94931 q^{65} -3.42732 q^{66} +12.6081 q^{67} -3.27108 q^{68} +2.21399 q^{70} -12.1241 q^{71} +2.88772 q^{72} -1.33182 q^{73} -0.0588714 q^{74} -1.00000 q^{75} +3.61596 q^{76} +9.14600 q^{77} -4.50811 q^{78} -7.35871 q^{79} -0.289619 q^{80} +1.00000 q^{81} +5.26079 q^{82} +2.04338 q^{83} -2.84472 q^{84} +2.79498 q^{85} -6.66156 q^{86} -3.02833 q^{87} -10.8658 q^{88} +7.99014 q^{89} -0.910856 q^{90} +12.0302 q^{91} -7.55866 q^{93} +2.10422 q^{94} -3.08967 q^{95} +5.51165 q^{96} -0.335046 q^{97} +0.994498 q^{98} -3.76274 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{3} + 12 q^{4} + 15 q^{5} + 5 q^{7} + 15 q^{9}+O(q^{10}) \) 15 * q - 15 * q^3 + 12 * q^4 + 15 * q^5 + 5 * q^7 + 15 * q^9	\( 15 q - 15 q^{3} + 12 q^{4} + 15 q^{5} + 5 q^{7} + 15 q^{9} - 13 q^{11} - 12 q^{12} - 24 q^{13} - 15 q^{14} - 15 q^{15} + 2 q^{16} - 2 q^{17} - 13 q^{19} + 12 q^{20} - 5 q^{21} + 9 q^{22} + 15 q^{25} - 9 q^{26} - 15 q^{27} - q^{28} - 3 q^{29} - 22 q^{31} + 13 q^{33} - q^{34} + 5 q^{35} + 12 q^{36} + 6 q^{37} + 17 q^{38} + 24 q^{39} - 20 q^{41} + 15 q^{42} + 4 q^{43} + 18 q^{44} + 15 q^{45} + 7 q^{47} - 2 q^{48} - 10 q^{49} + 2 q^{51} - 55 q^{52} - 4 q^{53} - 13 q^{55} - 25 q^{56} + 13 q^{57} + 2 q^{58} + 9 q^{59} - 12 q^{60} - 13 q^{61} - 7 q^{62} + 5 q^{63} - 26 q^{64} - 24 q^{65} - 9 q^{66} + 32 q^{67} - 27 q^{68} - 15 q^{70} + 14 q^{71} - 43 q^{73} + 11 q^{74} - 15 q^{75} - 88 q^{76} - 21 q^{77} + 9 q^{78} - 33 q^{79} + 2 q^{80} + 15 q^{81} - 35 q^{82} + 12 q^{83} + q^{84} - 2 q^{85} - 77 q^{86} + 3 q^{87} + 37 q^{88} - 29 q^{89} - 20 q^{91} + 22 q^{93} - 20 q^{94} - 13 q^{95} - 18 q^{97} - 19 q^{98} - 13 q^{99}+O(q^{100}) \) 15 * q - 15 * q^3 + 12 * q^4 + 15 * q^5 + 5 * q^7 + 15 * q^9 - 13 * q^11 - 12 * q^12 - 24 * q^13 - 15 * q^14 - 15 * q^15 + 2 * q^16 - 2 * q^17 - 13 * q^19 + 12 * q^20 - 5 * q^21 + 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 - q^28 - 3 * q^29 - 22 * q^31 + 13 * q^33 - q^34 + 5 * q^35 + 12 * q^36 + 6 * q^37 + 17 * q^38 + 24 * q^39 - 20 * q^41 + 15 * q^42 + 4 * q^43 + 18 * q^44 + 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 + 2 * q^51 - 55 * q^52 - 4 * q^53 - 13 * q^55 - 25 * q^56 + 13 * q^57 + 2 * q^58 + 9 * q^59 - 12 * q^60 - 13 * q^61 - 7 * q^62 + 5 * q^63 - 26 * q^64 - 24 * q^65 - 9 * q^66 + 32 * q^67 - 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 + 11 * q^74 - 15 * q^75 - 88 * q^76 - 21 * q^77 + 9 * q^78 - 33 * q^79 + 2 * q^80 + 15 * q^81 - 35 * q^82 + 12 * q^83 + q^84 - 2 * q^85 - 77 * q^86 + 3 * q^87 + 37 * q^88 - 29 * q^89 - 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 - 18 * q^97 - 19 * q^98 - 13 * q^99

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