LMFDB - Embedded newform 7935.2.a.bb.1.1

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:	$5$
Coefficient field:	5.5.3370660.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 9x^{3} - 2x^{2} + 16x + 6 $ x^5 - 9x^3 - 2x^2 + 16*x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.68673$ 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)

$f(q)$	$=$	$q-2.68673 q^{2} +1.00000 q^{3} +5.21850 q^{4} -1.00000 q^{5} -2.68673 q^{6} -4.21850 q^{7} -8.64724 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.68673 q^{2} +1.00000 q^{3} +5.21850 q^{4} -1.00000 q^{5} -2.68673 q^{6} -4.21850 q^{7} -8.64724 q^{8} +1.00000 q^{9} +2.68673 q^{10} -5.96051 q^{11} +5.21850 q^{12} -3.61675 q^{13} +11.3340 q^{14} -1.00000 q^{15} +12.7958 q^{16} -2.60175 q^{17} -2.68673 q^{18} +3.75671 q^{19} -5.21850 q^{20} -4.21850 q^{21} +16.0143 q^{22} -8.64724 q^{24} +1.00000 q^{25} +9.71722 q^{26} +1.00000 q^{27} -22.0143 q^{28} +10.1790 q^{29} +2.68673 q^{30} +2.21850 q^{31} -17.0842 q^{32} -5.96051 q^{33} +6.99020 q^{34} +4.21850 q^{35} +5.21850 q^{36} +8.73221 q^{37} -10.0932 q^{38} -3.61675 q^{39} +8.64724 q^{40} -2.60175 q^{41} +11.3340 q^{42} -1.65624 q^{43} -31.1049 q^{44} -1.00000 q^{45} -2.47649 q^{47} +12.7958 q^{48} +10.7958 q^{49} -2.68673 q^{50} -2.60175 q^{51} -18.8740 q^{52} +1.74201 q^{53} -2.68673 q^{54} +5.96051 q^{55} +36.4784 q^{56} +3.75671 q^{57} -27.3482 q^{58} +8.03905 q^{59} -5.21850 q^{60} +1.61675 q^{61} -5.96051 q^{62} -4.21850 q^{63} +20.3092 q^{64} +3.61675 q^{65} +16.0143 q^{66} +1.04885 q^{67} -13.5773 q^{68} -11.3340 q^{70} -6.25572 q^{71} -8.64724 q^{72} +7.13016 q^{73} -23.4611 q^{74} +1.00000 q^{75} +19.6044 q^{76} +25.1444 q^{77} +9.71722 q^{78} +10.3264 q^{79} -12.7958 q^{80} +1.00000 q^{81} +6.99020 q^{82} -13.0094 q^{83} -22.0143 q^{84} +2.60175 q^{85} +4.44986 q^{86} +10.1790 q^{87} +51.5419 q^{88} +0.127100 q^{89} +2.68673 q^{90} +15.2573 q^{91} +2.21850 q^{93} +6.65367 q^{94} -3.75671 q^{95} -17.0842 q^{96} +0.233200 q^{97} -29.0053 q^{98} -5.96051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9	$ 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9} - 6 q^{11} + 8 q^{12} - 6 q^{13} + 6 q^{14} - 5 q^{15} + 10 q^{16} - 7 q^{17} + 4 q^{19} - 8 q^{20} - 3 q^{21} + 8 q^{22} - 6 q^{24} + 5 q^{25} + 10 q^{26} + 5 q^{27} - 38 q^{28} + 9 q^{29} - 7 q^{31} - 12 q^{32} - 6 q^{33} - 4 q^{34} + 3 q^{35} + 8 q^{36} - q^{37} - 26 q^{38} - 6 q^{39} + 6 q^{40} - 7 q^{41} + 6 q^{42} - 20 q^{43} - 18 q^{44} - 5 q^{45} + 10 q^{48} - 7 q^{51} - 22 q^{52} + 3 q^{53} + 6 q^{55} + 18 q^{56} + 4 q^{57} - 14 q^{58} + q^{59} - 8 q^{60} - 4 q^{61} - 6 q^{62} - 3 q^{63} + 18 q^{64} + 6 q^{65} + 8 q^{66} + 5 q^{67} - 32 q^{68} - 6 q^{70} + q^{71} - 6 q^{72} - 6 q^{73} - 48 q^{74} + 5 q^{75} + 6 q^{76} + 12 q^{77} + 10 q^{78} - 10 q^{80} + 5 q^{81} - 4 q^{82} - 41 q^{83} - 38 q^{84} + 7 q^{85} + 2 q^{86} + 9 q^{87} + 84 q^{88} - 18 q^{89} + 16 q^{91} - 7 q^{93} + 4 q^{94} - 4 q^{95} - 12 q^{96} - 26 q^{97} - 24 q^{98} - 6 q^{99}+O(q^{100}) $ 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9 - 6 * q^11 + 8 * q^12 - 6 * q^13 + 6 * q^14 - 5 * q^15 + 10 * q^16 - 7 * q^17 + 4 * q^19 - 8 * q^20 - 3 * q^21 + 8 * q^22 - 6 * q^24 + 5 * q^25 + 10 * q^26 + 5 * q^27 - 38 * q^28 + 9 * q^29 - 7 * q^31 - 12 * q^32 - 6 * q^33 - 4 * q^34 + 3 * q^35 + 8 * q^36 - q^37 - 26 * q^38 - 6 * q^39 + 6 * q^40 - 7 * q^41 + 6 * q^42 - 20 * q^43 - 18 * q^44 - 5 * q^45 + 10 * q^48 - 7 * q^51 - 22 * q^52 + 3 * q^53 + 6 * q^55 + 18 * q^56 + 4 * q^57 - 14 * q^58 + q^59 - 8 * q^60 - 4 * q^61 - 6 * q^62 - 3 * q^63 + 18 * q^64 + 6 * q^65 + 8 * q^66 + 5 * q^67 - 32 * q^68 - 6 * q^70 + q^71 - 6 * q^72 - 6 * q^73 - 48 * q^74 + 5 * q^75 + 6 * q^76 + 12 * q^77 + 10 * q^78 - 10 * q^80 + 5 * q^81 - 4 * q^82 - 41 * q^83 - 38 * q^84 + 7 * q^85 + 2 * q^86 + 9 * q^87 + 84 * q^88 - 18 * q^89 + 16 * q^91 - 7 * q^93 + 4 * q^94 - 4 * q^95 - 12 * q^96 - 26 * q^97 - 24 * q^98 - 6 * 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 $

$2$	−2.68673	−1.89980	−0.949901	−	0.312550i	$-0.898817\pi$
$2$	−2.68673	−1.89980	−0.949901	+	0.312550i	$0.898817\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.21850	2.60925
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.68673	−1.09685
$7$	−4.21850	−1.59444	−0.797222	−	0.603686i	$-0.793698\pi$
$7$	−4.21850	−1.59444	−0.797222	+	0.603686i	$0.793698\pi$
$8$	−8.64724	−3.05726
$9$	1.00000	0.333333
$10$	2.68673	0.849618
$11$	−5.96051	−1.79716	−0.898581	−	0.438808i	$-0.855401\pi$
$11$	−5.96051	−1.79716	−0.898581	+	0.438808i	$0.855401\pi$
$12$	5.21850	1.50645
$13$	−3.61675	−1.00311	−0.501553	−	0.865127i	$-0.667238\pi$
$13$	−3.61675	−1.00311	−0.501553	+	0.865127i	$0.667238\pi$
$14$	11.3340	3.02913
$15$	−1.00000	−0.258199
$16$	12.7958	3.19894
$17$	−2.60175	−0.631018	−0.315509	−	0.948923i	$-0.602175\pi$
$17$	−2.60175	−0.631018	−0.315509	+	0.948923i	$0.602175\pi$
$18$	−2.68673	−0.633268
$19$	3.75671	0.861847	0.430924	−	0.902388i	$-0.358188\pi$
$19$	3.75671	0.861847	0.430924	+	0.902388i	$0.358188\pi$
$20$	−5.21850	−1.16689
$21$	−4.21850	−0.920553
$22$	16.0143	3.41425
$23$	0	0
$23$	0	0
$24$	−8.64724	−1.76511
$25$	1.00000	0.200000
$26$	9.71722	1.90570
$27$	1.00000	0.192450
$28$	−22.0143	−4.16030
$29$	10.1790	1.89019	0.945097	−	0.326788i	$-0.105966\pi$
$29$	10.1790	1.89019	0.945097	+	0.326788i	$0.105966\pi$
$30$	2.68673	0.490527
$31$	2.21850	0.398455	0.199227	−	0.979953i	$-0.436157\pi$
$31$	2.21850	0.398455	0.199227	+	0.979953i	$0.436157\pi$
$32$	−17.0842	−3.02010
$33$	−5.96051	−1.03759
$34$	6.99020	1.19881
$35$	4.21850	0.713057
$36$	5.21850	0.869750
$37$	8.73221	1.43557	0.717783	−	0.696267i	$-0.245157\pi$
$37$	8.73221	1.43557	0.717783	+	0.696267i	$0.245157\pi$
$38$	−10.0932	−1.63734
$39$	−3.61675	−0.579143
$40$	8.64724	1.36725
$41$	−2.60175	−0.406326	−0.203163	−	0.979145i	$-0.565122\pi$
$41$	−2.60175	−0.406326	−0.203163	+	0.979145i	$0.565122\pi$
$42$	11.3340	1.74887
$43$	−1.65624	−0.252574	−0.126287	−	0.991994i	$-0.540306\pi$
$43$	−1.65624	−0.252574	−0.126287	+	0.991994i	$0.540306\pi$
$44$	−31.1049	−4.68924
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−2.47649	−0.361234	−0.180617	−	0.983554i	$-0.557809\pi$
$47$	−2.47649	−0.361234	−0.180617	+	0.983554i	$0.557809\pi$
$48$	12.7958	1.84691
$49$	10.7958	1.54225
$50$	−2.68673	−0.379961
$51$	−2.60175	−0.364318
$52$	−18.8740	−2.61735
$53$	1.74201	0.239283	0.119642	−	0.992817i	$-0.461825\pi$
$53$	1.74201	0.239283	0.119642	+	0.992817i	$0.461825\pi$
$54$	−2.68673	−0.365617
$55$	5.96051	0.803715
$56$	36.4784	4.87463
$57$	3.75671	0.497588
$58$	−27.3482	−3.59100
$59$	8.03905	1.04660	0.523298	−	0.852150i	$-0.324702\pi$
$59$	8.03905	1.04660	0.523298	+	0.852150i	$0.324702\pi$
$60$	−5.21850	−0.673706
$61$	1.61675	0.207003	0.103502	−	0.994629i	$-0.466995\pi$
$61$	1.61675	0.207003	0.103502	+	0.994629i	$0.466995\pi$
$62$	−5.96051	−0.756985
$63$	−4.21850	−0.531481
$64$	20.3092	2.53865
$65$	3.61675	0.448602
$66$	16.0143	1.97122
$67$	1.04885	0.128138	0.0640688	−	0.997945i	$-0.479592\pi$
$67$	1.04885	0.128138	0.0640688	+	0.997945i	$0.479592\pi$
$68$	−13.5773	−1.64648
$69$	0	0
$70$	−11.3340	−1.35467
$71$	−6.25572	−0.742417	−0.371208	−	0.928550i	$-0.621056\pi$
$71$	−6.25572	−0.742417	−0.371208	+	0.928550i	$0.621056\pi$
$72$	−8.64724	−1.01909
$73$	7.13016	0.834522	0.417261	−	0.908787i	$-0.362990\pi$
$73$	7.13016	0.834522	0.417261	+	0.908787i	$0.362990\pi$
$74$	−23.4611	−2.72729
$75$	1.00000	0.115470
$76$	19.6044	2.24878
$77$	25.1444	2.86547
$78$	9.71722	1.10026
$79$	10.3264	1.16182	0.580908	−	0.813969i	$-0.302698\pi$
$79$	10.3264	1.16182	0.580908	+	0.813969i	$0.302698\pi$
$80$	−12.7958	−1.43061
$81$	1.00000	0.111111
$82$	6.99020	0.771939
$83$	−13.0094	−1.42796	−0.713981	−	0.700165i	$-0.753110\pi$
$83$	−13.0094	−1.42796	−0.713981	+	0.700165i	$0.753110\pi$
$84$	−22.0143	−2.40195
$85$	2.60175	0.282200
$86$	4.44986	0.479841
$87$	10.1790	1.09130
$88$	51.5419	5.49439
$89$	0.127100	0.0134726	0.00673630	−	0.999977i	$-0.497856\pi$
$89$	0.127100	0.0134726	0.00673630	+	0.999977i	$0.497856\pi$
$90$	2.68673	0.283206
$91$	15.2573	1.59940
$92$	0	0
$93$	2.21850	0.230048
$94$	6.65367	0.686273
$95$	−3.75671	−0.385430
$96$	−17.0842	−1.74365
$97$	0.233200	0.0236779	0.0118390	−	0.999930i	$-0.496231\pi$
$97$	0.233200	0.0236779	0.0118390	+	0.999930i	$0.496231\pi$
$98$	−29.0053	−2.92997
$99$	−5.96051	−0.599054
$100$	5.21850	0.521850
$101$	−6.08577	−0.605557	−0.302778	−	0.953061i	$-0.597914\pi$
$101$	−6.08577	−0.605557	−0.302778	+	0.953061i	$0.597914\pi$
$102$	6.99020	0.692133
$103$	12.3242	1.21434	0.607168	−	0.794573i	$-0.292305\pi$
$103$	12.3242	1.21434	0.607168	+	0.794573i	$0.292305\pi$
$104$	31.2749	3.06675
$105$	4.21850	0.411684
$106$	−4.68030	−0.454591
$107$	10.8965	1.05341	0.526703	−	0.850049i	$-0.323428\pi$
$107$	10.8965	1.05341	0.526703	+	0.850049i	$0.323428\pi$
$108$	5.21850	0.502151
$109$	−12.3637	−1.18422	−0.592112	−	0.805856i	$-0.701706\pi$
$109$	−12.3637	−1.18422	−0.592112	+	0.805856i	$0.701706\pi$
$110$	−16.0143	−1.52690
$111$	8.73221	0.828825
$112$	−53.9789	−5.10053
$113$	−19.7518	−1.85809	−0.929047	−	0.369962i	$-0.879371\pi$
$113$	−19.7518	−1.85809	−0.929047	+	0.369962i	$0.879371\pi$
$114$	−10.0932	−0.945319
$115$	0	0
$116$	53.1192	4.93199
$117$	−3.61675	−0.334368
$118$	−21.5987	−1.98833
$119$	10.9755	1.00612
$120$	8.64724	0.789381
$121$	24.5277	2.22979
$122$	−4.34376	−0.393266
$123$	−2.60175	−0.234592
$124$	11.5773	1.03967
$125$	−1.00000	−0.0894427
$126$	11.3340	1.00971
$127$	−1.64614	−0.146072	−0.0730359	−	0.997329i	$-0.523269\pi$
$127$	−1.64614	−0.146072	−0.0730359	+	0.997329i	$0.523269\pi$
$128$	−20.3967	−1.80283
$129$	−1.65624	−0.145824
$130$	−9.71722	−0.852256
$131$	19.8105	1.73085	0.865424	−	0.501040i	$-0.167049\pi$
$131$	19.8105	1.73085	0.865424	+	0.501040i	$0.167049\pi$
$132$	−31.1049	−2.70734
$133$	−15.8477	−1.37417
$134$	−2.81798	−0.243436
$135$	−1.00000	−0.0860663
$136$	22.4980	1.92919
$137$	6.53025	0.557917	0.278958	−	0.960303i	$-0.410011\pi$
$137$	6.53025	0.557917	0.278958	+	0.960303i	$0.410011\pi$
$138$	0	0
$139$	4.43516	0.376186	0.188093	−	0.982151i	$-0.439769\pi$
$139$	4.43516	0.376186	0.188093	+	0.982151i	$0.439769\pi$
$140$	22.0143	1.86054
$141$	−2.47649	−0.208558
$142$	16.8074	1.41045
$143$	21.5577	1.80274
$144$	12.7958	1.06631
$145$	−10.1790	−0.845321
$146$	−19.1568	−1.58543
$147$	10.7958	0.890419
$148$	45.5691	3.74575
$149$	−11.9605	−0.979843	−0.489922	−	0.871767i	$-0.662975\pi$
$149$	−11.9605	−0.979843	−0.489922	+	0.871767i	$0.662975\pi$
$150$	−2.68673	−0.219370
$151$	−16.7018	−1.35917	−0.679586	−	0.733596i	$-0.737841\pi$
$151$	−16.7018	−1.35917	−0.679586	+	0.733596i	$0.737841\pi$
$152$	−32.4851	−2.63489
$153$	−2.60175	−0.210339
$154$	−67.5562	−5.44383
$155$	−2.21850	−0.178194
$156$	−18.8740	−1.51113
$157$	4.46743	0.356540	0.178270	−	0.983982i	$-0.442950\pi$
$157$	4.46743	0.356540	0.178270	+	0.983982i	$0.442950\pi$
$158$	−27.7443	−2.20722
$159$	1.74201	0.138150
$160$	17.0842	1.35063
$161$	0	0
$162$	−2.68673	−0.211089
$163$	21.4644	1.68122	0.840612	−	0.541638i	$-0.182196\pi$
$163$	21.4644	1.68122	0.840612	+	0.541638i	$0.182196\pi$
$164$	−13.5773	−1.06021
$165$	5.96051	0.464025
$166$	34.9526	2.71285
$167$	4.70742	0.364271	0.182135	−	0.983273i	$-0.441699\pi$
$167$	4.70742	0.364271	0.182135	+	0.983273i	$0.441699\pi$
$168$	36.4784	2.81437
$169$	0.0808680	0.00622061
$170$	−6.99020	−0.536124
$171$	3.75671	0.287282
$172$	−8.64309	−0.659029
$173$	−12.0910	−0.919259	−0.459630	−	0.888111i	$-0.652018\pi$
$173$	−12.0910	−0.919259	−0.459630	+	0.888111i	$0.652018\pi$
$174$	−27.3482	−2.07326
$175$	−4.21850	−0.318889
$176$	−76.2692	−5.74901
$177$	8.03905	0.604252
$178$	−0.341484	−0.0255953
$179$	15.4667	1.15604	0.578018	−	0.816024i	$-0.303826\pi$
$179$	15.4667	1.15604	0.578018	+	0.816024i	$0.303826\pi$
$180$	−5.21850	−0.388964
$181$	−10.8259	−0.804682	−0.402341	−	0.915490i	$-0.631803\pi$
$181$	−10.8259	−0.804682	−0.402341	+	0.915490i	$0.631803\pi$
$182$	−40.9921	−3.03854
$183$	1.61675	0.119513
$184$	0	0
$185$	−8.73221	−0.642005
$186$	−5.96051	−0.437046
$187$	15.5078	1.13404
$188$	−12.9236	−0.942550
$189$	−4.21850	−0.306851
$190$	10.0932	0.732241
$191$	−0.757002	−0.0547747	−0.0273874	−	0.999625i	$-0.508719\pi$
$191$	−0.757002	−0.0547747	−0.0273874	+	0.999625i	$0.508719\pi$
$192$	20.3092	1.46569
$193$	1.07641	0.0774815	0.0387407	−	0.999249i	$-0.487665\pi$
$193$	1.07641	0.0774815	0.0387407	+	0.999249i	$0.487665\pi$
$194$	−0.626546	−0.0449834
$195$	3.61675	0.259001
$196$	56.3377	4.02412
$197$	−7.47116	−0.532298	−0.266149	−	0.963932i	$-0.585751\pi$
$197$	−7.47116	−0.532298	−0.266149	+	0.963932i	$0.585751\pi$
$198$	16.0143	1.13808
$199$	7.09295	0.502806	0.251403	−	0.967883i	$-0.419108\pi$
$199$	7.09295	0.502806	0.251403	+	0.967883i	$0.419108\pi$
$200$	−8.64724	−0.611452
$201$	1.04885	0.0739803
$202$	16.3508	1.15044
$203$	−42.9402	−3.01381
$204$	−13.5773	−0.950598
$205$	2.60175	0.181714
$206$	−33.1117	−2.30700
$207$	0	0
$208$	−46.2790	−3.20887
$209$	−22.3919	−1.54888
$210$	−11.3340	−0.782118
$211$	−4.76834	−0.328266	−0.164133	−	0.986438i	$-0.552483\pi$
$211$	−4.76834	−0.328266	−0.164133	+	0.986438i	$0.552483\pi$
$212$	9.09067	0.624350
$213$	−6.25572	−0.428635
$214$	−29.2760	−2.00126
$215$	1.65624	0.112955
$216$	−8.64724	−0.588370
$217$	−9.35876	−0.635314
$218$	33.2178	2.24979
$219$	7.13016	0.481812
$220$	31.1049	2.09709
$221$	9.40989	0.632978
$222$	−23.4611	−1.57460
$223$	10.3099	0.690402	0.345201	−	0.938529i	$-0.387811\pi$
$223$	10.3099	0.690402	0.345201	+	0.938529i	$0.387811\pi$
$224$	72.0699	4.81537
$225$	1.00000	0.0666667
$226$	53.0677	3.53001
$227$	−16.6198	−1.10310	−0.551548	−	0.834143i	$-0.685963\pi$
$227$	−16.6198	−1.10310	−0.551548	+	0.834143i	$0.685963\pi$
$228$	19.6044	1.29833
$229$	−11.9210	−0.787763	−0.393882	−	0.919161i	$-0.628868\pi$
$229$	−11.9210	−0.787763	−0.393882	+	0.919161i	$0.628868\pi$
$230$	0	0
$231$	25.1444	1.65438
$232$	−88.0203	−5.77882
$233$	−23.4216	−1.53440	−0.767199	−	0.641409i	$-0.778350\pi$
$233$	−23.4216	−1.53440	−0.767199	+	0.641409i	$0.778350\pi$
$234$	9.71722	0.635234
$235$	2.47649	0.161549
$236$	41.9518	2.73083
$237$	10.3264	0.670775
$238$	−29.4882	−1.91144
$239$	2.10231	0.135987	0.0679935	−	0.997686i	$-0.478340\pi$
$239$	2.10231	0.135987	0.0679935	+	0.997686i	$0.478340\pi$
$240$	−12.7958	−0.825963
$241$	−6.10334	−0.393150	−0.196575	−	0.980489i	$-0.562982\pi$
$241$	−6.10334	−0.393150	−0.196575	+	0.980489i	$0.562982\pi$
$242$	−65.8992	−4.23616
$243$	1.00000	0.0641500
$244$	8.43700	0.540124
$245$	−10.7958	−0.689716
$246$	6.99020	0.445679
$247$	−13.5871	−0.864524
$248$	−19.1839	−1.21818
$249$	−13.0094	−0.824435
$250$	2.68673	0.169924
$251$	−14.7763	−0.932672	−0.466336	−	0.884608i	$-0.654426\pi$
$251$	−14.7763	−0.932672	−0.466336	+	0.884608i	$0.654426\pi$
$252$	−22.0143	−1.38677
$253$	0	0
$254$	4.42274	0.277508
$255$	2.60175	0.162928
$256$	14.1821	0.886379
$257$	−8.44036	−0.526495	−0.263248	−	0.964728i	$-0.584794\pi$
$257$	−8.44036	−0.526495	−0.263248	+	0.964728i	$0.584794\pi$
$258$	4.44986	0.277036
$259$	−36.8368	−2.28893
$260$	18.8740	1.17052
$261$	10.1790	0.630065
$262$	−53.2253	−3.28827
$263$	−14.0813	−0.868291	−0.434145	−	0.900843i	$-0.642950\pi$
$263$	−14.0813	−0.868291	−0.434145	+	0.900843i	$0.642950\pi$
$264$	51.5419	3.17219
$265$	−1.74201	−0.107011
$266$	42.5784	2.61065
$267$	0.127100	0.00777841
$268$	5.47344	0.334343
$269$	9.38311	0.572098	0.286049	−	0.958215i	$-0.407658\pi$
$269$	9.38311	0.572098	0.286049	+	0.958215i	$0.407658\pi$
$270$	2.68673	0.163509
$271$	−7.15723	−0.434771	−0.217385	−	0.976086i	$-0.569753\pi$
$271$	−7.15723	−0.434771	−0.217385	+	0.976086i	$0.569753\pi$
$272$	−33.2914	−2.01859
$273$	15.2573	0.923411
$274$	−17.5450	−1.05993
$275$	−5.96051	−0.359432
$276$	0	0
$277$	−14.4664	−0.869202	−0.434601	−	0.900623i	$-0.643111\pi$
$277$	−14.4664	−0.869202	−0.434601	+	0.900623i	$0.643111\pi$
$278$	−11.9161	−0.714679
$279$	2.21850	0.132818
$280$	−36.4784	−2.18000
$281$	−19.6016	−1.16933	−0.584667	−	0.811273i	$-0.698775\pi$
$281$	−19.6016	−1.16933	−0.584667	+	0.811273i	$0.698775\pi$
$282$	6.65367	0.396220
$283$	−18.7036	−1.11182	−0.555908	−	0.831244i	$-0.687629\pi$
$283$	−18.7036	−1.11182	−0.555908	+	0.831244i	$0.687629\pi$
$284$	−32.6455	−1.93715
$285$	−3.75671	−0.222528
$286$	−57.9196	−3.42486
$287$	10.9755	0.647864
$288$	−17.0842	−1.00670
$289$	−10.2309	−0.601816
$290$	27.3482	1.60594
$291$	0.233200	0.0136705
$292$	37.2088	2.17748
$293$	−11.0388	−0.644891	−0.322446	−	0.946588i	$-0.604505\pi$
$293$	−11.0388	−0.644891	−0.322446	+	0.946588i	$0.604505\pi$
$294$	−29.0053	−1.69162
$295$	−8.03905	−0.468052
$296$	−75.5095	−4.38890
$297$	−5.96051	−0.345864
$298$	32.1346	1.86151
$299$	0	0
$300$	5.21850	0.301290
$301$	6.98685	0.402715
$302$	44.8731	2.58216
$303$	−6.08577	−0.349618
$304$	48.0699	2.75700
$305$	−1.61675	−0.0925747
$306$	6.99020	0.399603
$307$	−7.47838	−0.426814	−0.213407	−	0.976963i	$-0.568456\pi$
$307$	−7.47838	−0.426814	−0.213407	+	0.976963i	$0.568456\pi$
$308$	131.216	7.47674
$309$	12.3242	0.701097
$310$	5.96051	0.338534
$311$	8.98457	0.509468	0.254734	−	0.967011i	$-0.418012\pi$
$311$	8.98457	0.509468	0.254734	+	0.967011i	$0.418012\pi$
$312$	31.2749	1.77059
$313$	−28.1666	−1.59207	−0.796036	−	0.605249i	$-0.793074\pi$
$313$	−28.1666	−1.59207	−0.796036	+	0.605249i	$0.793074\pi$
$314$	−12.0028	−0.677355
$315$	4.21850	0.237686
$316$	53.8886	3.03147
$317$	7.51006	0.421807	0.210903	−	0.977507i	$-0.432359\pi$
$317$	7.51006	0.421807	0.210903	+	0.977507i	$0.432359\pi$
$318$	−4.68030	−0.262458
$319$	−60.6721	−3.39699
$320$	−20.3092	−1.13532
$321$	10.8965	0.608185
$322$	0	0
$323$	−9.77402	−0.543841
$324$	5.21850	0.289917
$325$	−3.61675	−0.200621
$326$	−57.6690	−3.19399
$327$	−12.3637	−0.683712
$328$	22.4980	1.24224
$329$	10.4471	0.575967
$330$	−16.0143	−0.881556
$331$	5.99738	0.329646	0.164823	−	0.986323i	$-0.447295\pi$
$331$	5.99738	0.329646	0.164823	+	0.986323i	$0.447295\pi$
$332$	−67.8894	−3.72591
$333$	8.73221	0.478522
$334$	−12.6475	−0.692043
$335$	−1.04885	−0.0573049
$336$	−53.9789	−2.94479
$337$	32.5274	1.77188	0.885940	−	0.463801i	$-0.153515\pi$
$337$	32.5274	1.77188	0.885940	+	0.463801i	$0.153515\pi$
$338$	−0.217270	−0.0118179
$339$	−19.7518	−1.07277
$340$	13.5773	0.736330
$341$	−13.2234	−0.716087
$342$	−10.0932	−0.545780
$343$	−16.0124	−0.864589
$344$	14.3219	0.772184
$345$	0	0
$346$	32.4851	1.74641
$347$	5.58172	0.299642	0.149821	−	0.988713i	$-0.452130\pi$
$347$	5.58172	0.299642	0.149821	+	0.988713i	$0.452130\pi$
$348$	53.1192	2.84749
$349$	−22.4343	−1.20088	−0.600440	−	0.799670i	$-0.705008\pi$
$349$	−22.4343	−1.20088	−0.600440	+	0.799670i	$0.705008\pi$
$350$	11.3340	0.605826
$351$	−3.61675	−0.193048
$352$	101.831	5.42760
$353$	18.2570	0.971720	0.485860	−	0.874037i	$-0.338506\pi$
$353$	18.2570	0.971720	0.485860	+	0.874037i	$0.338506\pi$
$354$	−21.5987	−1.14796
$355$	6.25572	0.332019
$356$	0.663273	0.0351534
$357$	10.9755	0.580885
$358$	−41.5548	−2.19624
$359$	32.3283	1.70622	0.853112	−	0.521728i	$-0.174712\pi$
$359$	32.3283	1.70622	0.853112	+	0.521728i	$0.174712\pi$
$360$	8.64724	0.455749
$361$	−4.88716	−0.257219
$362$	29.0862	1.52874
$363$	24.5277	1.28737
$364$	79.6200	4.17322
$365$	−7.13016	−0.373210
$366$	−4.34376	−0.227052
$367$	−15.0293	−0.784521	−0.392260	−	0.919854i	$-0.628307\pi$
$367$	−15.0293	−0.784521	−0.392260	+	0.919854i	$0.628307\pi$
$368$	0	0
$369$	−2.60175	−0.135442
$370$	23.4611	1.21968
$371$	−7.34866	−0.381524
$372$	11.5773	0.600253
$373$	27.6419	1.43124	0.715622	−	0.698488i	$-0.246143\pi$
$373$	27.6419	1.43124	0.715622	+	0.698488i	$0.246143\pi$
$374$	−41.6652	−2.15445
$375$	−1.00000	−0.0516398
$376$	21.4148	1.10439
$377$	−36.8149	−1.89606
$378$	11.3340	0.582956
$379$	−16.8281	−0.864400	−0.432200	−	0.901778i	$-0.642263\pi$
$379$	−16.8281	−0.864400	−0.432200	+	0.901778i	$0.642263\pi$
$380$	−19.6044	−1.00568
$381$	−1.64614	−0.0843346
$382$	2.03386	0.104061
$383$	36.1437	1.84686	0.923428	−	0.383771i	$-0.125375\pi$
$383$	36.1437	1.84686	0.923428	+	0.383771i	$0.125375\pi$
$384$	−20.3967	−1.04087
$385$	−25.1444	−1.28148
$386$	−2.89201	−0.147200
$387$	−1.65624	−0.0841913
$388$	1.21696	0.0617816
$389$	20.7356	1.05134	0.525669	−	0.850689i	$-0.323815\pi$
$389$	20.7356	1.05134	0.525669	+	0.850689i	$0.323815\pi$
$390$	−9.71722	−0.492050
$391$	0	0
$392$	−93.3535	−4.71506
$393$	19.8105	0.999305
$394$	20.0730	1.01126
$395$	−10.3264	−0.519580
$396$	−31.1049	−1.56308
$397$	−26.8740	−1.34877	−0.674384	−	0.738381i	$-0.735591\pi$
$397$	−26.8740	−1.34877	−0.674384	+	0.738381i	$0.735591\pi$
$398$	−19.0568	−0.955232
$399$	−15.8477	−0.793376
$400$	12.7958	0.639788
$401$	−5.49528	−0.274421	−0.137211	−	0.990542i	$-0.543814\pi$
$401$	−5.49528	−0.274421	−0.137211	+	0.990542i	$0.543814\pi$
$402$	−2.81798	−0.140548
$403$	−8.02376	−0.399692
$404$	−31.7586	−1.58005
$405$	−1.00000	−0.0496904
$406$	115.369	5.72564
$407$	−52.0484	−2.57994
$408$	22.4980	1.11382
$409$	32.8526	1.62446	0.812228	−	0.583341i	$-0.198255\pi$
$409$	32.8526	1.62446	0.812228	+	0.583341i	$0.198255\pi$
$410$	−6.99020	−0.345221
$411$	6.53025	0.322113
$412$	64.3137	3.16851
$413$	−33.9128	−1.66874
$414$	0	0
$415$	13.0094	0.638604
$416$	61.7894	3.02947
$417$	4.43516	0.217191
$418$	60.1609	2.94256
$419$	7.68000	0.375193	0.187596	−	0.982246i	$-0.439930\pi$
$419$	7.68000	0.375193	0.187596	+	0.982246i	$0.439930\pi$
$420$	22.0143	1.07419
$421$	20.4132	0.994880	0.497440	−	0.867498i	$-0.334273\pi$
$421$	20.4132	0.994880	0.497440	+	0.867498i	$0.334273\pi$
$422$	12.8112	0.623641
$423$	−2.47649	−0.120411
$424$	−15.0636	−0.731551
$425$	−2.60175	−0.126204
$426$	16.8074	0.814321
$427$	−6.82026	−0.330055
$428$	56.8635	2.74860
$429$	21.5577	1.04081
$430$	−4.44986	−0.214591
$431$	−3.40503	−0.164015	−0.0820074	−	0.996632i	$-0.526133\pi$
$431$	−3.40503	−0.164015	−0.0820074	+	0.996632i	$0.526133\pi$
$432$	12.7958	0.615636
$433$	19.8725	0.955010	0.477505	−	0.878629i	$-0.341541\pi$
$433$	19.8725	0.955010	0.477505	+	0.878629i	$0.341541\pi$
$434$	25.1444	1.20697
$435$	−10.1790	−0.488046
$436$	−64.5198	−3.08994
$437$	0	0
$438$	−19.1568	−0.915347
$439$	28.6341	1.36663	0.683315	−	0.730124i	$-0.260538\pi$
$439$	28.6341	1.36663	0.683315	+	0.730124i	$0.260538\pi$
$440$	−51.5419	−2.45717
$441$	10.7958	0.514084
$442$	−25.2818	−1.20253
$443$	−31.1438	−1.47969	−0.739844	−	0.672778i	$-0.765101\pi$
$443$	−31.1438	−1.47969	−0.739844	+	0.672778i	$0.765101\pi$
$444$	45.5691	2.16261
$445$	−0.127100	−0.00602513
$446$	−27.6999	−1.31163
$447$	−11.9605	−0.565713
$448$	−85.6743	−4.04773
$449$	−9.04322	−0.426776	−0.213388	−	0.976968i	$-0.568450\pi$
$449$	−9.04322	−0.426776	−0.213388	+	0.976968i	$0.568450\pi$
$450$	−2.68673	−0.126654
$451$	15.5078	0.730233
$452$	−103.075	−4.84823
$453$	−16.7018	−0.784718
$454$	44.6529	2.09566
$455$	−15.2573	−0.715271
$456$	−32.4851	−1.52126
$457$	26.1966	1.22543	0.612713	−	0.790305i	$-0.290078\pi$
$457$	26.1966	1.22543	0.612713	+	0.790305i	$0.290078\pi$
$458$	32.0285	1.49659
$459$	−2.60175	−0.121439
$460$	0	0
$461$	−10.3286	−0.481052	−0.240526	−	0.970643i	$-0.577320\pi$
$461$	−10.3286	−0.481052	−0.240526	+	0.970643i	$0.577320\pi$
$462$	−67.5562	−3.14300
$463$	23.0067	1.06921	0.534607	−	0.845101i	$-0.320460\pi$
$463$	23.0067	1.06921	0.534607	+	0.845101i	$0.320460\pi$
$464$	130.248	6.04662
$465$	−2.21850	−0.102881
$466$	62.9274	2.91505
$467$	28.6837	1.32732	0.663662	−	0.748032i	$-0.269001\pi$
$467$	28.6837	1.32732	0.663662	+	0.748032i	$0.269001\pi$
$468$	−18.8740	−0.872451
$469$	−4.42458	−0.204308
$470$	−6.65367	−0.306911
$471$	4.46743	0.205848
$472$	−69.5156	−3.19971
$473$	9.87203	0.453916
$474$	−27.7443	−1.27434
$475$	3.75671	0.172369
$476$	57.2757	2.62523
$477$	1.74201	0.0797610
$478$	−5.64833	−0.258349
$479$	10.2891	0.470123	0.235061	−	0.971981i	$-0.424471\pi$
$479$	10.2891	0.470123	0.235061	+	0.971981i	$0.424471\pi$
$480$	17.0842	0.779785
$481$	−31.5822	−1.44002
$482$	16.3980	0.746908
$483$	0	0
$484$	127.998	5.81808
$485$	−0.233200	−0.0105891
$486$	−2.68673	−0.121872
$487$	−33.4499	−1.51576	−0.757879	−	0.652395i	$-0.773764\pi$
$487$	−33.4499	−1.51576	−0.757879	+	0.652395i	$0.773764\pi$
$488$	−13.9804	−0.632863
$489$	21.4644	0.970655
$490$	29.0053	1.31032
$491$	−18.8011	−0.848482	−0.424241	−	0.905549i	$-0.639459\pi$
$491$	−18.8011	−0.848482	−0.424241	+	0.905549i	$0.639459\pi$
$492$	−13.5773	−0.612110
$493$	−26.4833	−1.19275
$494$	36.5047	1.64242
$495$	5.96051	0.267905
$496$	28.3874	1.27463
$497$	26.3897	1.18374
$498$	34.9526	1.56626
$499$	21.6566	0.969483	0.484742	−	0.874657i	$-0.338914\pi$
$499$	21.6566	0.969483	0.484742	+	0.874657i	$0.338914\pi$
$500$	−5.21850	−0.233379
$501$	4.70742	0.210312
$502$	39.6999	1.77189
$503$	15.9572	0.711497	0.355748	−	0.934582i	$-0.384226\pi$
$503$	15.9572	0.711497	0.355748	+	0.934582i	$0.384226\pi$
$504$	36.4784	1.62488
$505$	6.08577	0.270813
$506$	0	0
$507$	0.0808680	0.00359147
$508$	−8.59041	−0.381138
$509$	−38.5934	−1.71062	−0.855311	−	0.518114i	$-0.826634\pi$
$509$	−38.5934	−1.71062	−0.855311	+	0.518114i	$0.826634\pi$
$510$	−6.99020	−0.309531
$511$	−30.0786	−1.33060
$512$	2.69008	0.118886
$513$	3.75671	0.165863
$514$	22.6769	1.00024
$515$	−12.3242	−0.543068
$516$	−8.64309	−0.380491
$517$	14.7612	0.649196
$518$	98.9705	4.34852
$519$	−12.0910	−0.530734
$520$	−31.2749	−1.37149
$521$	37.6114	1.64779	0.823893	−	0.566745i	$-0.191798\pi$
$521$	37.6114	1.64779	0.823893	+	0.566745i	$0.191798\pi$
$522$	−27.3482	−1.19700
$523$	−15.2433	−0.666543	−0.333271	−	0.942831i	$-0.608153\pi$
$523$	−15.2433	−0.666543	−0.333271	+	0.942831i	$0.608153\pi$
$524$	103.381	4.51622
$525$	−4.21850	−0.184111
$526$	37.8326	1.64958
$527$	−5.77200	−0.251432
$528$	−76.2692	−3.31919
$529$	0	0
$530$	4.68030	0.203299
$531$	8.03905	0.348865
$532$	−82.7011	−3.58555
$533$	9.40989	0.407588
$534$	−0.341484	−0.0147774
$535$	−10.8965	−0.471098
$536$	−9.06967	−0.391750
$537$	15.4667	0.667437
$538$	−25.2099	−1.08687
$539$	−64.3482	−2.77167
$540$	−5.21850	−0.224569
$541$	36.8200	1.58301	0.791507	−	0.611160i	$-0.209297\pi$
$541$	36.8200	1.58301	0.791507	+	0.611160i	$0.209297\pi$
$542$	19.2295	0.825979
$543$	−10.8259	−0.464583
$544$	44.4490	1.90573
$545$	12.3637	0.529601
$546$	−40.9921	−1.75430
$547$	−4.77690	−0.204245	−0.102123	−	0.994772i	$-0.532563\pi$
$547$	−4.77690	−0.204245	−0.102123	+	0.994772i	$0.532563\pi$
$548$	34.0781	1.45574
$549$	1.61675	0.0690011
$550$	16.0143	0.682850
$551$	38.2396	1.62906
$552$	0	0
$553$	−43.5621	−1.85245
$554$	38.8673	1.65131
$555$	−8.73221	−0.370662
$556$	23.1449	0.981563
$557$	4.50910	0.191057	0.0955284	−	0.995427i	$-0.469546\pi$
$557$	4.50910	0.191057	0.0955284	+	0.995427i	$0.469546\pi$
$558$	−5.96051	−0.252328
$559$	5.99020	0.253358
$560$	53.9789	2.28103
$561$	15.5078	0.654739
$562$	52.6642	2.22150
$563$	17.4863	0.736961	0.368481	−	0.929635i	$-0.379878\pi$
$563$	17.4863	0.736961	0.368481	+	0.929635i	$0.379878\pi$
$564$	−12.9236	−0.544181
$565$	19.7518	0.830965
$566$	50.2515	2.11223
$567$	−4.21850	−0.177160
$568$	54.0946	2.26976
$569$	−33.9991	−1.42532	−0.712659	−	0.701511i	$-0.752509\pi$
$569$	−33.9991	−1.42532	−0.712659	+	0.701511i	$0.752509\pi$
$570$	10.0932	0.422759
$571$	−24.7878	−1.03734	−0.518669	−	0.854975i	$-0.673572\pi$
$571$	−24.7878	−1.03734	−0.518669	+	0.854975i	$0.673572\pi$
$572$	112.499	4.70381
$573$	−0.757002	−0.0316242
$574$	−29.4882	−1.23081
$575$	0	0
$576$	20.3092	0.846215
$577$	−45.8074	−1.90699	−0.953494	−	0.301413i	$-0.902542\pi$
$577$	−45.8074	−1.90699	−0.953494	+	0.301413i	$0.902542\pi$
$578$	27.4876	1.14333
$579$	1.07641	0.0447340
$580$	−53.1192	−2.20565
$581$	54.8800	2.27681
$582$	−0.626546	−0.0259712
$583$	−10.3833	−0.430030
$584$	−61.6562	−2.55135
$585$	3.61675	0.149534
$586$	29.6581	1.22517
$587$	−23.2923	−0.961376	−0.480688	−	0.876892i	$-0.659613\pi$
$587$	−23.2923	−0.961376	−0.480688	+	0.876892i	$0.659613\pi$
$588$	56.3377	2.32333
$589$	8.33426	0.343407
$590$	21.5987	0.889206
$591$	−7.47116	−0.307322
$592$	111.735	4.59229
$593$	−4.02604	−0.165330	−0.0826648	−	0.996577i	$-0.526343\pi$
$593$	−4.02604	−0.165330	−0.0826648	+	0.996577i	$0.526343\pi$
$594$	16.0143	0.657073
$595$	−10.9755	−0.449952
$596$	−62.4159	−2.55666
$597$	7.09295	0.290295
$598$	0	0
$599$	−10.6251	−0.434129	−0.217065	−	0.976157i	$-0.569648\pi$
$599$	−10.6251	−0.434129	−0.217065	+	0.976157i	$0.569648\pi$
$600$	−8.64724	−0.353022
$601$	−29.2934	−1.19490	−0.597452	−	0.801904i	$-0.703820\pi$
$601$	−29.2934	−1.19490	−0.597452	+	0.801904i	$0.703820\pi$
$602$	−18.7717	−0.765079
$603$	1.04885	0.0427125
$604$	−87.1583	−3.54642
$605$	−24.5277	−0.997192
$606$	16.3508	0.664206
$607$	31.9935	1.29858	0.649288	−	0.760543i	$-0.275067\pi$
$607$	31.9935	1.29858	0.649288	+	0.760543i	$0.275067\pi$
$608$	−64.1805	−2.60286
$609$	−42.9402	−1.74002
$610$	4.34376	0.175874
$611$	8.95686	0.362356
$612$	−13.5773	−0.548828
$613$	−6.67467	−0.269587	−0.134794	−	0.990874i	$-0.543037\pi$
$613$	−6.67467	−0.269587	−0.134794	+	0.990874i	$0.543037\pi$
$614$	20.0924	0.810862
$615$	2.60175	0.104913
$616$	−217.430	−8.76049
$617$	−1.25611	−0.0505689	−0.0252845	−	0.999680i	$-0.508049\pi$
$617$	−1.25611	−0.0505689	−0.0252845	+	0.999680i	$0.508049\pi$
$618$	−33.1117	−1.33195
$619$	20.0708	0.806713	0.403356	−	0.915043i	$-0.367844\pi$
$619$	20.0708	0.806713	0.403356	+	0.915043i	$0.367844\pi$
$620$	−11.5773	−0.464954
$621$	0	0
$622$	−24.1391	−0.967889
$623$	−0.536173	−0.0214813
$624$	−46.2790	−1.85264
$625$	1.00000	0.0400000
$626$	75.6761	3.02462
$627$	−22.3919	−0.894246
$628$	23.3133	0.930302
$629$	−22.7191	−0.905868
$630$	−11.3340	−0.451556
$631$	9.08791	0.361784	0.180892	−	0.983503i	$-0.442102\pi$
$631$	9.08791	0.361784	0.180892	+	0.983503i	$0.442102\pi$
$632$	−89.2952	−3.55197
$633$	−4.76834	−0.189525
$634$	−20.1775	−0.801350
$635$	1.64614	0.0653253
$636$	9.09067	0.360468
$637$	−39.0455	−1.54704
$638$	163.009	6.45360
$639$	−6.25572	−0.247472
$640$	20.3967	0.806251
$641$	9.99050	0.394601	0.197300	−	0.980343i	$-0.436783\pi$
$641$	9.99050	0.394601	0.197300	+	0.980343i	$0.436783\pi$
$642$	−29.2760	−1.15543
$643$	38.2772	1.50951	0.754753	−	0.656009i	$-0.227757\pi$
$643$	38.2772	1.50951	0.754753	+	0.656009i	$0.227757\pi$
$644$	0	0
$645$	1.65624	0.0652143
$646$	26.2601	1.03319
$647$	16.1170	0.633625	0.316812	−	0.948488i	$-0.397387\pi$
$647$	16.1170	0.633625	0.316812	+	0.948488i	$0.397387\pi$
$648$	−8.64724	−0.339696
$649$	−47.9169	−1.88090
$650$	9.71722	0.381141
$651$	−9.35876	−0.366799
$652$	112.012	4.38673
$653$	−29.1754	−1.14172	−0.570861	−	0.821047i	$-0.693390\pi$
$653$	−29.1754	−1.14172	−0.570861	+	0.821047i	$0.693390\pi$
$654$	33.2178	1.29892
$655$	−19.8105	−0.774059
$656$	−33.2914	−1.29981
$657$	7.13016	0.278174
$658$	−28.0685	−1.09422
$659$	−25.3511	−0.987538	−0.493769	−	0.869593i	$-0.664381\pi$
$659$	−25.3511	−0.987538	−0.493769	+	0.869593i	$0.664381\pi$
$660$	31.1049	1.21076
$661$	−36.7273	−1.42853	−0.714263	−	0.699877i	$-0.753238\pi$
$661$	−36.7273	−1.42853	−0.714263	+	0.699877i	$0.753238\pi$
$662$	−16.1133	−0.626262
$663$	9.40989	0.365450
$664$	112.495	4.36565
$665$	15.8477	0.614546
$666$	−23.4611	−0.909098
$667$	0	0
$668$	24.5657	0.950474
$669$	10.3099	0.398604
$670$	2.81798	0.108868
$671$	−9.63664	−0.372018
$672$	72.0699	2.78016
$673$	26.3524	1.01581	0.507905	−	0.861413i	$-0.330420\pi$
$673$	26.3524	1.01581	0.507905	+	0.861413i	$0.330420\pi$
$674$	−87.3922	−3.36622
$675$	1.00000	0.0384900
$676$	0.422010	0.0162311
$677$	−41.4961	−1.59483	−0.797413	−	0.603434i	$-0.793799\pi$
$677$	−41.4961	−1.59483	−0.797413	+	0.603434i	$0.793799\pi$
$678$	53.0677	2.03805
$679$	−0.983757	−0.0377531
$680$	−22.4980	−0.862758
$681$	−16.6198	−0.636872
$682$	35.5277	1.36042
$683$	−22.1651	−0.848125	−0.424062	−	0.905633i	$-0.639396\pi$
$683$	−22.1651	−0.848125	−0.424062	+	0.905633i	$0.639396\pi$
$684$	19.6044	0.749592
$685$	−6.53025	−0.249508
$686$	43.0210	1.64255
$687$	−11.9210	−0.454815
$688$	−21.1928	−0.807969
$689$	−6.30040	−0.240026
$690$	0	0
$691$	0.239939	0.00912769	0.00456385	−	0.999990i	$-0.498547\pi$
$691$	0.239939	0.00912769	0.00456385	+	0.999990i	$0.498547\pi$
$692$	−63.0967	−2.39858
$693$	25.1444	0.955158
$694$	−14.9966	−0.569261
$695$	−4.43516	−0.168235
$696$	−88.0203	−3.33640
$697$	6.76912	0.256399
$698$	60.2748	2.28144
$699$	−23.4216	−0.885885
$700$	−22.0143	−0.832061
$701$	23.3454	0.881742	0.440871	−	0.897570i	$-0.354670\pi$
$701$	23.3454	0.881742	0.440871	+	0.897570i	$0.354670\pi$
$702$	9.71722	0.366753
$703$	32.8043	1.23724
$704$	−121.053	−4.56236
$705$	2.47649	0.0932702
$706$	−49.0515	−1.84608
$707$	25.6728	0.965526
$708$	41.9518	1.57665
$709$	−14.8488	−0.557658	−0.278829	−	0.960341i	$-0.589946\pi$
$709$	−14.8488	−0.557658	−0.278829	+	0.960341i	$0.589946\pi$
$710$	−16.8074	−0.630770
$711$	10.3264	0.387272
$712$	−1.09907	−0.0411892
$713$	0	0
$714$	−29.4882	−1.10357
$715$	−21.5577	−0.806211
$716$	80.7130	3.01639
$717$	2.10231	0.0785121
$718$	−86.8574	−3.24149
$719$	25.1599	0.938306	0.469153	−	0.883117i	$-0.344559\pi$
$719$	25.1599	0.938306	0.469153	+	0.883117i	$0.344559\pi$
$720$	−12.7958	−0.476870
$721$	−51.9895	−1.93619
$722$	13.1305	0.488665
$723$	−6.10334	−0.226986
$724$	−56.4949	−2.09962
$725$	10.1790	0.378039
$726$	−65.8992	−2.44575
$727$	9.87920	0.366399	0.183200	−	0.983076i	$-0.441355\pi$
$727$	9.87920	0.366399	0.183200	+	0.983076i	$0.441355\pi$
$728$	−131.933	−4.88977
$729$	1.00000	0.0370370
$730$	19.1568	0.709025
$731$	4.30913	0.159379
$732$	8.43700	0.311841
$733$	−47.9793	−1.77216	−0.886078	−	0.463537i	$-0.846580\pi$
$733$	−47.9793	−1.77216	−0.886078	+	0.463537i	$0.846580\pi$
$734$	40.3795	1.49043
$735$	−10.7958	−0.398208
$736$	0	0
$737$	−6.25169	−0.230284
$738$	6.99020	0.257313
$739$	46.1479	1.69758	0.848788	−	0.528733i	$-0.177333\pi$
$739$	46.1479	1.69758	0.848788	+	0.528733i	$0.177333\pi$
$740$	−45.5691	−1.67515
$741$	−13.5871	−0.499133
$742$	19.7438	0.724819
$743$	−11.2133	−0.411376	−0.205688	−	0.978618i	$-0.565943\pi$
$743$	−11.2133	−0.411376	−0.205688	+	0.978618i	$0.565943\pi$
$744$	−19.1839	−0.703316
$745$	11.9605	0.438199
$746$	−74.2663	−2.71908
$747$	−13.0094	−0.475988
$748$	80.9274	2.95900
$749$	−45.9670	−1.67960
$750$	2.68673	0.0981054
$751$	−32.3395	−1.18009	−0.590043	−	0.807372i	$-0.700889\pi$
$751$	−32.3395	−1.18009	−0.590043	+	0.807372i	$0.700889\pi$
$752$	−31.6886	−1.15557
$753$	−14.7763	−0.538478
$754$	98.9116	3.60215
$755$	16.7018	0.607840
$756$	−22.0143	−0.800651
$757$	−3.20394	−0.116449	−0.0582247	−	0.998304i	$-0.518544\pi$
$757$	−3.20394	−0.116449	−0.0582247	+	0.998304i	$0.518544\pi$
$758$	45.2124	1.64219
$759$	0	0
$760$	32.4851	1.17836
$761$	2.07519	0.0752255	0.0376128	−	0.999292i	$-0.488025\pi$
$761$	2.07519	0.0752255	0.0376128	+	0.999292i	$0.488025\pi$
$762$	4.42274	0.160219
$763$	52.1561	1.88818
$764$	−3.95042	−0.142921
$765$	2.60175	0.0940666
$766$	−97.1082	−3.50866
$767$	−29.0752	−1.04985
$768$	14.1821	0.511751
$769$	4.68189	0.168833	0.0844166	−	0.996431i	$-0.473097\pi$
$769$	4.68189	0.168833	0.0844166	+	0.996431i	$0.473097\pi$
$770$	67.5562	2.43456
$771$	−8.44036	−0.303972
$772$	5.61723	0.202169
$773$	−5.73909	−0.206421	−0.103210	−	0.994660i	$-0.532911\pi$
$773$	−5.73909	−0.206421	−0.103210	+	0.994660i	$0.532911\pi$
$774$	4.44986	0.159947
$775$	2.21850	0.0796909
$776$	−2.01654	−0.0723895
$777$	−36.8368	−1.32151
$778$	−55.7110	−1.99734
$779$	−9.77402	−0.350191
$780$	18.8740	0.675798
$781$	37.2872	1.33424
$782$	0	0
$783$	10.1790	0.363768
$784$	138.140	4.93357
$785$	−4.46743	−0.159449
$786$	−53.2253	−1.89848
$787$	18.3449	0.653926	0.326963	−	0.945037i	$-0.393975\pi$
$787$	18.3449	0.653926	0.326963	+	0.945037i	$0.393975\pi$
$788$	−38.9883	−1.38890
$789$	−14.0813	−0.501308
$790$	27.7443	0.987099
$791$	83.3230	2.96263
$792$	51.5419	1.83146
$793$	−5.84737	−0.207646
$794$	72.2031	2.56239
$795$	−1.74201	−0.0617826
$796$	37.0146	1.31195
$797$	42.7529	1.51439	0.757193	−	0.653191i	$-0.226570\pi$
$797$	42.7529	1.51439	0.757193	+	0.653191i	$0.226570\pi$
$798$	42.5784	1.50726
$799$	6.44323	0.227945
$800$	−17.0842	−0.604019
$801$	0.127100	0.00449087
$802$	14.7643	0.521346
$803$	−42.4994	−1.49977
$804$	5.47344	0.193033
$805$	0	0
$806$	21.5577	0.759336
$807$	9.38311	0.330301
$808$	52.6251	1.85134
$809$	22.5340	0.792255	0.396127	−	0.918196i	$-0.370354\pi$
$809$	22.5340	0.792255	0.396127	+	0.918196i	$0.370354\pi$
$810$	2.68673	0.0944020
$811$	−40.0650	−1.40687	−0.703436	−	0.710758i	$-0.748352\pi$
$811$	−40.0650	−1.40687	−0.703436	+	0.710758i	$0.748352\pi$
$812$	−224.083	−7.86379
$813$	−7.15723	−0.251015
$814$	139.840	4.90139
$815$	−21.4644	−0.751866
$816$	−33.2914	−1.16543
$817$	−6.22200	−0.217680
$818$	−88.2659	−3.08614
$819$	15.2573	0.533132
$820$	13.5773	0.474138
$821$	22.8102	0.796080	0.398040	−	0.917368i	$-0.369690\pi$
$821$	22.8102	0.796080	0.398040	+	0.917368i	$0.369690\pi$
$822$	−17.5450	−0.611952
$823$	−11.2773	−0.393103	−0.196552	−	0.980493i	$-0.562974\pi$
$823$	−11.2773	−0.393103	−0.196552	+	0.980493i	$0.562974\pi$
$824$	−106.570	−3.71254
$825$	−5.96051	−0.207518
$826$	91.1143	3.17027
$827$	−27.5639	−0.958489	−0.479245	−	0.877681i	$-0.659089\pi$
$827$	−27.5639	−0.958489	−0.479245	+	0.877681i	$0.659089\pi$
$828$	0	0
$829$	−43.3122	−1.50429	−0.752147	−	0.658996i	$-0.770982\pi$
$829$	−43.3122	−1.50429	−0.752147	+	0.658996i	$0.770982\pi$
$830$	−34.9526	−1.21322
$831$	−14.4664	−0.501834
$832$	−73.4532	−2.54653
$833$	−28.0879	−0.973188
$834$	−11.9161	−0.412620
$835$	−4.70742	−0.162907
$836$	−116.852	−4.04141
$837$	2.21850	0.0766826
$838$	−20.6341	−0.712792
$839$	51.5870	1.78098	0.890490	−	0.455003i	$-0.150362\pi$
$839$	51.5870	1.78098	0.890490	+	0.455003i	$0.150362\pi$
$840$	−36.4784	−1.25862
$841$	74.6123	2.57284
$842$	−54.8448	−1.89008
$843$	−19.6016	−0.675115
$844$	−24.8836	−0.856529
$845$	−0.0808680	−0.00278194
$846$	6.65367	0.228758
$847$	−103.470	−3.55527
$848$	22.2903	0.765452
$849$	−18.7036	−0.641907
$850$	6.99020	0.239762
$851$	0	0
$852$	−32.6455	−1.11842
$853$	13.0418	0.446542	0.223271	−	0.974756i	$-0.428327\pi$
$853$	13.0418	0.446542	0.223271	+	0.974756i	$0.428327\pi$
$854$	18.3242	0.627040
$855$	−3.75671	−0.128477
$856$	−94.2248	−3.22054
$857$	−2.05177	−0.0700870	−0.0350435	−	0.999386i	$-0.511157\pi$
$857$	−2.05177	−0.0700870	−0.0350435	+	0.999386i	$0.511157\pi$
$858$	−57.9196	−1.97734
$859$	−12.4005	−0.423101	−0.211550	−	0.977367i	$-0.567851\pi$
$859$	−12.4005	−0.423101	−0.211550	+	0.977367i	$0.567851\pi$
$860$	8.64309	0.294727
$861$	10.9755	0.374044
$862$	9.14840	0.311596
$863$	55.3171	1.88302	0.941509	−	0.336989i	$-0.109409\pi$
$863$	55.3171	1.88302	0.941509	+	0.336989i	$0.109409\pi$
$864$	−17.0842	−0.581218
$865$	12.0910	0.411105
$866$	−53.3919	−1.81433
$867$	−10.2309	−0.347459
$868$	−48.8387	−1.65769
$869$	−61.5509	−2.08797
$870$	27.3482	0.927192
$871$	−3.79343	−0.128536
$872$	106.911	3.62048
$873$	0.233200	0.00789264
$874$	0	0
$875$	4.21850	0.142611
$876$	37.2088	1.25717
$877$	−57.0352	−1.92594	−0.962970	−	0.269608i	$-0.913106\pi$
$877$	−57.0352	−1.92594	−0.962970	+	0.269608i	$0.913106\pi$
$878$	−76.9319	−2.59633
$879$	−11.0388	−0.372328
$880$	76.2692	2.57104
$881$	−10.4532	−0.352178	−0.176089	−	0.984374i	$-0.556345\pi$
$881$	−10.4532	−0.352178	−0.176089	+	0.984374i	$0.556345\pi$
$882$	−29.0053	−0.976658
$883$	−21.6710	−0.729287	−0.364643	−	0.931147i	$-0.618809\pi$
$883$	−21.6710	−0.729287	−0.364643	+	0.931147i	$0.618809\pi$
$884$	49.1055	1.65160
$885$	−8.03905	−0.270230
$886$	83.6750	2.81112
$887$	41.6803	1.39949	0.699744	−	0.714394i	$-0.253297\pi$
$887$	41.6803	1.39949	0.699744	+	0.714394i	$0.253297\pi$
$888$	−75.5095	−2.53393
$889$	6.94427	0.232903
$890$	0.341484	0.0114466
$891$	−5.96051	−0.199685
$892$	53.8023	1.80143
$893$	−9.30346	−0.311328
$894$	32.1346	1.07474
$895$	−15.4667	−0.516995
$896$	86.0436	2.87451
$897$	0	0
$898$	24.2967	0.810790
$899$	22.5822	0.753157
$900$	5.21850	0.173950
$901$	−4.53227	−0.150992
$902$	−41.6652	−1.38730
$903$	6.98685	0.232508
$904$	170.799	5.68068
$905$	10.8259	0.359865
$906$	44.8731	1.49081
$907$	45.6228	1.51488	0.757439	−	0.652905i	$-0.226450\pi$
$907$	45.6228	1.51488	0.757439	+	0.652905i	$0.226450\pi$
$908$	−86.7305	−2.87825
$909$	−6.08577	−0.201852
$910$	40.9921	1.35887
$911$	−8.81521	−0.292061	−0.146031	−	0.989280i	$-0.546650\pi$
$911$	−8.81521	−0.292061	−0.146031	+	0.989280i	$0.546650\pi$
$912$	48.0699	1.59175
$913$	77.5424	2.56628
$914$	−70.3832	−2.32807
$915$	−1.61675	−0.0534480
$916$	−62.2099	−2.05547
$917$	−83.5705	−2.75974
$918$	6.99020	0.230711
$919$	−25.5735	−0.843592	−0.421796	−	0.906691i	$-0.638600\pi$
$919$	−25.5735	−0.843592	−0.421796	+	0.906691i	$0.638600\pi$
$920$	0	0
$921$	−7.47838	−0.246421
$922$	27.7502	0.913904
$923$	22.6253	0.744722
$924$	131.216	4.31670
$925$	8.73221	0.287113
$926$	−61.8128	−2.03130
$927$	12.3242	0.404779
$928$	−173.901	−5.70857
$929$	−31.3237	−1.02770	−0.513849	−	0.857881i	$-0.671781\pi$
$929$	−31.3237	−1.02770	−0.513849	+	0.857881i	$0.671781\pi$
$930$	5.96051	0.195453
$931$	40.5565	1.32919
$932$	−122.226	−4.00363
$933$	8.98457	0.294142
$934$	−77.0654	−2.52166
$935$	−15.5078	−0.507159
$936$	31.2749	1.02225
$937$	−40.8530	−1.33461	−0.667305	−	0.744785i	$-0.732552\pi$
$937$	−40.8530	−1.33461	−0.667305	+	0.744785i	$0.732552\pi$
$938$	11.8876	0.388145
$939$	−28.1666	−0.919184
$940$	12.9236	0.421521
$941$	−1.72871	−0.0563545	−0.0281772	−	0.999603i	$-0.508970\pi$
$941$	−1.72871	−0.0563545	−0.0281772	+	0.999603i	$0.508970\pi$
$942$	−12.0028	−0.391071
$943$	0	0
$944$	102.866	3.34800
$945$	4.21850	0.137228
$946$	−26.5234	−0.862351
$947$	28.5002	0.926131	0.463065	−	0.886324i	$-0.346749\pi$
$947$	28.5002	0.926131	0.463065	+	0.886324i	$0.346749\pi$
$948$	53.8886	1.75022
$949$	−25.7880	−0.837114
$950$	−10.0932	−0.327468
$951$	7.51006	0.243530
$952$	−94.9078	−3.07598
$953$	−34.1663	−1.10675	−0.553377	−	0.832931i	$-0.686661\pi$
$953$	−34.1663	−1.10675	−0.553377	+	0.832931i	$0.686661\pi$
$954$	−4.68030	−0.151530
$955$	0.757002	0.0244960
$956$	10.9709	0.354824
$957$	−60.6721	−1.96125
$958$	−27.6441	−0.893140
$959$	−27.5479	−0.889567
$960$	−20.3092	−0.655476
$961$	−26.0782	−0.841234
$962$	84.8528	2.73576
$963$	10.8965	0.351136
$964$	−31.8503	−1.02583
$965$	−1.07641	−0.0346508
$966$	0	0
$967$	7.66574	0.246514	0.123257	−	0.992375i	$-0.460666\pi$
$967$	7.66574	0.246514	0.123257	+	0.992375i	$0.460666\pi$
$968$	−212.097	−6.81704
$969$	−9.77402	−0.313987
$970$	0.626546	0.0201172
$971$	−50.5733	−1.62297	−0.811487	−	0.584370i	$-0.801342\pi$
$971$	−50.5733	−1.62297	−0.811487	+	0.584370i	$0.801342\pi$
$972$	5.21850	0.167384
$973$	−18.7097	−0.599807
$974$	89.8707	2.87964
$975$	−3.61675	−0.115829
$976$	20.6875	0.662191
$977$	−29.5847	−0.946499	−0.473250	−	0.880928i	$-0.656919\pi$
$977$	−29.5847	−0.946499	−0.473250	+	0.880928i	$0.656919\pi$
$978$	−57.6690	−1.84405
$979$	−0.757582	−0.0242124
$980$	−56.3377	−1.79964
$981$	−12.3637	−0.394741
$982$	50.5134	1.61195
$983$	−46.7574	−1.49133	−0.745664	−	0.666322i	$-0.767868\pi$
$983$	−46.7574	−1.49133	−0.745664	+	0.666322i	$0.767868\pi$
$984$	22.4980	0.717209
$985$	7.47116	0.238051
$986$	71.1534	2.26598
$987$	10.4471	0.332535
$988$	−70.9041	−2.25576
$989$	0	0
$990$	−16.0143	−0.508967
$991$	−46.4486	−1.47549	−0.737745	−	0.675080i	$-0.764109\pi$
$991$	−46.4486	−1.47549	−0.737745	+	0.675080i	$0.764109\pi$
$992$	−37.9014	−1.20337
$993$	5.99738	0.190321
$994$	−70.9020	−2.24888
$995$	−7.09295	−0.224862
$996$	−67.8894	−2.15116
$997$	−17.7676	−0.562706	−0.281353	−	0.959604i	$-0.590783\pi$
$997$	−17.7676	−0.562706	−0.281353	+	0.959604i	$0.590783\pi$
$998$	−58.1854	−1.84183
$999$	8.73221	0.276275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bb.1.1	✓	5
23.22	odd	2		7935.2.a.bc.1.1	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bb.1.1	✓	5	1.1	even	1	trivial
7935.2.a.bc.1.1	yes	5	23.22	odd	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68673 q^{2} +1.00000 q^{3} +5.21850 q^{4} -1.00000 q^{5} -2.68673 q^{6} -4.21850 q^{7} -8.64724 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.68673 q^{2} +1.00000 q^{3} +5.21850 q^{4} -1.00000 q^{5} -2.68673 q^{6} -4.21850 q^{7} -8.64724 q^{8} +1.00000 q^{9} +2.68673 q^{10} -5.96051 q^{11} +5.21850 q^{12} -3.61675 q^{13} +11.3340 q^{14} -1.00000 q^{15} +12.7958 q^{16} -2.60175 q^{17} -2.68673 q^{18} +3.75671 q^{19} -5.21850 q^{20} -4.21850 q^{21} +16.0143 q^{22} -8.64724 q^{24} +1.00000 q^{25} +9.71722 q^{26} +1.00000 q^{27} -22.0143 q^{28} +10.1790 q^{29} +2.68673 q^{30} +2.21850 q^{31} -17.0842 q^{32} -5.96051 q^{33} +6.99020 q^{34} +4.21850 q^{35} +5.21850 q^{36} +8.73221 q^{37} -10.0932 q^{38} -3.61675 q^{39} +8.64724 q^{40} -2.60175 q^{41} +11.3340 q^{42} -1.65624 q^{43} -31.1049 q^{44} -1.00000 q^{45} -2.47649 q^{47} +12.7958 q^{48} +10.7958 q^{49} -2.68673 q^{50} -2.60175 q^{51} -18.8740 q^{52} +1.74201 q^{53} -2.68673 q^{54} +5.96051 q^{55} +36.4784 q^{56} +3.75671 q^{57} -27.3482 q^{58} +8.03905 q^{59} -5.21850 q^{60} +1.61675 q^{61} -5.96051 q^{62} -4.21850 q^{63} +20.3092 q^{64} +3.61675 q^{65} +16.0143 q^{66} +1.04885 q^{67} -13.5773 q^{68} -11.3340 q^{70} -6.25572 q^{71} -8.64724 q^{72} +7.13016 q^{73} -23.4611 q^{74} +1.00000 q^{75} +19.6044 q^{76} +25.1444 q^{77} +9.71722 q^{78} +10.3264 q^{79} -12.7958 q^{80} +1.00000 q^{81} +6.99020 q^{82} -13.0094 q^{83} -22.0143 q^{84} +2.60175 q^{85} +4.44986 q^{86} +10.1790 q^{87} +51.5419 q^{88} +0.127100 q^{89} +2.68673 q^{90} +15.2573 q^{91} +2.21850 q^{93} +6.65367 q^{94} -3.75671 q^{95} -17.0842 q^{96} +0.233200 q^{97} -29.0053 q^{98} -5.96051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9	\( 5 q + 5 q^{3} + 8 q^{4} - 5 q^{5} - 3 q^{7} - 6 q^{8} + 5 q^{9} - 6 q^{11} + 8 q^{12} - 6 q^{13} + 6 q^{14} - 5 q^{15} + 10 q^{16} - 7 q^{17} + 4 q^{19} - 8 q^{20} - 3 q^{21} + 8 q^{22} - 6 q^{24} + 5 q^{25} + 10 q^{26} + 5 q^{27} - 38 q^{28} + 9 q^{29} - 7 q^{31} - 12 q^{32} - 6 q^{33} - 4 q^{34} + 3 q^{35} + 8 q^{36} - q^{37} - 26 q^{38} - 6 q^{39} + 6 q^{40} - 7 q^{41} + 6 q^{42} - 20 q^{43} - 18 q^{44} - 5 q^{45} + 10 q^{48} - 7 q^{51} - 22 q^{52} + 3 q^{53} + 6 q^{55} + 18 q^{56} + 4 q^{57} - 14 q^{58} + q^{59} - 8 q^{60} - 4 q^{61} - 6 q^{62} - 3 q^{63} + 18 q^{64} + 6 q^{65} + 8 q^{66} + 5 q^{67} - 32 q^{68} - 6 q^{70} + q^{71} - 6 q^{72} - 6 q^{73} - 48 q^{74} + 5 q^{75} + 6 q^{76} + 12 q^{77} + 10 q^{78} - 10 q^{80} + 5 q^{81} - 4 q^{82} - 41 q^{83} - 38 q^{84} + 7 q^{85} + 2 q^{86} + 9 q^{87} + 84 q^{88} - 18 q^{89} + 16 q^{91} - 7 q^{93} + 4 q^{94} - 4 q^{95} - 12 q^{96} - 26 q^{97} - 24 q^{98} - 6 q^{99}+O(q^{100}) \) 5 * q + 5 * q^3 + 8 * q^4 - 5 * q^5 - 3 * q^7 - 6 * q^8 + 5 * q^9 - 6 * q^11 + 8 * q^12 - 6 * q^13 + 6 * q^14 - 5 * q^15 + 10 * q^16 - 7 * q^17 + 4 * q^19 - 8 * q^20 - 3 * q^21 + 8 * q^22 - 6 * q^24 + 5 * q^25 + 10 * q^26 + 5 * q^27 - 38 * q^28 + 9 * q^29 - 7 * q^31 - 12 * q^32 - 6 * q^33 - 4 * q^34 + 3 * q^35 + 8 * q^36 - q^37 - 26 * q^38 - 6 * q^39 + 6 * q^40 - 7 * q^41 + 6 * q^42 - 20 * q^43 - 18 * q^44 - 5 * q^45 + 10 * q^48 - 7 * q^51 - 22 * q^52 + 3 * q^53 + 6 * q^55 + 18 * q^56 + 4 * q^57 - 14 * q^58 + q^59 - 8 * q^60 - 4 * q^61 - 6 * q^62 - 3 * q^63 + 18 * q^64 + 6 * q^65 + 8 * q^66 + 5 * q^67 - 32 * q^68 - 6 * q^70 + q^71 - 6 * q^72 - 6 * q^73 - 48 * q^74 + 5 * q^75 + 6 * q^76 + 12 * q^77 + 10 * q^78 - 10 * q^80 + 5 * q^81 - 4 * q^82 - 41 * q^83 - 38 * q^84 + 7 * q^85 + 2 * q^86 + 9 * q^87 + 84 * q^88 - 18 * q^89 + 16 * q^91 - 7 * q^93 + 4 * q^94 - 4 * q^95 - 12 * q^96 - 26 * q^97 - 24 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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