LMFDB - Embedded newform 7935.2.a.bc.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:	$0$
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	$-0.206302\pi$
$7$	4.21850	1.59444	0.797222	+	0.603686i	$0.206302\pi$
$8$	−8.64724	−3.05726
$9$	1.00000	0.333333
$10$	−2.68673	−0.849618
$11$	5.96051	1.79716	0.898581	−	0.438808i	$-0.144599\pi$
$11$	5.96051	1.79716	0.898581	+	0.438808i	$0.144599\pi$
$12$	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	$-0.397825\pi$
$17$	2.60175	0.631018	0.315509	+	0.948923i	$0.397825\pi$
$18$	−2.68673	−0.633268
$19$	−3.75671	−0.861847	−0.430924	−	0.902388i	$-0.641812\pi$
$19$	−3.75671	−0.861847	−0.430924	+	0.902388i	$0.641812\pi$
$20$	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	$-0.754843\pi$
$37$	−8.73221	−1.43557	−0.717783	+	0.696267i	$0.754843\pi$
$38$	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	$-0.459694\pi$
$43$	1.65624	0.252574	0.126287	+	0.991994i	$0.459694\pi$
$44$	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	$-0.538175\pi$
$53$	−1.74201	−0.239283	−0.119642	+	0.992817i	$0.538175\pi$
$54$	−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	$-0.533005\pi$
$61$	−1.61675	−0.207003	−0.103502	+	0.994629i	$0.533005\pi$
$62$	−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	$-0.520408\pi$
$67$	−1.04885	−0.128138	−0.0640688	+	0.997945i	$0.520408\pi$
$68$	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	$-0.697302\pi$
$79$	−10.3264	−1.16182	−0.580908	+	0.813969i	$0.697302\pi$
$80$	12.7958	1.43061
$81$	1.00000	0.111111
$82$	6.99020	0.771939
$83$	13.0094	1.42796	0.713981	−	0.700165i	$-0.246890\pi$
$83$	13.0094	1.42796	0.713981	+	0.700165i	$0.246890\pi$
$84$	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	$-0.502144\pi$
$89$	−0.127100	−0.0134726	−0.00673630	+	0.999977i	$0.502144\pi$
$90$	−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	$-0.503769\pi$
$97$	−0.233200	−0.0236779	−0.0118390	+	0.999930i	$0.503769\pi$
$98$	−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	$-0.707695\pi$
$103$	−12.3242	−1.21434	−0.607168	+	0.794573i	$0.707695\pi$
$104$	31.2749	3.06675
$105$	4.21850	0.411684
$106$	4.68030	0.454591
$107$	−10.8965	−1.05341	−0.526703	−	0.850049i	$-0.676572\pi$
$107$	−10.8965	−1.05341	−0.526703	+	0.850049i	$0.676572\pi$
$108$	5.21850	0.502151
$109$	12.3637	1.18422	0.592112	−	0.805856i	$-0.298294\pi$
$109$	12.3637	1.18422	0.592112	+	0.805856i	$0.298294\pi$
$110$	−16.0143	−1.52690
$111$	−8.73221	−0.828825
$112$	53.9789	5.10053
$113$	19.7518	1.85809	0.929047	−	0.369962i	$-0.120629\pi$
$113$	19.7518	1.85809	0.929047	+	0.369962i	$0.120629\pi$
$114$	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	$-0.589989\pi$
$137$	−6.53025	−0.557917	−0.278958	+	0.960303i	$0.589989\pi$
$138$	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	$-0.337025\pi$
$149$	11.9605	0.979843	0.489922	+	0.871767i	$0.337025\pi$
$150$	−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	$-0.557050\pi$
$157$	−4.46743	−0.356540	−0.178270	+	0.983982i	$0.557050\pi$
$158$	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	$-0.368197\pi$
$181$	10.8259	0.804682	0.402341	+	0.915490i	$0.368197\pi$
$182$	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	$-0.491281\pi$
$191$	0.757002	0.0547747	0.0273874	+	0.999625i	$0.491281\pi$
$192$	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	$-0.580892\pi$
$199$	−7.09295	−0.502806	−0.251403	+	0.967883i	$0.580892\pi$
$200$	−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	$-0.314037\pi$
$227$	16.6198	1.10310	0.551548	+	0.834143i	$0.314037\pi$
$228$	−19.6044	−1.29833
$229$	11.9210	0.787763	0.393882	−	0.919161i	$-0.371132\pi$
$229$	11.9210	0.787763	0.393882	+	0.919161i	$0.371132\pi$
$230$	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	$-0.437018\pi$
$241$	6.10334	0.393150	0.196575	+	0.980489i	$0.437018\pi$
$242$	−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	$-0.345574\pi$
$251$	14.7763	0.932672	0.466336	+	0.884608i	$0.345574\pi$
$252$	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	$-0.357050\pi$
$263$	14.0813	0.868291	0.434145	+	0.900843i	$0.357050\pi$
$264$	−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	$-0.301225\pi$
$281$	19.6016	1.16933	0.584667	+	0.811273i	$0.301225\pi$
$282$	6.65367	0.396220
$283$	18.7036	1.11182	0.555908	−	0.831244i	$-0.312371\pi$
$283$	18.7036	1.11182	0.555908	+	0.831244i	$0.312371\pi$
$284$	−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	$-0.395495\pi$
$293$	11.0388	0.644891	0.322446	+	0.946588i	$0.395495\pi$
$294$	−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	$-0.206926\pi$
$313$	28.1666	1.59207	0.796036	+	0.605249i	$0.206926\pi$
$314$	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	$-0.846485\pi$
$337$	−32.5274	−1.77188	−0.885940	+	0.463801i	$0.846485\pi$
$338$	−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	$-0.825288\pi$
$359$	−32.3283	−1.70622	−0.853112	+	0.521728i	$0.825288\pi$
$360$	−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	$-0.371693\pi$
$367$	15.0293	0.784521	0.392260	+	0.919854i	$0.371693\pi$
$368$	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	$-0.753857\pi$
$373$	−27.6419	−1.43124	−0.715622	+	0.698488i	$0.753857\pi$
$374$	−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	$-0.357737\pi$
$379$	16.8281	0.864400	0.432200	+	0.901778i	$0.357737\pi$
$380$	−19.6044	−1.00568
$381$	−1.64614	−0.0843346
$382$	−2.03386	−0.104061
$383$	−36.1437	−1.84686	−0.923428	−	0.383771i	$-0.874625\pi$
$383$	−36.1437	−1.84686	−0.923428	+	0.383771i	$0.874625\pi$
$384$	−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	$-0.676185\pi$
$389$	−20.7356	−1.05134	−0.525669	+	0.850689i	$0.676185\pi$
$390$	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	$-0.456186\pi$
$401$	5.49528	0.274421	0.137211	+	0.990542i	$0.456186\pi$
$402$	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	$-0.560070\pi$
$419$	−7.68000	−0.375193	−0.187596	+	0.982246i	$0.560070\pi$
$420$	22.0143	1.07419
$421$	−20.4132	−0.994880	−0.497440	−	0.867498i	$-0.665727\pi$
$421$	−20.4132	−0.994880	−0.497440	+	0.867498i	$0.665727\pi$
$422$	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	$-0.473867\pi$
$431$	3.40503	0.164015	0.0820074	+	0.996632i	$0.473867\pi$
$432$	12.7958	0.615636
$433$	−19.8725	−0.955010	−0.477505	−	0.878629i	$-0.658459\pi$
$433$	−19.8725	−0.955010	−0.477505	+	0.878629i	$0.658459\pi$
$434$	−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	$-0.709922\pi$
$457$	−26.1966	−1.22543	−0.612713	+	0.790305i	$0.709922\pi$
$458$	−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	$-0.730999\pi$
$467$	−28.6837	−1.32732	−0.663662	+	0.748032i	$0.730999\pi$
$468$	−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	$-0.575529\pi$
$479$	−10.2891	−0.470123	−0.235061	+	0.971981i	$0.575529\pi$
$480$	−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	$-0.615774\pi$
$503$	−15.9572	−0.711497	−0.355748	+	0.934582i	$0.615774\pi$
$504$	−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	$-0.808202\pi$
$521$	−37.6114	−1.64779	−0.823893	+	0.566745i	$0.808202\pi$
$522$	−27.3482	−1.19700
$523$	15.2433	0.666543	0.333271	−	0.942831i	$-0.391847\pi$
$523$	15.2433	0.666543	0.333271	+	0.942831i	$0.391847\pi$
$524$	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	$-0.530454\pi$
$557$	−4.50910	−0.191057	−0.0955284	+	0.995427i	$0.530454\pi$
$558$	−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	$-0.620122\pi$
$563$	−17.4863	−0.736961	−0.368481	+	0.929635i	$0.620122\pi$
$564$	−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	$-0.247491\pi$
$569$	33.9991	1.42532	0.712659	+	0.701511i	$0.247491\pi$
$570$	10.0932	0.422759
$571$	24.7878	1.03734	0.518669	−	0.854975i	$-0.326428\pi$
$571$	24.7878	1.03734	0.518669	+	0.854975i	$0.326428\pi$
$572$	−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	$-0.456963\pi$
$613$	6.67467	0.269587	0.134794	+	0.990874i	$0.456963\pi$
$614$	20.0924	0.810862
$615$	−2.60175	−0.104913
$616$	−217.430	−8.76049
$617$	1.25611	0.0505689	0.0252845	−	0.999680i	$-0.491951\pi$
$617$	1.25611	0.0505689	0.0252845	+	0.999680i	$0.491951\pi$
$618$	33.1117	1.33195
$619$	−20.0708	−0.806713	−0.403356	−	0.915043i	$-0.632156\pi$
$619$	−20.0708	−0.806713	−0.403356	+	0.915043i	$0.632156\pi$
$620$	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	$-0.557898\pi$
$631$	−9.08791	−0.361784	−0.180892	+	0.983503i	$0.557898\pi$
$632$	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	$-0.563217\pi$
$641$	−9.99050	−0.394601	−0.197300	+	0.980343i	$0.563217\pi$
$642$	29.2760	1.15543
$643$	−38.2772	−1.50951	−0.754753	−	0.656009i	$-0.772243\pi$
$643$	−38.2772	−1.50951	−0.754753	+	0.656009i	$0.772243\pi$
$644$	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	$-0.335619\pi$
$659$	25.3511	0.987538	0.493769	+	0.869593i	$0.335619\pi$
$660$	31.1049	1.21076
$661$	36.7273	1.42853	0.714263	−	0.699877i	$-0.246762\pi$
$661$	36.7273	1.42853	0.714263	+	0.699877i	$0.246762\pi$
$662$	−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	$-0.206201\pi$
$677$	41.4961	1.59483	0.797413	+	0.603434i	$0.206201\pi$
$678$	−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	$-0.645330\pi$
$701$	−23.3454	−0.881742	−0.440871	+	0.897570i	$0.645330\pi$
$702$	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	$-0.410054\pi$
$709$	14.8488	0.557658	0.278829	+	0.960341i	$0.410054\pi$
$710$	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	$-0.558645\pi$
$727$	−9.87920	−0.366399	−0.183200	+	0.983076i	$0.558645\pi$
$728$	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	$-0.153420\pi$
$733$	47.9793	1.77216	0.886078	+	0.463537i	$0.153420\pi$
$734$	−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	$-0.434057\pi$
$743$	11.2133	0.411376	0.205688	+	0.978618i	$0.434057\pi$
$744$	−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	$-0.299111\pi$
$751$	32.3395	1.18009	0.590043	+	0.807372i	$0.299111\pi$
$752$	−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	$-0.481456\pi$
$757$	3.20394	0.116449	0.0582247	+	0.998304i	$0.481456\pi$
$758$	−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	$-0.526903\pi$
$769$	−4.68189	−0.168833	−0.0844166	+	0.996431i	$0.526903\pi$
$770$	−67.5562	−2.43456
$771$	−8.44036	−0.303972
$772$	5.61723	0.202169
$773$	5.73909	0.206421	0.103210	−	0.994660i	$-0.467089\pi$
$773$	5.73909	0.206421	0.103210	+	0.994660i	$0.467089\pi$
$774$	−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	$-0.606025\pi$
$787$	−18.3449	−0.653926	−0.326963	+	0.945037i	$0.606025\pi$
$788$	−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	$-0.773430\pi$
$797$	−42.7529	−1.51439	−0.757193	+	0.653191i	$0.773430\pi$
$798$	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	$-0.340911\pi$
$827$	27.5639	0.958489	0.479245	+	0.877681i	$0.340911\pi$
$828$	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	$-0.849638\pi$
$839$	−51.5870	−1.78098	−0.890490	+	0.455003i	$0.849638\pi$
$840$	−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	$-0.443655\pi$
$881$	10.4532	0.352178	0.176089	+	0.984374i	$0.443655\pi$
$882$	−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	$-0.773550\pi$
$907$	−45.6228	−1.51488	−0.757439	+	0.652905i	$0.773550\pi$
$908$	86.7305	2.87825
$909$	−6.08577	−0.201852
$910$	40.9921	1.35887
$911$	8.81521	0.292061	0.146031	−	0.989280i	$-0.453350\pi$
$911$	8.81521	0.292061	0.146031	+	0.989280i	$0.453350\pi$
$912$	−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	$-0.361400\pi$
$919$	25.5735	0.843592	0.421796	+	0.906691i	$0.361400\pi$
$920$	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	$-0.267448\pi$
$937$	40.8530	1.33461	0.667305	+	0.744785i	$0.267448\pi$
$938$	11.8876	0.388145
$939$	28.1666	0.919184
$940$	−12.9236	−0.421521
$941$	1.72871	0.0563545	0.0281772	−	0.999603i	$-0.491030\pi$
$941$	1.72871	0.0563545	0.0281772	+	0.999603i	$0.491030\pi$
$942$	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	$-0.313339\pi$
$953$	34.1663	1.10675	0.553377	+	0.832931i	$0.313339\pi$
$954$	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	$-0.198658\pi$
$971$	50.5733	1.62297	0.811487	+	0.584370i	$0.198658\pi$
$972$	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	$-0.343081\pi$
$977$	29.5847	0.946499	0.473250	+	0.880928i	$0.343081\pi$
$978$	−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	$-0.232132\pi$
$983$	46.7574	1.49133	0.745664	+	0.666322i	$0.232132\pi$
$984$	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.bc.1.1	yes	5
23.22	odd	2		7935.2.a.bb.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bb.1.1	✓	5	23.22	odd	2
7935.2.a.bc.1.1	yes	5	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)

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

Related objects

Downloads

Learn more