LMFDB - Embedded newform 3971.2.a.k.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3971,2,Mod(1,3971)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3971, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3971.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3971 = 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3971.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:	$31.7085946427$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 13x^{7} + 12x^{6} + 51x^{5} - 38x^{4} - 70x^{3} + 30x^{2} + 27x + 3 $ x^9 - x^8 - 13x^7 + 12x^6 + 51x^5 - 38x^4 - 70x^3 + 30x^2 + 27*x + 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 209)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.23186$ of defining polynomial
Character	$\chi$	$=$	3971.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.23186 q^{2} -2.02769 q^{3} -0.482521 q^{4} +2.63096 q^{5} -2.49783 q^{6} +3.75846 q^{7} -3.05812 q^{8} +1.11154 q^{9} +3.24098 q^{10} -1.00000 q^{11} +0.978405 q^{12} -1.64954 q^{13} +4.62989 q^{14} -5.33478 q^{15} -2.80213 q^{16} -1.41204 q^{17} +1.36926 q^{18} -1.26950 q^{20} -7.62099 q^{21} -1.23186 q^{22} -2.42608 q^{23} +6.20092 q^{24} +1.92197 q^{25} -2.03200 q^{26} +3.82922 q^{27} -1.81354 q^{28} +7.21223 q^{29} -6.57171 q^{30} -9.66660 q^{31} +2.66441 q^{32} +2.02769 q^{33} -1.73944 q^{34} +9.88836 q^{35} -0.536340 q^{36} -9.68506 q^{37} +3.34475 q^{39} -8.04580 q^{40} -12.2344 q^{41} -9.38799 q^{42} -5.93610 q^{43} +0.482521 q^{44} +2.92441 q^{45} -2.98859 q^{46} +0.0866633 q^{47} +5.68186 q^{48} +7.12599 q^{49} +2.36759 q^{50} +2.86318 q^{51} +0.795937 q^{52} -1.19879 q^{53} +4.71707 q^{54} -2.63096 q^{55} -11.4938 q^{56} +8.88446 q^{58} -2.72279 q^{59} +2.57415 q^{60} +11.7585 q^{61} -11.9079 q^{62} +4.17766 q^{63} +8.88643 q^{64} -4.33987 q^{65} +2.49783 q^{66} +4.15566 q^{67} +0.681340 q^{68} +4.91935 q^{69} +12.1811 q^{70} +2.63868 q^{71} -3.39921 q^{72} +12.2328 q^{73} -11.9306 q^{74} -3.89716 q^{75} -3.75846 q^{77} +4.12027 q^{78} +3.17735 q^{79} -7.37230 q^{80} -11.0991 q^{81} -15.0711 q^{82} -1.23059 q^{83} +3.67729 q^{84} -3.71503 q^{85} -7.31244 q^{86} -14.6242 q^{87} +3.05812 q^{88} -15.2049 q^{89} +3.60246 q^{90} -6.19971 q^{91} +1.17064 q^{92} +19.6009 q^{93} +0.106757 q^{94} -5.40259 q^{96} -3.32141 q^{97} +8.77823 q^{98} -1.11154 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - q^{2} + 9 q^{4} + 3 q^{6} - 3 q^{7} + 11 q^{9} - 21 q^{10} - 9 q^{11} + 8 q^{12} - 11 q^{13} - q^{14} - 7 q^{15} + 13 q^{16} - 6 q^{17} - 4 q^{18} + 2 q^{20} - 24 q^{21} + q^{22} + q^{23} + 3 q^{24}+ \cdots - 11 q^{99}+O(q^{100}) $ 9 * q - q^2 + 9 * q^4 + 3 * q^6 - 3 * q^7 + 11 * q^9 - 21 * q^10 - 9 * q^11 + 8 * q^12 - 11 * q^13 - q^14 - 7 * q^15 + 13 * q^16 - 6 * q^17 - 4 * q^18 + 2 * q^20 - 24 * q^21 + q^22 + q^23 + 3 * q^24 + 7 * q^25 - 2 * q^26 + 3 * q^27 + 2 * q^28 - 13 * q^29 - 32 * q^30 - 16 * q^31 + 14 * q^32 - 8 * q^34 + 12 * q^35 - 10 * q^36 - 18 * q^37 + 10 * q^39 - 32 * q^40 - 4 * q^41 - 11 * q^42 - q^43 - 9 * q^44 + 11 * q^45 - 7 * q^46 + 14 * q^47 - 37 * q^48 - 6 * q^49 + 15 * q^50 + 16 * q^51 - 57 * q^52 + 4 * q^53 + 33 * q^54 - 17 * q^56 + 4 * q^58 - 31 * q^59 - 9 * q^60 - 3 * q^61 - 5 * q^62 - 50 * q^63 + 32 * q^64 - 28 * q^65 - 3 * q^66 + 2 * q^67 - 48 * q^68 + 58 * q^70 + 12 * q^71 - 5 * q^72 + 26 * q^73 - 35 * q^74 + 25 * q^75 + 3 * q^77 - 3 * q^78 - 31 * q^79 - 31 * q^80 + 21 * q^81 - 25 * q^82 + 18 * q^83 - 51 * q^84 + 11 * q^85 - 41 * q^86 - 62 * q^87 + 11 * q^89 - 51 * q^90 + 20 * q^91 + 33 * q^92 - 20 * q^93 - 43 * q^94 + 30 * q^96 - 16 * q^97 - 4 * q^98 - 11 * q^99

Coefficient data

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

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

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

$2$	1.23186	0.871056	0.435528	−	0.900175i	$-0.356562\pi$
$2$	1.23186	0.871056	0.435528	+	0.900175i	$0.356562\pi$
$3$	−2.02769	−1.17069	−0.585344	−	0.810785i	$-0.699041\pi$
$3$	−2.02769	−1.17069	−0.585344	+	0.810785i	$0.699041\pi$
$4$	−0.482521	−0.241261
$5$	2.63096	1.17660	0.588301	−	0.808642i	$-0.299797\pi$
$5$	2.63096	1.17660	0.588301	+	0.808642i	$0.299797\pi$
$6$	−2.49783	−1.01974
$7$	3.75846	1.42056	0.710281	−	0.703918i	$-0.248568\pi$
$7$	3.75846	1.42056	0.710281	+	0.703918i	$0.248568\pi$
$8$	−3.05812	−1.08121
$9$	1.11154	0.370512
$10$	3.24098	1.02489
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.978405	0.282441
$13$	−1.64954	−0.457499	−0.228750	−	0.973485i	$-0.573464\pi$
$13$	−1.64954	−0.457499	−0.228750	+	0.973485i	$0.573464\pi$
$14$	4.62989	1.23739
$15$	−5.33478	−1.37744
$16$	−2.80213	−0.700533
$17$	−1.41204	−0.342470	−0.171235	−	0.985230i	$-0.554776\pi$
$17$	−1.41204	−0.342470	−0.171235	+	0.985230i	$0.554776\pi$
$18$	1.36926	0.322737
$19$	0	0
$19$	0	0
$20$	−1.26950	−0.283868
$21$	−7.62099	−1.66304
$22$	−1.23186	−0.262633
$23$	−2.42608	−0.505873	−0.252937	−	0.967483i	$-0.581396\pi$
$23$	−2.42608	−0.505873	−0.252937	+	0.967483i	$0.581396\pi$
$24$	6.20092	1.26576
$25$	1.92197	0.384393
$26$	−2.03200	−0.398508
$27$	3.82922	0.736935
$28$	−1.81354	−0.342726
$29$	7.21223	1.33928	0.669639	−	0.742687i	$-0.266449\pi$
$29$	7.21223	1.33928	0.669639	+	0.742687i	$0.266449\pi$
$30$	−6.57171	−1.19982
$31$	−9.66660	−1.73617	−0.868086	−	0.496413i	$-0.834650\pi$
$31$	−9.66660	−1.73617	−0.868086	+	0.496413i	$0.834650\pi$
$32$	2.66441	0.471005
$33$	2.02769	0.352976
$34$	−1.73944	−0.298311
$35$	9.88836	1.67144
$36$	−0.536340	−0.0893899
$37$	−9.68506	−1.59221	−0.796107	−	0.605156i	$-0.793111\pi$
$37$	−9.68506	−1.59221	−0.796107	+	0.605156i	$0.793111\pi$
$38$	0	0
$39$	3.34475	0.535589
$40$	−8.04580	−1.27215
$41$	−12.2344	−1.91069	−0.955346	−	0.295489i	$-0.904517\pi$
$41$	−12.2344	−1.91069	−0.955346	+	0.295489i	$0.904517\pi$
$42$	−9.38799	−1.44860
$43$	−5.93610	−0.905246	−0.452623	−	0.891702i	$-0.649512\pi$
$43$	−5.93610	−0.905246	−0.452623	+	0.891702i	$0.649512\pi$
$44$	0.482521	0.0727428
$45$	2.92441	0.435945
$46$	−2.98859	−0.440644
$47$	0.0866633	0.0126411	0.00632057	−	0.999980i	$-0.497988\pi$
$47$	0.0866633	0.0126411	0.00632057	+	0.999980i	$0.497988\pi$
$48$	5.68186	0.820106
$49$	7.12599	1.01800
$50$	2.36759	0.334828
$51$	2.86318	0.400926
$52$	0.795937	0.110377
$53$	−1.19879	−0.164666	−0.0823332	−	0.996605i	$-0.526237\pi$
$53$	−1.19879	−0.164666	−0.0823332	+	0.996605i	$0.526237\pi$
$54$	4.71707	0.641912
$55$	−2.63096	−0.354759
$56$	−11.4938	−1.53592
$57$	0	0
$58$	8.88446	1.16659
$59$	−2.72279	−0.354478	−0.177239	−	0.984168i	$-0.556716\pi$
$59$	−2.72279	−0.354478	−0.177239	+	0.984168i	$0.556716\pi$
$60$	2.57415	0.332321
$61$	11.7585	1.50552	0.752760	−	0.658295i	$-0.228722\pi$
$61$	11.7585	1.50552	0.752760	+	0.658295i	$0.228722\pi$
$62$	−11.9079	−1.51230
$63$	4.17766	0.526335
$64$	8.88643	1.11080
$65$	−4.33987	−0.538295
$66$	2.49783	0.307462
$67$	4.15566	0.507694	0.253847	−	0.967244i	$-0.418304\pi$
$67$	4.15566	0.507694	0.253847	+	0.967244i	$0.418304\pi$
$68$	0.681340	0.0826246
$69$	4.91935	0.592220
$70$	12.1811	1.45592
$71$	2.63868	0.313154	0.156577	−	0.987666i	$-0.449954\pi$
$71$	2.63868	0.313154	0.156577	+	0.987666i	$0.449954\pi$
$72$	−3.39921	−0.400600
$73$	12.2328	1.43175	0.715873	−	0.698231i	$-0.246029\pi$
$73$	12.2328	1.43175	0.715873	+	0.698231i	$0.246029\pi$
$74$	−11.9306	−1.38691
$75$	−3.89716	−0.450005
$76$	0	0
$77$	−3.75846	−0.428316
$78$	4.12027	0.466528
$79$	3.17735	0.357480	0.178740	−	0.983896i	$-0.442798\pi$
$79$	3.17735	0.357480	0.178740	+	0.983896i	$0.442798\pi$
$80$	−7.37230	−0.824248
$81$	−11.0991	−1.23323
$82$	−15.0711	−1.66432
$83$	−1.23059	−0.135075	−0.0675373	−	0.997717i	$-0.521514\pi$
$83$	−1.23059	−0.135075	−0.0675373	+	0.997717i	$0.521514\pi$
$84$	3.67729	0.401225
$85$	−3.71503	−0.402951
$86$	−7.31244	−0.788521
$87$	−14.6242	−1.56788
$88$	3.05812	0.325997
$89$	−15.2049	−1.61172	−0.805858	−	0.592109i	$-0.798295\pi$
$89$	−15.2049	−1.61172	−0.805858	+	0.592109i	$0.798295\pi$
$90$	3.60246	0.379733
$91$	−6.19971	−0.649907
$92$	1.17064	0.122047
$93$	19.6009	2.03252
$94$	0.106757	0.0110112
$95$	0	0
$96$	−5.40259	−0.551400
$97$	−3.32141	−0.337238	−0.168619	−	0.985681i	$-0.553931\pi$
$97$	−3.32141	−0.337238	−0.168619	+	0.985681i	$0.553931\pi$
$98$	8.77823	0.886735
$99$	−1.11154	−0.111714
$100$	−0.927390	−0.0927390
$101$	−3.27090	−0.325467	−0.162733	−	0.986670i	$-0.552031\pi$
$101$	−3.27090	−0.325467	−0.162733	+	0.986670i	$0.552031\pi$
$102$	3.52704	0.349229
$103$	−4.53533	−0.446879	−0.223439	−	0.974718i	$-0.571729\pi$
$103$	−4.53533	−0.446879	−0.223439	+	0.974718i	$0.571729\pi$
$104$	5.04448	0.494652
$105$	−20.0505	−1.95673
$106$	−1.47674	−0.143434
$107$	4.59920	0.444621	0.222311	−	0.974976i	$-0.428640\pi$
$107$	4.59920	0.444621	0.222311	+	0.974976i	$0.428640\pi$
$108$	−1.84768	−0.177793
$109$	−12.2192	−1.17038	−0.585192	−	0.810895i	$-0.698981\pi$
$109$	−12.2192	−1.17038	−0.585192	+	0.810895i	$0.698981\pi$
$110$	−3.24098	−0.309015
$111$	19.6383	1.86399
$112$	−10.5317	−0.995151
$113$	0.758905	0.0713918	0.0356959	−	0.999363i	$-0.488635\pi$
$113$	0.758905	0.0713918	0.0356959	+	0.999363i	$0.488635\pi$
$114$	0	0
$115$	−6.38294	−0.595212
$116$	−3.48006	−0.323115
$117$	−1.83352	−0.169509
$118$	−3.35410	−0.308770
$119$	−5.30709	−0.486500
$120$	16.3144	1.48929
$121$	1.00000	0.0909091
$122$	14.4848	1.31139
$123$	24.8076	2.23683
$124$	4.66434	0.418870
$125$	−8.09819	−0.724324
$126$	5.14629	0.458468
$127$	−1.12935	−0.100214	−0.0501069	−	0.998744i	$-0.515956\pi$
$127$	−1.12935	−0.100214	−0.0501069	+	0.998744i	$0.515956\pi$
$128$	5.61803	0.496568
$129$	12.0366	1.05976
$130$	−5.34611	−0.468885
$131$	2.88213	0.251813	0.125907	−	0.992042i	$-0.459816\pi$
$131$	2.88213	0.251813	0.125907	+	0.992042i	$0.459816\pi$
$132$	−0.978405	−0.0851592
$133$	0	0
$134$	5.11919	0.442231
$135$	10.0745	0.867079
$136$	4.31819	0.370281
$137$	−22.7229	−1.94135	−0.970674	−	0.240398i	$-0.922722\pi$
$137$	−22.7229	−1.94135	−0.970674	+	0.240398i	$0.922722\pi$
$138$	6.05995	0.515857
$139$	1.30728	0.110882	0.0554411	−	0.998462i	$-0.482344\pi$
$139$	1.30728	0.110882	0.0554411	+	0.998462i	$0.482344\pi$
$140$	−4.77135	−0.403252
$141$	−0.175727	−0.0147988
$142$	3.25049	0.272775
$143$	1.64954	0.137941
$144$	−3.11467	−0.259556
$145$	18.9751	1.57580
$146$	15.0691	1.24713
$147$	−14.4493	−1.19176
$148$	4.67325	0.384139
$149$	5.05721	0.414303	0.207151	−	0.978309i	$-0.433581\pi$
$149$	5.05721	0.414303	0.207151	+	0.978309i	$0.433581\pi$
$150$	−4.80075	−0.391980
$151$	8.85980	0.721000	0.360500	−	0.932759i	$-0.382606\pi$
$151$	8.85980	0.721000	0.360500	+	0.932759i	$0.382606\pi$
$152$	0	0
$153$	−1.56953	−0.126889
$154$	−4.62989	−0.373087
$155$	−25.4325	−2.04278
$156$	−1.61392	−0.129217
$157$	−16.2238	−1.29480	−0.647399	−	0.762152i	$-0.724143\pi$
$157$	−16.2238	−1.29480	−0.647399	+	0.762152i	$0.724143\pi$
$158$	3.91405	0.311385
$159$	2.43078	0.192773
$160$	7.00995	0.554185
$161$	−9.11833	−0.718625
$162$	−13.6725	−1.07422
$163$	−21.9299	−1.71769	−0.858843	−	0.512239i	$-0.828816\pi$
$163$	−21.9299	−1.71769	−0.858843	+	0.512239i	$0.828816\pi$
$164$	5.90336	0.460975
$165$	5.33478	0.415312
$166$	−1.51591	−0.117658
$167$	−20.7195	−1.60332	−0.801662	−	0.597777i	$-0.796051\pi$
$167$	−20.7195	−1.60332	−0.801662	+	0.597777i	$0.796051\pi$
$168$	23.3059	1.79809
$169$	−10.2790	−0.790694
$170$	−4.57639	−0.350993
$171$	0	0
$172$	2.86429	0.218400
$173$	12.8417	0.976338	0.488169	−	0.872749i	$-0.337665\pi$
$173$	12.8417	0.976338	0.488169	+	0.872749i	$0.337665\pi$
$174$	−18.0149	−1.36571
$175$	7.22363	0.546055
$176$	2.80213	0.211219
$177$	5.52099	0.414983
$178$	−18.7303	−1.40390
$179$	0.801793	0.0599288	0.0299644	−	0.999551i	$-0.490461\pi$
$179$	0.801793	0.0599288	0.0299644	+	0.999551i	$0.490461\pi$
$180$	−1.41109	−0.105176
$181$	−11.2861	−0.838893	−0.419446	−	0.907780i	$-0.637776\pi$
$181$	−11.2861	−0.838893	−0.419446	+	0.907780i	$0.637776\pi$
$182$	−7.63718	−0.566105
$183$	−23.8426	−1.76250
$184$	7.41925	0.546954
$185$	−25.4810	−1.87340
$186$	24.1455	1.77044
$187$	1.41204	0.103259
$188$	−0.0418169	−0.00304981
$189$	14.3920	1.04686
$190$	0	0
$191$	7.65003	0.553536	0.276768	−	0.960937i	$-0.410737\pi$
$191$	7.65003	0.553536	0.276768	+	0.960937i	$0.410737\pi$
$192$	−18.0190	−1.30041
$193$	8.91369	0.641621	0.320811	−	0.947143i	$-0.396045\pi$
$193$	8.91369	0.641621	0.320811	+	0.947143i	$0.396045\pi$
$194$	−4.09151	−0.293753
$195$	8.79992	0.630176
$196$	−3.43844	−0.245603
$197$	2.10950	0.150296	0.0751480	−	0.997172i	$-0.476057\pi$
$197$	2.10950	0.150296	0.0751480	+	0.997172i	$0.476057\pi$
$198$	−1.36926	−0.0973088
$199$	5.51092	0.390659	0.195329	−	0.980738i	$-0.437422\pi$
$199$	5.51092	0.390659	0.195329	+	0.980738i	$0.437422\pi$
$200$	−5.87760	−0.415609
$201$	−8.42640	−0.594352
$202$	−4.02929	−0.283500
$203$	27.1069	1.90253
$204$	−1.38155	−0.0967276
$205$	−32.1883	−2.24812
$206$	−5.58689	−0.389257
$207$	−2.69668	−0.187432
$208$	4.62222	0.320493
$209$	0	0
$210$	−24.6995	−1.70443
$211$	−15.9616	−1.09884	−0.549421	−	0.835546i	$-0.685152\pi$
$211$	−15.9616	−1.09884	−0.549421	+	0.835546i	$0.685152\pi$
$212$	0.578441	0.0397275
$213$	−5.35043	−0.366606
$214$	5.66557	0.387290
$215$	−15.6177	−1.06512
$216$	−11.7102	−0.796780
$217$	−36.3315	−2.46634
$218$	−15.0523	−1.01947
$219$	−24.8044	−1.67613
$220$	1.26950	0.0855894
$221$	2.32921	0.156680
$222$	24.1917	1.62364
$223$	17.1293	1.14706	0.573531	−	0.819184i	$-0.305573\pi$
$223$	17.1293	1.14706	0.573531	+	0.819184i	$0.305573\pi$
$224$	10.0140	0.669092
$225$	2.13633	0.142422
$226$	0.934865	0.0621863
$227$	−22.3328	−1.48228	−0.741142	−	0.671349i	$-0.765715\pi$
$227$	−22.3328	−1.48228	−0.741142	+	0.671349i	$0.765715\pi$
$228$	0	0
$229$	−14.9912	−0.990645	−0.495322	−	0.868709i	$-0.664950\pi$
$229$	−14.9912	−0.990645	−0.495322	+	0.868709i	$0.664950\pi$
$230$	−7.86288	−0.518463
$231$	7.62099	0.501424
$232$	−22.0559	−1.44804
$233$	1.92394	0.126041	0.0630206	−	0.998012i	$-0.479927\pi$
$233$	1.92394	0.126041	0.0630206	+	0.998012i	$0.479927\pi$
$234$	−2.25864	−0.147652
$235$	0.228008	0.0148736
$236$	1.31381	0.0855215
$237$	−6.44269	−0.418498
$238$	−6.53759	−0.423769
$239$	3.30029	0.213478	0.106739	−	0.994287i	$-0.465959\pi$
$239$	3.30029	0.213478	0.106739	+	0.994287i	$0.465959\pi$
$240$	14.9488	0.964938
$241$	−17.1145	−1.10244	−0.551220	−	0.834360i	$-0.685838\pi$
$241$	−17.1145	−1.10244	−0.551220	+	0.834360i	$0.685838\pi$
$242$	1.23186	0.0791869
$243$	11.0179	0.706797
$244$	−5.67372	−0.363223
$245$	18.7482	1.19778
$246$	30.5595	1.94840
$247$	0	0
$248$	29.5616	1.87716
$249$	2.49525	0.158130
$250$	−9.97584	−0.630927
$251$	12.8202	0.809204	0.404602	−	0.914493i	$-0.367410\pi$
$251$	12.8202	0.809204	0.404602	+	0.914493i	$0.367410\pi$
$252$	−2.01581	−0.126984
$253$	2.42608	0.152527
$254$	−1.39120	−0.0872918
$255$	7.53293	0.471730
$256$	−10.8522	−0.678265
$257$	30.6098	1.90938	0.954692	−	0.297595i	$-0.0961846\pi$
$257$	30.6098	1.90938	0.954692	+	0.297595i	$0.0961846\pi$
$258$	14.8274	0.923112
$259$	−36.4009	−2.26184
$260$	2.09408	0.129869
$261$	8.01665	0.496218
$262$	3.55038	0.219343
$263$	−27.8774	−1.71900	−0.859498	−	0.511138i	$-0.829224\pi$
$263$	−27.8774	−1.71900	−0.859498	+	0.511138i	$0.829224\pi$
$264$	−6.20092	−0.381640
$265$	−3.15397	−0.193747
$266$	0	0
$267$	30.8308	1.88682
$268$	−2.00519	−0.122487
$269$	−1.55773	−0.0949766	−0.0474883	−	0.998872i	$-0.515122\pi$
$269$	−1.55773	−0.0949766	−0.0474883	+	0.998872i	$0.515122\pi$
$270$	12.4104	0.755275
$271$	−6.01455	−0.365358	−0.182679	−	0.983173i	$-0.558477\pi$
$271$	−6.01455	−0.365358	−0.182679	+	0.983173i	$0.558477\pi$
$272$	3.95672	0.239911
$273$	12.5711	0.760838
$274$	−27.9914	−1.69102
$275$	−1.92197	−0.115899
$276$	−2.37369	−0.142879
$277$	−16.1061	−0.967724	−0.483862	−	0.875144i	$-0.660766\pi$
$277$	−16.1061	−0.967724	−0.483862	+	0.875144i	$0.660766\pi$
$278$	1.61039	0.0965846
$279$	−10.7448	−0.643272
$280$	−30.2398	−1.80717
$281$	20.3244	1.21245	0.606226	−	0.795292i	$-0.292683\pi$
$281$	20.3244	1.21245	0.606226	+	0.795292i	$0.292683\pi$
$282$	−0.216470	−0.0128906
$283$	21.7917	1.29538	0.647692	−	0.761902i	$-0.275734\pi$
$283$	21.7917	1.29538	0.647692	+	0.761902i	$0.275734\pi$
$284$	−1.27322	−0.0755517
$285$	0	0
$286$	2.03200	0.120155
$287$	−45.9825	−2.71426
$288$	2.96158	0.174513
$289$	−15.0061	−0.882714
$290$	23.3747	1.37261
$291$	6.73480	0.394801
$292$	−5.90261	−0.345424
$293$	−1.41230	−0.0825073	−0.0412537	−	0.999149i	$-0.513135\pi$
$293$	−1.41230	−0.0825073	−0.0412537	+	0.999149i	$0.513135\pi$
$294$	−17.7995	−1.03809
$295$	−7.16357	−0.417079
$296$	29.6181	1.72151
$297$	−3.82922	−0.222194
$298$	6.22977	0.360881
$299$	4.00192	0.231437
$300$	1.88046	0.108569
$301$	−22.3106	−1.28596
$302$	10.9140	0.628032
$303$	6.63237	0.381020
$304$	0	0
$305$	30.9361	1.77140
$306$	−1.93344	−0.110528
$307$	28.8495	1.64653	0.823264	−	0.567659i	$-0.192151\pi$
$307$	28.8495	1.64653	0.823264	+	0.567659i	$0.192151\pi$
$308$	1.81354	0.103336
$309$	9.19624	0.523156
$310$	−31.3292	−1.77938
$311$	−14.9369	−0.846994	−0.423497	−	0.905897i	$-0.639198\pi$
$311$	−14.9369	−0.846994	−0.423497	+	0.905897i	$0.639198\pi$
$312$	−10.2287	−0.579083
$313$	24.3231	1.37482	0.687411	−	0.726269i	$-0.258747\pi$
$313$	24.3231	1.37482	0.687411	+	0.726269i	$0.258747\pi$
$314$	−19.9854	−1.12784
$315$	10.9913	0.619288
$316$	−1.53314	−0.0862459
$317$	−17.8218	−1.00097	−0.500486	−	0.865745i	$-0.666845\pi$
$317$	−17.8218	−1.00097	−0.500486	+	0.865745i	$0.666845\pi$
$318$	2.99437	0.167916
$319$	−7.21223	−0.403807
$320$	23.3799	1.30698
$321$	−9.32576	−0.520513
$322$	−11.2325	−0.625963
$323$	0	0
$324$	5.35555	0.297531
$325$	−3.17036	−0.175860
$326$	−27.0146	−1.49620
$327$	24.7767	1.37016
$328$	37.4142	2.06586
$329$	0.325720	0.0179575
$330$	6.57171	0.361760
$331$	18.2121	1.00103	0.500513	−	0.865729i	$-0.333145\pi$
$331$	18.2121	1.00103	0.500513	+	0.865729i	$0.333145\pi$
$332$	0.593785	0.0325882
$333$	−10.7653	−0.589934
$334$	−25.5235	−1.39659
$335$	10.9334	0.597355
$336$	21.3550	1.16501
$337$	−28.0190	−1.52629	−0.763147	−	0.646224i	$-0.776347\pi$
$337$	−28.0190	−1.52629	−0.763147	+	0.646224i	$0.776347\pi$
$338$	−12.6623	−0.688739
$339$	−1.53883	−0.0835776
$340$	1.79258	0.0972163
$341$	9.66660	0.523476
$342$	0	0
$343$	0.473542	0.0255689
$344$	18.1533	0.978760
$345$	12.9426	0.696808
$346$	15.8192	0.850446
$347$	28.3630	1.52261	0.761303	−	0.648396i	$-0.224560\pi$
$347$	28.3630	1.52261	0.761303	+	0.648396i	$0.224560\pi$
$348$	7.05648	0.378267
$349$	−4.77221	−0.255451	−0.127725	−	0.991810i	$-0.540768\pi$
$349$	−4.77221	−0.255451	−0.127725	+	0.991810i	$0.540768\pi$
$350$	8.89850	0.475645
$351$	−6.31645	−0.337147
$352$	−2.66441	−0.142013
$353$	−12.6727	−0.674498	−0.337249	−	0.941415i	$-0.609497\pi$
$353$	−12.6727	−0.674498	−0.337249	+	0.941415i	$0.609497\pi$
$354$	6.80108	0.361473
$355$	6.94227	0.368458
$356$	7.33669	0.388844
$357$	10.7611	0.569540
$358$	0.987696	0.0522014
$359$	1.24822	0.0658783	0.0329391	−	0.999457i	$-0.489513\pi$
$359$	1.24822	0.0658783	0.0329391	+	0.999457i	$0.489513\pi$
$360$	−8.94319	−0.471347
$361$	0	0
$362$	−13.9030	−0.730723
$363$	−2.02769	−0.106426
$364$	2.99149	0.156797
$365$	32.1841	1.68460
$366$	−29.3707	−1.53523
$367$	−33.9164	−1.77042	−0.885212	−	0.465188i	$-0.845987\pi$
$367$	−33.9164	−1.77042	−0.885212	+	0.465188i	$0.845987\pi$
$368$	6.79820	0.354381
$369$	−13.5990	−0.707934
$370$	−31.3891	−1.63184
$371$	−4.50560	−0.233919
$372$	−9.45785	−0.490367
$373$	−10.3937	−0.538167	−0.269083	−	0.963117i	$-0.586721\pi$
$373$	−10.3937	−0.538167	−0.269083	+	0.963117i	$0.586721\pi$
$374$	1.73944	0.0899441
$375$	16.4206	0.847958
$376$	−0.265027	−0.0136677
$377$	−11.8968	−0.612719
$378$	17.7289	0.911876
$379$	−0.456731	−0.0234607	−0.0117303	−	0.999931i	$-0.503734\pi$
$379$	−0.456731	−0.0234607	−0.0117303	+	0.999931i	$0.503734\pi$
$380$	0	0
$381$	2.28998	0.117319
$382$	9.42376	0.482161
$383$	21.0486	1.07554	0.537768	−	0.843093i	$-0.319268\pi$
$383$	21.0486	1.07554	0.537768	+	0.843093i	$0.319268\pi$
$384$	−11.3916	−0.581327
$385$	−9.88836	−0.503957
$386$	10.9804	0.558888
$387$	−6.59818	−0.335405
$388$	1.60265	0.0813623
$389$	−6.06998	−0.307760	−0.153880	−	0.988090i	$-0.549177\pi$
$389$	−6.06998	−0.307760	−0.153880	+	0.988090i	$0.549177\pi$
$390$	10.8403	0.548919
$391$	3.42573	0.173246
$392$	−21.7921	−1.10067
$393$	−5.84408	−0.294795
$394$	2.59861	0.130916
$395$	8.35949	0.420612
$396$	0.536340	0.0269521
$397$	19.8293	0.995203	0.497601	−	0.867406i	$-0.334214\pi$
$397$	19.8293	0.995203	0.497601	+	0.867406i	$0.334214\pi$
$398$	6.78868	0.340286
$399$	0	0
$400$	−5.38560	−0.269280
$401$	−18.8701	−0.942326	−0.471163	−	0.882046i	$-0.656166\pi$
$401$	−18.8701	−0.942326	−0.471163	+	0.882046i	$0.656166\pi$
$402$	−10.3801	−0.517714
$403$	15.9454	0.794298
$404$	1.57828	0.0785223
$405$	−29.2013	−1.45102
$406$	33.3918	1.65721
$407$	9.68506	0.480071
$408$	−8.75595	−0.433484
$409$	32.6139	1.61266	0.806328	−	0.591469i	$-0.201452\pi$
$409$	32.6139	1.61266	0.806328	+	0.591469i	$0.201452\pi$
$410$	−39.6514	−1.95824
$411$	46.0751	2.27271
$412$	2.18839	0.107814
$413$	−10.2335	−0.503558
$414$	−3.32193	−0.163264
$415$	−3.23763	−0.158929
$416$	−4.39504	−0.215484
$417$	−2.65076	−0.129808
$418$	0	0
$419$	−39.3439	−1.92208	−0.961039	−	0.276414i	$-0.910854\pi$
$419$	−39.3439	−1.92208	−0.961039	+	0.276414i	$0.910854\pi$
$420$	9.67482	0.472083
$421$	0.604068	0.0294404	0.0147202	−	0.999892i	$-0.495314\pi$
$421$	0.604068	0.0294404	0.0147202	+	0.999892i	$0.495314\pi$
$422$	−19.6625	−0.957153
$423$	0.0963294	0.00468369
$424$	3.66604	0.178039
$425$	−2.71389	−0.131643
$426$	−6.59099	−0.319334
$427$	44.1938	2.13869
$428$	−2.21921	−0.107270
$429$	−3.34475	−0.161486
$430$	−19.2388	−0.927775
$431$	−14.1289	−0.680564	−0.340282	−	0.940323i	$-0.610523\pi$
$431$	−14.1289	−0.680564	−0.340282	+	0.940323i	$0.610523\pi$
$432$	−10.7300	−0.516247
$433$	−18.8905	−0.907819	−0.453909	−	0.891048i	$-0.649971\pi$
$433$	−18.8905	−0.907819	−0.453909	+	0.891048i	$0.649971\pi$
$434$	−44.7553	−2.14832
$435$	−38.4757	−1.84477
$436$	5.89601	0.282368
$437$	0	0
$438$	−30.5556	−1.46000
$439$	34.8446	1.66304	0.831521	−	0.555494i	$-0.187471\pi$
$439$	34.8446	1.66304	0.831521	+	0.555494i	$0.187471\pi$
$440$	8.04580	0.383568
$441$	7.92080	0.377181
$442$	2.86926	0.136477
$443$	−4.42545	−0.210259	−0.105130	−	0.994459i	$-0.533526\pi$
$443$	−4.42545	−0.210259	−0.105130	+	0.994459i	$0.533526\pi$
$444$	−9.47591	−0.449707
$445$	−40.0035	−1.89635
$446$	21.1009	0.999155
$447$	−10.2545	−0.485020
$448$	33.3993	1.57797
$449$	27.5536	1.30033	0.650166	−	0.759792i	$-0.274699\pi$
$449$	27.5536	1.30033	0.650166	+	0.759792i	$0.274699\pi$
$450$	2.63166	0.124058
$451$	12.2344	0.576095
$452$	−0.366188	−0.0172240
$453$	−17.9649	−0.844067
$454$	−27.5109	−1.29115
$455$	−16.3112	−0.764682
$456$	0	0
$457$	30.7875	1.44018	0.720089	−	0.693881i	$-0.244101\pi$
$457$	30.7875	1.44018	0.720089	+	0.693881i	$0.244101\pi$
$458$	−18.4670	−0.862907
$459$	−5.40702	−0.252378
$460$	3.07990	0.143601
$461$	−24.7022	−1.15050	−0.575248	−	0.817979i	$-0.695094\pi$
$461$	−24.7022	−1.15050	−0.575248	+	0.817979i	$0.695094\pi$
$462$	9.38799	0.436769
$463$	13.4674	0.625885	0.312942	−	0.949772i	$-0.398685\pi$
$463$	13.4674	0.625885	0.312942	+	0.949772i	$0.398685\pi$
$464$	−20.2096	−0.938208
$465$	51.5692	2.39146
$466$	2.37002	0.109789
$467$	23.5735	1.09085	0.545425	−	0.838159i	$-0.316368\pi$
$467$	23.5735	1.09085	0.545425	+	0.838159i	$0.316368\pi$
$468$	0.884712	0.0408958
$469$	15.6189	0.721212
$470$	0.280874	0.0129557
$471$	32.8968	1.51580
$472$	8.32663	0.383264
$473$	5.93610	0.272942
$474$	−7.93649	−0.364535
$475$	0	0
$476$	2.56079	0.117373
$477$	−1.33250	−0.0610108
$478$	4.06550	0.185951
$479$	18.5653	0.848269	0.424135	−	0.905599i	$-0.360578\pi$
$479$	18.5653	0.848269	0.424135	+	0.905599i	$0.360578\pi$
$480$	−14.2140	−0.648778
$481$	15.9759	0.728437
$482$	−21.0826	−0.960288
$483$	18.4892	0.841286
$484$	−0.482521	−0.0219328
$485$	−8.73851	−0.396795
$486$	13.5725	0.615660
$487$	1.97914	0.0896835	0.0448417	−	0.998994i	$-0.485722\pi$
$487$	1.97914	0.0896835	0.0448417	+	0.998994i	$0.485722\pi$
$488$	−35.9588	−1.62778
$489$	44.4672	2.01087
$490$	23.0952	1.04333
$491$	21.2152	0.957431	0.478715	−	0.877970i	$-0.341103\pi$
$491$	21.2152	0.957431	0.478715	+	0.877970i	$0.341103\pi$
$492$	−11.9702	−0.539658
$493$	−10.1840	−0.458663
$494$	0	0
$495$	−2.92441	−0.131442
$496$	27.0871	1.21625
$497$	9.91737	0.444855
$498$	3.07380	0.137740
$499$	25.1247	1.12474	0.562368	−	0.826887i	$-0.309891\pi$
$499$	25.1247	1.12474	0.562368	+	0.826887i	$0.309891\pi$
$500$	3.90755	0.174751
$501$	42.0128	1.87699
$502$	15.7927	0.704862
$503$	−7.28460	−0.324804	−0.162402	−	0.986725i	$-0.551924\pi$
$503$	−7.28460	−0.324804	−0.162402	+	0.986725i	$0.551924\pi$
$504$	−12.7758	−0.569078
$505$	−8.60561	−0.382945
$506$	2.98859	0.132859
$507$	20.8427	0.925657
$508$	0.544936	0.0241776
$509$	30.3845	1.34677	0.673385	−	0.739292i	$-0.264840\pi$
$509$	30.3845	1.34677	0.673385	+	0.739292i	$0.264840\pi$
$510$	9.27951	0.410904
$511$	45.9766	2.03388
$512$	−24.6045	−1.08738
$513$	0	0
$514$	37.7069	1.66318
$515$	−11.9323	−0.525799
$516$	−5.80791	−0.255679
$517$	−0.0866633	−0.00381145
$518$	−44.8408	−1.97019
$519$	−26.0391	−1.14299
$520$	13.2718	0.582009
$521$	−8.26667	−0.362169	−0.181085	−	0.983468i	$-0.557961\pi$
$521$	−8.26667	−0.362169	−0.181085	+	0.983468i	$0.557961\pi$
$522$	9.87539	0.432234
$523$	−15.4759	−0.676714	−0.338357	−	0.941018i	$-0.609871\pi$
$523$	−15.4759	−0.676714	−0.338357	+	0.941018i	$0.609871\pi$
$524$	−1.39069	−0.0607526
$525$	−14.6473	−0.639260
$526$	−34.3411	−1.49734
$527$	13.6496	0.594587
$528$	−5.68186	−0.247271
$529$	−17.1141	−0.744092
$530$	−3.88525	−0.168764
$531$	−3.02648	−0.131338
$532$	0	0
$533$	20.1811	0.874140
$534$	37.9793	1.64352
$535$	12.1003	0.523143
$536$	−12.7085	−0.548923
$537$	−1.62579	−0.0701580
$538$	−1.91891	−0.0827300
$539$	−7.12599	−0.306938
$540$	−4.86119	−0.209192
$541$	13.3661	0.574656	0.287328	−	0.957832i	$-0.407233\pi$
$541$	13.3661	0.574656	0.287328	+	0.957832i	$0.407233\pi$
$542$	−7.40908	−0.318247
$543$	22.8848	0.982082
$544$	−3.76225	−0.161305
$545$	−32.1482	−1.37708
$546$	15.4858	0.662733
$547$	2.95631	0.126403	0.0632013	−	0.998001i	$-0.479869\pi$
$547$	2.95631	0.126403	0.0632013	+	0.998001i	$0.479869\pi$
$548$	10.9643	0.468371
$549$	13.0700	0.557813
$550$	−2.36759	−0.100955
$551$	0	0
$552$	−15.0440	−0.640313
$553$	11.9419	0.507823
$554$	−19.8405	−0.842942
$555$	51.6677	2.19317
$556$	−0.630791	−0.0267515
$557$	11.8388	0.501626	0.250813	−	0.968036i	$-0.419302\pi$
$557$	11.8388	0.501626	0.250813	+	0.968036i	$0.419302\pi$
$558$	−13.2360	−0.560327
$559$	9.79181	0.414150
$560$	−27.7085	−1.17090
$561$	−2.86318	−0.120884
$562$	25.0368	1.05611
$563$	1.82512	0.0769194	0.0384597	−	0.999260i	$-0.487755\pi$
$563$	1.82512	0.0769194	0.0384597	+	0.999260i	$0.487755\pi$
$564$	0.0847918	0.00357038
$565$	1.99665	0.0839998
$566$	26.8444	1.12835
$567$	−41.7155	−1.75188
$568$	−8.06940	−0.338585
$569$	−16.0290	−0.671971	−0.335986	−	0.941867i	$-0.609069\pi$
$569$	−16.0290	−0.671971	−0.335986	+	0.941867i	$0.609069\pi$
$570$	0	0
$571$	27.4663	1.14943	0.574714	−	0.818355i	$-0.305113\pi$
$571$	27.4663	1.14943	0.574714	+	0.818355i	$0.305113\pi$
$572$	−0.795937	−0.0332798
$573$	−15.5119	−0.648019
$574$	−56.6439	−2.36427
$575$	−4.66285	−0.194454
$576$	9.87759	0.411566
$577$	19.2841	0.802809	0.401405	−	0.915901i	$-0.368522\pi$
$577$	19.2841	0.802809	0.401405	+	0.915901i	$0.368522\pi$
$578$	−18.4855	−0.768894
$579$	−18.0742	−0.751139
$580$	−9.15590	−0.380178
$581$	−4.62511	−0.191882
$582$	8.29633	0.343894
$583$	1.19879	0.0496488
$584$	−37.4095	−1.54801
$585$	−4.82392	−0.199445
$586$	−1.73975	−0.0718685
$587$	−24.4297	−1.00832	−0.504160	−	0.863610i	$-0.668198\pi$
$587$	−24.4297	−1.00832	−0.504160	+	0.863610i	$0.668198\pi$
$588$	6.97211	0.287525
$589$	0	0
$590$	−8.82451	−0.363299
$591$	−4.27742	−0.175950
$592$	27.1388	1.11540
$593$	1.44069	0.0591620	0.0295810	−	0.999562i	$-0.490583\pi$
$593$	1.44069	0.0591620	0.0295810	+	0.999562i	$0.490583\pi$
$594$	−4.71707	−0.193544
$595$	−13.9628	−0.572417
$596$	−2.44021	−0.0999550
$597$	−11.1745	−0.457340
$598$	4.92980	0.201594
$599$	29.4218	1.20214	0.601072	−	0.799195i	$-0.294741\pi$
$599$	29.4218	1.20214	0.601072	+	0.799195i	$0.294741\pi$
$600$	11.9180	0.486549
$601$	−32.4389	−1.32321	−0.661605	−	0.749853i	$-0.730124\pi$
$601$	−32.4389	−1.32321	−0.661605	+	0.749853i	$0.730124\pi$
$602$	−27.4835	−1.12014
$603$	4.61916	0.188107
$604$	−4.27504	−0.173949
$605$	2.63096	0.106964
$606$	8.17016	0.331890
$607$	29.3851	1.19270	0.596352	−	0.802723i	$-0.296616\pi$
$607$	29.3851	1.19270	0.596352	+	0.802723i	$0.296616\pi$
$608$	0	0
$609$	−54.9644	−2.22727
$610$	38.1090	1.54299
$611$	−0.142954	−0.00578332
$612$	0.757333	0.0306134
$613$	−20.8384	−0.841654	−0.420827	−	0.907141i	$-0.638260\pi$
$613$	−20.8384	−0.841654	−0.420827	+	0.907141i	$0.638260\pi$
$614$	35.5385	1.43422
$615$	65.2679	2.63185
$616$	11.4938	0.463099
$617$	−32.3392	−1.30193	−0.650963	−	0.759109i	$-0.725635\pi$
$617$	−32.3392	−1.30193	−0.650963	+	0.759109i	$0.725635\pi$
$618$	11.3285	0.455698
$619$	32.8773	1.32145	0.660725	−	0.750628i	$-0.270249\pi$
$619$	32.8773	1.32145	0.660725	+	0.750628i	$0.270249\pi$
$620$	12.2717	0.492844
$621$	−9.29002	−0.372796
$622$	−18.4002	−0.737780
$623$	−57.1469	−2.28954
$624$	−9.37244	−0.375198
$625$	−30.9159	−1.23664
$626$	29.9626	1.19755
$627$	0	0
$628$	7.82831	0.312384
$629$	13.6757	0.545286
$630$	13.5397	0.539434
$631$	−27.3515	−1.08884	−0.544422	−	0.838811i	$-0.683251\pi$
$631$	−27.3515	−1.08884	−0.544422	+	0.838811i	$0.683251\pi$
$632$	−9.71672	−0.386510
$633$	32.3652	1.28640
$634$	−21.9540	−0.871903
$635$	−2.97128	−0.117912
$636$	−1.17290	−0.0465086
$637$	−11.7546	−0.465734
$638$	−8.88446	−0.351739
$639$	2.93299	0.116027
$640$	14.7808	0.584264
$641$	46.3007	1.82877	0.914383	−	0.404850i	$-0.132676\pi$
$641$	46.3007	1.82877	0.914383	+	0.404850i	$0.132676\pi$
$642$	−11.4880	−0.453396
$643$	20.7368	0.817780	0.408890	−	0.912584i	$-0.365916\pi$
$643$	20.7368	0.817780	0.408890	+	0.912584i	$0.365916\pi$
$644$	4.39979	0.173376
$645$	31.6678	1.24692
$646$	0	0
$647$	48.7337	1.91592	0.957959	−	0.286904i	$-0.0926262\pi$
$647$	48.7337	1.91592	0.957959	+	0.286904i	$0.0926262\pi$
$648$	33.9423	1.33338
$649$	2.72279	0.106879
$650$	−3.90543	−0.153184
$651$	73.6691	2.88732
$652$	10.5817	0.414410
$653$	−33.5147	−1.31153	−0.655765	−	0.754965i	$-0.727654\pi$
$653$	−33.5147	−1.31153	−0.655765	+	0.754965i	$0.727654\pi$
$654$	30.5214	1.19348
$655$	7.58279	0.296284
$656$	34.2824	1.33850
$657$	13.5972	0.530479
$658$	0.401242	0.0156420
$659$	22.3567	0.870892	0.435446	−	0.900215i	$-0.356591\pi$
$659$	22.3567	0.870892	0.435446	+	0.900215i	$0.356591\pi$
$660$	−2.57415	−0.100199
$661$	−17.1035	−0.665249	−0.332625	−	0.943059i	$-0.607934\pi$
$661$	−17.1035	−0.665249	−0.332625	+	0.943059i	$0.607934\pi$
$662$	22.4347	0.871950
$663$	−4.72293	−0.183423
$664$	3.76329	0.146044
$665$	0	0
$666$	−13.2613	−0.513866
$667$	−17.4975	−0.677505
$668$	9.99761	0.386819
$669$	−34.7329	−1.34285
$670$	13.4684	0.520330
$671$	−11.7585	−0.453931
$672$	−20.3054	−0.783298
$673$	14.4175	0.555752	0.277876	−	0.960617i	$-0.410370\pi$
$673$	14.4175	0.555752	0.277876	+	0.960617i	$0.410370\pi$
$674$	−34.5155	−1.32949
$675$	7.35964	0.283273
$676$	4.95985	0.190763
$677$	26.4020	1.01471	0.507355	−	0.861737i	$-0.330623\pi$
$677$	26.4020	1.01471	0.507355	+	0.861737i	$0.330623\pi$
$678$	−1.89562	−0.0728008
$679$	−12.4834	−0.479068
$680$	11.3610	0.435674
$681$	45.2841	1.73529
$682$	11.9079	0.455977
$683$	7.65175	0.292786	0.146393	−	0.989226i	$-0.453234\pi$
$683$	7.65175	0.292786	0.146393	+	0.989226i	$0.453234\pi$
$684$	0	0
$685$	−59.7831	−2.28420
$686$	0.583337	0.0222719
$687$	30.3975	1.15974
$688$	16.6337	0.634155
$689$	1.97745	0.0753348
$690$	15.9435	0.606959
$691$	−4.11843	−0.156672	−0.0783362	−	0.996927i	$-0.524961\pi$
$691$	−4.11843	−0.156672	−0.0783362	+	0.996927i	$0.524961\pi$
$692$	−6.19641	−0.235552
$693$	−4.17766	−0.158696
$694$	34.9392	1.32628
$695$	3.43941	0.130464
$696$	44.7225	1.69520
$697$	17.2755	0.654355
$698$	−5.87870	−0.222512
$699$	−3.90115	−0.147555
$700$	−3.48556	−0.131742
$701$	−3.49943	−0.132172	−0.0660858	−	0.997814i	$-0.521051\pi$
$701$	−3.49943	−0.132172	−0.0660858	+	0.997814i	$0.521051\pi$
$702$	−7.78098	−0.293674
$703$	0	0
$704$	−8.88643	−0.334920
$705$	−0.462330	−0.0174124
$706$	−15.6110	−0.587526
$707$	−12.2935	−0.462346
$708$	−2.66399	−0.100119
$709$	19.3216	0.725638	0.362819	−	0.931860i	$-0.381814\pi$
$709$	19.3216	0.725638	0.362819	+	0.931860i	$0.381814\pi$
$710$	8.55191	0.320947
$711$	3.53174	0.132451
$712$	46.4984	1.74260
$713$	23.4520	0.878283
$714$	13.2562	0.496102
$715$	4.33987	0.162302
$716$	−0.386882	−0.0144585
$717$	−6.69197	−0.249916
$718$	1.53763	0.0573837
$719$	7.62027	0.284188	0.142094	−	0.989853i	$-0.454616\pi$
$719$	7.62027	0.284188	0.142094	+	0.989853i	$0.454616\pi$
$720$	−8.19457	−0.305394
$721$	−17.0458	−0.634820
$722$	0	0
$723$	34.7029	1.29061
$724$	5.44581	0.202392
$725$	13.8617	0.514810
$726$	−2.49783	−0.0927033
$727$	−7.45853	−0.276622	−0.138311	−	0.990389i	$-0.544167\pi$
$727$	−7.45853	−0.276622	−0.138311	+	0.990389i	$0.544167\pi$
$728$	18.9595	0.702684
$729$	10.9564	0.405794
$730$	39.6464	1.46738
$731$	8.38201	0.310020
$732$	11.5046	0.425221
$733$	25.8079	0.953237	0.476618	−	0.879110i	$-0.341862\pi$
$733$	25.8079	0.953237	0.476618	+	0.879110i	$0.341862\pi$
$734$	−41.7803	−1.54214
$735$	−38.0156	−1.40223
$736$	−6.46407	−0.238269
$737$	−4.15566	−0.153076
$738$	−16.7520	−0.616650
$739$	−18.2186	−0.670180	−0.335090	−	0.942186i	$-0.608767\pi$
$739$	−18.2186	−0.670180	−0.335090	+	0.942186i	$0.608767\pi$
$740$	12.2951	0.451978
$741$	0	0
$742$	−5.55026	−0.203757
$743$	27.2606	1.00009	0.500047	−	0.865998i	$-0.333316\pi$
$743$	27.2606	1.00009	0.500047	+	0.865998i	$0.333316\pi$
$744$	−59.9418	−2.19757
$745$	13.3053	0.487470
$746$	−12.8036	−0.468774
$747$	−1.36784	−0.0500468
$748$	−0.681340	−0.0249122
$749$	17.2859	0.631613
$750$	20.2279	0.738619
$751$	11.8776	0.433422	0.216711	−	0.976236i	$-0.430467\pi$
$751$	11.8776	0.433422	0.216711	+	0.976236i	$0.430467\pi$
$752$	−0.242842	−0.00885553
$753$	−25.9954	−0.947326
$754$	−14.6552	−0.533713
$755$	23.3098	0.848330
$756$	−6.94444	−0.252567
$757$	−23.4833	−0.853516	−0.426758	−	0.904366i	$-0.640344\pi$
$757$	−23.4833	−0.853516	−0.426758	+	0.904366i	$0.640344\pi$
$758$	−0.562628	−0.0204356
$759$	−4.91935	−0.178561
$760$	0	0
$761$	−13.7958	−0.500097	−0.250049	−	0.968233i	$-0.580447\pi$
$761$	−13.7958	−0.500097	−0.250049	+	0.968233i	$0.580447\pi$
$762$	2.82093	0.102192
$763$	−45.9252	−1.66260
$764$	−3.69130	−0.133547
$765$	−4.12938	−0.149298
$766$	25.9290	0.936852
$767$	4.49135	0.162173
$768$	22.0050	0.794037
$769$	35.9440	1.29617	0.648087	−	0.761566i	$-0.275569\pi$
$769$	35.9440	1.29617	0.648087	+	0.761566i	$0.275569\pi$
$770$	−12.1811	−0.438975
$771$	−62.0672	−2.23529
$772$	−4.30105	−0.154798
$773$	−26.7394	−0.961749	−0.480874	−	0.876789i	$-0.659681\pi$
$773$	−26.7394	−0.961749	−0.480874	+	0.876789i	$0.659681\pi$
$774$	−8.12804	−0.292156
$775$	−18.5789	−0.667373
$776$	10.1573	0.364625
$777$	73.8098	2.64791
$778$	−7.47737	−0.268077
$779$	0	0
$780$	−4.24615	−0.152037
$781$	−2.63868	−0.0944195
$782$	4.22002	0.150907
$783$	27.6173	0.986960
$784$	−19.9680	−0.713142
$785$	−42.6841	−1.52346
$786$	−7.19909	−0.256783
$787$	−2.46597	−0.0879022	−0.0439511	−	0.999034i	$-0.513995\pi$
$787$	−2.46597	−0.0879022	−0.0439511	+	0.999034i	$0.513995\pi$
$788$	−1.01788	−0.0362605
$789$	56.5269	2.01241
$790$	10.2977	0.366377
$791$	2.85231	0.101417
$792$	3.39921	0.120786
$793$	−19.3961	−0.688774
$794$	24.4269	0.866878
$795$	6.39528	0.226817
$796$	−2.65914	−0.0942507
$797$	22.0167	0.779871	0.389936	−	0.920842i	$-0.372497\pi$
$797$	22.0167	0.779871	0.389936	+	0.920842i	$0.372497\pi$
$798$	0	0
$799$	−0.122372	−0.00432921
$800$	5.12090	0.181051
$801$	−16.9008	−0.597160
$802$	−23.2453	−0.820819
$803$	−12.2328	−0.431687
$804$	4.06592	0.143394
$805$	−23.9900	−0.845536
$806$	19.6425	0.691878
$807$	3.15860	0.111188
$808$	10.0028	0.351897
$809$	45.5853	1.60269	0.801347	−	0.598200i	$-0.204117\pi$
$809$	45.5853	1.60269	0.801347	+	0.598200i	$0.204117\pi$
$810$	−35.9719	−1.26392
$811$	−36.6835	−1.28813	−0.644067	−	0.764969i	$-0.722754\pi$
$811$	−36.6835	−1.28813	−0.644067	+	0.764969i	$0.722754\pi$
$812$	−13.0796	−0.459005
$813$	12.1957	0.427720
$814$	11.9306	0.418169
$815$	−57.6969	−2.02103
$816$	−8.02301	−0.280862
$817$	0	0
$818$	40.1758	1.40471
$819$	−6.89120	−0.240798
$820$	15.5315	0.542384
$821$	13.2959	0.464030	0.232015	−	0.972712i	$-0.425468\pi$
$821$	13.2959	0.464030	0.232015	+	0.972712i	$0.425468\pi$
$822$	56.7580	1.97966
$823$	28.2027	0.983084	0.491542	−	0.870854i	$-0.336433\pi$
$823$	28.2027	0.983084	0.491542	+	0.870854i	$0.336433\pi$
$824$	13.8696	0.483169
$825$	3.89716	0.135682
$826$	−12.6062	−0.438627
$827$	19.8716	0.691004	0.345502	−	0.938418i	$-0.387709\pi$
$827$	19.8716	0.691004	0.345502	+	0.938418i	$0.387709\pi$
$828$	1.30120	0.0452200
$829$	−32.7421	−1.13718	−0.568589	−	0.822622i	$-0.692511\pi$
$829$	−32.7421	−1.13718	−0.568589	+	0.822622i	$0.692511\pi$
$830$	−3.98831	−0.138436
$831$	32.6583	1.13290
$832$	−14.6585	−0.508192
$833$	−10.0622	−0.348634
$834$	−3.26537	−0.113070
$835$	−54.5123	−1.88648
$836$	0	0
$837$	−37.0156	−1.27945
$838$	−48.4662	−1.67424
$839$	32.5156	1.12256	0.561281	−	0.827625i	$-0.310309\pi$
$839$	32.5156	1.12256	0.561281	+	0.827625i	$0.310309\pi$
$840$	61.3170	2.11564
$841$	23.0163	0.793665
$842$	0.744126	0.0256443
$843$	−41.2116	−1.41940
$844$	7.70181	0.265107
$845$	−27.0437	−0.930333
$846$	0.118664	0.00407976
$847$	3.75846	0.129142
$848$	3.35916	0.115354
$849$	−44.1869	−1.51649
$850$	−3.34314	−0.114669
$851$	23.4968	0.805459
$852$	2.58170	0.0884476
$853$	−27.1348	−0.929078	−0.464539	−	0.885553i	$-0.653780\pi$
$853$	−27.1348	−0.929078	−0.464539	+	0.885553i	$0.653780\pi$
$854$	54.4405	1.86292
$855$	0	0
$856$	−14.0649	−0.480728
$857$	−21.7163	−0.741815	−0.370908	−	0.928670i	$-0.620953\pi$
$857$	−21.7163	−0.741815	−0.370908	+	0.928670i	$0.620953\pi$
$858$	−4.12027	−0.140664
$859$	−57.1926	−1.95139	−0.975693	−	0.219142i	$-0.929674\pi$
$859$	−57.1926	−1.95139	−0.975693	+	0.219142i	$0.929674\pi$
$860$	7.53585	0.256970
$861$	93.2383	3.17755
$862$	−17.4048	−0.592810
$863$	31.7815	1.08186	0.540928	−	0.841069i	$-0.318073\pi$
$863$	31.7815	1.08186	0.540928	+	0.841069i	$0.318073\pi$
$864$	10.2026	0.347100
$865$	33.7861	1.14876
$866$	−23.2704	−0.790761
$867$	30.4278	1.03338
$868$	17.5307	0.595031
$869$	−3.17735	−0.107784
$870$	−47.3967	−1.60690
$871$	−6.85491	−0.232270
$872$	37.3677	1.26543
$873$	−3.69187	−0.124951
$874$	0	0
$875$	−30.4367	−1.02895
$876$	11.9687	0.404384
$877$	−8.57500	−0.289557	−0.144779	−	0.989464i	$-0.546247\pi$
$877$	−8.57500	−0.289557	−0.144779	+	0.989464i	$0.546247\pi$
$878$	42.9237	1.44860
$879$	2.86371	0.0965904
$880$	7.37230	0.248520
$881$	−46.1073	−1.55339	−0.776697	−	0.629874i	$-0.783106\pi$
$881$	−46.1073	−1.55339	−0.776697	+	0.629874i	$0.783106\pi$
$882$	9.75731	0.328546
$883$	−30.5954	−1.02962	−0.514809	−	0.857305i	$-0.672137\pi$
$883$	−30.5954	−1.02962	−0.514809	+	0.857305i	$0.672137\pi$
$884$	−1.12390	−0.0378007
$885$	14.5255	0.488270
$886$	−5.45153	−0.183148
$887$	37.5358	1.26033	0.630164	−	0.776462i	$-0.282988\pi$
$887$	37.5358	1.26033	0.630164	+	0.776462i	$0.282988\pi$
$888$	−60.0563	−2.01536
$889$	−4.24462	−0.142360
$890$	−49.2787	−1.65183
$891$	11.0991	0.371834
$892$	−8.26524	−0.276741
$893$	0	0
$894$	−12.6321	−0.422479
$895$	2.10949	0.0705124
$896$	21.1151	0.705407
$897$	−8.11465	−0.270940
$898$	33.9421	1.13266
$899$	−69.7178	−2.32522
$900$	−1.03083	−0.0343609
$901$	1.69274	0.0563933
$902$	15.0711	0.501812
$903$	45.2390	1.50546
$904$	−2.32082	−0.0771894
$905$	−29.6934	−0.987043
$906$	−22.1303	−0.735230
$907$	−8.93894	−0.296813	−0.148406	−	0.988926i	$-0.547414\pi$
$907$	−8.93894	−0.296813	−0.148406	+	0.988926i	$0.547414\pi$
$908$	10.7761	0.357617
$909$	−3.63572	−0.120589
$910$	−20.0931	−0.666081
$911$	−25.3584	−0.840161	−0.420080	−	0.907487i	$-0.637998\pi$
$911$	−25.3584	−0.840161	−0.420080	+	0.907487i	$0.637998\pi$
$912$	0	0
$913$	1.23059	0.0407265
$914$	37.9259	1.25448
$915$	−62.7290	−2.07376
$916$	7.23356	0.239004
$917$	10.8324	0.357716
$918$	−6.66069	−0.219836
$919$	−14.6153	−0.482113	−0.241056	−	0.970511i	$-0.577494\pi$
$919$	−14.6153	−0.482113	−0.241056	+	0.970511i	$0.577494\pi$
$920$	19.5198	0.643548
$921$	−58.4979	−1.92757
$922$	−30.4296	−1.00215
$923$	−4.35260	−0.143268
$924$	−3.67729	−0.120974
$925$	−18.6144	−0.612036
$926$	16.5900	0.545181
$927$	−5.04118	−0.165574
$928$	19.2163	0.630806
$929$	−10.5585	−0.346412	−0.173206	−	0.984886i	$-0.555413\pi$
$929$	−10.5585	−0.346412	−0.173206	+	0.984886i	$0.555413\pi$
$930$	63.5260	2.08310
$931$	0	0
$932$	−0.928340	−0.0304088
$933$	30.2875	0.991567
$934$	29.0392	0.950192
$935$	3.71503	0.121494
$936$	5.60712	0.183274
$937$	5.86722	0.191674	0.0958369	−	0.995397i	$-0.469447\pi$
$937$	5.86722	0.191674	0.0958369	+	0.995397i	$0.469447\pi$
$938$	19.2402	0.628216
$939$	−49.3197	−1.60949
$940$	−0.110019	−0.00358842
$941$	13.7997	0.449857	0.224928	−	0.974375i	$-0.427785\pi$
$941$	13.7997	0.449857	0.224928	+	0.974375i	$0.427785\pi$
$942$	40.5242	1.32035
$943$	29.6817	0.966568
$944$	7.62962	0.248323
$945$	37.8648	1.23174
$946$	7.31244	0.237748
$947$	25.5398	0.829934	0.414967	−	0.909837i	$-0.363793\pi$
$947$	25.5398	0.829934	0.414967	+	0.909837i	$0.363793\pi$
$948$	3.10874	0.100967
$949$	−20.1785	−0.655023
$950$	0	0
$951$	36.1371	1.17183
$952$	16.2297	0.526008
$953$	57.9573	1.87742	0.938710	−	0.344709i	$-0.112022\pi$
$953$	57.9573	1.87742	0.938710	+	0.344709i	$0.112022\pi$
$954$	−1.64145	−0.0531439
$955$	20.1269	0.651292
$956$	−1.59246	−0.0515039
$957$	14.6242	0.472733
$958$	22.8698	0.738891
$959$	−85.4030	−2.75781
$960$	−47.4072	−1.53006
$961$	62.4431	2.01429
$962$	19.6800	0.634510
$963$	5.11217	0.164737
$964$	8.25810	0.265975
$965$	23.4516	0.754933
$966$	22.7761	0.732808
$967$	−7.02299	−0.225844	−0.112922	−	0.993604i	$-0.536021\pi$
$967$	−7.02299	−0.225844	−0.112922	+	0.993604i	$0.536021\pi$
$968$	−3.05812	−0.0982916
$969$	0	0
$970$	−10.7646	−0.345631
$971$	−13.0628	−0.419206	−0.209603	−	0.977787i	$-0.567217\pi$
$971$	−13.0628	−0.419206	−0.209603	+	0.977787i	$0.567217\pi$
$972$	−5.31636	−0.170522
$973$	4.91336	0.157515
$974$	2.43803	0.0781194
$975$	6.42851	0.205877
$976$	−32.9488	−1.05467
$977$	−31.2042	−0.998311	−0.499156	−	0.866512i	$-0.666356\pi$
$977$	−31.2042	−0.998311	−0.499156	+	0.866512i	$0.666356\pi$
$978$	54.7773	1.75159
$979$	15.2049	0.485951
$980$	−9.04642	−0.288977
$981$	−13.5820	−0.433641
$982$	26.1342	0.833976
$983$	26.6683	0.850587	0.425294	−	0.905055i	$-0.360171\pi$
$983$	26.6683	0.850587	0.425294	+	0.905055i	$0.360171\pi$
$984$	−75.8646	−2.41847
$985$	5.55003	0.176839
$986$	−12.5452	−0.399521
$987$	−0.660461	−0.0210227
$988$	0	0
$989$	14.4015	0.457940
$990$	−3.60246	−0.114494
$991$	41.2444	1.31017	0.655086	−	0.755554i	$-0.272632\pi$
$991$	41.2444	1.31017	0.655086	+	0.755554i	$0.272632\pi$
$992$	−25.7557	−0.817745
$993$	−36.9285	−1.17189
$994$	12.2168	0.387494
$995$	14.4990	0.459650
$996$	−1.20401	−0.0381506
$997$	−21.1364	−0.669396	−0.334698	−	0.942325i	$-0.608634\pi$
$997$	−21.1364	−0.669396	−0.334698	+	0.942325i	$0.608634\pi$
$998$	30.9501	0.979708
$999$	−37.0863	−1.17336

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3971.2.a.k.1.7		9
19.7	even	3		209.2.e.b.144.3	yes	18
19.11	even	3		209.2.e.b.45.3	✓	18
19.18	odd	2		3971.2.a.l.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.e.b.45.3	✓	18	19.11	even	3
209.2.e.b.144.3	yes	18	19.7	even	3
3971.2.a.k.1.7		9	1.1	even	1	trivial
3971.2.a.l.1.3		9	19.18	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:	\( N \)	\(=\)	\( 3971 = 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3971.a (trivial)

\(f(q)\)	\(=\)	\(q+1.23186 q^{2} -2.02769 q^{3} -0.482521 q^{4} +2.63096 q^{5} -2.49783 q^{6} +3.75846 q^{7} -3.05812 q^{8} +1.11154 q^{9} +3.24098 q^{10} -1.00000 q^{11} +0.978405 q^{12} -1.64954 q^{13} +4.62989 q^{14} -5.33478 q^{15} -2.80213 q^{16} -1.41204 q^{17} +1.36926 q^{18} -1.26950 q^{20} -7.62099 q^{21} -1.23186 q^{22} -2.42608 q^{23} +6.20092 q^{24} +1.92197 q^{25} -2.03200 q^{26} +3.82922 q^{27} -1.81354 q^{28} +7.21223 q^{29} -6.57171 q^{30} -9.66660 q^{31} +2.66441 q^{32} +2.02769 q^{33} -1.73944 q^{34} +9.88836 q^{35} -0.536340 q^{36} -9.68506 q^{37} +3.34475 q^{39} -8.04580 q^{40} -12.2344 q^{41} -9.38799 q^{42} -5.93610 q^{43} +0.482521 q^{44} +2.92441 q^{45} -2.98859 q^{46} +0.0866633 q^{47} +5.68186 q^{48} +7.12599 q^{49} +2.36759 q^{50} +2.86318 q^{51} +0.795937 q^{52} -1.19879 q^{53} +4.71707 q^{54} -2.63096 q^{55} -11.4938 q^{56} +8.88446 q^{58} -2.72279 q^{59} +2.57415 q^{60} +11.7585 q^{61} -11.9079 q^{62} +4.17766 q^{63} +8.88643 q^{64} -4.33987 q^{65} +2.49783 q^{66} +4.15566 q^{67} +0.681340 q^{68} +4.91935 q^{69} +12.1811 q^{70} +2.63868 q^{71} -3.39921 q^{72} +12.2328 q^{73} -11.9306 q^{74} -3.89716 q^{75} -3.75846 q^{77} +4.12027 q^{78} +3.17735 q^{79} -7.37230 q^{80} -11.0991 q^{81} -15.0711 q^{82} -1.23059 q^{83} +3.67729 q^{84} -3.71503 q^{85} -7.31244 q^{86} -14.6242 q^{87} +3.05812 q^{88} -15.2049 q^{89} +3.60246 q^{90} -6.19971 q^{91} +1.17064 q^{92} +19.6009 q^{93} +0.106757 q^{94} -5.40259 q^{96} -3.32141 q^{97} +8.77823 q^{98} -1.11154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - q^{2} + 9 q^{4} + 3 q^{6} - 3 q^{7} + 11 q^{9} - 21 q^{10} - 9 q^{11} + 8 q^{12} - 11 q^{13} - q^{14} - 7 q^{15} + 13 q^{16} - 6 q^{17} - 4 q^{18} + 2 q^{20} - 24 q^{21} + q^{22} + q^{23} + 3 q^{24}+ \cdots - 11 q^{99}+O(q^{100}) \) 9 * q - q^2 + 9 * q^4 + 3 * q^6 - 3 * q^7 + 11 * q^9 - 21 * q^10 - 9 * q^11 + 8 * q^12 - 11 * q^13 - q^14 - 7 * q^15 + 13 * q^16 - 6 * q^17 - 4 * q^18 + 2 * q^20 - 24 * q^21 + q^22 + q^23 + 3 * q^24 + 7 * q^25 - 2 * q^26 + 3 * q^27 + 2 * q^28 - 13 * q^29 - 32 * q^30 - 16 * q^31 + 14 * q^32 - 8 * q^34 + 12 * q^35 - 10 * q^36 - 18 * q^37 + 10 * q^39 - 32 * q^40 - 4 * q^41 - 11 * q^42 - q^43 - 9 * q^44 + 11 * q^45 - 7 * q^46 + 14 * q^47 - 37 * q^48 - 6 * q^49 + 15 * q^50 + 16 * q^51 - 57 * q^52 + 4 * q^53 + 33 * q^54 - 17 * q^56 + 4 * q^58 - 31 * q^59 - 9 * q^60 - 3 * q^61 - 5 * q^62 - 50 * q^63 + 32 * q^64 - 28 * q^65 - 3 * q^66 + 2 * q^67 - 48 * q^68 + 58 * q^70 + 12 * q^71 - 5 * q^72 + 26 * q^73 - 35 * q^74 + 25 * q^75 + 3 * q^77 - 3 * q^78 - 31 * q^79 - 31 * q^80 + 21 * q^81 - 25 * q^82 + 18 * q^83 - 51 * q^84 + 11 * q^85 - 41 * q^86 - 62 * q^87 + 11 * q^89 - 51 * q^90 + 20 * q^91 + 33 * q^92 - 20 * q^93 - 43 * q^94 + 30 * q^96 - 16 * q^97 - 4 * q^98 - 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more