LMFDB - Embedded newform 3751.2.a.l.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3751,2,Mod(1,3751)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3751, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3751.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3751 = 11^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3751.a (trivial)

Newform invariants

comment:select newform

sage:traces = [15,-1,2,17,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$29.9518857982$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 23 x^{13} + 21 x^{12} + 204 x^{11} - 160 x^{10} - 880 x^{9} + 535 x^{8} + 1918 x^{7} + \cdots + 4 $ x^15 - x^14 - 23x^13 + 21x^12 + 204x^11 - 160x^10 - 880x^9 + 535x^8 + 1918x^7 - 751x^6 - 1980x^5 + 313x^4 + 845x^3 + 37x^2 - 72*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 23 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.240763$ of defining polynomial
Character	$\chi$	$=$	3751.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.240763 q^{2} +0.685295 q^{3} -1.94203 q^{4} -1.44419 q^{5} -0.164993 q^{6} +4.65408 q^{7} +0.949094 q^{8} -2.53037 q^{9} +0.347707 q^{10} -1.33087 q^{12} +2.11164 q^{13} -1.12053 q^{14} -0.989697 q^{15} +3.65556 q^{16} +7.24162 q^{17} +0.609219 q^{18} +0.972100 q^{19} +2.80467 q^{20} +3.18942 q^{21} -0.403744 q^{23} +0.650409 q^{24} -2.91431 q^{25} -0.508403 q^{26} -3.78993 q^{27} -9.03838 q^{28} +10.6517 q^{29} +0.238282 q^{30} -1.00000 q^{31} -2.77831 q^{32} -1.74351 q^{34} -6.72139 q^{35} +4.91407 q^{36} -4.95782 q^{37} -0.234045 q^{38} +1.44709 q^{39} -1.37067 q^{40} -9.56967 q^{41} -0.767893 q^{42} -6.39348 q^{43} +3.65434 q^{45} +0.0972065 q^{46} -4.05721 q^{47} +2.50514 q^{48} +14.6605 q^{49} +0.701657 q^{50} +4.96264 q^{51} -4.10087 q^{52} +7.85349 q^{53} +0.912474 q^{54} +4.41716 q^{56} +0.666175 q^{57} -2.56453 q^{58} -5.89619 q^{59} +1.92202 q^{60} +5.92581 q^{61} +0.240763 q^{62} -11.7766 q^{63} -6.64221 q^{64} -3.04961 q^{65} -10.2449 q^{67} -14.0635 q^{68} -0.276684 q^{69} +1.61826 q^{70} +1.06019 q^{71} -2.40156 q^{72} +7.79694 q^{73} +1.19366 q^{74} -1.99716 q^{75} -1.88785 q^{76} -0.348406 q^{78} +14.5005 q^{79} -5.27933 q^{80} +4.99389 q^{81} +2.30402 q^{82} -4.42688 q^{83} -6.19396 q^{84} -10.4583 q^{85} +1.53931 q^{86} +7.29956 q^{87} +7.28573 q^{89} -0.879829 q^{90} +9.82773 q^{91} +0.784084 q^{92} -0.685295 q^{93} +0.976824 q^{94} -1.40390 q^{95} -1.90396 q^{96} +13.7014 q^{97} -3.52969 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - q^{2} + 2 q^{3} + 17 q^{4} + 8 q^{5} + 2 q^{6} - 3 q^{8} + 25 q^{9} + 15 q^{10} + 11 q^{12} + 4 q^{13} + 9 q^{14} + 15 q^{15} + 29 q^{16} + 2 q^{17} - 4 q^{18} - 5 q^{19} + 17 q^{20} + 15 q^{21}+ \cdots + 31 q^{98}+O(q^{100}) $ 15 * q - q^2 + 2 * q^3 + 17 * q^4 + 8 * q^5 + 2 * q^6 - 3 * q^8 + 25 * q^9 + 15 * q^10 + 11 * q^12 + 4 * q^13 + 9 * q^14 + 15 * q^15 + 29 * q^16 + 2 * q^17 - 4 * q^18 - 5 * q^19 + 17 * q^20 + 15 * q^21 + 17 * q^23 + 18 * q^24 + 27 * q^25 + 22 * q^26 + 17 * q^27 - 35 * q^28 - 7 * q^29 - 27 * q^30 - 15 * q^31 + 23 * q^32 + 15 * q^34 - 9 * q^35 - 3 * q^36 + 17 * q^37 + 4 * q^38 - 18 * q^39 + 51 * q^40 + 7 * q^41 - 17 * q^42 + 12 * q^43 + 18 * q^45 - 20 * q^46 - 8 * q^47 + 21 * q^48 + 37 * q^49 - 16 * q^50 + 52 * q^51 - 35 * q^52 + 26 * q^53 + 48 * q^54 + 8 * q^56 - 44 * q^57 - 55 * q^58 + 11 * q^59 + 108 * q^60 - 17 * q^61 + q^62 - 22 * q^63 - 3 * q^64 + 12 * q^65 - 31 * q^67 - 30 * q^68 - 16 * q^69 - 8 * q^70 + 35 * q^71 - 59 * q^72 + q^73 - 5 * q^74 + 61 * q^75 + 12 * q^76 + q^78 - 14 * q^79 + 27 * q^80 + 83 * q^81 + 39 * q^82 - 26 * q^83 + 46 * q^84 - 16 * q^85 + 51 * q^86 - 43 * q^87 + 73 * q^89 + 45 * q^90 - 23 * q^91 + 19 * q^92 - 2 * q^93 - 46 * q^94 + 59 * q^95 - 53 * q^96 + 34 * q^97 + 31 * q^98

Coefficient data

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

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

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

$2$	−0.240763	−0.170245	−0.0851224	−	0.996370i	$-0.527128\pi$
$2$	−0.240763	−0.170245	−0.0851224	+	0.996370i	$0.527128\pi$
$3$	0.685295	0.395655	0.197828	−	0.980237i	$-0.436611\pi$
$3$	0.685295	0.395655	0.197828	+	0.980237i	$0.436611\pi$
$4$	−1.94203	−0.971017
$5$	−1.44419	−0.645862	−0.322931	−	0.946422i	$-0.604668\pi$
$5$	−1.44419	−0.645862	−0.322931	+	0.946422i	$0.604668\pi$
$6$	−0.164993	−0.0673582
$7$	4.65408	1.75908	0.879539	−	0.475827i	$-0.157851\pi$
$7$	4.65408	1.75908	0.879539	+	0.475827i	$0.157851\pi$
$8$	0.949094	0.335555
$9$	−2.53037	−0.843457
$10$	0.347707	0.109955
$11$	0	0
$11$	0	0
$12$	−1.33087	−0.384188
$13$	2.11164	0.585663	0.292831	−	0.956164i	$-0.405403\pi$
$13$	2.11164	0.585663	0.292831	+	0.956164i	$0.405403\pi$
$14$	−1.12053	−0.299474
$15$	−0.989697	−0.255539
$16$	3.65556	0.913890
$17$	7.24162	1.75635	0.878175	−	0.478340i	$-0.158761\pi$
$17$	7.24162	1.75635	0.878175	+	0.478340i	$0.158761\pi$
$18$	0.609219	0.143594
$19$	0.972100	0.223015	0.111508	−	0.993764i	$-0.464432\pi$
$19$	0.972100	0.223015	0.111508	+	0.993764i	$0.464432\pi$
$20$	2.80467	0.627143
$21$	3.18942	0.695988
$22$	0	0
$23$	−0.403744	−0.0841864	−0.0420932	−	0.999114i	$-0.513403\pi$
$23$	−0.403744	−0.0841864	−0.0420932	+	0.999114i	$0.513403\pi$
$24$	0.650409	0.132764
$25$	−2.91431	−0.582862
$26$	−0.508403	−0.0997061
$27$	−3.78993	−0.729373
$28$	−9.03838	−1.70809
$29$	10.6517	1.97797	0.988986	−	0.148006i	$-0.0472856\pi$
$29$	10.6517	1.97797	0.988986	+	0.148006i	$0.0472856\pi$
$30$	0.238282	0.0435041
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−2.77831	−0.491141
$33$	0	0
$34$	−1.74351	−0.299010
$35$	−6.72139	−1.13612
$36$	4.91407	0.819011
$37$	−4.95782	−0.815060	−0.407530	−	0.913192i	$-0.633610\pi$
$37$	−4.95782	−0.815060	−0.407530	+	0.913192i	$0.633610\pi$
$38$	−0.234045	−0.0379672
$39$	1.44709	0.231720
$40$	−1.37067	−0.216723
$41$	−9.56967	−1.49453	−0.747265	−	0.664526i	$-0.768634\pi$
$41$	−9.56967	−1.49453	−0.747265	+	0.664526i	$0.768634\pi$
$42$	−0.767893	−0.118488
$43$	−6.39348	−0.974997	−0.487498	−	0.873124i	$-0.662091\pi$
$43$	−6.39348	−0.974997	−0.487498	+	0.873124i	$0.662091\pi$
$44$	0	0
$45$	3.65434	0.544757
$46$	0.0972065	0.0143323
$47$	−4.05721	−0.591805	−0.295902	−	0.955218i	$-0.595620\pi$
$47$	−4.05721	−0.591805	−0.295902	+	0.955218i	$0.595620\pi$
$48$	2.50514	0.361585
$49$	14.6605	2.09435
$50$	0.701657	0.0992293
$51$	4.96264	0.694909
$52$	−4.10087	−0.568688
$53$	7.85349	1.07876	0.539380	−	0.842063i	$-0.318659\pi$
$53$	7.85349	1.07876	0.539380	+	0.842063i	$0.318659\pi$
$54$	0.912474	0.124172
$55$	0	0
$56$	4.41716	0.590268
$57$	0.666175	0.0882371
$58$	−2.56453	−0.336740
$59$	−5.89619	−0.767619	−0.383809	−	0.923412i	$-0.625388\pi$
$59$	−5.89619	−0.767619	−0.383809	+	0.923412i	$0.625388\pi$
$60$	1.92202	0.248132
$61$	5.92581	0.758722	0.379361	−	0.925249i	$-0.376144\pi$
$61$	5.92581	0.758722	0.379361	+	0.925249i	$0.376144\pi$
$62$	0.240763	0.0305769
$63$	−11.7766	−1.48371
$64$	−6.64221	−0.830276
$65$	−3.04961	−0.378257
$66$	0	0
$67$	−10.2449	−1.25161	−0.625807	−	0.779978i	$-0.715230\pi$
$67$	−10.2449	−1.25161	−0.625807	+	0.779978i	$0.715230\pi$
$68$	−14.0635	−1.70544
$69$	−0.276684	−0.0333088
$70$	1.61826	0.193419
$71$	1.06019	0.125821	0.0629105	−	0.998019i	$-0.479962\pi$
$71$	1.06019	0.125821	0.0629105	+	0.998019i	$0.479962\pi$
$72$	−2.40156	−0.283027
$73$	7.79694	0.912563	0.456281	−	0.889835i	$-0.349181\pi$
$73$	7.79694	0.912563	0.456281	+	0.889835i	$0.349181\pi$
$74$	1.19366	0.138760
$75$	−1.99716	−0.230612
$76$	−1.88785	−0.216551
$77$	0	0
$78$	−0.348406	−0.0394492
$79$	14.5005	1.63143	0.815717	−	0.578451i	$-0.196343\pi$
$79$	14.5005	1.63143	0.815717	+	0.578451i	$0.196343\pi$
$80$	−5.27933	−0.590247
$81$	4.99389	0.554877
$82$	2.30402	0.254436
$83$	−4.42688	−0.485914	−0.242957	−	0.970037i	$-0.578117\pi$
$83$	−4.42688	−0.485914	−0.242957	+	0.970037i	$0.578117\pi$
$84$	−6.19396	−0.675816
$85$	−10.4583	−1.13436
$86$	1.53931	0.165988
$87$	7.29956	0.782595
$88$	0	0
$89$	7.28573	0.772285	0.386143	−	0.922439i	$-0.373807\pi$
$89$	7.28573	0.772285	0.386143	+	0.922439i	$0.373807\pi$
$90$	−0.879829	−0.0927421
$91$	9.82773	1.03023
$92$	0.784084	0.0817464
$93$	−0.685295	−0.0710618
$94$	0.976824	0.100752
$95$	−1.40390	−0.144037
$96$	−1.90396	−0.194322
$97$	13.7014	1.39116	0.695582	−	0.718447i	$-0.255147\pi$
$97$	13.7014	1.39116	0.695582	+	0.718447i	$0.255147\pi$
$98$	−3.52969	−0.356553
$99$	0	0
$100$	5.65969	0.565969
$101$	16.2469	1.61662	0.808312	−	0.588755i	$-0.200382\pi$
$101$	16.2469	1.61662	0.808312	+	0.588755i	$0.200382\pi$
$102$	−1.19482	−0.118305
$103$	13.6050	1.34054	0.670269	−	0.742118i	$-0.266179\pi$
$103$	13.6050	1.34054	0.670269	+	0.742118i	$0.266179\pi$
$104$	2.00414	0.196522
$105$	−4.60613	−0.449512
$106$	−1.89083	−0.183653
$107$	2.95670	0.285835	0.142917	−	0.989735i	$-0.454352\pi$
$107$	2.95670	0.285835	0.142917	+	0.989735i	$0.454352\pi$
$108$	7.36018	0.708234
$109$	19.3947	1.85768	0.928838	−	0.370486i	$-0.120809\pi$
$109$	19.3947	1.85768	0.928838	+	0.370486i	$0.120809\pi$
$110$	0	0
$111$	−3.39757	−0.322483
$112$	17.0133	1.60760
$113$	0.755335	0.0710559	0.0355280	−	0.999369i	$-0.488689\pi$
$113$	0.755335	0.0710559	0.0355280	+	0.999369i	$0.488689\pi$
$114$	−0.160390	−0.0150219
$115$	0.583084	0.0543728
$116$	−20.6860	−1.92064
$117$	−5.34323	−0.493981
$118$	1.41958	0.130683
$119$	33.7031	3.08956
$120$	−0.939316	−0.0857474
$121$	0	0
$122$	−1.42671	−0.129168
$123$	−6.55804	−0.591319
$124$	1.94203	0.174400
$125$	11.4298	1.02231
$126$	2.83535	0.252593
$127$	−17.9477	−1.59260	−0.796298	−	0.604904i	$-0.793211\pi$
$127$	−17.9477	−1.59260	−0.796298	+	0.604904i	$0.793211\pi$
$128$	7.15582	0.632491
$129$	−4.38142	−0.385763
$130$	0.734232	0.0643964
$131$	3.43573	0.300181	0.150090	−	0.988672i	$-0.452044\pi$
$131$	3.43573	0.300181	0.150090	+	0.988672i	$0.452044\pi$
$132$	0	0
$133$	4.52423	0.392301
$134$	2.46659	0.213081
$135$	5.47339	0.471075
$136$	6.87297	0.589353
$137$	−9.15594	−0.782245	−0.391122	−	0.920339i	$-0.627913\pi$
$137$	−9.15594	−0.782245	−0.391122	+	0.920339i	$0.627913\pi$
$138$	0.0666151	0.00567065
$139$	−6.69021	−0.567457	−0.283728	−	0.958905i	$-0.591571\pi$
$139$	−6.69021	−0.567457	−0.283728	+	0.958905i	$0.591571\pi$
$140$	13.0532	1.10319
$141$	−2.78038	−0.234151
$142$	−0.255253	−0.0214204
$143$	0	0
$144$	−9.24992	−0.770827
$145$	−15.3831	−1.27750
$146$	−1.87721	−0.155359
$147$	10.0467	0.828642
$148$	9.62825	0.791437
$149$	−3.83569	−0.314232	−0.157116	−	0.987580i	$-0.550220\pi$
$149$	−3.83569	−0.314232	−0.157116	+	0.987580i	$0.550220\pi$
$150$	0.480842	0.0392606
$151$	−12.6764	−1.03159	−0.515795	−	0.856712i	$-0.672503\pi$
$151$	−12.6764	−1.03159	−0.515795	+	0.856712i	$0.672503\pi$
$152$	0.922615	0.0748339
$153$	−18.3240	−1.48141
$154$	0	0
$155$	1.44419	0.116000
$156$	−2.81030	−0.225004
$157$	−10.6155	−0.847208	−0.423604	−	0.905848i	$-0.639235\pi$
$157$	−10.6155	−0.847208	−0.423604	+	0.905848i	$0.639235\pi$
$158$	−3.49118	−0.277743
$159$	5.38196	0.426817
$160$	4.01241	0.317209
$161$	−1.87906	−0.148090
$162$	−1.20234	−0.0944649
$163$	−13.5530	−1.06156	−0.530778	−	0.847511i	$-0.678100\pi$
$163$	−13.5530	−1.06156	−0.530778	+	0.847511i	$0.678100\pi$
$164$	18.5846	1.45121
$165$	0	0
$166$	1.06583	0.0827243
$167$	1.15677	0.0895136	0.0447568	−	0.998998i	$-0.485749\pi$
$167$	1.15677	0.0895136	0.0447568	+	0.998998i	$0.485749\pi$
$168$	3.02706	0.233543
$169$	−8.54099	−0.656999
$170$	2.51796	0.193119
$171$	−2.45977	−0.188104
$172$	12.4164	0.946738
$173$	10.3009	0.783161	0.391580	−	0.920144i	$-0.371928\pi$
$173$	10.3009	0.783161	0.391580	+	0.920144i	$0.371928\pi$
$174$	−1.75746	−0.133233
$175$	−13.5634	−1.02530
$176$	0	0
$177$	−4.04063	−0.303712
$178$	−1.75413	−0.131478
$179$	−8.60113	−0.642879	−0.321439	−	0.946930i	$-0.604167\pi$
$179$	−8.60113	−0.642879	−0.321439	+	0.946930i	$0.604167\pi$
$180$	−7.09685	−0.528968
$181$	−2.36287	−0.175631	−0.0878155	−	0.996137i	$-0.527989\pi$
$181$	−2.36287	−0.175631	−0.0878155	+	0.996137i	$0.527989\pi$
$182$	−2.36615	−0.175391
$183$	4.06092	0.300192
$184$	−0.383191	−0.0282492
$185$	7.16004	0.526417
$186$	0.164993	0.0120979
$187$	0	0
$188$	7.87923	0.574652
$189$	−17.6387	−1.28302
$190$	0.338006	0.0245216
$191$	25.9038	1.87434	0.937168	−	0.348879i	$-0.113438\pi$
$191$	25.9038	1.87434	0.937168	+	0.348879i	$0.113438\pi$
$192$	−4.55187	−0.328503
$193$	5.37296	0.386754	0.193377	−	0.981125i	$-0.438056\pi$
$193$	5.37296	0.386754	0.193377	+	0.981125i	$0.438056\pi$
$194$	−3.29878	−0.236838
$195$	−2.08988	−0.149659
$196$	−28.4711	−2.03365
$197$	13.2374	0.943125	0.471563	−	0.881833i	$-0.343690\pi$
$197$	13.2374	0.943125	0.471563	+	0.881833i	$0.343690\pi$
$198$	0	0
$199$	19.9091	1.41132	0.705660	−	0.708550i	$-0.250651\pi$
$199$	19.9091	1.41132	0.705660	+	0.708550i	$0.250651\pi$
$200$	−2.76596	−0.195583
$201$	−7.02078	−0.495208
$202$	−3.91164	−0.275222
$203$	49.5739	3.47941
$204$	−9.63761	−0.674768
$205$	13.8204	0.965261
$206$	−3.27557	−0.228220
$207$	1.02162	0.0710077
$208$	7.71922	0.535231
$209$	0	0
$210$	1.10898	0.0765272
$211$	−3.10581	−0.213813	−0.106906	−	0.994269i	$-0.534094\pi$
$211$	−3.10581	−0.213813	−0.106906	+	0.994269i	$0.534094\pi$
$212$	−15.2517	−1.04749
$213$	0.726540	0.0497817
$214$	−0.711863	−0.0486619
$215$	9.23341	0.629714
$216$	−3.59700	−0.244745
$217$	−4.65408	−0.315940
$218$	−4.66952	−0.316260
$219$	5.34320	0.361060
$220$	0	0
$221$	15.2917	1.02863
$222$	0.818007	0.0549010
$223$	2.17232	0.145469	0.0727347	−	0.997351i	$-0.476827\pi$
$223$	2.17232	0.145469	0.0727347	+	0.997351i	$0.476827\pi$
$224$	−12.9305	−0.863954
$225$	7.37429	0.491619
$226$	−0.181856	−0.0120969
$227$	6.13958	0.407498	0.203749	−	0.979023i	$-0.434687\pi$
$227$	6.13958	0.407498	0.203749	+	0.979023i	$0.434687\pi$
$228$	−1.29373	−0.0856797
$229$	−2.15039	−0.142102	−0.0710509	−	0.997473i	$-0.522635\pi$
$229$	−2.15039	−0.142102	−0.0710509	+	0.997473i	$0.522635\pi$
$230$	−0.140385	−0.00925670
$231$	0	0
$232$	10.1095	0.663720
$233$	22.4875	1.47320	0.736601	−	0.676327i	$-0.236430\pi$
$233$	22.4875	1.47320	0.736601	+	0.676327i	$0.236430\pi$
$234$	1.28645	0.0840978
$235$	5.85939	0.382224
$236$	11.4506	0.745370
$237$	9.93712	0.645485
$238$	−8.11444	−0.525981
$239$	28.0463	1.81416	0.907082	−	0.420954i	$-0.138305\pi$
$239$	28.0463	1.81416	0.907082	+	0.420954i	$0.138305\pi$
$240$	−3.61790	−0.233534
$241$	−4.12665	−0.265821	−0.132910	−	0.991128i	$-0.542432\pi$
$241$	−4.12665	−0.265821	−0.132910	+	0.991128i	$0.542432\pi$
$242$	0	0
$243$	14.7921	0.948913
$244$	−11.5081	−0.736731
$245$	−21.1725	−1.35266
$246$	1.57893	0.100669
$247$	2.05272	0.130612
$248$	−0.949094	−0.0602675
$249$	−3.03372	−0.192254
$250$	−2.75186	−0.174043
$251$	−13.5923	−0.857937	−0.428969	−	0.903319i	$-0.641123\pi$
$251$	−13.5923	−0.857937	−0.428969	+	0.903319i	$0.641123\pi$
$252$	22.8705	1.44070
$253$	0	0
$254$	4.32112	0.271131
$255$	−7.16700	−0.448815
$256$	11.5616	0.722598
$257$	−2.15904	−0.134678	−0.0673388	−	0.997730i	$-0.521451\pi$
$257$	−2.15904	−0.134678	−0.0673388	+	0.997730i	$0.521451\pi$
$258$	1.05488	0.0656741
$259$	−23.0741	−1.43375
$260$	5.92244	0.367294
$261$	−26.9528	−1.66834
$262$	−0.827194	−0.0511042
$263$	11.3990	0.702895	0.351447	−	0.936208i	$-0.385690\pi$
$263$	11.3990	0.702895	0.351447	+	0.936208i	$0.385690\pi$
$264$	0	0
$265$	−11.3419	−0.696730
$266$	−1.08927	−0.0667872
$267$	4.99287	0.305559
$268$	19.8959	1.21534
$269$	−19.3939	−1.18246	−0.591232	−	0.806501i	$-0.701358\pi$
$269$	−19.3939	−1.18246	−0.591232	+	0.806501i	$0.701358\pi$
$270$	−1.31779	−0.0801980
$271$	17.6839	1.07422	0.537111	−	0.843512i	$-0.319516\pi$
$271$	17.6839	1.07422	0.537111	+	0.843512i	$0.319516\pi$
$272$	26.4722	1.60511
$273$	6.73489	0.407614
$274$	2.20441	0.133173
$275$	0	0
$276$	0.537329	0.0323434
$277$	−9.20195	−0.552891	−0.276446	−	0.961030i	$-0.589157\pi$
$277$	−9.20195	−0.552891	−0.276446	+	0.961030i	$0.589157\pi$
$278$	1.61075	0.0966066
$279$	2.53037	0.151489
$280$	−6.37923	−0.381232
$281$	13.0580	0.778976	0.389488	−	0.921032i	$-0.372652\pi$
$281$	13.0580	0.778976	0.389488	+	0.921032i	$0.372652\pi$
$282$	0.669412	0.0398629
$283$	−18.3111	−1.08848	−0.544240	−	0.838930i	$-0.683182\pi$
$283$	−18.3111	−1.08848	−0.544240	+	0.838930i	$0.683182\pi$
$284$	−2.05892	−0.122174
$285$	−0.962085	−0.0569890
$286$	0	0
$287$	−44.5380	−2.62900
$288$	7.03016	0.414256
$289$	35.4410	2.08476
$290$	3.70368	0.217487
$291$	9.38948	0.550421
$292$	−15.1419	−0.886114
$293$	16.5243	0.965359	0.482680	−	0.875797i	$-0.339664\pi$
$293$	16.5243	0.965359	0.482680	+	0.875797i	$0.339664\pi$
$294$	−2.41888	−0.141072
$295$	8.51523	0.495776
$296$	−4.70544	−0.273498
$297$	0	0
$298$	0.923491	0.0534964
$299$	−0.852561	−0.0493049
$300$	3.87855	0.223928
$301$	−29.7558	−1.71510
$302$	3.05200	0.175623
$303$	11.1339	0.639625
$304$	3.55357	0.203811
$305$	−8.55800	−0.490030
$306$	4.41173	0.252202
$307$	19.9820	1.14043	0.570216	−	0.821495i	$-0.306859\pi$
$307$	19.9820	1.14043	0.570216	+	0.821495i	$0.306859\pi$
$308$	0	0
$309$	9.32342	0.530391
$310$	−0.347707	−0.0197484
$311$	−4.28152	−0.242782	−0.121391	−	0.992605i	$-0.538736\pi$
$311$	−4.28152	−0.242782	−0.121391	+	0.992605i	$0.538736\pi$
$312$	1.37343	0.0777551
$313$	−22.8941	−1.29405	−0.647026	−	0.762468i	$-0.723987\pi$
$313$	−22.8941	−1.29405	−0.647026	+	0.762468i	$0.723987\pi$
$314$	2.55581	0.144233
$315$	17.0076	0.958270
$316$	−28.1605	−1.58415
$317$	23.5110	1.32051	0.660255	−	0.751041i	$-0.270448\pi$
$317$	23.5110	1.32051	0.660255	+	0.751041i	$0.270448\pi$
$318$	−1.29577	−0.0726634
$319$	0	0
$320$	9.59262	0.536244
$321$	2.02621	0.113092
$322$	0.452407	0.0252116
$323$	7.03958	0.391692
$324$	−9.69830	−0.538795
$325$	−6.15397	−0.341361
$326$	3.26306	0.180724
$327$	13.2911	0.734999
$328$	−9.08251	−0.501498
$329$	−18.8826	−1.04103
$330$	0	0
$331$	16.7939	0.923074	0.461537	−	0.887121i	$-0.347298\pi$
$331$	16.7939	0.923074	0.461537	+	0.887121i	$0.347298\pi$
$332$	8.59716	0.471830
$333$	12.5451	0.687468
$334$	−0.278507	−0.0152392
$335$	14.7956	0.808370
$336$	11.6591	0.636057
$337$	1.42538	0.0776454	0.0388227	−	0.999246i	$-0.487639\pi$
$337$	1.42538	0.0776454	0.0388227	+	0.999246i	$0.487639\pi$
$338$	2.05635	0.111851
$339$	0.517627	0.0281136
$340$	20.3103	1.10148
$341$	0	0
$342$	0.592222	0.0320237
$343$	35.6525	1.92505
$344$	−6.06802	−0.327166
$345$	0.399584	0.0215129
$346$	−2.48006	−0.133329
$347$	−19.2227	−1.03193	−0.515964	−	0.856610i	$-0.672566\pi$
$347$	−19.2227	−1.03193	−0.515964	+	0.856610i	$0.672566\pi$
$348$	−14.1760	−0.759913
$349$	10.4815	0.561061	0.280530	−	0.959845i	$-0.409490\pi$
$349$	10.4815	0.561061	0.280530	+	0.959845i	$0.409490\pi$
$350$	3.26557	0.174552
$351$	−8.00297	−0.427167
$352$	0	0
$353$	12.8357	0.683178	0.341589	−	0.939850i	$-0.389035\pi$
$353$	12.8357	0.683178	0.341589	+	0.939850i	$0.389035\pi$
$354$	0.972832	0.0517054
$355$	−1.53111	−0.0812630
$356$	−14.1491	−0.749902
$357$	23.0965	1.22240
$358$	2.07083	0.109447
$359$	9.98297	0.526881	0.263441	−	0.964676i	$-0.415143\pi$
$359$	9.98297	0.526881	0.263441	+	0.964676i	$0.415143\pi$
$360$	3.46831	0.182796
$361$	−18.0550	−0.950264
$362$	0.568891	0.0299003
$363$	0	0
$364$	−19.0858	−1.00037
$365$	−11.2603	−0.589390
$366$	−0.977718	−0.0511062
$367$	−19.7915	−1.03311	−0.516554	−	0.856255i	$-0.672785\pi$
$367$	−19.7915	−1.03311	−0.516554	+	0.856255i	$0.672785\pi$
$368$	−1.47591	−0.0769372
$369$	24.2148	1.26057
$370$	−1.72387	−0.0896197
$371$	36.5508	1.89762
$372$	1.33087	0.0690022
$373$	18.0408	0.934117	0.467059	−	0.884226i	$-0.345314\pi$
$373$	18.0408	0.934117	0.467059	+	0.884226i	$0.345314\pi$
$374$	0	0
$375$	7.83277	0.404482
$376$	−3.85067	−0.198583
$377$	22.4925	1.15843
$378$	4.24673	0.218428
$379$	23.9558	1.23053	0.615263	−	0.788322i	$-0.289050\pi$
$379$	23.9558	1.23053	0.615263	+	0.788322i	$0.289050\pi$
$380$	2.72642	0.139862
$381$	−12.2994	−0.630119
$382$	−6.23667	−0.319096
$383$	−19.3629	−0.989396	−0.494698	−	0.869065i	$-0.664721\pi$
$383$	−19.3629	−0.989396	−0.494698	+	0.869065i	$0.664721\pi$
$384$	4.90384	0.250248
$385$	0	0
$386$	−1.29361	−0.0658429
$387$	16.1779	0.822368
$388$	−26.6085	−1.35084
$389$	−14.2744	−0.723742	−0.361871	−	0.932228i	$-0.617862\pi$
$389$	−14.2744	−0.723742	−0.361871	+	0.932228i	$0.617862\pi$
$390$	0.503165	0.0254788
$391$	−2.92376	−0.147861
$392$	13.9142	0.702772
$393$	2.35449	0.118768
$394$	−3.18707	−0.160562
$395$	−20.9415	−1.05368
$396$	0	0
$397$	13.8662	0.695927	0.347964	−	0.937508i	$-0.386873\pi$
$397$	13.8662	0.695927	0.347964	+	0.937508i	$0.386873\pi$
$398$	−4.79337	−0.240270
$399$	3.10043	0.155216
$400$	−10.6534	−0.532672
$401$	−8.15013	−0.406998	−0.203499	−	0.979075i	$-0.565231\pi$
$401$	−8.15013	−0.406998	−0.203499	+	0.979075i	$0.565231\pi$
$402$	1.69034	0.0843066
$403$	−2.11164	−0.105188
$404$	−31.5520	−1.56977
$405$	−7.21214	−0.358374
$406$	−11.9355	−0.592351
$407$	0	0
$408$	4.71001	0.233180
$409$	−21.1398	−1.04530	−0.522648	−	0.852549i	$-0.675056\pi$
$409$	−21.1398	−1.04530	−0.522648	+	0.852549i	$0.675056\pi$
$410$	−3.32744	−0.164331
$411$	−6.27452	−0.309499
$412$	−26.4213	−1.30168
$413$	−27.4414	−1.35030
$414$	−0.245968	−0.0120887
$415$	6.39327	0.313833
$416$	−5.86678	−0.287643
$417$	−4.58477	−0.224517
$418$	0	0
$419$	−1.23751	−0.0604562	−0.0302281	−	0.999543i	$-0.509623\pi$
$419$	−1.23751	−0.0604562	−0.0302281	+	0.999543i	$0.509623\pi$
$420$	8.94526	0.436484
$421$	−20.5242	−1.00029	−0.500145	−	0.865942i	$-0.666720\pi$
$421$	−20.5242	−1.00029	−0.500145	+	0.865942i	$0.666720\pi$
$422$	0.747762	0.0364005
$423$	10.2662	0.499162
$424$	7.45370	0.361984
$425$	−21.1043	−1.02371
$426$	−0.174924	−0.00847508
$427$	27.5792	1.33465
$428$	−5.74201	−0.277551
$429$	0	0
$430$	−2.22306	−0.107206
$431$	−23.8757	−1.15005	−0.575026	−	0.818135i	$-0.695008\pi$
$431$	−23.8757	−1.15005	−0.575026	+	0.818135i	$0.695008\pi$
$432$	−13.8543	−0.666567
$433$	−14.6737	−0.705174	−0.352587	−	0.935779i	$-0.614698\pi$
$433$	−14.6737	−0.705174	−0.352587	+	0.935779i	$0.614698\pi$
$434$	1.12053	0.0537871
$435$	−10.5420	−0.505449
$436$	−37.6652	−1.80383
$437$	−0.392480	−0.0187748
$438$	−1.28644	−0.0614686
$439$	−6.71158	−0.320326	−0.160163	−	0.987091i	$-0.551202\pi$
$439$	−6.71158	−0.320326	−0.160163	+	0.987091i	$0.551202\pi$
$440$	0	0
$441$	−37.0964	−1.76650
$442$	−3.68166	−0.175119
$443$	5.49444	0.261049	0.130524	−	0.991445i	$-0.458334\pi$
$443$	5.49444	0.261049	0.130524	+	0.991445i	$0.458334\pi$
$444$	6.59819	0.313136
$445$	−10.5220	−0.498790
$446$	−0.523014	−0.0247654
$447$	−2.62858	−0.124328
$448$	−30.9134	−1.46052
$449$	29.6446	1.39901	0.699507	−	0.714626i	$-0.253403\pi$
$449$	29.6446	1.39901	0.699507	+	0.714626i	$0.253403\pi$
$450$	−1.77545	−0.0836956
$451$	0	0
$452$	−1.46689	−0.0689965
$453$	−8.68706	−0.408153
$454$	−1.47818	−0.0693745
$455$	−14.1931	−0.665384
$456$	0.632263	0.0296084
$457$	13.6242	0.637314	0.318657	−	0.947870i	$-0.396768\pi$
$457$	13.6242	0.637314	0.318657	+	0.947870i	$0.396768\pi$
$458$	0.517734	0.0241921
$459$	−27.4452	−1.28103
$460$	−1.13237	−0.0527969
$461$	4.03538	0.187946	0.0939732	−	0.995575i	$-0.470043\pi$
$461$	4.03538	0.187946	0.0939732	+	0.995575i	$0.470043\pi$
$462$	0	0
$463$	−25.9409	−1.20558	−0.602789	−	0.797901i	$-0.705944\pi$
$463$	−25.9409	−1.20558	−0.602789	+	0.797901i	$0.705944\pi$
$464$	38.9380	1.80765
$465$	0.989697	0.0458961
$466$	−5.41414	−0.250805
$467$	−21.5932	−0.999214	−0.499607	−	0.866252i	$-0.666522\pi$
$467$	−21.5932	−0.999214	−0.499607	+	0.866252i	$0.666522\pi$
$468$	10.3767	0.479664
$469$	−47.6806	−2.20169
$470$	−1.41072	−0.0650717
$471$	−7.27474	−0.335202
$472$	−5.59604	−0.257579
$473$	0	0
$474$	−2.39249	−0.109891
$475$	−2.83300	−0.129987
$476$	−65.4525	−3.00001
$477$	−19.8722	−0.909887
$478$	−6.75250	−0.308852
$479$	17.0080	0.777115	0.388557	−	0.921425i	$-0.372974\pi$
$479$	17.0080	0.777115	0.388557	+	0.921425i	$0.372974\pi$
$480$	2.74969	0.125505
$481$	−10.4691	−0.477350
$482$	0.993543	0.0452546
$483$	−1.28771	−0.0585928
$484$	0	0
$485$	−19.7874	−0.898500
$486$	−3.56138	−0.161548
$487$	−27.5546	−1.24862	−0.624309	−	0.781178i	$-0.714619\pi$
$487$	−27.5546	−1.24862	−0.624309	+	0.781178i	$0.714619\pi$
$488$	5.62415	0.254593
$489$	−9.28782	−0.420010
$490$	5.09756	0.230284
$491$	7.98923	0.360549	0.180274	−	0.983616i	$-0.442301\pi$
$491$	7.98923	0.360549	0.180274	+	0.983616i	$0.442301\pi$
$492$	12.7359	0.574180
$493$	77.1356	3.47401
$494$	−0.494219	−0.0222360
$495$	0	0
$496$	−3.65556	−0.164140
$497$	4.93419	0.221329
$498$	0.730407	0.0327303
$499$	14.1884	0.635161	0.317580	−	0.948231i	$-0.397130\pi$
$499$	14.1884	0.635161	0.317580	+	0.948231i	$0.397130\pi$
$500$	−22.1970	−0.992681
$501$	0.792729	0.0354165
$502$	3.27251	0.146059
$503$	37.5543	1.67446	0.837232	−	0.546848i	$-0.184172\pi$
$503$	37.5543	1.67446	0.837232	+	0.546848i	$0.184172\pi$
$504$	−11.1771	−0.497866
$505$	−23.4636	−1.04412
$506$	0	0
$507$	−5.85309	−0.259945
$508$	34.8549	1.54644
$509$	29.4267	1.30431	0.652157	−	0.758084i	$-0.273864\pi$
$509$	29.4267	1.30431	0.652157	+	0.758084i	$0.273864\pi$
$510$	1.72555	0.0764085
$511$	36.2876	1.60527
$512$	−17.0952	−0.755509
$513$	−3.68420	−0.162661
$514$	0.519817	0.0229282
$515$	−19.6482	−0.865803
$516$	8.50886	0.374582
$517$	0	0
$518$	5.55538	0.244089
$519$	7.05913	0.309862
$520$	−2.89437	−0.126926
$521$	43.7591	1.91712	0.958561	−	0.284888i	$-0.0919563\pi$
$521$	43.7591	1.91712	0.958561	+	0.284888i	$0.0919563\pi$
$522$	6.48922	0.284025
$523$	39.9712	1.74782	0.873910	−	0.486088i	$-0.161577\pi$
$523$	39.9712	1.74782	0.873910	+	0.486088i	$0.161577\pi$
$524$	−6.67229	−0.291481
$525$	−9.29495	−0.405665
$526$	−2.74446	−0.119664
$527$	−7.24162	−0.315450
$528$	0	0
$529$	−22.8370	−0.992913
$530$	2.73072	0.118615
$531$	14.9195	0.647453
$532$	−8.78621	−0.380931
$533$	−20.2077	−0.875291
$534$	−1.20210	−0.0520198
$535$	−4.27004	−0.184610
$536$	−9.72338	−0.419986
$537$	−5.89431	−0.254358
$538$	4.66932	0.201309
$539$	0	0
$540$	−10.6295	−0.457421
$541$	−21.2029	−0.911586	−0.455793	−	0.890086i	$-0.650644\pi$
$541$	−21.2029	−0.911586	−0.455793	+	0.890086i	$0.650644\pi$
$542$	−4.25762	−0.182881
$543$	−1.61926	−0.0694893
$544$	−20.1195	−0.862615
$545$	−28.0097	−1.19980
$546$	−1.62151	−0.0693942
$547$	−17.0400	−0.728578	−0.364289	−	0.931286i	$-0.618688\pi$
$547$	−17.0400	−0.728578	−0.364289	+	0.931286i	$0.618688\pi$
$548$	17.7811	0.759573
$549$	−14.9945	−0.639949
$550$	0	0
$551$	10.3545	0.441118
$552$	−0.262599	−0.0111769
$553$	67.4865	2.86982
$554$	2.21548	0.0941269
$555$	4.90674	0.208279
$556$	12.9926	0.551010
$557$	−6.01265	−0.254764	−0.127382	−	0.991854i	$-0.540657\pi$
$557$	−6.01265	−0.254764	−0.127382	+	0.991854i	$0.540657\pi$
$558$	−0.609219	−0.0257903
$559$	−13.5007	−0.571019
$560$	−24.5704	−1.03829
$561$	0	0
$562$	−3.14388	−0.132617
$563$	−9.17313	−0.386601	−0.193301	−	0.981140i	$-0.561919\pi$
$563$	−9.17313	−0.386601	−0.193301	+	0.981140i	$0.561919\pi$
$564$	5.39960	0.227364
$565$	−1.09085	−0.0458923
$566$	4.40862	0.185308
$567$	23.2420	0.976071
$568$	1.00622	0.0422199
$569$	−8.31495	−0.348581	−0.174290	−	0.984694i	$-0.555763\pi$
$569$	−8.31495	−0.348581	−0.174290	+	0.984694i	$0.555763\pi$
$570$	0.231634	0.00970208
$571$	−46.7306	−1.95561	−0.977807	−	0.209506i	$-0.932814\pi$
$571$	−46.7306	−1.95561	−0.977807	+	0.209506i	$0.932814\pi$
$572$	0	0
$573$	17.7518	0.741590
$574$	10.7231	0.447573
$575$	1.17664	0.0490691
$576$	16.8072	0.700302
$577$	−25.0764	−1.04394	−0.521971	−	0.852963i	$-0.674803\pi$
$577$	−25.0764	−1.04394	−0.521971	+	0.852963i	$0.674803\pi$
$578$	−8.53287	−0.354920
$579$	3.68206	0.153021
$580$	29.8745	1.24047
$581$	−20.6031	−0.854760
$582$	−2.26063	−0.0937063
$583$	0	0
$584$	7.40003	0.306215
$585$	7.71664	0.319044
$586$	−3.97843	−0.164347
$587$	10.7760	0.444774	0.222387	−	0.974958i	$-0.428615\pi$
$587$	10.7760	0.444774	0.222387	+	0.974958i	$0.428615\pi$
$588$	−19.5111	−0.804625
$589$	−0.972100	−0.0400547
$590$	−2.05015	−0.0844033
$591$	9.07152	0.373152
$592$	−18.1236	−0.744875
$593$	−20.8971	−0.858141	−0.429071	−	0.903271i	$-0.641159\pi$
$593$	−20.8971	−0.858141	−0.429071	+	0.903271i	$0.641159\pi$
$594$	0	0
$595$	−48.6737	−1.99543
$596$	7.44904	0.305125
$597$	13.6436	0.558396
$598$	0.205265	0.00839390
$599$	−27.0298	−1.10441	−0.552204	−	0.833709i	$-0.686213\pi$
$599$	−27.0298	−1.10441	−0.552204	+	0.833709i	$0.686213\pi$
$600$	−1.89549	−0.0773832
$601$	−12.5663	−0.512592	−0.256296	−	0.966598i	$-0.582502\pi$
$601$	−12.5663	−0.512592	−0.256296	+	0.966598i	$0.582502\pi$
$602$	7.16408	0.291986
$603$	25.9234	1.05568
$604$	24.6180	1.00169
$605$	0	0
$606$	−2.68062	−0.108893
$607$	−10.3041	−0.418231	−0.209116	−	0.977891i	$-0.567058\pi$
$607$	−10.3041	−0.418231	−0.209116	+	0.977891i	$0.567058\pi$
$608$	−2.70080	−0.109532
$609$	33.9728	1.37665
$610$	2.06045	0.0834250
$611$	−8.56735	−0.346598
$612$	35.5858	1.43847
$613$	46.1388	1.86353	0.931764	−	0.363063i	$-0.118269\pi$
$613$	46.1388	1.86353	0.931764	+	0.363063i	$0.118269\pi$
$614$	−4.81092	−0.194153
$615$	9.47107	0.381910
$616$	0	0
$617$	1.40359	0.0565065	0.0282533	−	0.999601i	$-0.491006\pi$
$617$	1.40359	0.0565065	0.0282533	+	0.999601i	$0.491006\pi$
$618$	−2.24473	−0.0902963
$619$	−41.1842	−1.65533	−0.827667	−	0.561219i	$-0.810332\pi$
$619$	−41.1842	−1.65533	−0.827667	+	0.561219i	$0.810332\pi$
$620$	−2.80467	−0.112638
$621$	1.53016	0.0614033
$622$	1.03083	0.0413325
$623$	33.9084	1.35851
$624$	5.28994	0.211767
$625$	−1.93524	−0.0774096
$626$	5.51204	0.220306
$627$	0	0
$628$	20.6156	0.822653
$629$	−35.9026	−1.43153
$630$	−4.09479	−0.163140
$631$	−18.6894	−0.744012	−0.372006	−	0.928230i	$-0.621330\pi$
$631$	−18.6894	−0.744012	−0.372006	+	0.928230i	$0.621330\pi$
$632$	13.7623	0.547437
$633$	−2.12839	−0.0845960
$634$	−5.66058	−0.224810
$635$	25.9198	1.02860
$636$	−10.4519	−0.414446
$637$	30.9576	1.22659
$638$	0	0
$639$	−2.68266	−0.106125
$640$	−10.3344	−0.408502
$641$	−28.9420	−1.14314	−0.571570	−	0.820553i	$-0.693666\pi$
$641$	−28.9420	−1.14314	−0.571570	+	0.820553i	$0.693666\pi$
$642$	−0.487836	−0.0192533
$643$	−10.0620	−0.396805	−0.198402	−	0.980121i	$-0.563575\pi$
$643$	−10.0620	−0.396805	−0.198402	+	0.980121i	$0.563575\pi$
$644$	3.64919	0.143798
$645$	6.32761	0.249149
$646$	−1.69487	−0.0666836
$647$	20.8412	0.819352	0.409676	−	0.912231i	$-0.365642\pi$
$647$	20.8412	0.819352	0.409676	+	0.912231i	$0.365642\pi$
$648$	4.73967	0.186192
$649$	0	0
$650$	1.48164	0.0581149
$651$	−3.18942	−0.125003
$652$	26.3204	1.03079
$653$	−45.8533	−1.79438	−0.897189	−	0.441648i	$-0.854394\pi$
$653$	−45.8533	−1.79438	−0.897189	+	0.441648i	$0.854394\pi$
$654$	−3.20000	−0.125130
$655$	−4.96185	−0.193875
$656$	−34.9825	−1.36584
$657$	−19.7292	−0.769708
$658$	4.54622	0.177230
$659$	0.339852	0.0132388	0.00661938	−	0.999978i	$-0.497893\pi$
$659$	0.339852	0.0132388	0.00661938	+	0.999978i	$0.497893\pi$
$660$	0	0
$661$	18.7612	0.729724	0.364862	−	0.931062i	$-0.381116\pi$
$661$	18.7612	0.729724	0.364862	+	0.931062i	$0.381116\pi$
$662$	−4.04333	−0.157149
$663$	10.4793	0.406982
$664$	−4.20153	−0.163051
$665$	−6.53386	−0.253372
$666$	−3.02040	−0.117038
$667$	−4.30056	−0.166519
$668$	−2.24649	−0.0869192
$669$	1.48868	0.0575557
$670$	−3.56223	−0.137621
$671$	0	0
$672$	−8.86119	−0.341828
$673$	−8.42653	−0.324819	−0.162409	−	0.986723i	$-0.551927\pi$
$673$	−8.42653	−0.324819	−0.162409	+	0.986723i	$0.551927\pi$
$674$	−0.343178	−0.0132187
$675$	11.0450	0.425124
$676$	16.5869	0.637957
$677$	−4.87889	−0.187511	−0.0937555	−	0.995595i	$-0.529887\pi$
$677$	−4.87889	−0.187511	−0.0937555	+	0.995595i	$0.529887\pi$
$678$	−0.124625	−0.00478620
$679$	63.7673	2.44716
$680$	−9.92589	−0.380641
$681$	4.20742	0.161229
$682$	0	0
$683$	−4.05668	−0.155225	−0.0776123	−	0.996984i	$-0.524730\pi$
$683$	−4.05668	−0.155225	−0.0776123	+	0.996984i	$0.524730\pi$
$684$	4.77696	0.182652
$685$	13.2229	0.505222
$686$	−8.58379	−0.327730
$687$	−1.47365	−0.0562233
$688$	−23.3718	−0.891040
$689$	16.5837	0.631789
$690$	−0.0962049	−0.00366246
$691$	−45.4744	−1.72993	−0.864963	−	0.501836i	$-0.832658\pi$
$691$	−45.4744	−1.72993	−0.864963	+	0.501836i	$0.832658\pi$
$692$	−20.0046	−0.760462
$693$	0	0
$694$	4.62811	0.175681
$695$	9.66195	0.366499
$696$	6.92797	0.262604
$697$	−69.2998	−2.62492
$698$	−2.52355	−0.0955177
$699$	15.4105	0.582880
$700$	26.3407	0.995583
$701$	−25.8852	−0.977672	−0.488836	−	0.872376i	$-0.662578\pi$
$701$	−25.8852	−0.977672	−0.488836	+	0.872376i	$0.662578\pi$
$702$	1.92681	0.0727229
$703$	−4.81950	−0.181771
$704$	0	0
$705$	4.01541	0.151229
$706$	−3.09037	−0.116307
$707$	75.6142	2.84377
$708$	7.84704	0.294910
$709$	19.4320	0.729786	0.364893	−	0.931050i	$-0.381106\pi$
$709$	19.4320	0.729786	0.364893	+	0.931050i	$0.381106\pi$
$710$	0.368635	0.0138346
$711$	−36.6917	−1.37604
$712$	6.91484	0.259145
$713$	0.403744	0.0151203
$714$	−5.56078	−0.208107
$715$	0	0
$716$	16.7037	0.624246
$717$	19.2200	0.717783
$718$	−2.40353	−0.0896988
$719$	41.4188	1.54466	0.772330	−	0.635221i	$-0.219091\pi$
$719$	41.4188	1.54466	0.772330	+	0.635221i	$0.219091\pi$
$720$	13.3587	0.497848
$721$	63.3187	2.35811
$722$	4.34697	0.161778
$723$	−2.82797	−0.105173
$724$	4.58878	0.170541
$725$	−31.0424	−1.15289
$726$	0	0
$727$	−10.1085	−0.374902	−0.187451	−	0.982274i	$-0.560023\pi$
$727$	−10.1085	−0.374902	−0.187451	+	0.982274i	$0.560023\pi$
$728$	9.32744	0.345698
$729$	−4.84473	−0.179434
$730$	2.71105	0.100341
$731$	−46.2991	−1.71244
$732$	−7.88645	−0.291492
$733$	26.9428	0.995156	0.497578	−	0.867419i	$-0.334223\pi$
$733$	26.9428	0.995156	0.497578	+	0.867419i	$0.334223\pi$
$734$	4.76505	0.175881
$735$	−14.5094	−0.535188
$736$	1.12173	0.0413474
$737$	0	0
$738$	−5.83002	−0.214606
$739$	4.50951	0.165885	0.0829425	−	0.996554i	$-0.473568\pi$
$739$	4.50951	0.165885	0.0829425	+	0.996554i	$0.473568\pi$
$740$	−13.9050	−0.511159
$741$	1.40672	0.0516772
$742$	−8.80006	−0.323060
$743$	11.3739	0.417269	0.208635	−	0.977994i	$-0.433098\pi$
$743$	11.3739	0.417269	0.208635	+	0.977994i	$0.433098\pi$
$744$	−0.650409	−0.0238452
$745$	5.53947	0.202951
$746$	−4.34355	−0.159029
$747$	11.2017	0.409847
$748$	0	0
$749$	13.7607	0.502806
$750$	−1.88584	−0.0688611
$751$	−45.8888	−1.67451	−0.837253	−	0.546816i	$-0.815840\pi$
$751$	−45.8888	−1.67451	−0.837253	+	0.546816i	$0.815840\pi$
$752$	−14.8314	−0.540844
$753$	−9.31472	−0.339447
$754$	−5.41536	−0.197216
$755$	18.3071	0.666264
$756$	34.2549	1.24584
$757$	3.19914	0.116275	0.0581374	−	0.998309i	$-0.481484\pi$
$757$	3.19914	0.116275	0.0581374	+	0.998309i	$0.481484\pi$
$758$	−5.76766	−0.209491
$759$	0	0
$760$	−1.33243	−0.0483324
$761$	−12.9849	−0.470702	−0.235351	−	0.971910i	$-0.575624\pi$
$761$	−12.9849	−0.470702	−0.235351	+	0.971910i	$0.575624\pi$
$762$	2.96124	0.107275
$763$	90.2646	3.26780
$764$	−50.3061	−1.82001
$765$	26.4633	0.956784
$766$	4.66185	0.168440
$767$	−12.4506	−0.449566
$768$	7.92308	0.285899
$769$	−27.5944	−0.995080	−0.497540	−	0.867441i	$-0.665763\pi$
$769$	−27.5944	−0.995080	−0.497540	+	0.867441i	$0.665763\pi$
$770$	0	0
$771$	−1.47958	−0.0532858
$772$	−10.4345	−0.375544
$773$	25.8231	0.928793	0.464396	−	0.885627i	$-0.346271\pi$
$773$	25.8231	0.928793	0.464396	+	0.885627i	$0.346271\pi$
$774$	−3.89503	−0.140004
$775$	2.91431	0.104685
$776$	13.0039	0.466812
$777$	−15.8126	−0.567272
$778$	3.43675	0.123213
$779$	−9.30268	−0.333303
$780$	4.05862	0.145322
$781$	0	0
$782$	0.703932	0.0251725
$783$	−40.3693	−1.44268
$784$	53.5923	1.91401
$785$	15.3308	0.547179
$786$	−0.566872	−0.0202197
$787$	4.32407	0.154136	0.0770682	−	0.997026i	$-0.475444\pi$
$787$	4.32407	0.154136	0.0770682	+	0.997026i	$0.475444\pi$
$788$	−25.7075	−0.915790
$789$	7.81170	0.278104
$790$	5.04193	0.179384
$791$	3.51539	0.124993
$792$	0	0
$793$	12.5132	0.444355
$794$	−3.33847	−0.118478
$795$	−7.77257	−0.275665
$796$	−38.6642	−1.37042
$797$	−35.5665	−1.25983	−0.629915	−	0.776664i	$-0.716910\pi$
$797$	−35.5665	−1.25983	−0.629915	+	0.776664i	$0.716910\pi$
$798$	−0.746469	−0.0264247
$799$	−29.3807	−1.03942
$800$	8.09686	0.286267
$801$	−18.4356	−0.651390
$802$	1.96225	0.0692893
$803$	0	0
$804$	13.6346	0.480855
$805$	2.71372	0.0956460
$806$	0.508403	0.0179077
$807$	−13.2905	−0.467848
$808$	15.4198	0.542467
$809$	−36.4165	−1.28034	−0.640168	−	0.768235i	$-0.721135\pi$
$809$	−36.4165	−1.28034	−0.640168	+	0.768235i	$0.721135\pi$
$810$	1.73641	0.0610113
$811$	−9.13391	−0.320735	−0.160368	−	0.987057i	$-0.551268\pi$
$811$	−9.13391	−0.320735	−0.160368	+	0.987057i	$0.551268\pi$
$812$	−96.2742	−3.37856
$813$	12.1187	0.425021
$814$	0	0
$815$	19.5732	0.685619
$816$	18.1412	0.635070
$817$	−6.21511	−0.217439
$818$	5.08967	0.177956
$819$	−24.8678	−0.868952
$820$	−26.8397	−0.937284
$821$	−40.4505	−1.41173	−0.705866	−	0.708345i	$-0.749442\pi$
$821$	−40.4505	−1.41173	−0.705866	+	0.708345i	$0.749442\pi$
$822$	1.51067	0.0526906
$823$	39.6318	1.38148	0.690739	−	0.723104i	$-0.257285\pi$
$823$	39.6318	1.38148	0.690739	+	0.723104i	$0.257285\pi$
$824$	12.9124	0.449825
$825$	0	0
$826$	6.60685	0.229882
$827$	36.7460	1.27778	0.638892	−	0.769296i	$-0.279393\pi$
$827$	36.7460	1.27778	0.638892	+	0.769296i	$0.279393\pi$
$828$	−1.98402	−0.0689496
$829$	8.77892	0.304905	0.152452	−	0.988311i	$-0.451283\pi$
$829$	8.77892	0.304905	0.152452	+	0.988311i	$0.451283\pi$
$830$	−1.53926	−0.0534285
$831$	−6.30605	−0.218754
$832$	−14.0259	−0.486262
$833$	106.166	3.67842
$834$	1.10384	0.0382229
$835$	−1.67060	−0.0578134
$836$	0	0
$837$	3.78993	0.130999
$838$	0.297946	0.0102924
$839$	43.8498	1.51386	0.756931	−	0.653494i	$-0.226698\pi$
$839$	43.8498	1.51386	0.756931	+	0.653494i	$0.226698\pi$
$840$	−4.37165	−0.150836
$841$	84.4589	2.91238
$842$	4.94147	0.170294
$843$	8.94859	0.308206
$844$	6.03158	0.207616
$845$	12.3348	0.424331
$846$	−2.47173	−0.0849797
$847$	0	0
$848$	28.7089	0.985868
$849$	−12.5485	−0.430663
$850$	5.08113	0.174281
$851$	2.00169	0.0686170
$852$	−1.41097	−0.0483389
$853$	41.6678	1.42668	0.713339	−	0.700819i	$-0.247182\pi$
$853$	41.6678	1.42668	0.713339	+	0.700819i	$0.247182\pi$
$854$	−6.64004	−0.227217
$855$	3.55239	0.121489
$856$	2.80619	0.0959135
$857$	−40.4470	−1.38164	−0.690822	−	0.723025i	$-0.742751\pi$
$857$	−40.4470	−1.38164	−0.690822	+	0.723025i	$0.742751\pi$
$858$	0	0
$859$	−25.5186	−0.870685	−0.435342	−	0.900265i	$-0.643373\pi$
$859$	−25.5186	−0.870685	−0.435342	+	0.900265i	$0.643373\pi$
$860$	−17.9316	−0.611462
$861$	−30.5217	−1.04018
$862$	5.74837	0.195790
$863$	−24.3107	−0.827546	−0.413773	−	0.910380i	$-0.635789\pi$
$863$	−24.3107	−0.827546	−0.413773	+	0.910380i	$0.635789\pi$
$864$	10.5296	0.358225
$865$	−14.8764	−0.505814
$866$	3.53288	0.120052
$867$	24.2875	0.824848
$868$	9.03838	0.306783
$869$	0	0
$870$	2.53811	0.0860500
$871$	−21.6335	−0.733024
$872$	18.4074	0.623353
$873$	−34.6695	−1.17339
$874$	0.0944944	0.00319632
$875$	53.1951	1.79832
$876$	−10.3767	−0.350595
$877$	−44.6657	−1.50825	−0.754127	−	0.656729i	$-0.771940\pi$
$877$	−44.6657	−1.50825	−0.754127	+	0.656729i	$0.771940\pi$
$878$	1.61590	0.0545339
$879$	11.3240	0.381949
$880$	0	0
$881$	−13.6417	−0.459601	−0.229800	−	0.973238i	$-0.573807\pi$
$881$	−13.6417	−0.459601	−0.229800	+	0.973238i	$0.573807\pi$
$882$	8.93144	0.300737
$883$	−6.77650	−0.228047	−0.114024	−	0.993478i	$-0.536374\pi$
$883$	−6.77650	−0.228047	−0.114024	+	0.993478i	$0.536374\pi$
$884$	−29.6969	−0.998816
$885$	5.83544	0.196156
$886$	−1.32285	−0.0444422
$887$	29.4593	0.989146	0.494573	−	0.869136i	$-0.335324\pi$
$887$	29.4593	0.989146	0.494573	+	0.869136i	$0.335324\pi$
$888$	−3.22461	−0.108211
$889$	−83.5298	−2.80150
$890$	2.53330	0.0849164
$891$	0	0
$892$	−4.21872	−0.141253
$893$	−3.94401	−0.131981
$894$	0.632864	0.0211661
$895$	12.4217	0.415211
$896$	33.3038	1.11260
$897$	−0.584256	−0.0195077
$898$	−7.13730	−0.238175
$899$	−10.6517	−0.355254
$900$	−14.3211	−0.477370
$901$	56.8719	1.89468
$902$	0	0
$903$	−20.3915	−0.678586
$904$	0.716884	0.0238432
$905$	3.41244	0.113433
$906$	2.09152	0.0694860
$907$	−20.8554	−0.692491	−0.346246	−	0.938144i	$-0.612544\pi$
$907$	−20.8554	−0.692491	−0.346246	+	0.938144i	$0.612544\pi$
$908$	−11.9233	−0.395688
$909$	−41.1106	−1.36355
$910$	3.41717	0.113278
$911$	40.6343	1.34628	0.673138	−	0.739517i	$-0.264946\pi$
$911$	40.6343	1.34628	0.673138	+	0.739517i	$0.264946\pi$
$912$	2.43524	0.0806390
$913$	0	0
$914$	−3.28020	−0.108500
$915$	−5.86475	−0.193883
$916$	4.17613	0.137983
$917$	15.9902	0.528041
$918$	6.60779	0.218090
$919$	41.4755	1.36815	0.684076	−	0.729411i	$-0.260206\pi$
$919$	41.4755	1.36815	0.684076	+	0.729411i	$0.260206\pi$
$920$	0.553401	0.0182451
$921$	13.6936	0.451218
$922$	−0.971569	−0.0319969
$923$	2.23873	0.0736887
$924$	0	0
$925$	14.4486	0.475068
$926$	6.24561	0.205243
$927$	−34.4256	−1.13069
$928$	−29.5938	−0.971463
$929$	25.4975	0.836546	0.418273	−	0.908321i	$-0.362636\pi$
$929$	25.4975	0.836546	0.418273	+	0.908321i	$0.362636\pi$
$930$	−0.238282	−0.00781357
$931$	14.2515	0.467073
$932$	−43.6714	−1.43050
$933$	−2.93410	−0.0960581
$934$	5.19883	0.170111
$935$	0	0
$936$	−5.07122	−0.165758
$937$	19.3420	0.631875	0.315938	−	0.948780i	$-0.397681\pi$
$937$	19.3420	0.631875	0.315938	+	0.948780i	$0.397681\pi$
$938$	11.4797	0.374826
$939$	−15.6892	−0.511998
$940$	−11.3791	−0.371146
$941$	43.9326	1.43216	0.716080	−	0.698018i	$-0.245934\pi$
$941$	43.9326	1.43216	0.716080	+	0.698018i	$0.245934\pi$
$942$	1.75148	0.0570664
$943$	3.86370	0.125819
$944$	−21.5539	−0.701519
$945$	25.4736	0.828657
$946$	0	0
$947$	43.1838	1.40328	0.701642	−	0.712530i	$-0.252451\pi$
$947$	43.1838	1.40328	0.701642	+	0.712530i	$0.252451\pi$
$948$	−19.2982	−0.626777
$949$	16.4643	0.534454
$950$	0.682081	0.0221296
$951$	16.1120	0.522467
$952$	31.9874	1.03672
$953$	−20.0889	−0.650745	−0.325372	−	0.945586i	$-0.605490\pi$
$953$	−20.0889	−0.650745	−0.325372	+	0.945586i	$0.605490\pi$
$954$	4.78449	0.154904
$955$	−37.4101	−1.21056
$956$	−54.4668	−1.76158
$957$	0	0
$958$	−4.09489	−0.132300
$959$	−42.6125	−1.37603
$960$	6.57377	0.212168
$961$	1.00000	0.0322581
$962$	2.52057	0.0812665
$963$	−7.48155	−0.241090
$964$	8.01409	0.258117
$965$	−7.75958	−0.249790
$966$	0.310032	0.00997512
$967$	−20.2574	−0.651435	−0.325717	−	0.945467i	$-0.605606\pi$
$967$	−20.2574	−0.651435	−0.325717	+	0.945467i	$0.605606\pi$
$968$	0	0
$969$	4.82418	0.154975
$970$	4.76407	0.152965
$971$	31.1313	0.999050	0.499525	−	0.866300i	$-0.333508\pi$
$971$	31.1313	0.999050	0.499525	+	0.866300i	$0.333508\pi$
$972$	−28.7267	−0.921410
$973$	−31.1368	−0.998200
$974$	6.63411	0.212571
$975$	−4.21728	−0.135061
$976$	21.6621	0.693388
$977$	−16.3443	−0.522901	−0.261450	−	0.965217i	$-0.584201\pi$
$977$	−16.3443	−0.522901	−0.261450	+	0.965217i	$0.584201\pi$
$978$	2.23616	0.0715045
$979$	0	0
$980$	41.1178	1.31346
$981$	−49.0758	−1.56687
$982$	−1.92351	−0.0613816
$983$	46.7619	1.49147	0.745737	−	0.666241i	$-0.232098\pi$
$983$	46.7619	1.49147	0.745737	+	0.666241i	$0.232098\pi$
$984$	−6.22420	−0.198420
$985$	−19.1173	−0.609129
$986$	−18.5714	−0.591433
$987$	−12.9401	−0.411889
$988$	−3.98646	−0.126826
$989$	2.58133	0.0820815
$990$	0	0
$991$	13.4055	0.425841	0.212921	−	0.977069i	$-0.431702\pi$
$991$	13.4055	0.425841	0.212921	+	0.977069i	$0.431702\pi$
$992$	2.77831	0.0882114
$993$	11.5087	0.365219
$994$	−1.18797	−0.0376801
$995$	−28.7526	−0.911518
$996$	5.89159	0.186682
$997$	−22.3605	−0.708165	−0.354082	−	0.935214i	$-0.615207\pi$
$997$	−22.3605	−0.708165	−0.354082	+	0.935214i	$0.615207\pi$
$998$	−3.41604	−0.108133
$999$	18.7898	0.594483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3751.2.a.l.1.7	✓	15
11.10	odd	2		3751.2.a.m.1.9	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3751.2.a.l.1.7	✓	15	1.1	even	1	trivial
3751.2.a.m.1.9	yes	15	11.10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3751 = 11^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3751.a (trivial)

\(f(q)\)	\(=\)	\(q-0.240763 q^{2} +0.685295 q^{3} -1.94203 q^{4} -1.44419 q^{5} -0.164993 q^{6} +4.65408 q^{7} +0.949094 q^{8} -2.53037 q^{9} +0.347707 q^{10} -1.33087 q^{12} +2.11164 q^{13} -1.12053 q^{14} -0.989697 q^{15} +3.65556 q^{16} +7.24162 q^{17} +0.609219 q^{18} +0.972100 q^{19} +2.80467 q^{20} +3.18942 q^{21} -0.403744 q^{23} +0.650409 q^{24} -2.91431 q^{25} -0.508403 q^{26} -3.78993 q^{27} -9.03838 q^{28} +10.6517 q^{29} +0.238282 q^{30} -1.00000 q^{31} -2.77831 q^{32} -1.74351 q^{34} -6.72139 q^{35} +4.91407 q^{36} -4.95782 q^{37} -0.234045 q^{38} +1.44709 q^{39} -1.37067 q^{40} -9.56967 q^{41} -0.767893 q^{42} -6.39348 q^{43} +3.65434 q^{45} +0.0972065 q^{46} -4.05721 q^{47} +2.50514 q^{48} +14.6605 q^{49} +0.701657 q^{50} +4.96264 q^{51} -4.10087 q^{52} +7.85349 q^{53} +0.912474 q^{54} +4.41716 q^{56} +0.666175 q^{57} -2.56453 q^{58} -5.89619 q^{59} +1.92202 q^{60} +5.92581 q^{61} +0.240763 q^{62} -11.7766 q^{63} -6.64221 q^{64} -3.04961 q^{65} -10.2449 q^{67} -14.0635 q^{68} -0.276684 q^{69} +1.61826 q^{70} +1.06019 q^{71} -2.40156 q^{72} +7.79694 q^{73} +1.19366 q^{74} -1.99716 q^{75} -1.88785 q^{76} -0.348406 q^{78} +14.5005 q^{79} -5.27933 q^{80} +4.99389 q^{81} +2.30402 q^{82} -4.42688 q^{83} -6.19396 q^{84} -10.4583 q^{85} +1.53931 q^{86} +7.29956 q^{87} +7.28573 q^{89} -0.879829 q^{90} +9.82773 q^{91} +0.784084 q^{92} -0.685295 q^{93} +0.976824 q^{94} -1.40390 q^{95} -1.90396 q^{96} +13.7014 q^{97} -3.52969 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - q^{2} + 2 q^{3} + 17 q^{4} + 8 q^{5} + 2 q^{6} - 3 q^{8} + 25 q^{9} + 15 q^{10} + 11 q^{12} + 4 q^{13} + 9 q^{14} + 15 q^{15} + 29 q^{16} + 2 q^{17} - 4 q^{18} - 5 q^{19} + 17 q^{20} + 15 q^{21}+ \cdots + 31 q^{98}+O(q^{100}) \) 15 * q - q^2 + 2 * q^3 + 17 * q^4 + 8 * q^5 + 2 * q^6 - 3 * q^8 + 25 * q^9 + 15 * q^10 + 11 * q^12 + 4 * q^13 + 9 * q^14 + 15 * q^15 + 29 * q^16 + 2 * q^17 - 4 * q^18 - 5 * q^19 + 17 * q^20 + 15 * q^21 + 17 * q^23 + 18 * q^24 + 27 * q^25 + 22 * q^26 + 17 * q^27 - 35 * q^28 - 7 * q^29 - 27 * q^30 - 15 * q^31 + 23 * q^32 + 15 * q^34 - 9 * q^35 - 3 * q^36 + 17 * q^37 + 4 * q^38 - 18 * q^39 + 51 * q^40 + 7 * q^41 - 17 * q^42 + 12 * q^43 + 18 * q^45 - 20 * q^46 - 8 * q^47 + 21 * q^48 + 37 * q^49 - 16 * q^50 + 52 * q^51 - 35 * q^52 + 26 * q^53 + 48 * q^54 + 8 * q^56 - 44 * q^57 - 55 * q^58 + 11 * q^59 + 108 * q^60 - 17 * q^61 + q^62 - 22 * q^63 - 3 * q^64 + 12 * q^65 - 31 * q^67 - 30 * q^68 - 16 * q^69 - 8 * q^70 + 35 * q^71 - 59 * q^72 + q^73 - 5 * q^74 + 61 * q^75 + 12 * q^76 + q^78 - 14 * q^79 + 27 * q^80 + 83 * q^81 + 39 * q^82 - 26 * q^83 + 46 * q^84 - 16 * q^85 + 51 * q^86 - 43 * q^87 + 73 * q^89 + 45 * q^90 - 23 * q^91 + 19 * q^92 - 2 * q^93 - 46 * q^94 + 59 * q^95 - 53 * q^96 + 34 * q^97 + 31 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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