LMFDB - Embedded newform 3971.2.a.h.1.5

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:	$5$
Coefficient field:	5.5.246832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 $ x^5 - 2x^4 - 5x^3 + 6x^2 + 7x - 2
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			1.5
Root			$0.245526$ 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)

$f(q)$	$=$	\(q+2.18524 q^{2} -2.15766 q^{3} +2.77529 q^{4} -3.43077 q^{5} -4.71500 q^{6} +3.93972 q^{7} +1.69419 q^{8} +1.65548 q^{9} -7.49706 q^{10} +1.00000 q^{11} -5.98812 q^{12} -3.31182 q^{13} +8.60924 q^{14} +7.40242 q^{15} -1.84836 q^{16} +2.80637 q^{17} +3.61763 q^{18} -9.52137 q^{20} -8.50056 q^{21} +2.18524 q^{22} +6.88998 q^{23} -3.65548 q^{24} +6.77018 q^{25} -7.23713 q^{26} +2.90101 q^{27} +10.9338 q^{28} -5.67979 q^{29} +16.1761 q^{30} -2.51864 q^{31} -7.42749 q^{32} -2.15766 q^{33} +6.13259 q^{34} -13.5163 q^{35} +4.59444 q^{36} +6.39893 q^{37} +7.14577 q^{39} -5.81238 q^{40} -0.560629 q^{41} -18.5758 q^{42} -9.40080 q^{43} +2.77529 q^{44} -5.67958 q^{45} +15.0563 q^{46} -12.1742 q^{47} +3.98812 q^{48} +8.52137 q^{49} +14.7945 q^{50} -6.05517 q^{51} -9.19126 q^{52} -5.68316 q^{53} +6.33941 q^{54} -3.43077 q^{55} +6.67463 q^{56} -12.4117 q^{58} -4.35730 q^{59} +20.5438 q^{60} -3.56412 q^{61} -5.50384 q^{62} +6.52213 q^{63} -12.5342 q^{64} +11.3621 q^{65} -4.71500 q^{66} +9.95563 q^{67} +7.78847 q^{68} -14.8662 q^{69} -29.5363 q^{70} +11.4671 q^{71} +2.80470 q^{72} -8.95834 q^{73} +13.9832 q^{74} -14.6077 q^{75} +3.93972 q^{77} +15.6153 q^{78} -8.49105 q^{79} +6.34128 q^{80} -11.2258 q^{81} -1.22511 q^{82} -5.21960 q^{83} -23.5915 q^{84} -9.62799 q^{85} -20.5430 q^{86} +12.2550 q^{87} +1.69419 q^{88} +7.28423 q^{89} -12.4113 q^{90} -13.0476 q^{91} +19.1217 q^{92} +5.43436 q^{93} -26.6036 q^{94} +16.0260 q^{96} -10.6574 q^{97} +18.6213 q^{98} +1.65548 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{7} - 6 q^{8} + 4 q^{9} - 12 q^{10} + 5 q^{11} - 6 q^{12} - 4 q^{13} + 14 q^{14} - 3 q^{15} + 8 q^{16} - 4 q^{17} + 20 q^{18} - 8 q^{20} - 10 q^{21}+ \cdots + 4 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 - q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^7 - 6 * q^8 + 4 * q^9 - 12 * q^10 + 5 * q^11 - 6 * q^12 - 4 * q^13 + 14 * q^14 - 3 * q^15 + 8 * q^16 - 4 * q^17 + 20 * q^18 - 8 * q^20 - 10 * q^21 - 2 * q^22 + 3 * q^23 - 14 * q^24 + 6 * q^25 - 6 * q^26 + 11 * q^27 - 10 * q^28 - 10 * q^29 + 6 * q^30 - 11 * q^31 - 14 * q^32 - q^33 + 4 * q^34 - 8 * q^35 - 26 * q^36 - q^37 + 2 * q^39 + 16 * q^40 - 2 * q^41 - 16 * q^42 + 20 * q^43 + 6 * q^44 - 28 * q^45 + 4 * q^46 - 20 * q^47 - 4 * q^48 + 3 * q^49 + 32 * q^50 - 24 * q^51 - 6 * q^52 + 14 * q^53 + 16 * q^54 - 5 * q^55 + 38 * q^56 - 6 * q^58 - 3 * q^59 + 40 * q^60 - 10 * q^61 - 6 * q^62 + 24 * q^63 - 2 * q^66 - 9 * q^67 + 24 * q^68 + 5 * q^69 - 50 * q^70 - 23 * q^71 + 12 * q^72 + 8 * q^74 + 18 * q^75 + 6 * q^77 + 22 * q^78 - 44 * q^79 - 18 * q^80 + q^81 - 30 * q^82 - 14 * q^83 - 14 * q^84 - 12 * q^85 - 52 * q^86 + 28 * q^87 - 6 * q^88 + 27 * q^89 - 26 * q^90 - 24 * q^91 + 58 * q^92 - 27 * q^93 + 8 * q^94 + 50 * q^96 - 15 * q^97 + 10 * q^98 + 4 * 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 $

$2$	2.18524	1.54520	0.772600	−	0.634893i	$-0.218956\pi$
$2$	2.18524	1.54520	0.772600	+	0.634893i	$0.218956\pi$
$3$	−2.15766	−1.24572	−0.622862	−	0.782332i	$-0.714030\pi$
$3$	−2.15766	−1.24572	−0.622862	+	0.782332i	$0.714030\pi$
$4$	2.77529	1.38764
$5$	−3.43077	−1.53429	−0.767143	−	0.641476i	$-0.778322\pi$
$5$	−3.43077	−1.53429	−0.767143	+	0.641476i	$0.778322\pi$
$6$	−4.71500	−1.92489
$7$	3.93972	1.48907	0.744537	−	0.667582i	$-0.232671\pi$
$7$	3.93972	1.48907	0.744537	+	0.667582i	$0.232671\pi$
$8$	1.69419	0.598987
$9$	1.65548	0.551827
$10$	−7.49706	−2.37078
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−5.98812	−1.72862
$13$	−3.31182	−0.918534	−0.459267	−	0.888298i	$-0.651888\pi$
$13$	−3.31182	−0.918534	−0.459267	+	0.888298i	$0.651888\pi$
$14$	8.60924	2.30092
$15$	7.40242	1.91130
$16$	−1.84836	−0.462089
$17$	2.80637	0.680644	0.340322	−	0.940309i	$-0.389464\pi$
$17$	2.80637	0.680644	0.340322	+	0.940309i	$0.389464\pi$
$18$	3.61763	0.852684
$19$	0	0
$19$	0	0
$20$	−9.52137	−2.12904
$21$	−8.50056	−1.85497
$22$	2.18524	0.465895
$23$	6.88998	1.43666	0.718330	−	0.695702i	$-0.244907\pi$
$23$	6.88998	1.43666	0.718330	+	0.695702i	$0.244907\pi$
$24$	−3.65548	−0.746172
$25$	6.77018	1.35404
$26$	−7.23713	−1.41932
$27$	2.90101	0.558299
$28$	10.9338	2.06630
$29$	−5.67979	−1.05471	−0.527355	−	0.849645i	$-0.676816\pi$
$29$	−5.67979	−1.05471	−0.527355	+	0.849645i	$0.676816\pi$
$30$	16.1761	2.95334
$31$	−2.51864	−0.452361	−0.226180	−	0.974085i	$-0.572624\pi$
$31$	−2.51864	−0.452361	−0.226180	+	0.974085i	$0.572624\pi$
$32$	−7.42749	−1.31301
$33$	−2.15766	−0.375600
$34$	6.13259	1.05173
$35$	−13.5163	−2.28466
$36$	4.59444	0.765740
$37$	6.39893	1.05198	0.525989	−	0.850491i	$-0.323695\pi$
$37$	6.39893	1.05198	0.525989	+	0.850491i	$0.323695\pi$
$38$	0	0
$39$	7.14577	1.14424
$40$	−5.81238	−0.919018
$41$	−0.560629	−0.0875555	−0.0437778	−	0.999041i	$-0.513939\pi$
$41$	−0.560629	−0.0875555	−0.0437778	+	0.999041i	$0.513939\pi$
$42$	−18.5758	−2.86631
$43$	−9.40080	−1.43361	−0.716805	−	0.697274i	$-0.754396\pi$
$43$	−9.40080	−1.43361	−0.716805	+	0.697274i	$0.754396\pi$
$44$	2.77529	0.418390
$45$	−5.67958	−0.846661
$46$	15.0563	2.21993
$47$	−12.1742	−1.77579	−0.887896	−	0.460044i	$-0.847834\pi$
$47$	−12.1742	−1.77579	−0.887896	+	0.460044i	$0.847834\pi$
$48$	3.98812	0.575635
$49$	8.52137	1.21734
$50$	14.7945	2.09226
$51$	−6.05517	−0.847894
$52$	−9.19126	−1.27460
$53$	−5.68316	−0.780643	−0.390321	−	0.920679i	$-0.627636\pi$
$53$	−5.68316	−0.780643	−0.390321	+	0.920679i	$0.627636\pi$
$54$	6.33941	0.862684
$55$	−3.43077	−0.462605
$56$	6.67463	0.891935
$57$	0	0
$58$	−12.4117	−1.62974
$59$	−4.35730	−0.567273	−0.283636	−	0.958932i	$-0.591541\pi$
$59$	−4.35730	−0.567273	−0.283636	+	0.958932i	$0.591541\pi$
$60$	20.5438	2.65220
$61$	−3.56412	−0.456339	−0.228169	−	0.973621i	$-0.573274\pi$
$61$	−3.56412	−0.456339	−0.228169	+	0.973621i	$0.573274\pi$
$62$	−5.50384	−0.698988
$63$	6.52213	0.821711
$64$	−12.5342	−1.56677
$65$	11.3621	1.40929
$66$	−4.71500	−0.580377
$67$	9.95563	1.21627	0.608137	−	0.793832i	$-0.291917\pi$
$67$	9.95563	1.21627	0.608137	+	0.793832i	$0.291917\pi$
$68$	7.78847	0.944491
$69$	−14.8662	−1.78968
$70$	−29.5363	−3.53026
$71$	11.4671	1.36089	0.680447	−	0.732797i	$-0.261786\pi$
$71$	11.4671	1.36089	0.680447	+	0.732797i	$0.261786\pi$
$72$	2.80470	0.330537
$73$	−8.95834	−1.04849	−0.524247	−	0.851566i	$-0.675653\pi$
$73$	−8.95834	−1.04849	−0.524247	+	0.851566i	$0.675653\pi$
$74$	13.9832	1.62552
$75$	−14.6077	−1.68675
$76$	0	0
$77$	3.93972	0.448972
$78$	15.6153	1.76808
$79$	−8.49105	−0.955318	−0.477659	−	0.878545i	$-0.658515\pi$
$79$	−8.49105	−0.955318	−0.477659	+	0.878545i	$0.658515\pi$
$80$	6.34128	0.708977
$81$	−11.2258	−1.24731
$82$	−1.22511	−0.135291
$83$	−5.21960	−0.572926	−0.286463	−	0.958091i	$-0.592480\pi$
$83$	−5.21960	−0.572926	−0.286463	+	0.958091i	$0.592480\pi$
$84$	−23.5915	−2.57404
$85$	−9.62799	−1.04430
$86$	−20.5430	−2.21521
$87$	12.2550	1.31388
$88$	1.69419	0.180601
$89$	7.28423	0.772127	0.386064	−	0.922472i	$-0.373834\pi$
$89$	7.28423	0.772127	0.386064	+	0.922472i	$0.373834\pi$
$90$	−12.4113	−1.30826
$91$	−13.0476	−1.36776
$92$	19.1217	1.99357
$93$	5.43436	0.563517
$94$	−26.6036	−2.74395
$95$	0	0
$96$	16.0260	1.63564
$97$	−10.6574	−1.08209	−0.541045	−	0.840993i	$-0.681971\pi$
$97$	−10.6574	−1.08209	−0.541045	+	0.840993i	$0.681971\pi$
$98$	18.6213	1.88103
$99$	1.65548	0.166382
$100$	18.7892	1.87892
$101$	−11.4716	−1.14147	−0.570735	−	0.821134i	$-0.693342\pi$
$101$	−11.4716	−1.14147	−0.570735	+	0.821134i	$0.693342\pi$
$102$	−13.2320	−1.31017
$103$	−18.3034	−1.80349	−0.901745	−	0.432268i	$-0.857714\pi$
$103$	−18.3034	−1.80349	−0.901745	+	0.432268i	$0.857714\pi$
$104$	−5.61086	−0.550190
$105$	29.1634	2.84606
$106$	−12.4191	−1.20625
$107$	−1.38838	−0.134220	−0.0671100	−	0.997746i	$-0.521378\pi$
$107$	−1.38838	−0.134220	−0.0671100	+	0.997746i	$0.521378\pi$
$108$	8.05113	0.774720
$109$	0.412113	0.0394732	0.0197366	−	0.999805i	$-0.493717\pi$
$109$	0.412113	0.0394732	0.0197366	+	0.999805i	$0.493717\pi$
$110$	−7.49706	−0.714817
$111$	−13.8067	−1.31047
$112$	−7.28200	−0.688084
$113$	6.54003	0.615234	0.307617	−	0.951510i	$-0.400468\pi$
$113$	6.54003	0.615234	0.307617	+	0.951510i	$0.400468\pi$
$114$	0	0
$115$	−23.6379	−2.20425
$116$	−15.7630	−1.46356
$117$	−5.48266	−0.506872
$118$	−9.52177	−0.876550
$119$	11.0563	1.01353
$120$	12.5411	1.14484
$121$	1.00000	0.0909091
$122$	−7.78847	−0.705135
$123$	1.20964	0.109070
$124$	−6.98995	−0.627716
$125$	−6.07307	−0.543192
$126$	14.2524	1.26971
$127$	−9.08005	−0.805724	−0.402862	−	0.915261i	$-0.631985\pi$
$127$	−9.08005	−0.805724	−0.402862	+	0.915261i	$0.631985\pi$
$128$	−12.5352	−1.10797
$129$	20.2837	1.78588
$130$	24.8289	2.17764
$131$	−10.3876	−0.907571	−0.453785	−	0.891111i	$-0.649927\pi$
$131$	−10.3876	−0.907571	−0.453785	+	0.891111i	$0.649927\pi$
$132$	−5.98812	−0.521199
$133$	0	0
$134$	21.7555	1.87939
$135$	−9.95269	−0.856591
$136$	4.75452	0.407697
$137$	−0.798293	−0.0682028	−0.0341014	−	0.999418i	$-0.510857\pi$
$137$	−0.798293	−0.0682028	−0.0341014	+	0.999418i	$0.510857\pi$
$138$	−32.4863	−2.76542
$139$	5.03184	0.426795	0.213398	−	0.976965i	$-0.431547\pi$
$139$	5.03184	0.426795	0.213398	+	0.976965i	$0.431547\pi$
$140$	−37.5115	−3.17030
$141$	26.2678	2.21215
$142$	25.0584	2.10285
$143$	−3.31182	−0.276948
$144$	−3.05992	−0.254993
$145$	19.4860	1.61823
$146$	−19.5761	−1.62013
$147$	−18.3862	−1.51647
$148$	17.7589	1.45977
$149$	19.8351	1.62496	0.812479	−	0.582991i	$-0.198118\pi$
$149$	19.8351	1.62496	0.812479	+	0.582991i	$0.198118\pi$
$150$	−31.9214	−2.60637
$151$	−22.5447	−1.83466	−0.917331	−	0.398125i	$-0.869661\pi$
$151$	−22.5447	−1.83466	−0.917331	+	0.398125i	$0.869661\pi$
$152$	0	0
$153$	4.64589	0.375598
$154$	8.60924	0.693752
$155$	8.64087	0.694051
$156$	19.8316	1.58780
$157$	−11.8013	−0.941843	−0.470921	−	0.882175i	$-0.656078\pi$
$157$	−11.8013	−0.941843	−0.470921	+	0.882175i	$0.656078\pi$
$158$	−18.5550	−1.47616
$159$	12.2623	0.972465
$160$	25.4820	2.01453
$161$	27.1446	2.13929
$162$	−24.5312	−1.92735
$163$	−24.8395	−1.94558	−0.972789	−	0.231691i	$-0.925574\pi$
$163$	−24.8395	−1.94558	−0.972789	+	0.231691i	$0.925574\pi$
$164$	−1.55591	−0.121496
$165$	7.40242	0.576278
$166$	−11.4061	−0.885285
$167$	2.79938	0.216623	0.108311	−	0.994117i	$-0.465456\pi$
$167$	2.79938	0.216623	0.108311	+	0.994117i	$0.465456\pi$
$168$	−14.4016	−1.11110
$169$	−2.03184	−0.156295
$170$	−21.0395	−1.61366
$171$	0	0
$172$	−26.0899	−1.98934
$173$	6.43926	0.489568	0.244784	−	0.969578i	$-0.421283\pi$
$173$	6.43926	0.489568	0.244784	+	0.969578i	$0.421283\pi$
$174$	26.7802	2.03020
$175$	26.6726	2.01626
$176$	−1.84836	−0.139325
$177$	9.40156	0.706665
$178$	15.9178	1.19309
$179$	−12.5241	−0.936095	−0.468048	−	0.883703i	$-0.655042\pi$
$179$	−12.5241	−0.936095	−0.468048	+	0.883703i	$0.655042\pi$
$180$	−15.7625	−1.17486
$181$	−13.7515	−1.02214	−0.511071	−	0.859538i	$-0.670751\pi$
$181$	−13.7515	−1.02214	−0.511071	+	0.859538i	$0.670751\pi$
$182$	−28.5123	−2.11347
$183$	7.69015	0.568472
$184$	11.6729	0.860541
$185$	−21.9533	−1.61404
$186$	11.8754	0.870746
$187$	2.80637	0.205222
$188$	−33.7869	−2.46417
$189$	11.4292	0.831348
$190$	0	0
$191$	3.10678	0.224799	0.112399	−	0.993663i	$-0.464146\pi$
$191$	3.10678	0.224799	0.112399	+	0.993663i	$0.464146\pi$
$192$	27.0444	1.95176
$193$	0.747815	0.0538289	0.0269144	−	0.999638i	$-0.491432\pi$
$193$	0.747815	0.0538289	0.0269144	+	0.999638i	$0.491432\pi$
$194$	−23.2889	−1.67205
$195$	−24.5155	−1.75559
$196$	23.6492	1.68923
$197$	−3.41798	−0.243521	−0.121761	−	0.992559i	$-0.538854\pi$
$197$	−3.41798	−0.243521	−0.121761	+	0.992559i	$0.538854\pi$
$198$	3.61763	0.257094
$199$	5.36785	0.380517	0.190258	−	0.981734i	$-0.439067\pi$
$199$	5.36785	0.380517	0.190258	+	0.981734i	$0.439067\pi$
$200$	11.4700	0.811049
$201$	−21.4808	−1.51514
$202$	−25.0683	−1.76380
$203$	−22.3768	−1.57054
$204$	−16.8048	−1.17657
$205$	1.92339	0.134335
$206$	−39.9974	−2.78675
$207$	11.4062	0.792789
$208$	6.12142	0.424444
$209$	0	0
$210$	63.7292	4.39773
$211$	−2.55492	−0.175888	−0.0879441	−	0.996125i	$-0.528030\pi$
$211$	−2.55492	−0.175888	−0.0879441	+	0.996125i	$0.528030\pi$
$212$	−15.7724	−1.08325
$213$	−24.7421	−1.69530
$214$	−3.03395	−0.207397
$215$	32.2520	2.19957
$216$	4.91486	0.334414
$217$	−9.92272	−0.673598
$218$	0.900566	0.0609940
$219$	19.3290	1.30613
$220$	−9.52137	−0.641931
$221$	−9.29418	−0.625194
$222$	−30.1710	−2.02494
$223$	24.9404	1.67013	0.835066	−	0.550149i	$-0.185429\pi$
$223$	24.9404	1.67013	0.835066	+	0.550149i	$0.185429\pi$
$224$	−29.2622	−1.95516
$225$	11.2079	0.747194
$226$	14.2915	0.950660
$227$	22.8254	1.51497	0.757487	−	0.652851i	$-0.226427\pi$
$227$	22.8254	1.51497	0.757487	+	0.652851i	$0.226427\pi$
$228$	0	0
$229$	−0.603546	−0.0398834	−0.0199417	−	0.999801i	$-0.506348\pi$
$229$	−0.603546	−0.0398834	−0.0199417	+	0.999801i	$0.506348\pi$
$230$	−51.6546	−3.40601
$231$	−8.50056	−0.559296
$232$	−9.62264	−0.631757
$233$	17.3705	1.13798	0.568988	−	0.822346i	$-0.307335\pi$
$233$	17.3705	1.13798	0.568988	+	0.822346i	$0.307335\pi$
$234$	−11.9809	−0.783219
$235$	41.7669	2.72457
$236$	−12.0928	−0.787172
$237$	18.3208	1.19006
$238$	24.1607	1.56610
$239$	7.23486	0.467984	0.233992	−	0.972238i	$-0.424821\pi$
$239$	7.23486	0.467984	0.233992	+	0.972238i	$0.424821\pi$
$240$	−13.6823	−0.883189
$241$	12.2034	0.786090	0.393045	−	0.919519i	$-0.371422\pi$
$241$	12.2034	0.786090	0.393045	+	0.919519i	$0.371422\pi$
$242$	2.18524	0.140473
$243$	15.5185	0.995509
$244$	−9.89146	−0.633236
$245$	−29.2349	−1.86775
$246$	2.64337	0.168535
$247$	0	0
$248$	−4.26705	−0.270958
$249$	11.2621	0.713707
$250$	−13.2711	−0.839340
$251$	−14.0923	−0.889499	−0.444750	−	0.895655i	$-0.646707\pi$
$251$	−14.0923	−0.889499	−0.444750	+	0.895655i	$0.646707\pi$
$252$	18.1008	1.14024
$253$	6.88998	0.433169
$254$	−19.8421	−1.24501
$255$	20.7739	1.30091
$256$	−2.32415	−0.145259
$257$	−0.440920	−0.0275038	−0.0137519	−	0.999905i	$-0.504378\pi$
$257$	−0.440920	−0.0275038	−0.0137519	+	0.999905i	$0.504378\pi$
$258$	44.3248	2.75954
$259$	25.2100	1.56647
$260$	31.5331	1.95560
$261$	−9.40279	−0.582018
$262$	−22.6995	−1.40238
$263$	−15.0661	−0.929016	−0.464508	−	0.885569i	$-0.653769\pi$
$263$	−15.0661	−0.929016	−0.464508	+	0.885569i	$0.653769\pi$
$264$	−3.65548	−0.224979
$265$	19.4976	1.19773
$266$	0	0
$267$	−15.7169	−0.961857
$268$	27.6297	1.68775
$269$	7.25751	0.442498	0.221249	−	0.975217i	$-0.428987\pi$
$269$	7.25751	0.442498	0.221249	+	0.975217i	$0.428987\pi$
$270$	−21.7490	−1.32360
$271$	−16.8878	−1.02586	−0.512931	−	0.858430i	$-0.671440\pi$
$271$	−16.8878	−1.02586	−0.512931	+	0.858430i	$0.671440\pi$
$272$	−5.18716	−0.314518
$273$	28.1523	1.70386
$274$	−1.74446	−0.105387
$275$	6.77018	0.408257
$276$	−41.2580	−2.48344
$277$	−15.3818	−0.924204	−0.462102	−	0.886827i	$-0.652905\pi$
$277$	−15.3818	−0.924204	−0.462102	+	0.886827i	$0.652905\pi$
$278$	10.9958	0.659484
$279$	−4.16956	−0.249625
$280$	−22.8991	−1.36848
$281$	25.8974	1.54491	0.772456	−	0.635069i	$-0.219028\pi$
$281$	25.8974	1.54491	0.772456	+	0.635069i	$0.219028\pi$
$282$	57.4015	3.41821
$283$	18.6882	1.11090	0.555450	−	0.831550i	$-0.312546\pi$
$283$	18.6882	1.11090	0.555450	+	0.831550i	$0.312546\pi$
$284$	31.8245	1.88844
$285$	0	0
$286$	−7.23713	−0.427941
$287$	−2.20872	−0.130377
$288$	−12.2961	−0.724553
$289$	−9.12431	−0.536724
$290$	42.5817	2.50049
$291$	22.9949	1.34799
$292$	−24.8620	−1.45494
$293$	−26.7471	−1.56258	−0.781291	−	0.624167i	$-0.785439\pi$
$293$	−26.7471	−1.56258	−0.781291	+	0.624167i	$0.785439\pi$
$294$	−40.1783	−2.34325
$295$	14.9489	0.870359
$296$	10.8410	0.630121
$297$	2.90101	0.168334
$298$	43.3446	2.51088
$299$	−22.8184	−1.31962
$300$	−40.5406	−2.34061
$301$	−37.0365	−2.13475
$302$	−49.2657	−2.83492
$303$	24.7518	1.42196
$304$	0	0
$305$	12.2277	0.700155
$306$	10.1524	0.580374
$307$	−22.6415	−1.29222	−0.646109	−	0.763245i	$-0.723605\pi$
$307$	−22.6415	−1.29222	−0.646109	+	0.763245i	$0.723605\pi$
$308$	10.9338	0.623014
$309$	39.4925	2.24665
$310$	18.8824	1.07245
$311$	−1.38723	−0.0786628	−0.0393314	−	0.999226i	$-0.512523\pi$
$311$	−1.38723	−0.0786628	−0.0393314	+	0.999226i	$0.512523\pi$
$312$	12.1063	0.685384
$313$	12.9018	0.729255	0.364627	−	0.931153i	$-0.381196\pi$
$313$	12.9018	0.729255	0.364627	+	0.931153i	$0.381196\pi$
$314$	−25.7886	−1.45534
$315$	−22.3759	−1.26074
$316$	−23.5651	−1.32564
$317$	19.0712	1.07114	0.535572	−	0.844489i	$-0.320096\pi$
$317$	19.0712	1.07114	0.535572	+	0.844489i	$0.320096\pi$
$318$	26.7961	1.50265
$319$	−5.67979	−0.318007
$320$	43.0018	2.40387
$321$	2.99565	0.167201
$322$	59.3175	3.30564
$323$	0	0
$324$	−31.1549	−1.73083
$325$	−22.4216	−1.24373
$326$	−54.2803	−3.00631
$327$	−0.889197	−0.0491727
$328$	−0.949812	−0.0524446
$329$	−47.9630	−2.64428
$330$	16.1761	0.890464
$331$	12.4616	0.684952	0.342476	−	0.939527i	$-0.388735\pi$
$331$	12.4616	0.684952	0.342476	+	0.939527i	$0.388735\pi$
$332$	−14.4859	−0.795017
$333$	10.5933	0.580510
$334$	6.11733	0.334725
$335$	−34.1555	−1.86611
$336$	15.7121	0.857163
$337$	0.401035	0.0218458	0.0109229	−	0.999940i	$-0.496523\pi$
$337$	0.401035	0.0218458	0.0109229	+	0.999940i	$0.496523\pi$
$338$	−4.44006	−0.241508
$339$	−14.1111	−0.766411
$340$	−26.7204	−1.44912
$341$	−2.51864	−0.136392
$342$	0	0
$343$	5.99377	0.323633
$344$	−15.9268	−0.858713
$345$	51.0026	2.74589
$346$	14.0713	0.756480
$347$	1.06608	0.0572304	0.0286152	−	0.999591i	$-0.490890\pi$
$347$	1.06608	0.0572304	0.0286152	+	0.999591i	$0.490890\pi$
$348$	34.0112	1.82319
$349$	22.2695	1.19206	0.596029	−	0.802963i	$-0.296744\pi$
$349$	22.2695	1.19206	0.596029	+	0.802963i	$0.296744\pi$
$350$	58.2861	3.11552
$351$	−9.60762	−0.512817
$352$	−7.42749	−0.395886
$353$	12.3631	0.658023	0.329012	−	0.944326i	$-0.393284\pi$
$353$	12.3631	0.658023	0.329012	+	0.944326i	$0.393284\pi$
$354$	20.5447	1.09194
$355$	−39.3410	−2.08800
$356$	20.2158	1.07144
$357$	−23.8557	−1.26258
$358$	−27.3682	−1.44645
$359$	32.1914	1.69899	0.849497	−	0.527593i	$-0.176905\pi$
$359$	32.1914	1.69899	0.849497	+	0.527593i	$0.176905\pi$
$360$	−9.62229	−0.507139
$361$	0	0
$362$	−30.0504	−1.57941
$363$	−2.15766	−0.113248
$364$	−36.2109	−1.89797
$365$	30.7340	1.60869
$366$	16.8048	0.878403
$367$	−18.9777	−0.990628	−0.495314	−	0.868714i	$-0.664947\pi$
$367$	−18.9777	−0.990628	−0.495314	+	0.868714i	$0.664947\pi$
$368$	−12.7351	−0.663865
$369$	−0.928111	−0.0483155
$370$	−47.9732	−2.49401
$371$	−22.3901	−1.16243
$372$	15.0819	0.781960
$373$	−1.15238	−0.0596678	−0.0298339	−	0.999555i	$-0.509498\pi$
$373$	−1.15238	−0.0596678	−0.0298339	+	0.999555i	$0.509498\pi$
$374$	6.13259	0.317109
$375$	13.1036	0.676667
$376$	−20.6254	−1.06368
$377$	18.8104	0.968787
$378$	24.9755	1.28460
$379$	−13.5365	−0.695325	−0.347663	−	0.937620i	$-0.613025\pi$
$379$	−13.5365	−0.695325	−0.347663	+	0.937620i	$0.613025\pi$
$380$	0	0
$381$	19.5916	1.00371
$382$	6.78907	0.347359
$383$	−13.1671	−0.672809	−0.336404	−	0.941718i	$-0.609211\pi$
$383$	−13.1671	−0.672809	−0.336404	+	0.941718i	$0.609211\pi$
$384$	27.0467	1.38022
$385$	−13.5163	−0.688852
$386$	1.63416	0.0831764
$387$	−15.5629	−0.791105
$388$	−29.5772	−1.50156
$389$	0.223588	0.0113364	0.00566819	−	0.999984i	$-0.498196\pi$
$389$	0.223588	0.0113364	0.00566819	+	0.999984i	$0.498196\pi$
$390$	−53.5723	−2.71274
$391$	19.3358	0.977854
$392$	14.4368	0.729170
$393$	22.4129	1.13058
$394$	−7.46913	−0.376289
$395$	29.1308	1.46573
$396$	4.59444	0.230879
$397$	−21.6504	−1.08660	−0.543301	−	0.839538i	$-0.682826\pi$
$397$	−21.6504	−1.08660	−0.543301	+	0.839538i	$0.682826\pi$
$398$	11.7301	0.587975
$399$	0	0
$400$	−12.5137	−0.625685
$401$	−1.30180	−0.0650089	−0.0325045	−	0.999472i	$-0.510348\pi$
$401$	−1.30180	−0.0650089	−0.0325045	+	0.999472i	$0.510348\pi$
$402$	−46.9408	−2.34120
$403$	8.34128	0.415509
$404$	−31.8371	−1.58395
$405$	38.5132	1.91374
$406$	−48.8986	−2.42680
$407$	6.39893	0.317183
$408$	−10.2586	−0.507877
$409$	2.15631	0.106622	0.0533112	−	0.998578i	$-0.483022\pi$
$409$	2.15631	0.106622	0.0533112	+	0.998578i	$0.483022\pi$
$410$	4.20307	0.207575
$411$	1.72244	0.0849618
$412$	−50.7973	−2.50260
$413$	−17.1665	−0.844710
$414$	24.9254	1.22502
$415$	17.9073	0.879032
$416$	24.5985	1.20604
$417$	−10.8570	−0.531669
$418$	0	0
$419$	−29.6335	−1.44769	−0.723844	−	0.689963i	$-0.757627\pi$
$419$	−29.6335	−1.44769	−0.723844	+	0.689963i	$0.757627\pi$
$420$	80.9369	3.94932
$421$	5.25385	0.256057	0.128028	−	0.991770i	$-0.459135\pi$
$421$	5.25385	0.256057	0.128028	+	0.991770i	$0.459135\pi$
$422$	−5.58313	−0.271782
$423$	−20.1542	−0.979931
$424$	−9.62837	−0.467595
$425$	18.9996	0.921616
$426$	−54.0674	−2.61957
$427$	−14.0416	−0.679522
$428$	−3.85316	−0.186249
$429$	7.14577	0.345001
$430$	70.4784	3.39877
$431$	−17.8489	−0.859752	−0.429876	−	0.902888i	$-0.641443\pi$
$431$	−17.8489	−0.859752	−0.429876	+	0.902888i	$0.641443\pi$
$432$	−5.36209	−0.257984
$433$	0.696383	0.0334660	0.0167330	−	0.999860i	$-0.494673\pi$
$433$	0.696383	0.0334660	0.0167330	+	0.999860i	$0.494673\pi$
$434$	−21.6836	−1.04084
$435$	−42.0442	−2.01586
$436$	1.14373	0.0547748
$437$	0	0
$438$	42.2386	2.01824
$439$	24.8210	1.18464	0.592321	−	0.805702i	$-0.298212\pi$
$439$	24.8210	1.18464	0.592321	+	0.805702i	$0.298212\pi$
$440$	−5.81238	−0.277094
$441$	14.1070	0.671761
$442$	−20.3100	−0.966050
$443$	−3.93424	−0.186922	−0.0934608	−	0.995623i	$-0.529793\pi$
$443$	−3.93424	−0.186922	−0.0934608	+	0.995623i	$0.529793\pi$
$444$	−38.3175	−1.81847
$445$	−24.9905	−1.18466
$446$	54.5008	2.58069
$447$	−42.7974	−2.02425
$448$	−49.3810	−2.33303
$449$	−6.13394	−0.289479	−0.144739	−	0.989470i	$-0.546234\pi$
$449$	−6.13394	−0.289479	−0.144739	+	0.989470i	$0.546234\pi$
$450$	24.4920	1.15456
$451$	−0.560629	−0.0263990
$452$	18.1505	0.853725
$453$	48.6437	2.28548
$454$	49.8790	2.34094
$455$	44.7634	2.09854
$456$	0	0
$457$	8.40189	0.393024	0.196512	−	0.980501i	$-0.437039\pi$
$457$	8.40189	0.393024	0.196512	+	0.980501i	$0.437039\pi$
$458$	−1.31889	−0.0616279
$459$	8.14129	0.380003
$460$	−65.6021	−3.05871
$461$	25.9903	1.21049	0.605246	−	0.796039i	$-0.293075\pi$
$461$	25.9903	1.21049	0.605246	+	0.796039i	$0.293075\pi$
$462$	−18.5758	−0.864224
$463$	19.3724	0.900311	0.450155	−	0.892950i	$-0.351369\pi$
$463$	19.3724	0.900311	0.450155	+	0.892950i	$0.351369\pi$
$464$	10.4983	0.487370
$465$	−18.6440	−0.864596
$466$	37.9587	1.75840
$467$	−34.6720	−1.60443	−0.802214	−	0.597037i	$-0.796345\pi$
$467$	−34.6720	−1.60443	−0.802214	+	0.597037i	$0.796345\pi$
$468$	−15.2160	−0.703358
$469$	39.2224	1.81112
$470$	91.2709	4.21001
$471$	25.4631	1.17328
$472$	−7.38210	−0.339789
$473$	−9.40080	−0.432249
$474$	40.0353	1.83888
$475$	0	0
$476$	30.6844	1.40642
$477$	−9.40838	−0.430780
$478$	15.8099	0.723130
$479$	23.2352	1.06164	0.530821	−	0.847484i	$-0.321883\pi$
$479$	23.2352	1.06164	0.530821	+	0.847484i	$0.321883\pi$
$480$	−54.9814	−2.50955
$481$	−21.1921	−0.966277
$482$	26.6674	1.21467
$483$	−58.5687	−2.66497
$484$	2.77529	0.126149
$485$	36.5629	1.66024
$486$	33.9116	1.53826
$487$	−14.2680	−0.646545	−0.323272	−	0.946306i	$-0.604783\pi$
$487$	−14.2680	−0.646545	−0.323272	+	0.946306i	$0.604783\pi$
$488$	−6.03830	−0.273341
$489$	53.5951	2.42365
$490$	−63.8853	−2.88604
$491$	41.6168	1.87814	0.939071	−	0.343724i	$-0.111689\pi$
$491$	41.6168	1.87814	0.939071	+	0.343724i	$0.111689\pi$
$492$	3.35711	0.151350
$493$	−15.9396	−0.717882
$494$	0	0
$495$	−5.67958	−0.255278
$496$	4.65534	0.209031
$497$	45.1771	2.02647
$498$	24.6104	1.10282
$499$	19.9664	0.893820	0.446910	−	0.894579i	$-0.352524\pi$
$499$	19.9664	0.893820	0.446910	+	0.894579i	$0.352524\pi$
$500$	−16.8545	−0.753757
$501$	−6.04010	−0.269852
$502$	−30.7951	−1.37445
$503$	2.31362	0.103159	0.0515797	−	0.998669i	$-0.483574\pi$
$503$	2.31362	0.103159	0.0515797	+	0.998669i	$0.483574\pi$
$504$	11.0497	0.492194
$505$	39.3565	1.75134
$506$	15.0563	0.669334
$507$	4.38401	0.194701
$508$	−25.1998	−1.11806
$509$	13.2009	0.585120	0.292560	−	0.956247i	$-0.405493\pi$
$509$	13.2009	0.585120	0.292560	+	0.956247i	$0.405493\pi$
$510$	45.3960	2.01017
$511$	−35.2933	−1.56128
$512$	19.9916	0.883511
$513$	0	0
$514$	−0.963517	−0.0424989
$515$	62.7948	2.76707
$516$	56.2931	2.47817
$517$	−12.1742	−0.535421
$518$	55.0899	2.42051
$519$	−13.8937	−0.609866
$520$	19.2496	0.844149
$521$	15.6498	0.685629	0.342814	−	0.939403i	$-0.388620\pi$
$521$	15.6498	0.685629	0.342814	+	0.939403i	$0.388620\pi$
$522$	−20.5474	−0.899334
$523$	17.7350	0.775498	0.387749	−	0.921765i	$-0.373253\pi$
$523$	17.7350	0.775498	0.387749	+	0.921765i	$0.373253\pi$
$524$	−28.8286	−1.25938
$525$	−57.5503	−2.51170
$526$	−32.9231	−1.43552
$527$	−7.06822	−0.307897
$528$	3.98812	0.173560
$529$	24.4719	1.06399
$530$	42.6071	1.85073
$531$	−7.21344	−0.313037
$532$	0	0
$533$	1.85670	0.0804227
$534$	−34.3452	−1.48626
$535$	4.76322	0.205932
$536$	16.8667	0.728532
$537$	27.0227	1.16612
$538$	15.8594	0.683748
$539$	8.52137	0.367041
$540$	−27.6216	−1.18864
$541$	−34.5196	−1.48412	−0.742058	−	0.670336i	$-0.766150\pi$
$541$	−34.5196	−1.48412	−0.742058	+	0.670336i	$0.766150\pi$
$542$	−36.9040	−1.58516
$543$	29.6711	1.27331
$544$	−20.8442	−0.893690
$545$	−1.41386	−0.0605632
$546$	61.5197	2.63280
$547$	−1.99561	−0.0853263	−0.0426632	−	0.999090i	$-0.513584\pi$
$547$	−1.99561	−0.0853263	−0.0426632	+	0.999090i	$0.513584\pi$
$548$	−2.21549	−0.0946411
$549$	−5.90034	−0.251820
$550$	14.7945	0.630839
$551$	0	0
$552$	−25.1862	−1.07200
$553$	−33.4523	−1.42254
$554$	−33.6130	−1.42808
$555$	47.3676	2.01064
$556$	13.9648	0.592239
$557$	−23.5272	−0.996881	−0.498440	−	0.866924i	$-0.666094\pi$
$557$	−23.5272	−0.996881	−0.498440	+	0.866924i	$0.666094\pi$
$558$	−9.11150	−0.385721
$559$	31.1338	1.31682
$560$	24.9829	1.05572
$561$	−6.05517	−0.255650
$562$	56.5922	2.38720
$563$	−14.2122	−0.598972	−0.299486	−	0.954101i	$-0.596815\pi$
$563$	−14.2122	−0.598972	−0.299486	+	0.954101i	$0.596815\pi$
$564$	72.9006	3.06967
$565$	−22.4373	−0.943945
$566$	40.8383	1.71656
$567$	−44.2266	−1.85734
$568$	19.4275	0.815158
$569$	−22.1906	−0.930277	−0.465138	−	0.885238i	$-0.653995\pi$
$569$	−22.1906	−0.930277	−0.465138	+	0.885238i	$0.653995\pi$
$570$	0	0
$571$	8.67954	0.363227	0.181614	−	0.983370i	$-0.441868\pi$
$571$	8.67954	0.363227	0.181614	+	0.983370i	$0.441868\pi$
$572$	−9.19126	−0.384306
$573$	−6.70337	−0.280037
$574$	−4.82659	−0.201458
$575$	46.6464	1.94529
$576$	−20.7501	−0.864586
$577$	40.9150	1.70331	0.851657	−	0.524100i	$-0.175598\pi$
$577$	40.9150	1.70331	0.851657	+	0.524100i	$0.175598\pi$
$578$	−19.9388	−0.829346
$579$	−1.61353	−0.0670559
$580$	54.0794	2.24552
$581$	−20.5638	−0.853128
$582$	50.2495	2.08291
$583$	−5.68316	−0.235373
$584$	−15.1771	−0.628034
$585$	18.8097	0.777687
$586$	−58.4489	−2.41450
$587$	−21.2684	−0.877840	−0.438920	−	0.898526i	$-0.644639\pi$
$587$	−21.2684	−0.877840	−0.438920	+	0.898526i	$0.644639\pi$
$588$	−51.0270	−2.10432
$589$	0	0
$590$	32.6670	1.34488
$591$	7.37484	0.303360
$592$	−11.8275	−0.486107
$593$	−23.0212	−0.945368	−0.472684	−	0.881232i	$-0.656715\pi$
$593$	−23.0212	−0.945368	−0.472684	+	0.881232i	$0.656715\pi$
$594$	6.33941	0.260109
$595$	−37.9316	−1.55504
$596$	55.0482	2.25486
$597$	−11.5820	−0.474019
$598$	−49.8637	−2.03908
$599$	41.6249	1.70075	0.850374	−	0.526179i	$-0.176376\pi$
$599$	41.6249	1.70075	0.850374	+	0.526179i	$0.176376\pi$
$600$	−24.7483	−1.01034
$601$	20.8629	0.851016	0.425508	−	0.904955i	$-0.360095\pi$
$601$	20.8629	0.851016	0.425508	+	0.904955i	$0.360095\pi$
$602$	−80.9338	−3.29861
$603$	16.4814	0.671173
$604$	−62.5680	−2.54586
$605$	−3.43077	−0.139481
$606$	54.0888	2.19721
$607$	0.146703	0.00595450	0.00297725	−	0.999996i	$-0.499052\pi$
$607$	0.146703	0.00595450	0.00297725	+	0.999996i	$0.499052\pi$
$608$	0	0
$609$	48.2813	1.95646
$610$	26.7204	1.08188
$611$	40.3188	1.63113
$612$	12.8937	0.521196
$613$	−18.3393	−0.740716	−0.370358	−	0.928889i	$-0.620765\pi$
$613$	−18.3393	−0.740716	−0.370358	+	0.928889i	$0.620765\pi$
$614$	−49.4772	−1.99674
$615$	−4.15001	−0.167345
$616$	6.67463	0.268929
$617$	4.12050	0.165885	0.0829425	−	0.996554i	$-0.473568\pi$
$617$	4.12050	0.165885	0.0829425	+	0.996554i	$0.473568\pi$
$618$	86.3007	3.47153
$619$	28.5699	1.14832	0.574161	−	0.818743i	$-0.305328\pi$
$619$	28.5699	1.14832	0.574161	+	0.818743i	$0.305328\pi$
$620$	23.9809	0.963096
$621$	19.9879	0.802087
$622$	−3.03144	−0.121550
$623$	28.6978	1.14975
$624$	−13.2079	−0.528740
$625$	−13.0156	−0.520624
$626$	28.1937	1.12684
$627$	0	0
$628$	−32.7519	−1.30694
$629$	17.9577	0.716022
$630$	−48.8968	−1.94810
$631$	33.9323	1.35082	0.675412	−	0.737441i	$-0.263966\pi$
$631$	33.9323	1.35082	0.675412	+	0.737441i	$0.263966\pi$
$632$	−14.3855	−0.572223
$633$	5.51265	0.219108
$634$	41.6752	1.65513
$635$	31.1516	1.23621
$636$	34.0315	1.34943
$637$	−28.2213	−1.11817
$638$	−12.4117	−0.491385
$639$	18.9836	0.750979
$640$	43.0054	1.69994
$641$	−19.7694	−0.780844	−0.390422	−	0.920636i	$-0.627671\pi$
$641$	−19.7694	−0.780844	−0.390422	+	0.920636i	$0.627671\pi$
$642$	6.54623	0.258359
$643$	36.7642	1.44984	0.724920	−	0.688833i	$-0.241877\pi$
$643$	36.7642	1.44984	0.724920	+	0.688833i	$0.241877\pi$
$644$	75.3340	2.96858
$645$	−69.5887	−2.74005
$646$	0	0
$647$	24.9430	0.980610	0.490305	−	0.871551i	$-0.336885\pi$
$647$	24.9430	0.980610	0.490305	+	0.871551i	$0.336885\pi$
$648$	−19.0187	−0.747125
$649$	−4.35730	−0.171039
$650$	−48.9967	−1.92181
$651$	21.4098	0.839117
$652$	−68.9367	−2.69977
$653$	8.60802	0.336858	0.168429	−	0.985714i	$-0.446131\pi$
$653$	8.60802	0.336858	0.168429	+	0.985714i	$0.446131\pi$
$654$	−1.94311	−0.0759817
$655$	35.6375	1.39247
$656$	1.03624	0.0404584
$657$	−14.8304	−0.578588
$658$	−104.811	−4.08595
$659$	−27.7805	−1.08217	−0.541087	−	0.840967i	$-0.681987\pi$
$659$	−27.7805	−1.08217	−0.541087	+	0.840967i	$0.681987\pi$
$660$	20.5438	0.799668
$661$	−30.8037	−1.19812	−0.599062	−	0.800702i	$-0.704460\pi$
$661$	−30.8037	−1.19812	−0.599062	+	0.800702i	$0.704460\pi$
$662$	27.2316	1.05839
$663$	20.0537	0.778819
$664$	−8.84300	−0.343175
$665$	0	0
$666$	23.1490	0.897004
$667$	−39.1336	−1.51526
$668$	7.76909	0.300595
$669$	−53.8128	−2.08052
$670$	−74.6380	−2.88352
$671$	−3.56412	−0.137591
$672$	63.1378	2.43559
$673$	−15.2015	−0.585974	−0.292987	−	0.956116i	$-0.594649\pi$
$673$	−15.2015	−0.585974	−0.292987	+	0.956116i	$0.594649\pi$
$674$	0.876359	0.0337561
$675$	19.6403	0.755957
$676$	−5.63894	−0.216882
$677$	9.49027	0.364741	0.182370	−	0.983230i	$-0.441623\pi$
$677$	9.49027	0.364741	0.182370	+	0.983230i	$0.441623\pi$
$678$	−30.8362	−1.18426
$679$	−41.9870	−1.61131
$680$	−16.3117	−0.625523
$681$	−49.2493	−1.88724
$682$	−5.50384	−0.210753
$683$	−15.0960	−0.577631	−0.288816	−	0.957385i	$-0.593261\pi$
$683$	−15.0960	−0.577631	−0.288816	+	0.957385i	$0.593261\pi$
$684$	0	0
$685$	2.73876	0.104643
$686$	13.0978	0.500078
$687$	1.30224	0.0496837
$688$	17.3760	0.662455
$689$	18.8216	0.717047
$690$	111.453	4.24294
$691$	3.46673	0.131881	0.0659403	−	0.997824i	$-0.478995\pi$
$691$	3.46673	0.131881	0.0659403	+	0.997824i	$0.478995\pi$
$692$	17.8708	0.679345
$693$	6.52213	0.247755
$694$	2.32965	0.0884325
$695$	−17.2631	−0.654826
$696$	20.7624	0.786995
$697$	−1.57333	−0.0595941
$698$	48.6643	1.84197
$699$	−37.4795	−1.41760
$700$	74.0241	2.79785
$701$	−26.2612	−0.991872	−0.495936	−	0.868359i	$-0.665175\pi$
$701$	−26.2612	−0.991872	−0.495936	+	0.868359i	$0.665175\pi$
$702$	−20.9950	−0.792405
$703$	0	0
$704$	−12.5342	−0.472399
$705$	−90.1187	−3.39407
$706$	27.0165	1.01678
$707$	−45.1950	−1.69973
$708$	26.0920	0.980599
$709$	−20.1488	−0.756704	−0.378352	−	0.925662i	$-0.623509\pi$
$709$	−20.1488	−0.756704	−0.378352	+	0.925662i	$0.623509\pi$
$710$	−85.9696	−3.22638
$711$	−14.0568	−0.527171
$712$	12.3409	0.462494
$713$	−17.3534	−0.649889
$714$	−52.1304	−1.95093
$715$	11.3621	0.424918
$716$	−34.7580	−1.29897
$717$	−15.6104	−0.582979
$718$	70.3459	2.62529
$719$	−43.4738	−1.62130	−0.810650	−	0.585532i	$-0.800886\pi$
$719$	−43.4738	−1.62130	−0.810650	+	0.585532i	$0.800886\pi$
$720$	10.4979	0.391233
$721$	−72.1103	−2.68553
$722$	0	0
$723$	−26.3307	−0.979250
$724$	−38.1644	−1.41837
$725$	−38.4532	−1.42811
$726$	−4.71500	−0.174990
$727$	9.55640	0.354427	0.177214	−	0.984172i	$-0.443292\pi$
$727$	9.55640	0.354427	0.177214	+	0.984172i	$0.443292\pi$
$728$	−22.1052	−0.819273
$729$	0.193986	0.00718467
$730$	67.1612	2.48575
$731$	−26.3821	−0.975777
$732$	21.3424	0.788837
$733$	−20.3072	−0.750065	−0.375032	−	0.927012i	$-0.622368\pi$
$733$	−20.3072	−0.750065	−0.375032	+	0.927012i	$0.622368\pi$
$734$	−41.4709	−1.53072
$735$	63.0788	2.32670
$736$	−51.1753	−1.88635
$737$	9.95563	0.366720
$738$	−2.02815	−0.0746572
$739$	−6.60855	−0.243099	−0.121550	−	0.992585i	$-0.538786\pi$
$739$	−6.60855	−0.243099	−0.121550	+	0.992585i	$0.538786\pi$
$740$	−60.9266	−2.23971
$741$	0	0
$742$	−48.9277	−1.79619
$743$	39.1431	1.43602	0.718010	−	0.696033i	$-0.245053\pi$
$743$	39.1431	1.43602	0.718010	+	0.696033i	$0.245053\pi$
$744$	9.20684	0.337539
$745$	−68.0498	−2.49315
$746$	−2.51822	−0.0921988
$747$	−8.64096	−0.316156
$748$	7.78847	0.284775
$749$	−5.46983	−0.199863
$750$	28.6345	1.04559
$751$	−43.2173	−1.57702	−0.788511	−	0.615020i	$-0.789148\pi$
$751$	−43.2173	−1.57702	−0.788511	+	0.615020i	$0.789148\pi$
$752$	22.5023	0.820574
$753$	30.4064	1.10807
$754$	41.1054	1.49697
$755$	77.3457	2.81490
$756$	31.7192	1.15362
$757$	9.93714	0.361171	0.180586	−	0.983559i	$-0.442201\pi$
$757$	9.93714	0.361171	0.180586	+	0.983559i	$0.442201\pi$
$758$	−29.5806	−1.07442
$759$	−14.8662	−0.539609
$760$	0	0
$761$	14.5829	0.528630	0.264315	−	0.964436i	$-0.414854\pi$
$761$	14.5829	0.528630	0.264315	+	0.964436i	$0.414854\pi$
$762$	42.8125	1.55093
$763$	1.62361	0.0587785
$764$	8.62221	0.311941
$765$	−15.9390	−0.576275
$766$	−28.7734	−1.03962
$767$	14.4306	0.521059
$768$	5.01471	0.180953
$769$	−11.8924	−0.428853	−0.214426	−	0.976740i	$-0.568788\pi$
$769$	−11.8924	−0.428853	−0.214426	+	0.976740i	$0.568788\pi$
$770$	−29.5363	−1.06441
$771$	0.951354	0.0342622
$772$	2.07540	0.0746953
$773$	−15.0935	−0.542876	−0.271438	−	0.962456i	$-0.587499\pi$
$773$	−15.0935	−0.542876	−0.271438	+	0.962456i	$0.587499\pi$
$774$	−34.0086	−1.22242
$775$	−17.0516	−0.612513
$776$	−18.0556	−0.648158
$777$	−54.3945	−1.95139
$778$	0.488595	0.0175170
$779$	0	0
$780$	−68.0375	−2.43613
$781$	11.4671	0.410325
$782$	42.2534	1.51098
$783$	−16.4771	−0.588844
$784$	−15.7505	−0.562519
$785$	40.4874	1.44506
$786$	48.9777	1.74698
$787$	5.98214	0.213240	0.106620	−	0.994300i	$-0.465997\pi$
$787$	5.98214	0.213240	0.106620	+	0.994300i	$0.465997\pi$
$788$	−9.48589	−0.337921
$789$	32.5075	1.15730
$790$	63.6580	2.26485
$791$	25.7659	0.916128
$792$	2.80470	0.0996608
$793$	11.8037	0.419163
$794$	−47.3114	−1.67902
$795$	−42.0692	−1.49204
$796$	14.8973	0.528022
$797$	−24.2718	−0.859751	−0.429876	−	0.902888i	$-0.641443\pi$
$797$	−24.2718	−0.859751	−0.429876	+	0.902888i	$0.641443\pi$
$798$	0	0
$799$	−34.1653	−1.20868
$800$	−50.2854	−1.77786
$801$	12.0589	0.426081
$802$	−2.84476	−0.100452
$803$	−8.95834	−0.316133
$804$	−59.6155	−2.10248
$805$	−93.1268	−3.28229
$806$	18.2277	0.642044
$807$	−15.6592	−0.551230
$808$	−19.4351	−0.683726
$809$	−17.9557	−0.631289	−0.315644	−	0.948878i	$-0.602221\pi$
$809$	−17.9557	−0.631289	−0.315644	+	0.948878i	$0.602221\pi$
$810$	84.1607	2.95711
$811$	−5.48300	−0.192534	−0.0962671	−	0.995356i	$-0.530690\pi$
$811$	−5.48300	−0.192534	−0.0962671	+	0.995356i	$0.530690\pi$
$812$	−62.1019	−2.17935
$813$	36.4381	1.27794
$814$	13.9832	0.490111
$815$	85.2185	2.98508
$816$	11.1921	0.391802
$817$	0	0
$818$	4.71205	0.164753
$819$	−21.6001	−0.754770
$820$	5.33795	0.186409
$821$	52.6324	1.83688	0.918441	−	0.395558i	$-0.129449\pi$
$821$	52.6324	1.83688	0.918441	+	0.395558i	$0.129449\pi$
$822$	3.76395	0.131283
$823$	−20.4784	−0.713831	−0.356916	−	0.934137i	$-0.616172\pi$
$823$	−20.4784	−0.713831	−0.356916	+	0.934137i	$0.616172\pi$
$824$	−31.0095	−1.08027
$825$	−14.6077	−0.508575
$826$	−37.5131	−1.30525
$827$	0.359755	0.0125099	0.00625496	−	0.999980i	$-0.498009\pi$
$827$	0.359755	0.0125099	0.00625496	+	0.999980i	$0.498009\pi$
$828$	31.6556	1.10011
$829$	−22.7422	−0.789870	−0.394935	−	0.918709i	$-0.629233\pi$
$829$	−22.7422	−0.789870	−0.394935	+	0.918709i	$0.629233\pi$
$830$	39.1317	1.35828
$831$	33.1887	1.15130
$832$	41.5109	1.43913
$833$	23.9141	0.828574
$834$	−23.7251	−0.821535
$835$	−9.60403	−0.332361
$836$	0	0
$837$	−7.30659	−0.252553
$838$	−64.7563	−2.23697
$839$	−13.1616	−0.454388	−0.227194	−	0.973849i	$-0.572955\pi$
$839$	−13.1616	−0.454388	−0.227194	+	0.973849i	$0.572955\pi$
$840$	49.4084	1.70475
$841$	3.25998	0.112413
$842$	11.4809	0.395659
$843$	−55.8778	−1.92453
$844$	−7.09065	−0.244070
$845$	6.97077	0.239802
$846$	−44.0418	−1.51419
$847$	3.93972	0.135370
$848$	10.5045	0.360726
$849$	−40.3228	−1.38387
$850$	41.5187	1.42408
$851$	44.0885	1.51133
$852$	−68.6663	−2.35247
$853$	−36.9102	−1.26378	−0.631891	−	0.775057i	$-0.717721\pi$
$853$	−36.9102	−1.26378	−0.631891	+	0.775057i	$0.717721\pi$
$854$	−30.6844	−1.05000
$855$	0	0
$856$	−2.35218	−0.0803960
$857$	−24.3615	−0.832174	−0.416087	−	0.909325i	$-0.636599\pi$
$857$	−24.3615	−0.832174	−0.416087	+	0.909325i	$0.636599\pi$
$858$	15.6153	0.533096
$859$	−7.69750	−0.262635	−0.131318	−	0.991340i	$-0.541921\pi$
$859$	−7.69750	−0.262635	−0.131318	+	0.991340i	$0.541921\pi$
$860$	89.5085	3.05222
$861$	4.76566	0.162413
$862$	−39.0042	−1.32849
$863$	29.0225	0.987937	0.493969	−	0.869480i	$-0.335546\pi$
$863$	29.0225	0.987937	0.493969	+	0.869480i	$0.335546\pi$
$864$	−21.5472	−0.733051
$865$	−22.0916	−0.751137
$866$	1.52177	0.0517117
$867$	19.6871	0.668610
$868$	−27.5384	−0.934714
$869$	−8.49105	−0.288039
$870$	−91.8768	−3.11491
$871$	−32.9713	−1.11719
$872$	0.698197	0.0236439
$873$	−17.6431	−0.597127
$874$	0	0
$875$	−23.9262	−0.808852
$876$	53.6436	1.81245
$877$	36.0010	1.21567	0.607834	−	0.794064i	$-0.292039\pi$
$877$	36.0010	1.21567	0.607834	+	0.794064i	$0.292039\pi$
$878$	54.2399	1.83051
$879$	57.7111	1.94655
$880$	6.34128	0.213765
$881$	−15.3587	−0.517448	−0.258724	−	0.965951i	$-0.583302\pi$
$881$	−15.3587	−0.517448	−0.258724	+	0.965951i	$0.583302\pi$
$882$	30.8272	1.03800
$883$	40.2870	1.35577	0.677883	−	0.735170i	$-0.262898\pi$
$883$	40.2870	1.35577	0.677883	+	0.735170i	$0.262898\pi$
$884$	−25.7940	−0.867547
$885$	−32.2546	−1.08423
$886$	−8.59728	−0.288831
$887$	7.09855	0.238346	0.119173	−	0.992874i	$-0.461976\pi$
$887$	7.09855	0.238346	0.119173	+	0.992874i	$0.461976\pi$
$888$	−23.3912	−0.784956
$889$	−35.7728	−1.19978
$890$	−54.6104	−1.83054
$891$	−11.2258	−0.376079
$892$	69.2168	2.31755
$893$	0	0
$894$	−93.5228	−3.12787
$895$	42.9673	1.43624
$896$	−49.3851	−1.64984
$897$	49.2342	1.64388
$898$	−13.4042	−0.447302
$899$	14.3053	0.477110
$900$	31.1052	1.03684
$901$	−15.9490	−0.531339
$902$	−1.22511	−0.0407917
$903$	79.9121	2.65931
$904$	11.0801	0.368517
$905$	47.1783	1.56826
$906$	106.298	3.53153
$907$	−28.4435	−0.944452	−0.472226	−	0.881478i	$-0.656549\pi$
$907$	−28.4435	−0.944452	−0.472226	+	0.881478i	$0.656549\pi$
$908$	63.3470	2.10224
$909$	−18.9911	−0.629895
$910$	97.8190	3.24267
$911$	−49.5740	−1.64246	−0.821230	−	0.570598i	$-0.806712\pi$
$911$	−49.5740	−1.64246	−0.821230	+	0.570598i	$0.806712\pi$
$912$	0	0
$913$	−5.21960	−0.172744
$914$	18.3602	0.607301
$915$	−26.3831	−0.872199
$916$	−1.67501	−0.0553440
$917$	−40.9243	−1.35144
$918$	17.7907	0.587180
$919$	17.8421	0.588556	0.294278	−	0.955720i	$-0.404921\pi$
$919$	17.8421	0.588556	0.294278	+	0.955720i	$0.404921\pi$
$920$	−40.0472	−1.32032
$921$	48.8526	1.60975
$922$	56.7952	1.87045
$923$	−37.9770	−1.25003
$924$	−23.5915	−0.776103
$925$	43.3219	1.42441
$926$	42.3334	1.39116
$927$	−30.3010	−0.995215
$928$	42.1865	1.38484
$929$	36.0244	1.18192	0.590961	−	0.806700i	$-0.298749\pi$
$929$	36.0244	1.18192	0.590961	+	0.806700i	$0.298749\pi$
$930$	−40.7417	−1.33597
$931$	0	0
$932$	48.2080	1.57911
$933$	2.99317	0.0979921
$934$	−75.7667	−2.47916
$935$	−9.62799	−0.314869
$936$	−9.28867	−0.303610
$937$	−3.50371	−0.114461	−0.0572307	−	0.998361i	$-0.518227\pi$
$937$	−3.50371	−0.114461	−0.0572307	+	0.998361i	$0.518227\pi$
$938$	85.7104	2.79854
$939$	−27.8377	−0.908450
$940$	115.915	3.78074
$941$	−44.2074	−1.44112	−0.720560	−	0.693392i	$-0.756115\pi$
$941$	−44.2074	−1.44112	−0.720560	+	0.693392i	$0.756115\pi$
$942$	55.6430	1.81295
$943$	−3.86272	−0.125788
$944$	8.05385	0.262130
$945$	−39.2108	−1.27553
$946$	−20.5430	−0.667912
$947$	37.9515	1.23326	0.616629	−	0.787254i	$-0.288498\pi$
$947$	37.9515	1.23326	0.616629	+	0.787254i	$0.288498\pi$
$948$	50.8454	1.65138
$949$	29.6684	0.963077
$950$	0	0
$951$	−41.1491	−1.33435
$952$	18.7315	0.607090
$953$	−13.0303	−0.422094	−0.211047	−	0.977476i	$-0.567687\pi$
$953$	−13.0303	−0.422094	−0.211047	+	0.977476i	$0.567687\pi$
$954$	−20.5596	−0.665641
$955$	−10.6586	−0.344906
$956$	20.0788	0.649396
$957$	12.2550	0.396149
$958$	50.7745	1.64045
$959$	−3.14505	−0.101559
$960$	−92.7831	−2.99456
$961$	−24.6565	−0.795370
$962$	−46.3099	−1.49309
$963$	−2.29844	−0.0740662
$964$	33.8679	1.09081
$965$	−2.56558	−0.0825889
$966$	−127.987	−4.11791
$967$	24.0504	0.773409	0.386705	−	0.922204i	$-0.373613\pi$
$967$	24.0504	0.773409	0.386705	+	0.922204i	$0.373613\pi$
$968$	1.69419	0.0544534
$969$	0	0
$970$	79.8989	2.56540
$971$	−54.1335	−1.73723	−0.868614	−	0.495490i	$-0.834988\pi$
$971$	−54.1335	−1.73723	−0.868614	+	0.495490i	$0.834988\pi$
$972$	43.0682	1.38141
$973$	19.8240	0.635529
$974$	−31.1791	−0.999041
$975$	48.3781	1.54934
$976$	6.58776	0.210869
$977$	50.2507	1.60766	0.803832	−	0.594857i	$-0.202791\pi$
$977$	50.2507	1.60766	0.803832	+	0.594857i	$0.202791\pi$
$978$	117.118	3.74503
$979$	7.28423	0.232805
$980$	−81.1351	−2.59177
$981$	0.682245	0.0217824
$982$	90.9429	2.90210
$983$	−6.64633	−0.211985	−0.105993	−	0.994367i	$-0.533802\pi$
$983$	−6.64633	−0.211985	−0.105993	+	0.994367i	$0.533802\pi$
$984$	2.04937	0.0653315
$985$	11.7263	0.373631
$986$	−34.8318	−1.10927
$987$	103.488	3.29405
$988$	0	0
$989$	−64.7714	−2.05961
$990$	−12.4113	−0.394456
$991$	−51.7993	−1.64546	−0.822729	−	0.568434i	$-0.807549\pi$
$991$	−51.7993	−1.64546	−0.822729	+	0.568434i	$0.807549\pi$
$992$	18.7072	0.593953
$993$	−26.8879	−0.853260
$994$	98.7230	3.13130
$995$	−18.4159	−0.583822
$996$	31.2556	0.990371
$997$	−14.2042	−0.449851	−0.224925	−	0.974376i	$-0.572214\pi$
$997$	−14.2042	−0.449851	−0.224925	+	0.974376i	$0.572214\pi$
$998$	43.6315	1.38113
$999$	18.5633	0.587318

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3971.2.a.h.1.5		5
19.18	odd	2		209.2.a.c.1.1	✓	5
57.56	even	2		1881.2.a.k.1.5		5
76.75	even	2		3344.2.a.t.1.2		5
95.94	odd	2		5225.2.a.h.1.5		5
209.208	even	2		2299.2.a.n.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.a.c.1.1	✓	5	19.18	odd	2
1881.2.a.k.1.5		5	57.56	even	2
2299.2.a.n.1.5		5	209.208	even	2
3344.2.a.t.1.2		5	76.75	even	2
3971.2.a.h.1.5		5	1.1	even	1	trivial
5225.2.a.h.1.5		5	95.94	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)

\(f(q)\)	\(=\)	\(q+2.18524 q^{2} -2.15766 q^{3} +2.77529 q^{4} -3.43077 q^{5} -4.71500 q^{6} +3.93972 q^{7} +1.69419 q^{8} +1.65548 q^{9} -7.49706 q^{10} +1.00000 q^{11} -5.98812 q^{12} -3.31182 q^{13} +8.60924 q^{14} +7.40242 q^{15} -1.84836 q^{16} +2.80637 q^{17} +3.61763 q^{18} -9.52137 q^{20} -8.50056 q^{21} +2.18524 q^{22} +6.88998 q^{23} -3.65548 q^{24} +6.77018 q^{25} -7.23713 q^{26} +2.90101 q^{27} +10.9338 q^{28} -5.67979 q^{29} +16.1761 q^{30} -2.51864 q^{31} -7.42749 q^{32} -2.15766 q^{33} +6.13259 q^{34} -13.5163 q^{35} +4.59444 q^{36} +6.39893 q^{37} +7.14577 q^{39} -5.81238 q^{40} -0.560629 q^{41} -18.5758 q^{42} -9.40080 q^{43} +2.77529 q^{44} -5.67958 q^{45} +15.0563 q^{46} -12.1742 q^{47} +3.98812 q^{48} +8.52137 q^{49} +14.7945 q^{50} -6.05517 q^{51} -9.19126 q^{52} -5.68316 q^{53} +6.33941 q^{54} -3.43077 q^{55} +6.67463 q^{56} -12.4117 q^{58} -4.35730 q^{59} +20.5438 q^{60} -3.56412 q^{61} -5.50384 q^{62} +6.52213 q^{63} -12.5342 q^{64} +11.3621 q^{65} -4.71500 q^{66} +9.95563 q^{67} +7.78847 q^{68} -14.8662 q^{69} -29.5363 q^{70} +11.4671 q^{71} +2.80470 q^{72} -8.95834 q^{73} +13.9832 q^{74} -14.6077 q^{75} +3.93972 q^{77} +15.6153 q^{78} -8.49105 q^{79} +6.34128 q^{80} -11.2258 q^{81} -1.22511 q^{82} -5.21960 q^{83} -23.5915 q^{84} -9.62799 q^{85} -20.5430 q^{86} +12.2550 q^{87} +1.69419 q^{88} +7.28423 q^{89} -12.4113 q^{90} -13.0476 q^{91} +19.1217 q^{92} +5.43436 q^{93} -26.6036 q^{94} +16.0260 q^{96} -10.6574 q^{97} +18.6213 q^{98} +1.65548 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 6 q^{7} - 6 q^{8} + 4 q^{9} - 12 q^{10} + 5 q^{11} - 6 q^{12} - 4 q^{13} + 14 q^{14} - 3 q^{15} + 8 q^{16} - 4 q^{17} + 20 q^{18} - 8 q^{20} - 10 q^{21}+ \cdots + 4 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 6 * q^7 - 6 * q^8 + 4 * q^9 - 12 * q^10 + 5 * q^11 - 6 * q^12 - 4 * q^13 + 14 * q^14 - 3 * q^15 + 8 * q^16 - 4 * q^17 + 20 * q^18 - 8 * q^20 - 10 * q^21 - 2 * q^22 + 3 * q^23 - 14 * q^24 + 6 * q^25 - 6 * q^26 + 11 * q^27 - 10 * q^28 - 10 * q^29 + 6 * q^30 - 11 * q^31 - 14 * q^32 - q^33 + 4 * q^34 - 8 * q^35 - 26 * q^36 - q^37 + 2 * q^39 + 16 * q^40 - 2 * q^41 - 16 * q^42 + 20 * q^43 + 6 * q^44 - 28 * q^45 + 4 * q^46 - 20 * q^47 - 4 * q^48 + 3 * q^49 + 32 * q^50 - 24 * q^51 - 6 * q^52 + 14 * q^53 + 16 * q^54 - 5 * q^55 + 38 * q^56 - 6 * q^58 - 3 * q^59 + 40 * q^60 - 10 * q^61 - 6 * q^62 + 24 * q^63 - 2 * q^66 - 9 * q^67 + 24 * q^68 + 5 * q^69 - 50 * q^70 - 23 * q^71 + 12 * q^72 + 8 * q^74 + 18 * q^75 + 6 * q^77 + 22 * q^78 - 44 * q^79 - 18 * q^80 + q^81 - 30 * q^82 - 14 * q^83 - 14 * q^84 - 12 * q^85 - 52 * q^86 + 28 * q^87 - 6 * q^88 + 27 * q^89 - 26 * q^90 - 24 * q^91 + 58 * q^92 - 27 * q^93 + 8 * q^94 + 50 * q^96 - 15 * q^97 + 10 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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Groups

Database

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