LMFDB - Embedded newform 6031.2.a.c.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [6031,2,Mod(1,6031)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6031.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6031, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.a (trivial)

Newform invariants

comment:select newform

sage:traces = [110] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6031.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.45577 q^{2} -2.50707 q^{3} +4.03080 q^{4} -3.71982 q^{5} +6.15679 q^{6} -2.33961 q^{7} -4.98718 q^{8} +3.28541 q^{9} +9.13502 q^{10} +2.57303 q^{11} -10.1055 q^{12} +5.33790 q^{13} +5.74553 q^{14} +9.32586 q^{15} +4.18576 q^{16} +4.03274 q^{17} -8.06822 q^{18} -4.58211 q^{19} -14.9939 q^{20} +5.86556 q^{21} -6.31877 q^{22} -2.79877 q^{23} +12.5032 q^{24} +8.83707 q^{25} -13.1087 q^{26} -0.715550 q^{27} -9.43049 q^{28} -6.33486 q^{29} -22.9022 q^{30} +0.489920 q^{31} -0.304902 q^{32} -6.45077 q^{33} -9.90347 q^{34} +8.70291 q^{35} +13.2428 q^{36} -1.00000 q^{37} +11.2526 q^{38} -13.3825 q^{39} +18.5514 q^{40} -8.58242 q^{41} -14.4045 q^{42} +0.592609 q^{43} +10.3714 q^{44} -12.2211 q^{45} +6.87312 q^{46} -9.77727 q^{47} -10.4940 q^{48} -1.52625 q^{49} -21.7018 q^{50} -10.1104 q^{51} +21.5160 q^{52} -7.99488 q^{53} +1.75723 q^{54} -9.57121 q^{55} +11.6680 q^{56} +11.4877 q^{57} +15.5570 q^{58} +0.408646 q^{59} +37.5907 q^{60} +0.897776 q^{61} -1.20313 q^{62} -7.68657 q^{63} -7.62275 q^{64} -19.8560 q^{65} +15.8416 q^{66} -1.17207 q^{67} +16.2552 q^{68} +7.01671 q^{69} -21.3723 q^{70} +7.20994 q^{71} -16.3849 q^{72} +16.0979 q^{73} +2.45577 q^{74} -22.1552 q^{75} -18.4696 q^{76} -6.01987 q^{77} +32.8644 q^{78} +0.577220 q^{79} -15.5703 q^{80} -8.06230 q^{81} +21.0765 q^{82} +15.0091 q^{83} +23.6429 q^{84} -15.0011 q^{85} -1.45531 q^{86} +15.8820 q^{87} -12.8322 q^{88} +2.15432 q^{89} +30.0123 q^{90} -12.4886 q^{91} -11.2813 q^{92} -1.22827 q^{93} +24.0107 q^{94} +17.0446 q^{95} +0.764411 q^{96} +2.02030 q^{97} +3.74811 q^{98} +8.45346 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21}+ \cdots - 21 q^{99}+O(q^{100}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.45577	−1.73649	−0.868246	−	0.496135i	$-0.834752\pi$
$2$	−2.45577	−1.73649	−0.868246	+	0.496135i	$0.834752\pi$
$3$	−2.50707	−1.44746	−0.723730	−	0.690084i	$-0.757574\pi$
$3$	−2.50707	−1.44746	−0.723730	+	0.690084i	$0.757574\pi$
$4$	4.03080	2.01540
$5$	−3.71982	−1.66355	−0.831777	−	0.555110i	$-0.812676\pi$
$5$	−3.71982	−1.66355	−0.831777	+	0.555110i	$0.812676\pi$
$6$	6.15679	2.51350
$7$	−2.33961	−0.884288	−0.442144	−	0.896944i	$-0.645782\pi$
$7$	−2.33961	−0.884288	−0.442144	+	0.896944i	$0.645782\pi$
$8$	−4.98718	−1.76323
$9$	3.28541	1.09514
$10$	9.13502	2.88875
$11$	2.57303	0.775797	0.387899	−	0.921702i	$-0.373201\pi$
$11$	2.57303	0.775797	0.387899	+	0.921702i	$0.373201\pi$
$12$	−10.1055	−2.91721
$13$	5.33790	1.48047	0.740234	−	0.672349i	$-0.234715\pi$
$13$	5.33790	1.48047	0.740234	+	0.672349i	$0.234715\pi$
$14$	5.74553	1.53556
$15$	9.32586	2.40793
$16$	4.18576	1.04644
$17$	4.03274	0.978083	0.489041	−	0.872261i	$-0.337347\pi$
$17$	4.03274	0.978083	0.489041	+	0.872261i	$0.337347\pi$
$18$	−8.06822	−1.90170
$19$	−4.58211	−1.05121	−0.525604	−	0.850729i	$-0.676161\pi$
$19$	−4.58211	−1.05121	−0.525604	+	0.850729i	$0.676161\pi$
$20$	−14.9939	−3.35273
$21$	5.86556	1.27997
$22$	−6.31877	−1.34717
$23$	−2.79877	−0.583583	−0.291791	−	0.956482i	$-0.594251\pi$
$23$	−2.79877	−0.583583	−0.291791	+	0.956482i	$0.594251\pi$
$24$	12.5032	2.55221
$25$	8.83707	1.76741
$26$	−13.1087	−2.57082
$27$	−0.715550	−0.137708
$28$	−9.43049	−1.78219
$29$	−6.33486	−1.17635	−0.588177	−	0.808732i	$-0.700154\pi$
$29$	−6.33486	−1.17635	−0.588177	+	0.808732i	$0.700154\pi$
$30$	−22.9022	−4.18134
$31$	0.489920	0.0879922	0.0439961	−	0.999032i	$-0.485991\pi$
$31$	0.489920	0.0879922	0.0439961	+	0.999032i	$0.485991\pi$
$32$	−0.304902	−0.0538996
$33$	−6.45077	−1.12294
$34$	−9.90347	−1.69843
$35$	8.70291	1.47106
$36$	13.2428	2.20714
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	11.2526	1.82541
$39$	−13.3825	−2.14292
$40$	18.5514	2.93324
$41$	−8.58242	−1.34035	−0.670175	−	0.742203i	$-0.733781\pi$
$41$	−8.58242	−1.34035	−0.670175	+	0.742203i	$0.733781\pi$
$42$	−14.4045	−2.22266
$43$	0.592609	0.0903720	0.0451860	−	0.998979i	$-0.485612\pi$
$43$	0.592609	0.0903720	0.0451860	+	0.998979i	$0.485612\pi$
$44$	10.3714	1.56354
$45$	−12.2211	−1.82182
$46$	6.87312	1.01339
$47$	−9.77727	−1.42616	−0.713080	−	0.701082i	$-0.752701\pi$
$47$	−9.77727	−1.42616	−0.713080	+	0.701082i	$0.752701\pi$
$48$	−10.4940	−1.51468
$49$	−1.52625	−0.218035
$50$	−21.7018	−3.06910
$51$	−10.1104	−1.41573
$52$	21.5160	2.98374
$53$	−7.99488	−1.09818	−0.549091	−	0.835763i	$-0.685026\pi$
$53$	−7.99488	−1.09818	−0.549091	+	0.835763i	$0.685026\pi$
$54$	1.75723	0.239128
$55$	−9.57121	−1.29058
$56$	11.6680	1.55921
$57$	11.4877	1.52158
$58$	15.5570	2.04273
$59$	0.408646	0.0532012	0.0266006	−	0.999646i	$-0.491532\pi$
$59$	0.408646	0.0532012	0.0266006	+	0.999646i	$0.491532\pi$
$60$	37.5907	4.85294
$61$	0.897776	0.114948	0.0574742	−	0.998347i	$-0.481695\pi$
$61$	0.897776	0.114948	0.0574742	+	0.998347i	$0.481695\pi$
$62$	−1.20313	−0.152798
$63$	−7.68657	−0.968417
$64$	−7.62275	−0.952844
$65$	−19.8560	−2.46284
$66$	15.8416	1.94997
$67$	−1.17207	−0.143191	−0.0715954	−	0.997434i	$-0.522809\pi$
$67$	−1.17207	−0.143191	−0.0715954	+	0.997434i	$0.522809\pi$
$68$	16.2552	1.97123
$69$	7.01671	0.844712
$70$	−21.3723	−2.55448
$71$	7.20994	0.855662	0.427831	−	0.903859i	$-0.359278\pi$
$71$	7.20994	0.855662	0.427831	+	0.903859i	$0.359278\pi$
$72$	−16.3849	−1.93098
$73$	16.0979	1.88411	0.942057	−	0.335453i	$-0.108889\pi$
$73$	16.0979	1.88411	0.942057	+	0.335453i	$0.108889\pi$
$74$	2.45577	0.285477
$75$	−22.1552	−2.55826
$76$	−18.4696	−2.11861
$77$	−6.01987	−0.686028
$78$	32.8644	3.72115
$79$	0.577220	0.0649423	0.0324712	−	0.999473i	$-0.489662\pi$
$79$	0.577220	0.0649423	0.0324712	+	0.999473i	$0.489662\pi$
$80$	−15.5703	−1.74081
$81$	−8.06230	−0.895811
$82$	21.0765	2.32750
$83$	15.0091	1.64746	0.823731	−	0.566980i	$-0.191888\pi$
$83$	15.0091	1.64746	0.823731	+	0.566980i	$0.191888\pi$
$84$	23.6429	2.57965
$85$	−15.0011	−1.62709
$86$	−1.45531	−0.156930
$87$	15.8820	1.70273
$88$	−12.8322	−1.36791
$89$	2.15432	0.228357	0.114179	−	0.993460i	$-0.463576\pi$
$89$	2.15432	0.228357	0.114179	+	0.993460i	$0.463576\pi$
$90$	30.0123	3.16358
$91$	−12.4886	−1.30916
$92$	−11.2813	−1.17615
$93$	−1.22827	−0.127365
$94$	24.0107	2.47652
$95$	17.0446	1.74874
$96$	0.764411	0.0780174
$97$	2.02030	0.205131	0.102565	−	0.994726i	$-0.467295\pi$
$97$	2.02030	0.205131	0.102565	+	0.994726i	$0.467295\pi$
$98$	3.74811	0.378617
$99$	8.45346	0.849605
$100$	35.6205	3.56205
$101$	0.381656	0.0379762	0.0189881	−	0.999820i	$-0.493956\pi$
$101$	0.381656	0.0379762	0.0189881	+	0.999820i	$0.493956\pi$
$102$	24.8287	2.45841
$103$	2.19364	0.216146	0.108073	−	0.994143i	$-0.465532\pi$
$103$	2.19364	0.216146	0.108073	+	0.994143i	$0.465532\pi$
$104$	−26.6211	−2.61041
$105$	−21.8188	−2.12930
$106$	19.6336	1.90698
$107$	17.8638	1.72696	0.863479	−	0.504385i	$-0.168281\pi$
$107$	17.8638	1.72696	0.863479	+	0.504385i	$0.168281\pi$
$108$	−2.88424	−0.277536
$109$	5.26295	0.504099	0.252050	−	0.967714i	$-0.418895\pi$
$109$	5.26295	0.504099	0.252050	+	0.967714i	$0.418895\pi$
$110$	23.5047	2.24108
$111$	2.50707	0.237961
$112$	−9.79303	−0.925354
$113$	−10.3950	−0.977880	−0.488940	−	0.872317i	$-0.662616\pi$
$113$	−10.3950	−0.977880	−0.488940	+	0.872317i	$0.662616\pi$
$114$	−28.2111	−2.64221
$115$	10.4109	0.970822
$116$	−25.5346	−2.37083
$117$	17.5372	1.62132
$118$	−1.00354	−0.0923834
$119$	−9.43501	−0.864906
$120$	−46.5098	−4.24574
$121$	−4.37952	−0.398138
$122$	−2.20473	−0.199607
$123$	21.5168	1.94010
$124$	1.97477	0.177340
$125$	−14.2732	−1.27663
$126$	18.8764	1.68165
$127$	18.1699	1.61231	0.806157	−	0.591701i	$-0.201544\pi$
$127$	18.1699	1.61231	0.806157	+	0.591701i	$0.201544\pi$
$128$	19.3295	1.70851
$129$	−1.48571	−0.130810
$130$	48.7618	4.27670
$131$	−18.9556	−1.65615	−0.828077	−	0.560614i	$-0.810565\pi$
$131$	−18.9556	−1.65615	−0.828077	+	0.560614i	$0.810565\pi$
$132$	−26.0018	−2.26316
$133$	10.7203	0.929571
$134$	2.87833	0.248650
$135$	2.66172	0.229084
$136$	−20.1120	−1.72459
$137$	−21.1672	−1.80844	−0.904220	−	0.427068i	$-0.859547\pi$
$137$	−21.1672	−1.80844	−0.904220	+	0.427068i	$0.859547\pi$
$138$	−17.2314	−1.46684
$139$	13.0259	1.10484	0.552419	−	0.833566i	$-0.313705\pi$
$139$	13.0259	1.10484	0.552419	+	0.833566i	$0.313705\pi$
$140$	35.0797	2.96478
$141$	24.5123	2.06431
$142$	−17.7059	−1.48585
$143$	13.7346	1.14854
$144$	13.7520	1.14600
$145$	23.5646	1.95693
$146$	−39.5327	−3.27175
$147$	3.82641	0.315597
$148$	−4.03080	−0.331330
$149$	−3.12849	−0.256296	−0.128148	−	0.991755i	$-0.540903\pi$
$149$	−3.12849	−0.256296	−0.128148	+	0.991755i	$0.540903\pi$
$150$	54.4080	4.44239
$151$	−3.08038	−0.250677	−0.125339	−	0.992114i	$-0.540002\pi$
$151$	−3.08038	−0.250677	−0.125339	+	0.992114i	$0.540002\pi$
$152$	22.8518	1.85353
$153$	13.2492	1.07113
$154$	14.7834	1.19128
$155$	−1.82241	−0.146380
$156$	−53.9422	−4.31884
$157$	21.6881	1.73090	0.865450	−	0.500995i	$-0.167033\pi$
$157$	21.6881	1.73090	0.865450	+	0.500995i	$0.167033\pi$
$158$	−1.41752	−0.112772
$159$	20.0437	1.58957
$160$	1.13418	0.0896649
$161$	6.54801	0.516055
$162$	19.7992	1.55557
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	−34.5941	−2.70134
$165$	23.9957	1.86806
$166$	−36.8589	−2.86080
$167$	18.1507	1.40454	0.702270	−	0.711911i	$-0.252170\pi$
$167$	18.1507	1.40454	0.702270	+	0.711911i	$0.252170\pi$
$168$	−29.2526	−2.25689
$169$	15.4932	1.19178
$170$	36.8391	2.82543
$171$	−15.0541	−1.15122
$172$	2.38869	0.182136
$173$	−14.8938	−1.13236	−0.566178	−	0.824283i	$-0.691578\pi$
$173$	−14.8938	−1.13236	−0.566178	+	0.824283i	$0.691578\pi$
$174$	−39.0024	−2.95677
$175$	−20.6752	−1.56290
$176$	10.7701	0.811826
$177$	−1.02451	−0.0770066
$178$	−5.29051	−0.396541
$179$	−15.2482	−1.13971	−0.569853	−	0.821747i	$-0.693000\pi$
$179$	−15.2482	−1.13971	−0.569853	+	0.821747i	$0.693000\pi$
$180$	−49.2610	−3.67170
$181$	−22.5531	−1.67636	−0.838180	−	0.545394i	$-0.816380\pi$
$181$	−22.5531	−1.67636	−0.838180	+	0.545394i	$0.816380\pi$
$182$	30.6691	2.27334
$183$	−2.25079	−0.166383
$184$	13.9579	1.02899
$185$	3.71982	0.273487
$186$	3.01634	0.221168
$187$	10.3764	0.758794
$188$	−39.4102	−2.87429
$189$	1.67411	0.121773
$190$	−41.8577	−3.03668
$191$	−6.20408	−0.448912	−0.224456	−	0.974484i	$-0.572060\pi$
$191$	−6.20408	−0.448912	−0.224456	+	0.974484i	$0.572060\pi$
$192$	19.1108	1.37920
$193$	5.11788	0.368393	0.184196	−	0.982889i	$-0.441032\pi$
$193$	5.11788	0.368393	0.184196	+	0.982889i	$0.441032\pi$
$194$	−4.96139	−0.356207
$195$	49.7805	3.56486
$196$	−6.15200	−0.439429
$197$	−2.07974	−0.148175	−0.0740877	−	0.997252i	$-0.523604\pi$
$197$	−2.07974	−0.148175	−0.0740877	+	0.997252i	$0.523604\pi$
$198$	−20.7598	−1.47533
$199$	6.02258	0.426930	0.213465	−	0.976951i	$-0.431525\pi$
$199$	6.02258	0.426930	0.213465	+	0.976951i	$0.431525\pi$
$200$	−44.0720	−3.11636
$201$	2.93846	0.207263
$202$	−0.937258	−0.0659453
$203$	14.8211	1.04024
$204$	−40.7529	−2.85327
$205$	31.9251	2.22974
$206$	−5.38707	−0.375335
$207$	−9.19510	−0.639104
$208$	22.3432	1.54922
$209$	−11.7899	−0.815525
$210$	53.5820	3.69751
$211$	−2.87604	−0.197995	−0.0989973	−	0.995088i	$-0.531564\pi$
$211$	−2.87604	−0.197995	−0.0989973	+	0.995088i	$0.531564\pi$
$212$	−32.2258	−2.21328
$213$	−18.0758	−1.23854
$214$	−43.8693	−2.99885
$215$	−2.20440	−0.150339
$216$	3.56858	0.242811
$217$	−1.14622	−0.0778105
$218$	−12.9246	−0.875364
$219$	−40.3585	−2.72718
$220$	−38.5796	−2.60104
$221$	21.5264	1.44802
$222$	−6.15679	−0.413217
$223$	−3.25540	−0.217998	−0.108999	−	0.994042i	$-0.534765\pi$
$223$	−3.25540	−0.217998	−0.108999	+	0.994042i	$0.534765\pi$
$224$	0.713350	0.0476627
$225$	29.0334	1.93556
$226$	25.5277	1.69808
$227$	19.9280	1.32267	0.661333	−	0.750092i	$-0.269991\pi$
$227$	19.9280	1.32267	0.661333	+	0.750092i	$0.269991\pi$
$228$	46.3046	3.06660
$229$	−12.0532	−0.796501	−0.398250	−	0.917277i	$-0.630382\pi$
$229$	−12.0532	−0.796501	−0.398250	+	0.917277i	$0.630382\pi$
$230$	−25.5668	−1.68582
$231$	15.0923	0.992998
$232$	31.5931	2.07419
$233$	−6.90856	−0.452595	−0.226297	−	0.974058i	$-0.572662\pi$
$233$	−6.90856	−0.452595	−0.226297	+	0.974058i	$0.572662\pi$
$234$	−43.0673	−2.81540
$235$	36.3697	2.37250
$236$	1.64717	0.107222
$237$	−1.44713	−0.0940014
$238$	23.1702	1.50190
$239$	22.1606	1.43345	0.716723	−	0.697358i	$-0.245641\pi$
$239$	22.1606	1.43345	0.716723	+	0.697358i	$0.245641\pi$
$240$	39.0358	2.51975
$241$	−1.51312	−0.0974685	−0.0487343	−	0.998812i	$-0.515519\pi$
$241$	−1.51312	−0.0974685	−0.0487343	+	0.998812i	$0.515519\pi$
$242$	10.7551	0.691364
$243$	22.3594	1.43436
$244$	3.61876	0.231667
$245$	5.67737	0.362714
$246$	−52.8402	−3.36897
$247$	−24.4589	−1.55628
$248$	−2.44332	−0.155151
$249$	−37.6289	−2.38463
$250$	35.0517	2.21686
$251$	7.79981	0.492320	0.246160	−	0.969229i	$-0.420831\pi$
$251$	7.79981	0.492320	0.246160	+	0.969229i	$0.420831\pi$
$252$	−30.9830	−1.95175
$253$	−7.20130	−0.452742
$254$	−44.6210	−2.79977
$255$	37.6087	2.35515
$256$	−32.2234	−2.01396
$257$	−27.5057	−1.71576	−0.857880	−	0.513849i	$-0.828219\pi$
$257$	−27.5057	−1.71576	−0.857880	+	0.513849i	$0.828219\pi$
$258$	3.64857	0.227150
$259$	2.33961	0.145376
$260$	−80.0358	−4.96361
$261$	−20.8126	−1.28827
$262$	46.5505	2.87590
$263$	23.2339	1.43266	0.716332	−	0.697760i	$-0.245820\pi$
$263$	23.2339	1.43266	0.716332	+	0.697760i	$0.245820\pi$
$264$	32.1712	1.98000
$265$	29.7395	1.82688
$266$	−26.3267	−1.61419
$267$	−5.40103	−0.330538
$268$	−4.72437	−0.288587
$269$	7.08590	0.432035	0.216017	−	0.976389i	$-0.430693\pi$
$269$	7.08590	0.432035	0.216017	+	0.976389i	$0.430693\pi$
$270$	−6.53657	−0.397803
$271$	10.7026	0.650134	0.325067	−	0.945691i	$-0.394613\pi$
$271$	10.7026	0.650134	0.325067	+	0.945691i	$0.394613\pi$
$272$	16.8801	1.02351
$273$	31.3098	1.89495
$274$	51.9819	3.14034
$275$	22.7380	1.37115
$276$	28.2830	1.70243
$277$	19.0675	1.14565	0.572827	−	0.819677i	$-0.305847\pi$
$277$	19.0675	1.14565	0.572827	+	0.819677i	$0.305847\pi$
$278$	−31.9885	−1.91854
$279$	1.60959	0.0963636
$280$	−43.4030	−2.59383
$281$	13.8001	0.823243	0.411622	−	0.911355i	$-0.364963\pi$
$281$	13.8001	0.823243	0.411622	+	0.911355i	$0.364963\pi$
$282$	−60.1966	−3.58465
$283$	−15.6644	−0.931155	−0.465577	−	0.885007i	$-0.654153\pi$
$283$	−15.6644	−0.931155	−0.465577	+	0.885007i	$0.654153\pi$
$284$	29.0618	1.72450
$285$	−42.7321	−2.53123
$286$	−33.7290	−1.99443
$287$	20.0795	1.18525
$288$	−1.00173	−0.0590274
$289$	−0.737026	−0.0433544
$290$	−57.8691	−3.39819
$291$	−5.06504	−0.296918
$292$	64.8874	3.79725
$293$	−20.0490	−1.17128	−0.585639	−	0.810572i	$-0.699156\pi$
$293$	−20.0490	−1.17128	−0.585639	+	0.810572i	$0.699156\pi$
$294$	−9.39679	−0.548032
$295$	−1.52009	−0.0885031
$296$	4.98718	0.289874
$297$	−1.84113	−0.106833
$298$	7.68284	0.445055
$299$	−14.9395	−0.863976
$300$	−89.3031	−5.15592
$301$	−1.38647	−0.0799148
$302$	7.56469	0.435299
$303$	−0.956839	−0.0549689
$304$	−19.1796	−1.10003
$305$	−3.33957	−0.191223
$306$	−32.5370	−1.86002
$307$	−15.2943	−0.872893	−0.436447	−	0.899730i	$-0.643763\pi$
$307$	−15.2943	−0.872893	−0.436447	+	0.899730i	$0.643763\pi$
$308$	−24.2649	−1.38262
$309$	−5.49961	−0.312862
$310$	4.47543	0.254187
$311$	19.2053	1.08903	0.544516	−	0.838750i	$-0.316713\pi$
$311$	19.2053	1.08903	0.544516	+	0.838750i	$0.316713\pi$
$312$	66.7410	3.77846
$313$	−16.3505	−0.924186	−0.462093	−	0.886831i	$-0.652901\pi$
$313$	−16.3505	−0.924186	−0.462093	+	0.886831i	$0.652901\pi$
$314$	−53.2610	−3.00569
$315$	28.5927	1.61101
$316$	2.32666	0.130885
$317$	13.7975	0.774944	0.387472	−	0.921882i	$-0.373348\pi$
$317$	13.7975	0.774944	0.387472	+	0.921882i	$0.373348\pi$
$318$	−49.2228	−2.76028
$319$	−16.2998	−0.912613
$320$	28.3553	1.58511
$321$	−44.7858	−2.49970
$322$	−16.0804	−0.896125
$323$	−18.4785	−1.02817
$324$	−32.4975	−1.80542
$325$	47.1714	2.61660
$326$	2.45577	0.136012
$327$	−13.1946	−0.729663
$328$	42.8021	2.36335
$329$	22.8749	1.26114
$330$	−58.9279	−3.24388
$331$	22.2294	1.22184	0.610920	−	0.791693i	$-0.290800\pi$
$331$	22.2294	1.22184	0.610920	+	0.791693i	$0.290800\pi$
$332$	60.4987	3.32030
$333$	−3.28541	−0.180040
$334$	−44.5738	−2.43897
$335$	4.35988	0.238206
$336$	24.5518	1.33941
$337$	26.6404	1.45119	0.725596	−	0.688121i	$-0.241564\pi$
$337$	26.6404	1.45119	0.725596	+	0.688121i	$0.241564\pi$
$338$	−38.0477	−2.06952
$339$	26.0610	1.41544
$340$	−60.4663	−3.27925
$341$	1.26058	0.0682642
$342$	36.9695	1.99908
$343$	19.9481	1.07709
$344$	−2.95545	−0.159347
$345$	−26.1009	−1.40522
$346$	36.5757	1.96632
$347$	−12.3230	−0.661533	−0.330766	−	0.943713i	$-0.607307\pi$
$347$	−12.3230	−0.661533	−0.330766	+	0.943713i	$0.607307\pi$
$348$	64.0171	3.43167
$349$	20.9214	1.11990	0.559948	−	0.828528i	$-0.310821\pi$
$349$	20.9214	1.11990	0.559948	+	0.828528i	$0.310821\pi$
$350$	50.7736	2.71396
$351$	−3.81954	−0.203872
$352$	−0.784522	−0.0418151
$353$	−7.84095	−0.417332	−0.208666	−	0.977987i	$-0.566912\pi$
$353$	−7.84095	−0.417332	−0.208666	+	0.977987i	$0.566912\pi$
$354$	2.51595	0.133721
$355$	−26.8197	−1.42344
$356$	8.68363	0.460232
$357$	23.6543	1.25192
$358$	37.4461	1.97909
$359$	9.51169	0.502008	0.251004	−	0.967986i	$-0.419239\pi$
$359$	9.51169	0.502008	0.251004	+	0.967986i	$0.419239\pi$
$360$	60.9491	3.21230
$361$	1.99574	0.105039
$362$	55.3852	2.91098
$363$	10.9798	0.576289
$364$	−50.3390	−2.63848
$365$	−59.8812	−3.13433
$366$	5.52742	0.288923
$367$	18.6461	0.973316	0.486658	−	0.873593i	$-0.338216\pi$
$367$	18.6461	0.973316	0.486658	+	0.873593i	$0.338216\pi$
$368$	−11.7150	−0.610685
$369$	−28.1968	−1.46787
$370$	−9.13502	−0.474907
$371$	18.7049	0.971108
$372$	−4.95089	−0.256692
$373$	31.9281	1.65317	0.826586	−	0.562810i	$-0.190280\pi$
$373$	31.9281	1.65317	0.826586	+	0.562810i	$0.190280\pi$
$374$	−25.4819	−1.31764
$375$	35.7839	1.84787
$376$	48.7610	2.51466
$377$	−33.8149	−1.74156
$378$	−4.11122	−0.211458
$379$	23.2132	1.19238	0.596191	−	0.802842i	$-0.296680\pi$
$379$	23.2132	1.19238	0.596191	+	0.802842i	$0.296680\pi$
$380$	68.7035	3.52442
$381$	−45.5532	−2.33376
$382$	15.2358	0.779531
$383$	−6.54297	−0.334330	−0.167165	−	0.985929i	$-0.553461\pi$
$383$	−6.54297	−0.334330	−0.167165	+	0.985929i	$0.553461\pi$
$384$	−48.4605	−2.47299
$385$	22.3928	1.14125
$386$	−12.5683	−0.639711
$387$	1.94696	0.0989698
$388$	8.14344	0.413420
$389$	33.2338	1.68502	0.842511	−	0.538679i	$-0.181077\pi$
$389$	33.2338	1.68502	0.842511	+	0.538679i	$0.181077\pi$
$390$	−122.249	−6.19034
$391$	−11.2867	−0.570792
$392$	7.61167	0.384448
$393$	47.5230	2.39722
$394$	5.10736	0.257305
$395$	−2.14716	−0.108035
$396$	34.0742	1.71229
$397$	23.9110	1.20006	0.600028	−	0.799979i	$-0.295156\pi$
$397$	23.9110	1.20006	0.600028	+	0.799979i	$0.295156\pi$
$398$	−14.7901	−0.741359
$399$	−26.8766	−1.34552
$400$	36.9899	1.84949
$401$	16.8344	0.840669	0.420334	−	0.907369i	$-0.361913\pi$
$401$	16.8344	0.840669	0.420334	+	0.907369i	$0.361913\pi$
$402$	−7.21617	−0.359910
$403$	2.61515	0.130270
$404$	1.53838	0.0765372
$405$	29.9903	1.49023
$406$	−36.3972	−1.80636
$407$	−2.57303	−0.127540
$408$	50.4222	2.49627
$409$	−6.64296	−0.328473	−0.164237	−	0.986421i	$-0.552516\pi$
$409$	−6.64296	−0.328473	−0.164237	+	0.986421i	$0.552516\pi$
$410$	−78.4006	−3.87193
$411$	53.0678	2.61764
$412$	8.84212	0.435620
$413$	−0.956071	−0.0470452
$414$	22.5810	1.10980
$415$	−55.8312	−2.74064
$416$	−1.62754	−0.0797966
$417$	−32.6568	−1.59921
$418$	28.9533	1.41615
$419$	18.3741	0.897634	0.448817	−	0.893624i	$-0.351846\pi$
$419$	18.3741	0.897634	0.448817	+	0.893624i	$0.351846\pi$
$420$	−87.9474	−4.29139
$421$	−3.57601	−0.174284	−0.0871421	−	0.996196i	$-0.527773\pi$
$421$	−3.57601	−0.174284	−0.0871421	+	0.996196i	$0.527773\pi$
$422$	7.06289	0.343816
$423$	−32.1224	−1.56184
$424$	39.8719	1.93635
$425$	35.6376	1.72868
$426$	44.3901	2.15071
$427$	−2.10044	−0.101648
$428$	72.0054	3.48051
$429$	−34.4336	−1.66247
$430$	5.41349	0.261062
$431$	−15.4973	−0.746480	−0.373240	−	0.927735i	$-0.621753\pi$
$431$	−15.4973	−0.746480	−0.373240	+	0.927735i	$0.621753\pi$
$432$	−2.99512	−0.144103
$433$	−14.1594	−0.680457	−0.340228	−	0.940343i	$-0.610504\pi$
$433$	−14.1594	−0.680457	−0.340228	+	0.940343i	$0.610504\pi$
$434$	2.81485	0.135117
$435$	−59.0781	−2.83258
$436$	21.2139	1.01596
$437$	12.8243	0.613467
$438$	99.1113	4.73572
$439$	−28.7646	−1.37286	−0.686430	−	0.727196i	$-0.740823\pi$
$439$	−28.7646	−1.37286	−0.686430	+	0.727196i	$0.740823\pi$
$440$	47.7333	2.27560
$441$	−5.01435	−0.238779
$442$	−52.8638	−2.51447
$443$	−28.9522	−1.37556	−0.687780	−	0.725919i	$-0.741415\pi$
$443$	−28.9522	−1.37556	−0.687780	+	0.725919i	$0.741415\pi$
$444$	10.1055	0.479586
$445$	−8.01368	−0.379885
$446$	7.99452	0.378552
$447$	7.84334	0.370977
$448$	17.8342	0.842588
$449$	−17.5740	−0.829369	−0.414684	−	0.909965i	$-0.636108\pi$
$449$	−17.5740	−0.829369	−0.414684	+	0.909965i	$0.636108\pi$
$450$	−71.2993	−3.36108
$451$	−22.0828	−1.03984
$452$	−41.9002	−1.97082
$453$	7.72273	0.362845
$454$	−48.9385	−2.29680
$455$	46.4553	2.17786
$456$	−57.2912	−2.68290
$457$	−28.3952	−1.32827	−0.664137	−	0.747611i	$-0.731201\pi$
$457$	−28.3952	−1.32827	−0.664137	+	0.747611i	$0.731201\pi$
$458$	29.6000	1.38312
$459$	−2.88563	−0.134690
$460$	41.9643	1.95660
$461$	−23.4349	−1.09147	−0.545737	−	0.837957i	$-0.683750\pi$
$461$	−23.4349	−1.09147	−0.545737	+	0.837957i	$0.683750\pi$
$462$	−37.0631	−1.72433
$463$	−13.6729	−0.635432	−0.317716	−	0.948186i	$-0.602916\pi$
$463$	−13.6729	−0.635432	−0.317716	+	0.948186i	$0.602916\pi$
$464$	−26.5162	−1.23099
$465$	4.56893	0.211879
$466$	16.9658	0.785927
$467$	−29.5387	−1.36689	−0.683445	−	0.730002i	$-0.739519\pi$
$467$	−29.5387	−1.36689	−0.683445	+	0.730002i	$0.739519\pi$
$468$	70.6890	3.26760
$469$	2.74217	0.126622
$470$	−89.3155	−4.11982
$471$	−54.3737	−2.50541
$472$	−2.03799	−0.0938063
$473$	1.52480	0.0701104
$474$	3.55382	0.163233
$475$	−40.4924	−1.85792
$476$	−38.0307	−1.74313
$477$	−26.2665	−1.20266
$478$	−54.4212	−2.48917
$479$	16.9628	0.775051	0.387525	−	0.921859i	$-0.373330\pi$
$479$	16.9628	0.775051	0.387525	+	0.921859i	$0.373330\pi$
$480$	−2.84347	−0.129786
$481$	−5.33790	−0.243387
$482$	3.71587	0.169253
$483$	−16.4163	−0.746969
$484$	−17.6530	−0.802408
$485$	−7.51516	−0.341246
$486$	−54.9096	−2.49075
$487$	33.4512	1.51582	0.757909	−	0.652360i	$-0.226221\pi$
$487$	33.4512	1.51582	0.757909	+	0.652360i	$0.226221\pi$
$488$	−4.47737	−0.202681
$489$	2.50707	0.113374
$490$	−13.9423	−0.629849
$491$	−18.9378	−0.854651	−0.427325	−	0.904098i	$-0.640544\pi$
$491$	−18.9378	−0.854651	−0.427325	+	0.904098i	$0.640544\pi$
$492$	86.7298	3.91008
$493$	−25.5468	−1.15057
$494$	60.0653	2.70247
$495$	−31.4454	−1.41336
$496$	2.05069	0.0920786
$497$	−16.8684	−0.756652
$498$	92.4079	4.14090
$499$	10.6784	0.478030	0.239015	−	0.971016i	$-0.423176\pi$
$499$	10.6784	0.478030	0.239015	+	0.971016i	$0.423176\pi$
$500$	−57.5324	−2.57293
$501$	−45.5050	−2.03301
$502$	−19.1545	−0.854909
$503$	−19.1256	−0.852768	−0.426384	−	0.904542i	$-0.640213\pi$
$503$	−19.1256	−0.852768	−0.426384	+	0.904542i	$0.640213\pi$
$504$	38.3343	1.70755
$505$	−1.41969	−0.0631754
$506$	17.6847	0.786183
$507$	−38.8426	−1.72506
$508$	73.2391	3.24946
$509$	40.0760	1.77634	0.888170	−	0.459516i	$-0.151977\pi$
$509$	40.0760	1.77634	0.888170	+	0.459516i	$0.151977\pi$
$510$	−92.3584	−4.08970
$511$	−37.6627	−1.66610
$512$	40.4741	1.78872
$513$	3.27873	0.144760
$514$	67.5477	2.97940
$515$	−8.15994	−0.359570
$516$	−5.98862	−0.263634
$517$	−25.1572	−1.10641
$518$	−5.74553	−0.252444
$519$	37.3399	1.63904
$520$	99.0257	4.34256
$521$	−16.6678	−0.730232	−0.365116	−	0.930962i	$-0.618971\pi$
$521$	−16.6678	−0.730232	−0.365116	+	0.930962i	$0.618971\pi$
$522$	51.1110	2.23707
$523$	28.1816	1.23230	0.616148	−	0.787631i	$-0.288692\pi$
$523$	28.1816	1.23230	0.616148	+	0.787631i	$0.288692\pi$
$524$	−76.4061	−3.33782
$525$	51.8343	2.26224
$526$	−57.0571	−2.48781
$527$	1.97572	0.0860637
$528$	−27.0014	−1.17508
$529$	−15.1669	−0.659431
$530$	−73.0334	−3.17237
$531$	1.34257	0.0582627
$532$	43.2115	1.87346
$533$	−45.8121	−1.98434
$534$	13.2637	0.573976
$535$	−66.4501	−2.87289
$536$	5.84531	0.252479
$537$	38.2284	1.64968
$538$	−17.4013	−0.750225
$539$	−3.92708	−0.169151
$540$	10.7289	0.461697
$541$	24.7632	1.06465	0.532326	−	0.846539i	$-0.321318\pi$
$541$	24.7632	1.06465	0.532326	+	0.846539i	$0.321318\pi$
$542$	−26.2830	−1.12895
$543$	56.5423	2.42646
$544$	−1.22959	−0.0527182
$545$	−19.5772	−0.838597
$546$	−76.8896	−3.29057
$547$	8.42333	0.360155	0.180078	−	0.983652i	$-0.442365\pi$
$547$	8.42333	0.360155	0.180078	+	0.983652i	$0.442365\pi$
$548$	−85.3209	−3.64473
$549$	2.94957	0.125884
$550$	−55.8393	−2.38100
$551$	29.0271	1.23659
$552$	−34.9936	−1.48943
$553$	−1.35047	−0.0574277
$554$	−46.8253	−1.98942
$555$	−9.32586	−0.395861
$556$	52.5046	2.22669
$557$	27.1535	1.15053	0.575266	−	0.817967i	$-0.304899\pi$
$557$	27.1535	1.15053	0.575266	+	0.817967i	$0.304899\pi$
$558$	−3.95278	−0.167335
$559$	3.16329	0.133793
$560$	36.4283	1.53938
$561$	−26.0143	−1.09832
$562$	−33.8898	−1.42955
$563$	−18.5218	−0.780602	−0.390301	−	0.920687i	$-0.627629\pi$
$563$	−18.5218	−0.780602	−0.390301	+	0.920687i	$0.627629\pi$
$564$	98.8043	4.16041
$565$	38.6676	1.62676
$566$	38.4683	1.61694
$567$	18.8626	0.792155
$568$	−35.9573	−1.50873
$569$	15.8630	0.665012	0.332506	−	0.943101i	$-0.392106\pi$
$569$	15.8630	0.665012	0.332506	+	0.943101i	$0.392106\pi$
$570$	104.940	4.39546
$571$	−26.4240	−1.10581	−0.552904	−	0.833245i	$-0.686481\pi$
$571$	−26.4240	−1.10581	−0.552904	+	0.833245i	$0.686481\pi$
$572$	55.3614	2.31478
$573$	15.5541	0.649781
$574$	−49.3106	−2.05818
$575$	−24.7329	−1.03143
$576$	−25.0439	−1.04350
$577$	−5.19037	−0.216078	−0.108039	−	0.994147i	$-0.534457\pi$
$577$	−5.19037	−0.216078	−0.108039	+	0.994147i	$0.534457\pi$
$578$	1.80996	0.0752846
$579$	−12.8309	−0.533233
$580$	94.9841	3.94400
$581$	−35.1154	−1.45683
$582$	12.4386	0.515595
$583$	−20.5711	−0.851966
$584$	−80.2830	−3.32214
$585$	−65.2353	−2.69715
$586$	49.2358	2.03391
$587$	−15.8568	−0.654480	−0.327240	−	0.944941i	$-0.606119\pi$
$587$	−15.8568	−0.654480	−0.327240	+	0.944941i	$0.606119\pi$
$588$	15.4235	0.636055
$589$	−2.24487	−0.0924982
$590$	3.73299	0.153685
$591$	5.21406	0.214478
$592$	−4.18576	−0.172034
$593$	−38.1900	−1.56828	−0.784138	−	0.620587i	$-0.786895\pi$
$593$	−38.1900	−1.56828	−0.784138	+	0.620587i	$0.786895\pi$
$594$	4.52139	0.185515
$595$	35.0966	1.43882
$596$	−12.6103	−0.516539
$597$	−15.0991	−0.617963
$598$	36.6880	1.50029
$599$	−3.92586	−0.160406	−0.0802031	−	0.996779i	$-0.525557\pi$
$599$	−3.92586	−0.160406	−0.0802031	+	0.996779i	$0.525557\pi$
$600$	110.492	4.51081
$601$	8.65019	0.352849	0.176424	−	0.984314i	$-0.443547\pi$
$601$	8.65019	0.352849	0.176424	+	0.984314i	$0.443547\pi$
$602$	3.40485	0.138771
$603$	−3.85072	−0.156814
$604$	−12.4164	−0.505216
$605$	16.2910	0.662325
$606$	2.34977	0.0954531
$607$	−1.58272	−0.0642405	−0.0321202	−	0.999484i	$-0.510226\pi$
$607$	−1.58272	−0.0642405	−0.0321202	+	0.999484i	$0.510226\pi$
$608$	1.39709	0.0566597
$609$	−37.1575	−1.50570
$610$	8.20121	0.332057
$611$	−52.1901	−2.11139
$612$	53.4049	2.15877
$613$	2.10730	0.0851132	0.0425566	−	0.999094i	$-0.486450\pi$
$613$	2.10730	0.0851132	0.0425566	+	0.999094i	$0.486450\pi$
$614$	37.5593	1.51577
$615$	−80.0385	−3.22746
$616$	30.0222	1.20963
$617$	−2.71845	−0.109441	−0.0547203	−	0.998502i	$-0.517427\pi$
$617$	−2.71845	−0.109441	−0.0547203	+	0.998502i	$0.517427\pi$
$618$	13.5058	0.543282
$619$	−5.20074	−0.209035	−0.104518	−	0.994523i	$-0.533330\pi$
$619$	−5.20074	−0.209035	−0.104518	+	0.994523i	$0.533330\pi$
$620$	−7.34579	−0.295014
$621$	2.00266	0.0803639
$622$	−47.1638	−1.89110
$623$	−5.04026	−0.201934
$624$	−56.0160	−2.24243
$625$	8.90840	0.356336
$626$	40.1531	1.60484
$627$	29.5582	1.18044
$628$	87.4205	3.48846
$629$	−4.03274	−0.160796
$630$	−70.2170	−2.79751
$631$	29.4327	1.17170	0.585849	−	0.810421i	$-0.300761\pi$
$631$	29.4327	1.17170	0.585849	+	0.810421i	$0.300761\pi$
$632$	−2.87870	−0.114509
$633$	7.21044	0.286589
$634$	−33.8834	−1.34568
$635$	−67.5886	−2.68217
$636$	80.7924	3.20363
$637$	−8.14696	−0.322794
$638$	40.0285	1.58474
$639$	23.6876	0.937068
$640$	−71.9024	−2.84219
$641$	−14.8865	−0.587980	−0.293990	−	0.955808i	$-0.594983\pi$
$641$	−14.8865	−0.587980	−0.293990	+	0.955808i	$0.594983\pi$
$642$	109.984	4.34071
$643$	−50.6849	−1.99882	−0.999409	−	0.0343769i	$-0.989055\pi$
$643$	−50.6849	−1.99882	−0.999409	+	0.0343769i	$0.989055\pi$
$644$	26.3937	1.04006
$645$	5.52659	0.217609
$646$	45.3788	1.78541
$647$	−19.4552	−0.764864	−0.382432	−	0.923984i	$-0.624913\pi$
$647$	−19.4552	−0.764864	−0.382432	+	0.923984i	$0.624913\pi$
$648$	40.2082	1.57953
$649$	1.05146	0.0412734
$650$	−115.842	−4.54370
$651$	2.87366	0.112627
$652$	−4.03080	−0.157858
$653$	42.8763	1.67788	0.838939	−	0.544226i	$-0.183176\pi$
$653$	42.8763	1.67788	0.838939	+	0.544226i	$0.183176\pi$
$654$	32.4029	1.26705
$655$	70.5113	2.75510
$656$	−35.9240	−1.40260
$657$	52.8882	2.06336
$658$	−56.1756	−2.18995
$659$	40.4900	1.57727	0.788634	−	0.614863i	$-0.210789\pi$
$659$	40.4900	1.57727	0.788634	+	0.614863i	$0.210789\pi$
$660$	96.7220	3.76490
$661$	−42.7844	−1.66412	−0.832060	−	0.554685i	$-0.812839\pi$
$661$	−42.7844	−1.66412	−0.832060	+	0.554685i	$0.812839\pi$
$662$	−54.5903	−2.12171
$663$	−53.9681	−2.09595
$664$	−74.8531	−2.90486
$665$	−39.8777	−1.54639
$666$	8.06822	0.312637
$667$	17.7298	0.686500
$668$	73.1617	2.83071
$669$	8.16154	0.315543
$670$	−10.7069	−0.413642
$671$	2.31000	0.0891767
$672$	−1.78842	−0.0689898
$673$	38.7429	1.49343	0.746714	−	0.665146i	$-0.231631\pi$
$673$	38.7429	1.49343	0.746714	+	0.665146i	$0.231631\pi$
$674$	−65.4226	−2.51998
$675$	−6.32337	−0.243386
$676$	62.4500	2.40192
$677$	22.1962	0.853069	0.426535	−	0.904471i	$-0.359734\pi$
$677$	22.1962	0.853069	0.426535	+	0.904471i	$0.359734\pi$
$678$	−63.9999	−2.45790
$679$	−4.72671	−0.181394
$680$	74.8130	2.86895
$681$	−49.9609	−1.91451
$682$	−3.09569	−0.118540
$683$	−22.7313	−0.869789	−0.434894	−	0.900481i	$-0.643214\pi$
$683$	−22.7313	−0.869789	−0.434894	+	0.900481i	$0.643214\pi$
$684$	−60.6802	−2.32017
$685$	78.7383	3.00844
$686$	−48.9878	−1.87036
$687$	30.2184	1.15290
$688$	2.48052	0.0945689
$689$	−42.6759	−1.62582
$690$	64.0978	2.44016
$691$	0.341495	0.0129911	0.00649554	−	0.999979i	$-0.497932\pi$
$691$	0.341495	0.0129911	0.00649554	+	0.999979i	$0.497932\pi$
$692$	−60.0340	−2.28215
$693$	−19.7778	−0.751295
$694$	30.2624	1.14875
$695$	−48.4538	−1.83796
$696$	−79.2062	−3.00230
$697$	−34.6107	−1.31097
$698$	−51.3781	−1.94469
$699$	17.3203	0.655112
$700$	−83.3378	−3.14987
$701$	−12.3627	−0.466933	−0.233466	−	0.972365i	$-0.575007\pi$
$701$	−12.3627	−0.466933	−0.233466	+	0.972365i	$0.575007\pi$
$702$	9.37990	0.354022
$703$	4.58211	0.172818
$704$	−19.6136	−0.739214
$705$	−91.1814	−3.43409
$706$	19.2556	0.724693
$707$	−0.892924	−0.0335819
$708$	−4.12958	−0.155199
$709$	18.2554	0.685594	0.342797	−	0.939409i	$-0.388626\pi$
$709$	18.2554	0.685594	0.342797	+	0.939409i	$0.388626\pi$
$710$	65.8629	2.47179
$711$	1.89641	0.0711208
$712$	−10.7440	−0.402648
$713$	−1.37117	−0.0513508
$714$	−58.0894	−2.17394
$715$	−51.0902	−1.91066
$716$	−61.4625	−2.29696
$717$	−55.5581	−2.07486
$718$	−23.3585	−0.871732
$719$	23.1732	0.864216	0.432108	−	0.901822i	$-0.357770\pi$
$719$	23.1732	0.864216	0.432108	+	0.901822i	$0.357770\pi$
$720$	−51.1548	−1.90643
$721$	−5.13225	−0.191135
$722$	−4.90109	−0.182400
$723$	3.79350	0.141082
$724$	−90.9071	−3.37854
$725$	−55.9816	−2.07910
$726$	−26.9638	−1.00072
$727$	−13.2524	−0.491505	−0.245752	−	0.969333i	$-0.579035\pi$
$727$	−13.2524	−0.491505	−0.245752	+	0.969333i	$0.579035\pi$
$728$	62.2828	2.30836
$729$	−31.8698	−1.18036
$730$	147.054	5.44273
$731$	2.38984	0.0883913
$732$	−9.07249	−0.335329
$733$	43.6771	1.61325	0.806625	−	0.591063i	$-0.201291\pi$
$733$	43.6771	1.61325	0.806625	+	0.591063i	$0.201291\pi$
$734$	−45.7904	−1.69015
$735$	−14.2336	−0.525013
$736$	0.853349	0.0314549
$737$	−3.01576	−0.111087
$738$	69.2448	2.54894
$739$	36.8826	1.35675	0.678375	−	0.734716i	$-0.262684\pi$
$739$	36.8826	1.35675	0.678375	+	0.734716i	$0.262684\pi$
$740$	14.9939	0.551185
$741$	61.3201	2.25265
$742$	−45.9348	−1.68632
$743$	−16.4334	−0.602884	−0.301442	−	0.953484i	$-0.597468\pi$
$743$	−16.4334	−0.602884	−0.301442	+	0.953484i	$0.597468\pi$
$744$	6.12558	0.224575
$745$	11.6374	0.426362
$746$	−78.4080	−2.87072
$747$	49.3111	1.80420
$748$	41.8250	1.52927
$749$	−41.7942	−1.52713
$750$	−87.8771	−3.20882
$751$	−16.6189	−0.606431	−0.303216	−	0.952922i	$-0.598060\pi$
$751$	−16.6189	−0.606431	−0.303216	+	0.952922i	$0.598060\pi$
$752$	−40.9253	−1.49239
$753$	−19.5547	−0.712612
$754$	83.0416	3.02419
$755$	11.4584	0.417016
$756$	6.74799	0.245422
$757$	−10.3199	−0.375081	−0.187541	−	0.982257i	$-0.560052\pi$
$757$	−10.3199	−0.375081	−0.187541	+	0.982257i	$0.560052\pi$
$758$	−57.0063	−2.07056
$759$	18.0542	0.655326
$760$	−85.0047	−3.08344
$761$	−47.4336	−1.71947	−0.859734	−	0.510742i	$-0.829371\pi$
$761$	−47.4336	−1.71947	−0.859734	+	0.510742i	$0.829371\pi$
$762$	111.868	4.05255
$763$	−12.3132	−0.445769
$764$	−25.0074	−0.904737
$765$	−49.2847	−1.78189
$766$	16.0680	0.580561
$767$	2.18131	0.0787627
$768$	80.7863	2.91512
$769$	−31.8052	−1.14693	−0.573463	−	0.819232i	$-0.694400\pi$
$769$	−31.8052	−1.14693	−0.573463	+	0.819232i	$0.694400\pi$
$770$	−54.9917	−1.98176
$771$	68.9589	2.48349
$772$	20.6291	0.742459
$773$	38.2928	1.37730	0.688648	−	0.725096i	$-0.258205\pi$
$773$	38.2928	1.37730	0.688648	+	0.725096i	$0.258205\pi$
$774$	−4.78130	−0.171860
$775$	4.32946	0.155519
$776$	−10.0756	−0.361693
$777$	−5.86556	−0.210426
$778$	−81.6146	−2.92603
$779$	39.3256	1.40899
$780$	200.655	7.18462
$781$	18.5514	0.663821
$782$	27.7175	0.991176
$783$	4.53291	0.161993
$784$	−6.38851	−0.228161
$785$	−80.6759	−2.87945
$786$	−116.705	−4.16274
$787$	2.51440	0.0896287	0.0448144	−	0.998995i	$-0.485730\pi$
$787$	2.51440	0.0896287	0.0448144	+	0.998995i	$0.485730\pi$
$788$	−8.38302	−0.298633
$789$	−58.2491	−2.07372
$790$	5.27292	0.187602
$791$	24.3202	0.864727
$792$	−42.1590	−1.49805
$793$	4.79224	0.170178
$794$	−58.7198	−2.08389
$795$	−74.5591	−2.64434
$796$	24.2758	0.860434
$797$	11.8116	0.418389	0.209194	−	0.977874i	$-0.432916\pi$
$797$	11.8116	0.418389	0.209194	+	0.977874i	$0.432916\pi$
$798$	66.0028	2.33648
$799$	−39.4292	−1.39490
$800$	−2.69444	−0.0952628
$801$	7.07783	0.250083
$802$	−41.3414	−1.45981
$803$	41.4203	1.46169
$804$	11.8443	0.417718
$805$	−24.3574	−0.858486
$806$	−6.42219	−0.226212
$807$	−17.7649	−0.625353
$808$	−1.90339	−0.0669609
$809$	13.9959	0.492069	0.246034	−	0.969261i	$-0.420872\pi$
$809$	13.9959	0.492069	0.246034	+	0.969261i	$0.420872\pi$
$810$	−73.6493	−2.58777
$811$	35.7196	1.25429	0.627143	−	0.778904i	$-0.284224\pi$
$811$	35.7196	1.25429	0.627143	+	0.778904i	$0.284224\pi$
$812$	59.7408	2.09649
$813$	−26.8321	−0.941042
$814$	6.31877	0.221473
$815$	3.71982	0.130300
$816$	−42.3196	−1.48148
$817$	−2.71540	−0.0949998
$818$	16.3136	0.570391
$819$	−41.0302	−1.43371
$820$	128.684	4.49383
$821$	6.97985	0.243599	0.121799	−	0.992555i	$-0.461134\pi$
$821$	6.97985	0.243599	0.121799	+	0.992555i	$0.461134\pi$
$822$	−130.322	−4.54551
$823$	33.1183	1.15443	0.577215	−	0.816592i	$-0.304140\pi$
$823$	33.1183	1.15443	0.577215	+	0.816592i	$0.304140\pi$
$824$	−10.9401	−0.381115
$825$	−57.0059	−1.98469
$826$	2.34789	0.0816935
$827$	9.09095	0.316123	0.158062	−	0.987429i	$-0.449476\pi$
$827$	9.09095	0.316123	0.158062	+	0.987429i	$0.449476\pi$
$828$	−37.0636	−1.28805
$829$	−40.7321	−1.41468	−0.707342	−	0.706872i	$-0.750106\pi$
$829$	−40.7321	−1.41468	−0.707342	+	0.706872i	$0.750106\pi$
$830$	137.108	4.75910
$831$	−47.8035	−1.65829
$832$	−40.6895	−1.41066
$833$	−6.15496	−0.213257
$834$	80.1975	2.77701
$835$	−67.5172	−2.33653
$836$	−47.5228	−1.64361
$837$	−0.350562	−0.0121172
$838$	−45.1226	−1.55873
$839$	−26.0218	−0.898371	−0.449186	−	0.893438i	$-0.648286\pi$
$839$	−26.0218	−0.898371	−0.449186	+	0.893438i	$0.648286\pi$
$840$	108.814	3.75446
$841$	11.1305	0.383810
$842$	8.78186	0.302643
$843$	−34.5978	−1.19161
$844$	−11.5927	−0.399039
$845$	−57.6319	−1.98260
$846$	78.8851	2.71213
$847$	10.2463	0.352069
$848$	−33.4647	−1.14918
$849$	39.2719	1.34781
$850$	−87.5176	−3.00183
$851$	2.79877	0.0959404
$852$	−72.8601	−2.49615
$853$	−31.3585	−1.07369	−0.536847	−	0.843680i	$-0.680385\pi$
$853$	−31.3585	−1.07369	−0.536847	+	0.843680i	$0.680385\pi$
$854$	5.15820	0.176510
$855$	55.9987	1.91511
$856$	−89.0899	−3.04503
$857$	−26.8250	−0.916326	−0.458163	−	0.888868i	$-0.651492\pi$
$857$	−26.8250	−0.916326	−0.458163	+	0.888868i	$0.651492\pi$
$858$	84.5609	2.88686
$859$	−20.2078	−0.689482	−0.344741	−	0.938698i	$-0.612033\pi$
$859$	−20.2078	−0.689482	−0.344741	+	0.938698i	$0.612033\pi$
$860$	−8.88549	−0.302993
$861$	−50.3407	−1.71561
$862$	38.0578	1.29626
$863$	33.6918	1.14688	0.573441	−	0.819247i	$-0.305608\pi$
$863$	33.6918	1.14688	0.573441	+	0.819247i	$0.305608\pi$
$864$	0.218173	0.00742239
$865$	55.4023	1.88373
$866$	34.7722	1.18161
$867$	1.84778	0.0627538
$868$	−4.62018	−0.156819
$869$	1.48520	0.0503821
$870$	145.082	4.91874
$871$	−6.25638	−0.211989
$872$	−26.2473	−0.888846
$873$	6.63752	0.224646
$874$	−31.4934	−1.06528
$875$	33.3936	1.12891
$876$	−162.677	−5.49636
$877$	−0.734215	−0.0247927	−0.0123963	−	0.999923i	$-0.503946\pi$
$877$	−0.734215	−0.0247927	−0.0123963	+	0.999923i	$0.503946\pi$
$878$	70.6393	2.38396
$879$	50.2644	1.69538
$880$	−40.0628	−1.35052
$881$	23.9350	0.806392	0.403196	−	0.915114i	$-0.367899\pi$
$881$	23.9350	0.806392	0.403196	+	0.915114i	$0.367899\pi$
$882$	12.3141	0.414637
$883$	32.5452	1.09523	0.547616	−	0.836730i	$-0.315535\pi$
$883$	32.5452	1.09523	0.547616	+	0.836730i	$0.315535\pi$
$884$	86.7685	2.91834
$885$	3.81098	0.128105
$886$	71.0999	2.38865
$887$	−34.1782	−1.14759	−0.573796	−	0.818998i	$-0.694530\pi$
$887$	−34.1782	−1.14759	−0.573796	+	0.818998i	$0.694530\pi$
$888$	−12.5032	−0.419581
$889$	−42.5103	−1.42575
$890$	19.6797	0.659667
$891$	−20.7445	−0.694968
$892$	−13.1219	−0.439353
$893$	44.8005	1.49919
$894$	−19.2614	−0.644199
$895$	56.7206	1.89596
$896$	−45.2235	−1.51081
$897$	37.4545	1.25057
$898$	43.1577	1.44019
$899$	−3.10358	−0.103510
$900$	117.028	3.90093
$901$	−32.2413	−1.07411
$902$	54.2303	1.80567
$903$	3.47598	0.115673
$904$	51.8418	1.72423
$905$	83.8935	2.78871
$906$	−18.9652	−0.630078
$907$	−17.9826	−0.597104	−0.298552	−	0.954393i	$-0.596504\pi$
$907$	−17.9826	−0.597104	−0.298552	+	0.954393i	$0.596504\pi$
$908$	80.3258	2.66570
$909$	1.25390	0.0415891
$910$	−114.083	−3.78183
$911$	−0.862655	−0.0285811	−0.0142905	−	0.999898i	$-0.504549\pi$
$911$	−0.862655	−0.0285811	−0.0142905	+	0.999898i	$0.504549\pi$
$912$	48.0847	1.59224
$913$	38.6189	1.27810
$914$	69.7322	2.30654
$915$	8.37254	0.276788
$916$	−48.5842	−1.60527
$917$	44.3485	1.46452
$918$	7.08643	0.233887
$919$	54.1637	1.78670	0.893348	−	0.449366i	$-0.148350\pi$
$919$	54.1637	1.78670	0.893348	+	0.449366i	$0.148350\pi$
$920$	−51.9211	−1.71179
$921$	38.3440	1.26348
$922$	57.5508	1.89533
$923$	38.4860	1.26678
$924$	60.8339	2.00129
$925$	−8.83707	−0.290561
$926$	33.5774	1.10342
$927$	7.20701	0.236709
$928$	1.93151	0.0634050
$929$	11.9307	0.391434	0.195717	−	0.980660i	$-0.437297\pi$
$929$	11.9307	0.391434	0.195717	+	0.980660i	$0.437297\pi$
$930$	−11.2202	−0.367926
$931$	6.99344	0.229201
$932$	−27.8470	−0.912160
$933$	−48.1491	−1.57633
$934$	72.5403	2.37359
$935$	−38.5982	−1.26230
$936$	−87.4613	−2.85876
$937$	−32.4701	−1.06075	−0.530376	−	0.847763i	$-0.677949\pi$
$937$	−32.4701	−1.06075	−0.530376	+	0.847763i	$0.677949\pi$
$938$	−6.73415	−0.219878
$939$	40.9919	1.33772
$940$	146.599	4.78153
$941$	8.77454	0.286042	0.143021	−	0.989720i	$-0.454318\pi$
$941$	8.77454	0.286042	0.143021	+	0.989720i	$0.454318\pi$
$942$	133.529	4.35062
$943$	24.0202	0.782205
$944$	1.71050	0.0556719
$945$	−6.22737	−0.202576
$946$	−3.74456	−0.121746
$947$	21.7988	0.708367	0.354184	−	0.935176i	$-0.384759\pi$
$947$	21.7988	0.708367	0.354184	+	0.935176i	$0.384759\pi$
$948$	−5.83311	−0.189450
$949$	85.9289	2.78937
$950$	99.4400	3.22626
$951$	−34.5913	−1.12170
$952$	47.0541	1.52503
$953$	29.8250	0.966125	0.483063	−	0.875586i	$-0.339524\pi$
$953$	29.8250	0.966125	0.483063	+	0.875586i	$0.339524\pi$
$954$	64.5044	2.08841
$955$	23.0781	0.746789
$956$	89.3248	2.88897
$957$	40.8648	1.32097
$958$	−41.6567	−1.34587
$959$	49.5230	1.59918
$960$	−71.0887	−2.29438
$961$	−30.7600	−0.992257
$962$	13.1087	0.422640
$963$	58.6899	1.89126
$964$	−6.09908	−0.196438
$965$	−19.0376	−0.612841
$966$	40.3147	1.29710
$967$	14.9793	0.481701	0.240850	−	0.970562i	$-0.422574\pi$
$967$	14.9793	0.481701	0.240850	+	0.970562i	$0.422574\pi$
$968$	21.8415	0.702011
$969$	46.3268	1.48823
$970$	18.4555	0.592570
$971$	−39.9646	−1.28252	−0.641262	−	0.767322i	$-0.721589\pi$
$971$	−39.9646	−1.28252	−0.641262	+	0.767322i	$0.721589\pi$
$972$	90.1264	2.89081
$973$	−30.4754	−0.976995
$974$	−82.1484	−2.63220
$975$	−118.262	−3.78742
$976$	3.75788	0.120287
$977$	−13.8803	−0.444069	−0.222034	−	0.975039i	$-0.571270\pi$
$977$	−13.8803	−0.444069	−0.222034	+	0.975039i	$0.571270\pi$
$978$	−6.15679	−0.196872
$979$	5.54313	0.177159
$980$	22.8843	0.731014
$981$	17.2910	0.552058
$982$	46.5069	1.48409
$983$	0.0570295	0.00181896	0.000909479	−	1.00000i	$-0.499711\pi$
$983$	0.0570295	0.00181896	0.000909479		1.00000i	$0.499711\pi$
$984$	−107.308	−3.42085
$985$	7.73626	0.246498
$986$	62.7372	1.99796
$987$	−57.3491	−1.82544
$988$	−98.5888	−3.13653
$989$	−1.65857	−0.0527396
$990$	77.2226	2.45429
$991$	−0.787089	−0.0250027	−0.0125014	−	0.999922i	$-0.503979\pi$
$991$	−0.787089	−0.0250027	−0.0125014	+	0.999922i	$0.503979\pi$
$992$	−0.149378	−0.00474274
$993$	−55.7308	−1.76856
$994$	41.4249	1.31392
$995$	−22.4029	−0.710220
$996$	−151.675	−4.80600
$997$	41.3899	1.31083	0.655416	−	0.755268i	$-0.272493\pi$
$997$	41.3899	1.31083	0.655416	+	0.755268i	$0.272493\pi$
$998$	−26.2236	−0.830094
$999$	0.715550	0.0226390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.10	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.10	✓	110	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45577 q^{2} -2.50707 q^{3} +4.03080 q^{4} -3.71982 q^{5} +6.15679 q^{6} -2.33961 q^{7} -4.98718 q^{8} +3.28541 q^{9} +9.13502 q^{10} +2.57303 q^{11} -10.1055 q^{12} +5.33790 q^{13} +5.74553 q^{14} +9.32586 q^{15} +4.18576 q^{16} +4.03274 q^{17} -8.06822 q^{18} -4.58211 q^{19} -14.9939 q^{20} +5.86556 q^{21} -6.31877 q^{22} -2.79877 q^{23} +12.5032 q^{24} +8.83707 q^{25} -13.1087 q^{26} -0.715550 q^{27} -9.43049 q^{28} -6.33486 q^{29} -22.9022 q^{30} +0.489920 q^{31} -0.304902 q^{32} -6.45077 q^{33} -9.90347 q^{34} +8.70291 q^{35} +13.2428 q^{36} -1.00000 q^{37} +11.2526 q^{38} -13.3825 q^{39} +18.5514 q^{40} -8.58242 q^{41} -14.4045 q^{42} +0.592609 q^{43} +10.3714 q^{44} -12.2211 q^{45} +6.87312 q^{46} -9.77727 q^{47} -10.4940 q^{48} -1.52625 q^{49} -21.7018 q^{50} -10.1104 q^{51} +21.5160 q^{52} -7.99488 q^{53} +1.75723 q^{54} -9.57121 q^{55} +11.6680 q^{56} +11.4877 q^{57} +15.5570 q^{58} +0.408646 q^{59} +37.5907 q^{60} +0.897776 q^{61} -1.20313 q^{62} -7.68657 q^{63} -7.62275 q^{64} -19.8560 q^{65} +15.8416 q^{66} -1.17207 q^{67} +16.2552 q^{68} +7.01671 q^{69} -21.3723 q^{70} +7.20994 q^{71} -16.3849 q^{72} +16.0979 q^{73} +2.45577 q^{74} -22.1552 q^{75} -18.4696 q^{76} -6.01987 q^{77} +32.8644 q^{78} +0.577220 q^{79} -15.5703 q^{80} -8.06230 q^{81} +21.0765 q^{82} +15.0091 q^{83} +23.6429 q^{84} -15.0011 q^{85} -1.45531 q^{86} +15.8820 q^{87} -12.8322 q^{88} +2.15432 q^{89} +30.0123 q^{90} -12.4886 q^{91} -11.2813 q^{92} -1.22827 q^{93} +24.0107 q^{94} +17.0446 q^{95} +0.764411 q^{96} +2.02030 q^{97} +3.74811 q^{98} +8.45346 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21}+ \cdots - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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