LMFDB - Embedded newform 6031.2.a.c.1.8

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			1.8
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)

$f(q)$	$=$	\(q-2.51631 q^{2} +1.27091 q^{3} +4.33182 q^{4} +1.33976 q^{5} -3.19800 q^{6} +0.944830 q^{7} -5.86759 q^{8} -1.38479 q^{9} -3.37125 q^{10} -5.51551 q^{11} +5.50536 q^{12} +4.59866 q^{13} -2.37749 q^{14} +1.70271 q^{15} +6.10104 q^{16} +4.46947 q^{17} +3.48456 q^{18} +4.49981 q^{19} +5.80359 q^{20} +1.20079 q^{21} +13.8787 q^{22} -0.690017 q^{23} -7.45718 q^{24} -3.20505 q^{25} -11.5716 q^{26} -5.57267 q^{27} +4.09284 q^{28} -1.70940 q^{29} -4.28455 q^{30} -2.74062 q^{31} -3.61694 q^{32} -7.00971 q^{33} -11.2466 q^{34} +1.26584 q^{35} -5.99866 q^{36} -1.00000 q^{37} -11.3229 q^{38} +5.84448 q^{39} -7.86115 q^{40} -5.29292 q^{41} -3.02157 q^{42} -5.16303 q^{43} -23.8922 q^{44} -1.85528 q^{45} +1.73630 q^{46} -5.44119 q^{47} +7.75387 q^{48} -6.10730 q^{49} +8.06490 q^{50} +5.68029 q^{51} +19.9206 q^{52} -10.1943 q^{53} +14.0226 q^{54} -7.38944 q^{55} -5.54388 q^{56} +5.71885 q^{57} +4.30139 q^{58} +5.35440 q^{59} +7.37584 q^{60} +10.7183 q^{61} +6.89625 q^{62} -1.30839 q^{63} -3.10074 q^{64} +6.16108 q^{65} +17.6386 q^{66} -4.84439 q^{67} +19.3609 q^{68} -0.876950 q^{69} -3.18526 q^{70} -2.04359 q^{71} +8.12537 q^{72} -6.62627 q^{73} +2.51631 q^{74} -4.07333 q^{75} +19.4924 q^{76} -5.21122 q^{77} -14.7065 q^{78} +8.67316 q^{79} +8.17392 q^{80} -2.92800 q^{81} +13.3186 q^{82} +3.60041 q^{83} +5.20163 q^{84} +5.98800 q^{85} +12.9918 q^{86} -2.17250 q^{87} +32.3627 q^{88} -10.2191 q^{89} +4.66846 q^{90} +4.34495 q^{91} -2.98903 q^{92} -3.48308 q^{93} +13.6917 q^{94} +6.02865 q^{95} -4.59680 q^{96} +7.11283 q^{97} +15.3679 q^{98} +7.63781 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.51631	−1.77930	−0.889650	−	0.456642i	$-0.849052\pi$
$2$	−2.51631	−1.77930	−0.889650	+	0.456642i	$0.849052\pi$
$3$	1.27091	0.733760	0.366880	−	0.930268i	$-0.380426\pi$
$3$	1.27091	0.733760	0.366880	+	0.930268i	$0.380426\pi$
$4$	4.33182	2.16591
$5$	1.33976	0.599158	0.299579	−	0.954072i	$-0.403154\pi$
$5$	1.33976	0.599158	0.299579	+	0.954072i	$0.403154\pi$
$6$	−3.19800	−1.30558
$7$	0.944830	0.357112	0.178556	−	0.983930i	$-0.442857\pi$
$7$	0.944830	0.357112	0.178556	+	0.983930i	$0.442857\pi$
$8$	−5.86759	−2.07451
$9$	−1.38479	−0.461596
$10$	−3.37125	−1.06608
$11$	−5.51551	−1.66299	−0.831494	−	0.555534i	$-0.812514\pi$
$11$	−5.51551	−1.66299	−0.831494	+	0.555534i	$0.812514\pi$
$12$	5.50536	1.58926
$13$	4.59866	1.27544	0.637719	−	0.770269i	$-0.279878\pi$
$13$	4.59866	1.27544	0.637719	+	0.770269i	$0.279878\pi$
$14$	−2.37749	−0.635410
$15$	1.70271	0.439638
$16$	6.10104	1.52526
$17$	4.46947	1.08400	0.542002	−	0.840377i	$-0.317666\pi$
$17$	4.46947	1.08400	0.542002	+	0.840377i	$0.317666\pi$
$18$	3.48456	0.821318
$19$	4.49981	1.03233	0.516163	−	0.856490i	$-0.327360\pi$
$19$	4.49981	1.03233	0.516163	+	0.856490i	$0.327360\pi$
$20$	5.80359	1.29772
$21$	1.20079	0.262035
$22$	13.8787	2.95895
$23$	−0.690017	−0.143879	−0.0719393	−	0.997409i	$-0.522919\pi$
$23$	−0.690017	−0.143879	−0.0719393	+	0.997409i	$0.522919\pi$
$24$	−7.45718	−1.52219
$25$	−3.20505	−0.641010
$26$	−11.5716	−2.26939
$27$	−5.57267	−1.07246
$28$	4.09284	0.773474
$29$	−1.70940	−0.317428	−0.158714	−	0.987325i	$-0.550735\pi$
$29$	−1.70940	−0.317428	−0.158714	+	0.987325i	$0.550735\pi$
$30$	−4.28455	−0.782248
$31$	−2.74062	−0.492230	−0.246115	−	0.969241i	$-0.579154\pi$
$31$	−2.74062	−0.492230	−0.246115	+	0.969241i	$0.579154\pi$
$32$	−3.61694	−0.639390
$33$	−7.00971	−1.22023
$34$	−11.2466	−1.92877
$35$	1.26584	0.213967
$36$	−5.99866	−0.999776
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−11.3229	−1.83682
$39$	5.84448	0.935865
$40$	−7.86115	−1.24296
$41$	−5.29292	−0.826615	−0.413308	−	0.910591i	$-0.635627\pi$
$41$	−5.29292	−0.826615	−0.413308	+	0.910591i	$0.635627\pi$
$42$	−3.02157	−0.466239
$43$	−5.16303	−0.787355	−0.393678	−	0.919249i	$-0.628797\pi$
$43$	−5.16303	−0.787355	−0.393678	+	0.919249i	$0.628797\pi$
$44$	−23.8922	−3.60188
$45$	−1.85528	−0.276569
$46$	1.73630	0.256003
$47$	−5.44119	−0.793680	−0.396840	−	0.917888i	$-0.629893\pi$
$47$	−5.44119	−0.793680	−0.396840	+	0.917888i	$0.629893\pi$
$48$	7.75387	1.11918
$49$	−6.10730	−0.872471
$50$	8.06490	1.14055
$51$	5.68029	0.795399
$52$	19.9206	2.76248
$53$	−10.1943	−1.40030	−0.700148	−	0.713998i	$-0.746883\pi$
$53$	−10.1943	−1.40030	−0.700148	+	0.713998i	$0.746883\pi$
$54$	14.0226	1.90823
$55$	−7.38944	−0.996392
$56$	−5.54388	−0.740832
$57$	5.71885	0.757480
$58$	4.30139	0.564801
$59$	5.35440	0.697084	0.348542	−	0.937293i	$-0.386677\pi$
$59$	5.35440	0.697084	0.348542	+	0.937293i	$0.386677\pi$
$60$	7.37584	0.952217
$61$	10.7183	1.37233	0.686167	−	0.727444i	$-0.259292\pi$
$61$	10.7183	1.37233	0.686167	+	0.727444i	$0.259292\pi$
$62$	6.89625	0.875825
$63$	−1.30839	−0.164842
$64$	−3.10074	−0.387593
$65$	6.16108	0.764188
$66$	17.6386	2.17116
$67$	−4.84439	−0.591836	−0.295918	−	0.955213i	$-0.595626\pi$
$67$	−4.84439	−0.591836	−0.295918	+	0.955213i	$0.595626\pi$
$68$	19.3609	2.34786
$69$	−0.876950	−0.105572
$70$	−3.18526	−0.380711
$71$	−2.04359	−0.242530	−0.121265	−	0.992620i	$-0.538695\pi$
$71$	−2.04359	−0.242530	−0.121265	+	0.992620i	$0.538695\pi$
$72$	8.12537	0.957584
$73$	−6.62627	−0.775546	−0.387773	−	0.921755i	$-0.626756\pi$
$73$	−6.62627	−0.775546	−0.387773	+	0.921755i	$0.626756\pi$
$74$	2.51631	0.292515
$75$	−4.07333	−0.470348
$76$	19.4924	2.23593
$77$	−5.21122	−0.593873
$78$	−14.7065	−1.66519
$79$	8.67316	0.975807	0.487903	−	0.872898i	$-0.337762\pi$
$79$	8.67316	0.975807	0.487903	+	0.872898i	$0.337762\pi$
$80$	8.17392	0.913872
$81$	−2.92800	−0.325333
$82$	13.3186	1.47080
$83$	3.60041	0.395196	0.197598	−	0.980283i	$-0.436686\pi$
$83$	3.60041	0.395196	0.197598	+	0.980283i	$0.436686\pi$
$84$	5.20163	0.567544
$85$	5.98800	0.649490
$86$	12.9918	1.40094
$87$	−2.17250	−0.232916
$88$	32.3627	3.44988
$89$	−10.2191	−1.08322	−0.541610	−	0.840630i	$-0.682185\pi$
$89$	−10.2191	−1.08322	−0.541610	+	0.840630i	$0.682185\pi$
$90$	4.66846	0.492099
$91$	4.34495	0.455474
$92$	−2.98903	−0.311628
$93$	−3.48308	−0.361179
$94$	13.6917	1.41220
$95$	6.02865	0.618527
$96$	−4.59680	−0.469159
$97$	7.11283	0.722199	0.361099	−	0.932527i	$-0.382402\pi$
$97$	7.11283	0.722199	0.361099	+	0.932527i	$0.382402\pi$
$98$	15.3679	1.55239
$99$	7.63781	0.767628
$100$	−13.8837	−1.38837
$101$	3.76503	0.374635	0.187317	−	0.982299i	$-0.440021\pi$
$101$	3.76503	0.374635	0.187317	+	0.982299i	$0.440021\pi$
$102$	−14.2934	−1.41525
$103$	−13.9461	−1.37415	−0.687077	−	0.726584i	$-0.741107\pi$
$103$	−13.9461	−1.37415	−0.687077	+	0.726584i	$0.741107\pi$
$104$	−26.9830	−2.64590
$105$	1.60877	0.157000
$106$	25.6521	2.49155
$107$	−3.73079	−0.360669	−0.180335	−	0.983605i	$-0.557718\pi$
$107$	−3.73079	−0.360669	−0.180335	+	0.983605i	$0.557718\pi$
$108$	−24.1398	−2.32286
$109$	6.13227	0.587365	0.293683	−	0.955903i	$-0.405119\pi$
$109$	6.13227	0.587365	0.293683	+	0.955903i	$0.405119\pi$
$110$	18.5941	1.77288
$111$	−1.27091	−0.120629
$112$	5.76445	0.544689
$113$	−17.6030	−1.65596	−0.827978	−	0.560761i	$-0.810509\pi$
$113$	−17.6030	−1.65596	−0.827978	+	0.560761i	$0.810509\pi$
$114$	−14.3904	−1.34778
$115$	−0.924456	−0.0862059
$116$	−7.40484	−0.687522
$117$	−6.36816	−0.588737
$118$	−13.4733	−1.24032
$119$	4.22289	0.387111
$120$	−9.99081	−0.912032
$121$	19.4208	1.76553
$122$	−26.9705	−2.44180
$123$	−6.72682	−0.606537
$124$	−11.8719	−1.06613
$125$	−10.9928	−0.983224
$126$	3.29232	0.293303
$127$	4.18528	0.371384	0.185692	−	0.982608i	$-0.440547\pi$
$127$	4.18528	0.371384	0.185692	+	0.982608i	$0.440547\pi$
$128$	15.0363	1.32903
$129$	−6.56175	−0.577730
$130$	−15.5032	−1.35972
$131$	−7.32345	−0.639853	−0.319926	−	0.947442i	$-0.603658\pi$
$131$	−7.32345	−0.639853	−0.319926	+	0.947442i	$0.603658\pi$
$132$	−30.3648	−2.64292
$133$	4.25156	0.368657
$134$	12.1900	1.05306
$135$	−7.46603	−0.642573
$136$	−26.2250	−2.24878
$137$	1.18902	0.101585	0.0507923	−	0.998709i	$-0.483825\pi$
$137$	1.18902	0.101585	0.0507923	+	0.998709i	$0.483825\pi$
$138$	2.20668	0.187845
$139$	4.34773	0.368770	0.184385	−	0.982854i	$-0.440971\pi$
$139$	4.34773	0.368770	0.184385	+	0.982854i	$0.440971\pi$
$140$	5.48341	0.463433
$141$	−6.91527	−0.582371
$142$	5.14231	0.431533
$143$	−25.3639	−2.12104
$144$	−8.44865	−0.704054
$145$	−2.29019	−0.190190
$146$	16.6738	1.37993
$147$	−7.76182	−0.640184
$148$	−4.33182	−0.356074
$149$	−16.6117	−1.36089	−0.680443	−	0.732801i	$-0.738213\pi$
$149$	−16.6117	−1.36089	−0.680443	+	0.732801i	$0.738213\pi$
$150$	10.2498	0.836890
$151$	1.95178	0.158834	0.0794170	−	0.996841i	$-0.474694\pi$
$151$	1.95178	0.158834	0.0794170	+	0.996841i	$0.474694\pi$
$152$	−26.4030	−2.14157
$153$	−6.18926	−0.500372
$154$	13.1130	1.05668
$155$	−3.67177	−0.294923
$156$	25.3172	2.02700
$157$	8.28109	0.660903	0.330452	−	0.943823i	$-0.392799\pi$
$157$	8.28109	0.660903	0.330452	+	0.943823i	$0.392799\pi$
$158$	−21.8244	−1.73625
$159$	−12.9561	−1.02748
$160$	−4.84582	−0.383096
$161$	−0.651949	−0.0513808
$162$	7.36775	0.578865
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	−22.9280	−1.79038
$165$	−9.39131	−0.731113
$166$	−9.05974	−0.703173
$167$	−11.7602	−0.910030	−0.455015	−	0.890484i	$-0.650366\pi$
$167$	−11.7602	−0.910030	−0.455015	+	0.890484i	$0.650366\pi$
$168$	−7.04577	−0.543593
$169$	8.14763	0.626741
$170$	−15.0677	−1.15564
$171$	−6.23128	−0.476518
$172$	−22.3653	−1.70534
$173$	0.732287	0.0556747	0.0278374	−	0.999612i	$-0.491138\pi$
$173$	0.732287	0.0556747	0.0278374	+	0.999612i	$0.491138\pi$
$174$	5.46668	0.414428
$175$	−3.02823	−0.228913
$176$	−33.6503	−2.53649
$177$	6.80496	0.511492
$178$	25.7144	1.92738
$179$	7.29973	0.545608	0.272804	−	0.962070i	$-0.412049\pi$
$179$	7.29973	0.545608	0.272804	+	0.962070i	$0.412049\pi$
$180$	−8.03675	−0.599024
$181$	−4.38266	−0.325761	−0.162880	−	0.986646i	$-0.552078\pi$
$181$	−4.38266	−0.325761	−0.162880	+	0.986646i	$0.552078\pi$
$182$	−10.9332	−0.810426
$183$	13.6220	1.00696
$184$	4.04874	0.298477
$185$	−1.33976	−0.0985009
$186$	8.76451	0.642645
$187$	−24.6514	−1.80269
$188$	−23.5703	−1.71904
$189$	−5.26523	−0.382989
$190$	−15.1700	−1.10054
$191$	8.70678	0.630000	0.315000	−	0.949092i	$-0.397995\pi$
$191$	8.70678	0.630000	0.315000	+	0.949092i	$0.397995\pi$
$192$	−3.94076	−0.284400
$193$	5.10047	0.367140	0.183570	−	0.983007i	$-0.441235\pi$
$193$	5.10047	0.367140	0.183570	+	0.983007i	$0.441235\pi$
$194$	−17.8981	−1.28501
$195$	7.83018	0.560731
$196$	−26.4557	−1.88969
$197$	−15.7326	−1.12090	−0.560450	−	0.828188i	$-0.689372\pi$
$197$	−15.7326	−1.12090	−0.560450	+	0.828188i	$0.689372\pi$
$198$	−19.2191	−1.36584
$199$	12.0454	0.853876	0.426938	−	0.904281i	$-0.359592\pi$
$199$	12.0454	0.853876	0.426938	+	0.904281i	$0.359592\pi$
$200$	18.8059	1.32978
$201$	−6.15678	−0.434266
$202$	−9.47399	−0.666588
$203$	−1.61510	−0.113358
$204$	24.6060	1.72276
$205$	−7.09123	−0.495273
$206$	35.0928	2.44503
$207$	0.955528	0.0664138
$208$	28.0566	1.94537
$209$	−24.8187	−1.71675
$210$	−4.04817	−0.279351
$211$	−3.09653	−0.213174	−0.106587	−	0.994303i	$-0.533992\pi$
$211$	−3.09653	−0.213174	−0.106587	+	0.994303i	$0.533992\pi$
$212$	−44.1600	−3.03292
$213$	−2.59722	−0.177959
$214$	9.38783	0.641739
$215$	−6.91721	−0.471750
$216$	32.6982	2.22483
$217$	−2.58942	−0.175781
$218$	−15.4307	−1.04510
$219$	−8.42139	−0.569065
$220$	−32.0097	−2.15810
$221$	20.5535	1.38258
$222$	3.19800	0.214636
$223$	24.0868	1.61297	0.806485	−	0.591255i	$-0.201367\pi$
$223$	24.0868	1.61297	0.806485	+	0.591255i	$0.201367\pi$
$224$	−3.41739	−0.228334
$225$	4.43831	0.295888
$226$	44.2947	2.94644
$227$	10.6082	0.704088	0.352044	−	0.935983i	$-0.385487\pi$
$227$	10.6082	0.704088	0.352044	+	0.935983i	$0.385487\pi$
$228$	24.7730	1.64063
$229$	−4.84597	−0.320231	−0.160115	−	0.987098i	$-0.551187\pi$
$229$	−4.84597	−0.320231	−0.160115	+	0.987098i	$0.551187\pi$
$230$	2.32622	0.153386
$231$	−6.62299	−0.435761
$232$	10.0301	0.658508
$233$	−3.82485	−0.250574	−0.125287	−	0.992121i	$-0.539985\pi$
$233$	−3.82485	−0.250574	−0.125287	+	0.992121i	$0.539985\pi$
$234$	16.0243	1.04754
$235$	−7.28988	−0.475539
$236$	23.1943	1.50982
$237$	11.0228	0.716008
$238$	−10.6261	−0.688788
$239$	−0.184794	−0.0119533	−0.00597666	−	0.999982i	$-0.501902\pi$
$239$	−0.184794	−0.0119533	−0.00597666	+	0.999982i	$0.501902\pi$
$240$	10.3883	0.670563
$241$	−1.68358	−0.108449	−0.0542245	−	0.998529i	$-0.517269\pi$
$241$	−1.68358	−0.108449	−0.0542245	+	0.998529i	$0.517269\pi$
$242$	−48.8688	−3.14140
$243$	12.9968	0.833745
$244$	46.4297	2.97235
$245$	−8.18230	−0.522748
$246$	16.9268	1.07921
$247$	20.6931	1.31667
$248$	16.0808	1.02113
$249$	4.57579	0.289979
$250$	27.6612	1.74945
$251$	1.31589	0.0830585	0.0415292	−	0.999137i	$-0.486777\pi$
$251$	1.31589	0.0830585	0.0415292	+	0.999137i	$0.486777\pi$
$252$	−5.66771	−0.357032
$253$	3.80579	0.239268
$254$	−10.5315	−0.660803
$255$	7.61021	0.476570
$256$	−31.6345	−1.97716
$257$	12.6586	0.789621	0.394811	−	0.918762i	$-0.370810\pi$
$257$	12.6586	0.789621	0.394811	+	0.918762i	$0.370810\pi$
$258$	16.5114	1.02796
$259$	−0.944830	−0.0587089
$260$	26.6887	1.65516
$261$	2.36716	0.146524
$262$	18.4281	1.13849
$263$	13.4620	0.830100	0.415050	−	0.909799i	$-0.363764\pi$
$263$	13.4620	0.830100	0.415050	+	0.909799i	$0.363764\pi$
$264$	41.1301	2.53138
$265$	−13.6579	−0.838998
$266$	−10.6982	−0.655951
$267$	−12.9875	−0.794824
$268$	−20.9850	−1.28187
$269$	−24.8224	−1.51345	−0.756725	−	0.653733i	$-0.773202\pi$
$269$	−24.8224	−1.51345	−0.756725	+	0.653733i	$0.773202\pi$
$270$	18.7868	1.14333
$271$	−16.7039	−1.01469	−0.507344	−	0.861744i	$-0.669373\pi$
$271$	−16.7039	−1.01469	−0.507344	+	0.861744i	$0.669373\pi$
$272$	27.2684	1.65339
$273$	5.52204	0.334209
$274$	−2.99194	−0.180749
$275$	17.6775	1.06599
$276$	−3.79879	−0.228660
$277$	−21.8644	−1.31371	−0.656854	−	0.754018i	$-0.728113\pi$
$277$	−21.8644	−1.31371	−0.656854	+	0.754018i	$0.728113\pi$
$278$	−10.9402	−0.656152
$279$	3.79518	0.227211
$280$	−7.42745	−0.443875
$281$	30.3526	1.81068	0.905341	−	0.424685i	$-0.139615\pi$
$281$	30.3526	1.81068	0.905341	+	0.424685i	$0.139615\pi$
$282$	17.4010	1.03621
$283$	−9.00936	−0.535551	−0.267775	−	0.963481i	$-0.586288\pi$
$283$	−9.00936	−0.535551	−0.267775	+	0.963481i	$0.586288\pi$
$284$	−8.85247	−0.525298
$285$	7.66187	0.453850
$286$	63.8235	3.77396
$287$	−5.00091	−0.295194
$288$	5.00869	0.295140
$289$	2.97612	0.175066
$290$	5.76283	0.338405
$291$	9.03977	0.529920
$292$	−28.7038	−1.67976
$293$	−24.2877	−1.41890	−0.709450	−	0.704755i	$-0.751057\pi$
$293$	−24.2877	−1.41890	−0.709450	+	0.704755i	$0.751057\pi$
$294$	19.5312	1.13908
$295$	7.17360	0.417663
$296$	5.86759	0.341047
$297$	30.7361	1.78349
$298$	41.8003	2.42143
$299$	−3.17315	−0.183508
$300$	−17.6449	−1.01873
$301$	−4.87819	−0.281174
$302$	−4.91130	−0.282613
$303$	4.78502	0.274892
$304$	27.4535	1.57457
$305$	14.3599	0.822245
$306$	15.5741	0.890313
$307$	−32.0740	−1.83056	−0.915281	−	0.402817i	$-0.868031\pi$
$307$	−32.0740	−1.83056	−0.915281	+	0.402817i	$0.868031\pi$
$308$	−22.5741	−1.28628
$309$	−17.7243	−1.00830
$310$	9.23931	0.524757
$311$	−25.9238	−1.47000	−0.735001	−	0.678066i	$-0.762818\pi$
$311$	−25.9238	−1.47000	−0.735001	+	0.678066i	$0.762818\pi$
$312$	−34.2930	−1.94146
$313$	−25.4771	−1.44005	−0.720027	−	0.693946i	$-0.755870\pi$
$313$	−25.4771	−1.44005	−0.720027	+	0.693946i	$0.755870\pi$
$314$	−20.8378	−1.17595
$315$	−1.75293	−0.0987662
$316$	37.5706	2.11351
$317$	9.71399	0.545592	0.272796	−	0.962072i	$-0.412052\pi$
$317$	9.71399	0.545592	0.272796	+	0.962072i	$0.412052\pi$
$318$	32.6015	1.82820
$319$	9.42823	0.527880
$320$	−4.15424	−0.232229
$321$	−4.74150	−0.264645
$322$	1.64051	0.0914219
$323$	20.1117	1.11905
$324$	−12.6836	−0.704642
$325$	−14.7389	−0.817568
$326$	2.51631	0.139366
$327$	7.79357	0.430985
$328$	31.0567	1.71482
$329$	−5.14101	−0.283433
$330$	23.6315	1.30087
$331$	−7.68091	−0.422181	−0.211091	−	0.977467i	$-0.567701\pi$
$331$	−7.68091	−0.422181	−0.211091	+	0.977467i	$0.567701\pi$
$332$	15.5963	0.855959
$333$	1.38479	0.0758859
$334$	29.5923	1.61922
$335$	−6.49031	−0.354603
$336$	7.32610	0.399671
$337$	−25.7743	−1.40401	−0.702007	−	0.712170i	$-0.747713\pi$
$337$	−25.7743	−1.40401	−0.702007	+	0.712170i	$0.747713\pi$
$338$	−20.5020	−1.11516
$339$	−22.3719	−1.21507
$340$	25.9390	1.40674
$341$	15.1159	0.818572
$342$	15.6798	0.847869
$343$	−12.3842	−0.668682
$344$	30.2946	1.63337
$345$	−1.17490	−0.0632545
$346$	−1.84266	−0.0990621
$347$	34.9552	1.87649	0.938246	−	0.345970i	$-0.112450\pi$
$347$	34.9552	1.87649	0.938246	+	0.345970i	$0.112450\pi$
$348$	−9.41088	−0.504476
$349$	−3.43997	−0.184137	−0.0920687	−	0.995753i	$-0.529348\pi$
$349$	−3.43997	−0.184137	−0.0920687	+	0.995753i	$0.529348\pi$
$350$	7.61997	0.407304
$351$	−25.6268	−1.36786
$352$	19.9492	1.06330
$353$	−8.94045	−0.475852	−0.237926	−	0.971283i	$-0.576468\pi$
$353$	−8.94045	−0.475852	−0.237926	+	0.971283i	$0.576468\pi$
$354$	−17.1234	−0.910099
$355$	−2.73792	−0.145313
$356$	−44.2673	−2.34616
$357$	5.36691	0.284047
$358$	−18.3684	−0.970800
$359$	14.8573	0.784137	0.392068	−	0.919936i	$-0.371760\pi$
$359$	14.8573	0.784137	0.392068	+	0.919936i	$0.371760\pi$
$360$	10.8860	0.573744
$361$	1.24827	0.0656982
$362$	11.0281	0.579626
$363$	24.6821	1.29547
$364$	18.8216	0.986517
$365$	−8.87759	−0.464675
$366$	−34.2771	−1.79169
$367$	23.1680	1.20936	0.604680	−	0.796469i	$-0.293301\pi$
$367$	23.1680	1.20936	0.604680	+	0.796469i	$0.293301\pi$
$368$	−4.20982	−0.219452
$369$	7.32957	0.381562
$370$	3.37125	0.175263
$371$	−9.63190	−0.500063
$372$	−15.0881	−0.782281
$373$	2.23160	0.115548	0.0577740	−	0.998330i	$-0.481600\pi$
$373$	2.23160	0.115548	0.0577740	+	0.998330i	$0.481600\pi$
$374$	62.0305	3.20752
$375$	−13.9708	−0.721450
$376$	31.9267	1.64649
$377$	−7.86096	−0.404860
$378$	13.2490	0.681453
$379$	12.4129	0.637610	0.318805	−	0.947820i	$-0.396718\pi$
$379$	12.4129	0.637610	0.318805	+	0.947820i	$0.396718\pi$
$380$	26.1150	1.33967
$381$	5.31912	0.272507
$382$	−21.9090	−1.12096
$383$	3.31079	0.169174	0.0845868	−	0.996416i	$-0.473043\pi$
$383$	3.31079	0.169174	0.0845868	+	0.996416i	$0.473043\pi$
$384$	19.1098	0.975193
$385$	−6.98177	−0.355824
$386$	−12.8344	−0.653252
$387$	7.14971	0.363440
$388$	30.8115	1.56422
$389$	−35.6876	−1.80943	−0.904716	−	0.426016i	$-0.859917\pi$
$389$	−35.6876	−1.80943	−0.904716	+	0.426016i	$0.859917\pi$
$390$	−19.7032	−0.997709
$391$	−3.08401	−0.155965
$392$	35.8351	1.80995
$393$	−9.30745	−0.469499
$394$	39.5881	1.99442
$395$	11.6199	0.584662
$396$	33.0856	1.66262
$397$	7.19667	0.361190	0.180595	−	0.983558i	$-0.442198\pi$
$397$	7.19667	0.361190	0.180595	+	0.983558i	$0.442198\pi$
$398$	−30.3100	−1.51930
$399$	5.40334	0.270506
$400$	−19.5541	−0.977707
$401$	−11.0222	−0.550421	−0.275211	−	0.961384i	$-0.588748\pi$
$401$	−11.0222	−0.550421	−0.275211	+	0.961384i	$0.588748\pi$
$402$	15.4924	0.772690
$403$	−12.6032	−0.627808
$404$	16.3094	0.811425
$405$	−3.92281	−0.194926
$406$	4.06409	0.201697
$407$	5.51551	0.273393
$408$	−33.3296	−1.65006
$409$	5.09543	0.251953	0.125976	−	0.992033i	$-0.459794\pi$
$409$	5.09543	0.251953	0.125976	+	0.992033i	$0.459794\pi$
$410$	17.8437	0.881240
$411$	1.51113	0.0745387
$412$	−60.4122	−2.97630
$413$	5.05900	0.248937
$414$	−2.40441	−0.118170
$415$	4.82367	0.236785
$416$	−16.6331	−0.815502
$417$	5.52557	0.270588
$418$	62.4516	3.05461
$419$	4.28923	0.209543	0.104771	−	0.994496i	$-0.466589\pi$
$419$	4.28923	0.209543	0.104771	+	0.994496i	$0.466589\pi$
$420$	6.96892	0.340049
$421$	9.77782	0.476542	0.238271	−	0.971199i	$-0.423419\pi$
$421$	9.77782	0.476542	0.238271	+	0.971199i	$0.423419\pi$
$422$	7.79184	0.379301
$423$	7.53490	0.366359
$424$	59.8161	2.90492
$425$	−14.3249	−0.694858
$426$	6.53541	0.316642
$427$	10.1270	0.490078
$428$	−16.1611	−0.781178
$429$	−32.2352	−1.55633
$430$	17.4059	0.839385
$431$	7.15119	0.344461	0.172230	−	0.985057i	$-0.444903\pi$
$431$	7.15119	0.344461	0.172230	+	0.985057i	$0.444903\pi$
$432$	−33.9991	−1.63578
$433$	−2.45841	−0.118144	−0.0590719	−	0.998254i	$-0.518814\pi$
$433$	−2.45841	−0.118144	−0.0590719	+	0.998254i	$0.518814\pi$
$434$	6.51579	0.312768
$435$	−2.91062	−0.139554
$436$	26.5639	1.27218
$437$	−3.10494	−0.148530
$438$	21.1908	1.01254
$439$	−1.75112	−0.0835763	−0.0417881	−	0.999126i	$-0.513305\pi$
$439$	−1.75112	−0.0835763	−0.0417881	+	0.999126i	$0.513305\pi$
$440$	43.3582	2.06702
$441$	8.45731	0.402729
$442$	−51.7191	−2.46003
$443$	12.5026	0.594019	0.297009	−	0.954875i	$-0.404011\pi$
$443$	12.5026	0.594019	0.297009	+	0.954875i	$0.404011\pi$
$444$	−5.50536	−0.261273
$445$	−13.6911	−0.649020
$446$	−60.6098	−2.86996
$447$	−21.1120	−0.998564
$448$	−2.92968	−0.138414
$449$	2.02140	0.0953956	0.0476978	−	0.998862i	$-0.484812\pi$
$449$	2.02140	0.0953956	0.0476978	+	0.998862i	$0.484812\pi$
$450$	−11.1682	−0.526473
$451$	29.1931	1.37465
$452$	−76.2533	−3.58665
$453$	2.48054	0.116546
$454$	−26.6934	−1.25278
$455$	5.82118	0.272901
$456$	−33.5559	−1.57140
$457$	18.0880	0.846123	0.423062	−	0.906101i	$-0.360955\pi$
$457$	18.0880	0.846123	0.423062	+	0.906101i	$0.360955\pi$
$458$	12.1940	0.569787
$459$	−24.9069	−1.16255
$460$	−4.00458	−0.186714
$461$	−3.77816	−0.175967	−0.0879833	−	0.996122i	$-0.528042\pi$
$461$	−3.77816	−0.175967	−0.0879833	+	0.996122i	$0.528042\pi$
$462$	16.6655	0.775349
$463$	1.46342	0.0680108	0.0340054	−	0.999422i	$-0.489174\pi$
$463$	1.46342	0.0680108	0.0340054	+	0.999422i	$0.489174\pi$
$464$	−10.4291	−0.484161
$465$	−4.66648	−0.216403
$466$	9.62450	0.445846
$467$	38.7040	1.79101	0.895504	−	0.445054i	$-0.146816\pi$
$467$	38.7040	1.79101	0.895504	+	0.445054i	$0.146816\pi$
$468$	−27.5858	−1.27515
$469$	−4.57713	−0.211352
$470$	18.3436	0.846128
$471$	10.5245	0.484944
$472$	−31.4174	−1.44611
$473$	28.4767	1.30936
$474$	−27.7368	−1.27399
$475$	−14.4221	−0.661732
$476$	18.2928	0.838449
$477$	14.1170	0.646371
$478$	0.464999	0.0212686
$479$	−16.5769	−0.757419	−0.378709	−	0.925516i	$-0.623632\pi$
$479$	−16.5769	−0.757419	−0.378709	+	0.925516i	$0.623632\pi$
$480$	−6.15860	−0.281100
$481$	−4.59866	−0.209681
$482$	4.23642	0.192964
$483$	−0.828569	−0.0377012
$484$	84.1275	3.82398
$485$	9.52947	0.432711
$486$	−32.7040	−1.48348
$487$	−13.1919	−0.597782	−0.298891	−	0.954287i	$-0.596617\pi$
$487$	−13.1919	−0.597782	−0.298891	+	0.954287i	$0.596617\pi$
$488$	−62.8905	−2.84692
$489$	−1.27091	−0.0574725
$490$	20.5892	0.930125
$491$	−30.5758	−1.37987	−0.689933	−	0.723873i	$-0.742360\pi$
$491$	−30.5758	−1.37987	−0.689933	+	0.723873i	$0.742360\pi$
$492$	−29.1394	−1.31371
$493$	−7.64012	−0.344094
$494$	−52.0702	−2.34275
$495$	10.2328	0.459931
$496$	−16.7206	−0.750779
$497$	−1.93085	−0.0866103
$498$	−11.5141	−0.515960
$499$	−21.3430	−0.955444	−0.477722	−	0.878511i	$-0.658537\pi$
$499$	−21.3430	−0.955444	−0.477722	+	0.878511i	$0.658537\pi$
$500$	−47.6188	−2.12958
$501$	−14.9461	−0.667744
$502$	−3.31120	−0.147786
$503$	30.7941	1.37304	0.686520	−	0.727111i	$-0.259137\pi$
$503$	30.7941	1.37304	0.686520	+	0.727111i	$0.259137\pi$
$504$	7.67710	0.341965
$505$	5.04423	0.224465
$506$	−9.57656	−0.425730
$507$	10.3549	0.459877
$508$	18.1299	0.804384
$509$	−7.47722	−0.331422	−0.165711	−	0.986174i	$-0.552992\pi$
$509$	−7.47722	−0.331422	−0.165711	+	0.986174i	$0.552992\pi$
$510$	−19.1497	−0.847961
$511$	−6.26070	−0.276957
$512$	49.5298	2.18893
$513$	−25.0759	−1.10713
$514$	−31.8530	−1.40497
$515$	−18.6845	−0.823335
$516$	−28.4243	−1.25131
$517$	30.0109	1.31988
$518$	2.37749	0.104461
$519$	0.930670	0.0408519
$520$	−36.1507	−1.58531
$521$	16.1617	0.708057	0.354029	−	0.935235i	$-0.384812\pi$
$521$	16.1617	0.708057	0.354029	+	0.935235i	$0.384812\pi$
$522$	−5.95652	−0.260710
$523$	−36.0238	−1.57521	−0.787605	−	0.616180i	$-0.788679\pi$
$523$	−36.0238	−1.57521	−0.787605	+	0.616180i	$0.788679\pi$
$524$	−31.7239	−1.38586
$525$	−3.84861	−0.167967
$526$	−33.8745	−1.47700
$527$	−12.2491	−0.533579
$528$	−42.7665	−1.86117
$529$	−22.5239	−0.979299
$530$	34.3675	1.49283
$531$	−7.41471	−0.321771
$532$	18.4170	0.798477
$533$	−24.3403	−1.05430
$534$	32.6807	1.41423
$535$	−4.99836	−0.216098
$536$	28.4249	1.22777
$537$	9.27730	0.400345
$538$	62.4609	2.69288
$539$	33.6848	1.45091
$540$	−32.3415	−1.39176
$541$	−13.3161	−0.572506	−0.286253	−	0.958154i	$-0.592410\pi$
$541$	−13.3161	−0.572506	−0.286253	+	0.958154i	$0.592410\pi$
$542$	42.0321	1.80543
$543$	−5.56997	−0.239030
$544$	−16.1658	−0.693102
$545$	8.21576	0.351925
$546$	−13.8952	−0.594658
$547$	−20.4389	−0.873904	−0.436952	−	0.899485i	$-0.643942\pi$
$547$	−20.4389	−0.873904	−0.436952	+	0.899485i	$0.643942\pi$
$548$	5.15061	0.220023
$549$	−14.8425	−0.633464
$550$	−44.4820	−1.89672
$551$	−7.69199	−0.327690
$552$	5.14558	0.219011
$553$	8.19466	0.348473
$554$	55.0178	2.33748
$555$	−1.70271	−0.0722761
$556$	18.8336	0.798722
$557$	−45.0023	−1.90681	−0.953403	−	0.301698i	$-0.902447\pi$
$557$	−45.0023	−1.90681	−0.953403	+	0.301698i	$0.902447\pi$
$558$	−9.54985	−0.404277
$559$	−23.7430	−1.00422
$560$	7.72297	0.326355
$561$	−31.3297	−1.32274
$562$	−76.3765	−3.22175
$563$	28.6987	1.20951	0.604753	−	0.796413i	$-0.293272\pi$
$563$	28.6987	1.20951	0.604753	+	0.796413i	$0.293272\pi$
$564$	−29.9557	−1.26136
$565$	−23.5838	−0.992179
$566$	22.6703	0.952906
$567$	−2.76646	−0.116180
$568$	11.9910	0.503129
$569$	−14.6149	−0.612689	−0.306345	−	0.951921i	$-0.599106\pi$
$569$	−14.6149	−0.612689	−0.306345	+	0.951921i	$0.599106\pi$
$570$	−19.2797	−0.807536
$571$	13.9105	0.582134	0.291067	−	0.956703i	$-0.405990\pi$
$571$	13.9105	0.582134	0.291067	+	0.956703i	$0.405990\pi$
$572$	−109.872	−4.59398
$573$	11.0655	0.462269
$574$	12.5839	0.525240
$575$	2.21154	0.0922276
$576$	4.29387	0.178911
$577$	7.38262	0.307343	0.153671	−	0.988122i	$-0.450890\pi$
$577$	7.38262	0.307343	0.153671	+	0.988122i	$0.450890\pi$
$578$	−7.48885	−0.311495
$579$	6.48224	0.269393
$580$	−9.92069	−0.411934
$581$	3.40177	0.141129
$582$	−22.7469	−0.942888
$583$	56.2268	2.32868
$584$	38.8802	1.60888
$585$	−8.53179	−0.352746
$586$	61.1153	2.52465
$587$	−16.0656	−0.663099	−0.331550	−	0.943438i	$-0.607571\pi$
$587$	−16.0656	−0.663099	−0.331550	+	0.943438i	$0.607571\pi$
$588$	−33.6228	−1.38658
$589$	−12.3323	−0.508142
$590$	−18.0510	−0.743148
$591$	−19.9947	−0.822472
$592$	−6.10104	−0.250751
$593$	−0.479184	−0.0196777	−0.00983887	−	0.999952i	$-0.503132\pi$
$593$	−0.479184	−0.0196777	−0.00983887	+	0.999952i	$0.503132\pi$
$594$	−77.3416	−3.17336
$595$	5.65764	0.231941
$596$	−71.9591	−2.94756
$597$	15.3086	0.626540
$598$	7.98464	0.326516
$599$	−13.2676	−0.542101	−0.271051	−	0.962565i	$-0.587371\pi$
$599$	−13.2676	−0.542101	−0.271051	+	0.962565i	$0.587371\pi$
$600$	23.9006	0.975739
$601$	45.9011	1.87234	0.936172	−	0.351543i	$-0.114343\pi$
$601$	45.9011	1.87234	0.936172	+	0.351543i	$0.114343\pi$
$602$	12.2750	0.500294
$603$	6.70845	0.273189
$604$	8.45478	0.344020
$605$	26.0192	1.05783
$606$	−12.0406	−0.489115
$607$	11.5188	0.467532	0.233766	−	0.972293i	$-0.424895\pi$
$607$	11.5188	0.467532	0.233766	+	0.972293i	$0.424895\pi$
$608$	−16.2755	−0.660060
$609$	−2.05264	−0.0831773
$610$	−36.1339	−1.46302
$611$	−25.0222	−1.01229
$612$	−26.8108	−1.08376
$613$	6.69363	0.270353	0.135177	−	0.990822i	$-0.456840\pi$
$613$	6.69363	0.270353	0.135177	+	0.990822i	$0.456840\pi$
$614$	80.7082	3.25712
$615$	−9.01231	−0.363412
$616$	30.5773	1.23199
$617$	−21.3686	−0.860268	−0.430134	−	0.902765i	$-0.641534\pi$
$617$	−21.3686	−0.860268	−0.430134	+	0.902765i	$0.641534\pi$
$618$	44.5998	1.79407
$619$	−5.90911	−0.237507	−0.118754	−	0.992924i	$-0.537890\pi$
$619$	−5.90911	−0.237507	−0.118754	+	0.992924i	$0.537890\pi$
$620$	−15.9054	−0.638778
$621$	3.84524	0.154304
$622$	65.2323	2.61558
$623$	−9.65530	−0.386831
$624$	35.6574	1.42744
$625$	1.29759	0.0519037
$626$	64.1084	2.56229
$627$	−31.5423	−1.25968
$628$	35.8722	1.43146
$629$	−4.46947	−0.178209
$630$	4.41091	0.175735
$631$	39.8538	1.58656	0.793278	−	0.608860i	$-0.208373\pi$
$631$	39.8538	1.58656	0.793278	+	0.608860i	$0.208373\pi$
$632$	−50.8906	−2.02432
$633$	−3.93541	−0.156419
$634$	−24.4434	−0.970772
$635$	5.60726	0.222517
$636$	−56.1233	−2.22543
$637$	−28.0853	−1.11278
$638$	−23.7244	−0.939256
$639$	2.82994	0.111951
$640$	20.1450	0.796301
$641$	−24.0629	−0.950428	−0.475214	−	0.879870i	$-0.657629\pi$
$641$	−24.0629	−0.950428	−0.475214	+	0.879870i	$0.657629\pi$
$642$	11.9311	0.470883
$643$	30.4954	1.20262	0.601310	−	0.799016i	$-0.294646\pi$
$643$	30.4954	1.20262	0.601310	+	0.799016i	$0.294646\pi$
$644$	−2.82413	−0.111286
$645$	−8.79115	−0.346151
$646$	−50.6074	−1.99112
$647$	−12.7208	−0.500105	−0.250053	−	0.968232i	$-0.580448\pi$
$647$	−12.7208	−0.500105	−0.250053	+	0.968232i	$0.580448\pi$
$648$	17.1803	0.674906
$649$	−29.5322	−1.15924
$650$	37.0877	1.45470
$651$	−3.29092	−0.128981
$652$	−4.33182	−0.169647
$653$	25.2315	0.987384	0.493692	−	0.869637i	$-0.335647\pi$
$653$	25.2315	0.987384	0.493692	+	0.869637i	$0.335647\pi$
$654$	−19.6110	−0.766853
$655$	−9.81165	−0.383373
$656$	−32.2923	−1.26080
$657$	9.17598	0.357989
$658$	12.9364	0.504312
$659$	8.22627	0.320450	0.160225	−	0.987081i	$-0.448778\pi$
$659$	8.22627	0.320450	0.160225	+	0.987081i	$0.448778\pi$
$660$	−40.6815	−1.58353
$661$	−1.04179	−0.0405210	−0.0202605	−	0.999795i	$-0.506450\pi$
$661$	−1.04179	−0.0405210	−0.0202605	+	0.999795i	$0.506450\pi$
$662$	19.3276	0.751187
$663$	26.1217	1.01448
$664$	−21.1257	−0.819837
$665$	5.69605	0.220883
$666$	−3.48456	−0.135024
$667$	1.17952	0.0456711
$668$	−50.9430	−1.97104
$669$	30.6121	1.18353
$670$	16.3316	0.630946
$671$	−59.1167	−2.28217
$672$	−4.34320	−0.167543
$673$	16.7931	0.647325	0.323662	−	0.946173i	$-0.395086\pi$
$673$	16.7931	0.647325	0.323662	+	0.946173i	$0.395086\pi$
$674$	64.8561	2.49816
$675$	17.8607	0.687458
$676$	35.2941	1.35746
$677$	−35.1265	−1.35002	−0.675011	−	0.737808i	$-0.735861\pi$
$677$	−35.1265	−1.35002	−0.675011	+	0.737808i	$0.735861\pi$
$678$	56.2946	2.16198
$679$	6.72042	0.257906
$680$	−35.1351	−1.34737
$681$	13.4820	0.516632
$682$	−38.0363	−1.45649
$683$	5.42740	0.207674	0.103837	−	0.994594i	$-0.466888\pi$
$683$	5.42740	0.207674	0.103837	+	0.994594i	$0.466888\pi$
$684$	−26.9928	−1.03210
$685$	1.59299	0.0608652
$686$	31.1624	1.18979
$687$	−6.15880	−0.234973
$688$	−31.4999	−1.20092
$689$	−46.8801	−1.78599
$690$	2.95641	0.112549
$691$	−49.6085	−1.88720	−0.943598	−	0.331092i	$-0.892583\pi$
$691$	−49.6085	−1.88720	−0.943598	+	0.331092i	$0.892583\pi$
$692$	3.17214	0.120587
$693$	7.21643	0.274130
$694$	−87.9581	−3.33884
$695$	5.82490	0.220951
$696$	12.7473	0.483187
$697$	−23.6565	−0.896055
$698$	8.65604	0.327636
$699$	−4.86103	−0.183861
$700$	−13.1177	−0.495804
$701$	−35.2367	−1.33087	−0.665435	−	0.746456i	$-0.731754\pi$
$701$	−35.2367	−1.33087	−0.665435	+	0.746456i	$0.731754\pi$
$702$	64.4850	2.43383
$703$	−4.49981	−0.169713
$704$	17.1022	0.644562
$705$	−9.26478	−0.348932
$706$	22.4969	0.846684
$707$	3.55732	0.133787
$708$	29.4779	1.10785
$709$	14.5252	0.545506	0.272753	−	0.962084i	$-0.412066\pi$
$709$	14.5252	0.545506	0.272753	+	0.962084i	$0.412066\pi$
$710$	6.88945	0.258556
$711$	−12.0105	−0.450428
$712$	59.9614	2.24715
$713$	1.89107	0.0708213
$714$	−13.5048	−0.505405
$715$	−33.9815	−1.27084
$716$	31.6212	1.18174
$717$	−0.234856	−0.00877087
$718$	−37.3855	−1.39522
$719$	−26.8160	−1.00007	−0.500034	−	0.866006i	$-0.666679\pi$
$719$	−26.8160	−1.00007	−0.500034	+	0.866006i	$0.666679\pi$
$720$	−11.3191	−0.421840
$721$	−13.1767	−0.490728
$722$	−3.14103	−0.116897
$723$	−2.13968	−0.0795756
$724$	−18.9849	−0.705569
$725$	5.47873	0.203475
$726$	−62.1078	−2.30504
$727$	24.0361	0.891449	0.445725	−	0.895170i	$-0.352946\pi$
$727$	24.0361	0.891449	0.445725	+	0.895170i	$0.352946\pi$
$728$	−25.4944	−0.944885
$729$	25.3017	0.937102
$730$	22.3388	0.826796
$731$	−23.0760	−0.853497
$732$	59.0079	2.18100
$733$	−7.11404	−0.262763	−0.131381	−	0.991332i	$-0.541941\pi$
$733$	−7.11404	−0.262763	−0.131381	+	0.991332i	$0.541941\pi$
$734$	−58.2979	−2.15182
$735$	−10.3990	−0.383571
$736$	2.49575	0.0919946
$737$	26.7193	0.984217
$738$	−18.4435	−0.678914
$739$	10.0648	0.370239	0.185119	−	0.982716i	$-0.440733\pi$
$739$	10.0648	0.370239	0.185119	+	0.982716i	$0.440733\pi$
$740$	−5.80359	−0.213344
$741$	26.2990	0.966119
$742$	24.2368	0.889763
$743$	−7.91098	−0.290226	−0.145113	−	0.989415i	$-0.546354\pi$
$743$	−7.91098	−0.290226	−0.145113	+	0.989415i	$0.546354\pi$
$744$	20.4373	0.749268
$745$	−22.2557	−0.815386
$746$	−5.61541	−0.205595
$747$	−4.98580	−0.182421
$748$	−106.785	−3.90446
$749$	−3.52497	−0.128799
$750$	35.1550	1.28368
$751$	−6.73784	−0.245867	−0.122934	−	0.992415i	$-0.539230\pi$
$751$	−6.73784	−0.245867	−0.122934	+	0.992415i	$0.539230\pi$
$752$	−33.1970	−1.21057
$753$	1.67238	0.0609450
$754$	19.7806	0.720368
$755$	2.61492	0.0951666
$756$	−22.8080	−0.829520
$757$	18.3449	0.666755	0.333378	−	0.942793i	$-0.391812\pi$
$757$	18.3449	0.666755	0.333378	+	0.942793i	$0.391812\pi$
$758$	−31.2348	−1.13450
$759$	4.83682	0.175565
$760$	−35.3737	−1.28314
$761$	26.9508	0.976965	0.488482	−	0.872574i	$-0.337551\pi$
$761$	26.9508	0.976965	0.488482	+	0.872574i	$0.337551\pi$
$762$	−13.3846	−0.484871
$763$	5.79396	0.209755
$764$	37.7162	1.36452
$765$	−8.29211	−0.299802
$766$	−8.33098	−0.301011
$767$	24.6231	0.889087
$768$	−40.2047	−1.45076
$769$	13.3211	0.480373	0.240186	−	0.970727i	$-0.422791\pi$
$769$	13.3211	0.480373	0.240186	+	0.970727i	$0.422791\pi$
$770$	17.5683	0.633118
$771$	16.0879	0.579393
$772$	22.0943	0.795193
$773$	−38.3966	−1.38103	−0.690514	−	0.723319i	$-0.742616\pi$
$773$	−38.3966	−1.38103	−0.690514	+	0.723319i	$0.742616\pi$
$774$	−17.9909	−0.646669
$775$	8.78382	0.315524
$776$	−41.7352	−1.49821
$777$	−1.20079	−0.0430783
$778$	89.8010	3.21952
$779$	−23.8171	−0.853337
$780$	33.9190	1.21449
$781$	11.2714	0.403324
$782$	7.76032	0.277509
$783$	9.52595	0.340430
$784$	−37.2609	−1.33075
$785$	11.0947	0.395985
$786$	23.4204	0.835379
$787$	16.6153	0.592272	0.296136	−	0.955146i	$-0.404302\pi$
$787$	16.6153	0.592272	0.296136	+	0.955146i	$0.404302\pi$
$788$	−68.1508	−2.42777
$789$	17.1089	0.609094
$790$	−29.2394	−1.04029
$791$	−16.6319	−0.591362
$792$	−44.8155	−1.59245
$793$	49.2896	1.75033
$794$	−18.1090	−0.642666
$795$	−17.3580	−0.615624
$796$	52.1786	1.84942
$797$	−39.5554	−1.40113	−0.700563	−	0.713591i	$-0.747068\pi$
$797$	−39.5554	−1.40113	−0.700563	+	0.713591i	$0.747068\pi$
$798$	−13.5965	−0.481311
$799$	−24.3192	−0.860353
$800$	11.5925	0.409856
$801$	14.1513	0.500010
$802$	27.7352	0.979365
$803$	36.5472	1.28972
$804$	−26.6701	−0.940582
$805$	−0.873454	−0.0307852
$806$	31.7135	1.11706
$807$	−31.5471	−1.11051
$808$	−22.0917	−0.777182
$809$	36.7855	1.29331	0.646654	−	0.762783i	$-0.276168\pi$
$809$	36.7855	1.29331	0.646654	+	0.762783i	$0.276168\pi$
$810$	9.87100	0.346832
$811$	42.4513	1.49067	0.745334	−	0.666691i	$-0.232290\pi$
$811$	42.4513	1.49067	0.745334	+	0.666691i	$0.232290\pi$
$812$	−6.99632	−0.245523
$813$	−21.2291	−0.744537
$814$	−13.8787	−0.486449
$815$	−1.33976	−0.0469297
$816$	34.6557	1.21319
$817$	−23.2327	−0.812808
$818$	−12.8217	−0.448299
$819$	−6.01683	−0.210245
$820$	−30.7179	−1.07272
$821$	−0.876650	−0.0305953	−0.0152976	−	0.999883i	$-0.504870\pi$
$821$	−0.876650	−0.0305953	−0.0152976	+	0.999883i	$0.504870\pi$
$822$	−3.80248	−0.132627
$823$	−30.7344	−1.07133	−0.535667	−	0.844430i	$-0.679940\pi$
$823$	−30.7344	−1.07133	−0.535667	+	0.844430i	$0.679940\pi$
$824$	81.8303	2.85069
$825$	22.4665	0.782182
$826$	−12.7300	−0.442934
$827$	21.3093	0.740997	0.370499	−	0.928833i	$-0.379187\pi$
$827$	21.3093	0.740997	0.370499	+	0.928833i	$0.379187\pi$
$828$	4.13918	0.143846
$829$	−5.17379	−0.179693	−0.0898467	−	0.995956i	$-0.528638\pi$
$829$	−5.17379	−0.179693	−0.0898467	+	0.995956i	$0.528638\pi$
$830$	−12.1379	−0.421311
$831$	−27.7877	−0.963946
$832$	−14.2592	−0.494350
$833$	−27.2963	−0.945762
$834$	−13.9041	−0.481458
$835$	−15.7558	−0.545252
$836$	−107.510	−3.71832
$837$	15.2726	0.527897
$838$	−10.7930	−0.372839
$839$	7.42054	0.256186	0.128093	−	0.991762i	$-0.459114\pi$
$839$	7.42054	0.256186	0.128093	+	0.991762i	$0.459114\pi$
$840$	−9.43962	−0.325698
$841$	−26.0779	−0.899239
$842$	−24.6040	−0.847911
$843$	38.5754	1.32861
$844$	−13.4136	−0.461716
$845$	10.9158	0.375517
$846$	−18.9602	−0.651864
$847$	18.3494	0.630492
$848$	−62.1959	−2.13582
$849$	−11.4501	−0.392966
$850$	36.0458	1.23636
$851$	0.690017	0.0236535
$852$	−11.2507	−0.385442
$853$	41.3126	1.41452	0.707258	−	0.706956i	$-0.249932\pi$
$853$	41.3126	1.41452	0.707258	+	0.706956i	$0.249932\pi$
$854$	−25.4826	−0.871995
$855$	−8.34840	−0.285509
$856$	21.8908	0.748211
$857$	−7.62215	−0.260368	−0.130184	−	0.991490i	$-0.541557\pi$
$857$	−7.62215	−0.260368	−0.130184	+	0.991490i	$0.541557\pi$
$858$	81.1139	2.76918
$859$	−1.32702	−0.0452773	−0.0226387	−	0.999744i	$-0.507207\pi$
$859$	−1.32702	−0.0452773	−0.0226387	+	0.999744i	$0.507207\pi$
$860$	−29.9641	−1.02177
$861$	−6.35571	−0.216602
$862$	−17.9946	−0.612899
$863$	45.2045	1.53878	0.769389	−	0.638781i	$-0.220561\pi$
$863$	45.2045	1.53878	0.769389	+	0.638781i	$0.220561\pi$
$864$	20.1560	0.685721
$865$	0.981087	0.0333579
$866$	6.18613	0.210213
$867$	3.78238	0.128456
$868$	−11.2169	−0.380727
$869$	−47.8369	−1.62275
$870$	7.32403	0.248308
$871$	−22.2777	−0.754850
$872$	−35.9817	−1.21849
$873$	−9.84976	−0.333364
$874$	7.81301	0.264279
$875$	−10.3863	−0.351121
$876$	−36.4800	−1.23254
$877$	9.01613	0.304453	0.152227	−	0.988346i	$-0.451356\pi$
$877$	9.01613	0.304453	0.152227	+	0.988346i	$0.451356\pi$
$878$	4.40636	0.148707
$879$	−30.8674	−1.04113
$880$	−45.0833	−1.51976
$881$	−14.9177	−0.502591	−0.251295	−	0.967910i	$-0.580857\pi$
$881$	−14.9177	−0.502591	−0.251295	+	0.967910i	$0.580857\pi$
$882$	−21.2812	−0.716576
$883$	−0.649985	−0.0218737	−0.0109369	−	0.999940i	$-0.503481\pi$
$883$	−0.649985	−0.0218737	−0.0109369	+	0.999940i	$0.503481\pi$
$884$	89.0342	2.99455
$885$	9.11700	0.306465
$886$	−31.4605	−1.05694
$887$	−49.6056	−1.66559	−0.832796	−	0.553580i	$-0.813261\pi$
$887$	−49.6056	−1.66559	−0.832796	+	0.553580i	$0.813261\pi$
$888$	7.45718	0.250247
$889$	3.95438	0.132626
$890$	34.4511	1.15480
$891$	16.1494	0.541025
$892$	104.340	3.49355
$893$	−24.4843	−0.819337
$894$	53.1244	1.77675
$895$	9.77987	0.326905
$896$	14.2068	0.474615
$897$	−4.03279	−0.134651
$898$	−5.08646	−0.169737
$899$	4.68483	0.156248
$900$	19.2260	0.640866
$901$	−45.5631	−1.51793
$902$	−73.4590	−2.44592
$903$	−6.19974	−0.206314
$904$	103.287	3.43529
$905$	−5.87170	−0.195182
$906$	−6.24182	−0.207370
$907$	16.0169	0.531831	0.265915	−	0.963996i	$-0.414326\pi$
$907$	16.0169	0.531831	0.265915	+	0.963996i	$0.414326\pi$
$908$	45.9527	1.52499
$909$	−5.21377	−0.172930
$910$	−14.6479	−0.485573
$911$	−37.7233	−1.24983	−0.624914	−	0.780693i	$-0.714866\pi$
$911$	−37.7233	−1.24983	−0.624914	+	0.780693i	$0.714866\pi$
$912$	34.8909	1.15535
$913$	−19.8581	−0.657206
$914$	−45.5152	−1.50551
$915$	18.2501	0.603330
$916$	−20.9919	−0.693592
$917$	−6.91942	−0.228499
$918$	62.6734	2.06853
$919$	−26.2770	−0.866799	−0.433399	−	0.901202i	$-0.642686\pi$
$919$	−26.2770	−0.866799	−0.433399	+	0.901202i	$0.642686\pi$
$920$	5.42433	0.178835
$921$	−40.7632	−1.34319
$922$	9.50703	0.313097
$923$	−9.39777	−0.309331
$924$	−28.6896	−0.943819
$925$	3.20505	0.105381
$926$	−3.68242	−0.121012
$927$	19.3125	0.634304
$928$	6.18281	0.202961
$929$	−38.3851	−1.25937	−0.629687	−	0.776849i	$-0.716817\pi$
$929$	−38.3851	−1.25937	−0.629687	+	0.776849i	$0.716817\pi$
$930$	11.7423	0.385046
$931$	−27.4817	−0.900675
$932$	−16.5686	−0.542721
$933$	−32.9468	−1.07863
$934$	−97.3913	−3.18674
$935$	−33.0268	−1.08009
$936$	37.3658	1.22134
$937$	−20.9040	−0.682903	−0.341452	−	0.939899i	$-0.610919\pi$
$937$	−20.9040	−0.682903	−0.341452	+	0.939899i	$0.610919\pi$
$938$	11.5175	0.376059
$939$	−32.3792	−1.05665
$940$	−31.5785	−1.02998
$941$	−37.8154	−1.23275	−0.616373	−	0.787455i	$-0.711399\pi$
$941$	−37.8154	−1.23275	−0.616373	+	0.787455i	$0.711399\pi$
$942$	−26.4830	−0.862862
$943$	3.65221	0.118932
$944$	32.6674	1.06323
$945$	−7.05413	−0.229471
$946$	−71.6563	−2.32975
$947$	16.5748	0.538608	0.269304	−	0.963055i	$-0.413206\pi$
$947$	16.5748	0.538608	0.269304	+	0.963055i	$0.413206\pi$
$948$	47.7488	1.55081
$949$	−30.4719	−0.989161
$950$	36.2905	1.17742
$951$	12.3456	0.400334
$952$	−24.7782	−0.803065
$953$	−41.4797	−1.34366	−0.671830	−	0.740705i	$-0.734492\pi$
$953$	−41.4797	−1.34366	−0.671830	+	0.740705i	$0.734492\pi$
$954$	−35.5227	−1.15009
$955$	11.6650	0.377470
$956$	−0.800494	−0.0258898
$957$	11.9824	0.387337
$958$	41.7127	1.34768
$959$	1.12342	0.0362771
$960$	−5.27967	−0.170401
$961$	−23.4890	−0.757710
$962$	11.5716	0.373085
$963$	5.16636	0.166484
$964$	−7.29298	−0.234891
$965$	6.83340	0.219975
$966$	2.08494	0.0670817
$967$	−18.5153	−0.595413	−0.297706	−	0.954658i	$-0.596222\pi$
$967$	−18.5153	−0.595413	−0.297706	+	0.954658i	$0.596222\pi$
$968$	−113.953	−3.66260
$969$	25.5602	0.821112
$970$	−23.9791	−0.769923
$971$	−2.69210	−0.0863936	−0.0431968	−	0.999067i	$-0.513754\pi$
$971$	−2.69210	−0.0863936	−0.0431968	+	0.999067i	$0.513754\pi$
$972$	56.2998	1.80582
$973$	4.10787	0.131692
$974$	33.1949	1.06363
$975$	−18.7318	−0.599899
$976$	65.3926	2.09317
$977$	−40.0618	−1.28169	−0.640845	−	0.767670i	$-0.721416\pi$
$977$	−40.0618	−1.28169	−0.640845	+	0.767670i	$0.721416\pi$
$978$	3.19800	0.102261
$979$	56.3634	1.80138
$980$	−35.4443	−1.13223
$981$	−8.49190	−0.271126
$982$	76.9382	2.45520
$983$	4.82297	0.153829	0.0769145	−	0.997038i	$-0.475493\pi$
$983$	4.82297	0.153829	0.0769145	+	0.997038i	$0.475493\pi$
$984$	39.4703	1.25827
$985$	−21.0779	−0.671596
$986$	19.2249	0.612247
$987$	−6.53376	−0.207972
$988$	89.6387	2.85179
$989$	3.56258	0.113283
$990$	−25.7489	−0.818355
$991$	46.4468	1.47543	0.737716	−	0.675112i	$-0.235905\pi$
$991$	46.4468	1.47543	0.737716	+	0.675112i	$0.235905\pi$
$992$	9.91265	0.314727
$993$	−9.76175	−0.309780
$994$	4.85861	0.154106
$995$	16.1379	0.511606
$996$	19.8215	0.628069
$997$	34.6536	1.09749	0.548746	−	0.835989i	$-0.315105\pi$
$997$	34.6536	1.09749	0.548746	+	0.835989i	$0.315105\pi$
$998$	53.7056	1.70002
$999$	5.57267	0.176311

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.8	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.51631 q^{2} +1.27091 q^{3} +4.33182 q^{4} +1.33976 q^{5} -3.19800 q^{6} +0.944830 q^{7} -5.86759 q^{8} -1.38479 q^{9} -3.37125 q^{10} -5.51551 q^{11} +5.50536 q^{12} +4.59866 q^{13} -2.37749 q^{14} +1.70271 q^{15} +6.10104 q^{16} +4.46947 q^{17} +3.48456 q^{18} +4.49981 q^{19} +5.80359 q^{20} +1.20079 q^{21} +13.8787 q^{22} -0.690017 q^{23} -7.45718 q^{24} -3.20505 q^{25} -11.5716 q^{26} -5.57267 q^{27} +4.09284 q^{28} -1.70940 q^{29} -4.28455 q^{30} -2.74062 q^{31} -3.61694 q^{32} -7.00971 q^{33} -11.2466 q^{34} +1.26584 q^{35} -5.99866 q^{36} -1.00000 q^{37} -11.3229 q^{38} +5.84448 q^{39} -7.86115 q^{40} -5.29292 q^{41} -3.02157 q^{42} -5.16303 q^{43} -23.8922 q^{44} -1.85528 q^{45} +1.73630 q^{46} -5.44119 q^{47} +7.75387 q^{48} -6.10730 q^{49} +8.06490 q^{50} +5.68029 q^{51} +19.9206 q^{52} -10.1943 q^{53} +14.0226 q^{54} -7.38944 q^{55} -5.54388 q^{56} +5.71885 q^{57} +4.30139 q^{58} +5.35440 q^{59} +7.37584 q^{60} +10.7183 q^{61} +6.89625 q^{62} -1.30839 q^{63} -3.10074 q^{64} +6.16108 q^{65} +17.6386 q^{66} -4.84439 q^{67} +19.3609 q^{68} -0.876950 q^{69} -3.18526 q^{70} -2.04359 q^{71} +8.12537 q^{72} -6.62627 q^{73} +2.51631 q^{74} -4.07333 q^{75} +19.4924 q^{76} -5.21122 q^{77} -14.7065 q^{78} +8.67316 q^{79} +8.17392 q^{80} -2.92800 q^{81} +13.3186 q^{82} +3.60041 q^{83} +5.20163 q^{84} +5.98800 q^{85} +12.9918 q^{86} -2.17250 q^{87} +32.3627 q^{88} -10.2191 q^{89} +4.66846 q^{90} +4.34495 q^{91} -2.98903 q^{92} -3.48308 q^{93} +13.6917 q^{94} +6.02865 q^{95} -4.59680 q^{96} +7.11283 q^{97} +15.3679 q^{98} +7.63781 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21}+ \cdots - 21 q^{99}+O(q^{100}) \) 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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