LMFDB - Embedded newform 41.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,2,Mod(1,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("41.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	41.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$0.327386648287$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.193937 q^{2} +1.67513 q^{3} -1.96239 q^{4} -0.806063 q^{5} -0.324869 q^{6} +0.324869 q^{7} +0.768452 q^{8} -0.193937 q^{9} +O(q^{10})$	\(q-0.193937 q^{2} +1.67513 q^{3} -1.96239 q^{4} -0.806063 q^{5} -0.324869 q^{6} +0.324869 q^{7} +0.768452 q^{8} -0.193937 q^{9} +0.156325 q^{10} -4.63752 q^{11} -3.28726 q^{12} +2.96239 q^{13} -0.0630040 q^{14} -1.35026 q^{15} +3.77575 q^{16} -2.00000 q^{17} +0.0376114 q^{18} +6.63752 q^{19} +1.58181 q^{20} +0.544198 q^{21} +0.899385 q^{22} +8.31265 q^{23} +1.28726 q^{24} -4.35026 q^{25} -0.574515 q^{26} -5.35026 q^{27} -0.637519 q^{28} -5.35026 q^{29} +0.261865 q^{30} +5.61213 q^{31} -2.26916 q^{32} -7.76845 q^{33} +0.387873 q^{34} -0.261865 q^{35} +0.380579 q^{36} -2.41819 q^{37} -1.28726 q^{38} +4.96239 q^{39} -0.619421 q^{40} +1.00000 q^{41} -0.105540 q^{42} -4.96239 q^{43} +9.10062 q^{44} +0.156325 q^{45} -1.61213 q^{46} -5.86177 q^{47} +6.32487 q^{48} -6.89446 q^{49} +0.843675 q^{50} -3.35026 q^{51} -5.81336 q^{52} -1.35026 q^{53} +1.03761 q^{54} +3.73813 q^{55} +0.249646 q^{56} +11.1187 q^{57} +1.03761 q^{58} +4.31265 q^{59} +2.64974 q^{60} +4.57452 q^{61} -1.08840 q^{62} -0.0630040 q^{63} -7.11142 q^{64} -2.38787 q^{65} +1.50659 q^{66} +4.63752 q^{67} +3.92478 q^{68} +13.9248 q^{69} +0.0507852 q^{70} +12.2496 q^{71} -0.149031 q^{72} -15.0435 q^{73} +0.468976 q^{74} -7.28726 q^{75} -13.0254 q^{76} -1.50659 q^{77} -0.962389 q^{78} +8.71274 q^{79} -3.04349 q^{80} -8.38058 q^{81} -0.193937 q^{82} -6.70052 q^{83} -1.06793 q^{84} +1.61213 q^{85} +0.962389 q^{86} -8.96239 q^{87} -3.56371 q^{88} +12.2374 q^{89} -0.0303172 q^{90} +0.962389 q^{91} -16.3127 q^{92} +9.40105 q^{93} +1.13681 q^{94} -5.35026 q^{95} -3.80114 q^{96} +8.70052 q^{97} +1.33709 q^{98} +0.899385 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 5 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{7} - 9 q^{8} - q^{9}+O(q^{10}) $ 3 * q - q^2 + 5 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^7 - 9 * q^8 - q^9	\( 3 q - q^{2} + 5 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{7} - 9 q^{8} - q^{9} - 10 q^{10} + 2 q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} + 6 q^{15} + 13 q^{16} - 6 q^{17} + 11 q^{18} + 4 q^{19} + 6 q^{20} - 8 q^{21} - 4 q^{22} + 4 q^{23} - 2 q^{24} - 3 q^{25} + 10 q^{26} - 6 q^{27} + 14 q^{28} - 6 q^{29} + 10 q^{30} + 16 q^{31} - 29 q^{32} - 12 q^{33} + 2 q^{34} - 10 q^{35} - 11 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 14 q^{40} + 3 q^{41} - 20 q^{42} - 4 q^{43} + 34 q^{44} - 10 q^{45} - 4 q^{46} + 24 q^{48} - q^{49} + 13 q^{50} - 30 q^{52} + 6 q^{53} + 14 q^{54} + 2 q^{55} - 16 q^{56} + 12 q^{57} + 14 q^{58} - 8 q^{59} + 18 q^{60} + 2 q^{61} + 16 q^{62} + 4 q^{63} + 13 q^{64} - 8 q^{65} - 16 q^{66} - 2 q^{67} - 10 q^{68} + 20 q^{69} - 30 q^{70} + 20 q^{71} + 23 q^{72} - 2 q^{73} - 30 q^{74} - 16 q^{75} - 24 q^{76} + 16 q^{77} + 8 q^{78} + 32 q^{79} + 34 q^{80} - 13 q^{81} - q^{82} - 12 q^{84} + 4 q^{85} - 8 q^{86} - 16 q^{87} - 40 q^{88} - 6 q^{89} + 2 q^{90} - 8 q^{91} - 28 q^{92} - 12 q^{93} - 46 q^{94} - 6 q^{95} + 2 q^{96} + 6 q^{97} + 35 q^{98} - 4 q^{99}+O(q^{100}) \) 3 * q - q^2 + 5 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^7 - 9 * q^8 - q^9 - 10 * q^10 + 2 * q^11 - 4 * q^12 - 2 * q^13 + 4 * q^14 + 6 * q^15 + 13 * q^16 - 6 * q^17 + 11 * q^18 + 4 * q^19 + 6 * q^20 - 8 * q^21 - 4 * q^22 + 4 * q^23 - 2 * q^24 - 3 * q^25 + 10 * q^26 - 6 * q^27 + 14 * q^28 - 6 * q^29 + 10 * q^30 + 16 * q^31 - 29 * q^32 - 12 * q^33 + 2 * q^34 - 10 * q^35 - 11 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 14 * q^40 + 3 * q^41 - 20 * q^42 - 4 * q^43 + 34 * q^44 - 10 * q^45 - 4 * q^46 + 24 * q^48 - q^49 + 13 * q^50 - 30 * q^52 + 6 * q^53 + 14 * q^54 + 2 * q^55 - 16 * q^56 + 12 * q^57 + 14 * q^58 - 8 * q^59 + 18 * q^60 + 2 * q^61 + 16 * q^62 + 4 * q^63 + 13 * q^64 - 8 * q^65 - 16 * q^66 - 2 * q^67 - 10 * q^68 + 20 * q^69 - 30 * q^70 + 20 * q^71 + 23 * q^72 - 2 * q^73 - 30 * q^74 - 16 * q^75 - 24 * q^76 + 16 * q^77 + 8 * q^78 + 32 * q^79 + 34 * q^80 - 13 * q^81 - q^82 - 12 * q^84 + 4 * q^85 - 8 * q^86 - 16 * q^87 - 40 * q^88 - 6 * q^89 + 2 * q^90 - 8 * q^91 - 28 * q^92 - 12 * q^93 - 46 * q^94 - 6 * q^95 + 2 * q^96 + 6 * q^97 + 35 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.193937	−0.137134	−0.0685669	−	0.997647i	$-0.521843\pi$
$2$	−0.193937	−0.137134	−0.0685669	+	0.997647i	$0.521843\pi$
$3$	1.67513	0.967137	0.483569	−	0.875306i	$-0.339340\pi$
$3$	1.67513	0.967137	0.483569	+	0.875306i	$0.339340\pi$
$4$	−1.96239	−0.981194
$5$	−0.806063	−0.360483	−0.180241	−	0.983622i	$-0.557688\pi$
$5$	−0.806063	−0.360483	−0.180241	+	0.983622i	$0.557688\pi$
$6$	−0.324869	−0.132627
$7$	0.324869	0.122789	0.0613945	−	0.998114i	$-0.480445\pi$
$7$	0.324869	0.122789	0.0613945	+	0.998114i	$0.480445\pi$
$8$	0.768452	0.271689
$9$	−0.193937	−0.0646455
$10$	0.156325	0.0494344
$11$	−4.63752	−1.39826	−0.699132	−	0.714992i	$-0.746430\pi$
$11$	−4.63752	−1.39826	−0.699132	+	0.714992i	$0.746430\pi$
$12$	−3.28726	−0.948950
$13$	2.96239	0.821619	0.410809	−	0.911721i	$-0.365246\pi$
$13$	2.96239	0.821619	0.410809	+	0.911721i	$0.365246\pi$
$14$	−0.0630040	−0.0168385
$15$	−1.35026	−0.348636
$16$	3.77575	0.943937
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0.0376114	0.00886509
$19$	6.63752	1.52275	0.761376	−	0.648311i	$-0.224524\pi$
$19$	6.63752	1.52275	0.761376	+	0.648311i	$0.224524\pi$
$20$	1.58181	0.353703
$21$	0.544198	0.118754
$22$	0.899385	0.191749
$23$	8.31265	1.73331	0.866654	−	0.498910i	$-0.166266\pi$
$23$	8.31265	1.73331	0.866654	+	0.498910i	$0.166266\pi$
$24$	1.28726	0.262760
$25$	−4.35026	−0.870052
$26$	−0.574515	−0.112672
$27$	−5.35026	−1.02966
$28$	−0.637519	−0.120480
$29$	−5.35026	−0.993519	−0.496759	−	0.867888i	$-0.665477\pi$
$29$	−5.35026	−0.993519	−0.496759	+	0.867888i	$0.665477\pi$
$30$	0.261865	0.0478098
$31$	5.61213	1.00797	0.503984	−	0.863713i	$-0.331867\pi$
$31$	5.61213	1.00797	0.503984	+	0.863713i	$0.331867\pi$
$32$	−2.26916	−0.401134
$33$	−7.76845	−1.35231
$34$	0.387873	0.0665197
$35$	−0.261865	−0.0442633
$36$	0.380579	0.0634298
$37$	−2.41819	−0.397548	−0.198774	−	0.980045i	$-0.563696\pi$
$37$	−2.41819	−0.397548	−0.198774	+	0.980045i	$0.563696\pi$
$38$	−1.28726	−0.208821
$39$	4.96239	0.794618
$40$	−0.619421	−0.0979391
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	−0.105540	−0.0162852
$43$	−4.96239	−0.756757	−0.378379	−	0.925651i	$-0.623518\pi$
$43$	−4.96239	−0.756757	−0.378379	+	0.925651i	$0.623518\pi$
$44$	9.10062	1.37197
$45$	0.156325	0.0233036
$46$	−1.61213	−0.237695
$47$	−5.86177	−0.855027	−0.427514	−	0.904009i	$-0.640610\pi$
$47$	−5.86177	−0.855027	−0.427514	+	0.904009i	$0.640610\pi$
$48$	6.32487	0.912916
$49$	−6.89446	−0.984923
$50$	0.843675	0.119314
$51$	−3.35026	−0.469130
$52$	−5.81336	−0.806168
$53$	−1.35026	−0.185473	−0.0927364	−	0.995691i	$-0.529561\pi$
$53$	−1.35026	−0.185473	−0.0927364	+	0.995691i	$0.529561\pi$
$54$	1.03761	0.141201
$55$	3.73813	0.504050
$56$	0.249646	0.0333604
$57$	11.1187	1.47271
$58$	1.03761	0.136245
$59$	4.31265	0.561459	0.280730	−	0.959787i	$-0.409424\pi$
$59$	4.31265	0.561459	0.280730	+	0.959787i	$0.409424\pi$
$60$	2.64974	0.342080
$61$	4.57452	0.585707	0.292853	−	0.956157i	$-0.405395\pi$
$61$	4.57452	0.585707	0.292853	+	0.956157i	$0.405395\pi$
$62$	−1.08840	−0.138227
$63$	−0.0630040	−0.00793776
$64$	−7.11142	−0.888927
$65$	−2.38787	−0.296179
$66$	1.50659	0.185448
$67$	4.63752	0.566563	0.283282	−	0.959037i	$-0.408577\pi$
$67$	4.63752	0.566563	0.283282	+	0.959037i	$0.408577\pi$
$68$	3.92478	0.475949
$69$	13.9248	1.67635
$70$	0.0507852	0.00607000
$71$	12.2496	1.45377	0.726883	−	0.686762i	$-0.240968\pi$
$71$	12.2496	1.45377	0.726883	+	0.686762i	$0.240968\pi$
$72$	−0.149031	−0.0175635
$73$	−15.0435	−1.76071	−0.880354	−	0.474318i	$-0.842695\pi$
$73$	−15.0435	−1.76071	−0.880354	+	0.474318i	$0.842695\pi$
$74$	0.468976	0.0545173
$75$	−7.28726	−0.841460
$76$	−13.0254	−1.49412
$77$	−1.50659	−0.171692
$78$	−0.962389	−0.108969
$79$	8.71274	0.980260	0.490130	−	0.871649i	$-0.336949\pi$
$79$	8.71274	0.980260	0.490130	+	0.871649i	$0.336949\pi$
$80$	−3.04349	−0.340273
$81$	−8.38058	−0.931175
$82$	−0.193937	−0.0214167
$83$	−6.70052	−0.735478	−0.367739	−	0.929929i	$-0.619868\pi$
$83$	−6.70052	−0.735478	−0.367739	+	0.929929i	$0.619868\pi$
$84$	−1.06793	−0.116521
$85$	1.61213	0.174860
$86$	0.962389	0.103777
$87$	−8.96239	−0.960869
$88$	−3.56371	−0.379893
$89$	12.2374	1.29716	0.648582	−	0.761144i	$-0.275362\pi$
$89$	12.2374	1.29716	0.648582	+	0.761144i	$0.275362\pi$
$90$	−0.0303172	−0.00319571
$91$	0.962389	0.100886
$92$	−16.3127	−1.70071
$93$	9.40105	0.974843
$94$	1.13681	0.117253
$95$	−5.35026	−0.548925
$96$	−3.80114	−0.387952
$97$	8.70052	0.883404	0.441702	−	0.897162i	$-0.354375\pi$
$97$	8.70052	0.883404	0.441702	+	0.897162i	$0.354375\pi$
$98$	1.33709	0.135066
$99$	0.899385	0.0903916
$100$	8.53690	0.853690
$101$	−4.88717	−0.486291	−0.243146	−	0.969990i	$-0.578179\pi$
$101$	−4.88717	−0.486291	−0.243146	+	0.969990i	$0.578179\pi$
$102$	0.649738	0.0643337
$103$	−5.79877	−0.571370	−0.285685	−	0.958324i	$-0.592221\pi$
$103$	−5.79877	−0.571370	−0.285685	+	0.958324i	$0.592221\pi$
$104$	2.27645	0.223225
$105$	−0.438658	−0.0428087
$106$	0.261865	0.0254346
$107$	−4.77575	−0.461689	−0.230844	−	0.972991i	$-0.574149\pi$
$107$	−4.77575	−0.461689	−0.230844	+	0.972991i	$0.574149\pi$
$108$	10.4993	1.01029
$109$	−6.18664	−0.592573	−0.296286	−	0.955099i	$-0.595748\pi$
$109$	−6.18664	−0.592573	−0.296286	+	0.955099i	$0.595748\pi$
$110$	−0.724961	−0.0691223
$111$	−4.05079	−0.384484
$112$	1.22662	0.115905
$113$	15.8192	1.48815	0.744074	−	0.668097i	$-0.232891\pi$
$113$	15.8192	1.48815	0.744074	+	0.668097i	$0.232891\pi$
$114$	−2.15633	−0.201958
$115$	−6.70052	−0.624827
$116$	10.4993	0.974835
$117$	−0.574515	−0.0531140
$118$	−0.836381	−0.0769951
$119$	−0.649738	−0.0595614
$120$	−1.03761	−0.0947205
$121$	10.5066	0.955144
$122$	−0.887166	−0.0803202
$123$	1.67513	0.151041
$124$	−11.0132	−0.989012
$125$	7.53690	0.674121
$126$	0.0122188	0.00108854
$127$	12.3127	1.09257	0.546286	−	0.837599i	$-0.316041\pi$
$127$	12.3127	1.09257	0.546286	+	0.837599i	$0.316041\pi$
$128$	5.91748	0.523037
$129$	−8.31265	−0.731888
$130$	0.463096	0.0406162
$131$	−10.5745	−0.923900	−0.461950	−	0.886906i	$-0.652850\pi$
$131$	−10.5745	−0.923900	−0.461950	+	0.886906i	$0.652850\pi$
$132$	15.2447	1.32688
$133$	2.15633	0.186977
$134$	−0.899385	−0.0776950
$135$	4.31265	0.371174
$136$	−1.53690	−0.131788
$137$	19.4010	1.65754	0.828772	−	0.559587i	$-0.189040\pi$
$137$	19.4010	1.65754	0.828772	+	0.559587i	$0.189040\pi$
$138$	−2.70052	−0.229884
$139$	−9.86414	−0.836666	−0.418333	−	0.908294i	$-0.637385\pi$
$139$	−9.86414	−0.836666	−0.418333	+	0.908294i	$0.637385\pi$
$140$	0.513881	0.0434309
$141$	−9.81924	−0.826929
$142$	−2.37565	−0.199360
$143$	−13.7381	−1.14884
$144$	−0.732255	−0.0610213
$145$	4.31265	0.358146
$146$	2.91748	0.241453
$147$	−11.5491	−0.952556
$148$	4.74543	0.390072
$149$	−13.9756	−1.14492	−0.572461	−	0.819932i	$-0.694011\pi$
$149$	−13.9756	−1.14492	−0.572461	+	0.819932i	$0.694011\pi$
$150$	1.41327	0.115393
$151$	7.10062	0.577840	0.288920	−	0.957353i	$-0.406704\pi$
$151$	7.10062	0.577840	0.288920	+	0.957353i	$0.406704\pi$
$152$	5.10062	0.413715
$153$	0.387873	0.0313577
$154$	0.292182	0.0235447
$155$	−4.52373	−0.363355
$156$	−9.73813	−0.779675
$157$	−14.4387	−1.15233	−0.576165	−	0.817333i	$-0.695452\pi$
$157$	−14.4387	−1.15233	−0.576165	+	0.817333i	$0.695452\pi$
$158$	−1.68972	−0.134427
$159$	−2.26187	−0.179378
$160$	1.82909	0.144602
$161$	2.70052	0.212831
$162$	1.62530	0.127696
$163$	1.92478	0.150760	0.0753801	−	0.997155i	$-0.475983\pi$
$163$	1.92478	0.150760	0.0753801	+	0.997155i	$0.475983\pi$
$164$	−1.96239	−0.153237
$165$	6.26187	0.487486
$166$	1.29948	0.100859
$167$	−6.06300	−0.469169	−0.234585	−	0.972096i	$-0.575373\pi$
$167$	−6.06300	−0.469169	−0.234585	+	0.972096i	$0.575373\pi$
$168$	0.418190	0.0322641
$169$	−4.22425	−0.324943
$170$	−0.312650	−0.0239792
$171$	−1.28726	−0.0984391
$172$	9.73813	0.742526
$173$	−16.7005	−1.26972	−0.634859	−	0.772628i	$-0.718942\pi$
$173$	−16.7005	−1.26972	−0.634859	+	0.772628i	$0.718942\pi$
$174$	1.73813	0.131768
$175$	−1.41327	−0.106833
$176$	−17.5101	−1.31987
$177$	7.22425	0.543008
$178$	−2.37328	−0.177885
$179$	−2.12364	−0.158728	−0.0793641	−	0.996846i	$-0.525289\pi$
$179$	−2.12364	−0.158728	−0.0793641	+	0.996846i	$0.525289\pi$
$180$	−0.306771	−0.0228653
$181$	5.97556	0.444160	0.222080	−	0.975028i	$-0.428715\pi$
$181$	5.97556	0.444160	0.222080	+	0.975028i	$0.428715\pi$
$182$	−0.186642	−0.0138349
$183$	7.66291	0.566459
$184$	6.38787	0.470920
$185$	1.94921	0.143309
$186$	−1.82321	−0.133684
$187$	9.27504	0.678258
$188$	11.5031	0.838948
$189$	−1.73813	−0.126431
$190$	1.03761	0.0752762
$191$	7.73577	0.559740	0.279870	−	0.960038i	$-0.409709\pi$
$191$	7.73577	0.559740	0.279870	+	0.960038i	$0.409709\pi$
$192$	−11.9126	−0.859715
$193$	−1.68735	−0.121458	−0.0607290	−	0.998154i	$-0.519343\pi$
$193$	−1.68735	−0.121458	−0.0607290	+	0.998154i	$0.519343\pi$
$194$	−1.68735	−0.121145
$195$	−4.00000	−0.286446
$196$	13.5296	0.966401
$197$	20.5745	1.46587	0.732937	−	0.680297i	$-0.238149\pi$
$197$	20.5745	1.46587	0.732937	+	0.680297i	$0.238149\pi$
$198$	−0.174424	−0.0123957
$199$	10.5867	0.750474	0.375237	−	0.926929i	$-0.377561\pi$
$199$	10.5867	0.750474	0.375237	+	0.926929i	$0.377561\pi$
$200$	−3.34297	−0.236384
$201$	7.76845	0.547944
$202$	0.947800	0.0666870
$203$	−1.73813	−0.121993
$204$	6.57452	0.460308
$205$	−0.806063	−0.0562979
$206$	1.12459	0.0783541
$207$	−1.61213	−0.112051
$208$	11.1852	0.775556
$209$	−30.7816	−2.12921
$210$	0.0850719	0.00587052
$211$	7.80114	0.537053	0.268526	−	0.963272i	$-0.413463\pi$
$211$	7.80114	0.537053	0.268526	+	0.963272i	$0.413463\pi$
$212$	2.64974	0.181985
$213$	20.5198	1.40599
$214$	0.926192	0.0633132
$215$	4.00000	0.272798
$216$	−4.11142	−0.279747
$217$	1.82321	0.123767
$218$	1.19982	0.0812618
$219$	−25.1998	−1.70285
$220$	−7.33567	−0.494571
$221$	−5.92478	−0.398544
$222$	0.785595	0.0527257
$223$	−3.22425	−0.215912	−0.107956	−	0.994156i	$-0.534431\pi$
$223$	−3.22425	−0.215912	−0.107956	+	0.994156i	$0.534431\pi$
$224$	−0.737180	−0.0492549
$225$	0.843675	0.0562450
$226$	−3.06793	−0.204076
$227$	8.24965	0.547548	0.273774	−	0.961794i	$-0.411728\pi$
$227$	8.24965	0.547548	0.273774	+	0.961794i	$0.411728\pi$
$228$	−21.8192	−1.44501
$229$	−4.51388	−0.298286	−0.149143	−	0.988816i	$-0.547651\pi$
$229$	−4.51388	−0.298286	−0.149143	+	0.988816i	$0.547651\pi$
$230$	1.29948	0.0856849
$231$	−2.52373	−0.166049
$232$	−4.11142	−0.269928
$233$	−12.5501	−0.822183	−0.411091	−	0.911594i	$-0.634852\pi$
$233$	−12.5501	−0.822183	−0.411091	+	0.911594i	$0.634852\pi$
$234$	0.111420	0.00728372
$235$	4.72496	0.308222
$236$	−8.46310	−0.550901
$237$	14.5950	0.948046
$238$	0.126008	0.00816789
$239$	17.3380	1.12150	0.560752	−	0.827984i	$-0.310512\pi$
$239$	17.3380	1.12150	0.560752	+	0.827984i	$0.310512\pi$
$240$	−5.09825	−0.329090
$241$	18.7513	1.20788	0.603939	−	0.797031i	$-0.293597\pi$
$241$	18.7513	1.20788	0.603939	+	0.797031i	$0.293597\pi$
$242$	−2.03761	−0.130983
$243$	2.01222	0.129084
$244$	−8.97698	−0.574692
$245$	5.55737	0.355047
$246$	−0.324869	−0.0207129
$247$	19.6629	1.25112
$248$	4.31265	0.273854
$249$	−11.2243	−0.711308
$250$	−1.46168	−0.0924448
$251$	−5.42548	−0.342454	−0.171227	−	0.985232i	$-0.554773\pi$
$251$	−5.42548	−0.342454	−0.171227	+	0.985232i	$0.554773\pi$
$252$	0.123638	0.00778848
$253$	−38.5501	−2.42362
$254$	−2.38787	−0.149828
$255$	2.70052	0.169113
$256$	13.0752	0.817201
$257$	−11.4617	−0.714960	−0.357480	−	0.933921i	$-0.616364\pi$
$257$	−11.4617	−0.714960	−0.357480	+	0.933921i	$0.616364\pi$
$258$	1.61213	0.100367
$259$	−0.785595	−0.0488145
$260$	4.68594	0.290609
$261$	1.03761	0.0642265
$262$	2.05079	0.126698
$263$	−26.2760	−1.62025	−0.810124	−	0.586259i	$-0.800600\pi$
$263$	−26.2760	−1.62025	−0.810124	+	0.586259i	$0.800600\pi$
$264$	−5.96968	−0.367409
$265$	1.08840	0.0668597
$266$	−0.418190	−0.0256409
$267$	20.4993	1.25454
$268$	−9.10062	−0.555909
$269$	21.1998	1.29258	0.646288	−	0.763094i	$-0.276321\pi$
$269$	21.1998	1.29258	0.646288	+	0.763094i	$0.276321\pi$
$270$	−0.836381	−0.0509005
$271$	−1.61213	−0.0979297	−0.0489649	−	0.998801i	$-0.515592\pi$
$271$	−1.61213	−0.0979297	−0.0489649	+	0.998801i	$0.515592\pi$
$272$	−7.55149	−0.457876
$273$	1.61213	0.0975704
$274$	−3.76257	−0.227305
$275$	20.1744	1.21656
$276$	−27.3258	−1.64482
$277$	−21.7440	−1.30647	−0.653236	−	0.757155i	$-0.726589\pi$
$277$	−21.7440	−1.30647	−0.653236	+	0.757155i	$0.726589\pi$
$278$	1.91302	0.114735
$279$	−1.08840	−0.0651606
$280$	−0.201231	−0.0120258
$281$	19.9248	1.18861	0.594306	−	0.804239i	$-0.297427\pi$
$281$	19.9248	1.18861	0.594306	+	0.804239i	$0.297427\pi$
$282$	1.90431	0.113400
$283$	−21.7137	−1.29075	−0.645373	−	0.763868i	$-0.723298\pi$
$283$	−21.7137	−1.29075	−0.645373	+	0.763868i	$0.723298\pi$
$284$	−24.0386	−1.42643
$285$	−8.96239	−0.530886
$286$	2.66433	0.157545
$287$	0.324869	0.0191764
$288$	0.440073	0.0259315
$289$	−13.0000	−0.764706
$290$	−0.836381	−0.0491140
$291$	14.5745	0.854373
$292$	29.5212	1.72760
$293$	32.4241	1.89423	0.947117	−	0.320888i	$-0.103981\pi$
$293$	32.4241	1.89423	0.947117	+	0.320888i	$0.103981\pi$
$294$	2.23980	0.130628
$295$	−3.47627	−0.202396
$296$	−1.85826	−0.108009
$297$	24.8119	1.43973
$298$	2.71037	0.157008
$299$	24.6253	1.42412
$300$	14.3004	0.825636
$301$	−1.61213	−0.0929214
$302$	−1.37707	−0.0792414
$303$	−8.18664	−0.470310
$304$	25.0616	1.43738
$305$	−3.68735	−0.211137
$306$	−0.0752228	−0.00430020
$307$	−9.42548	−0.537941	−0.268970	−	0.963148i	$-0.586683\pi$
$307$	−9.42548	−0.537941	−0.268970	+	0.963148i	$0.586683\pi$
$308$	2.95651	0.168463
$309$	−9.71370	−0.552593
$310$	0.877317	0.0498282
$311$	26.2252	1.48710	0.743548	−	0.668683i	$-0.233142\pi$
$311$	26.2252	1.48710	0.743548	+	0.668683i	$0.233142\pi$
$312$	3.81336	0.215889
$313$	3.46168	0.195666	0.0978329	−	0.995203i	$-0.468809\pi$
$313$	3.46168	0.195666	0.0978329	+	0.995203i	$0.468809\pi$
$314$	2.80018	0.158024
$315$	0.0507852	0.00286142
$316$	−17.0978	−0.961826
$317$	−18.1866	−1.02146	−0.510732	−	0.859740i	$-0.670625\pi$
$317$	−18.1866	−1.02146	−0.510732	+	0.859740i	$0.670625\pi$
$318$	0.438658	0.0245987
$319$	24.8119	1.38920
$320$	5.73226	0.320443
$321$	−8.00000	−0.446516
$322$	−0.523730	−0.0291863
$323$	−13.2750	−0.738643
$324$	16.4460	0.913664
$325$	−12.8872	−0.714851
$326$	−0.373285	−0.0206743
$327$	−10.3634	−0.573099
$328$	0.768452	0.0424307
$329$	−1.90431	−0.104988
$330$	−1.21440	−0.0668508
$331$	−24.7997	−1.36312	−0.681558	−	0.731764i	$-0.738697\pi$
$331$	−24.7997	−1.36312	−0.681558	+	0.731764i	$0.738697\pi$
$332$	13.1490	0.721647
$333$	0.468976	0.0256997
$334$	1.17584	0.0643390
$335$	−3.73813	−0.204236
$336$	2.05475	0.112096
$337$	−18.6702	−1.01703	−0.508515	−	0.861053i	$-0.669806\pi$
$337$	−18.6702	−1.01703	−0.508515	+	0.861053i	$0.669806\pi$
$338$	0.819237	0.0445606
$339$	26.4993	1.43924
$340$	−3.16362	−0.171571
$341$	−26.0263	−1.40941
$342$	0.249646	0.0134993
$343$	−4.51388	−0.243727
$344$	−3.81336	−0.205602
$345$	−11.2243	−0.604294
$346$	3.23884	0.174121
$347$	−11.9126	−0.639500	−0.319750	−	0.947502i	$-0.603599\pi$
$347$	−11.9126	−0.639500	−0.319750	+	0.947502i	$0.603599\pi$
$348$	17.5877	0.942799
$349$	−16.8061	−0.899608	−0.449804	−	0.893127i	$-0.648506\pi$
$349$	−16.8061	−0.899608	−0.449804	+	0.893127i	$0.648506\pi$
$350$	0.274084	0.0146504
$351$	−15.8496	−0.845987
$352$	10.5233	0.560892
$353$	13.7440	0.731520	0.365760	−	0.930709i	$-0.380809\pi$
$353$	13.7440	0.731520	0.365760	+	0.930709i	$0.380809\pi$
$354$	−1.40105	−0.0744648
$355$	−9.87399	−0.524057
$356$	−24.0146	−1.27277
$357$	−1.08840	−0.0576041
$358$	0.411851	0.0217670
$359$	−23.0738	−1.21779	−0.608895	−	0.793251i	$-0.708387\pi$
$359$	−23.0738	−1.21779	−0.608895	+	0.793251i	$0.708387\pi$
$360$	0.120128	0.00633132
$361$	25.0567	1.31877
$362$	−1.15888	−0.0609094
$363$	17.5999	0.923756
$364$	−1.88858	−0.0989885
$365$	12.1260	0.634704
$366$	−1.48612	−0.0776807
$367$	−22.3634	−1.16736	−0.583681	−	0.811983i	$-0.698388\pi$
$367$	−22.3634	−1.16736	−0.583681	+	0.811983i	$0.698388\pi$
$368$	31.3865	1.63613
$369$	−0.193937	−0.0100959
$370$	−0.378024	−0.0196525
$371$	−0.438658	−0.0227740
$372$	−18.4485	−0.956511
$373$	−4.59895	−0.238125	−0.119062	−	0.992887i	$-0.537989\pi$
$373$	−4.59895	−0.238125	−0.119062	+	0.992887i	$0.537989\pi$
$374$	−1.79877	−0.0930121
$375$	12.6253	0.651968
$376$	−4.50449	−0.232301
$377$	−15.8496	−0.816294
$378$	0.337088	0.0173379
$379$	8.46310	0.434720	0.217360	−	0.976092i	$-0.430255\pi$
$379$	8.46310	0.434720	0.217360	+	0.976092i	$0.430255\pi$
$380$	10.4993	0.538602
$381$	20.6253	1.05667
$382$	−1.50025	−0.0767594
$383$	−11.8011	−0.603010	−0.301505	−	0.953465i	$-0.597489\pi$
$383$	−11.8011	−0.603010	−0.301505	+	0.953465i	$0.597489\pi$
$384$	9.91256	0.505848
$385$	1.21440	0.0618918
$386$	0.327239	0.0166560
$387$	0.962389	0.0489210
$388$	−17.0738	−0.866791
$389$	6.25202	0.316990	0.158495	−	0.987360i	$-0.449336\pi$
$389$	6.25202	0.316990	0.158495	+	0.987360i	$0.449336\pi$
$390$	0.775746	0.0392814
$391$	−16.6253	−0.840778
$392$	−5.29806	−0.267593
$393$	−17.7137	−0.893538
$394$	−3.99015	−0.201021
$395$	−7.02302	−0.353367
$396$	−1.76494	−0.0886917
$397$	17.6629	0.886476	0.443238	−	0.896404i	$-0.353830\pi$
$397$	17.6629	0.886476	0.443238	+	0.896404i	$0.353830\pi$
$398$	−2.05315	−0.102915
$399$	3.61213	0.180833
$400$	−16.4255	−0.821274
$401$	−7.44595	−0.371833	−0.185917	−	0.982566i	$-0.559525\pi$
$401$	−7.44595	−0.371833	−0.185917	+	0.982566i	$0.559525\pi$
$402$	−1.50659	−0.0751417
$403$	16.6253	0.828165
$404$	9.59052	0.477146
$405$	6.75528	0.335672
$406$	0.337088	0.0167294
$407$	11.2144	0.555877
$408$	−2.57452	−0.127458
$409$	−10.9829	−0.543067	−0.271534	−	0.962429i	$-0.587531\pi$
$409$	−10.9829	−0.543067	−0.271534	+	0.962429i	$0.587531\pi$
$410$	0.156325	0.00772035
$411$	32.4993	1.60307
$412$	11.3794	0.560625
$413$	1.40105	0.0689410
$414$	0.312650	0.0153659
$415$	5.40105	0.265127
$416$	−6.72213	−0.329580
$417$	−16.5237	−0.809171
$418$	5.96968	0.291987
$419$	0.0653737	0.00319371	0.00159686	−	0.999999i	$-0.499492\pi$
$419$	0.0653737	0.00319371	0.00159686	+	0.999999i	$0.499492\pi$
$420$	0.860818	0.0420036
$421$	11.7988	0.575037	0.287518	−	0.957775i	$-0.407170\pi$
$421$	11.7988	0.575037	0.287518	+	0.957775i	$0.407170\pi$
$422$	−1.51293	−0.0736481
$423$	1.13681	0.0552737
$424$	−1.03761	−0.0503909
$425$	8.70052	0.422037
$426$	−3.97953	−0.192809
$427$	1.48612	0.0719183
$428$	9.37187	0.453006
$429$	−23.0132	−1.11109
$430$	−0.775746	−0.0374098
$431$	20.2882	0.977249	0.488624	−	0.872494i	$-0.337499\pi$
$431$	20.2882	0.977249	0.488624	+	0.872494i	$0.337499\pi$
$432$	−20.2012	−0.971932
$433$	−31.8759	−1.53186	−0.765929	−	0.642925i	$-0.777721\pi$
$433$	−31.8759	−1.53186	−0.765929	+	0.642925i	$0.777721\pi$
$434$	−0.353586	−0.0169727
$435$	7.22425	0.346376
$436$	12.1406	0.581429
$437$	55.1754	2.63940
$438$	4.88717	0.233518
$439$	41.5148	1.98140	0.990698	−	0.136082i	$-0.0434512\pi$
$439$	41.5148	1.98140	0.990698	+	0.136082i	$0.0434512\pi$
$440$	2.87258	0.136945
$441$	1.33709	0.0636709
$442$	1.14903	0.0546538
$443$	37.2750	1.77099	0.885495	−	0.464648i	$-0.153819\pi$
$443$	37.2750	1.77099	0.885495	+	0.464648i	$0.153819\pi$
$444$	7.94921	0.377253
$445$	−9.86414	−0.467605
$446$	0.625301	0.0296088
$447$	−23.4109	−1.10730
$448$	−2.31028	−0.109151
$449$	−3.27504	−0.154559	−0.0772793	−	0.997009i	$-0.524623\pi$
$449$	−3.27504	−0.154559	−0.0772793	+	0.997009i	$0.524623\pi$
$450$	−0.163619	−0.00771309
$451$	−4.63752	−0.218372
$452$	−31.0435	−1.46016
$453$	11.8945	0.558850
$454$	−1.59991	−0.0750874
$455$	−0.775746	−0.0363675
$456$	8.54420	0.400119
$457$	−10.6253	−0.497031	−0.248515	−	0.968628i	$-0.579943\pi$
$457$	−10.6253	−0.497031	−0.248515	+	0.968628i	$0.579943\pi$
$458$	0.875407	0.0409051
$459$	10.7005	0.499458
$460$	13.1490	0.613077
$461$	−27.0435	−1.25954	−0.629770	−	0.776781i	$-0.716851\pi$
$461$	−27.0435	−1.25954	−0.629770	+	0.776781i	$0.716851\pi$
$462$	0.489444	0.0227710
$463$	2.57689	0.119758	0.0598790	−	0.998206i	$-0.480929\pi$
$463$	2.57689	0.119758	0.0598790	+	0.998206i	$0.480929\pi$
$464$	−20.2012	−0.937819
$465$	−7.57784	−0.351414
$466$	2.43392	0.112749
$467$	−18.3879	−0.850889	−0.425445	−	0.904984i	$-0.639882\pi$
$467$	−18.3879	−0.850889	−0.425445	+	0.904984i	$0.639882\pi$
$468$	1.12742	0.0521151
$469$	1.50659	0.0695677
$470$	−0.916343	−0.0422677
$471$	−24.1866	−1.11446
$472$	3.31406	0.152542
$473$	23.0132	1.05815
$474$	−2.83050	−0.130009
$475$	−28.8749	−1.32487
$476$	1.27504	0.0584413
$477$	0.261865	0.0119900
$478$	−3.36248	−0.153796
$479$	−16.3004	−0.744786	−0.372393	−	0.928075i	$-0.621463\pi$
$479$	−16.3004	−0.744786	−0.372393	+	0.928075i	$0.621463\pi$
$480$	3.06396	0.139850
$481$	−7.16362	−0.326633
$482$	−3.63656	−0.165641
$483$	4.52373	0.205837
$484$	−20.6180	−0.937182
$485$	−7.01317	−0.318452
$486$	−0.390243	−0.0177018
$487$	1.54675	0.0700901	0.0350450	−	0.999386i	$-0.488843\pi$
$487$	1.54675	0.0700901	0.0350450	+	0.999386i	$0.488843\pi$
$488$	3.51530	0.159130
$489$	3.22425	0.145806
$490$	−1.07778	−0.0486890
$491$	−15.7889	−0.712544	−0.356272	−	0.934382i	$-0.615952\pi$
$491$	−15.7889	−0.712544	−0.356272	+	0.934382i	$0.615952\pi$
$492$	−3.28726	−0.148201
$493$	10.7005	0.481927
$494$	−3.81336	−0.171571
$495$	−0.724961	−0.0325846
$496$	21.1900	0.951458
$497$	3.97953	0.178506
$498$	2.17679	0.0975444
$499$	17.6751	0.791248	0.395624	−	0.918413i	$-0.370528\pi$
$499$	17.6751	0.791248	0.395624	+	0.918413i	$0.370528\pi$
$500$	−14.7903	−0.661444
$501$	−10.1563	−0.453751
$502$	1.05220	0.0469620
$503$	6.48707	0.289244	0.144622	−	0.989487i	$-0.453803\pi$
$503$	6.48707	0.289244	0.144622	+	0.989487i	$0.453803\pi$
$504$	−0.0484156	−0.00215660
$505$	3.93937	0.175299
$506$	7.47627	0.332361
$507$	−7.07618	−0.314264
$508$	−24.1622	−1.07202
$509$	0.363436	0.0161090	0.00805450	−	0.999968i	$-0.497436\pi$
$509$	0.363436	0.0161090	0.00805450	+	0.999968i	$0.497436\pi$
$510$	−0.523730	−0.0231912
$511$	−4.88717	−0.216195
$512$	−14.3707	−0.635103
$513$	−35.5125	−1.56791
$514$	2.22284	0.0980452
$515$	4.67418	0.205969
$516$	16.3127	0.718124
$517$	27.1841	1.19555
$518$	0.152356	0.00669412
$519$	−27.9756	−1.22799
$520$	−1.83497	−0.0804686
$521$	−8.13586	−0.356438	−0.178219	−	0.983991i	$-0.557034\pi$
$521$	−8.13586	−0.356438	−0.178219	+	0.983991i	$0.557034\pi$
$522$	−0.201231	−0.00880763
$523$	35.6991	1.56101	0.780507	−	0.625148i	$-0.214961\pi$
$523$	35.6991	1.56101	0.780507	+	0.625148i	$0.214961\pi$
$524$	20.7513	0.906525
$525$	−2.36741	−0.103322
$526$	5.09588	0.222191
$527$	−11.2243	−0.488936
$528$	−29.3317	−1.27650
$529$	46.1002	2.00435
$530$	−0.211080	−0.00916873
$531$	−0.836381	−0.0362958
$532$	−4.23155	−0.183461
$533$	2.96239	0.128315
$534$	−3.97556	−0.172039
$535$	3.84955	0.166431
$536$	3.56371	0.153929
$537$	−3.55737	−0.153512
$538$	−4.11142	−0.177256
$539$	31.9732	1.37718
$540$	−8.46310	−0.364194
$541$	25.4920	1.09599	0.547993	−	0.836483i	$-0.315392\pi$
$541$	25.4920	1.09599	0.547993	+	0.836483i	$0.315392\pi$
$542$	0.312650	0.0134295
$543$	10.0098	0.429564
$544$	4.53832	0.194579
$545$	4.98683	0.213612
$546$	−0.312650	−0.0133802
$547$	−3.96143	−0.169379	−0.0846893	−	0.996407i	$-0.526990\pi$
$547$	−3.96143	−0.169379	−0.0846893	+	0.996407i	$0.526990\pi$
$548$	−38.0724	−1.62637
$549$	−0.887166	−0.0378633
$550$	−3.91256	−0.166832
$551$	−35.5125	−1.51288
$552$	10.7005	0.455445
$553$	2.83050	0.120365
$554$	4.21696	0.179161
$555$	3.26519	0.138600
$556$	19.3573	0.820932
$557$	−13.8740	−0.587860	−0.293930	−	0.955827i	$-0.594963\pi$
$557$	−13.8740	−0.587860	−0.293930	+	0.955827i	$0.594963\pi$
$558$	0.211080	0.00893572
$559$	−14.7005	−0.621766
$560$	−0.988736	−0.0417817
$561$	15.5369	0.655969
$562$	−3.86414	−0.162999
$563$	12.9140	0.544259	0.272130	−	0.962261i	$-0.412272\pi$
$563$	12.9140	0.544259	0.272130	+	0.962261i	$0.412272\pi$
$564$	19.2692	0.811378
$565$	−12.7513	−0.536452
$566$	4.21108	0.177005
$567$	−2.72259	−0.114338
$568$	9.41327	0.394972
$569$	7.50659	0.314692	0.157346	−	0.987543i	$-0.449706\pi$
$569$	7.50659	0.314692	0.157346	+	0.987543i	$0.449706\pi$
$570$	1.73813	0.0728025
$571$	35.6869	1.49345	0.746725	−	0.665133i	$-0.231625\pi$
$571$	35.6869	1.49345	0.746725	+	0.665133i	$0.231625\pi$
$572$	26.9596	1.12724
$573$	12.9584	0.541346
$574$	−0.0630040	−0.00262974
$575$	−36.1622	−1.50807
$576$	1.37916	0.0574652
$577$	−16.4485	−0.684760	−0.342380	−	0.939562i	$-0.611233\pi$
$577$	−16.4485	−0.684760	−0.342380	+	0.939562i	$0.611233\pi$
$578$	2.52118	0.104867
$579$	−2.82653	−0.117467
$580$	−8.46310	−0.351411
$581$	−2.17679	−0.0903086
$582$	−2.82653	−0.117163
$583$	6.26187	0.259340
$584$	−11.5602	−0.478365
$585$	0.463096	0.0191467
$586$	−6.28821	−0.259764
$587$	−4.32487	−0.178506	−0.0892532	−	0.996009i	$-0.528448\pi$
$587$	−4.32487	−0.178506	−0.0892532	+	0.996009i	$0.528448\pi$
$588$	22.6639	0.934642
$589$	37.2506	1.53488
$590$	0.674176	0.0277554
$591$	34.4650	1.41770
$592$	−9.13047	−0.375260
$593$	−10.7151	−0.440017	−0.220008	−	0.975498i	$-0.570608\pi$
$593$	−10.7151	−0.440017	−0.220008	+	0.975498i	$0.570608\pi$
$594$	−4.81194	−0.197436
$595$	0.523730	0.0214708
$596$	27.4255	1.12339
$597$	17.7342	0.725811
$598$	−4.77575	−0.195295
$599$	−48.7875	−1.99340	−0.996702	−	0.0811523i	$-0.974140\pi$
$599$	−48.7875	−1.99340	−0.996702	+	0.0811523i	$0.974140\pi$
$600$	−5.59991	−0.228615
$601$	7.55149	0.308032	0.154016	−	0.988068i	$-0.450779\pi$
$601$	7.55149	0.308032	0.154016	+	0.988068i	$0.450779\pi$
$602$	0.312650	0.0127427
$603$	−0.899385	−0.0366258
$604$	−13.9342	−0.566973
$605$	−8.46898	−0.344313
$606$	1.58769	0.0644955
$607$	−22.6351	−0.918732	−0.459366	−	0.888247i	$-0.651923\pi$
$607$	−22.6351	−0.918732	−0.459366	+	0.888247i	$0.651923\pi$
$608$	−15.0616	−0.610828
$609$	−2.91160	−0.117984
$610$	0.715112	0.0289540
$611$	−17.3649	−0.702507
$612$	−0.761158	−0.0307680
$613$	28.5950	1.15494	0.577470	−	0.816412i	$-0.304040\pi$
$613$	28.5950	1.15494	0.577470	+	0.816412i	$0.304040\pi$
$614$	1.82795	0.0737699
$615$	−1.35026	−0.0544478
$616$	−1.15774	−0.0466467
$617$	30.7757	1.23898	0.619492	−	0.785003i	$-0.287338\pi$
$617$	30.7757	1.23898	0.619492	+	0.785003i	$0.287338\pi$
$618$	1.88384	0.0757792
$619$	−7.38646	−0.296887	−0.148443	−	0.988921i	$-0.547426\pi$
$619$	−7.38646	−0.296887	−0.148443	+	0.988921i	$0.547426\pi$
$620$	8.87732	0.356522
$621$	−44.4749	−1.78471
$622$	−5.08603	−0.203931
$623$	3.97556	0.159278
$624$	18.7367	0.750069
$625$	15.6761	0.627043
$626$	−0.671347	−0.0268324
$627$	−51.5633	−2.05924
$628$	28.3343	1.13066
$629$	4.83638	0.192839
$630$	−0.00984911	−0.000392398 0
$631$	3.37470	0.134345	0.0671723	−	0.997741i	$-0.478602\pi$
$631$	3.37470	0.134345	0.0671723	+	0.997741i	$0.478602\pi$
$632$	6.69532	0.266326
$633$	13.0679	0.519404
$634$	3.52705	0.140077
$635$	−9.92478	−0.393853
$636$	4.43866	0.176004
$637$	−20.4241	−0.809231
$638$	−4.81194	−0.190507
$639$	−2.37565	−0.0939794
$640$	−4.76987	−0.188546
$641$	6.31265	0.249335	0.124667	−	0.992199i	$-0.460214\pi$
$641$	6.31265	0.249335	0.124667	+	0.992199i	$0.460214\pi$
$642$	1.55149	0.0612325
$643$	−22.5017	−0.887379	−0.443689	−	0.896181i	$-0.646331\pi$
$643$	−22.5017	−0.887379	−0.443689	+	0.896181i	$0.646331\pi$
$644$	−5.29948	−0.208829
$645$	6.70052	0.263833
$646$	2.57452	0.101293
$647$	−32.4993	−1.27768	−0.638840	−	0.769340i	$-0.720585\pi$
$647$	−32.4993	−1.27768	−0.638840	+	0.769340i	$0.720585\pi$
$648$	−6.44007	−0.252990
$649$	−20.0000	−0.785069
$650$	2.49929	0.0980303
$651$	3.05411	0.119700
$652$	−3.77716	−0.147925
$653$	−11.2144	−0.438854	−0.219427	−	0.975629i	$-0.570419\pi$
$653$	−11.2144	−0.438854	−0.219427	+	0.975629i	$0.570419\pi$
$654$	2.00985	0.0785913
$655$	8.52373	0.333050
$656$	3.77575	0.147418
$657$	2.91748	0.113822
$658$	0.369315	0.0143974
$659$	39.5101	1.53909	0.769547	−	0.638590i	$-0.220482\pi$
$659$	39.5101	1.53909	0.769547	+	0.638590i	$0.220482\pi$
$660$	−12.2882	−0.478318
$661$	−25.5329	−0.993116	−0.496558	−	0.868004i	$-0.665403\pi$
$661$	−25.5329	−0.993116	−0.496558	+	0.868004i	$0.665403\pi$
$662$	4.80957	0.186929
$663$	−9.92478	−0.385446
$664$	−5.14903	−0.199821
$665$	−1.73813	−0.0674020
$666$	−0.0909515	−0.00352430
$667$	−44.4749	−1.72207
$668$	11.8980	0.460346
$669$	−5.40105	−0.208817
$670$	0.724961	0.0280077
$671$	−21.2144	−0.818973
$672$	−1.23487	−0.0476362
$673$	−11.7137	−0.451530	−0.225765	−	0.974182i	$-0.572488\pi$
$673$	−11.7137	−0.451530	−0.225765	+	0.974182i	$0.572488\pi$
$674$	3.62084	0.139469
$675$	23.2750	0.895857
$676$	8.28963	0.318832
$677$	39.4168	1.51491	0.757455	−	0.652888i	$-0.226443\pi$
$677$	39.4168	1.51491	0.757455	+	0.652888i	$0.226443\pi$
$678$	−5.13918	−0.197369
$679$	2.82653	0.108472
$680$	1.23884	0.0475074
$681$	13.8192	0.529554
$682$	5.04746	0.193277
$683$	−19.6605	−0.752290	−0.376145	−	0.926561i	$-0.622751\pi$
$683$	−19.6605	−0.752290	−0.376145	+	0.926561i	$0.622751\pi$
$684$	2.52610	0.0965878
$685$	−15.6385	−0.597515
$686$	0.875407	0.0334232
$687$	−7.56134	−0.288483
$688$	−18.7367	−0.714331
$689$	−4.00000	−0.152388
$690$	2.17679	0.0828691
$691$	−13.4641	−0.512197	−0.256098	−	0.966651i	$-0.582437\pi$
$691$	−13.4641	−0.512197	−0.256098	+	0.966651i	$0.582437\pi$
$692$	32.7729	1.24584
$693$	0.292182	0.0110991
$694$	2.31028	0.0876971
$695$	7.95112	0.301603
$696$	−6.88717	−0.261057
$697$	−2.00000	−0.0757554
$698$	3.25931	0.123367
$699$	−21.0230	−0.795164
$700$	2.77338	0.104824
$701$	−39.8192	−1.50395	−0.751976	−	0.659191i	$-0.770899\pi$
$701$	−39.8192	−1.50395	−0.751976	+	0.659191i	$0.770899\pi$
$702$	3.07381	0.116013
$703$	−16.0508	−0.605367
$704$	32.9793	1.24296
$705$	7.91493	0.298093
$706$	−2.66547	−0.100316
$707$	−1.58769	−0.0597112
$708$	−14.1768	−0.532797
$709$	6.58910	0.247459	0.123729	−	0.992316i	$-0.460514\pi$
$709$	6.58910	0.247459	0.123729	+	0.992316i	$0.460514\pi$
$710$	1.91493	0.0718660
$711$	−1.68972	−0.0633694
$712$	9.40388	0.352425
$713$	46.6516	1.74712
$714$	0.211080	0.00789947
$715$	11.0738	0.414137
$716$	4.16740	0.155743
$717$	29.0435	1.08465
$718$	4.47486	0.167000
$719$	44.3874	1.65537	0.827686	−	0.561192i	$-0.189657\pi$
$719$	44.3874	1.65537	0.827686	+	0.561192i	$0.189657\pi$
$720$	0.590244	0.0219971
$721$	−1.88384	−0.0701579
$722$	−4.85940	−0.180848
$723$	31.4109	1.16818
$724$	−11.7264	−0.435807
$725$	23.2750	0.864413
$726$	−3.41327	−0.126678
$727$	35.6361	1.32167	0.660835	−	0.750531i	$-0.270202\pi$
$727$	35.6361	1.32167	0.660835	+	0.750531i	$0.270202\pi$
$728$	0.739549	0.0274095
$729$	28.5125	1.05602
$730$	−2.35168	−0.0870394
$731$	9.92478	0.367081
$732$	−15.0376	−0.555806
$733$	−16.5256	−0.610388	−0.305194	−	0.952290i	$-0.598721\pi$
$733$	−16.5256	−0.610388	−0.305194	+	0.952290i	$0.598721\pi$
$734$	4.33709	0.160085
$735$	9.30933	0.343380
$736$	−18.8627	−0.695289
$737$	−21.5066	−0.792205
$738$	0.0376114	0.00138449
$739$	30.7005	1.12934	0.564669	−	0.825318i	$-0.309004\pi$
$739$	30.7005	1.12934	0.564669	+	0.825318i	$0.309004\pi$
$740$	−3.82512	−0.140614
$741$	32.9380	1.21001
$742$	0.0850719	0.00312309
$743$	−39.9756	−1.46656	−0.733281	−	0.679926i	$-0.762012\pi$
$743$	−39.9756	−1.46656	−0.733281	+	0.679926i	$0.762012\pi$
$744$	7.22425	0.264854
$745$	11.2652	0.412725
$746$	0.891905	0.0326550
$747$	1.29948	0.0475454
$748$	−18.2012	−0.665503
$749$	−1.55149	−0.0566903
$750$	−2.44851	−0.0894069
$751$	21.4133	0.781381	0.390691	−	0.920522i	$-0.372236\pi$
$751$	21.4133	0.781381	0.390691	+	0.920522i	$0.372236\pi$
$752$	−22.1326	−0.807092
$753$	−9.08840	−0.331200
$754$	3.07381	0.111941
$755$	−5.72355	−0.208301
$756$	3.41090	0.124053
$757$	47.2868	1.71867	0.859334	−	0.511415i	$-0.170878\pi$
$757$	47.2868	1.71867	0.859334	+	0.511415i	$0.170878\pi$
$758$	−1.64130	−0.0596148
$759$	−64.5764	−2.34398
$760$	−4.11142	−0.149137
$761$	−6.20711	−0.225008	−0.112504	−	0.993651i	$-0.535887\pi$
$761$	−6.20711	−0.225008	−0.112504	+	0.993651i	$0.535887\pi$
$762$	−4.00000	−0.144905
$763$	−2.00985	−0.0727614
$764$	−15.1806	−0.549214
$765$	−0.312650	−0.0113039
$766$	2.28867	0.0826931
$767$	12.7757	0.461305
$768$	21.9027	0.790346
$769$	33.0738	1.19267	0.596336	−	0.802735i	$-0.296623\pi$
$769$	33.0738	1.19267	0.596336	+	0.802735i	$0.296623\pi$
$770$	−0.235517	−0.00848746
$771$	−19.1998	−0.691464
$772$	3.31124	0.119174
$773$	−24.4241	−0.878473	−0.439236	−	0.898372i	$-0.644751\pi$
$773$	−24.4241	−0.878473	−0.439236	+	0.898372i	$0.644751\pi$
$774$	−0.186642	−0.00670872
$775$	−24.4142	−0.876985
$776$	6.68594	0.240011
$777$	−1.31598	−0.0472103
$778$	−1.21249	−0.0434700
$779$	6.63752	0.237814
$780$	7.84955	0.281059
$781$	−56.8080	−2.03275
$782$	3.22425	0.115299
$783$	28.6253	1.02298
$784$	−26.0317	−0.929705
$785$	11.6385	0.415395
$786$	3.43533	0.122534
$787$	−21.7988	−0.777042	−0.388521	−	0.921440i	$-0.627014\pi$
$787$	−21.7988	−0.777042	−0.388521	+	0.921440i	$0.627014\pi$
$788$	−40.3752	−1.43831
$789$	−44.0157	−1.56700
$790$	1.36202	0.0484585
$791$	5.13918	0.182728
$792$	0.691134	0.0245584
$793$	13.5515	0.481228
$794$	−3.42548	−0.121566
$795$	1.82321	0.0646625
$796$	−20.7753	−0.736361
$797$	6.12601	0.216994	0.108497	−	0.994097i	$-0.465396\pi$
$797$	6.12601	0.216994	0.108497	+	0.994097i	$0.465396\pi$
$798$	−0.700523	−0.0247983
$799$	11.7235	0.414749
$800$	9.87144	0.349008
$801$	−2.37328	−0.0838559
$802$	1.44404	0.0509909
$803$	69.7645	2.46194
$804$	−15.2447	−0.537640
$805$	−2.17679	−0.0767219
$806$	−3.22425	−0.113569
$807$	35.5125	1.25010
$808$	−3.75555	−0.132120
$809$	−40.7005	−1.43095	−0.715477	−	0.698636i	$-0.753791\pi$
$809$	−40.7005	−1.43095	−0.715477	+	0.698636i	$0.753791\pi$
$810$	−1.31010	−0.0460321
$811$	−1.94921	−0.0684462	−0.0342231	−	0.999414i	$-0.510896\pi$
$811$	−1.94921	−0.0684462	−0.0342231	+	0.999414i	$0.510896\pi$
$812$	3.41090	0.119699
$813$	−2.70052	−0.0947115
$814$	−2.17488	−0.0762296
$815$	−1.55149	−0.0543464
$816$	−12.6497	−0.442829
$817$	−32.9380	−1.15235
$818$	2.12998	0.0744729
$819$	−0.186642	−0.00652181
$820$	1.58181	0.0552392
$821$	−25.3707	−0.885445	−0.442722	−	0.896659i	$-0.645987\pi$
$821$	−25.3707	−0.885445	−0.442722	+	0.896659i	$0.645987\pi$
$822$	−6.30280	−0.219835
$823$	5.48849	0.191317	0.0956583	−	0.995414i	$-0.469504\pi$
$823$	5.48849	0.191317	0.0956583	+	0.995414i	$0.469504\pi$
$824$	−4.45608	−0.155235
$825$	33.7948	1.17658
$826$	−0.271714	−0.00945415
$827$	44.3004	1.54048	0.770238	−	0.637756i	$-0.220137\pi$
$827$	44.3004	1.54048	0.770238	+	0.637756i	$0.220137\pi$
$828$	3.16362	0.109943
$829$	34.6213	1.20245	0.601224	−	0.799080i	$-0.294680\pi$
$829$	34.6213	1.20245	0.601224	+	0.799080i	$0.294680\pi$
$830$	−1.04746	−0.0363579
$831$	−36.4241	−1.26354
$832$	−21.0668	−0.730359
$833$	13.7889	0.477758
$834$	3.20456	0.110965
$835$	4.88717	0.169127
$836$	60.4055	2.08917
$837$	−30.0263	−1.03786
$838$	−0.0126783	−0.000437966 0
$839$	30.7489	1.06157	0.530786	−	0.847506i	$-0.321897\pi$
$839$	30.7489	1.06157	0.530786	+	0.847506i	$0.321897\pi$
$840$	−0.337088	−0.0116306
$841$	−0.374699	−0.0129207
$842$	−2.28821	−0.0788570
$843$	33.3766	1.14955
$844$	−15.3089	−0.526953
$845$	3.40502	0.117136
$846$	−0.220469	−0.00757990
$847$	3.41327	0.117281
$848$	−5.09825	−0.175074
$849$	−36.3733	−1.24833
$850$	−1.68735	−0.0578756
$851$	−20.1016	−0.689073
$852$	−40.2677	−1.37955
$853$	−57.0249	−1.95250	−0.976248	−	0.216655i	$-0.930485\pi$
$853$	−57.0249	−1.95250	−0.976248	+	0.216655i	$0.930485\pi$
$854$	−0.288213	−0.00986244
$855$	1.03761	0.0354856
$856$	−3.66993	−0.125436
$857$	−32.6067	−1.11383	−0.556913	−	0.830571i	$-0.688014\pi$
$857$	−32.6067	−1.11383	−0.556913	+	0.830571i	$0.688014\pi$
$858$	4.46310	0.152368
$859$	−21.9003	−0.747230	−0.373615	−	0.927584i	$-0.621882\pi$
$859$	−21.9003	−0.747230	−0.373615	+	0.927584i	$0.621882\pi$
$860$	−7.84955	−0.267668
$861$	0.544198	0.0185462
$862$	−3.93463	−0.134014
$863$	−8.03620	−0.273555	−0.136778	−	0.990602i	$-0.543675\pi$
$863$	−8.03620	−0.273555	−0.136778	+	0.990602i	$0.543675\pi$
$864$	12.1406	0.413031
$865$	13.4617	0.457711
$866$	6.18190	0.210070
$867$	−21.7767	−0.739576
$868$	−3.57784	−0.121440
$869$	−40.4055	−1.37066
$870$	−1.40105	−0.0474999
$871$	13.7381	0.465499
$872$	−4.75414	−0.160995
$873$	−1.68735	−0.0571081
$874$	−10.7005	−0.361951
$875$	2.44851	0.0827747
$876$	49.4518	1.67082
$877$	30.8726	1.04249	0.521246	−	0.853406i	$-0.325467\pi$
$877$	30.8726	1.04249	0.521246	+	0.853406i	$0.325467\pi$
$878$	−8.05124	−0.271716
$879$	54.3146	1.83198
$880$	14.1142	0.475791
$881$	21.7283	0.732045	0.366022	−	0.930606i	$-0.380719\pi$
$881$	21.7283	0.732045	0.366022	+	0.930606i	$0.380719\pi$
$882$	−0.259310	−0.00873143
$883$	−36.3465	−1.22316	−0.611578	−	0.791184i	$-0.709465\pi$
$883$	−36.3465	−1.22316	−0.611578	+	0.791184i	$0.709465\pi$
$884$	11.6267	0.391049
$885$	−5.82321	−0.195745
$886$	−7.22899	−0.242863
$887$	5.13681	0.172477	0.0862386	−	0.996275i	$-0.472515\pi$
$887$	5.13681	0.172477	0.0862386	+	0.996275i	$0.472515\pi$
$888$	−3.11283	−0.104460
$889$	4.00000	0.134156
$890$	1.91302	0.0641245
$891$	38.8651	1.30203
$892$	6.32724	0.211852
$893$	−38.9076	−1.30199
$894$	4.54023	0.151848
$895$	1.71179	0.0572187
$896$	1.92241	0.0642231
$897$	41.2506	1.37732
$898$	0.635150	0.0211952
$899$	−30.0263	−1.00143
$900$	−1.65562	−0.0551873
$901$	2.70052	0.0899675
$902$	0.899385	0.0299462
$903$	−2.70052	−0.0898678
$904$	12.1563	0.404313
$905$	−4.81668	−0.160112
$906$	−2.30677	−0.0766373
$907$	33.3766	1.10825	0.554126	−	0.832433i	$-0.313053\pi$
$907$	33.3766	1.10825	0.554126	+	0.832433i	$0.313053\pi$
$908$	−16.1890	−0.537251
$909$	0.947800	0.0314365
$910$	0.150446	0.00498722
$911$	28.1866	0.933865	0.466933	−	0.884293i	$-0.345359\pi$
$911$	28.1866	0.933865	0.466933	+	0.884293i	$0.345359\pi$
$912$	41.9814	1.39014
$913$	31.0738	1.02839
$914$	2.06063	0.0681597
$915$	−6.17679	−0.204198
$916$	8.85799	0.292676
$917$	−3.43533	−0.113445
$918$	−2.07522	−0.0684926
$919$	3.20028	0.105567	0.0527837	−	0.998606i	$-0.483191\pi$
$919$	3.20028	0.105567	0.0527837	+	0.998606i	$0.483191\pi$
$920$	−5.14903	−0.169759
$921$	−15.7889	−0.520263
$922$	5.24472	0.172726
$923$	36.2882	1.19444
$924$	4.95254	0.162927
$925$	10.5198	0.345888
$926$	−0.499752	−0.0164229
$927$	1.12459	0.0369365
$928$	12.1406	0.398535
$929$	−30.5647	−1.00279	−0.501397	−	0.865217i	$-0.667180\pi$
$929$	−30.5647	−1.00279	−0.501397	+	0.865217i	$0.667180\pi$
$930$	1.46962	0.0481907
$931$	−45.7621	−1.49979
$932$	24.6281	0.806721
$933$	43.9307	1.43823
$934$	3.56608	0.116686
$935$	−7.47627	−0.244500
$936$	−0.441488	−0.0144305
$937$	9.53690	0.311557	0.155779	−	0.987792i	$-0.450211\pi$
$937$	9.53690	0.311557	0.155779	+	0.987792i	$0.450211\pi$
$938$	−0.292182	−0.00954009
$939$	5.79877	0.189236
$940$	−9.27221	−0.302426
$941$	42.7269	1.39286	0.696428	−	0.717627i	$-0.254772\pi$
$941$	42.7269	1.39286	0.696428	+	0.717627i	$0.254772\pi$
$942$	4.69067	0.152830
$943$	8.31265	0.270697
$944$	16.2835	0.529982
$945$	1.40105	0.0455761
$946$	−4.46310	−0.145108
$947$	33.0395	1.07364	0.536820	−	0.843697i	$-0.319625\pi$
$947$	33.0395	1.07364	0.536820	+	0.843697i	$0.319625\pi$
$948$	−28.6410	−0.930217
$949$	−44.5647	−1.44663
$950$	5.59991	0.181685
$951$	−30.4650	−0.987896
$952$	−0.499293	−0.0161822
$953$	−43.1041	−1.39628	−0.698140	−	0.715961i	$-0.745989\pi$
$953$	−43.1041	−1.39628	−0.698140	+	0.715961i	$0.745989\pi$
$954$	−0.0507852	−0.00164423
$955$	−6.23552	−0.201777
$956$	−34.0240	−1.10041
$957$	41.5633	1.34355
$958$	3.16125	0.102135
$959$	6.30280	0.203528
$960$	9.60228	0.309912
$961$	0.495968	0.0159990
$962$	1.38929	0.0447924
$963$	0.926192	0.0298461
$964$	−36.7974	−1.18516
$965$	1.36011	0.0437835
$966$	−0.877317	−0.0282272
$967$	−2.81431	−0.0905022	−0.0452511	−	0.998976i	$-0.514409\pi$
$967$	−2.81431	−0.0905022	−0.0452511	+	0.998976i	$0.514409\pi$
$968$	8.07381	0.259502
$969$	−22.2374	−0.714369
$970$	1.36011	0.0436705
$971$	−7.25106	−0.232698	−0.116349	−	0.993208i	$-0.537119\pi$
$971$	−7.25106	−0.232698	−0.116349	+	0.993208i	$0.537119\pi$
$972$	−3.94876	−0.126656
$973$	−3.20456	−0.102733
$974$	−0.299972	−0.00961172
$975$	−21.5877	−0.691359
$976$	17.2722	0.552870
$977$	−2.83638	−0.0907439	−0.0453719	−	0.998970i	$-0.514447\pi$
$977$	−2.83638	−0.0907439	−0.0453719	+	0.998970i	$0.514447\pi$
$978$	−0.625301	−0.0199949
$979$	−56.7513	−1.81378
$980$	−10.9057	−0.348371
$981$	1.19982	0.0383072
$982$	3.06205	0.0977139
$983$	25.2388	0.804994	0.402497	−	0.915421i	$-0.368142\pi$
$983$	25.2388	0.804994	0.402497	+	0.915421i	$0.368142\pi$
$984$	1.28726	0.0410363
$985$	−16.5844	−0.528422
$986$	−2.07522	−0.0660886
$987$	−3.18997	−0.101538
$988$	−38.5863	−1.22759
$989$	−41.2506	−1.31169
$990$	0.140596	0.00446845
$991$	51.5755	1.63835	0.819174	−	0.573544i	$-0.194432\pi$
$991$	51.5755	1.63835	0.819174	+	0.573544i	$0.194432\pi$
$992$	−12.7348	−0.404331
$993$	−41.5428	−1.31832
$994$	−0.771777	−0.0244793
$995$	−8.53358	−0.270533
$996$	22.0263	0.697932
$997$	48.5256	1.53682	0.768411	−	0.639956i	$-0.221048\pi$
$997$	48.5256	1.53682	0.768411	+	0.639956i	$0.221048\pi$
$998$	−3.42785	−0.108507
$999$	12.9380	0.409339

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.a.a.1.2	✓	3
3.2	odd	2		369.2.a.f.1.2		3
4.3	odd	2		656.2.a.f.1.1		3
5.2	odd	4		1025.2.b.h.124.3		6
5.3	odd	4		1025.2.b.h.124.4		6
5.4	even	2		1025.2.a.j.1.2		3
7.6	odd	2		2009.2.a.g.1.2		3
8.3	odd	2		2624.2.a.q.1.3		3
8.5	even	2		2624.2.a.r.1.1		3
11.10	odd	2		4961.2.a.d.1.2		3
12.11	even	2		5904.2.a.bk.1.2		3
13.12	even	2		6929.2.a.b.1.2		3
15.14	odd	2		9225.2.a.bv.1.2		3
41.40	even	2		1681.2.a.d.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.a.a.1.2	✓	3	1.1	even	1	trivial
369.2.a.f.1.2		3	3.2	odd	2
656.2.a.f.1.1		3	4.3	odd	2
1025.2.a.j.1.2		3	5.4	even	2
1025.2.b.h.124.3		6	5.2	odd	4
1025.2.b.h.124.4		6	5.3	odd	4
1681.2.a.d.1.2		3	41.40	even	2
2009.2.a.g.1.2		3	7.6	odd	2
2624.2.a.q.1.3		3	8.3	odd	2
2624.2.a.r.1.1		3	8.5	even	2
4961.2.a.d.1.2		3	11.10	odd	2
5904.2.a.bk.1.2		3	12.11	even	2
6929.2.a.b.1.2		3	13.12	even	2
9225.2.a.bv.1.2		3	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.a (trivial)

\(f(q)\)	\(=\)	\(q-0.193937 q^{2} +1.67513 q^{3} -1.96239 q^{4} -0.806063 q^{5} -0.324869 q^{6} +0.324869 q^{7} +0.768452 q^{8} -0.193937 q^{9} +O(q^{10})\)	\(q-0.193937 q^{2} +1.67513 q^{3} -1.96239 q^{4} -0.806063 q^{5} -0.324869 q^{6} +0.324869 q^{7} +0.768452 q^{8} -0.193937 q^{9} +0.156325 q^{10} -4.63752 q^{11} -3.28726 q^{12} +2.96239 q^{13} -0.0630040 q^{14} -1.35026 q^{15} +3.77575 q^{16} -2.00000 q^{17} +0.0376114 q^{18} +6.63752 q^{19} +1.58181 q^{20} +0.544198 q^{21} +0.899385 q^{22} +8.31265 q^{23} +1.28726 q^{24} -4.35026 q^{25} -0.574515 q^{26} -5.35026 q^{27} -0.637519 q^{28} -5.35026 q^{29} +0.261865 q^{30} +5.61213 q^{31} -2.26916 q^{32} -7.76845 q^{33} +0.387873 q^{34} -0.261865 q^{35} +0.380579 q^{36} -2.41819 q^{37} -1.28726 q^{38} +4.96239 q^{39} -0.619421 q^{40} +1.00000 q^{41} -0.105540 q^{42} -4.96239 q^{43} +9.10062 q^{44} +0.156325 q^{45} -1.61213 q^{46} -5.86177 q^{47} +6.32487 q^{48} -6.89446 q^{49} +0.843675 q^{50} -3.35026 q^{51} -5.81336 q^{52} -1.35026 q^{53} +1.03761 q^{54} +3.73813 q^{55} +0.249646 q^{56} +11.1187 q^{57} +1.03761 q^{58} +4.31265 q^{59} +2.64974 q^{60} +4.57452 q^{61} -1.08840 q^{62} -0.0630040 q^{63} -7.11142 q^{64} -2.38787 q^{65} +1.50659 q^{66} +4.63752 q^{67} +3.92478 q^{68} +13.9248 q^{69} +0.0507852 q^{70} +12.2496 q^{71} -0.149031 q^{72} -15.0435 q^{73} +0.468976 q^{74} -7.28726 q^{75} -13.0254 q^{76} -1.50659 q^{77} -0.962389 q^{78} +8.71274 q^{79} -3.04349 q^{80} -8.38058 q^{81} -0.193937 q^{82} -6.70052 q^{83} -1.06793 q^{84} +1.61213 q^{85} +0.962389 q^{86} -8.96239 q^{87} -3.56371 q^{88} +12.2374 q^{89} -0.0303172 q^{90} +0.962389 q^{91} -16.3127 q^{92} +9.40105 q^{93} +1.13681 q^{94} -5.35026 q^{95} -3.80114 q^{96} +8.70052 q^{97} +1.33709 q^{98} +0.899385 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 5 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{7} - 9 q^{8} - q^{9}+O(q^{10}) \) 3 * q - q^2 + 5 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^7 - 9 * q^8 - q^9	\( 3 q - q^{2} + 5 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{7} - 9 q^{8} - q^{9} - 10 q^{10} + 2 q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} + 6 q^{15} + 13 q^{16} - 6 q^{17} + 11 q^{18} + 4 q^{19} + 6 q^{20} - 8 q^{21} - 4 q^{22} + 4 q^{23} - 2 q^{24} - 3 q^{25} + 10 q^{26} - 6 q^{27} + 14 q^{28} - 6 q^{29} + 10 q^{30} + 16 q^{31} - 29 q^{32} - 12 q^{33} + 2 q^{34} - 10 q^{35} - 11 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 14 q^{40} + 3 q^{41} - 20 q^{42} - 4 q^{43} + 34 q^{44} - 10 q^{45} - 4 q^{46} + 24 q^{48} - q^{49} + 13 q^{50} - 30 q^{52} + 6 q^{53} + 14 q^{54} + 2 q^{55} - 16 q^{56} + 12 q^{57} + 14 q^{58} - 8 q^{59} + 18 q^{60} + 2 q^{61} + 16 q^{62} + 4 q^{63} + 13 q^{64} - 8 q^{65} - 16 q^{66} - 2 q^{67} - 10 q^{68} + 20 q^{69} - 30 q^{70} + 20 q^{71} + 23 q^{72} - 2 q^{73} - 30 q^{74} - 16 q^{75} - 24 q^{76} + 16 q^{77} + 8 q^{78} + 32 q^{79} + 34 q^{80} - 13 q^{81} - q^{82} - 12 q^{84} + 4 q^{85} - 8 q^{86} - 16 q^{87} - 40 q^{88} - 6 q^{89} + 2 q^{90} - 8 q^{91} - 28 q^{92} - 12 q^{93} - 46 q^{94} - 6 q^{95} + 2 q^{96} + 6 q^{97} + 35 q^{98} - 4 q^{99}+O(q^{100}) \) 3 * q - q^2 + 5 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^7 - 9 * q^8 - q^9 - 10 * q^10 + 2 * q^11 - 4 * q^12 - 2 * q^13 + 4 * q^14 + 6 * q^15 + 13 * q^16 - 6 * q^17 + 11 * q^18 + 4 * q^19 + 6 * q^20 - 8 * q^21 - 4 * q^22 + 4 * q^23 - 2 * q^24 - 3 * q^25 + 10 * q^26 - 6 * q^27 + 14 * q^28 - 6 * q^29 + 10 * q^30 + 16 * q^31 - 29 * q^32 - 12 * q^33 + 2 * q^34 - 10 * q^35 - 11 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 14 * q^40 + 3 * q^41 - 20 * q^42 - 4 * q^43 + 34 * q^44 - 10 * q^45 - 4 * q^46 + 24 * q^48 - q^49 + 13 * q^50 - 30 * q^52 + 6 * q^53 + 14 * q^54 + 2 * q^55 - 16 * q^56 + 12 * q^57 + 14 * q^58 - 8 * q^59 + 18 * q^60 + 2 * q^61 + 16 * q^62 + 4 * q^63 + 13 * q^64 - 8 * q^65 - 16 * q^66 - 2 * q^67 - 10 * q^68 + 20 * q^69 - 30 * q^70 + 20 * q^71 + 23 * q^72 - 2 * q^73 - 30 * q^74 - 16 * q^75 - 24 * q^76 + 16 * q^77 + 8 * q^78 + 32 * q^79 + 34 * q^80 - 13 * q^81 - q^82 - 12 * q^84 + 4 * q^85 - 8 * q^86 - 16 * q^87 - 40 * q^88 - 6 * q^89 + 2 * q^90 - 8 * q^91 - 28 * q^92 - 12 * q^93 - 46 * q^94 - 6 * q^95 + 2 * q^96 + 6 * q^97 + 35 * q^98 - 4 * q^99

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