LMFDB - Embedded newform 8018.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.16496 q^{3} +1.00000 q^{4} -1.03983 q^{5} -3.16496 q^{6} -1.27872 q^{7} +1.00000 q^{8} +7.01700 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.16496 q^{3} +1.00000 q^{4} -1.03983 q^{5} -3.16496 q^{6} -1.27872 q^{7} +1.00000 q^{8} +7.01700 q^{9} -1.03983 q^{10} -3.87034 q^{11} -3.16496 q^{12} +2.19748 q^{13} -1.27872 q^{14} +3.29104 q^{15} +1.00000 q^{16} +5.42142 q^{17} +7.01700 q^{18} +1.00000 q^{19} -1.03983 q^{20} +4.04711 q^{21} -3.87034 q^{22} -0.224519 q^{23} -3.16496 q^{24} -3.91875 q^{25} +2.19748 q^{26} -12.7137 q^{27} -1.27872 q^{28} +8.40050 q^{29} +3.29104 q^{30} -2.19724 q^{31} +1.00000 q^{32} +12.2495 q^{33} +5.42142 q^{34} +1.32966 q^{35} +7.01700 q^{36} +6.76764 q^{37} +1.00000 q^{38} -6.95494 q^{39} -1.03983 q^{40} -7.27324 q^{41} +4.04711 q^{42} -2.43903 q^{43} -3.87034 q^{44} -7.29651 q^{45} -0.224519 q^{46} +1.16348 q^{47} -3.16496 q^{48} -5.36487 q^{49} -3.91875 q^{50} -17.1586 q^{51} +2.19748 q^{52} -2.65586 q^{53} -12.7137 q^{54} +4.02451 q^{55} -1.27872 q^{56} -3.16496 q^{57} +8.40050 q^{58} -8.57281 q^{59} +3.29104 q^{60} +1.81131 q^{61} -2.19724 q^{62} -8.97280 q^{63} +1.00000 q^{64} -2.28501 q^{65} +12.2495 q^{66} -3.87269 q^{67} +5.42142 q^{68} +0.710595 q^{69} +1.32966 q^{70} +7.52735 q^{71} +7.01700 q^{72} -11.8116 q^{73} +6.76764 q^{74} +12.4027 q^{75} +1.00000 q^{76} +4.94909 q^{77} -6.95494 q^{78} +7.42171 q^{79} -1.03983 q^{80} +19.1873 q^{81} -7.27324 q^{82} +0.0915083 q^{83} +4.04711 q^{84} -5.63738 q^{85} -2.43903 q^{86} -26.5873 q^{87} -3.87034 q^{88} +13.0974 q^{89} -7.29651 q^{90} -2.80997 q^{91} -0.224519 q^{92} +6.95420 q^{93} +1.16348 q^{94} -1.03983 q^{95} -3.16496 q^{96} +10.2588 q^{97} -5.36487 q^{98} -27.1582 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) $ 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9 + 17 * q^10 + 21 * q^11 + 13 * q^12 + 13 * q^13 + 22 * q^14 + 8 * q^15 + 49 * q^16 + 24 * q^17 + 66 * q^18 + 49 * q^19 + 17 * q^20 + 6 * q^21 + 21 * q^22 + 22 * q^23 + 13 * q^24 + 96 * q^25 + 13 * q^26 + 31 * q^27 + 22 * q^28 + 33 * q^29 + 8 * q^30 + 21 * q^31 + 49 * q^32 + 20 * q^33 + 24 * q^34 + 18 * q^35 + 66 * q^36 + 48 * q^37 + 49 * q^38 + 4 * q^39 + 17 * q^40 + 37 * q^41 + 6 * q^42 + 43 * q^43 + 21 * q^44 + 47 * q^45 + 22 * q^46 + 7 * q^47 + 13 * q^48 + 87 * q^49 + 96 * q^50 + 12 * q^51 + 13 * q^52 + 23 * q^53 + 31 * q^54 + 31 * q^55 + 22 * q^56 + 13 * q^57 + 33 * q^58 + 37 * q^59 + 8 * q^60 + 61 * q^61 + 21 * q^62 + 45 * q^63 + 49 * q^64 + 36 * q^65 + 20 * q^66 + 43 * q^67 + 24 * q^68 + 18 * q^69 + 18 * q^70 + 14 * q^71 + 66 * q^72 + 90 * q^73 + 48 * q^74 + 53 * q^75 + 49 * q^76 + 46 * q^77 + 4 * q^78 + 16 * q^79 + 17 * q^80 + 97 * q^81 + 37 * q^82 + 11 * q^83 + 6 * q^84 + 88 * q^85 + 43 * q^86 - 35 * q^87 + 21 * q^88 + 46 * q^89 + 47 * q^90 + 27 * q^91 + 22 * q^92 + 9 * q^93 + 7 * q^94 + 17 * q^95 + 13 * q^96 + 34 * q^97 + 87 * q^98 + 84 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.16496	−1.82729	−0.913647	−	0.406509i	$-0.866746\pi$
$3$	−3.16496	−1.82729	−0.913647	+	0.406509i	$0.866746\pi$
$4$	1.00000	0.500000
$5$	−1.03983	−0.465028	−0.232514	−	0.972593i	$-0.574695\pi$
$5$	−1.03983	−0.465028	−0.232514	+	0.972593i	$0.574695\pi$
$6$	−3.16496	−1.29209
$7$	−1.27872	−0.483312	−0.241656	−	0.970362i	$-0.577691\pi$
$7$	−1.27872	−0.483312	−0.241656	+	0.970362i	$0.577691\pi$
$8$	1.00000	0.353553
$9$	7.01700	2.33900
$10$	−1.03983	−0.328824
$11$	−3.87034	−1.16695	−0.583476	−	0.812131i	$-0.698308\pi$
$11$	−3.87034	−1.16695	−0.583476	+	0.812131i	$0.698308\pi$
$12$	−3.16496	−0.913647
$13$	2.19748	0.609471	0.304735	−	0.952437i	$-0.401432\pi$
$13$	2.19748	0.609471	0.304735	+	0.952437i	$0.401432\pi$
$14$	−1.27872	−0.341753
$15$	3.29104	0.849742
$16$	1.00000	0.250000
$17$	5.42142	1.31489	0.657444	−	0.753503i	$-0.271638\pi$
$17$	5.42142	1.31489	0.657444	+	0.753503i	$0.271638\pi$
$18$	7.01700	1.65392
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.03983	−0.232514
$21$	4.04711	0.883153
$22$	−3.87034	−0.825159
$23$	−0.224519	−0.0468154	−0.0234077	−	0.999726i	$-0.507452\pi$
$23$	−0.224519	−0.0468154	−0.0234077	+	0.999726i	$0.507452\pi$
$24$	−3.16496	−0.646046
$25$	−3.91875	−0.783749
$26$	2.19748	0.430961
$27$	−12.7137	−2.44675
$28$	−1.27872	−0.241656
$29$	8.40050	1.55993	0.779966	−	0.625821i	$-0.215236\pi$
$29$	8.40050	1.55993	0.779966	+	0.625821i	$0.215236\pi$
$30$	3.29104	0.600858
$31$	−2.19724	−0.394637	−0.197318	−	0.980339i	$-0.563223\pi$
$31$	−2.19724	−0.394637	−0.197318	+	0.980339i	$0.563223\pi$
$32$	1.00000	0.176777
$33$	12.2495	2.13236
$34$	5.42142	0.929766
$35$	1.32966	0.224753
$36$	7.01700	1.16950
$37$	6.76764	1.11259	0.556297	−	0.830984i	$-0.312222\pi$
$37$	6.76764	1.11259	0.556297	+	0.830984i	$0.312222\pi$
$38$	1.00000	0.162221
$39$	−6.95494	−1.11368
$40$	−1.03983	−0.164412
$41$	−7.27324	−1.13589	−0.567944	−	0.823067i	$-0.692261\pi$
$41$	−7.27324	−1.13589	−0.567944	+	0.823067i	$0.692261\pi$
$42$	4.04711	0.624483
$43$	−2.43903	−0.371948	−0.185974	−	0.982555i	$-0.559544\pi$
$43$	−2.43903	−0.371948	−0.185974	+	0.982555i	$0.559544\pi$
$44$	−3.87034	−0.583476
$45$	−7.29651	−1.08770
$46$	−0.224519	−0.0331035
$47$	1.16348	0.169711	0.0848555	−	0.996393i	$-0.472957\pi$
$47$	1.16348	0.169711	0.0848555	+	0.996393i	$0.472957\pi$
$48$	−3.16496	−0.456823
$49$	−5.36487	−0.766410
$50$	−3.91875	−0.554194
$51$	−17.1586	−2.40269
$52$	2.19748	0.304735
$53$	−2.65586	−0.364810	−0.182405	−	0.983224i	$-0.558388\pi$
$53$	−2.65586	−0.364810	−0.182405	+	0.983224i	$0.558388\pi$
$54$	−12.7137	−1.73011
$55$	4.02451	0.542665
$56$	−1.27872	−0.170877
$57$	−3.16496	−0.419210
$58$	8.40050	1.10304
$59$	−8.57281	−1.11609	−0.558043	−	0.829812i	$-0.688447\pi$
$59$	−8.57281	−1.11609	−0.558043	+	0.829812i	$0.688447\pi$
$60$	3.29104	0.424871
$61$	1.81131	0.231915	0.115957	−	0.993254i	$-0.463006\pi$
$61$	1.81131	0.231915	0.115957	+	0.993254i	$0.463006\pi$
$62$	−2.19724	−0.279050
$63$	−8.97280	−1.13047
$64$	1.00000	0.125000
$65$	−2.28501	−0.283421
$66$	12.2495	1.50781
$67$	−3.87269	−0.473124	−0.236562	−	0.971616i	$-0.576021\pi$
$67$	−3.87269	−0.473124	−0.236562	+	0.971616i	$0.576021\pi$
$68$	5.42142	0.657444
$69$	0.710595	0.0855455
$70$	1.32966	0.158925
$71$	7.52735	0.893332	0.446666	−	0.894701i	$-0.352611\pi$
$71$	7.52735	0.893332	0.446666	+	0.894701i	$0.352611\pi$
$72$	7.01700	0.826962
$73$	−11.8116	−1.38244	−0.691222	−	0.722642i	$-0.742927\pi$
$73$	−11.8116	−1.38244	−0.691222	+	0.722642i	$0.742927\pi$
$74$	6.76764	0.786722
$75$	12.4027	1.43214
$76$	1.00000	0.114708
$77$	4.94909	0.564001
$78$	−6.95494	−0.787492
$79$	7.42171	0.835007	0.417504	−	0.908675i	$-0.362905\pi$
$79$	7.42171	0.835007	0.417504	+	0.908675i	$0.362905\pi$
$80$	−1.03983	−0.116257
$81$	19.1873	2.13192
$82$	−7.27324	−0.803195
$83$	0.0915083	0.0100443	0.00502217	−	0.999987i	$-0.498401\pi$
$83$	0.0915083	0.0100443	0.00502217	+	0.999987i	$0.498401\pi$
$84$	4.04711	0.441576
$85$	−5.63738	−0.611459
$86$	−2.43903	−0.263007
$87$	−26.5873	−2.85045
$88$	−3.87034	−0.412580
$89$	13.0974	1.38833	0.694163	−	0.719817i	$-0.255774\pi$
$89$	13.0974	1.38833	0.694163	+	0.719817i	$0.255774\pi$
$90$	−7.29651	−0.769120
$91$	−2.80997	−0.294564
$92$	−0.224519	−0.0234077
$93$	6.95420	0.721117
$94$	1.16348	0.120004
$95$	−1.03983	−0.106685
$96$	−3.16496	−0.323023
$97$	10.2588	1.04163	0.520814	−	0.853670i	$-0.325629\pi$
$97$	10.2588	1.04163	0.520814	+	0.853670i	$0.325629\pi$
$98$	−5.36487	−0.541933
$99$	−27.1582	−2.72950
$100$	−3.91875	−0.391875
$101$	−7.66242	−0.762439	−0.381220	−	0.924485i	$-0.624496\pi$
$101$	−7.66242	−0.762439	−0.381220	+	0.924485i	$0.624496\pi$
$102$	−17.1586	−1.69896
$103$	−10.2345	−1.00844	−0.504219	−	0.863576i	$-0.668220\pi$
$103$	−10.2345	−1.00844	−0.504219	+	0.863576i	$0.668220\pi$
$104$	2.19748	0.215480
$105$	−4.20832	−0.410690
$106$	−2.65586	−0.257959
$107$	4.04902	0.391433	0.195717	−	0.980660i	$-0.437297\pi$
$107$	4.04902	0.391433	0.195717	+	0.980660i	$0.437297\pi$
$108$	−12.7137	−1.22337
$109$	−6.93498	−0.664251	−0.332125	−	0.943235i	$-0.607766\pi$
$109$	−6.93498	−0.664251	−0.332125	+	0.943235i	$0.607766\pi$
$110$	4.02451	0.383722
$111$	−21.4193	−2.03303
$112$	−1.27872	−0.120828
$113$	−3.00024	−0.282239	−0.141120	−	0.989993i	$-0.545070\pi$
$113$	−3.00024	−0.282239	−0.141120	+	0.989993i	$0.545070\pi$
$114$	−3.16496	−0.296426
$115$	0.233462	0.0217705
$116$	8.40050	0.779966
$117$	15.4197	1.42555
$118$	−8.57281	−0.789191
$119$	−6.93250	−0.635501
$120$	3.29104	0.300429
$121$	3.97953	0.361775
$122$	1.81131	0.163988
$123$	23.0195	2.07560
$124$	−2.19724	−0.197318
$125$	9.27401	0.829493
$126$	−8.97280	−0.799361
$127$	−13.7084	−1.21642	−0.608211	−	0.793776i	$-0.708112\pi$
$127$	−13.7084	−1.21642	−0.608211	+	0.793776i	$0.708112\pi$
$128$	1.00000	0.0883883
$129$	7.71944	0.679659
$130$	−2.28501	−0.200409
$131$	5.62606	0.491551	0.245775	−	0.969327i	$-0.420957\pi$
$131$	5.62606	0.491551	0.245775	+	0.969327i	$0.420957\pi$
$132$	12.2495	1.06618
$133$	−1.27872	−0.110879
$134$	−3.87269	−0.334549
$135$	13.2201	1.13781
$136$	5.42142	0.464883
$137$	−12.8264	−1.09583	−0.547916	−	0.836533i	$-0.684579\pi$
$137$	−12.8264	−1.09583	−0.547916	+	0.836533i	$0.684579\pi$
$138$	0.710595	0.0604898
$139$	−1.31591	−0.111614	−0.0558069	−	0.998442i	$-0.517773\pi$
$139$	−1.31591	−0.111614	−0.0558069	+	0.998442i	$0.517773\pi$
$140$	1.32966	0.112377
$141$	−3.68237	−0.310112
$142$	7.52735	0.631681
$143$	−8.50498	−0.711223
$144$	7.01700	0.584750
$145$	−8.73511	−0.725412
$146$	−11.8116	−0.977536
$147$	16.9796	1.40046
$148$	6.76764	0.556297
$149$	16.6678	1.36548	0.682738	−	0.730664i	$-0.260789\pi$
$149$	16.6678	1.36548	0.682738	+	0.730664i	$0.260789\pi$
$150$	12.4027	1.01268
$151$	6.29958	0.512653	0.256326	−	0.966590i	$-0.417488\pi$
$151$	6.29958	0.512653	0.256326	+	0.966590i	$0.417488\pi$
$152$	1.00000	0.0811107
$153$	38.0421	3.07552
$154$	4.94909	0.398809
$155$	2.28477	0.183517
$156$	−6.95494	−0.556841
$157$	15.1524	1.20929	0.604647	−	0.796494i	$-0.293314\pi$
$157$	15.1524	1.20929	0.604647	+	0.796494i	$0.293314\pi$
$158$	7.42171	0.590439
$159$	8.40569	0.666614
$160$	−1.03983	−0.0822060
$161$	0.287098	0.0226265
$162$	19.1873	1.50750
$163$	20.9903	1.64409	0.822043	−	0.569426i	$-0.192835\pi$
$163$	20.9903	1.64409	0.822043	+	0.569426i	$0.192835\pi$
$164$	−7.27324	−0.567944
$165$	−12.7374	−0.991607
$166$	0.0915083	0.00710242
$167$	−23.9336	−1.85204	−0.926019	−	0.377478i	$-0.876791\pi$
$167$	−23.9336	−1.85204	−0.926019	+	0.377478i	$0.876791\pi$
$168$	4.04711	0.312242
$169$	−8.17109	−0.628546
$170$	−5.63738	−0.432367
$171$	7.01700	0.536604
$172$	−2.43903	−0.185974
$173$	14.4621	1.09953	0.549766	−	0.835319i	$-0.314717\pi$
$173$	14.4621	1.09953	0.549766	+	0.835319i	$0.314717\pi$
$174$	−26.5873	−2.01558
$175$	5.01099	0.378795
$176$	−3.87034	−0.291738
$177$	27.1327	2.03942
$178$	13.0974	0.981695
$179$	5.19298	0.388141	0.194071	−	0.980988i	$-0.437831\pi$
$179$	5.19298	0.388141	0.194071	+	0.980988i	$0.437831\pi$
$180$	−7.29651	−0.543850
$181$	19.7882	1.47085	0.735423	−	0.677608i	$-0.236984\pi$
$181$	19.7882	1.47085	0.735423	+	0.677608i	$0.236984\pi$
$182$	−2.80997	−0.208288
$183$	−5.73274	−0.423776
$184$	−0.224519	−0.0165518
$185$	−7.03722	−0.517386
$186$	6.95420	0.509907
$187$	−20.9827	−1.53441
$188$	1.16348	0.0848555
$189$	16.2573	1.18254
$190$	−1.03983	−0.0754374
$191$	−14.6401	−1.05932	−0.529659	−	0.848211i	$-0.677680\pi$
$191$	−14.6401	−1.05932	−0.529659	+	0.848211i	$0.677680\pi$
$192$	−3.16496	−0.228412
$193$	18.6743	1.34421	0.672104	−	0.740457i	$-0.265391\pi$
$193$	18.6743	1.34421	0.672104	+	0.740457i	$0.265391\pi$
$194$	10.2588	0.736542
$195$	7.23198	0.517893
$196$	−5.36487	−0.383205
$197$	−5.91913	−0.421720	−0.210860	−	0.977516i	$-0.567626\pi$
$197$	−5.91913	−0.421720	−0.210860	+	0.977516i	$0.567626\pi$
$198$	−27.1582	−1.93005
$199$	19.9420	1.41365	0.706826	−	0.707387i	$-0.250126\pi$
$199$	19.9420	1.41365	0.706826	+	0.707387i	$0.250126\pi$
$200$	−3.91875	−0.277097
$201$	12.2569	0.864537
$202$	−7.66242	−0.539126
$203$	−10.7419	−0.753934
$204$	−17.1586	−1.20134
$205$	7.56295	0.528220
$206$	−10.2345	−0.713074
$207$	−1.57545	−0.109501
$208$	2.19748	0.152368
$209$	−3.87034	−0.267717
$210$	−4.20832	−0.290402
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−2.65586	−0.182405
$213$	−23.8238	−1.63238
$214$	4.04902	0.276785
$215$	2.53618	0.172966
$216$	−12.7137	−0.865056
$217$	2.80967	0.190733
$218$	−6.93498	−0.469696
$219$	37.3833	2.52613
$220$	4.02451	0.271332
$221$	11.9135	0.801386
$222$	−21.4193	−1.43757
$223$	−11.6643	−0.781098	−0.390549	−	0.920582i	$-0.627715\pi$
$223$	−11.6643	−0.781098	−0.390549	+	0.920582i	$0.627715\pi$
$224$	−1.27872	−0.0854383
$225$	−27.4979	−1.83319
$226$	−3.00024	−0.199573
$227$	11.3203	0.751356	0.375678	−	0.926750i	$-0.377410\pi$
$227$	11.3203	0.751356	0.375678	+	0.926750i	$0.377410\pi$
$228$	−3.16496	−0.209605
$229$	−13.5500	−0.895409	−0.447704	−	0.894182i	$-0.647758\pi$
$229$	−13.5500	−0.895409	−0.447704	+	0.894182i	$0.647758\pi$
$230$	0.233462	0.0153940
$231$	−15.6637	−1.03060
$232$	8.40050	0.551520
$233$	−9.81620	−0.643081	−0.321540	−	0.946896i	$-0.604201\pi$
$233$	−9.81620	−0.643081	−0.321540	+	0.946896i	$0.604201\pi$
$234$	15.4197	1.00802
$235$	−1.20982	−0.0789202
$236$	−8.57281	−0.558043
$237$	−23.4894	−1.52580
$238$	−6.93250	−0.449367
$239$	13.4248	0.868375	0.434187	−	0.900823i	$-0.357036\pi$
$239$	13.4248	0.868375	0.434187	+	0.900823i	$0.357036\pi$
$240$	3.29104	0.212435
$241$	−0.898157	−0.0578554	−0.0289277	−	0.999582i	$-0.509209\pi$
$241$	−0.898157	−0.0578554	−0.0289277	+	0.999582i	$0.509209\pi$
$242$	3.97953	0.255814
$243$	−22.5862	−1.44890
$244$	1.81131	0.115957
$245$	5.57857	0.356402
$246$	23.0195	1.46767
$247$	2.19748	0.139822
$248$	−2.19724	−0.139525
$249$	−0.289621	−0.0183540
$250$	9.27401	0.586540
$251$	−28.9852	−1.82953	−0.914765	−	0.403987i	$-0.867624\pi$
$251$	−28.9852	−1.82953	−0.914765	+	0.403987i	$0.867624\pi$
$252$	−8.97280	−0.565234
$253$	0.868965	0.0546313
$254$	−13.7084	−0.860140
$255$	17.8421	1.11732
$256$	1.00000	0.0625000
$257$	−11.0842	−0.691413	−0.345706	−	0.938343i	$-0.612361\pi$
$257$	−11.0842	−0.691413	−0.345706	+	0.938343i	$0.612361\pi$
$258$	7.71944	0.480592
$259$	−8.65394	−0.537730
$260$	−2.28501	−0.141710
$261$	58.9463	3.64868
$262$	5.62606	0.347579
$263$	28.4835	1.75637	0.878185	−	0.478321i	$-0.158754\pi$
$263$	28.4835	1.75637	0.878185	+	0.478321i	$0.158754\pi$
$264$	12.2495	0.753904
$265$	2.76165	0.169647
$266$	−1.27872	−0.0784035
$267$	−41.4530	−2.53688
$268$	−3.87269	−0.236562
$269$	9.96990	0.607876	0.303938	−	0.952692i	$-0.401698\pi$
$269$	9.96990	0.607876	0.303938	+	0.952692i	$0.401698\pi$
$270$	13.2201	0.804550
$271$	−4.64555	−0.282197	−0.141099	−	0.989996i	$-0.545063\pi$
$271$	−4.64555	−0.282197	−0.141099	+	0.989996i	$0.545063\pi$
$272$	5.42142	0.328722
$273$	8.89344	0.538256
$274$	−12.8264	−0.774870
$275$	15.1669	0.914597
$276$	0.710595	0.0427728
$277$	21.6404	1.30025	0.650124	−	0.759828i	$-0.274717\pi$
$277$	21.6404	1.30025	0.650124	+	0.759828i	$0.274717\pi$
$278$	−1.31591	−0.0789229
$279$	−15.4181	−0.923055
$280$	1.32966	0.0794623
$281$	6.21959	0.371030	0.185515	−	0.982641i	$-0.440605\pi$
$281$	6.21959	0.371030	0.185515	+	0.982641i	$0.440605\pi$
$282$	−3.68237	−0.219282
$283$	−9.33040	−0.554635	−0.277317	−	0.960778i	$-0.589445\pi$
$283$	−9.33040	−0.554635	−0.277317	+	0.960778i	$0.589445\pi$
$284$	7.52735	0.446666
$285$	3.29104	0.194944
$286$	−8.50498	−0.502910
$287$	9.30046	0.548989
$288$	7.01700	0.413481
$289$	12.3918	0.728931
$290$	−8.73511	−0.512944
$291$	−32.4689	−1.90336
$292$	−11.8116	−0.691222
$293$	16.3751	0.956642	0.478321	−	0.878185i	$-0.341246\pi$
$293$	16.3751	0.956642	0.478321	+	0.878185i	$0.341246\pi$
$294$	16.9796	0.990271
$295$	8.91430	0.519010
$296$	6.76764	0.393361
$297$	49.2062	2.85524
$298$	16.6678	0.965537
$299$	−0.493375	−0.0285326
$300$	12.4027	0.716070
$301$	3.11884	0.179767
$302$	6.29958	0.362500
$303$	24.2513	1.39320
$304$	1.00000	0.0573539
$305$	−1.88346	−0.107847
$306$	38.0421	2.17472
$307$	−11.6173	−0.663032	−0.331516	−	0.943450i	$-0.607560\pi$
$307$	−11.6173	−0.663032	−0.331516	+	0.943450i	$0.607560\pi$
$308$	4.94909	0.282001
$309$	32.3920	1.84271
$310$	2.28477	0.129766
$311$	24.5199	1.39039	0.695197	−	0.718819i	$-0.255317\pi$
$311$	24.5199	1.39039	0.695197	+	0.718819i	$0.255317\pi$
$312$	−6.95494	−0.393746
$313$	7.02519	0.397087	0.198544	−	0.980092i	$-0.436379\pi$
$313$	7.02519	0.397087	0.198544	+	0.980092i	$0.436379\pi$
$314$	15.1524	0.855100
$315$	9.33022	0.525698
$316$	7.42171	0.417504
$317$	−10.9818	−0.616801	−0.308401	−	0.951257i	$-0.599794\pi$
$317$	−10.9818	−0.616801	−0.308401	+	0.951257i	$0.599794\pi$
$318$	8.40569	0.471368
$319$	−32.5128	−1.82037
$320$	−1.03983	−0.0581284
$321$	−12.8150	−0.715264
$322$	0.287098	0.0159993
$323$	5.42142	0.301656
$324$	19.1873	1.06596
$325$	−8.61136	−0.477672
$326$	20.9903	1.16254
$327$	21.9490	1.21378
$328$	−7.27324	−0.401597
$329$	−1.48777	−0.0820233
$330$	−12.7374	−0.701172
$331$	−5.51968	−0.303389	−0.151694	−	0.988427i	$-0.548473\pi$
$331$	−5.51968	−0.303389	−0.151694	+	0.988427i	$0.548473\pi$
$332$	0.0915083	0.00502217
$333$	47.4886	2.60236
$334$	−23.9336	−1.30959
$335$	4.02695	0.220016
$336$	4.04711	0.220788
$337$	22.7373	1.23858	0.619291	−	0.785162i	$-0.287420\pi$
$337$	22.7373	1.23858	0.619291	+	0.785162i	$0.287420\pi$
$338$	−8.17109	−0.444449
$339$	9.49567	0.515734
$340$	−5.63738	−0.305730
$341$	8.50408	0.460522
$342$	7.01700	0.379436
$343$	15.8112	0.853727
$344$	−2.43903	−0.131504
$345$	−0.738900	−0.0397810
$346$	14.4621	0.777486
$347$	22.8804	1.22829	0.614143	−	0.789195i	$-0.289502\pi$
$347$	22.8804	1.22829	0.614143	+	0.789195i	$0.289502\pi$
$348$	−26.5873	−1.42523
$349$	22.3196	1.19474	0.597371	−	0.801965i	$-0.296212\pi$
$349$	22.3196	1.19474	0.597371	+	0.801965i	$0.296212\pi$
$350$	5.01099	0.267849
$351$	−27.9380	−1.49122
$352$	−3.87034	−0.206290
$353$	20.6758	1.10046	0.550231	−	0.835012i	$-0.314540\pi$
$353$	20.6758	1.10046	0.550231	+	0.835012i	$0.314540\pi$
$354$	27.1327	1.44208
$355$	−7.82719	−0.415424
$356$	13.0974	0.694163
$357$	21.9411	1.16125
$358$	5.19298	0.274457
$359$	15.8460	0.836319	0.418159	−	0.908374i	$-0.362675\pi$
$359$	15.8460	0.836319	0.418159	+	0.908374i	$0.362675\pi$
$360$	−7.29651	−0.384560
$361$	1.00000	0.0526316
$362$	19.7882	1.04004
$363$	−12.5951	−0.661070
$364$	−2.80997	−0.147282
$365$	12.2821	0.642875
$366$	−5.73274	−0.299655
$367$	7.08875	0.370030	0.185015	−	0.982736i	$-0.440767\pi$
$367$	7.08875	0.370030	0.185015	+	0.982736i	$0.440767\pi$
$368$	−0.224519	−0.0117039
$369$	−51.0363	−2.65685
$370$	−7.03722	−0.365848
$371$	3.39610	0.176317
$372$	6.95420	0.360558
$373$	14.2631	0.738515	0.369257	−	0.929327i	$-0.379612\pi$
$373$	14.2631	0.738515	0.369257	+	0.929327i	$0.379612\pi$
$374$	−20.9827	−1.08499
$375$	−29.3519	−1.51573
$376$	1.16348	0.0600019
$377$	18.4599	0.950733
$378$	16.2573	0.836184
$379$	14.9483	0.767842	0.383921	−	0.923366i	$-0.374573\pi$
$379$	14.9483	0.767842	0.383921	+	0.923366i	$0.374573\pi$
$380$	−1.03983	−0.0533423
$381$	43.3865	2.22276
$382$	−14.6401	−0.749051
$383$	2.07609	0.106083	0.0530416	−	0.998592i	$-0.483108\pi$
$383$	2.07609	0.106083	0.0530416	+	0.998592i	$0.483108\pi$
$384$	−3.16496	−0.161511
$385$	−5.14623	−0.262276
$386$	18.6743	0.950499
$387$	−17.1147	−0.869988
$388$	10.2588	0.520814
$389$	−13.8555	−0.702501	−0.351250	−	0.936282i	$-0.614243\pi$
$389$	−13.8555	−0.702501	−0.351250	+	0.936282i	$0.614243\pi$
$390$	7.23198	0.366205
$391$	−1.21721	−0.0615571
$392$	−5.36487	−0.270967
$393$	−17.8063	−0.898207
$394$	−5.91913	−0.298201
$395$	−7.71734	−0.388301
$396$	−27.1582	−1.36475
$397$	−12.0478	−0.604663	−0.302331	−	0.953203i	$-0.597765\pi$
$397$	−12.0478	−0.604663	−0.302331	+	0.953203i	$0.597765\pi$
$398$	19.9420	0.999603
$399$	4.04711	0.202609
$400$	−3.91875	−0.195937
$401$	−24.0091	−1.19896	−0.599479	−	0.800390i	$-0.704626\pi$
$401$	−24.0091	−1.19896	−0.599479	+	0.800390i	$0.704626\pi$
$402$	12.2569	0.611320
$403$	−4.82839	−0.240519
$404$	−7.66242	−0.381220
$405$	−19.9516	−0.991404
$406$	−10.7419	−0.533112
$407$	−26.1931	−1.29834
$408$	−17.1586	−0.849478
$409$	−27.3507	−1.35241	−0.676203	−	0.736715i	$-0.736376\pi$
$409$	−27.3507	−1.35241	−0.676203	+	0.736715i	$0.736376\pi$
$410$	7.56295	0.373508
$411$	40.5950	2.00241
$412$	−10.2345	−0.504219
$413$	10.9623	0.539417
$414$	−1.57545	−0.0774292
$415$	−0.0951534	−0.00467090
$416$	2.19748	0.107740
$417$	4.16480	0.203951
$418$	−3.87034	−0.189305
$419$	23.0356	1.12536	0.562682	−	0.826674i	$-0.309770\pi$
$419$	23.0356	1.12536	0.562682	+	0.826674i	$0.309770\pi$
$420$	−4.20832	−0.205345
$421$	36.6518	1.78630	0.893149	−	0.449761i	$-0.148491\pi$
$421$	36.6518	1.78630	0.893149	+	0.449761i	$0.148491\pi$
$422$	1.00000	0.0486792
$423$	8.16414	0.396954
$424$	−2.65586	−0.128980
$425$	−21.2452	−1.03054
$426$	−23.8238	−1.15427
$427$	−2.31617	−0.112087
$428$	4.04902	0.195717
$429$	26.9180	1.29961
$430$	2.53618	0.122306
$431$	2.24057	0.107925	0.0539623	−	0.998543i	$-0.482815\pi$
$431$	2.24057	0.107925	0.0539623	+	0.998543i	$0.482815\pi$
$432$	−12.7137	−0.611687
$433$	−0.411399	−0.0197706	−0.00988529	−	0.999951i	$-0.503147\pi$
$433$	−0.411399	−0.0197706	−0.00988529	+	0.999951i	$0.503147\pi$
$434$	2.80967	0.134868
$435$	27.6463	1.32554
$436$	−6.93498	−0.332125
$437$	−0.224519	−0.0107402
$438$	37.3833	1.78624
$439$	33.2877	1.58874	0.794368	−	0.607437i	$-0.207802\pi$
$439$	33.2877	1.58874	0.794368	+	0.607437i	$0.207802\pi$
$440$	4.02451	0.191861
$441$	−37.6453	−1.79263
$442$	11.9135	0.566665
$443$	15.7582	0.748693	0.374346	−	0.927289i	$-0.377867\pi$
$443$	15.7582	0.748693	0.374346	+	0.927289i	$0.377867\pi$
$444$	−21.4193	−1.01652
$445$	−13.6192	−0.645610
$446$	−11.6643	−0.552320
$447$	−52.7528	−2.49512
$448$	−1.27872	−0.0604140
$449$	−16.0654	−0.758174	−0.379087	−	0.925361i	$-0.623762\pi$
$449$	−16.0654	−0.758174	−0.379087	+	0.925361i	$0.623762\pi$
$450$	−27.4979	−1.29626
$451$	28.1499	1.32553
$452$	−3.00024	−0.141120
$453$	−19.9380	−0.936767
$454$	11.3203	0.531289
$455$	2.92190	0.136981
$456$	−3.16496	−0.148213
$457$	−9.45136	−0.442116	−0.221058	−	0.975261i	$-0.570951\pi$
$457$	−9.45136	−0.442116	−0.221058	+	0.975261i	$0.570951\pi$
$458$	−13.5500	−0.633150
$459$	−68.9262	−3.21720
$460$	0.233462	0.0108852
$461$	−12.1860	−0.567557	−0.283778	−	0.958890i	$-0.591588\pi$
$461$	−12.1860	−0.567557	−0.283778	+	0.958890i	$0.591588\pi$
$462$	−15.6637	−0.728742
$463$	37.0519	1.72195	0.860973	−	0.508651i	$-0.169856\pi$
$463$	37.0519	1.72195	0.860973	+	0.508651i	$0.169856\pi$
$464$	8.40050	0.389983
$465$	−7.23121	−0.335339
$466$	−9.81620	−0.454727
$467$	20.6966	0.957724	0.478862	−	0.877890i	$-0.341049\pi$
$467$	20.6966	0.957724	0.478862	+	0.877890i	$0.341049\pi$
$468$	15.4197	0.712776
$469$	4.95210	0.228667
$470$	−1.20982	−0.0558050
$471$	−47.9568	−2.20973
$472$	−8.57281	−0.394596
$473$	9.43987	0.434046
$474$	−23.4894	−1.07891
$475$	−3.91875	−0.179804
$476$	−6.93250	−0.317751
$477$	−18.6361	−0.853290
$478$	13.4248	0.614034
$479$	15.9742	0.729881	0.364940	−	0.931031i	$-0.381089\pi$
$479$	15.9742	0.729881	0.364940	+	0.931031i	$0.381089\pi$
$480$	3.29104	0.150215
$481$	14.8717	0.678093
$482$	−0.898157	−0.0409100
$483$	−0.908654	−0.0413452
$484$	3.97953	0.180888
$485$	−10.6675	−0.484385
$486$	−22.5862	−1.02453
$487$	−19.2800	−0.873660	−0.436830	−	0.899544i	$-0.643899\pi$
$487$	−19.2800	−0.873660	−0.436830	+	0.899544i	$0.643899\pi$
$488$	1.81131	0.0819942
$489$	−66.4335	−3.00423
$490$	5.57857	0.252014
$491$	−8.48176	−0.382776	−0.191388	−	0.981514i	$-0.561299\pi$
$491$	−8.48176	−0.382776	−0.191388	+	0.981514i	$0.561299\pi$
$492$	23.0195	1.03780
$493$	45.5426	2.05114
$494$	2.19748	0.0988692
$495$	28.2400	1.26929
$496$	−2.19724	−0.0986591
$497$	−9.62539	−0.431758
$498$	−0.289621	−0.0129782
$499$	7.41401	0.331897	0.165948	−	0.986134i	$-0.446932\pi$
$499$	7.41401	0.331897	0.165948	+	0.986134i	$0.446932\pi$
$500$	9.27401	0.414746
$501$	75.7490	3.38422
$502$	−28.9852	−1.29367
$503$	21.8189	0.972858	0.486429	−	0.873720i	$-0.338299\pi$
$503$	21.8189	0.972858	0.486429	+	0.873720i	$0.338299\pi$
$504$	−8.97280	−0.399680
$505$	7.96764	0.354555
$506$	0.868965	0.0386302
$507$	25.8612	1.14854
$508$	−13.7084	−0.608211
$509$	−12.6392	−0.560224	−0.280112	−	0.959967i	$-0.590372\pi$
$509$	−12.6392	−0.560224	−0.280112	+	0.959967i	$0.590372\pi$
$510$	17.8421	0.790061
$511$	15.1038	0.668152
$512$	1.00000	0.0441942
$513$	−12.7137	−0.561322
$514$	−11.0842	−0.488903
$515$	10.6422	0.468952
$516$	7.71944	0.339830
$517$	−4.50306	−0.198044
$518$	−8.65394	−0.380232
$519$	−45.7720	−2.00917
$520$	−2.28501	−0.100204
$521$	−17.2103	−0.753996	−0.376998	−	0.926214i	$-0.623044\pi$
$521$	−17.2103	−0.753996	−0.376998	+	0.926214i	$0.623044\pi$
$522$	58.9463	2.58001
$523$	40.7099	1.78012	0.890060	−	0.455844i	$-0.150662\pi$
$523$	40.7099	1.78012	0.890060	+	0.455844i	$0.150662\pi$
$524$	5.62606	0.245775
$525$	−15.8596	−0.692170
$526$	28.4835	1.24194
$527$	−11.9122	−0.518903
$528$	12.2495	0.533091
$529$	−22.9496	−0.997808
$530$	2.76165	0.119958
$531$	−60.1555	−2.61052
$532$	−1.27872	−0.0554397
$533$	−15.9828	−0.692291
$534$	−41.4530	−1.79385
$535$	−4.21030	−0.182027
$536$	−3.87269	−0.167275
$537$	−16.4356	−0.709248
$538$	9.96990	0.429833
$539$	20.7639	0.894363
$540$	13.2201	0.568903
$541$	10.8499	0.466476	0.233238	−	0.972420i	$-0.425068\pi$
$541$	10.8499	0.466476	0.233238	+	0.972420i	$0.425068\pi$
$542$	−4.64555	−0.199544
$543$	−62.6290	−2.68767
$544$	5.42142	0.232442
$545$	7.21122	0.308895
$546$	8.89344	0.380604
$547$	25.5903	1.09416	0.547080	−	0.837080i	$-0.315739\pi$
$547$	25.5903	1.09416	0.547080	+	0.837080i	$0.315739\pi$
$548$	−12.8264	−0.547916
$549$	12.7100	0.542449
$550$	15.1669	0.646718
$551$	8.40050	0.357873
$552$	0.710595	0.0302449
$553$	−9.49031	−0.403569
$554$	21.6404	0.919414
$555$	22.2725	0.945417
$556$	−1.31591	−0.0558069
$557$	12.9517	0.548781	0.274390	−	0.961618i	$-0.411524\pi$
$557$	12.9517	0.548781	0.274390	+	0.961618i	$0.411524\pi$
$558$	−15.4181	−0.652699
$559$	−5.35971	−0.226692
$560$	1.32966	0.0561883
$561$	66.4097	2.80382
$562$	6.21959	0.262358
$563$	−27.2513	−1.14851	−0.574253	−	0.818678i	$-0.694707\pi$
$563$	−27.2513	−1.14851	−0.574253	+	0.818678i	$0.694707\pi$
$564$	−3.68237	−0.155056
$565$	3.11975	0.131249
$566$	−9.33040	−0.392186
$567$	−24.5353	−1.03038
$568$	7.52735	0.315841
$569$	3.41691	0.143244	0.0716222	−	0.997432i	$-0.477182\pi$
$569$	3.41691	0.143244	0.0716222	+	0.997432i	$0.477182\pi$
$570$	3.29104	0.137846
$571$	1.56414	0.0654571	0.0327285	−	0.999464i	$-0.489580\pi$
$571$	1.56414	0.0654571	0.0327285	+	0.999464i	$0.489580\pi$
$572$	−8.50498	−0.355611
$573$	46.3353	1.93569
$574$	9.30046	0.388194
$575$	0.879833	0.0366916
$576$	7.01700	0.292375
$577$	23.1942	0.965585	0.482793	−	0.875735i	$-0.339623\pi$
$577$	23.1942	0.965585	0.482793	+	0.875735i	$0.339623\pi$
$578$	12.3918	0.515432
$579$	−59.1036	−2.45626
$580$	−8.73511	−0.362706
$581$	−0.117014	−0.00485455
$582$	−32.4689	−1.34588
$583$	10.2791	0.425715
$584$	−11.8116	−0.488768
$585$	−16.0339	−0.662921
$586$	16.3751	0.676448
$587$	−37.2538	−1.53763	−0.768814	−	0.639472i	$-0.779153\pi$
$587$	−37.2538	−1.53763	−0.768814	+	0.639472i	$0.779153\pi$
$588$	16.9796	0.700228
$589$	−2.19724	−0.0905358
$590$	8.91430	0.366996
$591$	18.7338	0.770607
$592$	6.76764	0.278148
$593$	−6.33930	−0.260324	−0.130162	−	0.991493i	$-0.541550\pi$
$593$	−6.33930	−0.260324	−0.130162	+	0.991493i	$0.541550\pi$
$594$	49.2062	2.01896
$595$	7.20864	0.295526
$596$	16.6678	0.682738
$597$	−63.1158	−2.58316
$598$	−0.493375	−0.0201756
$599$	9.14052	0.373471	0.186736	−	0.982410i	$-0.440209\pi$
$599$	9.14052	0.373471	0.186736	+	0.982410i	$0.440209\pi$
$600$	12.4027	0.506338
$601$	−30.0030	−1.22385	−0.611924	−	0.790917i	$-0.709604\pi$
$601$	−30.0030	−1.22385	−0.611924	+	0.790917i	$0.709604\pi$
$602$	3.11884	0.127115
$603$	−27.1747	−1.10664
$604$	6.29958	0.256326
$605$	−4.13805	−0.168236
$606$	24.2513	0.985141
$607$	32.0743	1.30186	0.650928	−	0.759139i	$-0.274380\pi$
$607$	32.0743	1.30186	0.650928	+	0.759139i	$0.274380\pi$
$608$	1.00000	0.0405554
$609$	33.9978	1.37766
$610$	−1.88346	−0.0762592
$611$	2.55672	0.103434
$612$	38.0421	1.53776
$613$	36.9120	1.49086	0.745430	−	0.666584i	$-0.232244\pi$
$613$	36.9120	1.49086	0.745430	+	0.666584i	$0.232244\pi$
$614$	−11.6173	−0.468835
$615$	−23.9365	−0.965212
$616$	4.94909	0.199405
$617$	−12.9235	−0.520281	−0.260140	−	0.965571i	$-0.583769\pi$
$617$	−12.9235	−0.520281	−0.260140	+	0.965571i	$0.583769\pi$
$618$	32.3920	1.30300
$619$	−9.38804	−0.377337	−0.188669	−	0.982041i	$-0.560417\pi$
$619$	−9.38804	−0.377337	−0.188669	+	0.982041i	$0.560417\pi$
$620$	2.28477	0.0917584
$621$	2.85446	0.114546
$622$	24.5199	0.983157
$623$	−16.7480	−0.670995
$624$	−6.95494	−0.278420
$625$	9.95031	0.398012
$626$	7.02519	0.280783
$627$	12.2495	0.489197
$628$	15.1524	0.604647
$629$	36.6902	1.46294
$630$	9.33022	0.371725
$631$	24.0967	0.959274	0.479637	−	0.877467i	$-0.340768\pi$
$631$	24.0967	0.959274	0.479637	+	0.877467i	$0.340768\pi$
$632$	7.42171	0.295220
$633$	−3.16496	−0.125796
$634$	−10.9818	−0.436145
$635$	14.2544	0.565669
$636$	8.40569	0.333307
$637$	−11.7892	−0.467104
$638$	−32.5128	−1.28719
$639$	52.8194	2.08950
$640$	−1.03983	−0.0411030
$641$	6.15525	0.243118	0.121559	−	0.992584i	$-0.461211\pi$
$641$	6.15525	0.243118	0.121559	+	0.992584i	$0.461211\pi$
$642$	−12.8150	−0.505768
$643$	−15.2159	−0.600056	−0.300028	−	0.953930i	$-0.596996\pi$
$643$	−15.2159	−0.600056	−0.300028	+	0.953930i	$0.596996\pi$
$644$	0.287098	0.0113132
$645$	−8.02693	−0.316060
$646$	5.42142	0.213303
$647$	−35.7186	−1.40424	−0.702121	−	0.712058i	$-0.747763\pi$
$647$	−35.7186	−1.40424	−0.702121	+	0.712058i	$0.747763\pi$
$648$	19.1873	0.753749
$649$	33.1797	1.30242
$650$	−8.61136	−0.337765
$651$	−8.89249	−0.348524
$652$	20.9903	0.822043
$653$	−13.3450	−0.522230	−0.261115	−	0.965308i	$-0.584090\pi$
$653$	−13.3450	−0.522230	−0.261115	+	0.965308i	$0.584090\pi$
$654$	21.9490	0.858272
$655$	−5.85016	−0.228585
$656$	−7.27324	−0.283972
$657$	−82.8821	−3.23354
$658$	−1.48777	−0.0579992
$659$	−3.89190	−0.151607	−0.0758034	−	0.997123i	$-0.524152\pi$
$659$	−3.89190	−0.151607	−0.0758034	+	0.997123i	$0.524152\pi$
$660$	−12.7374	−0.495804
$661$	−33.2884	−1.29477	−0.647384	−	0.762164i	$-0.724137\pi$
$661$	−33.2884	−1.29477	−0.647384	+	0.762164i	$0.724137\pi$
$662$	−5.51968	−0.214528
$663$	−37.7057	−1.46437
$664$	0.0915083	0.00355121
$665$	1.32966	0.0515620
$666$	47.4886	1.84014
$667$	−1.88607	−0.0730289
$668$	−23.9336	−0.926019
$669$	36.9170	1.42729
$670$	4.02695	0.155575
$671$	−7.01039	−0.270633
$672$	4.04711	0.156121
$673$	23.9313	0.922483	0.461242	−	0.887275i	$-0.347404\pi$
$673$	23.9313	0.922483	0.461242	+	0.887275i	$0.347404\pi$
$674$	22.7373	0.875809
$675$	49.8217	1.91764
$676$	−8.17109	−0.314273
$677$	24.2430	0.931733	0.465867	−	0.884855i	$-0.345743\pi$
$677$	24.2430	0.931733	0.465867	+	0.884855i	$0.345743\pi$
$678$	9.49567	0.364679
$679$	−13.1182	−0.503431
$680$	−5.63738	−0.216183
$681$	−35.8284	−1.37295
$682$	8.50408	0.325638
$683$	19.5809	0.749242	0.374621	−	0.927178i	$-0.377773\pi$
$683$	19.5809	0.749242	0.374621	+	0.927178i	$0.377773\pi$
$684$	7.01700	0.268302
$685$	13.3373	0.509592
$686$	15.8112	0.603676
$687$	42.8853	1.63617
$688$	−2.43903	−0.0929871
$689$	−5.83618	−0.222341
$690$	−0.738900	−0.0281294
$691$	35.2700	1.34173	0.670867	−	0.741578i	$-0.265922\pi$
$691$	35.2700	1.34173	0.670867	+	0.741578i	$0.265922\pi$
$692$	14.4621	0.549766
$693$	34.7278	1.31920
$694$	22.8804	0.868529
$695$	1.36832	0.0519035
$696$	−26.5873	−1.00779
$697$	−39.4313	−1.49357
$698$	22.3196	0.844810
$699$	31.0679	1.17510
$700$	5.01099	0.189398
$701$	25.3305	0.956719	0.478359	−	0.878164i	$-0.341232\pi$
$701$	25.3305	0.956719	0.478359	+	0.878164i	$0.341232\pi$
$702$	−27.9380	−1.05445
$703$	6.76764	0.255246
$704$	−3.87034	−0.145869
$705$	3.82905	0.144210
$706$	20.6758	0.778144
$707$	9.79811	0.368496
$708$	27.1327	1.01971
$709$	7.19871	0.270353	0.135177	−	0.990822i	$-0.456840\pi$
$709$	7.19871	0.270353	0.135177	+	0.990822i	$0.456840\pi$
$710$	−7.82719	−0.293749
$711$	52.0781	1.95308
$712$	13.0974	0.490848
$713$	0.493323	0.0184751
$714$	21.9411	0.821126
$715$	8.84377	0.330738
$716$	5.19298	0.194071
$717$	−42.4889	−1.58678
$718$	15.8460	0.591367
$719$	0.469681	0.0175162	0.00875808	−	0.999962i	$-0.497212\pi$
$719$	0.469681	0.0175162	0.00875808	+	0.999962i	$0.497212\pi$
$720$	−7.29651	−0.271925
$721$	13.0871	0.487391
$722$	1.00000	0.0372161
$723$	2.84264	0.105719
$724$	19.7882	0.735423
$725$	−32.9194	−1.22260
$726$	−12.5951	−0.467447
$727$	11.6180	0.430890	0.215445	−	0.976516i	$-0.430880\pi$
$727$	11.6180	0.430890	0.215445	+	0.976516i	$0.430880\pi$
$728$	−2.80997	−0.104144
$729$	13.9225	0.515648
$730$	12.2821	0.454581
$731$	−13.2230	−0.489071
$732$	−5.73274	−0.211888
$733$	39.5123	1.45942	0.729710	−	0.683757i	$-0.239655\pi$
$733$	39.5123	1.45942	0.729710	+	0.683757i	$0.239655\pi$
$734$	7.08875	0.261651
$735$	−17.6560	−0.651250
$736$	−0.224519	−0.00827588
$737$	14.9886	0.552113
$738$	−51.0363	−1.87867
$739$	15.1832	0.558523	0.279262	−	0.960215i	$-0.409910\pi$
$739$	15.1832	0.558523	0.279262	+	0.960215i	$0.409910\pi$
$740$	−7.03722	−0.258693
$741$	−6.95494	−0.255496
$742$	3.39610	0.124675
$743$	40.6555	1.49150	0.745752	−	0.666223i	$-0.232090\pi$
$743$	40.6555	1.49150	0.745752	+	0.666223i	$0.232090\pi$
$744$	6.95420	0.254953
$745$	−17.3317	−0.634984
$746$	14.2631	0.522209
$747$	0.642114	0.0234937
$748$	−20.9827	−0.767205
$749$	−5.17757	−0.189184
$750$	−29.3519	−1.07178
$751$	−9.97615	−0.364035	−0.182017	−	0.983295i	$-0.558263\pi$
$751$	−9.97615	−0.364035	−0.182017	+	0.983295i	$0.558263\pi$
$752$	1.16348	0.0424277
$753$	91.7371	3.34309
$754$	18.4599	0.672270
$755$	−6.55052	−0.238398
$756$	16.2573	0.591271
$757$	−10.9243	−0.397051	−0.198526	−	0.980096i	$-0.563615\pi$
$757$	−10.9243	−0.397051	−0.198526	+	0.980096i	$0.563615\pi$
$758$	14.9483	0.542946
$759$	−2.75024	−0.0998275
$760$	−1.03983	−0.0377187
$761$	−43.1632	−1.56466	−0.782332	−	0.622862i	$-0.785970\pi$
$761$	−43.1632	−1.56466	−0.782332	+	0.622862i	$0.785970\pi$
$762$	43.3865	1.57173
$763$	8.86792	0.321040
$764$	−14.6401	−0.529659
$765$	−39.5575	−1.43020
$766$	2.07609	0.0750121
$767$	−18.8386	−0.680221
$768$	−3.16496	−0.114206
$769$	−5.72807	−0.206559	−0.103280	−	0.994652i	$-0.532934\pi$
$769$	−5.72807	−0.206559	−0.103280	+	0.994652i	$0.532934\pi$
$770$	−5.14623	−0.185457
$771$	35.0811	1.26341
$772$	18.6743	0.672104
$773$	−15.2430	−0.548253	−0.274126	−	0.961694i	$-0.588389\pi$
$773$	−15.2430	−0.548253	−0.274126	+	0.961694i	$0.588389\pi$
$774$	−17.1147	−0.615174
$775$	8.61044	0.309296
$776$	10.2588	0.368271
$777$	27.3894	0.982590
$778$	−13.8555	−0.496743
$779$	−7.27324	−0.260591
$780$	7.23198	0.258946
$781$	−29.1334	−1.04247
$782$	−1.21721	−0.0435274
$783$	−106.801	−3.81676
$784$	−5.36487	−0.191602
$785$	−15.7560	−0.562355
$786$	−17.8063	−0.635129
$787$	−36.4330	−1.29870	−0.649348	−	0.760491i	$-0.724958\pi$
$787$	−36.4330	−1.29870	−0.649348	+	0.760491i	$0.724958\pi$
$788$	−5.91913	−0.210860
$789$	−90.1494	−3.20940
$790$	−7.71734	−0.274571
$791$	3.83648	0.136410
$792$	−27.1582	−0.965024
$793$	3.98032	0.141345
$794$	−12.0478	−0.427561
$795$	−8.74051	−0.309994
$796$	19.9420	0.706826
$797$	−1.58249	−0.0560547	−0.0280273	−	0.999607i	$-0.508923\pi$
$797$	−1.58249	−0.0560547	−0.0280273	+	0.999607i	$0.508923\pi$
$798$	4.04711	0.143266
$799$	6.30771	0.223151
$800$	−3.91875	−0.138549
$801$	91.9048	3.24730
$802$	−24.0091	−0.847792
$803$	45.7149	1.61325
$804$	12.2569	0.432269
$805$	−0.298534	−0.0105219
$806$	−4.82839	−0.170073
$807$	−31.5544	−1.11077
$808$	−7.66242	−0.269563
$809$	−35.9440	−1.26372	−0.631862	−	0.775081i	$-0.717709\pi$
$809$	−35.9440	−1.26372	−0.631862	+	0.775081i	$0.717709\pi$
$810$	−19.9516	−0.701028
$811$	−41.9008	−1.47134	−0.735668	−	0.677342i	$-0.763132\pi$
$811$	−41.9008	−1.47134	−0.735668	+	0.677342i	$0.763132\pi$
$812$	−10.7419	−0.376967
$813$	14.7030	0.515657
$814$	−26.1931	−0.918067
$815$	−21.8264	−0.764545
$816$	−17.1586	−0.600672
$817$	−2.43903	−0.0853308
$818$	−27.3507	−0.956296
$819$	−19.7175	−0.688986
$820$	7.56295	0.264110
$821$	46.6649	1.62861	0.814307	−	0.580434i	$-0.197117\pi$
$821$	46.6649	1.62861	0.814307	+	0.580434i	$0.197117\pi$
$822$	40.5950	1.41591
$823$	−18.6551	−0.650277	−0.325138	−	0.945666i	$-0.605411\pi$
$823$	−18.6551	−0.650277	−0.325138	+	0.945666i	$0.605411\pi$
$824$	−10.2345	−0.356537
$825$	−48.0026	−1.67124
$826$	10.9623	0.381426
$827$	−27.2509	−0.947605	−0.473803	−	0.880631i	$-0.657119\pi$
$827$	−27.2509	−0.947605	−0.473803	+	0.880631i	$0.657119\pi$
$828$	−1.57545	−0.0547507
$829$	21.7790	0.756417	0.378209	−	0.925720i	$-0.376540\pi$
$829$	21.7790	0.756417	0.378209	+	0.925720i	$0.376540\pi$
$830$	−0.0951534	−0.00330282
$831$	−68.4912	−2.37593
$832$	2.19748	0.0761838
$833$	−29.0852	−1.00774
$834$	4.16480	0.144215
$835$	24.8869	0.861248
$836$	−3.87034	−0.133858
$837$	27.9350	0.965576
$838$	23.0356	0.795752
$839$	−33.0914	−1.14244	−0.571222	−	0.820796i	$-0.693530\pi$
$839$	−33.0914	−1.14244	−0.571222	+	0.820796i	$0.693530\pi$
$840$	−4.20832	−0.145201
$841$	41.5683	1.43339
$842$	36.6518	1.26310
$843$	−19.6848	−0.677980
$844$	1.00000	0.0344214
$845$	8.49657	0.292291
$846$	8.16414	0.280689
$847$	−5.08872	−0.174850
$848$	−2.65586	−0.0912024
$849$	29.5304	1.01348
$850$	−21.2452	−0.728704
$851$	−1.51946	−0.0520865
$852$	−23.8238	−0.816190
$853$	−55.6894	−1.90677	−0.953384	−	0.301760i	$-0.902426\pi$
$853$	−55.6894	−1.90677	−0.953384	+	0.301760i	$0.902426\pi$
$854$	−2.31617	−0.0792576
$855$	−7.29651	−0.249535
$856$	4.04902	0.138393
$857$	−43.5076	−1.48619	−0.743096	−	0.669185i	$-0.766643\pi$
$857$	−43.5076	−1.48619	−0.743096	+	0.669185i	$0.766643\pi$
$858$	26.9180	0.918965
$859$	−6.23572	−0.212760	−0.106380	−	0.994326i	$-0.533926\pi$
$859$	−6.23572	−0.212760	−0.106380	+	0.994326i	$0.533926\pi$
$860$	2.53618	0.0864832
$861$	−29.4356	−1.00316
$862$	2.24057	0.0763142
$863$	49.0430	1.66944	0.834722	−	0.550672i	$-0.185628\pi$
$863$	49.0430	1.66944	0.834722	+	0.550672i	$0.185628\pi$
$864$	−12.7137	−0.432528
$865$	−15.0381	−0.511312
$866$	−0.411399	−0.0139799
$867$	−39.2197	−1.33197
$868$	2.80967	0.0953663
$869$	−28.7245	−0.974413
$870$	27.6463	0.937298
$871$	−8.51015	−0.288355
$872$	−6.93498	−0.234848
$873$	71.9863	2.43637
$874$	−0.224519	−0.00759447
$875$	−11.8589	−0.400904
$876$	37.3833	1.26307
$877$	46.0213	1.55403	0.777015	−	0.629482i	$-0.216733\pi$
$877$	46.0213	1.55403	0.777015	+	0.629482i	$0.216733\pi$
$878$	33.2877	1.12341
$879$	−51.8265	−1.74807
$880$	4.02451	0.135666
$881$	3.98373	0.134215	0.0671076	−	0.997746i	$-0.478623\pi$
$881$	3.98373	0.134215	0.0671076	+	0.997746i	$0.478623\pi$
$882$	−37.6453	−1.26758
$883$	42.8258	1.44120	0.720601	−	0.693350i	$-0.243866\pi$
$883$	42.8258	1.44120	0.720601	+	0.693350i	$0.243866\pi$
$884$	11.9135	0.400693
$885$	−28.2134	−0.948384
$886$	15.7582	0.529406
$887$	2.48408	0.0834073	0.0417036	−	0.999130i	$-0.486721\pi$
$887$	2.48408	0.0834073	0.0417036	+	0.999130i	$0.486721\pi$
$888$	−21.4193	−0.718786
$889$	17.5292	0.587911
$890$	−13.6192	−0.456515
$891$	−74.2615	−2.48785
$892$	−11.6643	−0.390549
$893$	1.16348	0.0389344
$894$	−52.7528	−1.76432
$895$	−5.39983	−0.180496
$896$	−1.27872	−0.0427191
$897$	1.56152	0.0521375
$898$	−16.0654	−0.536110
$899$	−18.4579	−0.615607
$900$	−27.4979	−0.916595
$901$	−14.3985	−0.479684
$902$	28.1499	0.937289
$903$	−9.87103	−0.328487
$904$	−3.00024	−0.0997867
$905$	−20.5764	−0.683984
$906$	−19.9380	−0.662395
$907$	32.9548	1.09425	0.547123	−	0.837052i	$-0.315723\pi$
$907$	32.9548	1.09425	0.547123	+	0.837052i	$0.315723\pi$
$908$	11.3203	0.375678
$909$	−53.7672	−1.78335
$910$	2.92190	0.0968599
$911$	−6.11873	−0.202723	−0.101361	−	0.994850i	$-0.532320\pi$
$911$	−6.11873	−0.202723	−0.101361	+	0.994850i	$0.532320\pi$
$912$	−3.16496	−0.104802
$913$	−0.354168	−0.0117213
$914$	−9.45136	−0.312623
$915$	5.96109	0.197068
$916$	−13.5500	−0.447704
$917$	−7.19417	−0.237572
$918$	−68.9262	−2.27490
$919$	−20.0404	−0.661072	−0.330536	−	0.943793i	$-0.607229\pi$
$919$	−20.0404	−0.661072	−0.330536	+	0.943793i	$0.607229\pi$
$920$	0.233462	0.00769702
$921$	36.7682	1.21155
$922$	−12.1860	−0.401323
$923$	16.5412	0.544460
$924$	−15.6637	−0.515298
$925$	−26.5207	−0.871994
$926$	37.0519	1.21760
$927$	−71.8158	−2.35874
$928$	8.40050	0.275760
$929$	−16.0027	−0.525033	−0.262517	−	0.964928i	$-0.584552\pi$
$929$	−16.0027	−0.525033	−0.262517	+	0.964928i	$0.584552\pi$
$930$	−7.23121	−0.237121
$931$	−5.36487	−0.175826
$932$	−9.81620	−0.321540
$933$	−77.6045	−2.54066
$934$	20.6966	0.677213
$935$	21.8186	0.713543
$936$	15.4197	0.504009
$937$	6.36687	0.207997	0.103998	−	0.994577i	$-0.466836\pi$
$937$	6.36687	0.207997	0.103998	+	0.994577i	$0.466836\pi$
$938$	4.95210	0.161692
$939$	−22.2345	−0.725595
$940$	−1.20982	−0.0394601
$941$	−25.0260	−0.815824	−0.407912	−	0.913021i	$-0.633743\pi$
$941$	−25.0260	−0.815824	−0.407912	+	0.913021i	$0.633743\pi$
$942$	−47.9568	−1.56252
$943$	1.63298	0.0531771
$944$	−8.57281	−0.279021
$945$	−16.9048	−0.549915
$946$	9.43987	0.306917
$947$	−11.6262	−0.377802	−0.188901	−	0.981996i	$-0.560493\pi$
$947$	−11.6262	−0.377802	−0.188901	+	0.981996i	$0.560493\pi$
$948$	−23.4894	−0.762902
$949$	−25.9557	−0.842559
$950$	−3.91875	−0.127141
$951$	34.7571	1.12708
$952$	−6.93250	−0.224684
$953$	26.1956	0.848559	0.424280	−	0.905531i	$-0.360527\pi$
$953$	26.1956	0.848559	0.424280	+	0.905531i	$0.360527\pi$
$954$	−18.6361	−0.603367
$955$	15.2232	0.492612
$956$	13.4248	0.434187
$957$	102.902	3.32634
$958$	15.9742	0.516103
$959$	16.4014	0.529629
$960$	3.29104	0.106218
$961$	−26.1721	−0.844262
$962$	14.8717	0.479484
$963$	28.4120	0.915563
$964$	−0.898157	−0.0289277
$965$	−19.4182	−0.625094
$966$	−0.908654	−0.0292355
$967$	−13.4514	−0.432566	−0.216283	−	0.976331i	$-0.569393\pi$
$967$	−13.4514	−0.432566	−0.216283	+	0.976331i	$0.569393\pi$
$968$	3.97953	0.127907
$969$	−17.1586	−0.551214
$970$	−10.6675	−0.342512
$971$	−5.71543	−0.183417	−0.0917084	−	0.995786i	$-0.529233\pi$
$971$	−5.71543	−0.183417	−0.0917084	+	0.995786i	$0.529233\pi$
$972$	−22.5862	−0.724452
$973$	1.68268	0.0539443
$974$	−19.2800	−0.617771
$975$	27.2546	0.872847
$976$	1.81131	0.0579787
$977$	51.4724	1.64675	0.823374	−	0.567499i	$-0.192089\pi$
$977$	51.4724	1.64675	0.823374	+	0.567499i	$0.192089\pi$
$978$	−66.4335	−2.12431
$979$	−50.6916	−1.62011
$980$	5.57857	0.178201
$981$	−48.6628	−1.55368
$982$	−8.48176	−0.270664
$983$	−51.5003	−1.64261	−0.821303	−	0.570492i	$-0.806752\pi$
$983$	−51.5003	−1.64261	−0.821303	+	0.570492i	$0.806752\pi$
$984$	23.0195	0.733836
$985$	6.15490	0.196112
$986$	45.5426	1.45037
$987$	4.70873	0.149881
$988$	2.19748	0.0699111
$989$	0.547608	0.0174129
$990$	28.2400	0.897526
$991$	48.4678	1.53963	0.769815	−	0.638267i	$-0.220348\pi$
$991$	48.4678	1.53963	0.769815	+	0.638267i	$0.220348\pi$
$992$	−2.19724	−0.0697626
$993$	17.4696	0.554380
$994$	−9.62539	−0.305299
$995$	−20.7364	−0.657387
$996$	−0.289621	−0.00917698
$997$	12.1529	0.384888	0.192444	−	0.981308i	$-0.438359\pi$
$997$	12.1529	0.384888	0.192444	+	0.981308i	$0.438359\pi$
$998$	7.41401	0.234686
$999$	−86.0416	−2.72223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.k.1.2	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.k.1.2	✓	49	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.16496 q^{3} +1.00000 q^{4} -1.03983 q^{5} -3.16496 q^{6} -1.27872 q^{7} +1.00000 q^{8} +7.01700 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.16496 q^{3} +1.00000 q^{4} -1.03983 q^{5} -3.16496 q^{6} -1.27872 q^{7} +1.00000 q^{8} +7.01700 q^{9} -1.03983 q^{10} -3.87034 q^{11} -3.16496 q^{12} +2.19748 q^{13} -1.27872 q^{14} +3.29104 q^{15} +1.00000 q^{16} +5.42142 q^{17} +7.01700 q^{18} +1.00000 q^{19} -1.03983 q^{20} +4.04711 q^{21} -3.87034 q^{22} -0.224519 q^{23} -3.16496 q^{24} -3.91875 q^{25} +2.19748 q^{26} -12.7137 q^{27} -1.27872 q^{28} +8.40050 q^{29} +3.29104 q^{30} -2.19724 q^{31} +1.00000 q^{32} +12.2495 q^{33} +5.42142 q^{34} +1.32966 q^{35} +7.01700 q^{36} +6.76764 q^{37} +1.00000 q^{38} -6.95494 q^{39} -1.03983 q^{40} -7.27324 q^{41} +4.04711 q^{42} -2.43903 q^{43} -3.87034 q^{44} -7.29651 q^{45} -0.224519 q^{46} +1.16348 q^{47} -3.16496 q^{48} -5.36487 q^{49} -3.91875 q^{50} -17.1586 q^{51} +2.19748 q^{52} -2.65586 q^{53} -12.7137 q^{54} +4.02451 q^{55} -1.27872 q^{56} -3.16496 q^{57} +8.40050 q^{58} -8.57281 q^{59} +3.29104 q^{60} +1.81131 q^{61} -2.19724 q^{62} -8.97280 q^{63} +1.00000 q^{64} -2.28501 q^{65} +12.2495 q^{66} -3.87269 q^{67} +5.42142 q^{68} +0.710595 q^{69} +1.32966 q^{70} +7.52735 q^{71} +7.01700 q^{72} -11.8116 q^{73} +6.76764 q^{74} +12.4027 q^{75} +1.00000 q^{76} +4.94909 q^{77} -6.95494 q^{78} +7.42171 q^{79} -1.03983 q^{80} +19.1873 q^{81} -7.27324 q^{82} +0.0915083 q^{83} +4.04711 q^{84} -5.63738 q^{85} -2.43903 q^{86} -26.5873 q^{87} -3.87034 q^{88} +13.0974 q^{89} -7.29651 q^{90} -2.80997 q^{91} -0.224519 q^{92} +6.95420 q^{93} +1.16348 q^{94} -1.03983 q^{95} -3.16496 q^{96} +10.2588 q^{97} -5.36487 q^{98} -27.1582 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9 + 17 * q^10 + 21 * q^11 + 13 * q^12 + 13 * q^13 + 22 * q^14 + 8 * q^15 + 49 * q^16 + 24 * q^17 + 66 * q^18 + 49 * q^19 + 17 * q^20 + 6 * q^21 + 21 * q^22 + 22 * q^23 + 13 * q^24 + 96 * q^25 + 13 * q^26 + 31 * q^27 + 22 * q^28 + 33 * q^29 + 8 * q^30 + 21 * q^31 + 49 * q^32 + 20 * q^33 + 24 * q^34 + 18 * q^35 + 66 * q^36 + 48 * q^37 + 49 * q^38 + 4 * q^39 + 17 * q^40 + 37 * q^41 + 6 * q^42 + 43 * q^43 + 21 * q^44 + 47 * q^45 + 22 * q^46 + 7 * q^47 + 13 * q^48 + 87 * q^49 + 96 * q^50 + 12 * q^51 + 13 * q^52 + 23 * q^53 + 31 * q^54 + 31 * q^55 + 22 * q^56 + 13 * q^57 + 33 * q^58 + 37 * q^59 + 8 * q^60 + 61 * q^61 + 21 * q^62 + 45 * q^63 + 49 * q^64 + 36 * q^65 + 20 * q^66 + 43 * q^67 + 24 * q^68 + 18 * q^69 + 18 * q^70 + 14 * q^71 + 66 * q^72 + 90 * q^73 + 48 * q^74 + 53 * q^75 + 49 * q^76 + 46 * q^77 + 4 * q^78 + 16 * q^79 + 17 * q^80 + 97 * q^81 + 37 * q^82 + 11 * q^83 + 6 * q^84 + 88 * q^85 + 43 * q^86 - 35 * q^87 + 21 * q^88 + 46 * q^89 + 47 * q^90 + 27 * q^91 + 22 * q^92 + 9 * q^93 + 7 * q^94 + 17 * q^95 + 13 * q^96 + 34 * q^97 + 87 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more