LMFDB - Embedded newform 4018.2.a.bs.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 17x^{8} + 36x^{7} + 75x^{6} - 174x^{5} - 69x^{4} + 260x^{3} - 104x^{2} - 24x + 14 $ x^10 - 2x^9 - 17x^8 + 36x^7 + 75x^6 - 174x^5 - 69x^4 + 260x^3 - 104x^2 - 24*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.06975$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.539617 q^{3} +1.00000 q^{4} +3.38661 q^{5} +0.539617 q^{6} -1.00000 q^{8} -2.70881 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.539617 q^{3} +1.00000 q^{4} +3.38661 q^{5} +0.539617 q^{6} -1.00000 q^{8} -2.70881 q^{9} -3.38661 q^{10} +2.98763 q^{11} -0.539617 q^{12} -0.00964170 q^{13} -1.82747 q^{15} +1.00000 q^{16} -0.0684206 q^{17} +2.70881 q^{18} +0.966028 q^{19} +3.38661 q^{20} -2.98763 q^{22} +1.61711 q^{23} +0.539617 q^{24} +6.46911 q^{25} +0.00964170 q^{26} +3.08057 q^{27} +0.701234 q^{29} +1.82747 q^{30} -7.29196 q^{31} -1.00000 q^{32} -1.61218 q^{33} +0.0684206 q^{34} -2.70881 q^{36} +4.88899 q^{37} -0.966028 q^{38} +0.00520283 q^{39} -3.38661 q^{40} +1.00000 q^{41} +1.84951 q^{43} +2.98763 q^{44} -9.17369 q^{45} -1.61711 q^{46} +3.16995 q^{47} -0.539617 q^{48} -6.46911 q^{50} +0.0369209 q^{51} -0.00964170 q^{52} -6.61947 q^{53} -3.08057 q^{54} +10.1179 q^{55} -0.521285 q^{57} -0.701234 q^{58} +3.16550 q^{59} -1.82747 q^{60} +8.67612 q^{61} +7.29196 q^{62} +1.00000 q^{64} -0.0326527 q^{65} +1.61218 q^{66} +8.55509 q^{67} -0.0684206 q^{68} -0.872619 q^{69} -3.64077 q^{71} +2.70881 q^{72} +3.52157 q^{73} -4.88899 q^{74} -3.49085 q^{75} +0.966028 q^{76} -0.00520283 q^{78} +13.6955 q^{79} +3.38661 q^{80} +6.46411 q^{81} -1.00000 q^{82} -6.62566 q^{83} -0.231714 q^{85} -1.84951 q^{86} -0.378398 q^{87} -2.98763 q^{88} +9.28595 q^{89} +9.17369 q^{90} +1.61711 q^{92} +3.93487 q^{93} -3.16995 q^{94} +3.27156 q^{95} +0.539617 q^{96} -4.17000 q^{97} -8.09294 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	$ 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * 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
$3$	−0.539617	−0.311548	−0.155774	−	0.987793i	$-0.549787\pi$
$3$	−0.539617	−0.311548	−0.155774	+	0.987793i	$0.549787\pi$
$4$	1.00000	0.500000
$5$	3.38661	1.51454	0.757269	−	0.653104i	$-0.226533\pi$
$5$	3.38661	1.51454	0.757269	+	0.653104i	$0.226533\pi$
$6$	0.539617	0.220298
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.70881	−0.902938
$10$	−3.38661	−1.07094
$11$	2.98763	0.900806	0.450403	−	0.892825i	$-0.351280\pi$
$11$	2.98763	0.900806	0.450403	+	0.892825i	$0.351280\pi$
$12$	−0.539617	−0.155774
$13$	−0.00964170	−0.00267413	−0.00133706	−	0.999999i	$-0.500426\pi$
$13$	−0.00964170	−0.00267413	−0.00133706	+	0.999999i	$0.500426\pi$
$14$	0	0
$15$	−1.82747	−0.471851
$16$	1.00000	0.250000
$17$	−0.0684206	−0.0165944	−0.00829721	−	0.999966i	$-0.502641\pi$
$17$	−0.0684206	−0.0165944	−0.00829721	+	0.999966i	$0.502641\pi$
$18$	2.70881	0.638473
$19$	0.966028	0.221622	0.110811	−	0.993841i	$-0.464655\pi$
$19$	0.966028	0.221622	0.110811	+	0.993841i	$0.464655\pi$
$20$	3.38661	0.757269
$21$	0	0
$22$	−2.98763	−0.636966
$23$	1.61711	0.337190	0.168595	−	0.985685i	$-0.446077\pi$
$23$	1.61711	0.337190	0.168595	+	0.985685i	$0.446077\pi$
$24$	0.539617	0.110149
$25$	6.46911	1.29382
$26$	0.00964170	0.00189089
$27$	3.08057	0.592857
$28$	0	0
$29$	0.701234	0.130216	0.0651080	−	0.997878i	$-0.479261\pi$
$29$	0.701234	0.130216	0.0651080	+	0.997878i	$0.479261\pi$
$30$	1.82747	0.333649
$31$	−7.29196	−1.30967	−0.654837	−	0.755770i	$-0.727263\pi$
$31$	−7.29196	−1.30967	−0.654837	+	0.755770i	$0.727263\pi$
$32$	−1.00000	−0.176777
$33$	−1.61218	−0.280644
$34$	0.0684206	0.0117340
$35$	0	0
$36$	−2.70881	−0.451469
$37$	4.88899	0.803745	0.401873	−	0.915696i	$-0.368359\pi$
$37$	4.88899	0.803745	0.401873	+	0.915696i	$0.368359\pi$
$38$	−0.966028	−0.156710
$39$	0.00520283	0.000833119 0
$40$	−3.38661	−0.535470
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	1.84951	0.282047	0.141023	−	0.990006i	$-0.454961\pi$
$43$	1.84951	0.282047	0.141023	+	0.990006i	$0.454961\pi$
$44$	2.98763	0.450403
$45$	−9.17369	−1.36753
$46$	−1.61711	−0.238429
$47$	3.16995	0.462385	0.231193	−	0.972908i	$-0.425737\pi$
$47$	3.16995	0.462385	0.231193	+	0.972908i	$0.425737\pi$
$48$	−0.539617	−0.0778870
$49$	0	0
$50$	−6.46911	−0.914871
$51$	0.0369209	0.00516996
$52$	−0.00964170	−0.00133706
$53$	−6.61947	−0.909254	−0.454627	−	0.890682i	$-0.650227\pi$
$53$	−6.61947	−0.909254	−0.454627	+	0.890682i	$0.650227\pi$
$54$	−3.08057	−0.419213
$55$	10.1179	1.36430
$56$	0	0
$57$	−0.521285	−0.0690459
$58$	−0.701234	−0.0920766
$59$	3.16550	0.412113	0.206057	−	0.978540i	$-0.433937\pi$
$59$	3.16550	0.412113	0.206057	+	0.978540i	$0.433937\pi$
$60$	−1.82747	−0.235926
$61$	8.67612	1.11086	0.555432	−	0.831562i	$-0.312553\pi$
$61$	8.67612	1.11086	0.555432	+	0.831562i	$0.312553\pi$
$62$	7.29196	0.926080
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.0326527	−0.00405007
$66$	1.61218	0.198446
$67$	8.55509	1.04517	0.522585	−	0.852587i	$-0.324968\pi$
$67$	8.55509	1.04517	0.522585	+	0.852587i	$0.324968\pi$
$68$	−0.0684206	−0.00829721
$69$	−0.872619	−0.105051
$70$	0	0
$71$	−3.64077	−0.432080	−0.216040	−	0.976384i	$-0.569314\pi$
$71$	−3.64077	−0.432080	−0.216040	+	0.976384i	$0.569314\pi$
$72$	2.70881	0.319237
$73$	3.52157	0.412168	0.206084	−	0.978534i	$-0.433928\pi$
$73$	3.52157	0.412168	0.206084	+	0.978534i	$0.433928\pi$
$74$	−4.88899	−0.568334
$75$	−3.49085	−0.403088
$76$	0.966028	0.110811
$77$	0	0
$78$	−0.00520283	−0.000589104 0
$79$	13.6955	1.54087	0.770434	−	0.637520i	$-0.220040\pi$
$79$	13.6955	1.54087	0.770434	+	0.637520i	$0.220040\pi$
$80$	3.38661	0.378634
$81$	6.46411	0.718234
$82$	−1.00000	−0.110432
$83$	−6.62566	−0.727261	−0.363631	−	0.931543i	$-0.618463\pi$
$83$	−6.62566	−0.727261	−0.363631	+	0.931543i	$0.618463\pi$
$84$	0	0
$85$	−0.231714	−0.0251329
$86$	−1.84951	−0.199437
$87$	−0.378398	−0.0405685
$88$	−2.98763	−0.318483
$89$	9.28595	0.984309	0.492154	−	0.870508i	$-0.336210\pi$
$89$	9.28595	0.984309	0.492154	+	0.870508i	$0.336210\pi$
$90$	9.17369	0.966992
$91$	0	0
$92$	1.61711	0.168595
$93$	3.93487	0.408027
$94$	−3.16995	−0.326956
$95$	3.27156	0.335655
$96$	0.539617	0.0550744
$97$	−4.17000	−0.423399	−0.211699	−	0.977335i	$-0.567900\pi$
$97$	−4.17000	−0.423399	−0.211699	+	0.977335i	$0.567900\pi$
$98$	0	0
$99$	−8.09294	−0.813372
$100$	6.46911	0.646911
$101$	5.41052	0.538367	0.269183	−	0.963089i	$-0.413246\pi$
$101$	5.41052	0.538367	0.269183	+	0.963089i	$0.413246\pi$
$102$	−0.0369209	−0.00365571
$103$	13.4966	1.32986	0.664929	−	0.746906i	$-0.268462\pi$
$103$	13.4966	1.32986	0.664929	+	0.746906i	$0.268462\pi$
$104$	0.00964170	0.000945447 0
$105$	0	0
$106$	6.61947	0.642940
$107$	9.54211	0.922470	0.461235	−	0.887278i	$-0.347406\pi$
$107$	9.54211	0.922470	0.461235	+	0.887278i	$0.347406\pi$
$108$	3.08057	0.296428
$109$	−2.65081	−0.253902	−0.126951	−	0.991909i	$-0.540519\pi$
$109$	−2.65081	−0.253902	−0.126951	+	0.991909i	$0.540519\pi$
$110$	−10.1179	−0.964708
$111$	−2.63818	−0.250405
$112$	0	0
$113$	−7.77537	−0.731445	−0.365723	−	0.930724i	$-0.619178\pi$
$113$	−7.77537	−0.731445	−0.365723	+	0.930724i	$0.619178\pi$
$114$	0.521285	0.0488228
$115$	5.47651	0.510687
$116$	0.701234	0.0651080
$117$	0.0261176	0.00241457
$118$	−3.16550	−0.291408
$119$	0	0
$120$	1.82747	0.166825
$121$	−2.07404	−0.188549
$122$	−8.67612	−0.785499
$123$	−0.539617	−0.0486556
$124$	−7.29196	−0.654837
$125$	4.97531	0.445006
$126$	0	0
$127$	−0.741046	−0.0657572	−0.0328786	−	0.999459i	$-0.510467\pi$
$127$	−0.741046	−0.0657572	−0.0328786	+	0.999459i	$0.510467\pi$
$128$	−1.00000	−0.0883883
$129$	−0.998025	−0.0878712
$130$	0.0326527	0.00286383
$131$	6.45083	0.563612	0.281806	−	0.959471i	$-0.409067\pi$
$131$	6.45083	0.563612	0.281806	+	0.959471i	$0.409067\pi$
$132$	−1.61218	−0.140322
$133$	0	0
$134$	−8.55509	−0.739047
$135$	10.4327	0.897903
$136$	0.0684206	0.00586701
$137$	−15.7049	−1.34176	−0.670881	−	0.741565i	$-0.734084\pi$
$137$	−15.7049	−1.34176	−0.670881	+	0.741565i	$0.734084\pi$
$138$	0.872619	0.0742823
$139$	7.14333	0.605890	0.302945	−	0.953008i	$-0.402030\pi$
$139$	7.14333	0.605890	0.302945	+	0.953008i	$0.402030\pi$
$140$	0	0
$141$	−1.71056	−0.144055
$142$	3.64077	0.305527
$143$	−0.0288059	−0.00240887
$144$	−2.70881	−0.225734
$145$	2.37481	0.197217
$146$	−3.52157	−0.291447
$147$	0	0
$148$	4.88899	0.401873
$149$	−11.1088	−0.910069	−0.455035	−	0.890474i	$-0.650373\pi$
$149$	−11.1088	−0.910069	−0.455035	+	0.890474i	$0.650373\pi$
$150$	3.49085	0.285026
$151$	−18.1410	−1.47629	−0.738147	−	0.674640i	$-0.764299\pi$
$151$	−18.1410	−1.47629	−0.738147	+	0.674640i	$0.764299\pi$
$152$	−0.966028	−0.0783552
$153$	0.185339	0.0149837
$154$	0	0
$155$	−24.6950	−1.98355
$156$	0.00520283	0.000416560 0
$157$	16.4130	1.30990	0.654952	−	0.755671i	$-0.272689\pi$
$157$	16.4130	1.30990	0.654952	+	0.755671i	$0.272689\pi$
$158$	−13.6955	−1.08956
$159$	3.57198	0.283276
$160$	−3.38661	−0.267735
$161$	0	0
$162$	−6.46411	−0.507868
$163$	−1.58395	−0.124064	−0.0620321	−	0.998074i	$-0.519758\pi$
$163$	−1.58395	−0.124064	−0.0620321	+	0.998074i	$0.519758\pi$
$164$	1.00000	0.0780869
$165$	−5.45982	−0.425046
$166$	6.62566	0.514251
$167$	8.09972	0.626775	0.313388	−	0.949625i	$-0.398536\pi$
$167$	8.09972	0.626775	0.313388	+	0.949625i	$0.398536\pi$
$168$	0	0
$169$	−12.9999	−0.999993
$170$	0.231714	0.0177716
$171$	−2.61679	−0.200111
$172$	1.84951	0.141023
$173$	15.1576	1.15241	0.576207	−	0.817304i	$-0.304532\pi$
$173$	15.1576	1.15241	0.576207	+	0.817304i	$0.304532\pi$
$174$	0.378398	0.0286863
$175$	0	0
$176$	2.98763	0.225201
$177$	−1.70816	−0.128393
$178$	−9.28595	−0.696011
$179$	17.0248	1.27249	0.636245	−	0.771487i	$-0.280487\pi$
$179$	17.0248	1.27249	0.636245	+	0.771487i	$0.280487\pi$
$180$	−9.17369	−0.683766
$181$	−11.2271	−0.834505	−0.417253	−	0.908790i	$-0.637007\pi$
$181$	−11.2271	−0.834505	−0.417253	+	0.908790i	$0.637007\pi$
$182$	0	0
$183$	−4.68178	−0.346087
$184$	−1.61711	−0.119215
$185$	16.5571	1.21730
$186$	−3.93487	−0.288518
$187$	−0.204416	−0.0149484
$188$	3.16995	0.231193
$189$	0	0
$190$	−3.27156	−0.237344
$191$	23.6031	1.70786	0.853929	−	0.520389i	$-0.174213\pi$
$191$	23.6031	1.70786	0.853929	+	0.520389i	$0.174213\pi$
$192$	−0.539617	−0.0389435
$193$	−8.41165	−0.605484	−0.302742	−	0.953073i	$-0.597902\pi$
$193$	−8.41165	−0.605484	−0.302742	+	0.953073i	$0.597902\pi$
$194$	4.17000	0.299388
$195$	0.0176199	0.00126179
$196$	0	0
$197$	−8.93787	−0.636797	−0.318399	−	0.947957i	$-0.603145\pi$
$197$	−8.93787	−0.636797	−0.318399	+	0.947957i	$0.603145\pi$
$198$	8.09294	0.575141
$199$	−20.9193	−1.48293	−0.741466	−	0.670990i	$-0.765869\pi$
$199$	−20.9193	−1.48293	−0.741466	+	0.670990i	$0.765869\pi$
$200$	−6.46911	−0.457435
$201$	−4.61647	−0.325621
$202$	−5.41052	−0.380683
$203$	0	0
$204$	0.0369209	0.00258498
$205$	3.38661	0.236531
$206$	−13.4966	−0.940352
$207$	−4.38044	−0.304462
$208$	−0.00964170	−0.000668532 0
$209$	2.88614	0.199638
$210$	0	0
$211$	10.5708	0.727722	0.363861	−	0.931453i	$-0.381458\pi$
$211$	10.5708	0.727722	0.363861	+	0.931453i	$0.381458\pi$
$212$	−6.61947	−0.454627
$213$	1.96462	0.134614
$214$	−9.54211	−0.652285
$215$	6.26355	0.427171
$216$	−3.08057	−0.209606
$217$	0	0
$218$	2.65081	0.179536
$219$	−1.90030	−0.128410
$220$	10.1179	0.682152
$221$	0.000659691 0	4.43756e−5 0
$222$	2.63818	0.177063
$223$	15.5890	1.04392	0.521959	−	0.852971i	$-0.325202\pi$
$223$	15.5890	1.04392	0.521959	+	0.852971i	$0.325202\pi$
$224$	0	0
$225$	−17.5236	−1.16824
$226$	7.77537	0.517210
$227$	−2.96125	−0.196545	−0.0982726	−	0.995160i	$-0.531332\pi$
$227$	−2.96125	−0.196545	−0.0982726	+	0.995160i	$0.531332\pi$
$228$	−0.521285	−0.0345230
$229$	24.3188	1.60703	0.803515	−	0.595284i	$-0.202961\pi$
$229$	24.3188	1.60703	0.803515	+	0.595284i	$0.202961\pi$
$230$	−5.47651	−0.361110
$231$	0	0
$232$	−0.701234	−0.0460383
$233$	−1.72516	−0.113019	−0.0565096	−	0.998402i	$-0.517997\pi$
$233$	−1.72516	−0.113019	−0.0565096	+	0.998402i	$0.517997\pi$
$234$	−0.0261176	−0.00170736
$235$	10.7354	0.700300
$236$	3.16550	0.206057
$237$	−7.39034	−0.480054
$238$	0	0
$239$	−9.61482	−0.621931	−0.310965	−	0.950421i	$-0.600652\pi$
$239$	−9.61482	−0.621931	−0.310965	+	0.950421i	$0.600652\pi$
$240$	−1.82747	−0.117963
$241$	−14.4222	−0.929014	−0.464507	−	0.885570i	$-0.653768\pi$
$241$	−14.4222	−0.929014	−0.464507	+	0.885570i	$0.653768\pi$
$242$	2.07404	0.133324
$243$	−12.7299	−0.816621
$244$	8.67612	0.555432
$245$	0	0
$246$	0.539617	0.0344047
$247$	−0.00931416	−0.000592646 0
$248$	7.29196	0.463040
$249$	3.57532	0.226577
$250$	−4.97531	−0.314666
$251$	−1.02742	−0.0648503	−0.0324251	−	0.999474i	$-0.510323\pi$
$251$	−1.02742	−0.0648503	−0.0324251	+	0.999474i	$0.510323\pi$
$252$	0	0
$253$	4.83133	0.303743
$254$	0.741046	0.0464974
$255$	0.125037	0.00783010
$256$	1.00000	0.0625000
$257$	5.56650	0.347229	0.173614	−	0.984814i	$-0.444455\pi$
$257$	5.56650	0.347229	0.173614	+	0.984814i	$0.444455\pi$
$258$	0.998025	0.0621343
$259$	0	0
$260$	−0.0326527	−0.00202503
$261$	−1.89951	−0.117577
$262$	−6.45083	−0.398534
$263$	−10.5040	−0.647705	−0.323853	−	0.946108i	$-0.604978\pi$
$263$	−10.5040	−0.647705	−0.323853	+	0.946108i	$0.604978\pi$
$264$	1.61218	0.0992228
$265$	−22.4175	−1.37710
$266$	0	0
$267$	−5.01086	−0.306660
$268$	8.55509	0.522585
$269$	27.8900	1.70049	0.850243	−	0.526391i	$-0.176455\pi$
$269$	27.8900	1.70049	0.850243	+	0.526391i	$0.176455\pi$
$270$	−10.4327	−0.634914
$271$	−11.8811	−0.721725	−0.360863	−	0.932619i	$-0.617518\pi$
$271$	−11.8811	−0.721725	−0.360863	+	0.932619i	$0.617518\pi$
$272$	−0.0684206	−0.00414861
$273$	0	0
$274$	15.7049	0.948768
$275$	19.3273	1.16548
$276$	−0.872619	−0.0525255
$277$	−5.89117	−0.353966	−0.176983	−	0.984214i	$-0.556634\pi$
$277$	−5.89117	−0.353966	−0.176983	+	0.984214i	$0.556634\pi$
$278$	−7.14333	−0.428429
$279$	19.7526	1.18255
$280$	0	0
$281$	−12.3163	−0.734726	−0.367363	−	0.930078i	$-0.619739\pi$
$281$	−12.3163	−0.734726	−0.367363	+	0.930078i	$0.619739\pi$
$282$	1.71056	0.101862
$283$	7.63451	0.453824	0.226912	−	0.973915i	$-0.427137\pi$
$283$	7.63451	0.453824	0.226912	+	0.973915i	$0.427137\pi$
$284$	−3.64077	−0.216040
$285$	−1.76539	−0.104573
$286$	0.0288059	0.00170333
$287$	0	0
$288$	2.70881	0.159618
$289$	−16.9953	−0.999725
$290$	−2.37481	−0.139453
$291$	2.25020	0.131909
$292$	3.52157	0.206084
$293$	26.4456	1.54497	0.772485	−	0.635034i	$-0.219014\pi$
$293$	26.4456	1.54497	0.772485	+	0.635034i	$0.219014\pi$
$294$	0	0
$295$	10.7203	0.624161
$296$	−4.88899	−0.284167
$297$	9.20363	0.534049
$298$	11.1088	0.643516
$299$	−0.0155917	−0.000901690 0
$300$	−3.49085	−0.201544
$301$	0	0
$302$	18.1410	1.04390
$303$	−2.91961	−0.167727
$304$	0.966028	0.0554055
$305$	29.3826	1.68244
$306$	−0.185339	−0.0105951
$307$	11.1342	0.635462	0.317731	−	0.948181i	$-0.397079\pi$
$307$	11.1342	0.635462	0.317731	+	0.948181i	$0.397079\pi$
$308$	0	0
$309$	−7.28299	−0.414315
$310$	24.6950	1.40258
$311$	−5.52223	−0.313137	−0.156569	−	0.987667i	$-0.550043\pi$
$311$	−5.52223	−0.313137	−0.156569	+	0.987667i	$0.550043\pi$
$312$	−0.00520283	−0.000294552 0
$313$	11.1544	0.630486	0.315243	−	0.949011i	$-0.397914\pi$
$313$	11.1544	0.630486	0.315243	+	0.949011i	$0.397914\pi$
$314$	−16.4130	−0.926242
$315$	0	0
$316$	13.6955	0.770434
$317$	3.17686	0.178430	0.0892151	−	0.996012i	$-0.471564\pi$
$317$	3.17686	0.178430	0.0892151	+	0.996012i	$0.471564\pi$
$318$	−3.57198	−0.200307
$319$	2.09503	0.117299
$320$	3.38661	0.189317
$321$	−5.14909	−0.287394
$322$	0	0
$323$	−0.0660962	−0.00367769
$324$	6.46411	0.359117
$325$	−0.0623733	−0.00345985
$326$	1.58395	0.0877266
$327$	1.43042	0.0791027
$328$	−1.00000	−0.0552158
$329$	0	0
$330$	5.45982	0.300553
$331$	13.3594	0.734298	0.367149	−	0.930162i	$-0.380334\pi$
$331$	13.3594	0.734298	0.367149	+	0.930162i	$0.380334\pi$
$332$	−6.62566	−0.363631
$333$	−13.2434	−0.725732
$334$	−8.09972	−0.443197
$335$	28.9727	1.58295
$336$	0	0
$337$	33.0885	1.80245	0.901224	−	0.433354i	$-0.142670\pi$
$337$	33.0885	1.80245	0.901224	+	0.433354i	$0.142670\pi$
$338$	12.9999	0.707102
$339$	4.19572	0.227880
$340$	−0.231714	−0.0125664
$341$	−21.7857	−1.17976
$342$	2.61679	0.141500
$343$	0	0
$344$	−1.84951	−0.0997187
$345$	−2.95522	−0.159104
$346$	−15.1576	−0.814880
$347$	3.93552	0.211270	0.105635	−	0.994405i	$-0.466313\pi$
$347$	3.93552	0.211270	0.105635	+	0.994405i	$0.466313\pi$
$348$	−0.378398	−0.0202843
$349$	−6.95104	−0.372080	−0.186040	−	0.982542i	$-0.559565\pi$
$349$	−6.95104	−0.372080	−0.186040	+	0.982542i	$0.559565\pi$
$350$	0	0
$351$	−0.0297020	−0.00158537
$352$	−2.98763	−0.159241
$353$	20.8201	1.10814	0.554072	−	0.832469i	$-0.313073\pi$
$353$	20.8201	1.10814	0.554072	+	0.832469i	$0.313073\pi$
$354$	1.70816	0.0907876
$355$	−12.3299	−0.654402
$356$	9.28595	0.492154
$357$	0	0
$358$	−17.0248	−0.899786
$359$	−21.1534	−1.11643	−0.558217	−	0.829695i	$-0.688514\pi$
$359$	−21.1534	−1.11643	−0.558217	+	0.829695i	$0.688514\pi$
$360$	9.17369	0.483496
$361$	−18.0668	−0.950884
$362$	11.2271	0.590084
$363$	1.11919	0.0587421
$364$	0	0
$365$	11.9262	0.624244
$366$	4.68178	0.244721
$367$	−8.46679	−0.441963	−0.220981	−	0.975278i	$-0.570926\pi$
$367$	−8.46679	−0.441963	−0.220981	+	0.975278i	$0.570926\pi$
$368$	1.61711	0.0842976
$369$	−2.70881	−0.141015
$370$	−16.5571	−0.860762
$371$	0	0
$372$	3.93487	0.204013
$373$	20.6334	1.06836	0.534179	−	0.845371i	$-0.320621\pi$
$373$	20.6334	1.06836	0.534179	+	0.845371i	$0.320621\pi$
$374$	0.204416	0.0105701
$375$	−2.68476	−0.138641
$376$	−3.16995	−0.163478
$377$	−0.00676109	−0.000348214 0
$378$	0	0
$379$	27.0545	1.38970	0.694848	−	0.719156i	$-0.255472\pi$
$379$	27.0545	1.38970	0.694848	+	0.719156i	$0.255472\pi$
$380$	3.27156	0.167827
$381$	0.399881	0.0204865
$382$	−23.6031	−1.20764
$383$	−9.98846	−0.510387	−0.255193	−	0.966890i	$-0.582139\pi$
$383$	−9.98846	−0.510387	−0.255193	+	0.966890i	$0.582139\pi$
$384$	0.539617	0.0275372
$385$	0	0
$386$	8.41165	0.428142
$387$	−5.00997	−0.254671
$388$	−4.17000	−0.211699
$389$	31.1899	1.58139	0.790696	−	0.612209i	$-0.209719\pi$
$389$	31.1899	1.58139	0.790696	+	0.612209i	$0.209719\pi$
$390$	−0.0176199	−0.000892221 0
$391$	−0.110643	−0.00559548
$392$	0	0
$393$	−3.48098	−0.175592
$394$	8.93787	0.450284
$395$	46.3814	2.33370
$396$	−8.09294	−0.406686
$397$	−19.7434	−0.990891	−0.495445	−	0.868639i	$-0.664995\pi$
$397$	−19.7434	−0.990891	−0.495445	+	0.868639i	$0.664995\pi$
$398$	20.9193	1.04859
$399$	0	0
$400$	6.46911	0.323456
$401$	−11.2580	−0.562196	−0.281098	−	0.959679i	$-0.590699\pi$
$401$	−11.2580	−0.562196	−0.281098	+	0.959679i	$0.590699\pi$
$402$	4.61647	0.230249
$403$	0.0703069	0.00350224
$404$	5.41052	0.269183
$405$	21.8914	1.08779
$406$	0	0
$407$	14.6065	0.724018
$408$	−0.0369209	−0.00182786
$409$	−7.27124	−0.359540	−0.179770	−	0.983709i	$-0.557535\pi$
$409$	−7.27124	−0.359540	−0.179770	+	0.983709i	$0.557535\pi$
$410$	−3.38661	−0.167253
$411$	8.47464	0.418023
$412$	13.4966	0.664929
$413$	0	0
$414$	4.38044	0.215287
$415$	−22.4385	−1.10146
$416$	0.00964170	0.000472723 0
$417$	−3.85467	−0.188764
$418$	−2.88614	−0.141166
$419$	24.3697	1.19054	0.595268	−	0.803527i	$-0.297046\pi$
$419$	24.3697	1.19054	0.595268	+	0.803527i	$0.297046\pi$
$420$	0	0
$421$	−11.6797	−0.569236	−0.284618	−	0.958641i	$-0.591867\pi$
$421$	−11.6797	−0.569236	−0.284618	+	0.958641i	$0.591867\pi$
$422$	−10.5708	−0.514577
$423$	−8.58681	−0.417505
$424$	6.61947	0.321470
$425$	−0.442620	−0.0214702
$426$	−1.96462	−0.0951863
$427$	0	0
$428$	9.54211	0.461235
$429$	0.0155442	0.000750479 0
$430$	−6.26355	−0.302055
$431$	14.2910	0.688374	0.344187	−	0.938901i	$-0.388155\pi$
$431$	14.2910	0.688374	0.344187	+	0.938901i	$0.388155\pi$
$432$	3.08057	0.148214
$433$	4.06751	0.195472	0.0977360	−	0.995212i	$-0.468840\pi$
$433$	4.06751	0.195472	0.0977360	+	0.995212i	$0.468840\pi$
$434$	0	0
$435$	−1.28149	−0.0614425
$436$	−2.65081	−0.126951
$437$	1.56217	0.0747288
$438$	1.90030	0.0907997
$439$	17.6381	0.841820	0.420910	−	0.907102i	$-0.361711\pi$
$439$	17.6381	0.841820	0.420910	+	0.907102i	$0.361711\pi$
$440$	−10.1179	−0.482354
$441$	0	0
$442$	−0.000659691 0	−3.13783e−5 0
$443$	2.09016	0.0993066	0.0496533	−	0.998767i	$-0.484188\pi$
$443$	2.09016	0.0993066	0.0496533	+	0.998767i	$0.484188\pi$
$444$	−2.63818	−0.125203
$445$	31.4479	1.49077
$446$	−15.5890	−0.738161
$447$	5.99451	0.283530
$448$	0	0
$449$	−11.1404	−0.525746	−0.262873	−	0.964830i	$-0.584670\pi$
$449$	−11.1404	−0.525746	−0.262873	+	0.964830i	$0.584670\pi$
$450$	17.5236	0.826071
$451$	2.98763	0.140682
$452$	−7.77537	−0.365723
$453$	9.78920	0.459937
$454$	2.96125	0.138978
$455$	0	0
$456$	0.521285	0.0244114
$457$	−26.4289	−1.23629	−0.618147	−	0.786063i	$-0.712116\pi$
$457$	−26.4289	−1.23629	−0.618147	+	0.786063i	$0.712116\pi$
$458$	−24.3188	−1.13634
$459$	−0.210775	−0.00983811
$460$	5.47651	0.255344
$461$	2.37152	0.110453	0.0552263	−	0.998474i	$-0.482412\pi$
$461$	2.37152	0.110453	0.0552263	+	0.998474i	$0.482412\pi$
$462$	0	0
$463$	19.8802	0.923912	0.461956	−	0.886903i	$-0.347148\pi$
$463$	19.8802	0.923912	0.461956	+	0.886903i	$0.347148\pi$
$464$	0.701234	0.0325540
$465$	13.3258	0.617971
$466$	1.72516	0.0799166
$467$	20.1463	0.932262	0.466131	−	0.884716i	$-0.345648\pi$
$467$	20.1463	0.932262	0.466131	+	0.884716i	$0.345648\pi$
$468$	0.0261176	0.00120729
$469$	0	0
$470$	−10.7354	−0.495187
$471$	−8.85676	−0.408098
$472$	−3.16550	−0.145704
$473$	5.52565	0.254070
$474$	7.39034	0.339450
$475$	6.24934	0.286740
$476$	0	0
$477$	17.9309	0.821000
$478$	9.61482	0.439771
$479$	42.0146	1.91970	0.959848	−	0.280521i	$-0.0905074\pi$
$479$	42.0146	1.91970	0.959848	+	0.280521i	$0.0905074\pi$
$480$	1.82747	0.0834123
$481$	−0.0471382	−0.00214932
$482$	14.4222	0.656912
$483$	0	0
$484$	−2.07404	−0.0942745
$485$	−14.1221	−0.641253
$486$	12.7299	0.577438
$487$	11.7506	0.532472	0.266236	−	0.963908i	$-0.414220\pi$
$487$	11.7506	0.532472	0.266236	+	0.963908i	$0.414220\pi$
$488$	−8.67612	−0.392750
$489$	0.854724	0.0386520
$490$	0	0
$491$	−19.2530	−0.868875	−0.434438	−	0.900702i	$-0.643053\pi$
$491$	−19.2530	−0.868875	−0.434438	+	0.900702i	$0.643053\pi$
$492$	−0.539617	−0.0243278
$493$	−0.0479788	−0.00216086
$494$	0.00931416	0.000419064 0
$495$	−27.4076	−1.23188
$496$	−7.29196	−0.327419
$497$	0	0
$498$	−3.57532	−0.160214
$499$	17.7083	0.792730	0.396365	−	0.918093i	$-0.370271\pi$
$499$	17.7083	0.792730	0.396365	+	0.918093i	$0.370271\pi$
$500$	4.97531	0.222503
$501$	−4.37075	−0.195271
$502$	1.02742	0.0458561
$503$	2.66677	0.118906	0.0594528	−	0.998231i	$-0.481064\pi$
$503$	2.66677	0.118906	0.0594528	+	0.998231i	$0.481064\pi$
$504$	0	0
$505$	18.3233	0.815377
$506$	−4.83133	−0.214779
$507$	7.01497	0.311546
$508$	−0.741046	−0.0328786
$509$	13.2720	0.588270	0.294135	−	0.955764i	$-0.404969\pi$
$509$	13.2720	0.588270	0.294135	+	0.955764i	$0.404969\pi$
$510$	−0.125037	−0.00553672
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	2.97592	0.131390
$514$	−5.56650	−0.245528
$515$	45.7077	2.01412
$516$	−0.998025	−0.0439356
$517$	9.47066	0.416519
$518$	0	0
$519$	−8.17932	−0.359032
$520$	0.0326527	0.00143191
$521$	−15.8768	−0.695575	−0.347788	−	0.937573i	$-0.613067\pi$
$521$	−15.8768	−0.695575	−0.347788	+	0.937573i	$0.613067\pi$
$522$	1.89951	0.0831394
$523$	30.0813	1.31537	0.657683	−	0.753295i	$-0.271537\pi$
$523$	30.0813	1.31537	0.657683	+	0.753295i	$0.271537\pi$
$524$	6.45083	0.281806
$525$	0	0
$526$	10.5040	0.457997
$527$	0.498920	0.0217333
$528$	−1.61218	−0.0701611
$529$	−20.3850	−0.886303
$530$	22.4175	0.973756
$531$	−8.57475	−0.372112
$532$	0	0
$533$	−0.00964170	−0.000417629 0
$534$	5.01086	0.216841
$535$	32.3154	1.39712
$536$	−8.55509	−0.369524
$537$	−9.18685	−0.396442
$538$	−27.8900	−1.20243
$539$	0	0
$540$	10.4327	0.448952
$541$	−45.8018	−1.96917	−0.984587	−	0.174893i	$-0.944042\pi$
$541$	−45.8018	−1.96917	−0.984587	+	0.174893i	$0.944042\pi$
$542$	11.8811	0.510337
$543$	6.05835	0.259989
$544$	0.0684206	0.00293351
$545$	−8.97727	−0.384544
$546$	0	0
$547$	15.7657	0.674091	0.337045	−	0.941488i	$-0.390572\pi$
$547$	15.7657	0.674091	0.337045	+	0.941488i	$0.390572\pi$
$548$	−15.7049	−0.670881
$549$	−23.5020	−1.00304
$550$	−19.3273	−0.824121
$551$	0.677412	0.0288587
$552$	0.872619	0.0371411
$553$	0	0
$554$	5.89117	0.250292
$555$	−8.93449	−0.379248
$556$	7.14333	0.302945
$557$	−31.7121	−1.34369	−0.671843	−	0.740694i	$-0.734497\pi$
$557$	−31.7121	−1.34369	−0.671843	+	0.740694i	$0.734497\pi$
$558$	−19.7526	−0.836192
$559$	−0.0178324	−0.000754230 0
$560$	0	0
$561$	0.110306	0.00465713
$562$	12.3163	0.519530
$563$	−1.89988	−0.0800705	−0.0400353	−	0.999198i	$-0.512747\pi$
$563$	−1.89988	−0.0800705	−0.0400353	+	0.999198i	$0.512747\pi$
$564$	−1.71056	−0.0720276
$565$	−26.3321	−1.10780
$566$	−7.63451	−0.320902
$567$	0	0
$568$	3.64077	0.152763
$569$	−21.2474	−0.890736	−0.445368	−	0.895348i	$-0.646927\pi$
$569$	−21.2474	−0.890736	−0.445368	+	0.895348i	$0.646927\pi$
$570$	1.76539	0.0739440
$571$	28.9274	1.21057	0.605287	−	0.796008i	$-0.293059\pi$
$571$	28.9274	1.21057	0.605287	+	0.796008i	$0.293059\pi$
$572$	−0.0288059	−0.00120443
$573$	−12.7366	−0.532080
$574$	0	0
$575$	10.4613	0.436264
$576$	−2.70881	−0.112867
$577$	−27.6536	−1.15123	−0.575617	−	0.817719i	$-0.695238\pi$
$577$	−27.6536	−1.15123	−0.575617	+	0.817719i	$0.695238\pi$
$578$	16.9953	0.706912
$579$	4.53907	0.188637
$580$	2.37481	0.0986084
$581$	0	0
$582$	−2.25020	−0.0932739
$583$	−19.7766	−0.819061
$584$	−3.52157	−0.145723
$585$	0.0884500	0.00365696
$586$	−26.4456	−1.09246
$587$	4.41980	0.182425	0.0912123	−	0.995831i	$-0.470926\pi$
$587$	4.41980	0.182425	0.0912123	+	0.995831i	$0.470926\pi$
$588$	0	0
$589$	−7.04423	−0.290253
$590$	−10.7203	−0.441348
$591$	4.82303	0.198393
$592$	4.88899	0.200936
$593$	11.6028	0.476468	0.238234	−	0.971208i	$-0.423431\pi$
$593$	11.6028	0.476468	0.238234	+	0.971208i	$0.423431\pi$
$594$	−9.20363	−0.377629
$595$	0	0
$596$	−11.1088	−0.455035
$597$	11.2884	0.462005
$598$	0.0155917	0.000637591 0
$599$	−15.2032	−0.621187	−0.310593	−	0.950543i	$-0.600528\pi$
$599$	−15.2032	−0.621187	−0.310593	+	0.950543i	$0.600528\pi$
$600$	3.49085	0.142513
$601$	−33.4852	−1.36589	−0.682944	−	0.730470i	$-0.739301\pi$
$601$	−33.4852	−1.36589	−0.682944	+	0.730470i	$0.739301\pi$
$602$	0	0
$603$	−23.1741	−0.943724
$604$	−18.1410	−0.738147
$605$	−7.02396	−0.285565
$606$	2.91961	0.118601
$607$	39.4996	1.60324	0.801620	−	0.597834i	$-0.203972\pi$
$607$	39.4996	1.60324	0.801620	+	0.597834i	$0.203972\pi$
$608$	−0.966028	−0.0391776
$609$	0	0
$610$	−29.3826	−1.18967
$611$	−0.0305638	−0.00123648
$612$	0.185339	0.00749187
$613$	21.6181	0.873146	0.436573	−	0.899669i	$-0.356192\pi$
$613$	21.6181	0.873146	0.436573	+	0.899669i	$0.356192\pi$
$614$	−11.1342	−0.449339
$615$	−1.82747	−0.0736908
$616$	0	0
$617$	−1.32602	−0.0533835	−0.0266918	−	0.999644i	$-0.508497\pi$
$617$	−1.32602	−0.0533835	−0.0266918	+	0.999644i	$0.508497\pi$
$618$	7.28299	0.292965
$619$	−39.2016	−1.57564	−0.787822	−	0.615903i	$-0.788791\pi$
$619$	−39.2016	−1.57564	−0.787822	+	0.615903i	$0.788791\pi$
$620$	−24.6950	−0.991775
$621$	4.98162	0.199905
$622$	5.52223	0.221421
$623$	0	0
$624$	0.00520283	0.000208280 0
$625$	−15.4961	−0.619845
$626$	−11.1544	−0.445821
$627$	−1.55741	−0.0621970
$628$	16.4130	0.654952
$629$	−0.334507	−0.0133377
$630$	0	0
$631$	−21.0119	−0.836469	−0.418235	−	0.908339i	$-0.637351\pi$
$631$	−21.0119	−0.836469	−0.418235	+	0.908339i	$0.637351\pi$
$632$	−13.6955	−0.544779
$633$	−5.70417	−0.226721
$634$	−3.17686	−0.126169
$635$	−2.50963	−0.0995917
$636$	3.57198	0.141638
$637$	0	0
$638$	−2.09503	−0.0829431
$639$	9.86217	0.390142
$640$	−3.38661	−0.133867
$641$	−9.17231	−0.362284	−0.181142	−	0.983457i	$-0.557979\pi$
$641$	−9.17231	−0.362284	−0.181142	+	0.983457i	$0.557979\pi$
$642$	5.14909	0.203218
$643$	18.2534	0.719845	0.359923	−	0.932982i	$-0.382803\pi$
$643$	18.2534	0.719845	0.359923	+	0.932982i	$0.382803\pi$
$644$	0	0
$645$	−3.37992	−0.133084
$646$	0.0660962	0.00260052
$647$	−21.6102	−0.849583	−0.424792	−	0.905291i	$-0.639653\pi$
$647$	−21.6102	−0.849583	−0.424792	+	0.905291i	$0.639653\pi$
$648$	−6.46411	−0.253934
$649$	9.45736	0.371234
$650$	0.0623733	0.00244648
$651$	0	0
$652$	−1.58395	−0.0620321
$653$	−37.3303	−1.46085	−0.730423	−	0.682995i	$-0.760677\pi$
$653$	−37.3303	−1.46085	−0.730423	+	0.682995i	$0.760677\pi$
$654$	−1.43042	−0.0559340
$655$	21.8464	0.853611
$656$	1.00000	0.0390434
$657$	−9.53927	−0.372162
$658$	0	0
$659$	4.38062	0.170645	0.0853224	−	0.996353i	$-0.472808\pi$
$659$	4.38062	0.170645	0.0853224	+	0.996353i	$0.472808\pi$
$660$	−5.45982	−0.212523
$661$	−42.5771	−1.65606	−0.828029	−	0.560685i	$-0.810538\pi$
$661$	−42.5771	−1.65606	−0.828029	+	0.560685i	$0.810538\pi$
$662$	−13.3594	−0.519227
$663$	−0.000355980 0	−1.38251e−5 0
$664$	6.62566	0.257126
$665$	0	0
$666$	13.2434	0.513170
$667$	1.13397	0.0439075
$668$	8.09972	0.313388
$669$	−8.41210	−0.325230
$670$	−28.9727	−1.11931
$671$	25.9211	1.00067
$672$	0	0
$673$	40.4996	1.56115	0.780573	−	0.625065i	$-0.214927\pi$
$673$	40.4996	1.56115	0.780573	+	0.625065i	$0.214927\pi$
$674$	−33.0885	−1.27452
$675$	19.9286	0.767052
$676$	−12.9999	−0.499996
$677$	−3.09659	−0.119012	−0.0595058	−	0.998228i	$-0.518952\pi$
$677$	−3.09659	−0.119012	−0.0595058	+	0.998228i	$0.518952\pi$
$678$	−4.19572	−0.161136
$679$	0	0
$680$	0.231714	0.00888581
$681$	1.59794	0.0612333
$682$	21.7857	0.834218
$683$	24.4003	0.933650	0.466825	−	0.884350i	$-0.345398\pi$
$683$	24.4003	0.933650	0.466825	+	0.884350i	$0.345398\pi$
$684$	−2.61679	−0.100055
$685$	−53.1864	−2.03215
$686$	0	0
$687$	−13.1228	−0.500667
$688$	1.84951	0.0705117
$689$	0.0638230	0.00243146
$690$	2.95522	0.112503
$691$	−0.130749	−0.00497394	−0.00248697	−	0.999997i	$-0.500792\pi$
$691$	−0.130749	−0.00497394	−0.00248697	+	0.999997i	$0.500792\pi$
$692$	15.1576	0.576207
$693$	0	0
$694$	−3.93552	−0.149390
$695$	24.1917	0.917643
$696$	0.378398	0.0143431
$697$	−0.0684206	−0.00259161
$698$	6.95104	0.263101
$699$	0.930927	0.0352109
$700$	0	0
$701$	−25.9200	−0.978985	−0.489493	−	0.872007i	$-0.662818\pi$
$701$	−25.9200	−0.978985	−0.489493	+	0.872007i	$0.662818\pi$
$702$	0.0297020	0.00112103
$703$	4.72290	0.178128
$704$	2.98763	0.112601
$705$	−5.79300	−0.218177
$706$	−20.8201	−0.783576
$707$	0	0
$708$	−1.70816	−0.0641965
$709$	−9.45952	−0.355260	−0.177630	−	0.984097i	$-0.556843\pi$
$709$	−9.45952	−0.355260	−0.177630	+	0.984097i	$0.556843\pi$
$710$	12.3299	0.462732
$711$	−37.0986	−1.39131
$712$	−9.28595	−0.348006
$713$	−11.7919	−0.441609
$714$	0	0
$715$	−0.0975543	−0.00364832
$716$	17.0248	0.636245
$717$	5.18832	0.193761
$718$	21.1534	0.789438
$719$	15.2451	0.568547	0.284274	−	0.958743i	$-0.408248\pi$
$719$	15.2451	0.568547	0.284274	+	0.958743i	$0.408248\pi$
$720$	−9.17369	−0.341883
$721$	0	0
$722$	18.0668	0.672376
$723$	7.78245	0.289432
$724$	−11.2271	−0.417253
$725$	4.53636	0.168476
$726$	−1.11919	−0.0415369
$727$	−32.6402	−1.21056	−0.605279	−	0.796013i	$-0.706939\pi$
$727$	−32.6402	−1.21056	−0.605279	+	0.796013i	$0.706939\pi$
$728$	0	0
$729$	−12.5231	−0.463818
$730$	−11.9262	−0.441407
$731$	−0.126544	−0.00468041
$732$	−4.68178	−0.173044
$733$	−10.7460	−0.396912	−0.198456	−	0.980110i	$-0.563593\pi$
$733$	−10.7460	−0.396912	−0.198456	+	0.980110i	$0.563593\pi$
$734$	8.46679	0.312515
$735$	0	0
$736$	−1.61711	−0.0596074
$737$	25.5595	0.941496
$738$	2.70881	0.0997128
$739$	−7.11218	−0.261626	−0.130813	−	0.991407i	$-0.541759\pi$
$739$	−7.11218	−0.261626	−0.130813	+	0.991407i	$0.541759\pi$
$740$	16.5571	0.608651
$741$	0.00502608	0.000184638 0
$742$	0	0
$743$	−29.2345	−1.07251	−0.536255	−	0.844056i	$-0.680162\pi$
$743$	−29.2345	−1.07251	−0.536255	+	0.844056i	$0.680162\pi$
$744$	−3.93487	−0.144259
$745$	−37.6212	−1.37833
$746$	−20.6334	−0.755444
$747$	17.9477	0.656671
$748$	−0.204416	−0.00747418
$749$	0	0
$750$	2.68476	0.0980337
$751$	−23.9539	−0.874091	−0.437046	−	0.899439i	$-0.643975\pi$
$751$	−23.9539	−0.874091	−0.437046	+	0.899439i	$0.643975\pi$
$752$	3.16995	0.115596
$753$	0.554414	0.0202040
$754$	0.00676109	0.000246225 0
$755$	−61.4365	−2.23590
$756$	0	0
$757$	−14.9884	−0.544761	−0.272380	−	0.962190i	$-0.587811\pi$
$757$	−14.9884	−0.544761	−0.272380	+	0.962190i	$0.587811\pi$
$758$	−27.0545	−0.982664
$759$	−2.60707	−0.0946305
$760$	−3.27156	−0.118672
$761$	−16.3237	−0.591733	−0.295867	−	0.955229i	$-0.595608\pi$
$761$	−16.3237	−0.591733	−0.295867	+	0.955229i	$0.595608\pi$
$762$	−0.399881	−0.0144862
$763$	0	0
$764$	23.6031	0.853929
$765$	0.627669	0.0226934
$766$	9.98846	0.360898
$767$	−0.0305208	−0.00110204
$768$	−0.539617	−0.0194718
$769$	−46.1029	−1.66251	−0.831256	−	0.555890i	$-0.812378\pi$
$769$	−46.1029	−1.66251	−0.831256	+	0.555890i	$0.812378\pi$
$770$	0	0
$771$	−3.00378	−0.108178
$772$	−8.41165	−0.302742
$773$	40.2629	1.44816	0.724078	−	0.689718i	$-0.242266\pi$
$773$	40.2629	1.44816	0.724078	+	0.689718i	$0.242266\pi$
$774$	5.00997	0.180079
$775$	−47.1725	−1.69449
$776$	4.17000	0.149694
$777$	0	0
$778$	−31.1899	−1.11821
$779$	0.966028	0.0346115
$780$	0.0176199	0.000630895 0
$781$	−10.8773	−0.389220
$782$	0.110643	0.00395660
$783$	2.16020	0.0771994
$784$	0	0
$785$	55.5845	1.98390
$786$	3.48098	0.124162
$787$	14.1353	0.503868	0.251934	−	0.967744i	$-0.418933\pi$
$787$	14.1353	0.503868	0.251934	+	0.967744i	$0.418933\pi$
$788$	−8.93787	−0.318399
$789$	5.66814	0.201791
$790$	−46.3814	−1.65018
$791$	0	0
$792$	8.09294	0.287570
$793$	−0.0836526	−0.00297059
$794$	19.7434	0.700666
$795$	12.0969	0.429033
$796$	−20.9193	−0.741466
$797$	20.7201	0.733943	0.366972	−	0.930232i	$-0.380395\pi$
$797$	20.7201	0.733943	0.366972	+	0.930232i	$0.380395\pi$
$798$	0	0
$799$	−0.216890	−0.00767301
$800$	−6.46911	−0.228718
$801$	−25.1539	−0.888769
$802$	11.2580	0.397533
$803$	10.5212	0.371283
$804$	−4.61647	−0.162810
$805$	0	0
$806$	−0.0703069	−0.00247646
$807$	−15.0499	−0.529783
$808$	−5.41052	−0.190341
$809$	33.2683	1.16965	0.584825	−	0.811159i	$-0.301163\pi$
$809$	33.2683	1.16965	0.584825	+	0.811159i	$0.301163\pi$
$810$	−21.8914	−0.769186
$811$	−41.8531	−1.46966	−0.734831	−	0.678250i	$-0.762739\pi$
$811$	−41.8531	−1.46966	−0.734831	+	0.678250i	$0.762739\pi$
$812$	0	0
$813$	6.41124	0.224852
$814$	−14.6065	−0.511958
$815$	−5.36420	−0.187900
$816$	0.0369209	0.00129249
$817$	1.78667	0.0625078
$818$	7.27124	0.254233
$819$	0	0
$820$	3.38661	0.118265
$821$	16.8738	0.588900	0.294450	−	0.955667i	$-0.404864\pi$
$821$	16.8738	0.588900	0.294450	+	0.955667i	$0.404864\pi$
$822$	−8.47464	−0.295587
$823$	−46.6603	−1.62648	−0.813238	−	0.581931i	$-0.802298\pi$
$823$	−46.6603	−1.62648	−0.813238	+	0.581931i	$0.802298\pi$
$824$	−13.4966	−0.470176
$825$	−10.4294	−0.363104
$826$	0	0
$827$	40.7692	1.41768	0.708841	−	0.705368i	$-0.249218\pi$
$827$	40.7692	1.41768	0.708841	+	0.705368i	$0.249218\pi$
$828$	−4.38044	−0.152231
$829$	20.5803	0.714783	0.357392	−	0.933955i	$-0.383666\pi$
$829$	20.5803	0.714783	0.357392	+	0.933955i	$0.383666\pi$
$830$	22.4385	0.778853
$831$	3.17898	0.110278
$832$	−0.00964170	−0.000334266 0
$833$	0	0
$834$	3.85467	0.133476
$835$	27.4306	0.949275
$836$	2.88614	0.0998192
$837$	−22.4634	−0.776449
$838$	−24.3697	−0.841836
$839$	−51.2811	−1.77042	−0.885210	−	0.465192i	$-0.845985\pi$
$839$	−51.2811	−1.77042	−0.885210	+	0.465192i	$0.845985\pi$
$840$	0	0
$841$	−28.5083	−0.983044
$842$	11.6797	0.402511
$843$	6.64606	0.228903
$844$	10.5708	0.363861
$845$	−44.0256	−1.51453
$846$	8.58681	0.295221
$847$	0	0
$848$	−6.61947	−0.227313
$849$	−4.11971	−0.141388
$850$	0.442620	0.0151818
$851$	7.90602	0.271015
$852$	1.96462	0.0673069
$853$	−41.1032	−1.40735	−0.703674	−	0.710523i	$-0.748458\pi$
$853$	−41.1032	−1.40735	−0.703674	+	0.710523i	$0.748458\pi$
$854$	0	0
$855$	−8.86204	−0.303075
$856$	−9.54211	−0.326143
$857$	26.8788	0.918164	0.459082	−	0.888394i	$-0.348178\pi$
$857$	26.8788	0.918164	0.459082	+	0.888394i	$0.348178\pi$
$858$	−0.0155442	−0.000530669 0
$859$	−40.3148	−1.37552	−0.687761	−	0.725937i	$-0.741406\pi$
$859$	−40.3148	−1.37552	−0.687761	+	0.725937i	$0.741406\pi$
$860$	6.26355	0.213585
$861$	0	0
$862$	−14.2910	−0.486754
$863$	−49.3950	−1.68143	−0.840713	−	0.541480i	$-0.817864\pi$
$863$	−49.3950	−1.68143	−0.840713	+	0.541480i	$0.817864\pi$
$864$	−3.08057	−0.104803
$865$	51.3330	1.74537
$866$	−4.06751	−0.138220
$867$	9.17097	0.311462
$868$	0	0
$869$	40.9172	1.38802
$870$	1.28149	0.0434464
$871$	−0.0824857	−0.00279492
$872$	2.65081	0.0897679
$873$	11.2957	0.382303
$874$	−1.56217	−0.0528412
$875$	0	0
$876$	−1.90030	−0.0642051
$877$	−26.3155	−0.888612	−0.444306	−	0.895875i	$-0.646550\pi$
$877$	−26.3155	−0.888612	−0.444306	+	0.895875i	$0.646550\pi$
$878$	−17.6381	−0.595257
$879$	−14.2705	−0.481332
$880$	10.1179	0.341076
$881$	−2.76108	−0.0930231	−0.0465116	−	0.998918i	$-0.514810\pi$
$881$	−2.76108	−0.0930231	−0.0465116	+	0.998918i	$0.514810\pi$
$882$	0	0
$883$	−37.8887	−1.27506	−0.637529	−	0.770427i	$-0.720043\pi$
$883$	−37.8887	−1.27506	−0.637529	+	0.770427i	$0.720043\pi$
$884$	0.000659691 0	2.21878e−5 0
$885$	−5.78486	−0.194456
$886$	−2.09016	−0.0702203
$887$	27.4974	0.923273	0.461637	−	0.887069i	$-0.347262\pi$
$887$	27.4974	0.923273	0.461637	+	0.887069i	$0.347262\pi$
$888$	2.63818	0.0885316
$889$	0	0
$890$	−31.4479	−1.05414
$891$	19.3124	0.646990
$892$	15.5890	0.521959
$893$	3.06226	0.102475
$894$	−5.99451	−0.200486
$895$	57.6562	1.92723
$896$	0	0
$897$	0.00841353	0.000280920 0
$898$	11.1404	0.371758
$899$	−5.11337	−0.170540
$900$	−17.5236	−0.584121
$901$	0.452908	0.0150885
$902$	−2.98763	−0.0994774
$903$	0	0
$904$	7.77537	0.258605
$905$	−38.0219	−1.26389
$906$	−9.78920	−0.325224
$907$	−41.3773	−1.37391	−0.686956	−	0.726699i	$-0.741053\pi$
$907$	−41.3773	−1.37391	−0.686956	+	0.726699i	$0.741053\pi$
$908$	−2.96125	−0.0982726
$909$	−14.6561	−0.486112
$910$	0	0
$911$	49.8447	1.65143	0.825715	−	0.564087i	$-0.190772\pi$
$911$	49.8447	1.65143	0.825715	+	0.564087i	$0.190772\pi$
$912$	−0.521285	−0.0172615
$913$	−19.7951	−0.655121
$914$	26.4289	0.874192
$915$	−15.8554	−0.524162
$916$	24.3188	0.803515
$917$	0	0
$918$	0.210775	0.00695660
$919$	4.40801	0.145407	0.0727035	−	0.997354i	$-0.476837\pi$
$919$	4.40801	0.145407	0.0727035	+	0.997354i	$0.476837\pi$
$920$	−5.47651	−0.180555
$921$	−6.00820	−0.197977
$922$	−2.37152	−0.0781017
$923$	0.0351033	0.00115544
$924$	0	0
$925$	31.6274	1.03990
$926$	−19.8802	−0.653304
$927$	−36.5597	−1.20078
$928$	−0.701234	−0.0230191
$929$	−16.9983	−0.557696	−0.278848	−	0.960335i	$-0.589953\pi$
$929$	−16.9983	−0.557696	−0.278848	+	0.960335i	$0.589953\pi$
$930$	−13.3258	−0.436972
$931$	0	0
$932$	−1.72516	−0.0565096
$933$	2.97989	0.0975573
$934$	−20.1463	−0.659209
$935$	−0.692276	−0.0226398
$936$	−0.0261176	−0.000853680 0
$937$	−13.3600	−0.436452	−0.218226	−	0.975898i	$-0.570027\pi$
$937$	−13.3600	−0.436452	−0.218226	+	0.975898i	$0.570027\pi$
$938$	0	0
$939$	−6.01912	−0.196427
$940$	10.7354	0.350150
$941$	−37.8940	−1.23531	−0.617654	−	0.786450i	$-0.711917\pi$
$941$	−37.8940	−1.23531	−0.617654	+	0.786450i	$0.711917\pi$
$942$	8.85676	0.288569
$943$	1.61711	0.0526603
$944$	3.16550	0.103028
$945$	0	0
$946$	−5.52565	−0.179654
$947$	33.5264	1.08946	0.544731	−	0.838611i	$-0.316632\pi$
$947$	33.5264	1.08946	0.544731	+	0.838611i	$0.316632\pi$
$948$	−7.39034	−0.240027
$949$	−0.0339539	−0.00110219
$950$	−6.24934	−0.202756
$951$	−1.71429	−0.0555896
$952$	0	0
$953$	36.9263	1.19616	0.598079	−	0.801437i	$-0.295931\pi$
$953$	36.9263	1.19616	0.598079	+	0.801437i	$0.295931\pi$
$954$	−17.9309	−0.580534
$955$	79.9344	2.58662
$956$	−9.61482	−0.310965
$957$	−1.13052	−0.0365444
$958$	−42.0146	−1.35743
$959$	0	0
$960$	−1.82747	−0.0589814
$961$	22.1726	0.715247
$962$	0.0471382	0.00151980
$963$	−25.8478	−0.832933
$964$	−14.4222	−0.464507
$965$	−28.4870	−0.917028
$966$	0	0
$967$	58.3356	1.87595	0.937973	−	0.346708i	$-0.112700\pi$
$967$	58.3356	1.87595	0.937973	+	0.346708i	$0.112700\pi$
$968$	2.07404	0.0666622
$969$	0.0356666	0.00114578
$970$	14.1221	0.453435
$971$	26.4840	0.849911	0.424955	−	0.905214i	$-0.360290\pi$
$971$	26.4840	0.849911	0.424955	+	0.905214i	$0.360290\pi$
$972$	−12.7299	−0.408311
$973$	0	0
$974$	−11.7506	−0.376514
$975$	0.0336577	0.00107791
$976$	8.67612	0.277716
$977$	24.6468	0.788522	0.394261	−	0.918999i	$-0.371001\pi$
$977$	24.6468	0.788522	0.394261	+	0.918999i	$0.371001\pi$
$978$	−0.854724	−0.0273311
$979$	27.7430	0.886671
$980$	0	0
$981$	7.18056	0.229258
$982$	19.2530	0.614388
$983$	−44.0018	−1.40344	−0.701720	−	0.712452i	$-0.747584\pi$
$983$	−44.0018	−1.40344	−0.701720	+	0.712452i	$0.747584\pi$
$984$	0.539617	0.0172024
$985$	−30.2691	−0.964453
$986$	0.0479788	0.00152796
$987$	0	0
$988$	−0.00931416	−0.000296323 0
$989$	2.99085	0.0951035
$990$	27.4076	0.871072
$991$	−33.7218	−1.07121	−0.535604	−	0.844470i	$-0.679916\pi$
$991$	−33.7218	−1.07121	−0.535604	+	0.844470i	$0.679916\pi$
$992$	7.29196	0.231520
$993$	−7.20895	−0.228769
$994$	0	0
$995$	−70.8456	−2.24596
$996$	3.57532	0.113288
$997$	−34.3401	−1.08756	−0.543781	−	0.839227i	$-0.683008\pi$
$997$	−34.3401	−1.08756	−0.543781	+	0.839227i	$0.683008\pi$
$998$	−17.7083	−0.560545
$999$	15.0609	0.476506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bs.1.4	yes	10
7.6	odd	2		4018.2.a.br.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.br.1.7	✓	10	7.6	odd	2
4018.2.a.bs.1.4	yes	10	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.539617 q^{3} +1.00000 q^{4} +3.38661 q^{5} +0.539617 q^{6} -1.00000 q^{8} -2.70881 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.539617 q^{3} +1.00000 q^{4} +3.38661 q^{5} +0.539617 q^{6} -1.00000 q^{8} -2.70881 q^{9} -3.38661 q^{10} +2.98763 q^{11} -0.539617 q^{12} -0.00964170 q^{13} -1.82747 q^{15} +1.00000 q^{16} -0.0684206 q^{17} +2.70881 q^{18} +0.966028 q^{19} +3.38661 q^{20} -2.98763 q^{22} +1.61711 q^{23} +0.539617 q^{24} +6.46911 q^{25} +0.00964170 q^{26} +3.08057 q^{27} +0.701234 q^{29} +1.82747 q^{30} -7.29196 q^{31} -1.00000 q^{32} -1.61218 q^{33} +0.0684206 q^{34} -2.70881 q^{36} +4.88899 q^{37} -0.966028 q^{38} +0.00520283 q^{39} -3.38661 q^{40} +1.00000 q^{41} +1.84951 q^{43} +2.98763 q^{44} -9.17369 q^{45} -1.61711 q^{46} +3.16995 q^{47} -0.539617 q^{48} -6.46911 q^{50} +0.0369209 q^{51} -0.00964170 q^{52} -6.61947 q^{53} -3.08057 q^{54} +10.1179 q^{55} -0.521285 q^{57} -0.701234 q^{58} +3.16550 q^{59} -1.82747 q^{60} +8.67612 q^{61} +7.29196 q^{62} +1.00000 q^{64} -0.0326527 q^{65} +1.61218 q^{66} +8.55509 q^{67} -0.0684206 q^{68} -0.872619 q^{69} -3.64077 q^{71} +2.70881 q^{72} +3.52157 q^{73} -4.88899 q^{74} -3.49085 q^{75} +0.966028 q^{76} -0.00520283 q^{78} +13.6955 q^{79} +3.38661 q^{80} +6.46411 q^{81} -1.00000 q^{82} -6.62566 q^{83} -0.231714 q^{85} -1.84951 q^{86} -0.378398 q^{87} -2.98763 q^{88} +9.28595 q^{89} +9.17369 q^{90} +1.61711 q^{92} +3.93487 q^{93} -3.16995 q^{94} +3.27156 q^{95} +0.539617 q^{96} -4.17000 q^{97} -8.09294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 4 * q^3 + 10 * q^4 + 4 * q^5 - 4 * q^6 - 10 * q^8 + 10 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 20 * q^17 - 10 * q^18 + 4 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 16 * q^27 - 4 * q^29 - 4 * q^30 - 4 * q^31 - 10 * q^32 + 36 * q^33 - 20 * q^34 + 10 * q^36 - 16 * q^37 + 20 * q^39 - 4 * q^40 + 10 * q^41 - 8 * q^43 + 4 * q^44 + 4 * q^45 - 4 * q^46 + 24 * q^47 + 4 * q^48 - 6 * q^50 + 20 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^54 + 20 * q^55 - 4 * q^57 + 4 * q^58 + 4 * q^60 + 4 * q^62 + 10 * q^64 - 12 * q^65 - 36 * q^66 + 8 * q^67 + 20 * q^68 + 4 * q^71 - 10 * q^72 - 24 * q^73 + 16 * q^74 + 48 * q^75 - 20 * q^78 + 24 * q^79 + 4 * q^80 - 18 * q^81 - 10 * q^82 + 48 * q^83 + 8 * q^85 + 8 * q^86 + 4 * q^87 - 4 * q^88 + 20 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 24 * q^94 - 4 * q^95 - 4 * q^96 + 4 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

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Database

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