LMFDB - Embedded newform 4018.2.a.br.1.5

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:	$1$
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			1.5
Root			$0.560789$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.748903 q^{3} +1.00000 q^{4} +1.86270 q^{5} +0.748903 q^{6} -1.00000 q^{8} -2.43914 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.748903 q^{3} +1.00000 q^{4} +1.86270 q^{5} +0.748903 q^{6} -1.00000 q^{8} -2.43914 q^{9} -1.86270 q^{10} +4.01593 q^{11} -0.748903 q^{12} -1.23814 q^{13} -1.39498 q^{15} +1.00000 q^{16} -0.0249841 q^{17} +2.43914 q^{18} -5.68255 q^{19} +1.86270 q^{20} -4.01593 q^{22} +8.15588 q^{23} +0.748903 q^{24} -1.53037 q^{25} +1.23814 q^{26} +4.07339 q^{27} -6.35687 q^{29} +1.39498 q^{30} -4.57801 q^{31} -1.00000 q^{32} -3.00754 q^{33} +0.0249841 q^{34} -2.43914 q^{36} -0.186536 q^{37} +5.68255 q^{38} +0.927248 q^{39} -1.86270 q^{40} -1.00000 q^{41} -12.3875 q^{43} +4.01593 q^{44} -4.54338 q^{45} -8.15588 q^{46} +0.593740 q^{47} -0.748903 q^{48} +1.53037 q^{50} +0.0187107 q^{51} -1.23814 q^{52} +9.94076 q^{53} -4.07339 q^{54} +7.48045 q^{55} +4.25568 q^{57} +6.35687 q^{58} +8.34796 q^{59} -1.39498 q^{60} +10.4690 q^{61} +4.57801 q^{62} +1.00000 q^{64} -2.30628 q^{65} +3.00754 q^{66} -13.2941 q^{67} -0.0249841 q^{68} -6.10796 q^{69} -3.37960 q^{71} +2.43914 q^{72} -14.7826 q^{73} +0.186536 q^{74} +1.14610 q^{75} -5.68255 q^{76} -0.927248 q^{78} -2.19932 q^{79} +1.86270 q^{80} +4.26685 q^{81} +1.00000 q^{82} -7.94255 q^{83} -0.0465377 q^{85} +12.3875 q^{86} +4.76068 q^{87} -4.01593 q^{88} -13.8087 q^{89} +4.54338 q^{90} +8.15588 q^{92} +3.42849 q^{93} -0.593740 q^{94} -10.5849 q^{95} +0.748903 q^{96} -15.4269 q^{97} -9.79542 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.748903	−0.432380	−0.216190	−	0.976351i	$-0.569363\pi$
$3$	−0.748903	−0.432380	−0.216190	+	0.976351i	$0.569363\pi$
$4$	1.00000	0.500000
$5$	1.86270	0.833023	0.416511	−	0.909131i	$-0.363253\pi$
$5$	1.86270	0.833023	0.416511	+	0.909131i	$0.363253\pi$
$6$	0.748903	0.305738
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.43914	−0.813048
$10$	−1.86270	−0.589036
$11$	4.01593	1.21085	0.605424	−	0.795903i	$-0.293004\pi$
$11$	4.01593	1.21085	0.605424	+	0.795903i	$0.293004\pi$
$12$	−0.748903	−0.216190
$13$	−1.23814	−0.343399	−0.171699	−	0.985149i	$-0.554926\pi$
$13$	−1.23814	−0.343399	−0.171699	+	0.985149i	$0.554926\pi$
$14$	0	0
$15$	−1.39498	−0.360182
$16$	1.00000	0.250000
$17$	−0.0249841	−0.00605953	−0.00302977	−	0.999995i	$-0.500964\pi$
$17$	−0.0249841	−0.00605953	−0.00302977	+	0.999995i	$0.500964\pi$
$18$	2.43914	0.574912
$19$	−5.68255	−1.30367	−0.651834	−	0.758362i	$-0.726000\pi$
$19$	−5.68255	−1.30367	−0.651834	+	0.758362i	$0.726000\pi$
$20$	1.86270	0.416511
$21$	0	0
$22$	−4.01593	−0.856198
$23$	8.15588	1.70062	0.850309	−	0.526284i	$-0.176415\pi$
$23$	8.15588	1.70062	0.850309	+	0.526284i	$0.176415\pi$
$24$	0.748903	0.152869
$25$	−1.53037	−0.306073
$26$	1.23814	0.242819
$27$	4.07339	0.783925
$28$	0	0
$29$	−6.35687	−1.18044	−0.590221	−	0.807242i	$-0.700959\pi$
$29$	−6.35687	−1.18044	−0.590221	+	0.807242i	$0.700959\pi$
$30$	1.39498	0.254687
$31$	−4.57801	−0.822235	−0.411118	−	0.911582i	$-0.634861\pi$
$31$	−4.57801	−0.822235	−0.411118	+	0.911582i	$0.634861\pi$
$32$	−1.00000	−0.176777
$33$	−3.00754	−0.523546
$34$	0.0249841	0.00428474
$35$	0	0
$36$	−2.43914	−0.406524
$37$	−0.186536	−0.0306664	−0.0153332	−	0.999882i	$-0.504881\pi$
$37$	−0.186536	−0.0306664	−0.0153332	+	0.999882i	$0.504881\pi$
$38$	5.68255	0.921832
$39$	0.927248	0.148478
$40$	−1.86270	−0.294518
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−12.3875	−1.88908	−0.944539	−	0.328399i	$-0.893491\pi$
$43$	−12.3875	−1.88908	−0.944539	+	0.328399i	$0.893491\pi$
$44$	4.01593	0.605424
$45$	−4.54338	−0.677287
$46$	−8.15588	−1.20252
$47$	0.593740	0.0866058	0.0433029	−	0.999062i	$-0.486212\pi$
$47$	0.593740	0.0866058	0.0433029	+	0.999062i	$0.486212\pi$
$48$	−0.748903	−0.108095
$49$	0	0
$50$	1.53037	0.216427
$51$	0.0187107	0.00262002
$52$	−1.23814	−0.171699
$53$	9.94076	1.36547	0.682734	−	0.730667i	$-0.260791\pi$
$53$	9.94076	1.36547	0.682734	+	0.730667i	$0.260791\pi$
$54$	−4.07339	−0.554319
$55$	7.48045	1.00866
$56$	0	0
$57$	4.25568	0.563679
$58$	6.35687	0.834698
$59$	8.34796	1.08681	0.543406	−	0.839470i	$-0.317135\pi$
$59$	8.34796	1.08681	0.543406	+	0.839470i	$0.317135\pi$
$60$	−1.39498	−0.180091
$61$	10.4690	1.34041	0.670206	−	0.742175i	$-0.266206\pi$
$61$	10.4690	1.34041	0.670206	+	0.742175i	$0.266206\pi$
$62$	4.57801	0.581408
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.30628	−0.286059
$66$	3.00754	0.370203
$67$	−13.2941	−1.62413	−0.812064	−	0.583569i	$-0.801656\pi$
$67$	−13.2941	−1.62413	−0.812064	+	0.583569i	$0.801656\pi$
$68$	−0.0249841	−0.00302977
$69$	−6.10796	−0.735312
$70$	0	0
$71$	−3.37960	−0.401085	−0.200542	−	0.979685i	$-0.564270\pi$
$71$	−3.37960	−0.401085	−0.200542	+	0.979685i	$0.564270\pi$
$72$	2.43914	0.287456
$73$	−14.7826	−1.73017	−0.865087	−	0.501621i	$-0.832737\pi$
$73$	−14.7826	−1.73017	−0.865087	+	0.501621i	$0.832737\pi$
$74$	0.186536	0.0216844
$75$	1.14610	0.132340
$76$	−5.68255	−0.651834
$77$	0	0
$78$	−0.927248	−0.104990
$79$	−2.19932	−0.247443	−0.123721	−	0.992317i	$-0.539483\pi$
$79$	−2.19932	−0.247443	−0.123721	+	0.992317i	$0.539483\pi$
$80$	1.86270	0.208256
$81$	4.26685	0.474095
$82$	1.00000	0.110432
$83$	−7.94255	−0.871808	−0.435904	−	0.899993i	$-0.643571\pi$
$83$	−7.94255	−0.871808	−0.435904	+	0.899993i	$0.643571\pi$
$84$	0	0
$85$	−0.0465377	−0.00504773
$86$	12.3875	1.33578
$87$	4.76068	0.510399
$88$	−4.01593	−0.428099
$89$	−13.8087	−1.46372	−0.731860	−	0.681455i	$-0.761348\pi$
$89$	−13.8087	−1.46372	−0.731860	+	0.681455i	$0.761348\pi$
$90$	4.54338	0.478914
$91$	0	0
$92$	8.15588	0.850309
$93$	3.42849	0.355518
$94$	−0.593740	−0.0612396
$95$	−10.5849	−1.08598
$96$	0.748903	0.0764346
$97$	−15.4269	−1.56636	−0.783180	−	0.621795i	$-0.786404\pi$
$97$	−15.4269	−1.56636	−0.783180	+	0.621795i	$0.786404\pi$
$98$	0	0
$99$	−9.79542	−0.984477
$100$	−1.53037	−0.153037
$101$	−10.9586	−1.09042	−0.545209	−	0.838300i	$-0.683550\pi$
$101$	−10.9586	−1.09042	−0.545209	+	0.838300i	$0.683550\pi$
$102$	−0.0187107	−0.00185263
$103$	11.1301	1.09668	0.548342	−	0.836254i	$-0.315259\pi$
$103$	11.1301	1.09668	0.548342	+	0.836254i	$0.315259\pi$
$104$	1.23814	0.121410
$105$	0	0
$106$	−9.94076	−0.965532
$107$	2.67167	0.258280	0.129140	−	0.991626i	$-0.458778\pi$
$107$	2.67167	0.258280	0.129140	+	0.991626i	$0.458778\pi$
$108$	4.07339	0.391962
$109$	7.68504	0.736093	0.368047	−	0.929807i	$-0.380027\pi$
$109$	7.68504	0.736093	0.368047	+	0.929807i	$0.380027\pi$
$110$	−7.48045	−0.713233
$111$	0.139698	0.0132595
$112$	0	0
$113$	−2.58320	−0.243007	−0.121503	−	0.992591i	$-0.538771\pi$
$113$	−2.58320	−0.243007	−0.121503	+	0.992591i	$0.538771\pi$
$114$	−4.25568	−0.398581
$115$	15.1919	1.41665
$116$	−6.35687	−0.590221
$117$	3.02000	0.279199
$118$	−8.34796	−0.768492
$119$	0	0
$120$	1.39498	0.127344
$121$	5.12767	0.466151
$122$	−10.4690	−0.947815
$123$	0.748903	0.0675263
$124$	−4.57801	−0.411118
$125$	−12.1641	−1.08799
$126$	0	0
$127$	6.57729	0.583640	0.291820	−	0.956473i	$-0.405739\pi$
$127$	6.57729	0.583640	0.291820	+	0.956473i	$0.405739\pi$
$128$	−1.00000	−0.0883883
$129$	9.27705	0.816799
$130$	2.30628	0.202274
$131$	−12.2620	−1.07133	−0.535667	−	0.844429i	$-0.679940\pi$
$131$	−12.2620	−1.07133	−0.535667	+	0.844429i	$0.679940\pi$
$132$	−3.00754	−0.261773
$133$	0	0
$134$	13.2941	1.14843
$135$	7.58749	0.653027
$136$	0.0249841	0.00214237
$137$	15.6827	1.33986	0.669931	−	0.742424i	$-0.266324\pi$
$137$	15.6827	1.33986	0.669931	+	0.742424i	$0.266324\pi$
$138$	6.10796	0.519944
$139$	−11.9368	−1.01246	−0.506232	−	0.862397i	$-0.668962\pi$
$139$	−11.9368	−1.01246	−0.506232	+	0.862397i	$0.668962\pi$
$140$	0	0
$141$	−0.444654	−0.0374466
$142$	3.37960	0.283610
$143$	−4.97228	−0.415803
$144$	−2.43914	−0.203262
$145$	−11.8409	−0.983334
$146$	14.7826	1.22342
$147$	0	0
$148$	−0.186536	−0.0153332
$149$	20.0368	1.64148	0.820739	−	0.571304i	$-0.193562\pi$
$149$	20.0368	1.64148	0.820739	+	0.571304i	$0.193562\pi$
$150$	−1.14610	−0.0935784
$151$	16.2272	1.32055	0.660276	−	0.751023i	$-0.270439\pi$
$151$	16.2272	1.32055	0.660276	+	0.751023i	$0.270439\pi$
$152$	5.68255	0.460916
$153$	0.0609398	0.00492669
$154$	0	0
$155$	−8.52744	−0.684941
$156$	0.927248	0.0742392
$157$	15.1295	1.20747	0.603733	−	0.797187i	$-0.293679\pi$
$157$	15.1295	1.20747	0.603733	+	0.797187i	$0.293679\pi$
$158$	2.19932	0.174969
$159$	−7.44467	−0.590401
$160$	−1.86270	−0.147259
$161$	0	0
$162$	−4.26685	−0.335236
$163$	21.0189	1.64632	0.823162	−	0.567807i	$-0.192208\pi$
$163$	21.0189	1.64632	0.823162	+	0.567807i	$0.192208\pi$
$164$	−1.00000	−0.0780869
$165$	−5.60213	−0.436125
$166$	7.94255	0.616461
$167$	−0.00695972	−0.000538559 0	−0.000269280	−	1.00000i	$-0.500086\pi$
$167$	−0.00695972	−0.000538559 0	−0.000269280		1.00000i	$0.500086\pi$
$168$	0	0
$169$	−11.4670	−0.882077
$170$	0.0465377	0.00356928
$171$	13.8606	1.05994
$172$	−12.3875	−0.944539
$173$	−16.2441	−1.23502	−0.617510	−	0.786563i	$-0.711858\pi$
$173$	−16.2441	−1.23502	−0.617510	+	0.786563i	$0.711858\pi$
$174$	−4.76068	−0.360906
$175$	0	0
$176$	4.01593	0.302712
$177$	−6.25181	−0.469915
$178$	13.8087	1.03501
$179$	8.82975	0.659967	0.329983	−	0.943987i	$-0.392957\pi$
$179$	8.82975	0.659967	0.329983	+	0.943987i	$0.392957\pi$
$180$	−4.54338	−0.338644
$181$	9.17435	0.681924	0.340962	−	0.940077i	$-0.389247\pi$
$181$	9.17435	0.681924	0.340962	+	0.940077i	$0.389247\pi$
$182$	0	0
$183$	−7.84024	−0.579567
$184$	−8.15588	−0.601259
$185$	−0.347460	−0.0255458
$186$	−3.42849	−0.251389
$187$	−0.100334	−0.00733717
$188$	0.593740	0.0433029
$189$	0	0
$190$	10.5849	0.767907
$191$	2.33977	0.169300	0.0846498	−	0.996411i	$-0.473023\pi$
$191$	2.33977	0.169300	0.0846498	+	0.996411i	$0.473023\pi$
$192$	−0.748903	−0.0540474
$193$	7.08033	0.509653	0.254827	−	0.966987i	$-0.417982\pi$
$193$	7.08033	0.509653	0.254827	+	0.966987i	$0.417982\pi$
$194$	15.4269	1.10758
$195$	1.72718	0.123686
$196$	0	0
$197$	−12.5563	−0.894597	−0.447298	−	0.894385i	$-0.647614\pi$
$197$	−12.5563	−0.894597	−0.447298	+	0.894385i	$0.647614\pi$
$198$	9.79542	0.696130
$199$	−25.2471	−1.78972	−0.894859	−	0.446349i	$-0.852724\pi$
$199$	−25.2471	−1.78972	−0.894859	+	0.446349i	$0.852724\pi$
$200$	1.53037	0.108213
$201$	9.95596	0.702240
$202$	10.9586	0.771042
$203$	0	0
$204$	0.0187107	0.00131001
$205$	−1.86270	−0.130096
$206$	−11.1301	−0.775472
$207$	−19.8934	−1.38268
$208$	−1.23814	−0.0858496
$209$	−22.8207	−1.57854
$210$	0	0
$211$	−20.8450	−1.43503	−0.717514	−	0.696544i	$-0.754720\pi$
$211$	−20.8450	−1.43503	−0.717514	+	0.696544i	$0.754720\pi$
$212$	9.94076	0.682734
$213$	2.53099	0.173421
$214$	−2.67167	−0.182631
$215$	−23.0742	−1.57364
$216$	−4.07339	−0.277159
$217$	0	0
$218$	−7.68504	−0.520497
$219$	11.0708	0.748092
$220$	7.48045	0.504332
$221$	0.0309338	0.00208083
$222$	−0.139698	−0.00937588
$223$	−19.3546	−1.29608	−0.648041	−	0.761605i	$-0.724411\pi$
$223$	−19.3546	−1.29608	−0.648041	+	0.761605i	$0.724411\pi$
$224$	0	0
$225$	3.73278	0.248852
$226$	2.58320	0.171832
$227$	−4.32774	−0.287242	−0.143621	−	0.989633i	$-0.545875\pi$
$227$	−4.32774	−0.287242	−0.143621	+	0.989633i	$0.545875\pi$
$228$	4.25568	0.281839
$229$	2.56052	0.169204	0.0846020	−	0.996415i	$-0.473038\pi$
$229$	2.56052	0.169204	0.0846020	+	0.996415i	$0.473038\pi$
$230$	−15.1919	−1.00172
$231$	0	0
$232$	6.35687	0.417349
$233$	−11.8749	−0.777948	−0.388974	−	0.921249i	$-0.627170\pi$
$233$	−11.8749	−0.777948	−0.388974	+	0.921249i	$0.627170\pi$
$234$	−3.02000	−0.197424
$235$	1.10596	0.0721446
$236$	8.34796	0.543406
$237$	1.64708	0.106989
$238$	0	0
$239$	−6.78691	−0.439009	−0.219505	−	0.975611i	$-0.570444\pi$
$239$	−6.78691	−0.439009	−0.219505	+	0.975611i	$0.570444\pi$
$240$	−1.39498	−0.0900455
$241$	6.20426	0.399652	0.199826	−	0.979831i	$-0.435962\pi$
$241$	6.20426	0.399652	0.199826	+	0.979831i	$0.435962\pi$
$242$	−5.12767	−0.329619
$243$	−15.4156	−0.988914
$244$	10.4690	0.670206
$245$	0	0
$246$	−0.748903	−0.0477483
$247$	7.03580	0.447677
$248$	4.57801	0.290704
$249$	5.94820	0.376952
$250$	12.1641	0.769324
$251$	0.343398	0.0216751	0.0108375	−	0.999941i	$-0.496550\pi$
$251$	0.343398	0.0216751	0.0108375	+	0.999941i	$0.496550\pi$
$252$	0	0
$253$	32.7534	2.05919
$254$	−6.57729	−0.412696
$255$	0.0348523	0.00218253
$256$	1.00000	0.0625000
$257$	−4.28196	−0.267102	−0.133551	−	0.991042i	$-0.542638\pi$
$257$	−4.28196	−0.267102	−0.133551	+	0.991042i	$0.542638\pi$
$258$	−9.27705	−0.577564
$259$	0	0
$260$	−2.30628	−0.143029
$261$	15.5053	0.959755
$262$	12.2620	0.757548
$263$	−3.94100	−0.243012	−0.121506	−	0.992591i	$-0.538772\pi$
$263$	−3.94100	−0.243012	−0.121506	+	0.992591i	$0.538772\pi$
$264$	3.00754	0.185101
$265$	18.5166	1.13747
$266$	0	0
$267$	10.3414	0.632883
$268$	−13.2941	−0.812064
$269$	−8.62142	−0.525657	−0.262829	−	0.964843i	$-0.584655\pi$
$269$	−8.62142	−0.525657	−0.262829	+	0.964843i	$0.584655\pi$
$270$	−7.58749	−0.461760
$271$	16.5660	1.00631	0.503156	−	0.864196i	$-0.332172\pi$
$271$	16.5660	1.00631	0.503156	+	0.864196i	$0.332172\pi$
$272$	−0.0249841	−0.00151488
$273$	0	0
$274$	−15.6827	−0.947425
$275$	−6.14584	−0.370608
$276$	−6.10796	−0.367656
$277$	−21.3808	−1.28465	−0.642324	−	0.766433i	$-0.722030\pi$
$277$	−21.3808	−1.28465	−0.642324	+	0.766433i	$0.722030\pi$
$278$	11.9368	0.715921
$279$	11.1664	0.668517
$280$	0	0
$281$	5.15438	0.307484	0.153742	−	0.988111i	$-0.450867\pi$
$281$	5.15438	0.307484	0.153742	+	0.988111i	$0.450867\pi$
$282$	0.444654	0.0264787
$283$	−32.5282	−1.93360	−0.966800	−	0.255533i	$-0.917749\pi$
$283$	−32.5282	−1.93360	−0.966800	+	0.255533i	$0.917749\pi$
$284$	−3.37960	−0.200542
$285$	7.92704	0.469557
$286$	4.97228	0.294017
$287$	0	0
$288$	2.43914	0.143728
$289$	−16.9994	−0.999963
$290$	11.8409	0.695322
$291$	11.5532	0.677262
$292$	−14.7826	−0.865087
$293$	−6.39063	−0.373345	−0.186672	−	0.982422i	$-0.559770\pi$
$293$	−6.39063	−0.373345	−0.186672	+	0.982422i	$0.559770\pi$
$294$	0	0
$295$	15.5497	0.905338
$296$	0.186536	0.0108422
$297$	16.3584	0.949213
$298$	−20.0368	−1.16070
$299$	−10.0981	−0.583990
$300$	1.14610	0.0661699
$301$	0	0
$302$	−16.2272	−0.933771
$303$	8.20691	0.471474
$304$	−5.68255	−0.325917
$305$	19.5005	1.11659
$306$	−0.0609398	−0.00348370
$307$	−17.5450	−1.00134	−0.500672	−	0.865637i	$-0.666914\pi$
$307$	−17.5450	−1.00134	−0.500672	+	0.865637i	$0.666914\pi$
$308$	0	0
$309$	−8.33538	−0.474183
$310$	8.52744	0.484326
$311$	31.7308	1.79929	0.899643	−	0.436626i	$-0.143827\pi$
$311$	31.7308	1.79929	0.899643	+	0.436626i	$0.143827\pi$
$312$	−0.927248	−0.0524951
$313$	4.47160	0.252750	0.126375	−	0.991983i	$-0.459666\pi$
$313$	4.47160	0.252750	0.126375	+	0.991983i	$0.459666\pi$
$314$	−15.1295	−0.853807
$315$	0	0
$316$	−2.19932	−0.123721
$317$	10.6100	0.595917	0.297959	−	0.954579i	$-0.403694\pi$
$317$	10.6100	0.595917	0.297959	+	0.954579i	$0.403694\pi$
$318$	7.44467	0.417476
$319$	−25.5287	−1.42933
$320$	1.86270	0.104128
$321$	−2.00082	−0.111675
$322$	0	0
$323$	0.141973	0.00789961
$324$	4.26685	0.237047
$325$	1.89481	0.105105
$326$	−21.0189	−1.16413
$327$	−5.75535	−0.318272
$328$	1.00000	0.0552158
$329$	0	0
$330$	5.60213	0.308387
$331$	−28.1254	−1.54591	−0.772956	−	0.634460i	$-0.781223\pi$
$331$	−28.1254	−1.54591	−0.772956	+	0.634460i	$0.781223\pi$
$332$	−7.94255	−0.435904
$333$	0.454988	0.0249332
$334$	0.00695972	0.000380819 0
$335$	−24.7628	−1.35294
$336$	0	0
$337$	12.6272	0.687848	0.343924	−	0.938998i	$-0.388244\pi$
$337$	12.6272	0.687848	0.343924	+	0.938998i	$0.388244\pi$
$338$	11.4670	0.623723
$339$	1.93456	0.105071
$340$	−0.0465377	−0.00252386
$341$	−18.3850	−0.995602
$342$	−13.8606	−0.749494
$343$	0	0
$344$	12.3875	0.667890
$345$	−11.3773	−0.612532
$346$	16.2441	0.873290
$347$	−22.5279	−1.20936	−0.604680	−	0.796469i	$-0.706699\pi$
$347$	−22.5279	−1.20936	−0.604680	+	0.796469i	$0.706699\pi$
$348$	4.76068	0.255199
$349$	−0.0549053	−0.00293901	−0.00146951	−	0.999999i	$-0.500468\pi$
$349$	−0.0549053	−0.00293901	−0.00146951	+	0.999999i	$0.500468\pi$
$350$	0	0
$351$	−5.04343	−0.269199
$352$	−4.01593	−0.214050
$353$	−15.9181	−0.847237	−0.423619	−	0.905841i	$-0.639240\pi$
$353$	−15.9181	−0.847237	−0.423619	+	0.905841i	$0.639240\pi$
$354$	6.25181	0.332280
$355$	−6.29516	−0.334113
$356$	−13.8087	−0.731860
$357$	0	0
$358$	−8.82975	−0.466667
$359$	−12.2372	−0.645857	−0.322928	−	0.946423i	$-0.604667\pi$
$359$	−12.2372	−0.645857	−0.322928	+	0.946423i	$0.604667\pi$
$360$	4.54338	0.239457
$361$	13.2914	0.699548
$362$	−9.17435	−0.482193
$363$	−3.84013	−0.201554
$364$	0	0
$365$	−27.5355	−1.44127
$366$	7.84024	0.409816
$367$	−35.2774	−1.84146	−0.920731	−	0.390197i	$-0.872407\pi$
$367$	−35.2774	−1.84146	−0.920731	+	0.390197i	$0.872407\pi$
$368$	8.15588	0.425154
$369$	2.43914	0.126977
$370$	0.347460	0.0180636
$371$	0	0
$372$	3.42849	0.177759
$373$	−22.8910	−1.18525	−0.592624	−	0.805479i	$-0.701908\pi$
$373$	−22.8910	−1.18525	−0.592624	+	0.805479i	$0.701908\pi$
$374$	0.100334	0.00518816
$375$	9.10972	0.470424
$376$	−0.593740	−0.0306198
$377$	7.87070	0.405362
$378$	0	0
$379$	−14.4612	−0.742822	−0.371411	−	0.928469i	$-0.621126\pi$
$379$	−14.4612	−0.742822	−0.371411	+	0.928469i	$0.621126\pi$
$380$	−10.5849	−0.542992
$381$	−4.92575	−0.252354
$382$	−2.33977	−0.119713
$383$	−14.7710	−0.754764	−0.377382	−	0.926058i	$-0.623176\pi$
$383$	−14.7710	−0.754764	−0.377382	+	0.926058i	$0.623176\pi$
$384$	0.748903	0.0382173
$385$	0	0
$386$	−7.08033	−0.360379
$387$	30.2149	1.53591
$388$	−15.4269	−0.783180
$389$	1.61052	0.0816564	0.0408282	−	0.999166i	$-0.487000\pi$
$389$	1.61052	0.0816564	0.0408282	+	0.999166i	$0.487000\pi$
$390$	−1.72718	−0.0874592
$391$	−0.203767	−0.0103049
$392$	0	0
$393$	9.18304	0.463223
$394$	12.5563	0.632575
$395$	−4.09667	−0.206126
$396$	−9.79542	−0.492239
$397$	26.8985	1.35000	0.674999	−	0.737819i	$-0.264144\pi$
$397$	26.8985	1.35000	0.674999	+	0.737819i	$0.264144\pi$
$398$	25.2471	1.26552
$399$	0	0
$400$	−1.53037	−0.0765183
$401$	−1.39064	−0.0694453	−0.0347227	−	0.999397i	$-0.511055\pi$
$401$	−1.39064	−0.0694453	−0.0347227	+	0.999397i	$0.511055\pi$
$402$	−9.95596	−0.496558
$403$	5.66823	0.282354
$404$	−10.9586	−0.545209
$405$	7.94785	0.394932
$406$	0	0
$407$	−0.749115	−0.0371323
$408$	−0.0187107	−0.000926316 0
$409$	6.27527	0.310292	0.155146	−	0.987892i	$-0.450415\pi$
$409$	6.27527	0.310292	0.155146	+	0.987892i	$0.450415\pi$
$410$	1.86270	0.0919920
$411$	−11.7448	−0.579329
$412$	11.1301	0.548342
$413$	0	0
$414$	19.8934	0.977705
$415$	−14.7945	−0.726236
$416$	1.23814	0.0607049
$417$	8.93950	0.437769
$418$	22.8207	1.11620
$419$	10.2750	0.501967	0.250984	−	0.967991i	$-0.419246\pi$
$419$	10.2750	0.501967	0.250984	+	0.967991i	$0.419246\pi$
$420$	0	0
$421$	35.0986	1.71060	0.855301	−	0.518132i	$-0.173372\pi$
$421$	35.0986	1.71060	0.855301	+	0.518132i	$0.173372\pi$
$422$	20.8450	1.01472
$423$	−1.44822	−0.0704147
$424$	−9.94076	−0.482766
$425$	0.0382348	0.00185466
$426$	−2.53099	−0.122627
$427$	0	0
$428$	2.67167	0.129140
$429$	3.72376	0.179785
$430$	23.0742	1.11273
$431$	−25.1735	−1.21257	−0.606284	−	0.795249i	$-0.707340\pi$
$431$	−25.1735	−1.21257	−0.606284	+	0.795249i	$0.707340\pi$
$432$	4.07339	0.195981
$433$	32.0992	1.54259	0.771293	−	0.636480i	$-0.219610\pi$
$433$	32.0992	1.54259	0.771293	+	0.636480i	$0.219610\pi$
$434$	0	0
$435$	8.86770	0.425174
$436$	7.68504	0.368047
$437$	−46.3462	−2.21704
$438$	−11.0708	−0.528981
$439$	−22.4145	−1.06978	−0.534892	−	0.844920i	$-0.679648\pi$
$439$	−22.4145	−1.06978	−0.534892	+	0.844920i	$0.679648\pi$
$440$	−7.48045	−0.356616
$441$	0	0
$442$	−0.0309338	−0.00147137
$443$	−14.6761	−0.697281	−0.348641	−	0.937256i	$-0.613357\pi$
$443$	−14.6761	−0.697281	−0.348641	+	0.937256i	$0.613357\pi$
$444$	0.139698	0.00662975
$445$	−25.7214	−1.21931
$446$	19.3546	0.916468
$447$	−15.0056	−0.709741
$448$	0	0
$449$	14.1839	0.669380	0.334690	−	0.942328i	$-0.391368\pi$
$449$	14.1839	0.669380	0.334690	+	0.942328i	$0.391368\pi$
$450$	−3.73278	−0.175965
$451$	−4.01593	−0.189103
$452$	−2.58320	−0.121503
$453$	−12.1526	−0.570980
$454$	4.32774	0.203111
$455$	0	0
$456$	−4.25568	−0.199291
$457$	−2.60020	−0.121632	−0.0608161	−	0.998149i	$-0.519370\pi$
$457$	−2.60020	−0.121632	−0.0608161	+	0.998149i	$0.519370\pi$
$458$	−2.56052	−0.119645
$459$	−0.101770	−0.00475022
$460$	15.1919	0.708326
$461$	12.9522	0.603245	0.301623	−	0.953427i	$-0.402472\pi$
$461$	12.9522	0.603245	0.301623	+	0.953427i	$0.402472\pi$
$462$	0	0
$463$	2.89466	0.134526	0.0672631	−	0.997735i	$-0.478573\pi$
$463$	2.89466	0.134526	0.0672631	+	0.997735i	$0.478573\pi$
$464$	−6.35687	−0.295110
$465$	6.38623	0.296154
$466$	11.8749	0.550092
$467$	−3.67570	−0.170091	−0.0850455	−	0.996377i	$-0.527104\pi$
$467$	−3.67570	−0.170091	−0.0850455	+	0.996377i	$0.527104\pi$
$468$	3.02000	0.139600
$469$	0	0
$470$	−1.10596	−0.0510140
$471$	−11.3305	−0.522084
$472$	−8.34796	−0.384246
$473$	−49.7473	−2.28739
$474$	−1.64708	−0.0756528
$475$	8.69639	0.399018
$476$	0	0
$477$	−24.2469	−1.11019
$478$	6.78691	0.310426
$479$	−18.1304	−0.828401	−0.414201	−	0.910186i	$-0.635939\pi$
$479$	−18.1304	−0.828401	−0.414201	+	0.910186i	$0.635939\pi$
$480$	1.39498	0.0636718
$481$	0.230958	0.0105308
$482$	−6.20426	−0.282596
$483$	0	0
$484$	5.12767	0.233076
$485$	−28.7355	−1.30481
$486$	15.4156	0.699268
$487$	9.18267	0.416107	0.208053	−	0.978117i	$-0.433287\pi$
$487$	9.18267	0.416107	0.208053	+	0.978117i	$0.433287\pi$
$488$	−10.4690	−0.473907
$489$	−15.7411	−0.711837
$490$	0	0
$491$	29.4648	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$491$	29.4648	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$492$	0.748903	0.0337632
$493$	0.158821	0.00715292
$494$	−7.03580	−0.316556
$495$	−18.2459	−0.820092
$496$	−4.57801	−0.205559
$497$	0	0
$498$	−5.94820	−0.266545
$499$	−36.0935	−1.61577	−0.807883	−	0.589343i	$-0.799387\pi$
$499$	−36.0935	−1.61577	−0.807883	+	0.589343i	$0.799387\pi$
$500$	−12.1641	−0.543994
$501$	0.00521216	0.000232862 0
$502$	−0.343398	−0.0153266
$503$	−19.0364	−0.848793	−0.424396	−	0.905477i	$-0.639514\pi$
$503$	−19.0364	−0.848793	−0.424396	+	0.905477i	$0.639514\pi$
$504$	0	0
$505$	−20.4125	−0.908343
$506$	−32.7534	−1.45607
$507$	8.58768	0.381392
$508$	6.57729	0.291820
$509$	−39.5967	−1.75509	−0.877547	−	0.479490i	$-0.840822\pi$
$509$	−39.5967	−1.75509	−0.877547	+	0.479490i	$0.840822\pi$
$510$	−0.0348523	−0.00154328
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−23.1473	−1.02198
$514$	4.28196	0.188869
$515$	20.7320	0.913562
$516$	9.27705	0.408399
$517$	2.38442	0.104866
$518$	0	0
$519$	12.1653	0.533997
$520$	2.30628	0.101137
$521$	−11.8193	−0.517814	−0.258907	−	0.965902i	$-0.583362\pi$
$521$	−11.8193	−0.517814	−0.258907	+	0.965902i	$0.583362\pi$
$522$	−15.5053	−0.678650
$523$	−13.4079	−0.586287	−0.293144	−	0.956068i	$-0.594701\pi$
$523$	−13.4079	−0.586287	−0.293144	+	0.956068i	$0.594701\pi$
$524$	−12.2620	−0.535667
$525$	0	0
$526$	3.94100	0.171836
$527$	0.114377	0.00498236
$528$	−3.00754	−0.130886
$529$	43.5183	1.89210
$530$	−18.5166	−0.804310
$531$	−20.3619	−0.883630
$532$	0	0
$533$	1.23814	0.0536298
$534$	−10.3414	−0.447516
$535$	4.97650	0.215153
$536$	13.2941	0.574216
$537$	−6.61263	−0.285356
$538$	8.62142	0.371696
$539$	0	0
$540$	7.58749	0.326514
$541$	44.2249	1.90138	0.950689	−	0.310144i	$-0.100377\pi$
$541$	44.2249	1.90138	0.950689	+	0.310144i	$0.100377\pi$
$542$	−16.5660	−0.711570
$543$	−6.87070	−0.294850
$544$	0.0249841	0.00107118
$545$	14.3149	0.613182
$546$	0	0
$547$	−36.0335	−1.54068	−0.770341	−	0.637633i	$-0.779914\pi$
$547$	−36.0335	−1.54068	−0.770341	+	0.637633i	$0.779914\pi$
$548$	15.6827	0.669931
$549$	−25.5353	−1.08982
$550$	6.14584	0.262060
$551$	36.1233	1.53890
$552$	6.10796	0.259972
$553$	0	0
$554$	21.3808	0.908384
$555$	0.260214	0.0110455
$556$	−11.9368	−0.506232
$557$	27.2515	1.15468	0.577342	−	0.816503i	$-0.304090\pi$
$557$	27.2515	1.15468	0.577342	+	0.816503i	$0.304090\pi$
$558$	−11.1664	−0.472713
$559$	15.3375	0.648707
$560$	0	0
$561$	0.0751406	0.00317244
$562$	−5.15438	−0.217424
$563$	−6.61694	−0.278871	−0.139435	−	0.990231i	$-0.544529\pi$
$563$	−6.61694	−0.278871	−0.139435	+	0.990231i	$0.544529\pi$
$564$	−0.444654	−0.0187233
$565$	−4.81170	−0.202430
$566$	32.5282	1.36726
$567$	0	0
$568$	3.37960	0.141805
$569$	−13.3689	−0.560453	−0.280226	−	0.959934i	$-0.590409\pi$
$569$	−13.3689	−0.560453	−0.280226	+	0.959934i	$0.590409\pi$
$570$	−7.92704	−0.332027
$571$	18.5736	0.777280	0.388640	−	0.921390i	$-0.372945\pi$
$571$	18.5736	0.777280	0.388640	+	0.921390i	$0.372945\pi$
$572$	−4.97228	−0.207902
$573$	−1.75226	−0.0732017
$574$	0	0
$575$	−12.4815	−0.520514
$576$	−2.43914	−0.101631
$577$	−18.4082	−0.766342	−0.383171	−	0.923677i	$-0.625168\pi$
$577$	−18.4082	−0.766342	−0.383171	+	0.923677i	$0.625168\pi$
$578$	16.9994	0.707081
$579$	−5.30248	−0.220364
$580$	−11.8409	−0.491667
$581$	0	0
$582$	−11.5532	−0.478897
$583$	39.9214	1.65337
$584$	14.7826	0.611709
$585$	5.62535	0.232579
$586$	6.39063	0.263994
$587$	−26.2965	−1.08537	−0.542687	−	0.839935i	$-0.682593\pi$
$587$	−26.2965	−1.08537	−0.542687	+	0.839935i	$0.682593\pi$
$588$	0	0
$589$	26.0148	1.07192
$590$	−15.5497	−0.640171
$591$	9.40343	0.386805
$592$	−0.186536	−0.00766659
$593$	−3.38522	−0.139015	−0.0695073	−	0.997581i	$-0.522143\pi$
$593$	−3.38522	−0.139015	−0.0695073	+	0.997581i	$0.522143\pi$
$594$	−16.3584	−0.671195
$595$	0	0
$596$	20.0368	0.820739
$597$	18.9076	0.773837
$598$	10.0981	0.412943
$599$	45.6931	1.86697	0.933484	−	0.358619i	$-0.116752\pi$
$599$	45.6931	1.86697	0.933484	+	0.358619i	$0.116752\pi$
$600$	−1.14610	−0.0467892
$601$	17.1184	0.698274	0.349137	−	0.937072i	$-0.386475\pi$
$601$	17.1184	0.698274	0.349137	+	0.937072i	$0.386475\pi$
$602$	0	0
$603$	32.4261	1.32049
$604$	16.2272	0.660276
$605$	9.55128	0.388315
$606$	−8.20691	−0.333383
$607$	8.91090	0.361682	0.180841	−	0.983512i	$-0.442118\pi$
$607$	8.91090	0.361682	0.180841	+	0.983512i	$0.442118\pi$
$608$	5.68255	0.230458
$609$	0	0
$610$	−19.5005	−0.789551
$611$	−0.735134	−0.0297403
$612$	0.0609398	0.00246334
$613$	21.0970	0.852099	0.426050	−	0.904700i	$-0.359905\pi$
$613$	21.0970	0.852099	0.426050	+	0.904700i	$0.359905\pi$
$614$	17.5450	0.708057
$615$	1.39498	0.0562510
$616$	0	0
$617$	−8.78533	−0.353684	−0.176842	−	0.984239i	$-0.556588\pi$
$617$	−8.78533	−0.353684	−0.176842	+	0.984239i	$0.556588\pi$
$618$	8.33538	0.335298
$619$	34.1596	1.37299	0.686496	−	0.727134i	$-0.259148\pi$
$619$	34.1596	1.37299	0.686496	+	0.727134i	$0.259148\pi$
$620$	−8.52744	−0.342470
$621$	33.2221	1.33316
$622$	−31.7308	−1.27229
$623$	0	0
$624$	0.927248	0.0371196
$625$	−15.0061	−0.600246
$626$	−4.47160	−0.178721
$627$	17.0905	0.682529
$628$	15.1295	0.603733
$629$	0.00466043	0.000185824 0
$630$	0	0
$631$	−11.7154	−0.466382	−0.233191	−	0.972431i	$-0.574917\pi$
$631$	−11.7154	−0.466382	−0.233191	+	0.972431i	$0.574917\pi$
$632$	2.19932	0.0874843
$633$	15.6109	0.620477
$634$	−10.6100	−0.421377
$635$	12.2515	0.486185
$636$	−7.44467	−0.295200
$637$	0	0
$638$	25.5287	1.01069
$639$	8.24333	0.326101
$640$	−1.86270	−0.0736295
$641$	17.6539	0.697288	0.348644	−	0.937255i	$-0.386642\pi$
$641$	17.6539	0.697288	0.348644	+	0.937255i	$0.386642\pi$
$642$	2.00082	0.0789661
$643$	26.5890	1.04857	0.524284	−	0.851544i	$-0.324333\pi$
$643$	26.5890	1.04857	0.524284	+	0.851544i	$0.324333\pi$
$644$	0	0
$645$	17.2803	0.680412
$646$	−0.141973	−0.00558587
$647$	−26.4141	−1.03844	−0.519222	−	0.854639i	$-0.673778\pi$
$647$	−26.4141	−1.03844	−0.519222	+	0.854639i	$0.673778\pi$
$648$	−4.26685	−0.167618
$649$	33.5248	1.31596
$650$	−1.89481	−0.0743206
$651$	0	0
$652$	21.0189	0.823162
$653$	22.9358	0.897548	0.448774	−	0.893645i	$-0.351861\pi$
$653$	22.9358	0.897548	0.448774	+	0.893645i	$0.351861\pi$
$654$	5.75535	0.225052
$655$	−22.8403	−0.892446
$656$	−1.00000	−0.0390434
$657$	36.0569	1.40672
$658$	0	0
$659$	−34.8489	−1.35752	−0.678760	−	0.734360i	$-0.737482\pi$
$659$	−34.8489	−1.35752	−0.678760	+	0.734360i	$0.737482\pi$
$660$	−5.60213	−0.218063
$661$	7.42961	0.288978	0.144489	−	0.989506i	$-0.453846\pi$
$661$	7.42961	0.288978	0.144489	+	0.989506i	$0.453846\pi$
$662$	28.1254	1.09312
$663$	−0.0231664	−0.000899710 0
$664$	7.94255	0.308231
$665$	0	0
$666$	−0.454988	−0.0176304
$667$	−51.8459	−2.00748
$668$	−0.00695972	−0.000269280 0
$669$	14.4947	0.560399
$670$	24.7628	0.956670
$671$	42.0426	1.62304
$672$	0	0
$673$	−37.2583	−1.43620	−0.718101	−	0.695939i	$-0.754988\pi$
$673$	−37.2583	−1.43620	−0.718101	+	0.695939i	$0.754988\pi$
$674$	−12.6272	−0.486382
$675$	−6.23378	−0.239938
$676$	−11.4670	−0.441039
$677$	−21.4147	−0.823033	−0.411517	−	0.911402i	$-0.635001\pi$
$677$	−21.4147	−0.823033	−0.411517	+	0.911402i	$0.635001\pi$
$678$	−1.93456	−0.0742965
$679$	0	0
$680$	0.0465377	0.00178464
$681$	3.24106	0.124198
$682$	18.3850	0.703997
$683$	2.12495	0.0813088	0.0406544	−	0.999173i	$-0.487056\pi$
$683$	2.12495	0.0813088	0.0406544	+	0.999173i	$0.487056\pi$
$684$	13.8606	0.529972
$685$	29.2120	1.11613
$686$	0	0
$687$	−1.91758	−0.0731603
$688$	−12.3875	−0.472269
$689$	−12.3081	−0.468900
$690$	11.3773	0.433125
$691$	−23.0955	−0.878595	−0.439297	−	0.898342i	$-0.644773\pi$
$691$	−23.0955	−0.878595	−0.439297	+	0.898342i	$0.644773\pi$
$692$	−16.2441	−0.617510
$693$	0	0
$694$	22.5279	0.855147
$695$	−22.2346	−0.843406
$696$	−4.76068	−0.180453
$697$	0.0249841	0.000946340 0
$698$	0.0549053	0.00207820
$699$	8.89312	0.336369
$700$	0	0
$701$	41.0987	1.55228	0.776138	−	0.630563i	$-0.217176\pi$
$701$	41.0987	1.55228	0.776138	+	0.630563i	$0.217176\pi$
$702$	5.04343	0.190352
$703$	1.06000	0.0399787
$704$	4.01593	0.151356
$705$	−0.828254	−0.0311939
$706$	15.9181	0.599087
$707$	0	0
$708$	−6.25181	−0.234957
$709$	10.9257	0.410322	0.205161	−	0.978728i	$-0.434228\pi$
$709$	10.9257	0.410322	0.205161	+	0.978728i	$0.434228\pi$
$710$	6.29516	0.236253
$711$	5.36446	0.201183
$712$	13.8087	0.517503
$713$	−37.3377	−1.39831
$714$	0	0
$715$	−9.26185	−0.346373
$716$	8.82975	0.329983
$717$	5.08274	0.189818
$718$	12.2372	0.456690
$719$	−16.4052	−0.611811	−0.305906	−	0.952062i	$-0.598959\pi$
$719$	−16.4052	−0.611811	−0.305906	+	0.952062i	$0.598959\pi$
$720$	−4.54338	−0.169322
$721$	0	0
$722$	−13.2914	−0.494655
$723$	−4.64639	−0.172801
$724$	9.17435	0.340962
$725$	9.72834	0.361302
$726$	3.84013	0.142520
$727$	21.5999	0.801094	0.400547	−	0.916276i	$-0.368820\pi$
$727$	21.5999	0.801094	0.400547	+	0.916276i	$0.368820\pi$
$728$	0	0
$729$	−1.25574	−0.0465089
$730$	27.5355	1.01914
$731$	0.309491	0.0114469
$732$	−7.84024	−0.289783
$733$	37.5774	1.38795	0.693976	−	0.719998i	$-0.255857\pi$
$733$	37.5774	1.38795	0.693976	+	0.719998i	$0.255857\pi$
$734$	35.2774	1.30211
$735$	0	0
$736$	−8.15588	−0.300630
$737$	−53.3880	−1.96657
$738$	−2.43914	−0.0897861
$739$	8.64328	0.317948	0.158974	−	0.987283i	$-0.449181\pi$
$739$	8.64328	0.317948	0.158974	+	0.987283i	$0.449181\pi$
$740$	−0.347460	−0.0127729
$741$	−5.26914	−0.193567
$742$	0	0
$743$	−10.1110	−0.370936	−0.185468	−	0.982650i	$-0.559380\pi$
$743$	−10.1110	−0.370936	−0.185468	+	0.982650i	$0.559380\pi$
$744$	−3.42849	−0.125694
$745$	37.3224	1.36739
$746$	22.8910	0.838097
$747$	19.3730	0.708822
$748$	−0.100334	−0.00366858
$749$	0	0
$750$	−9.10972	−0.332640
$751$	−8.82026	−0.321856	−0.160928	−	0.986966i	$-0.551449\pi$
$751$	−8.82026	−0.321856	−0.160928	+	0.986966i	$0.551449\pi$
$752$	0.593740	0.0216515
$753$	−0.257172	−0.00937186
$754$	−7.87070	−0.286634
$755$	30.2263	1.10005
$756$	0	0
$757$	31.4547	1.14324	0.571620	−	0.820518i	$-0.306315\pi$
$757$	31.4547	1.14324	0.571620	+	0.820518i	$0.306315\pi$
$758$	14.4612	0.525254
$759$	−24.5291	−0.890351
$760$	10.5849	0.383953
$761$	54.3544	1.97034	0.985172	−	0.171569i	$-0.0548836\pi$
$761$	54.3544	1.97034	0.985172	+	0.171569i	$0.0548836\pi$
$762$	4.92575	0.178441
$763$	0	0
$764$	2.33977	0.0846498
$765$	0.113512	0.00410404
$766$	14.7710	0.533698
$767$	−10.3359	−0.373209
$768$	−0.748903	−0.0270237
$769$	1.11188	0.0400953	0.0200476	−	0.999799i	$-0.493618\pi$
$769$	1.11188	0.0400953	0.0200476	+	0.999799i	$0.493618\pi$
$770$	0	0
$771$	3.20678	0.115489
$772$	7.08033	0.254827
$773$	10.1560	0.365285	0.182642	−	0.983179i	$-0.441535\pi$
$773$	10.1560	0.365285	0.182642	+	0.983179i	$0.441535\pi$
$774$	−30.2149	−1.08605
$775$	7.00604	0.251664
$776$	15.4269	0.553792
$777$	0	0
$778$	−1.61052	−0.0577398
$779$	5.68255	0.203599
$780$	1.72718	0.0618430
$781$	−13.5722	−0.485652
$782$	0.203767	0.00728670
$783$	−25.8940	−0.925377
$784$	0	0
$785$	28.1817	1.00585
$786$	−9.18304	−0.327548
$787$	−6.09117	−0.217127	−0.108563	−	0.994090i	$-0.534625\pi$
$787$	−6.09117	−0.217127	−0.108563	+	0.994090i	$0.534625\pi$
$788$	−12.5563	−0.447298
$789$	2.95143	0.105074
$790$	4.09667	0.145753
$791$	0	0
$792$	9.79542	0.348065
$793$	−12.9620	−0.460296
$794$	−26.8985	−0.954593
$795$	−13.8671	−0.491817
$796$	−25.2471	−0.894859
$797$	−41.3188	−1.46359	−0.731794	−	0.681526i	$-0.761317\pi$
$797$	−41.3188	−1.46359	−0.731794	+	0.681526i	$0.761317\pi$
$798$	0	0
$799$	−0.0148340	−0.000524791 0
$800$	1.53037	0.0541066
$801$	33.6814	1.19008
$802$	1.39064	0.0491053
$803$	−59.3659	−2.09498
$804$	9.95596	0.351120
$805$	0	0
$806$	−5.66823	−0.199655
$807$	6.45661	0.227283
$808$	10.9586	0.385521
$809$	14.1712	0.498235	0.249117	−	0.968473i	$-0.419860\pi$
$809$	14.1712	0.498235	0.249117	+	0.968473i	$0.419860\pi$
$810$	−7.94785	−0.279259
$811$	−20.1842	−0.708762	−0.354381	−	0.935101i	$-0.615308\pi$
$811$	−20.1842	−0.708762	−0.354381	+	0.935101i	$0.615308\pi$
$812$	0	0
$813$	−12.4063	−0.435108
$814$	0.749115	0.0262565
$815$	39.1517	1.37142
$816$	0.0187107	0.000655004 0
$817$	70.3927	2.46273
$818$	−6.27527	−0.219410
$819$	0	0
$820$	−1.86270	−0.0650481
$821$	−7.59767	−0.265161	−0.132580	−	0.991172i	$-0.542326\pi$
$821$	−7.59767	−0.265161	−0.132580	+	0.991172i	$0.542326\pi$
$822$	11.7448	0.409647
$823$	8.94087	0.311659	0.155830	−	0.987784i	$-0.450195\pi$
$823$	8.94087	0.311659	0.155830	+	0.987784i	$0.450195\pi$
$824$	−11.1301	−0.387736
$825$	4.60264	0.160243
$826$	0	0
$827$	−5.84653	−0.203304	−0.101652	−	0.994820i	$-0.532413\pi$
$827$	−5.84653	−0.203304	−0.101652	+	0.994820i	$0.532413\pi$
$828$	−19.8934	−0.691342
$829$	21.3152	0.740308	0.370154	−	0.928970i	$-0.379305\pi$
$829$	21.3152	0.740308	0.370154	+	0.928970i	$0.379305\pi$
$830$	14.7945	0.513526
$831$	16.0122	0.555456
$832$	−1.23814	−0.0429248
$833$	0	0
$834$	−8.93950	−0.309549
$835$	−0.0129638	−0.000448632 0
$836$	−22.8207	−0.789271
$837$	−18.6480	−0.644571
$838$	−10.2750	−0.354944
$839$	21.7442	0.750693	0.375347	−	0.926884i	$-0.377524\pi$
$839$	21.7442	0.750693	0.375347	+	0.926884i	$0.377524\pi$
$840$	0	0
$841$	11.4098	0.393442
$842$	−35.0986	−1.20958
$843$	−3.86013	−0.132950
$844$	−20.8450	−0.717514
$845$	−21.3595	−0.734790
$846$	1.44822	0.0497907
$847$	0	0
$848$	9.94076	0.341367
$849$	24.3605	0.836049
$850$	−0.0382348	−0.00131144
$851$	−1.52137	−0.0521517
$852$	2.53099	0.0867104
$853$	−9.17926	−0.314292	−0.157146	−	0.987575i	$-0.550229\pi$
$853$	−9.17926	−0.314292	−0.157146	+	0.987575i	$0.550229\pi$
$854$	0	0
$855$	25.8180	0.882957
$856$	−2.67167	−0.0913157
$857$	13.8352	0.472601	0.236300	−	0.971680i	$-0.424065\pi$
$857$	13.8352	0.472601	0.236300	+	0.971680i	$0.424065\pi$
$858$	−3.72376	−0.127127
$859$	37.8391	1.29105	0.645526	−	0.763738i	$-0.276638\pi$
$859$	37.8391	1.29105	0.645526	+	0.763738i	$0.276638\pi$
$860$	−23.0742	−0.786822
$861$	0	0
$862$	25.1735	0.857414
$863$	27.8741	0.948847	0.474423	−	0.880297i	$-0.342657\pi$
$863$	27.8741	0.948847	0.474423	+	0.880297i	$0.342657\pi$
$864$	−4.07339	−0.138580
$865$	−30.2579	−1.02880
$866$	−32.0992	−1.09077
$867$	12.7309	0.432364
$868$	0	0
$869$	−8.83231	−0.299616
$870$	−8.86770	−0.300643
$871$	16.4599	0.557723
$872$	−7.68504	−0.260248
$873$	37.6283	1.27353
$874$	46.3462	1.56768
$875$	0	0
$876$	11.0708	0.374046
$877$	−48.7795	−1.64717	−0.823583	−	0.567196i	$-0.808028\pi$
$877$	−48.7795	−1.64717	−0.823583	+	0.567196i	$0.808028\pi$
$878$	22.4145	0.756452
$879$	4.78596	0.161427
$880$	7.48045	0.252166
$881$	52.3044	1.76218	0.881091	−	0.472947i	$-0.156810\pi$
$881$	52.3044	1.76218	0.881091	+	0.472947i	$0.156810\pi$
$882$	0	0
$883$	0.682685	0.0229742	0.0114871	−	0.999934i	$-0.496343\pi$
$883$	0.682685	0.0229742	0.0114871	+	0.999934i	$0.496343\pi$
$884$	0.0309338	0.00104042
$885$	−11.6452	−0.391450
$886$	14.6761	0.493052
$887$	35.6411	1.19671	0.598355	−	0.801231i	$-0.295821\pi$
$887$	35.6411	1.19671	0.598355	+	0.801231i	$0.295821\pi$
$888$	−0.139698	−0.00468794
$889$	0	0
$890$	25.7214	0.862184
$891$	17.1354	0.574057
$892$	−19.3546	−0.648041
$893$	−3.37396	−0.112905
$894$	15.0056	0.501863
$895$	16.4471	0.549767
$896$	0	0
$897$	7.56252	0.252505
$898$	−14.1839	−0.473323
$899$	29.1018	0.970601
$900$	3.73278	0.124426
$901$	−0.248361	−0.00827410
$902$	4.01593	0.133716
$903$	0	0
$904$	2.58320	0.0859158
$905$	17.0890	0.568058
$906$	12.1526	0.403744
$907$	−55.8554	−1.85465	−0.927323	−	0.374261i	$-0.877896\pi$
$907$	−55.8554	−1.85465	−0.927323	+	0.374261i	$0.877896\pi$
$908$	−4.32774	−0.143621
$909$	26.7295	0.886562
$910$	0	0
$911$	−15.7393	−0.521467	−0.260734	−	0.965411i	$-0.583964\pi$
$911$	−15.7393	−0.521467	−0.260734	+	0.965411i	$0.583964\pi$
$912$	4.25568	0.140920
$913$	−31.8967	−1.05563
$914$	2.60020	0.0860070
$915$	−14.6040	−0.482792
$916$	2.56052	0.0846020
$917$	0	0
$918$	0.101770	0.00335891
$919$	35.8402	1.18226	0.591129	−	0.806577i	$-0.298682\pi$
$919$	35.8402	1.18226	0.591129	+	0.806577i	$0.298682\pi$
$920$	−15.1919	−0.500862
$921$	13.1395	0.432961
$922$	−12.9522	−0.426559
$923$	4.18442	0.137732
$924$	0	0
$925$	0.285469	0.00938615
$926$	−2.89466	−0.0951244
$927$	−27.1480	−0.891656
$928$	6.35687	0.208675
$929$	22.5270	0.739086	0.369543	−	0.929214i	$-0.379514\pi$
$929$	22.5270	0.739086	0.369543	+	0.929214i	$0.379514\pi$
$930$	−6.38623	−0.209413
$931$	0	0
$932$	−11.8749	−0.388974
$933$	−23.7633	−0.777974
$934$	3.67570	0.120273
$935$	−0.186892	−0.00611203
$936$	−3.02000	−0.0987119
$937$	12.3164	0.402358	0.201179	−	0.979555i	$-0.435523\pi$
$937$	12.3164	0.402358	0.201179	+	0.979555i	$0.435523\pi$
$938$	0	0
$939$	−3.34879	−0.109284
$940$	1.10596	0.0360723
$941$	15.8536	0.516813	0.258407	−	0.966036i	$-0.416803\pi$
$941$	15.8536	0.516813	0.258407	+	0.966036i	$0.416803\pi$
$942$	11.3305	0.369169
$943$	−8.15588	−0.265592
$944$	8.34796	0.271703
$945$	0	0
$946$	49.7473	1.61743
$947$	2.88925	0.0938881	0.0469440	−	0.998898i	$-0.485052\pi$
$947$	2.88925	0.0938881	0.0469440	+	0.998898i	$0.485052\pi$
$948$	1.64708	0.0534946
$949$	18.3030	0.594140
$950$	−8.69639	−0.282148
$951$	−7.94587	−0.257662
$952$	0	0
$953$	20.4341	0.661926	0.330963	−	0.943644i	$-0.392626\pi$
$953$	20.4341	0.661926	0.330963	+	0.943644i	$0.392626\pi$
$954$	24.2469	0.785024
$955$	4.35827	0.141030
$956$	−6.78691	−0.219505
$957$	19.1185	0.618015
$958$	18.1304	0.585768
$959$	0	0
$960$	−1.39498	−0.0450227
$961$	−10.0418	−0.323929
$962$	−0.230958	−0.00744639
$963$	−6.51658	−0.209994
$964$	6.20426	0.199826
$965$	13.1885	0.424553
$966$	0	0
$967$	33.7789	1.08626	0.543129	−	0.839649i	$-0.317240\pi$
$967$	33.7789	1.08626	0.543129	+	0.839649i	$0.317240\pi$
$968$	−5.12767	−0.164809
$969$	−0.106324	−0.00341563
$970$	28.7355	0.922642
$971$	45.5056	1.46034	0.730172	−	0.683264i	$-0.239440\pi$
$971$	45.5056	1.46034	0.730172	+	0.683264i	$0.239440\pi$
$972$	−15.4156	−0.494457
$973$	0	0
$974$	−9.18267	−0.294232
$975$	−1.41903	−0.0454453
$976$	10.4690	0.335103
$977$	−32.7507	−1.04779	−0.523893	−	0.851784i	$-0.675521\pi$
$977$	−32.7507	−1.04779	−0.523893	+	0.851784i	$0.675521\pi$
$978$	15.7411	0.503345
$979$	−55.4548	−1.77234
$980$	0	0
$981$	−18.7449	−0.598479
$982$	−29.4648	−0.940258
$983$	−32.7010	−1.04300	−0.521499	−	0.853252i	$-0.674627\pi$
$983$	−32.7010	−1.04300	−0.521499	+	0.853252i	$0.674627\pi$
$984$	−0.748903	−0.0238742
$985$	−23.3885	−0.745219
$986$	−0.158821	−0.00505788
$987$	0	0
$988$	7.03580	0.223839
$989$	−101.031	−3.21260
$990$	18.2459	0.579892
$991$	26.5964	0.844864	0.422432	−	0.906395i	$-0.361177\pi$
$991$	26.5964	0.844864	0.422432	+	0.906395i	$0.361177\pi$
$992$	4.57801	0.145352
$993$	21.0632	0.668421
$994$	0	0
$995$	−47.0276	−1.49088
$996$	5.94820	0.188476
$997$	26.1550	0.828338	0.414169	−	0.910200i	$-0.364072\pi$
$997$	26.1550	0.828338	0.414169	+	0.910200i	$0.364072\pi$
$998$	36.0935	1.14252
$999$	−0.759835	−0.0240401

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.br.1.5	✓	10
7.6	odd	2		4018.2.a.bs.1.6	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.br.1.5	✓	10	1.1	even	1	trivial
4018.2.a.bs.1.6	yes	10	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.748903 q^{3} +1.00000 q^{4} +1.86270 q^{5} +0.748903 q^{6} -1.00000 q^{8} -2.43914 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.748903 q^{3} +1.00000 q^{4} +1.86270 q^{5} +0.748903 q^{6} -1.00000 q^{8} -2.43914 q^{9} -1.86270 q^{10} +4.01593 q^{11} -0.748903 q^{12} -1.23814 q^{13} -1.39498 q^{15} +1.00000 q^{16} -0.0249841 q^{17} +2.43914 q^{18} -5.68255 q^{19} +1.86270 q^{20} -4.01593 q^{22} +8.15588 q^{23} +0.748903 q^{24} -1.53037 q^{25} +1.23814 q^{26} +4.07339 q^{27} -6.35687 q^{29} +1.39498 q^{30} -4.57801 q^{31} -1.00000 q^{32} -3.00754 q^{33} +0.0249841 q^{34} -2.43914 q^{36} -0.186536 q^{37} +5.68255 q^{38} +0.927248 q^{39} -1.86270 q^{40} -1.00000 q^{41} -12.3875 q^{43} +4.01593 q^{44} -4.54338 q^{45} -8.15588 q^{46} +0.593740 q^{47} -0.748903 q^{48} +1.53037 q^{50} +0.0187107 q^{51} -1.23814 q^{52} +9.94076 q^{53} -4.07339 q^{54} +7.48045 q^{55} +4.25568 q^{57} +6.35687 q^{58} +8.34796 q^{59} -1.39498 q^{60} +10.4690 q^{61} +4.57801 q^{62} +1.00000 q^{64} -2.30628 q^{65} +3.00754 q^{66} -13.2941 q^{67} -0.0249841 q^{68} -6.10796 q^{69} -3.37960 q^{71} +2.43914 q^{72} -14.7826 q^{73} +0.186536 q^{74} +1.14610 q^{75} -5.68255 q^{76} -0.927248 q^{78} -2.19932 q^{79} +1.86270 q^{80} +4.26685 q^{81} +1.00000 q^{82} -7.94255 q^{83} -0.0465377 q^{85} +12.3875 q^{86} +4.76068 q^{87} -4.01593 q^{88} -13.8087 q^{89} +4.54338 q^{90} +8.15588 q^{92} +3.42849 q^{93} -0.593740 q^{94} -10.5849 q^{95} +0.748903 q^{96} -15.4269 q^{97} -9.79542 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} - 4 q^{5} + 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 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

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