LMFDB - Embedded newform 4018.2.a.be.1.3

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:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.65544$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +3.05137 q^{3} +1.00000 q^{4} +2.65544 q^{5} -3.05137 q^{6} -1.00000 q^{8} +6.31088 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.05137 q^{3} +1.00000 q^{4} +2.65544 q^{5} -3.05137 q^{6} -1.00000 q^{8} +6.31088 q^{9} -2.65544 q^{10} -0.395932 q^{11} +3.05137 q^{12} +0.259511 q^{13} +8.10275 q^{15} +1.00000 q^{16} +0.948626 q^{17} -6.31088 q^{18} +2.25951 q^{19} +2.65544 q^{20} +0.395932 q^{22} -7.84324 q^{23} -3.05137 q^{24} +2.05137 q^{25} -0.259511 q^{26} +10.1027 q^{27} +9.01770 q^{29} -8.10275 q^{30} +1.20814 q^{31} -1.00000 q^{32} -1.20814 q^{33} -0.948626 q^{34} +6.31088 q^{36} -0.102748 q^{37} -2.25951 q^{38} +0.791864 q^{39} -2.65544 q^{40} -1.00000 q^{41} +2.10275 q^{43} -0.395932 q^{44} +16.7582 q^{45} +7.84324 q^{46} +8.25951 q^{47} +3.05137 q^{48} -2.05137 q^{50} +2.89461 q^{51} +0.259511 q^{52} +1.70682 q^{53} -10.1027 q^{54} -1.05137 q^{55} +6.89461 q^{57} -9.01770 q^{58} -1.96633 q^{59} +8.10275 q^{60} -14.2392 q^{61} -1.20814 q^{62} +1.00000 q^{64} +0.689115 q^{65} +1.20814 q^{66} +2.12309 q^{67} +0.948626 q^{68} -23.9327 q^{69} +6.89461 q^{71} -6.31088 q^{72} +10.1027 q^{73} +0.102748 q^{74} +6.25951 q^{75} +2.25951 q^{76} -0.791864 q^{78} +10.6218 q^{79} +2.65544 q^{80} +11.8946 q^{81} +1.00000 q^{82} -8.13642 q^{83} +2.51902 q^{85} -2.10275 q^{86} +27.5164 q^{87} +0.395932 q^{88} +2.27284 q^{89} -16.7582 q^{90} -7.84324 q^{92} +3.68648 q^{93} -8.25951 q^{94} +6.00000 q^{95} -3.05137 q^{96} -18.2055 q^{97} -2.49868 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} + 2 q^{5} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 + 2 * q^5 - 3 * q^8 + 7 * q^9	$ 3 q - 3 q^{2} + 3 q^{4} + 2 q^{5} - 3 q^{8} + 7 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{13} + 6 q^{15} + 3 q^{16} + 12 q^{17} - 7 q^{18} + 4 q^{19} + 2 q^{20} - 2 q^{22} - 8 q^{23} - 3 q^{25} + 2 q^{26} + 12 q^{27} - 6 q^{30} + 10 q^{31} - 3 q^{32} - 10 q^{33} - 12 q^{34} + 7 q^{36} + 18 q^{37} - 4 q^{38} - 4 q^{39} - 2 q^{40} - 3 q^{41} - 12 q^{43} + 2 q^{44} + 26 q^{45} + 8 q^{46} + 22 q^{47} + 3 q^{50} - 16 q^{51} - 2 q^{52} - 10 q^{53} - 12 q^{54} + 6 q^{55} - 4 q^{57} + 12 q^{59} + 6 q^{60} - 24 q^{61} - 10 q^{62} + 3 q^{64} + 14 q^{65} + 10 q^{66} + 4 q^{67} + 12 q^{68} - 36 q^{69} - 4 q^{71} - 7 q^{72} + 12 q^{73} - 18 q^{74} + 16 q^{75} + 4 q^{76} + 4 q^{78} + 8 q^{79} + 2 q^{80} + 11 q^{81} + 3 q^{82} - 24 q^{83} + 2 q^{85} + 12 q^{86} + 34 q^{87} - 2 q^{88} + 6 q^{89} - 26 q^{90} - 8 q^{92} - 20 q^{93} - 22 q^{94} + 18 q^{95} - 18 q^{97} + 14 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 + 2 * q^5 - 3 * q^8 + 7 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^13 + 6 * q^15 + 3 * q^16 + 12 * q^17 - 7 * q^18 + 4 * q^19 + 2 * q^20 - 2 * q^22 - 8 * q^23 - 3 * q^25 + 2 * q^26 + 12 * q^27 - 6 * q^30 + 10 * q^31 - 3 * q^32 - 10 * q^33 - 12 * q^34 + 7 * q^36 + 18 * q^37 - 4 * q^38 - 4 * q^39 - 2 * q^40 - 3 * q^41 - 12 * q^43 + 2 * q^44 + 26 * q^45 + 8 * q^46 + 22 * q^47 + 3 * q^50 - 16 * q^51 - 2 * q^52 - 10 * q^53 - 12 * q^54 + 6 * q^55 - 4 * q^57 + 12 * q^59 + 6 * q^60 - 24 * q^61 - 10 * q^62 + 3 * q^64 + 14 * q^65 + 10 * q^66 + 4 * q^67 + 12 * q^68 - 36 * q^69 - 4 * q^71 - 7 * q^72 + 12 * q^73 - 18 * q^74 + 16 * q^75 + 4 * q^76 + 4 * q^78 + 8 * q^79 + 2 * q^80 + 11 * q^81 + 3 * q^82 - 24 * q^83 + 2 * q^85 + 12 * q^86 + 34 * q^87 - 2 * q^88 + 6 * q^89 - 26 * q^90 - 8 * q^92 - 20 * q^93 - 22 * q^94 + 18 * q^95 - 18 * q^97 + 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.05137	1.76171	0.880856	−	0.473385i	$-0.156968\pi$
$3$	3.05137	1.76171	0.880856	+	0.473385i	$0.156968\pi$
$4$	1.00000	0.500000
$5$	2.65544	1.18755	0.593775	−	0.804631i	$-0.297637\pi$
$5$	2.65544	1.18755	0.593775	+	0.804631i	$0.297637\pi$
$6$	−3.05137	−1.24572
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	6.31088	2.10363
$10$	−2.65544	−0.839725
$11$	−0.395932	−0.119378	−0.0596890	−	0.998217i	$-0.519011\pi$
$11$	−0.395932	−0.119378	−0.0596890	+	0.998217i	$0.519011\pi$
$12$	3.05137	0.880856
$13$	0.259511	0.0719753	0.0359876	−	0.999352i	$-0.488542\pi$
$13$	0.259511	0.0719753	0.0359876	+	0.999352i	$0.488542\pi$
$14$	0	0
$15$	8.10275	2.09212
$16$	1.00000	0.250000
$17$	0.948626	0.230076	0.115038	−	0.993361i	$-0.463301\pi$
$17$	0.948626	0.230076	0.115038	+	0.993361i	$0.463301\pi$
$18$	−6.31088	−1.48749
$19$	2.25951	0.518367	0.259184	−	0.965828i	$-0.416547\pi$
$19$	2.25951	0.518367	0.259184	+	0.965828i	$0.416547\pi$
$20$	2.65544	0.593775
$21$	0	0
$22$	0.395932	0.0844130
$23$	−7.84324	−1.63543	−0.817714	−	0.575625i	$-0.804759\pi$
$23$	−7.84324	−1.63543	−0.817714	+	0.575625i	$0.804759\pi$
$24$	−3.05137	−0.622859
$25$	2.05137	0.410275
$26$	−0.259511	−0.0508942
$27$	10.1027	1.94427
$28$	0	0
$29$	9.01770	1.67455	0.837273	−	0.546786i	$-0.184149\pi$
$29$	9.01770	1.67455	0.837273	+	0.546786i	$0.184149\pi$
$30$	−8.10275	−1.47935
$31$	1.20814	0.216988	0.108494	−	0.994097i	$-0.465397\pi$
$31$	1.20814	0.216988	0.108494	+	0.994097i	$0.465397\pi$
$32$	−1.00000	−0.176777
$33$	−1.20814	−0.210310
$34$	−0.948626	−0.162688
$35$	0	0
$36$	6.31088	1.05181
$37$	−0.102748	−0.0168917	−0.00844587	−	0.999964i	$-0.502688\pi$
$37$	−0.102748	−0.0168917	−0.00844587	+	0.999964i	$0.502688\pi$
$38$	−2.25951	−0.366541
$39$	0.791864	0.126800
$40$	−2.65544	−0.419862
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	2.10275	0.320666	0.160333	−	0.987063i	$-0.448743\pi$
$43$	2.10275	0.320666	0.160333	+	0.987063i	$0.448743\pi$
$44$	−0.395932	−0.0596890
$45$	16.7582	2.49816
$46$	7.84324	1.15642
$47$	8.25951	1.20477	0.602387	−	0.798204i	$-0.294217\pi$
$47$	8.25951	1.20477	0.602387	+	0.798204i	$0.294217\pi$
$48$	3.05137	0.440428
$49$	0	0
$50$	−2.05137	−0.290108
$51$	2.89461	0.405327
$52$	0.259511	0.0359876
$53$	1.70682	0.234449	0.117225	−	0.993105i	$-0.462600\pi$
$53$	1.70682	0.234449	0.117225	+	0.993105i	$0.462600\pi$
$54$	−10.1027	−1.37481
$55$	−1.05137	−0.141767
$56$	0	0
$57$	6.89461	0.913214
$58$	−9.01770	−1.18408
$59$	−1.96633	−0.255994	−0.127997	−	0.991775i	$-0.540855\pi$
$59$	−1.96633	−0.255994	−0.127997	+	0.991775i	$0.540855\pi$
$60$	8.10275	1.04606
$61$	−14.2392	−1.82314	−0.911569	−	0.411146i	$-0.865129\pi$
$61$	−14.2392	−1.82314	−0.911569	+	0.411146i	$0.865129\pi$
$62$	−1.20814	−0.153433
$63$	0	0
$64$	1.00000	0.125000
$65$	0.689115	0.0854742
$66$	1.20814	0.148711
$67$	2.12309	0.259377	0.129688	−	0.991555i	$-0.458602\pi$
$67$	2.12309	0.259377	0.129688	+	0.991555i	$0.458602\pi$
$68$	0.948626	0.115038
$69$	−23.9327	−2.88115
$70$	0	0
$71$	6.89461	0.818240	0.409120	−	0.912481i	$-0.365836\pi$
$71$	6.89461	0.818240	0.409120	+	0.912481i	$0.365836\pi$
$72$	−6.31088	−0.743745
$73$	10.1027	1.18244	0.591219	−	0.806511i	$-0.298647\pi$
$73$	10.1027	1.18244	0.591219	+	0.806511i	$0.298647\pi$
$74$	0.102748	0.0119443
$75$	6.25951	0.722786
$76$	2.25951	0.259184
$77$	0	0
$78$	−0.791864	−0.0896609
$79$	10.6218	1.19504	0.597521	−	0.801853i	$-0.296152\pi$
$79$	10.6218	1.19504	0.597521	+	0.801853i	$0.296152\pi$
$80$	2.65544	0.296887
$81$	11.8946	1.32162
$82$	1.00000	0.110432
$83$	−8.13642	−0.893088	−0.446544	−	0.894762i	$-0.647345\pi$
$83$	−8.13642	−0.893088	−0.446544	+	0.894762i	$0.647345\pi$
$84$	0	0
$85$	2.51902	0.273226
$86$	−2.10275	−0.226745
$87$	27.5164	2.95007
$88$	0.395932	0.0422065
$89$	2.27284	0.240921	0.120460	−	0.992718i	$-0.461563\pi$
$89$	2.27284	0.240921	0.120460	+	0.992718i	$0.461563\pi$
$90$	−16.7582	−1.76647
$91$	0	0
$92$	−7.84324	−0.817714
$93$	3.68648	0.382270
$94$	−8.25951	−0.851903
$95$	6.00000	0.615587
$96$	−3.05137	−0.311430
$97$	−18.2055	−1.84849	−0.924244	−	0.381802i	$-0.875304\pi$
$97$	−18.2055	−1.84849	−0.924244	+	0.381802i	$0.875304\pi$
$98$	0	0
$99$	−2.49868	−0.251127
$100$	2.05137	0.205137
$101$	1.63774	0.162961	0.0814807	−	0.996675i	$-0.474035\pi$
$101$	1.63774	0.162961	0.0814807	+	0.996675i	$0.474035\pi$
$102$	−2.89461	−0.286609
$103$	−9.82991	−0.968569	−0.484285	−	0.874910i	$-0.660920\pi$
$103$	−9.82991	−0.968569	−0.484285	+	0.874910i	$0.660920\pi$
$104$	−0.259511	−0.0254471
$105$	0	0
$106$	−1.70682	−0.165781
$107$	3.20814	0.310142	0.155071	−	0.987903i	$-0.450439\pi$
$107$	3.20814	0.310142	0.155071	+	0.987903i	$0.450439\pi$
$108$	10.1027	0.972137
$109$	12.0824	1.15728	0.578642	−	0.815581i	$-0.303583\pi$
$109$	12.0824	1.15728	0.578642	+	0.815581i	$0.303583\pi$
$110$	1.05137	0.100245
$111$	−0.313524	−0.0297584
$112$	0	0
$113$	−13.0514	−1.22777	−0.613885	−	0.789395i	$-0.710394\pi$
$113$	−13.0514	−1.22777	−0.613885	+	0.789395i	$0.710394\pi$
$114$	−6.89461	−0.645740
$115$	−20.8273	−1.94215
$116$	9.01770	0.837273
$117$	1.63774	0.151409
$118$	1.96633	0.181015
$119$	0	0
$120$	−8.10275	−0.739676
$121$	−10.8432	−0.985749
$122$	14.2392	1.28915
$123$	−3.05137	−0.275133
$124$	1.20814	0.108494
$125$	−7.82991	−0.700328
$126$	0	0
$127$	19.8432	1.76080	0.880401	−	0.474229i	$-0.157273\pi$
$127$	19.8432	1.76080	0.880401	+	0.474229i	$0.157273\pi$
$128$	−1.00000	−0.0883883
$129$	6.41627	0.564921
$130$	−0.689115	−0.0604394
$131$	10.8609	0.948925	0.474462	−	0.880276i	$-0.342643\pi$
$131$	10.8609	0.948925	0.474462	+	0.880276i	$0.342643\pi$
$132$	−1.20814	−0.105155
$133$	0	0
$134$	−2.12309	−0.183407
$135$	26.8273	2.30892
$136$	−0.948626	−0.0813440
$137$	17.9327	1.53209	0.766045	−	0.642787i	$-0.222222\pi$
$137$	17.9327	1.53209	0.766045	+	0.642787i	$0.222222\pi$
$138$	23.9327	2.03728
$139$	3.44731	0.292397	0.146198	−	0.989255i	$-0.453296\pi$
$139$	3.44731	0.292397	0.146198	+	0.989255i	$0.453296\pi$
$140$	0	0
$141$	25.2029	2.12246
$142$	−6.89461	−0.578583
$143$	−0.102748	−0.00859226
$144$	6.31088	0.525907
$145$	23.9460	1.98861
$146$	−10.1027	−0.836109
$147$	0	0
$148$	−0.102748	−0.00844587
$149$	−10.1231	−0.829316	−0.414658	−	0.909977i	$-0.636099\pi$
$149$	−10.1231	−0.829316	−0.414658	+	0.909977i	$0.636099\pi$
$150$	−6.25951	−0.511087
$151$	−18.2055	−1.48154	−0.740771	−	0.671757i	$-0.765540\pi$
$151$	−18.2055	−1.48154	−0.740771	+	0.671757i	$0.765540\pi$
$152$	−2.25951	−0.183271
$153$	5.98667	0.483993
$154$	0	0
$155$	3.20814	0.257684
$156$	0.791864	0.0633998
$157$	13.2569	1.05801	0.529007	−	0.848618i	$-0.322565\pi$
$157$	13.2569	1.05801	0.529007	+	0.848618i	$0.322565\pi$
$158$	−10.6218	−0.845023
$159$	5.20814	0.413032
$160$	−2.65544	−0.209931
$161$	0	0
$162$	−11.8946	−0.934529
$163$	10.0354	0.786033	0.393017	−	0.919531i	$-0.371431\pi$
$163$	10.0354	0.786033	0.393017	+	0.919531i	$0.371431\pi$
$164$	−1.00000	−0.0780869
$165$	−3.20814	−0.249753
$166$	8.13642	0.631509
$167$	19.4136	1.50227	0.751136	−	0.660147i	$-0.229506\pi$
$167$	19.4136	1.50227	0.751136	+	0.660147i	$0.229506\pi$
$168$	0	0
$169$	−12.9327	−0.994820
$170$	−2.51902	−0.193200
$171$	14.2595	1.09045
$172$	2.10275	0.160333
$173$	−13.6528	−1.03800	−0.519002	−	0.854773i	$-0.673696\pi$
$173$	−13.6528	−1.03800	−0.519002	+	0.854773i	$0.673696\pi$
$174$	−27.5164	−2.08601
$175$	0	0
$176$	−0.395932	−0.0298445
$177$	−6.00000	−0.450988
$178$	−2.27284	−0.170357
$179$	−3.70682	−0.277060	−0.138530	−	0.990358i	$-0.544238\pi$
$179$	−3.70682	−0.277060	−0.138530	+	0.990358i	$0.544238\pi$
$180$	16.7582	1.24908
$181$	−5.84324	−0.434324	−0.217162	−	0.976136i	$-0.569680\pi$
$181$	−5.84324	−0.434324	−0.217162	+	0.976136i	$0.569680\pi$
$182$	0	0
$183$	−43.4490	−3.21185
$184$	7.84324	0.578211
$185$	−0.272843	−0.0200598
$186$	−3.68648	−0.270306
$187$	−0.375591	−0.0274659
$188$	8.25951	0.602387
$189$	0	0
$190$	−6.00000	−0.435286
$191$	−10.3489	−0.748822	−0.374411	−	0.927263i	$-0.622155\pi$
$191$	−10.3489	−0.748822	−0.374411	+	0.927263i	$0.622155\pi$
$192$	3.05137	0.220214
$193$	11.4136	0.821571	0.410786	−	0.911732i	$-0.365254\pi$
$193$	11.4136	0.821571	0.410786	+	0.911732i	$0.365254\pi$
$194$	18.2055	1.30708
$195$	2.10275	0.150581
$196$	0	0
$197$	−22.9707	−1.63659	−0.818297	−	0.574795i	$-0.805082\pi$
$197$	−22.9707	−1.63659	−0.818297	+	0.574795i	$0.805082\pi$
$198$	2.49868	0.177573
$199$	−20.9840	−1.48752	−0.743759	−	0.668448i	$-0.766959\pi$
$199$	−20.9840	−1.48752	−0.743759	+	0.668448i	$0.766959\pi$
$200$	−2.05137	−0.145054
$201$	6.47834	0.456947
$202$	−1.63774	−0.115231
$203$	0	0
$204$	2.89461	0.202663
$205$	−2.65544	−0.185464
$206$	9.82991	0.684882
$207$	−49.4978	−3.44033
$208$	0.259511	0.0179938
$209$	−0.894612	−0.0618816
$210$	0	0
$211$	−8.66877	−0.596783	−0.298392	−	0.954444i	$-0.596450\pi$
$211$	−8.66877	−0.596783	−0.298392	+	0.954444i	$0.596450\pi$
$212$	1.70682	0.117225
$213$	21.0380	1.44150
$214$	−3.20814	−0.219304
$215$	5.58373	0.380807
$216$	−10.1027	−0.687405
$217$	0	0
$218$	−12.0824	−0.818324
$219$	30.8273	2.08311
$220$	−1.05137	−0.0708836
$221$	0.246178	0.0165597
$222$	0.313524	0.0210424
$223$	14.8273	0.992907	0.496454	−	0.868063i	$-0.334635\pi$
$223$	14.8273	0.992907	0.496454	+	0.868063i	$0.334635\pi$
$224$	0	0
$225$	12.9460	0.863066
$226$	13.0514	0.868165
$227$	4.42960	0.294003	0.147002	−	0.989136i	$-0.453038\pi$
$227$	4.42960	0.294003	0.147002	+	0.989136i	$0.453038\pi$
$228$	6.89461	0.456607
$229$	−22.3623	−1.47774	−0.738870	−	0.673848i	$-0.764640\pi$
$229$	−22.3623	−1.47774	−0.738870	+	0.673848i	$0.764640\pi$
$230$	20.8273	1.37331
$231$	0	0
$232$	−9.01770	−0.592041
$233$	−22.9300	−1.50220	−0.751098	−	0.660191i	$-0.770475\pi$
$233$	−22.9300	−1.50220	−0.751098	+	0.660191i	$0.770475\pi$
$234$	−1.63774	−0.107062
$235$	21.9327	1.43073
$236$	−1.96633	−0.127997
$237$	32.4110	2.10532
$238$	0	0
$239$	−10.2055	−0.660139	−0.330069	−	0.943957i	$-0.607072\pi$
$239$	−10.2055	−0.660139	−0.330069	+	0.943957i	$0.607072\pi$
$240$	8.10275	0.523030
$241$	−25.1408	−1.61946	−0.809730	−	0.586802i	$-0.800387\pi$
$241$	−25.1408	−1.61946	−0.809730	+	0.586802i	$0.800387\pi$
$242$	10.8432	0.697030
$243$	5.98667	0.384045
$244$	−14.2392	−0.911569
$245$	0	0
$246$	3.05137	0.194549
$247$	0.586367	0.0373096
$248$	−1.20814	−0.0767167
$249$	−24.8273	−1.57336
$250$	7.82991	0.495207
$251$	0.901621	0.0569098	0.0284549	−	0.999595i	$-0.490941\pi$
$251$	0.901621	0.0569098	0.0284549	+	0.999595i	$0.490941\pi$
$252$	0	0
$253$	3.10539	0.195234
$254$	−19.8432	−1.24508
$255$	7.68648	0.481346
$256$	1.00000	0.0625000
$257$	−11.8566	−0.739593	−0.369796	−	0.929113i	$-0.620573\pi$
$257$	−11.8566	−0.739593	−0.369796	+	0.929113i	$0.620573\pi$
$258$	−6.41627	−0.399460
$259$	0	0
$260$	0.689115	0.0427371
$261$	56.9097	3.52262
$262$	−10.8609	−0.670991
$263$	0.519021	0.0320042	0.0160021	−	0.999872i	$-0.494906\pi$
$263$	0.519021	0.0320042	0.0160021	+	0.999872i	$0.494906\pi$
$264$	1.20814	0.0743556
$265$	4.53235	0.278420
$266$	0	0
$267$	6.93529	0.424433
$268$	2.12309	0.129688
$269$	−4.65544	−0.283847	−0.141924	−	0.989878i	$-0.545329\pi$
$269$	−4.65544	−0.283847	−0.141924	+	0.989878i	$0.545329\pi$
$270$	−26.8273	−1.63266
$271$	−7.24354	−0.440014	−0.220007	−	0.975498i	$-0.570608\pi$
$271$	−7.24354	−0.440014	−0.220007	+	0.975498i	$0.570608\pi$
$272$	0.948626	0.0575189
$273$	0	0
$274$	−17.9327	−1.08335
$275$	−0.812204	−0.0489778
$276$	−23.9327	−1.44058
$277$	6.27284	0.376899	0.188449	−	0.982083i	$-0.439654\pi$
$277$	6.27284	0.376899	0.188449	+	0.982083i	$0.439654\pi$
$278$	−3.44731	−0.206756
$279$	7.62441	0.456461
$280$	0	0
$281$	18.7245	1.11701	0.558506	−	0.829501i	$-0.311375\pi$
$281$	18.7245	1.11701	0.558506	+	0.829501i	$0.311375\pi$
$282$	−25.2029	−1.50081
$283$	13.6174	0.809470	0.404735	−	0.914434i	$-0.367364\pi$
$283$	13.6174	0.809470	0.404735	+	0.914434i	$0.367364\pi$
$284$	6.89461	0.409120
$285$	18.3082	1.08449
$286$	0.102748	0.00607565
$287$	0	0
$288$	−6.31088	−0.371872
$289$	−16.1001	−0.947065
$290$	−23.9460	−1.40616
$291$	−55.5518	−3.25650
$292$	10.1027	0.591219
$293$	13.0514	0.762469	0.381235	−	0.924478i	$-0.375499\pi$
$293$	13.0514	0.762469	0.381235	+	0.924478i	$0.375499\pi$
$294$	0	0
$295$	−5.22147	−0.304006
$296$	0.102748	0.00597213
$297$	−4.00000	−0.232104
$298$	10.1231	0.586415
$299$	−2.03540	−0.117710
$300$	6.25951	0.361393
$301$	0	0
$302$	18.2055	1.04761
$303$	4.99736	0.287091
$304$	2.25951	0.129592
$305$	−37.8113	−2.16507
$306$	−5.98667	−0.342235
$307$	−14.7936	−0.844315	−0.422157	−	0.906523i	$-0.638727\pi$
$307$	−14.7936	−0.844315	−0.422157	+	0.906523i	$0.638727\pi$
$308$	0	0
$309$	−29.9947	−1.70634
$310$	−3.20814	−0.182210
$311$	34.5678	1.96016	0.980079	−	0.198609i	$-0.0636424\pi$
$311$	34.5678	1.96016	0.980079	+	0.198609i	$0.0636424\pi$
$312$	−0.791864	−0.0448305
$313$	6.01333	0.339894	0.169947	−	0.985453i	$-0.445640\pi$
$313$	6.01333	0.339894	0.169947	+	0.985453i	$0.445640\pi$
$314$	−13.2569	−0.748129
$315$	0	0
$316$	10.6218	0.597521
$317$	−24.4313	−1.37220	−0.686100	−	0.727507i	$-0.740679\pi$
$317$	−24.4313	−1.37220	−0.686100	+	0.727507i	$0.740679\pi$
$318$	−5.20814	−0.292058
$319$	−3.57040	−0.199904
$320$	2.65544	0.148444
$321$	9.78922	0.546381
$322$	0	0
$323$	2.14343	0.119264
$324$	11.8946	0.660812
$325$	0.532353	0.0295296
$326$	−10.0354	−0.555810
$327$	36.8679	2.03880
$328$	1.00000	0.0552158
$329$	0	0
$330$	3.20814	0.176602
$331$	−23.1471	−1.27228	−0.636140	−	0.771573i	$-0.719470\pi$
$331$	−23.1471	−1.27228	−0.636140	+	0.771573i	$0.719470\pi$
$332$	−8.13642	−0.446544
$333$	−0.648434	−0.0355340
$334$	−19.4136	−1.06227
$335$	5.63774	0.308023
$336$	0	0
$337$	−25.6598	−1.39778	−0.698890	−	0.715230i	$-0.746322\pi$
$337$	−25.6598	−1.39778	−0.698890	+	0.715230i	$0.746322\pi$
$338$	12.9327	0.703444
$339$	−39.8246	−2.16298
$340$	2.51902	0.136613
$341$	−0.478340	−0.0259035
$342$	−14.2595	−0.771066
$343$	0	0
$344$	−2.10275	−0.113373
$345$	−63.5518	−3.42151
$346$	13.6528	0.733979
$347$	10.7715	0.578246	0.289123	−	0.957292i	$-0.406636\pi$
$347$	10.7715	0.578246	0.289123	+	0.957292i	$0.406636\pi$
$348$	27.5164	1.47503
$349$	−13.6935	−0.732995	−0.366498	−	0.930419i	$-0.619443\pi$
$349$	−13.6935	−0.732995	−0.366498	+	0.930419i	$0.619443\pi$
$350$	0	0
$351$	2.62177	0.139940
$352$	0.395932	0.0211032
$353$	−5.10011	−0.271451	−0.135726	−	0.990746i	$-0.543337\pi$
$353$	−5.10011	−0.271451	−0.135726	+	0.990746i	$0.543337\pi$
$354$	6.00000	0.318896
$355$	18.3082	0.971701
$356$	2.27284	0.120460
$357$	0	0
$358$	3.70682	0.195911
$359$	7.20814	0.380431	0.190215	−	0.981742i	$-0.439081\pi$
$359$	7.20814	0.380431	0.190215	+	0.981742i	$0.439081\pi$
$360$	−16.7582	−0.883234
$361$	−13.8946	−0.731295
$362$	5.84324	0.307114
$363$	−33.0868	−1.73661
$364$	0	0
$365$	26.8273	1.40420
$366$	43.4490	2.27112
$367$	33.0328	1.72430	0.862148	−	0.506656i	$-0.169119\pi$
$367$	33.0328	1.72430	0.862148	+	0.506656i	$0.169119\pi$
$368$	−7.84324	−0.408857
$369$	−6.31088	−0.328532
$370$	0.272843	0.0141844
$371$	0	0
$372$	3.68648	0.191135
$373$	28.2409	1.46226	0.731129	−	0.682239i	$-0.238994\pi$
$373$	28.2409	1.46226	0.731129	+	0.682239i	$0.238994\pi$
$374$	0.375591	0.0194214
$375$	−23.8920	−1.23378
$376$	−8.25951	−0.425952
$377$	2.34019	0.120526
$378$	0	0
$379$	−23.8920	−1.22725	−0.613624	−	0.789598i	$-0.710289\pi$
$379$	−23.8920	−1.22725	−0.613624	+	0.789598i	$0.710289\pi$
$380$	6.00000	0.307794
$381$	60.5491	3.10203
$382$	10.3489	0.529497
$383$	−30.2409	−1.54524	−0.772619	−	0.634870i	$-0.781054\pi$
$383$	−30.2409	−1.54524	−0.772619	+	0.634870i	$0.781054\pi$
$384$	−3.05137	−0.155715
$385$	0	0
$386$	−11.4136	−0.580939
$387$	13.2702	0.674562
$388$	−18.2055	−0.924244
$389$	11.7892	0.597737	0.298869	−	0.954294i	$-0.403391\pi$
$389$	11.7892	0.597737	0.298869	+	0.954294i	$0.403391\pi$
$390$	−2.10275	−0.106477
$391$	−7.44030	−0.376272
$392$	0	0
$393$	33.1408	1.67173
$394$	22.9707	1.15725
$395$	28.2055	1.41917
$396$	−2.49868	−0.125563
$397$	18.5678	0.931889	0.465944	−	0.884814i	$-0.345715\pi$
$397$	18.5678	0.931889	0.465944	+	0.884814i	$0.345715\pi$
$398$	20.9840	1.05183
$399$	0	0
$400$	2.05137	0.102569
$401$	−29.9814	−1.49720	−0.748600	−	0.663022i	$-0.769273\pi$
$401$	−29.9814	−1.49720	−0.748600	+	0.663022i	$0.769273\pi$
$402$	−6.47834	−0.323110
$403$	0.313524	0.0156177
$404$	1.63774	0.0814807
$405$	31.5855	1.56949
$406$	0	0
$407$	0.0406814	0.00201650
$408$	−2.89461	−0.143305
$409$	−30.2055	−1.49357	−0.746783	−	0.665068i	$-0.768403\pi$
$409$	−30.2055	−1.49357	−0.746783	+	0.665068i	$0.768403\pi$
$410$	2.65544	0.131143
$411$	54.7192	2.69910
$412$	−9.82991	−0.484285
$413$	0	0
$414$	49.4978	2.43268
$415$	−21.6058	−1.06059
$416$	−0.259511	−0.0127236
$417$	10.5190	0.515119
$418$	0.894612	0.0437569
$419$	5.82290	0.284467	0.142234	−	0.989833i	$-0.454572\pi$
$419$	5.82290	0.284467	0.142234	+	0.989833i	$0.454572\pi$
$420$	0	0
$421$	−2.91495	−0.142066	−0.0710331	−	0.997474i	$-0.522630\pi$
$421$	−2.91495	−0.142066	−0.0710331	+	0.997474i	$0.522630\pi$
$422$	8.66877	0.421989
$423$	52.1248	2.53440
$424$	−1.70682	−0.0828903
$425$	1.94599	0.0943942
$426$	−21.0380	−1.01930
$427$	0	0
$428$	3.20814	0.155071
$429$	−0.313524	−0.0151371
$430$	−5.58373	−0.269271
$431$	15.8432	0.763142	0.381571	−	0.924340i	$-0.375383\pi$
$431$	15.8432	0.763142	0.381571	+	0.924340i	$0.375383\pi$
$432$	10.1027	0.486069
$433$	7.89725	0.379518	0.189759	−	0.981831i	$-0.439229\pi$
$433$	7.89725	0.379518	0.189759	+	0.981831i	$0.439229\pi$
$434$	0	0
$435$	73.0682	3.50335
$436$	12.0824	0.578642
$437$	−17.7219	−0.847752
$438$	−30.8273	−1.47298
$439$	15.0868	0.720053	0.360026	−	0.932942i	$-0.382768\pi$
$439$	15.0868	0.720053	0.360026	+	0.932942i	$0.382768\pi$
$440$	1.05137	0.0501223
$441$	0	0
$442$	−0.246178	−0.0117095
$443$	−9.58373	−0.455337	−0.227668	−	0.973739i	$-0.573110\pi$
$443$	−9.58373	−0.455337	−0.227668	+	0.973739i	$0.573110\pi$
$444$	−0.313524	−0.0148792
$445$	6.03540	0.286106
$446$	−14.8273	−0.702091
$447$	−30.8893	−1.46102
$448$	0	0
$449$	−28.8946	−1.36362	−0.681811	−	0.731529i	$-0.738807\pi$
$449$	−28.8946	−1.36362	−0.681811	+	0.731529i	$0.738807\pi$
$450$	−12.9460	−0.610280
$451$	0.395932	0.0186437
$452$	−13.0514	−0.613885
$453$	−55.5518	−2.61005
$454$	−4.42960	−0.207892
$455$	0	0
$456$	−6.89461	−0.322870
$457$	18.3489	0.858327	0.429163	−	0.903227i	$-0.358808\pi$
$457$	18.3489	0.858327	0.429163	+	0.903227i	$0.358808\pi$
$458$	22.3623	1.04492
$459$	9.58373	0.447330
$460$	−20.8273	−0.971076
$461$	−10.7936	−0.502708	−0.251354	−	0.967895i	$-0.580876\pi$
$461$	−10.7936	−0.502708	−0.251354	+	0.967895i	$0.580876\pi$
$462$	0	0
$463$	−3.97334	−0.184657	−0.0923283	−	0.995729i	$-0.529431\pi$
$463$	−3.97334	−0.184657	−0.0923283	+	0.995729i	$0.529431\pi$
$464$	9.01770	0.418636
$465$	9.78922	0.453964
$466$	22.9300	1.06221
$467$	−12.9016	−0.597016	−0.298508	−	0.954407i	$-0.596489\pi$
$467$	−12.9016	−0.597016	−0.298508	+	0.954407i	$0.596489\pi$
$468$	1.63774	0.0757046
$469$	0	0
$470$	−21.9327	−1.01168
$471$	40.4517	1.86391
$472$	1.96633	0.0905075
$473$	−0.832545	−0.0382805
$474$	−32.4110	−1.48869
$475$	4.63510	0.212673
$476$	0	0
$477$	10.7715	0.493194
$478$	10.2055	0.466789
$479$	40.6438	1.85706	0.928532	−	0.371252i	$-0.121071\pi$
$479$	40.6438	1.85706	0.928532	+	0.371252i	$0.121071\pi$
$480$	−8.10275	−0.369838
$481$	−0.0266643	−0.00121579
$482$	25.1408	1.14513
$483$	0	0
$484$	−10.8432	−0.492874
$485$	−48.3436	−2.19517
$486$	−5.98667	−0.271561
$487$	−23.6191	−1.07028	−0.535142	−	0.844762i	$-0.679742\pi$
$487$	−23.6191	−1.07028	−0.535142	+	0.844762i	$0.679742\pi$
$488$	14.2392	0.644577
$489$	30.6218	1.38476
$490$	0	0
$491$	−0.519021	−0.0234231	−0.0117115	−	0.999931i	$-0.503728\pi$
$491$	−0.519021	−0.0234231	−0.0117115	+	0.999931i	$0.503728\pi$
$492$	−3.05137	−0.137567
$493$	8.55442	0.385272
$494$	−0.586367	−0.0263819
$495$	−6.63510	−0.298226
$496$	1.20814	0.0542469
$497$	0	0
$498$	24.8273	1.11254
$499$	14.8069	0.662849	0.331425	−	0.943482i	$-0.392471\pi$
$499$	14.8069	0.662849	0.331425	+	0.943482i	$0.392471\pi$
$500$	−7.82991	−0.350164
$501$	59.2383	2.64657
$502$	−0.901621	−0.0402413
$503$	29.5837	1.31907	0.659537	−	0.751672i	$-0.270753\pi$
$503$	29.5837	1.31907	0.659537	+	0.751672i	$0.270753\pi$
$504$	0	0
$505$	4.34893	0.193525
$506$	−3.10539	−0.138051
$507$	−39.4624	−1.75259
$508$	19.8432	0.880401
$509$	2.88128	0.127710	0.0638552	−	0.997959i	$-0.479660\pi$
$509$	2.88128	0.127710	0.0638552	+	0.997959i	$0.479660\pi$
$510$	−7.68648	−0.340363
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	22.8273	1.00785
$514$	11.8566	0.522971
$515$	−26.1027	−1.15022
$516$	6.41627	0.282461
$517$	−3.27020	−0.143823
$518$	0	0
$519$	−41.6598	−1.82866
$520$	−0.689115	−0.0302197
$521$	12.3216	0.539818	0.269909	−	0.962886i	$-0.413006\pi$
$521$	12.3216	0.539818	0.269909	+	0.962886i	$0.413006\pi$
$522$	−56.9097	−2.49087
$523$	−18.4447	−0.806529	−0.403264	−	0.915083i	$-0.632125\pi$
$523$	−18.4447	−0.806529	−0.403264	+	0.915083i	$0.632125\pi$
$524$	10.8609	0.474462
$525$	0	0
$526$	−0.519021	−0.0226304
$527$	1.14607	0.0499236
$528$	−1.20814	−0.0525774
$529$	38.5164	1.67463
$530$	−4.53235	−0.196873
$531$	−12.4093	−0.538516
$532$	0	0
$533$	−0.259511	−0.0112406
$534$	−6.93529	−0.300120
$535$	8.51902	0.368309
$536$	−2.12309	−0.0917035
$537$	−11.3109	−0.488101
$538$	4.65544	0.200710
$539$	0	0
$540$	26.8273	1.15446
$541$	20.0761	0.863138	0.431569	−	0.902080i	$-0.357960\pi$
$541$	20.0761	0.863138	0.431569	+	0.902080i	$0.357960\pi$
$542$	7.24354	0.311137
$543$	−17.8299	−0.765154
$544$	−0.948626	−0.0406720
$545$	32.0841	1.37433
$546$	0	0
$547$	−37.7068	−1.61223	−0.806114	−	0.591761i	$-0.798433\pi$
$547$	−37.7068	−1.61223	−0.806114	+	0.591761i	$0.798433\pi$
$548$	17.9327	0.766045
$549$	−89.8618	−3.83521
$550$	0.812204	0.0346325
$551$	20.3756	0.868029
$552$	23.9327	1.01864
$553$	0	0
$554$	−6.27284	−0.266508
$555$	−0.832545	−0.0353396
$556$	3.44731	0.146198
$557$	28.2879	1.19860	0.599298	−	0.800526i	$-0.295446\pi$
$557$	28.2879	1.19860	0.599298	+	0.800526i	$0.295446\pi$
$558$	−7.62441	−0.322767
$559$	0.545685	0.0230800
$560$	0	0
$561$	−1.14607	−0.0483871
$562$	−18.7245	−0.789846
$563$	30.5324	1.28679	0.643393	−	0.765536i	$-0.277526\pi$
$563$	30.5324	1.28679	0.643393	+	0.765536i	$0.277526\pi$
$564$	25.2029	1.06123
$565$	−34.6572	−1.45804
$566$	−13.6174	−0.572382
$567$	0	0
$568$	−6.89461	−0.289292
$569$	17.0514	0.714831	0.357415	−	0.933946i	$-0.383658\pi$
$569$	17.0514	0.714831	0.357415	+	0.933946i	$0.383658\pi$
$570$	−18.3082	−0.766848
$571$	−21.3312	−0.892684	−0.446342	−	0.894862i	$-0.647274\pi$
$571$	−21.3312	−0.892684	−0.446342	+	0.894862i	$0.647274\pi$
$572$	−0.102748	−0.00429613
$573$	−31.5784	−1.31921
$574$	0	0
$575$	−16.0894	−0.670975
$576$	6.31088	0.262954
$577$	−11.0780	−0.461185	−0.230592	−	0.973050i	$-0.574066\pi$
$577$	−11.0780	−0.461185	−0.230592	+	0.973050i	$0.574066\pi$
$578$	16.1001	0.669676
$579$	34.8273	1.44737
$580$	23.9460	0.994303
$581$	0	0
$582$	55.5518	2.30270
$583$	−0.675783	−0.0279881
$584$	−10.1027	−0.418055
$585$	4.34893	0.179806
$586$	−13.0514	−0.539147
$587$	14.4917	0.598135	0.299068	−	0.954232i	$-0.403324\pi$
$587$	14.4917	0.598135	0.299068	+	0.954232i	$0.403324\pi$
$588$	0	0
$589$	2.72980	0.112479
$590$	5.22147	0.214964
$591$	−70.0922	−2.88321
$592$	−0.102748	−0.00422294
$593$	−9.48098	−0.389337	−0.194669	−	0.980869i	$-0.562363\pi$
$593$	−9.48098	−0.389337	−0.194669	+	0.980869i	$0.562363\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	−10.1231	−0.414658
$597$	−64.0301	−2.62058
$598$	2.03540	0.0832338
$599$	−42.2409	−1.72592	−0.862958	−	0.505275i	$-0.831391\pi$
$599$	−42.2409	−1.72592	−0.862958	+	0.505275i	$0.831391\pi$
$600$	−6.25951	−0.255543
$601$	43.3277	1.76737	0.883686	−	0.468079i	$-0.155054\pi$
$601$	43.3277	1.76737	0.883686	+	0.468079i	$0.155054\pi$
$602$	0	0
$603$	13.3986	0.545632
$604$	−18.2055	−0.740771
$605$	−28.7936	−1.17063
$606$	−4.99736	−0.203004
$607$	−10.0000	−0.405887	−0.202944	−	0.979190i	$-0.565051\pi$
$607$	−10.0000	−0.405887	−0.202944	+	0.979190i	$0.565051\pi$
$608$	−2.25951	−0.0916353
$609$	0	0
$610$	37.8113	1.53093
$611$	2.14343	0.0867139
$612$	5.98667	0.241997
$613$	31.6545	1.27851	0.639257	−	0.768993i	$-0.279242\pi$
$613$	31.6545	1.27851	0.639257	+	0.768993i	$0.279242\pi$
$614$	14.7936	0.597021
$615$	−8.10275	−0.326734
$616$	0	0
$617$	20.8459	0.839223	0.419612	−	0.907704i	$-0.362166\pi$
$617$	20.8459	0.839223	0.419612	+	0.907704i	$0.362166\pi$
$618$	29.9947	1.20656
$619$	−0.177103	−0.00711836	−0.00355918	−	0.999994i	$-0.501133\pi$
$619$	−0.177103	−0.00711836	−0.00355918	+	0.999994i	$0.501133\pi$
$620$	3.20814	0.128842
$621$	−79.2383	−3.17972
$622$	−34.5678	−1.38604
$623$	0	0
$624$	0.791864	0.0316999
$625$	−31.0487	−1.24195
$626$	−6.01333	−0.240341
$627$	−2.72980	−0.109018
$628$	13.2569	0.529007
$629$	−0.0974699	−0.00388638
$630$	0	0
$631$	−8.63510	−0.343758	−0.171879	−	0.985118i	$-0.554984\pi$
$631$	−8.63510	−0.343758	−0.171879	+	0.985118i	$0.554984\pi$
$632$	−10.6218	−0.422511
$633$	−26.4517	−1.05136
$634$	24.4313	0.970292
$635$	52.6926	2.09104
$636$	5.20814	0.206516
$637$	0	0
$638$	3.57040	0.141353
$639$	43.5111	1.72127
$640$	−2.65544	−0.104966
$641$	49.4084	1.95151	0.975756	−	0.218860i	$-0.0702337\pi$
$641$	49.4084	1.95151	0.975756	+	0.218860i	$0.0702337\pi$
$642$	−9.78922	−0.386350
$643$	19.9106	0.785197	0.392598	−	0.919710i	$-0.371576\pi$
$643$	19.9106	0.785197	0.392598	+	0.919710i	$0.371576\pi$
$644$	0	0
$645$	17.0380	0.670872
$646$	−2.14343	−0.0843321
$647$	31.1001	1.22267	0.611336	−	0.791371i	$-0.290633\pi$
$647$	31.1001	1.22267	0.611336	+	0.791371i	$0.290633\pi$
$648$	−11.8946	−0.467264
$649$	0.778532	0.0305600
$650$	−0.532353	−0.0208806
$651$	0	0
$652$	10.0354	0.393017
$653$	28.9097	1.13132	0.565661	−	0.824638i	$-0.308621\pi$
$653$	28.9097	1.13132	0.565661	+	0.824638i	$0.308621\pi$
$654$	−36.8679	−1.44165
$655$	28.8406	1.12690
$656$	−1.00000	−0.0390434
$657$	63.7573	2.48741
$658$	0	0
$659$	32.2258	1.25534	0.627670	−	0.778479i	$-0.284009\pi$
$659$	32.2258	1.25534	0.627670	+	0.778479i	$0.284009\pi$
$660$	−3.20814	−0.124877
$661$	−15.6581	−0.609029	−0.304514	−	0.952508i	$-0.598494\pi$
$661$	−15.6581	−0.609029	−0.304514	+	0.952508i	$0.598494\pi$
$662$	23.1471	0.899638
$663$	0.751182	0.0291735
$664$	8.13642	0.315754
$665$	0	0
$666$	0.648434	0.0251263
$667$	−70.7280	−2.73860
$668$	19.4136	0.751136
$669$	45.2435	1.74922
$670$	−5.63774	−0.217805
$671$	5.63774	0.217643
$672$	0	0
$673$	−21.3870	−0.824407	−0.412204	−	0.911092i	$-0.635241\pi$
$673$	−21.3870	−0.824407	−0.412204	+	0.911092i	$0.635241\pi$
$674$	25.6598	0.988379
$675$	20.7245	0.797687
$676$	−12.9327	−0.497410
$677$	22.5614	0.867106	0.433553	−	0.901128i	$-0.357260\pi$
$677$	22.5614	0.867106	0.433553	+	0.901128i	$0.357260\pi$
$678$	39.8246	1.52946
$679$	0	0
$680$	−2.51902	−0.0966000
$681$	13.5164	0.517949
$682$	0.478340	0.0183166
$683$	42.8069	1.63796	0.818981	−	0.573821i	$-0.194539\pi$
$683$	42.8069	1.63796	0.818981	+	0.573821i	$0.194539\pi$
$684$	14.2595	0.545226
$685$	47.6191	1.81943
$686$	0	0
$687$	−68.2356	−2.60335
$688$	2.10275	0.0801665
$689$	0.442937	0.0168746
$690$	63.5518	2.41938
$691$	−41.6058	−1.58276	−0.791380	−	0.611325i	$-0.790637\pi$
$691$	−41.6058	−1.58276	−0.791380	+	0.611325i	$0.790637\pi$
$692$	−13.6528	−0.519002
$693$	0	0
$694$	−10.7715	−0.408881
$695$	9.15412	0.347236
$696$	−27.5164	−1.04301
$697$	−0.948626	−0.0359318
$698$	13.6935	0.518306
$699$	−69.9681	−2.64643
$700$	0	0
$701$	4.34893	0.164257	0.0821284	−	0.996622i	$-0.473828\pi$
$701$	4.34893	0.164257	0.0821284	+	0.996622i	$0.473828\pi$
$702$	−2.62177	−0.0989523
$703$	−0.232161	−0.00875613
$704$	−0.395932	−0.0149222
$705$	66.9247	2.52053
$706$	5.10011	0.191945
$707$	0	0
$708$	−6.00000	−0.225494
$709$	16.6421	0.625008	0.312504	−	0.949917i	$-0.398832\pi$
$709$	16.6421	0.625008	0.312504	+	0.949917i	$0.398832\pi$
$710$	−18.3082	−0.687096
$711$	67.0328	2.51393
$712$	−2.27284	−0.0851784
$713$	−9.47570	−0.354868
$714$	0	0
$715$	−0.272843	−0.0102037
$716$	−3.70682	−0.138530
$717$	−31.1408	−1.16297
$718$	−7.20814	−0.269005
$719$	−19.2081	−0.716343	−0.358171	−	0.933656i	$-0.616600\pi$
$719$	−19.2081	−0.716343	−0.358171	+	0.933656i	$0.616600\pi$
$720$	16.7582	0.624541
$721$	0	0
$722$	13.8946	0.517104
$723$	−76.7140	−2.85302
$724$	−5.84324	−0.217162
$725$	18.4987	0.687024
$726$	33.0868	1.22797
$727$	29.2029	1.08307	0.541537	−	0.840677i	$-0.317843\pi$
$727$	29.2029	1.08307	0.541537	+	0.840677i	$0.317843\pi$
$728$	0	0
$729$	−17.4163	−0.645047
$730$	−26.8273	−0.992922
$731$	1.99472	0.0737774
$732$	−43.4490	−1.60592
$733$	4.17182	0.154090	0.0770449	−	0.997028i	$-0.475452\pi$
$733$	4.17182	0.154090	0.0770449	+	0.997028i	$0.475452\pi$
$734$	−33.0328	−1.21926
$735$	0	0
$736$	7.84324	0.289106
$737$	−0.840599	−0.0309638
$738$	6.31088	0.232307
$739$	15.1408	0.556963	0.278481	−	0.960442i	$-0.410169\pi$
$739$	15.1408	0.556963	0.278481	+	0.960442i	$0.410169\pi$
$740$	−0.272843	−0.0100299
$741$	1.78922	0.0657288
$742$	0	0
$743$	−30.4871	−1.11846	−0.559231	−	0.829012i	$-0.688904\pi$
$743$	−30.4871	−1.11846	−0.559231	+	0.829012i	$0.688904\pi$
$744$	−3.68648	−0.135153
$745$	−26.8813	−0.984854
$746$	−28.2409	−1.03397
$747$	−51.3480	−1.87873
$748$	−0.375591	−0.0137330
$749$	0	0
$750$	23.8920	0.872411
$751$	−10.4924	−0.382872	−0.191436	−	0.981505i	$-0.561314\pi$
$751$	−10.4924	−0.382872	−0.191436	+	0.981505i	$0.561314\pi$
$752$	8.25951	0.301193
$753$	2.75118	0.100259
$754$	−2.34019	−0.0852246
$755$	−48.3436	−1.75941
$756$	0	0
$757$	−39.5721	−1.43827	−0.719137	−	0.694869i	$-0.755462\pi$
$757$	−39.5721	−1.43827	−0.719137	+	0.694869i	$0.755462\pi$
$758$	23.8920	0.867796
$759$	9.47570	0.343946
$760$	−6.00000	−0.217643
$761$	−22.6891	−0.822480	−0.411240	−	0.911527i	$-0.634904\pi$
$761$	−22.6891	−0.822480	−0.411240	+	0.911527i	$0.634904\pi$
$762$	−60.5491	−2.19346
$763$	0	0
$764$	−10.3489	−0.374411
$765$	15.8973	0.574766
$766$	30.2409	1.09265
$767$	−0.510283	−0.0184252
$768$	3.05137	0.110107
$769$	−4.55970	−0.164427	−0.0822135	−	0.996615i	$-0.526199\pi$
$769$	−4.55970	−0.164427	−0.0822135	+	0.996615i	$0.526199\pi$
$770$	0	0
$771$	−36.1788	−1.30295
$772$	11.4136	0.410786
$773$	55.2923	1.98872	0.994362	−	0.106035i	$-0.0338155\pi$
$773$	55.2923	1.98872	0.994362	+	0.106035i	$0.0338155\pi$
$774$	−13.2702	−0.476988
$775$	2.47834	0.0890246
$776$	18.2055	0.653539
$777$	0	0
$778$	−11.7892	−0.422664
$779$	−2.25951	−0.0809554
$780$	2.10275	0.0752905
$781$	−2.72980	−0.0976798
$782$	7.44030	0.266064
$783$	91.1036	3.25578
$784$	0	0
$785$	35.2029	1.25644
$786$	−33.1408	−1.18209
$787$	−45.9663	−1.63852	−0.819261	−	0.573420i	$-0.805616\pi$
$787$	−45.9663	−1.63852	−0.819261	+	0.573420i	$0.805616\pi$
$788$	−22.9707	−0.818297
$789$	1.58373	0.0563822
$790$	−28.2055	−1.00351
$791$	0	0
$792$	2.49868	0.0887867
$793$	−3.69521	−0.131221
$794$	−18.5678	−0.658945
$795$	13.8299	0.490496
$796$	−20.9840	−0.743759
$797$	27.4154	0.971102	0.485551	−	0.874208i	$-0.338619\pi$
$797$	27.4154	0.971102	0.485551	+	0.874208i	$0.338619\pi$
$798$	0	0
$799$	7.83518	0.277189
$800$	−2.05137	−0.0725270
$801$	14.3436	0.506808
$802$	29.9814	1.05868
$803$	−4.00000	−0.141157
$804$	6.47834	0.228473
$805$	0	0
$806$	−0.313524	−0.0110434
$807$	−14.2055	−0.500057
$808$	−1.63774	−0.0576155
$809$	20.8627	0.733492	0.366746	−	0.930321i	$-0.380472\pi$
$809$	20.8627	0.733492	0.366746	+	0.930321i	$0.380472\pi$
$810$	−31.5855	−1.10980
$811$	9.79623	0.343992	0.171996	−	0.985098i	$-0.444978\pi$
$811$	9.79623	0.343992	0.171996	+	0.985098i	$0.444978\pi$
$812$	0	0
$813$	−22.1027	−0.775177
$814$	−0.0406814	−0.00142588
$815$	26.6484	0.933454
$816$	2.89461	0.101332
$817$	4.75118	0.166223
$818$	30.2055	1.05611
$819$	0	0
$820$	−2.65544	−0.0927321
$821$	−46.5190	−1.62353	−0.811763	−	0.583988i	$-0.801492\pi$
$821$	−46.5190	−1.62353	−0.811763	+	0.583988i	$0.801492\pi$
$822$	−54.7192	−1.90855
$823$	−28.9707	−1.00985	−0.504927	−	0.863162i	$-0.668481\pi$
$823$	−28.9707	−1.00985	−0.504927	+	0.863162i	$0.668481\pi$
$824$	9.82991	0.342441
$825$	−2.47834	−0.0862847
$826$	0	0
$827$	34.6722	1.20567	0.602836	−	0.797865i	$-0.294037\pi$
$827$	34.6722	1.20567	0.602836	+	0.797865i	$0.294037\pi$
$828$	−49.4978	−1.72017
$829$	−22.2038	−0.771169	−0.385584	−	0.922673i	$-0.626000\pi$
$829$	−22.2038	−0.771169	−0.385584	+	0.922673i	$0.626000\pi$
$830$	21.6058	0.749948
$831$	19.1408	0.663987
$832$	0.259511	0.00899691
$833$	0	0
$834$	−10.5190	−0.364244
$835$	51.5518	1.78402
$836$	−0.894612	−0.0309408
$837$	12.2055	0.421884
$838$	−5.82290	−0.201149
$839$	34.5411	1.19249	0.596245	−	0.802802i	$-0.296659\pi$
$839$	34.5411	1.19249	0.596245	+	0.802802i	$0.296659\pi$
$840$	0	0
$841$	52.3189	1.80410
$842$	2.91495	0.100456
$843$	57.1355	1.96785
$844$	−8.66877	−0.298392
$845$	−34.3419	−1.18140
$846$	−52.1248	−1.79209
$847$	0	0
$848$	1.70682	0.0586123
$849$	41.5518	1.42605
$850$	−1.94599	−0.0667468
$851$	0.805881	0.0276252
$852$	21.0380	0.720751
$853$	−56.3454	−1.92923	−0.964615	−	0.263664i	$-0.915069\pi$
$853$	−56.3454	−1.92923	−0.964615	+	0.263664i	$0.915069\pi$
$854$	0	0
$855$	37.8653	1.29497
$856$	−3.20814	−0.109652
$857$	−11.2702	−0.384983	−0.192491	−	0.981299i	$-0.561657\pi$
$857$	−11.2702	−0.384983	−0.192491	+	0.981299i	$0.561657\pi$
$858$	0.313524	0.0107035
$859$	−1.30388	−0.0444877	−0.0222438	−	0.999753i	$-0.507081\pi$
$859$	−1.30388	−0.0444877	−0.0222438	+	0.999753i	$0.507081\pi$
$860$	5.58373	0.190404
$861$	0	0
$862$	−15.8432	−0.539623
$863$	−33.2029	−1.13024	−0.565119	−	0.825009i	$-0.691170\pi$
$863$	−33.2029	−1.13024	−0.565119	+	0.825009i	$0.691170\pi$
$864$	−10.1027	−0.343702
$865$	−36.2542	−1.23268
$866$	−7.89725	−0.268360
$867$	−49.1275	−1.66846
$868$	0	0
$869$	−4.20550	−0.142662
$870$	−73.0682	−2.47724
$871$	0.550964	0.0186687
$872$	−12.0824	−0.409162
$873$	−114.893	−3.88853
$874$	17.7219	0.599451
$875$	0	0
$876$	30.8273	1.04156
$877$	−41.3056	−1.39479	−0.697396	−	0.716686i	$-0.745658\pi$
$877$	−41.3056	−1.39479	−0.697396	+	0.716686i	$0.745658\pi$
$878$	−15.0868	−0.509154
$879$	39.8246	1.34325
$880$	−1.05137	−0.0354418
$881$	−21.1001	−0.710881	−0.355440	−	0.934699i	$-0.615669\pi$
$881$	−21.1001	−0.710881	−0.355440	+	0.934699i	$0.615669\pi$
$882$	0	0
$883$	−4.70946	−0.158486	−0.0792429	−	0.996855i	$-0.525250\pi$
$883$	−4.70946	−0.158486	−0.0792429	+	0.996855i	$0.525250\pi$
$884$	0.246178	0.00827987
$885$	−15.9327	−0.535570
$886$	9.58373	0.321972
$887$	−26.5411	−0.891163	−0.445581	−	0.895241i	$-0.647003\pi$
$887$	−26.5411	−0.891163	−0.445581	+	0.895241i	$0.647003\pi$
$888$	0.313524	0.0105212
$889$	0	0
$890$	−6.03540	−0.202307
$891$	−4.70946	−0.157773
$892$	14.8273	0.496454
$893$	18.6625	0.624515
$894$	30.8893	1.03309
$895$	−9.84324	−0.329023
$896$	0	0
$897$	−6.21078	−0.207372
$898$	28.8946	0.964226
$899$	10.8946	0.363356
$900$	12.9460	0.431533
$901$	1.61913	0.0539410
$902$	−0.395932	−0.0131831
$903$	0	0
$904$	13.0514	0.434082
$905$	−15.5164	−0.515782
$906$	55.5518	1.84558
$907$	4.83255	0.160462	0.0802310	−	0.996776i	$-0.474434\pi$
$907$	4.83255	0.160462	0.0802310	+	0.996776i	$0.474434\pi$
$908$	4.42960	0.147002
$909$	10.3356	0.342810
$910$	0	0
$911$	−21.8113	−0.722640	−0.361320	−	0.932442i	$-0.617674\pi$
$911$	−21.8113	−0.722640	−0.361320	+	0.932442i	$0.617674\pi$
$912$	6.89461	0.228303
$913$	3.22147	0.106615
$914$	−18.3489	−0.606929
$915$	−115.376	−3.81423
$916$	−22.3623	−0.738870
$917$	0	0
$918$	−9.58373	−0.316310
$919$	−22.6891	−0.748445	−0.374222	−	0.927339i	$-0.622090\pi$
$919$	−22.6891	−0.748445	−0.374222	+	0.927339i	$0.622090\pi$
$920$	20.8273	0.686655
$921$	−45.1408	−1.48744
$922$	10.7936	0.355468
$923$	1.78922	0.0588930
$924$	0	0
$925$	−0.210776	−0.00693026
$926$	3.97334	0.130572
$927$	−62.0354	−2.03751
$928$	−9.01770	−0.296021
$929$	−37.2081	−1.22076	−0.610380	−	0.792109i	$-0.708983\pi$
$929$	−37.2081	−1.22076	−0.610380	+	0.792109i	$0.708983\pi$
$930$	−9.78922	−0.321001
$931$	0	0
$932$	−22.9300	−0.751098
$933$	105.479	3.45323
$934$	12.9016	0.422154
$935$	−0.997361	−0.0326172
$936$	−1.63774	−0.0535312
$937$	39.9681	1.30570	0.652850	−	0.757487i	$-0.273573\pi$
$937$	39.9681	1.30570	0.652850	+	0.757487i	$0.273573\pi$
$938$	0	0
$939$	18.3489	0.598795
$940$	21.9327	0.715364
$941$	29.8316	0.972484	0.486242	−	0.873824i	$-0.338367\pi$
$941$	29.8316	0.972484	0.486242	+	0.873824i	$0.338367\pi$
$942$	−40.4517	−1.31799
$943$	7.84324	0.255411
$944$	−1.96633	−0.0639985
$945$	0	0
$946$	0.832545	0.0270684
$947$	1.01138	0.0328654	0.0164327	−	0.999865i	$-0.494769\pi$
$947$	1.01138	0.0328654	0.0164327	+	0.999865i	$0.494769\pi$
$948$	32.4110	1.05266
$949$	2.62177	0.0851062
$950$	−4.63510	−0.150383
$951$	−74.5491	−2.41742
$952$	0	0
$953$	35.2656	1.14237	0.571183	−	0.820823i	$-0.306485\pi$
$953$	35.2656	1.14237	0.571183	+	0.820823i	$0.306485\pi$
$954$	−10.7715	−0.348741
$955$	−27.4810	−0.889264
$956$	−10.2055	−0.330069
$957$	−10.8946	−0.352173
$958$	−40.6438	−1.31314
$959$	0	0
$960$	8.10275	0.261515
$961$	−29.5404	−0.952916
$962$	0.0266643	0.000859692 0
$963$	20.2462	0.652424
$964$	−25.1408	−0.809730
$965$	30.3082	0.975657
$966$	0	0
$967$	38.6838	1.24399	0.621994	−	0.783022i	$-0.286323\pi$
$967$	38.6838	1.24399	0.621994	+	0.783022i	$0.286323\pi$
$968$	10.8432	0.348515
$969$	6.54041	0.210108
$970$	48.3436	1.55222
$971$	−12.4703	−0.400191	−0.200095	−	0.979776i	$-0.564125\pi$
$971$	−12.4703	−0.400191	−0.200095	+	0.979776i	$0.564125\pi$
$972$	5.98667	0.192022
$973$	0	0
$974$	23.6191	0.756806
$975$	1.62441	0.0520227
$976$	−14.2392	−0.455785
$977$	−53.5111	−1.71197	−0.855986	−	0.516999i	$-0.827049\pi$
$977$	−53.5111	−1.71197	−0.855986	+	0.516999i	$0.827049\pi$
$978$	−30.6218	−0.979176
$979$	−0.899891	−0.0287606
$980$	0	0
$981$	76.2507	2.43450
$982$	0.519021	0.0165626
$983$	−28.7866	−0.918149	−0.459075	−	0.888398i	$-0.651819\pi$
$983$	−28.7866	−0.918149	−0.459075	+	0.888398i	$0.651819\pi$
$984$	3.05137	0.0972743
$985$	−60.9974	−1.94354
$986$	−8.55442	−0.272428
$987$	0	0
$988$	0.586367	0.0186548
$989$	−16.4924	−0.524426
$990$	6.63510	0.210877
$991$	−26.2409	−0.833570	−0.416785	−	0.909005i	$-0.636843\pi$
$991$	−26.2409	−0.833570	−0.416785	+	0.909005i	$0.636843\pi$
$992$	−1.20814	−0.0383584
$993$	−70.6305	−2.24139
$994$	0	0
$995$	−55.7219	−1.76650
$996$	−24.8273	−0.786682
$997$	−11.8078	−0.373958	−0.186979	−	0.982364i	$-0.559870\pi$
$997$	−11.8078	−0.373958	−0.186979	+	0.982364i	$0.559870\pi$
$998$	−14.8069	−0.468705
$999$	−1.03804	−0.0328422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.be.1.3	yes	3
7.6	odd	2		4018.2.a.bd.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4018.2.a.bd.1.1	✓	3	7.6	odd	2
4018.2.a.be.1.3	yes	3	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.05137 q^{3} +1.00000 q^{4} +2.65544 q^{5} -3.05137 q^{6} -1.00000 q^{8} +6.31088 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.05137 q^{3} +1.00000 q^{4} +2.65544 q^{5} -3.05137 q^{6} -1.00000 q^{8} +6.31088 q^{9} -2.65544 q^{10} -0.395932 q^{11} +3.05137 q^{12} +0.259511 q^{13} +8.10275 q^{15} +1.00000 q^{16} +0.948626 q^{17} -6.31088 q^{18} +2.25951 q^{19} +2.65544 q^{20} +0.395932 q^{22} -7.84324 q^{23} -3.05137 q^{24} +2.05137 q^{25} -0.259511 q^{26} +10.1027 q^{27} +9.01770 q^{29} -8.10275 q^{30} +1.20814 q^{31} -1.00000 q^{32} -1.20814 q^{33} -0.948626 q^{34} +6.31088 q^{36} -0.102748 q^{37} -2.25951 q^{38} +0.791864 q^{39} -2.65544 q^{40} -1.00000 q^{41} +2.10275 q^{43} -0.395932 q^{44} +16.7582 q^{45} +7.84324 q^{46} +8.25951 q^{47} +3.05137 q^{48} -2.05137 q^{50} +2.89461 q^{51} +0.259511 q^{52} +1.70682 q^{53} -10.1027 q^{54} -1.05137 q^{55} +6.89461 q^{57} -9.01770 q^{58} -1.96633 q^{59} +8.10275 q^{60} -14.2392 q^{61} -1.20814 q^{62} +1.00000 q^{64} +0.689115 q^{65} +1.20814 q^{66} +2.12309 q^{67} +0.948626 q^{68} -23.9327 q^{69} +6.89461 q^{71} -6.31088 q^{72} +10.1027 q^{73} +0.102748 q^{74} +6.25951 q^{75} +2.25951 q^{76} -0.791864 q^{78} +10.6218 q^{79} +2.65544 q^{80} +11.8946 q^{81} +1.00000 q^{82} -8.13642 q^{83} +2.51902 q^{85} -2.10275 q^{86} +27.5164 q^{87} +0.395932 q^{88} +2.27284 q^{89} -16.7582 q^{90} -7.84324 q^{92} +3.68648 q^{93} -8.25951 q^{94} +6.00000 q^{95} -3.05137 q^{96} -18.2055 q^{97} -2.49868 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} + 2 q^{5} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 + 2 * q^5 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} + 3 q^{4} + 2 q^{5} - 3 q^{8} + 7 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{13} + 6 q^{15} + 3 q^{16} + 12 q^{17} - 7 q^{18} + 4 q^{19} + 2 q^{20} - 2 q^{22} - 8 q^{23} - 3 q^{25} + 2 q^{26} + 12 q^{27} - 6 q^{30} + 10 q^{31} - 3 q^{32} - 10 q^{33} - 12 q^{34} + 7 q^{36} + 18 q^{37} - 4 q^{38} - 4 q^{39} - 2 q^{40} - 3 q^{41} - 12 q^{43} + 2 q^{44} + 26 q^{45} + 8 q^{46} + 22 q^{47} + 3 q^{50} - 16 q^{51} - 2 q^{52} - 10 q^{53} - 12 q^{54} + 6 q^{55} - 4 q^{57} + 12 q^{59} + 6 q^{60} - 24 q^{61} - 10 q^{62} + 3 q^{64} + 14 q^{65} + 10 q^{66} + 4 q^{67} + 12 q^{68} - 36 q^{69} - 4 q^{71} - 7 q^{72} + 12 q^{73} - 18 q^{74} + 16 q^{75} + 4 q^{76} + 4 q^{78} + 8 q^{79} + 2 q^{80} + 11 q^{81} + 3 q^{82} - 24 q^{83} + 2 q^{85} + 12 q^{86} + 34 q^{87} - 2 q^{88} + 6 q^{89} - 26 q^{90} - 8 q^{92} - 20 q^{93} - 22 q^{94} + 18 q^{95} - 18 q^{97} + 14 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 + 2 * q^5 - 3 * q^8 + 7 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^13 + 6 * q^15 + 3 * q^16 + 12 * q^17 - 7 * q^18 + 4 * q^19 + 2 * q^20 - 2 * q^22 - 8 * q^23 - 3 * q^25 + 2 * q^26 + 12 * q^27 - 6 * q^30 + 10 * q^31 - 3 * q^32 - 10 * q^33 - 12 * q^34 + 7 * q^36 + 18 * q^37 - 4 * q^38 - 4 * q^39 - 2 * q^40 - 3 * q^41 - 12 * q^43 + 2 * q^44 + 26 * q^45 + 8 * q^46 + 22 * q^47 + 3 * q^50 - 16 * q^51 - 2 * q^52 - 10 * q^53 - 12 * q^54 + 6 * q^55 - 4 * q^57 + 12 * q^59 + 6 * q^60 - 24 * q^61 - 10 * q^62 + 3 * q^64 + 14 * q^65 + 10 * q^66 + 4 * q^67 + 12 * q^68 - 36 * q^69 - 4 * q^71 - 7 * q^72 + 12 * q^73 - 18 * q^74 + 16 * q^75 + 4 * q^76 + 4 * q^78 + 8 * q^79 + 2 * q^80 + 11 * q^81 + 3 * q^82 - 24 * q^83 + 2 * q^85 + 12 * q^86 + 34 * q^87 - 2 * q^88 + 6 * q^89 - 26 * q^90 - 8 * q^92 - 20 * q^93 - 22 * q^94 + 18 * q^95 - 18 * q^97 + 14 * q^99

Introduction

L-functions

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