LMFDB - Embedded newform 3381.2.a.bf.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 15x^{6} + 11x^{5} + 75x^{4} - 35x^{3} - 141x^{2} + 37x + 80 $ x^8 - x^7 - 15x^6 + 11x^5 + 75x^4 - 35x^3 - 141x^2 + 37x + 80
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.67781$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67781 q^{2} +1.00000 q^{3} +0.815035 q^{4} +2.94824 q^{5} -1.67781 q^{6} +1.98814 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.67781 q^{2} +1.00000 q^{3} +0.815035 q^{4} +2.94824 q^{5} -1.67781 q^{6} +1.98814 q^{8} +1.00000 q^{9} -4.94658 q^{10} -3.66309 q^{11} +0.815035 q^{12} +1.91805 q^{13} +2.94824 q^{15} -4.96579 q^{16} +3.02844 q^{17} -1.67781 q^{18} +2.16450 q^{19} +2.40292 q^{20} +6.14595 q^{22} -1.00000 q^{23} +1.98814 q^{24} +3.69212 q^{25} -3.21812 q^{26} +1.00000 q^{27} -0.852794 q^{29} -4.94658 q^{30} +2.02344 q^{31} +4.35535 q^{32} -3.66309 q^{33} -5.08113 q^{34} +0.815035 q^{36} -5.43434 q^{37} -3.63162 q^{38} +1.91805 q^{39} +5.86152 q^{40} -1.41089 q^{41} +6.68453 q^{43} -2.98555 q^{44} +2.94824 q^{45} +1.67781 q^{46} +11.7223 q^{47} -4.96579 q^{48} -6.19467 q^{50} +3.02844 q^{51} +1.56328 q^{52} -6.80600 q^{53} -1.67781 q^{54} -10.7997 q^{55} +2.16450 q^{57} +1.43082 q^{58} +11.0956 q^{59} +2.40292 q^{60} -2.17302 q^{61} -3.39495 q^{62} +2.62414 q^{64} +5.65488 q^{65} +6.14595 q^{66} +11.4943 q^{67} +2.46828 q^{68} -1.00000 q^{69} -14.1534 q^{71} +1.98814 q^{72} +10.2300 q^{73} +9.11777 q^{74} +3.69212 q^{75} +1.76415 q^{76} -3.21812 q^{78} -4.40576 q^{79} -14.6403 q^{80} +1.00000 q^{81} +2.36721 q^{82} +14.2550 q^{83} +8.92856 q^{85} -11.2153 q^{86} -0.852794 q^{87} -7.28274 q^{88} +16.1850 q^{89} -4.94658 q^{90} -0.815035 q^{92} +2.02344 q^{93} -19.6678 q^{94} +6.38147 q^{95} +4.35535 q^{96} +7.01439 q^{97} -3.66309 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9} - 3 q^{10} + 10 q^{11} + 15 q^{12} - 6 q^{13} + 5 q^{15} + 13 q^{16} + 21 q^{17} + q^{18} + 5 q^{19} - q^{20} + 18 q^{22} - 8 q^{23} + 9 q^{24} + 27 q^{25} + 3 q^{26} + 8 q^{27} + 2 q^{29} - 3 q^{30} - 13 q^{31} + 29 q^{32} + 10 q^{33} - 19 q^{34} + 15 q^{36} + 13 q^{37} - 6 q^{38} - 6 q^{39} + 7 q^{40} + 16 q^{41} + 15 q^{43} + 24 q^{44} + 5 q^{45} - q^{46} - q^{47} + 13 q^{48} + 16 q^{50} + 21 q^{51} - 19 q^{52} + 3 q^{53} + q^{54} - 10 q^{55} + 5 q^{57} - 40 q^{58} + 26 q^{59} - q^{60} - 14 q^{61} - 14 q^{62} + 49 q^{64} - 3 q^{65} + 18 q^{66} + 38 q^{67} + 43 q^{68} - 8 q^{69} + 9 q^{71} + 9 q^{72} - 6 q^{73} + 32 q^{74} + 27 q^{75} - 14 q^{76} + 3 q^{78} + 23 q^{79} - 17 q^{80} + 8 q^{81} + 20 q^{82} + 30 q^{83} - 37 q^{85} - 28 q^{86} + 2 q^{87} + 86 q^{88} + 12 q^{89} - 3 q^{90} - 15 q^{92} - 13 q^{93} - 45 q^{94} + 16 q^{95} + 29 q^{96} + 14 q^{97} + 10 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9 - 3 * q^10 + 10 * q^11 + 15 * q^12 - 6 * q^13 + 5 * q^15 + 13 * q^16 + 21 * q^17 + q^18 + 5 * q^19 - q^20 + 18 * q^22 - 8 * q^23 + 9 * q^24 + 27 * q^25 + 3 * q^26 + 8 * q^27 + 2 * q^29 - 3 * q^30 - 13 * q^31 + 29 * q^32 + 10 * q^33 - 19 * q^34 + 15 * q^36 + 13 * q^37 - 6 * q^38 - 6 * q^39 + 7 * q^40 + 16 * q^41 + 15 * q^43 + 24 * q^44 + 5 * q^45 - q^46 - q^47 + 13 * q^48 + 16 * q^50 + 21 * q^51 - 19 * q^52 + 3 * q^53 + q^54 - 10 * q^55 + 5 * q^57 - 40 * q^58 + 26 * q^59 - q^60 - 14 * q^61 - 14 * q^62 + 49 * q^64 - 3 * q^65 + 18 * q^66 + 38 * q^67 + 43 * q^68 - 8 * q^69 + 9 * q^71 + 9 * q^72 - 6 * q^73 + 32 * q^74 + 27 * q^75 - 14 * q^76 + 3 * q^78 + 23 * q^79 - 17 * q^80 + 8 * q^81 + 20 * q^82 + 30 * q^83 - 37 * q^85 - 28 * q^86 + 2 * q^87 + 86 * q^88 + 12 * q^89 - 3 * q^90 - 15 * q^92 - 13 * q^93 - 45 * q^94 + 16 * q^95 + 29 * q^96 + 14 * q^97 + 10 * 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 $

$2$	−1.67781	−1.18639	−0.593194	−	0.805059i	$-0.702133\pi$
$2$	−1.67781	−1.18639	−0.593194	+	0.805059i	$0.702133\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.815035	0.407518
$5$	2.94824	1.31849	0.659247	−	0.751927i	$-0.270875\pi$
$5$	2.94824	1.31849	0.659247	+	0.751927i	$0.270875\pi$
$6$	−1.67781	−0.684962
$7$	0	0
$7$	0	0
$8$	1.98814	0.702914
$9$	1.00000	0.333333
$10$	−4.94658	−1.56425
$11$	−3.66309	−1.10446	−0.552231	−	0.833691i	$-0.686223\pi$
$11$	−3.66309	−1.10446	−0.552231	+	0.833691i	$0.686223\pi$
$12$	0.815035	0.235280
$13$	1.91805	0.531972	0.265986	−	0.963977i	$-0.414303\pi$
$13$	1.91805	0.531972	0.265986	+	0.963977i	$0.414303\pi$
$14$	0	0
$15$	2.94824	0.761232
$16$	−4.96579	−1.24145
$17$	3.02844	0.734504	0.367252	−	0.930122i	$-0.380299\pi$
$17$	3.02844	0.734504	0.367252	+	0.930122i	$0.380299\pi$
$18$	−1.67781	−0.395463
$19$	2.16450	0.496571	0.248285	−	0.968687i	$-0.420133\pi$
$19$	2.16450	0.496571	0.248285	+	0.968687i	$0.420133\pi$
$20$	2.40292	0.537309
$21$	0	0
$22$	6.14595	1.31032
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.98814	0.405828
$25$	3.69212	0.738425
$26$	−3.21812	−0.631125
$27$	1.00000	0.192450
$28$	0	0
$29$	−0.852794	−0.158360	−0.0791800	−	0.996860i	$-0.525230\pi$
$29$	−0.852794	−0.158360	−0.0791800	+	0.996860i	$0.525230\pi$
$30$	−4.94658	−0.903117
$31$	2.02344	0.363421	0.181711	−	0.983352i	$-0.441837\pi$
$31$	2.02344	0.363421	0.181711	+	0.983352i	$0.441837\pi$
$32$	4.35535	0.769924
$33$	−3.66309	−0.637662
$34$	−5.08113	−0.871407
$35$	0	0
$36$	0.815035	0.135839
$37$	−5.43434	−0.893399	−0.446700	−	0.894684i	$-0.647401\pi$
$37$	−5.43434	−0.893399	−0.446700	+	0.894684i	$0.647401\pi$
$38$	−3.63162	−0.589126
$39$	1.91805	0.307134
$40$	5.86152	0.926788
$41$	−1.41089	−0.220345	−0.110172	−	0.993913i	$-0.535140\pi$
$41$	−1.41089	−0.220345	−0.110172	+	0.993913i	$0.535140\pi$
$42$	0	0
$43$	6.68453	1.01938	0.509691	−	0.860358i	$-0.329760\pi$
$43$	6.68453	1.01938	0.509691	+	0.860358i	$0.329760\pi$
$44$	−2.98555	−0.450088
$45$	2.94824	0.439498
$46$	1.67781	0.247379
$47$	11.7223	1.70988	0.854938	−	0.518730i	$-0.173595\pi$
$47$	11.7223	1.70988	0.854938	+	0.518730i	$0.173595\pi$
$48$	−4.96579	−0.716750
$49$	0	0
$50$	−6.19467	−0.876058
$51$	3.02844	0.424066
$52$	1.56328	0.216788
$53$	−6.80600	−0.934877	−0.467438	−	0.884026i	$-0.654823\pi$
$53$	−6.80600	−0.934877	−0.467438	+	0.884026i	$0.654823\pi$
$54$	−1.67781	−0.228321
$55$	−10.7997	−1.45623
$56$	0	0
$57$	2.16450	0.286695
$58$	1.43082	0.187876
$59$	11.0956	1.44453	0.722265	−	0.691617i	$-0.243101\pi$
$59$	11.0956	1.44453	0.722265	+	0.691617i	$0.243101\pi$
$60$	2.40292	0.310216
$61$	−2.17302	−0.278226	−0.139113	−	0.990276i	$-0.544425\pi$
$61$	−2.17302	−0.278226	−0.139113	+	0.990276i	$0.544425\pi$
$62$	−3.39495	−0.431159
$63$	0	0
$64$	2.62414	0.328018
$65$	5.65488	0.701401
$66$	6.14595	0.756514
$67$	11.4943	1.40425	0.702126	−	0.712053i	$-0.252234\pi$
$67$	11.4943	1.40425	0.702126	+	0.712053i	$0.252234\pi$
$68$	2.46828	0.299323
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−14.1534	−1.67970	−0.839848	−	0.542822i	$-0.817356\pi$
$71$	−14.1534	−1.67970	−0.839848	+	0.542822i	$0.817356\pi$
$72$	1.98814	0.234305
$73$	10.2300	1.19733	0.598664	−	0.801000i	$-0.295699\pi$
$73$	10.2300	1.19733	0.598664	+	0.801000i	$0.295699\pi$
$74$	9.11777	1.05992
$75$	3.69212	0.426330
$76$	1.76415	0.202361
$77$	0	0
$78$	−3.21812	−0.364380
$79$	−4.40576	−0.495687	−0.247843	−	0.968800i	$-0.579722\pi$
$79$	−4.40576	−0.495687	−0.247843	+	0.968800i	$0.579722\pi$
$80$	−14.6403	−1.63684
$81$	1.00000	0.111111
$82$	2.36721	0.261414
$83$	14.2550	1.56469	0.782344	−	0.622847i	$-0.214024\pi$
$83$	14.2550	1.56469	0.782344	+	0.622847i	$0.214024\pi$
$84$	0	0
$85$	8.92856	0.968438
$86$	−11.2153	−1.20938
$87$	−0.852794	−0.0914292
$88$	−7.28274	−0.776342
$89$	16.1850	1.71560	0.857802	−	0.513981i	$-0.171830\pi$
$89$	16.1850	1.71560	0.857802	+	0.513981i	$0.171830\pi$
$90$	−4.94658	−0.521415
$91$	0	0
$92$	−0.815035	−0.0849733
$93$	2.02344	0.209821
$94$	−19.6678	−2.02858
$95$	6.38147	0.654725
$96$	4.35535	0.444516
$97$	7.01439	0.712203	0.356102	−	0.934447i	$-0.384106\pi$
$97$	7.01439	0.712203	0.356102	+	0.934447i	$0.384106\pi$
$98$	0	0
$99$	−3.66309	−0.368154
$100$	3.00921	0.300921
$101$	8.93684	0.889249	0.444625	−	0.895717i	$-0.353337\pi$
$101$	8.93684	0.889249	0.444625	+	0.895717i	$0.353337\pi$
$102$	−5.08113	−0.503107
$103$	1.14975	0.113288	0.0566439	−	0.998394i	$-0.481960\pi$
$103$	1.14975	0.113288	0.0566439	+	0.998394i	$0.481960\pi$
$104$	3.81336	0.373931
$105$	0	0
$106$	11.4192	1.10913
$107$	2.95186	0.285367	0.142684	−	0.989768i	$-0.454427\pi$
$107$	2.95186	0.285367	0.142684	+	0.989768i	$0.454427\pi$
$108$	0.815035	0.0784268
$109$	−10.7740	−1.03196	−0.515982	−	0.856599i	$-0.672573\pi$
$109$	−10.7740	−1.03196	−0.515982	+	0.856599i	$0.672573\pi$
$110$	18.1197	1.72765
$111$	−5.43434	−0.515804
$112$	0	0
$113$	−3.85957	−0.363078	−0.181539	−	0.983384i	$-0.558108\pi$
$113$	−3.85957	−0.363078	−0.181539	+	0.983384i	$0.558108\pi$
$114$	−3.63162	−0.340132
$115$	−2.94824	−0.274925
$116$	−0.695058	−0.0645345
$117$	1.91805	0.177324
$118$	−18.6163	−1.71377
$119$	0	0
$120$	5.86152	0.535081
$121$	2.41821	0.219837
$122$	3.64590	0.330084
$123$	−1.41089	−0.127216
$124$	1.64918	0.148101
$125$	−3.85594	−0.344885
$126$	0	0
$127$	−18.7188	−1.66102	−0.830512	−	0.557001i	$-0.811952\pi$
$127$	−18.7188	−1.66102	−0.830512	+	0.557001i	$0.811952\pi$
$128$	−13.1135	−1.15908
$129$	6.68453	0.588540
$130$	−9.48779	−0.832134
$131$	−12.7511	−1.11407	−0.557035	−	0.830489i	$-0.688061\pi$
$131$	−12.7511	−1.11407	−0.557035	+	0.830489i	$0.688061\pi$
$132$	−2.98555	−0.259858
$133$	0	0
$134$	−19.2852	−1.66599
$135$	2.94824	0.253744
$136$	6.02096	0.516293
$137$	19.5406	1.66947	0.834734	−	0.550653i	$-0.185621\pi$
$137$	19.5406	1.66947	0.834734	+	0.550653i	$0.185621\pi$
$138$	1.67781	0.142824
$139$	−7.65626	−0.649395	−0.324698	−	0.945818i	$-0.605263\pi$
$139$	−7.65626	−0.649395	−0.324698	+	0.945818i	$0.605263\pi$
$140$	0	0
$141$	11.7223	0.987197
$142$	23.7466	1.99277
$143$	−7.02599	−0.587543
$144$	−4.96579	−0.413816
$145$	−2.51424	−0.208797
$146$	−17.1639	−1.42050
$147$	0	0
$148$	−4.42918	−0.364076
$149$	−8.45147	−0.692371	−0.346186	−	0.938166i	$-0.612523\pi$
$149$	−8.45147	−0.692371	−0.346186	+	0.938166i	$0.612523\pi$
$150$	−6.19467	−0.505793
$151$	4.92644	0.400908	0.200454	−	0.979703i	$-0.435758\pi$
$151$	4.92644	0.400908	0.200454	+	0.979703i	$0.435758\pi$
$152$	4.30334	0.349047
$153$	3.02844	0.244835
$154$	0	0
$155$	5.96560	0.479168
$156$	1.56328	0.125163
$157$	−13.5380	−1.08045	−0.540227	−	0.841519i	$-0.681662\pi$
$157$	−13.5380	−1.08045	−0.540227	+	0.841519i	$0.681662\pi$
$158$	7.39201	0.588077
$159$	−6.80600	−0.539751
$160$	12.8406	1.01514
$161$	0	0
$162$	−1.67781	−0.131821
$163$	13.6773	1.07129	0.535645	−	0.844444i	$-0.320069\pi$
$163$	13.6773	1.07129	0.535645	+	0.844444i	$0.320069\pi$
$164$	−1.14993	−0.0897943
$165$	−10.7997	−0.840753
$166$	−23.9171	−1.85633
$167$	4.39959	0.340450	0.170225	−	0.985405i	$-0.445550\pi$
$167$	4.39959	0.340450	0.170225	+	0.985405i	$0.445550\pi$
$168$	0	0
$169$	−9.32108	−0.717006
$170$	−14.9804	−1.14894
$171$	2.16450	0.165524
$172$	5.44813	0.415416
$173$	1.80023	0.136869	0.0684343	−	0.997656i	$-0.478200\pi$
$173$	1.80023	0.136869	0.0684343	+	0.997656i	$0.478200\pi$
$174$	1.43082	0.108471
$175$	0	0
$176$	18.1901	1.37113
$177$	11.0956	0.833999
$178$	−27.1552	−2.03537
$179$	21.4810	1.60557	0.802783	−	0.596271i	$-0.203352\pi$
$179$	21.4810	1.60557	0.802783	+	0.596271i	$0.203352\pi$
$180$	2.40292	0.179103
$181$	−21.2920	−1.58262	−0.791310	−	0.611416i	$-0.790600\pi$
$181$	−21.2920	−1.58262	−0.791310	+	0.611416i	$0.790600\pi$
$182$	0	0
$183$	−2.17302	−0.160634
$184$	−1.98814	−0.146568
$185$	−16.0217	−1.17794
$186$	−3.39495	−0.248930
$187$	−11.0934	−0.811232
$188$	9.55410	0.696805
$189$	0	0
$190$	−10.7069	−0.776759
$191$	7.69448	0.556753	0.278376	−	0.960472i	$-0.410204\pi$
$191$	7.69448	0.556753	0.278376	+	0.960472i	$0.410204\pi$
$192$	2.62414	0.189381
$193$	−15.1469	−1.09030	−0.545149	−	0.838339i	$-0.683527\pi$
$193$	−15.1469	−1.09030	−0.545149	+	0.838339i	$0.683527\pi$
$194$	−11.7688	−0.844949
$195$	5.65488	0.404954
$196$	0	0
$197$	8.95690	0.638153	0.319076	−	0.947729i	$-0.396627\pi$
$197$	8.95690	0.638153	0.319076	+	0.947729i	$0.396627\pi$
$198$	6.14595	0.436774
$199$	16.6575	1.18082	0.590411	−	0.807103i	$-0.298966\pi$
$199$	16.6575	1.18082	0.590411	+	0.807103i	$0.298966\pi$
$200$	7.34046	0.519049
$201$	11.4943	0.810745
$202$	−14.9943	−1.05499
$203$	0	0
$204$	2.46828	0.172814
$205$	−4.15965	−0.290523
$206$	−1.92905	−0.134403
$207$	−1.00000	−0.0695048
$208$	−9.52464	−0.660415
$209$	−7.92876	−0.548444
$210$	0	0
$211$	−0.555224	−0.0382232	−0.0191116	−	0.999817i	$-0.506084\pi$
$211$	−0.555224	−0.0382232	−0.0191116	+	0.999817i	$0.506084\pi$
$212$	−5.54713	−0.380979
$213$	−14.1534	−0.969773
$214$	−4.95265	−0.338556
$215$	19.7076	1.34405
$216$	1.98814	0.135276
$217$	0	0
$218$	18.0767	1.22431
$219$	10.2300	0.691277
$220$	−8.80211	−0.593438
$221$	5.80870	0.390735
$222$	9.11777	0.611944
$223$	15.1938	1.01745	0.508727	−	0.860928i	$-0.330116\pi$
$223$	15.1938	1.01745	0.508727	+	0.860928i	$0.330116\pi$
$224$	0	0
$225$	3.69212	0.246142
$226$	6.47561	0.430751
$227$	27.1559	1.80240	0.901201	−	0.433400i	$-0.142686\pi$
$227$	27.1559	1.80240	0.901201	+	0.433400i	$0.142686\pi$
$228$	1.76415	0.116833
$229$	−22.1485	−1.46361	−0.731806	−	0.681513i	$-0.761322\pi$
$229$	−22.1485	−1.46361	−0.731806	+	0.681513i	$0.761322\pi$
$230$	4.94658	0.326168
$231$	0	0
$232$	−1.69548	−0.111313
$233$	−3.15821	−0.206901	−0.103451	−	0.994635i	$-0.532988\pi$
$233$	−3.15821	−0.206901	−0.103451	+	0.994635i	$0.532988\pi$
$234$	−3.21812	−0.210375
$235$	34.5602	2.25446
$236$	9.04334	0.588671
$237$	−4.40576	−0.286185
$238$	0	0
$239$	26.3726	1.70590	0.852952	−	0.521990i	$-0.174810\pi$
$239$	26.3726	1.70590	0.852952	+	0.521990i	$0.174810\pi$
$240$	−14.6403	−0.945030
$241$	−12.5445	−0.808063	−0.404032	−	0.914745i	$-0.632391\pi$
$241$	−12.5445	−0.808063	−0.404032	+	0.914745i	$0.632391\pi$
$242$	−4.05729	−0.260812
$243$	1.00000	0.0641500
$244$	−1.77109	−0.113382
$245$	0	0
$246$	2.36721	0.150928
$247$	4.15163	0.264162
$248$	4.02289	0.255454
$249$	14.2550	0.903373
$250$	6.46952	0.409168
$251$	20.5316	1.29595	0.647973	−	0.761663i	$-0.275617\pi$
$251$	20.5316	1.29595	0.647973	+	0.761663i	$0.275617\pi$
$252$	0	0
$253$	3.66309	0.230296
$254$	31.4065	1.97062
$255$	8.92856	0.559128
$256$	16.7536	1.04710
$257$	10.1070	0.630456	0.315228	−	0.949016i	$-0.397919\pi$
$257$	10.1070	0.630456	0.315228	+	0.949016i	$0.397919\pi$
$258$	−11.2153	−0.698237
$259$	0	0
$260$	4.60893	0.285833
$261$	−0.852794	−0.0527867
$262$	21.3939	1.32172
$263$	−7.29222	−0.449658	−0.224829	−	0.974398i	$-0.572182\pi$
$263$	−7.29222	−0.449658	−0.224829	+	0.974398i	$0.572182\pi$
$264$	−7.28274	−0.448221
$265$	−20.0657	−1.23263
$266$	0	0
$267$	16.1850	0.990504
$268$	9.36826	0.572257
$269$	−18.9937	−1.15807	−0.579034	−	0.815304i	$-0.696570\pi$
$269$	−18.9937	−1.15807	−0.579034	+	0.815304i	$0.696570\pi$
$270$	−4.94658	−0.301039
$271$	−8.35578	−0.507578	−0.253789	−	0.967260i	$-0.581677\pi$
$271$	−8.35578	−0.507578	−0.253789	+	0.967260i	$0.581677\pi$
$272$	−15.0386	−0.911847
$273$	0	0
$274$	−32.7854	−1.98064
$275$	−13.5246	−0.815562
$276$	−0.815035	−0.0490594
$277$	11.4500	0.687962	0.343981	−	0.938977i	$-0.388224\pi$
$277$	11.4500	0.687962	0.343981	+	0.938977i	$0.388224\pi$
$278$	12.8457	0.770435
$279$	2.02344	0.121140
$280$	0	0
$281$	−6.28234	−0.374773	−0.187387	−	0.982286i	$-0.560002\pi$
$281$	−6.28234	−0.374773	−0.187387	+	0.982286i	$0.560002\pi$
$282$	−19.6678	−1.17120
$283$	−15.5391	−0.923703	−0.461851	−	0.886957i	$-0.652815\pi$
$283$	−15.5391	−0.923703	−0.461851	+	0.886957i	$0.652815\pi$
$284$	−11.5355	−0.684506
$285$	6.38147	0.378006
$286$	11.7883	0.697054
$287$	0	0
$288$	4.35535	0.256641
$289$	−7.82858	−0.460504
$290$	4.21841	0.247714
$291$	7.01439	0.411191
$292$	8.33779	0.487932
$293$	13.8483	0.809026	0.404513	−	0.914532i	$-0.367441\pi$
$293$	13.8483	0.809026	0.404513	+	0.914532i	$0.367441\pi$
$294$	0	0
$295$	32.7126	1.90460
$296$	−10.8042	−0.627983
$297$	−3.66309	−0.212554
$298$	14.1799	0.821421
$299$	−1.91805	−0.110924
$300$	3.00921	0.173737
$301$	0	0
$302$	−8.26561	−0.475632
$303$	8.93684	0.513408
$304$	−10.7485	−0.616467
$305$	−6.40658	−0.366839
$306$	−5.08113	−0.290469
$307$	−20.5112	−1.17064	−0.585318	−	0.810804i	$-0.699030\pi$
$307$	−20.5112	−1.17064	−0.585318	+	0.810804i	$0.699030\pi$
$308$	0	0
$309$	1.14975	0.0654068
$310$	−10.0091	−0.568480
$311$	−0.981617	−0.0556624	−0.0278312	−	0.999613i	$-0.508860\pi$
$311$	−0.981617	−0.0556624	−0.0278312	+	0.999613i	$0.508860\pi$
$312$	3.81336	0.215889
$313$	−4.04432	−0.228598	−0.114299	−	0.993446i	$-0.536462\pi$
$313$	−4.04432	−0.228598	−0.114299	+	0.993446i	$0.536462\pi$
$314$	22.7142	1.28184
$315$	0	0
$316$	−3.59085	−0.202001
$317$	−14.9070	−0.837262	−0.418631	−	0.908156i	$-0.637490\pi$
$317$	−14.9070	−0.837262	−0.418631	+	0.908156i	$0.637490\pi$
$318$	11.4192	0.640355
$319$	3.12386	0.174903
$320$	7.73660	0.432489
$321$	2.95186	0.164757
$322$	0	0
$323$	6.55506	0.364733
$324$	0.815035	0.0452797
$325$	7.08168	0.392821
$326$	−22.9479	−1.27097
$327$	−10.7740	−0.595805
$328$	−2.80506	−0.154883
$329$	0	0
$330$	18.1197	0.997459
$331$	−8.12770	−0.446739	−0.223369	−	0.974734i	$-0.571706\pi$
$331$	−8.12770	−0.446739	−0.223369	+	0.974734i	$0.571706\pi$
$332$	11.6183	0.637638
$333$	−5.43434	−0.297800
$334$	−7.38166	−0.403907
$335$	33.8880	1.85150
$336$	0	0
$337$	3.74188	0.203833	0.101917	−	0.994793i	$-0.467503\pi$
$337$	3.74188	0.203833	0.101917	+	0.994793i	$0.467503\pi$
$338$	15.6390	0.850648
$339$	−3.85957	−0.209623
$340$	7.27709	0.394656
$341$	−7.41205	−0.401385
$342$	−3.63162	−0.196375
$343$	0	0
$344$	13.2898	0.716538
$345$	−2.94824	−0.158728
$346$	−3.02043	−0.162379
$347$	23.0525	1.23752	0.618760	−	0.785580i	$-0.287635\pi$
$347$	23.0525	1.23752	0.618760	+	0.785580i	$0.287635\pi$
$348$	−0.695058	−0.0372590
$349$	26.4338	1.41497	0.707484	−	0.706729i	$-0.249830\pi$
$349$	26.4338	1.41497	0.707484	+	0.706729i	$0.249830\pi$
$350$	0	0
$351$	1.91805	0.102378
$352$	−15.9540	−0.850352
$353$	−12.0448	−0.641077	−0.320539	−	0.947235i	$-0.603864\pi$
$353$	−12.0448	−0.641077	−0.320539	+	0.947235i	$0.603864\pi$
$354$	−18.6163	−0.989447
$355$	−41.7275	−2.21467
$356$	13.1913	0.699139
$357$	0	0
$358$	−36.0410	−1.90483
$359$	6.63503	0.350183	0.175092	−	0.984552i	$-0.443978\pi$
$359$	6.63503	0.350183	0.175092	+	0.984552i	$0.443978\pi$
$360$	5.86152	0.308929
$361$	−14.3149	−0.753417
$362$	35.7238	1.87760
$363$	2.41821	0.126923
$364$	0	0
$365$	30.1604	1.57867
$366$	3.64590	0.190574
$367$	35.7537	1.86633	0.933163	−	0.359452i	$-0.117037\pi$
$367$	35.7537	1.86633	0.933163	+	0.359452i	$0.117037\pi$
$368$	4.96579	0.258860
$369$	−1.41089	−0.0734482
$370$	26.8814	1.39750
$371$	0	0
$372$	1.64918	0.0855059
$373$	32.5253	1.68410	0.842048	−	0.539403i	$-0.181350\pi$
$373$	32.5253	1.68410	0.842048	+	0.539403i	$0.181350\pi$
$374$	18.6126	0.962436
$375$	−3.85594	−0.199120
$376$	23.3056	1.20190
$377$	−1.63570	−0.0842430
$378$	0	0
$379$	−8.00325	−0.411100	−0.205550	−	0.978647i	$-0.565898\pi$
$379$	−8.00325	−0.411100	−0.205550	+	0.978647i	$0.565898\pi$
$380$	5.20113	0.266812
$381$	−18.7188	−0.958992
$382$	−12.9098	−0.660525
$383$	−6.18518	−0.316048	−0.158024	−	0.987435i	$-0.550512\pi$
$383$	−6.18518	−0.316048	−0.158024	+	0.987435i	$0.550512\pi$
$384$	−13.1135	−0.669196
$385$	0	0
$386$	25.4136	1.29352
$387$	6.68453	0.339794
$388$	5.71697	0.290235
$389$	−4.94342	−0.250641	−0.125321	−	0.992116i	$-0.539996\pi$
$389$	−4.94342	−0.250641	−0.125321	+	0.992116i	$0.539996\pi$
$390$	−9.48779	−0.480433
$391$	−3.02844	−0.153155
$392$	0	0
$393$	−12.7511	−0.643208
$394$	−15.0279	−0.757097
$395$	−12.9892	−0.653559
$396$	−2.98555	−0.150029
$397$	21.8799	1.09812	0.549060	−	0.835783i	$-0.314986\pi$
$397$	21.8799	1.09812	0.549060	+	0.835783i	$0.314986\pi$
$398$	−27.9481	−1.40091
$399$	0	0
$400$	−18.3343	−0.916715
$401$	22.7730	1.13723	0.568615	−	0.822604i	$-0.307479\pi$
$401$	22.7730	1.13723	0.568615	+	0.822604i	$0.307479\pi$
$402$	−19.2852	−0.961859
$403$	3.88107	0.193330
$404$	7.28384	0.362385
$405$	2.94824	0.146499
$406$	0	0
$407$	19.9064	0.986726
$408$	6.02096	0.298082
$409$	−18.2807	−0.903923	−0.451962	−	0.892037i	$-0.649276\pi$
$409$	−18.2807	−0.903923	−0.451962	+	0.892037i	$0.649276\pi$
$410$	6.97910	0.344673
$411$	19.5406	0.963868
$412$	0.937084	0.0461668
$413$	0	0
$414$	1.67781	0.0824597
$415$	42.0271	2.06303
$416$	8.35378	0.409578
$417$	−7.65626	−0.374929
$418$	13.3029	0.650668
$419$	−7.08048	−0.345904	−0.172952	−	0.984930i	$-0.555331\pi$
$419$	−7.08048	−0.345904	−0.172952	+	0.984930i	$0.555331\pi$
$420$	0	0
$421$	23.8313	1.16147	0.580734	−	0.814093i	$-0.302766\pi$
$421$	23.8313	1.16147	0.580734	+	0.814093i	$0.302766\pi$
$422$	0.931558	0.0453476
$423$	11.7223	0.569959
$424$	−13.5313	−0.657138
$425$	11.1814	0.542376
$426$	23.7466	1.15053
$427$	0	0
$428$	2.40587	0.116292
$429$	−7.02599	−0.339218
$430$	−33.0655	−1.59456
$431$	−5.52782	−0.266266	−0.133133	−	0.991098i	$-0.542504\pi$
$431$	−5.52782	−0.266266	−0.133133	+	0.991098i	$0.542504\pi$
$432$	−4.96579	−0.238917
$433$	17.6961	0.850422	0.425211	−	0.905094i	$-0.360200\pi$
$433$	17.6961	0.850422	0.425211	+	0.905094i	$0.360200\pi$
$434$	0	0
$435$	−2.51424	−0.120549
$436$	−8.78121	−0.420544
$437$	−2.16450	−0.103542
$438$	−17.1639	−0.820123
$439$	−3.52980	−0.168468	−0.0842342	−	0.996446i	$-0.526844\pi$
$439$	−3.52980	−0.168468	−0.0842342	+	0.996446i	$0.526844\pi$
$440$	−21.4713	−1.02360
$441$	0	0
$442$	−9.74587	−0.463564
$443$	37.5974	1.78631	0.893154	−	0.449751i	$-0.148487\pi$
$443$	37.5974	1.78631	0.893154	+	0.449751i	$0.148487\pi$
$444$	−4.42918	−0.210199
$445$	47.7172	2.26201
$446$	−25.4923	−1.20710
$447$	−8.45147	−0.399741
$448$	0	0
$449$	−38.6628	−1.82461	−0.912305	−	0.409512i	$-0.865699\pi$
$449$	−38.6628	−1.82461	−0.912305	+	0.409512i	$0.865699\pi$
$450$	−6.19467	−0.292019
$451$	5.16823	0.243362
$452$	−3.14569	−0.147961
$453$	4.92644	0.231464
$454$	−45.5624	−2.13835
$455$	0	0
$456$	4.30334	0.201522
$457$	32.8960	1.53881	0.769405	−	0.638762i	$-0.220553\pi$
$457$	32.8960	1.53881	0.769405	+	0.638762i	$0.220553\pi$
$458$	37.1609	1.73641
$459$	3.02844	0.141355
$460$	−2.40292	−0.112037
$461$	33.3004	1.55095	0.775477	−	0.631376i	$-0.217509\pi$
$461$	33.3004	1.55095	0.775477	+	0.631376i	$0.217509\pi$
$462$	0	0
$463$	−41.9745	−1.95072	−0.975359	−	0.220622i	$-0.929191\pi$
$463$	−41.9745	−1.95072	−0.975359	+	0.220622i	$0.929191\pi$
$464$	4.23480	0.196595
$465$	5.96560	0.276648
$466$	5.29887	0.245466
$467$	−37.8708	−1.75245	−0.876226	−	0.481900i	$-0.839947\pi$
$467$	−37.8708	−1.75245	−0.876226	+	0.481900i	$0.839947\pi$
$468$	1.56328	0.0722626
$469$	0	0
$470$	−57.9854	−2.67467
$471$	−13.5380	−0.623800
$472$	22.0597	1.01538
$473$	−24.4860	−1.12587
$474$	7.39201	0.339526
$475$	7.99161	0.366680
$476$	0	0
$477$	−6.80600	−0.311626
$478$	−44.2482	−2.02386
$479$	−12.6552	−0.578229	−0.289115	−	0.957294i	$-0.593361\pi$
$479$	−12.6552	−0.578229	−0.289115	+	0.957294i	$0.593361\pi$
$480$	12.8406	0.586091
$481$	−10.4233	−0.475263
$482$	21.0473	0.958677
$483$	0	0
$484$	1.97092	0.0895875
$485$	20.6801	0.939035
$486$	−1.67781	−0.0761069
$487$	−18.7105	−0.847853	−0.423927	−	0.905696i	$-0.639349\pi$
$487$	−18.7105	−0.847853	−0.423927	+	0.905696i	$0.639349\pi$
$488$	−4.32026	−0.195569
$489$	13.6773	0.618509
$490$	0	0
$491$	41.6265	1.87858	0.939288	−	0.343129i	$-0.111487\pi$
$491$	41.6265	1.87858	0.939288	+	0.343129i	$0.111487\pi$
$492$	−1.14993	−0.0518428
$493$	−2.58263	−0.116316
$494$	−6.96563	−0.313398
$495$	−10.7997	−0.485409
$496$	−10.0480	−0.451168
$497$	0	0
$498$	−23.9171	−1.07175
$499$	23.7011	1.06101	0.530503	−	0.847683i	$-0.322003\pi$
$499$	23.7011	1.06101	0.530503	+	0.847683i	$0.322003\pi$
$500$	−3.14272	−0.140547
$501$	4.39959	0.196559
$502$	−34.4481	−1.53750
$503$	9.78650	0.436359	0.218179	−	0.975909i	$-0.429988\pi$
$503$	9.78650	0.436359	0.218179	+	0.975909i	$0.429988\pi$
$504$	0	0
$505$	26.3480	1.17247
$506$	−6.14595	−0.273221
$507$	−9.32108	−0.413964
$508$	−15.2565	−0.676896
$509$	−32.6888	−1.44890	−0.724452	−	0.689325i	$-0.757907\pi$
$509$	−32.6888	−1.44890	−0.724452	+	0.689325i	$0.757907\pi$
$510$	−14.9804	−0.663343
$511$	0	0
$512$	−1.88236	−0.0831892
$513$	2.16450	0.0955651
$514$	−16.9576	−0.747966
$515$	3.38973	0.149369
$516$	5.44813	0.239840
$517$	−42.9399	−1.88849
$518$	0	0
$519$	1.80023	0.0790211
$520$	11.2427	0.493025
$521$	9.37155	0.410575	0.205288	−	0.978702i	$-0.434187\pi$
$521$	9.37155	0.410575	0.205288	+	0.978702i	$0.434187\pi$
$522$	1.43082	0.0626255
$523$	30.3942	1.32905	0.664523	−	0.747268i	$-0.268635\pi$
$523$	30.3942	1.32905	0.664523	+	0.747268i	$0.268635\pi$
$524$	−10.3926	−0.454003
$525$	0	0
$526$	12.2349	0.533469
$527$	6.12787	0.266934
$528$	18.1901	0.791623
$529$	1.00000	0.0434783
$530$	33.6664	1.46238
$531$	11.0956	0.481510
$532$	0	0
$533$	−2.70617	−0.117217
$534$	−27.1552	−1.17512
$535$	8.70280	0.376255
$536$	22.8523	0.987069
$537$	21.4810	0.926974
$538$	31.8678	1.37392
$539$	0	0
$540$	2.40292	0.103405
$541$	13.5847	0.584053	0.292027	−	0.956410i	$-0.405670\pi$
$541$	13.5847	0.584053	0.292027	+	0.956410i	$0.405670\pi$
$542$	14.0194	0.602184
$543$	−21.2920	−0.913726
$544$	13.1899	0.565512
$545$	−31.7644	−1.36064
$546$	0	0
$547$	−38.4666	−1.64471	−0.822357	−	0.568971i	$-0.807341\pi$
$547$	−38.4666	−1.64471	−0.822357	+	0.568971i	$0.807341\pi$
$548$	15.9263	0.680338
$549$	−2.17302	−0.0927421
$550$	22.6916	0.967574
$551$	−1.84588	−0.0786370
$552$	−1.98814	−0.0846209
$553$	0	0
$554$	−19.2108	−0.816190
$555$	−16.0217	−0.680085
$556$	−6.24012	−0.264640
$557$	−36.1528	−1.53184	−0.765922	−	0.642934i	$-0.777717\pi$
$557$	−36.1528	−1.53184	−0.765922	+	0.642934i	$0.777717\pi$
$558$	−3.39495	−0.143720
$559$	12.8213	0.542282
$560$	0	0
$561$	−11.0934	−0.468365
$562$	10.5406	0.444627
$563$	9.11334	0.384081	0.192041	−	0.981387i	$-0.438489\pi$
$563$	9.11334	0.384081	0.192041	+	0.981387i	$0.438489\pi$
$564$	9.55410	0.402300
$565$	−11.3789	−0.478716
$566$	26.0716	1.09587
$567$	0	0
$568$	−28.1389	−1.18068
$569$	−6.84419	−0.286923	−0.143462	−	0.989656i	$-0.545823\pi$
$569$	−6.84419	−0.286923	−0.143462	+	0.989656i	$0.545823\pi$
$570$	−10.7069	−0.448462
$571$	−14.2712	−0.597232	−0.298616	−	0.954373i	$-0.596525\pi$
$571$	−14.2712	−0.597232	−0.298616	+	0.954373i	$0.596525\pi$
$572$	−5.72643	−0.239434
$573$	7.69448	0.321441
$574$	0	0
$575$	−3.69212	−0.153972
$576$	2.62414	0.109339
$577$	−13.6166	−0.566866	−0.283433	−	0.958992i	$-0.591473\pi$
$577$	−13.6166	−0.566866	−0.283433	+	0.958992i	$0.591473\pi$
$578$	13.1348	0.546337
$579$	−15.1469	−0.629483
$580$	−2.04920	−0.0850883
$581$	0	0
$582$	−11.7688	−0.487832
$583$	24.9310	1.03254
$584$	20.3386	0.841619
$585$	5.65488	0.233800
$586$	−23.2348	−0.959819
$587$	16.3493	0.674807	0.337403	−	0.941360i	$-0.390451\pi$
$587$	16.3493	0.674807	0.337403	+	0.941360i	$0.390451\pi$
$588$	0	0
$589$	4.37975	0.180464
$590$	−54.8855	−2.25960
$591$	8.95690	0.368438
$592$	26.9858	1.10911
$593$	−11.0436	−0.453507	−0.226754	−	0.973952i	$-0.572811\pi$
$593$	−11.0436	−0.453507	−0.226754	+	0.973952i	$0.572811\pi$
$594$	6.14595	0.252171
$595$	0	0
$596$	−6.88824	−0.282154
$597$	16.6575	0.681748
$598$	3.21812	0.131599
$599$	−1.46417	−0.0598244	−0.0299122	−	0.999553i	$-0.509523\pi$
$599$	−1.46417	−0.0598244	−0.0299122	+	0.999553i	$0.509523\pi$
$600$	7.34046	0.299673
$601$	−12.5553	−0.512141	−0.256071	−	0.966658i	$-0.582428\pi$
$601$	−12.5553	−0.512141	−0.256071	+	0.966658i	$0.582428\pi$
$602$	0	0
$603$	11.4943	0.468084
$604$	4.01522	0.163377
$605$	7.12946	0.289854
$606$	−14.9943	−0.609102
$607$	1.81528	0.0736799	0.0368399	−	0.999321i	$-0.488271\pi$
$607$	1.81528	0.0736799	0.0368399	+	0.999321i	$0.488271\pi$
$608$	9.42716	0.382322
$609$	0	0
$610$	10.7490	0.435214
$611$	22.4840	0.909606
$612$	2.46828	0.0997744
$613$	−48.7082	−1.96731	−0.983654	−	0.180071i	$-0.942367\pi$
$613$	−48.7082	−1.96731	−0.983654	+	0.180071i	$0.942367\pi$
$614$	34.4139	1.38883
$615$	−4.15965	−0.167733
$616$	0	0
$617$	−5.07884	−0.204466	−0.102233	−	0.994760i	$-0.532599\pi$
$617$	−5.07884	−0.204466	−0.102233	+	0.994760i	$0.532599\pi$
$618$	−1.92905	−0.0775979
$619$	−15.2756	−0.613980	−0.306990	−	0.951713i	$-0.599322\pi$
$619$	−15.2756	−0.613980	−0.306990	+	0.951713i	$0.599322\pi$
$620$	4.86217	0.195270
$621$	−1.00000	−0.0401286
$622$	1.64696	0.0660372
$623$	0	0
$624$	−9.52464	−0.381291
$625$	−29.8288	−1.19315
$626$	6.78559	0.271207
$627$	−7.92876	−0.316644
$628$	−11.0340	−0.440304
$629$	−16.4575	−0.656205
$630$	0	0
$631$	22.5888	0.899247	0.449623	−	0.893218i	$-0.351558\pi$
$631$	22.5888	0.899247	0.449623	+	0.893218i	$0.351558\pi$
$632$	−8.75927	−0.348425
$633$	−0.555224	−0.0220682
$634$	25.0111	0.993319
$635$	−55.1875	−2.19005
$636$	−5.54713	−0.219958
$637$	0	0
$638$	−5.24123	−0.207502
$639$	−14.1534	−0.559899
$640$	−38.6618	−1.52824
$641$	5.60065	0.221212	0.110606	−	0.993864i	$-0.464721\pi$
$641$	5.60065	0.221212	0.110606	+	0.993864i	$0.464721\pi$
$642$	−4.95265	−0.195466
$643$	−11.5110	−0.453951	−0.226975	−	0.973900i	$-0.572884\pi$
$643$	−11.5110	−0.453951	−0.226975	+	0.973900i	$0.572884\pi$
$644$	0	0
$645$	19.7076	0.775986
$646$	−10.9981	−0.432715
$647$	−15.5396	−0.610923	−0.305462	−	0.952204i	$-0.598811\pi$
$647$	−15.5396	−0.610923	−0.305462	+	0.952204i	$0.598811\pi$
$648$	1.98814	0.0781016
$649$	−40.6443	−1.59543
$650$	−11.8817	−0.466038
$651$	0	0
$652$	11.1475	0.436569
$653$	−31.6479	−1.23848	−0.619239	−	0.785202i	$-0.712559\pi$
$653$	−31.6479	−1.23848	−0.619239	+	0.785202i	$0.712559\pi$
$654$	18.0767	0.706856
$655$	−37.5933	−1.46889
$656$	7.00620	0.273546
$657$	10.2300	0.399109
$658$	0	0
$659$	−34.2553	−1.33440	−0.667199	−	0.744880i	$-0.732507\pi$
$659$	−34.2553	−1.33440	−0.667199	+	0.744880i	$0.732507\pi$
$660$	−8.80211	−0.342621
$661$	1.09146	0.0424528	0.0212264	−	0.999775i	$-0.493243\pi$
$661$	1.09146	0.0424528	0.0212264	+	0.999775i	$0.493243\pi$
$662$	13.6367	0.530006
$663$	5.80870	0.225591
$664$	28.3409	1.09984
$665$	0	0
$666$	9.11777	0.353306
$667$	0.852794	0.0330203
$668$	3.58582	0.138740
$669$	15.1938	0.587428
$670$	−56.8574	−2.19659
$671$	7.95995	0.307290
$672$	0	0
$673$	4.74037	0.182728	0.0913639	−	0.995818i	$-0.470877\pi$
$673$	4.74037	0.182728	0.0913639	+	0.995818i	$0.470877\pi$
$674$	−6.27815	−0.241825
$675$	3.69212	0.142110
$676$	−7.59701	−0.292193
$677$	40.7307	1.56541	0.782704	−	0.622394i	$-0.213840\pi$
$677$	40.7307	1.56541	0.782704	+	0.622394i	$0.213840\pi$
$678$	6.47561	0.248694
$679$	0	0
$680$	17.7512	0.680729
$681$	27.1559	1.04062
$682$	12.4360	0.476198
$683$	39.2028	1.50005	0.750026	−	0.661408i	$-0.230041\pi$
$683$	39.2028	1.50005	0.750026	+	0.661408i	$0.230041\pi$
$684$	1.76415	0.0674538
$685$	57.6105	2.20118
$686$	0	0
$687$	−22.1485	−0.845017
$688$	−33.1940	−1.26551
$689$	−13.0543	−0.497328
$690$	4.94658	0.188313
$691$	−13.4804	−0.512818	−0.256409	−	0.966568i	$-0.582539\pi$
$691$	−13.4804	−0.512818	−0.256409	+	0.966568i	$0.582539\pi$
$692$	1.46725	0.0557764
$693$	0	0
$694$	−38.6776	−1.46818
$695$	−22.5725	−0.856223
$696$	−1.69548	−0.0642669
$697$	−4.27280	−0.161844
$698$	−44.3508	−1.67870
$699$	−3.15821	−0.119455
$700$	0	0
$701$	13.4433	0.507745	0.253873	−	0.967238i	$-0.418296\pi$
$701$	13.4433	0.507745	0.253873	+	0.967238i	$0.418296\pi$
$702$	−3.21812	−0.121460
$703$	−11.7626	−0.443636
$704$	−9.61246	−0.362283
$705$	34.5602	1.30161
$706$	20.2088	0.760567
$707$	0	0
$708$	9.04334	0.339869
$709$	0.0451108	0.00169417	0.000847086	−	1.00000i	$-0.499730\pi$
$709$	0.0451108	0.00169417	0.000847086		1.00000i	$0.499730\pi$
$710$	70.0108	2.62746
$711$	−4.40576	−0.165229
$712$	32.1780	1.20592
$713$	−2.02344	−0.0757785
$714$	0	0
$715$	−20.7143	−0.774671
$716$	17.5078	0.654297
$717$	26.3726	0.984904
$718$	−11.1323	−0.415453
$719$	−30.5836	−1.14058	−0.570289	−	0.821444i	$-0.693169\pi$
$719$	−30.5836	−1.14058	−0.570289	+	0.821444i	$0.693169\pi$
$720$	−14.6403	−0.545613
$721$	0	0
$722$	24.0177	0.893846
$723$	−12.5445	−0.466535
$724$	−17.3537	−0.644945
$725$	−3.14862	−0.116937
$726$	−4.05729	−0.150580
$727$	−27.1973	−1.00869	−0.504347	−	0.863501i	$-0.668267\pi$
$727$	−27.1973	−1.00869	−0.504347	+	0.863501i	$0.668267\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−50.6033	−1.87291
$731$	20.2437	0.748739
$732$	−1.77109	−0.0654612
$733$	−35.8919	−1.32570	−0.662849	−	0.748753i	$-0.730653\pi$
$733$	−35.8919	−1.32570	−0.662849	+	0.748753i	$0.730653\pi$
$734$	−59.9878	−2.21419
$735$	0	0
$736$	−4.35535	−0.160540
$737$	−42.1046	−1.55094
$738$	2.36721	0.0871381
$739$	4.18412	0.153915	0.0769577	−	0.997034i	$-0.475479\pi$
$739$	4.18412	0.153915	0.0769577	+	0.997034i	$0.475479\pi$
$740$	−13.0583	−0.480032
$741$	4.15163	0.152514
$742$	0	0
$743$	17.5835	0.645075	0.322537	−	0.946557i	$-0.395464\pi$
$743$	17.5835	0.645075	0.322537	+	0.946557i	$0.395464\pi$
$744$	4.02289	0.147486
$745$	−24.9170	−0.912887
$746$	−54.5712	−1.99799
$747$	14.2550	0.521563
$748$	−9.04153	−0.330591
$749$	0	0
$750$	6.46952	0.236233
$751$	30.7378	1.12164	0.560819	−	0.827938i	$-0.310486\pi$
$751$	30.7378	1.12164	0.560819	+	0.827938i	$0.310486\pi$
$752$	−58.2105	−2.12272
$753$	20.5316	0.748215
$754$	2.74440	0.0999450
$755$	14.5243	0.528594
$756$	0	0
$757$	4.05528	0.147392	0.0736959	−	0.997281i	$-0.476521\pi$
$757$	4.05528	0.147392	0.0736959	+	0.997281i	$0.476521\pi$
$758$	13.4279	0.487724
$759$	3.66309	0.132962
$760$	12.6873	0.460216
$761$	28.8891	1.04723	0.523614	−	0.851956i	$-0.324583\pi$
$761$	28.8891	1.04723	0.523614	+	0.851956i	$0.324583\pi$
$762$	31.4065	1.13774
$763$	0	0
$764$	6.27127	0.226887
$765$	8.92856	0.322813
$766$	10.3775	0.374956
$767$	21.2820	0.768449
$768$	16.7536	0.604545
$769$	42.5217	1.53337	0.766685	−	0.642023i	$-0.221905\pi$
$769$	42.5217	1.53337	0.766685	+	0.642023i	$0.221905\pi$
$770$	0	0
$771$	10.1070	0.363994
$772$	−12.3452	−0.444315
$773$	−17.0065	−0.611682	−0.305841	−	0.952083i	$-0.598938\pi$
$773$	−17.0065	−0.611682	−0.305841	+	0.952083i	$0.598938\pi$
$774$	−11.2153	−0.403127
$775$	7.47080	0.268359
$776$	13.9456	0.500618
$777$	0	0
$778$	8.29411	0.297358
$779$	−3.05388	−0.109417
$780$	4.60893	0.165026
$781$	51.8450	1.85516
$782$	5.08113	0.181701
$783$	−0.852794	−0.0304764
$784$	0	0
$785$	−39.9134	−1.42457
$786$	21.3939	0.763095
$787$	19.3624	0.690194	0.345097	−	0.938567i	$-0.387846\pi$
$787$	19.3624	0.690194	0.345097	+	0.938567i	$0.387846\pi$
$788$	7.30019	0.260058
$789$	−7.29222	−0.259610
$790$	21.7934	0.775375
$791$	0	0
$792$	−7.28274	−0.258781
$793$	−4.16796	−0.148009
$794$	−36.7102	−1.30280
$795$	−20.0657	−0.711658
$796$	13.5765	0.481206
$797$	−20.7380	−0.734579	−0.367289	−	0.930107i	$-0.619714\pi$
$797$	−20.7380	−0.734579	−0.367289	+	0.930107i	$0.619714\pi$
$798$	0	0
$799$	35.5003	1.25591
$800$	16.0805	0.568531
$801$	16.1850	0.571868
$802$	−38.2087	−1.34920
$803$	−37.4733	−1.32240
$804$	9.36826	0.330393
$805$	0	0
$806$	−6.51168	−0.229364
$807$	−18.9937	−0.668610
$808$	17.7677	0.625066
$809$	−28.3202	−0.995685	−0.497843	−	0.867267i	$-0.665874\pi$
$809$	−28.3202	−0.995685	−0.497843	+	0.867267i	$0.665874\pi$
$810$	−4.94658	−0.173805
$811$	−18.6782	−0.655881	−0.327940	−	0.944698i	$-0.606354\pi$
$811$	−18.6782	−0.655881	−0.327940	+	0.944698i	$0.606354\pi$
$812$	0	0
$813$	−8.35578	−0.293050
$814$	−33.3992	−1.17064
$815$	40.3240	1.41249
$816$	−15.0386	−0.526455
$817$	14.4687	0.506195
$818$	30.6715	1.07240
$819$	0	0
$820$	−3.39026	−0.118393
$821$	−24.4161	−0.852127	−0.426063	−	0.904693i	$-0.640100\pi$
$821$	−24.4161	−0.852127	−0.426063	+	0.904693i	$0.640100\pi$
$822$	−32.7854	−1.14352
$823$	−37.0062	−1.28995	−0.644977	−	0.764202i	$-0.723133\pi$
$823$	−37.0062	−1.28995	−0.644977	+	0.764202i	$0.723133\pi$
$824$	2.28586	0.0796317
$825$	−13.5246	−0.470865
$826$	0	0
$827$	−42.8466	−1.48992	−0.744961	−	0.667108i	$-0.767532\pi$
$827$	−42.8466	−1.48992	−0.744961	+	0.667108i	$0.767532\pi$
$828$	−0.815035	−0.0283244
$829$	13.3749	0.464529	0.232265	−	0.972653i	$-0.425386\pi$
$829$	13.3749	0.464529	0.232265	+	0.972653i	$0.425386\pi$
$830$	−70.5134	−2.44756
$831$	11.4500	0.397195
$832$	5.03324	0.174496
$833$	0	0
$834$	12.8457	0.444811
$835$	12.9710	0.448882
$836$	−6.46222	−0.223501
$837$	2.02344	0.0699404
$838$	11.8797	0.410376
$839$	−53.2311	−1.83774	−0.918871	−	0.394559i	$-0.870897\pi$
$839$	−53.2311	−1.83774	−0.918871	+	0.394559i	$0.870897\pi$
$840$	0	0
$841$	−28.2727	−0.974922
$842$	−39.9844	−1.37795
$843$	−6.28234	−0.216375
$844$	−0.452527	−0.0155766
$845$	−27.4808	−0.945368
$846$	−19.6678	−0.676192
$847$	0	0
$848$	33.7972	1.16060
$849$	−15.5391	−0.533300
$850$	−18.7602	−0.643468
$851$	5.43434	0.186287
$852$	−11.5355	−0.395200
$853$	37.5791	1.28668	0.643341	−	0.765579i	$-0.277548\pi$
$853$	37.5791	1.28668	0.643341	+	0.765579i	$0.277548\pi$
$854$	0	0
$855$	6.38147	0.218242
$856$	5.86872	0.200589
$857$	−5.37406	−0.183574	−0.0917871	−	0.995779i	$-0.529258\pi$
$857$	−5.37406	−0.183574	−0.0917871	+	0.995779i	$0.529258\pi$
$858$	11.7883	0.402444
$859$	20.6749	0.705418	0.352709	−	0.935733i	$-0.385261\pi$
$859$	20.6749	0.705418	0.352709	+	0.935733i	$0.385261\pi$
$860$	16.0624	0.547723
$861$	0	0
$862$	9.27462	0.315895
$863$	−40.8060	−1.38905	−0.694526	−	0.719467i	$-0.744386\pi$
$863$	−40.8060	−1.38905	−0.694526	+	0.719467i	$0.744386\pi$
$864$	4.35535	0.148172
$865$	5.30750	0.180460
$866$	−29.6907	−1.00893
$867$	−7.82858	−0.265872
$868$	0	0
$869$	16.1387	0.547467
$870$	4.21841	0.143018
$871$	22.0467	0.747022
$872$	−21.4203	−0.725383
$873$	7.01439	0.237401
$874$	3.63162	0.122841
$875$	0	0
$876$	8.33779	0.281708
$877$	−42.2162	−1.42554	−0.712771	−	0.701397i	$-0.752560\pi$
$877$	−42.2162	−1.42554	−0.712771	+	0.701397i	$0.752560\pi$
$878$	5.92233	0.199869
$879$	13.8483	0.467091
$880$	53.6288	1.80783
$881$	−34.8993	−1.17579	−0.587893	−	0.808938i	$-0.700043\pi$
$881$	−34.8993	−1.17579	−0.587893	+	0.808938i	$0.700043\pi$
$882$	0	0
$883$	−56.9299	−1.91585	−0.957923	−	0.287027i	$-0.907333\pi$
$883$	−56.9299	−1.91585	−0.957923	+	0.287027i	$0.907333\pi$
$884$	4.73429	0.159231
$885$	32.7126	1.09962
$886$	−63.0812	−2.11925
$887$	40.8168	1.37049	0.685246	−	0.728311i	$-0.259694\pi$
$887$	40.8168	1.37049	0.685246	+	0.728311i	$0.259694\pi$
$888$	−10.8042	−0.362566
$889$	0	0
$890$	−80.0602	−2.68362
$891$	−3.66309	−0.122718
$892$	12.3835	0.414631
$893$	25.3730	0.849075
$894$	14.1799	0.474248
$895$	63.3312	2.11693
$896$	0	0
$897$	−1.91805	−0.0640419
$898$	64.8687	2.16470
$899$	−1.72558	−0.0575514
$900$	3.00921	0.100307
$901$	−20.6115	−0.686670
$902$	−8.67129	−0.288722
$903$	0	0
$904$	−7.67337	−0.255213
$905$	−62.7738	−2.08667
$906$	−8.26561	−0.274606
$907$	−49.6436	−1.64839	−0.824194	−	0.566307i	$-0.808372\pi$
$907$	−49.6436	−1.64839	−0.824194	+	0.566307i	$0.808372\pi$
$908$	22.1330	0.734511
$909$	8.93684	0.296416
$910$	0	0
$911$	−33.8661	−1.12203	−0.561016	−	0.827805i	$-0.689589\pi$
$911$	−33.8661	−1.12203	−0.561016	+	0.827805i	$0.689589\pi$
$912$	−10.7485	−0.355917
$913$	−52.2173	−1.72814
$914$	−55.1931	−1.82563
$915$	−6.40658	−0.211795
$916$	−18.0518	−0.596448
$917$	0	0
$918$	−5.08113	−0.167702
$919$	14.7590	0.486854	0.243427	−	0.969919i	$-0.421728\pi$
$919$	14.7590	0.486854	0.243427	+	0.969919i	$0.421728\pi$
$920$	−5.86152	−0.193249
$921$	−20.5112	−0.675868
$922$	−55.8716	−1.84003
$923$	−27.1469	−0.893551
$924$	0	0
$925$	−20.0642	−0.659708
$926$	70.4250	2.31431
$927$	1.14975	0.0377626
$928$	−3.71422	−0.121925
$929$	−25.1761	−0.826001	−0.413001	−	0.910731i	$-0.635519\pi$
$929$	−25.1761	−0.826001	−0.413001	+	0.910731i	$0.635519\pi$
$930$	−10.0091	−0.328212
$931$	0	0
$932$	−2.57406	−0.0843160
$933$	−0.981617	−0.0321367
$934$	63.5399	2.07909
$935$	−32.7061	−1.06960
$936$	3.81336	0.124644
$937$	1.20275	0.0392923	0.0196461	−	0.999807i	$-0.493746\pi$
$937$	1.20275	0.0392923	0.0196461	+	0.999807i	$0.493746\pi$
$938$	0	0
$939$	−4.04432	−0.131981
$940$	28.1678	0.918732
$941$	−8.27465	−0.269746	−0.134873	−	0.990863i	$-0.543063\pi$
$941$	−8.27465	−0.269746	−0.134873	+	0.990863i	$0.543063\pi$
$942$	22.7142	0.740069
$943$	1.41089	0.0459450
$944$	−55.0986	−1.79331
$945$	0	0
$946$	41.0828	1.33572
$947$	−33.1952	−1.07870	−0.539349	−	0.842082i	$-0.681330\pi$
$947$	−33.1952	−1.07870	−0.539349	+	0.842082i	$0.681330\pi$
$948$	−3.59085	−0.116625
$949$	19.6216	0.636944
$950$	−13.4084	−0.435025
$951$	−14.9070	−0.483394
$952$	0	0
$953$	14.3543	0.464982	0.232491	−	0.972599i	$-0.425312\pi$
$953$	14.3543	0.464982	0.232491	+	0.972599i	$0.425312\pi$
$954$	11.4192	0.369709
$955$	22.6852	0.734075
$956$	21.4946	0.695186
$957$	3.12386	0.100980
$958$	21.2329	0.686004
$959$	0	0
$960$	7.73660	0.249698
$961$	−26.9057	−0.867925
$962$	17.4883	0.563847
$963$	2.95186	0.0951224
$964$	−10.2242	−0.329300
$965$	−44.6567	−1.43755
$966$	0	0
$967$	−37.8148	−1.21604	−0.608021	−	0.793921i	$-0.708036\pi$
$967$	−37.8148	−1.21604	−0.608021	+	0.793921i	$0.708036\pi$
$968$	4.80774	0.154527
$969$	6.55506	0.210579
$970$	−34.6972	−1.11406
$971$	−31.0417	−0.996177	−0.498088	−	0.867126i	$-0.665965\pi$
$971$	−31.0417	−0.996177	−0.498088	+	0.867126i	$0.665965\pi$
$972$	0.815035	0.0261423
$973$	0	0
$974$	31.3926	1.00588
$975$	7.08168	0.226795
$976$	10.7907	0.345403
$977$	−52.9616	−1.69439	−0.847196	−	0.531281i	$-0.821711\pi$
$977$	−52.9616	−1.69439	−0.847196	+	0.531281i	$0.821711\pi$
$978$	−22.9479	−0.733792
$979$	−59.2869	−1.89482
$980$	0	0
$981$	−10.7740	−0.343988
$982$	−69.8412	−2.22872
$983$	−47.5142	−1.51547	−0.757734	−	0.652563i	$-0.773694\pi$
$983$	−47.5142	−1.51547	−0.757734	+	0.652563i	$0.773694\pi$
$984$	−2.80506	−0.0894219
$985$	26.4071	0.841400
$986$	4.33316	0.137996
$987$	0	0
$988$	3.38372	0.107651
$989$	−6.68453	−0.212556
$990$	18.1197	0.575883
$991$	−17.3201	−0.550192	−0.275096	−	0.961417i	$-0.588710\pi$
$991$	−17.3201	−0.550192	−0.275096	+	0.961417i	$0.588710\pi$
$992$	8.81280	0.279807
$993$	−8.12770	−0.257925
$994$	0	0
$995$	49.1104	1.55691
$996$	11.6183	0.368140
$997$	5.50089	0.174215	0.0871074	−	0.996199i	$-0.472238\pi$
$997$	5.50089	0.174215	0.0871074	+	0.996199i	$0.472238\pi$
$998$	−39.7658	−1.25877
$999$	−5.43434	−0.171935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bf.1.3		8
7.2	even	3		483.2.i.g.277.6	✓	16
7.4	even	3		483.2.i.g.415.6	yes	16
7.6	odd	2		3381.2.a.be.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.6	✓	16	7.2	even	3
483.2.i.g.415.6	yes	16	7.4	even	3
3381.2.a.be.1.3		8	7.6	odd	2
3381.2.a.bf.1.3		8	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67781 q^{2} +1.00000 q^{3} +0.815035 q^{4} +2.94824 q^{5} -1.67781 q^{6} +1.98814 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.67781 q^{2} +1.00000 q^{3} +0.815035 q^{4} +2.94824 q^{5} -1.67781 q^{6} +1.98814 q^{8} +1.00000 q^{9} -4.94658 q^{10} -3.66309 q^{11} +0.815035 q^{12} +1.91805 q^{13} +2.94824 q^{15} -4.96579 q^{16} +3.02844 q^{17} -1.67781 q^{18} +2.16450 q^{19} +2.40292 q^{20} +6.14595 q^{22} -1.00000 q^{23} +1.98814 q^{24} +3.69212 q^{25} -3.21812 q^{26} +1.00000 q^{27} -0.852794 q^{29} -4.94658 q^{30} +2.02344 q^{31} +4.35535 q^{32} -3.66309 q^{33} -5.08113 q^{34} +0.815035 q^{36} -5.43434 q^{37} -3.63162 q^{38} +1.91805 q^{39} +5.86152 q^{40} -1.41089 q^{41} +6.68453 q^{43} -2.98555 q^{44} +2.94824 q^{45} +1.67781 q^{46} +11.7223 q^{47} -4.96579 q^{48} -6.19467 q^{50} +3.02844 q^{51} +1.56328 q^{52} -6.80600 q^{53} -1.67781 q^{54} -10.7997 q^{55} +2.16450 q^{57} +1.43082 q^{58} +11.0956 q^{59} +2.40292 q^{60} -2.17302 q^{61} -3.39495 q^{62} +2.62414 q^{64} +5.65488 q^{65} +6.14595 q^{66} +11.4943 q^{67} +2.46828 q^{68} -1.00000 q^{69} -14.1534 q^{71} +1.98814 q^{72} +10.2300 q^{73} +9.11777 q^{74} +3.69212 q^{75} +1.76415 q^{76} -3.21812 q^{78} -4.40576 q^{79} -14.6403 q^{80} +1.00000 q^{81} +2.36721 q^{82} +14.2550 q^{83} +8.92856 q^{85} -11.2153 q^{86} -0.852794 q^{87} -7.28274 q^{88} +16.1850 q^{89} -4.94658 q^{90} -0.815035 q^{92} +2.02344 q^{93} -19.6678 q^{94} +6.38147 q^{95} +4.35535 q^{96} +7.01439 q^{97} -3.66309 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9} - 3 q^{10} + 10 q^{11} + 15 q^{12} - 6 q^{13} + 5 q^{15} + 13 q^{16} + 21 q^{17} + q^{18} + 5 q^{19} - q^{20} + 18 q^{22} - 8 q^{23} + 9 q^{24} + 27 q^{25} + 3 q^{26} + 8 q^{27} + 2 q^{29} - 3 q^{30} - 13 q^{31} + 29 q^{32} + 10 q^{33} - 19 q^{34} + 15 q^{36} + 13 q^{37} - 6 q^{38} - 6 q^{39} + 7 q^{40} + 16 q^{41} + 15 q^{43} + 24 q^{44} + 5 q^{45} - q^{46} - q^{47} + 13 q^{48} + 16 q^{50} + 21 q^{51} - 19 q^{52} + 3 q^{53} + q^{54} - 10 q^{55} + 5 q^{57} - 40 q^{58} + 26 q^{59} - q^{60} - 14 q^{61} - 14 q^{62} + 49 q^{64} - 3 q^{65} + 18 q^{66} + 38 q^{67} + 43 q^{68} - 8 q^{69} + 9 q^{71} + 9 q^{72} - 6 q^{73} + 32 q^{74} + 27 q^{75} - 14 q^{76} + 3 q^{78} + 23 q^{79} - 17 q^{80} + 8 q^{81} + 20 q^{82} + 30 q^{83} - 37 q^{85} - 28 q^{86} + 2 q^{87} + 86 q^{88} + 12 q^{89} - 3 q^{90} - 15 q^{92} - 13 q^{93} - 45 q^{94} + 16 q^{95} + 29 q^{96} + 14 q^{97} + 10 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9 - 3 * q^10 + 10 * q^11 + 15 * q^12 - 6 * q^13 + 5 * q^15 + 13 * q^16 + 21 * q^17 + q^18 + 5 * q^19 - q^20 + 18 * q^22 - 8 * q^23 + 9 * q^24 + 27 * q^25 + 3 * q^26 + 8 * q^27 + 2 * q^29 - 3 * q^30 - 13 * q^31 + 29 * q^32 + 10 * q^33 - 19 * q^34 + 15 * q^36 + 13 * q^37 - 6 * q^38 - 6 * q^39 + 7 * q^40 + 16 * q^41 + 15 * q^43 + 24 * q^44 + 5 * q^45 - q^46 - q^47 + 13 * q^48 + 16 * q^50 + 21 * q^51 - 19 * q^52 + 3 * q^53 + q^54 - 10 * q^55 + 5 * q^57 - 40 * q^58 + 26 * q^59 - q^60 - 14 * q^61 - 14 * q^62 + 49 * q^64 - 3 * q^65 + 18 * q^66 + 38 * q^67 + 43 * q^68 - 8 * q^69 + 9 * q^71 + 9 * q^72 - 6 * q^73 + 32 * q^74 + 27 * q^75 - 14 * q^76 + 3 * q^78 + 23 * q^79 - 17 * q^80 + 8 * q^81 + 20 * q^82 + 30 * q^83 - 37 * q^85 - 28 * q^86 + 2 * q^87 + 86 * q^88 + 12 * q^89 - 3 * q^90 - 15 * q^92 - 13 * q^93 - 45 * q^94 + 16 * q^95 + 29 * q^96 + 14 * q^97 + 10 * q^99

Introduction

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Modular forms

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