LMFDB - Embedded newform 3822.2.a.bu.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, 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("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.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:	$30.5188236525$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.585786 q^{10} -0.414214 q^{11} +1.00000 q^{12} -1.00000 q^{13} +0.585786 q^{15} +1.00000 q^{16} +2.41421 q^{17} +1.00000 q^{18} +2.17157 q^{19} +0.585786 q^{20} -0.414214 q^{22} +1.41421 q^{23} +1.00000 q^{24} -4.65685 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.82843 q^{29} +0.585786 q^{30} +8.48528 q^{31} +1.00000 q^{32} -0.414214 q^{33} +2.41421 q^{34} +1.00000 q^{36} +1.41421 q^{37} +2.17157 q^{38} -1.00000 q^{39} +0.585786 q^{40} +9.89949 q^{41} +6.48528 q^{43} -0.414214 q^{44} +0.585786 q^{45} +1.41421 q^{46} -1.00000 q^{47} +1.00000 q^{48} -4.65685 q^{50} +2.41421 q^{51} -1.00000 q^{52} +9.48528 q^{53} +1.00000 q^{54} -0.242641 q^{55} +2.17157 q^{57} -1.82843 q^{58} -2.07107 q^{59} +0.585786 q^{60} +4.41421 q^{61} +8.48528 q^{62} +1.00000 q^{64} -0.585786 q^{65} -0.414214 q^{66} +1.82843 q^{67} +2.41421 q^{68} +1.41421 q^{69} -5.00000 q^{71} +1.00000 q^{72} -1.41421 q^{73} +1.41421 q^{74} -4.65685 q^{75} +2.17157 q^{76} -1.00000 q^{78} -11.6569 q^{79} +0.585786 q^{80} +1.00000 q^{81} +9.89949 q^{82} -7.65685 q^{83} +1.41421 q^{85} +6.48528 q^{86} -1.82843 q^{87} -0.414214 q^{88} -2.58579 q^{89} +0.585786 q^{90} +1.41421 q^{92} +8.48528 q^{93} -1.00000 q^{94} +1.27208 q^{95} +1.00000 q^{96} +0.928932 q^{97} -0.414214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} + 4 q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 10 q^{19} + 4 q^{20} + 2 q^{22} + 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} + 2 q^{29} + 4 q^{30} + 2 q^{32} + 2 q^{33} + 2 q^{34} + 2 q^{36} + 10 q^{38} - 2 q^{39} + 4 q^{40} - 4 q^{43} + 2 q^{44} + 4 q^{45} - 2 q^{47} + 2 q^{48} + 2 q^{50} + 2 q^{51} - 2 q^{52} + 2 q^{53} + 2 q^{54} + 8 q^{55} + 10 q^{57} + 2 q^{58} + 10 q^{59} + 4 q^{60} + 6 q^{61} + 2 q^{64} - 4 q^{65} + 2 q^{66} - 2 q^{67} + 2 q^{68} - 10 q^{71} + 2 q^{72} + 2 q^{75} + 10 q^{76} - 2 q^{78} - 12 q^{79} + 4 q^{80} + 2 q^{81} - 4 q^{83} - 4 q^{86} + 2 q^{87} + 2 q^{88} - 8 q^{89} + 4 q^{90} - 2 q^{94} + 28 q^{95} + 2 q^{96} + 16 q^{97} + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 + 4 * q^10 + 2 * q^11 + 2 * q^12 - 2 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 10 * q^19 + 4 * q^20 + 2 * q^22 + 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 + 2 * q^29 + 4 * q^30 + 2 * q^32 + 2 * q^33 + 2 * q^34 + 2 * q^36 + 10 * q^38 - 2 * q^39 + 4 * q^40 - 4 * q^43 + 2 * q^44 + 4 * q^45 - 2 * q^47 + 2 * q^48 + 2 * q^50 + 2 * q^51 - 2 * q^52 + 2 * q^53 + 2 * q^54 + 8 * q^55 + 10 * q^57 + 2 * q^58 + 10 * q^59 + 4 * q^60 + 6 * q^61 + 2 * q^64 - 4 * q^65 + 2 * q^66 - 2 * q^67 + 2 * q^68 - 10 * q^71 + 2 * q^72 + 2 * q^75 + 10 * q^76 - 2 * q^78 - 12 * q^79 + 4 * q^80 + 2 * q^81 - 4 * q^83 - 4 * q^86 + 2 * q^87 + 2 * q^88 - 8 * q^89 + 4 * q^90 - 2 * q^94 + 28 * q^95 + 2 * q^96 + 16 * q^97 + 2 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.585786	0.261972	0.130986	−	0.991384i	$-0.458186\pi$
$5$	0.585786	0.261972	0.130986	+	0.991384i	$0.458186\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.585786	0.185242
$11$	−0.414214	−0.124890	−0.0624450	−	0.998048i	$-0.519890\pi$
$11$	−0.414214	−0.124890	−0.0624450	+	0.998048i	$0.519890\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	0.585786	0.151249
$16$	1.00000	0.250000
$17$	2.41421	0.585533	0.292766	−	0.956184i	$-0.405424\pi$
$17$	2.41421	0.585533	0.292766	+	0.956184i	$0.405424\pi$
$18$	1.00000	0.235702
$19$	2.17157	0.498193	0.249096	−	0.968479i	$-0.419866\pi$
$19$	2.17157	0.498193	0.249096	+	0.968479i	$0.419866\pi$
$20$	0.585786	0.130986
$21$	0	0
$22$	−0.414214	−0.0883106
$23$	1.41421	0.294884	0.147442	−	0.989071i	$-0.452896\pi$
$23$	1.41421	0.294884	0.147442	+	0.989071i	$0.452896\pi$
$24$	1.00000	0.204124
$25$	−4.65685	−0.931371
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	−1.82843	−0.339530	−0.169765	−	0.985485i	$-0.554301\pi$
$29$	−1.82843	−0.339530	−0.169765	+	0.985485i	$0.554301\pi$
$30$	0.585786	0.106949
$31$	8.48528	1.52400	0.762001	−	0.647576i	$-0.224217\pi$
$31$	8.48528	1.52400	0.762001	+	0.647576i	$0.224217\pi$
$32$	1.00000	0.176777
$33$	−0.414214	−0.0721053
$34$	2.41421	0.414034
$35$	0	0
$36$	1.00000	0.166667
$37$	1.41421	0.232495	0.116248	−	0.993220i	$-0.462913\pi$
$37$	1.41421	0.232495	0.116248	+	0.993220i	$0.462913\pi$
$38$	2.17157	0.352276
$39$	−1.00000	−0.160128
$40$	0.585786	0.0926210
$41$	9.89949	1.54604	0.773021	−	0.634381i	$-0.218745\pi$
$41$	9.89949	1.54604	0.773021	+	0.634381i	$0.218745\pi$
$42$	0	0
$43$	6.48528	0.988996	0.494498	−	0.869179i	$-0.335352\pi$
$43$	6.48528	0.988996	0.494498	+	0.869179i	$0.335352\pi$
$44$	−0.414214	−0.0624450
$45$	0.585786	0.0873239
$46$	1.41421	0.208514
$47$	−1.00000	−0.145865	−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000	−0.145865	−0.0729325	+	0.997337i	$0.523236\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−4.65685	−0.658579
$51$	2.41421	0.338058
$52$	−1.00000	−0.138675
$53$	9.48528	1.30290	0.651452	−	0.758690i	$-0.274160\pi$
$53$	9.48528	1.30290	0.651452	+	0.758690i	$0.274160\pi$
$54$	1.00000	0.136083
$55$	−0.242641	−0.0327177
$56$	0	0
$57$	2.17157	0.287632
$58$	−1.82843	−0.240084
$59$	−2.07107	−0.269630	−0.134815	−	0.990871i	$-0.543044\pi$
$59$	−2.07107	−0.269630	−0.134815	+	0.990871i	$0.543044\pi$
$60$	0.585786	0.0756247
$61$	4.41421	0.565182	0.282591	−	0.959240i	$-0.408806\pi$
$61$	4.41421	0.565182	0.282591	+	0.959240i	$0.408806\pi$
$62$	8.48528	1.07763
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.585786	−0.0726579
$66$	−0.414214	−0.0509862
$67$	1.82843	0.223378	0.111689	−	0.993743i	$-0.464374\pi$
$67$	1.82843	0.223378	0.111689	+	0.993743i	$0.464374\pi$
$68$	2.41421	0.292766
$69$	1.41421	0.170251
$70$	0	0
$71$	−5.00000	−0.593391	−0.296695	−	0.954972i	$-0.595885\pi$
$71$	−5.00000	−0.593391	−0.296695	+	0.954972i	$0.595885\pi$
$72$	1.00000	0.117851
$73$	−1.41421	−0.165521	−0.0827606	−	0.996569i	$-0.526374\pi$
$73$	−1.41421	−0.165521	−0.0827606	+	0.996569i	$0.526374\pi$
$74$	1.41421	0.164399
$75$	−4.65685	−0.537727
$76$	2.17157	0.249096
$77$	0	0
$78$	−1.00000	−0.113228
$79$	−11.6569	−1.31150	−0.655749	−	0.754979i	$-0.727647\pi$
$79$	−11.6569	−1.31150	−0.655749	+	0.754979i	$0.727647\pi$
$80$	0.585786	0.0654929
$81$	1.00000	0.111111
$82$	9.89949	1.09322
$83$	−7.65685	−0.840449	−0.420224	−	0.907420i	$-0.638049\pi$
$83$	−7.65685	−0.840449	−0.420224	+	0.907420i	$0.638049\pi$
$84$	0	0
$85$	1.41421	0.153393
$86$	6.48528	0.699326
$87$	−1.82843	−0.196028
$88$	−0.414214	−0.0441553
$89$	−2.58579	−0.274093	−0.137046	−	0.990565i	$-0.543761\pi$
$89$	−2.58579	−0.274093	−0.137046	+	0.990565i	$0.543761\pi$
$90$	0.585786	0.0617473
$91$	0	0
$92$	1.41421	0.147442
$93$	8.48528	0.879883
$94$	−1.00000	−0.103142
$95$	1.27208	0.130512
$96$	1.00000	0.102062
$97$	0.928932	0.0943188	0.0471594	−	0.998887i	$-0.484983\pi$
$97$	0.928932	0.0943188	0.0471594	+	0.998887i	$0.484983\pi$
$98$	0	0
$99$	−0.414214	−0.0416300
$100$	−4.65685	−0.465685
$101$	14.8284	1.47548	0.737742	−	0.675083i	$-0.235892\pi$
$101$	14.8284	1.47548	0.737742	+	0.675083i	$0.235892\pi$
$102$	2.41421	0.239043
$103$	16.8284	1.65815	0.829077	−	0.559134i	$-0.188866\pi$
$103$	16.8284	1.65815	0.829077	+	0.559134i	$0.188866\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	9.48528	0.921292
$107$	−19.3137	−1.86713	−0.933563	−	0.358412i	$-0.883318\pi$
$107$	−19.3137	−1.86713	−0.933563	+	0.358412i	$0.883318\pi$
$108$	1.00000	0.0962250
$109$	−9.65685	−0.924959	−0.462479	−	0.886630i	$-0.653040\pi$
$109$	−9.65685	−0.924959	−0.462479	+	0.886630i	$0.653040\pi$
$110$	−0.242641	−0.0231349
$111$	1.41421	0.134231
$112$	0	0
$113$	4.89949	0.460906	0.230453	−	0.973083i	$-0.425979\pi$
$113$	4.89949	0.460906	0.230453	+	0.973083i	$0.425979\pi$
$114$	2.17157	0.203386
$115$	0.828427	0.0772512
$116$	−1.82843	−0.169765
$117$	−1.00000	−0.0924500
$118$	−2.07107	−0.190657
$119$	0	0
$120$	0.585786	0.0534747
$121$	−10.8284	−0.984402
$122$	4.41421	0.399644
$123$	9.89949	0.892607
$124$	8.48528	0.762001
$125$	−5.65685	−0.505964
$126$	0	0
$127$	−7.89949	−0.700967	−0.350483	−	0.936569i	$-0.613983\pi$
$127$	−7.89949	−0.700967	−0.350483	+	0.936569i	$0.613983\pi$
$128$	1.00000	0.0883883
$129$	6.48528	0.570997
$130$	−0.585786	−0.0513769
$131$	9.55635	0.834942	0.417471	−	0.908690i	$-0.362917\pi$
$131$	9.55635	0.834942	0.417471	+	0.908690i	$0.362917\pi$
$132$	−0.414214	−0.0360527
$133$	0	0
$134$	1.82843	0.157952
$135$	0.585786	0.0504165
$136$	2.41421	0.207017
$137$	11.0711	0.945865	0.472933	−	0.881099i	$-0.343195\pi$
$137$	11.0711	0.945865	0.472933	+	0.881099i	$0.343195\pi$
$138$	1.41421	0.120386
$139$	13.0711	1.10867	0.554337	−	0.832292i	$-0.312972\pi$
$139$	13.0711	1.10867	0.554337	+	0.832292i	$0.312972\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	−5.00000	−0.419591
$143$	0.414214	0.0346383
$144$	1.00000	0.0833333
$145$	−1.07107	−0.0889473
$146$	−1.41421	−0.117041
$147$	0	0
$148$	1.41421	0.116248
$149$	−4.92893	−0.403794	−0.201897	−	0.979407i	$-0.564711\pi$
$149$	−4.92893	−0.403794	−0.201897	+	0.979407i	$0.564711\pi$
$150$	−4.65685	−0.380231
$151$	4.07107	0.331299	0.165649	−	0.986185i	$-0.447028\pi$
$151$	4.07107	0.331299	0.165649	+	0.986185i	$0.447028\pi$
$152$	2.17157	0.176138
$153$	2.41421	0.195178
$154$	0	0
$155$	4.97056	0.399245
$156$	−1.00000	−0.0800641
$157$	−9.72792	−0.776373	−0.388186	−	0.921581i	$-0.626898\pi$
$157$	−9.72792	−0.776373	−0.388186	+	0.921581i	$0.626898\pi$
$158$	−11.6569	−0.927370
$159$	9.48528	0.752232
$160$	0.585786	0.0463105
$161$	0	0
$162$	1.00000	0.0785674
$163$	−18.6569	−1.46132	−0.730659	−	0.682743i	$-0.760787\pi$
$163$	−18.6569	−1.46132	−0.730659	+	0.682743i	$0.760787\pi$
$164$	9.89949	0.773021
$165$	−0.242641	−0.0188896
$166$	−7.65685	−0.594287
$167$	0.656854	0.0508289	0.0254145	−	0.999677i	$-0.491909\pi$
$167$	0.656854	0.0508289	0.0254145	+	0.999677i	$0.491909\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	1.41421	0.108465
$171$	2.17157	0.166064
$172$	6.48528	0.494498
$173$	−5.48528	−0.417038	−0.208519	−	0.978018i	$-0.566864\pi$
$173$	−5.48528	−0.417038	−0.208519	+	0.978018i	$0.566864\pi$
$174$	−1.82843	−0.138613
$175$	0	0
$176$	−0.414214	−0.0312225
$177$	−2.07107	−0.155671
$178$	−2.58579	−0.193813
$179$	19.6569	1.46922	0.734611	−	0.678488i	$-0.237365\pi$
$179$	19.6569	1.46922	0.734611	+	0.678488i	$0.237365\pi$
$180$	0.585786	0.0436619
$181$	−2.89949	−0.215518	−0.107759	−	0.994177i	$-0.534367\pi$
$181$	−2.89949	−0.215518	−0.107759	+	0.994177i	$0.534367\pi$
$182$	0	0
$183$	4.41421	0.326308
$184$	1.41421	0.104257
$185$	0.828427	0.0609072
$186$	8.48528	0.622171
$187$	−1.00000	−0.0731272
$188$	−1.00000	−0.0729325
$189$	0	0
$190$	1.27208	0.0922862
$191$	−10.3431	−0.748404	−0.374202	−	0.927347i	$-0.622083\pi$
$191$	−10.3431	−0.748404	−0.374202	+	0.927347i	$0.622083\pi$
$192$	1.00000	0.0721688
$193$	−2.92893	−0.210829	−0.105415	−	0.994428i	$-0.533617\pi$
$193$	−2.92893	−0.210829	−0.105415	+	0.994428i	$0.533617\pi$
$194$	0.928932	0.0666934
$195$	−0.585786	−0.0419490
$196$	0	0
$197$	−15.5563	−1.10834	−0.554172	−	0.832402i	$-0.686965\pi$
$197$	−15.5563	−1.10834	−0.554172	+	0.832402i	$0.686965\pi$
$198$	−0.414214	−0.0294369
$199$	−2.72792	−0.193377	−0.0966886	−	0.995315i	$-0.530825\pi$
$199$	−2.72792	−0.193377	−0.0966886	+	0.995315i	$0.530825\pi$
$200$	−4.65685	−0.329289
$201$	1.82843	0.128967
$202$	14.8284	1.04332
$203$	0	0
$204$	2.41421	0.169029
$205$	5.79899	0.405019
$206$	16.8284	1.17249
$207$	1.41421	0.0982946
$208$	−1.00000	−0.0693375
$209$	−0.899495	−0.0622194
$210$	0	0
$211$	−12.9289	−0.890064	−0.445032	−	0.895515i	$-0.646808\pi$
$211$	−12.9289	−0.890064	−0.445032	+	0.895515i	$0.646808\pi$
$212$	9.48528	0.651452
$213$	−5.00000	−0.342594
$214$	−19.3137	−1.32026
$215$	3.79899	0.259089
$216$	1.00000	0.0680414
$217$	0	0
$218$	−9.65685	−0.654045
$219$	−1.41421	−0.0955637
$220$	−0.242641	−0.0163588
$221$	−2.41421	−0.162398
$222$	1.41421	0.0949158
$223$	7.92893	0.530961	0.265480	−	0.964116i	$-0.414469\pi$
$223$	7.92893	0.530961	0.265480	+	0.964116i	$0.414469\pi$
$224$	0	0
$225$	−4.65685	−0.310457
$226$	4.89949	0.325910
$227$	21.1716	1.40521	0.702603	−	0.711582i	$-0.252021\pi$
$227$	21.1716	1.40521	0.702603	+	0.711582i	$0.252021\pi$
$228$	2.17157	0.143816
$229$	−26.4853	−1.75020	−0.875098	−	0.483945i	$-0.839203\pi$
$229$	−26.4853	−1.75020	−0.875098	+	0.483945i	$0.839203\pi$
$230$	0.828427	0.0546249
$231$	0	0
$232$	−1.82843	−0.120042
$233$	−17.7279	−1.16139	−0.580697	−	0.814119i	$-0.697220\pi$
$233$	−17.7279	−1.16139	−0.580697	+	0.814119i	$0.697220\pi$
$234$	−1.00000	−0.0653720
$235$	−0.585786	−0.0382125
$236$	−2.07107	−0.134815
$237$	−11.6569	−0.757194
$238$	0	0
$239$	4.51472	0.292033	0.146016	−	0.989282i	$-0.453355\pi$
$239$	4.51472	0.292033	0.146016	+	0.989282i	$0.453355\pi$
$240$	0.585786	0.0378124
$241$	2.14214	0.137987	0.0689935	−	0.997617i	$-0.478021\pi$
$241$	2.14214	0.137987	0.0689935	+	0.997617i	$0.478021\pi$
$242$	−10.8284	−0.696078
$243$	1.00000	0.0641500
$244$	4.41421	0.282591
$245$	0	0
$246$	9.89949	0.631169
$247$	−2.17157	−0.138174
$248$	8.48528	0.538816
$249$	−7.65685	−0.485233
$250$	−5.65685	−0.357771
$251$	−24.8284	−1.56716	−0.783578	−	0.621293i	$-0.786608\pi$
$251$	−24.8284	−1.56716	−0.783578	+	0.621293i	$0.786608\pi$
$252$	0	0
$253$	−0.585786	−0.0368281
$254$	−7.89949	−0.495658
$255$	1.41421	0.0885615
$256$	1.00000	0.0625000
$257$	−26.4853	−1.65211	−0.826053	−	0.563592i	$-0.809419\pi$
$257$	−26.4853	−1.65211	−0.826053	+	0.563592i	$0.809419\pi$
$258$	6.48528	0.403756
$259$	0	0
$260$	−0.585786	−0.0363289
$261$	−1.82843	−0.113177
$262$	9.55635	0.590393
$263$	20.5858	1.26937	0.634687	−	0.772769i	$-0.281129\pi$
$263$	20.5858	1.26937	0.634687	+	0.772769i	$0.281129\pi$
$264$	−0.414214	−0.0254931
$265$	5.55635	0.341324
$266$	0	0
$267$	−2.58579	−0.158248
$268$	1.82843	0.111689
$269$	9.14214	0.557406	0.278703	−	0.960377i	$-0.410096\pi$
$269$	9.14214	0.557406	0.278703	+	0.960377i	$0.410096\pi$
$270$	0.585786	0.0356498
$271$	−26.2132	−1.59234	−0.796169	−	0.605074i	$-0.793144\pi$
$271$	−26.2132	−1.59234	−0.796169	+	0.605074i	$0.793144\pi$
$272$	2.41421	0.146383
$273$	0	0
$274$	11.0711	0.668828
$275$	1.92893	0.116319
$276$	1.41421	0.0851257
$277$	18.0711	1.08579	0.542893	−	0.839802i	$-0.317329\pi$
$277$	18.0711	1.08579	0.542893	+	0.839802i	$0.317329\pi$
$278$	13.0711	0.783951
$279$	8.48528	0.508001
$280$	0	0
$281$	0.686292	0.0409407	0.0204704	−	0.999790i	$-0.493484\pi$
$281$	0.686292	0.0409407	0.0204704	+	0.999790i	$0.493484\pi$
$282$	−1.00000	−0.0595491
$283$	15.7574	0.936678	0.468339	−	0.883549i	$-0.344853\pi$
$283$	15.7574	0.936678	0.468339	+	0.883549i	$0.344853\pi$
$284$	−5.00000	−0.296695
$285$	1.27208	0.0753514
$286$	0.414214	0.0244930
$287$	0	0
$288$	1.00000	0.0589256
$289$	−11.1716	−0.657151
$290$	−1.07107	−0.0628953
$291$	0.928932	0.0544550
$292$	−1.41421	−0.0827606
$293$	9.89949	0.578335	0.289167	−	0.957279i	$-0.406622\pi$
$293$	9.89949	0.578335	0.289167	+	0.957279i	$0.406622\pi$
$294$	0	0
$295$	−1.21320	−0.0706354
$296$	1.41421	0.0821995
$297$	−0.414214	−0.0240351
$298$	−4.92893	−0.285525
$299$	−1.41421	−0.0817861
$300$	−4.65685	−0.268864
$301$	0	0
$302$	4.07107	0.234264
$303$	14.8284	0.851871
$304$	2.17157	0.124548
$305$	2.58579	0.148062
$306$	2.41421	0.138011
$307$	28.1127	1.60448	0.802238	−	0.597004i	$-0.203642\pi$
$307$	28.1127	1.60448	0.802238	+	0.597004i	$0.203642\pi$
$308$	0	0
$309$	16.8284	0.957336
$310$	4.97056	0.282309
$311$	8.10051	0.459338	0.229669	−	0.973269i	$-0.426236\pi$
$311$	8.10051	0.459338	0.229669	+	0.973269i	$0.426236\pi$
$312$	−1.00000	−0.0566139
$313$	−3.51472	−0.198664	−0.0993318	−	0.995054i	$-0.531671\pi$
$313$	−3.51472	−0.198664	−0.0993318	+	0.995054i	$0.531671\pi$
$314$	−9.72792	−0.548978
$315$	0	0
$316$	−11.6569	−0.655749
$317$	29.7990	1.67368	0.836839	−	0.547449i	$-0.184401\pi$
$317$	29.7990	1.67368	0.836839	+	0.547449i	$0.184401\pi$
$318$	9.48528	0.531908
$319$	0.757359	0.0424040
$320$	0.585786	0.0327465
$321$	−19.3137	−1.07799
$322$	0	0
$323$	5.24264	0.291708
$324$	1.00000	0.0555556
$325$	4.65685	0.258316
$326$	−18.6569	−1.03331
$327$	−9.65685	−0.534025
$328$	9.89949	0.546608
$329$	0	0
$330$	−0.242641	−0.0133569
$331$	−22.4853	−1.23590	−0.617951	−	0.786216i	$-0.712037\pi$
$331$	−22.4853	−1.23590	−0.617951	+	0.786216i	$0.712037\pi$
$332$	−7.65685	−0.420224
$333$	1.41421	0.0774984
$334$	0.656854	0.0359415
$335$	1.07107	0.0585187
$336$	0	0
$337$	−20.3137	−1.10656	−0.553279	−	0.832996i	$-0.686624\pi$
$337$	−20.3137	−1.10656	−0.553279	+	0.832996i	$0.686624\pi$
$338$	1.00000	0.0543928
$339$	4.89949	0.266104
$340$	1.41421	0.0766965
$341$	−3.51472	−0.190333
$342$	2.17157	0.117425
$343$	0	0
$344$	6.48528	0.349663
$345$	0.828427	0.0446010
$346$	−5.48528	−0.294891
$347$	−8.72792	−0.468539	−0.234270	−	0.972172i	$-0.575270\pi$
$347$	−8.72792	−0.468539	−0.234270	+	0.972172i	$0.575270\pi$
$348$	−1.82843	−0.0980140
$349$	6.72792	0.360137	0.180069	−	0.983654i	$-0.442368\pi$
$349$	6.72792	0.360137	0.180069	+	0.983654i	$0.442368\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−0.414214	−0.0220777
$353$	−12.6274	−0.672090	−0.336045	−	0.941846i	$-0.609089\pi$
$353$	−12.6274	−0.672090	−0.336045	+	0.941846i	$0.609089\pi$
$354$	−2.07107	−0.110076
$355$	−2.92893	−0.155452
$356$	−2.58579	−0.137046
$357$	0	0
$358$	19.6569	1.03890
$359$	−0.828427	−0.0437227	−0.0218614	−	0.999761i	$-0.506959\pi$
$359$	−0.828427	−0.0437227	−0.0218614	+	0.999761i	$0.506959\pi$
$360$	0.585786	0.0308737
$361$	−14.2843	−0.751804
$362$	−2.89949	−0.152394
$363$	−10.8284	−0.568345
$364$	0	0
$365$	−0.828427	−0.0433619
$366$	4.41421	0.230735
$367$	−12.6274	−0.659146	−0.329573	−	0.944130i	$-0.606905\pi$
$367$	−12.6274	−0.659146	−0.329573	+	0.944130i	$0.606905\pi$
$368$	1.41421	0.0737210
$369$	9.89949	0.515347
$370$	0.828427	0.0430679
$371$	0	0
$372$	8.48528	0.439941
$373$	−5.58579	−0.289221	−0.144611	−	0.989489i	$-0.546193\pi$
$373$	−5.58579	−0.289221	−0.144611	+	0.989489i	$0.546193\pi$
$374$	−1.00000	−0.0517088
$375$	−5.65685	−0.292119
$376$	−1.00000	−0.0515711
$377$	1.82843	0.0941688
$378$	0	0
$379$	18.6274	0.956826	0.478413	−	0.878135i	$-0.341212\pi$
$379$	18.6274	0.956826	0.478413	+	0.878135i	$0.341212\pi$
$380$	1.27208	0.0652562
$381$	−7.89949	−0.404703
$382$	−10.3431	−0.529201
$383$	−11.1716	−0.570841	−0.285420	−	0.958402i	$-0.592133\pi$
$383$	−11.1716	−0.570841	−0.285420	+	0.958402i	$0.592133\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−2.92893	−0.149079
$387$	6.48528	0.329665
$388$	0.928932	0.0471594
$389$	−4.51472	−0.228905	−0.114453	−	0.993429i	$-0.536511\pi$
$389$	−4.51472	−0.228905	−0.114453	+	0.993429i	$0.536511\pi$
$390$	−0.585786	−0.0296624
$391$	3.41421	0.172664
$392$	0	0
$393$	9.55635	0.482054
$394$	−15.5563	−0.783718
$395$	−6.82843	−0.343575
$396$	−0.414214	−0.0208150
$397$	9.55635	0.479619	0.239810	−	0.970820i	$-0.422915\pi$
$397$	9.55635	0.479619	0.239810	+	0.970820i	$0.422915\pi$
$398$	−2.72792	−0.136738
$399$	0	0
$400$	−4.65685	−0.232843
$401$	19.8995	0.993733	0.496867	−	0.867827i	$-0.334484\pi$
$401$	19.8995	0.993733	0.496867	+	0.867827i	$0.334484\pi$
$402$	1.82843	0.0911937
$403$	−8.48528	−0.422682
$404$	14.8284	0.737742
$405$	0.585786	0.0291080
$406$	0	0
$407$	−0.585786	−0.0290364
$408$	2.41421	0.119521
$409$	−32.5858	−1.61126	−0.805632	−	0.592417i	$-0.798174\pi$
$409$	−32.5858	−1.61126	−0.805632	+	0.592417i	$0.798174\pi$
$410$	5.79899	0.286392
$411$	11.0711	0.546096
$412$	16.8284	0.829077
$413$	0	0
$414$	1.41421	0.0695048
$415$	−4.48528	−0.220174
$416$	−1.00000	−0.0490290
$417$	13.0711	0.640093
$418$	−0.899495	−0.0439957
$419$	−27.4558	−1.34131	−0.670653	−	0.741771i	$-0.733986\pi$
$419$	−27.4558	−1.34131	−0.670653	+	0.741771i	$0.733986\pi$
$420$	0	0
$421$	1.07107	0.0522007	0.0261003	−	0.999659i	$-0.491691\pi$
$421$	1.07107	0.0522007	0.0261003	+	0.999659i	$0.491691\pi$
$422$	−12.9289	−0.629371
$423$	−1.00000	−0.0486217
$424$	9.48528	0.460646
$425$	−11.2426	−0.545348
$426$	−5.00000	−0.242251
$427$	0	0
$428$	−19.3137	−0.933563
$429$	0.414214	0.0199984
$430$	3.79899	0.183204
$431$	30.4853	1.46842	0.734212	−	0.678920i	$-0.237552\pi$
$431$	30.4853	1.46842	0.734212	+	0.678920i	$0.237552\pi$
$432$	1.00000	0.0481125
$433$	−29.9706	−1.44029	−0.720147	−	0.693822i	$-0.755926\pi$
$433$	−29.9706	−1.44029	−0.720147	+	0.693822i	$0.755926\pi$
$434$	0	0
$435$	−1.07107	−0.0513538
$436$	−9.65685	−0.462479
$437$	3.07107	0.146909
$438$	−1.41421	−0.0675737
$439$	−16.5858	−0.791596	−0.395798	−	0.918338i	$-0.629532\pi$
$439$	−16.5858	−0.791596	−0.395798	+	0.918338i	$0.629532\pi$
$440$	−0.242641	−0.0115674
$441$	0	0
$442$	−2.41421	−0.114832
$443$	−33.6985	−1.60106	−0.800532	−	0.599290i	$-0.795449\pi$
$443$	−33.6985	−1.60106	−0.800532	+	0.599290i	$0.795449\pi$
$444$	1.41421	0.0671156
$445$	−1.51472	−0.0718045
$446$	7.92893	0.375446
$447$	−4.92893	−0.233130
$448$	0	0
$449$	24.9706	1.17843	0.589217	−	0.807975i	$-0.299436\pi$
$449$	24.9706	1.17843	0.589217	+	0.807975i	$0.299436\pi$
$450$	−4.65685	−0.219526
$451$	−4.10051	−0.193085
$452$	4.89949	0.230453
$453$	4.07107	0.191275
$454$	21.1716	0.993631
$455$	0	0
$456$	2.17157	0.101693
$457$	−3.07107	−0.143658	−0.0718292	−	0.997417i	$-0.522884\pi$
$457$	−3.07107	−0.143658	−0.0718292	+	0.997417i	$0.522884\pi$
$458$	−26.4853	−1.23758
$459$	2.41421	0.112686
$460$	0.828427	0.0386256
$461$	4.48528	0.208900	0.104450	−	0.994530i	$-0.466692\pi$
$461$	4.48528	0.208900	0.104450	+	0.994530i	$0.466692\pi$
$462$	0	0
$463$	−20.9706	−0.974585	−0.487292	−	0.873239i	$-0.662015\pi$
$463$	−20.9706	−0.974585	−0.487292	+	0.873239i	$0.662015\pi$
$464$	−1.82843	−0.0848826
$465$	4.97056	0.230504
$466$	−17.7279	−0.821230
$467$	11.4142	0.528187	0.264093	−	0.964497i	$-0.414927\pi$
$467$	11.4142	0.528187	0.264093	+	0.964497i	$0.414927\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	−0.585786	−0.0270203
$471$	−9.72792	−0.448239
$472$	−2.07107	−0.0953286
$473$	−2.68629	−0.123516
$474$	−11.6569	−0.535417
$475$	−10.1127	−0.464002
$476$	0	0
$477$	9.48528	0.434301
$478$	4.51472	0.206498
$479$	32.1127	1.46727	0.733633	−	0.679546i	$-0.237823\pi$
$479$	32.1127	1.46727	0.733633	+	0.679546i	$0.237823\pi$
$480$	0.585786	0.0267374
$481$	−1.41421	−0.0644826
$482$	2.14214	0.0975716
$483$	0	0
$484$	−10.8284	−0.492201
$485$	0.544156	0.0247088
$486$	1.00000	0.0453609
$487$	16.2132	0.734690	0.367345	−	0.930085i	$-0.380267\pi$
$487$	16.2132	0.734690	0.367345	+	0.930085i	$0.380267\pi$
$488$	4.41421	0.199822
$489$	−18.6569	−0.843692
$490$	0	0
$491$	23.6569	1.06762	0.533809	−	0.845605i	$-0.320760\pi$
$491$	23.6569	1.06762	0.533809	+	0.845605i	$0.320760\pi$
$492$	9.89949	0.446304
$493$	−4.41421	−0.198806
$494$	−2.17157	−0.0977037
$495$	−0.242641	−0.0109059
$496$	8.48528	0.381000
$497$	0	0
$498$	−7.65685	−0.343112
$499$	3.65685	0.163703	0.0818516	−	0.996645i	$-0.473917\pi$
$499$	3.65685	0.163703	0.0818516	+	0.996645i	$0.473917\pi$
$500$	−5.65685	−0.252982
$501$	0.656854	0.0293461
$502$	−24.8284	−1.10815
$503$	−26.1421	−1.16562	−0.582810	−	0.812608i	$-0.698047\pi$
$503$	−26.1421	−1.16562	−0.582810	+	0.812608i	$0.698047\pi$
$504$	0	0
$505$	8.68629	0.386535
$506$	−0.585786	−0.0260414
$507$	1.00000	0.0444116
$508$	−7.89949	−0.350483
$509$	−10.6274	−0.471052	−0.235526	−	0.971868i	$-0.575681\pi$
$509$	−10.6274	−0.471052	−0.235526	+	0.971868i	$0.575681\pi$
$510$	1.41421	0.0626224
$511$	0	0
$512$	1.00000	0.0441942
$513$	2.17157	0.0958773
$514$	−26.4853	−1.16822
$515$	9.85786	0.434389
$516$	6.48528	0.285499
$517$	0.414214	0.0182171
$518$	0	0
$519$	−5.48528	−0.240777
$520$	−0.585786	−0.0256884
$521$	−40.6274	−1.77992	−0.889960	−	0.456039i	$-0.849268\pi$
$521$	−40.6274	−1.77992	−0.889960	+	0.456039i	$0.849268\pi$
$522$	−1.82843	−0.0800281
$523$	16.8284	0.735856	0.367928	−	0.929854i	$-0.380067\pi$
$523$	16.8284	0.735856	0.367928	+	0.929854i	$0.380067\pi$
$524$	9.55635	0.417471
$525$	0	0
$526$	20.5858	0.897583
$527$	20.4853	0.892353
$528$	−0.414214	−0.0180263
$529$	−21.0000	−0.913043
$530$	5.55635	0.241352
$531$	−2.07107	−0.0898767
$532$	0	0
$533$	−9.89949	−0.428795
$534$	−2.58579	−0.111898
$535$	−11.3137	−0.489134
$536$	1.82843	0.0789760
$537$	19.6569	0.848256
$538$	9.14214	0.394145
$539$	0	0
$540$	0.585786	0.0252082
$541$	23.0711	0.991903	0.495951	−	0.868350i	$-0.334819\pi$
$541$	23.0711	0.991903	0.495951	+	0.868350i	$0.334819\pi$
$542$	−26.2132	−1.12595
$543$	−2.89949	−0.124429
$544$	2.41421	0.103509
$545$	−5.65685	−0.242313
$546$	0	0
$547$	−30.8701	−1.31991	−0.659954	−	0.751306i	$-0.729424\pi$
$547$	−30.8701	−1.31991	−0.659954	+	0.751306i	$0.729424\pi$
$548$	11.0711	0.472933
$549$	4.41421	0.188394
$550$	1.92893	0.0822499
$551$	−3.97056	−0.169152
$552$	1.41421	0.0601929
$553$	0	0
$554$	18.0711	0.767766
$555$	0.828427	0.0351648
$556$	13.0711	0.554337
$557$	−32.6274	−1.38247	−0.691234	−	0.722631i	$-0.742933\pi$
$557$	−32.6274	−1.38247	−0.691234	+	0.722631i	$0.742933\pi$
$558$	8.48528	0.359211
$559$	−6.48528	−0.274298
$560$	0	0
$561$	−1.00000	−0.0422200
$562$	0.686292	0.0289495
$563$	32.7696	1.38107	0.690536	−	0.723298i	$-0.257375\pi$
$563$	32.7696	1.38107	0.690536	+	0.723298i	$0.257375\pi$
$564$	−1.00000	−0.0421076
$565$	2.87006	0.120744
$566$	15.7574	0.662331
$567$	0	0
$568$	−5.00000	−0.209795
$569$	23.7279	0.994726	0.497363	−	0.867542i	$-0.334302\pi$
$569$	23.7279	0.994726	0.497363	+	0.867542i	$0.334302\pi$
$570$	1.27208	0.0532815
$571$	−31.3137	−1.31044	−0.655219	−	0.755439i	$-0.727424\pi$
$571$	−31.3137	−1.31044	−0.655219	+	0.755439i	$0.727424\pi$
$572$	0.414214	0.0173191
$573$	−10.3431	−0.432091
$574$	0	0
$575$	−6.58579	−0.274646
$576$	1.00000	0.0416667
$577$	−16.3431	−0.680374	−0.340187	−	0.940358i	$-0.610490\pi$
$577$	−16.3431	−0.680374	−0.340187	+	0.940358i	$0.610490\pi$
$578$	−11.1716	−0.464676
$579$	−2.92893	−0.121722
$580$	−1.07107	−0.0444737
$581$	0	0
$582$	0.928932	0.0385055
$583$	−3.92893	−0.162720
$584$	−1.41421	−0.0585206
$585$	−0.585786	−0.0242193
$586$	9.89949	0.408944
$587$	1.58579	0.0654524	0.0327262	−	0.999464i	$-0.489581\pi$
$587$	1.58579	0.0654524	0.0327262	+	0.999464i	$0.489581\pi$
$588$	0	0
$589$	18.4264	0.759247
$590$	−1.21320	−0.0499468
$591$	−15.5563	−0.639903
$592$	1.41421	0.0581238
$593$	34.3848	1.41201	0.706007	−	0.708205i	$-0.250495\pi$
$593$	34.3848	1.41201	0.706007	+	0.708205i	$0.250495\pi$
$594$	−0.414214	−0.0169954
$595$	0	0
$596$	−4.92893	−0.201897
$597$	−2.72792	−0.111646
$598$	−1.41421	−0.0578315
$599$	1.55635	0.0635907	0.0317954	−	0.999494i	$-0.489878\pi$
$599$	1.55635	0.0635907	0.0317954	+	0.999494i	$0.489878\pi$
$600$	−4.65685	−0.190115
$601$	−1.20101	−0.0489902	−0.0244951	−	0.999700i	$-0.507798\pi$
$601$	−1.20101	−0.0489902	−0.0244951	+	0.999700i	$0.507798\pi$
$602$	0	0
$603$	1.82843	0.0744593
$604$	4.07107	0.165649
$605$	−6.34315	−0.257886
$606$	14.8284	0.602364
$607$	−34.5269	−1.40140	−0.700702	−	0.713454i	$-0.747130\pi$
$607$	−34.5269	−1.40140	−0.700702	+	0.713454i	$0.747130\pi$
$608$	2.17157	0.0880689
$609$	0	0
$610$	2.58579	0.104695
$611$	1.00000	0.0404557
$612$	2.41421	0.0975888
$613$	−7.79899	−0.314998	−0.157499	−	0.987519i	$-0.550343\pi$
$613$	−7.79899	−0.314998	−0.157499	+	0.987519i	$0.550343\pi$
$614$	28.1127	1.13454
$615$	5.79899	0.233838
$616$	0	0
$617$	−24.1421	−0.971926	−0.485963	−	0.873979i	$-0.661531\pi$
$617$	−24.1421	−0.971926	−0.485963	+	0.873979i	$0.661531\pi$
$618$	16.8284	0.676939
$619$	−20.8284	−0.837165	−0.418583	−	0.908179i	$-0.637473\pi$
$619$	−20.8284	−0.837165	−0.418583	+	0.908179i	$0.637473\pi$
$620$	4.97056	0.199623
$621$	1.41421	0.0567504
$622$	8.10051	0.324801
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	19.9706	0.798823
$626$	−3.51472	−0.140476
$627$	−0.899495	−0.0359224
$628$	−9.72792	−0.388186
$629$	3.41421	0.136134
$630$	0	0
$631$	32.6274	1.29888	0.649438	−	0.760414i	$-0.275004\pi$
$631$	32.6274	1.29888	0.649438	+	0.760414i	$0.275004\pi$
$632$	−11.6569	−0.463685
$633$	−12.9289	−0.513879
$634$	29.7990	1.18347
$635$	−4.62742	−0.183633
$636$	9.48528	0.376116
$637$	0	0
$638$	0.757359	0.0299841
$639$	−5.00000	−0.197797
$640$	0.585786	0.0231552
$641$	31.7990	1.25598	0.627992	−	0.778220i	$-0.283877\pi$
$641$	31.7990	1.25598	0.627992	+	0.778220i	$0.283877\pi$
$642$	−19.3137	−0.762251
$643$	2.51472	0.0991708	0.0495854	−	0.998770i	$-0.484210\pi$
$643$	2.51472	0.0991708	0.0495854	+	0.998770i	$0.484210\pi$
$644$	0	0
$645$	3.79899	0.149585
$646$	5.24264	0.206269
$647$	9.02944	0.354984	0.177492	−	0.984122i	$-0.443202\pi$
$647$	9.02944	0.354984	0.177492	+	0.984122i	$0.443202\pi$
$648$	1.00000	0.0392837
$649$	0.857864	0.0336741
$650$	4.65685	0.182657
$651$	0	0
$652$	−18.6569	−0.730659
$653$	22.1421	0.866489	0.433244	−	0.901276i	$-0.357369\pi$
$653$	22.1421	0.866489	0.433244	+	0.901276i	$0.357369\pi$
$654$	−9.65685	−0.377613
$655$	5.59798	0.218731
$656$	9.89949	0.386510
$657$	−1.41421	−0.0551737
$658$	0	0
$659$	10.5858	0.412364	0.206182	−	0.978514i	$-0.433896\pi$
$659$	10.5858	0.412364	0.206182	+	0.978514i	$0.433896\pi$
$660$	−0.242641	−0.00944478
$661$	−40.2426	−1.56526	−0.782629	−	0.622489i	$-0.786122\pi$
$661$	−40.2426	−1.56526	−0.782629	+	0.622489i	$0.786122\pi$
$662$	−22.4853	−0.873915
$663$	−2.41421	−0.0937603
$664$	−7.65685	−0.297144
$665$	0	0
$666$	1.41421	0.0547997
$667$	−2.58579	−0.100122
$668$	0.656854	0.0254145
$669$	7.92893	0.306550
$670$	1.07107	0.0413790
$671$	−1.82843	−0.0705856
$672$	0	0
$673$	42.1421	1.62446	0.812230	−	0.583337i	$-0.198253\pi$
$673$	42.1421	1.62446	0.812230	+	0.583337i	$0.198253\pi$
$674$	−20.3137	−0.782455
$675$	−4.65685	−0.179242
$676$	1.00000	0.0384615
$677$	−15.0000	−0.576497	−0.288248	−	0.957556i	$-0.593073\pi$
$677$	−15.0000	−0.576497	−0.288248	+	0.957556i	$0.593073\pi$
$678$	4.89949	0.188164
$679$	0	0
$680$	1.41421	0.0542326
$681$	21.1716	0.811296
$682$	−3.51472	−0.134586
$683$	−14.1421	−0.541134	−0.270567	−	0.962701i	$-0.587211\pi$
$683$	−14.1421	−0.541134	−0.270567	+	0.962701i	$0.587211\pi$
$684$	2.17157	0.0830322
$685$	6.48528	0.247790
$686$	0	0
$687$	−26.4853	−1.01048
$688$	6.48528	0.247249
$689$	−9.48528	−0.361360
$690$	0.828427	0.0315377
$691$	20.6569	0.785824	0.392912	−	0.919576i	$-0.371468\pi$
$691$	20.6569	0.785824	0.392912	+	0.919576i	$0.371468\pi$
$692$	−5.48528	−0.208519
$693$	0	0
$694$	−8.72792	−0.331307
$695$	7.65685	0.290441
$696$	−1.82843	−0.0693064
$697$	23.8995	0.905258
$698$	6.72792	0.254656
$699$	−17.7279	−0.670532
$700$	0	0
$701$	−29.1716	−1.10180	−0.550898	−	0.834573i	$-0.685715\pi$
$701$	−29.1716	−1.10180	−0.550898	+	0.834573i	$0.685715\pi$
$702$	−1.00000	−0.0377426
$703$	3.07107	0.115828
$704$	−0.414214	−0.0156113
$705$	−0.585786	−0.0220620
$706$	−12.6274	−0.475239
$707$	0	0
$708$	−2.07107	−0.0778355
$709$	−36.8701	−1.38468	−0.692342	−	0.721569i	$-0.743421\pi$
$709$	−36.8701	−1.38468	−0.692342	+	0.721569i	$0.743421\pi$
$710$	−2.92893	−0.109921
$711$	−11.6569	−0.437166
$712$	−2.58579	−0.0969064
$713$	12.0000	0.449404
$714$	0	0
$715$	0.242641	0.00907425
$716$	19.6569	0.734611
$717$	4.51472	0.168605
$718$	−0.828427	−0.0309166
$719$	−9.31371	−0.347343	−0.173671	−	0.984804i	$-0.555563\pi$
$719$	−9.31371	−0.347343	−0.173671	+	0.984804i	$0.555563\pi$
$720$	0.585786	0.0218310
$721$	0	0
$722$	−14.2843	−0.531606
$723$	2.14214	0.0796669
$724$	−2.89949	−0.107759
$725$	8.51472	0.316229
$726$	−10.8284	−0.401881
$727$	50.4264	1.87021	0.935106	−	0.354368i	$-0.115304\pi$
$727$	50.4264	1.87021	0.935106	+	0.354368i	$0.115304\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.828427	−0.0306615
$731$	15.6569	0.579090
$732$	4.41421	0.163154
$733$	28.5858	1.05584	0.527920	−	0.849294i	$-0.322972\pi$
$733$	28.5858	1.05584	0.527920	+	0.849294i	$0.322972\pi$
$734$	−12.6274	−0.466086
$735$	0	0
$736$	1.41421	0.0521286
$737$	−0.757359	−0.0278977
$738$	9.89949	0.364405
$739$	−30.0000	−1.10357	−0.551784	−	0.833987i	$-0.686053\pi$
$739$	−30.0000	−1.10357	−0.551784	+	0.833987i	$0.686053\pi$
$740$	0.828427	0.0304536
$741$	−2.17157	−0.0797747
$742$	0	0
$743$	12.1716	0.446532	0.223266	−	0.974758i	$-0.428328\pi$
$743$	12.1716	0.446532	0.223266	+	0.974758i	$0.428328\pi$
$744$	8.48528	0.311086
$745$	−2.88730	−0.105783
$746$	−5.58579	−0.204510
$747$	−7.65685	−0.280150
$748$	−1.00000	−0.0365636
$749$	0	0
$750$	−5.65685	−0.206559
$751$	−19.3137	−0.704767	−0.352384	−	0.935856i	$-0.614629\pi$
$751$	−19.3137	−0.704767	−0.352384	+	0.935856i	$0.614629\pi$
$752$	−1.00000	−0.0364662
$753$	−24.8284	−0.904798
$754$	1.82843	0.0665874
$755$	2.38478	0.0867909
$756$	0	0
$757$	−30.7574	−1.11790	−0.558948	−	0.829203i	$-0.688795\pi$
$757$	−30.7574	−1.11790	−0.558948	+	0.829203i	$0.688795\pi$
$758$	18.6274	0.676578
$759$	−0.585786	−0.0212627
$760$	1.27208	0.0461431
$761$	−43.1127	−1.56283	−0.781417	−	0.624009i	$-0.785503\pi$
$761$	−43.1127	−1.56283	−0.781417	+	0.624009i	$0.785503\pi$
$762$	−7.89949	−0.286169
$763$	0	0
$764$	−10.3431	−0.374202
$765$	1.41421	0.0511310
$766$	−11.1716	−0.403645
$767$	2.07107	0.0747819
$768$	1.00000	0.0360844
$769$	−9.89949	−0.356985	−0.178492	−	0.983941i	$-0.557122\pi$
$769$	−9.89949	−0.356985	−0.178492	+	0.983941i	$0.557122\pi$
$770$	0	0
$771$	−26.4853	−0.953844
$772$	−2.92893	−0.105415
$773$	−18.9706	−0.682324	−0.341162	−	0.940005i	$-0.610820\pi$
$773$	−18.9706	−0.682324	−0.341162	+	0.940005i	$0.610820\pi$
$774$	6.48528	0.233109
$775$	−39.5147	−1.41941
$776$	0.928932	0.0333467
$777$	0	0
$778$	−4.51472	−0.161861
$779$	21.4975	0.770227
$780$	−0.585786	−0.0209745
$781$	2.07107	0.0741086
$782$	3.41421	0.122092
$783$	−1.82843	−0.0653427
$784$	0	0
$785$	−5.69848	−0.203388
$786$	9.55635	0.340864
$787$	26.3137	0.937982	0.468991	−	0.883203i	$-0.344618\pi$
$787$	26.3137	0.937982	0.468991	+	0.883203i	$0.344618\pi$
$788$	−15.5563	−0.554172
$789$	20.5858	0.732873
$790$	−6.82843	−0.242945
$791$	0	0
$792$	−0.414214	−0.0147184
$793$	−4.41421	−0.156753
$794$	9.55635	0.339142
$795$	5.55635	0.197063
$796$	−2.72792	−0.0966886
$797$	−34.3431	−1.21650	−0.608248	−	0.793747i	$-0.708128\pi$
$797$	−34.3431	−1.21650	−0.608248	+	0.793747i	$0.708128\pi$
$798$	0	0
$799$	−2.41421	−0.0854087
$800$	−4.65685	−0.164645
$801$	−2.58579	−0.0913643
$802$	19.8995	0.702676
$803$	0.585786	0.0206720
$804$	1.82843	0.0644837
$805$	0	0
$806$	−8.48528	−0.298881
$807$	9.14214	0.321818
$808$	14.8284	0.521662
$809$	−17.5858	−0.618283	−0.309142	−	0.951016i	$-0.600042\pi$
$809$	−17.5858	−0.618283	−0.309142	+	0.951016i	$0.600042\pi$
$810$	0.585786	0.0205824
$811$	−55.4558	−1.94732	−0.973659	−	0.228009i	$-0.926778\pi$
$811$	−55.4558	−1.94732	−0.973659	+	0.228009i	$0.926778\pi$
$812$	0	0
$813$	−26.2132	−0.919337
$814$	−0.585786	−0.0205318
$815$	−10.9289	−0.382824
$816$	2.41421	0.0845144
$817$	14.0833	0.492711
$818$	−32.5858	−1.13934
$819$	0	0
$820$	5.79899	0.202510
$821$	47.8995	1.67170	0.835852	−	0.548955i	$-0.184974\pi$
$821$	47.8995	1.67170	0.835852	+	0.548955i	$0.184974\pi$
$822$	11.0711	0.386148
$823$	−43.8406	−1.52819	−0.764094	−	0.645105i	$-0.776814\pi$
$823$	−43.8406	−1.52819	−0.764094	+	0.645105i	$0.776814\pi$
$824$	16.8284	0.586246
$825$	1.92893	0.0671568
$826$	0	0
$827$	46.3553	1.61193	0.805967	−	0.591961i	$-0.201646\pi$
$827$	46.3553	1.61193	0.805967	+	0.591961i	$0.201646\pi$
$828$	1.41421	0.0491473
$829$	26.6985	0.927277	0.463638	−	0.886025i	$-0.346544\pi$
$829$	26.6985	0.927277	0.463638	+	0.886025i	$0.346544\pi$
$830$	−4.48528	−0.155686
$831$	18.0711	0.626878
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	13.0711	0.452614
$835$	0.384776	0.0133157
$836$	−0.899495	−0.0311097
$837$	8.48528	0.293294
$838$	−27.4558	−0.948446
$839$	31.8284	1.09884	0.549420	−	0.835547i	$-0.314849\pi$
$839$	31.8284	1.09884	0.549420	+	0.835547i	$0.314849\pi$
$840$	0	0
$841$	−25.6569	−0.884719
$842$	1.07107	0.0369114
$843$	0.686292	0.0236371
$844$	−12.9289	−0.445032
$845$	0.585786	0.0201517
$846$	−1.00000	−0.0343807
$847$	0	0
$848$	9.48528	0.325726
$849$	15.7574	0.540791
$850$	−11.2426	−0.385619
$851$	2.00000	0.0685591
$852$	−5.00000	−0.171297
$853$	−6.72792	−0.230360	−0.115180	−	0.993345i	$-0.536744\pi$
$853$	−6.72792	−0.230360	−0.115180	+	0.993345i	$0.536744\pi$
$854$	0	0
$855$	1.27208	0.0435041
$856$	−19.3137	−0.660129
$857$	−20.5563	−0.702192	−0.351096	−	0.936340i	$-0.614191\pi$
$857$	−20.5563	−0.702192	−0.351096	+	0.936340i	$0.614191\pi$
$858$	0.414214	0.0141410
$859$	11.7990	0.402576	0.201288	−	0.979532i	$-0.435487\pi$
$859$	11.7990	0.402576	0.201288	+	0.979532i	$0.435487\pi$
$860$	3.79899	0.129544
$861$	0	0
$862$	30.4853	1.03833
$863$	39.3137	1.33825	0.669127	−	0.743148i	$-0.266668\pi$
$863$	39.3137	1.33825	0.669127	+	0.743148i	$0.266668\pi$
$864$	1.00000	0.0340207
$865$	−3.21320	−0.109252
$866$	−29.9706	−1.01844
$867$	−11.1716	−0.379407
$868$	0	0
$869$	4.82843	0.163793
$870$	−1.07107	−0.0363126
$871$	−1.82843	−0.0619539
$872$	−9.65685	−0.327022
$873$	0.928932	0.0314396
$874$	3.07107	0.103880
$875$	0	0
$876$	−1.41421	−0.0477818
$877$	−40.0416	−1.35211	−0.676055	−	0.736851i	$-0.736312\pi$
$877$	−40.0416	−1.35211	−0.676055	+	0.736851i	$0.736312\pi$
$878$	−16.5858	−0.559743
$879$	9.89949	0.333902
$880$	−0.242641	−0.00817942
$881$	−18.4853	−0.622785	−0.311392	−	0.950281i	$-0.600795\pi$
$881$	−18.4853	−0.622785	−0.311392	+	0.950281i	$0.600795\pi$
$882$	0	0
$883$	−9.75736	−0.328361	−0.164181	−	0.986430i	$-0.552498\pi$
$883$	−9.75736	−0.328361	−0.164181	+	0.986430i	$0.552498\pi$
$884$	−2.41421	−0.0811988
$885$	−1.21320	−0.0407814
$886$	−33.6985	−1.13212
$887$	−48.9117	−1.64229	−0.821147	−	0.570717i	$-0.806665\pi$
$887$	−48.9117	−1.64229	−0.821147	+	0.570717i	$0.806665\pi$
$888$	1.41421	0.0474579
$889$	0	0
$890$	−1.51472	−0.0507735
$891$	−0.414214	−0.0138767
$892$	7.92893	0.265480
$893$	−2.17157	−0.0726689
$894$	−4.92893	−0.164848
$895$	11.5147	0.384895
$896$	0	0
$897$	−1.41421	−0.0472192
$898$	24.9706	0.833278
$899$	−15.5147	−0.517445
$900$	−4.65685	−0.155228
$901$	22.8995	0.762893
$902$	−4.10051	−0.136532
$903$	0	0
$904$	4.89949	0.162955
$905$	−1.69848	−0.0564595
$906$	4.07107	0.135252
$907$	54.3848	1.80582	0.902908	−	0.429833i	$-0.141428\pi$
$907$	54.3848	1.80582	0.902908	+	0.429833i	$0.141428\pi$
$908$	21.1716	0.702603
$909$	14.8284	0.491828
$910$	0	0
$911$	−4.34315	−0.143895	−0.0719474	−	0.997408i	$-0.522921\pi$
$911$	−4.34315	−0.143895	−0.0719474	+	0.997408i	$0.522921\pi$
$912$	2.17157	0.0719080
$913$	3.17157	0.104964
$914$	−3.07107	−0.101582
$915$	2.58579	0.0854835
$916$	−26.4853	−0.875098
$917$	0	0
$918$	2.41421	0.0796809
$919$	1.79899	0.0593432	0.0296716	−	0.999560i	$-0.490554\pi$
$919$	1.79899	0.0593432	0.0296716	+	0.999560i	$0.490554\pi$
$920$	0.828427	0.0273124
$921$	28.1127	0.926345
$922$	4.48528	0.147715
$923$	5.00000	0.164577
$924$	0	0
$925$	−6.58579	−0.216539
$926$	−20.9706	−0.689135
$927$	16.8284	0.552718
$928$	−1.82843	−0.0600211
$929$	−34.6863	−1.13802	−0.569010	−	0.822330i	$-0.692673\pi$
$929$	−34.6863	−1.13802	−0.569010	+	0.822330i	$0.692673\pi$
$930$	4.97056	0.162991
$931$	0	0
$932$	−17.7279	−0.580697
$933$	8.10051	0.265199
$934$	11.4142	0.373484
$935$	−0.585786	−0.0191573
$936$	−1.00000	−0.0326860
$937$	−42.6569	−1.39354	−0.696769	−	0.717295i	$-0.745380\pi$
$937$	−42.6569	−1.39354	−0.696769	+	0.717295i	$0.745380\pi$
$938$	0	0
$939$	−3.51472	−0.114699
$940$	−0.585786	−0.0191062
$941$	12.9706	0.422828	0.211414	−	0.977397i	$-0.432193\pi$
$941$	12.9706	0.422828	0.211414	+	0.977397i	$0.432193\pi$
$942$	−9.72792	−0.316953
$943$	14.0000	0.455903
$944$	−2.07107	−0.0674075
$945$	0	0
$946$	−2.68629	−0.0873389
$947$	8.41421	0.273425	0.136713	−	0.990611i	$-0.456346\pi$
$947$	8.41421	0.273425	0.136713	+	0.990611i	$0.456346\pi$
$948$	−11.6569	−0.378597
$949$	1.41421	0.0459073
$950$	−10.1127	−0.328099
$951$	29.7990	0.966298
$952$	0	0
$953$	−41.5858	−1.34710	−0.673548	−	0.739144i	$-0.735230\pi$
$953$	−41.5858	−1.34710	−0.673548	+	0.739144i	$0.735230\pi$
$954$	9.48528	0.307097
$955$	−6.05887	−0.196061
$956$	4.51472	0.146016
$957$	0.757359	0.0244819
$958$	32.1127	1.03751
$959$	0	0
$960$	0.585786	0.0189062
$961$	41.0000	1.32258
$962$	−1.41421	−0.0455961
$963$	−19.3137	−0.622376
$964$	2.14214	0.0689935
$965$	−1.71573	−0.0552313
$966$	0	0
$967$	−13.5858	−0.436889	−0.218445	−	0.975849i	$-0.570098\pi$
$967$	−13.5858	−0.436889	−0.218445	+	0.975849i	$0.570098\pi$
$968$	−10.8284	−0.348039
$969$	5.24264	0.168418
$970$	0.544156	0.0174718
$971$	32.5269	1.04384	0.521919	−	0.852995i	$-0.325216\pi$
$971$	32.5269	1.04384	0.521919	+	0.852995i	$0.325216\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	16.2132	0.519505
$975$	4.65685	0.149139
$976$	4.41421	0.141296
$977$	43.1716	1.38118	0.690590	−	0.723246i	$-0.257351\pi$
$977$	43.1716	1.38118	0.690590	+	0.723246i	$0.257351\pi$
$978$	−18.6569	−0.596580
$979$	1.07107	0.0342315
$980$	0	0
$981$	−9.65685	−0.308320
$982$	23.6569	0.754921
$983$	29.4853	0.940434	0.470217	−	0.882551i	$-0.344176\pi$
$983$	29.4853	0.940434	0.470217	+	0.882551i	$0.344176\pi$
$984$	9.89949	0.315584
$985$	−9.11270	−0.290355
$986$	−4.41421	−0.140577
$987$	0	0
$988$	−2.17157	−0.0690869
$989$	9.17157	0.291639
$990$	−0.242641	−0.00771163
$991$	−0.686292	−0.0218008	−0.0109004	−	0.999941i	$-0.503470\pi$
$991$	−0.686292	−0.0218008	−0.0109004	+	0.999941i	$0.503470\pi$
$992$	8.48528	0.269408
$993$	−22.4853	−0.713549
$994$	0	0
$995$	−1.59798	−0.0506594
$996$	−7.65685	−0.242617
$997$	−52.4975	−1.66261	−0.831306	−	0.555815i	$-0.812406\pi$
$997$	−52.4975	−1.66261	−0.831306	+	0.555815i	$0.812406\pi$
$998$	3.65685	0.115756
$999$	1.41421	0.0447437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bu.1.1		2
7.3	odd	6		546.2.i.i.79.1	✓	4
7.5	odd	6		546.2.i.i.235.1	yes	4
7.6	odd	2		3822.2.a.bn.1.2		2
21.5	even	6		1638.2.j.m.235.2		4
21.17	even	6		1638.2.j.m.1171.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.i.79.1	✓	4	7.3	odd	6
546.2.i.i.235.1	yes	4	7.5	odd	6
1638.2.j.m.235.2		4	21.5	even	6
1638.2.j.m.1171.2		4	21.17	even	6
3822.2.a.bn.1.2		2	7.6	odd	2
3822.2.a.bu.1.1		2	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:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.585786 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.585786 q^{10} -0.414214 q^{11} +1.00000 q^{12} -1.00000 q^{13} +0.585786 q^{15} +1.00000 q^{16} +2.41421 q^{17} +1.00000 q^{18} +2.17157 q^{19} +0.585786 q^{20} -0.414214 q^{22} +1.41421 q^{23} +1.00000 q^{24} -4.65685 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.82843 q^{29} +0.585786 q^{30} +8.48528 q^{31} +1.00000 q^{32} -0.414214 q^{33} +2.41421 q^{34} +1.00000 q^{36} +1.41421 q^{37} +2.17157 q^{38} -1.00000 q^{39} +0.585786 q^{40} +9.89949 q^{41} +6.48528 q^{43} -0.414214 q^{44} +0.585786 q^{45} +1.41421 q^{46} -1.00000 q^{47} +1.00000 q^{48} -4.65685 q^{50} +2.41421 q^{51} -1.00000 q^{52} +9.48528 q^{53} +1.00000 q^{54} -0.242641 q^{55} +2.17157 q^{57} -1.82843 q^{58} -2.07107 q^{59} +0.585786 q^{60} +4.41421 q^{61} +8.48528 q^{62} +1.00000 q^{64} -0.585786 q^{65} -0.414214 q^{66} +1.82843 q^{67} +2.41421 q^{68} +1.41421 q^{69} -5.00000 q^{71} +1.00000 q^{72} -1.41421 q^{73} +1.41421 q^{74} -4.65685 q^{75} +2.17157 q^{76} -1.00000 q^{78} -11.6569 q^{79} +0.585786 q^{80} +1.00000 q^{81} +9.89949 q^{82} -7.65685 q^{83} +1.41421 q^{85} +6.48528 q^{86} -1.82843 q^{87} -0.414214 q^{88} -2.58579 q^{89} +0.585786 q^{90} +1.41421 q^{92} +8.48528 q^{93} -1.00000 q^{94} +1.27208 q^{95} +1.00000 q^{96} +0.928932 q^{97} -0.414214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} + 4 q^{10} + 2 q^{11} + 2 q^{12} - 2 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} + 10 q^{19} + 4 q^{20} + 2 q^{22} + 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} + 2 q^{29} + 4 q^{30} + 2 q^{32} + 2 q^{33} + 2 q^{34} + 2 q^{36} + 10 q^{38} - 2 q^{39} + 4 q^{40} - 4 q^{43} + 2 q^{44} + 4 q^{45} - 2 q^{47} + 2 q^{48} + 2 q^{50} + 2 q^{51} - 2 q^{52} + 2 q^{53} + 2 q^{54} + 8 q^{55} + 10 q^{57} + 2 q^{58} + 10 q^{59} + 4 q^{60} + 6 q^{61} + 2 q^{64} - 4 q^{65} + 2 q^{66} - 2 q^{67} + 2 q^{68} - 10 q^{71} + 2 q^{72} + 2 q^{75} + 10 q^{76} - 2 q^{78} - 12 q^{79} + 4 q^{80} + 2 q^{81} - 4 q^{83} - 4 q^{86} + 2 q^{87} + 2 q^{88} - 8 q^{89} + 4 q^{90} - 2 q^{94} + 28 q^{95} + 2 q^{96} + 16 q^{97} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 + 4 * q^10 + 2 * q^11 + 2 * q^12 - 2 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 + 10 * q^19 + 4 * q^20 + 2 * q^22 + 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 + 2 * q^29 + 4 * q^30 + 2 * q^32 + 2 * q^33 + 2 * q^34 + 2 * q^36 + 10 * q^38 - 2 * q^39 + 4 * q^40 - 4 * q^43 + 2 * q^44 + 4 * q^45 - 2 * q^47 + 2 * q^48 + 2 * q^50 + 2 * q^51 - 2 * q^52 + 2 * q^53 + 2 * q^54 + 8 * q^55 + 10 * q^57 + 2 * q^58 + 10 * q^59 + 4 * q^60 + 6 * q^61 + 2 * q^64 - 4 * q^65 + 2 * q^66 - 2 * q^67 + 2 * q^68 - 10 * q^71 + 2 * q^72 + 2 * q^75 + 10 * q^76 - 2 * q^78 - 12 * q^79 + 4 * q^80 + 2 * q^81 - 4 * q^83 - 4 * q^86 + 2 * q^87 + 2 * q^88 - 8 * q^89 + 4 * q^90 - 2 * q^94 + 28 * q^95 + 2 * q^96 + 16 * q^97 + 2 * q^99

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