LMFDB - Embedded newform 4018.2.a.bj.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.11348.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + x + 2 $ x^4 - x^3 - 5*x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.589216$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.39434 q^{3} +1.00000 q^{4} -1.47439 q^{5} -3.39434 q^{6} -1.00000 q^{8} +8.52156 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.39434 q^{3} +1.00000 q^{4} -1.47439 q^{5} -3.39434 q^{6} -1.00000 q^{8} +8.52156 q^{9} +1.47439 q^{10} -2.86874 q^{11} +3.39434 q^{12} +3.17843 q^{13} -5.00460 q^{15} +1.00000 q^{16} +1.91131 q^{17} -8.52156 q^{18} +1.17843 q^{19} -1.47439 q^{20} +2.86874 q^{22} +3.17843 q^{23} -3.39434 q^{24} -2.82616 q^{25} -3.17843 q^{26} +18.7421 q^{27} +8.13586 q^{29} +5.00460 q^{30} -9.00460 q^{31} -1.00000 q^{32} -9.73747 q^{33} -1.91131 q^{34} +8.52156 q^{36} +4.78868 q^{37} -1.17843 q^{38} +10.7887 q^{39} +1.47439 q^{40} -1.00000 q^{41} -1.78409 q^{43} -2.86874 q^{44} -12.5641 q^{45} -3.17843 q^{46} -4.66147 q^{47} +3.39434 q^{48} +2.82616 q^{50} +6.48763 q^{51} +3.17843 q^{52} +14.0334 q^{53} -18.7421 q^{54} +4.22964 q^{55} +4.00000 q^{57} -8.13586 q^{58} +4.47899 q^{59} -5.00460 q^{60} +4.69490 q^{61} +9.00460 q^{62} +1.00000 q^{64} -4.68626 q^{65} +9.73747 q^{66} -1.38570 q^{67} +1.91131 q^{68} +10.7887 q^{69} +12.3954 q^{71} -8.52156 q^{72} -12.6113 q^{73} -4.78868 q^{74} -9.59297 q^{75} +1.17843 q^{76} -10.7887 q^{78} -0.478439 q^{79} -1.47439 q^{80} +38.0523 q^{81} +1.00000 q^{82} +2.30970 q^{83} -2.81802 q^{85} +1.78409 q^{86} +27.6159 q^{87} +2.86874 q^{88} -9.26712 q^{89} +12.5641 q^{90} +3.17843 q^{92} -30.5647 q^{93} +4.66147 q^{94} -1.73747 q^{95} -3.39434 q^{96} +9.95338 q^{97} -24.4461 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + q^{3} + 4 q^{4} - 3 q^{5} - q^{6} - 4 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + q^3 + 4 * q^4 - 3 * q^5 - q^6 - 4 * q^8 + 9 * q^9	$ 4 q - 4 q^{2} + q^{3} + 4 q^{4} - 3 q^{5} - q^{6} - 4 q^{8} + 9 q^{9} + 3 q^{10} + 4 q^{11} + q^{12} + 6 q^{13} + 11 q^{15} + 4 q^{16} + q^{17} - 9 q^{18} - 2 q^{19} - 3 q^{20} - 4 q^{22} + 6 q^{23} - q^{24} + 13 q^{25} - 6 q^{26} + 13 q^{27} + 17 q^{29} - 11 q^{30} - 5 q^{31} - 4 q^{32} - 8 q^{33} - q^{34} + 9 q^{36} - 6 q^{37} + 2 q^{38} + 18 q^{39} + 3 q^{40} - 4 q^{41} - 13 q^{43} + 4 q^{44} - 34 q^{45} - 6 q^{46} - 6 q^{47} + q^{48} - 13 q^{50} - 11 q^{51} + 6 q^{52} + 29 q^{53} - 13 q^{54} + 16 q^{55} + 16 q^{57} - 17 q^{58} - 16 q^{59} + 11 q^{60} - 21 q^{61} + 5 q^{62} + 4 q^{64} + 18 q^{65} + 8 q^{66} + 4 q^{67} + q^{68} + 18 q^{69} + 17 q^{71} - 9 q^{72} - 12 q^{73} + 6 q^{74} - 26 q^{75} - 2 q^{76} - 18 q^{78} - 27 q^{79} - 3 q^{80} + 40 q^{81} + 4 q^{82} + 18 q^{83} - 29 q^{85} + 13 q^{86} + 41 q^{87} - 4 q^{88} - 37 q^{89} + 34 q^{90} + 6 q^{92} - 47 q^{93} + 6 q^{94} + 24 q^{95} - q^{96} + 3 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + q^3 + 4 * q^4 - 3 * q^5 - q^6 - 4 * q^8 + 9 * q^9 + 3 * q^10 + 4 * q^11 + q^12 + 6 * q^13 + 11 * q^15 + 4 * q^16 + q^17 - 9 * q^18 - 2 * q^19 - 3 * q^20 - 4 * q^22 + 6 * q^23 - q^24 + 13 * q^25 - 6 * q^26 + 13 * q^27 + 17 * q^29 - 11 * q^30 - 5 * q^31 - 4 * q^32 - 8 * q^33 - q^34 + 9 * q^36 - 6 * q^37 + 2 * q^38 + 18 * q^39 + 3 * q^40 - 4 * q^41 - 13 * q^43 + 4 * q^44 - 34 * q^45 - 6 * q^46 - 6 * q^47 + q^48 - 13 * q^50 - 11 * q^51 + 6 * q^52 + 29 * q^53 - 13 * q^54 + 16 * q^55 + 16 * q^57 - 17 * q^58 - 16 * q^59 + 11 * q^60 - 21 * q^61 + 5 * q^62 + 4 * q^64 + 18 * q^65 + 8 * q^66 + 4 * q^67 + q^68 + 18 * q^69 + 17 * q^71 - 9 * q^72 - 12 * q^73 + 6 * q^74 - 26 * q^75 - 2 * q^76 - 18 * q^78 - 27 * q^79 - 3 * q^80 + 40 * q^81 + 4 * q^82 + 18 * q^83 - 29 * q^85 + 13 * q^86 + 41 * q^87 - 4 * q^88 - 37 * q^89 + 34 * q^90 + 6 * q^92 - 47 * q^93 + 6 * q^94 + 24 * q^95 - q^96 + 3 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	3.39434	1.95972	0.979862	−	0.199675i	$-0.0639885\pi$
$3$	3.39434	1.95972	0.979862	+	0.199675i	$0.0639885\pi$
$4$	1.00000	0.500000
$5$	−1.47439	−0.659369	−0.329684	−	0.944091i	$-0.606942\pi$
$5$	−1.47439	−0.659369	−0.329684	+	0.944091i	$0.606942\pi$
$6$	−3.39434	−1.38573
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	8.52156	2.84052
$10$	1.47439	0.466244
$11$	−2.86874	−0.864956	−0.432478	−	0.901644i	$-0.642361\pi$
$11$	−2.86874	−0.864956	−0.432478	+	0.901644i	$0.642361\pi$
$12$	3.39434	0.979862
$13$	3.17843	0.881538	0.440769	−	0.897621i	$-0.354706\pi$
$13$	3.17843	0.881538	0.440769	+	0.897621i	$0.354706\pi$
$14$	0	0
$15$	−5.00460	−1.29218
$16$	1.00000	0.250000
$17$	1.91131	0.463560	0.231780	−	0.972768i	$-0.425545\pi$
$17$	1.91131	0.463560	0.231780	+	0.972768i	$0.425545\pi$
$18$	−8.52156	−2.00855
$19$	1.17843	0.270351	0.135175	−	0.990822i	$-0.456840\pi$
$19$	1.17843	0.270351	0.135175	+	0.990822i	$0.456840\pi$
$20$	−1.47439	−0.329684
$21$	0	0
$22$	2.86874	0.611617
$23$	3.17843	0.662749	0.331374	−	0.943499i	$-0.392488\pi$
$23$	3.17843	0.662749	0.331374	+	0.943499i	$0.392488\pi$
$24$	−3.39434	−0.692867
$25$	−2.82616	−0.565233
$26$	−3.17843	−0.623342
$27$	18.7421	3.60691
$28$	0	0
$29$	8.13586	1.51079	0.755396	−	0.655269i	$-0.227445\pi$
$29$	8.13586	1.51079	0.755396	+	0.655269i	$0.227445\pi$
$30$	5.00460	0.913710
$31$	−9.00460	−1.61727	−0.808637	−	0.588308i	$-0.799794\pi$
$31$	−9.00460	−1.61727	−0.808637	+	0.588308i	$0.799794\pi$
$32$	−1.00000	−0.176777
$33$	−9.73747	−1.69508
$34$	−1.91131	−0.327786
$35$	0	0
$36$	8.52156	1.42026
$37$	4.78868	0.787255	0.393627	−	0.919270i	$-0.371220\pi$
$37$	4.78868	0.787255	0.393627	+	0.919270i	$0.371220\pi$
$38$	−1.17843	−0.191167
$39$	10.7887	1.72757
$40$	1.47439	0.233122
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−1.78409	−0.272071	−0.136036	−	0.990704i	$-0.543436\pi$
$43$	−1.78409	−0.272071	−0.136036	+	0.990704i	$0.543436\pi$
$44$	−2.86874	−0.432478
$45$	−12.5641	−1.87295
$46$	−3.17843	−0.468634
$47$	−4.66147	−0.679945	−0.339972	−	0.940435i	$-0.610418\pi$
$47$	−4.66147	−0.679945	−0.339972	+	0.940435i	$0.610418\pi$
$48$	3.39434	0.489931
$49$	0	0
$50$	2.82616	0.399680
$51$	6.48763	0.908450
$52$	3.17843	0.440769
$53$	14.0334	1.92764	0.963820	−	0.266553i	$-0.0858849\pi$
$53$	14.0334	1.92764	0.963820	+	0.266553i	$0.0858849\pi$
$54$	−18.7421	−2.55047
$55$	4.22964	0.570325
$56$	0	0
$57$	4.00000	0.529813
$58$	−8.13586	−1.06829
$59$	4.47899	0.583115	0.291557	−	0.956553i	$-0.405827\pi$
$59$	4.47899	0.583115	0.291557	+	0.956553i	$0.405827\pi$
$60$	−5.00460	−0.646091
$61$	4.69490	0.601120	0.300560	−	0.953763i	$-0.402826\pi$
$61$	4.69490	0.601120	0.300560	+	0.953763i	$0.402826\pi$
$62$	9.00460	1.14358
$63$	0	0
$64$	1.00000	0.125000
$65$	−4.68626	−0.581259
$66$	9.73747	1.19860
$67$	−1.38570	−0.169290	−0.0846451	−	0.996411i	$-0.526976\pi$
$67$	−1.38570	−0.169290	−0.0846451	+	0.996411i	$0.526976\pi$
$68$	1.91131	0.231780
$69$	10.7887	1.29881
$70$	0	0
$71$	12.3954	1.47106	0.735531	−	0.677491i	$-0.236933\pi$
$71$	12.3954	1.47106	0.735531	+	0.677491i	$0.236933\pi$
$72$	−8.52156	−1.00428
$73$	−12.6113	−1.47604	−0.738020	−	0.674778i	$-0.764239\pi$
$73$	−12.6113	−1.47604	−0.738020	+	0.674778i	$0.764239\pi$
$74$	−4.78868	−0.556673
$75$	−9.59297	−1.10770
$76$	1.17843	0.135175
$77$	0	0
$78$	−10.7887	−1.22158
$79$	−0.478439	−0.0538286	−0.0269143	−	0.999638i	$-0.508568\pi$
$79$	−0.478439	−0.0538286	−0.0269143	+	0.999638i	$0.508568\pi$
$80$	−1.47439	−0.164842
$81$	38.0523	4.22803
$82$	1.00000	0.110432
$83$	2.30970	0.253522	0.126761	−	0.991933i	$-0.459542\pi$
$83$	2.30970	0.253522	0.126761	+	0.991933i	$0.459542\pi$
$84$	0	0
$85$	−2.81802	−0.305657
$86$	1.78409	0.192383
$87$	27.6159	2.96073
$88$	2.86874	0.305808
$89$	−9.26712	−0.982313	−0.491157	−	0.871071i	$-0.663426\pi$
$89$	−9.26712	−0.982313	−0.491157	+	0.871071i	$0.663426\pi$
$90$	12.5641	1.32438
$91$	0	0
$92$	3.17843	0.331374
$93$	−30.5647	−3.16941
$94$	4.66147	0.480794
$95$	−1.73747	−0.178261
$96$	−3.39434	−0.346434
$97$	9.95338	1.01061	0.505306	−	0.862940i	$-0.331379\pi$
$97$	9.95338	1.01061	0.505306	+	0.862940i	$0.331379\pi$
$98$	0	0
$99$	−24.4461	−2.45693
$100$	−2.82616	−0.282616
$101$	−6.55904	−0.652649	−0.326324	−	0.945258i	$-0.605810\pi$
$101$	−6.55904	−0.652649	−0.326324	+	0.945258i	$0.605810\pi$
$102$	−6.48763	−0.642371
$103$	−9.25903	−0.912320	−0.456160	−	0.889898i	$-0.650775\pi$
$103$	−9.25903	−0.912320	−0.456160	+	0.889898i	$0.650775\pi$
$104$	−3.17843	−0.311671
$105$	0	0
$106$	−14.0334	−1.36305
$107$	20.2078	1.95356	0.976782	−	0.214237i	$-0.0687264\pi$
$107$	20.2078	1.95356	0.976782	+	0.214237i	$0.0687264\pi$
$108$	18.7421	1.80346
$109$	−18.4461	−1.76682	−0.883408	−	0.468604i	$-0.844757\pi$
$109$	−18.4461	−1.76682	−0.883408	+	0.468604i	$0.844757\pi$
$110$	−4.22964	−0.403281
$111$	16.2544	1.54280
$112$	0	0
$113$	2.96252	0.278690	0.139345	−	0.990244i	$-0.455500\pi$
$113$	2.96252	0.278690	0.139345	+	0.990244i	$0.455500\pi$
$114$	−4.00000	−0.374634
$115$	−4.68626	−0.436996
$116$	8.13586	0.755396
$117$	27.0852	2.50403
$118$	−4.47899	−0.412324
$119$	0	0
$120$	5.00460	0.456855
$121$	−2.77036	−0.251850
$122$	−4.69490	−0.425056
$123$	−3.39434	−0.306058
$124$	−9.00460	−0.808637
$125$	11.5388	1.03207
$126$	0	0
$127$	2.39894	0.212871	0.106436	−	0.994320i	$-0.466056\pi$
$127$	2.39894	0.212871	0.106436	+	0.994320i	$0.466056\pi$
$128$	−1.00000	−0.0883883
$129$	−6.05581	−0.533184
$130$	4.68626	0.411012
$131$	14.8359	1.29621	0.648107	−	0.761549i	$-0.275561\pi$
$131$	14.8359	1.29621	0.648107	+	0.761549i	$0.275561\pi$
$132$	−9.73747	−0.847538
$133$	0	0
$134$	1.38570	0.119706
$135$	−27.6332	−2.37829
$136$	−1.91131	−0.163893
$137$	−17.3148	−1.47931	−0.739653	−	0.672988i	$-0.765011\pi$
$137$	−17.3148	−1.47931	−0.739653	+	0.672988i	$0.765011\pi$
$138$	−10.7887	−0.918394
$139$	4.63909	0.393483	0.196741	−	0.980455i	$-0.436964\pi$
$139$	4.63909	0.393483	0.196741	+	0.980455i	$0.436964\pi$
$140$	0	0
$141$	−15.8226	−1.33250
$142$	−12.3954	−1.04020
$143$	−9.11808	−0.762492
$144$	8.52156	0.710130
$145$	−11.9955	−0.996169
$146$	12.6113	1.04372
$147$	0	0
$148$	4.78868	0.393627
$149$	17.2539	1.41350	0.706749	−	0.707464i	$-0.250161\pi$
$149$	17.2539	1.41350	0.706749	+	0.707464i	$0.250161\pi$
$150$	9.59297	0.783263
$151$	20.5070	1.66884	0.834418	−	0.551132i	$-0.185804\pi$
$151$	20.5070	1.66884	0.834418	+	0.551132i	$0.185804\pi$
$152$	−1.17843	−0.0955834
$153$	16.2873	1.31675
$154$	0	0
$155$	13.2763	1.06638
$156$	10.7887	0.863786
$157$	−1.25339	−0.100031	−0.0500157	−	0.998748i	$-0.515927\pi$
$157$	−1.25339	−0.100031	−0.0500157	+	0.998748i	$0.515927\pi$
$158$	0.478439	0.0380626
$159$	47.6343	3.77764
$160$	1.47439	0.116561
$161$	0	0
$162$	−38.0523	−2.98967
$163$	4.87383	0.381748	0.190874	−	0.981615i	$-0.438868\pi$
$163$	4.87383	0.381748	0.190874	+	0.981615i	$0.438868\pi$
$164$	−1.00000	−0.0780869
$165$	14.3569	1.11768
$166$	−2.30970	−0.179267
$167$	−20.1887	−1.56225	−0.781123	−	0.624377i	$-0.785353\pi$
$167$	−20.1887	−1.56225	−0.781123	+	0.624377i	$0.785353\pi$
$168$	0	0
$169$	−2.89757	−0.222890
$170$	2.81802	0.216132
$171$	10.0421	0.767937
$172$	−1.78409	−0.136036
$173$	1.03239	0.0784910	0.0392455	−	0.999230i	$-0.487505\pi$
$173$	1.03239	0.0784910	0.0392455	+	0.999230i	$0.487505\pi$
$174$	−27.6159	−2.09356
$175$	0	0
$176$	−2.86874	−0.216239
$177$	15.2032	1.14274
$178$	9.26712	0.694600
$179$	20.3518	1.52116	0.760581	−	0.649243i	$-0.224914\pi$
$179$	20.3518	1.52116	0.760581	+	0.649243i	$0.224914\pi$
$180$	−12.5641	−0.936475
$181$	−5.34772	−0.397493	−0.198747	−	0.980051i	$-0.563687\pi$
$181$	−5.34772	−0.397493	−0.198747	+	0.980051i	$0.563687\pi$
$182$	0	0
$183$	15.9361	1.17803
$184$	−3.17843	−0.234317
$185$	−7.06040	−0.519091
$186$	30.5647	2.24111
$187$	−5.48304	−0.400959
$188$	−4.66147	−0.339972
$189$	0	0
$190$	1.73747	0.126049
$191$	9.86824	0.714041	0.357020	−	0.934097i	$-0.383793\pi$
$191$	9.86824	0.714041	0.357020	+	0.934097i	$0.383793\pi$
$192$	3.39434	0.244966
$193$	−13.9068	−1.00103	−0.500515	−	0.865728i	$-0.666856\pi$
$193$	−13.9068	−1.00103	−0.500515	+	0.865728i	$0.666856\pi$
$194$	−9.95338	−0.714611
$195$	−15.9068	−1.13911
$196$	0	0
$197$	19.5601	1.39360	0.696799	−	0.717266i	$-0.254607\pi$
$197$	19.5601	1.39360	0.696799	+	0.717266i	$0.254607\pi$
$198$	24.4461	1.73731
$199$	13.3477	0.946195	0.473098	−	0.881010i	$-0.343136\pi$
$199$	13.3477	0.946195	0.473098	+	0.881010i	$0.343136\pi$
$200$	2.82616	0.199840
$201$	−4.70354	−0.331762
$202$	6.55904	0.461492
$203$	0	0
$204$	6.48763	0.454225
$205$	1.47439	0.102976
$206$	9.25903	0.645107
$207$	27.0852	1.88255
$208$	3.17843	0.220385
$209$	−3.38061	−0.233842
$210$	0	0
$211$	−9.21541	−0.634415	−0.317208	−	0.948356i	$-0.602745\pi$
$211$	−9.21541	−0.634415	−0.317208	+	0.948356i	$0.602745\pi$
$212$	14.0334	0.963820
$213$	42.0742	2.88288
$214$	−20.2078	−1.38138
$215$	2.63045	0.179395
$216$	−18.7421	−1.27524
$217$	0	0
$218$	18.4461	1.24933
$219$	−42.8071	−2.89263
$220$	4.22964	0.285163
$221$	6.07496	0.408646
$222$	−16.2544	−1.09093
$223$	0.0191498	0.00128236	0.000641181	−	1.00000i	$-0.499796\pi$
$223$	0.0191498	0.00128236	0.000641181		1.00000i	$0.499796\pi$
$224$	0	0
$225$	−24.0833	−1.60556
$226$	−2.96252	−0.197064
$227$	21.9955	1.45989	0.729945	−	0.683506i	$-0.239546\pi$
$227$	21.9955	1.45989	0.729945	+	0.683506i	$0.239546\pi$
$228$	4.00000	0.264906
$229$	2.38165	0.157384	0.0786921	−	0.996899i	$-0.474926\pi$
$229$	2.38165	0.157384	0.0786921	+	0.996899i	$0.474926\pi$
$230$	4.68626	0.309003
$231$	0	0
$232$	−8.13586	−0.534145
$233$	−13.8226	−0.905550	−0.452775	−	0.891625i	$-0.649566\pi$
$233$	−13.8226	−0.905550	−0.452775	+	0.891625i	$0.649566\pi$
$234$	−27.0852	−1.77061
$235$	6.87284	0.448334
$236$	4.47899	0.291557
$237$	−1.62399	−0.105489
$238$	0	0
$239$	7.12617	0.460954	0.230477	−	0.973078i	$-0.425971\pi$
$239$	7.12617	0.460954	0.230477	+	0.973078i	$0.425971\pi$
$240$	−5.00460	−0.323045
$241$	−7.21132	−0.464522	−0.232261	−	0.972654i	$-0.574612\pi$
$241$	−7.21132	−0.464522	−0.232261	+	0.972654i	$0.574612\pi$
$242$	2.77036	0.178085
$243$	72.9364	4.67887
$244$	4.69490	0.300560
$245$	0	0
$246$	3.39434	0.216415
$247$	3.74556	0.238325
$248$	9.00460	0.571792
$249$	7.83990	0.496833
$250$	−11.5388	−0.729781
$251$	−5.08110	−0.320716	−0.160358	−	0.987059i	$-0.551265\pi$
$251$	−5.08110	−0.320716	−0.160358	+	0.987059i	$0.551265\pi$
$252$	0	0
$253$	−9.11808	−0.573249
$254$	−2.39894	−0.150523
$255$	−9.56532	−0.599004
$256$	1.00000	0.0625000
$257$	−21.0240	−1.31144	−0.655720	−	0.755004i	$-0.727635\pi$
$257$	−21.0240	−1.31144	−0.655720	+	0.755004i	$0.727635\pi$
$258$	6.05581	0.377018
$259$	0	0
$260$	−4.68626	−0.290629
$261$	69.3302	4.29143
$262$	−14.8359	−0.916562
$263$	−27.4749	−1.69418	−0.847089	−	0.531451i	$-0.821647\pi$
$263$	−27.4749	−1.69418	−0.847089	+	0.531451i	$0.821647\pi$
$264$	9.73747	0.599300
$265$	−20.6908	−1.27103
$266$	0	0
$267$	−31.4558	−1.92506
$268$	−1.38570	−0.0846451
$269$	3.00515	0.183227	0.0916135	−	0.995795i	$-0.470798\pi$
$269$	3.00515	0.183227	0.0916135	+	0.995795i	$0.470798\pi$
$270$	27.6332	1.68170
$271$	14.6113	0.887573	0.443787	−	0.896132i	$-0.353635\pi$
$271$	14.6113	0.887573	0.443787	+	0.896132i	$0.353635\pi$
$272$	1.91131	0.115890
$273$	0	0
$274$	17.3148	1.04603
$275$	8.10752	0.488902
$276$	10.7887	0.649403
$277$	−21.4922	−1.29134	−0.645671	−	0.763615i	$-0.723422\pi$
$277$	−21.4922	−1.29134	−0.645671	+	0.763615i	$0.723422\pi$
$278$	−4.63909	−0.278234
$279$	−76.7332	−4.59390
$280$	0	0
$281$	−9.47494	−0.565228	−0.282614	−	0.959234i	$-0.591201\pi$
$281$	−9.47494	−0.565228	−0.282614	+	0.959234i	$0.591201\pi$
$282$	15.8226	0.942223
$283$	13.6903	0.813804	0.406902	−	0.913472i	$-0.366609\pi$
$283$	13.6903	0.813804	0.406902	+	0.913472i	$0.366609\pi$
$284$	12.3954	0.735531
$285$	−5.89757	−0.349342
$286$	9.11808	0.539163
$287$	0	0
$288$	−8.52156	−0.502138
$289$	−13.3469	−0.785112
$290$	11.9955	0.704398
$291$	33.7852	1.98052
$292$	−12.6113	−0.738020
$293$	13.3579	0.780377	0.390189	−	0.920735i	$-0.372410\pi$
$293$	13.3579	0.780377	0.390189	+	0.920735i	$0.372410\pi$
$294$	0	0
$295$	−6.60379	−0.384488
$296$	−4.78868	−0.278337
$297$	−53.7660	−3.11982
$298$	−17.2539	−0.999494
$299$	10.1024	0.584238
$300$	−9.59297	−0.553850
$301$	0	0
$302$	−20.5070	−1.18005
$303$	−22.2636	−1.27901
$304$	1.17843	0.0675877
$305$	−6.92213	−0.396360
$306$	−16.2873	−0.931084
$307$	−11.1733	−0.637696	−0.318848	−	0.947806i	$-0.603296\pi$
$307$	−11.1733	−0.637696	−0.318848	+	0.947806i	$0.603296\pi$
$308$	0	0
$309$	−31.4283	−1.78789
$310$	−13.2763	−0.754044
$311$	−29.4593	−1.67049	−0.835243	−	0.549881i	$-0.814673\pi$
$311$	−29.4593	−1.67049	−0.835243	+	0.549881i	$0.814673\pi$
$312$	−10.7887	−0.610789
$313$	−31.4421	−1.77721	−0.888605	−	0.458673i	$-0.848325\pi$
$313$	−31.4421	−1.77721	−0.888605	+	0.458673i	$0.848325\pi$
$314$	1.25339	0.0707329
$315$	0	0
$316$	−0.478439	−0.0269143
$317$	−5.89248	−0.330955	−0.165477	−	0.986214i	$-0.552916\pi$
$317$	−5.89248	−0.330955	−0.165477	+	0.986214i	$0.552916\pi$
$318$	−47.6343	−2.67120
$319$	−23.3396	−1.30677
$320$	−1.47439	−0.0824211
$321$	68.5923	3.82845
$322$	0	0
$323$	2.25234	0.125324
$324$	38.0523	2.11402
$325$	−8.98277	−0.498274
$326$	−4.87383	−0.269936
$327$	−62.6124	−3.46247
$328$	1.00000	0.0552158
$329$	0	0
$330$	−14.3569	−0.790319
$331$	32.5232	1.78763	0.893817	−	0.448432i	$-0.148017\pi$
$331$	32.5232	1.78763	0.893817	+	0.448432i	$0.148017\pi$
$332$	2.30970	0.126761
$333$	40.8071	2.23621
$334$	20.1887	1.10467
$335$	2.04307	0.111625
$336$	0	0
$337$	20.0558	1.09251	0.546255	−	0.837619i	$-0.316053\pi$
$337$	20.0558	1.09251	0.546255	+	0.837619i	$0.316053\pi$
$338$	2.89757	0.157607
$339$	10.0558	0.546157
$340$	−2.81802	−0.152829
$341$	25.8318	1.39887
$342$	−10.0421	−0.543013
$343$	0	0
$344$	1.78409	0.0961916
$345$	−15.9068	−0.856391
$346$	−1.03239	−0.0555015
$347$	−11.9210	−0.639955	−0.319978	−	0.947425i	$-0.603675\pi$
$347$	−11.9210	−0.639955	−0.319978	+	0.947425i	$0.603675\pi$
$348$	27.6159	1.48037
$349$	−9.87688	−0.528697	−0.264349	−	0.964427i	$-0.585157\pi$
$349$	−9.87688	−0.528697	−0.264349	+	0.964427i	$0.585157\pi$
$350$	0	0
$351$	59.5704	3.17963
$352$	2.86874	0.152904
$353$	−15.1283	−0.805196	−0.402598	−	0.915377i	$-0.631893\pi$
$353$	−15.1283	−0.805196	−0.402598	+	0.915377i	$0.631893\pi$
$354$	−15.2032	−0.808042
$355$	−18.2757	−0.969972
$356$	−9.26712	−0.491157
$357$	0	0
$358$	−20.3518	−1.07562
$359$	1.32293	0.0698218	0.0349109	−	0.999390i	$-0.488885\pi$
$359$	1.32293	0.0698218	0.0349109	+	0.999390i	$0.488885\pi$
$360$	12.5641	0.662188
$361$	−17.6113	−0.926910
$362$	5.34772	0.281070
$363$	−9.40353	−0.493558
$364$	0	0
$365$	18.5940	0.973255
$366$	−15.9361	−0.832993
$367$	−6.31025	−0.329392	−0.164696	−	0.986344i	$-0.552664\pi$
$367$	−6.31025	−0.329392	−0.164696	+	0.986344i	$0.552664\pi$
$368$	3.17843	0.165687
$369$	−8.52156	−0.443615
$370$	7.06040	0.367053
$371$	0	0
$372$	−30.5647	−1.58470
$373$	−17.5024	−0.906240	−0.453120	−	0.891449i	$-0.649689\pi$
$373$	−17.5024	−0.906240	−0.453120	+	0.891449i	$0.649689\pi$
$374$	5.48304	0.283521
$375$	39.1668	2.02256
$376$	4.66147	0.240397
$377$	25.8593	1.33182
$378$	0	0
$379$	−36.6013	−1.88008	−0.940042	−	0.341058i	$-0.889215\pi$
$379$	−36.6013	−1.88008	−0.940042	+	0.341058i	$0.889215\pi$
$380$	−1.73747	−0.0891304
$381$	8.14282	0.417169
$382$	−9.86824	−0.504903
$383$	4.00000	0.204390	0.102195	−	0.994764i	$-0.467413\pi$
$383$	4.00000	0.204390	0.102195	+	0.994764i	$0.467413\pi$
$384$	−3.39434	−0.173217
$385$	0	0
$386$	13.9068	0.707836
$387$	−15.2032	−0.772823
$388$	9.95338	0.505306
$389$	−13.9068	−0.705101	−0.352550	−	0.935793i	$-0.614686\pi$
$389$	−13.9068	−0.705101	−0.352550	+	0.935793i	$0.614686\pi$
$390$	15.9068	0.805470
$391$	6.07496	0.307224
$392$	0	0
$393$	50.3580	2.54022
$394$	−19.5601	−0.985423
$395$	0.705408	0.0354929
$396$	−24.4461	−1.22846
$397$	−13.6296	−0.684051	−0.342026	−	0.939691i	$-0.611113\pi$
$397$	−13.6296	−0.684051	−0.342026	+	0.939691i	$0.611113\pi$
$398$	−13.3477	−0.669061
$399$	0	0
$400$	−2.82616	−0.141308
$401$	−29.9124	−1.49375	−0.746877	−	0.664962i	$-0.768448\pi$
$401$	−29.9124	−1.49375	−0.746877	+	0.664962i	$0.768448\pi$
$402$	4.70354	0.234591
$403$	−28.6205	−1.42569
$404$	−6.55904	−0.326324
$405$	−56.1041	−2.78783
$406$	0	0
$407$	−13.7375	−0.680941
$408$	−6.48763	−0.321186
$409$	6.36605	0.314781	0.157391	−	0.987536i	$-0.449692\pi$
$409$	6.36605	0.314781	0.157391	+	0.987536i	$0.449692\pi$
$410$	−1.47439	−0.0728151
$411$	−58.7725	−2.89903
$412$	−9.25903	−0.456160
$413$	0	0
$414$	−27.0852	−1.33116
$415$	−3.40540	−0.167165
$416$	−3.17843	−0.155835
$417$	15.7467	0.771117
$418$	3.38061	0.165351
$419$	−29.0822	−1.42076	−0.710379	−	0.703819i	$-0.751477\pi$
$419$	−29.0822	−1.42076	−0.710379	+	0.703819i	$0.751477\pi$
$420$	0	0
$421$	21.5257	1.04910	0.524548	−	0.851381i	$-0.324234\pi$
$421$	21.5257	1.04910	0.524548	+	0.851381i	$0.324234\pi$
$422$	9.21541	0.448599
$423$	−39.7230	−1.93140
$424$	−14.0334	−0.681524
$425$	−5.40167	−0.262019
$426$	−42.0742	−2.03850
$427$	0	0
$428$	20.2078	0.976782
$429$	−30.9499	−1.49427
$430$	−2.63045	−0.126852
$431$	23.7148	1.14230	0.571150	−	0.820846i	$-0.306497\pi$
$431$	23.7148	1.14230	0.571150	+	0.820846i	$0.306497\pi$
$432$	18.7421	0.901728
$433$	20.9499	1.00679	0.503394	−	0.864057i	$-0.332085\pi$
$433$	20.9499	1.00679	0.503394	+	0.864057i	$0.332085\pi$
$434$	0	0
$435$	−40.7167	−1.95222
$436$	−18.4461	−0.883408
$437$	3.74556	0.179175
$438$	42.8071	2.04540
$439$	7.97521	0.380636	0.190318	−	0.981723i	$-0.439048\pi$
$439$	7.97521	0.380636	0.190318	+	0.981723i	$0.439048\pi$
$440$	−4.22964	−0.201640
$441$	0	0
$442$	−6.07496	−0.288956
$443$	−26.9022	−1.27816	−0.639080	−	0.769140i	$-0.720685\pi$
$443$	−26.9022	−1.27816	−0.639080	+	0.769140i	$0.720685\pi$
$444$	16.2544	0.771401
$445$	13.6634	0.647707
$446$	−0.0191498	−0.000906767 0
$447$	58.5658	2.77007
$448$	0	0
$449$	−23.1760	−1.09374	−0.546871	−	0.837217i	$-0.684181\pi$
$449$	−23.1760	−1.09374	−0.546871	+	0.837217i	$0.684181\pi$
$450$	24.0833	1.13530
$451$	2.86874	0.135083
$452$	2.96252	0.139345
$453$	69.6078	3.27046
$454$	−21.9955	−1.03230
$455$	0	0
$456$	−4.00000	−0.187317
$457$	26.9478	1.26056	0.630282	−	0.776366i	$-0.282939\pi$
$457$	26.9478	1.26056	0.630282	+	0.776366i	$0.282939\pi$
$458$	−2.38165	−0.111287
$459$	35.8218	1.67202
$460$	−4.68626	−0.218498
$461$	12.7122	0.592065	0.296033	−	0.955178i	$-0.404336\pi$
$461$	12.7122	0.592065	0.296033	+	0.955178i	$0.404336\pi$
$462$	0	0
$463$	31.8685	1.48105	0.740527	−	0.672027i	$-0.234576\pi$
$463$	31.8685	1.48105	0.740527	+	0.672027i	$0.234576\pi$
$464$	8.13586	0.377698
$465$	45.0644	2.08981
$466$	13.8226	0.640320
$467$	−16.4963	−0.763356	−0.381678	−	0.924295i	$-0.624654\pi$
$467$	−16.4963	−0.763356	−0.381678	+	0.924295i	$0.624654\pi$
$468$	27.0852	1.25201
$469$	0	0
$470$	−6.87284	−0.317020
$471$	−4.25444	−0.196034
$472$	−4.47899	−0.206162
$473$	5.11808	0.235330
$474$	1.62399	0.0745922
$475$	−3.33044	−0.152811
$476$	0	0
$477$	119.587	5.47550
$478$	−7.12617	−0.325944
$479$	33.0001	1.50781	0.753905	−	0.656983i	$-0.228168\pi$
$479$	33.0001	1.50781	0.753905	+	0.656983i	$0.228168\pi$
$480$	5.00460	0.228428
$481$	15.2205	0.693995
$482$	7.21132	0.328466
$483$	0	0
$484$	−2.77036	−0.125925
$485$	−14.6752	−0.666367
$486$	−72.9364	−3.30846
$487$	23.4475	1.06251	0.531253	−	0.847213i	$-0.321721\pi$
$487$	23.4475	1.06251	0.531253	+	0.847213i	$0.321721\pi$
$488$	−4.69490	−0.212528
$489$	16.5434	0.748120
$490$	0	0
$491$	−10.4046	−0.469552	−0.234776	−	0.972049i	$-0.575436\pi$
$491$	−10.4046	−0.469552	−0.234776	+	0.972049i	$0.575436\pi$
$492$	−3.39434	−0.153029
$493$	15.5501	0.700343
$494$	−3.74556	−0.168521
$495$	36.0432	1.62002
$496$	−9.00460	−0.404318
$497$	0	0
$498$	−7.83990	−0.351314
$499$	3.20622	0.143530	0.0717651	−	0.997422i	$-0.477137\pi$
$499$	3.20622	0.143530	0.0717651	+	0.997422i	$0.477137\pi$
$500$	11.5388	0.516033
$501$	−68.5273	−3.06157
$502$	5.08110	0.226780
$503$	4.75203	0.211882	0.105941	−	0.994372i	$-0.466214\pi$
$503$	4.75203	0.211882	0.105941	+	0.994372i	$0.466214\pi$
$504$	0	0
$505$	9.67060	0.430336
$506$	9.11808	0.405348
$507$	−9.83536	−0.436803
$508$	2.39894	0.106436
$509$	−35.2566	−1.56272	−0.781360	−	0.624080i	$-0.785474\pi$
$509$	−35.2566	−1.56272	−0.781360	+	0.624080i	$0.785474\pi$
$510$	9.56532	0.423559
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	22.0862	0.975131
$514$	21.0240	0.927328
$515$	13.6515	0.601555
$516$	−6.05581	−0.266592
$517$	13.3725	0.588123
$518$	0	0
$519$	3.50428	0.153821
$520$	4.68626	0.205506
$521$	7.61235	0.333503	0.166751	−	0.985999i	$-0.446672\pi$
$521$	7.61235	0.333503	0.166751	+	0.985999i	$0.446672\pi$
$522$	−69.3302	−3.03450
$523$	−37.7857	−1.65225	−0.826127	−	0.563483i	$-0.809461\pi$
$523$	−37.7857	−1.65225	−0.826127	+	0.563483i	$0.809461\pi$
$524$	14.8359	0.648107
$525$	0	0
$526$	27.4749	1.19796
$527$	−17.2105	−0.749703
$528$	−9.73747	−0.423769
$529$	−12.8976	−0.560764
$530$	20.6908	0.898751
$531$	38.1680	1.65635
$532$	0	0
$533$	−3.17843	−0.137673
$534$	31.4558	1.36123
$535$	−29.7943	−1.28812
$536$	1.38570	0.0598531
$537$	69.0809	2.98106
$538$	−3.00515	−0.129561
$539$	0	0
$540$	−27.6332	−1.18914
$541$	23.6544	1.01698	0.508491	−	0.861067i	$-0.330203\pi$
$541$	23.6544	1.01698	0.508491	+	0.861067i	$0.330203\pi$
$542$	−14.6113	−0.627609
$543$	−18.1520	−0.778977
$544$	−1.91131	−0.0819466
$545$	27.1968	1.16498
$546$	0	0
$547$	−8.28600	−0.354284	−0.177142	−	0.984185i	$-0.556685\pi$
$547$	−8.28600	−0.354284	−0.177142	+	0.984185i	$0.556685\pi$
$548$	−17.3148	−0.739653
$549$	40.0079	1.70749
$550$	−8.10752	−0.345706
$551$	9.58755	0.408444
$552$	−10.7887	−0.459197
$553$	0	0
$554$	21.4922	0.913117
$555$	−23.9654	−1.01728
$556$	4.63909	0.196741
$557$	12.3730	0.524261	0.262131	−	0.965032i	$-0.415575\pi$
$557$	12.3730	0.524261	0.262131	+	0.965032i	$0.415575\pi$
$558$	76.7332	3.24838
$559$	−5.67060	−0.239841
$560$	0	0
$561$	−18.6113	−0.785770
$562$	9.47494	0.399676
$563$	11.5353	0.486155	0.243077	−	0.970007i	$-0.421843\pi$
$563$	11.5353	0.486155	0.243077	+	0.970007i	$0.421843\pi$
$564$	−15.8226	−0.666252
$565$	−4.36792	−0.183760
$566$	−13.6903	−0.575446
$567$	0	0
$568$	−12.3954	−0.520099
$569$	−3.97608	−0.166686	−0.0833430	−	0.996521i	$-0.526560\pi$
$569$	−3.97608	−0.166686	−0.0833430	+	0.996521i	$0.526560\pi$
$570$	5.89757	0.247022
$571$	−33.5815	−1.40534	−0.702670	−	0.711516i	$-0.748009\pi$
$571$	−33.5815	−1.40534	−0.702670	+	0.711516i	$0.748009\pi$
$572$	−9.11808	−0.381246
$573$	33.4962	1.39932
$574$	0	0
$575$	−8.98277	−0.374607
$576$	8.52156	0.355065
$577$	15.9013	0.661982	0.330991	−	0.943634i	$-0.392617\pi$
$577$	15.9013	0.661982	0.330991	+	0.943634i	$0.392617\pi$
$578$	13.3469	0.555158
$579$	−47.2043	−1.96174
$580$	−11.9955	−0.498084
$581$	0	0
$582$	−33.7852	−1.40044
$583$	−40.2582	−1.66732
$584$	12.6113	0.521859
$585$	−39.9342	−1.65108
$586$	−13.3579	−0.551810
$587$	−8.25799	−0.340844	−0.170422	−	0.985371i	$-0.554513\pi$
$587$	−8.25799	−0.340844	−0.170422	+	0.985371i	$0.554513\pi$
$588$	0	0
$589$	−10.6113	−0.437231
$590$	6.60379	0.271874
$591$	66.3936	2.73107
$592$	4.78868	0.196814
$593$	−33.6828	−1.38319	−0.691593	−	0.722288i	$-0.743091\pi$
$593$	−33.6828	−1.38319	−0.691593	+	0.722288i	$0.743091\pi$
$594$	53.7660	2.20605
$595$	0	0
$596$	17.2539	0.706749
$597$	45.3067	1.85428
$598$	−10.1024	−0.413119
$599$	−29.0798	−1.18817	−0.594084	−	0.804403i	$-0.702485\pi$
$599$	−29.0798	−1.18817	−0.594084	+	0.804403i	$0.702485\pi$
$600$	9.59297	0.391631
$601$	−30.8866	−1.25989	−0.629945	−	0.776640i	$-0.716922\pi$
$601$	−30.8866	−1.25989	−0.629945	+	0.776640i	$0.716922\pi$
$602$	0	0
$603$	−11.8083	−0.480872
$604$	20.5070	0.834418
$605$	4.08459	0.166062
$606$	22.2636	0.904398
$607$	−32.7787	−1.33045	−0.665224	−	0.746644i	$-0.731664\pi$
$607$	−32.7787	−1.33045	−0.665224	+	0.746644i	$0.731664\pi$
$608$	−1.17843	−0.0477917
$609$	0	0
$610$	6.92213	0.280269
$611$	−14.8162	−0.599397
$612$	16.2873	0.658376
$613$	20.8173	0.840801	0.420400	−	0.907339i	$-0.361890\pi$
$613$	20.8173	0.840801	0.420400	+	0.907339i	$0.361890\pi$
$614$	11.1733	0.450919
$615$	5.00460	0.201805
$616$	0	0
$617$	0.277136	0.0111571	0.00557854	−	0.999984i	$-0.498224\pi$
$617$	0.277136	0.0111571	0.00557854	+	0.999984i	$0.498224\pi$
$618$	31.4283	1.26423
$619$	−17.3253	−0.696365	−0.348182	−	0.937427i	$-0.613201\pi$
$619$	−17.3253	−0.696365	−0.348182	+	0.937427i	$0.613201\pi$
$620$	13.2763	0.533190
$621$	59.5704	2.39048
$622$	29.4593	1.18121
$623$	0	0
$624$	10.7887	0.431893
$625$	−2.88197	−0.115279
$626$	31.4421	1.25668
$627$	−11.4749	−0.458265
$628$	−1.25339	−0.0500157
$629$	9.15265	0.364940
$630$	0	0
$631$	17.8555	0.710816	0.355408	−	0.934711i	$-0.384342\pi$
$631$	17.8555	0.710816	0.355408	+	0.934711i	$0.384342\pi$
$632$	0.478439	0.0190313
$633$	−31.2803	−1.24328
$634$	5.89248	0.234020
$635$	−3.53698	−0.140361
$636$	47.6343	1.88882
$637$	0	0
$638$	23.3396	0.924025
$639$	105.628	4.17858
$640$	1.47439	0.0582805
$641$	7.98172	0.315259	0.157630	−	0.987498i	$-0.449615\pi$
$641$	7.98172	0.315259	0.157630	+	0.987498i	$0.449615\pi$
$642$	−68.5923	−2.70712
$643$	−38.2224	−1.50735	−0.753673	−	0.657250i	$-0.771720\pi$
$643$	−38.2224	−1.50735	−0.753673	+	0.657250i	$0.771720\pi$
$644$	0	0
$645$	8.92864	0.351565
$646$	−2.25234	−0.0886173
$647$	−13.7841	−0.541908	−0.270954	−	0.962592i	$-0.587339\pi$
$647$	−13.7841	−0.541908	−0.270954	+	0.962592i	$0.587339\pi$
$648$	−38.0523	−1.49484
$649$	−12.8490	−0.504369
$650$	8.98277	0.352333
$651$	0	0
$652$	4.87383	0.190874
$653$	13.3585	0.522757	0.261378	−	0.965236i	$-0.415823\pi$
$653$	13.3585	0.522757	0.261378	+	0.965236i	$0.415823\pi$
$654$	62.6124	2.44834
$655$	−21.8739	−0.854683
$656$	−1.00000	−0.0390434
$657$	−107.468	−4.19272
$658$	0	0
$659$	29.9464	1.16655	0.583274	−	0.812276i	$-0.301772\pi$
$659$	29.9464	1.16655	0.583274	+	0.812276i	$0.301772\pi$
$660$	14.3569	0.558840
$661$	8.48818	0.330152	0.165076	−	0.986281i	$-0.447213\pi$
$661$	8.48818	0.330152	0.165076	+	0.986281i	$0.447213\pi$
$662$	−32.5232	−1.26405
$663$	20.6205	0.800834
$664$	−2.30970	−0.0896336
$665$	0	0
$666$	−40.8071	−1.58124
$667$	25.8593	1.00128
$668$	−20.1887	−0.781123
$669$	0.0650008	0.00251308
$670$	−2.04307	−0.0789306
$671$	−13.4684	−0.519943
$672$	0	0
$673$	−3.40598	−0.131291	−0.0656455	−	0.997843i	$-0.520911\pi$
$673$	−3.40598	−0.131291	−0.0656455	+	0.997843i	$0.520911\pi$
$674$	−20.0558	−0.772521
$675$	−52.9682	−2.03875
$676$	−2.89757	−0.111445
$677$	17.7480	0.682110	0.341055	−	0.940043i	$-0.389216\pi$
$677$	17.7480	0.682110	0.341055	+	0.940043i	$0.389216\pi$
$678$	−10.0558	−0.386191
$679$	0	0
$680$	2.81802	0.108066
$681$	74.6601	2.86098
$682$	−25.8318	−0.989151
$683$	−30.4828	−1.16639	−0.583195	−	0.812332i	$-0.698198\pi$
$683$	−30.4828	−1.16639	−0.583195	+	0.812332i	$0.698198\pi$
$684$	10.0421	0.383968
$685$	25.5289	0.975409
$686$	0	0
$687$	8.08415	0.308430
$688$	−1.78409	−0.0680178
$689$	44.6043	1.69929
$690$	15.9068	0.605560
$691$	43.0580	1.63800	0.819001	−	0.573792i	$-0.194528\pi$
$691$	43.0580	1.63800	0.819001	+	0.573792i	$0.194528\pi$
$692$	1.03239	0.0392455
$693$	0	0
$694$	11.9210	0.452517
$695$	−6.83984	−0.259450
$696$	−27.6159	−1.04678
$697$	−1.91131	−0.0723959
$698$	9.87688	0.373845
$699$	−46.9187	−1.77463
$700$	0	0
$701$	−2.14992	−0.0812013	−0.0406006	−	0.999175i	$-0.512927\pi$
$701$	−2.14992	−0.0812013	−0.0406006	+	0.999175i	$0.512927\pi$
$702$	−59.5704	−2.24834
$703$	5.64314	0.212835
$704$	−2.86874	−0.108120
$705$	23.3288	0.878612
$706$	15.1283	0.569360
$707$	0	0
$708$	15.2032	0.571372
$709$	0.355729	0.0133597	0.00667983	−	0.999978i	$-0.497874\pi$
$709$	0.355729	0.0133597	0.00667983	+	0.999978i	$0.497874\pi$
$710$	18.2757	0.685874
$711$	−4.07705	−0.152901
$712$	9.26712	0.347300
$713$	−28.6205	−1.07185
$714$	0	0
$715$	13.4436	0.502763
$716$	20.3518	0.760581
$717$	24.1887	0.903342
$718$	−1.32293	−0.0493714
$719$	−24.6205	−0.918189	−0.459095	−	0.888387i	$-0.651826\pi$
$719$	−24.6205	−0.918189	−0.459095	+	0.888387i	$0.651826\pi$
$720$	−12.5641	−0.468238
$721$	0	0
$722$	17.6113	0.655425
$723$	−24.4777	−0.910334
$724$	−5.34772	−0.198747
$725$	−22.9933	−0.853949
$726$	9.40353	0.348998
$727$	33.2226	1.23216	0.616079	−	0.787684i	$-0.288720\pi$
$727$	33.2226	1.23216	0.616079	+	0.787684i	$0.288720\pi$
$728$	0	0
$729$	133.414	4.94126
$730$	−18.5940	−0.688195
$731$	−3.40994	−0.126121
$732$	15.9361	0.589015
$733$	−12.5623	−0.463998	−0.231999	−	0.972716i	$-0.574527\pi$
$733$	−12.5623	−0.463998	−0.231999	+	0.972716i	$0.574527\pi$
$734$	6.31025	0.232915
$735$	0	0
$736$	−3.17843	−0.117159
$737$	3.97521	0.146429
$738$	8.52156	0.313683
$739$	10.0456	0.369534	0.184767	−	0.982782i	$-0.440847\pi$
$739$	10.0456	0.369534	0.184767	+	0.982782i	$0.440847\pi$
$740$	−7.06040	−0.259546
$741$	12.7137	0.467050
$742$	0	0
$743$	43.7568	1.60528	0.802642	−	0.596462i	$-0.203427\pi$
$743$	43.7568	1.60528	0.802642	+	0.596462i	$0.203427\pi$
$744$	30.5647	1.12056
$745$	−25.4391	−0.932016
$746$	17.5024	0.640809
$747$	19.6822	0.720134
$748$	−5.48304	−0.200480
$749$	0	0
$750$	−39.1668	−1.43017
$751$	−16.6032	−0.605860	−0.302930	−	0.953013i	$-0.597965\pi$
$751$	−16.6032	−0.605860	−0.302930	+	0.953013i	$0.597965\pi$
$752$	−4.66147	−0.169986
$753$	−17.2470	−0.628515
$754$	−25.8593	−0.941739
$755$	−30.2354	−1.10038
$756$	0	0
$757$	35.2906	1.28266	0.641329	−	0.767266i	$-0.278383\pi$
$757$	35.2906	1.28266	0.641329	+	0.767266i	$0.278383\pi$
$758$	36.6013	1.32942
$759$	−30.9499	−1.12341
$760$	1.73747	0.0630247
$761$	−18.8738	−0.684176	−0.342088	−	0.939668i	$-0.611134\pi$
$761$	−18.8738	−0.684176	−0.342088	+	0.939668i	$0.611134\pi$
$762$	−8.14282	−0.294983
$763$	0	0
$764$	9.86824	0.357020
$765$	−24.0139	−0.868225
$766$	−4.00000	−0.144526
$767$	14.2362	0.514038
$768$	3.39434	0.122483
$769$	−46.8081	−1.68794	−0.843971	−	0.536389i	$-0.819788\pi$
$769$	−46.8081	−1.68794	−0.843971	+	0.536389i	$0.819788\pi$
$770$	0	0
$771$	−71.3626	−2.57006
$772$	−13.9068	−0.500515
$773$	15.3671	0.552716	0.276358	−	0.961055i	$-0.410872\pi$
$773$	15.3671	0.552716	0.276358	+	0.961055i	$0.410872\pi$
$774$	15.2032	0.546469
$775$	25.4485	0.914136
$776$	−9.95338	−0.357306
$777$	0	0
$778$	13.9068	0.498582
$779$	−1.17843	−0.0422217
$780$	−15.9068	−0.569554
$781$	−35.5591	−1.27240
$782$	−6.07496	−0.217240
$783$	152.483	5.44929
$784$	0	0
$785$	1.84799	0.0659576
$786$	−50.3580	−1.79621
$787$	42.8471	1.52734	0.763668	−	0.645609i	$-0.223397\pi$
$787$	42.8471	1.52734	0.763668	+	0.645609i	$0.223397\pi$
$788$	19.5601	0.696799
$789$	−93.2594	−3.32012
$790$	−0.705408	−0.0250973
$791$	0	0
$792$	24.4461	0.868655
$793$	14.9224	0.529911
$794$	13.6296	0.483697
$795$	−70.2317	−2.49086
$796$	13.3477	0.473098
$797$	−44.6464	−1.58146	−0.790729	−	0.612167i	$-0.790298\pi$
$797$	−44.6464	−1.58146	−0.790729	+	0.612167i	$0.790298\pi$
$798$	0	0
$799$	−8.90949	−0.315195
$800$	2.82616	0.0999200
$801$	−78.9704	−2.79028
$802$	29.9124	1.05624
$803$	36.1785	1.27671
$804$	−4.70354	−0.165881
$805$	0	0
$806$	28.6205	1.00811
$807$	10.2005	0.359074
$808$	6.55904	0.230746
$809$	−14.6367	−0.514598	−0.257299	−	0.966332i	$-0.582833\pi$
$809$	−14.6367	−0.514598	−0.257299	+	0.966332i	$0.582833\pi$
$810$	56.1041	1.97130
$811$	−2.02779	−0.0712054	−0.0356027	−	0.999366i	$-0.511335\pi$
$811$	−2.02779	−0.0712054	−0.0356027	+	0.999366i	$0.511335\pi$
$812$	0	0
$813$	49.5958	1.73940
$814$	13.7375	0.481498
$815$	−7.18594	−0.251712
$816$	6.48763	0.227113
$817$	−2.10243	−0.0735546
$818$	−6.36605	−0.222584
$819$	0	0
$820$	1.47439	0.0514880
$821$	−47.8329	−1.66938	−0.834690	−	0.550720i	$-0.814353\pi$
$821$	−47.8329	−1.66938	−0.834690	+	0.550720i	$0.814353\pi$
$822$	58.7725	2.04993
$823$	25.1933	0.878182	0.439091	−	0.898443i	$-0.355301\pi$
$823$	25.1933	0.878182	0.439091	+	0.898443i	$0.355301\pi$
$824$	9.25903	0.322554
$825$	27.5197	0.958113
$826$	0	0
$827$	3.22659	0.112200	0.0560998	−	0.998425i	$-0.482134\pi$
$827$	3.22659	0.112200	0.0560998	+	0.998425i	$0.482134\pi$
$828$	27.0852	0.941276
$829$	26.8642	0.933032	0.466516	−	0.884513i	$-0.345509\pi$
$829$	26.8642	0.933032	0.466516	+	0.884513i	$0.345509\pi$
$830$	3.40540	0.118203
$831$	−72.9520	−2.53068
$832$	3.17843	0.110192
$833$	0	0
$834$	−15.7467	−0.545262
$835$	29.7660	1.03010
$836$	−3.38061	−0.116921
$837$	−168.765	−5.83336
$838$	29.0822	1.00463
$839$	38.0453	1.31347	0.656734	−	0.754122i	$-0.271937\pi$
$839$	38.0453	1.31347	0.656734	+	0.754122i	$0.271937\pi$
$840$	0	0
$841$	37.1922	1.28249
$842$	−21.5257	−0.741823
$843$	−32.1612	−1.10769
$844$	−9.21541	−0.317208
$845$	4.27216	0.146967
$846$	39.7230	1.36570
$847$	0	0
$848$	14.0334	0.481910
$849$	46.4696	1.59483
$850$	5.40167	0.185276
$851$	15.2205	0.521752
$852$	42.0742	1.44144
$853$	15.4734	0.529799	0.264900	−	0.964276i	$-0.414661\pi$
$853$	15.4734	0.529799	0.264900	+	0.964276i	$0.414661\pi$
$854$	0	0
$855$	−14.8060	−0.506353
$856$	−20.2078	−0.690689
$857$	−54.7159	−1.86906	−0.934530	−	0.355884i	$-0.884180\pi$
$857$	−54.7159	−1.86906	−0.934530	+	0.355884i	$0.884180\pi$
$858$	30.9499	1.05661
$859$	−16.6181	−0.567001	−0.283501	−	0.958972i	$-0.591496\pi$
$859$	−16.6181	−0.567001	−0.283501	+	0.958972i	$0.591496\pi$
$860$	2.63045	0.0896976
$861$	0	0
$862$	−23.7148	−0.807728
$863$	−38.8071	−1.32101	−0.660504	−	0.750823i	$-0.729657\pi$
$863$	−38.8071	−1.32101	−0.660504	+	0.750823i	$0.729657\pi$
$864$	−18.7421	−0.637618
$865$	−1.52215	−0.0517545
$866$	−20.9499	−0.711906
$867$	−45.3040	−1.53860
$868$	0	0
$869$	1.37252	0.0465594
$870$	40.7167	1.38043
$871$	−4.40435	−0.149236
$872$	18.4461	0.624664
$873$	84.8184	2.87067
$874$	−3.74556	−0.126696
$875$	0	0
$876$	−42.8071	−1.44632
$877$	25.6971	0.867729	0.433864	−	0.900978i	$-0.357150\pi$
$877$	25.6971	0.867729	0.433864	+	0.900978i	$0.357150\pi$
$878$	−7.97521	−0.269150
$879$	45.3413	1.52932
$880$	4.22964	0.142581
$881$	22.3213	0.752024	0.376012	−	0.926615i	$-0.377295\pi$
$881$	22.3213	0.752024	0.376012	+	0.926615i	$0.377295\pi$
$882$	0	0
$883$	−6.22078	−0.209346	−0.104673	−	0.994507i	$-0.533380\pi$
$883$	−6.22078	−0.209346	−0.104673	+	0.994507i	$0.533380\pi$
$884$	6.07496	0.204323
$885$	−22.4155	−0.753490
$886$	26.9022	0.903796
$887$	−19.8474	−0.666411	−0.333205	−	0.942854i	$-0.608130\pi$
$887$	−19.8474	−0.666411	−0.333205	+	0.942854i	$0.608130\pi$
$888$	−16.2544	−0.545463
$889$	0	0
$890$	−13.6634	−0.457998
$891$	−109.162	−3.65707
$892$	0.0191498	0.000641181 0
$893$	−5.49322	−0.183824
$894$	−58.5658	−1.95873
$895$	−30.0065	−1.00301
$896$	0	0
$897$	34.2911	1.14495
$898$	23.1760	0.773393
$899$	−73.2601	−2.44336
$900$	−24.0833	−0.802778
$901$	26.8222	0.893577
$902$	−2.86874	−0.0955185
$903$	0	0
$904$	−2.96252	−0.0985320
$905$	7.88465	0.262095
$906$	−69.6078	−2.31256
$907$	−37.5135	−1.24561	−0.622807	−	0.782375i	$-0.714008\pi$
$907$	−37.5135	−1.24561	−0.622807	+	0.782375i	$0.714008\pi$
$908$	21.9955	0.729945
$909$	−55.8933	−1.85386
$910$	0	0
$911$	7.33963	0.243173	0.121586	−	0.992581i	$-0.461202\pi$
$911$	7.33963	0.243173	0.121586	+	0.992581i	$0.461202\pi$
$912$	4.00000	0.132453
$913$	−6.62591	−0.219286
$914$	−26.9478	−0.891354
$915$	−23.4961	−0.776756
$916$	2.38165	0.0786921
$917$	0	0
$918$	−35.8218	−1.18230
$919$	−13.6342	−0.449750	−0.224875	−	0.974388i	$-0.572197\pi$
$919$	−13.6342	−0.449750	−0.224875	+	0.974388i	$0.572197\pi$
$920$	4.68626	0.154501
$921$	−37.9261	−1.24971
$922$	−12.7122	−0.418653
$923$	39.3979	1.29680
$924$	0	0
$925$	−13.5336	−0.444982
$926$	−31.8685	−1.04726
$927$	−78.9014	−2.59146
$928$	−8.13586	−0.267073
$929$	46.2232	1.51654	0.758268	−	0.651943i	$-0.226046\pi$
$929$	46.2232	1.51654	0.758268	+	0.651943i	$0.226046\pi$
$930$	−45.0644	−1.47772
$931$	0	0
$932$	−13.8226	−0.452775
$933$	−99.9951	−3.27369
$934$	16.4963	0.539775
$935$	8.08415	0.264380
$936$	−27.0852	−0.885307
$937$	−45.6261	−1.49054	−0.745270	−	0.666763i	$-0.767679\pi$
$937$	−45.6261	−1.49054	−0.745270	+	0.666763i	$0.767679\pi$
$938$	0	0
$939$	−106.725	−3.48284
$940$	6.87284	0.224167
$941$	−16.0289	−0.522527	−0.261263	−	0.965268i	$-0.584139\pi$
$941$	−16.0289	−0.522527	−0.261263	+	0.965268i	$0.584139\pi$
$942$	4.25444	0.138617
$943$	−3.17843	−0.103504
$944$	4.47899	0.145779
$945$	0	0
$946$	−5.11808	−0.166403
$947$	−28.1995	−0.916361	−0.458180	−	0.888859i	$-0.651499\pi$
$947$	−28.1995	−0.916361	−0.458180	+	0.888859i	$0.651499\pi$
$948$	−1.62399	−0.0527447
$949$	−40.0842	−1.30119
$950$	3.33044	0.108054
$951$	−20.0011	−0.648580
$952$	0	0
$953$	−15.7412	−0.509909	−0.254955	−	0.966953i	$-0.582060\pi$
$953$	−15.7412	−0.509909	−0.254955	+	0.966953i	$0.582060\pi$
$954$	−119.587	−3.87176
$955$	−14.5497	−0.470816
$956$	7.12617	0.230477
$957$	−79.2227	−2.56091
$958$	−33.0001	−1.06618
$959$	0	0
$960$	−5.00460	−0.161523
$961$	50.0827	1.61557
$962$	−15.2205	−0.490729
$963$	172.202	5.54914
$964$	−7.21132	−0.232261
$965$	20.5040	0.660048
$966$	0	0
$967$	−27.9921	−0.900166	−0.450083	−	0.892987i	$-0.648606\pi$
$967$	−27.9921	−0.900166	−0.450083	+	0.892987i	$0.648606\pi$
$968$	2.77036	0.0890426
$969$	7.64523	0.245600
$970$	14.6752	0.471192
$971$	−48.7184	−1.56345	−0.781724	−	0.623625i	$-0.785659\pi$
$971$	−48.7184	−1.56345	−0.781724	+	0.623625i	$0.785659\pi$
$972$	72.9364	2.33944
$973$	0	0
$974$	−23.4475	−0.751306
$975$	−30.4906	−0.976481
$976$	4.69490	0.150280
$977$	−6.88466	−0.220260	−0.110130	−	0.993917i	$-0.535127\pi$
$977$	−6.88466	−0.220260	−0.110130	+	0.993917i	$0.535127\pi$
$978$	−16.5434	−0.529001
$979$	26.5849	0.849658
$980$	0	0
$981$	−157.190	−5.01868
$982$	10.4046	0.332023
$983$	−16.5453	−0.527713	−0.263857	−	0.964562i	$-0.584995\pi$
$983$	−16.5453	−0.527713	−0.263857	+	0.964562i	$0.584995\pi$
$984$	3.39434	0.108208
$985$	−28.8393	−0.918895
$986$	−15.5501	−0.495217
$987$	0	0
$988$	3.74556	0.119162
$989$	−5.67060	−0.180315
$990$	−36.0432	−1.14553
$991$	−8.97416	−0.285074	−0.142537	−	0.989789i	$-0.545526\pi$
$991$	−8.97416	−0.285074	−0.142537	+	0.989789i	$0.545526\pi$
$992$	9.00460	0.285896
$993$	110.395	3.50327
$994$	0	0
$995$	−19.6798	−0.623891
$996$	7.83990	0.248417
$997$	−55.3957	−1.75440	−0.877199	−	0.480127i	$-0.840591\pi$
$997$	−55.3957	−1.75440	−0.877199	+	0.480127i	$0.840591\pi$
$998$	−3.20622	−0.101491
$999$	89.7499	2.83956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bj.1.4		4
7.6	odd	2		574.2.a.m.1.1	✓	4
21.20	even	2		5166.2.a.bx.1.2		4
28.27	even	2		4592.2.a.ba.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.a.m.1.1	✓	4	7.6	odd	2
4018.2.a.bj.1.4		4	1.1	even	1	trivial
4592.2.a.ba.1.4		4	28.27	even	2
5166.2.a.bx.1.2		4	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.39434 q^{3} +1.00000 q^{4} -1.47439 q^{5} -3.39434 q^{6} -1.00000 q^{8} +8.52156 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.39434 q^{3} +1.00000 q^{4} -1.47439 q^{5} -3.39434 q^{6} -1.00000 q^{8} +8.52156 q^{9} +1.47439 q^{10} -2.86874 q^{11} +3.39434 q^{12} +3.17843 q^{13} -5.00460 q^{15} +1.00000 q^{16} +1.91131 q^{17} -8.52156 q^{18} +1.17843 q^{19} -1.47439 q^{20} +2.86874 q^{22} +3.17843 q^{23} -3.39434 q^{24} -2.82616 q^{25} -3.17843 q^{26} +18.7421 q^{27} +8.13586 q^{29} +5.00460 q^{30} -9.00460 q^{31} -1.00000 q^{32} -9.73747 q^{33} -1.91131 q^{34} +8.52156 q^{36} +4.78868 q^{37} -1.17843 q^{38} +10.7887 q^{39} +1.47439 q^{40} -1.00000 q^{41} -1.78409 q^{43} -2.86874 q^{44} -12.5641 q^{45} -3.17843 q^{46} -4.66147 q^{47} +3.39434 q^{48} +2.82616 q^{50} +6.48763 q^{51} +3.17843 q^{52} +14.0334 q^{53} -18.7421 q^{54} +4.22964 q^{55} +4.00000 q^{57} -8.13586 q^{58} +4.47899 q^{59} -5.00460 q^{60} +4.69490 q^{61} +9.00460 q^{62} +1.00000 q^{64} -4.68626 q^{65} +9.73747 q^{66} -1.38570 q^{67} +1.91131 q^{68} +10.7887 q^{69} +12.3954 q^{71} -8.52156 q^{72} -12.6113 q^{73} -4.78868 q^{74} -9.59297 q^{75} +1.17843 q^{76} -10.7887 q^{78} -0.478439 q^{79} -1.47439 q^{80} +38.0523 q^{81} +1.00000 q^{82} +2.30970 q^{83} -2.81802 q^{85} +1.78409 q^{86} +27.6159 q^{87} +2.86874 q^{88} -9.26712 q^{89} +12.5641 q^{90} +3.17843 q^{92} -30.5647 q^{93} +4.66147 q^{94} -1.73747 q^{95} -3.39434 q^{96} +9.95338 q^{97} -24.4461 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + q^{3} + 4 q^{4} - 3 q^{5} - q^{6} - 4 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + q^3 + 4 * q^4 - 3 * q^5 - q^6 - 4 * q^8 + 9 * q^9	\( 4 q - 4 q^{2} + q^{3} + 4 q^{4} - 3 q^{5} - q^{6} - 4 q^{8} + 9 q^{9} + 3 q^{10} + 4 q^{11} + q^{12} + 6 q^{13} + 11 q^{15} + 4 q^{16} + q^{17} - 9 q^{18} - 2 q^{19} - 3 q^{20} - 4 q^{22} + 6 q^{23} - q^{24} + 13 q^{25} - 6 q^{26} + 13 q^{27} + 17 q^{29} - 11 q^{30} - 5 q^{31} - 4 q^{32} - 8 q^{33} - q^{34} + 9 q^{36} - 6 q^{37} + 2 q^{38} + 18 q^{39} + 3 q^{40} - 4 q^{41} - 13 q^{43} + 4 q^{44} - 34 q^{45} - 6 q^{46} - 6 q^{47} + q^{48} - 13 q^{50} - 11 q^{51} + 6 q^{52} + 29 q^{53} - 13 q^{54} + 16 q^{55} + 16 q^{57} - 17 q^{58} - 16 q^{59} + 11 q^{60} - 21 q^{61} + 5 q^{62} + 4 q^{64} + 18 q^{65} + 8 q^{66} + 4 q^{67} + q^{68} + 18 q^{69} + 17 q^{71} - 9 q^{72} - 12 q^{73} + 6 q^{74} - 26 q^{75} - 2 q^{76} - 18 q^{78} - 27 q^{79} - 3 q^{80} + 40 q^{81} + 4 q^{82} + 18 q^{83} - 29 q^{85} + 13 q^{86} + 41 q^{87} - 4 q^{88} - 37 q^{89} + 34 q^{90} + 6 q^{92} - 47 q^{93} + 6 q^{94} + 24 q^{95} - q^{96} + 3 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + q^3 + 4 * q^4 - 3 * q^5 - q^6 - 4 * q^8 + 9 * q^9 + 3 * q^10 + 4 * q^11 + q^12 + 6 * q^13 + 11 * q^15 + 4 * q^16 + q^17 - 9 * q^18 - 2 * q^19 - 3 * q^20 - 4 * q^22 + 6 * q^23 - q^24 + 13 * q^25 - 6 * q^26 + 13 * q^27 + 17 * q^29 - 11 * q^30 - 5 * q^31 - 4 * q^32 - 8 * q^33 - q^34 + 9 * q^36 - 6 * q^37 + 2 * q^38 + 18 * q^39 + 3 * q^40 - 4 * q^41 - 13 * q^43 + 4 * q^44 - 34 * q^45 - 6 * q^46 - 6 * q^47 + q^48 - 13 * q^50 - 11 * q^51 + 6 * q^52 + 29 * q^53 - 13 * q^54 + 16 * q^55 + 16 * q^57 - 17 * q^58 - 16 * q^59 + 11 * q^60 - 21 * q^61 + 5 * q^62 + 4 * q^64 + 18 * q^65 + 8 * q^66 + 4 * q^67 + q^68 + 18 * q^69 + 17 * q^71 - 9 * q^72 - 12 * q^73 + 6 * q^74 - 26 * q^75 - 2 * q^76 - 18 * q^78 - 27 * q^79 - 3 * q^80 + 40 * q^81 + 4 * q^82 + 18 * q^83 - 29 * q^85 + 13 * q^86 + 41 * q^87 - 4 * q^88 - 37 * q^89 + 34 * q^90 + 6 * q^92 - 47 * q^93 + 6 * q^94 + 24 * q^95 - q^96 + 3 * q^97 - 32 * q^99

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