LMFDB - Embedded newform 147.4.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("147.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.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:	$8.67328077084$
Analytic rank:	$1$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41421 q^{2} +3.00000 q^{3} -2.17157 q^{4} -19.8995 q^{5} +7.24264 q^{6} -24.5563 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.41421 q^{2} +3.00000 q^{3} -2.17157 q^{4} -19.8995 q^{5} +7.24264 q^{6} -24.5563 q^{8} +9.00000 q^{9} -48.0416 q^{10} +23.9411 q^{11} -6.51472 q^{12} -87.3553 q^{13} -59.6985 q^{15} -41.9117 q^{16} +5.63961 q^{17} +21.7279 q^{18} -64.8873 q^{19} +43.2132 q^{20} +57.7990 q^{22} -25.5980 q^{23} -73.6690 q^{24} +270.990 q^{25} -210.894 q^{26} +27.0000 q^{27} +60.3188 q^{29} -144.125 q^{30} +122.711 q^{31} +95.2670 q^{32} +71.8234 q^{33} +13.6152 q^{34} -19.5442 q^{36} -56.1177 q^{37} -156.652 q^{38} -262.066 q^{39} +488.659 q^{40} +299.713 q^{41} -501.421 q^{43} -51.9899 q^{44} -179.095 q^{45} -61.7990 q^{46} -305.553 q^{47} -125.735 q^{48} +654.227 q^{50} +16.9188 q^{51} +189.698 q^{52} -375.117 q^{53} +65.1838 q^{54} -476.416 q^{55} -194.662 q^{57} +145.622 q^{58} +627.612 q^{59} +129.640 q^{60} -3.75736 q^{61} +296.250 q^{62} +565.288 q^{64} +1738.33 q^{65} +173.397 q^{66} -813.048 q^{67} -12.2468 q^{68} -76.7939 q^{69} +165.902 q^{71} -221.007 q^{72} -619.100 q^{73} -135.480 q^{74} +812.970 q^{75} +140.908 q^{76} -632.683 q^{78} -138.246 q^{79} +834.021 q^{80} +81.0000 q^{81} +723.571 q^{82} -621.137 q^{83} -112.225 q^{85} -1210.54 q^{86} +180.956 q^{87} -587.907 q^{88} -285.418 q^{89} -432.375 q^{90} +55.5879 q^{92} +368.132 q^{93} -737.671 q^{94} +1291.22 q^{95} +285.801 q^{96} +603.114 q^{97} +215.470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 6 q^{3} - 10 q^{4} - 20 q^{5} + 6 q^{6} - 18 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 6 * q^3 - 10 * q^4 - 20 * q^5 + 6 * q^6 - 18 * q^8 + 18 * q^9	\( 2 q + 2 q^{2} + 6 q^{3} - 10 q^{4} - 20 q^{5} + 6 q^{6} - 18 q^{8} + 18 q^{9} - 48 q^{10} - 20 q^{11} - 30 q^{12} - 104 q^{13} - 60 q^{15} + 18 q^{16} - 116 q^{17} + 18 q^{18} - 192 q^{19} + 44 q^{20} + 76 q^{22} + 28 q^{23} - 54 q^{24} + 146 q^{25} - 204 q^{26} + 54 q^{27} + 296 q^{29} - 144 q^{30} + 104 q^{31} + 18 q^{32} - 60 q^{33} + 64 q^{34} - 90 q^{36} - 248 q^{37} - 104 q^{38} - 312 q^{39} + 488 q^{40} - 20 q^{41} - 720 q^{43} + 292 q^{44} - 180 q^{45} - 84 q^{46} + 96 q^{47} + 54 q^{48} + 706 q^{50} - 348 q^{51} + 320 q^{52} + 268 q^{53} + 54 q^{54} - 472 q^{55} - 576 q^{57} + 48 q^{58} + 616 q^{59} + 132 q^{60} - 16 q^{61} + 304 q^{62} + 118 q^{64} + 1740 q^{65} + 228 q^{66} - 144 q^{67} + 940 q^{68} + 84 q^{69} + 988 q^{71} - 162 q^{72} - 104 q^{73} - 56 q^{74} + 438 q^{75} + 1136 q^{76} - 612 q^{78} - 944 q^{79} + 828 q^{80} + 162 q^{81} + 856 q^{82} - 1016 q^{83} - 100 q^{85} - 1120 q^{86} + 888 q^{87} - 876 q^{88} + 388 q^{89} - 432 q^{90} - 364 q^{92} + 312 q^{93} - 904 q^{94} + 1304 q^{95} + 54 q^{96} - 488 q^{97} - 180 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 6 * q^3 - 10 * q^4 - 20 * q^5 + 6 * q^6 - 18 * q^8 + 18 * q^9 - 48 * q^10 - 20 * q^11 - 30 * q^12 - 104 * q^13 - 60 * q^15 + 18 * q^16 - 116 * q^17 + 18 * q^18 - 192 * q^19 + 44 * q^20 + 76 * q^22 + 28 * q^23 - 54 * q^24 + 146 * q^25 - 204 * q^26 + 54 * q^27 + 296 * q^29 - 144 * q^30 + 104 * q^31 + 18 * q^32 - 60 * q^33 + 64 * q^34 - 90 * q^36 - 248 * q^37 - 104 * q^38 - 312 * q^39 + 488 * q^40 - 20 * q^41 - 720 * q^43 + 292 * q^44 - 180 * q^45 - 84 * q^46 + 96 * q^47 + 54 * q^48 + 706 * q^50 - 348 * q^51 + 320 * q^52 + 268 * q^53 + 54 * q^54 - 472 * q^55 - 576 * q^57 + 48 * q^58 + 616 * q^59 + 132 * q^60 - 16 * q^61 + 304 * q^62 + 118 * q^64 + 1740 * q^65 + 228 * q^66 - 144 * q^67 + 940 * q^68 + 84 * q^69 + 988 * q^71 - 162 * q^72 - 104 * q^73 - 56 * q^74 + 438 * q^75 + 1136 * q^76 - 612 * q^78 - 944 * q^79 + 828 * q^80 + 162 * q^81 + 856 * q^82 - 1016 * q^83 - 100 * q^85 - 1120 * q^86 + 888 * q^87 - 876 * q^88 + 388 * q^89 - 432 * q^90 - 364 * q^92 + 312 * q^93 - 904 * q^94 + 1304 * q^95 + 54 * q^96 - 488 * q^97 - 180 * 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 $

$2$	2.41421	0.853553	0.426777	−	0.904357i	$-0.359649\pi$
$2$	2.41421	0.853553	0.426777	+	0.904357i	$0.359649\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−2.17157	−0.271447
$5$	−19.8995	−1.77986	−0.889932	−	0.456092i	$-0.849249\pi$
$5$	−19.8995	−1.77986	−0.889932	+	0.456092i	$0.849249\pi$
$6$	7.24264	0.492799
$7$	0	0
$7$	0	0
$8$	−24.5563	−1.08525
$9$	9.00000	0.333333
$10$	−48.0416	−1.51921
$11$	23.9411	0.656229	0.328115	−	0.944638i	$-0.393587\pi$
$11$	23.9411	0.656229	0.328115	+	0.944638i	$0.393587\pi$
$12$	−6.51472	−0.156720
$13$	−87.3553	−1.86369	−0.931847	−	0.362852i	$-0.881803\pi$
$13$	−87.3553	−1.86369	−0.931847	+	0.362852i	$0.881803\pi$
$14$	0	0
$15$	−59.6985	−1.02761
$16$	−41.9117	−0.654870
$17$	5.63961	0.0804592	0.0402296	−	0.999190i	$-0.487191\pi$
$17$	5.63961	0.0804592	0.0402296	+	0.999190i	$0.487191\pi$
$18$	21.7279	0.284518
$19$	−64.8873	−0.783483	−0.391741	−	0.920075i	$-0.628127\pi$
$19$	−64.8873	−0.783483	−0.391741	+	0.920075i	$0.628127\pi$
$20$	43.2132	0.483138
$21$	0	0
$22$	57.7990	0.560127
$23$	−25.5980	−0.232067	−0.116034	−	0.993245i	$-0.537018\pi$
$23$	−25.5980	−0.232067	−0.116034	+	0.993245i	$0.537018\pi$
$24$	−73.6690	−0.626568
$25$	270.990	2.16792
$26$	−210.894	−1.59076
$27$	27.0000	0.192450
$28$	0	0
$29$	60.3188	0.386238	0.193119	−	0.981175i	$-0.438140\pi$
$29$	60.3188	0.386238	0.193119	+	0.981175i	$0.438140\pi$
$30$	−144.125	−0.877116
$31$	122.711	0.710951	0.355476	−	0.934686i	$-0.384319\pi$
$31$	122.711	0.710951	0.355476	+	0.934686i	$0.384319\pi$
$32$	95.2670	0.526281
$33$	71.8234	0.378874
$34$	13.6152	0.0686762
$35$	0	0
$36$	−19.5442	−0.0904822
$37$	−56.1177	−0.249343	−0.124672	−	0.992198i	$-0.539788\pi$
$37$	−56.1177	−0.249343	−0.124672	+	0.992198i	$0.539788\pi$
$38$	−156.652	−0.668744
$39$	−262.066	−1.07600
$40$	488.659	1.93159
$41$	299.713	1.14164	0.570820	−	0.821075i	$-0.306625\pi$
$41$	299.713	1.14164	0.570820	+	0.821075i	$0.306625\pi$
$42$	0	0
$43$	−501.421	−1.77828	−0.889140	−	0.457635i	$-0.848697\pi$
$43$	−501.421	−1.77828	−0.889140	+	0.457635i	$0.848697\pi$
$44$	−51.9899	−0.178131
$45$	−179.095	−0.593288
$46$	−61.7990	−0.198082
$47$	−305.553	−0.948288	−0.474144	−	0.880447i	$-0.657242\pi$
$47$	−305.553	−0.948288	−0.474144	+	0.880447i	$0.657242\pi$
$48$	−125.735	−0.378089
$49$	0	0
$50$	654.227	1.85043
$51$	16.9188	0.0464531
$52$	189.698	0.505893
$53$	−375.117	−0.972194	−0.486097	−	0.873905i	$-0.661580\pi$
$53$	−375.117	−0.972194	−0.486097	+	0.873905i	$0.661580\pi$
$54$	65.1838	0.164266
$55$	−476.416	−1.16800
$56$	0	0
$57$	−194.662	−0.452344
$58$	145.622	0.329675
$59$	627.612	1.38488	0.692442	−	0.721474i	$-0.256535\pi$
$59$	627.612	1.38488	0.692442	+	0.721474i	$0.256535\pi$
$60$	129.640	0.278940
$61$	−3.75736	−0.00788657	−0.00394328	−	0.999992i	$-0.501255\pi$
$61$	−3.75736	−0.00788657	−0.00394328	+	0.999992i	$0.501255\pi$
$62$	296.250	0.606835
$63$	0	0
$64$	565.288	1.10408
$65$	1738.33	3.31712
$66$	173.397	0.323389
$67$	−813.048	−1.48253	−0.741266	−	0.671212i	$-0.765774\pi$
$67$	−813.048	−1.48253	−0.741266	+	0.671212i	$0.765774\pi$
$68$	−12.2468	−0.0218404
$69$	−76.7939	−0.133984
$70$	0	0
$71$	165.902	0.277310	0.138655	−	0.990341i	$-0.455722\pi$
$71$	165.902	0.277310	0.138655	+	0.990341i	$0.455722\pi$
$72$	−221.007	−0.361749
$73$	−619.100	−0.992605	−0.496302	−	0.868150i	$-0.665309\pi$
$73$	−619.100	−0.992605	−0.496302	+	0.868150i	$0.665309\pi$
$74$	−135.480	−0.212828
$75$	812.970	1.25165
$76$	140.908	0.212674
$77$	0	0
$78$	−632.683	−0.918427
$79$	−138.246	−0.196884	−0.0984421	−	0.995143i	$-0.531386\pi$
$79$	−138.246	−0.196884	−0.0984421	+	0.995143i	$0.531386\pi$
$80$	834.021	1.16558
$81$	81.0000	0.111111
$82$	723.571	0.974451
$83$	−621.137	−0.821430	−0.410715	−	0.911764i	$-0.634721\pi$
$83$	−621.137	−0.821430	−0.410715	+	0.911764i	$0.634721\pi$
$84$	0	0
$85$	−112.225	−0.143207
$86$	−1210.54	−1.51786
$87$	180.956	0.222995
$88$	−587.907	−0.712171
$89$	−285.418	−0.339936	−0.169968	−	0.985450i	$-0.554366\pi$
$89$	−285.418	−0.339936	−0.169968	+	0.985450i	$0.554366\pi$
$90$	−432.375	−0.506403
$91$	0	0
$92$	55.5879	0.0629939
$93$	368.132	0.410468
$94$	−737.671	−0.809415
$95$	1291.22	1.39449
$96$	285.801	0.303848
$97$	603.114	0.631309	0.315654	−	0.948874i	$-0.397776\pi$
$97$	603.114	0.631309	0.315654	+	0.948874i	$0.397776\pi$
$98$	0	0
$99$	215.470	0.218743
$100$	−588.474	−0.588474
$101$	−457.209	−0.450436	−0.225218	−	0.974308i	$-0.572309\pi$
$101$	−457.209	−0.450436	−0.225218	+	0.974308i	$0.572309\pi$
$102$	40.8457	0.0396502
$103$	−786.045	−0.751954	−0.375977	−	0.926629i	$-0.622693\pi$
$103$	−786.045	−0.751954	−0.375977	+	0.926629i	$0.622693\pi$
$104$	2145.13	2.02257
$105$	0	0
$106$	−905.612	−0.829819
$107$	−196.461	−0.177501	−0.0887504	−	0.996054i	$-0.528287\pi$
$107$	−196.461	−0.177501	−0.0887504	+	0.996054i	$0.528287\pi$
$108$	−58.6325	−0.0522399
$109$	−306.343	−0.269196	−0.134598	−	0.990900i	$-0.542974\pi$
$109$	−306.343	−0.269196	−0.134598	+	0.990900i	$0.542974\pi$
$110$	−1150.17	−0.996950
$111$	−168.353	−0.143958
$112$	0	0
$113$	1997.63	1.66302	0.831508	−	0.555512i	$-0.187478\pi$
$113$	1997.63	1.66302	0.831508	+	0.555512i	$0.187478\pi$
$114$	−469.955	−0.386100
$115$	509.387	0.413048
$116$	−130.987	−0.104843
$117$	−786.198	−0.621231
$118$	1515.19	1.18207
$119$	0	0
$120$	1465.98	1.11521
$121$	−757.823	−0.569363
$122$	−9.07107	−0.00673161
$123$	899.138	0.659127
$124$	−266.475	−0.192985
$125$	−2905.13	−2.07874
$126$	0	0
$127$	−2311.40	−1.61499	−0.807494	−	0.589875i	$-0.799177\pi$
$127$	−2311.40	−1.61499	−0.807494	+	0.589875i	$0.799177\pi$
$128$	602.591	0.416109
$129$	−1504.26	−1.02669
$130$	4196.69	2.83134
$131$	155.018	0.103389	0.0516945	−	0.998663i	$-0.483538\pi$
$131$	155.018	0.103389	0.0516945	+	0.998663i	$0.483538\pi$
$132$	−155.970	−0.102844
$133$	0	0
$134$	−1962.87	−1.26542
$135$	−537.286	−0.342535
$136$	−138.488	−0.0873182
$137$	516.936	0.322371	0.161186	−	0.986924i	$-0.448468\pi$
$137$	516.936	0.322371	0.161186	+	0.986924i	$0.448468\pi$
$138$	−185.397	−0.114363
$139$	−958.067	−0.584620	−0.292310	−	0.956324i	$-0.594424\pi$
$139$	−958.067	−0.584620	−0.292310	+	0.956324i	$0.594424\pi$
$140$	0	0
$141$	−916.660	−0.547494
$142$	400.524	0.236699
$143$	−2091.39	−1.22301
$144$	−377.205	−0.218290
$145$	−1200.31	−0.687452
$146$	−1494.64	−0.847241
$147$	0	0
$148$	121.864	0.0676834
$149$	−1770.63	−0.973526	−0.486763	−	0.873534i	$-0.661822\pi$
$149$	−1770.63	−0.973526	−0.486763	+	0.873534i	$0.661822\pi$
$150$	1962.68	1.06835
$151$	−2540.24	−1.36902	−0.684508	−	0.729005i	$-0.739983\pi$
$151$	−2540.24	−1.36902	−0.684508	+	0.729005i	$0.739983\pi$
$152$	1593.40	0.850272
$153$	50.7565	0.0268197
$154$	0	0
$155$	−2441.88	−1.26540
$156$	569.095	0.292078
$157$	1083.34	0.550702	0.275351	−	0.961344i	$-0.411206\pi$
$157$	1083.34	0.550702	0.275351	+	0.961344i	$0.411206\pi$
$158$	−333.754	−0.168051
$159$	−1125.35	−0.561296
$160$	−1895.77	−0.936709
$161$	0	0
$162$	195.551	0.0948393
$163$	2968.72	1.42655	0.713277	−	0.700882i	$-0.247210\pi$
$163$	2968.72	1.42655	0.713277	+	0.700882i	$0.247210\pi$
$164$	−650.848	−0.309895
$165$	−1429.25	−0.674345
$166$	−1499.56	−0.701134
$167$	2091.53	0.969149	0.484574	−	0.874750i	$-0.338975\pi$
$167$	2091.53	0.969149	0.484574	+	0.874750i	$0.338975\pi$
$168$	0	0
$169$	5433.96	2.47335
$170$	−270.936	−0.122234
$171$	−583.986	−0.261161
$172$	1088.87	0.482708
$173$	470.148	0.206617	0.103308	−	0.994649i	$-0.467057\pi$
$173$	470.148	0.206617	0.103308	+	0.994649i	$0.467057\pi$
$174$	436.867	0.190338
$175$	0	0
$176$	−1003.41	−0.429745
$177$	1882.84	0.799563
$178$	−689.061	−0.290153
$179$	1056.46	0.441137	0.220569	−	0.975371i	$-0.429209\pi$
$179$	1056.46	0.441137	0.220569	+	0.975371i	$0.429209\pi$
$180$	388.919	0.161046
$181$	406.470	0.166921	0.0834605	−	0.996511i	$-0.473403\pi$
$181$	406.470	0.166921	0.0834605	+	0.996511i	$0.473403\pi$
$182$	0	0
$183$	−11.2721	−0.00455331
$184$	628.593	0.251850
$185$	1116.71	0.443797
$186$	888.749	0.350356
$187$	135.019	0.0527997
$188$	663.531	0.257410
$189$	0	0
$190$	3117.29	1.19027
$191$	179.410	0.0679666	0.0339833	−	0.999422i	$-0.489181\pi$
$191$	179.410	0.0679666	0.0339833	+	0.999422i	$0.489181\pi$
$192$	1695.87	0.637440
$193$	−2388.37	−0.890769	−0.445385	−	0.895339i	$-0.646933\pi$
$193$	−2388.37	−0.890769	−0.445385	+	0.895339i	$0.646933\pi$
$194$	1456.05	0.538856
$195$	5214.98	1.91514
$196$	0	0
$197$	−2665.35	−0.963952	−0.481976	−	0.876184i	$-0.660081\pi$
$197$	−2665.35	−0.963952	−0.481976	+	0.876184i	$0.660081\pi$
$198$	520.191	0.186709
$199$	1342.31	0.478159	0.239079	−	0.971000i	$-0.423154\pi$
$199$	1342.31	0.478159	0.239079	+	0.971000i	$0.423154\pi$
$200$	−6654.52	−2.35273
$201$	−2439.14	−0.855940
$202$	−1103.80	−0.384471
$203$	0	0
$204$	−36.7405	−0.0126095
$205$	−5964.13	−2.03197
$206$	−1897.68	−0.641833
$207$	−230.382	−0.0773558
$208$	3661.21	1.22048
$209$	−1553.48	−0.514144
$210$	0	0
$211$	628.442	0.205042	0.102521	−	0.994731i	$-0.467309\pi$
$211$	628.442	0.205042	0.102521	+	0.994731i	$0.467309\pi$
$212$	814.594	0.263899
$213$	497.707	0.160105
$214$	−474.299	−0.151506
$215$	9978.03	3.16510
$216$	−663.021	−0.208856
$217$	0	0
$218$	−739.578	−0.229773
$219$	−1857.30	−0.573081
$220$	1034.57	0.317049
$221$	−492.650	−0.149951
$222$	−406.441	−0.122876
$223$	969.970	0.291273	0.145637	−	0.989338i	$-0.453477\pi$
$223$	969.970	0.291273	0.145637	+	0.989338i	$0.453477\pi$
$224$	0	0
$225$	2438.91	0.722640
$226$	4822.70	1.41947
$227$	4748.64	1.38845	0.694225	−	0.719758i	$-0.255747\pi$
$227$	4748.64	1.38845	0.694225	+	0.719758i	$0.255747\pi$
$228$	422.723	0.122787
$229$	4801.99	1.38570	0.692848	−	0.721083i	$-0.256356\pi$
$229$	4801.99	1.38570	0.692848	+	0.721083i	$0.256356\pi$
$230$	1229.77	0.352559
$231$	0	0
$232$	−1481.21	−0.419164
$233$	−3155.29	−0.887166	−0.443583	−	0.896233i	$-0.646293\pi$
$233$	−3155.29	−0.887166	−0.443583	+	0.896233i	$0.646293\pi$
$234$	−1898.05	−0.530254
$235$	6080.36	1.68782
$236$	−1362.91	−0.375922
$237$	−414.737	−0.113671
$238$	0	0
$239$	4241.93	1.14806	0.574032	−	0.818833i	$-0.305378\pi$
$239$	4241.93	1.14806	0.574032	+	0.818833i	$0.305378\pi$
$240$	2502.06	0.672948
$241$	4342.99	1.16081	0.580407	−	0.814326i	$-0.302893\pi$
$241$	4342.99	1.16081	0.580407	+	0.814326i	$0.302893\pi$
$242$	−1829.55	−0.485982
$243$	243.000	0.0641500
$244$	8.15938	0.00214078
$245$	0	0
$246$	2170.71	0.562600
$247$	5668.25	1.46017
$248$	−3013.33	−0.771558
$249$	−1863.41	−0.474253
$250$	−7013.59	−1.77431
$251$	−3003.01	−0.755172	−0.377586	−	0.925974i	$-0.623246\pi$
$251$	−3003.01	−0.755172	−0.377586	+	0.925974i	$0.623246\pi$
$252$	0	0
$253$	−612.844	−0.152289
$254$	−5580.21	−1.37848
$255$	−336.676	−0.0826803
$256$	−3067.52	−0.748907
$257$	−4468.84	−1.08466	−0.542332	−	0.840164i	$-0.682459\pi$
$257$	−4468.84	−1.08466	−0.542332	+	0.840164i	$0.682459\pi$
$258$	−3631.61	−0.876335
$259$	0	0
$260$	−3774.90	−0.900422
$261$	542.869	0.128746
$262$	374.246	0.0882480
$263$	6160.13	1.44430	0.722148	−	0.691738i	$-0.243155\pi$
$263$	6160.13	1.44430	0.722148	+	0.691738i	$0.243155\pi$
$264$	−1763.72	−0.411172
$265$	7464.64	1.73037
$266$	0	0
$267$	−856.255	−0.196262
$268$	1765.59	0.402428
$269$	−4988.90	−1.13078	−0.565388	−	0.824825i	$-0.691274\pi$
$269$	−4988.90	−1.13078	−0.565388	+	0.824825i	$0.691274\pi$
$270$	−1297.12	−0.292372
$271$	−4433.73	−0.993837	−0.496918	−	0.867797i	$-0.665535\pi$
$271$	−4433.73	−0.993837	−0.496918	+	0.867797i	$0.665535\pi$
$272$	−236.366	−0.0526903
$273$	0	0
$274$	1247.99	0.275161
$275$	6487.80	1.42265
$276$	166.764	0.0363695
$277$	1112.37	0.241284	0.120642	−	0.992696i	$-0.461505\pi$
$277$	1112.37	0.241284	0.120642	+	0.992696i	$0.461505\pi$
$278$	−2312.98	−0.499005
$279$	1104.40	0.236984
$280$	0	0
$281$	2813.22	0.597233	0.298616	−	0.954373i	$-0.403475\pi$
$281$	2813.22	0.597233	0.298616	+	0.954373i	$0.403475\pi$
$282$	−2213.01	−0.467316
$283$	−3147.54	−0.661137	−0.330569	−	0.943782i	$-0.607241\pi$
$283$	−3147.54	−0.661137	−0.330569	+	0.943782i	$0.607241\pi$
$284$	−360.269	−0.0752748
$285$	3873.67	0.805111
$286$	−5049.05	−1.04390
$287$	0	0
$288$	857.403	0.175427
$289$	−4881.19	−0.993526
$290$	−2897.81	−0.586777
$291$	1809.34	0.364486
$292$	1344.42	0.269439
$293$	−9143.04	−1.82301	−0.911505	−	0.411289i	$-0.865079\pi$
$293$	−9143.04	−1.82301	−0.911505	+	0.411289i	$0.865079\pi$
$294$	0	0
$295$	−12489.2	−2.46491
$296$	1378.05	0.270599
$297$	646.410	0.126291
$298$	−4274.67	−0.830956
$299$	2236.12	0.432502
$300$	−1765.42	−0.339756
$301$	0	0
$302$	−6132.67	−1.16853
$303$	−1371.63	−0.260059
$304$	2719.54	0.513079
$305$	74.7696	0.0140370
$306$	122.537	0.0228921
$307$	4648.90	0.864257	0.432129	−	0.901812i	$-0.357763\pi$
$307$	4648.90	0.864257	0.432129	+	0.901812i	$0.357763\pi$
$308$	0	0
$309$	−2358.13	−0.434141
$310$	−5895.22	−1.08008
$311$	6417.18	1.17005	0.585024	−	0.811016i	$-0.301085\pi$
$311$	6417.18	1.17005	0.585024	+	0.811016i	$0.301085\pi$
$312$	6435.38	1.16773
$313$	−5868.22	−1.05972	−0.529858	−	0.848086i	$-0.677755\pi$
$313$	−5868.22	−1.05972	−0.529858	+	0.848086i	$0.677755\pi$
$314$	2615.42	0.470054
$315$	0	0
$316$	300.210	0.0534435
$317$	−3974.52	−0.704200	−0.352100	−	0.935962i	$-0.614532\pi$
$317$	−3974.52	−0.704200	−0.352100	+	0.935962i	$0.614532\pi$
$318$	−2716.84	−0.479096
$319$	1444.10	0.253461
$320$	−11249.0	−1.96511
$321$	−589.383	−0.102480
$322$	0	0
$323$	−365.939	−0.0630384
$324$	−175.897	−0.0301607
$325$	−23672.4	−4.04034
$326$	7167.13	1.21764
$327$	−919.029	−0.155420
$328$	−7359.85	−1.23896
$329$	0	0
$330$	−3450.51	−0.575589
$331$	−8912.82	−1.48004	−0.740020	−	0.672585i	$-0.765184\pi$
$331$	−8912.82	−1.48004	−0.740020	+	0.672585i	$0.765184\pi$
$332$	1348.84	0.222974
$333$	−505.060	−0.0831144
$334$	5049.41	0.827220
$335$	16179.2	2.63871
$336$	0	0
$337$	3977.06	0.642862	0.321431	−	0.946933i	$-0.395836\pi$
$337$	3977.06	0.642862	0.321431	+	0.946933i	$0.395836\pi$
$338$	13118.7	2.11114
$339$	5992.88	0.960143
$340$	243.706	0.0388729
$341$	2937.83	0.466547
$342$	−1409.87	−0.222915
$343$	0	0
$344$	12313.1	1.92987
$345$	1528.16	0.238474
$346$	1135.04	0.176358
$347$	6826.43	1.05609	0.528043	−	0.849218i	$-0.322926\pi$
$347$	6826.43	1.05609	0.528043	+	0.849218i	$0.322926\pi$
$348$	−392.960	−0.0605312
$349$	807.342	0.123828	0.0619141	−	0.998081i	$-0.480280\pi$
$349$	807.342	0.123828	0.0619141	+	0.998081i	$0.480280\pi$
$350$	0	0
$351$	−2358.59	−0.358668
$352$	2280.80	0.345361
$353$	7919.20	1.19404	0.597020	−	0.802226i	$-0.296351\pi$
$353$	7919.20	1.19404	0.597020	+	0.802226i	$0.296351\pi$
$354$	4545.57	0.682470
$355$	−3301.38	−0.493574
$356$	619.807	0.0922744
$357$	0	0
$358$	2550.52	0.376534
$359$	−8819.21	−1.29655	−0.648273	−	0.761408i	$-0.724509\pi$
$359$	−8819.21	−1.29655	−0.648273	+	0.761408i	$0.724509\pi$
$360$	4397.93	0.643865
$361$	−2648.64	−0.386155
$362$	981.307	0.142476
$363$	−2273.47	−0.328722
$364$	0	0
$365$	12319.8	1.76670
$366$	−27.2132	−0.00388649
$367$	11161.8	1.58758	0.793788	−	0.608194i	$-0.208106\pi$
$367$	11161.8	1.58758	0.793788	+	0.608194i	$0.208106\pi$
$368$	1072.85	0.151974
$369$	2697.41	0.380547
$370$	2695.99	0.378805
$371$	0	0
$372$	−799.426	−0.111420
$373$	2727.86	0.378668	0.189334	−	0.981913i	$-0.439367\pi$
$373$	2727.86	0.378668	0.189334	+	0.981913i	$0.439367\pi$
$374$	325.964	0.0450673
$375$	−8715.38	−1.20016
$376$	7503.28	1.02913
$377$	−5269.17	−0.719830
$378$	0	0
$379$	4086.49	0.553849	0.276924	−	0.960892i	$-0.410685\pi$
$379$	4086.49	0.553849	0.276924	+	0.960892i	$0.410685\pi$
$380$	−2803.99	−0.378530
$381$	−6934.20	−0.932414
$382$	433.133	0.0580131
$383$	−13032.9	−1.73878	−0.869389	−	0.494129i	$-0.835487\pi$
$383$	−13032.9	−1.73878	−0.869389	+	0.494129i	$0.835487\pi$
$384$	1807.77	0.240241
$385$	0	0
$386$	−5766.03	−0.760319
$387$	−4512.79	−0.592760
$388$	−1309.71	−0.171367
$389$	−194.991	−0.0254151	−0.0127075	−	0.999919i	$-0.504045\pi$
$389$	−194.991	−0.0254151	−0.0127075	+	0.999919i	$0.504045\pi$
$390$	12590.1	1.63468
$391$	−144.363	−0.0186719
$392$	0	0
$393$	465.053	0.0596916
$394$	−6434.73	−0.822785
$395$	2751.02	0.350427
$396$	−467.909	−0.0593771
$397$	14183.0	1.79300	0.896501	−	0.443042i	$-0.146101\pi$
$397$	14183.0	1.79300	0.896501	+	0.443042i	$0.146101\pi$
$398$	3240.61	0.408134
$399$	0	0
$400$	−11357.6	−1.41971
$401$	10005.0	1.24596	0.622978	−	0.782239i	$-0.285923\pi$
$401$	10005.0	1.24596	0.622978	+	0.782239i	$0.285923\pi$
$402$	−5888.61	−0.730590
$403$	−10719.4	−1.32500
$404$	992.863	0.122269
$405$	−1611.86	−0.197763
$406$	0	0
$407$	−1343.52	−0.163626
$408$	−415.465	−0.0504132
$409$	−4634.93	−0.560349	−0.280174	−	0.959949i	$-0.590392\pi$
$409$	−4634.93	−0.560349	−0.280174	+	0.959949i	$0.590392\pi$
$410$	−14398.7	−1.73439
$411$	1550.81	0.186121
$412$	1706.95	0.204115
$413$	0	0
$414$	−556.191	−0.0660273
$415$	12360.3	1.46203
$416$	−8322.08	−0.980826
$417$	−2874.20	−0.337531
$418$	−3750.42	−0.438849
$419$	−4998.31	−0.582777	−0.291388	−	0.956605i	$-0.594117\pi$
$419$	−4998.31	−0.582777	−0.291388	+	0.956605i	$0.594117\pi$
$420$	0	0
$421$	−704.160	−0.0815170	−0.0407585	−	0.999169i	$-0.512977\pi$
$421$	−704.160	−0.0815170	−0.0407585	+	0.999169i	$0.512977\pi$
$422$	1517.19	0.175014
$423$	−2749.98	−0.316096
$424$	9211.50	1.05507
$425$	1528.28	0.174429
$426$	1201.57	0.136658
$427$	0	0
$428$	426.629	0.0481820
$429$	−6274.16	−0.706105
$430$	24089.1	2.70158
$431$	−10332.8	−1.15479	−0.577393	−	0.816466i	$-0.695930\pi$
$431$	−10332.8	−1.15479	−0.577393	+	0.816466i	$0.695930\pi$
$432$	−1131.62	−0.126030
$433$	−11106.8	−1.23270	−0.616348	−	0.787474i	$-0.711389\pi$
$433$	−11106.8	−1.23270	−0.616348	+	0.787474i	$0.711389\pi$
$434$	0	0
$435$	−3600.94	−0.396901
$436$	665.246	0.0730723
$437$	1660.98	0.181821
$438$	−4483.92	−0.489155
$439$	7299.28	0.793566	0.396783	−	0.917912i	$-0.370126\pi$
$439$	7299.28	0.793566	0.396783	+	0.917912i	$0.370126\pi$
$440$	11699.0	1.26757
$441$	0	0
$442$	−1189.36	−0.127991
$443$	16089.7	1.72560	0.862802	−	0.505542i	$-0.168707\pi$
$443$	16089.7	1.72560	0.862802	+	0.505542i	$0.168707\pi$
$444$	365.591	0.0390770
$445$	5679.68	0.605040
$446$	2341.71	0.248617
$447$	−5311.88	−0.562065
$448$	0	0
$449$	13561.7	1.42543	0.712715	−	0.701454i	$-0.247466\pi$
$449$	13561.7	1.42543	0.712715	+	0.701454i	$0.247466\pi$
$450$	5888.05	0.616812
$451$	7175.46	0.749178
$452$	−4337.99	−0.451420
$453$	−7620.71	−0.790402
$454$	11464.2	1.18512
$455$	0	0
$456$	4780.19	0.490905
$457$	10848.6	1.11045	0.555224	−	0.831701i	$-0.312633\pi$
$457$	10848.6	1.11045	0.555224	+	0.831701i	$0.312633\pi$
$458$	11593.0	1.18277
$459$	152.269	0.0154844
$460$	−1106.17	−0.112121
$461$	1758.69	0.177679	0.0888397	−	0.996046i	$-0.471684\pi$
$461$	1758.69	0.177679	0.0888397	+	0.996046i	$0.471684\pi$
$462$	0	0
$463$	−5411.95	−0.543228	−0.271614	−	0.962406i	$-0.587557\pi$
$463$	−5411.95	−0.543228	−0.271614	+	0.962406i	$0.587557\pi$
$464$	−2528.06	−0.252936
$465$	−7325.64	−0.730577
$466$	−7617.54	−0.757244
$467$	−8111.34	−0.803744	−0.401872	−	0.915696i	$-0.631640\pi$
$467$	−8111.34	−0.803744	−0.401872	+	0.915696i	$0.631640\pi$
$468$	1707.29	0.168631
$469$	0	0
$470$	14679.3	1.44065
$471$	3250.03	0.317948
$472$	−15411.9	−1.50294
$473$	−12004.6	−1.16696
$474$	−1001.26	−0.0970244
$475$	−17583.8	−1.69853
$476$	0	0
$477$	−3376.05	−0.324065
$478$	10240.9	0.979935
$479$	−2095.76	−0.199912	−0.0999559	−	0.994992i	$-0.531870\pi$
$479$	−2095.76	−0.199912	−0.0999559	+	0.994992i	$0.531870\pi$
$480$	−5687.30	−0.540809
$481$	4902.18	0.464699
$482$	10484.9	0.990817
$483$	0	0
$484$	1645.67	0.154552
$485$	−12001.7	−1.12364
$486$	586.654	0.0547555
$487$	9610.08	0.894197	0.447099	−	0.894485i	$-0.352457\pi$
$487$	9610.08	0.894197	0.447099	+	0.894485i	$0.352457\pi$
$488$	92.2670	0.00855888
$489$	8906.17	0.823622
$490$	0	0
$491$	−11717.3	−1.07698	−0.538488	−	0.842633i	$-0.681004\pi$
$491$	−11717.3	−1.07698	−0.538488	+	0.842633i	$0.681004\pi$
$492$	−1952.54	−0.178918
$493$	340.174	0.0310764
$494$	13684.4	1.24633
$495$	−4287.75	−0.389333
$496$	−5143.01	−0.465581
$497$	0	0
$498$	−4498.67	−0.404800
$499$	−9195.19	−0.824916	−0.412458	−	0.910977i	$-0.635330\pi$
$499$	−9195.19	−0.824916	−0.412458	+	0.910977i	$0.635330\pi$
$500$	6308.69	0.564266
$501$	6274.60	0.559538
$502$	−7249.90	−0.644580
$503$	−16118.8	−1.42883	−0.714414	−	0.699724i	$-0.753307\pi$
$503$	−16118.8	−1.42883	−0.714414	+	0.699724i	$0.753307\pi$
$504$	0	0
$505$	9098.23	0.801715
$506$	−1479.54	−0.129987
$507$	16301.9	1.42799
$508$	5019.37	0.438383
$509$	−4918.78	−0.428333	−0.214166	−	0.976797i	$-0.568703\pi$
$509$	−4918.78	−0.428333	−0.214166	+	0.976797i	$0.568703\pi$
$510$	−812.808	−0.0705721
$511$	0	0
$512$	−12226.4	−1.05534
$513$	−1751.96	−0.150781
$514$	−10788.7	−0.925819
$515$	15641.9	1.33838
$516$	3266.62	0.278692
$517$	−7315.29	−0.622294
$518$	0	0
$519$	1410.44	0.119290
$520$	−42687.0	−3.59990
$521$	−13963.4	−1.17418	−0.587089	−	0.809522i	$-0.699726\pi$
$521$	−13963.4	−1.17418	−0.587089	+	0.809522i	$0.699726\pi$
$522$	1310.60	0.109892
$523$	13755.3	1.15005	0.575024	−	0.818136i	$-0.304993\pi$
$523$	13755.3	1.15005	0.575024	+	0.818136i	$0.304993\pi$
$524$	−336.632	−0.0280646
$525$	0	0
$526$	14871.9	1.23278
$527$	692.040	0.0572026
$528$	−3010.24	−0.248113
$529$	−11511.7	−0.946145
$530$	18021.2	1.47697
$531$	5648.51	0.461628
$532$	0	0
$533$	−26181.5	−2.12767
$534$	−2067.18	−0.167520
$535$	3909.47	0.315928
$536$	19965.5	1.60891
$537$	3169.38	0.254691
$538$	−12044.3	−0.965178
$539$	0	0
$540$	1166.76	0.0929800
$541$	14462.7	1.14935	0.574676	−	0.818381i	$-0.305128\pi$
$541$	14462.7	1.14935	0.574676	+	0.818381i	$0.305128\pi$
$542$	−10704.0	−0.848293
$543$	1219.41	0.0963719
$544$	537.269	0.0423441
$545$	6096.07	0.479132
$546$	0	0
$547$	13682.5	1.06951	0.534755	−	0.845007i	$-0.320404\pi$
$547$	13682.5	1.06951	0.534755	+	0.845007i	$0.320404\pi$
$548$	−1122.56	−0.0875065
$549$	−33.8162	−0.00262886
$550$	15662.9	1.21431
$551$	−3913.92	−0.302611
$552$	1885.78	0.145406
$553$	0	0
$554$	2685.49	0.205949
$555$	3350.14	0.256227
$556$	2080.51	0.158693
$557$	−7663.13	−0.582939	−0.291470	−	0.956580i	$-0.594144\pi$
$557$	−7663.13	−0.582939	−0.291470	+	0.956580i	$0.594144\pi$
$558$	2666.25	0.202278
$559$	43801.8	3.31417
$560$	0	0
$561$	405.056	0.0304839
$562$	6791.71	0.509770
$563$	−17470.5	−1.30780	−0.653902	−	0.756580i	$-0.726869\pi$
$563$	−17470.5	−1.30780	−0.653902	+	0.756580i	$0.726869\pi$
$564$	1990.59	0.148616
$565$	−39751.8	−2.95995
$566$	−7598.83	−0.564316
$567$	0	0
$568$	−4073.96	−0.300950
$569$	−13873.9	−1.02219	−0.511094	−	0.859525i	$-0.670760\pi$
$569$	−13873.9	−1.02219	−0.511094	+	0.859525i	$0.670760\pi$
$570$	9351.88	0.687205
$571$	−3777.52	−0.276855	−0.138428	−	0.990373i	$-0.544205\pi$
$571$	−3777.52	−0.276855	−0.138428	+	0.990373i	$0.544205\pi$
$572$	4541.60	0.331982
$573$	538.229	0.0392405
$574$	0	0
$575$	−6936.79	−0.503103
$576$	5087.60	0.368026
$577$	−13880.5	−1.00148	−0.500738	−	0.865599i	$-0.666938\pi$
$577$	−13880.5	−1.00148	−0.500738	+	0.865599i	$0.666938\pi$
$578$	−11784.2	−0.848028
$579$	−7165.10	−0.514286
$580$	2606.57	0.186607
$581$	0	0
$582$	4368.14	0.311108
$583$	−8980.72	−0.637982
$584$	15202.8	1.07722
$585$	15644.9	1.10571
$586$	−22073.2	−1.55604
$587$	2395.61	0.168445	0.0842227	−	0.996447i	$-0.473159\pi$
$587$	2395.61	0.168445	0.0842227	+	0.996447i	$0.473159\pi$
$588$	0	0
$589$	−7962.36	−0.557018
$590$	−30151.5	−2.10393
$591$	−7996.06	−0.556538
$592$	2351.99	0.163287
$593$	−6603.50	−0.457290	−0.228645	−	0.973510i	$-0.573430\pi$
$593$	−6603.50	−0.457290	−0.228645	+	0.973510i	$0.573430\pi$
$594$	1560.57	0.107796
$595$	0	0
$596$	3845.04	0.264260
$597$	4026.92	0.276065
$598$	5398.47	0.369164
$599$	17252.1	1.17680	0.588399	−	0.808571i	$-0.299759\pi$
$599$	17252.1	1.17680	0.588399	+	0.808571i	$0.299759\pi$
$600$	−19963.6	−1.35835
$601$	−12833.1	−0.871005	−0.435503	−	0.900187i	$-0.643429\pi$
$601$	−12833.1	−0.871005	−0.435503	+	0.900187i	$0.643429\pi$
$602$	0	0
$603$	−7317.43	−0.494177
$604$	5516.31	0.371615
$605$	15080.3	1.01339
$606$	−3311.40	−0.221974
$607$	−8620.16	−0.576411	−0.288206	−	0.957569i	$-0.593059\pi$
$607$	−8620.16	−0.576411	−0.288206	+	0.957569i	$0.593059\pi$
$608$	−6181.62	−0.412332
$609$	0	0
$610$	180.510	0.0119813
$611$	26691.7	1.76732
$612$	−110.221	−0.00728013
$613$	5136.73	0.338451	0.169226	−	0.985577i	$-0.445873\pi$
$613$	5136.73	0.338451	0.169226	+	0.985577i	$0.445873\pi$
$614$	11223.4	0.737690
$615$	−17892.4	−1.17316
$616$	0	0
$617$	−1759.82	−0.114826	−0.0574131	−	0.998351i	$-0.518285\pi$
$617$	−1759.82	−0.114826	−0.0574131	+	0.998351i	$0.518285\pi$
$618$	−5693.04	−0.370562
$619$	3560.24	0.231176	0.115588	−	0.993297i	$-0.463125\pi$
$619$	3560.24	0.231176	0.115588	+	0.993297i	$0.463125\pi$
$620$	5302.72	0.343488
$621$	−691.145	−0.0446614
$622$	15492.4	0.998698
$623$	0	0
$624$	10983.6	0.704643
$625$	23936.8	1.53195
$626$	−14167.1	−0.904524
$627$	−4660.43	−0.296841
$628$	−2352.56	−0.149486
$629$	−316.482	−0.0200620
$630$	0	0
$631$	−27321.4	−1.72369	−0.861845	−	0.507172i	$-0.830691\pi$
$631$	−27321.4	−1.72369	−0.861845	+	0.507172i	$0.830691\pi$
$632$	3394.81	0.213668
$633$	1885.33	0.118381
$634$	−9595.34	−0.601072
$635$	45995.7	2.87446
$636$	2443.78	0.152362
$637$	0	0
$638$	3486.36	0.216342
$639$	1493.12	0.0924366
$640$	−11991.3	−0.740619
$641$	−21927.0	−1.35112	−0.675558	−	0.737307i	$-0.736097\pi$
$641$	−21927.0	−1.35112	−0.675558	+	0.737307i	$0.736097\pi$
$642$	−1422.90	−0.0874723
$643$	5826.04	0.357320	0.178660	−	0.983911i	$-0.442824\pi$
$643$	5826.04	0.357320	0.178660	+	0.983911i	$0.442824\pi$
$644$	0	0
$645$	29934.1	1.82737
$646$	−883.455	−0.0538066
$647$	−24210.7	−1.47113	−0.735565	−	0.677454i	$-0.763083\pi$
$647$	−24210.7	−1.47113	−0.735565	+	0.677454i	$0.763083\pi$
$648$	−1989.06	−0.120583
$649$	15025.7	0.908801
$650$	−57150.3	−3.44864
$651$	0	0
$652$	−6446.80	−0.387233
$653$	−25623.3	−1.53556	−0.767778	−	0.640716i	$-0.778637\pi$
$653$	−25623.3	−1.53556	−0.767778	+	0.640716i	$0.778637\pi$
$654$	−2218.73	−0.132660
$655$	−3084.77	−0.184018
$656$	−12561.5	−0.747626
$657$	−5571.90	−0.330868
$658$	0	0
$659$	−23273.7	−1.37574	−0.687871	−	0.725833i	$-0.741455\pi$
$659$	−23273.7	−1.37574	−0.687871	+	0.725833i	$0.741455\pi$
$660$	3103.72	0.183049
$661$	20036.5	1.17902	0.589508	−	0.807763i	$-0.299322\pi$
$661$	20036.5	1.17902	0.589508	+	0.807763i	$0.299322\pi$
$662$	−21517.5	−1.26329
$663$	−1477.95	−0.0865744
$664$	15252.9	0.891454
$665$	0	0
$666$	−1219.32	−0.0709426
$667$	−1544.04	−0.0896333
$668$	−4541.92	−0.263072
$669$	2909.91	0.168167
$670$	39060.1	2.25228
$671$	−89.9554	−0.00517540
$672$	0	0
$673$	−18127.8	−1.03830	−0.519149	−	0.854684i	$-0.673751\pi$
$673$	−18127.8	−1.03830	−0.519149	+	0.854684i	$0.673751\pi$
$674$	9601.48	0.548717
$675$	7316.73	0.417216
$676$	−11800.2	−0.671383
$677$	−13815.5	−0.784301	−0.392150	−	0.919901i	$-0.628269\pi$
$677$	−13815.5	−0.784301	−0.392150	+	0.919901i	$0.628269\pi$
$678$	14468.1	0.819533
$679$	0	0
$680$	2755.85	0.155415
$681$	14245.9	0.801622
$682$	7092.55	0.398223
$683$	−4604.23	−0.257944	−0.128972	−	0.991648i	$-0.541168\pi$
$683$	−4604.23	−0.257944	−0.128972	+	0.991648i	$0.541168\pi$
$684$	1268.17	0.0708912
$685$	−10286.8	−0.573777
$686$	0	0
$687$	14406.0	0.800032
$688$	21015.4	1.16454
$689$	32768.5	1.81187
$690$	3689.31	0.203550
$691$	−17913.7	−0.986205	−0.493103	−	0.869971i	$-0.664137\pi$
$691$	−17913.7	−0.986205	−0.493103	+	0.869971i	$0.664137\pi$
$692$	−1020.96	−0.0560854
$693$	0	0
$694$	16480.5	0.901426
$695$	19065.1	1.04054
$696$	−4443.63	−0.242005
$697$	1690.26	0.0918555
$698$	1949.10	0.105694
$699$	−9465.86	−0.512206
$700$	0	0
$701$	11303.7	0.609035	0.304518	−	0.952507i	$-0.401505\pi$
$701$	11303.7	0.609035	0.304518	+	0.952507i	$0.401505\pi$
$702$	−5694.15	−0.306142
$703$	3641.33	0.195356
$704$	13533.6	0.724529
$705$	18241.1	0.974466
$706$	19118.6	1.01918
$707$	0	0
$708$	−4088.72	−0.217039
$709$	−16046.3	−0.849973	−0.424987	−	0.905200i	$-0.639721\pi$
$709$	−16046.3	−0.849973	−0.424987	+	0.905200i	$0.639721\pi$
$710$	−7970.22	−0.421292
$711$	−1244.21	−0.0656280
$712$	7008.83	0.368915
$713$	−3141.15	−0.164989
$714$	0	0
$715$	41617.5	2.17679
$716$	−2294.18	−0.119745
$717$	12725.8	0.662836
$718$	−21291.5	−1.10667
$719$	25190.5	1.30660	0.653300	−	0.757099i	$-0.273384\pi$
$719$	25190.5	1.30660	0.653300	+	0.757099i	$0.273384\pi$
$720$	7506.19	0.388527
$721$	0	0
$722$	−6394.38	−0.329604
$723$	13029.0	0.670197
$724$	−882.680	−0.0453102
$725$	16345.8	0.837334
$726$	−5488.64	−0.280582
$727$	−11277.2	−0.575307	−0.287653	−	0.957735i	$-0.592875\pi$
$727$	−11277.2	−0.575307	−0.287653	+	0.957735i	$0.592875\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	29742.6	1.50797
$731$	−2827.82	−0.143079
$732$	24.4781	0.00123598
$733$	−23720.0	−1.19525	−0.597626	−	0.801775i	$-0.703889\pi$
$733$	−23720.0	−1.19525	−0.597626	+	0.801775i	$0.703889\pi$
$734$	26946.9	1.35508
$735$	0	0
$736$	−2438.64	−0.122133
$737$	−19465.3	−0.972880
$738$	6512.14	0.324817
$739$	8124.72	0.404428	0.202214	−	0.979341i	$-0.435186\pi$
$739$	8124.72	0.404428	0.202214	+	0.979341i	$0.435186\pi$
$740$	−2425.03	−0.120467
$741$	17004.8	0.843030
$742$	0	0
$743$	20955.3	1.03469	0.517346	−	0.855777i	$-0.326920\pi$
$743$	20955.3	1.03469	0.517346	+	0.855777i	$0.326920\pi$
$744$	−9039.98	−0.445459
$745$	35234.6	1.73274
$746$	6585.63	0.323213
$747$	−5590.23	−0.273810
$748$	−293.203	−0.0143323
$749$	0	0
$750$	−21040.8	−1.02440
$751$	−38208.1	−1.85650	−0.928251	−	0.371954i	$-0.878688\pi$
$751$	−38208.1	−1.85650	−0.928251	+	0.371954i	$0.878688\pi$
$752$	12806.3	0.621006
$753$	−9009.02	−0.435999
$754$	−12720.9	−0.614413
$755$	50549.4	2.43666
$756$	0	0
$757$	30958.1	1.48638	0.743191	−	0.669079i	$-0.233311\pi$
$757$	30958.1	1.48638	0.743191	+	0.669079i	$0.233311\pi$
$758$	9865.65	0.472740
$759$	−1838.53	−0.0879243
$760$	−31707.8	−1.51337
$761$	40049.4	1.90774	0.953871	−	0.300218i	$-0.0970594\pi$
$761$	40049.4	1.90774	0.953871	+	0.300218i	$0.0970594\pi$
$762$	−16740.6	−0.795865
$763$	0	0
$764$	−389.601	−0.0184493
$765$	−1010.03	−0.0477355
$766$	−31464.3	−1.48414
$767$	−54825.3	−2.58100
$768$	−9202.57	−0.432382
$769$	8002.01	0.375240	0.187620	−	0.982242i	$-0.439923\pi$
$769$	8002.01	0.375240	0.187620	+	0.982242i	$0.439923\pi$
$770$	0	0
$771$	−13406.5	−0.626231
$772$	5186.52	0.241796
$773$	13933.4	0.648316	0.324158	−	0.946003i	$-0.394919\pi$
$773$	13933.4	0.648316	0.324158	+	0.946003i	$0.394919\pi$
$774$	−10894.8	−0.505952
$775$	33253.4	1.54128
$776$	−14810.3	−0.685126
$777$	0	0
$778$	−470.751	−0.0216931
$779$	−19447.6	−0.894456
$780$	−11324.7	−0.519859
$781$	3971.89	0.181979
$782$	−348.522	−0.0159375
$783$	1628.61	0.0743316
$784$	0	0
$785$	−21558.0	−0.980175
$786$	1122.74	0.0509500
$787$	−37581.7	−1.70222	−0.851108	−	0.524991i	$-0.824069\pi$
$787$	−37581.7	−1.70222	−0.851108	+	0.524991i	$0.824069\pi$
$788$	5788.01	0.261662
$789$	18480.4	0.833865
$790$	6641.54	0.299108
$791$	0	0
$792$	−5291.16	−0.237390
$793$	328.225	0.0146981
$794$	34240.7	1.53042
$795$	22393.9	0.999032
$796$	−2914.92	−0.129795
$797$	9458.78	0.420385	0.210193	−	0.977660i	$-0.432591\pi$
$797$	9458.78	0.420385	0.210193	+	0.977660i	$0.432591\pi$
$798$	0	0
$799$	−1723.20	−0.0762985
$800$	25816.4	1.14093
$801$	−2568.77	−0.113312
$802$	24154.3	1.06349
$803$	−14821.9	−0.651376
$804$	5296.78	0.232342
$805$	0	0
$806$	−25879.0	−1.13095
$807$	−14966.7	−0.652854
$808$	11227.4	0.488834
$809$	−1909.94	−0.0830034	−0.0415017	−	0.999138i	$-0.513214\pi$
$809$	−1909.94	−0.0830034	−0.0415017	+	0.999138i	$0.513214\pi$
$810$	−3891.37	−0.168801
$811$	−43110.6	−1.86661	−0.933303	−	0.359091i	$-0.883087\pi$
$811$	−43110.6	−1.86661	−0.933303	+	0.359091i	$0.883087\pi$
$812$	0	0
$813$	−13301.2	−0.573792
$814$	−3243.55	−0.139664
$815$	−59076.1	−2.53907
$816$	−709.097	−0.0304208
$817$	32535.9	1.39325
$818$	−11189.7	−0.478287
$819$	0	0
$820$	12951.5	0.551570
$821$	4026.56	0.171167	0.0855834	−	0.996331i	$-0.472725\pi$
$821$	4026.56	0.171167	0.0855834	+	0.996331i	$0.472725\pi$
$822$	3743.98	0.158864
$823$	39668.1	1.68012	0.840062	−	0.542491i	$-0.182519\pi$
$823$	39668.1	1.68012	0.840062	+	0.542491i	$0.182519\pi$
$824$	19302.4	0.816056
$825$	19463.4	0.821368
$826$	0	0
$827$	30137.7	1.26722	0.633611	−	0.773652i	$-0.281572\pi$
$827$	30137.7	1.26722	0.633611	+	0.773652i	$0.281572\pi$
$828$	500.291	0.0209980
$829$	−23278.0	−0.975245	−0.487622	−	0.873055i	$-0.662136\pi$
$829$	−23278.0	−0.975245	−0.487622	+	0.873055i	$0.662136\pi$
$830$	29840.4	1.24792
$831$	3337.10	0.139306
$832$	−49381.0	−2.05766
$833$	0	0
$834$	−6938.94	−0.288100
$835$	−41620.5	−1.72495
$836$	3373.48	0.139563
$837$	3313.19	0.136823
$838$	−12067.0	−0.497431
$839$	9494.43	0.390684	0.195342	−	0.980735i	$-0.437418\pi$
$839$	9494.43	0.390684	0.195342	+	0.980735i	$0.437418\pi$
$840$	0	0
$841$	−20750.6	−0.850820
$842$	−1699.99	−0.0695791
$843$	8439.65	0.344813
$844$	−1364.71	−0.0556578
$845$	−108133.	−4.40223
$846$	−6639.04	−0.269805
$847$	0	0
$848$	15721.8	0.636661
$849$	−9442.62	−0.381708
$850$	3689.59	0.148885
$851$	1436.50	0.0578644
$852$	−1080.81	−0.0434599
$853$	12692.4	0.509471	0.254736	−	0.967011i	$-0.418012\pi$
$853$	12692.4	0.509471	0.254736	+	0.967011i	$0.418012\pi$
$854$	0	0
$855$	11621.0	0.464831
$856$	4824.36	0.192632
$857$	−22206.0	−0.885114	−0.442557	−	0.896740i	$-0.645929\pi$
$857$	−22206.0	−0.885114	−0.442557	+	0.896740i	$0.645929\pi$
$858$	−15147.2	−0.602698
$859$	−19820.5	−0.787271	−0.393636	−	0.919267i	$-0.628783\pi$
$859$	−19820.5	−0.787271	−0.393636	+	0.919267i	$0.628783\pi$
$860$	−21668.0	−0.859155
$861$	0	0
$862$	−24945.5	−0.985671
$863$	36413.8	1.43631	0.718157	−	0.695881i	$-0.244986\pi$
$863$	36413.8	1.43631	0.718157	+	0.695881i	$0.244986\pi$
$864$	2572.21	0.101283
$865$	−9355.70	−0.367749
$866$	−26814.1	−1.05217
$867$	−14643.6	−0.573613
$868$	0	0
$869$	−3309.76	−0.129201
$870$	−8693.43	−0.338776
$871$	71024.1	2.76298
$872$	7522.67	0.292144
$873$	5428.03	0.210436
$874$	4009.97	0.155194
$875$	0	0
$876$	4033.26	0.155561
$877$	19442.6	0.748609	0.374305	−	0.927306i	$-0.377881\pi$
$877$	19442.6	0.748609	0.374305	+	0.927306i	$0.377881\pi$
$878$	17622.0	0.677351
$879$	−27429.1	−1.05252
$880$	19967.4	0.764888
$881$	25184.2	0.963082	0.481541	−	0.876423i	$-0.340077\pi$
$881$	25184.2	0.963082	0.481541	+	0.876423i	$0.340077\pi$
$882$	0	0
$883$	−4050.03	−0.154354	−0.0771769	−	0.997017i	$-0.524591\pi$
$883$	−4050.03	−0.154354	−0.0771769	+	0.997017i	$0.524591\pi$
$884$	1069.83	0.0407038
$885$	−37467.5	−1.42311
$886$	38843.9	1.47290
$887$	−41604.2	−1.57489	−0.787447	−	0.616383i	$-0.788598\pi$
$887$	−41604.2	−1.57489	−0.787447	+	0.616383i	$0.788598\pi$
$888$	4134.14	0.156231
$889$	0	0
$890$	13712.0	0.516434
$891$	1939.23	0.0729144
$892$	−2106.36	−0.0790652
$893$	19826.5	0.742967
$894$	−12824.0	−0.479753
$895$	−21023.0	−0.785165
$896$	0	0
$897$	6708.36	0.249705
$898$	32740.9	1.21668
$899$	7401.76	0.274597
$900$	−5296.27	−0.196158
$901$	−2115.51	−0.0782219
$902$	17323.1	0.639463
$903$	0	0
$904$	−49054.4	−1.80478
$905$	−8088.56	−0.297097
$906$	−18398.0	−0.674650
$907$	−3572.60	−0.130790	−0.0653949	−	0.997859i	$-0.520831\pi$
$907$	−3572.60	−0.130790	−0.0653949	+	0.997859i	$0.520831\pi$
$908$	−10312.0	−0.376890
$909$	−4114.88	−0.150145
$910$	0	0
$911$	29457.7	1.07133	0.535663	−	0.844432i	$-0.320062\pi$
$911$	29457.7	1.07133	0.535663	+	0.844432i	$0.320062\pi$
$912$	8158.61	0.296226
$913$	−14870.7	−0.539046
$914$	26190.8	0.947827
$915$	224.309	0.00810428
$916$	−10427.9	−0.376143
$917$	0	0
$918$	367.611	0.0132167
$919$	−3310.65	−0.118834	−0.0594168	−	0.998233i	$-0.518924\pi$
$919$	−3310.65	−0.118834	−0.0594168	+	0.998233i	$0.518924\pi$
$920$	−12508.7	−0.448260
$921$	13946.7	0.498979
$922$	4245.85	0.151659
$923$	−14492.5	−0.516820
$924$	0	0
$925$	−15207.3	−0.540556
$926$	−13065.6	−0.463674
$927$	−7074.40	−0.250651
$928$	5746.39	0.203270
$929$	31467.5	1.11132	0.555660	−	0.831410i	$-0.312466\pi$
$929$	31467.5	1.11132	0.555660	+	0.831410i	$0.312466\pi$
$930$	−17685.7	−0.623587
$931$	0	0
$932$	6851.94	0.240818
$933$	19251.5	0.675527
$934$	−19582.5	−0.686038
$935$	−2686.80	−0.0939763
$936$	19306.2	0.674190
$937$	17363.4	0.605375	0.302688	−	0.953090i	$-0.402116\pi$
$937$	17363.4	0.605375	0.302688	+	0.953090i	$0.402116\pi$
$938$	0	0
$939$	−17604.6	−0.611828
$940$	−13203.9	−0.458154
$941$	5547.77	0.192192	0.0960958	−	0.995372i	$-0.469364\pi$
$941$	5547.77	0.192192	0.0960958	+	0.995372i	$0.469364\pi$
$942$	7846.27	0.271386
$943$	−7672.04	−0.264937
$944$	−26304.3	−0.906919
$945$	0	0
$946$	−28981.6	−0.996062
$947$	−37960.3	−1.30258	−0.651290	−	0.758829i	$-0.725772\pi$
$947$	−37960.3	−1.30258	−0.651290	+	0.758829i	$0.725772\pi$
$948$	900.631	0.0308556
$949$	54081.7	1.84991
$950$	−42451.1	−1.44978
$951$	−11923.6	−0.406570
$952$	0	0
$953$	−10019.3	−0.340563	−0.170282	−	0.985395i	$-0.554468\pi$
$953$	−10019.3	−0.340563	−0.170282	+	0.985395i	$0.554468\pi$
$954$	−8150.51	−0.276606
$955$	−3570.16	−0.120971
$956$	−9211.65	−0.311638
$957$	4332.30	0.146336
$958$	−5059.61	−0.170635
$959$	0	0
$960$	−33746.9	−1.13456
$961$	−14733.1	−0.494548
$962$	11834.9	0.396646
$963$	−1768.15	−0.0591670
$964$	−9431.11	−0.315099
$965$	47527.3	1.58545
$966$	0	0
$967$	27834.4	0.925641	0.462820	−	0.886452i	$-0.346837\pi$
$967$	27834.4	0.925641	0.462820	+	0.886452i	$0.346837\pi$
$968$	18609.4	0.617900
$969$	−1097.82	−0.0363952
$970$	−28974.6	−0.959090
$971$	18275.3	0.604000	0.302000	−	0.953308i	$-0.402346\pi$
$971$	18275.3	0.604000	0.302000	+	0.953308i	$0.402346\pi$
$972$	−527.692	−0.0174133
$973$	0	0
$974$	23200.8	0.763245
$975$	−71017.2	−2.33269
$976$	157.477	0.00516468
$977$	−43028.9	−1.40903	−0.704513	−	0.709691i	$-0.748834\pi$
$977$	−43028.9	−1.40903	−0.704513	+	0.709691i	$0.748834\pi$
$978$	21501.4	0.703005
$979$	−6833.24	−0.223076
$980$	0	0
$981$	−2757.09	−0.0897320
$982$	−28288.1	−0.919256
$983$	−30559.2	−0.991544	−0.495772	−	0.868453i	$-0.665115\pi$
$983$	−30559.2	−0.991544	−0.495772	+	0.868453i	$0.665115\pi$
$984$	−22079.6	−0.715316
$985$	53039.2	1.71571
$986$	821.253	0.0265254
$987$	0	0
$988$	−12309.0	−0.396358
$989$	12835.4	0.412681
$990$	−10351.5	−0.332317
$991$	−44945.9	−1.44072	−0.720360	−	0.693600i	$-0.756024\pi$
$991$	−44945.9	−1.44072	−0.720360	+	0.693600i	$0.756024\pi$
$992$	11690.3	0.374160
$993$	−26738.5	−0.854501
$994$	0	0
$995$	−26711.2	−0.851058
$996$	4046.53	0.128734
$997$	−29006.1	−0.921397	−0.460698	−	0.887557i	$-0.652401\pi$
$997$	−29006.1	−0.921397	−0.460698	+	0.887557i	$0.652401\pi$
$998$	−22199.1	−0.704110
$999$	−1515.18	−0.0479861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.a.k.1.2	yes	2
3.2	odd	2		441.4.a.o.1.1		2
4.3	odd	2		2352.4.a.bl.1.1		2
7.2	even	3		147.4.e.j.67.1		4
7.3	odd	6		147.4.e.k.79.1		4
7.4	even	3		147.4.e.j.79.1		4
7.5	odd	6		147.4.e.k.67.1		4
7.6	odd	2		147.4.a.j.1.2	✓	2
21.2	odd	6		441.4.e.u.361.2		4
21.5	even	6		441.4.e.v.361.2		4
21.11	odd	6		441.4.e.u.226.2		4
21.17	even	6		441.4.e.v.226.2		4
21.20	even	2		441.4.a.n.1.1		2
28.27	even	2		2352.4.a.cf.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.j.1.2	✓	2	7.6	odd	2
147.4.a.k.1.2	yes	2	1.1	even	1	trivial
147.4.e.j.67.1		4	7.2	even	3
147.4.e.j.79.1		4	7.4	even	3
147.4.e.k.67.1		4	7.5	odd	6
147.4.e.k.79.1		4	7.3	odd	6
441.4.a.n.1.1		2	21.20	even	2
441.4.a.o.1.1		2	3.2	odd	2
441.4.e.u.226.2		4	21.11	odd	6
441.4.e.u.361.2		4	21.2	odd	6
441.4.e.v.226.2		4	21.17	even	6
441.4.e.v.361.2		4	21.5	even	6
2352.4.a.bl.1.1		2	4.3	odd	2
2352.4.a.cf.1.2		2	28.27	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

\(f(q)\)	\(=\)	\(q+2.41421 q^{2} +3.00000 q^{3} -2.17157 q^{4} -19.8995 q^{5} +7.24264 q^{6} -24.5563 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.41421 q^{2} +3.00000 q^{3} -2.17157 q^{4} -19.8995 q^{5} +7.24264 q^{6} -24.5563 q^{8} +9.00000 q^{9} -48.0416 q^{10} +23.9411 q^{11} -6.51472 q^{12} -87.3553 q^{13} -59.6985 q^{15} -41.9117 q^{16} +5.63961 q^{17} +21.7279 q^{18} -64.8873 q^{19} +43.2132 q^{20} +57.7990 q^{22} -25.5980 q^{23} -73.6690 q^{24} +270.990 q^{25} -210.894 q^{26} +27.0000 q^{27} +60.3188 q^{29} -144.125 q^{30} +122.711 q^{31} +95.2670 q^{32} +71.8234 q^{33} +13.6152 q^{34} -19.5442 q^{36} -56.1177 q^{37} -156.652 q^{38} -262.066 q^{39} +488.659 q^{40} +299.713 q^{41} -501.421 q^{43} -51.9899 q^{44} -179.095 q^{45} -61.7990 q^{46} -305.553 q^{47} -125.735 q^{48} +654.227 q^{50} +16.9188 q^{51} +189.698 q^{52} -375.117 q^{53} +65.1838 q^{54} -476.416 q^{55} -194.662 q^{57} +145.622 q^{58} +627.612 q^{59} +129.640 q^{60} -3.75736 q^{61} +296.250 q^{62} +565.288 q^{64} +1738.33 q^{65} +173.397 q^{66} -813.048 q^{67} -12.2468 q^{68} -76.7939 q^{69} +165.902 q^{71} -221.007 q^{72} -619.100 q^{73} -135.480 q^{74} +812.970 q^{75} +140.908 q^{76} -632.683 q^{78} -138.246 q^{79} +834.021 q^{80} +81.0000 q^{81} +723.571 q^{82} -621.137 q^{83} -112.225 q^{85} -1210.54 q^{86} +180.956 q^{87} -587.907 q^{88} -285.418 q^{89} -432.375 q^{90} +55.5879 q^{92} +368.132 q^{93} -737.671 q^{94} +1291.22 q^{95} +285.801 q^{96} +603.114 q^{97} +215.470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 6 q^{3} - 10 q^{4} - 20 q^{5} + 6 q^{6} - 18 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 6 * q^3 - 10 * q^4 - 20 * q^5 + 6 * q^6 - 18 * q^8 + 18 * q^9	\( 2 q + 2 q^{2} + 6 q^{3} - 10 q^{4} - 20 q^{5} + 6 q^{6} - 18 q^{8} + 18 q^{9} - 48 q^{10} - 20 q^{11} - 30 q^{12} - 104 q^{13} - 60 q^{15} + 18 q^{16} - 116 q^{17} + 18 q^{18} - 192 q^{19} + 44 q^{20} + 76 q^{22} + 28 q^{23} - 54 q^{24} + 146 q^{25} - 204 q^{26} + 54 q^{27} + 296 q^{29} - 144 q^{30} + 104 q^{31} + 18 q^{32} - 60 q^{33} + 64 q^{34} - 90 q^{36} - 248 q^{37} - 104 q^{38} - 312 q^{39} + 488 q^{40} - 20 q^{41} - 720 q^{43} + 292 q^{44} - 180 q^{45} - 84 q^{46} + 96 q^{47} + 54 q^{48} + 706 q^{50} - 348 q^{51} + 320 q^{52} + 268 q^{53} + 54 q^{54} - 472 q^{55} - 576 q^{57} + 48 q^{58} + 616 q^{59} + 132 q^{60} - 16 q^{61} + 304 q^{62} + 118 q^{64} + 1740 q^{65} + 228 q^{66} - 144 q^{67} + 940 q^{68} + 84 q^{69} + 988 q^{71} - 162 q^{72} - 104 q^{73} - 56 q^{74} + 438 q^{75} + 1136 q^{76} - 612 q^{78} - 944 q^{79} + 828 q^{80} + 162 q^{81} + 856 q^{82} - 1016 q^{83} - 100 q^{85} - 1120 q^{86} + 888 q^{87} - 876 q^{88} + 388 q^{89} - 432 q^{90} - 364 q^{92} + 312 q^{93} - 904 q^{94} + 1304 q^{95} + 54 q^{96} - 488 q^{97} - 180 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 6 * q^3 - 10 * q^4 - 20 * q^5 + 6 * q^6 - 18 * q^8 + 18 * q^9 - 48 * q^10 - 20 * q^11 - 30 * q^12 - 104 * q^13 - 60 * q^15 + 18 * q^16 - 116 * q^17 + 18 * q^18 - 192 * q^19 + 44 * q^20 + 76 * q^22 + 28 * q^23 - 54 * q^24 + 146 * q^25 - 204 * q^26 + 54 * q^27 + 296 * q^29 - 144 * q^30 + 104 * q^31 + 18 * q^32 - 60 * q^33 + 64 * q^34 - 90 * q^36 - 248 * q^37 - 104 * q^38 - 312 * q^39 + 488 * q^40 - 20 * q^41 - 720 * q^43 + 292 * q^44 - 180 * q^45 - 84 * q^46 + 96 * q^47 + 54 * q^48 + 706 * q^50 - 348 * q^51 + 320 * q^52 + 268 * q^53 + 54 * q^54 - 472 * q^55 - 576 * q^57 + 48 * q^58 + 616 * q^59 + 132 * q^60 - 16 * q^61 + 304 * q^62 + 118 * q^64 + 1740 * q^65 + 228 * q^66 - 144 * q^67 + 940 * q^68 + 84 * q^69 + 988 * q^71 - 162 * q^72 - 104 * q^73 - 56 * q^74 + 438 * q^75 + 1136 * q^76 - 612 * q^78 - 944 * q^79 + 828 * q^80 + 162 * q^81 + 856 * q^82 - 1016 * q^83 - 100 * q^85 - 1120 * q^86 + 888 * q^87 - 876 * q^88 + 388 * q^89 - 432 * q^90 - 364 * q^92 + 312 * q^93 - 904 * q^94 + 1304 * q^95 + 54 * q^96 - 488 * q^97 - 180 * q^99

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