LMFDB - Embedded newform 1617.2.a.z.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.11344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 4x + 3 $ x^4 - 2x^3 - 4x^2 + 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.51658$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.51658 q^{2} +1.00000 q^{3} +0.300014 q^{4} -2.33317 q^{5} -1.51658 q^{6} +2.57816 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.51658 q^{2} +1.00000 q^{3} +0.300014 q^{4} -2.33317 q^{5} -1.51658 q^{6} +2.57816 q^{8} +1.00000 q^{9} +3.53844 q^{10} -1.00000 q^{11} +0.300014 q^{12} -1.53844 q^{13} -2.33317 q^{15} -4.51002 q^{16} -0.116609 q^{17} -1.51658 q^{18} -3.61132 q^{19} -0.699986 q^{20} +1.51658 q^{22} +7.11005 q^{23} +2.57816 q^{24} +0.443701 q^{25} +2.33317 q^{26} +1.00000 q^{27} +5.05502 q^{29} +3.53844 q^{30} -4.37690 q^{31} +1.68348 q^{32} -1.00000 q^{33} +0.176846 q^{34} +0.300014 q^{36} -0.300014 q^{37} +5.47686 q^{38} -1.53844 q^{39} -6.01531 q^{40} +8.20479 q^{41} -4.18293 q^{43} -0.300014 q^{44} -2.33317 q^{45} -10.7830 q^{46} +2.30001 q^{47} -4.51002 q^{48} -0.672908 q^{50} -0.116609 q^{51} -0.461555 q^{52} -11.8869 q^{53} -1.51658 q^{54} +2.33317 q^{55} -3.61132 q^{57} -7.66635 q^{58} +4.95627 q^{59} -0.699986 q^{60} -4.57160 q^{61} +6.63792 q^{62} +6.46691 q^{64} +3.58946 q^{65} +1.51658 q^{66} +12.2894 q^{67} -0.0349842 q^{68} +7.11005 q^{69} +4.25628 q^{71} +2.57816 q^{72} +10.4380 q^{73} +0.454996 q^{74} +0.443701 q^{75} -1.08345 q^{76} +2.33317 q^{78} +14.3148 q^{79} +10.5227 q^{80} +1.00000 q^{81} -12.4432 q^{82} -11.1869 q^{83} +0.272068 q^{85} +6.34374 q^{86} +5.05502 q^{87} -2.57816 q^{88} +13.9327 q^{89} +3.53844 q^{90} +2.13312 q^{92} -4.37690 q^{93} -3.48816 q^{94} +8.42585 q^{95} +1.68348 q^{96} -16.4101 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 12 * q^8 + 4 * q^9	$ 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 12 q^{8} + 4 q^{9} + 10 q^{10} - 4 q^{11} + 4 q^{12} - 2 q^{13} + 4 q^{15} + 12 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{22} + 4 q^{23} + 12 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{27} + 8 q^{29} + 10 q^{30} - 12 q^{31} + 26 q^{32} - 4 q^{33} - 16 q^{34} + 4 q^{36} - 4 q^{37} + 8 q^{38} - 2 q^{39} - 6 q^{40} + 2 q^{41} + 18 q^{43} - 4 q^{44} + 4 q^{45} - 14 q^{46} + 12 q^{47} + 12 q^{48} + 2 q^{50} + 2 q^{51} - 6 q^{52} - 12 q^{53} + 2 q^{54} - 4 q^{55} - 4 q^{58} + 12 q^{59} + 2 q^{61} - 26 q^{62} + 56 q^{64} - 4 q^{65} - 2 q^{66} + 28 q^{67} - 48 q^{68} + 4 q^{69} + 12 q^{71} + 12 q^{72} + 6 q^{73} - 16 q^{74} + 4 q^{75} - 18 q^{76} - 4 q^{78} + 2 q^{79} + 16 q^{80} + 4 q^{81} - 12 q^{82} - 12 q^{83} + 18 q^{85} + 36 q^{86} + 8 q^{87} - 12 q^{88} + 8 q^{89} + 10 q^{90} - 16 q^{92} - 12 q^{93} + 20 q^{94} + 34 q^{95} + 26 q^{96} - 44 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 12 * q^8 + 4 * q^9 + 10 * q^10 - 4 * q^11 + 4 * q^12 - 2 * q^13 + 4 * q^15 + 12 * q^16 + 2 * q^17 + 2 * q^18 - 2 * q^22 + 4 * q^23 + 12 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^27 + 8 * q^29 + 10 * q^30 - 12 * q^31 + 26 * q^32 - 4 * q^33 - 16 * q^34 + 4 * q^36 - 4 * q^37 + 8 * q^38 - 2 * q^39 - 6 * q^40 + 2 * q^41 + 18 * q^43 - 4 * q^44 + 4 * q^45 - 14 * q^46 + 12 * q^47 + 12 * q^48 + 2 * q^50 + 2 * q^51 - 6 * q^52 - 12 * q^53 + 2 * q^54 - 4 * q^55 - 4 * q^58 + 12 * q^59 + 2 * q^61 - 26 * q^62 + 56 * q^64 - 4 * q^65 - 2 * q^66 + 28 * q^67 - 48 * q^68 + 4 * q^69 + 12 * q^71 + 12 * q^72 + 6 * q^73 - 16 * q^74 + 4 * q^75 - 18 * q^76 - 4 * q^78 + 2 * q^79 + 16 * q^80 + 4 * q^81 - 12 * q^82 - 12 * q^83 + 18 * q^85 + 36 * q^86 + 8 * q^87 - 12 * q^88 + 8 * q^89 + 10 * q^90 - 16 * q^92 - 12 * q^93 + 20 * q^94 + 34 * q^95 + 26 * q^96 - 44 * q^97 - 4 * 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 $

$2$	−1.51658	−1.07238	−0.536192	−	0.844096i	$-0.680138\pi$
$2$	−1.51658	−1.07238	−0.536192	+	0.844096i	$0.680138\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.300014	0.150007
$5$	−2.33317	−1.04343	−0.521714	−	0.853121i	$-0.674707\pi$
$5$	−2.33317	−1.04343	−0.521714	+	0.853121i	$0.674707\pi$
$6$	−1.51658	−0.619141
$7$	0	0
$7$	0	0
$8$	2.57816	0.911519
$9$	1.00000	0.333333
$10$	3.53844	1.11895
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.300014	0.0866067
$13$	−1.53844	−0.426688	−0.213344	−	0.976977i	$-0.568435\pi$
$13$	−1.53844	−0.426688	−0.213344	+	0.976977i	$0.568435\pi$
$14$	0	0
$15$	−2.33317	−0.602423
$16$	−4.51002	−1.12751
$17$	−0.116609	−0.0282817	−0.0141409	−	0.999900i	$-0.504501\pi$
$17$	−0.116609	−0.0282817	−0.0141409	+	0.999900i	$0.504501\pi$
$18$	−1.51658	−0.357461
$19$	−3.61132	−0.828494	−0.414247	−	0.910164i	$-0.635955\pi$
$19$	−3.61132	−0.828494	−0.414247	+	0.910164i	$0.635955\pi$
$20$	−0.699986	−0.156522
$21$	0	0
$22$	1.51658	0.323336
$23$	7.11005	1.48255	0.741274	−	0.671203i	$-0.234222\pi$
$23$	7.11005	1.48255	0.741274	+	0.671203i	$0.234222\pi$
$24$	2.57816	0.526266
$25$	0.443701	0.0887402
$26$	2.33317	0.457573
$27$	1.00000	0.192450
$28$	0	0
$29$	5.05502	0.938694	0.469347	−	0.883014i	$-0.344489\pi$
$29$	5.05502	0.938694	0.469347	+	0.883014i	$0.344489\pi$
$30$	3.53844	0.646029
$31$	−4.37690	−0.786115	−0.393058	−	0.919514i	$-0.628583\pi$
$31$	−4.37690	−0.786115	−0.393058	+	0.919514i	$0.628583\pi$
$32$	1.68348	0.297600
$33$	−1.00000	−0.174078
$34$	0.176846	0.0303289
$35$	0	0
$36$	0.300014	0.0500024
$37$	−0.300014	−0.0493221	−0.0246610	−	0.999696i	$-0.507851\pi$
$37$	−0.300014	−0.0493221	−0.0246610	+	0.999696i	$0.507851\pi$
$38$	5.47686	0.888464
$39$	−1.53844	−0.246348
$40$	−6.01531	−0.951103
$41$	8.20479	1.28137	0.640687	−	0.767802i	$-0.278650\pi$
$41$	8.20479	1.28137	0.640687	+	0.767802i	$0.278650\pi$
$42$	0	0
$43$	−4.18293	−0.637891	−0.318945	−	0.947773i	$-0.603329\pi$
$43$	−4.18293	−0.637891	−0.318945	+	0.947773i	$0.603329\pi$
$44$	−0.300014	−0.0452289
$45$	−2.33317	−0.347809
$46$	−10.7830	−1.58986
$47$	2.30001	0.335492	0.167746	−	0.985830i	$-0.446351\pi$
$47$	2.30001	0.335492	0.167746	+	0.985830i	$0.446351\pi$
$48$	−4.51002	−0.650965
$49$	0	0
$50$	−0.672908	−0.0951635
$51$	−0.116609	−0.0163285
$52$	−0.461555	−0.0640062
$53$	−11.8869	−1.63279	−0.816397	−	0.577491i	$-0.804032\pi$
$53$	−11.8869	−1.63279	−0.816397	+	0.577491i	$0.804032\pi$
$54$	−1.51658	−0.206380
$55$	2.33317	0.314605
$56$	0	0
$57$	−3.61132	−0.478331
$58$	−7.66635	−1.00664
$59$	4.95627	0.645251	0.322626	−	0.946527i	$-0.395434\pi$
$59$	4.95627	0.645251	0.322626	+	0.946527i	$0.395434\pi$
$60$	−0.699986	−0.0903678
$61$	−4.57160	−0.585334	−0.292667	−	0.956214i	$-0.594543\pi$
$61$	−4.57160	−0.585334	−0.292667	+	0.956214i	$0.594543\pi$
$62$	6.63792	0.843017
$63$	0	0
$64$	6.46691	0.808364
$65$	3.58946	0.445218
$66$	1.51658	0.186678
$67$	12.2894	1.50139	0.750697	−	0.660646i	$-0.229718\pi$
$67$	12.2894	1.50139	0.750697	+	0.660646i	$0.229718\pi$
$68$	−0.0349842	−0.00424246
$69$	7.11005	0.855949
$70$	0	0
$71$	4.25628	0.505128	0.252564	−	0.967580i	$-0.418726\pi$
$71$	4.25628	0.505128	0.252564	+	0.967580i	$0.418726\pi$
$72$	2.57816	0.303840
$73$	10.4380	1.22168	0.610838	−	0.791755i	$-0.290833\pi$
$73$	10.4380	1.22168	0.610838	+	0.791755i	$0.290833\pi$
$74$	0.454996	0.0528922
$75$	0.443701	0.0512342
$76$	−1.08345	−0.124280
$77$	0	0
$78$	2.33317	0.264180
$79$	14.3148	1.61055	0.805273	−	0.592905i	$-0.202019\pi$
$79$	14.3148	1.61055	0.805273	+	0.592905i	$0.202019\pi$
$80$	10.5227	1.17647
$81$	1.00000	0.111111
$82$	−12.4432	−1.37412
$83$	−11.1869	−1.22793	−0.613963	−	0.789335i	$-0.710426\pi$
$83$	−11.1869	−1.22793	−0.613963	+	0.789335i	$0.710426\pi$
$84$	0	0
$85$	0.272068	0.0295099
$86$	6.34374	0.684063
$87$	5.05502	0.541956
$88$	−2.57816	−0.274833
$89$	13.9327	1.47687	0.738433	−	0.674327i	$-0.235566\pi$
$89$	13.9327	1.47687	0.738433	+	0.674327i	$0.235566\pi$
$90$	3.53844	0.372985
$91$	0	0
$92$	2.13312	0.222393
$93$	−4.37690	−0.453864
$94$	−3.48816	−0.359776
$95$	8.42585	0.864474
$96$	1.68348	0.171819
$97$	−16.4101	−1.66619	−0.833095	−	0.553130i	$-0.813433\pi$
$97$	−16.4101	−1.66619	−0.833095	+	0.553130i	$0.813433\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	0.133117	0.0133117
$101$	9.65505	0.960714	0.480357	−	0.877073i	$-0.340507\pi$
$101$	9.65505	0.960714	0.480357	+	0.877073i	$0.340507\pi$
$102$	0.176846	0.0175104
$103$	8.82013	0.869073	0.434536	−	0.900654i	$-0.356912\pi$
$103$	8.82013	0.869073	0.434536	+	0.900654i	$0.356912\pi$
$104$	−3.96636	−0.388934
$105$	0	0
$106$	18.0275	1.75098
$107$	10.4841	1.01354	0.506770	−	0.862081i	$-0.330839\pi$
$107$	10.4841	1.01354	0.506770	+	0.862081i	$0.330839\pi$
$108$	0.300014	0.0288689
$109$	10.5279	1.00839	0.504194	−	0.863591i	$-0.331790\pi$
$109$	10.5279	1.00839	0.504194	+	0.863591i	$0.331790\pi$
$110$	−3.53844	−0.337377
$111$	−0.300014	−0.0284761
$112$	0	0
$113$	11.4327	1.07549	0.537747	−	0.843106i	$-0.319276\pi$
$113$	11.4327	1.07549	0.537747	+	0.843106i	$0.319276\pi$
$114$	5.47686	0.512955
$115$	−16.5890	−1.54693
$116$	1.51658	0.140811
$117$	−1.53844	−0.142229
$118$	−7.51658	−0.691957
$119$	0	0
$120$	−6.01531	−0.549120
$121$	1.00000	0.0909091
$122$	6.93320	0.627703
$123$	8.20479	0.739801
$124$	−1.31313	−0.117923
$125$	10.6306	0.950833
$126$	0	0
$127$	0.234898	0.0208438	0.0104219	−	0.999946i	$-0.496683\pi$
$127$	0.234898	0.0208438	0.0104219	+	0.999946i	$0.496683\pi$
$128$	−13.1745	−1.16448
$129$	−4.18293	−0.368286
$130$	−5.44370	−0.477444
$131$	−5.75854	−0.503126	−0.251563	−	0.967841i	$-0.580945\pi$
$131$	−5.75854	−0.503126	−0.251563	+	0.967841i	$0.580945\pi$
$132$	−0.300014	−0.0261129
$133$	0	0
$134$	−18.6379	−1.61007
$135$	−2.33317	−0.200808
$136$	−0.300636	−0.0257793
$137$	16.0865	1.37436	0.687181	−	0.726486i	$-0.258848\pi$
$137$	16.0865	1.37436	0.687181	+	0.726486i	$0.258848\pi$
$138$	−10.7830	−0.917906
$139$	−14.2930	−1.21231	−0.606157	−	0.795345i	$-0.707290\pi$
$139$	−14.2930	−1.21231	−0.606157	+	0.795345i	$0.707290\pi$
$140$	0	0
$141$	2.30001	0.193696
$142$	−6.45500	−0.541691
$143$	1.53844	0.128651
$144$	−4.51002	−0.375835
$145$	−11.7943	−0.979459
$146$	−15.8301	−1.31011
$147$	0	0
$148$	−0.0900086	−0.00739866
$149$	−0.672908	−0.0551267	−0.0275634	−	0.999620i	$-0.508775\pi$
$149$	−0.672908	−0.0551267	−0.0275634	+	0.999620i	$0.508775\pi$
$150$	−0.672908	−0.0549427
$151$	23.7724	1.93457	0.967285	−	0.253693i	$-0.0816454\pi$
$151$	23.7724	1.93457	0.967285	+	0.253693i	$0.0816454\pi$
$152$	−9.31058	−0.755188
$153$	−0.116609	−0.00942724
$154$	0	0
$155$	10.2121	0.820254
$156$	−0.461555	−0.0369540
$157$	−15.2558	−1.21755	−0.608773	−	0.793344i	$-0.708338\pi$
$157$	−15.2558	−1.21755	−0.608773	+	0.793344i	$0.708338\pi$
$158$	−21.7096	−1.72712
$159$	−11.8869	−0.942694
$160$	−3.92785	−0.310523
$161$	0	0
$162$	−1.51658	−0.119154
$163$	0.420633	0.0329465	0.0164733	−	0.999864i	$-0.494756\pi$
$163$	0.420633	0.0329465	0.0164733	+	0.999864i	$0.494756\pi$
$164$	2.46156	0.192215
$165$	2.33317	0.181637
$166$	16.9659	1.31681
$167$	16.4331	1.27163	0.635817	−	0.771840i	$-0.280663\pi$
$167$	16.4331	1.27163	0.635817	+	0.771840i	$0.280663\pi$
$168$	0	0
$169$	−10.6332	−0.817938
$170$	−0.412613	−0.0316460
$171$	−3.61132	−0.276165
$172$	−1.25494	−0.0956882
$173$	3.86153	0.293586	0.146793	−	0.989167i	$-0.453105\pi$
$173$	3.86153	0.293586	0.146793	+	0.989167i	$0.453105\pi$
$174$	−7.66635	−0.581184
$175$	0	0
$176$	4.51002	0.339956
$177$	4.95627	0.372536
$178$	−21.1301	−1.58377
$179$	−12.7096	−0.949960	−0.474980	−	0.879997i	$-0.657545\pi$
$179$	−12.7096	−0.949960	−0.474980	+	0.879997i	$0.657545\pi$
$180$	−0.699986	−0.0521739
$181$	16.5196	1.22789	0.613947	−	0.789347i	$-0.289581\pi$
$181$	16.5196	1.22789	0.613947	+	0.789347i	$0.289581\pi$
$182$	0	0
$183$	−4.57160	−0.337943
$184$	18.3309	1.35137
$185$	0.699986	0.0514640
$186$	6.63792	0.486716
$187$	0.116609	0.00852726
$188$	0.690037	0.0503261
$189$	0	0
$190$	−12.7785	−0.927048
$191$	−16.4096	−1.18736	−0.593678	−	0.804703i	$-0.702325\pi$
$191$	−16.4096	−1.18736	−0.593678	+	0.804703i	$0.702325\pi$
$192$	6.46691	0.466709
$193$	20.6532	1.48665	0.743326	−	0.668929i	$-0.233247\pi$
$193$	20.6532	1.48665	0.743326	+	0.668929i	$0.233247\pi$
$194$	24.8872	1.78679
$195$	3.58946	0.257046
$196$	0	0
$197$	26.3132	1.87474	0.937368	−	0.348342i	$-0.113255\pi$
$197$	26.3132	1.87474	0.937368	+	0.348342i	$0.113255\pi$
$198$	1.51658	0.107779
$199$	−11.0106	−0.780519	−0.390259	−	0.920705i	$-0.627615\pi$
$199$	−11.0106	−0.780519	−0.390259	+	0.920705i	$0.627615\pi$
$200$	1.14393	0.0808883
$201$	12.2894	0.866831
$202$	−14.6427	−1.03025
$203$	0	0
$204$	−0.0349842	−0.00244939
$205$	−19.1432	−1.33702
$206$	−13.3764	−0.931980
$207$	7.11005	0.494183
$208$	6.93842	0.481093
$209$	3.61132	0.249800
$210$	0	0
$211$	22.2476	1.53159	0.765793	−	0.643087i	$-0.222347\pi$
$211$	22.2476	1.53159	0.765793	+	0.643087i	$0.222347\pi$
$212$	−3.56625	−0.244931
$213$	4.25628	0.291636
$214$	−15.9000	−1.08690
$215$	9.75950	0.665592
$216$	2.57816	0.175422
$217$	0	0
$218$	−15.9664	−1.08138
$219$	10.4380	0.705335
$220$	0.699986	0.0471930
$221$	0.179396	0.0120675
$222$	0.454996	0.0305373
$223$	−16.8020	−1.12515	−0.562573	−	0.826748i	$-0.690188\pi$
$223$	−16.8020	−1.12515	−0.562573	+	0.826748i	$0.690188\pi$
$224$	0	0
$225$	0.443701	0.0295801
$226$	−17.3385	−1.15334
$227$	5.42015	0.359748	0.179874	−	0.983690i	$-0.442431\pi$
$227$	5.42015	0.359748	0.179874	+	0.983690i	$0.442431\pi$
$228$	−1.08345	−0.0717532
$229$	28.2323	1.86564	0.932820	−	0.360342i	$-0.117340\pi$
$229$	28.2323	1.86564	0.932820	+	0.360342i	$0.117340\pi$
$230$	25.1585	1.65890
$231$	0	0
$232$	13.0327	0.855637
$233$	5.61132	0.367610	0.183805	−	0.982963i	$-0.441158\pi$
$233$	5.61132	0.367610	0.183805	+	0.982963i	$0.441158\pi$
$234$	2.33317	0.152524
$235$	−5.36633	−0.350061
$236$	1.48695	0.0967923
$237$	14.3148	0.929849
$238$	0	0
$239$	12.0153	0.777205	0.388603	−	0.921405i	$-0.372958\pi$
$239$	12.0153	0.777205	0.388603	+	0.921405i	$0.372958\pi$
$240$	10.5227	0.679235
$241$	−20.7327	−1.33551	−0.667754	−	0.744382i	$-0.732744\pi$
$241$	−20.7327	−1.33551	−0.667754	+	0.744382i	$0.732744\pi$
$242$	−1.51658	−0.0974894
$243$	1.00000	0.0641500
$244$	−1.37155	−0.0878043
$245$	0	0
$246$	−12.4432	−0.793351
$247$	5.55582	0.353508
$248$	−11.2844	−0.716559
$249$	−11.1869	−0.708943
$250$	−16.1222	−1.01966
$251$	−27.2885	−1.72243	−0.861217	−	0.508237i	$-0.830297\pi$
$251$	−27.2885	−1.72243	−0.861217	+	0.508237i	$0.830297\pi$
$252$	0	0
$253$	−7.11005	−0.447005
$254$	−0.356242	−0.0223526
$255$	0.272068	0.0170376
$256$	7.04642	0.440401
$257$	8.90197	0.555290	0.277645	−	0.960684i	$-0.410446\pi$
$257$	8.90197	0.555290	0.277645	+	0.960684i	$0.410446\pi$
$258$	6.34374	0.394944
$259$	0	0
$260$	1.07689	0.0667858
$261$	5.05502	0.312898
$262$	8.73329	0.539544
$263$	−2.25581	−0.139099	−0.0695495	−	0.997579i	$-0.522156\pi$
$263$	−2.25581	−0.139099	−0.0695495	+	0.997579i	$0.522156\pi$
$264$	−2.57816	−0.158675
$265$	27.7343	1.70370
$266$	0	0
$267$	13.9327	0.852669
$268$	3.68701	0.225220
$269$	8.36888	0.510260	0.255130	−	0.966907i	$-0.417882\pi$
$269$	8.36888	0.510260	0.255130	+	0.966907i	$0.417882\pi$
$270$	3.53844	0.215343
$271$	8.89469	0.540314	0.270157	−	0.962816i	$-0.412924\pi$
$271$	8.89469	0.540314	0.270157	+	0.962816i	$0.412924\pi$
$272$	0.525907	0.0318878
$273$	0	0
$274$	−24.3965	−1.47384
$275$	−0.443701	−0.0267562
$276$	2.13312	0.128399
$277$	−5.39997	−0.324453	−0.162226	−	0.986754i	$-0.551867\pi$
$277$	−5.39997	−0.324453	−0.162226	+	0.986754i	$0.551867\pi$
$278$	21.6764	1.30007
$279$	−4.37690	−0.262038
$280$	0	0
$281$	−19.7416	−1.17768	−0.588841	−	0.808249i	$-0.700416\pi$
$281$	−19.7416	−1.17768	−0.588841	+	0.808249i	$0.700416\pi$
$282$	−3.48816	−0.207717
$283$	−10.1052	−0.600690	−0.300345	−	0.953831i	$-0.597102\pi$
$283$	−10.1052	−0.600690	−0.300345	+	0.953831i	$0.597102\pi$
$284$	1.27695	0.0757728
$285$	8.42585	0.499104
$286$	−2.33317	−0.137963
$287$	0	0
$288$	1.68348	0.0991999
$289$	−16.9864	−0.999200
$290$	17.8869	1.05036
$291$	−16.4101	−0.961975
$292$	3.13155	0.183260
$293$	−16.1108	−0.941201	−0.470601	−	0.882346i	$-0.655963\pi$
$293$	−16.1108	−0.941201	−0.470601	+	0.882346i	$0.655963\pi$
$294$	0	0
$295$	−11.5638	−0.673273
$296$	−0.773486	−0.0449580
$297$	−1.00000	−0.0580259
$298$	1.02052	0.0591170
$299$	−10.9384	−0.632585
$300$	0.133117	0.00768549
$301$	0	0
$302$	−36.0527	−2.07460
$303$	9.65505	0.554668
$304$	16.2871	0.934132
$305$	10.6663	0.610753
$306$	0.176846	0.0101096
$307$	27.8168	1.58759	0.793795	−	0.608185i	$-0.208102\pi$
$307$	27.8168	1.58759	0.793795	+	0.608185i	$0.208102\pi$
$308$	0	0
$309$	8.82013	0.501759
$310$	−15.4874	−0.879627
$311$	9.04277	0.512769	0.256384	−	0.966575i	$-0.417469\pi$
$311$	9.04277	0.512769	0.256384	+	0.966575i	$0.417469\pi$
$312$	−3.96636	−0.224551
$313$	−16.1768	−0.914369	−0.457185	−	0.889372i	$-0.651142\pi$
$313$	−16.1768	−0.914369	−0.457185	+	0.889372i	$0.651142\pi$
$314$	23.1366	1.30568
$315$	0	0
$316$	4.29466	0.241593
$317$	−5.23370	−0.293954	−0.146977	−	0.989140i	$-0.546954\pi$
$317$	−5.23370	−0.293954	−0.146977	+	0.989140i	$0.546954\pi$
$318$	18.0275	1.01093
$319$	−5.05502	−0.283027
$320$	−15.0884	−0.843469
$321$	10.4841	0.585168
$322$	0	0
$323$	0.421111	0.0234312
$324$	0.300014	0.0166675
$325$	−0.682609	−0.0378643
$326$	−0.637923	−0.0353313
$327$	10.5279	0.582193
$328$	21.1533	1.16800
$329$	0	0
$330$	−3.53844	−0.194785
$331$	−19.5302	−1.07348	−0.536739	−	0.843749i	$-0.680344\pi$
$331$	−19.5302	−1.07348	−0.536739	+	0.843749i	$0.680344\pi$
$332$	−3.35624	−0.184198
$333$	−0.300014	−0.0164407
$334$	−24.9222	−1.36368
$335$	−28.6734	−1.56660
$336$	0	0
$337$	−0.243643	−0.0132721	−0.00663605	−	0.999978i	$-0.502112\pi$
$337$	−0.243643	−0.0132721	−0.00663605	+	0.999978i	$0.502112\pi$
$338$	16.1261	0.877143
$339$	11.4327	0.620936
$340$	0.0816243	0.00442670
$341$	4.37690	0.237023
$342$	5.47686	0.296155
$343$	0	0
$344$	−10.7843	−0.581449
$345$	−16.5890	−0.893121
$346$	−5.85631	−0.314837
$347$	22.1611	1.18967	0.594834	−	0.803848i	$-0.297218\pi$
$347$	22.1611	1.18967	0.594834	+	0.803848i	$0.297218\pi$
$348$	1.51658	0.0812972
$349$	−16.1822	−0.866213	−0.433107	−	0.901343i	$-0.642583\pi$
$349$	−16.1822	−0.866213	−0.433107	+	0.901343i	$0.642583\pi$
$350$	0	0
$351$	−1.53844	−0.0821161
$352$	−1.68348	−0.0897297
$353$	−7.77687	−0.413921	−0.206961	−	0.978349i	$-0.566357\pi$
$353$	−7.77687	−0.413921	−0.206961	+	0.978349i	$0.566357\pi$
$354$	−7.51658	−0.399502
$355$	−9.93065	−0.527064
$356$	4.18002	0.221540
$357$	0	0
$358$	19.2751	1.01872
$359$	10.8128	0.570680	0.285340	−	0.958426i	$-0.407893\pi$
$359$	10.8128	0.570680	0.285340	+	0.958426i	$0.407893\pi$
$360$	−6.01531	−0.317034
$361$	−5.95834	−0.313597
$362$	−25.0533	−1.31677
$363$	1.00000	0.0524864
$364$	0	0
$365$	−24.3537	−1.27473
$366$	6.93320	0.362404
$367$	−1.75669	−0.0916985	−0.0458493	−	0.998948i	$-0.514599\pi$
$367$	−1.75669	−0.0916985	−0.0458493	+	0.998948i	$0.514599\pi$
$368$	−32.0665	−1.67158
$369$	8.20479	0.427124
$370$	−1.06158	−0.0551891
$371$	0	0
$372$	−1.31313	−0.0680828
$373$	−9.27366	−0.480172	−0.240086	−	0.970752i	$-0.577176\pi$
$373$	−9.27366	−0.480172	−0.240086	+	0.970752i	$0.577176\pi$
$374$	−0.176846	−0.00914449
$375$	10.6306	0.548964
$376$	5.92981	0.305807
$377$	−7.77687	−0.400529
$378$	0	0
$379$	−11.5130	−0.591386	−0.295693	−	0.955283i	$-0.595550\pi$
$379$	−11.5130	−0.591386	−0.295693	+	0.955283i	$0.595550\pi$
$380$	2.52787	0.129677
$381$	0.234898	0.0120342
$382$	24.8864	1.27330
$383$	−22.4785	−1.14860	−0.574298	−	0.818647i	$-0.694725\pi$
$383$	−22.4785	−1.14860	−0.574298	+	0.818647i	$0.694725\pi$
$384$	−13.1745	−0.672311
$385$	0	0
$386$	−31.3223	−1.59426
$387$	−4.18293	−0.212630
$388$	−4.92325	−0.249940
$389$	−34.3326	−1.74073	−0.870365	−	0.492408i	$-0.836117\pi$
$389$	−34.3326	−1.74073	−0.870365	+	0.492408i	$0.836117\pi$
$390$	−5.44370	−0.275653
$391$	−0.829092	−0.0419290
$392$	0	0
$393$	−5.75854	−0.290480
$394$	−39.9060	−2.01044
$395$	−33.3990	−1.68049
$396$	−0.300014	−0.0150763
$397$	−9.79961	−0.491828	−0.245914	−	0.969292i	$-0.579088\pi$
$397$	−9.79961	−0.491828	−0.245914	+	0.969292i	$0.579088\pi$
$398$	16.6984	0.837016
$399$	0	0
$400$	−2.00110	−0.100055
$401$	3.47638	0.173602	0.0868011	−	0.996226i	$-0.472336\pi$
$401$	3.47638	0.173602	0.0868011	+	0.996226i	$0.472336\pi$
$402$	−18.6379	−0.929575
$403$	6.73362	0.335426
$404$	2.89665	0.144114
$405$	−2.33317	−0.115936
$406$	0	0
$407$	0.300014	0.0148712
$408$	−0.300636	−0.0148837
$409$	35.1218	1.73666	0.868332	−	0.495984i	$-0.165192\pi$
$409$	35.1218	1.73666	0.868332	+	0.495984i	$0.165192\pi$
$410$	29.0322	1.43380
$411$	16.0865	0.793489
$412$	2.64616	0.130367
$413$	0	0
$414$	−10.7830	−0.529953
$415$	26.1011	1.28125
$416$	−2.58994	−0.126982
$417$	−14.2930	−0.699930
$418$	−5.47686	−0.267882
$419$	13.8100	0.674664	0.337332	−	0.941386i	$-0.390475\pi$
$419$	13.8100	0.674664	0.337332	+	0.941386i	$0.390475\pi$
$420$	0	0
$421$	9.72050	0.473748	0.236874	−	0.971540i	$-0.423877\pi$
$421$	9.72050	0.473748	0.236874	+	0.971540i	$0.423877\pi$
$422$	−33.7402	−1.64245
$423$	2.30001	0.111831
$424$	−30.6464	−1.48832
$425$	−0.0517393	−0.00250972
$426$	−6.45500	−0.312746
$427$	0	0
$428$	3.14539	0.152038
$429$	1.53844	0.0742768
$430$	−14.8011	−0.713770
$431$	−10.1917	−0.490916	−0.245458	−	0.969407i	$-0.578938\pi$
$431$	−10.1917	−0.490916	−0.245458	+	0.969407i	$0.578938\pi$
$432$	−4.51002	−0.216988
$433$	−21.0101	−1.00968	−0.504840	−	0.863213i	$-0.668449\pi$
$433$	−21.0101	−1.00968	−0.504840	+	0.863213i	$0.668449\pi$
$434$	0	0
$435$	−11.7943	−0.565491
$436$	3.15851	0.151265
$437$	−25.6767	−1.22828
$438$	−15.8301	−0.756390
$439$	9.84673	0.469959	0.234979	−	0.972000i	$-0.424498\pi$
$439$	9.84673	0.469959	0.234979	+	0.972000i	$0.424498\pi$
$440$	6.01531	0.286768
$441$	0	0
$442$	−0.272068	−0.0129410
$443$	15.5512	0.738860	0.369430	−	0.929259i	$-0.379553\pi$
$443$	15.5512	0.738860	0.369430	+	0.929259i	$0.379553\pi$
$444$	−0.0900086	−0.00427162
$445$	−32.5075	−1.54100
$446$	25.4816	1.20659
$447$	−0.672908	−0.0318274
$448$	0	0
$449$	2.62021	0.123655	0.0618277	−	0.998087i	$-0.480307\pi$
$449$	2.62021	0.123655	0.0618277	+	0.998087i	$0.480307\pi$
$450$	−0.672908	−0.0317212
$451$	−8.20479	−0.386349
$452$	3.42996	0.161332
$453$	23.7724	1.11692
$454$	−8.22010	−0.385788
$455$	0	0
$456$	−9.31058	−0.436008
$457$	7.62590	0.356725	0.178362	−	0.983965i	$-0.442920\pi$
$457$	7.62590	0.356725	0.178362	+	0.983965i	$0.442920\pi$
$458$	−42.8165	−2.00068
$459$	−0.116609	−0.00544282
$460$	−4.97693	−0.232051
$461$	−12.7392	−0.593325	−0.296662	−	0.954982i	$-0.595874\pi$
$461$	−12.7392	−0.593325	−0.296662	+	0.954982i	$0.595874\pi$
$462$	0	0
$463$	−8.76838	−0.407501	−0.203751	−	0.979023i	$-0.565313\pi$
$463$	−8.76838	−0.407501	−0.203751	+	0.979023i	$0.565313\pi$
$464$	−22.7983	−1.05838
$465$	10.2121	0.473574
$466$	−8.51002	−0.394219
$467$	−19.3683	−0.896256	−0.448128	−	0.893969i	$-0.647909\pi$
$467$	−19.3683	−0.896256	−0.448128	+	0.893969i	$0.647909\pi$
$468$	−0.461555	−0.0213354
$469$	0	0
$470$	8.13847	0.375400
$471$	−15.2558	−0.702950
$472$	12.7781	0.588159
$473$	4.18293	0.192331
$474$	−21.7096	−0.997155
$475$	−1.60235	−0.0735207
$476$	0	0
$477$	−11.8869	−0.544265
$478$	−18.2222	−0.833463
$479$	24.1990	1.10568	0.552839	−	0.833288i	$-0.313544\pi$
$479$	24.1990	1.10568	0.552839	+	0.833288i	$0.313544\pi$
$480$	−3.92785	−0.179281
$481$	0.461555	0.0210451
$482$	31.4427	1.43218
$483$	0	0
$484$	0.300014	0.0136370
$485$	38.2875	1.73855
$486$	−1.51658	−0.0687935
$487$	−21.2187	−0.961509	−0.480755	−	0.876855i	$-0.659637\pi$
$487$	−21.2187	−0.961509	−0.480755	+	0.876855i	$0.659637\pi$
$488$	−11.7863	−0.533543
$489$	0.420633	0.0190217
$490$	0	0
$491$	−28.2038	−1.27282	−0.636411	−	0.771350i	$-0.719582\pi$
$491$	−28.2038	−1.27282	−0.636411	+	0.771350i	$0.719582\pi$
$492$	2.46156	0.110975
$493$	−0.589459	−0.0265479
$494$	−8.42585	−0.379097
$495$	2.33317	0.104868
$496$	19.7399	0.886349
$497$	0	0
$498$	16.9659	0.760259
$499$	−35.4980	−1.58911	−0.794555	−	0.607193i	$-0.792296\pi$
$499$	−35.4980	−1.58911	−0.794555	+	0.607193i	$0.792296\pi$
$500$	3.18934	0.142632
$501$	16.4331	0.734178
$502$	41.3852	1.84711
$503$	16.0477	0.715529	0.357765	−	0.933812i	$-0.383539\pi$
$503$	16.0477	0.715529	0.357765	+	0.933812i	$0.383539\pi$
$504$	0	0
$505$	−22.5269	−1.00243
$506$	10.7830	0.479361
$507$	−10.6332	−0.472236
$508$	0.0704728	0.00312673
$509$	8.21303	0.364036	0.182018	−	0.983295i	$-0.441737\pi$
$509$	8.21303	0.364036	0.182018	+	0.983295i	$0.441737\pi$
$510$	−0.412613	−0.0182708
$511$	0	0
$512$	15.6626	0.692197
$513$	−3.61132	−0.159444
$514$	−13.5005	−0.595484
$515$	−20.5789	−0.906814
$516$	−1.25494	−0.0552456
$517$	−2.30001	−0.101155
$518$	0	0
$519$	3.86153	0.169502
$520$	9.25421	0.405824
$521$	−8.55534	−0.374816	−0.187408	−	0.982282i	$-0.560009\pi$
$521$	−8.55534	−0.374816	−0.187408	+	0.982282i	$0.560009\pi$
$522$	−7.66635	−0.335547
$523$	30.0369	1.31342	0.656712	−	0.754142i	$-0.271947\pi$
$523$	30.0369	1.31342	0.656712	+	0.754142i	$0.271947\pi$
$524$	−1.72765	−0.0754725
$525$	0	0
$526$	3.42111	0.149168
$527$	0.510384	0.0222327
$528$	4.51002	0.196273
$529$	27.5528	1.19795
$530$	−42.0612	−1.82702
$531$	4.95627	0.215084
$532$	0	0
$533$	−12.6226	−0.546746
$534$	−21.1301	−0.914388
$535$	−24.4613	−1.05756
$536$	31.6842	1.36855
$537$	−12.7096	−0.548460
$538$	−12.6921	−0.547194
$539$	0	0
$540$	−0.699986	−0.0301226
$541$	19.0169	0.817600	0.408800	−	0.912624i	$-0.365947\pi$
$541$	19.0169	0.817600	0.408800	+	0.912624i	$0.365947\pi$
$542$	−13.4895	−0.579424
$543$	16.5196	0.708925
$544$	−0.196308	−0.00841663
$545$	−24.5634	−1.05218
$546$	0	0
$547$	34.4968	1.47498	0.737489	−	0.675360i	$-0.236012\pi$
$547$	34.4968	1.47498	0.737489	+	0.675360i	$0.236012\pi$
$548$	4.82618	0.206164
$549$	−4.57160	−0.195111
$550$	0.672908	0.0286929
$551$	−18.2553	−0.777703
$552$	18.3309	0.780214
$553$	0	0
$554$	8.18949	0.347938
$555$	0.699986	0.0297127
$556$	−4.28810	−0.181856
$557$	5.42912	0.230039	0.115020	−	0.993363i	$-0.463307\pi$
$557$	5.42912	0.230039	0.115020	+	0.993363i	$0.463307\pi$
$558$	6.63792	0.281006
$559$	6.43520	0.272180
$560$	0	0
$561$	0.116609	0.00492321
$562$	29.9396	1.26293
$563$	−34.1681	−1.44001	−0.720007	−	0.693966i	$-0.755862\pi$
$563$	−34.1681	−1.44001	−0.720007	+	0.693966i	$0.755862\pi$
$564$	0.690037	0.0290558
$565$	−26.6744	−1.12220
$566$	15.3253	0.644170
$567$	0	0
$568$	10.9734	0.460434
$569$	−16.5925	−0.695594	−0.347797	−	0.937570i	$-0.613070\pi$
$569$	−16.5925	−0.695594	−0.347797	+	0.937570i	$0.613070\pi$
$570$	−12.7785	−0.535231
$571$	13.9344	0.583137	0.291568	−	0.956550i	$-0.405823\pi$
$571$	13.9344	0.583137	0.291568	+	0.956550i	$0.405823\pi$
$572$	0.461555	0.0192986
$573$	−16.4096	−0.685520
$574$	0	0
$575$	3.15473	0.131562
$576$	6.46691	0.269455
$577$	45.6774	1.90158	0.950788	−	0.309843i	$-0.100276\pi$
$577$	45.6774	1.90158	0.950788	+	0.309843i	$0.100276\pi$
$578$	25.7612	1.07153
$579$	20.6532	0.858319
$580$	−3.53844	−0.146926
$581$	0	0
$582$	24.8872	1.03161
$583$	11.8869	0.492306
$584$	26.9109	1.11358
$585$	3.58946	0.148406
$586$	24.4333	1.00933
$587$	29.3966	1.21333	0.606664	−	0.794958i	$-0.292507\pi$
$587$	29.3966	1.21333	0.606664	+	0.794958i	$0.292507\pi$
$588$	0	0
$589$	15.8064	0.651292
$590$	17.5375	0.722007
$591$	26.3132	1.08238
$592$	1.35307	0.0556109
$593$	−1.82436	−0.0749174	−0.0374587	−	0.999298i	$-0.511926\pi$
$593$	−1.82436	−0.0749174	−0.0374587	+	0.999298i	$0.511926\pi$
$594$	1.51658	0.0622260
$595$	0	0
$596$	−0.201882	−0.00826941
$597$	−11.0106	−0.450633
$598$	16.5890	0.678374
$599$	−22.4995	−0.919303	−0.459651	−	0.888099i	$-0.652026\pi$
$599$	−22.4995	−0.919303	−0.459651	+	0.888099i	$0.652026\pi$
$600$	1.14393	0.0467009
$601$	−10.3352	−0.421583	−0.210792	−	0.977531i	$-0.567604\pi$
$601$	−10.3352	−0.421583	−0.210792	+	0.977531i	$0.567604\pi$
$602$	0	0
$603$	12.2894	0.500465
$604$	7.13206	0.290199
$605$	−2.33317	−0.0948570
$606$	−14.6427	−0.594817
$607$	−32.6275	−1.32431	−0.662155	−	0.749367i	$-0.730358\pi$
$607$	−32.6275	−1.32431	−0.662155	+	0.749367i	$0.730358\pi$
$608$	−6.07958	−0.246560
$609$	0	0
$610$	−16.1764	−0.654962
$611$	−3.53844	−0.143150
$612$	−0.0349842	−0.00141415
$613$	−6.38700	−0.257968	−0.128984	−	0.991647i	$-0.541172\pi$
$613$	−6.38700	−0.257968	−0.128984	+	0.991647i	$0.541172\pi$
$614$	−42.1865	−1.70251
$615$	−19.1432	−0.771929
$616$	0	0
$617$	4.14609	0.166915	0.0834577	−	0.996511i	$-0.473404\pi$
$617$	4.14609	0.166915	0.0834577	+	0.996511i	$0.473404\pi$
$618$	−13.3764	−0.538079
$619$	−38.5960	−1.55131	−0.775653	−	0.631160i	$-0.782579\pi$
$619$	−38.5960	−1.55131	−0.775653	+	0.631160i	$0.782579\pi$
$620$	3.06377	0.123044
$621$	7.11005	0.285316
$622$	−13.7141	−0.549885
$623$	0	0
$624$	6.93842	0.277759
$625$	−27.0216	−1.08087
$626$	24.5335	0.980555
$627$	3.61132	0.144222
$628$	−4.57696	−0.182641
$629$	0.0349842	0.00139491
$630$	0	0
$631$	−8.89990	−0.354299	−0.177150	−	0.984184i	$-0.556688\pi$
$631$	−8.89990	−0.354299	−0.177150	+	0.984184i	$0.556688\pi$
$632$	36.9060	1.46804
$633$	22.2476	0.884261
$634$	7.93732	0.315231
$635$	−0.548058	−0.0217490
$636$	−3.56625	−0.141411
$637$	0	0
$638$	7.66635	0.303514
$639$	4.25628	0.168376
$640$	30.7385	1.21505
$641$	37.3297	1.47443	0.737217	−	0.675656i	$-0.236140\pi$
$641$	37.3297	1.47443	0.737217	+	0.675656i	$0.236140\pi$
$642$	−15.9000	−0.627525
$643$	15.9206	0.627846	0.313923	−	0.949449i	$-0.398357\pi$
$643$	15.9206	0.627846	0.313923	+	0.949449i	$0.398357\pi$
$644$	0	0
$645$	9.75950	0.384280
$646$	−0.638648	−0.0251273
$647$	17.5528	0.690072	0.345036	−	0.938590i	$-0.387867\pi$
$647$	17.5528	0.690072	0.345036	+	0.938590i	$0.387867\pi$
$648$	2.57816	0.101280
$649$	−4.95627	−0.194551
$650$	1.03523	0.0406051
$651$	0	0
$652$	0.126196	0.00494221
$653$	−23.9657	−0.937852	−0.468926	−	0.883237i	$-0.655359\pi$
$653$	−23.9657	−0.937852	−0.468926	+	0.883237i	$0.655359\pi$
$654$	−15.9664	−0.624334
$655$	13.4357	0.524975
$656$	−37.0038	−1.44475
$657$	10.4380	0.407226
$658$	0	0
$659$	−38.6166	−1.50429	−0.752144	−	0.658999i	$-0.770980\pi$
$659$	−38.6166	−1.50429	−0.752144	+	0.658999i	$0.770980\pi$
$660$	0.699986	0.0272469
$661$	10.3788	0.403690	0.201845	−	0.979418i	$-0.435306\pi$
$661$	10.3788	0.403690	0.201845	+	0.979418i	$0.435306\pi$
$662$	29.6191	1.15118
$663$	0.179396	0.00696715
$664$	−28.8418	−1.11928
$665$	0	0
$666$	0.454996	0.0176307
$667$	35.9415	1.39166
$668$	4.93017	0.190754
$669$	−16.8020	−0.649603
$670$	43.4855	1.67999
$671$	4.57160	0.176485
$672$	0	0
$673$	−11.8103	−0.455253	−0.227627	−	0.973748i	$-0.573097\pi$
$673$	−11.8103	−0.455253	−0.227627	+	0.973748i	$0.573097\pi$
$674$	0.369505	0.0142328
$675$	0.443701	0.0170781
$676$	−3.19011	−0.122697
$677$	41.9689	1.61300	0.806499	−	0.591236i	$-0.201360\pi$
$677$	41.9689	1.61300	0.806499	+	0.591236i	$0.201360\pi$
$678$	−17.3385	−0.665882
$679$	0	0
$680$	0.701436	0.0268988
$681$	5.42015	0.207701
$682$	−6.63792	−0.254179
$683$	24.1533	0.924200	0.462100	−	0.886828i	$-0.347096\pi$
$683$	24.1533	0.924200	0.462100	+	0.886828i	$0.347096\pi$
$684$	−1.08345	−0.0414267
$685$	−37.5326	−1.43405
$686$	0	0
$687$	28.2323	1.07713
$688$	18.8651	0.719225
$689$	18.2874	0.696693
$690$	25.1585	0.957768
$691$	−5.27440	−0.200648	−0.100324	−	0.994955i	$-0.531988\pi$
$691$	−5.27440	−0.200648	−0.100324	+	0.994955i	$0.531988\pi$
$692$	1.15851	0.0440401
$693$	0	0
$694$	−33.6090	−1.27578
$695$	33.3480	1.26496
$696$	13.0327	0.494003
$697$	−0.956749	−0.0362394
$698$	24.5416	0.928913
$699$	5.61132	0.212240
$700$	0	0
$701$	26.9166	1.01662	0.508312	−	0.861173i	$-0.330270\pi$
$701$	26.9166	1.01662	0.508312	+	0.861173i	$0.330270\pi$
$702$	2.33317	0.0880600
$703$	1.08345	0.0408630
$704$	−6.46691	−0.243731
$705$	−5.36633	−0.202108
$706$	11.7943	0.443883
$707$	0	0
$708$	1.48695	0.0558831
$709$	11.7428	0.441009	0.220504	−	0.975386i	$-0.429230\pi$
$709$	11.7428	0.441009	0.220504	+	0.975386i	$0.429230\pi$
$710$	15.0606	0.565215
$711$	14.3148	0.536848
$712$	35.9208	1.34619
$713$	−31.1200	−1.16545
$714$	0	0
$715$	−3.58946	−0.134238
$716$	−3.81306	−0.142501
$717$	12.0153	0.448720
$718$	−16.3985	−0.611988
$719$	28.1679	1.05048	0.525242	−	0.850953i	$-0.323975\pi$
$719$	28.1679	1.05048	0.525242	+	0.850953i	$0.323975\pi$
$720$	10.5227	0.392156
$721$	0	0
$722$	9.03630	0.336296
$723$	−20.7327	−0.771056
$724$	4.95613	0.184193
$725$	2.24292	0.0832999
$726$	−1.51658	−0.0562856
$727$	32.9885	1.22347	0.611737	−	0.791061i	$-0.290471\pi$
$727$	32.9885	1.22347	0.611737	+	0.791061i	$0.290471\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	36.9343	1.36700
$731$	0.487765	0.0180406
$732$	−1.37155	−0.0506938
$733$	1.90621	0.0704076	0.0352038	−	0.999380i	$-0.488792\pi$
$733$	1.90621	0.0704076	0.0352038	+	0.999380i	$0.488792\pi$
$734$	2.66416	0.0983360
$735$	0	0
$736$	11.9696	0.441206
$737$	−12.2894	−0.452688
$738$	−12.4432	−0.458041
$739$	−37.8273	−1.39150	−0.695749	−	0.718285i	$-0.744928\pi$
$739$	−37.8273	−1.39150	−0.695749	+	0.718285i	$0.744928\pi$
$740$	0.210006	0.00771996
$741$	5.55582	0.204098
$742$	0	0
$743$	46.4995	1.70590	0.852950	−	0.521993i	$-0.174811\pi$
$743$	46.4995	1.70590	0.852950	+	0.521993i	$0.174811\pi$
$744$	−11.2844	−0.413705
$745$	1.57001	0.0575207
$746$	14.0642	0.514929
$747$	−11.1869	−0.409309
$748$	0.0349842	0.00127915
$749$	0	0
$750$	−16.1222	−0.588700
$751$	4.14816	0.151369	0.0756843	−	0.997132i	$-0.475886\pi$
$751$	4.14816	0.151369	0.0756843	+	0.997132i	$0.475886\pi$
$752$	−10.3731	−0.378268
$753$	−27.2885	−0.994448
$754$	11.7943	0.429521
$755$	−55.4651	−2.01858
$756$	0	0
$757$	4.56418	0.165888	0.0829439	−	0.996554i	$-0.473568\pi$
$757$	4.56418	0.165888	0.0829439	+	0.996554i	$0.473568\pi$
$758$	17.4605	0.634192
$759$	−7.11005	−0.258078
$760$	21.7232	0.787984
$761$	−13.0509	−0.473094	−0.236547	−	0.971620i	$-0.576016\pi$
$761$	−13.0509	−0.473094	−0.236547	+	0.971620i	$0.576016\pi$
$762$	−0.356242	−0.0129053
$763$	0	0
$764$	−4.92311	−0.178112
$765$	0.272068	0.00983664
$766$	34.0904	1.23174
$767$	−7.62495	−0.275321
$768$	7.04642	0.254266
$769$	−4.40156	−0.158724	−0.0793622	−	0.996846i	$-0.525288\pi$
$769$	−4.40156	−0.158724	−0.0793622	+	0.996846i	$0.525288\pi$
$770$	0	0
$771$	8.90197	0.320597
$772$	6.19626	0.223008
$773$	22.4096	0.806017	0.403008	−	0.915196i	$-0.367965\pi$
$773$	22.4096	0.806017	0.403008	+	0.915196i	$0.367965\pi$
$774$	6.34374	0.228021
$775$	−1.94204	−0.0697600
$776$	−42.3078	−1.51876
$777$	0	0
$778$	52.0681	1.86673
$779$	−29.6302	−1.06161
$780$	1.07689	0.0385588
$781$	−4.25628	−0.152302
$782$	1.25738	0.0449640
$783$	5.05502	0.180652
$784$	0	0
$785$	35.5945	1.27042
$786$	8.73329	0.311506
$787$	−6.56286	−0.233941	−0.116970	−	0.993135i	$-0.537318\pi$
$787$	−6.56286	−0.233941	−0.116970	+	0.993135i	$0.537318\pi$
$788$	7.89433	0.281224
$789$	−2.25581	−0.0803088
$790$	50.6523	1.80213
$791$	0	0
$792$	−2.57816	−0.0916111
$793$	7.03316	0.249755
$794$	14.8619	0.527429
$795$	27.7343	0.983633
$796$	−3.30333	−0.117083
$797$	23.7974	0.842947	0.421473	−	0.906841i	$-0.361513\pi$
$797$	23.7974	0.842947	0.421473	+	0.906841i	$0.361513\pi$
$798$	0	0
$799$	−0.268201	−0.00948828
$800$	0.746960	0.0264090
$801$	13.9327	0.492289
$802$	−5.27221	−0.186168
$803$	−10.4380	−0.368349
$804$	3.68701	0.130031
$805$	0	0
$806$	−10.2121	−0.359705
$807$	8.36888	0.294599
$808$	24.8923	0.875708
$809$	−11.5953	−0.407669	−0.203834	−	0.979005i	$-0.565340\pi$
$809$	−11.5953	−0.407669	−0.203834	+	0.979005i	$0.565340\pi$
$810$	3.53844	0.124328
$811$	39.5907	1.39022	0.695109	−	0.718905i	$-0.255356\pi$
$811$	39.5907	1.39022	0.695109	+	0.718905i	$0.255356\pi$
$812$	0	0
$813$	8.89469	0.311950
$814$	−0.454996	−0.0159476
$815$	−0.981410	−0.0343773
$816$	0.525907	0.0184104
$817$	15.1059	0.528489
$818$	−53.2651	−1.86237
$819$	0	0
$820$	−5.74324	−0.200563
$821$	−5.14809	−0.179669	−0.0898347	−	0.995957i	$-0.528634\pi$
$821$	−5.14809	−0.179669	−0.0898347	+	0.995957i	$0.528634\pi$
$822$	−24.3965	−0.850924
$823$	22.1784	0.773092	0.386546	−	0.922270i	$-0.373668\pi$
$823$	22.1784	0.773092	0.386546	+	0.922270i	$0.373668\pi$
$824$	22.7397	0.792176
$825$	−0.443701	−0.0154477
$826$	0	0
$827$	−24.8915	−0.865564	−0.432782	−	0.901499i	$-0.642468\pi$
$827$	−24.8915	−0.865564	−0.432782	+	0.901499i	$0.642468\pi$
$828$	2.13312	0.0741309
$829$	32.1533	1.11673	0.558365	−	0.829595i	$-0.311429\pi$
$829$	32.1533	1.11673	0.558365	+	0.829595i	$0.311429\pi$
$830$	−39.5844	−1.37399
$831$	−5.39997	−0.187323
$832$	−9.94899	−0.344919
$833$	0	0
$834$	21.6764	0.750594
$835$	−38.3414	−1.32686
$836$	1.08345	0.0374719
$837$	−4.37690	−0.151288
$838$	−20.9440	−0.723499
$839$	23.6483	0.816429	0.408215	−	0.912886i	$-0.366152\pi$
$839$	23.6483	0.816429	0.408215	+	0.912886i	$0.366152\pi$
$840$	0	0
$841$	−3.44673	−0.118853
$842$	−14.7419	−0.508040
$843$	−19.7416	−0.679935
$844$	6.67459	0.229749
$845$	24.8091	0.853458
$846$	−3.48816	−0.119925
$847$	0	0
$848$	53.6103	1.84098
$849$	−10.1052	−0.346809
$850$	0.0784668	0.00269139
$851$	−2.13312	−0.0731223
$852$	1.27695	0.0437475
$853$	−27.0742	−0.927003	−0.463501	−	0.886096i	$-0.653407\pi$
$853$	−27.0742	−0.927003	−0.463501	+	0.886096i	$0.653407\pi$
$854$	0	0
$855$	8.42585	0.288158
$856$	27.0298	0.923861
$857$	−33.2977	−1.13743	−0.568714	−	0.822535i	$-0.692559\pi$
$857$	−33.2977	−1.13743	−0.568714	+	0.822535i	$0.692559\pi$
$858$	−2.33317	−0.0796532
$859$	−22.0306	−0.751675	−0.375837	−	0.926686i	$-0.622645\pi$
$859$	−22.0306	−0.751675	−0.375837	+	0.926686i	$0.622645\pi$
$860$	2.92799	0.0998436
$861$	0	0
$862$	15.4565	0.526450
$863$	−31.7851	−1.08198	−0.540988	−	0.841030i	$-0.681950\pi$
$863$	−31.7851	−1.08198	−0.540988	+	0.841030i	$0.681950\pi$
$864$	1.68348	0.0572731
$865$	−9.00961	−0.306336
$866$	31.8635	1.08277
$867$	−16.9864	−0.576888
$868$	0	0
$869$	−14.3148	−0.485598
$870$	17.8869	0.606424
$871$	−18.9066	−0.640627
$872$	27.1426	0.919164
$873$	−16.4101	−0.555396
$874$	38.9407	1.31719
$875$	0	0
$876$	3.13155	0.105805
$877$	29.3480	0.991012	0.495506	−	0.868605i	$-0.334983\pi$
$877$	29.3480	0.991012	0.495506	+	0.868605i	$0.334983\pi$
$878$	−14.9333	−0.503976
$879$	−16.1108	−0.543403
$880$	−10.5227	−0.354719
$881$	−43.4442	−1.46367	−0.731836	−	0.681481i	$-0.761336\pi$
$881$	−43.4442	−1.46367	−0.731836	+	0.681481i	$0.761336\pi$
$882$	0	0
$883$	26.4200	0.889104	0.444552	−	0.895753i	$-0.353363\pi$
$883$	26.4200	0.889104	0.444552	+	0.895753i	$0.353363\pi$
$884$	0.0538213	0.00181021
$885$	−11.5638	−0.388714
$886$	−23.5846	−0.792341
$887$	−12.8233	−0.430563	−0.215282	−	0.976552i	$-0.569067\pi$
$887$	−12.8233	−0.430563	−0.215282	+	0.976552i	$0.569067\pi$
$888$	−0.773486	−0.0259565
$889$	0	0
$890$	49.3002	1.65255
$891$	−1.00000	−0.0335013
$892$	−5.04085	−0.168780
$893$	−8.30610	−0.277953
$894$	1.02052	0.0341312
$895$	29.6537	0.991214
$896$	0	0
$897$	−10.9384	−0.365223
$898$	−3.97376	−0.132606
$899$	−22.1254	−0.737922
$900$	0.133117	0.00443722
$901$	1.38612	0.0461782
$902$	12.4432	0.414314
$903$	0	0
$904$	29.4753	0.980332
$905$	−38.5432	−1.28122
$906$	−36.0527	−1.19777
$907$	53.5384	1.77771	0.888856	−	0.458186i	$-0.151501\pi$
$907$	53.5384	1.77771	0.888856	+	0.458186i	$0.151501\pi$
$908$	1.62612	0.0539648
$909$	9.65505	0.320238
$910$	0	0
$911$	28.4552	0.942764	0.471382	−	0.881929i	$-0.343755\pi$
$911$	28.4552	0.942764	0.471382	+	0.881929i	$0.343755\pi$
$912$	16.2871	0.539321
$913$	11.1869	0.370234
$914$	−11.5653	−0.382546
$915$	10.6663	0.352619
$916$	8.47008	0.279859
$917$	0	0
$918$	0.176846	0.00583679
$919$	52.1851	1.72143	0.860714	−	0.509089i	$-0.170018\pi$
$919$	52.1851	1.72143	0.860714	+	0.509089i	$0.170018\pi$
$920$	−42.7691	−1.41006
$921$	27.8168	0.916596
$922$	19.3201	0.636272
$923$	−6.54806	−0.215532
$924$	0	0
$925$	−0.133117	−0.00437685
$926$	13.2979	0.436998
$927$	8.82013	0.289691
$928$	8.51002	0.279355
$929$	−35.7506	−1.17294	−0.586470	−	0.809971i	$-0.699483\pi$
$929$	−35.7506	−1.17294	−0.586470	+	0.809971i	$0.699483\pi$
$930$	−15.4874	−0.507853
$931$	0	0
$932$	1.68348	0.0551441
$933$	9.04277	0.296047
$934$	29.3735	0.961131
$935$	−0.272068	−0.00889757
$936$	−3.96636	−0.129645
$937$	−43.8725	−1.43325	−0.716626	−	0.697457i	$-0.754315\pi$
$937$	−43.8725	−1.43325	−0.716626	+	0.697457i	$0.754315\pi$
$938$	0	0
$939$	−16.1768	−0.527911
$940$	−1.60998	−0.0525117
$941$	28.9003	0.942123	0.471061	−	0.882100i	$-0.343871\pi$
$941$	28.9003	0.942123	0.471061	+	0.882100i	$0.343871\pi$
$942$	23.1366	0.753833
$943$	58.3365	1.89970
$944$	−22.3529	−0.727524
$945$	0	0
$946$	−6.34374	−0.206253
$947$	2.98044	0.0968512	0.0484256	−	0.998827i	$-0.484580\pi$
$947$	2.98044	0.0968512	0.0484256	+	0.998827i	$0.484580\pi$
$948$	4.29466	0.139484
$949$	−16.0583	−0.521274
$950$	2.43009	0.0788424
$951$	−5.23370	−0.169714
$952$	0	0
$953$	−31.6198	−1.02427	−0.512134	−	0.858906i	$-0.671145\pi$
$953$	−31.6198	−1.02427	−0.512134	+	0.858906i	$0.671145\pi$
$954$	18.0275	0.583661
$955$	38.2864	1.23892
$956$	3.60476	0.116586
$957$	−5.05502	−0.163406
$958$	−36.6997	−1.18571
$959$	0	0
$960$	−15.0884	−0.486977
$961$	−11.8427	−0.382023
$962$	−0.699986	−0.0225684
$963$	10.4841	0.337847
$964$	−6.22010	−0.200336
$965$	−48.1876	−1.55121
$966$	0	0
$967$	24.3425	0.782803	0.391402	−	0.920220i	$-0.371990\pi$
$967$	24.3425	0.782803	0.391402	+	0.920220i	$0.371990\pi$
$968$	2.57816	0.0828653
$969$	0.421111	0.0135280
$970$	−58.0661	−1.86439
$971$	4.20698	0.135008	0.0675042	−	0.997719i	$-0.478496\pi$
$971$	4.20698	0.135008	0.0675042	+	0.997719i	$0.478496\pi$
$972$	0.300014	0.00962296
$973$	0	0
$974$	32.1798	1.03111
$975$	−0.682609	−0.0218610
$976$	20.6180	0.659967
$977$	−6.83824	−0.218775	−0.109387	−	0.993999i	$-0.534889\pi$
$977$	−6.83824	−0.218775	−0.109387	+	0.993999i	$0.534889\pi$
$978$	−0.637923	−0.0203985
$979$	−13.9327	−0.445292
$980$	0	0
$981$	10.5279	0.336129
$982$	42.7734	1.36495
$983$	17.4463	0.556449	0.278224	−	0.960516i	$-0.410254\pi$
$983$	17.4463	0.556449	0.278224	+	0.960516i	$0.410254\pi$
$984$	21.1533	0.674343
$985$	−61.3932	−1.95615
$986$	0.893961	0.0284695
$987$	0	0
$988$	1.66683	0.0530288
$989$	−29.7408	−0.945703
$990$	−3.53844	−0.112459
$991$	27.3101	0.867534	0.433767	−	0.901025i	$-0.357184\pi$
$991$	27.3101	0.867534	0.433767	+	0.901025i	$0.357184\pi$
$992$	−7.36842	−0.233948
$993$	−19.5302	−0.619772
$994$	0	0
$995$	25.6896	0.814414
$996$	−3.35624	−0.106347
$997$	−30.4312	−0.963766	−0.481883	−	0.876235i	$-0.660047\pi$
$997$	−30.4312	−0.963766	−0.481883	+	0.876235i	$0.660047\pi$
$998$	53.8356	1.70414
$999$	−0.300014	−0.00949203

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.z.1.1		4
3.2	odd	2		4851.2.a.bt.1.4		4
7.2	even	3		231.2.i.e.67.4	✓	8
7.4	even	3		231.2.i.e.100.4	yes	8
7.6	odd	2		1617.2.a.x.1.1		4
21.2	odd	6		693.2.i.i.298.1		8
21.11	odd	6		693.2.i.i.100.1		8
21.20	even	2		4851.2.a.bu.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.e.67.4	✓	8	7.2	even	3
231.2.i.e.100.4	yes	8	7.4	even	3
693.2.i.i.100.1		8	21.11	odd	6
693.2.i.i.298.1		8	21.2	odd	6
1617.2.a.x.1.1		4	7.6	odd	2
1617.2.a.z.1.1		4	1.1	even	1	trivial
4851.2.a.bt.1.4		4	3.2	odd	2
4851.2.a.bu.1.4		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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-1.51658 q^{2} +1.00000 q^{3} +0.300014 q^{4} -2.33317 q^{5} -1.51658 q^{6} +2.57816 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.51658 q^{2} +1.00000 q^{3} +0.300014 q^{4} -2.33317 q^{5} -1.51658 q^{6} +2.57816 q^{8} +1.00000 q^{9} +3.53844 q^{10} -1.00000 q^{11} +0.300014 q^{12} -1.53844 q^{13} -2.33317 q^{15} -4.51002 q^{16} -0.116609 q^{17} -1.51658 q^{18} -3.61132 q^{19} -0.699986 q^{20} +1.51658 q^{22} +7.11005 q^{23} +2.57816 q^{24} +0.443701 q^{25} +2.33317 q^{26} +1.00000 q^{27} +5.05502 q^{29} +3.53844 q^{30} -4.37690 q^{31} +1.68348 q^{32} -1.00000 q^{33} +0.176846 q^{34} +0.300014 q^{36} -0.300014 q^{37} +5.47686 q^{38} -1.53844 q^{39} -6.01531 q^{40} +8.20479 q^{41} -4.18293 q^{43} -0.300014 q^{44} -2.33317 q^{45} -10.7830 q^{46} +2.30001 q^{47} -4.51002 q^{48} -0.672908 q^{50} -0.116609 q^{51} -0.461555 q^{52} -11.8869 q^{53} -1.51658 q^{54} +2.33317 q^{55} -3.61132 q^{57} -7.66635 q^{58} +4.95627 q^{59} -0.699986 q^{60} -4.57160 q^{61} +6.63792 q^{62} +6.46691 q^{64} +3.58946 q^{65} +1.51658 q^{66} +12.2894 q^{67} -0.0349842 q^{68} +7.11005 q^{69} +4.25628 q^{71} +2.57816 q^{72} +10.4380 q^{73} +0.454996 q^{74} +0.443701 q^{75} -1.08345 q^{76} +2.33317 q^{78} +14.3148 q^{79} +10.5227 q^{80} +1.00000 q^{81} -12.4432 q^{82} -11.1869 q^{83} +0.272068 q^{85} +6.34374 q^{86} +5.05502 q^{87} -2.57816 q^{88} +13.9327 q^{89} +3.53844 q^{90} +2.13312 q^{92} -4.37690 q^{93} -3.48816 q^{94} +8.42585 q^{95} +1.68348 q^{96} -16.4101 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 12 * q^8 + 4 * q^9	\( 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 2 q^{6} + 12 q^{8} + 4 q^{9} + 10 q^{10} - 4 q^{11} + 4 q^{12} - 2 q^{13} + 4 q^{15} + 12 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{22} + 4 q^{23} + 12 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{27} + 8 q^{29} + 10 q^{30} - 12 q^{31} + 26 q^{32} - 4 q^{33} - 16 q^{34} + 4 q^{36} - 4 q^{37} + 8 q^{38} - 2 q^{39} - 6 q^{40} + 2 q^{41} + 18 q^{43} - 4 q^{44} + 4 q^{45} - 14 q^{46} + 12 q^{47} + 12 q^{48} + 2 q^{50} + 2 q^{51} - 6 q^{52} - 12 q^{53} + 2 q^{54} - 4 q^{55} - 4 q^{58} + 12 q^{59} + 2 q^{61} - 26 q^{62} + 56 q^{64} - 4 q^{65} - 2 q^{66} + 28 q^{67} - 48 q^{68} + 4 q^{69} + 12 q^{71} + 12 q^{72} + 6 q^{73} - 16 q^{74} + 4 q^{75} - 18 q^{76} - 4 q^{78} + 2 q^{79} + 16 q^{80} + 4 q^{81} - 12 q^{82} - 12 q^{83} + 18 q^{85} + 36 q^{86} + 8 q^{87} - 12 q^{88} + 8 q^{89} + 10 q^{90} - 16 q^{92} - 12 q^{93} + 20 q^{94} + 34 q^{95} + 26 q^{96} - 44 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 2 * q^6 + 12 * q^8 + 4 * q^9 + 10 * q^10 - 4 * q^11 + 4 * q^12 - 2 * q^13 + 4 * q^15 + 12 * q^16 + 2 * q^17 + 2 * q^18 - 2 * q^22 + 4 * q^23 + 12 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^27 + 8 * q^29 + 10 * q^30 - 12 * q^31 + 26 * q^32 - 4 * q^33 - 16 * q^34 + 4 * q^36 - 4 * q^37 + 8 * q^38 - 2 * q^39 - 6 * q^40 + 2 * q^41 + 18 * q^43 - 4 * q^44 + 4 * q^45 - 14 * q^46 + 12 * q^47 + 12 * q^48 + 2 * q^50 + 2 * q^51 - 6 * q^52 - 12 * q^53 + 2 * q^54 - 4 * q^55 - 4 * q^58 + 12 * q^59 + 2 * q^61 - 26 * q^62 + 56 * q^64 - 4 * q^65 - 2 * q^66 + 28 * q^67 - 48 * q^68 + 4 * q^69 + 12 * q^71 + 12 * q^72 + 6 * q^73 - 16 * q^74 + 4 * q^75 - 18 * q^76 - 4 * q^78 + 2 * q^79 + 16 * q^80 + 4 * q^81 - 12 * q^82 - 12 * q^83 + 18 * q^85 + 36 * q^86 + 8 * q^87 - 12 * q^88 + 8 * q^89 + 10 * q^90 - 16 * q^92 - 12 * q^93 + 20 * q^94 + 34 * q^95 + 26 * q^96 - 44 * q^97 - 4 * q^99

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