LMFDB - Embedded newform 2695.2.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,2,Mod(1,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, 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("2695.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2695.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:	$21.5196833447$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 8x^{6} + 26x^{5} + 15x^{4} - 60x^{3} - 2x^{2} + 37x - 9 $ x^8 - 3x^7 - 8x^6 + 26x^5 + 15x^4 - 60x^3 - 2x^2 + 37*x - 9
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.47049$ of defining polynomial
Character	$\chi$	$=$	2695.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.47049 q^{2} +0.718935 q^{3} +0.162341 q^{4} +1.00000 q^{5} -1.05719 q^{6} +2.70226 q^{8} -2.48313 q^{9} +O(q^{10})$	\(q-1.47049 q^{2} +0.718935 q^{3} +0.162341 q^{4} +1.00000 q^{5} -1.05719 q^{6} +2.70226 q^{8} -2.48313 q^{9} -1.47049 q^{10} -1.00000 q^{11} +0.116713 q^{12} -1.35223 q^{13} +0.718935 q^{15} -4.29833 q^{16} -0.542152 q^{17} +3.65142 q^{18} +0.199247 q^{19} +0.162341 q^{20} +1.47049 q^{22} -3.97113 q^{23} +1.94275 q^{24} +1.00000 q^{25} +1.98844 q^{26} -3.94202 q^{27} +2.25572 q^{29} -1.05719 q^{30} +6.03274 q^{31} +0.916129 q^{32} -0.718935 q^{33} +0.797229 q^{34} -0.403114 q^{36} +7.76630 q^{37} -0.292991 q^{38} -0.972166 q^{39} +2.70226 q^{40} +4.07178 q^{41} -9.85011 q^{43} -0.162341 q^{44} -2.48313 q^{45} +5.83951 q^{46} +7.86148 q^{47} -3.09022 q^{48} -1.47049 q^{50} -0.389772 q^{51} -0.219522 q^{52} +9.02817 q^{53} +5.79670 q^{54} -1.00000 q^{55} +0.143246 q^{57} -3.31701 q^{58} -7.57418 q^{59} +0.116713 q^{60} +7.51073 q^{61} -8.87109 q^{62} +7.24950 q^{64} -1.35223 q^{65} +1.05719 q^{66} -8.01205 q^{67} -0.0880135 q^{68} -2.85498 q^{69} +6.96472 q^{71} -6.71007 q^{72} +14.8710 q^{73} -11.4203 q^{74} +0.718935 q^{75} +0.0323460 q^{76} +1.42956 q^{78} -0.363537 q^{79} -4.29833 q^{80} +4.61534 q^{81} -5.98752 q^{82} +3.87173 q^{83} -0.542152 q^{85} +14.4845 q^{86} +1.62172 q^{87} -2.70226 q^{88} -3.98228 q^{89} +3.65142 q^{90} -0.644677 q^{92} +4.33715 q^{93} -11.5602 q^{94} +0.199247 q^{95} +0.658638 q^{96} -16.6867 q^{97} +2.48313 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9	$ 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9} + 3 q^{10} - 8 q^{11} + 9 q^{12} + 14 q^{13} + q^{15} + 7 q^{16} + 5 q^{17} + 27 q^{18} + q^{19} + 9 q^{20} - 3 q^{22} - 2 q^{23} - 24 q^{24} + 8 q^{25} + 21 q^{26} - 5 q^{27} + 26 q^{29} - 3 q^{30} + 2 q^{31} + 16 q^{32} - q^{33} - 26 q^{34} + 54 q^{36} - q^{37} - 31 q^{38} + 19 q^{39} + 9 q^{40} - 3 q^{41} + 4 q^{43} - 9 q^{44} + 19 q^{45} + 10 q^{46} + q^{47} - 21 q^{48} + 3 q^{50} + 3 q^{51} + 37 q^{52} + 26 q^{53} - 5 q^{54} - 8 q^{55} + 20 q^{57} - q^{58} - 19 q^{59} + 9 q^{60} - 26 q^{62} + q^{64} + 14 q^{65} + 3 q^{66} - 13 q^{67} + 15 q^{68} - 14 q^{69} - 9 q^{71} + 32 q^{72} + 11 q^{73} + 24 q^{74} + q^{75} - 18 q^{76} - 33 q^{78} - 8 q^{79} + 7 q^{80} + 52 q^{81} + 41 q^{82} + 32 q^{83} + 5 q^{85} + 28 q^{86} - 16 q^{87} - 9 q^{88} + 5 q^{89} + 27 q^{90} + 30 q^{92} - 14 q^{93} - 5 q^{94} + q^{95} + q^{96} + 9 q^{97} - 19 q^{99}+O(q^{100}) $ 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9 + 3 * q^10 - 8 * q^11 + 9 * q^12 + 14 * q^13 + q^15 + 7 * q^16 + 5 * q^17 + 27 * q^18 + q^19 + 9 * q^20 - 3 * q^22 - 2 * q^23 - 24 * q^24 + 8 * q^25 + 21 * q^26 - 5 * q^27 + 26 * q^29 - 3 * q^30 + 2 * q^31 + 16 * q^32 - q^33 - 26 * q^34 + 54 * q^36 - q^37 - 31 * q^38 + 19 * q^39 + 9 * q^40 - 3 * q^41 + 4 * q^43 - 9 * q^44 + 19 * q^45 + 10 * q^46 + q^47 - 21 * q^48 + 3 * q^50 + 3 * q^51 + 37 * q^52 + 26 * q^53 - 5 * q^54 - 8 * q^55 + 20 * q^57 - q^58 - 19 * q^59 + 9 * q^60 - 26 * q^62 + q^64 + 14 * q^65 + 3 * q^66 - 13 * q^67 + 15 * q^68 - 14 * q^69 - 9 * q^71 + 32 * q^72 + 11 * q^73 + 24 * q^74 + q^75 - 18 * q^76 - 33 * q^78 - 8 * q^79 + 7 * q^80 + 52 * q^81 + 41 * q^82 + 32 * q^83 + 5 * q^85 + 28 * q^86 - 16 * q^87 - 9 * q^88 + 5 * q^89 + 27 * q^90 + 30 * q^92 - 14 * q^93 - 5 * q^94 + q^95 + q^96 + 9 * q^97 - 19 * 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 $

$2$	−1.47049	−1.03979	−0.519897	−	0.854229i	$-0.674030\pi$
$2$	−1.47049	−1.03979	−0.519897	+	0.854229i	$0.674030\pi$
$3$	0.718935	0.415078	0.207539	−	0.978227i	$-0.433455\pi$
$3$	0.718935	0.415078	0.207539	+	0.978227i	$0.433455\pi$
$4$	0.162341	0.0811705
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.05719	−0.431595
$7$	0	0
$7$	0	0
$8$	2.70226	0.955393
$9$	−2.48313	−0.827711
$10$	−1.47049	−0.465010
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.116713	0.0336921
$13$	−1.35223	−0.375041	−0.187521	−	0.982261i	$-0.560045\pi$
$13$	−1.35223	−0.375041	−0.187521	+	0.982261i	$0.560045\pi$
$14$	0	0
$15$	0.718935	0.185628
$16$	−4.29833	−1.07458
$17$	−0.542152	−0.131491	−0.0657456	−	0.997836i	$-0.520943\pi$
$17$	−0.542152	−0.131491	−0.0657456	+	0.997836i	$0.520943\pi$
$18$	3.65142	0.860648
$19$	0.199247	0.0457104	0.0228552	−	0.999739i	$-0.492724\pi$
$19$	0.199247	0.0457104	0.0228552	+	0.999739i	$0.492724\pi$
$20$	0.162341	0.0363006
$21$	0	0
$22$	1.47049	0.313510
$23$	−3.97113	−0.828038	−0.414019	−	0.910268i	$-0.635875\pi$
$23$	−3.97113	−0.828038	−0.414019	+	0.910268i	$0.635875\pi$
$24$	1.94275	0.396562
$25$	1.00000	0.200000
$26$	1.98844	0.389965
$27$	−3.94202	−0.758642
$28$	0	0
$29$	2.25572	0.418876	0.209438	−	0.977822i	$-0.432837\pi$
$29$	2.25572	0.418876	0.209438	+	0.977822i	$0.432837\pi$
$30$	−1.05719	−0.193015
$31$	6.03274	1.08351	0.541756	−	0.840536i	$-0.317760\pi$
$31$	6.03274	1.08351	0.541756	+	0.840536i	$0.317760\pi$
$32$	0.916129	0.161950
$33$	−0.718935	−0.125151
$34$	0.797229	0.136724
$35$	0	0
$36$	−0.403114	−0.0671857
$37$	7.76630	1.27677	0.638386	−	0.769716i	$-0.279602\pi$
$37$	7.76630	1.27677	0.638386	+	0.769716i	$0.279602\pi$
$38$	−0.292991	−0.0475294
$39$	−0.972166	−0.155671
$40$	2.70226	0.427265
$41$	4.07178	0.635906	0.317953	−	0.948106i	$-0.397005\pi$
$41$	4.07178	0.635906	0.317953	+	0.948106i	$0.397005\pi$
$42$	0	0
$43$	−9.85011	−1.50213	−0.751064	−	0.660230i	$-0.770459\pi$
$43$	−9.85011	−1.50213	−0.751064	+	0.660230i	$0.770459\pi$
$44$	−0.162341	−0.0244738
$45$	−2.48313	−0.370163
$46$	5.83951	0.860988
$47$	7.86148	1.14671	0.573357	−	0.819306i	$-0.305641\pi$
$47$	7.86148	1.14671	0.573357	+	0.819306i	$0.305641\pi$
$48$	−3.09022	−0.446035
$49$	0	0
$50$	−1.47049	−0.207959
$51$	−0.389772	−0.0545790
$52$	−0.219522	−0.0304423
$53$	9.02817	1.24011	0.620057	−	0.784557i	$-0.287109\pi$
$53$	9.02817	1.24011	0.620057	+	0.784557i	$0.287109\pi$
$54$	5.79670	0.788831
$55$	−1.00000	−0.134840
$56$	0	0
$57$	0.143246	0.0189733
$58$	−3.31701	−0.435545
$59$	−7.57418	−0.986074	−0.493037	−	0.870008i	$-0.664113\pi$
$59$	−7.57418	−0.986074	−0.493037	+	0.870008i	$0.664113\pi$
$60$	0.116713	0.0150675
$61$	7.51073	0.961651	0.480825	−	0.876816i	$-0.340337\pi$
$61$	7.51073	0.961651	0.480825	+	0.876816i	$0.340337\pi$
$62$	−8.87109	−1.12663
$63$	0	0
$64$	7.24950	0.906187
$65$	−1.35223	−0.167724
$66$	1.05719	0.130131
$67$	−8.01205	−0.978828	−0.489414	−	0.872052i	$-0.662789\pi$
$67$	−8.01205	−0.978828	−0.489414	+	0.872052i	$0.662789\pi$
$68$	−0.0880135	−0.0106732
$69$	−2.85498	−0.343700
$70$	0	0
$71$	6.96472	0.826560	0.413280	−	0.910604i	$-0.364383\pi$
$71$	6.96472	0.826560	0.413280	+	0.910604i	$0.364383\pi$
$72$	−6.71007	−0.790789
$73$	14.8710	1.74052	0.870259	−	0.492595i	$-0.163952\pi$
$73$	14.8710	1.74052	0.870259	+	0.492595i	$0.163952\pi$
$74$	−11.4203	−1.32758
$75$	0.718935	0.0830155
$76$	0.0323460	0.00371034
$77$	0	0
$78$	1.42956	0.161866
$79$	−0.363537	−0.0409011	−0.0204505	−	0.999791i	$-0.506510\pi$
$79$	−0.363537	−0.0409011	−0.0204505	+	0.999791i	$0.506510\pi$
$80$	−4.29833	−0.480568
$81$	4.61534	0.512816
$82$	−5.98752	−0.661211
$83$	3.87173	0.424978	0.212489	−	0.977163i	$-0.431843\pi$
$83$	3.87173	0.424978	0.212489	+	0.977163i	$0.431843\pi$
$84$	0	0
$85$	−0.542152	−0.0588046
$86$	14.4845	1.56190
$87$	1.62172	0.173866
$88$	−2.70226	−0.288062
$89$	−3.98228	−0.422120	−0.211060	−	0.977473i	$-0.567692\pi$
$89$	−3.98228	−0.422120	−0.211060	+	0.977473i	$0.567692\pi$
$90$	3.65142	0.384894
$91$	0	0
$92$	−0.644677	−0.0672123
$93$	4.33715	0.449742
$94$	−11.5602	−1.19235
$95$	0.199247	0.0204423
$96$	0.658638	0.0672219
$97$	−16.6867	−1.69427	−0.847137	−	0.531375i	$-0.821676\pi$
$97$	−16.6867	−1.69427	−0.847137	+	0.531375i	$0.821676\pi$
$98$	0	0
$99$	2.48313	0.249564
$100$	0.162341	0.0162341
$101$	4.82690	0.480295	0.240147	−	0.970736i	$-0.422804\pi$
$101$	4.82690	0.480295	0.240147	+	0.970736i	$0.422804\pi$
$102$	0.573156	0.0567509
$103$	16.5707	1.63276	0.816382	−	0.577513i	$-0.195977\pi$
$103$	16.5707	1.63276	0.816382	+	0.577513i	$0.195977\pi$
$104$	−3.65408	−0.358312
$105$	0	0
$106$	−13.2758	−1.28946
$107$	2.45150	0.236996	0.118498	−	0.992954i	$-0.462192\pi$
$107$	2.45150	0.236996	0.118498	+	0.992954i	$0.462192\pi$
$108$	−0.639951	−0.0615793
$109$	4.01540	0.384606	0.192303	−	0.981336i	$-0.438404\pi$
$109$	4.01540	0.384606	0.192303	+	0.981336i	$0.438404\pi$
$110$	1.47049	0.140206
$111$	5.58347	0.529959
$112$	0	0
$113$	−13.6765	−1.28658	−0.643290	−	0.765622i	$-0.722431\pi$
$113$	−13.6765	−1.28658	−0.643290	+	0.765622i	$0.722431\pi$
$114$	−0.210641	−0.0197284
$115$	−3.97113	−0.370310
$116$	0.366196	0.0340004
$117$	3.35777	0.310426
$118$	11.1378	1.02531
$119$	0	0
$120$	1.94275	0.177348
$121$	1.00000	0.0909091
$122$	−11.0445	−0.999918
$123$	2.92735	0.263950
$124$	0.979362	0.0879493
$125$	1.00000	0.0894427
$126$	0	0
$127$	15.7491	1.39750	0.698752	−	0.715364i	$-0.253739\pi$
$127$	15.7491	1.39750	0.698752	+	0.715364i	$0.253739\pi$
$128$	−12.4926	−1.10420
$129$	−7.08159	−0.623499
$130$	1.98844	0.174398
$131$	−7.32413	−0.639912	−0.319956	−	0.947432i	$-0.603668\pi$
$131$	−7.32413	−0.639912	−0.319956	+	0.947432i	$0.603668\pi$
$132$	−0.116713	−0.0101585
$133$	0	0
$134$	11.7816	1.01778
$135$	−3.94202	−0.339275
$136$	−1.46503	−0.125626
$137$	7.70716	0.658467	0.329233	−	0.944249i	$-0.393210\pi$
$137$	7.70716	0.658467	0.329233	+	0.944249i	$0.393210\pi$
$138$	4.19823	0.357377
$139$	−16.6345	−1.41092	−0.705461	−	0.708749i	$-0.749260\pi$
$139$	−16.6345	−1.41092	−0.705461	+	0.708749i	$0.749260\pi$
$140$	0	0
$141$	5.65189	0.475975
$142$	−10.2416	−0.859452
$143$	1.35223	0.113079
$144$	10.6733	0.889443
$145$	2.25572	0.187327
$146$	−21.8676	−1.80978
$147$	0	0
$148$	1.26079	0.103636
$149$	8.31172	0.680923	0.340461	−	0.940259i	$-0.389417\pi$
$149$	8.31172	0.680923	0.340461	+	0.940259i	$0.389417\pi$
$150$	−1.05719	−0.0863190
$151$	7.59875	0.618377	0.309189	−	0.951001i	$-0.399943\pi$
$151$	7.59875	0.618377	0.309189	+	0.951001i	$0.399943\pi$
$152$	0.538417	0.0436714
$153$	1.34623	0.108837
$154$	0	0
$155$	6.03274	0.484562
$156$	−0.157822	−0.0126359
$157$	7.67112	0.612222	0.306111	−	0.951996i	$-0.400972\pi$
$157$	7.67112	0.612222	0.306111	+	0.951996i	$0.400972\pi$
$158$	0.534577	0.0425287
$159$	6.49067	0.514743
$160$	0.916129	0.0724264
$161$	0	0
$162$	−6.78681	−0.533222
$163$	16.9402	1.32686	0.663428	−	0.748240i	$-0.269101\pi$
$163$	16.9402	1.32686	0.663428	+	0.748240i	$0.269101\pi$
$164$	0.661018	0.0516168
$165$	−0.718935	−0.0559690
$166$	−5.69334	−0.441889
$167$	12.0563	0.932945	0.466472	−	0.884536i	$-0.345525\pi$
$167$	12.0563	0.932945	0.466472	+	0.884536i	$0.345525\pi$
$168$	0	0
$169$	−11.1715	−0.859344
$170$	0.797229	0.0611447
$171$	−0.494756	−0.0378350
$172$	−1.59908	−0.121928
$173$	−9.21389	−0.700519	−0.350260	−	0.936653i	$-0.613907\pi$
$173$	−9.21389	−0.700519	−0.350260	+	0.936653i	$0.613907\pi$
$174$	−2.38472	−0.180785
$175$	0	0
$176$	4.29833	0.323999
$177$	−5.44534	−0.409297
$178$	5.85590	0.438918
$179$	4.32152	0.323006	0.161503	−	0.986872i	$-0.448366\pi$
$179$	4.32152	0.323006	0.161503	+	0.986872i	$0.448366\pi$
$180$	−0.403114	−0.0300464
$181$	−2.54375	−0.189075	−0.0945377	−	0.995521i	$-0.530137\pi$
$181$	−2.54375	−0.189075	−0.0945377	+	0.995521i	$0.530137\pi$
$182$	0	0
$183$	5.39973	0.399160
$184$	−10.7310	−0.791101
$185$	7.76630	0.570990
$186$	−6.37774	−0.467638
$187$	0.542152	0.0396461
$188$	1.27624	0.0930794
$189$	0	0
$190$	−0.292991	−0.0212558
$191$	2.92563	0.211691	0.105845	−	0.994383i	$-0.466245\pi$
$191$	2.92563	0.211691	0.105845	+	0.994383i	$0.466245\pi$
$192$	5.21192	0.376138
$193$	13.3599	0.961664	0.480832	−	0.876813i	$-0.340335\pi$
$193$	13.3599	0.961664	0.480832	+	0.876813i	$0.340335\pi$
$194$	24.5376	1.76169
$195$	−0.972166	−0.0696183
$196$	0	0
$197$	11.2489	0.801454	0.400727	−	0.916198i	$-0.368758\pi$
$197$	11.2489	0.801454	0.400727	+	0.916198i	$0.368758\pi$
$198$	−3.65142	−0.259495
$199$	−10.4913	−0.743709	−0.371855	−	0.928291i	$-0.621278\pi$
$199$	−10.4913	−0.743709	−0.371855	+	0.928291i	$0.621278\pi$
$200$	2.70226	0.191079
$201$	−5.76014	−0.406289
$202$	−7.09791	−0.499407
$203$	0	0
$204$	−0.0632760	−0.00443021
$205$	4.07178	0.284386
$206$	−24.3671	−1.69774
$207$	9.86084	0.685376
$208$	5.81233	0.403012
$209$	−0.199247	−0.0137822
$210$	0	0
$211$	8.48714	0.584279	0.292139	−	0.956376i	$-0.405633\pi$
$211$	8.48714	0.584279	0.292139	+	0.956376i	$0.405633\pi$
$212$	1.46564	0.100661
$213$	5.00718	0.343087
$214$	−3.60491	−0.246427
$215$	−9.85011	−0.671772
$216$	−10.6524	−0.724801
$217$	0	0
$218$	−5.90461	−0.399911
$219$	10.6913	0.722450
$220$	−0.162341	−0.0109450
$221$	0.733114	0.0493146
$222$	−8.21043	−0.551048
$223$	19.7906	1.32528	0.662640	−	0.748938i	$-0.269436\pi$
$223$	19.7906	1.32528	0.662640	+	0.748938i	$0.269436\pi$
$224$	0	0
$225$	−2.48313	−0.165542
$226$	20.1112	1.33778
$227$	−2.28445	−0.151624	−0.0758122	−	0.997122i	$-0.524155\pi$
$227$	−2.28445	−0.151624	−0.0758122	+	0.997122i	$0.524155\pi$
$228$	0.0232547	0.00154008
$229$	−26.2015	−1.73145	−0.865723	−	0.500524i	$-0.833141\pi$
$229$	−26.2015	−1.73145	−0.865723	+	0.500524i	$0.833141\pi$
$230$	5.83951	0.385046
$231$	0	0
$232$	6.09553	0.400191
$233$	18.0324	1.18134	0.590672	−	0.806912i	$-0.298863\pi$
$233$	18.0324	1.18134	0.590672	+	0.806912i	$0.298863\pi$
$234$	−4.93756	−0.322779
$235$	7.86148	0.512826
$236$	−1.22960	−0.0800401
$237$	−0.261359	−0.0169771
$238$	0	0
$239$	26.4144	1.70861	0.854304	−	0.519774i	$-0.173984\pi$
$239$	26.4144	1.70861	0.854304	+	0.519774i	$0.173984\pi$
$240$	−3.09022	−0.199473
$241$	14.3421	0.923857	0.461928	−	0.886917i	$-0.347158\pi$
$241$	14.3421	0.923857	0.461928	+	0.886917i	$0.347158\pi$
$242$	−1.47049	−0.0945267
$243$	15.1442	0.971500
$244$	1.21930	0.0780577
$245$	0	0
$246$	−4.30464	−0.274454
$247$	−0.269428	−0.0171433
$248$	16.3020	1.03518
$249$	2.78353	0.176399
$250$	−1.47049	−0.0930020
$251$	7.73165	0.488018	0.244009	−	0.969773i	$-0.421537\pi$
$251$	7.73165	0.488018	0.244009	+	0.969773i	$0.421537\pi$
$252$	0	0
$253$	3.97113	0.249663
$254$	−23.1588	−1.45312
$255$	−0.389772	−0.0244085
$256$	3.87121	0.241951
$257$	−7.72813	−0.482068	−0.241034	−	0.970517i	$-0.577486\pi$
$257$	−7.72813	−0.482068	−0.241034	+	0.970517i	$0.577486\pi$
$258$	10.4134	0.648311
$259$	0	0
$260$	−0.219522	−0.0136142
$261$	−5.60124	−0.346708
$262$	10.7701	0.665376
$263$	22.9661	1.41615	0.708076	−	0.706136i	$-0.249563\pi$
$263$	22.9661	1.41615	0.708076	+	0.706136i	$0.249563\pi$
$264$	−1.94275	−0.119568
$265$	9.02817	0.554596
$266$	0	0
$267$	−2.86300	−0.175213
$268$	−1.30068	−0.0794519
$269$	−21.4848	−1.30995	−0.654975	−	0.755650i	$-0.727321\pi$
$269$	−21.4848	−1.30995	−0.654975	+	0.755650i	$0.727321\pi$
$270$	5.79670	0.352776
$271$	−21.1324	−1.28370	−0.641851	−	0.766829i	$-0.721833\pi$
$271$	−21.1324	−1.28370	−0.641851	+	0.766829i	$0.721833\pi$
$272$	2.33035	0.141298
$273$	0	0
$274$	−11.3333	−0.684670
$275$	−1.00000	−0.0603023
$276$	−0.463481	−0.0278983
$277$	−11.8228	−0.710363	−0.355181	−	0.934797i	$-0.615581\pi$
$277$	−11.8228	−0.710363	−0.355181	+	0.934797i	$0.615581\pi$
$278$	24.4609	1.46707
$279$	−14.9801	−0.896835
$280$	0	0
$281$	26.7399	1.59517	0.797584	−	0.603209i	$-0.206111\pi$
$281$	26.7399	1.59517	0.797584	+	0.603209i	$0.206111\pi$
$282$	−8.31105	−0.494916
$283$	−11.7357	−0.697616	−0.348808	−	0.937194i	$-0.613414\pi$
$283$	−11.7357	−0.697616	−0.348808	+	0.937194i	$0.613414\pi$
$284$	1.13066	0.0670923
$285$	0.143246	0.00848514
$286$	−1.98844	−0.117579
$287$	0	0
$288$	−2.27487	−0.134048
$289$	−16.7061	−0.982710
$290$	−3.31701	−0.194782
$291$	−11.9966	−0.703255
$292$	2.41417	0.141279
$293$	14.9197	0.871621	0.435810	−	0.900039i	$-0.356462\pi$
$293$	14.9197	0.871621	0.435810	+	0.900039i	$0.356462\pi$
$294$	0	0
$295$	−7.57418	−0.440986
$296$	20.9866	1.21982
$297$	3.94202	0.228739
$298$	−12.2223	−0.708019
$299$	5.36988	0.310548
$300$	0.116713	0.00673841
$301$	0	0
$302$	−11.1739	−0.642985
$303$	3.47023	0.199360
$304$	−0.856429	−0.0491195
$305$	7.51073	0.430063
$306$	−1.97962	−0.113168
$307$	31.0065	1.76964	0.884818	−	0.465937i	$-0.154283\pi$
$307$	31.0065	1.76964	0.884818	+	0.465937i	$0.154283\pi$
$308$	0	0
$309$	11.9133	0.677723
$310$	−8.87109	−0.503844
$311$	−22.6575	−1.28479	−0.642394	−	0.766374i	$-0.722059\pi$
$311$	−22.6575	−1.28479	−0.642394	+	0.766374i	$0.722059\pi$
$312$	−2.62704	−0.148727
$313$	−10.4903	−0.592946	−0.296473	−	0.955041i	$-0.595811\pi$
$313$	−10.4903	−0.592946	−0.296473	+	0.955041i	$0.595811\pi$
$314$	−11.2803	−0.636585
$315$	0	0
$316$	−0.0590170	−0.00331996
$317$	33.9331	1.90588	0.952938	−	0.303166i	$-0.0980436\pi$
$317$	33.9331	1.90588	0.952938	+	0.303166i	$0.0980436\pi$
$318$	−9.54446	−0.535227
$319$	−2.25572	−0.126296
$320$	7.24950	0.405259
$321$	1.76247	0.0983716
$322$	0	0
$323$	−0.108022	−0.00601051
$324$	0.749259	0.0416255
$325$	−1.35223	−0.0750082
$326$	−24.9104	−1.37966
$327$	2.88681	0.159641
$328$	11.0030	0.607540
$329$	0	0
$330$	1.05719	0.0581962
$331$	15.4008	0.846507	0.423253	−	0.906011i	$-0.360888\pi$
$331$	15.4008	0.846507	0.423253	+	0.906011i	$0.360888\pi$
$332$	0.628541	0.0344957
$333$	−19.2847	−1.05680
$334$	−17.7287	−0.970070
$335$	−8.01205	−0.437745
$336$	0	0
$337$	−14.6257	−0.796710	−0.398355	−	0.917231i	$-0.630419\pi$
$337$	−14.6257	−0.796710	−0.398355	+	0.917231i	$0.630419\pi$
$338$	16.4275	0.893540
$339$	−9.83255	−0.534031
$340$	−0.0880135	−0.00477320
$341$	−6.03274	−0.326691
$342$	0.727534	0.0393406
$343$	0	0
$344$	−26.6175	−1.43512
$345$	−2.85498	−0.153707
$346$	13.5489	0.728395
$347$	1.11566	0.0598920	0.0299460	−	0.999552i	$-0.490466\pi$
$347$	1.11566	0.0598920	0.0299460	+	0.999552i	$0.490466\pi$
$348$	0.263271	0.0141128
$349$	25.7539	1.37858	0.689289	−	0.724487i	$-0.257923\pi$
$349$	25.7539	1.37858	0.689289	+	0.724487i	$0.257923\pi$
$350$	0	0
$351$	5.33051	0.284522
$352$	−0.916129	−0.0488299
$353$	15.2826	0.813413	0.406707	−	0.913559i	$-0.366677\pi$
$353$	15.2826	0.813413	0.406707	+	0.913559i	$0.366677\pi$
$354$	8.00732	0.425584
$355$	6.96472	0.369649
$356$	−0.646487	−0.0342637
$357$	0	0
$358$	−6.35476	−0.335859
$359$	6.82930	0.360437	0.180218	−	0.983627i	$-0.442320\pi$
$359$	6.82930	0.360437	0.180218	+	0.983627i	$0.442320\pi$
$360$	−6.71007	−0.353652
$361$	−18.9603	−0.997911
$362$	3.74056	0.196599
$363$	0.718935	0.0377343
$364$	0	0
$365$	14.8710	0.778383
$366$	−7.94025	−0.415044
$367$	−4.51629	−0.235748	−0.117874	−	0.993029i	$-0.537608\pi$
$367$	−4.51629	−0.235748	−0.117874	+	0.993029i	$0.537608\pi$
$368$	17.0692	0.889794
$369$	−10.1108	−0.526346
$370$	−11.4203	−0.593711
$371$	0	0
$372$	0.704098	0.0365058
$373$	4.25649	0.220392	0.110196	−	0.993910i	$-0.464852\pi$
$373$	4.25649	0.220392	0.110196	+	0.993910i	$0.464852\pi$
$374$	−0.797229	−0.0412237
$375$	0.718935	0.0371257
$376$	21.2437	1.09556
$377$	−3.05025	−0.157096
$378$	0	0
$379$	−12.2039	−0.626871	−0.313436	−	0.949609i	$-0.601480\pi$
$379$	−12.2039	−0.626871	−0.313436	+	0.949609i	$0.601480\pi$
$380$	0.0323460	0.00165931
$381$	11.3226	0.580072
$382$	−4.30211	−0.220115
$383$	11.0246	0.563332	0.281666	−	0.959512i	$-0.409113\pi$
$383$	11.0246	0.563332	0.281666	+	0.959512i	$0.409113\pi$
$384$	−8.98135	−0.458328
$385$	0	0
$386$	−19.6455	−0.999932
$387$	24.4591	1.24333
$388$	−2.70893	−0.137525
$389$	30.5673	1.54982	0.774911	−	0.632070i	$-0.217794\pi$
$389$	30.5673	1.54982	0.774911	+	0.632070i	$0.217794\pi$
$390$	1.42956	0.0723886
$391$	2.15295	0.108880
$392$	0	0
$393$	−5.26557	−0.265613
$394$	−16.5415	−0.833346
$395$	−0.363537	−0.0182915
$396$	0.403114	0.0202573
$397$	−17.7663	−0.891665	−0.445832	−	0.895116i	$-0.647092\pi$
$397$	−17.7663	−0.891665	−0.445832	+	0.895116i	$0.647092\pi$
$398$	15.4274	0.773304
$399$	0	0
$400$	−4.29833	−0.214916
$401$	25.1069	1.25378	0.626889	−	0.779108i	$-0.284328\pi$
$401$	25.1069	1.25378	0.626889	+	0.779108i	$0.284328\pi$
$402$	8.47024	0.422457
$403$	−8.15766	−0.406362
$404$	0.783604	0.0389858
$405$	4.61534	0.229338
$406$	0	0
$407$	−7.76630	−0.384961
$408$	−1.05327	−0.0521444
$409$	19.1247	0.945656	0.472828	−	0.881155i	$-0.343233\pi$
$409$	19.1247	0.945656	0.472828	+	0.881155i	$0.343233\pi$
$410$	−5.98752	−0.295702
$411$	5.54095	0.273315
$412$	2.69011	0.132532
$413$	0	0
$414$	−14.5003	−0.712649
$415$	3.87173	0.190056
$416$	−1.23882	−0.0607380
$417$	−11.9591	−0.585642
$418$	0.292991	0.0143306
$419$	−34.2881	−1.67508	−0.837542	−	0.546372i	$-0.816008\pi$
$419$	−34.2881	−1.67508	−0.837542	+	0.546372i	$0.816008\pi$
$420$	0	0
$421$	−13.2601	−0.646258	−0.323129	−	0.946355i	$-0.604735\pi$
$421$	−13.2601	−0.646258	−0.323129	+	0.946355i	$0.604735\pi$
$422$	−12.4803	−0.607529
$423$	−19.5211	−0.949148
$424$	24.3964	1.18480
$425$	−0.542152	−0.0262982
$426$	−7.36301	−0.356739
$427$	0	0
$428$	0.397980	0.0192371
$429$	0.972166	0.0469366
$430$	14.4845	0.698504
$431$	−19.3565	−0.932371	−0.466185	−	0.884687i	$-0.654372\pi$
$431$	−19.3565	−0.932371	−0.466185	+	0.884687i	$0.654372\pi$
$432$	16.9441	0.815222
$433$	14.8600	0.714127	0.357064	−	0.934080i	$-0.383778\pi$
$433$	14.8600	0.714127	0.357064	+	0.934080i	$0.383778\pi$
$434$	0	0
$435$	1.62172	0.0777553
$436$	0.651865	0.0312187
$437$	−0.791235	−0.0378499
$438$	−15.7214	−0.751198
$439$	−21.0593	−1.00511	−0.502554	−	0.864546i	$-0.667606\pi$
$439$	−21.0593	−1.00511	−0.502554	+	0.864546i	$0.667606\pi$
$440$	−2.70226	−0.128825
$441$	0	0
$442$	−1.07804	−0.0512770
$443$	−8.11188	−0.385407	−0.192704	−	0.981257i	$-0.561726\pi$
$443$	−8.11188	−0.385407	−0.192704	+	0.981257i	$0.561726\pi$
$444$	0.906426	0.0430171
$445$	−3.98228	−0.188778
$446$	−29.1019	−1.37802
$447$	5.97559	0.282636
$448$	0	0
$449$	35.4379	1.67242	0.836209	−	0.548411i	$-0.184767\pi$
$449$	35.4379	1.67242	0.836209	+	0.548411i	$0.184767\pi$
$450$	3.65142	0.172130
$451$	−4.07178	−0.191733
$452$	−2.22026	−0.104432
$453$	5.46301	0.256674
$454$	3.35926	0.157658
$455$	0	0
$456$	0.387087	0.0181270
$457$	32.6534	1.52746	0.763730	−	0.645536i	$-0.223366\pi$
$457$	32.6534	1.52746	0.763730	+	0.645536i	$0.223366\pi$
$458$	38.5291	1.80035
$459$	2.13717	0.0997546
$460$	−0.644677	−0.0300582
$461$	−1.18996	−0.0554219	−0.0277109	−	0.999616i	$-0.508822\pi$
$461$	−1.18996	−0.0554219	−0.0277109	+	0.999616i	$0.508822\pi$
$462$	0	0
$463$	−17.3660	−0.807068	−0.403534	−	0.914965i	$-0.632218\pi$
$463$	−17.3660	−0.807068	−0.403534	+	0.914965i	$0.632218\pi$
$464$	−9.69581	−0.450117
$465$	4.33715	0.201131
$466$	−26.5165	−1.22835
$467$	13.0818	0.605354	0.302677	−	0.953093i	$-0.402120\pi$
$467$	13.0818	0.605354	0.302677	+	0.953093i	$0.402120\pi$
$468$	0.545103	0.0251974
$469$	0	0
$470$	−11.5602	−0.533233
$471$	5.51504	0.254120
$472$	−20.4674	−0.942088
$473$	9.85011	0.452908
$474$	0.384327	0.0176527
$475$	0.199247	0.00914208
$476$	0	0
$477$	−22.4181	−1.02646
$478$	−38.8422	−1.77660
$479$	34.4109	1.57227	0.786136	−	0.618053i	$-0.212078\pi$
$479$	34.4109	1.57227	0.786136	+	0.618053i	$0.212078\pi$
$480$	0.658638	0.0300626
$481$	−10.5018	−0.478842
$482$	−21.0899	−0.960620
$483$	0	0
$484$	0.162341	0.00737914
$485$	−16.6867	−0.757702
$486$	−22.2694	−1.01016
$487$	−26.9669	−1.22199	−0.610994	−	0.791635i	$-0.709230\pi$
$487$	−26.9669	−1.22199	−0.610994	+	0.791635i	$0.709230\pi$
$488$	20.2959	0.918754
$489$	12.1789	0.550748
$490$	0	0
$491$	34.2270	1.54464	0.772322	−	0.635232i	$-0.219095\pi$
$491$	34.2270	1.54464	0.772322	+	0.635232i	$0.219095\pi$
$492$	0.475229	0.0214250
$493$	−1.22294	−0.0550785
$494$	0.396191	0.0178255
$495$	2.48313	0.111608
$496$	−25.9307	−1.16432
$497$	0	0
$498$	−4.09315	−0.183418
$499$	−35.3892	−1.58424	−0.792120	−	0.610366i	$-0.791022\pi$
$499$	−35.3892	−1.58424	−0.792120	+	0.610366i	$0.791022\pi$
$500$	0.162341	0.00726011
$501$	8.66770	0.387244
$502$	−11.3693	−0.507438
$503$	15.5682	0.694154	0.347077	−	0.937837i	$-0.387174\pi$
$503$	15.5682	0.694154	0.347077	+	0.937837i	$0.387174\pi$
$504$	0	0
$505$	4.82690	0.214794
$506$	−5.83951	−0.259598
$507$	−8.03157	−0.356694
$508$	2.55672	0.113436
$509$	−12.0948	−0.536092	−0.268046	−	0.963406i	$-0.586378\pi$
$509$	−12.0948	−0.536092	−0.268046	+	0.963406i	$0.586378\pi$
$510$	0.573156	0.0253798
$511$	0	0
$512$	19.2926	0.852619
$513$	−0.785435	−0.0346778
$514$	11.3641	0.501251
$515$	16.5707	0.730194
$516$	−1.14963	−0.0506098
$517$	−7.86148	−0.345747
$518$	0	0
$519$	−6.62419	−0.290770
$520$	−3.65408	−0.160242
$521$	9.54181	0.418034	0.209017	−	0.977912i	$-0.432974\pi$
$521$	9.54181	0.418034	0.209017	+	0.977912i	$0.432974\pi$
$522$	8.23658	0.360505
$523$	−34.6164	−1.51367	−0.756835	−	0.653606i	$-0.773256\pi$
$523$	−34.6164	−1.51367	−0.756835	+	0.653606i	$0.773256\pi$
$524$	−1.18901	−0.0519420
$525$	0	0
$526$	−33.7715	−1.47251
$527$	−3.27066	−0.142472
$528$	3.09022	0.134485
$529$	−7.23014	−0.314354
$530$	−13.2758	−0.576665
$531$	18.8077	0.816184
$532$	0	0
$533$	−5.50599	−0.238491
$534$	4.21001	0.182185
$535$	2.45150	0.105988
$536$	−21.6506	−0.935165
$537$	3.10690	0.134072
$538$	31.5932	1.36208
$539$	0	0
$540$	−0.639951	−0.0275391
$541$	2.48740	0.106942	0.0534708	−	0.998569i	$-0.482972\pi$
$541$	2.48740	0.106942	0.0534708	+	0.998569i	$0.482972\pi$
$542$	31.0750	1.33479
$543$	−1.82879	−0.0784810
$544$	−0.496681	−0.0212950
$545$	4.01540	0.172001
$546$	0	0
$547$	−27.1185	−1.15950	−0.579751	−	0.814794i	$-0.696850\pi$
$547$	−27.1185	−1.15950	−0.579751	+	0.814794i	$0.696850\pi$
$548$	1.25119	0.0534481
$549$	−18.6501	−0.795969
$550$	1.47049	0.0627019
$551$	0.449445	0.0191470
$552$	−7.71491	−0.328368
$553$	0	0
$554$	17.3853	0.738631
$555$	5.58347	0.237005
$556$	−2.70047	−0.114525
$557$	22.3081	0.945223	0.472612	−	0.881271i	$-0.343311\pi$
$557$	22.3081	0.945223	0.472612	+	0.881271i	$0.343311\pi$
$558$	22.0281	0.932523
$559$	13.3196	0.563360
$560$	0	0
$561$	0.389772	0.0164562
$562$	−39.3207	−1.65864
$563$	−8.81067	−0.371326	−0.185663	−	0.982614i	$-0.559443\pi$
$563$	−8.81067	−0.371326	−0.185663	+	0.982614i	$0.559443\pi$
$564$	0.917534	0.0386352
$565$	−13.6765	−0.575376
$566$	17.2573	0.725377
$567$	0	0
$568$	18.8205	0.789690
$569$	−17.8849	−0.749774	−0.374887	−	0.927070i	$-0.622319\pi$
$569$	−17.8849	−0.749774	−0.374887	+	0.927070i	$0.622319\pi$
$570$	−0.210641	−0.00882279
$571$	−5.45122	−0.228127	−0.114063	−	0.993473i	$-0.536387\pi$
$571$	−5.45122	−0.228127	−0.114063	+	0.993473i	$0.536387\pi$
$572$	0.219522	0.00917870
$573$	2.10334	0.0878682
$574$	0	0
$575$	−3.97113	−0.165608
$576$	−18.0015	−0.750061
$577$	−37.5399	−1.56281	−0.781403	−	0.624027i	$-0.785496\pi$
$577$	−37.5399	−1.56281	−0.781403	+	0.624027i	$0.785496\pi$
$578$	24.5661	1.02182
$579$	9.60488	0.399165
$580$	0.366196	0.0152054
$581$	0	0
$582$	17.6409	0.731240
$583$	−9.02817	−0.373908
$584$	40.1853	1.66288
$585$	3.35777	0.138827
$586$	−21.9393	−0.906305
$587$	−8.73112	−0.360372	−0.180186	−	0.983633i	$-0.557670\pi$
$587$	−8.73112	−0.360372	−0.180186	+	0.983633i	$0.557670\pi$
$588$	0	0
$589$	1.20201	0.0495278
$590$	11.1378	0.458534
$591$	8.08726	0.332665
$592$	−33.3821	−1.37200
$593$	−19.0152	−0.780862	−0.390431	−	0.920632i	$-0.627674\pi$
$593$	−19.0152	−0.780862	−0.390431	+	0.920632i	$0.627674\pi$
$594$	−5.79670	−0.237841
$595$	0	0
$596$	1.34933	0.0552708
$597$	−7.54257	−0.308697
$598$	−7.89636	−0.322906
$599$	−12.3635	−0.505160	−0.252580	−	0.967576i	$-0.581279\pi$
$599$	−12.3635	−0.505160	−0.252580	+	0.967576i	$0.581279\pi$
$600$	1.94275	0.0793124
$601$	−25.2886	−1.03154	−0.515772	−	0.856726i	$-0.672495\pi$
$601$	−25.2886	−1.03154	−0.515772	+	0.856726i	$0.672495\pi$
$602$	0	0
$603$	19.8950	0.810186
$604$	1.23359	0.0501940
$605$	1.00000	0.0406558
$606$	−5.10294	−0.207293
$607$	−9.56935	−0.388408	−0.194204	−	0.980961i	$-0.562212\pi$
$607$	−9.56935	−0.388408	−0.194204	+	0.980961i	$0.562212\pi$
$608$	0.182536	0.00740281
$609$	0	0
$610$	−11.0445	−0.447177
$611$	−10.6305	−0.430065
$612$	0.218549	0.00883433
$613$	1.65385	0.0667985	0.0333992	−	0.999442i	$-0.489367\pi$
$613$	1.65385	0.0667985	0.0333992	+	0.999442i	$0.489367\pi$
$614$	−45.5948	−1.84006
$615$	2.92735	0.118042
$616$	0	0
$617$	4.35949	0.175506	0.0877531	−	0.996142i	$-0.472031\pi$
$617$	4.35949	0.175506	0.0877531	+	0.996142i	$0.472031\pi$
$618$	−17.5184	−0.704692
$619$	−37.1991	−1.49516	−0.747579	−	0.664173i	$-0.768784\pi$
$619$	−37.1991	−1.49516	−0.747579	+	0.664173i	$0.768784\pi$
$620$	0.979362	0.0393321
$621$	15.6543	0.628184
$622$	33.3176	1.33591
$623$	0	0
$624$	4.17869	0.167281
$625$	1.00000	0.0400000
$626$	15.4259	0.616542
$627$	−0.143246	−0.00572068
$628$	1.24534	0.0496944
$629$	−4.21051	−0.167884
$630$	0	0
$631$	−35.1684	−1.40003	−0.700017	−	0.714126i	$-0.746824\pi$
$631$	−35.1684	−1.40003	−0.700017	+	0.714126i	$0.746824\pi$
$632$	−0.982371	−0.0390766
$633$	6.10170	0.242521
$634$	−49.8984	−1.98172
$635$	15.7491	0.624983
$636$	1.05370	0.0417820
$637$	0	0
$638$	3.31701	0.131322
$639$	−17.2943	−0.684153
$640$	−12.4926	−0.493812
$641$	−15.9052	−0.628217	−0.314108	−	0.949387i	$-0.601706\pi$
$641$	−15.9052	−0.628217	−0.314108	+	0.949387i	$0.601706\pi$
$642$	−2.59170	−0.102286
$643$	42.0439	1.65805	0.829024	−	0.559213i	$-0.188897\pi$
$643$	42.0439	1.65805	0.829024	+	0.559213i	$0.188897\pi$
$644$	0	0
$645$	−7.08159	−0.278837
$646$	0.158845	0.00624969
$647$	30.9656	1.21738	0.608692	−	0.793407i	$-0.291695\pi$
$647$	30.9656	1.21738	0.608692	+	0.793407i	$0.291695\pi$
$648$	12.4718	0.489940
$649$	7.57418	0.297312
$650$	1.98844	0.0779931
$651$	0	0
$652$	2.75009	0.107702
$653$	−16.8339	−0.658763	−0.329381	−	0.944197i	$-0.606840\pi$
$653$	−16.8339	−0.658763	−0.329381	+	0.944197i	$0.606840\pi$
$654$	−4.24503	−0.165994
$655$	−7.32413	−0.286177
$656$	−17.5019	−0.683333
$657$	−36.9266	−1.44064
$658$	0	0
$659$	−37.5268	−1.46184	−0.730918	−	0.682465i	$-0.760908\pi$
$659$	−37.5268	−1.46184	−0.730918	+	0.682465i	$0.760908\pi$
$660$	−0.116713	−0.00454304
$661$	7.98175	0.310454	0.155227	−	0.987879i	$-0.450389\pi$
$661$	7.98175	0.310454	0.155227	+	0.987879i	$0.450389\pi$
$662$	−22.6468	−0.880192
$663$	0.527062	0.0204694
$664$	10.4624	0.406021
$665$	0	0
$666$	28.3580	1.09885
$667$	−8.95775	−0.346845
$668$	1.95723	0.0757276
$669$	14.2282	0.550094
$670$	11.7816	0.455164
$671$	−7.51073	−0.289949
$672$	0	0
$673$	−30.3125	−1.16846	−0.584230	−	0.811588i	$-0.698603\pi$
$673$	−30.3125	−1.16846	−0.584230	+	0.811588i	$0.698603\pi$
$674$	21.5069	0.828414
$675$	−3.94202	−0.151728
$676$	−1.81359	−0.0697534
$677$	−17.4169	−0.669387	−0.334694	−	0.942327i	$-0.608633\pi$
$677$	−17.4169	−0.669387	−0.334694	+	0.942327i	$0.608633\pi$
$678$	14.4587	0.555282
$679$	0	0
$680$	−1.46503	−0.0561815
$681$	−1.64237	−0.0629359
$682$	8.87109	0.339692
$683$	−10.0042	−0.382802	−0.191401	−	0.981512i	$-0.561303\pi$
$683$	−10.0042	−0.382802	−0.191401	+	0.981512i	$0.561303\pi$
$684$	−0.0803193	−0.00307108
$685$	7.70716	0.294475
$686$	0	0
$687$	−18.8372	−0.718684
$688$	42.3390	1.61416
$689$	−12.2082	−0.465094
$690$	4.19823	0.159824
$691$	31.2753	1.18977	0.594884	−	0.803811i	$-0.297198\pi$
$691$	31.2753	1.18977	0.594884	+	0.803811i	$0.297198\pi$
$692$	−1.49579	−0.0568615
$693$	0	0
$694$	−1.64057	−0.0622753
$695$	−16.6345	−0.630984
$696$	4.38229	0.166110
$697$	−2.20753	−0.0836160
$698$	−37.8709	−1.43344
$699$	12.9642	0.490350
$700$	0	0
$701$	−14.8672	−0.561528	−0.280764	−	0.959777i	$-0.590588\pi$
$701$	−14.8672	−0.561528	−0.280764	+	0.959777i	$0.590588\pi$
$702$	−7.83847	−0.295844
$703$	1.54741	0.0583617
$704$	−7.24950	−0.273226
$705$	5.65189	0.212863
$706$	−22.4730	−0.845782
$707$	0	0
$708$	−0.884003	−0.0332229
$709$	25.8575	0.971097	0.485549	−	0.874210i	$-0.338620\pi$
$709$	25.8575	0.971097	0.485549	+	0.874210i	$0.338620\pi$
$710$	−10.2416	−0.384359
$711$	0.902710	0.0338543
$712$	−10.7611	−0.403291
$713$	−23.9568	−0.897189
$714$	0	0
$715$	1.35223	0.0505705
$716$	0.701561	0.0262186
$717$	18.9903	0.709204
$718$	−10.0424	−0.374780
$719$	−10.9108	−0.406903	−0.203452	−	0.979085i	$-0.565216\pi$
$719$	−10.9108	−0.406903	−0.203452	+	0.979085i	$0.565216\pi$
$720$	10.6733	0.397771
$721$	0	0
$722$	27.8809	1.03762
$723$	10.3111	0.383472
$724$	−0.412955	−0.0153474
$725$	2.25572	0.0837753
$726$	−1.05719	−0.0392359
$727$	−30.6727	−1.13759	−0.568794	−	0.822480i	$-0.692590\pi$
$727$	−30.6727	−1.13759	−0.568794	+	0.822480i	$0.692590\pi$
$728$	0	0
$729$	−2.95833	−0.109568
$730$	−21.8676	−0.809358
$731$	5.34025	0.197516
$732$	0.876598	0.0324000
$733$	38.8553	1.43515	0.717576	−	0.696480i	$-0.245252\pi$
$733$	38.8553	1.43515	0.717576	+	0.696480i	$0.245252\pi$
$734$	6.64116	0.245130
$735$	0	0
$736$	−3.63807	−0.134101
$737$	8.01205	0.295128
$738$	14.8678	0.547291
$739$	−24.1040	−0.886681	−0.443341	−	0.896353i	$-0.646207\pi$
$739$	−24.1040	−0.886681	−0.443341	+	0.896353i	$0.646207\pi$
$740$	1.26079	0.0463475
$741$	−0.193701	−0.00711579
$742$	0	0
$743$	1.57531	0.0577925	0.0288962	−	0.999582i	$-0.490801\pi$
$743$	1.57531	0.0577925	0.0288962	+	0.999582i	$0.490801\pi$
$744$	11.7201	0.429680
$745$	8.31172	0.304518
$746$	−6.25912	−0.229163
$747$	−9.61402	−0.351759
$748$	0.0880135	0.00321809
$749$	0	0
$750$	−1.05719	−0.0386030
$751$	−46.7635	−1.70642	−0.853212	−	0.521564i	$-0.825349\pi$
$751$	−46.7635	−1.70642	−0.853212	+	0.521564i	$0.825349\pi$
$752$	−33.7912	−1.23224
$753$	5.55856	0.202565
$754$	4.48536	0.163347
$755$	7.59875	0.276547
$756$	0	0
$757$	28.7476	1.04485	0.522425	−	0.852686i	$-0.325028\pi$
$757$	28.7476	1.04485	0.522425	+	0.852686i	$0.325028\pi$
$758$	17.9457	0.651817
$759$	2.85498	0.103629
$760$	0.538417	0.0195304
$761$	−28.7515	−1.04224	−0.521121	−	0.853483i	$-0.674486\pi$
$761$	−28.7515	−1.04224	−0.521121	+	0.853483i	$0.674486\pi$
$762$	−16.6497	−0.603155
$763$	0	0
$764$	0.474949	0.0171831
$765$	1.34623	0.0486732
$766$	−16.2116	−0.585749
$767$	10.2420	0.369818
$768$	2.78315	0.100428
$769$	−40.5398	−1.46190	−0.730951	−	0.682430i	$-0.760923\pi$
$769$	−40.5398	−1.46190	−0.730951	+	0.682430i	$0.760923\pi$
$770$	0	0
$771$	−5.55603	−0.200095
$772$	2.16885	0.0780588
$773$	35.3285	1.27068	0.635339	−	0.772233i	$-0.280860\pi$
$773$	35.3285	1.27068	0.635339	+	0.772233i	$0.280860\pi$
$774$	−35.9669	−1.29280
$775$	6.03274	0.216703
$776$	−45.0917	−1.61870
$777$	0	0
$778$	−44.9489	−1.61150
$779$	0.811291	0.0290675
$780$	−0.157822	−0.00565095
$781$	−6.96472	−0.249217
$782$	−3.16590	−0.113212
$783$	−8.89208	−0.317777
$784$	0	0
$785$	7.67112	0.273794
$786$	7.74297	0.276183
$787$	−17.8681	−0.636929	−0.318465	−	0.947935i	$-0.603167\pi$
$787$	−17.8681	−0.636929	−0.318465	+	0.947935i	$0.603167\pi$
$788$	1.82616	0.0650544
$789$	16.5112	0.587813
$790$	0.534577	0.0190194
$791$	0	0
$792$	6.71007	0.238432
$793$	−10.1562	−0.360659
$794$	26.1252	0.927147
$795$	6.49067	0.230200
$796$	−1.70317	−0.0603673
$797$	10.2292	0.362336	0.181168	−	0.983452i	$-0.442012\pi$
$797$	10.2292	0.362336	0.181168	+	0.983452i	$0.442012\pi$
$798$	0	0
$799$	−4.26211	−0.150783
$800$	0.916129	0.0323901
$801$	9.88852	0.349394
$802$	−36.9194	−1.30367
$803$	−14.8710	−0.524786
$804$	−0.935108	−0.0329787
$805$	0	0
$806$	11.9958	0.422532
$807$	−15.4462	−0.543731
$808$	13.0435	0.458870
$809$	−9.31168	−0.327381	−0.163691	−	0.986512i	$-0.552340\pi$
$809$	−9.31168	−0.327381	−0.163691	+	0.986512i	$0.552340\pi$
$810$	−6.78681	−0.238464
$811$	−19.7720	−0.694291	−0.347145	−	0.937811i	$-0.612849\pi$
$811$	−19.7720	−0.694291	−0.347145	+	0.937811i	$0.612849\pi$
$812$	0	0
$813$	−15.1928	−0.532836
$814$	11.4203	0.400280
$815$	16.9402	0.593388
$816$	1.67537	0.0586496
$817$	−1.96260	−0.0686628
$818$	−28.1227	−0.983287
$819$	0	0
$820$	0.661018	0.0230837
$821$	−22.5013	−0.785301	−0.392651	−	0.919688i	$-0.628442\pi$
$821$	−22.5013	−0.785301	−0.392651	+	0.919688i	$0.628442\pi$
$822$	−8.14791	−0.284191
$823$	−19.8463	−0.691800	−0.345900	−	0.938271i	$-0.612426\pi$
$823$	−19.8463	−0.691800	−0.345900	+	0.938271i	$0.612426\pi$
$824$	44.7784	1.55993
$825$	−0.718935	−0.0250301
$826$	0	0
$827$	−39.2944	−1.36640	−0.683200	−	0.730231i	$-0.739412\pi$
$827$	−39.2944	−1.36640	−0.683200	+	0.730231i	$0.739412\pi$
$828$	1.60082	0.0556323
$829$	−10.2729	−0.356792	−0.178396	−	0.983959i	$-0.557091\pi$
$829$	−10.2729	−0.356792	−0.178396	+	0.983959i	$0.557091\pi$
$830$	−5.69334	−0.197619
$831$	−8.49983	−0.294856
$832$	−9.80299	−0.339857
$833$	0	0
$834$	17.5858	0.608947
$835$	12.0563	0.417226
$836$	−0.0323460	−0.00111871
$837$	−23.7812	−0.821998
$838$	50.4204	1.74174
$839$	−15.4080	−0.531942	−0.265971	−	0.963981i	$-0.585693\pi$
$839$	−15.4080	−0.531942	−0.265971	+	0.963981i	$0.585693\pi$
$840$	0	0
$841$	−23.9117	−0.824543
$842$	19.4989	0.671975
$843$	19.2242	0.662118
$844$	1.37781	0.0474262
$845$	−11.1715	−0.384310
$846$	28.7056	0.986918
$847$	0	0
$848$	−38.8060	−1.33260
$849$	−8.43723	−0.289565
$850$	0.797229	0.0273447
$851$	−30.8410	−1.05722
$852$	0.812872	0.0278485
$853$	26.8003	0.917624	0.458812	−	0.888533i	$-0.348275\pi$
$853$	26.8003	0.917624	0.458812	+	0.888533i	$0.348275\pi$
$854$	0	0
$855$	−0.494756	−0.0169203
$856$	6.62460	0.226424
$857$	−2.84413	−0.0971535	−0.0485768	−	0.998819i	$-0.515469\pi$
$857$	−2.84413	−0.0971535	−0.0485768	+	0.998819i	$0.515469\pi$
$858$	−1.42956	−0.0488044
$859$	40.9313	1.39656	0.698279	−	0.715825i	$-0.253949\pi$
$859$	40.9313	1.39656	0.698279	+	0.715825i	$0.253949\pi$
$860$	−1.59908	−0.0545281
$861$	0	0
$862$	28.4636	0.969473
$863$	−23.6614	−0.805443	−0.402721	−	0.915323i	$-0.631936\pi$
$863$	−23.6614	−0.805443	−0.402721	+	0.915323i	$0.631936\pi$
$864$	−3.61140	−0.122862
$865$	−9.21389	−0.313282
$866$	−21.8515	−0.742545
$867$	−12.0106	−0.407901
$868$	0	0
$869$	0.363537	0.0123321
$870$	−2.38472	−0.0808494
$871$	10.8341	0.367101
$872$	10.8507	0.367450
$873$	41.4352	1.40237
$874$	1.16350	0.0393561
$875$	0	0
$876$	1.73563	0.0586416
$877$	22.3801	0.755724	0.377862	−	0.925862i	$-0.376659\pi$
$877$	22.3801	0.755724	0.377862	+	0.925862i	$0.376659\pi$
$878$	30.9675	1.04510
$879$	10.7263	0.361790
$880$	4.29833	0.144897
$881$	−37.3337	−1.25780	−0.628902	−	0.777485i	$-0.716495\pi$
$881$	−37.3337	−1.25780	−0.628902	+	0.777485i	$0.716495\pi$
$882$	0	0
$883$	1.75761	0.0591482	0.0295741	−	0.999563i	$-0.490585\pi$
$883$	1.75761	0.0591482	0.0295741	+	0.999563i	$0.490585\pi$
$884$	0.119015	0.00400289
$885$	−5.44534	−0.183043
$886$	11.9284	0.400744
$887$	−43.0230	−1.44457	−0.722286	−	0.691594i	$-0.756909\pi$
$887$	−43.0230	−1.44457	−0.722286	+	0.691594i	$0.756909\pi$
$888$	15.0880	0.506319
$889$	0	0
$890$	5.85590	0.196290
$891$	−4.61534	−0.154620
$892$	3.21283	0.107574
$893$	1.56638	0.0524167
$894$	−8.78704	−0.293883
$895$	4.32152	0.144453
$896$	0	0
$897$	3.86060	0.128902
$898$	−52.1111	−1.73897
$899$	13.6082	0.453858
$900$	−0.403114	−0.0134371
$901$	−4.89464	−0.163064
$902$	5.98752	0.199363
$903$	0	0
$904$	−36.9576	−1.22919
$905$	−2.54375	−0.0845571
$906$	−8.03330	−0.266888
$907$	7.35112	0.244090	0.122045	−	0.992525i	$-0.461055\pi$
$907$	7.35112	0.244090	0.122045	+	0.992525i	$0.461055\pi$
$908$	−0.370860	−0.0123074
$909$	−11.9858	−0.397545
$910$	0	0
$911$	55.4043	1.83563	0.917813	−	0.397014i	$-0.129953\pi$
$911$	55.4043	1.83563	0.917813	+	0.397014i	$0.129953\pi$
$912$	−0.615717	−0.0203884
$913$	−3.87173	−0.128136
$914$	−48.0164	−1.58824
$915$	5.39973	0.178510
$916$	−4.25358	−0.140542
$917$	0	0
$918$	−3.14269	−0.103724
$919$	41.8952	1.38199	0.690997	−	0.722858i	$-0.257172\pi$
$919$	41.8952	1.38199	0.690997	+	0.722858i	$0.257172\pi$
$920$	−10.7310	−0.353791
$921$	22.2917	0.734536
$922$	1.74982	0.0576273
$923$	−9.41791	−0.309994
$924$	0	0
$925$	7.76630	0.255354
$926$	25.5366	0.839185
$927$	−41.1473	−1.35146
$928$	2.06653	0.0678372
$929$	33.1475	1.08753	0.543767	−	0.839237i	$-0.316998\pi$
$929$	33.1475	1.08753	0.543767	+	0.839237i	$0.316998\pi$
$930$	−6.37774	−0.209134
$931$	0	0
$932$	2.92741	0.0958904
$933$	−16.2893	−0.533287
$934$	−19.2367	−0.629443
$935$	0.542152	0.0177303
$936$	9.07355	0.296578
$937$	41.2006	1.34597	0.672983	−	0.739658i	$-0.265013\pi$
$937$	41.2006	1.34597	0.672983	+	0.739658i	$0.265013\pi$
$938$	0	0
$939$	−7.54184	−0.246119
$940$	1.27624	0.0416264
$941$	−23.4424	−0.764202	−0.382101	−	0.924121i	$-0.624799\pi$
$941$	−23.4424	−0.764202	−0.382101	+	0.924121i	$0.624799\pi$
$942$	−8.10981	−0.264232
$943$	−16.1696	−0.526554
$944$	32.5563	1.05962
$945$	0	0
$946$	−14.4845	−0.470931
$947$	−14.3105	−0.465030	−0.232515	−	0.972593i	$-0.574695\pi$
$947$	−14.3105	−0.465030	−0.232515	+	0.972593i	$0.574695\pi$
$948$	−0.0424294	−0.00137804
$949$	−20.1090	−0.652766
$950$	−0.292991	−0.00950587
$951$	24.3957	0.791086
$952$	0	0
$953$	46.5779	1.50881	0.754403	−	0.656412i	$-0.227927\pi$
$953$	46.5779	1.50881	0.754403	+	0.656412i	$0.227927\pi$
$954$	32.9656	1.06730
$955$	2.92563	0.0946711
$956$	4.28815	0.138689
$957$	−1.62172	−0.0524226
$958$	−50.6008	−1.63484
$959$	0	0
$960$	5.21192	0.168214
$961$	5.39398	0.173999
$962$	15.4428	0.497897
$963$	−6.08741	−0.196164
$964$	2.32831	0.0749899
$965$	13.3599	0.430069
$966$	0	0
$967$	14.4707	0.465347	0.232674	−	0.972555i	$-0.425253\pi$
$967$	14.4707	0.465347	0.232674	+	0.972555i	$0.425253\pi$
$968$	2.70226	0.0868539
$969$	−0.0776609	−0.00249483
$970$	24.5376	0.787854
$971$	49.0353	1.57362	0.786809	−	0.617197i	$-0.211732\pi$
$971$	49.0353	1.57362	0.786809	+	0.617197i	$0.211732\pi$
$972$	2.45852	0.0788572
$973$	0	0
$974$	39.6546	1.27062
$975$	−0.972166	−0.0311342
$976$	−32.2836	−1.03337
$977$	51.3192	1.64185	0.820924	−	0.571038i	$-0.193459\pi$
$977$	51.3192	1.64185	0.820924	+	0.571038i	$0.193459\pi$
$978$	−17.9089	−0.572665
$979$	3.98228	0.127274
$980$	0	0
$981$	−9.97077	−0.318342
$982$	−50.3305	−1.60611
$983$	−51.7311	−1.64997	−0.824983	−	0.565158i	$-0.808815\pi$
$983$	−51.7311	−1.64997	−0.824983	+	0.565158i	$0.808815\pi$
$984$	7.91046	0.252176
$985$	11.2489	0.358421
$986$	1.79832	0.0572703
$987$	0	0
$988$	−0.0437392	−0.00139153
$989$	39.1161	1.24382
$990$	−3.65142	−0.116050
$991$	−16.4120	−0.521343	−0.260672	−	0.965428i	$-0.583944\pi$
$991$	−16.4120	−0.521343	−0.260672	+	0.965428i	$0.583944\pi$
$992$	5.52677	0.175475
$993$	11.0722	0.351366
$994$	0	0
$995$	−10.4913	−0.332597
$996$	0.451881	0.0143184
$997$	38.7004	1.22565	0.612827	−	0.790217i	$-0.290032\pi$
$997$	38.7004	1.22565	0.612827	+	0.790217i	$0.290032\pi$
$998$	52.0395	1.64728
$999$	−30.6149	−0.968612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.t.1.2		8
7.2	even	3		385.2.i.c.221.7	✓	16
7.4	even	3		385.2.i.c.331.7	yes	16
7.6	odd	2		2695.2.a.s.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.c.221.7	✓	16	7.2	even	3
385.2.i.c.331.7	yes	16	7.4	even	3
2695.2.a.s.1.2		8	7.6	odd	2
2695.2.a.t.1.2		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2695.a (trivial)

\(f(q)\)	\(=\)	\(q-1.47049 q^{2} +0.718935 q^{3} +0.162341 q^{4} +1.00000 q^{5} -1.05719 q^{6} +2.70226 q^{8} -2.48313 q^{9} +O(q^{10})\)	\(q-1.47049 q^{2} +0.718935 q^{3} +0.162341 q^{4} +1.00000 q^{5} -1.05719 q^{6} +2.70226 q^{8} -2.48313 q^{9} -1.47049 q^{10} -1.00000 q^{11} +0.116713 q^{12} -1.35223 q^{13} +0.718935 q^{15} -4.29833 q^{16} -0.542152 q^{17} +3.65142 q^{18} +0.199247 q^{19} +0.162341 q^{20} +1.47049 q^{22} -3.97113 q^{23} +1.94275 q^{24} +1.00000 q^{25} +1.98844 q^{26} -3.94202 q^{27} +2.25572 q^{29} -1.05719 q^{30} +6.03274 q^{31} +0.916129 q^{32} -0.718935 q^{33} +0.797229 q^{34} -0.403114 q^{36} +7.76630 q^{37} -0.292991 q^{38} -0.972166 q^{39} +2.70226 q^{40} +4.07178 q^{41} -9.85011 q^{43} -0.162341 q^{44} -2.48313 q^{45} +5.83951 q^{46} +7.86148 q^{47} -3.09022 q^{48} -1.47049 q^{50} -0.389772 q^{51} -0.219522 q^{52} +9.02817 q^{53} +5.79670 q^{54} -1.00000 q^{55} +0.143246 q^{57} -3.31701 q^{58} -7.57418 q^{59} +0.116713 q^{60} +7.51073 q^{61} -8.87109 q^{62} +7.24950 q^{64} -1.35223 q^{65} +1.05719 q^{66} -8.01205 q^{67} -0.0880135 q^{68} -2.85498 q^{69} +6.96472 q^{71} -6.71007 q^{72} +14.8710 q^{73} -11.4203 q^{74} +0.718935 q^{75} +0.0323460 q^{76} +1.42956 q^{78} -0.363537 q^{79} -4.29833 q^{80} +4.61534 q^{81} -5.98752 q^{82} +3.87173 q^{83} -0.542152 q^{85} +14.4845 q^{86} +1.62172 q^{87} -2.70226 q^{88} -3.98228 q^{89} +3.65142 q^{90} -0.644677 q^{92} +4.33715 q^{93} -11.5602 q^{94} +0.199247 q^{95} +0.658638 q^{96} -16.6867 q^{97} +2.48313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9	\( 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9} + 3 q^{10} - 8 q^{11} + 9 q^{12} + 14 q^{13} + q^{15} + 7 q^{16} + 5 q^{17} + 27 q^{18} + q^{19} + 9 q^{20} - 3 q^{22} - 2 q^{23} - 24 q^{24} + 8 q^{25} + 21 q^{26} - 5 q^{27} + 26 q^{29} - 3 q^{30} + 2 q^{31} + 16 q^{32} - q^{33} - 26 q^{34} + 54 q^{36} - q^{37} - 31 q^{38} + 19 q^{39} + 9 q^{40} - 3 q^{41} + 4 q^{43} - 9 q^{44} + 19 q^{45} + 10 q^{46} + q^{47} - 21 q^{48} + 3 q^{50} + 3 q^{51} + 37 q^{52} + 26 q^{53} - 5 q^{54} - 8 q^{55} + 20 q^{57} - q^{58} - 19 q^{59} + 9 q^{60} - 26 q^{62} + q^{64} + 14 q^{65} + 3 q^{66} - 13 q^{67} + 15 q^{68} - 14 q^{69} - 9 q^{71} + 32 q^{72} + 11 q^{73} + 24 q^{74} + q^{75} - 18 q^{76} - 33 q^{78} - 8 q^{79} + 7 q^{80} + 52 q^{81} + 41 q^{82} + 32 q^{83} + 5 q^{85} + 28 q^{86} - 16 q^{87} - 9 q^{88} + 5 q^{89} + 27 q^{90} + 30 q^{92} - 14 q^{93} - 5 q^{94} + q^{95} + q^{96} + 9 q^{97} - 19 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + q^3 + 9 * q^4 + 8 * q^5 - 3 * q^6 + 9 * q^8 + 19 * q^9 + 3 * q^10 - 8 * q^11 + 9 * q^12 + 14 * q^13 + q^15 + 7 * q^16 + 5 * q^17 + 27 * q^18 + q^19 + 9 * q^20 - 3 * q^22 - 2 * q^23 - 24 * q^24 + 8 * q^25 + 21 * q^26 - 5 * q^27 + 26 * q^29 - 3 * q^30 + 2 * q^31 + 16 * q^32 - q^33 - 26 * q^34 + 54 * q^36 - q^37 - 31 * q^38 + 19 * q^39 + 9 * q^40 - 3 * q^41 + 4 * q^43 - 9 * q^44 + 19 * q^45 + 10 * q^46 + q^47 - 21 * q^48 + 3 * q^50 + 3 * q^51 + 37 * q^52 + 26 * q^53 - 5 * q^54 - 8 * q^55 + 20 * q^57 - q^58 - 19 * q^59 + 9 * q^60 - 26 * q^62 + q^64 + 14 * q^65 + 3 * q^66 - 13 * q^67 + 15 * q^68 - 14 * q^69 - 9 * q^71 + 32 * q^72 + 11 * q^73 + 24 * q^74 + q^75 - 18 * q^76 - 33 * q^78 - 8 * q^79 + 7 * q^80 + 52 * q^81 + 41 * q^82 + 32 * q^83 + 5 * q^85 + 28 * q^86 - 16 * q^87 - 9 * q^88 + 5 * q^89 + 27 * q^90 + 30 * q^92 - 14 * q^93 - 5 * q^94 + q^95 + q^96 + 9 * q^97 - 19 * q^99

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