LMFDB - Embedded newform 2695.2.a.t.1.4

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			1.4
Root			$0.279211$ 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)

$f(q)$	$=$	$q+0.279211 q^{2} +0.275960 q^{3} -1.92204 q^{4} +1.00000 q^{5} +0.0770509 q^{6} -1.09508 q^{8} -2.92385 q^{9} +O(q^{10})$	\(q+0.279211 q^{2} +0.275960 q^{3} -1.92204 q^{4} +1.00000 q^{5} +0.0770509 q^{6} -1.09508 q^{8} -2.92385 q^{9} +0.279211 q^{10} -1.00000 q^{11} -0.530406 q^{12} +6.03636 q^{13} +0.275960 q^{15} +3.53833 q^{16} -4.48227 q^{17} -0.816369 q^{18} +6.17791 q^{19} -1.92204 q^{20} -0.279211 q^{22} -0.141046 q^{23} -0.302197 q^{24} +1.00000 q^{25} +1.68542 q^{26} -1.63474 q^{27} -5.06132 q^{29} +0.0770509 q^{30} -3.35347 q^{31} +3.17809 q^{32} -0.275960 q^{33} -1.25150 q^{34} +5.61975 q^{36} -9.49239 q^{37} +1.72494 q^{38} +1.66579 q^{39} -1.09508 q^{40} +1.23914 q^{41} +5.53959 q^{43} +1.92204 q^{44} -2.92385 q^{45} -0.0393815 q^{46} +6.92912 q^{47} +0.976435 q^{48} +0.279211 q^{50} -1.23692 q^{51} -11.6021 q^{52} +10.8073 q^{53} -0.456438 q^{54} -1.00000 q^{55} +1.70485 q^{57} -1.41318 q^{58} +10.0334 q^{59} -0.530406 q^{60} -9.17433 q^{61} -0.936325 q^{62} -6.18929 q^{64} +6.03636 q^{65} -0.0770509 q^{66} +10.4815 q^{67} +8.61510 q^{68} -0.0389230 q^{69} +9.66631 q^{71} +3.20183 q^{72} -4.06483 q^{73} -2.65038 q^{74} +0.275960 q^{75} -11.8742 q^{76} +0.465107 q^{78} +14.4849 q^{79} +3.53833 q^{80} +8.32042 q^{81} +0.345981 q^{82} +2.71493 q^{83} -4.48227 q^{85} +1.54671 q^{86} -1.39672 q^{87} +1.09508 q^{88} +17.8494 q^{89} -0.816369 q^{90} +0.271096 q^{92} -0.925422 q^{93} +1.93468 q^{94} +6.17791 q^{95} +0.877025 q^{96} -0.310934 q^{97} +2.92385 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.279211	0.197432	0.0987159	−	0.995116i	$-0.468526\pi$
$2$	0.279211	0.197432	0.0987159	+	0.995116i	$0.468526\pi$
$3$	0.275960	0.159325	0.0796627	−	0.996822i	$-0.474616\pi$
$3$	0.275960	0.159325	0.0796627	+	0.996822i	$0.474616\pi$
$4$	−1.92204	−0.961021
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.0770509	0.0314559
$7$	0	0
$7$	0	0
$8$	−1.09508	−0.387168
$9$	−2.92385	−0.974615
$10$	0.279211	0.0882942
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.530406	−0.153115
$13$	6.03636	1.67418	0.837092	−	0.547062i	$-0.184254\pi$
$13$	6.03636	1.67418	0.837092	+	0.547062i	$0.184254\pi$
$14$	0	0
$15$	0.275960	0.0712525
$16$	3.53833	0.884581
$17$	−4.48227	−1.08711	−0.543555	−	0.839374i	$-0.682922\pi$
$17$	−4.48227	−1.08711	−0.543555	+	0.839374i	$0.682922\pi$
$18$	−0.816369	−0.192420
$19$	6.17791	1.41731	0.708654	−	0.705556i	$-0.249303\pi$
$19$	6.17791	1.41731	0.708654	+	0.705556i	$0.249303\pi$
$20$	−1.92204	−0.429782
$21$	0	0
$22$	−0.279211	−0.0595279
$23$	−0.141046	−0.0294101	−0.0147051	−	0.999892i	$-0.504681\pi$
$23$	−0.141046	−0.0294101	−0.0147051	+	0.999892i	$0.504681\pi$
$24$	−0.302197	−0.0616857
$25$	1.00000	0.200000
$26$	1.68542	0.330537
$27$	−1.63474	−0.314606
$28$	0	0
$29$	−5.06132	−0.939864	−0.469932	−	0.882703i	$-0.655722\pi$
$29$	−5.06132	−0.939864	−0.469932	+	0.882703i	$0.655722\pi$
$30$	0.0770509	0.0140675
$31$	−3.35347	−0.602301	−0.301150	−	0.953577i	$-0.597371\pi$
$31$	−3.35347	−0.602301	−0.301150	+	0.953577i	$0.597371\pi$
$32$	3.17809	0.561812
$33$	−0.275960	−0.0480384
$34$	−1.25150	−0.214630
$35$	0	0
$36$	5.61975	0.936626
$37$	−9.49239	−1.56054	−0.780269	−	0.625443i	$-0.784918\pi$
$37$	−9.49239	−1.56054	−0.780269	+	0.625443i	$0.784918\pi$
$38$	1.72494	0.279822
$39$	1.66579	0.266740
$40$	−1.09508	−0.173147
$41$	1.23914	0.193521	0.0967605	−	0.995308i	$-0.469152\pi$
$41$	1.23914	0.193521	0.0967605	+	0.995308i	$0.469152\pi$
$42$	0	0
$43$	5.53959	0.844779	0.422389	−	0.906414i	$-0.361191\pi$
$43$	5.53959	0.844779	0.422389	+	0.906414i	$0.361191\pi$
$44$	1.92204	0.289759
$45$	−2.92385	−0.435861
$46$	−0.0393815	−0.00580649
$47$	6.92912	1.01072	0.505358	−	0.862910i	$-0.331360\pi$
$47$	6.92912	1.01072	0.505358	+	0.862910i	$0.331360\pi$
$48$	0.976435	0.140936
$49$	0	0
$50$	0.279211	0.0394864
$51$	−1.23692	−0.173204
$52$	−11.6021	−1.60893
$53$	10.8073	1.48449	0.742246	−	0.670128i	$-0.233761\pi$
$53$	10.8073	1.48449	0.742246	+	0.670128i	$0.233761\pi$
$54$	−0.456438	−0.0621133
$55$	−1.00000	−0.134840
$56$	0	0
$57$	1.70485	0.225813
$58$	−1.41318	−0.185559
$59$	10.0334	1.30623	0.653117	−	0.757257i	$-0.273461\pi$
$59$	10.0334	1.30623	0.653117	+	0.757257i	$0.273461\pi$
$60$	−0.530406	−0.0684751
$61$	−9.17433	−1.17465	−0.587327	−	0.809350i	$-0.699820\pi$
$61$	−9.17433	−1.17465	−0.587327	+	0.809350i	$0.699820\pi$
$62$	−0.936325	−0.118913
$63$	0	0
$64$	−6.18929	−0.773662
$65$	6.03636	0.748718
$66$	−0.0770509	−0.00948431
$67$	10.4815	1.28051	0.640257	−	0.768161i	$-0.278828\pi$
$67$	10.4815	1.28051	0.640257	+	0.768161i	$0.278828\pi$
$68$	8.61510	1.04473
$69$	−0.0389230	−0.00468578
$70$	0	0
$71$	9.66631	1.14718	0.573590	−	0.819143i	$-0.305550\pi$
$71$	9.66631	1.14718	0.573590	+	0.819143i	$0.305550\pi$
$72$	3.20183	0.377340
$73$	−4.06483	−0.475752	−0.237876	−	0.971295i	$-0.576451\pi$
$73$	−4.06483	−0.475752	−0.237876	+	0.971295i	$0.576451\pi$
$74$	−2.65038	−0.308100
$75$	0.275960	0.0318651
$76$	−11.8742	−1.36206
$77$	0	0
$78$	0.465107	0.0526629
$79$	14.4849	1.62968	0.814838	−	0.579689i	$-0.196826\pi$
$79$	14.4849	1.62968	0.814838	+	0.579689i	$0.196826\pi$
$80$	3.53833	0.395597
$81$	8.32042	0.924491
$82$	0.345981	0.0382072
$83$	2.71493	0.298002	0.149001	−	0.988837i	$-0.452394\pi$
$83$	2.71493	0.298002	0.149001	+	0.988837i	$0.452394\pi$
$84$	0	0
$85$	−4.48227	−0.486170
$86$	1.54671	0.166786
$87$	−1.39672	−0.149744
$88$	1.09508	0.116736
$89$	17.8494	1.89203	0.946014	−	0.324126i	$-0.105070\pi$
$89$	17.8494	1.89203	0.946014	+	0.324126i	$0.105070\pi$
$90$	−0.816369	−0.0860529
$91$	0	0
$92$	0.271096	0.0282637
$93$	−0.925422	−0.0959618
$94$	1.93468	0.199548
$95$	6.17791	0.633840
$96$	0.877025	0.0895110
$97$	−0.310934	−0.0315705	−0.0157853	−	0.999875i	$-0.505025\pi$
$97$	−0.310934	−0.0315705	−0.0157853	+	0.999875i	$0.505025\pi$
$98$	0	0
$99$	2.92385	0.293858
$100$	−1.92204	−0.192204
$101$	8.64712	0.860420	0.430210	−	0.902729i	$-0.358439\pi$
$101$	8.64712	0.860420	0.430210	+	0.902729i	$0.358439\pi$
$102$	−0.345363	−0.0341960
$103$	−7.22948	−0.712342	−0.356171	−	0.934421i	$-0.615918\pi$
$103$	−7.22948	−0.712342	−0.356171	+	0.934421i	$0.615918\pi$
$104$	−6.61027	−0.648190
$105$	0	0
$106$	3.01750	0.293086
$107$	8.42224	0.814209	0.407104	−	0.913382i	$-0.366539\pi$
$107$	8.42224	0.814209	0.407104	+	0.913382i	$0.366539\pi$
$108$	3.14204	0.302343
$109$	12.1265	1.16151	0.580756	−	0.814078i	$-0.302757\pi$
$109$	12.1265	1.16151	0.580756	+	0.814078i	$0.302757\pi$
$110$	−0.279211	−0.0266217
$111$	−2.61952	−0.248633
$112$	0	0
$113$	1.38668	0.130448	0.0652239	−	0.997871i	$-0.479224\pi$
$113$	1.38668	0.130448	0.0652239	+	0.997871i	$0.479224\pi$
$114$	0.476013	0.0445827
$115$	−0.141046	−0.0131526
$116$	9.72807	0.903229
$117$	−17.6494	−1.63169
$118$	2.80143	0.257892
$119$	0	0
$120$	−0.302197	−0.0275867
$121$	1.00000	0.0909091
$122$	−2.56157	−0.231914
$123$	0.341952	0.0308328
$124$	6.44551	0.578824
$125$	1.00000	0.0894427
$126$	0	0
$127$	−14.2544	−1.26487	−0.632437	−	0.774612i	$-0.717945\pi$
$127$	−14.2544	−1.26487	−0.632437	+	0.774612i	$0.717945\pi$
$128$	−8.08430	−0.714558
$129$	1.52870	0.134595
$130$	1.68542	0.147821
$131$	5.63904	0.492685	0.246343	−	0.969183i	$-0.420771\pi$
$131$	5.63904	0.492685	0.246343	+	0.969183i	$0.420771\pi$
$132$	0.530406	0.0461659
$133$	0	0
$134$	2.92654	0.252814
$135$	−1.63474	−0.140696
$136$	4.90842	0.420894
$137$	2.98167	0.254741	0.127371	−	0.991855i	$-0.459346\pi$
$137$	2.98167	0.254741	0.127371	+	0.991855i	$0.459346\pi$
$138$	−0.0108677	−0.000925121 0
$139$	−7.74208	−0.656675	−0.328337	−	0.944561i	$-0.606488\pi$
$139$	−7.74208	−0.656675	−0.328337	+	0.944561i	$0.606488\pi$
$140$	0	0
$141$	1.91216	0.161033
$142$	2.69894	0.226490
$143$	−6.03636	−0.504785
$144$	−10.3455	−0.862127
$145$	−5.06132	−0.420320
$146$	−1.13494	−0.0939286
$147$	0	0
$148$	18.2448	1.49971
$149$	5.41173	0.443346	0.221673	−	0.975121i	$-0.428848\pi$
$149$	5.41173	0.443346	0.221673	+	0.975121i	$0.428848\pi$
$150$	0.0770509	0.00629118
$151$	−17.7894	−1.44768	−0.723842	−	0.689966i	$-0.757626\pi$
$151$	−17.7894	−1.44768	−0.723842	+	0.689966i	$0.757626\pi$
$152$	−6.76528	−0.548736
$153$	13.1055	1.05951
$154$	0	0
$155$	−3.35347	−0.269357
$156$	−3.20172	−0.256343
$157$	7.64436	0.610086	0.305043	−	0.952339i	$-0.401329\pi$
$157$	7.64436	0.610086	0.305043	+	0.952339i	$0.401329\pi$
$158$	4.04433	0.321750
$159$	2.98237	0.236517
$160$	3.17809	0.251250
$161$	0	0
$162$	2.32315	0.182524
$163$	−7.71743	−0.604476	−0.302238	−	0.953233i	$-0.597734\pi$
$163$	−7.71743	−0.604476	−0.302238	+	0.953233i	$0.597734\pi$
$164$	−2.38168	−0.185978
$165$	−0.275960	−0.0214834
$166$	0.758038	0.0588352
$167$	−23.7258	−1.83596	−0.917978	−	0.396630i	$-0.870179\pi$
$167$	−23.7258	−1.83596	−0.917978	+	0.396630i	$0.870179\pi$
$168$	0	0
$169$	23.4376	1.80289
$170$	−1.25150	−0.0959855
$171$	−18.0632	−1.38133
$172$	−10.6473	−0.811850
$173$	11.7605	0.894132	0.447066	−	0.894501i	$-0.352469\pi$
$173$	11.7605	0.894132	0.447066	+	0.894501i	$0.352469\pi$
$174$	−0.389979	−0.0295643
$175$	0	0
$176$	−3.53833	−0.266711
$177$	2.76881	0.208116
$178$	4.98373	0.373547
$179$	14.1819	1.06000	0.530001	−	0.847997i	$-0.322192\pi$
$179$	14.1819	1.06000	0.530001	+	0.847997i	$0.322192\pi$
$180$	5.61975	0.418872
$181$	8.64623	0.642669	0.321335	−	0.946966i	$-0.395869\pi$
$181$	8.64623	0.642669	0.321335	+	0.946966i	$0.395869\pi$
$182$	0	0
$183$	−2.53175	−0.187152
$184$	0.154456	0.0113866
$185$	−9.49239	−0.697894
$186$	−0.258388	−0.0189459
$187$	4.48227	0.327776
$188$	−13.3181	−0.971319
$189$	0	0
$190$	1.72494	0.125140
$191$	3.12177	0.225883	0.112942	−	0.993602i	$-0.463973\pi$
$191$	3.12177	0.225883	0.112942	+	0.993602i	$0.463973\pi$
$192$	−1.70800	−0.123264
$193$	9.18481	0.661137	0.330568	−	0.943782i	$-0.392760\pi$
$193$	9.18481	0.661137	0.330568	+	0.943782i	$0.392760\pi$
$194$	−0.0868160	−0.00623303
$195$	1.66579	0.119290
$196$	0	0
$197$	14.7284	1.04935	0.524677	−	0.851301i	$-0.324186\pi$
$197$	14.7284	1.04935	0.524677	+	0.851301i	$0.324186\pi$
$198$	0.816369	0.0580168
$199$	−9.32644	−0.661134	−0.330567	−	0.943783i	$-0.607240\pi$
$199$	−9.32644	−0.661134	−0.330567	+	0.943783i	$0.607240\pi$
$200$	−1.09508	−0.0774336
$201$	2.89246	0.204018
$202$	2.41437	0.169874
$203$	0	0
$204$	2.37742	0.166453
$205$	1.23914	0.0865453
$206$	−2.01855	−0.140639
$207$	0.412397	0.0286635
$208$	21.3586	1.48095
$209$	−6.17791	−0.427335
$210$	0	0
$211$	−2.60436	−0.179291	−0.0896457	−	0.995974i	$-0.528573\pi$
$211$	−2.60436	−0.179291	−0.0896457	+	0.995974i	$0.528573\pi$
$212$	−20.7720	−1.42663
$213$	2.66751	0.182775
$214$	2.35158	0.160751
$215$	5.53959	0.377797
$216$	1.79017	0.121805
$217$	0	0
$218$	3.38586	0.229319
$219$	−1.12173	−0.0757994
$220$	1.92204	0.129584
$221$	−27.0566	−1.82002
$222$	−0.731397	−0.0490882
$223$	−4.65166	−0.311498	−0.155749	−	0.987797i	$-0.549779\pi$
$223$	−4.65166	−0.311498	−0.155749	+	0.987797i	$0.549779\pi$
$224$	0	0
$225$	−2.92385	−0.194923
$226$	0.387176	0.0257545
$227$	13.8037	0.916184	0.458092	−	0.888905i	$-0.348533\pi$
$227$	13.8037	0.916184	0.458092	+	0.888905i	$0.348533\pi$
$228$	−3.27680	−0.217011
$229$	−5.71282	−0.377514	−0.188757	−	0.982024i	$-0.560446\pi$
$229$	−5.71282	−0.377514	−0.188757	+	0.982024i	$0.560446\pi$
$230$	−0.0393815	−0.00259674
$231$	0	0
$232$	5.54253	0.363885
$233$	−4.17560	−0.273553	−0.136776	−	0.990602i	$-0.543674\pi$
$233$	−4.17560	−0.273553	−0.136776	+	0.990602i	$0.543674\pi$
$234$	−4.92790	−0.322147
$235$	6.92912	0.452006
$236$	−19.2846	−1.25532
$237$	3.99724	0.259649
$238$	0	0
$239$	13.1008	0.847419	0.423710	−	0.905798i	$-0.360728\pi$
$239$	13.1008	0.847419	0.423710	+	0.905798i	$0.360728\pi$
$240$	0.976435	0.0630286
$241$	−17.2821	−1.11324	−0.556620	−	0.830767i	$-0.687902\pi$
$241$	−17.2821	−1.11324	−0.556620	+	0.830767i	$0.687902\pi$
$242$	0.279211	0.0179483
$243$	7.20033	0.461901
$244$	17.6334	1.12887
$245$	0	0
$246$	0.0954768	0.00608738
$247$	37.2920	2.37284
$248$	3.67230	0.233192
$249$	0.749211	0.0474793
$250$	0.279211	0.0176588
$251$	−20.1119	−1.26945	−0.634725	−	0.772738i	$-0.718887\pi$
$251$	−20.1119	−1.26945	−0.634725	+	0.772738i	$0.718887\pi$
$252$	0	0
$253$	0.141046	0.00886748
$254$	−3.97998	−0.249726
$255$	−1.23692	−0.0774592
$256$	10.1214	0.632585
$257$	−30.7337	−1.91711	−0.958557	−	0.284901i	$-0.908039\pi$
$257$	−30.7337	−1.91711	−0.958557	+	0.284901i	$0.908039\pi$
$258$	0.426830	0.0265733
$259$	0	0
$260$	−11.6021	−0.719533
$261$	14.7985	0.916006
$262$	1.57448	0.0972718
$263$	11.2464	0.693480	0.346740	−	0.937961i	$-0.387289\pi$
$263$	11.2464	0.693480	0.346740	+	0.937961i	$0.387289\pi$
$264$	0.302197	0.0185989
$265$	10.8073	0.663885
$266$	0	0
$267$	4.92570	0.301448
$268$	−20.1458	−1.23060
$269$	8.94475	0.545371	0.272686	−	0.962103i	$-0.412088\pi$
$269$	8.94475	0.545371	0.272686	+	0.962103i	$0.412088\pi$
$270$	−0.456438	−0.0277779
$271$	13.1071	0.796198	0.398099	−	0.917342i	$-0.369670\pi$
$271$	13.1071	0.796198	0.398099	+	0.917342i	$0.369670\pi$
$272$	−15.8597	−0.961637
$273$	0	0
$274$	0.832514	0.0502940
$275$	−1.00000	−0.0603023
$276$	0.0748116	0.00450313
$277$	−8.66403	−0.520571	−0.260285	−	0.965532i	$-0.583817\pi$
$277$	−8.66403	−0.520571	−0.260285	+	0.965532i	$0.583817\pi$
$278$	−2.16167	−0.129648
$279$	9.80503	0.587012
$280$	0	0
$281$	7.01062	0.418218	0.209109	−	0.977892i	$-0.432944\pi$
$281$	7.01062	0.418218	0.209109	+	0.977892i	$0.432944\pi$
$282$	0.533895	0.0317930
$283$	−11.3097	−0.672289	−0.336145	−	0.941810i	$-0.609123\pi$
$283$	−11.3097	−0.672289	−0.336145	+	0.941810i	$0.609123\pi$
$284$	−18.5790	−1.10246
$285$	1.70485	0.100987
$286$	−1.68542	−0.0996607
$287$	0	0
$288$	−9.29225	−0.547551
$289$	3.09072	0.181807
$290$	−1.41318	−0.0829845
$291$	−0.0858051	−0.00502998
$292$	7.81277	0.457208
$293$	29.3418	1.71416	0.857082	−	0.515180i	$-0.172275\pi$
$293$	29.3418	1.71416	0.857082	+	0.515180i	$0.172275\pi$
$294$	0	0
$295$	10.0334	0.584166
$296$	10.3949	0.604191
$297$	1.63474	0.0948574
$298$	1.51101	0.0875307
$299$	−0.851403	−0.0492379
$300$	−0.530406	−0.0306230
$301$	0	0
$302$	−4.96700	−0.285819
$303$	2.38626	0.137087
$304$	21.8594	1.25372
$305$	−9.17433	−0.525321
$306$	3.65919	0.209182
$307$	19.8056	1.13036	0.565182	−	0.824967i	$-0.308806\pi$
$307$	19.8056	1.13036	0.565182	+	0.824967i	$0.308806\pi$
$308$	0	0
$309$	−1.99505	−0.113494
$310$	−0.936325	−0.0531797
$311$	−4.42538	−0.250940	−0.125470	−	0.992097i	$-0.540044\pi$
$311$	−4.42538	−0.250940	−0.125470	+	0.992097i	$0.540044\pi$
$312$	−1.82417	−0.103273
$313$	5.36849	0.303445	0.151722	−	0.988423i	$-0.451518\pi$
$313$	5.36849	0.303445	0.151722	+	0.988423i	$0.451518\pi$
$314$	2.13439	0.120450
$315$	0	0
$316$	−27.8405	−1.56615
$317$	14.9823	0.841488	0.420744	−	0.907179i	$-0.361769\pi$
$317$	14.9823	0.841488	0.420744	+	0.907179i	$0.361769\pi$
$318$	0.832709	0.0466960
$319$	5.06132	0.283380
$320$	−6.18929	−0.345992
$321$	2.32420	0.129724
$322$	0	0
$323$	−27.6910	−1.54077
$324$	−15.9922	−0.888455
$325$	6.03636	0.334837
$326$	−2.15479	−0.119343
$327$	3.34644	0.185058
$328$	−1.35695	−0.0749251
$329$	0	0
$330$	−0.0770509	−0.00424151
$331$	−19.1778	−1.05411	−0.527054	−	0.849832i	$-0.676703\pi$
$331$	−19.1778	−1.05411	−0.527054	+	0.849832i	$0.676703\pi$
$332$	−5.21821	−0.286386
$333$	27.7543	1.52093
$334$	−6.62450	−0.362476
$335$	10.4815	0.572663
$336$	0	0
$337$	−20.9041	−1.13872	−0.569359	−	0.822089i	$-0.692809\pi$
$337$	−20.9041	−1.13872	−0.569359	+	0.822089i	$0.692809\pi$
$338$	6.54403	0.355948
$339$	0.382667	0.0207836
$340$	8.61510	0.467220
$341$	3.35347	0.181601
$342$	−5.04345	−0.272719
$343$	0	0
$344$	−6.06627	−0.327071
$345$	−0.0389230	−0.00209554
$346$	3.28365	0.176530
$347$	11.9716	0.642667	0.321334	−	0.946966i	$-0.395869\pi$
$347$	11.9716	0.642667	0.321334	+	0.946966i	$0.395869\pi$
$348$	2.68455	0.143907
$349$	2.81828	0.150859	0.0754297	−	0.997151i	$-0.475967\pi$
$349$	2.81828	0.150859	0.0754297	+	0.997151i	$0.475967\pi$
$350$	0	0
$351$	−9.86789	−0.526709
$352$	−3.17809	−0.169393
$353$	18.2848	0.973204	0.486602	−	0.873624i	$-0.338236\pi$
$353$	18.2848	0.973204	0.486602	+	0.873624i	$0.338236\pi$
$354$	0.773081	0.0410888
$355$	9.66631	0.513034
$356$	−34.3072	−1.81828
$357$	0	0
$358$	3.95973	0.209278
$359$	−31.2691	−1.65032	−0.825159	−	0.564900i	$-0.808915\pi$
$359$	−31.2691	−1.65032	−0.825159	+	0.564900i	$0.808915\pi$
$360$	3.20183	0.168751
$361$	19.1665	1.00876
$362$	2.41412	0.126883
$363$	0.275960	0.0144841
$364$	0	0
$365$	−4.06483	−0.212763
$366$	−0.706891	−0.0369498
$367$	−1.01226	−0.0528397	−0.0264199	−	0.999651i	$-0.508411\pi$
$367$	−1.01226	−0.0528397	−0.0264199	+	0.999651i	$0.508411\pi$
$368$	−0.499066	−0.0260156
$369$	−3.62305	−0.188609
$370$	−2.65038	−0.137787
$371$	0	0
$372$	1.77870	0.0922213
$373$	−4.80505	−0.248796	−0.124398	−	0.992232i	$-0.539700\pi$
$373$	−4.80505	−0.248796	−0.124398	+	0.992232i	$0.539700\pi$
$374$	1.25150	0.0647134
$375$	0.275960	0.0142505
$376$	−7.58791	−0.391317
$377$	−30.5519	−1.57350
$378$	0	0
$379$	−28.9344	−1.48626	−0.743130	−	0.669147i	$-0.766660\pi$
$379$	−28.9344	−1.48626	−0.743130	+	0.669147i	$0.766660\pi$
$380$	−11.8742	−0.609133
$381$	−3.93364	−0.201526
$382$	0.871632	0.0445966
$383$	4.19297	0.214251	0.107125	−	0.994246i	$-0.465835\pi$
$383$	4.19297	0.214251	0.107125	+	0.994246i	$0.465835\pi$
$384$	−2.23094	−0.113847
$385$	0	0
$386$	2.56450	0.130529
$387$	−16.1969	−0.823335
$388$	0.597627	0.0303399
$389$	−38.9448	−1.97458	−0.987290	−	0.158929i	$-0.949196\pi$
$389$	−38.9448	−1.97458	−0.987290	+	0.158929i	$0.949196\pi$
$390$	0.465107	0.0235516
$391$	0.632206	0.0319720
$392$	0	0
$393$	1.55615	0.0784973
$394$	4.11233	0.207176
$395$	14.4849	0.728813
$396$	−5.61975	−0.282403
$397$	37.1497	1.86449	0.932245	−	0.361827i	$-0.117847\pi$
$397$	37.1497	1.86449	0.932245	+	0.361827i	$0.117847\pi$
$398$	−2.60404	−0.130529
$399$	0	0
$400$	3.53833	0.176916
$401$	8.77830	0.438367	0.219184	−	0.975684i	$-0.429661\pi$
$401$	8.77830	0.438367	0.219184	+	0.975684i	$0.429661\pi$
$402$	0.807606	0.0402797
$403$	−20.2427	−1.00836
$404$	−16.6201	−0.826882
$405$	8.32042	0.413445
$406$	0	0
$407$	9.49239	0.470520
$408$	1.35453	0.0670591
$409$	−22.3035	−1.10284	−0.551419	−	0.834229i	$-0.685913\pi$
$409$	−22.3035	−1.10284	−0.551419	+	0.834229i	$0.685913\pi$
$410$	0.345981	0.0170868
$411$	0.822821	0.0405867
$412$	13.8954	0.684576
$413$	0	0
$414$	0.115146	0.00565910
$415$	2.71493	0.133271
$416$	19.1841	0.940577
$417$	−2.13650	−0.104625
$418$	−1.72494	−0.0843695
$419$	−19.0544	−0.930869	−0.465434	−	0.885082i	$-0.654102\pi$
$419$	−19.0544	−0.930869	−0.465434	+	0.885082i	$0.654102\pi$
$420$	0	0
$421$	18.7130	0.912016	0.456008	−	0.889976i	$-0.349279\pi$
$421$	18.7130	0.912016	0.456008	+	0.889976i	$0.349279\pi$
$422$	−0.727164	−0.0353978
$423$	−20.2597	−0.985059
$424$	−11.8348	−0.574748
$425$	−4.48227	−0.217422
$426$	0.744797	0.0360856
$427$	0	0
$428$	−16.1879	−0.782471
$429$	−1.66579	−0.0804251
$430$	1.54671	0.0745891
$431$	−34.0933	−1.64222	−0.821108	−	0.570773i	$-0.806644\pi$
$431$	−34.0933	−1.64222	−0.821108	+	0.570773i	$0.806644\pi$
$432$	−5.78425	−0.278295
$433$	−11.2439	−0.540347	−0.270174	−	0.962812i	$-0.587081\pi$
$433$	−11.2439	−0.540347	−0.270174	+	0.962812i	$0.587081\pi$
$434$	0	0
$435$	−1.39672	−0.0669676
$436$	−23.3077	−1.11624
$437$	−0.871368	−0.0416832
$438$	−0.313199	−0.0149652
$439$	−15.0805	−0.719754	−0.359877	−	0.933000i	$-0.617181\pi$
$439$	−15.0805	−0.719754	−0.359877	+	0.933000i	$0.617181\pi$
$440$	1.09508	0.0522057
$441$	0	0
$442$	−7.55448	−0.359330
$443$	23.7848	1.13005	0.565026	−	0.825073i	$-0.308866\pi$
$443$	23.7848	1.13005	0.565026	+	0.825073i	$0.308866\pi$
$444$	5.03482	0.238942
$445$	17.8494	0.846141
$446$	−1.29879	−0.0614997
$447$	1.49342	0.0706363
$448$	0	0
$449$	26.2117	1.23701	0.618504	−	0.785781i	$-0.287739\pi$
$449$	26.2117	1.23701	0.618504	+	0.785781i	$0.287739\pi$
$450$	−0.816369	−0.0384840
$451$	−1.23914	−0.0583488
$452$	−2.66525	−0.125363
$453$	−4.90917	−0.230653
$454$	3.85414	0.180884
$455$	0	0
$456$	−1.86694	−0.0874276
$457$	−13.6132	−0.636799	−0.318399	−	0.947957i	$-0.603145\pi$
$457$	−13.6132	−0.636799	−0.318399	+	0.947957i	$0.603145\pi$
$458$	−1.59508	−0.0745332
$459$	7.32735	0.342012
$460$	0.271096	0.0126399
$461$	22.8464	1.06406	0.532032	−	0.846724i	$-0.321429\pi$
$461$	22.8464	1.06406	0.532032	+	0.846724i	$0.321429\pi$
$462$	0	0
$463$	−42.7331	−1.98598	−0.992989	−	0.118207i	$-0.962285\pi$
$463$	−42.7331	−1.98598	−0.992989	+	0.118207i	$0.962285\pi$
$464$	−17.9086	−0.831386
$465$	−0.925422	−0.0429154
$466$	−1.16587	−0.0540080
$467$	−11.5732	−0.535544	−0.267772	−	0.963482i	$-0.586287\pi$
$467$	−11.5732	−0.535544	−0.267772	+	0.963482i	$0.586287\pi$
$468$	33.9228	1.56808
$469$	0	0
$470$	1.93468	0.0892404
$471$	2.10953	0.0972022
$472$	−10.9873	−0.505732
$473$	−5.53959	−0.254710
$474$	1.11607	0.0512629
$475$	6.17791	0.283462
$476$	0	0
$477$	−31.5988	−1.44681
$478$	3.65788	0.167308
$479$	−31.2520	−1.42794	−0.713969	−	0.700177i	$-0.753104\pi$
$479$	−31.2520	−1.42794	−0.713969	+	0.700177i	$0.753104\pi$
$480$	0.877025	0.0400305
$481$	−57.2994	−2.61263
$482$	−4.82536	−0.219789
$483$	0	0
$484$	−1.92204	−0.0873655
$485$	−0.310934	−0.0141188
$486$	2.01041	0.0911940
$487$	−35.7949	−1.62202	−0.811012	−	0.585030i	$-0.801083\pi$
$487$	−35.7949	−1.62202	−0.811012	+	0.585030i	$0.801083\pi$
$488$	10.0466	0.454788
$489$	−2.12970	−0.0963083
$490$	0	0
$491$	23.3469	1.05363	0.526815	−	0.849980i	$-0.323386\pi$
$491$	23.3469	1.05363	0.526815	+	0.849980i	$0.323386\pi$
$492$	−0.657247	−0.0296310
$493$	22.6862	1.02173
$494$	10.4123	0.468473
$495$	2.92385	0.131417
$496$	−11.8657	−0.532784
$497$	0	0
$498$	0.209188	0.00937393
$499$	−7.97924	−0.357200	−0.178600	−	0.983922i	$-0.557157\pi$
$499$	−7.97924	−0.357200	−0.178600	+	0.983922i	$0.557157\pi$
$500$	−1.92204	−0.0859563
$501$	−6.54736	−0.292514
$502$	−5.61545	−0.250630
$503$	24.0054	1.07035	0.535173	−	0.844742i	$-0.320246\pi$
$503$	24.0054	1.07035	0.535173	+	0.844742i	$0.320246\pi$
$504$	0	0
$505$	8.64712	0.384792
$506$	0.0393815	0.00175072
$507$	6.46783	0.287246
$508$	27.3976	1.21557
$509$	−36.0113	−1.59617	−0.798086	−	0.602544i	$-0.794154\pi$
$509$	−36.0113	−1.59617	−0.798086	+	0.602544i	$0.794154\pi$
$510$	−0.345363	−0.0152929
$511$	0	0
$512$	18.9946	0.839450
$513$	−10.0993	−0.445894
$514$	−8.58117	−0.378499
$515$	−7.22948	−0.318569
$516$	−2.93823	−0.129348
$517$	−6.92912	−0.304742
$518$	0	0
$519$	3.24541	0.142458
$520$	−6.61027	−0.289879
$521$	−13.6970	−0.600076	−0.300038	−	0.953927i	$-0.596999\pi$
$521$	−13.6970	−0.600076	−0.300038	+	0.953927i	$0.596999\pi$
$522$	4.13191	0.180849
$523$	22.8824	1.00058	0.500289	−	0.865859i	$-0.333227\pi$
$523$	22.8824	1.00058	0.500289	+	0.865859i	$0.333227\pi$
$524$	−10.8385	−0.473481
$525$	0	0
$526$	3.14011	0.136915
$527$	15.0311	0.654767
$528$	−0.976435	−0.0424939
$529$	−22.9801	−0.999135
$530$	3.01750	0.131072
$531$	−29.3361	−1.27308
$532$	0	0
$533$	7.47989	0.323990
$534$	1.37531	0.0595154
$535$	8.42224	0.364125
$536$	−11.4780	−0.495774
$537$	3.91362	0.168885
$538$	2.49747	0.107674
$539$	0	0
$540$	3.14204	0.135212
$541$	35.8833	1.54274	0.771372	−	0.636385i	$-0.219571\pi$
$541$	35.8833	1.54274	0.771372	+	0.636385i	$0.219571\pi$
$542$	3.65964	0.157195
$543$	2.38601	0.102394
$544$	−14.2451	−0.610752
$545$	12.1265	0.519444
$546$	0	0
$547$	12.2566	0.524056	0.262028	−	0.965060i	$-0.415609\pi$
$547$	12.2566	0.524056	0.262028	+	0.965060i	$0.415609\pi$
$548$	−5.73089	−0.244812
$549$	26.8243	1.14484
$550$	−0.279211	−0.0119056
$551$	−31.2684	−1.33208
$552$	0.0426236	0.00181418
$553$	0	0
$554$	−2.41909	−0.102777
$555$	−2.61952	−0.111192
$556$	14.8806	0.631078
$557$	−42.0315	−1.78093	−0.890466	−	0.455049i	$-0.849622\pi$
$557$	−42.0315	−1.78093	−0.890466	+	0.455049i	$0.849622\pi$
$558$	2.73767	0.115895
$559$	33.4389	1.41432
$560$	0	0
$561$	1.23692	0.0522230
$562$	1.95744	0.0825696
$563$	6.37676	0.268748	0.134374	−	0.990931i	$-0.457098\pi$
$563$	6.37676	0.268748	0.134374	+	0.990931i	$0.457098\pi$
$564$	−3.67525	−0.154756
$565$	1.38668	0.0583380
$566$	−3.15778	−0.132731
$567$	0	0
$568$	−10.5853	−0.444151
$569$	28.0663	1.17660	0.588299	−	0.808643i	$-0.299798\pi$
$569$	28.0663	1.17660	0.588299	+	0.808643i	$0.299798\pi$
$570$	0.476013	0.0199380
$571$	18.6441	0.780231	0.390116	−	0.920766i	$-0.372435\pi$
$571$	18.6441	0.780231	0.390116	+	0.920766i	$0.372435\pi$
$572$	11.6021	0.485109
$573$	0.861482	0.0359889
$574$	0	0
$575$	−0.141046	−0.00588202
$576$	18.0965	0.754023
$577$	7.44336	0.309871	0.154936	−	0.987925i	$-0.450483\pi$
$577$	7.44336	0.309871	0.154936	+	0.987925i	$0.450483\pi$
$578$	0.862964	0.0358946
$579$	2.53464	0.105336
$580$	9.72807	0.403936
$581$	0	0
$582$	−0.0239577	−0.000993079 0
$583$	−10.8073	−0.447591
$584$	4.45130	0.184196
$585$	−17.6494	−0.729712
$586$	8.19253	0.338430
$587$	43.9273	1.81307	0.906536	−	0.422128i	$-0.138717\pi$
$587$	43.9273	1.81307	0.906536	+	0.422128i	$0.138717\pi$
$588$	0	0
$589$	−20.7174	−0.853646
$590$	2.80143	0.115333
$591$	4.06444	0.167189
$592$	−33.5872	−1.38042
$593$	−7.04574	−0.289334	−0.144667	−	0.989480i	$-0.546211\pi$
$593$	−7.04574	−0.289334	−0.144667	+	0.989480i	$0.546211\pi$
$594$	0.456438	0.0187279
$595$	0	0
$596$	−10.4016	−0.426065
$597$	−2.57372	−0.105335
$598$	−0.237721	−0.00972113
$599$	25.2758	1.03274	0.516371	−	0.856365i	$-0.327282\pi$
$599$	25.2758	1.03274	0.516371	+	0.856365i	$0.327282\pi$
$600$	−0.302197	−0.0123371
$601$	−35.8144	−1.46090	−0.730450	−	0.682967i	$-0.760689\pi$
$601$	−35.8144	−1.46090	−0.730450	+	0.682967i	$0.760689\pi$
$602$	0	0
$603$	−30.6462	−1.24801
$604$	34.1920	1.39125
$605$	1.00000	0.0406558
$606$	0.666268	0.0270653
$607$	−15.4769	−0.628190	−0.314095	−	0.949392i	$-0.601701\pi$
$607$	−15.4769	−0.628190	−0.314095	+	0.949392i	$0.601701\pi$
$608$	19.6339	0.796262
$609$	0	0
$610$	−2.56157	−0.103715
$611$	41.8266	1.69212
$612$	−25.1892	−1.01821
$613$	20.6694	0.834830	0.417415	−	0.908716i	$-0.362936\pi$
$613$	20.6694	0.834830	0.417415	+	0.908716i	$0.362936\pi$
$614$	5.52993	0.223170
$615$	0.341952	0.0137889
$616$	0	0
$617$	8.80214	0.354361	0.177180	−	0.984178i	$-0.443302\pi$
$617$	8.80214	0.354361	0.177180	+	0.984178i	$0.443302\pi$
$618$	−0.557038	−0.0224074
$619$	−25.5550	−1.02714	−0.513571	−	0.858047i	$-0.671678\pi$
$619$	−25.5550	−1.02714	−0.513571	+	0.858047i	$0.671678\pi$
$620$	6.44551	0.258858
$621$	0.230574	0.00925261
$622$	−1.23561	−0.0495436
$623$	0	0
$624$	5.89411	0.235953
$625$	1.00000	0.0400000
$626$	1.49894	0.0599097
$627$	−1.70485	−0.0680852
$628$	−14.6928	−0.586305
$629$	42.5474	1.69648
$630$	0	0
$631$	8.18725	0.325929	0.162965	−	0.986632i	$-0.447894\pi$
$631$	8.18725	0.325929	0.162965	+	0.986632i	$0.447894\pi$
$632$	−15.8620	−0.630958
$633$	−0.718697	−0.0285657
$634$	4.18321	0.166137
$635$	−14.2544	−0.565669
$636$	−5.73223	−0.227298
$637$	0	0
$638$	1.41318	0.0559481
$639$	−28.2628	−1.11806
$640$	−8.08430	−0.319560
$641$	0.789084	0.0311670	0.0155835	−	0.999879i	$-0.495039\pi$
$641$	0.789084	0.0311670	0.0155835	+	0.999879i	$0.495039\pi$
$642$	0.648941	0.0256117
$643$	9.03854	0.356445	0.178223	−	0.983990i	$-0.442965\pi$
$643$	9.03854	0.356445	0.178223	+	0.983990i	$0.442965\pi$
$644$	0	0
$645$	1.52870	0.0601926
$646$	−7.73163	−0.304197
$647$	−4.48207	−0.176208	−0.0881042	−	0.996111i	$-0.528081\pi$
$647$	−4.48207	−0.176208	−0.0881042	+	0.996111i	$0.528081\pi$
$648$	−9.11149	−0.357933
$649$	−10.0334	−0.393844
$650$	1.68542	0.0661074
$651$	0	0
$652$	14.8332	0.580914
$653$	1.25077	0.0489465	0.0244732	−	0.999700i	$-0.492209\pi$
$653$	1.25077	0.0489465	0.0244732	+	0.999700i	$0.492209\pi$
$654$	0.934361	0.0365364
$655$	5.63904	0.220336
$656$	4.38448	0.171185
$657$	11.8849	0.463676
$658$	0	0
$659$	−1.74776	−0.0680831	−0.0340416	−	0.999420i	$-0.510838\pi$
$659$	−1.74776	−0.0680831	−0.0340416	+	0.999420i	$0.510838\pi$
$660$	0.530406	0.0206460
$661$	37.8913	1.47380	0.736900	−	0.676002i	$-0.236289\pi$
$661$	37.8913	1.47380	0.736900	+	0.676002i	$0.236289\pi$
$662$	−5.35465	−0.208114
$663$	−7.46652	−0.289976
$664$	−2.97306	−0.115377
$665$	0	0
$666$	7.74929	0.300279
$667$	0.713879	0.0276415
$668$	45.6020	1.76439
$669$	−1.28367	−0.0496296
$670$	2.92654	0.113062
$671$	9.17433	0.354171
$672$	0	0
$673$	5.14338	0.198263	0.0991313	−	0.995074i	$-0.468394\pi$
$673$	5.14338	0.198263	0.0991313	+	0.995074i	$0.468394\pi$
$674$	−5.83665	−0.224819
$675$	−1.63474	−0.0629213
$676$	−45.0480	−1.73262
$677$	−22.0384	−0.847004	−0.423502	−	0.905895i	$-0.639199\pi$
$677$	−22.0384	−0.847004	−0.423502	+	0.905895i	$0.639199\pi$
$678$	0.106845	0.00410335
$679$	0	0
$680$	4.90842	0.188229
$681$	3.80926	0.145971
$682$	0.936325	0.0358537
$683$	23.5700	0.901880	0.450940	−	0.892554i	$-0.351089\pi$
$683$	23.5700	0.901880	0.450940	+	0.892554i	$0.351089\pi$
$684$	34.7183	1.32749
$685$	2.98167	0.113924
$686$	0	0
$687$	−1.57651	−0.0601475
$688$	19.6009	0.747276
$689$	65.2365	2.48531
$690$	−0.0108677	−0.000413727 0
$691$	7.52716	0.286347	0.143173	−	0.989698i	$-0.454269\pi$
$691$	7.52716	0.286347	0.143173	+	0.989698i	$0.454269\pi$
$692$	−22.6041	−0.859279
$693$	0	0
$694$	3.34259	0.126883
$695$	−7.74208	−0.293674
$696$	1.52952	0.0579761
$697$	−5.55416	−0.210379
$698$	0.786895	0.0297844
$699$	−1.15230	−0.0435839
$700$	0	0
$701$	26.0178	0.982678	0.491339	−	0.870968i	$-0.336508\pi$
$701$	26.0178	0.982678	0.491339	+	0.870968i	$0.336508\pi$
$702$	−2.75522	−0.103989
$703$	−58.6431	−2.21177
$704$	6.18929	0.233268
$705$	1.91216	0.0720160
$706$	5.10532	0.192141
$707$	0	0
$708$	−5.32176	−0.200004
$709$	40.9502	1.53792	0.768959	−	0.639298i	$-0.220775\pi$
$709$	40.9502	1.53792	0.768959	+	0.639298i	$0.220775\pi$
$710$	2.69894	0.101289
$711$	−42.3515	−1.58831
$712$	−19.5464	−0.732532
$713$	0.472993	0.0177137
$714$	0	0
$715$	−6.03636	−0.225747
$716$	−27.2581	−1.01868
$717$	3.61529	0.135015
$718$	−8.73066	−0.325825
$719$	−19.5476	−0.729003	−0.364502	−	0.931203i	$-0.618761\pi$
$719$	−19.5476	−0.729003	−0.364502	+	0.931203i	$0.618761\pi$
$720$	−10.3455	−0.385555
$721$	0	0
$722$	5.35150	0.199162
$723$	−4.76917	−0.177367
$724$	−16.6184	−0.617618
$725$	−5.06132	−0.187973
$726$	0.0770509	0.00285963
$727$	−9.16431	−0.339885	−0.169943	−	0.985454i	$-0.554358\pi$
$727$	−9.16431	−0.339885	−0.169943	+	0.985454i	$0.554358\pi$
$728$	0	0
$729$	−22.9742	−0.850898
$730$	−1.13494	−0.0420062
$731$	−24.8299	−0.918367
$732$	4.86612	0.179857
$733$	6.95073	0.256731	0.128366	−	0.991727i	$-0.459027\pi$
$733$	6.95073	0.256731	0.128366	+	0.991727i	$0.459027\pi$
$734$	−0.282635	−0.0104322
$735$	0	0
$736$	−0.448257	−0.0165230
$737$	−10.4815	−0.386089
$738$	−1.01160	−0.0372373
$739$	1.30073	0.0478483	0.0239242	−	0.999714i	$-0.492384\pi$
$739$	1.30073	0.0478483	0.0239242	+	0.999714i	$0.492384\pi$
$740$	18.2448	0.670691
$741$	10.2911	0.378053
$742$	0	0
$743$	31.0258	1.13823	0.569113	−	0.822260i	$-0.307287\pi$
$743$	31.0258	1.13823	0.569113	+	0.822260i	$0.307287\pi$
$744$	1.01341	0.0371533
$745$	5.41173	0.198270
$746$	−1.34162	−0.0491203
$747$	−7.93804	−0.290438
$748$	−8.61510	−0.314999
$749$	0	0
$750$	0.0770509	0.00281350
$751$	−1.32112	−0.0482084	−0.0241042	−	0.999709i	$-0.507673\pi$
$751$	−1.32112	−0.0482084	−0.0241042	+	0.999709i	$0.507673\pi$
$752$	24.5175	0.894061
$753$	−5.55006	−0.202256
$754$	−8.53043	−0.310660
$755$	−17.7894	−0.647424
$756$	0	0
$757$	6.28325	0.228368	0.114184	−	0.993460i	$-0.463575\pi$
$757$	6.28325	0.228368	0.114184	+	0.993460i	$0.463575\pi$
$758$	−8.07879	−0.293435
$759$	0.0389230	0.00141281
$760$	−6.76528	−0.245402
$761$	−17.8951	−0.648696	−0.324348	−	0.945938i	$-0.605145\pi$
$761$	−17.8951	−0.648696	−0.324348	+	0.945938i	$0.605145\pi$
$762$	−1.09831	−0.0397877
$763$	0	0
$764$	−6.00017	−0.217079
$765$	13.1055	0.473829
$766$	1.17072	0.0422999
$767$	60.5650	2.18688
$768$	2.79309	0.100787
$769$	−17.3712	−0.626421	−0.313210	−	0.949684i	$-0.601404\pi$
$769$	−17.3712	−0.626421	−0.313210	+	0.949684i	$0.601404\pi$
$770$	0	0
$771$	−8.48125	−0.305445
$772$	−17.6536	−0.635366
$773$	17.4251	0.626739	0.313369	−	0.949631i	$-0.398542\pi$
$773$	17.4251	0.626739	0.313369	+	0.949631i	$0.398542\pi$
$774$	−4.52235	−0.162552
$775$	−3.35347	−0.120460
$776$	0.340496	0.0122231
$777$	0	0
$778$	−10.8738	−0.389845
$779$	7.65529	0.274279
$780$	−3.20172	−0.114640
$781$	−9.66631	−0.345888
$782$	0.176519	0.00631229
$783$	8.27396	0.295687
$784$	0	0
$785$	7.64436	0.272839
$786$	0.434493	0.0154979
$787$	12.2339	0.436093	0.218047	−	0.975938i	$-0.430032\pi$
$787$	12.2339	0.436093	0.218047	+	0.975938i	$0.430032\pi$
$788$	−28.3086	−1.00845
$789$	3.10354	0.110489
$790$	4.04433	0.143891
$791$	0	0
$792$	−3.20183	−0.113772
$793$	−55.3795	−1.96659
$794$	10.3726	0.368110
$795$	2.98237	0.105774
$796$	17.9258	0.635363
$797$	10.3230	0.365658	0.182829	−	0.983145i	$-0.441475\pi$
$797$	10.3230	0.365658	0.182829	+	0.983145i	$0.441475\pi$
$798$	0	0
$799$	−31.0582	−1.09876
$800$	3.17809	0.112362
$801$	−52.1888	−1.84400
$802$	2.45100	0.0865476
$803$	4.06483	0.143445
$804$	−5.55943	−0.196066
$805$	0	0
$806$	−5.65199	−0.199083
$807$	2.46839	0.0868915
$808$	−9.46925	−0.333127
$809$	15.8950	0.558838	0.279419	−	0.960169i	$-0.409858\pi$
$809$	15.8950	0.558838	0.279419	+	0.960169i	$0.409858\pi$
$810$	2.32315	0.0816272
$811$	−1.63833	−0.0575295	−0.0287648	−	0.999586i	$-0.509157\pi$
$811$	−1.63833	−0.0575295	−0.0287648	+	0.999586i	$0.509157\pi$
$812$	0	0
$813$	3.61702	0.126855
$814$	2.65038	0.0928957
$815$	−7.71743	−0.270330
$816$	−4.37664	−0.153213
$817$	34.2230	1.19731
$818$	−6.22738	−0.217735
$819$	0	0
$820$	−2.38168	−0.0831718
$821$	15.9369	0.556201	0.278100	−	0.960552i	$-0.410295\pi$
$821$	15.9369	0.556201	0.278100	+	0.960552i	$0.410295\pi$
$822$	0.229740	0.00801311
$823$	50.4648	1.75909	0.879546	−	0.475813i	$-0.157846\pi$
$823$	50.4648	1.75909	0.879546	+	0.475813i	$0.157846\pi$
$824$	7.91684	0.275796
$825$	−0.275960	−0.00960768
$826$	0	0
$827$	0.696629	0.0242242	0.0121121	−	0.999927i	$-0.496145\pi$
$827$	0.696629	0.0242242	0.0121121	+	0.999927i	$0.496145\pi$
$828$	−0.792643	−0.0275463
$829$	−49.9264	−1.73402	−0.867008	−	0.498294i	$-0.833960\pi$
$829$	−49.9264	−1.73402	−0.867008	+	0.498294i	$0.833960\pi$
$830$	0.758038	0.0263119
$831$	−2.39092	−0.0829401
$832$	−37.3608	−1.29525
$833$	0	0
$834$	−0.596534	−0.0206563
$835$	−23.7258	−0.821065
$836$	11.8742	0.410677
$837$	5.48206	0.189488
$838$	−5.32020	−0.183783
$839$	−19.0422	−0.657409	−0.328704	−	0.944433i	$-0.606612\pi$
$839$	−19.0422	−0.657409	−0.328704	+	0.944433i	$0.606612\pi$
$840$	0	0
$841$	−3.38303	−0.116656
$842$	5.22487	0.180061
$843$	1.93465	0.0666328
$844$	5.00568	0.172303
$845$	23.4376	0.806277
$846$	−5.65672	−0.194482
$847$	0	0
$848$	38.2396	1.31315
$849$	−3.12101	−0.107113
$850$	−1.25150	−0.0429260
$851$	1.33886	0.0458956
$852$	−5.12706	−0.175650
$853$	3.57347	0.122353	0.0611767	−	0.998127i	$-0.480515\pi$
$853$	3.57347	0.122353	0.0611767	+	0.998127i	$0.480515\pi$
$854$	0	0
$855$	−18.0632	−0.617750
$856$	−9.22299	−0.315235
$857$	29.1336	0.995184	0.497592	−	0.867411i	$-0.334218\pi$
$857$	29.1336	0.995184	0.497592	+	0.867411i	$0.334218\pi$
$858$	−0.465107	−0.0158785
$859$	−33.1503	−1.13107	−0.565537	−	0.824723i	$-0.691331\pi$
$859$	−33.1503	−1.13107	−0.565537	+	0.824723i	$0.691331\pi$
$860$	−10.6473	−0.363070
$861$	0	0
$862$	−9.51921	−0.324226
$863$	−22.1126	−0.752723	−0.376361	−	0.926473i	$-0.622825\pi$
$863$	−22.1126	−0.752723	−0.376361	+	0.926473i	$0.622825\pi$
$864$	−5.19536	−0.176750
$865$	11.7605	0.399868
$866$	−3.13942	−0.106682
$867$	0.852915	0.0289665
$868$	0	0
$869$	−14.4849	−0.491366
$870$	−0.389979	−0.0132215
$871$	63.2698	2.14382
$872$	−13.2795	−0.449700
$873$	0.909122	0.0307691
$874$	−0.243295	−0.00822959
$875$	0	0
$876$	2.15601	0.0728448
$877$	18.2742	0.617076	0.308538	−	0.951212i	$-0.400160\pi$
$877$	18.2742	0.617076	0.308538	+	0.951212i	$0.400160\pi$
$878$	−4.21065	−0.142102
$879$	8.09714	0.273110
$880$	−3.53833	−0.119277
$881$	−40.8714	−1.37699	−0.688495	−	0.725241i	$-0.741728\pi$
$881$	−40.8714	−1.37699	−0.688495	+	0.725241i	$0.741728\pi$
$882$	0	0
$883$	−23.8690	−0.803256	−0.401628	−	0.915803i	$-0.631555\pi$
$883$	−23.8690	−0.803256	−0.401628	+	0.915803i	$0.631555\pi$
$884$	52.0038	1.74908
$885$	2.76881	0.0930724
$886$	6.64098	0.223108
$887$	−10.5896	−0.355565	−0.177783	−	0.984070i	$-0.556892\pi$
$887$	−10.5896	−0.355565	−0.177783	+	0.984070i	$0.556892\pi$
$888$	2.86857	0.0962629
$889$	0	0
$890$	4.98373	0.167055
$891$	−8.32042	−0.278744
$892$	8.94068	0.299356
$893$	42.8074	1.43250
$894$	0.416979	0.0139459
$895$	14.1819	0.474047
$896$	0	0
$897$	−0.234953	−0.00784485
$898$	7.31860	0.244225
$899$	16.9730	0.566081
$900$	5.61975	0.187325
$901$	−48.4410	−1.61381
$902$	−0.345981	−0.0115199
$903$	0	0
$904$	−1.51852	−0.0505052
$905$	8.64623	0.287410
$906$	−1.37069	−0.0455382
$907$	−33.5860	−1.11520	−0.557602	−	0.830109i	$-0.688278\pi$
$907$	−33.5860	−1.11520	−0.557602	+	0.830109i	$0.688278\pi$
$908$	−26.5313	−0.880471
$909$	−25.2828	−0.838579
$910$	0	0
$911$	−35.5767	−1.17871	−0.589355	−	0.807874i	$-0.700618\pi$
$911$	−35.5767	−1.17871	−0.589355	+	0.807874i	$0.700618\pi$
$912$	6.03232	0.199750
$913$	−2.71493	−0.0898511
$914$	−3.80095	−0.125724
$915$	−2.53175	−0.0836969
$916$	10.9803	0.362798
$917$	0	0
$918$	2.04588	0.0675240
$919$	35.2851	1.16395	0.581974	−	0.813207i	$-0.302280\pi$
$919$	35.2851	1.16395	0.581974	+	0.813207i	$0.302280\pi$
$920$	0.154456	0.00509226
$921$	5.46554	0.180096
$922$	6.37897	0.210080
$923$	58.3493	1.92059
$924$	0	0
$925$	−9.49239	−0.312108
$926$	−11.9316	−0.392095
$927$	21.1379	0.694260
$928$	−16.0853	−0.528027
$929$	2.52661	0.0828954	0.0414477	−	0.999141i	$-0.486803\pi$
$929$	2.52661	0.0828954	0.0414477	+	0.999141i	$0.486803\pi$
$930$	−0.258388	−0.00847287
$931$	0	0
$932$	8.02568	0.262890
$933$	−1.22123	−0.0399812
$934$	−3.23137	−0.105734
$935$	4.48227	0.146586
$936$	19.3274	0.631736
$937$	−37.6599	−1.23030	−0.615148	−	0.788411i	$-0.710904\pi$
$937$	−37.6599	−1.23030	−0.615148	+	0.788411i	$0.710904\pi$
$938$	0	0
$939$	1.48149	0.0483465
$940$	−13.3181	−0.434387
$941$	−26.3512	−0.859025	−0.429512	−	0.903061i	$-0.641315\pi$
$941$	−26.3512	−0.859025	−0.429512	+	0.903061i	$0.641315\pi$
$942$	0.589004	0.0191908
$943$	−0.174776	−0.00569148
$944$	35.5014	1.15547
$945$	0	0
$946$	−1.54671	−0.0502879
$947$	−31.5785	−1.02616	−0.513081	−	0.858340i	$-0.671496\pi$
$947$	−31.5785	−1.02616	−0.513081	+	0.858340i	$0.671496\pi$
$948$	−7.68286	−0.249528
$949$	−24.5368	−0.796497
$950$	1.72494	0.0559644
$951$	4.13450	0.134070
$952$	0	0
$953$	28.4947	0.923035	0.461518	−	0.887131i	$-0.347305\pi$
$953$	28.4947	0.923035	0.461518	+	0.887131i	$0.347305\pi$
$954$	−8.82272	−0.285646
$955$	3.12177	0.101018
$956$	−25.1803	−0.814388
$957$	1.39672	0.0451496
$958$	−8.72588	−0.281921
$959$	0	0
$960$	−1.70800	−0.0551253
$961$	−19.7542	−0.637234
$962$	−15.9986	−0.515816
$963$	−24.6253	−0.793540
$964$	33.2170	1.06985
$965$	9.18481	0.295669
$966$	0	0
$967$	32.5955	1.04820	0.524100	−	0.851657i	$-0.324402\pi$
$967$	32.5955	1.04820	0.524100	+	0.851657i	$0.324402\pi$
$968$	−1.09508	−0.0351971
$969$	−7.64160	−0.245484
$970$	−0.0868160	−0.00278749
$971$	5.49679	0.176400	0.0882002	−	0.996103i	$-0.471888\pi$
$971$	5.49679	0.176400	0.0882002	+	0.996103i	$0.471888\pi$
$972$	−13.8393	−0.443897
$973$	0	0
$974$	−9.99433	−0.320239
$975$	1.66579	0.0533480
$976$	−32.4618	−1.03908
$977$	−9.46911	−0.302944	−0.151472	−	0.988462i	$-0.548401\pi$
$977$	−9.46911	−0.302944	−0.151472	+	0.988462i	$0.548401\pi$
$978$	−0.594635	−0.0190143
$979$	−17.8494	−0.570468
$980$	0	0
$981$	−35.4562	−1.13203
$982$	6.51870	0.208020
$983$	2.35733	0.0751870	0.0375935	−	0.999293i	$-0.488031\pi$
$983$	2.35733	0.0751870	0.0375935	+	0.999293i	$0.488031\pi$
$984$	−0.374464	−0.0119375
$985$	14.7284	0.469286
$986$	6.33423	0.201723
$987$	0	0
$988$	−71.6768	−2.28034
$989$	−0.781336	−0.0248450
$990$	0.816369	0.0259459
$991$	−32.3759	−1.02845	−0.514227	−	0.857654i	$-0.671921\pi$
$991$	−32.3759	−1.02845	−0.514227	+	0.857654i	$0.671921\pi$
$992$	−10.6576	−0.338380
$993$	−5.29230	−0.167946
$994$	0	0
$995$	−9.32644	−0.295668
$996$	−1.44002	−0.0456286
$997$	−26.6087	−0.842705	−0.421353	−	0.906897i	$-0.638444\pi$
$997$	−26.6087	−0.842705	−0.421353	+	0.906897i	$0.638444\pi$
$998$	−2.22789	−0.0705227
$999$	15.5176	0.490955

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.t.1.4		8
7.2	even	3		385.2.i.c.221.5	✓	16
7.4	even	3		385.2.i.c.331.5	yes	16
7.6	odd	2		2695.2.a.s.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.c.221.5	✓	16	7.2	even	3
385.2.i.c.331.5	yes	16	7.4	even	3
2695.2.a.s.1.4		8	7.6	odd	2
2695.2.a.t.1.4		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)

\(f(q)\)	\(=\)	\(q+0.279211 q^{2} +0.275960 q^{3} -1.92204 q^{4} +1.00000 q^{5} +0.0770509 q^{6} -1.09508 q^{8} -2.92385 q^{9} +O(q^{10})\)	\(q+0.279211 q^{2} +0.275960 q^{3} -1.92204 q^{4} +1.00000 q^{5} +0.0770509 q^{6} -1.09508 q^{8} -2.92385 q^{9} +0.279211 q^{10} -1.00000 q^{11} -0.530406 q^{12} +6.03636 q^{13} +0.275960 q^{15} +3.53833 q^{16} -4.48227 q^{17} -0.816369 q^{18} +6.17791 q^{19} -1.92204 q^{20} -0.279211 q^{22} -0.141046 q^{23} -0.302197 q^{24} +1.00000 q^{25} +1.68542 q^{26} -1.63474 q^{27} -5.06132 q^{29} +0.0770509 q^{30} -3.35347 q^{31} +3.17809 q^{32} -0.275960 q^{33} -1.25150 q^{34} +5.61975 q^{36} -9.49239 q^{37} +1.72494 q^{38} +1.66579 q^{39} -1.09508 q^{40} +1.23914 q^{41} +5.53959 q^{43} +1.92204 q^{44} -2.92385 q^{45} -0.0393815 q^{46} +6.92912 q^{47} +0.976435 q^{48} +0.279211 q^{50} -1.23692 q^{51} -11.6021 q^{52} +10.8073 q^{53} -0.456438 q^{54} -1.00000 q^{55} +1.70485 q^{57} -1.41318 q^{58} +10.0334 q^{59} -0.530406 q^{60} -9.17433 q^{61} -0.936325 q^{62} -6.18929 q^{64} +6.03636 q^{65} -0.0770509 q^{66} +10.4815 q^{67} +8.61510 q^{68} -0.0389230 q^{69} +9.66631 q^{71} +3.20183 q^{72} -4.06483 q^{73} -2.65038 q^{74} +0.275960 q^{75} -11.8742 q^{76} +0.465107 q^{78} +14.4849 q^{79} +3.53833 q^{80} +8.32042 q^{81} +0.345981 q^{82} +2.71493 q^{83} -4.48227 q^{85} +1.54671 q^{86} -1.39672 q^{87} +1.09508 q^{88} +17.8494 q^{89} -0.816369 q^{90} +0.271096 q^{92} -0.925422 q^{93} +1.93468 q^{94} +6.17791 q^{95} +0.877025 q^{96} -0.310934 q^{97} +2.92385 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + q^{3} + 9 q^{4} + 8 q^{5} - 3 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) 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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