LMFDB - Embedded newform 2695.2.a.y.1.7

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 51x^{6} - 184x^{5} - 45x^{4} + 297x^{3} - 59x^{2} - 109x + 21 $ x^10 - 3x^9 - 13x^8 + 41x^7 + 51x^6 - 184x^5 - 45x^4 + 297x^3 - 59x^2 - 109*x + 21
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.7
Root			$1.29002$ 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)

$f(q)$	$=$	$q+1.29002 q^{2} +0.350856 q^{3} -0.335851 q^{4} -1.00000 q^{5} +0.452611 q^{6} -3.01329 q^{8} -2.87690 q^{9} +O(q^{10})$	\(q+1.29002 q^{2} +0.350856 q^{3} -0.335851 q^{4} -1.00000 q^{5} +0.452611 q^{6} -3.01329 q^{8} -2.87690 q^{9} -1.29002 q^{10} +1.00000 q^{11} -0.117835 q^{12} +3.47080 q^{13} -0.350856 q^{15} -3.21550 q^{16} +2.43891 q^{17} -3.71126 q^{18} -4.88344 q^{19} +0.335851 q^{20} +1.29002 q^{22} +6.56144 q^{23} -1.05723 q^{24} +1.00000 q^{25} +4.47739 q^{26} -2.06195 q^{27} +6.89952 q^{29} -0.452611 q^{30} -5.65800 q^{31} +1.87852 q^{32} +0.350856 q^{33} +3.14624 q^{34} +0.966209 q^{36} +8.05384 q^{37} -6.29973 q^{38} +1.21775 q^{39} +3.01329 q^{40} +5.48231 q^{41} +3.40659 q^{43} -0.335851 q^{44} +2.87690 q^{45} +8.46439 q^{46} +1.89060 q^{47} -1.12818 q^{48} +1.29002 q^{50} +0.855706 q^{51} -1.16567 q^{52} +8.60777 q^{53} -2.65995 q^{54} -1.00000 q^{55} -1.71338 q^{57} +8.90051 q^{58} -14.5510 q^{59} +0.117835 q^{60} +12.1195 q^{61} -7.29893 q^{62} +8.85434 q^{64} -3.47080 q^{65} +0.452611 q^{66} +13.9321 q^{67} -0.819110 q^{68} +2.30212 q^{69} -13.2480 q^{71} +8.66894 q^{72} +1.52912 q^{73} +10.3896 q^{74} +0.350856 q^{75} +1.64011 q^{76} +1.57092 q^{78} -7.58240 q^{79} +3.21550 q^{80} +7.90725 q^{81} +7.07228 q^{82} -6.63351 q^{83} -2.43891 q^{85} +4.39456 q^{86} +2.42074 q^{87} -3.01329 q^{88} -5.51625 q^{89} +3.71126 q^{90} -2.20367 q^{92} -1.98514 q^{93} +2.43891 q^{94} +4.88344 q^{95} +0.659092 q^{96} +9.66261 q^{97} -2.87690 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9	$ 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9} - 3 q^{10} + 10 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{15} + 21 q^{16} - 5 q^{17} + q^{18} + q^{19} - 15 q^{20} + 3 q^{22} + 18 q^{23} + 10 q^{24} + 10 q^{25} + 13 q^{26} - 15 q^{27} + 14 q^{29} - 5 q^{30} + 10 q^{31} + 46 q^{32} - 3 q^{33} - 2 q^{34} + 26 q^{36} + 13 q^{37} + 9 q^{38} + 3 q^{39} - 9 q^{40} - 7 q^{41} + 6 q^{43} + 15 q^{44} - 19 q^{45} + 10 q^{46} + q^{47} - 35 q^{48} + 3 q^{50} + 9 q^{51} - 17 q^{52} + 16 q^{53} + 73 q^{54} - 10 q^{55} + 12 q^{57} - 9 q^{58} + 13 q^{59} + 3 q^{60} + 18 q^{61} + 14 q^{62} + 43 q^{64} + 6 q^{65} + 5 q^{66} + 29 q^{67} + 13 q^{68} + 19 q^{71} - 48 q^{72} - 31 q^{73} - 8 q^{74} - 3 q^{75} - 8 q^{76} + 3 q^{78} - 21 q^{80} + 42 q^{81} + q^{82} - 2 q^{83} + 5 q^{85} + 10 q^{86} - 50 q^{87} + 9 q^{88} + 23 q^{89} - q^{90} + 14 q^{92} + 4 q^{93} - 5 q^{94} - q^{95} + 39 q^{96} - 43 q^{97} + 19 q^{99}+O(q^{100}) $ 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9 - 3 * q^10 + 10 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^15 + 21 * q^16 - 5 * q^17 + q^18 + q^19 - 15 * q^20 + 3 * q^22 + 18 * q^23 + 10 * q^24 + 10 * q^25 + 13 * q^26 - 15 * q^27 + 14 * q^29 - 5 * q^30 + 10 * q^31 + 46 * q^32 - 3 * q^33 - 2 * q^34 + 26 * q^36 + 13 * q^37 + 9 * q^38 + 3 * q^39 - 9 * q^40 - 7 * q^41 + 6 * q^43 + 15 * q^44 - 19 * q^45 + 10 * q^46 + q^47 - 35 * q^48 + 3 * q^50 + 9 * q^51 - 17 * q^52 + 16 * q^53 + 73 * q^54 - 10 * q^55 + 12 * q^57 - 9 * q^58 + 13 * q^59 + 3 * q^60 + 18 * q^61 + 14 * q^62 + 43 * q^64 + 6 * q^65 + 5 * q^66 + 29 * q^67 + 13 * q^68 + 19 * q^71 - 48 * q^72 - 31 * q^73 - 8 * q^74 - 3 * q^75 - 8 * q^76 + 3 * q^78 - 21 * q^80 + 42 * q^81 + q^82 - 2 * q^83 + 5 * q^85 + 10 * q^86 - 50 * q^87 + 9 * q^88 + 23 * q^89 - q^90 + 14 * q^92 + 4 * q^93 - 5 * q^94 - q^95 + 39 * q^96 - 43 * 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 $

$2$	1.29002	0.912181	0.456091	−	0.889933i	$-0.349249\pi$
$2$	1.29002	0.912181	0.456091	+	0.889933i	$0.349249\pi$
$3$	0.350856	0.202567	0.101283	−	0.994858i	$-0.467705\pi$
$3$	0.350856	0.202567	0.101283	+	0.994858i	$0.467705\pi$
$4$	−0.335851	−0.167925
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.452611	0.184778
$7$	0	0
$7$	0	0
$8$	−3.01329	−1.06536
$9$	−2.87690	−0.958967
$10$	−1.29002	−0.407940
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.117835	−0.0340161
$13$	3.47080	0.962626	0.481313	−	0.876549i	$-0.340160\pi$
$13$	3.47080	0.962626	0.481313	+	0.876549i	$0.340160\pi$
$14$	0	0
$15$	−0.350856	−0.0905906
$16$	−3.21550	−0.803876
$17$	2.43891	0.591523	0.295761	−	0.955262i	$-0.404427\pi$
$17$	2.43891	0.591523	0.295761	+	0.955262i	$0.404427\pi$
$18$	−3.71126	−0.874751
$19$	−4.88344	−1.12034	−0.560169	−	0.828378i	$-0.689264\pi$
$19$	−4.88344	−1.12034	−0.560169	+	0.828378i	$0.689264\pi$
$20$	0.335851	0.0750985
$21$	0	0
$22$	1.29002	0.275033
$23$	6.56144	1.36816	0.684078	−	0.729409i	$-0.260205\pi$
$23$	6.56144	1.36816	0.684078	+	0.729409i	$0.260205\pi$
$24$	−1.05723	−0.215806
$25$	1.00000	0.200000
$26$	4.47739	0.878089
$27$	−2.06195	−0.396822
$28$	0	0
$29$	6.89952	1.28121	0.640604	−	0.767871i	$-0.278684\pi$
$29$	6.89952	1.28121	0.640604	+	0.767871i	$0.278684\pi$
$30$	−0.452611	−0.0826351
$31$	−5.65800	−1.01621	−0.508104	−	0.861296i	$-0.669653\pi$
$31$	−5.65800	−1.01621	−0.508104	+	0.861296i	$0.669653\pi$
$32$	1.87852	0.332079
$33$	0.350856	0.0610762
$34$	3.14624	0.539576
$35$	0	0
$36$	0.966209	0.161035
$37$	8.05384	1.32404	0.662022	−	0.749485i	$-0.269699\pi$
$37$	8.05384	1.32404	0.662022	+	0.749485i	$0.269699\pi$
$38$	−6.29973	−1.02195
$39$	1.21775	0.194996
$40$	3.01329	0.476443
$41$	5.48231	0.856193	0.428096	−	0.903733i	$-0.359184\pi$
$41$	5.48231	0.856193	0.428096	+	0.903733i	$0.359184\pi$
$42$	0	0
$43$	3.40659	0.519500	0.259750	−	0.965676i	$-0.416360\pi$
$43$	3.40659	0.519500	0.259750	+	0.965676i	$0.416360\pi$
$44$	−0.335851	−0.0506314
$45$	2.87690	0.428863
$46$	8.46439	1.24801
$47$	1.89060	0.275772	0.137886	−	0.990448i	$-0.455969\pi$
$47$	1.89060	0.275772	0.137886	+	0.990448i	$0.455969\pi$
$48$	−1.12818	−0.162838
$49$	0	0
$50$	1.29002	0.182436
$51$	0.855706	0.119823
$52$	−1.16567	−0.161649
$53$	8.60777	1.18237	0.591184	−	0.806537i	$-0.298661\pi$
$53$	8.60777	1.18237	0.591184	+	0.806537i	$0.298661\pi$
$54$	−2.65995	−0.361973
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−1.71338	−0.226943
$58$	8.90051	1.16869
$59$	−14.5510	−1.89437	−0.947187	−	0.320681i	$-0.896088\pi$
$59$	−14.5510	−1.89437	−0.947187	+	0.320681i	$0.896088\pi$
$60$	0.117835	0.0152125
$61$	12.1195	1.55175	0.775874	−	0.630888i	$-0.217309\pi$
$61$	12.1195	1.55175	0.775874	+	0.630888i	$0.217309\pi$
$62$	−7.29893	−0.926965
$63$	0	0
$64$	8.85434	1.10679
$65$	−3.47080	−0.430499
$66$	0.452611	0.0557125
$67$	13.9321	1.70208	0.851039	−	0.525103i	$-0.175973\pi$
$67$	13.9321	1.70208	0.851039	+	0.525103i	$0.175973\pi$
$68$	−0.819110	−0.0993317
$69$	2.30212	0.277143
$70$	0	0
$71$	−13.2480	−1.57225	−0.786123	−	0.618070i	$-0.787915\pi$
$71$	−13.2480	−1.57225	−0.786123	+	0.618070i	$0.787915\pi$
$72$	8.66894	1.02164
$73$	1.52912	0.178970	0.0894851	−	0.995988i	$-0.471478\pi$
$73$	1.52912	0.178970	0.0894851	+	0.995988i	$0.471478\pi$
$74$	10.3896	1.20777
$75$	0.350856	0.0405134
$76$	1.64011	0.188133
$77$	0	0
$78$	1.57092	0.177872
$79$	−7.58240	−0.853087	−0.426543	−	0.904467i	$-0.640269\pi$
$79$	−7.58240	−0.853087	−0.426543	+	0.904467i	$0.640269\pi$
$80$	3.21550	0.359504
$81$	7.90725	0.878584
$82$	7.07228	0.781003
$83$	−6.63351	−0.728123	−0.364061	−	0.931375i	$-0.618610\pi$
$83$	−6.63351	−0.728123	−0.364061	+	0.931375i	$0.618610\pi$
$84$	0	0
$85$	−2.43891	−0.264537
$86$	4.39456	0.473878
$87$	2.42074	0.259530
$88$	−3.01329	−0.321218
$89$	−5.51625	−0.584722	−0.292361	−	0.956308i	$-0.594441\pi$
$89$	−5.51625	−0.584722	−0.292361	+	0.956308i	$0.594441\pi$
$90$	3.71126	0.391201
$91$	0	0
$92$	−2.20367	−0.229748
$93$	−1.98514	−0.205850
$94$	2.43891	0.251554
$95$	4.88344	0.501030
$96$	0.659092	0.0672682
$97$	9.66261	0.981090	0.490545	−	0.871416i	$-0.336798\pi$
$97$	9.66261	0.981090	0.490545	+	0.871416i	$0.336798\pi$
$98$	0	0
$99$	−2.87690	−0.289139
$100$	−0.335851	−0.0335851
$101$	9.62699	0.957922	0.478961	−	0.877836i	$-0.341014\pi$
$101$	9.62699	0.957922	0.478961	+	0.877836i	$0.341014\pi$
$102$	1.10388	0.109300
$103$	14.7598	1.45432	0.727162	−	0.686466i	$-0.240839\pi$
$103$	14.7598	1.45432	0.727162	+	0.686466i	$0.240839\pi$
$104$	−10.4585	−1.02554
$105$	0	0
$106$	11.1042	1.07853
$107$	5.37738	0.519851	0.259925	−	0.965629i	$-0.416302\pi$
$107$	5.37738	0.519851	0.259925	+	0.965629i	$0.416302\pi$
$108$	0.692506	0.0666364
$109$	5.23578	0.501496	0.250748	−	0.968052i	$-0.419323\pi$
$109$	5.23578	0.501496	0.250748	+	0.968052i	$0.419323\pi$
$110$	−1.29002	−0.122998
$111$	2.82574	0.268207
$112$	0	0
$113$	−4.62631	−0.435206	−0.217603	−	0.976037i	$-0.569824\pi$
$113$	−4.62631	−0.435206	−0.217603	+	0.976037i	$0.569824\pi$
$114$	−2.21030	−0.207013
$115$	−6.56144	−0.611858
$116$	−2.31721	−0.215148
$117$	−9.98513	−0.923126
$118$	−18.7710	−1.72801
$119$	0	0
$120$	1.05723	0.0965116
$121$	1.00000	0.0909091
$122$	15.6344	1.41547
$123$	1.92350	0.173436
$124$	1.90024	0.170647
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	12.4647	1.10606	0.553031	−	0.833161i	$-0.313471\pi$
$127$	12.4647	1.10606	0.553031	+	0.833161i	$0.313471\pi$
$128$	7.66521	0.677516
$129$	1.19522	0.105233
$130$	−4.47739	−0.392693
$131$	8.17335	0.714109	0.357054	−	0.934084i	$-0.383781\pi$
$131$	8.17335	0.714109	0.357054	+	0.934084i	$0.383781\pi$
$132$	−0.117835	−0.0102562
$133$	0	0
$134$	17.9727	1.55260
$135$	2.06195	0.177464
$136$	−7.34915	−0.630184
$137$	−13.6170	−1.16338	−0.581689	−	0.813412i	$-0.697608\pi$
$137$	−13.6170	−1.16338	−0.581689	+	0.813412i	$0.697608\pi$
$138$	2.96978	0.252805
$139$	−7.17921	−0.608933	−0.304466	−	0.952523i	$-0.598478\pi$
$139$	−7.17921	−0.608933	−0.304466	+	0.952523i	$0.598478\pi$
$140$	0	0
$141$	0.663328	0.0558623
$142$	−17.0901	−1.43417
$143$	3.47080	0.290243
$144$	9.25068	0.770890
$145$	−6.89952	−0.572974
$146$	1.97260	0.163253
$147$	0	0
$148$	−2.70489	−0.222341
$149$	1.17913	0.0965985	0.0482992	−	0.998833i	$-0.484620\pi$
$149$	1.17913	0.0965985	0.0482992	+	0.998833i	$0.484620\pi$
$150$	0.452611	0.0369555
$151$	3.15888	0.257066	0.128533	−	0.991705i	$-0.458973\pi$
$151$	3.15888	0.257066	0.128533	+	0.991705i	$0.458973\pi$
$152$	14.7152	1.19356
$153$	−7.01650	−0.567251
$154$	0	0
$155$	5.65800	0.454462
$156$	−0.408982	−0.0327448
$157$	−20.2341	−1.61486	−0.807428	−	0.589966i	$-0.799141\pi$
$157$	−20.2341	−1.61486	−0.807428	+	0.589966i	$0.799141\pi$
$158$	−9.78144	−0.778170
$159$	3.02009	0.239509
$160$	−1.87852	−0.148510
$161$	0	0
$162$	10.2005	0.801428
$163$	13.5384	1.06041	0.530204	−	0.847870i	$-0.322115\pi$
$163$	13.5384	1.06041	0.530204	+	0.847870i	$0.322115\pi$
$164$	−1.84124	−0.143777
$165$	−0.350856	−0.0273141
$166$	−8.55736	−0.664180
$167$	7.86088	0.608293	0.304147	−	0.952625i	$-0.401629\pi$
$167$	7.86088	0.608293	0.304147	+	0.952625i	$0.401629\pi$
$168$	0	0
$169$	−0.953575	−0.0733519
$170$	−3.14624	−0.241306
$171$	14.0492	1.07437
$172$	−1.14411	−0.0872372
$173$	−8.07813	−0.614169	−0.307085	−	0.951682i	$-0.599353\pi$
$173$	−8.07813	−0.614169	−0.307085	+	0.951682i	$0.599353\pi$
$174$	3.12280	0.236739
$175$	0	0
$176$	−3.21550	−0.242378
$177$	−5.10529	−0.383737
$178$	−7.11607	−0.533372
$179$	1.17176	0.0875813	0.0437907	−	0.999041i	$-0.486057\pi$
$179$	1.17176	0.0875813	0.0437907	+	0.999041i	$0.486057\pi$
$180$	−0.966209	−0.0720170
$181$	7.58860	0.564056	0.282028	−	0.959406i	$-0.408993\pi$
$181$	7.58860	0.564056	0.282028	+	0.959406i	$0.408993\pi$
$182$	0	0
$183$	4.25221	0.314332
$184$	−19.7715	−1.45758
$185$	−8.05384	−0.592130
$186$	−2.56087	−0.187772
$187$	2.43891	0.178351
$188$	−0.634960	−0.0463092
$189$	0	0
$190$	6.29973	0.457030
$191$	23.8285	1.72417	0.862085	−	0.506765i	$-0.169159\pi$
$191$	23.8285	1.72417	0.862085	+	0.506765i	$0.169159\pi$
$192$	3.10660	0.224199
$193$	−8.90873	−0.641264	−0.320632	−	0.947204i	$-0.603895\pi$
$193$	−8.90873	−0.641264	−0.320632	+	0.947204i	$0.603895\pi$
$194$	12.4650	0.894931
$195$	−1.21775	−0.0872048
$196$	0	0
$197$	1.46195	0.104159	0.0520797	−	0.998643i	$-0.483415\pi$
$197$	1.46195	0.104159	0.0520797	+	0.998643i	$0.483415\pi$
$198$	−3.71126	−0.263747
$199$	−25.3802	−1.79916	−0.899578	−	0.436760i	$-0.856126\pi$
$199$	−25.3802	−1.79916	−0.899578	+	0.436760i	$0.856126\pi$
$200$	−3.01329	−0.213072
$201$	4.88816	0.344784
$202$	12.4190	0.873798
$203$	0	0
$204$	−0.287390	−0.0201213
$205$	−5.48231	−0.382901
$206$	19.0404	1.32661
$207$	−18.8766	−1.31202
$208$	−11.1604	−0.773831
$209$	−4.88344	−0.337795
$210$	0	0
$211$	−16.8558	−1.16040	−0.580201	−	0.814473i	$-0.697026\pi$
$211$	−16.8558	−1.16040	−0.580201	+	0.814473i	$0.697026\pi$
$212$	−2.89093	−0.198550
$213$	−4.64813	−0.318485
$214$	6.93692	0.474198
$215$	−3.40659	−0.232327
$216$	6.21324	0.422758
$217$	0	0
$218$	6.75425	0.457456
$219$	0.536502	0.0362534
$220$	0.335851	0.0226431
$221$	8.46496	0.569415
$222$	3.64526	0.244654
$223$	1.51358	0.101357	0.0506783	−	0.998715i	$-0.483862\pi$
$223$	1.51358	0.101357	0.0506783	+	0.998715i	$0.483862\pi$
$224$	0	0
$225$	−2.87690	−0.191793
$226$	−5.96802	−0.396987
$227$	−20.5890	−1.36654	−0.683270	−	0.730166i	$-0.739443\pi$
$227$	−20.5890	−1.36654	−0.683270	+	0.730166i	$0.739443\pi$
$228$	0.575441	0.0381095
$229$	−13.0140	−0.859992	−0.429996	−	0.902831i	$-0.641485\pi$
$229$	−13.0140	−0.859992	−0.429996	+	0.902831i	$0.641485\pi$
$230$	−8.46439	−0.558125
$231$	0	0
$232$	−20.7903	−1.36495
$233$	−1.25412	−0.0821601	−0.0410801	−	0.999156i	$-0.513080\pi$
$233$	−1.25412	−0.0821601	−0.0410801	+	0.999156i	$0.513080\pi$
$234$	−12.8810	−0.842058
$235$	−1.89060	−0.123329
$236$	4.88695	0.318114
$237$	−2.66033	−0.172807
$238$	0	0
$239$	−7.02554	−0.454444	−0.227222	−	0.973843i	$-0.572964\pi$
$239$	−7.02554	−0.454444	−0.227222	+	0.973843i	$0.572964\pi$
$240$	1.12818	0.0728236
$241$	−4.66269	−0.300350	−0.150175	−	0.988659i	$-0.547984\pi$
$241$	−4.66269	−0.300350	−0.150175	+	0.988659i	$0.547984\pi$
$242$	1.29002	0.0829256
$243$	8.96014	0.574793
$244$	−4.07036	−0.260578
$245$	0	0
$246$	2.48135	0.158205
$247$	−16.9494	−1.07847
$248$	17.0492	1.08263
$249$	−2.32741	−0.147493
$250$	−1.29002	−0.0815880
$251$	−21.9908	−1.38805	−0.694024	−	0.719952i	$-0.744164\pi$
$251$	−21.9908	−1.38805	−0.694024	+	0.719952i	$0.744164\pi$
$252$	0	0
$253$	6.56144	0.412514
$254$	16.0797	1.00893
$255$	−0.855706	−0.0535864
$256$	−7.82040	−0.488775
$257$	−2.80644	−0.175061	−0.0875306	−	0.996162i	$-0.527898\pi$
$257$	−2.80644	−0.175061	−0.0875306	+	0.996162i	$0.527898\pi$
$258$	1.54186	0.0959919
$259$	0	0
$260$	1.16567	0.0722918
$261$	−19.8492	−1.22864
$262$	10.5438	0.651397
$263$	−4.28168	−0.264020	−0.132010	−	0.991248i	$-0.542143\pi$
$263$	−4.28168	−0.264020	−0.132010	+	0.991248i	$0.542143\pi$
$264$	−1.05723	−0.0650681
$265$	−8.60777	−0.528771
$266$	0	0
$267$	−1.93541	−0.118445
$268$	−4.67911	−0.285822
$269$	23.2869	1.41983	0.709914	−	0.704288i	$-0.248734\pi$
$269$	23.2869	1.41983	0.709914	+	0.704288i	$0.248734\pi$
$270$	2.65995	0.161879
$271$	12.7506	0.774545	0.387273	−	0.921965i	$-0.373417\pi$
$271$	12.7506	0.774545	0.387273	+	0.921965i	$0.373417\pi$
$272$	−7.84232	−0.475511
$273$	0	0
$274$	−17.5662	−1.06121
$275$	1.00000	0.0603023
$276$	−0.773170	−0.0465393
$277$	31.6913	1.90415	0.952074	−	0.305867i	$-0.0989464\pi$
$277$	31.6913	1.90415	0.952074	+	0.305867i	$0.0989464\pi$
$278$	−9.26132	−0.555457
$279$	16.2775	0.974509
$280$	0	0
$281$	21.6811	1.29339	0.646694	−	0.762749i	$-0.276151\pi$
$281$	21.6811	1.29339	0.646694	+	0.762749i	$0.276151\pi$
$282$	0.855706	0.0509566
$283$	19.8654	1.18087	0.590437	−	0.807084i	$-0.298956\pi$
$283$	19.8654	1.18087	0.590437	+	0.807084i	$0.298956\pi$
$284$	4.44935	0.264020
$285$	1.71338	0.101492
$286$	4.47739	0.264754
$287$	0	0
$288$	−5.40433	−0.318453
$289$	−11.0517	−0.650101
$290$	−8.90051	−0.522656
$291$	3.39018	0.198736
$292$	−0.513557	−0.0300536
$293$	26.2018	1.53072	0.765362	−	0.643600i	$-0.222560\pi$
$293$	26.2018	1.53072	0.765362	+	0.643600i	$0.222560\pi$
$294$	0	0
$295$	14.5510	0.847190
$296$	−24.2686	−1.41058
$297$	−2.06195	−0.119646
$298$	1.52111	0.0881153
$299$	22.7734	1.31702
$300$	−0.117835	−0.00680322
$301$	0	0
$302$	4.07501	0.234491
$303$	3.37769	0.194043
$304$	15.7027	0.900612
$305$	−12.1195	−0.693962
$306$	−9.05142	−0.517435
$307$	−8.71279	−0.497265	−0.248632	−	0.968598i	$-0.579981\pi$
$307$	−8.71279	−0.497265	−0.248632	+	0.968598i	$0.579981\pi$
$308$	0	0
$309$	5.17855	0.294598
$310$	7.29893	0.414551
$311$	−2.15875	−0.122411	−0.0612057	−	0.998125i	$-0.519495\pi$
$311$	−2.15875	−0.122411	−0.0612057	+	0.998125i	$0.519495\pi$
$312$	−3.66943	−0.207741
$313$	2.33128	0.131772	0.0658860	−	0.997827i	$-0.479013\pi$
$313$	2.33128	0.131772	0.0658860	+	0.997827i	$0.479013\pi$
$314$	−26.1024	−1.47304
$315$	0	0
$316$	2.54656	0.143255
$317$	25.8829	1.45373	0.726863	−	0.686782i	$-0.240977\pi$
$317$	25.8829	1.45373	0.726863	+	0.686782i	$0.240977\pi$
$318$	3.89597	0.218475
$319$	6.89952	0.386299
$320$	−8.85434	−0.494973
$321$	1.88669	0.105305
$322$	0	0
$323$	−11.9103	−0.662705
$324$	−2.65566	−0.147537
$325$	3.47080	0.192525
$326$	17.4648	0.967284
$327$	1.83700	0.101587
$328$	−16.5198	−0.912153
$329$	0	0
$330$	−0.452611	−0.0249154
$331$	3.61441	0.198666	0.0993330	−	0.995054i	$-0.468329\pi$
$331$	3.61441	0.198666	0.0993330	+	0.995054i	$0.468329\pi$
$332$	2.22787	0.122270
$333$	−23.1701	−1.26971
$334$	10.1407	0.554874
$335$	−13.9321	−0.761192
$336$	0	0
$337$	−7.79821	−0.424795	−0.212398	−	0.977183i	$-0.568127\pi$
$337$	−7.79821	−0.424795	−0.212398	+	0.977183i	$0.568127\pi$
$338$	−1.23013	−0.0669102
$339$	−1.62317	−0.0881583
$340$	0.819110	0.0444225
$341$	−5.65800	−0.306398
$342$	18.1237	0.980017
$343$	0	0
$344$	−10.2650	−0.553454
$345$	−2.30212	−0.123942
$346$	−10.4209	−0.560234
$347$	17.8459	0.958017	0.479008	−	0.877810i	$-0.340996\pi$
$347$	17.8459	0.958017	0.479008	+	0.877810i	$0.340996\pi$
$348$	−0.813007	−0.0435817
$349$	−17.0649	−0.913461	−0.456730	−	0.889605i	$-0.650980\pi$
$349$	−17.0649	−0.913461	−0.456730	+	0.889605i	$0.650980\pi$
$350$	0	0
$351$	−7.15659	−0.381991
$352$	1.87852	0.100126
$353$	18.9452	1.00835	0.504175	−	0.863602i	$-0.331797\pi$
$353$	18.9452	1.00835	0.504175	+	0.863602i	$0.331797\pi$
$354$	−6.58593	−0.350038
$355$	13.2480	0.703130
$356$	1.85264	0.0981896
$357$	0	0
$358$	1.51159	0.0798901
$359$	18.9242	0.998784	0.499392	−	0.866376i	$-0.333557\pi$
$359$	18.9242	0.998784	0.499392	+	0.866376i	$0.333557\pi$
$360$	−8.66894	−0.456893
$361$	4.84798	0.255157
$362$	9.78943	0.514521
$363$	0.350856	0.0184152
$364$	0	0
$365$	−1.52912	−0.0800379
$366$	5.48543	0.286728
$367$	3.97470	0.207478	0.103739	−	0.994605i	$-0.466919\pi$
$367$	3.97470	0.207478	0.103739	+	0.994605i	$0.466919\pi$
$368$	−21.0983	−1.09983
$369$	−15.7721	−0.821061
$370$	−10.3896	−0.540130
$371$	0	0
$372$	0.666712	0.0345674
$373$	29.2020	1.51202	0.756011	−	0.654559i	$-0.227145\pi$
$373$	29.2020	1.51202	0.756011	+	0.654559i	$0.227145\pi$
$374$	3.14624	0.162688
$375$	−0.350856	−0.0181181
$376$	−5.69693	−0.293797
$377$	23.9468	1.23332
$378$	0	0
$379$	−19.7847	−1.01627	−0.508135	−	0.861278i	$-0.669665\pi$
$379$	−19.7847	−1.01627	−0.508135	+	0.861278i	$0.669665\pi$
$380$	−1.64011	−0.0841357
$381$	4.37331	0.224051
$382$	30.7392	1.57275
$383$	−35.4585	−1.81185	−0.905923	−	0.423442i	$-0.860822\pi$
$383$	−35.4585	−1.81185	−0.905923	+	0.423442i	$0.860822\pi$
$384$	2.68939	0.137242
$385$	0	0
$386$	−11.4924	−0.584949
$387$	−9.80041	−0.498183
$388$	−3.24520	−0.164750
$389$	−17.8574	−0.905405	−0.452702	−	0.891662i	$-0.649540\pi$
$389$	−17.8574	−0.905405	−0.452702	+	0.891662i	$0.649540\pi$
$390$	−1.57092	−0.0795466
$391$	16.0028	0.809295
$392$	0	0
$393$	2.86767	0.144655
$394$	1.88594	0.0950122
$395$	7.58240	0.381512
$396$	0.966209	0.0485538
$397$	1.38803	0.0696630	0.0348315	−	0.999393i	$-0.488911\pi$
$397$	1.38803	0.0696630	0.0348315	+	0.999393i	$0.488911\pi$
$398$	−32.7410	−1.64116
$399$	0	0
$400$	−3.21550	−0.160775
$401$	−22.1904	−1.10813	−0.554067	−	0.832472i	$-0.686925\pi$
$401$	−22.1904	−1.10813	−0.554067	+	0.832472i	$0.686925\pi$
$402$	6.30582	0.314506
$403$	−19.6378	−0.978227
$404$	−3.23323	−0.160859
$405$	−7.90725	−0.392915
$406$	0	0
$407$	8.05384	0.399214
$408$	−2.57849	−0.127654
$409$	−27.6170	−1.36558	−0.682788	−	0.730617i	$-0.739233\pi$
$409$	−27.6170	−1.36558	−0.682788	+	0.730617i	$0.739233\pi$
$410$	−7.07228	−0.349275
$411$	−4.77760	−0.235662
$412$	−4.95708	−0.244218
$413$	0	0
$414$	−24.3512	−1.19680
$415$	6.63351	0.325626
$416$	6.51998	0.319668
$417$	−2.51887	−0.123350
$418$	−6.29973	−0.308130
$419$	30.2627	1.47843	0.739215	−	0.673470i	$-0.235197\pi$
$419$	30.2627	1.47843	0.739215	+	0.673470i	$0.235197\pi$
$420$	0	0
$421$	−19.2889	−0.940082	−0.470041	−	0.882645i	$-0.655761\pi$
$421$	−19.2889	−0.940082	−0.470041	+	0.882645i	$0.655761\pi$
$422$	−21.7443	−1.05850
$423$	−5.43907	−0.264457
$424$	−25.9377	−1.25965
$425$	2.43891	0.118305
$426$	−5.99618	−0.290516
$427$	0	0
$428$	−1.80600	−0.0872962
$429$	1.21775	0.0587935
$430$	−4.39456	−0.211925
$431$	−29.8047	−1.43564	−0.717820	−	0.696229i	$-0.754860\pi$
$431$	−29.8047	−1.43564	−0.717820	+	0.696229i	$0.754860\pi$
$432$	6.63019	0.318995
$433$	−15.4416	−0.742078	−0.371039	−	0.928617i	$-0.620998\pi$
$433$	−15.4416	−0.742078	−0.371039	+	0.928617i	$0.620998\pi$
$434$	0	0
$435$	−2.42074	−0.116065
$436$	−1.75844	−0.0842140
$437$	−32.0424	−1.53280
$438$	0.692097	0.0330697
$439$	31.8316	1.51924	0.759620	−	0.650367i	$-0.225385\pi$
$439$	31.8316	1.51924	0.759620	+	0.650367i	$0.225385\pi$
$440$	3.01329	0.143653
$441$	0	0
$442$	10.9200	0.519410
$443$	−8.01152	−0.380639	−0.190319	−	0.981722i	$-0.560952\pi$
$443$	−8.01152	−0.380639	−0.190319	+	0.981722i	$0.560952\pi$
$444$	−0.949027	−0.0450388
$445$	5.51625	0.261495
$446$	1.95254	0.0924555
$447$	0.413706	0.0195676
$448$	0	0
$449$	20.0142	0.944530	0.472265	−	0.881457i	$-0.343437\pi$
$449$	20.0142	0.944530	0.472265	+	0.881457i	$0.343437\pi$
$450$	−3.71126	−0.174950
$451$	5.48231	0.258152
$452$	1.55375	0.0730822
$453$	1.10831	0.0520730
$454$	−26.5602	−1.24653
$455$	0	0
$456$	5.16293	0.241776
$457$	−32.2462	−1.50841	−0.754207	−	0.656636i	$-0.771979\pi$
$457$	−32.2462	−1.50841	−0.754207	+	0.656636i	$0.771979\pi$
$458$	−16.7884	−0.784468
$459$	−5.02890	−0.234729
$460$	2.20367	0.102746
$461$	5.79564	0.269930	0.134965	−	0.990850i	$-0.456908\pi$
$461$	5.79564	0.269930	0.134965	+	0.990850i	$0.456908\pi$
$462$	0	0
$463$	12.9058	0.599783	0.299892	−	0.953973i	$-0.403049\pi$
$463$	12.9058	0.599783	0.299892	+	0.953973i	$0.403049\pi$
$464$	−22.1854	−1.02993
$465$	1.98514	0.0920588
$466$	−1.61784	−0.0749449
$467$	12.2821	0.568350	0.284175	−	0.958772i	$-0.408280\pi$
$467$	12.2821	0.568350	0.284175	+	0.958772i	$0.408280\pi$
$468$	3.35352	0.155016
$469$	0	0
$470$	−2.43891	−0.112499
$471$	−7.09925	−0.327116
$472$	43.8463	2.01819
$473$	3.40659	0.156635
$474$	−3.43188	−0.157631
$475$	−4.88344	−0.224068
$476$	0	0
$477$	−24.7637	−1.13385
$478$	−9.06307	−0.414535
$479$	7.70650	0.352119	0.176059	−	0.984380i	$-0.443665\pi$
$479$	7.70650	0.352119	0.176059	+	0.984380i	$0.443665\pi$
$480$	−0.659092	−0.0300833
$481$	27.9532	1.27456
$482$	−6.01496	−0.273974
$483$	0	0
$484$	−0.335851	−0.0152659
$485$	−9.66261	−0.438757
$486$	11.5588	0.524316
$487$	−0.173313	−0.00785358	−0.00392679	−	0.999992i	$-0.501250\pi$
$487$	−0.173313	−0.00785358	−0.00392679	+	0.999992i	$0.501250\pi$
$488$	−36.5197	−1.65317
$489$	4.75002	0.214803
$490$	0	0
$491$	0.789636	0.0356358	0.0178179	−	0.999841i	$-0.494328\pi$
$491$	0.789636	0.0356358	0.0178179	+	0.999841i	$0.494328\pi$
$492$	−0.646009	−0.0291244
$493$	16.8273	0.757864
$494$	−21.8651	−0.983756
$495$	2.87690	0.129307
$496$	18.1933	0.816904
$497$	0	0
$498$	−3.00240	−0.134541
$499$	−21.3761	−0.956926	−0.478463	−	0.878108i	$-0.658806\pi$
$499$	−21.3761	−0.956926	−0.478463	+	0.878108i	$0.658806\pi$
$500$	0.335851	0.0150197
$501$	2.75804	0.123220
$502$	−28.3686	−1.26615
$503$	34.5607	1.54098	0.770492	−	0.637449i	$-0.220010\pi$
$503$	34.5607	1.54098	0.770492	+	0.637449i	$0.220010\pi$
$504$	0	0
$505$	−9.62699	−0.428396
$506$	8.46439	0.376288
$507$	−0.334567	−0.0148587
$508$	−4.18628	−0.185736
$509$	−23.9075	−1.05968	−0.529841	−	0.848097i	$-0.677749\pi$
$509$	−23.9075	−1.05968	−0.529841	+	0.848097i	$0.677749\pi$
$510$	−1.10388	−0.0488805
$511$	0	0
$512$	−25.4189	−1.12337
$513$	10.0694	0.444574
$514$	−3.62037	−0.159688
$515$	−14.7598	−0.650393
$516$	−0.401416	−0.0176714
$517$	1.89060	0.0831485
$518$	0	0
$519$	−2.83426	−0.124410
$520$	10.4585	0.458637
$521$	10.7685	0.471775	0.235888	−	0.971780i	$-0.424200\pi$
$521$	10.7685	0.471775	0.235888	+	0.971780i	$0.424200\pi$
$522$	−25.6059	−1.12074
$523$	−27.2853	−1.19310	−0.596551	−	0.802575i	$-0.703463\pi$
$523$	−27.2853	−1.19310	−0.596551	+	0.802575i	$0.703463\pi$
$524$	−2.74503	−0.119917
$525$	0	0
$526$	−5.52345	−0.240834
$527$	−13.7994	−0.601110
$528$	−1.12818	−0.0490977
$529$	20.0526	0.871850
$530$	−11.1042	−0.482335
$531$	41.8617	1.81664
$532$	0	0
$533$	19.0280	0.824193
$534$	−2.49672	−0.108043
$535$	−5.37738	−0.232484
$536$	−41.9815	−1.81332
$537$	0.411118	0.0177411
$538$	30.0406	1.29514
$539$	0	0
$540$	−0.692506	−0.0298007
$541$	35.3355	1.51919	0.759595	−	0.650396i	$-0.225397\pi$
$541$	35.3355	1.51919	0.759595	+	0.650396i	$0.225397\pi$
$542$	16.4486	0.706526
$543$	2.66250	0.114259
$544$	4.58155	0.196432
$545$	−5.23578	−0.224276
$546$	0	0
$547$	−27.5149	−1.17645	−0.588227	−	0.808696i	$-0.700174\pi$
$547$	−27.5149	−1.17645	−0.588227	+	0.808696i	$0.700174\pi$
$548$	4.57328	0.195361
$549$	−34.8667	−1.48807
$550$	1.29002	0.0550066
$551$	−33.6934	−1.43539
$552$	−6.93697	−0.295257
$553$	0	0
$554$	40.8824	1.73693
$555$	−2.82574	−0.119946
$556$	2.41114	0.102255
$557$	14.2176	0.602420	0.301210	−	0.953558i	$-0.402609\pi$
$557$	14.2176	0.602420	0.301210	+	0.953558i	$0.402609\pi$
$558$	20.9983	0.888929
$559$	11.8236	0.500084
$560$	0	0
$561$	0.855706	0.0361279
$562$	27.9691	1.17980
$563$	14.4565	0.609269	0.304635	−	0.952469i	$-0.401466\pi$
$563$	14.4565	0.609269	0.304635	+	0.952469i	$0.401466\pi$
$564$	−0.222779	−0.00938070
$565$	4.62631	0.194630
$566$	25.6267	1.07717
$567$	0	0
$568$	39.9200	1.67501
$569$	0.918559	0.0385080	0.0192540	−	0.999815i	$-0.493871\pi$
$569$	0.918559	0.0385080	0.0192540	+	0.999815i	$0.493871\pi$
$570$	2.21030	0.0925792
$571$	12.9560	0.542190	0.271095	−	0.962553i	$-0.412614\pi$
$571$	12.9560	0.542190	0.271095	+	0.962553i	$0.412614\pi$
$572$	−1.16567	−0.0487391
$573$	8.36037	0.349259
$574$	0	0
$575$	6.56144	0.273631
$576$	−25.4730	−1.06138
$577$	−6.82850	−0.284274	−0.142137	−	0.989847i	$-0.545397\pi$
$577$	−6.82850	−0.284274	−0.142137	+	0.989847i	$0.545397\pi$
$578$	−14.2569	−0.593010
$579$	−3.12568	−0.129899
$580$	2.31721	0.0962169
$581$	0	0
$582$	4.37340	0.181283
$583$	8.60777	0.356497
$584$	−4.60769	−0.190668
$585$	9.98513	0.412834
$586$	33.8008	1.39630
$587$	26.0505	1.07522	0.537609	−	0.843194i	$-0.319328\pi$
$587$	26.0505	1.07522	0.537609	+	0.843194i	$0.319328\pi$
$588$	0	0
$589$	27.6305	1.13850
$590$	18.7710	0.772791
$591$	0.512933	0.0210992
$592$	−25.8972	−1.06437
$593$	−10.4487	−0.429078	−0.214539	−	0.976715i	$-0.568825\pi$
$593$	−10.4487	−0.429078	−0.214539	+	0.976715i	$0.568825\pi$
$594$	−2.65995	−0.109139
$595$	0	0
$596$	−0.396013	−0.0162213
$597$	−8.90480	−0.364449
$598$	29.3782	1.20136
$599$	7.54353	0.308220	0.154110	−	0.988054i	$-0.450749\pi$
$599$	7.54353	0.308220	0.154110	+	0.988054i	$0.450749\pi$
$600$	−1.05723	−0.0431613
$601$	29.2751	1.19416	0.597078	−	0.802183i	$-0.296328\pi$
$601$	29.2751	1.19416	0.597078	+	0.802183i	$0.296328\pi$
$602$	0	0
$603$	−40.0813	−1.63224
$604$	−1.06091	−0.0431679
$605$	−1.00000	−0.0406558
$606$	4.35728	0.177002
$607$	−22.0831	−0.896324	−0.448162	−	0.893952i	$-0.647921\pi$
$607$	−22.0831	−0.896324	−0.448162	+	0.893952i	$0.647921\pi$
$608$	−9.17366	−0.372041
$609$	0	0
$610$	−15.6344	−0.633019
$611$	6.56189	0.265466
$612$	2.35650	0.0952558
$613$	−27.7813	−1.12208	−0.561038	−	0.827790i	$-0.689598\pi$
$613$	−27.7813	−1.12208	−0.561038	+	0.827790i	$0.689598\pi$
$614$	−11.2397	−0.453596
$615$	−1.92350	−0.0775630
$616$	0	0
$617$	25.3923	1.02226	0.511129	−	0.859504i	$-0.329228\pi$
$617$	25.3923	1.02226	0.511129	+	0.859504i	$0.329228\pi$
$618$	6.68043	0.268726
$619$	−13.0972	−0.526420	−0.263210	−	0.964739i	$-0.584781\pi$
$619$	−13.0972	−0.526420	−0.263210	+	0.964739i	$0.584781\pi$
$620$	−1.90024	−0.0763157
$621$	−13.5293	−0.542914
$622$	−2.78483	−0.111661
$623$	0	0
$624$	−3.91568	−0.156753
$625$	1.00000	0.0400000
$626$	3.00740	0.120200
$627$	−1.71338	−0.0684260
$628$	6.79564	0.271175
$629$	19.6426	0.783202
$630$	0	0
$631$	−11.5720	−0.460676	−0.230338	−	0.973111i	$-0.573983\pi$
$631$	−11.5720	−0.460676	−0.230338	+	0.973111i	$0.573983\pi$
$632$	22.8480	0.908844
$633$	−5.91396	−0.235059
$634$	33.3894	1.32606
$635$	−12.4647	−0.494646
$636$	−1.01430	−0.0402196
$637$	0	0
$638$	8.90051	0.352375
$639$	38.1131	1.50773
$640$	−7.66521	−0.302994
$641$	38.1094	1.50523	0.752615	−	0.658461i	$-0.228792\pi$
$641$	38.1094	1.50523	0.752615	+	0.658461i	$0.228792\pi$
$642$	2.43386	0.0960568
$643$	−27.4359	−1.08197	−0.540983	−	0.841033i	$-0.681948\pi$
$643$	−27.4359	−1.08197	−0.540983	+	0.841033i	$0.681948\pi$
$644$	0	0
$645$	−1.19522	−0.0470618
$646$	−15.3645	−0.604507
$647$	16.9988	0.668291	0.334146	−	0.942521i	$-0.391552\pi$
$647$	16.9988	0.668291	0.334146	+	0.942521i	$0.391552\pi$
$648$	−23.8269	−0.936008
$649$	−14.5510	−0.571175
$650$	4.47739	0.175618
$651$	0	0
$652$	−4.54687	−0.178069
$653$	32.6461	1.27754	0.638770	−	0.769398i	$-0.279444\pi$
$653$	32.6461	1.27754	0.638770	+	0.769398i	$0.279444\pi$
$654$	2.36977	0.0926653
$655$	−8.17335	−0.319359
$656$	−17.6284	−0.688273
$657$	−4.39913	−0.171626
$658$	0	0
$659$	−27.4571	−1.06958	−0.534788	−	0.844986i	$-0.679608\pi$
$659$	−27.4571	−1.06958	−0.534788	+	0.844986i	$0.679608\pi$
$660$	0.117835	0.00458673
$661$	−22.5554	−0.877302	−0.438651	−	0.898658i	$-0.644543\pi$
$661$	−22.5554	−0.877302	−0.438651	+	0.898658i	$0.644543\pi$
$662$	4.66266	0.181219
$663$	2.96998	0.115345
$664$	19.9887	0.775712
$665$	0	0
$666$	−29.8899	−1.15821
$667$	45.2708	1.75289
$668$	−2.64008	−0.102148
$669$	0.531047	0.0205315
$670$	−17.9727	−0.694345
$671$	12.1195	0.467869
$672$	0	0
$673$	14.7077	0.566938	0.283469	−	0.958981i	$-0.408515\pi$
$673$	14.7077	0.566938	0.283469	+	0.958981i	$0.408515\pi$
$674$	−10.0598	−0.387490
$675$	−2.06195	−0.0793643
$676$	0.320259	0.0123176
$677$	−31.1356	−1.19664	−0.598320	−	0.801258i	$-0.704165\pi$
$677$	−31.1356	−1.19664	−0.598320	+	0.801258i	$0.704165\pi$
$678$	−2.09392	−0.0804164
$679$	0	0
$680$	7.34915	0.281827
$681$	−7.22377	−0.276816
$682$	−7.29893	−0.279490
$683$	−8.42769	−0.322477	−0.161238	−	0.986915i	$-0.551549\pi$
$683$	−8.42769	−0.322477	−0.161238	+	0.986915i	$0.551549\pi$
$684$	−4.71843	−0.180413
$685$	13.6170	0.520278
$686$	0	0
$687$	−4.56605	−0.174206
$688$	−10.9539	−0.417613
$689$	29.8758	1.13818
$690$	−2.96978	−0.113058
$691$	26.0643	0.991531	0.495765	−	0.868456i	$-0.334888\pi$
$691$	26.0643	0.991531	0.495765	+	0.868456i	$0.334888\pi$
$692$	2.71305	0.103135
$693$	0	0
$694$	23.0215	0.873885
$695$	7.17921	0.272323
$696$	−7.29439	−0.276493
$697$	13.3709	0.506458
$698$	−22.0140	−0.833242
$699$	−0.440015	−0.0166429
$700$	0	0
$701$	−19.4712	−0.735418	−0.367709	−	0.929941i	$-0.619858\pi$
$701$	−19.4712	−0.735418	−0.367709	+	0.929941i	$0.619858\pi$
$702$	−9.23214	−0.348445
$703$	−39.3305	−1.48338
$704$	8.85434	0.333710
$705$	−0.663328	−0.0249824
$706$	24.4396	0.919797
$707$	0	0
$708$	1.71462	0.0644393
$709$	14.3846	0.540225	0.270112	−	0.962829i	$-0.412939\pi$
$709$	14.3846	0.540225	0.270112	+	0.962829i	$0.412939\pi$
$710$	17.0901	0.641382
$711$	21.8138	0.818082
$712$	16.6221	0.622939
$713$	−37.1247	−1.39033
$714$	0	0
$715$	−3.47080	−0.129800
$716$	−0.393536	−0.0147071
$717$	−2.46495	−0.0920553
$718$	24.4126	0.911072
$719$	31.1328	1.16106	0.580529	−	0.814240i	$-0.302846\pi$
$719$	31.1328	1.16106	0.580529	+	0.814240i	$0.302846\pi$
$720$	−9.25068	−0.344752
$721$	0	0
$722$	6.25399	0.232749
$723$	−1.63593	−0.0608410
$724$	−2.54864	−0.0947193
$725$	6.89952	0.256242
$726$	0.452611	0.0167980
$727$	5.73167	0.212576	0.106288	−	0.994335i	$-0.466103\pi$
$727$	5.73167	0.212576	0.106288	+	0.994335i	$0.466103\pi$
$728$	0	0
$729$	−20.5780	−0.762150
$730$	−1.97260	−0.0730091
$731$	8.30836	0.307296
$732$	−1.42811	−0.0527844
$733$	−43.2728	−1.59832	−0.799159	−	0.601120i	$-0.794721\pi$
$733$	−43.2728	−1.59832	−0.799159	+	0.601120i	$0.794721\pi$
$734$	5.12744	0.189257
$735$	0	0
$736$	12.3258	0.454336
$737$	13.9321	0.513196
$738$	−20.3463	−0.748956
$739$	−13.1491	−0.483698	−0.241849	−	0.970314i	$-0.577754\pi$
$739$	−13.1491	−0.483698	−0.241849	+	0.970314i	$0.577754\pi$
$740$	2.70489	0.0994337
$741$	−5.94681	−0.218461
$742$	0	0
$743$	12.7721	0.468565	0.234282	−	0.972169i	$-0.424726\pi$
$743$	12.7721	0.468565	0.234282	+	0.972169i	$0.424726\pi$
$744$	5.98182	0.219304
$745$	−1.17913	−0.0432002
$746$	37.6711	1.37924
$747$	19.0840	0.698245
$748$	−0.819110	−0.0299496
$749$	0	0
$750$	−0.452611	−0.0165270
$751$	−21.7809	−0.794796	−0.397398	−	0.917646i	$-0.630087\pi$
$751$	−21.7809	−0.794796	−0.397398	+	0.917646i	$0.630087\pi$
$752$	−6.07923	−0.221687
$753$	−7.71561	−0.281172
$754$	30.8919	1.12502
$755$	−3.15888	−0.114963
$756$	0	0
$757$	14.4793	0.526261	0.263130	−	0.964760i	$-0.415245\pi$
$757$	14.4793	0.526261	0.263130	+	0.964760i	$0.415245\pi$
$758$	−25.5226	−0.927022
$759$	2.30212	0.0835617
$760$	−14.7152	−0.533778
$761$	11.9662	0.433775	0.216887	−	0.976197i	$-0.430410\pi$
$761$	11.9662	0.433775	0.216887	+	0.976197i	$0.430410\pi$
$762$	5.64165	0.204376
$763$	0	0
$764$	−8.00282	−0.289532
$765$	7.01650	0.253682
$766$	−45.7422	−1.65273
$767$	−50.5034	−1.82357
$768$	−2.74383	−0.0990096
$769$	−22.7511	−0.820425	−0.410213	−	0.911990i	$-0.634545\pi$
$769$	−22.7511	−0.820425	−0.410213	+	0.911990i	$0.634545\pi$
$770$	0	0
$771$	−0.984658	−0.0354616
$772$	2.99200	0.107685
$773$	−29.8261	−1.07277	−0.536385	−	0.843974i	$-0.680210\pi$
$773$	−29.8261	−1.07277	−0.536385	+	0.843974i	$0.680210\pi$
$774$	−12.6427	−0.454433
$775$	−5.65800	−0.203241
$776$	−29.1163	−1.04521
$777$	0	0
$778$	−23.0363	−0.825893
$779$	−26.7725	−0.959225
$780$	0.408982	0.0146439
$781$	−13.2480	−0.474050
$782$	20.6439	0.738224
$783$	−14.2264	−0.508411
$784$	0	0
$785$	20.2341	0.722186
$786$	3.69935	0.131951
$787$	20.6465	0.735968	0.367984	−	0.929832i	$-0.380048\pi$
$787$	20.6465	0.735968	0.367984	+	0.929832i	$0.380048\pi$
$788$	−0.490996	−0.0174910
$789$	−1.50225	−0.0534816
$790$	9.78144	0.348008
$791$	0	0
$792$	8.66894	0.308037
$793$	42.0644	1.49375
$794$	1.79058	0.0635453
$795$	−3.02009	−0.107111
$796$	8.52397	0.302124
$797$	31.5534	1.11768	0.558840	−	0.829276i	$-0.311247\pi$
$797$	31.5534	1.11768	0.558840	+	0.829276i	$0.311247\pi$
$798$	0	0
$799$	4.61101	0.163126
$800$	1.87852	0.0664159
$801$	15.8697	0.560729
$802$	−28.6260	−1.01082
$803$	1.52912	0.0539616
$804$	−1.64169	−0.0578981
$805$	0	0
$806$	−25.3331	−0.892320
$807$	8.17035	0.287610
$808$	−29.0089	−1.02053
$809$	14.9667	0.526200	0.263100	−	0.964769i	$-0.415255\pi$
$809$	14.9667	0.526200	0.263100	+	0.964769i	$0.415255\pi$
$810$	−10.2005	−0.358409
$811$	10.1647	0.356930	0.178465	−	0.983946i	$-0.442887\pi$
$811$	10.1647	0.356930	0.178465	+	0.983946i	$0.442887\pi$
$812$	0	0
$813$	4.47363	0.156897
$814$	10.3896	0.364156
$815$	−13.5384	−0.474229
$816$	−2.75153	−0.0963227
$817$	−16.6359	−0.582015
$818$	−35.6265	−1.24565
$819$	0	0
$820$	1.84124	0.0642988
$821$	30.2212	1.05473	0.527364	−	0.849640i	$-0.323181\pi$
$821$	30.2212	1.05473	0.527364	+	0.849640i	$0.323181\pi$
$822$	−6.16319	−0.214966
$823$	16.6960	0.581985	0.290992	−	0.956725i	$-0.406015\pi$
$823$	16.6960	0.581985	0.290992	+	0.956725i	$0.406015\pi$
$824$	−44.4755	−1.54938
$825$	0.350856	0.0122152
$826$	0	0
$827$	−1.82575	−0.0634875	−0.0317438	−	0.999496i	$-0.510106\pi$
$827$	−1.82575	−0.0634875	−0.0317438	+	0.999496i	$0.510106\pi$
$828$	6.33973	0.220321
$829$	54.2521	1.88425	0.942126	−	0.335258i	$-0.108824\pi$
$829$	54.2521	1.88425	0.942126	+	0.335258i	$0.108824\pi$
$830$	8.55736	0.297030
$831$	11.1191	0.385717
$832$	30.7316	1.06543
$833$	0	0
$834$	−3.24939	−0.112517
$835$	−7.86088	−0.272037
$836$	1.64011	0.0567243
$837$	11.6665	0.403253
$838$	39.0394	1.34860
$839$	33.4402	1.15448	0.577241	−	0.816574i	$-0.304129\pi$
$839$	33.4402	1.15448	0.577241	+	0.816574i	$0.304129\pi$
$840$	0	0
$841$	18.6034	0.641496
$842$	−24.8830	−0.857525
$843$	7.60696	0.261998
$844$	5.66104	0.194861
$845$	0.953575	0.0328040
$846$	−7.01650	−0.241232
$847$	0	0
$848$	−27.6783	−0.950477
$849$	6.96988	0.239206
$850$	3.14624	0.107915
$851$	52.8448	1.81150
$852$	1.56108	0.0534817
$853$	−42.0235	−1.43886	−0.719428	−	0.694567i	$-0.755596\pi$
$853$	−42.0235	−1.43886	−0.719428	+	0.694567i	$0.755596\pi$
$854$	0	0
$855$	−14.0492	−0.480471
$856$	−16.2036	−0.553828
$857$	19.5171	0.666691	0.333346	−	0.942805i	$-0.391822\pi$
$857$	19.5171	0.666691	0.333346	+	0.942805i	$0.391822\pi$
$858$	1.57092	0.0536303
$859$	−30.9964	−1.05758	−0.528791	−	0.848752i	$-0.677355\pi$
$859$	−30.9964	−1.05758	−0.528791	+	0.848752i	$0.677355\pi$
$860$	1.14411	0.0390137
$861$	0	0
$862$	−38.4486	−1.30956
$863$	−39.0212	−1.32830	−0.664149	−	0.747600i	$-0.731206\pi$
$863$	−39.0212	−1.32830	−0.664149	+	0.747600i	$0.731206\pi$
$864$	−3.87342	−0.131776
$865$	8.07813	0.274665
$866$	−19.9200	−0.676910
$867$	−3.87756	−0.131689
$868$	0	0
$869$	−7.58240	−0.257215
$870$	−3.12280	−0.105873
$871$	48.3555	1.63846
$872$	−15.7769	−0.534274
$873$	−27.7984	−0.940832
$874$	−41.3353	−1.39819
$875$	0	0
$876$	−0.180185	−0.00608787
$877$	−19.9741	−0.674476	−0.337238	−	0.941419i	$-0.609493\pi$
$877$	−19.9741	−0.674476	−0.337238	+	0.941419i	$0.609493\pi$
$878$	41.0634	1.38582
$879$	9.19305	0.310074
$880$	3.21550	0.108395
$881$	−20.5617	−0.692742	−0.346371	−	0.938098i	$-0.612586\pi$
$881$	−20.5617	−0.692742	−0.346371	+	0.938098i	$0.612586\pi$
$882$	0	0
$883$	−42.5960	−1.43347	−0.716735	−	0.697346i	$-0.754364\pi$
$883$	−42.5960	−1.43347	−0.716735	+	0.697346i	$0.754364\pi$
$884$	−2.84296	−0.0956192
$885$	5.10529	0.171613
$886$	−10.3350	−0.347212
$887$	−22.4612	−0.754172	−0.377086	−	0.926178i	$-0.623074\pi$
$887$	−22.4612	−0.754172	−0.377086	+	0.926178i	$0.623074\pi$
$888$	−8.51478	−0.285737
$889$	0	0
$890$	7.11607	0.238531
$891$	7.90725	0.264903
$892$	−0.508336	−0.0170203
$893$	−9.23263	−0.308958
$894$	0.533689	0.0178492
$895$	−1.17176	−0.0391676
$896$	0	0
$897$	7.99020	0.266785
$898$	25.8187	0.861582
$899$	−39.0375	−1.30197
$900$	0.966209	0.0322070
$901$	20.9936	0.699398
$902$	7.07228	0.235481
$903$	0	0
$904$	13.9404	0.463651
$905$	−7.58860	−0.252253
$906$	1.42974	0.0475000
$907$	18.6894	0.620572	0.310286	−	0.950643i	$-0.399575\pi$
$907$	18.6894	0.620572	0.310286	+	0.950643i	$0.399575\pi$
$908$	6.91483	0.229477
$909$	−27.6959	−0.918615
$910$	0	0
$911$	20.8893	0.692094	0.346047	−	0.938217i	$-0.387524\pi$
$911$	20.8893	0.692094	0.346047	+	0.938217i	$0.387524\pi$
$912$	5.50939	0.182434
$913$	−6.63351	−0.219537
$914$	−41.5982	−1.37595
$915$	−4.25221	−0.140574
$916$	4.37078	0.144414
$917$	0	0
$918$	−6.48738	−0.214115
$919$	−13.0488	−0.430439	−0.215220	−	0.976566i	$-0.569047\pi$
$919$	−13.0488	−0.430439	−0.215220	+	0.976566i	$0.569047\pi$
$920$	19.7715	0.651849
$921$	−3.05693	−0.100729
$922$	7.47649	0.246225
$923$	−45.9810	−1.51348
$924$	0	0
$925$	8.05384	0.264809
$926$	16.6487	0.547111
$927$	−42.4624	−1.39465
$928$	12.9609	0.425463
$929$	4.65571	0.152749	0.0763744	−	0.997079i	$-0.475666\pi$
$929$	4.65571	0.152749	0.0763744	+	0.997079i	$0.475666\pi$
$930$	2.56087	0.0839743
$931$	0	0
$932$	0.421197	0.0137968
$933$	−0.757410	−0.0247965
$934$	15.8442	0.518438
$935$	−2.43891	−0.0797609
$936$	30.0881	0.983461
$937$	−25.4926	−0.832806	−0.416403	−	0.909180i	$-0.636709\pi$
$937$	−25.4926	−0.832806	−0.416403	+	0.909180i	$0.636709\pi$
$938$	0	0
$939$	0.817945	0.0266926
$940$	0.634960	0.0207101
$941$	52.1737	1.70081	0.850407	−	0.526125i	$-0.176356\pi$
$941$	52.1737	1.70081	0.850407	+	0.526125i	$0.176356\pi$
$942$	−9.15817	−0.298389
$943$	35.9719	1.17141
$944$	46.7887	1.52284
$945$	0	0
$946$	4.39456	0.142880
$947$	16.3864	0.532485	0.266243	−	0.963906i	$-0.414218\pi$
$947$	16.3864	0.532485	0.266243	+	0.963906i	$0.414218\pi$
$948$	0.893474	0.0290187
$949$	5.30727	0.172281
$950$	−6.29973	−0.204390
$951$	9.08115	0.294477
$952$	0	0
$953$	37.8224	1.22519	0.612593	−	0.790398i	$-0.290126\pi$
$953$	37.8224	1.22519	0.612593	+	0.790398i	$0.290126\pi$
$954$	−31.9456	−1.03428
$955$	−23.8285	−0.771072
$956$	2.35953	0.0763127
$957$	2.42074	0.0782513
$958$	9.94153	0.321196
$959$	0	0
$960$	−3.10660	−0.100265
$961$	1.01298	0.0326768
$962$	36.0602	1.16263
$963$	−15.4702	−0.498520
$964$	1.56597	0.0504365
$965$	8.90873	0.286782
$966$	0	0
$967$	−12.8024	−0.411697	−0.205848	−	0.978584i	$-0.565995\pi$
$967$	−12.8024	−0.411697	−0.205848	+	0.978584i	$0.565995\pi$
$968$	−3.01329	−0.0968509
$969$	−4.17879	−0.134242
$970$	−12.4650	−0.400226
$971$	−58.7860	−1.88653	−0.943267	−	0.332035i	$-0.892265\pi$
$971$	−58.7860	−1.88653	−0.943267	+	0.332035i	$0.892265\pi$
$972$	−3.00927	−0.0965224
$973$	0	0
$974$	−0.223577	−0.00716388
$975$	1.21775	0.0389992
$976$	−38.9704	−1.24741
$977$	39.8191	1.27393	0.636964	−	0.770894i	$-0.280190\pi$
$977$	39.8191	1.27393	0.636964	+	0.770894i	$0.280190\pi$
$978$	6.12761	0.195940
$979$	−5.51625	−0.176300
$980$	0	0
$981$	−15.0628	−0.480918
$982$	1.01864	0.0325063
$983$	−37.2043	−1.18663	−0.593316	−	0.804970i	$-0.702181\pi$
$983$	−37.2043	−1.18663	−0.593316	+	0.804970i	$0.702181\pi$
$984$	−5.79607	−0.184772
$985$	−1.46195	−0.0465815
$986$	21.7076	0.691309
$987$	0	0
$988$	5.69248	0.181102
$989$	22.3521	0.710757
$990$	3.71126	0.117951
$991$	11.3441	0.360356	0.180178	−	0.983634i	$-0.442333\pi$
$991$	11.3441	0.360356	0.180178	+	0.983634i	$0.442333\pi$
$992$	−10.6287	−0.337461
$993$	1.26814	0.0402431
$994$	0	0
$995$	25.3802	0.804607
$996$	0.781662	0.0247679
$997$	−16.0926	−0.509656	−0.254828	−	0.966986i	$-0.582019\pi$
$997$	−16.0926	−0.509656	−0.254828	+	0.966986i	$0.582019\pi$
$998$	−27.5756	−0.872890
$999$	−16.6066	−0.525409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.y.1.7		10
7.2	even	3		385.2.i.d.221.4	✓	20
7.4	even	3		385.2.i.d.331.4	yes	20
7.6	odd	2		2695.2.a.z.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.d.221.4	✓	20	7.2	even	3
385.2.i.d.331.4	yes	20	7.4	even	3
2695.2.a.y.1.7		10	1.1	even	1	trivial
2695.2.a.z.1.7		10	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.29002 q^{2} +0.350856 q^{3} -0.335851 q^{4} -1.00000 q^{5} +0.452611 q^{6} -3.01329 q^{8} -2.87690 q^{9} +O(q^{10})\)	\(q+1.29002 q^{2} +0.350856 q^{3} -0.335851 q^{4} -1.00000 q^{5} +0.452611 q^{6} -3.01329 q^{8} -2.87690 q^{9} -1.29002 q^{10} +1.00000 q^{11} -0.117835 q^{12} +3.47080 q^{13} -0.350856 q^{15} -3.21550 q^{16} +2.43891 q^{17} -3.71126 q^{18} -4.88344 q^{19} +0.335851 q^{20} +1.29002 q^{22} +6.56144 q^{23} -1.05723 q^{24} +1.00000 q^{25} +4.47739 q^{26} -2.06195 q^{27} +6.89952 q^{29} -0.452611 q^{30} -5.65800 q^{31} +1.87852 q^{32} +0.350856 q^{33} +3.14624 q^{34} +0.966209 q^{36} +8.05384 q^{37} -6.29973 q^{38} +1.21775 q^{39} +3.01329 q^{40} +5.48231 q^{41} +3.40659 q^{43} -0.335851 q^{44} +2.87690 q^{45} +8.46439 q^{46} +1.89060 q^{47} -1.12818 q^{48} +1.29002 q^{50} +0.855706 q^{51} -1.16567 q^{52} +8.60777 q^{53} -2.65995 q^{54} -1.00000 q^{55} -1.71338 q^{57} +8.90051 q^{58} -14.5510 q^{59} +0.117835 q^{60} +12.1195 q^{61} -7.29893 q^{62} +8.85434 q^{64} -3.47080 q^{65} +0.452611 q^{66} +13.9321 q^{67} -0.819110 q^{68} +2.30212 q^{69} -13.2480 q^{71} +8.66894 q^{72} +1.52912 q^{73} +10.3896 q^{74} +0.350856 q^{75} +1.64011 q^{76} +1.57092 q^{78} -7.58240 q^{79} +3.21550 q^{80} +7.90725 q^{81} +7.07228 q^{82} -6.63351 q^{83} -2.43891 q^{85} +4.39456 q^{86} +2.42074 q^{87} -3.01329 q^{88} -5.51625 q^{89} +3.71126 q^{90} -2.20367 q^{92} -1.98514 q^{93} +2.43891 q^{94} +4.88344 q^{95} +0.659092 q^{96} +9.66261 q^{97} -2.87690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9	\( 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9} - 3 q^{10} + 10 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{15} + 21 q^{16} - 5 q^{17} + q^{18} + q^{19} - 15 q^{20} + 3 q^{22} + 18 q^{23} + 10 q^{24} + 10 q^{25} + 13 q^{26} - 15 q^{27} + 14 q^{29} - 5 q^{30} + 10 q^{31} + 46 q^{32} - 3 q^{33} - 2 q^{34} + 26 q^{36} + 13 q^{37} + 9 q^{38} + 3 q^{39} - 9 q^{40} - 7 q^{41} + 6 q^{43} + 15 q^{44} - 19 q^{45} + 10 q^{46} + q^{47} - 35 q^{48} + 3 q^{50} + 9 q^{51} - 17 q^{52} + 16 q^{53} + 73 q^{54} - 10 q^{55} + 12 q^{57} - 9 q^{58} + 13 q^{59} + 3 q^{60} + 18 q^{61} + 14 q^{62} + 43 q^{64} + 6 q^{65} + 5 q^{66} + 29 q^{67} + 13 q^{68} + 19 q^{71} - 48 q^{72} - 31 q^{73} - 8 q^{74} - 3 q^{75} - 8 q^{76} + 3 q^{78} - 21 q^{80} + 42 q^{81} + q^{82} - 2 q^{83} + 5 q^{85} + 10 q^{86} - 50 q^{87} + 9 q^{88} + 23 q^{89} - q^{90} + 14 q^{92} + 4 q^{93} - 5 q^{94} - q^{95} + 39 q^{96} - 43 q^{97} + 19 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 3 * q^3 + 15 * q^4 - 10 * q^5 + 5 * q^6 + 9 * q^8 + 19 * q^9 - 3 * q^10 + 10 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^15 + 21 * q^16 - 5 * q^17 + q^18 + q^19 - 15 * q^20 + 3 * q^22 + 18 * q^23 + 10 * q^24 + 10 * q^25 + 13 * q^26 - 15 * q^27 + 14 * q^29 - 5 * q^30 + 10 * q^31 + 46 * q^32 - 3 * q^33 - 2 * q^34 + 26 * q^36 + 13 * q^37 + 9 * q^38 + 3 * q^39 - 9 * q^40 - 7 * q^41 + 6 * q^43 + 15 * q^44 - 19 * q^45 + 10 * q^46 + q^47 - 35 * q^48 + 3 * q^50 + 9 * q^51 - 17 * q^52 + 16 * q^53 + 73 * q^54 - 10 * q^55 + 12 * q^57 - 9 * q^58 + 13 * q^59 + 3 * q^60 + 18 * q^61 + 14 * q^62 + 43 * q^64 + 6 * q^65 + 5 * q^66 + 29 * q^67 + 13 * q^68 + 19 * q^71 - 48 * q^72 - 31 * q^73 - 8 * q^74 - 3 * q^75 - 8 * q^76 + 3 * q^78 - 21 * q^80 + 42 * q^81 + q^82 - 2 * q^83 + 5 * q^85 + 10 * q^86 - 50 * q^87 + 9 * q^88 + 23 * q^89 - q^90 + 14 * q^92 + 4 * q^93 - 5 * q^94 - q^95 + 39 * q^96 - 43 * q^97 + 19 * q^99

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