LMFDB - Embedded newform 2695.2.a.j.1.3

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:	$1$
Dimension:	$4$
Coefficient field:	4.4.1957.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} - x + 1 $ x^4 - 4*x^2 - x + 1
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			1.3
Root			$-1.76401$ 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)

$f(q)$	$=$	$q+0.197126 q^{2} -1.56689 q^{3} -1.96114 q^{4} +1.00000 q^{5} -0.308875 q^{6} -0.780845 q^{8} -0.544860 q^{9} +O(q^{10})$	\(q+0.197126 q^{2} -1.56689 q^{3} -1.96114 q^{4} +1.00000 q^{5} -0.308875 q^{6} -0.780845 q^{8} -0.544860 q^{9} +0.197126 q^{10} +1.00000 q^{11} +3.07289 q^{12} +0.133777 q^{13} -1.56689 q^{15} +3.76836 q^{16} +3.07289 q^{17} -0.107406 q^{18} -6.46714 q^{19} -1.96114 q^{20} +0.197126 q^{22} +4.38176 q^{23} +1.22350 q^{24} +1.00000 q^{25} +0.0263710 q^{26} +5.55440 q^{27} -8.40379 q^{29} -0.308875 q^{30} +0.406740 q^{31} +2.30453 q^{32} -1.56689 q^{33} +0.605747 q^{34} +1.06855 q^{36} -2.73764 q^{37} -1.27484 q^{38} -0.209614 q^{39} -0.780845 q^{40} +9.66615 q^{41} +5.18898 q^{43} -1.96114 q^{44} -0.544860 q^{45} +0.863761 q^{46} +1.83690 q^{47} -5.90460 q^{48} +0.197126 q^{50} -4.81488 q^{51} -0.262356 q^{52} -5.21396 q^{53} +1.09492 q^{54} +1.00000 q^{55} +10.1333 q^{57} -1.65661 q^{58} +14.2162 q^{59} +3.07289 q^{60} +1.37222 q^{61} +0.0801792 q^{62} -7.08243 q^{64} +0.133777 q^{65} -0.308875 q^{66} -14.3886 q^{67} -6.02637 q^{68} -6.86574 q^{69} -6.88011 q^{71} +0.425451 q^{72} -0.396133 q^{73} -0.539662 q^{74} -1.56689 q^{75} +12.6830 q^{76} -0.0413204 q^{78} -13.8753 q^{79} +3.76836 q^{80} -7.06855 q^{81} +1.90545 q^{82} +9.46280 q^{83} +3.07289 q^{85} +1.02288 q^{86} +13.1678 q^{87} -0.780845 q^{88} -13.8460 q^{89} -0.107406 q^{90} -8.59326 q^{92} -0.637317 q^{93} +0.362102 q^{94} -6.46714 q^{95} -3.61095 q^{96} -11.9266 q^{97} -0.544860 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} + 7 q^{6} - 9 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 + 7 * q^6 - 9 * q^8 - q^9	$ 4 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} + 7 q^{6} - 9 q^{8} - q^{9} - 3 q^{10} + 4 q^{11} - 3 q^{12} - 6 q^{13} - 3 q^{15} + 5 q^{16} - 3 q^{17} + q^{18} - 3 q^{19} + 3 q^{20} - 3 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 5 q^{26} + 3 q^{27} - 8 q^{29} + 7 q^{30} + 10 q^{31} + 4 q^{32} - 3 q^{33} + 10 q^{34} - 8 q^{36} - 9 q^{37} - 23 q^{38} - 13 q^{39} - 9 q^{40} + 15 q^{41} - 2 q^{43} + 3 q^{44} - q^{45} + 16 q^{46} - 15 q^{47} - q^{48} - 3 q^{50} + q^{51} - 3 q^{52} - 30 q^{53} - 13 q^{54} + 4 q^{55} - 6 q^{57} - q^{58} + 17 q^{59} - 3 q^{60} + 16 q^{62} + 5 q^{64} - 6 q^{65} + 7 q^{66} - 25 q^{67} - 19 q^{68} + 6 q^{69} - 13 q^{71} + 26 q^{72} + 3 q^{73} - 16 q^{74} - 3 q^{75} + 40 q^{76} - 5 q^{78} - 4 q^{79} + 5 q^{80} - 16 q^{81} - 27 q^{82} + 18 q^{83} - 3 q^{85} - 10 q^{86} + 20 q^{87} - 9 q^{88} + 25 q^{89} + q^{90} - 26 q^{92} + 10 q^{93} + 23 q^{94} - 3 q^{95} - 7 q^{96} - 23 q^{97} - q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 + 7 * q^6 - 9 * q^8 - q^9 - 3 * q^10 + 4 * q^11 - 3 * q^12 - 6 * q^13 - 3 * q^15 + 5 * q^16 - 3 * q^17 + q^18 - 3 * q^19 + 3 * q^20 - 3 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 5 * q^26 + 3 * q^27 - 8 * q^29 + 7 * q^30 + 10 * q^31 + 4 * q^32 - 3 * q^33 + 10 * q^34 - 8 * q^36 - 9 * q^37 - 23 * q^38 - 13 * q^39 - 9 * q^40 + 15 * q^41 - 2 * q^43 + 3 * q^44 - q^45 + 16 * q^46 - 15 * q^47 - q^48 - 3 * q^50 + q^51 - 3 * q^52 - 30 * q^53 - 13 * q^54 + 4 * q^55 - 6 * q^57 - q^58 + 17 * q^59 - 3 * q^60 + 16 * q^62 + 5 * q^64 - 6 * q^65 + 7 * q^66 - 25 * q^67 - 19 * q^68 + 6 * q^69 - 13 * q^71 + 26 * q^72 + 3 * q^73 - 16 * q^74 - 3 * q^75 + 40 * q^76 - 5 * q^78 - 4 * q^79 + 5 * q^80 - 16 * q^81 - 27 * q^82 + 18 * q^83 - 3 * q^85 - 10 * q^86 + 20 * q^87 - 9 * q^88 + 25 * q^89 + q^90 - 26 * q^92 + 10 * q^93 + 23 * q^94 - 3 * q^95 - 7 * q^96 - 23 * q^97 - 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 $

$2$	0.197126	0.139389	0.0696947	−	0.997568i	$-0.477797\pi$
$2$	0.197126	0.139389	0.0696947	+	0.997568i	$0.477797\pi$
$3$	−1.56689	−0.904644	−0.452322	−	0.891855i	$-0.649404\pi$
$3$	−1.56689	−0.904644	−0.452322	+	0.891855i	$0.649404\pi$
$4$	−1.96114	−0.980571
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.308875	−0.126098
$7$	0	0
$7$	0	0
$8$	−0.780845	−0.276070
$9$	−0.544860	−0.181620
$10$	0.197126	0.0623368
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.07289	0.887067
$13$	0.133777	0.0371031	0.0185516	−	0.999828i	$-0.494095\pi$
$13$	0.133777	0.0371031	0.0185516	+	0.999828i	$0.494095\pi$
$14$	0	0
$15$	−1.56689	−0.404569
$16$	3.76836	0.942089
$17$	3.07289	0.745285	0.372643	−	0.927975i	$-0.378452\pi$
$17$	3.07289	0.745285	0.372643	+	0.927975i	$0.378452\pi$
$18$	−0.107406	−0.0253159
$19$	−6.46714	−1.48366	−0.741832	−	0.670586i	$-0.766043\pi$
$19$	−6.46714	−1.48366	−0.741832	+	0.670586i	$0.766043\pi$
$20$	−1.96114	−0.438525
$21$	0	0
$22$	0.197126	0.0420275
$23$	4.38176	0.913661	0.456831	−	0.889554i	$-0.348985\pi$
$23$	4.38176	0.913661	0.456831	+	0.889554i	$0.348985\pi$
$24$	1.22350	0.249745
$25$	1.00000	0.200000
$26$	0.0263710	0.00517178
$27$	5.55440	1.06894
$28$	0	0
$29$	−8.40379	−1.56055	−0.780273	−	0.625440i	$-0.784920\pi$
$29$	−8.40379	−1.56055	−0.780273	+	0.625440i	$0.784920\pi$
$30$	−0.308875	−0.0563926
$31$	0.406740	0.0730527	0.0365264	−	0.999333i	$-0.488371\pi$
$31$	0.406740	0.0730527	0.0365264	+	0.999333i	$0.488371\pi$
$32$	2.30453	0.407388
$33$	−1.56689	−0.272760
$34$	0.605747	0.103885
$35$	0	0
$36$	1.06855	0.178091
$37$	−2.73764	−0.450066	−0.225033	−	0.974351i	$-0.572249\pi$
$37$	−2.73764	−0.450066	−0.225033	+	0.974351i	$0.572249\pi$
$38$	−1.27484	−0.206807
$39$	−0.209614	−0.0335651
$40$	−0.780845	−0.123462
$41$	9.66615	1.50960	0.754799	−	0.655956i	$-0.227734\pi$
$41$	9.66615	1.50960	0.754799	+	0.655956i	$0.227734\pi$
$42$	0	0
$43$	5.18898	0.791312	0.395656	−	0.918399i	$-0.370517\pi$
$43$	5.18898	0.791312	0.395656	+	0.918399i	$0.370517\pi$
$44$	−1.96114	−0.295653
$45$	−0.544860	−0.0812229
$46$	0.863761	0.127355
$47$	1.83690	0.267940	0.133970	−	0.990985i	$-0.457227\pi$
$47$	1.83690	0.267940	0.133970	+	0.990985i	$0.457227\pi$
$48$	−5.90460	−0.852255
$49$	0	0
$50$	0.197126	0.0278779
$51$	−4.81488	−0.674218
$52$	−0.262356	−0.0363822
$53$	−5.21396	−0.716192	−0.358096	−	0.933685i	$-0.616574\pi$
$53$	−5.21396	−0.716192	−0.358096	+	0.933685i	$0.616574\pi$
$54$	1.09492	0.149000
$55$	1.00000	0.134840
$56$	0	0
$57$	10.1333	1.34219
$58$	−1.65661	−0.217523
$59$	14.2162	1.85079	0.925396	−	0.379001i	$-0.123732\pi$
$59$	14.2162	1.85079	0.925396	+	0.379001i	$0.123732\pi$
$60$	3.07289	0.396708
$61$	1.37222	0.175695	0.0878476	−	0.996134i	$-0.472001\pi$
$61$	1.37222	0.175695	0.0878476	+	0.996134i	$0.472001\pi$
$62$	0.0801792	0.0101828
$63$	0	0
$64$	−7.08243	−0.885304
$65$	0.133777	0.0165930
$66$	−0.308875	−0.0380199
$67$	−14.3886	−1.75784	−0.878922	−	0.476966i	$-0.841736\pi$
$67$	−14.3886	−1.75784	−0.878922	+	0.476966i	$0.841736\pi$
$68$	−6.02637	−0.730805
$69$	−6.86574	−0.826538
$70$	0	0
$71$	−6.88011	−0.816518	−0.408259	−	0.912866i	$-0.633864\pi$
$71$	−6.88011	−0.816518	−0.408259	+	0.912866i	$0.633864\pi$
$72$	0.425451	0.0501399
$73$	−0.396133	−0.0463639	−0.0231820	−	0.999731i	$-0.507380\pi$
$73$	−0.396133	−0.0463639	−0.0231820	+	0.999731i	$0.507380\pi$
$74$	−0.539662	−0.0627344
$75$	−1.56689	−0.180929
$76$	12.6830	1.45484
$77$	0	0
$78$	−0.0413204	−0.00467862
$79$	−13.8753	−1.56109	−0.780545	−	0.625099i	$-0.785059\pi$
$79$	−13.8753	−1.56109	−0.780545	+	0.625099i	$0.785059\pi$
$80$	3.76836	0.421315
$81$	−7.06855	−0.785394
$82$	1.90545	0.210422
$83$	9.46280	1.03868	0.519339	−	0.854569i	$-0.326178\pi$
$83$	9.46280	1.03868	0.519339	+	0.854569i	$0.326178\pi$
$84$	0	0
$85$	3.07289	0.333302
$86$	1.02288	0.110300
$87$	13.1678	1.41174
$88$	−0.780845	−0.0832384
$89$	−13.8460	−1.46767	−0.733834	−	0.679328i	$-0.762271\pi$
$89$	−13.8460	−1.46767	−0.733834	+	0.679328i	$0.762271\pi$
$90$	−0.107406	−0.0113216
$91$	0	0
$92$	−8.59326	−0.895909
$93$	−0.637317	−0.0660867
$94$	0.362102	0.0373480
$95$	−6.46714	−0.663515
$96$	−3.61095	−0.368541
$97$	−11.9266	−1.21097	−0.605483	−	0.795859i	$-0.707020\pi$
$97$	−11.9266	−1.21097	−0.605483	+	0.795859i	$0.707020\pi$
$98$	0	0
$99$	−0.544860	−0.0547605
$100$	−1.96114	−0.196114
$101$	−3.46988	−0.345266	−0.172633	−	0.984986i	$-0.555227\pi$
$101$	−3.46988	−0.345266	−0.172633	+	0.984986i	$0.555227\pi$
$102$	−0.949139	−0.0939787
$103$	−4.58950	−0.452217	−0.226108	−	0.974102i	$-0.572600\pi$
$103$	−4.58950	−0.452217	−0.226108	+	0.974102i	$0.572600\pi$
$104$	−0.104459	−0.0102431
$105$	0	0
$106$	−1.02781	−0.0998295
$107$	−11.6757	−1.12873	−0.564366	−	0.825525i	$-0.690879\pi$
$107$	−11.6757	−1.12873	−0.564366	+	0.825525i	$0.690879\pi$
$108$	−10.8930	−1.04818
$109$	13.8144	1.32318	0.661589	−	0.749866i	$-0.269882\pi$
$109$	13.8144	1.32318	0.661589	+	0.749866i	$0.269882\pi$
$110$	0.197126	0.0187953
$111$	4.28958	0.407149
$112$	0	0
$113$	−8.49400	−0.799048	−0.399524	−	0.916723i	$-0.630825\pi$
$113$	−8.49400	−0.799048	−0.399524	+	0.916723i	$0.630825\pi$
$114$	1.99754	0.187087
$115$	4.38176	0.408602
$116$	16.4810	1.53022
$117$	−0.0728899	−0.00673867
$118$	2.80239	0.257981
$119$	0	0
$120$	1.22350	0.111690
$121$	1.00000	0.0909091
$122$	0.270501	0.0244900
$123$	−15.1458	−1.36565
$124$	−0.797675	−0.0716334
$125$	1.00000	0.0894427
$126$	0	0
$127$	−11.3769	−1.00954	−0.504770	−	0.863254i	$-0.668423\pi$
$127$	−11.3769	−1.00954	−0.504770	+	0.863254i	$0.668423\pi$
$128$	−6.00520	−0.530790
$129$	−8.13056	−0.715855
$130$	0.0263710	0.00231289
$131$	−4.54106	−0.396754	−0.198377	−	0.980126i	$-0.563567\pi$
$131$	−4.54106	−0.396754	−0.198377	+	0.980126i	$0.563567\pi$
$132$	3.07289	0.267461
$133$	0	0
$134$	−2.83637	−0.245025
$135$	5.55440	0.478047
$136$	−2.39945	−0.205751
$137$	−11.8766	−1.01469	−0.507344	−	0.861744i	$-0.669373\pi$
$137$	−11.8766	−1.01469	−0.507344	+	0.861744i	$0.669373\pi$
$138$	−1.35342	−0.115211
$139$	−6.54572	−0.555200	−0.277600	−	0.960697i	$-0.589539\pi$
$139$	−6.54572	−0.555200	−0.277600	+	0.960697i	$0.589539\pi$
$140$	0	0
$141$	−2.87823	−0.242390
$142$	−1.35625	−0.113814
$143$	0.133777	0.0111870
$144$	−2.05323	−0.171102
$145$	−8.40379	−0.697897
$146$	−0.0780883	−0.00646263
$147$	0	0
$148$	5.36891	0.441321
$149$	14.1140	1.15626	0.578132	−	0.815943i	$-0.303782\pi$
$149$	14.1140	1.15626	0.578132	+	0.815943i	$0.303782\pi$
$150$	−0.308875	−0.0252195
$151$	−11.0724	−0.901060	−0.450530	−	0.892761i	$-0.648765\pi$
$151$	−11.0724	−0.901060	−0.450530	+	0.892761i	$0.648765\pi$
$152$	5.04984	0.409596
$153$	−1.67429	−0.135359
$154$	0	0
$155$	0.406740	0.0326702
$156$	0.411083	0.0329130
$157$	−11.7684	−0.939217	−0.469609	−	0.882875i	$-0.655605\pi$
$157$	−11.7684	−0.939217	−0.469609	+	0.882875i	$0.655605\pi$
$158$	−2.73518	−0.217599
$159$	8.16969	0.647898
$160$	2.30453	0.182189
$161$	0	0
$162$	−1.39340	−0.109476
$163$	11.3223	0.886829	0.443414	−	0.896317i	$-0.353767\pi$
$163$	11.3223	0.886829	0.443414	+	0.896317i	$0.353767\pi$
$164$	−18.9567	−1.48027
$165$	−1.56689	−0.121982
$166$	1.86537	0.144781
$167$	−0.457021	−0.0353653	−0.0176827	−	0.999844i	$-0.505629\pi$
$167$	−0.457021	−0.0353653	−0.0176827	+	0.999844i	$0.505629\pi$
$168$	0	0
$169$	−12.9821	−0.998623
$170$	0.605747	0.0464587
$171$	3.52369	0.269463
$172$	−10.1763	−0.775937
$173$	−9.08623	−0.690814	−0.345407	−	0.938453i	$-0.612259\pi$
$173$	−9.08623	−0.690814	−0.345407	+	0.938453i	$0.612259\pi$
$174$	2.59572	0.196781
$175$	0	0
$176$	3.76836	0.284051
$177$	−22.2752	−1.67431
$178$	−2.72940	−0.204577
$179$	1.40437	0.104968	0.0524839	−	0.998622i	$-0.483286\pi$
$179$	1.40437	0.104968	0.0524839	+	0.998622i	$0.483286\pi$
$180$	1.06855	0.0796448
$181$	11.8114	0.877934	0.438967	−	0.898503i	$-0.355345\pi$
$181$	11.8114	0.877934	0.438967	+	0.898503i	$0.355345\pi$
$182$	0	0
$183$	−2.15012	−0.158942
$184$	−3.42148	−0.252235
$185$	−2.73764	−0.201276
$186$	−0.125632	−0.00921178
$187$	3.07289	0.224712
$188$	−3.60243	−0.262734
$189$	0	0
$190$	−1.27484	−0.0924869
$191$	18.2429	1.32001	0.660007	−	0.751260i	$-0.270553\pi$
$191$	18.2429	1.32001	0.660007	+	0.751260i	$0.270553\pi$
$192$	11.0974	0.800884
$193$	−27.3438	−1.96825	−0.984125	−	0.177474i	$-0.943207\pi$
$193$	−27.3438	−1.96825	−0.984125	+	0.177474i	$0.943207\pi$
$194$	−2.35105	−0.168796
$195$	−0.209614	−0.0150108
$196$	0	0
$197$	0.779820	0.0555599	0.0277800	−	0.999614i	$-0.491156\pi$
$197$	0.779820	0.0555599	0.0277800	+	0.999614i	$0.491156\pi$
$198$	−0.107406	−0.00763303
$199$	15.5054	1.09915	0.549575	−	0.835444i	$-0.314790\pi$
$199$	15.5054	1.09915	0.549575	+	0.835444i	$0.314790\pi$
$200$	−0.780845	−0.0552141
$201$	22.5453	1.59022
$202$	−0.684004	−0.0481264
$203$	0	0
$204$	9.44265	0.661118
$205$	9.66615	0.675113
$206$	−0.904711	−0.0630342
$207$	−2.38745	−0.165939
$208$	0.504121	0.0349545
$209$	−6.46714	−0.447342
$210$	0	0
$211$	−5.84419	−0.402331	−0.201165	−	0.979557i	$-0.564473\pi$
$211$	−5.84419	−0.402331	−0.201165	+	0.979557i	$0.564473\pi$
$212$	10.2253	0.702277
$213$	10.7804	0.738658
$214$	−2.30159	−0.157333
$215$	5.18898	0.353886
$216$	−4.33713	−0.295104
$217$	0	0
$218$	2.72318	0.184437
$219$	0.620697	0.0419428
$220$	−1.96114	−0.132220
$221$	0.411083	0.0276524
$222$	0.845590	0.0567523
$223$	−26.7600	−1.79199	−0.895993	−	0.444069i	$-0.853534\pi$
$223$	−26.7600	−1.79199	−0.895993	+	0.444069i	$0.853534\pi$
$224$	0	0
$225$	−0.544860	−0.0363240
$226$	−1.67439	−0.111379
$227$	14.2891	0.948401	0.474200	−	0.880417i	$-0.342737\pi$
$227$	14.2891	0.948401	0.474200	+	0.880417i	$0.342737\pi$
$228$	−19.8728	−1.31611
$229$	−6.60907	−0.436739	−0.218370	−	0.975866i	$-0.570074\pi$
$229$	−6.60907	−0.436739	−0.218370	+	0.975866i	$0.570074\pi$
$230$	0.863761	0.0569547
$231$	0	0
$232$	6.56206	0.430820
$233$	−4.55489	−0.298401	−0.149200	−	0.988807i	$-0.547670\pi$
$233$	−4.55489	−0.298401	−0.149200	+	0.988807i	$0.547670\pi$
$234$	−0.0143685	−0.000939299 0
$235$	1.83690	0.119826
$236$	−27.8800	−1.81483
$237$	21.7410	1.41223
$238$	0	0
$239$	−0.249329	−0.0161277	−0.00806387	−	0.999967i	$-0.502567\pi$
$239$	−0.249329	−0.0161277	−0.00806387	+	0.999967i	$0.502567\pi$
$240$	−5.90460	−0.381140
$241$	−23.9846	−1.54498	−0.772491	−	0.635026i	$-0.780989\pi$
$241$	−23.9846	−1.54498	−0.772491	+	0.635026i	$0.780989\pi$
$242$	0.197126	0.0126718
$243$	−5.58758	−0.358443
$244$	−2.69113	−0.172282
$245$	0	0
$246$	−2.98563	−0.190357
$247$	−0.865157	−0.0550486
$248$	−0.317601	−0.0201677
$249$	−14.8272	−0.939633
$250$	0.197126	0.0124674
$251$	−4.49588	−0.283777	−0.141889	−	0.989883i	$-0.545318\pi$
$251$	−4.49588	−0.283777	−0.141889	+	0.989883i	$0.545318\pi$
$252$	0	0
$253$	4.38176	0.275479
$254$	−2.24269	−0.140719
$255$	−4.81488	−0.301519
$256$	12.9811	0.811317
$257$	11.4383	0.713502	0.356751	−	0.934199i	$-0.383884\pi$
$257$	11.4383	0.713502	0.356751	+	0.934199i	$0.383884\pi$
$258$	−1.60275	−0.0997826
$259$	0	0
$260$	−0.262356	−0.0162706
$261$	4.57889	0.283426
$262$	−0.895162	−0.0553033
$263$	15.2541	0.940608	0.470304	−	0.882505i	$-0.344144\pi$
$263$	15.2541	0.940608	0.470304	+	0.882505i	$0.344144\pi$
$264$	1.22350	0.0753011
$265$	−5.21396	−0.320291
$266$	0	0
$267$	21.6951	1.32772
$268$	28.2180	1.72369
$269$	−15.5980	−0.951025	−0.475513	−	0.879709i	$-0.657737\pi$
$269$	−15.5980	−0.951025	−0.475513	+	0.879709i	$0.657737\pi$
$270$	1.09492	0.0666346
$271$	−2.35454	−0.143028	−0.0715140	−	0.997440i	$-0.522783\pi$
$271$	−2.35454	−0.143028	−0.0715140	+	0.997440i	$0.522783\pi$
$272$	11.5797	0.702125
$273$	0	0
$274$	−2.34119	−0.141437
$275$	1.00000	0.0603023
$276$	13.4647	0.810479
$277$	6.18078	0.371367	0.185684	−	0.982610i	$-0.440550\pi$
$277$	6.18078	0.371367	0.185684	+	0.982610i	$0.440550\pi$
$278$	−1.29033	−0.0773890
$279$	−0.221617	−0.0132678
$280$	0	0
$281$	−28.0729	−1.67469	−0.837344	−	0.546676i	$-0.815893\pi$
$281$	−28.0729	−1.67469	−0.837344	+	0.546676i	$0.815893\pi$
$282$	−0.567374	−0.0337866
$283$	21.9487	1.30472	0.652359	−	0.757910i	$-0.273780\pi$
$283$	21.9487	1.30472	0.652359	+	0.757910i	$0.273780\pi$
$284$	13.4929	0.800654
$285$	10.1333	0.600244
$286$	0.0263710	0.00155935
$287$	0	0
$288$	−1.25565	−0.0739897
$289$	−7.55735	−0.444550
$290$	−1.65661	−0.0972794
$291$	18.6877	1.09549
$292$	0.776873	0.0454631
$293$	−17.3888	−1.01587	−0.507934	−	0.861396i	$-0.669590\pi$
$293$	−17.3888	−1.01587	−0.507934	+	0.861396i	$0.669590\pi$
$294$	0	0
$295$	14.2162	0.827700
$296$	2.13768	0.124250
$297$	5.55440	0.322299
$298$	2.78224	0.161171
$299$	0.586180	0.0338997
$300$	3.07289	0.177413
$301$	0	0
$302$	−2.18266	−0.125598
$303$	5.43691	0.312343
$304$	−24.3705	−1.39774
$305$	1.37222	0.0785733
$306$	−0.330048	−0.0188676
$307$	−21.7585	−1.24182	−0.620911	−	0.783881i	$-0.713237\pi$
$307$	−21.7585	−1.24182	−0.620911	+	0.783881i	$0.713237\pi$
$308$	0	0
$309$	7.19123	0.409095
$310$	0.0801792	0.00455387
$311$	5.91869	0.335618	0.167809	−	0.985820i	$-0.446331\pi$
$311$	5.91869	0.335618	0.167809	+	0.985820i	$0.446331\pi$
$312$	0.163676	0.00926634
$313$	−27.9510	−1.57988	−0.789942	−	0.613182i	$-0.789889\pi$
$313$	−27.9510	−1.57988	−0.789942	+	0.613182i	$0.789889\pi$
$314$	−2.31985	−0.130917
$315$	0	0
$316$	27.2114	1.53076
$317$	−25.9376	−1.45680	−0.728399	−	0.685153i	$-0.759735\pi$
$317$	−25.9376	−1.45680	−0.728399	+	0.685153i	$0.759735\pi$
$318$	1.61046	0.0903101
$319$	−8.40379	−0.470522
$320$	−7.08243	−0.395920
$321$	18.2945	1.02110
$322$	0	0
$323$	−19.8728	−1.10575
$324$	13.8624	0.770134
$325$	0.133777	0.00742063
$326$	2.23192	0.123614
$327$	−21.6456	−1.19701
$328$	−7.54777	−0.416756
$329$	0	0
$330$	−0.308875	−0.0170030
$331$	−22.8782	−1.25750	−0.628750	−	0.777607i	$-0.716433\pi$
$331$	−22.8782	−1.25750	−0.628750	+	0.777607i	$0.716433\pi$
$332$	−18.5579	−1.01850
$333$	1.49163	0.0817410
$334$	−0.0900908	−0.00492955
$335$	−14.3886	−0.786131
$336$	0	0
$337$	−17.0705	−0.929891	−0.464945	−	0.885339i	$-0.653926\pi$
$337$	−17.0705	−0.929891	−0.464945	+	0.885339i	$0.653926\pi$
$338$	−2.55911	−0.139197
$339$	13.3092	0.722854
$340$	−6.02637	−0.326826
$341$	0.406740	0.0220262
$342$	0.694611	0.0375603
$343$	0	0
$344$	−4.05179	−0.218458
$345$	−6.86574	−0.369639
$346$	−1.79114	−0.0962920
$347$	28.7693	1.54442	0.772209	−	0.635369i	$-0.219152\pi$
$347$	28.7693	1.54442	0.772209	+	0.635369i	$0.219152\pi$
$348$	−25.8239	−1.38431
$349$	17.4283	0.932915	0.466457	−	0.884544i	$-0.345530\pi$
$349$	17.4283	0.932915	0.466457	+	0.884544i	$0.345530\pi$
$350$	0	0
$351$	0.743053	0.0396612
$352$	2.30453	0.122832
$353$	−14.4872	−0.771078	−0.385539	−	0.922691i	$-0.625985\pi$
$353$	−14.4872	−0.771078	−0.385539	+	0.922691i	$0.625985\pi$
$354$	−4.39103	−0.233381
$355$	−6.88011	−0.365158
$356$	27.1539	1.43915
$357$	0	0
$358$	0.276839	0.0146314
$359$	0.186519	0.00984411	0.00492206	−	0.999988i	$-0.498433\pi$
$359$	0.186519	0.00984411	0.00492206	+	0.999988i	$0.498433\pi$
$360$	0.425451	0.0224233
$361$	22.8239	1.20126
$362$	2.32834	0.122375
$363$	−1.56689	−0.0822403
$364$	0	0
$365$	−0.396133	−0.0207346
$366$	−0.423846	−0.0221548
$367$	27.5782	1.43957	0.719785	−	0.694197i	$-0.244240\pi$
$367$	27.5782	1.43957	0.719785	+	0.694197i	$0.244240\pi$
$368$	16.5121	0.860750
$369$	−5.26670	−0.274173
$370$	−0.539662	−0.0280557
$371$	0	0
$372$	1.24987	0.0648027
$373$	4.81111	0.249110	0.124555	−	0.992213i	$-0.460250\pi$
$373$	4.81111	0.249110	0.124555	+	0.992213i	$0.460250\pi$
$374$	0.605747	0.0313225
$375$	−1.56689	−0.0809138
$376$	−1.43434	−0.0739703
$377$	−1.12424	−0.0579011
$378$	0	0
$379$	24.7198	1.26977	0.634887	−	0.772605i	$-0.281047\pi$
$379$	24.7198	1.26977	0.634887	+	0.772605i	$0.281047\pi$
$380$	12.6830	0.650623
$381$	17.8264	0.913274
$382$	3.59617	0.183996
$383$	27.2881	1.39436	0.697179	−	0.716897i	$-0.254438\pi$
$383$	27.2881	1.39436	0.697179	+	0.716897i	$0.254438\pi$
$384$	9.40948	0.480175
$385$	0	0
$386$	−5.39019	−0.274353
$387$	−2.82727	−0.143718
$388$	23.3898	1.18744
$389$	−16.5520	−0.839221	−0.419611	−	0.907704i	$-0.637833\pi$
$389$	−16.5520	−0.839221	−0.419611	+	0.907704i	$0.637833\pi$
$390$	−0.0413204	−0.00209234
$391$	13.4647	0.680938
$392$	0	0
$393$	7.11533	0.358921
$394$	0.153723	0.00774446
$395$	−13.8753	−0.698141
$396$	1.06855	0.0536965
$397$	23.2029	1.16452	0.582259	−	0.813003i	$-0.302169\pi$
$397$	23.2029	1.16452	0.582259	+	0.813003i	$0.302169\pi$
$398$	3.05653	0.153210
$399$	0	0
$400$	3.76836	0.188418
$401$	14.7190	0.735031	0.367516	−	0.930017i	$-0.380208\pi$
$401$	14.7190	0.735031	0.367516	+	0.930017i	$0.380208\pi$
$402$	4.44427	0.221660
$403$	0.0544126	0.00271049
$404$	6.80492	0.338558
$405$	−7.06855	−0.351239
$406$	0	0
$407$	−2.73764	−0.135700
$408$	3.75967	0.186132
$409$	26.0790	1.28952	0.644762	−	0.764384i	$-0.276957\pi$
$409$	26.0790	1.28952	0.644762	+	0.764384i	$0.276957\pi$
$410$	1.90545	0.0941036
$411$	18.6093	0.917931
$412$	9.00065	0.443430
$413$	0	0
$414$	−0.470629	−0.0231301
$415$	9.46280	0.464511
$416$	0.308294	0.0151154
$417$	10.2564	0.502258
$418$	−1.27484	−0.0623547
$419$	26.2464	1.28222	0.641111	−	0.767448i	$-0.278474\pi$
$419$	26.2464	1.28222	0.641111	+	0.767448i	$0.278474\pi$
$420$	0	0
$421$	18.6916	0.910972	0.455486	−	0.890243i	$-0.349465\pi$
$421$	18.6916	0.910972	0.455486	+	0.890243i	$0.349465\pi$
$422$	−1.15204	−0.0560806
$423$	−1.00086	−0.0486633
$424$	4.07129	0.197719
$425$	3.07289	0.149057
$426$	2.12509	0.102961
$427$	0	0
$428$	22.8977	1.10680
$429$	−0.209614	−0.0101203
$430$	1.02288	0.0493279
$431$	14.0020	0.674451	0.337226	−	0.941424i	$-0.390511\pi$
$431$	14.0020	0.674451	0.337226	+	0.941424i	$0.390511\pi$
$432$	20.9310	1.00704
$433$	−15.7376	−0.756303	−0.378151	−	0.925744i	$-0.623440\pi$
$433$	−15.7376	−0.756303	−0.378151	+	0.925744i	$0.623440\pi$
$434$	0	0
$435$	13.1678	0.631348
$436$	−27.0920	−1.29747
$437$	−28.3375	−1.35557
$438$	0.122356	0.00584638
$439$	14.7059	0.701873	0.350936	−	0.936399i	$-0.385863\pi$
$439$	14.7059	0.701873	0.350936	+	0.936399i	$0.385863\pi$
$440$	−0.780845	−0.0372253
$441$	0	0
$442$	0.0810352	0.00385445
$443$	−8.78224	−0.417257	−0.208628	−	0.977995i	$-0.566900\pi$
$443$	−8.78224	−0.417257	−0.208628	+	0.977995i	$0.566900\pi$
$444$	−8.41248	−0.399239
$445$	−13.8460	−0.656361
$446$	−5.27511	−0.249784
$447$	−22.1151	−1.04601
$448$	0	0
$449$	10.7075	0.505317	0.252658	−	0.967556i	$-0.418695\pi$
$449$	10.7075	0.505317	0.252658	+	0.967556i	$0.418695\pi$
$450$	−0.107406	−0.00506318
$451$	9.66615	0.455161
$452$	16.6579	0.783523
$453$	17.3492	0.815138
$454$	2.81676	0.132197
$455$	0	0
$456$	−7.91253	−0.370538
$457$	29.0361	1.35825	0.679125	−	0.734023i	$-0.262359\pi$
$457$	29.0361	1.35825	0.679125	+	0.734023i	$0.262359\pi$
$458$	−1.30282	−0.0608768
$459$	17.0681	0.796669
$460$	−8.59326	−0.400663
$461$	1.91548	0.0892127	0.0446064	−	0.999005i	$-0.485797\pi$
$461$	1.91548	0.0892127	0.0446064	+	0.999005i	$0.485797\pi$
$462$	0	0
$463$	−8.69638	−0.404155	−0.202077	−	0.979370i	$-0.564769\pi$
$463$	−8.69638	−0.404155	−0.202077	+	0.979370i	$0.564769\pi$
$464$	−31.6685	−1.47017
$465$	−0.637317	−0.0295549
$466$	−0.897888	−0.0415939
$467$	14.7885	0.684330	0.342165	−	0.939640i	$-0.388840\pi$
$467$	14.7885	0.684330	0.342165	+	0.939640i	$0.388840\pi$
$468$	0.142947	0.00660774
$469$	0	0
$470$	0.362102	0.0167025
$471$	18.4397	0.849657
$472$	−11.1007	−0.510949
$473$	5.18898	0.238590
$474$	4.28573	0.196850
$475$	−6.46714	−0.296733
$476$	0	0
$477$	2.84088	0.130075
$478$	−0.0491493	−0.00224804
$479$	−11.6279	−0.531291	−0.265646	−	0.964071i	$-0.585585\pi$
$479$	−11.6279	−0.531291	−0.265646	+	0.964071i	$0.585585\pi$
$480$	−3.61095	−0.164816
$481$	−0.366234	−0.0166989
$482$	−4.72799	−0.215354
$483$	0	0
$484$	−1.96114	−0.0891428
$485$	−11.9266	−0.541560
$486$	−1.10146	−0.0499632
$487$	22.3612	1.01328	0.506641	−	0.862157i	$-0.330887\pi$
$487$	22.3612	1.01328	0.506641	+	0.862157i	$0.330887\pi$
$488$	−1.07149	−0.0485043
$489$	−17.7407	−0.802264
$490$	0	0
$491$	8.82061	0.398069	0.199034	−	0.979993i	$-0.436219\pi$
$491$	8.82061	0.398069	0.199034	+	0.979993i	$0.436219\pi$
$492$	29.7030	1.33912
$493$	−25.8239	−1.16305
$494$	−0.170545	−0.00767319
$495$	−0.544860	−0.0244896
$496$	1.53274	0.0688222
$497$	0	0
$498$	−2.92282	−0.130975
$499$	−27.8906	−1.24855	−0.624276	−	0.781204i	$-0.714606\pi$
$499$	−27.8906	−1.24855	−0.624276	+	0.781204i	$0.714606\pi$
$500$	−1.96114	−0.0877049
$501$	0.716101	0.0319930
$502$	−0.886256	−0.0395555
$503$	−30.7069	−1.36915	−0.684576	−	0.728942i	$-0.740013\pi$
$503$	−30.7069	−1.36915	−0.684576	+	0.728942i	$0.740013\pi$
$504$	0	0
$505$	−3.46988	−0.154408
$506$	0.863761	0.0383989
$507$	20.3415	0.903398
$508$	22.3118	0.989925
$509$	19.9737	0.885320	0.442660	−	0.896690i	$-0.354035\pi$
$509$	19.9737	0.885320	0.442660	+	0.896690i	$0.354035\pi$
$510$	−0.949139	−0.0420286
$511$	0	0
$512$	14.5693	0.643879
$513$	−35.9211	−1.58596
$514$	2.25479	0.0994546
$515$	−4.58950	−0.202237
$516$	15.9452	0.701947
$517$	1.83690	0.0807870
$518$	0	0
$519$	14.2371	0.624940
$520$	−0.104459	−0.00458084
$521$	10.3751	0.454539	0.227270	−	0.973832i	$-0.427020\pi$
$521$	10.3751	0.454539	0.227270	+	0.973832i	$0.427020\pi$
$522$	0.902620	0.0395066
$523$	12.6196	0.551818	0.275909	−	0.961184i	$-0.411021\pi$
$523$	12.6196	0.551818	0.275909	+	0.961184i	$0.411021\pi$
$524$	8.90565	0.389045
$525$	0	0
$526$	3.00698	0.131111
$527$	1.24987	0.0544451
$528$	−5.90460	−0.256965
$529$	−3.80014	−0.165223
$530$	−1.02781	−0.0446451
$531$	−7.74584	−0.336141
$532$	0	0
$533$	1.29311	0.0560109
$534$	4.27667	0.185070
$535$	−11.6757	−0.504784
$536$	11.2352	0.485289
$537$	−2.20050	−0.0949585
$538$	−3.07477	−0.132563
$539$	0	0
$540$	−10.8930	−0.468759
$541$	−2.67220	−0.114887	−0.0574435	−	0.998349i	$-0.518295\pi$
$541$	−2.67220	−0.114887	−0.0574435	+	0.998349i	$0.518295\pi$
$542$	−0.464141	−0.0199366
$543$	−18.5071	−0.794217
$544$	7.08157	0.303620
$545$	13.8144	0.591743
$546$	0	0
$547$	−20.7633	−0.887775	−0.443888	−	0.896082i	$-0.646401\pi$
$547$	−20.7633	−0.887775	−0.443888	+	0.896082i	$0.646401\pi$
$548$	23.2917	0.994973
$549$	−0.747670	−0.0319098
$550$	0.197126	0.00840549
$551$	54.3485	2.31533
$552$	5.36108	0.228183
$553$	0	0
$554$	1.21839	0.0517646
$555$	4.28958	0.182083
$556$	12.8371	0.544413
$557$	−4.65907	−0.197411	−0.0987056	−	0.995117i	$-0.531470\pi$
$557$	−4.65907	−0.197411	−0.0987056	+	0.995117i	$0.531470\pi$
$558$	−0.0436865	−0.00184940
$559$	0.694168	0.0293602
$560$	0	0
$561$	−4.81488	−0.203284
$562$	−5.53390	−0.233434
$563$	−28.7816	−1.21300	−0.606500	−	0.795084i	$-0.707427\pi$
$563$	−28.7816	−1.21300	−0.606500	+	0.795084i	$0.707427\pi$
$564$	5.64461	0.237681
$565$	−8.49400	−0.357345
$566$	4.32668	0.181864
$567$	0	0
$568$	5.37230	0.225417
$569$	29.4306	1.23379	0.616897	−	0.787044i	$-0.288389\pi$
$569$	29.4306	1.23379	0.616897	+	0.787044i	$0.288389\pi$
$570$	1.99754	0.0836677
$571$	37.1221	1.55351	0.776757	−	0.629801i	$-0.216863\pi$
$571$	37.1221	1.55351	0.776757	+	0.629801i	$0.216863\pi$
$572$	−0.262356	−0.0109697
$573$	−28.5847	−1.19414
$574$	0	0
$575$	4.38176	0.182732
$576$	3.85893	0.160789
$577$	−14.6876	−0.611454	−0.305727	−	0.952119i	$-0.598900\pi$
$577$	−14.6876	−0.611454	−0.305727	+	0.952119i	$0.598900\pi$
$578$	−1.48975	−0.0619655
$579$	42.8447	1.78057
$580$	16.4810	0.684337
$581$	0	0
$582$	3.68384	0.152700
$583$	−5.21396	−0.215940
$584$	0.309319	0.0127997
$585$	−0.0728899	−0.00301363
$586$	−3.42780	−0.141601
$587$	42.3211	1.74678	0.873389	−	0.487023i	$-0.161917\pi$
$587$	42.3211	1.74678	0.873389	+	0.487023i	$0.161917\pi$
$588$	0	0
$589$	−2.63045	−0.108386
$590$	2.80239	0.115373
$591$	−1.22189	−0.0502619
$592$	−10.3164	−0.424002
$593$	−24.7463	−1.01621	−0.508105	−	0.861295i	$-0.669654\pi$
$593$	−24.7463	−1.01621	−0.508105	+	0.861295i	$0.669654\pi$
$594$	1.09492	0.0449250
$595$	0	0
$596$	−27.6795	−1.13380
$597$	−24.2953	−0.994339
$598$	0.115552	0.00472526
$599$	−28.9773	−1.18398	−0.591990	−	0.805946i	$-0.701657\pi$
$599$	−28.9773	−1.18398	−0.591990	+	0.805946i	$0.701657\pi$
$600$	1.22350	0.0499491
$601$	7.80190	0.318246	0.159123	−	0.987259i	$-0.449133\pi$
$601$	7.80190	0.318246	0.159123	+	0.987259i	$0.449133\pi$
$602$	0	0
$603$	7.83976	0.319260
$604$	21.7145	0.883552
$605$	1.00000	0.0406558
$606$	1.07176	0.0435372
$607$	−30.6030	−1.24214	−0.621069	−	0.783756i	$-0.713301\pi$
$607$	−30.6030	−1.24214	−0.621069	+	0.783756i	$0.713301\pi$
$608$	−14.9037	−0.604426
$609$	0	0
$610$	0.270501	0.0109523
$611$	0.245736	0.00994142
$612$	3.28353	0.132729
$613$	7.38912	0.298444	0.149222	−	0.988804i	$-0.452323\pi$
$613$	7.38912	0.298444	0.149222	+	0.988804i	$0.452323\pi$
$614$	−4.28917	−0.173097
$615$	−15.1458	−0.610737
$616$	0	0
$617$	−19.0956	−0.768760	−0.384380	−	0.923175i	$-0.625585\pi$
$617$	−19.0956	−0.768760	−0.384380	+	0.923175i	$0.625585\pi$
$618$	1.41758	0.0570235
$619$	−8.50900	−0.342006	−0.171003	−	0.985271i	$-0.554701\pi$
$619$	−8.50900	−0.342006	−0.171003	+	0.985271i	$0.554701\pi$
$620$	−0.797675	−0.0320354
$621$	24.3381	0.976653
$622$	1.16673	0.0467816
$623$	0	0
$624$	−0.789901	−0.0316213
$625$	1.00000	0.0400000
$626$	−5.50988	−0.220219
$627$	10.1333	0.404685
$628$	23.0794	0.920969
$629$	−8.41248	−0.335427
$630$	0	0
$631$	−14.3693	−0.572032	−0.286016	−	0.958225i	$-0.592331\pi$
$631$	−14.3693	−0.572032	−0.286016	+	0.958225i	$0.592331\pi$
$632$	10.8344	0.430971
$633$	9.15720	0.363966
$634$	−5.11298	−0.203062
$635$	−11.3769	−0.451480
$636$	−16.0219	−0.635310
$637$	0	0
$638$	−1.65661	−0.0655858
$639$	3.74869	0.148296
$640$	−6.00520	−0.237376
$641$	−21.2292	−0.838502	−0.419251	−	0.907870i	$-0.637707\pi$
$641$	−21.2292	−0.838502	−0.419251	+	0.907870i	$0.637707\pi$
$642$	3.60633	0.142330
$643$	18.4464	0.727455	0.363727	−	0.931505i	$-0.381504\pi$
$643$	18.4464	0.727455	0.363727	+	0.931505i	$0.381504\pi$
$644$	0	0
$645$	−8.13056	−0.320140
$646$	−3.91745	−0.154130
$647$	−39.3292	−1.54619	−0.773095	−	0.634290i	$-0.781292\pi$
$647$	−39.3292	−1.54619	−0.773095	+	0.634290i	$0.781292\pi$
$648$	5.51944	0.216824
$649$	14.2162	0.558035
$650$	0.0263710	0.00103436
$651$	0	0
$652$	−22.2046	−0.869598
$653$	3.41436	0.133614	0.0668071	−	0.997766i	$-0.478719\pi$
$653$	3.41436	0.133614	0.0668071	+	0.997766i	$0.478719\pi$
$654$	−4.26692	−0.166850
$655$	−4.54106	−0.177434
$656$	36.4255	1.42218
$657$	0.215837	0.00842061
$658$	0	0
$659$	8.15957	0.317852	0.158926	−	0.987291i	$-0.449197\pi$
$659$	8.15957	0.317852	0.158926	+	0.987291i	$0.449197\pi$
$660$	3.07289	0.119612
$661$	−24.2624	−0.943696	−0.471848	−	0.881680i	$-0.656413\pi$
$661$	−24.2624	−0.943696	−0.471848	+	0.881680i	$0.656413\pi$
$662$	−4.50990	−0.175282
$663$	−0.644121	−0.0250156
$664$	−7.38898	−0.286748
$665$	0	0
$666$	0.294040	0.0113938
$667$	−36.8234	−1.42581
$668$	0.896282	0.0346782
$669$	41.9300	1.62111
$670$	−2.83637	−0.109578
$671$	1.37222	0.0529741
$672$	0	0
$673$	24.9624	0.962229	0.481114	−	0.876658i	$-0.340232\pi$
$673$	24.9624	0.962229	0.481114	+	0.876658i	$0.340232\pi$
$674$	−3.36505	−0.129617
$675$	5.55440	0.213789
$676$	25.4597	0.979221
$677$	−4.24060	−0.162980	−0.0814898	−	0.996674i	$-0.525968\pi$
$677$	−4.24060	−0.162980	−0.0814898	+	0.996674i	$0.525968\pi$
$678$	2.62358	0.100758
$679$	0	0
$680$	−2.39945	−0.0920147
$681$	−22.3894	−0.857965
$682$	0.0801792	0.00307022
$683$	−48.1719	−1.84325	−0.921624	−	0.388085i	$-0.873137\pi$
$683$	−48.1719	−1.84325	−0.921624	+	0.388085i	$0.873137\pi$
$684$	−6.91045	−0.264228
$685$	−11.8766	−0.453782
$686$	0	0
$687$	10.3557	0.395093
$688$	19.5539	0.745487
$689$	−0.697509	−0.0265730
$690$	−1.35342	−0.0515237
$691$	0.295046	0.0112241	0.00561204	−	0.999984i	$-0.498214\pi$
$691$	0.295046	0.0112241	0.00561204	+	0.999984i	$0.498214\pi$
$692$	17.8194	0.677391
$693$	0	0
$694$	5.67119	0.215275
$695$	−6.54572	−0.248293
$696$	−10.2820	−0.389739
$697$	29.7030	1.12508
$698$	3.43557	0.130038
$699$	7.13700	0.269946
$700$	0	0
$701$	−14.8184	−0.559684	−0.279842	−	0.960046i	$-0.590282\pi$
$701$	−14.8184	−0.559684	−0.279842	+	0.960046i	$0.590282\pi$
$702$	0.146475	0.00552835
$703$	17.7047	0.667747
$704$	−7.08243	−0.266929
$705$	−2.87823	−0.108400
$706$	−2.85582	−0.107480
$707$	0	0
$708$	43.6848	1.64178
$709$	34.0554	1.27898	0.639488	−	0.768801i	$-0.279146\pi$
$709$	34.0554	1.27898	0.639488	+	0.768801i	$0.279146\pi$
$710$	−1.35625	−0.0508991
$711$	7.56008	0.283525
$712$	10.8116	0.405180
$713$	1.78224	0.0667454
$714$	0	0
$715$	0.133777	0.00500299
$716$	−2.75418	−0.102928
$717$	0.390671	0.0145899
$718$	0.0367679	0.00137216
$719$	−26.7437	−0.997370	−0.498685	−	0.866783i	$-0.666184\pi$
$719$	−26.7437	−0.997370	−0.498685	+	0.866783i	$0.666184\pi$
$720$	−2.05323	−0.0765193
$721$	0	0
$722$	4.49920	0.167443
$723$	37.5811	1.39766
$724$	−23.1638	−0.860876
$725$	−8.40379	−0.312109
$726$	−0.308875	−0.0114634
$727$	−32.6374	−1.21045	−0.605227	−	0.796053i	$-0.706917\pi$
$727$	−32.6374	−1.21045	−0.605227	+	0.796053i	$0.706917\pi$
$728$	0	0
$729$	29.9608	1.10966
$730$	−0.0780883	−0.00289018
$731$	15.9452	0.589753
$732$	4.21669	0.155853
$733$	−19.3614	−0.715130	−0.357565	−	0.933888i	$-0.616393\pi$
$733$	−19.3614	−0.715130	−0.357565	+	0.933888i	$0.616393\pi$
$734$	5.43639	0.200661
$735$	0	0
$736$	10.0979	0.372214
$737$	−14.3886	−0.530010
$738$	−1.03820	−0.0382168
$739$	9.71653	0.357428	0.178714	−	0.983901i	$-0.442806\pi$
$739$	9.71653	0.357428	0.178714	+	0.983901i	$0.442806\pi$
$740$	5.36891	0.197365
$741$	1.35560	0.0497994
$742$	0	0
$743$	24.4343	0.896407	0.448204	−	0.893931i	$-0.352064\pi$
$743$	24.4343	0.896407	0.448204	+	0.893931i	$0.352064\pi$
$744$	0.497646	0.0182446
$745$	14.1140	0.517097
$746$	0.948397	0.0347233
$747$	−5.15590	−0.188645
$748$	−6.02637	−0.220346
$749$	0	0
$750$	−0.308875	−0.0112785
$751$	−30.2712	−1.10461	−0.552307	−	0.833641i	$-0.686252\pi$
$751$	−30.2712	−1.10461	−0.552307	+	0.833641i	$0.686252\pi$
$752$	6.92211	0.252424
$753$	7.04454	0.256717
$754$	−0.221617	−0.00807080
$755$	−11.0724	−0.402966
$756$	0	0
$757$	−30.0921	−1.09371	−0.546857	−	0.837226i	$-0.684176\pi$
$757$	−30.0921	−1.09371	−0.546857	+	0.837226i	$0.684176\pi$
$758$	4.87293	0.176993
$759$	−6.86574	−0.249210
$760$	5.04984	0.183177
$761$	35.6872	1.29366	0.646831	−	0.762633i	$-0.276094\pi$
$761$	35.6872	1.29366	0.646831	+	0.762633i	$0.276094\pi$
$762$	3.51405	0.127301
$763$	0	0
$764$	−35.7770	−1.29437
$765$	−1.67429	−0.0605343
$766$	5.37921	0.194359
$767$	1.90181	0.0686702
$768$	−20.3399	−0.733953
$769$	14.5638	0.525183	0.262591	−	0.964907i	$-0.415423\pi$
$769$	14.5638	0.525183	0.262591	+	0.964907i	$0.415423\pi$
$770$	0	0
$771$	−17.9226	−0.645465
$772$	53.6251	1.93001
$773$	−21.0270	−0.756289	−0.378145	−	0.925747i	$-0.623438\pi$
$773$	−21.0270	−0.756289	−0.378145	+	0.925747i	$0.623438\pi$
$774$	−0.557329	−0.0200328
$775$	0.406740	0.0146105
$776$	9.31285	0.334312
$777$	0	0
$778$	−3.26284	−0.116979
$779$	−62.5124	−2.23974
$780$	0.411083	0.0147191
$781$	−6.88011	−0.246190
$782$	2.65424	0.0949155
$783$	−46.6780	−1.66814
$784$	0	0
$785$	−11.7684	−0.420031
$786$	1.40262	0.0500298
$787$	−35.7416	−1.27405	−0.637025	−	0.770843i	$-0.719835\pi$
$787$	−35.7416	−1.27405	−0.637025	+	0.770843i	$0.719835\pi$
$788$	−1.52934	−0.0544804
$789$	−23.9015	−0.850915
$790$	−2.73518	−0.0973134
$791$	0	0
$792$	0.425451	0.0151178
$793$	0.183572	0.00651885
$794$	4.57389	0.162321
$795$	8.16969	0.289749
$796$	−30.4083	−1.07779
$797$	29.7509	1.05383	0.526915	−	0.849918i	$-0.323349\pi$
$797$	29.7509	1.05383	0.526915	+	0.849918i	$0.323349\pi$
$798$	0	0
$799$	5.64461	0.199692
$800$	2.30453	0.0814775
$801$	7.54411	0.266558
$802$	2.90150	0.102456
$803$	−0.396133	−0.0139792
$804$	−44.2145	−1.55932
$805$	0	0
$806$	0.0107262	0.000377813 0
$807$	24.4403	0.860339
$808$	2.70944	0.0953177
$809$	8.52272	0.299643	0.149821	−	0.988713i	$-0.452130\pi$
$809$	8.52272	0.299643	0.149821	+	0.988713i	$0.452130\pi$
$810$	−1.39340	−0.0489590
$811$	−32.0970	−1.12708	−0.563538	−	0.826090i	$-0.690560\pi$
$811$	−32.0970	−1.12708	−0.563538	+	0.826090i	$0.690560\pi$
$812$	0	0
$813$	3.68930	0.129389
$814$	−0.539662	−0.0189151
$815$	11.3223	0.396602
$816$	−18.1442	−0.635173
$817$	−33.5579	−1.17404
$818$	5.14086	0.179746
$819$	0	0
$820$	−18.9567	−0.661996
$821$	−56.6538	−1.97723	−0.988615	−	0.150468i	$-0.951922\pi$
$821$	−56.6538	−1.97723	−0.988615	+	0.150468i	$0.951922\pi$
$822$	3.66839	0.127950
$823$	−48.5525	−1.69243	−0.846216	−	0.532839i	$-0.821125\pi$
$823$	−48.5525	−1.69243	−0.846216	+	0.532839i	$0.821125\pi$
$824$	3.58369	0.124844
$825$	−1.56689	−0.0545521
$826$	0	0
$827$	0.858467	0.0298518	0.0149259	−	0.999889i	$-0.495249\pi$
$827$	0.858467	0.0298518	0.0149259	+	0.999889i	$0.495249\pi$
$828$	4.68212	0.162715
$829$	32.4396	1.12667	0.563337	−	0.826227i	$-0.309517\pi$
$829$	32.4396	1.12667	0.563337	+	0.826227i	$0.309517\pi$
$830$	1.86537	0.0647478
$831$	−9.68460	−0.335955
$832$	−0.947468	−0.0328475
$833$	0	0
$834$	2.02181	0.0700095
$835$	−0.457021	−0.0158159
$836$	12.6830	0.438650
$837$	2.25920	0.0780893
$838$	5.17386	0.178728
$839$	−6.48494	−0.223885	−0.111943	−	0.993715i	$-0.535707\pi$
$839$	−6.48494	−0.223885	−0.111943	+	0.993715i	$0.535707\pi$
$840$	0	0
$841$	41.6237	1.43530
$842$	3.68460	0.126980
$843$	43.9871	1.51500
$844$	11.4613	0.394514
$845$	−12.9821	−0.446598
$846$	−0.197295	−0.00678314
$847$	0	0
$848$	−19.6481	−0.674717
$849$	−34.3912	−1.18030
$850$	0.605747	0.0207770
$851$	−11.9957	−0.411208
$852$	−21.1418	−0.724306
$853$	−6.35786	−0.217689	−0.108844	−	0.994059i	$-0.534715\pi$
$853$	−6.35786	−0.217689	−0.108844	+	0.994059i	$0.534715\pi$
$854$	0	0
$855$	3.52369	0.120508
$856$	9.11691	0.311609
$857$	−2.41435	−0.0824725	−0.0412362	−	0.999149i	$-0.513130\pi$
$857$	−2.41435	−0.0824725	−0.0412362	+	0.999149i	$0.513130\pi$
$858$	−0.0413204	−0.00141066
$859$	−8.65285	−0.295231	−0.147616	−	0.989045i	$-0.547160\pi$
$859$	−8.65285	−0.295231	−0.147616	+	0.989045i	$0.547160\pi$
$860$	−10.1763	−0.347010
$861$	0	0
$862$	2.76016	0.0940113
$863$	−17.6543	−0.600960	−0.300480	−	0.953788i	$-0.597147\pi$
$863$	−17.6543	−0.600960	−0.300480	+	0.953788i	$0.597147\pi$
$864$	12.8003	0.435475
$865$	−9.08623	−0.308941
$866$	−3.10230	−0.105421
$867$	11.8415	0.402159
$868$	0	0
$869$	−13.8753	−0.470687
$870$	2.59572	0.0880032
$871$	−1.92486	−0.0652215
$872$	−10.7869	−0.365291
$873$	6.49834	0.219936
$874$	−5.58607	−0.188951
$875$	0	0
$876$	−1.21727	−0.0411279
$877$	−27.1270	−0.916015	−0.458007	−	0.888948i	$-0.651437\pi$
$877$	−27.1270	−0.916015	−0.458007	+	0.888948i	$0.651437\pi$
$878$	2.89891	0.0978336
$879$	27.2464	0.918998
$880$	3.76836	0.127031
$881$	−38.7669	−1.30609	−0.653045	−	0.757319i	$-0.726509\pi$
$881$	−38.7669	−1.30609	−0.653045	+	0.757319i	$0.726509\pi$
$882$	0	0
$883$	−3.72070	−0.125211	−0.0626057	−	0.998038i	$-0.519941\pi$
$883$	−3.72070	−0.125211	−0.0626057	+	0.998038i	$0.519941\pi$
$884$	−0.806191	−0.0271152
$885$	−22.2752	−0.748773
$886$	−1.73121	−0.0581612
$887$	−34.1769	−1.14755	−0.573773	−	0.819014i	$-0.694521\pi$
$887$	−34.1769	−1.14755	−0.573773	+	0.819014i	$0.694521\pi$
$888$	−3.34950	−0.112402
$889$	0	0
$890$	−2.72940	−0.0914898
$891$	−7.06855	−0.236805
$892$	52.4802	1.75717
$893$	−11.8795	−0.397533
$894$	−4.35946	−0.145802
$895$	1.40437	0.0469431
$896$	0	0
$897$	−0.918480	−0.0306671
$898$	2.11072	0.0704358
$899$	−3.41816	−0.114002
$900$	1.06855	0.0356182
$901$	−16.0219	−0.533767
$902$	1.90545	0.0634446
$903$	0	0
$904$	6.63250	0.220594
$905$	11.8114	0.392624
$906$	3.41999	0.113622
$907$	41.7341	1.38576	0.692879	−	0.721054i	$-0.256342\pi$
$907$	41.7341	1.38576	0.692879	+	0.721054i	$0.256342\pi$
$908$	−28.0229	−0.929974
$909$	1.89060	0.0627072
$910$	0	0
$911$	54.2838	1.79850	0.899252	−	0.437431i	$-0.144111\pi$
$911$	54.2838	1.79850	0.899252	+	0.437431i	$0.144111\pi$
$912$	38.1859	1.26446
$913$	9.46280	0.313173
$914$	5.72377	0.189326
$915$	−2.15012	−0.0710808
$916$	12.9613	0.428254
$917$	0	0
$918$	3.36456	0.111047
$919$	57.3940	1.89325	0.946626	−	0.322333i	$-0.104467\pi$
$919$	57.3940	1.89325	0.946626	+	0.322333i	$0.104467\pi$
$920$	−3.42148	−0.112803
$921$	34.0931	1.12341
$922$	0.377591	0.0124353
$923$	−0.920402	−0.0302954
$924$	0	0
$925$	−2.73764	−0.0900132
$926$	−1.71428	−0.0563349
$927$	2.50063	0.0821316
$928$	−19.3668	−0.635747
$929$	38.0809	1.24939	0.624697	−	0.780867i	$-0.285222\pi$
$929$	38.0809	1.24939	0.624697	+	0.780867i	$0.285222\pi$
$930$	−0.125632	−0.00411963
$931$	0	0
$932$	8.93277	0.292603
$933$	−9.27393	−0.303615
$934$	2.91520	0.0953884
$935$	3.07289	0.100494
$936$	0.0569157	0.00186035
$937$	−52.9911	−1.73114	−0.865572	−	0.500785i	$-0.833045\pi$
$937$	−52.9911	−1.73114	−0.865572	+	0.500785i	$0.833045\pi$
$938$	0	0
$939$	43.7961	1.42923
$940$	−3.60243	−0.117498
$941$	−56.4978	−1.84178	−0.920888	−	0.389826i	$-0.872535\pi$
$941$	−56.4978	−1.84178	−0.920888	+	0.389826i	$0.872535\pi$
$942$	3.63495	0.118433
$943$	42.3548	1.37926
$944$	53.5718	1.74361
$945$	0	0
$946$	1.02288	0.0332568
$947$	20.1080	0.653422	0.326711	−	0.945124i	$-0.394060\pi$
$947$	20.1080	0.653422	0.326711	+	0.945124i	$0.394060\pi$
$948$	−42.6372	−1.38479
$949$	−0.0529936	−0.00172025
$950$	−1.27484	−0.0413614
$951$	40.6413	1.31788
$952$	0	0
$953$	−16.9646	−0.549536	−0.274768	−	0.961510i	$-0.588601\pi$
$953$	−16.9646	−0.549536	−0.274768	+	0.961510i	$0.588601\pi$
$954$	0.560011	0.0181310
$955$	18.2429	0.590328
$956$	0.488969	0.0158144
$957$	13.1678	0.425655
$958$	−2.29216	−0.0740563
$959$	0	0
$960$	11.0974	0.358166
$961$	−30.8346	−0.994663
$962$	−0.0721944	−0.00232764
$963$	6.36162	0.205000
$964$	47.0371	1.51496
$965$	−27.3438	−0.880229
$966$	0	0
$967$	53.0713	1.70666	0.853330	−	0.521372i	$-0.174580\pi$
$967$	53.0713	1.70666	0.853330	+	0.521372i	$0.174580\pi$
$968$	−0.780845	−0.0250973
$969$	31.1385	1.00031
$970$	−2.35105	−0.0754877
$971$	−4.43177	−0.142222	−0.0711111	−	0.997468i	$-0.522654\pi$
$971$	−4.43177	−0.142222	−0.0711111	+	0.997468i	$0.522654\pi$
$972$	10.9580	0.351479
$973$	0	0
$974$	4.40798	0.141241
$975$	−0.209614	−0.00671302
$976$	5.17103	0.165521
$977$	−0.543835	−0.0173988	−0.00869942	−	0.999962i	$-0.502769\pi$
$977$	−0.543835	−0.0173988	−0.00869942	+	0.999962i	$0.502769\pi$
$978$	−3.49717	−0.111827
$979$	−13.8460	−0.442519
$980$	0	0
$981$	−7.52691	−0.240316
$982$	1.73878	0.0554865
$983$	−58.4810	−1.86525	−0.932627	−	0.360841i	$-0.882490\pi$
$983$	−58.4810	−1.86525	−0.932627	+	0.360841i	$0.882490\pi$
$984$	11.8265	0.377015
$985$	0.779820	0.0248471
$986$	−5.09058	−0.162117
$987$	0	0
$988$	1.69669	0.0539790
$989$	22.7369	0.722991
$990$	−0.107406	−0.00341359
$991$	−47.4092	−1.50600	−0.753002	−	0.658018i	$-0.771395\pi$
$991$	−47.4092	−1.50600	−0.753002	+	0.658018i	$0.771395\pi$
$992$	0.937346	0.0297608
$993$	35.8476	1.13759
$994$	0	0
$995$	15.5054	0.491555
$996$	29.0781	0.921376
$997$	−50.0169	−1.58405	−0.792026	−	0.610487i	$-0.790974\pi$
$997$	−50.0169	−1.58405	−0.792026	+	0.610487i	$0.790974\pi$
$998$	−5.49796	−0.174035
$999$	−15.2060	−0.481096

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.j.1.3		4
7.2	even	3		385.2.i.a.221.2	✓	8
7.4	even	3		385.2.i.a.331.2	yes	8
7.6	odd	2		2695.2.a.k.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.a.221.2	✓	8	7.2	even	3
385.2.i.a.331.2	yes	8	7.4	even	3
2695.2.a.j.1.3		4	1.1	even	1	trivial
2695.2.a.k.1.3		4	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)

\(f(q)\)	\(=\)	\(q+0.197126 q^{2} -1.56689 q^{3} -1.96114 q^{4} +1.00000 q^{5} -0.308875 q^{6} -0.780845 q^{8} -0.544860 q^{9} +O(q^{10})\)	\(q+0.197126 q^{2} -1.56689 q^{3} -1.96114 q^{4} +1.00000 q^{5} -0.308875 q^{6} -0.780845 q^{8} -0.544860 q^{9} +0.197126 q^{10} +1.00000 q^{11} +3.07289 q^{12} +0.133777 q^{13} -1.56689 q^{15} +3.76836 q^{16} +3.07289 q^{17} -0.107406 q^{18} -6.46714 q^{19} -1.96114 q^{20} +0.197126 q^{22} +4.38176 q^{23} +1.22350 q^{24} +1.00000 q^{25} +0.0263710 q^{26} +5.55440 q^{27} -8.40379 q^{29} -0.308875 q^{30} +0.406740 q^{31} +2.30453 q^{32} -1.56689 q^{33} +0.605747 q^{34} +1.06855 q^{36} -2.73764 q^{37} -1.27484 q^{38} -0.209614 q^{39} -0.780845 q^{40} +9.66615 q^{41} +5.18898 q^{43} -1.96114 q^{44} -0.544860 q^{45} +0.863761 q^{46} +1.83690 q^{47} -5.90460 q^{48} +0.197126 q^{50} -4.81488 q^{51} -0.262356 q^{52} -5.21396 q^{53} +1.09492 q^{54} +1.00000 q^{55} +10.1333 q^{57} -1.65661 q^{58} +14.2162 q^{59} +3.07289 q^{60} +1.37222 q^{61} +0.0801792 q^{62} -7.08243 q^{64} +0.133777 q^{65} -0.308875 q^{66} -14.3886 q^{67} -6.02637 q^{68} -6.86574 q^{69} -6.88011 q^{71} +0.425451 q^{72} -0.396133 q^{73} -0.539662 q^{74} -1.56689 q^{75} +12.6830 q^{76} -0.0413204 q^{78} -13.8753 q^{79} +3.76836 q^{80} -7.06855 q^{81} +1.90545 q^{82} +9.46280 q^{83} +3.07289 q^{85} +1.02288 q^{86} +13.1678 q^{87} -0.780845 q^{88} -13.8460 q^{89} -0.107406 q^{90} -8.59326 q^{92} -0.637317 q^{93} +0.362102 q^{94} -6.46714 q^{95} -3.61095 q^{96} -11.9266 q^{97} -0.544860 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} + 7 q^{6} - 9 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 + 7 * q^6 - 9 * q^8 - q^9	\( 4 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 4 q^{5} + 7 q^{6} - 9 q^{8} - q^{9} - 3 q^{10} + 4 q^{11} - 3 q^{12} - 6 q^{13} - 3 q^{15} + 5 q^{16} - 3 q^{17} + q^{18} - 3 q^{19} + 3 q^{20} - 3 q^{22} - 6 q^{23} - 4 q^{24} + 4 q^{25} - 5 q^{26} + 3 q^{27} - 8 q^{29} + 7 q^{30} + 10 q^{31} + 4 q^{32} - 3 q^{33} + 10 q^{34} - 8 q^{36} - 9 q^{37} - 23 q^{38} - 13 q^{39} - 9 q^{40} + 15 q^{41} - 2 q^{43} + 3 q^{44} - q^{45} + 16 q^{46} - 15 q^{47} - q^{48} - 3 q^{50} + q^{51} - 3 q^{52} - 30 q^{53} - 13 q^{54} + 4 q^{55} - 6 q^{57} - q^{58} + 17 q^{59} - 3 q^{60} + 16 q^{62} + 5 q^{64} - 6 q^{65} + 7 q^{66} - 25 q^{67} - 19 q^{68} + 6 q^{69} - 13 q^{71} + 26 q^{72} + 3 q^{73} - 16 q^{74} - 3 q^{75} + 40 q^{76} - 5 q^{78} - 4 q^{79} + 5 q^{80} - 16 q^{81} - 27 q^{82} + 18 q^{83} - 3 q^{85} - 10 q^{86} + 20 q^{87} - 9 q^{88} + 25 q^{89} + q^{90} - 26 q^{92} + 10 q^{93} + 23 q^{94} - 3 q^{95} - 7 q^{96} - 23 q^{97} - q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 4 * q^5 + 7 * q^6 - 9 * q^8 - q^9 - 3 * q^10 + 4 * q^11 - 3 * q^12 - 6 * q^13 - 3 * q^15 + 5 * q^16 - 3 * q^17 + q^18 - 3 * q^19 + 3 * q^20 - 3 * q^22 - 6 * q^23 - 4 * q^24 + 4 * q^25 - 5 * q^26 + 3 * q^27 - 8 * q^29 + 7 * q^30 + 10 * q^31 + 4 * q^32 - 3 * q^33 + 10 * q^34 - 8 * q^36 - 9 * q^37 - 23 * q^38 - 13 * q^39 - 9 * q^40 + 15 * q^41 - 2 * q^43 + 3 * q^44 - q^45 + 16 * q^46 - 15 * q^47 - q^48 - 3 * q^50 + q^51 - 3 * q^52 - 30 * q^53 - 13 * q^54 + 4 * q^55 - 6 * q^57 - q^58 + 17 * q^59 - 3 * q^60 + 16 * q^62 + 5 * q^64 - 6 * q^65 + 7 * q^66 - 25 * q^67 - 19 * q^68 + 6 * q^69 - 13 * q^71 + 26 * q^72 + 3 * q^73 - 16 * q^74 - 3 * q^75 + 40 * q^76 - 5 * q^78 - 4 * q^79 + 5 * q^80 - 16 * q^81 - 27 * q^82 + 18 * q^83 - 3 * q^85 - 10 * q^86 + 20 * q^87 - 9 * q^88 + 25 * q^89 + q^90 - 26 * q^92 + 10 * q^93 + 23 * q^94 - 3 * q^95 - 7 * q^96 - 23 * q^97 - q^99

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