LMFDB - Embedded newform 2695.2.a.f.1.1

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:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ 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)

$f(q)$	$=$	$q-0.414214 q^{2} -2.82843 q^{3} -1.82843 q^{4} +1.00000 q^{5} +1.17157 q^{6} +1.58579 q^{8} +5.00000 q^{9} +O(q^{10})$	\(q-0.414214 q^{2} -2.82843 q^{3} -1.82843 q^{4} +1.00000 q^{5} +1.17157 q^{6} +1.58579 q^{8} +5.00000 q^{9} -0.414214 q^{10} +1.00000 q^{11} +5.17157 q^{12} +6.82843 q^{13} -2.82843 q^{15} +3.00000 q^{16} -1.17157 q^{17} -2.07107 q^{18} -1.82843 q^{20} -0.414214 q^{22} +2.82843 q^{23} -4.48528 q^{24} +1.00000 q^{25} -2.82843 q^{26} -5.65685 q^{27} +7.65685 q^{29} +1.17157 q^{30} -4.41421 q^{32} -2.82843 q^{33} +0.485281 q^{34} -9.14214 q^{36} +3.65685 q^{37} -19.3137 q^{39} +1.58579 q^{40} -6.00000 q^{41} -6.00000 q^{43} -1.82843 q^{44} +5.00000 q^{45} -1.17157 q^{46} +2.82843 q^{47} -8.48528 q^{48} -0.414214 q^{50} +3.31371 q^{51} -12.4853 q^{52} +0.343146 q^{53} +2.34315 q^{54} +1.00000 q^{55} -3.17157 q^{58} +9.65685 q^{59} +5.17157 q^{60} -13.3137 q^{61} -4.17157 q^{64} +6.82843 q^{65} +1.17157 q^{66} -4.48528 q^{67} +2.14214 q^{68} -8.00000 q^{69} -11.3137 q^{71} +7.92893 q^{72} +6.82843 q^{73} -1.51472 q^{74} -2.82843 q^{75} +8.00000 q^{78} +4.00000 q^{79} +3.00000 q^{80} +1.00000 q^{81} +2.48528 q^{82} +6.00000 q^{83} -1.17157 q^{85} +2.48528 q^{86} -21.6569 q^{87} +1.58579 q^{88} -9.31371 q^{89} -2.07107 q^{90} -5.17157 q^{92} -1.17157 q^{94} +12.4853 q^{96} +7.65685 q^{97} +5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 8 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 8 * q^6 + 6 * q^8 + 10 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 8 q^{6} + 6 q^{8} + 10 q^{9} + 2 q^{10} + 2 q^{11} + 16 q^{12} + 8 q^{13} + 6 q^{16} - 8 q^{17} + 10 q^{18} + 2 q^{20} + 2 q^{22} + 8 q^{24} + 2 q^{25} + 4 q^{29} + 8 q^{30} - 6 q^{32} - 16 q^{34} + 10 q^{36} - 4 q^{37} - 16 q^{39} + 6 q^{40} - 12 q^{41} - 12 q^{43} + 2 q^{44} + 10 q^{45} - 8 q^{46} + 2 q^{50} - 16 q^{51} - 8 q^{52} + 12 q^{53} + 16 q^{54} + 2 q^{55} - 12 q^{58} + 8 q^{59} + 16 q^{60} - 4 q^{61} - 14 q^{64} + 8 q^{65} + 8 q^{66} + 8 q^{67} - 24 q^{68} - 16 q^{69} + 30 q^{72} + 8 q^{73} - 20 q^{74} + 16 q^{78} + 8 q^{79} + 6 q^{80} + 2 q^{81} - 12 q^{82} + 12 q^{83} - 8 q^{85} - 12 q^{86} - 32 q^{87} + 6 q^{88} + 4 q^{89} + 10 q^{90} - 16 q^{92} - 8 q^{94} + 8 q^{96} + 4 q^{97} + 10 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 8 * q^6 + 6 * q^8 + 10 * q^9 + 2 * q^10 + 2 * q^11 + 16 * q^12 + 8 * q^13 + 6 * q^16 - 8 * q^17 + 10 * q^18 + 2 * q^20 + 2 * q^22 + 8 * q^24 + 2 * q^25 + 4 * q^29 + 8 * q^30 - 6 * q^32 - 16 * q^34 + 10 * q^36 - 4 * q^37 - 16 * q^39 + 6 * q^40 - 12 * q^41 - 12 * q^43 + 2 * q^44 + 10 * q^45 - 8 * q^46 + 2 * q^50 - 16 * q^51 - 8 * q^52 + 12 * q^53 + 16 * q^54 + 2 * q^55 - 12 * q^58 + 8 * q^59 + 16 * q^60 - 4 * q^61 - 14 * q^64 + 8 * q^65 + 8 * q^66 + 8 * q^67 - 24 * q^68 - 16 * q^69 + 30 * q^72 + 8 * q^73 - 20 * q^74 + 16 * q^78 + 8 * q^79 + 6 * q^80 + 2 * q^81 - 12 * q^82 + 12 * q^83 - 8 * q^85 - 12 * q^86 - 32 * q^87 + 6 * q^88 + 4 * q^89 + 10 * q^90 - 16 * q^92 - 8 * q^94 + 8 * q^96 + 4 * q^97 + 10 * 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 $

$2$	−0.414214	−0.292893	−0.146447	−	0.989219i	$-0.546784\pi$
$2$	−0.414214	−0.292893	−0.146447	+	0.989219i	$0.546784\pi$
$3$	−2.82843	−1.63299	−0.816497	−	0.577350i	$-0.804087\pi$
$3$	−2.82843	−1.63299	−0.816497	+	0.577350i	$0.804087\pi$
$4$	−1.82843	−0.914214
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.17157	0.478293
$7$	0	0
$7$	0	0
$8$	1.58579	0.560660
$9$	5.00000	1.66667
$10$	−0.414214	−0.130986
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.17157	1.49290
$13$	6.82843	1.89386	0.946932	−	0.321433i	$-0.104164\pi$
$13$	6.82843	1.89386	0.946932	+	0.321433i	$0.104164\pi$
$14$	0	0
$15$	−2.82843	−0.730297
$16$	3.00000	0.750000
$17$	−1.17157	−0.284148	−0.142074	−	0.989856i	$-0.545377\pi$
$17$	−1.17157	−0.284148	−0.142074	+	0.989856i	$0.545377\pi$
$18$	−2.07107	−0.488155
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−1.82843	−0.408849
$21$	0	0
$22$	−0.414214	−0.0883106
$23$	2.82843	0.589768	0.294884	−	0.955533i	$-0.404719\pi$
$23$	2.82843	0.589768	0.294884	+	0.955533i	$0.404719\pi$
$24$	−4.48528	−0.915554
$25$	1.00000	0.200000
$26$	−2.82843	−0.554700
$27$	−5.65685	−1.08866
$28$	0	0
$29$	7.65685	1.42184	0.710921	−	0.703272i	$-0.248278\pi$
$29$	7.65685	1.42184	0.710921	+	0.703272i	$0.248278\pi$
$30$	1.17157	0.213899
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−4.41421	−0.780330
$33$	−2.82843	−0.492366
$34$	0.485281	0.0832251
$35$	0	0
$36$	−9.14214	−1.52369
$37$	3.65685	0.601183	0.300592	−	0.953753i	$-0.402816\pi$
$37$	3.65685	0.601183	0.300592	+	0.953753i	$0.402816\pi$
$38$	0	0
$39$	−19.3137	−3.09267
$40$	1.58579	0.250735
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	−1.82843	−0.275646
$45$	5.00000	0.745356
$46$	−1.17157	−0.172739
$47$	2.82843	0.412568	0.206284	−	0.978492i	$-0.433863\pi$
$47$	2.82843	0.412568	0.206284	+	0.978492i	$0.433863\pi$
$48$	−8.48528	−1.22474
$49$	0	0
$50$	−0.414214	−0.0585786
$51$	3.31371	0.464012
$52$	−12.4853	−1.73140
$53$	0.343146	0.0471347	0.0235673	−	0.999722i	$-0.492498\pi$
$53$	0.343146	0.0471347	0.0235673	+	0.999722i	$0.492498\pi$
$54$	2.34315	0.318862
$55$	1.00000	0.134840
$56$	0	0
$57$	0	0
$58$	−3.17157	−0.416448
$59$	9.65685	1.25722	0.628608	−	0.777723i	$-0.283625\pi$
$59$	9.65685	1.25722	0.628608	+	0.777723i	$0.283625\pi$
$60$	5.17157	0.667647
$61$	−13.3137	−1.70465	−0.852323	−	0.523016i	$-0.824807\pi$
$61$	−13.3137	−1.70465	−0.852323	+	0.523016i	$0.824807\pi$
$62$	0	0
$63$	0	0
$64$	−4.17157	−0.521447
$65$	6.82843	0.846962
$66$	1.17157	0.144211
$67$	−4.48528	−0.547964	−0.273982	−	0.961735i	$-0.588341\pi$
$67$	−4.48528	−0.547964	−0.273982	+	0.961735i	$0.588341\pi$
$68$	2.14214	0.259772
$69$	−8.00000	−0.963087
$70$	0	0
$71$	−11.3137	−1.34269	−0.671345	−	0.741145i	$-0.734283\pi$
$71$	−11.3137	−1.34269	−0.671345	+	0.741145i	$0.734283\pi$
$72$	7.92893	0.934434
$73$	6.82843	0.799207	0.399603	−	0.916688i	$-0.369148\pi$
$73$	6.82843	0.799207	0.399603	+	0.916688i	$0.369148\pi$
$74$	−1.51472	−0.176082
$75$	−2.82843	−0.326599
$76$	0	0
$77$	0	0
$78$	8.00000	0.905822
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	3.00000	0.335410
$81$	1.00000	0.111111
$82$	2.48528	0.274453
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	−1.17157	−0.127075
$86$	2.48528	0.267995
$87$	−21.6569	−2.32186
$88$	1.58579	0.169045
$89$	−9.31371	−0.987251	−0.493626	−	0.869675i	$-0.664329\pi$
$89$	−9.31371	−0.987251	−0.493626	+	0.869675i	$0.664329\pi$
$90$	−2.07107	−0.218310
$91$	0	0
$92$	−5.17157	−0.539174
$93$	0	0
$94$	−1.17157	−0.120839
$95$	0	0
$96$	12.4853	1.27427
$97$	7.65685	0.777436	0.388718	−	0.921357i	$-0.372918\pi$
$97$	7.65685	0.777436	0.388718	+	0.921357i	$0.372918\pi$
$98$	0	0
$99$	5.00000	0.502519
$100$	−1.82843	−0.182843
$101$	13.3137	1.32476	0.662382	−	0.749166i	$-0.269546\pi$
$101$	13.3137	1.32476	0.662382	+	0.749166i	$0.269546\pi$
$102$	−1.37258	−0.135906
$103$	−1.17157	−0.115439	−0.0577193	−	0.998333i	$-0.518383\pi$
$103$	−1.17157	−0.115439	−0.0577193	+	0.998333i	$0.518383\pi$
$104$	10.8284	1.06181
$105$	0	0
$106$	−0.142136	−0.0138054
$107$	−3.65685	−0.353521	−0.176761	−	0.984254i	$-0.556562\pi$
$107$	−3.65685	−0.353521	−0.176761	+	0.984254i	$0.556562\pi$
$108$	10.3431	0.995270
$109$	3.65685	0.350263	0.175132	−	0.984545i	$-0.443965\pi$
$109$	3.65685	0.350263	0.175132	+	0.984545i	$0.443965\pi$
$110$	−0.414214	−0.0394937
$111$	−10.3431	−0.981728
$112$	0	0
$113$	8.34315	0.784857	0.392429	−	0.919782i	$-0.371635\pi$
$113$	8.34315	0.784857	0.392429	+	0.919782i	$0.371635\pi$
$114$	0	0
$115$	2.82843	0.263752
$116$	−14.0000	−1.29987
$117$	34.1421	3.15644
$118$	−4.00000	−0.368230
$119$	0	0
$120$	−4.48528	−0.409448
$121$	1.00000	0.0909091
$122$	5.51472	0.499279
$123$	16.9706	1.53018
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	15.6569	1.38932	0.694661	−	0.719338i	$-0.255555\pi$
$127$	15.6569	1.38932	0.694661	+	0.719338i	$0.255555\pi$
$128$	10.5563	0.933058
$129$	16.9706	1.49417
$130$	−2.82843	−0.248069
$131$	−11.3137	−0.988483	−0.494242	−	0.869325i	$-0.664554\pi$
$131$	−11.3137	−0.988483	−0.494242	+	0.869325i	$0.664554\pi$
$132$	5.17157	0.450128
$133$	0	0
$134$	1.85786	0.160495
$135$	−5.65685	−0.486864
$136$	−1.85786	−0.159311
$137$	22.9706	1.96251	0.981254	−	0.192720i	$-0.0617309\pi$
$137$	22.9706	1.96251	0.981254	+	0.192720i	$0.0617309\pi$
$138$	3.31371	0.282082
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	4.68629	0.393265
$143$	6.82843	0.571022
$144$	15.0000	1.25000
$145$	7.65685	0.635867
$146$	−2.82843	−0.234082
$147$	0	0
$148$	−6.68629	−0.549610
$149$	11.6569	0.954967	0.477483	−	0.878641i	$-0.341549\pi$
$149$	11.6569	0.954967	0.477483	+	0.878641i	$0.341549\pi$
$150$	1.17157	0.0956585
$151$	−12.0000	−0.976546	−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000	−0.976546	−0.488273	+	0.872691i	$0.662373\pi$
$152$	0	0
$153$	−5.85786	−0.473580
$154$	0	0
$155$	0	0
$156$	35.3137	2.82736
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	−1.65685	−0.131812
$159$	−0.970563	−0.0769706
$160$	−4.41421	−0.348974
$161$	0	0
$162$	−0.414214	−0.0325437
$163$	−0.485281	−0.0380102	−0.0190051	−	0.999819i	$-0.506050\pi$
$163$	−0.485281	−0.0380102	−0.0190051	+	0.999819i	$0.506050\pi$
$164$	10.9706	0.856657
$165$	−2.82843	−0.220193
$166$	−2.48528	−0.192895
$167$	−10.9706	−0.848928	−0.424464	−	0.905445i	$-0.639537\pi$
$167$	−10.9706	−0.848928	−0.424464	+	0.905445i	$0.639537\pi$
$168$	0	0
$169$	33.6274	2.58672
$170$	0.485281	0.0372194
$171$	0	0
$172$	10.9706	0.836498
$173$	−6.14214	−0.466978	−0.233489	−	0.972359i	$-0.575014\pi$
$173$	−6.14214	−0.466978	−0.233489	+	0.972359i	$0.575014\pi$
$174$	8.97056	0.680057
$175$	0	0
$176$	3.00000	0.226134
$177$	−27.3137	−2.05302
$178$	3.85786	0.289159
$179$	−1.65685	−0.123839	−0.0619196	−	0.998081i	$-0.519722\pi$
$179$	−1.65685	−0.123839	−0.0619196	+	0.998081i	$0.519722\pi$
$180$	−9.14214	−0.681415
$181$	1.31371	0.0976472	0.0488236	−	0.998807i	$-0.484453\pi$
$181$	1.31371	0.0976472	0.0488236	+	0.998807i	$0.484453\pi$
$182$	0	0
$183$	37.6569	2.78367
$184$	4.48528	0.330659
$185$	3.65685	0.268857
$186$	0	0
$187$	−1.17157	−0.0856739
$188$	−5.17157	−0.377176
$189$	0	0
$190$	0	0
$191$	−19.3137	−1.39749	−0.698745	−	0.715370i	$-0.746258\pi$
$191$	−19.3137	−1.39749	−0.698745	+	0.715370i	$0.746258\pi$
$192$	11.7990	0.851519
$193$	−6.82843	−0.491521	−0.245760	−	0.969331i	$-0.579038\pi$
$193$	−6.82843	−0.491521	−0.245760	+	0.969331i	$0.579038\pi$
$194$	−3.17157	−0.227706
$195$	−19.3137	−1.38308
$196$	0	0
$197$	−5.17157	−0.368459	−0.184230	−	0.982883i	$-0.558979\pi$
$197$	−5.17157	−0.368459	−0.184230	+	0.982883i	$0.558979\pi$
$198$	−2.07107	−0.147184
$199$	−21.6569	−1.53521	−0.767607	−	0.640921i	$-0.778553\pi$
$199$	−21.6569	−1.53521	−0.767607	+	0.640921i	$0.778553\pi$
$200$	1.58579	0.112132
$201$	12.6863	0.894822
$202$	−5.51472	−0.388014
$203$	0	0
$204$	−6.05887	−0.424206
$205$	−6.00000	−0.419058
$206$	0.485281	0.0338112
$207$	14.1421	0.982946
$208$	20.4853	1.42040
$209$	0	0
$210$	0	0
$211$	−16.0000	−1.10149	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000	−1.10149	−0.550743	+	0.834675i	$0.685655\pi$
$212$	−0.627417	−0.0430912
$213$	32.0000	2.19260
$214$	1.51472	0.103544
$215$	−6.00000	−0.409197
$216$	−8.97056	−0.610369
$217$	0	0
$218$	−1.51472	−0.102590
$219$	−19.3137	−1.30510
$220$	−1.82843	−0.123273
$221$	−8.00000	−0.538138
$222$	4.28427	0.287541
$223$	5.17157	0.346314	0.173157	−	0.984894i	$-0.444603\pi$
$223$	5.17157	0.346314	0.173157	+	0.984894i	$0.444603\pi$
$224$	0	0
$225$	5.00000	0.333333
$226$	−3.45584	−0.229879
$227$	−2.68629	−0.178295	−0.0891477	−	0.996018i	$-0.528414\pi$
$227$	−2.68629	−0.178295	−0.0891477	+	0.996018i	$0.528414\pi$
$228$	0	0
$229$	21.3137	1.40845	0.704225	−	0.709977i	$-0.251295\pi$
$229$	21.3137	1.40845	0.704225	+	0.709977i	$0.251295\pi$
$230$	−1.17157	−0.0772512
$231$	0	0
$232$	12.1421	0.797170
$233$	22.1421	1.45058	0.725290	−	0.688444i	$-0.241706\pi$
$233$	22.1421	1.45058	0.725290	+	0.688444i	$0.241706\pi$
$234$	−14.1421	−0.924500
$235$	2.82843	0.184506
$236$	−17.6569	−1.14936
$237$	−11.3137	−0.734904
$238$	0	0
$239$	−0.686292	−0.0443925	−0.0221963	−	0.999754i	$-0.507066\pi$
$239$	−0.686292	−0.0443925	−0.0221963	+	0.999754i	$0.507066\pi$
$240$	−8.48528	−0.547723
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	−0.414214	−0.0266267
$243$	14.1421	0.907218
$244$	24.3431	1.55841
$245$	0	0
$246$	−7.02944	−0.448181
$247$	0	0
$248$	0	0
$249$	−16.9706	−1.07547
$250$	−0.414214	−0.0261972
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	0	0
$253$	2.82843	0.177822
$254$	−6.48528	−0.406923
$255$	3.31371	0.207512
$256$	3.97056	0.248160
$257$	−13.3137	−0.830486	−0.415243	−	0.909710i	$-0.636304\pi$
$257$	−13.3137	−0.830486	−0.415243	+	0.909710i	$0.636304\pi$
$258$	−7.02944	−0.437634
$259$	0	0
$260$	−12.4853	−0.774304
$261$	38.2843	2.36974
$262$	4.68629	0.289520
$263$	22.9706	1.41643	0.708213	−	0.705999i	$-0.249502\pi$
$263$	22.9706	1.41643	0.708213	+	0.705999i	$0.249502\pi$
$264$	−4.48528	−0.276050
$265$	0.343146	0.0210793
$266$	0	0
$267$	26.3431	1.61217
$268$	8.20101	0.500956
$269$	5.31371	0.323983	0.161991	−	0.986792i	$-0.448208\pi$
$269$	5.31371	0.323983	0.161991	+	0.986792i	$0.448208\pi$
$270$	2.34315	0.142599
$271$	15.3137	0.930242	0.465121	−	0.885247i	$-0.346011\pi$
$271$	15.3137	0.930242	0.465121	+	0.885247i	$0.346011\pi$
$272$	−3.51472	−0.213111
$273$	0	0
$274$	−9.51472	−0.574805
$275$	1.00000	0.0603023
$276$	14.6274	0.880467
$277$	1.17157	0.0703930	0.0351965	−	0.999380i	$-0.488794\pi$
$277$	1.17157	0.0703930	0.0351965	+	0.999380i	$0.488794\pi$
$278$	−1.65685	−0.0993715
$279$	0	0
$280$	0	0
$281$	−5.31371	−0.316989	−0.158495	−	0.987360i	$-0.550664\pi$
$281$	−5.31371	−0.316989	−0.158495	+	0.987360i	$0.550664\pi$
$282$	3.31371	0.197328
$283$	12.6274	0.750622	0.375311	−	0.926899i	$-0.377536\pi$
$283$	12.6274	0.750622	0.375311	+	0.926899i	$0.377536\pi$
$284$	20.6863	1.22751
$285$	0	0
$286$	−2.82843	−0.167248
$287$	0	0
$288$	−22.0711	−1.30055
$289$	−15.6274	−0.919260
$290$	−3.17157	−0.186241
$291$	−21.6569	−1.26955
$292$	−12.4853	−0.730646
$293$	14.8284	0.866286	0.433143	−	0.901325i	$-0.357405\pi$
$293$	14.8284	0.866286	0.433143	+	0.901325i	$0.357405\pi$
$294$	0	0
$295$	9.65685	0.562244
$296$	5.79899	0.337059
$297$	−5.65685	−0.328244
$298$	−4.82843	−0.279703
$299$	19.3137	1.11694
$300$	5.17157	0.298581
$301$	0	0
$302$	4.97056	0.286024
$303$	−37.6569	−2.16333
$304$	0	0
$305$	−13.3137	−0.762341
$306$	2.42641	0.138708
$307$	27.6569	1.57846	0.789230	−	0.614098i	$-0.210480\pi$
$307$	27.6569	1.57846	0.789230	+	0.614098i	$0.210480\pi$
$308$	0	0
$309$	3.31371	0.188510
$310$	0	0
$311$	−27.3137	−1.54882	−0.774409	−	0.632685i	$-0.781953\pi$
$311$	−27.3137	−1.54882	−0.774409	+	0.632685i	$0.781953\pi$
$312$	−30.6274	−1.73394
$313$	−21.3137	−1.20472	−0.602361	−	0.798224i	$-0.705773\pi$
$313$	−21.3137	−1.20472	−0.602361	+	0.798224i	$0.705773\pi$
$314$	−5.79899	−0.327256
$315$	0	0
$316$	−7.31371	−0.411428
$317$	21.3137	1.19710	0.598549	−	0.801087i	$-0.295744\pi$
$317$	21.3137	1.19710	0.598549	+	0.801087i	$0.295744\pi$
$318$	0.402020	0.0225442
$319$	7.65685	0.428702
$320$	−4.17157	−0.233198
$321$	10.3431	0.577298
$322$	0	0
$323$	0	0
$324$	−1.82843	−0.101579
$325$	6.82843	0.378773
$326$	0.201010	0.0111329
$327$	−10.3431	−0.571977
$328$	−9.51472	−0.525362
$329$	0	0
$330$	1.17157	0.0644930
$331$	15.3137	0.841718	0.420859	−	0.907126i	$-0.361729\pi$
$331$	15.3137	0.841718	0.420859	+	0.907126i	$0.361729\pi$
$332$	−10.9706	−0.602088
$333$	18.2843	1.00197
$334$	4.54416	0.248645
$335$	−4.48528	−0.245057
$336$	0	0
$337$	−3.51472	−0.191459	−0.0957295	−	0.995407i	$-0.530518\pi$
$337$	−3.51472	−0.191459	−0.0957295	+	0.995407i	$0.530518\pi$
$338$	−13.9289	−0.757634
$339$	−23.5980	−1.28167
$340$	2.14214	0.116174
$341$	0	0
$342$	0	0
$343$	0	0
$344$	−9.51472	−0.512999
$345$	−8.00000	−0.430706
$346$	2.54416	0.136775
$347$	−22.9706	−1.23312	−0.616562	−	0.787306i	$-0.711475\pi$
$347$	−22.9706	−1.23312	−0.616562	+	0.787306i	$0.711475\pi$
$348$	39.5980	2.12267
$349$	6.97056	0.373126	0.186563	−	0.982443i	$-0.440265\pi$
$349$	6.97056	0.373126	0.186563	+	0.982443i	$0.440265\pi$
$350$	0	0
$351$	−38.6274	−2.06178
$352$	−4.41421	−0.235278
$353$	1.31371	0.0699216	0.0349608	−	0.999389i	$-0.488869\pi$
$353$	1.31371	0.0699216	0.0349608	+	0.999389i	$0.488869\pi$
$354$	11.3137	0.601317
$355$	−11.3137	−0.600469
$356$	17.0294	0.902558
$357$	0	0
$358$	0.686292	0.0362716
$359$	23.3137	1.23045	0.615225	−	0.788351i	$-0.289065\pi$
$359$	23.3137	1.23045	0.615225	+	0.788351i	$0.289065\pi$
$360$	7.92893	0.417891
$361$	−19.0000	−1.00000
$362$	−0.544156	−0.0286002
$363$	−2.82843	−0.148454
$364$	0	0
$365$	6.82843	0.357416
$366$	−15.5980	−0.815319
$367$	−8.48528	−0.442928	−0.221464	−	0.975169i	$-0.571084\pi$
$367$	−8.48528	−0.442928	−0.221464	+	0.975169i	$0.571084\pi$
$368$	8.48528	0.442326
$369$	−30.0000	−1.56174
$370$	−1.51472	−0.0787465
$371$	0	0
$372$	0	0
$373$	−3.79899	−0.196704	−0.0983521	−	0.995152i	$-0.531357\pi$
$373$	−3.79899	−0.196704	−0.0983521	+	0.995152i	$0.531357\pi$
$374$	0.485281	0.0250933
$375$	−2.82843	−0.146059
$376$	4.48528	0.231311
$377$	52.2843	2.69278
$378$	0	0
$379$	22.3431	1.14769	0.573845	−	0.818964i	$-0.305451\pi$
$379$	22.3431	1.14769	0.573845	+	0.818964i	$0.305451\pi$
$380$	0	0
$381$	−44.2843	−2.26875
$382$	8.00000	0.409316
$383$	34.1421	1.74458	0.872291	−	0.488987i	$-0.162634\pi$
$383$	34.1421	1.74458	0.872291	+	0.488987i	$0.162634\pi$
$384$	−29.8579	−1.52368
$385$	0	0
$386$	2.82843	0.143963
$387$	−30.0000	−1.52499
$388$	−14.0000	−0.710742
$389$	−24.6274	−1.24866	−0.624330	−	0.781161i	$-0.714628\pi$
$389$	−24.6274	−1.24866	−0.624330	+	0.781161i	$0.714628\pi$
$390$	8.00000	0.405096
$391$	−3.31371	−0.167581
$392$	0	0
$393$	32.0000	1.61419
$394$	2.14214	0.107919
$395$	4.00000	0.201262
$396$	−9.14214	−0.459410
$397$	−13.3137	−0.668196	−0.334098	−	0.942538i	$-0.608432\pi$
$397$	−13.3137	−0.668196	−0.334098	+	0.942538i	$0.608432\pi$
$398$	8.97056	0.449654
$399$	0	0
$400$	3.00000	0.150000
$401$	17.3137	0.864605	0.432303	−	0.901729i	$-0.357701\pi$
$401$	17.3137	0.864605	0.432303	+	0.901729i	$0.357701\pi$
$402$	−5.25483	−0.262087
$403$	0	0
$404$	−24.3431	−1.21112
$405$	1.00000	0.0496904
$406$	0	0
$407$	3.65685	0.181264
$408$	5.25483	0.260153
$409$	−34.9706	−1.72918	−0.864592	−	0.502475i	$-0.832423\pi$
$409$	−34.9706	−1.72918	−0.864592	+	0.502475i	$0.832423\pi$
$410$	2.48528	0.122739
$411$	−64.9706	−3.20476
$412$	2.14214	0.105535
$413$	0	0
$414$	−5.85786	−0.287898
$415$	6.00000	0.294528
$416$	−30.1421	−1.47784
$417$	−11.3137	−0.554035
$418$	0	0
$419$	14.3431	0.700709	0.350354	−	0.936617i	$-0.386061\pi$
$419$	14.3431	0.700709	0.350354	+	0.936617i	$0.386061\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	6.62742	0.322618
$423$	14.1421	0.687614
$424$	0.544156	0.0264265
$425$	−1.17157	−0.0568296
$426$	−13.2548	−0.642199
$427$	0	0
$428$	6.68629	0.323194
$429$	−19.3137	−0.932475
$430$	2.48528	0.119851
$431$	11.3137	0.544962	0.272481	−	0.962161i	$-0.412156\pi$
$431$	11.3137	0.544962	0.272481	+	0.962161i	$0.412156\pi$
$432$	−16.9706	−0.816497
$433$	−3.65685	−0.175737	−0.0878686	−	0.996132i	$-0.528006\pi$
$433$	−3.65685	−0.175737	−0.0878686	+	0.996132i	$0.528006\pi$
$434$	0	0
$435$	−21.6569	−1.03837
$436$	−6.68629	−0.320215
$437$	0	0
$438$	8.00000	0.382255
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	1.58579	0.0755994
$441$	0	0
$442$	3.31371	0.157617
$443$	−21.1716	−1.00589	−0.502946	−	0.864318i	$-0.667751\pi$
$443$	−21.1716	−1.00589	−0.502946	+	0.864318i	$0.667751\pi$
$444$	18.9117	0.897509
$445$	−9.31371	−0.441512
$446$	−2.14214	−0.101433
$447$	−32.9706	−1.55945
$448$	0	0
$449$	−16.6274	−0.784696	−0.392348	−	0.919817i	$-0.628337\pi$
$449$	−16.6274	−0.784696	−0.392348	+	0.919817i	$0.628337\pi$
$450$	−2.07107	−0.0976311
$451$	−6.00000	−0.282529
$452$	−15.2548	−0.717527
$453$	33.9411	1.59469
$454$	1.11270	0.0522215
$455$	0	0
$456$	0	0
$457$	−16.4853	−0.771149	−0.385574	−	0.922677i	$-0.625997\pi$
$457$	−16.4853	−0.771149	−0.385574	+	0.922677i	$0.625997\pi$
$458$	−8.82843	−0.412525
$459$	6.62742	0.309341
$460$	−5.17157	−0.241126
$461$	32.6274	1.51961	0.759805	−	0.650151i	$-0.225294\pi$
$461$	32.6274	1.51961	0.759805	+	0.650151i	$0.225294\pi$
$462$	0	0
$463$	22.1421	1.02903	0.514516	−	0.857481i	$-0.327972\pi$
$463$	22.1421	1.02903	0.514516	+	0.857481i	$0.327972\pi$
$464$	22.9706	1.06638
$465$	0	0
$466$	−9.17157	−0.424865
$467$	9.17157	0.424410	0.212205	−	0.977225i	$-0.431936\pi$
$467$	9.17157	0.424410	0.212205	+	0.977225i	$0.431936\pi$
$468$	−62.4264	−2.88566
$469$	0	0
$470$	−1.17157	−0.0540406
$471$	−39.5980	−1.82458
$472$	15.3137	0.704871
$473$	−6.00000	−0.275880
$474$	4.68629	0.215248
$475$	0	0
$476$	0	0
$477$	1.71573	0.0785578
$478$	0.284271	0.0130023
$479$	36.0000	1.64488	0.822441	−	0.568850i	$-0.192612\pi$
$479$	36.0000	1.64488	0.822441	+	0.568850i	$0.192612\pi$
$480$	12.4853	0.569873
$481$	24.9706	1.13856
$482$	2.48528	0.113201
$483$	0	0
$484$	−1.82843	−0.0831103
$485$	7.65685	0.347680
$486$	−5.85786	−0.265718
$487$	−7.51472	−0.340524	−0.170262	−	0.985399i	$-0.554461\pi$
$487$	−7.51472	−0.340524	−0.170262	+	0.985399i	$0.554461\pi$
$488$	−21.1127	−0.955727
$489$	1.37258	0.0620703
$490$	0	0
$491$	−23.3137	−1.05213	−0.526066	−	0.850443i	$-0.676334\pi$
$491$	−23.3137	−1.05213	−0.526066	+	0.850443i	$0.676334\pi$
$492$	−31.0294	−1.39892
$493$	−8.97056	−0.404014
$494$	0	0
$495$	5.00000	0.224733
$496$	0	0
$497$	0	0
$498$	7.02944	0.314997
$499$	−1.65685	−0.0741710	−0.0370855	−	0.999312i	$-0.511807\pi$
$499$	−1.65685	−0.0741710	−0.0370855	+	0.999312i	$0.511807\pi$
$500$	−1.82843	−0.0817697
$501$	31.0294	1.38629
$502$	4.97056	0.221847
$503$	28.6274	1.27643	0.638217	−	0.769857i	$-0.279672\pi$
$503$	28.6274	1.27643	0.638217	+	0.769857i	$0.279672\pi$
$504$	0	0
$505$	13.3137	0.592452
$506$	−1.17157	−0.0520828
$507$	−95.1127	−4.22410
$508$	−28.6274	−1.27014
$509$	−9.31371	−0.412823	−0.206411	−	0.978465i	$-0.566179\pi$
$509$	−9.31371	−0.412823	−0.206411	+	0.978465i	$0.566179\pi$
$510$	−1.37258	−0.0607790
$511$	0	0
$512$	−22.7574	−1.00574
$513$	0	0
$514$	5.51472	0.243244
$515$	−1.17157	−0.0516257
$516$	−31.0294	−1.36599
$517$	2.82843	0.124394
$518$	0	0
$519$	17.3726	0.762572
$520$	10.8284	0.474858
$521$	−2.68629	−0.117689	−0.0588443	−	0.998267i	$-0.518742\pi$
$521$	−2.68629	−0.117689	−0.0588443	+	0.998267i	$0.518742\pi$
$522$	−15.8579	−0.694080
$523$	−37.5980	−1.64404	−0.822022	−	0.569455i	$-0.807154\pi$
$523$	−37.5980	−1.64404	−0.822022	+	0.569455i	$0.807154\pi$
$524$	20.6863	0.903685
$525$	0	0
$526$	−9.51472	−0.414861
$527$	0	0
$528$	−8.48528	−0.369274
$529$	−15.0000	−0.652174
$530$	−0.142136	−0.00617398
$531$	48.2843	2.09536
$532$	0	0
$533$	−40.9706	−1.77463
$534$	−10.9117	−0.472195
$535$	−3.65685	−0.158100
$536$	−7.11270	−0.307222
$537$	4.68629	0.202228
$538$	−2.20101	−0.0948923
$539$	0	0
$540$	10.3431	0.445098
$541$	6.00000	0.257960	0.128980	−	0.991647i	$-0.458830\pi$
$541$	6.00000	0.257960	0.128980	+	0.991647i	$0.458830\pi$
$542$	−6.34315	−0.272461
$543$	−3.71573	−0.159457
$544$	5.17157	0.221729
$545$	3.65685	0.156642
$546$	0	0
$547$	−34.0000	−1.45374	−0.726868	−	0.686778i	$-0.759025\pi$
$547$	−34.0000	−1.45374	−0.726868	+	0.686778i	$0.759025\pi$
$548$	−42.0000	−1.79415
$549$	−66.5685	−2.84108
$550$	−0.414214	−0.0176621
$551$	0	0
$552$	−12.6863	−0.539964
$553$	0	0
$554$	−0.485281	−0.0206176
$555$	−10.3431	−0.439042
$556$	−7.31371	−0.310170
$557$	38.1421	1.61613	0.808067	−	0.589090i	$-0.200514\pi$
$557$	38.1421	1.61613	0.808067	+	0.589090i	$0.200514\pi$
$558$	0	0
$559$	−40.9706	−1.73287
$560$	0	0
$561$	3.31371	0.139905
$562$	2.20101	0.0928440
$563$	−11.6569	−0.491278	−0.245639	−	0.969361i	$-0.578998\pi$
$563$	−11.6569	−0.491278	−0.245639	+	0.969361i	$0.578998\pi$
$564$	14.6274	0.615925
$565$	8.34315	0.350999
$566$	−5.23045	−0.219852
$567$	0	0
$568$	−17.9411	−0.752793
$569$	20.3431	0.852829	0.426415	−	0.904528i	$-0.359776\pi$
$569$	20.3431	0.852829	0.426415	+	0.904528i	$0.359776\pi$
$570$	0	0
$571$	45.9411	1.92258	0.961288	−	0.275545i	$-0.0888584\pi$
$571$	45.9411	1.92258	0.961288	+	0.275545i	$0.0888584\pi$
$572$	−12.4853	−0.522036
$573$	54.6274	2.28209
$574$	0	0
$575$	2.82843	0.117954
$576$	−20.8579	−0.869078
$577$	−6.97056	−0.290188	−0.145094	−	0.989418i	$-0.546349\pi$
$577$	−6.97056	−0.290188	−0.145094	+	0.989418i	$0.546349\pi$
$578$	6.47309	0.269245
$579$	19.3137	0.802650
$580$	−14.0000	−0.581318
$581$	0	0
$582$	8.97056	0.371842
$583$	0.343146	0.0142116
$584$	10.8284	0.448084
$585$	34.1421	1.41160
$586$	−6.14214	−0.253729
$587$	−26.1421	−1.07900	−0.539501	−	0.841985i	$-0.681387\pi$
$587$	−26.1421	−1.07900	−0.539501	+	0.841985i	$0.681387\pi$
$588$	0	0
$589$	0	0
$590$	−4.00000	−0.164677
$591$	14.6274	0.601692
$592$	10.9706	0.450887
$593$	−20.4853	−0.841230	−0.420615	−	0.907239i	$-0.638186\pi$
$593$	−20.4853	−0.841230	−0.420615	+	0.907239i	$0.638186\pi$
$594$	2.34315	0.0961404
$595$	0	0
$596$	−21.3137	−0.873044
$597$	61.2548	2.50699
$598$	−8.00000	−0.327144
$599$	5.65685	0.231133	0.115566	−	0.993300i	$-0.463132\pi$
$599$	5.65685	0.231133	0.115566	+	0.993300i	$0.463132\pi$
$600$	−4.48528	−0.183111
$601$	43.9411	1.79240	0.896198	−	0.443654i	$-0.146318\pi$
$601$	43.9411	1.79240	0.896198	+	0.443654i	$0.146318\pi$
$602$	0	0
$603$	−22.4264	−0.913274
$604$	21.9411	0.892772
$605$	1.00000	0.0406558
$606$	15.5980	0.633625
$607$	18.2843	0.742136	0.371068	−	0.928606i	$-0.378992\pi$
$607$	18.2843	0.742136	0.371068	+	0.928606i	$0.378992\pi$
$608$	0	0
$609$	0	0
$610$	5.51472	0.223284
$611$	19.3137	0.781349
$612$	10.7107	0.432954
$613$	25.4558	1.02815	0.514076	−	0.857745i	$-0.328135\pi$
$613$	25.4558	1.02815	0.514076	+	0.857745i	$0.328135\pi$
$614$	−11.4558	−0.462320
$615$	16.9706	0.684319
$616$	0	0
$617$	11.6569	0.469287	0.234644	−	0.972081i	$-0.424608\pi$
$617$	11.6569	0.469287	0.234644	+	0.972081i	$0.424608\pi$
$618$	−1.37258	−0.0552134
$619$	25.6569	1.03124	0.515618	−	0.856819i	$-0.327562\pi$
$619$	25.6569	1.03124	0.515618	+	0.856819i	$0.327562\pi$
$620$	0	0
$621$	−16.0000	−0.642058
$622$	11.3137	0.453638
$623$	0	0
$624$	−57.9411	−2.31950
$625$	1.00000	0.0400000
$626$	8.82843	0.352855
$627$	0	0
$628$	−25.5980	−1.02147
$629$	−4.28427	−0.170825
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	6.34315	0.252317
$633$	45.2548	1.79872
$634$	−8.82843	−0.350622
$635$	15.6569	0.621323
$636$	1.77460	0.0703676
$637$	0	0
$638$	−3.17157	−0.125564
$639$	−56.5685	−2.23782
$640$	10.5563	0.417276
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	−4.28427	−0.169087
$643$	−49.4558	−1.95035	−0.975174	−	0.221440i	$-0.928924\pi$
$643$	−49.4558	−1.95035	−0.975174	+	0.221440i	$0.928924\pi$
$644$	0	0
$645$	16.9706	0.668215
$646$	0	0
$647$	35.1127	1.38042	0.690211	−	0.723608i	$-0.257518\pi$
$647$	35.1127	1.38042	0.690211	+	0.723608i	$0.257518\pi$
$648$	1.58579	0.0622956
$649$	9.65685	0.379065
$650$	−2.82843	−0.110940
$651$	0	0
$652$	0.887302	0.0347494
$653$	0.343146	0.0134283	0.00671417	−	0.999977i	$-0.497863\pi$
$653$	0.343146	0.0134283	0.00671417	+	0.999977i	$0.497863\pi$
$654$	4.28427	0.167528
$655$	−11.3137	−0.442063
$656$	−18.0000	−0.702782
$657$	34.1421	1.33201
$658$	0	0
$659$	−21.9411	−0.854705	−0.427352	−	0.904085i	$-0.640554\pi$
$659$	−21.9411	−0.854705	−0.427352	+	0.904085i	$0.640554\pi$
$660$	5.17157	0.201303
$661$	0.627417	0.0244037	0.0122018	−	0.999926i	$-0.496116\pi$
$661$	0.627417	0.0244037	0.0122018	+	0.999926i	$0.496116\pi$
$662$	−6.34315	−0.246533
$663$	22.6274	0.878776
$664$	9.51472	0.369243
$665$	0	0
$666$	−7.57359	−0.293471
$667$	21.6569	0.838557
$668$	20.0589	0.776101
$669$	−14.6274	−0.565529
$670$	1.85786	0.0717756
$671$	−13.3137	−0.513970
$672$	0	0
$673$	4.48528	0.172895	0.0864474	−	0.996256i	$-0.472449\pi$
$673$	4.48528	0.172895	0.0864474	+	0.996256i	$0.472449\pi$
$674$	1.45584	0.0560770
$675$	−5.65685	−0.217732
$676$	−61.4853	−2.36482
$677$	−17.1716	−0.659957	−0.329979	−	0.943988i	$-0.607042\pi$
$677$	−17.1716	−0.659957	−0.329979	+	0.943988i	$0.607042\pi$
$678$	9.77460	0.375391
$679$	0	0
$680$	−1.85786	−0.0712458
$681$	7.59798	0.291155
$682$	0	0
$683$	31.7990	1.21675	0.608377	−	0.793648i	$-0.291821\pi$
$683$	31.7990	1.21675	0.608377	+	0.793648i	$0.291821\pi$
$684$	0	0
$685$	22.9706	0.877660
$686$	0	0
$687$	−60.2843	−2.29999
$688$	−18.0000	−0.686244
$689$	2.34315	0.0892667
$690$	3.31371	0.126151
$691$	16.6863	0.634776	0.317388	−	0.948296i	$-0.397194\pi$
$691$	16.6863	0.634776	0.317388	+	0.948296i	$0.397194\pi$
$692$	11.2304	0.426918
$693$	0	0
$694$	9.51472	0.361174
$695$	4.00000	0.151729
$696$	−34.3431	−1.30177
$697$	7.02944	0.266259
$698$	−2.88730	−0.109286
$699$	−62.6274	−2.36879
$700$	0	0
$701$	32.6274	1.23232	0.616160	−	0.787621i	$-0.288687\pi$
$701$	32.6274	1.23232	0.616160	+	0.787621i	$0.288687\pi$
$702$	16.0000	0.603881
$703$	0	0
$704$	−4.17157	−0.157222
$705$	−8.00000	−0.301297
$706$	−0.544156	−0.0204796
$707$	0	0
$708$	49.9411	1.87690
$709$	−20.6274	−0.774679	−0.387339	−	0.921937i	$-0.626606\pi$
$709$	−20.6274	−0.774679	−0.387339	+	0.921937i	$0.626606\pi$
$710$	4.68629	0.175873
$711$	20.0000	0.750059
$712$	−14.7696	−0.553512
$713$	0	0
$714$	0	0
$715$	6.82843	0.255369
$716$	3.02944	0.113215
$717$	1.94113	0.0724927
$718$	−9.65685	−0.360391
$719$	−29.6569	−1.10601	−0.553007	−	0.833177i	$-0.686520\pi$
$719$	−29.6569	−1.10601	−0.553007	+	0.833177i	$0.686520\pi$
$720$	15.0000	0.559017
$721$	0	0
$722$	7.87006	0.292893
$723$	16.9706	0.631142
$724$	−2.40202	−0.0892704
$725$	7.65685	0.284368
$726$	1.17157	0.0434811
$727$	36.4853	1.35316	0.676582	−	0.736367i	$-0.263460\pi$
$727$	36.4853	1.35316	0.676582	+	0.736367i	$0.263460\pi$
$728$	0	0
$729$	−43.0000	−1.59259
$730$	−2.82843	−0.104685
$731$	7.02944	0.259993
$732$	−68.8528	−2.54487
$733$	−33.4558	−1.23572	−0.617860	−	0.786288i	$-0.712000\pi$
$733$	−33.4558	−1.23572	−0.617860	+	0.786288i	$0.712000\pi$
$734$	3.51472	0.129731
$735$	0	0
$736$	−12.4853	−0.460214
$737$	−4.48528	−0.165217
$738$	12.4264	0.457422
$739$	−37.9411	−1.39569	−0.697843	−	0.716250i	$-0.745857\pi$
$739$	−37.9411	−1.39569	−0.697843	+	0.716250i	$0.745857\pi$
$740$	−6.68629	−0.245793
$741$	0	0
$742$	0	0
$743$	29.5980	1.08584	0.542922	−	0.839783i	$-0.317318\pi$
$743$	29.5980	1.08584	0.542922	+	0.839783i	$0.317318\pi$
$744$	0	0
$745$	11.6569	0.427074
$746$	1.57359	0.0576133
$747$	30.0000	1.09764
$748$	2.14214	0.0783242
$749$	0	0
$750$	1.17157	0.0427798
$751$	−16.0000	−0.583848	−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000	−0.583848	−0.291924	+	0.956441i	$0.594295\pi$
$752$	8.48528	0.309426
$753$	33.9411	1.23688
$754$	−21.6569	−0.788696
$755$	−12.0000	−0.436725
$756$	0	0
$757$	−9.31371	−0.338512	−0.169256	−	0.985572i	$-0.554137\pi$
$757$	−9.31371	−0.338512	−0.169256	+	0.985572i	$0.554137\pi$
$758$	−9.25483	−0.336151
$759$	−8.00000	−0.290382
$760$	0	0
$761$	30.0000	1.08750	0.543750	−	0.839248i	$-0.317004\pi$
$761$	30.0000	1.08750	0.543750	+	0.839248i	$0.317004\pi$
$762$	18.3431	0.664502
$763$	0	0
$764$	35.3137	1.27761
$765$	−5.85786	−0.211792
$766$	−14.1421	−0.510976
$767$	65.9411	2.38100
$768$	−11.2304	−0.405244
$769$	−14.9706	−0.539852	−0.269926	−	0.962881i	$-0.586999\pi$
$769$	−14.9706	−0.539852	−0.269926	+	0.962881i	$0.586999\pi$
$770$	0	0
$771$	37.6569	1.35618
$772$	12.4853	0.449355
$773$	30.2843	1.08925	0.544625	−	0.838680i	$-0.316672\pi$
$773$	30.2843	1.08925	0.544625	+	0.838680i	$0.316672\pi$
$774$	12.4264	0.446658
$775$	0	0
$776$	12.1421	0.435877
$777$	0	0
$778$	10.2010	0.365724
$779$	0	0
$780$	35.3137	1.26443
$781$	−11.3137	−0.404836
$782$	1.37258	0.0490835
$783$	−43.3137	−1.54791
$784$	0	0
$785$	14.0000	0.499681
$786$	−13.2548	−0.472784
$787$	−18.9706	−0.676228	−0.338114	−	0.941105i	$-0.609789\pi$
$787$	−18.9706	−0.676228	−0.338114	+	0.941105i	$0.609789\pi$
$788$	9.45584	0.336850
$789$	−64.9706	−2.31301
$790$	−1.65685	−0.0589482
$791$	0	0
$792$	7.92893	0.281742
$793$	−90.9117	−3.22837
$794$	5.51472	0.195710
$795$	−0.970563	−0.0344223
$796$	39.5980	1.40351
$797$	12.6274	0.447286	0.223643	−	0.974671i	$-0.428205\pi$
$797$	12.6274	0.447286	0.223643	+	0.974671i	$0.428205\pi$
$798$	0	0
$799$	−3.31371	−0.117231
$800$	−4.41421	−0.156066
$801$	−46.5685	−1.64542
$802$	−7.17157	−0.253237
$803$	6.82843	0.240970
$804$	−23.1960	−0.818058
$805$	0	0
$806$	0	0
$807$	−15.0294	−0.529061
$808$	21.1127	0.742742
$809$	22.9706	0.807602	0.403801	−	0.914847i	$-0.367689\pi$
$809$	22.9706	0.807602	0.403801	+	0.914847i	$0.367689\pi$
$810$	−0.414214	−0.0145540
$811$	13.9411	0.489539	0.244770	−	0.969581i	$-0.421288\pi$
$811$	13.9411	0.489539	0.244770	+	0.969581i	$0.421288\pi$
$812$	0	0
$813$	−43.3137	−1.51908
$814$	−1.51472	−0.0530909
$815$	−0.485281	−0.0169987
$816$	9.94113	0.348009
$817$	0	0
$818$	14.4853	0.506466
$819$	0	0
$820$	10.9706	0.383109
$821$	−18.6863	−0.652156	−0.326078	−	0.945343i	$-0.605727\pi$
$821$	−18.6863	−0.652156	−0.326078	+	0.945343i	$0.605727\pi$
$822$	26.9117	0.938653
$823$	36.4853	1.27180	0.635898	−	0.771773i	$-0.280630\pi$
$823$	36.4853	1.27180	0.635898	+	0.771773i	$0.280630\pi$
$824$	−1.85786	−0.0647218
$825$	−2.82843	−0.0984732
$826$	0	0
$827$	−34.2843	−1.19218	−0.596090	−	0.802917i	$-0.703280\pi$
$827$	−34.2843	−1.19218	−0.596090	+	0.802917i	$0.703280\pi$
$828$	−25.8579	−0.898623
$829$	−18.0000	−0.625166	−0.312583	−	0.949890i	$-0.601194\pi$
$829$	−18.0000	−0.625166	−0.312583	+	0.949890i	$0.601194\pi$
$830$	−2.48528	−0.0862654
$831$	−3.31371	−0.114951
$832$	−28.4853	−0.987549
$833$	0	0
$834$	4.68629	0.162273
$835$	−10.9706	−0.379652
$836$	0	0
$837$	0	0
$838$	−5.94113	−0.205233
$839$	−37.6569	−1.30006	−0.650029	−	0.759909i	$-0.725243\pi$
$839$	−37.6569	−1.30006	−0.650029	+	0.759909i	$0.725243\pi$
$840$	0	0
$841$	29.6274	1.02164
$842$	2.48528	0.0856485
$843$	15.0294	0.517641
$844$	29.2548	1.00699
$845$	33.6274	1.15682
$846$	−5.85786	−0.201398
$847$	0	0
$848$	1.02944	0.0353510
$849$	−35.7157	−1.22576
$850$	0.485281	0.0166450
$851$	10.3431	0.354558
$852$	−58.5097	−2.00451
$853$	32.4853	1.11227	0.556137	−	0.831090i	$-0.312283\pi$
$853$	32.4853	1.11227	0.556137	+	0.831090i	$0.312283\pi$
$854$	0	0
$855$	0	0
$856$	−5.79899	−0.198205
$857$	48.7696	1.66594	0.832968	−	0.553321i	$-0.186640\pi$
$857$	48.7696	1.66594	0.832968	+	0.553321i	$0.186640\pi$
$858$	8.00000	0.273115
$859$	32.2843	1.10153	0.550763	−	0.834662i	$-0.314337\pi$
$859$	32.2843	1.10153	0.550763	+	0.834662i	$0.314337\pi$
$860$	10.9706	0.374093
$861$	0	0
$862$	−4.68629	−0.159616
$863$	−14.8284	−0.504766	−0.252383	−	0.967627i	$-0.581214\pi$
$863$	−14.8284	−0.504766	−0.252383	+	0.967627i	$0.581214\pi$
$864$	24.9706	0.849516
$865$	−6.14214	−0.208839
$866$	1.51472	0.0514722
$867$	44.2010	1.50115
$868$	0	0
$869$	4.00000	0.135691
$870$	8.97056	0.304131
$871$	−30.6274	−1.03777
$872$	5.79899	0.196379
$873$	38.2843	1.29573
$874$	0	0
$875$	0	0
$876$	35.3137	1.19314
$877$	1.45584	0.0491604	0.0245802	−	0.999698i	$-0.492175\pi$
$877$	1.45584	0.0491604	0.0245802	+	0.999698i	$0.492175\pi$
$878$	−6.62742	−0.223664
$879$	−41.9411	−1.41464
$880$	3.00000	0.101130
$881$	52.6274	1.77306	0.886531	−	0.462668i	$-0.153108\pi$
$881$	52.6274	1.77306	0.886531	+	0.462668i	$0.153108\pi$
$882$	0	0
$883$	42.8284	1.44129	0.720646	−	0.693304i	$-0.243845\pi$
$883$	42.8284	1.44129	0.720646	+	0.693304i	$0.243845\pi$
$884$	14.6274	0.491973
$885$	−27.3137	−0.918140
$886$	8.76955	0.294619
$887$	18.2843	0.613926	0.306963	−	0.951721i	$-0.400687\pi$
$887$	18.2843	0.613926	0.306963	+	0.951721i	$0.400687\pi$
$888$	−16.4020	−0.550416
$889$	0	0
$890$	3.85786	0.129316
$891$	1.00000	0.0335013
$892$	−9.45584	−0.316605
$893$	0	0
$894$	13.6569	0.456754
$895$	−1.65685	−0.0553825
$896$	0	0
$897$	−54.6274	−1.82396
$898$	6.88730	0.229832
$899$	0	0
$900$	−9.14214	−0.304738
$901$	−0.402020	−0.0133932
$902$	2.48528	0.0827508
$903$	0	0
$904$	13.2304	0.440038
$905$	1.31371	0.0436691
$906$	−14.0589	−0.467075
$907$	−44.4853	−1.47711	−0.738555	−	0.674193i	$-0.764491\pi$
$907$	−44.4853	−1.47711	−0.738555	+	0.674193i	$0.764491\pi$
$908$	4.91169	0.163000
$909$	66.5685	2.20794
$910$	0	0
$911$	57.9411	1.91968	0.959838	−	0.280556i	$-0.0905189\pi$
$911$	57.9411	1.91968	0.959838	+	0.280556i	$0.0905189\pi$
$912$	0	0
$913$	6.00000	0.198571
$914$	6.82843	0.225864
$915$	37.6569	1.24490
$916$	−38.9706	−1.28762
$917$	0	0
$918$	−2.74517	−0.0906040
$919$	−32.0000	−1.05558	−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000	−1.05558	−0.527791	+	0.849374i	$0.676980\pi$
$920$	4.48528	0.147875
$921$	−78.2254	−2.57761
$922$	−13.5147	−0.445084
$923$	−77.2548	−2.54287
$924$	0	0
$925$	3.65685	0.120237
$926$	−9.17157	−0.301397
$927$	−5.85786	−0.192398
$928$	−33.7990	−1.10951
$929$	17.3137	0.568044	0.284022	−	0.958818i	$-0.408331\pi$
$929$	17.3137	0.568044	0.284022	+	0.958818i	$0.408331\pi$
$930$	0	0
$931$	0	0
$932$	−40.4853	−1.32614
$933$	77.2548	2.52921
$934$	−3.79899	−0.124307
$935$	−1.17157	−0.0383145
$936$	54.1421	1.76969
$937$	−49.4558	−1.61565	−0.807826	−	0.589421i	$-0.799356\pi$
$937$	−49.4558	−1.61565	−0.807826	+	0.589421i	$0.799356\pi$
$938$	0	0
$939$	60.2843	1.96730
$940$	−5.17157	−0.168678
$941$	29.3137	0.955600	0.477800	−	0.878469i	$-0.341434\pi$
$941$	29.3137	0.955600	0.477800	+	0.878469i	$0.341434\pi$
$942$	16.4020	0.534407
$943$	−16.9706	−0.552638
$944$	28.9706	0.942912
$945$	0	0
$946$	2.48528	0.0808035
$947$	46.8284	1.52172	0.760860	−	0.648916i	$-0.224778\pi$
$947$	46.8284	1.52172	0.760860	+	0.648916i	$0.224778\pi$
$948$	20.6863	0.671860
$949$	46.6274	1.51359
$950$	0	0
$951$	−60.2843	−1.95485
$952$	0	0
$953$	58.8284	1.90564	0.952820	−	0.303536i	$-0.0981674\pi$
$953$	58.8284	1.90564	0.952820	+	0.303536i	$0.0981674\pi$
$954$	−0.710678	−0.0230091
$955$	−19.3137	−0.624977
$956$	1.25483	0.0405842
$957$	−21.6569	−0.700067
$958$	−14.9117	−0.481775
$959$	0	0
$960$	11.7990	0.380811
$961$	−31.0000	−1.00000
$962$	−10.3431	−0.333476
$963$	−18.2843	−0.589202
$964$	10.9706	0.353338
$965$	−6.82843	−0.219815
$966$	0	0
$967$	18.9706	0.610052	0.305026	−	0.952344i	$-0.401335\pi$
$967$	18.9706	0.610052	0.305026	+	0.952344i	$0.401335\pi$
$968$	1.58579	0.0509691
$969$	0	0
$970$	−3.17157	−0.101833
$971$	31.3137	1.00490	0.502452	−	0.864605i	$-0.332431\pi$
$971$	31.3137	1.00490	0.502452	+	0.864605i	$0.332431\pi$
$972$	−25.8579	−0.829391
$973$	0	0
$974$	3.11270	0.0997373
$975$	−19.3137	−0.618534
$976$	−39.9411	−1.27848
$977$	43.6569	1.39671	0.698353	−	0.715753i	$-0.253916\pi$
$977$	43.6569	1.39671	0.698353	+	0.715753i	$0.253916\pi$
$978$	−0.568542	−0.0181800
$979$	−9.31371	−0.297667
$980$	0	0
$981$	18.2843	0.583772
$982$	9.65685	0.308163
$983$	50.1421	1.59929	0.799643	−	0.600476i	$-0.205022\pi$
$983$	50.1421	1.59929	0.799643	+	0.600476i	$0.205022\pi$
$984$	26.9117	0.857913
$985$	−5.17157	−0.164780
$986$	3.71573	0.118333
$987$	0	0
$988$	0	0
$989$	−16.9706	−0.539633
$990$	−2.07107	−0.0658229
$991$	9.94113	0.315790	0.157895	−	0.987456i	$-0.449529\pi$
$991$	9.94113	0.315790	0.157895	+	0.987456i	$0.449529\pi$
$992$	0	0
$993$	−43.3137	−1.37452
$994$	0	0
$995$	−21.6569	−0.686568
$996$	31.0294	0.983205
$997$	−9.45584	−0.299470	−0.149735	−	0.988726i	$-0.547842\pi$
$997$	−9.45584	−0.299470	−0.149735	+	0.988726i	$0.547842\pi$
$998$	0.686292	0.0217242
$999$	−20.6863	−0.654485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.2.a.f.1.1		2
7.6	odd	2		55.2.a.b.1.1	✓	2
21.20	even	2		495.2.a.b.1.2		2
28.27	even	2		880.2.a.m.1.1		2
35.13	even	4		275.2.b.d.199.3		4
35.27	even	4		275.2.b.d.199.2		4
35.34	odd	2		275.2.a.c.1.2		2
56.13	odd	2		3520.2.a.bn.1.1		2
56.27	even	2		3520.2.a.bo.1.2		2
77.6	even	10		605.2.g.l.366.1		8
77.13	even	10		605.2.g.l.81.1		8
77.20	odd	10		605.2.g.f.81.2		8
77.27	odd	10		605.2.g.f.366.2		8
77.41	even	10		605.2.g.l.251.2		8
77.48	odd	10		605.2.g.f.511.1		8
77.62	even	10		605.2.g.l.511.2		8
77.69	odd	10		605.2.g.f.251.1		8
77.76	even	2		605.2.a.d.1.2		2
84.83	odd	2		7920.2.a.ch.1.1		2
91.90	odd	2		9295.2.a.g.1.2		2
105.62	odd	4		2475.2.c.l.199.3		4
105.83	odd	4		2475.2.c.l.199.2		4
105.104	even	2		2475.2.a.x.1.1		2
140.27	odd	4		4400.2.b.q.4049.4		4
140.83	odd	4		4400.2.b.q.4049.1		4
140.139	even	2		4400.2.a.bn.1.2		2
231.230	odd	2		5445.2.a.y.1.1		2
308.307	odd	2		9680.2.a.bn.1.1		2
385.384	even	2		3025.2.a.o.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.a.b.1.1	✓	2	7.6	odd	2
275.2.a.c.1.2		2	35.34	odd	2
275.2.b.d.199.2		4	35.27	even	4
275.2.b.d.199.3		4	35.13	even	4
495.2.a.b.1.2		2	21.20	even	2
605.2.a.d.1.2		2	77.76	even	2
605.2.g.f.81.2		8	77.20	odd	10
605.2.g.f.251.1		8	77.69	odd	10
605.2.g.f.366.2		8	77.27	odd	10
605.2.g.f.511.1		8	77.48	odd	10
605.2.g.l.81.1		8	77.13	even	10
605.2.g.l.251.2		8	77.41	even	10
605.2.g.l.366.1		8	77.6	even	10
605.2.g.l.511.2		8	77.62	even	10
880.2.a.m.1.1		2	28.27	even	2
2475.2.a.x.1.1		2	105.104	even	2
2475.2.c.l.199.2		4	105.83	odd	4
2475.2.c.l.199.3		4	105.62	odd	4
2695.2.a.f.1.1		2	1.1	even	1	trivial
3025.2.a.o.1.1		2	385.384	even	2
3520.2.a.bn.1.1		2	56.13	odd	2
3520.2.a.bo.1.2		2	56.27	even	2
4400.2.a.bn.1.2		2	140.139	even	2
4400.2.b.q.4049.1		4	140.83	odd	4
4400.2.b.q.4049.4		4	140.27	odd	4
5445.2.a.y.1.1		2	231.230	odd	2
7920.2.a.ch.1.1		2	84.83	odd	2
9295.2.a.g.1.2		2	91.90	odd	2
9680.2.a.bn.1.1		2	308.307	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)

\(f(q)\)	\(=\)	\(q-0.414214 q^{2} -2.82843 q^{3} -1.82843 q^{4} +1.00000 q^{5} +1.17157 q^{6} +1.58579 q^{8} +5.00000 q^{9} +O(q^{10})\)	\(q-0.414214 q^{2} -2.82843 q^{3} -1.82843 q^{4} +1.00000 q^{5} +1.17157 q^{6} +1.58579 q^{8} +5.00000 q^{9} -0.414214 q^{10} +1.00000 q^{11} +5.17157 q^{12} +6.82843 q^{13} -2.82843 q^{15} +3.00000 q^{16} -1.17157 q^{17} -2.07107 q^{18} -1.82843 q^{20} -0.414214 q^{22} +2.82843 q^{23} -4.48528 q^{24} +1.00000 q^{25} -2.82843 q^{26} -5.65685 q^{27} +7.65685 q^{29} +1.17157 q^{30} -4.41421 q^{32} -2.82843 q^{33} +0.485281 q^{34} -9.14214 q^{36} +3.65685 q^{37} -19.3137 q^{39} +1.58579 q^{40} -6.00000 q^{41} -6.00000 q^{43} -1.82843 q^{44} +5.00000 q^{45} -1.17157 q^{46} +2.82843 q^{47} -8.48528 q^{48} -0.414214 q^{50} +3.31371 q^{51} -12.4853 q^{52} +0.343146 q^{53} +2.34315 q^{54} +1.00000 q^{55} -3.17157 q^{58} +9.65685 q^{59} +5.17157 q^{60} -13.3137 q^{61} -4.17157 q^{64} +6.82843 q^{65} +1.17157 q^{66} -4.48528 q^{67} +2.14214 q^{68} -8.00000 q^{69} -11.3137 q^{71} +7.92893 q^{72} +6.82843 q^{73} -1.51472 q^{74} -2.82843 q^{75} +8.00000 q^{78} +4.00000 q^{79} +3.00000 q^{80} +1.00000 q^{81} +2.48528 q^{82} +6.00000 q^{83} -1.17157 q^{85} +2.48528 q^{86} -21.6569 q^{87} +1.58579 q^{88} -9.31371 q^{89} -2.07107 q^{90} -5.17157 q^{92} -1.17157 q^{94} +12.4853 q^{96} +7.65685 q^{97} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 8 q^{6} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 8 * q^6 + 6 * q^8 + 10 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{5} + 8 q^{6} + 6 q^{8} + 10 q^{9} + 2 q^{10} + 2 q^{11} + 16 q^{12} + 8 q^{13} + 6 q^{16} - 8 q^{17} + 10 q^{18} + 2 q^{20} + 2 q^{22} + 8 q^{24} + 2 q^{25} + 4 q^{29} + 8 q^{30} - 6 q^{32} - 16 q^{34} + 10 q^{36} - 4 q^{37} - 16 q^{39} + 6 q^{40} - 12 q^{41} - 12 q^{43} + 2 q^{44} + 10 q^{45} - 8 q^{46} + 2 q^{50} - 16 q^{51} - 8 q^{52} + 12 q^{53} + 16 q^{54} + 2 q^{55} - 12 q^{58} + 8 q^{59} + 16 q^{60} - 4 q^{61} - 14 q^{64} + 8 q^{65} + 8 q^{66} + 8 q^{67} - 24 q^{68} - 16 q^{69} + 30 q^{72} + 8 q^{73} - 20 q^{74} + 16 q^{78} + 8 q^{79} + 6 q^{80} + 2 q^{81} - 12 q^{82} + 12 q^{83} - 8 q^{85} - 12 q^{86} - 32 q^{87} + 6 q^{88} + 4 q^{89} + 10 q^{90} - 16 q^{92} - 8 q^{94} + 8 q^{96} + 4 q^{97} + 10 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^5 + 8 * q^6 + 6 * q^8 + 10 * q^9 + 2 * q^10 + 2 * q^11 + 16 * q^12 + 8 * q^13 + 6 * q^16 - 8 * q^17 + 10 * q^18 + 2 * q^20 + 2 * q^22 + 8 * q^24 + 2 * q^25 + 4 * q^29 + 8 * q^30 - 6 * q^32 - 16 * q^34 + 10 * q^36 - 4 * q^37 - 16 * q^39 + 6 * q^40 - 12 * q^41 - 12 * q^43 + 2 * q^44 + 10 * q^45 - 8 * q^46 + 2 * q^50 - 16 * q^51 - 8 * q^52 + 12 * q^53 + 16 * q^54 + 2 * q^55 - 12 * q^58 + 8 * q^59 + 16 * q^60 - 4 * q^61 - 14 * q^64 + 8 * q^65 + 8 * q^66 + 8 * q^67 - 24 * q^68 - 16 * q^69 + 30 * q^72 + 8 * q^73 - 20 * q^74 + 16 * q^78 + 8 * q^79 + 6 * q^80 + 2 * q^81 - 12 * q^82 + 12 * q^83 - 8 * q^85 - 12 * q^86 - 32 * q^87 + 6 * q^88 + 4 * q^89 + 10 * q^90 - 16 * q^92 - 8 * q^94 + 8 * q^96 + 4 * q^97 + 10 * q^99

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