LMFDB - Embedded newform 8281.2.a.bw.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8281,2,Mod(1,8281)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8281, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8281.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.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:	$66.1241179138$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.746052.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 7x^{3} + 8x + 2 $ x^5 - x^4 - 7x^3 + 8x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.265608$ of defining polynomial
Character	$\chi$	$=$	8281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.26561 q^{2} -2.62728 q^{3} -0.398235 q^{4} +2.90260 q^{5} +3.32511 q^{6} +3.03523 q^{8} +3.90260 q^{9} +O(q^{10})$	\(q-1.26561 q^{2} -2.62728 q^{3} -0.398235 q^{4} +2.90260 q^{5} +3.32511 q^{6} +3.03523 q^{8} +3.90260 q^{9} -3.67356 q^{10} -2.03656 q^{11} +1.04628 q^{12} -7.62594 q^{15} -3.04494 q^{16} +3.99866 q^{17} -4.93916 q^{18} -6.96210 q^{19} -1.15592 q^{20} +2.57749 q^{22} -0.627280 q^{23} -7.97439 q^{24} +3.42509 q^{25} -2.37138 q^{27} +1.09606 q^{29} +9.65146 q^{30} +10.4325 q^{31} -2.21675 q^{32} +5.35062 q^{33} -5.06074 q^{34} -1.55415 q^{36} +3.08537 q^{37} +8.81129 q^{38} +8.81005 q^{40} +0.521150 q^{41} +0.329024 q^{43} +0.811031 q^{44} +11.3277 q^{45} +0.793891 q^{46} -10.5457 q^{47} +7.99991 q^{48} -4.33482 q^{50} -10.5056 q^{51} +7.11900 q^{53} +3.00124 q^{54} -5.91133 q^{55} +18.2914 q^{57} -1.38719 q^{58} -2.03656 q^{59} +3.03692 q^{60} +2.40081 q^{61} -13.2034 q^{62} +8.89542 q^{64} -6.77179 q^{66} -14.6942 q^{67} -1.59241 q^{68} +1.64804 q^{69} -3.60141 q^{71} +11.8453 q^{72} -2.97573 q^{73} -3.90487 q^{74} -8.99866 q^{75} +2.77255 q^{76} -8.76150 q^{79} -8.83824 q^{80} -5.47751 q^{81} -0.659572 q^{82} -12.8039 q^{83} +11.6065 q^{85} -0.416416 q^{86} -2.87966 q^{87} -6.18143 q^{88} +2.68098 q^{89} -14.3364 q^{90} +0.249805 q^{92} -27.4090 q^{93} +13.3467 q^{94} -20.2082 q^{95} +5.82403 q^{96} +2.32902 q^{97} -7.94789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} + 5 q^{6} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 + 5 * q^6 - 9 * q^8 + 3 * q^9	$ 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} + 5 q^{6} - 9 q^{8} + 3 q^{9} - 5 q^{10} - 11 q^{11} + 5 q^{12} + 10 q^{16} - 5 q^{17} - 9 q^{18} - 9 q^{19} - q^{20} + 8 q^{22} + 10 q^{23} + 9 q^{25} - 3 q^{29} - 13 q^{30} + 6 q^{31} - 22 q^{32} - 8 q^{33} + 22 q^{34} + 7 q^{36} - 4 q^{37} - 10 q^{38} + 28 q^{40} - 14 q^{41} + 2 q^{43} + 32 q^{45} - 3 q^{46} - q^{47} - 23 q^{48} - 9 q^{50} - 8 q^{51} + 17 q^{53} - 23 q^{54} + 16 q^{57} + 27 q^{58} - 11 q^{59} + 29 q^{60} - 11 q^{61} - 23 q^{62} + 9 q^{64} + 21 q^{66} - 13 q^{67} - 32 q^{68} + 18 q^{69} - 15 q^{71} + 19 q^{72} - 33 q^{74} - 20 q^{75} - 8 q^{76} + 2 q^{79} - 55 q^{80} - 19 q^{81} + 34 q^{82} - 6 q^{83} + 22 q^{85} - 28 q^{86} - 8 q^{87} - 3 q^{88} + 4 q^{89} - 34 q^{90} + 21 q^{92} - 18 q^{93} + 20 q^{94} - 12 q^{95} + 37 q^{96} + 12 q^{97} - 11 q^{99}+O(q^{100}) $ 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 + 5 * q^6 - 9 * q^8 + 3 * q^9 - 5 * q^10 - 11 * q^11 + 5 * q^12 + 10 * q^16 - 5 * q^17 - 9 * q^18 - 9 * q^19 - q^20 + 8 * q^22 + 10 * q^23 + 9 * q^25 - 3 * q^29 - 13 * q^30 + 6 * q^31 - 22 * q^32 - 8 * q^33 + 22 * q^34 + 7 * q^36 - 4 * q^37 - 10 * q^38 + 28 * q^40 - 14 * q^41 + 2 * q^43 + 32 * q^45 - 3 * q^46 - q^47 - 23 * q^48 - 9 * q^50 - 8 * q^51 + 17 * q^53 - 23 * q^54 + 16 * q^57 + 27 * q^58 - 11 * q^59 + 29 * q^60 - 11 * q^61 - 23 * q^62 + 9 * q^64 + 21 * q^66 - 13 * q^67 - 32 * q^68 + 18 * q^69 - 15 * q^71 + 19 * q^72 - 33 * q^74 - 20 * q^75 - 8 * q^76 + 2 * q^79 - 55 * q^80 - 19 * q^81 + 34 * q^82 - 6 * q^83 + 22 * q^85 - 28 * q^86 - 8 * q^87 - 3 * q^88 + 4 * q^89 - 34 * q^90 + 21 * q^92 - 18 * q^93 + 20 * q^94 - 12 * q^95 + 37 * q^96 + 12 * q^97 - 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.26561	−0.894920	−0.447460	−	0.894304i	$-0.647671\pi$
$2$	−1.26561	−0.894920	−0.447460	+	0.894304i	$0.647671\pi$
$3$	−2.62728	−1.51686	−0.758430	−	0.651754i	$-0.774033\pi$
$3$	−2.62728	−1.51686	−0.758430	+	0.651754i	$0.774033\pi$
$4$	−0.398235	−0.199118
$5$	2.90260	1.29808	0.649041	−	0.760753i	$-0.275170\pi$
$5$	2.90260	1.29808	0.649041	+	0.760753i	$0.275170\pi$
$6$	3.32511	1.35747
$7$	0	0
$7$	0	0
$8$	3.03523	1.07311
$9$	3.90260	1.30087
$10$	−3.67356	−1.16168
$11$	−2.03656	−0.614047	−0.307024	−	0.951702i	$-0.599333\pi$
$11$	−2.03656	−0.614047	−0.307024	+	0.951702i	$0.599333\pi$
$12$	1.04628	0.302034
$13$	0	0
$13$	0	0
$14$	0	0
$15$	−7.62594	−1.96901
$16$	−3.04494	−0.761235
$17$	3.99866	0.969818	0.484909	−	0.874565i	$-0.338853\pi$
$17$	3.99866	0.969818	0.484909	+	0.874565i	$0.338853\pi$
$18$	−4.93916	−1.16417
$19$	−6.96210	−1.59722	−0.798608	−	0.601852i	$-0.794430\pi$
$19$	−6.96210	−1.59722	−0.798608	+	0.601852i	$0.794430\pi$
$20$	−1.15592	−0.258471
$21$	0	0
$22$	2.57749	0.549523
$23$	−0.627280	−0.130797	−0.0653985	−	0.997859i	$-0.520832\pi$
$23$	−0.627280	−0.130797	−0.0653985	+	0.997859i	$0.520832\pi$
$24$	−7.97439	−1.62777
$25$	3.42509	0.685017
$26$	0	0
$27$	−2.37138	−0.456373
$28$	0	0
$29$	1.09606	0.203534	0.101767	−	0.994808i	$-0.467550\pi$
$29$	1.09606	0.203534	0.101767	+	0.994808i	$0.467550\pi$
$30$	9.65146	1.76211
$31$	10.4325	1.87373	0.936864	−	0.349693i	$-0.113714\pi$
$31$	10.4325	1.87373	0.936864	+	0.349693i	$0.113714\pi$
$32$	−2.21675	−0.391870
$33$	5.35062	0.931424
$34$	−5.06074	−0.867910
$35$	0	0
$36$	−1.55415	−0.259025
$37$	3.08537	0.507232	0.253616	−	0.967305i	$-0.418380\pi$
$37$	3.08537	0.507232	0.253616	+	0.967305i	$0.418380\pi$
$38$	8.81129	1.42938
$39$	0	0
$40$	8.81005	1.39299
$41$	0.521150	0.0813900	0.0406950	−	0.999172i	$-0.487043\pi$
$41$	0.521150	0.0813900	0.0406950	+	0.999172i	$0.487043\pi$
$42$	0	0
$43$	0.329024	0.0501757	0.0250879	−	0.999685i	$-0.492013\pi$
$43$	0.329024	0.0501757	0.0250879	+	0.999685i	$0.492013\pi$
$44$	0.811031	0.122268
$45$	11.3277	1.68863
$46$	0.793891	0.117053
$47$	−10.5457	−1.53825	−0.769123	−	0.639101i	$-0.779307\pi$
$47$	−10.5457	−1.53825	−0.769123	+	0.639101i	$0.779307\pi$
$48$	7.99991	1.15469
$49$	0	0
$50$	−4.33482	−0.613036
$51$	−10.5056	−1.47108
$52$	0	0
$53$	7.11900	0.977870	0.488935	−	0.872320i	$-0.337386\pi$
$53$	7.11900	0.977870	0.488935	+	0.872320i	$0.337386\pi$
$54$	3.00124	0.408417
$55$	−5.91133	−0.797084
$56$	0	0
$57$	18.2914	2.42275
$58$	−1.38719	−0.182147
$59$	−2.03656	−0.265138	−0.132569	−	0.991174i	$-0.542323\pi$
$59$	−2.03656	−0.265138	−0.132569	+	0.991174i	$0.542323\pi$
$60$	3.03692	0.392065
$61$	2.40081	0.307393	0.153696	−	0.988118i	$-0.450882\pi$
$61$	2.40081	0.307393	0.153696	+	0.988118i	$0.450882\pi$
$62$	−13.2034	−1.67684
$63$	0	0
$64$	8.89542	1.11193
$65$	0	0
$66$	−6.77179	−0.833550
$67$	−14.6942	−1.79518	−0.897589	−	0.440832i	$-0.854683\pi$
$67$	−14.6942	−1.79518	−0.897589	+	0.440832i	$0.854683\pi$
$68$	−1.59241	−0.193108
$69$	1.64804	0.198401
$70$	0	0
$71$	−3.60141	−0.427409	−0.213704	−	0.976898i	$-0.568553\pi$
$71$	−3.60141	−0.427409	−0.213704	+	0.976898i	$0.568553\pi$
$72$	11.8453	1.39598
$73$	−2.97573	−0.348283	−0.174141	−	0.984721i	$-0.555715\pi$
$73$	−2.97573	−0.348283	−0.174141	+	0.984721i	$0.555715\pi$
$74$	−3.90487	−0.453932
$75$	−8.99866	−1.03908
$76$	2.77255	0.318034
$77$	0	0
$78$	0	0
$79$	−8.76150	−0.985746	−0.492873	−	0.870101i	$-0.664053\pi$
$79$	−8.76150	−0.985746	−0.492873	+	0.870101i	$0.664053\pi$
$80$	−8.83824	−0.988145
$81$	−5.47751	−0.608613
$82$	−0.659572	−0.0728376
$83$	−12.8039	−1.40541	−0.702703	−	0.711483i	$-0.748024\pi$
$83$	−12.8039	−1.40541	−0.702703	+	0.711483i	$0.748024\pi$
$84$	0	0
$85$	11.6065	1.25890
$86$	−0.416416	−0.0449033
$87$	−2.87966	−0.308732
$88$	−6.18143	−0.658943
$89$	2.68098	0.284184	0.142092	−	0.989853i	$-0.454617\pi$
$89$	2.68098	0.284184	0.142092	+	0.989853i	$0.454617\pi$
$90$	−14.3364	−1.51119
$91$	0	0
$92$	0.249805	0.0260440
$93$	−27.4090	−2.84219
$94$	13.3467	1.37661
$95$	−20.2082	−2.07332
$96$	5.82403	0.594413
$97$	2.32902	0.236477	0.118238	−	0.992985i	$-0.462275\pi$
$97$	2.32902	0.236477	0.118238	+	0.992985i	$0.462275\pi$
$98$	0	0
$99$	−7.94789	−0.798793
$100$	−1.36399	−0.136399
$101$	1.45324	0.144603	0.0723014	−	0.997383i	$-0.476966\pi$
$101$	1.45324	0.144603	0.0723014	+	0.997383i	$0.476966\pi$
$102$	13.2960	1.31650
$103$	−11.6353	−1.14646	−0.573230	−	0.819394i	$-0.694310\pi$
$103$	−11.6353	−1.14646	−0.573230	+	0.819394i	$0.694310\pi$
$104$	0	0
$105$	0	0
$106$	−9.00987	−0.875115
$107$	19.6259	1.89731	0.948656	−	0.316310i	$-0.102444\pi$
$107$	19.6259	1.89731	0.948656	+	0.316310i	$0.102444\pi$
$108$	0.944368	0.0908719
$109$	1.10676	0.106008	0.0530040	−	0.998594i	$-0.483120\pi$
$109$	1.10676	0.106008	0.0530040	+	0.998594i	$0.483120\pi$
$110$	7.48143	0.713326
$111$	−8.10613	−0.769400
$112$	0	0
$113$	−1.09606	−0.103109	−0.0515545	−	0.998670i	$-0.516418\pi$
$113$	−1.09606	−0.103109	−0.0515545	+	0.998670i	$0.516418\pi$
$114$	−23.1497	−2.16817
$115$	−1.82074	−0.169785
$116$	−0.436491	−0.0405272
$117$	0	0
$118$	2.57749	0.237277
$119$	0	0
$120$	−23.1465	−2.11297
$121$	−6.85241	−0.622946
$122$	−3.03849	−0.275092
$123$	−1.36921	−0.123457
$124$	−4.15458	−0.373092
$125$	−4.57134	−0.408873
$126$	0	0
$127$	5.18143	0.459778	0.229889	−	0.973217i	$-0.426164\pi$
$127$	5.18143	0.459778	0.229889	+	0.973217i	$0.426164\pi$
$128$	−6.82461	−0.603216
$129$	−0.864439	−0.0761096
$130$	0	0
$131$	10.5667	0.923217	0.461609	−	0.887084i	$-0.347272\pi$
$131$	10.5667	0.923217	0.461609	+	0.887084i	$0.347272\pi$
$132$	−2.13081	−0.185463
$133$	0	0
$134$	18.5971	1.60654
$135$	−6.88318	−0.592410
$136$	12.1368	1.04073
$137$	5.87177	0.501659	0.250830	−	0.968031i	$-0.419297\pi$
$137$	5.87177	0.501659	0.250830	+	0.968031i	$0.419297\pi$
$138$	−2.08577	−0.177553
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	27.7065	2.33331
$142$	4.55797	0.382497
$143$	0	0
$144$	−11.8832	−0.990265
$145$	3.18143	0.264204
$146$	3.76611	0.311685
$147$	0	0
$148$	−1.22870	−0.100999
$149$	10.1054	0.827868	0.413934	−	0.910307i	$-0.364154\pi$
$149$	10.1054	0.827868	0.413934	+	0.910307i	$0.364154\pi$
$150$	11.3888	0.929890
$151$	0.187726	0.0152769	0.00763847	−	0.999971i	$-0.497569\pi$
$151$	0.187726	0.0152769	0.00763847	+	0.999971i	$0.497569\pi$
$152$	−21.1316	−1.71400
$153$	15.6052	1.26160
$154$	0	0
$155$	30.2813	2.43225
$156$	0	0
$157$	−12.0718	−0.963434	−0.481717	−	0.876327i	$-0.659987\pi$
$157$	−12.0718	−0.963434	−0.481717	+	0.876327i	$0.659987\pi$
$158$	11.0886	0.882164
$159$	−18.7036	−1.48329
$160$	−6.43435	−0.508680
$161$	0	0
$162$	6.93239	0.544660
$163$	−14.9136	−1.16812	−0.584060	−	0.811711i	$-0.698537\pi$
$163$	−14.9136	−1.16812	−0.584060	+	0.811711i	$0.698537\pi$
$164$	−0.207540	−0.0162062
$165$	15.5307	1.20906
$166$	16.2047	1.25773
$167$	−5.05664	−0.391294	−0.195647	−	0.980674i	$-0.562681\pi$
$167$	−5.05664	−0.391294	−0.195647	+	0.980674i	$0.562681\pi$
$168$	0	0
$169$	0	0
$170$	−14.6893	−1.12662
$171$	−27.1703	−2.07776
$172$	−0.131029	−0.00999087
$173$	−0.595615	−0.0452837	−0.0226419	−	0.999744i	$-0.507208\pi$
$173$	−0.595615	−0.0452837	−0.0226419	+	0.999744i	$0.507208\pi$
$174$	3.64453	0.276291
$175$	0	0
$176$	6.20121	0.467434
$177$	5.35062	0.402177
$178$	−3.39308	−0.254322
$179$	8.07664	0.603676	0.301838	−	0.953359i	$-0.402400\pi$
$179$	8.07664	0.603676	0.301838	+	0.953359i	$0.402400\pi$
$180$	−4.51108	−0.336236
$181$	1.89324	0.140724	0.0703618	−	0.997522i	$-0.477585\pi$
$181$	1.89324	0.140724	0.0703618	+	0.997522i	$0.477585\pi$
$182$	0	0
$183$	−6.30761	−0.466272
$184$	−1.90394	−0.140360
$185$	8.95559	0.658428
$186$	34.6891	2.54353
$187$	−8.14353	−0.595514
$188$	4.19966	0.306292
$189$	0	0
$190$	25.5757	1.85545
$191$	3.70174	0.267849	0.133924	−	0.990992i	$-0.457242\pi$
$191$	3.70174	0.267849	0.133924	+	0.990992i	$0.457242\pi$
$192$	−23.3708	−1.68664
$193$	−13.5875	−0.978047	−0.489024	−	0.872271i	$-0.662647\pi$
$193$	−13.5875	−0.978047	−0.489024	+	0.872271i	$0.662647\pi$
$194$	−2.94763	−0.211628
$195$	0	0
$196$	0	0
$197$	9.70258	0.691280	0.345640	−	0.938367i	$-0.387662\pi$
$197$	9.70258	0.691280	0.345640	+	0.938367i	$0.387662\pi$
$198$	10.0589	0.714856
$199$	26.2720	1.86237	0.931185	−	0.364547i	$-0.118776\pi$
$199$	26.2720	1.86237	0.931185	+	0.364547i	$0.118776\pi$
$200$	10.3959	0.735102
$201$	38.6057	2.72304
$202$	−1.83923	−0.129408
$203$	0	0
$204$	4.18370	0.292918
$205$	1.51269	0.105651
$206$	14.7257	1.02599
$207$	−2.44802	−0.170149
$208$	0	0
$209$	14.1788	0.980765
$210$	0	0
$211$	10.0338	0.690758	0.345379	−	0.938463i	$-0.387750\pi$
$211$	10.0338	0.690758	0.345379	+	0.938463i	$0.387750\pi$
$212$	−2.83504	−0.194711
$213$	9.46191	0.648320
$214$	−24.8388	−1.69794
$215$	0.955026	0.0651322
$216$	−7.19769	−0.489740
$217$	0	0
$218$	−1.40072	−0.0948688
$219$	7.81807	0.528296
$220$	2.35410	0.158713
$221$	0	0
$222$	10.2592	0.688552
$223$	−17.4961	−1.17163	−0.585813	−	0.810446i	$-0.699225\pi$
$223$	−17.4961	−1.17163	−0.585813	+	0.810446i	$0.699225\pi$
$224$	0	0
$225$	13.3667	0.891116
$226$	1.38719	0.0922743
$227$	9.51630	0.631619	0.315810	−	0.948823i	$-0.397724\pi$
$227$	9.51630	0.631619	0.315810	+	0.948823i	$0.397724\pi$
$228$	−7.28427	−0.482413
$229$	−21.1170	−1.39545	−0.697725	−	0.716366i	$-0.745804\pi$
$229$	−21.1170	−1.39545	−0.697725	+	0.716366i	$0.745804\pi$
$230$	2.30435	0.151944
$231$	0	0
$232$	3.32680	0.218415
$233$	14.1788	0.928881	0.464441	−	0.885604i	$-0.346255\pi$
$233$	14.1788	0.928881	0.464441	+	0.885604i	$0.346255\pi$
$234$	0	0
$235$	−30.6099	−1.99677
$236$	0.811031	0.0527936
$237$	23.0189	1.49524
$238$	0	0
$239$	16.5275	1.06907	0.534536	−	0.845145i	$-0.320486\pi$
$239$	16.5275	1.06907	0.534536	+	0.845145i	$0.320486\pi$
$240$	23.2205	1.49888
$241$	13.6890	0.881786	0.440893	−	0.897560i	$-0.354662\pi$
$241$	13.6890	0.881786	0.440893	+	0.897560i	$0.354662\pi$
$242$	8.67247	0.557487
$243$	21.5051	1.37955
$244$	−0.956089	−0.0612073
$245$	0	0
$246$	1.73288	0.110484
$247$	0	0
$248$	31.6649	2.01073
$249$	33.6393	2.13181
$250$	5.78553	0.365909
$251$	−14.6603	−0.925349	−0.462674	−	0.886528i	$-0.653110\pi$
$251$	−14.6603	−0.925349	−0.462674	+	0.886528i	$0.653110\pi$
$252$	0	0
$253$	1.27750	0.0803155
$254$	−6.55767	−0.411464
$255$	−30.4936	−1.90958
$256$	−9.15355	−0.572097
$257$	−1.75277	−0.109335	−0.0546675	−	0.998505i	$-0.517410\pi$
$257$	−1.75277	−0.109335	−0.0546675	+	0.998505i	$0.517410\pi$
$258$	1.09404	0.0681120
$259$	0	0
$260$	0	0
$261$	4.27750	0.264770
$262$	−13.3733	−0.826206
$263$	26.9416	1.66129	0.830645	−	0.556802i	$-0.187972\pi$
$263$	26.9416	1.66129	0.830645	+	0.556802i	$0.187972\pi$
$264$	16.2404	0.999525
$265$	20.6636	1.26936
$266$	0	0
$267$	−7.04370	−0.431067
$268$	5.85174	0.357452
$269$	−22.0691	−1.34558	−0.672789	−	0.739835i	$-0.734904\pi$
$269$	−22.0691	−1.34558	−0.672789	+	0.739835i	$0.734904\pi$
$270$	8.71141	0.530159
$271$	8.96210	0.544409	0.272204	−	0.962239i	$-0.412247\pi$
$271$	8.96210	0.544409	0.272204	+	0.962239i	$0.412247\pi$
$272$	−12.1757	−0.738259
$273$	0	0
$274$	−7.43137	−0.448945
$275$	−6.97541	−0.420633
$276$	−0.656308	−0.0395051
$277$	−7.52925	−0.452389	−0.226194	−	0.974082i	$-0.572628\pi$
$277$	−7.52925	−0.452389	−0.226194	+	0.974082i	$0.572628\pi$
$278$	5.06243	0.303625
$279$	40.7138	2.43747
$280$	0	0
$281$	−29.7762	−1.77630	−0.888151	−	0.459553i	$-0.848010\pi$
$281$	−29.7762	−1.77630	−0.888151	+	0.459553i	$0.848010\pi$
$282$	−35.0655	−2.08812
$283$	0.301451	0.0179194	0.00895970	−	0.999960i	$-0.497148\pi$
$283$	0.301451	0.0179194	0.00895970	+	0.999960i	$0.497148\pi$
$284$	1.43421	0.0851046
$285$	53.0926	3.14493
$286$	0	0
$287$	0	0
$288$	−8.65110	−0.509771
$289$	−1.01069	−0.0594526
$290$	−4.02645	−0.236441
$291$	−6.11900	−0.358702
$292$	1.18504	0.0693492
$293$	19.2471	1.12443	0.562214	−	0.826992i	$-0.309950\pi$
$293$	19.2471	1.12443	0.562214	+	0.826992i	$0.309950\pi$
$294$	0	0
$295$	−5.91133	−0.344171
$296$	9.36480	0.544318
$297$	4.82947	0.280234
$298$	−12.7895	−0.740876
$299$	0	0
$300$	3.58358	0.206898
$301$	0	0
$302$	−0.237588	−0.0136716
$303$	−3.81807	−0.219342
$304$	21.1992	1.21586
$305$	6.96860	0.399021
$306$	−19.7501	−1.12904
$307$	3.57779	0.204195	0.102098	−	0.994774i	$-0.467445\pi$
$307$	3.57779	0.204195	0.102098	+	0.994774i	$0.467445\pi$
$308$	0	0
$309$	30.5692	1.73902
$310$	−38.3243	−2.17667
$311$	−23.8306	−1.35131	−0.675655	−	0.737218i	$-0.736139\pi$
$311$	−23.8306	−1.35131	−0.675655	+	0.737218i	$0.736139\pi$
$312$	0	0
$313$	−18.0814	−1.02202	−0.511009	−	0.859575i	$-0.670728\pi$
$313$	−18.0814	−1.02202	−0.511009	+	0.859575i	$0.670728\pi$
$314$	15.2782	0.862196
$315$	0	0
$316$	3.48914	0.196279
$317$	27.5482	1.54726	0.773630	−	0.633638i	$-0.218439\pi$
$317$	27.5482	1.54726	0.773630	+	0.633638i	$0.218439\pi$
$318$	23.6714	1.32743
$319$	−2.23220	−0.124979
$320$	25.8198	1.44337
$321$	−51.5628	−2.87796
$322$	0	0
$323$	−27.8391	−1.54901
$324$	2.18134	0.121185
$325$	0	0
$326$	18.8747	1.04537
$327$	−2.90776	−0.160799
$328$	1.58181	0.0873408
$329$	0	0
$330$	−19.6558	−1.08202
$331$	18.1814	0.999339	0.499669	−	0.866216i	$-0.333455\pi$
$331$	18.1814	0.999339	0.499669	+	0.866216i	$0.333455\pi$
$332$	5.09895	0.279841
$333$	12.0410	0.659841
$334$	6.39972	0.350177
$335$	−42.6513	−2.33029
$336$	0	0
$337$	−17.1381	−0.933572	−0.466786	−	0.884370i	$-0.654588\pi$
$337$	−17.1381	−0.933572	−0.466786	+	0.884370i	$0.654588\pi$
$338$	0	0
$339$	2.87966	0.156402
$340$	−4.62212	−0.250670
$341$	−21.2464	−1.15056
$342$	34.3869	1.85943
$343$	0	0
$344$	0.998663	0.0538443
$345$	4.78360	0.257540
$346$	0.753815	0.0405253
$347$	22.2688	1.19545	0.597725	−	0.801701i	$-0.296071\pi$
$347$	22.2688	1.19545	0.597725	+	0.801701i	$0.296071\pi$
$348$	1.14678	0.0614741
$349$	−19.9368	−1.06719	−0.533595	−	0.845740i	$-0.679159\pi$
$349$	−19.9368	−1.06719	−0.533595	+	0.845740i	$0.679159\pi$
$350$	0	0
$351$	0	0
$352$	4.51456	0.240627
$353$	−22.9152	−1.21965	−0.609825	−	0.792536i	$-0.708760\pi$
$353$	−22.9152	−1.21965	−0.609825	+	0.792536i	$0.708760\pi$
$354$	−6.77179	−0.359917
$355$	−10.4535	−0.554812
$356$	−1.06766	−0.0565860
$357$	0	0
$358$	−10.2219	−0.540242
$359$	−27.2314	−1.43722	−0.718610	−	0.695413i	$-0.755221\pi$
$359$	−27.2314	−1.43722	−0.718610	+	0.695413i	$0.755221\pi$
$360$	34.3821	1.81210
$361$	29.4708	1.55110
$362$	−2.39611	−0.125936
$363$	18.0032	0.944923
$364$	0	0
$365$	−8.63735	−0.452099
$366$	7.98297	0.417276
$367$	−10.8564	−0.566702	−0.283351	−	0.959016i	$-0.591446\pi$
$367$	−10.8564	−0.566702	−0.283351	+	0.959016i	$0.591446\pi$
$368$	1.91003	0.0995671
$369$	2.03384	0.105878
$370$	−11.3343	−0.589241
$371$	0	0
$372$	10.9152	0.565929
$373$	−2.37144	−0.122789	−0.0613943	−	0.998114i	$-0.519555\pi$
$373$	−2.37144	−0.122789	−0.0613943	+	0.998114i	$0.519555\pi$
$374$	10.3065	0.532938
$375$	12.0102	0.620204
$376$	−32.0085	−1.65071
$377$	0	0
$378$	0	0
$379$	29.2197	1.50092	0.750458	−	0.660918i	$-0.229833\pi$
$379$	29.2197	1.50092	0.750458	+	0.660918i	$0.229833\pi$
$380$	8.04761	0.412834
$381$	−13.6131	−0.697419
$382$	−4.68496	−0.239703
$383$	3.06595	0.156663	0.0783313	−	0.996927i	$-0.475041\pi$
$383$	3.06595	0.156663	0.0783313	+	0.996927i	$0.475041\pi$
$384$	17.9302	0.914995
$385$	0	0
$386$	17.1964	0.875274
$387$	1.28405	0.0652719
$388$	−0.927499	−0.0470866
$389$	27.7410	1.40652	0.703261	−	0.710932i	$-0.251726\pi$
$389$	27.7410	1.40652	0.703261	+	0.710932i	$0.251726\pi$
$390$	0	0
$391$	−2.50828	−0.126849
$392$	0	0
$393$	−27.7617	−1.40039
$394$	−12.2797	−0.618641
$395$	−25.4311	−1.27958
$396$	3.16513	0.159054
$397$	−17.2312	−0.864808	−0.432404	−	0.901680i	$-0.642335\pi$
$397$	−17.2312	−0.864808	−0.432404	+	0.901680i	$0.642335\pi$
$398$	−33.2500	−1.66667
$399$	0	0
$400$	−10.4292	−0.521459
$401$	−16.6440	−0.831163	−0.415582	−	0.909556i	$-0.636422\pi$
$401$	−16.6440	−0.831163	−0.415582	+	0.909556i	$0.636422\pi$
$402$	−48.8597	−2.43690
$403$	0	0
$404$	−0.578731	−0.0287930
$405$	−15.8990	−0.790029
$406$	0	0
$407$	−6.28355	−0.311464
$408$	−31.8869	−1.57864
$409$	13.6338	0.674147	0.337073	−	0.941478i	$-0.390563\pi$
$409$	13.6338	0.674147	0.337073	+	0.941478i	$0.390563\pi$
$410$	−1.91447	−0.0945491
$411$	−15.4268	−0.760948
$412$	4.63359	0.228280
$413$	0	0
$414$	3.09824	0.152270
$415$	−37.1645	−1.82433
$416$	0	0
$417$	10.5091	0.514634
$418$	−17.9448	−0.877707
$419$	−10.8502	−0.530066	−0.265033	−	0.964239i	$-0.585383\pi$
$419$	−10.8502	−0.530066	−0.265033	+	0.964239i	$0.585383\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	−12.6989	−0.618173
$423$	−41.1556	−2.00105
$424$	21.6078	1.04937
$425$	13.6958	0.664342
$426$	−11.9751	−0.580194
$427$	0	0
$428$	−7.81574	−0.377788
$429$	0	0
$430$	−1.20869	−0.0582881
$431$	−1.20953	−0.0582609	−0.0291304	−	0.999576i	$-0.509274\pi$
$431$	−1.20953	−0.0582609	−0.0291304	+	0.999576i	$0.509274\pi$
$432$	7.22072	0.347407
$433$	−5.56422	−0.267399	−0.133700	−	0.991022i	$-0.542686\pi$
$433$	−5.56422	−0.267399	−0.133700	+	0.991022i	$0.542686\pi$
$434$	0	0
$435$	−8.35851	−0.400760
$436$	−0.440749	−0.0211081
$437$	4.36719	0.208911
$438$	−9.89461	−0.472783
$439$	−19.7192	−0.941146	−0.470573	−	0.882361i	$-0.655953\pi$
$439$	−19.7192	−0.941146	−0.470573	+	0.882361i	$0.655953\pi$
$440$	−17.9422	−0.855362
$441$	0	0
$442$	0	0
$443$	22.2310	1.05623	0.528113	−	0.849174i	$-0.322900\pi$
$443$	22.2310	1.05623	0.528113	+	0.849174i	$0.322900\pi$
$444$	3.22815	0.153201
$445$	7.78182	0.368894
$446$	22.1432	1.04851
$447$	−26.5498	−1.25576
$448$	0	0
$449$	−18.4579	−0.871082	−0.435541	−	0.900169i	$-0.643443\pi$
$449$	−18.4579	−0.871082	−0.435541	+	0.900169i	$0.643443\pi$
$450$	−16.9171	−0.797478
$451$	−1.06136	−0.0499773
$452$	0.436491	0.0205308
$453$	−0.493209	−0.0231730
$454$	−12.0439	−0.565249
$455$	0	0
$456$	55.5185	2.59989
$457$	29.9819	1.40250	0.701248	−	0.712917i	$-0.252627\pi$
$457$	29.9819	1.40250	0.701248	+	0.712917i	$0.252627\pi$
$458$	26.7258	1.24882
$459$	−9.48236	−0.442599
$460$	0.725084	0.0338072
$461$	−29.1498	−1.35764	−0.678821	−	0.734304i	$-0.737509\pi$
$461$	−29.1498	−1.35764	−0.678821	+	0.734304i	$0.737509\pi$
$462$	0	0
$463$	−1.55900	−0.0724530	−0.0362265	−	0.999344i	$-0.511534\pi$
$463$	−1.55900	−0.0724530	−0.0362265	+	0.999344i	$0.511534\pi$
$464$	−3.33744	−0.154937
$465$	−79.5575	−3.68939
$466$	−17.9448	−0.831275
$467$	12.4231	0.574874	0.287437	−	0.957800i	$-0.407197\pi$
$467$	12.4231	0.574874	0.287437	+	0.957800i	$0.407197\pi$
$468$	0	0
$469$	0	0
$470$	38.7402	1.78695
$471$	31.7160	1.46139
$472$	−6.18143	−0.284523
$473$	−0.670079	−0.0308103
$474$	−29.1329	−1.33812
$475$	−23.8458	−1.09412
$476$	0	0
$477$	27.7826	1.27208
$478$	−20.9173	−0.956735
$479$	−36.0558	−1.64743	−0.823716	−	0.567003i	$-0.808103\pi$
$479$	−36.0558	−1.64743	−0.823716	+	0.567003i	$0.808103\pi$
$480$	16.9048	0.771597
$481$	0	0
$482$	−17.3249	−0.789128
$483$	0	0
$484$	2.72887	0.124040
$485$	6.76023	0.306966
$486$	−27.2170	−1.23459
$487$	−7.30004	−0.330796	−0.165398	−	0.986227i	$-0.552891\pi$
$487$	−7.30004	−0.330796	−0.165398	+	0.986227i	$0.552891\pi$
$488$	7.28702	0.329868
$489$	39.1821	1.77188
$490$	0	0
$491$	4.49178	0.202711	0.101356	−	0.994850i	$-0.467682\pi$
$491$	4.49178	0.202711	0.101356	+	0.994850i	$0.467682\pi$
$492$	0.545267	0.0245825
$493$	4.38279	0.197391
$494$	0	0
$495$	−23.0696	−1.03690
$496$	−31.7663	−1.42635
$497$	0	0
$498$	−42.5742	−1.90780
$499$	−11.3674	−0.508873	−0.254437	−	0.967089i	$-0.581890\pi$
$499$	−11.3674	−0.508873	−0.254437	+	0.967089i	$0.581890\pi$
$500$	1.82047	0.0814139
$501$	13.2852	0.593539
$502$	18.5542	0.828113
$503$	17.1080	0.762806	0.381403	−	0.924409i	$-0.375441\pi$
$503$	17.1080	0.762806	0.381403	+	0.924409i	$0.375441\pi$
$504$	0	0
$505$	4.21818	0.187706
$506$	−1.61681	−0.0718759
$507$	0	0
$508$	−2.06343	−0.0915498
$509$	−3.28284	−0.145509	−0.0727547	−	0.997350i	$-0.523179\pi$
$509$	−3.28284	−0.145509	−0.0727547	+	0.997350i	$0.523179\pi$
$510$	38.5929	1.70892
$511$	0	0
$512$	25.2340	1.11520
$513$	16.5098	0.728926
$514$	2.21833	0.0978462
$515$	−33.7726	−1.48820
$516$	0.344250	0.0151548
$517$	21.4770	0.944555
$518$	0	0
$519$	1.56485	0.0686891
$520$	0	0
$521$	−4.77061	−0.209004	−0.104502	−	0.994525i	$-0.533325\pi$
$521$	−4.77061	−0.209004	−0.104502	+	0.994525i	$0.533325\pi$
$522$	−5.41363	−0.236948
$523$	25.5124	1.11558	0.557789	−	0.829983i	$-0.311650\pi$
$523$	25.5124	1.11558	0.557789	+	0.829983i	$0.311650\pi$
$524$	−4.20803	−0.183829
$525$	0	0
$526$	−34.0975	−1.48672
$527$	41.7160	1.81718
$528$	−16.2923	−0.709032
$529$	−22.6065	−0.982892
$530$	−26.1520	−1.13597
$531$	−7.94789	−0.344909
$532$	0	0
$533$	0	0
$534$	8.91456	0.385771
$535$	56.9663	2.46287
$536$	−44.6001	−1.92643
$537$	−21.2196	−0.915693
$538$	27.9309	1.20418
$539$	0	0
$540$	2.74112	0.117959
$541$	16.5157	0.710064	0.355032	−	0.934854i	$-0.384470\pi$
$541$	16.5157	0.710064	0.355032	+	0.934854i	$0.384470\pi$
$542$	−11.3425	−0.487202
$543$	−4.97408	−0.213458
$544$	−8.86405	−0.380043
$545$	3.21247	0.137607
$546$	0	0
$547$	23.3317	0.997591	0.498796	−	0.866720i	$-0.333776\pi$
$547$	23.3317	0.997591	0.498796	+	0.866720i	$0.333776\pi$
$548$	−2.33835	−0.0998892
$549$	9.36942	0.399877
$550$	8.82814	0.376433
$551$	−7.63090	−0.325087
$552$	5.00218	0.212907
$553$	0	0
$554$	9.52909	0.404852
$555$	−23.5289	−0.998744
$556$	1.59294	0.0675557
$557$	20.0471	0.849422	0.424711	−	0.905329i	$-0.360376\pi$
$557$	20.0471	0.849422	0.424711	+	0.905329i	$0.360376\pi$
$558$	−51.5277	−2.18134
$559$	0	0
$560$	0	0
$561$	21.3953	0.903312
$562$	37.6851	1.58965
$563$	−40.5284	−1.70807	−0.854034	−	0.520218i	$-0.825851\pi$
$563$	−40.5284	−1.70807	−0.854034	+	0.520218i	$0.825851\pi$
$564$	−11.0337	−0.464602
$565$	−3.18143	−0.133844
$566$	−0.381519	−0.0160364
$567$	0	0
$568$	−10.9311	−0.458659
$569$	−21.4504	−0.899246	−0.449623	−	0.893219i	$-0.648442\pi$
$569$	−21.4504	−0.899246	−0.449623	+	0.893219i	$0.648442\pi$
$570$	−67.1944	−2.81446
$571$	−10.9559	−0.458489	−0.229244	−	0.973369i	$-0.573625\pi$
$571$	−10.9559	−0.458489	−0.229244	+	0.973369i	$0.573625\pi$
$572$	0	0
$573$	−9.72552	−0.406289
$574$	0	0
$575$	−2.14849	−0.0895982
$576$	34.7153	1.44647
$577$	−34.7415	−1.44631	−0.723154	−	0.690687i	$-0.757308\pi$
$577$	−34.7415	−1.44631	−0.723154	+	0.690687i	$0.757308\pi$
$578$	1.27914	0.0532053
$579$	35.6981	1.48356
$580$	−1.26696	−0.0526076
$581$	0	0
$582$	7.74426	0.321010
$583$	−14.4983	−0.600458
$584$	−9.03201	−0.373747
$585$	0	0
$586$	−24.3593	−1.00627
$587$	22.8463	0.942967	0.471483	−	0.881875i	$-0.343719\pi$
$587$	22.8463	0.942967	0.471483	+	0.881875i	$0.343719\pi$
$588$	0	0
$589$	−72.6320	−2.99275
$590$	7.48143	0.308006
$591$	−25.4914	−1.04858
$592$	−9.39476	−0.386122
$593$	−17.5935	−0.722480	−0.361240	−	0.932473i	$-0.617646\pi$
$593$	−17.5935	−0.722480	−0.361240	+	0.932473i	$0.617646\pi$
$594$	−6.11222	−0.250787
$595$	0	0
$596$	−4.02433	−0.164843
$597$	−69.0238	−2.82496
$598$	0	0
$599$	31.0073	1.26692	0.633461	−	0.773774i	$-0.281634\pi$
$599$	31.0073	1.26692	0.633461	+	0.773774i	$0.281634\pi$
$600$	−27.3130	−1.11505
$601$	−1.43754	−0.0586385	−0.0293193	−	0.999570i	$-0.509334\pi$
$601$	−1.43754	−0.0586385	−0.0293193	+	0.999570i	$0.509334\pi$
$602$	0	0
$603$	−57.3455	−2.33529
$604$	−0.0747591	−0.00304191
$605$	−19.8898	−0.808635
$606$	4.83218	0.196294
$607$	−33.0171	−1.34012	−0.670061	−	0.742306i	$-0.733732\pi$
$607$	−33.0171	−1.34012	−0.670061	+	0.742306i	$0.733732\pi$
$608$	15.4333	0.625901
$609$	0	0
$610$	−8.81953	−0.357092
$611$	0	0
$612$	−6.21453	−0.251208
$613$	43.1657	1.74345	0.871723	−	0.489999i	$-0.163003\pi$
$613$	43.1657	1.74345	0.871723	+	0.489999i	$0.163003\pi$
$614$	−4.52808	−0.182738
$615$	−3.97426	−0.160258
$616$	0	0
$617$	−2.45772	−0.0989441	−0.0494721	−	0.998776i	$-0.515754\pi$
$617$	−2.45772	−0.0989441	−0.0494721	+	0.998776i	$0.515754\pi$
$618$	−38.6886	−1.55628
$619$	−37.7789	−1.51846	−0.759231	−	0.650822i	$-0.774425\pi$
$619$	−37.7789	−1.51846	−0.759231	+	0.650822i	$0.774425\pi$
$620$	−12.0591	−0.484305
$621$	1.48752	0.0596922
$622$	30.1602	1.20932
$623$	0	0
$624$	0	0
$625$	−30.3942	−1.21577
$626$	22.8839	0.914625
$627$	−37.2516	−1.48768
$628$	4.80741	0.191837
$629$	12.3374	0.491922
$630$	0	0
$631$	28.4828	1.13388	0.566942	−	0.823758i	$-0.308126\pi$
$631$	28.4828	1.13388	0.566942	+	0.823758i	$0.308126\pi$
$632$	−26.5932	−1.05782
$633$	−26.3617	−1.04778
$634$	−34.8652	−1.38467
$635$	15.0396	0.596829
$636$	7.44843	0.295350
$637$	0	0
$638$	2.82509	0.111847
$639$	−14.0549	−0.556002
$640$	−19.8091	−0.783024
$641$	−27.1922	−1.07403	−0.537014	−	0.843573i	$-0.680448\pi$
$641$	−27.1922	−1.07403	−0.537014	+	0.843573i	$0.680448\pi$
$642$	65.2584	2.57554
$643$	37.1664	1.46570	0.732849	−	0.680391i	$-0.238190\pi$
$643$	37.1664	1.46570	0.732849	+	0.680391i	$0.238190\pi$
$644$	0	0
$645$	−2.50912	−0.0987965
$646$	35.2334	1.38624
$647$	18.8319	0.740357	0.370178	−	0.928961i	$-0.379297\pi$
$647$	18.8319	0.740357	0.370178	+	0.928961i	$0.379297\pi$
$648$	−16.6255	−0.653111
$649$	4.14759	0.162807
$650$	0	0
$651$	0	0
$652$	5.93910	0.232593
$653$	−26.0185	−1.01818	−0.509090	−	0.860713i	$-0.670018\pi$
$653$	−26.0185	−1.01818	−0.509090	+	0.860713i	$0.670018\pi$
$654$	3.68008	0.143903
$655$	30.6709	1.19841
$656$	−1.58687	−0.0619569
$657$	−11.6131	−0.453069
$658$	0	0
$659$	−33.3339	−1.29851	−0.649253	−	0.760573i	$-0.724918\pi$
$659$	−33.3339	−1.29851	−0.649253	+	0.760573i	$0.724918\pi$
$660$	−6.18488	−0.240746
$661$	−6.29841	−0.244980	−0.122490	−	0.992470i	$-0.539088\pi$
$661$	−6.29841	−0.244980	−0.122490	+	0.992470i	$0.539088\pi$
$662$	−23.0105	−0.894329
$663$	0	0
$664$	−38.8626	−1.50816
$665$	0	0
$666$	−15.2391	−0.590505
$667$	−0.687538	−0.0266216
$668$	2.01373	0.0779136
$669$	45.9672	1.77719
$670$	53.9799	2.08542
$671$	−4.88941	−0.188754
$672$	0	0
$673$	18.3188	0.706137	0.353068	−	0.935598i	$-0.385138\pi$
$673$	18.3188	0.706137	0.353068	+	0.935598i	$0.385138\pi$
$674$	21.6901	0.835473
$675$	−8.12219	−0.312623
$676$	0	0
$677$	24.3392	0.935430	0.467715	−	0.883879i	$-0.345077\pi$
$677$	24.3392	0.935430	0.467715	+	0.883879i	$0.345077\pi$
$678$	−3.64453	−0.139967
$679$	0	0
$680$	35.2284	1.35095
$681$	−25.0020	−0.958078
$682$	26.8896	1.02966
$683$	−11.7682	−0.450297	−0.225149	−	0.974324i	$-0.572287\pi$
$683$	−11.7682	−0.450297	−0.225149	+	0.974324i	$0.572287\pi$
$684$	10.8202	0.413719
$685$	17.0434	0.651195
$686$	0	0
$687$	55.4802	2.11670
$688$	−1.00186	−0.0381955
$689$	0	0
$690$	−6.05417	−0.230478
$691$	−1.17785	−0.0448074	−0.0224037	−	0.999749i	$-0.507132\pi$
$691$	−1.17785	−0.0448074	−0.0224037	+	0.999749i	$0.507132\pi$
$692$	0.237195	0.00901679
$693$	0	0
$694$	−28.1835	−1.06983
$695$	−11.6104	−0.440408
$696$	−8.74043	−0.331305
$697$	2.08390	0.0789335
$698$	25.2321	0.955050
$699$	−37.2516	−1.40898
$700$	0	0
$701$	−31.2867	−1.18168	−0.590841	−	0.806788i	$-0.701204\pi$
$701$	−31.2867	−1.18168	−0.590841	+	0.806788i	$0.701204\pi$
$702$	0	0
$703$	−21.4806	−0.810158
$704$	−18.1161	−0.682776
$705$	80.4208	3.02882
$706$	29.0016	1.09149
$707$	0	0
$708$	−2.13081	−0.0800806
$709$	−15.3748	−0.577411	−0.288706	−	0.957418i	$-0.593225\pi$
$709$	−15.3748	−0.577411	−0.288706	+	0.957418i	$0.593225\pi$
$710$	13.2300	0.496512
$711$	−34.1926	−1.28232
$712$	8.13739	0.304962
$713$	−6.54409	−0.245078
$714$	0	0
$715$	0	0
$716$	−3.21640	−0.120203
$717$	−43.4223	−1.62163
$718$	34.4643	1.28620
$719$	−11.1417	−0.415517	−0.207759	−	0.978180i	$-0.566617\pi$
$719$	−11.1417	−0.415517	−0.207759	+	0.978180i	$0.566617\pi$
$720$	−34.4921	−1.28545
$721$	0	0
$722$	−37.2985	−1.38811
$723$	−35.9648	−1.33755
$724$	−0.753956	−0.0280206
$725$	3.75411	0.139424
$726$	−22.7850	−0.845631
$727$	−6.24735	−0.231702	−0.115851	−	0.993267i	$-0.536959\pi$
$727$	−6.24735	−0.231702	−0.115851	+	0.993267i	$0.536959\pi$
$728$	0	0
$729$	−40.0674	−1.48398
$730$	10.9315	0.404593
$731$	1.31566	0.0486613
$732$	2.51191	0.0928430
$733$	−30.9669	−1.14379	−0.571894	−	0.820327i	$-0.693791\pi$
$733$	−30.9669	−1.14379	−0.571894	+	0.820327i	$0.693791\pi$
$734$	13.7400	0.507153
$735$	0	0
$736$	1.39053	0.0512554
$737$	29.9256	1.10232
$738$	−2.57405	−0.0947520
$739$	−2.33744	−0.0859843	−0.0429921	−	0.999075i	$-0.513689\pi$
$739$	−2.33744	−0.0859843	−0.0429921	+	0.999075i	$0.513689\pi$
$740$	−3.56643	−0.131105
$741$	0	0
$742$	0	0
$743$	−24.3612	−0.893726	−0.446863	−	0.894603i	$-0.647459\pi$
$743$	−24.3612	−0.893726	−0.446863	+	0.894603i	$0.647459\pi$
$744$	−83.1927	−3.04999
$745$	29.3320	1.07464
$746$	3.00132	0.109886
$747$	−49.9684	−1.82825
$748$	3.24304	0.118577
$749$	0	0
$750$	−15.2002	−0.555033
$751$	−12.0253	−0.438810	−0.219405	−	0.975634i	$-0.570412\pi$
$751$	−12.0253	−0.438810	−0.219405	+	0.975634i	$0.570412\pi$
$752$	32.1110	1.17097
$753$	38.5167	1.40363
$754$	0	0
$755$	0.544894	0.0198307
$756$	0	0
$757$	25.9905	0.944641	0.472321	−	0.881427i	$-0.343416\pi$
$757$	25.9905	0.944641	0.472321	+	0.881427i	$0.343416\pi$
$758$	−36.9807	−1.34320
$759$	−3.35634	−0.121827
$760$	−61.3364	−2.22491
$761$	−13.3270	−0.483103	−0.241552	−	0.970388i	$-0.577656\pi$
$761$	−13.3270	−0.483103	−0.241552	+	0.970388i	$0.577656\pi$
$762$	17.2288	0.624134
$763$	0	0
$764$	−1.47416	−0.0533334
$765$	45.2956	1.63767
$766$	−3.88029	−0.140200
$767$	0	0
$768$	24.0489	0.867792
$769$	−9.24486	−0.333378	−0.166689	−	0.986010i	$-0.553308\pi$
$769$	−9.24486	−0.333378	−0.166689	+	0.986010i	$0.553308\pi$
$770$	0	0
$771$	4.60503	0.165846
$772$	5.41101	0.194746
$773$	10.1419	0.364780	0.182390	−	0.983226i	$-0.441617\pi$
$773$	10.1419	0.364780	0.182390	+	0.983226i	$0.441617\pi$
$774$	−1.62510	−0.0584132
$775$	35.7322	1.28354
$776$	7.06912	0.253766
$777$	0	0
$778$	−35.1092	−1.25873
$779$	−3.62830	−0.129997
$780$	0	0
$781$	7.33450	0.262449
$782$	3.17450	0.113520
$783$	−2.59919	−0.0928873
$784$	0	0
$785$	−35.0396	−1.25062
$786$	35.1354	1.25324
$787$	−45.2823	−1.61414	−0.807070	−	0.590456i	$-0.798948\pi$
$787$	−45.2823	−1.61414	−0.807070	+	0.590456i	$0.798948\pi$
$788$	−3.86391	−0.137646
$789$	−70.7831	−2.51995
$790$	32.1859	1.14512
$791$	0	0
$792$	−24.1237	−0.857197
$793$	0	0
$794$	21.8079	0.773935
$795$	−54.2891	−1.92544
$796$	−10.4624	−0.370831
$797$	27.0784	0.959165	0.479583	−	0.877497i	$-0.340788\pi$
$797$	27.0784	0.959165	0.479583	+	0.877497i	$0.340788\pi$
$798$	0	0
$799$	−42.1686	−1.49182
$800$	−7.59257	−0.268438
$801$	10.4628	0.369685
$802$	21.0648	0.743825
$803$	6.06026	0.213862
$804$	−15.3741	−0.542204
$805$	0	0
$806$	0	0
$807$	57.9817	2.04105
$808$	4.41091	0.155175
$809$	−25.7798	−0.906370	−0.453185	−	0.891417i	$-0.649712\pi$
$809$	−25.7798	−0.906370	−0.453185	+	0.891417i	$0.649712\pi$
$810$	20.1219	0.707013
$811$	25.7829	0.905362	0.452681	−	0.891673i	$-0.350468\pi$
$811$	25.7829	0.905362	0.452681	+	0.891673i	$0.350468\pi$
$812$	0	0
$813$	−23.5459	−0.825792
$814$	7.95252	0.278736
$815$	−43.2881	−1.51632
$816$	31.9889	1.11984
$817$	−2.29070	−0.0801414
$818$	−17.2550	−0.603308
$819$	0	0
$820$	−0.602407	−0.0210370
$821$	1.71073	0.0597050	0.0298525	−	0.999554i	$-0.490496\pi$
$821$	1.71073	0.0597050	0.0298525	+	0.999554i	$0.490496\pi$
$822$	19.5243	0.680987
$823$	−40.3773	−1.40747	−0.703733	−	0.710465i	$-0.748485\pi$
$823$	−40.3773	−1.40747	−0.703733	+	0.710465i	$0.748485\pi$
$824$	−35.3158	−1.23028
$825$	18.3264	0.638042
$826$	0	0
$827$	−19.5698	−0.680509	−0.340254	−	0.940333i	$-0.610513\pi$
$827$	−19.5698	−0.680509	−0.340254	+	0.940333i	$0.610513\pi$
$828$	0.974889	0.0338797
$829$	41.5742	1.44393	0.721966	−	0.691928i	$-0.243239\pi$
$829$	41.5742	1.44393	0.721966	+	0.691928i	$0.243239\pi$
$830$	47.0357	1.63263
$831$	19.7815	0.686211
$832$	0	0
$833$	0	0
$834$	−13.3004	−0.460556
$835$	−14.6774	−0.507932
$836$	−5.64648	−0.195288
$837$	−24.7394	−0.855119
$838$	13.7321	0.474367
$839$	−45.8480	−1.58285	−0.791425	−	0.611266i	$-0.790660\pi$
$839$	−45.8480	−1.58285	−0.791425	+	0.611266i	$0.790660\pi$
$840$	0	0
$841$	−27.7986	−0.958574
$842$	−12.6561	−0.436157
$843$	78.2305	2.69440
$844$	−3.99583	−0.137542
$845$	0	0
$846$	52.0869	1.79078
$847$	0	0
$848$	−21.6769	−0.744388
$849$	−0.791997	−0.0271812
$850$	−17.3335	−0.594534
$851$	−1.93539	−0.0663443
$852$	−3.76807	−0.129092
$853$	−40.0236	−1.37038	−0.685191	−	0.728364i	$-0.740281\pi$
$853$	−40.0236	−1.37038	−0.685191	+	0.728364i	$0.740281\pi$
$854$	0	0
$855$	−78.8645	−2.69711
$856$	59.5692	2.03603
$857$	32.8702	1.12282	0.561412	−	0.827536i	$-0.310258\pi$
$857$	32.8702	1.12282	0.561412	+	0.827536i	$0.310258\pi$
$858$	0	0
$859$	−34.0503	−1.16178	−0.580891	−	0.813981i	$-0.697296\pi$
$859$	−34.0503	−1.16178	−0.580891	+	0.813981i	$0.697296\pi$
$860$	−0.380325	−0.0129690
$861$	0	0
$862$	1.53079	0.0521388
$863$	14.0642	0.478749	0.239375	−	0.970927i	$-0.423058\pi$
$863$	14.0642	0.478749	0.239375	+	0.970927i	$0.423058\pi$
$864$	5.25677	0.178839
$865$	−1.72883	−0.0587820
$866$	7.04212	0.239301
$867$	2.65537	0.0901813
$868$	0	0
$869$	17.8434	0.605295
$870$	10.5786	0.358648
$871$	0	0
$872$	3.35926	0.113759
$873$	9.08925	0.307625
$874$	−5.52715	−0.186959
$875$	0	0
$876$	−3.11343	−0.105193
$877$	−51.0669	−1.72441	−0.862204	−	0.506562i	$-0.830916\pi$
$877$	−51.0669	−1.72441	−0.862204	+	0.506562i	$0.830916\pi$
$878$	24.9568	0.842251
$879$	−50.5675	−1.70560
$880$	17.9996	0.606768
$881$	−18.4203	−0.620597	−0.310298	−	0.950639i	$-0.600429\pi$
$881$	−18.4203	−0.620597	−0.310298	+	0.950639i	$0.600429\pi$
$882$	0	0
$883$	0.126678	0.00426305	0.00213153	−	0.999998i	$-0.499322\pi$
$883$	0.126678	0.00426305	0.00213153	+	0.999998i	$0.499322\pi$
$884$	0	0
$885$	15.5307	0.522059
$886$	−28.1357	−0.945239
$887$	3.87470	0.130100	0.0650498	−	0.997882i	$-0.479279\pi$
$887$	3.87470	0.130100	0.0650498	+	0.997882i	$0.479279\pi$
$888$	−24.6039	−0.825654
$889$	0	0
$890$	−9.84874	−0.330131
$891$	11.1553	0.373717
$892$	6.96757	0.233291
$893$	73.4201	2.45691
$894$	33.6016	1.12381
$895$	23.4433	0.783622
$896$	0	0
$897$	0	0
$898$	23.3605	0.779549
$899$	11.4347	0.381367
$900$	−5.32311	−0.177437
$901$	28.4665	0.948356
$902$	1.34326	0.0447257
$903$	0	0
$904$	−3.32680	−0.110648
$905$	5.49533	0.182671
$906$	0.624210	0.0207380
$907$	−46.7741	−1.55311	−0.776555	−	0.630050i	$-0.783035\pi$
$907$	−46.7741	−1.55311	−0.776555	+	0.630050i	$0.783035\pi$
$908$	−3.78973	−0.125766
$909$	5.67142	0.188109
$910$	0	0
$911$	5.93675	0.196693	0.0983467	−	0.995152i	$-0.468645\pi$
$911$	5.93675	0.196693	0.0983467	+	0.995152i	$0.468645\pi$
$912$	−55.6961	−1.84428
$913$	26.0759	0.862986
$914$	−37.9454	−1.25512
$915$	−18.3085	−0.605260
$916$	8.40952	0.277858
$917$	0	0
$918$	12.0010	0.396091
$919$	−8.58701	−0.283259	−0.141630	−	0.989920i	$-0.545234\pi$
$919$	−8.58701	−0.283259	−0.141630	+	0.989920i	$0.545234\pi$
$920$	−5.52637	−0.182199
$921$	−9.39985	−0.309736
$922$	36.8922	1.21498
$923$	0	0
$924$	0	0
$925$	10.5677	0.347463
$926$	1.97309	0.0648396
$927$	−45.4079	−1.49139
$928$	−2.42970	−0.0797589
$929$	8.45945	0.277546	0.138773	−	0.990324i	$-0.455684\pi$
$929$	8.45945	0.277546	0.138773	+	0.990324i	$0.455684\pi$
$930$	100.689	3.30171
$931$	0	0
$932$	−5.64648	−0.184957
$933$	62.6097	2.04975
$934$	−15.7228	−0.514466
$935$	−23.6374	−0.773026
$936$	0	0
$937$	−33.3596	−1.08981	−0.544905	−	0.838498i	$-0.683434\pi$
$937$	−33.3596	−1.08981	−0.544905	+	0.838498i	$0.683434\pi$
$938$	0	0
$939$	47.5048	1.55026
$940$	12.1899	0.397592
$941$	13.4037	0.436949	0.218475	−	0.975843i	$-0.429892\pi$
$941$	13.4037	0.436949	0.218475	+	0.975843i	$0.429892\pi$
$942$	−40.1400	−1.30783
$943$	−0.326907	−0.0106456
$944$	6.20121	0.201832
$945$	0	0
$946$	0.848057	0.0275727
$947$	−43.0794	−1.39989	−0.699946	−	0.714196i	$-0.746793\pi$
$947$	−43.0794	−1.39989	−0.699946	+	0.714196i	$0.746793\pi$
$948$	−9.16695	−0.297729
$949$	0	0
$950$	30.1794	0.979150
$951$	−72.3768	−2.34698
$952$	0	0
$953$	16.7332	0.542040	0.271020	−	0.962574i	$-0.412639\pi$
$953$	16.7332	0.542040	0.271020	+	0.962574i	$0.412639\pi$
$954$	−35.1619	−1.13841
$955$	10.7447	0.347690
$956$	−6.58182	−0.212871
$957$	5.86462	0.189576
$958$	45.6325	1.47432
$959$	0	0
$960$	−67.8360	−2.18940
$961$	77.8366	2.51086
$962$	0	0
$963$	76.5922	2.46815
$964$	−5.45144	−0.175579
$965$	−39.4390	−1.26959
$966$	0	0
$967$	−44.7594	−1.43937	−0.719683	−	0.694303i	$-0.755713\pi$
$967$	−44.7594	−1.43937	−0.719683	+	0.694303i	$0.755713\pi$
$968$	−20.7986	−0.668493
$969$	73.1411	2.34963
$970$	−8.55580	−0.274710
$971$	−4.20259	−0.134867	−0.0674337	−	0.997724i	$-0.521481\pi$
$971$	−4.20259	−0.134867	−0.0674337	+	0.997724i	$0.521481\pi$
$972$	−8.56409	−0.274693
$973$	0	0
$974$	9.23899	0.296036
$975$	0	0
$976$	−7.31033	−0.233998
$977$	25.6899	0.821892	0.410946	−	0.911660i	$-0.365199\pi$
$977$	25.6899	0.821892	0.410946	+	0.911660i	$0.365199\pi$
$978$	−49.5892	−1.58569
$979$	−5.45999	−0.174502
$980$	0	0
$981$	4.31923	0.137902
$982$	−5.68483	−0.181410
$983$	31.8244	1.01504	0.507520	−	0.861640i	$-0.330562\pi$
$983$	31.8244	1.01504	0.507520	+	0.861640i	$0.330562\pi$
$984$	−4.15586	−0.132484
$985$	28.1627	0.897339
$986$	−5.54689	−0.176649
$987$	0	0
$988$	0	0
$989$	−0.206390	−0.00656283
$990$	29.1970	0.927942
$991$	9.47478	0.300976	0.150488	−	0.988612i	$-0.451915\pi$
$991$	9.47478	0.300976	0.150488	+	0.988612i	$0.451915\pi$
$992$	−23.1262	−0.734259
$993$	−47.7676	−1.51586
$994$	0	0
$995$	76.2570	2.41751
$996$	−13.3964	−0.424480
$997$	21.9511	0.695198	0.347599	−	0.937643i	$-0.386997\pi$
$997$	21.9511	0.695198	0.347599	+	0.937643i	$0.386997\pi$
$998$	14.3866	0.455401
$999$	−7.31659	−0.231487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.bw.1.3		5
7.2	even	3		1183.2.e.f.508.3		10
7.4	even	3		1183.2.e.f.170.3		10
7.6	odd	2		8281.2.a.bx.1.3		5
13.12	even	2		637.2.a.l.1.3		5
39.38	odd	2		5733.2.a.bl.1.3		5
91.12	odd	6		637.2.e.m.508.3		10
91.25	even	6		91.2.e.c.79.3	yes	10
91.38	odd	6		637.2.e.m.79.3		10
91.51	even	6		91.2.e.c.53.3	✓	10
91.90	odd	2		637.2.a.k.1.3		5
273.116	odd	6		819.2.j.h.352.3		10
273.233	odd	6		819.2.j.h.235.3		10
273.272	even	2		5733.2.a.bm.1.3		5
364.51	odd	6		1456.2.r.p.417.1		10
364.207	odd	6		1456.2.r.p.625.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.3	✓	10	91.51	even	6
91.2.e.c.79.3	yes	10	91.25	even	6
637.2.a.k.1.3		5	91.90	odd	2
637.2.a.l.1.3		5	13.12	even	2
637.2.e.m.79.3		10	91.38	odd	6
637.2.e.m.508.3		10	91.12	odd	6
819.2.j.h.235.3		10	273.233	odd	6
819.2.j.h.352.3		10	273.116	odd	6
1183.2.e.f.170.3		10	7.4	even	3
1183.2.e.f.508.3		10	7.2	even	3
1456.2.r.p.417.1		10	364.51	odd	6
1456.2.r.p.625.1		10	364.207	odd	6
5733.2.a.bl.1.3		5	39.38	odd	2
5733.2.a.bm.1.3		5	273.272	even	2
8281.2.a.bw.1.3		5	1.1	even	1	trivial
8281.2.a.bx.1.3		5	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:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q-1.26561 q^{2} -2.62728 q^{3} -0.398235 q^{4} +2.90260 q^{5} +3.32511 q^{6} +3.03523 q^{8} +3.90260 q^{9} +O(q^{10})\)	\(q-1.26561 q^{2} -2.62728 q^{3} -0.398235 q^{4} +2.90260 q^{5} +3.32511 q^{6} +3.03523 q^{8} +3.90260 q^{9} -3.67356 q^{10} -2.03656 q^{11} +1.04628 q^{12} -7.62594 q^{15} -3.04494 q^{16} +3.99866 q^{17} -4.93916 q^{18} -6.96210 q^{19} -1.15592 q^{20} +2.57749 q^{22} -0.627280 q^{23} -7.97439 q^{24} +3.42509 q^{25} -2.37138 q^{27} +1.09606 q^{29} +9.65146 q^{30} +10.4325 q^{31} -2.21675 q^{32} +5.35062 q^{33} -5.06074 q^{34} -1.55415 q^{36} +3.08537 q^{37} +8.81129 q^{38} +8.81005 q^{40} +0.521150 q^{41} +0.329024 q^{43} +0.811031 q^{44} +11.3277 q^{45} +0.793891 q^{46} -10.5457 q^{47} +7.99991 q^{48} -4.33482 q^{50} -10.5056 q^{51} +7.11900 q^{53} +3.00124 q^{54} -5.91133 q^{55} +18.2914 q^{57} -1.38719 q^{58} -2.03656 q^{59} +3.03692 q^{60} +2.40081 q^{61} -13.2034 q^{62} +8.89542 q^{64} -6.77179 q^{66} -14.6942 q^{67} -1.59241 q^{68} +1.64804 q^{69} -3.60141 q^{71} +11.8453 q^{72} -2.97573 q^{73} -3.90487 q^{74} -8.99866 q^{75} +2.77255 q^{76} -8.76150 q^{79} -8.83824 q^{80} -5.47751 q^{81} -0.659572 q^{82} -12.8039 q^{83} +11.6065 q^{85} -0.416416 q^{86} -2.87966 q^{87} -6.18143 q^{88} +2.68098 q^{89} -14.3364 q^{90} +0.249805 q^{92} -27.4090 q^{93} +13.3467 q^{94} -20.2082 q^{95} +5.82403 q^{96} +2.32902 q^{97} -7.94789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} + 5 q^{6} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 + 5 * q^6 - 9 * q^8 + 3 * q^9	\( 5 q - 4 q^{2} + 8 q^{4} - 2 q^{5} + 5 q^{6} - 9 q^{8} + 3 q^{9} - 5 q^{10} - 11 q^{11} + 5 q^{12} + 10 q^{16} - 5 q^{17} - 9 q^{18} - 9 q^{19} - q^{20} + 8 q^{22} + 10 q^{23} + 9 q^{25} - 3 q^{29} - 13 q^{30} + 6 q^{31} - 22 q^{32} - 8 q^{33} + 22 q^{34} + 7 q^{36} - 4 q^{37} - 10 q^{38} + 28 q^{40} - 14 q^{41} + 2 q^{43} + 32 q^{45} - 3 q^{46} - q^{47} - 23 q^{48} - 9 q^{50} - 8 q^{51} + 17 q^{53} - 23 q^{54} + 16 q^{57} + 27 q^{58} - 11 q^{59} + 29 q^{60} - 11 q^{61} - 23 q^{62} + 9 q^{64} + 21 q^{66} - 13 q^{67} - 32 q^{68} + 18 q^{69} - 15 q^{71} + 19 q^{72} - 33 q^{74} - 20 q^{75} - 8 q^{76} + 2 q^{79} - 55 q^{80} - 19 q^{81} + 34 q^{82} - 6 q^{83} + 22 q^{85} - 28 q^{86} - 8 q^{87} - 3 q^{88} + 4 q^{89} - 34 q^{90} + 21 q^{92} - 18 q^{93} + 20 q^{94} - 12 q^{95} + 37 q^{96} + 12 q^{97} - 11 q^{99}+O(q^{100}) \) 5 * q - 4 * q^2 + 8 * q^4 - 2 * q^5 + 5 * q^6 - 9 * q^8 + 3 * q^9 - 5 * q^10 - 11 * q^11 + 5 * q^12 + 10 * q^16 - 5 * q^17 - 9 * q^18 - 9 * q^19 - q^20 + 8 * q^22 + 10 * q^23 + 9 * q^25 - 3 * q^29 - 13 * q^30 + 6 * q^31 - 22 * q^32 - 8 * q^33 + 22 * q^34 + 7 * q^36 - 4 * q^37 - 10 * q^38 + 28 * q^40 - 14 * q^41 + 2 * q^43 + 32 * q^45 - 3 * q^46 - q^47 - 23 * q^48 - 9 * q^50 - 8 * q^51 + 17 * q^53 - 23 * q^54 + 16 * q^57 + 27 * q^58 - 11 * q^59 + 29 * q^60 - 11 * q^61 - 23 * q^62 + 9 * q^64 + 21 * q^66 - 13 * q^67 - 32 * q^68 + 18 * q^69 - 15 * q^71 + 19 * q^72 - 33 * q^74 - 20 * q^75 - 8 * q^76 + 2 * q^79 - 55 * q^80 - 19 * q^81 + 34 * q^82 - 6 * q^83 + 22 * q^85 - 28 * q^86 - 8 * q^87 - 3 * q^88 + 4 * q^89 - 34 * q^90 + 21 * q^92 - 18 * q^93 + 20 * q^94 - 12 * q^95 + 37 * q^96 + 12 * q^97 - 11 * q^99

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