LMFDB - Embedded newform 8281.2.a.bx.1.5

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:	$0$
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			1.5
Root			$3.00852$ 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)

$f(q)$	$=$	$q+2.00852 q^{2} -1.75906 q^{3} +2.03417 q^{4} +0.905722 q^{5} -3.53311 q^{6} +0.0686323 q^{8} +0.0942784 q^{9} +O(q^{10})$	\(q+2.00852 q^{2} -1.75906 q^{3} +2.03417 q^{4} +0.905722 q^{5} -3.53311 q^{6} +0.0686323 q^{8} +0.0942784 q^{9} +1.81916 q^{10} -0.716361 q^{11} -3.57822 q^{12} -1.59322 q^{15} -3.93049 q^{16} -2.35227 q^{17} +0.189360 q^{18} +6.63591 q^{19} +1.84239 q^{20} -1.43883 q^{22} +3.75906 q^{23} -0.120728 q^{24} -4.17967 q^{25} +5.11133 q^{27} +3.25799 q^{29} -3.20001 q^{30} +1.57050 q^{31} -8.03175 q^{32} +1.26012 q^{33} -4.72459 q^{34} +0.191778 q^{36} -5.20883 q^{37} +13.3284 q^{38} +0.0621618 q^{40} +4.92168 q^{41} -9.43766 q^{43} -1.45720 q^{44} +0.0853900 q^{45} +7.55016 q^{46} -8.31986 q^{47} +6.91395 q^{48} -8.39497 q^{50} +4.13778 q^{51} +14.0833 q^{53} +10.2662 q^{54} -0.648824 q^{55} -11.6729 q^{57} +6.54376 q^{58} +0.716361 q^{59} -3.24087 q^{60} +11.6527 q^{61} +3.15439 q^{62} -8.27099 q^{64} +2.53098 q^{66} -9.39174 q^{67} -4.78492 q^{68} -6.61239 q^{69} -10.9914 q^{71} +0.00647055 q^{72} -3.47300 q^{73} -10.4621 q^{74} +7.35227 q^{75} +13.4986 q^{76} +13.0082 q^{79} -3.55993 q^{80} -9.27395 q^{81} +9.88531 q^{82} +3.54083 q^{83} -2.13050 q^{85} -18.9558 q^{86} -5.73099 q^{87} -0.0491655 q^{88} +12.0501 q^{89} +0.171508 q^{90} +7.64656 q^{92} -2.76260 q^{93} -16.7106 q^{94} +6.01029 q^{95} +14.1283 q^{96} +7.43766 q^{97} -0.0675374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.00852	1.42024	0.710121	−	0.704080i	$-0.248640\pi$
$2$	2.00852	1.42024	0.710121	+	0.704080i	$0.248640\pi$
$3$	−1.75906	−1.01559	−0.507796	−	0.861477i	$-0.669540\pi$
$3$	−1.75906	−1.01559	−0.507796	+	0.861477i	$0.669540\pi$
$4$	2.03417	1.01709
$5$	0.905722	0.405051	0.202526	−	0.979277i	$-0.435085\pi$
$5$	0.905722	0.405051	0.202526	+	0.979277i	$0.435085\pi$
$6$	−3.53311	−1.44238
$7$	0	0
$7$	0	0
$8$	0.0686323	0.0242652
$9$	0.0942784	0.0314261
$10$	1.81916	0.575270
$11$	−0.716361	−0.215991	−0.107996	−	0.994151i	$-0.534443\pi$
$11$	−0.716361	−0.215991	−0.107996	+	0.994151i	$0.534443\pi$
$12$	−3.57822	−1.03294
$13$	0	0
$13$	0	0
$14$	0	0
$15$	−1.59322	−0.411366
$16$	−3.93049	−0.982623
$17$	−2.35227	−0.570510	−0.285255	−	0.958452i	$-0.592078\pi$
$17$	−2.35227	−0.570510	−0.285255	+	0.958452i	$0.592078\pi$
$18$	0.189360	0.0446327
$19$	6.63591	1.52238	0.761191	−	0.648528i	$-0.224615\pi$
$19$	6.63591	1.52238	0.761191	+	0.648528i	$0.224615\pi$
$20$	1.84239	0.411971
$21$	0	0
$22$	−1.43883	−0.306759
$23$	3.75906	0.783817	0.391909	−	0.920004i	$-0.371815\pi$
$23$	3.75906	0.783817	0.391909	+	0.920004i	$0.371815\pi$
$24$	−0.120728	−0.0246435
$25$	−4.17967	−0.835934
$26$	0	0
$27$	5.11133	0.983675
$28$	0	0
$29$	3.25799	0.604994	0.302497	−	0.953150i	$-0.402180\pi$
$29$	3.25799	0.604994	0.302497	+	0.953150i	$0.402180\pi$
$30$	−3.20001	−0.584239
$31$	1.57050	0.282070	0.141035	−	0.990005i	$-0.454957\pi$
$31$	1.57050	0.282070	0.141035	+	0.990005i	$0.454957\pi$
$32$	−8.03175	−1.41983
$33$	1.26012	0.219359
$34$	−4.72459	−0.810261
$35$	0	0
$36$	0.191778	0.0319631
$37$	−5.20883	−0.856326	−0.428163	−	0.903702i	$-0.640839\pi$
$37$	−5.20883	−0.856326	−0.428163	+	0.903702i	$0.640839\pi$
$38$	13.3284	2.16215
$39$	0	0
$40$	0.0621618	0.00982864
$41$	4.92168	0.768637	0.384318	−	0.923201i	$-0.374437\pi$
$41$	4.92168	0.768637	0.384318	+	0.923201i	$0.374437\pi$
$42$	0	0
$43$	−9.43766	−1.43923	−0.719615	−	0.694373i	$-0.755682\pi$
$43$	−9.43766	−1.43923	−0.719615	+	0.694373i	$0.755682\pi$
$44$	−1.45720	−0.219681
$45$	0.0853900	0.0127292
$46$	7.55016	1.11321
$47$	−8.31986	−1.21358	−0.606788	−	0.794863i	$-0.707542\pi$
$47$	−8.31986	−1.21358	−0.606788	+	0.794863i	$0.707542\pi$
$48$	6.91395	0.997943
$49$	0	0
$50$	−8.39497	−1.18723
$51$	4.13778	0.579405
$52$	0	0
$53$	14.0833	1.93449	0.967243	−	0.253854i	$-0.0816983\pi$
$53$	14.0833	1.93449	0.967243	+	0.253854i	$0.0816983\pi$
$54$	10.2662	1.39706
$55$	−0.648824	−0.0874874
$56$	0	0
$57$	−11.6729	−1.54612
$58$	6.54376	0.859238
$59$	0.716361	0.0932623	0.0466311	−	0.998912i	$-0.485151\pi$
$59$	0.716361	0.0932623	0.0466311	+	0.998912i	$0.485151\pi$
$60$	−3.24087	−0.418395
$61$	11.6527	1.49197	0.745986	−	0.665962i	$-0.231979\pi$
$61$	11.6527	1.49197	0.745986	+	0.665962i	$0.231979\pi$
$62$	3.15439	0.400607
$63$	0	0
$64$	−8.27099	−1.03387
$65$	0	0
$66$	2.53098	0.311542
$67$	−9.39174	−1.14738	−0.573692	−	0.819071i	$-0.694489\pi$
$67$	−9.39174	−1.14738	−0.573692	+	0.819071i	$0.694489\pi$
$68$	−4.78492	−0.580257
$69$	−6.61239	−0.796038
$70$	0	0
$71$	−10.9914	−1.30444	−0.652220	−	0.758030i	$-0.726162\pi$
$71$	−10.9914	−1.30444	−0.652220	+	0.758030i	$0.726162\pi$
$72$	0.00647055	0.000762561 0
$73$	−3.47300	−0.406484	−0.203242	−	0.979129i	$-0.565148\pi$
$73$	−3.47300	−0.406484	−0.203242	+	0.979129i	$0.565148\pi$
$74$	−10.4621	−1.21619
$75$	7.35227	0.848967
$76$	13.4986	1.54839
$77$	0	0
$78$	0	0
$79$	13.0082	1.46353	0.731766	−	0.681556i	$-0.238696\pi$
$79$	13.0082	1.46353	0.731766	+	0.681556i	$0.238696\pi$
$80$	−3.55993	−0.398012
$81$	−9.27395	−1.03044
$82$	9.88531	1.09165
$83$	3.54083	0.388656	0.194328	−	0.980937i	$-0.437747\pi$
$83$	3.54083	0.388656	0.194328	+	0.980937i	$0.437747\pi$
$84$	0	0
$85$	−2.13050	−0.231085
$86$	−18.9558	−2.04405
$87$	−5.73099	−0.614427
$88$	−0.0491655	−0.00524106
$89$	12.0501	1.27730	0.638651	−	0.769496i	$-0.279493\pi$
$89$	12.0501	1.27730	0.638651	+	0.769496i	$0.279493\pi$
$90$	0.171508	0.0180785
$91$	0	0
$92$	7.64656	0.797209
$93$	−2.76260	−0.286468
$94$	−16.7106	−1.72357
$95$	6.01029	0.616642
$96$	14.1283	1.44196
$97$	7.43766	0.755180	0.377590	−	0.925973i	$-0.376753\pi$
$97$	7.43766	0.755180	0.377590	+	0.925973i	$0.376753\pi$
$98$	0	0
$99$	−0.0675374	−0.00678776
$100$	−8.50216	−0.850216
$101$	1.19905	0.119310	0.0596551	−	0.998219i	$-0.481000\pi$
$101$	1.19905	0.119310	0.0596551	+	0.998219i	$0.481000\pi$
$102$	8.31083	0.822894
$103$	14.4123	1.42009	0.710043	−	0.704158i	$-0.248675\pi$
$103$	14.4123	1.42009	0.710043	+	0.704158i	$0.248675\pi$
$104$	0	0
$105$	0	0
$106$	28.2866	2.74744
$107$	13.5932	1.31411	0.657053	−	0.753845i	$-0.271803\pi$
$107$	13.5932	1.31411	0.657053	+	0.753845i	$0.271803\pi$
$108$	10.3973	1.00048
$109$	13.7248	1.31460	0.657299	−	0.753630i	$-0.271699\pi$
$109$	13.7248	1.31460	0.657299	+	0.753630i	$0.271699\pi$
$110$	−1.30318	−0.124253
$111$	9.16262	0.869677
$112$	0	0
$113$	−3.25799	−0.306486	−0.153243	−	0.988189i	$-0.548972\pi$
$113$	−3.25799	−0.306486	−0.153243	+	0.988189i	$0.548972\pi$
$114$	−23.4454	−2.19586
$115$	3.40466	0.317486
$116$	6.62731	0.615331
$117$	0	0
$118$	1.43883	0.132455
$119$	0	0
$120$	−0.109346	−0.00998189
$121$	−10.4868	−0.953348
$122$	23.4047	2.11896
$123$	−8.65750	−0.780621
$124$	3.19466	0.286889
$125$	−8.31422	−0.743647
$126$	0	0
$127$	−0.950834	−0.0843729	−0.0421865	−	0.999110i	$-0.513432\pi$
$127$	−0.950834	−0.0843729	−0.0421865	+	0.999110i	$0.513432\pi$
$128$	−0.548979	−0.0485233
$129$	16.6014	1.46167
$130$	0	0
$131$	18.8196	1.64428	0.822138	−	0.569288i	$-0.192781\pi$
$131$	18.8196	1.64428	0.822138	+	0.569288i	$0.192781\pi$
$132$	2.56330	0.223106
$133$	0	0
$134$	−18.8635	−1.62956
$135$	4.62944	0.398439
$136$	−0.161442	−0.0138435
$137$	−6.18179	−0.528146	−0.264073	−	0.964503i	$-0.585066\pi$
$137$	−6.18179	−0.528146	−0.264073	+	0.964503i	$0.585066\pi$
$138$	−13.2811	−1.13057
$139$	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
$141$	14.6351	1.23250
$142$	−22.0765	−1.85262
$143$	0	0
$144$	−0.370560	−0.0308800
$145$	2.95083	0.245053
$146$	−6.97560	−0.577305
$147$	0	0
$148$	−10.5956	−0.870956
$149$	21.0771	1.72670	0.863351	−	0.504604i	$-0.168361\pi$
$149$	21.0771	1.72670	0.863351	+	0.504604i	$0.168361\pi$
$150$	14.7672	1.20574
$151$	15.7234	1.27955	0.639777	−	0.768560i	$-0.279027\pi$
$151$	15.7234	1.27955	0.639777	+	0.768560i	$0.279027\pi$
$152$	0.455438	0.0369409
$153$	−0.221768	−0.0179289
$154$	0	0
$155$	1.42244	0.114253
$156$	0	0
$157$	7.78499	0.621310	0.310655	−	0.950523i	$-0.399452\pi$
$157$	7.78499	0.621310	0.310655	+	0.950523i	$0.399452\pi$
$158$	26.1272	2.07857
$159$	−24.7733	−1.96465
$160$	−7.27453	−0.575102
$161$	0	0
$162$	−18.6269	−1.46347
$163$	−1.68991	−0.132364	−0.0661820	−	0.997808i	$-0.521082\pi$
$163$	−1.68991	−0.132364	−0.0661820	+	0.997808i	$0.521082\pi$
$164$	10.0115	0.781769
$165$	1.14132	0.0888514
$166$	7.11184	0.551986
$167$	−21.8667	−1.69210	−0.846049	−	0.533105i	$-0.821025\pi$
$167$	−21.8667	−1.69210	−0.846049	+	0.533105i	$0.821025\pi$
$168$	0	0
$169$	0	0
$170$	−4.27917	−0.328197
$171$	0.625623	0.0478426
$172$	−19.1978	−1.46382
$173$	−5.84122	−0.444100	−0.222050	−	0.975035i	$-0.571275\pi$
$173$	−5.84122	−0.444100	−0.222050	+	0.975035i	$0.571275\pi$
$174$	−11.5108	−0.872634
$175$	0	0
$176$	2.81565	0.212238
$177$	−1.26012	−0.0947164
$178$	24.2028	1.81408
$179$	2.53427	0.189421	0.0947103	−	0.995505i	$-0.469808\pi$
$179$	2.53427	0.189421	0.0947103	+	0.995505i	$0.469808\pi$
$180$	0.173698	0.0129467
$181$	10.7248	0.797169	0.398585	−	0.917132i	$-0.369502\pi$
$181$	10.7248	0.797169	0.398585	+	0.917132i	$0.369502\pi$
$182$	0	0
$183$	−20.4977	−1.51523
$184$	0.257993	0.0190195
$185$	−4.71775	−0.346856
$186$	−5.54874	−0.406854
$187$	1.68508	0.123225
$188$	−16.9240	−1.23431
$189$	0	0
$190$	12.0718	0.875781
$191$	−1.67861	−0.121460	−0.0607298	−	0.998154i	$-0.519343\pi$
$191$	−1.67861	−0.121460	−0.0607298	+	0.998154i	$0.519343\pi$
$192$	14.5491	1.04999
$193$	6.44816	0.464148	0.232074	−	0.972698i	$-0.425449\pi$
$193$	6.44816	0.464148	0.232074	+	0.972698i	$0.425449\pi$
$194$	14.9387	1.07254
$195$	0	0
$196$	0	0
$197$	−1.87251	−0.133411	−0.0667054	−	0.997773i	$-0.521249\pi$
$197$	−1.87251	−0.133411	−0.0667054	+	0.997773i	$0.521249\pi$
$198$	−0.135650	−0.00964026
$199$	11.3967	0.807888	0.403944	−	0.914784i	$-0.367639\pi$
$199$	11.3967	0.807888	0.403944	+	0.914784i	$0.367639\pi$
$200$	−0.286860	−0.0202841
$201$	16.5206	1.16527
$202$	2.40833	0.169449
$203$	0	0
$204$	8.41694	0.589304
$205$	4.45767	0.311337
$206$	28.9475	2.01687
$207$	0.354398	0.0246324
$208$	0	0
$209$	−4.75371	−0.328821
$210$	0	0
$211$	7.53599	0.518799	0.259400	−	0.965770i	$-0.416475\pi$
$211$	7.53599	0.518799	0.259400	+	0.965770i	$0.416475\pi$
$212$	28.6478	1.96754
$213$	19.3345	1.32478
$214$	27.3023	1.86635
$215$	−8.54789	−0.582962
$216$	0.350802	0.0238691
$217$	0	0
$218$	27.5666	1.86705
$219$	6.10920	0.412822
$220$	−1.31982	−0.0889821
$221$	0	0
$222$	18.4033	1.23515
$223$	17.6349	1.18092	0.590459	−	0.807067i	$-0.298947\pi$
$223$	17.6349	1.18092	0.590459	+	0.807067i	$0.298947\pi$
$224$	0	0
$225$	−0.394052	−0.0262702
$226$	−6.54376	−0.435284
$227$	−5.32904	−0.353701	−0.176851	−	0.984238i	$-0.556591\pi$
$227$	−5.32904	−0.353701	−0.176851	+	0.984238i	$0.556591\pi$
$228$	−23.7447	−1.57253
$229$	−8.51900	−0.562951	−0.281476	−	0.959568i	$-0.590824\pi$
$229$	−8.51900	−0.562951	−0.281476	+	0.959568i	$0.590824\pi$
$230$	6.83834	0.450907
$231$	0	0
$232$	0.223604	0.0146803
$233$	4.75371	0.311426	0.155713	−	0.987802i	$-0.450233\pi$
$233$	4.75371	0.311426	0.155713	+	0.987802i	$0.450233\pi$
$234$	0	0
$235$	−7.53548	−0.491561
$236$	1.45720	0.0948557
$237$	−22.8821	−1.48635
$238$	0	0
$239$	−14.8314	−0.959365	−0.479682	−	0.877442i	$-0.659248\pi$
$239$	−14.8314	−0.959365	−0.479682	+	0.877442i	$0.659248\pi$
$240$	6.26212	0.404218
$241$	−6.12131	−0.394308	−0.197154	−	0.980373i	$-0.563170\pi$
$241$	−6.12131	−0.394308	−0.197154	+	0.980373i	$0.563170\pi$
$242$	−21.0630	−1.35398
$243$	0.979411	0.0628292
$244$	23.7035	1.51746
$245$	0	0
$246$	−17.3888	−1.10867
$247$	0	0
$248$	0.107787	0.00684448
$249$	−6.22852	−0.394716
$250$	−16.6993	−1.05616
$251$	13.9708	0.881832	0.440916	−	0.897548i	$-0.354654\pi$
$251$	13.9708	0.881832	0.440916	+	0.897548i	$0.354654\pi$
$252$	0	0
$253$	−2.69284	−0.169298
$254$	−1.90977	−0.119830
$255$	3.74767	0.234688
$256$	15.4393	0.964959
$257$	−17.2651	−1.07696	−0.538482	−	0.842637i	$-0.681002\pi$
$257$	−17.2651	−1.07696	−0.538482	+	0.842637i	$0.681002\pi$
$258$	33.3443	2.07592
$259$	0	0
$260$	0	0
$261$	0.307158	0.0190126
$262$	37.7996	2.33527
$263$	−2.60672	−0.160737	−0.0803687	−	0.996765i	$-0.525610\pi$
$263$	−2.60672	−0.160737	−0.0803687	+	0.996765i	$0.525610\pi$
$264$	0.0864849	0.00532278
$265$	12.7555	0.783565
$266$	0	0
$267$	−21.1967	−1.29722
$268$	−19.1044	−1.16699
$269$	14.4895	0.883443	0.441721	−	0.897152i	$-0.354368\pi$
$269$	14.4895	0.883443	0.441721	+	0.897152i	$0.354368\pi$
$270$	9.29834	0.565879
$271$	−8.63591	−0.524594	−0.262297	−	0.964987i	$-0.584480\pi$
$271$	−8.63591	−0.524594	−0.262297	+	0.964987i	$0.584480\pi$
$272$	9.24558	0.560596
$273$	0	0
$274$	−12.4163	−0.750095
$275$	2.99415	0.180554
$276$	−13.4507	−0.809639
$277$	12.2270	0.734647	0.367324	−	0.930093i	$-0.380274\pi$
$277$	12.2270	0.734647	0.367324	+	0.930093i	$0.380274\pi$
$278$	8.03410	0.481853
$279$	0.148064	0.00886437
$280$	0	0
$281$	24.1822	1.44259	0.721293	−	0.692630i	$-0.243548\pi$
$281$	24.1822	1.44259	0.721293	+	0.692630i	$0.243548\pi$
$282$	29.3950	1.75044
$283$	30.7683	1.82899	0.914493	−	0.404601i	$-0.132590\pi$
$283$	30.7683	1.82899	0.914493	+	0.404601i	$0.132590\pi$
$284$	−22.3584	−1.32673
$285$	−10.5724	−0.626257
$286$	0	0
$287$	0	0
$288$	−0.757221	−0.0446197
$289$	−11.4668	−0.674519
$290$	5.92682	0.348035
$291$	−13.0833	−0.766954
$292$	−7.06467	−0.413429
$293$	−31.8295	−1.85950	−0.929749	−	0.368193i	$-0.879976\pi$
$293$	−31.8295	−1.85950	−0.929749	+	0.368193i	$0.879976\pi$
$294$	0	0
$295$	0.648824	0.0377760
$296$	−0.357494	−0.0207789
$297$	−3.66156	−0.212465
$298$	42.3338	2.45233
$299$	0	0
$300$	14.9558	0.863472
$301$	0	0
$302$	31.5809	1.81728
$303$	−2.10920	−0.121170
$304$	−26.0824	−1.49593
$305$	10.5541	0.604324
$306$	−0.445427	−0.0254634
$307$	28.7884	1.64304	0.821520	−	0.570179i	$-0.193126\pi$
$307$	28.7884	1.64304	0.821520	+	0.570179i	$0.193126\pi$
$308$	0	0
$309$	−25.3521	−1.44223
$310$	2.85700	0.162266
$311$	−5.51862	−0.312932	−0.156466	−	0.987683i	$-0.550010\pi$
$311$	−5.51862	−0.312932	−0.156466	+	0.987683i	$0.550010\pi$
$312$	0	0
$313$	4.84799	0.274024	0.137012	−	0.990569i	$-0.456250\pi$
$313$	4.84799	0.274024	0.137012	+	0.990569i	$0.456250\pi$
$314$	15.6363	0.882410
$315$	0	0
$316$	26.4608	1.48854
$317$	7.65511	0.429954	0.214977	−	0.976619i	$-0.431032\pi$
$317$	7.65511	0.429954	0.214977	+	0.976619i	$0.431032\pi$
$318$	−49.7577	−2.79027
$319$	−2.33390	−0.130673
$320$	−7.49121	−0.418772
$321$	−23.9112	−1.33459
$322$	0	0
$323$	−15.6095	−0.868534
$324$	−18.8648	−1.04804
$325$	0	0
$326$	−3.39423	−0.187989
$327$	−24.1427	−1.33510
$328$	0.337786	0.0186511
$329$	0	0
$330$	2.29236	0.126190
$331$	−11.3432	−0.623477	−0.311739	−	0.950168i	$-0.600911\pi$
$331$	−11.3432	−0.623477	−0.311739	+	0.950168i	$0.600911\pi$
$332$	7.20265	0.395297
$333$	−0.491080	−0.0269110
$334$	−43.9199	−2.40319
$335$	−8.50631	−0.464749
$336$	0	0
$337$	1.74149	0.0948649	0.0474324	−	0.998874i	$-0.484896\pi$
$337$	1.74149	0.0948649	0.0474324	+	0.998874i	$0.484896\pi$
$338$	0	0
$339$	5.73099	0.311265
$340$	−4.33381	−0.235034
$341$	−1.12504	−0.0609246
$342$	1.25658	0.0679480
$343$	0	0
$344$	−0.647729	−0.0349232
$345$	−5.98898	−0.322436
$346$	−11.7322	−0.630729
$347$	21.0503	1.13004	0.565019	−	0.825078i	$-0.308869\pi$
$347$	21.0503	1.13004	0.565019	+	0.825078i	$0.308869\pi$
$348$	−11.6578	−0.624925
$349$	−8.35601	−0.447287	−0.223643	−	0.974671i	$-0.571795\pi$
$349$	−8.35601	−0.447287	−0.223643	+	0.974671i	$0.571795\pi$
$350$	0	0
$351$	0	0
$352$	5.75364	0.306670
$353$	−8.53355	−0.454195	−0.227097	−	0.973872i	$-0.572924\pi$
$353$	−8.53355	−0.454195	−0.227097	+	0.973872i	$0.572924\pi$
$354$	−2.53098	−0.134520
$355$	−9.95515	−0.528365
$356$	24.5119	1.29913
$357$	0	0
$358$	5.09015	0.269023
$359$	16.1713	0.853488	0.426744	−	0.904372i	$-0.359661\pi$
$359$	16.1713	0.853488	0.426744	+	0.904372i	$0.359661\pi$
$360$	0.00586051	0.000308876 0
$361$	25.0353	1.31765
$362$	21.5410	1.13217
$363$	18.4469	0.968212
$364$	0	0
$365$	−3.14557	−0.164647
$366$	−41.1701	−2.15200
$367$	−28.1540	−1.46963	−0.734813	−	0.678269i	$-0.762730\pi$
$367$	−28.1540	−1.46963	−0.734813	+	0.678269i	$0.762730\pi$
$368$	−14.7749	−0.770197
$369$	0.464008	0.0241553
$370$	−9.47571	−0.492619
$371$	0	0
$372$	−5.61959	−0.291362
$373$	−28.5037	−1.47586	−0.737932	−	0.674875i	$-0.764197\pi$
$373$	−28.5037	−1.47586	−0.737932	+	0.674875i	$0.764197\pi$
$374$	3.38452	0.175009
$375$	14.6252	0.755241
$376$	−0.571012	−0.0294477
$377$	0	0
$378$	0	0
$379$	7.26263	0.373056	0.186528	−	0.982450i	$-0.440276\pi$
$379$	7.26263	0.373056	0.186528	+	0.982450i	$0.440276\pi$
$380$	12.2259	0.627178
$381$	1.67257	0.0856884
$382$	−3.37152	−0.172502
$383$	12.9325	0.660822	0.330411	−	0.943837i	$-0.392813\pi$
$383$	12.9325	0.660822	0.330411	+	0.943837i	$0.392813\pi$
$384$	0.965684	0.0492799
$385$	0	0
$386$	12.9513	0.659203
$387$	−0.889768	−0.0452294
$388$	15.1295	0.768083
$389$	−21.1357	−1.07162	−0.535811	−	0.844338i	$-0.679994\pi$
$389$	−21.1357	−1.07162	−0.535811	+	0.844338i	$0.679994\pi$
$390$	0	0
$391$	−8.84232	−0.447175
$392$	0	0
$393$	−33.1047	−1.66991
$394$	−3.76098	−0.189476
$395$	11.7818	0.592805
$396$	−0.137383	−0.00690373
$397$	19.2073	0.963988	0.481994	−	0.876175i	$-0.339913\pi$
$397$	19.2073	0.963988	0.481994	+	0.876175i	$0.339913\pi$
$398$	22.8905	1.14740
$399$	0	0
$400$	16.4282	0.821408
$401$	−16.6692	−0.832420	−0.416210	−	0.909268i	$-0.636642\pi$
$401$	−16.6692	−0.832420	−0.416210	+	0.909268i	$0.636642\pi$
$402$	33.1820	1.65497
$403$	0	0
$404$	2.43908	0.121349
$405$	−8.39961	−0.417380
$406$	0	0
$407$	3.73140	0.184959
$408$	0.283985	0.0140594
$409$	12.3483	0.610585	0.305293	−	0.952259i	$-0.401246\pi$
$409$	12.3483	0.610585	0.305293	+	0.952259i	$0.401246\pi$
$410$	8.95333	0.442174
$411$	10.8741	0.536381
$412$	29.3171	1.44435
$413$	0	0
$414$	0.711817	0.0349839
$415$	3.20700	0.157426
$416$	0	0
$417$	−7.03622	−0.344565
$418$	−9.54794	−0.467005
$419$	−4.35934	−0.212968	−0.106484	−	0.994314i	$-0.533959\pi$
$419$	−4.35934	−0.212968	−0.106484	+	0.994314i	$0.533959\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	15.1362	0.736820
$423$	−0.784383	−0.0381380
$424$	0.966567	0.0469407
$425$	9.83171	0.476908
$426$	38.8338	1.88150
$427$	0	0
$428$	27.6509	1.33656
$429$	0	0
$430$	−17.1687	−0.827946
$431$	23.3626	1.12533	0.562667	−	0.826683i	$-0.309775\pi$
$431$	23.3626	1.12533	0.562667	+	0.826683i	$0.309775\pi$
$432$	−20.0900	−0.966582
$433$	2.71285	0.130371	0.0651856	−	0.997873i	$-0.479236\pi$
$433$	2.71285	0.130371	0.0651856	+	0.997873i	$0.479236\pi$
$434$	0	0
$435$	−5.19068	−0.248874
$436$	27.9186	1.33706
$437$	24.9448	1.19327
$438$	12.2705	0.586306
$439$	8.83519	0.421681	0.210840	−	0.977521i	$-0.432380\pi$
$439$	8.83519	0.421681	0.210840	+	0.977521i	$0.432380\pi$
$440$	−0.0445303	−0.00212290
$441$	0	0
$442$	0	0
$443$	−2.90558	−0.138048	−0.0690240	−	0.997615i	$-0.521989\pi$
$443$	−2.90558	−0.138048	−0.0690240	+	0.997615i	$0.521989\pi$
$444$	18.6383	0.884536
$445$	10.9140	0.517373
$446$	35.4201	1.67719
$447$	−37.0758	−1.75362
$448$	0	0
$449$	15.2777	0.720998	0.360499	−	0.932760i	$-0.382606\pi$
$449$	15.2777	0.720998	0.360499	+	0.932760i	$0.382606\pi$
$450$	−0.791464	−0.0373100
$451$	−3.52570	−0.166019
$452$	−6.62731	−0.311723
$453$	−27.6584	−1.29950
$454$	−10.7035	−0.502341
$455$	0	0
$456$	−0.801141	−0.0375169
$457$	−23.6600	−1.10677	−0.553384	−	0.832926i	$-0.686664\pi$
$457$	−23.6600	−1.10677	−0.553384	+	0.832926i	$0.686664\pi$
$458$	−17.1106	−0.799527
$459$	−12.0232	−0.561196
$460$	6.92566	0.322910
$461$	−26.6170	−1.23968	−0.619839	−	0.784729i	$-0.712802\pi$
$461$	−26.6170	−1.23968	−0.619839	+	0.784729i	$0.712802\pi$
$462$	0	0
$463$	1.44250	0.0670385	0.0335193	−	0.999438i	$-0.489328\pi$
$463$	1.44250	0.0670385	0.0335193	+	0.999438i	$0.489328\pi$
$464$	−12.8055	−0.594481
$465$	−2.50214	−0.116034
$466$	9.54794	0.442300
$467$	8.38959	0.388224	0.194112	−	0.980979i	$-0.437817\pi$
$467$	8.38959	0.388224	0.194112	+	0.980979i	$0.437817\pi$
$468$	0	0
$469$	0	0
$470$	−15.1352	−0.698135
$471$	−13.6942	−0.630997
$472$	0.0491655	0.00226303
$473$	6.76077	0.310861
$474$	−45.9592	−2.11098
$475$	−27.7359	−1.27261
$476$	0	0
$477$	1.32775	0.0607934
$478$	−29.7893	−1.36253
$479$	12.6122	0.576265	0.288132	−	0.957591i	$-0.406966\pi$
$479$	12.6122	0.576265	0.288132	+	0.957591i	$0.406966\pi$
$480$	12.7963	0.584069
$481$	0	0
$482$	−12.2948	−0.560013
$483$	0	0
$484$	−21.3320	−0.969636
$485$	6.73645	0.305886
$486$	1.96717	0.0892327
$487$	−21.5680	−0.977341	−0.488671	−	0.872468i	$-0.662518\pi$
$487$	−21.5680	−0.977341	−0.488671	+	0.872468i	$0.662518\pi$
$488$	0.799750	0.0362030
$489$	2.97265	0.134428
$490$	0	0
$491$	39.2347	1.77064	0.885318	−	0.464987i	$-0.153941\pi$
$491$	39.2347	1.77064	0.885318	+	0.464987i	$0.153941\pi$
$492$	−17.6108	−0.793958
$493$	−7.66368	−0.345155
$494$	0	0
$495$	−0.0611701	−0.00274939
$496$	−6.17283	−0.277168
$497$	0	0
$498$	−12.5101	−0.560592
$499$	−9.16814	−0.410422	−0.205211	−	0.978718i	$-0.565788\pi$
$499$	−9.16814	−0.410422	−0.205211	+	0.978718i	$0.565788\pi$
$500$	−16.9125	−0.756352
$501$	38.4648	1.71848
$502$	28.0608	1.25241
$503$	−24.9370	−1.11188	−0.555942	−	0.831221i	$-0.687642\pi$
$503$	−24.9370	−1.11188	−0.555942	+	0.831221i	$0.687642\pi$
$504$	0	0
$505$	1.08601	0.0483267
$506$	−5.40864	−0.240443
$507$	0	0
$508$	−1.93416	−0.0858144
$509$	5.89807	0.261428	0.130714	−	0.991420i	$-0.458273\pi$
$509$	5.89807	0.261428	0.130714	+	0.991420i	$0.458273\pi$
$510$	7.52730	0.333314
$511$	0	0
$512$	32.1083	1.41900
$513$	33.9183	1.49753
$514$	−34.6773	−1.52955
$515$	13.0535	0.575208
$516$	33.7700	1.48664
$517$	5.96003	0.262122
$518$	0	0
$519$	10.2750	0.451024
$520$	0	0
$521$	37.1895	1.62930	0.814652	−	0.579950i	$-0.196928\pi$
$521$	37.1895	1.62930	0.814652	+	0.579950i	$0.196928\pi$
$522$	0.616935	0.0270025
$523$	5.09080	0.222605	0.111303	−	0.993787i	$-0.464498\pi$
$523$	5.09080	0.222605	0.111303	+	0.993787i	$0.464498\pi$
$524$	38.2823	1.67237
$525$	0	0
$526$	−5.23567	−0.228286
$527$	−3.69424	−0.160924
$528$	−4.95289	−0.215547
$529$	−8.86950	−0.385630
$530$	25.6198	1.11285
$531$	0.0675374	0.00293087
$532$	0	0
$533$	0	0
$534$	−42.5741	−1.84236
$535$	12.3117	0.532280
$536$	−0.644577	−0.0278415
$537$	−4.45793	−0.192374
$538$	29.1026	1.25470
$539$	0	0
$540$	9.41707	0.405246
$541$	0.766850	0.0329694	0.0164847	−	0.999864i	$-0.494753\pi$
$541$	0.766850	0.0329694	0.0164847	+	0.999864i	$0.494753\pi$
$542$	−17.3454	−0.745050
$543$	−18.8655	−0.809598
$544$	18.8929	0.810025
$545$	12.4309	0.532480
$546$	0	0
$547$	14.1428	0.604702	0.302351	−	0.953197i	$-0.402229\pi$
$547$	14.1428	0.604702	0.302351	+	0.953197i	$0.402229\pi$
$548$	−12.5748	−0.537170
$549$	1.09859	0.0468869
$550$	6.01383	0.256430
$551$	21.6197	0.921032
$552$	−0.453824	−0.0193160
$553$	0	0
$554$	24.5582	1.04338
$555$	8.29878	0.352264
$556$	8.13668	0.345072
$557$	24.8627	1.05347	0.526733	−	0.850031i	$-0.323417\pi$
$557$	24.8627	1.05347	0.526733	+	0.850031i	$0.323417\pi$
$558$	0.297391	0.0125895
$559$	0	0
$560$	0	0
$561$	−2.96414	−0.125146
$562$	48.5705	2.04882
$563$	−44.0094	−1.85478	−0.927388	−	0.374101i	$-0.877951\pi$
$563$	−44.0094	−1.85478	−0.927388	+	0.374101i	$0.877951\pi$
$564$	29.7703	1.25356
$565$	−2.95083	−0.124143
$566$	61.7989	2.59760
$567$	0	0
$568$	−0.754366	−0.0316525
$569$	−33.2616	−1.39440	−0.697199	−	0.716877i	$-0.745571\pi$
$569$	−33.2616	−1.39440	−0.697199	+	0.716877i	$0.745571\pi$
$570$	−21.2350	−0.889436
$571$	−12.3540	−0.516998	−0.258499	−	0.966011i	$-0.583228\pi$
$571$	−12.3540	−0.516998	−0.258499	+	0.966011i	$0.583228\pi$
$572$	0	0
$573$	2.95276	0.123353
$574$	0	0
$575$	−15.7116	−0.655219
$576$	−0.779776	−0.0324907
$577$	−25.9659	−1.08097	−0.540486	−	0.841353i	$-0.681760\pi$
$577$	−25.9659	−1.08097	−0.540486	+	0.841353i	$0.681760\pi$
$578$	−23.0314	−0.957979
$579$	−11.3427	−0.471385
$580$	6.00250	0.249240
$581$	0	0
$582$	−26.2781	−1.08926
$583$	−10.0887	−0.417831
$584$	−0.238360	−0.00986341
$585$	0	0
$586$	−63.9303	−2.64094
$587$	−23.9747	−0.989543	−0.494771	−	0.869023i	$-0.664748\pi$
$587$	−23.9747	−0.989543	−0.494771	+	0.869023i	$0.664748\pi$
$588$	0	0
$589$	10.4217	0.429418
$590$	1.30318	0.0536510
$591$	3.29385	0.135491
$592$	20.4733	0.841445
$593$	47.0480	1.93203	0.966015	−	0.258484i	$-0.0832230\pi$
$593$	47.0480	1.93203	0.966015	+	0.258484i	$0.0832230\pi$
$594$	−7.35433	−0.301752
$595$	0	0
$596$	42.8744	1.75620
$597$	−20.0474	−0.820484
$598$	0	0
$599$	20.1736	0.824271	0.412135	−	0.911123i	$-0.364783\pi$
$599$	20.1736	0.824271	0.412135	+	0.911123i	$0.364783\pi$
$600$	0.504604	0.0206004
$601$	−29.5773	−1.20648	−0.603242	−	0.797558i	$-0.706125\pi$
$601$	−29.5773	−1.20648	−0.603242	+	0.797558i	$0.706125\pi$
$602$	0	0
$603$	−0.885439	−0.0360579
$604$	31.9841	1.30142
$605$	−9.49815	−0.386155
$606$	−4.23638	−0.172091
$607$	15.4420	0.626771	0.313385	−	0.949626i	$-0.398537\pi$
$607$	15.4420	0.626771	0.313385	+	0.949626i	$0.398537\pi$
$608$	−53.2980	−2.16152
$609$	0	0
$610$	21.1981	0.858287
$611$	0	0
$612$	−0.451115	−0.0182352
$613$	−1.99485	−0.0805711	−0.0402855	−	0.999188i	$-0.512827\pi$
$613$	−1.99485	−0.0805711	−0.0402855	+	0.999188i	$0.512827\pi$
$614$	57.8222	2.33351
$615$	−7.84129	−0.316191
$616$	0	0
$617$	2.85584	0.114972	0.0574858	−	0.998346i	$-0.481692\pi$
$617$	2.85584	0.114972	0.0574858	+	0.998346i	$0.481692\pi$
$618$	−50.9202	−2.04831
$619$	31.9823	1.28548	0.642738	−	0.766086i	$-0.277798\pi$
$619$	31.9823	1.28548	0.642738	+	0.766086i	$0.277798\pi$
$620$	2.89348	0.116205
$621$	19.2138	0.771022
$622$	−11.0843	−0.444440
$623$	0	0
$624$	0	0
$625$	13.3680	0.534719
$626$	9.73730	0.389181
$627$	8.36204	0.333948
$628$	15.8360	0.631925
$629$	12.2526	0.488542
$630$	0	0
$631$	−32.1115	−1.27834	−0.639169	−	0.769066i	$-0.720722\pi$
$631$	−32.1115	−1.27834	−0.639169	+	0.769066i	$0.720722\pi$
$632$	0.892781	0.0355129
$633$	−13.2562	−0.526888
$634$	15.3755	0.610638
$635$	−0.861191	−0.0341753
$636$	−50.3930	−1.99821
$637$	0	0
$638$	−4.68769	−0.185588
$639$	−1.03625	−0.0409935
$640$	−0.497222	−0.0196544
$641$	33.0248	1.30440	0.652200	−	0.758047i	$-0.273846\pi$
$641$	33.0248	1.30440	0.652200	+	0.758047i	$0.273846\pi$
$642$	−48.0263	−1.89545
$643$	15.7942	0.622863	0.311432	−	0.950269i	$-0.399192\pi$
$643$	15.7942	0.622863	0.311432	+	0.950269i	$0.399192\pi$
$644$	0	0
$645$	15.0362	0.592051
$646$	−31.3520	−1.23353
$647$	4.64072	0.182445	0.0912227	−	0.995831i	$-0.470922\pi$
$647$	4.64072	0.182445	0.0912227	+	0.995831i	$0.470922\pi$
$648$	−0.636493	−0.0250038
$649$	−0.513173	−0.0201438
$650$	0	0
$651$	0	0
$652$	−3.43757	−0.134626
$653$	26.8285	1.04988	0.524941	−	0.851139i	$-0.324087\pi$
$653$	26.8285	1.04988	0.524941	+	0.851139i	$0.324087\pi$
$654$	−48.4912	−1.89616
$655$	17.0453	0.666016
$656$	−19.3446	−0.755280
$657$	−0.327429	−0.0127742
$658$	0	0
$659$	−42.9889	−1.67461	−0.837306	−	0.546735i	$-0.815871\pi$
$659$	−42.9889	−1.67461	−0.837306	+	0.546735i	$0.815871\pi$
$660$	2.32163	0.0903695
$661$	−29.4698	−1.14624	−0.573122	−	0.819470i	$-0.694268\pi$
$661$	−29.4698	−1.14624	−0.573122	+	0.819470i	$0.694268\pi$
$662$	−22.7830	−0.885488
$663$	0	0
$664$	0.243015	0.00943082
$665$	0	0
$666$	−0.986346	−0.0382201
$667$	12.2470	0.474205
$668$	−44.4806	−1.72101
$669$	−31.0207	−1.19933
$670$	−17.0851	−0.660056
$671$	−8.34752	−0.322252
$672$	0	0
$673$	−20.1702	−0.777504	−0.388752	−	0.921342i	$-0.627094\pi$
$673$	−20.1702	−0.777504	−0.388752	+	0.921342i	$0.627094\pi$
$674$	3.49782	0.134731
$675$	−21.3637	−0.822287
$676$	0	0
$677$	6.20481	0.238470	0.119235	−	0.992866i	$-0.461956\pi$
$677$	6.20481	0.238470	0.119235	+	0.992866i	$0.461956\pi$
$678$	11.5108	0.442071
$679$	0	0
$680$	−0.146221	−0.00560733
$681$	9.37409	0.359216
$682$	−2.25968	−0.0865276
$683$	1.76952	0.0677087	0.0338543	−	0.999427i	$-0.489222\pi$
$683$	1.76952	0.0677087	0.0338543	+	0.999427i	$0.489222\pi$
$684$	1.27262	0.0486600
$685$	−5.59899	−0.213926
$686$	0	0
$687$	14.9854	0.571729
$688$	37.0946	1.41422
$689$	0	0
$690$	−12.0290	−0.457937
$691$	44.9317	1.70928	0.854641	−	0.519219i	$-0.173777\pi$
$691$	44.9317	1.70928	0.854641	+	0.519219i	$0.173777\pi$
$692$	−11.8820	−0.451688
$693$	0	0
$694$	42.2800	1.60493
$695$	3.62289	0.137424
$696$	−0.393331	−0.0149092
$697$	−11.5771	−0.438515
$698$	−16.7832	−0.635255
$699$	−8.36204	−0.316281
$700$	0	0
$701$	38.5707	1.45679	0.728397	−	0.685156i	$-0.240266\pi$
$701$	38.5707	1.45679	0.728397	+	0.685156i	$0.240266\pi$
$702$	0	0
$703$	−34.5653	−1.30366
$704$	5.92501	0.223307
$705$	13.2553	0.499225
$706$	−17.1398	−0.645066
$707$	0	0
$708$	−2.56330	−0.0963346
$709$	−8.77731	−0.329639	−0.164819	−	0.986324i	$-0.552704\pi$
$709$	−8.77731	−0.329639	−0.164819	+	0.986324i	$0.552704\pi$
$710$	−19.9952	−0.750405
$711$	1.22639	0.0459932
$712$	0.827023	0.0309940
$713$	5.90360	0.221091
$714$	0	0
$715$	0	0
$716$	5.15515	0.192657
$717$	26.0893	0.974323
$718$	32.4804	1.21216
$719$	−4.20437	−0.156796	−0.0783982	−	0.996922i	$-0.524981\pi$
$719$	−4.20437	−0.156796	−0.0783982	+	0.996922i	$0.524981\pi$
$720$	−0.335625	−0.0125080
$721$	0	0
$722$	50.2840	1.87138
$723$	10.7677	0.400456
$724$	21.8161	0.810789
$725$	−13.6173	−0.505735
$726$	37.0511	1.37509
$727$	28.9856	1.07502	0.537509	−	0.843258i	$-0.319366\pi$
$727$	28.9856	1.07502	0.537509	+	0.843258i	$0.319366\pi$
$728$	0	0
$729$	26.0990	0.966630
$730$	−6.31796	−0.233838
$731$	22.1999	0.821094
$732$	−41.6958	−1.54112
$733$	−24.0345	−0.887733	−0.443867	−	0.896093i	$-0.646394\pi$
$733$	−24.0345	−0.887733	−0.443867	+	0.896093i	$0.646394\pi$
$734$	−56.5480	−2.08722
$735$	0	0
$736$	−30.1918	−1.11288
$737$	6.72788	0.247825
$738$	0.931971	0.0343063
$739$	−11.8055	−0.434273	−0.217136	−	0.976141i	$-0.569672\pi$
$739$	−11.8055	−0.434273	−0.217136	+	0.976141i	$0.569672\pi$
$740$	−9.59670	−0.352782
$741$	0	0
$742$	0	0
$743$	−47.2786	−1.73448	−0.867241	−	0.497888i	$-0.834109\pi$
$743$	−47.2786	−1.73448	−0.867241	+	0.497888i	$0.834109\pi$
$744$	−0.189603	−0.00695120
$745$	19.0900	0.699402
$746$	−57.2503	−2.09608
$747$	0.333824	0.0122140
$748$	3.42773	0.125330
$749$	0	0
$750$	29.3750	1.07262
$751$	5.47700	0.199859	0.0999294	−	0.994995i	$-0.468138\pi$
$751$	5.47700	0.199859	0.0999294	+	0.994995i	$0.468138\pi$
$752$	32.7012	1.19249
$753$	−24.5755	−0.895581
$754$	0	0
$755$	14.2410	0.518285
$756$	0	0
$757$	10.7453	0.390546	0.195273	−	0.980749i	$-0.437441\pi$
$757$	10.7453	0.390546	0.195273	+	0.980749i	$0.437441\pi$
$758$	14.5872	0.529830
$759$	4.73686	0.171937
$760$	0.412500	0.0149630
$761$	−33.0399	−1.19770	−0.598848	−	0.800863i	$-0.704375\pi$
$761$	−33.0399	−1.19770	−0.598848	+	0.800863i	$0.704375\pi$
$762$	3.35940	0.121698
$763$	0	0
$764$	−3.41457	−0.123535
$765$	−0.200860	−0.00726212
$766$	25.9753	0.938527
$767$	0	0
$768$	−27.1587	−0.980004
$769$	2.98332	0.107581	0.0537907	−	0.998552i	$-0.482870\pi$
$769$	2.98332	0.107581	0.0537907	+	0.998552i	$0.482870\pi$
$770$	0	0
$771$	30.3702	1.09376
$772$	13.1167	0.472079
$773$	−21.9085	−0.787995	−0.393998	−	0.919111i	$-0.628908\pi$
$773$	−21.9085	−0.787995	−0.393998	+	0.919111i	$0.628908\pi$
$774$	−1.78712	−0.0642367
$775$	−6.56417	−0.235792
$776$	0.510464	0.0183246
$777$	0	0
$778$	−42.4516	−1.52196
$779$	32.6598	1.17016
$780$	0	0
$781$	7.87381	0.281747
$782$	−17.7600	−0.635097
$783$	16.6527	0.595118
$784$	0	0
$785$	7.05104	0.251662
$786$	−66.4917	−2.37168
$787$	−13.3632	−0.476347	−0.238174	−	0.971223i	$-0.576549\pi$
$787$	−13.3632	−0.476347	−0.238174	+	0.971223i	$0.576549\pi$
$788$	−3.80900	−0.135690
$789$	4.58537	0.163244
$790$	23.6640	0.841927
$791$	0	0
$792$	−0.00463525	−0.000164706 0
$793$	0	0
$794$	38.5784	1.36910
$795$	−22.4377	−0.795782
$796$	23.1827	0.821691
$797$	−32.5388	−1.15258	−0.576292	−	0.817244i	$-0.695501\pi$
$797$	−32.5388	−1.15258	−0.576292	+	0.817244i	$0.695501\pi$
$798$	0	0
$799$	19.5706	0.692357
$800$	33.5701	1.18688
$801$	1.13606	0.0401407
$802$	−33.4805	−1.18224
$803$	2.48792	0.0877969
$804$	33.6057	1.18518
$805$	0	0
$806$	0	0
$807$	−25.4879	−0.897217
$808$	0.0822938	0.00289509
$809$	7.68827	0.270305	0.135153	−	0.990825i	$-0.456848\pi$
$809$	7.68827	0.270305	0.135153	+	0.990825i	$0.456848\pi$
$810$	−16.8708	−0.592781
$811$	−48.3178	−1.69667	−0.848334	−	0.529461i	$-0.822394\pi$
$811$	−48.3178	−1.69667	−0.848334	+	0.529461i	$0.822394\pi$
$812$	0	0
$813$	15.1911	0.532773
$814$	7.49461	0.262686
$815$	−1.53059	−0.0536142
$816$	−16.2635	−0.569336
$817$	−62.6275	−2.19106
$818$	24.8019	0.867178
$819$	0	0
$820$	9.06766	0.316656
$821$	3.73442	0.130332	0.0651661	−	0.997874i	$-0.479242\pi$
$821$	3.73442	0.130332	0.0651661	+	0.997874i	$0.479242\pi$
$822$	21.8409	0.761790
$823$	14.2318	0.496089	0.248045	−	0.968749i	$-0.420212\pi$
$823$	14.2318	0.496089	0.248045	+	0.968749i	$0.420212\pi$
$824$	0.989150	0.0344587
$825$	−5.26688	−0.183369
$826$	0	0
$827$	−48.3016	−1.67961	−0.839805	−	0.542888i	$-0.817331\pi$
$827$	−48.3016	−1.67961	−0.839805	+	0.542888i	$0.817331\pi$
$828$	0.720906	0.0250532
$829$	−11.5101	−0.399763	−0.199882	−	0.979820i	$-0.564056\pi$
$829$	−11.5101	−0.399763	−0.199882	+	0.979820i	$0.564056\pi$
$830$	6.44135	0.223582
$831$	−21.5079	−0.746102
$832$	0	0
$833$	0	0
$834$	−14.1324	−0.489366
$835$	−19.8052	−0.685386
$836$	−9.66985	−0.334439
$837$	8.02734	0.277465
$838$	−8.75583	−0.302465
$839$	13.1103	0.452616	0.226308	−	0.974056i	$-0.427334\pi$
$839$	13.1103	0.452616	0.226308	+	0.974056i	$0.427334\pi$
$840$	0	0
$841$	−18.3855	−0.633982
$842$	20.0852	0.692183
$843$	−42.5378	−1.46508
$844$	15.3295	0.527663
$845$	0	0
$846$	−1.57545	−0.0541652
$847$	0	0
$848$	−55.3541	−1.90087
$849$	−54.1232	−1.85750
$850$	19.7472	0.677325
$851$	−19.5803	−0.671203
$852$	39.3297	1.34741
$853$	8.80346	0.301425	0.150712	−	0.988578i	$-0.451843\pi$
$853$	8.80346	0.301425	0.150712	+	0.988578i	$0.451843\pi$
$854$	0	0
$855$	0.566640	0.0193787
$856$	0.932934	0.0318870
$857$	−16.9651	−0.579516	−0.289758	−	0.957100i	$-0.593575\pi$
$857$	−16.9651	−0.579516	−0.289758	+	0.957100i	$0.593575\pi$
$858$	0	0
$859$	−14.5410	−0.496132	−0.248066	−	0.968743i	$-0.579795\pi$
$859$	−14.5410	−0.496132	−0.248066	+	0.968743i	$0.579795\pi$
$860$	−17.3879	−0.592922
$861$	0	0
$862$	46.9243	1.59825
$863$	−39.0444	−1.32909	−0.664544	−	0.747249i	$-0.731374\pi$
$863$	−39.0444	−1.32909	−0.664544	+	0.747249i	$0.731374\pi$
$864$	−41.0529	−1.39665
$865$	−5.29052	−0.179883
$866$	5.44882	0.185159
$867$	20.1708	0.685036
$868$	0	0
$869$	−9.31854	−0.316110
$870$	−10.4256	−0.353461
$871$	0	0
$872$	0.941966	0.0318990
$873$	0.701211	0.0237324
$874$	50.1022	1.69473
$875$	0	0
$876$	12.4272	0.419875
$877$	−32.5941	−1.10062	−0.550312	−	0.834959i	$-0.685491\pi$
$877$	−32.5941	−1.10062	−0.550312	+	0.834959i	$0.685491\pi$
$878$	17.7457	0.598888
$879$	55.9899	1.88849
$880$	2.55020	0.0859671
$881$	43.4141	1.46266	0.731330	−	0.682024i	$-0.238900\pi$
$881$	43.4141	1.46266	0.731330	+	0.682024i	$0.238900\pi$
$882$	0	0
$883$	28.2902	0.952040	0.476020	−	0.879434i	$-0.342079\pi$
$883$	28.2902	0.952040	0.476020	+	0.879434i	$0.342079\pi$
$884$	0	0
$885$	−1.14132	−0.0383650
$886$	−5.83592	−0.196062
$887$	50.2650	1.68773	0.843866	−	0.536554i	$-0.180274\pi$
$887$	50.2650	1.68773	0.843866	+	0.536554i	$0.180274\pi$
$888$	0.628852	0.0211029
$889$	0	0
$890$	21.9210	0.734794
$891$	6.64349	0.222565
$892$	35.8724	1.20110
$893$	−55.2099	−1.84753
$894$	−74.4676	−2.49057
$895$	2.29535	0.0767250
$896$	0	0
$897$	0	0
$898$	30.6856	1.02399
$899$	5.11668	0.170651
$900$	−0.801570	−0.0267190
$901$	−33.1277	−1.10364
$902$	−7.08145	−0.235786
$903$	0	0
$904$	−0.223604	−0.00743695
$905$	9.71369	0.322894
$906$	−55.5526	−1.84561
$907$	26.8277	0.890798	0.445399	−	0.895332i	$-0.353062\pi$
$907$	26.8277	0.890798	0.445399	+	0.895332i	$0.353062\pi$
$908$	−10.8402	−0.359744
$909$	0.113045	0.00374946
$910$	0	0
$911$	−22.3560	−0.740687	−0.370344	−	0.928895i	$-0.620760\pi$
$911$	−22.3560	−0.740687	−0.370344	+	0.928895i	$0.620760\pi$
$912$	45.8804	1.51925
$913$	−2.53651	−0.0839463
$914$	−47.5217	−1.57188
$915$	−18.5652	−0.613747
$916$	−17.3291	−0.572569
$917$	0	0
$918$	−24.1489	−0.797034
$919$	−8.62244	−0.284428	−0.142214	−	0.989836i	$-0.545422\pi$
$919$	−8.62244	−0.284428	−0.142214	+	0.989836i	$0.545422\pi$
$920$	0.233670	0.00770386
$921$	−50.6404	−1.66866
$922$	−53.4609	−1.76064
$923$	0	0
$924$	0	0
$925$	21.7712	0.715832
$926$	2.89729	0.0952109
$927$	1.35877	0.0446278
$928$	−26.1674	−0.858987
$929$	41.3861	1.35783	0.678916	−	0.734216i	$-0.262450\pi$
$929$	41.3861	1.35783	0.678916	+	0.734216i	$0.262450\pi$
$930$	−5.02562	−0.164796
$931$	0	0
$932$	9.66985	0.316747
$933$	9.70757	0.317812
$934$	16.8507	0.551372
$935$	1.52621	0.0499124
$936$	0	0
$937$	−21.3818	−0.698514	−0.349257	−	0.937027i	$-0.613566\pi$
$937$	−21.3818	−0.698514	−0.349257	+	0.937027i	$0.613566\pi$
$938$	0	0
$939$	−8.52788	−0.278297
$940$	−15.3285	−0.499959
$941$	−53.1480	−1.73258	−0.866288	−	0.499545i	$-0.833501\pi$
$941$	−53.1480	−1.73258	−0.866288	+	0.499545i	$0.833501\pi$
$942$	−27.5052	−0.896168
$943$	18.5009	0.602471
$944$	−2.81565	−0.0916416
$945$	0	0
$946$	13.5792	0.441497
$947$	8.86936	0.288216	0.144108	−	0.989562i	$-0.453969\pi$
$947$	8.86936	0.288216	0.144108	+	0.989562i	$0.453969\pi$
$948$	−46.5461	−1.51175
$949$	0	0
$950$	−55.7082	−1.80741
$951$	−13.4658	−0.436658
$952$	0	0
$953$	−39.8167	−1.28979	−0.644894	−	0.764272i	$-0.723099\pi$
$953$	−39.8167	−1.28979	−0.644894	+	0.764272i	$0.723099\pi$
$954$	2.66681	0.0863413
$955$	−1.52035	−0.0491973
$956$	−30.1696	−0.975756
$957$	4.10546	0.132711
$958$	25.3319	0.818435
$959$	0	0
$960$	13.1775	0.425301
$961$	−28.5335	−0.920437
$962$	0	0
$963$	1.28155	0.0412973
$964$	−12.4518	−0.401045
$965$	5.84024	0.188004
$966$	0	0
$967$	22.1611	0.712652	0.356326	−	0.934362i	$-0.384029\pi$
$967$	22.1611	0.712652	0.356326	+	0.934362i	$0.384029\pi$
$968$	−0.719735	−0.0231332
$969$	27.4579	0.882075
$970$	13.5303	0.434433
$971$	−36.0423	−1.15665	−0.578327	−	0.815805i	$-0.696294\pi$
$971$	−36.0423	−1.15665	−0.578327	+	0.815805i	$0.696294\pi$
$972$	1.99229	0.0639027
$973$	0	0
$974$	−43.3199	−1.38806
$975$	0	0
$976$	−45.8007	−1.46604
$977$	−32.9416	−1.05389	−0.526947	−	0.849898i	$-0.676664\pi$
$977$	−32.9416	−1.05389	−0.526947	+	0.849898i	$0.676664\pi$
$978$	5.97064	0.190920
$979$	−8.63219	−0.275886
$980$	0	0
$981$	1.29395	0.0413128
$982$	78.8038	2.51473
$983$	−4.19945	−0.133942	−0.0669709	−	0.997755i	$-0.521333\pi$
$983$	−4.19945	−0.133942	−0.0669709	+	0.997755i	$0.521333\pi$
$984$	−0.594185	−0.0189419
$985$	−1.69597	−0.0540382
$986$	−15.3927	−0.490203
$987$	0	0
$988$	0	0
$989$	−35.4767	−1.12809
$990$	−0.122862	−0.00390480
$991$	−13.4139	−0.426105	−0.213053	−	0.977041i	$-0.568341\pi$
$991$	−13.4139	−0.426105	−0.213053	+	0.977041i	$0.568341\pi$
$992$	−12.6139	−0.400491
$993$	19.9533	0.633198
$994$	0	0
$995$	10.3222	0.327236
$996$	−12.6699	−0.401460
$997$	47.8868	1.51659	0.758295	−	0.651911i	$-0.226033\pi$
$997$	47.8868	1.51659	0.758295	+	0.651911i	$0.226033\pi$
$998$	−18.4144	−0.582899
$999$	−26.6240	−0.842347

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.bx.1.5		5
7.3	odd	6		1183.2.e.f.170.1		10
7.5	odd	6		1183.2.e.f.508.1		10
7.6	odd	2		8281.2.a.bw.1.5		5
13.12	even	2		637.2.a.k.1.1		5
39.38	odd	2		5733.2.a.bm.1.5		5
91.12	odd	6		91.2.e.c.53.5	✓	10
91.25	even	6		637.2.e.m.79.5		10
91.38	odd	6		91.2.e.c.79.5	yes	10
91.51	even	6		637.2.e.m.508.5		10
91.90	odd	2		637.2.a.l.1.1		5
273.38	even	6		819.2.j.h.352.1		10
273.194	even	6		819.2.j.h.235.1		10
273.272	even	2		5733.2.a.bl.1.5		5
364.103	even	6		1456.2.r.p.417.4		10
364.311	even	6		1456.2.r.p.625.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.5	✓	10	91.12	odd	6
91.2.e.c.79.5	yes	10	91.38	odd	6
637.2.a.k.1.1		5	13.12	even	2
637.2.a.l.1.1		5	91.90	odd	2
637.2.e.m.79.5		10	91.25	even	6
637.2.e.m.508.5		10	91.51	even	6
819.2.j.h.235.1		10	273.194	even	6
819.2.j.h.352.1		10	273.38	even	6
1183.2.e.f.170.1		10	7.3	odd	6
1183.2.e.f.508.1		10	7.5	odd	6
1456.2.r.p.417.4		10	364.103	even	6
1456.2.r.p.625.4		10	364.311	even	6
5733.2.a.bl.1.5		5	273.272	even	2
5733.2.a.bm.1.5		5	39.38	odd	2
8281.2.a.bw.1.5		5	7.6	odd	2
8281.2.a.bx.1.5		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00852 q^{2} -1.75906 q^{3} +2.03417 q^{4} +0.905722 q^{5} -3.53311 q^{6} +0.0686323 q^{8} +0.0942784 q^{9} +O(q^{10})\)	\(q+2.00852 q^{2} -1.75906 q^{3} +2.03417 q^{4} +0.905722 q^{5} -3.53311 q^{6} +0.0686323 q^{8} +0.0942784 q^{9} +1.81916 q^{10} -0.716361 q^{11} -3.57822 q^{12} -1.59322 q^{15} -3.93049 q^{16} -2.35227 q^{17} +0.189360 q^{18} +6.63591 q^{19} +1.84239 q^{20} -1.43883 q^{22} +3.75906 q^{23} -0.120728 q^{24} -4.17967 q^{25} +5.11133 q^{27} +3.25799 q^{29} -3.20001 q^{30} +1.57050 q^{31} -8.03175 q^{32} +1.26012 q^{33} -4.72459 q^{34} +0.191778 q^{36} -5.20883 q^{37} +13.3284 q^{38} +0.0621618 q^{40} +4.92168 q^{41} -9.43766 q^{43} -1.45720 q^{44} +0.0853900 q^{45} +7.55016 q^{46} -8.31986 q^{47} +6.91395 q^{48} -8.39497 q^{50} +4.13778 q^{51} +14.0833 q^{53} +10.2662 q^{54} -0.648824 q^{55} -11.6729 q^{57} +6.54376 q^{58} +0.716361 q^{59} -3.24087 q^{60} +11.6527 q^{61} +3.15439 q^{62} -8.27099 q^{64} +2.53098 q^{66} -9.39174 q^{67} -4.78492 q^{68} -6.61239 q^{69} -10.9914 q^{71} +0.00647055 q^{72} -3.47300 q^{73} -10.4621 q^{74} +7.35227 q^{75} +13.4986 q^{76} +13.0082 q^{79} -3.55993 q^{80} -9.27395 q^{81} +9.88531 q^{82} +3.54083 q^{83} -2.13050 q^{85} -18.9558 q^{86} -5.73099 q^{87} -0.0491655 q^{88} +12.0501 q^{89} +0.171508 q^{90} +7.64656 q^{92} -2.76260 q^{93} -16.7106 q^{94} +6.01029 q^{95} +14.1283 q^{96} +7.43766 q^{97} -0.0675374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} + 8 q^{4} + 2 q^{5} - 5 q^{6} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 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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