LMFDB - Embedded newform 6027.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} -2.70928 q^{5} -2.17009 q^{6} -1.53919 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} -2.70928 q^{5} -2.17009 q^{6} -1.53919 q^{8} +1.00000 q^{9} +5.87936 q^{10} -3.07838 q^{11} +2.70928 q^{12} +5.24846 q^{13} -2.70928 q^{15} -2.07838 q^{16} -4.63090 q^{17} -2.17009 q^{18} +6.63090 q^{19} -7.34017 q^{20} +6.68035 q^{22} -5.43188 q^{23} -1.53919 q^{24} +2.34017 q^{25} -11.3896 q^{26} +1.00000 q^{27} +1.87936 q^{29} +5.87936 q^{30} +1.70928 q^{31} +7.58864 q^{32} -3.07838 q^{33} +10.0494 q^{34} +2.70928 q^{36} -3.29072 q^{37} -14.3896 q^{38} +5.24846 q^{39} +4.17009 q^{40} -1.00000 q^{41} +1.12783 q^{43} -8.34017 q^{44} -2.70928 q^{45} +11.7877 q^{46} -1.63090 q^{47} -2.07838 q^{48} -5.07838 q^{50} -4.63090 q^{51} +14.2195 q^{52} -3.24846 q^{53} -2.17009 q^{54} +8.34017 q^{55} +6.63090 q^{57} -4.07838 q^{58} +14.5464 q^{59} -7.34017 q^{60} -1.36910 q^{61} -3.70928 q^{62} -12.3112 q^{64} -14.2195 q^{65} +6.68035 q^{66} -8.86603 q^{67} -12.5464 q^{68} -5.43188 q^{69} +11.8082 q^{71} -1.53919 q^{72} +4.81432 q^{73} +7.14116 q^{74} +2.34017 q^{75} +17.9649 q^{76} -11.3896 q^{78} -16.4680 q^{79} +5.63090 q^{80} +1.00000 q^{81} +2.17009 q^{82} -13.9155 q^{83} +12.5464 q^{85} -2.44748 q^{86} +1.87936 q^{87} +4.73820 q^{88} +2.52359 q^{89} +5.87936 q^{90} -14.7165 q^{92} +1.70928 q^{93} +3.53919 q^{94} -17.9649 q^{95} +7.58864 q^{96} -3.87936 q^{97} -3.07838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 3 q^{3} + q^{4} - q^{5} - q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - q^2 + 3 * q^3 + q^4 - q^5 - q^6 - 3 * q^8 + 3 * q^9	$ 3 q - q^{2} + 3 q^{3} + q^{4} - q^{5} - q^{6} - 3 q^{8} + 3 q^{9} + 5 q^{10} - 6 q^{11} + q^{12} + 7 q^{13} - q^{15} - 3 q^{16} - 10 q^{17} - q^{18} + 16 q^{19} - 11 q^{20} - 2 q^{22} - 3 q^{23} - 3 q^{24} - 4 q^{25} - 5 q^{26} + 3 q^{27} - 7 q^{29} + 5 q^{30} - 2 q^{31} + 3 q^{32} - 6 q^{33} + 12 q^{34} + q^{36} - 17 q^{37} - 14 q^{38} + 7 q^{39} + 7 q^{40} - 3 q^{41} - 18 q^{43} - 14 q^{44} - q^{45} + 25 q^{46} - q^{47} - 3 q^{48} - 12 q^{50} - 10 q^{51} + 19 q^{52} - q^{53} - q^{54} + 14 q^{55} + 16 q^{57} - 9 q^{58} + 8 q^{59} - 11 q^{60} - 8 q^{61} - 4 q^{62} - 11 q^{64} - 19 q^{65} - 2 q^{66} - 13 q^{67} - 2 q^{68} - 3 q^{69} - 8 q^{71} - 3 q^{72} + 6 q^{73} + q^{74} - 4 q^{75} + 4 q^{76} - 5 q^{78} - 17 q^{79} + 13 q^{80} + 3 q^{81} + q^{82} - 10 q^{83} + 2 q^{85} - 8 q^{86} - 7 q^{87} + 22 q^{88} - 8 q^{89} + 5 q^{90} - 3 q^{92} - 2 q^{93} + 9 q^{94} - 4 q^{95} + 3 q^{96} + q^{97} - 6 q^{99}+O(q^{100}) $ 3 * q - q^2 + 3 * q^3 + q^4 - q^5 - q^6 - 3 * q^8 + 3 * q^9 + 5 * q^10 - 6 * q^11 + q^12 + 7 * q^13 - q^15 - 3 * q^16 - 10 * q^17 - q^18 + 16 * q^19 - 11 * q^20 - 2 * q^22 - 3 * q^23 - 3 * q^24 - 4 * q^25 - 5 * q^26 + 3 * q^27 - 7 * q^29 + 5 * q^30 - 2 * q^31 + 3 * q^32 - 6 * q^33 + 12 * q^34 + q^36 - 17 * q^37 - 14 * q^38 + 7 * q^39 + 7 * q^40 - 3 * q^41 - 18 * q^43 - 14 * q^44 - q^45 + 25 * q^46 - q^47 - 3 * q^48 - 12 * q^50 - 10 * q^51 + 19 * q^52 - q^53 - q^54 + 14 * q^55 + 16 * q^57 - 9 * q^58 + 8 * q^59 - 11 * q^60 - 8 * q^61 - 4 * q^62 - 11 * q^64 - 19 * q^65 - 2 * q^66 - 13 * q^67 - 2 * q^68 - 3 * q^69 - 8 * q^71 - 3 * q^72 + 6 * q^73 + q^74 - 4 * q^75 + 4 * q^76 - 5 * q^78 - 17 * q^79 + 13 * q^80 + 3 * q^81 + q^82 - 10 * q^83 + 2 * q^85 - 8 * q^86 - 7 * q^87 + 22 * q^88 - 8 * q^89 + 5 * q^90 - 3 * q^92 - 2 * q^93 + 9 * q^94 - 4 * q^95 + 3 * q^96 + q^97 - 6 * 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 $

$2$	−2.17009	−1.53448	−0.767241	−	0.641358i	$-0.778371\pi$
$2$	−2.17009	−1.53448	−0.767241	+	0.641358i	$0.778371\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.70928	1.35464
$5$	−2.70928	−1.21162	−0.605812	−	0.795608i	$-0.707152\pi$
$5$	−2.70928	−1.21162	−0.605812	+	0.795608i	$0.707152\pi$
$6$	−2.17009	−0.885934
$7$	0	0
$7$	0	0
$8$	−1.53919	−0.544185
$9$	1.00000	0.333333
$10$	5.87936	1.85922
$11$	−3.07838	−0.928166	−0.464083	−	0.885792i	$-0.653616\pi$
$11$	−3.07838	−0.928166	−0.464083	+	0.885792i	$0.653616\pi$
$12$	2.70928	0.782100
$13$	5.24846	1.45566	0.727831	−	0.685757i	$-0.240529\pi$
$13$	5.24846	1.45566	0.727831	+	0.685757i	$0.240529\pi$
$14$	0	0
$15$	−2.70928	−0.699532
$16$	−2.07838	−0.519594
$17$	−4.63090	−1.12316	−0.561579	−	0.827423i	$-0.689806\pi$
$17$	−4.63090	−1.12316	−0.561579	+	0.827423i	$0.689806\pi$
$18$	−2.17009	−0.511494
$19$	6.63090	1.52123	0.760616	−	0.649202i	$-0.224897\pi$
$19$	6.63090	1.52123	0.760616	+	0.649202i	$0.224897\pi$
$20$	−7.34017	−1.64131
$21$	0	0
$22$	6.68035	1.42425
$23$	−5.43188	−1.13263	−0.566313	−	0.824190i	$-0.691631\pi$
$23$	−5.43188	−1.13263	−0.566313	+	0.824190i	$0.691631\pi$
$24$	−1.53919	−0.314186
$25$	2.34017	0.468035
$26$	−11.3896	−2.23369
$27$	1.00000	0.192450
$28$	0	0
$29$	1.87936	0.348989	0.174494	−	0.984658i	$-0.444171\pi$
$29$	1.87936	0.348989	0.174494	+	0.984658i	$0.444171\pi$
$30$	5.87936	1.07342
$31$	1.70928	0.306995	0.153497	−	0.988149i	$-0.450946\pi$
$31$	1.70928	0.306995	0.153497	+	0.988149i	$0.450946\pi$
$32$	7.58864	1.34149
$33$	−3.07838	−0.535877
$34$	10.0494	1.72347
$35$	0	0
$36$	2.70928	0.451546
$37$	−3.29072	−0.540992	−0.270496	−	0.962721i	$-0.587188\pi$
$37$	−3.29072	−0.540992	−0.270496	+	0.962721i	$0.587188\pi$
$38$	−14.3896	−2.33430
$39$	5.24846	0.840427
$40$	4.17009	0.659349
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	1.12783	0.171992	0.0859959	−	0.996295i	$-0.472593\pi$
$43$	1.12783	0.171992	0.0859959	+	0.996295i	$0.472593\pi$
$44$	−8.34017	−1.25733
$45$	−2.70928	−0.403875
$46$	11.7877	1.73799
$47$	−1.63090	−0.237891	−0.118945	−	0.992901i	$-0.537951\pi$
$47$	−1.63090	−0.237891	−0.118945	+	0.992901i	$0.537951\pi$
$48$	−2.07838	−0.299988
$49$	0	0
$50$	−5.07838	−0.718191
$51$	−4.63090	−0.648455
$52$	14.2195	1.97189
$53$	−3.24846	−0.446211	−0.223105	−	0.974794i	$-0.571619\pi$
$53$	−3.24846	−0.446211	−0.223105	+	0.974794i	$0.571619\pi$
$54$	−2.17009	−0.295311
$55$	8.34017	1.12459
$56$	0	0
$57$	6.63090	0.878284
$58$	−4.07838	−0.535517
$59$	14.5464	1.89378	0.946888	−	0.321562i	$-0.104208\pi$
$59$	14.5464	1.89378	0.946888	+	0.321562i	$0.104208\pi$
$60$	−7.34017	−0.947612
$61$	−1.36910	−0.175296	−0.0876478	−	0.996152i	$-0.527935\pi$
$61$	−1.36910	−0.175296	−0.0876478	+	0.996152i	$0.527935\pi$
$62$	−3.70928	−0.471078
$63$	0	0
$64$	−12.3112	−1.53891
$65$	−14.2195	−1.76372
$66$	6.68035	0.822294
$67$	−8.86603	−1.08316	−0.541579	−	0.840650i	$-0.682173\pi$
$67$	−8.86603	−1.08316	−0.541579	+	0.840650i	$0.682173\pi$
$68$	−12.5464	−1.52147
$69$	−5.43188	−0.653922
$70$	0	0
$71$	11.8082	1.40137	0.700686	−	0.713470i	$-0.252877\pi$
$71$	11.8082	1.40137	0.700686	+	0.713470i	$0.252877\pi$
$72$	−1.53919	−0.181395
$73$	4.81432	0.563473	0.281736	−	0.959492i	$-0.409090\pi$
$73$	4.81432	0.563473	0.281736	+	0.959492i	$0.409090\pi$
$74$	7.14116	0.830143
$75$	2.34017	0.270220
$76$	17.9649	2.06072
$77$	0	0
$78$	−11.3896	−1.28962
$79$	−16.4680	−1.85279	−0.926397	−	0.376547i	$-0.877111\pi$
$79$	−16.4680	−1.85279	−0.926397	+	0.376547i	$0.877111\pi$
$80$	5.63090	0.629553
$81$	1.00000	0.111111
$82$	2.17009	0.239646
$83$	−13.9155	−1.52742	−0.763711	−	0.645558i	$-0.776625\pi$
$83$	−13.9155	−1.52742	−0.763711	+	0.645558i	$0.776625\pi$
$84$	0	0
$85$	12.5464	1.36085
$86$	−2.44748	−0.263919
$87$	1.87936	0.201489
$88$	4.73820	0.505094
$89$	2.52359	0.267500	0.133750	−	0.991015i	$-0.457298\pi$
$89$	2.52359	0.267500	0.133750	+	0.991015i	$0.457298\pi$
$90$	5.87936	0.619739
$91$	0	0
$92$	−14.7165	−1.53430
$93$	1.70928	0.177244
$94$	3.53919	0.365039
$95$	−17.9649	−1.84316
$96$	7.58864	0.774512
$97$	−3.87936	−0.393890	−0.196945	−	0.980415i	$-0.563102\pi$
$97$	−3.87936	−0.393890	−0.196945	+	0.980415i	$0.563102\pi$
$98$	0	0
$99$	−3.07838	−0.309389
$100$	6.34017	0.634017
$101$	12.4391	1.23773	0.618867	−	0.785496i	$-0.287592\pi$
$101$	12.4391	1.23773	0.618867	+	0.785496i	$0.287592\pi$
$102$	10.0494	0.995044
$103$	−2.80098	−0.275989	−0.137995	−	0.990433i	$-0.544066\pi$
$103$	−2.80098	−0.275989	−0.137995	+	0.990433i	$0.544066\pi$
$104$	−8.07838	−0.792150
$105$	0	0
$106$	7.04945	0.684703
$107$	0.957740	0.0925882	0.0462941	−	0.998928i	$-0.485259\pi$
$107$	0.957740	0.0925882	0.0462941	+	0.998928i	$0.485259\pi$
$108$	2.70928	0.260700
$109$	3.86603	0.370299	0.185149	−	0.982710i	$-0.440723\pi$
$109$	3.86603	0.370299	0.185149	+	0.982710i	$0.440723\pi$
$110$	−18.0989	−1.72566
$111$	−3.29072	−0.312342
$112$	0	0
$113$	−4.09890	−0.385592	−0.192796	−	0.981239i	$-0.561756\pi$
$113$	−4.09890	−0.385592	−0.192796	+	0.981239i	$0.561756\pi$
$114$	−14.3896	−1.34771
$115$	14.7165	1.37232
$116$	5.09171	0.472753
$117$	5.24846	0.485221
$118$	−31.5669	−2.90597
$119$	0	0
$120$	4.17009	0.380675
$121$	−1.52359	−0.138508
$122$	2.97107	0.268988
$123$	−1.00000	−0.0901670
$124$	4.63090	0.415867
$125$	7.20620	0.644542
$126$	0	0
$127$	10.4391	0.926318	0.463159	−	0.886275i	$-0.346716\pi$
$127$	10.4391	0.926318	0.463159	+	0.886275i	$0.346716\pi$
$128$	11.5392	1.01993
$129$	1.12783	0.0992995
$130$	30.8576	2.70639
$131$	9.89269	0.864329	0.432164	−	0.901795i	$-0.357750\pi$
$131$	9.89269	0.864329	0.432164	+	0.901795i	$0.357750\pi$
$132$	−8.34017	−0.725919
$133$	0	0
$134$	19.2401	1.66209
$135$	−2.70928	−0.233177
$136$	7.12783	0.611206
$137$	17.4813	1.49353	0.746765	−	0.665088i	$-0.231606\pi$
$137$	17.4813	1.49353	0.746765	+	0.665088i	$0.231606\pi$
$138$	11.7877	1.00343
$139$	12.5103	1.06111	0.530553	−	0.847652i	$-0.321984\pi$
$139$	12.5103	1.06111	0.530553	+	0.847652i	$0.321984\pi$
$140$	0	0
$141$	−1.63090	−0.137346
$142$	−25.6248	−2.15038
$143$	−16.1568	−1.35110
$144$	−2.07838	−0.173198
$145$	−5.09171	−0.422843
$146$	−10.4475	−0.864640
$147$	0	0
$148$	−8.91548	−0.732848
$149$	−18.7298	−1.53440	−0.767202	−	0.641405i	$-0.778352\pi$
$149$	−18.7298	−1.53440	−0.767202	+	0.641405i	$0.778352\pi$
$150$	−5.07838	−0.414648
$151$	−16.8638	−1.37235	−0.686177	−	0.727435i	$-0.740712\pi$
$151$	−16.8638	−1.37235	−0.686177	+	0.727435i	$0.740712\pi$
$152$	−10.2062	−0.827832
$153$	−4.63090	−0.374386
$154$	0	0
$155$	−4.63090	−0.371963
$156$	14.2195	1.13847
$157$	−7.62475	−0.608522	−0.304261	−	0.952589i	$-0.598409\pi$
$157$	−7.62475	−0.608522	−0.304261	+	0.952589i	$0.598409\pi$
$158$	35.7370	2.84308
$159$	−3.24846	−0.257620
$160$	−20.5597	−1.62539
$161$	0	0
$162$	−2.17009	−0.170498
$163$	15.2267	1.19265	0.596324	−	0.802743i	$-0.296627\pi$
$163$	15.2267	1.19265	0.596324	+	0.802743i	$0.296627\pi$
$164$	−2.70928	−0.211559
$165$	8.34017	0.649282
$166$	30.1978	2.34380
$167$	−13.5814	−1.05096	−0.525482	−	0.850805i	$-0.676115\pi$
$167$	−13.5814	−1.05096	−0.525482	+	0.850805i	$0.676115\pi$
$168$	0	0
$169$	14.5464	1.11895
$170$	−27.2267	−2.08819
$171$	6.63090	0.507077
$172$	3.05559	0.232987
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	−4.07838	−0.309181
$175$	0	0
$176$	6.39803	0.482270
$177$	14.5464	1.09337
$178$	−5.47641	−0.410474
$179$	−10.4475	−0.780881	−0.390441	−	0.920628i	$-0.627677\pi$
$179$	−10.4475	−0.780881	−0.390441	+	0.920628i	$0.627677\pi$
$180$	−7.34017	−0.547104
$181$	6.94441	0.516174	0.258087	−	0.966122i	$-0.416908\pi$
$181$	6.94441	0.516174	0.258087	+	0.966122i	$0.416908\pi$
$182$	0	0
$183$	−1.36910	−0.101207
$184$	8.36069	0.616358
$185$	8.91548	0.655479
$186$	−3.70928	−0.271977
$187$	14.2557	1.04248
$188$	−4.41855	−0.322256
$189$	0	0
$190$	38.9854	2.82830
$191$	12.5730	0.909753	0.454877	−	0.890554i	$-0.349683\pi$
$191$	12.5730	0.909753	0.454877	+	0.890554i	$0.349683\pi$
$192$	−12.3112	−0.888487
$193$	−15.0700	−1.08476	−0.542380	−	0.840133i	$-0.682477\pi$
$193$	−15.0700	−1.08476	−0.542380	+	0.840133i	$0.682477\pi$
$194$	8.41855	0.604417
$195$	−14.2195	−1.01828
$196$	0	0
$197$	18.0144	1.28347	0.641736	−	0.766926i	$-0.278215\pi$
$197$	18.0144	1.28347	0.641736	+	0.766926i	$0.278215\pi$
$198$	6.68035	0.474752
$199$	−22.8287	−1.61828	−0.809141	−	0.587614i	$-0.800067\pi$
$199$	−22.8287	−1.61828	−0.809141	+	0.587614i	$0.800067\pi$
$200$	−3.60197	−0.254698
$201$	−8.86603	−0.625362
$202$	−26.9939	−1.89928
$203$	0	0
$204$	−12.5464	−0.878422
$205$	2.70928	0.189224
$206$	6.07838	0.423501
$207$	−5.43188	−0.377542
$208$	−10.9083	−0.756354
$209$	−20.4124	−1.41196
$210$	0	0
$211$	−14.4680	−0.996018	−0.498009	−	0.867172i	$-0.665935\pi$
$211$	−14.4680	−0.996018	−0.498009	+	0.867172i	$0.665935\pi$
$212$	−8.80098	−0.604454
$213$	11.8082	0.809083
$214$	−2.07838	−0.142075
$215$	−3.05559	−0.208390
$216$	−1.53919	−0.104729
$217$	0	0
$218$	−8.38962	−0.568217
$219$	4.81432	0.325321
$220$	22.5958	1.52341
$221$	−24.3051	−1.63494
$222$	7.14116	0.479283
$223$	−12.5369	−0.839534	−0.419767	−	0.907632i	$-0.637888\pi$
$223$	−12.5369	−0.839534	−0.419767	+	0.907632i	$0.637888\pi$
$224$	0	0
$225$	2.34017	0.156012
$226$	8.89496	0.591684
$227$	19.5730	1.29911	0.649554	−	0.760315i	$-0.274956\pi$
$227$	19.5730	1.29911	0.649554	+	0.760315i	$0.274956\pi$
$228$	17.9649	1.18976
$229$	−9.66475	−0.638664	−0.319332	−	0.947643i	$-0.603459\pi$
$229$	−9.66475	−0.638664	−0.319332	+	0.947643i	$0.603459\pi$
$230$	−31.9360	−2.10580
$231$	0	0
$232$	−2.89269	−0.189915
$233$	−4.20620	−0.275558	−0.137779	−	0.990463i	$-0.543996\pi$
$233$	−4.20620	−0.275558	−0.137779	+	0.990463i	$0.543996\pi$
$234$	−11.3896	−0.744563
$235$	4.41855	0.288234
$236$	39.4101	2.56538
$237$	−16.4680	−1.06971
$238$	0	0
$239$	−17.4908	−1.13138	−0.565692	−	0.824616i	$-0.691391\pi$
$239$	−17.4908	−1.13138	−0.565692	+	0.824616i	$0.691391\pi$
$240$	5.63090	0.363473
$241$	−14.5958	−0.940200	−0.470100	−	0.882613i	$-0.655782\pi$
$241$	−14.5958	−0.940200	−0.470100	+	0.882613i	$0.655782\pi$
$242$	3.30632	0.212538
$243$	1.00000	0.0641500
$244$	−3.70928	−0.237462
$245$	0	0
$246$	2.17009	0.138360
$247$	34.8020	2.21440
$248$	−2.63090	−0.167062
$249$	−13.9155	−0.881858
$250$	−15.6381	−0.989039
$251$	−0.554787	−0.0350179	−0.0175089	−	0.999847i	$-0.505574\pi$
$251$	−0.554787	−0.0350179	−0.0175089	+	0.999847i	$0.505574\pi$
$252$	0	0
$253$	16.7214	1.05126
$254$	−22.6537	−1.42142
$255$	12.5464	0.785685
$256$	−0.418551	−0.0261594
$257$	−10.7070	−0.667885	−0.333942	−	0.942593i	$-0.608379\pi$
$257$	−10.7070	−0.667885	−0.333942	+	0.942593i	$0.608379\pi$
$258$	−2.44748	−0.152373
$259$	0	0
$260$	−38.5246	−2.38920
$261$	1.87936	0.116330
$262$	−21.4680	−1.32630
$263$	−24.6225	−1.51829	−0.759144	−	0.650923i	$-0.774382\pi$
$263$	−24.6225	−1.51829	−0.759144	+	0.650923i	$0.774382\pi$
$264$	4.73820	0.291616
$265$	8.80098	0.540640
$266$	0	0
$267$	2.52359	0.154441
$268$	−24.0205	−1.46729
$269$	−25.4391	−1.55105	−0.775524	−	0.631318i	$-0.782514\pi$
$269$	−25.4391	−1.55105	−0.775524	+	0.631318i	$0.782514\pi$
$270$	5.87936	0.357807
$271$	27.7454	1.68541	0.842706	−	0.538374i	$-0.180961\pi$
$271$	27.7454	1.68541	0.842706	+	0.538374i	$0.180961\pi$
$272$	9.62475	0.583586
$273$	0	0
$274$	−37.9360	−2.29180
$275$	−7.20394	−0.434414
$276$	−14.7165	−0.885827
$277$	13.7649	0.827051	0.413525	−	0.910493i	$-0.364297\pi$
$277$	13.7649	0.827051	0.413525	+	0.910493i	$0.364297\pi$
$278$	−27.1483	−1.62825
$279$	1.70928	0.102332
$280$	0	0
$281$	−16.9083	−1.00866	−0.504332	−	0.863510i	$-0.668261\pi$
$281$	−16.9083	−1.00866	−0.504332	+	0.863510i	$0.668261\pi$
$282$	3.53919	0.210756
$283$	18.8865	1.12269	0.561344	−	0.827582i	$-0.310284\pi$
$283$	18.8865	1.12269	0.561344	+	0.827582i	$0.310284\pi$
$284$	31.9916	1.89835
$285$	−17.9649	−1.06415
$286$	35.0616	2.07323
$287$	0	0
$288$	7.58864	0.447165
$289$	4.44521	0.261483
$290$	11.0494	0.648846
$291$	−3.87936	−0.227412
$292$	13.0433	0.763302
$293$	23.2001	1.35536	0.677681	−	0.735356i	$-0.262985\pi$
$293$	23.2001	1.35536	0.677681	+	0.735356i	$0.262985\pi$
$294$	0	0
$295$	−39.4101	−2.29455
$296$	5.06505	0.294400
$297$	−3.07838	−0.178626
$298$	40.6453	2.35452
$299$	−28.5090	−1.64872
$300$	6.34017	0.366050
$301$	0	0
$302$	36.5958	2.10585
$303$	12.4391	0.714606
$304$	−13.7815	−0.790424
$305$	3.70928	0.212392
$306$	10.0494	0.574489
$307$	−25.6069	−1.46146	−0.730731	−	0.682665i	$-0.760821\pi$
$307$	−25.6069	−1.46146	−0.730731	+	0.682665i	$0.760821\pi$
$308$	0	0
$309$	−2.80098	−0.159342
$310$	10.0494	0.570770
$311$	−4.80817	−0.272646	−0.136323	−	0.990664i	$-0.543529\pi$
$311$	−4.80817	−0.272646	−0.136323	+	0.990664i	$0.543529\pi$
$312$	−8.07838	−0.457348
$313$	0.823770	0.0465623	0.0232811	−	0.999729i	$-0.492589\pi$
$313$	0.823770	0.0465623	0.0232811	+	0.999729i	$0.492589\pi$
$314$	16.5464	0.933766
$315$	0	0
$316$	−44.6163	−2.50987
$317$	−19.8443	−1.11457	−0.557283	−	0.830323i	$-0.688156\pi$
$317$	−19.8443	−1.11457	−0.557283	+	0.830323i	$0.688156\pi$
$318$	7.04945	0.395313
$319$	−5.78539	−0.323919
$320$	33.3545	1.86458
$321$	0.957740	0.0534558
$322$	0	0
$323$	−30.7070	−1.70858
$324$	2.70928	0.150515
$325$	12.2823	0.681300
$326$	−33.0433	−1.83010
$327$	3.86603	0.213792
$328$	1.53919	0.0849875
$329$	0	0
$330$	−18.0989	−0.996311
$331$	−9.43907	−0.518818	−0.259409	−	0.965768i	$-0.583528\pi$
$331$	−9.43907	−0.518818	−0.259409	+	0.965768i	$0.583528\pi$
$332$	−37.7009	−2.06910
$333$	−3.29072	−0.180331
$334$	29.4729	1.61269
$335$	24.0205	1.31238
$336$	0	0
$337$	−20.6248	−1.12350	−0.561751	−	0.827306i	$-0.689872\pi$
$337$	−20.6248	−1.12350	−0.561751	+	0.827306i	$0.689872\pi$
$338$	−31.5669	−1.71701
$339$	−4.09890	−0.222622
$340$	33.9916	1.84345
$341$	−5.26180	−0.284942
$342$	−14.3896	−0.778102
$343$	0	0
$344$	−1.73594	−0.0935955
$345$	14.7165	0.792308
$346$	−19.5308	−1.04998
$347$	4.70313	0.252477	0.126239	−	0.992000i	$-0.459709\pi$
$347$	4.70313	0.252477	0.126239	+	0.992000i	$0.459709\pi$
$348$	5.09171	0.272944
$349$	−30.7031	−1.64350	−0.821750	−	0.569847i	$-0.807002\pi$
$349$	−30.7031	−1.64350	−0.821750	+	0.569847i	$0.807002\pi$
$350$	0	0
$351$	5.24846	0.280142
$352$	−23.3607	−1.24513
$353$	−34.2290	−1.82183	−0.910913	−	0.412599i	$-0.864621\pi$
$353$	−34.2290	−1.82183	−0.910913	+	0.412599i	$0.864621\pi$
$354$	−31.5669	−1.67776
$355$	−31.9916	−1.69794
$356$	6.83710	0.362366
$357$	0	0
$358$	22.6719	1.19825
$359$	−30.1883	−1.59328	−0.796640	−	0.604454i	$-0.793391\pi$
$359$	−30.1883	−1.59328	−0.796640	+	0.604454i	$0.793391\pi$
$360$	4.17009	0.219783
$361$	24.9688	1.31415
$362$	−15.0700	−0.792060
$363$	−1.52359	−0.0799678
$364$	0	0
$365$	−13.0433	−0.682718
$366$	2.97107	0.155300
$367$	30.2606	1.57959	0.789795	−	0.613372i	$-0.210187\pi$
$367$	30.2606	1.57959	0.789795	+	0.613372i	$0.210187\pi$
$368$	11.2895	0.588506
$369$	−1.00000	−0.0520579
$370$	−19.3474	−1.00582
$371$	0	0
$372$	4.63090	0.240101
$373$	18.1012	0.937243	0.468621	−	0.883399i	$-0.344751\pi$
$373$	18.1012	0.937243	0.468621	+	0.883399i	$0.344751\pi$
$374$	−30.9360	−1.59966
$375$	7.20620	0.372127
$376$	2.51026	0.129457
$377$	9.86376	0.508010
$378$	0	0
$379$	23.7503	1.21997	0.609986	−	0.792412i	$-0.291175\pi$
$379$	23.7503	1.21997	0.609986	+	0.792412i	$0.291175\pi$
$380$	−48.6719	−2.49682
$381$	10.4391	0.534810
$382$	−27.2846	−1.39600
$383$	6.61038	0.337775	0.168887	−	0.985635i	$-0.445983\pi$
$383$	6.61038	0.337775	0.168887	+	0.985635i	$0.445983\pi$
$384$	11.5392	0.588857
$385$	0	0
$386$	32.7031	1.66455
$387$	1.12783	0.0573306
$388$	−10.5103	−0.533578
$389$	18.9444	0.960520	0.480260	−	0.877126i	$-0.340542\pi$
$389$	18.9444	0.960520	0.480260	+	0.877126i	$0.340542\pi$
$390$	30.8576	1.56254
$391$	25.1545	1.27212
$392$	0	0
$393$	9.89269	0.499020
$394$	−39.0928	−1.96946
$395$	44.6163	2.24489
$396$	−8.34017	−0.419109
$397$	−5.36910	−0.269468	−0.134734	−	0.990882i	$-0.543018\pi$
$397$	−5.36910	−0.269468	−0.134734	+	0.990882i	$0.543018\pi$
$398$	49.5402	2.48323
$399$	0	0
$400$	−4.86376	−0.243188
$401$	23.1506	1.15609	0.578043	−	0.816006i	$-0.303817\pi$
$401$	23.1506	1.15609	0.578043	+	0.816006i	$0.303817\pi$
$402$	19.2401	0.959607
$403$	8.97107	0.446881
$404$	33.7009	1.67668
$405$	−2.70928	−0.134625
$406$	0	0
$407$	10.1301	0.502130
$408$	7.12783	0.352880
$409$	−27.7152	−1.37043	−0.685215	−	0.728341i	$-0.740292\pi$
$409$	−27.7152	−1.37043	−0.685215	+	0.728341i	$0.740292\pi$
$410$	−5.87936	−0.290361
$411$	17.4813	0.862290
$412$	−7.58864	−0.373865
$413$	0	0
$414$	11.7877	0.579332
$415$	37.7009	1.85066
$416$	39.8287	1.95276
$417$	12.5103	0.612630
$418$	44.2967	2.16662
$419$	−0.165166	−0.00806889	−0.00403444	−	0.999992i	$-0.501284\pi$
$419$	−0.165166	−0.00806889	−0.00403444	+	0.999992i	$0.501284\pi$
$420$	0	0
$421$	−29.2267	−1.42442	−0.712212	−	0.701965i	$-0.752306\pi$
$421$	−29.2267	−1.42442	−0.712212	+	0.701965i	$0.752306\pi$
$422$	31.3968	1.52837
$423$	−1.63090	−0.0792970
$424$	5.00000	0.242821
$425$	−10.8371	−0.525677
$426$	−25.6248	−1.24152
$427$	0	0
$428$	2.59478	0.125423
$429$	−16.1568	−0.780056
$430$	6.63090	0.319770
$431$	13.9071	0.669880	0.334940	−	0.942239i	$-0.391284\pi$
$431$	13.9071	0.669880	0.334940	+	0.942239i	$0.391284\pi$
$432$	−2.07838	−0.0999960
$433$	14.2290	0.683802	0.341901	−	0.939736i	$-0.388929\pi$
$433$	14.2290	0.683802	0.341901	+	0.939736i	$0.388929\pi$
$434$	0	0
$435$	−5.09171	−0.244129
$436$	10.4741	0.501620
$437$	−36.0183	−1.72299
$438$	−10.4475	−0.499200
$439$	29.4947	1.40770	0.703852	−	0.710347i	$-0.251462\pi$
$439$	29.4947	1.40770	0.703852	+	0.710347i	$0.251462\pi$
$440$	−12.8371	−0.611985
$441$	0	0
$442$	52.7442	2.50878
$443$	9.44134	0.448571	0.224286	−	0.974523i	$-0.427995\pi$
$443$	9.44134	0.448571	0.224286	+	0.974523i	$0.427995\pi$
$444$	−8.91548	−0.423110
$445$	−6.83710	−0.324110
$446$	27.2062	1.28825
$447$	−18.7298	−0.885889
$448$	0	0
$449$	13.5259	0.638325	0.319162	−	0.947700i	$-0.396598\pi$
$449$	13.5259	0.638325	0.319162	+	0.947700i	$0.396598\pi$
$450$	−5.07838	−0.239397
$451$	3.07838	0.144955
$452$	−11.1050	−0.522337
$453$	−16.8638	−0.792329
$454$	−42.4752	−1.99346
$455$	0	0
$456$	−10.2062	−0.477949
$457$	−15.8310	−0.740541	−0.370270	−	0.928924i	$-0.620735\pi$
$457$	−15.8310	−0.740541	−0.370270	+	0.928924i	$0.620735\pi$
$458$	20.9733	0.980020
$459$	−4.63090	−0.216152
$460$	39.8710	1.85899
$461$	−4.34632	−0.202428	−0.101214	−	0.994865i	$-0.532273\pi$
$461$	−4.34632	−0.202428	−0.101214	+	0.994865i	$0.532273\pi$
$462$	0	0
$463$	−24.6970	−1.14777	−0.573883	−	0.818937i	$-0.694564\pi$
$463$	−24.6970	−1.14777	−0.573883	+	0.818937i	$0.694564\pi$
$464$	−3.90602	−0.181333
$465$	−4.63090	−0.214753
$466$	9.12783	0.422838
$467$	−37.9071	−1.75413	−0.877065	−	0.480372i	$-0.840502\pi$
$467$	−37.9071	−1.75413	−0.877065	+	0.480372i	$0.840502\pi$
$468$	14.2195	0.657298
$469$	0	0
$470$	−9.58864	−0.442291
$471$	−7.62475	−0.351330
$472$	−22.3896	−1.03057
$473$	−3.47187	−0.159637
$474$	35.7370	1.64145
$475$	15.5174	0.711989
$476$	0	0
$477$	−3.24846	−0.148737
$478$	37.9565	1.73609
$479$	−40.1666	−1.83526	−0.917629	−	0.397437i	$-0.869900\pi$
$479$	−40.1666	−1.83526	−0.917629	+	0.397437i	$0.869900\pi$
$480$	−20.5597	−0.938418
$481$	−17.2713	−0.787501
$482$	31.6742	1.44272
$483$	0	0
$484$	−4.12783	−0.187628
$485$	10.5103	0.477246
$486$	−2.17009	−0.0984371
$487$	−17.6286	−0.798829	−0.399415	−	0.916770i	$-0.630787\pi$
$487$	−17.6286	−0.798829	−0.399415	+	0.916770i	$0.630787\pi$
$488$	2.10731	0.0953933
$489$	15.2267	0.688576
$490$	0	0
$491$	29.8225	1.34587	0.672936	−	0.739700i	$-0.265033\pi$
$491$	29.8225	1.34587	0.672936	+	0.739700i	$0.265033\pi$
$492$	−2.70928	−0.122144
$493$	−8.70313	−0.391969
$494$	−75.5234	−3.39796
$495$	8.34017	0.374863
$496$	−3.55252	−0.159513
$497$	0	0
$498$	30.1978	1.35320
$499$	34.9048	1.56255	0.781277	−	0.624185i	$-0.214569\pi$
$499$	34.9048	1.56255	0.781277	+	0.624185i	$0.214569\pi$
$500$	19.5236	0.873122
$501$	−13.5814	−0.606774
$502$	1.20394	0.0537343
$503$	−42.6163	−1.90017	−0.950084	−	0.311993i	$-0.899003\pi$
$503$	−42.6163	−1.90017	−0.950084	+	0.311993i	$0.899003\pi$
$504$	0	0
$505$	−33.7009	−1.49967
$506$	−36.2868	−1.61315
$507$	14.5464	0.646027
$508$	28.2823	1.25482
$509$	33.9337	1.50409	0.752043	−	0.659114i	$-0.229069\pi$
$509$	33.9337	1.50409	0.752043	+	0.659114i	$0.229069\pi$
$510$	−27.2267	−1.20562
$511$	0	0
$512$	−22.1701	−0.979789
$513$	6.63090	0.292761
$514$	23.2351	1.02486
$515$	7.58864	0.334395
$516$	3.05559	0.134515
$517$	5.02052	0.220802
$518$	0	0
$519$	9.00000	0.395056
$520$	21.8865	0.959789
$521$	−22.3668	−0.979909	−0.489954	−	0.871748i	$-0.662987\pi$
$521$	−22.3668	−0.979909	−0.489954	+	0.871748i	$0.662987\pi$
$522$	−4.07838	−0.178506
$523$	20.1340	0.880397	0.440199	−	0.897900i	$-0.354908\pi$
$523$	20.1340	0.880397	0.440199	+	0.897900i	$0.354908\pi$
$524$	26.8020	1.17085
$525$	0	0
$526$	53.4329	2.32979
$527$	−7.91548	−0.344804
$528$	6.39803	0.278439
$529$	6.50534	0.282841
$530$	−19.0989	−0.829603
$531$	14.5464	0.631259
$532$	0	0
$533$	−5.24846	−0.227336
$534$	−5.47641	−0.236987
$535$	−2.59478	−0.112182
$536$	13.6465	0.589439
$537$	−10.4475	−0.450842
$538$	55.2050	2.38006
$539$	0	0
$540$	−7.34017	−0.315871
$541$	−1.02279	−0.0439730	−0.0219865	−	0.999758i	$-0.506999\pi$
$541$	−1.02279	−0.0439730	−0.0219865	+	0.999758i	$0.506999\pi$
$542$	−60.2099	−2.58624
$543$	6.94441	0.298013
$544$	−35.1422	−1.50671
$545$	−10.4741	−0.448663
$546$	0	0
$547$	−27.8326	−1.19003	−0.595017	−	0.803713i	$-0.702855\pi$
$547$	−27.8326	−1.19003	−0.595017	+	0.803713i	$0.702855\pi$
$548$	47.3617	2.02319
$549$	−1.36910	−0.0584319
$550$	15.6332	0.666600
$551$	12.4619	0.530893
$552$	8.36069	0.355855
$553$	0	0
$554$	−29.8710	−1.26910
$555$	8.91548	0.378441
$556$	33.8937	1.43741
$557$	−16.5197	−0.699963	−0.349981	−	0.936757i	$-0.613812\pi$
$557$	−16.5197	−0.699963	−0.349981	+	0.936757i	$0.613812\pi$
$558$	−3.70928	−0.157026
$559$	5.91935	0.250362
$560$	0	0
$561$	14.2557	0.601874
$562$	36.6925	1.54778
$563$	−35.3812	−1.49114	−0.745570	−	0.666427i	$-0.767823\pi$
$563$	−35.3812	−1.49114	−0.745570	+	0.666427i	$0.767823\pi$
$564$	−4.41855	−0.186055
$565$	11.1050	0.467193
$566$	−40.9854	−1.72275
$567$	0	0
$568$	−18.1750	−0.762606
$569$	−39.2846	−1.64690	−0.823448	−	0.567392i	$-0.807952\pi$
$569$	−39.2846	−1.64690	−0.823448	+	0.567392i	$0.807952\pi$
$570$	38.9854	1.63292
$571$	−21.1773	−0.886241	−0.443121	−	0.896462i	$-0.646129\pi$
$571$	−21.1773	−0.886241	−0.443121	+	0.896462i	$0.646129\pi$
$572$	−43.7731	−1.83025
$573$	12.5730	0.525246
$574$	0	0
$575$	−12.7115	−0.530108
$576$	−12.3112	−0.512968
$577$	17.8348	0.742474	0.371237	−	0.928538i	$-0.378934\pi$
$577$	17.8348	0.742474	0.371237	+	0.928538i	$0.378934\pi$
$578$	−9.64650	−0.401241
$579$	−15.0700	−0.626286
$580$	−13.7948	−0.572800
$581$	0	0
$582$	8.41855	0.348960
$583$	10.0000	0.414158
$584$	−7.41014	−0.306634
$585$	−14.2195	−0.587905
$586$	−50.3461	−2.07978
$587$	−33.3074	−1.37474	−0.687371	−	0.726306i	$-0.741235\pi$
$587$	−33.3074	−1.37474	−0.687371	+	0.726306i	$0.741235\pi$
$588$	0	0
$589$	11.3340	0.467011
$590$	85.5234	3.52094
$591$	18.0144	0.741012
$592$	6.83937	0.281096
$593$	−39.2495	−1.61178	−0.805892	−	0.592062i	$-0.798314\pi$
$593$	−39.2495	−1.61178	−0.805892	+	0.592062i	$0.798314\pi$
$594$	6.68035	0.274098
$595$	0	0
$596$	−50.7442	−2.07856
$597$	−22.8287	−0.934316
$598$	61.8671	2.52993
$599$	45.1471	1.84466	0.922331	−	0.386401i	$-0.126282\pi$
$599$	45.1471	1.84466	0.922331	+	0.386401i	$0.126282\pi$
$600$	−3.60197	−0.147050
$601$	10.6176	0.433100	0.216550	−	0.976272i	$-0.430520\pi$
$601$	10.6176	0.433100	0.216550	+	0.976272i	$0.430520\pi$
$602$	0	0
$603$	−8.86603	−0.361053
$604$	−45.6886	−1.85904
$605$	4.12783	0.167820
$606$	−26.9939	−1.09655
$607$	−40.1171	−1.62830	−0.814152	−	0.580651i	$-0.802798\pi$
$607$	−40.1171	−1.62830	−0.814152	+	0.580651i	$0.802798\pi$
$608$	50.3195	2.04072
$609$	0	0
$610$	−8.04945	−0.325913
$611$	−8.55971	−0.346289
$612$	−12.5464	−0.507157
$613$	−23.3545	−0.943281	−0.471641	−	0.881791i	$-0.656338\pi$
$613$	−23.3545	−0.943281	−0.471641	+	0.881791i	$0.656338\pi$
$614$	55.5692	2.24259
$615$	2.70928	0.109249
$616$	0	0
$617$	−1.20847	−0.0486512	−0.0243256	−	0.999704i	$-0.507744\pi$
$617$	−1.20847	−0.0486512	−0.0243256	+	0.999704i	$0.507744\pi$
$618$	6.07838	0.244508
$619$	−43.3656	−1.74301	−0.871506	−	0.490386i	$-0.836856\pi$
$619$	−43.3656	−1.74301	−0.871506	+	0.490386i	$0.836856\pi$
$620$	−12.5464	−0.503875
$621$	−5.43188	−0.217974
$622$	10.4341	0.418371
$623$	0	0
$624$	−10.9083	−0.436681
$625$	−31.2245	−1.24898
$626$	−1.78765	−0.0714490
$627$	−20.4124	−0.815193
$628$	−20.6576	−0.824326
$629$	15.2390	0.607619
$630$	0	0
$631$	6.24128	0.248461	0.124231	−	0.992253i	$-0.460354\pi$
$631$	6.24128	0.248461	0.124231	+	0.992253i	$0.460354\pi$
$632$	25.3474	1.00826
$633$	−14.4680	−0.575051
$634$	43.0638	1.71028
$635$	−28.2823	−1.12235
$636$	−8.80098	−0.348982
$637$	0	0
$638$	12.5548	0.497049
$639$	11.8082	0.467124
$640$	−31.2628	−1.23577
$641$	34.0326	1.34421	0.672104	−	0.740457i	$-0.265391\pi$
$641$	34.0326	1.34421	0.672104	+	0.740457i	$0.265391\pi$
$642$	−2.07838	−0.0820270
$643$	−14.4885	−0.571371	−0.285686	−	0.958323i	$-0.592221\pi$
$643$	−14.4885	−0.571371	−0.285686	+	0.958323i	$0.592221\pi$
$644$	0	0
$645$	−3.05559	−0.120314
$646$	66.6369	2.62179
$647$	18.1529	0.713663	0.356832	−	0.934169i	$-0.383857\pi$
$647$	18.1529	0.713663	0.356832	+	0.934169i	$0.383857\pi$
$648$	−1.53919	−0.0604650
$649$	−44.7792	−1.75774
$650$	−26.6537	−1.04544
$651$	0	0
$652$	41.2534	1.61561
$653$	−4.97107	−0.194533	−0.0972665	−	0.995258i	$-0.531010\pi$
$653$	−4.97107	−0.194533	−0.0972665	+	0.995258i	$0.531010\pi$
$654$	−8.38962	−0.328060
$655$	−26.8020	−1.04724
$656$	2.07838	0.0811470
$657$	4.81432	0.187824
$658$	0	0
$659$	−22.1445	−0.862626	−0.431313	−	0.902202i	$-0.641950\pi$
$659$	−22.1445	−0.862626	−0.431313	+	0.902202i	$0.641950\pi$
$660$	22.5958	0.879541
$661$	19.0349	0.740372	0.370186	−	0.928958i	$-0.379294\pi$
$661$	19.0349	0.740372	0.370186	+	0.928958i	$0.379294\pi$
$662$	20.4836	0.796118
$663$	−24.3051	−0.943932
$664$	21.4186	0.831201
$665$	0	0
$666$	7.14116	0.276714
$667$	−10.2085	−0.395274
$668$	−36.7959	−1.42368
$669$	−12.5369	−0.484705
$670$	−52.1266	−2.01383
$671$	4.21461	0.162703
$672$	0	0
$673$	6.17501	0.238029	0.119015	−	0.992893i	$-0.462026\pi$
$673$	6.17501	0.238029	0.119015	+	0.992893i	$0.462026\pi$
$674$	44.7575	1.72399
$675$	2.34017	0.0900733
$676$	39.4101	1.51577
$677$	−27.0784	−1.04071	−0.520353	−	0.853951i	$-0.674200\pi$
$677$	−27.0784	−1.04071	−0.520353	+	0.853951i	$0.674200\pi$
$678$	8.89496	0.341609
$679$	0	0
$680$	−19.3112	−0.740552
$681$	19.5730	0.750040
$682$	11.4186	0.437239
$683$	−37.9421	−1.45182	−0.725908	−	0.687792i	$-0.758580\pi$
$683$	−37.9421	−1.45182	−0.725908	+	0.687792i	$0.758580\pi$
$684$	17.9649	0.686906
$685$	−47.3617	−1.80960
$686$	0	0
$687$	−9.66475	−0.368733
$688$	−2.34405	−0.0893660
$689$	−17.0494	−0.649532
$690$	−31.9360	−1.21578
$691$	−14.1034	−0.536520	−0.268260	−	0.963347i	$-0.586449\pi$
$691$	−14.1034	−0.536520	−0.268260	+	0.963347i	$0.586449\pi$
$692$	24.3835	0.926921
$693$	0	0
$694$	−10.2062	−0.387422
$695$	−33.8937	−1.28566
$696$	−2.89269	−0.109647
$697$	4.63090	0.175408
$698$	66.6285	2.52192
$699$	−4.20620	−0.159093
$700$	0	0
$701$	24.1133	0.910746	0.455373	−	0.890301i	$-0.349506\pi$
$701$	24.1133	0.910746	0.455373	+	0.890301i	$0.349506\pi$
$702$	−11.3896	−0.429874
$703$	−21.8205	−0.822974
$704$	37.8987	1.42836
$705$	4.41855	0.166412
$706$	74.2799	2.79556
$707$	0	0
$708$	39.4101	1.48112
$709$	0.890425	0.0334406	0.0167203	−	0.999860i	$-0.494678\pi$
$709$	0.890425	0.0334406	0.0167203	+	0.999860i	$0.494678\pi$
$710$	69.4245	2.60546
$711$	−16.4680	−0.617598
$712$	−3.88428	−0.145570
$713$	−9.28458	−0.347710
$714$	0	0
$715$	43.7731	1.63702
$716$	−28.3051	−1.05781
$717$	−17.4908	−0.653205
$718$	65.5113	2.44486
$719$	38.0722	1.41985	0.709927	−	0.704275i	$-0.248728\pi$
$719$	38.0722	1.41985	0.709927	+	0.704275i	$0.248728\pi$
$720$	5.63090	0.209851
$721$	0	0
$722$	−54.1845	−2.01654
$723$	−14.5958	−0.542825
$724$	18.8143	0.699229
$725$	4.39803	0.163339
$726$	3.30632	0.122709
$727$	−17.4908	−0.648697	−0.324349	−	0.945938i	$-0.605145\pi$
$727$	−17.4908	−0.648697	−0.324349	+	0.945938i	$0.605145\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	28.3051	1.04762
$731$	−5.22285	−0.193174
$732$	−3.70928	−0.137099
$733$	−1.94214	−0.0717346	−0.0358673	−	0.999357i	$-0.511419\pi$
$733$	−1.94214	−0.0717346	−0.0358673	+	0.999357i	$0.511419\pi$
$734$	−65.6681	−2.42385
$735$	0	0
$736$	−41.2206	−1.51941
$737$	27.2930	1.00535
$738$	2.17009	0.0798820
$739$	−17.6391	−0.648866	−0.324433	−	0.945909i	$-0.605173\pi$
$739$	−17.6391	−0.648866	−0.324433	+	0.945909i	$0.605173\pi$
$740$	24.1545	0.887937
$741$	34.8020	1.27848
$742$	0	0
$743$	−0.913212	−0.0335025	−0.0167512	−	0.999860i	$-0.505332\pi$
$743$	−0.913212	−0.0335025	−0.0167512	+	0.999860i	$0.505332\pi$
$744$	−2.63090	−0.0964534
$745$	50.7442	1.85912
$746$	−39.2811	−1.43818
$747$	−13.9155	−0.509141
$748$	38.6225	1.41218
$749$	0	0
$750$	−15.6381	−0.571022
$751$	34.4413	1.25678	0.628391	−	0.777898i	$-0.283714\pi$
$751$	34.4413	1.25678	0.628391	+	0.777898i	$0.283714\pi$
$752$	3.38962	0.123607
$753$	−0.554787	−0.0202176
$754$	−21.4052	−0.779532
$755$	45.6886	1.66278
$756$	0	0
$757$	−10.1834	−0.370123	−0.185061	−	0.982727i	$-0.559248\pi$
$757$	−10.1834	−0.370123	−0.185061	+	0.982727i	$0.559248\pi$
$758$	−51.5402	−1.87203
$759$	16.7214	0.606948
$760$	27.6514	1.00302
$761$	−5.00841	−0.181555	−0.0907774	−	0.995871i	$-0.528935\pi$
$761$	−5.00841	−0.181555	−0.0907774	+	0.995871i	$0.528935\pi$
$762$	−22.6537	−0.820656
$763$	0	0
$764$	34.0638	1.23239
$765$	12.5464	0.453615
$766$	−14.3451	−0.518309
$767$	76.3461	2.75670
$768$	−0.418551	−0.0151031
$769$	−40.2290	−1.45069	−0.725347	−	0.688383i	$-0.758321\pi$
$769$	−40.2290	−1.45069	−0.725347	+	0.688383i	$0.758321\pi$
$770$	0	0
$771$	−10.7070	−0.385603
$772$	−40.8287	−1.46946
$773$	−37.8888	−1.36277	−0.681383	−	0.731927i	$-0.738621\pi$
$773$	−37.8888	−1.36277	−0.681383	+	0.731927i	$0.738621\pi$
$774$	−2.44748	−0.0879729
$775$	4.00000	0.143684
$776$	5.97107	0.214349
$777$	0	0
$778$	−41.1110	−1.47390
$779$	−6.63090	−0.237577
$780$	−38.5246	−1.37940
$781$	−36.3500	−1.30071
$782$	−54.5874	−1.95204
$783$	1.87936	0.0671629
$784$	0	0
$785$	20.6576	0.737300
$786$	−21.4680	−0.765738
$787$	25.1327	0.895886	0.447943	−	0.894062i	$-0.352157\pi$
$787$	25.1327	0.895886	0.447943	+	0.894062i	$0.352157\pi$
$788$	48.8059	1.73864
$789$	−24.6225	−0.876584
$790$	−96.8213	−3.44475
$791$	0	0
$792$	4.73820	0.168365
$793$	−7.18568	−0.255171
$794$	11.6514	0.413493
$795$	8.80098	0.312139
$796$	−61.8492	−2.19219
$797$	−31.8264	−1.12735	−0.563675	−	0.825997i	$-0.690613\pi$
$797$	−31.8264	−1.12735	−0.563675	+	0.825997i	$0.690613\pi$
$798$	0	0
$799$	7.55252	0.267189
$800$	17.7587	0.627866
$801$	2.52359	0.0891667
$802$	−50.2388	−1.77399
$803$	−14.8203	−0.522996
$804$	−24.0205	−0.847138
$805$	0	0
$806$	−19.4680	−0.685731
$807$	−25.4391	−0.895498
$808$	−19.1461	−0.673557
$809$	14.3412	0.504210	0.252105	−	0.967700i	$-0.418877\pi$
$809$	14.3412	0.504210	0.252105	+	0.967700i	$0.418877\pi$
$810$	5.87936	0.206580
$811$	−7.42347	−0.260673	−0.130337	−	0.991470i	$-0.541606\pi$
$811$	−7.42347	−0.260673	−0.130337	+	0.991470i	$0.541606\pi$
$812$	0	0
$813$	27.7454	0.973073
$814$	−21.9832	−0.770510
$815$	−41.2534	−1.44504
$816$	9.62475	0.336934
$817$	7.47850	0.261640
$818$	60.1445	2.10290
$819$	0	0
$820$	7.34017	0.256330
$821$	−28.2206	−0.984905	−0.492453	−	0.870339i	$-0.663899\pi$
$821$	−28.2206	−0.984905	−0.492453	+	0.870339i	$0.663899\pi$
$822$	−37.9360	−1.32317
$823$	−50.5523	−1.76214	−0.881072	−	0.472982i	$-0.843177\pi$
$823$	−50.5523	−1.76214	−0.881072	+	0.472982i	$0.843177\pi$
$824$	4.31124	0.150189
$825$	−7.20394	−0.250809
$826$	0	0
$827$	2.29460	0.0797911	0.0398955	−	0.999204i	$-0.487297\pi$
$827$	2.29460	0.0797911	0.0398955	+	0.999204i	$0.487297\pi$
$828$	−14.7165	−0.511432
$829$	−28.3545	−0.984794	−0.492397	−	0.870371i	$-0.663879\pi$
$829$	−28.3545	−0.984794	−0.492397	+	0.870371i	$0.663879\pi$
$830$	−81.8141	−2.83981
$831$	13.7649	0.477498
$832$	−64.6151	−2.24013
$833$	0	0
$834$	−27.1483	−0.940070
$835$	36.7959	1.27337
$836$	−55.3028	−1.91269
$837$	1.70928	0.0590812
$838$	0.358424	0.0123816
$839$	−29.8515	−1.03059	−0.515294	−	0.857014i	$-0.672317\pi$
$839$	−29.8515	−1.03059	−0.515294	+	0.857014i	$0.672317\pi$
$840$	0	0
$841$	−25.4680	−0.878207
$842$	63.4245	2.18575
$843$	−16.9083	−0.582352
$844$	−39.1978	−1.34924
$845$	−39.4101	−1.35575
$846$	3.53919	0.121680
$847$	0	0
$848$	6.75154	0.231849
$849$	18.8865	0.648185
$850$	23.5174	0.806642
$851$	17.8748	0.612741
$852$	31.9916	1.09601
$853$	11.5753	0.396331	0.198165	−	0.980169i	$-0.436502\pi$
$853$	11.5753	0.396331	0.198165	+	0.980169i	$0.436502\pi$
$854$	0	0
$855$	−17.9649	−0.614388
$856$	−1.47414	−0.0503851
$857$	20.2990	0.693399	0.346700	−	0.937976i	$-0.387302\pi$
$857$	20.2990	0.693399	0.346700	+	0.937976i	$0.387302\pi$
$858$	35.0616	1.19698
$859$	−55.3929	−1.88998	−0.944991	−	0.327096i	$-0.893930\pi$
$859$	−55.3929	−1.88998	−0.944991	+	0.327096i	$0.893930\pi$
$860$	−8.27844	−0.282292
$861$	0	0
$862$	−30.1795	−1.02792
$863$	−32.6274	−1.11065	−0.555325	−	0.831633i	$-0.687406\pi$
$863$	−32.6274	−1.11065	−0.555325	+	0.831633i	$0.687406\pi$
$864$	7.58864	0.258171
$865$	−24.3835	−0.829063
$866$	−30.8781	−1.04928
$867$	4.44521	0.150967
$868$	0	0
$869$	50.6947	1.71970
$870$	11.0494	0.374611
$871$	−46.5330	−1.57671
$872$	−5.95055	−0.201511
$873$	−3.87936	−0.131297
$874$	78.1627	2.64389
$875$	0	0
$876$	13.0433	0.440692
$877$	29.0517	0.981007	0.490503	−	0.871439i	$-0.336813\pi$
$877$	29.0517	0.981007	0.490503	+	0.871439i	$0.336813\pi$
$878$	−64.0060	−2.16010
$879$	23.2001	0.782519
$880$	−17.3340	−0.584330
$881$	16.2411	0.547177	0.273588	−	0.961847i	$-0.411789\pi$
$881$	16.2411	0.547177	0.273588	+	0.961847i	$0.411789\pi$
$882$	0	0
$883$	−19.2245	−0.646954	−0.323477	−	0.946236i	$-0.604852\pi$
$883$	−19.2245	−0.646954	−0.323477	+	0.946236i	$0.604852\pi$
$884$	−65.8492	−2.21475
$885$	−39.4101	−1.32476
$886$	−20.4885	−0.688325
$887$	14.6475	0.491816	0.245908	−	0.969293i	$-0.420914\pi$
$887$	14.6475	0.491816	0.245908	+	0.969293i	$0.420914\pi$
$888$	5.06505	0.169972
$889$	0	0
$890$	14.8371	0.497341
$891$	−3.07838	−0.103130
$892$	−33.9660	−1.13726
$893$	−10.8143	−0.361887
$894$	40.6453	1.35938
$895$	28.3051	0.946135
$896$	0	0
$897$	−28.5090	−0.951889
$898$	−29.3523	−0.979498
$899$	3.21235	0.107138
$900$	6.34017	0.211339
$901$	15.0433	0.501165
$902$	−6.68035	−0.222431
$903$	0	0
$904$	6.30898	0.209833
$905$	−18.8143	−0.625409
$906$	36.5958	1.21581
$907$	15.5609	0.516692	0.258346	−	0.966052i	$-0.416823\pi$
$907$	15.5609	0.516692	0.258346	+	0.966052i	$0.416823\pi$
$908$	53.0288	1.75982
$909$	12.4391	0.412578
$910$	0	0
$911$	−10.2062	−0.338147	−0.169073	−	0.985603i	$-0.554077\pi$
$911$	−10.2062	−0.338147	−0.169073	+	0.985603i	$0.554077\pi$
$912$	−13.7815	−0.456351
$913$	42.8371	1.41770
$914$	34.3545	1.13635
$915$	3.70928	0.122625
$916$	−26.1845	−0.865159
$917$	0	0
$918$	10.0494	0.331681
$919$	−29.6681	−0.978659	−0.489329	−	0.872099i	$-0.662758\pi$
$919$	−29.6681	−0.978659	−0.489329	+	0.872099i	$0.662758\pi$
$920$	−22.6514	−0.746795
$921$	−25.6069	−0.843776
$922$	9.43188	0.310622
$923$	61.9748	2.03992
$924$	0	0
$925$	−7.70086	−0.253203
$926$	53.5946	1.76123
$927$	−2.80098	−0.0919964
$928$	14.2618	0.468166
$929$	1.23901	0.0406506	0.0203253	−	0.999793i	$-0.493530\pi$
$929$	1.23901	0.0406506	0.0203253	+	0.999793i	$0.493530\pi$
$930$	10.0494	0.329534
$931$	0	0
$932$	−11.3958	−0.373281
$933$	−4.80817	−0.157412
$934$	82.2616	2.69168
$935$	−38.6225	−1.26309
$936$	−8.07838	−0.264050
$937$	42.4619	1.38717	0.693584	−	0.720376i	$-0.256031\pi$
$937$	42.4619	1.38717	0.693584	+	0.720376i	$0.256031\pi$
$938$	0	0
$939$	0.823770	0.0268827
$940$	11.9711	0.390453
$941$	8.31512	0.271065	0.135533	−	0.990773i	$-0.456725\pi$
$941$	8.31512	0.271065	0.135533	+	0.990773i	$0.456725\pi$
$942$	16.5464	0.539110
$943$	5.43188	0.176886
$944$	−30.2329	−0.983996
$945$	0	0
$946$	7.53427	0.244960
$947$	−3.39681	−0.110381	−0.0551907	−	0.998476i	$-0.517577\pi$
$947$	−3.39681	−0.110381	−0.0551907	+	0.998476i	$0.517577\pi$
$948$	−44.6163	−1.44907
$949$	25.2678	0.820226
$950$	−33.6742	−1.09254
$951$	−19.8443	−0.643495
$952$	0	0
$953$	−24.7708	−0.802406	−0.401203	−	0.915989i	$-0.631408\pi$
$953$	−24.7708	−0.802406	−0.401203	+	0.915989i	$0.631408\pi$
$954$	7.04945	0.228234
$955$	−34.0638	−1.10228
$956$	−47.3874	−1.53262
$957$	−5.78539	−0.187015
$958$	87.1650	2.81617
$959$	0	0
$960$	33.3545	1.07651
$961$	−28.0784	−0.905754
$962$	37.4801	1.20841
$963$	0.957740	0.0308627
$964$	−39.5441	−1.27363
$965$	40.8287	1.31432
$966$	0	0
$967$	1.78378	0.0573624	0.0286812	−	0.999589i	$-0.490869\pi$
$967$	1.78378	0.0573624	0.0286812	+	0.999589i	$0.490869\pi$
$968$	2.34509	0.0753742
$969$	−30.7070	−0.986451
$970$	−22.8082	−0.732326
$971$	38.1545	1.22444	0.612218	−	0.790689i	$-0.290278\pi$
$971$	38.1545	1.22444	0.612218	+	0.790689i	$0.290278\pi$
$972$	2.70928	0.0869000
$973$	0	0
$974$	38.2557	1.22579
$975$	12.2823	0.393349
$976$	2.84551	0.0910826
$977$	−14.7831	−0.472954	−0.236477	−	0.971637i	$-0.575993\pi$
$977$	−14.7831	−0.472954	−0.236477	+	0.971637i	$0.575993\pi$
$978$	−33.0433	−1.05661
$979$	−7.76856	−0.248284
$980$	0	0
$981$	3.86603	0.123433
$982$	−64.7175	−2.06522
$983$	9.73594	0.310528	0.155264	−	0.987873i	$-0.450377\pi$
$983$	9.73594	0.310528	0.155264	+	0.987873i	$0.450377\pi$
$984$	1.53919	0.0490675
$985$	−48.8059	−1.55509
$986$	18.8865	0.601470
$987$	0	0
$988$	94.2883	2.99971
$989$	−6.12622	−0.194802
$990$	−18.0989	−0.575221
$991$	−40.3028	−1.28026	−0.640131	−	0.768266i	$-0.721120\pi$
$991$	−40.3028	−1.28026	−0.640131	+	0.768266i	$0.721120\pi$
$992$	12.9711	0.411832
$993$	−9.43907	−0.299540
$994$	0	0
$995$	61.8492	1.96075
$996$	−37.7009	−1.19460
$997$	23.4013	0.741128	0.370564	−	0.928807i	$-0.379164\pi$
$997$	23.4013	0.741128	0.370564	+	0.928807i	$0.379164\pi$
$998$	−75.7464	−2.39771
$999$	−3.29072	−0.104114

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.o.1.1		3
7.6	odd	2		861.2.a.h.1.1	✓	3
21.20	even	2		2583.2.a.n.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.h.1.1	✓	3	7.6	odd	2
2583.2.a.n.1.3		3	21.20	even	2
6027.2.a.o.1.1		3	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} -2.70928 q^{5} -2.17009 q^{6} -1.53919 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} -2.70928 q^{5} -2.17009 q^{6} -1.53919 q^{8} +1.00000 q^{9} +5.87936 q^{10} -3.07838 q^{11} +2.70928 q^{12} +5.24846 q^{13} -2.70928 q^{15} -2.07838 q^{16} -4.63090 q^{17} -2.17009 q^{18} +6.63090 q^{19} -7.34017 q^{20} +6.68035 q^{22} -5.43188 q^{23} -1.53919 q^{24} +2.34017 q^{25} -11.3896 q^{26} +1.00000 q^{27} +1.87936 q^{29} +5.87936 q^{30} +1.70928 q^{31} +7.58864 q^{32} -3.07838 q^{33} +10.0494 q^{34} +2.70928 q^{36} -3.29072 q^{37} -14.3896 q^{38} +5.24846 q^{39} +4.17009 q^{40} -1.00000 q^{41} +1.12783 q^{43} -8.34017 q^{44} -2.70928 q^{45} +11.7877 q^{46} -1.63090 q^{47} -2.07838 q^{48} -5.07838 q^{50} -4.63090 q^{51} +14.2195 q^{52} -3.24846 q^{53} -2.17009 q^{54} +8.34017 q^{55} +6.63090 q^{57} -4.07838 q^{58} +14.5464 q^{59} -7.34017 q^{60} -1.36910 q^{61} -3.70928 q^{62} -12.3112 q^{64} -14.2195 q^{65} +6.68035 q^{66} -8.86603 q^{67} -12.5464 q^{68} -5.43188 q^{69} +11.8082 q^{71} -1.53919 q^{72} +4.81432 q^{73} +7.14116 q^{74} +2.34017 q^{75} +17.9649 q^{76} -11.3896 q^{78} -16.4680 q^{79} +5.63090 q^{80} +1.00000 q^{81} +2.17009 q^{82} -13.9155 q^{83} +12.5464 q^{85} -2.44748 q^{86} +1.87936 q^{87} +4.73820 q^{88} +2.52359 q^{89} +5.87936 q^{90} -14.7165 q^{92} +1.70928 q^{93} +3.53919 q^{94} -17.9649 q^{95} +7.58864 q^{96} -3.87936 q^{97} -3.07838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 3 q^{3} + q^{4} - q^{5} - q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - q^2 + 3 * q^3 + q^4 - q^5 - q^6 - 3 * q^8 + 3 * q^9	\( 3 q - q^{2} + 3 q^{3} + q^{4} - q^{5} - q^{6} - 3 q^{8} + 3 q^{9} + 5 q^{10} - 6 q^{11} + q^{12} + 7 q^{13} - q^{15} - 3 q^{16} - 10 q^{17} - q^{18} + 16 q^{19} - 11 q^{20} - 2 q^{22} - 3 q^{23} - 3 q^{24} - 4 q^{25} - 5 q^{26} + 3 q^{27} - 7 q^{29} + 5 q^{30} - 2 q^{31} + 3 q^{32} - 6 q^{33} + 12 q^{34} + q^{36} - 17 q^{37} - 14 q^{38} + 7 q^{39} + 7 q^{40} - 3 q^{41} - 18 q^{43} - 14 q^{44} - q^{45} + 25 q^{46} - q^{47} - 3 q^{48} - 12 q^{50} - 10 q^{51} + 19 q^{52} - q^{53} - q^{54} + 14 q^{55} + 16 q^{57} - 9 q^{58} + 8 q^{59} - 11 q^{60} - 8 q^{61} - 4 q^{62} - 11 q^{64} - 19 q^{65} - 2 q^{66} - 13 q^{67} - 2 q^{68} - 3 q^{69} - 8 q^{71} - 3 q^{72} + 6 q^{73} + q^{74} - 4 q^{75} + 4 q^{76} - 5 q^{78} - 17 q^{79} + 13 q^{80} + 3 q^{81} + q^{82} - 10 q^{83} + 2 q^{85} - 8 q^{86} - 7 q^{87} + 22 q^{88} - 8 q^{89} + 5 q^{90} - 3 q^{92} - 2 q^{93} + 9 q^{94} - 4 q^{95} + 3 q^{96} + q^{97} - 6 q^{99}+O(q^{100}) \) 3 * q - q^2 + 3 * q^3 + q^4 - q^5 - q^6 - 3 * q^8 + 3 * q^9 + 5 * q^10 - 6 * q^11 + q^12 + 7 * q^13 - q^15 - 3 * q^16 - 10 * q^17 - q^18 + 16 * q^19 - 11 * q^20 - 2 * q^22 - 3 * q^23 - 3 * q^24 - 4 * q^25 - 5 * q^26 + 3 * q^27 - 7 * q^29 + 5 * q^30 - 2 * q^31 + 3 * q^32 - 6 * q^33 + 12 * q^34 + q^36 - 17 * q^37 - 14 * q^38 + 7 * q^39 + 7 * q^40 - 3 * q^41 - 18 * q^43 - 14 * q^44 - q^45 + 25 * q^46 - q^47 - 3 * q^48 - 12 * q^50 - 10 * q^51 + 19 * q^52 - q^53 - q^54 + 14 * q^55 + 16 * q^57 - 9 * q^58 + 8 * q^59 - 11 * q^60 - 8 * q^61 - 4 * q^62 - 11 * q^64 - 19 * q^65 - 2 * q^66 - 13 * q^67 - 2 * q^68 - 3 * q^69 - 8 * q^71 - 3 * q^72 + 6 * q^73 + q^74 - 4 * q^75 + 4 * q^76 - 5 * q^78 - 17 * q^79 + 13 * q^80 + 3 * q^81 + q^82 - 10 * q^83 + 2 * q^85 - 8 * q^86 - 7 * q^87 + 22 * q^88 - 8 * q^89 + 5 * q^90 - 3 * q^92 - 2 * q^93 + 9 * q^94 - 4 * q^95 + 3 * q^96 + q^97 - 6 * q^99

Introduction

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