LMFDB - Embedded newform 4998.2.a.cl.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4998,2,Mod(1,4998)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4998, 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("4998.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4998.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:	$39.9092309302$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.31808.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 11x^{2} + 12x + 28 $ x^4 - 2x^3 - 11x^2 + 12*x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.34975$ of defining polynomial
Character	$\chi$	$=$	4998.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.34975 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.34975 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.34975 q^{10} +3.25858 q^{11} -1.00000 q^{12} -3.34975 q^{13} +1.34975 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +2.73726 q^{19} -1.34975 q^{20} -3.25858 q^{22} +1.32305 q^{23} +1.00000 q^{24} -3.17818 q^{25} +3.34975 q^{26} -1.00000 q^{27} -1.90883 q^{29} -1.34975 q^{30} -2.09117 q^{31} -1.00000 q^{32} -3.25858 q^{33} -1.00000 q^{34} +1.00000 q^{36} +5.84437 q^{37} -2.73726 q^{38} +3.34975 q^{39} +1.34975 q^{40} -7.43676 q^{41} +6.91544 q^{43} +3.25858 q^{44} -1.34975 q^{45} -1.32305 q^{46} +11.5657 q^{47} -1.00000 q^{48} +3.17818 q^{50} -1.00000 q^{51} -3.34975 q^{52} +7.34975 q^{53} +1.00000 q^{54} -4.39827 q^{55} -2.73726 q^{57} +1.90883 q^{58} -6.15147 q^{59} +1.34975 q^{60} -3.68874 q^{61} +2.09117 q^{62} +1.00000 q^{64} +4.52132 q^{65} +3.25858 q^{66} -6.78651 q^{67} +1.00000 q^{68} -1.32305 q^{69} +2.37157 q^{71} -1.00000 q^{72} -11.0066 q^{73} -5.84437 q^{74} +3.17818 q^{75} +2.73726 q^{76} -3.34975 q^{78} +1.38751 q^{79} -1.34975 q^{80} +1.00000 q^{81} +7.43676 q^{82} -4.76396 q^{83} -1.34975 q^{85} -6.91544 q^{86} +1.90883 q^{87} -3.25858 q^{88} +4.43603 q^{89} +1.34975 q^{90} +1.32305 q^{92} +2.09117 q^{93} -11.5657 q^{94} -3.69462 q^{95} +1.00000 q^{96} +5.16742 q^{97} +3.25858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{10} - 2 q^{11} - 4 q^{12} - 6 q^{13} - 2 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - 8 q^{19} + 2 q^{20} + 2 q^{22} - 8 q^{23} + 4 q^{24} + 6 q^{25} + 6 q^{26} - 4 q^{27} + 2 q^{30} - 16 q^{31} - 4 q^{32} + 2 q^{33} - 4 q^{34} + 4 q^{36} + 14 q^{37} + 8 q^{38} + 6 q^{39} - 2 q^{40} + 4 q^{41} - 10 q^{43} - 2 q^{44} + 2 q^{45} + 8 q^{46} + 16 q^{47} - 4 q^{48} - 6 q^{50} - 4 q^{51} - 6 q^{52} + 22 q^{53} + 4 q^{54} - 10 q^{55} + 8 q^{57} - 2 q^{60} + 4 q^{61} + 16 q^{62} + 4 q^{64} + 22 q^{65} - 2 q^{66} + 14 q^{67} + 4 q^{68} + 8 q^{69} - 4 q^{71} - 4 q^{72} - 14 q^{73} - 14 q^{74} - 6 q^{75} - 8 q^{76} - 6 q^{78} - 6 q^{79} + 2 q^{80} + 4 q^{81} - 4 q^{82} - 6 q^{83} + 2 q^{85} + 10 q^{86} + 2 q^{88} + 6 q^{89} - 2 q^{90} - 8 q^{92} + 16 q^{93} - 16 q^{94} + 12 q^{95} + 4 q^{96} - 2 q^{97} - 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^10 - 2 * q^11 - 4 * q^12 - 6 * q^13 - 2 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - 8 * q^19 + 2 * q^20 + 2 * q^22 - 8 * q^23 + 4 * q^24 + 6 * q^25 + 6 * q^26 - 4 * q^27 + 2 * q^30 - 16 * q^31 - 4 * q^32 + 2 * q^33 - 4 * q^34 + 4 * q^36 + 14 * q^37 + 8 * q^38 + 6 * q^39 - 2 * q^40 + 4 * q^41 - 10 * q^43 - 2 * q^44 + 2 * q^45 + 8 * q^46 + 16 * q^47 - 4 * q^48 - 6 * q^50 - 4 * q^51 - 6 * q^52 + 22 * q^53 + 4 * q^54 - 10 * q^55 + 8 * q^57 - 2 * q^60 + 4 * q^61 + 16 * q^62 + 4 * q^64 + 22 * q^65 - 2 * q^66 + 14 * q^67 + 4 * q^68 + 8 * q^69 - 4 * q^71 - 4 * q^72 - 14 * q^73 - 14 * q^74 - 6 * q^75 - 8 * q^76 - 6 * q^78 - 6 * q^79 + 2 * q^80 + 4 * q^81 - 4 * q^82 - 6 * q^83 + 2 * q^85 + 10 * q^86 + 2 * q^88 + 6 * q^89 - 2 * q^90 - 8 * q^92 + 16 * q^93 - 16 * q^94 + 12 * q^95 + 4 * q^96 - 2 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.34975	−0.603626	−0.301813	−	0.953367i	$-0.597592\pi$
$5$	−1.34975	−0.603626	−0.301813	+	0.953367i	$0.597592\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.34975	0.426828
$11$	3.25858	0.982500	0.491250	−	0.871019i	$-0.336540\pi$
$11$	3.25858	0.982500	0.491250	+	0.871019i	$0.336540\pi$
$12$	−1.00000	−0.288675
$13$	−3.34975	−0.929053	−0.464527	−	0.885559i	$-0.653776\pi$
$13$	−3.34975	−0.929053	−0.464527	+	0.885559i	$0.653776\pi$
$14$	0	0
$15$	1.34975	0.348504
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	2.73726	0.627971	0.313985	−	0.949428i	$-0.398336\pi$
$19$	2.73726	0.627971	0.313985	+	0.949428i	$0.398336\pi$
$20$	−1.34975	−0.301813
$21$	0	0
$22$	−3.25858	−0.694732
$23$	1.32305	0.275874	0.137937	−	0.990441i	$-0.455953\pi$
$23$	1.32305	0.275874	0.137937	+	0.990441i	$0.455953\pi$
$24$	1.00000	0.204124
$25$	−3.17818	−0.635635
$26$	3.34975	0.656940
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−1.90883	−0.354462	−0.177231	−	0.984169i	$-0.556714\pi$
$29$	−1.90883	−0.354462	−0.177231	+	0.984169i	$0.556714\pi$
$30$	−1.34975	−0.246429
$31$	−2.09117	−0.375585	−0.187792	−	0.982209i	$-0.560133\pi$
$31$	−2.09117	−0.375585	−0.187792	+	0.982209i	$0.560133\pi$
$32$	−1.00000	−0.176777
$33$	−3.25858	−0.567247
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	5.84437	0.960808	0.480404	−	0.877047i	$-0.340490\pi$
$37$	5.84437	0.960808	0.480404	+	0.877047i	$0.340490\pi$
$38$	−2.73726	−0.444042
$39$	3.34975	0.536389
$40$	1.34975	0.213414
$41$	−7.43676	−1.16143	−0.580713	−	0.814108i	$-0.697226\pi$
$41$	−7.43676	−1.16143	−0.580713	+	0.814108i	$0.697226\pi$
$42$	0	0
$43$	6.91544	1.05459	0.527297	−	0.849681i	$-0.323205\pi$
$43$	6.91544	1.05459	0.527297	+	0.849681i	$0.323205\pi$
$44$	3.25858	0.491250
$45$	−1.34975	−0.201209
$46$	−1.32305	−0.195073
$47$	11.5657	1.68703	0.843515	−	0.537106i	$-0.180483\pi$
$47$	11.5657	1.68703	0.843515	+	0.537106i	$0.180483\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	3.17818	0.449462
$51$	−1.00000	−0.140028
$52$	−3.34975	−0.464527
$53$	7.34975	1.00957	0.504783	−	0.863246i	$-0.331573\pi$
$53$	7.34975	1.00957	0.504783	+	0.863246i	$0.331573\pi$
$54$	1.00000	0.136083
$55$	−4.39827	−0.593063
$56$	0	0
$57$	−2.73726	−0.362559
$58$	1.90883	0.250642
$59$	−6.15147	−0.800854	−0.400427	−	0.916329i	$-0.631138\pi$
$59$	−6.15147	−0.800854	−0.400427	+	0.916329i	$0.631138\pi$
$60$	1.34975	0.174252
$61$	−3.68874	−0.472295	−0.236147	−	0.971717i	$-0.575885\pi$
$61$	−3.68874	−0.472295	−0.236147	+	0.971717i	$0.575885\pi$
$62$	2.09117	0.265578
$63$	0	0
$64$	1.00000	0.125000
$65$	4.52132	0.560801
$66$	3.25858	0.401104
$67$	−6.78651	−0.829104	−0.414552	−	0.910026i	$-0.636062\pi$
$67$	−6.78651	−0.829104	−0.414552	+	0.910026i	$0.636062\pi$
$68$	1.00000	0.121268
$69$	−1.32305	−0.159276
$70$	0	0
$71$	2.37157	0.281453	0.140727	−	0.990048i	$-0.455056\pi$
$71$	2.37157	0.281453	0.140727	+	0.990048i	$0.455056\pi$
$72$	−1.00000	−0.117851
$73$	−11.0066	−1.28823	−0.644113	−	0.764931i	$-0.722773\pi$
$73$	−11.0066	−1.28823	−0.644113	+	0.764931i	$0.722773\pi$
$74$	−5.84437	−0.679394
$75$	3.17818	0.366984
$76$	2.73726	0.313985
$77$	0	0
$78$	−3.34975	−0.379284
$79$	1.38751	0.156107	0.0780536	−	0.996949i	$-0.475129\pi$
$79$	1.38751	0.156107	0.0780536	+	0.996949i	$0.475129\pi$
$80$	−1.34975	−0.150907
$81$	1.00000	0.111111
$82$	7.43676	0.821253
$83$	−4.76396	−0.522913	−0.261456	−	0.965215i	$-0.584203\pi$
$83$	−4.76396	−0.522913	−0.261456	+	0.965215i	$0.584203\pi$
$84$	0	0
$85$	−1.34975	−0.146401
$86$	−6.91544	−0.745711
$87$	1.90883	0.204648
$88$	−3.25858	−0.347366
$89$	4.43603	0.470219	0.235109	−	0.971969i	$-0.424455\pi$
$89$	4.43603	0.470219	0.235109	+	0.971969i	$0.424455\pi$
$90$	1.34975	0.142276
$91$	0	0
$92$	1.32305	0.137937
$93$	2.09117	0.216844
$94$	−11.5657	−1.19291
$95$	−3.69462	−0.379060
$96$	1.00000	0.102062
$97$	5.16742	0.524672	0.262336	−	0.964977i	$-0.415507\pi$
$97$	5.16742	0.524672	0.262336	+	0.964977i	$0.415507\pi$
$98$	0	0
$99$	3.25858	0.327500
$100$	−3.17818	−0.317818
$101$	−5.07107	−0.504590	−0.252295	−	0.967650i	$-0.581185\pi$
$101$	−5.07107	−0.504590	−0.252295	+	0.967650i	$0.581185\pi$
$102$	1.00000	0.0990148
$103$	−2.09635	−0.206559	−0.103280	−	0.994652i	$-0.532934\pi$
$103$	−2.09635	−0.206559	−0.103280	+	0.994652i	$0.532934\pi$
$104$	3.34975	0.328470
$105$	0	0
$106$	−7.34975	−0.713871
$107$	−0.646095	−0.0624604	−0.0312302	−	0.999512i	$-0.509942\pi$
$107$	−0.646095	−0.0624604	−0.0312302	+	0.999512i	$0.509942\pi$
$108$	−1.00000	−0.0962250
$109$	−9.42154	−0.902420	−0.451210	−	0.892418i	$-0.649008\pi$
$109$	−9.42154	−0.902420	−0.451210	+	0.892418i	$0.649008\pi$
$110$	4.39827	0.419359
$111$	−5.84437	−0.554723
$112$	0	0
$113$	−6.54387	−0.615595	−0.307798	−	0.951452i	$-0.599592\pi$
$113$	−6.54387	−0.615595	−0.307798	+	0.951452i	$0.599592\pi$
$114$	2.73726	0.256368
$115$	−1.78578	−0.166525
$116$	−1.90883	−0.177231
$117$	−3.34975	−0.309684
$118$	6.15147	0.566289
$119$	0	0
$120$	−1.34975	−0.123215
$121$	−0.381635	−0.0346941
$122$	3.68874	0.333963
$123$	7.43676	0.670550
$124$	−2.09117	−0.187792
$125$	11.0385	0.987312
$126$	0	0
$127$	4.82843	0.428454	0.214227	−	0.976784i	$-0.431277\pi$
$127$	4.82843	0.428454	0.214227	+	0.976784i	$0.431277\pi$
$128$	−1.00000	−0.0883883
$129$	−6.91544	−0.608870
$130$	−4.52132	−0.396546
$131$	21.8309	1.90737	0.953686	−	0.300803i	$-0.0972548\pi$
$131$	21.8309	1.90737	0.953686	+	0.300803i	$0.0972548\pi$
$132$	−3.25858	−0.283623
$133$	0	0
$134$	6.78651	0.586265
$135$	1.34975	0.116168
$136$	−1.00000	−0.0857493
$137$	13.7480	1.17457	0.587286	−	0.809379i	$-0.300196\pi$
$137$	13.7480	1.17457	0.587286	+	0.809379i	$0.300196\pi$
$138$	1.32305	0.112625
$139$	−10.1404	−0.860099	−0.430049	−	0.902805i	$-0.641504\pi$
$139$	−10.1404	−0.860099	−0.430049	+	0.902805i	$0.641504\pi$
$140$	0	0
$141$	−11.5657	−0.974007
$142$	−2.37157	−0.199018
$143$	−10.9154	−0.912795
$144$	1.00000	0.0833333
$145$	2.57645	0.213962
$146$	11.0066	0.910913
$147$	0	0
$148$	5.84437	0.480404
$149$	−6.87768	−0.563441	−0.281721	−	0.959496i	$-0.590905\pi$
$149$	−6.87768	−0.563441	−0.281721	+	0.959496i	$0.590905\pi$
$150$	−3.17818	−0.259497
$151$	14.6402	1.19140	0.595702	−	0.803206i	$-0.296874\pi$
$151$	14.6402	1.19140	0.595702	+	0.803206i	$0.296874\pi$
$152$	−2.73726	−0.222021
$153$	1.00000	0.0808452
$154$	0	0
$155$	2.82255	0.226713
$156$	3.34975	0.268195
$157$	−13.2167	−1.05480	−0.527402	−	0.849616i	$-0.676834\pi$
$157$	−13.2167	−1.05480	−0.527402	+	0.849616i	$0.676834\pi$
$158$	−1.38751	−0.110384
$159$	−7.34975	−0.582873
$160$	1.34975	0.106707
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	7.12447	0.558032	0.279016	−	0.960286i	$-0.409992\pi$
$163$	7.12447	0.558032	0.279016	+	0.960286i	$0.409992\pi$
$164$	−7.43676	−0.580713
$165$	4.39827	0.342405
$166$	4.76396	0.369755
$167$	11.6683	0.902923	0.451462	−	0.892291i	$-0.350903\pi$
$167$	11.6683	0.902923	0.451462	+	0.892291i	$0.350903\pi$
$168$	0	0
$169$	−1.77918	−0.136860
$170$	1.34975	0.103521
$171$	2.73726	0.209324
$172$	6.91544	0.527297
$173$	17.9917	1.36788	0.683941	−	0.729537i	$-0.260264\pi$
$173$	17.9917	1.36788	0.683941	+	0.729537i	$0.260264\pi$
$174$	−1.90883	−0.144708
$175$	0	0
$176$	3.25858	0.245625
$177$	6.15147	0.462373
$178$	−4.43603	−0.332495
$179$	21.4284	1.60164	0.800819	−	0.598907i	$-0.204398\pi$
$179$	21.4284	1.60164	0.800819	+	0.598907i	$0.204398\pi$
$180$	−1.34975	−0.100604
$181$	−9.26274	−0.688494	−0.344247	−	0.938879i	$-0.611866\pi$
$181$	−9.26274	−0.688494	−0.344247	+	0.938879i	$0.611866\pi$
$182$	0	0
$183$	3.68874	0.272679
$184$	−1.32305	−0.0975364
$185$	−7.88843	−0.579969
$186$	−2.09117	−0.153332
$187$	3.25858	0.238291
$188$	11.5657	0.843515
$189$	0	0
$190$	3.69462	0.268036
$191$	−5.07625	−0.367305	−0.183652	−	0.982991i	$-0.558792\pi$
$191$	−5.07625	−0.367305	−0.183652	+	0.982991i	$0.558792\pi$
$192$	−1.00000	−0.0721688
$193$	13.3834	0.963355	0.481678	−	0.876349i	$-0.340028\pi$
$193$	13.3834	0.963355	0.481678	+	0.876349i	$0.340028\pi$
$194$	−5.16742	−0.370999
$195$	−4.52132	−0.323779
$196$	0	0
$197$	−3.25443	−0.231868	−0.115934	−	0.993257i	$-0.536986\pi$
$197$	−3.25443	−0.231868	−0.115934	+	0.993257i	$0.536986\pi$
$198$	−3.25858	−0.231577
$199$	−15.3834	−1.09050	−0.545249	−	0.838274i	$-0.683565\pi$
$199$	−15.3834	−1.09050	−0.545249	+	0.838274i	$0.683565\pi$
$200$	3.17818	0.224731
$201$	6.78651	0.478683
$202$	5.07107	0.356799
$203$	0	0
$204$	−1.00000	−0.0700140
$205$	10.0378	0.701068
$206$	2.09635	0.146060
$207$	1.32305	0.0919582
$208$	−3.34975	−0.232263
$209$	8.91959	0.616981
$210$	0	0
$211$	−20.1588	−1.38779	−0.693895	−	0.720077i	$-0.744107\pi$
$211$	−20.1588	−1.38779	−0.693895	+	0.720077i	$0.744107\pi$
$212$	7.34975	0.504783
$213$	−2.37157	−0.162497
$214$	0.646095	0.0441661
$215$	−9.33411	−0.636581
$216$	1.00000	0.0680414
$217$	0	0
$218$	9.42154	0.638107
$219$	11.0066	0.743757
$220$	−4.39827	−0.296531
$221$	−3.34975	−0.225329
$222$	5.84437	0.392248
$223$	−13.3986	−0.897235	−0.448617	−	0.893724i	$-0.648083\pi$
$223$	−13.3986	−0.897235	−0.448617	+	0.893724i	$0.648083\pi$
$224$	0	0
$225$	−3.17818	−0.211878
$226$	6.54387	0.435292
$227$	15.0559	0.999292	0.499646	−	0.866230i	$-0.333463\pi$
$227$	15.0559	0.999292	0.499646	+	0.866230i	$0.333463\pi$
$228$	−2.73726	−0.181280
$229$	−11.2429	−0.742955	−0.371477	−	0.928442i	$-0.621149\pi$
$229$	−11.2429	−0.742955	−0.371477	+	0.928442i	$0.621149\pi$
$230$	1.78578	0.117751
$231$	0	0
$232$	1.90883	0.125321
$233$	24.9321	1.63336	0.816678	−	0.577093i	$-0.195813\pi$
$233$	24.9321	1.63336	0.816678	+	0.577093i	$0.195813\pi$
$234$	3.34975	0.218980
$235$	−15.6108	−1.01834
$236$	−6.15147	−0.400427
$237$	−1.38751	−0.0901286
$238$	0	0
$239$	−2.83991	−0.183699	−0.0918494	−	0.995773i	$-0.529278\pi$
$239$	−2.83991	−0.183699	−0.0918494	+	0.995773i	$0.529278\pi$
$240$	1.34975	0.0871259
$241$	−12.7750	−0.822912	−0.411456	−	0.911430i	$-0.634980\pi$
$241$	−12.7750	−0.822912	−0.411456	+	0.911430i	$0.634980\pi$
$242$	0.381635	0.0245324
$243$	−1.00000	−0.0641500
$244$	−3.68874	−0.236147
$245$	0	0
$246$	−7.43676	−0.474150
$247$	−9.16914	−0.583418
$248$	2.09117	0.132789
$249$	4.76396	0.301904
$250$	−11.0385	−0.698135
$251$	−6.05615	−0.382261	−0.191130	−	0.981565i	$-0.561215\pi$
$251$	−6.05615	−0.382261	−0.191130	+	0.981565i	$0.561215\pi$
$252$	0	0
$253$	4.31126	0.271047
$254$	−4.82843	−0.302962
$255$	1.34975	0.0845246
$256$	1.00000	0.0625000
$257$	22.3307	1.39295	0.696475	−	0.717581i	$-0.254751\pi$
$257$	22.3307	1.39295	0.696475	+	0.717581i	$0.254751\pi$
$258$	6.91544	0.430536
$259$	0	0
$260$	4.52132	0.280401
$261$	−1.90883	−0.118154
$262$	−21.8309	−1.34872
$263$	3.98851	0.245942	0.122971	−	0.992410i	$-0.460758\pi$
$263$	3.98851	0.245942	0.122971	+	0.992410i	$0.460758\pi$
$264$	3.25858	0.200552
$265$	−9.92032	−0.609400
$266$	0	0
$267$	−4.43603	−0.271481
$268$	−6.78651	−0.414552
$269$	26.7231	1.62933	0.814667	−	0.579929i	$-0.196920\pi$
$269$	26.7231	1.62933	0.814667	+	0.579929i	$0.196920\pi$
$270$	−1.34975	−0.0821431
$271$	20.4125	1.23997	0.619986	−	0.784613i	$-0.287138\pi$
$271$	20.4125	1.23997	0.619986	+	0.784613i	$0.287138\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	−13.7480	−0.830548
$275$	−10.3564	−0.624512
$276$	−1.32305	−0.0796381
$277$	18.4108	1.10620	0.553098	−	0.833116i	$-0.313445\pi$
$277$	18.4108	1.10620	0.553098	+	0.833116i	$0.313445\pi$
$278$	10.1404	0.608182
$279$	−2.09117	−0.125195
$280$	0	0
$281$	15.7019	0.936700	0.468350	−	0.883543i	$-0.344849\pi$
$281$	15.7019	0.936700	0.468350	+	0.883543i	$0.344849\pi$
$282$	11.5657	0.688727
$283$	5.43260	0.322935	0.161467	−	0.986878i	$-0.448377\pi$
$283$	5.43260	0.322935	0.161467	+	0.986878i	$0.448377\pi$
$284$	2.37157	0.140727
$285$	3.69462	0.218850
$286$	10.9154	0.645443
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−2.57645	−0.151294
$291$	−5.16742	−0.302919
$292$	−11.0066	−0.644113
$293$	16.2049	0.946699	0.473350	−	0.880875i	$-0.343045\pi$
$293$	16.2049	0.946699	0.473350	+	0.880875i	$0.343045\pi$
$294$	0	0
$295$	8.30295	0.483416
$296$	−5.84437	−0.339697
$297$	−3.25858	−0.189082
$298$	6.87768	0.398413
$299$	−4.43188	−0.256302
$300$	3.17818	0.183492
$301$	0	0
$302$	−14.6402	−0.842450
$303$	5.07107	0.291325
$304$	2.73726	0.156993
$305$	4.97887	0.285089
$306$	−1.00000	−0.0571662
$307$	23.0877	1.31769	0.658843	−	0.752280i	$-0.271046\pi$
$307$	23.0877	1.31769	0.658843	+	0.752280i	$0.271046\pi$
$308$	0	0
$309$	2.09635	0.119257
$310$	−2.82255	−0.160310
$311$	9.44092	0.535345	0.267673	−	0.963510i	$-0.413745\pi$
$311$	9.44092	0.535345	0.267673	+	0.963510i	$0.413745\pi$
$312$	−3.34975	−0.189642
$313$	9.44264	0.533729	0.266865	−	0.963734i	$-0.414012\pi$
$313$	9.44264	0.533729	0.266865	+	0.963734i	$0.414012\pi$
$314$	13.2167	0.745860
$315$	0	0
$316$	1.38751	0.0780536
$317$	−6.01321	−0.337735	−0.168868	−	0.985639i	$-0.554011\pi$
$317$	−6.01321	−0.337735	−0.168868	+	0.985639i	$0.554011\pi$
$318$	7.34975	0.412153
$319$	−6.22009	−0.348258
$320$	−1.34975	−0.0754533
$321$	0.646095	0.0360615
$322$	0	0
$323$	2.73726	0.152305
$324$	1.00000	0.0555556
$325$	10.6461	0.590539
$326$	−7.12447	−0.394588
$327$	9.42154	0.521013
$328$	7.43676	0.410626
$329$	0	0
$330$	−4.39827	−0.242117
$331$	5.19481	0.285533	0.142766	−	0.989756i	$-0.454400\pi$
$331$	5.19481	0.285533	0.142766	+	0.989756i	$0.454400\pi$
$332$	−4.76396	−0.261456
$333$	5.84437	0.320269
$334$	−11.6683	−0.638463
$335$	9.16009	0.500469
$336$	0	0
$337$	12.3431	0.672374	0.336187	−	0.941795i	$-0.390863\pi$
$337$	12.3431	0.672374	0.336187	+	0.941795i	$0.390863\pi$
$338$	1.77918	0.0967746
$339$	6.54387	0.355414
$340$	−1.34975	−0.0732004
$341$	−6.81424	−0.369012
$342$	−2.73726	−0.148014
$343$	0	0
$344$	−6.91544	−0.372855
$345$	1.78578	0.0961433
$346$	−17.9917	−0.967239
$347$	−0.582057	−0.0312464	−0.0156232	−	0.999878i	$-0.504973\pi$
$347$	−0.582057	−0.0312464	−0.0156232	+	0.999878i	$0.504973\pi$
$348$	1.90883	0.102324
$349$	4.01736	0.215045	0.107522	−	0.994203i	$-0.465708\pi$
$349$	4.01736	0.215045	0.107522	+	0.994203i	$0.465708\pi$
$350$	0	0
$351$	3.34975	0.178796
$352$	−3.25858	−0.173683
$353$	−5.44825	−0.289981	−0.144990	−	0.989433i	$-0.546315\pi$
$353$	−5.44825	−0.289981	−0.144990	+	0.989433i	$0.546315\pi$
$354$	−6.15147	−0.326947
$355$	−3.20102	−0.169893
$356$	4.43603	0.235109
$357$	0	0
$358$	−21.4284	−1.13253
$359$	3.81767	0.201489	0.100744	−	0.994912i	$-0.467878\pi$
$359$	3.81767	0.201489	0.100744	+	0.994912i	$0.467878\pi$
$360$	1.34975	0.0711380
$361$	−11.5074	−0.605653
$362$	9.26274	0.486839
$363$	0.381635	0.0200306
$364$	0	0
$365$	14.8562	0.777607
$366$	−3.68874	−0.192814
$367$	5.91471	0.308745	0.154373	−	0.988013i	$-0.450664\pi$
$367$	5.91471	0.308745	0.154373	+	0.988013i	$0.450664\pi$
$368$	1.32305	0.0689686
$369$	−7.43676	−0.387142
$370$	7.88843	0.410100
$371$	0	0
$372$	2.09117	0.108422
$373$	35.5893	1.84274	0.921371	−	0.388684i	$-0.127070\pi$
$373$	35.5893	1.84274	0.921371	+	0.388684i	$0.127070\pi$
$374$	−3.25858	−0.168497
$375$	−11.0385	−0.570025
$376$	−11.5657	−0.596455
$377$	6.39412	0.329314
$378$	0	0
$379$	33.5578	1.72375	0.861874	−	0.507122i	$-0.169291\pi$
$379$	33.5578	1.72375	0.861874	+	0.507122i	$0.169291\pi$
$380$	−3.69462	−0.189530
$381$	−4.82843	−0.247368
$382$	5.07625	0.259724
$383$	−6.13626	−0.313548	−0.156774	−	0.987634i	$-0.550109\pi$
$383$	−6.13626	−0.313548	−0.156774	+	0.987634i	$0.550109\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−13.3834	−0.681195
$387$	6.91544	0.351531
$388$	5.16742	0.262336
$389$	12.6676	0.642274	0.321137	−	0.947033i	$-0.395935\pi$
$389$	12.6676	0.642274	0.321137	+	0.947033i	$0.395935\pi$
$390$	4.52132	0.228946
$391$	1.32305	0.0669094
$392$	0	0
$393$	−21.8309	−1.10122
$394$	3.25443	0.163956
$395$	−1.87279	−0.0942304
$396$	3.25858	0.163750
$397$	8.98924	0.451157	0.225579	−	0.974225i	$-0.427573\pi$
$397$	8.98924	0.451157	0.225579	+	0.974225i	$0.427573\pi$
$398$	15.3834	0.771098
$399$	0	0
$400$	−3.17818	−0.158909
$401$	13.2378	0.661062	0.330531	−	0.943795i	$-0.392772\pi$
$401$	13.2378	0.661062	0.330531	+	0.943795i	$0.392772\pi$
$402$	−6.78651	−0.338480
$403$	7.00488	0.348938
$404$	−5.07107	−0.252295
$405$	−1.34975	−0.0670696
$406$	0	0
$407$	19.0444	0.943994
$408$	1.00000	0.0495074
$409$	11.9397	0.590380	0.295190	−	0.955439i	$-0.404617\pi$
$409$	11.9397	0.590380	0.295190	+	0.955439i	$0.404617\pi$
$410$	−10.0378	−0.495730
$411$	−13.7480	−0.678140
$412$	−2.09635	−0.103280
$413$	0	0
$414$	−1.32305	−0.0650242
$415$	6.43016	0.315644
$416$	3.34975	0.164235
$417$	10.1404	0.496578
$418$	−8.91959	−0.436272
$419$	−2.95148	−0.144189	−0.0720946	−	0.997398i	$-0.522968\pi$
$419$	−2.95148	−0.144189	−0.0720946	+	0.997398i	$0.522968\pi$
$420$	0	0
$421$	15.7612	0.768155	0.384078	−	0.923301i	$-0.374520\pi$
$421$	15.7612	0.768155	0.384078	+	0.923301i	$0.374520\pi$
$422$	20.1588	0.981315
$423$	11.5657	0.562343
$424$	−7.34975	−0.356935
$425$	−3.17818	−0.154164
$426$	2.37157	0.114903
$427$	0	0
$428$	−0.646095	−0.0312302
$429$	10.9154	0.527002
$430$	9.33411	0.450131
$431$	−10.7383	−0.517245	−0.258623	−	0.965978i	$-0.583269\pi$
$431$	−10.7383	−0.517245	−0.258623	+	0.965978i	$0.583269\pi$
$432$	−1.00000	−0.0481125
$433$	−20.5235	−0.986295	−0.493147	−	0.869946i	$-0.664154\pi$
$433$	−20.5235	−0.986295	−0.493147	+	0.869946i	$0.664154\pi$
$434$	0	0
$435$	−2.57645	−0.123531
$436$	−9.42154	−0.451210
$437$	3.62153	0.173241
$438$	−11.0066	−0.525916
$439$	23.9324	1.14223	0.571116	−	0.820870i	$-0.306511\pi$
$439$	23.9324	1.14223	0.571116	+	0.820870i	$0.306511\pi$
$440$	4.39827	0.209679
$441$	0	0
$442$	3.34975	0.159331
$443$	−28.7637	−1.36660	−0.683302	−	0.730136i	$-0.739457\pi$
$443$	−28.7637	−1.36660	−0.683302	+	0.730136i	$0.739457\pi$
$444$	−5.84437	−0.277362
$445$	−5.98753	−0.283836
$446$	13.3986	0.634441
$447$	6.87768	0.325303
$448$	0	0
$449$	−27.2032	−1.28380	−0.641899	−	0.766790i	$-0.721853\pi$
$449$	−27.2032	−1.28380	−0.641899	+	0.766790i	$0.721853\pi$
$450$	3.17818	0.149821
$451$	−24.2333	−1.14110
$452$	−6.54387	−0.307798
$453$	−14.6402	−0.687857
$454$	−15.0559	−0.706606
$455$	0	0
$456$	2.73726	0.128184
$457$	31.4919	1.47313	0.736564	−	0.676368i	$-0.236447\pi$
$457$	31.4919	1.47313	0.736564	+	0.676368i	$0.236447\pi$
$458$	11.2429	0.525348
$459$	−1.00000	−0.0466760
$460$	−1.78578	−0.0832625
$461$	−19.8319	−0.923664	−0.461832	−	0.886967i	$-0.652808\pi$
$461$	−19.8319	−0.923664	−0.461832	+	0.886967i	$0.652808\pi$
$462$	0	0
$463$	−16.7446	−0.778187	−0.389094	−	0.921198i	$-0.627212\pi$
$463$	−16.7446	−0.778187	−0.389094	+	0.921198i	$0.627212\pi$
$464$	−1.90883	−0.0886154
$465$	−2.82255	−0.130893
$466$	−24.9321	−1.15496
$467$	−11.8187	−0.546904	−0.273452	−	0.961886i	$-0.588165\pi$
$467$	−11.8187	−0.546904	−0.273452	+	0.961886i	$0.588165\pi$
$468$	−3.34975	−0.154842
$469$	0	0
$470$	15.6108	0.720072
$471$	13.2167	0.608992
$472$	6.15147	0.283145
$473$	22.5345	1.03614
$474$	1.38751	0.0637305
$475$	−8.69950	−0.399160
$476$	0	0
$477$	7.34975	0.336522
$478$	2.83991	0.129895
$479$	−19.1934	−0.876970	−0.438485	−	0.898739i	$-0.644485\pi$
$479$	−19.1934	−0.876970	−0.438485	+	0.898739i	$0.644485\pi$
$480$	−1.34975	−0.0616073
$481$	−19.5772	−0.892642
$482$	12.7750	0.581886
$483$	0	0
$484$	−0.381635	−0.0173470
$485$	−6.97472	−0.316706
$486$	1.00000	0.0453609
$487$	25.0458	1.13493	0.567467	−	0.823396i	$-0.307923\pi$
$487$	25.0458	1.13493	0.567467	+	0.823396i	$0.307923\pi$
$488$	3.68874	0.166981
$489$	−7.12447	−0.322180
$490$	0	0
$491$	9.52060	0.429658	0.214829	−	0.976652i	$-0.431081\pi$
$491$	9.52060	0.429658	0.214829	+	0.976652i	$0.431081\pi$
$492$	7.43676	0.335275
$493$	−1.90883	−0.0859696
$494$	9.16914	0.412539
$495$	−4.39827	−0.197688
$496$	−2.09117	−0.0938961
$497$	0	0
$498$	−4.76396	−0.213478
$499$	−31.3740	−1.40449	−0.702247	−	0.711933i	$-0.747820\pi$
$499$	−31.3740	−1.40449	−0.702247	+	0.711933i	$0.747820\pi$
$500$	11.0385	0.493656
$501$	−11.6683	−0.521303
$502$	6.05615	0.270299
$503$	13.1417	0.585961	0.292981	−	0.956118i	$-0.405353\pi$
$503$	13.1417	0.585961	0.292981	+	0.956118i	$0.405353\pi$
$504$	0	0
$505$	6.84467	0.304584
$506$	−4.31126	−0.191659
$507$	1.77918	0.0790161
$508$	4.82843	0.214227
$509$	32.8745	1.45714	0.728569	−	0.684972i	$-0.240186\pi$
$509$	32.8745	1.45714	0.728569	+	0.684972i	$0.240186\pi$
$510$	−1.34975	−0.0597679
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−2.73726	−0.120853
$514$	−22.3307	−0.984964
$515$	2.82955	0.124685
$516$	−6.91544	−0.304435
$517$	37.6878	1.65751
$518$	0	0
$519$	−17.9917	−0.789747
$520$	−4.52132	−0.198273
$521$	8.47109	0.371125	0.185563	−	0.982632i	$-0.440589\pi$
$521$	8.47109	0.371125	0.185563	+	0.982632i	$0.440589\pi$
$522$	1.90883	0.0835474
$523$	4.65441	0.203523	0.101761	−	0.994809i	$-0.467552\pi$
$523$	4.65441	0.203523	0.101761	+	0.994809i	$0.467552\pi$
$524$	21.8309	0.953686
$525$	0	0
$526$	−3.98851	−0.173907
$527$	−2.09117	−0.0910926
$528$	−3.25858	−0.141812
$529$	−21.2495	−0.923893
$530$	9.92032	0.430911
$531$	−6.15147	−0.266951
$532$	0	0
$533$	24.9113	1.07903
$534$	4.43603	0.191966
$535$	0.872066	0.0377027
$536$	6.78651	0.293133
$537$	−21.4284	−0.924706
$538$	−26.7231	−1.15211
$539$	0	0
$540$	1.34975	0.0580840
$541$	35.9865	1.54718	0.773590	−	0.633686i	$-0.218459\pi$
$541$	35.9865	1.54718	0.773590	+	0.633686i	$0.218459\pi$
$542$	−20.4125	−0.876792
$543$	9.26274	0.397502
$544$	−1.00000	−0.0428746
$545$	12.7167	0.544725
$546$	0	0
$547$	34.0039	1.45390	0.726950	−	0.686690i	$-0.240937\pi$
$547$	34.0039	1.45390	0.726950	+	0.686690i	$0.240937\pi$
$548$	13.7480	0.587286
$549$	−3.68874	−0.157432
$550$	10.3564	0.441596
$551$	−5.22498	−0.222591
$552$	1.32305	0.0563126
$553$	0	0
$554$	−18.4108	−0.782199
$555$	7.88843	0.334845
$556$	−10.1404	−0.430049
$557$	1.38579	0.0587178	0.0293589	−	0.999569i	$-0.490653\pi$
$557$	1.38579	0.0587178	0.0293589	+	0.999569i	$0.490653\pi$
$558$	2.09117	0.0885261
$559$	−23.1650	−0.979774
$560$	0	0
$561$	−3.25858	−0.137577
$562$	−15.7019	−0.662347
$563$	24.5630	1.03521	0.517603	−	0.855621i	$-0.326825\pi$
$563$	24.5630	1.03521	0.517603	+	0.855621i	$0.326825\pi$
$564$	−11.5657	−0.487003
$565$	8.83258	0.371590
$566$	−5.43260	−0.228349
$567$	0	0
$568$	−2.37157	−0.0995088
$569$	0.967722	0.0405690	0.0202845	−	0.999794i	$-0.493543\pi$
$569$	0.967722	0.0405690	0.0202845	+	0.999794i	$0.493543\pi$
$570$	−3.69462	−0.154750
$571$	−24.8798	−1.04119	−0.520594	−	0.853804i	$-0.674289\pi$
$571$	−24.8798	−1.04119	−0.520594	+	0.853804i	$0.674289\pi$
$572$	−10.9154	−0.456397
$573$	5.07625	0.212063
$574$	0	0
$575$	−4.20488	−0.175356
$576$	1.00000	0.0416667
$577$	−11.1303	−0.463362	−0.231681	−	0.972792i	$-0.574423\pi$
$577$	−11.1303	−0.463362	−0.231681	+	0.972792i	$0.574423\pi$
$578$	−1.00000	−0.0415945
$579$	−13.3834	−0.556193
$580$	2.57645	0.106981
$581$	0	0
$582$	5.16742	0.214196
$583$	23.9498	0.991898
$584$	11.0066	0.455457
$585$	4.52132	0.186934
$586$	−16.2049	−0.669417
$587$	5.50366	0.227160	0.113580	−	0.993529i	$-0.463768\pi$
$587$	5.50366	0.227160	0.113580	+	0.993529i	$0.463768\pi$
$588$	0	0
$589$	−5.72407	−0.235856
$590$	−8.30295	−0.341827
$591$	3.25443	0.133869
$592$	5.84437	0.240202
$593$	14.6593	0.601985	0.300993	−	0.953626i	$-0.402682\pi$
$593$	14.6593	0.601985	0.300993	+	0.953626i	$0.402682\pi$
$594$	3.25858	0.133701
$595$	0	0
$596$	−6.87768	−0.281721
$597$	15.3834	0.629599
$598$	4.43188	0.181233
$599$	46.9858	1.91979	0.959894	−	0.280362i	$-0.0904544\pi$
$599$	46.9858	1.91979	0.959894	+	0.280362i	$0.0904544\pi$
$600$	−3.17818	−0.129749
$601$	−16.7980	−0.685205	−0.342602	−	0.939481i	$-0.611308\pi$
$601$	−16.7980	−0.685205	−0.342602	+	0.939481i	$0.611308\pi$
$602$	0	0
$603$	−6.78651	−0.276368
$604$	14.6402	0.595702
$605$	0.515111	0.0209422
$606$	−5.07107	−0.205998
$607$	−11.0617	−0.448982	−0.224491	−	0.974476i	$-0.572072\pi$
$607$	−11.0617	−0.448982	−0.224491	+	0.974476i	$0.572072\pi$
$608$	−2.73726	−0.111011
$609$	0	0
$610$	−4.97887	−0.201589
$611$	−38.7422	−1.56734
$612$	1.00000	0.0404226
$613$	38.9334	1.57251	0.786253	−	0.617905i	$-0.212018\pi$
$613$	38.9334	1.57251	0.786253	+	0.617905i	$0.212018\pi$
$614$	−23.0877	−0.931745
$615$	−10.0378	−0.404762
$616$	0	0
$617$	0.704682	0.0283694	0.0141847	−	0.999899i	$-0.495485\pi$
$617$	0.704682	0.0283694	0.0141847	+	0.999899i	$0.495485\pi$
$618$	−2.09635	−0.0843275
$619$	33.1880	1.33394	0.666968	−	0.745086i	$-0.267592\pi$
$619$	33.1880	1.33394	0.666968	+	0.745086i	$0.267592\pi$
$620$	2.82255	0.113356
$621$	−1.32305	−0.0530921
$622$	−9.44092	−0.378546
$623$	0	0
$624$	3.34975	0.134097
$625$	0.991689	0.0396675
$626$	−9.44264	−0.377404
$627$	−8.91959	−0.356214
$628$	−13.2167	−0.527402
$629$	5.84437	0.233030
$630$	0	0
$631$	−1.64952	−0.0656665	−0.0328333	−	0.999461i	$-0.510453\pi$
$631$	−1.64952	−0.0656665	−0.0328333	+	0.999461i	$0.510453\pi$
$632$	−1.38751	−0.0551922
$633$	20.1588	0.801241
$634$	6.01321	0.238815
$635$	−6.51717	−0.258626
$636$	−7.34975	−0.291437
$637$	0	0
$638$	6.22009	0.246256
$639$	2.37157	0.0938178
$640$	1.34975	0.0533535
$641$	15.8561	0.626279	0.313140	−	0.949707i	$-0.398619\pi$
$641$	15.8561	0.626279	0.313140	+	0.949707i	$0.398619\pi$
$642$	−0.646095	−0.0254993
$643$	−39.0596	−1.54036	−0.770181	−	0.637826i	$-0.779834\pi$
$643$	−39.0596	−1.54036	−0.770181	+	0.637826i	$0.779834\pi$
$644$	0	0
$645$	9.33411	0.367530
$646$	−2.73726	−0.107696
$647$	10.8343	0.425940	0.212970	−	0.977059i	$-0.431686\pi$
$647$	10.8343	0.425940	0.212970	+	0.977059i	$0.431686\pi$
$648$	−1.00000	−0.0392837
$649$	−20.0451	−0.786839
$650$	−10.6461	−0.417574
$651$	0	0
$652$	7.12447	0.279016
$653$	−32.4465	−1.26973	−0.634866	−	0.772623i	$-0.718945\pi$
$653$	−32.4465	−1.26973	−0.634866	+	0.772623i	$0.718945\pi$
$654$	−9.42154	−0.368412
$655$	−29.4662	−1.15134
$656$	−7.43676	−0.290357
$657$	−11.0066	−0.429409
$658$	0	0
$659$	27.3269	1.06451	0.532253	−	0.846585i	$-0.321346\pi$
$659$	27.3269	1.06451	0.532253	+	0.846585i	$0.321346\pi$
$660$	4.39827	0.171202
$661$	23.5294	0.915187	0.457593	−	0.889162i	$-0.348712\pi$
$661$	23.5294	0.915187	0.457593	+	0.889162i	$0.348712\pi$
$662$	−5.19481	−0.201902
$663$	3.34975	0.130093
$664$	4.76396	0.184878
$665$	0	0
$666$	−5.84437	−0.226465
$667$	−2.52548	−0.0977869
$668$	11.6683	0.451462
$669$	13.3986	0.518019
$670$	−9.16009	−0.353885
$671$	−12.0201	−0.464029
$672$	0	0
$673$	12.3824	0.477305	0.238652	−	0.971105i	$-0.423294\pi$
$673$	12.3824	0.477305	0.238652	+	0.971105i	$0.423294\pi$
$674$	−12.3431	−0.475440
$675$	3.17818	0.122328
$676$	−1.77918	−0.0684300
$677$	9.98264	0.383664	0.191832	−	0.981428i	$-0.438557\pi$
$677$	9.98264	0.383664	0.191832	+	0.981428i	$0.438557\pi$
$678$	−6.54387	−0.251316
$679$	0	0
$680$	1.34975	0.0517605
$681$	−15.0559	−0.576941
$682$	6.81424	0.260931
$683$	6.02212	0.230430	0.115215	−	0.993341i	$-0.463244\pi$
$683$	6.02212	0.230430	0.115215	+	0.993341i	$0.463244\pi$
$684$	2.73726	0.104662
$685$	−18.5564	−0.709003
$686$	0	0
$687$	11.2429	0.428945
$688$	6.91544	0.263649
$689$	−24.6198	−0.937940
$690$	−1.78578	−0.0679836
$691$	−13.6232	−0.518253	−0.259126	−	0.965843i	$-0.583435\pi$
$691$	−13.6232	−0.518253	−0.259126	+	0.965843i	$0.583435\pi$
$692$	17.9917	0.683941
$693$	0	0
$694$	0.582057	0.0220946
$695$	13.6870	0.519178
$696$	−1.90883	−0.0723542
$697$	−7.43676	−0.281687
$698$	−4.01736	−0.152059
$699$	−24.9321	−0.943019
$700$	0	0
$701$	−5.84394	−0.220723	−0.110361	−	0.993892i	$-0.535201\pi$
$701$	−5.84394	−0.220723	−0.110361	+	0.993892i	$0.535201\pi$
$702$	−3.34975	−0.126428
$703$	15.9976	0.603360
$704$	3.25858	0.122812
$705$	15.6108	0.587936
$706$	5.44825	0.205047
$707$	0	0
$708$	6.15147	0.231187
$709$	24.5786	0.923068	0.461534	−	0.887122i	$-0.347299\pi$
$709$	24.5786	0.923068	0.461534	+	0.887122i	$0.347299\pi$
$710$	3.20102	0.120132
$711$	1.38751	0.0520358
$712$	−4.43603	−0.166247
$713$	−2.76671	−0.103614
$714$	0	0
$715$	14.7331	0.550987
$716$	21.4284	0.800819
$717$	2.83991	0.106058
$718$	−3.81767	−0.142474
$719$	0.958809	0.0357575	0.0178788	−	0.999840i	$-0.494309\pi$
$719$	0.958809	0.0357575	0.0178788	+	0.999840i	$0.494309\pi$
$720$	−1.34975	−0.0503022
$721$	0	0
$722$	11.5074	0.428261
$723$	12.7750	0.475108
$724$	−9.26274	−0.344247
$725$	6.06661	0.225308
$726$	−0.381635	−0.0141638
$727$	0.171272	0.00635212	0.00317606	−	0.999995i	$-0.498989\pi$
$727$	0.171272	0.00635212	0.00317606	+	0.999995i	$0.498989\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−14.8562	−0.549851
$731$	6.91544	0.255777
$732$	3.68874	0.136340
$733$	9.13283	0.337329	0.168664	−	0.985674i	$-0.446055\pi$
$733$	9.13283	0.337329	0.168664	+	0.985674i	$0.446055\pi$
$734$	−5.91471	−0.218316
$735$	0	0
$736$	−1.32305	−0.0487682
$737$	−22.1144	−0.814595
$738$	7.43676	0.273751
$739$	−33.8877	−1.24658	−0.623290	−	0.781991i	$-0.714204\pi$
$739$	−33.8877	−1.24658	−0.623290	+	0.781991i	$0.714204\pi$
$740$	−7.88843	−0.289985
$741$	9.16914	0.336837
$742$	0	0
$743$	−31.8015	−1.16668	−0.583341	−	0.812227i	$-0.698255\pi$
$743$	−31.8015	−1.16668	−0.583341	+	0.812227i	$0.698255\pi$
$744$	−2.09117	−0.0766659
$745$	9.28314	0.340108
$746$	−35.5893	−1.30302
$747$	−4.76396	−0.174304
$748$	3.25858	0.119146
$749$	0	0
$750$	11.0385	0.403069
$751$	−21.8843	−0.798569	−0.399284	−	0.916827i	$-0.630741\pi$
$751$	−21.8843	−0.798569	−0.399284	+	0.916827i	$0.630741\pi$
$752$	11.5657	0.421757
$753$	6.05615	0.220698
$754$	−6.39412	−0.232860
$755$	−19.7606	−0.719163
$756$	0	0
$757$	34.2146	1.24355	0.621776	−	0.783195i	$-0.286411\pi$
$757$	34.2146	1.24355	0.621776	+	0.783195i	$0.286411\pi$
$758$	−33.5578	−1.21887
$759$	−4.31126	−0.156489
$760$	3.69462	0.134018
$761$	38.8243	1.40738	0.703689	−	0.710508i	$-0.251535\pi$
$761$	38.8243	1.40738	0.703689	+	0.710508i	$0.251535\pi$
$762$	4.82843	0.174915
$763$	0	0
$764$	−5.07625	−0.183652
$765$	−1.34975	−0.0488003
$766$	6.13626	0.221712
$767$	20.6059	0.744036
$768$	−1.00000	−0.0360844
$769$	−28.2877	−1.02008	−0.510041	−	0.860150i	$-0.670370\pi$
$769$	−28.2877	−1.02008	−0.510041	+	0.860150i	$0.670370\pi$
$770$	0	0
$771$	−22.3307	−0.804220
$772$	13.3834	0.481678
$773$	−2.09317	−0.0752863	−0.0376431	−	0.999291i	$-0.511985\pi$
$773$	−2.09317	−0.0752863	−0.0376431	+	0.999291i	$0.511985\pi$
$774$	−6.91544	−0.248570
$775$	6.64609	0.238735
$776$	−5.16742	−0.185499
$777$	0	0
$778$	−12.6676	−0.454156
$779$	−20.3564	−0.729342
$780$	−4.52132	−0.161889
$781$	7.72796	0.276528
$782$	−1.32305	−0.0473121
$783$	1.90883	0.0682162
$784$	0	0
$785$	17.8392	0.636708
$786$	21.8309	0.778682
$787$	39.8007	1.41874	0.709371	−	0.704835i	$-0.248979\pi$
$787$	39.8007	1.41874	0.709371	+	0.704835i	$0.248979\pi$
$788$	−3.25443	−0.115934
$789$	−3.98851	−0.141995
$790$	1.87279	0.0666310
$791$	0	0
$792$	−3.25858	−0.115789
$793$	12.3564	0.438787
$794$	−8.98924	−0.319016
$795$	9.92032	0.351837
$796$	−15.3834	−0.545249
$797$	48.1779	1.70655	0.853274	−	0.521463i	$-0.174613\pi$
$797$	48.1779	1.70655	0.853274	+	0.521463i	$0.174613\pi$
$798$	0	0
$799$	11.5657	0.409165
$800$	3.17818	0.112366
$801$	4.43603	0.156740
$802$	−13.2378	−0.467441
$803$	−35.8659	−1.26568
$804$	6.78651	0.239342
$805$	0	0
$806$	−7.00488	−0.246736
$807$	−26.7231	−0.940697
$808$	5.07107	0.178400
$809$	−9.92405	−0.348911	−0.174456	−	0.984665i	$-0.555817\pi$
$809$	−9.92405	−0.348911	−0.174456	+	0.984665i	$0.555817\pi$
$810$	1.34975	0.0474254
$811$	31.0188	1.08922	0.544609	−	0.838690i	$-0.316678\pi$
$811$	31.0188	1.08922	0.544609	+	0.838690i	$0.316678\pi$
$812$	0	0
$813$	−20.4125	−0.715898
$814$	−19.0444	−0.667505
$815$	−9.61625	−0.336843
$816$	−1.00000	−0.0350070
$817$	18.9294	0.662254
$818$	−11.9397	−0.417462
$819$	0	0
$820$	10.0378	0.350534
$821$	−39.6225	−1.38284	−0.691418	−	0.722455i	$-0.743014\pi$
$821$	−39.6225	−1.38284	−0.691418	+	0.722455i	$0.743014\pi$
$822$	13.7480	0.479517
$823$	15.9698	0.556673	0.278337	−	0.960484i	$-0.410217\pi$
$823$	15.9698	0.556673	0.278337	+	0.960484i	$0.410217\pi$
$824$	2.09635	0.0730298
$825$	10.3564	0.360562
$826$	0	0
$827$	6.75462	0.234881	0.117441	−	0.993080i	$-0.462531\pi$
$827$	6.75462	0.234881	0.117441	+	0.993080i	$0.462531\pi$
$828$	1.32305	0.0459791
$829$	35.1404	1.22048	0.610239	−	0.792218i	$-0.291074\pi$
$829$	35.1404	1.22048	0.610239	+	0.792218i	$0.291074\pi$
$830$	−6.43016	−0.223194
$831$	−18.4108	−0.638663
$832$	−3.34975	−0.116132
$833$	0	0
$834$	−10.1404	−0.351134
$835$	−15.7493	−0.545028
$836$	8.91959	0.308491
$837$	2.09117	0.0722813
$838$	2.95148	0.101957
$839$	47.1532	1.62791	0.813955	−	0.580928i	$-0.197310\pi$
$839$	47.1532	1.62791	0.813955	+	0.580928i	$0.197310\pi$
$840$	0	0
$841$	−25.3564	−0.874357
$842$	−15.7612	−0.543168
$843$	−15.7019	−0.540804
$844$	−20.1588	−0.693895
$845$	2.40145	0.0826122
$846$	−11.5657	−0.397637
$847$	0	0
$848$	7.34975	0.252391
$849$	−5.43260	−0.186446
$850$	3.17818	0.109011
$851$	7.73238	0.265063
$852$	−2.37157	−0.0812486
$853$	−24.6118	−0.842691	−0.421346	−	0.906900i	$-0.638442\pi$
$853$	−24.6118	−0.842691	−0.421346	+	0.906900i	$0.638442\pi$
$854$	0	0
$855$	−3.69462	−0.126353
$856$	0.646095	0.0220831
$857$	−23.0260	−0.786554	−0.393277	−	0.919420i	$-0.628659\pi$
$857$	−23.0260	−0.786554	−0.393277	+	0.919420i	$0.628659\pi$
$858$	−10.9154	−0.372647
$859$	24.5089	0.836231	0.418116	−	0.908394i	$-0.362691\pi$
$859$	24.5089	0.836231	0.418116	+	0.908394i	$0.362691\pi$
$860$	−9.33411	−0.318290
$861$	0	0
$862$	10.7383	0.365748
$863$	−51.2856	−1.74578	−0.872891	−	0.487915i	$-0.837758\pi$
$863$	−51.2856	−1.74578	−0.872891	+	0.487915i	$0.837758\pi$
$864$	1.00000	0.0340207
$865$	−24.2843	−0.825690
$866$	20.5235	0.697416
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	4.52132	0.153375
$870$	2.57645	0.0873497
$871$	22.7331	0.770282
$872$	9.42154	0.319054
$873$	5.16742	0.174891
$874$	−3.62153	−0.122500
$875$	0	0
$876$	11.0066	0.371879
$877$	34.8497	1.17679	0.588395	−	0.808574i	$-0.299760\pi$
$877$	34.8497	1.17679	0.588395	+	0.808574i	$0.299760\pi$
$878$	−23.9324	−0.807680
$879$	−16.2049	−0.546577
$880$	−4.39827	−0.148266
$881$	−4.67798	−0.157605	−0.0788026	−	0.996890i	$-0.525110\pi$
$881$	−4.67798	−0.157605	−0.0788026	+	0.996890i	$0.525110\pi$
$882$	0	0
$883$	30.9304	1.04089	0.520445	−	0.853895i	$-0.325766\pi$
$883$	30.9304	1.04089	0.520445	+	0.853895i	$0.325766\pi$
$884$	−3.34975	−0.112664
$885$	−8.30295	−0.279101
$886$	28.7637	0.966335
$887$	−49.0389	−1.64656	−0.823282	−	0.567632i	$-0.807860\pi$
$887$	−49.0389	−1.64656	−0.823282	+	0.567632i	$0.807860\pi$
$888$	5.84437	0.196124
$889$	0	0
$890$	5.98753	0.200703
$891$	3.25858	0.109167
$892$	−13.3986	−0.448617
$893$	31.6583	1.05940
$894$	−6.87768	−0.230024
$895$	−28.9230	−0.966790
$896$	0	0
$897$	4.43188	0.147976
$898$	27.2032	0.907782
$899$	3.99169	0.133130
$900$	−3.17818	−0.105939
$901$	7.34975	0.244856
$902$	24.2333	0.806881
$903$	0	0
$904$	6.54387	0.217646
$905$	12.5024	0.415593
$906$	14.6402	0.486389
$907$	−44.1730	−1.46674	−0.733370	−	0.679830i	$-0.762054\pi$
$907$	−44.1730	−1.46674	−0.733370	+	0.679830i	$0.762054\pi$
$908$	15.0559	0.499646
$909$	−5.07107	−0.168197
$910$	0	0
$911$	−16.4627	−0.545435	−0.272717	−	0.962094i	$-0.587922\pi$
$911$	−16.4627	−0.545435	−0.272717	+	0.962094i	$0.587922\pi$
$912$	−2.73726	−0.0906398
$913$	−15.5238	−0.513762
$914$	−31.4919	−1.04166
$915$	−4.97887	−0.164596
$916$	−11.2429	−0.371477
$917$	0	0
$918$	1.00000	0.0330049
$919$	−33.3671	−1.10068	−0.550340	−	0.834941i	$-0.685502\pi$
$919$	−33.3671	−1.10068	−0.550340	+	0.834941i	$0.685502\pi$
$920$	1.78578	0.0588755
$921$	−23.0877	−0.760767
$922$	19.8319	0.653129
$923$	−7.94416	−0.261485
$924$	0	0
$925$	−18.5744	−0.610724
$926$	16.7446	0.550261
$927$	−2.09635	−0.0688531
$928$	1.90883	0.0626605
$929$	−17.2152	−0.564813	−0.282406	−	0.959295i	$-0.591133\pi$
$929$	−17.2152	−0.564813	−0.282406	+	0.959295i	$0.591133\pi$
$930$	2.82255	0.0925551
$931$	0	0
$932$	24.9321	0.816678
$933$	−9.44092	−0.309082
$934$	11.8187	0.386720
$935$	−4.39827	−0.143839
$936$	3.34975	0.109490
$937$	−4.34272	−0.141870	−0.0709352	−	0.997481i	$-0.522598\pi$
$937$	−4.34272	−0.141870	−0.0709352	+	0.997481i	$0.522598\pi$
$938$	0	0
$939$	−9.44264	−0.308149
$940$	−15.6108	−0.509168
$941$	20.2233	0.659260	0.329630	−	0.944110i	$-0.393076\pi$
$941$	20.2233	0.659260	0.329630	+	0.944110i	$0.393076\pi$
$942$	−13.2167	−0.430622
$943$	−9.83919	−0.320408
$944$	−6.15147	−0.200213
$945$	0	0
$946$	−22.5345	−0.732661
$947$	−53.7485	−1.74659	−0.873296	−	0.487191i	$-0.838022\pi$
$947$	−53.7485	−1.74659	−0.873296	+	0.487191i	$0.838022\pi$
$948$	−1.38751	−0.0450643
$949$	36.8694	1.19683
$950$	8.69950	0.282249
$951$	6.01321	0.194992
$952$	0	0
$953$	57.0681	1.84862	0.924308	−	0.381647i	$-0.124643\pi$
$953$	57.0681	1.84862	0.924308	+	0.381647i	$0.124643\pi$
$954$	−7.34975	−0.237957
$955$	6.85167	0.221715
$956$	−2.83991	−0.0918494
$957$	6.22009	0.201067
$958$	19.1934	0.620111
$959$	0	0
$960$	1.34975	0.0435630
$961$	−26.6270	−0.858936
$962$	19.5772	0.631193
$963$	−0.646095	−0.0208201
$964$	−12.7750	−0.411456
$965$	−18.0642	−0.581506
$966$	0	0
$967$	4.91959	0.158203	0.0791017	−	0.996867i	$-0.474795\pi$
$967$	4.91959	0.158203	0.0791017	+	0.996867i	$0.474795\pi$
$968$	0.381635	0.0122662
$969$	−2.73726	−0.0879335
$970$	6.97472	0.223945
$971$	−53.3311	−1.71148	−0.855739	−	0.517409i	$-0.826897\pi$
$971$	−53.3311	−1.71148	−0.855739	+	0.517409i	$0.826897\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−25.0458	−0.802520
$975$	−10.6461	−0.340948
$976$	−3.68874	−0.118074
$977$	−51.6039	−1.65096	−0.825478	−	0.564434i	$-0.809094\pi$
$977$	−51.6039	−1.65096	−0.825478	+	0.564434i	$0.809094\pi$
$978$	7.12447	0.227815
$979$	14.4552	0.461990
$980$	0	0
$981$	−9.42154	−0.300807
$982$	−9.52060	−0.303814
$983$	−8.67798	−0.276785	−0.138392	−	0.990377i	$-0.544193\pi$
$983$	−8.67798	−0.276785	−0.138392	+	0.990377i	$0.544193\pi$
$984$	−7.43676	−0.237075
$985$	4.39266	0.139962
$986$	1.90883	0.0607897
$987$	0	0
$988$	−9.16914	−0.291709
$989$	9.14945	0.290936
$990$	4.39827	0.139786
$991$	−9.45959	−0.300494	−0.150247	−	0.988648i	$-0.548007\pi$
$991$	−9.45959	−0.300494	−0.150247	+	0.988648i	$0.548007\pi$
$992$	2.09117	0.0663946
$993$	−5.19481	−0.164852
$994$	0	0
$995$	20.7637	0.658253
$996$	4.76396	0.150952
$997$	−3.41180	−0.108053	−0.0540264	−	0.998540i	$-0.517206\pi$
$997$	−3.41180	−0.108053	−0.0540264	+	0.998540i	$0.517206\pi$
$998$	31.3740	0.993127
$999$	−5.84437	−0.184908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4998.2.a.cl.1.2	✓	4
7.6	odd	2		4998.2.a.cm.1.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4998.2.a.cl.1.2	✓	4	1.1	even	1	trivial
4998.2.a.cm.1.3	yes	4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4998.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.34975 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.34975 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.34975 q^{10} +3.25858 q^{11} -1.00000 q^{12} -3.34975 q^{13} +1.34975 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +2.73726 q^{19} -1.34975 q^{20} -3.25858 q^{22} +1.32305 q^{23} +1.00000 q^{24} -3.17818 q^{25} +3.34975 q^{26} -1.00000 q^{27} -1.90883 q^{29} -1.34975 q^{30} -2.09117 q^{31} -1.00000 q^{32} -3.25858 q^{33} -1.00000 q^{34} +1.00000 q^{36} +5.84437 q^{37} -2.73726 q^{38} +3.34975 q^{39} +1.34975 q^{40} -7.43676 q^{41} +6.91544 q^{43} +3.25858 q^{44} -1.34975 q^{45} -1.32305 q^{46} +11.5657 q^{47} -1.00000 q^{48} +3.17818 q^{50} -1.00000 q^{51} -3.34975 q^{52} +7.34975 q^{53} +1.00000 q^{54} -4.39827 q^{55} -2.73726 q^{57} +1.90883 q^{58} -6.15147 q^{59} +1.34975 q^{60} -3.68874 q^{61} +2.09117 q^{62} +1.00000 q^{64} +4.52132 q^{65} +3.25858 q^{66} -6.78651 q^{67} +1.00000 q^{68} -1.32305 q^{69} +2.37157 q^{71} -1.00000 q^{72} -11.0066 q^{73} -5.84437 q^{74} +3.17818 q^{75} +2.73726 q^{76} -3.34975 q^{78} +1.38751 q^{79} -1.34975 q^{80} +1.00000 q^{81} +7.43676 q^{82} -4.76396 q^{83} -1.34975 q^{85} -6.91544 q^{86} +1.90883 q^{87} -3.25858 q^{88} +4.43603 q^{89} +1.34975 q^{90} +1.32305 q^{92} +2.09117 q^{93} -11.5657 q^{94} -3.69462 q^{95} +1.00000 q^{96} +5.16742 q^{97} +3.25858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{10} - 2 q^{11} - 4 q^{12} - 6 q^{13} - 2 q^{15} + 4 q^{16} + 4 q^{17} - 4 q^{18} - 8 q^{19} + 2 q^{20} + 2 q^{22} - 8 q^{23} + 4 q^{24} + 6 q^{25} + 6 q^{26} - 4 q^{27} + 2 q^{30} - 16 q^{31} - 4 q^{32} + 2 q^{33} - 4 q^{34} + 4 q^{36} + 14 q^{37} + 8 q^{38} + 6 q^{39} - 2 q^{40} + 4 q^{41} - 10 q^{43} - 2 q^{44} + 2 q^{45} + 8 q^{46} + 16 q^{47} - 4 q^{48} - 6 q^{50} - 4 q^{51} - 6 q^{52} + 22 q^{53} + 4 q^{54} - 10 q^{55} + 8 q^{57} - 2 q^{60} + 4 q^{61} + 16 q^{62} + 4 q^{64} + 22 q^{65} - 2 q^{66} + 14 q^{67} + 4 q^{68} + 8 q^{69} - 4 q^{71} - 4 q^{72} - 14 q^{73} - 14 q^{74} - 6 q^{75} - 8 q^{76} - 6 q^{78} - 6 q^{79} + 2 q^{80} + 4 q^{81} - 4 q^{82} - 6 q^{83} + 2 q^{85} + 10 q^{86} + 2 q^{88} + 6 q^{89} - 2 q^{90} - 8 q^{92} + 16 q^{93} - 16 q^{94} + 12 q^{95} + 4 q^{96} - 2 q^{97} - 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^10 - 2 * q^11 - 4 * q^12 - 6 * q^13 - 2 * q^15 + 4 * q^16 + 4 * q^17 - 4 * q^18 - 8 * q^19 + 2 * q^20 + 2 * q^22 - 8 * q^23 + 4 * q^24 + 6 * q^25 + 6 * q^26 - 4 * q^27 + 2 * q^30 - 16 * q^31 - 4 * q^32 + 2 * q^33 - 4 * q^34 + 4 * q^36 + 14 * q^37 + 8 * q^38 + 6 * q^39 - 2 * q^40 + 4 * q^41 - 10 * q^43 - 2 * q^44 + 2 * q^45 + 8 * q^46 + 16 * q^47 - 4 * q^48 - 6 * q^50 - 4 * q^51 - 6 * q^52 + 22 * q^53 + 4 * q^54 - 10 * q^55 + 8 * q^57 - 2 * q^60 + 4 * q^61 + 16 * q^62 + 4 * q^64 + 22 * q^65 - 2 * q^66 + 14 * q^67 + 4 * q^68 + 8 * q^69 - 4 * q^71 - 4 * q^72 - 14 * q^73 - 14 * q^74 - 6 * q^75 - 8 * q^76 - 6 * q^78 - 6 * q^79 + 2 * q^80 + 4 * q^81 - 4 * q^82 - 6 * q^83 + 2 * q^85 + 10 * q^86 + 2 * q^88 + 6 * q^89 - 2 * q^90 - 8 * q^92 + 16 * q^93 - 16 * q^94 + 12 * q^95 + 4 * q^96 - 2 * q^97 - 2 * q^99

Introduction

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