LMFDB - Embedded newform 4998.2.a.cl.1.1

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			1.1
Root			$-2.51304$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.51304 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.51304 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.51304 q^{10} -1.04094 q^{11} -1.00000 q^{12} -4.51304 q^{13} +2.51304 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -8.38241 q^{19} -2.51304 q^{20} +1.04094 q^{22} -6.96819 q^{23} +1.00000 q^{24} +1.31538 q^{25} +4.51304 q^{26} -1.00000 q^{27} +3.55398 q^{29} -2.51304 q^{30} -7.55398 q^{31} -1.00000 q^{32} +1.04094 q^{33} -1.00000 q^{34} +1.00000 q^{36} +4.37328 q^{37} +8.38241 q^{38} +4.51304 q^{39} +2.51304 q^{40} +1.35632 q^{41} -8.69779 q^{43} -1.04094 q^{44} -2.51304 q^{45} +6.96819 q^{46} -5.21083 q^{47} -1.00000 q^{48} -1.31538 q^{50} -1.00000 q^{51} -4.51304 q^{52} +8.51304 q^{53} +1.00000 q^{54} +2.61592 q^{55} +8.38241 q^{57} -3.55398 q^{58} +7.79662 q^{59} +2.51304 q^{60} -0.746554 q^{61} +7.55398 q^{62} +1.00000 q^{64} +11.3415 q^{65} -1.04094 q^{66} +0.843278 q^{67} +1.00000 q^{68} +6.96819 q^{69} -14.0972 q^{71} -1.00000 q^{72} -0.856189 q^{73} -4.37328 q^{74} -1.31538 q^{75} -8.38241 q^{76} -4.51304 q^{78} -10.8954 q^{79} -2.51304 q^{80} +1.00000 q^{81} -1.35632 q^{82} -3.09883 q^{83} -2.51304 q^{85} +8.69779 q^{86} -3.55398 q^{87} +1.04094 q^{88} -16.0244 q^{89} +2.51304 q^{90} -6.96819 q^{92} +7.55398 q^{93} +5.21083 q^{94} +21.0653 q^{95} +1.00000 q^{96} -4.59492 q^{97} -1.04094 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.51304	−1.12387	−0.561933	−	0.827182i	$-0.689942\pi$
$5$	−2.51304	−1.12387	−0.561933	+	0.827182i	$0.689942\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.51304	0.794694
$11$	−1.04094	−0.313854	−0.156927	−	0.987610i	$-0.550159\pi$
$11$	−1.04094	−0.313854	−0.156927	+	0.987610i	$0.550159\pi$
$12$	−1.00000	−0.288675
$13$	−4.51304	−1.25169	−0.625846	−	0.779946i	$-0.715246\pi$
$13$	−4.51304	−1.25169	−0.625846	+	0.779946i	$0.715246\pi$
$14$	0	0
$15$	2.51304	0.648865
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−8.38241	−1.92306	−0.961528	−	0.274707i	$-0.911419\pi$
$19$	−8.38241	−1.92306	−0.961528	+	0.274707i	$0.911419\pi$
$20$	−2.51304	−0.561933
$21$	0	0
$22$	1.04094	0.221928
$23$	−6.96819	−1.45297	−0.726484	−	0.687183i	$-0.758847\pi$
$23$	−6.96819	−1.45297	−0.726484	+	0.687183i	$0.758847\pi$
$24$	1.00000	0.204124
$25$	1.31538	0.263077
$26$	4.51304	0.885081
$27$	−1.00000	−0.192450
$28$	0	0
$29$	3.55398	0.659957	0.329979	−	0.943988i	$-0.392958\pi$
$29$	3.55398	0.659957	0.329979	+	0.943988i	$0.392958\pi$
$30$	−2.51304	−0.458817
$31$	−7.55398	−1.35673	−0.678367	−	0.734723i	$-0.737312\pi$
$31$	−7.55398	−1.35673	−0.678367	+	0.734723i	$0.737312\pi$
$32$	−1.00000	−0.176777
$33$	1.04094	0.181204
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	4.37328	0.718962	0.359481	−	0.933152i	$-0.382954\pi$
$37$	4.37328	0.718962	0.359481	+	0.933152i	$0.382954\pi$
$38$	8.38241	1.35981
$39$	4.51304	0.722665
$40$	2.51304	0.397347
$41$	1.35632	0.211822	0.105911	−	0.994376i	$-0.466224\pi$
$41$	1.35632	0.211822	0.105911	+	0.994376i	$0.466224\pi$
$42$	0	0
$43$	−8.69779	−1.32640	−0.663200	−	0.748442i	$-0.730802\pi$
$43$	−8.69779	−1.32640	−0.663200	+	0.748442i	$0.730802\pi$
$44$	−1.04094	−0.156927
$45$	−2.51304	−0.374622
$46$	6.96819	1.02740
$47$	−5.21083	−0.760078	−0.380039	−	0.924970i	$-0.624089\pi$
$47$	−5.21083	−0.760078	−0.380039	+	0.924970i	$0.624089\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−1.31538	−0.186023
$51$	−1.00000	−0.140028
$52$	−4.51304	−0.625846
$53$	8.51304	1.16936	0.584678	−	0.811265i	$-0.301221\pi$
$53$	8.51304	1.16936	0.584678	+	0.811265i	$0.301221\pi$
$54$	1.00000	0.136083
$55$	2.61592	0.352730
$56$	0	0
$57$	8.38241	1.11028
$58$	−3.55398	−0.466660
$59$	7.79662	1.01503	0.507517	−	0.861642i	$-0.330564\pi$
$59$	7.79662	1.01503	0.507517	+	0.861642i	$0.330564\pi$
$60$	2.51304	0.324432
$61$	−0.746554	−0.0955865	−0.0477932	−	0.998857i	$-0.515219\pi$
$61$	−0.746554	−0.0955865	−0.0477932	+	0.998857i	$0.515219\pi$
$62$	7.55398	0.959356
$63$	0	0
$64$	1.00000	0.125000
$65$	11.3415	1.40674
$66$	−1.04094	−0.128130
$67$	0.843278	0.103023	0.0515114	−	0.998672i	$-0.483596\pi$
$67$	0.843278	0.103023	0.0515114	+	0.998672i	$0.483596\pi$
$68$	1.00000	0.121268
$69$	6.96819	0.838872
$70$	0	0
$71$	−14.0972	−1.67302	−0.836512	−	0.547948i	$-0.815409\pi$
$71$	−14.0972	−1.67302	−0.836512	+	0.547948i	$0.815409\pi$
$72$	−1.00000	−0.117851
$73$	−0.856189	−0.100209	−0.0501046	−	0.998744i	$-0.515955\pi$
$73$	−0.856189	−0.100209	−0.0501046	+	0.998744i	$0.515955\pi$
$74$	−4.37328	−0.508383
$75$	−1.31538	−0.151887
$76$	−8.38241	−0.961528
$77$	0	0
$78$	−4.51304	−0.511001
$79$	−10.8954	−1.22583	−0.612917	−	0.790147i	$-0.710004\pi$
$79$	−10.8954	−1.22583	−0.612917	+	0.790147i	$0.710004\pi$
$80$	−2.51304	−0.280967
$81$	1.00000	0.111111
$82$	−1.35632	−0.149781
$83$	−3.09883	−0.340141	−0.170070	−	0.985432i	$-0.554399\pi$
$83$	−3.09883	−0.340141	−0.170070	+	0.985432i	$0.554399\pi$
$84$	0	0
$85$	−2.51304	−0.272578
$86$	8.69779	0.937907
$87$	−3.55398	−0.381027
$88$	1.04094	0.110964
$89$	−16.0244	−1.69858	−0.849292	−	0.527923i	$-0.822971\pi$
$89$	−16.0244	−1.69858	−0.849292	+	0.527923i	$0.822971\pi$
$90$	2.51304	0.264898
$91$	0	0
$92$	−6.96819	−0.726484
$93$	7.55398	0.783311
$94$	5.21083	0.537456
$95$	21.0653	2.16126
$96$	1.00000	0.102062
$97$	−4.59492	−0.466543	−0.233272	−	0.972412i	$-0.574943\pi$
$97$	−4.59492	−0.466543	−0.233272	+	0.972412i	$0.574943\pi$
$98$	0	0
$99$	−1.04094	−0.104618
$100$	1.31538	0.131538
$101$	9.07107	0.902605	0.451302	−	0.892371i	$-0.350960\pi$
$101$	9.07107	0.902605	0.451302	+	0.892371i	$0.350960\pi$
$102$	1.00000	0.0990148
$103$	−6.47615	−0.638114	−0.319057	−	0.947735i	$-0.603366\pi$
$103$	−6.47615	−0.638114	−0.319057	+	0.947735i	$0.603366\pi$
$104$	4.51304	0.442540
$105$	0	0
$106$	−8.51304	−0.826860
$107$	15.9364	1.54063	0.770314	−	0.637664i	$-0.220099\pi$
$107$	15.9364	1.54063	0.770314	+	0.637664i	$0.220099\pi$
$108$	−1.00000	−0.0962250
$109$	−8.11006	−0.776803	−0.388402	−	0.921490i	$-0.626973\pi$
$109$	−8.11006	−0.776803	−0.388402	+	0.921490i	$0.626973\pi$
$110$	−2.61592	−0.249418
$111$	−4.37328	−0.415093
$112$	0	0
$113$	−7.39936	−0.696074	−0.348037	−	0.937481i	$-0.613152\pi$
$113$	−7.39936	−0.696074	−0.348037	+	0.937481i	$0.613152\pi$
$114$	−8.38241	−0.785084
$115$	17.5114	1.63294
$116$	3.55398	0.329979
$117$	−4.51304	−0.417231
$118$	−7.79662	−0.717737
$119$	0	0
$120$	−2.51304	−0.229408
$121$	−9.91645	−0.901496
$122$	0.746554	0.0675898
$123$	−1.35632	−0.122295
$124$	−7.55398	−0.678367
$125$	9.25960	0.828204
$126$	0	0
$127$	−0.828427	−0.0735110	−0.0367555	−	0.999324i	$-0.511702\pi$
$127$	−0.828427	−0.0735110	−0.0367555	+	0.999324i	$0.511702\pi$
$128$	−1.00000	−0.0883883
$129$	8.69779	0.765798
$130$	−11.3415	−0.994713
$131$	−9.39558	−0.820896	−0.410448	−	0.911884i	$-0.634628\pi$
$131$	−9.39558	−0.820896	−0.410448	+	0.911884i	$0.634628\pi$
$132$	1.04094	0.0906019
$133$	0	0
$134$	−0.843278	−0.0728481
$135$	2.51304	0.216288
$136$	−1.00000	−0.0857493
$137$	7.89713	0.674697	0.337348	−	0.941380i	$-0.390470\pi$
$137$	7.89713	0.674697	0.337348	+	0.941380i	$0.390470\pi$
$138$	−6.96819	−0.593172
$139$	−19.0931	−1.61946	−0.809728	−	0.586805i	$-0.800385\pi$
$139$	−19.0931	−1.61946	−0.809728	+	0.586805i	$0.800385\pi$
$140$	0	0
$141$	5.21083	0.438831
$142$	14.0972	1.18301
$143$	4.69779	0.392849
$144$	1.00000	0.0833333
$145$	−8.93130	−0.741704
$146$	0.856189	0.0708587
$147$	0	0
$148$	4.37328	0.359481
$149$	−4.71070	−0.385916	−0.192958	−	0.981207i	$-0.561808\pi$
$149$	−4.71070	−0.385916	−0.192958	+	0.981207i	$0.561808\pi$
$150$	1.31538	0.107401
$151$	19.8755	1.61745	0.808723	−	0.588189i	$-0.200159\pi$
$151$	19.8755	1.61745	0.808723	+	0.588189i	$0.200159\pi$
$152$	8.38241	0.679903
$153$	1.00000	0.0808452
$154$	0	0
$155$	18.9835	1.52479
$156$	4.51304	0.361333
$157$	−6.94421	−0.554209	−0.277104	−	0.960840i	$-0.589375\pi$
$157$	−6.94421	−0.554209	−0.277104	+	0.960840i	$0.589375\pi$
$158$	10.8954	0.866795
$159$	−8.51304	−0.675128
$160$	2.51304	0.198673
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	11.8914	0.931407	0.465703	−	0.884941i	$-0.345801\pi$
$163$	11.8914	0.931407	0.465703	+	0.884941i	$0.345801\pi$
$164$	1.35632	0.105911
$165$	−2.61592	−0.203649
$166$	3.09883	0.240516
$167$	17.2908	1.33800	0.669000	−	0.743263i	$-0.266723\pi$
$167$	17.2908	1.33800	0.669000	+	0.743263i	$0.266723\pi$
$168$	0	0
$169$	7.36756	0.566735
$170$	2.51304	0.192742
$171$	−8.38241	−0.641019
$172$	−8.69779	−0.663200
$173$	−12.8467	−0.976715	−0.488358	−	0.872644i	$-0.662404\pi$
$173$	−12.8467	−0.976715	−0.488358	+	0.872644i	$0.662404\pi$
$174$	3.55398	0.269426
$175$	0	0
$176$	−1.04094	−0.0784635
$177$	−7.79662	−0.586030
$178$	16.0244	1.20108
$179$	−18.2030	−1.36056	−0.680278	−	0.732954i	$-0.738141\pi$
$179$	−18.2030	−1.36056	−0.680278	+	0.732954i	$0.738141\pi$
$180$	−2.51304	−0.187311
$181$	−20.3824	−1.51501	−0.757506	−	0.652828i	$-0.773582\pi$
$181$	−20.3824	−1.51501	−0.757506	+	0.652828i	$0.773582\pi$
$182$	0	0
$183$	0.746554	0.0551869
$184$	6.96819	0.513702
$185$	−10.9902	−0.808018
$186$	−7.55398	−0.553885
$187$	−1.04094	−0.0761208
$188$	−5.21083	−0.380039
$189$	0	0
$190$	−21.0653	−1.52824
$191$	10.1489	0.734348	0.367174	−	0.930152i	$-0.380325\pi$
$191$	10.1489	0.734348	0.367174	+	0.930152i	$0.380325\pi$
$192$	−1.00000	−0.0721688
$193$	−14.3188	−1.03069	−0.515345	−	0.856983i	$-0.672336\pi$
$193$	−14.3188	−1.03069	−0.515345	+	0.856983i	$0.672336\pi$
$194$	4.59492	0.329896
$195$	−11.3415	−0.812180
$196$	0	0
$197$	16.4643	1.17303	0.586516	−	0.809938i	$-0.300499\pi$
$197$	16.4643	1.17303	0.586516	+	0.809938i	$0.300499\pi$
$198$	1.04094	0.0739761
$199$	12.3188	0.873256	0.436628	−	0.899642i	$-0.356173\pi$
$199$	12.3188	0.873256	0.436628	+	0.899642i	$0.356173\pi$
$200$	−1.31538	−0.0930117
$201$	−0.843278	−0.0594802
$202$	−9.07107	−0.638238
$203$	0	0
$204$	−1.00000	−0.0700140
$205$	−3.40849	−0.238059
$206$	6.47615	0.451215
$207$	−6.96819	−0.484323
$208$	−4.51304	−0.312923
$209$	8.72555	0.603559
$210$	0	0
$211$	−7.72766	−0.531994	−0.265997	−	0.963974i	$-0.585701\pi$
$211$	−7.72766	−0.531994	−0.265997	+	0.963974i	$0.585701\pi$
$212$	8.51304	0.584678
$213$	14.0972	0.965921
$214$	−15.9364	−1.08939
$215$	21.8579	1.49070
$216$	1.00000	0.0680414
$217$	0	0
$218$	8.11006	0.549283
$219$	0.856189	0.0578559
$220$	2.61592	0.176365
$221$	−4.51304	−0.303580
$222$	4.37328	0.293515
$223$	21.7852	1.45884	0.729422	−	0.684064i	$-0.239789\pi$
$223$	21.7852	1.45884	0.729422	+	0.684064i	$0.239789\pi$
$224$	0	0
$225$	1.31538	0.0876923
$226$	7.39936	0.492198
$227$	8.39532	0.557217	0.278608	−	0.960405i	$-0.410127\pi$
$227$	8.39532	0.557217	0.278608	+	0.960405i	$0.410127\pi$
$228$	8.38241	0.555138
$229$	25.4119	1.67927	0.839633	−	0.543154i	$-0.182770\pi$
$229$	25.4119	1.67927	0.839633	+	0.543154i	$0.182770\pi$
$230$	−17.5114	−1.15467
$231$	0	0
$232$	−3.55398	−0.233330
$233$	25.1720	1.64907	0.824536	−	0.565809i	$-0.191436\pi$
$233$	25.1720	1.64907	0.824536	+	0.565809i	$0.191436\pi$
$234$	4.51304	0.295027
$235$	13.0950	0.854227
$236$	7.79662	0.507517
$237$	10.8954	0.707735
$238$	0	0
$239$	−14.1192	−0.913295	−0.456647	−	0.889648i	$-0.650950\pi$
$239$	−14.1192	−0.913295	−0.456647	+	0.889648i	$0.650950\pi$
$240$	2.51304	0.162216
$241$	11.7909	0.759519	0.379759	−	0.925085i	$-0.376007\pi$
$241$	11.7909	0.759519	0.379759	+	0.925085i	$0.376007\pi$
$242$	9.91645	0.637454
$243$	−1.00000	−0.0641500
$244$	−0.746554	−0.0477932
$245$	0	0
$246$	1.35632	0.0864759
$247$	37.8302	2.40708
$248$	7.55398	0.479678
$249$	3.09883	0.196380
$250$	−9.25960	−0.585628
$251$	28.7739	1.81620	0.908098	−	0.418759i	$-0.137535\pi$
$251$	28.7739	1.81620	0.908098	+	0.418759i	$0.137535\pi$
$252$	0	0
$253$	7.25345	0.456020
$254$	0.828427	0.0519801
$255$	2.51304	0.157373
$256$	1.00000	0.0625000
$257$	−12.6132	−0.786788	−0.393394	−	0.919370i	$-0.628699\pi$
$257$	−12.6132	−0.786788	−0.393394	+	0.919370i	$0.628699\pi$
$258$	−8.69779	−0.541501
$259$	0	0
$260$	11.3415	0.703368
$261$	3.55398	0.219986
$262$	9.39558	0.580461
$263$	−12.9476	−0.798384	−0.399192	−	0.916867i	$-0.630709\pi$
$263$	−12.9476	−0.798384	−0.399192	+	0.916867i	$0.630709\pi$
$264$	−1.04094	−0.0640652
$265$	−21.3936	−1.31420
$266$	0	0
$267$	16.0244	0.980678
$268$	0.843278	0.0515114
$269$	6.58281	0.401361	0.200680	−	0.979657i	$-0.435685\pi$
$269$	6.58281	0.401361	0.200680	+	0.979657i	$0.435685\pi$
$270$	−2.51304	−0.152939
$271$	−23.4047	−1.42173	−0.710867	−	0.703326i	$-0.751697\pi$
$271$	−23.4047	−1.42173	−0.710867	+	0.703326i	$0.751697\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	−7.89713	−0.477083
$275$	−1.36923	−0.0825678
$276$	6.96819	0.419436
$277$	11.8305	0.710828	0.355414	−	0.934709i	$-0.384340\pi$
$277$	11.8305	0.710828	0.355414	+	0.934709i	$0.384340\pi$
$278$	19.0931	1.14513
$279$	−7.55398	−0.452245
$280$	0	0
$281$	−7.54107	−0.449862	−0.224931	−	0.974375i	$-0.572216\pi$
$281$	−7.54107	−0.449862	−0.224931	+	0.974375i	$0.572216\pi$
$282$	−5.21083	−0.310301
$283$	−18.7797	−1.11634	−0.558168	−	0.829728i	$-0.688495\pi$
$283$	−18.7797	−1.11634	−0.558168	+	0.829728i	$0.688495\pi$
$284$	−14.0972	−0.836512
$285$	−21.0653	−1.24780
$286$	−4.69779	−0.277786
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	8.93130	0.524464
$291$	4.59492	0.269359
$292$	−0.856189	−0.0501046
$293$	21.1659	1.23652	0.618261	−	0.785973i	$-0.287837\pi$
$293$	21.1659	1.23652	0.618261	+	0.785973i	$0.287837\pi$
$294$	0	0
$295$	−19.5932	−1.14076
$296$	−4.37328	−0.254192
$297$	1.04094	0.0604013
$298$	4.71070	0.272884
$299$	31.4478	1.81867
$300$	−1.31538	−0.0759437
$301$	0	0
$302$	−19.8755	−1.14371
$303$	−9.07107	−0.521119
$304$	−8.38241	−0.480764
$305$	1.87612	0.107426
$306$	−1.00000	−0.0571662
$307$	24.7987	1.41534	0.707669	−	0.706544i	$-0.249747\pi$
$307$	24.7987	1.41534	0.707669	+	0.706544i	$0.249747\pi$
$308$	0	0
$309$	6.47615	0.368415
$310$	−18.9835	−1.07819
$311$	16.0670	0.911077	0.455539	−	0.890216i	$-0.349447\pi$
$311$	16.0670	0.911077	0.455539	+	0.890216i	$0.349447\pi$
$312$	−4.51304	−0.255501
$313$	−21.1682	−1.19650	−0.598249	−	0.801310i	$-0.704137\pi$
$313$	−21.1682	−1.19650	−0.598249	+	0.801310i	$0.704137\pi$
$314$	6.94421	0.391885
$315$	0	0
$316$	−10.8954	−0.612917
$317$	14.2876	0.802473	0.401236	−	0.915975i	$-0.368581\pi$
$317$	14.2876	0.802473	0.401236	+	0.915975i	$0.368581\pi$
$318$	8.51304	0.477388
$319$	−3.69947	−0.207130
$320$	−2.51304	−0.140483
$321$	−15.9364	−0.889482
$322$	0	0
$323$	−8.38241	−0.466410
$324$	1.00000	0.0555556
$325$	−5.93639	−0.329291
$326$	−11.8914	−0.658604
$327$	8.11006	0.448488
$328$	−1.35632	−0.0748903
$329$	0	0
$330$	2.61592	0.144002
$331$	−15.8478	−0.871071	−0.435536	−	0.900171i	$-0.643441\pi$
$331$	−15.8478	−0.871071	−0.435536	+	0.900171i	$0.643441\pi$
$332$	−3.09883	−0.170070
$333$	4.37328	0.239654
$334$	−17.2908	−0.946109
$335$	−2.11919	−0.115784
$336$	0	0
$337$	23.6569	1.28867	0.644335	−	0.764743i	$-0.277134\pi$
$337$	23.6569	1.28867	0.644335	+	0.764743i	$0.277134\pi$
$338$	−7.36756	−0.400742
$339$	7.39936	0.401878
$340$	−2.51304	−0.136289
$341$	7.86321	0.425817
$342$	8.38241	0.453269
$343$	0	0
$344$	8.69779	0.468953
$345$	−17.5114	−0.942780
$346$	12.8467	0.690642
$347$	−27.8282	−1.49390	−0.746949	−	0.664882i	$-0.768482\pi$
$347$	−27.8282	−1.49390	−0.746949	+	0.664882i	$0.768482\pi$
$348$	−3.55398	−0.190513
$349$	−0.864280	−0.0462638	−0.0231319	−	0.999732i	$-0.507364\pi$
$349$	−0.864280	−0.0462638	−0.0231319	+	0.999732i	$0.507364\pi$
$350$	0	0
$351$	4.51304	0.240888
$352$	1.04094	0.0554821
$353$	−13.5913	−0.723392	−0.361696	−	0.932296i	$-0.617802\pi$
$353$	−13.5913	−0.723392	−0.361696	+	0.932296i	$0.617802\pi$
$354$	7.79662	0.414386
$355$	35.4268	1.88026
$356$	−16.0244	−0.849292
$357$	0	0
$358$	18.2030	0.962059
$359$	−7.10796	−0.375144	−0.187572	−	0.982251i	$-0.560062\pi$
$359$	−7.10796	−0.375144	−0.187572	+	0.982251i	$0.560062\pi$
$360$	2.51304	0.132449
$361$	51.2647	2.69814
$362$	20.3824	1.07128
$363$	9.91645	0.520479
$364$	0	0
$365$	2.15164	0.112622
$366$	−0.746554	−0.0390230
$367$	−21.3659	−1.11529	−0.557645	−	0.830080i	$-0.688295\pi$
$367$	−21.3659	−1.11529	−0.557645	+	0.830080i	$0.688295\pi$
$368$	−6.96819	−0.363242
$369$	1.35632	0.0706072
$370$	10.9902	0.571355
$371$	0	0
$372$	7.55398	0.391656
$373$	−3.65411	−0.189203	−0.0946013	−	0.995515i	$-0.530158\pi$
$373$	−3.65411	−0.189203	−0.0946013	+	0.995515i	$0.530158\pi$
$374$	1.04094	0.0538255
$375$	−9.25960	−0.478164
$376$	5.21083	0.268728
$377$	−16.0393	−0.826064
$378$	0	0
$379$	25.7798	1.32422	0.662110	−	0.749406i	$-0.269661\pi$
$379$	25.7798	1.32422	0.662110	+	0.749406i	$0.269661\pi$
$380$	21.0653	1.08063
$381$	0.828427	0.0424416
$382$	−10.1489	−0.519263
$383$	0.330235	0.0168742	0.00843711	−	0.999964i	$-0.497314\pi$
$383$	0.330235	0.0168742	0.00843711	+	0.999964i	$0.497314\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	14.3188	0.728807
$387$	−8.69779	−0.442134
$388$	−4.59492	−0.233272
$389$	6.62268	0.335783	0.167892	−	0.985805i	$-0.446304\pi$
$389$	6.62268	0.335783	0.167892	+	0.985805i	$0.446304\pi$
$390$	11.3415	0.574298
$391$	−6.96819	−0.352397
$392$	0	0
$393$	9.39558	0.473944
$394$	−16.4643	−0.829458
$395$	27.3807	1.37767
$396$	−1.04094	−0.0523090
$397$	3.72047	0.186725	0.0933625	−	0.995632i	$-0.470238\pi$
$397$	3.72047	0.186725	0.0933625	+	0.995632i	$0.470238\pi$
$398$	−12.3188	−0.617485
$399$	0	0
$400$	1.31538	0.0657692
$401$	−22.3341	−1.11531	−0.557655	−	0.830073i	$-0.688299\pi$
$401$	−22.3341	−1.11531	−0.557655	+	0.830073i	$0.688299\pi$
$402$	0.843278	0.0420589
$403$	34.0914	1.69822
$404$	9.07107	0.451302
$405$	−2.51304	−0.124874
$406$	0	0
$407$	−4.55230	−0.225649
$408$	1.00000	0.0495074
$409$	31.3506	1.55019	0.775094	−	0.631846i	$-0.217703\pi$
$409$	31.3506	1.55019	0.775094	+	0.631846i	$0.217703\pi$
$410$	3.40849	0.168333
$411$	−7.89713	−0.389536
$412$	−6.47615	−0.319057
$413$	0	0
$414$	6.96819	0.342468
$415$	7.78749	0.382273
$416$	4.51304	0.221270
$417$	19.0931	0.934994
$418$	−8.72555	−0.426781
$419$	−11.1290	−0.543685	−0.271843	−	0.962342i	$-0.587633\pi$
$419$	−11.1290	−0.543685	−0.271843	+	0.962342i	$0.587633\pi$
$420$	0	0
$421$	−10.3905	−0.506402	−0.253201	−	0.967414i	$-0.581483\pi$
$421$	−10.3905	−0.506402	−0.253201	+	0.967414i	$0.581483\pi$
$422$	7.72766	0.376176
$423$	−5.21083	−0.253359
$424$	−8.51304	−0.413430
$425$	1.31538	0.0638055
$426$	−14.0972	−0.683009
$427$	0	0
$428$	15.9364	0.770314
$429$	−4.69779	−0.226811
$430$	−21.8579	−1.05408
$431$	16.8836	0.813253	0.406627	−	0.913594i	$-0.366705\pi$
$431$	16.8836	0.813253	0.406627	+	0.913594i	$0.366705\pi$
$432$	−1.00000	−0.0481125
$433$	−29.9436	−1.43900	−0.719498	−	0.694494i	$-0.755628\pi$
$433$	−29.9436	−1.43900	−0.719498	+	0.694494i	$0.755628\pi$
$434$	0	0
$435$	8.93130	0.428223
$436$	−8.11006	−0.388402
$437$	58.4102	2.79414
$438$	−0.856189	−0.0409103
$439$	−3.99726	−0.190779	−0.0953893	−	0.995440i	$-0.530410\pi$
$439$	−3.99726	−0.190779	−0.0953893	+	0.995440i	$0.530410\pi$
$440$	−2.61592	−0.124709
$441$	0	0
$442$	4.51304	0.214664
$443$	22.9577	1.09075	0.545375	−	0.838192i	$-0.316387\pi$
$443$	22.9577	1.09075	0.545375	+	0.838192i	$0.316387\pi$
$444$	−4.37328	−0.207547
$445$	40.2700	1.90898
$446$	−21.7852	−1.03156
$447$	4.71070	0.222809
$448$	0	0
$449$	8.82465	0.416461	0.208230	−	0.978080i	$-0.433230\pi$
$449$	8.82465	0.416461	0.208230	+	0.978080i	$0.433230\pi$
$450$	−1.31538	−0.0620078
$451$	−1.41184	−0.0664811
$452$	−7.39936	−0.348037
$453$	−19.8755	−0.933833
$454$	−8.39532	−0.394012
$455$	0	0
$456$	−8.38241	−0.392542
$457$	4.37091	0.204462	0.102231	−	0.994761i	$-0.467402\pi$
$457$	4.37091	0.204462	0.102231	+	0.994761i	$0.467402\pi$
$458$	−25.4119	−1.18742
$459$	−1.00000	−0.0466760
$460$	17.5114	0.816472
$461$	27.8968	1.29928	0.649641	−	0.760241i	$-0.274919\pi$
$461$	27.8968	1.29928	0.649641	+	0.760241i	$0.274919\pi$
$462$	0	0
$463$	−7.14187	−0.331911	−0.165955	−	0.986133i	$-0.553071\pi$
$463$	−7.14187	−0.331911	−0.165955	+	0.986133i	$0.553071\pi$
$464$	3.55398	0.164989
$465$	−18.9835	−0.880338
$466$	−25.1720	−1.16607
$467$	15.6091	0.722304	0.361152	−	0.932507i	$-0.382383\pi$
$467$	15.6091	0.722304	0.361152	+	0.932507i	$0.382383\pi$
$468$	−4.51304	−0.208615
$469$	0	0
$470$	−13.0950	−0.604030
$471$	6.94421	0.319972
$472$	−7.79662	−0.358869
$473$	9.05385	0.416296
$474$	−10.8954	−0.500445
$475$	−11.0261	−0.505912
$476$	0	0
$477$	8.51304	0.389785
$478$	14.1192	0.645797
$479$	−39.6204	−1.81030	−0.905151	−	0.425090i	$-0.860242\pi$
$479$	−39.6204	−1.81030	−0.905151	+	0.425090i	$0.860242\pi$
$480$	−2.51304	−0.114704
$481$	−19.7368	−0.899920
$482$	−11.7909	−0.537061
$483$	0	0
$484$	−9.91645	−0.450748
$485$	11.5472	0.524332
$486$	1.00000	0.0453609
$487$	24.7839	1.12306	0.561532	−	0.827455i	$-0.310212\pi$
$487$	24.7839	1.12306	0.561532	+	0.827455i	$0.310212\pi$
$488$	0.746554	0.0337949
$489$	−11.8914	−0.537748
$490$	0	0
$491$	4.67338	0.210907	0.105453	−	0.994424i	$-0.466371\pi$
$491$	4.67338	0.210907	0.105453	+	0.994424i	$0.466371\pi$
$492$	−1.35632	−0.0611477
$493$	3.55398	0.160063
$494$	−37.8302	−1.70206
$495$	2.61592	0.117577
$496$	−7.55398	−0.339184
$497$	0	0
$498$	−3.09883	−0.138862
$499$	10.6643	0.477400	0.238700	−	0.971093i	$-0.423279\pi$
$499$	10.6643	0.477400	0.238700	+	0.971093i	$0.423279\pi$
$500$	9.25960	0.414102
$501$	−17.2908	−0.772494
$502$	−28.7739	−1.28424
$503$	−22.5773	−1.00667	−0.503337	−	0.864090i	$-0.667894\pi$
$503$	−22.5773	−1.00667	−0.503337	+	0.864090i	$0.667894\pi$
$504$	0	0
$505$	−22.7960	−1.01441
$506$	−7.25345	−0.322455
$507$	−7.36756	−0.327205
$508$	−0.828427	−0.0367555
$509$	−1.21381	−0.0538012	−0.0269006	−	0.999638i	$-0.508564\pi$
$509$	−1.21381	−0.0538012	−0.0269006	+	0.999638i	$0.508564\pi$
$510$	−2.51304	−0.111279
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	8.38241	0.370092
$514$	12.6132	0.556343
$515$	16.2748	0.717155
$516$	8.69779	0.382899
$517$	5.42415	0.238554
$518$	0	0
$519$	12.8467	0.563907
$520$	−11.3415	−0.497356
$521$	−17.5201	−0.767568	−0.383784	−	0.923423i	$-0.625379\pi$
$521$	−17.5201	−0.767568	−0.383784	+	0.923423i	$0.625379\pi$
$522$	−3.55398	−0.155553
$523$	18.9103	0.826890	0.413445	−	0.910529i	$-0.364325\pi$
$523$	18.9103	0.826890	0.413445	+	0.910529i	$0.364325\pi$
$524$	−9.39558	−0.410448
$525$	0	0
$526$	12.9476	0.564543
$527$	−7.55398	−0.329057
$528$	1.04094	0.0453009
$529$	25.5557	1.11112
$530$	21.3936	0.929280
$531$	7.79662	0.338344
$532$	0	0
$533$	−6.12113	−0.265136
$534$	−16.0244	−0.693444
$535$	−40.0488	−1.73146
$536$	−0.843278	−0.0364241
$537$	18.2030	0.785518
$538$	−6.58281	−0.283805
$539$	0	0
$540$	2.51304	0.108144
$541$	6.23114	0.267898	0.133949	−	0.990988i	$-0.457234\pi$
$541$	6.23114	0.267898	0.133949	+	0.990988i	$0.457234\pi$
$542$	23.4047	1.00532
$543$	20.3824	0.874693
$544$	−1.00000	−0.0428746
$545$	20.3809	0.873023
$546$	0	0
$547$	−0.633139	−0.0270710	−0.0135355	−	0.999908i	$-0.504309\pi$
$547$	−0.633139	−0.0270710	−0.0135355	+	0.999908i	$0.504309\pi$
$548$	7.89713	0.337348
$549$	−0.746554	−0.0318622
$550$	1.36923	0.0583842
$551$	−29.7909	−1.26913
$552$	−6.96819	−0.296586
$553$	0	0
$554$	−11.8305	−0.502631
$555$	10.9902	0.466509
$556$	−19.0931	−0.809728
$557$	26.3398	1.11605	0.558026	−	0.829823i	$-0.311559\pi$
$557$	26.3398	1.11605	0.558026	+	0.829823i	$0.311559\pi$
$558$	7.55398	0.319785
$559$	39.2535	1.66025
$560$	0	0
$561$	1.04094	0.0439484
$562$	7.54107	0.318101
$563$	−16.7002	−0.703828	−0.351914	−	0.936032i	$-0.614469\pi$
$563$	−16.7002	−0.703828	−0.351914	+	0.936032i	$0.614469\pi$
$564$	5.21083	0.219416
$565$	18.5949	0.782294
$566$	18.7797	0.789368
$567$	0	0
$568$	14.0972	0.591503
$569$	−14.8386	−0.622066	−0.311033	−	0.950399i	$-0.600675\pi$
$569$	−14.8386	−0.622066	−0.311033	+	0.950399i	$0.600675\pi$
$570$	21.0653	0.882330
$571$	−25.3128	−1.05931	−0.529654	−	0.848214i	$-0.677678\pi$
$571$	−25.3128	−1.05931	−0.529654	+	0.848214i	$0.677678\pi$
$572$	4.69779	0.196424
$573$	−10.1489	−0.423976
$574$	0	0
$575$	−9.16585	−0.382242
$576$	1.00000	0.0416667
$577$	5.92050	0.246474	0.123237	−	0.992377i	$-0.460673\pi$
$577$	5.92050	0.246474	0.123237	+	0.992377i	$0.460673\pi$
$578$	−1.00000	−0.0415945
$579$	14.3188	0.595069
$580$	−8.93130	−0.370852
$581$	0	0
$582$	−4.59492	−0.190465
$583$	−8.86154	−0.367007
$584$	0.856189	0.0354293
$585$	11.3415	0.468912
$586$	−21.1659	−0.874353
$587$	45.3750	1.87283	0.936414	−	0.350898i	$-0.114124\pi$
$587$	45.3750	1.87283	0.936414	+	0.350898i	$0.114124\pi$
$588$	0	0
$589$	63.3205	2.60908
$590$	19.5932	0.806641
$591$	−16.4643	−0.677250
$592$	4.37328	0.179741
$593$	−22.2240	−0.912631	−0.456315	−	0.889818i	$-0.650831\pi$
$593$	−22.2240	−0.912631	−0.456315	+	0.889818i	$0.650831\pi$
$594$	−1.04094	−0.0427101
$595$	0	0
$596$	−4.71070	−0.192958
$597$	−12.3188	−0.504175
$598$	−31.4478	−1.28599
$599$	−40.2605	−1.64500	−0.822500	−	0.568765i	$-0.807421\pi$
$599$	−40.2605	−1.64500	−0.822500	+	0.568765i	$0.807421\pi$
$600$	1.31538	0.0537003
$601$	−26.1043	−1.06482	−0.532409	−	0.846487i	$-0.678713\pi$
$601$	−26.1043	−1.06482	−0.532409	+	0.846487i	$0.678713\pi$
$602$	0	0
$603$	0.843278	0.0343409
$604$	19.8755	0.808723
$605$	24.9205	1.01316
$606$	9.07107	0.368487
$607$	17.4166	0.706917	0.353459	−	0.935450i	$-0.385006\pi$
$607$	17.4166	0.706917	0.353459	+	0.935450i	$0.385006\pi$
$608$	8.38241	0.339951
$609$	0	0
$610$	−1.87612	−0.0759620
$611$	23.5167	0.951384
$612$	1.00000	0.0404226
$613$	−37.9006	−1.53079	−0.765395	−	0.643561i	$-0.777456\pi$
$613$	−37.9006	−1.53079	−0.765395	+	0.643561i	$0.777456\pi$
$614$	−24.7987	−1.00080
$615$	3.40849	0.137444
$616$	0	0
$617$	1.94826	0.0784339	0.0392170	−	0.999231i	$-0.487514\pi$
$617$	1.94826	0.0784339	0.0392170	+	0.999231i	$0.487514\pi$
$618$	−6.47615	−0.260509
$619$	4.64174	0.186567	0.0932836	−	0.995640i	$-0.470264\pi$
$619$	4.64174	0.186567	0.0932836	+	0.995640i	$0.470264\pi$
$620$	18.9835	0.762395
$621$	6.96819	0.279624
$622$	−16.0670	−0.644229
$623$	0	0
$624$	4.51304	0.180666
$625$	−29.8467	−1.19387
$626$	21.1682	0.846052
$627$	−8.72555	−0.348465
$628$	−6.94421	−0.277104
$629$	4.37328	0.174374
$630$	0	0
$631$	11.1811	0.445114	0.222557	−	0.974920i	$-0.428560\pi$
$631$	11.1811	0.445114	0.222557	+	0.974920i	$0.428560\pi$
$632$	10.8954	0.433398
$633$	7.72766	0.307147
$634$	−14.2876	−0.567434
$635$	2.08187	0.0826166
$636$	−8.51304	−0.337564
$637$	0	0
$638$	3.69947	0.146463
$639$	−14.0972	−0.557675
$640$	2.51304	0.0993367
$641$	−29.2505	−1.15533	−0.577663	−	0.816275i	$-0.696035\pi$
$641$	−29.2505	−1.15533	−0.577663	+	0.816275i	$0.696035\pi$
$642$	15.9364	0.628959
$643$	37.8423	1.49235	0.746177	−	0.665748i	$-0.231887\pi$
$643$	37.8423	1.49235	0.746177	+	0.665748i	$0.231887\pi$
$644$	0	0
$645$	−21.8579	−0.860655
$646$	8.38241	0.329801
$647$	−16.6403	−0.654199	−0.327099	−	0.944990i	$-0.606071\pi$
$647$	−16.6403	−0.654199	−0.327099	+	0.944990i	$0.606071\pi$
$648$	−1.00000	−0.0392837
$649$	−8.11579	−0.318572
$650$	5.93639	0.232844
$651$	0	0
$652$	11.8914	0.465703
$653$	0.399197	0.0156218	0.00781090	−	0.999969i	$-0.497514\pi$
$653$	0.399197	0.0156218	0.00781090	+	0.999969i	$0.497514\pi$
$654$	−8.11006	−0.317129
$655$	23.6115	0.922578
$656$	1.35632	0.0529554
$657$	−0.856189	−0.0334031
$658$	0	0
$659$	−15.6013	−0.607742	−0.303871	−	0.952713i	$-0.598279\pi$
$659$	−15.6013	−0.607742	−0.303871	+	0.952713i	$0.598279\pi$
$660$	−2.61592	−0.101824
$661$	43.5338	1.69327	0.846635	−	0.532174i	$-0.178625\pi$
$661$	43.5338	1.69327	0.846635	+	0.532174i	$0.178625\pi$
$662$	15.8478	0.615940
$663$	4.51304	0.175272
$664$	3.09883	0.120258
$665$	0	0
$666$	−4.37328	−0.169461
$667$	−24.7648	−0.958897
$668$	17.2908	0.669000
$669$	−21.7852	−0.842264
$670$	2.11919	0.0818716
$671$	0.777116	0.0300002
$672$	0	0
$673$	33.5845	1.29459	0.647294	−	0.762240i	$-0.275900\pi$
$673$	33.5845	1.29459	0.647294	+	0.762240i	$0.275900\pi$
$674$	−23.6569	−0.911228
$675$	−1.31538	−0.0506292
$676$	7.36756	0.283368
$677$	14.8643	0.571281	0.285640	−	0.958337i	$-0.407794\pi$
$677$	14.8643	0.571281	0.285640	+	0.958337i	$0.407794\pi$
$678$	−7.39936	−0.284171
$679$	0	0
$680$	2.51304	0.0963708
$681$	−8.39532	−0.321709
$682$	−7.86321	−0.301098
$683$	−39.7795	−1.52212	−0.761059	−	0.648682i	$-0.775320\pi$
$683$	−39.7795	−1.52212	−0.761059	+	0.648682i	$0.775320\pi$
$684$	−8.38241	−0.320509
$685$	−19.8458	−0.758270
$686$	0	0
$687$	−25.4119	−0.969524
$688$	−8.69779	−0.331600
$689$	−38.4197	−1.46368
$690$	17.5114	0.666646
$691$	−31.1750	−1.18595	−0.592976	−	0.805220i	$-0.702047\pi$
$691$	−31.1750	−1.18595	−0.592976	+	0.805220i	$0.702047\pi$
$692$	−12.8467	−0.488358
$693$	0	0
$694$	27.8282	1.05634
$695$	47.9818	1.82005
$696$	3.55398	0.134713
$697$	1.35632	0.0513743
$698$	0.864280	0.0327135
$699$	−25.1720	−0.952093
$700$	0	0
$701$	35.4641	1.33946	0.669730	−	0.742605i	$-0.266410\pi$
$701$	35.4641	1.33946	0.669730	+	0.742605i	$0.266410\pi$
$702$	−4.51304	−0.170334
$703$	−36.6586	−1.38260
$704$	−1.04094	−0.0392318
$705$	−13.0950	−0.493188
$706$	13.5913	0.511515
$707$	0	0
$708$	−7.79662	−0.293015
$709$	15.6708	0.588529	0.294265	−	0.955724i	$-0.404925\pi$
$709$	15.6708	0.588529	0.294265	+	0.955724i	$0.404925\pi$
$710$	−35.4268	−1.32954
$711$	−10.8954	−0.408611
$712$	16.0244	0.600540
$713$	52.6376	1.97129
$714$	0	0
$715$	−11.8057	−0.441510
$716$	−18.2030	−0.680278
$717$	14.1192	0.527291
$718$	7.10796	0.265267
$719$	10.6532	0.397299	0.198649	−	0.980071i	$-0.436345\pi$
$719$	10.6532	0.397299	0.198649	+	0.980071i	$0.436345\pi$
$720$	−2.51304	−0.0936556
$721$	0	0
$722$	−51.2647	−1.90788
$723$	−11.7909	−0.438508
$724$	−20.3824	−0.757506
$725$	4.67485	0.173620
$726$	−9.91645	−0.368034
$727$	33.9977	1.26090	0.630452	−	0.776228i	$-0.282869\pi$
$727$	33.9977	1.26090	0.630452	+	0.776228i	$0.282869\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−2.15164	−0.0796357
$731$	−8.69779	−0.321699
$732$	0.746554	0.0275934
$733$	−1.08549	−0.0400934	−0.0200467	−	0.999799i	$-0.506381\pi$
$733$	−1.08549	−0.0400934	−0.0200467	+	0.999799i	$0.506381\pi$
$734$	21.3659	0.788629
$735$	0	0
$736$	6.96819	0.256851
$737$	−0.877799	−0.0323341
$738$	−1.35632	−0.0499269
$739$	52.9036	1.94609	0.973045	−	0.230615i	$-0.0740737\pi$
$739$	52.9036	1.94609	0.973045	+	0.230615i	$0.0740737\pi$
$740$	−10.9902	−0.404009
$741$	−37.8302	−1.38973
$742$	0	0
$743$	0.963981	0.0353651	0.0176825	−	0.999844i	$-0.494371\pi$
$743$	0.963981	0.0353651	0.0176825	+	0.999844i	$0.494371\pi$
$744$	−7.55398	−0.276942
$745$	11.8382	0.433718
$746$	3.65411	0.133786
$747$	−3.09883	−0.113380
$748$	−1.04094	−0.0380604
$749$	0	0
$750$	9.25960	0.338113
$751$	−9.56689	−0.349101	−0.174550	−	0.984648i	$-0.555847\pi$
$751$	−9.56689	−0.349101	−0.174550	+	0.984648i	$0.555847\pi$
$752$	−5.21083	−0.190020
$753$	−28.7739	−1.04858
$754$	16.0393	0.584115
$755$	−49.9480	−1.81779
$756$	0	0
$757$	−17.2792	−0.628023	−0.314011	−	0.949419i	$-0.601673\pi$
$757$	−17.2792	−0.628023	−0.314011	+	0.949419i	$0.601673\pi$
$758$	−25.7798	−0.936366
$759$	−7.25345	−0.263283
$760$	−21.0653	−0.764120
$761$	17.7482	0.643373	0.321686	−	0.946846i	$-0.395750\pi$
$761$	17.7482	0.643373	0.321686	+	0.946846i	$0.395750\pi$
$762$	−0.828427	−0.0300107
$763$	0	0
$764$	10.1489	0.367174
$765$	−2.51304	−0.0908593
$766$	−0.330235	−0.0119319
$767$	−35.1865	−1.27051
$768$	−1.00000	−0.0360844
$769$	−7.87315	−0.283913	−0.141956	−	0.989873i	$-0.545339\pi$
$769$	−7.87315	−0.283913	−0.141956	+	0.989873i	$0.545339\pi$
$770$	0	0
$771$	12.6132	0.454252
$772$	−14.3188	−0.515345
$773$	−20.3752	−0.732846	−0.366423	−	0.930448i	$-0.619418\pi$
$773$	−20.3752	−0.732846	−0.366423	+	0.930448i	$0.619418\pi$
$774$	8.69779	0.312636
$775$	−9.93639	−0.356926
$776$	4.59492	0.164948
$777$	0	0
$778$	−6.62268	−0.237434
$779$	−11.3692	−0.407345
$780$	−11.3415	−0.406090
$781$	14.6742	0.525086
$782$	6.96819	0.249182
$783$	−3.55398	−0.127009
$784$	0	0
$785$	17.4511	0.622857
$786$	−9.39558	−0.335129
$787$	−37.0342	−1.32013	−0.660064	−	0.751209i	$-0.729471\pi$
$787$	−37.0342	−1.32013	−0.660064	+	0.751209i	$0.729471\pi$
$788$	16.4643	0.586516
$789$	12.9476	0.460947
$790$	−27.3807	−0.974163
$791$	0	0
$792$	1.04094	0.0369881
$793$	3.36923	0.119645
$794$	−3.72047	−0.132034
$795$	21.3936	0.758754
$796$	12.3188	0.436628
$797$	−6.37187	−0.225703	−0.112852	−	0.993612i	$-0.535998\pi$
$797$	−6.37187	−0.225703	−0.112852	+	0.993612i	$0.535998\pi$
$798$	0	0
$799$	−5.21083	−0.184346
$800$	−1.31538	−0.0465059
$801$	−16.0244	−0.566195
$802$	22.3341	0.788644
$803$	0.891238	0.0314511
$804$	−0.843278	−0.0297401
$805$	0	0
$806$	−34.0914	−1.20082
$807$	−6.58281	−0.231726
$808$	−9.07107	−0.319119
$809$	3.02036	0.106190	0.0530952	−	0.998589i	$-0.483091\pi$
$809$	3.02036	0.106190	0.0530952	+	0.998589i	$0.483091\pi$
$810$	2.51304	0.0882993
$811$	−28.7538	−1.00968	−0.504842	−	0.863212i	$-0.668449\pi$
$811$	−28.7538	−1.00968	−0.504842	+	0.863212i	$0.668449\pi$
$812$	0	0
$813$	23.4047	0.820839
$814$	4.55230	0.159558
$815$	−29.8836	−1.04678
$816$	−1.00000	−0.0350070
$817$	72.9084	2.55074
$818$	−31.3506	−1.09615
$819$	0	0
$820$	−3.40849	−0.119030
$821$	32.7188	1.14190	0.570948	−	0.820986i	$-0.306576\pi$
$821$	32.7188	1.14190	0.570948	+	0.820986i	$0.306576\pi$
$822$	7.89713	0.275444
$823$	−29.6387	−1.03314	−0.516569	−	0.856245i	$-0.672791\pi$
$823$	−29.6387	−1.03314	−0.516569	+	0.856245i	$0.672791\pi$
$824$	6.47615	0.225607
$825$	1.36923	0.0476705
$826$	0	0
$827$	−9.24669	−0.321539	−0.160769	−	0.986992i	$-0.551398\pi$
$827$	−9.24669	−0.321539	−0.160769	+	0.986992i	$0.551398\pi$
$828$	−6.96819	−0.242161
$829$	−34.1326	−1.18548	−0.592738	−	0.805396i	$-0.701953\pi$
$829$	−34.1326	−1.18548	−0.592738	+	0.805396i	$0.701953\pi$
$830$	−7.78749	−0.270308
$831$	−11.8305	−0.410397
$832$	−4.51304	−0.156462
$833$	0	0
$834$	−19.0931	−0.661140
$835$	−43.4524	−1.50373
$836$	8.72555	0.301780
$837$	7.55398	0.261104
$838$	11.1290	0.384444
$839$	28.3703	0.979452	0.489726	−	0.871877i	$-0.337097\pi$
$839$	28.3703	0.979452	0.489726	+	0.871877i	$0.337097\pi$
$840$	0	0
$841$	−16.3692	−0.564456
$842$	10.3905	0.358080
$843$	7.54107	0.259728
$844$	−7.72766	−0.265997
$845$	−18.5150	−0.636935
$846$	5.21083	0.179152
$847$	0	0
$848$	8.51304	0.292339
$849$	18.7797	0.644516
$850$	−1.31538	−0.0451173
$851$	−30.4738	−1.04463
$852$	14.0972	0.482961
$853$	52.9984	1.81463	0.907315	−	0.420452i	$-0.138128\pi$
$853$	52.9984	1.81463	0.907315	+	0.420452i	$0.138128\pi$
$854$	0	0
$855$	21.0653	0.720420
$856$	−15.9364	−0.544694
$857$	25.0104	0.854340	0.427170	−	0.904171i	$-0.359511\pi$
$857$	25.0104	0.854340	0.427170	+	0.904171i	$0.359511\pi$
$858$	4.69779	0.160380
$859$	−14.9286	−0.509356	−0.254678	−	0.967026i	$-0.581969\pi$
$859$	−14.9286	−0.509356	−0.254678	+	0.967026i	$0.581969\pi$
$860$	21.8579	0.745349
$861$	0	0
$862$	−16.8836	−0.575057
$863$	49.9547	1.70048	0.850239	−	0.526397i	$-0.176457\pi$
$863$	49.9547	1.70048	0.850239	+	0.526397i	$0.176457\pi$
$864$	1.00000	0.0340207
$865$	32.2843	1.09770
$866$	29.9436	1.01752
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	11.3415	0.384733
$870$	−8.93130	−0.302800
$871$	−3.80575	−0.128953
$872$	8.11006	0.274641
$873$	−4.59492	−0.155514
$874$	−58.4102	−1.97576
$875$	0	0
$876$	0.856189	0.0289279
$877$	−10.3258	−0.348679	−0.174340	−	0.984686i	$-0.555779\pi$
$877$	−10.3258	−0.348679	−0.174340	+	0.984686i	$0.555779\pi$
$878$	3.99726	0.134901
$879$	−21.1659	−0.713906
$880$	2.61592	0.0881826
$881$	3.53298	0.119029	0.0595145	−	0.998227i	$-0.481045\pi$
$881$	3.53298	0.119029	0.0595145	+	0.998227i	$0.481045\pi$
$882$	0	0
$883$	−42.2207	−1.42084	−0.710419	−	0.703779i	$-0.751495\pi$
$883$	−42.2207	−1.42084	−0.710419	+	0.703779i	$0.751495\pi$
$884$	−4.51304	−0.151790
$885$	19.5932	0.658620
$886$	−22.9577	−0.771277
$887$	23.5310	0.790092	0.395046	−	0.918661i	$-0.370729\pi$
$887$	23.5310	0.790092	0.395046	+	0.918661i	$0.370729\pi$
$888$	4.37328	0.146758
$889$	0	0
$890$	−40.2700	−1.34985
$891$	−1.04094	−0.0348727
$892$	21.7852	0.729422
$893$	43.6793	1.46167
$894$	−4.71070	−0.157549
$895$	45.7449	1.52908
$896$	0	0
$897$	−31.4478	−1.05001
$898$	−8.82465	−0.294482
$899$	−26.8467	−0.895387
$900$	1.31538	0.0438461
$901$	8.51304	0.283611
$902$	1.41184	0.0470093
$903$	0	0
$904$	7.39936	0.246099
$905$	51.2219	1.70267
$906$	19.8755	0.660320
$907$	−40.7624	−1.35349	−0.676747	−	0.736215i	$-0.736611\pi$
$907$	−40.7624	−1.35349	−0.676747	+	0.736215i	$0.736611\pi$
$908$	8.39532	0.278608
$909$	9.07107	0.300868
$910$	0	0
$911$	−5.45683	−0.180793	−0.0903964	−	0.995906i	$-0.528813\pi$
$911$	−5.45683	−0.180793	−0.0903964	+	0.995906i	$0.528813\pi$
$912$	8.38241	0.277569
$913$	3.22568	0.106755
$914$	−4.37091	−0.144577
$915$	−1.87612	−0.0620227
$916$	25.4119	0.839633
$917$	0	0
$918$	1.00000	0.0330049
$919$	−29.6488	−0.978022	−0.489011	−	0.872277i	$-0.662642\pi$
$919$	−29.6488	−0.978022	−0.489011	+	0.872277i	$0.662642\pi$
$920$	−17.5114	−0.577333
$921$	−24.7987	−0.817146
$922$	−27.8968	−0.918731
$923$	63.6211	2.09411
$924$	0	0
$925$	5.75254	0.189142
$926$	7.14187	0.234696
$927$	−6.47615	−0.212705
$928$	−3.55398	−0.116665
$929$	12.3920	0.406567	0.203284	−	0.979120i	$-0.434839\pi$
$929$	12.3920	0.406567	0.203284	+	0.979120i	$0.434839\pi$
$930$	18.9835	0.622493
$931$	0	0
$932$	25.1720	0.824536
$933$	−16.0670	−0.526011
$934$	−15.6091	−0.510746
$935$	2.61592	0.0855497
$936$	4.51304	0.147513
$937$	24.1805	0.789942	0.394971	−	0.918694i	$-0.370755\pi$
$937$	24.1805	0.789942	0.394971	+	0.918694i	$0.370755\pi$
$938$	0	0
$939$	21.1682	0.690799
$940$	13.0950	0.427113
$941$	3.80040	0.123890	0.0619448	−	0.998080i	$-0.480270\pi$
$941$	3.80040	0.123890	0.0619448	+	0.998080i	$0.480270\pi$
$942$	−6.94421	−0.226255
$943$	−9.45110	−0.307770
$944$	7.79662	0.253758
$945$	0	0
$946$	−9.05385	−0.294366
$947$	−41.9109	−1.36192	−0.680961	−	0.732320i	$-0.738437\pi$
$947$	−41.9109	−1.36192	−0.680961	+	0.732320i	$0.738437\pi$
$948$	10.8954	0.353868
$949$	3.86402	0.125431
$950$	11.0261	0.357733
$951$	−14.2876	−0.463308
$952$	0	0
$953$	0.785286	0.0254379	0.0127190	−	0.999919i	$-0.495951\pi$
$953$	0.785286	0.0254379	0.0127190	+	0.999919i	$0.495951\pi$
$954$	−8.51304	−0.275620
$955$	−25.5046	−0.825310
$956$	−14.1192	−0.456647
$957$	3.69947	0.119587
$958$	39.6204	1.28008
$959$	0	0
$960$	2.51304	0.0811081
$961$	26.0626	0.840729
$962$	19.7368	0.636340
$963$	15.9364	0.513543
$964$	11.7909	0.379759
$965$	35.9837	1.15836
$966$	0	0
$967$	4.72555	0.151964	0.0759818	−	0.997109i	$-0.475791\pi$
$967$	4.72555	0.151964	0.0759818	+	0.997109i	$0.475791\pi$
$968$	9.91645	0.318727
$969$	8.38241	0.269282
$970$	−11.5472	−0.370759
$971$	20.0016	0.641881	0.320940	−	0.947099i	$-0.396001\pi$
$971$	20.0016	0.641881	0.320940	+	0.947099i	$0.396001\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−24.7839	−0.794127
$975$	5.93639	0.190116
$976$	−0.746554	−0.0238966
$977$	−15.3944	−0.492512	−0.246256	−	0.969205i	$-0.579200\pi$
$977$	−15.3944	−0.492512	−0.246256	+	0.969205i	$0.579200\pi$
$978$	11.8914	0.380245
$979$	16.6804	0.533108
$980$	0	0
$981$	−8.11006	−0.258934
$982$	−4.67338	−0.149134
$983$	−0.467023	−0.0148957	−0.00744786	−	0.999972i	$-0.502371\pi$
$983$	−0.467023	−0.0148957	−0.00744786	+	0.999972i	$0.502371\pi$
$984$	1.35632	0.0432379
$985$	−41.3754	−1.31833
$986$	−3.55398	−0.113182
$987$	0	0
$988$	37.8302	1.20354
$989$	60.6079	1.92722
$990$	−2.61592	−0.0831393
$991$	−44.7581	−1.42179	−0.710893	−	0.703300i	$-0.751709\pi$
$991$	−44.7581	−1.42179	−0.710893	+	0.703300i	$0.751709\pi$
$992$	7.55398	0.239839
$993$	15.8478	0.502913
$994$	0	0
$995$	−30.9577	−0.981424
$996$	3.09883	0.0981902
$997$	−58.5551	−1.85446	−0.927229	−	0.374494i	$-0.877816\pi$
$997$	−58.5551	−1.85446	−0.927229	+	0.374494i	$0.877816\pi$
$998$	−10.6643	−0.337573
$999$	−4.37328	−0.138364

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4998.2.a.cl.1.1	✓	4
7.6	odd	2		4998.2.a.cm.1.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4998.2.a.cl.1.1	✓	4	1.1	even	1	trivial
4998.2.a.cm.1.4	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.51304 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.51304 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.51304 q^{10} -1.04094 q^{11} -1.00000 q^{12} -4.51304 q^{13} +2.51304 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -8.38241 q^{19} -2.51304 q^{20} +1.04094 q^{22} -6.96819 q^{23} +1.00000 q^{24} +1.31538 q^{25} +4.51304 q^{26} -1.00000 q^{27} +3.55398 q^{29} -2.51304 q^{30} -7.55398 q^{31} -1.00000 q^{32} +1.04094 q^{33} -1.00000 q^{34} +1.00000 q^{36} +4.37328 q^{37} +8.38241 q^{38} +4.51304 q^{39} +2.51304 q^{40} +1.35632 q^{41} -8.69779 q^{43} -1.04094 q^{44} -2.51304 q^{45} +6.96819 q^{46} -5.21083 q^{47} -1.00000 q^{48} -1.31538 q^{50} -1.00000 q^{51} -4.51304 q^{52} +8.51304 q^{53} +1.00000 q^{54} +2.61592 q^{55} +8.38241 q^{57} -3.55398 q^{58} +7.79662 q^{59} +2.51304 q^{60} -0.746554 q^{61} +7.55398 q^{62} +1.00000 q^{64} +11.3415 q^{65} -1.04094 q^{66} +0.843278 q^{67} +1.00000 q^{68} +6.96819 q^{69} -14.0972 q^{71} -1.00000 q^{72} -0.856189 q^{73} -4.37328 q^{74} -1.31538 q^{75} -8.38241 q^{76} -4.51304 q^{78} -10.8954 q^{79} -2.51304 q^{80} +1.00000 q^{81} -1.35632 q^{82} -3.09883 q^{83} -2.51304 q^{85} +8.69779 q^{86} -3.55398 q^{87} +1.04094 q^{88} -16.0244 q^{89} +2.51304 q^{90} -6.96819 q^{92} +7.55398 q^{93} +5.21083 q^{94} +21.0653 q^{95} +1.00000 q^{96} -4.59492 q^{97} -1.04094 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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

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