LMFDB - Embedded newform 4998.2.a.cl.1.4

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			1.4
Root			$3.51304$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.51304 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.51304 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -3.51304 q^{10} +1.45515 q^{11} -1.00000 q^{12} +1.51304 q^{13} -3.51304 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +0.139766 q^{19} +3.51304 q^{20} -1.45515 q^{22} +1.55398 q^{23} +1.00000 q^{24} +7.34147 q^{25} -1.51304 q^{26} -1.00000 q^{27} -4.96819 q^{29} +3.51304 q^{30} +0.968193 q^{31} -1.00000 q^{32} -1.45515 q^{33} -1.00000 q^{34} +1.00000 q^{36} +6.86936 q^{37} -0.139766 q^{38} -1.51304 q^{39} -3.51304 q^{40} +4.88632 q^{41} -6.20170 q^{43} +1.45515 q^{44} +3.51304 q^{45} -1.55398 q^{46} +3.31134 q^{47} -1.00000 q^{48} -7.34147 q^{50} -1.00000 q^{51} +1.51304 q^{52} +2.48696 q^{53} +1.00000 q^{54} +5.11200 q^{55} -0.139766 q^{57} +4.96819 q^{58} -0.725552 q^{59} -3.51304 q^{60} -5.73873 q^{61} -0.968193 q^{62} +1.00000 q^{64} +5.31538 q^{65} +1.45515 q^{66} +10.3994 q^{67} +1.00000 q^{68} -1.55398 q^{69} -2.04498 q^{71} -1.00000 q^{72} +5.16990 q^{73} -6.86936 q^{74} -7.34147 q^{75} +0.139766 q^{76} +1.51304 q^{78} +3.65281 q^{79} +3.51304 q^{80} +1.00000 q^{81} -4.88632 q^{82} +2.92726 q^{83} +3.51304 q^{85} +6.20170 q^{86} +4.96819 q^{87} -1.45515 q^{88} +2.05385 q^{89} -3.51304 q^{90} +1.55398 q^{92} -0.968193 q^{93} -3.31134 q^{94} +0.491003 q^{95} +1.00000 q^{96} +6.42334 q^{97} +1.45515 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.51304	1.57108	0.785540	−	0.618811i	$-0.212385\pi$
$5$	3.51304	1.57108	0.785540	+	0.618811i	$0.212385\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.51304	−1.11092
$11$	1.45515	0.438744	0.219372	−	0.975641i	$-0.429599\pi$
$11$	1.45515	0.438744	0.219372	+	0.975641i	$0.429599\pi$
$12$	−1.00000	−0.288675
$13$	1.51304	0.419643	0.209821	−	0.977740i	$-0.432712\pi$
$13$	1.51304	0.419643	0.209821	+	0.977740i	$0.432712\pi$
$14$	0	0
$15$	−3.51304	−0.907064
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	0.139766	0.0320645	0.0160322	−	0.999871i	$-0.494897\pi$
$19$	0.139766	0.0320645	0.0160322	+	0.999871i	$0.494897\pi$
$20$	3.51304	0.785540
$21$	0	0
$22$	−1.45515	−0.310239
$23$	1.55398	0.324027	0.162014	−	0.986789i	$-0.448201\pi$
$23$	1.55398	0.324027	0.162014	+	0.986789i	$0.448201\pi$
$24$	1.00000	0.204124
$25$	7.34147	1.46829
$26$	−1.51304	−0.296732
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−4.96819	−0.922570	−0.461285	−	0.887252i	$-0.652611\pi$
$29$	−4.96819	−0.922570	−0.461285	+	0.887252i	$0.652611\pi$
$30$	3.51304	0.641391
$31$	0.968193	0.173893	0.0869463	−	0.996213i	$-0.472289\pi$
$31$	0.968193	0.173893	0.0869463	+	0.996213i	$0.472289\pi$
$32$	−1.00000	−0.176777
$33$	−1.45515	−0.253309
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	6.86936	1.12932	0.564658	−	0.825325i	$-0.309008\pi$
$37$	6.86936	1.12932	0.564658	+	0.825325i	$0.309008\pi$
$38$	−0.139766	−0.0226730
$39$	−1.51304	−0.242281
$40$	−3.51304	−0.555461
$41$	4.88632	0.763115	0.381557	−	0.924345i	$-0.375388\pi$
$41$	4.88632	0.763115	0.381557	+	0.924345i	$0.375388\pi$
$42$	0	0
$43$	−6.20170	−0.945751	−0.472876	−	0.881129i	$-0.656784\pi$
$43$	−6.20170	−0.945751	−0.472876	+	0.881129i	$0.656784\pi$
$44$	1.45515	0.219372
$45$	3.51304	0.523694
$46$	−1.55398	−0.229122
$47$	3.31134	0.483008	0.241504	−	0.970400i	$-0.422359\pi$
$47$	3.31134	0.483008	0.241504	+	0.970400i	$0.422359\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−7.34147	−1.03824
$51$	−1.00000	−0.140028
$52$	1.51304	0.209821
$53$	2.48696	0.341610	0.170805	−	0.985305i	$-0.445363\pi$
$53$	2.48696	0.341610	0.170805	+	0.985305i	$0.445363\pi$
$54$	1.00000	0.136083
$55$	5.11200	0.689303
$56$	0	0
$57$	−0.139766	−0.0185124
$58$	4.96819	0.652356
$59$	−0.725552	−0.0944588	−0.0472294	−	0.998884i	$-0.515039\pi$
$59$	−0.725552	−0.0944588	−0.0472294	+	0.998884i	$0.515039\pi$
$60$	−3.51304	−0.453532
$61$	−5.73873	−0.734769	−0.367384	−	0.930069i	$-0.619747\pi$
$61$	−5.73873	−0.734769	−0.367384	+	0.930069i	$0.619747\pi$
$62$	−0.968193	−0.122961
$63$	0	0
$64$	1.00000	0.125000
$65$	5.31538	0.659292
$66$	1.45515	0.179117
$67$	10.3994	1.27048	0.635242	−	0.772313i	$-0.280900\pi$
$67$	10.3994	1.27048	0.635242	+	0.772313i	$0.280900\pi$
$68$	1.00000	0.121268
$69$	−1.55398	−0.187077
$70$	0	0
$71$	−2.04498	−0.242695	−0.121347	−	0.992610i	$-0.538721\pi$
$71$	−2.04498	−0.242695	−0.121347	+	0.992610i	$0.538721\pi$
$72$	−1.00000	−0.117851
$73$	5.16990	0.605091	0.302545	−	0.953135i	$-0.402164\pi$
$73$	5.16990	0.605091	0.302545	+	0.953135i	$0.402164\pi$
$74$	−6.86936	−0.798547
$75$	−7.34147	−0.847720
$76$	0.139766	0.0160322
$77$	0	0
$78$	1.51304	0.171318
$79$	3.65281	0.410973	0.205487	−	0.978660i	$-0.434122\pi$
$79$	3.65281	0.410973	0.205487	+	0.978660i	$0.434122\pi$
$80$	3.51304	0.392770
$81$	1.00000	0.111111
$82$	−4.88632	−0.539604
$83$	2.92726	0.321308	0.160654	−	0.987011i	$-0.448640\pi$
$83$	2.92726	0.321308	0.160654	+	0.987011i	$0.448640\pi$
$84$	0	0
$85$	3.51304	0.381043
$86$	6.20170	0.668747
$87$	4.96819	0.532646
$88$	−1.45515	−0.155120
$89$	2.05385	0.217707	0.108854	−	0.994058i	$-0.465282\pi$
$89$	2.05385	0.217707	0.108854	+	0.994058i	$0.465282\pi$
$90$	−3.51304	−0.370307
$91$	0	0
$92$	1.55398	0.162014
$93$	−0.968193	−0.100397
$94$	−3.31134	−0.341538
$95$	0.491003	0.0503758
$96$	1.00000	0.102062
$97$	6.42334	0.652192	0.326096	−	0.945337i	$-0.394267\pi$
$97$	6.42334	0.652192	0.326096	+	0.945337i	$0.394267\pi$
$98$	0	0
$99$	1.45515	0.146248
$100$	7.34147	0.734147
$101$	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
$103$	−17.4944	−1.72378	−0.861888	−	0.507099i	$-0.830718\pi$
$103$	−17.4944	−1.72378	−0.861888	+	0.507099i	$0.830718\pi$
$104$	−1.51304	−0.148366
$105$	0	0
$106$	−2.48696	−0.241555
$107$	−1.10796	−0.107110	−0.0535552	−	0.998565i	$-0.517055\pi$
$107$	−1.10796	−0.107110	−0.0535552	+	0.998565i	$0.517055\pi$
$108$	−1.00000	−0.0962250
$109$	19.5243	1.87009	0.935043	−	0.354533i	$-0.115360\pi$
$109$	19.5243	1.87009	0.935043	+	0.354533i	$0.115360\pi$
$110$	−5.11200	−0.487410
$111$	−6.86936	−0.652011
$112$	0	0
$113$	2.15672	0.202887	0.101444	−	0.994841i	$-0.467654\pi$
$113$	2.15672	0.202887	0.101444	+	0.994841i	$0.467654\pi$
$114$	0.139766	0.0130903
$115$	5.45920	0.509073
$116$	−4.96819	−0.461285
$117$	1.51304	0.139881
$118$	0.725552	0.0667925
$119$	0	0
$120$	3.51304	0.320695
$121$	−8.88254	−0.807504
$122$	5.73873	0.519560
$123$	−4.88632	−0.440585
$124$	0.968193	0.0869463
$125$	8.22568	0.735728
$126$	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
$129$	6.20170	0.546030
$130$	−5.31538	−0.466190
$131$	−4.40341	−0.384728	−0.192364	−	0.981324i	$-0.561615\pi$
$131$	−4.40341	−0.384728	−0.192364	+	0.981324i	$0.561615\pi$
$132$	−1.45515	−0.126655
$133$	0	0
$134$	−10.3994	−0.898368
$135$	−3.51304	−0.302355
$136$	−1.00000	−0.0857493
$137$	−0.625047	−0.0534014	−0.0267007	−	0.999643i	$-0.508500\pi$
$137$	−0.625047	−0.0534014	−0.0267007	+	0.999643i	$0.508500\pi$
$138$	1.55398	0.132283
$139$	7.50732	0.636763	0.318381	−	0.947963i	$-0.396861\pi$
$139$	7.50732	0.636763	0.318381	+	0.947963i	$0.396861\pi$
$140$	0	0
$141$	−3.31134	−0.278865
$142$	2.04498	0.171611
$143$	2.20170	0.184116
$144$	1.00000	0.0833333
$145$	−17.4535	−1.44943
$146$	−5.16990	−0.427864
$147$	0	0
$148$	6.86936	0.564658
$149$	13.3676	1.09511	0.547556	−	0.836769i	$-0.315558\pi$
$149$	13.3676	1.09511	0.547556	+	0.836769i	$0.315558\pi$
$150$	7.34147	0.599429
$151$	21.3377	1.73644	0.868218	−	0.496183i	$-0.165265\pi$
$151$	21.3377	1.73644	0.868218	+	0.496183i	$0.165265\pi$
$152$	−0.139766	−0.0113365
$153$	1.00000	0.0808452
$154$	0	0
$155$	3.40130	0.273199
$156$	−1.51304	−0.121140
$157$	0.115786	0.00924070	0.00462035	−	0.999989i	$-0.498529\pi$
$157$	0.115786	0.00924070	0.00462035	+	0.999989i	$0.498529\pi$
$158$	−3.65281	−0.290602
$159$	−2.48696	−0.197229
$160$	−3.51304	−0.277730
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−17.2051	−1.34761	−0.673804	−	0.738910i	$-0.735341\pi$
$163$	−17.2051	−1.34761	−0.673804	+	0.738910i	$0.735341\pi$
$164$	4.88632	0.381557
$165$	−5.11200	−0.397969
$166$	−2.92726	−0.227199
$167$	−21.3618	−1.65303	−0.826514	−	0.562916i	$-0.809679\pi$
$167$	−21.3618	−1.65303	−0.826514	+	0.562916i	$0.809679\pi$
$168$	0	0
$169$	−10.7107	−0.823900
$170$	−3.51304	−0.269438
$171$	0.139766	0.0106882
$172$	−6.20170	−0.472876
$173$	9.18983	0.698690	0.349345	−	0.936994i	$-0.386404\pi$
$173$	9.18983	0.698690	0.349345	+	0.936994i	$0.386404\pi$
$174$	−4.96819	−0.376638
$175$	0	0
$176$	1.45515	0.109686
$177$	0.725552	0.0545358
$178$	−2.05385	−0.153942
$179$	0.303511	0.0226855	0.0113428	−	0.999936i	$-0.496389\pi$
$179$	0.303511	0.0226855	0.0113428	+	0.999936i	$0.496389\pi$
$180$	3.51304	0.261847
$181$	−11.8602	−0.881564	−0.440782	−	0.897614i	$-0.645299\pi$
$181$	−11.8602	−0.881564	−0.440782	+	0.897614i	$0.645299\pi$
$182$	0	0
$183$	5.73873	0.424219
$184$	−1.55398	−0.114561
$185$	24.1324	1.77425
$186$	0.968193	0.0709913
$187$	1.45515	0.106411
$188$	3.31134	0.241504
$189$	0	0
$190$	−0.491003	−0.0356211
$191$	−9.39154	−0.679548	−0.339774	−	0.940507i	$-0.610351\pi$
$191$	−9.39154	−0.679548	−0.339774	+	0.940507i	$0.610351\pi$
$192$	−1.00000	−0.0721688
$193$	11.2477	0.809629	0.404814	−	0.914399i	$-0.367336\pi$
$193$	11.2477	0.809629	0.404814	+	0.914399i	$0.367336\pi$
$194$	−6.42334	−0.461169
$195$	−5.31538	−0.380643
$196$	0	0
$197$	2.94993	0.210174	0.105087	−	0.994463i	$-0.466488\pi$
$197$	2.94993	0.210174	0.105087	+	0.994463i	$0.466488\pi$
$198$	−1.45515	−0.103413
$199$	−13.2477	−0.939106	−0.469553	−	0.882904i	$-0.655585\pi$
$199$	−13.2477	−0.939106	−0.469553	+	0.882904i	$0.655585\pi$
$200$	−7.34147	−0.519120
$201$	−10.3994	−0.733514
$202$	−9.07107	−0.638238
$203$	0	0
$204$	−1.00000	−0.0700140
$205$	17.1659	1.19892
$206$	17.4944	1.21889
$207$	1.55398	0.108009
$208$	1.51304	0.104911
$209$	0.203380	0.0140681
$210$	0	0
$211$	11.3845	0.783742	0.391871	−	0.920020i	$-0.371828\pi$
$211$	11.3845	0.783742	0.391871	+	0.920020i	$0.371828\pi$
$212$	2.48696	0.170805
$213$	2.04498	0.140120
$214$	1.10796	0.0757385
$215$	−21.7869	−1.48585
$216$	1.00000	0.0680414
$217$	0	0
$218$	−19.5243	−1.32235
$219$	−5.16990	−0.349349
$220$	5.11200	0.344651
$221$	1.51304	0.101778
$222$	6.86936	0.461041
$223$	−27.8857	−1.86736	−0.933682	−	0.358104i	$-0.883423\pi$
$223$	−27.8857	−1.86736	−0.933682	+	0.358104i	$0.883423\pi$
$224$	0	0
$225$	7.34147	0.489431
$226$	−2.15672	−0.143463
$227$	−15.7090	−1.04264	−0.521322	−	0.853360i	$-0.674561\pi$
$227$	−15.7090	−1.04264	−0.521322	+	0.853360i	$0.674561\pi$
$228$	−0.139766	−0.00925621
$229$	−26.7550	−1.76802	−0.884012	−	0.467465i	$-0.845167\pi$
$229$	−26.7550	−1.76802	−0.884012	+	0.467465i	$0.845167\pi$
$230$	−5.45920	−0.359969
$231$	0	0
$232$	4.96819	0.326178
$233$	8.55592	0.560517	0.280258	−	0.959925i	$-0.409580\pi$
$233$	8.55592	0.560517	0.280258	+	0.959925i	$0.409580\pi$
$234$	−1.51304	−0.0989107
$235$	11.6329	0.758845
$236$	−0.725552	−0.0472294
$237$	−3.65281	−0.237275
$238$	0	0
$239$	24.5334	1.58693	0.793467	−	0.608613i	$-0.208274\pi$
$239$	24.5334	1.58693	0.793467	+	0.608613i	$0.208274\pi$
$240$	−3.51304	−0.226766
$241$	−17.3056	−1.11475	−0.557376	−	0.830260i	$-0.688192\pi$
$241$	−17.3056	−1.11475	−0.557376	+	0.830260i	$0.688192\pi$
$242$	8.88254	0.570991
$243$	−1.00000	−0.0641500
$244$	−5.73873	−0.367384
$245$	0	0
$246$	4.88632	0.311540
$247$	0.211471	0.0134556
$248$	−0.968193	−0.0614803
$249$	−2.92726	−0.185507
$250$	−8.22568	−0.520238
$251$	0.711339	0.0448993	0.0224497	−	0.999748i	$-0.492853\pi$
$251$	0.711339	0.0448993	0.0224497	+	0.999748i	$0.492853\pi$
$252$	0	0
$253$	2.26127	0.142165
$254$	0.828427	0.0519801
$255$	−3.51304	−0.219995
$256$	1.00000	0.0625000
$257$	20.4416	1.27511	0.637556	−	0.770404i	$-0.279945\pi$
$257$	20.4416	1.27511	0.637556	+	0.770404i	$0.279945\pi$
$258$	−6.20170	−0.386101
$259$	0	0
$260$	5.31538	0.329646
$261$	−4.96819	−0.307523
$262$	4.40341	0.272043
$263$	25.7050	1.58504	0.792518	−	0.609848i	$-0.208769\pi$
$263$	25.7050	1.58504	0.792518	+	0.609848i	$0.208769\pi$
$264$	1.45515	0.0895583
$265$	8.73679	0.536697
$266$	0	0
$267$	−2.05385	−0.125693
$268$	10.3994	0.635242
$269$	21.5593	1.31450	0.657248	−	0.753675i	$-0.271721\pi$
$269$	21.5593	1.31450	0.657248	+	0.753675i	$0.271721\pi$
$270$	3.51304	0.213797
$271$	−7.39428	−0.449170	−0.224585	−	0.974454i	$-0.572103\pi$
$271$	−7.39428	−0.449170	−0.224585	+	0.974454i	$0.572103\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	0.625047	0.0377605
$275$	10.6829	0.644206
$276$	−1.55398	−0.0935386
$277$	1.24054	0.0745365	0.0372683	−	0.999305i	$-0.488134\pi$
$277$	1.24054	0.0745365	0.0372683	+	0.999305i	$0.488134\pi$
$278$	−7.50732	−0.450259
$279$	0.968193	0.0579642
$280$	0	0
$281$	−14.6011	−0.871027	−0.435513	−	0.900182i	$-0.643433\pi$
$281$	−14.6011	−0.871027	−0.435513	+	0.900182i	$0.643433\pi$
$282$	3.31134	0.197187
$283$	−11.2914	−0.671204	−0.335602	−	0.942004i	$-0.608940\pi$
$283$	−11.2914	−0.671204	−0.335602	+	0.942004i	$0.608940\pi$
$284$	−2.04498	−0.121347
$285$	−0.491003	−0.0290845
$286$	−2.20170	−0.130190
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	17.4535	1.02490
$291$	−6.42334	−0.376543
$292$	5.16990	0.302545
$293$	0.591508	0.0345563	0.0172781	−	0.999851i	$-0.494500\pi$
$293$	0.591508	0.0345563	0.0172781	+	0.999851i	$0.494500\pi$
$294$	0	0
$295$	−2.54890	−0.148402
$296$	−6.86936	−0.399274
$297$	−1.45515	−0.0844364
$298$	−13.3676	−0.774362
$299$	2.35124	0.135976
$300$	−7.34147	−0.423860
$301$	0	0
$302$	−21.3377	−1.22785
$303$	−9.07107	−0.521119
$304$	0.139766	0.00801611
$305$	−20.1604	−1.15438
$306$	−1.00000	−0.0571662
$307$	5.68656	0.324549	0.162274	−	0.986746i	$-0.448117\pi$
$307$	5.68656	0.324549	0.162274	+	0.986746i	$0.448117\pi$
$308$	0	0
$309$	17.4944	0.995222
$310$	−3.40130	−0.193181
$311$	1.51876	0.0861212	0.0430606	−	0.999072i	$-0.486289\pi$
$311$	1.51876	0.0861212	0.0430606	+	0.999072i	$0.486289\pi$
$312$	1.51304	0.0856592
$313$	−9.11605	−0.515270	−0.257635	−	0.966242i	$-0.582943\pi$
$313$	−9.11605	−0.515270	−0.257635	+	0.966242i	$0.582943\pi$
$314$	−0.115786	−0.00653416
$315$	0	0
$316$	3.65281	0.205487
$317$	26.3398	1.47939	0.739695	−	0.672942i	$-0.234970\pi$
$317$	26.3398	1.47939	0.739695	+	0.672942i	$0.234970\pi$
$318$	2.48696	0.139462
$319$	−7.22947	−0.404772
$320$	3.51304	0.196385
$321$	1.10796	0.0618402
$322$	0	0
$323$	0.139766	0.00777677
$324$	1.00000	0.0555556
$325$	11.1080	0.616159
$326$	17.2051	0.952903
$327$	−19.5243	−1.07970
$328$	−4.88632	−0.269802
$329$	0	0
$330$	5.11200	0.281407
$331$	−23.3360	−1.28266	−0.641332	−	0.767264i	$-0.721618\pi$
$331$	−23.3360	−1.28266	−0.641332	+	0.767264i	$0.721618\pi$
$332$	2.92726	0.160654
$333$	6.86936	0.376439
$334$	21.3618	1.16887
$335$	36.5334	1.99603
$336$	0	0
$337$	23.6569	1.28867	0.644335	−	0.764743i	$-0.277134\pi$
$337$	23.6569	1.28867	0.644335	+	0.764743i	$0.277134\pi$
$338$	10.7107	0.582585
$339$	−2.15672	−0.117137
$340$	3.51304	0.190521
$341$	1.40887	0.0762944
$342$	−0.139766	−0.00755766
$343$	0	0
$344$	6.20170	0.334373
$345$	−5.45920	−0.293913
$346$	−9.18983	−0.494048
$347$	34.9287	1.87507	0.937536	−	0.347888i	$-0.113101\pi$
$347$	34.9287	1.87507	0.937536	+	0.347888i	$0.113101\pi$
$348$	4.96819	0.266323
$349$	−23.9347	−1.28120	−0.640598	−	0.767877i	$-0.721313\pi$
$349$	−23.9347	−1.28120	−0.640598	+	0.767877i	$0.721313\pi$
$350$	0	0
$351$	−1.51304	−0.0807603
$352$	−1.45515	−0.0775598
$353$	28.5913	1.52176	0.760881	−	0.648892i	$-0.224767\pi$
$353$	28.5913	1.52176	0.760881	+	0.648892i	$0.224767\pi$
$354$	−0.725552	−0.0385627
$355$	−7.18411	−0.381293
$356$	2.05385	0.108854
$357$	0	0
$358$	−0.303511	−0.0160411
$359$	9.93639	0.524422	0.262211	−	0.965011i	$-0.415548\pi$
$359$	9.93639	0.524422	0.262211	+	0.965011i	$0.415548\pi$
$360$	−3.51304	−0.185154
$361$	−18.9805	−0.998972
$362$	11.8602	0.623360
$363$	8.88254	0.466212
$364$	0	0
$365$	18.1621	0.950646
$366$	−5.73873	−0.299968
$367$	2.73846	0.142947	0.0714733	−	0.997443i	$-0.477230\pi$
$367$	2.73846	0.142947	0.0714733	+	0.997443i	$0.477230\pi$
$368$	1.55398	0.0810068
$369$	4.88632	0.254372
$370$	−24.1324	−1.25458
$371$	0	0
$372$	−0.968193	−0.0501985
$373$	31.8968	1.65155	0.825776	−	0.563999i	$-0.190738\pi$
$373$	31.8968	1.65155	0.825776	+	0.563999i	$0.190738\pi$
$374$	−1.45515	−0.0752440
$375$	−8.22568	−0.424773
$376$	−3.31134	−0.170769
$377$	−7.51709	−0.387150
$378$	0	0
$379$	−17.4367	−0.895662	−0.447831	−	0.894118i	$-0.647803\pi$
$379$	−17.4367	−0.895662	−0.447831	+	0.894118i	$0.647803\pi$
$380$	0.491003	0.0251879
$381$	0.828427	0.0424416
$382$	9.39154	0.480513
$383$	15.9124	0.813086	0.406543	−	0.913632i	$-0.366734\pi$
$383$	15.9124	0.813086	0.406543	+	0.913632i	$0.366734\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−11.2477	−0.572494
$387$	−6.20170	−0.315250
$388$	6.42334	0.326096
$389$	−10.4217	−0.528399	−0.264200	−	0.964468i	$-0.585108\pi$
$389$	−10.4217	−0.528399	−0.264200	+	0.964468i	$0.585108\pi$
$390$	5.31538	0.269155
$391$	1.55398	0.0785881
$392$	0	0
$393$	4.40341	0.222123
$394$	−2.94993	−0.148616
$395$	12.8325	0.645672
$396$	1.45515	0.0731240
$397$	20.7648	1.04216	0.521078	−	0.853509i	$-0.325530\pi$
$397$	20.7648	1.04216	0.521078	+	0.853509i	$0.325530\pi$
$398$	13.2477	0.664048
$399$	0	0
$400$	7.34147	0.367073
$401$	10.2924	0.513980	0.256990	−	0.966414i	$-0.417269\pi$
$401$	10.2924	0.513980	0.256990	+	0.966414i	$0.417269\pi$
$402$	10.3994	0.518673
$403$	1.46492	0.0729727
$404$	9.07107	0.451302
$405$	3.51304	0.174565
$406$	0	0
$407$	9.99595	0.495481
$408$	1.00000	0.0495074
$409$	14.3063	0.707399	0.353699	−	0.935359i	$-0.384924\pi$
$409$	14.3063	0.707399	0.353699	+	0.935359i	$0.384924\pi$
$410$	−17.1659	−0.847761
$411$	0.625047	0.0308313
$412$	−17.4944	−0.861888
$413$	0	0
$414$	−1.55398	−0.0763739
$415$	10.2836	0.504801
$416$	−1.51304	−0.0741830
$417$	−7.50732	−0.367635
$418$	−0.203380	−0.00994764
$419$	−7.59896	−0.371234	−0.185617	−	0.982622i	$-0.559428\pi$
$419$	−7.59896	−0.371234	−0.185617	+	0.982622i	$0.559428\pi$
$420$	0	0
$421$	−30.9648	−1.50913	−0.754567	−	0.656223i	$-0.772153\pi$
$421$	−30.9648	−1.50913	−0.754567	+	0.656223i	$0.772153\pi$
$422$	−11.3845	−0.554189
$423$	3.31134	0.161003
$424$	−2.48696	−0.120777
$425$	7.34147	0.356114
$426$	−2.04498	−0.0990797
$427$	0	0
$428$	−1.10796	−0.0535552
$429$	−2.20170	−0.106299
$430$	21.7869	1.05066
$431$	−22.1973	−1.06921	−0.534603	−	0.845103i	$-0.679539\pi$
$431$	−22.1973	−1.06921	−0.534603	+	0.845103i	$0.679539\pi$
$432$	−1.00000	−0.0481125
$433$	23.2573	1.11767	0.558837	−	0.829278i	$-0.311248\pi$
$433$	23.2573	1.11767	0.558837	+	0.829278i	$0.311248\pi$
$434$	0	0
$435$	17.4535	0.836830
$436$	19.5243	0.935043
$437$	0.217193	0.0103897
$438$	5.16990	0.247027
$439$	31.5536	1.50597	0.752986	−	0.658037i	$-0.228613\pi$
$439$	31.5536	1.50597	0.752986	+	0.658037i	$0.228613\pi$
$440$	−5.11200	−0.243705
$441$	0	0
$442$	−1.51304	−0.0719681
$443$	38.5398	1.83108	0.915541	−	0.402224i	$-0.131763\pi$
$443$	38.5398	1.83108	0.915541	+	0.402224i	$0.131763\pi$
$444$	−6.86936	−0.326006
$445$	7.21525	0.342036
$446$	27.8857	1.32043
$447$	−13.3676	−0.632264
$448$	0	0
$449$	13.3886	0.631845	0.315923	−	0.948785i	$-0.397686\pi$
$449$	13.3886	0.631845	0.315923	+	0.948785i	$0.397686\pi$
$450$	−7.34147	−0.346080
$451$	7.11033	0.334812
$452$	2.15672	0.101444
$453$	−21.3377	−1.00253
$454$	15.7090	0.737261
$455$	0	0
$456$	0.139766	0.00654513
$457$	−1.65518	−0.0774260	−0.0387130	−	0.999250i	$-0.512326\pi$
$457$	−1.65518	−0.0774260	−0.0387130	+	0.999250i	$0.512326\pi$
$458$	26.7550	1.25018
$459$	−1.00000	−0.0466760
$460$	5.45920	0.254536
$461$	−7.65411	−0.356487	−0.178244	−	0.983986i	$-0.557042\pi$
$461$	−7.65411	−0.356487	−0.178244	+	0.983986i	$0.557042\pi$
$462$	0	0
$463$	11.9703	0.556307	0.278153	−	0.960537i	$-0.410278\pi$
$463$	11.9703	0.556307	0.278153	+	0.960537i	$0.410278\pi$
$464$	−4.96819	−0.230643
$465$	−3.40130	−0.157732
$466$	−8.55592	−0.396345
$467$	−31.9939	−1.48050	−0.740251	−	0.672331i	$-0.765293\pi$
$467$	−31.9939	−1.48050	−0.740251	+	0.672331i	$0.765293\pi$
$468$	1.51304	0.0699404
$469$	0	0
$470$	−11.6329	−0.536584
$471$	−0.115786	−0.00533512
$472$	0.725552	0.0333962
$473$	−9.02441	−0.414943
$474$	3.65281	0.167779
$475$	1.02609	0.0470800
$476$	0	0
$477$	2.48696	0.113870
$478$	−24.5334	−1.12213
$479$	−40.0487	−1.82987	−0.914935	−	0.403602i	$-0.867758\pi$
$479$	−40.0487	−1.82987	−0.914935	+	0.403602i	$0.867758\pi$
$480$	3.51304	0.160348
$481$	10.3936	0.473909
$482$	17.3056	0.788249
$483$	0	0
$484$	−8.88254	−0.403752
$485$	22.5655	1.02465
$486$	1.00000	0.0453609
$487$	−3.88438	−0.176018	−0.0880090	−	0.996120i	$-0.528050\pi$
$487$	−3.88438	−0.176018	−0.0880090	+	0.996120i	$0.528050\pi$
$488$	5.73873	0.259780
$489$	17.2051	0.778042
$490$	0	0
$491$	20.2556	0.914120	0.457060	−	0.889436i	$-0.348902\pi$
$491$	20.2556	0.914120	0.457060	+	0.889436i	$0.348902\pi$
$492$	−4.88632	−0.220292
$493$	−4.96819	−0.223756
$494$	−0.211471	−0.00951455
$495$	5.11200	0.229768
$496$	0.968193	0.0434731
$497$	0	0
$498$	2.92726	0.131173
$499$	−6.38004	−0.285610	−0.142805	−	0.989751i	$-0.545612\pi$
$499$	−6.38004	−0.285610	−0.142805	+	0.989751i	$0.545612\pi$
$500$	8.22568	0.367864
$501$	21.3618	0.954376
$502$	−0.711339	−0.0317486
$503$	33.5479	1.49583	0.747913	−	0.663797i	$-0.231056\pi$
$503$	33.5479	1.49583	0.747913	+	0.663797i	$0.231056\pi$
$504$	0	0
$505$	31.8670	1.41807
$506$	−2.26127	−0.100526
$507$	10.7107	0.475679
$508$	−0.828427	−0.0367555
$509$	22.2849	0.987760	0.493880	−	0.869530i	$-0.335578\pi$
$509$	22.2849	0.987760	0.493880	+	0.869530i	$0.335578\pi$
$510$	3.51304	0.155560
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−0.139766	−0.00617081
$514$	−20.4416	−0.901640
$515$	−61.4586	−2.70819
$516$	6.20170	0.273015
$517$	4.81849	0.211917
$518$	0	0
$519$	−9.18983	−0.403389
$520$	−5.31538	−0.233095
$521$	−11.0657	−0.484798	−0.242399	−	0.970177i	$-0.577934\pi$
$521$	−11.0657	−0.484798	−0.242399	+	0.970177i	$0.577934\pi$
$522$	4.96819	0.217452
$523$	13.9181	0.608597	0.304299	−	0.952577i	$-0.401578\pi$
$523$	13.9181	0.608597	0.304299	+	0.952577i	$0.401578\pi$
$524$	−4.40341	−0.192364
$525$	0	0
$526$	−25.7050	−1.12079
$527$	0.968193	0.0421751
$528$	−1.45515	−0.0633273
$529$	−20.5851	−0.895006
$530$	−8.73679	−0.379502
$531$	−0.725552	−0.0314863
$532$	0	0
$533$	7.39321	0.320236
$534$	2.05385	0.0888787
$535$	−3.89231	−0.168279
$536$	−10.3994	−0.449184
$537$	−0.303511	−0.0130975
$538$	−21.5593	−0.929489
$539$	0	0
$540$	−3.51304	−0.151177
$541$	8.72723	0.375213	0.187606	−	0.982244i	$-0.439927\pi$
$541$	8.72723	0.375213	0.187606	+	0.982244i	$0.439927\pi$
$542$	7.39428	0.317611
$543$	11.8602	0.508971
$544$	−1.00000	−0.0428746
$545$	68.5896	2.93806
$546$	0	0
$547$	−21.2075	−0.906766	−0.453383	−	0.891316i	$-0.649783\pi$
$547$	−21.2075	−0.906766	−0.453383	+	0.891316i	$0.649783\pi$
$548$	−0.625047	−0.0267007
$549$	−5.73873	−0.244923
$550$	−10.6829	−0.455522
$551$	−0.694383	−0.0295817
$552$	1.55398	0.0661417
$553$	0	0
$554$	−1.24054	−0.0527053
$555$	−24.1324	−1.02436
$556$	7.50732	0.318381
$557$	14.2876	0.605386	0.302693	−	0.953088i	$-0.402114\pi$
$557$	14.2876	0.605386	0.302693	+	0.953088i	$0.402114\pi$
$558$	−0.968193	−0.0409869
$559$	−9.38344	−0.396877
$560$	0	0
$561$	−1.45515	−0.0614365
$562$	14.6011	0.615909
$563$	−22.7262	−0.957797	−0.478899	−	0.877870i	$-0.658964\pi$
$563$	−22.7262	−0.957797	−0.478899	+	0.877870i	$0.658964\pi$
$564$	−3.31134	−0.139433
$565$	7.57666	0.318752
$566$	11.2914	0.474613
$567$	0	0
$568$	2.04498	0.0858055
$569$	36.2944	1.52154	0.760771	−	0.649020i	$-0.224821\pi$
$569$	36.2944	1.52154	0.760771	+	0.649020i	$0.224821\pi$
$570$	0.491003	0.0205658
$571$	39.9402	1.67145	0.835723	−	0.549151i	$-0.185049\pi$
$571$	39.9402	1.67145	0.835723	+	0.549151i	$0.185049\pi$
$572$	2.20170	0.0920579
$573$	9.39154	0.392337
$574$	0	0
$575$	11.4085	0.475767
$576$	1.00000	0.0416667
$577$	19.4348	0.809083	0.404542	−	0.914520i	$-0.367431\pi$
$577$	19.4348	0.809083	0.404542	+	0.914520i	$0.367431\pi$
$578$	−1.00000	−0.0415945
$579$	−11.2477	−0.467439
$580$	−17.4535	−0.724716
$581$	0	0
$582$	6.42334	0.266256
$583$	3.61890	0.149879
$584$	−5.16990	−0.213932
$585$	5.31538	0.219764
$586$	−0.591508	−0.0244350
$587$	10.2524	0.423162	0.211581	−	0.977360i	$-0.432139\pi$
$587$	10.2524	0.423162	0.211581	+	0.977360i	$0.432139\pi$
$588$	0	0
$589$	0.135320	0.00557577
$590$	2.54890	0.104936
$591$	−2.94993	−0.121344
$592$	6.86936	0.282329
$593$	−17.2318	−0.707627	−0.353813	−	0.935316i	$-0.615115\pi$
$593$	−17.2318	−0.707627	−0.353813	+	0.935316i	$0.615115\pi$
$594$	1.45515	0.0597055
$595$	0	0
$596$	13.3676	0.547556
$597$	13.2477	0.542193
$598$	−2.35124	−0.0961492
$599$	8.80468	0.359750	0.179875	−	0.983690i	$-0.442431\pi$
$599$	8.80468	0.359750	0.179875	+	0.983690i	$0.442431\pi$
$600$	7.34147	0.299714
$601$	22.1043	0.901655	0.450827	−	0.892611i	$-0.351129\pi$
$601$	22.1043	0.901655	0.450827	+	0.892611i	$0.351129\pi$
$602$	0	0
$603$	10.3994	0.423495
$604$	21.3377	0.868218
$605$	−31.2047	−1.26865
$606$	9.07107	0.368487
$607$	25.9388	1.05282	0.526411	−	0.850230i	$-0.323537\pi$
$607$	25.9388	1.05282	0.526411	+	0.850230i	$0.323537\pi$
$608$	−0.139766	−0.00566825
$609$	0	0
$610$	20.1604	0.816270
$611$	5.01020	0.202691
$612$	1.00000	0.0404226
$613$	45.8590	1.85223	0.926113	−	0.377246i	$-0.123129\pi$
$613$	45.8590	1.85223	0.926113	+	0.377246i	$0.123129\pi$
$614$	−5.68656	−0.229491
$615$	−17.1659	−0.692194
$616$	0	0
$617$	9.43652	0.379900	0.189950	−	0.981794i	$-0.439167\pi$
$617$	9.43652	0.379900	0.189950	+	0.981794i	$0.439167\pi$
$618$	−17.4944	−0.703728
$619$	−24.0265	−0.965707	−0.482854	−	0.875701i	$-0.660400\pi$
$619$	−24.0265	−0.965707	−0.482854	+	0.875701i	$0.660400\pi$
$620$	3.40130	0.136600
$621$	−1.55398	−0.0623590
$622$	−1.51876	−0.0608969
$623$	0	0
$624$	−1.51304	−0.0605702
$625$	−7.81017	−0.312407
$626$	9.11605	0.364351
$627$	−0.203380	−0.00812222
$628$	0.115786	0.00462035
$629$	6.86936	0.273899
$630$	0	0
$631$	−16.4532	−0.654992	−0.327496	−	0.944853i	$-0.606205\pi$
$631$	−16.4532	−0.654992	−0.327496	+	0.944853i	$0.606205\pi$
$632$	−3.65281	−0.145301
$633$	−11.3845	−0.452494
$634$	−26.3398	−1.04609
$635$	−2.91030	−0.115492
$636$	−2.48696	−0.0986143
$637$	0	0
$638$	7.22947	0.286217
$639$	−2.04498	−0.0808982
$640$	−3.51304	−0.138865
$641$	4.40990	0.174181	0.0870904	−	0.996200i	$-0.472243\pi$
$641$	4.40990	0.174181	0.0870904	+	0.996200i	$0.472243\pi$
$642$	−1.10796	−0.0437276
$643$	−25.7712	−1.01632	−0.508158	−	0.861264i	$-0.669674\pi$
$643$	−25.7712	−1.01632	−0.508158	+	0.861264i	$0.669674\pi$
$644$	0	0
$645$	21.7869	0.857856
$646$	−0.139766	−0.00549901
$647$	−1.05816	−0.0416004	−0.0208002	−	0.999784i	$-0.506621\pi$
$647$	−1.05816	−0.0416004	−0.0208002	+	0.999784i	$0.506621\pi$
$648$	−1.00000	−0.0392837
$649$	−1.05579	−0.0414433
$650$	−11.1080	−0.435690
$651$	0	0
$652$	−17.2051	−0.673804
$653$	26.5714	1.03982	0.519909	−	0.854222i	$-0.325966\pi$
$653$	26.5714	1.03982	0.519909	+	0.854222i	$0.325966\pi$
$654$	19.5243	0.763460
$655$	−15.4694	−0.604438
$656$	4.88632	0.190779
$657$	5.16990	0.201697
$658$	0	0
$659$	−27.6535	−1.07723	−0.538614	−	0.842553i	$-0.681052\pi$
$659$	−27.6535	−1.07723	−0.538614	+	0.842553i	$0.681052\pi$
$660$	−5.11200	−0.198984
$661$	−11.7348	−0.456433	−0.228216	−	0.973610i	$-0.573289\pi$
$661$	−11.7348	−0.456433	−0.228216	+	0.973610i	$0.573289\pi$
$662$	23.3360	0.906980
$663$	−1.51304	−0.0587617
$664$	−2.92726	−0.113600
$665$	0	0
$666$	−6.86936	−0.266182
$667$	−7.72047	−0.298938
$668$	−21.3618	−0.826514
$669$	27.8857	1.07812
$670$	−36.5334	−1.41141
$671$	−8.35071	−0.322376
$672$	0	0
$673$	10.9424	0.421797	0.210899	−	0.977508i	$-0.432361\pi$
$673$	10.9424	0.421797	0.210899	+	0.977508i	$0.432361\pi$
$674$	−23.6569	−0.911228
$675$	−7.34147	−0.282573
$676$	−10.7107	−0.411950
$677$	37.9347	1.45795	0.728975	−	0.684541i	$-0.239997\pi$
$677$	37.9347	1.45795	0.728975	+	0.684541i	$0.239997\pi$
$678$	2.15672	0.0828284
$679$	0	0
$680$	−3.51304	−0.134719
$681$	15.7090	0.601971
$682$	−1.40887	−0.0539483
$683$	30.4657	1.16574	0.582870	−	0.812566i	$-0.301930\pi$
$683$	30.4657	1.16574	0.582870	+	0.812566i	$0.301930\pi$
$684$	0.139766	0.00534408
$685$	−2.19582	−0.0838979
$686$	0	0
$687$	26.7550	1.02077
$688$	−6.20170	−0.236438
$689$	3.76287	0.143354
$690$	5.45920	0.207828
$691$	0.417621	0.0158871	0.00794353	−	0.999968i	$-0.497471\pi$
$691$	0.417621	0.0158871	0.00794353	+	0.999968i	$0.497471\pi$
$692$	9.18983	0.349345
$693$	0	0
$694$	−34.9287	−1.32588
$695$	26.3735	1.00041
$696$	−4.96819	−0.188319
$697$	4.88632	0.185083
$698$	23.9347	0.905942
$699$	−8.55592	−0.323615
$700$	0	0
$701$	−40.8072	−1.54127	−0.770634	−	0.637278i	$-0.780060\pi$
$701$	−40.8072	−1.54127	−0.770634	+	0.637278i	$0.780060\pi$
$702$	1.51304	0.0571061
$703$	0.960101	0.0362109
$704$	1.45515	0.0548430
$705$	−11.6329	−0.438119
$706$	−28.5913	−1.07605
$707$	0	0
$708$	0.725552	0.0272679
$709$	−40.0261	−1.50321	−0.751607	−	0.659612i	$-0.770721\pi$
$709$	−40.0261	−1.50321	−0.751607	+	0.659612i	$0.770721\pi$
$710$	7.18411	0.269615
$711$	3.65281	0.136991
$712$	−2.05385	−0.0769712
$713$	1.50455	0.0563459
$714$	0	0
$715$	7.73468	0.289261
$716$	0.303511	0.0113428
$717$	−24.5334	−0.916217
$718$	−9.93639	−0.370823
$719$	−20.5111	−0.764935	−0.382468	−	0.923969i	$-0.624926\pi$
$719$	−20.5111	−0.764935	−0.382468	+	0.923969i	$0.624926\pi$
$720$	3.51304	0.130923
$721$	0	0
$722$	18.9805	0.706380
$723$	17.3056	0.643603
$724$	−11.8602	−0.440782
$725$	−36.4738	−1.35460
$726$	−8.88254	−0.329662
$727$	−18.1693	−0.673861	−0.336930	−	0.941530i	$-0.609389\pi$
$727$	−18.1693	−0.673861	−0.336930	+	0.941530i	$0.609389\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−18.1621	−0.672208
$731$	−6.20170	−0.229378
$732$	5.73873	0.212109
$733$	−27.2577	−1.00678	−0.503392	−	0.864058i	$-0.667915\pi$
$733$	−27.2577	−1.00678	−0.503392	+	0.864058i	$0.667915\pi$
$734$	−2.73846	−0.101079
$735$	0	0
$736$	−1.55398	−0.0572804
$737$	15.1326	0.557418
$738$	−4.88632	−0.179868
$739$	23.8071	0.875758	0.437879	−	0.899034i	$-0.355730\pi$
$739$	23.8071	0.875758	0.437879	+	0.899034i	$0.355730\pi$
$740$	24.1324	0.887124
$741$	−0.211471	−0.00776860
$742$	0	0
$743$	13.6218	0.499736	0.249868	−	0.968280i	$-0.419613\pi$
$743$	13.6218	0.499736	0.249868	+	0.968280i	$0.419613\pi$
$744$	0.968193	0.0354957
$745$	46.9608	1.72051
$746$	−31.8968	−1.16782
$747$	2.92726	0.107103
$748$	1.45515	0.0532056
$749$	0	0
$750$	8.22568	0.300360
$751$	14.5375	0.530479	0.265240	−	0.964183i	$-0.414549\pi$
$751$	14.5375	0.530479	0.265240	+	0.964183i	$0.414549\pi$
$752$	3.31134	0.120752
$753$	−0.711339	−0.0259226
$754$	7.51709	0.273756
$755$	74.9602	2.72808
$756$	0	0
$757$	−42.8457	−1.55725	−0.778627	−	0.627487i	$-0.784083\pi$
$757$	−42.8457	−1.55725	−0.778627	+	0.627487i	$0.784083\pi$
$758$	17.4367	0.633329
$759$	−2.26127	−0.0820790
$760$	−0.491003	−0.0178105
$761$	28.7665	1.04278	0.521392	−	0.853317i	$-0.325413\pi$
$761$	28.7665	1.04278	0.521392	+	0.853317i	$0.325413\pi$
$762$	−0.828427	−0.0300107
$763$	0	0
$764$	−9.39154	−0.339774
$765$	3.51304	0.127014
$766$	−15.9124	−0.574939
$767$	−1.09779	−0.0396390
$768$	−1.00000	−0.0360844
$769$	−0.813146	−0.0293228	−0.0146614	−	0.999893i	$-0.504667\pi$
$769$	−0.813146	−0.0293228	−0.0146614	+	0.999893i	$0.504667\pi$
$770$	0	0
$771$	−20.4416	−0.736186
$772$	11.2477	0.404814
$773$	−48.0096	−1.72678	−0.863392	−	0.504534i	$-0.831664\pi$
$773$	−48.0096	−1.72678	−0.863392	+	0.504534i	$0.831664\pi$
$774$	6.20170	0.222916
$775$	7.10796	0.255325
$776$	−6.42334	−0.230585
$777$	0	0
$778$	10.4217	0.373635
$779$	0.682940	0.0244689
$780$	−5.31538	−0.190321
$781$	−2.97576	−0.106481
$782$	−1.55398	−0.0555702
$783$	4.96819	0.177549
$784$	0	0
$785$	0.406760	0.0145179
$786$	−4.40341	−0.157064
$787$	−10.4338	−0.371925	−0.185962	−	0.982557i	$-0.559540\pi$
$787$	−10.4338	−0.371925	−0.185962	+	0.982557i	$0.559540\pi$
$788$	2.94993	0.105087
$789$	−25.7050	−0.915122
$790$	−12.8325	−0.456559
$791$	0	0
$792$	−1.45515	−0.0517065
$793$	−8.68294	−0.308340
$794$	−20.7648	−0.736916
$795$	−8.73679	−0.309862
$796$	−13.2477	−0.469553
$797$	−21.9540	−0.777652	−0.388826	−	0.921311i	$-0.627119\pi$
$797$	−21.9540	−0.777652	−0.388826	+	0.921311i	$0.627119\pi$
$798$	0	0
$799$	3.31134	0.117147
$800$	−7.34147	−0.259560
$801$	2.05385	0.0725691
$802$	−10.2924	−0.363439
$803$	7.52298	0.265480
$804$	−10.3994	−0.366757
$805$	0	0
$806$	−1.46492	−0.0515995
$807$	−21.5593	−0.758924
$808$	−9.07107	−0.319119
$809$	−29.6062	−1.04090	−0.520448	−	0.853893i	$-0.674235\pi$
$809$	−29.6062	−1.04090	−0.520448	+	0.853893i	$0.674235\pi$
$810$	−3.51304	−0.123436
$811$	−52.4299	−1.84106	−0.920532	−	0.390668i	$-0.872244\pi$
$811$	−52.4299	−1.84106	−0.920532	+	0.390668i	$0.872244\pi$
$812$	0	0
$813$	7.39428	0.259329
$814$	−9.99595	−0.350358
$815$	−60.4423	−2.11720
$816$	−1.00000	−0.0350070
$817$	−0.866786	−0.0303250
$818$	−14.3063	−0.500206
$819$	0	0
$820$	17.1659	0.599458
$821$	0.0923342	0.00322249	0.00161124	−	0.999999i	$-0.499487\pi$
$821$	0.0923342	0.00322249	0.00161124	+	0.999999i	$0.499487\pi$
$822$	−0.625047	−0.0218010
$823$	−8.03040	−0.279922	−0.139961	−	0.990157i	$-0.544698\pi$
$823$	−8.03040	−0.279922	−0.139961	+	0.990157i	$0.544698\pi$
$824$	17.4944	0.609447
$825$	−10.6829	−0.371932
$826$	0	0
$827$	−23.7949	−0.827431	−0.413716	−	0.910406i	$-0.635769\pi$
$827$	−23.7949	−0.827431	−0.413716	+	0.910406i	$0.635769\pi$
$828$	1.55398	0.0540045
$829$	−18.1222	−0.629410	−0.314705	−	0.949190i	$-0.601906\pi$
$829$	−18.1222	−0.629410	−0.314705	+	0.949190i	$0.601906\pi$
$830$	−10.2836	−0.356948
$831$	−1.24054	−0.0430337
$832$	1.51304	0.0524553
$833$	0	0
$834$	7.50732	0.259957
$835$	−75.0450	−2.59704
$836$	0.203380	0.00703405
$837$	−0.968193	−0.0334656
$838$	7.59896	0.262502
$839$	45.8429	1.58267	0.791336	−	0.611381i	$-0.209386\pi$
$839$	45.8429	1.58267	0.791336	+	0.611381i	$0.209386\pi$
$840$	0	0
$841$	−4.31706	−0.148864
$842$	30.9648	1.06712
$843$	14.6011	0.502887
$844$	11.3845	0.391871
$845$	−37.6272	−1.29441
$846$	−3.31134	−0.113846
$847$	0	0
$848$	2.48696	0.0854025
$849$	11.2914	0.387520
$850$	−7.34147	−0.251810
$851$	10.6748	0.365929
$852$	2.04498	0.0700599
$853$	3.32752	0.113932	0.0569661	−	0.998376i	$-0.481857\pi$
$853$	3.32752	0.113932	0.0569661	+	0.998376i	$0.481857\pi$
$854$	0	0
$855$	0.491003	0.0167919
$856$	1.10796	0.0378692
$857$	−7.01043	−0.239472	−0.119736	−	0.992806i	$-0.538205\pi$
$857$	−7.01043	−0.239472	−0.119736	+	0.992806i	$0.538205\pi$
$858$	2.20170	0.0751649
$859$	12.1001	0.412851	0.206426	−	0.978462i	$-0.433817\pi$
$859$	12.1001	0.412851	0.206426	+	0.978462i	$0.433817\pi$
$860$	−21.7869	−0.742926
$861$	0	0
$862$	22.1973	0.756043
$863$	−32.7709	−1.11554	−0.557768	−	0.829997i	$-0.688342\pi$
$863$	−32.7709	−1.11554	−0.557768	+	0.829997i	$0.688342\pi$
$864$	1.00000	0.0340207
$865$	32.2843	1.09770
$866$	−23.2573	−0.790315
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	5.31538	0.180312
$870$	−17.4535	−0.591728
$871$	15.7347	0.533149
$872$	−19.5243	−0.661175
$873$	6.42334	0.217397
$874$	−0.217193	−0.00734666
$875$	0	0
$876$	−5.16990	−0.174675
$877$	−53.9706	−1.82246	−0.911229	−	0.411900i	$-0.864865\pi$
$877$	−53.9706	−1.82246	−0.911229	+	0.411900i	$0.864865\pi$
$878$	−31.5536	−1.06488
$879$	−0.591508	−0.0199511
$880$	5.11200	0.172326
$881$	−18.5035	−0.623400	−0.311700	−	0.950181i	$-0.600898\pi$
$881$	−18.5035	−0.623400	−0.311700	+	0.950181i	$0.600898\pi$
$882$	0	0
$883$	−25.1763	−0.847250	−0.423625	−	0.905838i	$-0.639243\pi$
$883$	−25.1763	−0.847250	−0.423625	+	0.905838i	$0.639243\pi$
$884$	1.51304	0.0508891
$885$	2.54890	0.0856802
$886$	−38.5398	−1.29477
$887$	38.0792	1.27857	0.639287	−	0.768968i	$-0.279229\pi$
$887$	38.0792	1.27857	0.639287	+	0.768968i	$0.279229\pi$
$888$	6.86936	0.230521
$889$	0	0
$890$	−7.21525	−0.241856
$891$	1.45515	0.0487494
$892$	−27.8857	−0.933682
$893$	0.462812	0.0154874
$894$	13.3676	0.447078
$895$	1.06625	0.0356408
$896$	0	0
$897$	−2.35124	−0.0785055
$898$	−13.3886	−0.446782
$899$	−4.81017	−0.160428
$900$	7.34147	0.244716
$901$	2.48696	0.0828526
$902$	−7.11033	−0.236748
$903$	0	0
$904$	−2.15672	−0.0717315
$905$	−41.6655	−1.38501
$906$	21.3377	0.708897
$907$	−15.1959	−0.504572	−0.252286	−	0.967653i	$-0.581182\pi$
$907$	−15.1959	−0.504572	−0.252286	+	0.967653i	$0.581182\pi$
$908$	−15.7090	−0.521322
$909$	9.07107	0.300868
$910$	0	0
$911$	−8.98683	−0.297747	−0.148873	−	0.988856i	$-0.547565\pi$
$911$	−8.98683	−0.297747	−0.148873	+	0.988856i	$0.547565\pi$
$912$	−0.139766	−0.00462810
$913$	4.25960	0.140972
$914$	1.65518	0.0547484
$915$	20.1604	0.666482
$916$	−26.7550	−0.884012
$917$	0	0
$918$	1.00000	0.0330049
$919$	−0.552247	−0.0182170	−0.00910848	−	0.999959i	$-0.502899\pi$
$919$	−0.552247	−0.0182170	−0.00910848	+	0.999959i	$0.502899\pi$
$920$	−5.45920	−0.179984
$921$	−5.68656	−0.187378
$922$	7.65411	0.252075
$923$	−3.09415	−0.101845
$924$	0	0
$925$	50.4312	1.65817
$926$	−11.9703	−0.393368
$927$	−17.4944	−0.574592
$928$	4.96819	0.163089
$929$	−23.7645	−0.779690	−0.389845	−	0.920881i	$-0.627471\pi$
$929$	−23.7645	−0.779690	−0.389845	+	0.920881i	$0.627471\pi$
$930$	3.40130	0.111533
$931$	0	0
$932$	8.55592	0.280258
$933$	−1.51876	−0.0497221
$934$	31.9939	1.04687
$935$	5.11200	0.167180
$936$	−1.51304	−0.0494554
$937$	−49.5947	−1.62019	−0.810094	−	0.586300i	$-0.800584\pi$
$937$	−49.5947	−1.62019	−0.810094	+	0.586300i	$0.800584\pi$
$938$	0	0
$939$	9.11605	0.297491
$940$	11.6329	0.379423
$941$	−9.28568	−0.302705	−0.151352	−	0.988480i	$-0.548363\pi$
$941$	−9.28568	−0.302705	−0.151352	+	0.988480i	$0.548363\pi$
$942$	0.115786	0.00377250
$943$	7.59324	0.247270
$944$	−0.725552	−0.0236147
$945$	0	0
$946$	9.02441	0.293409
$947$	15.4256	0.501265	0.250633	−	0.968082i	$-0.419361\pi$
$947$	15.4256	0.501265	0.250633	+	0.968082i	$0.419361\pi$
$948$	−3.65281	−0.118638
$949$	7.82228	0.253922
$950$	−1.02609	−0.0332906
$951$	−26.3398	−0.854126
$952$	0	0
$953$	−40.9691	−1.32712	−0.663559	−	0.748124i	$-0.730955\pi$
$953$	−40.9691	−1.32712	−0.663559	+	0.748124i	$0.730955\pi$
$954$	−2.48696	−0.0805182
$955$	−32.9929	−1.06762
$956$	24.5334	0.793467
$957$	7.22947	0.233695
$958$	40.0487	1.29391
$959$	0	0
$960$	−3.51304	−0.113383
$961$	−30.0626	−0.969761
$962$	−10.3936	−0.335104
$963$	−1.10796	−0.0357035
$964$	−17.3056	−0.557376
$965$	39.5137	1.27199
$966$	0	0
$967$	−3.79662	−0.122091	−0.0610455	−	0.998135i	$-0.519443\pi$
$967$	−3.79662	−0.122091	−0.0610455	+	0.998135i	$0.519443\pi$
$968$	8.88254	0.285496
$969$	−0.139766	−0.00448992
$970$	−22.5655	−0.724534
$971$	18.1111	0.581214	0.290607	−	0.956843i	$-0.406143\pi$
$971$	18.1111	0.581214	0.290607	+	0.956843i	$0.406143\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	3.88438	0.124464
$975$	−11.1080	−0.355739
$976$	−5.73873	−0.183692
$977$	4.32338	0.138317	0.0691585	−	0.997606i	$-0.477969\pi$
$977$	4.32338	0.138317	0.0691585	+	0.997606i	$0.477969\pi$
$978$	−17.2051	−0.550159
$979$	2.98866	0.0955178
$980$	0	0
$981$	19.5243	0.623362
$982$	−20.2556	−0.646381
$983$	−22.5035	−0.717751	−0.358876	−	0.933385i	$-0.616840\pi$
$983$	−22.5035	−0.717751	−0.358876	+	0.933385i	$0.616840\pi$
$984$	4.88632	0.155770
$985$	10.3632	0.330200
$986$	4.96819	0.158219
$987$	0	0
$988$	0.211471	0.00672780
$989$	−9.63732	−0.306449
$990$	−5.11200	−0.162470
$991$	−47.2541	−1.50108	−0.750539	−	0.660827i	$-0.770206\pi$
$991$	−47.2541	−1.50108	−0.750539	+	0.660827i	$0.770206\pi$
$992$	−0.968193	−0.0307402
$993$	23.3360	0.740546
$994$	0	0
$995$	−46.5398	−1.47541
$996$	−2.92726	−0.0927537
$997$	−35.9129	−1.13737	−0.568687	−	0.822554i	$-0.692548\pi$
$997$	−35.9129	−1.13737	−0.568687	+	0.822554i	$0.692548\pi$
$998$	6.38004	0.201957
$999$	−6.86936	−0.217337

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.51304 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.51304 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -3.51304 q^{10} +1.45515 q^{11} -1.00000 q^{12} +1.51304 q^{13} -3.51304 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +0.139766 q^{19} +3.51304 q^{20} -1.45515 q^{22} +1.55398 q^{23} +1.00000 q^{24} +7.34147 q^{25} -1.51304 q^{26} -1.00000 q^{27} -4.96819 q^{29} +3.51304 q^{30} +0.968193 q^{31} -1.00000 q^{32} -1.45515 q^{33} -1.00000 q^{34} +1.00000 q^{36} +6.86936 q^{37} -0.139766 q^{38} -1.51304 q^{39} -3.51304 q^{40} +4.88632 q^{41} -6.20170 q^{43} +1.45515 q^{44} +3.51304 q^{45} -1.55398 q^{46} +3.31134 q^{47} -1.00000 q^{48} -7.34147 q^{50} -1.00000 q^{51} +1.51304 q^{52} +2.48696 q^{53} +1.00000 q^{54} +5.11200 q^{55} -0.139766 q^{57} +4.96819 q^{58} -0.725552 q^{59} -3.51304 q^{60} -5.73873 q^{61} -0.968193 q^{62} +1.00000 q^{64} +5.31538 q^{65} +1.45515 q^{66} +10.3994 q^{67} +1.00000 q^{68} -1.55398 q^{69} -2.04498 q^{71} -1.00000 q^{72} +5.16990 q^{73} -6.86936 q^{74} -7.34147 q^{75} +0.139766 q^{76} +1.51304 q^{78} +3.65281 q^{79} +3.51304 q^{80} +1.00000 q^{81} -4.88632 q^{82} +2.92726 q^{83} +3.51304 q^{85} +6.20170 q^{86} +4.96819 q^{87} -1.45515 q^{88} +2.05385 q^{89} -3.51304 q^{90} +1.55398 q^{92} -0.968193 q^{93} -3.31134 q^{94} +0.491003 q^{95} +1.00000 q^{96} +6.42334 q^{97} +1.45515 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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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