LMFDB - Embedded newform 4998.2.a.bs.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{41}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 10 $ x^2 - x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 714)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.70156$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.70156 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.70156 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +3.70156 q^{10} +3.70156 q^{11} -1.00000 q^{12} +1.70156 q^{13} +3.70156 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -6.00000 q^{19} -3.70156 q^{20} -3.70156 q^{22} -3.40312 q^{23} +1.00000 q^{24} +8.70156 q^{25} -1.70156 q^{26} -1.00000 q^{27} -7.40312 q^{29} -3.70156 q^{30} -1.00000 q^{32} -3.70156 q^{33} -1.00000 q^{34} +1.00000 q^{36} +1.70156 q^{37} +6.00000 q^{38} -1.70156 q^{39} +3.70156 q^{40} +1.40312 q^{41} +2.29844 q^{43} +3.70156 q^{44} -3.70156 q^{45} +3.40312 q^{46} +8.00000 q^{47} -1.00000 q^{48} -8.70156 q^{50} -1.00000 q^{51} +1.70156 q^{52} -7.70156 q^{53} +1.00000 q^{54} -13.7016 q^{55} +6.00000 q^{57} +7.40312 q^{58} -5.40312 q^{59} +3.70156 q^{60} +2.00000 q^{61} +1.00000 q^{64} -6.29844 q^{65} +3.70156 q^{66} +9.70156 q^{67} +1.00000 q^{68} +3.40312 q^{69} +10.8062 q^{71} -1.00000 q^{72} +11.7016 q^{73} -1.70156 q^{74} -8.70156 q^{75} -6.00000 q^{76} +1.70156 q^{78} +13.7016 q^{79} -3.70156 q^{80} +1.00000 q^{81} -1.40312 q^{82} -8.29844 q^{83} -3.70156 q^{85} -2.29844 q^{86} +7.40312 q^{87} -3.70156 q^{88} -8.29844 q^{89} +3.70156 q^{90} -3.40312 q^{92} -8.00000 q^{94} +22.2094 q^{95} +1.00000 q^{96} -0.298438 q^{97} +3.70156 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} + q^{11} - 2 q^{12} - 3 q^{13} + q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 12 q^{19} - q^{20} - q^{22} + 6 q^{23} + 2 q^{24} + 11 q^{25} + 3 q^{26} - 2 q^{27} - 2 q^{29} - q^{30} - 2 q^{32} - q^{33} - 2 q^{34} + 2 q^{36} - 3 q^{37} + 12 q^{38} + 3 q^{39} + q^{40} - 10 q^{41} + 11 q^{43} + q^{44} - q^{45} - 6 q^{46} + 16 q^{47} - 2 q^{48} - 11 q^{50} - 2 q^{51} - 3 q^{52} - 9 q^{53} + 2 q^{54} - 21 q^{55} + 12 q^{57} + 2 q^{58} + 2 q^{59} + q^{60} + 4 q^{61} + 2 q^{64} - 19 q^{65} + q^{66} + 13 q^{67} + 2 q^{68} - 6 q^{69} - 4 q^{71} - 2 q^{72} + 17 q^{73} + 3 q^{74} - 11 q^{75} - 12 q^{76} - 3 q^{78} + 21 q^{79} - q^{80} + 2 q^{81} + 10 q^{82} - 23 q^{83} - q^{85} - 11 q^{86} + 2 q^{87} - q^{88} - 23 q^{89} + q^{90} + 6 q^{92} - 16 q^{94} + 6 q^{95} + 2 q^{96} - 7 q^{97} + q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 + q^11 - 2 * q^12 - 3 * q^13 + q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 12 * q^19 - q^20 - q^22 + 6 * q^23 + 2 * q^24 + 11 * q^25 + 3 * q^26 - 2 * q^27 - 2 * q^29 - q^30 - 2 * q^32 - q^33 - 2 * q^34 + 2 * q^36 - 3 * q^37 + 12 * q^38 + 3 * q^39 + q^40 - 10 * q^41 + 11 * q^43 + q^44 - q^45 - 6 * q^46 + 16 * q^47 - 2 * q^48 - 11 * q^50 - 2 * q^51 - 3 * q^52 - 9 * q^53 + 2 * q^54 - 21 * q^55 + 12 * q^57 + 2 * q^58 + 2 * q^59 + q^60 + 4 * q^61 + 2 * q^64 - 19 * q^65 + q^66 + 13 * q^67 + 2 * q^68 - 6 * q^69 - 4 * q^71 - 2 * q^72 + 17 * q^73 + 3 * q^74 - 11 * q^75 - 12 * q^76 - 3 * q^78 + 21 * q^79 - q^80 + 2 * q^81 + 10 * q^82 - 23 * q^83 - q^85 - 11 * q^86 + 2 * q^87 - q^88 - 23 * q^89 + q^90 + 6 * q^92 - 16 * q^94 + 6 * q^95 + 2 * q^96 - 7 * q^97 + 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
$5$	−3.70156	−1.65539	−0.827694	−	0.561179i	$-0.810348\pi$
$5$	−3.70156	−1.65539	−0.827694	+	0.561179i	$0.810348\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.70156	1.17054
$11$	3.70156	1.11606	0.558031	−	0.829820i	$-0.311557\pi$
$11$	3.70156	1.11606	0.558031	+	0.829820i	$0.311557\pi$
$12$	−1.00000	−0.288675
$13$	1.70156	0.471928	0.235964	−	0.971762i	$-0.424175\pi$
$13$	1.70156	0.471928	0.235964	+	0.971762i	$0.424175\pi$
$14$	0	0
$15$	3.70156	0.955739
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	−3.70156	−0.827694
$21$	0	0
$22$	−3.70156	−0.789176
$23$	−3.40312	−0.709600	−0.354800	−	0.934942i	$-0.615451\pi$
$23$	−3.40312	−0.709600	−0.354800	+	0.934942i	$0.615451\pi$
$24$	1.00000	0.204124
$25$	8.70156	1.74031
$26$	−1.70156	−0.333704
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−7.40312	−1.37473	−0.687363	−	0.726314i	$-0.741232\pi$
$29$	−7.40312	−1.37473	−0.687363	+	0.726314i	$0.741232\pi$
$30$	−3.70156	−0.675810
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−1.00000	−0.176777
$33$	−3.70156	−0.644359
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	1.70156	0.279735	0.139868	−	0.990170i	$-0.455332\pi$
$37$	1.70156	0.279735	0.139868	+	0.990170i	$0.455332\pi$
$38$	6.00000	0.973329
$39$	−1.70156	−0.272468
$40$	3.70156	0.585268
$41$	1.40312	0.219131	0.109566	−	0.993980i	$-0.465054\pi$
$41$	1.40312	0.219131	0.109566	+	0.993980i	$0.465054\pi$
$42$	0	0
$43$	2.29844	0.350508	0.175254	−	0.984523i	$-0.443925\pi$
$43$	2.29844	0.350508	0.175254	+	0.984523i	$0.443925\pi$
$44$	3.70156	0.558031
$45$	−3.70156	−0.551796
$46$	3.40312	0.501763
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−8.70156	−1.23059
$51$	−1.00000	−0.140028
$52$	1.70156	0.235964
$53$	−7.70156	−1.05789	−0.528945	−	0.848656i	$-0.677412\pi$
$53$	−7.70156	−1.05789	−0.528945	+	0.848656i	$0.677412\pi$
$54$	1.00000	0.136083
$55$	−13.7016	−1.84752
$56$	0	0
$57$	6.00000	0.794719
$58$	7.40312	0.972078
$59$	−5.40312	−0.703427	−0.351713	−	0.936108i	$-0.614401\pi$
$59$	−5.40312	−0.703427	−0.351713	+	0.936108i	$0.614401\pi$
$60$	3.70156	0.477870
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	0.125000
$65$	−6.29844	−0.781225
$66$	3.70156	0.455631
$67$	9.70156	1.18523	0.592617	−	0.805484i	$-0.298095\pi$
$67$	9.70156	1.18523	0.592617	+	0.805484i	$0.298095\pi$
$68$	1.00000	0.121268
$69$	3.40312	0.409688
$70$	0	0
$71$	10.8062	1.28247	0.641233	−	0.767346i	$-0.278423\pi$
$71$	10.8062	1.28247	0.641233	+	0.767346i	$0.278423\pi$
$72$	−1.00000	−0.117851
$73$	11.7016	1.36956	0.684782	−	0.728748i	$-0.259897\pi$
$73$	11.7016	1.36956	0.684782	+	0.728748i	$0.259897\pi$
$74$	−1.70156	−0.197803
$75$	−8.70156	−1.00477
$76$	−6.00000	−0.688247
$77$	0	0
$78$	1.70156	0.192664
$79$	13.7016	1.54155	0.770773	−	0.637110i	$-0.219870\pi$
$79$	13.7016	1.54155	0.770773	+	0.637110i	$0.219870\pi$
$80$	−3.70156	−0.413847
$81$	1.00000	0.111111
$82$	−1.40312	−0.154949
$83$	−8.29844	−0.910872	−0.455436	−	0.890269i	$-0.650517\pi$
$83$	−8.29844	−0.910872	−0.455436	+	0.890269i	$0.650517\pi$
$84$	0	0
$85$	−3.70156	−0.401491
$86$	−2.29844	−0.247847
$87$	7.40312	0.793698
$88$	−3.70156	−0.394588
$89$	−8.29844	−0.879633	−0.439816	−	0.898088i	$-0.644956\pi$
$89$	−8.29844	−0.879633	−0.439816	+	0.898088i	$0.644956\pi$
$90$	3.70156	0.390179
$91$	0	0
$92$	−3.40312	−0.354800
$93$	0	0
$94$	−8.00000	−0.825137
$95$	22.2094	2.27863
$96$	1.00000	0.102062
$97$	−0.298438	−0.0303018	−0.0151509	−	0.999885i	$-0.504823\pi$
$97$	−0.298438	−0.0303018	−0.0151509	+	0.999885i	$0.504823\pi$
$98$	0	0
$99$	3.70156	0.372021
$100$	8.70156	0.870156
$101$	18.8062	1.87129	0.935646	−	0.352940i	$-0.114818\pi$
$101$	18.8062	1.87129	0.935646	+	0.352940i	$0.114818\pi$
$102$	1.00000	0.0990148
$103$	12.5078	1.23243	0.616216	−	0.787578i	$-0.288665\pi$
$103$	12.5078	1.23243	0.616216	+	0.787578i	$0.288665\pi$
$104$	−1.70156	−0.166852
$105$	0	0
$106$	7.70156	0.748042
$107$	−17.4031	−1.68242	−0.841212	−	0.540706i	$-0.818157\pi$
$107$	−17.4031	−1.68242	−0.841212	+	0.540706i	$0.818157\pi$
$108$	−1.00000	−0.0962250
$109$	7.40312	0.709091	0.354545	−	0.935039i	$-0.384636\pi$
$109$	7.40312	0.709091	0.354545	+	0.935039i	$0.384636\pi$
$110$	13.7016	1.30639
$111$	−1.70156	−0.161505
$112$	0	0
$113$	15.1047	1.42093	0.710465	−	0.703733i	$-0.248485\pi$
$113$	15.1047	1.42093	0.710465	+	0.703733i	$0.248485\pi$
$114$	−6.00000	−0.561951
$115$	12.5969	1.17466
$116$	−7.40312	−0.687363
$117$	1.70156	0.157309
$118$	5.40312	0.497398
$119$	0	0
$120$	−3.70156	−0.337905
$121$	2.70156	0.245597
$122$	−2.00000	−0.181071
$123$	−1.40312	−0.126515
$124$	0	0
$125$	−13.7016	−1.22550
$126$	0	0
$127$	−4.59688	−0.407907	−0.203953	−	0.978981i	$-0.565379\pi$
$127$	−4.59688	−0.407907	−0.203953	+	0.978981i	$0.565379\pi$
$128$	−1.00000	−0.0883883
$129$	−2.29844	−0.202366
$130$	6.29844	0.552410
$131$	7.40312	0.646814	0.323407	−	0.946260i	$-0.395172\pi$
$131$	7.40312	0.646814	0.323407	+	0.946260i	$0.395172\pi$
$132$	−3.70156	−0.322180
$133$	0	0
$134$	−9.70156	−0.838087
$135$	3.70156	0.318580
$136$	−1.00000	−0.0857493
$137$	−13.4031	−1.14511	−0.572553	−	0.819868i	$-0.694047\pi$
$137$	−13.4031	−1.14511	−0.572553	+	0.819868i	$0.694047\pi$
$138$	−3.40312	−0.289693
$139$	−1.70156	−0.144325	−0.0721623	−	0.997393i	$-0.522990\pi$
$139$	−1.70156	−0.144325	−0.0721623	+	0.997393i	$0.522990\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	−10.8062	−0.906840
$143$	6.29844	0.526702
$144$	1.00000	0.0833333
$145$	27.4031	2.27571
$146$	−11.7016	−0.968428
$147$	0	0
$148$	1.70156	0.139868
$149$	−19.7016	−1.61401	−0.807007	−	0.590541i	$-0.798914\pi$
$149$	−19.7016	−1.61401	−0.807007	+	0.590541i	$0.798914\pi$
$150$	8.70156	0.710480
$151$	−6.80625	−0.553885	−0.276942	−	0.960887i	$-0.589321\pi$
$151$	−6.80625	−0.553885	−0.276942	+	0.960887i	$0.589321\pi$
$152$	6.00000	0.486664
$153$	1.00000	0.0808452
$154$	0	0
$155$	0	0
$156$	−1.70156	−0.136234
$157$	−22.2094	−1.77250	−0.886250	−	0.463206i	$-0.846699\pi$
$157$	−22.2094	−1.77250	−0.886250	+	0.463206i	$0.846699\pi$
$158$	−13.7016	−1.09004
$159$	7.70156	0.610774
$160$	3.70156	0.292634
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	1.40312	0.109566
$165$	13.7016	1.06667
$166$	8.29844	0.644084
$167$	−16.5078	−1.27741	−0.638706	−	0.769451i	$-0.720530\pi$
$167$	−16.5078	−1.27741	−0.638706	+	0.769451i	$0.720530\pi$
$168$	0	0
$169$	−10.1047	−0.777284
$170$	3.70156	0.283897
$171$	−6.00000	−0.458831
$172$	2.29844	0.175254
$173$	10.0000	0.760286	0.380143	−	0.924928i	$-0.375875\pi$
$173$	10.0000	0.760286	0.380143	+	0.924928i	$0.375875\pi$
$174$	−7.40312	−0.561229
$175$	0	0
$176$	3.70156	0.279016
$177$	5.40312	0.406124
$178$	8.29844	0.621994
$179$	−14.2094	−1.06206	−0.531029	−	0.847354i	$-0.678195\pi$
$179$	−14.2094	−1.06206	−0.531029	+	0.847354i	$0.678195\pi$
$180$	−3.70156	−0.275898
$181$	9.40312	0.698929	0.349464	−	0.936950i	$-0.386364\pi$
$181$	9.40312	0.698929	0.349464	+	0.936950i	$0.386364\pi$
$182$	0	0
$183$	−2.00000	−0.147844
$184$	3.40312	0.250882
$185$	−6.29844	−0.463070
$186$	0	0
$187$	3.70156	0.270685
$188$	8.00000	0.583460
$189$	0	0
$190$	−22.2094	−1.61124
$191$	−13.1047	−0.948222	−0.474111	−	0.880465i	$-0.657230\pi$
$191$	−13.1047	−0.948222	−0.474111	+	0.880465i	$0.657230\pi$
$192$	−1.00000	−0.0721688
$193$	16.2094	1.16678	0.583388	−	0.812194i	$-0.301727\pi$
$193$	16.2094	1.16678	0.583388	+	0.812194i	$0.301727\pi$
$194$	0.298438	0.0214266
$195$	6.29844	0.451041
$196$	0	0
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	−3.70156	−0.263059
$199$	−6.80625	−0.482482	−0.241241	−	0.970465i	$-0.577554\pi$
$199$	−6.80625	−0.482482	−0.241241	+	0.970465i	$0.577554\pi$
$200$	−8.70156	−0.615293
$201$	−9.70156	−0.684295
$202$	−18.8062	−1.32320
$203$	0	0
$204$	−1.00000	−0.0700140
$205$	−5.19375	−0.362747
$206$	−12.5078	−0.871460
$207$	−3.40312	−0.236533
$208$	1.70156	0.117982
$209$	−22.2094	−1.53625
$210$	0	0
$211$	−16.8062	−1.15699	−0.578495	−	0.815686i	$-0.696360\pi$
$211$	−16.8062	−1.15699	−0.578495	+	0.815686i	$0.696360\pi$
$212$	−7.70156	−0.528945
$213$	−10.8062	−0.740432
$214$	17.4031	1.18965
$215$	−8.50781	−0.580228
$216$	1.00000	0.0680414
$217$	0	0
$218$	−7.40312	−0.501403
$219$	−11.7016	−0.790718
$220$	−13.7016	−0.923759
$221$	1.70156	0.114459
$222$	1.70156	0.114201
$223$	−26.8062	−1.79508	−0.897540	−	0.440934i	$-0.854647\pi$
$223$	−26.8062	−1.79508	−0.897540	+	0.440934i	$0.854647\pi$
$224$	0	0
$225$	8.70156	0.580104
$226$	−15.1047	−1.00475
$227$	2.80625	0.186257	0.0931286	−	0.995654i	$-0.470313\pi$
$227$	2.80625	0.186257	0.0931286	+	0.995654i	$0.470313\pi$
$228$	6.00000	0.397360
$229$	17.1047	1.13031	0.565155	−	0.824985i	$-0.308816\pi$
$229$	17.1047	1.13031	0.565155	+	0.824985i	$0.308816\pi$
$230$	−12.5969	−0.830613
$231$	0	0
$232$	7.40312	0.486039
$233$	−23.7016	−1.55274	−0.776370	−	0.630277i	$-0.782941\pi$
$233$	−23.7016	−1.55274	−0.776370	+	0.630277i	$0.782941\pi$
$234$	−1.70156	−0.111235
$235$	−29.6125	−1.93171
$236$	−5.40312	−0.351713
$237$	−13.7016	−0.890012
$238$	0	0
$239$	29.1047	1.88263	0.941313	−	0.337535i	$-0.109593\pi$
$239$	29.1047	1.88263	0.941313	+	0.337535i	$0.109593\pi$
$240$	3.70156	0.238935
$241$	24.8062	1.59791	0.798955	−	0.601390i	$-0.205386\pi$
$241$	24.8062	1.59791	0.798955	+	0.601390i	$0.205386\pi$
$242$	−2.70156	−0.173663
$243$	−1.00000	−0.0641500
$244$	2.00000	0.128037
$245$	0	0
$246$	1.40312	0.0894599
$247$	−10.2094	−0.649607
$248$	0	0
$249$	8.29844	0.525892
$250$	13.7016	0.866563
$251$	13.9109	0.878050	0.439025	−	0.898475i	$-0.355324\pi$
$251$	13.9109	0.878050	0.439025	+	0.898475i	$0.355324\pi$
$252$	0	0
$253$	−12.5969	−0.791959
$254$	4.59688	0.288434
$255$	3.70156	0.231801
$256$	1.00000	0.0625000
$257$	−26.5078	−1.65351	−0.826756	−	0.562561i	$-0.809816\pi$
$257$	−26.5078	−1.65351	−0.826756	+	0.562561i	$0.809816\pi$
$258$	2.29844	0.143094
$259$	0	0
$260$	−6.29844	−0.390613
$261$	−7.40312	−0.458242
$262$	−7.40312	−0.457367
$263$	−29.1047	−1.79467	−0.897336	−	0.441348i	$-0.854500\pi$
$263$	−29.1047	−1.79467	−0.897336	+	0.441348i	$0.854500\pi$
$264$	3.70156	0.227815
$265$	28.5078	1.75122
$266$	0	0
$267$	8.29844	0.507856
$268$	9.70156	0.592617
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	−3.70156	−0.225270
$271$	−12.5078	−0.759795	−0.379898	−	0.925029i	$-0.624041\pi$
$271$	−12.5078	−0.759795	−0.379898	+	0.925029i	$0.624041\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	13.4031	0.809712
$275$	32.2094	1.94230
$276$	3.40312	0.204844
$277$	3.40312	0.204474	0.102237	−	0.994760i	$-0.467400\pi$
$277$	3.40312	0.204474	0.102237	+	0.994760i	$0.467400\pi$
$278$	1.70156	0.102053
$279$	0	0
$280$	0	0
$281$	4.80625	0.286717	0.143358	−	0.989671i	$-0.454210\pi$
$281$	4.80625	0.286717	0.143358	+	0.989671i	$0.454210\pi$
$282$	8.00000	0.476393
$283$	−2.89531	−0.172109	−0.0860543	−	0.996290i	$-0.527426\pi$
$283$	−2.89531	−0.172109	−0.0860543	+	0.996290i	$0.527426\pi$
$284$	10.8062	0.641233
$285$	−22.2094	−1.31557
$286$	−6.29844	−0.372434
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−27.4031	−1.60917
$291$	0.298438	0.0174947
$292$	11.7016	0.684782
$293$	−8.00000	−0.467365	−0.233682	−	0.972313i	$-0.575078\pi$
$293$	−8.00000	−0.467365	−0.233682	+	0.972313i	$0.575078\pi$
$294$	0	0
$295$	20.0000	1.16445
$296$	−1.70156	−0.0989013
$297$	−3.70156	−0.214786
$298$	19.7016	1.14128
$299$	−5.79063	−0.334881
$300$	−8.70156	−0.502385
$301$	0	0
$302$	6.80625	0.391656
$303$	−18.8062	−1.08039
$304$	−6.00000	−0.344124
$305$	−7.40312	−0.423902
$306$	−1.00000	−0.0571662
$307$	12.2094	0.696826	0.348413	−	0.937341i	$-0.386721\pi$
$307$	12.2094	0.696826	0.348413	+	0.937341i	$0.386721\pi$
$308$	0	0
$309$	−12.5078	−0.711544
$310$	0	0
$311$	13.1047	0.743099	0.371549	−	0.928413i	$-0.378827\pi$
$311$	13.1047	0.743099	0.371549	+	0.928413i	$0.378827\pi$
$312$	1.70156	0.0963320
$313$	20.8062	1.17604	0.588019	−	0.808847i	$-0.299908\pi$
$313$	20.8062	1.17604	0.588019	+	0.808847i	$0.299908\pi$
$314$	22.2094	1.25335
$315$	0	0
$316$	13.7016	0.770773
$317$	−15.4031	−0.865126	−0.432563	−	0.901604i	$-0.642391\pi$
$317$	−15.4031	−0.865126	−0.432563	+	0.901604i	$0.642391\pi$
$318$	−7.70156	−0.431882
$319$	−27.4031	−1.53428
$320$	−3.70156	−0.206924
$321$	17.4031	0.971348
$322$	0	0
$323$	−6.00000	−0.333849
$324$	1.00000	0.0555556
$325$	14.8062	0.821303
$326$	10.0000	0.553849
$327$	−7.40312	−0.409394
$328$	−1.40312	−0.0774746
$329$	0	0
$330$	−13.7016	−0.754246
$331$	13.7016	0.753106	0.376553	−	0.926395i	$-0.377109\pi$
$331$	13.7016	0.753106	0.376553	+	0.926395i	$0.377109\pi$
$332$	−8.29844	−0.455436
$333$	1.70156	0.0932450
$334$	16.5078	0.903267
$335$	−35.9109	−1.96202
$336$	0	0
$337$	−7.19375	−0.391869	−0.195934	−	0.980617i	$-0.562774\pi$
$337$	−7.19375	−0.391869	−0.195934	+	0.980617i	$0.562774\pi$
$338$	10.1047	0.549622
$339$	−15.1047	−0.820374
$340$	−3.70156	−0.200745
$341$	0	0
$342$	6.00000	0.324443
$343$	0	0
$344$	−2.29844	−0.123923
$345$	−12.5969	−0.678193
$346$	−10.0000	−0.537603
$347$	19.1047	1.02559	0.512797	−	0.858510i	$-0.328609\pi$
$347$	19.1047	1.02559	0.512797	+	0.858510i	$0.328609\pi$
$348$	7.40312	0.396849
$349$	−24.5078	−1.31187	−0.655937	−	0.754816i	$-0.727726\pi$
$349$	−24.5078	−1.31187	−0.655937	+	0.754816i	$0.727726\pi$
$350$	0	0
$351$	−1.70156	−0.0908227
$352$	−3.70156	−0.197294
$353$	6.50781	0.346376	0.173188	−	0.984889i	$-0.444593\pi$
$353$	6.50781	0.346376	0.173188	+	0.984889i	$0.444593\pi$
$354$	−5.40312	−0.287173
$355$	−40.0000	−2.12298
$356$	−8.29844	−0.439816
$357$	0	0
$358$	14.2094	0.750989
$359$	−29.6125	−1.56289	−0.781444	−	0.623975i	$-0.785516\pi$
$359$	−29.6125	−1.56289	−0.781444	+	0.623975i	$0.785516\pi$
$360$	3.70156	0.195089
$361$	17.0000	0.894737
$362$	−9.40312	−0.494217
$363$	−2.70156	−0.141795
$364$	0	0
$365$	−43.3141	−2.26716
$366$	2.00000	0.104542
$367$	−14.8062	−0.772880	−0.386440	−	0.922315i	$-0.626295\pi$
$367$	−14.8062	−0.772880	−0.386440	+	0.922315i	$0.626295\pi$
$368$	−3.40312	−0.177400
$369$	1.40312	0.0730437
$370$	6.29844	0.327440
$371$	0	0
$372$	0	0
$373$	−9.40312	−0.486875	−0.243438	−	0.969917i	$-0.578275\pi$
$373$	−9.40312	−0.486875	−0.243438	+	0.969917i	$0.578275\pi$
$374$	−3.70156	−0.191403
$375$	13.7016	0.707546
$376$	−8.00000	−0.412568
$377$	−12.5969	−0.648772
$378$	0	0
$379$	31.6125	1.62382	0.811912	−	0.583779i	$-0.198427\pi$
$379$	31.6125	1.62382	0.811912	+	0.583779i	$0.198427\pi$
$380$	22.2094	1.13932
$381$	4.59688	0.235505
$382$	13.1047	0.670494
$383$	−2.80625	−0.143393	−0.0716963	−	0.997427i	$-0.522841\pi$
$383$	−2.80625	−0.143393	−0.0716963	+	0.997427i	$0.522841\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−16.2094	−0.825035
$387$	2.29844	0.116836
$388$	−0.298438	−0.0151509
$389$	24.8062	1.25773	0.628863	−	0.777516i	$-0.283520\pi$
$389$	24.8062	1.25773	0.628863	+	0.777516i	$0.283520\pi$
$390$	−6.29844	−0.318934
$391$	−3.40312	−0.172103
$392$	0	0
$393$	−7.40312	−0.373438
$394$	12.0000	0.604551
$395$	−50.7172	−2.55186
$396$	3.70156	0.186010
$397$	−21.4031	−1.07419	−0.537096	−	0.843521i	$-0.680479\pi$
$397$	−21.4031	−1.07419	−0.537096	+	0.843521i	$0.680479\pi$
$398$	6.80625	0.341166
$399$	0	0
$400$	8.70156	0.435078
$401$	22.0000	1.09863	0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000	1.09863	0.549314	+	0.835616i	$0.314889\pi$
$402$	9.70156	0.483870
$403$	0	0
$404$	18.8062	0.935646
$405$	−3.70156	−0.183932
$406$	0	0
$407$	6.29844	0.312202
$408$	1.00000	0.0495074
$409$	−12.8062	−0.633228	−0.316614	−	0.948554i	$-0.602546\pi$
$409$	−12.8062	−0.633228	−0.316614	+	0.948554i	$0.602546\pi$
$410$	5.19375	0.256501
$411$	13.4031	0.661127
$412$	12.5078	0.616216
$413$	0	0
$414$	3.40312	0.167254
$415$	30.7172	1.50785
$416$	−1.70156	−0.0834259
$417$	1.70156	0.0833259
$418$	22.2094	1.08630
$419$	18.2094	0.889586	0.444793	−	0.895633i	$-0.353277\pi$
$419$	18.2094	0.889586	0.444793	+	0.895633i	$0.353277\pi$
$420$	0	0
$421$	−22.0000	−1.07221	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000	−1.07221	−0.536107	+	0.844150i	$0.680106\pi$
$422$	16.8062	0.818115
$423$	8.00000	0.388973
$424$	7.70156	0.374021
$425$	8.70156	0.422088
$426$	10.8062	0.523564
$427$	0	0
$428$	−17.4031	−0.841212
$429$	−6.29844	−0.304091
$430$	8.50781	0.410283
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	−1.00000	−0.0481125
$433$	−16.2094	−0.778973	−0.389486	−	0.921032i	$-0.627347\pi$
$433$	−16.2094	−0.778973	−0.389486	+	0.921032i	$0.627347\pi$
$434$	0	0
$435$	−27.4031	−1.31388
$436$	7.40312	0.354545
$437$	20.4187	0.976761
$438$	11.7016	0.559122
$439$	−30.8062	−1.47030	−0.735151	−	0.677903i	$-0.762889\pi$
$439$	−30.8062	−1.47030	−0.735151	+	0.677903i	$0.762889\pi$
$440$	13.7016	0.653196
$441$	0	0
$442$	−1.70156	−0.0809351
$443$	13.6125	0.646749	0.323375	−	0.946271i	$-0.395183\pi$
$443$	13.6125	0.646749	0.323375	+	0.946271i	$0.395183\pi$
$444$	−1.70156	−0.0807526
$445$	30.7172	1.45613
$446$	26.8062	1.26931
$447$	19.7016	0.931852
$448$	0	0
$449$	12.2984	0.580399	0.290200	−	0.956966i	$-0.406278\pi$
$449$	12.2984	0.580399	0.290200	+	0.956966i	$0.406278\pi$
$450$	−8.70156	−0.410196
$451$	5.19375	0.244564
$452$	15.1047	0.710465
$453$	6.80625	0.319785
$454$	−2.80625	−0.131704
$455$	0	0
$456$	−6.00000	−0.280976
$457$	8.89531	0.416105	0.208053	−	0.978118i	$-0.433287\pi$
$457$	8.89531	0.416105	0.208053	+	0.978118i	$0.433287\pi$
$458$	−17.1047	−0.799250
$459$	−1.00000	−0.0466760
$460$	12.5969	0.587332
$461$	27.4031	1.27629	0.638145	−	0.769916i	$-0.279702\pi$
$461$	27.4031	1.27629	0.638145	+	0.769916i	$0.279702\pi$
$462$	0	0
$463$	−29.6125	−1.37621	−0.688105	−	0.725611i	$-0.741557\pi$
$463$	−29.6125	−1.37621	−0.688105	+	0.725611i	$0.741557\pi$
$464$	−7.40312	−0.343681
$465$	0	0
$466$	23.7016	1.09795
$467$	20.2094	0.935178	0.467589	−	0.883946i	$-0.345123\pi$
$467$	20.2094	0.935178	0.467589	+	0.883946i	$0.345123\pi$
$468$	1.70156	0.0786547
$469$	0	0
$470$	29.6125	1.36592
$471$	22.2094	1.02335
$472$	5.40312	0.248699
$473$	8.50781	0.391190
$474$	13.7016	0.629334
$475$	−52.2094	−2.39553
$476$	0	0
$477$	−7.70156	−0.352630
$478$	−29.1047	−1.33122
$479$	−37.1047	−1.69536	−0.847678	−	0.530511i	$-0.822000\pi$
$479$	−37.1047	−1.69536	−0.847678	+	0.530511i	$0.822000\pi$
$480$	−3.70156	−0.168952
$481$	2.89531	0.132015
$482$	−24.8062	−1.12989
$483$	0	0
$484$	2.70156	0.122798
$485$	1.10469	0.0501612
$486$	1.00000	0.0453609
$487$	−18.8953	−0.856228	−0.428114	−	0.903725i	$-0.640822\pi$
$487$	−18.8953	−0.856228	−0.428114	+	0.903725i	$0.640822\pi$
$488$	−2.00000	−0.0905357
$489$	10.0000	0.452216
$490$	0	0
$491$	31.4031	1.41720	0.708602	−	0.705609i	$-0.249326\pi$
$491$	31.4031	1.41720	0.708602	+	0.705609i	$0.249326\pi$
$492$	−1.40312	−0.0632577
$493$	−7.40312	−0.333420
$494$	10.2094	0.459341
$495$	−13.7016	−0.615839
$496$	0	0
$497$	0	0
$498$	−8.29844	−0.371862
$499$	9.40312	0.420942	0.210471	−	0.977600i	$-0.432500\pi$
$499$	9.40312	0.420942	0.210471	+	0.977600i	$0.432500\pi$
$500$	−13.7016	−0.612752
$501$	16.5078	0.737515
$502$	−13.9109	−0.620875
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	0	0
$505$	−69.6125	−3.09772
$506$	12.5969	0.559999
$507$	10.1047	0.448765
$508$	−4.59688	−0.203953
$509$	−18.8062	−0.833572	−0.416786	−	0.909005i	$-0.636844\pi$
$509$	−18.8062	−0.833572	−0.416786	+	0.909005i	$0.636844\pi$
$510$	−3.70156	−0.163908
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	6.00000	0.264906
$514$	26.5078	1.16921
$515$	−46.2984	−2.04015
$516$	−2.29844	−0.101183
$517$	29.6125	1.30236
$518$	0	0
$519$	−10.0000	−0.438951
$520$	6.29844	0.276205
$521$	6.59688	0.289014	0.144507	−	0.989504i	$-0.453840\pi$
$521$	6.59688	0.289014	0.144507	+	0.989504i	$0.453840\pi$
$522$	7.40312	0.324026
$523$	−27.0156	−1.18131	−0.590655	−	0.806924i	$-0.701131\pi$
$523$	−27.0156	−1.18131	−0.590655	+	0.806924i	$0.701131\pi$
$524$	7.40312	0.323407
$525$	0	0
$526$	29.1047	1.26902
$527$	0	0
$528$	−3.70156	−0.161090
$529$	−11.4187	−0.496467
$530$	−28.5078	−1.23830
$531$	−5.40312	−0.234476
$532$	0	0
$533$	2.38750	0.103414
$534$	−8.29844	−0.359109
$535$	64.4187	2.78507
$536$	−9.70156	−0.419044
$537$	14.2094	0.613180
$538$	14.0000	0.603583
$539$	0	0
$540$	3.70156	0.159290
$541$	−31.9109	−1.37196	−0.685979	−	0.727621i	$-0.740626\pi$
$541$	−31.9109	−1.37196	−0.685979	+	0.727621i	$0.740626\pi$
$542$	12.5078	0.537256
$543$	−9.40312	−0.403527
$544$	−1.00000	−0.0428746
$545$	−27.4031	−1.17382
$546$	0	0
$547$	−16.8062	−0.718583	−0.359292	−	0.933225i	$-0.616982\pi$
$547$	−16.8062	−0.718583	−0.359292	+	0.933225i	$0.616982\pi$
$548$	−13.4031	−0.572553
$549$	2.00000	0.0853579
$550$	−32.2094	−1.37341
$551$	44.4187	1.89230
$552$	−3.40312	−0.144847
$553$	0	0
$554$	−3.40312	−0.144585
$555$	6.29844	0.267354
$556$	−1.70156	−0.0721623
$557$	−22.0000	−0.932170	−0.466085	−	0.884740i	$-0.654336\pi$
$557$	−22.0000	−0.932170	−0.466085	+	0.884740i	$0.654336\pi$
$558$	0	0
$559$	3.91093	0.165415
$560$	0	0
$561$	−3.70156	−0.156280
$562$	−4.80625	−0.202739
$563$	25.3141	1.06686	0.533430	−	0.845844i	$-0.320903\pi$
$563$	25.3141	1.06686	0.533430	+	0.845844i	$0.320903\pi$
$564$	−8.00000	−0.336861
$565$	−55.9109	−2.35219
$566$	2.89531	0.121699
$567$	0	0
$568$	−10.8062	−0.453420
$569$	3.61250	0.151444	0.0757219	−	0.997129i	$-0.475874\pi$
$569$	3.61250	0.151444	0.0757219	+	0.997129i	$0.475874\pi$
$570$	22.2094	0.930248
$571$	−27.0156	−1.13057	−0.565284	−	0.824896i	$-0.691234\pi$
$571$	−27.0156	−1.13057	−0.565284	+	0.824896i	$0.691234\pi$
$572$	6.29844	0.263351
$573$	13.1047	0.547456
$574$	0	0
$575$	−29.6125	−1.23493
$576$	1.00000	0.0416667
$577$	27.6125	1.14952	0.574762	−	0.818321i	$-0.305095\pi$
$577$	27.6125	1.14952	0.574762	+	0.818321i	$0.305095\pi$
$578$	−1.00000	−0.0415945
$579$	−16.2094	−0.673639
$580$	27.4031	1.13785
$581$	0	0
$582$	−0.298438	−0.0123706
$583$	−28.5078	−1.18067
$584$	−11.7016	−0.484214
$585$	−6.29844	−0.260408
$586$	8.00000	0.330477
$587$	−24.2984	−1.00290	−0.501452	−	0.865186i	$-0.667201\pi$
$587$	−24.2984	−1.00290	−0.501452	+	0.865186i	$0.667201\pi$
$588$	0	0
$589$	0	0
$590$	−20.0000	−0.823387
$591$	12.0000	0.493614
$592$	1.70156	0.0699338
$593$	−7.61250	−0.312608	−0.156304	−	0.987709i	$-0.549958\pi$
$593$	−7.61250	−0.312608	−0.156304	+	0.987709i	$0.549958\pi$
$594$	3.70156	0.151877
$595$	0	0
$596$	−19.7016	−0.807007
$597$	6.80625	0.278561
$598$	5.79063	0.236796
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	8.70156	0.355240
$601$	−32.8062	−1.33819	−0.669097	−	0.743175i	$-0.733319\pi$
$601$	−32.8062	−1.33819	−0.669097	+	0.743175i	$0.733319\pi$
$602$	0	0
$603$	9.70156	0.395078
$604$	−6.80625	−0.276942
$605$	−10.0000	−0.406558
$606$	18.8062	0.763952
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	6.00000	0.243332
$609$	0	0
$610$	7.40312	0.299744
$611$	13.6125	0.550703
$612$	1.00000	0.0404226
$613$	−41.4031	−1.67226	−0.836128	−	0.548534i	$-0.815186\pi$
$613$	−41.4031	−1.67226	−0.836128	+	0.548534i	$0.815186\pi$
$614$	−12.2094	−0.492730
$615$	5.19375	0.209432
$616$	0	0
$617$	−15.7016	−0.632121	−0.316061	−	0.948739i	$-0.602360\pi$
$617$	−15.7016	−0.632121	−0.316061	+	0.948739i	$0.602360\pi$
$618$	12.5078	0.503138
$619$	−18.2984	−0.735476	−0.367738	−	0.929929i	$-0.619868\pi$
$619$	−18.2984	−0.735476	−0.367738	+	0.929929i	$0.619868\pi$
$620$	0	0
$621$	3.40312	0.136563
$622$	−13.1047	−0.525450
$623$	0	0
$624$	−1.70156	−0.0681170
$625$	7.20937	0.288375
$626$	−20.8062	−0.831585
$627$	22.2094	0.886957
$628$	−22.2094	−0.886250
$629$	1.70156	0.0678457
$630$	0	0
$631$	30.8062	1.22638	0.613189	−	0.789936i	$-0.289887\pi$
$631$	30.8062	1.22638	0.613189	+	0.789936i	$0.289887\pi$
$632$	−13.7016	−0.545019
$633$	16.8062	0.667988
$634$	15.4031	0.611736
$635$	17.0156	0.675244
$636$	7.70156	0.305387
$637$	0	0
$638$	27.4031	1.08490
$639$	10.8062	0.427489
$640$	3.70156	0.146317
$641$	25.9109	1.02342	0.511710	−	0.859158i	$-0.329012\pi$
$641$	25.9109	1.02342	0.511710	+	0.859158i	$0.329012\pi$
$642$	−17.4031	−0.686847
$643$	10.2984	0.406131	0.203065	−	0.979165i	$-0.434910\pi$
$643$	10.2984	0.406131	0.203065	+	0.979165i	$0.434910\pi$
$644$	0	0
$645$	8.50781	0.334995
$646$	6.00000	0.236067
$647$	−45.6125	−1.79321	−0.896606	−	0.442829i	$-0.853975\pi$
$647$	−45.6125	−1.79321	−0.896606	+	0.442829i	$0.853975\pi$
$648$	−1.00000	−0.0392837
$649$	−20.0000	−0.785069
$650$	−14.8062	−0.580749
$651$	0	0
$652$	−10.0000	−0.391630
$653$	−46.2094	−1.80831	−0.904156	−	0.427202i	$-0.859499\pi$
$653$	−46.2094	−1.80831	−0.904156	+	0.427202i	$0.859499\pi$
$654$	7.40312	0.289485
$655$	−27.4031	−1.07073
$656$	1.40312	0.0547828
$657$	11.7016	0.456521
$658$	0	0
$659$	45.6125	1.77681	0.888405	−	0.459060i	$-0.151814\pi$
$659$	45.6125	1.77681	0.888405	+	0.459060i	$0.151814\pi$
$660$	13.7016	0.533333
$661$	−15.4031	−0.599112	−0.299556	−	0.954079i	$-0.596839\pi$
$661$	−15.4031	−0.599112	−0.299556	+	0.954079i	$0.596839\pi$
$662$	−13.7016	−0.532526
$663$	−1.70156	−0.0660832
$664$	8.29844	0.322042
$665$	0	0
$666$	−1.70156	−0.0659342
$667$	25.1938	0.975506
$668$	−16.5078	−0.638706
$669$	26.8062	1.03639
$670$	35.9109	1.38736
$671$	7.40312	0.285794
$672$	0	0
$673$	8.20937	0.316448	0.158224	−	0.987403i	$-0.449423\pi$
$673$	8.20937	0.316448	0.158224	+	0.987403i	$0.449423\pi$
$674$	7.19375	0.277093
$675$	−8.70156	−0.334923
$676$	−10.1047	−0.388642
$677$	−41.3141	−1.58783	−0.793914	−	0.608030i	$-0.791960\pi$
$677$	−41.3141	−1.58783	−0.793914	+	0.608030i	$0.791960\pi$
$678$	15.1047	0.580092
$679$	0	0
$680$	3.70156	0.141948
$681$	−2.80625	−0.107536
$682$	0	0
$683$	−14.5969	−0.558534	−0.279267	−	0.960213i	$-0.590091\pi$
$683$	−14.5969	−0.558534	−0.279267	+	0.960213i	$0.590091\pi$
$684$	−6.00000	−0.229416
$685$	49.6125	1.89560
$686$	0	0
$687$	−17.1047	−0.652584
$688$	2.29844	0.0876271
$689$	−13.1047	−0.499249
$690$	12.5969	0.479555
$691$	−42.7172	−1.62504	−0.812519	−	0.582935i	$-0.801904\pi$
$691$	−42.7172	−1.62504	−0.812519	+	0.582935i	$0.801904\pi$
$692$	10.0000	0.380143
$693$	0	0
$694$	−19.1047	−0.725204
$695$	6.29844	0.238913
$696$	−7.40312	−0.280615
$697$	1.40312	0.0531471
$698$	24.5078	0.927634
$699$	23.7016	0.896475
$700$	0	0
$701$	46.5078	1.75658	0.878288	−	0.478132i	$-0.158686\pi$
$701$	46.5078	1.75658	0.878288	+	0.478132i	$0.158686\pi$
$702$	1.70156	0.0642213
$703$	−10.2094	−0.385054
$704$	3.70156	0.139508
$705$	29.6125	1.11527
$706$	−6.50781	−0.244925
$707$	0	0
$708$	5.40312	0.203062
$709$	−30.7172	−1.15361	−0.576804	−	0.816883i	$-0.695700\pi$
$709$	−30.7172	−1.15361	−0.576804	+	0.816883i	$0.695700\pi$
$710$	40.0000	1.50117
$711$	13.7016	0.513849
$712$	8.29844	0.310997
$713$	0	0
$714$	0	0
$715$	−23.3141	−0.871896
$716$	−14.2094	−0.531029
$717$	−29.1047	−1.08693
$718$	29.6125	1.10513
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	−3.70156	−0.137949
$721$	0	0
$722$	−17.0000	−0.632674
$723$	−24.8062	−0.922554
$724$	9.40312	0.349464
$725$	−64.4187	−2.39245
$726$	2.70156	0.100264
$727$	−3.91093	−0.145049	−0.0725243	−	0.997367i	$-0.523105\pi$
$727$	−3.91093	−0.145049	−0.0725243	+	0.997367i	$0.523105\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	43.3141	1.60313
$731$	2.29844	0.0850108
$732$	−2.00000	−0.0739221
$733$	−53.0156	−1.95818	−0.979088	−	0.203436i	$-0.934789\pi$
$733$	−53.0156	−1.95818	−0.979088	+	0.203436i	$0.934789\pi$
$734$	14.8062	0.546509
$735$	0	0
$736$	3.40312	0.125441
$737$	35.9109	1.32280
$738$	−1.40312	−0.0516497
$739$	30.8062	1.13323	0.566613	−	0.823984i	$-0.308253\pi$
$739$	30.8062	1.13323	0.566613	+	0.823984i	$0.308253\pi$
$740$	−6.29844	−0.231535
$741$	10.2094	0.375051
$742$	0	0
$743$	14.2094	0.521291	0.260646	−	0.965435i	$-0.416065\pi$
$743$	14.2094	0.521291	0.260646	+	0.965435i	$0.416065\pi$
$744$	0	0
$745$	72.9266	2.67182
$746$	9.40312	0.344273
$747$	−8.29844	−0.303624
$748$	3.70156	0.135343
$749$	0	0
$750$	−13.7016	−0.500310
$751$	17.1938	0.627409	0.313704	−	0.949521i	$-0.398430\pi$
$751$	17.1938	0.627409	0.313704	+	0.949521i	$0.398430\pi$
$752$	8.00000	0.291730
$753$	−13.9109	−0.506943
$754$	12.5969	0.458751
$755$	25.1938	0.916894
$756$	0	0
$757$	28.2094	1.02529	0.512644	−	0.858602i	$-0.328666\pi$
$757$	28.2094	1.02529	0.512644	+	0.858602i	$0.328666\pi$
$758$	−31.6125	−1.14822
$759$	12.5969	0.457238
$760$	−22.2094	−0.805619
$761$	−24.8953	−0.902454	−0.451227	−	0.892409i	$-0.649014\pi$
$761$	−24.8953	−0.902454	−0.451227	+	0.892409i	$0.649014\pi$
$762$	−4.59688	−0.166527
$763$	0	0
$764$	−13.1047	−0.474111
$765$	−3.70156	−0.133830
$766$	2.80625	0.101394
$767$	−9.19375	−0.331967
$768$	−1.00000	−0.0360844
$769$	16.8062	0.606049	0.303024	−	0.952983i	$-0.402004\pi$
$769$	16.8062	0.606049	0.303024	+	0.952983i	$0.402004\pi$
$770$	0	0
$771$	26.5078	0.954655
$772$	16.2094	0.583388
$773$	−28.4187	−1.02215	−0.511076	−	0.859536i	$-0.670753\pi$
$773$	−28.4187	−1.02215	−0.511076	+	0.859536i	$0.670753\pi$
$774$	−2.29844	−0.0826156
$775$	0	0
$776$	0.298438	0.0107133
$777$	0	0
$778$	−24.8062	−0.889347
$779$	−8.41875	−0.301633
$780$	6.29844	0.225520
$781$	40.0000	1.43131
$782$	3.40312	0.121695
$783$	7.40312	0.264566
$784$	0	0
$785$	82.2094	2.93418
$786$	7.40312	0.264061
$787$	−47.9109	−1.70784	−0.853920	−	0.520404i	$-0.825781\pi$
$787$	−47.9109	−1.70784	−0.853920	+	0.520404i	$0.825781\pi$
$788$	−12.0000	−0.427482
$789$	29.1047	1.03615
$790$	50.7172	1.80444
$791$	0	0
$792$	−3.70156	−0.131529
$793$	3.40312	0.120848
$794$	21.4031	0.759568
$795$	−28.5078	−1.01107
$796$	−6.80625	−0.241241
$797$	−43.4031	−1.53742	−0.768709	−	0.639599i	$-0.779100\pi$
$797$	−43.4031	−1.53742	−0.768709	+	0.639599i	$0.779100\pi$
$798$	0	0
$799$	8.00000	0.283020
$800$	−8.70156	−0.307647
$801$	−8.29844	−0.293211
$802$	−22.0000	−0.776847
$803$	43.3141	1.52852
$804$	−9.70156	−0.342148
$805$	0	0
$806$	0	0
$807$	14.0000	0.492823
$808$	−18.8062	−0.661602
$809$	−8.80625	−0.309611	−0.154806	−	0.987945i	$-0.549475\pi$
$809$	−8.80625	−0.309611	−0.154806	+	0.987945i	$0.549475\pi$
$810$	3.70156	0.130060
$811$	5.10469	0.179250	0.0896249	−	0.995976i	$-0.471433\pi$
$811$	5.10469	0.179250	0.0896249	+	0.995976i	$0.471433\pi$
$812$	0	0
$813$	12.5078	0.438668
$814$	−6.29844	−0.220760
$815$	37.0156	1.29660
$816$	−1.00000	−0.0350070
$817$	−13.7906	−0.482473
$818$	12.8062	0.447760
$819$	0	0
$820$	−5.19375	−0.181374
$821$	−8.59688	−0.300033	−0.150017	−	0.988683i	$-0.547933\pi$
$821$	−8.59688	−0.300033	−0.150017	+	0.988683i	$0.547933\pi$
$822$	−13.4031	−0.467488
$823$	29.7016	1.03533	0.517666	−	0.855583i	$-0.326801\pi$
$823$	29.7016	1.03533	0.517666	+	0.855583i	$0.326801\pi$
$824$	−12.5078	−0.435730
$825$	−32.2094	−1.12139
$826$	0	0
$827$	−37.9109	−1.31829	−0.659146	−	0.752015i	$-0.729082\pi$
$827$	−37.9109	−1.31829	−0.659146	+	0.752015i	$0.729082\pi$
$828$	−3.40312	−0.118267
$829$	33.7016	1.17050	0.585252	−	0.810852i	$-0.300996\pi$
$829$	33.7016	1.17050	0.585252	+	0.810852i	$0.300996\pi$
$830$	−30.7172	−1.06621
$831$	−3.40312	−0.118053
$832$	1.70156	0.0589911
$833$	0	0
$834$	−1.70156	−0.0589203
$835$	61.1047	2.11461
$836$	−22.2094	−0.768127
$837$	0	0
$838$	−18.2094	−0.629032
$839$	26.8953	0.928529	0.464265	−	0.885697i	$-0.346319\pi$
$839$	26.8953	0.928529	0.464265	+	0.885697i	$0.346319\pi$
$840$	0	0
$841$	25.8062	0.889871
$842$	22.0000	0.758170
$843$	−4.80625	−0.165536
$844$	−16.8062	−0.578495
$845$	37.4031	1.28671
$846$	−8.00000	−0.275046
$847$	0	0
$848$	−7.70156	−0.264473
$849$	2.89531	0.0993669
$850$	−8.70156	−0.298461
$851$	−5.79063	−0.198500
$852$	−10.8062	−0.370216
$853$	7.61250	0.260647	0.130323	−	0.991472i	$-0.458398\pi$
$853$	7.61250	0.260647	0.130323	+	0.991472i	$0.458398\pi$
$854$	0	0
$855$	22.2094	0.759545
$856$	17.4031	0.594827
$857$	−43.0156	−1.46939	−0.734693	−	0.678400i	$-0.762674\pi$
$857$	−43.0156	−1.46939	−0.734693	+	0.678400i	$0.762674\pi$
$858$	6.29844	0.215025
$859$	18.0000	0.614152	0.307076	−	0.951685i	$-0.400649\pi$
$859$	18.0000	0.614152	0.307076	+	0.951685i	$0.400649\pi$
$860$	−8.50781	−0.290114
$861$	0	0
$862$	0	0
$863$	1.70156	0.0579218	0.0289609	−	0.999581i	$-0.490780\pi$
$863$	1.70156	0.0579218	0.0289609	+	0.999581i	$0.490780\pi$
$864$	1.00000	0.0340207
$865$	−37.0156	−1.25857
$866$	16.2094	0.550817
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	50.7172	1.72046
$870$	27.4031	0.929053
$871$	16.5078	0.559346
$872$	−7.40312	−0.250701
$873$	−0.298438	−0.0101006
$874$	−20.4187	−0.690674
$875$	0	0
$876$	−11.7016	−0.395359
$877$	2.29844	0.0776127	0.0388064	−	0.999247i	$-0.487644\pi$
$877$	2.29844	0.0776127	0.0388064	+	0.999247i	$0.487644\pi$
$878$	30.8062	1.03966
$879$	8.00000	0.269833
$880$	−13.7016	−0.461880
$881$	−40.8062	−1.37480	−0.687399	−	0.726280i	$-0.741247\pi$
$881$	−40.8062	−1.37480	−0.687399	+	0.726280i	$0.741247\pi$
$882$	0	0
$883$	54.8062	1.84438	0.922189	−	0.386741i	$-0.126399\pi$
$883$	54.8062	1.84438	0.922189	+	0.386741i	$0.126399\pi$
$884$	1.70156	0.0572297
$885$	−20.0000	−0.672293
$886$	−13.6125	−0.457321
$887$	46.1203	1.54857	0.774284	−	0.632838i	$-0.218110\pi$
$887$	46.1203	1.54857	0.774284	+	0.632838i	$0.218110\pi$
$888$	1.70156	0.0571007
$889$	0	0
$890$	−30.7172	−1.02964
$891$	3.70156	0.124007
$892$	−26.8062	−0.897540
$893$	−48.0000	−1.60626
$894$	−19.7016	−0.658919
$895$	52.5969	1.75812
$896$	0	0
$897$	5.79063	0.193343
$898$	−12.2984	−0.410404
$899$	0	0
$900$	8.70156	0.290052
$901$	−7.70156	−0.256576
$902$	−5.19375	−0.172933
$903$	0	0
$904$	−15.1047	−0.502374
$905$	−34.8062	−1.15700
$906$	−6.80625	−0.226122
$907$	−7.79063	−0.258684	−0.129342	−	0.991600i	$-0.541286\pi$
$907$	−7.79063	−0.258684	−0.129342	+	0.991600i	$0.541286\pi$
$908$	2.80625	0.0931286
$909$	18.8062	0.623764
$910$	0	0
$911$	−48.4187	−1.60418	−0.802092	−	0.597200i	$-0.796280\pi$
$911$	−48.4187	−1.60418	−0.802092	+	0.597200i	$0.796280\pi$
$912$	6.00000	0.198680
$913$	−30.7172	−1.01659
$914$	−8.89531	−0.294231
$915$	7.40312	0.244740
$916$	17.1047	0.565155
$917$	0	0
$918$	1.00000	0.0330049
$919$	13.6125	0.449035	0.224517	−	0.974470i	$-0.427919\pi$
$919$	13.6125	0.449035	0.224517	+	0.974470i	$0.427919\pi$
$920$	−12.5969	−0.415307
$921$	−12.2094	−0.402313
$922$	−27.4031	−0.902474
$923$	18.3875	0.605232
$924$	0	0
$925$	14.8062	0.486826
$926$	29.6125	0.973127
$927$	12.5078	0.410810
$928$	7.40312	0.243019
$929$	30.5969	1.00385	0.501925	−	0.864911i	$-0.332625\pi$
$929$	30.5969	1.00385	0.501925	+	0.864911i	$0.332625\pi$
$930$	0	0
$931$	0	0
$932$	−23.7016	−0.776370
$933$	−13.1047	−0.429028
$934$	−20.2094	−0.661271
$935$	−13.7016	−0.448089
$936$	−1.70156	−0.0556173
$937$	−41.8219	−1.36626	−0.683130	−	0.730296i	$-0.739382\pi$
$937$	−41.8219	−1.36626	−0.683130	+	0.730296i	$0.739382\pi$
$938$	0	0
$939$	−20.8062	−0.678986
$940$	−29.6125	−0.965853
$941$	−43.1047	−1.40517	−0.702586	−	0.711599i	$-0.747972\pi$
$941$	−43.1047	−1.40517	−0.702586	+	0.711599i	$0.747972\pi$
$942$	−22.2094	−0.723620
$943$	−4.77501	−0.155496
$944$	−5.40312	−0.175857
$945$	0	0
$946$	−8.50781	−0.276613
$947$	16.2094	0.526734	0.263367	−	0.964696i	$-0.415167\pi$
$947$	16.2094	0.526734	0.263367	+	0.964696i	$0.415167\pi$
$948$	−13.7016	−0.445006
$949$	19.9109	0.646336
$950$	52.2094	1.69390
$951$	15.4031	0.499481
$952$	0	0
$953$	−20.8062	−0.673980	−0.336990	−	0.941508i	$-0.609409\pi$
$953$	−20.8062	−0.673980	−0.336990	+	0.941508i	$0.609409\pi$
$954$	7.70156	0.249347
$955$	48.5078	1.56968
$956$	29.1047	0.941313
$957$	27.4031	0.885817
$958$	37.1047	1.19880
$959$	0	0
$960$	3.70156	0.119467
$961$	−31.0000	−1.00000
$962$	−2.89531	−0.0933487
$963$	−17.4031	−0.560808
$964$	24.8062	0.798955
$965$	−60.0000	−1.93147
$966$	0	0
$967$	60.4187	1.94294	0.971468	−	0.237171i	$-0.0762201\pi$
$967$	60.4187	1.94294	0.971468	+	0.237171i	$0.0762201\pi$
$968$	−2.70156	−0.0868315
$969$	6.00000	0.192748
$970$	−1.10469	−0.0354693
$971$	−52.7172	−1.69177	−0.845887	−	0.533361i	$-0.820929\pi$
$971$	−52.7172	−1.69177	−0.845887	+	0.533361i	$0.820929\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	18.8953	0.605445
$975$	−14.8062	−0.474179
$976$	2.00000	0.0640184
$977$	37.4031	1.19663	0.598316	−	0.801260i	$-0.295837\pi$
$977$	37.4031	1.19663	0.598316	+	0.801260i	$0.295837\pi$
$978$	−10.0000	−0.319765
$979$	−30.7172	−0.981725
$980$	0	0
$981$	7.40312	0.236364
$982$	−31.4031	−1.00211
$983$	24.0000	0.765481	0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000	0.765481	0.382741	+	0.923856i	$0.374980\pi$
$984$	1.40312	0.0447300
$985$	44.4187	1.41530
$986$	7.40312	0.235764
$987$	0	0
$988$	−10.2094	−0.324803
$989$	−7.82187	−0.248721
$990$	13.7016	0.435464
$991$	−23.9109	−0.759556	−0.379778	−	0.925078i	$-0.624000\pi$
$991$	−23.9109	−0.759556	−0.379778	+	0.925078i	$0.624000\pi$
$992$	0	0
$993$	−13.7016	−0.434806
$994$	0	0
$995$	25.1938	0.798696
$996$	8.29844	0.262946
$997$	−15.0156	−0.475549	−0.237775	−	0.971320i	$-0.576418\pi$
$997$	−15.0156	−0.475549	−0.237775	+	0.971320i	$0.576418\pi$
$998$	−9.40312	−0.297651
$999$	−1.70156	−0.0538350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4998.2.a.bs.1.1		2
7.6	odd	2		714.2.a.k.1.2	✓	2
21.20	even	2		2142.2.a.y.1.1		2
28.27	even	2		5712.2.a.bi.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.a.k.1.2	✓	2	7.6	odd	2
2142.2.a.y.1.1		2	21.20	even	2
4998.2.a.bs.1.1		2	1.1	even	1	trivial
5712.2.a.bi.1.2		2	28.27	even	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.70156 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.70156 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +3.70156 q^{10} +3.70156 q^{11} -1.00000 q^{12} +1.70156 q^{13} +3.70156 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -6.00000 q^{19} -3.70156 q^{20} -3.70156 q^{22} -3.40312 q^{23} +1.00000 q^{24} +8.70156 q^{25} -1.70156 q^{26} -1.00000 q^{27} -7.40312 q^{29} -3.70156 q^{30} -1.00000 q^{32} -3.70156 q^{33} -1.00000 q^{34} +1.00000 q^{36} +1.70156 q^{37} +6.00000 q^{38} -1.70156 q^{39} +3.70156 q^{40} +1.40312 q^{41} +2.29844 q^{43} +3.70156 q^{44} -3.70156 q^{45} +3.40312 q^{46} +8.00000 q^{47} -1.00000 q^{48} -8.70156 q^{50} -1.00000 q^{51} +1.70156 q^{52} -7.70156 q^{53} +1.00000 q^{54} -13.7016 q^{55} +6.00000 q^{57} +7.40312 q^{58} -5.40312 q^{59} +3.70156 q^{60} +2.00000 q^{61} +1.00000 q^{64} -6.29844 q^{65} +3.70156 q^{66} +9.70156 q^{67} +1.00000 q^{68} +3.40312 q^{69} +10.8062 q^{71} -1.00000 q^{72} +11.7016 q^{73} -1.70156 q^{74} -8.70156 q^{75} -6.00000 q^{76} +1.70156 q^{78} +13.7016 q^{79} -3.70156 q^{80} +1.00000 q^{81} -1.40312 q^{82} -8.29844 q^{83} -3.70156 q^{85} -2.29844 q^{86} +7.40312 q^{87} -3.70156 q^{88} -8.29844 q^{89} +3.70156 q^{90} -3.40312 q^{92} -8.00000 q^{94} +22.2094 q^{95} +1.00000 q^{96} -0.298438 q^{97} +3.70156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} + q^{11} - 2 q^{12} - 3 q^{13} + q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} - 12 q^{19} - q^{20} - q^{22} + 6 q^{23} + 2 q^{24} + 11 q^{25} + 3 q^{26} - 2 q^{27} - 2 q^{29} - q^{30} - 2 q^{32} - q^{33} - 2 q^{34} + 2 q^{36} - 3 q^{37} + 12 q^{38} + 3 q^{39} + q^{40} - 10 q^{41} + 11 q^{43} + q^{44} - q^{45} - 6 q^{46} + 16 q^{47} - 2 q^{48} - 11 q^{50} - 2 q^{51} - 3 q^{52} - 9 q^{53} + 2 q^{54} - 21 q^{55} + 12 q^{57} + 2 q^{58} + 2 q^{59} + q^{60} + 4 q^{61} + 2 q^{64} - 19 q^{65} + q^{66} + 13 q^{67} + 2 q^{68} - 6 q^{69} - 4 q^{71} - 2 q^{72} + 17 q^{73} + 3 q^{74} - 11 q^{75} - 12 q^{76} - 3 q^{78} + 21 q^{79} - q^{80} + 2 q^{81} + 10 q^{82} - 23 q^{83} - q^{85} - 11 q^{86} + 2 q^{87} - q^{88} - 23 q^{89} + q^{90} + 6 q^{92} - 16 q^{94} + 6 q^{95} + 2 q^{96} - 7 q^{97} + q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 + q^11 - 2 * q^12 - 3 * q^13 + q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 - 12 * q^19 - q^20 - q^22 + 6 * q^23 + 2 * q^24 + 11 * q^25 + 3 * q^26 - 2 * q^27 - 2 * q^29 - q^30 - 2 * q^32 - q^33 - 2 * q^34 + 2 * q^36 - 3 * q^37 + 12 * q^38 + 3 * q^39 + q^40 - 10 * q^41 + 11 * q^43 + q^44 - q^45 - 6 * q^46 + 16 * q^47 - 2 * q^48 - 11 * q^50 - 2 * q^51 - 3 * q^52 - 9 * q^53 + 2 * q^54 - 21 * q^55 + 12 * q^57 + 2 * q^58 + 2 * q^59 + q^60 + 4 * q^61 + 2 * q^64 - 19 * q^65 + q^66 + 13 * q^67 + 2 * q^68 - 6 * q^69 - 4 * q^71 - 2 * q^72 + 17 * q^73 + 3 * q^74 - 11 * q^75 - 12 * q^76 - 3 * q^78 + 21 * q^79 - q^80 + 2 * q^81 + 10 * q^82 - 23 * q^83 - q^85 - 11 * q^86 + 2 * q^87 - q^88 - 23 * q^89 + q^90 + 6 * q^92 - 16 * q^94 + 6 * q^95 + 2 * q^96 - 7 * q^97 + q^99

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