LMFDB - Embedded newform 4025.2.a.bd.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.475047 q^{2} +0.568069 q^{3} -1.77433 q^{4} -0.269859 q^{6} -1.00000 q^{7} +1.79298 q^{8} -2.67730 q^{9} +O(q^{10})$	\(q-0.475047 q^{2} +0.568069 q^{3} -1.77433 q^{4} -0.269859 q^{6} -1.00000 q^{7} +1.79298 q^{8} -2.67730 q^{9} +3.62393 q^{11} -1.00794 q^{12} -0.366330 q^{13} +0.475047 q^{14} +2.69691 q^{16} +4.72015 q^{17} +1.27184 q^{18} +2.25210 q^{19} -0.568069 q^{21} -1.72153 q^{22} -1.00000 q^{23} +1.01854 q^{24} +0.174024 q^{26} -3.22510 q^{27} +1.77433 q^{28} -1.38003 q^{29} -6.19921 q^{31} -4.86712 q^{32} +2.05864 q^{33} -2.24229 q^{34} +4.75041 q^{36} -1.74136 q^{37} -1.06985 q^{38} -0.208101 q^{39} -2.66442 q^{41} +0.269859 q^{42} +3.44974 q^{43} -6.43005 q^{44} +0.475047 q^{46} +6.94831 q^{47} +1.53203 q^{48} +1.00000 q^{49} +2.68137 q^{51} +0.649991 q^{52} -3.64904 q^{53} +1.53207 q^{54} -1.79298 q^{56} +1.27935 q^{57} +0.655580 q^{58} -3.54909 q^{59} -1.04697 q^{61} +2.94491 q^{62} +2.67730 q^{63} -3.08171 q^{64} -0.977951 q^{66} -7.17892 q^{67} -8.37511 q^{68} -0.568069 q^{69} +1.85410 q^{71} -4.80035 q^{72} -8.97042 q^{73} +0.827227 q^{74} -3.99596 q^{76} -3.62393 q^{77} +0.0988577 q^{78} +8.42912 q^{79} +6.19981 q^{81} +1.26572 q^{82} -3.02053 q^{83} +1.00794 q^{84} -1.63879 q^{86} -0.783955 q^{87} +6.49764 q^{88} +14.5728 q^{89} +0.366330 q^{91} +1.77433 q^{92} -3.52158 q^{93} -3.30077 q^{94} -2.76486 q^{96} -2.17489 q^{97} -0.475047 q^{98} -9.70233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 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 $

$2$	−0.475047	−0.335909	−0.167954	−	0.985795i	$-0.553716\pi$
$2$	−0.475047	−0.335909	−0.167954	+	0.985795i	$0.553716\pi$
$3$	0.568069	0.327975	0.163987	−	0.986462i	$-0.447564\pi$
$3$	0.568069	0.327975	0.163987	+	0.986462i	$0.447564\pi$
$4$	−1.77433	−0.887165
$5$	0	0
$5$	0	0
$6$	−0.269859	−0.110170
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.79298	0.633915
$9$	−2.67730	−0.892432
$10$	0	0
$11$	3.62393	1.09266	0.546328	−	0.837572i	$-0.316025\pi$
$11$	3.62393	1.09266	0.546328	+	0.837572i	$0.316025\pi$
$12$	−1.00794	−0.290968
$13$	−0.366330	−0.101602	−0.0508009	−	0.998709i	$-0.516177\pi$
$13$	−0.366330	−0.101602	−0.0508009	+	0.998709i	$0.516177\pi$
$14$	0.475047	0.126962
$15$	0	0
$16$	2.69691	0.674228
$17$	4.72015	1.14480	0.572402	−	0.819973i	$-0.306012\pi$
$17$	4.72015	1.14480	0.572402	+	0.819973i	$0.306012\pi$
$18$	1.27184	0.299776
$19$	2.25210	0.516666	0.258333	−	0.966056i	$-0.416827\pi$
$19$	2.25210	0.516666	0.258333	+	0.966056i	$0.416827\pi$
$20$	0	0
$21$	−0.568069	−0.123963
$22$	−1.72153	−0.367032
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.01854	0.207908
$25$	0	0
$26$	0.174024	0.0341289
$27$	−3.22510	−0.620670
$28$	1.77433	0.335317
$29$	−1.38003	−0.256266	−0.128133	−	0.991757i	$-0.540898\pi$
$29$	−1.38003	−0.256266	−0.128133	+	0.991757i	$0.540898\pi$
$30$	0	0
$31$	−6.19921	−1.11341	−0.556705	−	0.830710i	$-0.687935\pi$
$31$	−6.19921	−1.11341	−0.556705	+	0.830710i	$0.687935\pi$
$32$	−4.86712	−0.860394
$33$	2.05864	0.358364
$34$	−2.24229	−0.384550
$35$	0	0
$36$	4.75041	0.791735
$37$	−1.74136	−0.286278	−0.143139	−	0.989703i	$-0.545720\pi$
$37$	−1.74136	−0.286278	−0.143139	+	0.989703i	$0.545720\pi$
$38$	−1.06985	−0.173553
$39$	−0.208101	−0.0333228
$40$	0	0
$41$	−2.66442	−0.416113	−0.208056	−	0.978117i	$-0.566714\pi$
$41$	−2.66442	−0.416113	−0.208056	+	0.978117i	$0.566714\pi$
$42$	0.269859	0.0416402
$43$	3.44974	0.526080	0.263040	−	0.964785i	$-0.415275\pi$
$43$	3.44974	0.526080	0.263040	+	0.964785i	$0.415275\pi$
$44$	−6.43005	−0.969366
$45$	0	0
$46$	0.475047	0.0700418
$47$	6.94831	1.01352	0.506758	−	0.862088i	$-0.330844\pi$
$47$	6.94831	1.01352	0.506758	+	0.862088i	$0.330844\pi$
$48$	1.53203	0.221130
$49$	1.00000	0.142857
$50$	0	0
$51$	2.68137	0.375467
$52$	0.649991	0.0901376
$53$	−3.64904	−0.501234	−0.250617	−	0.968086i	$-0.580634\pi$
$53$	−3.64904	−0.501234	−0.250617	+	0.968086i	$0.580634\pi$
$54$	1.53207	0.208489
$55$	0	0
$56$	−1.79298	−0.239597
$57$	1.27935	0.169454
$58$	0.655580	0.0860819
$59$	−3.54909	−0.462052	−0.231026	−	0.972948i	$-0.574208\pi$
$59$	−3.54909	−0.462052	−0.231026	+	0.972948i	$0.574208\pi$
$60$	0	0
$61$	−1.04697	−0.134051	−0.0670255	−	0.997751i	$-0.521351\pi$
$61$	−1.04697	−0.134051	−0.0670255	+	0.997751i	$0.521351\pi$
$62$	2.94491	0.374004
$63$	2.67730	0.337308
$64$	−3.08171	−0.385214
$65$	0	0
$66$	−0.977951	−0.120377
$67$	−7.17892	−0.877045	−0.438523	−	0.898720i	$-0.644498\pi$
$67$	−7.17892	−0.877045	−0.438523	+	0.898720i	$0.644498\pi$
$68$	−8.37511	−1.01563
$69$	−0.568069	−0.0683875
$70$	0	0
$71$	1.85410	0.220042	0.110021	−	0.993929i	$-0.464908\pi$
$71$	1.85410	0.220042	0.110021	+	0.993929i	$0.464908\pi$
$72$	−4.80035	−0.565727
$73$	−8.97042	−1.04991	−0.524954	−	0.851131i	$-0.675917\pi$
$73$	−8.97042	−1.04991	−0.524954	+	0.851131i	$0.675917\pi$
$74$	0.827227	0.0961631
$75$	0	0
$76$	−3.99596	−0.458368
$77$	−3.62393	−0.412985
$78$	0.0988577	0.0111934
$79$	8.42912	0.948350	0.474175	−	0.880431i	$-0.342746\pi$
$79$	8.42912	0.948350	0.474175	+	0.880431i	$0.342746\pi$
$80$	0	0
$81$	6.19981	0.688868
$82$	1.26572	0.139776
$83$	−3.02053	−0.331546	−0.165773	−	0.986164i	$-0.553012\pi$
$83$	−3.02053	−0.331546	−0.165773	+	0.986164i	$0.553012\pi$
$84$	1.00794	0.109976
$85$	0	0
$86$	−1.63879	−0.176715
$87$	−0.783955	−0.0840488
$88$	6.49764	0.692651
$89$	14.5728	1.54471	0.772356	−	0.635190i	$-0.219078\pi$
$89$	14.5728	1.54471	0.772356	+	0.635190i	$0.219078\pi$
$90$	0	0
$91$	0.366330	0.0384019
$92$	1.77433	0.184987
$93$	−3.52158	−0.365171
$94$	−3.30077	−0.340449
$95$	0	0
$96$	−2.76486	−0.282188
$97$	−2.17489	−0.220826	−0.110413	−	0.993886i	$-0.535217\pi$
$97$	−2.17489	−0.220826	−0.110413	+	0.993886i	$0.535217\pi$
$98$	−0.475047	−0.0479870
$99$	−9.70233	−0.975121
$100$	0	0
$101$	17.1405	1.70555	0.852773	−	0.522282i	$-0.174919\pi$
$101$	17.1405	1.70555	0.852773	+	0.522282i	$0.174919\pi$
$102$	−1.27378	−0.126123
$103$	5.42016	0.534064	0.267032	−	0.963688i	$-0.413957\pi$
$103$	5.42016	0.534064	0.267032	+	0.963688i	$0.413957\pi$
$104$	−0.656824	−0.0644069
$105$	0	0
$106$	1.73346	0.168369
$107$	8.75692	0.846563	0.423281	−	0.905998i	$-0.360878\pi$
$107$	8.75692	0.846563	0.423281	+	0.905998i	$0.360878\pi$
$108$	5.72239	0.550637
$109$	14.1208	1.35252	0.676262	−	0.736661i	$-0.263599\pi$
$109$	14.1208	1.35252	0.676262	+	0.736661i	$0.263599\pi$
$110$	0	0
$111$	−0.989212	−0.0938919
$112$	−2.69691	−0.254834
$113$	6.24934	0.587889	0.293944	−	0.955823i	$-0.405032\pi$
$113$	6.24934	0.587889	0.293944	+	0.955823i	$0.405032\pi$
$114$	−0.607749	−0.0569209
$115$	0	0
$116$	2.44864	0.227350
$117$	0.980775	0.0906727
$118$	1.68598	0.155207
$119$	−4.72015	−0.432695
$120$	0	0
$121$	2.13285	0.193896
$122$	0.497360	0.0450289
$123$	−1.51358	−0.136474
$124$	10.9994	0.987780
$125$	0	0
$126$	−1.27184	−0.113305
$127$	−7.14552	−0.634062	−0.317031	−	0.948415i	$-0.602686\pi$
$127$	−7.14552	−0.634062	−0.317031	+	0.948415i	$0.602686\pi$
$128$	11.1982	0.989791
$129$	1.95969	0.172541
$130$	0	0
$131$	17.2298	1.50537	0.752685	−	0.658380i	$-0.228758\pi$
$131$	17.2298	1.50537	0.752685	+	0.658380i	$0.228758\pi$
$132$	−3.65271	−0.317928
$133$	−2.25210	−0.195281
$134$	3.41032	0.294607
$135$	0	0
$136$	8.46315	0.725709
$137$	21.8791	1.86926	0.934630	−	0.355621i	$-0.115731\pi$
$137$	21.8791	1.86926	0.934630	+	0.355621i	$0.115731\pi$
$138$	0.269859	0.0229720
$139$	9.49823	0.805630	0.402815	−	0.915281i	$-0.368032\pi$
$139$	9.49823	0.805630	0.402815	+	0.915281i	$0.368032\pi$
$140$	0	0
$141$	3.94712	0.332408
$142$	−0.880786	−0.0739139
$143$	−1.32755	−0.111016
$144$	−7.22043	−0.601703
$145$	0	0
$146$	4.26137	0.352673
$147$	0.568069	0.0468536
$148$	3.08975	0.253976
$149$	21.0603	1.72533	0.862665	−	0.505776i	$-0.168794\pi$
$149$	21.0603	1.72533	0.862665	+	0.505776i	$0.168794\pi$
$150$	0	0
$151$	2.70376	0.220029	0.110015	−	0.993930i	$-0.464910\pi$
$151$	2.70376	0.220029	0.110015	+	0.993930i	$0.464910\pi$
$152$	4.03797	0.327523
$153$	−12.6372	−1.02166
$154$	1.72153	0.138725
$155$	0	0
$156$	0.369240	0.0295629
$157$	0.260067	0.0207556	0.0103778	−	0.999946i	$-0.496697\pi$
$157$	0.260067	0.0207556	0.0103778	+	0.999946i	$0.496697\pi$
$158$	−4.00422	−0.318559
$159$	−2.07291	−0.164392
$160$	0	0
$161$	1.00000	0.0788110
$162$	−2.94520	−0.231397
$163$	−15.3158	−1.19963	−0.599814	−	0.800140i	$-0.704759\pi$
$163$	−15.3158	−1.19963	−0.599814	+	0.800140i	$0.704759\pi$
$164$	4.72756	0.369161
$165$	0	0
$166$	1.43489	0.111369
$167$	7.47626	0.578531	0.289265	−	0.957249i	$-0.406589\pi$
$167$	7.47626	0.578531	0.289265	+	0.957249i	$0.406589\pi$
$168$	−1.01854	−0.0785819
$169$	−12.8658	−0.989677
$170$	0	0
$171$	−6.02953	−0.461090
$172$	−6.12098	−0.466720
$173$	−11.2814	−0.857708	−0.428854	−	0.903374i	$-0.641083\pi$
$173$	−11.2814	−0.857708	−0.428854	+	0.903374i	$0.641083\pi$
$174$	0.372415	0.0282327
$175$	0	0
$176$	9.77341	0.736699
$177$	−2.01613	−0.151541
$178$	−6.92275	−0.518882
$179$	−3.17351	−0.237199	−0.118600	−	0.992942i	$-0.537841\pi$
$179$	−3.17351	−0.237199	−0.118600	+	0.992942i	$0.537841\pi$
$180$	0	0
$181$	11.1059	0.825493	0.412747	−	0.910846i	$-0.364570\pi$
$181$	11.1059	0.825493	0.412747	+	0.910846i	$0.364570\pi$
$182$	−0.174024	−0.0128995
$183$	−0.594752	−0.0439653
$184$	−1.79298	−0.132180
$185$	0	0
$186$	1.67291	0.122664
$187$	17.1055	1.25088
$188$	−12.3286	−0.899156
$189$	3.22510	0.234591
$190$	0	0
$191$	11.6272	0.841314	0.420657	−	0.907220i	$-0.361800\pi$
$191$	11.6272	0.841314	0.420657	+	0.907220i	$0.361800\pi$
$192$	−1.75062	−0.126340
$193$	−19.1682	−1.37976	−0.689879	−	0.723924i	$-0.742336\pi$
$193$	−19.1682	−1.37976	−0.689879	+	0.723924i	$0.742336\pi$
$194$	1.03317	0.0741775
$195$	0	0
$196$	−1.77433	−0.126738
$197$	12.7813	0.910632	0.455316	−	0.890330i	$-0.349526\pi$
$197$	12.7813	0.910632	0.455316	+	0.890330i	$0.349526\pi$
$198$	4.60906	0.327552
$199$	−11.3322	−0.803317	−0.401659	−	0.915790i	$-0.631566\pi$
$199$	−11.3322	−0.803317	−0.401659	+	0.915790i	$0.631566\pi$
$200$	0	0
$201$	−4.07813	−0.287649
$202$	−8.14255	−0.572908
$203$	1.38003	0.0968594
$204$	−4.75764	−0.333101
$205$	0	0
$206$	−2.57483	−0.179397
$207$	2.67730	0.186085
$208$	−0.987960	−0.0685027
$209$	8.16143	0.564538
$210$	0	0
$211$	22.4696	1.54687	0.773435	−	0.633876i	$-0.218537\pi$
$211$	22.4696	1.54687	0.773435	+	0.633876i	$0.218537\pi$
$212$	6.47460	0.444678
$213$	1.05326	0.0721681
$214$	−4.15994	−0.284368
$215$	0	0
$216$	−5.78255	−0.393452
$217$	6.19921	0.420830
$218$	−6.70802	−0.454324
$219$	−5.09582	−0.344343
$220$	0	0
$221$	−1.72913	−0.116314
$222$	0.469922	0.0315391
$223$	23.7740	1.59203	0.796013	−	0.605279i	$-0.206939\pi$
$223$	23.7740	1.59203	0.796013	+	0.605279i	$0.206939\pi$
$224$	4.86712	0.325198
$225$	0	0
$226$	−2.96873	−0.197477
$227$	−12.2752	−0.814734	−0.407367	−	0.913265i	$-0.633553\pi$
$227$	−12.2752	−0.814734	−0.407367	+	0.913265i	$0.633553\pi$
$228$	−2.26998	−0.150333
$229$	23.4129	1.54717	0.773585	−	0.633693i	$-0.218462\pi$
$229$	23.4129	1.54717	0.773585	+	0.633693i	$0.218462\pi$
$230$	0	0
$231$	−2.05864	−0.135449
$232$	−2.47438	−0.162451
$233$	−23.2138	−1.52079	−0.760393	−	0.649463i	$-0.774994\pi$
$233$	−23.2138	−1.52079	−0.760393	+	0.649463i	$0.774994\pi$
$234$	−0.465914	−0.0304578
$235$	0	0
$236$	6.29725	0.409916
$237$	4.78832	0.311035
$238$	2.24229	0.145346
$239$	9.48945	0.613821	0.306911	−	0.951738i	$-0.400705\pi$
$239$	9.48945	0.613821	0.306911	+	0.951738i	$0.400705\pi$
$240$	0	0
$241$	11.7032	0.753869	0.376934	−	0.926240i	$-0.376978\pi$
$241$	11.7032	0.753869	0.376934	+	0.926240i	$0.376978\pi$
$242$	−1.01320	−0.0651313
$243$	13.1972	0.846602
$244$	1.85767	0.118925
$245$	0	0
$246$	0.719019	0.0458430
$247$	−0.825011	−0.0524942
$248$	−11.1151	−0.705808
$249$	−1.71587	−0.108739
$250$	0	0
$251$	−12.6949	−0.801295	−0.400648	−	0.916232i	$-0.631215\pi$
$251$	−12.6949	−0.801295	−0.400648	+	0.916232i	$0.631215\pi$
$252$	−4.75041	−0.299248
$253$	−3.62393	−0.227834
$254$	3.39446	0.212987
$255$	0	0
$256$	0.843751	0.0527345
$257$	−9.06991	−0.565765	−0.282883	−	0.959155i	$-0.591291\pi$
$257$	−9.06991	−0.565765	−0.282883	+	0.959155i	$0.591291\pi$
$258$	−0.930944	−0.0579581
$259$	1.74136	0.108203
$260$	0	0
$261$	3.69476	0.228700
$262$	−8.18494	−0.505667
$263$	16.4561	1.01473	0.507363	−	0.861732i	$-0.330620\pi$
$263$	16.4561	1.01473	0.507363	+	0.861732i	$0.330620\pi$
$264$	3.69111	0.227172
$265$	0	0
$266$	1.06985	0.0655967
$267$	8.27834	0.506626
$268$	12.7378	0.778084
$269$	−27.0742	−1.65074	−0.825372	−	0.564589i	$-0.809035\pi$
$269$	−27.0742	−1.65074	−0.825372	+	0.564589i	$0.809035\pi$
$270$	0	0
$271$	−15.2991	−0.929355	−0.464677	−	0.885480i	$-0.653830\pi$
$271$	−15.2991	−0.929355	−0.464677	+	0.885480i	$0.653830\pi$
$272$	12.7298	0.771859
$273$	0.208101	0.0125948
$274$	−10.3936	−0.627901
$275$	0	0
$276$	1.00794	0.0606710
$277$	−12.0456	−0.723752	−0.361876	−	0.932226i	$-0.617864\pi$
$277$	−12.0456	−0.723752	−0.361876	+	0.932226i	$0.617864\pi$
$278$	−4.51210	−0.270618
$279$	16.5971	0.993644
$280$	0	0
$281$	27.7280	1.65411	0.827057	−	0.562119i	$-0.190014\pi$
$281$	27.7280	1.65411	0.827057	+	0.562119i	$0.190014\pi$
$282$	−1.87507	−0.111659
$283$	−14.7837	−0.878798	−0.439399	−	0.898292i	$-0.644808\pi$
$283$	−14.7837	−0.878798	−0.439399	+	0.898292i	$0.644808\pi$
$284$	−3.28979	−0.195213
$285$	0	0
$286$	0.630650	0.0372911
$287$	2.66442	0.157276
$288$	13.0307	0.767844
$289$	5.27981	0.310577
$290$	0	0
$291$	−1.23549	−0.0724255
$292$	15.9165	0.931442
$293$	6.20650	0.362588	0.181294	−	0.983429i	$-0.441972\pi$
$293$	6.20650	0.362588	0.181294	+	0.983429i	$0.441972\pi$
$294$	−0.269859	−0.0157385
$295$	0	0
$296$	−3.12223	−0.181476
$297$	−11.6875	−0.678179
$298$	−10.0046	−0.579553
$299$	0.366330	0.0211854
$300$	0	0
$301$	−3.44974	−0.198840
$302$	−1.28441	−0.0739097
$303$	9.73700	0.559376
$304$	6.07370	0.348351
$305$	0	0
$306$	6.00328	0.343185
$307$	−17.9829	−1.02634	−0.513169	−	0.858288i	$-0.671529\pi$
$307$	−17.9829	−1.02634	−0.513169	+	0.858288i	$0.671529\pi$
$308$	6.43005	0.366386
$309$	3.07902	0.175160
$310$	0	0
$311$	18.1349	1.02834	0.514168	−	0.857690i	$-0.328101\pi$
$311$	18.1349	1.02834	0.514168	+	0.857690i	$0.328101\pi$
$312$	−0.373122	−0.0211238
$313$	17.7307	1.00220	0.501098	−	0.865391i	$-0.332930\pi$
$313$	17.7307	1.00220	0.501098	+	0.865391i	$0.332930\pi$
$314$	−0.123544	−0.00697198
$315$	0	0
$316$	−14.9560	−0.841343
$317$	−24.9852	−1.40331	−0.701653	−	0.712519i	$-0.747554\pi$
$317$	−24.9852	−1.40331	−0.701653	+	0.712519i	$0.747554\pi$
$318$	0.984727	0.0552208
$319$	−5.00114	−0.280010
$320$	0	0
$321$	4.97453	0.277651
$322$	−0.475047	−0.0264733
$323$	10.6302	0.591482
$324$	−11.0005	−0.611140
$325$	0	0
$326$	7.27573	0.402965
$327$	8.02157	0.443594
$328$	−4.77726	−0.263780
$329$	−6.94831	−0.383073
$330$	0	0
$331$	−6.82136	−0.374936	−0.187468	−	0.982271i	$-0.560028\pi$
$331$	−6.82136	−0.374936	−0.187468	+	0.982271i	$0.560028\pi$
$332$	5.35942	0.294136
$333$	4.66213	0.255483
$334$	−3.55157	−0.194333
$335$	0	0
$336$	−1.53203	−0.0835792
$337$	35.0659	1.91016	0.955081	−	0.296346i	$-0.0957681\pi$
$337$	35.0659	1.91016	0.955081	+	0.296346i	$0.0957681\pi$
$338$	6.11186	0.332441
$339$	3.55006	0.192813
$340$	0	0
$341$	−22.4655	−1.21657
$342$	2.86431	0.154884
$343$	−1.00000	−0.0539949
$344$	6.18532	0.333490
$345$	0	0
$346$	5.35919	0.288112
$347$	−1.75166	−0.0940342	−0.0470171	−	0.998894i	$-0.514972\pi$
$347$	−1.75166	−0.0940342	−0.0470171	+	0.998894i	$0.514972\pi$
$348$	1.39099	0.0745652
$349$	12.3350	0.660280	0.330140	−	0.943932i	$-0.392904\pi$
$349$	12.3350	0.660280	0.330140	+	0.943932i	$0.392904\pi$
$350$	0	0
$351$	1.18145	0.0630612
$352$	−17.6381	−0.940114
$353$	4.48809	0.238877	0.119438	−	0.992842i	$-0.461891\pi$
$353$	4.48809	0.238877	0.119438	+	0.992842i	$0.461891\pi$
$354$	0.957754	0.0509040
$355$	0	0
$356$	−25.8569	−1.37041
$357$	−2.68137	−0.141913
$358$	1.50757	0.0796773
$359$	34.5757	1.82484	0.912418	−	0.409260i	$-0.134213\pi$
$359$	34.5757	1.82484	0.912418	+	0.409260i	$0.134213\pi$
$360$	0	0
$361$	−13.9281	−0.733056
$362$	−5.27581	−0.277290
$363$	1.21161	0.0635929
$364$	−0.649991	−0.0340688
$365$	0	0
$366$	0.282535	0.0147683
$367$	−23.7888	−1.24176	−0.620881	−	0.783905i	$-0.713225\pi$
$367$	−23.7888	−1.24176	−0.620881	+	0.783905i	$0.713225\pi$
$368$	−2.69691	−0.140586
$369$	7.13345	0.371352
$370$	0	0
$371$	3.64904	0.189449
$372$	6.24845	0.323967
$373$	3.32047	0.171927	0.0859636	−	0.996298i	$-0.472603\pi$
$373$	3.32047	0.171927	0.0859636	+	0.996298i	$0.472603\pi$
$374$	−8.12590	−0.420180
$375$	0	0
$376$	12.4582	0.642483
$377$	0.505548	0.0260371
$378$	−1.53207	−0.0788013
$379$	11.9530	0.613986	0.306993	−	0.951712i	$-0.400677\pi$
$379$	11.9530	0.613986	0.306993	+	0.951712i	$0.400677\pi$
$380$	0	0
$381$	−4.05915	−0.207957
$382$	−5.52346	−0.282605
$383$	33.4131	1.70733	0.853664	−	0.520825i	$-0.174375\pi$
$383$	33.4131	1.70733	0.853664	+	0.520825i	$0.174375\pi$
$384$	6.36135	0.324627
$385$	0	0
$386$	9.10580	0.463473
$387$	−9.23598	−0.469491
$388$	3.85897	0.195909
$389$	19.6070	0.994116	0.497058	−	0.867717i	$-0.334414\pi$
$389$	19.6070	0.994116	0.497058	+	0.867717i	$0.334414\pi$
$390$	0	0
$391$	−4.72015	−0.238708
$392$	1.79298	0.0905593
$393$	9.78769	0.493724
$394$	−6.07173	−0.305889
$395$	0	0
$396$	17.2151	0.865094
$397$	14.4686	0.726157	0.363079	−	0.931759i	$-0.381726\pi$
$397$	14.4686	0.726157	0.363079	+	0.931759i	$0.381726\pi$
$398$	5.38331	0.269841
$399$	−1.27935	−0.0640474
$400$	0	0
$401$	−23.7511	−1.18607	−0.593037	−	0.805176i	$-0.702071\pi$
$401$	−23.7511	−1.18607	−0.593037	+	0.805176i	$0.702071\pi$
$402$	1.93730	0.0966237
$403$	2.27096	0.113125
$404$	−30.4129	−1.51310
$405$	0	0
$406$	−0.655580	−0.0325359
$407$	−6.31056	−0.312803
$408$	4.80765	0.238014
$409$	−8.88455	−0.439313	−0.219656	−	0.975577i	$-0.570494\pi$
$409$	−8.88455	−0.439313	−0.219656	+	0.975577i	$0.570494\pi$
$410$	0	0
$411$	12.4289	0.613070
$412$	−9.61715	−0.473803
$413$	3.54909	0.174639
$414$	−1.27184	−0.0625076
$415$	0	0
$416$	1.78298	0.0874176
$417$	5.39565	0.264226
$418$	−3.87706	−0.189633
$419$	−22.8044	−1.11407	−0.557034	−	0.830490i	$-0.688061\pi$
$419$	−22.8044	−1.11407	−0.557034	+	0.830490i	$0.688061\pi$
$420$	0	0
$421$	31.4849	1.53448	0.767239	−	0.641361i	$-0.221630\pi$
$421$	31.4849	1.53448	0.767239	+	0.641361i	$0.221630\pi$
$422$	−10.6741	−0.519607
$423$	−18.6027	−0.904494
$424$	−6.54267	−0.317740
$425$	0	0
$426$	−0.500347	−0.0242419
$427$	1.04697	0.0506665
$428$	−15.5377	−0.751041
$429$	−0.754143	−0.0364104
$430$	0	0
$431$	−11.9042	−0.573407	−0.286703	−	0.958019i	$-0.592559\pi$
$431$	−11.9042	−0.573407	−0.286703	+	0.958019i	$0.592559\pi$
$432$	−8.69780	−0.418473
$433$	−3.93648	−0.189175	−0.0945875	−	0.995517i	$-0.530153\pi$
$433$	−3.93648	−0.189175	−0.0945875	+	0.995517i	$0.530153\pi$
$434$	−2.94491	−0.141360
$435$	0	0
$436$	−25.0549	−1.19991
$437$	−2.25210	−0.107732
$438$	2.42075	0.115668
$439$	15.3783	0.733965	0.366983	−	0.930228i	$-0.380391\pi$
$439$	15.3783	0.733965	0.366983	+	0.930228i	$0.380391\pi$
$440$	0	0
$441$	−2.67730	−0.127490
$442$	0.821419	0.0390709
$443$	−26.0062	−1.23559	−0.617796	−	0.786339i	$-0.711974\pi$
$443$	−26.0062	−1.23559	−0.617796	+	0.786339i	$0.711974\pi$
$444$	1.75519	0.0832976
$445$	0	0
$446$	−11.2938	−0.534775
$447$	11.9637	0.565865
$448$	3.08171	0.145597
$449$	−22.2693	−1.05096	−0.525478	−	0.850807i	$-0.676113\pi$
$449$	−22.2693	−1.05096	−0.525478	+	0.850807i	$0.676113\pi$
$450$	0	0
$451$	−9.65567	−0.454668
$452$	−11.0884	−0.521555
$453$	1.53592	0.0721640
$454$	5.83129	0.273676
$455$	0	0
$456$	2.29385	0.107419
$457$	22.7054	1.06211	0.531056	−	0.847337i	$-0.321795\pi$
$457$	22.7054	1.06211	0.531056	+	0.847337i	$0.321795\pi$
$458$	−11.1222	−0.519708
$459$	−15.2229	−0.710546
$460$	0	0
$461$	1.21906	0.0567773	0.0283886	−	0.999597i	$-0.490962\pi$
$461$	1.21906	0.0567773	0.0283886	+	0.999597i	$0.490962\pi$
$462$	0.977951	0.0454984
$463$	24.1230	1.12109	0.560546	−	0.828123i	$-0.310591\pi$
$463$	24.1230	1.12109	0.560546	+	0.828123i	$0.310591\pi$
$464$	−3.72183	−0.172782
$465$	0	0
$466$	11.0276	0.510845
$467$	−3.92815	−0.181773	−0.0908865	−	0.995861i	$-0.528970\pi$
$467$	−3.92815	−0.181773	−0.0908865	+	0.995861i	$0.528970\pi$
$468$	−1.74022	−0.0804417
$469$	7.17892	0.331492
$470$	0	0
$471$	0.147736	0.00680731
$472$	−6.36345	−0.292902
$473$	12.5016	0.574824
$474$	−2.27468	−0.104479
$475$	0	0
$476$	8.37511	0.383872
$477$	9.76957	0.447318
$478$	−4.50793	−0.206188
$479$	4.77900	0.218358	0.109179	−	0.994022i	$-0.465178\pi$
$479$	4.77900	0.218358	0.109179	+	0.994022i	$0.465178\pi$
$480$	0	0
$481$	0.637913	0.0290863
$482$	−5.55956	−0.253231
$483$	0.568069	0.0258480
$484$	−3.78439	−0.172018
$485$	0	0
$486$	−6.26929	−0.284381
$487$	−34.2446	−1.55177	−0.775885	−	0.630875i	$-0.782696\pi$
$487$	−34.2446	−1.55177	−0.775885	+	0.630875i	$0.782696\pi$
$488$	−1.87720	−0.0849769
$489$	−8.70044	−0.393448
$490$	0	0
$491$	3.20102	0.144460	0.0722301	−	0.997388i	$-0.476988\pi$
$491$	3.20102	0.144460	0.0722301	+	0.997388i	$0.476988\pi$
$492$	2.68558	0.121075
$493$	−6.51397	−0.293374
$494$	0.391919	0.0176333
$495$	0	0
$496$	−16.7187	−0.750692
$497$	−1.85410	−0.0831679
$498$	0.815118	0.0365263
$499$	−1.27276	−0.0569766	−0.0284883	−	0.999594i	$-0.509069\pi$
$499$	−1.27276	−0.0569766	−0.0284883	+	0.999594i	$0.509069\pi$
$500$	0	0
$501$	4.24703	0.189743
$502$	6.03067	0.269162
$503$	42.1380	1.87884	0.939420	−	0.342768i	$-0.111364\pi$
$503$	42.1380	1.87884	0.939420	+	0.342768i	$0.111364\pi$
$504$	4.80035	0.213825
$505$	0	0
$506$	1.72153	0.0765316
$507$	−7.30867	−0.324589
$508$	12.6785	0.562518
$509$	12.8431	0.569261	0.284631	−	0.958637i	$-0.408129\pi$
$509$	12.8431	0.569261	0.284631	+	0.958637i	$0.408129\pi$
$510$	0	0
$511$	8.97042	0.396828
$512$	−22.7972	−1.00750
$513$	−7.26323	−0.320679
$514$	4.30863	0.190045
$515$	0	0
$516$	−3.47714	−0.153073
$517$	25.1802	1.10742
$518$	−0.827227	−0.0363462
$519$	−6.40861	−0.281307
$520$	0	0
$521$	22.3272	0.978171	0.489085	−	0.872236i	$-0.337331\pi$
$521$	22.3272	0.978171	0.489085	+	0.872236i	$0.337331\pi$
$522$	−1.75518	−0.0768223
$523$	7.37589	0.322525	0.161262	−	0.986912i	$-0.448443\pi$
$523$	7.37589	0.322525	0.161262	+	0.986912i	$0.448443\pi$
$524$	−30.5713	−1.33551
$525$	0	0
$526$	−7.81741	−0.340855
$527$	−29.2612	−1.27464
$528$	5.55197	0.241619
$529$	1.00000	0.0434783
$530$	0	0
$531$	9.50196	0.412350
$532$	3.99596	0.173247
$533$	0.976058	0.0422778
$534$	−3.93260	−0.170180
$535$	0	0
$536$	−12.8717	−0.555972
$537$	−1.80277	−0.0777954
$538$	12.8615	0.554499
$539$	3.62393	0.156094
$540$	0	0
$541$	35.2120	1.51388	0.756942	−	0.653482i	$-0.226692\pi$
$541$	35.2120	1.51388	0.756942	+	0.653482i	$0.226692\pi$
$542$	7.26779	0.312178
$543$	6.30890	0.270741
$544$	−22.9736	−0.984983
$545$	0	0
$546$	−0.0988577	−0.00423072
$547$	11.3825	0.486680	0.243340	−	0.969941i	$-0.421757\pi$
$547$	11.3825	0.486680	0.243340	+	0.969941i	$0.421757\pi$
$548$	−38.8208	−1.65834
$549$	2.80305	0.119631
$550$	0	0
$551$	−3.10797	−0.132404
$552$	−1.01854	−0.0433519
$553$	−8.42912	−0.358443
$554$	5.72224	0.243115
$555$	0	0
$556$	−16.8530	−0.714727
$557$	−3.15042	−0.133488	−0.0667439	−	0.997770i	$-0.521261\pi$
$557$	−3.15042	−0.133488	−0.0667439	+	0.997770i	$0.521261\pi$
$558$	−7.88441	−0.333774
$559$	−1.26374	−0.0534507
$560$	0	0
$561$	9.71710	0.410256
$562$	−13.1721	−0.555631
$563$	−29.5286	−1.24448	−0.622241	−	0.782826i	$-0.713778\pi$
$563$	−29.5286	−1.24448	−0.622241	+	0.782826i	$0.713778\pi$
$564$	−7.00350	−0.294901
$565$	0	0
$566$	7.02293	0.295196
$567$	−6.19981	−0.260368
$568$	3.32438	0.139488
$569$	22.1717	0.929487	0.464744	−	0.885445i	$-0.346146\pi$
$569$	22.1717	0.929487	0.464744	+	0.885445i	$0.346146\pi$
$570$	0	0
$571$	−20.8328	−0.871827	−0.435913	−	0.899989i	$-0.643575\pi$
$571$	−20.8328	−0.871827	−0.435913	+	0.899989i	$0.643575\pi$
$572$	2.35552	0.0984893
$573$	6.60505	0.275930
$574$	−1.26572	−0.0528303
$575$	0	0
$576$	8.25066	0.343777
$577$	−13.8892	−0.578214	−0.289107	−	0.957297i	$-0.593358\pi$
$577$	−13.8892	−0.578214	−0.289107	+	0.957297i	$0.593358\pi$
$578$	−2.50816	−0.104326
$579$	−10.8889	−0.452526
$580$	0	0
$581$	3.02053	0.125313
$582$	0.586913	0.0243283
$583$	−13.2239	−0.547676
$584$	−16.0838	−0.665553
$585$	0	0
$586$	−2.94838	−0.121796
$587$	12.5350	0.517374	0.258687	−	0.965961i	$-0.416710\pi$
$587$	12.5350	0.517374	0.258687	+	0.965961i	$0.416710\pi$
$588$	−1.00794	−0.0415668
$589$	−13.9612	−0.575262
$590$	0	0
$591$	7.26068	0.298664
$592$	−4.69629	−0.193016
$593$	−13.1123	−0.538459	−0.269229	−	0.963076i	$-0.586769\pi$
$593$	−13.1123	−0.538459	−0.269229	+	0.963076i	$0.586769\pi$
$594$	5.55212	0.227806
$595$	0	0
$596$	−37.3680	−1.53065
$597$	−6.43746	−0.263468
$598$	−0.174024	−0.00711637
$599$	9.36785	0.382760	0.191380	−	0.981516i	$-0.438704\pi$
$599$	9.36785	0.382760	0.191380	+	0.981516i	$0.438704\pi$
$600$	0	0
$601$	−36.4694	−1.48762	−0.743809	−	0.668392i	$-0.766983\pi$
$601$	−36.4694	−1.48762	−0.743809	+	0.668392i	$0.766983\pi$
$602$	1.63879	0.0667920
$603$	19.2201	0.782704
$604$	−4.79737	−0.195202
$605$	0	0
$606$	−4.62553	−0.187899
$607$	12.8526	0.521673	0.260836	−	0.965383i	$-0.416002\pi$
$607$	12.8526	0.521673	0.260836	+	0.965383i	$0.416002\pi$
$608$	−10.9612	−0.444537
$609$	0.783955	0.0317674
$610$	0	0
$611$	−2.54538	−0.102975
$612$	22.4227	0.906382
$613$	33.0378	1.33438	0.667192	−	0.744886i	$-0.267496\pi$
$613$	33.0378	1.33438	0.667192	+	0.744886i	$0.267496\pi$
$614$	8.54271	0.344756
$615$	0	0
$616$	−6.49764	−0.261797
$617$	19.4844	0.784413	0.392206	−	0.919877i	$-0.371712\pi$
$617$	19.4844	0.784413	0.392206	+	0.919877i	$0.371712\pi$
$618$	−1.46268	−0.0588376
$619$	15.3321	0.616249	0.308124	−	0.951346i	$-0.400299\pi$
$619$	15.3321	0.616249	0.308124	+	0.951346i	$0.400299\pi$
$620$	0	0
$621$	3.22510	0.129419
$622$	−8.61492	−0.345427
$623$	−14.5728	−0.583846
$624$	−0.561230	−0.0224672
$625$	0	0
$626$	−8.42289	−0.336646
$627$	4.63626	0.185154
$628$	−0.461444	−0.0184136
$629$	−8.21947	−0.327732
$630$	0	0
$631$	−26.9810	−1.07410	−0.537048	−	0.843552i	$-0.680460\pi$
$631$	−26.9810	−1.07410	−0.537048	+	0.843552i	$0.680460\pi$
$632$	15.1133	0.601173
$633$	12.7643	0.507334
$634$	11.8691	0.471383
$635$	0	0
$636$	3.67802	0.145843
$637$	−0.366330	−0.0145145
$638$	2.37578	0.0940579
$639$	−4.96399	−0.196372
$640$	0	0
$641$	−9.22751	−0.364465	−0.182232	−	0.983256i	$-0.558332\pi$
$641$	−9.22751	−0.364465	−0.182232	+	0.983256i	$0.558332\pi$
$642$	−2.36314	−0.0932655
$643$	36.1832	1.42692	0.713462	−	0.700694i	$-0.247126\pi$
$643$	36.1832	1.42692	0.713462	+	0.700694i	$0.247126\pi$
$644$	−1.77433	−0.0699184
$645$	0	0
$646$	−5.04985	−0.198684
$647$	−24.2754	−0.954365	−0.477183	−	0.878804i	$-0.658342\pi$
$647$	−24.2754	−0.954365	−0.477183	+	0.878804i	$0.658342\pi$
$648$	11.1162	0.436684
$649$	−12.8616	−0.504863
$650$	0	0
$651$	3.52158	0.138022
$652$	27.1753	1.06427
$653$	7.13233	0.279110	0.139555	−	0.990214i	$-0.455433\pi$
$653$	7.13233	0.279110	0.139555	+	0.990214i	$0.455433\pi$
$654$	−3.81062	−0.149007
$655$	0	0
$656$	−7.18571	−0.280555
$657$	24.0165	0.936972
$658$	3.30077	0.128678
$659$	−21.6547	−0.843546	−0.421773	−	0.906702i	$-0.638592\pi$
$659$	−21.6547	−0.843546	−0.421773	+	0.906702i	$0.638592\pi$
$660$	0	0
$661$	−39.8293	−1.54918	−0.774590	−	0.632464i	$-0.782044\pi$
$661$	−39.8293	−1.54918	−0.774590	+	0.632464i	$0.782044\pi$
$662$	3.24046	0.125944
$663$	−0.982268	−0.0381481
$664$	−5.41576	−0.210172
$665$	0	0
$666$	−2.21473	−0.0858191
$667$	1.38003	0.0534351
$668$	−13.2654	−0.513252
$669$	13.5053	0.522145
$670$	0	0
$671$	−3.79415	−0.146471
$672$	2.76486	0.106657
$673$	−1.32432	−0.0510489	−0.0255245	−	0.999674i	$-0.508126\pi$
$673$	−1.32432	−0.0510489	−0.0255245	+	0.999674i	$0.508126\pi$
$674$	−16.6579	−0.641640
$675$	0	0
$676$	22.8282	0.878007
$677$	43.7310	1.68072	0.840360	−	0.542029i	$-0.182344\pi$
$677$	43.7310	1.68072	0.840360	+	0.542029i	$0.182344\pi$
$678$	−1.68644	−0.0647675
$679$	2.17489	0.0834645
$680$	0	0
$681$	−6.97316	−0.267212
$682$	10.6722	0.408658
$683$	11.1134	0.425243	0.212621	−	0.977135i	$-0.431800\pi$
$683$	11.1134	0.425243	0.212621	+	0.977135i	$0.431800\pi$
$684$	10.6984	0.409063
$685$	0	0
$686$	0.475047	0.0181374
$687$	13.3002	0.507433
$688$	9.30364	0.354698
$689$	1.33675	0.0509263
$690$	0	0
$691$	−15.2547	−0.580318	−0.290159	−	0.956978i	$-0.593708\pi$
$691$	−15.2547	−0.580318	−0.290159	+	0.956978i	$0.593708\pi$
$692$	20.0169	0.760929
$693$	9.70233	0.368561
$694$	0.832122	0.0315869
$695$	0	0
$696$	−1.40562	−0.0532798
$697$	−12.5765	−0.476368
$698$	−5.85972	−0.221794
$699$	−13.1870	−0.498780
$700$	0	0
$701$	5.12760	0.193667	0.0968333	−	0.995301i	$-0.469129\pi$
$701$	5.12760	0.193667	0.0968333	+	0.995301i	$0.469129\pi$
$702$	−0.561244	−0.0211828
$703$	−3.92171	−0.147910
$704$	−11.1679	−0.420906
$705$	0	0
$706$	−2.13205	−0.0802408
$707$	−17.1405	−0.644636
$708$	3.57727	0.134442
$709$	−14.3015	−0.537104	−0.268552	−	0.963265i	$-0.586545\pi$
$709$	−14.3015	−0.537104	−0.268552	+	0.963265i	$0.586545\pi$
$710$	0	0
$711$	−22.5673	−0.846338
$712$	26.1287	0.979216
$713$	6.19921	0.232162
$714$	1.27378	0.0476699
$715$	0	0
$716$	5.63086	0.210435
$717$	5.39066	0.201318
$718$	−16.4251	−0.612978
$719$	−31.0157	−1.15669	−0.578346	−	0.815792i	$-0.696302\pi$
$719$	−31.0157	−1.15669	−0.578346	+	0.815792i	$0.696302\pi$
$720$	0	0
$721$	−5.42016	−0.201857
$722$	6.61648	0.246240
$723$	6.64822	0.247250
$724$	−19.7055	−0.732349
$725$	0	0
$726$	−0.575570	−0.0213614
$727$	19.5886	0.726501	0.363250	−	0.931692i	$-0.381667\pi$
$727$	19.5886	0.726501	0.363250	+	0.931692i	$0.381667\pi$
$728$	0.656824	0.0243435
$729$	−11.1025	−0.411204
$730$	0	0
$731$	16.2833	0.602259
$732$	1.05529	0.0390045
$733$	−6.45996	−0.238604	−0.119302	−	0.992858i	$-0.538066\pi$
$733$	−6.45996	−0.238604	−0.119302	+	0.992858i	$0.538066\pi$
$734$	11.3008	0.417119
$735$	0	0
$736$	4.86712	0.179405
$737$	−26.0159	−0.958308
$738$	−3.38872	−0.124740
$739$	51.2185	1.88410	0.942052	−	0.335467i	$-0.108894\pi$
$739$	51.2185	1.88410	0.942052	+	0.335467i	$0.108894\pi$
$740$	0	0
$741$	−0.468663	−0.0172168
$742$	−1.73346	−0.0636375
$743$	−8.59918	−0.315474	−0.157737	−	0.987481i	$-0.550420\pi$
$743$	−8.59918	−0.315474	−0.157737	+	0.987481i	$0.550420\pi$
$744$	−6.31413	−0.231487
$745$	0	0
$746$	−1.57738	−0.0577518
$747$	8.08686	0.295883
$748$	−30.3508	−1.10973
$749$	−8.75692	−0.319971
$750$	0	0
$751$	25.0478	0.914007	0.457003	−	0.889465i	$-0.348923\pi$
$751$	25.0478	0.914007	0.457003	+	0.889465i	$0.348923\pi$
$752$	18.7390	0.683340
$753$	−7.21158	−0.262805
$754$	−0.240159	−0.00874608
$755$	0	0
$756$	−5.72239	−0.208121
$757$	−12.1778	−0.442609	−0.221304	−	0.975205i	$-0.571031\pi$
$757$	−12.1778	−0.442609	−0.221304	+	0.975205i	$0.571031\pi$
$758$	−5.67825	−0.206243
$759$	−2.05864	−0.0747240
$760$	0	0
$761$	−30.8963	−1.11999	−0.559996	−	0.828495i	$-0.689197\pi$
$761$	−30.8963	−1.11999	−0.559996	+	0.828495i	$0.689197\pi$
$762$	1.92829	0.0698544
$763$	−14.1208	−0.511206
$764$	−20.6305	−0.746384
$765$	0	0
$766$	−15.8728	−0.573506
$767$	1.30014	0.0469453
$768$	0.479309	0.0172956
$769$	−43.6733	−1.57490	−0.787449	−	0.616380i	$-0.788599\pi$
$769$	−43.6733	−1.57490	−0.787449	+	0.616380i	$0.788599\pi$
$770$	0	0
$771$	−5.15233	−0.185557
$772$	34.0108	1.22407
$773$	−25.6391	−0.922175	−0.461088	−	0.887355i	$-0.652541\pi$
$773$	−25.6391	−0.922175	−0.461088	+	0.887355i	$0.652541\pi$
$774$	4.38752	0.157706
$775$	0	0
$776$	−3.89953	−0.139985
$777$	0.989212	0.0354878
$778$	−9.31426	−0.333932
$779$	−6.00053	−0.214991
$780$	0	0
$781$	6.71914	0.240430
$782$	2.24229	0.0801842
$783$	4.45074	0.159057
$784$	2.69691	0.0963182
$785$	0	0
$786$	−4.64961	−0.165846
$787$	−11.0965	−0.395547	−0.197773	−	0.980248i	$-0.563371\pi$
$787$	−11.0965	−0.395547	−0.197773	+	0.980248i	$0.563371\pi$
$788$	−22.6783	−0.807881
$789$	9.34820	0.332805
$790$	0	0
$791$	−6.24934	−0.222201
$792$	−17.3961	−0.618144
$793$	0.383537	0.0136198
$794$	−6.87325	−0.243922
$795$	0	0
$796$	20.1070	0.712675
$797$	24.4287	0.865309	0.432654	−	0.901560i	$-0.357577\pi$
$797$	24.4287	0.865309	0.432654	+	0.901560i	$0.357577\pi$
$798$	0.607749	0.0215141
$799$	32.7971	1.16028
$800$	0	0
$801$	−39.0157	−1.37855
$802$	11.2829	0.398412
$803$	−32.5081	−1.14719
$804$	7.23594	0.255192
$805$	0	0
$806$	−1.07881	−0.0379995
$807$	−15.3800	−0.541403
$808$	30.7327	1.08117
$809$	18.7033	0.657575	0.328787	−	0.944404i	$-0.393360\pi$
$809$	18.7033	0.657575	0.328787	+	0.944404i	$0.393360\pi$
$810$	0	0
$811$	46.1449	1.62037	0.810183	−	0.586177i	$-0.199368\pi$
$811$	46.1449	1.62037	0.810183	+	0.586177i	$0.199368\pi$
$812$	−2.44864	−0.0859303
$813$	−8.69095	−0.304805
$814$	2.99781	0.105073
$815$	0	0
$816$	7.23142	0.253150
$817$	7.76914	0.271808
$818$	4.22058	0.147569
$819$	−0.980775	−0.0342711
$820$	0	0
$821$	26.0602	0.909507	0.454753	−	0.890617i	$-0.349727\pi$
$821$	26.0602	0.909507	0.454753	+	0.890617i	$0.349727\pi$
$822$	−5.90429	−0.205936
$823$	−4.12617	−0.143829	−0.0719147	−	0.997411i	$-0.522911\pi$
$823$	−4.12617	−0.143829	−0.0719147	+	0.997411i	$0.522911\pi$
$824$	9.71825	0.338551
$825$	0	0
$826$	−1.68598	−0.0586628
$827$	−2.45081	−0.0852232	−0.0426116	−	0.999092i	$-0.513568\pi$
$827$	−2.45081	−0.0852232	−0.0426116	+	0.999092i	$0.513568\pi$
$828$	−4.75041	−0.165088
$829$	44.6503	1.55077	0.775384	−	0.631490i	$-0.217556\pi$
$829$	44.6503	1.55077	0.775384	+	0.631490i	$0.217556\pi$
$830$	0	0
$831$	−6.84275	−0.237372
$832$	1.12892	0.0391384
$833$	4.72015	0.163543
$834$	−2.56319	−0.0887559
$835$	0	0
$836$	−14.4811	−0.500839
$837$	19.9931	0.691061
$838$	10.8332	0.374225
$839$	−27.4553	−0.947863	−0.473931	−	0.880562i	$-0.657166\pi$
$839$	−27.4553	−0.947863	−0.473931	+	0.880562i	$0.657166\pi$
$840$	0	0
$841$	−27.0955	−0.934328
$842$	−14.9568	−0.515444
$843$	15.7514	0.542508
$844$	−39.8685	−1.37233
$845$	0	0
$846$	8.83715	0.303828
$847$	−2.13285	−0.0732857
$848$	−9.84114	−0.337946
$849$	−8.39814	−0.288224
$850$	0	0
$851$	1.74136	0.0596930
$852$	−1.86883	−0.0640251
$853$	−48.9511	−1.67605	−0.838026	−	0.545630i	$-0.816290\pi$
$853$	−48.9511	−1.67605	−0.838026	+	0.545630i	$0.816290\pi$
$854$	−0.497360	−0.0170193
$855$	0	0
$856$	15.7010	0.536649
$857$	−7.57790	−0.258856	−0.129428	−	0.991589i	$-0.541314\pi$
$857$	−7.57790	−0.258856	−0.129428	+	0.991589i	$0.541314\pi$
$858$	0.358253	0.0122306
$859$	51.2498	1.74862	0.874310	−	0.485368i	$-0.161315\pi$
$859$	51.2498	1.74862	0.874310	+	0.485368i	$0.161315\pi$
$860$	0	0
$861$	1.51358	0.0515825
$862$	5.65506	0.192612
$863$	−37.1356	−1.26411	−0.632054	−	0.774924i	$-0.717788\pi$
$863$	−37.1356	−1.26411	−0.632054	+	0.774924i	$0.717788\pi$
$864$	15.6970	0.534021
$865$	0	0
$866$	1.87001	0.0635455
$867$	2.99930	0.101862
$868$	−10.9994	−0.373346
$869$	30.5465	1.03622
$870$	0	0
$871$	2.62986	0.0891093
$872$	25.3183	0.857385
$873$	5.82282	0.197073
$874$	1.06985	0.0361882
$875$	0	0
$876$	9.04166	0.305490
$877$	28.2268	0.953150	0.476575	−	0.879134i	$-0.341878\pi$
$877$	28.2268	0.953150	0.476575	+	0.879134i	$0.341878\pi$
$878$	−7.30540	−0.246545
$879$	3.52572	0.118920
$880$	0	0
$881$	−58.7511	−1.97937	−0.989687	−	0.143249i	$-0.954245\pi$
$881$	−58.7511	−1.97937	−0.989687	+	0.143249i	$0.954245\pi$
$882$	1.27184	0.0428251
$883$	−27.3977	−0.922007	−0.461004	−	0.887398i	$-0.652510\pi$
$883$	−27.3977	−0.922007	−0.461004	+	0.887398i	$0.652510\pi$
$884$	3.06806	0.103190
$885$	0	0
$886$	12.3542	0.415046
$887$	20.6528	0.693454	0.346727	−	0.937966i	$-0.387293\pi$
$887$	20.6528	0.693454	0.346727	+	0.937966i	$0.387293\pi$
$888$	−1.77364	−0.0595195
$889$	7.14552	0.239653
$890$	0	0
$891$	22.4677	0.752696
$892$	−42.1830	−1.41239
$893$	15.6483	0.523649
$894$	−5.68333	−0.190079
$895$	0	0
$896$	−11.1982	−0.374106
$897$	0.208101	0.00694829
$898$	10.5790	0.353025
$899$	8.55512	0.285329
$900$	0	0
$901$	−17.2240	−0.573815
$902$	4.58689	0.152727
$903$	−1.95969	−0.0652144
$904$	11.2050	0.372672
$905$	0	0
$906$	−0.729636	−0.0242405
$907$	−28.7744	−0.955438	−0.477719	−	0.878513i	$-0.658536\pi$
$907$	−28.7744	−0.955438	−0.477719	+	0.878513i	$0.658536\pi$
$908$	21.7803	0.722804
$909$	−45.8903	−1.52208
$910$	0	0
$911$	−47.9708	−1.58934	−0.794672	−	0.607039i	$-0.792357\pi$
$911$	−47.9708	−1.58934	−0.794672	+	0.607039i	$0.792357\pi$
$912$	3.45028	0.114250
$913$	−10.9462	−0.362266
$914$	−10.7861	−0.356773
$915$	0	0
$916$	−41.5423	−1.37259
$917$	−17.2298	−0.568977
$918$	7.23161	0.238679
$919$	21.2002	0.699331	0.349666	−	0.936875i	$-0.386295\pi$
$919$	21.2002	0.699331	0.349666	+	0.936875i	$0.386295\pi$
$920$	0	0
$921$	−10.2155	−0.336613
$922$	−0.579110	−0.0190720
$923$	−0.679215	−0.0223566
$924$	3.65271	0.120165
$925$	0	0
$926$	−11.4596	−0.376585
$927$	−14.5114	−0.476616
$928$	6.71680	0.220490
$929$	−42.4523	−1.39281	−0.696407	−	0.717647i	$-0.745219\pi$
$929$	−42.4523	−1.39281	−0.696407	+	0.717647i	$0.745219\pi$
$930$	0	0
$931$	2.25210	0.0738094
$932$	41.1889	1.34919
$933$	10.3019	0.337268
$934$	1.86605	0.0610592
$935$	0	0
$936$	1.75851	0.0574788
$937$	−10.1453	−0.331432	−0.165716	−	0.986174i	$-0.552994\pi$
$937$	−10.1453	−0.331432	−0.165716	+	0.986174i	$0.552994\pi$
$938$	−3.41032	−0.111351
$939$	10.0722	0.328695
$940$	0	0
$941$	−14.4224	−0.470158	−0.235079	−	0.971976i	$-0.575535\pi$
$941$	−14.4224	−0.470158	−0.235079	+	0.971976i	$0.575535\pi$
$942$	−0.0701814	−0.00228663
$943$	2.66442	0.0867655
$944$	−9.57157	−0.311528
$945$	0	0
$946$	−5.93885	−0.193089
$947$	−57.0861	−1.85505	−0.927524	−	0.373763i	$-0.878067\pi$
$947$	−57.0861	−1.85505	−0.927524	+	0.373763i	$0.878067\pi$
$948$	−8.49607	−0.275939
$949$	3.28614	0.106672
$950$	0	0
$951$	−14.1933	−0.460249
$952$	−8.46315	−0.274292
$953$	11.1297	0.360525	0.180263	−	0.983618i	$-0.442305\pi$
$953$	11.1297	0.360525	0.180263	+	0.983618i	$0.442305\pi$
$954$	−4.64100	−0.150258
$955$	0	0
$956$	−16.8374	−0.544561
$957$	−2.84100	−0.0918363
$958$	−2.27025	−0.0733484
$959$	−21.8791	−0.706514
$960$	0	0
$961$	7.43020	0.239684
$962$	−0.303038	−0.00977034
$963$	−23.4449	−0.755500
$964$	−20.7653	−0.668806
$965$	0	0
$966$	−0.269859	−0.00868258
$967$	−1.42443	−0.0458066	−0.0229033	−	0.999738i	$-0.507291\pi$
$967$	−1.42443	−0.0458066	−0.0229033	+	0.999738i	$0.507291\pi$
$968$	3.82417	0.122913
$969$	6.03870	0.193991
$970$	0	0
$971$	43.7712	1.40469	0.702343	−	0.711839i	$-0.252137\pi$
$971$	43.7712	1.40469	0.702343	+	0.711839i	$0.252137\pi$
$972$	−23.4162	−0.751076
$973$	−9.49823	−0.304499
$974$	16.2678	0.521253
$975$	0	0
$976$	−2.82359	−0.0903808
$977$	−50.0127	−1.60005	−0.800025	−	0.599967i	$-0.795180\pi$
$977$	−50.0127	−1.60005	−0.800025	+	0.599967i	$0.795180\pi$
$978$	4.13311	0.132162
$979$	52.8107	1.68784
$980$	0	0
$981$	−37.8055	−1.20704
$982$	−1.52064	−0.0485254
$983$	50.8384	1.62149	0.810747	−	0.585397i	$-0.199061\pi$
$983$	50.8384	1.62149	0.810747	+	0.585397i	$0.199061\pi$
$984$	−2.71381	−0.0865133
$985$	0	0
$986$	3.09444	0.0985470
$987$	−3.94712	−0.125638
$988$	1.46384	0.0465710
$989$	−3.44974	−0.109695
$990$	0	0
$991$	−0.692213	−0.0219889	−0.0109944	−	0.999940i	$-0.503500\pi$
$991$	−0.692213	−0.0219889	−0.0109944	+	0.999940i	$0.503500\pi$
$992$	30.1723	0.957972
$993$	−3.87500	−0.122970
$994$	0.880786	0.0279368
$995$	0	0
$996$	3.04452	0.0964693
$997$	9.43143	0.298696	0.149348	−	0.988785i	$-0.452282\pi$
$997$	9.43143	0.298696	0.149348	+	0.988785i	$0.452282\pi$
$998$	0.604620	0.0191389
$999$	5.61605	0.177684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bd.1.10		21
5.2	odd	4		805.2.c.c.484.19	✓	42
5.3	odd	4		805.2.c.c.484.24	yes	42
5.4	even	2		4025.2.a.be.1.12		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.c.484.19	✓	42	5.2	odd	4
805.2.c.c.484.24	yes	42	5.3	odd	4
4025.2.a.bd.1.10		21	1.1	even	1	trivial
4025.2.a.be.1.12		21	5.4	even	2

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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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.475047 q^{2} +0.568069 q^{3} -1.77433 q^{4} -0.269859 q^{6} -1.00000 q^{7} +1.79298 q^{8} -2.67730 q^{9} +O(q^{10})\)	\(q-0.475047 q^{2} +0.568069 q^{3} -1.77433 q^{4} -0.269859 q^{6} -1.00000 q^{7} +1.79298 q^{8} -2.67730 q^{9} +3.62393 q^{11} -1.00794 q^{12} -0.366330 q^{13} +0.475047 q^{14} +2.69691 q^{16} +4.72015 q^{17} +1.27184 q^{18} +2.25210 q^{19} -0.568069 q^{21} -1.72153 q^{22} -1.00000 q^{23} +1.01854 q^{24} +0.174024 q^{26} -3.22510 q^{27} +1.77433 q^{28} -1.38003 q^{29} -6.19921 q^{31} -4.86712 q^{32} +2.05864 q^{33} -2.24229 q^{34} +4.75041 q^{36} -1.74136 q^{37} -1.06985 q^{38} -0.208101 q^{39} -2.66442 q^{41} +0.269859 q^{42} +3.44974 q^{43} -6.43005 q^{44} +0.475047 q^{46} +6.94831 q^{47} +1.53203 q^{48} +1.00000 q^{49} +2.68137 q^{51} +0.649991 q^{52} -3.64904 q^{53} +1.53207 q^{54} -1.79298 q^{56} +1.27935 q^{57} +0.655580 q^{58} -3.54909 q^{59} -1.04697 q^{61} +2.94491 q^{62} +2.67730 q^{63} -3.08171 q^{64} -0.977951 q^{66} -7.17892 q^{67} -8.37511 q^{68} -0.568069 q^{69} +1.85410 q^{71} -4.80035 q^{72} -8.97042 q^{73} +0.827227 q^{74} -3.99596 q^{76} -3.62393 q^{77} +0.0988577 q^{78} +8.42912 q^{79} +6.19981 q^{81} +1.26572 q^{82} -3.02053 q^{83} +1.00794 q^{84} -1.63879 q^{86} -0.783955 q^{87} +6.49764 q^{88} +14.5728 q^{89} +0.366330 q^{91} +1.77433 q^{92} -3.52158 q^{93} -3.30077 q^{94} -2.76486 q^{96} -2.17489 q^{97} -0.475047 q^{98} -9.70233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 2 * q^99

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