LMFDB - Embedded newform 4998.2.a.ci.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4998, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4998.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$39.9092309302$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.469.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 4 $ x^3 - x^2 - 5*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.772866$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.17554 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.17554 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.17554 q^{10} -1.62981 q^{11} -1.00000 q^{12} -3.62981 q^{13} -3.17554 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +6.80536 q^{19} +3.17554 q^{20} -1.62981 q^{22} +2.00000 q^{23} -1.00000 q^{24} +5.08408 q^{25} -3.62981 q^{26} -1.00000 q^{27} +1.54573 q^{29} -3.17554 q^{30} -7.25963 q^{31} +1.00000 q^{32} +1.62981 q^{33} +1.00000 q^{34} +1.00000 q^{36} +4.72128 q^{37} +6.80536 q^{38} +3.62981 q^{39} +3.17554 q^{40} -5.09146 q^{41} +5.17554 q^{43} -1.62981 q^{44} +3.17554 q^{45} +2.00000 q^{46} +6.35109 q^{47} -1.00000 q^{48} +5.08408 q^{50} -1.00000 q^{51} -3.62981 q^{52} +7.17554 q^{53} -1.00000 q^{54} -5.17554 q^{55} -6.80536 q^{57} +1.54573 q^{58} +2.45427 q^{59} -3.17554 q^{60} +1.09146 q^{61} -7.25963 q^{62} +1.00000 q^{64} -11.5266 q^{65} +1.62981 q^{66} +5.91592 q^{67} +1.00000 q^{68} -2.00000 q^{69} +15.6107 q^{71} +1.00000 q^{72} +4.08408 q^{73} +4.72128 q^{74} -5.08408 q^{75} +6.80536 q^{76} +3.62981 q^{78} +15.6948 q^{79} +3.17554 q^{80} +1.00000 q^{81} -5.09146 q^{82} +0.538351 q^{83} +3.17554 q^{85} +5.17554 q^{86} -1.54573 q^{87} -1.62981 q^{88} -13.5266 q^{89} +3.17554 q^{90} +2.00000 q^{92} +7.25963 q^{93} +6.35109 q^{94} +21.6107 q^{95} -1.00000 q^{96} -10.4352 q^{97} -1.62981 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} - 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 - 3 * q^6 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} - 3 q^{6} + 3 q^{8} + 3 q^{9} - q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{13} + q^{15} + 3 q^{16} + 3 q^{17} + 3 q^{18} + 2 q^{19} - q^{20} + 3 q^{22} + 6 q^{23} - 3 q^{24} + 10 q^{25} - 3 q^{26} - 3 q^{27} + 2 q^{29} + q^{30} - 6 q^{31} + 3 q^{32} - 3 q^{33} + 3 q^{34} + 3 q^{36} + q^{37} + 2 q^{38} + 3 q^{39} - q^{40} - 10 q^{41} + 5 q^{43} + 3 q^{44} - q^{45} + 6 q^{46} - 2 q^{47} - 3 q^{48} + 10 q^{50} - 3 q^{51} - 3 q^{52} + 11 q^{53} - 3 q^{54} - 5 q^{55} - 2 q^{57} + 2 q^{58} + 10 q^{59} + q^{60} - 2 q^{61} - 6 q^{62} + 3 q^{64} - 3 q^{65} - 3 q^{66} + 23 q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{71} + 3 q^{72} + 7 q^{73} + q^{74} - 10 q^{75} + 2 q^{76} + 3 q^{78} + 5 q^{79} - q^{80} + 3 q^{81} - 10 q^{82} - q^{83} - q^{85} + 5 q^{86} - 2 q^{87} + 3 q^{88} - 9 q^{89} - q^{90} + 6 q^{92} + 6 q^{93} - 2 q^{94} + 28 q^{95} - 3 q^{96} - 5 q^{97} + 3 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 - 3 * q^6 + 3 * q^8 + 3 * q^9 - q^10 + 3 * q^11 - 3 * q^12 - 3 * q^13 + q^15 + 3 * q^16 + 3 * q^17 + 3 * q^18 + 2 * q^19 - q^20 + 3 * q^22 + 6 * q^23 - 3 * q^24 + 10 * q^25 - 3 * q^26 - 3 * q^27 + 2 * q^29 + q^30 - 6 * q^31 + 3 * q^32 - 3 * q^33 + 3 * q^34 + 3 * q^36 + q^37 + 2 * q^38 + 3 * q^39 - q^40 - 10 * q^41 + 5 * q^43 + 3 * q^44 - q^45 + 6 * q^46 - 2 * q^47 - 3 * q^48 + 10 * q^50 - 3 * q^51 - 3 * q^52 + 11 * q^53 - 3 * q^54 - 5 * q^55 - 2 * q^57 + 2 * q^58 + 10 * q^59 + q^60 - 2 * q^61 - 6 * q^62 + 3 * q^64 - 3 * q^65 - 3 * q^66 + 23 * q^67 + 3 * q^68 - 6 * q^69 + 10 * q^71 + 3 * q^72 + 7 * q^73 + q^74 - 10 * q^75 + 2 * q^76 + 3 * q^78 + 5 * q^79 - q^80 + 3 * q^81 - 10 * q^82 - q^83 - q^85 + 5 * q^86 - 2 * q^87 + 3 * q^88 - 9 * q^89 - q^90 + 6 * q^92 + 6 * q^93 - 2 * q^94 + 28 * q^95 - 3 * q^96 - 5 * q^97 + 3 * 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
$5$	3.17554	1.42015	0.710073	−	0.704128i	$-0.248662\pi$
$5$	3.17554	1.42015	0.710073	+	0.704128i	$0.248662\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.17554	1.00420
$11$	−1.62981	−0.491407	−0.245704	−	0.969345i	$-0.579019\pi$
$11$	−1.62981	−0.491407	−0.245704	+	0.969345i	$0.579019\pi$
$12$	−1.00000	−0.288675
$13$	−3.62981	−1.00673	−0.503365	−	0.864074i	$-0.667905\pi$
$13$	−3.62981	−1.00673	−0.503365	+	0.864074i	$0.667905\pi$
$14$	0	0
$15$	−3.17554	−0.819922
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	6.80536	1.56126	0.780628	−	0.624996i	$-0.214899\pi$
$19$	6.80536	1.56126	0.780628	+	0.624996i	$0.214899\pi$
$20$	3.17554	0.710073
$21$	0	0
$22$	−1.62981	−0.347477
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	−1.00000	−0.204124
$25$	5.08408	1.01682
$26$	−3.62981	−0.711865
$27$	−1.00000	−0.192450
$28$	0	0
$29$	1.54573	0.287035	0.143518	−	0.989648i	$-0.454159\pi$
$29$	1.54573	0.287035	0.143518	+	0.989648i	$0.454159\pi$
$30$	−3.17554	−0.579772
$31$	−7.25963	−1.30387	−0.651934	−	0.758276i	$-0.726042\pi$
$31$	−7.25963	−1.30387	−0.651934	+	0.758276i	$0.726042\pi$
$32$	1.00000	0.176777
$33$	1.62981	0.283714
$34$	1.00000	0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	4.72128	0.776173	0.388086	−	0.921623i	$-0.373136\pi$
$37$	4.72128	0.776173	0.388086	+	0.921623i	$0.373136\pi$
$38$	6.80536	1.10397
$39$	3.62981	0.581235
$40$	3.17554	0.502098
$41$	−5.09146	−0.795153	−0.397576	−	0.917569i	$-0.630149\pi$
$41$	−5.09146	−0.795153	−0.397576	+	0.917569i	$0.630149\pi$
$42$	0	0
$43$	5.17554	0.789263	0.394632	−	0.918839i	$-0.370872\pi$
$43$	5.17554	0.789263	0.394632	+	0.918839i	$0.370872\pi$
$44$	−1.62981	−0.245704
$45$	3.17554	0.473382
$46$	2.00000	0.294884
$47$	6.35109	0.926402	0.463201	−	0.886253i	$-0.346701\pi$
$47$	6.35109	0.926402	0.463201	+	0.886253i	$0.346701\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	5.08408	0.718998
$51$	−1.00000	−0.140028
$52$	−3.62981	−0.503365
$53$	7.17554	0.985637	0.492818	−	0.870132i	$-0.335967\pi$
$53$	7.17554	0.985637	0.492818	+	0.870132i	$0.335967\pi$
$54$	−1.00000	−0.136083
$55$	−5.17554	−0.697870
$56$	0	0
$57$	−6.80536	−0.901392
$58$	1.54573	0.202964
$59$	2.45427	0.319519	0.159759	−	0.987156i	$-0.448928\pi$
$59$	2.45427	0.319519	0.159759	+	0.987156i	$0.448928\pi$
$60$	−3.17554	−0.409961
$61$	1.09146	0.139747	0.0698737	−	0.997556i	$-0.477740\pi$
$61$	1.09146	0.139747	0.0698737	+	0.997556i	$0.477740\pi$
$62$	−7.25963	−0.921973
$63$	0	0
$64$	1.00000	0.125000
$65$	−11.5266	−1.42970
$66$	1.62981	0.200616
$67$	5.91592	0.722744	0.361372	−	0.932422i	$-0.382308\pi$
$67$	5.91592	0.722744	0.361372	+	0.932422i	$0.382308\pi$
$68$	1.00000	0.121268
$69$	−2.00000	−0.240772
$70$	0	0
$71$	15.6107	1.85265	0.926326	−	0.376724i	$-0.122949\pi$
$71$	15.6107	1.85265	0.926326	+	0.376724i	$0.122949\pi$
$72$	1.00000	0.117851
$73$	4.08408	0.478006	0.239003	−	0.971019i	$-0.423179\pi$
$73$	4.08408	0.478006	0.239003	+	0.971019i	$0.423179\pi$
$74$	4.72128	0.548837
$75$	−5.08408	−0.587059
$76$	6.80536	0.780628
$77$	0	0
$78$	3.62981	0.410995
$79$	15.6948	1.76580	0.882901	−	0.469559i	$-0.155587\pi$
$79$	15.6948	1.76580	0.882901	+	0.469559i	$0.155587\pi$
$80$	3.17554	0.355037
$81$	1.00000	0.111111
$82$	−5.09146	−0.562258
$83$	0.538351	0.0590917	0.0295459	−	0.999563i	$-0.490594\pi$
$83$	0.538351	0.0590917	0.0295459	+	0.999563i	$0.490594\pi$
$84$	0	0
$85$	3.17554	0.344436
$86$	5.17554	0.558093
$87$	−1.54573	−0.165720
$88$	−1.62981	−0.173739
$89$	−13.5266	−1.43382	−0.716910	−	0.697166i	$-0.754444\pi$
$89$	−13.5266	−1.43382	−0.716910	+	0.697166i	$0.754444\pi$
$90$	3.17554	0.334732
$91$	0	0
$92$	2.00000	0.208514
$93$	7.25963	0.752788
$94$	6.35109	0.655065
$95$	21.6107	2.21721
$96$	−1.00000	−0.102062
$97$	−10.4352	−1.05953	−0.529766	−	0.848144i	$-0.677720\pi$
$97$	−10.4352	−1.05953	−0.529766	+	0.848144i	$0.677720\pi$
$98$	0	0
$99$	−1.62981	−0.163802
$100$	5.08408	0.508408
$101$	11.5457	1.14884	0.574422	−	0.818560i	$-0.305227\pi$
$101$	11.5457	1.14884	0.574422	+	0.818560i	$0.305227\pi$
$102$	−1.00000	−0.0990148
$103$	0.824456	0.0812360	0.0406180	−	0.999175i	$-0.487067\pi$
$103$	0.824456	0.0812360	0.0406180	+	0.999175i	$0.487067\pi$
$104$	−3.62981	−0.355932
$105$	0	0
$106$	7.17554	0.696950
$107$	−9.89682	−0.956762	−0.478381	−	0.878152i	$-0.658776\pi$
$107$	−9.89682	−0.956762	−0.478381	+	0.878152i	$0.658776\pi$
$108$	−1.00000	−0.0962250
$109$	−5.15645	−0.493898	−0.246949	−	0.969028i	$-0.579428\pi$
$109$	−5.15645	−0.493898	−0.246949	+	0.969028i	$0.579428\pi$
$110$	−5.17554	−0.493469
$111$	−4.72128	−0.448124
$112$	0	0
$113$	−11.5266	−1.08433	−0.542167	−	0.840271i	$-0.682396\pi$
$113$	−11.5266	−1.08433	−0.542167	+	0.840271i	$0.682396\pi$
$114$	−6.80536	−0.637380
$115$	6.35109	0.592242
$116$	1.54573	0.143518
$117$	−3.62981	−0.335576
$118$	2.45427	0.225934
$119$	0	0
$120$	−3.17554	−0.289886
$121$	−8.34371	−0.758519
$122$	1.09146	0.0988163
$123$	5.09146	0.459082
$124$	−7.25963	−0.651934
$125$	0.267007	0.0238818
$126$	0	0
$127$	20.8703	1.85194	0.925972	−	0.377593i	$-0.123248\pi$
$127$	20.8703	1.85194	0.925972	+	0.377593i	$0.123248\pi$
$128$	1.00000	0.0883883
$129$	−5.17554	−0.455681
$130$	−11.5266	−1.01095
$131$	11.2596	0.983758	0.491879	−	0.870664i	$-0.336310\pi$
$131$	11.2596	0.983758	0.491879	+	0.870664i	$0.336310\pi$
$132$	1.62981	0.141857
$133$	0	0
$134$	5.91592	0.511057
$135$	−3.17554	−0.273307
$136$	1.00000	0.0857493
$137$	−6.70218	−0.572606	−0.286303	−	0.958139i	$-0.592426\pi$
$137$	−6.70218	−0.572606	−0.286303	+	0.958139i	$0.592426\pi$
$138$	−2.00000	−0.170251
$139$	−4.43517	−0.376186	−0.188093	−	0.982151i	$-0.560231\pi$
$139$	−4.43517	−0.376186	−0.188093	+	0.982151i	$0.560231\pi$
$140$	0	0
$141$	−6.35109	−0.534858
$142$	15.6107	1.31002
$143$	5.91592	0.494714
$144$	1.00000	0.0833333
$145$	4.90854	0.407632
$146$	4.08408	0.338001
$147$	0	0
$148$	4.72128	0.388086
$149$	3.17554	0.260151	0.130075	−	0.991504i	$-0.458478\pi$
$149$	3.17554	0.260151	0.130075	+	0.991504i	$0.458478\pi$
$150$	−5.08408	−0.415114
$151$	1.64891	0.134186	0.0670932	−	0.997747i	$-0.478628\pi$
$151$	1.64891	0.134186	0.0670932	+	0.997747i	$0.478628\pi$
$152$	6.80536	0.551987
$153$	1.00000	0.0808452
$154$	0	0
$155$	−23.0533	−1.85168
$156$	3.62981	0.290618
$157$	−10.9883	−0.876960	−0.438480	−	0.898741i	$-0.644483\pi$
$157$	−10.9883	−0.876960	−0.438480	+	0.898741i	$0.644483\pi$
$158$	15.6948	1.24861
$159$	−7.17554	−0.569058
$160$	3.17554	0.251049
$161$	0	0
$162$	1.00000	0.0785674
$163$	7.15645	0.560536	0.280268	−	0.959922i	$-0.409577\pi$
$163$	7.15645	0.560536	0.280268	+	0.959922i	$0.409577\pi$
$164$	−5.09146	−0.397576
$165$	5.17554	0.402916
$166$	0.538351	0.0417841
$167$	−12.6033	−0.975275	−0.487638	−	0.873046i	$-0.662141\pi$
$167$	−12.6033	−0.975275	−0.487638	+	0.873046i	$0.662141\pi$
$168$	0	0
$169$	0.175544	0.0135034
$170$	3.17554	0.243553
$171$	6.80536	0.520419
$172$	5.17554	0.394632
$173$	2.00000	0.152057	0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000	0.152057	0.0760286	+	0.997106i	$0.475776\pi$
$174$	−1.54573	−0.117182
$175$	0	0
$176$	−1.62981	−0.122852
$177$	−2.45427	−0.184474
$178$	−13.5266	−1.01386
$179$	19.0915	1.42696	0.713481	−	0.700674i	$-0.247117\pi$
$179$	19.0915	1.42696	0.713481	+	0.700674i	$0.247117\pi$
$180$	3.17554	0.236691
$181$	26.1300	1.94223	0.971113	−	0.238622i	$-0.0766956\pi$
$181$	26.1300	1.94223	0.971113	+	0.238622i	$0.0766956\pi$
$182$	0	0
$183$	−1.09146	−0.0806832
$184$	2.00000	0.147442
$185$	14.9926	1.10228
$186$	7.25963	0.532302
$187$	−1.62981	−0.119184
$188$	6.35109	0.463201
$189$	0	0
$190$	21.6107	1.56781
$191$	−22.9544	−1.66092	−0.830462	−	0.557075i	$-0.811923\pi$
$191$	−22.9544	−1.66092	−0.830462	+	0.557075i	$0.811923\pi$
$192$	−1.00000	−0.0721688
$193$	19.6107	1.41161	0.705805	−	0.708406i	$-0.250585\pi$
$193$	19.6107	1.41161	0.705805	+	0.708406i	$0.250585\pi$
$194$	−10.4352	−0.749202
$195$	11.5266	0.825439
$196$	0	0
$197$	−6.62243	−0.471829	−0.235914	−	0.971774i	$-0.575809\pi$
$197$	−6.62243	−0.471829	−0.235914	+	0.971774i	$0.575809\pi$
$198$	−1.62981	−0.115826
$199$	−16.1682	−1.14613	−0.573065	−	0.819510i	$-0.694246\pi$
$199$	−16.1682	−1.14613	−0.573065	+	0.819510i	$0.694246\pi$
$200$	5.08408	0.359499
$201$	−5.91592	−0.417277
$202$	11.5457	0.812355
$203$	0	0
$204$	−1.00000	−0.0700140
$205$	−16.1682	−1.12923
$206$	0.824456	0.0574425
$207$	2.00000	0.139010
$208$	−3.62981	−0.251682
$209$	−11.0915	−0.767212
$210$	0	0
$211$	0.637193	0.0438662	0.0219331	−	0.999759i	$-0.493018\pi$
$211$	0.637193	0.0438662	0.0219331	+	0.999759i	$0.493018\pi$
$212$	7.17554	0.492818
$213$	−15.6107	−1.06963
$214$	−9.89682	−0.676533
$215$	16.4352	1.12087
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−5.15645	−0.349239
$219$	−4.08408	−0.275977
$220$	−5.17554	−0.348935
$221$	−3.62981	−0.244168
$222$	−4.72128	−0.316871
$223$	2.74037	0.183509	0.0917545	−	0.995782i	$-0.470753\pi$
$223$	2.74037	0.183509	0.0917545	+	0.995782i	$0.470753\pi$
$224$	0	0
$225$	5.08408	0.338939
$226$	−11.5266	−0.766740
$227$	−15.2214	−1.01028	−0.505141	−	0.863037i	$-0.668559\pi$
$227$	−15.2214	−1.01028	−0.505141	+	0.863037i	$0.668559\pi$
$228$	−6.80536	−0.450696
$229$	−19.5916	−1.29465	−0.647325	−	0.762214i	$-0.724112\pi$
$229$	−19.5916	−1.29465	−0.647325	+	0.762214i	$0.724112\pi$
$230$	6.35109	0.418778
$231$	0	0
$232$	1.54573	0.101482
$233$	−1.00738	−0.0659957	−0.0329978	−	0.999455i	$-0.510505\pi$
$233$	−1.00738	−0.0659957	−0.0329978	+	0.999455i	$0.510505\pi$
$234$	−3.62981	−0.237288
$235$	20.1682	1.31563
$236$	2.45427	0.159759
$237$	−15.6948	−1.01949
$238$	0	0
$239$	−5.17554	−0.334778	−0.167389	−	0.985891i	$-0.553534\pi$
$239$	−5.17554	−0.334778	−0.167389	+	0.985891i	$0.553534\pi$
$240$	−3.17554	−0.204981
$241$	−18.7022	−1.20471	−0.602357	−	0.798227i	$-0.705771\pi$
$241$	−18.7022	−1.20471	−0.602357	+	0.798227i	$0.705771\pi$
$242$	−8.34371	−0.536354
$243$	−1.00000	−0.0641500
$244$	1.09146	0.0698737
$245$	0	0
$246$	5.09146	0.324620
$247$	−24.7022	−1.57176
$248$	−7.25963	−0.460987
$249$	−0.538351	−0.0341166
$250$	0.267007	0.0168870
$251$	3.46165	0.218497	0.109249	−	0.994014i	$-0.465156\pi$
$251$	3.46165	0.218497	0.109249	+	0.994014i	$0.465156\pi$
$252$	0	0
$253$	−3.25963	−0.204931
$254$	20.8703	1.30952
$255$	−3.17554	−0.198860
$256$	1.00000	0.0625000
$257$	−15.8777	−0.990425	−0.495213	−	0.868772i	$-0.664910\pi$
$257$	−15.8777	−0.990425	−0.495213	+	0.868772i	$0.664910\pi$
$258$	−5.17554	−0.322215
$259$	0	0
$260$	−11.5266	−0.714851
$261$	1.54573	0.0956784
$262$	11.2596	0.695622
$263$	4.47337	0.275840	0.137920	−	0.990443i	$-0.455958\pi$
$263$	4.47337	0.275840	0.137920	+	0.990443i	$0.455958\pi$
$264$	1.62981	0.100308
$265$	22.7863	1.39975
$266$	0	0
$267$	13.5266	0.827817
$268$	5.91592	0.361372
$269$	−3.61072	−0.220149	−0.110075	−	0.993923i	$-0.535109\pi$
$269$	−3.61072	−0.220149	−0.110075	+	0.993923i	$0.535109\pi$
$270$	−3.17554	−0.193257
$271$	−3.34371	−0.203116	−0.101558	−	0.994830i	$-0.532383\pi$
$271$	−3.34371	−0.203116	−0.101558	+	0.994830i	$0.532383\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	−6.70218	−0.404893
$275$	−8.28610	−0.499671
$276$	−2.00000	−0.120386
$277$	19.3394	1.16199	0.580995	−	0.813907i	$-0.302664\pi$
$277$	19.3394	1.16199	0.580995	+	0.813907i	$0.302664\pi$
$278$	−4.43517	−0.266004
$279$	−7.25963	−0.434622
$280$	0	0
$281$	20.5193	1.22408	0.612038	−	0.790828i	$-0.290350\pi$
$281$	20.5193	1.22408	0.612038	+	0.790828i	$0.290350\pi$
$282$	−6.35109	−0.378202
$283$	−22.8245	−1.35677	−0.678387	−	0.734705i	$-0.737320\pi$
$283$	−22.8245	−1.35677	−0.678387	+	0.734705i	$0.737320\pi$
$284$	15.6107	0.926326
$285$	−21.6107	−1.28011
$286$	5.91592	0.349816
$287$	0	0
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	4.90854	0.288239
$291$	10.4352	0.611721
$292$	4.08408	0.239003
$293$	22.0268	1.28682	0.643409	−	0.765522i	$-0.277519\pi$
$293$	22.0268	1.28682	0.643409	+	0.765522i	$0.277519\pi$
$294$	0	0
$295$	7.79364	0.453763
$296$	4.72128	0.274419
$297$	1.62981	0.0945714
$298$	3.17554	0.183954
$299$	−7.25963	−0.419835
$300$	−5.08408	−0.293530
$301$	0	0
$302$	1.64891	0.0948842
$303$	−11.5457	−0.663285
$304$	6.80536	0.390314
$305$	3.46599	0.198462
$306$	1.00000	0.0571662
$307$	4.62243	0.263816	0.131908	−	0.991262i	$-0.457890\pi$
$307$	4.62243	0.263816	0.131908	+	0.991262i	$0.457890\pi$
$308$	0	0
$309$	−0.824456	−0.0469016
$310$	−23.0533	−1.30934
$311$	28.4352	1.61241	0.806205	−	0.591636i	$-0.201518\pi$
$311$	28.4352	1.61241	0.806205	+	0.591636i	$0.201518\pi$
$312$	3.62981	0.205498
$313$	12.5193	0.707630	0.353815	−	0.935315i	$-0.384884\pi$
$313$	12.5193	0.707630	0.353815	+	0.935315i	$0.384884\pi$
$314$	−10.9883	−0.620105
$315$	0	0
$316$	15.6948	0.882901
$317$	−0.103180	−0.00579517	−0.00289759	−	0.999996i	$-0.500922\pi$
$317$	−0.103180	−0.00579517	−0.00289759	+	0.999996i	$0.500922\pi$
$318$	−7.17554	−0.402385
$319$	−2.51925	−0.141051
$320$	3.17554	0.177518
$321$	9.89682	0.552387
$322$	0	0
$323$	6.80536	0.378660
$324$	1.00000	0.0555556
$325$	−18.4543	−1.02366
$326$	7.15645	0.396359
$327$	5.15645	0.285152
$328$	−5.09146	−0.281129
$329$	0	0
$330$	5.17554	0.284904
$331$	29.8395	1.64013	0.820064	−	0.572271i	$-0.193938\pi$
$331$	29.8395	1.64013	0.820064	+	0.572271i	$0.193938\pi$
$332$	0.538351	0.0295459
$333$	4.72128	0.258724
$334$	−12.6033	−0.689624
$335$	18.7863	1.02640
$336$	0	0
$337$	−23.4044	−1.27492	−0.637458	−	0.770485i	$-0.720014\pi$
$337$	−23.4044	−1.27492	−0.637458	+	0.770485i	$0.720014\pi$
$338$	0.175544	0.00954836
$339$	11.5266	0.626041
$340$	3.17554	0.172218
$341$	11.8318	0.640730
$342$	6.80536	0.367992
$343$	0	0
$344$	5.17554	0.279047
$345$	−6.35109	−0.341931
$346$	2.00000	0.107521
$347$	−9.59162	−0.514905	−0.257452	−	0.966291i	$-0.582883\pi$
$347$	−9.59162	−0.514905	−0.257452	+	0.966291i	$0.582883\pi$
$348$	−1.54573	−0.0828599
$349$	10.7213	0.573897	0.286948	−	0.957946i	$-0.407359\pi$
$349$	10.7213	0.573897	0.286948	+	0.957946i	$0.407359\pi$
$350$	0	0
$351$	3.62981	0.193745
$352$	−1.62981	−0.0868693
$353$	11.1755	0.594814	0.297407	−	0.954751i	$-0.403878\pi$
$353$	11.1755	0.594814	0.297407	+	0.954751i	$0.403878\pi$
$354$	−2.45427	−0.130443
$355$	49.5725	2.63104
$356$	−13.5266	−0.716910
$357$	0	0
$358$	19.0915	1.00902
$359$	−32.4958	−1.71506	−0.857532	−	0.514431i	$-0.828003\pi$
$359$	−32.4958	−1.71506	−0.857532	+	0.514431i	$0.828003\pi$
$360$	3.17554	0.167366
$361$	27.3129	1.43752
$362$	26.1300	1.37336
$363$	8.34371	0.437931
$364$	0	0
$365$	12.9692	0.678838
$366$	−1.09146	−0.0570516
$367$	24.8321	1.29623	0.648114	−	0.761544i	$-0.275558\pi$
$367$	24.8321	1.29623	0.648114	+	0.761544i	$0.275558\pi$
$368$	2.00000	0.104257
$369$	−5.09146	−0.265051
$370$	14.9926	0.779429
$371$	0	0
$372$	7.25963	0.376394
$373$	−26.7022	−1.38259	−0.691293	−	0.722574i	$-0.742959\pi$
$373$	−26.7022	−1.38259	−0.691293	+	0.722574i	$0.742959\pi$
$374$	−1.62981	−0.0842756
$375$	−0.267007	−0.0137882
$376$	6.35109	0.327532
$377$	−5.61072	−0.288967
$378$	0	0
$379$	−0.637193	−0.0327304	−0.0163652	−	0.999866i	$-0.505209\pi$
$379$	−0.637193	−0.0327304	−0.0163652	+	0.999866i	$0.505209\pi$
$380$	21.6107	1.10861
$381$	−20.8703	−1.06922
$382$	−22.9544	−1.17445
$383$	20.7404	1.05978	0.529892	−	0.848065i	$-0.322233\pi$
$383$	20.7404	1.05978	0.529892	+	0.848065i	$0.322233\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	19.6107	0.998159
$387$	5.17554	0.263088
$388$	−10.4352	−0.529766
$389$	−5.09146	−0.258147	−0.129074	−	0.991635i	$-0.541200\pi$
$389$	−5.09146	−0.258147	−0.129074	+	0.991635i	$0.541200\pi$
$390$	11.5266	0.583674
$391$	2.00000	0.101144
$392$	0	0
$393$	−11.2596	−0.567973
$394$	−6.62243	−0.333633
$395$	49.8395	2.50770
$396$	−1.62981	−0.0819012
$397$	−6.53401	−0.327933	−0.163966	−	0.986466i	$-0.552429\pi$
$397$	−6.53401	−0.327933	−0.163966	+	0.986466i	$0.552429\pi$
$398$	−16.1682	−0.810437
$399$	0	0
$400$	5.08408	0.254204
$401$	17.5725	0.877530	0.438765	−	0.898602i	$-0.355416\pi$
$401$	17.5725	0.877530	0.438765	+	0.898602i	$0.355416\pi$
$402$	−5.91592	−0.295059
$403$	26.3511	1.31264
$404$	11.5457	0.574422
$405$	3.17554	0.157794
$406$	0	0
$407$	−7.69480	−0.381417
$408$	−1.00000	−0.0495074
$409$	−8.90854	−0.440499	−0.220249	−	0.975444i	$-0.570687\pi$
$409$	−8.90854	−0.440499	−0.220249	+	0.975444i	$0.570687\pi$
$410$	−16.1682	−0.798489
$411$	6.70218	0.330594
$412$	0.824456	0.0406180
$413$	0	0
$414$	2.00000	0.0982946
$415$	1.70956	0.0839189
$416$	−3.62981	−0.177966
$417$	4.43517	0.217191
$418$	−11.0915	−0.542501
$419$	−19.7936	−0.966983	−0.483491	−	0.875349i	$-0.660632\pi$
$419$	−19.7936	−0.966983	−0.483491	+	0.875349i	$0.660632\pi$
$420$	0	0
$421$	−36.1447	−1.76159	−0.880793	−	0.473501i	$-0.842990\pi$
$421$	−36.1447	−1.76159	−0.880793	+	0.473501i	$0.842990\pi$
$422$	0.637193	0.0310181
$423$	6.35109	0.308801
$424$	7.17554	0.348475
$425$	5.08408	0.246614
$426$	−15.6107	−0.756342
$427$	0	0
$428$	−9.89682	−0.478381
$429$	−5.91592	−0.285623
$430$	16.4352	0.792574
$431$	−12.1829	−0.586831	−0.293415	−	0.955985i	$-0.594792\pi$
$431$	−12.1829	−0.586831	−0.293415	+	0.955985i	$0.594792\pi$
$432$	−1.00000	−0.0481125
$433$	8.74037	0.420036	0.210018	−	0.977698i	$-0.432648\pi$
$433$	8.74037	0.420036	0.210018	+	0.977698i	$0.432648\pi$
$434$	0	0
$435$	−4.90854	−0.235346
$436$	−5.15645	−0.246949
$437$	13.6107	0.651089
$438$	−4.08408	−0.195145
$439$	−12.7404	−0.608065	−0.304032	−	0.952662i	$-0.598333\pi$
$439$	−12.7404	−0.608065	−0.304032	+	0.952662i	$0.598333\pi$
$440$	−5.17554	−0.246734
$441$	0	0
$442$	−3.62981	−0.172653
$443$	−10.5574	−0.501600	−0.250800	−	0.968039i	$-0.580694\pi$
$443$	−10.5574	−0.501600	−0.250800	+	0.968039i	$0.580694\pi$
$444$	−4.72128	−0.224062
$445$	−42.9544	−2.03623
$446$	2.74037	0.129760
$447$	−3.17554	−0.150198
$448$	0	0
$449$	34.0077	1.60492	0.802461	−	0.596704i	$-0.203524\pi$
$449$	34.0077	1.60492	0.802461	+	0.596704i	$0.203524\pi$
$450$	5.08408	0.239666
$451$	8.29813	0.390744
$452$	−11.5266	−0.542167
$453$	−1.64891	−0.0774726
$454$	−15.2214	−0.714377
$455$	0	0
$456$	−6.80536	−0.318690
$457$	3.51187	0.164278	0.0821392	−	0.996621i	$-0.473825\pi$
$457$	3.51187	0.164278	0.0821392	+	0.996621i	$0.473825\pi$
$458$	−19.5916	−0.915456
$459$	−1.00000	−0.0466760
$460$	6.35109	0.296121
$461$	−7.54573	−0.351440	−0.175720	−	0.984440i	$-0.556225\pi$
$461$	−7.54573	−0.351440	−0.175720	+	0.984440i	$0.556225\pi$
$462$	0	0
$463$	−19.2214	−0.893296	−0.446648	−	0.894710i	$-0.647382\pi$
$463$	−19.2214	−0.893296	−0.446648	+	0.894710i	$0.647382\pi$
$464$	1.54573	0.0717588
$465$	23.0533	1.06907
$466$	−1.00738	−0.0466660
$467$	9.54573	0.441724	0.220862	−	0.975305i	$-0.429113\pi$
$467$	9.54573	0.441724	0.220862	+	0.975305i	$0.429113\pi$
$468$	−3.62981	−0.167788
$469$	0	0
$470$	20.1682	0.930288
$471$	10.9883	0.506313
$472$	2.45427	0.112967
$473$	−8.43517	−0.387850
$474$	−15.6948	−0.720886
$475$	34.5990	1.58751
$476$	0	0
$477$	7.17554	0.328546
$478$	−5.17554	−0.236724
$479$	20.9692	0.958106	0.479053	−	0.877786i	$-0.340980\pi$
$479$	20.9692	0.958106	0.479053	+	0.877786i	$0.340980\pi$
$480$	−3.17554	−0.144943
$481$	−17.1373	−0.781396
$482$	−18.7022	−0.851861
$483$	0	0
$484$	−8.34371	−0.379259
$485$	−33.1373	−1.50469
$486$	−1.00000	−0.0453609
$487$	20.7715	0.941246	0.470623	−	0.882334i	$-0.344029\pi$
$487$	20.7715	0.941246	0.470623	+	0.882334i	$0.344029\pi$
$488$	1.09146	0.0494082
$489$	−7.15645	−0.323626
$490$	0	0
$491$	−7.79364	−0.351722	−0.175861	−	0.984415i	$-0.556271\pi$
$491$	−7.79364	−0.351722	−0.175861	+	0.984415i	$0.556271\pi$
$492$	5.09146	0.229541
$493$	1.54573	0.0696162
$494$	−24.7022	−1.11140
$495$	−5.17554	−0.232623
$496$	−7.25963	−0.325967
$497$	0	0
$498$	−0.538351	−0.0241241
$499$	9.14169	0.409238	0.204619	−	0.978842i	$-0.434404\pi$
$499$	9.14169	0.409238	0.204619	+	0.978842i	$0.434404\pi$
$500$	0.267007	0.0119409
$501$	12.6033	0.563075
$502$	3.46165	0.154501
$503$	−39.9236	−1.78011	−0.890053	−	0.455857i	$-0.849333\pi$
$503$	−39.9236	−1.78011	−0.890053	+	0.455857i	$0.849333\pi$
$504$	0	0
$505$	36.6640	1.63153
$506$	−3.25963	−0.144908
$507$	−0.175544	−0.00779620
$508$	20.8703	0.925972
$509$	32.4161	1.43682	0.718409	−	0.695621i	$-0.244871\pi$
$509$	32.4161	1.43682	0.718409	+	0.695621i	$0.244871\pi$
$510$	−3.17554	−0.140615
$511$	0	0
$512$	1.00000	0.0441942
$513$	−6.80536	−0.300464
$514$	−15.8777	−0.700336
$515$	2.61810	0.115367
$516$	−5.17554	−0.227841
$517$	−10.3511	−0.455240
$518$	0	0
$519$	−2.00000	−0.0877903
$520$	−11.5266	−0.505476
$521$	10.7022	0.468871	0.234435	−	0.972132i	$-0.424676\pi$
$521$	10.7022	0.468871	0.234435	+	0.972132i	$0.424676\pi$
$522$	1.54573	0.0676548
$523$	22.5990	0.988185	0.494093	−	0.869409i	$-0.335500\pi$
$523$	22.5990	0.988185	0.494093	+	0.869409i	$0.335500\pi$
$524$	11.2596	0.491879
$525$	0	0
$526$	4.47337	0.195048
$527$	−7.25963	−0.316234
$528$	1.62981	0.0709285
$529$	−19.0000	−0.826087
$530$	22.7863	0.989772
$531$	2.45427	0.106506
$532$	0	0
$533$	18.4811	0.800503
$534$	13.5266	0.585355
$535$	−31.4278	−1.35874
$536$	5.91592	0.255529
$537$	−19.0915	−0.823857
$538$	−3.61072	−0.155669
$539$	0	0
$540$	−3.17554	−0.136654
$541$	−37.9575	−1.63192	−0.815959	−	0.578109i	$-0.803791\pi$
$541$	−37.9575	−1.63192	−0.815959	+	0.578109i	$0.803791\pi$
$542$	−3.34371	−0.143625
$543$	−26.1300	−1.12134
$544$	1.00000	0.0428746
$545$	−16.3745	−0.701408
$546$	0	0
$547$	10.2861	0.439802	0.219901	−	0.975522i	$-0.429427\pi$
$547$	10.2861	0.439802	0.219901	+	0.975522i	$0.429427\pi$
$548$	−6.70218	−0.286303
$549$	1.09146	0.0465825
$550$	−8.28610	−0.353321
$551$	10.5193	0.448135
$552$	−2.00000	−0.0851257
$553$	0	0
$554$	19.3394	0.821651
$555$	−14.9926	−0.636401
$556$	−4.43517	−0.188093
$557$	−24.5193	−1.03891	−0.519457	−	0.854497i	$-0.673866\pi$
$557$	−24.5193	−1.03891	−0.519457	+	0.854497i	$0.673866\pi$
$558$	−7.25963	−0.307324
$559$	−18.7863	−0.794574
$560$	0	0
$561$	1.62981	0.0688108
$562$	20.5193	0.865552
$563$	−20.7065	−0.872676	−0.436338	−	0.899783i	$-0.643725\pi$
$563$	−20.7065	−0.872676	−0.436338	+	0.899783i	$0.643725\pi$
$564$	−6.35109	−0.267429
$565$	−36.6033	−1.53991
$566$	−22.8245	−0.959383
$567$	0	0
$568$	15.6107	0.655011
$569$	24.8851	1.04324	0.521619	−	0.853179i	$-0.325328\pi$
$569$	24.8851	1.04324	0.521619	+	0.853179i	$0.325328\pi$
$570$	−21.6107	−0.905173
$571$	−25.7139	−1.07609	−0.538047	−	0.842915i	$-0.680838\pi$
$571$	−25.7139	−1.07609	−0.538047	+	0.842915i	$0.680838\pi$
$572$	5.91592	0.247357
$573$	22.9544	0.958935
$574$	0	0
$575$	10.1682	0.424042
$576$	1.00000	0.0416667
$577$	14.0148	0.583442	0.291721	−	0.956503i	$-0.405772\pi$
$577$	14.0148	0.583442	0.291721	+	0.956503i	$0.405772\pi$
$578$	1.00000	0.0415945
$579$	−19.6107	−0.814994
$580$	4.90854	0.203816
$581$	0	0
$582$	10.4352	0.432552
$583$	−11.6948	−0.484349
$584$	4.08408	0.169001
$585$	−11.5266	−0.476568
$586$	22.0268	0.909918
$587$	31.7598	1.31087	0.655433	−	0.755253i	$-0.272486\pi$
$587$	31.7598	1.31087	0.655433	+	0.755253i	$0.272486\pi$
$588$	0	0
$589$	−49.4044	−2.03567
$590$	7.79364	0.320859
$591$	6.62243	0.272411
$592$	4.72128	0.194043
$593$	−6.12997	−0.251728	−0.125864	−	0.992048i	$-0.540170\pi$
$593$	−6.12997	−0.251728	−0.125864	+	0.992048i	$0.540170\pi$
$594$	1.62981	0.0668720
$595$	0	0
$596$	3.17554	0.130075
$597$	16.1682	0.661719
$598$	−7.25963	−0.296868
$599$	22.3129	0.911680	0.455840	−	0.890062i	$-0.349339\pi$
$599$	22.3129	0.911680	0.455840	+	0.890062i	$0.349339\pi$
$600$	−5.08408	−0.207557
$601$	−39.4044	−1.60734	−0.803669	−	0.595077i	$-0.797121\pi$
$601$	−39.4044	−1.60734	−0.803669	+	0.595077i	$0.797121\pi$
$602$	0	0
$603$	5.91592	0.240915
$604$	1.64891	0.0670932
$605$	−26.4958	−1.07721
$606$	−11.5457	−0.469013
$607$	−3.46599	−0.140680	−0.0703400	−	0.997523i	$-0.522408\pi$
$607$	−3.46599	−0.140680	−0.0703400	+	0.997523i	$0.522408\pi$
$608$	6.80536	0.275994
$609$	0	0
$610$	3.46599	0.140334
$611$	−23.0533	−0.932635
$612$	1.00000	0.0404226
$613$	−42.1300	−1.70161	−0.850807	−	0.525479i	$-0.823886\pi$
$613$	−42.1300	−1.70161	−0.850807	+	0.525479i	$0.823886\pi$
$614$	4.62243	0.186546
$615$	16.1682	0.651963
$616$	0	0
$617$	−44.5651	−1.79412	−0.897062	−	0.441904i	$-0.854303\pi$
$617$	−44.5651	−1.79412	−0.897062	+	0.441904i	$0.854303\pi$
$618$	−0.824456	−0.0331645
$619$	−37.8777	−1.52243	−0.761217	−	0.648497i	$-0.775398\pi$
$619$	−37.8777	−1.52243	−0.761217	+	0.648497i	$0.775398\pi$
$620$	−23.0533	−0.925841
$621$	−2.00000	−0.0802572
$622$	28.4352	1.14015
$623$	0	0
$624$	3.62981	0.145309
$625$	−24.5725	−0.982901
$626$	12.5193	0.500370
$627$	11.0915	0.442950
$628$	−10.9883	−0.438480
$629$	4.72128	0.188250
$630$	0	0
$631$	−31.7554	−1.26416	−0.632082	−	0.774901i	$-0.717799\pi$
$631$	−31.7554	−1.26416	−0.632082	+	0.774901i	$0.717799\pi$
$632$	15.6948	0.624306
$633$	−0.637193	−0.0253262
$634$	−0.103180	−0.00409781
$635$	66.2747	2.63003
$636$	−7.17554	−0.284529
$637$	0	0
$638$	−2.51925	−0.0997382
$639$	15.6107	0.617550
$640$	3.17554	0.125524
$641$	−11.7330	−0.463425	−0.231713	−	0.972784i	$-0.574433\pi$
$641$	−11.7330	−0.463425	−0.231713	+	0.972784i	$0.574433\pi$
$642$	9.89682	0.390596
$643$	15.6948	0.618942	0.309471	−	0.950909i	$-0.399848\pi$
$643$	15.6948	0.618942	0.309471	+	0.950909i	$0.399848\pi$
$644$	0	0
$645$	−16.4352	−0.647134
$646$	6.80536	0.267753
$647$	42.6874	1.67822	0.839108	−	0.543965i	$-0.183078\pi$
$647$	42.6874	1.67822	0.839108	+	0.543965i	$0.183078\pi$
$648$	1.00000	0.0392837
$649$	−4.00000	−0.157014
$650$	−18.4543	−0.723836
$651$	0	0
$652$	7.15645	0.280268
$653$	39.8204	1.55829	0.779147	−	0.626841i	$-0.215653\pi$
$653$	39.8204	1.55829	0.779147	+	0.626841i	$0.215653\pi$
$654$	5.15645	0.201633
$655$	35.7554	1.39708
$656$	−5.09146	−0.198788
$657$	4.08408	0.159335
$658$	0	0
$659$	−45.7407	−1.78180	−0.890902	−	0.454196i	$-0.849927\pi$
$659$	−45.7407	−1.78180	−0.890902	+	0.454196i	$0.849927\pi$
$660$	5.17554	0.201458
$661$	−25.1417	−0.977898	−0.488949	−	0.872312i	$-0.662620\pi$
$661$	−25.1417	−0.977898	−0.488949	+	0.872312i	$0.662620\pi$
$662$	29.8395	1.15975
$663$	3.62981	0.140970
$664$	0.538351	0.0208921
$665$	0	0
$666$	4.72128	0.182946
$667$	3.09146	0.119702
$668$	−12.6033	−0.487638
$669$	−2.74037	−0.105949
$670$	18.7863	0.725777
$671$	−1.77888	−0.0686729
$672$	0	0
$673$	−0.389285	−0.0150058	−0.00750291	−	0.999972i	$-0.502388\pi$
$673$	−0.389285	−0.0150058	−0.00750291	+	0.999972i	$0.502388\pi$
$674$	−23.4044	−0.901502
$675$	−5.08408	−0.195686
$676$	0.175544	0.00675171
$677$	−42.4352	−1.63092	−0.815458	−	0.578816i	$-0.803515\pi$
$677$	−42.4352	−1.63092	−0.815458	+	0.578816i	$0.803515\pi$
$678$	11.5266	0.442678
$679$	0	0
$680$	3.17554	0.121777
$681$	15.2214	0.583286
$682$	11.8318	0.453064
$683$	−16.9883	−0.650039	−0.325019	−	0.945707i	$-0.605371\pi$
$683$	−16.9883	−0.650039	−0.325019	+	0.945707i	$0.605371\pi$
$684$	6.80536	0.260209
$685$	−21.2831	−0.813184
$686$	0	0
$687$	19.5916	0.747467
$688$	5.17554	0.197316
$689$	−26.0459	−0.992269
$690$	−6.35109	−0.241782
$691$	−34.2436	−1.30269	−0.651343	−	0.758783i	$-0.725794\pi$
$691$	−34.2436	−1.30269	−0.651343	+	0.758783i	$0.725794\pi$
$692$	2.00000	0.0760286
$693$	0	0
$694$	−9.59162	−0.364093
$695$	−14.0841	−0.534240
$696$	−1.54573	−0.0585908
$697$	−5.09146	−0.192853
$698$	10.7213	0.405806
$699$	1.00738	0.0381026
$700$	0	0
$701$	37.6566	1.42227	0.711135	−	0.703055i	$-0.248181\pi$
$701$	37.6566	1.42227	0.711135	+	0.703055i	$0.248181\pi$
$702$	3.62981	0.136998
$703$	32.1300	1.21180
$704$	−1.62981	−0.0614259
$705$	−20.1682	−0.759577
$706$	11.1755	0.420597
$707$	0	0
$708$	−2.45427	−0.0922371
$709$	−0.889440	−0.0334036	−0.0167018	−	0.999861i	$-0.505317\pi$
$709$	−0.889440	−0.0334036	−0.0167018	+	0.999861i	$0.505317\pi$
$710$	49.5725	1.86042
$711$	15.6948	0.588601
$712$	−13.5266	−0.506932
$713$	−14.5193	−0.543750
$714$	0	0
$715$	18.7863	0.702566
$716$	19.0915	0.713481
$717$	5.17554	0.193284
$718$	−32.4958	−1.21273
$719$	18.1829	0.678109	0.339054	−	0.940767i	$-0.389893\pi$
$719$	18.1829	0.678109	0.339054	+	0.940767i	$0.389893\pi$
$720$	3.17554	0.118346
$721$	0	0
$722$	27.3129	1.01648
$723$	18.7022	0.695541
$724$	26.1300	0.971113
$725$	7.85862	0.291862
$726$	8.34371	0.309664
$727$	36.2522	1.34452	0.672261	−	0.740314i	$-0.265323\pi$
$727$	36.2522	1.34452	0.672261	+	0.740314i	$0.265323\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	12.9692	0.480011
$731$	5.17554	0.191424
$732$	−1.09146	−0.0403416
$733$	25.3012	0.934520	0.467260	−	0.884120i	$-0.345241\pi$
$733$	25.3012	0.934520	0.467260	+	0.884120i	$0.345241\pi$
$734$	24.8321	0.916571
$735$	0	0
$736$	2.00000	0.0737210
$737$	−9.64184	−0.355162
$738$	−5.09146	−0.187419
$739$	4.00000	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$740$	14.9926	0.551140
$741$	24.7022	0.907457
$742$	0	0
$743$	23.9766	0.879615	0.439807	−	0.898092i	$-0.355047\pi$
$743$	23.9766	0.879615	0.439807	+	0.898092i	$0.355047\pi$
$744$	7.25963	0.266151
$745$	10.0841	0.369452
$746$	−26.7022	−0.977636
$747$	0.538351	0.0196972
$748$	−1.62981	−0.0595919
$749$	0	0
$750$	−0.267007	−0.00974970
$751$	−43.9236	−1.60280	−0.801398	−	0.598132i	$-0.795910\pi$
$751$	−43.9236	−1.60280	−0.801398	+	0.598132i	$0.795910\pi$
$752$	6.35109	0.231600
$753$	−3.46165	−0.126150
$754$	−5.61072	−0.204330
$755$	5.23619	0.190564
$756$	0	0
$757$	−51.5343	−1.87305	−0.936523	−	0.350605i	$-0.885976\pi$
$757$	−51.5343	−1.87305	−0.936523	+	0.350605i	$0.885976\pi$
$758$	−0.637193	−0.0231439
$759$	3.25963	0.118317
$760$	21.6107	0.783903
$761$	−17.4884	−0.633955	−0.316978	−	0.948433i	$-0.602668\pi$
$761$	−17.4884	−0.633955	−0.316978	+	0.948433i	$0.602668\pi$
$762$	−20.8703	−0.756053
$763$	0	0
$764$	−22.9544	−0.830462
$765$	3.17554	0.114812
$766$	20.7404	0.749380
$767$	−8.90854	−0.321669
$768$	−1.00000	−0.0360844
$769$	−36.1300	−1.30288	−0.651440	−	0.758700i	$-0.725835\pi$
$769$	−36.1300	−1.30288	−0.651440	+	0.758700i	$0.725835\pi$
$770$	0	0
$771$	15.8777	0.571822
$772$	19.6107	0.705805
$773$	19.1417	0.688479	0.344239	−	0.938882i	$-0.388137\pi$
$773$	19.1417	0.688479	0.344239	+	0.938882i	$0.388137\pi$
$774$	5.17554	0.186031
$775$	−36.9085	−1.32579
$776$	−10.4352	−0.374601
$777$	0	0
$778$	−5.09146	−0.182538
$779$	−34.6492	−1.24144
$780$	11.5266	0.412720
$781$	−25.4426	−0.910406
$782$	2.00000	0.0715199
$783$	−1.54573	−0.0552399
$784$	0	0
$785$	−34.8938	−1.24541
$786$	−11.2596	−0.401618
$787$	−1.17554	−0.0419036	−0.0209518	−	0.999780i	$-0.506670\pi$
$787$	−1.17554	−0.0419036	−0.0209518	+	0.999780i	$0.506670\pi$
$788$	−6.62243	−0.235914
$789$	−4.47337	−0.159256
$790$	49.8395	1.77321
$791$	0	0
$792$	−1.62981	−0.0579129
$793$	−3.96180	−0.140688
$794$	−6.53401	−0.231883
$795$	−22.7863	−0.808145
$796$	−16.1682	−0.573065
$797$	−7.54573	−0.267284	−0.133642	−	0.991030i	$-0.542667\pi$
$797$	−7.54573	−0.267284	−0.133642	+	0.991030i	$0.542667\pi$
$798$	0	0
$799$	6.35109	0.224685
$800$	5.08408	0.179749
$801$	−13.5266	−0.477940
$802$	17.5725	0.620507
$803$	−6.65629	−0.234895
$804$	−5.91592	−0.208638
$805$	0	0
$806$	26.3511	0.928178
$807$	3.61072	0.127103
$808$	11.5457	0.406177
$809$	−20.5340	−0.721937	−0.360969	−	0.932578i	$-0.617554\pi$
$809$	−20.5340	−0.721937	−0.360969	+	0.932578i	$0.617554\pi$
$810$	3.17554	0.111577
$811$	−34.9544	−1.22742	−0.613708	−	0.789533i	$-0.710323\pi$
$811$	−34.9544	−1.22742	−0.613708	+	0.789533i	$0.710323\pi$
$812$	0	0
$813$	3.34371	0.117269
$814$	−7.69480	−0.269703
$815$	22.7256	0.796044
$816$	−1.00000	−0.0350070
$817$	35.2214	1.23224
$818$	−8.90854	−0.311480
$819$	0	0
$820$	−16.1682	−0.564617
$821$	−14.8201	−0.517226	−0.258613	−	0.965981i	$-0.583265\pi$
$821$	−14.8201	−0.517226	−0.258613	+	0.965981i	$0.583265\pi$
$822$	6.70218	0.233765
$823$	−4.22881	−0.147407	−0.0737035	−	0.997280i	$-0.523482\pi$
$823$	−4.22881	−0.147407	−0.0737035	+	0.997280i	$0.523482\pi$
$824$	0.824456	0.0287213
$825$	8.28610	0.288485
$826$	0	0
$827$	−15.2405	−0.529965	−0.264983	−	0.964253i	$-0.585366\pi$
$827$	−15.2405	−0.529965	−0.264983	+	0.964253i	$0.585366\pi$
$828$	2.00000	0.0695048
$829$	−25.0342	−0.869473	−0.434736	−	0.900558i	$-0.643158\pi$
$829$	−25.0342	−0.869473	−0.434736	+	0.900558i	$0.643158\pi$
$830$	1.70956	0.0593396
$831$	−19.3394	−0.670875
$832$	−3.62981	−0.125841
$833$	0	0
$834$	4.43517	0.153577
$835$	−40.0225	−1.38503
$836$	−11.0915	−0.383606
$837$	7.25963	0.250929
$838$	−19.7936	−0.683760
$839$	−28.8010	−0.994322	−0.497161	−	0.867658i	$-0.665624\pi$
$839$	−28.8010	−0.994322	−0.497161	+	0.867658i	$0.665624\pi$
$840$	0	0
$841$	−26.6107	−0.917611
$842$	−36.1447	−1.24563
$843$	−20.5193	−0.706721
$844$	0.637193	0.0219331
$845$	0.557449	0.0191768
$846$	6.35109	0.218355
$847$	0	0
$848$	7.17554	0.246409
$849$	22.8245	0.783333
$850$	5.08408	0.174383
$851$	9.44255	0.323686
$852$	−15.6107	−0.534814
$853$	27.4426	0.939615	0.469808	−	0.882769i	$-0.344323\pi$
$853$	27.4426	0.939615	0.469808	+	0.882769i	$0.344323\pi$
$854$	0	0
$855$	21.6107	0.739071
$856$	−9.89682	−0.338266
$857$	41.1832	1.40679	0.703396	−	0.710798i	$-0.251666\pi$
$857$	41.1832	1.40679	0.703396	+	0.710798i	$0.251666\pi$
$858$	−5.91592	−0.201966
$859$	20.1179	0.686415	0.343208	−	0.939260i	$-0.388487\pi$
$859$	20.1179	0.686415	0.343208	+	0.939260i	$0.388487\pi$
$860$	16.4352	0.560435
$861$	0	0
$862$	−12.1829	−0.414952
$863$	11.3289	0.385642	0.192821	−	0.981234i	$-0.438236\pi$
$863$	11.3289	0.385642	0.192821	+	0.981234i	$0.438236\pi$
$864$	−1.00000	−0.0340207
$865$	6.35109	0.215943
$866$	8.74037	0.297010
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	−25.5796	−0.867728
$870$	−4.90854	−0.166415
$871$	−21.4737	−0.727608
$872$	−5.15645	−0.174619
$873$	−10.4352	−0.353177
$874$	13.6107	0.460389
$875$	0	0
$876$	−4.08408	−0.137988
$877$	46.8660	1.58255	0.791276	−	0.611459i	$-0.209417\pi$
$877$	46.8660	1.58255	0.791276	+	0.611459i	$0.209417\pi$
$878$	−12.7404	−0.429967
$879$	−22.0268	−0.742945
$880$	−5.17554	−0.174468
$881$	−9.45731	−0.318625	−0.159312	−	0.987228i	$-0.550928\pi$
$881$	−9.45731	−0.318625	−0.159312	+	0.987228i	$0.550928\pi$
$882$	0	0
$883$	−18.1829	−0.611904	−0.305952	−	0.952047i	$-0.598975\pi$
$883$	−18.1829	−0.611904	−0.305952	+	0.952047i	$0.598975\pi$
$884$	−3.62981	−0.122084
$885$	−7.79364	−0.261980
$886$	−10.5574	−0.354684
$887$	−31.6566	−1.06292	−0.531462	−	0.847082i	$-0.678357\pi$
$887$	−31.6566	−1.06292	−0.531462	+	0.847082i	$0.678357\pi$
$888$	−4.72128	−0.158436
$889$	0	0
$890$	−42.9544	−1.43984
$891$	−1.62981	−0.0546008
$892$	2.74037	0.0917545
$893$	43.2214	1.44635
$894$	−3.17554	−0.106206
$895$	60.6258	2.02650
$896$	0	0
$897$	7.25963	0.242392
$898$	34.0077	1.13485
$899$	−11.2214	−0.374256
$900$	5.08408	0.169469
$901$	7.17554	0.239052
$902$	8.29813	0.276298
$903$	0	0
$904$	−11.5266	−0.383370
$905$	82.9769	2.75824
$906$	−1.64891	−0.0547814
$907$	−51.2864	−1.70294	−0.851469	−	0.524405i	$-0.824288\pi$
$907$	−51.2864	−1.70294	−0.851469	+	0.524405i	$0.824288\pi$
$908$	−15.2214	−0.505141
$909$	11.5457	0.382948
$910$	0	0
$911$	38.2981	1.26887	0.634437	−	0.772975i	$-0.281232\pi$
$911$	38.2981	1.26887	0.634437	+	0.772975i	$0.281232\pi$
$912$	−6.80536	−0.225348
$913$	−0.877412	−0.0290381
$914$	3.51187	0.116162
$915$	−3.46599	−0.114582
$916$	−19.5916	−0.647325
$917$	0	0
$918$	−1.00000	−0.0330049
$919$	42.1065	1.38897	0.694483	−	0.719509i	$-0.255633\pi$
$919$	42.1065	1.38897	0.694483	+	0.719509i	$0.255633\pi$
$920$	6.35109	0.209389
$921$	−4.62243	−0.152314
$922$	−7.54573	−0.248505
$923$	−56.6640	−1.86512
$924$	0	0
$925$	24.0034	0.789225
$926$	−19.2214	−0.631655
$927$	0.824456	0.0270787
$928$	1.54573	0.0507411
$929$	−18.1682	−0.596078	−0.298039	−	0.954554i	$-0.596333\pi$
$929$	−18.1682	−0.596078	−0.298039	+	0.954554i	$0.596333\pi$
$930$	23.0533	0.755946
$931$	0	0
$932$	−1.00738	−0.0329978
$933$	−28.4352	−0.930926
$934$	9.54573	0.312346
$935$	−5.17554	−0.169258
$936$	−3.62981	−0.118644
$937$	−53.4044	−1.74464	−0.872322	−	0.488932i	$-0.837387\pi$
$937$	−53.4044	−1.74464	−0.872322	+	0.488932i	$0.837387\pi$
$938$	0	0
$939$	−12.5193	−0.408550
$940$	20.1682	0.657813
$941$	−39.8013	−1.29749	−0.648743	−	0.761007i	$-0.724705\pi$
$941$	−39.8013	−1.29749	−0.648743	+	0.761007i	$0.724705\pi$
$942$	10.9883	0.358018
$943$	−10.1829	−0.331602
$944$	2.45427	0.0798796
$945$	0	0
$946$	−8.43517	−0.274251
$947$	49.4546	1.60706	0.803529	−	0.595266i	$-0.202953\pi$
$947$	49.4546	1.60706	0.803529	+	0.595266i	$0.202953\pi$
$948$	−15.6948	−0.509743
$949$	−14.8245	−0.481222
$950$	34.5990	1.12254
$951$	0.103180	0.00334584
$952$	0	0
$953$	3.57252	0.115725	0.0578626	−	0.998325i	$-0.481571\pi$
$953$	3.57252	0.115725	0.0578626	+	0.998325i	$0.481571\pi$
$954$	7.17554	0.232317
$955$	−72.8928	−2.35876
$956$	−5.17554	−0.167389
$957$	2.51925	0.0814359
$958$	20.9692	0.677484
$959$	0	0
$960$	−3.17554	−0.102490
$961$	21.7022	0.700070
$962$	−17.1373	−0.552530
$963$	−9.89682	−0.318921
$964$	−18.7022	−0.602357
$965$	62.2747	2.00469
$966$	0	0
$967$	12.1682	0.391302	0.195651	−	0.980674i	$-0.437318\pi$
$967$	12.1682	0.391302	0.195651	+	0.980674i	$0.437318\pi$
$968$	−8.34371	−0.268177
$969$	−6.80536	−0.218620
$970$	−33.1373	−1.06398
$971$	−21.2023	−0.680415	−0.340208	−	0.940350i	$-0.610497\pi$
$971$	−21.2023	−0.680415	−0.340208	+	0.940350i	$0.610497\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	20.7715	0.665562
$975$	18.4543	0.591010
$976$	1.09146	0.0349369
$977$	6.36585	0.203662	0.101831	−	0.994802i	$-0.467530\pi$
$977$	6.36585	0.203662	0.101831	+	0.994802i	$0.467530\pi$
$978$	−7.15645	−0.228838
$979$	22.0459	0.704590
$980$	0	0
$981$	−5.15645	−0.164633
$982$	−7.79364	−0.248705
$983$	−2.51925	−0.0803517	−0.0401758	−	0.999193i	$-0.512792\pi$
$983$	−2.51925	−0.0803517	−0.0401758	+	0.999193i	$0.512792\pi$
$984$	5.09146	0.162310
$985$	−21.0298	−0.670066
$986$	1.54573	0.0492261
$987$	0	0
$988$	−24.7022	−0.785881
$989$	10.3511	0.329145
$990$	−5.17554	−0.164490
$991$	−32.2288	−1.02378	−0.511891	−	0.859050i	$-0.671055\pi$
$991$	−32.2288	−1.02378	−0.511891	+	0.859050i	$0.671055\pi$
$992$	−7.25963	−0.230493
$993$	−29.8395	−0.946929
$994$	0	0
$995$	−51.3427	−1.62767
$996$	−0.538351	−0.0170583
$997$	−35.4044	−1.12127	−0.560634	−	0.828064i	$-0.689442\pi$
$997$	−35.4044	−1.12127	−0.560634	+	0.828064i	$0.689442\pi$
$998$	9.14169	0.289375
$999$	−4.72128	−0.149375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4998.2.a.ci.1.3	✓	3
7.6	odd	2		4998.2.a.cj.1.1	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4998.2.a.ci.1.3	✓	3	1.1	even	1	trivial
4998.2.a.cj.1.1	yes	3	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.17554 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.17554 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.17554 q^{10} -1.62981 q^{11} -1.00000 q^{12} -3.62981 q^{13} -3.17554 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +6.80536 q^{19} +3.17554 q^{20} -1.62981 q^{22} +2.00000 q^{23} -1.00000 q^{24} +5.08408 q^{25} -3.62981 q^{26} -1.00000 q^{27} +1.54573 q^{29} -3.17554 q^{30} -7.25963 q^{31} +1.00000 q^{32} +1.62981 q^{33} +1.00000 q^{34} +1.00000 q^{36} +4.72128 q^{37} +6.80536 q^{38} +3.62981 q^{39} +3.17554 q^{40} -5.09146 q^{41} +5.17554 q^{43} -1.62981 q^{44} +3.17554 q^{45} +2.00000 q^{46} +6.35109 q^{47} -1.00000 q^{48} +5.08408 q^{50} -1.00000 q^{51} -3.62981 q^{52} +7.17554 q^{53} -1.00000 q^{54} -5.17554 q^{55} -6.80536 q^{57} +1.54573 q^{58} +2.45427 q^{59} -3.17554 q^{60} +1.09146 q^{61} -7.25963 q^{62} +1.00000 q^{64} -11.5266 q^{65} +1.62981 q^{66} +5.91592 q^{67} +1.00000 q^{68} -2.00000 q^{69} +15.6107 q^{71} +1.00000 q^{72} +4.08408 q^{73} +4.72128 q^{74} -5.08408 q^{75} +6.80536 q^{76} +3.62981 q^{78} +15.6948 q^{79} +3.17554 q^{80} +1.00000 q^{81} -5.09146 q^{82} +0.538351 q^{83} +3.17554 q^{85} +5.17554 q^{86} -1.54573 q^{87} -1.62981 q^{88} -13.5266 q^{89} +3.17554 q^{90} +2.00000 q^{92} +7.25963 q^{93} +6.35109 q^{94} +21.6107 q^{95} -1.00000 q^{96} -10.4352 q^{97} -1.62981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} - 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 - 3 * q^6 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} - 3 q^{6} + 3 q^{8} + 3 q^{9} - q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{13} + q^{15} + 3 q^{16} + 3 q^{17} + 3 q^{18} + 2 q^{19} - q^{20} + 3 q^{22} + 6 q^{23} - 3 q^{24} + 10 q^{25} - 3 q^{26} - 3 q^{27} + 2 q^{29} + q^{30} - 6 q^{31} + 3 q^{32} - 3 q^{33} + 3 q^{34} + 3 q^{36} + q^{37} + 2 q^{38} + 3 q^{39} - q^{40} - 10 q^{41} + 5 q^{43} + 3 q^{44} - q^{45} + 6 q^{46} - 2 q^{47} - 3 q^{48} + 10 q^{50} - 3 q^{51} - 3 q^{52} + 11 q^{53} - 3 q^{54} - 5 q^{55} - 2 q^{57} + 2 q^{58} + 10 q^{59} + q^{60} - 2 q^{61} - 6 q^{62} + 3 q^{64} - 3 q^{65} - 3 q^{66} + 23 q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{71} + 3 q^{72} + 7 q^{73} + q^{74} - 10 q^{75} + 2 q^{76} + 3 q^{78} + 5 q^{79} - q^{80} + 3 q^{81} - 10 q^{82} - q^{83} - q^{85} + 5 q^{86} - 2 q^{87} + 3 q^{88} - 9 q^{89} - q^{90} + 6 q^{92} + 6 q^{93} - 2 q^{94} + 28 q^{95} - 3 q^{96} - 5 q^{97} + 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 - 3 * q^6 + 3 * q^8 + 3 * q^9 - q^10 + 3 * q^11 - 3 * q^12 - 3 * q^13 + q^15 + 3 * q^16 + 3 * q^17 + 3 * q^18 + 2 * q^19 - q^20 + 3 * q^22 + 6 * q^23 - 3 * q^24 + 10 * q^25 - 3 * q^26 - 3 * q^27 + 2 * q^29 + q^30 - 6 * q^31 + 3 * q^32 - 3 * q^33 + 3 * q^34 + 3 * q^36 + q^37 + 2 * q^38 + 3 * q^39 - q^40 - 10 * q^41 + 5 * q^43 + 3 * q^44 - q^45 + 6 * q^46 - 2 * q^47 - 3 * q^48 + 10 * q^50 - 3 * q^51 - 3 * q^52 + 11 * q^53 - 3 * q^54 - 5 * q^55 - 2 * q^57 + 2 * q^58 + 10 * q^59 + q^60 - 2 * q^61 - 6 * q^62 + 3 * q^64 - 3 * q^65 - 3 * q^66 + 23 * q^67 + 3 * q^68 - 6 * q^69 + 10 * q^71 + 3 * q^72 + 7 * q^73 + q^74 - 10 * q^75 + 2 * q^76 + 3 * q^78 + 5 * q^79 - q^80 + 3 * q^81 - 10 * q^82 - q^83 - q^85 + 5 * q^86 - 2 * q^87 + 3 * q^88 - 9 * q^89 - q^90 + 6 * q^92 + 6 * q^93 - 2 * q^94 + 28 * q^95 - 3 * q^96 - 5 * q^97 + 3 * q^99

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