LMFDB - Embedded newform 2166.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,2,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2166.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2166.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:	$17.2955970778$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.61803 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.61803 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.61803 q^{10} -4.00000 q^{11} +1.00000 q^{12} -0.618034 q^{13} -1.61803 q^{15} +1.00000 q^{16} +7.09017 q^{17} -1.00000 q^{18} -1.61803 q^{20} +4.00000 q^{22} -4.00000 q^{23} -1.00000 q^{24} -2.38197 q^{25} +0.618034 q^{26} +1.00000 q^{27} -2.14590 q^{29} +1.61803 q^{30} +10.4721 q^{31} -1.00000 q^{32} -4.00000 q^{33} -7.09017 q^{34} +1.00000 q^{36} -0.854102 q^{37} -0.618034 q^{39} +1.61803 q^{40} -0.854102 q^{41} -1.52786 q^{43} -4.00000 q^{44} -1.61803 q^{45} +4.00000 q^{46} -12.9443 q^{47} +1.00000 q^{48} -7.00000 q^{49} +2.38197 q^{50} +7.09017 q^{51} -0.618034 q^{52} -6.38197 q^{53} -1.00000 q^{54} +6.47214 q^{55} +2.14590 q^{58} -6.47214 q^{59} -1.61803 q^{60} -7.38197 q^{61} -10.4721 q^{62} +1.00000 q^{64} +1.00000 q^{65} +4.00000 q^{66} +15.4164 q^{67} +7.09017 q^{68} -4.00000 q^{69} -2.47214 q^{71} -1.00000 q^{72} -13.0344 q^{73} +0.854102 q^{74} -2.38197 q^{75} +0.618034 q^{78} +4.00000 q^{79} -1.61803 q^{80} +1.00000 q^{81} +0.854102 q^{82} -8.00000 q^{83} -11.4721 q^{85} +1.52786 q^{86} -2.14590 q^{87} +4.00000 q^{88} -10.3820 q^{89} +1.61803 q^{90} -4.00000 q^{92} +10.4721 q^{93} +12.9443 q^{94} -1.00000 q^{96} +14.7984 q^{97} +7.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} - 8 q^{11} + 2 q^{12} + q^{13} - q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - q^{20} + 8 q^{22} - 8 q^{23} - 2 q^{24} - 7 q^{25} - q^{26} + 2 q^{27} - 11 q^{29} + q^{30} + 12 q^{31} - 2 q^{32} - 8 q^{33} - 3 q^{34} + 2 q^{36} + 5 q^{37} + q^{39} + q^{40} + 5 q^{41} - 12 q^{43} - 8 q^{44} - q^{45} + 8 q^{46} - 8 q^{47} + 2 q^{48} - 14 q^{49} + 7 q^{50} + 3 q^{51} + q^{52} - 15 q^{53} - 2 q^{54} + 4 q^{55} + 11 q^{58} - 4 q^{59} - q^{60} - 17 q^{61} - 12 q^{62} + 2 q^{64} + 2 q^{65} + 8 q^{66} + 4 q^{67} + 3 q^{68} - 8 q^{69} + 4 q^{71} - 2 q^{72} + 3 q^{73} - 5 q^{74} - 7 q^{75} - q^{78} + 8 q^{79} - q^{80} + 2 q^{81} - 5 q^{82} - 16 q^{83} - 14 q^{85} + 12 q^{86} - 11 q^{87} + 8 q^{88} - 23 q^{89} + q^{90} - 8 q^{92} + 12 q^{93} + 8 q^{94} - 2 q^{96} + 5 q^{97} + 14 q^{98} - 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 - 8 * q^11 + 2 * q^12 + q^13 - q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - q^20 + 8 * q^22 - 8 * q^23 - 2 * q^24 - 7 * q^25 - q^26 + 2 * q^27 - 11 * q^29 + q^30 + 12 * q^31 - 2 * q^32 - 8 * q^33 - 3 * q^34 + 2 * q^36 + 5 * q^37 + q^39 + q^40 + 5 * q^41 - 12 * q^43 - 8 * q^44 - q^45 + 8 * q^46 - 8 * q^47 + 2 * q^48 - 14 * q^49 + 7 * q^50 + 3 * q^51 + q^52 - 15 * q^53 - 2 * q^54 + 4 * q^55 + 11 * q^58 - 4 * q^59 - q^60 - 17 * q^61 - 12 * q^62 + 2 * q^64 + 2 * q^65 + 8 * q^66 + 4 * q^67 + 3 * q^68 - 8 * q^69 + 4 * q^71 - 2 * q^72 + 3 * q^73 - 5 * q^74 - 7 * q^75 - q^78 + 8 * q^79 - q^80 + 2 * q^81 - 5 * q^82 - 16 * q^83 - 14 * q^85 + 12 * q^86 - 11 * q^87 + 8 * q^88 - 23 * q^89 + q^90 - 8 * q^92 + 12 * q^93 + 8 * q^94 - 2 * q^96 + 5 * q^97 + 14 * q^98 - 8 * 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
$5$	−1.61803	−0.723607	−0.361803	−	0.932254i	$-0.617839\pi$
$5$	−1.61803	−0.723607	−0.361803	+	0.932254i	$0.617839\pi$
$6$	−1.00000	−0.408248
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.61803	0.511667
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.00000	0.288675
$13$	−0.618034	−0.171412	−0.0857059	−	0.996320i	$-0.527315\pi$
$13$	−0.618034	−0.171412	−0.0857059	+	0.996320i	$0.527315\pi$
$14$	0	0
$15$	−1.61803	−0.417775
$16$	1.00000	0.250000
$17$	7.09017	1.71962	0.859809	−	0.510615i	$-0.170582\pi$
$17$	7.09017	1.71962	0.859809	+	0.510615i	$0.170582\pi$
$18$	−1.00000	−0.235702
$19$	0	0
$19$	0	0
$20$	−1.61803	−0.361803
$21$	0	0
$22$	4.00000	0.852803
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−1.00000	−0.204124
$25$	−2.38197	−0.476393
$26$	0.618034	0.121206
$27$	1.00000	0.192450
$28$	0	0
$29$	−2.14590	−0.398483	−0.199242	−	0.979950i	$-0.563848\pi$
$29$	−2.14590	−0.398483	−0.199242	+	0.979950i	$0.563848\pi$
$30$	1.61803	0.295411
$31$	10.4721	1.88085	0.940426	−	0.340000i	$-0.110427\pi$
$31$	10.4721	1.88085	0.940426	+	0.340000i	$0.110427\pi$
$32$	−1.00000	−0.176777
$33$	−4.00000	−0.696311
$34$	−7.09017	−1.21595
$35$	0	0
$36$	1.00000	0.166667
$37$	−0.854102	−0.140413	−0.0702067	−	0.997532i	$-0.522366\pi$
$37$	−0.854102	−0.140413	−0.0702067	+	0.997532i	$0.522366\pi$
$38$	0	0
$39$	−0.618034	−0.0989646
$40$	1.61803	0.255834
$41$	−0.854102	−0.133388	−0.0666942	−	0.997773i	$-0.521245\pi$
$41$	−0.854102	−0.133388	−0.0666942	+	0.997773i	$0.521245\pi$
$42$	0	0
$43$	−1.52786	−0.232997	−0.116499	−	0.993191i	$-0.537167\pi$
$43$	−1.52786	−0.232997	−0.116499	+	0.993191i	$0.537167\pi$
$44$	−4.00000	−0.603023
$45$	−1.61803	−0.241202
$46$	4.00000	0.589768
$47$	−12.9443	−1.88812	−0.944058	−	0.329779i	$-0.893026\pi$
$47$	−12.9443	−1.88812	−0.944058	+	0.329779i	$0.893026\pi$
$48$	1.00000	0.144338
$49$	−7.00000	−1.00000
$50$	2.38197	0.336861
$51$	7.09017	0.992822
$52$	−0.618034	−0.0857059
$53$	−6.38197	−0.876630	−0.438315	−	0.898821i	$-0.644425\pi$
$53$	−6.38197	−0.876630	−0.438315	+	0.898821i	$0.644425\pi$
$54$	−1.00000	−0.136083
$55$	6.47214	0.872703
$56$	0	0
$57$	0	0
$58$	2.14590	0.281770
$59$	−6.47214	−0.842600	−0.421300	−	0.906921i	$-0.638426\pi$
$59$	−6.47214	−0.842600	−0.421300	+	0.906921i	$0.638426\pi$
$60$	−1.61803	−0.208887
$61$	−7.38197	−0.945164	−0.472582	−	0.881287i	$-0.656678\pi$
$61$	−7.38197	−0.945164	−0.472582	+	0.881287i	$0.656678\pi$
$62$	−10.4721	−1.32996
$63$	0	0
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	4.00000	0.492366
$67$	15.4164	1.88341	0.941707	−	0.336434i	$-0.109221\pi$
$67$	15.4164	1.88341	0.941707	+	0.336434i	$0.109221\pi$
$68$	7.09017	0.859809
$69$	−4.00000	−0.481543
$70$	0	0
$71$	−2.47214	−0.293389	−0.146694	−	0.989182i	$-0.546863\pi$
$71$	−2.47214	−0.293389	−0.146694	+	0.989182i	$0.546863\pi$
$72$	−1.00000	−0.117851
$73$	−13.0344	−1.52557	−0.762783	−	0.646655i	$-0.776168\pi$
$73$	−13.0344	−1.52557	−0.762783	+	0.646655i	$0.776168\pi$
$74$	0.854102	0.0992873
$75$	−2.38197	−0.275046
$76$	0	0
$77$	0	0
$78$	0.618034	0.0699786
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	−1.61803	−0.180902
$81$	1.00000	0.111111
$82$	0.854102	0.0943198
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	0	0
$85$	−11.4721	−1.24433
$86$	1.52786	0.164754
$87$	−2.14590	−0.230064
$88$	4.00000	0.426401
$89$	−10.3820	−1.10049	−0.550243	−	0.835005i	$-0.685465\pi$
$89$	−10.3820	−1.10049	−0.550243	+	0.835005i	$0.685465\pi$
$90$	1.61803	0.170556
$91$	0	0
$92$	−4.00000	−0.417029
$93$	10.4721	1.08591
$94$	12.9443	1.33510
$95$	0	0
$96$	−1.00000	−0.102062
$97$	14.7984	1.50255	0.751274	−	0.659991i	$-0.229440\pi$
$97$	14.7984	1.50255	0.751274	+	0.659991i	$0.229440\pi$
$98$	7.00000	0.707107
$99$	−4.00000	−0.402015
$100$	−2.38197	−0.238197
$101$	−16.0902	−1.60103	−0.800516	−	0.599312i	$-0.795441\pi$
$101$	−16.0902	−1.60103	−0.800516	+	0.599312i	$0.795441\pi$
$102$	−7.09017	−0.702031
$103$	−11.4164	−1.12489	−0.562446	−	0.826834i	$-0.690140\pi$
$103$	−11.4164	−1.12489	−0.562446	+	0.826834i	$0.690140\pi$
$104$	0.618034	0.0606032
$105$	0	0
$106$	6.38197	0.619871
$107$	−4.94427	−0.477981	−0.238990	−	0.971022i	$-0.576816\pi$
$107$	−4.94427	−0.477981	−0.238990	+	0.971022i	$0.576816\pi$
$108$	1.00000	0.0962250
$109$	−13.7984	−1.32164	−0.660822	−	0.750542i	$-0.729792\pi$
$109$	−13.7984	−1.32164	−0.660822	+	0.750542i	$0.729792\pi$
$110$	−6.47214	−0.617094
$111$	−0.854102	−0.0810678
$112$	0	0
$113$	8.32624	0.783267	0.391633	−	0.920121i	$-0.371910\pi$
$113$	8.32624	0.783267	0.391633	+	0.920121i	$0.371910\pi$
$114$	0	0
$115$	6.47214	0.603530
$116$	−2.14590	−0.199242
$117$	−0.618034	−0.0571373
$118$	6.47214	0.595808
$119$	0	0
$120$	1.61803	0.147706
$121$	5.00000	0.454545
$122$	7.38197	0.668332
$123$	−0.854102	−0.0770118
$124$	10.4721	0.940426
$125$	11.9443	1.06833
$126$	0	0
$127$	−11.4164	−1.01304	−0.506521	−	0.862228i	$-0.669069\pi$
$127$	−11.4164	−1.01304	−0.506521	+	0.862228i	$0.669069\pi$
$128$	−1.00000	−0.0883883
$129$	−1.52786	−0.134521
$130$	−1.00000	−0.0877058
$131$	15.4164	1.34694	0.673469	−	0.739216i	$-0.264804\pi$
$131$	15.4164	1.34694	0.673469	+	0.739216i	$0.264804\pi$
$132$	−4.00000	−0.348155
$133$	0	0
$134$	−15.4164	−1.33177
$135$	−1.61803	−0.139258
$136$	−7.09017	−0.607977
$137$	−12.0902	−1.03293	−0.516466	−	0.856307i	$-0.672753\pi$
$137$	−12.0902	−1.03293	−0.516466	+	0.856307i	$0.672753\pi$
$138$	4.00000	0.340503
$139$	3.05573	0.259183	0.129592	−	0.991567i	$-0.458633\pi$
$139$	3.05573	0.259183	0.129592	+	0.991567i	$0.458633\pi$
$140$	0	0
$141$	−12.9443	−1.09010
$142$	2.47214	0.207457
$143$	2.47214	0.206730
$144$	1.00000	0.0833333
$145$	3.47214	0.288345
$146$	13.0344	1.07874
$147$	−7.00000	−0.577350
$148$	−0.854102	−0.0702067
$149$	7.09017	0.580849	0.290425	−	0.956898i	$-0.406203\pi$
$149$	7.09017	0.580849	0.290425	+	0.956898i	$0.406203\pi$
$150$	2.38197	0.194487
$151$	14.4721	1.17773	0.588863	−	0.808233i	$-0.299576\pi$
$151$	14.4721	1.17773	0.588863	+	0.808233i	$0.299576\pi$
$152$	0	0
$153$	7.09017	0.573206
$154$	0	0
$155$	−16.9443	−1.36100
$156$	−0.618034	−0.0494823
$157$	18.5066	1.47699	0.738493	−	0.674261i	$-0.235538\pi$
$157$	18.5066	1.47699	0.738493	+	0.674261i	$0.235538\pi$
$158$	−4.00000	−0.318223
$159$	−6.38197	−0.506123
$160$	1.61803	0.127917
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−23.4164	−1.83411	−0.917057	−	0.398755i	$-0.869442\pi$
$163$	−23.4164	−1.83411	−0.917057	+	0.398755i	$0.869442\pi$
$164$	−0.854102	−0.0666942
$165$	6.47214	0.503855
$166$	8.00000	0.620920
$167$	3.41641	0.264370	0.132185	−	0.991225i	$-0.457801\pi$
$167$	3.41641	0.264370	0.132185	+	0.991225i	$0.457801\pi$
$168$	0	0
$169$	−12.6180	−0.970618
$170$	11.4721	0.879873
$171$	0	0
$172$	−1.52786	−0.116499
$173$	−11.3262	−0.861118	−0.430559	−	0.902562i	$-0.641684\pi$
$173$	−11.3262	−0.861118	−0.430559	+	0.902562i	$0.641684\pi$
$174$	2.14590	0.162680
$175$	0	0
$176$	−4.00000	−0.301511
$177$	−6.47214	−0.486476
$178$	10.3820	0.778161
$179$	8.00000	0.597948	0.298974	−	0.954261i	$-0.403356\pi$
$179$	8.00000	0.597948	0.298974	+	0.954261i	$0.403356\pi$
$180$	−1.61803	−0.120601
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	0	0
$183$	−7.38197	−0.545691
$184$	4.00000	0.294884
$185$	1.38197	0.101604
$186$	−10.4721	−0.767854
$187$	−28.3607	−2.07394
$188$	−12.9443	−0.944058
$189$	0	0
$190$	0	0
$191$	7.41641	0.536632	0.268316	−	0.963331i	$-0.413533\pi$
$191$	7.41641	0.536632	0.268316	+	0.963331i	$0.413533\pi$
$192$	1.00000	0.0721688
$193$	23.8885	1.71954	0.859768	−	0.510686i	$-0.170608\pi$
$193$	23.8885	1.71954	0.859768	+	0.510686i	$0.170608\pi$
$194$	−14.7984	−1.06246
$195$	1.00000	0.0716115
$196$	−7.00000	−0.500000
$197$	−21.2705	−1.51546	−0.757731	−	0.652568i	$-0.773692\pi$
$197$	−21.2705	−1.51546	−0.757731	+	0.652568i	$0.773692\pi$
$198$	4.00000	0.284268
$199$	7.41641	0.525735	0.262868	−	0.964832i	$-0.415332\pi$
$199$	7.41641	0.525735	0.262868	+	0.964832i	$0.415332\pi$
$200$	2.38197	0.168430
$201$	15.4164	1.08739
$202$	16.0902	1.13210
$203$	0	0
$204$	7.09017	0.496411
$205$	1.38197	0.0965207
$206$	11.4164	0.795419
$207$	−4.00000	−0.278019
$208$	−0.618034	−0.0428529
$209$	0	0
$210$	0	0
$211$	−15.4164	−1.06131	−0.530655	−	0.847588i	$-0.678054\pi$
$211$	−15.4164	−1.06131	−0.530655	+	0.847588i	$0.678054\pi$
$212$	−6.38197	−0.438315
$213$	−2.47214	−0.169388
$214$	4.94427	0.337983
$215$	2.47214	0.168598
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	13.7984	0.934544
$219$	−13.0344	−0.880786
$220$	6.47214	0.436351
$221$	−4.38197	−0.294763
$222$	0.854102	0.0573236
$223$	2.47214	0.165546	0.0827732	−	0.996568i	$-0.473622\pi$
$223$	2.47214	0.165546	0.0827732	+	0.996568i	$0.473622\pi$
$224$	0	0
$225$	−2.38197	−0.158798
$226$	−8.32624	−0.553853
$227$	0.944272	0.0626735	0.0313368	−	0.999509i	$-0.490024\pi$
$227$	0.944272	0.0626735	0.0313368	+	0.999509i	$0.490024\pi$
$228$	0	0
$229$	−2.56231	−0.169322	−0.0846610	−	0.996410i	$-0.526981\pi$
$229$	−2.56231	−0.169322	−0.0846610	+	0.996410i	$0.526981\pi$
$230$	−6.47214	−0.426760
$231$	0	0
$232$	2.14590	0.140885
$233$	18.1459	1.18878	0.594389	−	0.804178i	$-0.297394\pi$
$233$	18.1459	1.18878	0.594389	+	0.804178i	$0.297394\pi$
$234$	0.618034	0.0404021
$235$	20.9443	1.36625
$236$	−6.47214	−0.421300
$237$	4.00000	0.259828
$238$	0	0
$239$	−11.4164	−0.738466	−0.369233	−	0.929337i	$-0.620380\pi$
$239$	−11.4164	−0.738466	−0.369233	+	0.929337i	$0.620380\pi$
$240$	−1.61803	−0.104444
$241$	−27.8885	−1.79646	−0.898230	−	0.439527i	$-0.855146\pi$
$241$	−27.8885	−1.79646	−0.898230	+	0.439527i	$0.855146\pi$
$242$	−5.00000	−0.321412
$243$	1.00000	0.0641500
$244$	−7.38197	−0.472582
$245$	11.3262	0.723607
$246$	0.854102	0.0544556
$247$	0	0
$248$	−10.4721	−0.664981
$249$	−8.00000	−0.506979
$250$	−11.9443	−0.755422
$251$	−2.47214	−0.156040	−0.0780199	−	0.996952i	$-0.524860\pi$
$251$	−2.47214	−0.156040	−0.0780199	+	0.996952i	$0.524860\pi$
$252$	0	0
$253$	16.0000	1.00591
$254$	11.4164	0.716329
$255$	−11.4721	−0.718413
$256$	1.00000	0.0625000
$257$	−3.90983	−0.243888	−0.121944	−	0.992537i	$-0.538913\pi$
$257$	−3.90983	−0.243888	−0.121944	+	0.992537i	$0.538913\pi$
$258$	1.52786	0.0951207
$259$	0	0
$260$	1.00000	0.0620174
$261$	−2.14590	−0.132828
$262$	−15.4164	−0.952429
$263$	22.4721	1.38569	0.692846	−	0.721086i	$-0.256357\pi$
$263$	22.4721	1.38569	0.692846	+	0.721086i	$0.256357\pi$
$264$	4.00000	0.246183
$265$	10.3262	0.634336
$266$	0	0
$267$	−10.3820	−0.635366
$268$	15.4164	0.941707
$269$	13.2705	0.809117	0.404559	−	0.914512i	$-0.367425\pi$
$269$	13.2705	0.809117	0.404559	+	0.914512i	$0.367425\pi$
$270$	1.61803	0.0984704
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	7.09017	0.429905
$273$	0	0
$274$	12.0902	0.730394
$275$	9.52786	0.574552
$276$	−4.00000	−0.240772
$277$	−4.09017	−0.245754	−0.122877	−	0.992422i	$-0.539212\pi$
$277$	−4.09017	−0.245754	−0.122877	+	0.992422i	$0.539212\pi$
$278$	−3.05573	−0.183270
$279$	10.4721	0.626950
$280$	0	0
$281$	23.7426	1.41637	0.708184	−	0.706028i	$-0.249515\pi$
$281$	23.7426	1.41637	0.708184	+	0.706028i	$0.249515\pi$
$282$	12.9443	0.770820
$283$	0.944272	0.0561311	0.0280656	−	0.999606i	$-0.491065\pi$
$283$	0.944272	0.0561311	0.0280656	+	0.999606i	$0.491065\pi$
$284$	−2.47214	−0.146694
$285$	0	0
$286$	−2.47214	−0.146180
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	33.2705	1.95709
$290$	−3.47214	−0.203891
$291$	14.7984	0.867496
$292$	−13.0344	−0.762783
$293$	−22.0000	−1.28525	−0.642627	−	0.766179i	$-0.722155\pi$
$293$	−22.0000	−1.28525	−0.642627	+	0.766179i	$0.722155\pi$
$294$	7.00000	0.408248
$295$	10.4721	0.609711
$296$	0.854102	0.0496437
$297$	−4.00000	−0.232104
$298$	−7.09017	−0.410723
$299$	2.47214	0.142967
$300$	−2.38197	−0.137523
$301$	0	0
$302$	−14.4721	−0.832778
$303$	−16.0902	−0.924356
$304$	0	0
$305$	11.9443	0.683927
$306$	−7.09017	−0.405318
$307$	−22.4721	−1.28255	−0.641276	−	0.767310i	$-0.721595\pi$
$307$	−22.4721	−1.28255	−0.641276	+	0.767310i	$0.721595\pi$
$308$	0	0
$309$	−11.4164	−0.649457
$310$	16.9443	0.962370
$311$	−21.5279	−1.22073	−0.610367	−	0.792119i	$-0.708978\pi$
$311$	−21.5279	−1.22073	−0.610367	+	0.792119i	$0.708978\pi$
$312$	0.618034	0.0349893
$313$	3.32624	0.188010	0.0940050	−	0.995572i	$-0.470033\pi$
$313$	3.32624	0.188010	0.0940050	+	0.995572i	$0.470033\pi$
$314$	−18.5066	−1.04439
$315$	0	0
$316$	4.00000	0.225018
$317$	−29.2148	−1.64087	−0.820433	−	0.571743i	$-0.806267\pi$
$317$	−29.2148	−1.64087	−0.820433	+	0.571743i	$0.806267\pi$
$318$	6.38197	0.357883
$319$	8.58359	0.480589
$320$	−1.61803	−0.0904508
$321$	−4.94427	−0.275962
$322$	0	0
$323$	0	0
$324$	1.00000	0.0555556
$325$	1.47214	0.0816594
$326$	23.4164	1.29691
$327$	−13.7984	−0.763052
$328$	0.854102	0.0471599
$329$	0	0
$330$	−6.47214	−0.356279
$331$	1.88854	0.103804	0.0519019	−	0.998652i	$-0.483472\pi$
$331$	1.88854	0.103804	0.0519019	+	0.998652i	$0.483472\pi$
$332$	−8.00000	−0.439057
$333$	−0.854102	−0.0468045
$334$	−3.41641	−0.186938
$335$	−24.9443	−1.36285
$336$	0	0
$337$	−0.270510	−0.0147356	−0.00736780	−	0.999973i	$-0.502345\pi$
$337$	−0.270510	−0.0147356	−0.00736780	+	0.999973i	$0.502345\pi$
$338$	12.6180	0.686331
$339$	8.32624	0.452219
$340$	−11.4721	−0.622164
$341$	−41.8885	−2.26839
$342$	0	0
$343$	0	0
$344$	1.52786	0.0823769
$345$	6.47214	0.348448
$346$	11.3262	0.608902
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	−2.14590	−0.115032
$349$	27.0902	1.45010	0.725052	−	0.688694i	$-0.241816\pi$
$349$	27.0902	1.45010	0.725052	+	0.688694i	$0.241816\pi$
$350$	0	0
$351$	−0.618034	−0.0329882
$352$	4.00000	0.213201
$353$	−3.38197	−0.180004	−0.0900019	−	0.995942i	$-0.528687\pi$
$353$	−3.38197	−0.180004	−0.0900019	+	0.995942i	$0.528687\pi$
$354$	6.47214	0.343990
$355$	4.00000	0.212298
$356$	−10.3820	−0.550243
$357$	0	0
$358$	−8.00000	−0.422813
$359$	−20.3607	−1.07460	−0.537298	−	0.843393i	$-0.680555\pi$
$359$	−20.3607	−1.07460	−0.537298	+	0.843393i	$0.680555\pi$
$360$	1.61803	0.0852779
$361$	0	0
$362$	6.00000	0.315353
$363$	5.00000	0.262432
$364$	0	0
$365$	21.0902	1.10391
$366$	7.38197	0.385862
$367$	12.0000	0.626395	0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000	0.626395	0.313197	+	0.949688i	$0.398600\pi$
$368$	−4.00000	−0.208514
$369$	−0.854102	−0.0444628
$370$	−1.38197	−0.0718450
$371$	0	0
$372$	10.4721	0.542955
$373$	−1.20163	−0.0622178	−0.0311089	−	0.999516i	$-0.509904\pi$
$373$	−1.20163	−0.0622178	−0.0311089	+	0.999516i	$0.509904\pi$
$374$	28.3607	1.46650
$375$	11.9443	0.616800
$376$	12.9443	0.667550
$377$	1.32624	0.0683047
$378$	0	0
$379$	−7.41641	−0.380955	−0.190478	−	0.981692i	$-0.561004\pi$
$379$	−7.41641	−0.380955	−0.190478	+	0.981692i	$0.561004\pi$
$380$	0	0
$381$	−11.4164	−0.584880
$382$	−7.41641	−0.379456
$383$	−28.3607	−1.44916	−0.724582	−	0.689189i	$-0.757967\pi$
$383$	−28.3607	−1.44916	−0.724582	+	0.689189i	$0.757967\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−23.8885	−1.21589
$387$	−1.52786	−0.0776657
$388$	14.7984	0.751274
$389$	2.14590	0.108801	0.0544007	−	0.998519i	$-0.482675\pi$
$389$	2.14590	0.108801	0.0544007	+	0.998519i	$0.482675\pi$
$390$	−1.00000	−0.0506370
$391$	−28.3607	−1.43426
$392$	7.00000	0.353553
$393$	15.4164	0.777655
$394$	21.2705	1.07159
$395$	−6.47214	−0.325649
$396$	−4.00000	−0.201008
$397$	−27.8885	−1.39969	−0.699843	−	0.714297i	$-0.746747\pi$
$397$	−27.8885	−1.39969	−0.699843	+	0.714297i	$0.746747\pi$
$398$	−7.41641	−0.371751
$399$	0	0
$400$	−2.38197	−0.119098
$401$	14.0000	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$402$	−15.4164	−0.768901
$403$	−6.47214	−0.322400
$404$	−16.0902	−0.800516
$405$	−1.61803	−0.0804008
$406$	0	0
$407$	3.41641	0.169345
$408$	−7.09017	−0.351016
$409$	−11.3262	−0.560046	−0.280023	−	0.959993i	$-0.590342\pi$
$409$	−11.3262	−0.560046	−0.280023	+	0.959993i	$0.590342\pi$
$410$	−1.38197	−0.0682504
$411$	−12.0902	−0.596364
$412$	−11.4164	−0.562446
$413$	0	0
$414$	4.00000	0.196589
$415$	12.9443	0.635409
$416$	0.618034	0.0303016
$417$	3.05573	0.149640
$418$	0	0
$419$	2.47214	0.120772	0.0603859	−	0.998175i	$-0.480767\pi$
$419$	2.47214	0.120772	0.0603859	+	0.998175i	$0.480767\pi$
$420$	0	0
$421$	−13.4377	−0.654913	−0.327457	−	0.944866i	$-0.606192\pi$
$421$	−13.4377	−0.654913	−0.327457	+	0.944866i	$0.606192\pi$
$422$	15.4164	0.750459
$423$	−12.9443	−0.629372
$424$	6.38197	0.309936
$425$	−16.8885	−0.819215
$426$	2.47214	0.119775
$427$	0	0
$428$	−4.94427	−0.238990
$429$	2.47214	0.119356
$430$	−2.47214	−0.119217
$431$	27.4164	1.32060	0.660301	−	0.751001i	$-0.270429\pi$
$431$	27.4164	1.32060	0.660301	+	0.751001i	$0.270429\pi$
$432$	1.00000	0.0481125
$433$	32.0902	1.54216	0.771078	−	0.636741i	$-0.219718\pi$
$433$	32.0902	1.54216	0.771078	+	0.636741i	$0.219718\pi$
$434$	0	0
$435$	3.47214	0.166476
$436$	−13.7984	−0.660822
$437$	0	0
$438$	13.0344	0.622810
$439$	27.4164	1.30851	0.654257	−	0.756272i	$-0.272982\pi$
$439$	27.4164	1.30851	0.654257	+	0.756272i	$0.272982\pi$
$440$	−6.47214	−0.308547
$441$	−7.00000	−0.333333
$442$	4.38197	0.208429
$443$	34.4721	1.63782	0.818910	−	0.573922i	$-0.194579\pi$
$443$	34.4721	1.63782	0.818910	+	0.573922i	$0.194579\pi$
$444$	−0.854102	−0.0405339
$445$	16.7984	0.796319
$446$	−2.47214	−0.117059
$447$	7.09017	0.335354
$448$	0	0
$449$	10.7984	0.509607	0.254803	−	0.966993i	$-0.417989\pi$
$449$	10.7984	0.509607	0.254803	+	0.966993i	$0.417989\pi$
$450$	2.38197	0.112287
$451$	3.41641	0.160872
$452$	8.32624	0.391633
$453$	14.4721	0.679960
$454$	−0.944272	−0.0443169
$455$	0	0
$456$	0	0
$457$	11.3262	0.529819	0.264910	−	0.964273i	$-0.414658\pi$
$457$	11.3262	0.529819	0.264910	+	0.964273i	$0.414658\pi$
$458$	2.56231	0.119729
$459$	7.09017	0.330941
$460$	6.47214	0.301765
$461$	4.11146	0.191490	0.0957448	−	0.995406i	$-0.469477\pi$
$461$	4.11146	0.191490	0.0957448	+	0.995406i	$0.469477\pi$
$462$	0	0
$463$	33.3050	1.54781	0.773906	−	0.633300i	$-0.218300\pi$
$463$	33.3050	1.54781	0.773906	+	0.633300i	$0.218300\pi$
$464$	−2.14590	−0.0996208
$465$	−16.9443	−0.785772
$466$	−18.1459	−0.840592
$467$	25.5279	1.18129	0.590644	−	0.806932i	$-0.298874\pi$
$467$	25.5279	1.18129	0.590644	+	0.806932i	$0.298874\pi$
$468$	−0.618034	−0.0285686
$469$	0	0
$470$	−20.9443	−0.966087
$471$	18.5066	0.852738
$472$	6.47214	0.297904
$473$	6.11146	0.281005
$474$	−4.00000	−0.183726
$475$	0	0
$476$	0	0
$477$	−6.38197	−0.292210
$478$	11.4164	0.522174
$479$	12.9443	0.591439	0.295719	−	0.955275i	$-0.404441\pi$
$479$	12.9443	0.591439	0.295719	+	0.955275i	$0.404441\pi$
$480$	1.61803	0.0738528
$481$	0.527864	0.0240685
$482$	27.8885	1.27029
$483$	0	0
$484$	5.00000	0.227273
$485$	−23.9443	−1.08725
$486$	−1.00000	−0.0453609
$487$	21.5279	0.975521	0.487760	−	0.872978i	$-0.337814\pi$
$487$	21.5279	0.975521	0.487760	+	0.872978i	$0.337814\pi$
$488$	7.38197	0.334166
$489$	−23.4164	−1.05893
$490$	−11.3262	−0.511667
$491$	32.3607	1.46042	0.730209	−	0.683224i	$-0.239423\pi$
$491$	32.3607	1.46042	0.730209	+	0.683224i	$0.239423\pi$
$492$	−0.854102	−0.0385059
$493$	−15.2148	−0.685239
$494$	0	0
$495$	6.47214	0.290901
$496$	10.4721	0.470213
$497$	0	0
$498$	8.00000	0.358489
$499$	−8.94427	−0.400401	−0.200200	−	0.979755i	$-0.564159\pi$
$499$	−8.94427	−0.400401	−0.200200	+	0.979755i	$0.564159\pi$
$500$	11.9443	0.534164
$501$	3.41641	0.152634
$502$	2.47214	0.110337
$503$	7.05573	0.314599	0.157300	−	0.987551i	$-0.449721\pi$
$503$	7.05573	0.314599	0.157300	+	0.987551i	$0.449721\pi$
$504$	0	0
$505$	26.0344	1.15852
$506$	−16.0000	−0.711287
$507$	−12.6180	−0.560387
$508$	−11.4164	−0.506521
$509$	−16.9787	−0.752568	−0.376284	−	0.926504i	$-0.622798\pi$
$509$	−16.9787	−0.752568	−0.376284	+	0.926504i	$0.622798\pi$
$510$	11.4721	0.507995
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	3.90983	0.172455
$515$	18.4721	0.813980
$516$	−1.52786	−0.0672605
$517$	51.7771	2.27715
$518$	0	0
$519$	−11.3262	−0.497167
$520$	−1.00000	−0.0438529
$521$	24.3262	1.06575	0.532876	−	0.846193i	$-0.321111\pi$
$521$	24.3262	1.06575	0.532876	+	0.846193i	$0.321111\pi$
$522$	2.14590	0.0939234
$523$	9.52786	0.416624	0.208312	−	0.978062i	$-0.433203\pi$
$523$	9.52786	0.416624	0.208312	+	0.978062i	$0.433203\pi$
$524$	15.4164	0.673469
$525$	0	0
$526$	−22.4721	−0.979832
$527$	74.2492	3.23435
$528$	−4.00000	−0.174078
$529$	−7.00000	−0.304348
$530$	−10.3262	−0.448543
$531$	−6.47214	−0.280867
$532$	0	0
$533$	0.527864	0.0228643
$534$	10.3820	0.449272
$535$	8.00000	0.345870
$536$	−15.4164	−0.665887
$537$	8.00000	0.345225
$538$	−13.2705	−0.572132
$539$	28.0000	1.20605
$540$	−1.61803	−0.0696291
$541$	−17.8541	−0.767608	−0.383804	−	0.923415i	$-0.625386\pi$
$541$	−17.8541	−0.767608	−0.383804	+	0.923415i	$0.625386\pi$
$542$	8.00000	0.343629
$543$	−6.00000	−0.257485
$544$	−7.09017	−0.303989
$545$	22.3262	0.956351
$546$	0	0
$547$	39.4164	1.68532	0.842662	−	0.538443i	$-0.180987\pi$
$547$	39.4164	1.68532	0.842662	+	0.538443i	$0.180987\pi$
$548$	−12.0902	−0.516466
$549$	−7.38197	−0.315055
$550$	−9.52786	−0.406269
$551$	0	0
$552$	4.00000	0.170251
$553$	0	0
$554$	4.09017	0.173775
$555$	1.38197	0.0586612
$556$	3.05573	0.129592
$557$	−8.11146	−0.343693	−0.171847	−	0.985124i	$-0.554973\pi$
$557$	−8.11146	−0.343693	−0.171847	+	0.985124i	$0.554973\pi$
$558$	−10.4721	−0.443321
$559$	0.944272	0.0399384
$560$	0	0
$561$	−28.3607	−1.19739
$562$	−23.7426	−1.00152
$563$	−5.88854	−0.248173	−0.124086	−	0.992271i	$-0.539600\pi$
$563$	−5.88854	−0.248173	−0.124086	+	0.992271i	$0.539600\pi$
$564$	−12.9443	−0.545052
$565$	−13.4721	−0.566777
$566$	−0.944272	−0.0396907
$567$	0	0
$568$	2.47214	0.103729
$569$	−21.7984	−0.913835	−0.456918	−	0.889509i	$-0.651047\pi$
$569$	−21.7984	−0.913835	−0.456918	+	0.889509i	$0.651047\pi$
$570$	0	0
$571$	−8.94427	−0.374306	−0.187153	−	0.982331i	$-0.559926\pi$
$571$	−8.94427	−0.374306	−0.187153	+	0.982331i	$0.559926\pi$
$572$	2.47214	0.103365
$573$	7.41641	0.309825
$574$	0	0
$575$	9.52786	0.397339
$576$	1.00000	0.0416667
$577$	11.6738	0.485985	0.242993	−	0.970028i	$-0.421871\pi$
$577$	11.6738	0.485985	0.242993	+	0.970028i	$0.421871\pi$
$578$	−33.2705	−1.38387
$579$	23.8885	0.992774
$580$	3.47214	0.144173
$581$	0	0
$582$	−14.7984	−0.613412
$583$	25.5279	1.05726
$584$	13.0344	0.539369
$585$	1.00000	0.0413449
$586$	22.0000	0.908812
$587$	32.0000	1.32078	0.660391	−	0.750922i	$-0.270391\pi$
$587$	32.0000	1.32078	0.660391	+	0.750922i	$0.270391\pi$
$588$	−7.00000	−0.288675
$589$	0	0
$590$	−10.4721	−0.431131
$591$	−21.2705	−0.874952
$592$	−0.854102	−0.0351034
$593$	13.7984	0.566631	0.283316	−	0.959027i	$-0.408566\pi$
$593$	13.7984	0.566631	0.283316	+	0.959027i	$0.408566\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	7.09017	0.290425
$597$	7.41641	0.303533
$598$	−2.47214	−0.101093
$599$	16.5836	0.677587	0.338794	−	0.940861i	$-0.389981\pi$
$599$	16.5836	0.677587	0.338794	+	0.940861i	$0.389981\pi$
$600$	2.38197	0.0972434
$601$	−45.7771	−1.86729	−0.933643	−	0.358204i	$-0.883389\pi$
$601$	−45.7771	−1.86729	−0.933643	+	0.358204i	$0.883389\pi$
$602$	0	0
$603$	15.4164	0.627805
$604$	14.4721	0.588863
$605$	−8.09017	−0.328912
$606$	16.0902	0.653618
$607$	27.4164	1.11280	0.556399	−	0.830915i	$-0.312183\pi$
$607$	27.4164	1.11280	0.556399	+	0.830915i	$0.312183\pi$
$608$	0	0
$609$	0	0
$610$	−11.9443	−0.483609
$611$	8.00000	0.323645
$612$	7.09017	0.286603
$613$	−23.5066	−0.949422	−0.474711	−	0.880142i	$-0.657447\pi$
$613$	−23.5066	−0.949422	−0.474711	+	0.880142i	$0.657447\pi$
$614$	22.4721	0.906902
$615$	1.38197	0.0557262
$616$	0	0
$617$	19.8885	0.800683	0.400341	−	0.916366i	$-0.368892\pi$
$617$	19.8885	0.800683	0.400341	+	0.916366i	$0.368892\pi$
$618$	11.4164	0.459235
$619$	7.41641	0.298091	0.149045	−	0.988830i	$-0.452380\pi$
$619$	7.41641	0.298091	0.149045	+	0.988830i	$0.452380\pi$
$620$	−16.9443	−0.680498
$621$	−4.00000	−0.160514
$622$	21.5279	0.863189
$623$	0	0
$624$	−0.618034	−0.0247412
$625$	−7.41641	−0.296656
$626$	−3.32624	−0.132943
$627$	0	0
$628$	18.5066	0.738493
$629$	−6.05573	−0.241458
$630$	0	0
$631$	−32.3607	−1.28826	−0.644129	−	0.764917i	$-0.722780\pi$
$631$	−32.3607	−1.28826	−0.644129	+	0.764917i	$0.722780\pi$
$632$	−4.00000	−0.159111
$633$	−15.4164	−0.612747
$634$	29.2148	1.16027
$635$	18.4721	0.733044
$636$	−6.38197	−0.253061
$637$	4.32624	0.171412
$638$	−8.58359	−0.339828
$639$	−2.47214	−0.0977962
$640$	1.61803	0.0639584
$641$	26.7984	1.05847	0.529236	−	0.848475i	$-0.322479\pi$
$641$	26.7984	1.05847	0.529236	+	0.848475i	$0.322479\pi$
$642$	4.94427	0.195135
$643$	−4.94427	−0.194983	−0.0974915	−	0.995236i	$-0.531082\pi$
$643$	−4.94427	−0.194983	−0.0974915	+	0.995236i	$0.531082\pi$
$644$	0	0
$645$	2.47214	0.0973403
$646$	0	0
$647$	24.9443	0.980661	0.490330	−	0.871537i	$-0.336876\pi$
$647$	24.9443	0.980661	0.490330	+	0.871537i	$0.336876\pi$
$648$	−1.00000	−0.0392837
$649$	25.8885	1.01621
$650$	−1.47214	−0.0577419
$651$	0	0
$652$	−23.4164	−0.917057
$653$	14.3820	0.562810	0.281405	−	0.959589i	$-0.409200\pi$
$653$	14.3820	0.562810	0.281405	+	0.959589i	$0.409200\pi$
$654$	13.7984	0.539559
$655$	−24.9443	−0.974653
$656$	−0.854102	−0.0333471
$657$	−13.0344	−0.508522
$658$	0	0
$659$	27.4164	1.06799	0.533996	−	0.845487i	$-0.320690\pi$
$659$	27.4164	1.06799	0.533996	+	0.845487i	$0.320690\pi$
$660$	6.47214	0.251928
$661$	−22.0000	−0.855701	−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000	−0.855701	−0.427850	+	0.903850i	$0.640729\pi$
$662$	−1.88854	−0.0734003
$663$	−4.38197	−0.170181
$664$	8.00000	0.310460
$665$	0	0
$666$	0.854102	0.0330958
$667$	8.58359	0.332358
$668$	3.41641	0.132185
$669$	2.47214	0.0955783
$670$	24.9443	0.963681
$671$	29.5279	1.13991
$672$	0	0
$673$	3.14590	0.121265	0.0606327	−	0.998160i	$-0.480688\pi$
$673$	3.14590	0.121265	0.0606327	+	0.998160i	$0.480688\pi$
$674$	0.270510	0.0104196
$675$	−2.38197	−0.0916819
$676$	−12.6180	−0.485309
$677$	34.2148	1.31498	0.657490	−	0.753463i	$-0.271618\pi$
$677$	34.2148	1.31498	0.657490	+	0.753463i	$0.271618\pi$
$678$	−8.32624	−0.319767
$679$	0	0
$680$	11.4721	0.439936
$681$	0.944272	0.0361846
$682$	41.8885	1.60400
$683$	1.52786	0.0584621	0.0292310	−	0.999573i	$-0.490694\pi$
$683$	1.52786	0.0584621	0.0292310	+	0.999573i	$0.490694\pi$
$684$	0	0
$685$	19.5623	0.747437
$686$	0	0
$687$	−2.56231	−0.0977581
$688$	−1.52786	−0.0582493
$689$	3.94427	0.150265
$690$	−6.47214	−0.246390
$691$	−30.4721	−1.15921	−0.579607	−	0.814896i	$-0.696794\pi$
$691$	−30.4721	−1.15921	−0.579607	+	0.814896i	$0.696794\pi$
$692$	−11.3262	−0.430559
$693$	0	0
$694$	0	0
$695$	−4.94427	−0.187547
$696$	2.14590	0.0813401
$697$	−6.05573	−0.229377
$698$	−27.0902	−1.02538
$699$	18.1459	0.686341
$700$	0	0
$701$	−29.0344	−1.09662	−0.548308	−	0.836277i	$-0.684728\pi$
$701$	−29.0344	−1.09662	−0.548308	+	0.836277i	$0.684728\pi$
$702$	0.618034	0.0233262
$703$	0	0
$704$	−4.00000	−0.150756
$705$	20.9443	0.788807
$706$	3.38197	0.127282
$707$	0	0
$708$	−6.47214	−0.243238
$709$	−28.9098	−1.08573	−0.542866	−	0.839820i	$-0.682661\pi$
$709$	−28.9098	−1.08573	−0.542866	+	0.839820i	$0.682661\pi$
$710$	−4.00000	−0.150117
$711$	4.00000	0.150012
$712$	10.3820	0.389081
$713$	−41.8885	−1.56874
$714$	0	0
$715$	−4.00000	−0.149592
$716$	8.00000	0.298974
$717$	−11.4164	−0.426354
$718$	20.3607	0.759854
$719$	−26.4721	−0.987244	−0.493622	−	0.869677i	$-0.664327\pi$
$719$	−26.4721	−0.987244	−0.493622	+	0.869677i	$0.664327\pi$
$720$	−1.61803	−0.0603006
$721$	0	0
$722$	0	0
$723$	−27.8885	−1.03719
$724$	−6.00000	−0.222988
$725$	5.11146	0.189835
$726$	−5.00000	−0.185567
$727$	18.8328	0.698470	0.349235	−	0.937035i	$-0.386441\pi$
$727$	18.8328	0.698470	0.349235	+	0.937035i	$0.386441\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−21.0902	−0.780582
$731$	−10.8328	−0.400666
$732$	−7.38197	−0.272845
$733$	−4.32624	−0.159793	−0.0798966	−	0.996803i	$-0.525459\pi$
$733$	−4.32624	−0.159793	−0.0798966	+	0.996803i	$0.525459\pi$
$734$	−12.0000	−0.442928
$735$	11.3262	0.417775
$736$	4.00000	0.147442
$737$	−61.6656	−2.27148
$738$	0.854102	0.0314399
$739$	−37.8885	−1.39375	−0.696876	−	0.717191i	$-0.745427\pi$
$739$	−37.8885	−1.39375	−0.696876	+	0.717191i	$0.745427\pi$
$740$	1.38197	0.0508021
$741$	0	0
$742$	0	0
$743$	19.0557	0.699087	0.349543	−	0.936920i	$-0.386337\pi$
$743$	19.0557	0.699087	0.349543	+	0.936920i	$0.386337\pi$
$744$	−10.4721	−0.383927
$745$	−11.4721	−0.420307
$746$	1.20163	0.0439947
$747$	−8.00000	−0.292705
$748$	−28.3607	−1.03697
$749$	0	0
$750$	−11.9443	−0.436143
$751$	−30.8328	−1.12511	−0.562553	−	0.826761i	$-0.690181\pi$
$751$	−30.8328	−1.12511	−0.562553	+	0.826761i	$0.690181\pi$
$752$	−12.9443	−0.472029
$753$	−2.47214	−0.0900896
$754$	−1.32624	−0.0482987
$755$	−23.4164	−0.852210
$756$	0	0
$757$	41.3394	1.50251	0.751253	−	0.660014i	$-0.229450\pi$
$757$	41.3394	1.50251	0.751253	+	0.660014i	$0.229450\pi$
$758$	7.41641	0.269376
$759$	16.0000	0.580763
$760$	0	0
$761$	−12.1115	−0.439040	−0.219520	−	0.975608i	$-0.570449\pi$
$761$	−12.1115	−0.439040	−0.219520	+	0.975608i	$0.570449\pi$
$762$	11.4164	0.413573
$763$	0	0
$764$	7.41641	0.268316
$765$	−11.4721	−0.414776
$766$	28.3607	1.02471
$767$	4.00000	0.144432
$768$	1.00000	0.0360844
$769$	32.6312	1.17671	0.588355	−	0.808602i	$-0.299776\pi$
$769$	32.6312	1.17671	0.588355	+	0.808602i	$0.299776\pi$
$770$	0	0
$771$	−3.90983	−0.140809
$772$	23.8885	0.859768
$773$	−52.0344	−1.87155	−0.935774	−	0.352599i	$-0.885298\pi$
$773$	−52.0344	−1.87155	−0.935774	+	0.352599i	$0.885298\pi$
$774$	1.52786	0.0549179
$775$	−24.9443	−0.896025
$776$	−14.7984	−0.531231
$777$	0	0
$778$	−2.14590	−0.0769342
$779$	0	0
$780$	1.00000	0.0358057
$781$	9.88854	0.353840
$782$	28.3607	1.01418
$783$	−2.14590	−0.0766881
$784$	−7.00000	−0.250000
$785$	−29.9443	−1.06876
$786$	−15.4164	−0.549885
$787$	43.4164	1.54763	0.773814	−	0.633413i	$-0.218347\pi$
$787$	43.4164	1.54763	0.773814	+	0.633413i	$0.218347\pi$
$788$	−21.2705	−0.757731
$789$	22.4721	0.800029
$790$	6.47214	0.230268
$791$	0	0
$792$	4.00000	0.142134
$793$	4.56231	0.162012
$794$	27.8885	0.989727
$795$	10.3262	0.366234
$796$	7.41641	0.262868
$797$	−21.2016	−0.751000	−0.375500	−	0.926822i	$-0.622529\pi$
$797$	−21.2016	−0.751000	−0.375500	+	0.926822i	$0.622529\pi$
$798$	0	0
$799$	−91.7771	−3.24684
$800$	2.38197	0.0842152
$801$	−10.3820	−0.366829
$802$	−14.0000	−0.494357
$803$	52.1378	1.83990
$804$	15.4164	0.543695
$805$	0	0
$806$	6.47214	0.227971
$807$	13.2705	0.467144
$808$	16.0902	0.566050
$809$	47.6869	1.67658	0.838291	−	0.545223i	$-0.183555\pi$
$809$	47.6869	1.67658	0.838291	+	0.545223i	$0.183555\pi$
$810$	1.61803	0.0568519
$811$	20.3607	0.714960	0.357480	−	0.933921i	$-0.383636\pi$
$811$	20.3607	0.714960	0.357480	+	0.933921i	$0.383636\pi$
$812$	0	0
$813$	−8.00000	−0.280572
$814$	−3.41641	−0.119745
$815$	37.8885	1.32718
$816$	7.09017	0.248206
$817$	0	0
$818$	11.3262	0.396013
$819$	0	0
$820$	1.38197	0.0482603
$821$	−5.85410	−0.204310	−0.102155	−	0.994769i	$-0.532574\pi$
$821$	−5.85410	−0.204310	−0.102155	+	0.994769i	$0.532574\pi$
$822$	12.0902	0.421693
$823$	−3.05573	−0.106516	−0.0532580	−	0.998581i	$-0.516961\pi$
$823$	−3.05573	−0.106516	−0.0532580	+	0.998581i	$0.516961\pi$
$824$	11.4164	0.397709
$825$	9.52786	0.331718
$826$	0	0
$827$	14.8328	0.515788	0.257894	−	0.966173i	$-0.416972\pi$
$827$	14.8328	0.515788	0.257894	+	0.966173i	$0.416972\pi$
$828$	−4.00000	−0.139010
$829$	39.5066	1.37212	0.686060	−	0.727545i	$-0.259339\pi$
$829$	39.5066	1.37212	0.686060	+	0.727545i	$0.259339\pi$
$830$	−12.9443	−0.449302
$831$	−4.09017	−0.141886
$832$	−0.618034	−0.0214265
$833$	−49.6312	−1.71962
$834$	−3.05573	−0.105811
$835$	−5.52786	−0.191300
$836$	0	0
$837$	10.4721	0.361970
$838$	−2.47214	−0.0853985
$839$	−30.8328	−1.06447	−0.532234	−	0.846598i	$-0.678647\pi$
$839$	−30.8328	−1.06447	−0.532234	+	0.846598i	$0.678647\pi$
$840$	0	0
$841$	−24.3951	−0.841211
$842$	13.4377	0.463094
$843$	23.7426	0.817740
$844$	−15.4164	−0.530655
$845$	20.4164	0.702346
$846$	12.9443	0.445033
$847$	0	0
$848$	−6.38197	−0.219158
$849$	0.944272	0.0324073
$850$	16.8885	0.579272
$851$	3.41641	0.117113
$852$	−2.47214	−0.0846940
$853$	−33.2705	−1.13916	−0.569580	−	0.821936i	$-0.692894\pi$
$853$	−33.2705	−1.13916	−0.569580	+	0.821936i	$0.692894\pi$
$854$	0	0
$855$	0	0
$856$	4.94427	0.168992
$857$	−9.56231	−0.326642	−0.163321	−	0.986573i	$-0.552221\pi$
$857$	−9.56231	−0.326642	−0.163321	+	0.986573i	$0.552221\pi$
$858$	−2.47214	−0.0843973
$859$	−47.1935	−1.61022	−0.805111	−	0.593125i	$-0.797894\pi$
$859$	−47.1935	−1.61022	−0.805111	+	0.593125i	$0.797894\pi$
$860$	2.47214	0.0842991
$861$	0	0
$862$	−27.4164	−0.933807
$863$	−19.4164	−0.660942	−0.330471	−	0.943816i	$-0.607208\pi$
$863$	−19.4164	−0.660942	−0.330471	+	0.943816i	$0.607208\pi$
$864$	−1.00000	−0.0340207
$865$	18.3262	0.623111
$866$	−32.0902	−1.09047
$867$	33.2705	1.12993
$868$	0	0
$869$	−16.0000	−0.542763
$870$	−3.47214	−0.117716
$871$	−9.52786	−0.322839
$872$	13.7984	0.467272
$873$	14.7984	0.500849
$874$	0	0
$875$	0	0
$876$	−13.0344	−0.440393
$877$	−4.97871	−0.168119	−0.0840596	−	0.996461i	$-0.526789\pi$
$877$	−4.97871	−0.168119	−0.0840596	+	0.996461i	$0.526789\pi$
$878$	−27.4164	−0.925259
$879$	−22.0000	−0.742042
$880$	6.47214	0.218176
$881$	−44.8115	−1.50974	−0.754869	−	0.655875i	$-0.772300\pi$
$881$	−44.8115	−1.50974	−0.754869	+	0.655875i	$0.772300\pi$
$882$	7.00000	0.235702
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	−4.38197	−0.147381
$885$	10.4721	0.352017
$886$	−34.4721	−1.15811
$887$	−5.88854	−0.197718	−0.0988590	−	0.995101i	$-0.531519\pi$
$887$	−5.88854	−0.197718	−0.0988590	+	0.995101i	$0.531519\pi$
$888$	0.854102	0.0286618
$889$	0	0
$890$	−16.7984	−0.563083
$891$	−4.00000	−0.134005
$892$	2.47214	0.0827732
$893$	0	0
$894$	−7.09017	−0.237131
$895$	−12.9443	−0.432679
$896$	0	0
$897$	2.47214	0.0825422
$898$	−10.7984	−0.360346
$899$	−22.4721	−0.749488
$900$	−2.38197	−0.0793989
$901$	−45.2492	−1.50747
$902$	−3.41641	−0.113754
$903$	0	0
$904$	−8.32624	−0.276927
$905$	9.70820	0.322712
$906$	−14.4721	−0.480805
$907$	27.0557	0.898371	0.449185	−	0.893439i	$-0.351714\pi$
$907$	27.0557	0.898371	0.449185	+	0.893439i	$0.351714\pi$
$908$	0.944272	0.0313368
$909$	−16.0902	−0.533677
$910$	0	0
$911$	28.3607	0.939631	0.469816	−	0.882765i	$-0.344320\pi$
$911$	28.3607	0.939631	0.469816	+	0.882765i	$0.344320\pi$
$912$	0	0
$913$	32.0000	1.05905
$914$	−11.3262	−0.374639
$915$	11.9443	0.394865
$916$	−2.56231	−0.0846610
$917$	0	0
$918$	−7.09017	−0.234010
$919$	−32.0000	−1.05558	−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000	−1.05558	−0.527791	+	0.849374i	$0.676980\pi$
$920$	−6.47214	−0.213380
$921$	−22.4721	−0.740482
$922$	−4.11146	−0.135404
$923$	1.52786	0.0502903
$924$	0	0
$925$	2.03444	0.0668920
$926$	−33.3050	−1.09447
$927$	−11.4164	−0.374964
$928$	2.14590	0.0704426
$929$	−37.8541	−1.24195	−0.620976	−	0.783829i	$-0.713264\pi$
$929$	−37.8541	−1.24195	−0.620976	+	0.783829i	$0.713264\pi$
$930$	16.9443	0.555625
$931$	0	0
$932$	18.1459	0.594389
$933$	−21.5279	−0.704791
$934$	−25.5279	−0.835297
$935$	45.8885	1.50072
$936$	0.618034	0.0202011
$937$	−31.8885	−1.04175	−0.520877	−	0.853632i	$-0.674395\pi$
$937$	−31.8885	−1.04175	−0.520877	+	0.853632i	$0.674395\pi$
$938$	0	0
$939$	3.32624	0.108548
$940$	20.9443	0.683127
$941$	53.7771	1.75308	0.876541	−	0.481326i	$-0.159845\pi$
$941$	53.7771	1.75308	0.876541	+	0.481326i	$0.159845\pi$
$942$	−18.5066	−0.602977
$943$	3.41641	0.111254
$944$	−6.47214	−0.210650
$945$	0	0
$946$	−6.11146	−0.198701
$947$	−14.8328	−0.482002	−0.241001	−	0.970525i	$-0.577476\pi$
$947$	−14.8328	−0.482002	−0.241001	+	0.970525i	$0.577476\pi$
$948$	4.00000	0.129914
$949$	8.05573	0.261500
$950$	0	0
$951$	−29.2148	−0.947354
$952$	0	0
$953$	39.1591	1.26849	0.634243	−	0.773134i	$-0.281312\pi$
$953$	39.1591	1.26849	0.634243	+	0.773134i	$0.281312\pi$
$954$	6.38197	0.206624
$955$	−12.0000	−0.388311
$956$	−11.4164	−0.369233
$957$	8.58359	0.277468
$958$	−12.9443	−0.418210
$959$	0	0
$960$	−1.61803	−0.0522218
$961$	78.6656	2.53760
$962$	−0.527864	−0.0170190
$963$	−4.94427	−0.159327
$964$	−27.8885	−0.898230
$965$	−38.6525	−1.24427
$966$	0	0
$967$	43.7771	1.40778	0.703888	−	0.710311i	$-0.251446\pi$
$967$	43.7771	1.40778	0.703888	+	0.710311i	$0.251446\pi$
$968$	−5.00000	−0.160706
$969$	0	0
$970$	23.9443	0.768804
$971$	−28.5836	−0.917291	−0.458646	−	0.888619i	$-0.651665\pi$
$971$	−28.5836	−0.917291	−0.458646	+	0.888619i	$0.651665\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−21.5279	−0.689797
$975$	1.47214	0.0471461
$976$	−7.38197	−0.236291
$977$	0.673762	0.0215556	0.0107778	−	0.999942i	$-0.496569\pi$
$977$	0.673762	0.0215556	0.0107778	+	0.999942i	$0.496569\pi$
$978$	23.4164	0.748774
$979$	41.5279	1.32724
$980$	11.3262	0.361803
$981$	−13.7984	−0.440548
$982$	−32.3607	−1.03267
$983$	−33.8885	−1.08088	−0.540438	−	0.841384i	$-0.681742\pi$
$983$	−33.8885	−1.08088	−0.540438	+	0.841384i	$0.681742\pi$
$984$	0.854102	0.0272278
$985$	34.4164	1.09660
$986$	15.2148	0.484537
$987$	0	0
$988$	0	0
$989$	6.11146	0.194333
$990$	−6.47214	−0.205698
$991$	−10.8328	−0.344116	−0.172058	−	0.985087i	$-0.555042\pi$
$991$	−10.8328	−0.344116	−0.172058	+	0.985087i	$0.555042\pi$
$992$	−10.4721	−0.332491
$993$	1.88854	0.0599311
$994$	0	0
$995$	−12.0000	−0.380426
$996$	−8.00000	−0.253490
$997$	−30.3394	−0.960858	−0.480429	−	0.877034i	$-0.659519\pi$
$997$	−30.3394	−0.960858	−0.480429	+	0.877034i	$0.659519\pi$
$998$	8.94427	0.283126
$999$	−0.854102	−0.0270226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.2.a.k.1.1	✓	2
3.2	odd	2		6498.2.a.bj.1.2		2
19.18	odd	2		2166.2.a.l.1.1	yes	2
57.56	even	2		6498.2.a.bd.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2166.2.a.k.1.1	✓	2	1.1	even	1	trivial
2166.2.a.l.1.1	yes	2	19.18	odd	2
6498.2.a.bd.1.2		2	57.56	even	2
6498.2.a.bj.1.2		2	3.2	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:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.61803 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.61803 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.61803 q^{10} -4.00000 q^{11} +1.00000 q^{12} -0.618034 q^{13} -1.61803 q^{15} +1.00000 q^{16} +7.09017 q^{17} -1.00000 q^{18} -1.61803 q^{20} +4.00000 q^{22} -4.00000 q^{23} -1.00000 q^{24} -2.38197 q^{25} +0.618034 q^{26} +1.00000 q^{27} -2.14590 q^{29} +1.61803 q^{30} +10.4721 q^{31} -1.00000 q^{32} -4.00000 q^{33} -7.09017 q^{34} +1.00000 q^{36} -0.854102 q^{37} -0.618034 q^{39} +1.61803 q^{40} -0.854102 q^{41} -1.52786 q^{43} -4.00000 q^{44} -1.61803 q^{45} +4.00000 q^{46} -12.9443 q^{47} +1.00000 q^{48} -7.00000 q^{49} +2.38197 q^{50} +7.09017 q^{51} -0.618034 q^{52} -6.38197 q^{53} -1.00000 q^{54} +6.47214 q^{55} +2.14590 q^{58} -6.47214 q^{59} -1.61803 q^{60} -7.38197 q^{61} -10.4721 q^{62} +1.00000 q^{64} +1.00000 q^{65} +4.00000 q^{66} +15.4164 q^{67} +7.09017 q^{68} -4.00000 q^{69} -2.47214 q^{71} -1.00000 q^{72} -13.0344 q^{73} +0.854102 q^{74} -2.38197 q^{75} +0.618034 q^{78} +4.00000 q^{79} -1.61803 q^{80} +1.00000 q^{81} +0.854102 q^{82} -8.00000 q^{83} -11.4721 q^{85} +1.52786 q^{86} -2.14590 q^{87} +4.00000 q^{88} -10.3820 q^{89} +1.61803 q^{90} -4.00000 q^{92} +10.4721 q^{93} +12.9443 q^{94} -1.00000 q^{96} +14.7984 q^{97} +7.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} - 8 q^{11} + 2 q^{12} + q^{13} - q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - q^{20} + 8 q^{22} - 8 q^{23} - 2 q^{24} - 7 q^{25} - q^{26} + 2 q^{27} - 11 q^{29} + q^{30} + 12 q^{31} - 2 q^{32} - 8 q^{33} - 3 q^{34} + 2 q^{36} + 5 q^{37} + q^{39} + q^{40} + 5 q^{41} - 12 q^{43} - 8 q^{44} - q^{45} + 8 q^{46} - 8 q^{47} + 2 q^{48} - 14 q^{49} + 7 q^{50} + 3 q^{51} + q^{52} - 15 q^{53} - 2 q^{54} + 4 q^{55} + 11 q^{58} - 4 q^{59} - q^{60} - 17 q^{61} - 12 q^{62} + 2 q^{64} + 2 q^{65} + 8 q^{66} + 4 q^{67} + 3 q^{68} - 8 q^{69} + 4 q^{71} - 2 q^{72} + 3 q^{73} - 5 q^{74} - 7 q^{75} - q^{78} + 8 q^{79} - q^{80} + 2 q^{81} - 5 q^{82} - 16 q^{83} - 14 q^{85} + 12 q^{86} - 11 q^{87} + 8 q^{88} - 23 q^{89} + q^{90} - 8 q^{92} + 12 q^{93} + 8 q^{94} - 2 q^{96} + 5 q^{97} + 14 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 - 8 * q^11 + 2 * q^12 + q^13 - q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - q^20 + 8 * q^22 - 8 * q^23 - 2 * q^24 - 7 * q^25 - q^26 + 2 * q^27 - 11 * q^29 + q^30 + 12 * q^31 - 2 * q^32 - 8 * q^33 - 3 * q^34 + 2 * q^36 + 5 * q^37 + q^39 + q^40 + 5 * q^41 - 12 * q^43 - 8 * q^44 - q^45 + 8 * q^46 - 8 * q^47 + 2 * q^48 - 14 * q^49 + 7 * q^50 + 3 * q^51 + q^52 - 15 * q^53 - 2 * q^54 + 4 * q^55 + 11 * q^58 - 4 * q^59 - q^60 - 17 * q^61 - 12 * q^62 + 2 * q^64 + 2 * q^65 + 8 * q^66 + 4 * q^67 + 3 * q^68 - 8 * q^69 + 4 * q^71 - 2 * q^72 + 3 * q^73 - 5 * q^74 - 7 * q^75 - q^78 + 8 * q^79 - q^80 + 2 * q^81 - 5 * q^82 - 16 * q^83 - 14 * q^85 + 12 * q^86 - 11 * q^87 + 8 * q^88 - 23 * q^89 + q^90 - 8 * q^92 + 12 * q^93 + 8 * q^94 - 2 * q^96 + 5 * q^97 + 14 * q^98 - 8 * q^99

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