LMFDB - Embedded newform 2541.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -2.61803 q^{5} -1.61803 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -2.61803 q^{5} -1.61803 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +4.23607 q^{10} +0.618034 q^{12} +1.00000 q^{13} +1.61803 q^{14} -2.61803 q^{15} -4.85410 q^{16} -0.236068 q^{17} -1.61803 q^{18} -1.61803 q^{20} -1.00000 q^{21} +1.23607 q^{23} +2.23607 q^{24} +1.85410 q^{25} -1.61803 q^{26} +1.00000 q^{27} -0.618034 q^{28} +6.70820 q^{29} +4.23607 q^{30} -5.76393 q^{31} +3.38197 q^{32} +0.381966 q^{34} +2.61803 q^{35} +0.618034 q^{36} -10.9443 q^{37} +1.00000 q^{39} -5.85410 q^{40} +6.09017 q^{41} +1.61803 q^{42} +1.00000 q^{43} -2.61803 q^{45} -2.00000 q^{46} +8.32624 q^{47} -4.85410 q^{48} +1.00000 q^{49} -3.00000 q^{50} -0.236068 q^{51} +0.618034 q^{52} +5.38197 q^{53} -1.61803 q^{54} -2.23607 q^{56} -10.8541 q^{58} -10.8541 q^{59} -1.61803 q^{60} +10.2361 q^{61} +9.32624 q^{62} -1.00000 q^{63} +4.23607 q^{64} -2.61803 q^{65} -4.76393 q^{67} -0.145898 q^{68} +1.23607 q^{69} -4.23607 q^{70} +1.47214 q^{71} +2.23607 q^{72} +8.56231 q^{73} +17.7082 q^{74} +1.85410 q^{75} -1.61803 q^{78} -4.14590 q^{79} +12.7082 q^{80} +1.00000 q^{81} -9.85410 q^{82} +6.00000 q^{83} -0.618034 q^{84} +0.618034 q^{85} -1.61803 q^{86} +6.70820 q^{87} -8.61803 q^{89} +4.23607 q^{90} -1.00000 q^{91} +0.763932 q^{92} -5.76393 q^{93} -13.4721 q^{94} +3.38197 q^{96} -17.0000 q^{97} -1.61803 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} - q^{4} - 3 q^{5} - q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 - q^4 - 3 * q^5 - q^6 - 2 * q^7 + 2 * q^9	$ 2 q - q^{2} + 2 q^{3} - q^{4} - 3 q^{5} - q^{6} - 2 q^{7} + 2 q^{9} + 4 q^{10} - q^{12} + 2 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - q^{18} - q^{20} - 2 q^{21} - 2 q^{23} - 3 q^{25} - q^{26} + 2 q^{27} + q^{28} + 4 q^{30} - 16 q^{31} + 9 q^{32} + 3 q^{34} + 3 q^{35} - q^{36} - 4 q^{37} + 2 q^{39} - 5 q^{40} + q^{41} + q^{42} + 2 q^{43} - 3 q^{45} - 4 q^{46} + q^{47} - 3 q^{48} + 2 q^{49} - 6 q^{50} + 4 q^{51} - q^{52} + 13 q^{53} - q^{54} - 15 q^{58} - 15 q^{59} - q^{60} + 16 q^{61} + 3 q^{62} - 2 q^{63} + 4 q^{64} - 3 q^{65} - 14 q^{67} - 7 q^{68} - 2 q^{69} - 4 q^{70} - 6 q^{71} - 3 q^{73} + 22 q^{74} - 3 q^{75} - q^{78} - 15 q^{79} + 12 q^{80} + 2 q^{81} - 13 q^{82} + 12 q^{83} + q^{84} - q^{85} - q^{86} - 15 q^{89} + 4 q^{90} - 2 q^{91} + 6 q^{92} - 16 q^{93} - 18 q^{94} + 9 q^{96} - 34 q^{97} - q^{98}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 - q^4 - 3 * q^5 - q^6 - 2 * q^7 + 2 * q^9 + 4 * q^10 - q^12 + 2 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - q^18 - q^20 - 2 * q^21 - 2 * q^23 - 3 * q^25 - q^26 + 2 * q^27 + q^28 + 4 * q^30 - 16 * q^31 + 9 * q^32 + 3 * q^34 + 3 * q^35 - q^36 - 4 * q^37 + 2 * q^39 - 5 * q^40 + q^41 + q^42 + 2 * q^43 - 3 * q^45 - 4 * q^46 + q^47 - 3 * q^48 + 2 * q^49 - 6 * q^50 + 4 * q^51 - q^52 + 13 * q^53 - q^54 - 15 * q^58 - 15 * q^59 - q^60 + 16 * q^61 + 3 * q^62 - 2 * q^63 + 4 * q^64 - 3 * q^65 - 14 * q^67 - 7 * q^68 - 2 * q^69 - 4 * q^70 - 6 * q^71 - 3 * q^73 + 22 * q^74 - 3 * q^75 - q^78 - 15 * q^79 + 12 * q^80 + 2 * q^81 - 13 * q^82 + 12 * q^83 + q^84 - q^85 - q^86 - 15 * q^89 + 4 * q^90 - 2 * q^91 + 6 * q^92 - 16 * q^93 - 18 * q^94 + 9 * q^96 - 34 * q^97 - q^98

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 $

$2$	−1.61803	−1.14412	−0.572061	−	0.820211i	$-0.693856\pi$
$2$	−1.61803	−1.14412	−0.572061	+	0.820211i	$0.693856\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.618034	0.309017
$5$	−2.61803	−1.17082	−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803	−1.17082	−0.585410	+	0.810737i	$0.699067\pi$
$6$	−1.61803	−0.660560
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.23607	0.790569
$9$	1.00000	0.333333
$10$	4.23607	1.33956
$11$	0	0
$11$	0	0
$12$	0.618034	0.178411
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	1.61803	0.432438
$15$	−2.61803	−0.675973
$16$	−4.85410	−1.21353
$17$	−0.236068	−0.0572549	−0.0286274	−	0.999590i	$-0.509114\pi$
$17$	−0.236068	−0.0572549	−0.0286274	+	0.999590i	$0.509114\pi$
$18$	−1.61803	−0.381374
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−1.61803	−0.361803
$21$	−1.00000	−0.218218
$22$	0	0
$23$	1.23607	0.257738	0.128869	−	0.991662i	$-0.458865\pi$
$23$	1.23607	0.257738	0.128869	+	0.991662i	$0.458865\pi$
$24$	2.23607	0.456435
$25$	1.85410	0.370820
$26$	−1.61803	−0.317323
$27$	1.00000	0.192450
$28$	−0.618034	−0.116797
$29$	6.70820	1.24568	0.622841	−	0.782348i	$-0.285978\pi$
$29$	6.70820	1.24568	0.622841	+	0.782348i	$0.285978\pi$
$30$	4.23607	0.773397
$31$	−5.76393	−1.03523	−0.517616	−	0.855613i	$-0.673181\pi$
$31$	−5.76393	−1.03523	−0.517616	+	0.855613i	$0.673181\pi$
$32$	3.38197	0.597853
$33$	0	0
$34$	0.381966	0.0655066
$35$	2.61803	0.442529
$36$	0.618034	0.103006
$37$	−10.9443	−1.79923	−0.899614	−	0.436687i	$-0.856152\pi$
$37$	−10.9443	−1.79923	−0.899614	+	0.436687i	$0.856152\pi$
$38$	0	0
$39$	1.00000	0.160128
$40$	−5.85410	−0.925615
$41$	6.09017	0.951125	0.475562	−	0.879682i	$-0.342245\pi$
$41$	6.09017	0.951125	0.475562	+	0.879682i	$0.342245\pi$
$42$	1.61803	0.249668
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	0	0
$45$	−2.61803	−0.390273
$46$	−2.00000	−0.294884
$47$	8.32624	1.21451	0.607253	−	0.794508i	$-0.292271\pi$
$47$	8.32624	1.21451	0.607253	+	0.794508i	$0.292271\pi$
$48$	−4.85410	−0.700629
$49$	1.00000	0.142857
$50$	−3.00000	−0.424264
$51$	−0.236068	−0.0330561
$52$	0.618034	0.0857059
$53$	5.38197	0.739270	0.369635	−	0.929177i	$-0.379483\pi$
$53$	5.38197	0.739270	0.369635	+	0.929177i	$0.379483\pi$
$54$	−1.61803	−0.220187
$55$	0	0
$56$	−2.23607	−0.298807
$57$	0	0
$58$	−10.8541	−1.42521
$59$	−10.8541	−1.41308	−0.706542	−	0.707671i	$-0.749746\pi$
$59$	−10.8541	−1.41308	−0.706542	+	0.707671i	$0.749746\pi$
$60$	−1.61803	−0.208887
$61$	10.2361	1.31059	0.655297	−	0.755371i	$-0.272543\pi$
$61$	10.2361	1.31059	0.655297	+	0.755371i	$0.272543\pi$
$62$	9.32624	1.18443
$63$	−1.00000	−0.125988
$64$	4.23607	0.529508
$65$	−2.61803	−0.324727
$66$	0	0
$67$	−4.76393	−0.582007	−0.291003	−	0.956722i	$-0.593989\pi$
$67$	−4.76393	−0.582007	−0.291003	+	0.956722i	$0.593989\pi$
$68$	−0.145898	−0.0176927
$69$	1.23607	0.148805
$70$	−4.23607	−0.506307
$71$	1.47214	0.174710	0.0873552	−	0.996177i	$-0.472158\pi$
$71$	1.47214	0.174710	0.0873552	+	0.996177i	$0.472158\pi$
$72$	2.23607	0.263523
$73$	8.56231	1.00214	0.501071	−	0.865406i	$-0.332940\pi$
$73$	8.56231	1.00214	0.501071	+	0.865406i	$0.332940\pi$
$74$	17.7082	2.05854
$75$	1.85410	0.214093
$76$	0	0
$77$	0	0
$78$	−1.61803	−0.183206
$79$	−4.14590	−0.466450	−0.233225	−	0.972423i	$-0.574928\pi$
$79$	−4.14590	−0.466450	−0.233225	+	0.972423i	$0.574928\pi$
$80$	12.7082	1.42082
$81$	1.00000	0.111111
$82$	−9.85410	−1.08820
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	−0.618034	−0.0674330
$85$	0.618034	0.0670352
$86$	−1.61803	−0.174477
$87$	6.70820	0.719195
$88$	0	0
$89$	−8.61803	−0.913510	−0.456755	−	0.889593i	$-0.650988\pi$
$89$	−8.61803	−0.913510	−0.456755	+	0.889593i	$0.650988\pi$
$90$	4.23607	0.446521
$91$	−1.00000	−0.104828
$92$	0.763932	0.0796454
$93$	−5.76393	−0.597692
$94$	−13.4721	−1.38954
$95$	0	0
$96$	3.38197	0.345170
$97$	−17.0000	−1.72609	−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000	−1.72609	−0.863044	+	0.505128i	$0.831445\pi$
$98$	−1.61803	−0.163446
$99$	0	0
$100$	1.14590	0.114590
$101$	−18.1803	−1.80901	−0.904506	−	0.426461i	$-0.859760\pi$
$101$	−18.1803	−1.80901	−0.904506	+	0.426461i	$0.859760\pi$
$102$	0.381966	0.0378203
$103$	0.708204	0.0697814	0.0348907	−	0.999391i	$-0.488892\pi$
$103$	0.708204	0.0697814	0.0348907	+	0.999391i	$0.488892\pi$
$104$	2.23607	0.219265
$105$	2.61803	0.255494
$106$	−8.70820	−0.845816
$107$	−20.2361	−1.95629	−0.978147	−	0.207913i	$-0.933333\pi$
$107$	−20.2361	−1.95629	−0.978147	+	0.207913i	$0.933333\pi$
$108$	0.618034	0.0594703
$109$	−12.5623	−1.20325	−0.601625	−	0.798778i	$-0.705480\pi$
$109$	−12.5623	−1.20325	−0.601625	+	0.798778i	$0.705480\pi$
$110$	0	0
$111$	−10.9443	−1.03878
$112$	4.85410	0.458670
$113$	19.6525	1.84875	0.924375	−	0.381486i	$-0.124587\pi$
$113$	19.6525	1.84875	0.924375	+	0.381486i	$0.124587\pi$
$114$	0	0
$115$	−3.23607	−0.301765
$116$	4.14590	0.384937
$117$	1.00000	0.0924500
$118$	17.5623	1.61674
$119$	0.236068	0.0216403
$120$	−5.85410	−0.534404
$121$	0	0
$122$	−16.5623	−1.49948
$123$	6.09017	0.549132
$124$	−3.56231	−0.319905
$125$	8.23607	0.736656
$126$	1.61803	0.144146
$127$	−8.32624	−0.738834	−0.369417	−	0.929264i	$-0.620443\pi$
$127$	−8.32624	−0.738834	−0.369417	+	0.929264i	$0.620443\pi$
$128$	−13.6180	−1.20368
$129$	1.00000	0.0880451
$130$	4.23607	0.371528
$131$	−12.3262	−1.07695	−0.538474	−	0.842642i	$-0.680999\pi$
$131$	−12.3262	−1.07695	−0.538474	+	0.842642i	$0.680999\pi$
$132$	0	0
$133$	0	0
$134$	7.70820	0.665887
$135$	−2.61803	−0.225324
$136$	−0.527864	−0.0452640
$137$	−20.9443	−1.78939	−0.894695	−	0.446678i	$-0.852607\pi$
$137$	−20.9443	−1.78939	−0.894695	+	0.446678i	$0.852607\pi$
$138$	−2.00000	−0.170251
$139$	−2.56231	−0.217332	−0.108666	−	0.994078i	$-0.534658\pi$
$139$	−2.56231	−0.217332	−0.108666	+	0.994078i	$0.534658\pi$
$140$	1.61803	0.136749
$141$	8.32624	0.701196
$142$	−2.38197	−0.199890
$143$	0	0
$144$	−4.85410	−0.404508
$145$	−17.5623	−1.45847
$146$	−13.8541	−1.14657
$147$	1.00000	0.0824786
$148$	−6.76393	−0.555992
$149$	1.90983	0.156459	0.0782297	−	0.996935i	$-0.475073\pi$
$149$	1.90983	0.156459	0.0782297	+	0.996935i	$0.475073\pi$
$150$	−3.00000	−0.244949
$151$	9.90983	0.806451	0.403225	−	0.915101i	$-0.367889\pi$
$151$	9.90983	0.806451	0.403225	+	0.915101i	$0.367889\pi$
$152$	0	0
$153$	−0.236068	−0.0190850
$154$	0	0
$155$	15.0902	1.21207
$156$	0.618034	0.0494823
$157$	−17.3262	−1.38278	−0.691392	−	0.722480i	$-0.743002\pi$
$157$	−17.3262	−1.38278	−0.691392	+	0.722480i	$0.743002\pi$
$158$	6.70820	0.533676
$159$	5.38197	0.426818
$160$	−8.85410	−0.699978
$161$	−1.23607	−0.0974158
$162$	−1.61803	−0.127125
$163$	−23.0344	−1.80420	−0.902098	−	0.431530i	$-0.857974\pi$
$163$	−23.0344	−1.80420	−0.902098	+	0.431530i	$0.857974\pi$
$164$	3.76393	0.293914
$165$	0	0
$166$	−9.70820	−0.753503
$167$	−11.6180	−0.899030	−0.449515	−	0.893273i	$-0.648403\pi$
$167$	−11.6180	−0.899030	−0.449515	+	0.893273i	$0.648403\pi$
$168$	−2.23607	−0.172516
$169$	−12.0000	−0.923077
$170$	−1.00000	−0.0766965
$171$	0	0
$172$	0.618034	0.0471246
$173$	12.3820	0.941383	0.470692	−	0.882298i	$-0.344004\pi$
$173$	12.3820	0.941383	0.470692	+	0.882298i	$0.344004\pi$
$174$	−10.8541	−0.822847
$175$	−1.85410	−0.140157
$176$	0	0
$177$	−10.8541	−0.815844
$178$	13.9443	1.04517
$179$	2.23607	0.167132	0.0835658	−	0.996502i	$-0.473369\pi$
$179$	2.23607	0.167132	0.0835658	+	0.996502i	$0.473369\pi$
$180$	−1.61803	−0.120601
$181$	4.23607	0.314864	0.157432	−	0.987530i	$-0.449678\pi$
$181$	4.23607	0.314864	0.157432	+	0.987530i	$0.449678\pi$
$182$	1.61803	0.119937
$183$	10.2361	0.756672
$184$	2.76393	0.203760
$185$	28.6525	2.10657
$186$	9.32624	0.683833
$187$	0	0
$188$	5.14590	0.375303
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	14.2361	1.03009	0.515043	−	0.857164i	$-0.327776\pi$
$191$	14.2361	1.03009	0.515043	+	0.857164i	$0.327776\pi$
$192$	4.23607	0.305712
$193$	−22.9443	−1.65156	−0.825782	−	0.563989i	$-0.809266\pi$
$193$	−22.9443	−1.65156	−0.825782	+	0.563989i	$0.809266\pi$
$194$	27.5066	1.97486
$195$	−2.61803	−0.187481
$196$	0.618034	0.0441453
$197$	4.76393	0.339416	0.169708	−	0.985494i	$-0.445718\pi$
$197$	4.76393	0.339416	0.169708	+	0.985494i	$0.445718\pi$
$198$	0	0
$199$	12.5623	0.890518	0.445259	−	0.895402i	$-0.353112\pi$
$199$	12.5623	0.890518	0.445259	+	0.895402i	$0.353112\pi$
$200$	4.14590	0.293159
$201$	−4.76393	−0.336022
$202$	29.4164	2.06973
$203$	−6.70820	−0.470824
$204$	−0.145898	−0.0102149
$205$	−15.9443	−1.11360
$206$	−1.14590	−0.0798385
$207$	1.23607	0.0859127
$208$	−4.85410	−0.336571
$209$	0	0
$210$	−4.23607	−0.292316
$211$	−18.7082	−1.28793	−0.643963	−	0.765057i	$-0.722711\pi$
$211$	−18.7082	−1.28793	−0.643963	+	0.765057i	$0.722711\pi$
$212$	3.32624	0.228447
$213$	1.47214	0.100869
$214$	32.7426	2.23824
$215$	−2.61803	−0.178548
$216$	2.23607	0.152145
$217$	5.76393	0.391281
$218$	20.3262	1.37667
$219$	8.56231	0.578587
$220$	0	0
$221$	−0.236068	−0.0158797
$222$	17.7082	1.18850
$223$	0.708204	0.0474248	0.0237124	−	0.999719i	$-0.492451\pi$
$223$	0.708204	0.0474248	0.0237124	+	0.999719i	$0.492451\pi$
$224$	−3.38197	−0.225967
$225$	1.85410	0.123607
$226$	−31.7984	−2.11520
$227$	27.9787	1.85701	0.928506	−	0.371317i	$-0.121094\pi$
$227$	27.9787	1.85701	0.928506	+	0.371317i	$0.121094\pi$
$228$	0	0
$229$	1.70820	0.112881	0.0564406	−	0.998406i	$-0.482025\pi$
$229$	1.70820	0.112881	0.0564406	+	0.998406i	$0.482025\pi$
$230$	5.23607	0.345256
$231$	0	0
$232$	15.0000	0.984798
$233$	−1.76393	−0.115559	−0.0577795	−	0.998329i	$-0.518402\pi$
$233$	−1.76393	−0.115559	−0.0577795	+	0.998329i	$0.518402\pi$
$234$	−1.61803	−0.105774
$235$	−21.7984	−1.42197
$236$	−6.70820	−0.436667
$237$	−4.14590	−0.269305
$238$	−0.381966	−0.0247592
$239$	−25.8541	−1.67236	−0.836181	−	0.548453i	$-0.815217\pi$
$239$	−25.8541	−1.67236	−0.836181	+	0.548453i	$0.815217\pi$
$240$	12.7082	0.820311
$241$	11.2918	0.727369	0.363684	−	0.931522i	$-0.381519\pi$
$241$	11.2918	0.727369	0.363684	+	0.931522i	$0.381519\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	6.32624	0.404996
$245$	−2.61803	−0.167260
$246$	−9.85410	−0.628275
$247$	0	0
$248$	−12.8885	−0.818423
$249$	6.00000	0.380235
$250$	−13.3262	−0.842825
$251$	−22.5967	−1.42629	−0.713147	−	0.701014i	$-0.752731\pi$
$251$	−22.5967	−1.42629	−0.713147	+	0.701014i	$0.752731\pi$
$252$	−0.618034	−0.0389325
$253$	0	0
$254$	13.4721	0.845317
$255$	0.618034	0.0387028
$256$	13.5623	0.847644
$257$	9.05573	0.564881	0.282440	−	0.959285i	$-0.408856\pi$
$257$	9.05573	0.564881	0.282440	+	0.959285i	$0.408856\pi$
$258$	−1.61803	−0.100734
$259$	10.9443	0.680044
$260$	−1.61803	−0.100346
$261$	6.70820	0.415227
$262$	19.9443	1.23216
$263$	12.7082	0.783621	0.391811	−	0.920046i	$-0.371849\pi$
$263$	12.7082	0.783621	0.391811	+	0.920046i	$0.371849\pi$
$264$	0	0
$265$	−14.0902	−0.865552
$266$	0	0
$267$	−8.61803	−0.527415
$268$	−2.94427	−0.179850
$269$	6.05573	0.369224	0.184612	−	0.982811i	$-0.440897\pi$
$269$	6.05573	0.369224	0.184612	+	0.982811i	$0.440897\pi$
$270$	4.23607	0.257799
$271$	−20.4164	−1.24021	−0.620104	−	0.784519i	$-0.712910\pi$
$271$	−20.4164	−1.24021	−0.620104	+	0.784519i	$0.712910\pi$
$272$	1.14590	0.0694803
$273$	−1.00000	−0.0605228
$274$	33.8885	2.04728
$275$	0	0
$276$	0.763932	0.0459833
$277$	−1.41641	−0.0851037	−0.0425519	−	0.999094i	$-0.513549\pi$
$277$	−1.41641	−0.0851037	−0.0425519	+	0.999094i	$0.513549\pi$
$278$	4.14590	0.248654
$279$	−5.76393	−0.345078
$280$	5.85410	0.349850
$281$	−13.3820	−0.798301	−0.399151	−	0.916885i	$-0.630695\pi$
$281$	−13.3820	−0.798301	−0.399151	+	0.916885i	$0.630695\pi$
$282$	−13.4721	−0.802254
$283$	−20.7082	−1.23097	−0.615487	−	0.788147i	$-0.711041\pi$
$283$	−20.7082	−1.23097	−0.615487	+	0.788147i	$0.711041\pi$
$284$	0.909830	0.0539885
$285$	0	0
$286$	0	0
$287$	−6.09017	−0.359491
$288$	3.38197	0.199284
$289$	−16.9443	−0.996722
$290$	28.4164	1.66867
$291$	−17.0000	−0.996558
$292$	5.29180	0.309679
$293$	8.76393	0.511994	0.255997	−	0.966678i	$-0.417596\pi$
$293$	8.76393	0.511994	0.255997	+	0.966678i	$0.417596\pi$
$294$	−1.61803	−0.0943657
$295$	28.4164	1.65447
$296$	−24.4721	−1.42241
$297$	0	0
$298$	−3.09017	−0.179009
$299$	1.23607	0.0714837
$300$	1.14590	0.0661585
$301$	−1.00000	−0.0576390
$302$	−16.0344	−0.922678
$303$	−18.1803	−1.04443
$304$	0	0
$305$	−26.7984	−1.53447
$306$	0.381966	0.0218355
$307$	3.18034	0.181512	0.0907558	−	0.995873i	$-0.471072\pi$
$307$	3.18034	0.181512	0.0907558	+	0.995873i	$0.471072\pi$
$308$	0	0
$309$	0.708204	0.0402883
$310$	−24.4164	−1.38676
$311$	−7.79837	−0.442205	−0.221103	−	0.975251i	$-0.570966\pi$
$311$	−7.79837	−0.442205	−0.221103	+	0.975251i	$0.570966\pi$
$312$	2.23607	0.126592
$313$	8.79837	0.497313	0.248657	−	0.968592i	$-0.420011\pi$
$313$	8.79837	0.497313	0.248657	+	0.968592i	$0.420011\pi$
$314$	28.0344	1.58208
$315$	2.61803	0.147510
$316$	−2.56231	−0.144141
$317$	−19.3607	−1.08740	−0.543702	−	0.839278i	$-0.682978\pi$
$317$	−19.3607	−1.08740	−0.543702	+	0.839278i	$0.682978\pi$
$318$	−8.70820	−0.488332
$319$	0	0
$320$	−11.0902	−0.619959
$321$	−20.2361	−1.12947
$322$	2.00000	0.111456
$323$	0	0
$324$	0.618034	0.0343352
$325$	1.85410	0.102847
$326$	37.2705	2.06422
$327$	−12.5623	−0.694697
$328$	13.6180	0.751930
$329$	−8.32624	−0.459040
$330$	0	0
$331$	−1.29180	−0.0710035	−0.0355018	−	0.999370i	$-0.511303\pi$
$331$	−1.29180	−0.0710035	−0.0355018	+	0.999370i	$0.511303\pi$
$332$	3.70820	0.203514
$333$	−10.9443	−0.599742
$334$	18.7984	1.02860
$335$	12.4721	0.681426
$336$	4.85410	0.264813
$337$	−14.7082	−0.801207	−0.400603	−	0.916252i	$-0.631199\pi$
$337$	−14.7082	−0.801207	−0.400603	+	0.916252i	$0.631199\pi$
$338$	19.4164	1.05611
$339$	19.6525	1.06738
$340$	0.381966	0.0207150
$341$	0	0
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	2.23607	0.120561
$345$	−3.23607	−0.174224
$346$	−20.0344	−1.07706
$347$	−1.41641	−0.0760368	−0.0380184	−	0.999277i	$-0.512105\pi$
$347$	−1.41641	−0.0760368	−0.0380184	+	0.999277i	$0.512105\pi$
$348$	4.14590	0.222243
$349$	29.9230	1.60174	0.800870	−	0.598838i	$-0.204371\pi$
$349$	29.9230	1.60174	0.800870	+	0.598838i	$0.204371\pi$
$350$	3.00000	0.160357
$351$	1.00000	0.0533761
$352$	0	0
$353$	−16.5279	−0.879689	−0.439845	−	0.898074i	$-0.644967\pi$
$353$	−16.5279	−0.879689	−0.439845	+	0.898074i	$0.644967\pi$
$354$	17.5623	0.933426
$355$	−3.85410	−0.204554
$356$	−5.32624	−0.282290
$357$	0.236068	0.0124940
$358$	−3.61803	−0.191219
$359$	−18.2148	−0.961339	−0.480670	−	0.876902i	$-0.659606\pi$
$359$	−18.2148	−0.961339	−0.480670	+	0.876902i	$0.659606\pi$
$360$	−5.85410	−0.308538
$361$	−19.0000	−1.00000
$362$	−6.85410	−0.360244
$363$	0	0
$364$	−0.618034	−0.0323938
$365$	−22.4164	−1.17333
$366$	−16.5623	−0.865726
$367$	24.7082	1.28976	0.644879	−	0.764285i	$-0.276908\pi$
$367$	24.7082	1.28976	0.644879	+	0.764285i	$0.276908\pi$
$368$	−6.00000	−0.312772
$369$	6.09017	0.317042
$370$	−46.3607	−2.41018
$371$	−5.38197	−0.279418
$372$	−3.56231	−0.184697
$373$	−7.81966	−0.404887	−0.202443	−	0.979294i	$-0.564888\pi$
$373$	−7.81966	−0.404887	−0.202443	+	0.979294i	$0.564888\pi$
$374$	0	0
$375$	8.23607	0.425309
$376$	18.6180	0.960152
$377$	6.70820	0.345490
$378$	1.61803	0.0832227
$379$	−4.14590	−0.212960	−0.106480	−	0.994315i	$-0.533958\pi$
$379$	−4.14590	−0.212960	−0.106480	+	0.994315i	$0.533958\pi$
$380$	0	0
$381$	−8.32624	−0.426566
$382$	−23.0344	−1.17854
$383$	−19.0902	−0.975462	−0.487731	−	0.872994i	$-0.662175\pi$
$383$	−19.0902	−0.975462	−0.487731	+	0.872994i	$0.662175\pi$
$384$	−13.6180	−0.694942
$385$	0	0
$386$	37.1246	1.88959
$387$	1.00000	0.0508329
$388$	−10.5066	−0.533391
$389$	−10.6525	−0.540102	−0.270051	−	0.962846i	$-0.587041\pi$
$389$	−10.6525	−0.540102	−0.270051	+	0.962846i	$0.587041\pi$
$390$	4.23607	0.214502
$391$	−0.291796	−0.0147568
$392$	2.23607	0.112938
$393$	−12.3262	−0.621776
$394$	−7.70820	−0.388334
$395$	10.8541	0.546129
$396$	0	0
$397$	−34.6869	−1.74089	−0.870443	−	0.492269i	$-0.836168\pi$
$397$	−34.6869	−1.74089	−0.870443	+	0.492269i	$0.836168\pi$
$398$	−20.3262	−1.01886
$399$	0	0
$400$	−9.00000	−0.450000
$401$	27.3262	1.36461	0.682304	−	0.731069i	$-0.260978\pi$
$401$	27.3262	1.36461	0.682304	+	0.731069i	$0.260978\pi$
$402$	7.70820	0.384450
$403$	−5.76393	−0.287122
$404$	−11.2361	−0.559015
$405$	−2.61803	−0.130091
$406$	10.8541	0.538680
$407$	0	0
$408$	−0.527864	−0.0261332
$409$	28.6180	1.41507	0.707535	−	0.706678i	$-0.249807\pi$
$409$	28.6180	1.41507	0.707535	+	0.706678i	$0.249807\pi$
$410$	25.7984	1.27409
$411$	−20.9443	−1.03310
$412$	0.437694	0.0215636
$413$	10.8541	0.534095
$414$	−2.00000	−0.0982946
$415$	−15.7082	−0.771085
$416$	3.38197	0.165815
$417$	−2.56231	−0.125477
$418$	0	0
$419$	0.326238	0.0159378	0.00796888	−	0.999968i	$-0.497463\pi$
$419$	0.326238	0.0159378	0.00796888	+	0.999968i	$0.497463\pi$
$420$	1.61803	0.0789520
$421$	36.2705	1.76772	0.883858	−	0.467755i	$-0.154937\pi$
$421$	36.2705	1.76772	0.883858	+	0.467755i	$0.154937\pi$
$422$	30.2705	1.47355
$423$	8.32624	0.404836
$424$	12.0344	0.584444
$425$	−0.437694	−0.0212313
$426$	−2.38197	−0.115407
$427$	−10.2361	−0.495358
$428$	−12.5066	−0.604528
$429$	0	0
$430$	4.23607	0.204281
$431$	13.2016	0.635900	0.317950	−	0.948107i	$-0.397006\pi$
$431$	13.2016	0.635900	0.317950	+	0.948107i	$0.397006\pi$
$432$	−4.85410	−0.233543
$433$	−29.4164	−1.41366	−0.706831	−	0.707382i	$-0.749876\pi$
$433$	−29.4164	−1.41366	−0.706831	+	0.707382i	$0.749876\pi$
$434$	−9.32624	−0.447674
$435$	−17.5623	−0.842048
$436$	−7.76393	−0.371825
$437$	0	0
$438$	−13.8541	−0.661975
$439$	−9.47214	−0.452080	−0.226040	−	0.974118i	$-0.572578\pi$
$439$	−9.47214	−0.452080	−0.226040	+	0.974118i	$0.572578\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	0.381966	0.0181683
$443$	−5.34752	−0.254069	−0.127034	−	0.991898i	$-0.540546\pi$
$443$	−5.34752	−0.254069	−0.127034	+	0.991898i	$0.540546\pi$
$444$	−6.76393	−0.321002
$445$	22.5623	1.06956
$446$	−1.14590	−0.0542598
$447$	1.90983	0.0903319
$448$	−4.23607	−0.200135
$449$	−15.6525	−0.738686	−0.369343	−	0.929293i	$-0.620417\pi$
$449$	−15.6525	−0.738686	−0.369343	+	0.929293i	$0.620417\pi$
$450$	−3.00000	−0.141421
$451$	0	0
$452$	12.1459	0.571295
$453$	9.90983	0.465604
$454$	−45.2705	−2.12465
$455$	2.61803	0.122735
$456$	0	0
$457$	21.2705	0.994992	0.497496	−	0.867466i	$-0.334253\pi$
$457$	21.2705	0.994992	0.497496	+	0.867466i	$0.334253\pi$
$458$	−2.76393	−0.129150
$459$	−0.236068	−0.0110187
$460$	−2.00000	−0.0932505
$461$	−0.819660	−0.0381754	−0.0190877	−	0.999818i	$-0.506076\pi$
$461$	−0.819660	−0.0381754	−0.0190877	+	0.999818i	$0.506076\pi$
$462$	0	0
$463$	28.9230	1.34417	0.672083	−	0.740476i	$-0.265400\pi$
$463$	28.9230	1.34417	0.672083	+	0.740476i	$0.265400\pi$
$464$	−32.5623	−1.51167
$465$	15.0902	0.699790
$466$	2.85410	0.132214
$467$	14.0557	0.650422	0.325211	−	0.945642i	$-0.394565\pi$
$467$	14.0557	0.650422	0.325211	+	0.945642i	$0.394565\pi$
$468$	0.618034	0.0285686
$469$	4.76393	0.219978
$470$	35.2705	1.62691
$471$	−17.3262	−0.798351
$472$	−24.2705	−1.11714
$473$	0	0
$474$	6.70820	0.308118
$475$	0	0
$476$	0.145898	0.00668723
$477$	5.38197	0.246423
$478$	41.8328	1.91339
$479$	16.5066	0.754205	0.377102	−	0.926172i	$-0.376920\pi$
$479$	16.5066	0.754205	0.377102	+	0.926172i	$0.376920\pi$
$480$	−8.85410	−0.404133
$481$	−10.9443	−0.499016
$482$	−18.2705	−0.832199
$483$	−1.23607	−0.0562430
$484$	0	0
$485$	44.5066	2.02094
$486$	−1.61803	−0.0733955
$487$	14.3820	0.651709	0.325855	−	0.945420i	$-0.394348\pi$
$487$	14.3820	0.651709	0.325855	+	0.945420i	$0.394348\pi$
$488$	22.8885	1.03612
$489$	−23.0344	−1.04165
$490$	4.23607	0.191366
$491$	9.70820	0.438125	0.219063	−	0.975711i	$-0.429700\pi$
$491$	9.70820	0.438125	0.219063	+	0.975711i	$0.429700\pi$
$492$	3.76393	0.169691
$493$	−1.58359	−0.0713214
$494$	0	0
$495$	0	0
$496$	27.9787	1.25628
$497$	−1.47214	−0.0660343
$498$	−9.70820	−0.435035
$499$	−5.00000	−0.223831	−0.111915	−	0.993718i	$-0.535699\pi$
$499$	−5.00000	−0.223831	−0.111915	+	0.993718i	$0.535699\pi$
$500$	5.09017	0.227639
$501$	−11.6180	−0.519055
$502$	36.5623	1.63186
$503$	−30.3050	−1.35123	−0.675616	−	0.737254i	$-0.736122\pi$
$503$	−30.3050	−1.35123	−0.675616	+	0.737254i	$0.736122\pi$
$504$	−2.23607	−0.0996024
$505$	47.5967	2.11803
$506$	0	0
$507$	−12.0000	−0.532939
$508$	−5.14590	−0.228312
$509$	−11.8328	−0.524480	−0.262240	−	0.965003i	$-0.584461\pi$
$509$	−11.8328	−0.524480	−0.262240	+	0.965003i	$0.584461\pi$
$510$	−1.00000	−0.0442807
$511$	−8.56231	−0.378774
$512$	5.29180	0.233867
$513$	0	0
$514$	−14.6525	−0.646293
$515$	−1.85410	−0.0817015
$516$	0.618034	0.0272074
$517$	0	0
$518$	−17.7082	−0.778054
$519$	12.3820	0.543508
$520$	−5.85410	−0.256719
$521$	3.18034	0.139333	0.0696666	−	0.997570i	$-0.477806\pi$
$521$	3.18034	0.139333	0.0696666	+	0.997570i	$0.477806\pi$
$522$	−10.8541	−0.475071
$523$	42.3050	1.84987	0.924933	−	0.380130i	$-0.124121\pi$
$523$	42.3050	1.84987	0.924933	+	0.380130i	$0.124121\pi$
$524$	−7.61803	−0.332795
$525$	−1.85410	−0.0809196
$526$	−20.5623	−0.896559
$527$	1.36068	0.0592721
$528$	0	0
$529$	−21.4721	−0.933571
$530$	22.7984	0.990298
$531$	−10.8541	−0.471028
$532$	0	0
$533$	6.09017	0.263795
$534$	13.9443	0.603428
$535$	52.9787	2.29047
$536$	−10.6525	−0.460117
$537$	2.23607	0.0964935
$538$	−9.79837	−0.422438
$539$	0	0
$540$	−1.61803	−0.0696291
$541$	−8.90983	−0.383064	−0.191532	−	0.981486i	$-0.561345\pi$
$541$	−8.90983	−0.383064	−0.191532	+	0.981486i	$0.561345\pi$
$542$	33.0344	1.41895
$543$	4.23607	0.181787
$544$	−0.798374	−0.0342300
$545$	32.8885	1.40879
$546$	1.61803	0.0692455
$547$	26.5967	1.13719	0.568597	−	0.822616i	$-0.307486\pi$
$547$	26.5967	1.13719	0.568597	+	0.822616i	$0.307486\pi$
$548$	−12.9443	−0.552952
$549$	10.2361	0.436865
$550$	0	0
$551$	0	0
$552$	2.76393	0.117641
$553$	4.14590	0.176302
$554$	2.29180	0.0973691
$555$	28.6525	1.21623
$556$	−1.58359	−0.0671593
$557$	−5.23607	−0.221859	−0.110930	−	0.993828i	$-0.535383\pi$
$557$	−5.23607	−0.221859	−0.110930	+	0.993828i	$0.535383\pi$
$558$	9.32624	0.394811
$559$	1.00000	0.0422955
$560$	−12.7082	−0.537020
$561$	0	0
$562$	21.6525	0.913355
$563$	−13.0689	−0.550788	−0.275394	−	0.961331i	$-0.588808\pi$
$563$	−13.0689	−0.550788	−0.275394	+	0.961331i	$0.588808\pi$
$564$	5.14590	0.216681
$565$	−51.4508	−2.16455
$566$	33.5066	1.40839
$567$	−1.00000	−0.0419961
$568$	3.29180	0.138121
$569$	19.0689	0.799409	0.399705	−	0.916644i	$-0.369113\pi$
$569$	19.0689	0.799409	0.399705	+	0.916644i	$0.369113\pi$
$570$	0	0
$571$	−7.00000	−0.292941	−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000	−0.292941	−0.146470	+	0.989215i	$0.546791\pi$
$572$	0	0
$573$	14.2361	0.594720
$574$	9.85410	0.411302
$575$	2.29180	0.0955745
$576$	4.23607	0.176503
$577$	−29.5623	−1.23069	−0.615347	−	0.788256i	$-0.710984\pi$
$577$	−29.5623	−1.23069	−0.615347	+	0.788256i	$0.710984\pi$
$578$	27.4164	1.14037
$579$	−22.9443	−0.953531
$580$	−10.8541	−0.450692
$581$	−6.00000	−0.248922
$582$	27.5066	1.14018
$583$	0	0
$584$	19.1459	0.792263
$585$	−2.61803	−0.108242
$586$	−14.1803	−0.585784
$587$	0.111456	0.00460029	0.00230014	−	0.999997i	$-0.499268\pi$
$587$	0.111456	0.00460029	0.00230014	+	0.999997i	$0.499268\pi$
$588$	0.618034	0.0254873
$589$	0	0
$590$	−45.9787	−1.89291
$591$	4.76393	0.195962
$592$	53.1246	2.18341
$593$	−11.8885	−0.488204	−0.244102	−	0.969750i	$-0.578493\pi$
$593$	−11.8885	−0.488204	−0.244102	+	0.969750i	$0.578493\pi$
$594$	0	0
$595$	−0.618034	−0.0253369
$596$	1.18034	0.0483486
$597$	12.5623	0.514141
$598$	−2.00000	−0.0817861
$599$	−6.50658	−0.265852	−0.132926	−	0.991126i	$-0.542437\pi$
$599$	−6.50658	−0.265852	−0.132926	+	0.991126i	$0.542437\pi$
$600$	4.14590	0.169256
$601$	−38.8328	−1.58402	−0.792012	−	0.610506i	$-0.790966\pi$
$601$	−38.8328	−1.58402	−0.792012	+	0.610506i	$0.790966\pi$
$602$	1.61803	0.0659461
$603$	−4.76393	−0.194002
$604$	6.12461	0.249207
$605$	0	0
$606$	29.4164	1.19496
$607$	22.8541	0.927619	0.463810	−	0.885935i	$-0.346482\pi$
$607$	22.8541	0.927619	0.463810	+	0.885935i	$0.346482\pi$
$608$	0	0
$609$	−6.70820	−0.271830
$610$	43.3607	1.75562
$611$	8.32624	0.336844
$612$	−0.145898	−0.00589758
$613$	21.4508	0.866392	0.433196	−	0.901300i	$-0.357386\pi$
$613$	21.4508	0.866392	0.433196	+	0.901300i	$0.357386\pi$
$614$	−5.14590	−0.207672
$615$	−15.9443	−0.642935
$616$	0	0
$617$	1.09017	0.0438886	0.0219443	−	0.999759i	$-0.493014\pi$
$617$	1.09017	0.0438886	0.0219443	+	0.999759i	$0.493014\pi$
$618$	−1.14590	−0.0460948
$619$	−5.12461	−0.205976	−0.102988	−	0.994683i	$-0.532840\pi$
$619$	−5.12461	−0.205976	−0.102988	+	0.994683i	$0.532840\pi$
$620$	9.32624	0.374551
$621$	1.23607	0.0496017
$622$	12.6180	0.505937
$623$	8.61803	0.345274
$624$	−4.85410	−0.194320
$625$	−30.8328	−1.23331
$626$	−14.2361	−0.568988
$627$	0	0
$628$	−10.7082	−0.427304
$629$	2.58359	0.103015
$630$	−4.23607	−0.168769
$631$	13.1803	0.524701	0.262351	−	0.964973i	$-0.415502\pi$
$631$	13.1803	0.524701	0.262351	+	0.964973i	$0.415502\pi$
$632$	−9.27051	−0.368761
$633$	−18.7082	−0.743584
$634$	31.3262	1.24412
$635$	21.7984	0.865042
$636$	3.32624	0.131894
$637$	1.00000	0.0396214
$638$	0	0
$639$	1.47214	0.0582368
$640$	35.6525	1.40929
$641$	−18.9787	−0.749614	−0.374807	−	0.927103i	$-0.622291\pi$
$641$	−18.9787	−0.749614	−0.374807	+	0.927103i	$0.622291\pi$
$642$	32.7426	1.29225
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	−0.763932	−0.0301031
$645$	−2.61803	−0.103085
$646$	0	0
$647$	33.6525	1.32302	0.661508	−	0.749938i	$-0.269917\pi$
$647$	33.6525	1.32302	0.661508	+	0.749938i	$0.269917\pi$
$648$	2.23607	0.0878410
$649$	0	0
$650$	−3.00000	−0.117670
$651$	5.76393	0.225906
$652$	−14.2361	−0.557527
$653$	−12.7082	−0.497310	−0.248655	−	0.968592i	$-0.579989\pi$
$653$	−12.7082	−0.497310	−0.248655	+	0.968592i	$0.579989\pi$
$654$	20.3262	0.794819
$655$	32.2705	1.26091
$656$	−29.5623	−1.15421
$657$	8.56231	0.334047
$658$	13.4721	0.525199
$659$	11.8328	0.460941	0.230471	−	0.973079i	$-0.425973\pi$
$659$	11.8328	0.460941	0.230471	+	0.973079i	$0.425973\pi$
$660$	0	0
$661$	−3.00000	−0.116686	−0.0583432	−	0.998297i	$-0.518582\pi$
$661$	−3.00000	−0.116686	−0.0583432	+	0.998297i	$0.518582\pi$
$662$	2.09017	0.0812368
$663$	−0.236068	−0.00916812
$664$	13.4164	0.520658
$665$	0	0
$666$	17.7082	0.686179
$667$	8.29180	0.321060
$668$	−7.18034	−0.277816
$669$	0.708204	0.0273807
$670$	−20.1803	−0.779635
$671$	0	0
$672$	−3.38197	−0.130462
$673$	34.4164	1.32666	0.663328	−	0.748329i	$-0.269144\pi$
$673$	34.4164	1.32666	0.663328	+	0.748329i	$0.269144\pi$
$674$	23.7984	0.916679
$675$	1.85410	0.0713644
$676$	−7.41641	−0.285246
$677$	32.4508	1.24719	0.623594	−	0.781749i	$-0.285672\pi$
$677$	32.4508	1.24719	0.623594	+	0.781749i	$0.285672\pi$
$678$	−31.7984	−1.22121
$679$	17.0000	0.652400
$680$	1.38197	0.0529960
$681$	27.9787	1.07215
$682$	0	0
$683$	30.3050	1.15959	0.579793	−	0.814764i	$-0.303133\pi$
$683$	30.3050	1.15959	0.579793	+	0.814764i	$0.303133\pi$
$684$	0	0
$685$	54.8328	2.09505
$686$	1.61803	0.0617768
$687$	1.70820	0.0651720
$688$	−4.85410	−0.185061
$689$	5.38197	0.205037
$690$	5.23607	0.199334
$691$	−5.56231	−0.211600	−0.105800	−	0.994387i	$-0.533740\pi$
$691$	−5.56231	−0.211600	−0.105800	+	0.994387i	$0.533740\pi$
$692$	7.65248	0.290903
$693$	0	0
$694$	2.29180	0.0869954
$695$	6.70820	0.254457
$696$	15.0000	0.568574
$697$	−1.43769	−0.0544565
$698$	−48.4164	−1.83259
$699$	−1.76393	−0.0667180
$700$	−1.14590	−0.0433109
$701$	−27.0000	−1.01978	−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000	−1.01978	−0.509888	+	0.860241i	$0.670313\pi$
$702$	−1.61803	−0.0610688
$703$	0	0
$704$	0	0
$705$	−21.7984	−0.820974
$706$	26.7426	1.00647
$707$	18.1803	0.683742
$708$	−6.70820	−0.252110
$709$	−19.3475	−0.726612	−0.363306	−	0.931670i	$-0.618352\pi$
$709$	−19.3475	−0.726612	−0.363306	+	0.931670i	$0.618352\pi$
$710$	6.23607	0.234035
$711$	−4.14590	−0.155483
$712$	−19.2705	−0.722193
$713$	−7.12461	−0.266819
$714$	−0.381966	−0.0142947
$715$	0	0
$716$	1.38197	0.0516465
$717$	−25.8541	−0.965539
$718$	29.4721	1.09989
$719$	−6.38197	−0.238007	−0.119004	−	0.992894i	$-0.537970\pi$
$719$	−6.38197	−0.238007	−0.119004	+	0.992894i	$0.537970\pi$
$720$	12.7082	0.473607
$721$	−0.708204	−0.0263749
$722$	30.7426	1.14412
$723$	11.2918	0.419946
$724$	2.61803	0.0972985
$725$	12.4377	0.461924
$726$	0	0
$727$	28.8541	1.07014	0.535070	−	0.844808i	$-0.320285\pi$
$727$	28.8541	1.07014	0.535070	+	0.844808i	$0.320285\pi$
$728$	−2.23607	−0.0828742
$729$	1.00000	0.0370370
$730$	36.2705	1.34243
$731$	−0.236068	−0.00873129
$732$	6.32624	0.233824
$733$	36.1246	1.33429	0.667146	−	0.744927i	$-0.267516\pi$
$733$	36.1246	1.33429	0.667146	+	0.744927i	$0.267516\pi$
$734$	−39.9787	−1.47564
$735$	−2.61803	−0.0965676
$736$	4.18034	0.154089
$737$	0	0
$738$	−9.85410	−0.362735
$739$	17.6869	0.650624	0.325312	−	0.945607i	$-0.394531\pi$
$739$	17.6869	0.650624	0.325312	+	0.945607i	$0.394531\pi$
$740$	17.7082	0.650967
$741$	0	0
$742$	8.70820	0.319688
$743$	−37.0902	−1.36071	−0.680353	−	0.732884i	$-0.738174\pi$
$743$	−37.0902	−1.36071	−0.680353	+	0.732884i	$0.738174\pi$
$744$	−12.8885	−0.472517
$745$	−5.00000	−0.183186
$746$	12.6525	0.463240
$747$	6.00000	0.219529
$748$	0	0
$749$	20.2361	0.739410
$750$	−13.3262	−0.486605
$751$	−22.1459	−0.808115	−0.404058	−	0.914734i	$-0.632400\pi$
$751$	−22.1459	−0.808115	−0.404058	+	0.914734i	$0.632400\pi$
$752$	−40.4164	−1.47383
$753$	−22.5967	−0.823471
$754$	−10.8541	−0.395283
$755$	−25.9443	−0.944209
$756$	−0.618034	−0.0224777
$757$	40.7639	1.48159	0.740795	−	0.671731i	$-0.234449\pi$
$757$	40.7639	1.48159	0.740795	+	0.671731i	$0.234449\pi$
$758$	6.70820	0.243653
$759$	0	0
$760$	0	0
$761$	11.0902	0.402018	0.201009	−	0.979589i	$-0.435578\pi$
$761$	11.0902	0.402018	0.201009	+	0.979589i	$0.435578\pi$
$762$	13.4721	0.488044
$763$	12.5623	0.454786
$764$	8.79837	0.318314
$765$	0.618034	0.0223451
$766$	30.8885	1.11605
$767$	−10.8541	−0.391919
$768$	13.5623	0.489388
$769$	−35.5279	−1.28117	−0.640584	−	0.767888i	$-0.721308\pi$
$769$	−35.5279	−1.28117	−0.640584	+	0.767888i	$0.721308\pi$
$770$	0	0
$771$	9.05573	0.326134
$772$	−14.1803	−0.510362
$773$	37.4164	1.34577	0.672887	−	0.739745i	$-0.265054\pi$
$773$	37.4164	1.34577	0.672887	+	0.739745i	$0.265054\pi$
$774$	−1.61803	−0.0581590
$775$	−10.6869	−0.383885
$776$	−38.0132	−1.36459
$777$	10.9443	0.392624
$778$	17.2361	0.617943
$779$	0	0
$780$	−1.61803	−0.0579349
$781$	0	0
$782$	0.472136	0.0168835
$783$	6.70820	0.239732
$784$	−4.85410	−0.173361
$785$	45.3607	1.61899
$786$	19.9443	0.711389
$787$	26.1459	0.932001	0.466000	−	0.884785i	$-0.345695\pi$
$787$	26.1459	0.932001	0.466000	+	0.884785i	$0.345695\pi$
$788$	2.94427	0.104885
$789$	12.7082	0.452424
$790$	−17.5623	−0.624839
$791$	−19.6525	−0.698762
$792$	0	0
$793$	10.2361	0.363493
$794$	56.1246	1.99179
$795$	−14.0902	−0.499727
$796$	7.76393	0.275185
$797$	23.4508	0.830672	0.415336	−	0.909668i	$-0.363664\pi$
$797$	23.4508	0.830672	0.415336	+	0.909668i	$0.363664\pi$
$798$	0	0
$799$	−1.96556	−0.0695364
$800$	6.27051	0.221696
$801$	−8.61803	−0.304503
$802$	−44.2148	−1.56128
$803$	0	0
$804$	−2.94427	−0.103836
$805$	3.23607	0.114056
$806$	9.32624	0.328503
$807$	6.05573	0.213172
$808$	−40.6525	−1.43015
$809$	15.9787	0.561782	0.280891	−	0.959740i	$-0.409370\pi$
$809$	15.9787	0.561782	0.280891	+	0.959740i	$0.409370\pi$
$810$	4.23607	0.148840
$811$	−17.1246	−0.601326	−0.300663	−	0.953730i	$-0.597208\pi$
$811$	−17.1246	−0.601326	−0.300663	+	0.953730i	$0.597208\pi$
$812$	−4.14590	−0.145492
$813$	−20.4164	−0.716035
$814$	0	0
$815$	60.3050	2.11239
$816$	1.14590	0.0401145
$817$	0	0
$818$	−46.3050	−1.61901
$819$	−1.00000	−0.0349428
$820$	−9.85410	−0.344120
$821$	−28.1803	−0.983501	−0.491750	−	0.870736i	$-0.663643\pi$
$821$	−28.1803	−0.983501	−0.491750	+	0.870736i	$0.663643\pi$
$822$	33.8885	1.18200
$823$	54.2492	1.89101	0.945505	−	0.325609i	$-0.105569\pi$
$823$	54.2492	1.89101	0.945505	+	0.325609i	$0.105569\pi$
$824$	1.58359	0.0551670
$825$	0	0
$826$	−17.5623	−0.611071
$827$	−40.8885	−1.42183	−0.710917	−	0.703276i	$-0.751720\pi$
$827$	−40.8885	−1.42183	−0.710917	+	0.703276i	$0.751720\pi$
$828$	0.763932	0.0265485
$829$	−22.6869	−0.787949	−0.393975	−	0.919121i	$-0.628900\pi$
$829$	−22.6869	−0.787949	−0.393975	+	0.919121i	$0.628900\pi$
$830$	25.4164	0.882216
$831$	−1.41641	−0.0491346
$832$	4.23607	0.146859
$833$	−0.236068	−0.00817927
$834$	4.14590	0.143561
$835$	30.4164	1.05260
$836$	0	0
$837$	−5.76393	−0.199231
$838$	−0.527864	−0.0182348
$839$	−29.0689	−1.00357	−0.501785	−	0.864993i	$-0.667323\pi$
$839$	−29.0689	−1.00357	−0.501785	+	0.864993i	$0.667323\pi$
$840$	5.85410	0.201986
$841$	16.0000	0.551724
$842$	−58.6869	−2.02248
$843$	−13.3820	−0.460899
$844$	−11.5623	−0.397991
$845$	31.4164	1.08076
$846$	−13.4721	−0.463182
$847$	0	0
$848$	−26.1246	−0.897123
$849$	−20.7082	−0.710704
$850$	0.708204	0.0242912
$851$	−13.5279	−0.463729
$852$	0.909830	0.0311703
$853$	−33.7984	−1.15723	−0.578617	−	0.815599i	$-0.696407\pi$
$853$	−33.7984	−1.15723	−0.578617	+	0.815599i	$0.696407\pi$
$854$	16.5623	0.566750
$855$	0	0
$856$	−45.2492	−1.54659
$857$	49.7639	1.69990	0.849952	−	0.526861i	$-0.176631\pi$
$857$	49.7639	1.69990	0.849952	+	0.526861i	$0.176631\pi$
$858$	0	0
$859$	11.8328	0.403730	0.201865	−	0.979413i	$-0.435300\pi$
$859$	11.8328	0.403730	0.201865	+	0.979413i	$0.435300\pi$
$860$	−1.61803	−0.0551745
$861$	−6.09017	−0.207552
$862$	−21.3607	−0.727548
$863$	−13.3607	−0.454803	−0.227401	−	0.973801i	$-0.573023\pi$
$863$	−13.3607	−0.454803	−0.227401	+	0.973801i	$0.573023\pi$
$864$	3.38197	0.115057
$865$	−32.4164	−1.10219
$866$	47.5967	1.61740
$867$	−16.9443	−0.575458
$868$	3.56231	0.120913
$869$	0	0
$870$	28.4164	0.963406
$871$	−4.76393	−0.161420
$872$	−28.0902	−0.951253
$873$	−17.0000	−0.575363
$874$	0	0
$875$	−8.23607	−0.278430
$876$	5.29180	0.178793
$877$	0.742646	0.0250774	0.0125387	−	0.999921i	$-0.496009\pi$
$877$	0.742646	0.0250774	0.0125387	+	0.999921i	$0.496009\pi$
$878$	15.3262	0.517235
$879$	8.76393	0.295600
$880$	0	0
$881$	5.94427	0.200268	0.100134	−	0.994974i	$-0.468073\pi$
$881$	5.94427	0.200268	0.100134	+	0.994974i	$0.468073\pi$
$882$	−1.61803	−0.0544820
$883$	−3.96556	−0.133452	−0.0667258	−	0.997771i	$-0.521255\pi$
$883$	−3.96556	−0.133452	−0.0667258	+	0.997771i	$0.521255\pi$
$884$	−0.145898	−0.00490708
$885$	28.4164	0.955207
$886$	8.65248	0.290686
$887$	12.5279	0.420645	0.210322	−	0.977632i	$-0.432549\pi$
$887$	12.5279	0.420645	0.210322	+	0.977632i	$0.432549\pi$
$888$	−24.4721	−0.821231
$889$	8.32624	0.279253
$890$	−36.5066	−1.22370
$891$	0	0
$892$	0.437694	0.0146551
$893$	0	0
$894$	−3.09017	−0.103351
$895$	−5.85410	−0.195681
$896$	13.6180	0.454947
$897$	1.23607	0.0412711
$898$	25.3262	0.845148
$899$	−38.6656	−1.28957
$900$	1.14590	0.0381966
$901$	−1.27051	−0.0423268
$902$	0	0
$903$	−1.00000	−0.0332779
$904$	43.9443	1.46156
$905$	−11.0902	−0.368650
$906$	−16.0344	−0.532709
$907$	−27.9787	−0.929018	−0.464509	−	0.885568i	$-0.653769\pi$
$907$	−27.9787	−0.929018	−0.464509	+	0.885568i	$0.653769\pi$
$908$	17.2918	0.573848
$909$	−18.1803	−0.603004
$910$	−4.23607	−0.140424
$911$	−48.3262	−1.60112	−0.800560	−	0.599253i	$-0.795464\pi$
$911$	−48.3262	−1.60112	−0.800560	+	0.599253i	$0.795464\pi$
$912$	0	0
$913$	0	0
$914$	−34.4164	−1.13839
$915$	−26.7984	−0.885927
$916$	1.05573	0.0348822
$917$	12.3262	0.407048
$918$	0.381966	0.0126068
$919$	43.4164	1.43218	0.716088	−	0.698010i	$-0.245931\pi$
$919$	43.4164	1.43218	0.716088	+	0.698010i	$0.245931\pi$
$920$	−7.23607	−0.238566
$921$	3.18034	0.104796
$922$	1.32624	0.0436773
$923$	1.47214	0.0484559
$924$	0	0
$925$	−20.2918	−0.667190
$926$	−46.7984	−1.53789
$927$	0.708204	0.0232605
$928$	22.6869	0.744735
$929$	55.7771	1.82999	0.914993	−	0.403469i	$-0.132196\pi$
$929$	55.7771	1.82999	0.914993	+	0.403469i	$0.132196\pi$
$930$	−24.4164	−0.800646
$931$	0	0
$932$	−1.09017	−0.0357097
$933$	−7.79837	−0.255307
$934$	−22.7426	−0.744162
$935$	0	0
$936$	2.23607	0.0730882
$937$	7.00000	0.228680	0.114340	−	0.993442i	$-0.463525\pi$
$937$	7.00000	0.228680	0.114340	+	0.993442i	$0.463525\pi$
$938$	−7.70820	−0.251682
$939$	8.79837	0.287124
$940$	−13.4721	−0.439413
$941$	31.8197	1.03729	0.518646	−	0.854989i	$-0.326436\pi$
$941$	31.8197	1.03729	0.518646	+	0.854989i	$0.326436\pi$
$942$	28.0344	0.913411
$943$	7.52786	0.245141
$944$	52.6869	1.71481
$945$	2.61803	0.0851647
$946$	0	0
$947$	1.61803	0.0525790	0.0262895	−	0.999654i	$-0.491631\pi$
$947$	1.61803	0.0525790	0.0262895	+	0.999654i	$0.491631\pi$
$948$	−2.56231	−0.0832198
$949$	8.56231	0.277944
$950$	0	0
$951$	−19.3607	−0.627813
$952$	0.527864	0.0171082
$953$	−43.7984	−1.41877	−0.709384	−	0.704822i	$-0.751027\pi$
$953$	−43.7984	−1.41877	−0.709384	+	0.704822i	$0.751027\pi$
$954$	−8.70820	−0.281939
$955$	−37.2705	−1.20605
$956$	−15.9787	−0.516789
$957$	0	0
$958$	−26.7082	−0.862903
$959$	20.9443	0.676326
$960$	−11.0902	−0.357934
$961$	2.22291	0.0717069
$962$	17.7082	0.570935
$963$	−20.2361	−0.652098
$964$	6.97871	0.224769
$965$	60.0689	1.93369
$966$	2.00000	0.0643489
$967$	−49.7082	−1.59851	−0.799254	−	0.600993i	$-0.794772\pi$
$967$	−49.7082	−1.59851	−0.799254	+	0.600993i	$0.794772\pi$
$968$	0	0
$969$	0	0
$970$	−72.0132	−2.31220
$971$	−11.2918	−0.362371	−0.181185	−	0.983449i	$-0.557993\pi$
$971$	−11.2918	−0.362371	−0.181185	+	0.983449i	$0.557993\pi$
$972$	0.618034	0.0198234
$973$	2.56231	0.0821438
$974$	−23.2705	−0.745635
$975$	1.85410	0.0593788
$976$	−49.6869	−1.59044
$977$	33.0000	1.05576	0.527882	−	0.849318i	$-0.322986\pi$
$977$	33.0000	1.05576	0.527882	+	0.849318i	$0.322986\pi$
$978$	37.2705	1.19178
$979$	0	0
$980$	−1.61803	−0.0516862
$981$	−12.5623	−0.401084
$982$	−15.7082	−0.501269
$983$	−12.0557	−0.384518	−0.192259	−	0.981344i	$-0.561581\pi$
$983$	−12.0557	−0.384518	−0.192259	+	0.981344i	$0.561581\pi$
$984$	13.6180	0.434127
$985$	−12.4721	−0.397395
$986$	2.56231	0.0816004
$987$	−8.32624	−0.265027
$988$	0	0
$989$	1.23607	0.0393047
$990$	0	0
$991$	−44.6312	−1.41776	−0.708878	−	0.705331i	$-0.750798\pi$
$991$	−44.6312	−1.41776	−0.708878	+	0.705331i	$0.750798\pi$
$992$	−19.4934	−0.618917
$993$	−1.29180	−0.0409939
$994$	2.38197	0.0755514
$995$	−32.8885	−1.04264
$996$	3.70820	0.117499
$997$	25.4164	0.804946	0.402473	−	0.915432i	$-0.368151\pi$
$997$	25.4164	0.804946	0.402473	+	0.915432i	$0.368151\pi$
$998$	8.09017	0.256090
$999$	−10.9443	−0.346261

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.s.1.1		2
3.2	odd	2		7623.2.a.bp.1.2		2
11.7	odd	10		231.2.j.d.148.1	yes	4
11.8	odd	10		231.2.j.d.64.1	✓	4
11.10	odd	2		2541.2.a.bb.1.2		2
33.8	even	10		693.2.m.b.64.1		4
33.29	even	10		693.2.m.b.379.1		4
33.32	even	2		7623.2.a.ba.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.d.64.1	✓	4	11.8	odd	10
231.2.j.d.148.1	yes	4	11.7	odd	10
693.2.m.b.64.1		4	33.8	even	10
693.2.m.b.379.1		4	33.29	even	10
2541.2.a.s.1.1		2	1.1	even	1	trivial
2541.2.a.bb.1.2		2	11.10	odd	2
7623.2.a.ba.1.1		2	33.32	even	2
7623.2.a.bp.1.2		2	3.2	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -2.61803 q^{5} -1.61803 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.61803 q^{2} +1.00000 q^{3} +0.618034 q^{4} -2.61803 q^{5} -1.61803 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +4.23607 q^{10} +0.618034 q^{12} +1.00000 q^{13} +1.61803 q^{14} -2.61803 q^{15} -4.85410 q^{16} -0.236068 q^{17} -1.61803 q^{18} -1.61803 q^{20} -1.00000 q^{21} +1.23607 q^{23} +2.23607 q^{24} +1.85410 q^{25} -1.61803 q^{26} +1.00000 q^{27} -0.618034 q^{28} +6.70820 q^{29} +4.23607 q^{30} -5.76393 q^{31} +3.38197 q^{32} +0.381966 q^{34} +2.61803 q^{35} +0.618034 q^{36} -10.9443 q^{37} +1.00000 q^{39} -5.85410 q^{40} +6.09017 q^{41} +1.61803 q^{42} +1.00000 q^{43} -2.61803 q^{45} -2.00000 q^{46} +8.32624 q^{47} -4.85410 q^{48} +1.00000 q^{49} -3.00000 q^{50} -0.236068 q^{51} +0.618034 q^{52} +5.38197 q^{53} -1.61803 q^{54} -2.23607 q^{56} -10.8541 q^{58} -10.8541 q^{59} -1.61803 q^{60} +10.2361 q^{61} +9.32624 q^{62} -1.00000 q^{63} +4.23607 q^{64} -2.61803 q^{65} -4.76393 q^{67} -0.145898 q^{68} +1.23607 q^{69} -4.23607 q^{70} +1.47214 q^{71} +2.23607 q^{72} +8.56231 q^{73} +17.7082 q^{74} +1.85410 q^{75} -1.61803 q^{78} -4.14590 q^{79} +12.7082 q^{80} +1.00000 q^{81} -9.85410 q^{82} +6.00000 q^{83} -0.618034 q^{84} +0.618034 q^{85} -1.61803 q^{86} +6.70820 q^{87} -8.61803 q^{89} +4.23607 q^{90} -1.00000 q^{91} +0.763932 q^{92} -5.76393 q^{93} -13.4721 q^{94} +3.38197 q^{96} -17.0000 q^{97} -1.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} - q^{4} - 3 q^{5} - q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 - q^4 - 3 * q^5 - q^6 - 2 * q^7 + 2 * q^9	\( 2 q - q^{2} + 2 q^{3} - q^{4} - 3 q^{5} - q^{6} - 2 q^{7} + 2 q^{9} + 4 q^{10} - q^{12} + 2 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - q^{18} - q^{20} - 2 q^{21} - 2 q^{23} - 3 q^{25} - q^{26} + 2 q^{27} + q^{28} + 4 q^{30} - 16 q^{31} + 9 q^{32} + 3 q^{34} + 3 q^{35} - q^{36} - 4 q^{37} + 2 q^{39} - 5 q^{40} + q^{41} + q^{42} + 2 q^{43} - 3 q^{45} - 4 q^{46} + q^{47} - 3 q^{48} + 2 q^{49} - 6 q^{50} + 4 q^{51} - q^{52} + 13 q^{53} - q^{54} - 15 q^{58} - 15 q^{59} - q^{60} + 16 q^{61} + 3 q^{62} - 2 q^{63} + 4 q^{64} - 3 q^{65} - 14 q^{67} - 7 q^{68} - 2 q^{69} - 4 q^{70} - 6 q^{71} - 3 q^{73} + 22 q^{74} - 3 q^{75} - q^{78} - 15 q^{79} + 12 q^{80} + 2 q^{81} - 13 q^{82} + 12 q^{83} + q^{84} - q^{85} - q^{86} - 15 q^{89} + 4 q^{90} - 2 q^{91} + 6 q^{92} - 16 q^{93} - 18 q^{94} + 9 q^{96} - 34 q^{97} - q^{98}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 - q^4 - 3 * q^5 - q^6 - 2 * q^7 + 2 * q^9 + 4 * q^10 - q^12 + 2 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - q^18 - q^20 - 2 * q^21 - 2 * q^23 - 3 * q^25 - q^26 + 2 * q^27 + q^28 + 4 * q^30 - 16 * q^31 + 9 * q^32 + 3 * q^34 + 3 * q^35 - q^36 - 4 * q^37 + 2 * q^39 - 5 * q^40 + q^41 + q^42 + 2 * q^43 - 3 * q^45 - 4 * q^46 + q^47 - 3 * q^48 + 2 * q^49 - 6 * q^50 + 4 * q^51 - q^52 + 13 * q^53 - q^54 - 15 * q^58 - 15 * q^59 - q^60 + 16 * q^61 + 3 * q^62 - 2 * q^63 + 4 * q^64 - 3 * q^65 - 14 * q^67 - 7 * q^68 - 2 * q^69 - 4 * q^70 - 6 * q^71 - 3 * q^73 + 22 * q^74 - 3 * q^75 - q^78 - 15 * q^79 + 12 * q^80 + 2 * q^81 - 13 * q^82 + 12 * q^83 + q^84 - q^85 - q^86 - 15 * q^89 + 4 * q^90 - 2 * q^91 + 6 * q^92 - 16 * q^93 - 18 * q^94 + 9 * q^96 - 34 * q^97 - q^98

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