LMFDB - Embedded newform 2541.2.a.bg.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:	$0$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*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			$2.11491$ 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)

$f(q)$	$=$	$q-2.47283 q^{2} +1.00000 q^{3} +4.11491 q^{4} -2.58774 q^{5} -2.47283 q^{6} +1.00000 q^{7} -5.22982 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.47283 q^{2} +1.00000 q^{3} +4.11491 q^{4} -2.58774 q^{5} -2.47283 q^{6} +1.00000 q^{7} -5.22982 q^{8} +1.00000 q^{9} +6.39905 q^{10} +4.11491 q^{12} +5.87189 q^{13} -2.47283 q^{14} -2.58774 q^{15} +4.70265 q^{16} -7.51396 q^{17} -2.47283 q^{18} +2.35793 q^{19} -10.6483 q^{20} +1.00000 q^{21} +6.94567 q^{23} -5.22982 q^{24} +1.69641 q^{25} -14.5202 q^{26} +1.00000 q^{27} +4.11491 q^{28} +5.87189 q^{29} +6.39905 q^{30} -3.66152 q^{31} -1.16924 q^{32} +18.5808 q^{34} -2.58774 q^{35} +4.11491 q^{36} +3.30359 q^{37} -5.83076 q^{38} +5.87189 q^{39} +13.5334 q^{40} -5.28415 q^{41} -2.47283 q^{42} -7.40530 q^{43} -2.58774 q^{45} -17.1755 q^{46} +7.53341 q^{47} +4.70265 q^{48} +1.00000 q^{49} -4.19493 q^{50} -7.51396 q^{51} +24.1623 q^{52} -4.22982 q^{53} -2.47283 q^{54} -5.22982 q^{56} +2.35793 q^{57} -14.5202 q^{58} -0.926221 q^{59} -10.6483 q^{60} +2.00000 q^{61} +9.05433 q^{62} +1.00000 q^{63} -6.51396 q^{64} -15.1949 q^{65} -10.1017 q^{67} -30.9193 q^{68} +6.94567 q^{69} +6.39905 q^{70} +4.45963 q^{71} -5.22982 q^{72} +2.12811 q^{73} -8.16924 q^{74} +1.69641 q^{75} +9.70265 q^{76} -14.5202 q^{78} +4.45963 q^{79} -12.1692 q^{80} +1.00000 q^{81} +13.0668 q^{82} +10.6894 q^{83} +4.11491 q^{84} +19.4442 q^{85} +18.3121 q^{86} +5.87189 q^{87} +15.8913 q^{89} +6.39905 q^{90} +5.87189 q^{91} +28.5808 q^{92} -3.66152 q^{93} -18.6289 q^{94} -6.10170 q^{95} -1.16924 q^{96} +10.1212 q^{97} -2.47283 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} + 3 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 + 3 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 2 q^{2} + 3 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 11 q^{10} + 6 q^{12} + 4 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 8 q^{17} - 2 q^{18} + 8 q^{19} - 3 q^{20} + 3 q^{21} + 10 q^{23} - 3 q^{24} + 15 q^{25} - q^{26} + 3 q^{27} + 6 q^{28} + 4 q^{29} + 11 q^{30} - 2 q^{31} - 8 q^{32} - 4 q^{34} + 4 q^{35} + 6 q^{36} - 13 q^{38} + 4 q^{39} + 18 q^{40} - 14 q^{41} - 2 q^{42} + 14 q^{43} + 4 q^{45} - 28 q^{46} - 4 q^{48} + 3 q^{49} + 19 q^{50} - 8 q^{51} + 29 q^{52} - 2 q^{54} - 3 q^{56} + 8 q^{57} - q^{58} - 3 q^{60} + 6 q^{61} + 38 q^{62} + 3 q^{63} - 5 q^{64} - 14 q^{65} - 4 q^{67} - 42 q^{68} + 10 q^{69} + 11 q^{70} - 12 q^{71} - 3 q^{72} + 20 q^{73} - 29 q^{74} + 15 q^{75} + 11 q^{76} - q^{78} - 12 q^{79} - 41 q^{80} + 3 q^{81} - 6 q^{82} - 6 q^{83} + 6 q^{84} + 6 q^{85} + 24 q^{86} + 4 q^{87} + 26 q^{89} + 11 q^{90} + 4 q^{91} + 26 q^{92} - 2 q^{93} - 35 q^{94} + 8 q^{95} - 8 q^{96} - 4 q^{97} - 2 q^{98}+O(q^{100}) $ 3 * q - 2 * q^2 + 3 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 11 * q^10 + 6 * q^12 + 4 * q^13 - 2 * q^14 + 4 * q^15 - 4 * q^16 - 8 * q^17 - 2 * q^18 + 8 * q^19 - 3 * q^20 + 3 * q^21 + 10 * q^23 - 3 * q^24 + 15 * q^25 - q^26 + 3 * q^27 + 6 * q^28 + 4 * q^29 + 11 * q^30 - 2 * q^31 - 8 * q^32 - 4 * q^34 + 4 * q^35 + 6 * q^36 - 13 * q^38 + 4 * q^39 + 18 * q^40 - 14 * q^41 - 2 * q^42 + 14 * q^43 + 4 * q^45 - 28 * q^46 - 4 * q^48 + 3 * q^49 + 19 * q^50 - 8 * q^51 + 29 * q^52 - 2 * q^54 - 3 * q^56 + 8 * q^57 - q^58 - 3 * q^60 + 6 * q^61 + 38 * q^62 + 3 * q^63 - 5 * q^64 - 14 * q^65 - 4 * q^67 - 42 * q^68 + 10 * q^69 + 11 * q^70 - 12 * q^71 - 3 * q^72 + 20 * q^73 - 29 * q^74 + 15 * q^75 + 11 * q^76 - q^78 - 12 * q^79 - 41 * q^80 + 3 * q^81 - 6 * q^82 - 6 * q^83 + 6 * q^84 + 6 * q^85 + 24 * q^86 + 4 * q^87 + 26 * q^89 + 11 * q^90 + 4 * q^91 + 26 * q^92 - 2 * q^93 - 35 * q^94 + 8 * q^95 - 8 * q^96 - 4 * q^97 - 2 * 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 $

$2$	−2.47283	−1.74856	−0.874279	−	0.485424i	$-0.838665\pi$
$2$	−2.47283	−1.74856	−0.874279	+	0.485424i	$0.838665\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.11491	2.05745
$5$	−2.58774	−1.15727	−0.578637	−	0.815586i	$-0.696415\pi$
$5$	−2.58774	−1.15727	−0.578637	+	0.815586i	$0.696415\pi$
$6$	−2.47283	−1.00953
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−5.22982	−1.84902
$9$	1.00000	0.333333
$10$	6.39905	2.02356
$11$	0	0
$11$	0	0
$12$	4.11491	1.18787
$13$	5.87189	1.62857	0.814284	−	0.580466i	$-0.197130\pi$
$13$	5.87189	1.62857	0.814284	+	0.580466i	$0.197130\pi$
$14$	−2.47283	−0.660893
$15$	−2.58774	−0.668152
$16$	4.70265	1.17566
$17$	−7.51396	−1.82240	−0.911202	−	0.411960i	$-0.864844\pi$
$17$	−7.51396	−1.82240	−0.911202	+	0.411960i	$0.864844\pi$
$18$	−2.47283	−0.582853
$19$	2.35793	0.540945	0.270473	−	0.962728i	$-0.412820\pi$
$19$	2.35793	0.540945	0.270473	+	0.962728i	$0.412820\pi$
$20$	−10.6483	−2.38104
$21$	1.00000	0.218218
$22$	0	0
$23$	6.94567	1.44827	0.724136	−	0.689657i	$-0.242239\pi$
$23$	6.94567	1.44827	0.724136	+	0.689657i	$0.242239\pi$
$24$	−5.22982	−1.06753
$25$	1.69641	0.339281
$26$	−14.5202	−2.84765
$27$	1.00000	0.192450
$28$	4.11491	0.777644
$29$	5.87189	1.09038	0.545191	−	0.838312i	$-0.316457\pi$
$29$	5.87189	1.09038	0.545191	+	0.838312i	$0.316457\pi$
$30$	6.39905	1.16830
$31$	−3.66152	−0.657629	−0.328814	−	0.944395i	$-0.606649\pi$
$31$	−3.66152	−0.657629	−0.328814	+	0.944395i	$0.606649\pi$
$32$	−1.16924	−0.206694
$33$	0	0
$34$	18.5808	3.18658
$35$	−2.58774	−0.437408
$36$	4.11491	0.685818
$37$	3.30359	0.543108	0.271554	−	0.962423i	$-0.412463\pi$
$37$	3.30359	0.543108	0.271554	+	0.962423i	$0.412463\pi$
$38$	−5.83076	−0.945874
$39$	5.87189	0.940255
$40$	13.5334	2.13982
$41$	−5.28415	−0.825245	−0.412623	−	0.910902i	$-0.635387\pi$
$41$	−5.28415	−0.825245	−0.412623	+	0.910902i	$0.635387\pi$
$42$	−2.47283	−0.381567
$43$	−7.40530	−1.12930	−0.564649	−	0.825331i	$-0.690988\pi$
$43$	−7.40530	−1.12930	−0.564649	+	0.825331i	$0.690988\pi$
$44$	0	0
$45$	−2.58774	−0.385758
$46$	−17.1755	−2.53239
$47$	7.53341	1.09886	0.549430	−	0.835540i	$-0.314845\pi$
$47$	7.53341	1.09886	0.549430	+	0.835540i	$0.314845\pi$
$48$	4.70265	0.678769
$49$	1.00000	0.142857
$50$	−4.19493	−0.593253
$51$	−7.51396	−1.05217
$52$	24.1623	3.35071
$53$	−4.22982	−0.581010	−0.290505	−	0.956874i	$-0.593823\pi$
$53$	−4.22982	−0.581010	−0.290505	+	0.956874i	$0.593823\pi$
$54$	−2.47283	−0.336510
$55$	0	0
$56$	−5.22982	−0.698863
$57$	2.35793	0.312315
$58$	−14.5202	−1.90660
$59$	−0.926221	−0.120584	−0.0602918	−	0.998181i	$-0.519203\pi$
$59$	−0.926221	−0.120584	−0.0602918	+	0.998181i	$0.519203\pi$
$60$	−10.6483	−1.37469
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	9.05433	1.14990
$63$	1.00000	0.125988
$64$	−6.51396	−0.814245
$65$	−15.1949	−1.88470
$66$	0	0
$67$	−10.1017	−1.23412	−0.617060	−	0.786916i	$-0.711676\pi$
$67$	−10.1017	−1.23412	−0.617060	+	0.786916i	$0.711676\pi$
$68$	−30.9193	−3.74951
$69$	6.94567	0.836160
$70$	6.39905	0.764833
$71$	4.45963	0.529261	0.264630	−	0.964350i	$-0.414750\pi$
$71$	4.45963	0.529261	0.264630	+	0.964350i	$0.414750\pi$
$72$	−5.22982	−0.616340
$73$	2.12811	0.249077	0.124538	−	0.992215i	$-0.460255\pi$
$73$	2.12811	0.249077	0.124538	+	0.992215i	$0.460255\pi$
$74$	−8.16924	−0.949655
$75$	1.69641	0.195884
$76$	9.70265	1.11297
$77$	0	0
$78$	−14.5202	−1.64409
$79$	4.45963	0.501748	0.250874	−	0.968020i	$-0.419282\pi$
$79$	4.45963	0.501748	0.250874	+	0.968020i	$0.419282\pi$
$80$	−12.1692	−1.36056
$81$	1.00000	0.111111
$82$	13.0668	1.44299
$83$	10.6894	1.17332	0.586660	−	0.809834i	$-0.300443\pi$
$83$	10.6894	1.17332	0.586660	+	0.809834i	$0.300443\pi$
$84$	4.11491	0.448973
$85$	19.4442	2.10902
$86$	18.3121	1.97464
$87$	5.87189	0.629533
$88$	0	0
$89$	15.8913	1.68448	0.842239	−	0.539104i	$-0.181237\pi$
$89$	15.8913	1.68448	0.842239	+	0.539104i	$0.181237\pi$
$90$	6.39905	0.674520
$91$	5.87189	0.615541
$92$	28.5808	2.97975
$93$	−3.66152	−0.379682
$94$	−18.6289	−1.92142
$95$	−6.10170	−0.626022
$96$	−1.16924	−0.119335
$97$	10.1212	1.02765	0.513824	−	0.857896i	$-0.328229\pi$
$97$	10.1212	1.02765	0.513824	+	0.857896i	$0.328229\pi$
$98$	−2.47283	−0.249794
$99$	0	0
$100$	6.98055	0.698055
$101$	13.4053	1.33388	0.666939	−	0.745113i	$-0.267604\pi$
$101$	13.4053	1.33388	0.666939	+	0.745113i	$0.267604\pi$
$102$	18.5808	1.83977
$103$	−4.71585	−0.464667	−0.232333	−	0.972636i	$-0.574636\pi$
$103$	−4.71585	−0.464667	−0.232333	+	0.972636i	$0.574636\pi$
$104$	−30.7089	−3.01125
$105$	−2.58774	−0.252538
$106$	10.4596	1.01593
$107$	−7.07378	−0.683848	−0.341924	−	0.939728i	$-0.611079\pi$
$107$	−7.07378	−0.683848	−0.341924	+	0.939728i	$0.611079\pi$
$108$	4.11491	0.395957
$109$	−18.8370	−1.80426	−0.902129	−	0.431467i	$-0.857996\pi$
$109$	−18.8370	−1.80426	−0.902129	+	0.431467i	$0.857996\pi$
$110$	0	0
$111$	3.30359	0.313563
$112$	4.70265	0.444359
$113$	−9.02792	−0.849276	−0.424638	−	0.905363i	$-0.639599\pi$
$113$	−9.02792	−0.849276	−0.424638	+	0.905363i	$0.639599\pi$
$114$	−5.83076	−0.546101
$115$	−17.9736	−1.67605
$116$	24.1623	2.24341
$117$	5.87189	0.542856
$118$	2.29039	0.210848
$119$	−7.51396	−0.688804
$120$	13.5334	1.23543
$121$	0	0
$122$	−4.94567	−0.447760
$123$	−5.28415	−0.476456
$124$	−15.0668	−1.35304
$125$	8.54885	0.764632
$126$	−2.47283	−0.220298
$127$	10.2298	0.907749	0.453875	−	0.891066i	$-0.350041\pi$
$127$	10.2298	0.907749	0.453875	+	0.891066i	$0.350041\pi$
$128$	18.4464	1.63045
$129$	−7.40530	−0.652000
$130$	37.5745	3.29550
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	0	0
$133$	2.35793	0.204458
$134$	24.9798	2.15793
$135$	−2.58774	−0.222717
$136$	39.2966	3.36966
$137$	−10.8370	−0.925868	−0.462934	−	0.886393i	$-0.653203\pi$
$137$	−10.8370	−0.925868	−0.462934	+	0.886393i	$0.653203\pi$
$138$	−17.1755	−1.46207
$139$	−0.459630	−0.0389853	−0.0194927	−	0.999810i	$-0.506205\pi$
$139$	−0.459630	−0.0389853	−0.0194927	+	0.999810i	$0.506205\pi$
$140$	−10.6483	−0.899947
$141$	7.53341	0.634428
$142$	−11.0279	−0.925443
$143$	0	0
$144$	4.70265	0.391887
$145$	−15.1949	−1.26187
$146$	−5.26247	−0.435525
$147$	1.00000	0.0824786
$148$	13.5940	1.11742
$149$	−11.0474	−0.905036	−0.452518	−	0.891755i	$-0.649474\pi$
$149$	−11.0474	−0.905036	−0.452518	+	0.891755i	$0.649474\pi$
$150$	−4.19493	−0.342515
$151$	16.1212	1.31192	0.655960	−	0.754795i	$-0.272264\pi$
$151$	16.1212	1.31192	0.655960	+	0.754795i	$0.272264\pi$
$152$	−12.3315	−1.00022
$153$	−7.51396	−0.607468
$154$	0	0
$155$	9.47507	0.761056
$156$	24.1623	1.93453
$157$	13.0668	1.04285	0.521423	−	0.853298i	$-0.325401\pi$
$157$	13.0668	1.04285	0.521423	+	0.853298i	$0.325401\pi$
$158$	−11.0279	−0.877335
$159$	−4.22982	−0.335446
$160$	3.02569	0.239202
$161$	6.94567	0.547395
$162$	−2.47283	−0.194284
$163$	−10.1017	−0.791227	−0.395613	−	0.918417i	$-0.629468\pi$
$163$	−10.1017	−0.791227	−0.395613	+	0.918417i	$0.629468\pi$
$164$	−21.7438	−1.69790
$165$	0	0
$166$	−26.4332	−2.05162
$167$	10.4860	0.811434	0.405717	−	0.913999i	$-0.367022\pi$
$167$	10.4860	0.811434	0.405717	+	0.913999i	$0.367022\pi$
$168$	−5.22982	−0.403489
$169$	21.4791	1.65224
$170$	−48.0823	−3.68774
$171$	2.35793	0.180315
$172$	−30.4721	−2.32348
$173$	−14.4985	−1.10230	−0.551151	−	0.834405i	$-0.685811\pi$
$173$	−14.4985	−1.10230	−0.551151	+	0.834405i	$0.685811\pi$
$174$	−14.5202	−1.10077
$175$	1.69641	0.128236
$176$	0	0
$177$	−0.926221	−0.0696190
$178$	−39.2966	−2.94541
$179$	14.3510	1.07264	0.536321	−	0.844014i	$-0.319814\pi$
$179$	14.3510	1.07264	0.536321	+	0.844014i	$0.319814\pi$
$180$	−10.6483	−0.793679
$181$	9.66152	0.718135	0.359068	−	0.933312i	$-0.383095\pi$
$181$	9.66152	0.718135	0.359068	+	0.933312i	$0.383095\pi$
$182$	−14.5202	−1.07631
$183$	2.00000	0.147844
$184$	−36.3246	−2.67788
$185$	−8.54885	−0.628524
$186$	9.05433	0.663896
$187$	0	0
$188$	30.9993	2.26086
$189$	1.00000	0.0727393
$190$	15.0885	1.09463
$191$	−9.55286	−0.691220	−0.345610	−	0.938378i	$-0.612328\pi$
$191$	−9.55286	−0.691220	−0.345610	+	0.938378i	$0.612328\pi$
$192$	−6.51396	−0.470105
$193$	22.1212	1.59232	0.796158	−	0.605089i	$-0.206863\pi$
$193$	22.1212	1.59232	0.796158	+	0.605089i	$0.206863\pi$
$194$	−25.0279	−1.79690
$195$	−15.1949	−1.08813
$196$	4.11491	0.293922
$197$	26.2423	1.86969	0.934843	−	0.355061i	$-0.115540\pi$
$197$	26.2423	1.86969	0.934843	+	0.355061i	$0.115540\pi$
$198$	0	0
$199$	1.05433	0.0747396	0.0373698	−	0.999302i	$-0.488102\pi$
$199$	1.05433	0.0747396	0.0373698	+	0.999302i	$0.488102\pi$
$200$	−8.87189	−0.627337
$201$	−10.1017	−0.712519
$202$	−33.1491	−2.33236
$203$	5.87189	0.412126
$204$	−30.9193	−2.16478
$205$	13.6740	0.955034
$206$	11.6615	0.812497
$207$	6.94567	0.482757
$208$	27.6134	1.91465
$209$	0	0
$210$	6.39905	0.441577
$211$	8.71585	0.600024	0.300012	−	0.953935i	$-0.403009\pi$
$211$	8.71585	0.600024	0.300012	+	0.953935i	$0.403009\pi$
$212$	−17.4053	−1.19540
$213$	4.45963	0.305569
$214$	17.4923	1.19575
$215$	19.1630	1.30691
$216$	−5.22982	−0.355844
$217$	−3.66152	−0.248560
$218$	46.5808	3.15485
$219$	2.12811	0.143804
$220$	0	0
$221$	−44.1212	−2.96791
$222$	−8.16924	−0.548283
$223$	−23.7438	−1.59000	−0.795000	−	0.606609i	$-0.792529\pi$
$223$	−23.7438	−1.59000	−0.795000	+	0.606609i	$0.792529\pi$
$224$	−1.16924	−0.0781231
$225$	1.69641	0.113094
$226$	22.3246	1.48501
$227$	13.1755	0.874488	0.437244	−	0.899343i	$-0.355955\pi$
$227$	13.1755	0.874488	0.437244	+	0.899343i	$0.355955\pi$
$228$	9.70265	0.642574
$229$	13.3664	0.883277	0.441638	−	0.897193i	$-0.354397\pi$
$229$	13.3664	0.883277	0.441638	+	0.897193i	$0.354397\pi$
$230$	44.4457	2.93066
$231$	0	0
$232$	−30.7089	−2.01614
$233$	−7.13659	−0.467533	−0.233767	−	0.972293i	$-0.575105\pi$
$233$	−7.13659	−0.467533	−0.233767	+	0.972293i	$0.575105\pi$
$234$	−14.5202	−0.949216
$235$	−19.4945	−1.27168
$236$	−3.81131	−0.248095
$237$	4.45963	0.289684
$238$	18.5808	1.20441
$239$	19.9930	1.29324	0.646621	−	0.762811i	$-0.276182\pi$
$239$	19.9930	1.29324	0.646621	+	0.762811i	$0.276182\pi$
$240$	−12.1692	−0.785521
$241$	9.19493	0.592297	0.296149	−	0.955142i	$-0.404298\pi$
$241$	9.19493	0.592297	0.296149	+	0.955142i	$0.404298\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	8.22982	0.526860
$245$	−2.58774	−0.165325
$246$	13.0668	0.833110
$247$	13.8455	0.880967
$248$	19.1491	1.21597
$249$	10.6894	0.677416
$250$	−21.1399	−1.33700
$251$	−9.42474	−0.594885	−0.297442	−	0.954740i	$-0.596134\pi$
$251$	−9.42474	−0.594885	−0.297442	+	0.954740i	$0.596134\pi$
$252$	4.11491	0.259215
$253$	0	0
$254$	−25.2966	−1.58725
$255$	19.4442	1.21764
$256$	−32.5870	−2.03669
$257$	−0.0194469	−0.00121307	−0.000606533	−	1.00000i	$-0.500193\pi$
$257$	−0.0194469	−0.00121307	−0.000606533		1.00000i	$0.500193\pi$
$258$	18.3121	1.14006
$259$	3.30359	0.205275
$260$	−62.5257	−3.87768
$261$	5.87189	0.363461
$262$	9.89134	0.611089
$263$	−27.9930	−1.72612	−0.863062	−	0.505097i	$-0.831457\pi$
$263$	−27.9930	−1.72612	−0.863062	+	0.505097i	$0.831457\pi$
$264$	0	0
$265$	10.9457	0.672387
$266$	−5.83076	−0.357507
$267$	15.8913	0.972534
$268$	−41.5676	−2.53914
$269$	30.9193	1.88518	0.942590	−	0.333951i	$-0.108382\pi$
$269$	30.9193	1.88518	0.942590	+	0.333951i	$0.108382\pi$
$270$	6.39905	0.389434
$271$	22.3579	1.35815	0.679074	−	0.734070i	$-0.262382\pi$
$271$	22.3579	1.35815	0.679074	+	0.734070i	$0.262382\pi$
$272$	−35.3355	−2.14253
$273$	5.87189	0.355383
$274$	26.7981	1.61893
$275$	0	0
$276$	28.5808	1.72036
$277$	−24.7717	−1.48839	−0.744194	−	0.667964i	$-0.767166\pi$
$277$	−24.7717	−1.48839	−0.744194	+	0.667964i	$0.767166\pi$
$278$	1.13659	0.0681681
$279$	−3.66152	−0.219210
$280$	13.5334	0.808776
$281$	1.19493	0.0712835	0.0356418	−	0.999365i	$-0.488652\pi$
$281$	1.19493	0.0712835	0.0356418	+	0.999365i	$0.488652\pi$
$282$	−18.6289	−1.10933
$283$	15.5723	0.925677	0.462839	−	0.886443i	$-0.346831\pi$
$283$	15.5723	0.925677	0.462839	+	0.886443i	$0.346831\pi$
$284$	18.3510	1.08893
$285$	−6.10170	−0.361434
$286$	0	0
$287$	−5.28415	−0.311913
$288$	−1.16924	−0.0688981
$289$	39.4596	2.32115
$290$	37.5745	2.20645
$291$	10.1212	0.593312
$292$	8.75698	0.512464
$293$	9.74378	0.569238	0.284619	−	0.958641i	$-0.408133\pi$
$293$	9.74378	0.569238	0.284619	+	0.958641i	$0.408133\pi$
$294$	−2.47283	−0.144219
$295$	2.39682	0.139548
$296$	−17.2772	−1.00422
$297$	0	0
$298$	27.3183	1.58251
$299$	40.7842	2.35861
$300$	6.98055	0.403022
$301$	−7.40530	−0.426834
$302$	−39.8649	−2.29397
$303$	13.4053	0.770114
$304$	11.0885	0.635969
$305$	−5.17548	−0.296347
$306$	18.5808	1.06219
$307$	−6.35097	−0.362469	−0.181234	−	0.983440i	$-0.558009\pi$
$307$	−6.35097	−0.362469	−0.181234	+	0.983440i	$0.558009\pi$
$308$	0	0
$309$	−4.71585	−0.268275
$310$	−23.4303	−1.33075
$311$	8.00000	0.453638	0.226819	−	0.973937i	$-0.427167\pi$
$311$	8.00000	0.453638	0.226819	+	0.973937i	$0.427167\pi$
$312$	−30.7089	−1.73855
$313$	16.9457	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$313$	16.9457	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$314$	−32.3121	−1.82348
$315$	−2.58774	−0.145803
$316$	18.3510	1.03232
$317$	20.0125	1.12401	0.562007	−	0.827133i	$-0.310030\pi$
$317$	20.0125	1.12401	0.562007	+	0.827133i	$0.310030\pi$
$318$	10.4596	0.586547
$319$	0	0
$320$	16.8565	0.942304
$321$	−7.07378	−0.394820
$322$	−17.1755	−0.957152
$323$	−17.7174	−0.985821
$324$	4.11491	0.228606
$325$	9.96111	0.552543
$326$	24.9798	1.38351
$327$	−18.8370	−1.04169
$328$	27.6351	1.52589
$329$	7.53341	0.415330
$330$	0	0
$331$	7.54037	0.414456	0.207228	−	0.978293i	$-0.433556\pi$
$331$	7.54037	0.414456	0.207228	+	0.978293i	$0.433556\pi$
$332$	43.9861	2.41405
$333$	3.30359	0.181036
$334$	−25.9302	−1.41884
$335$	26.1406	1.42821
$336$	4.70265	0.256551
$337$	12.6894	0.691238	0.345619	−	0.938375i	$-0.387669\pi$
$337$	12.6894	0.691238	0.345619	+	0.938375i	$0.387669\pi$
$338$	−53.1142	−2.88903
$339$	−9.02792	−0.490330
$340$	80.0111	4.33921
$341$	0	0
$342$	−5.83076	−0.315291
$343$	1.00000	0.0539949
$344$	38.7283	2.08809
$345$	−17.9736	−0.967666
$346$	35.8524	1.92744
$347$	−1.13659	−0.0610153	−0.0305076	−	0.999535i	$-0.509712\pi$
$347$	−1.13659	−0.0610153	−0.0305076	+	0.999535i	$0.509712\pi$
$348$	24.1623	1.29523
$349$	14.7911	0.791752	0.395876	−	0.918304i	$-0.370441\pi$
$349$	14.7911	0.791752	0.395876	+	0.918304i	$0.370441\pi$
$350$	−4.19493	−0.224228
$351$	5.87189	0.313418
$352$	0	0
$353$	−7.52092	−0.400298	−0.200149	−	0.979765i	$-0.564143\pi$
$353$	−7.52092	−0.400298	−0.200149	+	0.979765i	$0.564143\pi$
$354$	2.29039	0.121733
$355$	−11.5404	−0.612499
$356$	65.3914	3.46574
$357$	−7.51396	−0.397681
$358$	−35.4876	−1.87558
$359$	17.5962	0.928693	0.464346	−	0.885654i	$-0.346289\pi$
$359$	17.5962	0.928693	0.464346	+	0.885654i	$0.346289\pi$
$360$	13.5334	0.713273
$361$	−13.4402	−0.707378
$362$	−23.8913	−1.25570
$363$	0	0
$364$	24.1623	1.26645
$365$	−5.50700	−0.288250
$366$	−4.94567	−0.258514
$367$	14.3121	0.747084	0.373542	−	0.927613i	$-0.378143\pi$
$367$	14.3121	0.747084	0.373542	+	0.927613i	$0.378143\pi$
$368$	32.6630	1.70268
$369$	−5.28415	−0.275082
$370$	21.1399	1.09901
$371$	−4.22982	−0.219601
$372$	−15.0668	−0.781178
$373$	16.4332	0.850880	0.425440	−	0.904987i	$-0.360119\pi$
$373$	16.4332	0.850880	0.425440	+	0.904987i	$0.360119\pi$
$374$	0	0
$375$	8.54885	0.441461
$376$	−39.3983	−2.03181
$377$	34.4791	1.77576
$378$	−2.47283	−0.127189
$379$	19.5334	1.00336	0.501682	−	0.865052i	$-0.332715\pi$
$379$	19.5334	1.00336	0.501682	+	0.865052i	$0.332715\pi$
$380$	−25.1079	−1.28801
$381$	10.2298	0.524089
$382$	23.6226	1.20864
$383$	2.35097	0.120129	0.0600644	−	0.998195i	$-0.480869\pi$
$383$	2.35097	0.120129	0.0600644	+	0.998195i	$0.480869\pi$
$384$	18.4464	0.941340
$385$	0	0
$386$	−54.7019	−2.78426
$387$	−7.40530	−0.376432
$388$	41.6476	2.11434
$389$	−1.74378	−0.0884130	−0.0442065	−	0.999022i	$-0.514076\pi$
$389$	−1.74378	−0.0884130	−0.0442065	+	0.999022i	$0.514076\pi$
$390$	37.5745	1.90266
$391$	−52.1895	−2.63934
$392$	−5.22982	−0.264146
$393$	−4.00000	−0.201773
$394$	−64.8929	−3.26925
$395$	−11.5404	−0.580659
$396$	0	0
$397$	6.54189	0.328328	0.164164	−	0.986433i	$-0.447507\pi$
$397$	6.54189	0.328328	0.164164	+	0.986433i	$0.447507\pi$
$398$	−2.60719	−0.130687
$399$	2.35793	0.118044
$400$	7.97760	0.398880
$401$	5.66152	0.282723	0.141361	−	0.989958i	$-0.454852\pi$
$401$	5.66152	0.282723	0.141361	+	0.989958i	$0.454852\pi$
$402$	24.9798	1.24588
$403$	−21.5000	−1.07099
$404$	55.1616	2.74439
$405$	−2.58774	−0.128586
$406$	−14.5202	−0.720626
$407$	0	0
$408$	39.2966	1.94547
$409$	5.48755	0.271342	0.135671	−	0.990754i	$-0.456681\pi$
$409$	5.48755	0.271342	0.135671	+	0.990754i	$0.456681\pi$
$410$	−33.8135	−1.66993
$411$	−10.8370	−0.534550
$412$	−19.4053	−0.956030
$413$	−0.926221	−0.0455764
$414$	−17.1755	−0.844129
$415$	−27.6615	−1.35785
$416$	−6.86565	−0.336616
$417$	−0.459630	−0.0225082
$418$	0	0
$419$	8.24926	0.403003	0.201501	−	0.979488i	$-0.435418\pi$
$419$	8.24926	0.403003	0.201501	+	0.979488i	$0.435418\pi$
$420$	−10.6483	−0.519585
$421$	32.2617	1.57234	0.786171	−	0.618009i	$-0.212061\pi$
$421$	32.2617	1.57234	0.786171	+	0.618009i	$0.212061\pi$
$422$	−21.5529	−1.04918
$423$	7.53341	0.366287
$424$	22.1212	1.07430
$425$	−12.7467	−0.618307
$426$	−11.0279	−0.534305
$427$	2.00000	0.0967868
$428$	−29.1079	−1.40699
$429$	0	0
$430$	−47.3869	−2.28520
$431$	23.2772	1.12122	0.560611	−	0.828079i	$-0.310566\pi$
$431$	23.2772	1.12122	0.560611	+	0.828079i	$0.310566\pi$
$432$	4.70265	0.226256
$433$	−15.9302	−0.765558	−0.382779	−	0.923840i	$-0.625033\pi$
$433$	−15.9302	−0.765558	−0.382779	+	0.923840i	$0.625033\pi$
$434$	9.05433	0.434622
$435$	−15.1949	−0.728541
$436$	−77.5125	−3.71218
$437$	16.3774	0.783436
$438$	−5.26247	−0.251450
$439$	−22.8565	−1.09088	−0.545439	−	0.838150i	$-0.683637\pi$
$439$	−22.8565	−1.09088	−0.545439	+	0.838150i	$0.683637\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	109.104	5.18956
$443$	21.5962	1.02607	0.513034	−	0.858368i	$-0.328522\pi$
$443$	21.5962	1.02607	0.513034	+	0.858368i	$0.328522\pi$
$444$	13.5940	0.645142
$445$	−41.1227	−1.94940
$446$	58.7144	2.78021
$447$	−11.0474	−0.522523
$448$	−6.51396	−0.307756
$449$	18.6630	0.880763	0.440382	−	0.897811i	$-0.354843\pi$
$449$	18.6630	0.880763	0.440382	+	0.897811i	$0.354843\pi$
$450$	−4.19493	−0.197751
$451$	0	0
$452$	−37.1491	−1.74735
$453$	16.1212	0.757438
$454$	−32.5808	−1.52909
$455$	−15.1949	−0.712349
$456$	−12.3315	−0.577476
$457$	−36.4721	−1.70609	−0.853047	−	0.521834i	$-0.825248\pi$
$457$	−36.4721	−1.70609	−0.853047	+	0.521834i	$0.825248\pi$
$458$	−33.0529	−1.54446
$459$	−7.51396	−0.350722
$460$	−73.9597	−3.44839
$461$	−7.17548	−0.334196	−0.167098	−	0.985940i	$-0.553440\pi$
$461$	−7.17548	−0.334196	−0.167098	+	0.985940i	$0.553440\pi$
$462$	0	0
$463$	−0.452670	−0.0210373	−0.0105187	−	0.999945i	$-0.503348\pi$
$463$	−0.452670	−0.0210373	−0.0105187	+	0.999945i	$0.503348\pi$
$464$	27.6134	1.28192
$465$	9.47507	0.439396
$466$	17.6476	0.817509
$467$	−9.68097	−0.447982	−0.223991	−	0.974591i	$-0.571909\pi$
$467$	−9.68097	−0.447982	−0.223991	+	0.974591i	$0.571909\pi$
$468$	24.1623	1.11690
$469$	−10.1017	−0.466453
$470$	48.2067	2.22361
$471$	13.0668	0.602087
$472$	4.84396	0.222962
$473$	0	0
$474$	−11.0279	−0.506529
$475$	4.00000	0.183533
$476$	−30.9193	−1.41718
$477$	−4.22982	−0.193670
$478$	−49.4395	−2.26131
$479$	−24.3635	−1.11319	−0.556597	−	0.830782i	$-0.687893\pi$
$479$	−24.3635	−1.11319	−0.556597	+	0.830782i	$0.687893\pi$
$480$	3.02569	0.138103
$481$	19.3983	0.884488
$482$	−22.7375	−1.03567
$483$	6.94567	0.316039
$484$	0	0
$485$	−26.1909	−1.18927
$486$	−2.47283	−0.112170
$487$	−19.2702	−0.873217	−0.436609	−	0.899652i	$-0.643821\pi$
$487$	−19.2702	−0.873217	−0.436609	+	0.899652i	$0.643821\pi$
$488$	−10.4596	−0.473485
$489$	−10.1017	−0.456815
$490$	6.39905	0.289080
$491$	−29.6421	−1.33773	−0.668864	−	0.743385i	$-0.733219\pi$
$491$	−29.6421	−1.33773	−0.668864	+	0.743385i	$0.733219\pi$
$492$	−21.7438	−0.980285
$493$	−44.1212	−1.98712
$494$	−34.2376	−1.54042
$495$	0	0
$496$	−17.2188	−0.773149
$497$	4.45963	0.200042
$498$	−26.4332	−1.18450
$499$	29.3719	1.31487	0.657434	−	0.753512i	$-0.271642\pi$
$499$	29.3719	1.31487	0.657434	+	0.753512i	$0.271642\pi$
$500$	35.1777	1.57320
$501$	10.4860	0.468482
$502$	23.3058	1.04019
$503$	−12.5947	−0.561570	−0.280785	−	0.959771i	$-0.590595\pi$
$503$	−12.5947	−0.561570	−0.280785	+	0.959771i	$0.590595\pi$
$504$	−5.22982	−0.232954
$505$	−34.6894	−1.54366
$506$	0	0
$507$	21.4791	0.953919
$508$	42.0947	1.86765
$509$	−15.2144	−0.674365	−0.337183	−	0.941439i	$-0.609474\pi$
$509$	−15.2144	−0.674365	−0.337183	+	0.941439i	$0.609474\pi$
$510$	−48.0823	−2.12912
$511$	2.12811	0.0941421
$512$	43.6894	1.93082
$513$	2.35793	0.104105
$514$	0.0480890	0.00212112
$515$	12.2034	0.537746
$516$	−30.4721	−1.34146
$517$	0	0
$518$	−8.16924	−0.358936
$519$	−14.4985	−0.636415
$520$	79.4667	3.48484
$521$	20.5180	0.898909	0.449454	−	0.893303i	$-0.351618\pi$
$521$	20.5180	0.898909	0.449454	+	0.893303i	$0.351618\pi$
$522$	−14.5202	−0.635532
$523$	29.8844	1.30675	0.653376	−	0.757033i	$-0.273352\pi$
$523$	29.8844	1.30675	0.653376	+	0.757033i	$0.273352\pi$
$524$	−16.4596	−0.719042
$525$	1.69641	0.0740372
$526$	69.2221	3.01823
$527$	27.5125	1.19846
$528$	0	0
$529$	25.2423	1.09749
$530$	−27.0668	−1.17571
$531$	−0.926221	−0.0401946
$532$	9.70265	0.420663
$533$	−31.0279	−1.34397
$534$	−39.2966	−1.70053
$535$	18.3051	0.791399
$536$	52.8300	2.28191
$537$	14.3510	0.619290
$538$	−76.4582	−3.29635
$539$	0	0
$540$	−10.6483	−0.458231
$541$	−26.9582	−1.15902	−0.579511	−	0.814965i	$-0.696756\pi$
$541$	−26.9582	−1.15902	−0.579511	+	0.814965i	$0.696756\pi$
$542$	−55.2874	−2.37480
$543$	9.66152	0.414616
$544$	8.78562	0.376680
$545$	48.7453	2.08802
$546$	−14.5202	−0.621407
$547$	−26.0558	−1.11407	−0.557034	−	0.830490i	$-0.688061\pi$
$547$	−26.0558	−1.11407	−0.557034	+	0.830490i	$0.688061\pi$
$548$	−44.5933	−1.90493
$549$	2.00000	0.0853579
$550$	0	0
$551$	13.8455	0.589837
$552$	−36.3246	−1.54608
$553$	4.45963	0.189643
$554$	61.2563	2.60253
$555$	−8.54885	−0.362878
$556$	−1.89134	−0.0802105
$557$	−8.01945	−0.339795	−0.169897	−	0.985462i	$-0.554344\pi$
$557$	−8.01945	−0.339795	−0.169897	+	0.985462i	$0.554344\pi$
$558$	9.05433	0.383300
$559$	−43.4831	−1.83914
$560$	−12.1692	−0.514244
$561$	0	0
$562$	−2.95486	−0.124643
$563$	−21.9736	−0.926077	−0.463038	−	0.886338i	$-0.653241\pi$
$563$	−21.9736	−0.926077	−0.463038	+	0.886338i	$0.653241\pi$
$564$	30.9993	1.30531
$565$	23.3619	0.982844
$566$	−38.5077	−1.61860
$567$	1.00000	0.0419961
$568$	−23.3230	−0.978613
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	15.0885	0.631988
$571$	−37.6740	−1.57661	−0.788304	−	0.615286i	$-0.789041\pi$
$571$	−37.6740	−1.57661	−0.788304	+	0.615286i	$0.789041\pi$
$572$	0	0
$573$	−9.55286	−0.399076
$574$	13.0668	0.545398
$575$	11.7827	0.491371
$576$	−6.51396	−0.271415
$577$	−7.80908	−0.325096	−0.162548	−	0.986701i	$-0.551971\pi$
$577$	−7.80908	−0.325096	−0.162548	+	0.986701i	$0.551971\pi$
$578$	−97.5771	−4.05867
$579$	22.1212	0.919324
$580$	−62.5257	−2.59624
$581$	10.6894	0.443473
$582$	−25.0279	−1.03744
$583$	0	0
$584$	−11.1296	−0.460547
$585$	−15.1949	−0.628233
$586$	−24.0947	−0.995345
$587$	−43.2633	−1.78567	−0.892833	−	0.450388i	$-0.851286\pi$
$587$	−43.2633	−1.78567	−0.892833	+	0.450388i	$0.851286\pi$
$588$	4.11491	0.169696
$589$	−8.63360	−0.355741
$590$	−5.92694	−0.244008
$591$	26.2423	1.07946
$592$	15.5356	0.638511
$593$	29.7438	1.22143	0.610715	−	0.791850i	$-0.290882\pi$
$593$	29.7438	1.22143	0.610715	+	0.791850i	$0.290882\pi$
$594$	0	0
$595$	19.4442	0.797134
$596$	−45.4589	−1.86207
$597$	1.05433	0.0431509
$598$	−100.853	−4.12417
$599$	11.5404	0.471527	0.235763	−	0.971810i	$-0.424241\pi$
$599$	11.5404	0.471527	0.235763	+	0.971810i	$0.424241\pi$
$600$	−8.87189	−0.362193
$601$	−7.06129	−0.288036	−0.144018	−	0.989575i	$-0.546002\pi$
$601$	−7.06129	−0.288036	−0.144018	+	0.989575i	$0.546002\pi$
$602$	18.3121	0.746344
$603$	−10.1017	−0.411373
$604$	66.3370	2.69922
$605$	0	0
$606$	−33.1491	−1.34659
$607$	17.3859	0.705670	0.352835	−	0.935686i	$-0.385218\pi$
$607$	17.3859	0.705670	0.352835	+	0.935686i	$0.385218\pi$
$608$	−2.75698	−0.111810
$609$	5.87189	0.237941
$610$	12.7981	0.518180
$611$	44.2353	1.78957
$612$	−30.9193	−1.24984
$613$	−39.4611	−1.59382	−0.796910	−	0.604098i	$-0.793534\pi$
$613$	−39.4611	−1.59382	−0.796910	+	0.604098i	$0.793534\pi$
$614$	15.7049	0.633798
$615$	13.6740	0.551389
$616$	0	0
$617$	−4.40378	−0.177290	−0.0886448	−	0.996063i	$-0.528254\pi$
$617$	−4.40378	−0.177290	−0.0886448	+	0.996063i	$0.528254\pi$
$618$	11.6615	0.469095
$619$	16.4163	0.659825	0.329913	−	0.944011i	$-0.392981\pi$
$619$	16.4163	0.659825	0.329913	+	0.944011i	$0.392981\pi$
$620$	38.9890	1.56584
$621$	6.94567	0.278720
$622$	−19.7827	−0.793213
$623$	15.8913	0.636673
$624$	27.6134	1.10542
$625$	−30.6042	−1.22417
$626$	−41.9038	−1.67481
$627$	0	0
$628$	53.7688	2.14561
$629$	−24.8231	−0.989761
$630$	6.39905	0.254944
$631$	44.4596	1.76991	0.884955	−	0.465677i	$-0.154189\pi$
$631$	44.4596	1.76991	0.884955	+	0.465677i	$0.154189\pi$
$632$	−23.3230	−0.927741
$633$	8.71585	0.346424
$634$	−49.4876	−1.96540
$635$	−26.4721	−1.05051
$636$	−17.4053	−0.690165
$637$	5.87189	0.232653
$638$	0	0
$639$	4.45963	0.176420
$640$	−47.7346	−1.88688
$641$	10.5419	0.416380	0.208190	−	0.978088i	$-0.433243\pi$
$641$	10.5419	0.416380	0.208190	+	0.978088i	$0.433243\pi$
$642$	17.4923	0.690365
$643$	−23.4053	−0.923015	−0.461507	−	0.887136i	$-0.652691\pi$
$643$	−23.4053	−0.923015	−0.461507	+	0.887136i	$0.652691\pi$
$644$	28.5808	1.12624
$645$	19.1630	0.754542
$646$	43.8121	1.72376
$647$	11.4945	0.451896	0.225948	−	0.974139i	$-0.427452\pi$
$647$	11.4945	0.451896	0.225948	+	0.974139i	$0.427452\pi$
$648$	−5.22982	−0.205447
$649$	0	0
$650$	−24.6322	−0.966153
$651$	−3.66152	−0.143506
$652$	−41.5676	−1.62791
$653$	19.8774	0.777863	0.388932	−	0.921267i	$-0.372844\pi$
$653$	19.8774	0.777863	0.388932	+	0.921267i	$0.372844\pi$
$654$	46.5808	1.82145
$655$	10.3510	0.404446
$656$	−24.8495	−0.970210
$657$	2.12811	0.0830255
$658$	−18.6289	−0.726229
$659$	−15.0738	−0.587191	−0.293596	−	0.955930i	$-0.594852\pi$
$659$	−15.0738	−0.587191	−0.293596	+	0.955930i	$0.594852\pi$
$660$	0	0
$661$	−4.74226	−0.184453	−0.0922263	−	0.995738i	$-0.529398\pi$
$661$	−4.74226	−0.184453	−0.0922263	+	0.995738i	$0.529398\pi$
$662$	−18.6461	−0.724701
$663$	−44.1212	−1.71352
$664$	−55.9038	−2.16949
$665$	−6.10170	−0.236614
$666$	−8.16924	−0.316552
$667$	40.7842	1.57917
$668$	43.1491	1.66949
$669$	−23.7438	−0.917987
$670$	−64.6414	−2.49731
$671$	0	0
$672$	−1.16924	−0.0451044
$673$	−9.87885	−0.380802	−0.190401	−	0.981706i	$-0.560979\pi$
$673$	−9.87885	−0.380802	−0.190401	+	0.981706i	$0.560979\pi$
$674$	−31.3789	−1.20867
$675$	1.69641	0.0652947
$676$	88.3844	3.39940
$677$	29.0279	1.11563	0.557817	−	0.829964i	$-0.311639\pi$
$677$	29.0279	1.11563	0.557817	+	0.829964i	$0.311639\pi$
$678$	22.3246	0.857369
$679$	10.1212	0.388414
$680$	−101.690	−3.89962
$681$	13.1755	0.504886
$682$	0	0
$683$	−37.9597	−1.45249	−0.726243	−	0.687438i	$-0.758735\pi$
$683$	−37.9597	−1.45249	−0.726243	+	0.687438i	$0.758735\pi$
$684$	9.70265	0.370990
$685$	28.0434	1.07148
$686$	−2.47283	−0.0944132
$687$	13.3664	0.509960
$688$	−34.8245	−1.32767
$689$	−24.8370	−0.946214
$690$	44.4457	1.69202
$691$	−15.5264	−0.590654	−0.295327	−	0.955396i	$-0.595429\pi$
$691$	−15.5264	−0.590654	−0.295327	+	0.955396i	$0.595429\pi$
$692$	−59.6601	−2.26794
$693$	0	0
$694$	2.81060	0.106689
$695$	1.18940	0.0451167
$696$	−30.7089	−1.16402
$697$	39.7049	1.50393
$698$	−36.5761	−1.38442
$699$	−7.13659	−0.269931
$700$	6.98055	0.263840
$701$	27.4317	1.03608	0.518041	−	0.855356i	$-0.326662\pi$
$701$	27.4317	1.03608	0.518041	+	0.855356i	$0.326662\pi$
$702$	−14.5202	−0.548030
$703$	7.78963	0.293792
$704$	0	0
$705$	−19.4945	−0.734206
$706$	18.5980	0.699945
$707$	13.4053	0.504158
$708$	−3.81131	−0.143238
$709$	−44.5180	−1.67191	−0.835954	−	0.548800i	$-0.815085\pi$
$709$	−44.5180	−1.67191	−0.835954	+	0.548800i	$0.815085\pi$
$710$	28.5374	1.07099
$711$	4.45963	0.167249
$712$	−83.1087	−3.11463
$713$	−25.4317	−0.952425
$714$	18.5808	0.695368
$715$	0	0
$716$	59.0529	2.20691
$717$	19.9930	0.746654
$718$	−43.5125	−1.62387
$719$	17.3859	0.648383	0.324191	−	0.945992i	$-0.394908\pi$
$719$	17.3859	0.648383	0.324191	+	0.945992i	$0.394908\pi$
$720$	−12.1692	−0.453521
$721$	−4.71585	−0.175628
$722$	33.2353	1.23689
$723$	9.19493	0.341963
$724$	39.7563	1.47753
$725$	9.96111	0.369946
$726$	0	0
$727$	−18.6506	−0.691711	−0.345855	−	0.938288i	$-0.612411\pi$
$727$	−18.6506	−0.691711	−0.345855	+	0.938288i	$0.612411\pi$
$728$	−30.7089	−1.13815
$729$	1.00000	0.0370370
$730$	13.6179	0.504021
$731$	55.6431	2.05804
$732$	8.22982	0.304183
$733$	−16.3510	−0.603937	−0.301968	−	0.953318i	$-0.597644\pi$
$733$	−16.3510	−0.603937	−0.301968	+	0.953318i	$0.597644\pi$
$734$	−35.3914	−1.30632
$735$	−2.58774	−0.0954503
$736$	−8.12115	−0.299350
$737$	0	0
$738$	13.0668	0.480996
$739$	32.8370	1.20793	0.603964	−	0.797011i	$-0.293587\pi$
$739$	32.8370	1.20793	0.603964	+	0.797011i	$0.293587\pi$
$740$	−35.1777	−1.29316
$741$	13.8455	0.508626
$742$	10.4596	0.383985
$743$	−20.9123	−0.767198	−0.383599	−	0.923500i	$-0.625315\pi$
$743$	−20.9123	−0.767198	−0.383599	+	0.923500i	$0.625315\pi$
$744$	19.1491	0.702039
$745$	28.5877	1.04737
$746$	−40.6366	−1.48781
$747$	10.6894	0.391106
$748$	0	0
$749$	−7.07378	−0.258470
$750$	−21.1399	−0.771919
$751$	−39.2633	−1.43274	−0.716368	−	0.697722i	$-0.754197\pi$
$751$	−39.2633	−1.43274	−0.716368	+	0.697722i	$0.754197\pi$
$752$	35.4270	1.29189
$753$	−9.42474	−0.343457
$754$	−85.2610	−3.10502
$755$	−41.7174	−1.51825
$756$	4.11491	0.149658
$757$	−10.3454	−0.376011	−0.188006	−	0.982168i	$-0.560202\pi$
$757$	−10.3454	−0.376011	−0.188006	+	0.982168i	$0.560202\pi$
$758$	−48.3029	−1.75444
$759$	0	0
$760$	31.9108	1.15753
$761$	−30.9582	−1.12223	−0.561116	−	0.827737i	$-0.689628\pi$
$761$	−30.9582	−1.12223	−0.561116	+	0.827737i	$0.689628\pi$
$762$	−25.2966	−0.916400
$763$	−18.8370	−0.681945
$764$	−39.3091	−1.42215
$765$	19.4442	0.703006
$766$	−5.81355	−0.210052
$767$	−5.43867	−0.196379
$768$	−32.5870	−1.17588
$769$	28.8998	1.04215	0.521077	−	0.853510i	$-0.325530\pi$
$769$	28.8998	1.04215	0.521077	+	0.853510i	$0.325530\pi$
$770$	0	0
$771$	−0.0194469	−0.000700364 0
$772$	91.0265	3.27612
$773$	−26.7523	−0.962212	−0.481106	−	0.876663i	$-0.659765\pi$
$773$	−26.7523	−0.962212	−0.481106	+	0.876663i	$0.659765\pi$
$774$	18.3121	0.658214
$775$	−6.21142	−0.223121
$776$	−52.9317	−1.90014
$777$	3.30359	0.118516
$778$	4.31207	0.154595
$779$	−12.4596	−0.446413
$780$	−62.5257	−2.23878
$781$	0	0
$782$	129.056	4.61503
$783$	5.87189	0.209844
$784$	4.70265	0.167952
$785$	−33.8135	−1.20686
$786$	9.89134	0.352812
$787$	−22.1406	−0.789227	−0.394614	−	0.918847i	$-0.629122\pi$
$787$	−22.1406	−0.789227	−0.394614	+	0.918847i	$0.629122\pi$
$788$	107.985	3.84679
$789$	−27.9930	−0.996579
$790$	28.5374	1.01532
$791$	−9.02792	−0.320996
$792$	0	0
$793$	11.7438	0.417034
$794$	−16.1770	−0.574100
$795$	10.9457	0.388203
$796$	4.33848	0.153773
$797$	8.18396	0.289891	0.144945	−	0.989440i	$-0.453699\pi$
$797$	8.18396	0.289891	0.144945	+	0.989440i	$0.453699\pi$
$798$	−5.83076	−0.206407
$799$	−56.6058	−2.00257
$800$	−1.98351	−0.0701275
$801$	15.8913	0.561493
$802$	−14.0000	−0.494357
$803$	0	0
$804$	−41.5676	−1.46598
$805$	−17.9736	−0.633486
$806$	53.1660	1.87269
$807$	30.9193	1.08841
$808$	−70.1072	−2.46636
$809$	−17.6685	−0.621191	−0.310595	−	0.950542i	$-0.600528\pi$
$809$	−17.6685	−0.621191	−0.310595	+	0.950542i	$0.600528\pi$
$810$	6.39905	0.224840
$811$	43.0210	1.51067	0.755335	−	0.655339i	$-0.227474\pi$
$811$	43.0210	1.51067	0.755335	+	0.655339i	$0.227474\pi$
$812$	24.1623	0.847930
$813$	22.3579	0.784127
$814$	0	0
$815$	26.1406	0.915665
$816$	−35.3355	−1.23699
$817$	−17.4611	−0.610888
$818$	−13.5698	−0.474457
$819$	5.87189	0.205180
$820$	56.2673	1.96494
$821$	−18.0364	−0.629475	−0.314737	−	0.949179i	$-0.601916\pi$
$821$	−18.0364	−0.629475	−0.314737	+	0.949179i	$0.601916\pi$
$822$	26.7981	0.934691
$823$	−8.21037	−0.286195	−0.143098	−	0.989709i	$-0.545706\pi$
$823$	−8.21037	−0.286195	−0.143098	+	0.989709i	$0.545706\pi$
$824$	24.6630	0.859178
$825$	0	0
$826$	2.29039	0.0796929
$827$	−6.83148	−0.237554	−0.118777	−	0.992921i	$-0.537897\pi$
$827$	−6.83148	−0.237554	−0.118777	+	0.992921i	$0.537897\pi$
$828$	28.5808	0.993251
$829$	−25.7438	−0.894118	−0.447059	−	0.894504i	$-0.647529\pi$
$829$	−25.7438	−0.894118	−0.447059	+	0.894504i	$0.647529\pi$
$830$	68.4023	2.37428
$831$	−24.7717	−0.859321
$832$	−38.2493	−1.32605
$833$	−7.51396	−0.260343
$834$	1.13659	0.0393569
$835$	−27.1352	−0.939051
$836$	0	0
$837$	−3.66152	−0.126561
$838$	−20.3991	−0.704674
$839$	−30.6002	−1.05644	−0.528219	−	0.849108i	$-0.677140\pi$
$839$	−30.6002	−1.05644	−0.528219	+	0.849108i	$0.677140\pi$
$840$	13.5334	0.466947
$841$	5.47908	0.188934
$842$	−79.7779	−2.74933
$843$	1.19493	0.0411556
$844$	35.8649	1.23452
$845$	−55.5823	−1.91209
$846$	−18.6289	−0.640474
$847$	0	0
$848$	−19.8913	−0.683071
$849$	15.5723	0.534440
$850$	31.5205	1.08115
$851$	22.9457	0.786567
$852$	18.3510	0.628694
$853$	30.4596	1.04292	0.521459	−	0.853276i	$-0.325388\pi$
$853$	30.4596	1.04292	0.521459	+	0.853276i	$0.325388\pi$
$854$	−4.94567	−0.169237
$855$	−6.10170	−0.208674
$856$	36.9946	1.26445
$857$	41.2702	1.40976	0.704882	−	0.709325i	$-0.251000\pi$
$857$	41.2702	1.40976	0.704882	+	0.709325i	$0.251000\pi$
$858$	0	0
$859$	−28.9193	−0.986712	−0.493356	−	0.869827i	$-0.664230\pi$
$859$	−28.9193	−0.986712	−0.493356	+	0.869827i	$0.664230\pi$
$860$	78.8540	2.68890
$861$	−5.28415	−0.180083
$862$	−57.5606	−1.96052
$863$	37.0015	1.25955	0.629773	−	0.776779i	$-0.283148\pi$
$863$	37.0015	1.25955	0.629773	+	0.776779i	$0.283148\pi$
$864$	−1.16924	−0.0397783
$865$	37.5184	1.27566
$866$	39.3928	1.33862
$867$	39.4596	1.34012
$868$	−15.0668	−0.511401
$869$	0	0
$870$	37.5745	1.27390
$871$	−59.3161	−2.00985
$872$	98.5140	3.33611
$873$	10.1212	0.342549
$874$	−40.4985	−1.36988
$875$	8.54885	0.289004
$876$	8.75698	0.295871
$877$	6.12562	0.206847	0.103424	−	0.994637i	$-0.467020\pi$
$877$	6.12562	0.206847	0.103424	+	0.994637i	$0.467020\pi$
$878$	56.5202	1.90746
$879$	9.74378	0.328649
$880$	0	0
$881$	25.4123	0.856161	0.428080	−	0.903741i	$-0.359190\pi$
$881$	25.4123	0.856161	0.428080	+	0.903741i	$0.359190\pi$
$882$	−2.47283	−0.0832646
$883$	−17.0040	−0.572230	−0.286115	−	0.958195i	$-0.592364\pi$
$883$	−17.0040	−0.572230	−0.286115	+	0.958195i	$0.592364\pi$
$884$	−181.554	−6.10634
$885$	2.39682	0.0805682
$886$	−53.4039	−1.79414
$887$	−35.2269	−1.18280	−0.591401	−	0.806378i	$-0.701425\pi$
$887$	−35.2269	−1.18280	−0.591401	+	0.806378i	$0.701425\pi$
$888$	−17.2772	−0.579784
$889$	10.2298	0.343097
$890$	101.690	3.40864
$891$	0	0
$892$	−97.7034	−3.27135
$893$	17.7632	0.594424
$894$	27.3183	0.913661
$895$	−37.1366	−1.24134
$896$	18.4464	0.616252
$897$	40.7842	1.36174
$898$	−46.1506	−1.54007
$899$	−21.5000	−0.717067
$900$	6.98055	0.232685
$901$	31.7827	1.05883
$902$	0	0
$903$	−7.40530	−0.246433
$904$	47.2144	1.57033
$905$	−25.0015	−0.831079
$906$	−39.8649	−1.32442
$907$	−9.72682	−0.322974	−0.161487	−	0.986875i	$-0.551629\pi$
$907$	−9.72682	−0.322974	−0.161487	+	0.986875i	$0.551629\pi$
$908$	54.2159	1.79922
$909$	13.4053	0.444626
$910$	37.5745	1.24558
$911$	−42.7717	−1.41709	−0.708545	−	0.705666i	$-0.750648\pi$
$911$	−42.7717	−1.41709	−0.708545	+	0.705666i	$0.750648\pi$
$912$	11.0885	0.367177
$913$	0	0
$914$	90.1895	2.98320
$915$	−5.17548	−0.171096
$916$	55.0015	1.81730
$917$	−4.00000	−0.132092
$918$	18.5808	0.613257
$919$	−6.26871	−0.206786	−0.103393	−	0.994641i	$-0.532970\pi$
$919$	−6.26871	−0.206786	−0.103393	+	0.994641i	$0.532970\pi$
$920$	93.9986	3.09904
$921$	−6.35097	−0.209271
$922$	17.7438	0.584360
$923$	26.1865	0.861938
$924$	0	0
$925$	5.60424	0.184266
$926$	1.11938	0.0367850
$927$	−4.71585	−0.154889
$928$	−6.86565	−0.225376
$929$	20.0194	0.656817	0.328408	−	0.944536i	$-0.393488\pi$
$929$	20.0194	0.656817	0.328408	+	0.944536i	$0.393488\pi$
$930$	−23.4303	−0.768309
$931$	2.35793	0.0772779
$932$	−29.3664	−0.961929
$933$	8.00000	0.261908
$934$	23.9394	0.783322
$935$	0	0
$936$	−30.7089	−1.00375
$937$	11.2144	0.366358	0.183179	−	0.983080i	$-0.441361\pi$
$937$	11.2144	0.366358	0.183179	+	0.983080i	$0.441361\pi$
$938$	24.9798	0.815621
$939$	16.9457	0.553001
$940$	−80.2181	−2.61643
$941$	−31.3400	−1.02165	−0.510827	−	0.859683i	$-0.670661\pi$
$941$	−31.3400	−1.02165	−0.510827	+	0.859683i	$0.670661\pi$
$942$	−32.3121	−1.05278
$943$	−36.7019	−1.19518
$944$	−4.35569	−0.141766
$945$	−2.58774	−0.0841792
$946$	0	0
$947$	−23.2841	−0.756633	−0.378317	−	0.925676i	$-0.623497\pi$
$947$	−23.2841	−0.756633	−0.378317	+	0.925676i	$0.623497\pi$
$948$	18.3510	0.596012
$949$	12.4960	0.405638
$950$	−9.89134	−0.320917
$951$	20.0125	0.648949
$952$	39.2966	1.27361
$953$	−26.8300	−0.869110	−0.434555	−	0.900645i	$-0.643094\pi$
$953$	−26.8300	−0.869110	−0.434555	+	0.900645i	$0.643094\pi$
$954$	10.4596	0.338643
$955$	24.7203	0.799931
$956$	82.2695	2.66079
$957$	0	0
$958$	60.2468	1.94648
$959$	−10.8370	−0.349945
$960$	16.8565	0.544040
$961$	−17.5933	−0.567525
$962$	−47.9689	−1.54658
$963$	−7.07378	−0.227949
$964$	37.8363	1.21862
$965$	−57.2438	−1.84274
$966$	−17.1755	−0.552612
$967$	−36.2034	−1.16422	−0.582112	−	0.813109i	$-0.697773\pi$
$967$	−36.2034	−1.16422	−0.582112	+	0.813109i	$0.697773\pi$
$968$	0	0
$969$	−17.7174	−0.569164
$970$	64.7658	2.07950
$971$	6.06281	0.194565	0.0972824	−	0.995257i	$-0.468985\pi$
$971$	6.06281	0.194565	0.0972824	+	0.995257i	$0.468985\pi$
$972$	4.11491	0.131986
$973$	−0.459630	−0.0147351
$974$	47.6521	1.52687
$975$	9.96111	0.319011
$976$	9.40530	0.301056
$977$	−4.28263	−0.137013	−0.0685067	−	0.997651i	$-0.521823\pi$
$977$	−4.28263	−0.137013	−0.0685067	+	0.997651i	$0.521823\pi$
$978$	24.9798	0.798767
$979$	0	0
$980$	−10.6483	−0.340148
$981$	−18.8370	−0.601419
$982$	73.2999	2.33909
$983$	−17.1894	−0.548257	−0.274128	−	0.961693i	$-0.588389\pi$
$983$	−17.1894	−0.548257	−0.274128	+	0.961693i	$0.588389\pi$
$984$	27.6351	0.880975
$985$	−67.9083	−2.16374
$986$	109.104	3.47459
$987$	7.53341	0.239791
$988$	56.9729	1.81255
$989$	−51.4347	−1.63553
$990$	0	0
$991$	35.4945	1.12752	0.563760	−	0.825939i	$-0.309354\pi$
$991$	35.4945	1.12752	0.563760	+	0.825939i	$0.309354\pi$
$992$	4.28120	0.135928
$993$	7.54037	0.239286
$994$	−11.0279	−0.349785
$995$	−2.72834	−0.0864942
$996$	43.9861	1.39375
$997$	−30.4068	−0.962993	−0.481497	−	0.876448i	$-0.659907\pi$
$997$	−30.4068	−0.962993	−0.481497	+	0.876448i	$0.659907\pi$
$998$	−72.6319	−2.29912
$999$	3.30359	0.104521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bg.1.1		3
3.2	odd	2		7623.2.a.cd.1.3		3
11.10	odd	2		231.2.a.e.1.3	✓	3
33.32	even	2		693.2.a.l.1.1		3
44.43	even	2		3696.2.a.bo.1.1		3
55.54	odd	2		5775.2.a.bp.1.1		3
77.76	even	2		1617.2.a.t.1.3		3
231.230	odd	2		4851.2.a.bi.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.a.e.1.3	✓	3	11.10	odd	2
693.2.a.l.1.1		3	33.32	even	2
1617.2.a.t.1.3		3	77.76	even	2
2541.2.a.bg.1.1		3	1.1	even	1	trivial
3696.2.a.bo.1.1		3	44.43	even	2
4851.2.a.bi.1.1		3	231.230	odd	2
5775.2.a.bp.1.1		3	55.54	odd	2
7623.2.a.cd.1.3		3	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:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47283 q^{2} +1.00000 q^{3} +4.11491 q^{4} -2.58774 q^{5} -2.47283 q^{6} +1.00000 q^{7} -5.22982 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.47283 q^{2} +1.00000 q^{3} +4.11491 q^{4} -2.58774 q^{5} -2.47283 q^{6} +1.00000 q^{7} -5.22982 q^{8} +1.00000 q^{9} +6.39905 q^{10} +4.11491 q^{12} +5.87189 q^{13} -2.47283 q^{14} -2.58774 q^{15} +4.70265 q^{16} -7.51396 q^{17} -2.47283 q^{18} +2.35793 q^{19} -10.6483 q^{20} +1.00000 q^{21} +6.94567 q^{23} -5.22982 q^{24} +1.69641 q^{25} -14.5202 q^{26} +1.00000 q^{27} +4.11491 q^{28} +5.87189 q^{29} +6.39905 q^{30} -3.66152 q^{31} -1.16924 q^{32} +18.5808 q^{34} -2.58774 q^{35} +4.11491 q^{36} +3.30359 q^{37} -5.83076 q^{38} +5.87189 q^{39} +13.5334 q^{40} -5.28415 q^{41} -2.47283 q^{42} -7.40530 q^{43} -2.58774 q^{45} -17.1755 q^{46} +7.53341 q^{47} +4.70265 q^{48} +1.00000 q^{49} -4.19493 q^{50} -7.51396 q^{51} +24.1623 q^{52} -4.22982 q^{53} -2.47283 q^{54} -5.22982 q^{56} +2.35793 q^{57} -14.5202 q^{58} -0.926221 q^{59} -10.6483 q^{60} +2.00000 q^{61} +9.05433 q^{62} +1.00000 q^{63} -6.51396 q^{64} -15.1949 q^{65} -10.1017 q^{67} -30.9193 q^{68} +6.94567 q^{69} +6.39905 q^{70} +4.45963 q^{71} -5.22982 q^{72} +2.12811 q^{73} -8.16924 q^{74} +1.69641 q^{75} +9.70265 q^{76} -14.5202 q^{78} +4.45963 q^{79} -12.1692 q^{80} +1.00000 q^{81} +13.0668 q^{82} +10.6894 q^{83} +4.11491 q^{84} +19.4442 q^{85} +18.3121 q^{86} +5.87189 q^{87} +15.8913 q^{89} +6.39905 q^{90} +5.87189 q^{91} +28.5808 q^{92} -3.66152 q^{93} -18.6289 q^{94} -6.10170 q^{95} -1.16924 q^{96} +10.1212 q^{97} -2.47283 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} + 3 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 + 3 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 2 q^{2} + 3 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 11 q^{10} + 6 q^{12} + 4 q^{13} - 2 q^{14} + 4 q^{15} - 4 q^{16} - 8 q^{17} - 2 q^{18} + 8 q^{19} - 3 q^{20} + 3 q^{21} + 10 q^{23} - 3 q^{24} + 15 q^{25} - q^{26} + 3 q^{27} + 6 q^{28} + 4 q^{29} + 11 q^{30} - 2 q^{31} - 8 q^{32} - 4 q^{34} + 4 q^{35} + 6 q^{36} - 13 q^{38} + 4 q^{39} + 18 q^{40} - 14 q^{41} - 2 q^{42} + 14 q^{43} + 4 q^{45} - 28 q^{46} - 4 q^{48} + 3 q^{49} + 19 q^{50} - 8 q^{51} + 29 q^{52} - 2 q^{54} - 3 q^{56} + 8 q^{57} - q^{58} - 3 q^{60} + 6 q^{61} + 38 q^{62} + 3 q^{63} - 5 q^{64} - 14 q^{65} - 4 q^{67} - 42 q^{68} + 10 q^{69} + 11 q^{70} - 12 q^{71} - 3 q^{72} + 20 q^{73} - 29 q^{74} + 15 q^{75} + 11 q^{76} - q^{78} - 12 q^{79} - 41 q^{80} + 3 q^{81} - 6 q^{82} - 6 q^{83} + 6 q^{84} + 6 q^{85} + 24 q^{86} + 4 q^{87} + 26 q^{89} + 11 q^{90} + 4 q^{91} + 26 q^{92} - 2 q^{93} - 35 q^{94} + 8 q^{95} - 8 q^{96} - 4 q^{97} - 2 q^{98}+O(q^{100}) \) 3 * q - 2 * q^2 + 3 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 + 11 * q^10 + 6 * q^12 + 4 * q^13 - 2 * q^14 + 4 * q^15 - 4 * q^16 - 8 * q^17 - 2 * q^18 + 8 * q^19 - 3 * q^20 + 3 * q^21 + 10 * q^23 - 3 * q^24 + 15 * q^25 - q^26 + 3 * q^27 + 6 * q^28 + 4 * q^29 + 11 * q^30 - 2 * q^31 - 8 * q^32 - 4 * q^34 + 4 * q^35 + 6 * q^36 - 13 * q^38 + 4 * q^39 + 18 * q^40 - 14 * q^41 - 2 * q^42 + 14 * q^43 + 4 * q^45 - 28 * q^46 - 4 * q^48 + 3 * q^49 + 19 * q^50 - 8 * q^51 + 29 * q^52 - 2 * q^54 - 3 * q^56 + 8 * q^57 - q^58 - 3 * q^60 + 6 * q^61 + 38 * q^62 + 3 * q^63 - 5 * q^64 - 14 * q^65 - 4 * q^67 - 42 * q^68 + 10 * q^69 + 11 * q^70 - 12 * q^71 - 3 * q^72 + 20 * q^73 - 29 * q^74 + 15 * q^75 + 11 * q^76 - q^78 - 12 * q^79 - 41 * q^80 + 3 * q^81 - 6 * q^82 - 6 * q^83 + 6 * q^84 + 6 * q^85 + 24 * q^86 + 4 * q^87 + 26 * q^89 + 11 * q^90 + 4 * q^91 + 26 * q^92 - 2 * q^93 - 35 * q^94 + 8 * q^95 - 8 * q^96 - 4 * q^97 - 2 * q^98

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