LMFDB - Embedded newform 2541.2.a.bq.1.10

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 $ x^10 - 19x^8 - x^7 + 124x^6 + 6x^5 - 316x^4 + 17x^3 + 253x^2 - 70*x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.79866$ 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)

$f(q)$	$=$	$q+2.79866 q^{2} +1.00000 q^{3} +5.83249 q^{4} -1.67767 q^{5} +2.79866 q^{6} -1.00000 q^{7} +10.7258 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.79866 q^{2} +1.00000 q^{3} +5.83249 q^{4} -1.67767 q^{5} +2.79866 q^{6} -1.00000 q^{7} +10.7258 q^{8} +1.00000 q^{9} -4.69523 q^{10} +5.83249 q^{12} +5.87113 q^{13} -2.79866 q^{14} -1.67767 q^{15} +18.3530 q^{16} -0.304169 q^{17} +2.79866 q^{18} -4.62860 q^{19} -9.78502 q^{20} -1.00000 q^{21} -1.38164 q^{23} +10.7258 q^{24} -2.18541 q^{25} +16.4313 q^{26} +1.00000 q^{27} -5.83249 q^{28} +3.96868 q^{29} -4.69523 q^{30} +0.764099 q^{31} +29.9121 q^{32} -0.851264 q^{34} +1.67767 q^{35} +5.83249 q^{36} +3.21023 q^{37} -12.9539 q^{38} +5.87113 q^{39} -17.9945 q^{40} -8.31274 q^{41} -2.79866 q^{42} -1.01069 q^{43} -1.67767 q^{45} -3.86674 q^{46} -2.58688 q^{47} +18.3530 q^{48} +1.00000 q^{49} -6.11623 q^{50} -0.304169 q^{51} +34.2434 q^{52} -1.45374 q^{53} +2.79866 q^{54} -10.7258 q^{56} -4.62860 q^{57} +11.1070 q^{58} -2.49444 q^{59} -9.78502 q^{60} +3.39295 q^{61} +2.13845 q^{62} -1.00000 q^{63} +47.0078 q^{64} -9.84984 q^{65} +6.16878 q^{67} -1.77406 q^{68} -1.38164 q^{69} +4.69523 q^{70} +7.59943 q^{71} +10.7258 q^{72} -12.7455 q^{73} +8.98434 q^{74} -2.18541 q^{75} -26.9963 q^{76} +16.4313 q^{78} -6.15519 q^{79} -30.7903 q^{80} +1.00000 q^{81} -23.2645 q^{82} -2.01266 q^{83} -5.83249 q^{84} +0.510295 q^{85} -2.82859 q^{86} +3.96868 q^{87} +0.0843908 q^{89} -4.69523 q^{90} -5.87113 q^{91} -8.05840 q^{92} +0.764099 q^{93} -7.23980 q^{94} +7.76527 q^{95} +29.9121 q^{96} +1.03775 q^{97} +2.79866 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} - 10 q^{7} + 3 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 - 10 * q^7 + 3 * q^8 + 10 * q^9	$ 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} - 10 q^{7} + 3 q^{8} + 10 q^{9} + 6 q^{10} + 18 q^{12} - 6 q^{13} + 5 q^{15} + 38 q^{16} - 8 q^{17} + 7 q^{20} - 10 q^{21} + 3 q^{24} + 31 q^{25} + q^{26} + 10 q^{27} - 18 q^{28} + 14 q^{29} + 6 q^{30} + 26 q^{31} + 41 q^{32} + 21 q^{34} - 5 q^{35} + 18 q^{36} + 24 q^{37} + 8 q^{38} - 6 q^{39} + 5 q^{40} - 19 q^{41} + 6 q^{43} + 5 q^{45} + q^{46} + 15 q^{47} + 38 q^{48} + 10 q^{49} + q^{50} - 8 q^{51} + 25 q^{52} - q^{53} - 3 q^{56} + 11 q^{58} + 23 q^{59} + 7 q^{60} - 11 q^{62} - 10 q^{63} + 53 q^{64} + 29 q^{65} + 38 q^{67} - 87 q^{68} - 6 q^{70} + 26 q^{71} + 3 q^{72} + q^{73} + 39 q^{74} + 31 q^{75} + 2 q^{76} + q^{78} - 5 q^{79} + 6 q^{80} + 10 q^{81} + 5 q^{82} - 6 q^{83} - 18 q^{84} + q^{85} - 41 q^{86} + 14 q^{87} - 9 q^{89} + 6 q^{90} + 6 q^{91} - 48 q^{92} + 26 q^{93} + 42 q^{95} + 41 q^{96} + 24 q^{97}+O(q^{100}) $ 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 - 10 * q^7 + 3 * q^8 + 10 * q^9 + 6 * q^10 + 18 * q^12 - 6 * q^13 + 5 * q^15 + 38 * q^16 - 8 * q^17 + 7 * q^20 - 10 * q^21 + 3 * q^24 + 31 * q^25 + q^26 + 10 * q^27 - 18 * q^28 + 14 * q^29 + 6 * q^30 + 26 * q^31 + 41 * q^32 + 21 * q^34 - 5 * q^35 + 18 * q^36 + 24 * q^37 + 8 * q^38 - 6 * q^39 + 5 * q^40 - 19 * q^41 + 6 * q^43 + 5 * q^45 + q^46 + 15 * q^47 + 38 * q^48 + 10 * q^49 + q^50 - 8 * q^51 + 25 * q^52 - q^53 - 3 * q^56 + 11 * q^58 + 23 * q^59 + 7 * q^60 - 11 * q^62 - 10 * q^63 + 53 * q^64 + 29 * q^65 + 38 * q^67 - 87 * q^68 - 6 * q^70 + 26 * q^71 + 3 * q^72 + q^73 + 39 * q^74 + 31 * q^75 + 2 * q^76 + q^78 - 5 * q^79 + 6 * q^80 + 10 * q^81 + 5 * q^82 - 6 * q^83 - 18 * q^84 + q^85 - 41 * q^86 + 14 * q^87 - 9 * q^89 + 6 * q^90 + 6 * q^91 - 48 * q^92 + 26 * q^93 + 42 * q^95 + 41 * q^96 + 24 * q^97

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 $

$2$	2.79866	1.97895	0.989476	−	0.144700i	$-0.0462218\pi$
$2$	2.79866	1.97895	0.989476	+	0.144700i	$0.0462218\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.83249	2.91625
$5$	−1.67767	−0.750278	−0.375139	−	0.926969i	$-0.622405\pi$
$5$	−1.67767	−0.750278	−0.375139	+	0.926969i	$0.622405\pi$
$6$	2.79866	1.14255
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	10.7258	3.79216
$9$	1.00000	0.333333
$10$	−4.69523	−1.48476
$11$	0	0
$11$	0	0
$12$	5.83249	1.68370
$13$	5.87113	1.62836	0.814180	−	0.580613i	$-0.197187\pi$
$13$	5.87113	1.62836	0.814180	+	0.580613i	$0.197187\pi$
$14$	−2.79866	−0.747973
$15$	−1.67767	−0.433173
$16$	18.3530	4.58825
$17$	−0.304169	−0.0737717	−0.0368859	−	0.999319i	$-0.511744\pi$
$17$	−0.304169	−0.0737717	−0.0368859	+	0.999319i	$0.511744\pi$
$18$	2.79866	0.659650
$19$	−4.62860	−1.06187	−0.530937	−	0.847411i	$-0.678160\pi$
$19$	−4.62860	−1.06187	−0.530937	+	0.847411i	$0.678160\pi$
$20$	−9.78502	−2.18800
$21$	−1.00000	−0.218218
$22$	0	0
$23$	−1.38164	−0.288092	−0.144046	−	0.989571i	$-0.546011\pi$
$23$	−1.38164	−0.288092	−0.144046	+	0.989571i	$0.546011\pi$
$24$	10.7258	2.18940
$25$	−2.18541	−0.437083
$26$	16.4313	3.22244
$27$	1.00000	0.192450
$28$	−5.83249	−1.10224
$29$	3.96868	0.736965	0.368483	−	0.929635i	$-0.379877\pi$
$29$	3.96868	0.736965	0.368483	+	0.929635i	$0.379877\pi$
$30$	−4.69523	−0.857229
$31$	0.764099	0.137236	0.0686181	−	0.997643i	$-0.478141\pi$
$31$	0.764099	0.137236	0.0686181	+	0.997643i	$0.478141\pi$
$32$	29.9121	5.28776
$33$	0	0
$34$	−0.851264	−0.145991
$35$	1.67767	0.283578
$36$	5.83249	0.972082
$37$	3.21023	0.527759	0.263879	−	0.964556i	$-0.414998\pi$
$37$	3.21023	0.527759	0.263879	+	0.964556i	$0.414998\pi$
$38$	−12.9539	−2.10140
$39$	5.87113	0.940134
$40$	−17.9945	−2.84517
$41$	−8.31274	−1.29823	−0.649116	−	0.760690i	$-0.724861\pi$
$41$	−8.31274	−1.29823	−0.649116	+	0.760690i	$0.724861\pi$
$42$	−2.79866	−0.431843
$43$	−1.01069	−0.154129	−0.0770647	−	0.997026i	$-0.524555\pi$
$43$	−1.01069	−0.154129	−0.0770647	+	0.997026i	$0.524555\pi$
$44$	0	0
$45$	−1.67767	−0.250093
$46$	−3.86674	−0.570119
$47$	−2.58688	−0.377335	−0.188668	−	0.982041i	$-0.560417\pi$
$47$	−2.58688	−0.377335	−0.188668	+	0.982041i	$0.560417\pi$
$48$	18.3530	2.64903
$49$	1.00000	0.142857
$50$	−6.11623	−0.864966
$51$	−0.304169	−0.0425921
$52$	34.2434	4.74870
$53$	−1.45374	−0.199686	−0.0998430	−	0.995003i	$-0.531834\pi$
$53$	−1.45374	−0.199686	−0.0998430	+	0.995003i	$0.531834\pi$
$54$	2.79866	0.380849
$55$	0	0
$56$	−10.7258	−1.43330
$57$	−4.62860	−0.613073
$58$	11.1070	1.45842
$59$	−2.49444	−0.324749	−0.162374	−	0.986729i	$-0.551915\pi$
$59$	−2.49444	−0.324749	−0.162374	+	0.986729i	$0.551915\pi$
$60$	−9.78502	−1.26324
$61$	3.39295	0.434423	0.217211	−	0.976125i	$-0.430304\pi$
$61$	3.39295	0.434423	0.217211	+	0.976125i	$0.430304\pi$
$62$	2.13845	0.271584
$63$	−1.00000	−0.125988
$64$	47.0078	5.87598
$65$	−9.84984	−1.22172
$66$	0	0
$67$	6.16878	0.753636	0.376818	−	0.926287i	$-0.377018\pi$
$67$	6.16878	0.753636	0.376818	+	0.926287i	$0.377018\pi$
$68$	−1.77406	−0.215137
$69$	−1.38164	−0.166330
$70$	4.69523	0.561188
$71$	7.59943	0.901886	0.450943	−	0.892553i	$-0.351088\pi$
$71$	7.59943	0.901886	0.450943	+	0.892553i	$0.351088\pi$
$72$	10.7258	1.26405
$73$	−12.7455	−1.49175	−0.745877	−	0.666084i	$-0.767969\pi$
$73$	−12.7455	−1.49175	−0.745877	+	0.666084i	$0.767969\pi$
$74$	8.98434	1.04441
$75$	−2.18541	−0.252350
$76$	−26.9963	−3.09669
$77$	0	0
$78$	16.4313	1.86048
$79$	−6.15519	−0.692512	−0.346256	−	0.938140i	$-0.612547\pi$
$79$	−6.15519	−0.692512	−0.346256	+	0.938140i	$0.612547\pi$
$80$	−30.7903	−3.44246
$81$	1.00000	0.111111
$82$	−23.2645	−2.56914
$83$	−2.01266	−0.220918	−0.110459	−	0.993881i	$-0.535232\pi$
$83$	−2.01266	−0.220918	−0.110459	+	0.993881i	$0.535232\pi$
$84$	−5.83249	−0.636377
$85$	0.510295	0.0553493
$86$	−2.82859	−0.305014
$87$	3.96868	0.425487
$88$	0	0
$89$	0.0843908	0.00894541	0.00447270	−	0.999990i	$-0.498576\pi$
$89$	0.0843908	0.00894541	0.00447270	+	0.999990i	$0.498576\pi$
$90$	−4.69523	−0.494921
$91$	−5.87113	−0.615462
$92$	−8.05840	−0.840146
$93$	0.764099	0.0792334
$94$	−7.23980	−0.746728
$95$	7.76527	0.796700
$96$	29.9121	3.05289
$97$	1.03775	0.105367	0.0526837	−	0.998611i	$-0.483223\pi$
$97$	1.03775	0.105367	0.0526837	+	0.998611i	$0.483223\pi$
$98$	2.79866	0.282707
$99$	0	0
$100$	−12.7464	−1.27464
$101$	−19.6972	−1.95994	−0.979971	−	0.199139i	$-0.936185\pi$
$101$	−19.6972	−1.95994	−0.979971	+	0.199139i	$0.936185\pi$
$102$	−0.851264	−0.0842877
$103$	−2.41267	−0.237727	−0.118864	−	0.992911i	$-0.537925\pi$
$103$	−2.41267	−0.237727	−0.118864	+	0.992911i	$0.537925\pi$
$104$	62.9729	6.17500
$105$	1.67767	0.163724
$106$	−4.06851	−0.395169
$107$	−9.26256	−0.895445	−0.447723	−	0.894172i	$-0.647765\pi$
$107$	−9.26256	−0.895445	−0.447723	+	0.894172i	$0.647765\pi$
$108$	5.83249	0.561232
$109$	−8.30530	−0.795503	−0.397752	−	0.917493i	$-0.630209\pi$
$109$	−8.30530	−0.795503	−0.397752	+	0.917493i	$0.630209\pi$
$110$	0	0
$111$	3.21023	0.304702
$112$	−18.3530	−1.73420
$113$	5.47962	0.515479	0.257740	−	0.966214i	$-0.417022\pi$
$113$	5.47962	0.515479	0.257740	+	0.966214i	$0.417022\pi$
$114$	−12.9539	−1.21324
$115$	2.31794	0.216149
$116$	23.1473	2.14917
$117$	5.87113	0.542787
$118$	−6.98110	−0.642662
$119$	0.304169	0.0278831
$120$	−17.9945	−1.64266
$121$	0	0
$122$	9.49572	0.859702
$123$	−8.31274	−0.749534
$124$	4.45660	0.400215
$125$	12.0548	1.07821
$126$	−2.79866	−0.249324
$127$	20.0576	1.77983	0.889913	−	0.456130i	$-0.150765\pi$
$127$	20.0576	1.77983	0.889913	+	0.456130i	$0.150765\pi$
$128$	71.7346	6.34050
$129$	−1.01069	−0.0889866
$130$	−27.5664	−2.41773
$131$	4.22096	0.368787	0.184394	−	0.982852i	$-0.440968\pi$
$131$	4.22096	0.368787	0.184394	+	0.982852i	$0.440968\pi$
$132$	0	0
$133$	4.62860	0.401350
$134$	17.2643	1.49141
$135$	−1.67767	−0.144391
$136$	−3.26247	−0.279754
$137$	−14.5361	−1.24191	−0.620953	−	0.783848i	$-0.713254\pi$
$137$	−14.5361	−1.24191	−0.620953	+	0.783848i	$0.713254\pi$
$138$	−3.86674	−0.329159
$139$	6.94615	0.589165	0.294583	−	0.955626i	$-0.404819\pi$
$139$	6.94615	0.589165	0.294583	+	0.955626i	$0.404819\pi$
$140$	9.78502	0.826985
$141$	−2.58688	−0.217855
$142$	21.2682	1.78479
$143$	0	0
$144$	18.3530	1.52942
$145$	−6.65814	−0.552929
$146$	−35.6704	−2.95211
$147$	1.00000	0.0824786
$148$	18.7236	1.53907
$149$	−13.9640	−1.14398	−0.571989	−	0.820262i	$-0.693828\pi$
$149$	−13.9640	−1.14398	−0.571989	+	0.820262i	$0.693828\pi$
$150$	−6.11623	−0.499388
$151$	−1.37080	−0.111554	−0.0557771	−	0.998443i	$-0.517764\pi$
$151$	−1.37080	−0.111554	−0.0557771	+	0.998443i	$0.517764\pi$
$152$	−49.6456	−4.02679
$153$	−0.304169	−0.0245906
$154$	0	0
$155$	−1.28191	−0.102965
$156$	34.2434	2.74166
$157$	−15.8997	−1.26894	−0.634469	−	0.772949i	$-0.718781\pi$
$157$	−15.8997	−1.26894	−0.634469	+	0.772949i	$0.718781\pi$
$158$	−17.2263	−1.37045
$159$	−1.45374	−0.115289
$160$	−50.1827	−3.96729
$161$	1.38164	0.108888
$162$	2.79866	0.219883
$163$	10.4685	0.819957	0.409978	−	0.912095i	$-0.365536\pi$
$163$	10.4685	0.819957	0.409978	+	0.912095i	$0.365536\pi$
$164$	−48.4840	−3.78596
$165$	0	0
$166$	−5.63275	−0.437186
$167$	8.57355	0.663442	0.331721	−	0.943378i	$-0.392371\pi$
$167$	8.57355	0.663442	0.331721	+	0.943378i	$0.392371\pi$
$168$	−10.7258	−0.827517
$169$	21.4702	1.65156
$170$	1.42814	0.109534
$171$	−4.62860	−0.353958
$172$	−5.89486	−0.449479
$173$	−13.7471	−1.04517	−0.522586	−	0.852587i	$-0.675033\pi$
$173$	−13.7471	−1.04517	−0.522586	+	0.852587i	$0.675033\pi$
$174$	11.1070	0.842018
$175$	2.18541	0.165202
$176$	0	0
$177$	−2.49444	−0.187494
$178$	0.236181	0.0177025
$179$	−3.85014	−0.287773	−0.143887	−	0.989594i	$-0.545960\pi$
$179$	−3.85014	−0.287773	−0.143887	+	0.989594i	$0.545960\pi$
$180$	−9.78502	−0.729332
$181$	−19.5568	−1.45365	−0.726823	−	0.686825i	$-0.759004\pi$
$181$	−19.5568	−1.45365	−0.726823	+	0.686825i	$0.759004\pi$
$182$	−16.4313	−1.21797
$183$	3.39295	0.250814
$184$	−14.8192	−1.09249
$185$	−5.38571	−0.395966
$186$	2.13845	0.156799
$187$	0	0
$188$	−15.0880	−1.10040
$189$	−1.00000	−0.0727393
$190$	21.7324	1.57663
$191$	−2.54502	−0.184151	−0.0920755	−	0.995752i	$-0.529350\pi$
$191$	−2.54502	−0.184151	−0.0920755	+	0.995752i	$0.529350\pi$
$192$	47.0078	3.39250
$193$	21.6282	1.55683	0.778415	−	0.627750i	$-0.216024\pi$
$193$	21.6282	1.55683	0.778415	+	0.627750i	$0.216024\pi$
$194$	2.90430	0.208517
$195$	−9.84984	−0.705362
$196$	5.83249	0.416607
$197$	−22.0693	−1.57237	−0.786187	−	0.617989i	$-0.787948\pi$
$197$	−22.0693	−1.57237	−0.786187	+	0.617989i	$0.787948\pi$
$198$	0	0
$199$	−12.8315	−0.909598	−0.454799	−	0.890594i	$-0.650289\pi$
$199$	−12.8315	−0.909598	−0.454799	+	0.890594i	$0.650289\pi$
$200$	−23.4404	−1.65749
$201$	6.16878	0.435112
$202$	−55.1257	−3.87863
$203$	−3.96868	−0.278547
$204$	−1.77406	−0.124209
$205$	13.9461	0.974035
$206$	−6.75224	−0.470451
$207$	−1.38164	−0.0960305
$208$	107.753	7.47132
$209$	0	0
$210$	4.69523	0.324002
$211$	−17.7406	−1.22131	−0.610655	−	0.791897i	$-0.709094\pi$
$211$	−17.7406	−1.22131	−0.610655	+	0.791897i	$0.709094\pi$
$212$	−8.47891	−0.582334
$213$	7.59943	0.520704
$214$	−25.9227	−1.77204
$215$	1.69561	0.115640
$216$	10.7258	0.729801
$217$	−0.764099	−0.0518704
$218$	−23.2437	−1.57426
$219$	−12.7455	−0.861264
$220$	0	0
$221$	−1.78581	−0.120127
$222$	8.98434	0.602989
$223$	17.1174	1.14627	0.573133	−	0.819462i	$-0.305728\pi$
$223$	17.1174	1.14627	0.573133	+	0.819462i	$0.305728\pi$
$224$	−29.9121	−1.99859
$225$	−2.18541	−0.145694
$226$	15.3356	1.02011
$227$	−20.4871	−1.35978	−0.679888	−	0.733316i	$-0.737971\pi$
$227$	−20.4871	−1.35978	−0.679888	+	0.733316i	$0.737971\pi$
$228$	−26.9963	−1.78787
$229$	24.4342	1.61466	0.807328	−	0.590103i	$-0.200913\pi$
$229$	24.4342	1.61466	0.807328	+	0.590103i	$0.200913\pi$
$230$	6.48712	0.427748
$231$	0	0
$232$	42.5674	2.79469
$233$	−23.7053	−1.55298	−0.776491	−	0.630128i	$-0.783002\pi$
$233$	−23.7053	−1.55298	−0.776491	+	0.630128i	$0.783002\pi$
$234$	16.4313	1.07415
$235$	4.33994	0.283106
$236$	−14.5488	−0.947048
$237$	−6.15519	−0.399822
$238$	0.851264	0.0551793
$239$	−1.57997	−0.102200	−0.0510998	−	0.998694i	$-0.516273\pi$
$239$	−1.57997	−0.102200	−0.0510998	+	0.998694i	$0.516273\pi$
$240$	−30.7903	−1.98751
$241$	−12.2382	−0.788333	−0.394167	−	0.919039i	$-0.628967\pi$
$241$	−12.2382	−0.788333	−0.394167	+	0.919039i	$0.628967\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	19.7894	1.26688
$245$	−1.67767	−0.107183
$246$	−23.2645	−1.48329
$247$	−27.1751	−1.72911
$248$	8.19561	0.520422
$249$	−2.01266	−0.127547
$250$	33.7372	2.13373
$251$	19.4107	1.22520	0.612598	−	0.790395i	$-0.290125\pi$
$251$	19.4107	1.22520	0.612598	+	0.790395i	$0.290125\pi$
$252$	−5.83249	−0.367413
$253$	0	0
$254$	56.1345	3.52219
$255$	0.510295	0.0319559
$256$	106.745	6.67157
$257$	−0.270104	−0.0168486	−0.00842431	−	0.999965i	$-0.502682\pi$
$257$	−0.270104	−0.0168486	−0.00842431	+	0.999965i	$0.502682\pi$
$258$	−2.82859	−0.176100
$259$	−3.21023	−0.199474
$260$	−57.4491	−3.56284
$261$	3.96868	0.245655
$262$	11.8130	0.729812
$263$	27.9927	1.72611	0.863053	−	0.505113i	$-0.168549\pi$
$263$	27.9927	1.72611	0.863053	+	0.505113i	$0.168549\pi$
$264$	0	0
$265$	2.43889	0.149820
$266$	12.9539	0.794253
$267$	0.0843908	0.00516463
$268$	35.9794	2.19779
$269$	1.11686	0.0680960	0.0340480	−	0.999420i	$-0.489160\pi$
$269$	1.11686	0.0680960	0.0340480	+	0.999420i	$0.489160\pi$
$270$	−4.69523	−0.285743
$271$	24.8310	1.50837	0.754187	−	0.656660i	$-0.228031\pi$
$271$	24.8310	1.50837	0.754187	+	0.656660i	$0.228031\pi$
$272$	−5.58241	−0.338483
$273$	−5.87113	−0.355337
$274$	−40.6817	−2.45767
$275$	0	0
$276$	−8.05840	−0.485059
$277$	−12.4335	−0.747057	−0.373528	−	0.927619i	$-0.621852\pi$
$277$	−12.4335	−0.747057	−0.373528	+	0.927619i	$0.621852\pi$
$278$	19.4399	1.16593
$279$	0.764099	0.0457454
$280$	17.9945	1.07537
$281$	−6.73560	−0.401812	−0.200906	−	0.979611i	$-0.564389\pi$
$281$	−6.73560	−0.401812	−0.200906	+	0.979611i	$0.564389\pi$
$282$	−7.23980	−0.431124
$283$	−11.1606	−0.663430	−0.331715	−	0.943380i	$-0.607627\pi$
$283$	−11.1606	−0.663430	−0.331715	+	0.943380i	$0.607627\pi$
$284$	44.3236	2.63012
$285$	7.76527	0.459975
$286$	0	0
$287$	8.31274	0.490685
$288$	29.9121	1.76259
$289$	−16.9075	−0.994558
$290$	−18.6339	−1.09422
$291$	1.03775	0.0608338
$292$	−74.3383	−4.35032
$293$	−16.9009	−0.987363	−0.493682	−	0.869643i	$-0.664349\pi$
$293$	−16.9009	−0.987363	−0.493682	+	0.869643i	$0.664349\pi$
$294$	2.79866	0.163221
$295$	4.18486	0.243652
$296$	34.4324	2.00134
$297$	0	0
$298$	−39.0805	−2.26388
$299$	−8.11179	−0.469117
$300$	−12.7464	−0.735915
$301$	1.01069	0.0582554
$302$	−3.83640	−0.220760
$303$	−19.6972	−1.13157
$304$	−84.9487	−4.87214
$305$	−5.69226	−0.325938
$306$	−0.851264	−0.0486635
$307$	−11.3453	−0.647511	−0.323755	−	0.946141i	$-0.604946\pi$
$307$	−11.3453	−0.647511	−0.323755	+	0.946141i	$0.604946\pi$
$308$	0	0
$309$	−2.41267	−0.137252
$310$	−3.58762	−0.203763
$311$	23.8487	1.35234	0.676169	−	0.736747i	$-0.263639\pi$
$311$	23.8487	1.35234	0.676169	+	0.736747i	$0.263639\pi$
$312$	62.9729	3.56514
$313$	30.9666	1.75034	0.875169	−	0.483818i	$-0.160750\pi$
$313$	30.9666	1.75034	0.875169	+	0.483818i	$0.160750\pi$
$314$	−44.4980	−2.51116
$315$	1.67767	0.0945261
$316$	−35.9001	−2.01954
$317$	3.20875	0.180221	0.0901106	−	0.995932i	$-0.471278\pi$
$317$	3.20875	0.180221	0.0901106	+	0.995932i	$0.471278\pi$
$318$	−4.06851	−0.228151
$319$	0	0
$320$	−78.8637	−4.40862
$321$	−9.26256	−0.516986
$322$	3.86674	0.215485
$323$	1.40787	0.0783362
$324$	5.83249	0.324027
$325$	−12.8309	−0.711728
$326$	29.2978	1.62265
$327$	−8.30530	−0.459284
$328$	−89.1612	−4.92310
$329$	2.58688	0.142619
$330$	0	0
$331$	−3.98424	−0.218994	−0.109497	−	0.993987i	$-0.534924\pi$
$331$	−3.98424	−0.218994	−0.109497	+	0.993987i	$0.534924\pi$
$332$	−11.7388	−0.644252
$333$	3.21023	0.175920
$334$	23.9945	1.31292
$335$	−10.3492	−0.565437
$336$	−18.3530	−1.00124
$337$	−11.3006	−0.615582	−0.307791	−	0.951454i	$-0.599590\pi$
$337$	−11.3006	−0.615582	−0.307791	+	0.951454i	$0.599590\pi$
$338$	60.0878	3.26835
$339$	5.47962	0.297612
$340$	2.97629	0.161412
$341$	0	0
$342$	−12.9539	−0.700465
$343$	−1.00000	−0.0539949
$344$	−10.8405	−0.584483
$345$	2.31794	0.124794
$346$	−38.4734	−2.06834
$347$	6.58840	0.353684	0.176842	−	0.984239i	$-0.443412\pi$
$347$	6.58840	0.353684	0.176842	+	0.984239i	$0.443412\pi$
$348$	23.1473	1.24083
$349$	20.4343	1.09382	0.546912	−	0.837190i	$-0.315803\pi$
$349$	20.4343	1.09382	0.546912	+	0.837190i	$0.315803\pi$
$350$	6.11623	0.326926
$351$	5.87113	0.313378
$352$	0	0
$353$	36.5457	1.94513	0.972565	−	0.232630i	$-0.0747330\pi$
$353$	36.5457	1.94513	0.972565	+	0.232630i	$0.0747330\pi$
$354$	−6.98110	−0.371041
$355$	−12.7494	−0.676665
$356$	0.492209	0.0260870
$357$	0.304169	0.0160983
$358$	−10.7752	−0.569489
$359$	0.314474	0.0165973	0.00829864	−	0.999966i	$-0.497358\pi$
$359$	0.314474	0.0165973	0.00829864	+	0.999966i	$0.497358\pi$
$360$	−17.9945	−0.948391
$361$	2.42393	0.127575
$362$	−54.7328	−2.87669
$363$	0	0
$364$	−34.2434	−1.79484
$365$	21.3829	1.11923
$366$	9.49572	0.496349
$367$	22.6952	1.18468	0.592340	−	0.805688i	$-0.298204\pi$
$367$	22.6952	1.18468	0.592340	+	0.805688i	$0.298204\pi$
$368$	−25.3572	−1.32184
$369$	−8.31274	−0.432744
$370$	−15.0728	−0.783597
$371$	1.45374	0.0754742
$372$	4.45660	0.231064
$373$	32.8020	1.69843	0.849213	−	0.528051i	$-0.177077\pi$
$373$	32.8020	1.69843	0.849213	+	0.528051i	$0.177077\pi$
$374$	0	0
$375$	12.0548	0.622506
$376$	−27.7465	−1.43092
$377$	23.3006	1.20004
$378$	−2.79866	−0.143948
$379$	25.4514	1.30735	0.653675	−	0.756776i	$-0.273227\pi$
$379$	25.4514	1.30735	0.653675	+	0.756776i	$0.273227\pi$
$380$	45.2909	2.32338
$381$	20.0576	1.02758
$382$	−7.12264	−0.364426
$383$	−13.9526	−0.712944	−0.356472	−	0.934306i	$-0.616021\pi$
$383$	−13.9526	−0.712944	−0.356472	+	0.934306i	$0.616021\pi$
$384$	71.7346	3.66069
$385$	0	0
$386$	60.5299	3.08089
$387$	−1.01069	−0.0513764
$388$	6.05266	0.307277
$389$	−9.06975	−0.459855	−0.229927	−	0.973208i	$-0.573849\pi$
$389$	−9.06975	−0.459855	−0.229927	+	0.973208i	$0.573849\pi$
$390$	−27.5664	−1.39588
$391$	0.420251	0.0212530
$392$	10.7258	0.541737
$393$	4.22096	0.212919
$394$	−61.7645	−3.11165
$395$	10.3264	0.519577
$396$	0	0
$397$	24.1849	1.21381	0.606904	−	0.794775i	$-0.292411\pi$
$397$	24.1849	1.21381	0.606904	+	0.794775i	$0.292411\pi$
$398$	−35.9109	−1.80005
$399$	4.62860	0.231720
$400$	−40.1089	−2.00545
$401$	3.86368	0.192943	0.0964715	−	0.995336i	$-0.469244\pi$
$401$	3.86368	0.192943	0.0964715	+	0.995336i	$0.469244\pi$
$402$	17.2643	0.861065
$403$	4.48613	0.223470
$404$	−114.884	−5.71568
$405$	−1.67767	−0.0833642
$406$	−11.1070	−0.551230
$407$	0	0
$408$	−3.26247	−0.161516
$409$	20.0985	0.993806	0.496903	−	0.867806i	$-0.334470\pi$
$409$	20.0985	0.993806	0.496903	+	0.867806i	$0.334470\pi$
$410$	39.0303	1.92757
$411$	−14.5361	−0.717015
$412$	−14.0719	−0.693272
$413$	2.49444	0.122744
$414$	−3.86674	−0.190040
$415$	3.37659	0.165750
$416$	175.618	8.61038
$417$	6.94615	0.340155
$418$	0	0
$419$	−2.12825	−0.103972	−0.0519859	−	0.998648i	$-0.516555\pi$
$419$	−2.12825	−0.103972	−0.0519859	+	0.998648i	$0.516555\pi$
$420$	9.78502	0.477460
$421$	−3.84998	−0.187636	−0.0938182	−	0.995589i	$-0.529907\pi$
$421$	−3.84998	−0.187636	−0.0938182	+	0.995589i	$0.529907\pi$
$422$	−49.6498	−2.41691
$423$	−2.58688	−0.125778
$424$	−15.5926	−0.757242
$425$	0.664734	0.0322443
$426$	21.2682	1.03045
$427$	−3.39295	−0.164196
$428$	−54.0238	−2.61134
$429$	0	0
$430$	4.74544	0.228846
$431$	−16.7030	−0.804555	−0.402278	−	0.915518i	$-0.631781\pi$
$431$	−16.7030	−0.804555	−0.402278	+	0.915518i	$0.631781\pi$
$432$	18.3530	0.883009
$433$	16.9215	0.813196	0.406598	−	0.913607i	$-0.366715\pi$
$433$	16.9215	0.813196	0.406598	+	0.913607i	$0.366715\pi$
$434$	−2.13845	−0.102649
$435$	−6.65814	−0.319234
$436$	−48.4406	−2.31988
$437$	6.39505	0.305917
$438$	−35.6704	−1.70440
$439$	−26.7946	−1.27883	−0.639417	−	0.768860i	$-0.720824\pi$
$439$	−26.7946	−1.27883	−0.639417	+	0.768860i	$0.720824\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−4.99789	−0.237725
$443$	−3.92408	−0.186439	−0.0932194	−	0.995646i	$-0.529716\pi$
$443$	−3.92408	−0.186439	−0.0932194	+	0.995646i	$0.529716\pi$
$444$	18.7236	0.888585
$445$	−0.141580	−0.00671154
$446$	47.9058	2.26841
$447$	−13.9640	−0.660476
$448$	−47.0078	−2.22091
$449$	19.6785	0.928686	0.464343	−	0.885655i	$-0.346291\pi$
$449$	19.6785	0.928686	0.464343	+	0.885655i	$0.346291\pi$
$450$	−6.11623	−0.288322
$451$	0	0
$452$	31.9598	1.50326
$453$	−1.37080	−0.0644058
$454$	−57.3364	−2.69093
$455$	9.84984	0.461768
$456$	−49.6456	−2.32487
$457$	19.7725	0.924921	0.462460	−	0.886640i	$-0.346967\pi$
$457$	19.7725	0.924921	0.462460	+	0.886640i	$0.346967\pi$
$458$	68.3830	3.19533
$459$	−0.304169	−0.0141974
$460$	13.5194	0.630343
$461$	9.69184	0.451394	0.225697	−	0.974198i	$-0.427534\pi$
$461$	9.69184	0.451394	0.225697	+	0.974198i	$0.427534\pi$
$462$	0	0
$463$	7.21162	0.335152	0.167576	−	0.985859i	$-0.446406\pi$
$463$	7.21162	0.335152	0.167576	+	0.985859i	$0.446406\pi$
$464$	72.8372	3.38138
$465$	−1.28191	−0.0594471
$466$	−66.3429	−3.07328
$467$	36.5718	1.69234	0.846171	−	0.532912i	$-0.178902\pi$
$467$	36.5718	1.69234	0.846171	+	0.532912i	$0.178902\pi$
$468$	34.2434	1.58290
$469$	−6.16878	−0.284848
$470$	12.1460	0.560253
$471$	−15.8997	−0.732621
$472$	−26.7550	−1.23150
$473$	0	0
$474$	−17.2263	−0.791229
$475$	10.1154	0.464127
$476$	1.77406	0.0813140
$477$	−1.45374	−0.0665620
$478$	−4.42179	−0.202248
$479$	38.9699	1.78058	0.890290	−	0.455394i	$-0.150502\pi$
$479$	38.9699	1.78058	0.890290	+	0.455394i	$0.150502\pi$
$480$	−50.1827	−2.29052
$481$	18.8477	0.859381
$482$	−34.2506	−1.56007
$483$	1.38164	0.0628667
$484$	0	0
$485$	−1.74100	−0.0790548
$486$	2.79866	0.126950
$487$	−23.9835	−1.08679	−0.543397	−	0.839476i	$-0.682862\pi$
$487$	−23.9835	−1.08679	−0.543397	+	0.839476i	$0.682862\pi$
$488$	36.3923	1.64740
$489$	10.4685	0.473402
$490$	−4.69523	−0.212109
$491$	3.19310	0.144103	0.0720513	−	0.997401i	$-0.477045\pi$
$491$	3.19310	0.144103	0.0720513	+	0.997401i	$0.477045\pi$
$492$	−48.4840	−2.18583
$493$	−1.20715	−0.0543672
$494$	−76.0539	−3.42183
$495$	0	0
$496$	14.0235	0.629674
$497$	−7.59943	−0.340881
$498$	−5.63275	−0.252410
$499$	27.5331	1.23255	0.616275	−	0.787531i	$-0.288641\pi$
$499$	27.5331	1.23255	0.616275	+	0.787531i	$0.288641\pi$
$500$	70.3094	3.14433
$501$	8.57355	0.383038
$502$	54.3241	2.42460
$503$	−33.1568	−1.47839	−0.739195	−	0.673492i	$-0.764794\pi$
$503$	−33.1568	−1.47839	−0.739195	+	0.673492i	$0.764794\pi$
$504$	−10.7258	−0.477767
$505$	33.0454	1.47050
$506$	0	0
$507$	21.4702	0.953526
$508$	116.986	5.19042
$509$	−7.69479	−0.341066	−0.170533	−	0.985352i	$-0.554549\pi$
$509$	−7.69479	−0.341066	−0.170533	+	0.985352i	$0.554549\pi$
$510$	1.42814	0.0632392
$511$	12.7455	0.563830
$512$	155.274	6.86221
$513$	−4.62860	−0.204358
$514$	−0.755929	−0.0333426
$515$	4.04767	0.178362
$516$	−5.89486	−0.259507
$517$	0	0
$518$	−8.98434	−0.394749
$519$	−13.7471	−0.603430
$520$	−105.648	−4.63297
$521$	−8.09827	−0.354792	−0.177396	−	0.984140i	$-0.556767\pi$
$521$	−8.09827	−0.354792	−0.177396	+	0.984140i	$0.556767\pi$
$522$	11.1070	0.486139
$523$	19.3528	0.846241	0.423120	−	0.906073i	$-0.360935\pi$
$523$	19.3528	0.846241	0.423120	+	0.906073i	$0.360935\pi$
$524$	24.6187	1.07547
$525$	2.18541	0.0953793
$526$	78.3422	3.41588
$527$	−0.232415	−0.0101241
$528$	0	0
$529$	−21.0911	−0.917003
$530$	6.82563	0.296487
$531$	−2.49444	−0.108250
$532$	26.9963	1.17044
$533$	−48.8052	−2.11399
$534$	0.236181	0.0102206
$535$	15.5395	0.671833
$536$	66.1654	2.85791
$537$	−3.85014	−0.166146
$538$	3.12571	0.134759
$539$	0	0
$540$	−9.78502	−0.421080
$541$	−28.5883	−1.22911	−0.614554	−	0.788875i	$-0.710664\pi$
$541$	−28.5883	−1.22911	−0.614554	+	0.788875i	$0.710664\pi$
$542$	69.4934	2.98500
$543$	−19.5568	−0.839263
$544$	−9.09832	−0.390087
$545$	13.9336	0.596849
$546$	−16.4313	−0.703195
$547$	23.3917	1.00016	0.500078	−	0.865980i	$-0.333305\pi$
$547$	23.3917	1.00016	0.500078	+	0.865980i	$0.333305\pi$
$548$	−84.7820	−3.62171
$549$	3.39295	0.144808
$550$	0	0
$551$	−18.3694	−0.782564
$552$	−14.8192	−0.630749
$553$	6.15519	0.261745
$554$	−34.7971	−1.47839
$555$	−5.38571	−0.228611
$556$	40.5134	1.71815
$557$	25.4361	1.07776	0.538881	−	0.842382i	$-0.318847\pi$
$557$	25.4361	1.07776	0.538881	+	0.842382i	$0.318847\pi$
$558$	2.13845	0.0905279
$559$	−5.93392	−0.250978
$560$	30.7903	1.30113
$561$	0	0
$562$	−18.8506	−0.795167
$563$	39.8791	1.68070	0.840352	−	0.542041i	$-0.182348\pi$
$563$	39.8791	1.68070	0.840352	+	0.542041i	$0.182348\pi$
$564$	−15.0880	−0.635318
$565$	−9.19301	−0.386753
$566$	−31.2348	−1.31290
$567$	−1.00000	−0.0419961
$568$	81.5103	3.42010
$569$	32.2487	1.35194	0.675968	−	0.736931i	$-0.263726\pi$
$569$	32.2487	1.35194	0.675968	+	0.736931i	$0.263726\pi$
$570$	21.7324	0.910268
$571$	−20.6844	−0.865615	−0.432807	−	0.901486i	$-0.642477\pi$
$571$	−20.6844	−0.865615	−0.432807	+	0.901486i	$0.642477\pi$
$572$	0	0
$573$	−2.54502	−0.106320
$574$	23.2645	0.971043
$575$	3.01945	0.125920
$576$	47.0078	1.95866
$577$	15.7198	0.654424	0.327212	−	0.944951i	$-0.393891\pi$
$577$	15.7198	0.654424	0.327212	+	0.944951i	$0.393891\pi$
$578$	−47.3183	−1.96818
$579$	21.6282	0.898836
$580$	−38.8336	−1.61248
$581$	2.01266	0.0834993
$582$	2.90430	0.120387
$583$	0	0
$584$	−136.707	−5.65697
$585$	−9.84984	−0.407241
$586$	−47.3000	−1.95394
$587$	20.5683	0.848946	0.424473	−	0.905441i	$-0.360459\pi$
$587$	20.5683	0.848946	0.424473	+	0.905441i	$0.360459\pi$
$588$	5.83249	0.240528
$589$	−3.53671	−0.145727
$590$	11.7120	0.482175
$591$	−22.0693	−0.907810
$592$	58.9174	2.42149
$593$	21.1496	0.868511	0.434255	−	0.900790i	$-0.357012\pi$
$593$	21.1496	0.868511	0.434255	+	0.900790i	$0.357012\pi$
$594$	0	0
$595$	−0.510295	−0.0209201
$596$	−81.4451	−3.33612
$597$	−12.8315	−0.525156
$598$	−22.7021	−0.928359
$599$	−33.6993	−1.37691	−0.688457	−	0.725277i	$-0.741712\pi$
$599$	−33.6993	−1.37691	−0.688457	+	0.725277i	$0.741712\pi$
$600$	−23.4404	−0.956951
$601$	−36.7888	−1.50065	−0.750324	−	0.661070i	$-0.770103\pi$
$601$	−36.7888	−1.50065	−0.750324	+	0.661070i	$0.770103\pi$
$602$	2.82859	0.115285
$603$	6.16878	0.251212
$604$	−7.99519	−0.325320
$605$	0	0
$606$	−55.1257	−2.23933
$607$	12.0614	0.489558	0.244779	−	0.969579i	$-0.421285\pi$
$607$	12.0614	0.489558	0.244779	+	0.969579i	$0.421285\pi$
$608$	−138.451	−5.61494
$609$	−3.96868	−0.160819
$610$	−15.9307	−0.645015
$611$	−15.1879	−0.614437
$612$	−1.77406	−0.0717122
$613$	8.57642	0.346398	0.173199	−	0.984887i	$-0.444590\pi$
$613$	8.57642	0.346398	0.173199	+	0.984887i	$0.444590\pi$
$614$	−31.7517	−1.28139
$615$	13.9461	0.562359
$616$	0	0
$617$	−0.0309560	−0.00124624	−0.000623121	−	1.00000i	$-0.500198\pi$
$617$	−0.0309560	−0.00124624	−0.000623121		1.00000i	$0.500198\pi$
$618$	−6.75224	−0.271615
$619$	−21.2938	−0.855869	−0.427934	−	0.903810i	$-0.640759\pi$
$619$	−21.2938	−0.855869	−0.427934	+	0.903810i	$0.640759\pi$
$620$	−7.47672	−0.300272
$621$	−1.38164	−0.0554433
$622$	66.7445	2.67621
$623$	−0.0843908	−0.00338105
$624$	107.753	4.31357
$625$	−9.29689	−0.371876
$626$	86.6650	3.46383
$627$	0	0
$628$	−92.7351	−3.70053
$629$	−0.976451	−0.0389336
$630$	4.69523	0.187063
$631$	21.7895	0.867426	0.433713	−	0.901051i	$-0.357203\pi$
$631$	21.7895	0.867426	0.433713	+	0.901051i	$0.357203\pi$
$632$	−66.0196	−2.62612
$633$	−17.7406	−0.705124
$634$	8.98019	0.356649
$635$	−33.6501	−1.33536
$636$	−8.47891	−0.336211
$637$	5.87113	0.232623
$638$	0	0
$639$	7.59943	0.300629
$640$	−120.347	−4.75714
$641$	−39.8969	−1.57583	−0.787916	−	0.615783i	$-0.788840\pi$
$641$	−39.8969	−1.57583	−0.787916	+	0.615783i	$0.788840\pi$
$642$	−25.9227	−1.02309
$643$	7.15604	0.282207	0.141103	−	0.989995i	$-0.454935\pi$
$643$	7.15604	0.282207	0.141103	+	0.989995i	$0.454935\pi$
$644$	8.05840	0.317546
$645$	1.69561	0.0667647
$646$	3.94016	0.155024
$647$	−4.74897	−0.186701	−0.0933506	−	0.995633i	$-0.529758\pi$
$647$	−4.74897	−0.186701	−0.0933506	+	0.995633i	$0.529758\pi$
$648$	10.7258	0.421351
$649$	0	0
$650$	−35.9092	−1.40848
$651$	−0.764099	−0.0299474
$652$	61.0575	2.39120
$653$	−5.03380	−0.196988	−0.0984938	−	0.995138i	$-0.531402\pi$
$653$	−5.03380	−0.196988	−0.0984938	+	0.995138i	$0.531402\pi$
$654$	−23.2437	−0.908900
$655$	−7.08139	−0.276693
$656$	−152.564	−5.95661
$657$	−12.7455	−0.497251
$658$	7.23980	0.282237
$659$	6.55136	0.255205	0.127602	−	0.991825i	$-0.459272\pi$
$659$	6.55136	0.255205	0.127602	+	0.991825i	$0.459272\pi$
$660$	0	0
$661$	36.4255	1.41679	0.708394	−	0.705818i	$-0.249420\pi$
$661$	36.4255	1.41679	0.708394	+	0.705818i	$0.249420\pi$
$662$	−11.1505	−0.433378
$663$	−1.78581	−0.0693553
$664$	−21.5875	−0.837757
$665$	−7.76527	−0.301124
$666$	8.98434	0.348136
$667$	−5.48328	−0.212313
$668$	50.0052	1.93476
$669$	17.1174	0.661797
$670$	−28.9639	−1.11897
$671$	0	0
$672$	−29.9121	−1.15388
$673$	31.9908	1.23315	0.616577	−	0.787295i	$-0.288519\pi$
$673$	31.9908	1.23315	0.616577	+	0.787295i	$0.288519\pi$
$674$	−31.6265	−1.21821
$675$	−2.18541	−0.0841166
$676$	125.225	4.81634
$677$	−21.6417	−0.831760	−0.415880	−	0.909420i	$-0.636526\pi$
$677$	−21.6417	−0.831760	−0.415880	+	0.909420i	$0.636526\pi$
$678$	15.3356	0.588960
$679$	−1.03775	−0.0398251
$680$	5.47335	0.209893
$681$	−20.4871	−0.785067
$682$	0	0
$683$	−23.1587	−0.886144	−0.443072	−	0.896486i	$-0.646111\pi$
$683$	−23.1587	−0.886144	−0.443072	+	0.896486i	$0.646111\pi$
$684$	−26.9963	−1.03223
$685$	24.3869	0.931775
$686$	−2.79866	−0.106853
$687$	24.4342	0.932222
$688$	−18.5493	−0.707184
$689$	−8.53508	−0.325161
$690$	6.48712	0.246960
$691$	2.69598	0.102560	0.0512800	−	0.998684i	$-0.483670\pi$
$691$	2.69598	0.102560	0.0512800	+	0.998684i	$0.483670\pi$
$692$	−80.1798	−3.04798
$693$	0	0
$694$	18.4387	0.699923
$695$	−11.6534	−0.442038
$696$	42.5674	1.61351
$697$	2.52847	0.0957728
$698$	57.1887	2.16463
$699$	−23.7053	−0.896615
$700$	12.7464	0.481769
$701$	0.447285	0.0168937	0.00844686	−	0.999964i	$-0.497311\pi$
$701$	0.447285	0.0168937	0.00844686	+	0.999964i	$0.497311\pi$
$702$	16.4313	0.620160
$703$	−14.8589	−0.560413
$704$	0	0
$705$	4.33994	0.163451
$706$	102.279	3.84932
$707$	19.6972	0.740789
$708$	−14.5488	−0.546778
$709$	11.2291	0.421718	0.210859	−	0.977517i	$-0.432374\pi$
$709$	11.2291	0.421718	0.210859	+	0.977517i	$0.432374\pi$
$710$	−35.6811	−1.33909
$711$	−6.15519	−0.230837
$712$	0.905163	0.0339224
$713$	−1.05571	−0.0395366
$714$	0.851264	0.0318578
$715$	0	0
$716$	−22.4559	−0.839218
$717$	−1.57997	−0.0590050
$718$	0.880105	0.0328452
$719$	9.04358	0.337268	0.168634	−	0.985679i	$-0.446064\pi$
$719$	9.04358	0.337268	0.168634	+	0.985679i	$0.446064\pi$
$720$	−30.7903	−1.14749
$721$	2.41267	0.0898525
$722$	6.78375	0.252465
$723$	−12.2382	−0.455144
$724$	−114.065	−4.23919
$725$	−8.67321	−0.322115
$726$	0	0
$727$	−44.1368	−1.63694	−0.818471	−	0.574548i	$-0.805178\pi$
$727$	−44.1368	−1.63694	−0.818471	+	0.574548i	$0.805178\pi$
$728$	−62.9729	−2.33393
$729$	1.00000	0.0370370
$730$	59.8433	2.21490
$731$	0.307421	0.0113704
$732$	19.7894	0.731436
$733$	−28.0438	−1.03582	−0.517911	−	0.855435i	$-0.673290\pi$
$733$	−28.0438	−1.03582	−0.517911	+	0.855435i	$0.673290\pi$
$734$	63.5161	2.34442
$735$	−1.67767	−0.0618819
$736$	−41.3277	−1.52336
$737$	0	0
$738$	−23.2645	−0.856379
$739$	−43.7065	−1.60777	−0.803886	−	0.594784i	$-0.797238\pi$
$739$	−43.7065	−1.60777	−0.803886	+	0.594784i	$0.797238\pi$
$740$	−31.4122	−1.15473
$741$	−27.1751	−0.998303
$742$	4.06851	0.149360
$743$	−21.3676	−0.783901	−0.391950	−	0.919986i	$-0.628199\pi$
$743$	−21.3676	−0.783901	−0.391950	+	0.919986i	$0.628199\pi$
$744$	8.19561	0.300466
$745$	23.4271	0.858301
$746$	91.8017	3.36110
$747$	−2.01266	−0.0736394
$748$	0	0
$749$	9.26256	0.338446
$750$	33.7372	1.23191
$751$	2.23940	0.0817169	0.0408585	−	0.999165i	$-0.486991\pi$
$751$	2.23940	0.0817169	0.0408585	+	0.999165i	$0.486991\pi$
$752$	−47.4770	−1.73131
$753$	19.4107	0.707367
$754$	65.2106	2.37483
$755$	2.29976	0.0836967
$756$	−5.83249	−0.212126
$757$	47.7090	1.73401	0.867007	−	0.498296i	$-0.166041\pi$
$757$	47.7090	1.73401	0.867007	+	0.498296i	$0.166041\pi$
$758$	71.2297	2.58718
$759$	0	0
$760$	83.2891	3.02121
$761$	−35.6430	−1.29206	−0.646029	−	0.763313i	$-0.723572\pi$
$761$	−35.6430	−1.29206	−0.646029	+	0.763313i	$0.723572\pi$
$762$	56.1345	2.03354
$763$	8.30530	0.300672
$764$	−14.8438	−0.537030
$765$	0.510295	0.0184498
$766$	−39.0486	−1.41088
$767$	−14.6452	−0.528808
$768$	106.745	3.85183
$769$	22.0645	0.795665	0.397832	−	0.917458i	$-0.369763\pi$
$769$	22.0645	0.795665	0.397832	+	0.917458i	$0.369763\pi$
$770$	0	0
$771$	−0.270104	−0.00972755
$772$	126.146	4.54010
$773$	−18.9064	−0.680016	−0.340008	−	0.940423i	$-0.610430\pi$
$773$	−18.9064	−0.680016	−0.340008	+	0.940423i	$0.610430\pi$
$774$	−2.82859	−0.101671
$775$	−1.66987	−0.0599836
$776$	11.1307	0.399570
$777$	−3.21023	−0.115166
$778$	−25.3832	−0.910030
$779$	38.4763	1.37856
$780$	−57.4491	−2.05701
$781$	0	0
$782$	1.17614	0.0420587
$783$	3.96868	0.141829
$784$	18.3530	0.655464
$785$	26.6746	0.952056
$786$	11.8130	0.421357
$787$	6.64396	0.236832	0.118416	−	0.992964i	$-0.462218\pi$
$787$	6.64396	0.236832	0.118416	+	0.992964i	$0.462218\pi$
$788$	−128.719	−4.58543
$789$	27.9927	0.996568
$790$	28.9000	1.02822
$791$	−5.47962	−0.194833
$792$	0	0
$793$	19.9205	0.707397
$794$	67.6854	2.40207
$795$	2.43889	0.0864987
$796$	−74.8394	−2.65261
$797$	−15.3017	−0.542014	−0.271007	−	0.962577i	$-0.587357\pi$
$797$	−15.3017	−0.542014	−0.271007	+	0.962577i	$0.587357\pi$
$798$	12.9539	0.458562
$799$	0.786847	0.0278367
$800$	−65.3704	−2.31119
$801$	0.0843908	0.00298180
$802$	10.8131	0.381825
$803$	0	0
$804$	35.9794	1.26889
$805$	−2.31794	−0.0816966
$806$	12.5551	0.442236
$807$	1.11686	0.0393153
$808$	−211.269	−7.43241
$809$	24.7092	0.868728	0.434364	−	0.900737i	$-0.356973\pi$
$809$	24.7092	0.868728	0.434364	+	0.900737i	$0.356973\pi$
$810$	−4.69523	−0.164974
$811$	25.7880	0.905539	0.452770	−	0.891628i	$-0.350436\pi$
$811$	25.7880	0.905539	0.452770	+	0.891628i	$0.350436\pi$
$812$	−23.1473	−0.812311
$813$	24.8310	0.870860
$814$	0	0
$815$	−17.5627	−0.615195
$816$	−5.58241	−0.195423
$817$	4.67810	0.163666
$818$	56.2488	1.96669
$819$	−5.87113	−0.205154
$820$	81.3403	2.84053
$821$	−18.3066	−0.638905	−0.319452	−	0.947602i	$-0.603499\pi$
$821$	−18.3066	−0.638905	−0.319452	+	0.947602i	$0.603499\pi$
$822$	−40.6817	−1.41894
$823$	−4.84388	−0.168847	−0.0844235	−	0.996430i	$-0.526905\pi$
$823$	−4.84388	−0.168847	−0.0844235	+	0.996430i	$0.526905\pi$
$824$	−25.8779	−0.901500
$825$	0	0
$826$	6.98110	0.242903
$827$	25.8818	0.900000	0.450000	−	0.893029i	$-0.351424\pi$
$827$	25.8818	0.900000	0.450000	+	0.893029i	$0.351424\pi$
$828$	−8.05840	−0.280049
$829$	54.1465	1.88058	0.940292	−	0.340368i	$-0.110552\pi$
$829$	54.1465	1.88058	0.940292	+	0.340368i	$0.110552\pi$
$830$	9.44992	0.328011
$831$	−12.4335	−0.431313
$832$	275.989	9.56820
$833$	−0.304169	−0.0105388
$834$	19.4399	0.673149
$835$	−14.3836	−0.497766
$836$	0	0
$837$	0.764099	0.0264111
$838$	−5.95625	−0.205755
$839$	32.3629	1.11729	0.558645	−	0.829407i	$-0.311321\pi$
$839$	32.3629	1.11729	0.558645	+	0.829407i	$0.311321\pi$
$840$	17.9945	0.620868
$841$	−13.2496	−0.456882
$842$	−10.7748	−0.371323
$843$	−6.73560	−0.231986
$844$	−103.472	−3.56164
$845$	−36.0200	−1.23913
$846$	−7.23980	−0.248909
$847$	0	0
$848$	−26.6804	−0.916210
$849$	−11.1606	−0.383031
$850$	1.86036	0.0638100
$851$	−4.43538	−0.152043
$852$	44.3236	1.51850
$853$	6.12615	0.209755	0.104878	−	0.994485i	$-0.466555\pi$
$853$	6.12615	0.209755	0.104878	+	0.994485i	$0.466555\pi$
$854$	−9.49572	−0.324937
$855$	7.76527	0.265567
$856$	−99.3488	−3.39567
$857$	−22.6396	−0.773354	−0.386677	−	0.922215i	$-0.626377\pi$
$857$	−22.6396	−0.773354	−0.386677	+	0.922215i	$0.626377\pi$
$858$	0	0
$859$	−13.7204	−0.468134	−0.234067	−	0.972220i	$-0.575204\pi$
$859$	−13.7204	−0.468134	−0.234067	+	0.972220i	$0.575204\pi$
$860$	9.88965	0.337234
$861$	8.31274	0.283297
$862$	−46.7460	−1.59218
$863$	43.6306	1.48520	0.742601	−	0.669734i	$-0.233592\pi$
$863$	43.6306	1.48520	0.742601	+	0.669734i	$0.233592\pi$
$864$	29.9121	1.01763
$865$	23.0631	0.784170
$866$	47.3575	1.60927
$867$	−16.9075	−0.574208
$868$	−4.45660	−0.151267
$869$	0	0
$870$	−18.6339	−0.631748
$871$	36.2177	1.22719
$872$	−89.0813	−3.01667
$873$	1.03775	0.0351224
$874$	17.8976	0.605394
$875$	−12.0548	−0.407526
$876$	−74.3383	−2.51166
$877$	33.9122	1.14513	0.572567	−	0.819858i	$-0.305948\pi$
$877$	33.9122	1.14513	0.572567	+	0.819858i	$0.305948\pi$
$878$	−74.9889	−2.53075
$879$	−16.9009	−0.570055
$880$	0	0
$881$	12.7514	0.429605	0.214803	−	0.976657i	$-0.431089\pi$
$881$	12.7514	0.429605	0.214803	+	0.976657i	$0.431089\pi$
$882$	2.79866	0.0942358
$883$	0.882229	0.0296894	0.0148447	−	0.999890i	$-0.495275\pi$
$883$	0.882229	0.0296894	0.0148447	+	0.999890i	$0.495275\pi$
$884$	−10.4158	−0.350320
$885$	4.18486	0.140673
$886$	−10.9822	−0.368953
$887$	34.4245	1.15586	0.577931	−	0.816086i	$-0.303860\pi$
$887$	34.4245	1.15586	0.577931	+	0.816086i	$0.303860\pi$
$888$	34.4324	1.15548
$889$	−20.0576	−0.672711
$890$	−0.396235	−0.0132818
$891$	0	0
$892$	99.8372	3.34280
$893$	11.9736	0.400682
$894$	−39.0805	−1.30705
$895$	6.45928	0.215910
$896$	−71.7346	−2.39649
$897$	−8.11179	−0.270845
$898$	55.0734	1.83782
$899$	3.03246	0.101138
$900$	−12.7464	−0.424881
$901$	0.442181	0.0147312
$902$	0	0
$903$	1.01069	0.0336338
$904$	58.7736	1.95478
$905$	32.8099	1.09064
$906$	−3.83640	−0.127456
$907$	37.1339	1.23301	0.616505	−	0.787351i	$-0.288548\pi$
$907$	37.1339	1.23301	0.616505	+	0.787351i	$0.288548\pi$
$908$	−119.491	−3.96544
$909$	−19.6972	−0.653314
$910$	27.5664	0.913816
$911$	−38.9275	−1.28973	−0.644864	−	0.764298i	$-0.723086\pi$
$911$	−38.9275	−1.28973	−0.644864	+	0.764298i	$0.723086\pi$
$912$	−84.9487	−2.81293
$913$	0	0
$914$	55.3366	1.83037
$915$	−5.69226	−0.188180
$916$	142.512	4.70874
$917$	−4.22096	−0.139388
$918$	−0.851264	−0.0280959
$919$	−29.1897	−0.962881	−0.481440	−	0.876479i	$-0.659886\pi$
$919$	−29.1897	−0.962881	−0.481440	+	0.876479i	$0.659886\pi$
$920$	24.8618	0.819671
$921$	−11.3453	−0.373841
$922$	27.1242	0.893287
$923$	44.6173	1.46860
$924$	0	0
$925$	−7.01568	−0.230674
$926$	20.1829	0.663250
$927$	−2.41267	−0.0792425
$928$	118.712	3.89690
$929$	18.9850	0.622879	0.311440	−	0.950266i	$-0.399189\pi$
$929$	18.9850	0.622879	0.311440	+	0.950266i	$0.399189\pi$
$930$	−3.58762	−0.117643
$931$	−4.62860	−0.151696
$932$	−138.261	−4.52888
$933$	23.8487	0.780772
$934$	102.352	3.34906
$935$	0	0
$936$	62.9729	2.05833
$937$	−19.8921	−0.649847	−0.324924	−	0.945740i	$-0.605339\pi$
$937$	−19.8921	−0.649847	−0.324924	+	0.945740i	$0.605339\pi$
$938$	−17.2643	−0.563700
$939$	30.9666	1.01056
$940$	25.3127	0.825608
$941$	−10.9695	−0.357595	−0.178797	−	0.983886i	$-0.557221\pi$
$941$	−10.9695	−0.357595	−0.178797	+	0.983886i	$0.557221\pi$
$942$	−44.4980	−1.44982
$943$	11.4852	0.374010
$944$	−45.7805	−1.49003
$945$	1.67767	0.0545747
$946$	0	0
$947$	−40.5321	−1.31712	−0.658558	−	0.752530i	$-0.728833\pi$
$947$	−40.5321	−1.31712	−0.658558	+	0.752530i	$0.728833\pi$
$948$	−35.9001	−1.16598
$949$	−74.8308	−2.42911
$950$	28.3096	0.918484
$951$	3.20875	0.104051
$952$	3.26247	0.105737
$953$	−46.6243	−1.51031	−0.755154	−	0.655547i	$-0.772438\pi$
$953$	−46.6243	−1.51031	−0.755154	+	0.655547i	$0.772438\pi$
$954$	−4.06851	−0.131723
$955$	4.26971	0.138164
$956$	−9.21516	−0.298039
$957$	0	0
$958$	109.063	3.52368
$959$	14.5361	0.469396
$960$	−78.8637	−2.54532
$961$	−30.4162	−0.981166
$962$	52.7483	1.70067
$963$	−9.26256	−0.298482
$964$	−71.3794	−2.29897
$965$	−36.2850	−1.16806
$966$	3.86674	0.124410
$967$	27.2512	0.876338	0.438169	−	0.898893i	$-0.355627\pi$
$967$	27.2512	0.876338	0.438169	+	0.898893i	$0.355627\pi$
$968$	0	0
$969$	1.40787	0.0452274
$970$	−4.87247	−0.156446
$971$	23.2361	0.745683	0.372842	−	0.927895i	$-0.378383\pi$
$971$	23.2361	0.745683	0.372842	+	0.927895i	$0.378383\pi$
$972$	5.83249	0.187077
$973$	−6.94615	−0.222684
$974$	−67.1215	−2.15071
$975$	−12.8309	−0.410916
$976$	62.2709	1.99324
$977$	−28.7747	−0.920583	−0.460292	−	0.887768i	$-0.652255\pi$
$977$	−28.7747	−0.920583	−0.460292	+	0.887768i	$0.652255\pi$
$978$	29.2978	0.936840
$979$	0	0
$980$	−9.78502	−0.312571
$981$	−8.30530	−0.265168
$982$	8.93640	0.285172
$983$	−28.1922	−0.899192	−0.449596	−	0.893232i	$-0.648432\pi$
$983$	−28.1922	−0.899192	−0.449596	+	0.893232i	$0.648432\pi$
$984$	−89.1612	−2.84235
$985$	37.0251	1.17972
$986$	−3.37839	−0.107590
$987$	2.58688	0.0823413
$988$	−158.499	−5.04252
$989$	1.39641	0.0444034
$990$	0	0
$991$	−47.6676	−1.51421	−0.757106	−	0.653293i	$-0.773387\pi$
$991$	−47.6676	−1.51421	−0.757106	+	0.653293i	$0.773387\pi$
$992$	22.8558	0.725673
$993$	−3.98424	−0.126436
$994$	−21.2682	−0.674587
$995$	21.5270	0.682451
$996$	−11.7388	−0.371959
$997$	−18.6624	−0.591046	−0.295523	−	0.955336i	$-0.595494\pi$
$997$	−18.6624	−0.591046	−0.295523	+	0.955336i	$0.595494\pi$
$998$	77.0557	2.43916
$999$	3.21023	0.101567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bq.1.10		10
3.2	odd	2		7623.2.a.cx.1.1		10
11.3	even	5		231.2.j.g.64.5	✓	20
11.4	even	5		231.2.j.g.148.5	yes	20
11.10	odd	2		2541.2.a.br.1.1		10
33.14	odd	10		693.2.m.j.64.1		20
33.26	odd	10		693.2.m.j.379.1		20
33.32	even	2		7623.2.a.cy.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.64.5	✓	20	11.3	even	5
231.2.j.g.148.5	yes	20	11.4	even	5
693.2.m.j.64.1		20	33.14	odd	10
693.2.m.j.379.1		20	33.26	odd	10
2541.2.a.bq.1.10		10	1.1	even	1	trivial
2541.2.a.br.1.1		10	11.10	odd	2
7623.2.a.cx.1.1		10	3.2	odd	2
7623.2.a.cy.1.10		10	33.32	even	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)

\(f(q)\)	\(=\)	\(q+2.79866 q^{2} +1.00000 q^{3} +5.83249 q^{4} -1.67767 q^{5} +2.79866 q^{6} -1.00000 q^{7} +10.7258 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.79866 q^{2} +1.00000 q^{3} +5.83249 q^{4} -1.67767 q^{5} +2.79866 q^{6} -1.00000 q^{7} +10.7258 q^{8} +1.00000 q^{9} -4.69523 q^{10} +5.83249 q^{12} +5.87113 q^{13} -2.79866 q^{14} -1.67767 q^{15} +18.3530 q^{16} -0.304169 q^{17} +2.79866 q^{18} -4.62860 q^{19} -9.78502 q^{20} -1.00000 q^{21} -1.38164 q^{23} +10.7258 q^{24} -2.18541 q^{25} +16.4313 q^{26} +1.00000 q^{27} -5.83249 q^{28} +3.96868 q^{29} -4.69523 q^{30} +0.764099 q^{31} +29.9121 q^{32} -0.851264 q^{34} +1.67767 q^{35} +5.83249 q^{36} +3.21023 q^{37} -12.9539 q^{38} +5.87113 q^{39} -17.9945 q^{40} -8.31274 q^{41} -2.79866 q^{42} -1.01069 q^{43} -1.67767 q^{45} -3.86674 q^{46} -2.58688 q^{47} +18.3530 q^{48} +1.00000 q^{49} -6.11623 q^{50} -0.304169 q^{51} +34.2434 q^{52} -1.45374 q^{53} +2.79866 q^{54} -10.7258 q^{56} -4.62860 q^{57} +11.1070 q^{58} -2.49444 q^{59} -9.78502 q^{60} +3.39295 q^{61} +2.13845 q^{62} -1.00000 q^{63} +47.0078 q^{64} -9.84984 q^{65} +6.16878 q^{67} -1.77406 q^{68} -1.38164 q^{69} +4.69523 q^{70} +7.59943 q^{71} +10.7258 q^{72} -12.7455 q^{73} +8.98434 q^{74} -2.18541 q^{75} -26.9963 q^{76} +16.4313 q^{78} -6.15519 q^{79} -30.7903 q^{80} +1.00000 q^{81} -23.2645 q^{82} -2.01266 q^{83} -5.83249 q^{84} +0.510295 q^{85} -2.82859 q^{86} +3.96868 q^{87} +0.0843908 q^{89} -4.69523 q^{90} -5.87113 q^{91} -8.05840 q^{92} +0.764099 q^{93} -7.23980 q^{94} +7.76527 q^{95} +29.9121 q^{96} +1.03775 q^{97} +2.79866 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} - 10 q^{7} + 3 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 - 10 * q^7 + 3 * q^8 + 10 * q^9	\( 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} - 10 q^{7} + 3 q^{8} + 10 q^{9} + 6 q^{10} + 18 q^{12} - 6 q^{13} + 5 q^{15} + 38 q^{16} - 8 q^{17} + 7 q^{20} - 10 q^{21} + 3 q^{24} + 31 q^{25} + q^{26} + 10 q^{27} - 18 q^{28} + 14 q^{29} + 6 q^{30} + 26 q^{31} + 41 q^{32} + 21 q^{34} - 5 q^{35} + 18 q^{36} + 24 q^{37} + 8 q^{38} - 6 q^{39} + 5 q^{40} - 19 q^{41} + 6 q^{43} + 5 q^{45} + q^{46} + 15 q^{47} + 38 q^{48} + 10 q^{49} + q^{50} - 8 q^{51} + 25 q^{52} - q^{53} - 3 q^{56} + 11 q^{58} + 23 q^{59} + 7 q^{60} - 11 q^{62} - 10 q^{63} + 53 q^{64} + 29 q^{65} + 38 q^{67} - 87 q^{68} - 6 q^{70} + 26 q^{71} + 3 q^{72} + q^{73} + 39 q^{74} + 31 q^{75} + 2 q^{76} + q^{78} - 5 q^{79} + 6 q^{80} + 10 q^{81} + 5 q^{82} - 6 q^{83} - 18 q^{84} + q^{85} - 41 q^{86} + 14 q^{87} - 9 q^{89} + 6 q^{90} + 6 q^{91} - 48 q^{92} + 26 q^{93} + 42 q^{95} + 41 q^{96} + 24 q^{97}+O(q^{100}) \) 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 - 10 * q^7 + 3 * q^8 + 10 * q^9 + 6 * q^10 + 18 * q^12 - 6 * q^13 + 5 * q^15 + 38 * q^16 - 8 * q^17 + 7 * q^20 - 10 * q^21 + 3 * q^24 + 31 * q^25 + q^26 + 10 * q^27 - 18 * q^28 + 14 * q^29 + 6 * q^30 + 26 * q^31 + 41 * q^32 + 21 * q^34 - 5 * q^35 + 18 * q^36 + 24 * q^37 + 8 * q^38 - 6 * q^39 + 5 * q^40 - 19 * q^41 + 6 * q^43 + 5 * q^45 + q^46 + 15 * q^47 + 38 * q^48 + 10 * q^49 + q^50 - 8 * q^51 + 25 * q^52 - q^53 - 3 * q^56 + 11 * q^58 + 23 * q^59 + 7 * q^60 - 11 * q^62 - 10 * q^63 + 53 * q^64 + 29 * q^65 + 38 * q^67 - 87 * q^68 - 6 * q^70 + 26 * q^71 + 3 * q^72 + q^73 + 39 * q^74 + 31 * q^75 + 2 * q^76 + q^78 - 5 * q^79 + 6 * q^80 + 10 * q^81 + 5 * q^82 - 6 * q^83 - 18 * q^84 + q^85 - 41 * q^86 + 14 * q^87 - 9 * q^89 + 6 * q^90 + 6 * q^91 - 48 * q^92 + 26 * q^93 + 42 * q^95 + 41 * q^96 + 24 * q^97

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