LMFDB - Embedded newform 2541.2.a.br.1.2

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			1.2
Root			$2.63994$ 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)

$f(q)$	$=$	$q-2.63994 q^{2} +1.00000 q^{3} +4.96928 q^{4} +3.08369 q^{5} -2.63994 q^{6} +1.00000 q^{7} -7.83871 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.63994 q^{2} +1.00000 q^{3} +4.96928 q^{4} +3.08369 q^{5} -2.63994 q^{6} +1.00000 q^{7} -7.83871 q^{8} +1.00000 q^{9} -8.14075 q^{10} +4.96928 q^{12} +5.64097 q^{13} -2.63994 q^{14} +3.08369 q^{15} +10.7552 q^{16} +5.60085 q^{17} -2.63994 q^{18} -0.122652 q^{19} +15.3237 q^{20} +1.00000 q^{21} +1.67325 q^{23} -7.83871 q^{24} +4.50913 q^{25} -14.8918 q^{26} +1.00000 q^{27} +4.96928 q^{28} -8.85038 q^{29} -8.14075 q^{30} +1.59773 q^{31} -12.7156 q^{32} -14.7859 q^{34} +3.08369 q^{35} +4.96928 q^{36} +4.17268 q^{37} +0.323795 q^{38} +5.64097 q^{39} -24.1721 q^{40} -3.48859 q^{41} -2.63994 q^{42} +5.10698 q^{43} +3.08369 q^{45} -4.41727 q^{46} -1.59400 q^{47} +10.7552 q^{48} +1.00000 q^{49} -11.9038 q^{50} +5.60085 q^{51} +28.0316 q^{52} -11.8564 q^{53} -2.63994 q^{54} -7.83871 q^{56} -0.122652 q^{57} +23.3645 q^{58} +6.61445 q^{59} +15.3237 q^{60} +8.48918 q^{61} -4.21790 q^{62} +1.00000 q^{63} +12.0580 q^{64} +17.3950 q^{65} -8.04949 q^{67} +27.8322 q^{68} +1.67325 q^{69} -8.14075 q^{70} +6.24379 q^{71} -7.83871 q^{72} -3.51005 q^{73} -11.0156 q^{74} +4.50913 q^{75} -0.609494 q^{76} -14.8918 q^{78} +9.39769 q^{79} +33.1656 q^{80} +1.00000 q^{81} +9.20967 q^{82} +9.43386 q^{83} +4.96928 q^{84} +17.2713 q^{85} -13.4821 q^{86} -8.85038 q^{87} -8.45556 q^{89} -8.14075 q^{90} +5.64097 q^{91} +8.31482 q^{92} +1.59773 q^{93} +4.20807 q^{94} -0.378222 q^{95} -12.7156 q^{96} -5.68478 q^{97} -2.63994 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.63994	−1.86672	−0.933359	−	0.358943i	$-0.883137\pi$
$2$	−2.63994	−1.86672	−0.933359	+	0.358943i	$0.883137\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.96928	2.48464
$5$	3.08369	1.37907	0.689534	−	0.724254i	$-0.257816\pi$
$5$	3.08369	1.37907	0.689534	+	0.724254i	$0.257816\pi$
$6$	−2.63994	−1.07775
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−7.83871	−2.77140
$9$	1.00000	0.333333
$10$	−8.14075	−2.57433
$11$	0	0
$11$	0	0
$12$	4.96928	1.43451
$13$	5.64097	1.56452	0.782262	−	0.622949i	$-0.214066\pi$
$13$	5.64097	1.56452	0.782262	+	0.622949i	$0.214066\pi$
$14$	−2.63994	−0.705553
$15$	3.08369	0.796205
$16$	10.7552	2.68879
$17$	5.60085	1.35841	0.679203	−	0.733951i	$-0.262326\pi$
$17$	5.60085	1.35841	0.679203	+	0.733951i	$0.262326\pi$
$18$	−2.63994	−0.622240
$19$	−0.122652	−0.0281384	−0.0140692	−	0.999901i	$-0.504479\pi$
$19$	−0.122652	−0.0281384	−0.0140692	+	0.999901i	$0.504479\pi$
$20$	15.3237	3.42648
$21$	1.00000	0.218218
$22$	0	0
$23$	1.67325	0.348896	0.174448	−	0.984666i	$-0.444186\pi$
$23$	1.67325	0.348896	0.174448	+	0.984666i	$0.444186\pi$
$24$	−7.83871	−1.60007
$25$	4.50913	0.901826
$26$	−14.8918	−2.92053
$27$	1.00000	0.192450
$28$	4.96928	0.939105
$29$	−8.85038	−1.64347	−0.821737	−	0.569867i	$-0.806995\pi$
$29$	−8.85038	−1.64347	−0.821737	+	0.569867i	$0.806995\pi$
$30$	−8.14075	−1.48629
$31$	1.59773	0.286960	0.143480	−	0.989653i	$-0.454171\pi$
$31$	1.59773	0.286960	0.143480	+	0.989653i	$0.454171\pi$
$32$	−12.7156	−2.24782
$33$	0	0
$34$	−14.7859	−2.53576
$35$	3.08369	0.521238
$36$	4.96928	0.828213
$37$	4.17268	0.685984	0.342992	−	0.939338i	$-0.388560\pi$
$37$	4.17268	0.685984	0.342992	+	0.939338i	$0.388560\pi$
$38$	0.323795	0.0525265
$39$	5.64097	0.903278
$40$	−24.1721	−3.82195
$41$	−3.48859	−0.544827	−0.272413	−	0.962180i	$-0.587822\pi$
$41$	−3.48859	−0.544827	−0.272413	+	0.962180i	$0.587822\pi$
$42$	−2.63994	−0.407351
$43$	5.10698	0.778807	0.389403	−	0.921067i	$-0.372681\pi$
$43$	5.10698	0.778807	0.389403	+	0.921067i	$0.372681\pi$
$44$	0	0
$45$	3.08369	0.459689
$46$	−4.41727	−0.651290
$47$	−1.59400	−0.232509	−0.116255	−	0.993219i	$-0.537089\pi$
$47$	−1.59400	−0.232509	−0.116255	+	0.993219i	$0.537089\pi$
$48$	10.7552	1.55238
$49$	1.00000	0.142857
$50$	−11.9038	−1.68346
$51$	5.60085	0.784276
$52$	28.0316	3.88728
$53$	−11.8564	−1.62861	−0.814303	−	0.580440i	$-0.802881\pi$
$53$	−11.8564	−1.62861	−0.814303	+	0.580440i	$0.802881\pi$
$54$	−2.63994	−0.359250
$55$	0	0
$56$	−7.83871	−1.04749
$57$	−0.122652	−0.0162457
$58$	23.3645	3.06790
$59$	6.61445	0.861128	0.430564	−	0.902560i	$-0.358315\pi$
$59$	6.61445	0.861128	0.430564	+	0.902560i	$0.358315\pi$
$60$	15.3237	1.97828
$61$	8.48918	1.08693	0.543464	−	0.839432i	$-0.317112\pi$
$61$	8.48918	1.08693	0.543464	+	0.839432i	$0.317112\pi$
$62$	−4.21790	−0.535674
$63$	1.00000	0.125988
$64$	12.0580	1.50725
$65$	17.3950	2.15758
$66$	0	0
$67$	−8.04949	−0.983402	−0.491701	−	0.870764i	$-0.663625\pi$
$67$	−8.04949	−0.983402	−0.491701	+	0.870764i	$0.663625\pi$
$68$	27.8322	3.37515
$69$	1.67325	0.201435
$70$	−8.14075	−0.973006
$71$	6.24379	0.741001	0.370501	−	0.928832i	$-0.379186\pi$
$71$	6.24379	0.741001	0.370501	+	0.928832i	$0.379186\pi$
$72$	−7.83871	−0.923801
$73$	−3.51005	−0.410820	−0.205410	−	0.978676i	$-0.565853\pi$
$73$	−3.51005	−0.410820	−0.205410	+	0.978676i	$0.565853\pi$
$74$	−11.0156	−1.28054
$75$	4.50913	0.520670
$76$	−0.609494	−0.0699138
$77$	0	0
$78$	−14.8918	−1.68617
$79$	9.39769	1.05732	0.528661	−	0.848833i	$-0.322694\pi$
$79$	9.39769	1.05732	0.528661	+	0.848833i	$0.322694\pi$
$80$	33.1656	3.70803
$81$	1.00000	0.111111
$82$	9.20967	1.01704
$83$	9.43386	1.03550	0.517750	−	0.855532i	$-0.326770\pi$
$83$	9.43386	1.03550	0.517750	+	0.855532i	$0.326770\pi$
$84$	4.96928	0.542193
$85$	17.2713	1.87333
$86$	−13.4821	−1.45381
$87$	−8.85038	−0.948860
$88$	0	0
$89$	−8.45556	−0.896288	−0.448144	−	0.893961i	$-0.647915\pi$
$89$	−8.45556	−0.896288	−0.448144	+	0.893961i	$0.647915\pi$
$90$	−8.14075	−0.858110
$91$	5.64097	0.591335
$92$	8.31482	0.866880
$93$	1.59773	0.165677
$94$	4.20807	0.434030
$95$	−0.378222	−0.0388047
$96$	−12.7156	−1.29778
$97$	−5.68478	−0.577202	−0.288601	−	0.957449i	$-0.593190\pi$
$97$	−5.68478	−0.577202	−0.288601	+	0.957449i	$0.593190\pi$
$98$	−2.63994	−0.266674
$99$	0	0
$100$	22.4071	2.24071
$101$	−16.8776	−1.67938	−0.839690	−	0.543066i	$-0.817263\pi$
$101$	−16.8776	−1.67938	−0.839690	+	0.543066i	$0.817263\pi$
$102$	−14.7859	−1.46402
$103$	−13.2172	−1.30233	−0.651163	−	0.758938i	$-0.725719\pi$
$103$	−13.2172	−1.30233	−0.651163	+	0.758938i	$0.725719\pi$
$104$	−44.2180	−4.33593
$105$	3.08369	0.300937
$106$	31.3003	3.04015
$107$	−11.0745	−1.07061	−0.535307	−	0.844658i	$-0.679804\pi$
$107$	−11.0745	−1.07061	−0.535307	+	0.844658i	$0.679804\pi$
$108$	4.96928	0.478169
$109$	4.87369	0.466815	0.233407	−	0.972379i	$-0.425012\pi$
$109$	4.87369	0.466815	0.233407	+	0.972379i	$0.425012\pi$
$110$	0	0
$111$	4.17268	0.396053
$112$	10.7552	1.01627
$113$	−5.28263	−0.496948	−0.248474	−	0.968639i	$-0.579929\pi$
$113$	−5.28263	−0.496948	−0.248474	+	0.968639i	$0.579929\pi$
$114$	0.323795	0.0303262
$115$	5.15977	0.481151
$116$	−43.9800	−4.08344
$117$	5.64097	0.521508
$118$	−17.4617	−1.60748
$119$	5.60085	0.513429
$120$	−24.1721	−2.20661
$121$	0	0
$122$	−22.4109	−2.02899
$123$	−3.48859	−0.314556
$124$	7.93955	0.712992
$125$	−1.51368	−0.135388
$126$	−2.63994	−0.235184
$127$	11.3400	1.00627	0.503133	−	0.864209i	$-0.332181\pi$
$127$	11.3400	1.00627	0.503133	+	0.864209i	$0.332181\pi$
$128$	−6.40120	−0.565792
$129$	5.10698	0.449644
$130$	−45.9217	−4.02760
$131$	0.970284	0.0847741	0.0423870	−	0.999101i	$-0.486504\pi$
$131$	0.970284	0.0847741	0.0423870	+	0.999101i	$0.486504\pi$
$132$	0	0
$133$	−0.122652	−0.0106353
$134$	21.2502	1.83574
$135$	3.08369	0.265402
$136$	−43.9035	−3.76469
$137$	−0.125101	−0.0106881	−0.00534403	−	0.999986i	$-0.501701\pi$
$137$	−0.125101	−0.0106881	−0.00534403	+	0.999986i	$0.501701\pi$
$138$	−4.41727	−0.376023
$139$	1.67835	0.142355	0.0711777	−	0.997464i	$-0.477324\pi$
$139$	1.67835	0.142355	0.0711777	+	0.997464i	$0.477324\pi$
$140$	15.3237	1.29509
$141$	−1.59400	−0.134239
$142$	−16.4832	−1.38324
$143$	0	0
$144$	10.7552	0.896264
$145$	−27.2918	−2.26646
$146$	9.26631	0.766885
$147$	1.00000	0.0824786
$148$	20.7352	1.70442
$149$	−14.1791	−1.16160	−0.580800	−	0.814046i	$-0.697260\pi$
$149$	−14.1791	−1.16160	−0.580800	+	0.814046i	$0.697260\pi$
$150$	−11.9038	−0.971944
$151$	−15.8823	−1.29249	−0.646243	−	0.763132i	$-0.723661\pi$
$151$	−15.8823	−1.29249	−0.646243	+	0.763132i	$0.723661\pi$
$152$	0.961437	0.0779829
$153$	5.60085	0.452802
$154$	0	0
$155$	4.92689	0.395737
$156$	28.0316	2.24432
$157$	−9.19854	−0.734124	−0.367062	−	0.930197i	$-0.619636\pi$
$157$	−9.19854	−0.734124	−0.367062	+	0.930197i	$0.619636\pi$
$158$	−24.8093	−1.97372
$159$	−11.8564	−0.940276
$160$	−39.2108	−3.09989
$161$	1.67325	0.131870
$162$	−2.63994	−0.207413
$163$	9.76942	0.765200	0.382600	−	0.923914i	$-0.375029\pi$
$163$	9.76942	0.765200	0.382600	+	0.923914i	$0.375029\pi$
$164$	−17.3358	−1.35370
$165$	0	0
$166$	−24.9048	−1.93299
$167$	−6.10236	−0.472215	−0.236107	−	0.971727i	$-0.575872\pi$
$167$	−6.10236	−0.472215	−0.236107	+	0.971727i	$0.575872\pi$
$168$	−7.83871	−0.604770
$169$	18.8206	1.44774
$170$	−45.5951	−3.49699
$171$	−0.122652	−0.00937947
$172$	25.3780	1.93505
$173$	−6.73818	−0.512294	−0.256147	−	0.966638i	$-0.582453\pi$
$173$	−6.73818	−0.512294	−0.256147	+	0.966638i	$0.582453\pi$
$174$	23.3645	1.77126
$175$	4.50913	0.340858
$176$	0	0
$177$	6.61445	0.497173
$178$	22.3222	1.67312
$179$	12.9936	0.971184	0.485592	−	0.874186i	$-0.338604\pi$
$179$	12.9936	0.971184	0.485592	+	0.874186i	$0.338604\pi$
$180$	15.3237	1.14216
$181$	−4.09819	−0.304616	−0.152308	−	0.988333i	$-0.548671\pi$
$181$	−4.09819	−0.304616	−0.152308	+	0.988333i	$0.548671\pi$
$182$	−14.8918	−1.10386
$183$	8.48918	0.627538
$184$	−13.1161	−0.966931
$185$	12.8672	0.946018
$186$	−4.21790	−0.309271
$187$	0	0
$188$	−7.92105	−0.577702
$189$	1.00000	0.0727393
$190$	0.998483	0.0724375
$191$	21.5036	1.55595	0.777973	−	0.628297i	$-0.216248\pi$
$191$	21.5036	1.55595	0.777973	+	0.628297i	$0.216248\pi$
$192$	12.0580	0.870210
$193$	−17.7964	−1.28101	−0.640506	−	0.767953i	$-0.721275\pi$
$193$	−17.7964	−1.28101	−0.640506	+	0.767953i	$0.721275\pi$
$194$	15.0075	1.07747
$195$	17.3950	1.24568
$196$	4.96928	0.354948
$197$	−18.1083	−1.29016	−0.645080	−	0.764115i	$-0.723176\pi$
$197$	−18.1083	−1.29016	−0.645080	+	0.764115i	$0.723176\pi$
$198$	0	0
$199$	2.67139	0.189370	0.0946848	−	0.995507i	$-0.469816\pi$
$199$	2.67139	0.189370	0.0946848	+	0.995507i	$0.469816\pi$
$200$	−35.3458	−2.49933
$201$	−8.04949	−0.567768
$202$	44.5557	3.13493
$203$	−8.85038	−0.621175
$204$	27.8322	1.94864
$205$	−10.7577	−0.751352
$206$	34.8925	2.43108
$207$	1.67325	0.116299
$208$	60.6696	4.20668
$209$	0	0
$210$	−8.14075	−0.561765
$211$	8.15447	0.561377	0.280688	−	0.959799i	$-0.409437\pi$
$211$	8.15447	0.561377	0.280688	+	0.959799i	$0.409437\pi$
$212$	−58.9179	−4.04650
$213$	6.24379	0.427817
$214$	29.2360	1.99853
$215$	15.7483	1.07403
$216$	−7.83871	−0.533357
$217$	1.59773	0.108461
$218$	−12.8662	−0.871412
$219$	−3.51005	−0.237187
$220$	0	0
$221$	31.5942	2.12526
$222$	−11.0156	−0.739319
$223$	8.48763	0.568374	0.284187	−	0.958769i	$-0.408276\pi$
$223$	8.48763	0.568374	0.284187	+	0.958769i	$0.408276\pi$
$224$	−12.7156	−0.849595
$225$	4.50913	0.300609
$226$	13.9458	0.927662
$227$	22.1524	1.47031	0.735154	−	0.677900i	$-0.237110\pi$
$227$	22.1524	1.47031	0.735154	+	0.677900i	$0.237110\pi$
$228$	−0.609494	−0.0403647
$229$	−8.98014	−0.593424	−0.296712	−	0.954967i	$-0.595890\pi$
$229$	−8.98014	−0.593424	−0.296712	+	0.954967i	$0.595890\pi$
$230$	−13.6215	−0.898173
$231$	0	0
$232$	69.3756	4.55473
$233$	−19.8909	−1.30309	−0.651547	−	0.758608i	$-0.725880\pi$
$233$	−19.8909	−1.30309	−0.651547	+	0.758608i	$0.725880\pi$
$234$	−14.8918	−0.973509
$235$	−4.91541	−0.320646
$236$	32.8690	2.13959
$237$	9.39769	0.610445
$238$	−14.7859	−0.958428
$239$	9.21976	0.596377	0.298188	−	0.954507i	$-0.403618\pi$
$239$	9.21976	0.596377	0.298188	+	0.954507i	$0.403618\pi$
$240$	33.1656	2.14083
$241$	0.802919	0.0517206	0.0258603	−	0.999666i	$-0.491767\pi$
$241$	0.802919	0.0517206	0.0258603	+	0.999666i	$0.491767\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	42.1851	2.70062
$245$	3.08369	0.197010
$246$	9.20967	0.587187
$247$	−0.691879	−0.0440232
$248$	−12.5241	−0.795282
$249$	9.43386	0.597847
$250$	3.99603	0.252731
$251$	0.459277	0.0289893	0.0144947	−	0.999895i	$-0.495386\pi$
$251$	0.459277	0.0289893	0.0144947	+	0.999895i	$0.495386\pi$
$252$	4.96928	0.313035
$253$	0	0
$254$	−29.9370	−1.87842
$255$	17.2713	1.08157
$256$	−7.21718	−0.451073
$257$	−23.3574	−1.45699	−0.728496	−	0.685050i	$-0.759780\pi$
$257$	−23.3574	−1.45699	−0.728496	+	0.685050i	$0.759780\pi$
$258$	−13.4821	−0.839359
$259$	4.17268	0.259277
$260$	86.4406	5.36082
$261$	−8.85038	−0.547825
$262$	−2.56149	−0.158249
$263$	4.96169	0.305951	0.152975	−	0.988230i	$-0.451114\pi$
$263$	4.96169	0.305951	0.152975	+	0.988230i	$0.451114\pi$
$264$	0	0
$265$	−36.5615	−2.24596
$266$	0.323795	0.0198531
$267$	−8.45556	−0.517472
$268$	−40.0002	−2.44340
$269$	1.03203	0.0629239	0.0314620	−	0.999505i	$-0.489984\pi$
$269$	1.03203	0.0629239	0.0314620	+	0.999505i	$0.489984\pi$
$270$	−8.14075	−0.495430
$271$	−15.1427	−0.919856	−0.459928	−	0.887956i	$-0.652125\pi$
$271$	−15.1427	−0.919856	−0.459928	+	0.887956i	$0.652125\pi$
$272$	60.2381	3.65247
$273$	5.64097	0.341407
$274$	0.330258	0.0199516
$275$	0	0
$276$	8.31482	0.500494
$277$	1.07001	0.0642909	0.0321455	−	0.999483i	$-0.489766\pi$
$277$	1.07001	0.0642909	0.0321455	+	0.999483i	$0.489766\pi$
$278$	−4.43073	−0.265737
$279$	1.59773	0.0956534
$280$	−24.1721	−1.44456
$281$	31.3090	1.86774	0.933868	−	0.357617i	$-0.116411\pi$
$281$	31.3090	1.86774	0.933868	+	0.357617i	$0.116411\pi$
$282$	4.20807	0.250587
$283$	−31.9651	−1.90013	−0.950063	−	0.312059i	$-0.898981\pi$
$283$	−31.9651	−1.90013	−0.950063	+	0.312059i	$0.898981\pi$
$284$	31.0271	1.84112
$285$	−0.378222	−0.0224039
$286$	0	0
$287$	−3.48859	−0.205925
$288$	−12.7156	−0.749272
$289$	14.3695	0.845266
$290$	72.0487	4.23085
$291$	−5.68478	−0.333248
$292$	−17.4424	−1.02074
$293$	0.472963	0.0276308	0.0138154	−	0.999905i	$-0.495602\pi$
$293$	0.472963	0.0276308	0.0138154	+	0.999905i	$0.495602\pi$
$294$	−2.63994	−0.153964
$295$	20.3969	1.18755
$296$	−32.7084	−1.90114
$297$	0	0
$298$	37.4321	2.16838
$299$	9.43873	0.545856
$300$	22.4071	1.29368
$301$	5.10698	0.294361
$302$	41.9284	2.41271
$303$	−16.8776	−0.969591
$304$	−1.31915	−0.0756583
$305$	26.1780	1.49895
$306$	−14.7859	−0.845254
$307$	22.3522	1.27571	0.637854	−	0.770158i	$-0.279823\pi$
$307$	22.3522	1.27571	0.637854	+	0.770158i	$0.279823\pi$
$308$	0	0
$309$	−13.2172	−0.751898
$310$	−13.0067	−0.738730
$311$	21.9838	1.24659	0.623293	−	0.781988i	$-0.285794\pi$
$311$	21.9838	1.24659	0.623293	+	0.781988i	$0.285794\pi$
$312$	−44.2180	−2.50335
$313$	−7.95027	−0.449376	−0.224688	−	0.974431i	$-0.572136\pi$
$313$	−7.95027	−0.449376	−0.224688	+	0.974431i	$0.572136\pi$
$314$	24.2836	1.37040
$315$	3.08369	0.173746
$316$	46.6997	2.62707
$317$	−15.1227	−0.849374	−0.424687	−	0.905340i	$-0.639616\pi$
$317$	−15.1227	−0.849374	−0.424687	+	0.905340i	$0.639616\pi$
$318$	31.3003	1.75523
$319$	0	0
$320$	37.1831	2.07860
$321$	−11.0745	−0.618119
$322$	−4.41727	−0.246165
$323$	−0.686958	−0.0382234
$324$	4.96928	0.276071
$325$	25.4359	1.41093
$326$	−25.7907	−1.42841
$327$	4.87369	0.269516
$328$	27.3461	1.50993
$329$	−1.59400	−0.0878803
$330$	0	0
$331$	−6.02542	−0.331187	−0.165594	−	0.986194i	$-0.552954\pi$
$331$	−6.02542	−0.331187	−0.165594	+	0.986194i	$0.552954\pi$
$332$	46.8795	2.57285
$333$	4.17268	0.228661
$334$	16.1099	0.881492
$335$	−24.8221	−1.35618
$336$	10.7552	0.586743
$337$	−20.8494	−1.13574	−0.567869	−	0.823119i	$-0.692232\pi$
$337$	−20.8494	−1.13574	−0.567869	+	0.823119i	$0.692232\pi$
$338$	−49.6851	−2.70252
$339$	−5.28263	−0.286913
$340$	85.8258	4.65456
$341$	0	0
$342$	0.323795	0.0175088
$343$	1.00000	0.0539949
$344$	−40.0321	−2.15839
$345$	5.15977	0.277793
$346$	17.7884	0.956309
$347$	−1.49329	−0.0801643	−0.0400821	−	0.999196i	$-0.512762\pi$
$347$	−1.49329	−0.0801643	−0.0400821	+	0.999196i	$0.512762\pi$
$348$	−43.9800	−2.35758
$349$	21.4795	1.14977	0.574886	−	0.818234i	$-0.305046\pi$
$349$	21.4795	1.14977	0.574886	+	0.818234i	$0.305046\pi$
$350$	−11.9038	−0.636287
$351$	5.64097	0.301093
$352$	0	0
$353$	11.4760	0.610808	0.305404	−	0.952223i	$-0.401208\pi$
$353$	11.4760	0.610808	0.305404	+	0.952223i	$0.401208\pi$
$354$	−17.4617	−0.928081
$355$	19.2539	1.02189
$356$	−42.0180	−2.22695
$357$	5.60085	0.296428
$358$	−34.3022	−1.81293
$359$	5.72481	0.302144	0.151072	−	0.988523i	$-0.451727\pi$
$359$	5.72481	0.302144	0.151072	+	0.988523i	$0.451727\pi$
$360$	−24.1721	−1.27398
$361$	−18.9850	−0.999208
$362$	10.8190	0.568632
$363$	0	0
$364$	28.0316	1.46925
$365$	−10.8239	−0.566548
$366$	−22.4109	−1.17144
$367$	17.4991	0.913445	0.456723	−	0.889609i	$-0.349023\pi$
$367$	17.4991	0.913445	0.456723	+	0.889609i	$0.349023\pi$
$368$	17.9960	0.938109
$369$	−3.48859	−0.181609
$370$	−33.9687	−1.76595
$371$	−11.8564	−0.615555
$372$	7.93955	0.411646
$373$	9.54362	0.494150	0.247075	−	0.968996i	$-0.420531\pi$
$373$	9.54362	0.494150	0.247075	+	0.968996i	$0.420531\pi$
$374$	0	0
$375$	−1.51368	−0.0781662
$376$	12.4949	0.644377
$377$	−49.9247	−2.57126
$378$	−2.63994	−0.135784
$379$	31.9605	1.64170	0.820850	−	0.571144i	$-0.193500\pi$
$379$	31.9605	1.64170	0.820850	+	0.571144i	$0.193500\pi$
$380$	−1.87949	−0.0964158
$381$	11.3400	0.580968
$382$	−56.7682	−2.90452
$383$	−9.82236	−0.501899	−0.250950	−	0.968000i	$-0.580743\pi$
$383$	−9.82236	−0.501899	−0.250950	+	0.968000i	$0.580743\pi$
$384$	−6.40120	−0.326660
$385$	0	0
$386$	46.9814	2.39129
$387$	5.10698	0.259602
$388$	−28.2493	−1.43414
$389$	33.1998	1.68330	0.841648	−	0.540027i	$-0.181586\pi$
$389$	33.1998	1.68330	0.841648	+	0.540027i	$0.181586\pi$
$390$	−45.9217	−2.32534
$391$	9.37160	0.473942
$392$	−7.83871	−0.395915
$393$	0.970284	0.0489443
$394$	47.8047	2.40837
$395$	28.9795	1.45812
$396$	0	0
$397$	23.6535	1.18713	0.593566	−	0.804785i	$-0.297719\pi$
$397$	23.6535	1.18713	0.593566	+	0.804785i	$0.297719\pi$
$398$	−7.05230	−0.353500
$399$	−0.122652	−0.00614030
$400$	48.4965	2.42482
$401$	25.2737	1.26211	0.631054	−	0.775739i	$-0.282623\pi$
$401$	25.2737	1.26211	0.631054	+	0.775739i	$0.282623\pi$
$402$	21.2502	1.05986
$403$	9.01273	0.448956
$404$	−83.8693	−4.17265
$405$	3.08369	0.153230
$406$	23.3645	1.15956
$407$	0	0
$408$	−43.9035	−2.17355
$409$	−13.9735	−0.690947	−0.345474	−	0.938428i	$-0.612282\pi$
$409$	−13.9735	−0.690947	−0.345474	+	0.938428i	$0.612282\pi$
$410$	28.3998	1.40256
$411$	−0.125101	−0.00617076
$412$	−65.6798	−3.23581
$413$	6.61445	0.325476
$414$	−4.41727	−0.217097
$415$	29.0911	1.42803
$416$	−71.7282	−3.51676
$417$	1.67835	0.0821889
$418$	0	0
$419$	29.7445	1.45311	0.726556	−	0.687107i	$-0.241120\pi$
$419$	29.7445	1.45311	0.726556	+	0.687107i	$0.241120\pi$
$420$	15.3237	0.747720
$421$	36.2675	1.76757	0.883786	−	0.467892i	$-0.154986\pi$
$421$	36.2675	1.76757	0.883786	+	0.467892i	$0.154986\pi$
$422$	−21.5273	−1.04793
$423$	−1.59400	−0.0775031
$424$	92.9392	4.51353
$425$	25.2550	1.22505
$426$	−16.4832	−0.798615
$427$	8.48918	0.410820
$428$	−55.0323	−2.66009
$429$	0	0
$430$	−41.5746	−2.00491
$431$	−35.8066	−1.72474	−0.862372	−	0.506275i	$-0.831022\pi$
$431$	−35.8066	−1.72474	−0.862372	+	0.506275i	$0.831022\pi$
$432$	10.7552	0.517458
$433$	−23.0958	−1.10992	−0.554958	−	0.831879i	$-0.687266\pi$
$433$	−23.0958	−1.10992	−0.554958	+	0.831879i	$0.687266\pi$
$434$	−4.21790	−0.202466
$435$	−27.2918	−1.30854
$436$	24.2187	1.15987
$437$	−0.205228	−0.00981737
$438$	9.26631	0.442761
$439$	−24.7837	−1.18286	−0.591431	−	0.806356i	$-0.701437\pi$
$439$	−24.7837	−1.18286	−0.591431	+	0.806356i	$0.701437\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−83.4069	−3.96726
$443$	13.2945	0.631642	0.315821	−	0.948819i	$-0.397720\pi$
$443$	13.2945	0.631642	0.315821	+	0.948819i	$0.397720\pi$
$444$	20.7352	0.984049
$445$	−26.0743	−1.23604
$446$	−22.4068	−1.06099
$447$	−14.1791	−0.670650
$448$	12.0580	0.569686
$449$	20.8714	0.984981	0.492490	−	0.870318i	$-0.336087\pi$
$449$	20.8714	0.984981	0.492490	+	0.870318i	$0.336087\pi$
$450$	−11.9038	−0.561152
$451$	0	0
$452$	−26.2509	−1.23474
$453$	−15.8823	−0.746217
$454$	−58.4810	−2.74465
$455$	17.3950	0.815490
$456$	0.961437	0.0450234
$457$	28.2344	1.32075	0.660375	−	0.750936i	$-0.270397\pi$
$457$	28.2344	1.32075	0.660375	+	0.750936i	$0.270397\pi$
$458$	23.7070	1.10776
$459$	5.60085	0.261425
$460$	25.6403	1.19549
$461$	13.5432	0.630770	0.315385	−	0.948964i	$-0.397866\pi$
$461$	13.5432	0.630770	0.315385	+	0.948964i	$0.397866\pi$
$462$	0	0
$463$	−33.9584	−1.57818	−0.789090	−	0.614277i	$-0.789448\pi$
$463$	−33.9584	−1.57818	−0.789090	+	0.614277i	$0.789448\pi$
$464$	−95.1873	−4.41896
$465$	4.92689	0.228479
$466$	52.5107	2.43251
$467$	12.5809	0.582172	0.291086	−	0.956697i	$-0.405983\pi$
$467$	12.5809	0.582172	0.291086	+	0.956697i	$0.405983\pi$
$468$	28.0316	1.29576
$469$	−8.04949	−0.371691
$470$	12.9764	0.598556
$471$	−9.19854	−0.423847
$472$	−51.8488	−2.38653
$473$	0	0
$474$	−24.8093	−1.13953
$475$	−0.553056	−0.0253759
$476$	27.8322	1.27569
$477$	−11.8564	−0.542869
$478$	−24.3396	−1.11327
$479$	−28.8916	−1.32009	−0.660046	−	0.751225i	$-0.729463\pi$
$479$	−28.8916	−1.32009	−0.660046	+	0.751225i	$0.729463\pi$
$480$	−39.2108	−1.78972
$481$	23.5380	1.07324
$482$	−2.11966	−0.0965478
$483$	1.67325	0.0761353
$484$	0	0
$485$	−17.5301	−0.796001
$486$	−2.63994	−0.119750
$487$	25.5077	1.15586	0.577932	−	0.816085i	$-0.303860\pi$
$487$	25.5077	1.15586	0.577932	+	0.816085i	$0.303860\pi$
$488$	−66.5443	−3.01232
$489$	9.76942	0.441789
$490$	−8.14075	−0.367762
$491$	−4.66598	−0.210573	−0.105286	−	0.994442i	$-0.533576\pi$
$491$	−4.66598	−0.210573	−0.105286	+	0.994442i	$0.533576\pi$
$492$	−17.3358	−0.781558
$493$	−49.5697	−2.23250
$494$	1.82652	0.0821789
$495$	0	0
$496$	17.1838	0.771576
$497$	6.24379	0.280072
$498$	−24.9048	−1.11601
$499$	−18.4958	−0.827987	−0.413994	−	0.910280i	$-0.635866\pi$
$499$	−18.4958	−0.827987	−0.413994	+	0.910280i	$0.635866\pi$
$500$	−7.52191	−0.336390
$501$	−6.10236	−0.272633
$502$	−1.21246	−0.0541149
$503$	23.1076	1.03032	0.515159	−	0.857094i	$-0.327733\pi$
$503$	23.1076	1.03032	0.515159	+	0.857094i	$0.327733\pi$
$504$	−7.83871	−0.349164
$505$	−52.0451	−2.31598
$506$	0	0
$507$	18.8206	0.835851
$508$	56.3518	2.50021
$509$	−28.6541	−1.27007	−0.635036	−	0.772483i	$-0.719015\pi$
$509$	−28.6541	−1.27007	−0.635036	+	0.772483i	$0.719015\pi$
$510$	−45.5951	−2.01899
$511$	−3.51005	−0.155275
$512$	31.8553	1.40782
$513$	−0.122652	−0.00541524
$514$	61.6620	2.71979
$515$	−40.7576	−1.79600
$516$	25.3780	1.11720
$517$	0	0
$518$	−11.0156	−0.483998
$519$	−6.73818	−0.295773
$520$	−136.354	−5.97954
$521$	−7.99220	−0.350144	−0.175072	−	0.984556i	$-0.556016\pi$
$521$	−7.99220	−0.350144	−0.175072	+	0.984556i	$0.556016\pi$
$522$	23.3645	1.02263
$523$	−37.2399	−1.62839	−0.814194	−	0.580592i	$-0.802821\pi$
$523$	−37.2399	−1.62839	−0.814194	+	0.580592i	$0.802821\pi$
$524$	4.82161	0.210633
$525$	4.50913	0.196795
$526$	−13.0986	−0.571124
$527$	8.94863	0.389808
$528$	0	0
$529$	−20.2002	−0.878272
$530$	96.5202	4.19257
$531$	6.61445	0.287043
$532$	−0.609494	−0.0264249
$533$	−19.6791	−0.852394
$534$	22.3222	0.965975
$535$	−34.1503	−1.47645
$536$	63.0977	2.72541
$537$	12.9936	0.560713
$538$	−2.72449	−0.117461
$539$	0	0
$540$	15.3237	0.659427
$541$	22.9890	0.988376	0.494188	−	0.869355i	$-0.335465\pi$
$541$	22.9890	0.988376	0.494188	+	0.869355i	$0.335465\pi$
$542$	39.9759	1.71711
$543$	−4.09819	−0.175870
$544$	−71.2180	−3.05345
$545$	15.0289	0.643769
$546$	−14.8918	−0.637311
$547$	−30.4285	−1.30103	−0.650515	−	0.759493i	$-0.725447\pi$
$547$	−30.4285	−1.30103	−0.650515	+	0.759493i	$0.725447\pi$
$548$	−0.621660	−0.0265560
$549$	8.48918	0.362309
$550$	0	0
$551$	1.08552	0.0462447
$552$	−13.1161	−0.558258
$553$	9.39769	0.399630
$554$	−2.82477	−0.120013
$555$	12.8672	0.546184
$556$	8.34016	0.353702
$557$	42.4812	1.79998	0.899992	−	0.435906i	$-0.143572\pi$
$557$	42.4812	1.79998	0.899992	+	0.435906i	$0.143572\pi$
$558$	−4.21790	−0.178558
$559$	28.8083	1.21846
$560$	33.1656	1.40150
$561$	0	0
$562$	−82.6538	−3.48654
$563$	−12.0958	−0.509777	−0.254888	−	0.966971i	$-0.582039\pi$
$563$	−12.0958	−0.509777	−0.254888	+	0.966971i	$0.582039\pi$
$564$	−7.92105	−0.333536
$565$	−16.2900	−0.685325
$566$	84.3858	3.54700
$567$	1.00000	0.0419961
$568$	−48.9433	−2.05361
$569$	34.0054	1.42558	0.712789	−	0.701378i	$-0.247432\pi$
$569$	34.0054	1.42558	0.712789	+	0.701378i	$0.247432\pi$
$570$	0.998483	0.0418218
$571$	−16.0762	−0.672767	−0.336383	−	0.941725i	$-0.609204\pi$
$571$	−16.0762	−0.672767	−0.336383	+	0.941725i	$0.609204\pi$
$572$	0	0
$573$	21.5036	0.898326
$574$	9.20967	0.384404
$575$	7.54489	0.314643
$576$	12.0580	0.502416
$577$	3.94068	0.164053	0.0820264	−	0.996630i	$-0.473861\pi$
$577$	3.94068	0.164053	0.0820264	+	0.996630i	$0.473861\pi$
$578$	−37.9347	−1.57787
$579$	−17.7964	−0.739592
$580$	−135.621	−5.63134
$581$	9.43386	0.391383
$582$	15.0075	0.622080
$583$	0	0
$584$	27.5142	1.13855
$585$	17.3950	0.719195
$586$	−1.24859	−0.0515789
$587$	9.92820	0.409781	0.204890	−	0.978785i	$-0.434316\pi$
$587$	9.92820	0.409781	0.204890	+	0.978785i	$0.434316\pi$
$588$	4.96928	0.204930
$589$	−0.195965	−0.00807460
$590$	−53.8466	−2.21683
$591$	−18.1083	−0.744874
$592$	44.8778	1.84447
$593$	−1.35512	−0.0556480	−0.0278240	−	0.999613i	$-0.508858\pi$
$593$	−1.35512	−0.0556480	−0.0278240	+	0.999613i	$0.508858\pi$
$594$	0	0
$595$	17.2713	0.708053
$596$	−70.4601	−2.88616
$597$	2.67139	0.109333
$598$	−24.9177	−1.01896
$599$	−30.7682	−1.25716	−0.628578	−	0.777747i	$-0.716363\pi$
$599$	−30.7682	−1.25716	−0.628578	+	0.777747i	$0.716363\pi$
$600$	−35.3458	−1.44299
$601$	13.2165	0.539113	0.269557	−	0.962985i	$-0.413123\pi$
$601$	13.2165	0.539113	0.269557	+	0.962985i	$0.413123\pi$
$602$	−13.4821	−0.549490
$603$	−8.04949	−0.327801
$604$	−78.9237	−3.21136
$605$	0	0
$606$	44.5557	1.80995
$607$	5.83308	0.236757	0.118379	−	0.992969i	$-0.462230\pi$
$607$	5.83308	0.236757	0.118379	+	0.992969i	$0.462230\pi$
$608$	1.55960	0.0632499
$609$	−8.85038	−0.358635
$610$	−69.1083	−2.79811
$611$	−8.99173	−0.363767
$612$	27.8322	1.12505
$613$	−6.67731	−0.269694	−0.134847	−	0.990866i	$-0.543054\pi$
$613$	−6.67731	−0.269694	−0.134847	+	0.990866i	$0.543054\pi$
$614$	−59.0084	−2.38139
$615$	−10.7577	−0.433794
$616$	0	0
$617$	15.1716	0.610785	0.305392	−	0.952227i	$-0.401212\pi$
$617$	15.1716	0.610785	0.305392	+	0.952227i	$0.401212\pi$
$618$	34.8925	1.40358
$619$	27.9902	1.12502	0.562510	−	0.826790i	$-0.309836\pi$
$619$	27.9902	1.12502	0.562510	+	0.826790i	$0.309836\pi$
$620$	24.4831	0.983264
$621$	1.67325	0.0671450
$622$	−58.0359	−2.32703
$623$	−8.45556	−0.338765
$624$	60.6696	2.42873
$625$	−27.2134	−1.08854
$626$	20.9882	0.838858
$627$	0	0
$628$	−45.7101	−1.82403
$629$	23.3705	0.931844
$630$	−8.14075	−0.324335
$631$	−5.58035	−0.222150	−0.111075	−	0.993812i	$-0.535429\pi$
$631$	−5.58035	−0.222150	−0.111075	+	0.993812i	$0.535429\pi$
$632$	−73.6658	−2.93027
$633$	8.15447	0.324111
$634$	39.9230	1.58554
$635$	34.9692	1.38771
$636$	−58.9179	−2.33625
$637$	5.64097	0.223503
$638$	0	0
$639$	6.24379	0.247000
$640$	−19.7393	−0.780265
$641$	10.9667	0.433158	0.216579	−	0.976265i	$-0.430510\pi$
$641$	10.9667	0.433158	0.216579	+	0.976265i	$0.430510\pi$
$642$	29.2360	1.15385
$643$	0.399143	0.0157406	0.00787032	−	0.999969i	$-0.497495\pi$
$643$	0.399143	0.0157406	0.00787032	+	0.999969i	$0.497495\pi$
$644$	8.31482	0.327650
$645$	15.7483	0.620090
$646$	1.81353	0.0713523
$647$	31.2956	1.23036	0.615178	−	0.788389i	$-0.289084\pi$
$647$	31.2956	1.23036	0.615178	+	0.788389i	$0.289084\pi$
$648$	−7.83871	−0.307934
$649$	0	0
$650$	−67.1492	−2.63381
$651$	1.59773	0.0626198
$652$	48.5470	1.90125
$653$	−26.1788	−1.02446	−0.512228	−	0.858849i	$-0.671180\pi$
$653$	−26.1788	−1.02446	−0.512228	+	0.858849i	$0.671180\pi$
$654$	−12.8662	−0.503110
$655$	2.99205	0.116909
$656$	−37.5204	−1.46493
$657$	−3.51005	−0.136940
$658$	4.20807	0.164048
$659$	5.84482	0.227682	0.113841	−	0.993499i	$-0.463685\pi$
$659$	5.84482	0.227682	0.113841	+	0.993499i	$0.463685\pi$
$660$	0	0
$661$	−6.32811	−0.246135	−0.123067	−	0.992398i	$-0.539273\pi$
$661$	−6.32811	−0.246135	−0.123067	+	0.992398i	$0.539273\pi$
$662$	15.9067	0.618233
$663$	31.5942	1.22702
$664$	−73.9494	−2.86979
$665$	−0.378222	−0.0146668
$666$	−11.0156	−0.426846
$667$	−14.8089	−0.573401
$668$	−30.3243	−1.17328
$669$	8.48763	0.328151
$670$	65.5289	2.53160
$671$	0	0
$672$	−12.7156	−0.490514
$673$	−4.21912	−0.162635	−0.0813176	−	0.996688i	$-0.525913\pi$
$673$	−4.21912	−0.162635	−0.0813176	+	0.996688i	$0.525913\pi$
$674$	55.0411	2.12010
$675$	4.50913	0.173557
$676$	93.5246	3.59710
$677$	−17.9247	−0.688902	−0.344451	−	0.938804i	$-0.611935\pi$
$677$	−17.9247	−0.688902	−0.344451	+	0.938804i	$0.611935\pi$
$678$	13.9458	0.535586
$679$	−5.68478	−0.218162
$680$	−135.385	−5.19176
$681$	22.1524	0.848883
$682$	0	0
$683$	−5.96513	−0.228249	−0.114125	−	0.993466i	$-0.536406\pi$
$683$	−5.96513	−0.228249	−0.114125	+	0.993466i	$0.536406\pi$
$684$	−0.609494	−0.0233046
$685$	−0.385771	−0.0147396
$686$	−2.63994	−0.100793
$687$	−8.98014	−0.342614
$688$	54.9264	2.09405
$689$	−66.8818	−2.54799
$690$	−13.6215	−0.518561
$691$	−39.4084	−1.49917	−0.749583	−	0.661910i	$-0.769746\pi$
$691$	−39.4084	−1.49917	−0.749583	+	0.661910i	$0.769746\pi$
$692$	−33.4839	−1.27287
$693$	0	0
$694$	3.94221	0.149644
$695$	5.17549	0.196318
$696$	69.3756	2.62968
$697$	−19.5391	−0.740096
$698$	−56.7046	−2.14630
$699$	−19.8909	−0.752342
$700$	22.4071	0.846910
$701$	25.4284	0.960417	0.480208	−	0.877154i	$-0.340561\pi$
$701$	25.4284	0.960417	0.480208	+	0.877154i	$0.340561\pi$
$702$	−14.8918	−0.562056
$703$	−0.511789	−0.0193025
$704$	0	0
$705$	−4.91541	−0.185125
$706$	−30.2961	−1.14021
$707$	−16.8776	−0.634746
$708$	32.8690	1.23529
$709$	7.08068	0.265921	0.132960	−	0.991121i	$-0.457552\pi$
$709$	7.08068	0.265921	0.132960	+	0.991121i	$0.457552\pi$
$710$	−50.8291	−1.90758
$711$	9.39769	0.352441
$712$	66.2807	2.48398
$713$	2.67339	0.100119
$714$	−14.7859	−0.553349
$715$	0	0
$716$	64.5686	2.41304
$717$	9.21976	0.344318
$718$	−15.1132	−0.564018
$719$	−21.5811	−0.804840	−0.402420	−	0.915455i	$-0.631831\pi$
$719$	−21.5811	−0.804840	−0.402420	+	0.915455i	$0.631831\pi$
$720$	33.1656	1.23601
$721$	−13.2172	−0.492233
$722$	50.1191	1.86524
$723$	0.802919	0.0298609
$724$	−20.3650	−0.756861
$725$	−39.9075	−1.48213
$726$	0	0
$727$	35.7114	1.32446	0.662231	−	0.749300i	$-0.269610\pi$
$727$	35.7114	1.32446	0.662231	+	0.749300i	$0.269610\pi$
$728$	−44.2180	−1.63883
$729$	1.00000	0.0370370
$730$	28.5744	1.05759
$731$	28.6034	1.05794
$732$	42.1851	1.55921
$733$	−6.34501	−0.234358	−0.117179	−	0.993111i	$-0.537385\pi$
$733$	−6.34501	−0.234358	−0.117179	+	0.993111i	$0.537385\pi$
$734$	−46.1965	−1.70515
$735$	3.08369	0.113744
$736$	−21.2763	−0.784254
$737$	0	0
$738$	9.20967	0.339013
$739$	−10.9804	−0.403922	−0.201961	−	0.979394i	$-0.564731\pi$
$739$	−10.9804	−0.403922	−0.201961	+	0.979394i	$0.564731\pi$
$740$	63.9409	2.35051
$741$	−0.691879	−0.0254168
$742$	31.3003	1.14907
$743$	18.4186	0.675711	0.337856	−	0.941198i	$-0.390298\pi$
$743$	18.4186	0.675711	0.337856	+	0.941198i	$0.390298\pi$
$744$	−12.5241	−0.459157
$745$	−43.7240	−1.60192
$746$	−25.1946	−0.922438
$747$	9.43386	0.345167
$748$	0	0
$749$	−11.0745	−0.404654
$750$	3.99603	0.145914
$751$	4.96566	0.181200	0.0905998	−	0.995887i	$-0.471122\pi$
$751$	4.96566	0.181200	0.0905998	+	0.995887i	$0.471122\pi$
$752$	−17.1438	−0.625170
$753$	0.459277	0.0167370
$754$	131.798	4.79981
$755$	−48.9761	−1.78242
$756$	4.96928	0.180731
$757$	−1.04107	−0.0378384	−0.0189192	−	0.999821i	$-0.506023\pi$
$757$	−1.04107	−0.0378384	−0.0189192	+	0.999821i	$0.506023\pi$
$758$	−84.3737	−3.06459
$759$	0	0
$760$	2.96477	0.107544
$761$	42.0282	1.52352	0.761760	−	0.647860i	$-0.224336\pi$
$761$	42.0282	1.52352	0.761760	+	0.647860i	$0.224336\pi$
$762$	−29.9370	−1.08450
$763$	4.87369	0.176439
$764$	106.857	3.86597
$765$	17.2713	0.624444
$766$	25.9304	0.936905
$767$	37.3119	1.34726
$768$	−7.21718	−0.260427
$769$	−44.1300	−1.59137	−0.795684	−	0.605712i	$-0.792888\pi$
$769$	−44.1300	−1.59137	−0.795684	+	0.605712i	$0.792888\pi$
$770$	0	0
$771$	−23.3574	−0.841195
$772$	−88.4352	−3.18285
$773$	−37.3027	−1.34168	−0.670842	−	0.741600i	$-0.734067\pi$
$773$	−37.3027	−1.34168	−0.670842	+	0.741600i	$0.734067\pi$
$774$	−13.4821	−0.484604
$775$	7.20436	0.258788
$776$	44.5614	1.59966
$777$	4.17268	0.149694
$778$	−87.6454	−3.14224
$779$	0.427884	0.0153305
$780$	86.4406	3.09507
$781$	0	0
$782$	−24.7404	−0.884717
$783$	−8.85038	−0.316287
$784$	10.7552	0.384113
$785$	−28.3654	−1.01241
$786$	−2.56149	−0.0913653
$787$	−7.35809	−0.262288	−0.131144	−	0.991363i	$-0.541865\pi$
$787$	−7.35809	−0.262288	−0.131144	+	0.991363i	$0.541865\pi$
$788$	−89.9850	−3.20558
$789$	4.96169	0.176641
$790$	−76.5042	−2.72190
$791$	−5.28263	−0.187829
$792$	0	0
$793$	47.8872	1.70053
$794$	−62.4437	−2.21604
$795$	−36.5615	−1.29670
$796$	13.2749	0.470515
$797$	6.00177	0.212594	0.106297	−	0.994334i	$-0.466101\pi$
$797$	6.00177	0.212594	0.106297	+	0.994334i	$0.466101\pi$
$798$	0.323795	0.0114622
$799$	−8.92778	−0.315842
$800$	−57.3362	−2.02714
$801$	−8.45556	−0.298763
$802$	−66.7210	−2.35600
$803$	0	0
$804$	−40.0002	−1.41070
$805$	5.15977	0.181858
$806$	−23.7931	−0.838075
$807$	1.03203	0.0363291
$808$	132.298	4.65424
$809$	28.3939	0.998278	0.499139	−	0.866522i	$-0.333650\pi$
$809$	28.3939	0.998278	0.499139	+	0.866522i	$0.333650\pi$
$810$	−8.14075	−0.286037
$811$	−31.9066	−1.12039	−0.560196	−	0.828360i	$-0.689274\pi$
$811$	−31.9066	−1.12039	−0.560196	+	0.828360i	$0.689274\pi$
$812$	−43.9800	−1.54340
$813$	−15.1427	−0.531079
$814$	0	0
$815$	30.1259	1.05526
$816$	60.2381	2.10876
$817$	−0.626383	−0.0219144
$818$	36.8893	1.28980
$819$	5.64097	0.197112
$820$	−53.4582	−1.86684
$821$	4.55941	0.159125	0.0795623	−	0.996830i	$-0.474648\pi$
$821$	4.55941	0.159125	0.0795623	+	0.996830i	$0.474648\pi$
$822$	0.330258	0.0115191
$823$	46.5932	1.62414	0.812069	−	0.583562i	$-0.198341\pi$
$823$	46.5932	1.62414	0.812069	+	0.583562i	$0.198341\pi$
$824$	103.606	3.60927
$825$	0	0
$826$	−17.4617	−0.607572
$827$	1.00246	0.0348589	0.0174294	−	0.999848i	$-0.494452\pi$
$827$	1.00246	0.0348589	0.0174294	+	0.999848i	$0.494452\pi$
$828$	8.31482	0.288960
$829$	−50.4845	−1.75340	−0.876699	−	0.481039i	$-0.840260\pi$
$829$	−50.4845	−1.75340	−0.876699	+	0.481039i	$0.840260\pi$
$830$	−76.7987	−2.66572
$831$	1.07001	0.0371184
$832$	68.0187	2.35813
$833$	5.60085	0.194058
$834$	−4.43073	−0.153424
$835$	−18.8178	−0.651216
$836$	0	0
$837$	1.59773	0.0552255
$838$	−78.5236	−2.71255
$839$	−26.0614	−0.899739	−0.449869	−	0.893094i	$-0.648529\pi$
$839$	−26.0614	−0.899739	−0.449869	+	0.893094i	$0.648529\pi$
$840$	−24.1721	−0.834018
$841$	49.3292	1.70101
$842$	−95.7441	−3.29956
$843$	31.3090	1.07834
$844$	40.5218	1.39482
$845$	58.0368	1.99652
$846$	4.20807	0.144677
$847$	0	0
$848$	−127.518	−4.37898
$849$	−31.9651	−1.09704
$850$	−66.6716	−2.28682
$851$	6.98191	0.239337
$852$	31.0271	1.06297
$853$	30.1888	1.03364	0.516822	−	0.856093i	$-0.327115\pi$
$853$	30.1888	1.03364	0.516822	+	0.856093i	$0.327115\pi$
$854$	−22.4109	−0.766886
$855$	−0.378222	−0.0129349
$856$	86.8099	2.96710
$857$	25.3151	0.864748	0.432374	−	0.901694i	$-0.357676\pi$
$857$	25.3151	0.864748	0.432374	+	0.901694i	$0.357676\pi$
$858$	0	0
$859$	−10.7680	−0.367399	−0.183699	−	0.982982i	$-0.558807\pi$
$859$	−10.7680	−0.367399	−0.183699	+	0.982982i	$0.558807\pi$
$860$	78.2578	2.66857
$861$	−3.48859	−0.118891
$862$	94.5273	3.21961
$863$	−35.3003	−1.20163	−0.600817	−	0.799386i	$-0.705158\pi$
$863$	−35.3003	−1.20163	−0.600817	+	0.799386i	$0.705158\pi$
$864$	−12.7156	−0.432592
$865$	−20.7784	−0.706488
$866$	60.9716	2.07190
$867$	14.3695	0.488015
$868$	7.93955	0.269486
$869$	0	0
$870$	72.0487	2.44268
$871$	−45.4070	−1.53856
$872$	−38.2035	−1.29373
$873$	−5.68478	−0.192401
$874$	0.541788	0.0183263
$875$	−1.51368	−0.0511718
$876$	−17.4424	−0.589324
$877$	4.16706	0.140712	0.0703558	−	0.997522i	$-0.477587\pi$
$877$	4.16706	0.140712	0.0703558	+	0.997522i	$0.477587\pi$
$878$	65.4275	2.20807
$879$	0.472963	0.0159526
$880$	0	0
$881$	−40.6561	−1.36974	−0.684870	−	0.728665i	$-0.740141\pi$
$881$	−40.6561	−1.36974	−0.684870	+	0.728665i	$0.740141\pi$
$882$	−2.63994	−0.0888914
$883$	−19.1697	−0.645113	−0.322556	−	0.946550i	$-0.604542\pi$
$883$	−19.1697	−0.645113	−0.322556	+	0.946550i	$0.604542\pi$
$884$	157.001	5.28050
$885$	20.3969	0.685634
$886$	−35.0967	−1.17910
$887$	37.0380	1.24362	0.621808	−	0.783170i	$-0.286398\pi$
$887$	37.0380	1.24362	0.621808	+	0.783170i	$0.286398\pi$
$888$	−32.7084	−1.09762
$889$	11.3400	0.380333
$890$	68.8346	2.30734
$891$	0	0
$892$	42.1774	1.41220
$893$	0.195508	0.00654244
$894$	37.4321	1.25192
$895$	40.0681	1.33933
$896$	−6.40120	−0.213849
$897$	9.43873	0.315150
$898$	−55.0992	−1.83868
$899$	−14.1405	−0.471612
$900$	22.4071	0.746904
$901$	−66.4061	−2.21231
$902$	0	0
$903$	5.10698	0.169950
$904$	41.4090	1.37724
$905$	−12.6375	−0.420086
$906$	41.9284	1.39298
$907$	−28.7583	−0.954905	−0.477452	−	0.878658i	$-0.658440\pi$
$907$	−28.7583	−0.954905	−0.477452	+	0.878658i	$0.658440\pi$
$908$	110.082	3.65318
$909$	−16.8776	−0.559793
$910$	−45.9217	−1.52229
$911$	44.7716	1.48335	0.741675	−	0.670759i	$-0.234032\pi$
$911$	44.7716	1.48335	0.741675	+	0.670759i	$0.234032\pi$
$912$	−1.31915	−0.0436813
$913$	0	0
$914$	−74.5371	−2.46547
$915$	26.1780	0.865418
$916$	−44.6248	−1.47445
$917$	0.970284	0.0320416
$918$	−14.7859	−0.488008
$919$	−19.3392	−0.637943	−0.318971	−	0.947764i	$-0.603337\pi$
$919$	−19.3392	−0.637943	−0.318971	+	0.947764i	$0.603337\pi$
$920$	−40.4459	−1.33346
$921$	22.3522	0.736530
$922$	−35.7533	−1.17747
$923$	35.2210	1.15931
$924$	0	0
$925$	18.8152	0.618638
$926$	89.6481	2.94602
$927$	−13.2172	−0.434109
$928$	112.538	3.69423
$929$	−26.9129	−0.882985	−0.441493	−	0.897265i	$-0.645551\pi$
$929$	−26.9129	−0.882985	−0.441493	+	0.897265i	$0.645551\pi$
$930$	−13.0067	−0.426506
$931$	−0.122652	−0.00401977
$932$	−98.8433	−3.23772
$933$	21.9838	0.719717
$934$	−33.2127	−1.08675
$935$	0	0
$936$	−44.2180	−1.44531
$937$	−42.5349	−1.38956	−0.694778	−	0.719224i	$-0.744497\pi$
$937$	−42.5349	−1.38956	−0.694778	+	0.719224i	$0.744497\pi$
$938$	21.2502	0.693843
$939$	−7.95027	−0.259447
$940$	−24.4260	−0.796690
$941$	48.7704	1.58987	0.794934	−	0.606695i	$-0.207505\pi$
$941$	48.7704	1.58987	0.794934	+	0.606695i	$0.207505\pi$
$942$	24.2836	0.791202
$943$	−5.83727	−0.190088
$944$	71.1395	2.31540
$945$	3.08369	0.100312
$946$	0	0
$947$	0.641845	0.0208572	0.0104286	−	0.999946i	$-0.496680\pi$
$947$	0.641845	0.0208572	0.0104286	+	0.999946i	$0.496680\pi$
$948$	46.6997	1.51674
$949$	−19.8001	−0.642738
$950$	1.46003	0.0473698
$951$	−15.1227	−0.490387
$952$	−43.9035	−1.42292
$953$	−7.65944	−0.248114	−0.124057	−	0.992275i	$-0.539591\pi$
$953$	−7.65944	−0.248114	−0.124057	+	0.992275i	$0.539591\pi$
$954$	31.3003	1.01338
$955$	66.3104	2.14576
$956$	45.8156	1.48178
$957$	0	0
$958$	76.2721	2.46424
$959$	−0.125101	−0.00403971
$960$	37.1831	1.20008
$961$	−28.4473	−0.917654
$962$	−62.1388	−2.00343
$963$	−11.0745	−0.356871
$964$	3.98993	0.128507
$965$	−54.8785	−1.76660
$966$	−4.41727	−0.142123
$967$	29.7387	0.956333	0.478166	−	0.878269i	$-0.341302\pi$
$967$	29.7387	0.956333	0.478166	+	0.878269i	$0.341302\pi$
$968$	0	0
$969$	−0.686958	−0.0220683
$970$	46.2784	1.48591
$971$	−34.9188	−1.12060	−0.560299	−	0.828291i	$-0.689314\pi$
$971$	−34.9188	−1.12060	−0.560299	+	0.828291i	$0.689314\pi$
$972$	4.96928	0.159390
$973$	1.67835	0.0538053
$974$	−67.3388	−2.15767
$975$	25.4359	0.814600
$976$	91.3026	2.92253
$977$	31.9341	1.02166	0.510832	−	0.859681i	$-0.329338\pi$
$977$	31.9341	1.02166	0.510832	+	0.859681i	$0.329338\pi$
$978$	−25.7907	−0.824695
$979$	0	0
$980$	15.3237	0.489498
$981$	4.87369	0.155605
$982$	12.3179	0.393080
$983$	−33.9111	−1.08159	−0.540797	−	0.841153i	$-0.681877\pi$
$983$	−33.9111	−1.08159	−0.540797	+	0.841153i	$0.681877\pi$
$984$	27.3461	0.871761
$985$	−55.8402	−1.77922
$986$	130.861	4.16746
$987$	−1.59400	−0.0507377
$988$	−3.43814	−0.109382
$989$	8.54523	0.271722
$990$	0	0
$991$	−13.3101	−0.422809	−0.211404	−	0.977399i	$-0.567804\pi$
$991$	−13.3101	−0.422809	−0.211404	+	0.977399i	$0.567804\pi$
$992$	−20.3160	−0.645034
$993$	−6.02542	−0.191211
$994$	−16.4832	−0.522816
$995$	8.23772	0.261153
$996$	46.8795	1.48543
$997$	2.95257	0.0935088	0.0467544	−	0.998906i	$-0.485112\pi$
$997$	2.95257	0.0935088	0.0467544	+	0.998906i	$0.485112\pi$
$998$	48.8279	1.54562
$999$	4.17268	0.132018

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.br.1.2		10
3.2	odd	2		7623.2.a.cy.1.9		10
11.2	odd	10		231.2.j.g.169.1	✓	20
11.6	odd	10		231.2.j.g.190.1	yes	20
11.10	odd	2		2541.2.a.bq.1.9		10
33.2	even	10		693.2.m.j.631.5		20
33.17	even	10		693.2.m.j.190.5		20
33.32	even	2		7623.2.a.cx.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.1	✓	20	11.2	odd	10
231.2.j.g.190.1	yes	20	11.6	odd	10
693.2.m.j.190.5		20	33.17	even	10
693.2.m.j.631.5		20	33.2	even	10
2541.2.a.bq.1.9		10	11.10	odd	2
2541.2.a.br.1.2		10	1.1	even	1	trivial
7623.2.a.cx.1.2		10	33.32	even	2
7623.2.a.cy.1.9		10	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)

\(f(q)\)	\(=\)	\(q-2.63994 q^{2} +1.00000 q^{3} +4.96928 q^{4} +3.08369 q^{5} -2.63994 q^{6} +1.00000 q^{7} -7.83871 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.63994 q^{2} +1.00000 q^{3} +4.96928 q^{4} +3.08369 q^{5} -2.63994 q^{6} +1.00000 q^{7} -7.83871 q^{8} +1.00000 q^{9} -8.14075 q^{10} +4.96928 q^{12} +5.64097 q^{13} -2.63994 q^{14} +3.08369 q^{15} +10.7552 q^{16} +5.60085 q^{17} -2.63994 q^{18} -0.122652 q^{19} +15.3237 q^{20} +1.00000 q^{21} +1.67325 q^{23} -7.83871 q^{24} +4.50913 q^{25} -14.8918 q^{26} +1.00000 q^{27} +4.96928 q^{28} -8.85038 q^{29} -8.14075 q^{30} +1.59773 q^{31} -12.7156 q^{32} -14.7859 q^{34} +3.08369 q^{35} +4.96928 q^{36} +4.17268 q^{37} +0.323795 q^{38} +5.64097 q^{39} -24.1721 q^{40} -3.48859 q^{41} -2.63994 q^{42} +5.10698 q^{43} +3.08369 q^{45} -4.41727 q^{46} -1.59400 q^{47} +10.7552 q^{48} +1.00000 q^{49} -11.9038 q^{50} +5.60085 q^{51} +28.0316 q^{52} -11.8564 q^{53} -2.63994 q^{54} -7.83871 q^{56} -0.122652 q^{57} +23.3645 q^{58} +6.61445 q^{59} +15.3237 q^{60} +8.48918 q^{61} -4.21790 q^{62} +1.00000 q^{63} +12.0580 q^{64} +17.3950 q^{65} -8.04949 q^{67} +27.8322 q^{68} +1.67325 q^{69} -8.14075 q^{70} +6.24379 q^{71} -7.83871 q^{72} -3.51005 q^{73} -11.0156 q^{74} +4.50913 q^{75} -0.609494 q^{76} -14.8918 q^{78} +9.39769 q^{79} +33.1656 q^{80} +1.00000 q^{81} +9.20967 q^{82} +9.43386 q^{83} +4.96928 q^{84} +17.2713 q^{85} -13.4821 q^{86} -8.85038 q^{87} -8.45556 q^{89} -8.14075 q^{90} +5.64097 q^{91} +8.31482 q^{92} +1.59773 q^{93} +4.20807 q^{94} -0.378222 q^{95} -12.7156 q^{96} -5.68478 q^{97} -2.63994 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 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

Introduction

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