LMFDB - Embedded newform 2541.2.a.bq.1.8

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			1.8
Root			$1.80545$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.80545 q^{2} +1.00000 q^{3} +1.25966 q^{4} +2.77715 q^{5} +1.80545 q^{6} -1.00000 q^{7} -1.33666 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.80545 q^{2} +1.00000 q^{3} +1.25966 q^{4} +2.77715 q^{5} +1.80545 q^{6} -1.00000 q^{7} -1.33666 q^{8} +1.00000 q^{9} +5.01400 q^{10} +1.25966 q^{12} +2.31311 q^{13} -1.80545 q^{14} +2.77715 q^{15} -4.93258 q^{16} +2.66163 q^{17} +1.80545 q^{18} +8.08270 q^{19} +3.49825 q^{20} -1.00000 q^{21} -2.43007 q^{23} -1.33666 q^{24} +2.71254 q^{25} +4.17621 q^{26} +1.00000 q^{27} -1.25966 q^{28} -7.55762 q^{29} +5.01400 q^{30} +9.24567 q^{31} -6.23222 q^{32} +4.80544 q^{34} -2.77715 q^{35} +1.25966 q^{36} +11.1976 q^{37} +14.5929 q^{38} +2.31311 q^{39} -3.71209 q^{40} -0.299894 q^{41} -1.80545 q^{42} -7.29328 q^{43} +2.77715 q^{45} -4.38737 q^{46} +0.457855 q^{47} -4.93258 q^{48} +1.00000 q^{49} +4.89737 q^{50} +2.66163 q^{51} +2.91372 q^{52} -5.19340 q^{53} +1.80545 q^{54} +1.33666 q^{56} +8.08270 q^{57} -13.6449 q^{58} +12.2826 q^{59} +3.49825 q^{60} -1.81788 q^{61} +16.6926 q^{62} -1.00000 q^{63} -1.38682 q^{64} +6.42384 q^{65} -1.42267 q^{67} +3.35273 q^{68} -2.43007 q^{69} -5.01400 q^{70} +0.558099 q^{71} -1.33666 q^{72} -9.66283 q^{73} +20.2168 q^{74} +2.71254 q^{75} +10.1814 q^{76} +4.17621 q^{78} -10.3200 q^{79} -13.6985 q^{80} +1.00000 q^{81} -0.541445 q^{82} -8.51075 q^{83} -1.25966 q^{84} +7.39173 q^{85} -13.1677 q^{86} -7.55762 q^{87} -1.56616 q^{89} +5.01400 q^{90} -2.31311 q^{91} -3.06105 q^{92} +9.24567 q^{93} +0.826634 q^{94} +22.4468 q^{95} -6.23222 q^{96} -0.533862 q^{97} +1.80545 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.80545	1.27665	0.638324	−	0.769768i	$-0.279628\pi$
$2$	1.80545	1.27665	0.638324	+	0.769768i	$0.279628\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.25966	0.629828
$5$	2.77715	1.24198	0.620989	−	0.783819i	$-0.286731\pi$
$5$	2.77715	1.24198	0.620989	+	0.783819i	$0.286731\pi$
$6$	1.80545	0.737073
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.33666	−0.472579
$9$	1.00000	0.333333
$10$	5.01400	1.58557
$11$	0	0
$11$	0	0
$12$	1.25966	0.363631
$13$	2.31311	0.641541	0.320771	−	0.947157i	$-0.396058\pi$
$13$	2.31311	0.641541	0.320771	+	0.947157i	$0.396058\pi$
$14$	−1.80545	−0.482527
$15$	2.77715	0.717056
$16$	−4.93258	−1.23314
$17$	2.66163	0.645539	0.322770	−	0.946478i	$-0.395386\pi$
$17$	2.66163	0.645539	0.322770	+	0.946478i	$0.395386\pi$
$18$	1.80545	0.425549
$19$	8.08270	1.85430	0.927149	−	0.374693i	$-0.122252\pi$
$19$	8.08270	1.85430	0.927149	+	0.374693i	$0.122252\pi$
$20$	3.49825	0.782232
$21$	−1.00000	−0.218218
$22$	0	0
$23$	−2.43007	−0.506704	−0.253352	−	0.967374i	$-0.581533\pi$
$23$	−2.43007	−0.506704	−0.253352	+	0.967374i	$0.581533\pi$
$24$	−1.33666	−0.272844
$25$	2.71254	0.542509
$26$	4.17621	0.819022
$27$	1.00000	0.192450
$28$	−1.25966	−0.238053
$29$	−7.55762	−1.40342	−0.701708	−	0.712465i	$-0.747579\pi$
$29$	−7.55762	−1.40342	−0.701708	+	0.712465i	$0.747579\pi$
$30$	5.01400	0.915428
$31$	9.24567	1.66057	0.830285	−	0.557339i	$-0.188177\pi$
$31$	9.24567	1.66057	0.830285	+	0.557339i	$0.188177\pi$
$32$	−6.23222	−1.10171
$33$	0	0
$34$	4.80544	0.824126
$35$	−2.77715	−0.469423
$36$	1.25966	0.209943
$37$	11.1976	1.84088	0.920438	−	0.390888i	$-0.127832\pi$
$37$	11.1976	1.84088	0.920438	+	0.390888i	$0.127832\pi$
$38$	14.5929	2.36728
$39$	2.31311	0.370394
$40$	−3.71209	−0.586933
$41$	−0.299894	−0.0468356	−0.0234178	−	0.999726i	$-0.507455\pi$
$41$	−0.299894	−0.0468356	−0.0234178	+	0.999726i	$0.507455\pi$
$42$	−1.80545	−0.278587
$43$	−7.29328	−1.11221	−0.556107	−	0.831110i	$-0.687706\pi$
$43$	−7.29328	−1.11221	−0.556107	+	0.831110i	$0.687706\pi$
$44$	0	0
$45$	2.77715	0.413993
$46$	−4.38737	−0.646882
$47$	0.457855	0.0667849	0.0333925	−	0.999442i	$-0.489369\pi$
$47$	0.457855	0.0667849	0.0333925	+	0.999442i	$0.489369\pi$
$48$	−4.93258	−0.711956
$49$	1.00000	0.142857
$50$	4.89737	0.692592
$51$	2.66163	0.372702
$52$	2.91372	0.404060
$53$	−5.19340	−0.713369	−0.356684	−	0.934225i	$-0.616093\pi$
$53$	−5.19340	−0.713369	−0.356684	+	0.934225i	$0.616093\pi$
$54$	1.80545	0.245691
$55$	0	0
$56$	1.33666	0.178618
$57$	8.08270	1.07058
$58$	−13.6449	−1.79167
$59$	12.2826	1.59906	0.799532	−	0.600623i	$-0.205081\pi$
$59$	12.2826	1.59906	0.799532	+	0.600623i	$0.205081\pi$
$60$	3.49825	0.451622
$61$	−1.81788	−0.232755	−0.116378	−	0.993205i	$-0.537128\pi$
$61$	−1.81788	−0.232755	−0.116378	+	0.993205i	$0.537128\pi$
$62$	16.6926	2.11996
$63$	−1.00000	−0.125988
$64$	−1.38682	−0.173352
$65$	6.42384	0.796780
$66$	0	0
$67$	−1.42267	−0.173807	−0.0869036	−	0.996217i	$-0.527697\pi$
$67$	−1.42267	−0.173807	−0.0869036	+	0.996217i	$0.527697\pi$
$68$	3.35273	0.406579
$69$	−2.43007	−0.292546
$70$	−5.01400	−0.599288
$71$	0.558099	0.0662342	0.0331171	−	0.999451i	$-0.489457\pi$
$71$	0.558099	0.0662342	0.0331171	+	0.999451i	$0.489457\pi$
$72$	−1.33666	−0.157526
$73$	−9.66283	−1.13095	−0.565474	−	0.824766i	$-0.691307\pi$
$73$	−9.66283	−1.13095	−0.565474	+	0.824766i	$0.691307\pi$
$74$	20.2168	2.35015
$75$	2.71254	0.313218
$76$	10.1814	1.16789
$77$	0	0
$78$	4.17621	0.472862
$79$	−10.3200	−1.16109	−0.580544	−	0.814229i	$-0.697160\pi$
$79$	−10.3200	−1.16109	−0.580544	+	0.814229i	$0.697160\pi$
$80$	−13.6985	−1.53154
$81$	1.00000	0.111111
$82$	−0.541445	−0.0597926
$83$	−8.51075	−0.934177	−0.467088	−	0.884211i	$-0.654697\pi$
$83$	−8.51075	−0.934177	−0.467088	+	0.884211i	$0.654697\pi$
$84$	−1.25966	−0.137440
$85$	7.39173	0.801745
$86$	−13.1677	−1.41991
$87$	−7.55762	−0.810262
$88$	0	0
$89$	−1.56616	−0.166012	−0.0830062	−	0.996549i	$-0.526452\pi$
$89$	−1.56616	−0.166012	−0.0830062	+	0.996549i	$0.526452\pi$
$90$	5.01400	0.528522
$91$	−2.31311	−0.242480
$92$	−3.06105	−0.319136
$93$	9.24567	0.958731
$94$	0.826634	0.0852608
$95$	22.4468	2.30300
$96$	−6.23222	−0.636073
$97$	−0.533862	−0.0542055	−0.0271027	−	0.999633i	$-0.508628\pi$
$97$	−0.533862	−0.0542055	−0.0271027	+	0.999633i	$0.508628\pi$
$98$	1.80545	0.182378
$99$	0	0
$100$	3.41687	0.341687
$101$	−5.31761	−0.529122	−0.264561	−	0.964369i	$-0.585227\pi$
$101$	−5.31761	−0.529122	−0.264561	+	0.964369i	$0.585227\pi$
$102$	4.80544	0.475809
$103$	18.5606	1.82883	0.914414	−	0.404781i	$-0.132652\pi$
$103$	18.5606	1.82883	0.914414	+	0.404781i	$0.132652\pi$
$104$	−3.09183	−0.303179
$105$	−2.77715	−0.271022
$106$	−9.37644	−0.910720
$107$	−9.42725	−0.911367	−0.455683	−	0.890142i	$-0.650605\pi$
$107$	−9.42725	−0.911367	−0.455683	+	0.890142i	$0.650605\pi$
$108$	1.25966	0.121210
$109$	1.11200	0.106511	0.0532553	−	0.998581i	$-0.483040\pi$
$109$	1.11200	0.106511	0.0532553	+	0.998581i	$0.483040\pi$
$110$	0	0
$111$	11.1976	1.06283
$112$	4.93258	0.466085
$113$	−9.02473	−0.848975	−0.424488	−	0.905434i	$-0.639546\pi$
$113$	−9.02473	−0.848975	−0.424488	+	0.905434i	$0.639546\pi$
$114$	14.5929	1.36675
$115$	−6.74866	−0.629315
$116$	−9.52000	−0.883910
$117$	2.31311	0.213847
$118$	22.1757	2.04144
$119$	−2.66163	−0.243991
$120$	−3.71209	−0.338866
$121$	0	0
$122$	−3.28209	−0.297146
$123$	−0.299894	−0.0270406
$124$	11.6464	1.04587
$125$	−6.35260	−0.568194
$126$	−1.80545	−0.160842
$127$	−8.33542	−0.739649	−0.369824	−	0.929102i	$-0.620582\pi$
$127$	−8.33542	−0.739649	−0.369824	+	0.929102i	$0.620582\pi$
$128$	9.96061	0.880402
$129$	−7.29328	−0.642137
$130$	11.5979	1.01721
$131$	7.97862	0.697095	0.348548	−	0.937291i	$-0.386675\pi$
$131$	7.97862	0.697095	0.348548	+	0.937291i	$0.386675\pi$
$132$	0	0
$133$	−8.08270	−0.700859
$134$	−2.56857	−0.221891
$135$	2.77715	0.239019
$136$	−3.55768	−0.305068
$137$	−10.3316	−0.882691	−0.441345	−	0.897337i	$-0.645499\pi$
$137$	−10.3316	−0.882691	−0.441345	+	0.897337i	$0.645499\pi$
$138$	−4.38737	−0.373478
$139$	−5.53964	−0.469866	−0.234933	−	0.972012i	$-0.575487\pi$
$139$	−5.53964	−0.469866	−0.234933	+	0.972012i	$0.575487\pi$
$140$	−3.49825	−0.295656
$141$	0.457855	0.0385583
$142$	1.00762	0.0845576
$143$	0	0
$144$	−4.93258	−0.411048
$145$	−20.9886	−1.74301
$146$	−17.4458	−1.44382
$147$	1.00000	0.0824786
$148$	14.1051	1.15944
$149$	21.9883	1.80136	0.900678	−	0.434488i	$-0.143071\pi$
$149$	21.9883	1.80136	0.900678	+	0.434488i	$0.143071\pi$
$150$	4.89737	0.399868
$151$	−14.1658	−1.15280	−0.576400	−	0.817168i	$-0.695543\pi$
$151$	−14.1658	−1.15280	−0.576400	+	0.817168i	$0.695543\pi$
$152$	−10.8038	−0.876303
$153$	2.66163	0.215180
$154$	0	0
$155$	25.6766	2.06239
$156$	2.91372	0.233284
$157$	−1.37897	−0.110054	−0.0550270	−	0.998485i	$-0.517524\pi$
$157$	−1.37897	−0.110054	−0.0550270	+	0.998485i	$0.517524\pi$
$158$	−18.6322	−1.48230
$159$	−5.19340	−0.411864
$160$	−17.3078	−1.36830
$161$	2.43007	0.191516
$162$	1.80545	0.141850
$163$	−17.0408	−1.33474	−0.667370	−	0.744727i	$-0.732580\pi$
$163$	−17.0408	−1.33474	−0.667370	+	0.744727i	$0.732580\pi$
$164$	−0.377764	−0.0294984
$165$	0	0
$166$	−15.3658	−1.19261
$167$	−7.96033	−0.615989	−0.307995	−	0.951388i	$-0.599658\pi$
$167$	−7.96033	−0.615989	−0.307995	+	0.951388i	$0.599658\pi$
$168$	1.33666	0.103125
$169$	−7.64953	−0.588425
$170$	13.3454	1.02355
$171$	8.08270	0.618099
$172$	−9.18702	−0.700504
$173$	−10.2300	−0.777774	−0.388887	−	0.921285i	$-0.627140\pi$
$173$	−10.2300	−0.777774	−0.388887	+	0.921285i	$0.627140\pi$
$174$	−13.6449	−1.03442
$175$	−2.71254	−0.205049
$176$	0	0
$177$	12.2826	0.923220
$178$	−2.82762	−0.211939
$179$	1.75709	0.131331	0.0656656	−	0.997842i	$-0.479083\pi$
$179$	1.75709	0.131331	0.0656656	+	0.997842i	$0.479083\pi$
$180$	3.49825	0.260744
$181$	12.5171	0.930386	0.465193	−	0.885209i	$-0.345985\pi$
$181$	12.5171	0.930386	0.465193	+	0.885209i	$0.345985\pi$
$182$	−4.17621	−0.309561
$183$	−1.81788	−0.134381
$184$	3.24816	0.239458
$185$	31.0974	2.28633
$186$	16.6926	1.22396
$187$	0	0
$188$	0.576739	0.0420630
$189$	−1.00000	−0.0727393
$190$	40.5267	2.94011
$191$	−19.6079	−1.41878	−0.709389	−	0.704818i	$-0.751029\pi$
$191$	−19.6079	−1.41878	−0.709389	+	0.704818i	$0.751029\pi$
$192$	−1.38682	−0.100085
$193$	−0.612533	−0.0440911	−0.0220455	−	0.999757i	$-0.507018\pi$
$193$	−0.612533	−0.0440911	−0.0220455	+	0.999757i	$0.507018\pi$
$194$	−0.963862	−0.0692013
$195$	6.42384	0.460021
$196$	1.25966	0.0899754
$197$	−13.5754	−0.967204	−0.483602	−	0.875288i	$-0.660672\pi$
$197$	−13.5754	−0.967204	−0.483602	+	0.875288i	$0.660672\pi$
$198$	0	0
$199$	4.17314	0.295826	0.147913	−	0.989000i	$-0.452744\pi$
$199$	4.17314	0.295826	0.147913	+	0.989000i	$0.452744\pi$
$200$	−3.62574	−0.256378
$201$	−1.42267	−0.100348
$202$	−9.60069	−0.675502
$203$	7.55762	0.530441
$204$	3.35273	0.234738
$205$	−0.832851	−0.0581688
$206$	33.5102	2.33477
$207$	−2.43007	−0.168901
$208$	−11.4096	−0.791113
$209$	0	0
$210$	−5.01400	−0.345999
$211$	10.6630	0.734073	0.367037	−	0.930206i	$-0.380372\pi$
$211$	10.6630	0.734073	0.367037	+	0.930206i	$0.380372\pi$
$212$	−6.54190	−0.449300
$213$	0.558099	0.0382403
$214$	−17.0204	−1.16349
$215$	−20.2545	−1.38135
$216$	−1.33666	−0.0909479
$217$	−9.24567	−0.627637
$218$	2.00767	0.135976
$219$	−9.66283	−0.652954
$220$	0	0
$221$	6.15663	0.414140
$222$	20.2168	1.35686
$223$	3.64321	0.243967	0.121984	−	0.992532i	$-0.461074\pi$
$223$	3.64321	0.243967	0.121984	+	0.992532i	$0.461074\pi$
$224$	6.23222	0.416408
$225$	2.71254	0.180836
$226$	−16.2937	−1.08384
$227$	20.9279	1.38904	0.694518	−	0.719475i	$-0.255618\pi$
$227$	20.9279	1.38904	0.694518	+	0.719475i	$0.255618\pi$
$228$	10.1814	0.674281
$229$	−16.5049	−1.09068	−0.545338	−	0.838216i	$-0.683599\pi$
$229$	−16.5049	−1.09068	−0.545338	+	0.838216i	$0.683599\pi$
$230$	−12.1844	−0.803414
$231$	0	0
$232$	10.1019	0.663225
$233$	7.28683	0.477376	0.238688	−	0.971096i	$-0.423283\pi$
$233$	7.28683	0.477376	0.238688	+	0.971096i	$0.423283\pi$
$234$	4.17621	0.273007
$235$	1.27153	0.0829454
$236$	15.4719	1.00714
$237$	−10.3200	−0.670355
$238$	−4.80544	−0.311490
$239$	−11.9626	−0.773798	−0.386899	−	0.922122i	$-0.626454\pi$
$239$	−11.9626	−0.773798	−0.386899	+	0.922122i	$0.626454\pi$
$240$	−13.6985	−0.884234
$241$	−4.39102	−0.282850	−0.141425	−	0.989949i	$-0.545168\pi$
$241$	−4.39102	−0.282850	−0.141425	+	0.989949i	$0.545168\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−2.28990	−0.146596
$245$	2.77715	0.177425
$246$	−0.541445	−0.0345213
$247$	18.6962	1.18961
$248$	−12.3583	−0.784751
$249$	−8.51075	−0.539347
$250$	−11.4693	−0.725383
$251$	−13.5401	−0.854643	−0.427322	−	0.904100i	$-0.640543\pi$
$251$	−13.5401	−0.854643	−0.427322	+	0.904100i	$0.640543\pi$
$252$	−1.25966	−0.0793509
$253$	0	0
$254$	−15.0492	−0.944271
$255$	7.39173	0.462888
$256$	20.7570	1.29731
$257$	0.121519	0.00758013	0.00379006	−	0.999993i	$-0.498794\pi$
$257$	0.121519	0.00758013	0.00379006	+	0.999993i	$0.498794\pi$
$258$	−13.1677	−0.819783
$259$	−11.1976	−0.695786
$260$	8.09183	0.501834
$261$	−7.55762	−0.467805
$262$	14.4050	0.889944
$263$	5.88836	0.363092	0.181546	−	0.983382i	$-0.441890\pi$
$263$	5.88836	0.363092	0.181546	+	0.983382i	$0.441890\pi$
$264$	0	0
$265$	−14.4228	−0.885988
$266$	−14.5929	−0.894749
$267$	−1.56616	−0.0958473
$268$	−1.79208	−0.109469
$269$	−2.21155	−0.134841	−0.0674203	−	0.997725i	$-0.521477\pi$
$269$	−2.21155	−0.134841	−0.0674203	+	0.997725i	$0.521477\pi$
$270$	5.01400	0.305143
$271$	−7.59429	−0.461321	−0.230660	−	0.973034i	$-0.574089\pi$
$271$	−7.59429	−0.461321	−0.230660	+	0.973034i	$0.574089\pi$
$272$	−13.1287	−0.796043
$273$	−2.31311	−0.139996
$274$	−18.6533	−1.12688
$275$	0	0
$276$	−3.06105	−0.184254
$277$	−24.1488	−1.45096	−0.725481	−	0.688243i	$-0.758382\pi$
$277$	−24.1488	−1.45096	−0.725481	+	0.688243i	$0.758382\pi$
$278$	−10.0016	−0.599854
$279$	9.24567	0.553524
$280$	3.71209	0.221840
$281$	27.2967	1.62838	0.814192	−	0.580595i	$-0.197180\pi$
$281$	27.2967	1.62838	0.814192	+	0.580595i	$0.197180\pi$
$282$	0.826634	0.0492254
$283$	25.6085	1.52227	0.761135	−	0.648594i	$-0.224643\pi$
$283$	25.6085	1.52227	0.761135	+	0.648594i	$0.224643\pi$
$284$	0.703012	0.0417161
$285$	22.4468	1.32964
$286$	0	0
$287$	0.299894	0.0177022
$288$	−6.23222	−0.367237
$289$	−9.91574	−0.583279
$290$	−37.8939	−2.22521
$291$	−0.533862	−0.0312956
$292$	−12.1718	−0.712303
$293$	−11.6993	−0.683482	−0.341741	−	0.939794i	$-0.611017\pi$
$293$	−11.6993	−0.683482	−0.341741	+	0.939794i	$0.611017\pi$
$294$	1.80545	0.105296
$295$	34.1107	1.98600
$296$	−14.9674	−0.869960
$297$	0	0
$298$	39.6989	2.29969
$299$	−5.62101	−0.325072
$300$	3.41687	0.197273
$301$	7.29328	0.420378
$302$	−25.5757	−1.47172
$303$	−5.31761	−0.305489
$304$	−39.8685	−2.28662
$305$	−5.04851	−0.289077
$306$	4.80544	0.274709
$307$	28.0637	1.60168	0.800839	−	0.598880i	$-0.204387\pi$
$307$	28.0637	1.60168	0.800839	+	0.598880i	$0.204387\pi$
$308$	0	0
$309$	18.5606	1.05587
$310$	46.3578	2.63295
$311$	28.7137	1.62820	0.814102	−	0.580722i	$-0.197230\pi$
$311$	28.7137	1.62820	0.814102	+	0.580722i	$0.197230\pi$
$312$	−3.09183	−0.175040
$313$	−29.4483	−1.66451	−0.832257	−	0.554390i	$-0.812952\pi$
$313$	−29.4483	−1.66451	−0.832257	+	0.554390i	$0.812952\pi$
$314$	−2.48967	−0.140500
$315$	−2.77715	−0.156474
$316$	−12.9996	−0.731286
$317$	−0.0336526	−0.00189012	−0.000945058	−	1.00000i	$-0.500301\pi$
$317$	−0.0336526	−0.00189012	−0.000945058		1.00000i	$0.500301\pi$
$318$	−9.37644	−0.525805
$319$	0	0
$320$	−3.85139	−0.215299
$321$	−9.42725	−0.526178
$322$	4.38737	0.244499
$323$	21.5131	1.19702
$324$	1.25966	0.0699809
$325$	6.27441	0.348042
$326$	−30.7664	−1.70399
$327$	1.11200	0.0614939
$328$	0.400856	0.0221335
$329$	−0.457855	−0.0252423
$330$	0	0
$331$	16.4575	0.904588	0.452294	−	0.891869i	$-0.350606\pi$
$331$	16.4575	0.904588	0.452294	+	0.891869i	$0.350606\pi$
$332$	−10.7206	−0.588371
$333$	11.1976	0.613626
$334$	−14.3720	−0.786401
$335$	−3.95097	−0.215865
$336$	4.93258	0.269094
$337$	13.2223	0.720262	0.360131	−	0.932902i	$-0.382732\pi$
$337$	13.2223	0.720262	0.360131	+	0.932902i	$0.382732\pi$
$338$	−13.8108	−0.751211
$339$	−9.02473	−0.490156
$340$	9.31103	0.504962
$341$	0	0
$342$	14.5929	0.789095
$343$	−1.00000	−0.0539949
$344$	9.74860	0.525609
$345$	−6.74866	−0.363335
$346$	−18.4698	−0.992943
$347$	17.1944	0.923045	0.461523	−	0.887128i	$-0.347303\pi$
$347$	17.1944	0.923045	0.461523	+	0.887128i	$0.347303\pi$
$348$	−9.52000	−0.510326
$349$	−25.2943	−1.35397	−0.676987	−	0.735995i	$-0.736715\pi$
$349$	−25.2943	−1.35397	−0.676987	+	0.735995i	$0.736715\pi$
$350$	−4.89737	−0.261775
$351$	2.31311	0.123465
$352$	0	0
$353$	6.60477	0.351536	0.175768	−	0.984432i	$-0.443759\pi$
$353$	6.60477	0.351536	0.175768	+	0.984432i	$0.443759\pi$
$354$	22.1757	1.17863
$355$	1.54992	0.0822613
$356$	−1.97282	−0.104559
$357$	−2.66163	−0.140868
$358$	3.17234	0.167664
$359$	36.4260	1.92249	0.961246	−	0.275692i	$-0.0889070\pi$
$359$	36.4260	1.92249	0.961246	+	0.275692i	$0.0889070\pi$
$360$	−3.71209	−0.195644
$361$	46.3300	2.43842
$362$	22.5990	1.18777
$363$	0	0
$364$	−2.91372	−0.152720
$365$	−26.8351	−1.40461
$366$	−3.28209	−0.171557
$367$	9.80019	0.511566	0.255783	−	0.966734i	$-0.417667\pi$
$367$	9.80019	0.511566	0.255783	+	0.966734i	$0.417667\pi$
$368$	11.9865	0.624840
$369$	−0.299894	−0.0156119
$370$	56.1449	2.91883
$371$	5.19340	0.269628
$372$	11.6464	0.603835
$373$	11.7043	0.606027	0.303013	−	0.952986i	$-0.402007\pi$
$373$	11.7043	0.606027	0.303013	+	0.952986i	$0.402007\pi$
$374$	0	0
$375$	−6.35260	−0.328047
$376$	−0.611994	−0.0315612
$377$	−17.4816	−0.900348
$378$	−1.80545	−0.0928624
$379$	22.0823	1.13429	0.567146	−	0.823617i	$-0.308047\pi$
$379$	22.0823	1.13429	0.567146	+	0.823617i	$0.308047\pi$
$380$	28.2753	1.45049
$381$	−8.33542	−0.427037
$382$	−35.4011	−1.81128
$383$	−21.7965	−1.11375	−0.556874	−	0.830597i	$-0.687999\pi$
$383$	−21.7965	−1.11375	−0.556874	+	0.830597i	$0.687999\pi$
$384$	9.96061	0.508300
$385$	0	0
$386$	−1.10590	−0.0562887
$387$	−7.29328	−0.370738
$388$	−0.672483	−0.0341401
$389$	−18.6044	−0.943280	−0.471640	−	0.881791i	$-0.656338\pi$
$389$	−18.6044	−0.943280	−0.471640	+	0.881791i	$0.656338\pi$
$390$	11.5979	0.587284
$391$	−6.46793	−0.327097
$392$	−1.33666	−0.0675113
$393$	7.97862	0.402468
$394$	−24.5096	−1.23478
$395$	−28.6601	−1.44205
$396$	0	0
$397$	−17.4492	−0.875750	−0.437875	−	0.899036i	$-0.644269\pi$
$397$	−17.4492	−0.875750	−0.437875	+	0.899036i	$0.644269\pi$
$398$	7.53440	0.377665
$399$	−8.08270	−0.404641
$400$	−13.3798	−0.668992
$401$	−37.4603	−1.87068	−0.935339	−	0.353754i	$-0.884905\pi$
$401$	−37.4603	−1.87068	−0.935339	+	0.353754i	$0.884905\pi$
$402$	−2.56857	−0.128109
$403$	21.3862	1.06532
$404$	−6.69836	−0.333256
$405$	2.77715	0.137998
$406$	13.6449	0.677186
$407$	0	0
$408$	−3.55768	−0.176131
$409$	1.93760	0.0958083	0.0479041	−	0.998852i	$-0.484746\pi$
$409$	1.93760	0.0958083	0.0479041	+	0.998852i	$0.484746\pi$
$410$	−1.50367	−0.0742611
$411$	−10.3316	−0.509622
$412$	23.3799	1.15185
$413$	−12.2826	−0.604389
$414$	−4.38737	−0.215627
$415$	−23.6356	−1.16023
$416$	−14.4158	−0.706793
$417$	−5.53964	−0.271277
$418$	0	0
$419$	−17.2226	−0.841378	−0.420689	−	0.907205i	$-0.638212\pi$
$419$	−17.2226	−0.841378	−0.420689	+	0.907205i	$0.638212\pi$
$420$	−3.49825	−0.170697
$421$	7.23823	0.352770	0.176385	−	0.984321i	$-0.443560\pi$
$421$	7.23823	0.352770	0.176385	+	0.984321i	$0.443560\pi$
$422$	19.2516	0.937153
$423$	0.457855	0.0222616
$424$	6.94179	0.337123
$425$	7.21978	0.350211
$426$	1.00762	0.0488194
$427$	1.81788	0.0879732
$428$	−11.8751	−0.574004
$429$	0	0
$430$	−36.5685	−1.76349
$431$	−32.4557	−1.56334	−0.781668	−	0.623695i	$-0.785631\pi$
$431$	−32.4557	−1.56334	−0.781668	+	0.623695i	$0.785631\pi$
$432$	−4.93258	−0.237319
$433$	22.7744	1.09447	0.547235	−	0.836979i	$-0.315680\pi$
$433$	22.7744	1.09447	0.547235	+	0.836979i	$0.315680\pi$
$434$	−16.6926	−0.801271
$435$	−20.9886	−1.00633
$436$	1.40074	0.0670833
$437$	−19.6415	−0.939581
$438$	−17.4458	−0.833591
$439$	30.4359	1.45263	0.726314	−	0.687363i	$-0.241232\pi$
$439$	30.4359	1.45263	0.726314	+	0.687363i	$0.241232\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	11.1155	0.528711
$443$	−19.9801	−0.949285	−0.474643	−	0.880179i	$-0.657423\pi$
$443$	−19.9801	−0.949285	−0.474643	+	0.880179i	$0.657423\pi$
$444$	14.1051	0.669400
$445$	−4.34945	−0.206184
$446$	6.57764	0.311460
$447$	21.9883	1.04001
$448$	1.38682	0.0655209
$449$	11.8269	0.558148	0.279074	−	0.960270i	$-0.409973\pi$
$449$	11.8269	0.558148	0.279074	+	0.960270i	$0.409973\pi$
$450$	4.89737	0.230864
$451$	0	0
$452$	−11.3681	−0.534708
$453$	−14.1658	−0.665569
$454$	37.7844	1.77331
$455$	−6.42384	−0.301154
$456$	−10.8038	−0.505934
$457$	−1.96299	−0.0918248	−0.0459124	−	0.998945i	$-0.514620\pi$
$457$	−1.96299	−0.0918248	−0.0459124	+	0.998945i	$0.514620\pi$
$458$	−29.7988	−1.39241
$459$	2.66163	0.124234
$460$	−8.50098	−0.396360
$461$	−15.5498	−0.724226	−0.362113	−	0.932134i	$-0.617945\pi$
$461$	−15.5498	−0.724226	−0.362113	+	0.932134i	$0.617945\pi$
$462$	0	0
$463$	−3.73913	−0.173772	−0.0868860	−	0.996218i	$-0.527692\pi$
$463$	−3.73913	−0.173772	−0.0868860	+	0.996218i	$0.527692\pi$
$464$	37.2786	1.73061
$465$	25.6766	1.19072
$466$	13.1560	0.609441
$467$	10.1969	0.471857	0.235929	−	0.971770i	$-0.424187\pi$
$467$	10.1969	0.471857	0.235929	+	0.971770i	$0.424187\pi$
$468$	2.91372	0.134687
$469$	1.42267	0.0656930
$470$	2.29568	0.105892
$471$	−1.37897	−0.0635397
$472$	−16.4177	−0.755684
$473$	0	0
$474$	−18.6322	−0.855807
$475$	21.9247	1.00597
$476$	−3.35273	−0.153672
$477$	−5.19340	−0.237790
$478$	−21.5980	−0.987867
$479$	22.6431	1.03459	0.517296	−	0.855807i	$-0.326939\pi$
$479$	22.6431	1.03459	0.517296	+	0.855807i	$0.326939\pi$
$480$	−17.3078	−0.789989
$481$	25.9013	1.18100
$482$	−7.92777	−0.361100
$483$	2.43007	0.110572
$484$	0	0
$485$	−1.48261	−0.0673220
$486$	1.80545	0.0818970
$487$	−23.1079	−1.04712	−0.523559	−	0.851989i	$-0.675396\pi$
$487$	−23.1079	−1.04712	−0.523559	+	0.851989i	$0.675396\pi$
$488$	2.42987	0.109995
$489$	−17.0408	−0.770612
$490$	5.01400	0.226510
$491$	−32.7793	−1.47931	−0.739653	−	0.672988i	$-0.765011\pi$
$491$	−32.7793	−1.47931	−0.739653	+	0.672988i	$0.765011\pi$
$492$	−0.377764	−0.0170309
$493$	−20.1156	−0.905960
$494$	33.7550	1.51871
$495$	0	0
$496$	−45.6050	−2.04772
$497$	−0.558099	−0.0250342
$498$	−15.3658	−0.688556
$499$	17.7759	0.795757	0.397878	−	0.917438i	$-0.369747\pi$
$499$	17.7759	0.795757	0.397878	+	0.917438i	$0.369747\pi$
$500$	−8.00209	−0.357864
$501$	−7.96033	−0.355641
$502$	−24.4460	−1.09108
$503$	−15.0014	−0.668879	−0.334439	−	0.942417i	$-0.608547\pi$
$503$	−15.0014	−0.668879	−0.334439	+	0.942417i	$0.608547\pi$
$504$	1.33666	0.0595394
$505$	−14.7678	−0.657158
$506$	0	0
$507$	−7.64953	−0.339727
$508$	−10.4998	−0.465852
$509$	−24.3906	−1.08109	−0.540547	−	0.841314i	$-0.681783\pi$
$509$	−24.3906	−1.08109	−0.540547	+	0.841314i	$0.681783\pi$
$510$	13.3454	0.590945
$511$	9.66283	0.427459
$512$	17.5546	0.775811
$513$	8.08270	0.356860
$514$	0.219396	0.00967715
$515$	51.5454	2.27136
$516$	−9.18702	−0.404436
$517$	0	0
$518$	−20.2168	−0.888273
$519$	−10.2300	−0.449048
$520$	−8.58647	−0.376542
$521$	8.07185	0.353634	0.176817	−	0.984244i	$-0.443420\pi$
$521$	8.07185	0.353634	0.176817	+	0.984244i	$0.443420\pi$
$522$	−13.6449	−0.597222
$523$	−0.370242	−0.0161895	−0.00809477	−	0.999967i	$-0.502577\pi$
$523$	−0.370242	−0.0161895	−0.00809477	+	0.999967i	$0.502577\pi$
$524$	10.0503	0.439050
$525$	−2.71254	−0.118385
$526$	10.6311	0.463540
$527$	24.6085	1.07196
$528$	0	0
$529$	−17.0948	−0.743251
$530$	−26.0398	−1.13109
$531$	12.2826	0.533021
$532$	−10.1814	−0.441420
$533$	−0.693689	−0.0300470
$534$	−2.82762	−0.122363
$535$	−26.1809	−1.13190
$536$	1.90163	0.0821377
$537$	1.75709	0.0758241
$538$	−3.99285	−0.172144
$539$	0	0
$540$	3.49825	0.150541
$541$	−2.96946	−0.127667	−0.0638336	−	0.997961i	$-0.520333\pi$
$541$	−2.96946	−0.127667	−0.0638336	+	0.997961i	$0.520333\pi$
$542$	−13.7111	−0.588943
$543$	12.5171	0.537159
$544$	−16.5878	−0.711198
$545$	3.08819	0.132284
$546$	−4.17621	−0.178725
$547$	16.6650	0.712545	0.356273	−	0.934382i	$-0.384047\pi$
$547$	16.6650	0.712545	0.356273	+	0.934382i	$0.384047\pi$
$548$	−13.0143	−0.555943
$549$	−1.81788	−0.0775851
$550$	0	0
$551$	−61.0860	−2.60235
$552$	3.24816	0.138251
$553$	10.3200	0.438850
$554$	−43.5995	−1.85237
$555$	31.0974	1.32001
$556$	−6.97804	−0.295935
$557$	−30.1565	−1.27777	−0.638885	−	0.769302i	$-0.720604\pi$
$557$	−30.1565	−1.27777	−0.638885	+	0.769302i	$0.720604\pi$
$558$	16.6926	0.706654
$559$	−16.8702	−0.713531
$560$	13.6985	0.578867
$561$	0	0
$562$	49.2829	2.07887
$563$	−4.22354	−0.178001	−0.0890004	−	0.996032i	$-0.528367\pi$
$563$	−4.22354	−0.178001	−0.0890004	+	0.996032i	$0.528367\pi$
$564$	0.576739	0.0242851
$565$	−25.0630	−1.05441
$566$	46.2350	1.94340
$567$	−1.00000	−0.0419961
$568$	−0.745986	−0.0313009
$569$	25.2216	1.05735	0.528673	−	0.848826i	$-0.322690\pi$
$569$	25.2216	1.05735	0.528673	+	0.848826i	$0.322690\pi$
$570$	40.5267	1.69748
$571$	−42.9041	−1.79548	−0.897740	−	0.440525i	$-0.854792\pi$
$571$	−42.9041	−1.79548	−0.897740	+	0.440525i	$0.854792\pi$
$572$	0	0
$573$	−19.6079	−0.819131
$574$	0.541445	0.0225995
$575$	−6.59167	−0.274892
$576$	−1.38682	−0.0577840
$577$	−28.8359	−1.20045	−0.600227	−	0.799830i	$-0.704923\pi$
$577$	−28.8359	−1.20045	−0.600227	+	0.799830i	$0.704923\pi$
$578$	−17.9024	−0.744642
$579$	−0.612533	−0.0254560
$580$	−26.4384	−1.09780
$581$	8.51075	0.353086
$582$	−0.963862	−0.0399534
$583$	0	0
$584$	12.9159	0.534463
$585$	6.42384	0.265593
$586$	−21.1226	−0.872566
$587$	−37.7758	−1.55918	−0.779588	−	0.626293i	$-0.784571\pi$
$587$	−37.7758	−1.55918	−0.779588	+	0.626293i	$0.784571\pi$
$588$	1.25966	0.0519473
$589$	74.7299	3.07919
$590$	61.5852	2.53542
$591$	−13.5754	−0.558415
$592$	−55.2331	−2.27007
$593$	−10.8394	−0.445119	−0.222559	−	0.974919i	$-0.571441\pi$
$593$	−10.8394	−0.445119	−0.222559	+	0.974919i	$0.571441\pi$
$594$	0	0
$595$	−7.39173	−0.303031
$596$	27.6977	1.13454
$597$	4.17314	0.170795
$598$	−10.1485	−0.415002
$599$	43.4225	1.77420	0.887098	−	0.461582i	$-0.152718\pi$
$599$	43.4225	1.77420	0.887098	+	0.461582i	$0.152718\pi$
$600$	−3.62574	−0.148020
$601$	0.476391	0.0194324	0.00971619	−	0.999953i	$-0.496907\pi$
$601$	0.476391	0.0194324	0.00971619	+	0.999953i	$0.496907\pi$
$602$	13.1677	0.536674
$603$	−1.42267	−0.0579358
$604$	−17.8441	−0.726065
$605$	0	0
$606$	−9.60069	−0.390001
$607$	−4.90638	−0.199144	−0.0995720	−	0.995030i	$-0.531747\pi$
$607$	−4.90638	−0.199144	−0.0995720	+	0.995030i	$0.531747\pi$
$608$	−50.3732	−2.04290
$609$	7.55762	0.306250
$610$	−9.11484	−0.369049
$611$	1.05907	0.0428453
$612$	3.35273	0.135526
$613$	−6.14615	−0.248241	−0.124120	−	0.992267i	$-0.539611\pi$
$613$	−6.14615	−0.248241	−0.124120	+	0.992267i	$0.539611\pi$
$614$	50.6676	2.04478
$615$	−0.832851	−0.0335838
$616$	0	0
$617$	−11.2456	−0.452730	−0.226365	−	0.974043i	$-0.572684\pi$
$617$	−11.2456	−0.452730	−0.226365	+	0.974043i	$0.572684\pi$
$618$	33.5102	1.34798
$619$	−33.3779	−1.34157	−0.670786	−	0.741651i	$-0.734043\pi$
$619$	−33.3779	−1.34157	−0.670786	+	0.741651i	$0.734043\pi$
$620$	32.3436	1.29895
$621$	−2.43007	−0.0975153
$622$	51.8412	2.07864
$623$	1.56616	0.0627468
$624$	−11.4096	−0.456749
$625$	−31.2048	−1.24819
$626$	−53.1674	−2.12500
$627$	0	0
$628$	−1.73703	−0.0693151
$629$	29.8039	1.18836
$630$	−5.01400	−0.199763
$631$	37.0130	1.47346	0.736731	−	0.676186i	$-0.236368\pi$
$631$	37.0130	1.47346	0.736731	+	0.676186i	$0.236368\pi$
$632$	13.7943	0.548706
$633$	10.6630	0.423817
$634$	−0.0607581	−0.00241301
$635$	−23.1487	−0.918628
$636$	−6.54190	−0.259403
$637$	2.31311	0.0916487
$638$	0	0
$639$	0.558099	0.0220781
$640$	27.6621	1.09344
$641$	−18.0178	−0.711662	−0.355831	−	0.934550i	$-0.615802\pi$
$641$	−18.0178	−0.711662	−0.355831	+	0.934550i	$0.615802\pi$
$642$	−17.0204	−0.671744
$643$	6.89603	0.271953	0.135976	−	0.990712i	$-0.456583\pi$
$643$	6.89603	0.271953	0.135976	+	0.990712i	$0.456583\pi$
$644$	3.06105	0.120622
$645$	−20.2545	−0.797520
$646$	38.8409	1.52818
$647$	37.6477	1.48008	0.740041	−	0.672561i	$-0.234806\pi$
$647$	37.6477	1.48008	0.740041	+	0.672561i	$0.234806\pi$
$648$	−1.33666	−0.0525088
$649$	0	0
$650$	11.3281	0.444326
$651$	−9.24567	−0.362366
$652$	−21.4656	−0.840656
$653$	−6.97518	−0.272960	−0.136480	−	0.990643i	$-0.543579\pi$
$653$	−6.97518	−0.272960	−0.136480	+	0.990643i	$0.543579\pi$
$654$	2.00767	0.0785060
$655$	22.1578	0.865777
$656$	1.47925	0.0577551
$657$	−9.66283	−0.376983
$658$	−0.826634	−0.0322256
$659$	−0.567182	−0.0220943	−0.0110471	−	0.999939i	$-0.503516\pi$
$659$	−0.567182	−0.0220943	−0.0110471	+	0.999939i	$0.503516\pi$
$660$	0	0
$661$	0.107429	0.00417852	0.00208926	−	0.999998i	$-0.499335\pi$
$661$	0.107429	0.00417852	0.00208926	+	0.999998i	$0.499335\pi$
$662$	29.7133	1.15484
$663$	6.15663	0.239104
$664$	11.3759	0.441472
$665$	−22.4468	−0.870451
$666$	20.2168	0.783383
$667$	18.3655	0.711116
$668$	−10.0273	−0.387967
$669$	3.64321	0.140855
$670$	−7.13329	−0.275583
$671$	0	0
$672$	6.23222	0.240413
$673$	20.1725	0.777591	0.388795	−	0.921324i	$-0.372891\pi$
$673$	20.1725	0.777591	0.388795	+	0.921324i	$0.372891\pi$
$674$	23.8721	0.919520
$675$	2.71254	0.104406
$676$	−9.63577	−0.370607
$677$	10.0671	0.386910	0.193455	−	0.981109i	$-0.438031\pi$
$677$	10.0671	0.386910	0.193455	+	0.981109i	$0.438031\pi$
$678$	−16.2937	−0.625756
$679$	0.533862	0.0204877
$680$	−9.88019	−0.378888
$681$	20.9279	0.801961
$682$	0	0
$683$	−32.4580	−1.24197	−0.620985	−	0.783822i	$-0.713267\pi$
$683$	−32.4580	−1.24197	−0.620985	+	0.783822i	$0.713267\pi$
$684$	10.1814	0.389296
$685$	−28.6925	−1.09628
$686$	−1.80545	−0.0689325
$687$	−16.5049	−0.629702
$688$	35.9747	1.37152
$689$	−12.0129	−0.457655
$690$	−12.1844	−0.463851
$691$	47.1070	1.79204	0.896018	−	0.444018i	$-0.146447\pi$
$691$	47.1070	1.79204	0.896018	+	0.444018i	$0.146447\pi$
$692$	−12.8863	−0.489864
$693$	0	0
$694$	31.0437	1.17840
$695$	−15.3844	−0.583564
$696$	10.1019	0.382913
$697$	−0.798207	−0.0302342
$698$	−45.6677	−1.72855
$699$	7.28683	0.275613
$700$	−3.41687	−0.129146
$701$	20.4498	0.772379	0.386190	−	0.922419i	$-0.373791\pi$
$701$	20.4498	0.772379	0.386190	+	0.922419i	$0.373791\pi$
$702$	4.17621	0.157621
$703$	90.5070	3.41353
$704$	0	0
$705$	1.27153	0.0478886
$706$	11.9246	0.448788
$707$	5.31761	0.199989
$708$	15.4719	0.581470
$709$	−9.94643	−0.373546	−0.186773	−	0.982403i	$-0.559803\pi$
$709$	−9.94643	−0.373546	−0.186773	+	0.982403i	$0.559803\pi$
$710$	2.79831	0.105019
$711$	−10.3200	−0.387030
$712$	2.09341	0.0784540
$713$	−22.4676	−0.841418
$714$	−4.80544	−0.179839
$715$	0	0
$716$	2.21333	0.0827160
$717$	−11.9626	−0.446753
$718$	65.7654	2.45434
$719$	6.83696	0.254975	0.127488	−	0.991840i	$-0.459309\pi$
$719$	6.83696	0.254975	0.127488	+	0.991840i	$0.459309\pi$
$720$	−13.6985	−0.510513
$721$	−18.5606	−0.691232
$722$	83.6466	3.11300
$723$	−4.39102	−0.163304
$724$	15.7672	0.585983
$725$	−20.5004	−0.761365
$726$	0	0
$727$	49.3919	1.83184	0.915922	−	0.401357i	$-0.131461\pi$
$727$	49.3919	1.83184	0.915922	+	0.401357i	$0.131461\pi$
$728$	3.09183	0.114591
$729$	1.00000	0.0370370
$730$	−48.4495	−1.79320
$731$	−19.4120	−0.717978
$732$	−2.28990	−0.0846371
$733$	39.7282	1.46739	0.733697	−	0.679477i	$-0.237793\pi$
$733$	39.7282	1.46739	0.733697	+	0.679477i	$0.237793\pi$
$734$	17.6938	0.653089
$735$	2.77715	0.102437
$736$	15.1447	0.558242
$737$	0	0
$738$	−0.541445	−0.0199309
$739$	31.1915	1.14740	0.573698	−	0.819067i	$-0.305508\pi$
$739$	31.1915	1.14740	0.573698	+	0.819067i	$0.305508\pi$
$740$	39.1721	1.43999
$741$	18.6962	0.686821
$742$	9.37644	0.344220
$743$	30.9041	1.13376	0.566880	−	0.823800i	$-0.308150\pi$
$743$	30.9041	1.13376	0.566880	+	0.823800i	$0.308150\pi$
$744$	−12.3583	−0.453076
$745$	61.0649	2.23724
$746$	21.1316	0.773682
$747$	−8.51075	−0.311392
$748$	0	0
$749$	9.42725	0.344464
$750$	−11.4693	−0.418800
$751$	−17.1976	−0.627549	−0.313775	−	0.949497i	$-0.601594\pi$
$751$	−17.1976	−0.627549	−0.313775	+	0.949497i	$0.601594\pi$
$752$	−2.25840	−0.0823555
$753$	−13.5401	−0.493428
$754$	−31.5622	−1.14943
$755$	−39.3406	−1.43175
$756$	−1.25966	−0.0458132
$757$	5.67500	0.206261	0.103131	−	0.994668i	$-0.467114\pi$
$757$	5.67500	0.206261	0.103131	+	0.994668i	$0.467114\pi$
$758$	39.8686	1.44809
$759$	0	0
$760$	−30.0037	−1.08835
$761$	8.73463	0.316630	0.158315	−	0.987389i	$-0.449394\pi$
$761$	8.73463	0.316630	0.158315	+	0.987389i	$0.449394\pi$
$762$	−15.0492	−0.545175
$763$	−1.11200	−0.0402572
$764$	−24.6992	−0.893585
$765$	7.39173	0.267248
$766$	−39.3525	−1.42186
$767$	28.4111	1.02587
$768$	20.7570	0.749005
$769$	7.76277	0.279933	0.139966	−	0.990156i	$-0.455301\pi$
$769$	7.76277	0.279933	0.139966	+	0.990156i	$0.455301\pi$
$770$	0	0
$771$	0.121519	0.00437639
$772$	−0.771580	−0.0277698
$773$	32.9829	1.18631	0.593156	−	0.805087i	$-0.297882\pi$
$773$	32.9829	1.18631	0.593156	+	0.805087i	$0.297882\pi$
$774$	−13.1677	−0.473302
$775$	25.0793	0.900874
$776$	0.713590	0.0256164
$777$	−11.1976	−0.401712
$778$	−33.5893	−1.20424
$779$	−2.42396	−0.0868472
$780$	8.09183	0.289734
$781$	0	0
$782$	−11.6775	−0.417588
$783$	−7.55762	−0.270087
$784$	−4.93258	−0.176164
$785$	−3.82961	−0.136685
$786$	14.4050	0.513810
$787$	16.4069	0.584845	0.292422	−	0.956289i	$-0.405539\pi$
$787$	16.4069	0.584845	0.292422	+	0.956289i	$0.405539\pi$
$788$	−17.1003	−0.609172
$789$	5.88836	0.209631
$790$	−51.7444	−1.84098
$791$	9.02473	0.320882
$792$	0	0
$793$	−4.20495	−0.149322
$794$	−31.5037	−1.11802
$795$	−14.4228	−0.511526
$796$	5.25672	0.186319
$797$	−5.86473	−0.207740	−0.103870	−	0.994591i	$-0.533123\pi$
$797$	−5.86473	−0.207740	−0.103870	+	0.994591i	$0.533123\pi$
$798$	−14.5929	−0.516584
$799$	1.21864	0.0431123
$800$	−16.9052	−0.597688
$801$	−1.56616	−0.0553375
$802$	−67.6327	−2.38819
$803$	0	0
$804$	−1.79208	−0.0632018
$805$	6.74866	0.237859
$806$	38.6118	1.36004
$807$	−2.21155	−0.0778503
$808$	7.10782	0.250052
$809$	−17.9373	−0.630643	−0.315322	−	0.948985i	$-0.602112\pi$
$809$	−17.9373	−0.630643	−0.315322	+	0.948985i	$0.602112\pi$
$810$	5.01400	0.176174
$811$	−27.2249	−0.955996	−0.477998	−	0.878361i	$-0.658637\pi$
$811$	−27.2249	−0.955996	−0.477998	+	0.878361i	$0.658637\pi$
$812$	9.52000	0.334087
$813$	−7.59429	−0.266344
$814$	0	0
$815$	−47.3248	−1.65772
$816$	−13.1287	−0.459596
$817$	−58.9494	−2.06238
$818$	3.49825	0.122313
$819$	−2.31311	−0.0808266
$820$	−1.04911	−0.0366363
$821$	4.06642	0.141919	0.0709595	−	0.997479i	$-0.477394\pi$
$821$	4.06642	0.141919	0.0709595	+	0.997479i	$0.477394\pi$
$822$	−18.6533	−0.650607
$823$	−32.5150	−1.13340	−0.566700	−	0.823924i	$-0.691780\pi$
$823$	−32.5150	−1.13340	−0.566700	+	0.823924i	$0.691780\pi$
$824$	−24.8091	−0.864266
$825$	0	0
$826$	−22.1757	−0.771592
$827$	18.6162	0.647349	0.323674	−	0.946169i	$-0.395082\pi$
$827$	18.6162	0.647349	0.323674	+	0.946169i	$0.395082\pi$
$828$	−3.06105	−0.106379
$829$	48.9304	1.69942	0.849712	−	0.527247i	$-0.176776\pi$
$829$	48.9304	1.69942	0.849712	+	0.527247i	$0.176776\pi$
$830$	−42.6730	−1.48120
$831$	−24.1488	−0.837713
$832$	−3.20786	−0.111212
$833$	2.66163	0.0922199
$834$	−10.0016	−0.346326
$835$	−22.1070	−0.765045
$836$	0	0
$837$	9.24567	0.319577
$838$	−31.0945	−1.07414
$839$	−2.90781	−0.100389	−0.0501944	−	0.998739i	$-0.515984\pi$
$839$	−2.90781	−0.100389	−0.0501944	+	0.998739i	$0.515984\pi$
$840$	3.71209	0.128079
$841$	28.1176	0.969574
$842$	13.0683	0.450363
$843$	27.2967	0.940148
$844$	13.4317	0.462340
$845$	−21.2439	−0.730811
$846$	0.826634	0.0284203
$847$	0	0
$848$	25.6169	0.879687
$849$	25.6085	0.878883
$850$	13.0350	0.447096
$851$	−27.2110	−0.932780
$852$	0.703012	0.0240848
$853$	26.5311	0.908406	0.454203	−	0.890898i	$-0.349924\pi$
$853$	26.5311	0.908406	0.454203	+	0.890898i	$0.349924\pi$
$854$	3.28209	0.112311
$855$	22.4468	0.767666
$856$	12.6010	0.430693
$857$	32.5818	1.11297	0.556487	−	0.830856i	$-0.312149\pi$
$857$	32.5818	1.11297	0.556487	+	0.830856i	$0.312149\pi$
$858$	0	0
$859$	30.4695	1.03961	0.519803	−	0.854286i	$-0.326005\pi$
$859$	30.4695	1.03961	0.519803	+	0.854286i	$0.326005\pi$
$860$	−25.5137	−0.870010
$861$	0.299894	0.0102204
$862$	−58.5972	−1.99583
$863$	21.0577	0.716814	0.358407	−	0.933566i	$-0.383320\pi$
$863$	21.0577	0.716814	0.358407	+	0.933566i	$0.383320\pi$
$864$	−6.23222	−0.212024
$865$	−28.4103	−0.965978
$866$	41.1182	1.39725
$867$	−9.91574	−0.336756
$868$	−11.6464	−0.395303
$869$	0	0
$870$	−37.8939	−1.28473
$871$	−3.29080	−0.111504
$872$	−1.48636	−0.0503347
$873$	−0.533862	−0.0180685
$874$	−35.4618	−1.19951
$875$	6.35260	0.214757
$876$	−12.1718	−0.411248
$877$	9.82296	0.331698	0.165849	−	0.986151i	$-0.446964\pi$
$877$	9.82296	0.331698	0.165849	+	0.986151i	$0.446964\pi$
$878$	54.9506	1.85449
$879$	−11.6993	−0.394609
$880$	0	0
$881$	16.4077	0.552789	0.276394	−	0.961044i	$-0.410860\pi$
$881$	16.4077	0.552789	0.276394	+	0.961044i	$0.410860\pi$
$882$	1.80545	0.0607927
$883$	27.7229	0.932949	0.466475	−	0.884535i	$-0.345524\pi$
$883$	27.7229	0.932949	0.466475	+	0.884535i	$0.345524\pi$
$884$	7.75524	0.260837
$885$	34.1107	1.14662
$886$	−36.0732	−1.21190
$887$	−33.1490	−1.11304	−0.556518	−	0.830836i	$-0.687863\pi$
$887$	−33.1490	−1.11304	−0.556518	+	0.830836i	$0.687863\pi$
$888$	−14.9674	−0.502272
$889$	8.33542	0.279561
$890$	−7.85272	−0.263224
$891$	0	0
$892$	4.58919	0.153657
$893$	3.70070	0.123839
$894$	39.6989	1.32773
$895$	4.87970	0.163110
$896$	−9.96061	−0.332761
$897$	−5.62101	−0.187680
$898$	21.3530	0.712558
$899$	−69.8752	−2.33047
$900$	3.41687	0.113896
$901$	−13.8229	−0.460508
$902$	0	0
$903$	7.29328	0.242705
$904$	12.0630	0.401208
$905$	34.7617	1.15552
$906$	−25.5757	−0.849697
$907$	2.69837	0.0895980	0.0447990	−	0.998996i	$-0.485735\pi$
$907$	2.69837	0.0895980	0.0447990	+	0.998996i	$0.485735\pi$
$908$	26.3620	0.874854
$909$	−5.31761	−0.176374
$910$	−11.5979	−0.384468
$911$	30.2768	1.00312	0.501558	−	0.865124i	$-0.332761\pi$
$911$	30.2768	1.00312	0.501558	+	0.865124i	$0.332761\pi$
$912$	−39.8685	−1.32018
$913$	0	0
$914$	−3.54408	−0.117228
$915$	−5.04851	−0.166899
$916$	−20.7905	−0.686938
$917$	−7.97862	−0.263477
$918$	4.80544	0.158603
$919$	38.2913	1.26311	0.631557	−	0.775329i	$-0.282416\pi$
$919$	38.2913	1.26311	0.631557	+	0.775329i	$0.282416\pi$
$920$	9.02063	0.297401
$921$	28.0637	0.924729
$922$	−28.0744	−0.924581
$923$	1.29094	0.0424919
$924$	0	0
$925$	30.3740	0.998692
$926$	−6.75081	−0.221845
$927$	18.5606	0.609609
$928$	47.1008	1.54616
$929$	−1.97036	−0.0646453	−0.0323227	−	0.999477i	$-0.510290\pi$
$929$	−1.97036	−0.0646453	−0.0323227	+	0.999477i	$0.510290\pi$
$930$	46.3578	1.52013
$931$	8.08270	0.264900
$932$	9.17890	0.300665
$933$	28.7137	0.940044
$934$	18.4101	0.602395
$935$	0	0
$936$	−3.09183	−0.101060
$937$	37.2007	1.21529	0.607647	−	0.794207i	$-0.292114\pi$
$937$	37.2007	1.21529	0.607647	+	0.794207i	$0.292114\pi$
$938$	2.56857	0.0838667
$939$	−29.4483	−0.961008
$940$	1.60169	0.0522413
$941$	−30.1836	−0.983957	−0.491979	−	0.870607i	$-0.663726\pi$
$941$	−30.1836	−0.983957	−0.491979	+	0.870607i	$0.663726\pi$
$942$	−2.48967	−0.0811178
$943$	0.728764	0.0237318
$944$	−60.5851	−1.97188
$945$	−2.77715	−0.0903406
$946$	0	0
$947$	54.8775	1.78328	0.891639	−	0.452746i	$-0.149556\pi$
$947$	54.8775	1.78328	0.891639	+	0.452746i	$0.149556\pi$
$948$	−12.9996	−0.422208
$949$	−22.3512	−0.725550
$950$	39.5839	1.28427
$951$	−0.0336526	−0.00109126
$952$	3.55768	0.115305
$953$	−25.5001	−0.826028	−0.413014	−	0.910725i	$-0.635524\pi$
$953$	−25.5001	−0.826028	−0.413014	+	0.910725i	$0.635524\pi$
$954$	−9.37644	−0.303573
$955$	−54.4540	−1.76209
$956$	−15.0688	−0.487360
$957$	0	0
$958$	40.8811	1.32081
$959$	10.3316	0.333626
$960$	−3.85139	−0.124303
$961$	54.4823	1.75749
$962$	46.7636	1.50772
$963$	−9.42725	−0.303789
$964$	−5.53117	−0.178147
$965$	−1.70109	−0.0547601
$966$	4.38737	0.141161
$967$	−52.7171	−1.69527	−0.847633	−	0.530583i	$-0.821973\pi$
$967$	−52.7171	−1.69527	−0.847633	+	0.530583i	$0.821973\pi$
$968$	0	0
$969$	21.5131	0.691101
$970$	−2.67679	−0.0859465
$971$	33.0543	1.06076	0.530382	−	0.847759i	$-0.322049\pi$
$971$	33.0543	1.06076	0.530382	+	0.847759i	$0.322049\pi$
$972$	1.25966	0.0404035
$973$	5.53964	0.177593
$974$	−41.7202	−1.33680
$975$	6.27441	0.200942
$976$	8.96682	0.287021
$977$	−31.6423	−1.01233	−0.506164	−	0.862437i	$-0.668937\pi$
$977$	−31.6423	−1.01233	−0.506164	+	0.862437i	$0.668937\pi$
$978$	−30.7664	−0.983800
$979$	0	0
$980$	3.49825	0.111747
$981$	1.11200	0.0355035
$982$	−59.1814	−1.88855
$983$	14.0077	0.446778	0.223389	−	0.974729i	$-0.428288\pi$
$983$	14.0077	0.446778	0.223389	+	0.974729i	$0.428288\pi$
$984$	0.400856	0.0127788
$985$	−37.7007	−1.20125
$986$	−36.3177	−1.15659
$987$	−0.457855	−0.0145737
$988$	23.5507	0.749249
$989$	17.7232	0.563564
$990$	0	0
$991$	21.2818	0.676038	0.338019	−	0.941139i	$-0.390243\pi$
$991$	21.2818	0.676038	0.338019	+	0.941139i	$0.390243\pi$
$992$	−57.6210	−1.82947
$993$	16.4575	0.522264
$994$	−1.00762	−0.0319598
$995$	11.5894	0.367409
$996$	−10.7206	−0.339696
$997$	−21.9094	−0.693876	−0.346938	−	0.937888i	$-0.612779\pi$
$997$	−21.9094	−0.693876	−0.346938	+	0.937888i	$0.612779\pi$
$998$	32.0935	1.01590
$999$	11.1976	0.354277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bq.1.8		10
3.2	odd	2		7623.2.a.cx.1.3		10
11.3	even	5		231.2.j.g.64.4	✓	20
11.4	even	5		231.2.j.g.148.4	yes	20
11.10	odd	2		2541.2.a.br.1.3		10
33.14	odd	10		693.2.m.j.64.2		20
33.26	odd	10		693.2.m.j.379.2		20
33.32	even	2		7623.2.a.cy.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.64.4	✓	20	11.3	even	5
231.2.j.g.148.4	yes	20	11.4	even	5
693.2.m.j.64.2		20	33.14	odd	10
693.2.m.j.379.2		20	33.26	odd	10
2541.2.a.bq.1.8		10	1.1	even	1	trivial
2541.2.a.br.1.3		10	11.10	odd	2
7623.2.a.cx.1.3		10	3.2	odd	2
7623.2.a.cy.1.8		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)

\(f(q)\)	\(=\)	\(q+1.80545 q^{2} +1.00000 q^{3} +1.25966 q^{4} +2.77715 q^{5} +1.80545 q^{6} -1.00000 q^{7} -1.33666 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.80545 q^{2} +1.00000 q^{3} +1.25966 q^{4} +2.77715 q^{5} +1.80545 q^{6} -1.00000 q^{7} -1.33666 q^{8} +1.00000 q^{9} +5.01400 q^{10} +1.25966 q^{12} +2.31311 q^{13} -1.80545 q^{14} +2.77715 q^{15} -4.93258 q^{16} +2.66163 q^{17} +1.80545 q^{18} +8.08270 q^{19} +3.49825 q^{20} -1.00000 q^{21} -2.43007 q^{23} -1.33666 q^{24} +2.71254 q^{25} +4.17621 q^{26} +1.00000 q^{27} -1.25966 q^{28} -7.55762 q^{29} +5.01400 q^{30} +9.24567 q^{31} -6.23222 q^{32} +4.80544 q^{34} -2.77715 q^{35} +1.25966 q^{36} +11.1976 q^{37} +14.5929 q^{38} +2.31311 q^{39} -3.71209 q^{40} -0.299894 q^{41} -1.80545 q^{42} -7.29328 q^{43} +2.77715 q^{45} -4.38737 q^{46} +0.457855 q^{47} -4.93258 q^{48} +1.00000 q^{49} +4.89737 q^{50} +2.66163 q^{51} +2.91372 q^{52} -5.19340 q^{53} +1.80545 q^{54} +1.33666 q^{56} +8.08270 q^{57} -13.6449 q^{58} +12.2826 q^{59} +3.49825 q^{60} -1.81788 q^{61} +16.6926 q^{62} -1.00000 q^{63} -1.38682 q^{64} +6.42384 q^{65} -1.42267 q^{67} +3.35273 q^{68} -2.43007 q^{69} -5.01400 q^{70} +0.558099 q^{71} -1.33666 q^{72} -9.66283 q^{73} +20.2168 q^{74} +2.71254 q^{75} +10.1814 q^{76} +4.17621 q^{78} -10.3200 q^{79} -13.6985 q^{80} +1.00000 q^{81} -0.541445 q^{82} -8.51075 q^{83} -1.25966 q^{84} +7.39173 q^{85} -13.1677 q^{86} -7.55762 q^{87} -1.56616 q^{89} +5.01400 q^{90} -2.31311 q^{91} -3.06105 q^{92} +9.24567 q^{93} +0.826634 q^{94} +22.4468 q^{95} -6.23222 q^{96} -0.533862 q^{97} +1.80545 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} - 10 q^{7} + 3 q^{8} + 10 q^{9}+O(q^{10}) \) 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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