LMFDB - Embedded newform 3549.2.a.bf.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 11x^{7} + 8x^{6} + 37x^{5} - 18x^{4} - 41x^{3} + 12x^{2} + 6x - 1 $ x^9 - x^8 - 11x^7 + 8x^6 + 37x^5 - 18x^4 - 41x^3 + 12x^2 + 6*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.90042$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.90042 q^{2} -1.00000 q^{3} +1.61158 q^{4} -1.76582 q^{5} -1.90042 q^{6} -1.00000 q^{7} -0.738153 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.90042 q^{2} -1.00000 q^{3} +1.61158 q^{4} -1.76582 q^{5} -1.90042 q^{6} -1.00000 q^{7} -0.738153 q^{8} +1.00000 q^{9} -3.35579 q^{10} +3.13241 q^{11} -1.61158 q^{12} -1.90042 q^{14} +1.76582 q^{15} -4.62597 q^{16} -0.934195 q^{17} +1.90042 q^{18} -2.13289 q^{19} -2.84577 q^{20} +1.00000 q^{21} +5.95289 q^{22} +5.87145 q^{23} +0.738153 q^{24} -1.88188 q^{25} -1.00000 q^{27} -1.61158 q^{28} -2.37261 q^{29} +3.35579 q^{30} +6.06765 q^{31} -7.31496 q^{32} -3.13241 q^{33} -1.77536 q^{34} +1.76582 q^{35} +1.61158 q^{36} +2.02644 q^{37} -4.05338 q^{38} +1.30344 q^{40} +6.16399 q^{41} +1.90042 q^{42} +5.68247 q^{43} +5.04815 q^{44} -1.76582 q^{45} +11.1582 q^{46} -5.26708 q^{47} +4.62597 q^{48} +1.00000 q^{49} -3.57636 q^{50} +0.934195 q^{51} +10.5891 q^{53} -1.90042 q^{54} -5.53127 q^{55} +0.738153 q^{56} +2.13289 q^{57} -4.50895 q^{58} -4.83882 q^{59} +2.84577 q^{60} +12.6018 q^{61} +11.5311 q^{62} -1.00000 q^{63} -4.64954 q^{64} -5.95289 q^{66} +6.65056 q^{67} -1.50553 q^{68} -5.87145 q^{69} +3.35579 q^{70} +7.17531 q^{71} -0.738153 q^{72} -4.85580 q^{73} +3.85108 q^{74} +1.88188 q^{75} -3.43733 q^{76} -3.13241 q^{77} +12.0565 q^{79} +8.16862 q^{80} +1.00000 q^{81} +11.7142 q^{82} -11.7189 q^{83} +1.61158 q^{84} +1.64962 q^{85} +10.7991 q^{86} +2.37261 q^{87} -2.31220 q^{88} -8.30211 q^{89} -3.35579 q^{90} +9.46233 q^{92} -6.06765 q^{93} -10.0096 q^{94} +3.76630 q^{95} +7.31496 q^{96} +18.2921 q^{97} +1.90042 q^{98} +3.13241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9	$ 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9} + q^{10} + q^{11} - 5 q^{12} - q^{14} + 9 q^{15} + 5 q^{16} + 11 q^{17} + q^{18} - 7 q^{19} - 23 q^{20} + 9 q^{21} - 3 q^{22} + 22 q^{23} - 6 q^{24} - 8 q^{25} - 9 q^{27} - 5 q^{28} + 11 q^{29} - q^{30} - 7 q^{31} + 18 q^{32} - q^{33} + 6 q^{34} + 9 q^{35} + 5 q^{36} + q^{37} - 6 q^{38} - 14 q^{40} - 16 q^{41} + q^{42} + 32 q^{43} - 18 q^{44} - 9 q^{45} + 9 q^{46} + 12 q^{47} - 5 q^{48} + 9 q^{49} - 10 q^{50} - 11 q^{51} + 13 q^{53} - q^{54} + 9 q^{55} - 6 q^{56} + 7 q^{57} - 4 q^{58} - 29 q^{59} + 23 q^{60} - 12 q^{61} + 30 q^{62} - 9 q^{63} + 6 q^{64} + 3 q^{66} + 20 q^{67} + 34 q^{68} - 22 q^{69} - q^{70} + 2 q^{71} + 6 q^{72} - q^{73} + 43 q^{74} + 8 q^{75} - 13 q^{76} - q^{77} + 3 q^{79} + 39 q^{80} + 9 q^{81} - 19 q^{82} - 24 q^{83} + 5 q^{84} - 15 q^{85} + 28 q^{86} - 11 q^{87} - 19 q^{88} - 11 q^{89} + q^{90} + 73 q^{92} + 7 q^{93} + 15 q^{94} + 39 q^{95} - 18 q^{96} - 20 q^{97} + q^{98} + q^{99}+O(q^{100}) $ 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9 + q^10 + q^11 - 5 * q^12 - q^14 + 9 * q^15 + 5 * q^16 + 11 * q^17 + q^18 - 7 * q^19 - 23 * q^20 + 9 * q^21 - 3 * q^22 + 22 * q^23 - 6 * q^24 - 8 * q^25 - 9 * q^27 - 5 * q^28 + 11 * q^29 - q^30 - 7 * q^31 + 18 * q^32 - q^33 + 6 * q^34 + 9 * q^35 + 5 * q^36 + q^37 - 6 * q^38 - 14 * q^40 - 16 * q^41 + q^42 + 32 * q^43 - 18 * q^44 - 9 * q^45 + 9 * q^46 + 12 * q^47 - 5 * q^48 + 9 * q^49 - 10 * q^50 - 11 * q^51 + 13 * q^53 - q^54 + 9 * q^55 - 6 * q^56 + 7 * q^57 - 4 * q^58 - 29 * q^59 + 23 * q^60 - 12 * q^61 + 30 * q^62 - 9 * q^63 + 6 * q^64 + 3 * q^66 + 20 * q^67 + 34 * q^68 - 22 * q^69 - q^70 + 2 * q^71 + 6 * q^72 - q^73 + 43 * q^74 + 8 * q^75 - 13 * q^76 - q^77 + 3 * q^79 + 39 * q^80 + 9 * q^81 - 19 * q^82 - 24 * q^83 + 5 * q^84 - 15 * q^85 + 28 * q^86 - 11 * q^87 - 19 * q^88 - 11 * q^89 + q^90 + 73 * q^92 + 7 * q^93 + 15 * q^94 + 39 * q^95 - 18 * q^96 - 20 * q^97 + q^98 + q^99

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 $

$2$	1.90042	1.34380	0.671899	−	0.740643i	$-0.265479\pi$
$2$	1.90042	1.34380	0.671899	+	0.740643i	$0.265479\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.61158	0.805792
$5$	−1.76582	−0.789698	−0.394849	−	0.918746i	$-0.629203\pi$
$5$	−1.76582	−0.789698	−0.394849	+	0.918746i	$0.629203\pi$
$6$	−1.90042	−0.775842
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.738153	−0.260976
$9$	1.00000	0.333333
$10$	−3.35579	−1.06119
$11$	3.13241	0.944458	0.472229	−	0.881476i	$-0.343450\pi$
$11$	3.13241	0.944458	0.472229	+	0.881476i	$0.343450\pi$
$12$	−1.61158	−0.465224
$13$	0	0
$13$	0	0
$14$	−1.90042	−0.507908
$15$	1.76582	0.455932
$16$	−4.62597	−1.15649
$17$	−0.934195	−0.226576	−0.113288	−	0.993562i	$-0.536138\pi$
$17$	−0.934195	−0.226576	−0.113288	+	0.993562i	$0.536138\pi$
$18$	1.90042	0.447933
$19$	−2.13289	−0.489319	−0.244659	−	0.969609i	$-0.578676\pi$
$19$	−2.13289	−0.489319	−0.244659	+	0.969609i	$0.578676\pi$
$20$	−2.84577	−0.636332
$21$	1.00000	0.218218
$22$	5.95289	1.26916
$23$	5.87145	1.22428	0.612141	−	0.790749i	$-0.290309\pi$
$23$	5.87145	1.22428	0.612141	+	0.790749i	$0.290309\pi$
$24$	0.738153	0.150675
$25$	−1.88188	−0.376377
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.61158	−0.304561
$29$	−2.37261	−0.440583	−0.220292	−	0.975434i	$-0.570701\pi$
$29$	−2.37261	−0.440583	−0.220292	+	0.975434i	$0.570701\pi$
$30$	3.35579	0.612681
$31$	6.06765	1.08978	0.544891	−	0.838507i	$-0.316571\pi$
$31$	6.06765	1.08978	0.544891	+	0.838507i	$0.316571\pi$
$32$	−7.31496	−1.29311
$33$	−3.13241	−0.545283
$34$	−1.77536	−0.304472
$35$	1.76582	0.298478
$36$	1.61158	0.268597
$37$	2.02644	0.333145	0.166572	−	0.986029i	$-0.446730\pi$
$37$	2.02644	0.333145	0.166572	+	0.986029i	$0.446730\pi$
$38$	−4.05338	−0.657546
$39$	0	0
$40$	1.30344	0.206093
$41$	6.16399	0.962654	0.481327	−	0.876541i	$-0.340155\pi$
$41$	6.16399	0.962654	0.481327	+	0.876541i	$0.340155\pi$
$42$	1.90042	0.293241
$43$	5.68247	0.866569	0.433284	−	0.901257i	$-0.357355\pi$
$43$	5.68247	0.866569	0.433284	+	0.901257i	$0.357355\pi$
$44$	5.04815	0.761037
$45$	−1.76582	−0.263233
$46$	11.1582	1.64519
$47$	−5.26708	−0.768283	−0.384141	−	0.923274i	$-0.625502\pi$
$47$	−5.26708	−0.768283	−0.384141	+	0.923274i	$0.625502\pi$
$48$	4.62597	0.667701
$49$	1.00000	0.142857
$50$	−3.57636	−0.505774
$51$	0.934195	0.130813
$52$	0	0
$53$	10.5891	1.45452	0.727260	−	0.686362i	$-0.240794\pi$
$53$	10.5891	1.45452	0.727260	+	0.686362i	$0.240794\pi$
$54$	−1.90042	−0.258614
$55$	−5.53127	−0.745837
$56$	0.738153	0.0986398
$57$	2.13289	0.282508
$58$	−4.50895	−0.592055
$59$	−4.83882	−0.629960	−0.314980	−	0.949098i	$-0.601998\pi$
$59$	−4.83882	−0.629960	−0.314980	+	0.949098i	$0.601998\pi$
$60$	2.84577	0.367387
$61$	12.6018	1.61350	0.806749	−	0.590894i	$-0.201225\pi$
$61$	12.6018	1.61350	0.806749	+	0.590894i	$0.201225\pi$
$62$	11.5311	1.46445
$63$	−1.00000	−0.125988
$64$	−4.64954	−0.581192
$65$	0	0
$66$	−5.95289	−0.732750
$67$	6.65056	0.812495	0.406248	−	0.913763i	$-0.366837\pi$
$67$	6.65056	0.812495	0.406248	+	0.913763i	$0.366837\pi$
$68$	−1.50553	−0.182573
$69$	−5.87145	−0.706839
$70$	3.35579	0.401094
$71$	7.17531	0.851552	0.425776	−	0.904829i	$-0.360001\pi$
$71$	7.17531	0.851552	0.425776	+	0.904829i	$0.360001\pi$
$72$	−0.738153	−0.0869921
$73$	−4.85580	−0.568328	−0.284164	−	0.958776i	$-0.591716\pi$
$73$	−4.85580	−0.568328	−0.284164	+	0.958776i	$0.591716\pi$
$74$	3.85108	0.447679
$75$	1.88188	0.217301
$76$	−3.43733	−0.394289
$77$	−3.13241	−0.356972
$78$	0	0
$79$	12.0565	1.35646	0.678231	−	0.734848i	$-0.262747\pi$
$79$	12.0565	1.35646	0.678231	+	0.734848i	$0.262747\pi$
$80$	8.16862	0.913279
$81$	1.00000	0.111111
$82$	11.7142	1.29361
$83$	−11.7189	−1.28632	−0.643160	−	0.765732i	$-0.722377\pi$
$83$	−11.7189	−1.28632	−0.643160	+	0.765732i	$0.722377\pi$
$84$	1.61158	0.175838
$85$	1.64962	0.178926
$86$	10.7991	1.16449
$87$	2.37261	0.254371
$88$	−2.31220	−0.246481
$89$	−8.30211	−0.880021	−0.440011	−	0.897993i	$-0.645025\pi$
$89$	−8.30211	−0.880021	−0.440011	+	0.897993i	$0.645025\pi$
$90$	−3.35579	−0.353731
$91$	0	0
$92$	9.46233	0.986516
$93$	−6.06765	−0.629186
$94$	−10.0096	−1.03242
$95$	3.76630	0.386414
$96$	7.31496	0.746580
$97$	18.2921	1.85728	0.928642	−	0.370977i	$-0.120977\pi$
$97$	18.2921	1.85728	0.928642	+	0.370977i	$0.120977\pi$
$98$	1.90042	0.191971
$99$	3.13241	0.314819
$100$	−3.03281	−0.303281
$101$	12.5967	1.25342	0.626710	−	0.779252i	$-0.284401\pi$
$101$	12.5967	1.25342	0.626710	+	0.779252i	$0.284401\pi$
$102$	1.77536	0.175787
$103$	−4.92445	−0.485220	−0.242610	−	0.970124i	$-0.578004\pi$
$103$	−4.92445	−0.485220	−0.242610	+	0.970124i	$0.578004\pi$
$104$	0	0
$105$	−1.76582	−0.172326
$106$	20.1236	1.95458
$107$	−3.69523	−0.357231	−0.178616	−	0.983919i	$-0.557162\pi$
$107$	−3.69523	−0.357231	−0.178616	+	0.983919i	$0.557162\pi$
$108$	−1.61158	−0.155075
$109$	14.6664	1.40479	0.702393	−	0.711789i	$-0.252115\pi$
$109$	14.6664	1.40479	0.702393	+	0.711789i	$0.252115\pi$
$110$	−10.5117	−1.00225
$111$	−2.02644	−0.192341
$112$	4.62597	0.437113
$113$	14.4311	1.35756	0.678780	−	0.734342i	$-0.262509\pi$
$113$	14.4311	1.35756	0.678780	+	0.734342i	$0.262509\pi$
$114$	4.05338	0.379634
$115$	−10.3679	−0.966813
$116$	−3.82366	−0.355018
$117$	0	0
$118$	−9.19577	−0.846539
$119$	0.934195	0.0856375
$120$	−1.30344	−0.118988
$121$	−1.18799	−0.107999
$122$	23.9487	2.16821
$123$	−6.16399	−0.555789
$124$	9.77853	0.878138
$125$	12.1522	1.08692
$126$	−1.90042	−0.169303
$127$	−4.80045	−0.425971	−0.212986	−	0.977055i	$-0.568319\pi$
$127$	−4.80045	−0.425971	−0.212986	+	0.977055i	$0.568319\pi$
$128$	5.79386	0.512110
$129$	−5.68247	−0.500314
$130$	0	0
$131$	−7.33712	−0.641047	−0.320524	−	0.947241i	$-0.603859\pi$
$131$	−7.33712	−0.641047	−0.320524	+	0.947241i	$0.603859\pi$
$132$	−5.04815	−0.439385
$133$	2.13289	0.184945
$134$	12.6388	1.09183
$135$	1.76582	0.151977
$136$	0.689579	0.0591309
$137$	−0.951272	−0.0812726	−0.0406363	−	0.999174i	$-0.512939\pi$
$137$	−0.951272	−0.0812726	−0.0406363	+	0.999174i	$0.512939\pi$
$138$	−11.1582	−0.949849
$139$	−9.89366	−0.839169	−0.419584	−	0.907716i	$-0.637824\pi$
$139$	−9.89366	−0.839169	−0.419584	+	0.907716i	$0.637824\pi$
$140$	2.84577	0.240511
$141$	5.26708	0.443568
$142$	13.6361	1.14431
$143$	0	0
$144$	−4.62597	−0.385497
$145$	4.18960	0.347928
$146$	−9.22804	−0.763718
$147$	−1.00000	−0.0824786
$148$	3.26578	0.268445
$149$	19.7207	1.61558	0.807792	−	0.589467i	$-0.200662\pi$
$149$	19.7207	1.61558	0.807792	+	0.589467i	$0.200662\pi$
$150$	3.57636	0.292009
$151$	−12.6508	−1.02951	−0.514753	−	0.857338i	$-0.672116\pi$
$151$	−12.6508	−1.02951	−0.514753	+	0.857338i	$0.672116\pi$
$152$	1.57440	0.127701
$153$	−0.934195	−0.0755252
$154$	−5.95289	−0.479698
$155$	−10.7144	−0.860599
$156$	0	0
$157$	−15.9485	−1.27283	−0.636413	−	0.771348i	$-0.719583\pi$
$157$	−15.9485	−1.27283	−0.636413	+	0.771348i	$0.719583\pi$
$158$	22.9124	1.82281
$159$	−10.5891	−0.839767
$160$	12.9169	1.02117
$161$	−5.87145	−0.462735
$162$	1.90042	0.149311
$163$	9.44073	0.739455	0.369727	−	0.929140i	$-0.379451\pi$
$163$	9.44073	0.739455	0.369727	+	0.929140i	$0.379451\pi$
$164$	9.93379	0.775699
$165$	5.53127	0.430609
$166$	−22.2708	−1.72855
$167$	−4.14823	−0.320999	−0.160500	−	0.987036i	$-0.551311\pi$
$167$	−4.14823	−0.320999	−0.160500	+	0.987036i	$0.551311\pi$
$168$	−0.738153	−0.0569497
$169$	0	0
$170$	3.13496	0.240441
$171$	−2.13289	−0.163106
$172$	9.15778	0.698274
$173$	3.23618	0.246042	0.123021	−	0.992404i	$-0.460742\pi$
$173$	3.23618	0.246042	0.123021	+	0.992404i	$0.460742\pi$
$174$	4.50895	0.341823
$175$	1.88188	0.142257
$176$	−14.4904	−1.09226
$177$	4.83882	0.363708
$178$	−15.7775	−1.18257
$179$	19.8786	1.48579	0.742896	−	0.669406i	$-0.233452\pi$
$179$	19.8786	1.48579	0.742896	+	0.669406i	$0.233452\pi$
$180$	−2.84577	−0.212111
$181$	8.91114	0.662360	0.331180	−	0.943568i	$-0.392553\pi$
$181$	8.91114	0.662360	0.331180	+	0.943568i	$0.392553\pi$
$182$	0	0
$183$	−12.6018	−0.931553
$184$	−4.33403	−0.319509
$185$	−3.57833	−0.263084
$186$	−11.5311	−0.845499
$187$	−2.92629	−0.213991
$188$	−8.48834	−0.619076
$189$	1.00000	0.0727393
$190$	7.15754	0.519262
$191$	17.4590	1.26329	0.631646	−	0.775257i	$-0.282380\pi$
$191$	17.4590	1.26329	0.631646	+	0.775257i	$0.282380\pi$
$192$	4.64954	0.335551
$193$	−19.3101	−1.38997	−0.694984	−	0.719025i	$-0.744589\pi$
$193$	−19.3101	−1.38997	−0.694984	+	0.719025i	$0.744589\pi$
$194$	34.7627	2.49581
$195$	0	0
$196$	1.61158	0.115113
$197$	−25.9848	−1.85134	−0.925669	−	0.378334i	$-0.876497\pi$
$197$	−25.9848	−1.85134	−0.925669	+	0.378334i	$0.876497\pi$
$198$	5.95289	0.423054
$199$	20.1033	1.42508	0.712542	−	0.701629i	$-0.247544\pi$
$199$	20.1033	1.42508	0.712542	+	0.701629i	$0.247544\pi$
$200$	1.38912	0.0982254
$201$	−6.65056	−0.469094
$202$	23.9390	1.68434
$203$	2.37261	0.166525
$204$	1.50553	0.105408
$205$	−10.8845	−0.760206
$206$	−9.35850	−0.652038
$207$	5.87145	0.408094
$208$	0	0
$209$	−6.68110	−0.462141
$210$	−3.35579	−0.231572
$211$	−7.25390	−0.499379	−0.249689	−	0.968326i	$-0.580329\pi$
$211$	−7.25390	−0.499379	−0.249689	+	0.968326i	$0.580329\pi$
$212$	17.0652	1.17204
$213$	−7.17531	−0.491644
$214$	−7.02247	−0.480046
$215$	−10.0342	−0.684328
$216$	0.738153	0.0502249
$217$	−6.06765	−0.411899
$218$	27.8723	1.88775
$219$	4.85580	0.328124
$220$	−8.91411	−0.600989
$221$	0	0
$222$	−3.85108	−0.258468
$223$	8.41784	0.563701	0.281850	−	0.959458i	$-0.409052\pi$
$223$	8.41784	0.563701	0.281850	+	0.959458i	$0.409052\pi$
$224$	7.31496	0.488751
$225$	−1.88188	−0.125459
$226$	27.4250	1.82429
$227$	10.4603	0.694275	0.347138	−	0.937814i	$-0.387154\pi$
$227$	10.4603	0.694275	0.347138	+	0.937814i	$0.387154\pi$
$228$	3.43733	0.227643
$229$	−10.6287	−0.702362	−0.351181	−	0.936308i	$-0.614220\pi$
$229$	−10.6287	−0.702362	−0.351181	+	0.936308i	$0.614220\pi$
$230$	−19.7034	−1.29920
$231$	3.13241	0.206098
$232$	1.75135	0.114982
$233$	22.9731	1.50502	0.752510	−	0.658580i	$-0.228843\pi$
$233$	22.9731	1.50502	0.752510	+	0.658580i	$0.228843\pi$
$234$	0	0
$235$	9.30071	0.606711
$236$	−7.79816	−0.507617
$237$	−12.0565	−0.783154
$238$	1.77536	0.115079
$239$	−15.7349	−1.01781	−0.508904	−	0.860823i	$-0.669949\pi$
$239$	−15.7349	−1.01781	−0.508904	+	0.860823i	$0.669949\pi$
$240$	−8.16862	−0.527282
$241$	−9.04536	−0.582663	−0.291331	−	0.956622i	$-0.594098\pi$
$241$	−9.04536	−0.582663	−0.291331	+	0.956622i	$0.594098\pi$
$242$	−2.25767	−0.145128
$243$	−1.00000	−0.0641500
$244$	20.3089	1.30014
$245$	−1.76582	−0.112814
$246$	−11.7142	−0.746867
$247$	0	0
$248$	−4.47885	−0.284407
$249$	11.7189	0.742657
$250$	23.0942	1.46060
$251$	17.0593	1.07677	0.538386	−	0.842698i	$-0.319034\pi$
$251$	17.0593	1.07677	0.538386	+	0.842698i	$0.319034\pi$
$252$	−1.61158	−0.101520
$253$	18.3918	1.15628
$254$	−9.12286	−0.572419
$255$	−1.64962	−0.103303
$256$	20.3098	1.26936
$257$	−7.93028	−0.494677	−0.247339	−	0.968929i	$-0.579556\pi$
$257$	−7.93028	−0.494677	−0.247339	+	0.968929i	$0.579556\pi$
$258$	−10.7991	−0.672320
$259$	−2.02644	−0.125917
$260$	0	0
$261$	−2.37261	−0.146861
$262$	−13.9436	−0.861438
$263$	18.4617	1.13840	0.569199	−	0.822200i	$-0.307253\pi$
$263$	18.4617	1.13840	0.569199	+	0.822200i	$0.307253\pi$
$264$	2.31220	0.142306
$265$	−18.6984	−1.14863
$266$	4.05338	0.248529
$267$	8.30211	0.508081
$268$	10.7179	0.654702
$269$	−10.2133	−0.622716	−0.311358	−	0.950293i	$-0.600784\pi$
$269$	−10.2133	−0.622716	−0.311358	+	0.950293i	$0.600784\pi$
$270$	3.35579	0.204227
$271$	−24.1804	−1.46886	−0.734428	−	0.678687i	$-0.762549\pi$
$271$	−24.1804	−1.46886	−0.734428	+	0.678687i	$0.762549\pi$
$272$	4.32155	0.262033
$273$	0	0
$274$	−1.80781	−0.109214
$275$	−5.89484	−0.355472
$276$	−9.46233	−0.569565
$277$	−18.3142	−1.10039	−0.550195	−	0.835036i	$-0.685447\pi$
$277$	−18.3142	−1.10039	−0.550195	+	0.835036i	$0.685447\pi$
$278$	−18.8021	−1.12767
$279$	6.06765	0.363261
$280$	−1.30344	−0.0778957
$281$	−9.11661	−0.543852	−0.271926	−	0.962318i	$-0.587661\pi$
$281$	−9.11661	−0.543852	−0.271926	+	0.962318i	$0.587661\pi$
$282$	10.0096	0.596066
$283$	−9.22502	−0.548371	−0.274185	−	0.961677i	$-0.588408\pi$
$283$	−9.22502	−0.548371	−0.274185	+	0.961677i	$0.588408\pi$
$284$	11.5636	0.686174
$285$	−3.76630	−0.223096
$286$	0	0
$287$	−6.16399	−0.363849
$288$	−7.31496	−0.431038
$289$	−16.1273	−0.948664
$290$	7.96199	0.467544
$291$	−18.2921	−1.07230
$292$	−7.82553	−0.457954
$293$	18.0748	1.05594	0.527970	−	0.849263i	$-0.322953\pi$
$293$	18.0748	1.05594	0.527970	+	0.849263i	$0.322953\pi$
$294$	−1.90042	−0.110835
$295$	8.54448	0.497479
$296$	−1.49582	−0.0869429
$297$	−3.13241	−0.181761
$298$	37.4776	2.17102
$299$	0	0
$300$	3.03281	0.175100
$301$	−5.68247	−0.327532
$302$	−24.0418	−1.38345
$303$	−12.5967	−0.723663
$304$	9.86668	0.565893
$305$	−22.2525	−1.27418
$306$	−1.77536	−0.101491
$307$	−15.5831	−0.889373	−0.444686	−	0.895686i	$-0.646685\pi$
$307$	−15.5831	−0.889373	−0.444686	+	0.895686i	$0.646685\pi$
$308$	−5.04815	−0.287645
$309$	4.92445	0.280142
$310$	−20.3618	−1.15647
$311$	−2.20637	−0.125112	−0.0625558	−	0.998041i	$-0.519925\pi$
$311$	−2.20637	−0.125112	−0.0625558	+	0.998041i	$0.519925\pi$
$312$	0	0
$313$	26.6495	1.50632	0.753160	−	0.657837i	$-0.228528\pi$
$313$	26.6495	1.50632	0.753160	+	0.657837i	$0.228528\pi$
$314$	−30.3087	−1.71042
$315$	1.76582	0.0994926
$316$	19.4301	1.09303
$317$	−22.8415	−1.28291	−0.641455	−	0.767161i	$-0.721669\pi$
$317$	−22.8415	−1.28291	−0.641455	+	0.767161i	$0.721669\pi$
$318$	−20.1236	−1.12848
$319$	−7.43200	−0.416112
$320$	8.21024	0.458966
$321$	3.69523	0.206247
$322$	−11.1582	−0.621822
$323$	1.99254	0.110868
$324$	1.61158	0.0895324
$325$	0	0
$326$	17.9413	0.993678
$327$	−14.6664	−0.811054
$328$	−4.54997	−0.251230
$329$	5.26708	0.290383
$330$	10.5117	0.578652
$331$	−3.66559	−0.201479	−0.100739	−	0.994913i	$-0.532121\pi$
$331$	−3.66559	−0.201479	−0.100739	+	0.994913i	$0.532121\pi$
$332$	−18.8860	−1.03651
$333$	2.02644	0.111048
$334$	−7.88336	−0.431358
$335$	−11.7437	−0.641626
$336$	−4.62597	−0.252367
$337$	−32.6505	−1.77859	−0.889293	−	0.457339i	$-0.848803\pi$
$337$	−32.6505	−1.77859	−0.889293	+	0.457339i	$0.848803\pi$
$338$	0	0
$339$	−14.4311	−0.783788
$340$	2.65850	0.144177
$341$	19.0064	1.02925
$342$	−4.05338	−0.219182
$343$	−1.00000	−0.0539949
$344$	−4.19453	−0.226154
$345$	10.3679	0.558190
$346$	6.15009	0.330631
$347$	21.9592	1.17883	0.589417	−	0.807829i	$-0.299358\pi$
$347$	21.9592	1.17883	0.589417	+	0.807829i	$0.299358\pi$
$348$	3.82366	0.204970
$349$	−35.8913	−1.92121	−0.960607	−	0.277909i	$-0.910359\pi$
$349$	−35.8913	−1.92121	−0.960607	+	0.277909i	$0.910359\pi$
$350$	3.57636	0.191165
$351$	0	0
$352$	−22.9135	−1.22129
$353$	5.10983	0.271969	0.135984	−	0.990711i	$-0.456580\pi$
$353$	5.10983	0.271969	0.135984	+	0.990711i	$0.456580\pi$
$354$	9.19577	0.488750
$355$	−12.6703	−0.672469
$356$	−13.3795	−0.709114
$357$	−0.934195	−0.0494428
$358$	37.7775	1.99660
$359$	2.15127	0.113540	0.0567698	−	0.998387i	$-0.481920\pi$
$359$	2.15127	0.113540	0.0567698	+	0.998387i	$0.481920\pi$
$360$	1.30344	0.0686975
$361$	−14.4508	−0.760567
$362$	16.9349	0.890077
$363$	1.18799	0.0623531
$364$	0	0
$365$	8.57446	0.448808
$366$	−23.9487	−1.25182
$367$	19.3500	1.01006	0.505031	−	0.863101i	$-0.331481\pi$
$367$	19.3500	1.01006	0.505031	+	0.863101i	$0.331481\pi$
$368$	−27.1611	−1.41587
$369$	6.16399	0.320885
$370$	−6.80031	−0.353532
$371$	−10.5891	−0.549757
$372$	−9.77853	−0.506993
$373$	−16.3147	−0.844741	−0.422371	−	0.906423i	$-0.638802\pi$
$373$	−16.3147	−0.844741	−0.422371	+	0.906423i	$0.638802\pi$
$374$	−5.56116	−0.287561
$375$	−12.1522	−0.627535
$376$	3.88791	0.200504
$377$	0	0
$378$	1.90042	0.0977469
$379$	8.99682	0.462135	0.231068	−	0.972938i	$-0.425778\pi$
$379$	8.99682	0.462135	0.231068	+	0.972938i	$0.425778\pi$
$380$	6.06971	0.311369
$381$	4.80045	0.245935
$382$	33.1794	1.69761
$383$	−35.9745	−1.83821	−0.919105	−	0.394012i	$-0.871087\pi$
$383$	−35.9745	−1.83821	−0.919105	+	0.394012i	$0.871087\pi$
$384$	−5.79386	−0.295667
$385$	5.53127	0.281900
$386$	−36.6972	−1.86784
$387$	5.68247	0.288856
$388$	29.4793	1.49658
$389$	21.7976	1.10518	0.552591	−	0.833453i	$-0.313639\pi$
$389$	21.7976	1.10518	0.552591	+	0.833453i	$0.313639\pi$
$390$	0	0
$391$	−5.48508	−0.277392
$392$	−0.738153	−0.0372823
$393$	7.33712	0.370109
$394$	−49.3819	−2.48782
$395$	−21.2896	−1.07120
$396$	5.04815	0.253679
$397$	25.9786	1.30383	0.651913	−	0.758293i	$-0.273967\pi$
$397$	25.9786	1.30383	0.651913	+	0.758293i	$0.273967\pi$
$398$	38.2046	1.91503
$399$	−2.13289	−0.106778
$400$	8.70553	0.435276
$401$	24.2479	1.21088	0.605442	−	0.795890i	$-0.292996\pi$
$401$	24.2479	1.21088	0.605442	+	0.795890i	$0.292996\pi$
$402$	−12.6388	−0.630368
$403$	0	0
$404$	20.3007	1.01000
$405$	−1.76582	−0.0877442
$406$	4.50895	0.223776
$407$	6.34765	0.314641
$408$	−0.689579	−0.0341392
$409$	21.5639	1.06627	0.533134	−	0.846031i	$-0.321014\pi$
$409$	21.5639	1.06627	0.533134	+	0.846031i	$0.321014\pi$
$410$	−20.6851	−1.02156
$411$	0.951272	0.0469228
$412$	−7.93616	−0.390987
$413$	4.83882	0.238103
$414$	11.1582	0.548396
$415$	20.6935	1.01580
$416$	0	0
$417$	9.89366	0.484494
$418$	−12.6969	−0.621024
$419$	0.199171	0.00973014	0.00486507	−	0.999988i	$-0.498451\pi$
$419$	0.199171	0.00973014	0.00486507	+	0.999988i	$0.498451\pi$
$420$	−2.84577	−0.138859
$421$	−20.8702	−1.01715	−0.508576	−	0.861017i	$-0.669828\pi$
$421$	−20.8702	−1.01715	−0.508576	+	0.861017i	$0.669828\pi$
$422$	−13.7854	−0.671064
$423$	−5.26708	−0.256094
$424$	−7.81634	−0.379595
$425$	1.75805	0.0852778
$426$	−13.6361	−0.660670
$427$	−12.6018	−0.609845
$428$	−5.95517	−0.287854
$429$	0	0
$430$	−19.0692	−0.919598
$431$	13.2296	0.637246	0.318623	−	0.947882i	$-0.396780\pi$
$431$	13.2296	0.637246	0.318623	+	0.947882i	$0.396780\pi$
$432$	4.62597	0.222567
$433$	−31.5518	−1.51628	−0.758142	−	0.652090i	$-0.773892\pi$
$433$	−31.5518	−1.51628	−0.758142	+	0.652090i	$0.773892\pi$
$434$	−11.5311	−0.553509
$435$	−4.18960	−0.200876
$436$	23.6361	1.13197
$437$	−12.5232	−0.599064
$438$	9.22804	0.440933
$439$	27.1399	1.29532	0.647658	−	0.761931i	$-0.275748\pi$
$439$	27.1399	1.29532	0.647658	+	0.761931i	$0.275748\pi$
$440$	4.08292	0.194646
$441$	1.00000	0.0476190
$442$	0	0
$443$	−0.825961	−0.0392426	−0.0196213	−	0.999807i	$-0.506246\pi$
$443$	−0.825961	−0.0392426	−0.0196213	+	0.999807i	$0.506246\pi$
$444$	−3.26578	−0.154987
$445$	14.6600	0.694951
$446$	15.9974	0.757499
$447$	−19.7207	−0.932758
$448$	4.64954	0.219670
$449$	−27.5595	−1.30061	−0.650306	−	0.759673i	$-0.725359\pi$
$449$	−27.5595	−1.30061	−0.650306	+	0.759673i	$0.725359\pi$
$450$	−3.57636	−0.168591
$451$	19.3082	0.909187
$452$	23.2569	1.09391
$453$	12.6508	0.594386
$454$	19.8789	0.932965
$455$	0	0
$456$	−1.57440	−0.0737280
$457$	0.0445936	0.00208600	0.00104300	−	0.999999i	$-0.499668\pi$
$457$	0.0445936	0.00208600	0.00104300	+	0.999999i	$0.499668\pi$
$458$	−20.1989	−0.943833
$459$	0.934195	0.0436045
$460$	−16.7088	−0.779050
$461$	−2.86714	−0.133536	−0.0667680	−	0.997769i	$-0.521269\pi$
$461$	−2.86714	−0.133536	−0.0667680	+	0.997769i	$0.521269\pi$
$462$	5.95289	0.276954
$463$	11.7612	0.546590	0.273295	−	0.961930i	$-0.411886\pi$
$463$	11.7612	0.546590	0.273295	+	0.961930i	$0.411886\pi$
$464$	10.9756	0.509531
$465$	10.7144	0.496867
$466$	43.6586	2.02244
$467$	39.3716	1.82190	0.910949	−	0.412518i	$-0.135351\pi$
$467$	39.3716	1.82190	0.910949	+	0.412518i	$0.135351\pi$
$468$	0	0
$469$	−6.65056	−0.307094
$470$	17.6752	0.815297
$471$	15.9485	0.734867
$472$	3.57179	0.164405
$473$	17.7999	0.818438
$474$	−22.9124	−1.05240
$475$	4.01385	0.184168
$476$	1.50553	0.0690060
$477$	10.5891	0.484840
$478$	−29.9029	−1.36773
$479$	−15.5574	−0.710835	−0.355417	−	0.934708i	$-0.615661\pi$
$479$	−15.5574	−0.710835	−0.355417	+	0.934708i	$0.615661\pi$
$480$	−12.9169	−0.589573
$481$	0	0
$482$	−17.1900	−0.782981
$483$	5.87145	0.267160
$484$	−1.91454	−0.0870245
$485$	−32.3006	−1.46669
$486$	−1.90042	−0.0862047
$487$	−23.7460	−1.07604	−0.538018	−	0.842933i	$-0.680827\pi$
$487$	−23.7460	−1.07604	−0.538018	+	0.842933i	$0.680827\pi$
$488$	−9.30207	−0.421085
$489$	−9.44073	−0.426924
$490$	−3.35579	−0.151599
$491$	−5.86527	−0.264696	−0.132348	−	0.991203i	$-0.542252\pi$
$491$	−5.86527	−0.264696	−0.132348	+	0.991203i	$0.542252\pi$
$492$	−9.93379	−0.447850
$493$	2.21648	0.0998254
$494$	0	0
$495$	−5.53127	−0.248612
$496$	−28.0687	−1.26032
$497$	−7.17531	−0.321856
$498$	22.2708	0.997981
$499$	−7.79729	−0.349054	−0.174527	−	0.984652i	$-0.555840\pi$
$499$	−7.79729	−0.349054	−0.174527	+	0.984652i	$0.555840\pi$
$500$	19.5842	0.875833
$501$	4.14823	0.185329
$502$	32.4197	1.44696
$503$	−34.3648	−1.53225	−0.766126	−	0.642690i	$-0.777818\pi$
$503$	−34.3648	−1.53225	−0.766126	+	0.642690i	$0.777818\pi$
$504$	0.738153	0.0328799
$505$	−22.2435	−0.989824
$506$	34.9521	1.55381
$507$	0	0
$508$	−7.73633	−0.343244
$509$	10.4900	0.464960	0.232480	−	0.972601i	$-0.425316\pi$
$509$	10.4900	0.464960	0.232480	+	0.972601i	$0.425316\pi$
$510$	−3.13496	−0.138819
$511$	4.85580	0.214808
$512$	27.0094	1.19366
$513$	2.13289	0.0941695
$514$	−15.0708	−0.664746
$515$	8.69568	0.383178
$516$	−9.15778	−0.403149
$517$	−16.4987	−0.725611
$518$	−3.85108	−0.169207
$519$	−3.23618	−0.142053
$520$	0	0
$521$	−2.34072	−0.102549	−0.0512743	−	0.998685i	$-0.516328\pi$
$521$	−2.34072	−0.102549	−0.0512743	+	0.998685i	$0.516328\pi$
$522$	−4.50895	−0.197352
$523$	32.9438	1.44053	0.720266	−	0.693698i	$-0.244020\pi$
$523$	32.9438	1.44053	0.720266	+	0.693698i	$0.244020\pi$
$524$	−11.8244	−0.516551
$525$	−1.88188	−0.0821321
$526$	35.0849	1.52978
$527$	−5.66837	−0.246918
$528$	14.4904	0.630615
$529$	11.4739	0.498866
$530$	−35.5347	−1.54353
$531$	−4.83882	−0.209987
$532$	3.43733	0.149027
$533$	0	0
$534$	15.7775	0.682758
$535$	6.52510	0.282105
$536$	−4.90913	−0.212042
$537$	−19.8786	−0.857823
$538$	−19.4095	−0.836805
$539$	3.13241	0.134923
$540$	2.84577	0.122462
$541$	−7.71023	−0.331489	−0.165744	−	0.986169i	$-0.553003\pi$
$541$	−7.71023	−0.331489	−0.165744	+	0.986169i	$0.553003\pi$
$542$	−45.9529	−1.97384
$543$	−8.91114	−0.382414
$544$	6.83360	0.292988
$545$	−25.8982	−1.10936
$546$	0	0
$547$	23.6877	1.01281	0.506407	−	0.862294i	$-0.330973\pi$
$547$	23.6877	1.01281	0.506407	+	0.862294i	$0.330973\pi$
$548$	−1.53305	−0.0654888
$549$	12.6018	0.537833
$550$	−11.2027	−0.477683
$551$	5.06053	0.215586
$552$	4.33403	0.184468
$553$	−12.0565	−0.512695
$554$	−34.8045	−1.47870
$555$	3.57833	0.151892
$556$	−15.9445	−0.676195
$557$	11.8899	0.503792	0.251896	−	0.967754i	$-0.418946\pi$
$557$	11.8899	0.503792	0.251896	+	0.967754i	$0.418946\pi$
$558$	11.5311	0.488149
$559$	0	0
$560$	−8.16862	−0.345187
$561$	2.92629	0.123548
$562$	−17.3254	−0.730826
$563$	45.2378	1.90655	0.953273	−	0.302109i	$-0.0976907\pi$
$563$	45.2378	1.90655	0.953273	+	0.302109i	$0.0976907\pi$
$564$	8.48834	0.357424
$565$	−25.4826	−1.07206
$566$	−17.5314	−0.736899
$567$	−1.00000	−0.0419961
$568$	−5.29647	−0.222235
$569$	−17.7145	−0.742629	−0.371314	−	0.928507i	$-0.621093\pi$
$569$	−17.7145	−0.742629	−0.371314	+	0.928507i	$0.621093\pi$
$570$	−7.15754	−0.299796
$571$	20.5380	0.859487	0.429743	−	0.902951i	$-0.358604\pi$
$571$	20.5380	0.859487	0.429743	+	0.902951i	$0.358604\pi$
$572$	0	0
$573$	−17.4590	−0.729361
$574$	−11.7142	−0.488940
$575$	−11.0494	−0.460791
$576$	−4.64954	−0.193731
$577$	11.9204	0.496253	0.248127	−	0.968728i	$-0.420185\pi$
$577$	11.9204	0.496253	0.248127	+	0.968728i	$0.420185\pi$
$578$	−30.6486	−1.27481
$579$	19.3101	0.802499
$580$	6.75190	0.280357
$581$	11.7189	0.486183
$582$	−34.7627	−1.44096
$583$	33.1693	1.37373
$584$	3.58432	0.148320
$585$	0	0
$586$	34.3496	1.41897
$587$	−18.9993	−0.784185	−0.392093	−	0.919926i	$-0.628249\pi$
$587$	−18.9993	−0.784185	−0.392093	+	0.919926i	$0.628249\pi$
$588$	−1.61158	−0.0664606
$589$	−12.9416	−0.533251
$590$	16.2381	0.668511
$591$	25.9848	1.06887
$592$	−9.37425	−0.385279
$593$	14.9494	0.613899	0.306949	−	0.951726i	$-0.400692\pi$
$593$	14.9494	0.613899	0.306949	+	0.951726i	$0.400692\pi$
$594$	−5.95289	−0.244250
$595$	−1.64962	−0.0676278
$596$	31.7816	1.30183
$597$	−20.1033	−0.822773
$598$	0	0
$599$	45.5130	1.85961	0.929806	−	0.368051i	$-0.119975\pi$
$599$	45.5130	1.85961	0.929806	+	0.368051i	$0.119975\pi$
$600$	−1.38912	−0.0567105
$601$	31.0256	1.26556	0.632781	−	0.774331i	$-0.281913\pi$
$601$	31.0256	1.26556	0.632781	+	0.774331i	$0.281913\pi$
$602$	−10.7991	−0.440137
$603$	6.65056	0.270832
$604$	−20.3878	−0.829568
$605$	2.09777	0.0852864
$606$	−23.9390	−0.972456
$607$	−1.55815	−0.0632435	−0.0316218	−	0.999500i	$-0.510067\pi$
$607$	−1.55815	−0.0632435	−0.0316218	+	0.999500i	$0.510067\pi$
$608$	15.6020	0.632745
$609$	−2.37261	−0.0961431
$610$	−42.2891	−1.71224
$611$	0	0
$612$	−1.50553	−0.0608576
$613$	17.4821	0.706096	0.353048	−	0.935605i	$-0.385145\pi$
$613$	17.4821	0.706096	0.353048	+	0.935605i	$0.385145\pi$
$614$	−29.6143	−1.19514
$615$	10.8845	0.438905
$616$	2.31220	0.0931612
$617$	31.7640	1.27877	0.639385	−	0.768887i	$-0.279189\pi$
$617$	31.7640	1.27877	0.639385	+	0.768887i	$0.279189\pi$
$618$	9.35850	0.376454
$619$	−1.58220	−0.0635941	−0.0317970	−	0.999494i	$-0.510123\pi$
$619$	−1.58220	−0.0635941	−0.0317970	+	0.999494i	$0.510123\pi$
$620$	−17.2671	−0.693464
$621$	−5.87145	−0.235613
$622$	−4.19301	−0.168125
$623$	8.30211	0.332617
$624$	0	0
$625$	−12.0491	−0.481964
$626$	50.6452	2.02419
$627$	6.68110	0.266817
$628$	−25.7023	−1.02563
$629$	−1.89309	−0.0754825
$630$	3.35579	0.133698
$631$	3.86214	0.153749	0.0768746	−	0.997041i	$-0.475506\pi$
$631$	3.86214	0.153749	0.0768746	+	0.997041i	$0.475506\pi$
$632$	−8.89954	−0.354005
$633$	7.25390	0.288317
$634$	−43.4085	−1.72397
$635$	8.47673	0.336389
$636$	−17.0652	−0.676678
$637$	0	0
$638$	−14.1239	−0.559171
$639$	7.17531	0.283851
$640$	−10.2309	−0.404412
$641$	−17.1008	−0.675442	−0.337721	−	0.941246i	$-0.609656\pi$
$641$	−17.1008	−0.675442	−0.337721	+	0.941246i	$0.609656\pi$
$642$	7.02247	0.277155
$643$	49.0673	1.93503	0.967513	−	0.252821i	$-0.0813583\pi$
$643$	49.0673	1.93503	0.967513	+	0.252821i	$0.0813583\pi$
$644$	−9.46233	−0.372868
$645$	10.0342	0.395097
$646$	3.78665	0.148984
$647$	−18.3702	−0.722209	−0.361104	−	0.932525i	$-0.617600\pi$
$647$	−18.3702	−0.722209	−0.361104	+	0.932525i	$0.617600\pi$
$648$	−0.738153	−0.0289974
$649$	−15.1572	−0.594971
$650$	0	0
$651$	6.06765	0.237810
$652$	15.2145	0.595847
$653$	18.7518	0.733814	0.366907	−	0.930258i	$-0.380417\pi$
$653$	18.7518	0.733814	0.366907	+	0.930258i	$0.380417\pi$
$654$	−27.8723	−1.08989
$655$	12.9560	0.506234
$656$	−28.5144	−1.11330
$657$	−4.85580	−0.189443
$658$	10.0096	0.390217
$659$	27.0220	1.05263	0.526315	−	0.850290i	$-0.323573\pi$
$659$	27.0220	1.05263	0.526315	+	0.850290i	$0.323573\pi$
$660$	8.91411	0.346981
$661$	−17.3755	−0.675830	−0.337915	−	0.941177i	$-0.609722\pi$
$661$	−17.3755	−0.675830	−0.337915	+	0.941177i	$0.609722\pi$
$662$	−6.96614	−0.270747
$663$	0	0
$664$	8.65036	0.335699
$665$	−3.76630	−0.146051
$666$	3.85108	0.149226
$667$	−13.9307	−0.539398
$668$	−6.68522	−0.258659
$669$	−8.41784	−0.325453
$670$	−22.3179	−0.862216
$671$	39.4741	1.52388
$672$	−7.31496	−0.282181
$673$	8.26424	0.318563	0.159281	−	0.987233i	$-0.449082\pi$
$673$	8.26424	0.318563	0.159281	+	0.987233i	$0.449082\pi$
$674$	−62.0495	−2.39006
$675$	1.88188	0.0724337
$676$	0	0
$677$	−33.9430	−1.30454	−0.652268	−	0.757988i	$-0.726182\pi$
$677$	−33.9430	−1.30454	−0.652268	+	0.757988i	$0.726182\pi$
$678$	−27.4250	−1.05325
$679$	−18.2921	−0.701988
$680$	−1.21767	−0.0466955
$681$	−10.4603	−0.400840
$682$	36.1201	1.38311
$683$	3.32745	0.127321	0.0636606	−	0.997972i	$-0.479722\pi$
$683$	3.32745	0.127321	0.0636606	+	0.997972i	$0.479722\pi$
$684$	−3.43733	−0.131430
$685$	1.67977	0.0641809
$686$	−1.90042	−0.0725582
$687$	10.6287	0.405509
$688$	−26.2869	−1.00218
$689$	0	0
$690$	19.7034	0.750094
$691$	−13.6990	−0.521133	−0.260567	−	0.965456i	$-0.583909\pi$
$691$	−13.6990	−0.521133	−0.260567	+	0.965456i	$0.583909\pi$
$692$	5.21538	0.198259
$693$	−3.13241	−0.118991
$694$	41.7317	1.58411
$695$	17.4704	0.662690
$696$	−1.75135	−0.0663848
$697$	−5.75837	−0.218114
$698$	−68.2083	−2.58172
$699$	−22.9731	−0.868924
$700$	3.03281	0.114630
$701$	−25.4300	−0.960478	−0.480239	−	0.877138i	$-0.659450\pi$
$701$	−25.4300	−0.960478	−0.480239	+	0.877138i	$0.659450\pi$
$702$	0	0
$703$	−4.32218	−0.163014
$704$	−14.5643	−0.548911
$705$	−9.30071	−0.350285
$706$	9.71081	0.365471
$707$	−12.5967	−0.473749
$708$	7.79816	0.293073
$709$	−28.2448	−1.06076	−0.530378	−	0.847761i	$-0.677950\pi$
$709$	−28.2448	−1.06076	−0.530378	+	0.847761i	$0.677950\pi$
$710$	−24.0788	−0.903662
$711$	12.0565	0.452154
$712$	6.12822	0.229665
$713$	35.6259	1.33420
$714$	−1.77536	−0.0664412
$715$	0	0
$716$	32.0360	1.19724
$717$	15.7349	0.587631
$718$	4.08831	0.152574
$719$	16.4857	0.614812	0.307406	−	0.951578i	$-0.400539\pi$
$719$	16.4857	0.614812	0.307406	+	0.951578i	$0.400539\pi$
$720$	8.16862	0.304426
$721$	4.92445	0.183396
$722$	−27.4625	−1.02205
$723$	9.04536	0.336401
$724$	14.3610	0.533724
$725$	4.46498	0.165825
$726$	2.25767	0.0837899
$727$	−34.4487	−1.27763	−0.638816	−	0.769359i	$-0.720576\pi$
$727$	−34.4487	−1.27763	−0.638816	+	0.769359i	$0.720576\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	16.2950	0.603107
$731$	−5.30854	−0.196343
$732$	−20.3089	−0.750638
$733$	−51.0217	−1.88453	−0.942265	−	0.334869i	$-0.891308\pi$
$733$	−51.0217	−1.88453	−0.942265	+	0.334869i	$0.891308\pi$
$734$	36.7731	1.35732
$735$	1.76582	0.0651332
$736$	−42.9494	−1.58314
$737$	20.8323	0.767368
$738$	11.7142	0.431204
$739$	33.2683	1.22379	0.611897	−	0.790938i	$-0.290407\pi$
$739$	33.2683	1.22379	0.611897	+	0.790938i	$0.290407\pi$
$740$	−5.76678	−0.211991
$741$	0	0
$742$	−20.1236	−0.738762
$743$	48.4232	1.77648	0.888238	−	0.459384i	$-0.151930\pi$
$743$	48.4232	1.77648	0.888238	+	0.459384i	$0.151930\pi$
$744$	4.47885	0.164203
$745$	−34.8232	−1.27582
$746$	−31.0047	−1.13516
$747$	−11.7189	−0.428773
$748$	−4.71595	−0.172432
$749$	3.69523	0.135021
$750$	−23.0942	−0.843280
$751$	51.7999	1.89021	0.945103	−	0.326771i	$-0.105961\pi$
$751$	51.7999	1.89021	0.945103	+	0.326771i	$0.105961\pi$
$752$	24.3653	0.888512
$753$	−17.0593	−0.621675
$754$	0	0
$755$	22.3390	0.812999
$756$	1.61158	0.0586127
$757$	−2.92984	−0.106487	−0.0532434	−	0.998582i	$-0.516956\pi$
$757$	−2.92984	−0.106487	−0.0532434	+	0.998582i	$0.516956\pi$
$758$	17.0977	0.621016
$759$	−18.3918	−0.667580
$760$	−2.78010	−0.100845
$761$	18.2514	0.661613	0.330806	−	0.943699i	$-0.392679\pi$
$761$	18.2514	0.661613	0.330806	+	0.943699i	$0.392679\pi$
$762$	9.12286	0.330486
$763$	−14.6664	−0.530959
$764$	28.1367	1.01795
$765$	1.64962	0.0596421
$766$	−68.3665	−2.47018
$767$	0	0
$768$	−20.3098	−0.732867
$769$	−10.3062	−0.371652	−0.185826	−	0.982583i	$-0.559496\pi$
$769$	−10.3062	−0.371652	−0.185826	+	0.982583i	$0.559496\pi$
$770$	10.5117	0.378816
$771$	7.93028	0.285602
$772$	−31.1198	−1.12003
$773$	41.7219	1.50063	0.750316	−	0.661079i	$-0.229901\pi$
$773$	41.7219	1.50063	0.750316	+	0.661079i	$0.229901\pi$
$774$	10.7991	0.388164
$775$	−11.4186	−0.410169
$776$	−13.5024	−0.484707
$777$	2.02644	0.0726982
$778$	41.4245	1.48514
$779$	−13.1471	−0.471045
$780$	0	0
$781$	22.4760	0.804255
$782$	−10.4239	−0.372759
$783$	2.37261	0.0847903
$784$	−4.62597	−0.165213
$785$	28.1621	1.00515
$786$	13.9436	0.497351
$787$	−22.8437	−0.814289	−0.407144	−	0.913364i	$-0.633475\pi$
$787$	−22.8437	−0.814289	−0.407144	+	0.913364i	$0.633475\pi$
$788$	−41.8766	−1.49179
$789$	−18.4617	−0.657254
$790$	−40.4591	−1.43947
$791$	−14.4311	−0.513110
$792$	−2.31220	−0.0821604
$793$	0	0
$794$	49.3701	1.75208
$795$	18.6984	0.663163
$796$	32.3981	1.14832
$797$	30.3269	1.07423	0.537116	−	0.843508i	$-0.319514\pi$
$797$	30.3269	1.07423	0.537116	+	0.843508i	$0.319514\pi$
$798$	−4.05338	−0.143488
$799$	4.92048	0.174074
$800$	13.7659	0.486698
$801$	−8.30211	−0.293340
$802$	46.0812	1.62718
$803$	−15.2104	−0.536762
$804$	−10.7179	−0.377992
$805$	10.3679	0.365421
$806$	0	0
$807$	10.2133	0.359525
$808$	−9.29830	−0.327113
$809$	27.4074	0.963594	0.481797	−	0.876283i	$-0.339984\pi$
$809$	27.4074	0.963594	0.481797	+	0.876283i	$0.339984\pi$
$810$	−3.35579	−0.117910
$811$	−10.9233	−0.383568	−0.191784	−	0.981437i	$-0.561427\pi$
$811$	−10.9233	−0.383568	−0.191784	+	0.981437i	$0.561427\pi$
$812$	3.82366	0.134184
$813$	24.1804	0.848044
$814$	12.0632	0.422814
$815$	−16.6706	−0.583946
$816$	−4.32155	−0.151285
$817$	−12.1201	−0.424028
$818$	40.9804	1.43285
$819$	0	0
$820$	−17.5413	−0.612568
$821$	3.84174	0.134078	0.0670388	−	0.997750i	$-0.478645\pi$
$821$	3.84174	0.134078	0.0670388	+	0.997750i	$0.478645\pi$
$822$	1.80781	0.0630547
$823$	46.5183	1.62153	0.810764	−	0.585373i	$-0.199052\pi$
$823$	46.5183	1.62153	0.810764	+	0.585373i	$0.199052\pi$
$824$	3.63499	0.126631
$825$	5.89484	0.205232
$826$	9.19577	0.319962
$827$	−1.60867	−0.0559390	−0.0279695	−	0.999609i	$-0.508904\pi$
$827$	−1.60867	−0.0559390	−0.0279695	+	0.999609i	$0.508904\pi$
$828$	9.46233	0.328839
$829$	40.8933	1.42028	0.710142	−	0.704058i	$-0.248631\pi$
$829$	40.8933	1.42028	0.710142	+	0.704058i	$0.248631\pi$
$830$	39.3263	1.36504
$831$	18.3142	0.635311
$832$	0	0
$833$	−0.934195	−0.0323679
$834$	18.8021	0.651062
$835$	7.32502	0.253493
$836$	−10.7671	−0.372390
$837$	−6.06765	−0.209729
$838$	0.378508	0.0130753
$839$	−45.4468	−1.56900	−0.784499	−	0.620130i	$-0.787080\pi$
$839$	−45.4468	−1.56900	−0.784499	+	0.620130i	$0.787080\pi$
$840$	1.30344	0.0449731
$841$	−23.3707	−0.805886
$842$	−39.6621	−1.36685
$843$	9.11661	0.313993
$844$	−11.6903	−0.402396
$845$	0	0
$846$	−10.0096	−0.344139
$847$	1.18799	0.0408197
$848$	−48.9846	−1.68214
$849$	9.22502	0.316602
$850$	3.34102	0.114596
$851$	11.8981	0.407863
$852$	−11.5636	−0.396163
$853$	−34.0573	−1.16610	−0.583050	−	0.812436i	$-0.698141\pi$
$853$	−34.0573	−1.16610	−0.583050	+	0.812436i	$0.698141\pi$
$854$	−23.9487	−0.819508
$855$	3.76630	0.128805
$856$	2.72764	0.0932289
$857$	−30.3420	−1.03646	−0.518231	−	0.855240i	$-0.673409\pi$
$857$	−30.3420	−1.03646	−0.518231	+	0.855240i	$0.673409\pi$
$858$	0	0
$859$	54.1644	1.84806	0.924032	−	0.382315i	$-0.124873\pi$
$859$	54.1644	1.84806	0.924032	+	0.382315i	$0.124873\pi$
$860$	−16.1710	−0.551426
$861$	6.16399	0.210068
$862$	25.1417	0.856329
$863$	−53.2784	−1.81362	−0.906808	−	0.421543i	$-0.861489\pi$
$863$	−53.2784	−1.81362	−0.906808	+	0.421543i	$0.861489\pi$
$864$	7.31496	0.248860
$865$	−5.71451	−0.194299
$866$	−59.9616	−2.03758
$867$	16.1273	0.547711
$868$	−9.77853	−0.331905
$869$	37.7660	1.28112
$870$	−7.96199	−0.269937
$871$	0	0
$872$	−10.8260	−0.366616
$873$	18.2921	0.619095
$874$	−23.7992	−0.805021
$875$	−12.1522	−0.410818
$876$	7.82553	0.264400
$877$	−32.5325	−1.09854	−0.549272	−	0.835643i	$-0.685095\pi$
$877$	−32.5325	−1.09854	−0.549272	+	0.835643i	$0.685095\pi$
$878$	51.5771	1.74064
$879$	−18.0748	−0.609647
$880$	25.5875	0.862554
$881$	−12.1091	−0.407965	−0.203983	−	0.978975i	$-0.565389\pi$
$881$	−12.1091	−0.407965	−0.203983	+	0.978975i	$0.565389\pi$
$882$	1.90042	0.0639904
$883$	−39.1408	−1.31719	−0.658596	−	0.752497i	$-0.728849\pi$
$883$	−39.1408	−1.31719	−0.658596	+	0.752497i	$0.728849\pi$
$884$	0	0
$885$	−8.54448	−0.287219
$886$	−1.56967	−0.0527341
$887$	−18.8647	−0.633414	−0.316707	−	0.948523i	$-0.602577\pi$
$887$	−18.8647	−0.633414	−0.316707	+	0.948523i	$0.602577\pi$
$888$	1.49582	0.0501965
$889$	4.80045	0.161002
$890$	27.8601	0.933874
$891$	3.13241	0.104940
$892$	13.5661	0.454225
$893$	11.2341	0.375935
$894$	−37.4776	−1.25344
$895$	−35.1019	−1.17333
$896$	−5.79386	−0.193559
$897$	0	0
$898$	−52.3744	−1.74776
$899$	−14.3962	−0.480140
$900$	−3.03281	−0.101094
$901$	−9.89225	−0.329559
$902$	36.6936	1.22176
$903$	5.68247	0.189101
$904$	−10.6523	−0.354291
$905$	−15.7355	−0.523064
$906$	24.0418	0.798734
$907$	−7.69608	−0.255544	−0.127772	−	0.991804i	$-0.540783\pi$
$907$	−7.69608	−0.255544	−0.127772	+	0.991804i	$0.540783\pi$
$908$	16.8577	0.559441
$909$	12.5967	0.417807
$910$	0	0
$911$	−37.7524	−1.25079	−0.625396	−	0.780307i	$-0.715063\pi$
$911$	−37.7524	−1.25079	−0.625396	+	0.780307i	$0.715063\pi$
$912$	−9.86668	−0.326718
$913$	−36.7085	−1.21488
$914$	0.0847464	0.00280316
$915$	22.2525	0.735646
$916$	−17.1290	−0.565958
$917$	7.33712	0.242293
$918$	1.77536	0.0585956
$919$	−55.4581	−1.82939	−0.914696	−	0.404142i	$-0.867570\pi$
$919$	−55.4581	−1.82939	−0.914696	+	0.404142i	$0.867570\pi$
$920$	7.65310	0.252315
$921$	15.5831	0.513480
$922$	−5.44876	−0.179445
$923$	0	0
$924$	5.04815	0.166072
$925$	−3.81353	−0.125388
$926$	22.3512	0.734507
$927$	−4.92445	−0.161740
$928$	17.3556	0.569724
$929$	25.9014	0.849799	0.424899	−	0.905241i	$-0.360309\pi$
$929$	25.9014	0.849799	0.424899	+	0.905241i	$0.360309\pi$
$930$	20.3618	0.667689
$931$	−2.13289	−0.0699027
$932$	37.0232	1.21273
$933$	2.20637	0.0722332
$934$	74.8224	2.44826
$935$	5.16729	0.168988
$936$	0	0
$937$	−52.0461	−1.70027	−0.850136	−	0.526562i	$-0.823481\pi$
$937$	−52.0461	−1.70027	−0.850136	+	0.526562i	$0.823481\pi$
$938$	−12.6388	−0.412673
$939$	−26.6495	−0.869675
$940$	14.9889	0.488883
$941$	16.0103	0.521921	0.260960	−	0.965349i	$-0.415961\pi$
$941$	16.0103	0.521921	0.260960	+	0.965349i	$0.415961\pi$
$942$	30.3087	0.987512
$943$	36.1916	1.17856
$944$	22.3842	0.728544
$945$	−1.76582	−0.0574421
$946$	33.8271	1.09982
$947$	12.0064	0.390155	0.195078	−	0.980788i	$-0.437504\pi$
$947$	12.0064	0.390155	0.195078	+	0.980788i	$0.437504\pi$
$948$	−19.4301	−0.631059
$949$	0	0
$950$	7.62800	0.247485
$951$	22.8415	0.740688
$952$	−0.689579	−0.0223494
$953$	−0.168086	−0.00544483	−0.00272241	−	0.999996i	$-0.500867\pi$
$953$	−0.168086	−0.00544483	−0.00272241	+	0.999996i	$0.500867\pi$
$954$	20.1236	0.651527
$955$	−30.8295	−0.997619
$956$	−25.3581	−0.820141
$957$	7.43200	0.240243
$958$	−29.5655	−0.955218
$959$	0.951272	0.0307182
$960$	−8.21024	−0.264984
$961$	5.81638	0.187625
$962$	0	0
$963$	−3.69523	−0.119077
$964$	−14.5774	−0.469505
$965$	34.0981	1.09766
$966$	11.1582	0.359009
$967$	−13.9167	−0.447531	−0.223766	−	0.974643i	$-0.571835\pi$
$967$	−13.9167	−0.447531	−0.223766	+	0.974643i	$0.571835\pi$
$968$	0.876915	0.0281851
$969$	−1.99254	−0.0640095
$970$	−61.3846	−1.97094
$971$	46.8956	1.50495	0.752476	−	0.658619i	$-0.228859\pi$
$971$	46.8956	1.50495	0.752476	+	0.658619i	$0.228859\pi$
$972$	−1.61158	−0.0516916
$973$	9.89366	0.317176
$974$	−45.1274	−1.44597
$975$	0	0
$976$	−58.2956	−1.86600
$977$	5.97584	0.191184	0.0955920	−	0.995421i	$-0.469526\pi$
$977$	5.97584	0.191184	0.0955920	+	0.995421i	$0.469526\pi$
$978$	−17.9413	−0.573700
$979$	−26.0056	−0.831144
$980$	−2.84577	−0.0909046
$981$	14.6664	0.468262
$982$	−11.1465	−0.355698
$983$	36.0862	1.15097	0.575485	−	0.817812i	$-0.304813\pi$
$983$	36.0862	1.15097	0.575485	+	0.817812i	$0.304813\pi$
$984$	4.54997	0.145048
$985$	45.8844	1.46200
$986$	4.21224	0.134145
$987$	−5.26708	−0.167653
$988$	0	0
$989$	33.3643	1.06092
$990$	−10.5117	−0.334085
$991$	−45.0778	−1.43194	−0.715972	−	0.698129i	$-0.754016\pi$
$991$	−45.0778	−1.43194	−0.715972	+	0.698129i	$0.754016\pi$
$992$	−44.3846	−1.40921
$993$	3.66559	0.116324
$994$	−13.6361	−0.432510
$995$	−35.4988	−1.12539
$996$	18.8860	0.598427
$997$	15.1512	0.479842	0.239921	−	0.970792i	$-0.422878\pi$
$997$	15.1512	0.479842	0.239921	+	0.970792i	$0.422878\pi$
$998$	−14.8181	−0.469059
$999$	−2.02644	−0.0641138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bf.1.8	yes	9
13.12	even	2		3549.2.a.be.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.be.1.2	✓	9	13.12	even	2
3549.2.a.bf.1.8	yes	9	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+1.90042 q^{2} -1.00000 q^{3} +1.61158 q^{4} -1.76582 q^{5} -1.90042 q^{6} -1.00000 q^{7} -0.738153 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.90042 q^{2} -1.00000 q^{3} +1.61158 q^{4} -1.76582 q^{5} -1.90042 q^{6} -1.00000 q^{7} -0.738153 q^{8} +1.00000 q^{9} -3.35579 q^{10} +3.13241 q^{11} -1.61158 q^{12} -1.90042 q^{14} +1.76582 q^{15} -4.62597 q^{16} -0.934195 q^{17} +1.90042 q^{18} -2.13289 q^{19} -2.84577 q^{20} +1.00000 q^{21} +5.95289 q^{22} +5.87145 q^{23} +0.738153 q^{24} -1.88188 q^{25} -1.00000 q^{27} -1.61158 q^{28} -2.37261 q^{29} +3.35579 q^{30} +6.06765 q^{31} -7.31496 q^{32} -3.13241 q^{33} -1.77536 q^{34} +1.76582 q^{35} +1.61158 q^{36} +2.02644 q^{37} -4.05338 q^{38} +1.30344 q^{40} +6.16399 q^{41} +1.90042 q^{42} +5.68247 q^{43} +5.04815 q^{44} -1.76582 q^{45} +11.1582 q^{46} -5.26708 q^{47} +4.62597 q^{48} +1.00000 q^{49} -3.57636 q^{50} +0.934195 q^{51} +10.5891 q^{53} -1.90042 q^{54} -5.53127 q^{55} +0.738153 q^{56} +2.13289 q^{57} -4.50895 q^{58} -4.83882 q^{59} +2.84577 q^{60} +12.6018 q^{61} +11.5311 q^{62} -1.00000 q^{63} -4.64954 q^{64} -5.95289 q^{66} +6.65056 q^{67} -1.50553 q^{68} -5.87145 q^{69} +3.35579 q^{70} +7.17531 q^{71} -0.738153 q^{72} -4.85580 q^{73} +3.85108 q^{74} +1.88188 q^{75} -3.43733 q^{76} -3.13241 q^{77} +12.0565 q^{79} +8.16862 q^{80} +1.00000 q^{81} +11.7142 q^{82} -11.7189 q^{83} +1.61158 q^{84} +1.64962 q^{85} +10.7991 q^{86} +2.37261 q^{87} -2.31220 q^{88} -8.30211 q^{89} -3.35579 q^{90} +9.46233 q^{92} -6.06765 q^{93} -10.0096 q^{94} +3.76630 q^{95} +7.31496 q^{96} +18.2921 q^{97} +1.90042 q^{98} +3.13241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9	\( 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9} + q^{10} + q^{11} - 5 q^{12} - q^{14} + 9 q^{15} + 5 q^{16} + 11 q^{17} + q^{18} - 7 q^{19} - 23 q^{20} + 9 q^{21} - 3 q^{22} + 22 q^{23} - 6 q^{24} - 8 q^{25} - 9 q^{27} - 5 q^{28} + 11 q^{29} - q^{30} - 7 q^{31} + 18 q^{32} - q^{33} + 6 q^{34} + 9 q^{35} + 5 q^{36} + q^{37} - 6 q^{38} - 14 q^{40} - 16 q^{41} + q^{42} + 32 q^{43} - 18 q^{44} - 9 q^{45} + 9 q^{46} + 12 q^{47} - 5 q^{48} + 9 q^{49} - 10 q^{50} - 11 q^{51} + 13 q^{53} - q^{54} + 9 q^{55} - 6 q^{56} + 7 q^{57} - 4 q^{58} - 29 q^{59} + 23 q^{60} - 12 q^{61} + 30 q^{62} - 9 q^{63} + 6 q^{64} + 3 q^{66} + 20 q^{67} + 34 q^{68} - 22 q^{69} - q^{70} + 2 q^{71} + 6 q^{72} - q^{73} + 43 q^{74} + 8 q^{75} - 13 q^{76} - q^{77} + 3 q^{79} + 39 q^{80} + 9 q^{81} - 19 q^{82} - 24 q^{83} + 5 q^{84} - 15 q^{85} + 28 q^{86} - 11 q^{87} - 19 q^{88} - 11 q^{89} + q^{90} + 73 q^{92} + 7 q^{93} + 15 q^{94} + 39 q^{95} - 18 q^{96} - 20 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9 + q^10 + q^11 - 5 * q^12 - q^14 + 9 * q^15 + 5 * q^16 + 11 * q^17 + q^18 - 7 * q^19 - 23 * q^20 + 9 * q^21 - 3 * q^22 + 22 * q^23 - 6 * q^24 - 8 * q^25 - 9 * q^27 - 5 * q^28 + 11 * q^29 - q^30 - 7 * q^31 + 18 * q^32 - q^33 + 6 * q^34 + 9 * q^35 + 5 * q^36 + q^37 - 6 * q^38 - 14 * q^40 - 16 * q^41 + q^42 + 32 * q^43 - 18 * q^44 - 9 * q^45 + 9 * q^46 + 12 * q^47 - 5 * q^48 + 9 * q^49 - 10 * q^50 - 11 * q^51 + 13 * q^53 - q^54 + 9 * q^55 - 6 * q^56 + 7 * q^57 - 4 * q^58 - 29 * q^59 + 23 * q^60 - 12 * q^61 + 30 * q^62 - 9 * q^63 + 6 * q^64 + 3 * q^66 + 20 * q^67 + 34 * q^68 - 22 * q^69 - q^70 + 2 * q^71 + 6 * q^72 - q^73 + 43 * q^74 + 8 * q^75 - 13 * q^76 - q^77 + 3 * q^79 + 39 * q^80 + 9 * q^81 - 19 * q^82 - 24 * q^83 + 5 * q^84 - 15 * q^85 + 28 * q^86 - 11 * q^87 - 19 * q^88 - 11 * q^89 + q^90 + 73 * q^92 + 7 * q^93 + 15 * q^94 + 39 * q^95 - 18 * q^96 - 20 * q^97 + q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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