LMFDB - Embedded newform 6027.2.a.z.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 8x^{6} + 14x^{5} + 18x^{4} - 24x^{3} - 10x^{2} + 10x - 1 $ x^8 - 2x^7 - 8x^6 + 14x^5 + 18x^4 - 24x^3 - 10x^2 + 10*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.41849$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41849 q^{2} -1.00000 q^{3} +0.0121162 q^{4} -2.27752 q^{5} -1.41849 q^{6} -2.81979 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.41849 q^{2} -1.00000 q^{3} +0.0121162 q^{4} -2.27752 q^{5} -1.41849 q^{6} -2.81979 q^{8} +1.00000 q^{9} -3.23064 q^{10} -2.51338 q^{11} -0.0121162 q^{12} +0.793613 q^{13} +2.27752 q^{15} -4.02409 q^{16} +5.45234 q^{17} +1.41849 q^{18} +3.19026 q^{19} -0.0275949 q^{20} -3.56521 q^{22} +0.533334 q^{23} +2.81979 q^{24} +0.187104 q^{25} +1.12573 q^{26} -1.00000 q^{27} +7.94974 q^{29} +3.23064 q^{30} +4.75167 q^{31} -0.0685386 q^{32} +2.51338 q^{33} +7.73409 q^{34} +0.0121162 q^{36} -10.8168 q^{37} +4.52535 q^{38} -0.793613 q^{39} +6.42214 q^{40} +1.00000 q^{41} +7.87530 q^{43} -0.0304526 q^{44} -2.27752 q^{45} +0.756530 q^{46} +10.2295 q^{47} +4.02409 q^{48} +0.265405 q^{50} -5.45234 q^{51} +0.00961557 q^{52} -9.61970 q^{53} -1.41849 q^{54} +5.72428 q^{55} -3.19026 q^{57} +11.2766 q^{58} -8.28879 q^{59} +0.0275949 q^{60} +8.46622 q^{61} +6.74020 q^{62} +7.95095 q^{64} -1.80747 q^{65} +3.56521 q^{66} -6.45159 q^{67} +0.0660616 q^{68} -0.533334 q^{69} -10.8662 q^{71} -2.81979 q^{72} -14.1377 q^{73} -15.3436 q^{74} -0.187104 q^{75} +0.0386538 q^{76} -1.12573 q^{78} -12.8150 q^{79} +9.16494 q^{80} +1.00000 q^{81} +1.41849 q^{82} -16.8165 q^{83} -12.4178 q^{85} +11.1710 q^{86} -7.94974 q^{87} +7.08722 q^{88} -8.93140 q^{89} -3.23064 q^{90} +0.00646199 q^{92} -4.75167 q^{93} +14.5105 q^{94} -7.26588 q^{95} +0.0685386 q^{96} +3.67076 q^{97} -2.51338 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9	$ 8 q - 2 q^{2} - 8 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9} - 2 q^{10} - 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{15} + 8 q^{17} - 2 q^{18} + 6 q^{19} + 4 q^{20} - 14 q^{22} - 12 q^{23} + 6 q^{24} - 4 q^{25} + 4 q^{26} - 8 q^{27} - 4 q^{29} + 2 q^{30} - 10 q^{31} - 4 q^{32} + 2 q^{33} + 4 q^{34} + 4 q^{36} - 20 q^{37} - 18 q^{38} - 4 q^{39} + 12 q^{40} + 8 q^{41} - 8 q^{43} + 20 q^{44} + 2 q^{45} - 12 q^{46} + 24 q^{47} - 22 q^{50} - 8 q^{51} - 30 q^{52} - 36 q^{53} + 2 q^{54} + 4 q^{55} - 6 q^{57} + 14 q^{58} + 10 q^{59} - 4 q^{60} - 22 q^{61} + 30 q^{62} - 24 q^{64} + 8 q^{65} + 14 q^{66} - 14 q^{67} + 38 q^{68} + 12 q^{69} - 10 q^{71} - 6 q^{72} - 12 q^{73} - 2 q^{74} + 4 q^{75} + 32 q^{76} - 4 q^{78} + 16 q^{79} - 14 q^{80} + 8 q^{81} - 2 q^{82} + 24 q^{83} - 44 q^{85} + 36 q^{86} + 4 q^{87} - 34 q^{88} + 2 q^{89} - 2 q^{90} - 48 q^{92} + 10 q^{93} - 34 q^{94} - 24 q^{95} + 4 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 8 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9 - 2 * q^10 - 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^15 + 8 * q^17 - 2 * q^18 + 6 * q^19 + 4 * q^20 - 14 * q^22 - 12 * q^23 + 6 * q^24 - 4 * q^25 + 4 * q^26 - 8 * q^27 - 4 * q^29 + 2 * q^30 - 10 * q^31 - 4 * q^32 + 2 * q^33 + 4 * q^34 + 4 * q^36 - 20 * q^37 - 18 * q^38 - 4 * q^39 + 12 * q^40 + 8 * q^41 - 8 * q^43 + 20 * q^44 + 2 * q^45 - 12 * q^46 + 24 * q^47 - 22 * q^50 - 8 * q^51 - 30 * q^52 - 36 * q^53 + 2 * q^54 + 4 * q^55 - 6 * q^57 + 14 * q^58 + 10 * q^59 - 4 * q^60 - 22 * q^61 + 30 * q^62 - 24 * q^64 + 8 * q^65 + 14 * q^66 - 14 * q^67 + 38 * q^68 + 12 * q^69 - 10 * q^71 - 6 * q^72 - 12 * q^73 - 2 * q^74 + 4 * q^75 + 32 * q^76 - 4 * q^78 + 16 * q^79 - 14 * q^80 + 8 * q^81 - 2 * q^82 + 24 * q^83 - 44 * q^85 + 36 * q^86 + 4 * q^87 - 34 * q^88 + 2 * q^89 - 2 * q^90 - 48 * q^92 + 10 * q^93 - 34 * q^94 - 24 * q^95 + 4 * q^96 + 16 * q^97 - 2 * 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 $

$2$	1.41849	1.00302	0.501512	−	0.865151i	$-0.332777\pi$
$2$	1.41849	1.00302	0.501512	+	0.865151i	$0.332777\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.0121162	0.00605810
$5$	−2.27752	−1.01854	−0.509269	−	0.860607i	$-0.670084\pi$
$5$	−2.27752	−1.01854	−0.509269	+	0.860607i	$0.670084\pi$
$6$	−1.41849	−0.579096
$7$	0	0
$7$	0	0
$8$	−2.81979	−0.996948
$9$	1.00000	0.333333
$10$	−3.23064	−1.02162
$11$	−2.51338	−0.757813	−0.378907	−	0.925435i	$-0.623700\pi$
$11$	−2.51338	−0.757813	−0.378907	+	0.925435i	$0.623700\pi$
$12$	−0.0121162	−0.00349765
$13$	0.793613	0.220109	0.110054	−	0.993926i	$-0.464898\pi$
$13$	0.793613	0.220109	0.110054	+	0.993926i	$0.464898\pi$
$14$	0	0
$15$	2.27752	0.588054
$16$	−4.02409	−1.00602
$17$	5.45234	1.32239	0.661193	−	0.750216i	$-0.270050\pi$
$17$	5.45234	1.32239	0.661193	+	0.750216i	$0.270050\pi$
$18$	1.41849	0.334341
$19$	3.19026	0.731895	0.365948	−	0.930635i	$-0.380745\pi$
$19$	3.19026	0.731895	0.365948	+	0.930635i	$0.380745\pi$
$20$	−0.0275949	−0.00617041
$21$	0	0
$22$	−3.56521	−0.760105
$23$	0.533334	0.111208	0.0556040	−	0.998453i	$-0.482292\pi$
$23$	0.533334	0.111208	0.0556040	+	0.998453i	$0.482292\pi$
$24$	2.81979	0.575588
$25$	0.187104	0.0374208
$26$	1.12573	0.220774
$27$	−1.00000	−0.192450
$28$	0	0
$29$	7.94974	1.47623	0.738115	−	0.674675i	$-0.235716\pi$
$29$	7.94974	1.47623	0.738115	+	0.674675i	$0.235716\pi$
$30$	3.23064	0.589832
$31$	4.75167	0.853425	0.426712	−	0.904387i	$-0.359672\pi$
$31$	4.75167	0.853425	0.426712	+	0.904387i	$0.359672\pi$
$32$	−0.0685386	−0.0121160
$33$	2.51338	0.437524
$34$	7.73409	1.32639
$35$	0	0
$36$	0.0121162	0.00201937
$37$	−10.8168	−1.77828	−0.889139	−	0.457638i	$-0.848696\pi$
$37$	−10.8168	−1.77828	−0.889139	+	0.457638i	$0.848696\pi$
$38$	4.52535	0.734109
$39$	−0.793613	−0.127080
$40$	6.42214	1.01543
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	7.87530	1.20097	0.600486	−	0.799635i	$-0.294974\pi$
$43$	7.87530	1.20097	0.600486	+	0.799635i	$0.294974\pi$
$44$	−0.0304526	−0.00459091
$45$	−2.27752	−0.339513
$46$	0.756530	0.111544
$47$	10.2295	1.49213	0.746064	−	0.665875i	$-0.231941\pi$
$47$	10.2295	1.49213	0.746064	+	0.665875i	$0.231941\pi$
$48$	4.02409	0.580827
$49$	0	0
$50$	0.265405	0.0375340
$51$	−5.45234	−0.763480
$52$	0.00961557	0.00133344
$53$	−9.61970	−1.32137	−0.660684	−	0.750664i	$-0.729734\pi$
$53$	−9.61970	−1.32137	−0.660684	+	0.750664i	$0.729734\pi$
$54$	−1.41849	−0.193032
$55$	5.72428	0.771862
$56$	0	0
$57$	−3.19026	−0.422560
$58$	11.2766	1.48069
$59$	−8.28879	−1.07911	−0.539554	−	0.841951i	$-0.681407\pi$
$59$	−8.28879	−1.07911	−0.539554	+	0.841951i	$0.681407\pi$
$60$	0.0275949	0.00356249
$61$	8.46622	1.08399	0.541994	−	0.840382i	$-0.317669\pi$
$61$	8.46622	1.08399	0.541994	+	0.840382i	$0.317669\pi$
$62$	6.74020	0.856006
$63$	0	0
$64$	7.95095	0.993869
$65$	−1.80747	−0.224189
$66$	3.56521	0.438847
$67$	−6.45159	−0.788188	−0.394094	−	0.919070i	$-0.628941\pi$
$67$	−6.45159	−0.788188	−0.394094	+	0.919070i	$0.628941\pi$
$68$	0.0660616	0.00801115
$69$	−0.533334	−0.0642059
$70$	0	0
$71$	−10.8662	−1.28959	−0.644793	−	0.764357i	$-0.723056\pi$
$71$	−10.8662	−1.28959	−0.644793	+	0.764357i	$0.723056\pi$
$72$	−2.81979	−0.332316
$73$	−14.1377	−1.65469	−0.827345	−	0.561694i	$-0.810150\pi$
$73$	−14.1377	−1.65469	−0.827345	+	0.561694i	$0.810150\pi$
$74$	−15.3436	−1.78366
$75$	−0.187104	−0.0216049
$76$	0.0386538	0.00443390
$77$	0	0
$78$	−1.12573	−0.127464
$79$	−12.8150	−1.44180	−0.720900	−	0.693039i	$-0.756272\pi$
$79$	−12.8150	−1.44180	−0.720900	+	0.693039i	$0.756272\pi$
$80$	9.16494	1.02467
$81$	1.00000	0.111111
$82$	1.41849	0.156646
$83$	−16.8165	−1.84585	−0.922927	−	0.384976i	$-0.874210\pi$
$83$	−16.8165	−1.84585	−0.922927	+	0.384976i	$0.874210\pi$
$84$	0	0
$85$	−12.4178	−1.34690
$86$	11.1710	1.20460
$87$	−7.94974	−0.852301
$88$	7.08722	0.755500
$89$	−8.93140	−0.946727	−0.473363	−	0.880867i	$-0.656960\pi$
$89$	−8.93140	−0.946727	−0.473363	+	0.880867i	$0.656960\pi$
$90$	−3.23064	−0.340540
$91$	0	0
$92$	0.00646199	0.000673709 0
$93$	−4.75167	−0.492725
$94$	14.5105	1.49664
$95$	−7.26588	−0.745464
$96$	0.0685386	0.00699520
$97$	3.67076	0.372709	0.186355	−	0.982483i	$-0.440333\pi$
$97$	3.67076	0.372709	0.186355	+	0.982483i	$0.440333\pi$
$98$	0	0
$99$	−2.51338	−0.252604
$100$	0.00226699	0.000226699 0
$101$	15.1892	1.51138	0.755690	−	0.654930i	$-0.227302\pi$
$101$	15.1892	1.51138	0.755690	+	0.654930i	$0.227302\pi$
$102$	−7.73409	−0.765789
$103$	−7.55116	−0.744038	−0.372019	−	0.928225i	$-0.621334\pi$
$103$	−7.55116	−0.744038	−0.372019	+	0.928225i	$0.621334\pi$
$104$	−2.23783	−0.219437
$105$	0	0
$106$	−13.6455	−1.32536
$107$	−9.00884	−0.870918	−0.435459	−	0.900209i	$-0.643414\pi$
$107$	−9.00884	−0.870918	−0.435459	+	0.900209i	$0.643414\pi$
$108$	−0.0121162	−0.00116588
$109$	−6.16075	−0.590093	−0.295046	−	0.955483i	$-0.595335\pi$
$109$	−6.16075	−0.590093	−0.295046	+	0.955483i	$0.595335\pi$
$110$	8.11984	0.774196
$111$	10.8168	1.02669
$112$	0	0
$113$	18.4202	1.73282	0.866412	−	0.499329i	$-0.166420\pi$
$113$	18.4202	1.73282	0.866412	+	0.499329i	$0.166420\pi$
$114$	−4.52535	−0.423838
$115$	−1.21468	−0.113270
$116$	0.0963206	0.00894314
$117$	0.793613	0.0733695
$118$	−11.7576	−1.08237
$119$	0	0
$120$	−6.42214	−0.586259
$121$	−4.68291	−0.425719
$122$	12.0093	1.08727
$123$	−1.00000	−0.0901670
$124$	0.0575722	0.00517013
$125$	10.9615	0.980424
$126$	0	0
$127$	12.0740	1.07140	0.535699	−	0.844409i	$-0.320048\pi$
$127$	12.0740	1.07140	0.535699	+	0.844409i	$0.320048\pi$
$128$	11.4154	1.00899
$129$	−7.87530	−0.693382
$130$	−2.56388	−0.224867
$131$	13.6702	1.19437	0.597185	−	0.802103i	$-0.296286\pi$
$131$	13.6702	1.19437	0.597185	+	0.802103i	$0.296286\pi$
$132$	0.0304526	0.00265056
$133$	0	0
$134$	−9.15153	−0.790571
$135$	2.27752	0.196018
$136$	−15.3745	−1.31835
$137$	−12.5675	−1.07371	−0.536857	−	0.843673i	$-0.680388\pi$
$137$	−12.5675	−1.07371	−0.536857	+	0.843673i	$0.680388\pi$
$138$	−0.756530	−0.0644001
$139$	7.52482	0.638247	0.319124	−	0.947713i	$-0.396611\pi$
$139$	7.52482	0.638247	0.319124	+	0.947713i	$0.396611\pi$
$140$	0	0
$141$	−10.2295	−0.861480
$142$	−15.4137	−1.29349
$143$	−1.99465	−0.166801
$144$	−4.02409	−0.335340
$145$	−18.1057	−1.50360
$146$	−20.0542	−1.65969
$147$	0	0
$148$	−0.131059	−0.0107730
$149$	−4.30227	−0.352456	−0.176228	−	0.984349i	$-0.556390\pi$
$149$	−4.30227	−0.352456	−0.176228	+	0.984349i	$0.556390\pi$
$150$	−0.265405	−0.0216702
$151$	−12.8508	−1.04578	−0.522890	−	0.852400i	$-0.675146\pi$
$151$	−12.8508	−1.04578	−0.522890	+	0.852400i	$0.675146\pi$
$152$	−8.99587	−0.729662
$153$	5.45234	0.440795
$154$	0	0
$155$	−10.8220	−0.869246
$156$	−0.00961557	−0.000769862 0
$157$	−12.2828	−0.980276	−0.490138	−	0.871645i	$-0.663054\pi$
$157$	−12.2828	−0.980276	−0.490138	+	0.871645i	$0.663054\pi$
$158$	−18.1780	−1.44616
$159$	9.61970	0.762892
$160$	0.156098	0.0123406
$161$	0	0
$162$	1.41849	0.111447
$163$	17.2057	1.34766	0.673829	−	0.738887i	$-0.264648\pi$
$163$	17.2057	1.34766	0.673829	+	0.738887i	$0.264648\pi$
$164$	0.0121162	0.000946116 0
$165$	−5.72428	−0.445635
$166$	−23.8541	−1.85144
$167$	−3.81224	−0.295000	−0.147500	−	0.989062i	$-0.547123\pi$
$167$	−3.81224	−0.295000	−0.147500	+	0.989062i	$0.547123\pi$
$168$	0	0
$169$	−12.3702	−0.951552
$170$	−17.6146	−1.35098
$171$	3.19026	0.243965
$172$	0.0954188	0.00727561
$173$	11.0232	0.838077	0.419038	−	0.907969i	$-0.362367\pi$
$173$	11.0232	0.838077	0.419038	+	0.907969i	$0.362367\pi$
$174$	−11.2766	−0.854879
$175$	0	0
$176$	10.1141	0.762376
$177$	8.28879	0.623023
$178$	−12.6691	−0.949590
$179$	12.9395	0.967140	0.483570	−	0.875306i	$-0.339340\pi$
$179$	12.9395	0.967140	0.483570	+	0.875306i	$0.339340\pi$
$180$	−0.0275949	−0.00205680
$181$	−6.58317	−0.489324	−0.244662	−	0.969608i	$-0.578677\pi$
$181$	−6.58317	−0.489324	−0.244662	+	0.969608i	$0.578677\pi$
$182$	0	0
$183$	−8.46622	−0.625841
$184$	−1.50389	−0.110869
$185$	24.6356	1.81124
$186$	−6.74020	−0.494215
$187$	−13.7038	−1.00212
$188$	0.123943	0.00903946
$189$	0	0
$190$	−10.3066	−0.747718
$191$	16.3300	1.18160	0.590800	−	0.806818i	$-0.298812\pi$
$191$	16.3300	1.18160	0.590800	+	0.806818i	$0.298812\pi$
$192$	−7.95095	−0.573810
$193$	−0.871945	−0.0627639	−0.0313820	−	0.999507i	$-0.509991\pi$
$193$	−0.871945	−0.0627639	−0.0313820	+	0.999507i	$0.509991\pi$
$194$	5.20694	0.373837
$195$	1.80747	0.129436
$196$	0	0
$197$	3.48366	0.248201	0.124100	−	0.992270i	$-0.460396\pi$
$197$	3.48366	0.248201	0.124100	+	0.992270i	$0.460396\pi$
$198$	−3.56521	−0.253368
$199$	−3.48060	−0.246733	−0.123367	−	0.992361i	$-0.539369\pi$
$199$	−3.48060	−0.246733	−0.123367	+	0.992361i	$0.539369\pi$
$200$	−0.527595	−0.0373066
$201$	6.45159	0.455060
$202$	21.5457	1.51595
$203$	0	0
$204$	−0.0660616	−0.00462524
$205$	−2.27752	−0.159069
$206$	−10.7113	−0.746288
$207$	0.533334	0.0370693
$208$	−3.19357	−0.221434
$209$	−8.01834	−0.554640
$210$	0	0
$211$	2.34385	0.161357	0.0806786	−	0.996740i	$-0.474291\pi$
$211$	2.34385	0.161357	0.0806786	+	0.996740i	$0.474291\pi$
$212$	−0.116554	−0.00800497
$213$	10.8662	0.744543
$214$	−12.7790	−0.873552
$215$	−17.9362	−1.22324
$216$	2.81979	0.191863
$217$	0	0
$218$	−8.73897	−0.591878
$219$	14.1377	0.955336
$220$	0.0693565	0.00467602
$221$	4.32705	0.291069
$222$	15.3436	1.02979
$223$	−2.63120	−0.176198	−0.0880989	−	0.996112i	$-0.528079\pi$
$223$	−2.63120	−0.176198	−0.0880989	+	0.996112i	$0.528079\pi$
$224$	0	0
$225$	0.187104	0.0124736
$226$	26.1289	1.73807
$227$	−14.5503	−0.965740	−0.482870	−	0.875692i	$-0.660406\pi$
$227$	−14.5503	−0.965740	−0.482870	+	0.875692i	$0.660406\pi$
$228$	−0.0386538	−0.00255991
$229$	−14.8353	−0.980346	−0.490173	−	0.871625i	$-0.663066\pi$
$229$	−14.8353	−0.980346	−0.490173	+	0.871625i	$0.663066\pi$
$230$	−1.72301	−0.113612
$231$	0	0
$232$	−22.4166	−1.47172
$233$	−7.77864	−0.509596	−0.254798	−	0.966994i	$-0.582009\pi$
$233$	−7.77864	−0.509596	−0.254798	+	0.966994i	$0.582009\pi$
$234$	1.12573	0.0735914
$235$	−23.2979	−1.51979
$236$	−0.100429	−0.00653734
$237$	12.8150	0.832424
$238$	0	0
$239$	−12.3165	−0.796687	−0.398343	−	0.917236i	$-0.630415\pi$
$239$	−12.3165	−0.796687	−0.398343	+	0.917236i	$0.630415\pi$
$240$	−9.16494	−0.591594
$241$	−30.1689	−1.94335	−0.971673	−	0.236328i	$-0.924056\pi$
$241$	−30.1689	−1.94335	−0.971673	+	0.236328i	$0.924056\pi$
$242$	−6.64267	−0.427007
$243$	−1.00000	−0.0641500
$244$	0.102578	0.00656691
$245$	0	0
$246$	−1.41849	−0.0904397
$247$	2.53183	0.161096
$248$	−13.3987	−0.850820
$249$	16.8165	1.06570
$250$	15.5488	0.983389
$251$	−6.97910	−0.440517	−0.220259	−	0.975442i	$-0.570690\pi$
$251$	−6.97910	−0.440517	−0.220259	+	0.975442i	$0.570690\pi$
$252$	0	0
$253$	−1.34047	−0.0842748
$254$	17.1269	1.07464
$255$	12.4178	0.777634
$256$	0.290778	0.0181736
$257$	−26.1325	−1.63010	−0.815050	−	0.579391i	$-0.803290\pi$
$257$	−26.1325	−1.63010	−0.815050	+	0.579391i	$0.803290\pi$
$258$	−11.1710	−0.695479
$259$	0	0
$260$	−0.0218997	−0.00135816
$261$	7.94974	0.492076
$262$	19.3911	1.19798
$263$	−21.8909	−1.34985	−0.674925	−	0.737887i	$-0.735824\pi$
$263$	−21.8909	−1.34985	−0.674925	+	0.737887i	$0.735824\pi$
$264$	−7.08722	−0.436188
$265$	21.9091	1.34586
$266$	0	0
$267$	8.93140	0.546593
$268$	−0.0781688	−0.00477492
$269$	−11.4098	−0.695667	−0.347833	−	0.937556i	$-0.613082\pi$
$269$	−11.4098	−0.695667	−0.347833	+	0.937556i	$0.613082\pi$
$270$	3.23064	0.196611
$271$	19.2441	1.16899	0.584497	−	0.811396i	$-0.301292\pi$
$271$	19.2441	1.16899	0.584497	+	0.811396i	$0.301292\pi$
$272$	−21.9407	−1.33035
$273$	0	0
$274$	−17.8269	−1.07696
$275$	−0.470264	−0.0283580
$276$	−0.00646199	−0.000388966 0
$277$	−30.8885	−1.85591	−0.927956	−	0.372690i	$-0.878436\pi$
$277$	−30.8885	−1.85591	−0.927956	+	0.372690i	$0.878436\pi$
$278$	10.6739	0.640178
$279$	4.75167	0.284475
$280$	0	0
$281$	28.9922	1.72953	0.864764	−	0.502178i	$-0.167468\pi$
$281$	28.9922	1.72953	0.864764	+	0.502178i	$0.167468\pi$
$282$	−14.5105	−0.864086
$283$	−6.79869	−0.404140	−0.202070	−	0.979371i	$-0.564767\pi$
$283$	−6.79869	−0.404140	−0.202070	+	0.979371i	$0.564767\pi$
$284$	−0.131658	−0.00781244
$285$	7.26588	0.430394
$286$	−2.82940	−0.167306
$287$	0	0
$288$	−0.0685386	−0.00403868
$289$	12.7280	0.748706
$290$	−25.6828	−1.50814
$291$	−3.67076	−0.215184
$292$	−0.171295	−0.0100243
$293$	5.90390	0.344909	0.172455	−	0.985017i	$-0.444830\pi$
$293$	5.90390	0.344909	0.172455	+	0.985017i	$0.444830\pi$
$294$	0	0
$295$	18.8779	1.09911
$296$	30.5013	1.77285
$297$	2.51338	0.145841
$298$	−6.10274	−0.353522
$299$	0.423261	0.0244778
$300$	−0.00226699	−0.000130885 0
$301$	0	0
$302$	−18.2287	−1.04894
$303$	−15.1892	−0.872595
$304$	−12.8379	−0.736302
$305$	−19.2820	−1.10408
$306$	7.73409	0.442129
$307$	−7.75244	−0.442455	−0.221228	−	0.975222i	$-0.571006\pi$
$307$	−7.75244	−0.442455	−0.221228	+	0.975222i	$0.571006\pi$
$308$	0	0
$309$	7.55116	0.429571
$310$	−15.3509	−0.871875
$311$	18.1162	1.02727	0.513636	−	0.858008i	$-0.328298\pi$
$311$	18.1162	1.02727	0.513636	+	0.858008i	$0.328298\pi$
$312$	2.23783	0.126692
$313$	17.6100	0.995378	0.497689	−	0.867356i	$-0.334182\pi$
$313$	17.6100	0.995378	0.497689	+	0.867356i	$0.334182\pi$
$314$	−17.4231	−0.983241
$315$	0	0
$316$	−0.155269	−0.00873457
$317$	−17.8320	−1.00154	−0.500771	−	0.865580i	$-0.666950\pi$
$317$	−17.8320	−1.00154	−0.500771	+	0.865580i	$0.666950\pi$
$318$	13.6455	0.765199
$319$	−19.9807	−1.11871
$320$	−18.1085	−1.01229
$321$	9.00884	0.502825
$322$	0	0
$323$	17.3944	0.967848
$324$	0.0121162	0.000673122 0
$325$	0.148488	0.00823664
$326$	24.4062	1.35173
$327$	6.16075	0.340690
$328$	−2.81979	−0.155697
$329$	0	0
$330$	−8.11984	−0.446983
$331$	−18.6479	−1.02498	−0.512491	−	0.858693i	$-0.671277\pi$
$331$	−18.6479	−1.02498	−0.512491	+	0.858693i	$0.671277\pi$
$332$	−0.203752	−0.0111824
$333$	−10.8168	−0.592759
$334$	−5.40763	−0.295892
$335$	14.6936	0.802799
$336$	0	0
$337$	1.56830	0.0854309	0.0427155	−	0.999087i	$-0.486399\pi$
$337$	1.56830	0.0854309	0.0427155	+	0.999087i	$0.486399\pi$
$338$	−17.5470	−0.954430
$339$	−18.4202	−1.00045
$340$	−0.150457	−0.00815966
$341$	−11.9428	−0.646737
$342$	4.52535	0.244703
$343$	0	0
$344$	−22.2067	−1.19731
$345$	1.21468	0.0653962
$346$	15.6363	0.840611
$347$	−4.03178	−0.216437	−0.108219	−	0.994127i	$-0.534515\pi$
$347$	−4.03178	−0.216437	−0.108219	+	0.994127i	$0.534515\pi$
$348$	−0.0963206	−0.00516333
$349$	20.5796	1.10160	0.550800	−	0.834637i	$-0.314323\pi$
$349$	20.5796	1.10160	0.550800	+	0.834637i	$0.314323\pi$
$350$	0	0
$351$	−0.793613	−0.0423599
$352$	0.172264	0.00918169
$353$	24.2125	1.28870	0.644349	−	0.764731i	$-0.277128\pi$
$353$	24.2125	1.28870	0.644349	+	0.764731i	$0.277128\pi$
$354$	11.7576	0.624908
$355$	24.7481	1.31349
$356$	−0.108215	−0.00573536
$357$	0	0
$358$	18.3545	0.970065
$359$	16.4275	0.867013	0.433506	−	0.901150i	$-0.357276\pi$
$359$	16.4275	0.867013	0.433506	+	0.901150i	$0.357276\pi$
$360$	6.42214	0.338477
$361$	−8.82225	−0.464329
$362$	−9.33817	−0.490803
$363$	4.68291	0.245789
$364$	0	0
$365$	32.1989	1.68537
$366$	−12.0093	−0.627734
$367$	−13.9928	−0.730416	−0.365208	−	0.930926i	$-0.619002\pi$
$367$	−13.9928	−0.730416	−0.365208	+	0.930926i	$0.619002\pi$
$368$	−2.14618	−0.111878
$369$	1.00000	0.0520579
$370$	34.9453	1.81672
$371$	0	0
$372$	−0.0575722	−0.00298498
$373$	−17.3616	−0.898950	−0.449475	−	0.893293i	$-0.648389\pi$
$373$	−17.3616	−0.898950	−0.449475	+	0.893293i	$0.648389\pi$
$374$	−19.4387	−1.00515
$375$	−10.9615	−0.566048
$376$	−28.8451	−1.48757
$377$	6.30901	0.324931
$378$	0	0
$379$	−31.6095	−1.62367	−0.811835	−	0.583887i	$-0.801531\pi$
$379$	−31.6095	−1.62367	−0.811835	+	0.583887i	$0.801531\pi$
$380$	−0.0880349	−0.00451609
$381$	−12.0740	−0.618572
$382$	23.1640	1.18517
$383$	16.9284	0.865002	0.432501	−	0.901633i	$-0.357631\pi$
$383$	16.9284	0.865002	0.432501	+	0.901633i	$0.357631\pi$
$384$	−11.4154	−0.582541
$385$	0	0
$386$	−1.23685	−0.0629538
$387$	7.87530	0.400324
$388$	0.0444757	0.00225791
$389$	2.87047	0.145538	0.0727692	−	0.997349i	$-0.476816\pi$
$389$	2.87047	0.145538	0.0727692	+	0.997349i	$0.476816\pi$
$390$	2.56388	0.129827
$391$	2.90792	0.147060
$392$	0	0
$393$	−13.6702	−0.689570
$394$	4.94154	0.248951
$395$	29.1865	1.46853
$396$	−0.0304526	−0.00153030
$397$	−30.0965	−1.51050	−0.755249	−	0.655438i	$-0.772484\pi$
$397$	−30.0965	−1.51050	−0.755249	+	0.655438i	$0.772484\pi$
$398$	−4.93720	−0.247480
$399$	0	0
$400$	−0.752922	−0.0376461
$401$	10.4674	0.522718	0.261359	−	0.965242i	$-0.415829\pi$
$401$	10.4674	0.522718	0.261359	+	0.965242i	$0.415829\pi$
$402$	9.15153	0.456437
$403$	3.77098	0.187846
$404$	0.184035	0.00915609
$405$	−2.27752	−0.113171
$406$	0	0
$407$	27.1868	1.34760
$408$	15.3745	0.761150
$409$	19.0601	0.942464	0.471232	−	0.882009i	$-0.343809\pi$
$409$	19.0601	0.942464	0.471232	+	0.882009i	$0.343809\pi$
$410$	−3.23064	−0.159550
$411$	12.5675	0.619909
$412$	−0.0914914	−0.00450746
$413$	0	0
$414$	0.756530	0.0371814
$415$	38.3000	1.88007
$416$	−0.0543931	−0.00266684
$417$	−7.52482	−0.368492
$418$	−11.3739	−0.556317
$419$	−24.2844	−1.18637	−0.593185	−	0.805066i	$-0.702130\pi$
$419$	−24.2844	−1.18637	−0.593185	+	0.805066i	$0.702130\pi$
$420$	0	0
$421$	−6.12221	−0.298378	−0.149189	−	0.988809i	$-0.547666\pi$
$421$	−6.12221	−0.298378	−0.149189	+	0.988809i	$0.547666\pi$
$422$	3.32473	0.161845
$423$	10.2295	0.497376
$424$	27.1256	1.31733
$425$	1.02015	0.0494847
$426$	15.4137	0.746795
$427$	0	0
$428$	−0.109153	−0.00527611
$429$	1.99465	0.0963027
$430$	−25.4423	−1.22694
$431$	31.6823	1.52608	0.763042	−	0.646348i	$-0.223705\pi$
$431$	31.6823	1.52608	0.763042	+	0.646348i	$0.223705\pi$
$432$	4.02409	0.193609
$433$	−0.374506	−0.0179976	−0.00899880	−	0.999960i	$-0.502864\pi$
$433$	−0.374506	−0.0179976	−0.00899880	+	0.999960i	$0.502864\pi$
$434$	0	0
$435$	18.1057	0.868102
$436$	−0.0746449	−0.00357484
$437$	1.70147	0.0813926
$438$	20.0542	0.958225
$439$	−17.2502	−0.823305	−0.411652	−	0.911341i	$-0.635048\pi$
$439$	−17.2502	−0.823305	−0.411652	+	0.911341i	$0.635048\pi$
$440$	−16.1413	−0.769506
$441$	0	0
$442$	6.13787	0.291949
$443$	−19.7611	−0.938878	−0.469439	−	0.882965i	$-0.655544\pi$
$443$	−19.7611	−0.938878	−0.469439	+	0.882965i	$0.655544\pi$
$444$	0.131059	0.00621978
$445$	20.3415	0.964278
$446$	−3.73233	−0.176731
$447$	4.30227	0.203491
$448$	0	0
$449$	−39.2383	−1.85177	−0.925885	−	0.377804i	$-0.876679\pi$
$449$	−39.2383	−1.85177	−0.925885	+	0.377804i	$0.876679\pi$
$450$	0.265405	0.0125113
$451$	−2.51338	−0.118351
$452$	0.223183	0.0104976
$453$	12.8508	0.603781
$454$	−20.6395	−0.968661
$455$	0	0
$456$	8.99587	0.421270
$457$	31.6706	1.48149	0.740743	−	0.671789i	$-0.234474\pi$
$457$	31.6706	1.48149	0.740743	+	0.671789i	$0.234474\pi$
$458$	−21.0438	−0.983311
$459$	−5.45234	−0.254493
$460$	−0.0147173	−0.000686198 0
$461$	26.9528	1.25532	0.627659	−	0.778488i	$-0.284013\pi$
$461$	26.9528	1.25532	0.627659	+	0.778488i	$0.284013\pi$
$462$	0	0
$463$	−3.72526	−0.173128	−0.0865639	−	0.996246i	$-0.527589\pi$
$463$	−3.72526	−0.173128	−0.0865639	+	0.996246i	$0.527589\pi$
$464$	−31.9904	−1.48512
$465$	10.8220	0.501859
$466$	−11.0339	−0.511137
$467$	−25.7032	−1.18940	−0.594702	−	0.803946i	$-0.702730\pi$
$467$	−25.7032	−1.18940	−0.594702	+	0.803946i	$0.702730\pi$
$468$	0.00961557	0.000444480 0
$469$	0	0
$470$	−33.0479	−1.52439
$471$	12.2828	0.565963
$472$	23.3727	1.07581
$473$	−19.7936	−0.910113
$474$	18.1780	0.834942
$475$	0.596910	0.0273881
$476$	0	0
$477$	−9.61970	−0.440456
$478$	−17.4708	−0.799096
$479$	−8.16418	−0.373031	−0.186516	−	0.982452i	$-0.559719\pi$
$479$	−8.16418	−0.373031	−0.186516	+	0.982452i	$0.559719\pi$
$480$	−0.156098	−0.00712488
$481$	−8.58438	−0.391414
$482$	−42.7942	−1.94922
$483$	0	0
$484$	−0.0567391	−0.00257905
$485$	−8.36024	−0.379619
$486$	−1.41849	−0.0643441
$487$	14.7420	0.668022	0.334011	−	0.942569i	$-0.391598\pi$
$487$	14.7420	0.668022	0.334011	+	0.942569i	$0.391598\pi$
$488$	−23.8730	−1.08068
$489$	−17.2057	−0.778071
$490$	0	0
$491$	22.3751	1.00977	0.504887	−	0.863186i	$-0.331534\pi$
$491$	22.3751	1.00977	0.504887	+	0.863186i	$0.331534\pi$
$492$	−0.0121162	−0.000546240 0
$493$	43.3447	1.95215
$494$	3.59138	0.161584
$495$	5.72428	0.257287
$496$	−19.1211	−0.858564
$497$	0	0
$498$	23.8541	1.06893
$499$	7.49969	0.335732	0.167866	−	0.985810i	$-0.446312\pi$
$499$	7.49969	0.335732	0.167866	+	0.985810i	$0.446312\pi$
$500$	0.132811	0.00593951
$501$	3.81224	0.170318
$502$	−9.89979	−0.441849
$503$	0.450312	0.0200784	0.0100392	−	0.999950i	$-0.496804\pi$
$503$	0.450312	0.0200784	0.0100392	+	0.999950i	$0.496804\pi$
$504$	0	0
$505$	−34.5937	−1.53940
$506$	−1.90145	−0.0845297
$507$	12.3702	0.549379
$508$	0.146291	0.00649063
$509$	−31.2669	−1.38588	−0.692940	−	0.720995i	$-0.743685\pi$
$509$	−31.2669	−1.38588	−0.692940	+	0.720995i	$0.743685\pi$
$510$	17.6146	0.779986
$511$	0	0
$512$	−22.4184	−0.990762
$513$	−3.19026	−0.140853
$514$	−37.0687	−1.63503
$515$	17.1979	0.757831
$516$	−0.0954188	−0.00420058
$517$	−25.7107	−1.13075
$518$	0	0
$519$	−11.0232	−0.483864
$520$	5.09669	0.223505
$521$	13.3439	0.584609	0.292304	−	0.956325i	$-0.405578\pi$
$521$	13.3439	0.584609	0.292304	+	0.956325i	$0.405578\pi$
$522$	11.2766	0.493565
$523$	19.5524	0.854965	0.427483	−	0.904024i	$-0.359401\pi$
$523$	19.5524	0.854965	0.427483	+	0.904024i	$0.359401\pi$
$524$	0.165631	0.00723562
$525$	0	0
$526$	−31.0520	−1.35393
$527$	25.9077	1.12856
$528$	−10.1141	−0.440158
$529$	−22.7156	−0.987633
$530$	31.0778	1.34993
$531$	−8.28879	−0.359703
$532$	0	0
$533$	0.793613	0.0343752
$534$	12.6691	0.548246
$535$	20.5178	0.887063
$536$	18.1922	0.785782
$537$	−12.9395	−0.558379
$538$	−16.1847	−0.697771
$539$	0	0
$540$	0.0275949	0.00118750
$541$	−10.1164	−0.434940	−0.217470	−	0.976067i	$-0.569780\pi$
$541$	−10.1164	−0.434940	−0.217470	+	0.976067i	$0.569780\pi$
$542$	27.2976	1.17253
$543$	6.58317	0.282511
$544$	−0.373696	−0.0160221
$545$	14.0312	0.601032
$546$	0	0
$547$	−0.569282	−0.0243408	−0.0121704	−	0.999926i	$-0.503874\pi$
$547$	−0.569282	−0.0243408	−0.0121704	+	0.999926i	$0.503874\pi$
$548$	−0.152270	−0.00650466
$549$	8.46622	0.361329
$550$	−0.667065	−0.0284437
$551$	25.3617	1.08045
$552$	1.50389	0.0640100
$553$	0	0
$554$	−43.8151	−1.86153
$555$	−24.6356	−1.04572
$556$	0.0911723	0.00386657
$557$	−28.8745	−1.22345	−0.611726	−	0.791070i	$-0.709524\pi$
$557$	−28.8745	−1.22345	−0.611726	+	0.791070i	$0.709524\pi$
$558$	6.74020	0.285335
$559$	6.24994	0.264344
$560$	0	0
$561$	13.7038	0.578575
$562$	41.1251	1.73476
$563$	−3.84753	−0.162154	−0.0810770	−	0.996708i	$-0.525836\pi$
$563$	−3.84753	−0.162154	−0.0810770	+	0.996708i	$0.525836\pi$
$564$	−0.123943	−0.00521893
$565$	−41.9523	−1.76495
$566$	−9.64388	−0.405362
$567$	0	0
$568$	30.6406	1.28565
$569$	27.2780	1.14355	0.571777	−	0.820409i	$-0.306254\pi$
$569$	27.2780	1.14355	0.571777	+	0.820409i	$0.306254\pi$
$570$	10.3066	0.431695
$571$	5.74811	0.240551	0.120275	−	0.992741i	$-0.461622\pi$
$571$	5.74811	0.240551	0.120275	+	0.992741i	$0.461622\pi$
$572$	−0.0241676	−0.00101050
$573$	−16.3300	−0.682197
$574$	0	0
$575$	0.0997890	0.00416149
$576$	7.95095	0.331290
$577$	−24.5967	−1.02398	−0.511988	−	0.858993i	$-0.671091\pi$
$577$	−24.5967	−1.02398	−0.511988	+	0.858993i	$0.671091\pi$
$578$	18.0545	0.750970
$579$	0.871945	0.0362368
$580$	−0.219372	−0.00910894
$581$	0	0
$582$	−5.20694	−0.215835
$583$	24.1780	1.00135
$584$	39.8653	1.64964
$585$	−1.80747	−0.0747297
$586$	8.37462	0.345952
$587$	−31.0440	−1.28132	−0.640662	−	0.767823i	$-0.721340\pi$
$587$	−31.0440	−1.28132	−0.640662	+	0.767823i	$0.721340\pi$
$588$	0	0
$589$	15.1590	0.624618
$590$	26.7781	1.10244
$591$	−3.48366	−0.143299
$592$	43.5279	1.78899
$593$	19.5644	0.803413	0.401707	−	0.915768i	$-0.368417\pi$
$593$	19.5644	0.803413	0.401707	+	0.915768i	$0.368417\pi$
$594$	3.56521	0.146282
$595$	0	0
$596$	−0.0521272	−0.00213521
$597$	3.48060	0.142452
$598$	0.600392	0.0245519
$599$	14.6078	0.596857	0.298428	−	0.954432i	$-0.403538\pi$
$599$	14.6078	0.596857	0.298428	+	0.954432i	$0.403538\pi$
$600$	0.527595	0.0215390
$601$	21.0836	0.860018	0.430009	−	0.902825i	$-0.358510\pi$
$601$	21.0836	0.860018	0.430009	+	0.902825i	$0.358510\pi$
$602$	0	0
$603$	−6.45159	−0.262729
$604$	−0.155702	−0.00633544
$605$	10.6654	0.433611
$606$	−21.5457	−0.875234
$607$	13.1367	0.533204	0.266602	−	0.963807i	$-0.414099\pi$
$607$	13.1367	0.533204	0.266602	+	0.963807i	$0.414099\pi$
$608$	−0.218656	−0.00886767
$609$	0	0
$610$	−27.3513	−1.10742
$611$	8.11827	0.328430
$612$	0.0660616	0.00267038
$613$	−14.3758	−0.580634	−0.290317	−	0.956930i	$-0.593761\pi$
$613$	−14.3758	−0.580634	−0.290317	+	0.956930i	$0.593761\pi$
$614$	−10.9968	−0.443793
$615$	2.27752	0.0918385
$616$	0	0
$617$	−20.2383	−0.814764	−0.407382	−	0.913258i	$-0.633558\pi$
$617$	−20.2383	−0.814764	−0.407382	+	0.913258i	$0.633558\pi$
$618$	10.7113	0.430870
$619$	5.06250	0.203479	0.101740	−	0.994811i	$-0.467559\pi$
$619$	5.06250	0.203479	0.101740	+	0.994811i	$0.467559\pi$
$620$	−0.131122	−0.00526598
$621$	−0.533334	−0.0214020
$622$	25.6976	1.03038
$623$	0	0
$624$	3.19357	0.127845
$625$	−25.9005	−1.03602
$626$	24.9797	0.998388
$627$	8.01834	0.320222
$628$	−0.148821	−0.00593861
$629$	−58.9771	−2.35157
$630$	0	0
$631$	7.11493	0.283241	0.141620	−	0.989921i	$-0.454769\pi$
$631$	7.11493	0.283241	0.141620	+	0.989921i	$0.454769\pi$
$632$	36.1357	1.43740
$633$	−2.34385	−0.0931596
$634$	−25.2945	−1.00457
$635$	−27.4989	−1.09126
$636$	0.116554	0.00462167
$637$	0	0
$638$	−28.3425	−1.12209
$639$	−10.8662	−0.429862
$640$	−25.9989	−1.02770
$641$	−21.4618	−0.847689	−0.423845	−	0.905735i	$-0.639320\pi$
$641$	−21.4618	−0.847689	−0.423845	+	0.905735i	$0.639320\pi$
$642$	12.7790	0.504345
$643$	−5.81048	−0.229143	−0.114571	−	0.993415i	$-0.536549\pi$
$643$	−5.81048	−0.229143	−0.114571	+	0.993415i	$0.536549\pi$
$644$	0	0
$645$	17.9362	0.706236
$646$	24.6737	0.970776
$647$	43.3465	1.70413	0.852064	−	0.523438i	$-0.175351\pi$
$647$	43.3465	1.70413	0.852064	+	0.523438i	$0.175351\pi$
$648$	−2.81979	−0.110772
$649$	20.8329	0.817762
$650$	0.210629	0.00826155
$651$	0	0
$652$	0.208468	0.00816425
$653$	5.57320	0.218096	0.109048	−	0.994036i	$-0.465220\pi$
$653$	5.57320	0.218096	0.109048	+	0.994036i	$0.465220\pi$
$654$	8.73897	0.341721
$655$	−31.1342	−1.21651
$656$	−4.02409	−0.157114
$657$	−14.1377	−0.551563
$658$	0	0
$659$	−39.6392	−1.54412	−0.772062	−	0.635547i	$-0.780775\pi$
$659$	−39.6392	−1.54412	−0.772062	+	0.635547i	$0.780775\pi$
$660$	−0.0693565	−0.00269970
$661$	−44.5800	−1.73396	−0.866980	−	0.498344i	$-0.833942\pi$
$661$	−44.5800	−1.73396	−0.866980	+	0.498344i	$0.833942\pi$
$662$	−26.4519	−1.02808
$663$	−4.32705	−0.168049
$664$	47.4191	1.84022
$665$	0	0
$666$	−15.3436	−0.594552
$667$	4.23987	0.164168
$668$	−0.0461899	−0.00178714
$669$	2.63120	0.101728
$670$	20.8428	0.805227
$671$	−21.2788	−0.821461
$672$	0	0
$673$	7.83183	0.301895	0.150947	−	0.988542i	$-0.451768\pi$
$673$	7.83183	0.301895	0.150947	+	0.988542i	$0.451768\pi$
$674$	2.22462	0.0856893
$675$	−0.187104	−0.00720163
$676$	−0.149880	−0.00576460
$677$	−25.6670	−0.986464	−0.493232	−	0.869898i	$-0.664185\pi$
$677$	−25.6670	−0.986464	−0.493232	+	0.869898i	$0.664185\pi$
$678$	−26.1289	−1.00347
$679$	0	0
$680$	35.0157	1.34279
$681$	14.5503	0.557570
$682$	−16.9407	−0.648693
$683$	18.7719	0.718285	0.359143	−	0.933283i	$-0.383069\pi$
$683$	18.7719	0.718285	0.359143	+	0.933283i	$0.383069\pi$
$684$	0.0386538	0.00147797
$685$	28.6227	1.09362
$686$	0	0
$687$	14.8353	0.566003
$688$	−31.6909	−1.20820
$689$	−7.63432	−0.290844
$690$	1.72301	0.0655940
$691$	−8.94894	−0.340434	−0.170217	−	0.985407i	$-0.554447\pi$
$691$	−8.94894	−0.340434	−0.170217	+	0.985407i	$0.554447\pi$
$692$	0.133559	0.00507715
$693$	0	0
$694$	−5.71904	−0.217092
$695$	−17.1379	−0.650079
$696$	22.4166	0.849700
$697$	5.45234	0.206522
$698$	29.1919	1.10493
$699$	7.77864	0.294215
$700$	0	0
$701$	−49.7538	−1.87917	−0.939587	−	0.342311i	$-0.888790\pi$
$701$	−49.7538	−1.87917	−0.939587	+	0.342311i	$0.888790\pi$
$702$	−1.12573	−0.0424880
$703$	−34.5085	−1.30151
$704$	−19.9838	−0.753167
$705$	23.2979	0.877451
$706$	34.3451	1.29260
$707$	0	0
$708$	0.100429	0.00377434
$709$	−39.9666	−1.50098	−0.750488	−	0.660884i	$-0.770181\pi$
$709$	−39.9666	−1.50098	−0.750488	+	0.660884i	$0.770181\pi$
$710$	35.1050	1.31747
$711$	−12.8150	−0.480600
$712$	25.1847	0.943837
$713$	2.53423	0.0949076
$714$	0	0
$715$	4.54286	0.169893
$716$	0.156777	0.00585903
$717$	12.3165	0.459967
$718$	23.3023	0.869635
$719$	21.8678	0.815532	0.407766	−	0.913086i	$-0.366308\pi$
$719$	21.8678	0.815532	0.407766	+	0.913086i	$0.366308\pi$
$720$	9.16494	0.341557
$721$	0	0
$722$	−12.5143	−0.465734
$723$	30.1689	1.12199
$724$	−0.0797631	−0.00296437
$725$	1.48743	0.0552417
$726$	6.64267	0.246532
$727$	16.3310	0.605684	0.302842	−	0.953041i	$-0.402065\pi$
$727$	16.3310	0.605684	0.302842	+	0.953041i	$0.402065\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	45.6738	1.69046
$731$	42.9388	1.58815
$732$	−0.102578	−0.00379141
$733$	−47.6725	−1.76082	−0.880412	−	0.474209i	$-0.842734\pi$
$733$	−47.6725	−1.76082	−0.880412	+	0.474209i	$0.842734\pi$
$734$	−19.8486	−0.732625
$735$	0	0
$736$	−0.0365540	−0.00134740
$737$	16.2153	0.597299
$738$	1.41849	0.0522154
$739$	43.1339	1.58671	0.793354	−	0.608761i	$-0.208333\pi$
$739$	43.1339	1.58671	0.793354	+	0.608761i	$0.208333\pi$
$740$	0.298490	0.0109727
$741$	−2.53183	−0.0930091
$742$	0	0
$743$	−6.73942	−0.247245	−0.123623	−	0.992329i	$-0.539451\pi$
$743$	−6.73942	−0.247245	−0.123623	+	0.992329i	$0.539451\pi$
$744$	13.3987	0.491221
$745$	9.79852	0.358990
$746$	−24.6273	−0.901668
$747$	−16.8165	−0.615284
$748$	−0.166038	−0.00607095
$749$	0	0
$750$	−15.5488	−0.567760
$751$	−6.80536	−0.248331	−0.124166	−	0.992262i	$-0.539625\pi$
$751$	−6.80536	−0.248331	−0.124166	+	0.992262i	$0.539625\pi$
$752$	−41.1644	−1.50111
$753$	6.97910	0.254333
$754$	8.94928	0.325913
$755$	29.2679	1.06517
$756$	0	0
$757$	13.0431	0.474058	0.237029	−	0.971503i	$-0.423826\pi$
$757$	13.0431	0.474058	0.237029	+	0.971503i	$0.423826\pi$
$758$	−44.8378	−1.62858
$759$	1.34047	0.0486561
$760$	20.4883	0.743189
$761$	16.4668	0.596922	0.298461	−	0.954422i	$-0.403527\pi$
$761$	16.4668	0.596922	0.298461	+	0.954422i	$0.403527\pi$
$762$	−17.1269	−0.620442
$763$	0	0
$764$	0.197858	0.00715825
$765$	−12.4178	−0.448967
$766$	24.0128	0.867618
$767$	−6.57809	−0.237521
$768$	−0.290778	−0.0104926
$769$	6.99481	0.252239	0.126120	−	0.992015i	$-0.459748\pi$
$769$	6.99481	0.252239	0.126120	+	0.992015i	$0.459748\pi$
$770$	0	0
$771$	26.1325	0.941138
$772$	−0.0105647	−0.000380230 0
$773$	3.99169	0.143571	0.0717856	−	0.997420i	$-0.477130\pi$
$773$	3.99169	0.143571	0.0717856	+	0.997420i	$0.477130\pi$
$774$	11.1710	0.401535
$775$	0.889056	0.0319358
$776$	−10.3508	−0.371572
$777$	0	0
$778$	4.07173	0.145979
$779$	3.19026	0.114303
$780$	0.0218997	0.000784134 0
$781$	27.3110	0.977265
$782$	4.12486	0.147505
$783$	−7.94974	−0.284100
$784$	0	0
$785$	27.9744	0.998449
$786$	−19.3911	−0.691656
$787$	12.9580	0.461902	0.230951	−	0.972965i	$-0.425816\pi$
$787$	12.9580	0.461902	0.230951	+	0.972965i	$0.425816\pi$
$788$	0.0422088	0.00150362
$789$	21.8909	0.779336
$790$	41.4007	1.47297
$791$	0	0
$792$	7.08722	0.251833
$793$	6.71890	0.238595
$794$	−42.6916	−1.51507
$795$	−21.9091	−0.777035
$796$	−0.0421717	−0.00149473
$797$	36.8015	1.30357	0.651787	−	0.758402i	$-0.274020\pi$
$797$	36.8015	1.30357	0.651787	+	0.758402i	$0.274020\pi$
$798$	0	0
$799$	55.7748	1.97317
$800$	−0.0128239	−0.000453392 0
$801$	−8.93140	−0.315576
$802$	14.8479	0.524299
$803$	35.5334	1.25395
$804$	0.0781688	0.00275680
$805$	0	0
$806$	5.34911	0.188414
$807$	11.4098	0.401643
$808$	−42.8304	−1.50677
$809$	49.6230	1.74465	0.872326	−	0.488925i	$-0.162611\pi$
$809$	49.6230	1.74465	0.872326	+	0.488925i	$0.162611\pi$
$810$	−3.23064	−0.113513
$811$	−51.6163	−1.81249	−0.906247	−	0.422749i	$-0.861065\pi$
$811$	−51.6163	−1.81249	−0.906247	+	0.422749i	$0.861065\pi$
$812$	0	0
$813$	−19.2441	−0.674919
$814$	38.5643	1.35168
$815$	−39.1865	−1.37264
$816$	21.9407	0.768077
$817$	25.1242	0.878986
$818$	27.0366	0.945314
$819$	0	0
$820$	−0.0275949	−0.000963656 0
$821$	20.8079	0.726202	0.363101	−	0.931750i	$-0.381718\pi$
$821$	20.8079	0.726202	0.363101	+	0.931750i	$0.381718\pi$
$822$	17.8269	0.621784
$823$	11.9886	0.417895	0.208947	−	0.977927i	$-0.432996\pi$
$823$	11.9886	0.417895	0.208947	+	0.977927i	$0.432996\pi$
$824$	21.2927	0.741767
$825$	0.470264	0.0163725
$826$	0	0
$827$	23.2213	0.807484	0.403742	−	0.914873i	$-0.367709\pi$
$827$	23.2213	0.807484	0.403742	+	0.914873i	$0.367709\pi$
$828$	0.00646199	0.000224570 0
$829$	−22.6028	−0.785027	−0.392513	−	0.919746i	$-0.628394\pi$
$829$	−22.6028	−0.785027	−0.392513	+	0.919746i	$0.628394\pi$
$830$	54.3282	1.88576
$831$	30.8885	1.07151
$832$	6.30998	0.218759
$833$	0	0
$834$	−10.6739	−0.369607
$835$	8.68246	0.300469
$836$	−0.0971518	−0.00336006
$837$	−4.75167	−0.164242
$838$	−34.4472	−1.18996
$839$	5.81382	0.200715	0.100358	−	0.994951i	$-0.468001\pi$
$839$	5.81382	0.200715	0.100358	+	0.994951i	$0.468001\pi$
$840$	0	0
$841$	34.1983	1.17925
$842$	−8.68429	−0.299280
$843$	−28.9922	−0.998543
$844$	0.0283985	0.000977517 0
$845$	28.1733	0.969193
$846$	14.5105	0.498880
$847$	0	0
$848$	38.7105	1.32932
$849$	6.79869	0.233330
$850$	1.44708	0.0496344
$851$	−5.76899	−0.197759
$852$	0.131658	0.00451051
$853$	−39.8961	−1.36602	−0.683008	−	0.730411i	$-0.739329\pi$
$853$	−39.8961	−1.36602	−0.683008	+	0.730411i	$0.739329\pi$
$854$	0	0
$855$	−7.26588	−0.248488
$856$	25.4031	0.868260
$857$	5.88044	0.200872	0.100436	−	0.994944i	$-0.467976\pi$
$857$	5.88044	0.200872	0.100436	+	0.994944i	$0.467976\pi$
$858$	2.82940	0.0965940
$859$	−18.4535	−0.629624	−0.314812	−	0.949154i	$-0.601941\pi$
$859$	−18.4535	−0.629624	−0.314812	+	0.949154i	$0.601941\pi$
$860$	−0.217318	−0.00741049
$861$	0	0
$862$	44.9411	1.53070
$863$	−43.6308	−1.48521	−0.742605	−	0.669730i	$-0.766410\pi$
$863$	−43.6308	−1.48521	−0.742605	+	0.669730i	$0.766410\pi$
$864$	0.0685386	0.00233173
$865$	−25.1055	−0.853613
$866$	−0.531233	−0.0180520
$867$	−12.7280	−0.432265
$868$	0	0
$869$	32.2090	1.09262
$870$	25.6828	0.870727
$871$	−5.12007	−0.173487
$872$	17.3721	0.588292
$873$	3.67076	0.124236
$874$	2.41353	0.0816387
$875$	0	0
$876$	0.171295	0.00578752
$877$	−3.03547	−0.102501	−0.0512503	−	0.998686i	$-0.516321\pi$
$877$	−3.03547	−0.102501	−0.0512503	+	0.998686i	$0.516321\pi$
$878$	−24.4692	−0.825795
$879$	−5.90390	−0.199133
$880$	−23.0350	−0.776510
$881$	11.9431	0.402373	0.201186	−	0.979553i	$-0.435520\pi$
$881$	11.9431	0.402373	0.201186	+	0.979553i	$0.435520\pi$
$882$	0	0
$883$	20.5683	0.692178	0.346089	−	0.938202i	$-0.387509\pi$
$883$	20.5683	0.692178	0.346089	+	0.938202i	$0.387509\pi$
$884$	0.0524273	0.00176332
$885$	−18.8779	−0.634573
$886$	−28.0309	−0.941717
$887$	1.59581	0.0535822	0.0267911	−	0.999641i	$-0.491471\pi$
$887$	1.59581	0.0535822	0.0267911	+	0.999641i	$0.491471\pi$
$888$	−30.5013	−1.02356
$889$	0	0
$890$	28.8542	0.967194
$891$	−2.51338	−0.0842015
$892$	−0.0318801	−0.00106742
$893$	32.6348	1.09208
$894$	6.10274	0.204106
$895$	−29.4699	−0.985069
$896$	0	0
$897$	−0.423261	−0.0141323
$898$	−55.6592	−1.85737
$899$	37.7745	1.25985
$900$	0.00226699	7.55663e−5 0
$901$	−52.4499	−1.74736
$902$	−3.56521	−0.118708
$903$	0	0
$904$	−51.9411	−1.72754
$905$	14.9933	0.498395
$906$	18.2287	0.605607
$907$	−23.1391	−0.768323	−0.384161	−	0.923266i	$-0.625509\pi$
$907$	−23.1391	−0.768323	−0.384161	+	0.923266i	$0.625509\pi$
$908$	−0.176295	−0.00585055
$909$	15.1892	0.503793
$910$	0	0
$911$	2.82733	0.0936736	0.0468368	−	0.998903i	$-0.485086\pi$
$911$	2.82733	0.0936736	0.0468368	+	0.998903i	$0.485086\pi$
$912$	12.8379	0.425104
$913$	42.2663	1.39881
$914$	44.9244	1.48597
$915$	19.2820	0.637443
$916$	−0.179748	−0.00593903
$917$	0	0
$918$	−7.73409	−0.255263
$919$	−18.1925	−0.600115	−0.300057	−	0.953921i	$-0.597006\pi$
$919$	−18.1925	−0.600115	−0.300057	+	0.953921i	$0.597006\pi$
$920$	3.42515	0.112924
$921$	7.75244	0.255452
$922$	38.2323	1.25911
$923$	−8.62359	−0.283849
$924$	0	0
$925$	−2.02387	−0.0665445
$926$	−5.28425	−0.173651
$927$	−7.55116	−0.248013
$928$	−0.544864	−0.0178860
$929$	26.3903	0.865839	0.432919	−	0.901433i	$-0.357483\pi$
$929$	26.3903	0.865839	0.432919	+	0.901433i	$0.357483\pi$
$930$	15.3509	0.503377
$931$	0	0
$932$	−0.0942475	−0.00308718
$933$	−18.1162	−0.593096
$934$	−36.4598	−1.19300
$935$	31.2107	1.02070
$936$	−2.23783	−0.0731456
$937$	48.9344	1.59862	0.799309	−	0.600921i	$-0.205199\pi$
$937$	48.9344	1.59862	0.799309	+	0.600921i	$0.205199\pi$
$938$	0	0
$939$	−17.6100	−0.574682
$940$	−0.282282	−0.00920704
$941$	−1.87882	−0.0612479	−0.0306240	−	0.999531i	$-0.509749\pi$
$941$	−1.87882	−0.0612479	−0.0306240	+	0.999531i	$0.509749\pi$
$942$	17.4231	0.567675
$943$	0.533334	0.0173678
$944$	33.3548	1.08561
$945$	0	0
$946$	−28.0771	−0.912865
$947$	−14.2085	−0.461715	−0.230858	−	0.972988i	$-0.574153\pi$
$947$	−14.2085	−0.461715	−0.230858	+	0.972988i	$0.574153\pi$
$948$	0.155269	0.00504291
$949$	−11.2198	−0.364211
$950$	0.846711	0.0274709
$951$	17.8320	0.578241
$952$	0	0
$953$	−52.8253	−1.71118	−0.855590	−	0.517655i	$-0.826805\pi$
$953$	−52.8253	−1.71118	−0.855590	+	0.517655i	$0.826805\pi$
$954$	−13.6455	−0.441788
$955$	−37.1920	−1.20351
$956$	−0.149229	−0.00482641
$957$	19.9807	0.645885
$958$	−11.5808	−0.374159
$959$	0	0
$960$	18.1085	0.584448
$961$	−8.42165	−0.271666
$962$	−12.1769	−0.392598
$963$	−9.00884	−0.290306
$964$	−0.365532	−0.0117730
$965$	1.98587	0.0639275
$966$	0	0
$967$	−6.02265	−0.193675	−0.0968377	−	0.995300i	$-0.530873\pi$
$967$	−6.02265	−0.193675	−0.0968377	+	0.995300i	$0.530873\pi$
$968$	13.2048	0.424420
$969$	−17.3944	−0.558788
$970$	−11.8589	−0.380767
$971$	−57.1229	−1.83316	−0.916581	−	0.399849i	$-0.869063\pi$
$971$	−57.1229	−1.83316	−0.916581	+	0.399849i	$0.869063\pi$
$972$	−0.0121162	−0.000388627 0
$973$	0	0
$974$	20.9113	0.670042
$975$	−0.148488	−0.00475542
$976$	−34.0688	−1.09052
$977$	−10.8810	−0.348114	−0.174057	−	0.984736i	$-0.555688\pi$
$977$	−10.8810	−0.348114	−0.174057	+	0.984736i	$0.555688\pi$
$978$	−24.4062	−0.780424
$979$	22.4480	0.717442
$980$	0	0
$981$	−6.16075	−0.196698
$982$	31.7389	1.01283
$983$	−31.6456	−1.00934	−0.504669	−	0.863313i	$-0.668385\pi$
$983$	−31.6456	−1.00934	−0.504669	+	0.863313i	$0.668385\pi$
$984$	2.81979	0.0898918
$985$	−7.93412	−0.252802
$986$	61.4840	1.95805
$987$	0	0
$988$	0.0306761	0.000975938 0
$989$	4.20017	0.133558
$990$	8.11984	0.258065
$991$	12.9502	0.411378	0.205689	−	0.978617i	$-0.434057\pi$
$991$	12.9502	0.411378	0.205689	+	0.978617i	$0.434057\pi$
$992$	−0.325673	−0.0103401
$993$	18.6479	0.591773
$994$	0	0
$995$	7.92714	0.251307
$996$	0.203752	0.00645614
$997$	9.40141	0.297746	0.148873	−	0.988856i	$-0.452435\pi$
$997$	9.40141	0.297746	0.148873	+	0.988856i	$0.452435\pi$
$998$	10.6382	0.336748
$999$	10.8168	0.342230

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.z.1.7	✓	8
7.6	odd	2		6027.2.a.ba.1.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.z.1.7	✓	8	1.1	even	1	trivial
6027.2.a.ba.1.7	yes	8	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+1.41849 q^{2} -1.00000 q^{3} +0.0121162 q^{4} -2.27752 q^{5} -1.41849 q^{6} -2.81979 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.41849 q^{2} -1.00000 q^{3} +0.0121162 q^{4} -2.27752 q^{5} -1.41849 q^{6} -2.81979 q^{8} +1.00000 q^{9} -3.23064 q^{10} -2.51338 q^{11} -0.0121162 q^{12} +0.793613 q^{13} +2.27752 q^{15} -4.02409 q^{16} +5.45234 q^{17} +1.41849 q^{18} +3.19026 q^{19} -0.0275949 q^{20} -3.56521 q^{22} +0.533334 q^{23} +2.81979 q^{24} +0.187104 q^{25} +1.12573 q^{26} -1.00000 q^{27} +7.94974 q^{29} +3.23064 q^{30} +4.75167 q^{31} -0.0685386 q^{32} +2.51338 q^{33} +7.73409 q^{34} +0.0121162 q^{36} -10.8168 q^{37} +4.52535 q^{38} -0.793613 q^{39} +6.42214 q^{40} +1.00000 q^{41} +7.87530 q^{43} -0.0304526 q^{44} -2.27752 q^{45} +0.756530 q^{46} +10.2295 q^{47} +4.02409 q^{48} +0.265405 q^{50} -5.45234 q^{51} +0.00961557 q^{52} -9.61970 q^{53} -1.41849 q^{54} +5.72428 q^{55} -3.19026 q^{57} +11.2766 q^{58} -8.28879 q^{59} +0.0275949 q^{60} +8.46622 q^{61} +6.74020 q^{62} +7.95095 q^{64} -1.80747 q^{65} +3.56521 q^{66} -6.45159 q^{67} +0.0660616 q^{68} -0.533334 q^{69} -10.8662 q^{71} -2.81979 q^{72} -14.1377 q^{73} -15.3436 q^{74} -0.187104 q^{75} +0.0386538 q^{76} -1.12573 q^{78} -12.8150 q^{79} +9.16494 q^{80} +1.00000 q^{81} +1.41849 q^{82} -16.8165 q^{83} -12.4178 q^{85} +11.1710 q^{86} -7.94974 q^{87} +7.08722 q^{88} -8.93140 q^{89} -3.23064 q^{90} +0.00646199 q^{92} -4.75167 q^{93} +14.5105 q^{94} -7.26588 q^{95} +0.0685386 q^{96} +3.67076 q^{97} -2.51338 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} - 8 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9} - 2 q^{10} - 2 q^{11} - 4 q^{12} + 4 q^{13} - 2 q^{15} + 8 q^{17} - 2 q^{18} + 6 q^{19} + 4 q^{20} - 14 q^{22} - 12 q^{23} + 6 q^{24} - 4 q^{25} + 4 q^{26} - 8 q^{27} - 4 q^{29} + 2 q^{30} - 10 q^{31} - 4 q^{32} + 2 q^{33} + 4 q^{34} + 4 q^{36} - 20 q^{37} - 18 q^{38} - 4 q^{39} + 12 q^{40} + 8 q^{41} - 8 q^{43} + 20 q^{44} + 2 q^{45} - 12 q^{46} + 24 q^{47} - 22 q^{50} - 8 q^{51} - 30 q^{52} - 36 q^{53} + 2 q^{54} + 4 q^{55} - 6 q^{57} + 14 q^{58} + 10 q^{59} - 4 q^{60} - 22 q^{61} + 30 q^{62} - 24 q^{64} + 8 q^{65} + 14 q^{66} - 14 q^{67} + 38 q^{68} + 12 q^{69} - 10 q^{71} - 6 q^{72} - 12 q^{73} - 2 q^{74} + 4 q^{75} + 32 q^{76} - 4 q^{78} + 16 q^{79} - 14 q^{80} + 8 q^{81} - 2 q^{82} + 24 q^{83} - 44 q^{85} + 36 q^{86} + 4 q^{87} - 34 q^{88} + 2 q^{89} - 2 q^{90} - 48 q^{92} + 10 q^{93} - 34 q^{94} - 24 q^{95} + 4 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^3 + 4 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9 - 2 * q^10 - 2 * q^11 - 4 * q^12 + 4 * q^13 - 2 * q^15 + 8 * q^17 - 2 * q^18 + 6 * q^19 + 4 * q^20 - 14 * q^22 - 12 * q^23 + 6 * q^24 - 4 * q^25 + 4 * q^26 - 8 * q^27 - 4 * q^29 + 2 * q^30 - 10 * q^31 - 4 * q^32 + 2 * q^33 + 4 * q^34 + 4 * q^36 - 20 * q^37 - 18 * q^38 - 4 * q^39 + 12 * q^40 + 8 * q^41 - 8 * q^43 + 20 * q^44 + 2 * q^45 - 12 * q^46 + 24 * q^47 - 22 * q^50 - 8 * q^51 - 30 * q^52 - 36 * q^53 + 2 * q^54 + 4 * q^55 - 6 * q^57 + 14 * q^58 + 10 * q^59 - 4 * q^60 - 22 * q^61 + 30 * q^62 - 24 * q^64 + 8 * q^65 + 14 * q^66 - 14 * q^67 + 38 * q^68 + 12 * q^69 - 10 * q^71 - 6 * q^72 - 12 * q^73 - 2 * q^74 + 4 * q^75 + 32 * q^76 - 4 * q^78 + 16 * q^79 - 14 * q^80 + 8 * q^81 - 2 * q^82 + 24 * q^83 - 44 * q^85 + 36 * q^86 + 4 * q^87 - 34 * q^88 + 2 * q^89 - 2 * q^90 - 48 * q^92 + 10 * q^93 - 34 * q^94 - 24 * q^95 + 4 * q^96 + 16 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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