LMFDB - Embedded newform 6018.2.a.x.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 $ x^10 - x^9 - 34x^8 + 30x^7 + 341x^6 - 276x^5 - 1032x^4 + 1176x^3 + 416x^2 - 896x + 272
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.54849$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.54849 q^{5} +1.00000 q^{6} +4.63796 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.54849 q^{5} +1.00000 q^{6} +4.63796 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.54849 q^{10} +3.82518 q^{11} -1.00000 q^{12} -5.99795 q^{13} -4.63796 q^{14} +2.54849 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +0.762270 q^{19} -2.54849 q^{20} -4.63796 q^{21} -3.82518 q^{22} +2.86752 q^{23} +1.00000 q^{24} +1.49481 q^{25} +5.99795 q^{26} -1.00000 q^{27} +4.63796 q^{28} -9.70128 q^{29} -2.54849 q^{30} +1.94903 q^{31} -1.00000 q^{32} -3.82518 q^{33} -1.00000 q^{34} -11.8198 q^{35} +1.00000 q^{36} +11.3843 q^{37} -0.762270 q^{38} +5.99795 q^{39} +2.54849 q^{40} +3.77294 q^{41} +4.63796 q^{42} +7.13039 q^{43} +3.82518 q^{44} -2.54849 q^{45} -2.86752 q^{46} -8.60402 q^{47} -1.00000 q^{48} +14.5107 q^{49} -1.49481 q^{50} -1.00000 q^{51} -5.99795 q^{52} +5.21830 q^{53} +1.00000 q^{54} -9.74843 q^{55} -4.63796 q^{56} -0.762270 q^{57} +9.70128 q^{58} -1.00000 q^{59} +2.54849 q^{60} +1.28666 q^{61} -1.94903 q^{62} +4.63796 q^{63} +1.00000 q^{64} +15.2857 q^{65} +3.82518 q^{66} +5.70701 q^{67} +1.00000 q^{68} -2.86752 q^{69} +11.8198 q^{70} +13.9465 q^{71} -1.00000 q^{72} -8.60878 q^{73} -11.3843 q^{74} -1.49481 q^{75} +0.762270 q^{76} +17.7410 q^{77} -5.99795 q^{78} -7.61639 q^{79} -2.54849 q^{80} +1.00000 q^{81} -3.77294 q^{82} -14.7833 q^{83} -4.63796 q^{84} -2.54849 q^{85} -7.13039 q^{86} +9.70128 q^{87} -3.82518 q^{88} -6.97875 q^{89} +2.54849 q^{90} -27.8182 q^{91} +2.86752 q^{92} -1.94903 q^{93} +8.60402 q^{94} -1.94264 q^{95} +1.00000 q^{96} +17.5660 q^{97} -14.5107 q^{98} +3.82518 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9 - q^10 + 2 * q^11 - 10 * q^12 - 10 * q^14 - q^15 + 10 * q^16 + 10 * q^17 - 10 * q^18 + 15 * q^19 + q^20 - 10 * q^21 - 2 * q^22 + 19 * q^23 + 10 * q^24 + 19 * q^25 - 10 * q^27 + 10 * q^28 - q^29 + q^30 + 15 * q^31 - 10 * q^32 - 2 * q^33 - 10 * q^34 - 14 * q^35 + 10 * q^36 + q^37 - 15 * q^38 - q^40 - 5 * q^41 + 10 * q^42 + 26 * q^43 + 2 * q^44 + q^45 - 19 * q^46 + 14 * q^47 - 10 * q^48 + 20 * q^49 - 19 * q^50 - 10 * q^51 - 2 * q^53 + 10 * q^54 + 4 * q^55 - 10 * q^56 - 15 * q^57 + q^58 - 10 * q^59 - q^60 + 4 * q^61 - 15 * q^62 + 10 * q^63 + 10 * q^64 - 20 * q^65 + 2 * q^66 + 15 * q^67 + 10 * q^68 - 19 * q^69 + 14 * q^70 + 14 * q^71 - 10 * q^72 + 43 * q^73 - q^74 - 19 * q^75 + 15 * q^76 + 20 * q^77 + q^80 + 10 * q^81 + 5 * q^82 - 4 * q^83 - 10 * q^84 + q^85 - 26 * q^86 + q^87 - 2 * q^88 - 22 * q^89 - q^90 - q^91 + 19 * q^92 - 15 * q^93 - 14 * q^94 - 37 * q^95 + 10 * q^96 + 37 * q^97 - 20 * q^98 + 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.54849	−1.13972	−0.569860	−	0.821742i	$-0.693003\pi$
$5$	−2.54849	−1.13972	−0.569860	+	0.821742i	$0.693003\pi$
$6$	1.00000	0.408248
$7$	4.63796	1.75298	0.876492	−	0.481416i	$-0.159877\pi$
$7$	4.63796	1.75298	0.876492	+	0.481416i	$0.159877\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.54849	0.805904
$11$	3.82518	1.15333	0.576667	−	0.816979i	$-0.304353\pi$
$11$	3.82518	1.15333	0.576667	+	0.816979i	$0.304353\pi$
$12$	−1.00000	−0.288675
$13$	−5.99795	−1.66353	−0.831765	−	0.555127i	$-0.812670\pi$
$13$	−5.99795	−1.66353	−0.831765	+	0.555127i	$0.812670\pi$
$14$	−4.63796	−1.23955
$15$	2.54849	0.658018
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	0.762270	0.174877	0.0874383	−	0.996170i	$-0.472132\pi$
$19$	0.762270	0.174877	0.0874383	+	0.996170i	$0.472132\pi$
$20$	−2.54849	−0.569860
$21$	−4.63796	−1.01209
$22$	−3.82518	−0.815530
$23$	2.86752	0.597919	0.298960	−	0.954266i	$-0.403360\pi$
$23$	2.86752	0.597919	0.298960	+	0.954266i	$0.403360\pi$
$24$	1.00000	0.204124
$25$	1.49481	0.298963
$26$	5.99795	1.17629
$27$	−1.00000	−0.192450
$28$	4.63796	0.876492
$29$	−9.70128	−1.80148	−0.900741	−	0.434356i	$-0.856976\pi$
$29$	−9.70128	−1.80148	−0.900741	+	0.434356i	$0.856976\pi$
$30$	−2.54849	−0.465289
$31$	1.94903	0.350057	0.175028	−	0.984563i	$-0.443998\pi$
$31$	1.94903	0.350057	0.175028	+	0.984563i	$0.443998\pi$
$32$	−1.00000	−0.176777
$33$	−3.82518	−0.665878
$34$	−1.00000	−0.171499
$35$	−11.8198	−1.99791
$36$	1.00000	0.166667
$37$	11.3843	1.87157	0.935786	−	0.352567i	$-0.114691\pi$
$37$	11.3843	1.87157	0.935786	+	0.352567i	$0.114691\pi$
$38$	−0.762270	−0.123656
$39$	5.99795	0.960440
$40$	2.54849	0.402952
$41$	3.77294	0.589234	0.294617	−	0.955615i	$-0.404808\pi$
$41$	3.77294	0.589234	0.294617	+	0.955615i	$0.404808\pi$
$42$	4.63796	0.715653
$43$	7.13039	1.08737	0.543687	−	0.839288i	$-0.317028\pi$
$43$	7.13039	1.08737	0.543687	+	0.839288i	$0.317028\pi$
$44$	3.82518	0.576667
$45$	−2.54849	−0.379907
$46$	−2.86752	−0.422793
$47$	−8.60402	−1.25503	−0.627513	−	0.778606i	$-0.715927\pi$
$47$	−8.60402	−1.25503	−0.627513	+	0.778606i	$0.715927\pi$
$48$	−1.00000	−0.144338
$49$	14.5107	2.07295
$50$	−1.49481	−0.211399
$51$	−1.00000	−0.140028
$52$	−5.99795	−0.831765
$53$	5.21830	0.716789	0.358395	−	0.933570i	$-0.383324\pi$
$53$	5.21830	0.716789	0.358395	+	0.933570i	$0.383324\pi$
$54$	1.00000	0.136083
$55$	−9.74843	−1.31448
$56$	−4.63796	−0.619773
$57$	−0.762270	−0.100965
$58$	9.70128	1.27384
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	2.54849	0.329009
$61$	1.28666	0.164739	0.0823697	−	0.996602i	$-0.473751\pi$
$61$	1.28666	0.164739	0.0823697	+	0.996602i	$0.473751\pi$
$62$	−1.94903	−0.247527
$63$	4.63796	0.584328
$64$	1.00000	0.125000
$65$	15.2857	1.89596
$66$	3.82518	0.470847
$67$	5.70701	0.697222	0.348611	−	0.937268i	$-0.386653\pi$
$67$	5.70701	0.697222	0.348611	+	0.937268i	$0.386653\pi$
$68$	1.00000	0.121268
$69$	−2.86752	−0.345209
$70$	11.8198	1.41274
$71$	13.9465	1.65514	0.827572	−	0.561360i	$-0.189722\pi$
$71$	13.9465	1.65514	0.827572	+	0.561360i	$0.189722\pi$
$72$	−1.00000	−0.117851
$73$	−8.60878	−1.00758	−0.503791	−	0.863826i	$-0.668062\pi$
$73$	−8.60878	−1.00758	−0.503791	+	0.863826i	$0.668062\pi$
$74$	−11.3843	−1.32340
$75$	−1.49481	−0.172606
$76$	0.762270	0.0874383
$77$	17.7410	2.02178
$78$	−5.99795	−0.679134
$79$	−7.61639	−0.856911	−0.428455	−	0.903563i	$-0.640942\pi$
$79$	−7.61639	−0.856911	−0.428455	+	0.903563i	$0.640942\pi$
$80$	−2.54849	−0.284930
$81$	1.00000	0.111111
$82$	−3.77294	−0.416651
$83$	−14.7833	−1.62268	−0.811339	−	0.584576i	$-0.801261\pi$
$83$	−14.7833	−1.62268	−0.811339	+	0.584576i	$0.801261\pi$
$84$	−4.63796	−0.506043
$85$	−2.54849	−0.276423
$86$	−7.13039	−0.768890
$87$	9.70128	1.04009
$88$	−3.82518	−0.407765
$89$	−6.97875	−0.739746	−0.369873	−	0.929082i	$-0.620599\pi$
$89$	−6.97875	−0.739746	−0.369873	+	0.929082i	$0.620599\pi$
$90$	2.54849	0.268635
$91$	−27.8182	−2.91614
$92$	2.86752	0.298960
$93$	−1.94903	−0.202105
$94$	8.60402	0.887437
$95$	−1.94264	−0.199311
$96$	1.00000	0.102062
$97$	17.5660	1.78355	0.891777	−	0.452476i	$-0.149459\pi$
$97$	17.5660	1.78355	0.891777	+	0.452476i	$0.149459\pi$
$98$	−14.5107	−1.46580
$99$	3.82518	0.384445
$100$	1.49481	0.149481
$101$	−0.682590	−0.0679202	−0.0339601	−	0.999423i	$-0.510812\pi$
$101$	−0.682590	−0.0679202	−0.0339601	+	0.999423i	$0.510812\pi$
$102$	1.00000	0.0990148
$103$	0.439469	0.0433022	0.0216511	−	0.999766i	$-0.493108\pi$
$103$	0.439469	0.0433022	0.0216511	+	0.999766i	$0.493108\pi$
$104$	5.99795	0.588147
$105$	11.8198	1.15350
$106$	−5.21830	−0.506846
$107$	−11.8128	−1.14199	−0.570994	−	0.820954i	$-0.693442\pi$
$107$	−11.8128	−1.14199	−0.570994	+	0.820954i	$0.693442\pi$
$108$	−1.00000	−0.0962250
$109$	13.4758	1.29075	0.645376	−	0.763865i	$-0.276701\pi$
$109$	13.4758	1.29075	0.645376	+	0.763865i	$0.276701\pi$
$110$	9.74843	0.929476
$111$	−11.3843	−1.08055
$112$	4.63796	0.438246
$113$	5.72384	0.538454	0.269227	−	0.963077i	$-0.413232\pi$
$113$	5.72384	0.538454	0.269227	+	0.963077i	$0.413232\pi$
$114$	0.762270	0.0713931
$115$	−7.30786	−0.681461
$116$	−9.70128	−0.900741
$117$	−5.99795	−0.554510
$118$	1.00000	0.0920575
$119$	4.63796	0.425161
$120$	−2.54849	−0.232644
$121$	3.63197	0.330179
$122$	−1.28666	−0.116488
$123$	−3.77294	−0.340194
$124$	1.94903	0.175028
$125$	8.93294	0.798986
$126$	−4.63796	−0.413182
$127$	4.33400	0.384581	0.192290	−	0.981338i	$-0.438408\pi$
$127$	4.33400	0.384581	0.192290	+	0.981338i	$0.438408\pi$
$128$	−1.00000	−0.0883883
$129$	−7.13039	−0.627796
$130$	−15.2857	−1.34065
$131$	−3.59336	−0.313953	−0.156977	−	0.987602i	$-0.550175\pi$
$131$	−3.59336	−0.313953	−0.156977	+	0.987602i	$0.550175\pi$
$132$	−3.82518	−0.332939
$133$	3.53538	0.306556
$134$	−5.70701	−0.493010
$135$	2.54849	0.219339
$136$	−1.00000	−0.0857493
$137$	−6.46145	−0.552039	−0.276019	−	0.961152i	$-0.589015\pi$
$137$	−6.46145	−0.552039	−0.276019	+	0.961152i	$0.589015\pi$
$138$	2.86752	0.244100
$139$	−6.71562	−0.569612	−0.284806	−	0.958585i	$-0.591929\pi$
$139$	−6.71562	−0.569612	−0.284806	+	0.958585i	$0.591929\pi$
$140$	−11.8198	−0.998956
$141$	8.60402	0.724590
$142$	−13.9465	−1.17036
$143$	−22.9432	−1.91861
$144$	1.00000	0.0833333
$145$	24.7236	2.05319
$146$	8.60878	0.712467
$147$	−14.5107	−1.19682
$148$	11.3843	0.935786
$149$	−0.592891	−0.0485715	−0.0242858	−	0.999705i	$-0.507731\pi$
$149$	−0.592891	−0.0485715	−0.0242858	+	0.999705i	$0.507731\pi$
$150$	1.49481	0.122051
$151$	−5.91828	−0.481623	−0.240811	−	0.970572i	$-0.577413\pi$
$151$	−5.91828	−0.481623	−0.240811	+	0.970572i	$0.577413\pi$
$152$	−0.762270	−0.0618282
$153$	1.00000	0.0808452
$154$	−17.7410	−1.42961
$155$	−4.96710	−0.398967
$156$	5.99795	0.480220
$157$	−23.5975	−1.88329	−0.941643	−	0.336612i	$-0.890719\pi$
$157$	−23.5975	−1.88329	−0.941643	+	0.336612i	$0.890719\pi$
$158$	7.61639	0.605927
$159$	−5.21830	−0.413838
$160$	2.54849	0.201476
$161$	13.2994	1.04814
$162$	−1.00000	−0.0785674
$163$	16.0752	1.25911	0.629554	−	0.776957i	$-0.283238\pi$
$163$	16.0752	1.25911	0.629554	+	0.776957i	$0.283238\pi$
$164$	3.77294	0.294617
$165$	9.74843	0.758914
$166$	14.7833	1.14741
$167$	12.2184	0.945490	0.472745	−	0.881199i	$-0.343263\pi$
$167$	12.2184	0.945490	0.472745	+	0.881199i	$0.343263\pi$
$168$	4.63796	0.357826
$169$	22.9754	1.76734
$170$	2.54849	0.195460
$171$	0.762270	0.0582922
$172$	7.13039	0.543687
$173$	−11.8307	−0.899469	−0.449734	−	0.893162i	$-0.648481\pi$
$173$	−11.8307	−0.899469	−0.449734	+	0.893162i	$0.648481\pi$
$174$	−9.70128	−0.735452
$175$	6.93289	0.524077
$176$	3.82518	0.288333
$177$	1.00000	0.0751646
$178$	6.97875	0.523079
$179$	−19.7618	−1.47706	−0.738532	−	0.674218i	$-0.764481\pi$
$179$	−19.7618	−1.47706	−0.738532	+	0.674218i	$0.764481\pi$
$180$	−2.54849	−0.189953
$181$	−12.0473	−0.895467	−0.447734	−	0.894167i	$-0.647769\pi$
$181$	−12.0473	−0.895467	−0.447734	+	0.894167i	$0.647769\pi$
$182$	27.8182	2.06202
$183$	−1.28666	−0.0951123
$184$	−2.86752	−0.211396
$185$	−29.0129	−2.13307
$186$	1.94903	0.142910
$187$	3.82518	0.279725
$188$	−8.60402	−0.627513
$189$	−4.63796	−0.337362
$190$	1.94264	0.140934
$191$	8.89380	0.643533	0.321767	−	0.946819i	$-0.395723\pi$
$191$	8.89380	0.643533	0.321767	+	0.946819i	$0.395723\pi$
$192$	−1.00000	−0.0721688
$193$	17.3211	1.24680	0.623402	−	0.781902i	$-0.285750\pi$
$193$	17.3211	1.24680	0.623402	+	0.781902i	$0.285750\pi$
$194$	−17.5660	−1.26116
$195$	−15.2857	−1.09463
$196$	14.5107	1.03648
$197$	3.65868	0.260670	0.130335	−	0.991470i	$-0.458395\pi$
$197$	3.65868	0.260670	0.130335	+	0.991470i	$0.458395\pi$
$198$	−3.82518	−0.271843
$199$	1.27579	0.0904384	0.0452192	−	0.998977i	$-0.485601\pi$
$199$	1.27579	0.0904384	0.0452192	+	0.998977i	$0.485601\pi$
$200$	−1.49481	−0.105699
$201$	−5.70701	−0.402541
$202$	0.682590	0.0480269
$203$	−44.9942	−3.15797
$204$	−1.00000	−0.0700140
$205$	−9.61530	−0.671562
$206$	−0.439469	−0.0306193
$207$	2.86752	0.199306
$208$	−5.99795	−0.415883
$209$	2.91581	0.201691
$210$	−11.8198	−0.815644
$211$	−9.91164	−0.682345	−0.341173	−	0.940001i	$-0.610824\pi$
$211$	−9.91164	−0.682345	−0.341173	+	0.940001i	$0.610824\pi$
$212$	5.21830	0.358395
$213$	−13.9465	−0.955597
$214$	11.8128	0.807508
$215$	−18.1718	−1.23930
$216$	1.00000	0.0680414
$217$	9.03954	0.613644
$218$	−13.4758	−0.912699
$219$	8.60878	0.581727
$220$	−9.74843	−0.657239
$221$	−5.99795	−0.403466
$222$	11.3843	0.764066
$223$	14.7168	0.985508	0.492754	−	0.870169i	$-0.335990\pi$
$223$	14.7168	0.985508	0.492754	+	0.870169i	$0.335990\pi$
$224$	−4.63796	−0.309887
$225$	1.49481	0.0996543
$226$	−5.72384	−0.380744
$227$	−7.54209	−0.500586	−0.250293	−	0.968170i	$-0.580527\pi$
$227$	−7.54209	−0.500586	−0.250293	+	0.968170i	$0.580527\pi$
$228$	−0.762270	−0.0504825
$229$	4.21611	0.278608	0.139304	−	0.990250i	$-0.455513\pi$
$229$	4.21611	0.278608	0.139304	+	0.990250i	$0.455513\pi$
$230$	7.30786	0.481866
$231$	−17.7410	−1.16727
$232$	9.70128	0.636920
$233$	15.8761	1.04008	0.520039	−	0.854143i	$-0.325917\pi$
$233$	15.8761	1.04008	0.520039	+	0.854143i	$0.325917\pi$
$234$	5.99795	0.392098
$235$	21.9273	1.43038
$236$	−1.00000	−0.0650945
$237$	7.61639	0.494738
$238$	−4.63796	−0.300634
$239$	16.5846	1.07277	0.536383	−	0.843974i	$-0.319790\pi$
$239$	16.5846	1.07277	0.536383	+	0.843974i	$0.319790\pi$
$240$	2.54849	0.164504
$241$	18.6176	1.19927	0.599633	−	0.800275i	$-0.295313\pi$
$241$	18.6176	1.19927	0.599633	+	0.800275i	$0.295313\pi$
$242$	−3.63197	−0.233472
$243$	−1.00000	−0.0641500
$244$	1.28666	0.0823697
$245$	−36.9803	−2.36259
$246$	3.77294	0.240554
$247$	−4.57205	−0.290913
$248$	−1.94903	−0.123764
$249$	14.7833	0.936854
$250$	−8.93294	−0.564969
$251$	20.5014	1.29403	0.647017	−	0.762475i	$-0.276016\pi$
$251$	20.5014	1.29403	0.647017	+	0.762475i	$0.276016\pi$
$252$	4.63796	0.292164
$253$	10.9688	0.689601
$254$	−4.33400	−0.271940
$255$	2.54849	0.159593
$256$	1.00000	0.0625000
$257$	−30.5722	−1.90704	−0.953520	−	0.301329i	$-0.902570\pi$
$257$	−30.5722	−1.90704	−0.953520	+	0.301329i	$0.902570\pi$
$258$	7.13039	0.443919
$259$	52.8001	3.28084
$260$	15.2857	0.947980
$261$	−9.70128	−0.600494
$262$	3.59336	0.221998
$263$	−18.8943	−1.16507	−0.582536	−	0.812805i	$-0.697939\pi$
$263$	−18.8943	−1.16507	−0.582536	+	0.812805i	$0.697939\pi$
$264$	3.82518	0.235423
$265$	−13.2988	−0.816939
$266$	−3.53538	−0.216768
$267$	6.97875	0.427092
$268$	5.70701	0.348611
$269$	22.1179	1.34855	0.674277	−	0.738479i	$-0.264456\pi$
$269$	22.1179	1.34855	0.674277	+	0.738479i	$0.264456\pi$
$270$	−2.54849	−0.155096
$271$	−8.25394	−0.501391	−0.250696	−	0.968066i	$-0.580659\pi$
$271$	−8.25394	−0.501391	−0.250696	+	0.968066i	$0.580659\pi$
$272$	1.00000	0.0606339
$273$	27.8182	1.68364
$274$	6.46145	0.390350
$275$	5.71793	0.344804
$276$	−2.86752	−0.172604
$277$	21.6324	1.29977	0.649884	−	0.760033i	$-0.274818\pi$
$277$	21.6324	1.29977	0.649884	+	0.760033i	$0.274818\pi$
$278$	6.71562	0.402776
$279$	1.94903	0.116686
$280$	11.8198	0.706369
$281$	−12.2357	−0.729918	−0.364959	−	0.931024i	$-0.618917\pi$
$281$	−12.2357	−0.729918	−0.364959	+	0.931024i	$0.618917\pi$
$282$	−8.60402	−0.512362
$283$	24.1666	1.43656	0.718278	−	0.695756i	$-0.244930\pi$
$283$	24.1666	1.43656	0.718278	+	0.695756i	$0.244930\pi$
$284$	13.9465	0.827572
$285$	1.94264	0.115072
$286$	22.9432	1.35666
$287$	17.4987	1.03292
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−24.7236	−1.45182
$291$	−17.5660	−1.02973
$292$	−8.60878	−0.503791
$293$	7.87369	0.459986	0.229993	−	0.973192i	$-0.426130\pi$
$293$	7.87369	0.459986	0.229993	+	0.973192i	$0.426130\pi$
$294$	14.5107	0.846280
$295$	2.54849	0.148379
$296$	−11.3843	−0.661701
$297$	−3.82518	−0.221959
$298$	0.592891	0.0343453
$299$	−17.1992	−0.994657
$300$	−1.49481	−0.0863032
$301$	33.0705	1.90615
$302$	5.91828	0.340559
$303$	0.682590	0.0392138
$304$	0.762270	0.0437192
$305$	−3.27903	−0.187757
$306$	−1.00000	−0.0571662
$307$	−5.01048	−0.285963	−0.142982	−	0.989725i	$-0.545669\pi$
$307$	−5.01048	−0.285963	−0.142982	+	0.989725i	$0.545669\pi$
$308$	17.7410	1.01089
$309$	−0.439469	−0.0250005
$310$	4.96710	0.282112
$311$	−20.6925	−1.17336	−0.586681	−	0.809818i	$-0.699566\pi$
$311$	−20.6925	−1.17336	−0.586681	+	0.809818i	$0.699566\pi$
$312$	−5.99795	−0.339567
$313$	3.30664	0.186902	0.0934512	−	0.995624i	$-0.470210\pi$
$313$	3.30664	0.186902	0.0934512	+	0.995624i	$0.470210\pi$
$314$	23.5975	1.33168
$315$	−11.8198	−0.665971
$316$	−7.61639	−0.428455
$317$	21.2869	1.19559	0.597795	−	0.801649i	$-0.296044\pi$
$317$	21.2869	1.19559	0.597795	+	0.801649i	$0.296044\pi$
$318$	5.21830	0.292628
$319$	−37.1091	−2.07771
$320$	−2.54849	−0.142465
$321$	11.8128	0.659328
$322$	−13.2994	−0.741149
$323$	0.762270	0.0424138
$324$	1.00000	0.0555556
$325$	−8.96582	−0.497334
$326$	−16.0752	−0.890324
$327$	−13.4758	−0.745216
$328$	−3.77294	−0.208326
$329$	−39.9051	−2.20004
$330$	−9.74843	−0.536633
$331$	−31.6518	−1.73974	−0.869869	−	0.493282i	$-0.835797\pi$
$331$	−31.6518	−1.73974	−0.869869	+	0.493282i	$0.835797\pi$
$332$	−14.7833	−0.811339
$333$	11.3843	0.623858
$334$	−12.2184	−0.668562
$335$	−14.5443	−0.794638
$336$	−4.63796	−0.253021
$337$	23.9923	1.30694	0.653472	−	0.756951i	$-0.273312\pi$
$337$	23.9923	1.30694	0.653472	+	0.756951i	$0.273312\pi$
$338$	−22.9754	−1.24969
$339$	−5.72384	−0.310876
$340$	−2.54849	−0.138211
$341$	7.45539	0.403732
$342$	−0.762270	−0.0412188
$343$	34.8342	1.88087
$344$	−7.13039	−0.384445
$345$	7.30786	0.393442
$346$	11.8307	0.636020
$347$	32.8100	1.76133	0.880666	−	0.473737i	$-0.157095\pi$
$347$	32.8100	1.76133	0.880666	+	0.473737i	$0.157095\pi$
$348$	9.70128	0.520043
$349$	34.7365	1.85940	0.929702	−	0.368313i	$-0.120064\pi$
$349$	34.7365	1.85940	0.929702	+	0.368313i	$0.120064\pi$
$350$	−6.93289	−0.370579
$351$	5.99795	0.320147
$352$	−3.82518	−0.203883
$353$	14.4903	0.771239	0.385620	−	0.922658i	$-0.373988\pi$
$353$	14.4903	0.771239	0.385620	+	0.922658i	$0.373988\pi$
$354$	−1.00000	−0.0531494
$355$	−35.5425	−1.88640
$356$	−6.97875	−0.369873
$357$	−4.63796	−0.245467
$358$	19.7618	1.04444
$359$	28.7973	1.51986	0.759931	−	0.650003i	$-0.225233\pi$
$359$	28.7973	1.51986	0.759931	+	0.650003i	$0.225233\pi$
$360$	2.54849	0.134317
$361$	−18.4189	−0.969418
$362$	12.0473	0.633191
$363$	−3.63197	−0.190629
$364$	−27.8182	−1.45807
$365$	21.9394	1.14836
$366$	1.28666	0.0672546
$367$	29.0220	1.51494	0.757468	−	0.652872i	$-0.226436\pi$
$367$	29.0220	1.51494	0.757468	+	0.652872i	$0.226436\pi$
$368$	2.86752	0.149480
$369$	3.77294	0.196411
$370$	29.0129	1.50831
$371$	24.2023	1.25652
$372$	−1.94903	−0.101053
$373$	−11.0958	−0.574517	−0.287259	−	0.957853i	$-0.592744\pi$
$373$	−11.0958	−0.574517	−0.287259	+	0.957853i	$0.592744\pi$
$374$	−3.82518	−0.197795
$375$	−8.93294	−0.461295
$376$	8.60402	0.443719
$377$	58.1878	2.99682
$378$	4.63796	0.238551
$379$	13.4270	0.689698	0.344849	−	0.938658i	$-0.387930\pi$
$379$	13.4270	0.689698	0.344849	+	0.938658i	$0.387930\pi$
$380$	−1.94264	−0.0996553
$381$	−4.33400	−0.222038
$382$	−8.89380	−0.455047
$383$	18.8502	0.963198	0.481599	−	0.876392i	$-0.340056\pi$
$383$	18.8502	0.963198	0.481599	+	0.876392i	$0.340056\pi$
$384$	1.00000	0.0510310
$385$	−45.2128	−2.30426
$386$	−17.3211	−0.881623
$387$	7.13039	0.362458
$388$	17.5660	0.891777
$389$	30.4095	1.54182	0.770912	−	0.636942i	$-0.219801\pi$
$389$	30.4095	1.54182	0.770912	+	0.636942i	$0.219801\pi$
$390$	15.2857	0.774023
$391$	2.86752	0.145017
$392$	−14.5107	−0.732900
$393$	3.59336	0.181261
$394$	−3.65868	−0.184321
$395$	19.4103	0.976639
$396$	3.82518	0.192222
$397$	−2.12187	−0.106494	−0.0532469	−	0.998581i	$-0.516957\pi$
$397$	−2.12187	−0.106494	−0.0532469	+	0.998581i	$0.516957\pi$
$398$	−1.27579	−0.0639496
$399$	−3.53538	−0.176990
$400$	1.49481	0.0747407
$401$	−37.8596	−1.89062	−0.945308	−	0.326179i	$-0.894239\pi$
$401$	−37.8596	−1.89062	−0.945308	+	0.326179i	$0.894239\pi$
$402$	5.70701	0.284640
$403$	−11.6902	−0.582330
$404$	−0.682590	−0.0339601
$405$	−2.54849	−0.126636
$406$	44.9942	2.23302
$407$	43.5471	2.15855
$408$	1.00000	0.0495074
$409$	−20.2018	−0.998914	−0.499457	−	0.866339i	$-0.666467\pi$
$409$	−20.2018	−0.998914	−0.499457	+	0.866339i	$0.666467\pi$
$410$	9.61530	0.474866
$411$	6.46145	0.318720
$412$	0.439469	0.0216511
$413$	−4.63796	−0.228219
$414$	−2.86752	−0.140931
$415$	37.6751	1.84940
$416$	5.99795	0.294073
$417$	6.71562	0.328866
$418$	−2.91581	−0.142617
$419$	−12.3079	−0.601281	−0.300640	−	0.953738i	$-0.597200\pi$
$419$	−12.3079	−0.601281	−0.300640	+	0.953738i	$0.597200\pi$
$420$	11.8198	0.576748
$421$	−19.3946	−0.945236	−0.472618	−	0.881267i	$-0.656691\pi$
$421$	−19.3946	−0.945236	−0.472618	+	0.881267i	$0.656691\pi$
$422$	9.91164	0.482491
$423$	−8.60402	−0.418342
$424$	−5.21830	−0.253423
$425$	1.49481	0.0725092
$426$	13.9465	0.675709
$427$	5.96746	0.288785
$428$	−11.8128	−0.570994
$429$	22.9432	1.10771
$430$	18.1718	0.876320
$431$	34.0357	1.63944	0.819721	−	0.572764i	$-0.194129\pi$
$431$	34.0357	1.63944	0.819721	+	0.572764i	$0.194129\pi$
$432$	−1.00000	−0.0481125
$433$	−4.99483	−0.240036	−0.120018	−	0.992772i	$-0.538295\pi$
$433$	−4.99483	−0.240036	−0.120018	+	0.992772i	$0.538295\pi$
$434$	−9.03954	−0.433912
$435$	−24.7236	−1.18541
$436$	13.4758	0.645376
$437$	2.18582	0.104562
$438$	−8.60878	−0.411343
$439$	6.83701	0.326312	0.163156	−	0.986600i	$-0.447833\pi$
$439$	6.83701	0.326312	0.163156	+	0.986600i	$0.447833\pi$
$440$	9.74843	0.464738
$441$	14.5107	0.690984
$442$	5.99795	0.285293
$443$	−19.9406	−0.947408	−0.473704	−	0.880684i	$-0.657083\pi$
$443$	−19.9406	−0.947408	−0.473704	+	0.880684i	$0.657083\pi$
$444$	−11.3843	−0.540277
$445$	17.7853	0.843103
$446$	−14.7168	−0.696860
$447$	0.592891	0.0280428
$448$	4.63796	0.219123
$449$	16.6045	0.783614	0.391807	−	0.920048i	$-0.371850\pi$
$449$	16.6045	0.783614	0.391807	+	0.920048i	$0.371850\pi$
$450$	−1.49481	−0.0704662
$451$	14.4321	0.679583
$452$	5.72384	0.269227
$453$	5.91828	0.278065
$454$	7.54209	0.353968
$455$	70.8946	3.32359
$456$	0.762270	0.0356965
$457$	27.9950	1.30955	0.654776	−	0.755823i	$-0.272763\pi$
$457$	27.9950	1.30955	0.654776	+	0.755823i	$0.272763\pi$
$458$	−4.21611	−0.197006
$459$	−1.00000	−0.0466760
$460$	−7.30786	−0.340731
$461$	21.7097	1.01112	0.505560	−	0.862791i	$-0.331286\pi$
$461$	21.7097	1.01112	0.505560	+	0.862791i	$0.331286\pi$
$462$	17.7410	0.825386
$463$	30.2922	1.40780	0.703900	−	0.710299i	$-0.251440\pi$
$463$	30.2922	1.40780	0.703900	+	0.710299i	$0.251440\pi$
$464$	−9.70128	−0.450371
$465$	4.96710	0.230344
$466$	−15.8761	−0.735446
$467$	18.5442	0.858124	0.429062	−	0.903275i	$-0.358844\pi$
$467$	18.5442	0.858124	0.429062	+	0.903275i	$0.358844\pi$
$468$	−5.99795	−0.277255
$469$	26.4689	1.22222
$470$	−21.9273	−1.01143
$471$	23.5975	1.08732
$472$	1.00000	0.0460287
$473$	27.2750	1.25411
$474$	−7.61639	−0.349832
$475$	1.13945	0.0522816
$476$	4.63796	0.212581
$477$	5.21830	0.238930
$478$	−16.5846	−0.758561
$479$	1.71688	0.0784463	0.0392232	−	0.999230i	$-0.487512\pi$
$479$	1.71688	0.0784463	0.0392232	+	0.999230i	$0.487512\pi$
$480$	−2.54849	−0.116322
$481$	−68.2826	−3.11342
$482$	−18.6176	−0.848009
$483$	−13.2994	−0.605146
$484$	3.63197	0.165089
$485$	−44.7667	−2.03275
$486$	1.00000	0.0453609
$487$	14.2393	0.645243	0.322622	−	0.946528i	$-0.395436\pi$
$487$	14.2393	0.645243	0.322622	+	0.946528i	$0.395436\pi$
$488$	−1.28666	−0.0582442
$489$	−16.0752	−0.726946
$490$	36.9803	1.67060
$491$	−16.3779	−0.739122	−0.369561	−	0.929206i	$-0.620492\pi$
$491$	−16.3779	−0.739122	−0.369561	+	0.929206i	$0.620492\pi$
$492$	−3.77294	−0.170097
$493$	−9.70128	−0.436924
$494$	4.57205	0.205706
$495$	−9.74843	−0.438159
$496$	1.94903	0.0875142
$497$	64.6832	2.90144
$498$	−14.7833	−0.662456
$499$	−11.1972	−0.501257	−0.250628	−	0.968083i	$-0.580637\pi$
$499$	−11.1972	−0.501257	−0.250628	+	0.968083i	$0.580637\pi$
$500$	8.93294	0.399493
$501$	−12.2184	−0.545879
$502$	−20.5014	−0.915020
$503$	32.4393	1.44640	0.723198	−	0.690641i	$-0.242672\pi$
$503$	32.4393	1.44640	0.723198	+	0.690641i	$0.242672\pi$
$504$	−4.63796	−0.206591
$505$	1.73958	0.0774101
$506$	−10.9688	−0.487621
$507$	−22.9754	−1.02037
$508$	4.33400	0.192290
$509$	4.36844	0.193628	0.0968139	−	0.995303i	$-0.469135\pi$
$509$	4.36844	0.193628	0.0968139	+	0.995303i	$0.469135\pi$
$510$	−2.54849	−0.112849
$511$	−39.9272	−1.76627
$512$	−1.00000	−0.0441942
$513$	−0.762270	−0.0336550
$514$	30.5722	1.34848
$515$	−1.11998	−0.0493524
$516$	−7.13039	−0.313898
$517$	−32.9119	−1.44746
$518$	−52.8001	−2.31990
$519$	11.8307	0.519308
$520$	−15.2857	−0.670323
$521$	−15.3232	−0.671320	−0.335660	−	0.941983i	$-0.608959\pi$
$521$	−15.3232	−0.671320	−0.335660	+	0.941983i	$0.608959\pi$
$522$	9.70128	0.424614
$523$	−6.06787	−0.265329	−0.132665	−	0.991161i	$-0.542353\pi$
$523$	−6.06787	−0.265329	−0.132665	+	0.991161i	$0.542353\pi$
$524$	−3.59336	−0.156977
$525$	−6.93289	−0.302576
$526$	18.8943	0.823830
$527$	1.94903	0.0849012
$528$	−3.82518	−0.166469
$529$	−14.7773	−0.642492
$530$	13.2988	0.577663
$531$	−1.00000	−0.0433963
$532$	3.53538	0.153278
$533$	−22.6299	−0.980208
$534$	−6.97875	−0.302000
$535$	30.1049	1.30155
$536$	−5.70701	−0.246505
$537$	19.7618	0.852784
$538$	−22.1179	−0.953571
$539$	55.5059	2.39081
$540$	2.54849	0.109670
$541$	3.15210	0.135519	0.0677597	−	0.997702i	$-0.478415\pi$
$541$	3.15210	0.135519	0.0677597	+	0.997702i	$0.478415\pi$
$542$	8.25394	0.354537
$543$	12.0473	0.516998
$544$	−1.00000	−0.0428746
$545$	−34.3431	−1.47110
$546$	−27.8182	−1.19051
$547$	−34.1028	−1.45813	−0.729066	−	0.684444i	$-0.760045\pi$
$547$	−34.1028	−1.45813	−0.729066	+	0.684444i	$0.760045\pi$
$548$	−6.46145	−0.276019
$549$	1.28666	0.0549131
$550$	−5.71793	−0.243813
$551$	−7.39499	−0.315037
$552$	2.86752	0.122050
$553$	−35.3245	−1.50215
$554$	−21.6324	−0.919075
$555$	29.0129	1.23153
$556$	−6.71562	−0.284806
$557$	−14.9518	−0.633526	−0.316763	−	0.948505i	$-0.602596\pi$
$557$	−14.9518	−0.633526	−0.316763	+	0.948505i	$0.602596\pi$
$558$	−1.94903	−0.0825091
$559$	−42.7677	−1.80888
$560$	−11.8198	−0.499478
$561$	−3.82518	−0.161499
$562$	12.2357	0.516130
$563$	−41.0404	−1.72965	−0.864824	−	0.502075i	$-0.832570\pi$
$563$	−41.0404	−1.72965	−0.864824	+	0.502075i	$0.832570\pi$
$564$	8.60402	0.362295
$565$	−14.5872	−0.613687
$566$	−24.1666	−1.01580
$567$	4.63796	0.194776
$568$	−13.9465	−0.585181
$569$	45.3508	1.90120	0.950602	−	0.310412i	$-0.100467\pi$
$569$	45.3508	1.90120	0.950602	+	0.310412i	$0.100467\pi$
$570$	−1.94264	−0.0813682
$571$	1.35462	0.0566891	0.0283445	−	0.999598i	$-0.490976\pi$
$571$	1.35462	0.0566891	0.0283445	+	0.999598i	$0.490976\pi$
$572$	−22.9432	−0.959303
$573$	−8.89380	−0.371544
$574$	−17.4987	−0.730383
$575$	4.28641	0.178756
$576$	1.00000	0.0416667
$577$	36.5251	1.52056	0.760280	−	0.649595i	$-0.225062\pi$
$577$	36.5251	1.52056	0.760280	+	0.649595i	$0.225062\pi$
$578$	−1.00000	−0.0415945
$579$	−17.3211	−0.719842
$580$	24.7236	1.02659
$581$	−68.5644	−2.84453
$582$	17.5660	0.728133
$583$	19.9609	0.826697
$584$	8.60878	0.356234
$585$	15.2857	0.631987
$586$	−7.87369	−0.325259
$587$	3.84129	0.158547	0.0792735	−	0.996853i	$-0.474740\pi$
$587$	3.84129	0.158547	0.0792735	+	0.996853i	$0.474740\pi$
$588$	−14.5107	−0.598410
$589$	1.48569	0.0612167
$590$	−2.54849	−0.104920
$591$	−3.65868	−0.150498
$592$	11.3843	0.467893
$593$	25.5457	1.04904	0.524519	−	0.851399i	$-0.324245\pi$
$593$	25.5457	1.04904	0.524519	+	0.851399i	$0.324245\pi$
$594$	3.82518	0.156949
$595$	−11.8198	−0.484565
$596$	−0.592891	−0.0242858
$597$	−1.27579	−0.0522146
$598$	17.1992	0.703329
$599$	9.94840	0.406480	0.203240	−	0.979129i	$-0.434853\pi$
$599$	9.94840	0.406480	0.203240	+	0.979129i	$0.434853\pi$
$600$	1.49481	0.0610256
$601$	4.71246	0.192225	0.0961127	−	0.995370i	$-0.469359\pi$
$601$	4.71246	0.192225	0.0961127	+	0.995370i	$0.469359\pi$
$602$	−33.0705	−1.34785
$603$	5.70701	0.232407
$604$	−5.91828	−0.240811
$605$	−9.25604	−0.376312
$606$	−0.682590	−0.0277283
$607$	10.3558	0.420330	0.210165	−	0.977666i	$-0.432600\pi$
$607$	10.3558	0.420330	0.210165	+	0.977666i	$0.432600\pi$
$608$	−0.762270	−0.0309141
$609$	44.9942	1.82326
$610$	3.27903	0.132764
$611$	51.6065	2.08777
$612$	1.00000	0.0404226
$613$	2.49428	0.100743	0.0503714	−	0.998731i	$-0.483959\pi$
$613$	2.49428	0.100743	0.0503714	+	0.998731i	$0.483959\pi$
$614$	5.01048	0.202206
$615$	9.61530	0.387726
$616$	−17.7410	−0.714806
$617$	−29.4330	−1.18493	−0.592463	−	0.805598i	$-0.701844\pi$
$617$	−29.4330	−1.18493	−0.592463	+	0.805598i	$0.701844\pi$
$618$	0.439469	0.0176780
$619$	−38.1785	−1.53452	−0.767262	−	0.641334i	$-0.778381\pi$
$619$	−38.1785	−1.53452	−0.767262	+	0.641334i	$0.778381\pi$
$620$	−4.96710	−0.199483
$621$	−2.86752	−0.115070
$622$	20.6925	0.829693
$623$	−32.3671	−1.29676
$624$	5.99795	0.240110
$625$	−30.2396	−1.20958
$626$	−3.30664	−0.132160
$627$	−2.91581	−0.116446
$628$	−23.5975	−0.941643
$629$	11.3843	0.453923
$630$	11.8198	0.470912
$631$	22.9868	0.915091	0.457545	−	0.889186i	$-0.348729\pi$
$631$	22.9868	0.915091	0.457545	+	0.889186i	$0.348729\pi$
$632$	7.61639	0.302964
$633$	9.91164	0.393952
$634$	−21.2869	−0.845410
$635$	−11.0452	−0.438314
$636$	−5.21830	−0.206919
$637$	−87.0342	−3.44842
$638$	37.1091	1.46916
$639$	13.9465	0.551714
$640$	2.54849	0.100738
$641$	8.67850	0.342780	0.171390	−	0.985203i	$-0.445174\pi$
$641$	8.67850	0.342780	0.171390	+	0.985203i	$0.445174\pi$
$642$	−11.8128	−0.466215
$643$	−15.7953	−0.622907	−0.311454	−	0.950261i	$-0.600816\pi$
$643$	−15.7953	−0.622907	−0.311454	+	0.950261i	$0.600816\pi$
$644$	13.2994	0.524072
$645$	18.1718	0.715512
$646$	−0.762270	−0.0299911
$647$	41.7112	1.63984	0.819919	−	0.572479i	$-0.194018\pi$
$647$	41.7112	1.63984	0.819919	+	0.572479i	$0.194018\pi$
$648$	−1.00000	−0.0392837
$649$	−3.82518	−0.150151
$650$	8.96582	0.351668
$651$	−9.03954	−0.354287
$652$	16.0752	0.629554
$653$	19.3693	0.757980	0.378990	−	0.925401i	$-0.376271\pi$
$653$	19.3693	0.757980	0.378990	+	0.925401i	$0.376271\pi$
$654$	13.4758	0.526947
$655$	9.15765	0.357819
$656$	3.77294	0.147308
$657$	−8.60878	−0.335860
$658$	39.9051	1.55566
$659$	0.580138	0.0225990	0.0112995	−	0.999936i	$-0.496403\pi$
$659$	0.580138	0.0225990	0.0112995	+	0.999936i	$0.496403\pi$
$660$	9.74843	0.379457
$661$	−0.100726	−0.00391780	−0.00195890	−	0.999998i	$-0.500624\pi$
$661$	−0.100726	−0.00391780	−0.00195890	+	0.999998i	$0.500624\pi$
$662$	31.6518	1.23018
$663$	5.99795	0.232941
$664$	14.7833	0.573703
$665$	−9.00988	−0.349388
$666$	−11.3843	−0.441134
$667$	−27.8186	−1.07714
$668$	12.2184	0.472745
$669$	−14.7168	−0.568984
$670$	14.5443	0.561894
$671$	4.92168	0.189999
$672$	4.63796	0.178913
$673$	−18.7350	−0.722180	−0.361090	−	0.932531i	$-0.617595\pi$
$673$	−18.7350	−0.722180	−0.361090	+	0.932531i	$0.617595\pi$
$674$	−23.9923	−0.924149
$675$	−1.49481	−0.0575354
$676$	22.9754	0.883668
$677$	23.6543	0.909110	0.454555	−	0.890719i	$-0.349798\pi$
$677$	23.6543	0.909110	0.454555	+	0.890719i	$0.349798\pi$
$678$	5.72384	0.219823
$679$	81.4702	3.12654
$680$	2.54849	0.0977302
$681$	7.54209	0.289014
$682$	−7.45539	−0.285482
$683$	−33.5301	−1.28299	−0.641496	−	0.767126i	$-0.721686\pi$
$683$	−33.5301	−1.28299	−0.641496	+	0.767126i	$0.721686\pi$
$684$	0.762270	0.0291461
$685$	16.4670	0.629170
$686$	−34.8342	−1.32998
$687$	−4.21611	−0.160855
$688$	7.13039	0.271844
$689$	−31.2991	−1.19240
$690$	−7.30786	−0.278205
$691$	48.7963	1.85630	0.928150	−	0.372207i	$-0.121399\pi$
$691$	48.7963	1.85630	0.928150	+	0.372207i	$0.121399\pi$
$692$	−11.8307	−0.449734
$693$	17.7410	0.673925
$694$	−32.8100	−1.24545
$695$	17.1147	0.649198
$696$	−9.70128	−0.367726
$697$	3.77294	0.142910
$698$	−34.7365	−1.31480
$699$	−15.8761	−0.600489
$700$	6.93289	0.262039
$701$	15.2136	0.574611	0.287305	−	0.957839i	$-0.407241\pi$
$701$	15.2136	0.574611	0.287305	+	0.957839i	$0.407241\pi$
$702$	−5.99795	−0.226378
$703$	8.67793	0.327294
$704$	3.82518	0.144167
$705$	−21.9273	−0.825830
$706$	−14.4903	−0.545348
$707$	−3.16582	−0.119063
$708$	1.00000	0.0375823
$709$	0.529329	0.0198794	0.00993968	−	0.999951i	$-0.496836\pi$
$709$	0.529329	0.0198794	0.00993968	+	0.999951i	$0.496836\pi$
$710$	35.5425	1.33389
$711$	−7.61639	−0.285637
$712$	6.97875	0.261540
$713$	5.58889	0.209306
$714$	4.63796	0.173571
$715$	58.4706	2.18668
$716$	−19.7618	−0.738532
$717$	−16.5846	−0.619362
$718$	−28.7973	−1.07471
$719$	−37.9170	−1.41407	−0.707034	−	0.707180i	$-0.749967\pi$
$719$	−37.9170	−1.41407	−0.707034	+	0.707180i	$0.749967\pi$
$720$	−2.54849	−0.0949767
$721$	2.03824	0.0759080
$722$	18.4189	0.685482
$723$	−18.6176	−0.692397
$724$	−12.0473	−0.447734
$725$	−14.5016	−0.538577
$726$	3.63197	0.134795
$727$	32.0489	1.18863	0.594314	−	0.804233i	$-0.297424\pi$
$727$	32.0489	1.18863	0.594314	+	0.804233i	$0.297424\pi$
$728$	27.8182	1.03101
$729$	1.00000	0.0370370
$730$	−21.9394	−0.812014
$731$	7.13039	0.263727
$732$	−1.28666	−0.0475562
$733$	−26.1824	−0.967067	−0.483534	−	0.875326i	$-0.660647\pi$
$733$	−26.1824	−0.967067	−0.483534	+	0.875326i	$0.660647\pi$
$734$	−29.0220	−1.07122
$735$	36.9803	1.36404
$736$	−2.86752	−0.105698
$737$	21.8303	0.804129
$738$	−3.77294	−0.138884
$739$	12.1686	0.447628	0.223814	−	0.974632i	$-0.428149\pi$
$739$	12.1686	0.447628	0.223814	+	0.974632i	$0.428149\pi$
$740$	−29.0129	−1.06654
$741$	4.57205	0.167959
$742$	−24.2023	−0.888494
$743$	34.3740	1.26106	0.630530	−	0.776165i	$-0.282838\pi$
$743$	34.3740	1.26106	0.630530	+	0.776165i	$0.282838\pi$
$744$	1.94903	0.0714550
$745$	1.51098	0.0553580
$746$	11.0958	0.406245
$747$	−14.7833	−0.540893
$748$	3.82518	0.139862
$749$	−54.7874	−2.00189
$750$	8.93294	0.326185
$751$	−5.96957	−0.217833	−0.108916	−	0.994051i	$-0.534738\pi$
$751$	−5.96957	−0.217833	−0.108916	+	0.994051i	$0.534738\pi$
$752$	−8.60402	−0.313756
$753$	−20.5014	−0.747111
$754$	−58.1878	−2.11907
$755$	15.0827	0.548915
$756$	−4.63796	−0.168681
$757$	−12.2269	−0.444395	−0.222198	−	0.975002i	$-0.571323\pi$
$757$	−12.2269	−0.444395	−0.222198	+	0.975002i	$0.571323\pi$
$758$	−13.4270	−0.487690
$759$	−10.9688	−0.398141
$760$	1.94264	0.0704669
$761$	23.9650	0.868731	0.434365	−	0.900737i	$-0.356973\pi$
$761$	23.9650	0.868731	0.434365	+	0.900737i	$0.356973\pi$
$762$	4.33400	0.157004
$763$	62.5004	2.26267
$764$	8.89380	0.321767
$765$	−2.54849	−0.0921409
$766$	−18.8502	−0.681084
$767$	5.99795	0.216573
$768$	−1.00000	−0.0360844
$769$	−20.5777	−0.742050	−0.371025	−	0.928623i	$-0.620994\pi$
$769$	−20.5777	−0.742050	−0.371025	+	0.928623i	$0.620994\pi$
$770$	45.2128	1.62936
$771$	30.5722	1.10103
$772$	17.3211	0.623402
$773$	−47.9219	−1.72363	−0.861815	−	0.507222i	$-0.830672\pi$
$773$	−47.9219	−1.72363	−0.861815	+	0.507222i	$0.830672\pi$
$774$	−7.13039	−0.256297
$775$	2.91344	0.104654
$776$	−17.5660	−0.630581
$777$	−52.8001	−1.89419
$778$	−30.4095	−1.09023
$779$	2.87599	0.103043
$780$	−15.2857	−0.547317
$781$	53.3477	1.90893
$782$	−2.86752	−0.102542
$783$	9.70128	0.346696
$784$	14.5107	0.518238
$785$	60.1381	2.14642
$786$	−3.59336	−0.128171
$787$	−8.11613	−0.289309	−0.144654	−	0.989482i	$-0.546207\pi$
$787$	−8.11613	−0.289309	−0.144654	+	0.989482i	$0.546207\pi$
$788$	3.65868	0.130335
$789$	18.8943	0.672654
$790$	−19.4103	−0.690588
$791$	26.5470	0.943901
$792$	−3.82518	−0.135922
$793$	−7.71729	−0.274049
$794$	2.12187	0.0753025
$795$	13.2988	0.471660
$796$	1.27579	0.0452192
$797$	52.2418	1.85050	0.925249	−	0.379360i	$-0.123856\pi$
$797$	52.2418	1.85050	0.925249	+	0.379360i	$0.123856\pi$
$798$	3.53538	0.125151
$799$	−8.60402	−0.304388
$800$	−1.49481	−0.0528497
$801$	−6.97875	−0.246582
$802$	37.8596	1.33687
$803$	−32.9301	−1.16208
$804$	−5.70701	−0.201271
$805$	−33.8935	−1.19459
$806$	11.6902	0.411769
$807$	−22.1179	−0.778587
$808$	0.682590	0.0240134
$809$	−9.12135	−0.320690	−0.160345	−	0.987061i	$-0.551261\pi$
$809$	−9.12135	−0.320690	−0.160345	+	0.987061i	$0.551261\pi$
$810$	2.54849	0.0895449
$811$	32.0055	1.12387	0.561933	−	0.827183i	$-0.310058\pi$
$811$	32.0055	1.12387	0.561933	+	0.827183i	$0.310058\pi$
$812$	−44.9942	−1.57899
$813$	8.25394	0.289478
$814$	−43.5471	−1.52632
$815$	−40.9676	−1.43503
$816$	−1.00000	−0.0350070
$817$	5.43528	0.190156
$818$	20.2018	0.706339
$819$	−27.8182	−0.972048
$820$	−9.61530	−0.335781
$821$	−43.0180	−1.50134	−0.750670	−	0.660678i	$-0.770269\pi$
$821$	−43.0180	−1.50134	−0.750670	+	0.660678i	$0.770269\pi$
$822$	−6.46145	−0.225369
$823$	−46.1202	−1.60765	−0.803825	−	0.594866i	$-0.797205\pi$
$823$	−46.1202	−1.60765	−0.803825	+	0.594866i	$0.797205\pi$
$824$	−0.439469	−0.0153096
$825$	−5.71793	−0.199073
$826$	4.63796	0.161375
$827$	37.9834	1.32081	0.660407	−	0.750908i	$-0.270384\pi$
$827$	37.9834	1.32081	0.660407	+	0.750908i	$0.270384\pi$
$828$	2.86752	0.0996532
$829$	−28.6322	−0.994438	−0.497219	−	0.867625i	$-0.665645\pi$
$829$	−28.6322	−0.994438	−0.497219	+	0.867625i	$0.665645\pi$
$830$	−37.6751	−1.30772
$831$	−21.6324	−0.750421
$832$	−5.99795	−0.207941
$833$	14.5107	0.502765
$834$	−6.71562	−0.232543
$835$	−31.1386	−1.07759
$836$	2.91581	0.100846
$837$	−1.94903	−0.0673684
$838$	12.3079	0.425170
$839$	−18.4056	−0.635430	−0.317715	−	0.948186i	$-0.602916\pi$
$839$	−18.4056	−0.635430	−0.317715	+	0.948186i	$0.602916\pi$
$840$	−11.8198	−0.407822
$841$	65.1149	2.24534
$842$	19.3946	0.668383
$843$	12.2357	0.421418
$844$	−9.91164	−0.341173
$845$	−58.5525	−2.01427
$846$	8.60402	0.295812
$847$	16.8449	0.578798
$848$	5.21830	0.179197
$849$	−24.1666	−0.829396
$850$	−1.49481	−0.0512717
$851$	32.6448	1.11905
$852$	−13.9465	−0.477799
$853$	52.3271	1.79165	0.895824	−	0.444410i	$-0.146587\pi$
$853$	52.3271	1.79165	0.895824	+	0.444410i	$0.146587\pi$
$854$	−5.96746	−0.204202
$855$	−1.94264	−0.0664368
$856$	11.8128	0.403754
$857$	55.4946	1.89566	0.947830	−	0.318777i	$-0.103272\pi$
$857$	55.4946	1.89566	0.947830	+	0.318777i	$0.103272\pi$
$858$	−22.9432	−0.783268
$859$	29.9388	1.02150	0.510750	−	0.859729i	$-0.329368\pi$
$859$	29.9388	1.02150	0.510750	+	0.859729i	$0.329368\pi$
$860$	−18.1718	−0.619652
$861$	−17.4987	−0.596355
$862$	−34.0357	−1.15926
$863$	18.2073	0.619784	0.309892	−	0.950772i	$-0.399707\pi$
$863$	18.2073	0.619784	0.309892	+	0.950772i	$0.399707\pi$
$864$	1.00000	0.0340207
$865$	30.1504	1.02514
$866$	4.99483	0.169731
$867$	−1.00000	−0.0339618
$868$	9.03954	0.306822
$869$	−29.1340	−0.988304
$870$	24.7236	0.838210
$871$	−34.2303	−1.15985
$872$	−13.4758	−0.456350
$873$	17.5660	0.594518
$874$	−2.18582	−0.0739366
$875$	41.4306	1.40061
$876$	8.60878	0.290864
$877$	−18.4858	−0.624220	−0.312110	−	0.950046i	$-0.601036\pi$
$877$	−18.4858	−0.624220	−0.312110	+	0.950046i	$0.601036\pi$
$878$	−6.83701	−0.230738
$879$	−7.87369	−0.265573
$880$	−9.74843	−0.328620
$881$	9.52164	0.320792	0.160396	−	0.987053i	$-0.448723\pi$
$881$	9.52164	0.320792	0.160396	+	0.987053i	$0.448723\pi$
$882$	−14.5107	−0.488600
$883$	−16.6415	−0.560032	−0.280016	−	0.959995i	$-0.590340\pi$
$883$	−16.6415	−0.560032	−0.280016	+	0.959995i	$0.590340\pi$
$884$	−5.99795	−0.201733
$885$	−2.54849	−0.0856666
$886$	19.9406	0.669919
$887$	8.26123	0.277385	0.138692	−	0.990335i	$-0.455710\pi$
$887$	8.26123	0.277385	0.138692	+	0.990335i	$0.455710\pi$
$888$	11.3843	0.382033
$889$	20.1009	0.674164
$890$	−17.7853	−0.596164
$891$	3.82518	0.128148
$892$	14.7168	0.492754
$893$	−6.55859	−0.219475
$894$	−0.592891	−0.0198292
$895$	50.3627	1.68344
$896$	−4.63796	−0.154943
$897$	17.1992	0.574266
$898$	−16.6045	−0.554099
$899$	−18.9081	−0.630621
$900$	1.49481	0.0498272
$901$	5.21830	0.173847
$902$	−14.4321	−0.480538
$903$	−33.0705	−1.10052
$904$	−5.72384	−0.190372
$905$	30.7024	1.02058
$906$	−5.91828	−0.196622
$907$	−21.7046	−0.720689	−0.360344	−	0.932819i	$-0.617341\pi$
$907$	−21.7046	−0.720689	−0.360344	+	0.932819i	$0.617341\pi$
$908$	−7.54209	−0.250293
$909$	−0.682590	−0.0226401
$910$	−70.8946	−2.35013
$911$	−36.5255	−1.21014	−0.605071	−	0.796171i	$-0.706855\pi$
$911$	−36.5255	−1.21014	−0.605071	+	0.796171i	$0.706855\pi$
$912$	−0.762270	−0.0252413
$913$	−56.5487	−1.87149
$914$	−27.9950	−0.925993
$915$	3.27903	0.108401
$916$	4.21611	0.139304
$917$	−16.6659	−0.550355
$918$	1.00000	0.0330049
$919$	−16.0561	−0.529642	−0.264821	−	0.964298i	$-0.585313\pi$
$919$	−16.0561	−0.529642	−0.264821	+	0.964298i	$0.585313\pi$
$920$	7.30786	0.240933
$921$	5.01048	0.165101
$922$	−21.7097	−0.714970
$923$	−83.6503	−2.75338
$924$	−17.7410	−0.583636
$925$	17.0175	0.559531
$926$	−30.2922	−0.995465
$927$	0.439469	0.0144341
$928$	9.70128	0.318460
$929$	−15.8831	−0.521108	−0.260554	−	0.965459i	$-0.583905\pi$
$929$	−15.8831	−0.521108	−0.260554	+	0.965459i	$0.583905\pi$
$930$	−4.96710	−0.162877
$931$	11.0610	0.362511
$932$	15.8761	0.520039
$933$	20.6925	0.677441
$934$	−18.5442	−0.606785
$935$	−9.74843	−0.318808
$936$	5.99795	0.196049
$937$	16.2989	0.532463	0.266231	−	0.963909i	$-0.414221\pi$
$937$	16.2989	0.532463	0.266231	+	0.963909i	$0.414221\pi$
$938$	−26.4689	−0.864239
$939$	−3.30664	−0.107908
$940$	21.9273	0.715189
$941$	56.6960	1.84824	0.924118	−	0.382108i	$-0.124802\pi$
$941$	56.6960	1.84824	0.924118	+	0.382108i	$0.124802\pi$
$942$	−23.5975	−0.768849
$943$	10.8190	0.352314
$944$	−1.00000	−0.0325472
$945$	11.8198	0.384498
$946$	−27.2750	−0.886787
$947$	29.2311	0.949882	0.474941	−	0.880018i	$-0.342469\pi$
$947$	29.2311	0.949882	0.474941	+	0.880018i	$0.342469\pi$
$948$	7.61639	0.247369
$949$	51.6350	1.67614
$950$	−1.13945	−0.0369687
$951$	−21.2869	−0.690274
$952$	−4.63796	−0.150317
$953$	−5.30319	−0.171787	−0.0858935	−	0.996304i	$-0.527374\pi$
$953$	−5.30319	−0.171787	−0.0858935	+	0.996304i	$0.527374\pi$
$954$	−5.21830	−0.168949
$955$	−22.6658	−0.733448
$956$	16.5846	0.536383
$957$	37.1091	1.19957
$958$	−1.71688	−0.0554699
$959$	−29.9679	−0.967715
$960$	2.54849	0.0822522
$961$	−27.2013	−0.877460
$962$	68.2826	2.20152
$963$	−11.8128	−0.380663
$964$	18.6176	0.599633
$965$	−44.1428	−1.42101
$966$	13.2994	0.427903
$967$	45.9410	1.47736	0.738681	−	0.674055i	$-0.235449\pi$
$967$	45.9410	1.47736	0.738681	+	0.674055i	$0.235449\pi$
$968$	−3.63197	−0.116736
$969$	−0.762270	−0.0244876
$970$	44.7667	1.43737
$971$	−12.4092	−0.398229	−0.199114	−	0.979976i	$-0.563807\pi$
$971$	−12.4092	−0.398229	−0.199114	+	0.979976i	$0.563807\pi$
$972$	−1.00000	−0.0320750
$973$	−31.1468	−0.998521
$974$	−14.2393	−0.456256
$975$	8.96582	0.287136
$976$	1.28666	0.0411848
$977$	−7.64754	−0.244667	−0.122333	−	0.992489i	$-0.539038\pi$
$977$	−7.64754	−0.244667	−0.122333	+	0.992489i	$0.539038\pi$
$978$	16.0752	0.514029
$979$	−26.6949	−0.853173
$980$	−36.9803	−1.18129
$981$	13.4758	0.430251
$982$	16.3779	0.522638
$983$	18.7156	0.596935	0.298467	−	0.954420i	$-0.403525\pi$
$983$	18.7156	0.596935	0.298467	+	0.954420i	$0.403525\pi$
$984$	3.77294	0.120277
$985$	−9.32411	−0.297091
$986$	9.70128	0.308952
$987$	39.9051	1.27019
$988$	−4.57205	−0.145456
$989$	20.4466	0.650163
$990$	9.74843	0.309825
$991$	−35.6483	−1.13241	−0.566203	−	0.824266i	$-0.691588\pi$
$991$	−35.6483	−1.13241	−0.566203	+	0.824266i	$0.691588\pi$
$992$	−1.94903	−0.0618819
$993$	31.6518	1.00444
$994$	−64.6832	−2.05163
$995$	−3.25134	−0.103075
$996$	14.7833	0.468427
$997$	62.0991	1.96670	0.983349	−	0.181726i	$-0.0581685\pi$
$997$	62.0991	1.96670	0.983349	+	0.181726i	$0.0581685\pi$
$998$	11.1972	0.354442
$999$	−11.3843	−0.360184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.x.1.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.x.1.3	✓	10	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.54849 q^{5} +1.00000 q^{6} +4.63796 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.54849 q^{5} +1.00000 q^{6} +4.63796 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.54849 q^{10} +3.82518 q^{11} -1.00000 q^{12} -5.99795 q^{13} -4.63796 q^{14} +2.54849 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +0.762270 q^{19} -2.54849 q^{20} -4.63796 q^{21} -3.82518 q^{22} +2.86752 q^{23} +1.00000 q^{24} +1.49481 q^{25} +5.99795 q^{26} -1.00000 q^{27} +4.63796 q^{28} -9.70128 q^{29} -2.54849 q^{30} +1.94903 q^{31} -1.00000 q^{32} -3.82518 q^{33} -1.00000 q^{34} -11.8198 q^{35} +1.00000 q^{36} +11.3843 q^{37} -0.762270 q^{38} +5.99795 q^{39} +2.54849 q^{40} +3.77294 q^{41} +4.63796 q^{42} +7.13039 q^{43} +3.82518 q^{44} -2.54849 q^{45} -2.86752 q^{46} -8.60402 q^{47} -1.00000 q^{48} +14.5107 q^{49} -1.49481 q^{50} -1.00000 q^{51} -5.99795 q^{52} +5.21830 q^{53} +1.00000 q^{54} -9.74843 q^{55} -4.63796 q^{56} -0.762270 q^{57} +9.70128 q^{58} -1.00000 q^{59} +2.54849 q^{60} +1.28666 q^{61} -1.94903 q^{62} +4.63796 q^{63} +1.00000 q^{64} +15.2857 q^{65} +3.82518 q^{66} +5.70701 q^{67} +1.00000 q^{68} -2.86752 q^{69} +11.8198 q^{70} +13.9465 q^{71} -1.00000 q^{72} -8.60878 q^{73} -11.3843 q^{74} -1.49481 q^{75} +0.762270 q^{76} +17.7410 q^{77} -5.99795 q^{78} -7.61639 q^{79} -2.54849 q^{80} +1.00000 q^{81} -3.77294 q^{82} -14.7833 q^{83} -4.63796 q^{84} -2.54849 q^{85} -7.13039 q^{86} +9.70128 q^{87} -3.82518 q^{88} -6.97875 q^{89} +2.54849 q^{90} -27.8182 q^{91} +2.86752 q^{92} -1.94903 q^{93} +8.60402 q^{94} -1.94264 q^{95} +1.00000 q^{96} +17.5660 q^{97} -14.5107 q^{98} +3.82518 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + q^5 + 10 * q^6 + 10 * q^7 - 10 * q^8 + 10 * q^9 - q^10 + 2 * q^11 - 10 * q^12 - 10 * q^14 - q^15 + 10 * q^16 + 10 * q^17 - 10 * q^18 + 15 * q^19 + q^20 - 10 * q^21 - 2 * q^22 + 19 * q^23 + 10 * q^24 + 19 * q^25 - 10 * q^27 + 10 * q^28 - q^29 + q^30 + 15 * q^31 - 10 * q^32 - 2 * q^33 - 10 * q^34 - 14 * q^35 + 10 * q^36 + q^37 - 15 * q^38 - q^40 - 5 * q^41 + 10 * q^42 + 26 * q^43 + 2 * q^44 + q^45 - 19 * q^46 + 14 * q^47 - 10 * q^48 + 20 * q^49 - 19 * q^50 - 10 * q^51 - 2 * q^53 + 10 * q^54 + 4 * q^55 - 10 * q^56 - 15 * q^57 + q^58 - 10 * q^59 - q^60 + 4 * q^61 - 15 * q^62 + 10 * q^63 + 10 * q^64 - 20 * q^65 + 2 * q^66 + 15 * q^67 + 10 * q^68 - 19 * q^69 + 14 * q^70 + 14 * q^71 - 10 * q^72 + 43 * q^73 - q^74 - 19 * q^75 + 15 * q^76 + 20 * q^77 + q^80 + 10 * q^81 + 5 * q^82 - 4 * q^83 - 10 * q^84 + q^85 - 26 * q^86 + q^87 - 2 * q^88 - 22 * q^89 - q^90 - q^91 + 19 * q^92 - 15 * q^93 - 14 * q^94 - 37 * q^95 + 10 * q^96 + 37 * q^97 - 20 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more